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 | 29.2 | ||
Character | \(\chi\) | \(=\) | 108.29 |
Dual form | 108.5.k.a.41.2 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{1}{18}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −8.23149 | + | 3.63904i | −0.914610 | + | 0.404338i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 18.1168 | + | 21.5908i | 0.724674 | + | 0.863632i | 0.995076 | − | 0.0991149i | \(-0.0316011\pi\) |
−0.270402 | + | 0.962747i | \(0.587157\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 22.9581 | − | 8.35608i | 0.468534 | − | 0.170532i | −0.0969544 | − | 0.995289i | \(-0.530910\pi\) |
0.565488 | + | 0.824757i | \(0.308688\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 54.5147 | − | 59.9095i | 0.673022 | − | 0.739623i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −73.4456 | + | 87.5290i | −0.606988 | + | 0.723380i | −0.978775 | − | 0.204938i | \(-0.934301\pi\) |
0.371787 | + | 0.928318i | \(0.378745\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.427402 | − | 2.42392i | −0.00252901 | − | 0.0143427i | 0.983517 | − | 0.180815i | \(-0.0578735\pi\) |
−0.986046 | + | 0.166472i | \(0.946762\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −227.698 | − | 111.797i | −1.01199 | − | 0.496873i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −208.105 | + | 120.150i | −0.720088 | + | 0.415743i | −0.814785 | − | 0.579763i | \(-0.803145\pi\) |
0.0946973 | + | 0.995506i | \(0.469812\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −246.932 | + | 427.698i | −0.684021 | + | 1.18476i | 0.289722 | + | 0.957111i | \(0.406437\pi\) |
−0.973743 | + | 0.227649i | \(0.926896\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −158.572 | + | 152.329i | −0.359573 | + | 0.345416i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −179.414 | + | 492.937i | −0.339158 | + | 0.931828i | 0.646477 | + | 0.762934i | \(0.276242\pi\) |
−0.985634 | + | 0.168894i | \(0.945980\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −29.4131 | + | 166.810i | −0.0470609 | + | 0.266896i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −230.724 | + | 691.525i | −0.316494 | + | 0.948594i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −95.9782 | − | 16.9236i | −0.114124 | − | 0.0201231i | 0.116294 | − | 0.993215i | \(-0.462898\pi\) |
−0.230418 | + | 0.973092i | \(0.574009\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1499.65 | − | 545.827i | −1.56051 | − | 0.567978i | −0.589654 | − | 0.807656i | \(-0.700736\pi\) |
−0.970852 | + | 0.239679i | \(0.922958\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 286.044 | − | 987.765i | 0.262667 | − | 0.907039i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 596.344 | + | 344.299i | 0.486811 | + | 0.281061i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 414.251 | + | 717.504i | 0.302594 | + | 0.524108i | 0.976723 | − | 0.214506i | \(-0.0688141\pi\) |
−0.674129 | + | 0.738614i | \(0.735481\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12.3389 | + | 18.3971i | 0.00811236 | + | 0.0120954i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2401.19 | − | 423.394i | 1.42843 | − | 0.251870i | 0.594656 | − | 0.803980i | \(-0.297288\pi\) |
0.833772 | + | 0.552110i | \(0.186177\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1294.95 | − | 1086.59i | −0.700351 | − | 0.587664i | 0.221523 | − | 0.975155i | \(-0.428897\pi\) |
−0.921873 | + | 0.387491i | \(0.873342\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2281.13 | + | 91.6475i | 1.12648 | + | 0.0452580i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −379.164 | − | 1041.74i | −0.171645 | − | 0.471591i | 0.823805 | − | 0.566873i | \(-0.191847\pi\) |
−0.995450 | + | 0.0952820i | \(0.969625\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1382.02 | + | 1159.65i | −0.575602 | + | 0.482987i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1275.79 | − | 1746.31i | 0.490498 | − | 0.671401i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3880.06i | 1.38130i | 0.723191 | + | 0.690648i | \(0.242675\pi\) | ||||
−0.723191 | + | 0.690648i | \(0.757325\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3220.42 | −1.06460 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 476.203 | − | 4419.19i | 0.146569 | − | 1.36017i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2429.52 | + | 2895.39i | 0.697939 | + | 0.831771i | 0.992291 | − | 0.123926i | \(-0.0395485\pi\) |
−0.294353 | + | 0.955697i | \(0.595104\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1823.41 | − | 663.667i | 0.490032 | − | 0.178357i | −0.0851732 | − | 0.996366i | \(-0.527144\pi\) |
0.575205 | + | 0.818009i | \(0.304922\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 750.949 | − | 1830.94i | 0.189204 | − | 0.461310i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 44.5912 | − | 53.1417i | 0.0105541 | − | 0.0125779i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −145.480 | − | 825.059i | −0.0324082 | − | 0.183796i | 0.964307 | − | 0.264788i | \(-0.0853021\pi\) |
−0.996715 | + | 0.0809926i | \(0.974191\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −316.971 | − | 4710.50i | −0.0665766 | − | 0.989393i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1966.62 | − | 1135.43i | 0.390126 | − | 0.225239i | −0.292089 | − | 0.956391i | \(-0.594350\pi\) |
0.682215 | + | 0.731152i | \(0.261017\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2940.78 | − | 5093.57i | 0.551844 | − | 0.955822i | −0.446298 | − | 0.894885i | \(-0.647258\pi\) |
0.998142 | − | 0.0609373i | \(-0.0194090\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −364.915 | − | 1480.13i | −0.0648737 | − | 0.263134i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −954.774 | + | 2623.22i | −0.161035 | + | 0.442439i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −988.613 | + | 5606.70i | −0.158406 | + | 0.898366i | 0.797199 | + | 0.603717i | \(0.206314\pi\) |
−0.955605 | + | 0.294650i | \(0.904797\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −617.285 | − | 6531.90i | −0.0940840 | − | 0.995564i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7283.42 | + | 1284.26i | 1.05725 | + | 0.186422i | 0.675137 | − | 0.737692i | \(-0.264084\pi\) |
0.382116 | + | 0.924114i | \(0.375196\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6364.34 | − | 2316.43i | −0.880877 | − | 0.320613i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 851.629 | − | 209.963i | 0.112515 | − | 0.0277398i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10189.8 | + | 5883.10i | 1.28643 | + | 0.742722i | 0.978016 | − | 0.208530i | \(-0.0668678\pi\) |
0.308416 | + | 0.951252i | \(0.400201\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −30.0668 | − | 52.0773i | −0.00363082 | − | 0.00628877i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 14330.6 | − | 964.312i | 1.65691 | − | 0.111494i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −13708.0 | + | 2417.09i | −1.51889 | + | 0.267821i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2197.40 | + | 1843.84i | 0.233542 | + | 0.195965i | 0.752047 | − | 0.659110i | \(-0.229067\pi\) |
−0.518505 | + | 0.855075i | \(0.673511\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1239.95 | + | 9171.70i | 0.126513 | + | 0.935793i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 573.994 | + | 1577.03i | 0.0562684 | + | 0.154596i | 0.964642 | − | 0.263563i | \(-0.0848977\pi\) |
−0.908374 | + | 0.418159i | \(0.862675\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11083.9 | + | 9300.48i | −1.04476 | + | 0.876659i | −0.992533 | − | 0.121976i | \(-0.961077\pi\) |
−0.0522289 | + | 0.998635i | \(0.516633\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6161.71 | − | 663.974i | −0.558886 | − | 0.0602244i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 6102.13i | − | 0.532983i | −0.963837 | − | 0.266492i | \(-0.914136\pi\) | ||
0.963837 | − | 0.266492i | \(-0.0858645\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19211.9 | −1.61703 | −0.808513 | − | 0.588479i | \(-0.799727\pi\) | ||||
−0.808513 | + | 0.588479i | \(0.799727\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6020.93 | − | 4398.65i | −0.488672 | − | 0.357004i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 176.048 | + | 209.806i | 0.0137871 | + | 0.0164309i | 0.772894 | − | 0.634535i | \(-0.218808\pi\) |
−0.759107 | + | 0.650966i | \(0.774364\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13893.3 | + | 5056.76i | −1.05054 | + | 0.382364i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −168.515 | − | 106.534i | −0.0123103 | − | 0.00778244i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3773.73 | + | 4497.36i | −0.266488 | + | 0.317588i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 275.306 | + | 1561.34i | 0.0188037 | + | 0.106641i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −18224.6 | + | 12223.2i | −1.20461 | + | 0.807931i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11121.0 | − | 6420.74i | 0.711747 | − | 0.410927i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14641.1 | − | 25359.1i | 0.907749 | − | 1.57227i | 0.0905660 | − | 0.995890i | \(-0.471132\pi\) |
0.817183 | − | 0.576378i | \(-0.195534\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 14613.5 | + | 4231.88i | 0.878162 | + | 0.254305i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8692.53 | + | 23882.5i | −0.506528 | + | 1.39167i | 0.378268 | + | 0.925696i | \(0.376520\pi\) |
−0.884796 | + | 0.465979i | \(0.845702\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2095.21 | + | 11882.5i | −0.118447 | + | 0.671747i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −19110.6 | + | 7546.73i | −1.04859 | + | 0.414087i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12879.6 | − | 2271.01i | −0.686214 | − | 0.120998i | −0.180339 | − | 0.983605i | \(-0.557719\pi\) |
−0.505875 | + | 0.862607i | \(0.668830\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8423.60 | + | 3065.94i | 0.435982 | + | 0.158684i | 0.550681 | − | 0.834716i | \(-0.314368\pi\) |
−0.114699 | + | 0.993400i | \(0.536590\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6912.04 | + | 7195.31i | 0.347670 | + | 0.361919i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 243.554 | + | 140.616i | 0.0119103 | + | 0.00687642i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1373.43 | − | 2378.85i | −0.0653236 | − | 0.113144i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7156.06 | − | 14574.9i | 0.331161 | − | 0.674483i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2532.71 | − | 446.586i | 0.114081 | − | 0.0201156i | −0.116316 | − | 0.993212i | \(-0.537109\pi\) |
0.230397 | + | 0.973097i | \(0.425997\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 27267.3 | + | 22880.0i | 1.19588 | + | 1.00347i | 0.999738 | + | 0.0228908i | \(0.00728701\pi\) |
0.196146 | + | 0.980575i | \(0.437157\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4146.71 | + | 19017.4i | −0.177142 | + | 0.812397i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15384.0 | − | 42267.2i | −0.640334 | − | 1.75930i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6637.42 | − | 5569.46i | 0.269277 | − | 0.225951i | −0.498143 | − | 0.867095i | \(-0.665984\pi\) |
0.767420 | + | 0.641144i | \(0.221540\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14119.7 | − | 31938.7i | −0.558511 | − | 1.26335i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12816.1i | 0.494430i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 44505.1 | 1.67508 | 0.837538 | − | 0.546380i | \(-0.183994\pi\) | ||||
0.837538 | + | 0.546380i | \(0.183994\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 26508.9 | − | 11719.3i | 0.973696 | − | 0.430459i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20696.9 | − | 24665.6i | −0.742116 | − | 0.884420i | 0.254461 | − | 0.967083i | \(-0.418102\pi\) |
−0.996578 | + | 0.0826633i | \(0.973657\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 26832.9 | − | 9766.37i | 0.939493 | − | 0.341948i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12161.7 | + | 38109.4i | 0.415914 | + | 1.30329i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19826.3 | − | 23628.1i | 0.662445 | − | 0.789472i | −0.325289 | − | 0.945615i | \(-0.605462\pi\) |
0.987734 | + | 0.156143i | \(0.0499060\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 718.607 | + | 4075.42i | 0.0234647 | + | 0.133075i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −30535.1 | − | 14992.3i | −0.974658 | − | 0.478543i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 26159.6 | − | 15103.2i | 0.816441 | − | 0.471372i | −0.0327469 | − | 0.999464i | \(-0.510426\pi\) |
0.849187 | + | 0.528091i | \(0.177092\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 26379.0 | − | 45689.8i | 0.805196 | − | 1.39464i | −0.110963 | − | 0.993824i | \(-0.535394\pi\) |
0.916159 | − | 0.400815i | \(-0.131273\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12594.3 | + | 12098.4i | −0.376072 | + | 0.361266i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7986.57 | + | 21942.9i | −0.233355 | + | 0.641137i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4767.83 | − | 27039.7i | 0.136344 | − | 0.773248i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 481.439 | + | 17804.1i | 0.0134777 | + | 0.498421i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −43117.1 | − | 7602.71i | −1.18191 | − | 0.208402i | −0.452043 | − | 0.891996i | \(-0.649305\pi\) |
−0.729862 | + | 0.683594i | \(0.760416\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −65952.9 | − | 24004.9i | −1.77060 | − | 0.644444i | −0.999974 | − | 0.00715076i | \(-0.997724\pi\) |
−0.770621 | − | 0.637293i | \(-0.780054\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −173.667 | + | 599.705i | −0.00456718 | + | 0.0157713i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24057.2 | + | 13889.5i | 0.619888 | + | 0.357893i | 0.776825 | − | 0.629716i | \(-0.216829\pi\) |
−0.156937 | + | 0.987609i | \(0.550162\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15512.8 | + | 26868.9i | 0.391727 | + | 0.678491i | 0.992677 | − | 0.120795i | \(-0.0385445\pi\) |
−0.600951 | + | 0.799286i | \(0.705211\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4199.94 | + | 6262.05i | 0.103956 | + | 0.154998i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2344.90 | + | 413.469i | −0.0569025 | + | 0.0100335i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 52643.4 | + | 44173.0i | 1.25267 | + | 1.05111i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 19750.9 | + | 37620.9i | 0.460941 | + | 0.877989i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −19300.0 | − | 53026.2i | −0.441839 | − | 1.21394i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19010.7 | + | 15951.9i | −0.427005 | + | 0.358300i | −0.830820 | − | 0.556541i | \(-0.812128\pi\) |
0.403815 | + | 0.914841i | \(0.367684\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12056.4 | + | 16502.9i | −0.265740 | + | 0.363749i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 47644.6i | − | 1.03071i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −38990.1 | −0.828008 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5671.23 | + | 52629.3i | −0.118247 | + | 1.09734i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 380.178 | + | 453.078i | 0.00778399 | + | 0.00927659i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 74226.5 | − | 27016.2i | 1.49262 | − | 0.543269i | 0.538482 | − | 0.842637i | \(-0.318998\pi\) |
0.954138 | + | 0.299368i | \(0.0967760\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8390.04 | + | 10855.7i | 0.165729 | + | 0.214434i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 48220.6 | − | 57467.1i | 0.935795 | − | 1.11524i | −0.0573506 | − | 0.998354i | \(-0.518265\pi\) |
0.993146 | − | 0.116883i | \(-0.0372903\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2505.13 | − | 14207.3i | −0.0477705 | − | 0.270920i | 0.951562 | − | 0.307458i | \(-0.0994782\pi\) |
−0.999332 | + | 0.0365377i | \(0.988367\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1686.80 | − | 25067.5i | −0.0316111 | − | 0.469771i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −21793.0 | + | 12582.2i | −0.401425 | + | 0.231763i | −0.687099 | − | 0.726564i | \(-0.741116\pi\) |
0.285674 | + | 0.958327i | \(0.407783\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15622.9 | − | 27059.6i | 0.282895 | − | 0.489988i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12265.3 | − | 49749.1i | −0.218364 | − | 0.885704i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12305.3 | + | 33808.6i | −0.215425 | + | 0.591876i | −0.999589 | − | 0.0286783i | \(-0.990870\pi\) |
0.784163 | + | 0.620554i | \(0.213092\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11393.0 | + | 64612.9i | −0.196157 | + | 1.11246i | 0.714605 | + | 0.699529i | \(0.246607\pi\) |
−0.910762 | + | 0.412933i | \(0.864504\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 28851.0 | + | 51520.9i | 0.488595 | + | 0.872511i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −50075.7 | − | 8829.70i | −0.834247 | − | 0.147100i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1142.24 | + | 415.743i | 0.0187226 | + | 0.00681445i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −64626.8 | + | 15933.3i | −1.04235 | + | 0.256984i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 35938.0 | + | 20748.8i | 0.570435 | + | 0.329341i | 0.757323 | − | 0.653040i | \(-0.226507\pi\) |
−0.186888 | + | 0.982381i | \(0.559840\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −29969.1 | − | 51908.0i | −0.468201 | − | 0.810948i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 60817.6 | − | 4092.44i | 0.935295 | − | 0.0629364i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −67142.0 | + | 11838.9i | −1.01655 | + | 0.179245i | −0.657007 | − | 0.753884i | \(-0.728178\pi\) |
−0.359541 | + | 0.933129i | \(0.617067\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15506.0 | + | 13011.0i | 0.231153 | + | 0.193960i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6246.11 | + | 4827.42i | −0.0916914 | + | 0.0708654i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10711.9 | − | 29430.8i | −0.154866 | − | 0.425492i | 0.837860 | − | 0.545885i | \(-0.183807\pi\) |
−0.992726 | + | 0.120394i | \(0.961584\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −83773.7 | + | 70294.5i | −1.19293 | + | 1.00099i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −105286. | − | 11345.4i | −1.47689 | − | 0.159147i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 136677.i | 1.88882i | 0.328766 | + | 0.944411i | \(0.393367\pi\) | ||||
−0.328766 | + | 0.944411i | \(0.606633\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 122527. | 1.66837 | 0.834187 | − | 0.551481i | \(-0.185937\pi\) | ||||
0.834187 | + | 0.551481i | \(0.185937\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 437.006 | + | 319.259i | 0.00586357 | + | 0.00428369i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12440.4 | − | 14825.9i | −0.164502 | − | 0.196046i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −39521.0 | + | 14384.5i | −0.515073 | + | 0.187471i | −0.586461 | − | 0.809978i | \(-0.699479\pi\) |
0.0713884 | + | 0.997449i | \(0.477257\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −114453. | + | 60087.4i | −1.47034 | + | 0.771925i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −36512.2 | + | 43513.5i | −0.462408 | + | 0.551076i | −0.945979 | − | 0.324229i | \(-0.894895\pi\) |
0.483571 | + | 0.875305i | \(0.339340\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1441.88 | + | 8177.30i | 0.0180035 | + | 0.102103i | 0.992485 | − | 0.122363i | \(-0.0390473\pi\) |
−0.974482 | + | 0.224466i | \(0.927936\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 104041. | − | 69780.1i | 1.28090 | − | 0.859096i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 51588.9 | − | 29784.9i | 0.626314 | − | 0.361603i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12888.6 | + | 22323.7i | −0.154316 | + | 0.267283i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −24797.7 | − | 7181.09i | −0.292836 | − | 0.0848017i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −51954.9 | + | 142745.i | −0.605189 | + | 1.66274i | 0.135404 | + | 0.990791i | \(0.456767\pi\) |
−0.740593 | + | 0.671954i | \(0.765455\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −18498.6 | + | 104911.i | −0.212567 | + | 1.20553i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −43582.8 | − | 70984.5i | −0.494086 | − | 0.804731i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1271.52 | + | 224.203i | 0.0142227 | + | 0.00250784i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −38809.2 | − | 14125.4i | −0.428353 | − | 0.155908i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10463.7 | − | 10892.5i | −0.113973 | − | 0.118644i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 47363.5 | + | 27345.3i | 0.509148 | + | 0.293957i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −90294.2 | − | 156394.i | −0.958039 | − | 1.65937i | −0.727255 | − | 0.686367i | \(-0.759204\pi\) |
−0.230783 | − | 0.973005i | \(-0.574129\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 57392.0 | − | 116891.i | 0.601083 | − | 1.22424i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 71897.1 | − | 12677.4i | 0.743345 | − | 0.131072i | 0.210866 | − | 0.977515i | \(-0.432372\pi\) |
0.532479 | + | 0.846443i | \(0.321260\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −74410.2 | − | 62437.5i | −0.759528 | − | 0.637319i | 0.178476 | − | 0.983944i | \(-0.442883\pi\) |
−0.938004 | + | 0.346625i | \(0.887328\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 53136.3 | − | 16957.2i | 0.535513 | − | 0.170897i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27314.7 | + | 75046.5i | 0.271818 | + | 0.746813i | 0.998225 | + | 0.0595488i | \(0.0189662\pi\) |
−0.726408 | + | 0.687264i | \(0.758812\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8530.48 | − | 7157.92i | 0.0838286 | − | 0.0703405i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 22205.9 | + | 50229.6i | 0.215505 | + | 0.487472i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 118675.i | − | 1.13751i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 416.905 | 0.00394703 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 158142. | − | 69912.8i | 1.47895 | − | 0.653825i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17409.8 | − | 20748.2i | −0.160843 | − | 0.191685i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −51094.6 | + | 18596.9i | −0.466357 | + | 0.169740i | −0.564502 | − | 0.825432i | \(-0.690932\pi\) |
0.0981442 | + | 0.995172i | \(0.468709\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 65568.0 | + | 14297.0i | 0.591294 | + | 0.128931i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15178.1 | − | 18088.5i | 0.135247 | − | 0.161181i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3454.56 | + | 19591.8i | 0.0304181 | + | 0.172510i | 0.996232 | − | 0.0867260i | \(-0.0276405\pi\) |
−0.965814 | + | 0.259236i | \(0.916529\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2212.63 | − | 1086.37i | −0.0192535 | − | 0.00945317i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 157918. | − | 91174.0i | 1.35807 | − | 0.784083i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −51368.5 | + | 88972.9i | −0.436625 | + | 0.756257i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 95961.0 | − | 92183.1i | 0.806226 | − | 0.774485i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19743.2 | + | 54243.9i | −0.163967 | + | 0.450497i | −0.994280 | − | 0.106801i | \(-0.965939\pi\) |
0.830313 | + | 0.557297i | \(0.188162\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4802.56 | − | 27236.6i | 0.0394295 | − | 0.223616i | −0.958725 | − | 0.284333i | \(-0.908228\pi\) |
0.998155 | + | 0.0607175i | \(0.0193389\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1774.81 | + | 263.698i | 0.0144058 | + | 0.00214039i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 163139. | + | 28765.8i | 1.30921 | + | 0.230848i | 0.784337 | − | 0.620334i | \(-0.213003\pi\) |
0.524869 | + | 0.851183i | \(0.324114\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 60143.9 | + | 21890.6i | 0.477238 | + | 0.173700i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 14697.3 | − | 50752.7i | 0.115319 | − | 0.398220i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20895.8 | + | 12064.2i | 0.162133 | + | 0.0936074i | 0.578871 | − | 0.815419i | \(-0.303493\pi\) |
−0.416738 | + | 0.909027i | \(0.636827\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −56789.9 | − | 98363.1i | −0.435770 | − | 0.754775i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7947.94 | − | 11850.3i | −0.0603172 | − | 0.0899321i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 163252. | − | 28785.7i | 1.22539 | − | 0.216069i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7464.93 | + | 6263.82i | 0.0554235 | + | 0.0465058i | 0.670079 | − | 0.742290i | \(-0.266260\pi\) |
−0.614655 | + | 0.788796i | \(0.710705\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 105535. | − | 166935.i | 0.775074 | − | 1.22601i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 32422.1 | + | 89079.0i | 0.235556 | + | 0.647184i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19173.2 | − | 16088.2i | 0.137809 | − | 0.115635i | −0.571278 | − | 0.820757i | \(-0.693552\pi\) |
0.709086 | + | 0.705122i | \(0.249108\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −68177.4 | + | 93322.1i | −0.484817 | + | 0.663624i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 239.877i | 0.00168774i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −57436.8 | −0.399863 | −0.199932 | − | 0.979810i | \(-0.564072\pi\) | ||||
−0.199932 | + | 0.979810i | \(0.564072\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −28235.1 | + | 262023.i | −0.194509 | + | 1.80505i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −82991.0 | − | 98904.8i | −0.565762 | − | 0.674249i | 0.404994 | − | 0.914319i | \(-0.367274\pi\) |
−0.970755 | + | 0.240071i | \(0.922829\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −73935.0 | + | 26910.1i | −0.498802 | + | 0.181549i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −135691. | + | 18344.4i | −0.906001 | + | 0.122485i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24505.0 | − | 29203.9i | 0.161941 | − | 0.192993i | −0.678972 | − | 0.734164i | \(-0.737574\pi\) |
0.840913 | + | 0.541171i | \(0.182019\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21889.1 | − | 124139.i | −0.143177 | − | 0.812000i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15357.1 | − | 228221.i | −0.0994315 | − | 1.47765i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −138964. | + | 80230.8i | −0.890651 | + | 0.514218i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5111.47 | − | 8853.33i | 0.0324313 | − | 0.0561727i | −0.849354 | − | 0.527823i | \(-0.823008\pi\) |
0.881786 | + | 0.471651i | \(0.156342\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −25994.3 | − | 105435.i | −0.163280 | − | 0.662279i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −92985.8 | + | 255477.i | −0.578267 | + | 1.58877i | 0.212834 | + | 0.977088i | \(0.431731\pi\) |
−0.791101 | + | 0.611686i | \(0.790492\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −682.087 | + | 3868.31i | −0.00419981 | + | 0.0238183i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 129846. | − | 131665.i | 0.791621 | − | 0.802713i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −93227.3 | − | 16438.5i | −0.562800 | − | 0.0992368i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −236318. | − | 86012.7i | −1.41270 | − | 0.514181i | −0.480779 | − | 0.876842i | \(-0.659646\pi\) |
−0.931921 | + | 0.362661i | \(0.881868\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 114282. | − | 28175.4i | 0.676542 | − | 0.166796i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 79971.5 | + | 46171.6i | 0.468851 | + | 0.270692i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 104224. | + | 180522.i | 0.605163 | + | 1.04817i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −80495.9 | + | 5416.60i | −0.462915 | + | 0.0311497i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 226077. | − | 39863.4i | 1.28774 | − | 0.227063i | 0.512476 | − | 0.858702i | \(-0.328728\pi\) |
0.775263 | + | 0.631638i | \(0.217617\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34300.2 | + | 28781.3i | 0.193523 | + | 0.162385i | 0.734401 | − | 0.678716i | \(-0.237463\pi\) |
−0.540878 | + | 0.841101i | \(0.681908\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −83080.4 | − | 34074.9i | −0.464320 | − | 0.190438i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −13921.1 | − | 38248.0i | −0.0770720 | − | 0.211754i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 36316.4 | − | 30473.1i | 0.199181 | − | 0.167133i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2516.52 | − | 271.175i | −0.0136737 | − | 0.00147345i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 128951.i | 0.694176i | 0.937833 | + | 0.347088i | \(0.112830\pi\) | ||||
−0.937833 | + | 0.347088i | \(0.887170\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 68399.9 | 0.364821 | 0.182410 | − | 0.983222i | \(-0.441610\pi\) | ||||
0.182410 | + | 0.983222i | \(0.441610\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 19962.1 | + | 14583.5i | 0.105494 | + | 0.0770696i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −166525. | − | 198457.i | −0.872001 | − | 1.03921i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6048.33 | − | 2201.41i | 0.0313839 | − | 0.0114228i | −0.326281 | − | 0.945273i | \(-0.605795\pi\) |
0.357664 | + | 0.933850i | \(0.383573\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5866.32 | + | 146014.i | −0.0301640 | + | 0.750789i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −181179. | + | 215921.i | −0.923212 | + | 1.10024i | 0.0714898 | + | 0.997441i | \(0.477225\pi\) |
−0.994702 | + | 0.102800i | \(0.967220\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 57586.6 | + | 326590.i | 0.290805 | + | 1.64924i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19222.8 | + | 12892.7i | −0.0962061 | + | 0.0645252i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −250048. | + | 144365.i | −1.24031 | + | 0.716094i | −0.969158 | − | 0.246442i | \(-0.920739\pi\) |
−0.271154 | + | 0.962536i | \(0.587405\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −139297. | + | 241270.i | −0.684841 | + | 1.18618i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −307712. | − | 89109.6i | −1.49951 | − | 0.434238i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 579.675 | − | 1592.64i | 0.00280002 | − | 0.00769300i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 56283.2 | − | 319198.i | 0.269492 | − | 1.52837i | −0.486438 | − | 0.873715i | \(-0.661704\pi\) |
0.755930 | − | 0.654652i | \(-0.227185\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −35071.6 | − | 171632.i | −0.166468 | − | 0.814651i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 254561. | + | 44886.0i | 1.19782 | + | 0.211207i | 0.736754 | − | 0.676161i | \(-0.236358\pi\) |
0.461062 | + | 0.887368i | \(0.347469\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 249634. | + | 90859.5i | 1.16451 | + | 0.423846i | 0.850706 | − | 0.525642i | \(-0.176175\pi\) |
0.313802 | + | 0.949488i | \(0.398397\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 280446. | + | 291939.i | 1.29701 | + | 1.35016i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −234369. | − | 135313.i | −1.07465 | − | 0.620448i | −0.145200 | − | 0.989402i | \(-0.546383\pi\) |
−0.929448 | + | 0.368954i | \(0.879716\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10234.2 | − | 17726.2i | −0.0465274 | − | 0.0805878i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −34368.3 | + | 69998.7i | −0.154923 | + | 0.315536i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 190216. | − | 33540.3i | 0.850209 | − | 0.149915i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −64081.2 | − | 53770.5i | −0.284017 | − | 0.238318i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 232452. | + | 211521.i | 1.02164 | + | 0.929643i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −43361.6 | − | 119135.i | −0.188988 | − | 0.519240i | 0.808623 | − | 0.588328i | \(-0.200213\pi\) |
−0.997611 | + | 0.0690874i | \(0.977991\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1562.12 | − | 1310.77i | 0.00675187 | − | 0.00566549i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −46638.4 | − | 105496.i | −0.199917 | − | 0.452210i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 80848.2i | 0.343706i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −99411.6 | −0.419159 | −0.209580 | − | 0.977792i | \(-0.567210\pi\) | ||||
−0.209580 | + | 0.977792i | \(0.567210\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −366343. | + | 161956.i | −1.53204 | + | 0.677297i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 59612.1 | + | 71043.0i | 0.247270 | + | 0.294685i | 0.875376 | − | 0.483443i | \(-0.160614\pi\) |
−0.628106 | + | 0.778128i | \(0.716169\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22006.9 | − | 8009.87i | 0.0905453 | − | 0.0329558i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −175561. | + | 192934.i | −0.716501 | + | 0.787405i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 35662.3 | − | 42500.7i | 0.144376 | − | 0.172061i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −58901.1 | − | 334045.i | −0.236550 | − | 1.34154i | −0.839326 | − | 0.543629i | \(-0.817050\pi\) |
0.602776 | − | 0.797910i | \(-0.294061\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 260125. | + | 127718.i | 1.03635 | + | 0.508833i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22048.1 | + | 12729.5i | −0.0871435 | + | 0.0503123i | −0.542939 | − | 0.839772i | \(-0.682688\pi\) |
0.455795 | + | 0.890085i | \(0.349355\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23650.5 | + | 40963.9i | −0.0927380 | + | 0.160627i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −185334. | + | 178038.i | −0.721007 | + | 0.692621i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 149571. | − | 410944.i | 0.577315 | − | 1.58616i | −0.215373 | − | 0.976532i | \(-0.569097\pi\) |
0.792688 | − | 0.609628i | \(-0.208681\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24952.5 | − | 141512.i | 0.0955590 | − | 0.541942i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −238791. | − | 269440.i | −0.907367 | − | 1.02383i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −401610. | − | 70814.6i | −1.51422 | − | 0.266998i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 119031. | + | 43323.7i | 0.445326 | + | 0.162085i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −77216.5 | + | 266643.i | −0.286666 | + | 0.989910i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −389228. | − | 224721.i | −1.43393 | − | 0.827882i | −0.436515 | − | 0.899697i | \(-0.643787\pi\) |
−0.997418 | + | 0.0718152i | \(0.977121\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 179231. | + | 310437.i | 0.655254 | + | 1.13493i | 0.981830 | + | 0.189762i | \(0.0607717\pi\) |
−0.326576 | + | 0.945171i | \(0.605895\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −20745.8 | − | 30931.7i | −0.0752683 | − | 0.112224i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 377665. | − | 66592.6i | 1.35983 | − | 0.239775i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3573.37 | + | 2998.41i | 0.0127693 | + | 0.0107147i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 305906. | + | 12290.2i | 1.08492 | + | 0.0435883i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2052.55 | − | 5639.32i | −0.00722501 | − | 0.0198506i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 131750. | − | 110551.i | 0.460302 | − | 0.386239i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −160371. | + | 219518.i | −0.556131 | + | 0.761240i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 206138.i | − | 0.709547i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 116585. | 0.398333 | 0.199167 | − | 0.979966i | \(-0.436177\pi\) | ||||
0.199167 | + | 0.979966i | \(0.436177\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −50871.4 | + | 472089.i | −0.172534 | + | 1.60112i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −348059. | − | 414800.i | −1.17182 | − | 1.39652i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −51478.9 | + | 18736.8i | −0.172050 | + | 0.0626210i | −0.426609 | − | 0.904436i | \(-0.640292\pi\) |
0.254559 | + | 0.967057i | \(0.418070\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 59642.8 | − | 145419.i | 0.197885 | − | 0.482477i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 30938.2 | − | 36870.8i | 0.101904 | − | 0.121445i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24153.4 | + | 136980.i | 0.0789818 | + | 0.447928i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −14109.9 | − | 209686.i | −0.0458075 | − | 0.680744i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −30508.0 | + | 17613.8i | −0.0983339 | + | 0.0567731i | −0.548360 | − | 0.836242i | \(-0.684748\pi\) |
0.450027 | + | 0.893015i | \(0.351414\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2080.34 | + | 3603.26i | −0.00665750 | + | 0.0115311i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 59152.3 | + | 239927.i | 0.187952 | + | 0.762349i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −61925.1 | + | 170138.i | −0.195366 | + | 0.536765i | −0.998235 | − | 0.0593917i | \(-0.981084\pi\) |
0.802868 | + | 0.596156i | \(0.203306\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1340.44 | + | 7602.04i | −0.00419906 | + | 0.0238140i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −68752.8 | − | 144802.i | −0.213857 | − | 0.450411i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 368377. | + | 64954.7i | 1.13780 | + | 0.200626i | 0.710645 | − | 0.703551i | \(-0.248403\pi\) |
0.427159 | + | 0.904176i | \(0.359514\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 459788. | + | 167349.i | 1.41022 | + | 0.513277i | 0.931193 | − | 0.364526i | \(-0.118769\pi\) |
0.479023 | + | 0.877803i | \(0.340991\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 382584. | − | 94323.3i | 1.16525 | − | 0.287283i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −76949.6 | − | 44426.9i | −0.232740 | − | 0.134372i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 113291. | + | 196225.i | 0.340285 | + | 0.589390i | 0.984485 | − | 0.175466i | \(-0.0561433\pi\) |
−0.644201 | + | 0.764856i | \(0.722810\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 630245. | − | 42409.4i | 1.87998 | − | 0.126504i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 177945. | − | 31376.5i | 0.527149 | − | 0.0929507i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −339618. | − | 284973.i | −0.999203 | − | 0.838431i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −752.814 | − | 5568.44i | −0.00219976 | − | 0.0162713i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 136938. | + | 376234.i | 0.397418 | + | 1.09190i | 0.963538 | + | 0.267573i | \(0.0862217\pi\) |
−0.566120 | + | 0.824323i | \(0.691556\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 603759. | − | 506614.i | 1.74034 | − | 1.46032i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −248571. | − | 26785.5i | −0.711665 | − | 0.0766877i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 332164.i | − | 0.944590i | −0.881441 | − | 0.472295i | \(-0.843426\pi\) | ||
0.881441 | − | 0.472295i | \(-0.156574\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −165470. | −0.467396 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −225470. | − | 164719.i | −0.632617 | − | 0.462164i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −403032. | − | 480315.i | −1.12327 | − | 1.33867i | −0.934219 | − | 0.356700i | \(-0.883902\pi\) |
−0.189056 | − | 0.981966i | \(-0.560543\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 565600. | − | 205862.i | 1.56589 | − | 0.569936i | 0.593811 | − | 0.804604i | \(-0.297623\pi\) |
0.972076 | + | 0.234668i | \(0.0754003\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −57359.7 | − | 36262.2i | −0.157751 | − | 0.0997287i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −28722.8 | + | 34230.6i | −0.0784724 | + | 0.0935197i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −72553.0 | − | 411469.i | −0.196915 | − | 1.11676i | −0.909665 | − | 0.415342i | \(-0.863662\pi\) |
0.712751 | − | 0.701417i | \(-0.247449\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 17797.4 | − | 11936.6i | 0.0479867 | − | 0.0321846i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2363.05 | + | 1364.31i | −0.00632980 | + | 0.00365451i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 165625. | − | 286871.i | 0.440764 | − | 0.763425i | −0.556983 | − | 0.830524i | \(-0.688041\pi\) |
0.997746 | + | 0.0670991i | \(0.0213744\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −594081. | − | 172038.i | −1.57071 | − | 0.454857i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −182752. | + | 502108.i | −0.480057 | + | 1.31895i | 0.429387 | + | 0.903120i | \(0.358730\pi\) |
−0.909444 | + | 0.415826i | \(0.863493\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18382.4 | − | 104252.i | 0.0479756 | − | 0.272083i | −0.951378 | − | 0.308025i | \(-0.900332\pi\) |
0.999354 | + | 0.0359418i | \(0.0114431\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −299483. | − | 237802.i | −0.776585 | − | 0.616641i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 283099. | + | 49918.0i | 0.729395 | + | 0.128612i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 439587. | + | 159997.i | 1.12534 | + | 0.409591i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 351832. | + | 366251.i | 0.894953 | + | 0.931631i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −172416. | − | 99544.2i | −0.435788 | − | 0.251602i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 288702. | + | 500047.i | 0.725089 | + | 1.25589i | 0.958937 | + | 0.283618i | \(0.0915348\pi\) |
−0.233848 | + | 0.972273i | \(0.575132\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 98436.7 | − | 200488.i | 0.245669 | − | 0.500359i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 812774. | − | 143314.i | 2.01568 | − | 0.355419i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3401.58 | + | 2854.27i | 0.00838305 | + | 0.00703422i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 39187.0 | − | 179717.i | 0.0959710 | − | 0.440137i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 181206. | + | 497859.i | 0.441018 | + | 1.21169i | 0.938824 | + | 0.344397i | \(0.111917\pi\) |
−0.497806 | + | 0.867288i | \(0.665861\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 68330.7 | − | 57336.3i | 0.165270 | − | 0.138678i | −0.556402 | − | 0.830913i | \(-0.687818\pi\) |
0.721672 | + | 0.692235i | \(0.243374\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 173381. | + | 392186.i | 0.416755 | + | 0.942697i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 690108.i | − | 1.64857i | −0.566172 | − | 0.824287i | \(-0.691576\pi\) | ||
0.566172 | − | 0.824287i | \(-0.308424\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −431869. | −1.02533 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 320946. | − | 141886.i | 0.757304 | − | 0.334795i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −360793. | − | 429977.i | −0.846121 | − | 1.00837i | −0.999795 | − | 0.0202458i | \(-0.993555\pi\) |
0.153674 | − | 0.988122i | \(-0.450889\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −673125. | + | 244997.i | −1.56896 | + | 0.571056i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −144838. | − | 453855.i | −0.335545 | − | 1.05145i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −470549. | + | 560778.i | −1.08351 | + | 1.29128i | −0.129479 | + | 0.991582i | \(0.541330\pi\) |
−0.954034 | + | 0.299698i | \(0.903114\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 118352. | + | 671209.i | 0.270878 | + | 1.53623i | 0.751758 | + | 0.659439i | \(0.229206\pi\) |
−0.480880 | + | 0.876786i | \(0.659683\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4778.20 | − | 2346.02i | −0.0108702 | − | 0.00533710i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −294512. | + | 170037.i | −0.665978 | + | 0.384503i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25562.1 | − | 44274.9i | 0.0574573 | − | 0.0995190i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −512681. | + | 492497.i | −1.14550 | + | 1.10040i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −75831.2 | + | 208345.i | −0.168424 | + | 0.462740i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −50789.8 | + | 288043.i | −0.112136 | + | 0.635957i | 0.875992 | + | 0.482326i | \(0.160208\pi\) |
−0.988128 | + | 0.153631i | \(0.950903\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −108567. | − | 58827.0i | −0.238281 | − | 0.129113i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −547224. | − | 96490.4i | −1.19396 | − | 0.210527i | −0.458871 | − | 0.888503i | \(-0.651746\pi\) |
−0.735084 | + | 0.677976i | \(0.762857\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 65855.5 | + | 23969.4i | 0.142841 | + | 0.0519898i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −187802. | + | 648516.i | −0.404954 | + | 1.39838i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8476.38 | − | 4893.84i | −0.0181706 | − | 0.0104908i | 0.490887 | − | 0.871223i | \(-0.336673\pi\) |
−0.509058 | + | 0.860732i | \(0.670006\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −184304. | − | 319224.i | −0.392783 | − | 0.680321i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 72321.9 | + | 107831.i | 0.153235 | + | 0.228470i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9404.96 | − | 1658.35i | 0.0198115 | − | 0.00349331i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −604854. | − | 507533.i | −1.26676 | − | 1.06294i | −0.994928 | − | 0.100594i | \(-0.967926\pi\) |
−0.271833 | − | 0.962344i | \(-0.587630\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 105106. | + | 200204.i | 0.218858 | + | 0.416876i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 86412.9 | + | 237418.i | 0.178900 | + | 0.491522i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −448829. | + | 376612.i | −0.923880 | + | 0.775227i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 133601. | − | 182876.i | 0.273437 | − | 0.374284i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 765720.i | 1.55824i | 0.626876 | + | 0.779119i | \(0.284333\pi\) | ||||
−0.626876 | + | 0.779119i | \(0.715667\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −409167. | −0.827922 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −30128.4 | + | 279593.i | −0.0606174 | + | 0.562533i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 26355.6 | + | 31409.4i | 0.0527272 | + | 0.0628379i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −132595. | + | 48260.7i | −0.263776 | + | 0.0960066i | −0.470523 | − | 0.882388i | \(-0.655935\pi\) |
0.206747 | + | 0.978394i | \(0.433712\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 282001. | + | 364875.i | 0.557842 | + | 0.721781i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 538116. | − | 641302.i | 1.05851 | − | 1.26149i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1376.42 | + | 7806.05i | 0.00269239 | + | 0.0152693i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21739.8 | − | 323074.i | −0.0422880 | − | 0.628440i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 76955.1 | − | 44430.1i | 0.148861 | − | 0.0859447i | −0.423720 | − | 0.905793i | \(-0.639276\pi\) |
0.572580 | + | 0.819849i | \(0.305942\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −176750. | + | 306140.i | −0.340007 | + | 0.588910i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −141348. | − | 573319.i | −0.270403 | − | 1.09678i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5646.03 | − | 15512.3i | 0.0107416 | − | 0.0295122i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2153.14 | + | 12211.1i | −0.00407384 | + | 0.0231039i | −0.986777 | − | 0.162084i | \(-0.948178\pi\) |
0.982703 | + | 0.185188i | \(0.0592895\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −424974. | − | 319103.i | −0.799663 | − | 0.600449i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 400039. | + | 70537.7i | 0.748631 | + | 0.132004i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −405994. | − | 147770.i | −0.755634 | − | 0.275028i | −0.0646595 | − | 0.997907i | \(-0.520596\pi\) |
−0.690975 | + | 0.722879i | \(0.742818\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 444329. | − | 109546.i | 0.822489 | − | 0.202779i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 82901.5 | + | 47863.2i | 0.152626 | + | 0.0881184i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 95170.2 | + | 164840.i | 0.174266 | + | 0.301837i | 0.939907 | − | 0.341431i | \(-0.110911\pi\) |
−0.765641 | + | 0.643268i | \(0.777578\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10915.3 | + | 734.493i | −0.0198792 | + | 0.00133768i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 920487. | − | 162307.i | 1.66740 | − | 0.294008i | 0.741269 | − | 0.671208i | \(-0.234224\pi\) |
0.926132 | + | 0.377200i | \(0.123113\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 55526.9 | + | 46592.6i | 0.100044 | + | 0.0839469i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 473993. | − | 366334.i | 0.849436 | − | 0.656502i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −50989.9 | − | 140093.i | −0.0908908 | − | 0.249721i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 193215. | − | 162126.i | 0.342578 | − | 0.287457i | −0.455223 | − | 0.890377i | \(-0.650441\pi\) |
0.797802 | + | 0.602920i | \(0.205996\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −371329. | − | 40013.7i | −0.654890 | − | 0.0705697i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.00324e6i | 1.75999i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −449009. | −0.783544 | −0.391772 | − | 0.920062i | \(-0.628138\pi\) | ||||
−0.391772 | + | 0.920062i | \(0.628138\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 435586. | + | 318221.i | 0.756119 | + | 0.552390i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −380749. | − | 453759.i | −0.657460 | − | 0.783530i | 0.329559 | − | 0.944135i | \(-0.393100\pi\) |
−0.987019 | + | 0.160605i | \(0.948656\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −441069. | + | 160536.i | −0.757631 | + | 0.275755i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −485726. | + | 255005.i | −0.829982 | + | 0.435738i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5979.82 | − | 7126.47i | 0.0101648 | − | 0.0121139i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35286.0 | − | 200117.i | −0.0596692 | − | 0.338401i | 0.940329 | − | 0.340267i | \(-0.110517\pi\) |
−0.999998 | + | 0.00186555i | \(0.999406\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 509596. | − | 341785.i | 0.857269 | − | 0.574968i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −93598.2 | + | 54039.0i | −0.156642 | + | 0.0904374i | −0.576272 | − | 0.817258i | \(-0.695493\pi\) |
0.419630 | + | 0.907695i | \(0.362160\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 135158. | − | 234101.i | 0.225030 | − | 0.389763i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −174985. | − | 50673.4i | −0.289840 | − | 0.0839340i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −411844. | + | 1.13153e6i | −0.678669 | + | 1.86463i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −45056.7 | + | 255529.i | −0.0738681 | + | 0.418927i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 33847.6 | − | 62466.7i | 0.0552083 | − | 0.101888i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 240498. | + | 42406.3i | 0.390277 | + | 0.0688163i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −819692. | − | 298343.i | −1.32343 | − | 0.481689i | −0.418874 | − | 0.908044i | \(-0.637575\pi\) |
−0.904556 | + | 0.426355i | \(0.859797\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 195275. | + | 203278.i | 0.313685 | + | 0.326540i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5794.89 | + | 3345.68i | 0.00926173 | + | 0.00534726i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2388.00 | − | 4136.14i | −0.00379742 | − | 0.00657732i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 433778. | − | 883484.i | 0.686330 | − | 1.39786i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 105519. | − | 18605.8i | 0.166116 | − | 0.0292908i | −0.0899713 | − | 0.995944i | \(-0.528678\pi\) |
0.256088 | + | 0.966654i | \(0.417566\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 204071. | + | 171236.i | 0.319660 | + | 0.268227i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 907949. | − | 289751.i | 1.41513 | − | 0.451607i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 229849. | + | 631504.i | 0.356460 | + | 0.979366i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −276710. | + | 232188.i | −0.427006 | + | 0.358300i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −497374. | − | 1.12506e6i | −0.763723 | − | 1.72754i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 15837.0i | − | 0.0241977i | −0.999927 | − | 0.0120989i | \(-0.996149\pi\) | ||
0.999927 | − | 0.0120989i | \(-0.00385128\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 77890.8 | 0.118425 | 0.0592127 | − | 0.998245i | \(-0.481141\pi\) | ||||
0.0592127 | + | 0.998245i | \(0.481141\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.00858e6 | + | 445881.i | −1.52591 | + | 0.674587i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 806291. | + | 960901.i | 1.21388 | + | 1.44665i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 784496. | − | 285533.i | 1.17529 | − | 0.427772i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4759.01 | − | 1037.69i | −0.00709493 | − | 0.00154704i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −281744. | + | 335769.i | −0.417992 | + | 0.498143i | −0.933418 | − | 0.358791i | \(-0.883189\pi\) |
0.515426 | + | 0.856934i | \(0.327634\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 43692.6 | + | 247793.i | 0.0645072 | + | 0.365838i | 0.999924 | + | 0.0122928i | \(0.00391301\pi\) |
−0.935417 | + | 0.353546i | \(0.884976\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 156356. | + | 76768.2i | 0.229724 | + | 0.112791i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 317420. | − | 183262.i | 0.464112 | − | 0.267955i | −0.249660 | − | 0.968334i | \(-0.580319\pi\) |
0.713772 | + | 0.700379i | \(0.246985\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −260535. | + | 451260.i | −0.379103 | + | 0.656625i | −0.990932 | − | 0.134365i | \(-0.957101\pi\) |
0.611829 | + | 0.790990i | \(0.290434\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 272971. | − | 262224.i | 0.395289 | − | 0.379726i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 148274. | − | 407379.i | 0.213685 | − | 0.587096i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 157588. | − | 893725.i | 0.226021 | − | 1.28183i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 723458. | − | 911108.i | 1.03267 | − | 1.30053i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −488823. | − | 86192.7i | −0.694429 | − | 0.122447i | −0.184717 | − | 0.982792i | \(-0.559137\pi\) |
−0.509712 | + | 0.860345i | \(0.670248\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −655701. | − | 238656.i | −0.927073 | − | 0.337427i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 142202. | − | 491050.i | 0.200102 | − | 0.690989i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 696991. | + | 402408.i | 0.976143 | + | 0.563577i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19367.2 | + | 33544.9i | 0.0269960 | + | 0.0467584i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −41626.4 | − | 62064.3i | −0.0577502 | − | 0.0861046i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −428007. | + | 75469.1i | −0.591005 | + | 0.104210i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 740679. | + | 621504.i | 1.01796 | + | 0.854172i | 0.989370 | − | 0.145419i | \(-0.0464529\pi\) |
0.0285928 | + | 0.999591i | \(0.490897\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −602480. | + | 953004.i | −0.824158 | + | 1.30365i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −396643. | − | 1.08977e6i | −0.540055 | − | 1.48379i | −0.846755 | − | 0.531982i | \(-0.821447\pi\) |
0.306701 | − | 0.951806i | \(-0.400775\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −138587. | + | 116288.i | −0.187817 | + | 0.157597i | −0.731848 | − | 0.681468i | \(-0.761342\pi\) |
0.544031 | + | 0.839065i | \(0.316897\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −316265. | + | 432908.i | −0.426623 | + | 0.583968i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 941281.i | − | 1.26386i | −0.775027 | − | 0.631928i | \(-0.782264\pi\) | ||
0.775027 | − | 0.631928i | \(-0.217736\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 869340. | 1.16187 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 24855.5 | − | 230660.i | 0.0330661 | − | 0.306855i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −418140. | − | 498320.i | −0.553710 | − | 0.659886i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1937.70 | + | 705.264i | −0.00255417 | + | 0.000929642i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 230254. | − | 31128.7i | 0.302120 | − | 0.0408444i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 201666. | − | 240336.i | 0.263401 | − | 0.313909i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −123251. | − | 698994.i | −0.160248 | − | 0.908812i | −0.953830 | − | 0.300348i | \(-0.902897\pi\) |
0.793582 | − | 0.608464i | \(-0.208214\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −91788.7 | − | 1.36407e6i | −0.118799 | − | 1.76546i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −479040. | + | 276574.i | −0.617191 | + | 0.356336i | −0.775775 | − | 0.631010i | \(-0.782641\pi\) |
0.158583 | + | 0.987346i | \(0.449307\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −567258. | + | 982519.i | −0.727543 | + | 1.26014i | 0.230375 | + | 0.973102i | \(0.426005\pi\) |
−0.957919 | + | 0.287040i | \(0.907329\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −229504. | − | 930889.i | −0.293024 | − | 1.18853i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −201922. | + | 554777.i | −0.256648 | + | 0.705133i | 0.742721 | + | 0.669601i | \(0.233535\pi\) |
−0.999369 | + | 0.0355323i | \(0.988687\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 124229. | − | 704540.i | 0.157189 | − | 0.891461i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 617067. | + | 425708.i | 0.777279 | + | 0.536237i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 539180. | + | 95071.9i | 0.676131 | + | 0.119220i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 800020. | + | 291183.i | 0.998745 | + | 0.363514i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −11282.4 | + | 2781.59i | −0.0140222 | + | 0.00345707i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 134696. | + | 77766.8i | 0.166662 | + | 0.0962221i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −466188. | − | 807462.i | −0.574264 | − | 0.994655i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 370861. | − | 24955.4i | 0.454816 | − | 0.0306047i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.46438e6 | − | 258210.i | 1.78796 | − | 0.315266i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −452398. | − | 379607.i | −0.549928 | − | 0.461444i | 0.324989 | − | 0.945718i | \(-0.394639\pi\) |
−0.874917 | + | 0.484274i | \(0.839084\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 125770. | + | 51584.0i | 0.152213 | + | 0.0624291i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 56684.2 | + | 155738.i | 0.0683007 | + | 0.187655i | 0.969147 | − | 0.246484i | \(-0.0792752\pi\) |
−0.900846 | + | 0.434138i | \(0.857053\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −647345. | + | 543187.i | −0.776594 | + | 0.651640i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −489383. | − | 52735.0i | −0.584530 | − | 0.0629878i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 620934.i | 0.738426i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.06675e6 | 1.26309 | 0.631543 | − | 0.775341i | \(-0.282422\pi\) | ||||
0.631543 | + | 0.775341i | \(0.282422\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.31238e6 | + | 958772.i | 1.54718 | + | 1.13031i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3592.73 | − | 4281.65i | −0.00421717 | − | 0.00502583i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −131871. | + | 47997.2i | −0.154123 | + | 0.0560960i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −47048.2 | + | 1.17104e6i | −0.0547500 | + | 1.36274i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 389468. | − | 464150.i | 0.451274 | − | 0.537807i | −0.491660 | − | 0.870787i | \(-0.663610\pi\) |
0.942934 | + | 0.332980i | \(0.108054\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −154717. | − | 877443.i | −0.178500 | − | 1.01232i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −545686. | + | 365990.i | −0.626873 | + | 0.420442i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 670187. | − | 386933.i | 0.766607 | − | 0.442601i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 650792. | − | 1.12720e6i | 0.741247 | − | 1.28388i | −0.210681 | − | 0.977555i | \(-0.567568\pi\) |
0.951928 | − | 0.306323i | \(-0.0990987\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 839719. | + | 243172.i | 0.952364 | + | 0.275793i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −285013. | + | 783067.i | −0.321874 | + | 0.884341i | 0.668224 | + | 0.743960i | \(0.267055\pi\) |
−0.990098 | + | 0.140381i | \(0.955167\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −222101. | + | 1.25960e6i | −0.249762 | + | 1.41647i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −375683. | + | 332949.i | −0.420685 | + | 0.372832i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.02383e6 | − | 180529.i | −1.14164 | − | 0.201302i | −0.429317 | − | 0.903154i | \(-0.641246\pi\) |
−0.712323 | + | 0.701852i | \(0.752357\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13603.3 | − | 4951.20i | −0.0151047 | − | 0.00549766i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −497938. | − | 518345.i | −0.550572 | − | 0.573136i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.26089e6 | + | 727976.i | 1.38833 | + | 0.801551i | 0.993127 | − | 0.117044i | \(-0.0373418\pi\) |
0.395200 | + | 0.918595i | \(0.370675\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −616997. | − | 1.06867e6i | −0.676513 | − | 1.17176i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −44170.5 | + | 89963.1i | −0.0482291 | + | 0.0982292i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −314667. | + | 55484.3i | −0.342148 | + | 0.0603300i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.24355e6 | + | 1.04347e6i | 1.34654 | + | 1.12988i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −365575. | − | 332656.i | −0.394207 | − | 0.358709i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −676573. | − | 1.85887e6i | −0.726541 | − | 1.99616i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −215918. | + | 181176.i | −0.230906 | + | 0.193753i | −0.750898 | − | 0.660418i | \(-0.770379\pi\) |
0.519992 | + | 0.854171i | \(0.325935\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 431863. | + | 976872.i | 0.459937 | + | 1.04038i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 450143.i | − | 0.477433i | −0.971089 | − | 0.238716i | \(-0.923273\pi\) | ||
0.971089 | − | 0.238716i | \(-0.0767267\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 219010. | 0.231333 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3431.75 | + | 1517.13i | −0.00360999 | + | 0.00159593i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −601049. | − | 716302.i | −0.629681 | − | 0.750424i | 0.353022 | − | 0.935615i | \(-0.385154\pi\) |
−0.982703 | + | 0.185191i | \(0.940710\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.26334e6 | + | 459818.i | −1.31812 | + | 0.479756i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.04733e6 | + | 1.15097e6i | −1.08829 | + | 1.19599i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −32996.0 | + | 39323.2i | −0.0341472 | + | 0.0406950i | −0.782848 | − | 0.622213i | \(-0.786234\pi\) |
0.748701 | + | 0.662908i | \(0.230678\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 135957. | + | 771048.i | 0.140129 | + | 0.794711i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 218812. | + | 107433.i | 0.224614 | + | 0.110282i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 767953. | − | 443378.i | 0.785131 | − | 0.453295i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 124272. | − | 215246.i | 0.126540 | − | 0.219173i | −0.795794 | − | 0.605567i | \(-0.792946\pi\) |
0.922334 | + | 0.386394i | \(0.126280\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 352909. | − | 339015.i | 0.357902 | − | 0.343812i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −299079. | + | 821713.i | −0.302093 | + | 0.829992i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −209863. | + | 1.19019e6i | −0.211128 | + | 1.19737i | 0.676373 | + | 0.736560i | \(0.263551\pi\) |
−0.887501 | + | 0.460807i | \(0.847560\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −591750. | + | 120919.i | −0.592935 | + | 0.121162i |
(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.29.2 | ✓ | 72 | |
3.2 | odd | 2 | 324.5.k.a.89.3 | 72 | |||
27.13 | even | 9 | 324.5.k.a.233.3 | 72 | |||
27.14 | odd | 18 | inner | 108.5.k.a.41.2 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.5.k.a.29.2 | ✓ | 72 | 1.1 | even | 1 | trivial | |
108.5.k.a.41.2 | yes | 72 | 27.14 | odd | 18 | inner | |
324.5.k.a.89.3 | 72 | 3.2 | odd | 2 | |||
324.5.k.a.233.3 | 72 | 27.13 | even | 9 |