Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,8,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(55.2921495107\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 2 x^{16} - 1669 x^{15} + 2385 x^{14} + 1108684 x^{13} - 848131 x^{12} - 377920980 x^{11} + 12724944 x^{10} + 71331230512 x^{9} + \cdots + 24\!\cdots\!16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{31}]\) |
Coefficient ring index: | multiple of \( 2^{10}\cdot 3^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Root | \(16.5905\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 16.5905 | 1.46641 | 0.733206 | − | 0.680007i | \(-0.238023\pi\) | ||||
0.733206 | + | 0.680007i | \(0.238023\pi\) | |||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | 147.246 | 1.15036 | ||||||||
\(5\) | 174.998 | 0.626091 | 0.313045 | − | 0.949738i | \(-0.398651\pi\) | ||||
0.313045 | + | 0.949738i | \(0.398651\pi\) | |||||||
\(6\) | −447.945 | −0.846633 | ||||||||
\(7\) | 1111.07 | 1.22433 | 0.612164 | − | 0.790731i | \(-0.290299\pi\) | ||||
0.612164 | + | 0.790731i | \(0.290299\pi\) | |||||||
\(8\) | 319.307 | 0.220493 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 2903.31 | 0.918107 | ||||||||
\(11\) | 3459.76 | 0.783738 | 0.391869 | − | 0.920021i | \(-0.371829\pi\) | ||||
0.391869 | + | 0.920021i | \(0.371829\pi\) | |||||||
\(12\) | −3975.65 | −0.664162 | ||||||||
\(13\) | −368.734 | −0.0465491 | −0.0232746 | − | 0.999729i | \(-0.507409\pi\) | ||||
−0.0232746 | + | 0.999729i | \(0.507409\pi\) | |||||||
\(14\) | 18433.2 | 1.79537 | ||||||||
\(15\) | −4724.94 | −0.361474 | ||||||||
\(16\) | −13550.0 | −0.827029 | ||||||||
\(17\) | 12018.6 | 0.593310 | 0.296655 | − | 0.954985i | \(-0.404129\pi\) | ||||
0.296655 | + | 0.954985i | \(0.404129\pi\) | |||||||
\(18\) | 12094.5 | 0.488804 | ||||||||
\(19\) | −20398.0 | −0.682259 | −0.341129 | − | 0.940016i | \(-0.610809\pi\) | ||||
−0.341129 | + | 0.940016i | \(0.610809\pi\) | |||||||
\(20\) | 25767.8 | 0.720231 | ||||||||
\(21\) | −29998.9 | −0.706866 | ||||||||
\(22\) | 57399.3 | 1.14928 | ||||||||
\(23\) | 27686.4 | 0.474481 | 0.237241 | − | 0.971451i | \(-0.423757\pi\) | ||||
0.237241 | + | 0.971451i | \(0.423757\pi\) | |||||||
\(24\) | −8621.30 | −0.127301 | ||||||||
\(25\) | −47500.8 | −0.608010 | ||||||||
\(26\) | −6117.50 | −0.0682602 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | 163601. | 1.40842 | ||||||||
\(29\) | 141983. | 1.08105 | 0.540523 | − | 0.841329i | \(-0.318227\pi\) | ||||
0.540523 | + | 0.841329i | \(0.318227\pi\) | |||||||
\(30\) | −78389.3 | −0.530069 | ||||||||
\(31\) | 224521. | 1.35360 | 0.676801 | − | 0.736166i | \(-0.263366\pi\) | ||||
0.676801 | + | 0.736166i | \(0.263366\pi\) | |||||||
\(32\) | −265674. | −1.43326 | ||||||||
\(33\) | −93413.4 | −0.452492 | ||||||||
\(34\) | 199395. | 0.870037 | ||||||||
\(35\) | 194434. | 0.766541 | ||||||||
\(36\) | 107343. | 0.383454 | ||||||||
\(37\) | 433168. | 1.40589 | 0.702944 | − | 0.711246i | \(-0.251869\pi\) | ||||
0.702944 | + | 0.711246i | \(0.251869\pi\) | |||||||
\(38\) | −338413. | −1.00047 | ||||||||
\(39\) | 9955.82 | 0.0268751 | ||||||||
\(40\) | 55878.1 | 0.138048 | ||||||||
\(41\) | 286012. | 0.648097 | 0.324049 | − | 0.946040i | \(-0.394956\pi\) | ||||
0.324049 | + | 0.946040i | \(0.394956\pi\) | |||||||
\(42\) | −497698. | −1.03656 | ||||||||
\(43\) | −152357. | −0.292229 | −0.146115 | − | 0.989268i | \(-0.546677\pi\) | ||||
−0.146115 | + | 0.989268i | \(0.546677\pi\) | |||||||
\(44\) | 509436. | 0.901583 | ||||||||
\(45\) | 127573. | 0.208697 | ||||||||
\(46\) | 459333. | 0.695785 | ||||||||
\(47\) | 449388. | 0.631363 | 0.315682 | − | 0.948865i | \(-0.397767\pi\) | ||||
0.315682 | + | 0.948865i | \(0.397767\pi\) | |||||||
\(48\) | 365851. | 0.477486 | ||||||||
\(49\) | 410931. | 0.498980 | ||||||||
\(50\) | −788065. | −0.891593 | ||||||||
\(51\) | −324502. | −0.342548 | ||||||||
\(52\) | −54294.7 | −0.0535483 | ||||||||
\(53\) | 141405. | 0.130467 | 0.0652335 | − | 0.997870i | \(-0.479221\pi\) | ||||
0.0652335 | + | 0.997870i | \(0.479221\pi\) | |||||||
\(54\) | −326552. | −0.282211 | ||||||||
\(55\) | 605449. | 0.490691 | ||||||||
\(56\) | 354773. | 0.269955 | ||||||||
\(57\) | 550745. | 0.393902 | ||||||||
\(58\) | 2.35558e6 | 1.58526 | ||||||||
\(59\) | −205379. | −0.130189 | ||||||||
\(60\) | −695730. | −0.415826 | ||||||||
\(61\) | −522147. | −0.294536 | −0.147268 | − | 0.989097i | \(-0.547048\pi\) | ||||
−0.147268 | + | 0.989097i | \(0.547048\pi\) | |||||||
\(62\) | 3.72492e6 | 1.98494 | ||||||||
\(63\) | 809969. | 0.408109 | ||||||||
\(64\) | −2.67327e6 | −1.27472 | ||||||||
\(65\) | −64527.6 | −0.0291440 | ||||||||
\(66\) | −1.54978e6 | −0.663539 | ||||||||
\(67\) | 1.89319e6 | 0.769010 | 0.384505 | − | 0.923123i | \(-0.374372\pi\) | ||||
0.384505 | + | 0.923123i | \(0.374372\pi\) | |||||||
\(68\) | 1.76969e6 | 0.682522 | ||||||||
\(69\) | −747533. | −0.273942 | ||||||||
\(70\) | 3.22578e6 | 1.12406 | ||||||||
\(71\) | 3.16299e6 | 1.04880 | 0.524400 | − | 0.851472i | \(-0.324289\pi\) | ||||
0.524400 | + | 0.851472i | \(0.324289\pi\) | |||||||
\(72\) | 232775. | 0.0734975 | ||||||||
\(73\) | 3.37201e6 | 1.01452 | 0.507258 | − | 0.861794i | \(-0.330659\pi\) | ||||
0.507258 | + | 0.861794i | \(0.330659\pi\) | |||||||
\(74\) | 7.18650e6 | 2.06161 | ||||||||
\(75\) | 1.28252e6 | 0.351035 | ||||||||
\(76\) | −3.00352e6 | −0.784844 | ||||||||
\(77\) | 3.84403e6 | 0.959553 | ||||||||
\(78\) | 165172. | 0.0394100 | ||||||||
\(79\) | −1.64311e6 | −0.374949 | −0.187475 | − | 0.982269i | \(-0.560030\pi\) | ||||
−0.187475 | + | 0.982269i | \(0.560030\pi\) | |||||||
\(80\) | −2.37123e6 | −0.517795 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 4.74509e6 | 0.950377 | ||||||||
\(83\) | −6.36325e6 | −1.22153 | −0.610767 | − | 0.791810i | \(-0.709139\pi\) | ||||
−0.610767 | + | 0.791810i | \(0.709139\pi\) | |||||||
\(84\) | −4.41722e6 | −0.813152 | ||||||||
\(85\) | 2.10322e6 | 0.371466 | ||||||||
\(86\) | −2.52769e6 | −0.428528 | ||||||||
\(87\) | −3.83355e6 | −0.624142 | ||||||||
\(88\) | 1.10473e6 | 0.172809 | ||||||||
\(89\) | 5.43034e6 | 0.816511 | 0.408256 | − | 0.912868i | \(-0.366137\pi\) | ||||
0.408256 | + | 0.912868i | \(0.366137\pi\) | |||||||
\(90\) | 2.11651e6 | 0.306036 | ||||||||
\(91\) | −409689. | −0.0569914 | ||||||||
\(92\) | 4.07672e6 | 0.545825 | ||||||||
\(93\) | −6.06206e6 | −0.781502 | ||||||||
\(94\) | 7.45560e6 | 0.925838 | ||||||||
\(95\) | −3.56959e6 | −0.427156 | ||||||||
\(96\) | 7.17320e6 | 0.827492 | ||||||||
\(97\) | −2.91053e6 | −0.323796 | −0.161898 | − | 0.986807i | \(-0.551762\pi\) | ||||
−0.161898 | + | 0.986807i | \(0.551762\pi\) | |||||||
\(98\) | 6.81757e6 | 0.731709 | ||||||||
\(99\) | 2.52216e6 | 0.261246 | ||||||||
\(100\) | −6.99432e6 | −0.699432 | ||||||||
\(101\) | −1.20381e7 | −1.16261 | −0.581305 | − | 0.813686i | \(-0.697458\pi\) | ||||
−0.581305 | + | 0.813686i | \(0.697458\pi\) | |||||||
\(102\) | −5.38366e6 | −0.502316 | ||||||||
\(103\) | −4.50334e6 | −0.406074 | −0.203037 | − | 0.979171i | \(-0.565081\pi\) | ||||
−0.203037 | + | 0.979171i | \(0.565081\pi\) | |||||||
\(104\) | −117739. | −0.0102637 | ||||||||
\(105\) | −5.24973e6 | −0.442562 | ||||||||
\(106\) | 2.34599e6 | 0.191318 | ||||||||
\(107\) | −1.38674e6 | −0.109434 | −0.0547171 | − | 0.998502i | \(-0.517426\pi\) | ||||
−0.0547171 | + | 0.998502i | \(0.517426\pi\) | |||||||
\(108\) | −2.89825e6 | −0.221387 | ||||||||
\(109\) | −1.51322e7 | −1.11920 | −0.559602 | − | 0.828761i | \(-0.689046\pi\) | ||||
−0.559602 | + | 0.828761i | \(0.689046\pi\) | |||||||
\(110\) | 1.00447e7 | 0.719555 | ||||||||
\(111\) | −1.16955e7 | −0.811689 | ||||||||
\(112\) | −1.50550e7 | −1.01256 | ||||||||
\(113\) | −1.74988e7 | −1.14086 | −0.570432 | − | 0.821345i | \(-0.693224\pi\) | ||||
−0.570432 | + | 0.821345i | \(0.693224\pi\) | |||||||
\(114\) | 9.13716e6 | 0.577623 | ||||||||
\(115\) | 4.84506e6 | 0.297068 | ||||||||
\(116\) | 2.09065e7 | 1.24359 | ||||||||
\(117\) | −268807. | −0.0155164 | ||||||||
\(118\) | −3.40735e6 | −0.190910 | ||||||||
\(119\) | 1.33535e7 | 0.726407 | ||||||||
\(120\) | −1.50871e6 | −0.0797023 | ||||||||
\(121\) | −7.51726e6 | −0.385754 | ||||||||
\(122\) | −8.66270e6 | −0.431911 | ||||||||
\(123\) | −7.72232e6 | −0.374179 | ||||||||
\(124\) | 3.30599e7 | 1.55713 | ||||||||
\(125\) | −2.19842e7 | −1.00676 | ||||||||
\(126\) | 1.34378e7 | 0.598456 | ||||||||
\(127\) | −2.00254e7 | −0.867495 | −0.433748 | − | 0.901034i | \(-0.642809\pi\) | ||||
−0.433748 | + | 0.901034i | \(0.642809\pi\) | |||||||
\(128\) | −1.03448e7 | −0.436000 | ||||||||
\(129\) | 4.11365e6 | 0.168719 | ||||||||
\(130\) | −1.07055e6 | −0.0427370 | ||||||||
\(131\) | 1.77758e7 | 0.690845 | 0.345422 | − | 0.938447i | \(-0.387736\pi\) | ||||
0.345422 | + | 0.938447i | \(0.387736\pi\) | |||||||
\(132\) | −1.37548e7 | −0.520529 | ||||||||
\(133\) | −2.26635e7 | −0.835308 | ||||||||
\(134\) | 3.14090e7 | 1.12769 | ||||||||
\(135\) | −3.44448e6 | −0.120491 | ||||||||
\(136\) | 3.83762e6 | 0.130821 | ||||||||
\(137\) | 4.37881e7 | 1.45490 | 0.727451 | − | 0.686159i | \(-0.240705\pi\) | ||||
0.727451 | + | 0.686159i | \(0.240705\pi\) | |||||||
\(138\) | −1.24020e7 | −0.401712 | ||||||||
\(139\) | −2.03284e7 | −0.642024 | −0.321012 | − | 0.947075i | \(-0.604023\pi\) | ||||
−0.321012 | + | 0.947075i | \(0.604023\pi\) | |||||||
\(140\) | 2.86298e7 | 0.881799 | ||||||||
\(141\) | −1.21335e7 | −0.364518 | ||||||||
\(142\) | 5.24757e7 | 1.53797 | ||||||||
\(143\) | −1.27573e6 | −0.0364823 | ||||||||
\(144\) | −9.87798e6 | −0.275676 | ||||||||
\(145\) | 2.48467e7 | 0.676832 | ||||||||
\(146\) | 5.59435e7 | 1.48770 | ||||||||
\(147\) | −1.10951e7 | −0.288086 | ||||||||
\(148\) | 6.37824e7 | 1.61728 | ||||||||
\(149\) | 6.14768e7 | 1.52251 | 0.761254 | − | 0.648454i | \(-0.224584\pi\) | ||||
0.761254 | + | 0.648454i | \(0.224584\pi\) | |||||||
\(150\) | 2.12777e7 | 0.514762 | ||||||||
\(151\) | 6.11417e6 | 0.144517 | 0.0722583 | − | 0.997386i | \(-0.476979\pi\) | ||||
0.0722583 | + | 0.997386i | \(0.476979\pi\) | |||||||
\(152\) | −6.51322e6 | −0.150433 | ||||||||
\(153\) | 8.76155e6 | 0.197770 | ||||||||
\(154\) | 6.37745e7 | 1.40710 | ||||||||
\(155\) | 3.92906e7 | 0.847477 | ||||||||
\(156\) | 1.46596e6 | 0.0309161 | ||||||||
\(157\) | 3.59609e7 | 0.741621 | 0.370810 | − | 0.928709i | \(-0.379080\pi\) | ||||
0.370810 | + | 0.928709i | \(0.379080\pi\) | |||||||
\(158\) | −2.72601e7 | −0.549830 | ||||||||
\(159\) | −3.81795e6 | −0.0753251 | ||||||||
\(160\) | −4.64923e7 | −0.897349 | ||||||||
\(161\) | 3.07615e7 | 0.580921 | ||||||||
\(162\) | 8.81690e6 | 0.162935 | ||||||||
\(163\) | −3.88451e7 | −0.702553 | −0.351277 | − | 0.936272i | \(-0.614252\pi\) | ||||
−0.351277 | + | 0.936272i | \(0.614252\pi\) | |||||||
\(164\) | 4.21142e7 | 0.745547 | ||||||||
\(165\) | −1.63471e7 | −0.283301 | ||||||||
\(166\) | −1.05570e8 | −1.79127 | ||||||||
\(167\) | −8.48288e7 | −1.40940 | −0.704702 | − | 0.709503i | \(-0.748919\pi\) | ||||
−0.704702 | + | 0.709503i | \(0.748919\pi\) | |||||||
\(168\) | −9.57886e6 | −0.155859 | ||||||||
\(169\) | −6.26126e7 | −0.997833 | ||||||||
\(170\) | 3.48936e7 | 0.544722 | ||||||||
\(171\) | −1.48701e7 | −0.227420 | ||||||||
\(172\) | −2.24341e7 | −0.336169 | ||||||||
\(173\) | −2.04205e7 | −0.299850 | −0.149925 | − | 0.988697i | \(-0.547903\pi\) | ||||
−0.149925 | + | 0.988697i | \(0.547903\pi\) | |||||||
\(174\) | −6.36006e7 | −0.915249 | ||||||||
\(175\) | −5.27767e7 | −0.744404 | ||||||||
\(176\) | −4.68799e7 | −0.648175 | ||||||||
\(177\) | 5.54523e6 | 0.0751646 | ||||||||
\(178\) | 9.00924e7 | 1.19734 | ||||||||
\(179\) | −2.15476e7 | −0.280811 | −0.140405 | − | 0.990094i | \(-0.544841\pi\) | ||||
−0.140405 | + | 0.990094i | \(0.544841\pi\) | |||||||
\(180\) | 1.87847e7 | 0.240077 | ||||||||
\(181\) | −6.19200e7 | −0.776168 | −0.388084 | − | 0.921624i | \(-0.626863\pi\) | ||||
−0.388084 | + | 0.921624i | \(0.626863\pi\) | |||||||
\(182\) | −6.79696e6 | −0.0835728 | ||||||||
\(183\) | 1.40980e7 | 0.170050 | ||||||||
\(184\) | 8.84047e6 | 0.104620 | ||||||||
\(185\) | 7.58034e7 | 0.880213 | ||||||||
\(186\) | −1.00573e8 | −1.14600 | ||||||||
\(187\) | 4.15814e7 | 0.465000 | ||||||||
\(188\) | 6.61708e7 | 0.726296 | ||||||||
\(189\) | −2.18692e7 | −0.235622 | ||||||||
\(190\) | −5.92215e7 | −0.626386 | ||||||||
\(191\) | −1.83254e8 | −1.90300 | −0.951498 | − | 0.307656i | \(-0.900456\pi\) | ||||
−0.951498 | + | 0.307656i | \(0.900456\pi\) | |||||||
\(192\) | 7.21784e7 | 0.735958 | ||||||||
\(193\) | −2.51674e7 | −0.251993 | −0.125996 | − | 0.992031i | \(-0.540213\pi\) | ||||
−0.125996 | + | 0.992031i | \(0.540213\pi\) | |||||||
\(194\) | −4.82873e7 | −0.474818 | ||||||||
\(195\) | 1.74225e6 | 0.0168263 | ||||||||
\(196\) | 6.05081e7 | 0.574007 | ||||||||
\(197\) | 4.11501e7 | 0.383477 | 0.191738 | − | 0.981446i | \(-0.438588\pi\) | ||||
0.191738 | + | 0.981446i | \(0.438588\pi\) | |||||||
\(198\) | 4.18441e7 | 0.383094 | ||||||||
\(199\) | 1.20872e8 | 1.08728 | 0.543638 | − | 0.839320i | \(-0.317047\pi\) | ||||
0.543638 | + | 0.839320i | \(0.317047\pi\) | |||||||
\(200\) | −1.51674e7 | −0.134062 | ||||||||
\(201\) | −5.11161e7 | −0.443988 | ||||||||
\(202\) | −1.99719e8 | −1.70486 | ||||||||
\(203\) | 1.57753e8 | 1.32355 | ||||||||
\(204\) | −4.77817e7 | −0.394054 | ||||||||
\(205\) | 5.00514e7 | 0.405768 | ||||||||
\(206\) | −7.47129e7 | −0.595471 | ||||||||
\(207\) | 2.01834e7 | 0.158160 | ||||||||
\(208\) | 4.99636e6 | 0.0384975 | ||||||||
\(209\) | −7.05720e7 | −0.534712 | ||||||||
\(210\) | −8.70959e7 | −0.648978 | ||||||||
\(211\) | −1.24225e8 | −0.910379 | −0.455189 | − | 0.890395i | \(-0.650428\pi\) | ||||
−0.455189 | + | 0.890395i | \(0.650428\pi\) | |||||||
\(212\) | 2.08214e7 | 0.150084 | ||||||||
\(213\) | −8.54006e7 | −0.605525 | ||||||||
\(214\) | −2.30068e7 | −0.160475 | ||||||||
\(215\) | −2.66622e7 | −0.182962 | ||||||||
\(216\) | −6.28493e6 | −0.0424338 | ||||||||
\(217\) | 2.49458e8 | 1.65725 | ||||||||
\(218\) | −2.51052e8 | −1.64121 | ||||||||
\(219\) | −9.10443e7 | −0.585731 | ||||||||
\(220\) | 8.91502e7 | 0.564473 | ||||||||
\(221\) | −4.43166e6 | −0.0276181 | ||||||||
\(222\) | −1.94035e8 | −1.19027 | ||||||||
\(223\) | −4.32331e6 | −0.0261065 | −0.0130533 | − | 0.999915i | \(-0.504155\pi\) | ||||
−0.0130533 | + | 0.999915i | \(0.504155\pi\) | |||||||
\(224\) | −2.95182e8 | −1.75478 | ||||||||
\(225\) | −3.46281e7 | −0.202670 | ||||||||
\(226\) | −2.90315e8 | −1.67298 | ||||||||
\(227\) | −1.29928e8 | −0.737244 | −0.368622 | − | 0.929579i | \(-0.620170\pi\) | ||||
−0.368622 | + | 0.929579i | \(0.620170\pi\) | |||||||
\(228\) | 8.10952e7 | 0.453130 | ||||||||
\(229\) | −6.03820e7 | −0.332264 | −0.166132 | − | 0.986103i | \(-0.553128\pi\) | ||||
−0.166132 | + | 0.986103i | \(0.553128\pi\) | |||||||
\(230\) | 8.03821e7 | 0.435624 | ||||||||
\(231\) | −1.03789e8 | −0.553998 | ||||||||
\(232\) | 4.53363e7 | 0.238362 | ||||||||
\(233\) | −2.38228e8 | −1.23381 | −0.616904 | − | 0.787038i | \(-0.711613\pi\) | ||||
−0.616904 | + | 0.787038i | \(0.711613\pi\) | |||||||
\(234\) | −4.45966e6 | −0.0227534 | ||||||||
\(235\) | 7.86419e7 | 0.395291 | ||||||||
\(236\) | −3.02413e7 | −0.149764 | ||||||||
\(237\) | 4.43640e7 | 0.216477 | ||||||||
\(238\) | 2.21541e8 | 1.06521 | ||||||||
\(239\) | −3.08535e7 | −0.146188 | −0.0730940 | − | 0.997325i | \(-0.523287\pi\) | ||||
−0.0730940 | + | 0.997325i | \(0.523287\pi\) | |||||||
\(240\) | 6.40231e7 | 0.298949 | ||||||||
\(241\) | 9.76207e6 | 0.0449244 | 0.0224622 | − | 0.999748i | \(-0.492849\pi\) | ||||
0.0224622 | + | 0.999748i | \(0.492849\pi\) | |||||||
\(242\) | −1.24715e8 | −0.565674 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | −7.68842e7 | −0.338823 | ||||||||
\(245\) | 7.19120e7 | 0.312407 | ||||||||
\(246\) | −1.28117e8 | −0.548701 | ||||||||
\(247\) | 7.52142e6 | 0.0317585 | ||||||||
\(248\) | 7.16912e7 | 0.298459 | ||||||||
\(249\) | 1.71808e8 | 0.705253 | ||||||||
\(250\) | −3.64730e8 | −1.47632 | ||||||||
\(251\) | 2.04882e8 | 0.817798 | 0.408899 | − | 0.912580i | \(-0.365913\pi\) | ||||
0.408899 | + | 0.912580i | \(0.365913\pi\) | |||||||
\(252\) | 1.19265e8 | 0.469474 | ||||||||
\(253\) | 9.57882e7 | 0.371869 | ||||||||
\(254\) | −3.32232e8 | −1.27211 | ||||||||
\(255\) | −5.67870e7 | −0.214466 | ||||||||
\(256\) | 1.70553e8 | 0.635360 | ||||||||
\(257\) | −7.58629e7 | −0.278781 | −0.139391 | − | 0.990237i | \(-0.544514\pi\) | ||||
−0.139391 | + | 0.990237i | \(0.544514\pi\) | |||||||
\(258\) | 6.82477e7 | 0.247411 | ||||||||
\(259\) | 4.81280e8 | 1.72127 | ||||||||
\(260\) | −9.50145e6 | −0.0335261 | ||||||||
\(261\) | 1.03506e8 | 0.360348 | ||||||||
\(262\) | 2.94911e8 | 1.01306 | ||||||||
\(263\) | −3.76186e8 | −1.27514 | −0.637569 | − | 0.770393i | \(-0.720060\pi\) | ||||
−0.637569 | + | 0.770393i | \(0.720060\pi\) | |||||||
\(264\) | −2.98276e7 | −0.0997710 | ||||||||
\(265\) | 2.47456e7 | 0.0816842 | ||||||||
\(266\) | −3.76000e8 | −1.22491 | ||||||||
\(267\) | −1.46619e8 | −0.471413 | ||||||||
\(268\) | 2.78765e8 | 0.884640 | ||||||||
\(269\) | −5.43241e8 | −1.70161 | −0.850804 | − | 0.525483i | \(-0.823885\pi\) | ||||
−0.850804 | + | 0.525483i | \(0.823885\pi\) | |||||||
\(270\) | −5.71458e7 | −0.176690 | ||||||||
\(271\) | 5.59119e8 | 1.70652 | 0.853261 | − | 0.521484i | \(-0.174621\pi\) | ||||
0.853261 | + | 0.521484i | \(0.174621\pi\) | |||||||
\(272\) | −1.62852e8 | −0.490685 | ||||||||
\(273\) | 1.10616e7 | 0.0329040 | ||||||||
\(274\) | 7.26468e8 | 2.13349 | ||||||||
\(275\) | −1.64341e8 | −0.476521 | ||||||||
\(276\) | −1.10071e8 | −0.315132 | ||||||||
\(277\) | 4.08022e8 | 1.15346 | 0.576732 | − | 0.816933i | \(-0.304328\pi\) | ||||
0.576732 | + | 0.816933i | \(0.304328\pi\) | |||||||
\(278\) | −3.37259e8 | −0.941472 | ||||||||
\(279\) | 1.63676e8 | 0.451200 | ||||||||
\(280\) | 6.20844e7 | 0.169017 | ||||||||
\(281\) | 3.46395e8 | 0.931321 | 0.465660 | − | 0.884964i | \(-0.345817\pi\) | ||||
0.465660 | + | 0.884964i | \(0.345817\pi\) | |||||||
\(282\) | −2.01301e8 | −0.534533 | ||||||||
\(283\) | 1.32435e8 | 0.347337 | 0.173669 | − | 0.984804i | \(-0.444438\pi\) | ||||
0.173669 | + | 0.984804i | \(0.444438\pi\) | |||||||
\(284\) | 4.65738e8 | 1.20650 | ||||||||
\(285\) | 9.63791e7 | 0.246619 | ||||||||
\(286\) | −2.11651e7 | −0.0534981 | ||||||||
\(287\) | 3.17779e8 | 0.793484 | ||||||||
\(288\) | −1.93676e8 | −0.477753 | ||||||||
\(289\) | −2.65892e8 | −0.647983 | ||||||||
\(290\) | 4.12221e8 | 0.992515 | ||||||||
\(291\) | 7.85844e7 | 0.186944 | ||||||||
\(292\) | 4.96516e8 | 1.16706 | ||||||||
\(293\) | −6.11894e8 | −1.42115 | −0.710574 | − | 0.703622i | \(-0.751565\pi\) | ||||
−0.710574 | + | 0.703622i | \(0.751565\pi\) | |||||||
\(294\) | −1.84075e8 | −0.422453 | ||||||||
\(295\) | −3.59408e7 | −0.0815101 | ||||||||
\(296\) | 1.38314e8 | 0.309988 | ||||||||
\(297\) | −6.80984e7 | −0.150831 | ||||||||
\(298\) | 1.01993e9 | 2.23262 | ||||||||
\(299\) | −1.02089e7 | −0.0220867 | ||||||||
\(300\) | 1.88847e8 | 0.403817 | ||||||||
\(301\) | −1.69279e8 | −0.357785 | ||||||||
\(302\) | 1.01437e8 | 0.211921 | ||||||||
\(303\) | 3.25029e8 | 0.671233 | ||||||||
\(304\) | 2.76393e8 | 0.564248 | ||||||||
\(305\) | −9.13745e7 | −0.184406 | ||||||||
\(306\) | 1.45359e8 | 0.290012 | ||||||||
\(307\) | 1.61294e8 | 0.318151 | 0.159075 | − | 0.987266i | \(-0.449149\pi\) | ||||
0.159075 | + | 0.987266i | \(0.449149\pi\) | |||||||
\(308\) | 5.66019e8 | 1.10383 | ||||||||
\(309\) | 1.21590e8 | 0.234447 | ||||||||
\(310\) | 6.51853e8 | 1.24275 | ||||||||
\(311\) | 5.52921e8 | 1.04232 | 0.521160 | − | 0.853459i | \(-0.325499\pi\) | ||||
0.521160 | + | 0.853459i | \(0.325499\pi\) | |||||||
\(312\) | 3.17897e6 | 0.00592577 | ||||||||
\(313\) | 3.45307e8 | 0.636503 | 0.318252 | − | 0.948006i | \(-0.396904\pi\) | ||||
0.318252 | + | 0.948006i | \(0.396904\pi\) | |||||||
\(314\) | 5.96611e8 | 1.08752 | ||||||||
\(315\) | 1.41743e8 | 0.255514 | ||||||||
\(316\) | −2.41942e8 | −0.431327 | ||||||||
\(317\) | −5.61715e8 | −0.990395 | −0.495198 | − | 0.868780i | \(-0.664904\pi\) | ||||
−0.495198 | + | 0.868780i | \(0.664904\pi\) | |||||||
\(318\) | −6.33418e7 | −0.110458 | ||||||||
\(319\) | 4.91227e8 | 0.847257 | ||||||||
\(320\) | −4.67817e8 | −0.798088 | ||||||||
\(321\) | 3.74421e7 | 0.0631818 | ||||||||
\(322\) | 5.10350e8 | 0.851869 | ||||||||
\(323\) | −2.45154e8 | −0.404791 | ||||||||
\(324\) | 7.82527e7 | 0.127818 | ||||||||
\(325\) | 1.75152e7 | 0.0283023 | ||||||||
\(326\) | −6.44461e8 | −1.03023 | ||||||||
\(327\) | 4.08570e8 | 0.646173 | ||||||||
\(328\) | 9.13256e7 | 0.142901 | ||||||||
\(329\) | 4.99302e8 | 0.772996 | ||||||||
\(330\) | −2.71208e8 | −0.415435 | ||||||||
\(331\) | −7.48834e8 | −1.13498 | −0.567489 | − | 0.823381i | \(-0.692085\pi\) | ||||
−0.567489 | + | 0.823381i | \(0.692085\pi\) | |||||||
\(332\) | −9.36965e8 | −1.40521 | ||||||||
\(333\) | 3.15780e8 | 0.468629 | ||||||||
\(334\) | −1.40736e9 | −2.06677 | ||||||||
\(335\) | 3.31304e8 | 0.481470 | ||||||||
\(336\) | 4.06486e8 | 0.584599 | ||||||||
\(337\) | 3.77520e8 | 0.537322 | 0.268661 | − | 0.963235i | \(-0.413419\pi\) | ||||
0.268661 | + | 0.963235i | \(0.413419\pi\) | |||||||
\(338\) | −1.03878e9 | −1.46323 | ||||||||
\(339\) | 4.72468e8 | 0.658678 | ||||||||
\(340\) | 3.09692e8 | 0.427321 | ||||||||
\(341\) | 7.76787e8 | 1.06087 | ||||||||
\(342\) | −2.46703e8 | −0.333491 | ||||||||
\(343\) | −4.58440e8 | −0.613413 | ||||||||
\(344\) | −4.86488e7 | −0.0644344 | ||||||||
\(345\) | −1.30817e8 | −0.171512 | ||||||||
\(346\) | −3.38787e8 | −0.439703 | ||||||||
\(347\) | 2.25075e8 | 0.289185 | 0.144592 | − | 0.989491i | \(-0.453813\pi\) | ||||
0.144592 | + | 0.989491i | \(0.453813\pi\) | |||||||
\(348\) | −5.64476e8 | −0.717989 | ||||||||
\(349\) | 2.00272e8 | 0.252192 | 0.126096 | − | 0.992018i | \(-0.459755\pi\) | ||||
0.126096 | + | 0.992018i | \(0.459755\pi\) | |||||||
\(350\) | −8.75594e8 | −1.09160 | ||||||||
\(351\) | 7.25779e6 | 0.00895838 | ||||||||
\(352\) | −9.19168e8 | −1.12330 | ||||||||
\(353\) | −9.69527e6 | −0.0117314 | −0.00586568 | − | 0.999983i | \(-0.501867\pi\) | ||||
−0.00586568 | + | 0.999983i | \(0.501867\pi\) | |||||||
\(354\) | 9.19985e7 | 0.110222 | ||||||||
\(355\) | 5.53515e8 | 0.656645 | ||||||||
\(356\) | 7.99598e8 | 0.939284 | ||||||||
\(357\) | −3.60544e8 | −0.419391 | ||||||||
\(358\) | −3.57487e8 | −0.411784 | ||||||||
\(359\) | 1.59435e9 | 1.81867 | 0.909334 | − | 0.416067i | \(-0.136592\pi\) | ||||
0.909334 | + | 0.416067i | \(0.136592\pi\) | |||||||
\(360\) | 4.07351e7 | 0.0460161 | ||||||||
\(361\) | −4.77795e8 | −0.534523 | ||||||||
\(362\) | −1.02729e9 | −1.13818 | ||||||||
\(363\) | 2.02966e8 | 0.222715 | ||||||||
\(364\) | −6.03252e7 | −0.0655607 | ||||||||
\(365\) | 5.90094e8 | 0.635179 | ||||||||
\(366\) | 2.33893e8 | 0.249364 | ||||||||
\(367\) | 4.36226e8 | 0.460660 | 0.230330 | − | 0.973113i | \(-0.426019\pi\) | ||||
0.230330 | + | 0.973113i | \(0.426019\pi\) | |||||||
\(368\) | −3.75152e8 | −0.392410 | ||||||||
\(369\) | 2.08503e8 | 0.216032 | ||||||||
\(370\) | 1.25762e9 | 1.29075 | ||||||||
\(371\) | 1.57111e8 | 0.159734 | ||||||||
\(372\) | −8.92616e8 | −0.899010 | ||||||||
\(373\) | 8.71065e8 | 0.869100 | 0.434550 | − | 0.900648i | \(-0.356907\pi\) | ||||
0.434550 | + | 0.900648i | \(0.356907\pi\) | |||||||
\(374\) | 6.89858e8 | 0.681882 | ||||||||
\(375\) | 5.93574e8 | 0.581253 | ||||||||
\(376\) | 1.43493e8 | 0.139211 | ||||||||
\(377\) | −5.23540e7 | −0.0503217 | ||||||||
\(378\) | −3.62822e8 | −0.345519 | ||||||||
\(379\) | 1.10371e9 | 1.04140 | 0.520702 | − | 0.853739i | \(-0.325670\pi\) | ||||
0.520702 | + | 0.853739i | \(0.325670\pi\) | |||||||
\(380\) | −5.25610e8 | −0.491384 | ||||||||
\(381\) | 5.40685e8 | 0.500849 | ||||||||
\(382\) | −3.04029e9 | −2.79057 | ||||||||
\(383\) | 3.23348e8 | 0.294086 | 0.147043 | − | 0.989130i | \(-0.453024\pi\) | ||||
0.147043 | + | 0.989130i | \(0.453024\pi\) | |||||||
\(384\) | 2.79309e8 | 0.251725 | ||||||||
\(385\) | 6.72696e8 | 0.600767 | ||||||||
\(386\) | −4.17541e8 | −0.369525 | ||||||||
\(387\) | −1.11068e8 | −0.0974098 | ||||||||
\(388\) | −4.28565e8 | −0.372483 | ||||||||
\(389\) | 1.09065e9 | 0.939423 | 0.469711 | − | 0.882820i | \(-0.344358\pi\) | ||||
0.469711 | + | 0.882820i | \(0.344358\pi\) | |||||||
\(390\) | 2.89048e7 | 0.0246742 | ||||||||
\(391\) | 3.32751e8 | 0.281515 | ||||||||
\(392\) | 1.31213e8 | 0.110021 | ||||||||
\(393\) | −4.79948e8 | −0.398859 | ||||||||
\(394\) | 6.82702e8 | 0.562334 | ||||||||
\(395\) | −2.87541e8 | −0.234752 | ||||||||
\(396\) | 3.71379e8 | 0.300528 | ||||||||
\(397\) | −2.19755e9 | −1.76268 | −0.881338 | − | 0.472487i | \(-0.843356\pi\) | ||||
−0.881338 | + | 0.472487i | \(0.843356\pi\) | |||||||
\(398\) | 2.00533e9 | 1.59439 | ||||||||
\(399\) | 6.11915e8 | 0.482266 | ||||||||
\(400\) | 6.43638e8 | 0.502842 | ||||||||
\(401\) | −2.55403e9 | −1.97797 | −0.988987 | − | 0.148004i | \(-0.952715\pi\) | ||||
−0.988987 | + | 0.148004i | \(0.952715\pi\) | |||||||
\(402\) | −8.48044e8 | −0.651069 | ||||||||
\(403\) | −8.27885e7 | −0.0630089 | ||||||||
\(404\) | −1.77257e9 | −1.33742 | ||||||||
\(405\) | 9.30009e7 | 0.0695656 | ||||||||
\(406\) | 2.61721e9 | 1.94087 | ||||||||
\(407\) | 1.49866e9 | 1.10185 | ||||||||
\(408\) | −1.03616e8 | −0.0755293 | ||||||||
\(409\) | −2.88636e8 | −0.208602 | −0.104301 | − | 0.994546i | \(-0.533261\pi\) | ||||
−0.104301 | + | 0.994546i | \(0.533261\pi\) | |||||||
\(410\) | 8.30380e8 | 0.595022 | ||||||||
\(411\) | −1.18228e9 | −0.839989 | ||||||||
\(412\) | −6.63101e8 | −0.467132 | ||||||||
\(413\) | −2.28190e8 | −0.159394 | ||||||||
\(414\) | 3.34854e8 | 0.231928 | ||||||||
\(415\) | −1.11355e9 | −0.764791 | ||||||||
\(416\) | 9.79631e7 | 0.0667169 | ||||||||
\(417\) | 5.48867e8 | 0.370673 | ||||||||
\(418\) | −1.17083e9 | −0.784108 | ||||||||
\(419\) | −5.30993e8 | −0.352647 | −0.176323 | − | 0.984332i | \(-0.556420\pi\) | ||||
−0.176323 | + | 0.984332i | \(0.556420\pi\) | |||||||
\(420\) | −7.73004e8 | −0.509107 | ||||||||
\(421\) | −2.15095e9 | −1.40489 | −0.702445 | − | 0.711738i | \(-0.747908\pi\) | ||||
−0.702445 | + | 0.711738i | \(0.747908\pi\) | |||||||
\(422\) | −2.06097e9 | −1.33499 | ||||||||
\(423\) | 3.27604e8 | 0.210454 | ||||||||
\(424\) | 4.51518e7 | 0.0287670 | ||||||||
\(425\) | −5.70892e8 | −0.360739 | ||||||||
\(426\) | −1.41684e9 | −0.887949 | ||||||||
\(427\) | −5.80141e8 | −0.360609 | ||||||||
\(428\) | −2.04193e8 | −0.125889 | ||||||||
\(429\) | 3.44447e7 | 0.0210631 | ||||||||
\(430\) | −4.42340e8 | −0.268298 | ||||||||
\(431\) | −3.30976e8 | −0.199125 | −0.0995624 | − | 0.995031i | \(-0.531744\pi\) | ||||
−0.0995624 | + | 0.995031i | \(0.531744\pi\) | |||||||
\(432\) | 2.66706e8 | 0.159162 | ||||||||
\(433\) | 2.05100e9 | 1.21411 | 0.607056 | − | 0.794659i | \(-0.292350\pi\) | ||||
0.607056 | + | 0.794659i | \(0.292350\pi\) | |||||||
\(434\) | 4.13865e9 | 2.43021 | ||||||||
\(435\) | −6.70862e8 | −0.390769 | ||||||||
\(436\) | −2.22816e9 | −1.28749 | ||||||||
\(437\) | −5.64746e8 | −0.323719 | ||||||||
\(438\) | −1.51047e9 | −0.858922 | ||||||||
\(439\) | 1.57643e9 | 0.889299 | 0.444649 | − | 0.895705i | \(-0.353328\pi\) | ||||
0.444649 | + | 0.895705i | \(0.353328\pi\) | |||||||
\(440\) | 1.93324e8 | 0.108194 | ||||||||
\(441\) | 2.99569e8 | 0.166327 | ||||||||
\(442\) | −7.35237e7 | −0.0404995 | ||||||||
\(443\) | 3.27614e8 | 0.179040 | 0.0895199 | − | 0.995985i | \(-0.471467\pi\) | ||||
0.0895199 | + | 0.995985i | \(0.471467\pi\) | |||||||
\(444\) | −1.72213e9 | −0.933737 | ||||||||
\(445\) | 9.50297e8 | 0.511210 | ||||||||
\(446\) | −7.17261e7 | −0.0382829 | ||||||||
\(447\) | −1.65987e9 | −0.879020 | ||||||||
\(448\) | −2.97019e9 | −1.56067 | ||||||||
\(449\) | −3.76746e7 | −0.0196420 | −0.00982101 | − | 0.999952i | \(-0.503126\pi\) | ||||
−0.00982101 | + | 0.999952i | \(0.503126\pi\) | |||||||
\(450\) | −5.74499e8 | −0.297198 | ||||||||
\(451\) | 9.89531e8 | 0.507939 | ||||||||
\(452\) | −2.57664e9 | −1.31241 | ||||||||
\(453\) | −1.65082e8 | −0.0834367 | ||||||||
\(454\) | −2.15557e9 | −1.08110 | ||||||||
\(455\) | −7.16946e7 | −0.0356818 | ||||||||
\(456\) | 1.75857e8 | 0.0868525 | ||||||||
\(457\) | 1.95746e8 | 0.0959372 | 0.0479686 | − | 0.998849i | \(-0.484725\pi\) | ||||
0.0479686 | + | 0.998849i | \(0.484725\pi\) | |||||||
\(458\) | −1.00177e9 | −0.487236 | ||||||||
\(459\) | −2.36562e8 | −0.114183 | ||||||||
\(460\) | 7.13417e8 | 0.341736 | ||||||||
\(461\) | −1.06215e9 | −0.504931 | −0.252465 | − | 0.967606i | \(-0.581241\pi\) | ||||
−0.252465 | + | 0.967606i | \(0.581241\pi\) | |||||||
\(462\) | −1.72191e9 | −0.812389 | ||||||||
\(463\) | 1.12424e9 | 0.526412 | 0.263206 | − | 0.964740i | \(-0.415220\pi\) | ||||
0.263206 | + | 0.964740i | \(0.415220\pi\) | |||||||
\(464\) | −1.92388e9 | −0.894056 | ||||||||
\(465\) | −1.06085e9 | −0.489291 | ||||||||
\(466\) | −3.95234e9 | −1.80927 | ||||||||
\(467\) | −1.93669e9 | −0.879936 | −0.439968 | − | 0.898013i | \(-0.645010\pi\) | ||||
−0.439968 | + | 0.898013i | \(0.645010\pi\) | |||||||
\(468\) | −3.95809e7 | −0.0178494 | ||||||||
\(469\) | 2.10346e9 | 0.941521 | ||||||||
\(470\) | 1.30471e9 | 0.579659 | ||||||||
\(471\) | −9.70945e8 | −0.428175 | ||||||||
\(472\) | −6.55790e7 | −0.0287057 | ||||||||
\(473\) | −5.27119e8 | −0.229031 | ||||||||
\(474\) | 7.36024e8 | 0.317444 | ||||||||
\(475\) | 9.68919e8 | 0.414820 | ||||||||
\(476\) | 1.96625e9 | 0.835631 | ||||||||
\(477\) | 1.03085e8 | 0.0434890 | ||||||||
\(478\) | −5.11877e8 | −0.214372 | ||||||||
\(479\) | 2.67237e9 | 1.11102 | 0.555510 | − | 0.831510i | \(-0.312523\pi\) | ||||
0.555510 | + | 0.831510i | \(0.312523\pi\) | |||||||
\(480\) | 1.25529e9 | 0.518085 | ||||||||
\(481\) | −1.59724e8 | −0.0654428 | ||||||||
\(482\) | 1.61958e8 | 0.0658777 | ||||||||
\(483\) | −8.30561e8 | −0.335395 | ||||||||
\(484\) | −1.10689e9 | −0.443757 | ||||||||
\(485\) | −5.09337e8 | −0.202726 | ||||||||
\(486\) | −2.38056e8 | −0.0940703 | ||||||||
\(487\) | 9.86225e8 | 0.386923 | 0.193462 | − | 0.981108i | \(-0.438029\pi\) | ||||
0.193462 | + | 0.981108i | \(0.438029\pi\) | |||||||
\(488\) | −1.66725e8 | −0.0649430 | ||||||||
\(489\) | 1.04882e9 | 0.405619 | ||||||||
\(490\) | 1.19306e9 | 0.458116 | ||||||||
\(491\) | −3.33799e9 | −1.27262 | −0.636312 | − | 0.771431i | \(-0.719541\pi\) | ||||
−0.636312 | + | 0.771431i | \(0.719541\pi\) | |||||||
\(492\) | −1.13708e9 | −0.430442 | ||||||||
\(493\) | 1.70644e9 | 0.641395 | ||||||||
\(494\) | 1.24784e8 | 0.0465711 | ||||||||
\(495\) | 4.41373e8 | 0.163564 | ||||||||
\(496\) | −3.04227e9 | −1.11947 | ||||||||
\(497\) | 3.51430e9 | 1.28408 | ||||||||
\(498\) | 2.85039e9 | 1.03419 | ||||||||
\(499\) | 4.31622e9 | 1.55508 | 0.777539 | − | 0.628835i | \(-0.216468\pi\) | ||||
0.777539 | + | 0.628835i | \(0.216468\pi\) | |||||||
\(500\) | −3.23710e9 | −1.15814 | ||||||||
\(501\) | 2.29038e9 | 0.813720 | ||||||||
\(502\) | 3.39911e9 | 1.19923 | ||||||||
\(503\) | −3.79261e9 | −1.32877 | −0.664386 | − | 0.747389i | \(-0.731307\pi\) | ||||
−0.664386 | + | 0.747389i | \(0.731307\pi\) | |||||||
\(504\) | 2.58629e8 | 0.0899851 | ||||||||
\(505\) | −2.10664e9 | −0.727899 | ||||||||
\(506\) | 1.58918e9 | 0.545313 | ||||||||
\(507\) | 1.69054e9 | 0.576099 | ||||||||
\(508\) | −2.94866e9 | −0.997934 | ||||||||
\(509\) | 1.85516e9 | 0.623548 | 0.311774 | − | 0.950156i | \(-0.399077\pi\) | ||||
0.311774 | + | 0.950156i | \(0.399077\pi\) | |||||||
\(510\) | −9.42128e8 | −0.314496 | ||||||||
\(511\) | 3.74653e9 | 1.24210 | ||||||||
\(512\) | 4.15370e9 | 1.36770 | ||||||||
\(513\) | 4.01493e8 | 0.131301 | ||||||||
\(514\) | −1.25861e9 | −0.408808 | ||||||||
\(515\) | −7.88075e8 | −0.254239 | ||||||||
\(516\) | 6.05720e8 | 0.194088 | ||||||||
\(517\) | 1.55477e9 | 0.494824 | ||||||||
\(518\) | 7.98470e9 | 2.52409 | ||||||||
\(519\) | 5.51352e8 | 0.173118 | ||||||||
\(520\) | −2.06041e7 | −0.00642603 | ||||||||
\(521\) | −2.97325e8 | −0.0921083 | −0.0460542 | − | 0.998939i | \(-0.514665\pi\) | ||||
−0.0460542 | + | 0.998939i | \(0.514665\pi\) | |||||||
\(522\) | 1.71722e9 | 0.528419 | ||||||||
\(523\) | 2.48461e9 | 0.759456 | 0.379728 | − | 0.925098i | \(-0.376018\pi\) | ||||
0.379728 | + | 0.925098i | \(0.376018\pi\) | |||||||
\(524\) | 2.61743e9 | 0.794722 | ||||||||
\(525\) | 1.42497e9 | 0.429782 | ||||||||
\(526\) | −6.24113e9 | −1.86988 | ||||||||
\(527\) | 2.69842e9 | 0.803106 | ||||||||
\(528\) | 1.26576e9 | 0.374224 | ||||||||
\(529\) | −2.63829e9 | −0.774867 | ||||||||
\(530\) | 4.10544e8 | 0.119783 | ||||||||
\(531\) | −1.49721e8 | −0.0433963 | ||||||||
\(532\) | −3.33712e9 | −0.960907 | ||||||||
\(533\) | −1.05462e8 | −0.0301684 | ||||||||
\(534\) | −2.43249e9 | −0.691285 | ||||||||
\(535\) | −2.42677e8 | −0.0685157 | ||||||||
\(536\) | 6.04509e8 | 0.169561 | ||||||||
\(537\) | 5.81786e8 | 0.162126 | ||||||||
\(538\) | −9.01267e9 | −2.49526 | ||||||||
\(539\) | 1.42172e9 | 0.391070 | ||||||||
\(540\) | −5.07187e8 | −0.138609 | ||||||||
\(541\) | −4.16187e9 | −1.13005 | −0.565026 | − | 0.825073i | \(-0.691134\pi\) | ||||
−0.565026 | + | 0.825073i | \(0.691134\pi\) | |||||||
\(542\) | 9.27610e9 | 2.50246 | ||||||||
\(543\) | 1.67184e9 | 0.448121 | ||||||||
\(544\) | −3.19303e9 | −0.850367 | ||||||||
\(545\) | −2.64810e9 | −0.700724 | ||||||||
\(546\) | 1.83518e8 | 0.0482508 | ||||||||
\(547\) | 6.75557e9 | 1.76484 | 0.882422 | − | 0.470459i | \(-0.155912\pi\) | ||||
0.882422 | + | 0.470459i | \(0.155912\pi\) | |||||||
\(548\) | 6.44764e9 | 1.67367 | ||||||||
\(549\) | −3.80645e8 | −0.0981786 | ||||||||
\(550\) | −2.72651e9 | −0.698776 | ||||||||
\(551\) | −2.89617e9 | −0.737552 | ||||||||
\(552\) | −2.38693e8 | −0.0604022 | ||||||||
\(553\) | −1.82561e9 | −0.459061 | ||||||||
\(554\) | 6.76931e9 | 1.69145 | ||||||||
\(555\) | −2.04669e9 | −0.508191 | ||||||||
\(556\) | −2.99328e9 | −0.738560 | ||||||||
\(557\) | 3.44498e9 | 0.844681 | 0.422341 | − | 0.906437i | \(-0.361209\pi\) | ||||
0.422341 | + | 0.906437i | \(0.361209\pi\) | |||||||
\(558\) | 2.71547e9 | 0.661645 | ||||||||
\(559\) | 5.61793e7 | 0.0136030 | ||||||||
\(560\) | −2.63460e9 | −0.633951 | ||||||||
\(561\) | −1.12270e9 | −0.268468 | ||||||||
\(562\) | 5.74688e9 | 1.36570 | ||||||||
\(563\) | −2.05492e9 | −0.485306 | −0.242653 | − | 0.970113i | \(-0.578018\pi\) | ||||
−0.242653 | + | 0.970113i | \(0.578018\pi\) | |||||||
\(564\) | −1.78661e9 | −0.419327 | ||||||||
\(565\) | −3.06225e9 | −0.714284 | ||||||||
\(566\) | 2.19717e9 | 0.509339 | ||||||||
\(567\) | 5.90468e8 | 0.136036 | ||||||||
\(568\) | 1.00996e9 | 0.231253 | ||||||||
\(569\) | 7.09854e8 | 0.161538 | 0.0807692 | − | 0.996733i | \(-0.474262\pi\) | ||||
0.0807692 | + | 0.996733i | \(0.474262\pi\) | |||||||
\(570\) | 1.59898e9 | 0.361644 | ||||||||
\(571\) | −3.56358e7 | −0.00801051 | −0.00400525 | − | 0.999992i | \(-0.501275\pi\) | ||||
−0.00400525 | + | 0.999992i | \(0.501275\pi\) | |||||||
\(572\) | −1.87847e8 | −0.0419679 | ||||||||
\(573\) | 4.94787e9 | 1.09869 | ||||||||
\(574\) | 5.27212e9 | 1.16357 | ||||||||
\(575\) | −1.31513e9 | −0.288490 | ||||||||
\(576\) | −1.94882e9 | −0.424905 | ||||||||
\(577\) | −1.37806e9 | −0.298644 | −0.149322 | − | 0.988789i | \(-0.547709\pi\) | ||||
−0.149322 | + | 0.988789i | \(0.547709\pi\) | |||||||
\(578\) | −4.41130e9 | −0.950209 | ||||||||
\(579\) | 6.79520e8 | 0.145488 | ||||||||
\(580\) | 3.65859e9 | 0.778602 | ||||||||
\(581\) | −7.07001e9 | −1.49556 | ||||||||
\(582\) | 1.30376e9 | 0.274136 | ||||||||
\(583\) | 4.89228e8 | 0.102252 | ||||||||
\(584\) | 1.07671e9 | 0.223693 | ||||||||
\(585\) | −4.70406e7 | −0.00971466 | ||||||||
\(586\) | −1.01517e10 | −2.08399 | ||||||||
\(587\) | 2.82850e9 | 0.577195 | 0.288597 | − | 0.957451i | \(-0.406811\pi\) | ||||
0.288597 | + | 0.957451i | \(0.406811\pi\) | |||||||
\(588\) | −1.63372e9 | −0.331403 | ||||||||
\(589\) | −4.57977e9 | −0.923506 | ||||||||
\(590\) | −5.96278e8 | −0.119527 | ||||||||
\(591\) | −1.11105e9 | −0.221400 | ||||||||
\(592\) | −5.86945e9 | −1.16271 | ||||||||
\(593\) | −4.23981e9 | −0.834940 | −0.417470 | − | 0.908691i | \(-0.637083\pi\) | ||||
−0.417470 | + | 0.908691i | \(0.637083\pi\) | |||||||
\(594\) | −1.12979e9 | −0.221180 | ||||||||
\(595\) | 2.33683e9 | 0.454797 | ||||||||
\(596\) | 9.05224e9 | 1.75143 | ||||||||
\(597\) | −3.26354e9 | −0.627739 | ||||||||
\(598\) | −1.69372e8 | −0.0323882 | ||||||||
\(599\) | −7.47951e9 | −1.42193 | −0.710967 | − | 0.703225i | \(-0.751742\pi\) | ||||
−0.710967 | + | 0.703225i | \(0.751742\pi\) | |||||||
\(600\) | 4.09519e8 | 0.0774006 | ||||||||
\(601\) | 2.42694e9 | 0.456034 | 0.228017 | − | 0.973657i | \(-0.426776\pi\) | ||||
0.228017 | + | 0.973657i | \(0.426776\pi\) | |||||||
\(602\) | −2.80844e9 | −0.524659 | ||||||||
\(603\) | 1.38013e9 | 0.256337 | ||||||||
\(604\) | 9.00288e8 | 0.166246 | ||||||||
\(605\) | −1.31550e9 | −0.241517 | ||||||||
\(606\) | 5.39241e9 | 0.984304 | ||||||||
\(607\) | −6.09411e9 | −1.10599 | −0.552993 | − | 0.833186i | \(-0.686514\pi\) | ||||
−0.552993 | + | 0.833186i | \(0.686514\pi\) | |||||||
\(608\) | 5.41921e9 | 0.977852 | ||||||||
\(609\) | −4.25933e9 | −0.764154 | ||||||||
\(610\) | −1.51595e9 | −0.270415 | ||||||||
\(611\) | −1.65705e8 | −0.0293894 | ||||||||
\(612\) | 1.29011e9 | 0.227507 | ||||||||
\(613\) | −6.89396e9 | −1.20881 | −0.604403 | − | 0.796678i | \(-0.706588\pi\) | ||||
−0.604403 | + | 0.796678i | \(0.706588\pi\) | |||||||
\(614\) | 2.67595e9 | 0.466540 | ||||||||
\(615\) | −1.35139e9 | −0.234270 | ||||||||
\(616\) | 1.22743e9 | 0.211574 | ||||||||
\(617\) | −1.05989e10 | −1.81661 | −0.908304 | − | 0.418311i | \(-0.862622\pi\) | ||||
−0.908304 | + | 0.418311i | \(0.862622\pi\) | |||||||
\(618\) | 2.01725e9 | 0.343795 | ||||||||
\(619\) | 7.11095e9 | 1.20507 | 0.602533 | − | 0.798094i | \(-0.294158\pi\) | ||||
0.602533 | + | 0.798094i | \(0.294158\pi\) | |||||||
\(620\) | 5.78540e9 | 0.974905 | ||||||||
\(621\) | −5.44951e8 | −0.0913140 | ||||||||
\(622\) | 9.17326e9 | 1.52847 | ||||||||
\(623\) | 6.03349e9 | 0.999678 | ||||||||
\(624\) | −1.34902e8 | −0.0222265 | ||||||||
\(625\) | −1.36187e8 | −0.0223130 | ||||||||
\(626\) | 5.72884e9 | 0.933375 | ||||||||
\(627\) | 1.90544e9 | 0.308716 | ||||||||
\(628\) | 5.29511e9 | 0.853133 | ||||||||
\(629\) | 5.20607e9 | 0.834128 | ||||||||
\(630\) | 2.35159e9 | 0.374688 | ||||||||
\(631\) | −3.97705e9 | −0.630170 | −0.315085 | − | 0.949063i | \(-0.602033\pi\) | ||||
−0.315085 | + | 0.949063i | \(0.602033\pi\) | |||||||
\(632\) | −5.24658e8 | −0.0826735 | ||||||||
\(633\) | 3.35409e9 | 0.525607 | ||||||||
\(634\) | −9.31916e9 | −1.45233 | ||||||||
\(635\) | −3.50439e9 | −0.543131 | ||||||||
\(636\) | −5.62179e8 | −0.0866512 | ||||||||
\(637\) | −1.51524e8 | −0.0232271 | ||||||||
\(638\) | 8.14973e9 | 1.24243 | ||||||||
\(639\) | 2.30582e9 | 0.349600 | ||||||||
\(640\) | −1.81031e9 | −0.272976 | ||||||||
\(641\) | 5.39534e8 | 0.0809125 | 0.0404563 | − | 0.999181i | \(-0.487119\pi\) | ||||
0.0404563 | + | 0.999181i | \(0.487119\pi\) | |||||||
\(642\) | 6.21185e8 | 0.0926506 | ||||||||
\(643\) | 6.57420e8 | 0.0975225 | 0.0487612 | − | 0.998810i | \(-0.484473\pi\) | ||||
0.0487612 | + | 0.998810i | \(0.484473\pi\) | |||||||
\(644\) | 4.52952e9 | 0.668269 | ||||||||
\(645\) | 7.19879e8 | 0.105633 | ||||||||
\(646\) | −4.06725e9 | −0.593590 | ||||||||
\(647\) | −2.49688e9 | −0.362437 | −0.181219 | − | 0.983443i | \(-0.558004\pi\) | ||||
−0.181219 | + | 0.983443i | \(0.558004\pi\) | |||||||
\(648\) | 1.69693e8 | 0.0244992 | ||||||||
\(649\) | −7.10561e8 | −0.102034 | ||||||||
\(650\) | 2.90586e8 | 0.0415029 | ||||||||
\(651\) | −6.73537e9 | −0.956815 | ||||||||
\(652\) | −5.71979e9 | −0.808191 | ||||||||
\(653\) | −9.29237e9 | −1.30596 | −0.652981 | − | 0.757374i | \(-0.726482\pi\) | ||||
−0.652981 | + | 0.757374i | \(0.726482\pi\) | |||||||
\(654\) | 6.77840e9 | 0.947556 | ||||||||
\(655\) | 3.11073e9 | 0.432532 | ||||||||
\(656\) | −3.87547e9 | −0.535995 | ||||||||
\(657\) | 2.45819e9 | 0.338172 | ||||||||
\(658\) | 8.28369e9 | 1.13353 | ||||||||
\(659\) | −6.58505e9 | −0.896315 | −0.448157 | − | 0.893955i | \(-0.647920\pi\) | ||||
−0.448157 | + | 0.893955i | \(0.647920\pi\) | |||||||
\(660\) | −2.40706e9 | −0.325898 | ||||||||
\(661\) | −3.64989e9 | −0.491558 | −0.245779 | − | 0.969326i | \(-0.579044\pi\) | ||||
−0.245779 | + | 0.969326i | \(0.579044\pi\) | |||||||
\(662\) | −1.24236e10 | −1.66434 | ||||||||
\(663\) | 1.19655e8 | 0.0159453 | ||||||||
\(664\) | −2.03183e9 | −0.269339 | ||||||||
\(665\) | −3.96607e9 | −0.522979 | ||||||||
\(666\) | 5.23896e9 | 0.687203 | ||||||||
\(667\) | 3.93100e9 | 0.512936 | ||||||||
\(668\) | −1.24907e10 | −1.62132 | ||||||||
\(669\) | 1.16729e8 | 0.0150726 | ||||||||
\(670\) | 5.49651e9 | 0.706033 | ||||||||
\(671\) | −1.80650e9 | −0.230839 | ||||||||
\(672\) | 7.96992e9 | 1.01312 | ||||||||
\(673\) | 7.02119e9 | 0.887887 | 0.443944 | − | 0.896055i | \(-0.353579\pi\) | ||||
0.443944 | + | 0.896055i | \(0.353579\pi\) | |||||||
\(674\) | 6.26326e9 | 0.787936 | ||||||||
\(675\) | 9.34958e8 | 0.117012 | ||||||||
\(676\) | −9.21947e9 | −1.14787 | ||||||||
\(677\) | 8.84175e9 | 1.09516 | 0.547580 | − | 0.836753i | \(-0.315549\pi\) | ||||
0.547580 | + | 0.836753i | \(0.315549\pi\) | |||||||
\(678\) | 7.83850e9 | 0.965893 | ||||||||
\(679\) | −3.23380e9 | −0.396433 | ||||||||
\(680\) | 6.71575e8 | 0.0819055 | ||||||||
\(681\) | 3.50805e9 | 0.425648 | ||||||||
\(682\) | 1.28873e10 | 1.55567 | ||||||||
\(683\) | 3.28325e9 | 0.394304 | 0.197152 | − | 0.980373i | \(-0.436831\pi\) | ||||
0.197152 | + | 0.980373i | \(0.436831\pi\) | |||||||
\(684\) | −2.18957e9 | −0.261615 | ||||||||
\(685\) | 7.66281e9 | 0.910901 | ||||||||
\(686\) | −7.60577e9 | −0.899516 | ||||||||
\(687\) | 1.63032e9 | 0.191833 | ||||||||
\(688\) | 2.06445e9 | 0.241682 | ||||||||
\(689\) | −5.21410e7 | −0.00607312 | ||||||||
\(690\) | −2.17032e9 | −0.251508 | ||||||||
\(691\) | 3.72206e9 | 0.429151 | 0.214576 | − | 0.976707i | \(-0.431163\pi\) | ||||
0.214576 | + | 0.976707i | \(0.431163\pi\) | |||||||
\(692\) | −3.00684e9 | −0.344936 | ||||||||
\(693\) | 2.80230e9 | 0.319851 | ||||||||
\(694\) | 3.73413e9 | 0.424063 | ||||||||
\(695\) | −3.55742e9 | −0.401965 | ||||||||
\(696\) | −1.22408e9 | −0.137619 | ||||||||
\(697\) | 3.43745e9 | 0.384523 | ||||||||
\(698\) | 3.32263e9 | 0.369818 | ||||||||
\(699\) | 6.43216e9 | 0.712339 | ||||||||
\(700\) | −7.77117e9 | −0.856334 | ||||||||
\(701\) | 2.70122e9 | 0.296174 | 0.148087 | − | 0.988974i | \(-0.452688\pi\) | ||||
0.148087 | + | 0.988974i | \(0.452688\pi\) | |||||||
\(702\) | 1.20411e8 | 0.0131367 | ||||||||
\(703\) | −8.83575e9 | −0.959179 | ||||||||
\(704\) | −9.24887e9 | −0.999044 | ||||||||
\(705\) | −2.12333e9 | −0.228221 | ||||||||
\(706\) | −1.60850e8 | −0.0172030 | ||||||||
\(707\) | −1.33752e10 | −1.42342 | ||||||||
\(708\) | 8.16515e8 | 0.0864665 | ||||||||
\(709\) | 4.56678e8 | 0.0481225 | 0.0240613 | − | 0.999710i | \(-0.492340\pi\) | ||||
0.0240613 | + | 0.999710i | \(0.492340\pi\) | |||||||
\(710\) | 9.18312e9 | 0.962911 | ||||||||
\(711\) | −1.19783e9 | −0.124983 | ||||||||
\(712\) | 1.73395e9 | 0.180035 | ||||||||
\(713\) | 6.21617e9 | 0.642258 | ||||||||
\(714\) | −5.98162e9 | −0.615000 | ||||||||
\(715\) | −2.23250e8 | −0.0228412 | ||||||||
\(716\) | −3.17281e9 | −0.323034 | ||||||||
\(717\) | 8.33045e8 | 0.0844017 | ||||||||
\(718\) | 2.64512e10 | 2.66692 | ||||||||
\(719\) | 4.28395e9 | 0.429827 | 0.214913 | − | 0.976633i | \(-0.431053\pi\) | ||||
0.214913 | + | 0.976633i | \(0.431053\pi\) | |||||||
\(720\) | −1.72862e9 | −0.172598 | ||||||||
\(721\) | −5.00352e9 | −0.497167 | ||||||||
\(722\) | −7.92689e9 | −0.783831 | ||||||||
\(723\) | −2.63576e8 | −0.0259371 | ||||||||
\(724\) | −9.11749e9 | −0.892874 | ||||||||
\(725\) | −6.74432e9 | −0.657287 | ||||||||
\(726\) | 3.36732e9 | 0.326592 | ||||||||
\(727\) | 9.46884e9 | 0.913958 | 0.456979 | − | 0.889477i | \(-0.348931\pi\) | ||||
0.456979 | + | 0.889477i | \(0.348931\pi\) | |||||||
\(728\) | −1.30817e8 | −0.0125662 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 9.78998e9 | 0.931433 | ||||||||
\(731\) | −1.83112e9 | −0.173383 | ||||||||
\(732\) | 2.07587e9 | 0.195619 | ||||||||
\(733\) | −7.31501e9 | −0.686043 | −0.343021 | − | 0.939328i | \(-0.611450\pi\) | ||||
−0.343021 | + | 0.939328i | \(0.611450\pi\) | |||||||
\(734\) | 7.23723e9 | 0.675517 | ||||||||
\(735\) | −1.94162e9 | −0.180368 | ||||||||
\(736\) | −7.35556e9 | −0.680054 | ||||||||
\(737\) | 6.54997e9 | 0.602703 | ||||||||
\(738\) | 3.45917e9 | 0.316792 | ||||||||
\(739\) | −9.28262e9 | −0.846087 | −0.423043 | − | 0.906109i | \(-0.639038\pi\) | ||||
−0.423043 | + | 0.906109i | \(0.639038\pi\) | |||||||
\(740\) | 1.11618e10 | 1.01256 | ||||||||
\(741\) | −2.03078e8 | −0.0183358 | ||||||||
\(742\) | 2.60656e9 | 0.234236 | ||||||||
\(743\) | −8.15117e9 | −0.729053 | −0.364526 | − | 0.931193i | \(-0.618769\pi\) | ||||
−0.364526 | + | 0.931193i | \(0.618769\pi\) | |||||||
\(744\) | −1.93566e9 | −0.172315 | ||||||||
\(745\) | 1.07583e10 | 0.953228 | ||||||||
\(746\) | 1.44515e10 | 1.27446 | ||||||||
\(747\) | −4.63881e9 | −0.407178 | ||||||||
\(748\) | 6.12270e9 | 0.534919 | ||||||||
\(749\) | −1.54077e9 | −0.133983 | ||||||||
\(750\) | 9.84772e9 | 0.852357 | ||||||||
\(751\) | −1.21007e10 | −1.04248 | −0.521242 | − | 0.853409i | \(-0.674531\pi\) | ||||
−0.521242 | + | 0.853409i | \(0.674531\pi\) | |||||||
\(752\) | −6.08923e9 | −0.522156 | ||||||||
\(753\) | −5.53182e9 | −0.472156 | ||||||||
\(754\) | −8.68582e8 | −0.0737923 | ||||||||
\(755\) | 1.06996e9 | 0.0904805 | ||||||||
\(756\) | −3.22016e9 | −0.271051 | ||||||||
\(757\) | −2.15810e10 | −1.80816 | −0.904078 | − | 0.427367i | \(-0.859441\pi\) | ||||
−0.904078 | + | 0.427367i | \(0.859441\pi\) | |||||||
\(758\) | 1.83112e10 | 1.52713 | ||||||||
\(759\) | −2.58628e9 | −0.214699 | ||||||||
\(760\) | −1.13980e9 | −0.0941847 | ||||||||
\(761\) | 2.06853e9 | 0.170144 | 0.0850719 | − | 0.996375i | \(-0.472888\pi\) | ||||
0.0850719 | + | 0.996375i | \(0.472888\pi\) | |||||||
\(762\) | 8.97025e9 | 0.734450 | ||||||||
\(763\) | −1.68129e10 | −1.37027 | ||||||||
\(764\) | −2.69835e10 | −2.18913 | ||||||||
\(765\) | 1.53325e9 | 0.123822 | ||||||||
\(766\) | 5.36452e9 | 0.431251 | ||||||||
\(767\) | 7.57302e7 | 0.00606018 | ||||||||
\(768\) | −4.60494e9 | −0.366825 | ||||||||
\(769\) | 1.90437e10 | 1.51011 | 0.755055 | − | 0.655662i | \(-0.227610\pi\) | ||||
0.755055 | + | 0.655662i | \(0.227610\pi\) | |||||||
\(770\) | 1.11604e10 | 0.880972 | ||||||||
\(771\) | 2.04830e9 | 0.160954 | ||||||||
\(772\) | −3.70581e9 | −0.289883 | ||||||||
\(773\) | 7.43503e9 | 0.578968 | 0.289484 | − | 0.957183i | \(-0.406516\pi\) | ||||
0.289484 | + | 0.957183i | \(0.406516\pi\) | |||||||
\(774\) | −1.84269e9 | −0.142843 | ||||||||
\(775\) | −1.06649e10 | −0.823003 | ||||||||
\(776\) | −9.29355e8 | −0.0713946 | ||||||||
\(777\) | −1.29946e10 | −0.993774 | ||||||||
\(778\) | 1.80945e10 | 1.37758 | ||||||||
\(779\) | −5.83405e9 | −0.442170 | ||||||||
\(780\) | 2.56539e8 | 0.0193563 | ||||||||
\(781\) | 1.09432e10 | 0.821986 | ||||||||
\(782\) | 5.52053e9 | 0.412816 | ||||||||
\(783\) | −2.79465e9 | −0.208047 | ||||||||
\(784\) | −5.56814e9 | −0.412671 | ||||||||
\(785\) | 6.29308e9 | 0.464322 | ||||||||
\(786\) | −7.96259e9 | −0.584892 | ||||||||
\(787\) | 9.17424e9 | 0.670901 | 0.335451 | − | 0.942058i | \(-0.391111\pi\) | ||||
0.335451 | + | 0.942058i | \(0.391111\pi\) | |||||||
\(788\) | 6.05920e9 | 0.441137 | ||||||||
\(789\) | 1.01570e10 | 0.736201 | ||||||||
\(790\) | −4.77046e9 | −0.344243 | ||||||||
\(791\) | −1.94424e10 | −1.39679 | ||||||||
\(792\) | 8.05345e8 | 0.0576028 | ||||||||
\(793\) | 1.92533e8 | 0.0137104 | ||||||||
\(794\) | −3.64586e10 | −2.58481 | ||||||||
\(795\) | −6.68132e8 | −0.0471604 | ||||||||
\(796\) | 1.77979e10 | 1.25076 | ||||||||
\(797\) | −2.11317e10 | −1.47853 | −0.739265 | − | 0.673415i | \(-0.764827\pi\) | ||||
−0.739265 | + | 0.673415i | \(0.764827\pi\) | |||||||
\(798\) | 1.01520e10 | 0.707200 | ||||||||
\(799\) | 5.40101e9 | 0.374594 | ||||||||
\(800\) | 1.26197e10 | 0.871436 | ||||||||
\(801\) | 3.95872e9 | 0.272170 | ||||||||
\(802\) | −4.23727e10 | −2.90052 | ||||||||
\(803\) | 1.16663e10 | 0.795115 | ||||||||
\(804\) | −7.52666e9 | −0.510747 | ||||||||
\(805\) | 5.38319e9 | 0.363709 | ||||||||
\(806\) | −1.37351e9 | −0.0923970 | ||||||||
\(807\) | 1.46675e10 | 0.982424 | ||||||||
\(808\) | −3.84386e9 | −0.256347 | ||||||||
\(809\) | −2.83173e9 | −0.188032 | −0.0940161 | − | 0.995571i | \(-0.529971\pi\) | ||||
−0.0940161 | + | 0.995571i | \(0.529971\pi\) | |||||||
\(810\) | 1.54294e9 | 0.102012 | ||||||||
\(811\) | 2.43178e10 | 1.60085 | 0.800427 | − | 0.599430i | \(-0.204606\pi\) | ||||
0.800427 | + | 0.599430i | \(0.204606\pi\) | |||||||
\(812\) | 2.32286e10 | 1.52257 | ||||||||
\(813\) | −1.50962e10 | −0.985261 | ||||||||
\(814\) | 2.48635e10 | 1.61576 | ||||||||
\(815\) | −6.79780e9 | −0.439862 | ||||||||
\(816\) | 4.39701e9 | 0.283297 | ||||||||
\(817\) | 3.10778e9 | 0.199376 | ||||||||
\(818\) | −4.78863e9 | −0.305897 | ||||||||
\(819\) | −2.98663e8 | −0.0189971 | ||||||||
\(820\) | 7.36988e9 | 0.466780 | ||||||||
\(821\) | −2.00983e10 | −1.26753 | −0.633765 | − | 0.773525i | \(-0.718491\pi\) | ||||
−0.633765 | + | 0.773525i | \(0.718491\pi\) | |||||||
\(822\) | −1.96146e10 | −1.23177 | ||||||||
\(823\) | 1.63406e10 | 1.02180 | 0.510902 | − | 0.859639i | \(-0.329312\pi\) | ||||
0.510902 | + | 0.859639i | \(0.329312\pi\) | |||||||
\(824\) | −1.43795e9 | −0.0895362 | ||||||||
\(825\) | 4.43721e9 | 0.275120 | ||||||||
\(826\) | −3.78580e9 | −0.233737 | ||||||||
\(827\) | −9.17251e9 | −0.563922 | −0.281961 | − | 0.959426i | \(-0.590985\pi\) | ||||
−0.281961 | + | 0.959426i | \(0.590985\pi\) | |||||||
\(828\) | 2.97193e9 | 0.181942 | ||||||||
\(829\) | −2.43239e10 | −1.48283 | −0.741417 | − | 0.671045i | \(-0.765846\pi\) | ||||
−0.741417 | + | 0.671045i | \(0.765846\pi\) | |||||||
\(830\) | −1.84745e10 | −1.12150 | ||||||||
\(831\) | −1.10166e10 | −0.665953 | ||||||||
\(832\) | 9.85727e8 | 0.0593369 | ||||||||
\(833\) | 4.93881e9 | 0.296050 | ||||||||
\(834\) | 9.10600e9 | 0.543559 | ||||||||
\(835\) | −1.48448e10 | −0.882415 | ||||||||
\(836\) | −1.03915e10 | −0.615113 | ||||||||
\(837\) | −4.41924e9 | −0.260501 | ||||||||
\(838\) | −8.80946e9 | −0.517125 | ||||||||
\(839\) | 1.35860e9 | 0.0794193 | 0.0397096 | − | 0.999211i | \(-0.487357\pi\) | ||||
0.0397096 | + | 0.999211i | \(0.487357\pi\) | |||||||
\(840\) | −1.67628e9 | −0.0975817 | ||||||||
\(841\) | 2.90934e9 | 0.168659 | ||||||||
\(842\) | −3.56854e10 | −2.06015 | ||||||||
\(843\) | −9.35266e9 | −0.537698 | ||||||||
\(844\) | −1.82917e10 | −1.04726 | ||||||||
\(845\) | −1.09571e10 | −0.624734 | ||||||||
\(846\) | 5.43513e9 | 0.308613 | ||||||||
\(847\) | −8.35219e9 | −0.472290 | ||||||||
\(848\) | −1.91605e9 | −0.107900 | ||||||||
\(849\) | −3.57575e9 | −0.200535 | ||||||||
\(850\) | −9.47142e9 | −0.528992 | ||||||||
\(851\) | 1.19929e10 | 0.667067 | ||||||||
\(852\) | −1.25749e10 | −0.696574 | ||||||||
\(853\) | −1.40851e10 | −0.777031 | −0.388516 | − | 0.921442i | \(-0.627012\pi\) | ||||
−0.388516 | + | 0.921442i | \(0.627012\pi\) | |||||||
\(854\) | −9.62486e9 | −0.528800 | ||||||||
\(855\) | −2.60223e9 | −0.142385 | ||||||||
\(856\) | −4.42797e8 | −0.0241294 | ||||||||
\(857\) | 2.25854e10 | 1.22573 | 0.612865 | − | 0.790188i | \(-0.290017\pi\) | ||||
0.612865 | + | 0.790188i | \(0.290017\pi\) | |||||||
\(858\) | 5.71457e8 | 0.0308871 | ||||||||
\(859\) | 3.28621e10 | 1.76897 | 0.884483 | − | 0.466572i | \(-0.154511\pi\) | ||||
0.884483 | + | 0.466572i | \(0.154511\pi\) | |||||||
\(860\) | −3.92591e9 | −0.210473 | ||||||||
\(861\) | −8.58002e9 | −0.458118 | ||||||||
\(862\) | −5.49107e9 | −0.291999 | ||||||||
\(863\) | −7.68268e9 | −0.406888 | −0.203444 | − | 0.979087i | \(-0.565213\pi\) | ||||
−0.203444 | + | 0.979087i | \(0.565213\pi\) | |||||||
\(864\) | 5.22926e9 | 0.275831 | ||||||||
\(865\) | −3.57353e9 | −0.187733 | ||||||||
\(866\) | 3.40273e10 | 1.78039 | ||||||||
\(867\) | 7.17909e9 | 0.374113 | ||||||||
\(868\) | 3.67318e10 | 1.90644 | ||||||||
\(869\) | −5.68477e9 | −0.293862 | ||||||||
\(870\) | −1.11300e10 | −0.573029 | ||||||||
\(871\) | −6.98083e8 | −0.0357967 | ||||||||
\(872\) | −4.83183e9 | −0.246776 | ||||||||
\(873\) | −2.12178e9 | −0.107932 | ||||||||
\(874\) | −9.36945e9 | −0.474705 | ||||||||
\(875\) | −2.44260e10 | −1.23261 | ||||||||
\(876\) | −1.34059e10 | −0.673803 | ||||||||
\(877\) | 3.95364e10 | 1.97924 | 0.989621 | − | 0.143702i | \(-0.0459008\pi\) | ||||
0.989621 | + | 0.143702i | \(0.0459008\pi\) | |||||||
\(878\) | 2.61538e10 | 1.30408 | ||||||||
\(879\) | 1.65211e10 | 0.820500 | ||||||||
\(880\) | −8.20387e9 | −0.405816 | ||||||||
\(881\) | 1.90800e10 | 0.940074 | 0.470037 | − | 0.882647i | \(-0.344241\pi\) | ||||
0.470037 | + | 0.882647i | \(0.344241\pi\) | |||||||
\(882\) | 4.97001e9 | 0.243903 | ||||||||
\(883\) | −4.60772e9 | −0.225228 | −0.112614 | − | 0.993639i | \(-0.535922\pi\) | ||||
−0.112614 | + | 0.993639i | \(0.535922\pi\) | |||||||
\(884\) | −6.52546e8 | −0.0317708 | ||||||||
\(885\) | 9.70403e8 | 0.0470599 | ||||||||
\(886\) | 5.43530e9 | 0.262546 | ||||||||
\(887\) | −1.44107e10 | −0.693349 | −0.346674 | − | 0.937986i | \(-0.612689\pi\) | ||||
−0.346674 | + | 0.937986i | \(0.612689\pi\) | |||||||
\(888\) | −3.73447e9 | −0.178972 | ||||||||
\(889\) | −2.22495e10 | −1.06210 | ||||||||
\(890\) | 1.57660e10 | 0.749644 | ||||||||
\(891\) | 1.83866e9 | 0.0870820 | ||||||||
\(892\) | −6.36591e8 | −0.0300320 | ||||||||
\(893\) | −9.16660e9 | −0.430753 | ||||||||
\(894\) | −2.75382e10 | −1.28901 | ||||||||
\(895\) | −3.77078e9 | −0.175813 | ||||||||
\(896\) | −1.14938e10 | −0.533807 | ||||||||
\(897\) | 2.75641e8 | 0.0127518 | ||||||||
\(898\) | −6.25042e8 | −0.0288033 | ||||||||
\(899\) | 3.18782e10 | 1.46330 | ||||||||
\(900\) | −5.09886e9 | −0.233144 | ||||||||
\(901\) | 1.69949e9 | 0.0774074 | ||||||||
\(902\) | 1.64169e10 | 0.744847 | ||||||||
\(903\) | 4.57055e9 | 0.206567 | ||||||||
\(904\) | −5.58750e9 | −0.251552 | ||||||||
\(905\) | −1.08358e10 | −0.485951 | ||||||||
\(906\) | −2.73881e9 | −0.122353 | ||||||||
\(907\) | 3.03408e10 | 1.35021 | 0.675105 | − | 0.737721i | \(-0.264098\pi\) | ||||
0.675105 | + | 0.737721i | \(0.264098\pi\) | |||||||
\(908\) | −1.91314e10 | −0.848098 | ||||||||
\(909\) | −8.77579e9 | −0.387537 | ||||||||
\(910\) | −1.18945e9 | −0.0523242 | ||||||||
\(911\) | −3.82951e9 | −0.167814 | −0.0839072 | − | 0.996474i | \(-0.526740\pi\) | ||||
−0.0839072 | + | 0.996474i | \(0.526740\pi\) | |||||||
\(912\) | −7.46262e9 | −0.325769 | ||||||||
\(913\) | −2.20153e10 | −0.957363 | ||||||||
\(914\) | 3.24754e9 | 0.140683 | ||||||||
\(915\) | 2.46711e9 | 0.106467 | ||||||||
\(916\) | −8.89104e9 | −0.382224 | ||||||||
\(917\) | 1.97502e10 | 0.845821 | ||||||||
\(918\) | −3.92469e9 | −0.167439 | ||||||||
\(919\) | 2.78817e10 | 1.18499 | 0.592495 | − | 0.805574i | \(-0.298143\pi\) | ||||
0.592495 | + | 0.805574i | \(0.298143\pi\) | |||||||
\(920\) | 1.54706e9 | 0.0655014 | ||||||||
\(921\) | −4.35493e9 | −0.183684 | ||||||||
\(922\) | −1.76216e10 | −0.740436 | ||||||||
\(923\) | −1.16630e9 | −0.0488208 | ||||||||
\(924\) | −1.52825e10 | −0.637299 | ||||||||
\(925\) | −2.05758e10 | −0.854794 | ||||||||
\(926\) | 1.86518e10 | 0.771936 | ||||||||
\(927\) | −3.28294e9 | −0.135358 | ||||||||
\(928\) | −3.77212e10 | −1.54942 | ||||||||
\(929\) | 1.44369e10 | 0.590770 | 0.295385 | − | 0.955378i | \(-0.404552\pi\) | ||||
0.295385 | + | 0.955378i | \(0.404552\pi\) | |||||||
\(930\) | −1.76000e10 | −0.717502 | ||||||||
\(931\) | −8.38216e9 | −0.340433 | ||||||||
\(932\) | −3.50782e10 | −1.41933 | ||||||||
\(933\) | −1.49289e10 | −0.601784 | ||||||||
\(934\) | −3.21308e10 | −1.29035 | ||||||||
\(935\) | 7.27664e9 | 0.291132 | ||||||||
\(936\) | −8.58321e7 | −0.00342125 | ||||||||
\(937\) | −3.25299e10 | −1.29180 | −0.645898 | − | 0.763424i | \(-0.723517\pi\) | ||||
−0.645898 | + | 0.763424i | \(0.723517\pi\) | |||||||
\(938\) | 3.48976e10 | 1.38066 | ||||||||
\(939\) | −9.32330e9 | −0.367485 | ||||||||
\(940\) | 1.15797e10 | 0.454727 | ||||||||
\(941\) | −1.74946e9 | −0.0684448 | −0.0342224 | − | 0.999414i | \(-0.510895\pi\) | ||||
−0.0342224 | + | 0.999414i | \(0.510895\pi\) | |||||||
\(942\) | −1.61085e10 | −0.627881 | ||||||||
\(943\) | 7.91863e9 | 0.307510 | ||||||||
\(944\) | 2.78290e9 | 0.107670 | ||||||||
\(945\) | −3.82705e9 | −0.147521 | ||||||||
\(946\) | −8.74520e9 | −0.335854 | ||||||||
\(947\) | −2.65135e10 | −1.01448 | −0.507239 | − | 0.861805i | \(-0.669334\pi\) | ||||
−0.507239 | + | 0.861805i | \(0.669334\pi\) | |||||||
\(948\) | 6.53244e9 | 0.249027 | ||||||||
\(949\) | −1.24337e9 | −0.0472248 | ||||||||
\(950\) | 1.60749e10 | 0.608297 | ||||||||
\(951\) | 1.51663e10 | 0.571805 | ||||||||
\(952\) | 4.26386e9 | 0.160167 | ||||||||
\(953\) | 3.31597e10 | 1.24104 | 0.620519 | − | 0.784191i | \(-0.286922\pi\) | ||||
0.620519 | + | 0.784191i | \(0.286922\pi\) | |||||||
\(954\) | 1.71023e9 | 0.0637727 | ||||||||
\(955\) | −3.20691e10 | −1.19145 | ||||||||
\(956\) | −4.54307e9 | −0.168169 | ||||||||
\(957\) | −1.32631e10 | −0.489164 | ||||||||
\(958\) | 4.43361e10 | 1.62921 | ||||||||
\(959\) | 4.86516e10 | 1.78128 | ||||||||
\(960\) | 1.26310e10 | 0.460776 | ||||||||
\(961\) | 2.28970e10 | 0.832236 | ||||||||
\(962\) | −2.64991e9 | −0.0959661 | ||||||||
\(963\) | −1.01094e9 | −0.0364780 | ||||||||
\(964\) | 1.43743e9 | 0.0516793 | ||||||||
\(965\) | −4.40424e9 | −0.157770 | ||||||||
\(966\) | −1.37795e10 | −0.491827 | ||||||||
\(967\) | 1.58334e9 | 0.0563095 | 0.0281547 | − | 0.999604i | \(-0.491037\pi\) | ||||
0.0281547 | + | 0.999604i | \(0.491037\pi\) | |||||||
\(968\) | −2.40032e9 | −0.0850559 | ||||||||
\(969\) | 6.61917e9 | 0.233706 | ||||||||
\(970\) | −8.45017e9 | −0.297279 | ||||||||
\(971\) | −7.55884e9 | −0.264965 | −0.132482 | − | 0.991185i | \(-0.542295\pi\) | ||||
−0.132482 | + | 0.991185i | \(0.542295\pi\) | |||||||
\(972\) | −2.11282e9 | −0.0737958 | ||||||||
\(973\) | −2.25863e10 | −0.786048 | ||||||||
\(974\) | 1.63620e10 | 0.567388 | ||||||||
\(975\) | −4.72909e8 | −0.0163404 | ||||||||
\(976\) | 7.07511e9 | 0.243590 | ||||||||
\(977\) | 1.24479e9 | 0.0427036 | 0.0213518 | − | 0.999772i | \(-0.493203\pi\) | ||||
0.0213518 | + | 0.999772i | \(0.493203\pi\) | |||||||
\(978\) | 1.74004e10 | 0.594805 | ||||||||
\(979\) | 1.87877e10 | 0.639931 | ||||||||
\(980\) | 1.05888e10 | 0.359381 | ||||||||
\(981\) | −1.10314e10 | −0.373068 | ||||||||
\(982\) | −5.53792e10 | −1.86619 | ||||||||
\(983\) | 1.03091e10 | 0.346166 | 0.173083 | − | 0.984907i | \(-0.444627\pi\) | ||||
0.173083 | + | 0.984907i | \(0.444627\pi\) | |||||||
\(984\) | −2.46579e9 | −0.0825037 | ||||||||
\(985\) | 7.20117e9 | 0.240091 | ||||||||
\(986\) | 2.83107e10 | 0.940550 | ||||||||
\(987\) | −1.34811e10 | −0.446289 | ||||||||
\(988\) | 1.10750e9 | 0.0365338 | ||||||||
\(989\) | −4.21823e9 | −0.138657 | ||||||||
\(990\) | 7.32261e9 | 0.239852 | ||||||||
\(991\) | −1.42062e10 | −0.463683 | −0.231842 | − | 0.972754i | \(-0.574475\pi\) | ||||
−0.231842 | + | 0.972754i | \(0.574475\pi\) | |||||||
\(992\) | −5.96494e10 | −1.94006 | ||||||||
\(993\) | 2.02185e10 | 0.655280 | ||||||||
\(994\) | 5.83041e10 | 1.88298 | ||||||||
\(995\) | 2.11523e10 | 0.680733 | ||||||||
\(996\) | 2.52981e10 | 0.811296 | ||||||||
\(997\) | 8.79297e9 | 0.280998 | 0.140499 | − | 0.990081i | \(-0.455129\pi\) | ||||
0.140499 | + | 0.990081i | \(0.455129\pi\) | |||||||
\(998\) | 7.16085e10 | 2.28038 | ||||||||
\(999\) | −8.52605e9 | −0.270563 |
(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 | 177.8.a.c.1.15 | ✓ | 17 | |
3.2 | odd | 2 | 531.8.a.c.1.3 | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.c.1.15 | ✓ | 17 | 1.1 | even | 1 | trivial | |
531.8.a.c.1.3 | 17 | 3.2 | odd | 2 |