Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [23,14,Mod(1,23)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(23, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("23.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 23 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 23.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: | \(24.6631136589\) |
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: | \( x^{14} - 6 x^{13} - 91997 x^{12} + 766599 x^{11} + 3278769040 x^{10} - 30986318669 x^{9} - 56829440072404 x^{8} + 496745885608086 x^{7} + \cdots - 45\!\cdots\!18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{19}\cdot 3^{4}\cdot 11 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(167.770\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 23.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −162.770 | −1.79838 | −0.899188 | − | 0.437562i | \(-0.855842\pi\) | ||||
−0.899188 | + | 0.437562i | \(0.855842\pi\) | |||||||
\(3\) | −2381.17 | −1.88583 | −0.942915 | − | 0.333033i | \(-0.891928\pi\) | ||||
−0.942915 | + | 0.333033i | \(0.891928\pi\) | |||||||
\(4\) | 18302.2 | 2.23416 | ||||||||
\(5\) | 37078.1 | 1.06124 | 0.530618 | − | 0.847611i | \(-0.321960\pi\) | ||||
0.530618 | + | 0.847611i | \(0.321960\pi\) | |||||||
\(6\) | 387584. | 3.39143 | ||||||||
\(7\) | 189022. | 0.607262 | 0.303631 | − | 0.952790i | \(-0.401801\pi\) | ||||
0.303631 | + | 0.952790i | \(0.401801\pi\) | |||||||
\(8\) | −1.64565e6 | −2.21948 | ||||||||
\(9\) | 4.07566e6 | 2.55636 | ||||||||
\(10\) | −6.03522e6 | −1.90850 | ||||||||
\(11\) | −8.01372e6 | −1.36390 | −0.681948 | − | 0.731400i | \(-0.738867\pi\) | ||||
−0.681948 | + | 0.731400i | \(0.738867\pi\) | |||||||
\(12\) | −4.35807e7 | −4.21324 | ||||||||
\(13\) | 3.13553e7 | 1.80169 | 0.900844 | − | 0.434142i | \(-0.142949\pi\) | ||||
0.900844 | + | 0.434142i | \(0.142949\pi\) | |||||||
\(14\) | −3.07673e7 | −1.09209 | ||||||||
\(15\) | −8.82893e7 | −2.00131 | ||||||||
\(16\) | 1.17931e8 | 1.75730 | ||||||||
\(17\) | 8.72430e7 | 0.876622 | 0.438311 | − | 0.898823i | \(-0.355577\pi\) | ||||
0.438311 | + | 0.898823i | \(0.355577\pi\) | |||||||
\(18\) | −6.63397e8 | −4.59729 | ||||||||
\(19\) | −6.54013e7 | −0.318925 | −0.159462 | − | 0.987204i | \(-0.550976\pi\) | ||||
−0.159462 | + | 0.987204i | \(0.550976\pi\) | |||||||
\(20\) | 6.78611e8 | 2.37097 | ||||||||
\(21\) | −4.50095e8 | −1.14519 | ||||||||
\(22\) | 1.30440e9 | 2.45280 | ||||||||
\(23\) | 1.48036e8 | 0.208514 | ||||||||
\(24\) | 3.91857e9 | 4.18556 | ||||||||
\(25\) | 1.54082e8 | 0.126224 | ||||||||
\(26\) | −5.10372e9 | −3.24011 | ||||||||
\(27\) | −5.90848e9 | −2.93502 | ||||||||
\(28\) | 3.45953e9 | 1.35672 | ||||||||
\(29\) | −1.62740e9 | −0.508051 | −0.254026 | − | 0.967197i | \(-0.581755\pi\) | ||||
−0.254026 | + | 0.967197i | \(0.581755\pi\) | |||||||
\(30\) | 1.43709e10 | 3.59911 | ||||||||
\(31\) | 1.26677e9 | 0.256357 | 0.128179 | − | 0.991751i | \(-0.459087\pi\) | ||||
0.128179 | + | 0.991751i | \(0.459087\pi\) | |||||||
\(32\) | −5.71450e9 | −0.940813 | ||||||||
\(33\) | 1.90820e10 | 2.57208 | ||||||||
\(34\) | −1.42006e10 | −1.57650 | ||||||||
\(35\) | 7.00859e9 | 0.644449 | ||||||||
\(36\) | 7.45936e10 | 5.71130 | ||||||||
\(37\) | 1.32290e10 | 0.847651 | 0.423826 | − | 0.905744i | \(-0.360687\pi\) | ||||
0.423826 | + | 0.905744i | \(0.360687\pi\) | |||||||
\(38\) | 1.06454e10 | 0.573547 | ||||||||
\(39\) | −7.46625e10 | −3.39768 | ||||||||
\(40\) | −6.10174e10 | −2.35539 | ||||||||
\(41\) | 7.60558e9 | 0.250056 | 0.125028 | − | 0.992153i | \(-0.460098\pi\) | ||||
0.125028 | + | 0.992153i | \(0.460098\pi\) | |||||||
\(42\) | 7.32621e10 | 2.05949 | ||||||||
\(43\) | −5.09971e9 | −0.123027 | −0.0615135 | − | 0.998106i | \(-0.519593\pi\) | ||||
−0.0615135 | + | 0.998106i | \(0.519593\pi\) | |||||||
\(44\) | −1.46669e11 | −3.04716 | ||||||||
\(45\) | 1.51118e11 | 2.71290 | ||||||||
\(46\) | −2.40959e10 | −0.374987 | ||||||||
\(47\) | −7.63675e10 | −1.03341 | −0.516705 | − | 0.856164i | \(-0.672841\pi\) | ||||
−0.516705 | + | 0.856164i | \(0.672841\pi\) | |||||||
\(48\) | −2.80813e11 | −3.31398 | ||||||||
\(49\) | −6.11595e10 | −0.631233 | ||||||||
\(50\) | −2.50799e10 | −0.226998 | ||||||||
\(51\) | −2.07741e11 | −1.65316 | ||||||||
\(52\) | 5.73872e11 | 4.02526 | ||||||||
\(53\) | 7.15348e9 | 0.0443327 | 0.0221664 | − | 0.999754i | \(-0.492944\pi\) | ||||
0.0221664 | + | 0.999754i | \(0.492944\pi\) | |||||||
\(54\) | 9.61727e11 | 5.27828 | ||||||||
\(55\) | −2.97133e11 | −1.44742 | ||||||||
\(56\) | −3.11064e11 | −1.34781 | ||||||||
\(57\) | 1.55732e11 | 0.601438 | ||||||||
\(58\) | 2.64893e11 | 0.913668 | ||||||||
\(59\) | 1.05569e11 | 0.325836 | 0.162918 | − | 0.986640i | \(-0.447909\pi\) | ||||
0.162918 | + | 0.986640i | \(0.447909\pi\) | |||||||
\(60\) | −1.61589e12 | −4.47125 | ||||||||
\(61\) | 3.01020e10 | 0.0748086 | 0.0374043 | − | 0.999300i | \(-0.488091\pi\) | ||||
0.0374043 | + | 0.999300i | \(0.488091\pi\) | |||||||
\(62\) | −2.06192e11 | −0.461026 | ||||||||
\(63\) | 7.70390e11 | 1.55238 | ||||||||
\(64\) | −3.59361e10 | −0.0653674 | ||||||||
\(65\) | 1.16260e12 | 1.91202 | ||||||||
\(66\) | −3.10599e12 | −4.62557 | ||||||||
\(67\) | 1.15435e12 | 1.55902 | 0.779512 | − | 0.626387i | \(-0.215467\pi\) | ||||
0.779512 | + | 0.626387i | \(0.215467\pi\) | |||||||
\(68\) | 1.59674e12 | 1.95851 | ||||||||
\(69\) | −3.52499e11 | −0.393223 | ||||||||
\(70\) | −1.14079e12 | −1.15896 | ||||||||
\(71\) | 5.97518e11 | 0.553569 | 0.276785 | − | 0.960932i | \(-0.410731\pi\) | ||||
0.276785 | + | 0.960932i | \(0.410731\pi\) | |||||||
\(72\) | −6.70709e12 | −5.67378 | ||||||||
\(73\) | 4.44729e11 | 0.343951 | 0.171976 | − | 0.985101i | \(-0.444985\pi\) | ||||
0.171976 | + | 0.985101i | \(0.444985\pi\) | |||||||
\(74\) | −2.15330e12 | −1.52440 | ||||||||
\(75\) | −3.66895e11 | −0.238036 | ||||||||
\(76\) | −1.19699e12 | −0.712528 | ||||||||
\(77\) | −1.51477e12 | −0.828243 | ||||||||
\(78\) | 1.21528e13 | 6.11031 | ||||||||
\(79\) | 2.62211e12 | 1.21360 | 0.606798 | − | 0.794856i | \(-0.292454\pi\) | ||||
0.606798 | + | 0.794856i | \(0.292454\pi\) | |||||||
\(80\) | 4.37264e12 | 1.86492 | ||||||||
\(81\) | 7.57120e12 | 2.97860 | ||||||||
\(82\) | −1.23796e12 | −0.449695 | ||||||||
\(83\) | −4.10881e12 | −1.37946 | −0.689729 | − | 0.724067i | \(-0.742270\pi\) | ||||
−0.689729 | + | 0.724067i | \(0.742270\pi\) | |||||||
\(84\) | −8.23774e12 | −2.55854 | ||||||||
\(85\) | 3.23480e12 | 0.930304 | ||||||||
\(86\) | 8.30082e11 | 0.221249 | ||||||||
\(87\) | 3.87512e12 | 0.958099 | ||||||||
\(88\) | 1.31877e13 | 3.02714 | ||||||||
\(89\) | 9.87837e10 | 0.0210693 | 0.0105347 | − | 0.999945i | \(-0.496647\pi\) | ||||
0.0105347 | + | 0.999945i | \(0.496647\pi\) | |||||||
\(90\) | −2.45975e13 | −4.87881 | ||||||||
\(91\) | 5.92686e12 | 1.09410 | ||||||||
\(92\) | 2.70939e12 | 0.465854 | ||||||||
\(93\) | −3.01639e12 | −0.483446 | ||||||||
\(94\) | 1.24304e13 | 1.85846 | ||||||||
\(95\) | −2.42496e12 | −0.338455 | ||||||||
\(96\) | 1.36072e13 | 1.77421 | ||||||||
\(97\) | 9.35623e12 | 1.14047 | 0.570236 | − | 0.821481i | \(-0.306852\pi\) | ||||
0.570236 | + | 0.821481i | \(0.306852\pi\) | |||||||
\(98\) | 9.95497e12 | 1.13519 | ||||||||
\(99\) | −3.26612e13 | −3.48661 | ||||||||
\(100\) | 2.82003e12 | 0.282003 | ||||||||
\(101\) | −1.76126e13 | −1.65095 | −0.825475 | − | 0.564439i | \(-0.809093\pi\) | ||||
−0.825475 | + | 0.564439i | \(0.809093\pi\) | |||||||
\(102\) | 3.38140e13 | 2.97301 | ||||||||
\(103\) | 2.02756e13 | 1.67314 | 0.836568 | − | 0.547864i | \(-0.184559\pi\) | ||||
0.836568 | + | 0.547864i | \(0.184559\pi\) | |||||||
\(104\) | −5.15998e13 | −3.99881 | ||||||||
\(105\) | −1.66887e13 | −1.21532 | ||||||||
\(106\) | −1.16438e12 | −0.0797269 | ||||||||
\(107\) | 1.68773e13 | 1.08720 | 0.543599 | − | 0.839345i | \(-0.317061\pi\) | ||||
0.543599 | + | 0.839345i | \(0.317061\pi\) | |||||||
\(108\) | −1.08138e14 | −6.55731 | ||||||||
\(109\) | −1.34752e13 | −0.769597 | −0.384799 | − | 0.923001i | \(-0.625729\pi\) | ||||
−0.384799 | + | 0.923001i | \(0.625729\pi\) | |||||||
\(110\) | 4.83645e13 | 2.60300 | ||||||||
\(111\) | −3.15006e13 | −1.59853 | ||||||||
\(112\) | 2.22915e13 | 1.06714 | ||||||||
\(113\) | −2.89653e13 | −1.30879 | −0.654393 | − | 0.756155i | \(-0.727076\pi\) | ||||
−0.654393 | + | 0.756155i | \(0.727076\pi\) | |||||||
\(114\) | −2.53485e13 | −1.08161 | ||||||||
\(115\) | 5.48889e12 | 0.221283 | ||||||||
\(116\) | −2.97851e13 | −1.13507 | ||||||||
\(117\) | 1.27794e14 | 4.60576 | ||||||||
\(118\) | −1.71836e13 | −0.585977 | ||||||||
\(119\) | 1.64909e13 | 0.532339 | ||||||||
\(120\) | 1.45293e14 | 4.44187 | ||||||||
\(121\) | 2.96970e13 | 0.860215 | ||||||||
\(122\) | −4.89972e12 | −0.134534 | ||||||||
\(123\) | −1.81102e13 | −0.471563 | ||||||||
\(124\) | 2.31846e13 | 0.572742 | ||||||||
\(125\) | −3.95483e13 | −0.927284 | ||||||||
\(126\) | −1.25397e14 | −2.79176 | ||||||||
\(127\) | −3.35902e13 | −0.710377 | −0.355189 | − | 0.934795i | \(-0.615583\pi\) | ||||
−0.355189 | + | 0.934795i | \(0.615583\pi\) | |||||||
\(128\) | 5.26625e13 | 1.05837 | ||||||||
\(129\) | 1.21433e13 | 0.232008 | ||||||||
\(130\) | −1.89236e14 | −3.43853 | ||||||||
\(131\) | 5.17174e13 | 0.894074 | 0.447037 | − | 0.894515i | \(-0.352479\pi\) | ||||
0.447037 | + | 0.894515i | \(0.352479\pi\) | |||||||
\(132\) | 3.49244e14 | 5.74643 | ||||||||
\(133\) | −1.23623e13 | −0.193671 | ||||||||
\(134\) | −1.87895e14 | −2.80371 | ||||||||
\(135\) | −2.19075e14 | −3.11476 | ||||||||
\(136\) | −1.43571e14 | −1.94565 | ||||||||
\(137\) | 1.28569e14 | 1.66132 | 0.830659 | − | 0.556781i | \(-0.187964\pi\) | ||||
0.830659 | + | 0.556781i | \(0.187964\pi\) | |||||||
\(138\) | 5.73764e13 | 0.707163 | ||||||||
\(139\) | −2.89383e13 | −0.340311 | −0.170156 | − | 0.985417i | \(-0.554427\pi\) | ||||
−0.170156 | + | 0.985417i | \(0.554427\pi\) | |||||||
\(140\) | 1.28273e14 | 1.43980 | ||||||||
\(141\) | 1.81844e14 | 1.94883 | ||||||||
\(142\) | −9.72583e13 | −0.995526 | ||||||||
\(143\) | −2.51273e14 | −2.45732 | ||||||||
\(144\) | 4.80645e14 | 4.49229 | ||||||||
\(145\) | −6.03409e13 | −0.539163 | ||||||||
\(146\) | −7.23887e13 | −0.618554 | ||||||||
\(147\) | 1.45631e14 | 1.19040 | ||||||||
\(148\) | 2.42121e14 | 1.89379 | ||||||||
\(149\) | −1.55111e14 | −1.16127 | −0.580634 | − | 0.814165i | \(-0.697195\pi\) | ||||
−0.580634 | + | 0.814165i | \(0.697195\pi\) | |||||||
\(150\) | 5.97196e13 | 0.428079 | ||||||||
\(151\) | 1.20273e14 | 0.825691 | 0.412846 | − | 0.910801i | \(-0.364535\pi\) | ||||
0.412846 | + | 0.910801i | \(0.364535\pi\) | |||||||
\(152\) | 1.07627e14 | 0.707847 | ||||||||
\(153\) | 3.55573e14 | 2.24096 | ||||||||
\(154\) | 2.46560e14 | 1.48949 | ||||||||
\(155\) | 4.69692e13 | 0.272056 | ||||||||
\(156\) | −1.36649e15 | −7.59095 | ||||||||
\(157\) | 1.49045e14 | 0.794272 | 0.397136 | − | 0.917760i | \(-0.370004\pi\) | ||||
0.397136 | + | 0.917760i | \(0.370004\pi\) | |||||||
\(158\) | −4.26801e14 | −2.18250 | ||||||||
\(159\) | −1.70337e13 | −0.0836040 | ||||||||
\(160\) | −2.11883e14 | −0.998426 | ||||||||
\(161\) | 2.79821e13 | 0.126623 | ||||||||
\(162\) | −1.23237e15 | −5.35665 | ||||||||
\(163\) | 1.73639e14 | 0.725150 | 0.362575 | − | 0.931955i | \(-0.381898\pi\) | ||||
0.362575 | + | 0.931955i | \(0.381898\pi\) | |||||||
\(164\) | 1.39199e14 | 0.558664 | ||||||||
\(165\) | 7.07526e14 | 2.72958 | ||||||||
\(166\) | 6.68793e14 | 2.48079 | ||||||||
\(167\) | 2.43080e14 | 0.867146 | 0.433573 | − | 0.901118i | \(-0.357253\pi\) | ||||
0.433573 | + | 0.901118i | \(0.357253\pi\) | |||||||
\(168\) | 7.40696e14 | 2.54173 | ||||||||
\(169\) | 6.80282e14 | 2.24608 | ||||||||
\(170\) | −5.26530e14 | −1.67304 | ||||||||
\(171\) | −2.66553e14 | −0.815285 | ||||||||
\(172\) | −9.33360e13 | −0.274862 | ||||||||
\(173\) | −1.35247e14 | −0.383556 | −0.191778 | − | 0.981438i | \(-0.561425\pi\) | ||||
−0.191778 | + | 0.981438i | \(0.561425\pi\) | |||||||
\(174\) | −6.30755e14 | −1.72302 | ||||||||
\(175\) | 2.91249e13 | 0.0766508 | ||||||||
\(176\) | −9.45063e14 | −2.39678 | ||||||||
\(177\) | −2.51379e14 | −0.614472 | ||||||||
\(178\) | −1.60791e13 | −0.0378905 | ||||||||
\(179\) | 1.88153e14 | 0.427531 | 0.213765 | − | 0.976885i | \(-0.431427\pi\) | ||||
0.213765 | + | 0.976885i | \(0.431427\pi\) | |||||||
\(180\) | 2.76579e15 | 6.06105 | ||||||||
\(181\) | −2.56029e13 | −0.0541226 | −0.0270613 | − | 0.999634i | \(-0.508615\pi\) | ||||
−0.0270613 | + | 0.999634i | \(0.508615\pi\) | |||||||
\(182\) | −9.64718e14 | −1.96760 | ||||||||
\(183\) | −7.16781e13 | −0.141076 | ||||||||
\(184\) | −2.43615e14 | −0.462794 | ||||||||
\(185\) | 4.90508e14 | 0.899559 | ||||||||
\(186\) | 4.90979e14 | 0.869418 | ||||||||
\(187\) | −6.99141e14 | −1.19562 | ||||||||
\(188\) | −1.39769e15 | −2.30880 | ||||||||
\(189\) | −1.11684e15 | −1.78233 | ||||||||
\(190\) | 3.94711e14 | 0.608669 | ||||||||
\(191\) | 1.03200e15 | 1.53802 | 0.769009 | − | 0.639238i | \(-0.220750\pi\) | ||||
0.769009 | + | 0.639238i | \(0.220750\pi\) | |||||||
\(192\) | 8.55701e13 | 0.123272 | ||||||||
\(193\) | −5.29871e14 | −0.737985 | −0.368992 | − | 0.929432i | \(-0.620297\pi\) | ||||
−0.368992 | + | 0.929432i | \(0.620297\pi\) | |||||||
\(194\) | −1.52292e15 | −2.05100 | ||||||||
\(195\) | −2.76834e15 | −3.60574 | ||||||||
\(196\) | −1.11936e15 | −1.41027 | ||||||||
\(197\) | 5.75465e14 | 0.701437 | 0.350718 | − | 0.936481i | \(-0.385937\pi\) | ||||
0.350718 | + | 0.936481i | \(0.385937\pi\) | |||||||
\(198\) | 5.31627e15 | 6.27023 | ||||||||
\(199\) | 4.03658e14 | 0.460754 | 0.230377 | − | 0.973101i | \(-0.426004\pi\) | ||||
0.230377 | + | 0.973101i | \(0.426004\pi\) | |||||||
\(200\) | −2.53564e14 | −0.280151 | ||||||||
\(201\) | −2.74872e15 | −2.94006 | ||||||||
\(202\) | 2.86681e15 | 2.96903 | ||||||||
\(203\) | −3.07615e14 | −0.308520 | ||||||||
\(204\) | −3.80211e15 | −3.69342 | ||||||||
\(205\) | 2.82000e14 | 0.265368 | ||||||||
\(206\) | −3.30026e15 | −3.00893 | ||||||||
\(207\) | 6.03344e14 | 0.533037 | ||||||||
\(208\) | 3.69776e15 | 3.16611 | ||||||||
\(209\) | 5.24108e14 | 0.434981 | ||||||||
\(210\) | 2.71642e15 | 2.18560 | ||||||||
\(211\) | 1.42907e15 | 1.11485 | 0.557425 | − | 0.830227i | \(-0.311789\pi\) | ||||
0.557425 | + | 0.830227i | \(0.311789\pi\) | |||||||
\(212\) | 1.30925e14 | 0.0990463 | ||||||||
\(213\) | −1.42279e15 | −1.04394 | ||||||||
\(214\) | −2.74713e15 | −1.95519 | ||||||||
\(215\) | −1.89087e14 | −0.130561 | ||||||||
\(216\) | 9.72327e15 | 6.51423 | ||||||||
\(217\) | 2.39447e14 | 0.155676 | ||||||||
\(218\) | 2.19337e15 | 1.38403 | ||||||||
\(219\) | −1.05898e15 | −0.648634 | ||||||||
\(220\) | −5.43820e15 | −3.23376 | ||||||||
\(221\) | 2.73553e15 | 1.57940 | ||||||||
\(222\) | 5.12737e15 | 2.87475 | ||||||||
\(223\) | −2.19961e15 | −1.19775 | −0.598873 | − | 0.800844i | \(-0.704385\pi\) | ||||
−0.598873 | + | 0.800844i | \(0.704385\pi\) | |||||||
\(224\) | −1.08017e15 | −0.571320 | ||||||||
\(225\) | 6.27984e14 | 0.322672 | ||||||||
\(226\) | 4.71470e15 | 2.35369 | ||||||||
\(227\) | 4.52431e14 | 0.219474 | 0.109737 | − | 0.993961i | \(-0.464999\pi\) | ||||
0.109737 | + | 0.993961i | \(0.464999\pi\) | |||||||
\(228\) | 2.85024e15 | 1.34371 | ||||||||
\(229\) | 2.17418e15 | 0.996242 | 0.498121 | − | 0.867108i | \(-0.334024\pi\) | ||||
0.498121 | + | 0.867108i | \(0.334024\pi\) | |||||||
\(230\) | −8.93429e14 | −0.397950 | ||||||||
\(231\) | 3.60693e15 | 1.56192 | ||||||||
\(232\) | 2.67813e15 | 1.12761 | ||||||||
\(233\) | 2.29330e15 | 0.938961 | 0.469480 | − | 0.882943i | \(-0.344441\pi\) | ||||
0.469480 | + | 0.882943i | \(0.344441\pi\) | |||||||
\(234\) | −2.08010e16 | −8.28289 | ||||||||
\(235\) | −2.83156e15 | −1.09669 | ||||||||
\(236\) | 1.93215e15 | 0.727970 | ||||||||
\(237\) | −6.24368e15 | −2.28864 | ||||||||
\(238\) | −2.68423e15 | −0.957346 | ||||||||
\(239\) | −1.19066e15 | −0.413239 | −0.206620 | − | 0.978421i | \(-0.566246\pi\) | ||||
−0.206620 | + | 0.978421i | \(0.566246\pi\) | |||||||
\(240\) | −1.04120e16 | −3.51691 | ||||||||
\(241\) | 2.21497e15 | 0.728210 | 0.364105 | − | 0.931358i | \(-0.381375\pi\) | ||||
0.364105 | + | 0.931358i | \(0.381375\pi\) | |||||||
\(242\) | −4.83379e15 | −1.54699 | ||||||||
\(243\) | −8.60831e15 | −2.68211 | ||||||||
\(244\) | 5.50934e14 | 0.167134 | ||||||||
\(245\) | −2.26768e15 | −0.669888 | ||||||||
\(246\) | 2.94780e15 | 0.848048 | ||||||||
\(247\) | −2.05068e15 | −0.574603 | ||||||||
\(248\) | −2.08465e15 | −0.568980 | ||||||||
\(249\) | 9.78379e15 | 2.60143 | ||||||||
\(250\) | 6.43729e15 | 1.66761 | ||||||||
\(251\) | −2.19417e15 | −0.553848 | −0.276924 | − | 0.960892i | \(-0.589315\pi\) | ||||
−0.276924 | + | 0.960892i | \(0.589315\pi\) | |||||||
\(252\) | 1.40999e16 | 3.46826 | ||||||||
\(253\) | −1.18632e15 | −0.284392 | ||||||||
\(254\) | 5.46750e15 | 1.27753 | ||||||||
\(255\) | −7.70262e15 | −1.75440 | ||||||||
\(256\) | −8.27752e15 | −1.83798 | ||||||||
\(257\) | 4.57805e15 | 0.991095 | 0.495548 | − | 0.868581i | \(-0.334967\pi\) | ||||
0.495548 | + | 0.868581i | \(0.334967\pi\) | |||||||
\(258\) | −1.97657e15 | −0.417238 | ||||||||
\(259\) | 2.50059e15 | 0.514746 | ||||||||
\(260\) | 2.12781e16 | 4.27175 | ||||||||
\(261\) | −6.63273e15 | −1.29876 | ||||||||
\(262\) | −8.41807e15 | −1.60788 | ||||||||
\(263\) | 8.12564e15 | 1.51407 | 0.757034 | − | 0.653376i | \(-0.226648\pi\) | ||||
0.757034 | + | 0.653376i | \(0.226648\pi\) | |||||||
\(264\) | −3.14023e16 | −5.70868 | ||||||||
\(265\) | 2.65237e14 | 0.0470475 | ||||||||
\(266\) | 2.01222e15 | 0.348293 | ||||||||
\(267\) | −2.35221e14 | −0.0397331 | ||||||||
\(268\) | 2.11273e16 | 3.48311 | ||||||||
\(269\) | −7.05029e14 | −0.113453 | −0.0567267 | − | 0.998390i | \(-0.518066\pi\) | ||||
−0.0567267 | + | 0.998390i | \(0.518066\pi\) | |||||||
\(270\) | 3.56590e16 | 5.60150 | ||||||||
\(271\) | −5.16985e15 | −0.792825 | −0.396412 | − | 0.918073i | \(-0.629745\pi\) | ||||
−0.396412 | + | 0.918073i | \(0.629745\pi\) | |||||||
\(272\) | 1.02886e16 | 1.54049 | ||||||||
\(273\) | −1.41129e16 | −2.06328 | ||||||||
\(274\) | −2.09273e16 | −2.98768 | ||||||||
\(275\) | −1.23477e15 | −0.172156 | ||||||||
\(276\) | −6.45151e15 | −0.878522 | ||||||||
\(277\) | −4.92917e15 | −0.655625 | −0.327812 | − | 0.944743i | \(-0.606311\pi\) | ||||
−0.327812 | + | 0.944743i | \(0.606311\pi\) | |||||||
\(278\) | 4.71029e15 | 0.612007 | ||||||||
\(279\) | 5.16290e15 | 0.655340 | ||||||||
\(280\) | −1.15337e16 | −1.43034 | ||||||||
\(281\) | 1.52979e16 | 1.85371 | 0.926854 | − | 0.375422i | \(-0.122502\pi\) | ||||
0.926854 | + | 0.375422i | \(0.122502\pi\) | |||||||
\(282\) | −2.95988e16 | −3.50474 | ||||||||
\(283\) | 1.54101e16 | 1.78317 | 0.891586 | − | 0.452852i | \(-0.149593\pi\) | ||||
0.891586 | + | 0.452852i | \(0.149593\pi\) | |||||||
\(284\) | 1.09359e16 | 1.23676 | ||||||||
\(285\) | 5.77424e15 | 0.638268 | ||||||||
\(286\) | 4.08998e16 | 4.41918 | ||||||||
\(287\) | 1.43762e15 | 0.151849 | ||||||||
\(288\) | −2.32903e16 | −2.40505 | ||||||||
\(289\) | −2.29324e15 | −0.231533 | ||||||||
\(290\) | 9.82172e15 | 0.969618 | ||||||||
\(291\) | −2.22788e16 | −2.15074 | ||||||||
\(292\) | 8.13953e15 | 0.768441 | ||||||||
\(293\) | −7.92823e15 | −0.732044 | −0.366022 | − | 0.930606i | \(-0.619280\pi\) | ||||
−0.366022 | + | 0.930606i | \(0.619280\pi\) | |||||||
\(294\) | −2.37045e16 | −2.14078 | ||||||||
\(295\) | 3.91431e15 | 0.345790 | ||||||||
\(296\) | −2.17703e16 | −1.88135 | ||||||||
\(297\) | 4.73489e16 | 4.00307 | ||||||||
\(298\) | 2.52475e16 | 2.08840 | ||||||||
\(299\) | 4.64172e15 | 0.375678 | ||||||||
\(300\) | −6.71499e15 | −0.531811 | ||||||||
\(301\) | −9.63959e14 | −0.0747096 | ||||||||
\(302\) | −1.95769e16 | −1.48490 | ||||||||
\(303\) | 4.19386e16 | 3.11341 | ||||||||
\(304\) | −7.71282e15 | −0.560448 | ||||||||
\(305\) | 1.11613e15 | 0.0793897 | ||||||||
\(306\) | −5.78767e16 | −4.03009 | ||||||||
\(307\) | −1.91914e16 | −1.30830 | −0.654151 | − | 0.756364i | \(-0.726974\pi\) | ||||
−0.654151 | + | 0.756364i | \(0.726974\pi\) | |||||||
\(308\) | −2.77237e16 | −1.85042 | ||||||||
\(309\) | −4.82796e16 | −3.15525 | ||||||||
\(310\) | −7.64521e15 | −0.489258 | ||||||||
\(311\) | −1.45504e16 | −0.911869 | −0.455934 | − | 0.890013i | \(-0.650695\pi\) | ||||
−0.455934 | + | 0.890013i | \(0.650695\pi\) | |||||||
\(312\) | 1.22868e17 | 7.54108 | ||||||||
\(313\) | −1.66747e16 | −1.00235 | −0.501177 | − | 0.865345i | \(-0.667099\pi\) | ||||
−0.501177 | + | 0.865345i | \(0.667099\pi\) | |||||||
\(314\) | −2.42601e16 | −1.42840 | ||||||||
\(315\) | 2.85646e16 | 1.64744 | ||||||||
\(316\) | 4.79903e16 | 2.71136 | ||||||||
\(317\) | −1.42181e16 | −0.786966 | −0.393483 | − | 0.919332i | \(-0.628730\pi\) | ||||
−0.393483 | + | 0.919332i | \(0.628730\pi\) | |||||||
\(318\) | 2.77258e15 | 0.150351 | ||||||||
\(319\) | 1.30415e16 | 0.692930 | ||||||||
\(320\) | −1.33244e15 | −0.0693703 | ||||||||
\(321\) | −4.01878e16 | −2.05027 | ||||||||
\(322\) | −4.55466e15 | −0.227716 | ||||||||
\(323\) | −5.70581e15 | −0.279577 | ||||||||
\(324\) | 1.38570e17 | 6.65466 | ||||||||
\(325\) | 4.83128e15 | 0.227416 | ||||||||
\(326\) | −2.82633e16 | −1.30409 | ||||||||
\(327\) | 3.20868e16 | 1.45133 | ||||||||
\(328\) | −1.25161e16 | −0.554994 | ||||||||
\(329\) | −1.44352e16 | −0.627550 | ||||||||
\(330\) | −1.15164e17 | −4.90882 | ||||||||
\(331\) | 2.48098e16 | 1.03691 | 0.518455 | − | 0.855105i | \(-0.326508\pi\) | ||||
0.518455 | + | 0.855105i | \(0.326508\pi\) | |||||||
\(332\) | −7.52004e16 | −3.08193 | ||||||||
\(333\) | 5.39170e16 | 2.16690 | ||||||||
\(334\) | −3.95662e16 | −1.55945 | ||||||||
\(335\) | 4.28013e16 | 1.65449 | ||||||||
\(336\) | −5.30800e16 | −2.01245 | ||||||||
\(337\) | −1.84939e16 | −0.687755 | −0.343877 | − | 0.939015i | \(-0.611740\pi\) | ||||
−0.343877 | + | 0.939015i | \(0.611740\pi\) | |||||||
\(338\) | −1.10730e17 | −4.03930 | ||||||||
\(339\) | 6.89714e16 | 2.46815 | ||||||||
\(340\) | 5.92041e16 | 2.07845 | ||||||||
\(341\) | −1.01515e16 | −0.349645 | ||||||||
\(342\) | 4.33870e16 | 1.46619 | ||||||||
\(343\) | −2.98747e16 | −0.990586 | ||||||||
\(344\) | 8.39231e15 | 0.273056 | ||||||||
\(345\) | −1.30700e16 | −0.417303 | ||||||||
\(346\) | 2.20142e16 | 0.689777 | ||||||||
\(347\) | 2.57363e16 | 0.791416 | 0.395708 | − | 0.918376i | \(-0.370499\pi\) | ||||
0.395708 | + | 0.918376i | \(0.370499\pi\) | |||||||
\(348\) | 7.09233e16 | 2.14054 | ||||||||
\(349\) | 6.00461e16 | 1.77877 | 0.889384 | − | 0.457161i | \(-0.151134\pi\) | ||||
0.889384 | + | 0.457161i | \(0.151134\pi\) | |||||||
\(350\) | −4.74067e15 | −0.137847 | ||||||||
\(351\) | −1.85263e17 | −5.28800 | ||||||||
\(352\) | 4.57944e16 | 1.28317 | ||||||||
\(353\) | 2.06395e16 | 0.567759 | 0.283880 | − | 0.958860i | \(-0.408378\pi\) | ||||
0.283880 | + | 0.958860i | \(0.408378\pi\) | |||||||
\(354\) | 4.09170e16 | 1.10505 | ||||||||
\(355\) | 2.21548e16 | 0.587468 | ||||||||
\(356\) | 1.80796e15 | 0.0470722 | ||||||||
\(357\) | −3.92676e16 | −1.00390 | ||||||||
\(358\) | −3.06258e16 | −0.768861 | ||||||||
\(359\) | 2.66939e16 | 0.658109 | 0.329054 | − | 0.944311i | \(-0.393270\pi\) | ||||
0.329054 | + | 0.944311i | \(0.393270\pi\) | |||||||
\(360\) | −2.48686e17 | −6.02123 | ||||||||
\(361\) | −3.77756e16 | −0.898287 | ||||||||
\(362\) | 4.16740e15 | 0.0973329 | ||||||||
\(363\) | −7.07136e16 | −1.62222 | ||||||||
\(364\) | 1.08475e17 | 2.44438 | ||||||||
\(365\) | 1.64897e16 | 0.365014 | ||||||||
\(366\) | 1.16671e16 | 0.253708 | ||||||||
\(367\) | 2.30658e16 | 0.492763 | 0.246382 | − | 0.969173i | \(-0.420758\pi\) | ||||
0.246382 | + | 0.969173i | \(0.420758\pi\) | |||||||
\(368\) | 1.74580e16 | 0.366423 | ||||||||
\(369\) | 3.09977e16 | 0.639232 | ||||||||
\(370\) | −7.98401e16 | −1.61775 | ||||||||
\(371\) | 1.35217e15 | 0.0269216 | ||||||||
\(372\) | −5.52066e16 | −1.08009 | ||||||||
\(373\) | 3.39408e16 | 0.652552 | 0.326276 | − | 0.945275i | \(-0.394206\pi\) | ||||
0.326276 | + | 0.945275i | \(0.394206\pi\) | |||||||
\(374\) | 1.13799e17 | 2.15018 | ||||||||
\(375\) | 9.41713e16 | 1.74870 | ||||||||
\(376\) | 1.25674e17 | 2.29363 | ||||||||
\(377\) | −5.10277e16 | −0.915350 | ||||||||
\(378\) | 1.81788e17 | 3.20530 | ||||||||
\(379\) | −7.43215e16 | −1.28813 | −0.644065 | − | 0.764971i | \(-0.722753\pi\) | ||||
−0.644065 | + | 0.764971i | \(0.722753\pi\) | |||||||
\(380\) | −4.43821e16 | −0.756161 | ||||||||
\(381\) | 7.99842e16 | 1.33965 | ||||||||
\(382\) | −1.67979e17 | −2.76594 | ||||||||
\(383\) | −3.24509e16 | −0.525333 | −0.262666 | − | 0.964887i | \(-0.584602\pi\) | ||||
−0.262666 | + | 0.964887i | \(0.584602\pi\) | |||||||
\(384\) | −1.25399e17 | −1.99590 | ||||||||
\(385\) | −5.61648e16 | −0.878961 | ||||||||
\(386\) | 8.62473e16 | 1.32717 | ||||||||
\(387\) | −2.07847e16 | −0.314501 | ||||||||
\(388\) | 1.71240e17 | 2.54799 | ||||||||
\(389\) | 4.26831e16 | 0.624573 | 0.312287 | − | 0.949988i | \(-0.398905\pi\) | ||||
0.312287 | + | 0.949988i | \(0.398905\pi\) | |||||||
\(390\) | 4.50604e17 | 6.48448 | ||||||||
\(391\) | 1.29151e16 | 0.182788 | ||||||||
\(392\) | 1.00647e17 | 1.40101 | ||||||||
\(393\) | −1.23148e17 | −1.68607 | ||||||||
\(394\) | −9.36687e16 | −1.26145 | ||||||||
\(395\) | 9.72226e16 | 1.28791 | ||||||||
\(396\) | −5.97772e17 | −7.78963 | ||||||||
\(397\) | −5.73276e16 | −0.734895 | −0.367448 | − | 0.930044i | \(-0.619768\pi\) | ||||
−0.367448 | + | 0.930044i | \(0.619768\pi\) | |||||||
\(398\) | −6.57036e16 | −0.828609 | ||||||||
\(399\) | 2.94368e16 | 0.365230 | ||||||||
\(400\) | 1.81709e16 | 0.221813 | ||||||||
\(401\) | −2.84487e16 | −0.341684 | −0.170842 | − | 0.985298i | \(-0.554649\pi\) | ||||
−0.170842 | + | 0.985298i | \(0.554649\pi\) | |||||||
\(402\) | 4.47410e17 | 5.28733 | ||||||||
\(403\) | 3.97199e16 | 0.461876 | ||||||||
\(404\) | −3.22349e17 | −3.68848 | ||||||||
\(405\) | 2.80726e17 | 3.16100 | ||||||||
\(406\) | 5.00707e16 | 0.554835 | ||||||||
\(407\) | −1.06014e17 | −1.15611 | ||||||||
\(408\) | 3.41867e17 | 3.66916 | ||||||||
\(409\) | −5.23729e15 | −0.0553229 | −0.0276615 | − | 0.999617i | \(-0.508806\pi\) | ||||
−0.0276615 | + | 0.999617i | \(0.508806\pi\) | |||||||
\(410\) | −4.59013e16 | −0.477232 | ||||||||
\(411\) | −3.06145e17 | −3.13297 | ||||||||
\(412\) | 3.71088e17 | 3.73805 | ||||||||
\(413\) | 1.99550e16 | 0.197868 | ||||||||
\(414\) | −9.82065e16 | −0.958601 | ||||||||
\(415\) | −1.52347e17 | −1.46393 | ||||||||
\(416\) | −1.79180e17 | −1.69505 | ||||||||
\(417\) | 6.89070e16 | 0.641769 | ||||||||
\(418\) | −8.53093e16 | −0.782259 | ||||||||
\(419\) | −1.67230e16 | −0.150982 | −0.0754908 | − | 0.997147i | \(-0.524052\pi\) | ||||
−0.0754908 | + | 0.997147i | \(0.524052\pi\) | |||||||
\(420\) | −3.05439e17 | −2.71522 | ||||||||
\(421\) | 7.74959e16 | 0.678337 | 0.339168 | − | 0.940726i | \(-0.389854\pi\) | ||||
0.339168 | + | 0.940726i | \(0.389854\pi\) | |||||||
\(422\) | −2.32610e17 | −2.00492 | ||||||||
\(423\) | −3.11248e17 | −2.64176 | ||||||||
\(424\) | −1.17721e16 | −0.0983956 | ||||||||
\(425\) | 1.34425e16 | 0.110650 | ||||||||
\(426\) | 2.31589e17 | 1.87739 | ||||||||
\(427\) | 5.68995e15 | 0.0454284 | ||||||||
\(428\) | 3.08892e17 | 2.42897 | ||||||||
\(429\) | 5.98324e17 | 4.63408 | ||||||||
\(430\) | 3.07779e16 | 0.234797 | ||||||||
\(431\) | −9.90993e16 | −0.744678 | −0.372339 | − | 0.928097i | \(-0.621444\pi\) | ||||
−0.372339 | + | 0.928097i | \(0.621444\pi\) | |||||||
\(432\) | −6.96792e17 | −5.15773 | ||||||||
\(433\) | 7.08003e16 | 0.516254 | 0.258127 | − | 0.966111i | \(-0.416895\pi\) | ||||
0.258127 | + | 0.966111i | \(0.416895\pi\) | |||||||
\(434\) | −3.89749e16 | −0.279964 | ||||||||
\(435\) | 1.43682e17 | 1.01677 | ||||||||
\(436\) | −2.46626e17 | −1.71940 | ||||||||
\(437\) | −9.68175e15 | −0.0665004 | ||||||||
\(438\) | 1.72370e17 | 1.16649 | ||||||||
\(439\) | 1.98677e17 | 1.32474 | 0.662368 | − | 0.749179i | \(-0.269552\pi\) | ||||
0.662368 | + | 0.749179i | \(0.269552\pi\) | |||||||
\(440\) | 4.88976e17 | 3.21252 | ||||||||
\(441\) | −2.49265e17 | −1.61366 | ||||||||
\(442\) | −4.45264e17 | −2.84036 | ||||||||
\(443\) | 1.81878e16 | 0.114329 | 0.0571646 | − | 0.998365i | \(-0.481794\pi\) | ||||
0.0571646 | + | 0.998365i | \(0.481794\pi\) | |||||||
\(444\) | −5.76531e17 | −3.57136 | ||||||||
\(445\) | 3.66271e15 | 0.0223595 | ||||||||
\(446\) | 3.58032e17 | 2.15400 | ||||||||
\(447\) | 3.69346e17 | 2.18995 | ||||||||
\(448\) | −6.79273e15 | −0.0396951 | ||||||||
\(449\) | 3.99244e16 | 0.229952 | 0.114976 | − | 0.993368i | \(-0.463321\pi\) | ||||
0.114976 | + | 0.993368i | \(0.463321\pi\) | |||||||
\(450\) | −1.02217e17 | −0.580287 | ||||||||
\(451\) | −6.09489e16 | −0.341050 | ||||||||
\(452\) | −5.30130e17 | −2.92403 | ||||||||
\(453\) | −2.86390e17 | −1.55711 | ||||||||
\(454\) | −7.36424e16 | −0.394698 | ||||||||
\(455\) | 2.19757e17 | 1.16110 | ||||||||
\(456\) | −2.56279e17 | −1.33488 | ||||||||
\(457\) | −8.13503e16 | −0.417738 | −0.208869 | − | 0.977944i | \(-0.566978\pi\) | ||||
−0.208869 | + | 0.977944i | \(0.566978\pi\) | |||||||
\(458\) | −3.53892e17 | −1.79162 | ||||||||
\(459\) | −5.15474e17 | −2.57291 | ||||||||
\(460\) | 1.00459e17 | 0.494382 | ||||||||
\(461\) | 4.00641e17 | 1.94401 | 0.972006 | − | 0.234955i | \(-0.0754943\pi\) | ||||
0.972006 | + | 0.234955i | \(0.0754943\pi\) | |||||||
\(462\) | −5.87102e17 | −2.80893 | ||||||||
\(463\) | 1.77015e17 | 0.835090 | 0.417545 | − | 0.908656i | \(-0.362891\pi\) | ||||
0.417545 | + | 0.908656i | \(0.362891\pi\) | |||||||
\(464\) | −1.91920e17 | −0.892801 | ||||||||
\(465\) | −1.11842e17 | −0.513051 | ||||||||
\(466\) | −3.73282e17 | −1.68860 | ||||||||
\(467\) | −3.59491e17 | −1.60372 | −0.801861 | − | 0.597511i | \(-0.796156\pi\) | ||||
−0.801861 | + | 0.597511i | \(0.796156\pi\) | |||||||
\(468\) | 2.33891e18 | 10.2900 | ||||||||
\(469\) | 2.18199e17 | 0.946736 | ||||||||
\(470\) | 4.60894e17 | 1.97226 | ||||||||
\(471\) | −3.54901e17 | −1.49786 | ||||||||
\(472\) | −1.73730e17 | −0.723188 | ||||||||
\(473\) | 4.08676e16 | 0.167796 | ||||||||
\(474\) | 1.01629e18 | 4.11583 | ||||||||
\(475\) | −1.00771e16 | −0.0402558 | ||||||||
\(476\) | 3.01820e17 | 1.18933 | ||||||||
\(477\) | 2.91551e16 | 0.113330 | ||||||||
\(478\) | 1.93804e17 | 0.743159 | ||||||||
\(479\) | 7.55857e16 | 0.285929 | 0.142965 | − | 0.989728i | \(-0.454336\pi\) | ||||
0.142965 | + | 0.989728i | \(0.454336\pi\) | |||||||
\(480\) | 5.04529e17 | 1.88286 | ||||||||
\(481\) | 4.14801e17 | 1.52720 | ||||||||
\(482\) | −3.60532e17 | −1.30960 | ||||||||
\(483\) | −6.66302e16 | −0.238789 | ||||||||
\(484\) | 5.43520e17 | 1.92186 | ||||||||
\(485\) | 3.46911e17 | 1.21031 | ||||||||
\(486\) | 1.40118e18 | 4.82345 | ||||||||
\(487\) | 4.43593e17 | 1.50677 | 0.753384 | − | 0.657581i | \(-0.228420\pi\) | ||||
0.753384 | + | 0.657581i | \(0.228420\pi\) | |||||||
\(488\) | −4.95372e16 | −0.166036 | ||||||||
\(489\) | −4.13464e17 | −1.36751 | ||||||||
\(490\) | 3.69111e17 | 1.20471 | ||||||||
\(491\) | −6.02305e17 | −1.93993 | −0.969966 | − | 0.243240i | \(-0.921790\pi\) | ||||
−0.969966 | + | 0.243240i | \(0.921790\pi\) | |||||||
\(492\) | −3.31457e17 | −1.05355 | ||||||||
\(493\) | −1.41979e17 | −0.445369 | ||||||||
\(494\) | 3.33790e17 | 1.03335 | ||||||||
\(495\) | −1.21101e18 | −3.70012 | ||||||||
\(496\) | 1.49391e17 | 0.450497 | ||||||||
\(497\) | 1.12944e17 | 0.336161 | ||||||||
\(498\) | −1.59251e18 | −4.67834 | ||||||||
\(499\) | −6.24220e17 | −1.81002 | −0.905011 | − | 0.425387i | \(-0.860138\pi\) | ||||
−0.905011 | + | 0.425387i | \(0.860138\pi\) | |||||||
\(500\) | −7.23822e17 | −2.07170 | ||||||||
\(501\) | −5.78815e17 | −1.63529 | ||||||||
\(502\) | 3.57146e17 | 0.996027 | ||||||||
\(503\) | 1.59160e17 | 0.438168 | 0.219084 | − | 0.975706i | \(-0.429693\pi\) | ||||
0.219084 | + | 0.975706i | \(0.429693\pi\) | |||||||
\(504\) | −1.26779e18 | −3.44547 | ||||||||
\(505\) | −6.53040e17 | −1.75205 | ||||||||
\(506\) | 1.93097e17 | 0.511444 | ||||||||
\(507\) | −1.61987e18 | −4.23573 | ||||||||
\(508\) | −6.14776e17 | −1.58709 | ||||||||
\(509\) | 4.29007e17 | 1.09345 | 0.546725 | − | 0.837312i | \(-0.315874\pi\) | ||||
0.546725 | + | 0.837312i | \(0.315874\pi\) | |||||||
\(510\) | 1.25376e18 | 3.15506 | ||||||||
\(511\) | 8.40637e16 | 0.208868 | ||||||||
\(512\) | 9.15923e17 | 2.24701 | ||||||||
\(513\) | 3.86423e17 | 0.936052 | ||||||||
\(514\) | −7.45172e17 | −1.78236 | ||||||||
\(515\) | 7.51779e17 | 1.77559 | ||||||||
\(516\) | 2.22249e17 | 0.518343 | ||||||||
\(517\) | 6.11987e17 | 1.40946 | ||||||||
\(518\) | −4.07021e17 | −0.925708 | ||||||||
\(519\) | 3.22047e17 | 0.723321 | ||||||||
\(520\) | −1.91322e18 | −4.24369 | ||||||||
\(521\) | 8.00451e17 | 1.75343 | 0.876717 | − | 0.481006i | \(-0.159728\pi\) | ||||
0.876717 | + | 0.481006i | \(0.159728\pi\) | |||||||
\(522\) | 1.07961e18 | 2.33566 | ||||||||
\(523\) | −2.10512e17 | −0.449797 | −0.224898 | − | 0.974382i | \(-0.572205\pi\) | ||||
−0.224898 | + | 0.974382i | \(0.572205\pi\) | |||||||
\(524\) | 9.46544e17 | 1.99750 | ||||||||
\(525\) | −6.93513e16 | −0.144550 | ||||||||
\(526\) | −1.32261e18 | −2.72286 | ||||||||
\(527\) | 1.10516e17 | 0.224728 | ||||||||
\(528\) | 2.25036e18 | 4.51992 | ||||||||
\(529\) | 2.19146e16 | 0.0434783 | ||||||||
\(530\) | −4.31728e16 | −0.0846091 | ||||||||
\(531\) | 4.30264e17 | 0.832954 | ||||||||
\(532\) | −2.26258e17 | −0.432691 | ||||||||
\(533\) | 2.38475e17 | 0.450523 | ||||||||
\(534\) | 3.82870e16 | 0.0714551 | ||||||||
\(535\) | 6.25779e17 | 1.15378 | ||||||||
\(536\) | −1.89966e18 | −3.46022 | ||||||||
\(537\) | −4.48026e17 | −0.806250 | ||||||||
\(538\) | 1.14758e17 | 0.204032 | ||||||||
\(539\) | 4.90115e17 | 0.860937 | ||||||||
\(540\) | −4.00956e18 | −6.95886 | ||||||||
\(541\) | 8.80059e17 | 1.50914 | 0.754570 | − | 0.656220i | \(-0.227845\pi\) | ||||
0.754570 | + | 0.656220i | \(0.227845\pi\) | |||||||
\(542\) | 8.41498e17 | 1.42580 | ||||||||
\(543\) | 6.09650e16 | 0.102066 | ||||||||
\(544\) | −4.98550e17 | −0.824738 | ||||||||
\(545\) | −4.99635e17 | −0.816725 | ||||||||
\(546\) | 2.29716e18 | 3.71056 | ||||||||
\(547\) | −8.28017e17 | −1.32167 | −0.660833 | − | 0.750533i | \(-0.729797\pi\) | ||||
−0.660833 | + | 0.750533i | \(0.729797\pi\) | |||||||
\(548\) | 2.35310e18 | 3.71165 | ||||||||
\(549\) | 1.22686e17 | 0.191237 | ||||||||
\(550\) | 2.00983e17 | 0.309601 | ||||||||
\(551\) | 1.06434e17 | 0.162030 | ||||||||
\(552\) | 5.80088e17 | 0.872750 | ||||||||
\(553\) | 4.95637e17 | 0.736970 | ||||||||
\(554\) | 8.02323e17 | 1.17906 | ||||||||
\(555\) | −1.16798e18 | −1.69642 | ||||||||
\(556\) | −5.29634e17 | −0.760309 | ||||||||
\(557\) | −3.64214e17 | −0.516771 | −0.258386 | − | 0.966042i | \(-0.583190\pi\) | ||||
−0.258386 | + | 0.966042i | \(0.583190\pi\) | |||||||
\(558\) | −8.40368e17 | −1.17855 | ||||||||
\(559\) | −1.59903e17 | −0.221656 | ||||||||
\(560\) | 8.26528e17 | 1.13249 | ||||||||
\(561\) | 1.66477e18 | 2.25474 | ||||||||
\(562\) | −2.49005e18 | −3.33366 | ||||||||
\(563\) | 9.72416e17 | 1.28691 | 0.643454 | − | 0.765485i | \(-0.277501\pi\) | ||||
0.643454 | + | 0.765485i | \(0.277501\pi\) | |||||||
\(564\) | 3.32815e18 | 4.35400 | ||||||||
\(565\) | −1.07398e18 | −1.38893 | ||||||||
\(566\) | −2.50831e18 | −3.20681 | ||||||||
\(567\) | 1.43113e18 | 1.80879 | ||||||||
\(568\) | −9.83303e17 | −1.22864 | ||||||||
\(569\) | 5.07825e16 | 0.0627313 | 0.0313656 | − | 0.999508i | \(-0.490014\pi\) | ||||
0.0313656 | + | 0.999508i | \(0.490014\pi\) | |||||||
\(570\) | −9.39876e17 | −1.14785 | ||||||||
\(571\) | −1.89682e17 | −0.229030 | −0.114515 | − | 0.993422i | \(-0.536531\pi\) | ||||
−0.114515 | + | 0.993422i | \(0.536531\pi\) | |||||||
\(572\) | −4.59885e18 | −5.49004 | ||||||||
\(573\) | −2.45736e18 | −2.90044 | ||||||||
\(574\) | −2.34003e17 | −0.273082 | ||||||||
\(575\) | 2.28096e16 | 0.0263194 | ||||||||
\(576\) | −1.46463e17 | −0.167102 | ||||||||
\(577\) | −8.27893e17 | −0.933966 | −0.466983 | − | 0.884266i | \(-0.654659\pi\) | ||||
−0.466983 | + | 0.884266i | \(0.654659\pi\) | |||||||
\(578\) | 3.73271e17 | 0.416384 | ||||||||
\(579\) | 1.26171e18 | 1.39171 | ||||||||
\(580\) | −1.10437e18 | −1.20457 | ||||||||
\(581\) | −7.76657e17 | −0.837693 | ||||||||
\(582\) | 3.62633e18 | 3.86783 | ||||||||
\(583\) | −5.73260e16 | −0.0604652 | ||||||||
\(584\) | −7.31866e17 | −0.763393 | ||||||||
\(585\) | 4.73834e18 | 4.88780 | ||||||||
\(586\) | 1.29048e18 | 1.31649 | ||||||||
\(587\) | 7.80410e17 | 0.787364 | 0.393682 | − | 0.919247i | \(-0.371201\pi\) | ||||
0.393682 | + | 0.919247i | \(0.371201\pi\) | |||||||
\(588\) | 2.66538e18 | 2.65954 | ||||||||
\(589\) | −8.28482e16 | −0.0817586 | ||||||||
\(590\) | −6.37134e17 | −0.621860 | ||||||||
\(591\) | −1.37028e18 | −1.32279 | ||||||||
\(592\) | 1.56011e18 | 1.48958 | ||||||||
\(593\) | 1.70361e18 | 1.60885 | 0.804425 | − | 0.594054i | \(-0.202474\pi\) | ||||
0.804425 | + | 0.594054i | \(0.202474\pi\) | |||||||
\(594\) | −7.70701e18 | −7.19903 | ||||||||
\(595\) | 6.11450e17 | 0.564938 | ||||||||
\(596\) | −2.83888e18 | −2.59446 | ||||||||
\(597\) | −9.61180e17 | −0.868903 | ||||||||
\(598\) | −7.55534e17 | −0.675611 | ||||||||
\(599\) | 6.34568e17 | 0.561311 | 0.280655 | − | 0.959809i | \(-0.409448\pi\) | ||||
0.280655 | + | 0.959809i | \(0.409448\pi\) | |||||||
\(600\) | 6.03778e17 | 0.528317 | ||||||||
\(601\) | −1.58119e18 | −1.36867 | −0.684336 | − | 0.729167i | \(-0.739908\pi\) | ||||
−0.684336 | + | 0.729167i | \(0.739908\pi\) | |||||||
\(602\) | 1.56904e17 | 0.134356 | ||||||||
\(603\) | 4.70475e18 | 3.98542 | ||||||||
\(604\) | 2.20126e18 | 1.84472 | ||||||||
\(605\) | 1.10111e18 | 0.912892 | ||||||||
\(606\) | −6.82636e18 | −5.59909 | ||||||||
\(607\) | 1.14804e18 | 0.931602 | 0.465801 | − | 0.884889i | \(-0.345766\pi\) | ||||
0.465801 | + | 0.884889i | \(0.345766\pi\) | |||||||
\(608\) | 3.73736e17 | 0.300049 | ||||||||
\(609\) | 7.32485e17 | 0.581817 | ||||||||
\(610\) | −1.81672e17 | −0.142773 | ||||||||
\(611\) | −2.39453e18 | −1.86188 | ||||||||
\(612\) | 6.50777e18 | 5.00666 | ||||||||
\(613\) | 2.01236e17 | 0.153184 | 0.0765919 | − | 0.997063i | \(-0.475596\pi\) | ||||
0.0765919 | + | 0.997063i | \(0.475596\pi\) | |||||||
\(614\) | 3.12380e18 | 2.35282 | ||||||||
\(615\) | −6.71491e17 | −0.500440 | ||||||||
\(616\) | 2.49278e18 | 1.83827 | ||||||||
\(617\) | 1.46232e18 | 1.06706 | 0.533530 | − | 0.845781i | \(-0.320865\pi\) | ||||
0.533530 | + | 0.845781i | \(0.320865\pi\) | |||||||
\(618\) | 7.85849e18 | 5.67433 | ||||||||
\(619\) | −1.45866e17 | −0.104223 | −0.0521116 | − | 0.998641i | \(-0.516595\pi\) | ||||
−0.0521116 | + | 0.998641i | \(0.516595\pi\) | |||||||
\(620\) | 8.59642e17 | 0.607815 | ||||||||
\(621\) | −8.74668e17 | −0.611995 | ||||||||
\(622\) | 2.36837e18 | 1.63988 | ||||||||
\(623\) | 1.86723e16 | 0.0127946 | ||||||||
\(624\) | −8.80499e18 | −5.97075 | ||||||||
\(625\) | −1.65446e18 | −1.11029 | ||||||||
\(626\) | 2.71415e18 | 1.80261 | ||||||||
\(627\) | −1.24799e18 | −0.820300 | ||||||||
\(628\) | 2.72785e18 | 1.77453 | ||||||||
\(629\) | 1.15414e18 | 0.743070 | ||||||||
\(630\) | −4.64947e18 | −2.96272 | ||||||||
\(631\) | −1.33503e18 | −0.841977 | −0.420988 | − | 0.907066i | \(-0.638317\pi\) | ||||
−0.420988 | + | 0.907066i | \(0.638317\pi\) | |||||||
\(632\) | −4.31506e18 | −2.69355 | ||||||||
\(633\) | −3.40286e18 | −2.10242 | ||||||||
\(634\) | 2.31428e18 | 1.41526 | ||||||||
\(635\) | −1.24546e18 | −0.753878 | ||||||||
\(636\) | −3.11754e17 | −0.186784 | ||||||||
\(637\) | −1.91768e18 | −1.13729 | ||||||||
\(638\) | −2.12278e18 | −1.24615 | ||||||||
\(639\) | 2.43528e18 | 1.41512 | ||||||||
\(640\) | 1.95263e18 | 1.12318 | ||||||||
\(641\) | 1.08968e18 | 0.620469 | 0.310235 | − | 0.950660i | \(-0.399592\pi\) | ||||
0.310235 | + | 0.950660i | \(0.399592\pi\) | |||||||
\(642\) | 6.54139e18 | 3.68716 | ||||||||
\(643\) | −6.30973e17 | −0.352079 | −0.176039 | − | 0.984383i | \(-0.556329\pi\) | ||||
−0.176039 | + | 0.984383i | \(0.556329\pi\) | |||||||
\(644\) | 5.12135e17 | 0.282895 | ||||||||
\(645\) | 4.50250e17 | 0.246215 | ||||||||
\(646\) | 9.28737e17 | 0.502784 | ||||||||
\(647\) | 5.64504e17 | 0.302545 | 0.151272 | − | 0.988492i | \(-0.451663\pi\) | ||||
0.151272 | + | 0.988492i | \(0.451663\pi\) | |||||||
\(648\) | −1.24595e19 | −6.61095 | ||||||||
\(649\) | −8.46003e17 | −0.444407 | ||||||||
\(650\) | −7.86389e17 | −0.408979 | ||||||||
\(651\) | −5.70165e17 | −0.293578 | ||||||||
\(652\) | 3.17798e18 | 1.62010 | ||||||||
\(653\) | −2.48932e18 | −1.25645 | −0.628224 | − | 0.778033i | \(-0.716218\pi\) | ||||
−0.628224 | + | 0.778033i | \(0.716218\pi\) | |||||||
\(654\) | −5.22278e18 | −2.61004 | ||||||||
\(655\) | 1.91758e18 | 0.948824 | ||||||||
\(656\) | 8.96931e17 | 0.439424 | ||||||||
\(657\) | 1.81256e18 | 0.879262 | ||||||||
\(658\) | 2.34962e18 | 1.12857 | ||||||||
\(659\) | −2.89893e18 | −1.37874 | −0.689370 | − | 0.724410i | \(-0.742112\pi\) | ||||
−0.689370 | + | 0.724410i | \(0.742112\pi\) | |||||||
\(660\) | 1.29493e19 | 6.09832 | ||||||||
\(661\) | −3.27467e18 | −1.52707 | −0.763534 | − | 0.645768i | \(-0.776537\pi\) | ||||
−0.763534 | + | 0.645768i | \(0.776537\pi\) | |||||||
\(662\) | −4.03830e18 | −1.86475 | ||||||||
\(663\) | −6.51378e18 | −2.97848 | ||||||||
\(664\) | 6.76165e18 | 3.06168 | ||||||||
\(665\) | −4.58371e17 | −0.205531 | ||||||||
\(666\) | −8.77610e18 | −3.89690 | ||||||||
\(667\) | −2.40914e17 | −0.105936 | ||||||||
\(668\) | 4.44890e18 | 1.93734 | ||||||||
\(669\) | 5.23766e18 | 2.25875 | ||||||||
\(670\) | −6.96678e18 | −2.97540 | ||||||||
\(671\) | −2.41229e17 | −0.102031 | ||||||||
\(672\) | 2.57207e18 | 1.07741 | ||||||||
\(673\) | −3.53625e18 | −1.46705 | −0.733525 | − | 0.679663i | \(-0.762126\pi\) | ||||
−0.733525 | + | 0.679663i | \(0.762126\pi\) | |||||||
\(674\) | 3.01026e18 | 1.23684 | ||||||||
\(675\) | −9.10388e17 | −0.370469 | ||||||||
\(676\) | 1.24507e19 | 5.01810 | ||||||||
\(677\) | 2.85848e18 | 1.14106 | 0.570531 | − | 0.821276i | \(-0.306737\pi\) | ||||
0.570531 | + | 0.821276i | \(0.306737\pi\) | |||||||
\(678\) | −1.12265e19 | −4.43866 | ||||||||
\(679\) | 1.76854e18 | 0.692565 | ||||||||
\(680\) | −5.32334e18 | −2.06479 | ||||||||
\(681\) | −1.07732e18 | −0.413892 | ||||||||
\(682\) | 1.65236e18 | 0.628793 | ||||||||
\(683\) | −2.67594e18 | −1.00865 | −0.504326 | − | 0.863513i | \(-0.668259\pi\) | ||||
−0.504326 | + | 0.863513i | \(0.668259\pi\) | |||||||
\(684\) | −4.87852e18 | −1.82148 | ||||||||
\(685\) | 4.76710e18 | 1.76305 | ||||||||
\(686\) | 4.86272e18 | 1.78145 | ||||||||
\(687\) | −5.17710e18 | −1.87874 | ||||||||
\(688\) | −6.01412e17 | −0.216196 | ||||||||
\(689\) | 2.24300e17 | 0.0798737 | ||||||||
\(690\) | 2.12741e18 | 0.750467 | ||||||||
\(691\) | 1.96852e18 | 0.687913 | 0.343956 | − | 0.938986i | \(-0.388233\pi\) | ||||
0.343956 | + | 0.938986i | \(0.388233\pi\) | |||||||
\(692\) | −2.47532e18 | −0.856924 | ||||||||
\(693\) | −6.17369e18 | −2.11728 | ||||||||
\(694\) | −4.18911e18 | −1.42326 | ||||||||
\(695\) | −1.07298e18 | −0.361151 | ||||||||
\(696\) | −6.37708e18 | −2.12648 | ||||||||
\(697\) | 6.63533e17 | 0.219205 | ||||||||
\(698\) | −9.77372e18 | −3.19889 | ||||||||
\(699\) | −5.46074e18 | −1.77072 | ||||||||
\(700\) | 5.33050e17 | 0.171250 | ||||||||
\(701\) | 3.82780e18 | 1.21838 | 0.609189 | − | 0.793025i | \(-0.291495\pi\) | ||||
0.609189 | + | 0.793025i | \(0.291495\pi\) | |||||||
\(702\) | 3.01553e19 | 9.50981 | ||||||||
\(703\) | −8.65197e17 | −0.270337 | ||||||||
\(704\) | 2.87982e17 | 0.0891544 | ||||||||
\(705\) | 6.74243e18 | 2.06817 | ||||||||
\(706\) | −3.35951e18 | −1.02104 | ||||||||
\(707\) | −3.32917e18 | −1.00256 | ||||||||
\(708\) | −4.60079e18 | −1.37283 | ||||||||
\(709\) | −1.30255e18 | −0.385117 | −0.192558 | − | 0.981286i | \(-0.561679\pi\) | ||||
−0.192558 | + | 0.981286i | \(0.561679\pi\) | |||||||
\(710\) | −3.60615e18 | −1.05649 | ||||||||
\(711\) | 1.06868e19 | 3.10238 | ||||||||
\(712\) | −1.62563e17 | −0.0467629 | ||||||||
\(713\) | 1.87527e17 | 0.0534541 | ||||||||
\(714\) | 6.39161e18 | 1.80539 | ||||||||
\(715\) | −9.31672e18 | −2.60780 | ||||||||
\(716\) | 3.44362e18 | 0.955171 | ||||||||
\(717\) | 2.83517e18 | 0.779299 | ||||||||
\(718\) | −4.34497e18 | −1.18353 | ||||||||
\(719\) | 1.60657e18 | 0.433674 | 0.216837 | − | 0.976208i | \(-0.430426\pi\) | ||||
0.216837 | + | 0.976208i | \(0.430426\pi\) | |||||||
\(720\) | 1.78214e19 | 4.76739 | ||||||||
\(721\) | 3.83254e18 | 1.01603 | ||||||||
\(722\) | 6.14876e18 | 1.61546 | ||||||||
\(723\) | −5.27422e18 | −1.37328 | ||||||||
\(724\) | −4.68590e17 | −0.120918 | ||||||||
\(725\) | −2.50752e17 | −0.0641281 | ||||||||
\(726\) | 1.15101e19 | 2.91736 | ||||||||
\(727\) | 1.70155e18 | 0.427435 | 0.213718 | − | 0.976895i | \(-0.431443\pi\) | ||||
0.213718 | + | 0.976895i | \(0.431443\pi\) | |||||||
\(728\) | −9.75351e18 | −2.42833 | ||||||||
\(729\) | 8.42691e18 | 2.07941 | ||||||||
\(730\) | −2.68404e18 | −0.656432 | ||||||||
\(731\) | −4.44914e17 | −0.107848 | ||||||||
\(732\) | −1.31187e18 | −0.315187 | ||||||||
\(733\) | 5.61258e16 | 0.0133656 | 0.00668278 | − | 0.999978i | \(-0.497873\pi\) | ||||
0.00668278 | + | 0.999978i | \(0.497873\pi\) | |||||||
\(734\) | −3.75443e18 | −0.886174 | ||||||||
\(735\) | 5.39973e18 | 1.26329 | ||||||||
\(736\) | −8.45951e17 | −0.196173 | ||||||||
\(737\) | −9.25067e18 | −2.12635 | ||||||||
\(738\) | −5.04551e18 | −1.14958 | ||||||||
\(739\) | 1.36630e18 | 0.308572 | 0.154286 | − | 0.988026i | \(-0.450692\pi\) | ||||
0.154286 | + | 0.988026i | \(0.450692\pi\) | |||||||
\(740\) | 8.97738e18 | 2.00976 | ||||||||
\(741\) | 4.88302e18 | 1.08360 | ||||||||
\(742\) | −2.20093e17 | −0.0484151 | ||||||||
\(743\) | 6.30358e18 | 1.37455 | 0.687274 | − | 0.726399i | \(-0.258807\pi\) | ||||
0.687274 | + | 0.726399i | \(0.258807\pi\) | |||||||
\(744\) | 4.96390e18 | 1.07300 | ||||||||
\(745\) | −5.75123e18 | −1.23238 | ||||||||
\(746\) | −5.52456e18 | −1.17353 | ||||||||
\(747\) | −1.67461e19 | −3.52639 | ||||||||
\(748\) | −1.27958e19 | −2.67121 | ||||||||
\(749\) | 3.19019e18 | 0.660214 | ||||||||
\(750\) | −1.53283e19 | −3.14482 | ||||||||
\(751\) | 6.46039e18 | 1.31401 | 0.657006 | − | 0.753886i | \(-0.271823\pi\) | ||||
0.657006 | + | 0.753886i | \(0.271823\pi\) | |||||||
\(752\) | −9.00607e18 | −1.81601 | ||||||||
\(753\) | 5.22469e18 | 1.04446 | ||||||||
\(754\) | 8.30580e18 | 1.64614 | ||||||||
\(755\) | 4.45949e18 | 0.876254 | ||||||||
\(756\) | −2.04406e19 | −3.98200 | ||||||||
\(757\) | −2.01550e18 | −0.389278 | −0.194639 | − | 0.980875i | \(-0.562354\pi\) | ||||
−0.194639 | + | 0.980875i | \(0.562354\pi\) | |||||||
\(758\) | 1.20974e19 | 2.31654 | ||||||||
\(759\) | 2.82483e18 | 0.536315 | ||||||||
\(760\) | 3.99062e18 | 0.751194 | ||||||||
\(761\) | 5.12180e17 | 0.0955923 | 0.0477961 | − | 0.998857i | \(-0.484780\pi\) | ||||
0.0477961 | + | 0.998857i | \(0.484780\pi\) | |||||||
\(762\) | −1.30191e19 | −2.40920 | ||||||||
\(763\) | −2.54712e18 | −0.467347 | ||||||||
\(764\) | 1.88878e19 | 3.43618 | ||||||||
\(765\) | 1.31840e19 | 2.37819 | ||||||||
\(766\) | 5.28204e18 | 0.944746 | ||||||||
\(767\) | 3.31016e18 | 0.587056 | ||||||||
\(768\) | 1.97102e19 | 3.46611 | ||||||||
\(769\) | −3.57203e18 | −0.622865 | −0.311432 | − | 0.950268i | \(-0.600809\pi\) | ||||
−0.311432 | + | 0.950268i | \(0.600809\pi\) | |||||||
\(770\) | 9.14198e18 | 1.58070 | ||||||||
\(771\) | −1.09011e19 | −1.86904 | ||||||||
\(772\) | −9.69781e18 | −1.64877 | ||||||||
\(773\) | −3.36335e18 | −0.567030 | −0.283515 | − | 0.958968i | \(-0.591501\pi\) | ||||
−0.283515 | + | 0.958968i | \(0.591501\pi\) | |||||||
\(774\) | 3.38313e18 | 0.565591 | ||||||||
\(775\) | 1.95185e17 | 0.0323583 | ||||||||
\(776\) | −1.53970e19 | −2.53125 | ||||||||
\(777\) | −5.95432e18 | −0.970724 | ||||||||
\(778\) | −6.94754e18 | −1.12322 | ||||||||
\(779\) | −4.97415e17 | −0.0797490 | ||||||||
\(780\) | −5.06668e19 | −8.05580 | ||||||||
\(781\) | −4.78834e18 | −0.755011 | ||||||||
\(782\) | −2.10220e18 | −0.328722 | ||||||||
\(783\) | 9.61547e18 | 1.49114 | ||||||||
\(784\) | −7.21259e18 | −1.10927 | ||||||||
\(785\) | 5.52630e18 | 0.842911 | ||||||||
\(786\) | 2.00449e19 | 3.03219 | ||||||||
\(787\) | 1.14381e19 | 1.71601 | 0.858005 | − | 0.513641i | \(-0.171704\pi\) | ||||
0.858005 | + | 0.513641i | \(0.171704\pi\) | |||||||
\(788\) | 1.05323e19 | 1.56712 | ||||||||
\(789\) | −1.93485e19 | −2.85527 | ||||||||
\(790\) | −1.58250e19 | −2.31615 | ||||||||
\(791\) | −5.47510e18 | −0.794776 | ||||||||
\(792\) | 5.37487e19 | 7.73846 | ||||||||
\(793\) | 9.43859e17 | 0.134782 | ||||||||
\(794\) | 9.33124e18 | 1.32162 | ||||||||
\(795\) | −6.31576e17 | −0.0887236 | ||||||||
\(796\) | 7.38784e18 | 1.02940 | ||||||||
\(797\) | −6.36200e18 | −0.879255 | −0.439627 | − | 0.898180i | \(-0.644889\pi\) | ||||
−0.439627 | + | 0.898180i | \(0.644889\pi\) | |||||||
\(798\) | −4.79144e18 | −0.656822 | ||||||||
\(799\) | −6.66253e18 | −0.905910 | ||||||||
\(800\) | −8.80499e17 | −0.118753 | ||||||||
\(801\) | 4.02609e17 | 0.0538607 | ||||||||
\(802\) | 4.63061e18 | 0.614476 | ||||||||
\(803\) | −3.56393e18 | −0.469114 | ||||||||
\(804\) | −5.03076e19 | −6.56855 | ||||||||
\(805\) | 1.03752e18 | 0.134377 | ||||||||
\(806\) | −6.46522e18 | −0.830626 | ||||||||
\(807\) | 1.67880e18 | 0.213954 | ||||||||
\(808\) | 2.89840e19 | 3.66425 | ||||||||
\(809\) | 5.78945e18 | 0.726060 | 0.363030 | − | 0.931778i | \(-0.381742\pi\) | ||||
0.363030 | + | 0.931778i | \(0.381742\pi\) | |||||||
\(810\) | −4.56939e19 | −5.68467 | ||||||||
\(811\) | −4.83603e18 | −0.596833 | −0.298417 | − | 0.954436i | \(-0.596459\pi\) | ||||
−0.298417 | + | 0.954436i | \(0.596459\pi\) | |||||||
\(812\) | −5.63004e18 | −0.689283 | ||||||||
\(813\) | 1.23103e19 | 1.49513 | ||||||||
\(814\) | 1.72559e19 | 2.07912 | ||||||||
\(815\) | 6.43820e18 | 0.769556 | ||||||||
\(816\) | −2.44990e19 | −2.90511 | ||||||||
\(817\) | 3.33528e17 | 0.0392364 | ||||||||
\(818\) | 8.52476e17 | 0.0994915 | ||||||||
\(819\) | 2.41559e19 | 2.79690 | ||||||||
\(820\) | 5.16123e18 | 0.592875 | ||||||||
\(821\) | −9.30560e18 | −1.06051 | −0.530254 | − | 0.847839i | \(-0.677903\pi\) | ||||
−0.530254 | + | 0.847839i | \(0.677903\pi\) | |||||||
\(822\) | 4.98314e19 | 5.63425 | ||||||||
\(823\) | −6.35671e18 | −0.713072 | −0.356536 | − | 0.934282i | \(-0.616042\pi\) | ||||
−0.356536 | + | 0.934282i | \(0.616042\pi\) | |||||||
\(824\) | −3.33664e19 | −3.71349 | ||||||||
\(825\) | 2.94019e18 | 0.324657 | ||||||||
\(826\) | −3.24808e18 | −0.355841 | ||||||||
\(827\) | 3.51042e18 | 0.381569 | 0.190785 | − | 0.981632i | \(-0.438897\pi\) | ||||
0.190785 | + | 0.981632i | \(0.438897\pi\) | |||||||
\(828\) | 1.10425e19 | 1.19089 | ||||||||
\(829\) | 1.30969e19 | 1.40140 | 0.700701 | − | 0.713455i | \(-0.252871\pi\) | ||||
0.700701 | + | 0.713455i | \(0.252871\pi\) | |||||||
\(830\) | 2.47976e19 | 2.63270 | ||||||||
\(831\) | 1.17372e19 | 1.23640 | ||||||||
\(832\) | −1.12679e18 | −0.117772 | ||||||||
\(833\) | −5.33574e18 | −0.553353 | ||||||||
\(834\) | −1.12160e19 | −1.15414 | ||||||||
\(835\) | 9.01294e18 | 0.920247 | ||||||||
\(836\) | 9.59234e18 | 0.971815 | ||||||||
\(837\) | −7.48467e18 | −0.752414 | ||||||||
\(838\) | 2.72202e18 | 0.271522 | ||||||||
\(839\) | −1.05635e19 | −1.04558 | −0.522789 | − | 0.852462i | \(-0.675108\pi\) | ||||
−0.522789 | + | 0.852462i | \(0.675108\pi\) | |||||||
\(840\) | 2.74636e19 | 2.69738 | ||||||||
\(841\) | −7.61219e18 | −0.741884 | ||||||||
\(842\) | −1.26140e19 | −1.21990 | ||||||||
\(843\) | −3.64270e19 | −3.49578 | ||||||||
\(844\) | 2.61551e19 | 2.49075 | ||||||||
\(845\) | 2.52236e19 | 2.38362 | ||||||||
\(846\) | 5.06619e19 | 4.75088 | ||||||||
\(847\) | 5.61339e18 | 0.522376 | ||||||||
\(848\) | 8.43615e17 | 0.0779060 | ||||||||
\(849\) | −3.66941e19 | −3.36276 | ||||||||
\(850\) | −2.18805e18 | −0.198991 | ||||||||
\(851\) | 1.95837e18 | 0.176748 | ||||||||
\(852\) | −2.60403e19 | −2.33232 | ||||||||
\(853\) | 6.70695e18 | 0.596151 | 0.298076 | − | 0.954542i | \(-0.403655\pi\) | ||||
0.298076 | + | 0.954542i | \(0.403655\pi\) | |||||||
\(854\) | −9.26157e17 | −0.0816974 | ||||||||
\(855\) | −9.88329e18 | −0.865211 | ||||||||
\(856\) | −2.77741e19 | −2.41302 | ||||||||
\(857\) | 8.12179e18 | 0.700288 | 0.350144 | − | 0.936696i | \(-0.386133\pi\) | ||||
0.350144 | + | 0.936696i | \(0.386133\pi\) | |||||||
\(858\) | −9.73894e19 | −8.33383 | ||||||||
\(859\) | 1.31202e19 | 1.11426 | 0.557129 | − | 0.830426i | \(-0.311903\pi\) | ||||
0.557129 | + | 0.830426i | \(0.311903\pi\) | |||||||
\(860\) | −3.46072e18 | −0.291693 | ||||||||
\(861\) | −3.42323e18 | −0.286362 | ||||||||
\(862\) | 1.61304e19 | 1.33921 | ||||||||
\(863\) | 2.07543e19 | 1.71016 | 0.855082 | − | 0.518493i | \(-0.173507\pi\) | ||||
0.855082 | + | 0.518493i | \(0.173507\pi\) | |||||||
\(864\) | 3.37640e19 | 2.76131 | ||||||||
\(865\) | −5.01470e18 | −0.407043 | ||||||||
\(866\) | −1.15242e19 | −0.928420 | ||||||||
\(867\) | 5.46059e18 | 0.436632 | ||||||||
\(868\) | 4.38241e18 | 0.347804 | ||||||||
\(869\) | −2.10128e19 | −1.65522 | ||||||||
\(870\) | −2.33872e19 | −1.82853 | ||||||||
\(871\) | 3.61952e19 | 2.80888 | ||||||||
\(872\) | 2.21754e19 | 1.70811 | ||||||||
\(873\) | 3.81328e19 | 2.91545 | ||||||||
\(874\) | 1.57590e18 | 0.119593 | ||||||||
\(875\) | −7.47551e18 | −0.563104 | ||||||||
\(876\) | −1.93816e19 | −1.44915 | ||||||||
\(877\) | 3.78205e17 | 0.0280692 | 0.0140346 | − | 0.999902i | \(-0.495533\pi\) | ||||
0.0140346 | + | 0.999902i | \(0.495533\pi\) | |||||||
\(878\) | −3.23388e19 | −2.38237 | ||||||||
\(879\) | 1.88785e19 | 1.38051 | ||||||||
\(880\) | −3.50411e19 | −2.54355 | ||||||||
\(881\) | −3.37859e18 | −0.243440 | −0.121720 | − | 0.992564i | \(-0.538841\pi\) | ||||
−0.121720 | + | 0.992564i | \(0.538841\pi\) | |||||||
\(882\) | 4.05730e19 | 2.90196 | ||||||||
\(883\) | −2.54109e18 | −0.180416 | −0.0902082 | − | 0.995923i | \(-0.528753\pi\) | ||||
−0.0902082 | + | 0.995923i | \(0.528753\pi\) | |||||||
\(884\) | 5.00663e19 | 3.52863 | ||||||||
\(885\) | −9.32064e18 | −0.652101 | ||||||||
\(886\) | −2.96044e18 | −0.205607 | ||||||||
\(887\) | 3.03810e18 | 0.209459 | 0.104729 | − | 0.994501i | \(-0.466602\pi\) | ||||
0.104729 | + | 0.994501i | \(0.466602\pi\) | |||||||
\(888\) | 5.18389e19 | 3.54790 | ||||||||
\(889\) | −6.34931e18 | −0.431385 | ||||||||
\(890\) | −5.96181e17 | −0.0402108 | ||||||||
\(891\) | −6.06735e19 | −4.06250 | ||||||||
\(892\) | −4.02578e19 | −2.67595 | ||||||||
\(893\) | 4.99454e18 | 0.329580 | ||||||||
\(894\) | −6.01187e19 | −3.93836 | ||||||||
\(895\) | 6.97637e18 | 0.453711 | ||||||||
\(896\) | 9.95440e18 | 0.642707 | ||||||||
\(897\) | −1.10527e19 | −0.708465 | ||||||||
\(898\) | −6.49852e18 | −0.413541 | ||||||||
\(899\) | −2.06154e18 | −0.130243 | ||||||||
\(900\) | 1.14935e19 | 0.720901 | ||||||||
\(901\) | 6.24091e17 | 0.0388630 | ||||||||
\(902\) | 9.92069e18 | 0.613337 | ||||||||
\(903\) | 2.29535e18 | 0.140890 | ||||||||
\(904\) | 4.76667e19 | 2.90483 | ||||||||
\(905\) | −9.49308e17 | −0.0574369 | ||||||||
\(906\) | 4.66159e19 | 2.80028 | ||||||||
\(907\) | −1.76653e19 | −1.05360 | −0.526798 | − | 0.849991i | \(-0.676607\pi\) | ||||
−0.526798 | + | 0.849991i | \(0.676607\pi\) | |||||||
\(908\) | 8.28049e18 | 0.490341 | ||||||||
\(909\) | −7.17828e19 | −4.22042 | ||||||||
\(910\) | −3.57699e19 | −2.08809 | ||||||||
\(911\) | −2.96918e19 | −1.72094 | −0.860471 | − | 0.509499i | \(-0.829831\pi\) | ||||
−0.860471 | + | 0.509499i | \(0.829831\pi\) | |||||||
\(912\) | 1.83656e19 | 1.05691 | ||||||||
\(913\) | 3.29269e19 | 1.88144 | ||||||||
\(914\) | 1.32414e19 | 0.751250 | ||||||||
\(915\) | −2.65769e18 | −0.149715 | ||||||||
\(916\) | 3.97923e19 | 2.22576 | ||||||||
\(917\) | 9.77575e18 | 0.542937 | ||||||||
\(918\) | 8.39039e19 | 4.62706 | ||||||||
\(919\) | −2.40974e19 | −1.31953 | −0.659766 | − | 0.751471i | \(-0.729344\pi\) | ||||
−0.659766 | + | 0.751471i | \(0.729344\pi\) | |||||||
\(920\) | −9.03276e18 | −0.491134 | ||||||||
\(921\) | 4.56981e19 | 2.46723 | ||||||||
\(922\) | −6.52125e19 | −3.49607 | ||||||||
\(923\) | 1.87354e19 | 0.997359 | ||||||||
\(924\) | 6.60149e19 | 3.48959 | ||||||||
\(925\) | 2.03835e18 | 0.106994 | ||||||||
\(926\) | −2.88128e19 | −1.50181 | ||||||||
\(927\) | 8.26363e19 | 4.27713 | ||||||||
\(928\) | 9.29978e18 | 0.477981 | ||||||||
\(929\) | −1.44715e19 | −0.738605 | −0.369302 | − | 0.929309i | \(-0.620403\pi\) | ||||
−0.369302 | + | 0.929309i | \(0.620403\pi\) | |||||||
\(930\) | 1.82046e19 | 0.922658 | ||||||||
\(931\) | 3.99992e18 | 0.201316 | ||||||||
\(932\) | 4.19725e19 | 2.09779 | ||||||||
\(933\) | 3.46470e19 | 1.71963 | ||||||||
\(934\) | 5.85146e19 | 2.88409 | ||||||||
\(935\) | −2.59228e19 | −1.26884 | ||||||||
\(936\) | −2.10303e20 | −10.2224 | ||||||||
\(937\) | −1.83486e19 | −0.885718 | −0.442859 | − | 0.896591i | \(-0.646036\pi\) | ||||
−0.442859 | + | 0.896591i | \(0.646036\pi\) | |||||||
\(938\) | −3.55163e19 | −1.70259 | ||||||||
\(939\) | 3.97054e19 | 1.89027 | ||||||||
\(940\) | −5.18238e19 | −2.45018 | ||||||||
\(941\) | −4.09261e19 | −1.92162 | −0.960810 | − | 0.277209i | \(-0.910590\pi\) | ||||
−0.960810 | + | 0.277209i | \(0.910590\pi\) | |||||||
\(942\) | 5.77675e19 | 2.69372 | ||||||||
\(943\) | 1.12590e18 | 0.0521403 | ||||||||
\(944\) | 1.24499e19 | 0.572594 | ||||||||
\(945\) | −4.14101e19 | −1.89147 | ||||||||
\(946\) | −6.65204e18 | −0.301761 | ||||||||
\(947\) | 1.28440e19 | 0.578664 | 0.289332 | − | 0.957229i | \(-0.406567\pi\) | ||||
0.289332 | + | 0.957229i | \(0.406567\pi\) | |||||||
\(948\) | −1.14273e20 | −5.11317 | ||||||||
\(949\) | 1.39446e19 | 0.619693 | ||||||||
\(950\) | 1.64026e18 | 0.0723951 | ||||||||
\(951\) | 3.38557e19 | 1.48408 | ||||||||
\(952\) | −2.71381e19 | −1.18152 | ||||||||
\(953\) | 2.24332e18 | 0.0970033 | 0.0485017 | − | 0.998823i | \(-0.484555\pi\) | ||||
0.0485017 | + | 0.998823i | \(0.484555\pi\) | |||||||
\(954\) | −4.74560e18 | −0.203810 | ||||||||
\(955\) | 3.82645e19 | 1.63220 | ||||||||
\(956\) | −2.17917e19 | −0.923241 | ||||||||
\(957\) | −3.10541e19 | −1.30675 | ||||||||
\(958\) | −1.23031e19 | −0.514208 | ||||||||
\(959\) | 2.43024e19 | 1.00886 | ||||||||
\(960\) | 3.17278e18 | 0.130821 | ||||||||
\(961\) | −2.28129e19 | −0.934281 | ||||||||
\(962\) | −6.75174e19 | −2.74649 | ||||||||
\(963\) | 6.87862e19 | 2.77927 | ||||||||
\(964\) | 4.05389e19 | 1.62694 | ||||||||
\(965\) | −1.96466e19 | −0.783177 | ||||||||
\(966\) | 1.08454e19 | 0.429433 | ||||||||
\(967\) | −3.11794e19 | −1.22630 | −0.613148 | − | 0.789968i | \(-0.710097\pi\) | ||||
−0.613148 | + | 0.789968i | \(0.710097\pi\) | |||||||
\(968\) | −4.88707e19 | −1.90923 | ||||||||
\(969\) | 1.35865e19 | 0.527234 | ||||||||
\(970\) | −5.64669e19 | −2.17659 | ||||||||
\(971\) | −1.54433e19 | −0.591310 | −0.295655 | − | 0.955295i | \(-0.595538\pi\) | ||||
−0.295655 | + | 0.955295i | \(0.595538\pi\) | |||||||
\(972\) | −1.57551e20 | −5.99226 | ||||||||
\(973\) | −5.46998e18 | −0.206658 | ||||||||
\(974\) | −7.22038e19 | −2.70974 | ||||||||
\(975\) | −1.15041e19 | −0.428867 | ||||||||
\(976\) | 3.54995e18 | 0.131461 | ||||||||
\(977\) | 2.59027e19 | 0.952863 | 0.476431 | − | 0.879212i | \(-0.341930\pi\) | ||||
0.476431 | + | 0.879212i | \(0.341930\pi\) | |||||||
\(978\) | 6.72998e19 | 2.45930 | ||||||||
\(979\) | −7.91625e17 | −0.0287364 | ||||||||
\(980\) | −4.15036e19 | −1.49664 | ||||||||
\(981\) | −5.49204e19 | −1.96736 | ||||||||
\(982\) | 9.80374e19 | 3.48873 | ||||||||
\(983\) | 2.25386e19 | 0.796762 | 0.398381 | − | 0.917220i | \(-0.369572\pi\) | ||||
0.398381 | + | 0.917220i | \(0.369572\pi\) | |||||||
\(984\) | 2.98029e19 | 1.04662 | ||||||||
\(985\) | 2.13371e19 | 0.744390 | ||||||||
\(986\) | 2.31100e19 | 0.800941 | ||||||||
\(987\) | 3.43726e19 | 1.18345 | ||||||||
\(988\) | −3.75320e19 | −1.28375 | ||||||||
\(989\) | −7.54940e17 | −0.0256529 | ||||||||
\(990\) | 1.97117e20 | 6.65420 | ||||||||
\(991\) | 1.01248e17 | 0.00339553 | 0.00169776 | − | 0.999999i | \(-0.499460\pi\) | ||||
0.00169776 | + | 0.999999i | \(0.499460\pi\) | |||||||
\(992\) | −7.23893e18 | −0.241184 | ||||||||
\(993\) | −5.90763e19 | −1.95543 | ||||||||
\(994\) | −1.83840e19 | −0.604545 | ||||||||
\(995\) | 1.49669e19 | 0.488969 | ||||||||
\(996\) | 1.79065e20 | 5.81199 | ||||||||
\(997\) | 3.91495e18 | 0.126243 | 0.0631216 | − | 0.998006i | \(-0.479894\pi\) | ||||
0.0631216 | + | 0.998006i | \(0.479894\pi\) | |||||||
\(998\) | 1.01605e20 | 3.25510 | ||||||||
\(999\) | −7.81636e19 | −2.48788 |
(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 | 23.14.a.b.1.1 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
23.14.a.b.1.1 | ✓ | 14 | 1.1 | even | 1 | trivial |