Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [175,4,Mod(99,175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(175, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("175.99");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.b (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: | \(10.3253342510\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.2 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 175.99 |
Dual form | 175.4.b.c.99.3 |
$q$-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 \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.58579i | − 0.914214i | −0.889412 | − | 0.457107i | \(-0.848886\pi\) | ||||
0.889412 | − | 0.457107i | \(-0.151114\pi\) | |||||||
\(3\) | 6.65685i | 1.28111i | 0.767911 | + | 0.640556i | \(0.221296\pi\) | ||||
−0.767911 | + | 0.640556i | \(0.778704\pi\) | |||||||
\(4\) | 1.31371 | 0.164214 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 17.2132 | 1.17121 | ||||||||
\(7\) | 7.00000i | 0.377964i | ||||||||
\(8\) | − 24.0833i | − 1.06434i | ||||||||
\(9\) | −17.3137 | −0.641248 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 38.2548 | 1.04857 | 0.524285 | − | 0.851543i | \(-0.324333\pi\) | ||||
0.524285 | + | 0.851543i | \(0.324333\pi\) | |||||||
\(12\) | 8.74517i | 0.210376i | ||||||||
\(13\) | 19.3431i | 0.412679i | 0.978480 | + | 0.206339i | \(0.0661551\pi\) | ||||
−0.978480 | + | 0.206339i | \(0.933845\pi\) | |||||||
\(14\) | 18.1005 | 0.345540 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −51.7645 | −0.808820 | ||||||||
\(17\) | 87.2254i | 1.24443i | 0.782847 | + | 0.622214i | \(0.213767\pi\) | ||||
−0.782847 | + | 0.622214i | \(0.786233\pi\) | |||||||
\(18\) | 44.7696i | 0.586238i | ||||||||
\(19\) | 44.2254 | 0.534000 | 0.267000 | − | 0.963697i | \(-0.413968\pi\) | ||||
0.267000 | + | 0.963697i | \(0.413968\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −46.5980 | −0.484215 | ||||||||
\(22\) | − 98.9188i | − 0.958617i | ||||||||
\(23\) | 218.167i | 1.97786i | 0.148371 | + | 0.988932i | \(0.452597\pi\) | ||||
−0.148371 | + | 0.988932i | \(0.547403\pi\) | |||||||
\(24\) | 160.319 | 1.36354 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 50.0172 | 0.377276 | ||||||||
\(27\) | 64.4802i | 0.459601i | ||||||||
\(28\) | 9.19596i | 0.0620669i | ||||||||
\(29\) | 46.9411 | 0.300578 | 0.150289 | − | 0.988642i | \(-0.451980\pi\) | ||||
0.150289 | + | 0.988642i | \(0.451980\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 194.558 | 1.12722 | 0.563609 | − | 0.826042i | \(-0.309413\pi\) | ||||
0.563609 | + | 0.826042i | \(0.309413\pi\) | |||||||
\(32\) | − 58.8141i | − 0.324905i | ||||||||
\(33\) | 254.657i | 1.34334i | ||||||||
\(34\) | 225.546 | 1.13767 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −22.7452 | −0.105302 | ||||||||
\(37\) | − 366.853i | − 1.63001i | −0.579457 | − | 0.815003i | \(-0.696735\pi\) | ||||
0.579457 | − | 0.815003i | \(-0.303265\pi\) | |||||||
\(38\) | − 114.357i | − 0.488190i | ||||||||
\(39\) | −128.765 | −0.528688 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −339.362 | −1.29267 | −0.646336 | − | 0.763053i | \(-0.723699\pi\) | ||||
−0.646336 | + | 0.763053i | \(0.723699\pi\) | |||||||
\(42\) | 120.492i | 0.442676i | ||||||||
\(43\) | − 226.167i | − 0.802095i | −0.916057 | − | 0.401047i | \(-0.868646\pi\) | ||||
0.916057 | − | 0.401047i | \(-0.131354\pi\) | |||||||
\(44\) | 50.2557 | 0.172189 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 564.132 | 1.80819 | ||||||||
\(47\) | − 11.6762i | − 0.0362372i | −0.999836 | − | 0.0181186i | \(-0.994232\pi\) | ||||
0.999836 | − | 0.0181186i | \(-0.00576764\pi\) | |||||||
\(48\) | − 344.589i | − 1.03619i | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −580.647 | −1.59425 | ||||||||
\(52\) | 25.4113i | 0.0677674i | ||||||||
\(53\) | − 209.019i | − 0.541717i | −0.962619 | − | 0.270859i | \(-0.912692\pi\) | ||||
0.962619 | − | 0.270859i | \(-0.0873076\pi\) | |||||||
\(54\) | 166.732 | 0.420173 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 168.583 | 0.402283 | ||||||||
\(57\) | 294.402i | 0.684114i | ||||||||
\(58\) | − 121.380i | − 0.274792i | ||||||||
\(59\) | 616.000 | 1.35926 | 0.679630 | − | 0.733555i | \(-0.262140\pi\) | ||||
0.679630 | + | 0.733555i | \(0.262140\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 320.735 | 0.673212 | 0.336606 | − | 0.941646i | \(-0.390721\pi\) | ||||
0.336606 | + | 0.941646i | \(0.390721\pi\) | |||||||
\(62\) | − 503.087i | − 1.03052i | ||||||||
\(63\) | − 121.196i | − 0.242369i | ||||||||
\(64\) | −566.197 | −1.10585 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 658.488 | 1.22810 | ||||||||
\(67\) | − 14.5097i | − 0.0264573i | −0.999912 | − | 0.0132286i | \(-0.995789\pi\) | ||||
0.999912 | − | 0.0132286i | \(-0.00421093\pi\) | |||||||
\(68\) | 114.589i | 0.204352i | ||||||||
\(69\) | −1452.30 | −2.53387 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −952.000 | −1.59129 | −0.795645 | − | 0.605763i | \(-0.792868\pi\) | ||||
−0.795645 | + | 0.605763i | \(0.792868\pi\) | |||||||
\(72\) | 416.971i | 0.682506i | ||||||||
\(73\) | 824.489i | 1.32191i | 0.750427 | + | 0.660953i | \(0.229848\pi\) | ||||
−0.750427 | + | 0.660953i | \(0.770152\pi\) | |||||||
\(74\) | −948.603 | −1.49017 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 58.0993 | 0.0876901 | ||||||||
\(77\) | 267.784i | 0.396322i | ||||||||
\(78\) | 332.958i | 0.483334i | ||||||||
\(79\) | −156.275 | −0.222561 | −0.111280 | − | 0.993789i | \(-0.535495\pi\) | ||||
−0.111280 | + | 0.993789i | \(0.535495\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −896.706 | −1.23005 | ||||||||
\(82\) | 877.519i | 1.18178i | ||||||||
\(83\) | − 1036.53i | − 1.37077i | −0.728182 | − | 0.685384i | \(-0.759634\pi\) | ||||
0.728182 | − | 0.685384i | \(-0.240366\pi\) | |||||||
\(84\) | −61.2162 | −0.0795147 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −584.818 | −0.733286 | ||||||||
\(87\) | 312.480i | 0.385074i | ||||||||
\(88\) | − 921.301i | − 1.11603i | ||||||||
\(89\) | 170.225 | 0.202740 | 0.101370 | − | 0.994849i | \(-0.467677\pi\) | ||||
0.101370 | + | 0.994849i | \(0.467677\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −135.402 | −0.155978 | ||||||||
\(92\) | 286.607i | 0.324792i | ||||||||
\(93\) | 1295.15i | 1.44409i | ||||||||
\(94\) | −30.1921 | −0.0331285 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 391.517 | 0.416240 | ||||||||
\(97\) | − 1059.87i | − 1.10942i | −0.832044 | − | 0.554710i | \(-0.812829\pi\) | ||||
0.832044 | − | 0.554710i | \(-0.187171\pi\) | |||||||
\(98\) | 126.704i | 0.130602i | ||||||||
\(99\) | −662.333 | −0.672394 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −241.833 | −0.238251 | −0.119125 | − | 0.992879i | \(-0.538009\pi\) | ||||
−0.119125 | + | 0.992879i | \(0.538009\pi\) | |||||||
\(102\) | 1501.43i | 1.45749i | ||||||||
\(103\) | − 1679.58i | − 1.60673i | −0.595484 | − | 0.803367i | \(-0.703040\pi\) | ||||
0.595484 | − | 0.803367i | \(-0.296960\pi\) | |||||||
\(104\) | 465.846 | 0.439230 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −540.479 | −0.495245 | ||||||||
\(107\) | − 1506.88i | − 1.36146i | −0.732537 | − | 0.680728i | \(-0.761664\pi\) | ||||
0.732537 | − | 0.680728i | \(-0.238336\pi\) | |||||||
\(108\) | 84.7082i | 0.0754727i | ||||||||
\(109\) | 1252.41 | 1.10054 | 0.550271 | − | 0.834986i | \(-0.314524\pi\) | ||||
0.550271 | + | 0.834986i | \(0.314524\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2442.09 | 2.08822 | ||||||||
\(112\) | − 362.352i | − 0.305705i | ||||||||
\(113\) | 1370.20i | 1.14069i | 0.821405 | + | 0.570345i | \(0.193190\pi\) | ||||
−0.821405 | + | 0.570345i | \(0.806810\pi\) | |||||||
\(114\) | 761.261 | 0.625426 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 61.6670 | 0.0493589 | ||||||||
\(117\) | − 334.902i | − 0.264630i | ||||||||
\(118\) | − 1592.84i | − 1.24265i | ||||||||
\(119\) | −610.578 | −0.470349 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 132.432 | 0.0994984 | ||||||||
\(122\) | − 829.352i | − 0.615459i | ||||||||
\(123\) | − 2259.09i | − 1.65606i | ||||||||
\(124\) | 255.593 | 0.185104 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −313.387 | −0.221577 | ||||||||
\(127\) | − 1213.49i | − 0.847873i | −0.905692 | − | 0.423936i | \(-0.860648\pi\) | ||||
0.905692 | − | 0.423936i | \(-0.139352\pi\) | |||||||
\(128\) | 993.551i | 0.686081i | ||||||||
\(129\) | 1505.56 | 1.02757 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1982.42 | −1.32217 | −0.661087 | − | 0.750309i | \(-0.729904\pi\) | ||||
−0.661087 | + | 0.750309i | \(0.729904\pi\) | |||||||
\(132\) | 334.545i | 0.220594i | ||||||||
\(133\) | 309.578i | 0.201833i | ||||||||
\(134\) | −37.5189 | −0.0241876 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2100.67 | 1.32449 | ||||||||
\(137\) | − 2210.95i | − 1.37879i | −0.724386 | − | 0.689394i | \(-0.757877\pi\) | ||||
0.724386 | − | 0.689394i | \(-0.242123\pi\) | |||||||
\(138\) | 3755.34i | 2.31649i | ||||||||
\(139\) | −528.039 | −0.322213 | −0.161107 | − | 0.986937i | \(-0.551506\pi\) | ||||
−0.161107 | + | 0.986937i | \(0.551506\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 77.7267 | 0.0464239 | ||||||||
\(142\) | 2461.67i | 1.45478i | ||||||||
\(143\) | 739.969i | 0.432722i | ||||||||
\(144\) | 896.235 | 0.518655 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2131.95 | 1.20851 | ||||||||
\(147\) | − 326.186i | − 0.183016i | ||||||||
\(148\) | − 481.938i | − 0.267669i | ||||||||
\(149\) | 328.372 | 0.180545 | 0.0902727 | − | 0.995917i | \(-0.471226\pi\) | ||||
0.0902727 | + | 0.995917i | \(0.471226\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1029.43 | 0.554793 | 0.277396 | − | 0.960756i | \(-0.410528\pi\) | ||||
0.277396 | + | 0.960756i | \(0.410528\pi\) | |||||||
\(152\) | − 1065.09i | − 0.568358i | ||||||||
\(153\) | − 1510.20i | − 0.797987i | ||||||||
\(154\) | 692.432 | 0.362323 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −169.159 | −0.0868177 | ||||||||
\(157\) | − 525.098i | − 0.266926i | −0.991054 | − | 0.133463i | \(-0.957390\pi\) | ||||
0.991054 | − | 0.133463i | \(-0.0426098\pi\) | |||||||
\(158\) | 404.094i | 0.203468i | ||||||||
\(159\) | 1391.41 | 0.694001 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1527.17 | −0.747562 | ||||||||
\(162\) | 2318.69i | 1.12453i | ||||||||
\(163\) | 1002.63i | 0.481790i | 0.970551 | + | 0.240895i | \(0.0774409\pi\) | ||||
−0.970551 | + | 0.240895i | \(0.922559\pi\) | |||||||
\(164\) | −445.823 | −0.212274 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2680.24 | −1.25317 | ||||||||
\(167\) | 359.422i | 0.166544i | 0.996527 | + | 0.0832722i | \(0.0265371\pi\) | ||||
−0.996527 | + | 0.0832722i | \(0.973463\pi\) | |||||||
\(168\) | 1122.23i | 0.515369i | ||||||||
\(169\) | 1822.84 | 0.829696 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −765.706 | −0.342427 | ||||||||
\(172\) | − 297.117i | − 0.131715i | ||||||||
\(173\) | 3293.65i | 1.44747i | 0.690080 | + | 0.723733i | \(0.257575\pi\) | ||||
−0.690080 | + | 0.723733i | \(0.742425\pi\) | |||||||
\(174\) | 808.007 | 0.352039 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1980.24 | −0.848104 | ||||||||
\(177\) | 4100.62i | 1.74137i | ||||||||
\(178\) | − 440.167i | − 0.185348i | ||||||||
\(179\) | −2978.82 | −1.24384 | −0.621921 | − | 0.783080i | \(-0.713647\pi\) | ||||
−0.621921 | + | 0.783080i | \(0.713647\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1462.31 | 0.600514 | 0.300257 | − | 0.953858i | \(-0.402928\pi\) | ||||
0.300257 | + | 0.953858i | \(0.402928\pi\) | |||||||
\(182\) | 350.121i | 0.142597i | ||||||||
\(183\) | 2135.09i | 0.862460i | ||||||||
\(184\) | 5254.16 | 2.10512 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3348.97 | 1.32021 | ||||||||
\(187\) | 3336.79i | 1.30487i | ||||||||
\(188\) | − 15.3391i | − 0.00595064i | ||||||||
\(189\) | −451.362 | −0.173713 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −374.923 | −0.142034 | −0.0710169 | − | 0.997475i | \(-0.522624\pi\) | ||||
−0.0710169 | + | 0.997475i | \(0.522624\pi\) | |||||||
\(192\) | − 3769.09i | − 1.41672i | ||||||||
\(193\) | 733.028i | 0.273391i | 0.990613 | + | 0.136696i | \(0.0436482\pi\) | ||||
−0.990613 | + | 0.136696i | \(0.956352\pi\) | |||||||
\(194\) | −2740.61 | −1.01425 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −64.3717 | −0.0234591 | ||||||||
\(197\) | 2093.24i | 0.757043i | 0.925593 | + | 0.378521i | \(0.123567\pi\) | ||||
−0.925593 | + | 0.378521i | \(0.876433\pi\) | |||||||
\(198\) | 1712.65i | 0.614711i | ||||||||
\(199\) | −2865.04 | −1.02059 | −0.510295 | − | 0.860000i | \(-0.670464\pi\) | ||||
−0.510295 | + | 0.860000i | \(0.670464\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 96.5887 | 0.0338948 | ||||||||
\(202\) | 625.330i | 0.217812i | ||||||||
\(203\) | 328.588i | 0.113608i | ||||||||
\(204\) | −762.801 | −0.261798 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4343.03 | −1.46890 | ||||||||
\(207\) | − 3777.27i | − 1.26830i | ||||||||
\(208\) | − 1001.29i | − 0.333783i | ||||||||
\(209\) | 1691.84 | 0.559936 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5643.65 | 1.84135 | 0.920674 | − | 0.390331i | \(-0.127640\pi\) | ||||
0.920674 | + | 0.390331i | \(0.127640\pi\) | |||||||
\(212\) | − 274.590i | − 0.0889573i | ||||||||
\(213\) | − 6337.33i | − 2.03862i | ||||||||
\(214\) | −3896.47 | −1.24466 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1552.89 | 0.489172 | ||||||||
\(217\) | 1361.91i | 0.426048i | ||||||||
\(218\) | − 3238.46i | − 1.00613i | ||||||||
\(219\) | −5488.51 | −1.69351 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1687.21 | −0.513549 | ||||||||
\(222\) | − 6314.71i | − 1.90908i | ||||||||
\(223\) | − 6369.16i | − 1.91260i | −0.292381 | − | 0.956302i | \(-0.594448\pi\) | ||||
0.292381 | − | 0.956302i | \(-0.405552\pi\) | |||||||
\(224\) | 411.699 | 0.122803 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3543.05 | 1.04283 | ||||||||
\(227\) | 1015.67i | 0.296972i | 0.988914 | + | 0.148486i | \(0.0474400\pi\) | ||||
−0.988914 | + | 0.148486i | \(0.952560\pi\) | |||||||
\(228\) | 386.758i | 0.112341i | ||||||||
\(229\) | −4108.35 | −1.18554 | −0.592768 | − | 0.805373i | \(-0.701965\pi\) | ||||
−0.592768 | + | 0.805373i | \(0.701965\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1782.60 | −0.507733 | ||||||||
\(232\) | − 1130.50i | − 0.319917i | ||||||||
\(233\) | 608.431i | 0.171071i | 0.996335 | + | 0.0855357i | \(0.0272602\pi\) | ||||
−0.996335 | + | 0.0855357i | \(0.972740\pi\) | |||||||
\(234\) | −865.984 | −0.241928 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 809.244 | 0.223209 | ||||||||
\(237\) | − 1040.30i | − 0.285126i | ||||||||
\(238\) | 1578.82i | 0.430000i | ||||||||
\(239\) | 5054.44 | 1.36797 | 0.683985 | − | 0.729496i | \(-0.260245\pi\) | ||||
0.683985 | + | 0.729496i | \(0.260245\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.86782 | 0.00130109 | 0.000650547 | − | 1.00000i | \(-0.499793\pi\) | ||||
0.000650547 | 1.00000i | \(0.499793\pi\) | ||||||||
\(242\) | − 342.442i | − 0.0909628i | ||||||||
\(243\) | − 4228.27i | − 1.11623i | ||||||||
\(244\) | 421.352 | 0.110551 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5841.52 | −1.51399 | ||||||||
\(247\) | 855.458i | 0.220370i | ||||||||
\(248\) | − 4685.60i | − 1.19974i | ||||||||
\(249\) | 6900.02 | 1.75611 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −547.921 | −0.137787 | −0.0688934 | − | 0.997624i | \(-0.521947\pi\) | ||||
−0.0688934 | + | 0.997624i | \(0.521947\pi\) | |||||||
\(252\) | − 159.216i | − 0.0398003i | ||||||||
\(253\) | 8345.92i | 2.07393i | ||||||||
\(254\) | −3137.83 | −0.775137 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1960.46 | −0.478629 | ||||||||
\(257\) | 1774.61i | 0.430729i | 0.976534 | + | 0.215364i | \(0.0690939\pi\) | ||||
−0.976534 | + | 0.215364i | \(0.930906\pi\) | |||||||
\(258\) | − 3893.05i | − 0.939421i | ||||||||
\(259\) | 2567.97 | 0.616084 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −812.725 | −0.192745 | ||||||||
\(262\) | 5126.11i | 1.20875i | ||||||||
\(263\) | − 1199.09i | − 0.281138i | −0.990071 | − | 0.140569i | \(-0.955107\pi\) | ||||
0.990071 | − | 0.140569i | \(-0.0448932\pi\) | |||||||
\(264\) | 6132.97 | 1.42977 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 800.502 | 0.184519 | ||||||||
\(267\) | 1133.17i | 0.259733i | ||||||||
\(268\) | − 19.0615i | − 0.00434464i | ||||||||
\(269\) | −3250.29 | −0.736706 | −0.368353 | − | 0.929686i | \(-0.620078\pi\) | ||||
−0.368353 | + | 0.929686i | \(0.620078\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −896.143 | −0.200874 | −0.100437 | − | 0.994943i | \(-0.532024\pi\) | ||||
−0.100437 | + | 0.994943i | \(0.532024\pi\) | |||||||
\(272\) | − 4515.18i | − 1.00652i | ||||||||
\(273\) | − 901.352i | − 0.199825i | ||||||||
\(274\) | −5717.04 | −1.26051 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1907.90 | −0.416095 | ||||||||
\(277\) | 386.562i | 0.0838492i | 0.999121 | + | 0.0419246i | \(0.0133489\pi\) | ||||
−0.999121 | + | 0.0419246i | \(0.986651\pi\) | |||||||
\(278\) | 1365.40i | 0.294572i | ||||||||
\(279\) | −3368.53 | −0.722826 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3335.10 | −0.708025 | −0.354013 | − | 0.935241i | \(-0.615183\pi\) | ||||
−0.354013 | + | 0.935241i | \(0.615183\pi\) | |||||||
\(282\) | − 200.985i | − 0.0424414i | ||||||||
\(283\) | 5412.26i | 1.13684i | 0.822739 | + | 0.568419i | \(0.192445\pi\) | ||||
−0.822739 | + | 0.568419i | \(0.807555\pi\) | |||||||
\(284\) | −1250.65 | −0.261311 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1913.40 | 0.395601 | ||||||||
\(287\) | − 2375.54i | − 0.488584i | ||||||||
\(288\) | 1018.29i | 0.208345i | ||||||||
\(289\) | −2695.27 | −0.548600 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7055.42 | 1.42129 | ||||||||
\(292\) | 1083.14i | 0.217075i | ||||||||
\(293\) | 282.211i | 0.0562695i | 0.999604 | + | 0.0281347i | \(0.00895675\pi\) | ||||
−0.999604 | + | 0.0281347i | \(0.991043\pi\) | |||||||
\(294\) | −843.447 | −0.167316 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8835.01 | −1.73488 | ||||||||
\(297\) | 2466.68i | 0.481924i | ||||||||
\(298\) | − 849.099i | − 0.165057i | ||||||||
\(299\) | −4220.03 | −0.816222 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1583.17 | 0.303163 | ||||||||
\(302\) | − 2661.88i | − 0.507199i | ||||||||
\(303\) | − 1609.85i | − 0.305226i | ||||||||
\(304\) | −2289.31 | −0.431910 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3905.04 | −0.729531 | ||||||||
\(307\) | − 1919.67i | − 0.356878i | −0.983951 | − | 0.178439i | \(-0.942895\pi\) | ||||
0.983951 | − | 0.178439i | \(-0.0571048\pi\) | |||||||
\(308\) | 351.790i | 0.0650815i | ||||||||
\(309\) | 11180.7 | 2.05841 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1213.31 | 0.221223 | 0.110612 | − | 0.993864i | \(-0.464719\pi\) | ||||
0.110612 | + | 0.993864i | \(0.464719\pi\) | |||||||
\(312\) | 3101.07i | 0.562703i | ||||||||
\(313\) | − 1434.00i | − 0.258960i | −0.991582 | − | 0.129480i | \(-0.958669\pi\) | ||||
0.991582 | − | 0.129480i | \(-0.0413309\pi\) | |||||||
\(314\) | −1357.79 | −0.244028 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −205.300 | −0.0365475 | ||||||||
\(317\) | − 6496.95i | − 1.15112i | −0.817760 | − | 0.575560i | \(-0.804784\pi\) | ||||
0.817760 | − | 0.575560i | \(-0.195216\pi\) | |||||||
\(318\) | − 3597.89i | − 0.634465i | ||||||||
\(319\) | 1795.72 | 0.315176 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10031.1 | 1.74418 | ||||||||
\(322\) | 3948.92i | 0.683432i | ||||||||
\(323\) | 3857.58i | 0.664524i | ||||||||
\(324\) | −1178.01 | −0.201991 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2592.58 | 0.440459 | ||||||||
\(327\) | 8337.11i | 1.40992i | ||||||||
\(328\) | 8172.96i | 1.37584i | ||||||||
\(329\) | 81.7333 | 0.0136964 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9683.88 | −1.60808 | −0.804039 | − | 0.594576i | \(-0.797320\pi\) | ||||
−0.804039 | + | 0.594576i | \(0.797320\pi\) | |||||||
\(332\) | − 1361.70i | − 0.225099i | ||||||||
\(333\) | 6351.58i | 1.04524i | ||||||||
\(334\) | 929.389 | 0.152257 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2412.12 | 0.391643 | ||||||||
\(337\) | − 29.1319i | − 0.00470895i | −0.999997 | − | 0.00235447i | \(-0.999251\pi\) | ||||
0.999997 | − | 0.00235447i | \(-0.000749453\pi\) | |||||||
\(338\) | − 4713.48i | − 0.758520i | ||||||||
\(339\) | −9121.24 | −1.46135 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7442.80 | 1.18197 | ||||||||
\(342\) | 1979.95i | 0.313051i | ||||||||
\(343\) | − 343.000i | − 0.0539949i | ||||||||
\(344\) | −5446.83 | −0.853701 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8516.68 | 1.32329 | ||||||||
\(347\) | 7848.58i | 1.21422i | 0.794618 | + | 0.607110i | \(0.207671\pi\) | ||||
−0.794618 | + | 0.607110i | \(0.792329\pi\) | |||||||
\(348\) | 410.508i | 0.0632343i | ||||||||
\(349\) | 10269.6 | 1.57513 | 0.787567 | − | 0.616229i | \(-0.211341\pi\) | ||||
0.787567 | + | 0.616229i | \(0.211341\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1247.25 | −0.189668 | ||||||||
\(352\) | − 2249.93i | − 0.340686i | ||||||||
\(353\) | 2799.93i | 0.422168i | 0.977468 | + | 0.211084i | \(0.0676994\pi\) | ||||
−0.977468 | + | 0.211084i | \(0.932301\pi\) | |||||||
\(354\) | 10603.3 | 1.59198 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 223.627 | 0.0332927 | ||||||||
\(357\) | − 4064.53i | − 0.602570i | ||||||||
\(358\) | 7702.60i | 1.13714i | ||||||||
\(359\) | 3163.29 | 0.465048 | 0.232524 | − | 0.972591i | \(-0.425302\pi\) | ||||
0.232524 | + | 0.972591i | \(0.425302\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4903.11 | −0.714844 | ||||||||
\(362\) | − 3781.23i | − 0.548998i | ||||||||
\(363\) | 881.583i | 0.127469i | ||||||||
\(364\) | −177.879 | −0.0256137 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5520.88 | 0.788472 | ||||||||
\(367\) | − 3182.85i | − 0.452706i | −0.974045 | − | 0.226353i | \(-0.927320\pi\) | ||||
0.974045 | − | 0.226353i | \(-0.0726803\pi\) | |||||||
\(368\) | − 11293.3i | − 1.59974i | ||||||||
\(369\) | 5875.62 | 0.828923 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1463.14 | 0.204750 | ||||||||
\(372\) | 1701.45i | 0.237139i | ||||||||
\(373\) | − 2615.14i | − 0.363021i | −0.983389 | − | 0.181510i | \(-0.941901\pi\) | ||||
0.983389 | − | 0.181510i | \(-0.0580986\pi\) | |||||||
\(374\) | 8628.23 | 1.19293 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −281.201 | −0.0385687 | ||||||||
\(377\) | 907.989i | 0.124042i | ||||||||
\(378\) | 1167.12i | 0.158811i | ||||||||
\(379\) | 672.434 | 0.0911362 | 0.0455681 | − | 0.998961i | \(-0.485490\pi\) | ||||
0.0455681 | + | 0.998961i | \(0.485490\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8078.03 | 1.08622 | ||||||||
\(382\) | 969.470i | 0.129849i | ||||||||
\(383\) | 1169.86i | 0.156075i | 0.996950 | + | 0.0780377i | \(0.0248655\pi\) | ||||
−0.996950 | + | 0.0780377i | \(0.975135\pi\) | |||||||
\(384\) | −6613.92 | −0.878946 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1895.45 | 0.249938 | ||||||||
\(387\) | 3915.78i | 0.514342i | ||||||||
\(388\) | − 1392.36i | − 0.182182i | ||||||||
\(389\) | 1122.22 | 0.146269 | 0.0731347 | − | 0.997322i | \(-0.476700\pi\) | ||||
0.0731347 | + | 0.997322i | \(0.476700\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19029.7 | −2.46131 | ||||||||
\(392\) | 1180.08i | 0.152049i | ||||||||
\(393\) | − 13196.7i | − 1.69385i | ||||||||
\(394\) | 5412.68 | 0.692099 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −870.113 | −0.110416 | ||||||||
\(397\) | 1985.93i | 0.251060i | 0.992090 | + | 0.125530i | \(0.0400631\pi\) | ||||
−0.992090 | + | 0.125530i | \(0.959937\pi\) | |||||||
\(398\) | 7408.38i | 0.933037i | ||||||||
\(399\) | −2060.81 | −0.258571 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4172.38 | −0.519597 | −0.259799 | − | 0.965663i | \(-0.583656\pi\) | ||||
−0.259799 | + | 0.965663i | \(0.583656\pi\) | |||||||
\(402\) | − 249.758i | − 0.0309870i | ||||||||
\(403\) | 3763.37i | 0.465178i | ||||||||
\(404\) | −317.699 | −0.0391240 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 849.658 | 0.103862 | ||||||||
\(407\) | − 14033.9i | − 1.70918i | ||||||||
\(408\) | 13983.9i | 1.69682i | ||||||||
\(409\) | 11700.8 | 1.41459 | 0.707295 | − | 0.706919i | \(-0.249915\pi\) | ||||
0.707295 | + | 0.706919i | \(0.249915\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14718.0 | 1.76638 | ||||||||
\(412\) | − 2206.47i | − 0.263848i | ||||||||
\(413\) | 4312.00i | 0.513752i | ||||||||
\(414\) | −9767.22 | −1.15950 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1137.65 | 0.134082 | ||||||||
\(417\) | − 3515.08i | − 0.412791i | ||||||||
\(418\) | − 4374.72i | − 0.511901i | ||||||||
\(419\) | −2733.20 | −0.318677 | −0.159339 | − | 0.987224i | \(-0.550936\pi\) | ||||
−0.159339 | + | 0.987224i | \(0.550936\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13549.4 | 1.56854 | 0.784272 | − | 0.620417i | \(-0.213037\pi\) | ||||
0.784272 | + | 0.620417i | \(0.213037\pi\) | |||||||
\(422\) | − 14593.3i | − 1.68339i | ||||||||
\(423\) | 202.158i | 0.0232370i | ||||||||
\(424\) | −5033.87 | −0.576571 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −16387.0 | −1.86374 | ||||||||
\(427\) | 2245.15i | 0.254450i | ||||||||
\(428\) | − 1979.60i | − 0.223569i | ||||||||
\(429\) | −4925.86 | −0.554366 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6429.25 | −0.718530 | −0.359265 | − | 0.933236i | \(-0.616973\pi\) | ||||
−0.359265 | + | 0.933236i | \(0.616973\pi\) | |||||||
\(432\) | − 3337.79i | − 0.371735i | ||||||||
\(433\) | 8022.03i | 0.890333i | 0.895448 | + | 0.445166i | \(0.146855\pi\) | ||||
−0.895448 | + | 0.445166i | \(0.853145\pi\) | |||||||
\(434\) | 3521.61 | 0.389499 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1645.30 | 0.180724 | ||||||||
\(437\) | 9648.50i | 1.05618i | ||||||||
\(438\) | 14192.1i | 1.54823i | ||||||||
\(439\) | 5569.88 | 0.605549 | 0.302774 | − | 0.953062i | \(-0.402087\pi\) | ||||
0.302774 | + | 0.953062i | \(0.402087\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 848.372 | 0.0916069 | ||||||||
\(442\) | 4362.77i | 0.469493i | ||||||||
\(443\) | − 5486.21i | − 0.588392i | −0.955745 | − | 0.294196i | \(-0.904948\pi\) | ||||
0.955745 | − | 0.294196i | \(-0.0950519\pi\) | |||||||
\(444\) | 3208.19 | 0.342914 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −16469.3 | −1.74853 | ||||||||
\(447\) | 2185.92i | 0.231299i | ||||||||
\(448\) | − 3963.38i | − 0.417973i | ||||||||
\(449\) | 7232.67 | 0.760203 | 0.380101 | − | 0.924945i | \(-0.375889\pi\) | ||||
0.380101 | + | 0.924945i | \(0.375889\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12982.3 | −1.35546 | ||||||||
\(452\) | 1800.05i | 0.187317i | ||||||||
\(453\) | 6852.76i | 0.710752i | ||||||||
\(454\) | 2626.32 | 0.271496 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7090.16 | 0.728130 | ||||||||
\(457\) | 2900.51i | 0.296893i | 0.988920 | + | 0.148446i | \(0.0474272\pi\) | ||||
−0.988920 | + | 0.148446i | \(0.952573\pi\) | |||||||
\(458\) | 10623.3i | 1.08383i | ||||||||
\(459\) | −5624.31 | −0.571940 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6073.57 | 0.613611 | 0.306805 | − | 0.951772i | \(-0.400740\pi\) | ||||
0.306805 | + | 0.951772i | \(0.400740\pi\) | |||||||
\(462\) | 4609.42i | 0.464176i | ||||||||
\(463\) | − 18922.8i | − 1.89939i | −0.313183 | − | 0.949693i | \(-0.601395\pi\) | ||||
0.313183 | − | 0.949693i | \(-0.398605\pi\) | |||||||
\(464\) | −2429.88 | −0.243113 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1573.27 | 0.156396 | ||||||||
\(467\) | 6776.71i | 0.671496i | 0.941952 | + | 0.335748i | \(0.108989\pi\) | ||||
−0.941952 | + | 0.335748i | \(0.891011\pi\) | |||||||
\(468\) | − 439.963i | − 0.0434558i | ||||||||
\(469\) | 101.568 | 0.00999991 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3495.50 | 0.341962 | ||||||||
\(472\) | − 14835.3i | − 1.44672i | ||||||||
\(473\) | − 8651.96i | − 0.841052i | ||||||||
\(474\) | −2689.99 | −0.260666 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −802.121 | −0.0772377 | ||||||||
\(477\) | 3618.90i | 0.347375i | ||||||||
\(478\) | − 13069.7i | − 1.25062i | ||||||||
\(479\) | −2397.32 | −0.228677 | −0.114338 | − | 0.993442i | \(-0.536475\pi\) | ||||
−0.114338 | + | 0.993442i | \(0.536475\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7096.09 | 0.672669 | ||||||||
\(482\) | − 12.5871i | − 0.00118948i | ||||||||
\(483\) | − 10166.1i | − 0.957711i | ||||||||
\(484\) | 173.977 | 0.0163390 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −10933.4 | −1.02047 | ||||||||
\(487\) | − 5586.17i | − 0.519781i | −0.965638 | − | 0.259890i | \(-0.916314\pi\) | ||||
0.965638 | − | 0.259890i | \(-0.0836865\pi\) | |||||||
\(488\) | − 7724.35i | − 0.716526i | ||||||||
\(489\) | −6674.33 | −0.617227 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 537.392 | 0.0493934 | 0.0246967 | − | 0.999695i | \(-0.492138\pi\) | ||||
0.0246967 | + | 0.999695i | \(0.492138\pi\) | |||||||
\(492\) | − 2967.78i | − 0.271947i | ||||||||
\(493\) | 4094.46i | 0.374047i | ||||||||
\(494\) | 2212.03 | 0.201466 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10071.2 | −0.911716 | ||||||||
\(497\) | − 6664.00i | − 0.601451i | ||||||||
\(498\) | − 17842.0i | − 1.60546i | ||||||||
\(499\) | −598.965 | −0.0537342 | −0.0268671 | − | 0.999639i | \(-0.508553\pi\) | ||||
−0.0268671 | + | 0.999639i | \(0.508553\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2392.62 | −0.213362 | ||||||||
\(502\) | 1416.81i | 0.125966i | ||||||||
\(503\) | 4426.76i | 0.392405i | 0.980563 | + | 0.196202i | \(0.0628610\pi\) | ||||
−0.980563 | + | 0.196202i | \(0.937139\pi\) | |||||||
\(504\) | −2918.79 | −0.257963 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 21580.8 | 1.89601 | ||||||||
\(507\) | 12134.4i | 1.06293i | ||||||||
\(508\) | − 1594.17i | − 0.139232i | ||||||||
\(509\) | −17727.7 | −1.54374 | −0.771872 | − | 0.635779i | \(-0.780679\pi\) | ||||
−0.771872 | + | 0.635779i | \(0.780679\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5771.43 | −0.499634 | ||||||||
\(512\) | 13017.7i | 1.12365i | ||||||||
\(513\) | 2851.66i | 0.245427i | ||||||||
\(514\) | 4588.77 | 0.393778 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1977.86 | 0.168741 | ||||||||
\(517\) | − 446.671i | − 0.0379972i | ||||||||
\(518\) | − 6640.22i | − 0.563233i | ||||||||
\(519\) | −21925.4 | −1.85437 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8662.79 | 0.728453 | 0.364226 | − | 0.931310i | \(-0.381333\pi\) | ||||
0.364226 | + | 0.931310i | \(0.381333\pi\) | |||||||
\(522\) | 2101.53i | 0.176210i | ||||||||
\(523\) | − 7770.40i | − 0.649667i | −0.945771 | − | 0.324833i | \(-0.894692\pi\) | ||||
0.945771 | − | 0.324833i | \(-0.105308\pi\) | |||||||
\(524\) | −2604.32 | −0.217119 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3100.60 | −0.257020 | ||||||||
\(527\) | 16970.4i | 1.40274i | ||||||||
\(528\) | − 13182.2i | − 1.08652i | ||||||||
\(529\) | −35429.6 | −2.91194 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10665.2 | −0.871624 | ||||||||
\(532\) | 406.695i | 0.0331437i | ||||||||
\(533\) | − 6564.34i | − 0.533458i | ||||||||
\(534\) | 2930.12 | 0.237451 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −349.440 | −0.0281595 | ||||||||
\(537\) | − 19829.6i | − 1.59350i | ||||||||
\(538\) | 8404.56i | 0.673506i | ||||||||
\(539\) | −1874.49 | −0.149796 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21641.0 | 1.71981 | 0.859906 | − | 0.510453i | \(-0.170522\pi\) | ||||
0.859906 | + | 0.510453i | \(0.170522\pi\) | |||||||
\(542\) | 2317.23i | 0.183642i | ||||||||
\(543\) | 9734.41i | 0.769325i | ||||||||
\(544\) | 5130.09 | 0.404321 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2330.70 | −0.182683 | ||||||||
\(547\) | − 7489.29i | − 0.585409i | −0.956203 | − | 0.292705i | \(-0.905445\pi\) | ||||
0.956203 | − | 0.292705i | \(-0.0945552\pi\) | |||||||
\(548\) | − 2904.54i | − 0.226416i | ||||||||
\(549\) | −5553.11 | −0.431696 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2075.99 | 0.160508 | ||||||||
\(552\) | 34976.2i | 2.69689i | ||||||||
\(553\) | − 1093.93i | − 0.0841201i | ||||||||
\(554\) | 999.566 | 0.0766561 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −693.689 | −0.0529118 | ||||||||
\(557\) | − 25297.9i | − 1.92443i | −0.272295 | − | 0.962214i | \(-0.587783\pi\) | ||||
0.272295 | − | 0.962214i | \(-0.412217\pi\) | |||||||
\(558\) | 8710.29i | 0.660817i | ||||||||
\(559\) | 4374.77 | 0.331007 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22212.5 | −1.67168 | ||||||||
\(562\) | 8623.85i | 0.647286i | ||||||||
\(563\) | 15661.3i | 1.17237i | 0.810177 | + | 0.586186i | \(0.199371\pi\) | ||||
−0.810177 | + | 0.586186i | \(0.800629\pi\) | |||||||
\(564\) | 102.110 | 0.00762343 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 13994.9 | 1.03931 | ||||||||
\(567\) | − 6276.94i | − 0.464915i | ||||||||
\(568\) | 22927.3i | 1.69367i | ||||||||
\(569\) | 9982.75 | 0.735498 | 0.367749 | − | 0.929925i | \(-0.380129\pi\) | ||||
0.367749 | + | 0.929925i | \(0.380129\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11583.6 | −0.848966 | −0.424483 | − | 0.905436i | \(-0.639544\pi\) | ||||
−0.424483 | + | 0.905436i | \(0.639544\pi\) | |||||||
\(572\) | 972.103i | 0.0710589i | ||||||||
\(573\) | − 2495.81i | − 0.181961i | ||||||||
\(574\) | −6142.63 | −0.446670 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 9802.97 | 0.709127 | ||||||||
\(577\) | 595.378i | 0.0429565i | 0.999769 | + | 0.0214783i | \(0.00683727\pi\) | ||||
−0.999769 | + | 0.0214783i | \(0.993163\pi\) | |||||||
\(578\) | 6969.39i | 0.501537i | ||||||||
\(579\) | −4879.66 | −0.350245 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7255.70 | 0.518102 | ||||||||
\(582\) | − 18243.8i | − 1.29936i | ||||||||
\(583\) | − 7996.00i | − 0.568028i | ||||||||
\(584\) | 19856.4 | 1.40696 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 729.738 | 0.0514423 | ||||||||
\(587\) | 15750.3i | 1.10747i | 0.832693 | + | 0.553736i | \(0.186798\pi\) | ||||
−0.832693 | + | 0.553736i | \(0.813202\pi\) | |||||||
\(588\) | − 428.513i | − 0.0300537i | ||||||||
\(589\) | 8604.42 | 0.601934 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13934.4 | −0.969856 | ||||||||
\(592\) | 18990.0i | 1.31838i | ||||||||
\(593\) | − 417.878i | − 0.0289379i | −0.999895 | − | 0.0144690i | \(-0.995394\pi\) | ||||
0.999895 | − | 0.0144690i | \(-0.00460577\pi\) | |||||||
\(594\) | 6378.31 | 0.440581 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 431.385 | 0.0296480 | ||||||||
\(597\) | − 19072.2i | − 1.30749i | ||||||||
\(598\) | 10912.1i | 0.746201i | ||||||||
\(599\) | 19997.3 | 1.36406 | 0.682028 | − | 0.731326i | \(-0.261098\pi\) | ||||
0.682028 | + | 0.731326i | \(0.261098\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15992.6 | −1.08545 | −0.542723 | − | 0.839912i | \(-0.682607\pi\) | ||||
−0.542723 | + | 0.839912i | \(0.682607\pi\) | |||||||
\(602\) | − 4093.73i | − 0.277156i | ||||||||
\(603\) | 251.216i | 0.0169657i | ||||||||
\(604\) | 1352.37 | 0.0911045 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4162.73 | −0.279042 | ||||||||
\(607\) | − 14159.2i | − 0.946793i | −0.880850 | − | 0.473396i | \(-0.843028\pi\) | ||||
0.880850 | − | 0.473396i | \(-0.156972\pi\) | |||||||
\(608\) | − 2601.08i | − 0.173499i | ||||||||
\(609\) | −2187.36 | −0.145544 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 225.854 | 0.0149543 | ||||||||
\(612\) | − 1983.96i | − 0.131040i | ||||||||
\(613\) | − 4629.41i | − 0.305025i | −0.988302 | − | 0.152512i | \(-0.951264\pi\) | ||||
0.988302 | − | 0.152512i | \(-0.0487364\pi\) | |||||||
\(614\) | −4963.87 | −0.326263 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6449.11 | 0.421821 | ||||||||
\(617\) | 23165.3i | 1.51151i | 0.654857 | + | 0.755753i | \(0.272729\pi\) | ||||
−0.654857 | + | 0.755753i | \(0.727271\pi\) | |||||||
\(618\) | − 28910.9i | − 1.88182i | ||||||||
\(619\) | −12370.6 | −0.803258 | −0.401629 | − | 0.915803i | \(-0.631556\pi\) | ||||
−0.401629 | + | 0.915803i | \(0.631556\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14067.4 | −0.909028 | ||||||||
\(622\) | − 3137.36i | − 0.202245i | ||||||||
\(623\) | 1191.58i | 0.0766285i | ||||||||
\(624\) | 6665.43 | 0.427613 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3708.02 | −0.236745 | ||||||||
\(627\) | 11262.3i | 0.717341i | ||||||||
\(628\) | − 689.826i | − 0.0438329i | ||||||||
\(629\) | 31998.9 | 2.02842 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13980.2 | 0.882002 | 0.441001 | − | 0.897507i | \(-0.354623\pi\) | ||||
0.441001 | + | 0.897507i | \(0.354623\pi\) | |||||||
\(632\) | 3763.61i | 0.236880i | ||||||||
\(633\) | 37568.9i | 2.35897i | ||||||||
\(634\) | −16799.7 | −1.05237 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1827.91 | 0.113964 | ||||||||
\(637\) | − 947.814i | − 0.0589541i | ||||||||
\(638\) | − 4643.36i | − 0.288139i | ||||||||
\(639\) | 16482.7 | 1.02041 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16060.9 | −0.989655 | −0.494828 | − | 0.868991i | \(-0.664769\pi\) | ||||
−0.494828 | + | 0.868991i | \(0.664769\pi\) | |||||||
\(642\) | − 25938.3i | − 1.59455i | ||||||||
\(643\) | − 4502.17i | − 0.276125i | −0.990424 | − | 0.138063i | \(-0.955913\pi\) | ||||
0.990424 | − | 0.138063i | \(-0.0440875\pi\) | |||||||
\(644\) | −2006.25 | −0.122760 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9974.87 | 0.607517 | ||||||||
\(647\) | − 29414.8i | − 1.78735i | −0.448715 | − | 0.893675i | \(-0.648118\pi\) | ||||
0.448715 | − | 0.893675i | \(-0.351882\pi\) | |||||||
\(648\) | 21595.6i | 1.30919i | ||||||||
\(649\) | 23565.0 | 1.42528 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9066.03 | −0.545815 | ||||||||
\(652\) | 1317.16i | 0.0791164i | ||||||||
\(653\) | 13013.6i | 0.779882i | 0.920840 | + | 0.389941i | \(0.127505\pi\) | ||||
−0.920840 | + | 0.389941i | \(0.872495\pi\) | |||||||
\(654\) | 21558.0 | 1.28897 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 17566.9 | 1.04554 | ||||||||
\(657\) | − 14275.0i | − 0.847671i | ||||||||
\(658\) | − 211.345i | − 0.0125214i | ||||||||
\(659\) | −23474.2 | −1.38759 | −0.693797 | − | 0.720171i | \(-0.744063\pi\) | ||||
−0.693797 | + | 0.720171i | \(0.744063\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9266.36 | −0.545264 | −0.272632 | − | 0.962118i | \(-0.587894\pi\) | ||||
−0.272632 | + | 0.962118i | \(0.587894\pi\) | |||||||
\(662\) | 25040.4i | 1.47013i | ||||||||
\(663\) | − 11231.5i | − 0.657914i | ||||||||
\(664\) | −24963.0 | −1.45896 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 16423.8 | 0.955572 | ||||||||
\(667\) | 10241.0i | 0.594501i | ||||||||
\(668\) | 472.176i | 0.0273489i | ||||||||
\(669\) | 42398.6 | 2.45026 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12269.7 | 0.705909 | ||||||||
\(672\) | 2740.62i | 0.157324i | ||||||||
\(673\) | − 25067.2i | − 1.43576i | −0.696164 | − | 0.717882i | \(-0.745112\pi\) | ||||
0.696164 | − | 0.717882i | \(-0.254888\pi\) | |||||||
\(674\) | −75.3288 | −0.00430498 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2394.68 | 0.136247 | ||||||||
\(677\) | 22409.6i | 1.27219i | 0.771613 | + | 0.636093i | \(0.219450\pi\) | ||||
−0.771613 | + | 0.636093i | \(0.780550\pi\) | |||||||
\(678\) | 23585.6i | 1.33599i | ||||||||
\(679\) | 7419.11 | 0.419322 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6761.20 | −0.380455 | ||||||||
\(682\) | − 19245.5i | − 1.08057i | ||||||||
\(683\) | − 8757.53i | − 0.490626i | −0.969444 | − | 0.245313i | \(-0.921109\pi\) | ||||
0.969444 | − | 0.245313i | \(-0.0788908\pi\) | |||||||
\(684\) | −1005.91 | −0.0562311 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −886.925 | −0.0493629 | ||||||||
\(687\) | − 27348.7i | − 1.51880i | ||||||||
\(688\) | 11707.4i | 0.648750i | ||||||||
\(689\) | 4043.09 | 0.223555 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8468.42 | 0.466214 | 0.233107 | − | 0.972451i | \(-0.425111\pi\) | ||||
0.233107 | + | 0.972451i | \(0.425111\pi\) | |||||||
\(692\) | 4326.90i | 0.237694i | ||||||||
\(693\) | − 4636.33i | − 0.254141i | ||||||||
\(694\) | 20294.8 | 1.11006 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7525.54 | 0.409849 | ||||||||
\(697\) | − 29601.0i | − 1.60864i | ||||||||
\(698\) | − 26555.1i | − 1.44001i | ||||||||
\(699\) | −4050.23 | −0.219162 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15996.9 | 0.861906 | 0.430953 | − | 0.902374i | \(-0.358177\pi\) | ||||
0.430953 | + | 0.902374i | \(0.358177\pi\) | |||||||
\(702\) | 3225.12i | 0.173397i | ||||||||
\(703\) | − 16224.2i | − 0.870423i | ||||||||
\(704\) | −21659.8 | −1.15956 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7240.03 | 0.385952 | ||||||||
\(707\) | − 1692.83i | − 0.0900503i | ||||||||
\(708\) | 5387.02i | 0.285956i | ||||||||
\(709\) | −19903.0 | −1.05426 | −0.527131 | − | 0.849784i | \(-0.676732\pi\) | ||||
−0.527131 | + | 0.849784i | \(0.676732\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2705.70 | 0.142717 | ||||||||
\(712\) | − 4099.58i | − 0.215784i | ||||||||
\(713\) | 42446.1i | 2.22948i | ||||||||
\(714\) | −10510.0 | −0.550878 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3913.30 | −0.204256 | ||||||||
\(717\) | 33646.7i | 1.75252i | ||||||||
\(718\) | − 8179.59i | − 0.425153i | ||||||||
\(719\) | 11073.1 | 0.574347 | 0.287174 | − | 0.957879i | \(-0.407284\pi\) | ||||
0.287174 | + | 0.957879i | \(0.407284\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11757.0 | 0.607288 | ||||||||
\(722\) | 12678.4i | 0.653520i | ||||||||
\(723\) | 32.4043i | 0.00166685i | ||||||||
\(724\) | 1921.06 | 0.0986125 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2279.58 | 0.116533 | ||||||||
\(727\) | − 31652.7i | − 1.61476i | −0.590029 | − | 0.807382i | \(-0.700884\pi\) | ||||
0.590029 | − | 0.807382i | \(-0.299116\pi\) | |||||||
\(728\) | 3260.92i | 0.166013i | ||||||||
\(729\) | 3935.94 | 0.199967 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19727.5 | 0.998149 | ||||||||
\(732\) | 2804.88i | 0.141628i | ||||||||
\(733\) | 16958.3i | 0.854528i | 0.904127 | + | 0.427264i | \(0.140523\pi\) | ||||
−0.904127 | + | 0.427264i | \(0.859477\pi\) | |||||||
\(734\) | −8230.16 | −0.413870 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12831.3 | 0.642618 | ||||||||
\(737\) | − 555.065i | − 0.0277423i | ||||||||
\(738\) | − 15193.1i | − 0.757813i | ||||||||
\(739\) | 11616.6 | 0.578245 | 0.289123 | − | 0.957292i | \(-0.406636\pi\) | ||||
0.289123 | + | 0.957292i | \(0.406636\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5694.66 | −0.282319 | ||||||||
\(742\) | − 3783.36i | − 0.187185i | ||||||||
\(743\) | 15928.0i | 0.786464i | 0.919439 | + | 0.393232i | \(0.128643\pi\) | ||||
−0.919439 | + | 0.393232i | \(0.871357\pi\) | |||||||
\(744\) | 31191.4 | 1.53700 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −6762.19 | −0.331879 | ||||||||
\(747\) | 17946.1i | 0.879003i | ||||||||
\(748\) | 4383.57i | 0.214277i | ||||||||
\(749\) | 10548.2 | 0.514582 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25571.9 | 1.24252 | 0.621260 | − | 0.783604i | \(-0.286621\pi\) | ||||
0.621260 | + | 0.783604i | \(0.286621\pi\) | |||||||
\(752\) | 604.412i | 0.0293094i | ||||||||
\(753\) | − 3647.43i | − 0.176520i | ||||||||
\(754\) | 2347.87 | 0.113401 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −592.958 | −0.0285260 | ||||||||
\(757\) | − 6202.41i | − 0.297794i | −0.988853 | − | 0.148897i | \(-0.952428\pi\) | ||||
0.988853 | − | 0.148897i | \(-0.0475723\pi\) | |||||||
\(758\) | − 1738.77i | − 0.0833179i | ||||||||
\(759\) | −55557.6 | −2.65693 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29199.1 | −1.39089 | −0.695444 | − | 0.718580i | \(-0.744792\pi\) | ||||
−0.695444 | + | 0.718580i | \(0.744792\pi\) | |||||||
\(762\) | − 20888.1i | − 0.993037i | ||||||||
\(763\) | 8766.87i | 0.415966i | ||||||||
\(764\) | −492.539 | −0.0233239 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3025.00 | 0.142686 | ||||||||
\(767\) | 11915.4i | 0.560938i | ||||||||
\(768\) | − 13050.5i | − 0.613177i | ||||||||
\(769\) | −21838.2 | −1.02407 | −0.512033 | − | 0.858966i | \(-0.671108\pi\) | ||||
−0.512033 | + | 0.858966i | \(0.671108\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11813.3 | −0.551812 | ||||||||
\(772\) | 962.985i | 0.0448945i | ||||||||
\(773\) | − 25544.8i | − 1.18859i | −0.804246 | − | 0.594296i | \(-0.797431\pi\) | ||||
0.804246 | − | 0.594296i | \(-0.202569\pi\) | |||||||
\(774\) | 10125.4 | 0.470218 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −25525.2 | −1.18080 | ||||||||
\(777\) | 17094.6i | 0.789273i | ||||||||
\(778\) | − 2901.82i | − 0.133721i | ||||||||
\(779\) | −15008.4 | −0.690286 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36418.6 | −1.66858 | ||||||||
\(782\) | 49206.6i | 2.25016i | ||||||||
\(783\) | 3026.77i | 0.138146i | ||||||||
\(784\) | 2536.46 | 0.115546 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −34123.8 | −1.54854 | ||||||||
\(787\) | 37223.2i | 1.68598i | 0.537931 | + | 0.842989i | \(0.319206\pi\) | ||||
−0.537931 | + | 0.842989i | \(0.680794\pi\) | |||||||
\(788\) | 2749.91i | 0.124317i | ||||||||
\(789\) | 7982.19 | 0.360169 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9591.42 | −0.431140 | ||||||||
\(792\) | 15951.1i | 0.715655i | ||||||||
\(793\) | 6204.03i | 0.277820i | ||||||||
\(794\) | 5135.18 | 0.229522 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3763.83 | −0.167595 | ||||||||
\(797\) | 40384.6i | 1.79485i | 0.441168 | + | 0.897425i | \(0.354564\pi\) | ||||
−0.441168 | + | 0.897425i | \(0.645436\pi\) | |||||||
\(798\) | 5328.83i | 0.236389i | ||||||||
\(799\) | 1018.46 | 0.0450945 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2947.23 | −0.130007 | ||||||||
\(802\) | 10788.9i | 0.475023i | ||||||||
\(803\) | 31540.7i | 1.38611i | ||||||||
\(804\) | 126.889 | 0.00556598 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9731.28 | 0.425272 | ||||||||
\(807\) | − 21636.7i | − 0.943803i | ||||||||
\(808\) | 5824.14i | 0.253580i | ||||||||
\(809\) | 1955.76 | 0.0849948 | 0.0424974 | − | 0.999097i | \(-0.486469\pi\) | ||||
0.0424974 | + | 0.999097i | \(0.486469\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34301.8 | −1.48520 | −0.742600 | − | 0.669735i | \(-0.766408\pi\) | ||||
−0.742600 | + | 0.669735i | \(0.766408\pi\) | |||||||
\(812\) | 431.669i | 0.0186559i | ||||||||
\(813\) | − 5965.49i | − 0.257342i | ||||||||
\(814\) | −36288.7 | −1.56255 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 30056.9 | 1.28946 | ||||||||
\(817\) | − 10002.3i | − 0.428319i | ||||||||
\(818\) | − 30255.8i | − 1.29324i | ||||||||
\(819\) | 2344.31 | 0.100021 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13665.6 | −0.580918 | −0.290459 | − | 0.956887i | \(-0.593808\pi\) | ||||
−0.290459 | + | 0.956887i | \(0.593808\pi\) | |||||||
\(822\) | − 38057.5i | − 1.61485i | ||||||||
\(823\) | − 21519.5i | − 0.911449i | −0.890121 | − | 0.455724i | \(-0.849380\pi\) | ||||
0.890121 | − | 0.455724i | \(-0.150620\pi\) | |||||||
\(824\) | −40449.7 | −1.71011 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11149.9 | 0.469679 | ||||||||
\(827\) | − 35220.6i | − 1.48094i | −0.672088 | − | 0.740471i | \(-0.734602\pi\) | ||||
0.672088 | − | 0.740471i | \(-0.265398\pi\) | |||||||
\(828\) | − 4962.23i | − 0.208272i | ||||||||
\(829\) | −31365.5 | −1.31408 | −0.657039 | − | 0.753857i | \(-0.728191\pi\) | ||||
−0.657039 | + | 0.753857i | \(0.728191\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2573.28 | −0.107420 | ||||||||
\(832\) | − 10952.0i | − 0.456362i | ||||||||
\(833\) | − 4274.04i | − 0.177775i | ||||||||
\(834\) | −9089.24 | −0.377380 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2222.58 | 0.0919491 | ||||||||
\(837\) | 12545.2i | 0.518070i | ||||||||
\(838\) | 7067.48i | 0.291339i | ||||||||
\(839\) | 28287.1 | 1.16398 | 0.581990 | − | 0.813196i | \(-0.302274\pi\) | ||||
0.581990 | + | 0.813196i | \(0.302274\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22185.5 | −0.909653 | ||||||||
\(842\) | − 35035.8i | − 1.43398i | ||||||||
\(843\) | − 22201.2i | − 0.907060i | ||||||||
\(844\) | 7414.11 | 0.302374 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 522.738 | 0.0212436 | ||||||||
\(847\) | 927.026i | 0.0376068i | ||||||||
\(848\) | 10819.8i | 0.438152i | ||||||||
\(849\) | −36028.6 | −1.45642 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 80035.0 | 3.22393 | ||||||||
\(852\) | − 8325.40i | − 0.334769i | ||||||||
\(853\) | 9405.41i | 0.377533i | 0.982022 | + | 0.188766i | \(0.0604489\pi\) | ||||
−0.982022 | + | 0.188766i | \(0.939551\pi\) | |||||||
\(854\) | 5805.47 | 0.232622 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −36290.6 | −1.44905 | ||||||||
\(857\) | 27966.9i | 1.11474i | 0.830265 | + | 0.557369i | \(0.188189\pi\) | ||||
−0.830265 | + | 0.557369i | \(0.811811\pi\) | |||||||
\(858\) | 12737.2i | 0.506809i | ||||||||
\(859\) | −6281.11 | −0.249486 | −0.124743 | − | 0.992189i | \(-0.539811\pi\) | ||||
−0.124743 | + | 0.992189i | \(0.539811\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15813.6 | 0.625931 | ||||||||
\(862\) | 16624.7i | 0.656890i | ||||||||
\(863\) | − 4757.13i | − 0.187642i | −0.995589 | − | 0.0938208i | \(-0.970092\pi\) | ||||
0.995589 | − | 0.0938208i | \(-0.0299081\pi\) | |||||||
\(864\) | 3792.35 | 0.149327 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 20743.3 | 0.813954 | ||||||||
\(867\) | − 17942.0i | − 0.702818i | ||||||||
\(868\) | 1789.15i | 0.0699629i | ||||||||
\(869\) | −5978.28 | −0.233371 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 280.663 | 0.0109184 | ||||||||
\(872\) | − 30162.1i | − 1.17135i | ||||||||
\(873\) | 18350.3i | 0.711414i | ||||||||
\(874\) | 24949.0 | 0.965574 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7210.30 | −0.278097 | ||||||||
\(877\) | 30240.5i | 1.16437i | 0.813057 | + | 0.582184i | \(0.197802\pi\) | ||||
−0.813057 | + | 0.582184i | \(0.802198\pi\) | |||||||
\(878\) | − 14402.5i | − 0.553601i | ||||||||
\(879\) | −1878.64 | −0.0720875 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44875.5 | 1.71611 | 0.858056 | − | 0.513556i | \(-0.171672\pi\) | ||||
0.858056 | + | 0.513556i | \(0.171672\pi\) | |||||||
\(882\) | − 2193.71i | − 0.0837483i | ||||||||
\(883\) | 4892.13i | 0.186448i | 0.995645 | + | 0.0932238i | \(0.0297172\pi\) | ||||
−0.995645 | + | 0.0932238i | \(0.970283\pi\) | |||||||
\(884\) | −2216.51 | −0.0843317 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14186.2 | −0.537916 | ||||||||
\(887\) | − 1761.40i | − 0.0666765i | −0.999444 | − | 0.0333382i | \(-0.989386\pi\) | ||||
0.999444 | − | 0.0333382i | \(-0.0106139\pi\) | |||||||
\(888\) | − 58813.4i | − 2.22258i | ||||||||
\(889\) | 8494.43 | 0.320466 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −34303.3 | −1.28979 | ||||||||
\(892\) | − 8367.22i | − 0.314075i | ||||||||
\(893\) | − 516.384i | − 0.0193507i | ||||||||
\(894\) | 5652.33 | 0.211457 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −6954.86 | −0.259314 | ||||||||
\(897\) | − 28092.1i | − 1.04567i | ||||||||
\(898\) | − 18702.2i | − 0.694988i | ||||||||
\(899\) | 9132.79 | 0.338816 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18231.8 | 0.674128 | ||||||||
\(902\) | 33569.3i | 1.23918i | ||||||||
\(903\) | 10538.9i | 0.388386i | ||||||||
\(904\) | 32999.0 | 1.21408 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 17719.8 | 0.649779 | ||||||||
\(907\) | − 23689.1i | − 0.867238i | −0.901096 | − | 0.433619i | \(-0.857236\pi\) | ||||
0.901096 | − | 0.433619i | \(-0.142764\pi\) | |||||||
\(908\) | 1334.30i | 0.0487669i | ||||||||
\(909\) | 4187.03 | 0.152778 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13877.3 | −0.504692 | −0.252346 | − | 0.967637i | \(-0.581202\pi\) | ||||
−0.252346 | + | 0.967637i | \(0.581202\pi\) | |||||||
\(912\) | − 15239.6i | − 0.553325i | ||||||||
\(913\) | − 39652.2i | − 1.43735i | ||||||||
\(914\) | 7500.09 | 0.271423 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5397.18 | −0.194681 | ||||||||
\(917\) | − 13876.9i | − 0.499735i | ||||||||
\(918\) | 14543.3i | 0.522875i | ||||||||
\(919\) | −14331.6 | −0.514426 | −0.257213 | − | 0.966355i | \(-0.582804\pi\) | ||||
−0.257213 | + | 0.966355i | \(0.582804\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12779.0 | 0.457201 | ||||||||
\(922\) | − 15705.0i | − 0.560971i | ||||||||
\(923\) | − 18414.7i | − 0.656692i | ||||||||
\(924\) | −2341.81 | −0.0833767 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −48930.2 | −1.73644 | ||||||||
\(927\) | 29079.7i | 1.03032i | ||||||||
\(928\) | − 2760.80i | − 0.0976592i | ||||||||
\(929\) | −16668.4 | −0.588668 | −0.294334 | − | 0.955703i | \(-0.595098\pi\) | ||||
−0.294334 | + | 0.955703i | \(0.595098\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2167.04 | −0.0762857 | ||||||||
\(932\) | 799.300i | 0.0280922i | ||||||||
\(933\) | 8076.82i | 0.283412i | ||||||||
\(934\) | 17523.1 | 0.613891 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −8065.52 | −0.281656 | ||||||||
\(937\) | − 30384.9i | − 1.05937i | −0.848194 | − | 0.529685i | \(-0.822310\pi\) | ||||
0.848194 | − | 0.529685i | \(-0.177690\pi\) | |||||||
\(938\) | − 262.632i | − 0.00914206i | ||||||||
\(939\) | 9545.94 | 0.331757 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1196.35 | −0.0414452 | −0.0207226 | − | 0.999785i | \(-0.506597\pi\) | ||||
−0.0207226 | + | 0.999785i | \(0.506597\pi\) | |||||||
\(942\) | − 9038.63i | − 0.312627i | ||||||||
\(943\) | − 74037.5i | − 2.55673i | ||||||||
\(944\) | −31886.9 | −1.09940 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −22372.1 | −0.768901 | ||||||||
\(947\) | − 1788.41i | − 0.0613681i | −0.999529 | − | 0.0306840i | \(-0.990231\pi\) | ||||
0.999529 | − | 0.0306840i | \(-0.00976856\pi\) | |||||||
\(948\) | − 1366.65i | − 0.0468215i | ||||||||
\(949\) | −15948.2 | −0.545523 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 43249.2 | 1.47471 | ||||||||
\(952\) | 14704.7i | 0.500612i | ||||||||
\(953\) | 8578.60i | 0.291593i | 0.989315 | + | 0.145796i | \(0.0465744\pi\) | ||||
−0.989315 | + | 0.145796i | \(0.953426\pi\) | |||||||
\(954\) | 9357.70 | 0.317575 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6640.06 | 0.224639 | ||||||||
\(957\) | 11953.9i | 0.403776i | ||||||||
\(958\) | 6198.95i | 0.209059i | ||||||||
\(959\) | 15476.6 | 0.521133 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8061.99 | 0.270618 | ||||||||
\(962\) | − 18349.0i | − 0.614963i | ||||||||
\(963\) | 26089.7i | 0.873031i | ||||||||
\(964\) | 6.39489 | 0.000213657 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −26287.4 | −0.875552 | ||||||||
\(967\) | 55459.3i | 1.84431i | 0.386818 | + | 0.922156i | \(0.373574\pi\) | ||||
−0.386818 | + | 0.922156i | \(0.626426\pi\) | |||||||
\(968\) | − 3189.40i | − 0.105900i | ||||||||
\(969\) | −25679.3 | −0.851330 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22047.3 | 0.728662 | 0.364331 | − | 0.931270i | \(-0.381298\pi\) | ||||
0.364331 | + | 0.931270i | \(0.381298\pi\) | |||||||
\(972\) | − 5554.72i | − 0.183300i | ||||||||
\(973\) | − 3696.27i | − 0.121785i | ||||||||
\(974\) | −14444.6 | −0.475191 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16602.7 | −0.544507 | ||||||||
\(977\) | − 14402.3i | − 0.471617i | −0.971800 | − | 0.235809i | \(-0.924226\pi\) | ||||
0.971800 | − | 0.235809i | \(-0.0757738\pi\) | |||||||
\(978\) | 17258.4i | 0.564277i | ||||||||
\(979\) | 6511.94 | 0.212587 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −21683.9 | −0.705721 | ||||||||
\(982\) | − 1389.58i | − 0.0451561i | ||||||||
\(983\) | 7817.11i | 0.253639i | 0.991926 | + | 0.126819i | \(0.0404769\pi\) | ||||
−0.991926 | + | 0.126819i | \(0.959523\pi\) | |||||||
\(984\) | −54406.2 | −1.76261 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 10587.4 | 0.341959 | ||||||||
\(987\) | 544.087i | 0.0175466i | ||||||||
\(988\) | 1123.82i | 0.0361878i | ||||||||
\(989\) | 49342.0 | 1.58643 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24501.6 | 0.785386 | 0.392693 | − | 0.919670i | \(-0.371543\pi\) | ||||
0.392693 | + | 0.919670i | \(0.371543\pi\) | |||||||
\(992\) | − 11442.8i | − 0.366239i | ||||||||
\(993\) | − 64464.2i | − 2.06013i | ||||||||
\(994\) | −17231.7 | −0.549855 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 9064.61 | 0.288377 | ||||||||
\(997\) | 50696.0i | 1.61039i | 0.593010 | + | 0.805195i | \(0.297940\pi\) | ||||
−0.593010 | + | 0.805195i | \(0.702060\pi\) | |||||||
\(998\) | 1548.80i | 0.0491245i | ||||||||
\(999\) | 23654.8 | 0.749152 |
(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 | 175.4.b.c.99.2 | 4 | ||
5.2 | odd | 4 | 35.4.a.b.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 175.4.a.c.1.2 | 2 | |||
5.4 | even | 2 | inner | 175.4.b.c.99.3 | 4 | ||
15.2 | even | 4 | 315.4.a.f.1.2 | 2 | |||
15.8 | even | 4 | 1575.4.a.z.1.1 | 2 | |||
20.7 | even | 4 | 560.4.a.r.1.1 | 2 | |||
35.2 | odd | 12 | 245.4.e.h.116.2 | 4 | |||
35.12 | even | 12 | 245.4.e.i.116.2 | 4 | |||
35.13 | even | 4 | 1225.4.a.m.1.2 | 2 | |||
35.17 | even | 12 | 245.4.e.i.226.2 | 4 | |||
35.27 | even | 4 | 245.4.a.k.1.1 | 2 | |||
35.32 | odd | 12 | 245.4.e.h.226.2 | 4 | |||
40.27 | even | 4 | 2240.4.a.bo.1.2 | 2 | |||
40.37 | odd | 4 | 2240.4.a.bn.1.1 | 2 | |||
105.62 | odd | 4 | 2205.4.a.u.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.4.a.b.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
175.4.a.c.1.2 | 2 | 5.3 | odd | 4 | |||
175.4.b.c.99.2 | 4 | 1.1 | even | 1 | trivial | ||
175.4.b.c.99.3 | 4 | 5.4 | even | 2 | inner | ||
245.4.a.k.1.1 | 2 | 35.27 | even | 4 | |||
245.4.e.h.116.2 | 4 | 35.2 | odd | 12 | |||
245.4.e.h.226.2 | 4 | 35.32 | odd | 12 | |||
245.4.e.i.116.2 | 4 | 35.12 | even | 12 | |||
245.4.e.i.226.2 | 4 | 35.17 | even | 12 | |||
315.4.a.f.1.2 | 2 | 15.2 | even | 4 | |||
560.4.a.r.1.1 | 2 | 20.7 | even | 4 | |||
1225.4.a.m.1.2 | 2 | 35.13 | even | 4 | |||
1575.4.a.z.1.1 | 2 | 15.8 | even | 4 | |||
2205.4.a.u.1.2 | 2 | 105.62 | odd | 4 | |||
2240.4.a.bn.1.1 | 2 | 40.37 | odd | 4 | |||
2240.4.a.bo.1.2 | 2 | 40.27 | even | 4 |