Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,6,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, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
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: | \(28.3879361069\) |
Analytic rank: | \(1\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 5 x^{10} - 238 x^{9} + 1067 x^{8} + 20782 x^{7} - 79077 x^{6} - 813818 x^{5} + 2364885 x^{4} + \cdots - 14846072 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-9.21944\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −10.2194 | −1.80656 | −0.903280 | − | 0.429052i | \(-0.858848\pi\) | ||||
−0.903280 | + | 0.429052i | \(0.858848\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 72.4370 | 2.26366 | ||||||||
\(5\) | −99.2561 | −1.77555 | −0.887773 | − | 0.460281i | \(-0.847749\pi\) | ||||
−0.887773 | + | 0.460281i | \(0.847749\pi\) | |||||||
\(6\) | −91.9750 | −1.04302 | ||||||||
\(7\) | 109.985 | 0.848373 | 0.424187 | − | 0.905575i | \(-0.360560\pi\) | ||||
0.424187 | + | 0.905575i | \(0.360560\pi\) | |||||||
\(8\) | −413.244 | −2.28287 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 1014.34 | 3.20763 | ||||||||
\(11\) | −193.795 | −0.482905 | −0.241453 | − | 0.970413i | \(-0.577624\pi\) | ||||
−0.241453 | + | 0.970413i | \(0.577624\pi\) | |||||||
\(12\) | 651.933 | 1.30692 | ||||||||
\(13\) | 577.502 | 0.947752 | 0.473876 | − | 0.880591i | \(-0.342854\pi\) | ||||
0.473876 | + | 0.880591i | \(0.342854\pi\) | |||||||
\(14\) | −1123.98 | −1.53264 | ||||||||
\(15\) | −893.304 | −1.02511 | ||||||||
\(16\) | 1905.14 | 1.86049 | ||||||||
\(17\) | −332.271 | −0.278850 | −0.139425 | − | 0.990233i | \(-0.544525\pi\) | ||||
−0.139425 | + | 0.990233i | \(0.544525\pi\) | |||||||
\(18\) | −827.775 | −0.602187 | ||||||||
\(19\) | −2111.75 | −1.34202 | −0.671010 | − | 0.741448i | \(-0.734139\pi\) | ||||
−0.671010 | + | 0.741448i | \(0.734139\pi\) | |||||||
\(20\) | −7189.82 | −4.01923 | ||||||||
\(21\) | 989.862 | 0.489808 | ||||||||
\(22\) | 1980.48 | 0.872397 | ||||||||
\(23\) | 3186.50 | 1.25601 | 0.628007 | − | 0.778208i | \(-0.283871\pi\) | ||||
0.628007 | + | 0.778208i | \(0.283871\pi\) | |||||||
\(24\) | −3719.20 | −1.31802 | ||||||||
\(25\) | 6726.76 | 2.15256 | ||||||||
\(26\) | −5901.75 | −1.71217 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 7966.96 | 1.92043 | ||||||||
\(29\) | 6111.58 | 1.34946 | 0.674728 | − | 0.738067i | \(-0.264261\pi\) | ||||
0.674728 | + | 0.738067i | \(0.264261\pi\) | |||||||
\(30\) | 9129.08 | 1.85193 | ||||||||
\(31\) | −2024.27 | −0.378324 | −0.189162 | − | 0.981946i | \(-0.560577\pi\) | ||||
−0.189162 | + | 0.981946i | \(0.560577\pi\) | |||||||
\(32\) | −6245.66 | −1.07821 | ||||||||
\(33\) | −1744.16 | −0.278805 | ||||||||
\(34\) | 3395.63 | 0.503759 | ||||||||
\(35\) | −10916.6 | −1.50633 | ||||||||
\(36\) | 5867.40 | 0.754553 | ||||||||
\(37\) | 3581.82 | 0.430129 | 0.215065 | − | 0.976600i | \(-0.431004\pi\) | ||||
0.215065 | + | 0.976600i | \(0.431004\pi\) | |||||||
\(38\) | 21580.9 | 2.42444 | ||||||||
\(39\) | 5197.52 | 0.547185 | ||||||||
\(40\) | 41017.0 | 4.05335 | ||||||||
\(41\) | 4115.68 | 0.382369 | 0.191184 | − | 0.981554i | \(-0.438767\pi\) | ||||
0.191184 | + | 0.981554i | \(0.438767\pi\) | |||||||
\(42\) | −10115.8 | −0.884868 | ||||||||
\(43\) | −23103.3 | −1.90547 | −0.952737 | − | 0.303795i | \(-0.901746\pi\) | ||||
−0.952737 | + | 0.303795i | \(0.901746\pi\) | |||||||
\(44\) | −14038.0 | −1.09313 | ||||||||
\(45\) | −8039.74 | −0.591849 | ||||||||
\(46\) | −32564.3 | −2.26906 | ||||||||
\(47\) | −6685.33 | −0.441447 | −0.220723 | − | 0.975336i | \(-0.570842\pi\) | ||||
−0.220723 | + | 0.975336i | \(0.570842\pi\) | |||||||
\(48\) | 17146.3 | 1.07415 | ||||||||
\(49\) | −4710.38 | −0.280263 | ||||||||
\(50\) | −68743.8 | −3.88874 | ||||||||
\(51\) | −2990.44 | −0.160994 | ||||||||
\(52\) | 41832.5 | 2.14539 | ||||||||
\(53\) | 18280.2 | 0.893904 | 0.446952 | − | 0.894558i | \(-0.352509\pi\) | ||||
0.446952 | + | 0.894558i | \(0.352509\pi\) | |||||||
\(54\) | −7449.98 | −0.347673 | ||||||||
\(55\) | 19235.4 | 0.857420 | ||||||||
\(56\) | −45450.5 | −1.93673 | ||||||||
\(57\) | −19005.8 | −0.774815 | ||||||||
\(58\) | −62457.0 | −2.43787 | ||||||||
\(59\) | 3481.00 | 0.130189 | ||||||||
\(60\) | −64708.3 | −2.32050 | ||||||||
\(61\) | −14865.7 | −0.511516 | −0.255758 | − | 0.966741i | \(-0.582325\pi\) | ||||
−0.255758 | + | 0.966741i | \(0.582325\pi\) | |||||||
\(62\) | 20686.9 | 0.683465 | ||||||||
\(63\) | 8908.76 | 0.282791 | ||||||||
\(64\) | 2862.70 | 0.0873628 | ||||||||
\(65\) | −57320.5 | −1.68278 | ||||||||
\(66\) | 17824.3 | 0.503679 | ||||||||
\(67\) | −10836.8 | −0.294926 | −0.147463 | − | 0.989068i | \(-0.547111\pi\) | ||||
−0.147463 | + | 0.989068i | \(0.547111\pi\) | |||||||
\(68\) | −24068.8 | −0.631221 | ||||||||
\(69\) | 28678.5 | 0.725160 | ||||||||
\(70\) | 111562. | 2.72127 | ||||||||
\(71\) | −80021.9 | −1.88392 | −0.941961 | − | 0.335722i | \(-0.891020\pi\) | ||||
−0.941961 | + | 0.335722i | \(0.891020\pi\) | |||||||
\(72\) | −33472.8 | −0.760958 | ||||||||
\(73\) | −22189.8 | −0.487357 | −0.243678 | − | 0.969856i | \(-0.578354\pi\) | ||||
−0.243678 | + | 0.969856i | \(0.578354\pi\) | |||||||
\(74\) | −36604.2 | −0.777054 | ||||||||
\(75\) | 60540.9 | 1.24278 | ||||||||
\(76\) | −152969. | −3.03787 | ||||||||
\(77\) | −21314.5 | −0.409684 | ||||||||
\(78\) | −53115.7 | −0.988522 | ||||||||
\(79\) | −57520.3 | −1.03694 | −0.518470 | − | 0.855096i | \(-0.673498\pi\) | ||||
−0.518470 | + | 0.855096i | \(0.673498\pi\) | |||||||
\(80\) | −189097. | −3.30338 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −42060.0 | −0.690772 | ||||||||
\(83\) | −98908.2 | −1.57593 | −0.787966 | − | 0.615719i | \(-0.788866\pi\) | ||||
−0.787966 | + | 0.615719i | \(0.788866\pi\) | |||||||
\(84\) | 71702.7 | 1.10876 | ||||||||
\(85\) | 32979.9 | 0.495111 | ||||||||
\(86\) | 236103. | 3.44235 | ||||||||
\(87\) | 55004.2 | 0.779109 | ||||||||
\(88\) | 80084.8 | 1.10241 | ||||||||
\(89\) | −91785.6 | −1.22829 | −0.614143 | − | 0.789195i | \(-0.710498\pi\) | ||||
−0.614143 | + | 0.789195i | \(0.710498\pi\) | |||||||
\(90\) | 82161.7 | 1.06921 | ||||||||
\(91\) | 63516.3 | 0.804048 | ||||||||
\(92\) | 230821. | 2.84319 | ||||||||
\(93\) | −18218.4 | −0.218426 | ||||||||
\(94\) | 68320.4 | 0.797500 | ||||||||
\(95\) | 209604. | 2.38282 | ||||||||
\(96\) | −56211.0 | −0.622505 | ||||||||
\(97\) | 49151.1 | 0.530400 | 0.265200 | − | 0.964193i | \(-0.414562\pi\) | ||||
0.265200 | + | 0.964193i | \(0.414562\pi\) | |||||||
\(98\) | 48137.5 | 0.506312 | ||||||||
\(99\) | −15697.4 | −0.160968 | ||||||||
\(100\) | 487267. | 4.87267 | ||||||||
\(101\) | −24936.4 | −0.243237 | −0.121619 | − | 0.992577i | \(-0.538809\pi\) | ||||
−0.121619 | + | 0.992577i | \(0.538809\pi\) | |||||||
\(102\) | 30560.7 | 0.290845 | ||||||||
\(103\) | −134019. | −1.24472 | −0.622361 | − | 0.782731i | \(-0.713826\pi\) | ||||
−0.622361 | + | 0.782731i | \(0.713826\pi\) | |||||||
\(104\) | −238649. | −2.16360 | ||||||||
\(105\) | −98249.8 | −0.869678 | ||||||||
\(106\) | −186813. | −1.61489 | ||||||||
\(107\) | 106814. | 0.901924 | 0.450962 | − | 0.892543i | \(-0.351081\pi\) | ||||
0.450962 | + | 0.892543i | \(0.351081\pi\) | |||||||
\(108\) | 52806.6 | 0.435641 | ||||||||
\(109\) | 186806. | 1.50600 | 0.752998 | − | 0.658023i | \(-0.228607\pi\) | ||||
0.752998 | + | 0.658023i | \(0.228607\pi\) | |||||||
\(110\) | −196575. | −1.54898 | ||||||||
\(111\) | 32236.4 | 0.248335 | ||||||||
\(112\) | 209536. | 1.57839 | ||||||||
\(113\) | −129207. | −0.951900 | −0.475950 | − | 0.879472i | \(-0.657896\pi\) | ||||
−0.475950 | + | 0.879472i | \(0.657896\pi\) | |||||||
\(114\) | 194228. | 1.39975 | ||||||||
\(115\) | −316279. | −2.23011 | ||||||||
\(116\) | 442705. | 3.05471 | ||||||||
\(117\) | 46777.6 | 0.315917 | ||||||||
\(118\) | −35573.9 | −0.235194 | ||||||||
\(119\) | −36544.7 | −0.236569 | ||||||||
\(120\) | 369153. | 2.34020 | ||||||||
\(121\) | −123494. | −0.766803 | ||||||||
\(122\) | 151919. | 0.924085 | ||||||||
\(123\) | 37041.2 | 0.220761 | ||||||||
\(124\) | −146632. | −0.856396 | ||||||||
\(125\) | −357497. | −2.04643 | ||||||||
\(126\) | −91042.5 | −0.510879 | ||||||||
\(127\) | −221537. | −1.21881 | −0.609406 | − | 0.792858i | \(-0.708592\pi\) | ||||
−0.609406 | + | 0.792858i | \(0.708592\pi\) | |||||||
\(128\) | 170606. | 0.920384 | ||||||||
\(129\) | −207930. | −1.10013 | ||||||||
\(130\) | 585784. | 3.04004 | ||||||||
\(131\) | 103256. | 0.525700 | 0.262850 | − | 0.964837i | \(-0.415338\pi\) | ||||
0.262850 | + | 0.964837i | \(0.415338\pi\) | |||||||
\(132\) | −126342. | −0.631120 | ||||||||
\(133\) | −232260. | −1.13853 | ||||||||
\(134\) | 110746. | 0.532801 | ||||||||
\(135\) | −72357.7 | −0.341704 | ||||||||
\(136\) | 137309. | 0.636579 | ||||||||
\(137\) | −395523. | −1.80041 | −0.900204 | − | 0.435469i | \(-0.856582\pi\) | ||||
−0.900204 | + | 0.435469i | \(0.856582\pi\) | |||||||
\(138\) | −293078. | −1.31004 | ||||||||
\(139\) | 239860. | 1.05298 | 0.526492 | − | 0.850180i | \(-0.323507\pi\) | ||||
0.526492 | + | 0.850180i | \(0.323507\pi\) | |||||||
\(140\) | −790769. | −3.40981 | ||||||||
\(141\) | −60168.0 | −0.254869 | ||||||||
\(142\) | 817779. | 3.40342 | ||||||||
\(143\) | −111917. | −0.457674 | ||||||||
\(144\) | 154316. | 0.620163 | ||||||||
\(145\) | −606611. | −2.39602 | ||||||||
\(146\) | 226768. | 0.880439 | ||||||||
\(147\) | −42393.4 | −0.161810 | ||||||||
\(148\) | 259456. | 0.973666 | ||||||||
\(149\) | −265499. | −0.979708 | −0.489854 | − | 0.871804i | \(-0.662950\pi\) | ||||
−0.489854 | + | 0.871804i | \(0.662950\pi\) | |||||||
\(150\) | −618694. | −2.24516 | ||||||||
\(151\) | 481345. | 1.71796 | 0.858982 | − | 0.512005i | \(-0.171097\pi\) | ||||
0.858982 | + | 0.512005i | \(0.171097\pi\) | |||||||
\(152\) | 872669. | 3.06366 | ||||||||
\(153\) | −26914.0 | −0.0929500 | ||||||||
\(154\) | 217823. | 0.740118 | ||||||||
\(155\) | 200921. | 0.671732 | ||||||||
\(156\) | 376493. | 1.23864 | ||||||||
\(157\) | 108460. | 0.351173 | 0.175587 | − | 0.984464i | \(-0.443818\pi\) | ||||
0.175587 | + | 0.984464i | \(0.443818\pi\) | |||||||
\(158\) | 587826. | 1.87329 | ||||||||
\(159\) | 164522. | 0.516096 | ||||||||
\(160\) | 619920. | 1.91441 | ||||||||
\(161\) | 350466. | 1.06557 | ||||||||
\(162\) | −67049.8 | −0.200729 | ||||||||
\(163\) | 167294. | 0.493187 | 0.246594 | − | 0.969119i | \(-0.420689\pi\) | ||||
0.246594 | + | 0.969119i | \(0.420689\pi\) | |||||||
\(164\) | 298128. | 0.865552 | ||||||||
\(165\) | 173118. | 0.495032 | ||||||||
\(166\) | 1.01079e6 | 2.84701 | ||||||||
\(167\) | −700984. | −1.94499 | −0.972494 | − | 0.232930i | \(-0.925169\pi\) | ||||
−0.972494 | + | 0.232930i | \(0.925169\pi\) | |||||||
\(168\) | −409055. | −1.11817 | ||||||||
\(169\) | −37784.8 | −0.101765 | ||||||||
\(170\) | −337037. | −0.894448 | ||||||||
\(171\) | −171052. | −0.447340 | ||||||||
\(172\) | −1.67354e6 | −4.31334 | ||||||||
\(173\) | −375116. | −0.952906 | −0.476453 | − | 0.879200i | \(-0.658078\pi\) | ||||
−0.476453 | + | 0.879200i | \(0.658078\pi\) | |||||||
\(174\) | −562113. | −1.40751 | ||||||||
\(175\) | 739841. | 1.82618 | ||||||||
\(176\) | −369207. | −0.898439 | ||||||||
\(177\) | 31329.0 | 0.0751646 | ||||||||
\(178\) | 937998. | 2.21897 | ||||||||
\(179\) | 252271. | 0.588485 | 0.294242 | − | 0.955731i | \(-0.404933\pi\) | ||||
0.294242 | + | 0.955731i | \(0.404933\pi\) | |||||||
\(180\) | −582375. | −1.33974 | ||||||||
\(181\) | 737343. | 1.67291 | 0.836456 | − | 0.548033i | \(-0.184623\pi\) | ||||
0.836456 | + | 0.548033i | \(0.184623\pi\) | |||||||
\(182\) | −649101. | −1.45256 | ||||||||
\(183\) | −133791. | −0.295324 | ||||||||
\(184\) | −1.31680e6 | −2.86732 | ||||||||
\(185\) | −355517. | −0.763715 | ||||||||
\(186\) | 186182. | 0.394599 | ||||||||
\(187\) | 64392.7 | 0.134658 | ||||||||
\(188\) | −484266. | −0.999285 | ||||||||
\(189\) | 80178.8 | 0.163269 | ||||||||
\(190\) | −2.14204e6 | −4.30470 | ||||||||
\(191\) | 984468. | 1.95262 | 0.976311 | − | 0.216370i | \(-0.0694217\pi\) | ||||
0.976311 | + | 0.216370i | \(0.0694217\pi\) | |||||||
\(192\) | 25764.3 | 0.0504389 | ||||||||
\(193\) | 3026.14 | 0.00584785 | 0.00292392 | − | 0.999996i | \(-0.499069\pi\) | ||||
0.00292392 | + | 0.999996i | \(0.499069\pi\) | |||||||
\(194\) | −502297. | −0.958200 | ||||||||
\(195\) | −515885. | −0.971552 | ||||||||
\(196\) | −341206. | −0.634419 | ||||||||
\(197\) | −416621. | −0.764848 | −0.382424 | − | 0.923987i | \(-0.624911\pi\) | ||||
−0.382424 | + | 0.923987i | \(0.624911\pi\) | |||||||
\(198\) | 160419. | 0.290799 | ||||||||
\(199\) | −1.00316e6 | −1.79572 | −0.897861 | − | 0.440280i | \(-0.854879\pi\) | ||||
−0.897861 | + | 0.440280i | \(0.854879\pi\) | |||||||
\(200\) | −2.77980e6 | −4.91403 | ||||||||
\(201\) | −97530.8 | −0.170275 | ||||||||
\(202\) | 254836. | 0.439423 | ||||||||
\(203\) | 672180. | 1.14484 | ||||||||
\(204\) | −216619. | −0.364436 | ||||||||
\(205\) | −408506. | −0.678913 | ||||||||
\(206\) | 1.36960e6 | 2.24866 | ||||||||
\(207\) | 258107. | 0.418671 | ||||||||
\(208\) | 1.10022e6 | 1.76328 | ||||||||
\(209\) | 409248. | 0.648068 | ||||||||
\(210\) | 1.00406e6 | 1.57112 | ||||||||
\(211\) | 241371. | 0.373231 | 0.186616 | − | 0.982433i | \(-0.440248\pi\) | ||||
0.186616 | + | 0.982433i | \(0.440248\pi\) | |||||||
\(212\) | 1.32416e6 | 2.02349 | ||||||||
\(213\) | −720197. | −1.08768 | ||||||||
\(214\) | −1.09158e6 | −1.62938 | ||||||||
\(215\) | 2.29314e6 | 3.38326 | ||||||||
\(216\) | −301255. | −0.439339 | ||||||||
\(217\) | −222639. | −0.320960 | ||||||||
\(218\) | −1.90905e6 | −2.72067 | ||||||||
\(219\) | −199708. | −0.281375 | ||||||||
\(220\) | 1.39335e6 | 1.94091 | ||||||||
\(221\) | −191887. | −0.264281 | ||||||||
\(222\) | −329438. | −0.448633 | ||||||||
\(223\) | 227725. | 0.306654 | 0.153327 | − | 0.988176i | \(-0.451001\pi\) | ||||
0.153327 | + | 0.988176i | \(0.451001\pi\) | |||||||
\(224\) | −686927. | −0.914725 | ||||||||
\(225\) | 544868. | 0.717522 | ||||||||
\(226\) | 1.32043e6 | 1.71966 | ||||||||
\(227\) | 1.00306e6 | 1.29200 | 0.645998 | − | 0.763339i | \(-0.276442\pi\) | ||||
0.645998 | + | 0.763339i | \(0.276442\pi\) | |||||||
\(228\) | −1.37672e6 | −1.75392 | ||||||||
\(229\) | −682918. | −0.860558 | −0.430279 | − | 0.902696i | \(-0.641585\pi\) | ||||
−0.430279 | + | 0.902696i | \(0.641585\pi\) | |||||||
\(230\) | 3.23220e6 | 4.02883 | ||||||||
\(231\) | −191831. | −0.236531 | ||||||||
\(232\) | −2.52558e6 | −3.08064 | ||||||||
\(233\) | 1.32745e6 | 1.60187 | 0.800935 | − | 0.598752i | \(-0.204336\pi\) | ||||
0.800935 | + | 0.598752i | \(0.204336\pi\) | |||||||
\(234\) | −478041. | −0.570724 | ||||||||
\(235\) | 663560. | 0.783809 | ||||||||
\(236\) | 252153. | 0.294703 | ||||||||
\(237\) | −517683. | −0.598677 | ||||||||
\(238\) | 373467. | 0.427376 | ||||||||
\(239\) | −1.27290e6 | −1.44145 | −0.720727 | − | 0.693220i | \(-0.756192\pi\) | ||||
−0.720727 | + | 0.693220i | \(0.756192\pi\) | |||||||
\(240\) | −1.70187e6 | −1.90721 | ||||||||
\(241\) | 641199. | 0.711132 | 0.355566 | − | 0.934651i | \(-0.384288\pi\) | ||||
0.355566 | + | 0.934651i | \(0.384288\pi\) | |||||||
\(242\) | 1.26204e6 | 1.38527 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | −1.07682e6 | −1.15790 | ||||||||
\(245\) | 467534. | 0.497620 | ||||||||
\(246\) | −378540. | −0.398817 | ||||||||
\(247\) | −1.21954e6 | −1.27190 | ||||||||
\(248\) | 836518. | 0.863666 | ||||||||
\(249\) | −890174. | −0.909864 | ||||||||
\(250\) | 3.65342e6 | 3.69700 | ||||||||
\(251\) | −1.79177e6 | −1.79514 | −0.897571 | − | 0.440870i | \(-0.854670\pi\) | ||||
−0.897571 | + | 0.440870i | \(0.854670\pi\) | |||||||
\(252\) | 645324. | 0.640142 | ||||||||
\(253\) | −617529. | −0.606536 | ||||||||
\(254\) | 2.26398e6 | 2.20186 | ||||||||
\(255\) | 296820. | 0.285853 | ||||||||
\(256\) | −1.83510e6 | −1.75009 | ||||||||
\(257\) | −511016. | −0.482616 | −0.241308 | − | 0.970449i | \(-0.577576\pi\) | ||||
−0.241308 | + | 0.970449i | \(0.577576\pi\) | |||||||
\(258\) | 2.12493e6 | 1.98744 | ||||||||
\(259\) | 393945. | 0.364910 | ||||||||
\(260\) | −4.15213e6 | −3.80923 | ||||||||
\(261\) | 495038. | 0.449819 | ||||||||
\(262\) | −1.05522e6 | −0.949708 | ||||||||
\(263\) | 453523. | 0.404306 | 0.202153 | − | 0.979354i | \(-0.435206\pi\) | ||||
0.202153 | + | 0.979354i | \(0.435206\pi\) | |||||||
\(264\) | 720763. | 0.636477 | ||||||||
\(265\) | −1.81442e6 | −1.58717 | ||||||||
\(266\) | 2.37357e6 | 2.05683 | ||||||||
\(267\) | −826070. | −0.709151 | ||||||||
\(268\) | −784983. | −0.667611 | ||||||||
\(269\) | 1.74732e6 | 1.47229 | 0.736144 | − | 0.676825i | \(-0.236645\pi\) | ||||
0.736144 | + | 0.676825i | \(0.236645\pi\) | |||||||
\(270\) | 739455. | 0.617309 | ||||||||
\(271\) | −223578. | −0.184929 | −0.0924647 | − | 0.995716i | \(-0.529475\pi\) | ||||
−0.0924647 | + | 0.995716i | \(0.529475\pi\) | |||||||
\(272\) | −633024. | −0.518797 | ||||||||
\(273\) | 571647. | 0.464217 | ||||||||
\(274\) | 4.04203e6 | 3.25254 | ||||||||
\(275\) | −1.30362e6 | −1.03948 | ||||||||
\(276\) | 2.07739e6 | 1.64151 | ||||||||
\(277\) | 588786. | 0.461061 | 0.230530 | − | 0.973065i | \(-0.425954\pi\) | ||||
0.230530 | + | 0.973065i | \(0.425954\pi\) | |||||||
\(278\) | −2.45124e6 | −1.90228 | ||||||||
\(279\) | −163966. | −0.126108 | ||||||||
\(280\) | 4.51124e6 | 3.43875 | ||||||||
\(281\) | 815660. | 0.616231 | 0.308115 | − | 0.951349i | \(-0.400302\pi\) | ||||
0.308115 | + | 0.951349i | \(0.400302\pi\) | |||||||
\(282\) | 614884. | 0.460437 | ||||||||
\(283\) | −1.08887e6 | −0.808186 | −0.404093 | − | 0.914718i | \(-0.632413\pi\) | ||||
−0.404093 | + | 0.914718i | \(0.632413\pi\) | |||||||
\(284\) | −5.79655e6 | −4.26455 | ||||||||
\(285\) | 1.88644e6 | 1.37572 | ||||||||
\(286\) | 1.14373e6 | 0.826816 | ||||||||
\(287\) | 452662. | 0.324391 | ||||||||
\(288\) | −505899. | −0.359403 | ||||||||
\(289\) | −1.30945e6 | −0.922243 | ||||||||
\(290\) | 6.19923e6 | 4.32855 | ||||||||
\(291\) | 442360. | 0.306227 | ||||||||
\(292\) | −1.60737e6 | −1.10321 | ||||||||
\(293\) | −1.13966e6 | −0.775541 | −0.387770 | − | 0.921756i | \(-0.626755\pi\) | ||||
−0.387770 | + | 0.921756i | \(0.626755\pi\) | |||||||
\(294\) | 433237. | 0.292319 | ||||||||
\(295\) | −345510. | −0.231156 | ||||||||
\(296\) | −1.48017e6 | −0.981931 | ||||||||
\(297\) | −141277. | −0.0929351 | ||||||||
\(298\) | 2.71325e6 | 1.76990 | ||||||||
\(299\) | 1.84021e6 | 1.19039 | ||||||||
\(300\) | 4.38540e6 | 2.81324 | ||||||||
\(301\) | −2.54101e6 | −1.61655 | ||||||||
\(302\) | −4.91908e6 | −3.10361 | ||||||||
\(303\) | −224428. | −0.140433 | ||||||||
\(304\) | −4.02318e6 | −2.49681 | ||||||||
\(305\) | 1.47551e6 | 0.908221 | ||||||||
\(306\) | 275046. | 0.167920 | ||||||||
\(307\) | −1.27600e6 | −0.772688 | −0.386344 | − | 0.922355i | \(-0.626262\pi\) | ||||
−0.386344 | + | 0.922355i | \(0.626262\pi\) | |||||||
\(308\) | −1.54396e6 | −0.927384 | ||||||||
\(309\) | −1.20617e6 | −0.718640 | ||||||||
\(310\) | −2.05330e6 | −1.21352 | ||||||||
\(311\) | −1.30216e6 | −0.763422 | −0.381711 | − | 0.924282i | \(-0.624665\pi\) | ||||
−0.381711 | + | 0.924282i | \(0.624665\pi\) | |||||||
\(312\) | −2.14784e6 | −1.24915 | ||||||||
\(313\) | −2.37612e6 | −1.37090 | −0.685452 | − | 0.728118i | \(-0.740395\pi\) | ||||
−0.685452 | + | 0.728118i | \(0.740395\pi\) | |||||||
\(314\) | −1.10840e6 | −0.634416 | ||||||||
\(315\) | −884248. | −0.502109 | ||||||||
\(316\) | −4.16660e6 | −2.34728 | ||||||||
\(317\) | 2.63675e6 | 1.47374 | 0.736869 | − | 0.676035i | \(-0.236303\pi\) | ||||
0.736869 | + | 0.676035i | \(0.236303\pi\) | |||||||
\(318\) | −1.68132e6 | −0.932358 | ||||||||
\(319\) | −1.18440e6 | −0.651659 | ||||||||
\(320\) | −284141. | −0.155117 | ||||||||
\(321\) | 961328. | 0.520726 | ||||||||
\(322\) | −3.58157e6 | −1.92501 | ||||||||
\(323\) | 701675. | 0.374222 | ||||||||
\(324\) | 475259. | 0.251518 | ||||||||
\(325\) | 3.88472e6 | 2.04010 | ||||||||
\(326\) | −1.70965e6 | −0.890972 | ||||||||
\(327\) | 1.68125e6 | 0.869487 | ||||||||
\(328\) | −1.70078e6 | −0.872899 | ||||||||
\(329\) | −735284. | −0.374512 | ||||||||
\(330\) | −1.76917e6 | −0.894305 | ||||||||
\(331\) | 345030. | 0.173096 | 0.0865480 | − | 0.996248i | \(-0.472416\pi\) | ||||
0.0865480 | + | 0.996248i | \(0.472416\pi\) | |||||||
\(332\) | −7.16462e6 | −3.56737 | ||||||||
\(333\) | 290127. | 0.143376 | ||||||||
\(334\) | 7.16366e6 | 3.51374 | ||||||||
\(335\) | 1.07561e6 | 0.523654 | ||||||||
\(336\) | 1.88583e6 | 0.911283 | ||||||||
\(337\) | 1.21026e6 | 0.580503 | 0.290251 | − | 0.956950i | \(-0.406261\pi\) | ||||
0.290251 | + | 0.956950i | \(0.406261\pi\) | |||||||
\(338\) | 386140. | 0.183845 | ||||||||
\(339\) | −1.16287e6 | −0.549580 | ||||||||
\(340\) | 2.38897e6 | 1.12076 | ||||||||
\(341\) | 392294. | 0.182695 | ||||||||
\(342\) | 1.74806e6 | 0.808146 | ||||||||
\(343\) | −2.36658e6 | −1.08614 | ||||||||
\(344\) | 9.54731e6 | 4.34996 | ||||||||
\(345\) | −2.84652e6 | −1.28756 | ||||||||
\(346\) | 3.83348e6 | 1.72148 | ||||||||
\(347\) | −3.75698e6 | −1.67500 | −0.837500 | − | 0.546437i | \(-0.815984\pi\) | ||||
−0.837500 | + | 0.546437i | \(0.815984\pi\) | |||||||
\(348\) | 3.98434e6 | 1.76364 | ||||||||
\(349\) | 402933. | 0.177080 | 0.0885399 | − | 0.996073i | \(-0.471780\pi\) | ||||
0.0885399 | + | 0.996073i | \(0.471780\pi\) | |||||||
\(350\) | −7.56076e6 | −3.29910 | ||||||||
\(351\) | 420999. | 0.182395 | ||||||||
\(352\) | 1.21038e6 | 0.520673 | ||||||||
\(353\) | −2.57154e6 | −1.09839 | −0.549196 | − | 0.835694i | \(-0.685066\pi\) | ||||
−0.549196 | + | 0.835694i | \(0.685066\pi\) | |||||||
\(354\) | −320165. | −0.135789 | ||||||||
\(355\) | 7.94266e6 | 3.34499 | ||||||||
\(356\) | −6.64868e6 | −2.78042 | ||||||||
\(357\) | −328903. | −0.136583 | ||||||||
\(358\) | −2.57807e6 | −1.06313 | ||||||||
\(359\) | 181007. | 0.0741241 | 0.0370620 | − | 0.999313i | \(-0.488200\pi\) | ||||
0.0370620 | + | 0.999313i | \(0.488200\pi\) | |||||||
\(360\) | 3.32238e6 | 1.35112 | ||||||||
\(361\) | 1.98340e6 | 0.801017 | ||||||||
\(362\) | −7.53524e6 | −3.02222 | ||||||||
\(363\) | −1.11145e6 | −0.442714 | ||||||||
\(364\) | 4.60093e6 | 1.82009 | ||||||||
\(365\) | 2.20248e6 | 0.865324 | ||||||||
\(366\) | 1.36727e6 | 0.533521 | ||||||||
\(367\) | −395859. | −0.153418 | −0.0767089 | − | 0.997054i | \(-0.524441\pi\) | ||||
−0.0767089 | + | 0.997054i | \(0.524441\pi\) | |||||||
\(368\) | 6.07073e6 | 2.33680 | ||||||||
\(369\) | 333370. | 0.127456 | ||||||||
\(370\) | 3.63319e6 | 1.37970 | ||||||||
\(371\) | 2.01054e6 | 0.758365 | ||||||||
\(372\) | −1.31969e6 | −0.494441 | ||||||||
\(373\) | −1.17285e6 | −0.436486 | −0.218243 | − | 0.975894i | \(-0.570033\pi\) | ||||
−0.218243 | + | 0.975894i | \(0.570033\pi\) | |||||||
\(374\) | −658057. | −0.243268 | ||||||||
\(375\) | −3.21747e6 | −1.18151 | ||||||||
\(376\) | 2.76267e6 | 1.00777 | ||||||||
\(377\) | 3.52945e6 | 1.27895 | ||||||||
\(378\) | −819383. | −0.294956 | ||||||||
\(379\) | −1.54397e6 | −0.552130 | −0.276065 | − | 0.961139i | \(-0.589030\pi\) | ||||
−0.276065 | + | 0.961139i | \(0.589030\pi\) | |||||||
\(380\) | 1.51831e7 | 5.39388 | ||||||||
\(381\) | −1.99383e6 | −0.703681 | ||||||||
\(382\) | −1.00607e7 | −3.52753 | ||||||||
\(383\) | −5.57141e6 | −1.94074 | −0.970371 | − | 0.241619i | \(-0.922322\pi\) | ||||
−0.970371 | + | 0.241619i | \(0.922322\pi\) | |||||||
\(384\) | 1.53545e6 | 0.531384 | ||||||||
\(385\) | 2.11560e6 | 0.727412 | ||||||||
\(386\) | −30925.5 | −0.0105645 | ||||||||
\(387\) | −1.87137e6 | −0.635158 | ||||||||
\(388\) | 3.56036e6 | 1.20064 | ||||||||
\(389\) | −1.44734e6 | −0.484949 | −0.242474 | − | 0.970158i | \(-0.577959\pi\) | ||||
−0.242474 | + | 0.970158i | \(0.577959\pi\) | |||||||
\(390\) | 5.27206e6 | 1.75517 | ||||||||
\(391\) | −1.05878e6 | −0.350239 | ||||||||
\(392\) | 1.94654e6 | 0.639805 | ||||||||
\(393\) | 929306. | 0.303513 | ||||||||
\(394\) | 4.25763e6 | 1.38174 | ||||||||
\(395\) | 5.70924e6 | 1.84113 | ||||||||
\(396\) | −1.13708e6 | −0.364377 | ||||||||
\(397\) | 5.20211e6 | 1.65654 | 0.828272 | − | 0.560326i | \(-0.189324\pi\) | ||||
0.828272 | + | 0.560326i | \(0.189324\pi\) | |||||||
\(398\) | 1.02518e7 | 3.24408 | ||||||||
\(399\) | −2.09034e6 | −0.657333 | ||||||||
\(400\) | 1.28154e7 | 4.00482 | ||||||||
\(401\) | 1.93344e6 | 0.600439 | 0.300220 | − | 0.953870i | \(-0.402940\pi\) | ||||
0.300220 | + | 0.953870i | \(0.402940\pi\) | |||||||
\(402\) | 996711. | 0.307613 | ||||||||
\(403\) | −1.16902e6 | −0.358558 | ||||||||
\(404\) | −1.80632e6 | −0.550606 | ||||||||
\(405\) | −651219. | −0.197283 | ||||||||
\(406\) | −6.86931e6 | −2.06823 | ||||||||
\(407\) | −694140. | −0.207712 | ||||||||
\(408\) | 1.23578e6 | 0.367529 | ||||||||
\(409\) | −4.68677e6 | −1.38537 | −0.692684 | − | 0.721241i | \(-0.743572\pi\) | ||||
−0.692684 | + | 0.721241i | \(0.743572\pi\) | |||||||
\(410\) | 4.17471e6 | 1.22650 | ||||||||
\(411\) | −3.55971e6 | −1.03947 | ||||||||
\(412\) | −9.70791e6 | −2.81762 | ||||||||
\(413\) | 382857. | 0.110449 | ||||||||
\(414\) | −2.63771e6 | −0.756355 | ||||||||
\(415\) | 9.81724e6 | 2.79814 | ||||||||
\(416\) | −3.60688e6 | −1.02188 | ||||||||
\(417\) | 2.15874e6 | 0.607940 | ||||||||
\(418\) | −4.18229e6 | −1.17077 | ||||||||
\(419\) | 5.57751e6 | 1.55205 | 0.776025 | − | 0.630703i | \(-0.217233\pi\) | ||||
0.776025 | + | 0.630703i | \(0.217233\pi\) | |||||||
\(420\) | −7.11692e6 | −1.96865 | ||||||||
\(421\) | −1.52289e6 | −0.418759 | −0.209379 | − | 0.977834i | \(-0.567144\pi\) | ||||
−0.209379 | + | 0.977834i | \(0.567144\pi\) | |||||||
\(422\) | −2.46667e6 | −0.674265 | ||||||||
\(423\) | −541512. | −0.147149 | ||||||||
\(424\) | −7.55418e6 | −2.04067 | ||||||||
\(425\) | −2.23511e6 | −0.600243 | ||||||||
\(426\) | 7.36001e6 | 1.96496 | ||||||||
\(427\) | −1.63499e6 | −0.433957 | ||||||||
\(428\) | 7.73731e6 | 2.04165 | ||||||||
\(429\) | −1.00725e6 | −0.264238 | ||||||||
\(430\) | −2.34347e7 | −6.11206 | ||||||||
\(431\) | −1.32186e6 | −0.342761 | −0.171380 | − | 0.985205i | \(-0.554823\pi\) | ||||
−0.171380 | + | 0.985205i | \(0.554823\pi\) | |||||||
\(432\) | 1.38885e6 | 0.358051 | ||||||||
\(433\) | 4.13752e6 | 1.06052 | 0.530262 | − | 0.847834i | \(-0.322094\pi\) | ||||
0.530262 | + | 0.847834i | \(0.322094\pi\) | |||||||
\(434\) | 2.27524e6 | 0.579834 | ||||||||
\(435\) | −5.45950e6 | −1.38334 | ||||||||
\(436\) | 1.35316e7 | 3.40906 | ||||||||
\(437\) | −6.72910e6 | −1.68560 | ||||||||
\(438\) | 2.04091e6 | 0.508322 | ||||||||
\(439\) | −916784. | −0.227042 | −0.113521 | − | 0.993536i | \(-0.536213\pi\) | ||||
−0.113521 | + | 0.993536i | \(0.536213\pi\) | |||||||
\(440\) | −7.94890e6 | −1.95738 | ||||||||
\(441\) | −381541. | −0.0934210 | ||||||||
\(442\) | 1.96098e6 | 0.477439 | ||||||||
\(443\) | 1.86032e6 | 0.450378 | 0.225189 | − | 0.974315i | \(-0.427700\pi\) | ||||
0.225189 | + | 0.974315i | \(0.427700\pi\) | |||||||
\(444\) | 2.33511e6 | 0.562146 | ||||||||
\(445\) | 9.11027e6 | 2.18088 | ||||||||
\(446\) | −2.32722e6 | −0.553989 | ||||||||
\(447\) | −2.38949e6 | −0.565635 | ||||||||
\(448\) | 314854. | 0.0741163 | ||||||||
\(449\) | 2.38131e6 | 0.557442 | 0.278721 | − | 0.960372i | \(-0.410090\pi\) | ||||
0.278721 | + | 0.960372i | \(0.410090\pi\) | |||||||
\(450\) | −5.56825e6 | −1.29625 | ||||||||
\(451\) | −797601. | −0.184648 | ||||||||
\(452\) | −9.35940e6 | −2.15478 | ||||||||
\(453\) | 4.33211e6 | 0.991867 | ||||||||
\(454\) | −1.02507e7 | −2.33407 | ||||||||
\(455\) | −6.30438e6 | −1.42762 | ||||||||
\(456\) | 7.85402e6 | 1.76881 | ||||||||
\(457\) | 679422. | 0.152177 | 0.0760885 | − | 0.997101i | \(-0.475757\pi\) | ||||
0.0760885 | + | 0.997101i | \(0.475757\pi\) | |||||||
\(458\) | 6.97905e6 | 1.55465 | ||||||||
\(459\) | −242226. | −0.0536647 | ||||||||
\(460\) | −2.29104e7 | −5.04821 | ||||||||
\(461\) | −278818. | −0.0611039 | −0.0305520 | − | 0.999533i | \(-0.509727\pi\) | ||||
−0.0305520 | + | 0.999533i | \(0.509727\pi\) | |||||||
\(462\) | 1.96040e6 | 0.427307 | ||||||||
\(463\) | 5.43255e6 | 1.17774 | 0.588872 | − | 0.808226i | \(-0.299572\pi\) | ||||
0.588872 | + | 0.808226i | \(0.299572\pi\) | |||||||
\(464\) | 1.16434e7 | 2.51065 | ||||||||
\(465\) | 1.80829e6 | 0.387825 | ||||||||
\(466\) | −1.35658e7 | −2.89387 | ||||||||
\(467\) | −373892. | −0.0793330 | −0.0396665 | − | 0.999213i | \(-0.512630\pi\) | ||||
−0.0396665 | + | 0.999213i | \(0.512630\pi\) | |||||||
\(468\) | 3.38843e6 | 0.715129 | ||||||||
\(469\) | −1.19188e6 | −0.250207 | ||||||||
\(470\) | −6.78121e6 | −1.41600 | ||||||||
\(471\) | 976143. | 0.202750 | ||||||||
\(472\) | −1.43850e6 | −0.297205 | ||||||||
\(473\) | 4.47732e6 | 0.920164 | ||||||||
\(474\) | 5.29043e6 | 1.08155 | ||||||||
\(475\) | −1.42053e7 | −2.88878 | ||||||||
\(476\) | −2.64719e6 | −0.535511 | ||||||||
\(477\) | 1.48070e6 | 0.297968 | ||||||||
\(478\) | 1.30084e7 | 2.60407 | ||||||||
\(479\) | −526098. | −0.104768 | −0.0523839 | − | 0.998627i | \(-0.516682\pi\) | ||||
−0.0523839 | + | 0.998627i | \(0.516682\pi\) | |||||||
\(480\) | 5.57928e6 | 1.10529 | ||||||||
\(481\) | 2.06851e6 | 0.407656 | ||||||||
\(482\) | −6.55270e6 | −1.28470 | ||||||||
\(483\) | 3.15420e6 | 0.615206 | ||||||||
\(484\) | −8.94556e6 | −1.73578 | ||||||||
\(485\) | −4.87854e6 | −0.941750 | ||||||||
\(486\) | −603448. | −0.115891 | ||||||||
\(487\) | −5.03131e6 | −0.961299 | −0.480650 | − | 0.876913i | \(-0.659599\pi\) | ||||
−0.480650 | + | 0.876913i | \(0.659599\pi\) | |||||||
\(488\) | 6.14315e6 | 1.16773 | ||||||||
\(489\) | 1.50565e6 | 0.284742 | ||||||||
\(490\) | −4.77793e6 | −0.898980 | ||||||||
\(491\) | 4.50265e6 | 0.842878 | 0.421439 | − | 0.906857i | \(-0.361525\pi\) | ||||
0.421439 | + | 0.906857i | \(0.361525\pi\) | |||||||
\(492\) | 2.68315e6 | 0.499727 | ||||||||
\(493\) | −2.03070e6 | −0.376296 | ||||||||
\(494\) | 1.24630e7 | 2.29777 | ||||||||
\(495\) | 1.55806e6 | 0.285807 | ||||||||
\(496\) | −3.85652e6 | −0.703868 | ||||||||
\(497\) | −8.80118e6 | −1.59827 | ||||||||
\(498\) | 9.09709e6 | 1.64372 | ||||||||
\(499\) | 4.33681e6 | 0.779685 | 0.389842 | − | 0.920882i | \(-0.372529\pi\) | ||||
0.389842 | + | 0.920882i | \(0.372529\pi\) | |||||||
\(500\) | −2.58960e7 | −4.63242 | ||||||||
\(501\) | −6.30885e6 | −1.12294 | ||||||||
\(502\) | 1.83109e7 | 3.24303 | ||||||||
\(503\) | −4.73584e6 | −0.834597 | −0.417299 | − | 0.908769i | \(-0.637023\pi\) | ||||
−0.417299 | + | 0.908769i | \(0.637023\pi\) | |||||||
\(504\) | −3.68149e6 | −0.645576 | ||||||||
\(505\) | 2.47509e6 | 0.431879 | ||||||||
\(506\) | 6.31081e6 | 1.09574 | ||||||||
\(507\) | −340063. | −0.0587543 | ||||||||
\(508\) | −1.60475e7 | −2.75897 | ||||||||
\(509\) | 5.24411e6 | 0.897175 | 0.448587 | − | 0.893739i | \(-0.351927\pi\) | ||||
0.448587 | + | 0.893739i | \(0.351927\pi\) | |||||||
\(510\) | −3.03333e6 | −0.516410 | ||||||||
\(511\) | −2.44054e6 | −0.413460 | ||||||||
\(512\) | 1.32944e7 | 2.24126 | ||||||||
\(513\) | −1.53947e6 | −0.258272 | ||||||||
\(514\) | 5.22230e6 | 0.871875 | ||||||||
\(515\) | 1.33022e7 | 2.21006 | ||||||||
\(516\) | −1.50618e7 | −2.49031 | ||||||||
\(517\) | 1.29559e6 | 0.213177 | ||||||||
\(518\) | −4.02590e6 | −0.659232 | ||||||||
\(519\) | −3.37604e6 | −0.550161 | ||||||||
\(520\) | 2.36874e7 | 3.84157 | ||||||||
\(521\) | 1.11744e7 | 1.80356 | 0.901781 | − | 0.432194i | \(-0.142261\pi\) | ||||
0.901781 | + | 0.432194i | \(0.142261\pi\) | |||||||
\(522\) | −5.05901e6 | −0.812624 | ||||||||
\(523\) | 7.05297e6 | 1.12750 | 0.563752 | − | 0.825944i | \(-0.309357\pi\) | ||||
0.563752 | + | 0.825944i | \(0.309357\pi\) | |||||||
\(524\) | 7.47957e6 | 1.19000 | ||||||||
\(525\) | 6.65857e6 | 1.05434 | ||||||||
\(526\) | −4.63476e6 | −0.730403 | ||||||||
\(527\) | 672607. | 0.105496 | ||||||||
\(528\) | −3.32287e6 | −0.518714 | ||||||||
\(529\) | 3.71744e6 | 0.577571 | ||||||||
\(530\) | 1.85424e7 | 2.86731 | ||||||||
\(531\) | 281961. | 0.0433963 | ||||||||
\(532\) | −1.68242e7 | −2.57725 | ||||||||
\(533\) | 2.37681e6 | 0.362391 | ||||||||
\(534\) | 8.44198e6 | 1.28112 | ||||||||
\(535\) | −1.06020e7 | −1.60141 | ||||||||
\(536\) | 4.47823e6 | 0.673278 | ||||||||
\(537\) | 2.27044e6 | 0.339762 | ||||||||
\(538\) | −1.78567e7 | −2.65978 | ||||||||
\(539\) | 912850. | 0.135340 | ||||||||
\(540\) | −5.24138e6 | −0.773501 | ||||||||
\(541\) | −734520. | −0.107897 | −0.0539486 | − | 0.998544i | \(-0.517181\pi\) | ||||
−0.0539486 | + | 0.998544i | \(0.517181\pi\) | |||||||
\(542\) | 2.28484e6 | 0.334086 | ||||||||
\(543\) | 6.63609e6 | 0.965857 | ||||||||
\(544\) | 2.07525e6 | 0.300659 | ||||||||
\(545\) | −1.85416e7 | −2.67397 | ||||||||
\(546\) | −5.84191e6 | −0.838636 | ||||||||
\(547\) | −5.09324e6 | −0.727824 | −0.363912 | − | 0.931433i | \(-0.618559\pi\) | ||||
−0.363912 | + | 0.931433i | \(0.618559\pi\) | |||||||
\(548\) | −2.86505e7 | −4.07551 | ||||||||
\(549\) | −1.20412e6 | −0.170505 | ||||||||
\(550\) | 1.33222e7 | 1.87789 | ||||||||
\(551\) | −1.29061e7 | −1.81100 | ||||||||
\(552\) | −1.18512e7 | −1.65545 | ||||||||
\(553\) | −6.32635e6 | −0.879712 | ||||||||
\(554\) | −6.01707e6 | −0.832934 | ||||||||
\(555\) | −3.19965e6 | −0.440931 | ||||||||
\(556\) | 1.73748e7 | 2.38359 | ||||||||
\(557\) | −3.78806e6 | −0.517343 | −0.258672 | − | 0.965965i | \(-0.583285\pi\) | ||||
−0.258672 | + | 0.965965i | \(0.583285\pi\) | |||||||
\(558\) | 1.67564e6 | 0.227822 | ||||||||
\(559\) | −1.33422e7 | −1.80592 | ||||||||
\(560\) | −2.07977e7 | −2.80250 | ||||||||
\(561\) | 579534. | 0.0777449 | ||||||||
\(562\) | −8.33559e6 | −1.11326 | ||||||||
\(563\) | −8.41523e6 | −1.11891 | −0.559455 | − | 0.828861i | \(-0.688989\pi\) | ||||
−0.559455 | + | 0.828861i | \(0.688989\pi\) | |||||||
\(564\) | −4.35839e6 | −0.576937 | ||||||||
\(565\) | 1.28246e7 | 1.69014 | ||||||||
\(566\) | 1.11277e7 | 1.46004 | ||||||||
\(567\) | 721609. | 0.0942637 | ||||||||
\(568\) | 3.30686e7 | 4.30075 | ||||||||
\(569\) | −4.34598e6 | −0.562739 | −0.281370 | − | 0.959599i | \(-0.590789\pi\) | ||||
−0.281370 | + | 0.959599i | \(0.590789\pi\) | |||||||
\(570\) | −1.92783e7 | −2.48532 | ||||||||
\(571\) | 766497. | 0.0983830 | 0.0491915 | − | 0.998789i | \(-0.484336\pi\) | ||||
0.0491915 | + | 0.998789i | \(0.484336\pi\) | |||||||
\(572\) | −8.10695e6 | −1.03602 | ||||||||
\(573\) | 8.86022e6 | 1.12735 | ||||||||
\(574\) | −4.62595e6 | −0.586032 | ||||||||
\(575\) | 2.14348e7 | 2.70365 | ||||||||
\(576\) | 231879. | 0.0291209 | ||||||||
\(577\) | 460709. | 0.0576086 | 0.0288043 | − | 0.999585i | \(-0.490830\pi\) | ||||
0.0288043 | + | 0.999585i | \(0.490830\pi\) | |||||||
\(578\) | 1.33819e7 | 1.66609 | ||||||||
\(579\) | 27235.3 | 0.00337626 | ||||||||
\(580\) | −4.39411e7 | −5.42377 | ||||||||
\(581\) | −1.08784e7 | −1.33698 | ||||||||
\(582\) | −4.52067e6 | −0.553217 | ||||||||
\(583\) | −3.54262e6 | −0.431671 | ||||||||
\(584\) | 9.16982e6 | 1.11257 | ||||||||
\(585\) | −4.64296e6 | −0.560926 | ||||||||
\(586\) | 1.16467e7 | 1.40106 | ||||||||
\(587\) | 279534. | 0.0334841 | 0.0167421 | − | 0.999860i | \(-0.494671\pi\) | ||||
0.0167421 | + | 0.999860i | \(0.494671\pi\) | |||||||
\(588\) | −3.07085e6 | −0.366282 | ||||||||
\(589\) | 4.27475e6 | 0.507718 | ||||||||
\(590\) | 3.53092e6 | 0.417598 | ||||||||
\(591\) | −3.74959e6 | −0.441585 | ||||||||
\(592\) | 6.82386e6 | 0.800251 | ||||||||
\(593\) | 4.02162e6 | 0.469639 | 0.234819 | − | 0.972039i | \(-0.424550\pi\) | ||||
0.234819 | + | 0.972039i | \(0.424550\pi\) | |||||||
\(594\) | 1.44377e6 | 0.167893 | ||||||||
\(595\) | 3.62729e6 | 0.420039 | ||||||||
\(596\) | −1.92319e7 | −2.21772 | ||||||||
\(597\) | −9.02847e6 | −1.03676 | ||||||||
\(598\) | −1.88059e7 | −2.15051 | ||||||||
\(599\) | −60227.1 | −0.00685843 | −0.00342922 | − | 0.999994i | \(-0.501092\pi\) | ||||
−0.00342922 | + | 0.999994i | \(0.501092\pi\) | |||||||
\(600\) | −2.50182e7 | −2.83712 | ||||||||
\(601\) | 4.60932e6 | 0.520536 | 0.260268 | − | 0.965536i | \(-0.416189\pi\) | ||||
0.260268 | + | 0.965536i | \(0.416189\pi\) | |||||||
\(602\) | 2.59677e7 | 2.92040 | ||||||||
\(603\) | −877778. | −0.0983085 | ||||||||
\(604\) | 3.48672e7 | 3.88888 | ||||||||
\(605\) | 1.22576e7 | 1.36149 | ||||||||
\(606\) | 2.29353e6 | 0.253701 | ||||||||
\(607\) | −6.23116e6 | −0.686431 | −0.343216 | − | 0.939257i | \(-0.611516\pi\) | ||||
−0.343216 | + | 0.939257i | \(0.611516\pi\) | |||||||
\(608\) | 1.31893e7 | 1.44698 | ||||||||
\(609\) | 6.04962e6 | 0.660975 | ||||||||
\(610\) | −1.50789e7 | −1.64076 | ||||||||
\(611\) | −3.86079e6 | −0.418382 | ||||||||
\(612\) | −1.94957e6 | −0.210407 | ||||||||
\(613\) | 5.27500e6 | 0.566984 | 0.283492 | − | 0.958975i | \(-0.408507\pi\) | ||||
0.283492 | + | 0.958975i | \(0.408507\pi\) | |||||||
\(614\) | 1.30400e7 | 1.39591 | ||||||||
\(615\) | −3.67656e6 | −0.391971 | ||||||||
\(616\) | 8.80810e6 | 0.935256 | ||||||||
\(617\) | −1.43161e7 | −1.51395 | −0.756975 | − | 0.653444i | \(-0.773323\pi\) | ||||
−0.756975 | + | 0.653444i | \(0.773323\pi\) | |||||||
\(618\) | 1.23264e7 | 1.29827 | ||||||||
\(619\) | 1.67507e7 | 1.75714 | 0.878569 | − | 0.477615i | \(-0.158499\pi\) | ||||
0.878569 | + | 0.477615i | \(0.158499\pi\) | |||||||
\(620\) | 1.45541e7 | 1.52057 | ||||||||
\(621\) | 2.32296e6 | 0.241720 | ||||||||
\(622\) | 1.33074e7 | 1.37917 | ||||||||
\(623\) | −1.00950e7 | −1.04204 | ||||||||
\(624\) | 9.90199e6 | 1.01803 | ||||||||
\(625\) | 1.44626e7 | 1.48097 | ||||||||
\(626\) | 2.42826e7 | 2.47662 | ||||||||
\(627\) | 3.68323e6 | 0.374162 | ||||||||
\(628\) | 7.85654e6 | 0.794936 | ||||||||
\(629\) | −1.19014e6 | −0.119942 | ||||||||
\(630\) | 9.03652e6 | 0.907089 | ||||||||
\(631\) | 7.91210e6 | 0.791076 | 0.395538 | − | 0.918450i | \(-0.370558\pi\) | ||||
0.395538 | + | 0.918450i | \(0.370558\pi\) | |||||||
\(632\) | 2.37699e7 | 2.36720 | ||||||||
\(633\) | 2.17233e6 | 0.215485 | ||||||||
\(634\) | −2.69461e7 | −2.66240 | ||||||||
\(635\) | 2.19889e7 | 2.16406 | ||||||||
\(636\) | 1.19175e7 | 1.16826 | ||||||||
\(637\) | −2.72025e6 | −0.265620 | ||||||||
\(638\) | 1.21039e7 | 1.17726 | ||||||||
\(639\) | −6.48177e6 | −0.627974 | ||||||||
\(640\) | −1.69337e7 | −1.63418 | ||||||||
\(641\) | −1.24774e7 | −1.19945 | −0.599723 | − | 0.800208i | \(-0.704722\pi\) | ||||
−0.599723 | + | 0.800208i | \(0.704722\pi\) | |||||||
\(642\) | −9.82424e6 | −0.940722 | ||||||||
\(643\) | 1.49984e6 | 0.143060 | 0.0715299 | − | 0.997438i | \(-0.477212\pi\) | ||||
0.0715299 | + | 0.997438i | \(0.477212\pi\) | |||||||
\(644\) | 2.53867e7 | 2.41208 | ||||||||
\(645\) | 2.06383e7 | 1.95333 | ||||||||
\(646\) | −7.17073e6 | −0.676055 | ||||||||
\(647\) | −6.33662e6 | −0.595109 | −0.297555 | − | 0.954705i | \(-0.596171\pi\) | ||||
−0.297555 | + | 0.954705i | \(0.596171\pi\) | |||||||
\(648\) | −2.71129e6 | −0.253653 | ||||||||
\(649\) | −674602. | −0.0628689 | ||||||||
\(650\) | −3.96997e7 | −3.68556 | ||||||||
\(651\) | −2.00375e6 | −0.185306 | ||||||||
\(652\) | 1.21183e7 | 1.11641 | ||||||||
\(653\) | −6.01496e6 | −0.552014 | −0.276007 | − | 0.961156i | \(-0.589011\pi\) | ||||
−0.276007 | + | 0.961156i | \(0.589011\pi\) | |||||||
\(654\) | −1.71814e7 | −1.57078 | ||||||||
\(655\) | −1.02488e7 | −0.933404 | ||||||||
\(656\) | 7.84095e6 | 0.711393 | ||||||||
\(657\) | −1.79738e6 | −0.162452 | ||||||||
\(658\) | 7.51419e6 | 0.676578 | ||||||||
\(659\) | 9.61791e6 | 0.862714 | 0.431357 | − | 0.902181i | \(-0.358035\pi\) | ||||
0.431357 | + | 0.902181i | \(0.358035\pi\) | |||||||
\(660\) | 1.25402e7 | 1.12058 | ||||||||
\(661\) | −8.42469e6 | −0.749981 | −0.374990 | − | 0.927029i | \(-0.622354\pi\) | ||||
−0.374990 | + | 0.927029i | \(0.622354\pi\) | |||||||
\(662\) | −3.52601e6 | −0.312708 | ||||||||
\(663\) | −1.72699e6 | −0.152583 | ||||||||
\(664\) | 4.08733e7 | 3.59765 | ||||||||
\(665\) | 2.30532e7 | 2.02152 | ||||||||
\(666\) | −2.96494e6 | −0.259018 | ||||||||
\(667\) | 1.94746e7 | 1.69494 | ||||||||
\(668\) | −5.07772e7 | −4.40278 | ||||||||
\(669\) | 2.04952e6 | 0.177047 | ||||||||
\(670\) | −1.09922e7 | −0.946012 | ||||||||
\(671\) | 2.88090e6 | 0.247014 | ||||||||
\(672\) | −6.18234e6 | −0.528117 | ||||||||
\(673\) | 4.81831e6 | 0.410069 | 0.205035 | − | 0.978755i | \(-0.434269\pi\) | ||||
0.205035 | + | 0.978755i | \(0.434269\pi\) | |||||||
\(674\) | −1.23682e7 | −1.04871 | ||||||||
\(675\) | 4.90381e6 | 0.414261 | ||||||||
\(676\) | −2.73702e6 | −0.230362 | ||||||||
\(677\) | −1.49503e7 | −1.25365 | −0.626826 | − | 0.779159i | \(-0.715647\pi\) | ||||
−0.626826 | + | 0.779159i | \(0.715647\pi\) | |||||||
\(678\) | 1.18839e7 | 0.992849 | ||||||||
\(679\) | 5.40586e6 | 0.449977 | ||||||||
\(680\) | −1.36288e7 | −1.13028 | ||||||||
\(681\) | 9.02751e6 | 0.745934 | ||||||||
\(682\) | −4.00903e6 | −0.330049 | ||||||||
\(683\) | 1.14545e6 | 0.0939559 | 0.0469780 | − | 0.998896i | \(-0.485041\pi\) | ||||
0.0469780 | + | 0.998896i | \(0.485041\pi\) | |||||||
\(684\) | −1.23905e7 | −1.01262 | ||||||||
\(685\) | 3.92581e7 | 3.19671 | ||||||||
\(686\) | 2.41851e7 | 1.96218 | ||||||||
\(687\) | −6.14627e6 | −0.496843 | ||||||||
\(688\) | −4.40151e7 | −3.54511 | ||||||||
\(689\) | 1.05568e7 | 0.847200 | ||||||||
\(690\) | 2.90898e7 | 2.32604 | ||||||||
\(691\) | 1.14659e7 | 0.913511 | 0.456755 | − | 0.889592i | \(-0.349011\pi\) | ||||
0.456755 | + | 0.889592i | \(0.349011\pi\) | |||||||
\(692\) | −2.71723e7 | −2.15705 | ||||||||
\(693\) | −1.72648e6 | −0.136561 | ||||||||
\(694\) | 3.83942e7 | 3.02599 | ||||||||
\(695\) | −2.38076e7 | −1.86962 | ||||||||
\(696\) | −2.27302e7 | −1.77861 | ||||||||
\(697\) | −1.36752e6 | −0.106624 | ||||||||
\(698\) | −4.11775e6 | −0.319905 | ||||||||
\(699\) | 1.19470e7 | 0.924840 | ||||||||
\(700\) | 5.35919e7 | 4.13384 | ||||||||
\(701\) | −5.89914e6 | −0.453413 | −0.226706 | − | 0.973963i | \(-0.572796\pi\) | ||||
−0.226706 | + | 0.973963i | \(0.572796\pi\) | |||||||
\(702\) | −4.30237e6 | −0.329507 | ||||||||
\(703\) | −7.56391e6 | −0.577242 | ||||||||
\(704\) | −554779. | −0.0421880 | ||||||||
\(705\) | 5.97204e6 | 0.452532 | ||||||||
\(706\) | 2.62798e7 | 1.98431 | ||||||||
\(707\) | −2.74262e6 | −0.206356 | ||||||||
\(708\) | 2.26938e6 | 0.170147 | ||||||||
\(709\) | 1.68552e6 | 0.125927 | 0.0629636 | − | 0.998016i | \(-0.479945\pi\) | ||||
0.0629636 | + | 0.998016i | \(0.479945\pi\) | |||||||
\(710\) | −8.11695e7 | −6.04293 | ||||||||
\(711\) | −4.65914e6 | −0.345647 | ||||||||
\(712\) | 3.79299e7 | 2.80402 | ||||||||
\(713\) | −6.45034e6 | −0.475180 | ||||||||
\(714\) | 3.36120e6 | 0.246746 | ||||||||
\(715\) | 1.11085e7 | 0.812622 | ||||||||
\(716\) | 1.82738e7 | 1.33213 | ||||||||
\(717\) | −1.14561e7 | −0.832223 | ||||||||
\(718\) | −1.84979e6 | −0.133910 | ||||||||
\(719\) | 1.79183e7 | 1.29263 | 0.646314 | − | 0.763072i | \(-0.276310\pi\) | ||||
0.646314 | + | 0.763072i | \(0.276310\pi\) | |||||||
\(720\) | −1.53168e7 | −1.10113 | ||||||||
\(721\) | −1.47400e7 | −1.05599 | ||||||||
\(722\) | −2.02692e7 | −1.44708 | ||||||||
\(723\) | 5.77079e6 | 0.410573 | ||||||||
\(724\) | 5.34110e7 | 3.78690 | ||||||||
\(725\) | 4.11112e7 | 2.90479 | ||||||||
\(726\) | 1.13584e7 | 0.799789 | ||||||||
\(727\) | −8.60696e6 | −0.603968 | −0.301984 | − | 0.953313i | \(-0.597649\pi\) | ||||
−0.301984 | + | 0.953313i | \(0.597649\pi\) | |||||||
\(728\) | −2.62477e7 | −1.83554 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −2.25081e7 | −1.56326 | ||||||||
\(731\) | 7.67657e6 | 0.531342 | ||||||||
\(732\) | −9.69142e6 | −0.668513 | ||||||||
\(733\) | −4.93390e6 | −0.339180 | −0.169590 | − | 0.985515i | \(-0.554244\pi\) | ||||
−0.169590 | + | 0.985515i | \(0.554244\pi\) | |||||||
\(734\) | 4.04546e6 | 0.277158 | ||||||||
\(735\) | 4.20780e6 | 0.287301 | ||||||||
\(736\) | −1.99018e7 | −1.35425 | ||||||||
\(737\) | 2.10011e6 | 0.142421 | ||||||||
\(738\) | −3.40686e6 | −0.230257 | ||||||||
\(739\) | −6.04050e6 | −0.406876 | −0.203438 | − | 0.979088i | \(-0.565212\pi\) | ||||
−0.203438 | + | 0.979088i | \(0.565212\pi\) | |||||||
\(740\) | −2.57526e7 | −1.72879 | ||||||||
\(741\) | −1.09759e7 | −0.734333 | ||||||||
\(742\) | −2.05466e7 | −1.37003 | ||||||||
\(743\) | −7.90866e6 | −0.525570 | −0.262785 | − | 0.964854i | \(-0.584641\pi\) | ||||
−0.262785 | + | 0.964854i | \(0.584641\pi\) | |||||||
\(744\) | 7.52866e6 | 0.498638 | ||||||||
\(745\) | 2.63524e7 | 1.73952 | ||||||||
\(746\) | 1.19859e7 | 0.788539 | ||||||||
\(747\) | −8.01157e6 | −0.525310 | ||||||||
\(748\) | 4.66442e6 | 0.304820 | ||||||||
\(749\) | 1.17479e7 | 0.765168 | ||||||||
\(750\) | 3.28808e7 | 2.13446 | ||||||||
\(751\) | −6.20100e6 | −0.401201 | −0.200601 | − | 0.979673i | \(-0.564289\pi\) | ||||
−0.200601 | + | 0.979673i | \(0.564289\pi\) | |||||||
\(752\) | −1.27365e7 | −0.821307 | ||||||||
\(753\) | −1.61260e7 | −1.03643 | ||||||||
\(754\) | −3.60690e7 | −2.31050 | ||||||||
\(755\) | −4.77764e7 | −3.05033 | ||||||||
\(756\) | 5.80792e6 | 0.369586 | ||||||||
\(757\) | 6.28292e6 | 0.398494 | 0.199247 | − | 0.979949i | \(-0.436150\pi\) | ||||
0.199247 | + | 0.979949i | \(0.436150\pi\) | |||||||
\(758\) | 1.57785e7 | 0.997455 | ||||||||
\(759\) | −5.55776e6 | −0.350183 | ||||||||
\(760\) | −8.66177e7 | −5.43967 | ||||||||
\(761\) | −4.81278e6 | −0.301255 | −0.150627 | − | 0.988591i | \(-0.548129\pi\) | ||||
−0.150627 | + | 0.988591i | \(0.548129\pi\) | |||||||
\(762\) | 2.03758e7 | 1.27124 | ||||||||
\(763\) | 2.05458e7 | 1.27765 | ||||||||
\(764\) | 7.13120e7 | 4.42007 | ||||||||
\(765\) | 2.67138e6 | 0.165037 | ||||||||
\(766\) | 5.69367e7 | 3.50607 | ||||||||
\(767\) | 2.01028e6 | 0.123387 | ||||||||
\(768\) | −1.65159e7 | −1.01042 | ||||||||
\(769\) | −7.75895e6 | −0.473137 | −0.236569 | − | 0.971615i | \(-0.576023\pi\) | ||||
−0.236569 | + | 0.971615i | \(0.576023\pi\) | |||||||
\(770\) | −2.16202e7 | −1.31411 | ||||||||
\(771\) | −4.59915e6 | −0.278639 | ||||||||
\(772\) | 219205. | 0.0132375 | ||||||||
\(773\) | 1.00740e7 | 0.606389 | 0.303195 | − | 0.952929i | \(-0.401947\pi\) | ||||
0.303195 | + | 0.952929i | \(0.401947\pi\) | |||||||
\(774\) | 1.91243e7 | 1.14745 | ||||||||
\(775\) | −1.36168e7 | −0.814367 | ||||||||
\(776\) | −2.03114e7 | −1.21084 | ||||||||
\(777\) | 3.54550e6 | 0.210681 | ||||||||
\(778\) | 1.47910e7 | 0.876089 | ||||||||
\(779\) | −8.69130e6 | −0.513146 | ||||||||
\(780\) | −3.73692e7 | −2.19926 | ||||||||
\(781\) | 1.55079e7 | 0.909756 | ||||||||
\(782\) | 1.08202e7 | 0.632728 | ||||||||
\(783\) | 4.45534e6 | 0.259703 | ||||||||
\(784\) | −8.97393e6 | −0.521426 | ||||||||
\(785\) | −1.07653e7 | −0.623525 | ||||||||
\(786\) | −9.49699e6 | −0.548314 | ||||||||
\(787\) | −8.19431e6 | −0.471602 | −0.235801 | − | 0.971801i | \(-0.575771\pi\) | ||||
−0.235801 | + | 0.971801i | \(0.575771\pi\) | |||||||
\(788\) | −3.01788e7 | −1.73136 | ||||||||
\(789\) | 4.08171e6 | 0.233426 | ||||||||
\(790\) | −5.83452e7 | −3.32612 | ||||||||
\(791\) | −1.42108e7 | −0.807567 | ||||||||
\(792\) | 6.48687e6 | 0.367470 | ||||||||
\(793\) | −8.58494e6 | −0.484791 | ||||||||
\(794\) | −5.31626e7 | −2.99265 | ||||||||
\(795\) | −1.63298e7 | −0.916352 | ||||||||
\(796\) | −7.26662e7 | −4.06490 | ||||||||
\(797\) | −1.92457e7 | −1.07322 | −0.536610 | − | 0.843830i | \(-0.680295\pi\) | ||||
−0.536610 | + | 0.843830i | \(0.680295\pi\) | |||||||
\(798\) | 2.13621e7 | 1.18751 | ||||||||
\(799\) | 2.22134e6 | 0.123097 | ||||||||
\(800\) | −4.20131e7 | −2.32092 | ||||||||
\(801\) | −7.43463e6 | −0.409429 | ||||||||
\(802\) | −1.97587e7 | −1.08473 | ||||||||
\(803\) | 4.30029e6 | 0.235347 | ||||||||
\(804\) | −7.06485e6 | −0.385445 | ||||||||
\(805\) | −3.47859e7 | −1.89197 | ||||||||
\(806\) | 1.19467e7 | 0.647756 | ||||||||
\(807\) | 1.57259e7 | 0.850026 | ||||||||
\(808\) | 1.03048e7 | 0.555280 | ||||||||
\(809\) | −3.71300e6 | −0.199459 | −0.0997296 | − | 0.995015i | \(-0.531798\pi\) | ||||
−0.0997296 | + | 0.995015i | \(0.531798\pi\) | |||||||
\(810\) | 6.65510e6 | 0.356403 | ||||||||
\(811\) | −2.16439e7 | −1.15553 | −0.577767 | − | 0.816201i | \(-0.696076\pi\) | ||||
−0.577767 | + | 0.816201i | \(0.696076\pi\) | |||||||
\(812\) | 4.86907e7 | 2.59153 | ||||||||
\(813\) | −2.01220e6 | −0.106769 | ||||||||
\(814\) | 7.09372e6 | 0.375244 | ||||||||
\(815\) | −1.66050e7 | −0.875677 | ||||||||
\(816\) | −5.69721e6 | −0.299528 | ||||||||
\(817\) | 4.87885e7 | 2.55718 | ||||||||
\(818\) | 4.78962e7 | 2.50275 | ||||||||
\(819\) | 5.14482e6 | 0.268016 | ||||||||
\(820\) | −2.95910e7 | −1.53683 | ||||||||
\(821\) | −2.51582e7 | −1.30263 | −0.651316 | − | 0.758807i | \(-0.725783\pi\) | ||||
−0.651316 | + | 0.758807i | \(0.725783\pi\) | |||||||
\(822\) | 3.63783e7 | 1.87786 | ||||||||
\(823\) | −1.27945e7 | −0.658451 | −0.329225 | − | 0.944251i | \(-0.606788\pi\) | ||||
−0.329225 | + | 0.944251i | \(0.606788\pi\) | |||||||
\(824\) | 5.53824e7 | 2.84154 | ||||||||
\(825\) | −1.17325e7 | −0.600147 | ||||||||
\(826\) | −3.91258e6 | −0.199532 | ||||||||
\(827\) | −4.64226e6 | −0.236029 | −0.118015 | − | 0.993012i | \(-0.537653\pi\) | ||||
−0.118015 | + | 0.993012i | \(0.537653\pi\) | |||||||
\(828\) | 1.86965e7 | 0.947728 | ||||||||
\(829\) | −1.53561e7 | −0.776059 | −0.388029 | − | 0.921647i | \(-0.626844\pi\) | ||||
−0.388029 | + | 0.921647i | \(0.626844\pi\) | |||||||
\(830\) | −1.00327e8 | −5.05500 | ||||||||
\(831\) | 5.29908e6 | 0.266194 | ||||||||
\(832\) | 1.65322e6 | 0.0827983 | ||||||||
\(833\) | 1.56512e6 | 0.0781513 | ||||||||
\(834\) | −2.20612e7 | −1.09828 | ||||||||
\(835\) | 6.95769e7 | 3.45341 | ||||||||
\(836\) | 2.96447e7 | 1.46700 | ||||||||
\(837\) | −1.47569e6 | −0.0728085 | ||||||||
\(838\) | −5.69991e7 | −2.80387 | ||||||||
\(839\) | −1.78634e6 | −0.0876112 | −0.0438056 | − | 0.999040i | \(-0.513948\pi\) | ||||
−0.0438056 | + | 0.999040i | \(0.513948\pi\) | |||||||
\(840\) | 4.06011e7 | 1.98536 | ||||||||
\(841\) | 1.68403e7 | 0.821031 | ||||||||
\(842\) | 1.55631e7 | 0.756513 | ||||||||
\(843\) | 7.34094e6 | 0.355781 | ||||||||
\(844\) | 1.74842e7 | 0.844868 | ||||||||
\(845\) | 3.75037e6 | 0.180689 | ||||||||
\(846\) | 5.53395e6 | 0.265833 | ||||||||
\(847\) | −1.35825e7 | −0.650535 | ||||||||
\(848\) | 3.48263e7 | 1.66310 | ||||||||
\(849\) | −9.79986e6 | −0.466606 | ||||||||
\(850\) | 2.28416e7 | 1.08437 | ||||||||
\(851\) | 1.14135e7 | 0.540248 | ||||||||
\(852\) | −5.21689e7 | −2.46214 | ||||||||
\(853\) | −2.41934e7 | −1.13848 | −0.569239 | − | 0.822172i | \(-0.692762\pi\) | ||||
−0.569239 | + | 0.822172i | \(0.692762\pi\) | |||||||
\(854\) | 1.67087e7 | 0.783969 | ||||||||
\(855\) | 1.69779e7 | 0.794273 | ||||||||
\(856\) | −4.41404e7 | −2.05898 | ||||||||
\(857\) | −2.04166e6 | −0.0949578 | −0.0474789 | − | 0.998872i | \(-0.515119\pi\) | ||||
−0.0474789 | + | 0.998872i | \(0.515119\pi\) | |||||||
\(858\) | 1.02936e7 | 0.477363 | ||||||||
\(859\) | 4.39878e6 | 0.203399 | 0.101700 | − | 0.994815i | \(-0.467572\pi\) | ||||
0.101700 | + | 0.994815i | \(0.467572\pi\) | |||||||
\(860\) | 1.66109e8 | 7.65854 | ||||||||
\(861\) | 4.07396e6 | 0.187287 | ||||||||
\(862\) | 1.35086e7 | 0.619217 | ||||||||
\(863\) | 2.14857e7 | 0.982023 | 0.491012 | − | 0.871153i | \(-0.336627\pi\) | ||||
0.491012 | + | 0.871153i | \(0.336627\pi\) | |||||||
\(864\) | −4.55309e6 | −0.207502 | ||||||||
\(865\) | 3.72325e7 | 1.69193 | ||||||||
\(866\) | −4.22832e7 | −1.91590 | ||||||||
\(867\) | −1.17851e7 | −0.532457 | ||||||||
\(868\) | −1.61273e7 | −0.726544 | ||||||||
\(869\) | 1.11472e7 | 0.500743 | ||||||||
\(870\) | 5.57931e7 | 2.49909 | ||||||||
\(871\) | −6.25825e6 | −0.279516 | ||||||||
\(872\) | −7.71963e7 | −3.43800 | ||||||||
\(873\) | 3.98124e6 | 0.176800 | ||||||||
\(874\) | 6.87676e7 | 3.04513 | ||||||||
\(875\) | −3.93192e7 | −1.73614 | ||||||||
\(876\) | −1.44663e7 | −0.636938 | ||||||||
\(877\) | 3.80492e7 | 1.67050 | 0.835251 | − | 0.549869i | \(-0.185322\pi\) | ||||
0.835251 | + | 0.549869i | \(0.185322\pi\) | |||||||
\(878\) | 9.36902e6 | 0.410164 | ||||||||
\(879\) | −1.02569e7 | −0.447759 | ||||||||
\(880\) | 3.66461e7 | 1.59522 | ||||||||
\(881\) | −2.79654e7 | −1.21390 | −0.606949 | − | 0.794741i | \(-0.707607\pi\) | ||||
−0.606949 | + | 0.794741i | \(0.707607\pi\) | |||||||
\(882\) | 3.89913e6 | 0.168771 | ||||||||
\(883\) | −4.11323e7 | −1.77534 | −0.887669 | − | 0.460481i | \(-0.847677\pi\) | ||||
−0.887669 | + | 0.460481i | \(0.847677\pi\) | |||||||
\(884\) | −1.38997e7 | −0.598241 | ||||||||
\(885\) | −3.10959e6 | −0.133458 | ||||||||
\(886\) | −1.90114e7 | −0.813635 | ||||||||
\(887\) | −2.45600e7 | −1.04814 | −0.524070 | − | 0.851675i | \(-0.675587\pi\) | ||||
−0.524070 | + | 0.851675i | \(0.675587\pi\) | |||||||
\(888\) | −1.33215e7 | −0.566918 | ||||||||
\(889\) | −2.43656e7 | −1.03401 | ||||||||
\(890\) | −9.31019e7 | −3.93989 | ||||||||
\(891\) | −1.27149e6 | −0.0536561 | ||||||||
\(892\) | 1.64957e7 | 0.694159 | ||||||||
\(893\) | 1.41178e7 | 0.592430 | ||||||||
\(894\) | 2.44192e7 | 1.02185 | ||||||||
\(895\) | −2.50394e7 | −1.04488 | ||||||||
\(896\) | 1.87640e7 | 0.780829 | ||||||||
\(897\) | 1.65619e7 | 0.687272 | ||||||||
\(898\) | −2.43356e7 | −1.00705 | ||||||||
\(899\) | −1.23715e7 | −0.510532 | ||||||||
\(900\) | 3.94686e7 | 1.62422 | ||||||||
\(901\) | −6.07399e6 | −0.249265 | ||||||||
\(902\) | 8.15104e6 | 0.333577 | ||||||||
\(903\) | −2.28691e7 | −0.933318 | ||||||||
\(904\) | 5.33942e7 | 2.17307 | ||||||||
\(905\) | −7.31858e7 | −2.97033 | ||||||||
\(906\) | −4.42717e7 | −1.79187 | ||||||||
\(907\) | 2.64205e7 | 1.06640 | 0.533202 | − | 0.845988i | \(-0.320988\pi\) | ||||
0.533202 | + | 0.845988i | \(0.320988\pi\) | |||||||
\(908\) | 7.26585e7 | 2.92463 | ||||||||
\(909\) | −2.01985e6 | −0.0810792 | ||||||||
\(910\) | 6.44272e7 | 2.57909 | ||||||||
\(911\) | 4.37194e7 | 1.74533 | 0.872666 | − | 0.488317i | \(-0.162389\pi\) | ||||
0.872666 | + | 0.488317i | \(0.162389\pi\) | |||||||
\(912\) | −3.62086e7 | −1.44154 | ||||||||
\(913\) | 1.91680e7 | 0.761025 | ||||||||
\(914\) | −6.94331e6 | −0.274917 | ||||||||
\(915\) | 1.32796e7 | 0.524362 | ||||||||
\(916\) | −4.94686e7 | −1.94801 | ||||||||
\(917\) | 1.13566e7 | 0.445990 | ||||||||
\(918\) | 2.47541e6 | 0.0969485 | ||||||||
\(919\) | −3.62009e7 | −1.41394 | −0.706969 | − | 0.707245i | \(-0.749938\pi\) | ||||
−0.706969 | + | 0.707245i | \(0.749938\pi\) | |||||||
\(920\) | 1.30701e8 | 5.09106 | ||||||||
\(921\) | −1.14840e7 | −0.446112 | ||||||||
\(922\) | 2.84937e6 | 0.110388 | ||||||||
\(923\) | −4.62128e7 | −1.78549 | ||||||||
\(924\) | −1.38956e7 | −0.535425 | ||||||||
\(925\) | 2.40940e7 | 0.925881 | ||||||||
\(926\) | −5.55176e7 | −2.12767 | ||||||||
\(927\) | −1.08555e7 | −0.414907 | ||||||||
\(928\) | −3.81709e7 | −1.45500 | ||||||||
\(929\) | 2.73689e7 | 1.04044 | 0.520221 | − | 0.854032i | \(-0.325850\pi\) | ||||
0.520221 | + | 0.854032i | \(0.325850\pi\) | |||||||
\(930\) | −1.84797e7 | −0.700628 | ||||||||
\(931\) | 9.94715e6 | 0.376118 | ||||||||
\(932\) | 9.61563e7 | 3.62608 | ||||||||
\(933\) | −1.17195e7 | −0.440762 | ||||||||
\(934\) | 3.82097e6 | 0.143320 | ||||||||
\(935\) | −6.39136e6 | −0.239092 | ||||||||
\(936\) | −1.93306e7 | −0.721199 | ||||||||
\(937\) | 4.36536e7 | 1.62432 | 0.812158 | − | 0.583437i | \(-0.198292\pi\) | ||||
0.812158 | + | 0.583437i | \(0.198292\pi\) | |||||||
\(938\) | 1.21803e7 | 0.452014 | ||||||||
\(939\) | −2.13850e7 | −0.791491 | ||||||||
\(940\) | 4.80663e7 | 1.77428 | ||||||||
\(941\) | 9.38560e6 | 0.345532 | 0.172766 | − | 0.984963i | \(-0.444730\pi\) | ||||
0.172766 | + | 0.984963i | \(0.444730\pi\) | |||||||
\(942\) | −9.97564e6 | −0.366280 | ||||||||
\(943\) | 1.31146e7 | 0.480260 | ||||||||
\(944\) | 6.63179e6 | 0.242215 | ||||||||
\(945\) | −7.95823e6 | −0.289893 | ||||||||
\(946\) | −4.57557e7 | −1.66233 | ||||||||
\(947\) | 1.33282e7 | 0.482942 | 0.241471 | − | 0.970408i | \(-0.422370\pi\) | ||||
0.241471 | + | 0.970408i | \(0.422370\pi\) | |||||||
\(948\) | −3.74994e7 | −1.35520 | ||||||||
\(949\) | −1.28147e7 | −0.461893 | ||||||||
\(950\) | 1.45170e8 | 5.21876 | ||||||||
\(951\) | 2.37307e7 | 0.850864 | ||||||||
\(952\) | 1.51019e7 | 0.540057 | ||||||||
\(953\) | 3.84674e7 | 1.37202 | 0.686010 | − | 0.727592i | \(-0.259361\pi\) | ||||
0.686010 | + | 0.727592i | \(0.259361\pi\) | |||||||
\(954\) | −1.51319e7 | −0.538297 | ||||||||
\(955\) | −9.77145e7 | −3.46697 | ||||||||
\(956\) | −9.22053e7 | −3.26296 | ||||||||
\(957\) | −1.06596e7 | −0.376236 | ||||||||
\(958\) | 5.37643e6 | 0.189269 | ||||||||
\(959\) | −4.35015e7 | −1.52742 | ||||||||
\(960\) | −2.55727e6 | −0.0895567 | ||||||||
\(961\) | −2.45315e7 | −0.856871 | ||||||||
\(962\) | −2.11390e7 | −0.736455 | ||||||||
\(963\) | 8.65195e6 | 0.300641 | ||||||||
\(964\) | 4.64466e7 | 1.60976 | ||||||||
\(965\) | −300363. | −0.0103831 | ||||||||
\(966\) | −3.22341e7 | −1.11141 | ||||||||
\(967\) | −4.34724e7 | −1.49502 | −0.747511 | − | 0.664249i | \(-0.768751\pi\) | ||||
−0.747511 | + | 0.664249i | \(0.768751\pi\) | |||||||
\(968\) | 5.10333e7 | 1.75051 | ||||||||
\(969\) | 6.31507e6 | 0.216057 | ||||||||
\(970\) | 4.98560e7 | 1.70133 | ||||||||
\(971\) | −1.32711e6 | −0.0451710 | −0.0225855 | − | 0.999745i | \(-0.507190\pi\) | ||||
−0.0225855 | + | 0.999745i | \(0.507190\pi\) | |||||||
\(972\) | 4.27734e6 | 0.145214 | ||||||||
\(973\) | 2.63810e7 | 0.893323 | ||||||||
\(974\) | 5.14172e7 | 1.73664 | ||||||||
\(975\) | 3.49625e7 | 1.17785 | ||||||||
\(976\) | −2.83212e7 | −0.951670 | ||||||||
\(977\) | −2.29185e7 | −0.768158 | −0.384079 | − | 0.923300i | \(-0.625481\pi\) | ||||
−0.384079 | + | 0.923300i | \(0.625481\pi\) | |||||||
\(978\) | −1.53869e7 | −0.514403 | ||||||||
\(979\) | 1.77876e7 | 0.593146 | ||||||||
\(980\) | 3.38668e7 | 1.12644 | ||||||||
\(981\) | 1.51313e7 | 0.501999 | ||||||||
\(982\) | −4.60146e7 | −1.52271 | ||||||||
\(983\) | 5.50750e7 | 1.81790 | 0.908952 | − | 0.416900i | \(-0.136884\pi\) | ||||
0.908952 | + | 0.416900i | \(0.136884\pi\) | |||||||
\(984\) | −1.53070e7 | −0.503969 | ||||||||
\(985\) | 4.13521e7 | 1.35802 | ||||||||
\(986\) | 2.07527e7 | 0.679801 | ||||||||
\(987\) | −6.61756e6 | −0.216224 | ||||||||
\(988\) | −8.83399e7 | −2.87915 | ||||||||
\(989\) | −7.36187e7 | −2.39330 | ||||||||
\(990\) | −1.59226e7 | −0.516327 | ||||||||
\(991\) | 5.09544e7 | 1.64815 | 0.824077 | − | 0.566478i | \(-0.191694\pi\) | ||||
0.824077 | + | 0.566478i | \(0.191694\pi\) | |||||||
\(992\) | 1.26429e7 | 0.407913 | ||||||||
\(993\) | 3.10527e6 | 0.0999370 | ||||||||
\(994\) | 8.99432e7 | 2.88737 | ||||||||
\(995\) | 9.95700e7 | 3.18839 | ||||||||
\(996\) | −6.44816e7 | −2.05962 | ||||||||
\(997\) | −3.69215e7 | −1.17636 | −0.588181 | − | 0.808729i | \(-0.700156\pi\) | ||||
−0.588181 | + | 0.808729i | \(0.700156\pi\) | |||||||
\(998\) | −4.43198e7 | −1.40855 | ||||||||
\(999\) | 2.61114e6 | 0.0827784 |
(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 | 177.6.a.a.1.1 | ✓ | 11 | |
3.2 | odd | 2 | 531.6.a.b.1.11 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.6.a.a.1.1 | ✓ | 11 | 1.1 | even | 1 | trivial | |
531.6.a.b.1.11 | 11 | 3.2 | odd | 2 |