Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,6,Mod(1,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("320.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.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: | \(51.3228223402\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.39180.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 36x - 24 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 160) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-5.11788\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 18.4715 | 1.18495 | 0.592474 | − | 0.805590i | \(-0.298151\pi\) | ||||
0.592474 | + | 0.805590i | \(0.298151\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 121.899 | 0.940275 | 0.470138 | − | 0.882593i | \(-0.344204\pi\) | ||||
0.470138 | + | 0.882593i | \(0.344204\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 98.1968 | 0.404102 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 438.282 | 1.09213 | 0.546063 | − | 0.837744i | \(-0.316126\pi\) | ||||
0.546063 | + | 0.837744i | \(0.316126\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 758.285 | 1.24444 | 0.622220 | − | 0.782842i | \(-0.286231\pi\) | ||||
0.622220 | + | 0.782842i | \(0.286231\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 461.788 | 0.529925 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1534.86 | −1.28809 | −0.644044 | − | 0.764989i | \(-0.722744\pi\) | ||||
−0.644044 | + | 0.764989i | \(0.722744\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −75.8518 | −0.0482039 | −0.0241019 | − | 0.999710i | \(-0.507673\pi\) | ||||
−0.0241019 | + | 0.999710i | \(0.507673\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2251.66 | 1.11418 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3694.27 | 1.45616 | 0.728079 | − | 0.685493i | \(-0.240413\pi\) | ||||
0.728079 | + | 0.685493i | \(0.240413\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2674.73 | −0.706108 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6323.09 | −1.39616 | −0.698079 | − | 0.716021i | \(-0.745961\pi\) | ||||
−0.698079 | + | 0.716021i | \(0.745961\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2691.35 | 0.502998 | 0.251499 | − | 0.967857i | \(-0.419076\pi\) | ||||
0.251499 | + | 0.967857i | \(0.419076\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8095.74 | 1.29411 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3047.47 | 0.420504 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7252.19 | 0.870893 | 0.435446 | − | 0.900215i | \(-0.356591\pi\) | ||||
0.435446 | + | 0.900215i | \(0.356591\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 14006.7 | 1.47460 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4913.34 | 0.456475 | 0.228238 | − | 0.973605i | \(-0.426704\pi\) | ||||
0.228238 | + | 0.973605i | \(0.426704\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2533.81 | −0.208979 | −0.104490 | − | 0.994526i | \(-0.533321\pi\) | ||||
−0.104490 | + | 0.994526i | \(0.533321\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2454.92 | 0.180720 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11380.6 | 0.751487 | 0.375743 | − | 0.926724i | \(-0.377387\pi\) | ||||
0.375743 | + | 0.926724i | \(0.377387\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1947.64 | −0.115882 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −28351.1 | −1.52632 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −29442.3 | −1.43973 | −0.719866 | − | 0.694113i | \(-0.755797\pi\) | ||||
−0.719866 | + | 0.694113i | \(0.755797\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10957.1 | 0.488413 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1401.10 | −0.0571191 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5681.08 | 0.212472 | 0.106236 | − | 0.994341i | \(-0.466120\pi\) | ||||
0.106236 | + | 0.994341i | \(0.466120\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 48039.8 | 1.65301 | 0.826507 | − | 0.562926i | \(-0.190324\pi\) | ||||
0.826507 | + | 0.562926i | \(0.190324\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11970.1 | 0.379967 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 18957.1 | 0.556531 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −39570.6 | −1.07693 | −0.538463 | − | 0.842649i | \(-0.680995\pi\) | ||||
−0.538463 | + | 0.842649i | \(0.680995\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 68238.7 | 1.72547 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12622.3 | 0.297161 | 0.148581 | − | 0.988900i | \(-0.452530\pi\) | ||||
0.148581 | + | 0.988900i | \(0.452530\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 57959.2 | 1.27296 | 0.636481 | − | 0.771292i | \(-0.280389\pi\) | ||||
0.636481 | + | 0.771292i | \(0.280389\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 11544.7 | 0.236990 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 53426.2 | 1.02690 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −29504.0 | −0.531879 | −0.265939 | − | 0.963990i | \(-0.585682\pi\) | ||||
−0.265939 | + | 0.963990i | \(0.585682\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −73268.2 | −1.24080 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −112209. | −1.78786 | −0.893928 | − | 0.448211i | \(-0.852061\pi\) | ||||
−0.893928 | + | 0.448211i | \(0.852061\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −38371.4 | −0.576050 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −116797. | −1.65437 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 66969.5 | 0.896194 | 0.448097 | − | 0.893985i | \(-0.352102\pi\) | ||||
0.448097 | + | 0.893985i | \(0.352102\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 92434.2 | 1.17012 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 49713.4 | 0.596027 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1896.30 | −0.0215574 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 131833. | 1.42264 | 0.711322 | − | 0.702867i | \(-0.248097\pi\) | ||||
0.711322 | + | 0.702867i | \(0.248097\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 43037.9 | 0.441330 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 30688.2 | 0.299343 | 0.149671 | − | 0.988736i | \(-0.452178\pi\) | ||||
0.149671 | + | 0.988736i | \(0.452178\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −140744. | −1.30718 | −0.653591 | − | 0.756848i | \(-0.726738\pi\) | ||||
−0.653591 | + | 0.756848i | \(0.726738\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 56291.5 | 0.498275 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14196.9 | −0.119876 | −0.0599381 | − | 0.998202i | \(-0.519090\pi\) | ||||
−0.0599381 | + | 0.998202i | \(0.519090\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9873.09 | −0.0795952 | −0.0397976 | − | 0.999208i | \(-0.512671\pi\) | ||||
−0.0397976 | + | 0.999208i | \(0.512671\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 133959. | 1.03196 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 245866. | 1.81135 | 0.905675 | − | 0.423973i | \(-0.139365\pi\) | ||||
0.905675 | + | 0.423973i | \(0.139365\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 92356.7 | 0.651214 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 74461.2 | 0.502881 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −187097. | −1.21116 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 31040.5 | 0.192737 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 90756.9 | 0.540900 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 88403.3 | 0.486361 | 0.243181 | − | 0.969981i | \(-0.421809\pi\) | ||||
0.243181 | + | 0.969981i | \(0.421809\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −46803.3 | −0.247630 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 274297. | 1.39651 | 0.698253 | − | 0.715851i | \(-0.253961\pi\) | ||||
0.698253 | + | 0.715851i | \(0.253961\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9246.26 | −0.0453249 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −66868.4 | −0.315781 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −309183. | −1.40739 | −0.703694 | − | 0.710503i | \(-0.748467\pi\) | ||||
−0.703694 | + | 0.710503i | \(0.748467\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 381380. | 1.67425 | 0.837125 | − | 0.547011i | \(-0.184235\pi\) | ||||
0.837125 | + | 0.547011i | \(0.184235\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 210217. | 0.890473 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 332343. | 1.35908 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −158077. | −0.624381 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −35975.8 | −0.137315 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 101742. | 0.375436 | 0.187718 | − | 0.982223i | \(-0.439891\pi\) | ||||
0.187718 | + | 0.982223i | \(0.439891\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 338843. | 1.20936 | 0.604680 | − | 0.796469i | \(-0.293301\pi\) | ||||
0.604680 | + | 0.796469i | \(0.293301\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −150718. | −0.520519 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 67283.9 | 0.224948 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −101650. | −0.329123 | −0.164561 | − | 0.986367i | \(-0.552621\pi\) | ||||
−0.164561 | + | 0.986367i | \(0.552621\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −543843. | −1.70601 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 450327. | 1.36919 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −214136. | −0.631279 | −0.315640 | − | 0.948879i | \(-0.602219\pi\) | ||||
−0.315640 | + | 0.948879i | \(0.602219\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 202393. | 0.578744 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −606370. | −1.68247 | −0.841234 | − | 0.540672i | \(-0.818170\pi\) | ||||
−0.841234 | + | 0.540672i | \(0.818170\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 203703. | 0.548633 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7448.41 | −0.0194793 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 426958. | 1.08460 | 0.542301 | − | 0.840184i | \(-0.317553\pi\) | ||||
0.542301 | + | 0.840184i | \(0.317553\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 76186.9 | 0.188055 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 104938. | 0.251768 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −682764. | −1.59271 | −0.796357 | − | 0.604826i | \(-0.793243\pi\) | ||||
−0.796357 | + | 0.604826i | \(0.793243\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −725666. | −1.64642 | −0.823209 | − | 0.567738i | \(-0.807819\pi\) | ||||
−0.823209 | + | 0.567738i | \(0.807819\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 887368. | 1.95874 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 181305. | 0.389475 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −672700. | −1.40675 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −326047. | −0.663936 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 662000. | 1.31303 | 0.656515 | − | 0.754313i | \(-0.272030\pi\) | ||||
0.656515 | + | 0.754313i | \(0.272030\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −481557. | −0.930582 | −0.465291 | − | 0.885158i | \(-0.654050\pi\) | ||||
−0.465291 | + | 0.885158i | \(0.654050\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 350167. | 0.659460 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −569264. | −1.04508 | −0.522538 | − | 0.852616i | \(-0.675015\pi\) | ||||
−0.522538 | + | 0.852616i | \(0.675015\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −850151. | −1.52182 | −0.760911 | − | 0.648857i | \(-0.775247\pi\) | ||||
−0.760911 | + | 0.648857i | \(0.775247\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −730930. | −1.27610 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −770778. | −1.31277 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 122834. | 0.204142 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 362765. | 0.588437 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −33244.5 | −0.0526447 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −285552. | −0.441548 | −0.220774 | − | 0.975325i | \(-0.570858\pi\) | ||||
−0.220774 | + | 0.975325i | \(0.570858\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 233153. | 0.352120 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −63345.3 | −0.0934583 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 328073. | 0.472957 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.07059e6 | 1.50839 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.16386e6 | −1.60295 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 279669. | 0.376602 | 0.188301 | − | 0.982111i | \(-0.439702\pi\) | ||||
0.188301 | + | 0.982111i | \(0.439702\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 61373.0 | 0.0808204 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.27295e6 | −1.63964 | −0.819819 | − | 0.572623i | \(-0.805926\pi\) | ||||
−0.819819 | + | 0.572623i | \(0.805926\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −584351. | −0.736352 | −0.368176 | − | 0.929756i | \(-0.620018\pi\) | ||||
−0.368176 | + | 0.929756i | \(0.620018\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 986863. | 1.21682 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −658722. | −0.794900 | −0.397450 | − | 0.917624i | \(-0.630105\pi\) | ||||
−0.397450 | + | 0.917624i | \(0.630105\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 284515. | 0.336075 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −544983. | −0.630248 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −664166. | −0.752111 | −0.376055 | − | 0.926597i | \(-0.622720\pi\) | ||||
−0.376055 | + | 0.926597i | \(0.622720\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −192140. | −0.213095 | −0.106548 | − | 0.994308i | \(-0.533980\pi\) | ||||
−0.106548 | + | 0.994308i | \(0.533980\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −703414. | −0.764180 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −48690.9 | −0.0518242 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −57517.3 | −0.0599869 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.07267e6 | −2.11852 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.20021e6 | −1.20246 | −0.601231 | − | 0.799075i | \(-0.705323\pi\) | ||||
−0.601231 | + | 0.799075i | \(0.705323\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.61913e6 | 1.59031 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −708778. | −0.682589 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −494440. | −0.466961 | −0.233481 | − | 0.972361i | \(-0.575012\pi\) | ||||
−0.233481 | + | 0.972361i | \(0.575012\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 884034. | 0.818879 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −620907. | −0.564190 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 535899. | 0.477742 | 0.238871 | − | 0.971051i | \(-0.423223\pi\) | ||||
0.238871 | + | 0.971051i | \(0.423223\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −736056. | −0.643867 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.23703e6 | 1.06194 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 886621. | 0.747063 | 0.373532 | − | 0.927617i | \(-0.378147\pi\) | ||||
0.373532 | + | 0.927617i | \(0.378147\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.31305e6 | −1.08607 | −0.543036 | − | 0.839710i | \(-0.682725\pi\) | ||||
−0.543036 | + | 0.839710i | \(0.682725\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.70740e6 | 1.38653 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 273927. | 0.218425 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −175211. | −0.137203 | −0.0686013 | − | 0.997644i | \(-0.521854\pi\) | ||||
−0.0686013 | + | 0.997644i | \(0.521854\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 264282. | 0.203263 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.78398e6 | −1.34779 | −0.673897 | − | 0.738826i | \(-0.735381\pi\) | ||||
−0.673897 | + | 0.738826i | \(0.735381\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.98478e6 | −1.47315 | −0.736573 | − | 0.676358i | \(-0.763557\pi\) | ||||
−0.736573 | + | 0.676358i | \(0.763557\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −35027.4 | −0.0255444 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 598931. | 0.429212 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 935925. | 0.659168 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.43516e6 | 1.68576 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.44146e6 | −1.66143 | −0.830714 | − | 0.556700i | \(-0.812067\pi\) | ||||
−0.830714 | + | 0.556700i | \(0.812067\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 142027. | 0.0950202 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.17229e6 | −0.771158 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.80131e6 | 1.81210 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −308869. | −0.196498 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 566858. | 0.354706 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.20100e6 | 0.739251 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.53943e6 | 1.53777 | 0.768883 | − | 0.639390i | \(-0.220813\pi\) | ||||
0.768883 | + | 0.639390i | \(0.220813\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.59975e6 | −1.54894 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.86583e6 | 1.09388 | 0.546941 | − | 0.837171i | \(-0.315792\pi\) | ||||
0.546941 | + | 0.837171i | \(0.315792\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.17459e6 | 1.25463 | 0.627316 | − | 0.778765i | \(-0.284153\pi\) | ||||
0.627316 | + | 0.778765i | \(0.284153\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 299252. | 0.169926 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.48421e6 | 0.829557 | 0.414779 | − | 0.909922i | \(-0.363859\pi\) | ||||
0.414779 | + | 0.909922i | \(0.363859\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.77130e6 | −1.52478 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −262238. | −0.142047 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 116422. | 0.0620908 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 473928. | 0.248888 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −182371. | −0.0943162 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.38729e6 | 0.706604 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.02880e6 | −1.01782 | −0.508908 | − | 0.860821i | \(-0.669950\pi\) | ||||
−0.508908 | + | 0.860821i | \(0.669950\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 712141. | 0.351930 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −989266. | −0.481616 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.34355e6 | −0.644435 | −0.322218 | − | 0.946666i | \(-0.604428\pi\) | ||||
−0.322218 | + | 0.946666i | \(0.604428\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.54152e6 | 2.14636 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.17957e6 | 0.549337 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.28617e6 | −1.04924 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.70597e6 | 0.771655 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.52038e6 | −0.677843 | −0.338921 | − | 0.940815i | \(-0.610062\pi\) | ||||
−0.338921 | + | 0.940815i | \(0.610062\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.80948e6 | 0.795224 | 0.397612 | − | 0.917554i | \(-0.369839\pi\) | ||||
0.397612 | + | 0.917554i | \(0.369839\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.02821e6 | −0.878710 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.48843e6 | 1.06289 | 0.531446 | − | 0.847092i | \(-0.321649\pi\) | ||||
0.531446 | + | 0.847092i | \(0.321649\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 315557. | 0.132894 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.45597e6 | −1.43516 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.44154e6 | 0.590324 | 0.295162 | − | 0.955447i | \(-0.404626\pi\) | ||||
0.295162 | + | 0.955447i | \(0.404626\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.47035e6 | −0.997676 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 573365. | 0.228383 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.44898e6 | 0.569286 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 257353. | 0.0997388 | 0.0498694 | − | 0.998756i | \(-0.484119\pi\) | ||||
0.0498694 | + | 0.998756i | \(0.484119\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 482474. | 0.184463 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.58898e6 | −1.35374 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.55163e6 | 1.69393 | 0.846964 | − | 0.531651i | \(-0.178428\pi\) | ||||
0.846964 | + | 0.531651i | \(0.178428\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 288617. | 0.105985 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.79471e6 | −1.73743 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.96634e6 | −1.06077 | −0.530387 | − | 0.847756i | \(-0.677953\pi\) | ||||
−0.530387 | + | 0.847756i | \(0.677953\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.63294e6 | 0.576313 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.57107e6 | 1.24395 | 0.621973 | − | 0.783039i | \(-0.286331\pi\) | ||||
0.621973 | + | 0.783039i | \(0.286331\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.33565e6 | 0.459243 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −248812. | −0.0844489 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 881685. | 0.295420 | 0.147710 | − | 0.989031i | \(-0.452810\pi\) | ||||
0.147710 | + | 0.989031i | \(0.452810\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.67017e6 | −1.87566 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.06668e6 | 1.65479 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −737599. | −0.237863 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.56117e6 | 0.815570 | 0.407785 | − | 0.913078i | \(-0.366301\pi\) | ||||
0.407785 | + | 0.913078i | \(0.366301\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −170792. | −0.0537077 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.37596e6 | −1.04842 | −0.524211 | − | 0.851589i | \(-0.675640\pi\) | ||||
−0.524211 | + | 0.851589i | \(0.675640\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.04081e6 | 0.625952 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.83171e6 | −0.554904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.17851e6 | 0.951124 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.56437e6 | −0.758006 | −0.379003 | − | 0.925395i | \(-0.623733\pi\) | ||||
−0.379003 | + | 0.925395i | \(0.623733\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.71107e6 | −1.66768 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 692518. | 0.199782 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.80522e6 | −0.799553 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.04466e6 | 1.98390 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.64881e6 | −1.85016 | −0.925079 | − | 0.379775i | \(-0.876001\pi\) | ||||
−0.925079 | + | 0.379775i | \(0.876001\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.98840e6 | −1.37169 | −0.685846 | − | 0.727747i | \(-0.740568\pi\) | ||||
−0.685846 | + | 0.727747i | \(0.740568\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.11754e6 | 0.303677 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −959285. | −0.257617 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.85600e6 | 1.55429 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.13888e6 | 1.61045 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 802200. | 0.208012 | 0.104006 | − | 0.994577i | \(-0.466834\pi\) | ||||
0.104006 | + | 0.994577i | \(0.466834\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.80978e6 | 1.48916 | 0.744578 | − | 0.667535i | \(-0.232651\pi\) | ||||
0.744578 | + | 0.667535i | \(0.232651\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.91993e6 | −0.739859 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −280217. | −0.0701925 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 585972. | 0.145116 | 0.0725581 | − | 0.997364i | \(-0.476884\pi\) | ||||
0.0725581 | + | 0.997364i | \(0.476884\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −191252. | −0.0468283 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.41675e6 | −1.06929 | −0.534643 | − | 0.845078i | \(-0.679554\pi\) | ||||
−0.534643 | + | 0.845078i | \(0.679554\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.67424e6 | 0.400790 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.87934e6 | 0.444872 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.28408e6 | 0.534681 | 0.267340 | − | 0.963602i | \(-0.413855\pi\) | ||||
0.267340 | + | 0.963602i | \(0.413855\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.15343e6 | 0.498528 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.25893e6 | 1.43303 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.31086e6 | 0.523292 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.43086e6 | 0.768444 | 0.384222 | − | 0.923241i | \(-0.374470\pi\) | ||||
0.384222 | + | 0.923241i | \(0.374470\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.10533e6 | 0.909529 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −674699. | −0.147862 | −0.0739311 | − | 0.997263i | \(-0.523555\pi\) | ||||
−0.0739311 | + | 0.997263i | \(0.523555\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.78627e6 | 1.25443 | 0.627215 | − | 0.778846i | \(-0.284195\pi\) | ||||
0.627215 | + | 0.778846i | \(0.284195\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.24283e6 | 0.266551 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.88097e6 | −1.46002 | −0.730008 | − | 0.683439i | \(-0.760484\pi\) | ||||
−0.730008 | + | 0.683439i | \(0.760484\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.82362e6 | −1.01261 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.87763e6 | −0.389993 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.11052e6 | −0.228231 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −47407.4 | −0.00964078 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.89114e6 | −0.581798 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.94000e6 | 0.983757 | 0.491879 | − | 0.870664i | \(-0.336310\pi\) | ||||
0.491879 | + | 0.870664i | \(0.336310\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.49923e6 | 1.08377 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.31823e6 | 1.62242 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.29583e6 | 0.636225 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.21802e6 | 0.996973 | 0.498487 | − | 0.866897i | \(-0.333889\pi\) | ||||
0.498487 | + | 0.866897i | \(0.333889\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.95542e6 | −0.748033 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.20805e6 | 0.787730 | 0.393865 | − | 0.919168i | \(-0.371138\pi\) | ||||
0.393865 | + | 0.919168i | \(0.371138\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.70503e6 | 1.79837 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.07595e6 | 0.197369 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.53864e6 | 0.279413 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.74013e6 | −1.39154 | −0.695771 | − | 0.718263i | \(-0.744937\pi\) | ||||
−0.695771 | + | 0.718263i | \(0.744937\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.12006e7 | −1.99364 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.20893e6 | −1.09420 | −0.547100 | − | 0.837067i | \(-0.684268\pi\) | ||||
−0.547100 | + | 0.837067i | \(0.684268\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 767206. | 0.133870 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.76271e6 | 0.650101 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.43892e6 | −1.44375 | −0.721876 | − | 0.692022i | \(-0.756720\pi\) | ||||
−0.721876 | + | 0.692022i | \(0.756720\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.06517e6 | 1.19693 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 202883. | 0.0340372 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.51859e6 | −0.584590 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.98793e6 | 0.820717 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.88657e6 | 1.28520 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.61888e6 | −1.06829 | −0.534146 | − | 0.845392i | \(-0.679367\pi\) | ||||
−0.534146 | + | 0.845392i | \(0.679367\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.48657e6 | 0.877095 | 0.438548 | − | 0.898708i | \(-0.355493\pi\) | ||||
0.438548 | + | 0.898708i | \(0.355493\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.40729e6 | 0.222835 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.13084e6 | −0.647906 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.21127e6 | 1.12040 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 557864. | 0.0858602 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.72571e6 | 0.568057 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −354922. | −0.0536103 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.26117e7 | −1.88728 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −853614. | −0.126558 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 427673. | 0.0628230 | 0.0314115 | − | 0.999507i | \(-0.490000\pi\) | ||||
0.0314115 | + | 0.999507i | \(0.490000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.34041e7 | −1.95092 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −246827. | −0.0355960 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.94393e6 | 1.27809 | 0.639043 | − | 0.769171i | \(-0.279331\pi\) | ||||
0.639043 | + | 0.769171i | \(0.279331\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.71736e6 | 0.667987 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 479618. | 0.0673002 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.59650e6 | −0.500112 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.34897e6 | 0.461508 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.93887e6 | −1.08423 | −0.542114 | − | 0.840305i | \(-0.682376\pi\) | ||||
−0.542114 | + | 0.840305i | \(0.682376\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.92135e6 | −0.260062 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.24258e7 | −1.66693 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.61543e6 | 0.214792 | 0.107396 | − | 0.994216i | \(-0.465749\pi\) | ||||
0.107396 | + | 0.994216i | \(0.465749\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.14665e6 | 0.810060 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.93132e6 | −1.16670 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.97353e6 | 0.255543 | 0.127771 | − | 0.991804i | \(-0.459218\pi\) | ||||
0.127771 | + | 0.991804i | \(0.459218\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.18140e6 | 0.921762 | 0.460881 | − | 0.887462i | \(-0.347533\pi\) | ||||
0.460881 | + | 0.887462i | \(0.347533\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.22281e7 | 1.55587 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.30892e6 | 0.291232 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.61498e6 | −1.20229 | −0.601145 | − | 0.799140i | \(-0.705288\pi\) | ||||
−0.601145 | + | 0.799140i | \(0.705288\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.89509e6 | −1.10269 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.36782e7 | −1.68108 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.29040e7 | −1.57237 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.86153e6 | 0.224895 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.66522e6 | −0.319255 | −0.159627 | − | 0.987177i | \(-0.551029\pi\) | ||||
−0.159627 | + | 0.987177i | \(0.551029\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −204144. | −0.0242465 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.05152e7 | −1.23836 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.83235e6 | 0.681093 | 0.340547 | − | 0.940228i | \(-0.389388\pi\) | ||||
0.340547 | + | 0.940228i | \(0.389388\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.67743e6 | −0.541646 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.57036e7 | −1.80328 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.39890e6 | 0.728683 | 0.364341 | − | 0.931265i | \(-0.381294\pi\) | ||||
0.364341 | + | 0.931265i | \(0.381294\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.00505e7 | 1.13502 | 0.567509 | − | 0.823367i | \(-0.307907\pi\) | ||||
0.567509 | + | 0.823367i | \(0.307907\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.88571e6 | −0.435188 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 776012. | 0.0861946 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.83636e6 | 0.202295 | 0.101148 | − | 0.994871i | \(-0.467749\pi\) | ||||
0.101148 | + | 0.994871i | \(0.467749\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.42374e7 | −1.55557 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.62976e6 | 0.935181 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.33155e7 | −1.43122 | −0.715611 | − | 0.698499i | \(-0.753852\pi\) | ||||
−0.715611 | + | 0.698499i | \(0.753852\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.26892e6 | 0.241898 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.09296e6 | 0.327085 | 0.163543 | − | 0.986536i | \(-0.447708\pi\) | ||||
0.163543 | + | 0.986536i | \(0.447708\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.64802e6 | 1.01207 | 0.506036 | − | 0.862512i | \(-0.331110\pi\) | ||||
0.506036 | + | 0.862512i | \(0.331110\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.88118e6 | −1.02821 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.16352e6 | 0.842669 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −614077. | −0.0623812 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.11311e7 | −1.12179 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.72048e7 | −1.72019 | −0.860096 | − | 0.510132i | \(-0.829597\pi\) | ||||
−0.860096 | + | 0.510132i | \(0.829597\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.27457e6 | −0.523212 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.21008e6 | 0.217507 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.47686e6 | −0.144209 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.23947e6 | 0.120083 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.86292e6 | 0.179081 | 0.0895403 | − | 0.995983i | \(-0.471460\pi\) | ||||
0.0895403 | + | 0.995983i | \(0.471460\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.39819e7 | 1.33364 | 0.666821 | − | 0.745218i | \(-0.267655\pi\) | ||||
0.666821 | + | 0.745218i | \(0.267655\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.17008e6 | −0.110743 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.28310e7 | −1.20504 | −0.602520 | − | 0.798104i | \(-0.705837\pi\) | ||||
−0.602520 | + | 0.798104i | \(0.705837\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.48992e6 | 0.232045 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.06001e6 | 0.560430 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −423926. | −0.0389051 | −0.0194526 | − | 0.999811i | \(-0.506192\pi\) | ||||
−0.0194526 | + | 0.999811i | \(0.506192\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.85743e6 | 0.624537 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.69141e6 | 0.514406 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.64781e7 | −1.47807 | −0.739035 | − | 0.673668i | \(-0.764718\pi\) | ||||
−0.739035 | + | 0.673668i | \(0.764718\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.71556e7 | 1.52723 | 0.763613 | − | 0.645674i | \(-0.223423\pi\) | ||||
0.763613 | + | 0.645674i | \(0.223423\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.14982e7 | −1.89941 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −231157. | −0.0202699 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.33592e7 | −2.03303 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.16592e6 | 0.446254 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.10550e7 | 1.80530 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.24172e7 | 1.90785 | 0.953923 | − | 0.300053i | \(-0.0970043\pi\) | ||||
0.953923 | + | 0.300053i | \(0.0970043\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.67171e6 | −0.141222 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.63329e6 | 0.472379 | 0.236190 | − | 0.971707i | \(-0.424101\pi\) | ||||
0.236190 | + | 0.971707i | \(0.424101\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.60704e7 | 1.33768 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.35134e7 | −1.94289 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.27876e6 | 0.104891 | 0.0524453 | − | 0.998624i | \(-0.483298\pi\) | ||||
0.0524453 | + | 0.998624i | \(0.483298\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.72957e6 | −0.629403 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.07939e7 | −0.872539 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.23256e7 | −1.79166 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 712345. | 0.0567539 | 0.0283769 | − | 0.999597i | \(-0.490966\pi\) | ||||
0.0283769 | + | 0.999597i | \(0.490966\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.24628e6 | 0.414972 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.53449e6 | 0.748748 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.54127e6 | −0.587980 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.21676e7 | −0.941915 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.89586e6 | −0.606882 | −0.303441 | − | 0.952850i | \(-0.598136\pi\) | ||||
−0.303441 | + | 0.952850i | \(0.598136\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −550091. | −0.0419804 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.25543e6 | 0.398231 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.74087e6 | 0.281464 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 812363. | 0.0606924 | 0.0303462 | − | 0.999539i | \(-0.490339\pi\) | ||||
0.0303462 | + | 0.999539i | \(0.490339\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.89719e6 | −0.214933 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.94258e6 | 0.732446 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.30858e6 | 0.607801 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.22681e7 | −0.891212 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.46975e7 | −1.06028 | −0.530142 | − | 0.847909i | \(-0.677861\pi\) | ||||
−0.530142 | + | 0.847909i | \(0.677861\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.71565e7 | −1.22911 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.54911e6 | −0.252507 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.95193e6 | −0.279231 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 946478. | 0.0664163 | 0.0332081 | − | 0.999448i | \(-0.489428\pi\) | ||||
0.0332081 | + | 0.999448i | \(0.489428\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.81105e6 | 0.335290 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.88903e6 | 0.269183 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.33370e6 | −0.160430 | −0.0802150 | − | 0.996778i | \(-0.525561\pi\) | ||||
−0.0802150 | + | 0.996778i | \(0.525561\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −899394. | −0.0614090 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.73431e7 | −1.17614 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.17842e7 | −0.793757 | −0.396878 | − | 0.917871i | \(-0.629906\pi\) | ||||
−0.396878 | + | 0.917871i | \(0.629906\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.06243e6 | −0.0710813 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.02537e7 | 0.681413 | 0.340706 | − | 0.940170i | \(-0.389334\pi\) | ||||
0.340706 | + | 0.940170i | \(0.389334\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.54356e6 | 0.167900 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.10186e7 | −0.722476 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.73058e6 | −0.112717 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.02684e7 | 1.31135 | 0.655676 | − | 0.755043i | \(-0.272384\pi\) | ||||
0.655676 | + | 0.755043i | \(0.272384\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.21696e7 | −1.42486 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.47106e6 | 0.540842 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.54478e7 | 0.979776 | 0.489888 | − | 0.871785i | \(-0.337038\pi\) | ||||
0.489888 | + | 0.871785i | \(0.337038\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.99078e7 | 1.88443 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.68238e7 | −1.05308 | −0.526540 | − | 0.850150i | \(-0.676511\pi\) | ||||
−0.526540 | + | 0.850150i | \(0.676511\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.20352e6 | −0.0748414 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.76795e6 | −0.232783 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.30788e6 | 0.264408 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.25563e7 | 1.37547 | 0.687737 | − | 0.725960i | \(-0.258604\pi\) | ||||
0.687737 | + | 0.725960i | \(0.258604\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.13305e6 | −0.553325 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.87038e6 | 0.353360 | 0.176680 | − | 0.984268i | \(-0.443464\pi\) | ||||
0.176680 | + | 0.984268i | \(0.443464\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.68210e6 | 0.100600 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.63294e7 | 0.970329 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −372686. | −0.0220039 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.53212e6 | 0.324537 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.69126e7 | 0.985838 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.54125e6 | −0.147188 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.45154e6 | 0.141092 | 0.0705459 | − | 0.997509i | \(-0.477526\pi\) | ||||
0.0705459 | + | 0.997509i | \(0.477526\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.89886e6 | 0.566099 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.99708e7 | 1.70317 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.64279e7 | 2.05708 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.35961e7 | −0.762949 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.18622e7 | 1.21913 | 0.609564 | − | 0.792737i | \(-0.291345\pi\) | ||||
0.609564 | + | 0.792737i | \(0.291345\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.74676e7 | −0.967980 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.57619e6 | 0.362154 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.54025e7 | 1.39023 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.12582e7 | 0.612320 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.63772e7 | 0.885231 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.66048e7 | 1.42919 | 0.714593 | − | 0.699541i | \(-0.246612\pi\) | ||||
0.714593 | + | 0.699541i | \(0.246612\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.44067e7 | 0.769152 | 0.384576 | − | 0.923093i | \(-0.374348\pi\) | ||||
0.384576 | + | 0.923093i | \(0.374348\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.42540e7 | −1.28694 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.35341e6 | −0.282317 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 192194. | 0.0100736 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.07674e6 | 0.472847 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.88597e6 | −0.0976508 | −0.0488254 | − | 0.998807i | \(-0.515548\pi\) | ||||
−0.0488254 | + | 0.998807i | \(0.515548\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.52832e7 | 0.786530 | 0.393265 | − | 0.919425i | \(-0.371346\pi\) | ||||
0.393265 | + | 0.919425i | \(0.371346\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.05984e6 | 0.258822 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.78935e6 | 0.141821 | 0.0709103 | − | 0.997483i | \(-0.477410\pi\) | ||||
0.0709103 | + | 0.997483i | \(0.477410\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.87077e6 | 0.0945440 | 0.0472720 | − | 0.998882i | \(-0.484947\pi\) | ||||
0.0472720 | + | 0.998882i | \(0.484947\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.23641e6 | −0.162578 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.98934e6 | 0.149267 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.51593e7 | −0.752422 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.19866e6 | −0.355171 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.01293e6 | −0.0987244 | −0.0493622 | − | 0.998781i | \(-0.515719\pi\) | ||||
−0.0493622 | + | 0.998781i | \(0.515719\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.94703e7 | 0.949255 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.29527e7 | −1.59706 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.09259e6 | 0.245356 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.78381e6 | 0.181226 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.66618e7 | −1.74560 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.67915e7 | 1.26816 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.09443e7 | −0.515008 | −0.257504 | − | 0.966277i | \(-0.582900\pi\) | ||||
−0.257504 | + | 0.966277i | \(0.582900\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −186210. | −0.00871140 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.17692e7 | −1.01249 | −0.506245 | − | 0.862390i | \(-0.668967\pi\) | ||||
−0.506245 | + | 0.862390i | \(0.668967\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.86741e6 | 0.317549 | 0.158774 | − | 0.987315i | \(-0.449246\pi\) | ||||
0.158774 | + | 0.987315i | \(0.449246\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.10632e7 | 0.508595 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.75635e7 | −0.802755 | −0.401378 | − | 0.915913i | \(-0.631468\pi\) | ||||
−0.401378 | + | 0.915913i | \(0.631468\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.06740e7 | 0.485049 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.72880e7 | 0.781080 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.29311e7 | −0.580878 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.00058e7 | −1.34017 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.29456e7 | 0.574893 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.90467e6 | 0.0841008 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.95517e6 | 0.129743 | 0.0648715 | − | 0.997894i | \(-0.479336\pi\) | ||||
0.0648715 | + | 0.997894i | \(0.479336\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.50975e7 | −1.96870 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.53773e7 | 1.53562 | 0.767811 | − | 0.640676i | \(-0.221346\pi\) | ||||
0.767811 | + | 0.640676i | \(0.221346\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.26106e7 | −0.975912 | −0.487956 | − | 0.872868i | \(-0.662257\pi\) | ||||
−0.487956 | + | 0.872868i | \(0.662257\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.62345e6 | 0.112594 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.57410e6 | −0.365914 | −0.182957 | − | 0.983121i | \(-0.558567\pi\) | ||||
−0.182957 | + | 0.983121i | \(0.558567\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.07763e7 | 0.457314 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.21122e7 | −1.35511 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −863241. | −0.0362246 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.70691e7 | −0.712284 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.17444e7 | 2.14725 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.70177e7 | −0.702265 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.51896e7 | 1.85450 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.70528e6 | −0.232840 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.81416e7 | −0.736301 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.76363e7 | −0.711852 | −0.355926 | − | 0.934514i | \(-0.615834\pi\) | ||||
−0.355926 | + | 0.934514i | \(0.615834\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.01349e6 | 0.120965 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.48438e7 | −0.592585 | −0.296292 | − | 0.955097i | \(-0.595750\pi\) | ||||
−0.296292 | + | 0.955097i | \(0.595750\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.91792e7 | −1.95256 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.21842e7 | 0.875973 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.34365e7 | 1.31310 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −448602. | −0.0175215 | −0.00876077 | − | 0.999962i | \(-0.502789\pi\) | ||||
−0.00876077 | + | 0.999962i | \(0.502789\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.69071e7 | 1.82217 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.57129e6 | 0.369799 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.53262e6 | 0.174179 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.38206e7 | −0.528235 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.11976e6 | 0.0805836 | 0.0402918 | − | 0.999188i | \(-0.487171\pi\) | ||||
0.0402918 | + | 0.999188i | \(0.487171\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 147732. | 0.00558598 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.44647e7 | 1.29619 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.68175e7 | −0.629119 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.54945e6 | 0.206491 | 0.103245 | − | 0.994656i | \(-0.467077\pi\) | ||||
0.103245 | + | 0.994656i | \(0.467077\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.01680e7 | 1.48667 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.00433e6 | −0.221050 | −0.110525 | − | 0.993873i | \(-0.535253\pi\) | ||||
−0.110525 | + | 0.993873i | \(0.535253\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.81512e7 | 0.664701 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.15119e6 | −0.296921 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.19597e7 | 0.433357 | 0.216679 | − | 0.976243i | \(-0.430478\pi\) | ||||
0.216679 | + | 0.976243i | \(0.430478\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.39496e7 | 1.58413 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.74156e7 | 0.982982 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.84885e7 | −1.01610 | −0.508051 | − | 0.861327i | \(-0.669634\pi\) | ||||
−0.508051 | + | 0.861327i | \(0.669634\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.65500e7 | 0.587205 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.11901e7 | −1.80678 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.76891e7 | −1.32333 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.13858e7 | −0.746993 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.39409e6 | −0.0484422 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.20389e7 | −0.416169 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.44173e6 | 0.0839714 | 0.0419857 | − | 0.999118i | \(-0.486632\pi\) | ||||
0.0419857 | + | 0.999118i | \(0.486632\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.15048e6 | 0.0735744 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.63888e7 | −0.898198 | −0.449099 | − | 0.893482i | \(-0.648255\pi\) | ||||
−0.449099 | + | 0.893482i | \(0.648255\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.64898e7 | 1.57426 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.75417e6 | 0.294920 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.67324e6 | −0.223666 | −0.111833 | − | 0.993727i | \(-0.535672\pi\) | ||||
−0.111833 | + | 0.993727i | \(0.535672\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.93516e7 | 0.978756 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −969506. | −0.0321646 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.21646e7 | −0.401528 | −0.200764 | − | 0.979640i | \(-0.564342\pi\) | ||||
−0.200764 | + | 0.979640i | \(0.564342\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.42316e7 | −0.467372 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.56253e7 | 0.837289 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.36057e6 | −0.304307 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.16204e7 | −0.375869 | −0.187935 | − | 0.982182i | \(-0.560179\pi\) | ||||
−0.187935 | + | 0.982182i | \(0.560179\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.74750e7 | −1.20606 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.12538e7 | −0.680579 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.61789e7 | 1.47132 | 0.735658 | − | 0.677354i | \(-0.236873\pi\) | ||||
0.735658 | + | 0.677354i | \(0.236873\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.93977e7 | −0.614944 |
(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 | 320.6.a.x.1.3 | 3 | ||
4.3 | odd | 2 | 320.6.a.y.1.1 | 3 | |||
8.3 | odd | 2 | 160.6.a.f.1.3 | ✓ | 3 | ||
8.5 | even | 2 | 160.6.a.g.1.1 | yes | 3 | ||
40.3 | even | 4 | 800.6.c.k.449.5 | 6 | |||
40.13 | odd | 4 | 800.6.c.j.449.2 | 6 | |||
40.19 | odd | 2 | 800.6.a.o.1.1 | 3 | |||
40.27 | even | 4 | 800.6.c.k.449.2 | 6 | |||
40.29 | even | 2 | 800.6.a.n.1.3 | 3 | |||
40.37 | odd | 4 | 800.6.c.j.449.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.6.a.f.1.3 | ✓ | 3 | 8.3 | odd | 2 | ||
160.6.a.g.1.1 | yes | 3 | 8.5 | even | 2 | ||
320.6.a.x.1.3 | 3 | 1.1 | even | 1 | trivial | ||
320.6.a.y.1.1 | 3 | 4.3 | odd | 2 | |||
800.6.a.n.1.3 | 3 | 40.29 | even | 2 | |||
800.6.a.o.1.1 | 3 | 40.19 | odd | 2 | |||
800.6.c.j.449.2 | 6 | 40.13 | odd | 4 | |||
800.6.c.j.449.5 | 6 | 40.37 | odd | 4 | |||
800.6.c.k.449.2 | 6 | 40.27 | even | 4 | |||
800.6.c.k.449.5 | 6 | 40.3 | even | 4 |