Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [304,5,Mod(113,304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("304.113");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 304 = 2^{4} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 304.e (of order \(2\), degree \(1\), not 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: | \(31.4244687775\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 996 x^{18} + 408854 x^{16} + 89661524 x^{14} + 11414409521 x^{12} + 861580608848 x^{10} + \cdots + 34\!\cdots\!64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{50} \) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 113.9 | ||
Root | \(-1.51452i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 304.113 |
Dual form | 304.5.e.f.113.12 |
$q$-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 \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(191\) | \(229\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − | 1.51452i | − | 0.168279i | −0.996454 | − | 0.0841397i | \(-0.973186\pi\) | ||
0.996454 | − | 0.0841397i | \(-0.0268142\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 15.8064 | 0.632257 | 0.316129 | − | 0.948716i | \(-0.397617\pi\) | ||||
0.316129 | + | 0.948716i | \(0.397617\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 74.7269 | 1.52504 | 0.762520 | − | 0.646965i | \(-0.223962\pi\) | ||||
0.762520 | + | 0.646965i | \(0.223962\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 78.7062 | 0.971682 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.49946 | −0.0702434 | −0.0351217 | − | 0.999383i | \(-0.511182\pi\) | ||||
−0.0351217 | + | 0.999383i | \(0.511182\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 283.924i | 1.68003i | 0.542566 | + | 0.840013i | \(0.317453\pi\) | ||||
−0.542566 | + | 0.840013i | \(0.682547\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 23.9391i | − | 0.106396i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −36.0953 | −0.124897 | −0.0624486 | − | 0.998048i | \(-0.519891\pi\) | ||||
−0.0624486 | + | 0.998048i | \(0.519891\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 345.662 | − | 104.111i | 0.957511 | − | 0.288396i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 113.175i | − | 0.256633i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −488.441 | −0.923330 | −0.461665 | − | 0.887054i | \(-0.652748\pi\) | ||||
−0.461665 | + | 0.887054i | \(0.652748\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −375.157 | −0.600251 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 241.878i | − | 0.331794i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 492.463i | 0.585568i | 0.956179 | + | 0.292784i | \(0.0945817\pi\) | ||||
−0.956179 | + | 0.292784i | \(0.905418\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1281.73i | − | 1.33375i | −0.745170 | − | 0.666875i | \(-0.767631\pi\) | ||
0.745170 | − | 0.666875i | \(-0.232369\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.8726i | 0.0118205i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1181.17 | 0.964217 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2139.58i | 1.56288i | 0.623983 | + | 0.781438i | \(0.285514\pi\) | ||||
−0.623983 | + | 0.781438i | \(0.714486\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 430.008 | 0.282714 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2076.32i | 1.23517i | 0.786505 | + | 0.617584i | \(0.211888\pi\) | ||||
−0.786505 | + | 0.617584i | \(0.788112\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3051.37 | 1.65028 | 0.825139 | − | 0.564929i | \(-0.191097\pi\) | ||||
0.825139 | + | 0.564929i | \(0.191097\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1244.06 | 0.614353 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1218.81 | −0.551747 | −0.275873 | − | 0.961194i | \(-0.588967\pi\) | ||||
−0.275873 | + | 0.961194i | \(0.588967\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3183.11 | 1.32575 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 54.6669i | 0.0210176i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 4680.27i | − | 1.66617i | −0.553145 | − | 0.833085i | \(-0.686572\pi\) | ||
0.553145 | − | 0.833085i | \(-0.313428\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −134.346 | −0.0444119 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −157.678 | − | 523.510i | −0.0485312 | − | 0.161129i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3207.19i | 0.921342i | 0.887571 | + | 0.460671i | \(0.152391\pi\) | ||||
−0.887571 | + | 0.460671i | \(0.847609\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2169.77 | 0.583115 | 0.291558 | − | 0.956553i | \(-0.405826\pi\) | ||||
0.291558 | + | 0.956553i | \(0.405826\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5881.48 | 1.48185 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4487.83i | 1.06221i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 6862.25i | − | 1.52868i | −0.644813 | − | 0.764340i | \(-0.723065\pi\) | ||
0.644813 | − | 0.764340i | \(-0.276935\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 739.752i | 0.155377i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6267.19i | 1.24324i | 0.783317 | + | 0.621622i | \(0.213526\pi\) | ||||
−0.783317 | + | 0.621622i | \(0.786474\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2394.57 | 0.449348 | 0.224674 | − | 0.974434i | \(-0.427868\pi\) | ||||
0.224674 | + | 0.974434i | \(0.427868\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 568.181i | 0.101010i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −635.138 | −0.107124 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1312.83i | 0.210356i | 0.994453 | + | 0.105178i | \(0.0335413\pi\) | ||||
−0.994453 | + | 0.105178i | \(0.966459\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6008.88 | 0.915848 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −672.952 | −0.0976850 | −0.0488425 | − | 0.998806i | \(-0.515553\pi\) | ||||
−0.0488425 | + | 0.998806i | \(0.515553\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −570.537 | −0.0789671 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 745.843 | 0.0985391 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 11177.3i | − | 1.41110i | −0.708661 | − | 0.705550i | \(-0.750700\pi\) | ||
0.708661 | − | 0.705550i | \(-0.249300\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 21216.8i | 2.56211i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1941.21 | −0.224443 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5463.67 | − | 1645.62i | 0.605393 | − | 0.182341i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10698.0i | − | 1.13700i | −0.822684 | − | 0.568499i | \(-0.807524\pi\) | ||
0.822684 | − | 0.568499i | \(-0.192476\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −668.960 | −0.0682543 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17196.2 | 1.68574 | 0.842869 | − | 0.538119i | \(-0.180865\pi\) | ||||
0.842869 | + | 0.538119i | \(0.180865\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10868.1i | 1.02442i | 0.858860 | + | 0.512210i | \(0.171173\pi\) | ||||
−0.858860 | + | 0.512210i | \(0.828827\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 1788.89i | − | 0.162258i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 17778.1i | − | 1.55281i | −0.630235 | − | 0.776404i | \(-0.717042\pi\) | ||
0.630235 | − | 0.776404i | \(-0.282958\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 7047.87i | − | 0.593205i | −0.955001 | − | 0.296603i | \(-0.904146\pi\) | ||
0.955001 | − | 0.296603i | \(-0.0958537\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3240.42 | 0.263000 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10151.4i | 0.795001i | 0.917602 | + | 0.397501i | \(0.130122\pi\) | ||||
−0.917602 | + | 0.397501i | \(0.869878\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7720.51 | −0.583782 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 22346.6i | 1.63245i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2697.29 | −0.190473 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14568.8 | −0.995066 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3144.61 | 0.207853 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −15808.9 | −1.01177 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1075.85i | 0.0667025i | 0.999444 | + | 0.0333513i | \(0.0106180\pi\) | ||||
−0.999444 | + | 0.0333513i | \(0.989382\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 4621.34i | − | 0.277708i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16149.5 | −0.941057 | −0.470528 | − | 0.882385i | \(-0.655937\pi\) | ||||
−0.470528 | + | 0.882385i | \(0.655937\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 25830.2 | − | 7779.90i | 1.46024 | − | 0.439816i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 3823.22i | − | 0.209779i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −31949.1 | −1.70223 | −0.851113 | − | 0.524983i | \(-0.824072\pi\) | ||||
−0.851113 | + | 0.524983i | \(0.824072\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6268.09 | 0.324419 | 0.162209 | − | 0.986756i | \(-0.448138\pi\) | ||||
0.162209 | + | 0.986756i | \(0.448138\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1845.90i | 0.0928476i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 2413.20i | − | 0.118011i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7784.08i | 0.370230i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 4820.87i | − | 0.223096i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 25057.7 | 1.12868 | 0.564338 | − | 0.825544i | \(-0.309132\pi\) | ||||
0.564338 | + | 0.825544i | \(0.309132\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1553.62i | − | 0.0681383i | −0.999419 | − | 0.0340691i | \(-0.989153\pi\) | ||
0.999419 | − | 0.0340691i | \(-0.0108466\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2840.92 | −0.121360 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 20259.6i | − | 0.843273i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6295.54 | 0.255408 | 0.127704 | − | 0.991812i | \(-0.459239\pi\) | ||||
0.127704 | + | 0.991812i | \(0.459239\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7088.34 | −0.280382 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −36499.7 | −1.40811 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11459.2 | −0.431299 | −0.215650 | − | 0.976471i | \(-0.569187\pi\) | ||||
−0.215650 | + | 0.976471i | \(0.569187\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 203.469i | 0.00747361i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 47855.8i | − | 1.71594i | −0.513700 | − | 0.857970i | \(-0.671726\pi\) | ||
0.513700 | − | 0.857970i | \(-0.328274\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −52052.0 | −1.82249 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 27205.7 | − | 8194.19i | 0.930396 | − | 0.280229i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21330.4i | 0.712701i | 0.934352 | + | 0.356351i | \(0.115979\pi\) | ||||
−0.934352 | + | 0.356351i | \(0.884021\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −28034.3 | −0.915407 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4857.34 | 0.155043 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8485.13i | 0.264821i | 0.991195 | + | 0.132411i | \(0.0422717\pi\) | ||||
−0.991195 | + | 0.132411i | \(0.957728\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6499.58i | 0.198394i | 0.995068 | + | 0.0991969i | \(0.0316274\pi\) | ||||
−0.995068 | + | 0.0991969i | \(0.968373\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 3286.15i | − | 0.0981263i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 33819.1i | 0.988140i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 306.790 | 0.00877321 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 18074.8i | − | 0.505998i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6129.39 | −0.168016 | −0.0840079 | − | 0.996465i | \(-0.526772\pi\) | ||||
−0.0840079 | + | 0.996465i | \(0.526772\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 18414.1i | − | 0.494353i | −0.968970 | − | 0.247176i | \(-0.920497\pi\) | ||
0.968970 | − | 0.247176i | \(-0.0795027\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6796.88 | 0.178748 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13128.9 | −0.338294 | −0.169147 | − | 0.985591i | \(-0.554101\pi\) | ||||
−0.169147 | + | 0.985591i | \(0.554101\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −50573.2 | −1.27707 | −0.638534 | − | 0.769593i | \(-0.720459\pi\) | ||||
−0.638534 | + | 0.769593i | \(0.720459\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10393.0 | −0.257246 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 36800.2i | 0.893015i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 32819.2i | 0.780944i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −38443.4 | −0.897183 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2937.94 | + | 884.887i | −0.0672589 | + | 0.0202579i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 42125.2i | − | 0.946186i | −0.881012 | − | 0.473093i | \(-0.843137\pi\) | ||
0.881012 | − | 0.473093i | \(-0.156863\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9491.76 | 0.209212 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 48231.2 | 1.04340 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 95780.0i | − | 2.03402i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 3626.62i | − | 0.0756160i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 10248.3i | − | 0.209830i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 22513.9i | − | 0.452731i | −0.974042 | − | 0.226366i | \(-0.927316\pi\) | ||
0.974042 | − | 0.226366i | \(-0.0726844\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −29527.2 | −0.583253 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 29584.8i | 0.574138i | 0.957910 | + | 0.287069i | \(0.0926809\pi\) | ||||
−0.957910 | + | 0.287069i | \(0.907319\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16727.2 | −0.318973 | −0.159486 | − | 0.987200i | \(-0.550984\pi\) | ||||
−0.159486 | + | 0.987200i | \(0.550984\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 961.927i | 0.0180268i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1427.44 | −0.0262933 | −0.0131467 | − | 0.999914i | \(-0.504185\pi\) | ||||
−0.0131467 | + | 0.999914i | \(0.504185\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −19265.0 | −0.348846 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1988.31 | 0.0353987 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −69656.3 | −1.21945 | −0.609726 | − | 0.792613i | \(-0.708720\pi\) | ||||
−0.609726 | + | 0.792613i | \(0.708720\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 17559.7i | − | 0.302331i | −0.988508 | − | 0.151166i | \(-0.951697\pi\) | ||
0.988508 | − | 0.151166i | \(-0.0483027\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 28692.6i | − | 0.485912i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 50313.7 | 0.838212 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 29559.7 | + | 98141.7i | 0.484513 | + | 1.60864i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1019.20i | 0.0164384i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −73019.0 | −1.15901 | −0.579507 | − | 0.814968i | \(-0.696755\pi\) | ||||
−0.579507 | + | 0.814968i | \(0.696755\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4151.49 | 0.0648579 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 864.088i | 0.0132885i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14644.7i | 0.221724i | 0.993836 | + | 0.110862i | \(0.0353612\pi\) | ||||
−0.993836 | + | 0.110862i | \(0.964639\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 159884.i | 2.38345i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 38759.9i | 0.568986i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 94182.6 | 1.36163 | 0.680815 | − | 0.732455i | \(-0.261626\pi\) | ||||
0.680815 | + | 0.732455i | \(0.261626\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 73978.4i | − | 1.05345i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −16928.2 | −0.237459 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 79750.0i | − | 1.10211i | −0.834468 | − | 0.551057i | \(-0.814225\pi\) | ||
0.834468 | − | 0.551057i | \(-0.185775\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 68908.9 | 0.938289 | 0.469145 | − | 0.883121i | \(-0.344562\pi\) | ||||
0.469145 | + | 0.883121i | \(0.344562\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 32133.2 | 0.431150 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3188.63 | 0.0421637 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 90990.1 | 1.18586 | 0.592931 | − | 0.805253i | \(-0.297971\pi\) | ||||
0.592931 | + | 0.805253i | \(0.297971\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 100880.i | − | 1.29598i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 72273.8i | 0.915311i | 0.889130 | + | 0.457655i | \(0.151311\pi\) | ||||
−0.889130 | + | 0.457655i | \(0.848689\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 63191.7 | 0.789019 | 0.394509 | − | 0.918892i | \(-0.370915\pi\) | ||||
0.394509 | + | 0.918892i | \(0.370915\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2492.32 | − | 8274.82i | −0.0306842 | − | 0.101875i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 155157.i | 1.88368i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −82218.1 | −0.984401 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16202.3 | −0.191333 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 26746.7i | − | 0.311556i | −0.987792 | − | 0.155778i | \(-0.950212\pi\) | ||
0.987792 | − | 0.155778i | \(-0.0497884\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 50694.2i | 0.582525i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2055.83i | 0.0233063i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 138680.i | − | 1.55122i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 228019. | 2.51674 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 26043.9i | − | 0.283675i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 34296.3 | 0.368679 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 20047.9i | − | 0.212713i | −0.994328 | − | 0.106356i | \(-0.966082\pi\) | ||
0.994328 | − | 0.106356i | \(-0.0339184\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16459.9 | 0.172389 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 91473.1 | 0.945742 | 0.472871 | − | 0.881132i | \(-0.343218\pi\) | ||||
0.472871 | + | 0.881132i | \(0.343218\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3767.82 | 0.0384593 | 0.0192297 | − | 0.999815i | \(-0.493879\pi\) | ||||
0.0192297 | + | 0.999815i | \(0.493879\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 92965.1 | 0.936912 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 104893.i | 1.04382i | 0.853000 | + | 0.521911i | \(0.174781\pi\) | ||||
−0.853000 | + | 0.521911i | \(0.825219\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 4185.67i | − | 0.0411323i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −26925.2 | −0.261306 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12476.8 | + | 3757.92i | −0.119590 | + | 0.0360199i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 106516.i | − | 1.00844i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10674.1 | −0.0998242 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −91077.8 | −0.841435 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 58070.6i | 0.530030i | 0.964244 | + | 0.265015i | \(0.0853769\pi\) | ||||
−0.964244 | + | 0.265015i | \(0.914623\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 168398.i | 1.51862i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 108468.i | − | 0.966519i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27715.4i | 0.244040i | 0.992528 | + | 0.122020i | \(0.0389372\pi\) | ||||
−0.992528 | + | 0.122020i | \(0.961063\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15374.4 | 0.133782 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10894.0i | 0.0936872i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 58445.0 | 0.496774 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11692.8i | 0.0982385i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −148847. | −1.23618 | −0.618089 | − | 0.786108i | \(-0.712093\pi\) | ||||
−0.618089 | + | 0.786108i | \(0.712093\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 113003. | 0.927764 | 0.463882 | − | 0.885897i | \(-0.346456\pi\) | ||||
0.463882 | + | 0.885897i | \(0.346456\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 68674.9 | 0.557422 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −173058. | −1.38881 | −0.694404 | − | 0.719585i | \(-0.744332\pi\) | ||||
−0.694404 | + | 0.719585i | \(0.744332\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 99061.9i | 0.786050i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4085.09i | 0.0320527i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 33967.3 | 0.263555 | 0.131778 | − | 0.991279i | \(-0.457932\pi\) | ||||
0.131778 | + | 0.991279i | \(0.457932\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 108643. | − | 71974.3i | 0.833655 | − | 0.552285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 22064.6i | 0.167449i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 37849.7 | 0.284103 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −132869. | −0.986490 | −0.493245 | − | 0.869891i | \(-0.664189\pi\) | ||||
−0.493245 | + | 0.869891i | \(0.664189\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 163419.i | 1.20019i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 349742.i | − | 2.54097i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 76178.5i | 0.547539i | 0.961795 | + | 0.273769i | \(0.0882705\pi\) | ||||
−0.961795 | + | 0.273769i | \(0.911730\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 23942.8i | 0.170260i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −139822. | −0.983770 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 83156.8i | 0.578921i | 0.957190 | + | 0.289461i | \(0.0934759\pi\) | ||||
−0.957190 | + | 0.289461i | \(0.906524\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1629.38 | 0.0112247 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 169744.i | − | 1.15717i | −0.815622 | − | 0.578586i | \(-0.803605\pi\) | ||
0.815622 | − | 0.578586i | \(-0.196395\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10039.3 | −0.0677299 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 240162. | 1.60355 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15312.4 | 0.101191 | 0.0505956 | − | 0.998719i | \(-0.483888\pi\) | ||||
0.0505956 | + | 0.998719i | \(0.483888\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17630.4 | 0.115321 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 24458.6i | 0.158360i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 20751.2i | 0.132999i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 131462. | 0.834100 | 0.417050 | − | 0.908884i | \(-0.363064\pi\) | ||||
0.417050 | + | 0.908884i | \(0.363064\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11782.8 | − | 39120.3i | −0.0740119 | − | 0.245729i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 284670.i | − | 1.77032i | −0.465284 | − | 0.885162i | \(-0.654048\pi\) | ||
0.465284 | − | 0.885162i | \(-0.345952\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 363915. | 2.24073 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 94978.9 | 0.579051 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 18185.3i | − | 0.109782i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 183642.i | 1.09781i | 0.835886 | + | 0.548903i | \(0.184954\pi\) | ||||
−0.835886 | + | 0.548903i | \(0.815046\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 48387.4i | 0.286450i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 239663.i | 1.40508i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10637.0 | −0.0617620 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 9493.12i | − | 0.0545930i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −82365.8 | −0.469157 | −0.234579 | − | 0.972097i | \(-0.575371\pi\) | ||||
−0.234579 | + | 0.972097i | \(0.575371\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 293141.i | 1.65391i | 0.562266 | + | 0.826957i | \(0.309930\pi\) | ||||
−0.562266 | + | 0.826957i | \(0.690070\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −95927.8 | −0.536122 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13541.4 | 0.0749697 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 162140. | 0.889274 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3654.83 | −0.0198588 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 66323.1i | − | 0.357035i | −0.983937 | − | 0.178517i | \(-0.942870\pi\) | ||
0.983937 | − | 0.178517i | \(-0.0571301\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 137702.i | − | 0.734452i | −0.930132 | − | 0.367226i | \(-0.880308\pi\) | ||
0.930132 | − | 0.367226i | \(-0.119692\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11789.1 | 0.0623020 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −168835. | + | 50852.1i | −0.884099 | + | 0.266285i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 311507.i | 1.61636i | 0.588935 | + | 0.808180i | \(0.299547\pi\) | ||||
−0.588935 | + | 0.808180i | \(0.700453\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 250531. | 1.28820 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −320788. | −1.63460 | −0.817299 | − | 0.576214i | \(-0.804530\pi\) | ||||
−0.817299 | + | 0.576214i | \(0.804530\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 176673.i | − | 0.892177i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 37950.3i | − | 0.189933i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 119322.i | − | 0.591873i | −0.955208 | − | 0.295936i | \(-0.904368\pi\) | ||
0.955208 | − | 0.295936i | \(-0.0956316\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 17647.6i | − | 0.0867625i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2352.98 | −0.0114663 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 335362.i | 1.61991i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 44310.8 | 0.212167 | 0.106083 | − | 0.994357i | \(-0.466169\pi\) | ||||
0.106083 | + | 0.994357i | \(0.466169\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8730.64i | 0.0414401i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −292702. | −1.37729 | −0.688643 | − | 0.725101i | \(-0.741793\pi\) | ||||
−0.688643 | + | 0.725101i | \(0.741793\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −293714. | −1.37013 | −0.685067 | − | 0.728480i | \(-0.740227\pi\) | ||||
−0.685067 | + | 0.728480i | \(0.740227\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −30683.5 | −0.141906 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −67231.3 | −0.308275 | −0.154137 | − | 0.988049i | \(-0.549260\pi\) | ||||
−0.154137 | + | 0.988049i | \(0.549260\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 512795.i | − | 2.33130i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 9534.70i | − | 0.0429799i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −25934.9 | −0.115921 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −129677. | + | 39058.0i | −0.574747 | + | 0.173110i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 368367.i | − | 1.61899i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −104619. | −0.455973 | −0.227986 | − | 0.973664i | \(-0.573214\pi\) | ||||
−0.227986 | + | 0.973664i | \(0.573214\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −607478. | −2.62567 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 55279.4i | 0.236957i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 169097.i | − | 0.718875i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 432894.i | − | 1.82526i | −0.408789 | − | 0.912629i | \(-0.634049\pi\) | ||
0.408789 | − | 0.912629i | \(-0.365951\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17355.1i | 0.0725788i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −198985. | −0.825387 | −0.412694 | − | 0.910870i | \(-0.635412\pi\) | ||||
−0.412694 | + | 0.910870i | \(0.635412\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 17775.6i | − | 0.0731358i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10573.9 | −0.0431543 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 468328.i | 1.89600i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −111012. | −0.445828 | −0.222914 | − | 0.974838i | \(-0.571557\pi\) | ||||
−0.222914 | + | 0.974838i | \(0.571557\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −72478.4 | −0.288757 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −413050. | −1.63255 | −0.816276 | − | 0.577662i | \(-0.803965\pi\) | ||||
−0.816276 | + | 0.577662i | \(0.803965\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 271811. | 1.06582 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 78833.6i | 0.306687i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 93319.0i | 0.360193i | 0.983649 | + | 0.180096i | \(0.0576409\pi\) | ||||
−0.983649 | + | 0.180096i | \(0.942359\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 178939. | 0.685273 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −25182.1 | − | 83607.8i | −0.0956880 | − | 0.317696i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 171785.i | 0.647697i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10359.2 | 0.0387566 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 32305.3 | 0.119933 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 381971.i | − | 1.40720i | −0.710598 | − | 0.703598i | \(-0.751576\pi\) | ||
0.710598 | − | 0.703598i | \(-0.248424\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 395430.i | − | 1.44566i | −0.691027 | − | 0.722829i | \(-0.742841\pi\) | ||
0.691027 | − | 0.722829i | \(-0.257159\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 42458.4i | 0.154044i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 46264.6i | 0.166582i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −41265.9 | −0.147462 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 252426.i | 0.895251i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −589517. | −2.07511 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 281008.i | − | 0.981774i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12850.9 | 0.0445639 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −27054.7 | −0.0931249 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 263394. | 0.899934 | 0.449967 | − | 0.893045i | \(-0.351436\pi\) | ||||
0.449967 | + | 0.893045i | \(0.351436\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9843.71 | 0.0333856 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 111402.i | − | 0.375058i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 122704.i | 0.410093i | 0.978752 | + | 0.205047i | \(0.0657346\pi\) | ||||
−0.978752 | + | 0.205047i | \(0.934265\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 170775. | 0.566603 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 51270.8 | + | 170225.i | 0.168876 | + | 0.560688i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 98104.1i | 0.320802i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 51219.5 | 0.166284 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29020.6 | 0.0935397 | 0.0467698 | − | 0.998906i | \(-0.485107\pi\) | ||||
0.0467698 | + | 0.998906i | \(0.485107\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 866357.i | 2.77251i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 464.639i | − | 0.00147635i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 79705.3i | − | 0.251461i | −0.992064 | − | 0.125731i | \(-0.959873\pi\) | ||
0.992064 | − | 0.125731i | \(-0.0401275\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 160457.i | 0.502645i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 449025. | 1.39670 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 449751.i | − | 1.38914i | −0.719423 | − | 0.694572i | \(-0.755594\pi\) | ||
0.719423 | − | 0.694572i | \(-0.244406\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −346869. | −1.06388 | −0.531941 | − | 0.846781i | \(-0.678537\pi\) | ||||
−0.531941 | + | 0.846781i | \(0.678537\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9283.05i | 0.0282736i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 183242. | 0.554230 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 407905. | 1.22520 | 0.612600 | − | 0.790393i | \(-0.290124\pi\) | ||||
0.612600 | + | 0.790393i | \(0.290124\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −27888.5 | −0.0831894 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −50287.6 | −0.148973 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 39779.8i | 0.117038i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 353220.i | 1.03213i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −120671. | −0.350209 | −0.175104 | − | 0.984550i | \(-0.556026\pi\) | ||||
−0.175104 | + | 0.984550i | \(0.556026\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −133443. | − | 443046.i | −0.384648 | − | 1.27708i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19883.9i | 0.0569280i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 671576. | 1.90979 | 0.954896 | − | 0.296942i | \(-0.0959668\pi\) | ||||
0.954896 | + | 0.296942i | \(0.0959668\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −42634.5 | −0.120428 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 76593.9i | 0.214904i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 159147.i | − | 0.443554i | −0.975097 | − | 0.221777i | \(-0.928814\pi\) | ||
0.975097 | − | 0.221777i | \(-0.0711856\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 321439.i | 0.889918i | 0.895551 | + | 0.444959i | \(0.146782\pi\) | ||||
−0.895551 | + | 0.444959i | \(0.853218\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 540102.i | − | 1.48539i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −230280. | −0.629137 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 440276.i | − | 1.19494i | −0.801890 | − | 0.597472i | \(-0.796172\pi\) | ||
0.801890 | − | 0.597472i | \(-0.203828\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 55734.5 | 0.150276 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 346049.i | − | 0.926949i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −516045. | −1.37330 | −0.686652 | − | 0.726986i | \(-0.740920\pi\) | ||||
−0.686652 | + | 0.726986i | \(0.740920\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 49705.1 | 0.131417 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −646632. | −1.69858 | −0.849292 | − | 0.527924i | \(-0.822971\pi\) | ||||
−0.849292 | + | 0.527924i | \(0.822971\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 202214. | 0.527751 | 0.263876 | − | 0.964557i | \(-0.414999\pi\) | ||||
0.263876 | + | 0.964557i | \(0.414999\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 118143.i | 0.306355i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 835247.i | − | 2.15198i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15409.2 | −0.0394476 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1340.17 | + | 4449.55i | 0.00340900 | + | 0.0113183i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 77228.7i | − | 0.195199i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 338994. | 0.851399 | 0.425700 | − | 0.904864i | \(-0.360028\pi\) | ||||
0.425700 | + | 0.904864i | \(0.360028\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −63799.2 | −0.159224 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17005.3i | 0.0421731i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 903764.i | 2.22729i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 493267.i | 1.20804i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 633633.i | 1.54213i | 0.636754 | + | 0.771067i | \(0.280277\pi\) | ||||
−0.636754 | + | 0.771067i | \(0.719723\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −203816. | −0.492965 | −0.246483 | − | 0.969147i | \(-0.579275\pi\) | ||||
−0.246483 | + | 0.969147i | \(0.579275\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 73046.8i | − | 0.175583i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −347996. | −0.831314 | −0.415657 | − | 0.909521i | \(-0.636448\pi\) | ||||
−0.415657 | + | 0.909521i | \(0.636448\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 27259.4i | − | 0.0647182i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −145060. | −0.342284 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −645403. | −1.51358 | −0.756789 | − | 0.653659i | \(-0.773233\pi\) | ||||
−0.756789 | + | 0.653659i | \(0.773233\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −255265. | −0.594990 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 188468. | 0.436623 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 373142.i | 0.859217i | 0.903015 | + | 0.429609i | \(0.141349\pi\) | ||||
−0.903015 | + | 0.429609i | \(0.858651\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 297605.i | 0.681141i | 0.940219 | + | 0.340571i | \(0.110620\pi\) | ||||
−0.940219 | + | 0.340571i | \(0.889380\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −15521.3 | −0.0353102 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 408284. | − | 122972.i | 0.923248 | − | 0.278076i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 240539.i | − | 0.540673i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −34097.6 | −0.0761853 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18441.9 | −0.0409600 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 410131.i | − | 0.905509i | −0.891635 | − | 0.452755i | \(-0.850441\pi\) | ||
0.891635 | − | 0.452755i | \(-0.149559\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 90742.0i | 0.199159i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 308448.i | − | 0.672984i | −0.941686 | − | 0.336492i | \(-0.890759\pi\) | ||
0.941686 | − | 0.336492i | \(-0.109241\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 799429.i | − | 1.73397i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 44806.6 | 0.0966156 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 461976.i | 0.990325i | 0.868800 | + | 0.495162i | \(0.164891\pi\) | ||||
−0.868800 | + | 0.495162i | \(0.835109\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −505001. | −1.07624 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25333.7i | 0.0536765i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.32884e6 | 2.79921 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 365047. | 0.764526 | 0.382263 | − | 0.924054i | \(-0.375145\pi\) | ||||
0.382263 | + | 0.924054i | \(0.375145\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −49989.4 | −0.104090 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 99076.1 | 0.205116 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 74945.3i | − | 0.154269i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2161.88i | 0.00442463i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 174714. | 0.355544 | 0.177772 | − | 0.984072i | \(-0.443111\pi\) | ||||
0.177772 | + | 0.984072i | \(0.443111\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 222754. | + | 739570.i | 0.450728 | + | 1.49647i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 29177.1i | 0.0587036i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.28502e6 | 2.57082 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 624205. | 1.24175 | 0.620876 | − | 0.783909i | \(-0.286777\pi\) | ||||
0.620876 | + | 0.783909i | \(0.286777\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 103328.i | 0.204400i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 626052.i | 1.23149i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 38144.1i | − | 0.0746132i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 105495.i | 0.205209i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −116573. | −0.225496 | −0.112748 | − | 0.993624i | \(-0.535965\pi\) | ||||
−0.112748 | + | 0.993624i | \(0.535965\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 812138.i | 1.56228i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −26594.4 | −0.0508762 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 184751.i | − | 0.351488i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 632724. | 1.19714 | 0.598571 | − | 0.801070i | \(-0.295735\pi\) | ||||
0.598571 | + | 0.801070i | \(0.295735\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 443264. | 0.834079 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −110140. | −0.206115 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −672228. | −1.25115 | −0.625574 | − | 0.780165i | \(-0.715135\pi\) | ||||
−0.625574 | + | 0.780165i | \(0.715135\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 76200.8i | − | 0.141054i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 58325.4i | 0.107380i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 850121. | 1.55665 | 0.778327 | − | 0.627860i | \(-0.216069\pi\) | ||||
0.778327 | + | 0.627860i | \(0.216069\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 148637. | − | 44768.5i | 0.270702 | − | 0.0815336i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 105660.i | 0.191396i | 0.995410 | + | 0.0956980i | \(0.0305083\pi\) | ||||
−0.995410 | + | 0.0956980i | \(0.969492\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 396073. | 0.713613 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −52965.5 | −0.0949188 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1.32850e6i | − | 2.36809i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 783330.i | − | 1.38888i | −0.719550 | − | 0.694441i | \(-0.755652\pi\) | ||
0.719550 | − | 0.694441i | \(-0.244348\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 110588.i | 0.195038i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 24557.2i | − | 0.0430809i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 813155. | 1.41900 | 0.709499 | − | 0.704706i | \(-0.248921\pi\) | ||||
0.709499 | + | 0.704706i | \(0.248921\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 6287.49i | − | 0.0109142i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 74387.2 | 0.128448 | 0.0642242 | − | 0.997935i | \(-0.479543\pi\) | ||||
0.0642242 | + | 0.997935i | \(0.479543\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 526666.i | − | 0.904661i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −44904.9 | −0.0767309 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −910599. | −1.54788 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −228356. | −0.386153 | −0.193076 | − | 0.981184i | \(-0.561846\pi\) | ||||
−0.193076 | + | 0.981184i | \(0.561846\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22179.6 | 0.0373117 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 732635.i | 1.22611i | 0.790041 | + | 0.613054i | \(0.210059\pi\) | ||||
−0.790041 | + | 0.613054i | \(0.789941\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 480851.i | 0.800585i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 242147. | 0.401085 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 216168. | + | 717703.i | 0.356218 | + | 1.18269i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 53267.7i | − | 0.0873297i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 119116. | 0.194288 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 99510.0 | 0.161483 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 759258.i | 1.22586i | 0.790138 | + | 0.612929i | \(0.210009\pi\) | ||||
−0.790138 | + | 0.612929i | \(0.789991\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 142641.i | − | 0.229134i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 758581.i | 1.21241i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 616051.i | 0.979649i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −112041. | −0.177274 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1.10047e6i | − | 1.73245i | −0.499650 | − | 0.866227i | \(-0.666538\pi\) | ||
0.499650 | − | 0.866227i | \(-0.333462\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 43993.2 | 0.0689116 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 879725.i | − | 1.37114i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −20352.6 | −0.0315637 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −576930. | −0.890290 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −120783. | −0.185463 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −687697. | −1.05075 | −0.525375 | − | 0.850871i | \(-0.676075\pi\) | ||||
−0.525375 | + | 0.850871i | \(0.676075\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 194733.i | − | 0.296073i | −0.988982 | − | 0.148036i | \(-0.952705\pi\) | ||
0.988982 | − | 0.148036i | \(-0.0472953\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 104364.i | − | 0.157895i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −181129. | −0.272692 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.05474e6 | − | 317681.i | 1.58016 | − | 0.475934i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.66989e6i | 2.48955i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 341765. | 0.507039 | 0.253519 | − | 0.967330i | \(-0.418412\pi\) | ||||
0.253519 | + | 0.967330i | \(0.418412\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 76669.7 | 0.113194 | 0.0565971 | − | 0.998397i | \(-0.481975\pi\) | ||||
0.0565971 | + | 0.998397i | \(0.481975\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 4829.23i | − | 0.00709529i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25522.2i | 0.0373171i | 0.999826 | + | 0.0186585i | \(0.00593954\pi\) | ||||
−0.999826 | + | 0.0186585i | \(0.994060\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 341385.i | 0.496747i | 0.968664 | + | 0.248374i | \(0.0798961\pi\) | ||||
−0.968664 | + | 0.248374i | \(0.920104\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 137806.i | − | 0.199556i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −114895. | −0.165582 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 756430.i | − | 1.08492i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −310023. | −0.442530 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 617409.i | 0.877099i | 0.898707 | + | 0.438550i | \(0.144508\pi\) | ||||
−0.898707 | + | 0.438550i | \(0.855492\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 464761. | 0.657110 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 109460. | 0.154028 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −822757. | −1.15228 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.08868e6 | −1.51751 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 95704.8i | − | 0.132776i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1.04506e6i | − | 1.44305i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 517750. | 0.711577 | 0.355789 | − | 0.934566i | \(-0.384212\pi\) | ||||
0.355789 | + | 0.934566i | \(0.384212\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 430025. | − | 129521.i | 0.588250 | − | 0.177177i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.44446e6i | − | 1.96673i | −0.181647 | − | 0.983364i | \(-0.558143\pi\) | ||
0.181647 | − | 0.983364i | \(-0.441857\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −836422. | −1.13355 | −0.566773 | − | 0.823874i | \(-0.691808\pi\) | ||||
−0.566773 | + | 0.823874i | \(0.691808\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 234987. | 0.316985 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1.13241e6i | − | 1.52048i | −0.649641 | − | 0.760241i | \(-0.725081\pi\) | ||
0.649641 | − | 0.760241i | \(-0.274919\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 337158.i | 0.450610i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 124521.i | 0.165654i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 11158.4i | − | 0.0147762i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.94836e6 | 2.56822 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 842000.i | − | 1.10480i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.18135e6 | −1.54299 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.06124e6i | 1.37980i | 0.723905 | + | 0.689899i | \(0.242345\pi\) | ||||
−0.723905 | + | 0.689899i | \(0.757655\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −40508.3 | −0.0524284 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38098.7 | 0.0490861 | 0.0245430 | − | 0.999699i | \(-0.492187\pi\) | ||||
0.0245430 | + | 0.999699i | \(0.492187\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −300580. | −0.385513 | −0.192756 | − | 0.981247i | \(-0.561743\pi\) | ||||
−0.192756 | + | 0.981247i | \(0.561743\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 76777.1 | 0.0980269 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 928047.i | 1.17957i | 0.807561 | + | 0.589784i | \(0.200787\pi\) | ||||
−0.807561 | + | 0.589784i | \(0.799213\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 80394.6i | 0.101724i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −51072.2 | −0.0643323 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −421295. | + | 126891.i | −0.528304 | + | 0.159122i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 134120.i | 0.167435i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −210034. | −0.261038 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 631206. | 0.781002 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 168936.i | 0.208100i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 345338.i | − | 0.423516i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 102735.i | 0.125436i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 129940.i | − | 0.157953i | −0.996876 | − | 0.0789764i | \(-0.974835\pi\) | ||
0.996876 | − | 0.0789764i | \(-0.0251652\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.35345e6 | 1.63800 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.14347e6i | 1.37781i | 0.724853 | + | 0.688904i | \(0.241908\pi\) | ||||
−0.724853 | + | 0.688904i | \(0.758092\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5719.73 | 0.00686173 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 51942.3i | − | 0.0620411i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.20680e6 | −1.43515 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 723426. | 0.856571 | 0.428285 | − | 0.903643i | \(-0.359118\pi\) | ||||
0.428285 | + | 0.903643i | \(0.359118\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30362.9 | −0.0357952 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.77941e6 | −2.08868 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 802677.i | − | 0.938118i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 855385.i | 0.995411i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −223643. | −0.259133 | −0.129567 | − | 0.991571i | \(-0.541359\pi\) | ||||
−0.129567 | + | 0.991571i | \(0.541359\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.10028e6 | − | 331397.i | 1.26942 | − | 0.382340i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 138537.i | − | 0.159149i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4849.26 | 0.00554692 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −980898. | −1.11723 | −0.558617 | − | 0.829425i | \(-0.688668\pi\) | ||||
−0.558617 | + | 0.829425i | \(0.688668\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 5706.42i | − | 0.00647192i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 482742.i | 0.545175i | 0.962131 | + | 0.272588i | \(0.0878794\pi\) | ||||
−0.962131 | + | 0.272588i | \(0.912121\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.01416e6i | − | 1.14047i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 285697.i | − | 0.319921i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 325880. | 0.363377 | 0.181688 | − | 0.983356i | \(-0.441844\pi\) | ||||
0.181688 | + | 0.983356i | \(0.441844\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 679878.i | 0.754916i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 158861. | 0.175654 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.78316e6i | 1.96338i | 0.190491 | + | 0.981689i | \(0.438992\pi\) | ||||
−0.190491 | + | 0.981689i | \(0.561008\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −96883.7 | −0.106229 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6339.26 | −0.00692173 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.38746e6 | −2.59596 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −719321. | −0.778890 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 1.39925e6i | − | 1.50884i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 291062.i | − | 0.312558i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −138031. | −0.147613 | −0.0738063 | − | 0.997273i | \(-0.523515\pi\) | ||||
−0.0738063 | + | 0.997273i | \(0.523515\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5691.42 | + | 18896.2i | 0.00606140 | + | 0.0201246i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 497346.i | 0.527498i | 0.964591 | + | 0.263749i | \(0.0849590\pi\) | ||||
−0.964591 | + | 0.263749i | \(0.915041\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 468395. | 0.494751 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −161320. | −0.169699 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 795595.i | 0.833495i | 0.909022 | + | 0.416747i | \(0.136830\pi\) | ||||
−0.909022 | + | 0.416747i | \(0.863170\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 95001.1i | 0.0991205i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 554711.i | − | 0.576407i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 501529.i | − | 0.519026i | −0.965740 | − | 0.259513i | \(-0.916438\pi\) | ||
0.965740 | − | 0.259513i | \(-0.0835621\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −207520. | −0.213889 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 137939.i | 0.141596i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.49041e6 | −1.52375 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.71173e6i | − | 1.74297i | −0.490426 | − | 0.871483i | \(-0.663159\pi\) | ||
0.490426 | − | 0.871483i | \(-0.336841\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 87948.8 | 0.0891931 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −799381. | −0.807436 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.42725e6 | −1.43586 | −0.717928 | − | 0.696118i | \(-0.754909\pi\) | ||||
−0.717928 | + | 0.696118i | \(0.754909\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 517516. | 0.518552 |
(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 | 304.5.e.f.113.9 | 20 | ||
4.3 | odd | 2 | 152.5.e.a.113.12 | yes | 20 | ||
12.11 | even | 2 | 1368.5.o.a.721.8 | 20 | |||
19.18 | odd | 2 | inner | 304.5.e.f.113.12 | 20 | ||
76.75 | even | 2 | 152.5.e.a.113.9 | ✓ | 20 | ||
228.227 | odd | 2 | 1368.5.o.a.721.7 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.5.e.a.113.9 | ✓ | 20 | 76.75 | even | 2 | ||
152.5.e.a.113.12 | yes | 20 | 4.3 | odd | 2 | ||
304.5.e.f.113.9 | 20 | 1.1 | even | 1 | trivial | ||
304.5.e.f.113.12 | 20 | 19.18 | odd | 2 | inner | ||
1368.5.o.a.721.7 | 20 | 228.227 | odd | 2 | |||
1368.5.o.a.721.8 | 20 | 12.11 | even | 2 |