Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,5,Mod(31,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.31");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.f (of order \(4\), degree \(2\), 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: | \(13.2313552747\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + 11456 x^{6} - 19968 x^{5} + 31744 x^{4} - 139264 x^{3} + 491520 x^{2} + \cdots + 2097152 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{42} \) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 95.1 | ||
Root | \(0.153862 + 2.82424i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 128.95 |
Dual form | 128.5.f.a.31.1 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −9.42589 | + | 9.42589i | −1.04732 | + | 1.04732i | −0.0484980 | + | 0.998823i | \(0.515443\pi\) |
−0.998823 | + | 0.0484980i | \(0.984557\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.84710 | − | 2.84710i | 0.113884 | − | 0.113884i | −0.647868 | − | 0.761752i | \(-0.724339\pi\) |
0.761752 | + | 0.647868i | \(0.224339\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 76.7794 | 1.56693 | 0.783463 | − | 0.621439i | \(-0.213451\pi\) | ||||
0.783463 | + | 0.621439i | \(0.213451\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 96.6949i | − | 1.19376i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 121.488 | + | 121.488i | 1.00403 | + | 1.00403i | 0.999992 | + | 0.00403849i | \(0.00128549\pi\) |
0.00403849 | + | 0.999992i | \(0.498715\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −27.1604 | − | 27.1604i | −0.160712 | − | 0.160712i | 0.622170 | − | 0.782882i | \(-0.286251\pi\) |
−0.782882 | + | 0.622170i | \(0.786251\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 53.6729i | 0.238546i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −88.0613 | −0.304710 | −0.152355 | − | 0.988326i | \(-0.548686\pi\) | ||||
−0.152355 | + | 0.988326i | \(0.548686\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −261.112 | + | 261.112i | −0.723302 | + | 0.723302i | −0.969276 | − | 0.245974i | \(-0.920892\pi\) |
0.245974 | + | 0.969276i | \(0.420892\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −723.714 | + | 723.714i | −1.64107 | + | 1.64107i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −93.4210 | −0.176599 | −0.0882996 | − | 0.996094i | \(-0.528143\pi\) | ||||
−0.0882996 | + | 0.996094i | \(0.528143\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 608.788i | 0.974061i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 147.938 | + | 147.938i | 0.202933 | + | 0.202933i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −272.522 | − | 272.522i | −0.324045 | − | 0.324045i | 0.526272 | − | 0.850316i | \(-0.323590\pi\) |
−0.850316 | + | 0.526272i | \(0.823590\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1232.20i | 1.28220i | 0.767455 | + | 0.641102i | \(0.221523\pi\) | ||||
−0.767455 | + | 0.641102i | \(0.778477\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2290.26 | −2.10308 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 218.599 | − | 218.599i | 0.178448 | − | 0.178448i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1046.16 | − | 1046.16i | 0.764177 | − | 0.764177i | −0.212898 | − | 0.977075i | \(-0.568290\pi\) |
0.977075 | + | 0.212898i | \(0.0682901\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 512.021 | 0.336635 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 915.267i | 0.544478i | 0.962230 | + | 0.272239i | \(0.0877641\pi\) | ||||
−0.962230 | + | 0.272239i | \(0.912236\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1116.82 | + | 1116.82i | 0.604013 | + | 0.604013i | 0.941375 | − | 0.337362i | \(-0.109535\pi\) |
−0.337362 | + | 0.941375i | \(0.609535\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −275.300 | − | 275.300i | −0.135951 | − | 0.135951i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1720.70i | 0.778949i | 0.921037 | + | 0.389475i | \(0.127343\pi\) | ||||
−0.921037 | + | 0.389475i | \(0.872657\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3494.07 | 1.45526 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 830.056 | − | 830.056i | 0.319130 | − | 0.319130i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −734.019 | + | 734.019i | −0.261310 | + | 0.261310i | −0.825586 | − | 0.564276i | \(-0.809155\pi\) |
0.564276 | + | 0.825586i | \(0.309155\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 691.775 | 0.228686 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 4922.43i | − | 1.51506i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1202.73 | − | 1202.73i | −0.345512 | − | 0.345512i | 0.512923 | − | 0.858435i | \(-0.328563\pi\) |
−0.858435 | + | 0.512923i | \(0.828563\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −580.221 | − | 580.221i | −0.155932 | − | 0.155932i | 0.624830 | − | 0.780761i | \(-0.285168\pi\) |
−0.780761 | + | 0.624830i | \(0.785168\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 7424.17i | − | 1.87054i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −154.657 | −0.0366051 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1483.97 | + | 1483.97i | −0.330580 | + | 0.330580i | −0.852807 | − | 0.522227i | \(-0.825101\pi\) |
0.522227 | + | 0.852807i | \(0.325101\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 880.576 | − | 880.576i | 0.184956 | − | 0.184956i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5571.73 | −1.10528 | −0.552641 | − | 0.833419i | \(-0.686380\pi\) | ||||
−0.552641 | + | 0.833419i | \(0.686380\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6615.21i | 1.24136i | 0.784064 | + | 0.620681i | \(0.213144\pi\) | ||||
−0.784064 | + | 0.620681i | \(0.786856\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5738.37 | − | 5738.37i | −1.02015 | − | 1.02015i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9327.75 | + | 9327.75i | 1.57324 | + | 1.57324i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 5391.66i | − | 0.863910i | −0.901895 | − | 0.431955i | \(-0.857824\pi\) | ||
0.901895 | − | 0.431955i | \(-0.142176\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5043.39 | 0.768692 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2554.07 | + | 2554.07i | −0.370747 | + | 0.370747i | −0.867749 | − | 0.497002i | \(-0.834434\pi\) |
0.497002 | + | 0.867749i | \(0.334434\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −250.719 | + | 250.719i | −0.0347017 | + | 0.0347017i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5137.52 | 0.678758 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 10962.7i | − | 1.38400i | −0.721898 | − | 0.691999i | \(-0.756730\pi\) | ||
0.721898 | − | 0.691999i | \(-0.243270\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2085.35 | − | 2085.35i | −0.251824 | − | 0.251824i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −11614.6 | − | 11614.6i | −1.34288 | − | 1.34288i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1486.83i | 0.164745i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4713.20 | 0.500925 | 0.250462 | − | 0.968126i | \(-0.419417\pi\) | ||||
0.250462 | + | 0.968126i | \(0.419417\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11747.2 | − | 11747.2i | 1.19858 | − | 1.19858i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11381.0 | − | 11381.0i | 1.11568 | − | 1.11568i | 0.123307 | − | 0.992369i | \(-0.460650\pi\) |
0.992369 | − | 0.123307i | \(-0.0393499\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −175.758 | −0.0165668 | −0.00828342 | − | 0.999966i | \(-0.502637\pi\) | ||||
−0.00828342 | + | 0.999966i | \(0.502637\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4120.97i | 0.373784i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15151.8 | + | 15151.8i | 1.32342 | + | 1.32342i | 0.910988 | + | 0.412432i | \(0.135321\pi\) |
0.412432 | + | 0.910988i | \(0.364679\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2349.51 | + | 2349.51i | 0.197754 | + | 0.197754i | 0.799036 | − | 0.601283i | \(-0.205343\pi\) |
−0.601283 | + | 0.799036i | \(0.705343\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 19721.9i | 1.60068i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8526.30 | −0.667734 | −0.333867 | − | 0.942620i | \(-0.608354\pi\) | ||||
−0.333867 | + | 0.942620i | \(0.608354\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −265.979 | + | 265.979i | −0.0201118 | + | 0.0201118i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2626.27 | + | 2626.27i | −0.191852 | + | 0.191852i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6761.29 | −0.477459 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14877.5i | 1.01615i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8627.21 | − | 8627.21i | −0.570243 | − | 0.570243i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3512.72 | + | 3512.72i | 0.224814 | + | 0.224814i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2844.31i | 0.176347i | 0.996105 | + | 0.0881737i | \(0.0281031\pi\) | ||||
−0.996105 | + | 0.0881737i | \(0.971897\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −21054.1 | −1.26519 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6989.87 | + | 6989.87i | −0.407311 | + | 0.407311i | −0.880800 | − | 0.473489i | \(-0.842994\pi\) |
0.473489 | + | 0.880800i | \(0.342994\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −20048.0 | + | 20048.0i | −1.13336 | + | 1.13336i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 842.390 | 0.0462217 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 3669.69i | − | 0.195519i | −0.995210 | − | 0.0977594i | \(-0.968832\pi\) | ||
0.995210 | − | 0.0977594i | \(-0.0311676\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4401.33 | + | 4401.33i | 0.227800 | + | 0.227800i | 0.811773 | − | 0.583973i | \(-0.198503\pi\) |
−0.583973 | + | 0.811773i | \(0.698503\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16219.1 | − | 16219.1i | −0.815810 | − | 0.815810i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 6599.30i | − | 0.322720i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1551.79 | −0.0738071 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −32934.7 | + | 32934.7i | −1.52412 | + | 1.52412i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15737.5 | + | 15737.5i | −0.708863 | + | 0.708863i | −0.966296 | − | 0.257433i | \(-0.917123\pi\) |
0.257433 | + | 0.966296i | \(0.417123\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 41972.2 | 1.84080 | 0.920402 | − | 0.390974i | \(-0.127862\pi\) | ||||
0.920402 | + | 0.390974i | \(0.127862\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8515.08i | 0.363752i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3508.19 | + | 3508.19i | 0.146023 | + | 0.146023i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24735.4 | + | 24735.4i | 1.00351 | + | 1.00351i | 0.999994 | + | 0.00351271i | \(0.00111813\pi\) |
0.00351271 | + | 0.999994i | \(0.498882\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 13837.6i | − | 0.547350i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7172.80 | −0.276718 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24429.8 | − | 24429.8i | 0.919483 | − | 0.919483i | −0.0775084 | − | 0.996992i | \(-0.524696\pi\) |
0.996992 | + | 0.0775084i | \(0.0246965\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6520.60 | + | 6520.60i | −0.239508 | + | 0.239508i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −52178.2 | −1.87093 | −0.935463 | − | 0.353425i | \(-0.885017\pi\) | ||||
−0.935463 | + | 0.353425i | \(0.885017\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 27085.6i | − | 0.948343i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 25248.2 | + | 25248.2i | 0.863452 | + | 0.863452i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −26316.2 | − | 26316.2i | −0.879289 | − | 0.879289i | 0.114172 | − | 0.993461i | \(-0.463578\pi\) |
−0.993461 | + | 0.114172i | \(0.963578\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 46742.4i | 1.52628i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 22673.5 | 0.723723 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4815.78 | − | 4815.78i | 0.150301 | − | 0.150301i | −0.627952 | − | 0.778252i | \(-0.716106\pi\) |
0.778252 | + | 0.627952i | \(0.216106\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23924.9 | − | 23924.9i | 0.730286 | − | 0.730286i | −0.240391 | − | 0.970676i | \(-0.577276\pi\) |
0.970676 | + | 0.240391i | \(0.0772755\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10938.2 | 0.326621 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 5957.04i | − | 0.174055i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10698.4 | − | 10698.4i | −0.305939 | − | 0.305939i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 11358.6 | + | 11358.6i | 0.317981 | + | 0.317981i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 45079.4i | − | 1.23569i | −0.786298 | − | 0.617847i | \(-0.788005\pi\) | ||
0.786298 | − | 0.617847i | \(-0.211995\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 50286.0 | 1.34999 | 0.674997 | − | 0.737820i | \(-0.264145\pi\) | ||||
0.674997 | + | 0.737820i | \(0.264145\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1457.78 | − | 1457.78i | 0.0383373 | − | 0.0383373i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25662.2 | − | 25662.2i | 0.661243 | − | 0.661243i | −0.294430 | − | 0.955673i | \(-0.595130\pi\) |
0.955673 | + | 0.294430i | \(0.0951297\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 44599.1 | 1.12621 | 0.563106 | − | 0.826385i | \(-0.309606\pi\) | ||||
0.563106 | + | 0.826385i | \(0.309606\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 27975.5i | − | 0.692447i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −20924.0 | − | 20924.0i | −0.507754 | − | 0.507754i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2605.86 | + | 2605.86i | 0.0620073 | + | 0.0620073i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9033.33i | 0.210818i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −63443.8 | −1.45244 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25828.5 | − | 25828.5i | 0.580143 | − | 0.580143i | −0.354800 | − | 0.934942i | \(-0.615451\pi\) |
0.934942 | + | 0.354800i | \(0.115451\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 52518.5 | − | 52518.5i | 1.15759 | − | 1.15759i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6359.40 | 0.137575 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 94607.4i | 2.00912i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −62354.3 | − | 62354.3i | −1.30010 | − | 1.30010i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2391.78 | + | 2391.78i | 0.0489707 | + | 0.0489707i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 72650.0i | − | 1.46092i | −0.682957 | − | 0.730459i | \(-0.739306\pi\) | ||
0.682957 | − | 0.730459i | \(-0.260694\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 58866.7 | 1.16280 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18858.2 | − | 18858.2i | 0.365972 | − | 0.365972i | −0.500034 | − | 0.866006i | \(-0.666679\pi\) |
0.866006 | + | 0.500034i | \(0.166679\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −41675.9 | + | 41675.9i | −0.794721 | + | 0.794721i | −0.982258 | − | 0.187537i | \(-0.939950\pi\) |
0.187537 | + | 0.982258i | \(0.439950\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −175845. | −3.29538 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 2767.61i | − | 0.0509792i | −0.999675 | − | 0.0254896i | \(-0.991886\pi\) | ||
0.999675 | − | 0.0254896i | \(-0.00811447\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4899.00 | + | 4899.00i | 0.0887099 | + | 0.0887099i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 50821.2 | + | 50821.2i | 0.904791 | + | 0.904791i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 49981.8i | 0.875016i | 0.899215 | + | 0.437508i | \(0.144139\pi\) | ||||
−0.899215 | + | 0.437508i | \(0.855861\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −44076.0 | −0.758872 | −0.379436 | − | 0.925218i | \(-0.623882\pi\) | ||||
−0.379436 | + | 0.925218i | \(0.623882\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −59521.4 | + | 59521.4i | −1.00800 | + | 1.00800i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9947.97 | − | 9947.97i | 0.165730 | − | 0.165730i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14183.8 | 0.232487 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 48148.8i | − | 0.776582i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −31786.2 | − | 31786.2i | −0.504534 | − | 0.504534i | 0.408309 | − | 0.912844i | \(-0.366119\pi\) |
−0.912844 | + | 0.408309i | \(0.866119\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11349.5 | − | 11349.5i | −0.177311 | − | 0.177311i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 4726.51i | − | 0.0726876i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 70865.6 | 1.07292 | 0.536462 | − | 0.843924i | \(-0.319760\pi\) | ||||
0.536462 | + | 0.843924i | \(0.319760\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 80323.4 | − | 80323.4i | 1.19741 | − | 1.19741i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −26351.5 | + | 26351.5i | −0.386833 | + | 0.386833i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 113289. | 1.63786 | 0.818929 | − | 0.573894i | \(-0.194568\pi\) | ||||
0.818929 | + | 0.573894i | \(0.194568\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4179.65i | 0.0595180i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 103333. | + | 103333.i | 1.44949 | + | 1.44949i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −70652.7 | − | 70652.7i | −0.976393 | − | 0.976393i | 0.0233352 | − | 0.999728i | \(-0.492572\pi\) |
−0.999728 | + | 0.0233352i | \(0.992572\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 110180.i | − | 1.50025i | −0.661294 | − | 0.750126i | \(-0.729993\pi\) | ||
0.661294 | − | 0.750126i | \(-0.270007\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 39312.7 | 0.527481 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −73960.2 | + | 73960.2i | −0.977987 | + | 0.977987i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −34611.0 | + | 34611.0i | −0.451081 | + | 0.451081i | −0.895713 | − | 0.444632i | \(-0.853334\pi\) |
0.444632 | + | 0.895713i | \(0.353334\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 119147. | 1.53065 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 147980.i | − | 1.87408i | −0.349216 | − | 0.937042i | \(-0.613552\pi\) | ||
0.349216 | − | 0.937042i | \(-0.386448\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 39761.2 | + | 39761.2i | 0.496463 | + | 0.496463i | 0.910335 | − | 0.413872i | \(-0.135824\pi\) |
−0.413872 | + | 0.910335i | \(0.635824\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −14014.7 | − | 14014.7i | −0.172541 | − | 0.172541i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 70273.6i | 0.853156i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −75766.2 | −0.907152 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −44426.1 | + | 44426.1i | −0.524629 | + | 0.524629i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 708.909 | − | 708.909i | 0.00825763 | − | 0.00825763i | −0.702966 | − | 0.711224i | \(-0.748141\pi\) |
0.711224 | + | 0.702966i | \(0.248141\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6848.56 | −0.0786965 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 35945.3i | 0.407502i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2537.35 | + | 2537.35i | 0.0283816 | + | 0.0283816i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 85748.8 | + | 85748.8i | 0.946444 | + | 0.946444i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 214552.i | 2.33694i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3303.90 | −0.0355162 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20597.1 | + | 20597.1i | −0.218539 | + | 0.218539i | −0.807883 | − | 0.589344i | \(-0.799386\pi\) |
0.589344 | + | 0.807883i | \(0.299386\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1656.67 | − | 1656.67i | 0.0173508 | − | 0.0173508i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −82310.6 | −0.851011 | −0.425505 | − | 0.904956i | \(-0.639904\pi\) | ||||
−0.425505 | + | 0.904956i | \(0.639904\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 120415.i | 1.22911i | 0.788872 | + | 0.614557i | \(0.210665\pi\) | ||||
−0.788872 | + | 0.614557i | \(0.789335\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −21137.4 | − | 21137.4i | −0.213025 | − | 0.213025i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14795.3 | − | 14795.3i | −0.147233 | − | 0.147233i | 0.629648 | − | 0.776881i | \(-0.283199\pi\) |
−0.776881 | + | 0.629648i | \(0.783199\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 66216.1i | − | 0.650702i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −285639. | −2.77209 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 22993.9 | − | 22993.9i | 0.220398 | − | 0.220398i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16534.9 | − | 16534.9i | 0.156543 | − | 0.156543i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −44292.5 | −0.414224 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 132114.i | 1.22056i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 82868.2 | + | 82868.2i | 0.756366 | + | 0.756366i | 0.975659 | − | 0.219293i | \(-0.0703752\pi\) |
−0.219293 | + | 0.975659i | \(0.570375\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −101158. | − | 101158.i | −0.912247 | − | 0.912247i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8450.04i | 0.0752955i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 78854.4 | 0.694331 | 0.347165 | − | 0.937804i | \(-0.387144\pi\) | ||||
0.347165 | + | 0.937804i | \(0.387144\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 80368.0 | − | 80368.0i | 0.699332 | − | 0.699332i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −149697. | + | 149697.i | −1.28737 | + | 1.28737i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 83925.2 | 0.713352 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 5014.18i | − | 0.0421271i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −59543.0 | − | 59543.0i | −0.494506 | − | 0.494506i | 0.415216 | − | 0.909723i | \(-0.363706\pi\) |
−0.909723 | + | 0.415216i | \(0.863706\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 756.172 | + | 756.172i | 0.00620826 | + | 0.00620826i | 0.710204 | − | 0.703996i | \(-0.248603\pi\) |
−0.703996 | + | 0.710204i | \(0.748603\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 8036.11i | − | 0.0652276i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23723.5 | 0.190384 | 0.0951918 | − | 0.995459i | \(-0.469654\pi\) | ||||
0.0951918 | + | 0.995459i | \(0.469654\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15863.3 | + | 15863.3i | −0.125874 | + | 0.125874i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 63731.2 | − | 63731.2i | 0.500053 | − | 0.500053i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −146064. | −1.13333 | −0.566663 | − | 0.823950i | \(-0.691766\pi\) | ||||
−0.566663 | + | 0.823950i | \(0.691766\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 6038.12i | − | 0.0463327i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −140234. | − | 140234.i | −1.06424 | − | 1.06424i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18834.2 | + | 18834.2i | 0.141371 | + | 0.141371i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 151129.i | 1.12206i | 0.827797 | + | 0.561028i | \(0.189594\pi\) | ||||
−0.827797 | + | 0.561028i | \(0.810406\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 88501.7 | 0.649978 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −56357.5 | + | 56357.5i | −0.409453 | + | 0.409453i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26207.7 | + | 26207.7i | −0.188370 | + | 0.188370i | −0.794991 | − | 0.606621i | \(-0.792524\pi\) |
0.606621 | + | 0.794991i | \(0.292524\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −66221.0 | −0.470905 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14803.6i | 0.104156i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 110424. | + | 110424.i | 0.768752 | + | 0.768752i | 0.977887 | − | 0.209135i | \(-0.0670647\pi\) |
−0.209135 | + | 0.977887i | \(0.567065\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −26810.1 | − | 26810.1i | −0.184692 | − | 0.184692i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 10514.9i | − | 0.0716819i | −0.999358 | − | 0.0358409i | \(-0.988589\pi\) | ||
0.999358 | − | 0.0358409i | \(-0.0114110\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 53114.1 | 0.358334 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 107991. | − | 107991.i | 0.721049 | − | 0.721049i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 166762. | − | 166762.i | 1.10204 | − | 1.10204i | 0.107877 | − | 0.994164i | \(-0.465595\pi\) |
0.994164 | − | 0.107877i | \(-0.0344054\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8226.78 | 0.0538116 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 131772.i | − | 0.853172i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15350.6 | − | 15350.6i | −0.0983855 | − | 0.0983855i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 192542. | + | 192542.i | 1.22164 | + | 1.22164i | 0.967048 | + | 0.254594i | \(0.0819419\pi\) |
0.254594 | + | 0.967048i | \(0.418058\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 377941.i | − | 2.37399i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 91157.6 | 0.566897 | 0.283448 | − | 0.958987i | \(-0.408522\pi\) | ||||
0.283448 | + | 0.958987i | \(0.408522\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 33467.0 | − | 33467.0i | 0.206066 | − | 0.206066i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14359.0 | − | 14359.0i | 0.0875417 | − | 0.0875417i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 254191. | 1.53451 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 107774.i | − | 0.644272i | −0.946693 | − | 0.322136i | \(-0.895599\pi\) | ||
0.946693 | − | 0.322136i | \(-0.104401\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 34590.1 | + | 34590.1i | 0.204771 | + | 0.204771i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −92344.5 | − | 92344.5i | −0.541391 | − | 0.541391i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14543.4i | 0.0844442i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −82972.9 | −0.477160 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −118524. | + | 118524.i | −0.675115 | + | 0.675115i | −0.958891 | − | 0.283776i | \(-0.908413\pi\) |
0.283776 | + | 0.958891i | \(0.408413\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 226616. | − | 226616.i | 1.27858 | − | 1.27858i | 0.337113 | − | 0.941464i | \(-0.390549\pi\) |
0.941464 | − | 0.337113i | \(-0.109451\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 166383. | 0.929882 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 53610.7i | − | 0.296807i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −44549.0 | − | 44549.0i | −0.244333 | − | 0.244333i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 62204.3 | + | 62204.3i | 0.337991 | + | 0.337991i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5397.51i | 0.0290562i | 0.999894 | + | 0.0145281i | \(0.00462460\pi\) | ||||
−0.999894 | + | 0.0145281i | \(0.995375\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 163835. | 0.873840 | 0.436920 | − | 0.899500i | \(-0.356069\pi\) | ||||
0.436920 | + | 0.899500i | \(0.356069\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14627.0 | − | 14627.0i | 0.0772997 | − | 0.0772997i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 24393.4 | − | 24393.4i | 0.127735 | − | 0.127735i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −158472. | −0.822289 | −0.411144 | − | 0.911570i | \(-0.634871\pi\) | ||||
−0.411144 | + | 0.911570i | \(0.634871\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 337859.i | − | 1.73723i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −137929. | − | 137929.i | −0.702826 | − | 0.702826i | 0.262190 | − | 0.965016i | \(-0.415555\pi\) |
−0.965016 | + | 0.262190i | \(0.915555\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −31211.8 | − | 31211.8i | −0.157615 | − | 0.157615i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 296680.i | − | 1.48482i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 327336. | 1.62368 | 0.811841 | − | 0.583879i | \(-0.198466\pi\) | ||||
0.811841 | + | 0.583879i | \(0.198466\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −111194. | + | 111194.i | −0.546672 | + | 0.546672i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −395625. | + | 395625.i | −1.92791 | + | 1.92791i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11874.4 | −0.0573575 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 154510.i | 0.739817i | 0.929068 | + | 0.369909i | \(0.120611\pi\) | ||||
−0.929068 | + | 0.369909i | \(0.879389\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13027.6 | − | 13027.6i | −0.0618358 | − | 0.0618358i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19296.3 | − | 19296.3i | −0.0907971 | − | 0.0907971i | 0.660249 | − | 0.751046i | \(-0.270451\pi\) |
−0.751046 | + | 0.660249i | \(0.770451\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 26503.6i | − | 0.123635i | −0.998087 | − | 0.0618176i | \(-0.980310\pi\) | ||
0.998087 | − | 0.0618176i | \(-0.0196897\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −66135.7 | −0.305865 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 111797. | − | 111797.i | 0.512622 | − | 0.512622i | −0.402707 | − | 0.915329i | \(-0.631931\pi\) |
0.915329 | + | 0.402707i | \(0.131931\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −113939. | + | 113939.i | −0.517994 | + | 0.517994i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −466307. | −2.10199 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 271360.i | 1.21290i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −158962. | − | 158962.i | −0.704541 | − | 0.704541i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 70975.8 | + | 70975.8i | 0.311942 | + | 0.311942i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 225380.i | 0.982301i | 0.871075 | + | 0.491150i | \(0.163423\pi\) | ||||
−0.871075 | + | 0.491150i | \(0.836577\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −56828.1 | −0.245625 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 67610.1 | − | 67610.1i | 0.289813 | − | 0.289813i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13419.0 | − | 13419.0i | 0.0570473 | − | 0.0570473i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8483.58 | −0.0357702 | −0.0178851 | − | 0.999840i | \(-0.505693\pi\) | ||||
−0.0178851 | + | 0.999840i | \(0.505693\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 460544.i | 1.92599i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 69265.0 | + | 69265.0i | 0.287310 | + | 0.287310i | 0.836016 | − | 0.548706i | \(-0.184879\pi\) |
−0.548706 | + | 0.836016i | \(0.684879\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23998.6 | + | 23998.6i | 0.0987399 | + | 0.0987399i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 66891.1i | − | 0.272997i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −427794. | −1.73190 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 86869.4 | − | 86869.4i | 0.348872 | − | 0.348872i | −0.510817 | − | 0.859689i | \(-0.670657\pi\) |
0.859689 | + | 0.510817i | \(0.170657\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 491827. | − | 491827.i | 1.95946 | − | 1.95946i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −112271. | −0.443745 | −0.221872 | − | 0.975076i | \(-0.571217\pi\) | ||||
−0.221872 | + | 0.975076i | \(0.571217\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 64805.7i | − | 0.254115i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 255306. | + | 255306.i | 0.993220 | + | 0.993220i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 167589. | + | 167589.i | 0.646861 | + | 0.646861i | 0.952233 | − | 0.305372i | \(-0.0987808\pi\) |
−0.305372 | + | 0.952233i | \(0.598781\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 507912.i | 1.94512i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −77256.9 | −0.293564 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −500.399 | + | 500.399i | −0.00188670 | + | 0.00188670i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −209044. | + | 209044.i | −0.782089 | + | 0.782089i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 496108. | 1.84180 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 287463.i | − | 1.05903i | −0.848302 | − | 0.529513i | \(-0.822375\pi\) | ||
0.848302 | − | 0.529513i | \(-0.177625\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −203069. | − | 203069.i | −0.742404 | − | 0.742404i | 0.230636 | − | 0.973040i | \(-0.425919\pi\) |
−0.973040 | + | 0.230636i | \(0.925919\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −440588. | − | 440588.i | −1.59851 | − | 1.59851i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 108509.i | − | 0.390701i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −271114. | −0.968813 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −116297. | + | 116297.i | −0.412459 | + | 0.412459i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24859.0 | − | 24859.0i | 0.0875042 | − | 0.0875042i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 86277.6 | 0.301433 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 90786.1i | 0.314826i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 424486. | + | 424486.i | 1.46112 | + | 1.46112i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −308972. | − | 308972.i | −1.05566 | − | 1.05566i | −0.998357 | − | 0.0573036i | \(-0.981750\pi\) |
−0.0573036 | − | 0.998357i | \(-0.518250\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 451027.i | 1.52969i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13378.6 | 0.0450420 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8623.13 | + | 8623.13i | −0.0288198 | + | 0.0288198i | −0.721370 | − | 0.692550i | \(-0.756487\pi\) |
0.692550 | + | 0.721370i | \(0.256487\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −56104.4 | + | 56104.4i | −0.186145 | + | 0.186145i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 142317. | 0.468765 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 413968.i | − | 1.35368i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 56150.4 | + | 56150.4i | 0.182292 | + | 0.182292i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 208785. | + | 208785.i | 0.672961 | + | 0.672961i | 0.958398 | − | 0.285437i | \(-0.0921387\pi\) |
−0.285437 | + | 0.958398i | \(0.592139\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 60666.5i | − | 0.194145i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 201683. | 0.640832 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 127891. | − | 127891.i | 0.403480 | − | 0.403480i | −0.475977 | − | 0.879458i | \(-0.657906\pi\) |
0.879458 | + | 0.475977i | \(0.157906\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −24275.2 | + | 24275.2i | −0.0760443 | + | 0.0760443i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 387228. | 1.20448 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 488561.i | 1.50902i | 0.656290 | + | 0.754509i | \(0.272125\pi\) | ||||
−0.656290 | + | 0.754509i | \(0.727875\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17324.2 | − | 17324.2i | −0.0531352 | − | 0.0531352i | 0.680040 | − | 0.733175i | \(-0.261962\pi\) |
−0.733175 | + | 0.680040i | \(0.761962\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 424913. | + | 424913.i | 1.29417 | + | 1.29417i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 56873.6i | − | 0.172018i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9362.93 | −0.0281229 | −0.0140615 | − | 0.999901i | \(-0.504476\pi\) | ||||
−0.0140615 | + | 0.999901i | \(0.504476\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −473990. | + | 473990.i | −1.41388 | + | 1.41388i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −196100. | + | 196100.i | −0.580932 | + | 0.580932i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −178348. | −0.524725 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 14954.5i | 0.0436978i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 46301.5 | + | 46301.5i | 0.134375 | + | 0.134375i | 0.771095 | − | 0.636720i | \(-0.219709\pi\) |
−0.636720 | + | 0.771095i | \(0.719709\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −321742. | − | 321742.i | −0.927422 | − | 0.927422i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 483778.i | 1.38507i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −194145. | −0.552099 | −0.276049 | − | 0.961143i | \(-0.589025\pi\) | ||||
−0.276049 | + | 0.961143i | \(0.589025\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19250.1 | + | 19250.1i | −0.0543749 | + | 0.0543749i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −420387. | + | 420387.i | −1.17951 | + | 1.17951i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −474516. | −1.32250 | −0.661252 | − | 0.750164i | \(-0.729975\pi\) | ||||
−0.661252 | + | 0.750164i | \(0.729975\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 87515.3i | − | 0.242290i | −0.992635 | − | 0.121145i | \(-0.961343\pi\) | ||
0.992635 | − | 0.121145i | \(-0.0386566\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 143493. | + | 143493.i | 0.394634 | + | 0.394634i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 42357.8 | + | 42357.8i | 0.115724 | + | 0.115724i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 687260.i | − | 1.86528i | −0.360808 | − | 0.932640i | \(-0.617499\pi\) | ||
0.360808 | − | 0.932640i | \(-0.382501\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 394456. | 1.06356 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 46734.8 | − | 46734.8i | 0.125187 | − | 0.125187i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 220862. | − | 220862.i | 0.587761 | − | 0.587761i | −0.349263 | − | 0.937025i | \(-0.613568\pi\) |
0.937025 | + | 0.349263i | \(0.113568\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −49125.1 | −0.129883 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 518967.i | − | 1.36323i | −0.731711 | − | 0.681615i | \(-0.761278\pi\) | ||
0.731711 | − | 0.681615i | \(-0.238722\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −77555.3 | − | 77555.3i | −0.202409 | − | 0.202409i | 0.598622 | − | 0.801031i | \(-0.295715\pi\) |
−0.801031 | + | 0.598622i | \(0.795715\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13820.5 | − | 13820.5i | −0.0358378 | − | 0.0358378i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 841705.i | − | 2.16862i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −360490. | −0.922855 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 598015. | − | 598015.i | 1.52117 | − | 1.52117i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −92126.1 | + | 92126.1i | −0.232853 | + | 0.232853i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −344653. | −0.865612 | −0.432806 | − | 0.901487i | \(-0.642477\pi\) | ||||
−0.432806 | + | 0.901487i | \(0.642477\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 486914.i | 1.21519i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8098.03 | + | 8098.03i | 0.0200832 | + | 0.0200832i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −94900.2 | − | 94900.2i | −0.233877 | − | 0.233877i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 538758.i | 1.31945i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −183353. | −0.446243 | −0.223122 | − | 0.974791i | \(-0.571625\pi\) | ||||
−0.223122 | + | 0.974791i | \(0.571625\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −541900. | + | 541900.i | −1.31068 | + | 1.31068i | −0.389768 | + | 0.920913i | \(0.627445\pi\) |
−0.920913 | + | 0.389768i | \(0.872555\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −59943.0 | + | 59943.0i | −0.144085 | + | 0.144085i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 358562. | 0.856555 | 0.428278 | − | 0.903647i | \(-0.359121\pi\) | ||||
0.428278 | + | 0.903647i | \(0.359121\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 292233.i | − | 0.693808i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −891760. | − | 891760.i | −2.10419 | − | 2.10419i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 73642.4 | + | 73642.4i | 0.172704 | + | 0.172704i | 0.788166 | − | 0.615463i | \(-0.211031\pi\) |
−0.615463 | + | 0.788166i | \(0.711031\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 39801.7i | 0.0927725i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 639657. | 1.48189 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22081.7 | − | 22081.7i | 0.0508467 | − | 0.0508467i | −0.681226 | − | 0.732073i | \(-0.738553\pi\) |
0.732073 | + | 0.681226i | \(0.238553\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20869.3 | + | 20869.3i | −0.0477644 | + | 0.0477644i | −0.730586 | − | 0.682821i | \(-0.760753\pi\) |
0.682821 | + | 0.730586i | \(0.260753\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −45089.3 | −0.102576 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 114157.i | 0.258143i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25459.3 | + | 25459.3i | 0.0572261 | + | 0.0572261i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 684791. | + | 684791.i | 1.53005 | + | 1.53005i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 140979.i | − | 0.313120i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 379771. | 0.838479 | 0.419239 | − | 0.907876i | \(-0.362297\pi\) | ||||
0.419239 | + | 0.907876i | \(0.362297\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −90063.0 | + | 90063.0i | −0.197669 | + | 0.197669i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 156167. | − | 156167.i | 0.340731 | − | 0.340731i | −0.515911 | − | 0.856642i | \(-0.672546\pi\) |
0.856642 | + | 0.515911i | \(0.172546\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 361877. | 0.784912 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 355511.i | 0.766581i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 164044. | + | 164044.i | 0.351656 | + | 0.351656i | 0.860725 | − | 0.509070i | \(-0.170010\pi\) |
−0.509070 | + | 0.860725i | \(0.670010\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10448.0 | − | 10448.0i | −0.0222665 | − | 0.0222665i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 785666.i | − | 1.66466i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 39872.4 | 0.0839912 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −288207. | + | 288207.i | −0.603599 | + | 0.603599i | −0.941266 | − | 0.337667i | \(-0.890362\pi\) |
0.337667 | + | 0.941266i | \(0.390362\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 901945. | − | 901945.i | 1.87808 | − | 1.87808i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 25062.1 | 0.0518856 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 80599.7i | − | 0.165908i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 26087.2 | + | 26087.2i | 0.0533916 | + | 0.0533916i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −323248. | − | 323248.i | −0.657808 | − | 0.657808i | 0.297053 | − | 0.954861i | \(-0.403996\pi\) |
−0.954861 | + | 0.297053i | \(0.903996\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 546329.i | 1.10546i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −92355.0 | −0.185816 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 873826. | − | 873826.i | 1.74818 | − | 1.74818i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 580085. | − | 580085.i | 1.15398 | − | 1.15398i | 0.168235 | − | 0.985747i | \(-0.446193\pi\) |
0.985747 | − | 0.168235i | \(-0.0538067\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −521346. | −1.03130 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 115113.i | − | 0.226436i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18788.9 | − | 18788.9i | −0.0367526 | − | 0.0367526i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −471123. | − | 471123.i | −0.916423 | − | 0.916423i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 332243.i | 0.642684i | 0.946963 | + | 0.321342i | \(0.104134\pi\) | ||||
−0.946963 | + | 0.321342i | \(0.895866\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13494.5 | −0.0259590 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 415456. | − | 415456.i | 0.794783 | − | 0.794783i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 165908. | − | 165908.i | 0.315639 | − | 0.315639i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −362311. | −0.685508 | −0.342754 | − | 0.939425i | \(-0.611360\pi\) | ||||
−0.342754 | + | 0.939425i | \(0.611360\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 713570.i | − | 1.34271i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −98348.7 | − | 98348.7i | −0.184049 | − | 0.184049i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −377844. | − | 377844.i | −0.703242 | − | 0.703242i | 0.261863 | − | 0.965105i | \(-0.415663\pi\) |
−0.965105 | + | 0.261863i | \(0.915663\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 187537.i | 0.347146i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −360569. | −0.663825 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 467502. | − | 467502.i | 0.856042 | − | 0.856042i | −0.134828 | − | 0.990869i | \(-0.543048\pi\) |
0.990869 | + | 0.134828i | \(0.0430480\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −133695. | + | 133695.i | −0.243489 | + | 0.243489i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 555820. | 1.00683 | 0.503415 | − | 0.864045i | \(-0.332077\pi\) | ||||
0.503415 | + | 0.864045i | \(0.332077\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 89612.4i | 0.161456i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 246966. | + | 246966.i | 0.442584 | + | 0.442584i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.16335e6 | + | 1.16335e6i | 2.07370 | + | 2.07370i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 308308.i | − | 0.546644i | −0.961923 | − | 0.273322i | \(-0.911878\pi\) | ||
0.961923 | − | 0.273322i | \(-0.0881224\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 599226. | 1.05682 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 119499. | − | 119499.i | 0.209638 | − | 0.209638i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34980.2 | + | 34980.2i | −0.0610423 | + | 0.0610423i | −0.736969 | − | 0.675927i | \(-0.763744\pi\) |
0.675927 | + | 0.736969i | \(0.263744\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 213958. | 0.371403 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 545745.i | − | 0.942368i | −0.882035 | − | 0.471184i | \(-0.843827\pi\) | ||
0.882035 | − | 0.471184i | \(-0.156173\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 180394. | + | 180394.i | 0.309866 | + | 0.309866i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 24243.3 | + | 24243.3i | 0.0414256 | + | 0.0414256i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 65332.9i | 0.111056i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 510362. | 0.863030 | 0.431515 | − | 0.902106i | \(-0.357979\pi\) | ||||
0.431515 | + | 0.902106i | \(0.357979\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −667972. | + | 667972.i | −1.12370 | + | 1.12370i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −596763. | + | 596763.i | −0.998718 | + | 0.998718i | −0.999999 | − | 0.00128103i | \(-0.999592\pi\) |
0.00128103 | + | 0.999999i | \(0.499592\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −750148. | −1.24895 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.51424e6i | 2.50814i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −238987. | − | 238987.i | −0.393822 | − | 0.393822i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −676897. | − | 676897.i | −1.10974 | − | 1.10974i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 80632.7i | − | 0.131519i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 140849. | 0.228567 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −463254. | + | 463254.i | −0.747945 | + | 0.747945i | −0.974093 | − | 0.226148i | \(-0.927387\pi\) |
0.226148 | + | 0.974093i | \(0.427387\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.06785e6 | + | 1.06785e6i | −1.71536 | + | 1.71536i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −654644. | −1.04629 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31518.0i | 0.0501202i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −39396.9 | − | 39396.9i | −0.0623344 | − | 0.0623344i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −406283. | − | 406283.i | −0.639605 | − | 0.639605i | 0.310853 | − | 0.950458i | \(-0.399385\pi\) |
−0.950458 | + | 0.310853i | \(0.899385\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 151527.i | − | 0.237354i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.06003e6 | −1.65217 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −803667. | + | 803667.i | −1.24636 | + | 1.24636i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20421.7 | + | 20421.7i | −0.0315137 | + | 0.0315137i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.33193e6 | 2.04519 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 766553.i | 1.17124i | 0.810587 | + | 0.585619i | \(0.199148\pi\) | ||||
−0.810587 | + | 0.585619i | \(0.800852\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −418641. | − | 418641.i | −0.636503 | − | 0.636503i | 0.313188 | − | 0.949691i | \(-0.398603\pi\) |
−0.949691 | + | 0.313188i | \(0.898603\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.03855e6 | + | 1.03855e6i | 1.57125 | + | 1.57125i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 139108.i | − | 0.209429i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −583231. | −0.873769 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −201643. | + | 201643.i | −0.300618 | + | 0.300618i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23229.7 | − | 23229.7i | 0.0344633 | − | 0.0344633i | −0.689665 | − | 0.724128i | \(-0.742242\pi\) |
0.724128 | + | 0.689665i | \(0.242242\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41797.3 | 0.0617090 | 0.0308545 | − | 0.999524i | \(-0.490177\pi\) | ||||
0.0308545 | + | 0.999524i | \(0.490177\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 1.39428e6i | − | 2.04853i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −349889. | − | 349889.i | −0.511587 | − | 0.511587i | 0.403425 | − | 0.915013i | \(-0.367820\pi\) |
−0.915013 | + | 0.403425i | \(0.867820\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −213369. | − | 213369.i | −0.310472 | − | 0.310472i | 0.534621 | − | 0.845092i | \(-0.320455\pi\) |
−0.845092 | + | 0.534621i | \(0.820455\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 652479.i | − | 0.944853i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −307692. | −0.443432 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −148557. | + | 148557.i | −0.213069 | + | 0.213069i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −182289. | + | 182289.i | −0.260202 | + | 0.260202i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7789.74 | 0.0110662 | 0.00553311 | − | 0.999985i | \(-0.498239\pi\) | ||||
0.00553311 | + | 0.999985i | \(0.498239\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 558745.i | − | 0.789990i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.39484e6 | + | 1.39484e6i | 1.96277 | + | 1.96277i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −77115.5 | − | 77115.5i | −0.108001 | − | 0.108001i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.14229e6i | 1.59224i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −749570. | −1.03991 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −97733.2 | + | 97733.2i | −0.134953 | + | 0.134953i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −485860. | + | 485860.i | −0.667749 | + | 0.667749i | −0.957195 | − | 0.289445i | \(-0.906529\pi\) |
0.289445 | + | 0.957195i | \(0.406529\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 143768. | 0.196667 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.01914e6i | 1.38763i | 0.720154 | + | 0.693814i | \(0.244071\pi\) | ||||
−0.720154 | + | 0.693814i | \(0.755929\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 232567. | + | 232567.i | 0.315182 | + | 0.315182i | 0.846913 | − | 0.531731i | \(-0.178458\pi\) |
−0.531731 | + | 0.846913i | \(0.678458\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −662392. | − | 662392.i | −0.893529 | − | 0.893529i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 739852.i | 0.993398i | 0.867923 | + | 0.496699i | \(0.165455\pi\) | ||||
−0.867923 | + | 0.496699i | \(0.834545\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −149850. | −0.200274 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 714164. | − | 714164.i | 0.950079 | − | 0.950079i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 655020. | − | 655020.i | 0.867392 | − | 0.867392i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 80610.5 | 0.106256 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 455742.i | − | 0.597986i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 269704. | + | 269704.i | 0.352267 | + | 0.352267i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 828805. | + | 828805.i | 1.07759 | + | 1.07759i | 0.996725 | + | 0.0808636i | \(0.0257678\pi\) |
0.0808636 | + | 0.996725i | \(0.474232\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13364.2i | 0.0172968i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.20631e6 | 1.55420 | 0.777099 | − | 0.629379i | \(-0.216690\pi\) | ||||
0.777099 | + | 0.629379i | \(0.216690\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 381765. | − | 381765.i | 0.489637 | − | 0.489637i | −0.418555 | − | 0.908192i | \(-0.637463\pi\) |
0.908192 | + | 0.418555i | \(0.137463\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 64553.8 | − | 64553.8i | 0.0824205 | − | 0.0824205i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.44154e6 | 1.83223 | 0.916113 | − | 0.400919i | \(-0.131309\pi\) | ||||
0.916113 | + | 0.400919i | \(0.131309\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 218384.i | 0.276323i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 612709. | + | 612709.i | 0.771790 | + | 0.771790i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −449295. | − | 449295.i | −0.563416 | − | 0.563416i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 27422.0i | − | 0.0342337i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −47833.5 | −0.0594494 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 335801. | − | 335801.i | 0.415492 | − | 0.415492i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 64638.6 | − | 64638.6i | 0.0796238 | − | 0.0796238i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.61652e6 | −1.98246 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 136233.i | − | 0.166336i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −208093. | − | 208093.i | −0.252955 | − | 0.252955i | 0.569226 | − | 0.822181i | \(-0.307243\pi\) |
−0.822181 | + | 0.569226i | \(0.807243\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.10048e6 | − | 1.10048e6i | −1.33185 | − | 1.33185i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 861726.i | 1.03832i | 0.854676 | + | 0.519162i | \(0.173756\pi\) | ||||
−0.854676 | + | 0.519162i | \(0.826244\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −620577. | −0.744482 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 31142.2 | − | 31142.2i | 0.0371969 | − | 0.0371969i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −536678. | + | 536678.i | −0.638227 | + | 0.638227i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 368829. | 0.436711 | 0.218355 | − | 0.975869i | \(-0.429931\pi\) | ||||
0.218355 | + | 0.975869i | \(0.429931\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 388292.i | − | 0.457761i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 151330. | + | 151330.i | 0.177632 | + | 0.177632i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 636889. | + | 636889.i | 0.744355 | + | 0.744355i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16994.8i | 0.0197769i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 842458. | 0.976151 | 0.488076 | − | 0.872801i | \(-0.337699\pi\) | ||||
0.488076 | + | 0.872801i | \(0.337699\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −912344. | + | 912344.i | −1.05259 | + | 1.05259i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 775851. | − | 775851.i | 0.891282 | − | 0.891282i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −60918.6 | −0.0696830 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41186.1i | 0.0469107i | 0.999725 | + | 0.0234553i | \(0.00746675\pi\) | ||||
−0.999725 | + | 0.0234553i | \(0.992533\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.13502e6 | − | 1.13502e6i | −1.28728 | − | 1.28728i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −495362. | − | 495362.i | −0.559427 | − | 0.559427i | 0.369717 | − | 0.929144i | \(-0.379454\pi\) |
−0.929144 | + | 0.369717i | \(0.879454\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 85505.2i | − | 0.0961544i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 64678.2 | 0.0724259 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −825578. | + | 825578.i | −0.920573 | + | 0.920573i | −0.997070 | − | 0.0764965i | \(-0.975627\pi\) |
0.0764965 | + | 0.997070i | \(0.475627\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 179672. | − | 179672.i | 0.199502 | − | 0.199502i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 278918. | 0.308401 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.06311e6i | 1.17055i | 0.810834 | + | 0.585276i | \(0.199014\pi\) | ||||
−0.810834 | + | 0.585276i | \(0.800986\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −128345. | − | 128345.i | −0.140726 | − | 0.140726i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 624145. | + | 624145.i | 0.681494 | + | 0.681494i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 281757.i | − | 0.306364i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −594793. | −0.644050 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.46511e6 | − | 1.46511e6i | 1.57985 | − | 1.57985i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 143169. | − | 143169.i | 0.153743 | − | 0.153743i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.03910e6 | −1.11123 | −0.555615 | − | 0.831440i | \(-0.687517\pi\) | ||||
−0.555615 | + | 0.831440i | \(0.687517\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 433476.i | 0.461655i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 624932. | + | 624932.i | 0.662818 | + | 0.662818i | 0.956043 | − | 0.293225i | \(-0.0947285\pi\) |
−0.293225 | + | 0.956043i | \(0.594729\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 337931. | + | 337931.i | 0.356946 | + | 0.356946i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 311712.i | 0.327903i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.37121e6 | 1.43653 | 0.718264 | − | 0.695771i | \(-0.244937\pi\) | ||||
0.718264 | + | 0.695771i | \(0.244937\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.33183e6 | − | 1.33183e6i | 1.38958 | − | 1.38958i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 227186. | − | 227186.i | 0.236071 | − | 0.236071i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −838159. | −0.867400 | −0.433700 | − | 0.901057i | \(-0.642792\pi\) | ||||
−0.433700 | + | 0.901057i | \(0.642792\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 146126.i | − | 0.150610i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.24529e6 | − | 1.24529e6i | −1.27831 | − | 1.27831i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −104335. | − | 104335.i | −0.106668 | − | 0.106668i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 817540.i | − | 0.832457i | −0.909260 | − | 0.416228i | \(-0.863352\pi\) | ||
0.909260 | − | 0.416228i | \(-0.136648\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.56221e6 | −1.58432 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 126978. | − | 126978.i | 0.128258 | − | 0.128258i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 243046. | − | 243046.i | 0.244511 | − | 0.244511i | −0.574203 | − | 0.818713i | \(-0.694688\pi\) |
0.818713 | + | 0.574203i | \(0.194688\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 309534. | 0.310154 |
(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 | 128.5.f.a.95.1 | 14 | ||
4.3 | odd | 2 | 128.5.f.b.95.7 | 14 | |||
8.3 | odd | 2 | 16.5.f.a.3.2 | ✓ | 14 | ||
8.5 | even | 2 | 64.5.f.a.47.7 | 14 | |||
16.3 | odd | 4 | 64.5.f.a.15.7 | 14 | |||
16.5 | even | 4 | 128.5.f.b.31.7 | 14 | |||
16.11 | odd | 4 | inner | 128.5.f.a.31.1 | 14 | ||
16.13 | even | 4 | 16.5.f.a.11.2 | yes | 14 | ||
24.5 | odd | 2 | 576.5.m.a.559.4 | 14 | |||
24.11 | even | 2 | 144.5.m.a.19.6 | 14 | |||
48.29 | odd | 4 | 144.5.m.a.91.6 | 14 | |||
48.35 | even | 4 | 576.5.m.a.271.4 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.5.f.a.3.2 | ✓ | 14 | 8.3 | odd | 2 | ||
16.5.f.a.11.2 | yes | 14 | 16.13 | even | 4 | ||
64.5.f.a.15.7 | 14 | 16.3 | odd | 4 | |||
64.5.f.a.47.7 | 14 | 8.5 | even | 2 | |||
128.5.f.a.31.1 | 14 | 16.11 | odd | 4 | inner | ||
128.5.f.a.95.1 | 14 | 1.1 | even | 1 | trivial | ||
128.5.f.b.31.7 | 14 | 16.5 | even | 4 | |||
128.5.f.b.95.7 | 14 | 4.3 | odd | 2 | |||
144.5.m.a.19.6 | 14 | 24.11 | even | 2 | |||
144.5.m.a.91.6 | 14 | 48.29 | odd | 4 | |||
576.5.m.a.271.4 | 14 | 48.35 | even | 4 | |||
576.5.m.a.559.4 | 14 | 24.5 | odd | 2 |