Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,5,Mod(5,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.5");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.k (of order \(18\), degree \(6\), 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: | \(11.1639560131\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 5.6 | ||
Character | \(\chi\) | \(=\) | 108.5 |
Dual form | 108.5.k.a.65.6 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{5}{18}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −1.23486 | − | 8.91488i | −0.137206 | − | 0.990542i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.87553 | + | 16.1429i | 0.235021 | + | 0.645716i | 0.999999 | + | 0.00165851i | \(0.000527920\pi\) |
−0.764977 | + | 0.644057i | \(0.777250\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.12577 | + | 46.0835i | 0.165832 | + | 0.940480i | 0.948202 | + | 0.317667i | \(0.102899\pi\) |
−0.782370 | + | 0.622813i | \(0.785990\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −77.9503 | + | 22.0172i | −0.962349 | + | 0.271818i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −21.9431 | + | 60.2882i | −0.181348 | + | 0.498250i | −0.996742 | − | 0.0806569i | \(-0.974298\pi\) |
0.815394 | + | 0.578907i | \(0.196520\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 26.5065 | + | 22.2416i | 0.156843 | + | 0.131607i | 0.717832 | − | 0.696216i | \(-0.245135\pi\) |
−0.560989 | + | 0.827823i | \(0.689579\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 136.657 | − | 72.3139i | 0.607362 | − | 0.321395i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 211.894 | + | 122.337i | 0.733196 | + | 0.423311i | 0.819590 | − | 0.572950i | \(-0.194201\pi\) |
−0.0863944 | + | 0.996261i | \(0.527535\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 215.694 | + | 373.592i | 0.597489 | + | 1.03488i | 0.993190 | + | 0.116502i | \(0.0371682\pi\) |
−0.395701 | + | 0.918379i | \(0.629498\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 400.795 | − | 129.347i | 0.908832 | − | 0.293304i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 364.888 | + | 64.3396i | 0.689770 | + | 0.121625i | 0.507536 | − | 0.861630i | \(-0.330556\pi\) |
0.182233 | + | 0.983255i | \(0.441667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 252.707 | − | 212.046i | 0.404331 | − | 0.339274i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 292.538 | + | 667.729i | 0.401287 | + | 0.915952i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −478.762 | − | 570.567i | −0.569277 | − | 0.678438i | 0.402205 | − | 0.915550i | \(-0.368244\pi\) |
−0.971483 | + | 0.237111i | \(0.923799\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −232.834 | + | 1320.47i | −0.242283 | + | 1.37405i | 0.584436 | + | 0.811440i | \(0.301316\pi\) |
−0.826719 | + | 0.562615i | \(0.809795\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 564.559 | + | 121.173i | 0.518420 | + | 0.111270i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −696.178 | + | 401.939i | −0.568309 | + | 0.328113i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 27.6012 | − | 47.8066i | 0.0201615 | − | 0.0349208i | −0.855769 | − | 0.517359i | \(-0.826915\pi\) |
0.875930 | + | 0.482438i | \(0.160249\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 165.550 | − | 263.768i | 0.108843 | − | 0.173417i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −603.231 | + | 718.902i | −0.358852 | + | 0.427664i | −0.915021 | − | 0.403406i | \(-0.867826\pi\) |
0.556169 | + | 0.831069i | \(0.312271\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1586.08 | + | 577.286i | 0.857805 | + | 0.312215i | 0.733218 | − | 0.679993i | \(-0.238017\pi\) |
0.124586 | + | 0.992209i | \(0.460240\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −813.421 | − | 1128.98i | −0.401689 | − | 0.557521i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3718.42 | + | 655.657i | −1.68330 | + | 0.296812i | −0.931814 | − | 0.362935i | \(-0.881775\pi\) |
−0.751488 | + | 0.659747i | \(0.770664\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 198.539 | − | 72.2624i | 0.0826903 | − | 0.0300968i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 828.960 | − | 2040.07i | 0.318708 | − | 0.784343i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1222.43i | − | 0.435185i | −0.976040 | − | 0.217592i | \(-0.930180\pi\) | ||
0.976040 | − | 0.217592i | \(-0.0698203\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1102.15 | −0.364348 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3064.18 | − | 2384.22i | 0.943115 | − | 0.733831i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1312.00 | − | 3604.69i | −0.376904 | − | 1.03553i | −0.972633 | − | 0.232349i | \(-0.925359\pi\) |
0.595729 | − | 0.803185i | \(-0.296863\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 308.780 | + | 1751.18i | 0.0829831 | + | 0.470620i | 0.997774 | + | 0.0666918i | \(0.0212444\pi\) |
−0.914791 | + | 0.403928i | \(0.867644\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1648.04 | − | 3413.32i | −0.415227 | − | 0.859994i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −203.304 | + | 558.573i | −0.0481193 | + | 0.132207i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3270.92 | + | 2744.63i | 0.728652 | + | 0.611411i | 0.929764 | − | 0.368157i | \(-0.120011\pi\) |
−0.201112 | + | 0.979568i | \(0.564455\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 122.995 | − | 3332.39i | 0.0258339 | − | 0.699934i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4353.90 | − | 2513.72i | −0.863697 | − | 0.498656i | 0.00155135 | − | 0.999999i | \(-0.499506\pi\) |
−0.865249 | + | 0.501343i | \(0.832840\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −496.098 | − | 859.268i | −0.0930941 | − | 0.161244i | 0.815717 | − | 0.578451i | \(-0.196342\pi\) |
−0.908812 | + | 0.417207i | \(0.863009\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2202.42 | − | 1991.00i | −0.391542 | − | 0.353956i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2956.60 | − | 521.328i | −0.498667 | − | 0.0879285i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8677.93 | + | 7281.65i | −1.39047 | + | 1.16674i | −0.425323 | + | 0.905042i | \(0.639840\pi\) |
−0.965149 | + | 0.261703i | \(0.915716\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5591.48 | − | 3432.50i | 0.852230 | − | 0.523167i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2884.98 | − | 3438.18i | −0.418780 | − | 0.499083i | 0.514870 | − | 0.857268i | \(-0.327840\pi\) |
−0.933651 | + | 0.358185i | \(0.883396\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −729.883 | + | 4139.37i | −0.101022 | + | 0.572923i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4495.33 | + | 4972.68i | −0.593914 | + | 0.656980i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1220.28 | − | 704.528i | 0.154056 | − | 0.0889443i | −0.420990 | − | 0.907065i | \(-0.638317\pi\) |
0.575046 | + | 0.818121i | \(0.304984\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −809.586 | + | 1402.24i | −0.0977643 | + | 0.169333i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 12059.3 | + | 445.098i | 1.39430 | + | 0.0514623i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4763.55 | + | 5676.97i | −0.527817 | + | 0.629027i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5073.22 | + | 1846.50i | 0.539188 | + | 0.196248i | 0.597236 | − | 0.802065i | \(-0.296265\pi\) |
−0.0580481 | + | 0.998314i | \(0.518488\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 383.092 | − | 5182.61i | 0.0390870 | − | 0.528784i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2412.93 | + | 425.465i | −0.236539 | + | 0.0417082i | −0.290661 | − | 0.956826i | \(-0.593875\pi\) |
0.0541220 | + | 0.998534i | \(0.482764\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15177.4 | − | 5524.12i | 1.43061 | − | 0.520701i | 0.493507 | − | 0.869742i | \(-0.335715\pi\) |
0.937107 | + | 0.349041i | \(0.113493\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4442.92 | + | 5710.01i | 0.402986 | + | 0.517915i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16847.5i | 1.47153i | 0.677238 | + | 0.735764i | \(0.263177\pi\) | ||||
−0.677238 | + | 0.735764i | \(0.736823\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7711.13 | 0.649031 | 0.324515 | − | 0.945880i | \(-0.394799\pi\) | ||||
0.324515 | + | 0.945880i | \(0.394799\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −460.274 | − | 187.027i | −0.0373568 | − | 0.0151795i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7240.01 | − | 19891.8i | −0.566999 | − | 1.55782i | −0.809165 | − | 0.587582i | \(-0.800080\pi\) |
0.242166 | − | 0.970235i | \(-0.422142\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1105.28 | + | 6268.38i | 0.0835754 | + | 0.473980i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2555.89 | − | 1150.14i | −0.186711 | − | 0.0840192i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3915.91 | + | 10758.9i | −0.276528 | + | 0.759754i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8062.49 | + | 6765.23i | 0.550679 | + | 0.462074i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7153.83 | + | 4489.99i | 0.472856 | + | 0.296780i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 14206.2 | + | 8201.94i | 0.909196 | + | 0.524924i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2846.78 | − | 4930.77i | −0.176501 | − | 0.305709i | 0.764179 | − | 0.645005i | \(-0.223145\pi\) |
−0.940680 | + | 0.339296i | \(0.889811\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3187.85 | − | 14852.6i | 0.191566 | − | 0.892530i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21524.9 | + | 3795.42i | 1.25429 | + | 0.221165i | 0.761030 | − | 0.648716i | \(-0.224694\pi\) |
0.493260 | + | 0.869882i | \(0.335805\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15463.8 | + | 12975.6i | −0.874203 | + | 0.733543i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9060.26 | + | 8645.68i | −0.497134 | + | 0.474386i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1116.26 | − | 1330.31i | −0.0594739 | − | 0.0708782i | 0.735487 | − | 0.677538i | \(-0.236953\pi\) |
−0.794961 | + | 0.606660i | \(0.792509\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2361.73 | − | 13394.0i | 0.122236 | − | 0.693236i | −0.860675 | − | 0.509155i | \(-0.829958\pi\) |
0.982911 | − | 0.184081i | \(-0.0589310\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10436.8 | + | 32339.6i | 0.524965 | + | 1.62666i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1922.54 | + | 1109.98i | −0.0940165 | + | 0.0542804i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6397.61 | − | 11081.0i | 0.304286 | − | 0.527039i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −889.379 | − | 1680.72i | −0.0411578 | − | 0.0777788i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 27688.4 | − | 32997.8i | 1.24717 | − | 1.48632i | 0.437744 | − | 0.899100i | \(-0.355778\pi\) |
0.809427 | − | 0.587221i | \(-0.199778\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10633.6 | − | 3870.31i | −0.466365 | − | 0.169743i | 0.0981399 | − | 0.995173i | \(-0.468711\pi\) |
−0.564505 | + | 0.825430i | \(0.690933\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −19210.7 | − | 4870.88i | −0.820653 | − | 0.208077i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −22684.2 | + | 3999.83i | −0.944190 | + | 0.166486i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18511.2 | + | 6737.53i | −0.750992 | + | 0.273339i | −0.689023 | − | 0.724739i | \(-0.741960\pi\) |
−0.0619689 | + | 0.998078i | \(0.519738\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10897.9 | + | 1509.53i | −0.431069 | + | 0.0597101i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 17338.1i | 0.668884i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22213.1 | −0.836055 | −0.418027 | − | 0.908434i | \(-0.637278\pi\) | ||||
−0.418027 | + | 0.908434i | \(0.637278\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1361.00 | + | 9825.57i | 0.0499909 | + | 0.360902i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 45.4798 | + | 124.955i | 0.00163074 | + | 0.00448043i | 0.940505 | − | 0.339779i | \(-0.110352\pi\) |
−0.938875 | + | 0.344259i | \(0.888130\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4751.66 | − | 26948.0i | −0.166369 | − | 0.943524i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −25038.8 | − | 24372.6i | −0.856292 | − | 0.833509i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4304.21 | − | 11825.7i | 0.143814 | − | 0.395126i | −0.846783 | − | 0.531939i | \(-0.821464\pi\) |
0.990597 | + | 0.136813i | \(0.0436859\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11825.3 | + | 9922.58i | 0.386131 | + | 0.324002i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −30515.3 | + | 16147.6i | −0.974027 | + | 0.515421i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 38910.8 | + | 22465.2i | 1.21441 | + | 0.701138i | 0.963716 | − | 0.266929i | \(-0.0860088\pi\) |
0.250691 | + | 0.968067i | \(0.419342\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −30521.8 | − | 52865.4i | −0.931652 | − | 1.61367i | −0.780498 | − | 0.625158i | \(-0.785035\pi\) |
−0.151154 | − | 0.988510i | \(-0.548299\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15230.2 | − | 4915.19i | 0.454784 | − | 0.146770i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 933.908 | + | 164.673i | 0.0272873 | + | 0.00481149i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12025.1 | + | 10090.2i | −0.343878 | + | 0.288548i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −28394.2 | + | 18907.0i | −0.794888 | + | 0.529297i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13921.7 | − | 16591.2i | −0.381614 | − | 0.454790i | 0.540709 | − | 0.841210i | \(-0.318156\pi\) |
−0.922323 | + | 0.386420i | \(0.873712\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2671.39 | − | 15150.2i | 0.0717171 | − | 0.406728i | −0.927723 | − | 0.373269i | \(-0.878237\pi\) |
0.999440 | − | 0.0334585i | \(-0.0106521\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5230.67 | + | 1122.67i | 0.137559 | + | 0.0295246i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 42526.8 | − | 24552.9i | 1.09580 | − | 0.632659i | 0.160684 | − | 0.987006i | \(-0.448630\pi\) |
0.935114 | + | 0.354347i | \(0.115297\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 38457.1 | − | 66609.6i | 0.971114 | − | 1.68202i | 0.278910 | − | 0.960317i | \(-0.410027\pi\) |
0.692204 | − | 0.721702i | \(-0.256640\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 20428.9 | − | 32549.1i | 0.505653 | − | 0.805650i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 22403.4 | − | 26699.3i | 0.543653 | − | 0.647901i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15149.5 | − | 5513.95i | −0.360487 | − | 0.131207i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −29859.7 | + | 3018.54i | −0.696859 | + | 0.0704459i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −27256.2 | + | 4806.00i | −0.623983 | + | 0.110025i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 80895.2 | − | 29443.4i | 1.81701 | − | 0.661338i | 0.821123 | − | 0.570751i | \(-0.193348\pi\) |
0.995889 | − | 0.0905869i | \(-0.0288743\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −17033.1 | + | 41918.6i | −0.375435 | + | 0.923948i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 28995.8i | 0.627275i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −62743.7 | −1.33245 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7047.66 | + | 5483.73i | −0.146946 | + | 0.114337i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2895.59 | + | 7955.58i | 0.0592861 | + | 0.162887i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4374.88 | + | 24811.2i | 0.0879743 | + | 0.498927i | 0.996675 | + | 0.0814790i | \(0.0259644\pi\) |
−0.908701 | + | 0.417448i | \(0.862925\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −15029.9 | + | 22092.9i | −0.296887 | + | 0.436404i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −25727.7 | + | 70686.3i | −0.499286 | + | 1.37178i | 0.392680 | + | 0.919675i | \(0.371548\pi\) |
−0.891966 | + | 0.452103i | \(0.850674\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13639.0 | + | 11444.5i | 0.260083 | + | 0.218236i | 0.763500 | − | 0.645808i | \(-0.223479\pi\) |
−0.503416 | + | 0.864044i | \(0.667924\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −996.599 | + | 27001.5i | −0.0186765 | + | 0.506015i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5151.21 | + | 2974.05i | 0.0948850 | + | 0.0547819i | 0.546692 | − | 0.837334i | \(-0.315887\pi\) |
−0.451807 | + | 0.892116i | \(0.649220\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −32431.9 | − | 56173.6i | −0.587268 | − | 1.01718i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 75631.1 | + | 68370.9i | 1.34649 | + | 1.21724i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6503.03 | − | 1146.66i | −0.113847 | − | 0.0200742i | 0.116435 | − | 0.993198i | \(-0.462853\pi\) |
−0.230281 | + | 0.973124i | \(0.573965\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −66257.5 | + | 55596.7i | −1.14078 | + | 0.957226i | −0.999464 | − | 0.0327387i | \(-0.989577\pi\) |
−0.141314 | + | 0.989965i | \(0.545133\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −37505.0 | − | 45608.8i | −0.635150 | − | 0.772389i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2333.05 | + | 2780.42i | 0.0388680 | + | 0.0463210i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2592.01 | + | 14700.0i | −0.0424857 | + | 0.240948i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −27088.5 | + | 29964.9i | −0.436904 | + | 0.483297i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 77901.6 | − | 44976.5i | 1.23651 | − | 0.713901i | 0.268133 | − | 0.963382i | \(-0.413593\pi\) |
0.968380 | + | 0.249481i | \(0.0802599\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11885.7 | + | 20586.6i | −0.185688 | + | 0.321621i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 37803.3 | + | 1395.28i | 0.581366 | + | 0.0214576i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 54004.6 | − | 64360.2i | 0.817645 | − | 0.974432i | −0.182316 | − | 0.983240i | \(-0.558359\pi\) |
0.999961 | + | 0.00880836i | \(0.00280382\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2427.38 | + | 883.493i | 0.0361858 | + | 0.0131705i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 49881.9 | + | 33934.8i | 0.732255 | + | 0.498155i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1424.17 | + | 251.119i | −0.0205897 | + | 0.00363052i | −0.183934 | − | 0.982939i | \(-0.558883\pi\) |
0.163344 | + | 0.986569i | \(0.447772\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19733.6 | − | 7182.45i | 0.281006 | − | 0.102278i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7787.65 | − | 10008.6i | −0.109241 | − | 0.140395i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 124679.i | 1.72301i | 0.507748 | + | 0.861506i | \(0.330478\pi\) | ||||
−0.507748 | + | 0.861506i | \(0.669522\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 75336.2 | 1.02581 | 0.512903 | − | 0.858447i | \(-0.328570\pi\) | ||||
0.512903 | + | 0.858447i | \(0.328570\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13500.6 | + | 5485.79i | 0.181145 | + | 0.0736061i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7238.71 | + | 19888.2i | 0.0957184 | + | 0.262984i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18002.8 | + | 102099.i | 0.234629 | + | 1.33064i | 0.843395 | + | 0.537295i | \(0.180554\pi\) |
−0.608766 | + | 0.793350i | \(0.708335\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10923.5 | − | 108057.i | −0.140332 | − | 1.38818i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18849.0 | − | 51787.1i | 0.238712 | − | 0.655857i | −0.761260 | − | 0.648447i | \(-0.775419\pi\) |
0.999973 | − | 0.00741027i | \(-0.00235878\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 74274.8 | + | 62323.9i | 0.927403 | + | 0.778183i | 0.975349 | − | 0.220667i | \(-0.0708232\pi\) |
−0.0479465 | + | 0.998850i | \(0.515268\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 56491.8 | + | 35456.2i | 0.695498 | + | 0.436518i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −38031.3 | − | 21957.4i | −0.461718 | − | 0.266573i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11827.9 | − | 20486.5i | −0.141616 | − | 0.245286i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10196.6 | − | 47507.3i | 0.120412 | − | 0.561015i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3384.94 | − | 596.856i | −0.0394290 | − | 0.00695240i | 0.153899 | − | 0.988087i | \(-0.450817\pi\) |
−0.193328 | + | 0.981134i | \(0.561928\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 50481.5 | − | 42359.0i | 0.580080 | − | 0.486745i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −46675.4 | + | 2984.56i | −0.529146 | + | 0.0338351i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8240.90 | + | 9821.12i | 0.0921790 | + | 0.109855i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13715.3 | + | 77783.1i | −0.151381 | + | 0.858523i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6772.60 | + | 20985.6i | 0.0737683 | + | 0.228579i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −26454.8 | + | 15273.7i | −0.284384 | + | 0.164189i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2091.41 | + | 3622.43i | −0.0221903 | + | 0.0384347i | −0.876907 | − | 0.480660i | \(-0.840397\pi\) |
0.854717 | + | 0.519094i | \(0.173731\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −67988.8 | − | 128483.i | −0.712066 | − | 1.34564i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7930.44 | − | 9451.12i | 0.0819929 | − | 0.0977153i | −0.723488 | − | 0.690337i | \(-0.757462\pi\) |
0.805481 | + | 0.592621i | \(0.201907\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −91607.2 | − | 33342.3i | −0.935064 | − | 0.340335i | −0.170849 | − | 0.985297i | \(-0.554651\pi\) |
−0.764215 | + | 0.644962i | \(0.776873\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 45417.7 | − | 46659.1i | 0.457724 | − | 0.470236i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −169962. | + | 29968.9i | −1.69135 | + | 0.298230i | −0.934659 | − | 0.355545i | \(-0.884295\pi\) |
−0.756689 | + | 0.653775i | \(0.773184\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 44904.0 | − | 16343.7i | 0.441269 | − | 0.160609i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 150194. | − | 20804.3i | 1.45761 | − | 0.201903i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 105549.i | 1.01169i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11414.6 | 0.108067 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9522.15 | − | 68743.8i | −0.0890512 | − | 0.642892i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −60430.0 | − | 166030.i | −0.558291 | − | 1.53389i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15558.1 | + | 88234.6i | 0.142004 | + | 0.805347i | 0.969724 | + | 0.244204i | \(0.0785268\pi\) |
−0.827719 | + | 0.561142i | \(0.810362\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1098.95 | + | 4334.24i | −0.00991034 | + | 0.0390863i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −25087.8 | + | 68928.2i | −0.223549 | + | 0.614197i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −64856.8 | − | 54421.3i | −0.571078 | − | 0.479191i | 0.310925 | − | 0.950434i | \(-0.399361\pi\) |
−0.882003 | + | 0.471243i | \(0.843806\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −168392. | + | 89107.3i | −1.46529 | + | 0.775379i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −74499.4 | − | 43012.3i | −0.640685 | − | 0.369899i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 61120.1 | + | 105863.i | 0.519512 | + | 0.899822i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 54517.0 | − | 17594.0i | 0.458030 | − | 0.147818i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −169395. | − | 29868.8i | −1.40683 | − | 0.248062i | −0.581881 | − | 0.813274i | \(-0.697683\pi\) |
−0.824946 | + | 0.565212i | \(0.808794\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12779.7 | + | 10723.4i | −0.104923 | + | 0.0880405i | −0.693740 | − | 0.720226i | \(-0.744038\pi\) |
0.588817 | + | 0.808266i | \(0.299594\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7097.20 | + | 24205.7i | −0.0576066 | + | 0.196473i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −122460. | − | 145943.i | −0.982757 | − | 1.17120i | −0.985235 | − | 0.171207i | \(-0.945233\pi\) |
0.00247824 | − | 0.999997i | \(-0.499211\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14997.3 | − | 85054.0i | 0.119003 | − | 0.674898i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 100750. | + | 21624.2i | 0.790510 | + | 0.169670i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −53628.4 | + | 30962.4i | −0.416108 | + | 0.240240i | −0.693411 | − | 0.720542i | \(-0.743893\pi\) |
0.277303 | + | 0.960783i | \(0.410560\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −27887.0 | + | 48301.6i | −0.213987 | + | 0.370636i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 50355.2 | − | 80230.2i | 0.382148 | − | 0.608870i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10956.2 | − | 13057.1i | 0.0822385 | − | 0.0980080i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22340.3 | − | 8131.21i | −0.165866 | − | 0.0603703i | 0.257753 | − | 0.966211i | \(-0.417018\pi\) |
−0.423618 | + | 0.905841i | \(0.639240\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 31193.7 | − | 69320.1i | 0.229095 | − | 0.509104i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 56334.0 | − | 9933.21i | 0.409282 | − | 0.0721675i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −61939.6 | + | 22544.2i | −0.445195 | + | 0.162038i | −0.554883 | − | 0.831928i | \(-0.687237\pi\) |
0.109688 | + | 0.993966i | \(0.465015\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 55576.7 | − | 136775.i | 0.395212 | − | 0.972620i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 25772.2i | − | 0.181330i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25944.4 | −0.180620 | −0.0903099 | − | 0.995914i | \(-0.528786\pi\) | ||||
−0.0903099 | + | 0.995914i | \(0.528786\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −40441.9 | + | 31467.5i | −0.278600 | + | 0.216777i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7650.34 | − | 21019.1i | −0.0521535 | − | 0.143290i | 0.910881 | − | 0.412670i | \(-0.135404\pi\) |
−0.963034 | + | 0.269379i | \(0.913181\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8955.84 | − | 50791.1i | −0.0604206 | − | 0.342662i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −136346. | − | 10078.5i | −0.910373 | − | 0.0672937i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31551.4 | − | 86686.7i | 0.208506 | − | 0.572866i | −0.790721 | − | 0.612177i | \(-0.790294\pi\) |
0.999227 | + | 0.0393109i | \(0.0125163\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 69446.4 | + | 58272.4i | 0.454251 | + | 0.381162i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7255.53 | − | 196579.i | 0.0469768 | − | 1.27277i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −168534. | − | 97303.4i | −1.08018 | − | 0.623640i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 60496.9 | + | 104784.i | 0.383842 | + | 0.664834i | 0.991608 | − | 0.129283i | \(-0.0412674\pi\) |
−0.607766 | + | 0.794116i | \(0.707934\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 134772. | + | 121835.i | 0.846552 | + | 0.765288i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 177505. | + | 31298.9i | 1.10388 | + | 0.194644i | 0.695753 | − | 0.718281i | \(-0.255071\pi\) |
0.408127 | + | 0.912925i | \(0.366182\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −35540.9 | + | 29822.4i | −0.218836 | + | 0.183625i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 88263.4 | + | 70095.0i | 0.538109 | + | 0.427343i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2276.52 | + | 2713.05i | 0.0137430 | + | 0.0163783i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10648.4 | + | 60390.1i | −0.0636558 | + | 0.361010i | 0.936296 | + | 0.351211i | \(0.114230\pi\) |
−0.999952 | + | 0.00979857i | \(0.996881\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10481.2 | + | 11594.1i | −0.0620476 | + | 0.0686363i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 155456. | − | 89752.5i | 0.911396 | − | 0.526195i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 38551.4 | − | 66773.1i | 0.223843 | − | 0.387708i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −122323. | − | 4514.81i | −0.703452 | − | 0.0259637i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −190265. | + | 226748.i | −1.08375 | + | 1.29157i | −0.129821 | + | 0.991537i | \(0.541440\pi\) |
−0.953930 | + | 0.300028i | \(0.903004\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 103730. | + | 37754.5i | 0.585246 | + | 0.213012i | 0.617637 | − | 0.786463i | \(-0.288090\pi\) |
−0.0323910 | + | 0.999475i | \(0.510312\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 275416. | − | 132978.i | 1.53925 | − | 0.743188i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 79488.0 | − | 14015.9i | 0.440072 | − | 0.0775965i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −78191.4 | + | 28459.3i | −0.428848 | + | 0.156088i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12269.4 | + | 15768.6i | 0.0666667 | + | 0.0856797i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 114346.i | 0.615556i | 0.951458 | + | 0.307778i | \(0.0995854\pi\) | ||||
−0.951458 | + | 0.307778i | \(0.900415\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 68905.4 | 0.367517 | 0.183759 | − | 0.982971i | \(-0.441174\pi\) | ||||
0.183759 | + | 0.982971i | \(0.441174\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −106686. | − | 43350.5i | −0.563804 | − | 0.229095i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 54667.3 | + | 150197.i | 0.286262 | + | 0.786500i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19037.3 | + | 107966.i | 0.0987818 | + | 0.560220i | 0.993523 | + | 0.113634i | \(0.0362491\pi\) |
−0.894741 | + | 0.446586i | \(0.852640\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13885.2 | + | 10004.2i | −0.0713961 | + | 0.0514403i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −58654.2 | + | 161151.i | −0.298876 | + | 0.821156i | 0.695812 | + | 0.718224i | \(0.255045\pi\) |
−0.994688 | + | 0.102932i | \(0.967178\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18542.9 | + | 15559.3i | 0.0936392 | + | 0.0785726i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −328363. | − | 206092.i | −1.64338 | − | 1.03144i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −134746. | − | 77795.9i | −0.668381 | − | 0.385890i | 0.127082 | − | 0.991892i | \(-0.459439\pi\) |
−0.795463 | + | 0.606002i | \(0.792772\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −30104.6 | − | 52142.7i | −0.148006 | − | 0.256354i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −21372.4 | + | 99576.5i | −0.104149 | + | 0.485244i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −27393.0 | − | 4830.13i | −0.132317 | − | 0.0233311i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 242462. | − | 203450.i | 1.16094 | − | 0.974147i | 0.161026 | − | 0.986950i | \(-0.448520\pi\) |
0.999918 | + | 0.0128029i | \(0.00407542\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −19700.8 | + | 177276.i | −0.0935103 | + | 0.841442i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 180926. | + | 215619.i | 0.851332 | + | 1.01458i | 0.999671 | + | 0.0256412i | \(0.00816273\pi\) |
−0.148339 | + | 0.988936i | \(0.547393\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18880.2 | + | 107075.i | −0.0880732 | + | 0.499488i | 0.908578 | + | 0.417716i | \(0.137169\pi\) |
−0.996651 | + | 0.0817723i | \(0.973942\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 63669.7 | + | 197287.i | 0.294461 | + | 0.912417i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 323907. | − | 187008.i | 1.48520 | − | 0.857483i | 0.485346 | − | 0.874322i | \(-0.338693\pi\) |
0.999858 | + | 0.0168386i | \(0.00536014\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −99903.3 | + | 173038.i | −0.454186 | + | 0.786674i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 82923.0 | + | 156705.i | 0.373795 | + | 0.706386i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −69607.1 | + | 82954.5i | −0.311122 | + | 0.370781i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 133726. | + | 48672.3i | 0.592691 | + | 0.215722i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 26914.6 | + | 95289.0i | 0.118291 | + | 0.418799i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 257523. | − | 45408.3i | 1.12239 | − | 0.197909i | 0.418503 | − | 0.908215i | \(-0.362555\pi\) |
0.703892 | + | 0.710307i | \(0.251444\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1794.91 | − | 653.293i | 0.00775803 | − | 0.00282369i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 154567. | − | 21410.1i | 0.662558 | − | 0.0917752i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 92745.7i | 0.394285i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −325076. | −1.37065 | −0.685325 | − | 0.728237i | \(-0.740340\pi\) | ||||
−0.685325 | + | 0.728237i | \(0.740340\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 27430.1 | + | 198028.i | 0.114712 | + | 0.828148i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16561.1 | + | 45501.1i | 0.0686950 | + | 0.188738i | 0.969290 | − | 0.245922i | \(-0.0790908\pi\) |
−0.900595 | + | 0.434660i | \(0.856869\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −31645.3 | − | 179470.i | −0.130202 | − | 0.738409i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 85913.1 | − | 24266.4i | 0.350630 | − | 0.0990363i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 80462.5 | − | 221069.i | 0.325747 | − | 0.894983i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −111893. | − | 93889.6i | −0.449369 | − | 0.377065i | 0.389833 | − | 0.920886i | \(-0.372533\pi\) |
−0.839202 | + | 0.543820i | \(0.816977\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1057.80 | − | 559.748i | 0.00421431 | − | 0.00223006i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −404971. | − | 233810.i | −1.60062 | − | 0.924117i | −0.991364 | − | 0.131141i | \(-0.958136\pi\) |
−0.609253 | − | 0.792976i | \(-0.708531\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21045.5 | − | 36451.9i | −0.0825233 | − | 0.142934i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −234371. | + | 75637.4i | −0.911774 | + | 0.294253i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 292320. | + | 51543.9i | 1.12830 | + | 0.198949i | 0.706480 | − | 0.707733i | \(-0.250282\pi\) |
0.421815 | + | 0.906682i | \(0.361393\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 35566.9 | − | 29844.2i | 0.136208 | − | 0.114292i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −186360. | + | 253315.i | −0.708137 | + | 0.962556i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 178350. | + | 212550.i | 0.672450 | + | 0.801394i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 42065.2 | − | 238564.i | 0.157377 | − | 0.892531i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −110740. | − | 23768.4i | −0.411121 | − | 0.0882401i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 343568. | − | 198359.i | 1.26572 | − | 0.730763i | 0.291544 | − | 0.956558i | \(-0.405831\pi\) |
0.974175 | + | 0.225795i | \(0.0724978\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 101598. | − | 175973.i | 0.371433 | − | 0.643342i | −0.618353 | − | 0.785901i | \(-0.712200\pi\) |
0.989786 | + | 0.142559i | \(0.0455331\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 73856.1 | − | 117674.i | 0.267959 | − | 0.426934i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −210878. | + | 251314.i | −0.759293 | + | 0.904890i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −133961. | − | 48757.7i | −0.478703 | − | 0.174234i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 181636. | + | 252100.i | 0.644189 | + | 0.894096i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −31979.1 | + | 5638.78i | −0.112567 | + | 0.0198486i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −271968. | + | 98988.2i | −0.950189 | + | 0.345841i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 152225. | − | 374627.i | 0.527883 | − | 1.29912i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13555.2i | 0.0466584i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 545062. | 1.86231 | 0.931153 | − | 0.364628i | \(-0.118804\pi\) | ||||
0.931153 | + | 0.364628i | \(0.118804\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −433599. | + | 337380.i | −1.47058 | + | 1.14425i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 45307.0 | + | 124480.i | 0.152536 | + | 0.419089i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −77497.0 | − | 439507.i | −0.259006 | − | 1.46890i | −0.785576 | − | 0.618765i | \(-0.787633\pi\) |
0.526570 | − | 0.850132i | \(-0.323478\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −62625.6 | − | 129706.i | −0.207782 | − | 0.430345i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 109893. | − | 301929.i | 0.361966 | − | 0.994494i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −406079. | − | 340741.i | −1.32788 | − | 1.11423i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 314.798 | − | 8529.03i | 0.00102199 | − | 0.0276894i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −336771. | − | 194435.i | −1.08549 | − | 0.626705i | −0.153115 | − | 0.988208i | \(-0.548930\pi\) |
−0.932371 | + | 0.361503i | \(0.882264\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 29201.7 | + | 50578.8i | 0.0934511 | + | 0.161862i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 104802. | + | 94742.1i | 0.333001 | + | 0.301035i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 178666. | + | 31503.7i | 0.563671 | + | 0.0993904i | 0.448221 | − | 0.893923i | \(-0.352058\pi\) |
0.115450 | + | 0.993313i | \(0.463169\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 278572. | − | 233749.i | 0.872650 | − | 0.732240i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 203617. | + | 229784.i | 0.633355 | + | 0.714748i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −104051. | − | 124003.i | −0.321382 | − | 0.383009i | 0.581030 | − | 0.813882i | \(-0.302650\pi\) |
−0.902412 | + | 0.430874i | \(0.858205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 44974.8 | − | 255065.i | 0.137942 | − | 0.782308i | −0.834824 | − | 0.550518i | \(-0.814430\pi\) |
0.972766 | − | 0.231791i | \(-0.0744585\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −130717. | + | 144598.i | −0.398129 | + | 0.440405i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 105853. | − | 61114.0i | 0.320159 | − | 0.184844i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −173118. | + | 299850.i | −0.519986 | + | 0.900642i | 0.479744 | + | 0.877409i | \(0.340730\pi\) |
−0.999730 | + | 0.0232338i | \(0.992604\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −138361. | − | 5106.77i | −0.412721 | − | 0.0152331i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 135001. | − | 160888.i | 0.399930 | − | 0.476619i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 73698.3 | + | 26824.0i | 0.216831 | + | 0.0789199i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3549.37 | − | 48017.1i | 0.0103714 | − | 0.140309i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 496369. | − | 87523.2i | 1.44055 | − | 0.254008i | 0.601853 | − | 0.798607i | \(-0.294429\pi\) |
0.838697 | + | 0.544599i | \(0.183318\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −543537. | + | 197831.i | −1.56674 | + | 0.570249i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −271400. | − | 348802.i | −0.777026 | − | 0.998629i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 637062.i | 1.81164i | 0.423661 | + | 0.905821i | \(0.360745\pi\) | ||||
−0.423661 | + | 0.905821i | \(0.639255\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −196688. | −0.555575 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −641306. | − | 260587.i | −1.79935 | − | 0.731146i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 63233.8 | + | 173734.i | 0.176236 | + | 0.484206i | 0.996088 | − | 0.0883710i | \(-0.0281661\pi\) |
−0.819851 | + | 0.572577i | \(0.805944\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −121142. | − | 687032.i | −0.335388 | − | 1.90208i | −0.423373 | − | 0.905956i | \(-0.639154\pi\) |
0.0879853 | − | 0.996122i | \(-0.471957\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −315398. | − | 141928.i | −0.867410 | − | 0.390331i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −61839.0 | + | 169901.i | −0.168947 | + | 0.464179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −224939. | − | 188746.i | −0.610502 | − | 0.512272i | 0.284300 | − | 0.958735i | \(-0.408239\pi\) |
−0.894802 | + | 0.446463i | \(0.852683\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −265687. | − | 166754.i | −0.716366 | − | 0.449616i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −113145. | − | 65324.4i | −0.303077 | − | 0.174982i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 281442. | + | 487472.i | 0.748976 | + | 1.29726i | 0.948314 | + | 0.317333i | \(0.102787\pi\) |
−0.199338 | + | 0.979931i | \(0.563879\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −30448.8 | + | 141865.i | −0.0805045 | + | 0.375080i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −572112. | − | 100879.i | −1.50283 | − | 0.264990i | −0.639172 | − | 0.769064i | \(-0.720723\pi\) |
−0.863660 | + | 0.504074i | \(0.831834\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −168647. | + | 141511.i | −0.440146 | + | 0.369326i | −0.835764 | − | 0.549089i | \(-0.814975\pi\) |
0.395618 | + | 0.918415i | \(0.370530\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 63782.4 | + | 262468.i | 0.165393 | + | 0.680603i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 42382.8 | + | 50509.9i | 0.109198 | + | 0.130137i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13131.7 | + | 74473.7i | −0.0336172 | + | 0.190653i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 76502.5 | + | 237051.i | 0.194599 | + | 0.602985i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11697.0 | − | 6753.27i | 0.0295647 | − | 0.0170692i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −143576. | + | 248680.i | −0.360597 | + | 0.624572i | −0.988059 | − | 0.154075i | \(-0.950760\pi\) |
0.627462 | + | 0.778647i | \(0.284094\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −362379. | − | 684812.i | −0.904389 | − | 1.70909i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 62870.6 | − | 74926.2i | 0.155919 | − | 0.185817i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6869.82 | + | 2500.41i | 0.0169304 | + | 0.00616215i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 394733. | + | 100085.i | 0.966722 | + | 0.245113i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 348199. | − | 61396.9i | 0.847446 | − | 0.149428i | 0.266970 | − | 0.963705i | \(-0.413978\pi\) |
0.580476 | + | 0.814277i | \(0.302867\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 604456. | − | 220004.i | 1.46198 | − | 0.532119i | 0.516073 | − | 0.856545i | \(-0.327393\pi\) |
0.945911 | + | 0.324426i | \(0.105171\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 258494. | − | 35805.7i | 0.621343 | − | 0.0860662i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 343334.i | − | 0.820179i | −0.912045 | − | 0.410089i | \(-0.865497\pi\) | ||
0.912045 | − | 0.410089i | \(-0.134503\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 246110. | 0.584305 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 77479.5 | + | 559353.i | 0.182821 | + | 1.31985i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 141240. | + | 388054.i | 0.331231 | + | 0.910050i | 0.987792 | + | 0.155777i | \(0.0497883\pi\) |
−0.656561 | + | 0.754273i | \(0.727990\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 65201.1 | + | 369774.i | 0.151975 | + | 0.861894i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 57589.7 | + | 56057.4i | 0.133418 | + | 0.129868i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 140053. | − | 384794.i | 0.322495 | − | 0.886048i | −0.667458 | − | 0.744648i | \(-0.732617\pi\) |
0.989953 | − | 0.141400i | \(-0.0451603\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −223989. | − | 187949.i | −0.512654 | − | 0.430168i | 0.349408 | − | 0.936971i | \(-0.386383\pi\) |
−0.862062 | + | 0.506803i | \(0.830827\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 67347.4 | − | 35637.9i | 0.153212 | − | 0.0810746i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −300322. | − | 173391.i | −0.679117 | − | 0.392088i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −137985. | − | 238996.i | −0.310155 | − | 0.537205i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 215786. | − | 69639.7i | 0.482138 | − | 0.155598i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −112351. | − | 19810.5i | −0.249535 | − | 0.0439998i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 193341. | − | 162232.i | 0.426868 | − | 0.358185i | −0.403900 | − | 0.914803i | \(-0.632346\pi\) |
0.830769 | + | 0.556618i | \(0.187901\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 215516. | + | 106708.i | 0.473011 | + | 0.234201i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 123728. | + | 147453.i | 0.269954 | + | 0.321719i | 0.883942 | − | 0.467597i | \(-0.154880\pi\) |
−0.613988 | + | 0.789316i | \(0.710436\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −43869.5 | + | 248796.i | −0.0951531 | + | 0.539640i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 661930. | + | 142072.i | 1.42731 | + | 0.306348i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 382344. | − | 220747.i | 0.819622 | − | 0.473209i | −0.0306644 | − | 0.999530i | \(-0.509762\pi\) |
0.850286 | + | 0.526321i | \(0.176429\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14916.4 | − | 25836.0i | 0.0317895 | − | 0.0550611i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 85184.2 | − | 135723.i | 0.180487 | − | 0.287567i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 27188.9 | − | 32402.5i | 0.0572734 | − | 0.0682558i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 450725. | + | 164051.i | 0.943964 | + | 0.343575i | 0.767730 | − | 0.640773i | \(-0.221386\pi\) |
0.176234 | + | 0.984348i | \(0.443608\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 241946. | − | 24458.4i | 0.503792 | − | 0.0509287i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 230095. | − | 40571.9i | 0.476362 | − | 0.0839954i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −215769. | + | 78533.5i | −0.444144 | + | 0.161655i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 20152.3 | − | 49595.0i | 0.0412450 | − | 0.101504i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 486026.i | 0.989063i | 0.869160 | + | 0.494531i | \(0.164660\pi\) | ||||
−0.869160 | + | 0.494531i | \(0.835340\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23813.6 | 0.0481852 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −460733. | + | 358493.i | −0.926981 | + | 0.721277i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −39213.8 | − | 107739.i | −0.0784514 | − | 0.215543i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −38195.6 | − | 216618.i | −0.0759838 | − | 0.430926i | −0.998940 | − | 0.0460216i | \(-0.985346\pi\) |
0.922957 | − | 0.384904i | \(-0.125765\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 516125. | − | 758671.i | 1.02098 | − | 1.50077i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −169917. | + | 466842.i | −0.334239 | + | 0.918313i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −29214.3 | − | 24513.7i | −0.0571456 | − | 0.0479508i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2192.02 | + | 59389.7i | −0.00426389 | + | 0.115524i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −757816. | − | 437526.i | −1.46591 | − | 0.846341i | −0.466633 | − | 0.884451i | \(-0.654533\pi\) |
−0.999274 | + | 0.0381097i | \(0.987866\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 377899. | + | 654540.i | 0.726950 | + | 1.25911i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 577456. | + | 522024.i | 1.10470 | + | 0.998651i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −241973. | − | 42666.3i | −0.460353 | − | 0.0811726i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −523516. | + | 439282.i | −0.990515 | + | 0.831141i | −0.985642 | − | 0.168847i | \(-0.945995\pi\) |
−0.00487274 | + | 0.999988i | \(0.501551\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −360283. | + | 390673.i | −0.677937 | + | 0.735120i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 265457. | + | 316359.i | 0.496775 | + | 0.592033i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −89439.8 | + | 507239.i | −0.166465 | + | 0.944070i | 0.781076 | + | 0.624436i | \(0.214671\pi\) |
−0.947541 | + | 0.319634i | \(0.896440\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 21906.1 | − | 24232.3i | 0.0405500 | − | 0.0448559i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −237243. | + | 136972.i | −0.436775 | + | 0.252172i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 134409. | − | 232804.i | 0.246116 | − | 0.426286i | −0.716329 | − | 0.697763i | \(-0.754179\pi\) |
0.962445 | + | 0.271477i | \(0.0875122\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 134250. | + | 4955.02i | 0.244499 | + | 0.00902421i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −367472. | + | 437936.i | −0.665651 | + | 0.793292i | −0.988185 | − | 0.153266i | \(-0.951021\pi\) |
0.322534 | + | 0.946558i | \(0.395465\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 695364. | + | 253092.i | 1.25285 | + | 0.456001i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 300584. | + | 204488.i | 0.538672 | + | 0.366460i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −776394. | + | 136899.i | −1.38394 | + | 0.244027i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 161443. | − | 58760.5i | 0.286246 | − | 0.104185i | −0.194907 | − | 0.980822i | \(-0.562440\pi\) |
0.481153 | + | 0.876637i | \(0.340218\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −497157. | − | 638944.i | −0.876807 | − | 1.12687i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 194397.i | − | 0.341033i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 87387.1 | 0.152495 | 0.0762475 | − | 0.997089i | \(-0.475706\pi\) | ||||
0.0762475 | + | 0.997089i | \(0.475706\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 198205. | + | 80538.1i | 0.344057 | + | 0.139803i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 182574. | + | 501618.i | 0.315260 | + | 0.866171i | 0.991572 | + | 0.129555i | \(0.0413550\pi\) |
−0.676312 | + | 0.736616i | \(0.736423\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 62658.9 | + | 355356.i | 0.107630 | + | 0.610400i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −34242.9 | − | 338735.i | −0.0585124 | − | 0.578811i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 45397.6 | − | 124729.i | 0.0771689 | − | 0.212020i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 770270. | + | 646334.i | 1.30254 | + | 1.09296i | 0.989701 | + | 0.143153i | \(0.0457241\pi\) |
0.312838 | + | 0.949807i | \(0.398720\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −640452. | − | 401969.i | −1.07740 | − | 0.676214i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −540306. | − | 311946.i | −0.904234 | − | 0.522060i | −0.0256627 | − | 0.999671i | \(-0.508170\pi\) |
−0.878572 | + | 0.477611i | \(0.841503\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 221161. | + | 383062.i | 0.368218 | + | 0.637772i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4878.77 | − | 22730.8i | 0.00808106 | − | 0.0376506i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −398689. | − | 70299.7i | −0.656991 | − | 0.115845i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 247086. | − | 207330.i | 0.405085 | − | 0.339907i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 240928. | − | 486596.i | 0.392973 | − | 0.793680i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −217526. | − | 259238.i | −0.352998 | − | 0.420687i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 74917.1 | − | 424876.i | 0.120957 | − | 0.685982i | −0.862670 | − | 0.505767i | \(-0.831210\pi\) |
0.983627 | − | 0.180215i | \(-0.0576793\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3997.34 | + | 12386.2i | 0.00642122 | + | 0.0198968i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 857852. | − | 495281.i | 1.37107 | − | 0.791587i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30764.3 | + | 53285.4i | −0.0489217 | + | 0.0847348i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −88398.9 | − | 167054.i | −0.139866 | − | 0.264315i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 31827.0 | − | 37929.9i | 0.0501047 | − | 0.0597125i | −0.740410 | − | 0.672155i | \(-0.765369\pi\) |
0.790515 | + | 0.612443i | \(0.209813\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −868119. | − | 315970.i | −1.35983 | − | 0.494939i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −79609.2 | + | 81785.3i | −0.124079 | + | 0.127471i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 62689.7 | − | 11053.9i | 0.0972220 | − | 0.0171429i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −279888. | + | 101871.i | −0.431909 | + | 0.157202i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.11150e6 | − | 153961.i | 1.70672 | − | 0.236408i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.19267e6i | 1.82231i | 0.412061 | + | 0.911156i | \(0.364809\pi\) | ||||
−0.412061 | + | 0.911156i | \(0.635191\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −760675. | −1.15653 | −0.578265 | − | 0.815849i | \(-0.696270\pi\) | ||||
−0.578265 | + | 0.815849i | \(0.696270\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −93029.5 | − | 671613.i | −0.140747 | − | 1.01610i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −130514. | − | 358584.i | −0.196491 | − | 0.539854i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 126438. | + | 717064.i | 0.189423 | + | 1.07427i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 32233.9 | − | 127130.i | 0.0480557 | − | 0.189531i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 88627.7 | − | 243503.i | 0.131487 | − | 0.361258i | −0.856425 | − | 0.516271i | \(-0.827320\pi\) |
0.987912 | + | 0.155013i | \(0.0495420\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 732235. | + | 614418.i | 1.08106 | + | 0.907119i | 0.996009 | − | 0.0892572i | \(-0.0284493\pi\) |
0.0850539 | + | 0.996376i | \(0.472894\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 168362. | − | 89091.3i | 0.247364 | − | 0.130896i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −716837. | − | 413866.i | −1.04812 | − | 0.605130i | −0.125994 | − | 0.992031i | \(-0.540212\pi\) |
−0.922121 | + | 0.386901i | \(0.873545\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −432183. | − | 748564.i | −0.628867 | − | 1.08923i | −0.987779 | − | 0.155859i | \(-0.950186\pi\) |
0.358912 | − | 0.933371i | \(-0.383148\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 887970. | − | 286571.i | 1.28587 | − | 0.414983i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 50909.6 | + | 8976.73i | 0.0733685 | + | 0.0129368i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1749.91 | + | 1468.35i | −0.00250982 | + | 0.00210599i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −949827. | + | 230817.i | −1.35579 | + | 0.329471i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −445949. | − | 531461.i | −0.633521 | − | 0.755001i | 0.349811 | − | 0.936820i | \(-0.386246\pi\) |
−0.983332 | + | 0.181819i | \(0.941801\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26485.1 | − | 150204.i | 0.0374463 | − | 0.212368i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −484952. | − | 104087.i | −0.682407 | − | 0.146467i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 407100. | − | 235039.i | 0.570148 | − | 0.329175i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −246252. | + | 426521.i | −0.343252 | + | 0.594529i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 463892. | − | 739112.i | 0.643578 | − | 1.02540i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13147.2 | − | 15668.2i | 0.0181541 | − | 0.0216352i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 542954. | + | 197619.i | 0.746217 | + | 0.271601i | 0.687013 | − | 0.726645i | \(-0.258922\pi\) |
0.0592040 | + | 0.998246i | \(0.481144\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 246328. | − | 547401.i | 0.336963 | − | 0.748814i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −549610. | + | 96911.1i | −0.748330 | + | 0.131951i | −0.534792 | − | 0.844984i | \(-0.679610\pi\) |
−0.213538 | + | 0.976935i | \(0.568499\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −268789. | + | 97831.2i | −0.364271 | + | 0.132584i | −0.517670 | − | 0.855580i | \(-0.673200\pi\) |
0.153398 | + | 0.988164i | \(0.450978\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −148784. | + | 366158.i | −0.200701 | + | 0.493927i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 193853.i | − | 0.260286i | −0.991495 | − | 0.130143i | \(-0.958456\pi\) | ||
0.991495 | − | 0.130143i | \(-0.0415437\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 216191. | 0.288938 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −168029. | + | 130742.i | −0.223536 | + | 0.173931i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −248577. | − | 682959.i | −0.329171 | − | 0.904389i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25655.7 | + | 145501.i | 0.0338180 | + | 0.191792i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −436114. | − | 32237.0i | −0.572231 | − | 0.0422986i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −262538. | + | 721318.i | −0.342907 | + | 0.942129i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −731376. | − | 613697.i | −0.950915 | − | 0.797912i | 0.0285366 | − | 0.999593i | \(-0.490915\pi\) |
−0.979451 | + | 0.201681i | \(0.935360\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1140.98 | + | 30913.4i | −0.00147673 | + | 0.0400100i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 662276. | + | 382365.i | 0.853271 | + | 0.492636i | 0.861753 | − | 0.507328i | \(-0.169367\pi\) |
−0.00848230 | + | 0.999964i | \(0.502700\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −395228. | − | 684556.i | −0.506905 | − | 0.877985i | −0.999968 | − | 0.00799177i | \(-0.997456\pi\) |
0.493063 | − | 0.869994i | \(-0.335877\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −439963. | − | 397729.i | −0.561732 | − | 0.507810i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −189753. | − | 33458.5i | −0.241180 | − | 0.0425265i | 0.0517515 | − | 0.998660i | \(-0.483520\pi\) |
−0.292931 | + | 0.956133i | \(0.594631\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 204095. | − | 171256.i | 0.258243 | − | 0.216692i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 84244.5 | + | 412420.i | 0.106117 | + | 0.519499i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.04699e6 | − | 1.24775e6i | −1.31292 | − | 1.56468i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −134031. | + | 760128.i | −0.167324 | + | 0.948944i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 77377.8 | − | 85594.3i | 0.0961682 | − | 0.106380i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 864886. | − | 499342.i | 1.07014 | − | 0.617844i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 149549. | − | 259026.i | 0.184218 | − | 0.319076i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 710363. | + | 26218.8i | 0.871174 | + | 0.0321542i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 674068. | − | 803323.i | 0.823013 | − | 0.980829i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −902536. | − | 328496.i | −1.09711 | − | 0.399315i | −0.270860 | − | 0.962619i | \(-0.587308\pi\) |
−0.826250 | + | 0.563304i | \(0.809530\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 178721. | − | 86291.2i | 0.216296 | − | 0.104433i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.08169e6 | + | 190732.i | −1.30337 | + | 0.229819i | −0.781875 | − | 0.623435i | \(-0.785737\pi\) |
−0.521495 | + | 0.853254i | \(0.674626\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 270587. | − | 98485.7i | 0.324613 | − | 0.118149i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 168831. | + | 216981.i | 0.201656 | + | 0.259167i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.02278e6i | 1.21631i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 278278. | 0.329495 | 0.164747 | − | 0.986336i | \(-0.447319\pi\) | ||||
0.164747 | + | 0.986336i | \(0.447319\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 34876.1 | + | 14171.5i | 0.0411158 | + | 0.0167069i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −59497.4 | − | 163468.i | −0.0698385 | − | 0.191880i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3162.21 | − | 17933.8i | −0.00369579 | − | 0.0209598i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.06146e6 | + | 764770.i | −1.23521 | + | 0.889962i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10559.2 | − | 29011.1i | 0.0122348 | − | 0.0336150i | −0.933425 | − | 0.358773i | \(-0.883195\pi\) |
0.945660 | + | 0.325158i | \(0.105417\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 69820.4 | + | 58586.2i | 0.0805532 | + | 0.0675921i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −94048.6 | − | 59028.1i | −0.108041 | − | 0.0678103i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −233539. | − | 134834.i | −0.267139 | − | 0.154233i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 249027. | + | 431327.i | 0.283639 | + | 0.491278i | 0.972278 | − | 0.233827i | \(-0.0751248\pi\) |
−0.688639 | + | 0.725104i | \(0.741791\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −184121. | + | 857841.i | −0.208820 | + | 0.972916i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 774493. | + | 136564.i | 0.874658 | + | 0.154226i | 0.592916 | − | 0.805264i | \(-0.297977\pi\) |
0.281742 | + | 0.959490i | \(0.409088\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −266366. | + | 223507.i | −0.299540 | + | 0.251344i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −472045. | − | 347276.i | −0.528591 | − | 0.388876i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 904077. | + | 1.07744e6i | 1.00810 | + | 1.20141i | 0.979422 | + | 0.201823i | \(0.0646866\pi\) |
0.0286819 | + | 0.999589i | \(0.490869\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5961.66 | − | 33810.2i | 0.00661964 | − | 0.0375418i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 477048. | + | 1.47818e6i | 0.527474 | + | 1.63443i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.50741e6 | + | 870301.i | −1.65976 | + | 0.958261i | −0.686930 | + | 0.726723i | \(0.741042\pi\) |
−0.972826 | + | 0.231537i | \(0.925624\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 186033. | − | 322218.i | 0.203978 | − | 0.353300i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −201152. | − | 380131.i | −0.219635 | − | 0.415059i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 52235.0 | − | 62251.2i | 0.0567968 | − | 0.0676878i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −821594. | − | 299036.i | −0.889632 | − | 0.323799i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −370936. | − | 1.31327e6i | −0.399987 | − | 1.41612i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 260264. | − | 45891.6i | 0.279486 | − | 0.0492808i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 986414. | − | 359025.i | 1.05489 | − | 0.383948i | 0.244382 | − | 0.969679i | \(-0.421415\pi\) |
0.810505 | + | 0.585731i | \(0.199193\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 940958. | − | 130338.i | 1.00213 | − | 0.138811i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 936946.i | 0.993748i | 0.867823 | + | 0.496874i | \(0.165519\pi\) | ||||
−0.867823 | + | 0.496874i | \(0.834481\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 636434. | 0.672246 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −14095.4 | − | 101760.i | −0.0148275 | − | 0.107045i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16333.4 | − | 44875.6i | −0.0171115 | − | 0.0470134i | 0.930843 | − | 0.365420i | \(-0.119075\pi\) |
−0.947954 | + | 0.318406i | \(0.896852\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15698.0 | + | 89027.9i | 0.0163787 | + | 0.0928882i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −601085. | + | 169778.i | −0.624594 | + | 0.176418i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14168.9 | + | 38928.8i | −0.0146632 | + | 0.0402869i | −0.946808 | − | 0.321798i | \(-0.895713\pi\) |
0.932145 | + | 0.362085i | \(0.117935\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 646222. | + | 542245.i | 0.666054 | + | 0.558885i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.40552e6 | + | 743749.i | −1.44278 | + | 0.763471i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 541600. | + | 312693.i | 0.553714 | + | 0.319687i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −679417. | − | 1.17678e6i | −0.691814 | − | 1.19826i | −0.971243 | − | 0.238090i | \(-0.923479\pi\) |
0.279429 | − | 0.960166i | \(-0.409855\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 767389. | − | 247656.i | 0.778246 | − | 0.251160i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.30123e6 | + | 229442.i | 1.31434 | + | 0.231753i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 134572. | − | 112919.i | 0.135383 | − | 0.113600i | −0.572582 | − | 0.819848i | \(-0.694058\pi\) |
0.707965 | + | 0.706248i | \(0.249614\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 39996.3 | + | 4444.83i | 0.0400764 | + | 0.00445373i |
(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 | 108.5.k.a.5.6 | ✓ | 72 | |
3.2 | odd | 2 | 324.5.k.a.125.4 | 72 | |||
27.11 | odd | 18 | inner | 108.5.k.a.65.6 | yes | 72 | |
27.16 | even | 9 | 324.5.k.a.197.4 | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.5.k.a.5.6 | ✓ | 72 | 1.1 | even | 1 | trivial | |
108.5.k.a.65.6 | yes | 72 | 27.11 | odd | 18 | inner | |
324.5.k.a.125.4 | 72 | 3.2 | odd | 2 | |||
324.5.k.a.197.4 | 72 | 27.16 | even | 9 |