Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,6,Mod(161,320)]
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, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.161");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(51.3228223402\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 343 x^{10} - 696 x^{9} + 44406 x^{8} + 179640 x^{7} - 2401691 x^{6} - 15554592 x^{5} + \cdots + 653157349 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{30} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.5 | ||
Root | \(-7.49748 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.161 |
Dual form | 320.6.d.d.161.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 5.06676i | − 0.325033i | −0.986706 | − | 0.162516i | \(-0.948039\pi\) | ||||
0.986706 | − | 0.162516i | \(-0.0519611\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 25.0000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 250.333 | 1.93096 | 0.965479 | − | 0.260481i | \(-0.0838812\pi\) | ||||
0.965479 | + | 0.260481i | \(0.0838812\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 217.328 | 0.894354 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 94.5683i | 0.235648i | 0.993034 | + | 0.117824i | \(0.0375919\pi\) | ||||
−0.993034 | + | 0.117824i | \(0.962408\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 887.073i | − 1.45580i | −0.685684 | − | 0.727899i | \(-0.740497\pi\) | ||||
0.685684 | − | 0.727899i | \(-0.259503\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 126.669 | 0.145359 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1448.19 | 1.21536 | 0.607679 | − | 0.794182i | \(-0.292101\pi\) | ||||
0.607679 | + | 0.794182i | \(0.292101\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 611.677i | 0.388721i | 0.980930 | + | 0.194361i | \(0.0622632\pi\) | ||||
−0.980930 | + | 0.194361i | \(0.937737\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 1268.38i | − 0.627625i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −814.118 | −0.320899 | −0.160449 | − | 0.987044i | \(-0.551294\pi\) | ||||
−0.160449 | + | 0.987044i | \(0.551294\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −625.000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 2332.37i | − 0.615727i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5291.31i | 1.16834i | 0.811633 | + | 0.584168i | \(0.198579\pi\) | ||||
−0.811633 | + | 0.584168i | \(0.801421\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3614.36 | −0.675502 | −0.337751 | − | 0.941236i | \(-0.609666\pi\) | ||||
−0.337751 | + | 0.941236i | \(0.609666\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 479.155 | 0.0765934 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6258.32i | 0.863551i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9480.98i | 1.13854i | 0.822150 | + | 0.569271i | \(0.192774\pi\) | ||||
−0.822150 | + | 0.569271i | \(0.807226\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4494.59 | −0.473182 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9910.48 | −0.920736 | −0.460368 | − | 0.887728i | \(-0.652282\pi\) | ||||
−0.460368 | + | 0.887728i | \(0.652282\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 20213.1i | − 1.66710i | −0.552445 | − | 0.833549i | \(-0.686305\pi\) | ||||
0.552445 | − | 0.833549i | \(-0.313695\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5433.20i | 0.399967i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 20765.1 | 1.37116 | 0.685581 | − | 0.727996i | \(-0.259548\pi\) | ||||
0.685581 | + | 0.727996i | \(0.259548\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 45859.5 | 2.72860 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 7337.66i | − 0.395032i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 13009.9i | − 0.636187i | −0.948059 | − | 0.318094i | \(-0.896957\pi\) | ||||
0.948059 | − | 0.318094i | \(-0.103043\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2364.21 | −0.105385 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3099.22 | 0.126347 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 16632.8i | 0.622065i | 0.950399 | + | 0.311032i | \(0.100675\pi\) | ||||
−0.950399 | + | 0.311032i | \(0.899325\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 715.975i | − 0.0246362i | −0.999924 | − | 0.0123181i | \(-0.996079\pi\) | ||||
0.999924 | − | 0.0123181i | \(-0.00392107\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 54404.3 | 1.72696 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 22176.8 | 0.651053 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 21955.0i | − 0.597513i | −0.954329 | − | 0.298756i | \(-0.903428\pi\) | ||||
0.954329 | − | 0.298756i | \(-0.0965718\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4124.94i | 0.104303i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 38473.5 | 0.905765 | 0.452883 | − | 0.891570i | \(-0.350396\pi\) | ||||
0.452883 | + | 0.891570i | \(0.350396\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −40857.0 | −0.897344 | −0.448672 | − | 0.893696i | \(-0.648103\pi\) | ||||
−0.448672 | + | 0.893696i | \(0.648103\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3166.73i | 0.0650066i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 23673.5i | 0.455026i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −84846.9 | −1.52957 | −0.764783 | − | 0.644288i | \(-0.777154\pi\) | ||||
−0.764783 | + | 0.644288i | \(0.777154\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 40993.1 | 0.694222 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 116115.i | − 1.85010i | −0.379851 | − | 0.925048i | \(-0.624025\pi\) | ||||
0.379851 | − | 0.925048i | \(-0.375975\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 36204.9i | 0.543525i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 26809.8 | 0.379748 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 121182. | 1.62168 | 0.810838 | − | 0.585271i | \(-0.199012\pi\) | ||||
0.810838 | + | 0.585271i | \(0.199012\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 222064.i | − 2.81108i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 18313.1i | 0.219560i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15291.9 | −0.173841 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 21598.7 | 0.233077 | 0.116538 | − | 0.993186i | \(-0.462820\pi\) | ||||
0.116538 | + | 0.993186i | \(0.462820\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 20552.3i | 0.210753i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 105401.i | 1.02811i | 0.857756 | + | 0.514057i | \(0.171858\pi\) | ||||
−0.857756 | + | 0.514057i | \(0.828142\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15362.8 | 0.142684 | 0.0713421 | − | 0.997452i | \(-0.477272\pi\) | ||||
0.0713421 | + | 0.997452i | \(0.477272\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 31709.4 | 0.280682 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 14774.1i | − 0.124750i | −0.998053 | − | 0.0623750i | \(-0.980133\pi\) | ||||
0.998053 | − | 0.0623750i | \(-0.0198675\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 165494.i | 1.33419i | 0.744973 | + | 0.667094i | \(0.232462\pi\) | ||||
−0.744973 | + | 0.667094i | \(0.767538\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 48037.9 | 0.370064 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 72833.6 | 0.536582 | 0.268291 | − | 0.963338i | \(-0.413541\pi\) | ||||
0.268291 | + | 0.963338i | \(0.413541\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 20352.9i | − 0.143510i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 192786.i | − 1.30200i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 362531. | 2.34681 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 152108. | 0.944470 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 50214.0i | 0.299269i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 15625.0i | − 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8287.17 | −0.0455929 | −0.0227964 | − | 0.999740i | \(-0.507257\pi\) | ||||
−0.0227964 | + | 0.999740i | \(0.507257\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −102415. | −0.541862 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 177213.i | 0.902231i | 0.892466 | + | 0.451115i | \(0.148974\pi\) | ||||
−0.892466 | + | 0.451115i | \(0.851026\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 153123.i | 0.750605i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 58309.3 | 0.275362 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 352108. | 1.60278 | 0.801391 | − | 0.598141i | \(-0.204094\pi\) | ||||
0.801391 | + | 0.598141i | \(0.204094\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 145465.i | − 0.638589i | −0.947656 | − | 0.319294i | \(-0.896554\pi\) | ||||
0.947656 | − | 0.319294i | \(-0.103446\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 105212.i | − 0.445673i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 83889.0 | 0.343056 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −132283. | −0.522496 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 232359.i | − 0.886884i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 162250.i | − 0.598712i | −0.954142 | − | 0.299356i | \(-0.903228\pi\) | ||||
0.954142 | − | 0.299356i | \(-0.0967718\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −427740. | −1.52664 | −0.763321 | − | 0.646019i | \(-0.776433\pi\) | ||||
−0.763321 | + | 0.646019i | \(0.776433\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 314733. | 1.08696 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 90358.9i | − 0.302094i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 278644.i | 0.902194i | 0.892475 | + | 0.451097i | \(0.148967\pi\) | ||||
−0.892475 | + | 0.451097i | \(0.851033\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −65918.2 | −0.206782 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −203800. | −0.619642 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 276615.i | 0.815467i | 0.913101 | + | 0.407733i | \(0.133681\pi\) | ||||
−0.913101 | + | 0.407733i | \(0.866319\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 11978.9i | 0.0342536i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3008.18 | 0.00834667 | 0.00417334 | − | 0.999991i | \(-0.498672\pi\) | ||||
0.00417334 | + | 0.999991i | \(0.498672\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −415606. | −1.11935 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 132935.i | 0.347654i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 473850.i | 1.20372i | 0.798602 | + | 0.601860i | \(0.205573\pi\) | ||||
−0.798602 | + | 0.601860i | \(0.794427\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −156458. | −0.386192 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 84274.5 | 0.202192 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 661760.i | − 1.54372i | −0.635794 | − | 0.771859i | \(-0.719327\pi\) | ||||
0.635794 | − | 0.771859i | \(-0.280673\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 390057.i | 0.884977i | 0.896774 | + | 0.442488i | \(0.145904\pi\) | ||||
−0.896774 | + | 0.442488i | \(0.854096\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3627.67 | −0.00800757 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −237025. | −0.509171 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 136953.i | 0.286397i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 583869.i | − 1.18894i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −456202. | −0.904845 | −0.452422 | − | 0.891804i | \(-0.649440\pi\) | ||||
−0.452422 | + | 0.891804i | \(0.649440\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −28265.7 | −0.0546218 | −0.0273109 | − | 0.999627i | \(-0.508694\pi\) | ||||
−0.0273109 | + | 0.999627i | \(0.508694\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 112365.i | − 0.211614i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 746684.i | − 1.37079i | −0.728171 | − | 0.685396i | \(-0.759629\pi\) | ||||
0.728171 | − | 0.685396i | \(-0.240371\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 271671. | 0.486307 | 0.243153 | − | 0.969988i | \(-0.421818\pi\) | ||||
0.243153 | + | 0.969988i | \(0.421818\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −111241. | −0.194211 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.32459e6i | 2.25601i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 247762.i | − 0.411766i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −176931. | −0.286997 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −57845.3 | −0.0916014 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 20283.2i | − 0.0313640i | −0.999877 | − | 0.0156820i | \(-0.995008\pi\) | ||||
0.999877 | − | 0.0156820i | \(-0.00499194\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 194936.i | − 0.294404i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 505327. | 0.745549 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −904792. | −1.30437 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 207013.i | 0.291667i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 1.28465e6i | − 1.76932i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 30380.0 | 0.0409096 | 0.0204548 | − | 0.999791i | \(-0.493489\pi\) | ||||
0.0204548 | + | 0.999791i | \(0.493489\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −135830. | −0.178871 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.45723e6i | 1.87699i | 0.345286 | + | 0.938497i | \(0.387782\pi\) | ||||
−0.345286 | + | 0.938497i | \(0.612218\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 963464.i | − 1.21408i | −0.794672 | − | 0.607039i | \(-0.792357\pi\) | ||||
0.794672 | − | 0.607039i | \(-0.207643\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 119948. | 0.147899 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.31864e6 | −1.59125 | −0.795623 | − | 0.605792i | \(-0.792856\pi\) | ||||
−0.795623 | + | 0.605792i | \(0.792856\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 519127.i | 0.613202i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 429899.i | 0.497159i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.17974e6 | −1.33595 | −0.667974 | − | 0.744184i | \(-0.732838\pi\) | ||||
−0.667974 | + | 0.744184i | \(0.732838\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 785926. | 0.871644 | 0.435822 | − | 0.900033i | \(-0.356458\pi\) | ||||
0.435822 | + | 0.900033i | \(0.356458\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 774469.i | − 0.841372i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.14649e6i | 1.22027i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 542603. | 0.565900 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −588329. | −0.601342 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 923722.i | − 0.925459i | −0.886500 | − | 0.462729i | \(-0.846870\pi\) | ||||
0.886500 | − | 0.462729i | \(-0.153130\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 76989.7i | − 0.0756191i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 183441. | 0.176664 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −497776. | −0.470112 | −0.235056 | − | 0.971982i | \(-0.575527\pi\) | ||||
−0.235056 | + | 0.971982i | \(0.575527\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.37340e6i | 2.19848i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.14995e6i | 1.04491i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 745381. | 0.664491 | 0.332245 | − | 0.943193i | \(-0.392194\pi\) | ||||
0.332245 | + | 0.943193i | \(0.392194\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 325248. | 0.284512 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 614002.i | − 0.527098i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.80992e6i | 1.52503i | 0.646970 | + | 0.762516i | \(0.276036\pi\) | ||||
−0.646970 | + | 0.762516i | \(0.723964\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.20319e6 | −1.82234 | −0.911169 | − | 0.412032i | \(-0.864819\pi\) | ||||
−0.911169 | + | 0.412032i | \(0.864819\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.12514e6 | −0.913695 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 59105.2i | − 0.0471296i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1.85372e6i | − 1.45159i | −0.687912 | − | 0.725795i | \(-0.741472\pi\) | ||||
0.687912 | − | 0.725795i | \(-0.258528\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −785500. | −0.604138 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.06542e6 | −0.804926 | −0.402463 | − | 0.915436i | \(-0.631846\pi\) | ||||
−0.402463 | + | 0.915436i | \(0.631846\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 38350.4i | 0.0284645i | 0.999899 | + | 0.0142323i | \(0.00453042\pi\) | ||||
−0.999899 | + | 0.0142323i | \(0.995470\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 77480.6i | 0.0565042i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.48092e6 | −1.77790 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 677410. | 0.477097 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 109436.i | − 0.0757576i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 463895.i | 0.315683i | 0.987464 | + | 0.157841i | \(0.0504534\pi\) | ||||
−0.987464 | + | 0.157841i | \(0.949547\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −415820. | −0.278196 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 220568. | 0.145095 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 722182.i | 0.467164i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 5.06000e6i | − 3.21910i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 534042. | 0.334171 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 17899.4 | 0.0110176 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 203618.i | − 0.123302i | −0.998098 | − | 0.0616509i | \(-0.980363\pi\) | ||||
0.998098 | − | 0.0616509i | \(-0.0196365\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 77839.4i | − 0.0463771i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.32625e6 | 0.777541 | 0.388770 | − | 0.921335i | \(-0.372900\pi\) | ||||
0.388770 | + | 0.921335i | \(0.372900\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.62292e6 | −0.936344 | −0.468172 | − | 0.883637i | \(-0.655087\pi\) | ||||
−0.468172 | + | 0.883637i | \(0.655087\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.36011e6i | 0.772320i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 920943.i | 0.514736i | 0.966313 | + | 0.257368i | \(0.0828553\pi\) | ||||
−0.966313 | + | 0.257368i | \(0.917145\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −500390. | −0.275316 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −74856.7 | −0.0405479 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 885828.i | 0.472436i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 554421.i | 0.291160i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 838521. | 0.433655 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.19818e6 | 2.64766 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 689680.i | 0.346001i | 0.984922 | + | 0.173001i | \(0.0553463\pi\) | ||||
−0.984922 | + | 0.173001i | \(0.944654\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.06048e6i | 1.01826i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 548876. | 0.267216 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.23442e6 | 0.592089 | 0.296045 | − | 0.955174i | \(-0.404332\pi\) | ||||
0.296045 | + | 0.955174i | \(0.404332\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 369031.i | − 0.174407i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 341803.i | − 0.159181i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.27281e6 | 3.33785 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −103124. | −0.0466455 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 2.59951e6i | − 1.15896i | −0.814987 | − | 0.579480i | \(-0.803256\pi\) | ||||
0.814987 | − | 0.579480i | \(-0.196744\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 277542.i | 0.121974i | 0.998139 | + | 0.0609868i | \(0.0194247\pi\) | ||||
−0.998139 | + | 0.0609868i | \(0.980575\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.06899e6 | −0.896375 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.51736e6 | −1.07525 | −0.537624 | − | 0.843184i | \(-0.680678\pi\) | ||||
−0.537624 | + | 0.843184i | \(0.680678\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 961837.i | 0.405071i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 1.83686e6i | − 0.762790i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 899617. | 0.368402 | 0.184201 | − | 0.982889i | \(-0.441030\pi\) | ||||
0.184201 | + | 0.982889i | \(0.441030\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.10195e6 | 0.848896 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 770694.i | − 0.306984i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 1.02142e6i | − 0.401305i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.07519e6 | −0.804253 | −0.402126 | − | 0.915584i | \(-0.631729\pi\) | ||||
−0.402126 | + | 0.915584i | \(0.631729\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.15382e6 | −0.823463 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 3.25681e6i | − 1.22845i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.12372e6i | 1.90684i | 0.301651 | + | 0.953419i | \(0.402462\pi\) | ||||
−0.301651 | + | 0.953419i | \(0.597538\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −79168.2 | −0.0290718 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.69378e6 | 1.70086 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 1.55330e6i | − 0.555465i | −0.960659 | − | 0.277732i | \(-0.910417\pi\) | ||||
0.960659 | − | 0.277732i | \(-0.0895828\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 41989.1i | 0.0148192i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.17661e6 | −0.409861 | −0.204930 | − | 0.978777i | \(-0.565697\pi\) | ||||
−0.204930 | + | 0.978777i | \(0.565697\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −591839. | −0.203494 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 4.39287e6i | − 1.49098i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.56804e6i | 0.525392i | 0.964879 | + | 0.262696i | \(0.0846116\pi\) | ||||
−0.964879 | + | 0.262696i | \(0.915388\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.17900e6 | −0.390007 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 897897. | 0.293255 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 2.12117e6i | − 0.684043i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.55070e6i | 0.493799i | 0.969041 | + | 0.246900i | \(0.0794118\pi\) | ||||
−0.969041 | + | 0.246900i | \(0.920588\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 775838. | 0.243971 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.78114e6 | 0.553144 | 0.276572 | − | 0.960993i | \(-0.410802\pi\) | ||||
0.276572 | + | 0.960993i | \(0.410802\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.20620e6i | 0.983394i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.02483e6i | 0.310465i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −896600. | −0.268295 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.19593e6 | −1.53587 | −0.767936 | − | 0.640527i | \(-0.778716\pi\) | ||||
−0.767936 | + | 0.640527i | \(0.778716\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 1.78405e6i | − 0.520957i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.16374e6i | 1.20118i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.90288e6 | 0.827388 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −737036. | −0.207562 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 6.45443e6i | − 1.79607i | −0.439927 | − | 0.898033i | \(-0.644996\pi\) | ||||
0.439927 | − | 0.898033i | \(-0.355004\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 1.41145e6i | − 0.388114i | −0.980990 | − | 0.194057i | \(-0.937835\pi\) | ||||
0.980990 | − | 0.194057i | \(-0.0621646\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.51283e6 | 1.22630 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −905121. | −0.243072 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 179232.i | − 0.0475714i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 425046.i | − 0.111504i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.94825e6 | −0.764488 | −0.382244 | − | 0.924061i | \(-0.624849\pi\) | ||||
−0.382244 | + | 0.924061i | \(0.624849\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.63564e6 | 1.18820 | 0.594100 | − | 0.804391i | \(-0.297508\pi\) | ||||
0.594100 | + | 0.804391i | \(0.297508\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 670245.i | 0.169828i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 497978.i | − 0.124740i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.15825e6 | 0.534491 | 0.267245 | − | 0.963629i | \(-0.413887\pi\) | ||||
0.267245 | + | 0.963629i | \(0.413887\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.96656e6 | 2.44033 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.27689e6i | 1.03543i | 0.855554 | + | 0.517713i | \(0.173217\pi\) | ||||
−0.855554 | + | 0.517713i | \(0.826783\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.02956e6i | 0.725236i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −822080. | −0.194601 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.31292e6 | 0.307342 | 0.153671 | − | 0.988122i | \(-0.450890\pi\) | ||||
0.153671 | + | 0.988122i | \(0.450890\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 937217.i | − 0.216969i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.16726e6i | 0.496209i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.55159e6 | 1.25716 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.14752e6 | −1.15294 | −0.576471 | − | 0.817117i | \(-0.695571\pi\) | ||||
−0.576471 | + | 0.817117i | \(0.695571\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 3.37773e6i | − 0.748330i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 7.94846e6i | − 1.74193i | −0.491346 | − | 0.870965i | \(-0.663495\pi\) | ||||
0.491346 | − | 0.870965i | \(-0.336505\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −374404. | −0.0811687 | −0.0405843 | − | 0.999176i | \(-0.512922\pi\) | ||||
−0.0405843 | + | 0.999176i | \(0.512922\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −457827. | −0.0981904 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.84308e6i | 0.815432i | 0.913109 | + | 0.407716i | \(0.133675\pi\) | ||||
−0.913109 | + | 0.407716i | \(0.866325\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 5.49607e6i | − 1.15377i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.41182e6 | 0.293243 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.91152e6 | 0.392848 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 382298.i | − 0.0777443i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 2.82742e6i | − 0.568977i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.08933e6 | 0.216930 | 0.108465 | − | 0.994100i | \(-0.465406\pi\) | ||||
0.108465 | + | 0.994100i | \(0.465406\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.41033e6 | 1.65749 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.03261e6i | 0.201404i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 539968.i | 0.104235i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.02078e6 | −0.386098 | −0.193049 | − | 0.981189i | \(-0.561838\pi\) | ||||
−0.193049 | + | 0.981189i | \(0.561838\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.40154e6 | 0.265054 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 9.05818e6i | − 1.69565i | −0.530273 | − | 0.847827i | \(-0.677911\pi\) | ||||
0.530273 | − | 0.847827i | \(-0.322089\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.66284e6i | 1.41995i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −513808. | −0.0942514 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.63118e6 | 1.74899 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 2.83503e6i | − 0.509690i | −0.966982 | − | 0.254845i | \(-0.917976\pi\) | ||||
0.966982 | − | 0.254845i | \(-0.0820245\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 15241.8i | − 0.00271294i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.09022e6 | 1.24951 | 0.624755 | − | 0.780821i | \(-0.285199\pi\) | ||||
0.624755 | + | 0.780821i | \(0.285199\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.63503e6 | −0.459787 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.10578e6i | 0.363825i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 3.09922e6i | − 0.530222i | −0.964218 | − | 0.265111i | \(-0.914591\pi\) | ||||
0.964218 | − | 0.265111i | \(-0.0854086\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.02278e7 | −1.73273 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.42666e6 | 0.239346 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 384069.i | 0.0638103i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.96372e6i | 0.323112i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.40088e6 | 0.391248 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.38166e6 | −1.03000 | −0.515002 | − | 0.857189i | \(-0.672209\pi\) | ||||
−0.515002 | + | 0.857189i | \(0.672209\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.15218e6i | 0.663776i | 0.943319 | + | 0.331888i | \(0.107686\pi\) | ||||
−0.943319 | + | 0.331888i | \(0.892314\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 792736.i | 0.125525i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.23429e6 | −0.820977 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.77355e6 | −0.897024 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.61477e6i | 0.556346i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.79132e6i | 1.34041i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 369352. | 0.0557899 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.35298e6 | −0.501759 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.33686e6i | 0.642989i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.36079e6i | 0.934367i | 0.884160 | + | 0.467184i | \(0.154731\pi\) | ||||
−0.884160 | + | 0.467184i | \(0.845269\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.97633e6 | 0.287647 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.13736e6 | −0.596667 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 9.40603e6i | − 1.34412i | −0.740497 | − | 0.672060i | \(-0.765410\pi\) | ||||
0.740497 | − | 0.672060i | \(-0.234590\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 155601.i | − 0.0220334i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.23657e6 | −0.454157 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.12400e7 | −2.95353 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.20095e6i | 0.165497i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.24324e6i | 0.442936i | 0.975168 | + | 0.221468i | \(0.0710848\pi\) | ||||
−0.975168 | + | 0.221468i | \(0.928915\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.79305e7 | −2.42696 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 693910. | 0.0930884 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.80932e6i | 1.17131i | 0.810561 | + | 0.585654i | \(0.199162\pi\) | ||||
−0.810561 | + | 0.585654i | \(0.800838\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.82084e6i | 0.239967i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.02619e7 | 1.34051 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.59867e6 | 1.24288 | 0.621441 | − | 0.783461i | \(-0.286547\pi\) | ||||
0.621441 | + | 0.783461i | \(0.286547\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.28215e7i | 1.64569i | 0.568262 | + | 0.822847i | \(0.307616\pi\) | ||||
−0.568262 | + | 0.822847i | \(0.692384\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.31147e6i | 0.294104i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 508824. | 0.0641797 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.39655e6 | −0.674803 | −0.337401 | − | 0.941361i | \(-0.609548\pi\) | ||||
−0.337401 | + | 0.941361i | \(0.609548\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 143216.i | 0.0177539i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 2.90675e7i | − 3.57246i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.23033e6 | 0.149916 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.81965e6 | 0.582271 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.42415e6i | 0.290379i | 0.989404 | + | 0.145189i | \(0.0463792\pi\) | ||||
−0.989404 | + | 0.145189i | \(0.953621\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 2.21082e6i | − 0.262582i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.78327e6 | −0.445552 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.84341e6 | −1.14950 | −0.574750 | − | 0.818329i | \(-0.694901\pi\) | ||||
−0.574750 | + | 0.818329i | \(0.694901\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.06327e6i | 1.04952i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 1.37649e6i | − 0.158066i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.63365e6 | −0.186034 | −0.0930169 | − | 0.995665i | \(-0.529651\pi\) | ||||
−0.0930169 | + | 0.995665i | \(0.529651\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.99906e6 | −1.01627 | −0.508137 | − | 0.861276i | \(-0.669666\pi\) | ||||
−0.508137 | + | 0.861276i | \(0.669666\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 4.77144e6i | − 0.534388i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.80270e6i | 0.422380i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.70178e6 | −0.738276 | −0.369138 | − | 0.929375i | \(-0.620347\pi\) | ||||
−0.369138 | + | 0.929375i | \(0.620347\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.71137e6 | 0.733277 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 1.84201e7i | − 1.99613i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 5.70585e6i | − 0.613294i | −0.951823 | − | 0.306647i | \(-0.900793\pi\) | ||||
0.951823 | − | 0.306647i | \(-0.0992072\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.25535e6 | −0.133837 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.55652e7 | 1.64605 | 0.823023 | − | 0.568008i | \(-0.192286\pi\) | ||||
0.823023 | + | 0.568008i | \(0.192286\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.26590e7i | 1.32792i | 0.747766 | + | 0.663962i | \(0.231126\pi\) | ||||
−0.747766 | + | 0.663962i | \(0.768874\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.89883e6i | 0.197586i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.03359e7 | 3.13139 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 293088.i | 0.0297735i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.37303e7i | 1.38374i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.23076e7 | −1.23055 | −0.615274 | − | 0.788313i | \(-0.710955\pi\) | ||||
−0.615274 | + | 0.788313i | \(0.710955\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −102770. | −0.0101943 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 207179.i | − 0.0203897i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 4.06808e7i | − 3.97229i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.36136e6 | 0.810075 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.25160e7 | −1.20315 | −0.601576 | − | 0.798816i | \(-0.705460\pi\) | ||||
−0.601576 | + | 0.798816i | \(0.705460\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.85603e6i | 0.558568i | 0.960209 | + | 0.279284i | \(0.0900970\pi\) | ||||
−0.960209 | + | 0.279284i | \(0.909903\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 2.56037e6i | − 0.242328i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.02686e7 | −0.964387 | −0.482194 | − | 0.876065i | \(-0.660160\pi\) | ||||
−0.482194 | + | 0.876065i | \(0.660160\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.57294e6 | −0.146588 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.58437e6i | 0.423962i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 6277.16i | 0 0.000576076i | −1.00000 | 0.000288038i | \(-0.999908\pi\) | |||||
1.00000 | 0.000288038i | \(-9.16854e-5\pi\) | ||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.43033e6 | −0.403490 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.87936e6 | −0.802543 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.90209e7i | 1.70615i | 0.521784 | + | 0.853077i | \(0.325267\pi\) | ||||
−0.521784 | + | 0.853077i | \(0.674733\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 9.84622e6i | − 0.876528i | −0.898846 | − | 0.438264i | \(-0.855594\pi\) | ||||
0.898846 | − | 0.438264i | \(-0.144406\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.50904e6 | −0.575086 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.82807e6 | −0.335681 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 4.30775e6i | − 0.374918i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 153928.i | − 0.0132970i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 67708.5 | 0.00580546 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.82184e7 | −1.55050 | −0.775252 | − | 0.631652i | \(-0.782377\pi\) | ||||
−0.775252 | + | 0.631652i | \(0.782377\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.45773e6i | 0.123145i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.10909e6i | 0.679987i | 0.940428 | + | 0.339993i | \(0.110425\pi\) | ||||
−0.940428 | + | 0.339993i | \(0.889575\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.40687e6 | 0.450061 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.38343e6 | 0.610085 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1.11760e7i | − 0.916717i | −0.888767 | − | 0.458358i | \(-0.848438\pi\) | ||||
0.888767 | − | 0.458358i | \(-0.151562\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.80269e6i | 0.716785i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.88164e6 | −0.394616 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.15408e7 | −0.926161 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.40751e6i | 0.112139i | 0.998427 | + | 0.0560695i | \(0.0178568\pi\) | ||||
−0.998427 | + | 0.0560695i | \(0.982143\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.14492e6i | 0.406954i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.63662e6 | 0.285586 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.43523e7 | −1.11902 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.68125e6i | 0.517208i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.40860e7i | 1.08266i | 0.840809 | + | 0.541331i | \(0.182079\pi\) | ||||
−0.840809 | + | 0.541331i | \(0.817921\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.79930e6 | −0.442576 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.63029e6 | 0.199311 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.63854e7i | 1.98525i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 1.38968e6i | − 0.103824i | −0.998652 | − | 0.0519122i | \(-0.983468\pi\) | ||||
0.998652 | − | 0.0519122i | \(-0.0165316\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.84396e7 | −1.36797 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.94251e6 | 0.216768 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.09722e6i | 0.153419i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.97744e6i | 0.434227i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.91426e7 | −1.38096 | −0.690478 | − | 0.723354i | \(-0.742600\pi\) | ||||
−0.690478 | + | 0.723354i | \(0.742600\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.84580e6 | 0.275517 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 3.98210e6i | − 0.283313i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 3.30707e6i | − 0.233667i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.38873e7 | −0.974497 | −0.487248 | − | 0.873263i | \(-0.661999\pi\) | ||||
−0.487248 | + | 0.873263i | \(0.661999\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6.03727e6 | 0.420748 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 2.92725e7i | − 2.02612i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 9.41321e6i | − 0.647110i | −0.946209 | − | 0.323555i | \(-0.895122\pi\) | ||||
0.946209 | − | 0.323555i | \(-0.104878\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.80899e6 | 0.396627 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.07625e6 | 0.140803 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 118264.i | 0.00796605i | 0.999992 | + | 0.00398302i | \(0.00126784\pi\) | ||||
−0.999992 | + | 0.00398302i | \(0.998732\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 2.74924e6i | − 0.183936i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.62763e6 | −0.108164 | −0.0540820 | − | 0.998537i | \(-0.517223\pi\) | ||||
−0.0540820 | + | 0.998537i | \(0.517223\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.05624e6 | 0.267752 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 2.52351e7i | − 1.65464i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 3.69843e6i | − 0.240887i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.02408e6 | 0.583853 | 0.291926 | − | 0.956441i | \(-0.405704\pi\) | ||||
0.291926 | + | 0.956441i | \(0.405704\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.68028e6 | −0.300805 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 1.06935e7i | − 0.682735i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 645135.i | 0.0409177i | 0.999791 | + | 0.0204588i | \(0.00651271\pi\) | ||||
−0.999791 | + | 0.0204588i | \(0.993487\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −390089. | −0.0245787 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.61414e6 | 0.288821 | 0.144411 | − | 0.989518i | \(-0.453871\pi\) | ||||
0.144411 | + | 0.989518i | \(0.453871\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.14287e7i | 2.57626i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.86833e6i | 0.486104i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.47545e7 | 0.905601 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 59875.3 | 0.00365117 | 0.00182559 | − | 0.999998i | \(-0.499419\pi\) | ||||
0.00182559 | + | 0.999998i | \(0.499419\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.52211e6i | 0.152802i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.78468e7i | 1.07426i | 0.843499 | + | 0.537132i | \(0.180492\pi\) | ||||
−0.843499 | + | 0.537132i | \(0.819508\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.25897e6 | 0.135100 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.20255e7 | 0.714577 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 6.06202e6i | − 0.357910i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.63837e6i | 0.213442i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.23413e7 | 0.719377 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.96609e6 | −0.403473 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.87666e7i | 1.08006i | 0.841645 | + | 0.540031i | \(0.181588\pi\) | ||||
−0.841645 | + | 0.540031i | \(0.818412\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 3.77667e6i | − 0.215981i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.82326e7 | 1.03612 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −635122. | −0.0358653 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 1.64796e6i | − 0.0924757i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 3.95963e6i | − 0.220805i | −0.993887 | − | 0.110403i | \(-0.964786\pi\) | ||||
0.993887 | − | 0.110403i | \(-0.0352140\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.00719e7 | 1.66645 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.63363e7 | 1.45035 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 3.86377e6i | − 0.211457i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 5.09501e6i | − 0.277112i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.17044e6 | 0.495685 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.74535e6 | −0.469792 | −0.234896 | − | 0.972020i | \(-0.575475\pi\) | ||||
−0.234896 | + | 0.972020i | \(0.575475\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.74240e7i | 1.46413i | 0.681236 | + | 0.732064i | \(0.261443\pi\) | ||||
−0.681236 | + | 0.732064i | \(0.738557\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.11631e7i | 0.592320i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.91537e6 | −0.364688 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.23639e7 | 0.648037 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 4.82606e7i | − 2.51410i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.48659e7i | 0.769719i | 0.922975 | + | 0.384859i | \(0.125750\pi\) | ||||
−0.922975 | + | 0.384859i | \(0.874250\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.27591e6 | 0.477372 | 0.238686 | − | 0.971097i | \(-0.423283\pi\) | ||||
0.238686 | + | 0.971097i | \(0.423283\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −299472. | −0.0153187 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 6.99433e6i | − 0.355617i | −0.984065 | − | 0.177808i | \(-0.943099\pi\) | ||||
0.984065 | − | 0.177808i | \(-0.0569007\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 3.29484e7i | − 1.66513i | −0.553929 | − | 0.832564i | \(-0.686872\pi\) | ||||
0.553929 | − | 0.832564i | \(-0.313128\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.39234e6 | −0.471814 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.64135e7 | 3.31623 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 75204.6i | 0.00373274i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.43002e6i | 0.415925i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.29215e6 | −0.308599 | −0.154299 | − | 0.988024i | \(-0.549312\pi\) | ||||
−0.154299 | + | 0.988024i | \(0.549312\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.48678e6 | −0.365010 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.39824e6i | 0.261627i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1.03902e7i | − 0.500588i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.80776e7 | 1.82373 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 194312. | 0.00925191 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 7.71864e6i | − 0.365356i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 2.28452e6i | − 0.107504i | −0.998554 | − | 0.0537518i | \(-0.982882\pi\) | ||||
0.998554 | − | 0.0537518i | \(-0.0171180\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.32336e6 | −0.155476 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.33739e6 | 0.0622023 | 0.0311012 | − | 0.999516i | \(-0.490099\pi\) | ||||
0.0311012 | + | 0.999516i | \(0.490099\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 3.12847e7i | − 1.44660i | −0.690533 | − | 0.723301i | \(-0.742624\pi\) | ||||
0.690533 | − | 0.723301i | \(-0.257376\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.25702e7i | 0.577877i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.83963e7 | −1.75494 | −0.877469 | − | 0.479633i | \(-0.840770\pi\) | ||||
−0.877469 | + | 0.479633i | \(0.840770\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.18462e7 | −0.538320 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 3.43228e6i | − 0.155072i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 8.02382e6i | − 0.360439i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.94757e7 | −0.869858 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.69401e6 | 0.208453 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 3.91145e6i | − 0.172710i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.62074e7i | 0.711565i | 0.934569 | + | 0.355783i | \(0.115786\pi\) | ||||
−0.934569 | + | 0.355783i | \(0.884214\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.35045e6 | 0.102607 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.64879e6 | −0.158383 | −0.0791916 | − | 0.996859i | \(-0.525234\pi\) | ||||
−0.0791916 | + | 0.996859i | \(0.525234\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 3.21031e7i | − 1.38562i | −0.721119 | − | 0.692811i | \(-0.756372\pi\) | ||||
0.721119 | − | 0.692811i | \(-0.243628\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.10686e6i | 0.0904228i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.29249e7 | −0.551594 | −0.275797 | − | 0.961216i | \(-0.588942\pi\) | ||||
−0.275797 | + | 0.961216i | \(0.588942\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.07455e6 | −0.0880379 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.87665e6i | 0.163592i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.27015e7i | 0.533000i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.65440e7 | 0.690372 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.65913e6 | 0.151844 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 1.91247e7i | − 0.789214i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 1.88409e7i | − 0.773196i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.56378e7 | −1.04631 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.75143e6 | −0.395774 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 541993.i | 0.0218764i | 0.999940 | + | 0.0109382i | \(0.00348181\pi\) | ||||
−0.999940 | + | 0.0109382i | \(0.996518\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.29066e7i | 0.919498i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.25168e7 | 1.29811 | 0.649055 | − | 0.760741i | \(-0.275164\pi\) | ||||
0.649055 | + | 0.760741i | \(0.275164\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.09808e7 | 0.435971 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 90691.8i | − 0.00358109i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.43623e7i | 1.74217i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.14025e7 | −1.22652 | −0.613261 | − | 0.789880i | \(-0.710143\pi\) | ||||
−0.613261 | + | 0.789880i | \(0.710143\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.03168e6 | −0.0400772 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 3.41288e7i | − 1.31861i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 5.92561e6i | − 0.227708i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.33876e6 | 0.127610 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.06286e7 | 0.404052 | 0.202026 | − | 0.979380i | \(-0.435247\pi\) | ||||
0.202026 | + | 0.979380i | \(0.435247\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.80513e7i | 1.06066i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 6.71978e6i | − 0.252726i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.42383e6 | −0.128081 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.41673e7 | −0.527154 | −0.263577 | − | 0.964638i | \(-0.584902\pi\) | ||||
−0.263577 | + | 0.964638i | \(0.584902\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.22293e6i | 0.304343i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.78895e6i | 0.176306i | 0.996107 | + | 0.0881528i | \(0.0280964\pi\) | ||||
−0.996107 | + | 0.0881528i | \(0.971904\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.06830e6 | 0.295463 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.45967e7 | 0.531712 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 4.35818e7i | − 1.57917i | −0.613639 | − | 0.789587i | \(-0.710295\pi\) | ||||
0.613639 | − | 0.789587i | \(-0.289705\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.62431e7i | 1.30635i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.66620e6 | 0.167306 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −639034. | −0.0227925 | −0.0113962 | − | 0.999935i | \(-0.503628\pi\) | ||||
−0.0113962 | + | 0.999935i | \(0.503628\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 1.14051e7i | − 0.404659i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.53536e6i | 0.0894868i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.81442e7 | 3.09490 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.55656e7 | −0.543697 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 3.21082e6i | − 0.111571i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 706642.i | − 0.0244276i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.89639e6 | −0.0652172 | −0.0326086 | − | 0.999468i | \(-0.510381\pi\) | ||||
−0.0326086 | + | 0.999468i | \(0.510381\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.48828e6 | 0.153557 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 2.30710e7i | − 0.785268i | −0.919695 | − | 0.392634i | \(-0.871564\pi\) | ||||
0.919695 | − | 0.392634i | \(-0.128436\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 3.64147e7i | − 1.23309i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.80912e6 | 0.0946365 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.36091e7 | 1.46164 | 0.730820 | − | 0.682571i | \(-0.239138\pi\) | ||||
0.730820 | + | 0.682571i | \(0.239138\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.14600e7i | 0.382145i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.59666e7i | 1.19324i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.07856e6 | 0.167632 | 0.0838160 | − | 0.996481i | \(-0.473289\pi\) | ||||
0.0838160 | + | 0.996481i | \(0.473289\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.86671e7 | 0.613036 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 2.63379e7i | − 0.860575i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.64558e7i | 0.534970i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.28580e7 | 0.415901 | 0.207950 | − | 0.978139i | \(-0.433321\pi\) | ||||
0.207950 | + | 0.978139i | \(0.433321\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.49445e6 | 0.112462 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.79177e6i | 0.217483i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 3.44037e7i | − 1.09614i | −0.836431 | − | 0.548072i | \(-0.815362\pi\) | ||||
0.836431 | − | 0.548072i | \(-0.184638\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.21132e7 | 0.701031 |
(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.d.d.161.5 | yes | 12 | |
4.3 | odd | 2 | 320.6.d.c.161.8 | yes | 12 | ||
8.3 | odd | 2 | 320.6.d.c.161.5 | ✓ | 12 | ||
8.5 | even | 2 | inner | 320.6.d.d.161.8 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
320.6.d.c.161.5 | ✓ | 12 | 8.3 | odd | 2 | ||
320.6.d.c.161.8 | yes | 12 | 4.3 | odd | 2 | ||
320.6.d.d.161.5 | yes | 12 | 1.1 | even | 1 | trivial | |
320.6.d.d.161.8 | yes | 12 | 8.5 | even | 2 | inner |