Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,7,Mod(42,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.42");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.b (of order \(2\), degree \(1\), 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: | \(9.89232559565\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 1038 x^{18} + 455829 x^{16} + 110435384 x^{14} + 16133606976 x^{12} + 1458210485616 x^{10} + \cdots + 64\!\cdots\!40 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{15} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.7 | ||
Root | \(-7.14115i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.7.b.b.42.14 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 7.14115i | − | 0.892644i | −0.894872 | − | 0.446322i | \(-0.852734\pi\) | ||
0.894872 | − | 0.446322i | \(-0.147266\pi\) | |||||||
\(3\) | − | 19.7617i | − | 0.731916i | −0.930631 | − | 0.365958i | \(-0.880741\pi\) | ||
0.930631 | − | 0.365958i | \(-0.119259\pi\) | |||||||
\(4\) | 13.0039 | 0.203186 | ||||||||
\(5\) | − | 151.678i | − | 1.21343i | −0.794920 | − | 0.606714i | \(-0.792487\pi\) | ||
0.794920 | − | 0.606714i | \(-0.207513\pi\) | |||||||
\(6\) | −141.122 | −0.653340 | ||||||||
\(7\) | 62.8896i | 0.183352i | 0.995789 | + | 0.0916759i | \(0.0292224\pi\) | ||||
−0.995789 | + | 0.0916759i | \(0.970778\pi\) | |||||||
\(8\) | − | 549.897i | − | 1.07402i | ||||||
\(9\) | 338.474 | 0.464299 | ||||||||
\(10\) | −1083.16 | −1.08316 | ||||||||
\(11\) | −497.851 | −0.374043 | −0.187021 | − | 0.982356i | \(-0.559883\pi\) | ||||
−0.187021 | + | 0.982356i | \(0.559883\pi\) | |||||||
\(12\) | − | 256.980i | − | 0.148715i | ||||||
\(13\) | 850.633 | 0.387179 | 0.193590 | − | 0.981083i | \(-0.437987\pi\) | ||||
0.193590 | + | 0.981083i | \(0.437987\pi\) | |||||||
\(14\) | 449.105 | 0.163668 | ||||||||
\(15\) | −2997.43 | −0.888127 | ||||||||
\(16\) | −3094.65 | −0.755529 | ||||||||
\(17\) | −8046.00 | −1.63770 | −0.818848 | − | 0.574010i | \(-0.805387\pi\) | ||||
−0.818848 | + | 0.574010i | \(0.805387\pi\) | |||||||
\(18\) | − | 2417.10i | − | 0.414454i | ||||||
\(19\) | 11446.3i | 1.66880i | 0.551156 | + | 0.834402i | \(0.314187\pi\) | ||||
−0.551156 | + | 0.834402i | \(0.685813\pi\) | |||||||
\(20\) | − | 1972.42i | − | 0.246552i | ||||||
\(21\) | 1242.81 | 0.134198 | ||||||||
\(22\) | 3555.23i | 0.333887i | ||||||||
\(23\) | 6206.07 | 0.510074 | 0.255037 | − | 0.966931i | \(-0.417912\pi\) | ||||
0.255037 | + | 0.966931i | \(0.417912\pi\) | |||||||
\(24\) | −10866.9 | −0.786090 | ||||||||
\(25\) | −7381.34 | −0.472406 | ||||||||
\(26\) | − | 6074.50i | − | 0.345613i | ||||||
\(27\) | − | 21095.1i | − | 1.07174i | ||||||
\(28\) | 817.813i | 0.0372546i | ||||||||
\(29\) | − | 23809.8i | − | 0.976253i | −0.872773 | − | 0.488126i | \(-0.837680\pi\) | ||
0.872773 | − | 0.488126i | \(-0.162320\pi\) | |||||||
\(30\) | 21405.1i | 0.792781i | ||||||||
\(31\) | 26939.3 | 0.904275 | 0.452138 | − | 0.891948i | \(-0.350662\pi\) | ||||
0.452138 | + | 0.891948i | \(0.350662\pi\) | |||||||
\(32\) | − | 13094.1i | − | 0.399599i | ||||||
\(33\) | 9838.40i | 0.273768i | ||||||||
\(34\) | 57457.7i | 1.46188i | ||||||||
\(35\) | 9539.00 | 0.222484 | ||||||||
\(36\) | 4401.49 | 0.0943393 | ||||||||
\(37\) | − | 23588.9i | − | 0.465696i | −0.972513 | − | 0.232848i | \(-0.925196\pi\) | ||
0.972513 | − | 0.232848i | \(-0.0748044\pi\) | |||||||
\(38\) | 81740.0 | 1.48965 | ||||||||
\(39\) | − | 16810.0i | − | 0.283383i | ||||||
\(40\) | −83407.5 | −1.30324 | ||||||||
\(41\) | 87352.8 | 1.26743 | 0.633717 | − | 0.773565i | \(-0.281528\pi\) | ||||
0.633717 | + | 0.773565i | \(0.281528\pi\) | |||||||
\(42\) | − | 8875.08i | − | 0.119791i | ||||||
\(43\) | 79070.1 | − | 8323.35i | 0.994505 | − | 0.104687i | ||||
\(44\) | −6474.02 | −0.0760004 | ||||||||
\(45\) | − | 51339.2i | − | 0.563393i | ||||||
\(46\) | − | 44318.5i | − | 0.455314i | ||||||
\(47\) | −39004.6 | −0.375684 | −0.187842 | − | 0.982199i | \(-0.560149\pi\) | ||||
−0.187842 | + | 0.982199i | \(0.560149\pi\) | |||||||
\(48\) | 61155.6i | 0.552984i | ||||||||
\(49\) | 113694. | 0.966382 | ||||||||
\(50\) | 52711.3i | 0.421690i | ||||||||
\(51\) | 159003.i | 1.19866i | ||||||||
\(52\) | 11061.6 | 0.0786696 | ||||||||
\(53\) | −178171. | −1.19676 | −0.598382 | − | 0.801211i | \(-0.704190\pi\) | ||||
−0.598382 | + | 0.801211i | \(0.704190\pi\) | |||||||
\(54\) | −150644. | −0.956686 | ||||||||
\(55\) | 75513.3i | 0.453874i | ||||||||
\(56\) | 34582.8 | 0.196923 | ||||||||
\(57\) | 226199. | 1.22142 | ||||||||
\(58\) | −170030. | −0.871446 | ||||||||
\(59\) | 19938.3 | 0.0970806 | 0.0485403 | − | 0.998821i | \(-0.484543\pi\) | ||||
0.0485403 | + | 0.998821i | \(0.484543\pi\) | |||||||
\(60\) | −38978.3 | −0.180455 | ||||||||
\(61\) | 34949.8i | 0.153977i | 0.997032 | + | 0.0769885i | \(0.0245305\pi\) | ||||
−0.997032 | + | 0.0769885i | \(0.975470\pi\) | |||||||
\(62\) | − | 192377.i | − | 0.807196i | ||||||
\(63\) | 21286.5i | 0.0851301i | ||||||||
\(64\) | −291564. | −1.11223 | ||||||||
\(65\) | − | 129023.i | − | 0.469814i | ||||||
\(66\) | 70257.5 | 0.244377 | ||||||||
\(67\) | −299904. | −0.997143 | −0.498572 | − | 0.866849i | \(-0.666142\pi\) | ||||
−0.498572 | + | 0.866849i | \(0.666142\pi\) | |||||||
\(68\) | −104630. | −0.332758 | ||||||||
\(69\) | − | 122643.i | − | 0.373331i | ||||||
\(70\) | − | 68119.5i | − | 0.198599i | ||||||
\(71\) | − | 362351.i | − | 1.01241i | −0.862414 | − | 0.506203i | \(-0.831049\pi\) | ||
0.862414 | − | 0.506203i | \(-0.168951\pi\) | |||||||
\(72\) | − | 186126.i | − | 0.498665i | ||||||
\(73\) | − | 89951.1i | − | 0.231227i | −0.993294 | − | 0.115613i | \(-0.963117\pi\) | ||
0.993294 | − | 0.115613i | \(-0.0368833\pi\) | |||||||
\(74\) | −168452. | −0.415701 | ||||||||
\(75\) | 145868.i | 0.345761i | ||||||||
\(76\) | 148847.i | 0.339078i | ||||||||
\(77\) | − | 31309.7i | − | 0.0685814i | ||||||
\(78\) | −120043. | −0.252960 | ||||||||
\(79\) | 434327. | 0.880917 | 0.440459 | − | 0.897773i | \(-0.354816\pi\) | ||||
0.440459 | + | 0.897773i | \(0.354816\pi\) | |||||||
\(80\) | 469391.i | 0.916779i | ||||||||
\(81\) | −170129. | −0.320127 | ||||||||
\(82\) | − | 623800.i | − | 1.13137i | ||||||
\(83\) | 662276. | 1.15826 | 0.579128 | − | 0.815236i | \(-0.303393\pi\) | ||||
0.579128 | + | 0.815236i | \(0.303393\pi\) | |||||||
\(84\) | 16161.4 | 0.0272672 | ||||||||
\(85\) | 1.22041e6i | 1.98723i | ||||||||
\(86\) | −59438.3 | − | 564652.i | −0.0934483 | − | 0.887739i | ||||
\(87\) | −470523. | −0.714535 | ||||||||
\(88\) | 273767.i | 0.401729i | ||||||||
\(89\) | 1.26108e6i | 1.78884i | 0.447223 | + | 0.894422i | \(0.352413\pi\) | ||||
−0.447223 | + | 0.894422i | \(0.647587\pi\) | |||||||
\(90\) | −366621. | −0.502910 | ||||||||
\(91\) | 53496.0i | 0.0709900i | ||||||||
\(92\) | 80703.2 | 0.103640 | ||||||||
\(93\) | − | 532366.i | − | 0.661853i | ||||||
\(94\) | 278538.i | 0.335352i | ||||||||
\(95\) | 1.73616e6 | 2.02497 | ||||||||
\(96\) | −258761. | −0.292473 | ||||||||
\(97\) | 83771.3 | 0.0917868 | 0.0458934 | − | 0.998946i | \(-0.485387\pi\) | ||||
0.0458934 | + | 0.998946i | \(0.485387\pi\) | |||||||
\(98\) | − | 811906.i | − | 0.862635i | ||||||
\(99\) | −168510. | −0.173668 | ||||||||
\(100\) | −95986.5 | −0.0959865 | ||||||||
\(101\) | 1.19842e6 | 1.16318 | 0.581588 | − | 0.813483i | \(-0.302432\pi\) | ||||
0.581588 | + | 0.813483i | \(0.302432\pi\) | |||||||
\(102\) | 1.13546e6 | 1.06997 | ||||||||
\(103\) | 737144. | 0.674592 | 0.337296 | − | 0.941399i | \(-0.390488\pi\) | ||||
0.337296 | + | 0.941399i | \(0.390488\pi\) | |||||||
\(104\) | − | 467760.i | − | 0.415837i | ||||||
\(105\) | − | 188507.i | − | 0.162840i | ||||||
\(106\) | 1.27234e6i | 1.06829i | ||||||||
\(107\) | −604874. | −0.493758 | −0.246879 | − | 0.969046i | \(-0.579405\pi\) | ||||
−0.246879 | + | 0.969046i | \(0.579405\pi\) | |||||||
\(108\) | − | 274320.i | − | 0.217764i | ||||||
\(109\) | −1.09966e6 | −0.849137 | −0.424569 | − | 0.905396i | \(-0.639574\pi\) | ||||
−0.424569 | + | 0.905396i | \(0.639574\pi\) | |||||||
\(110\) | 539252. | 0.405148 | ||||||||
\(111\) | −466157. | −0.340850 | ||||||||
\(112\) | − | 194621.i | − | 0.138528i | ||||||
\(113\) | 543549.i | 0.376707i | 0.982101 | + | 0.188354i | \(0.0603151\pi\) | ||||
−0.982101 | + | 0.188354i | \(0.939685\pi\) | |||||||
\(114\) | − | 1.61532e6i | − | 1.09030i | ||||||
\(115\) | − | 941326.i | − | 0.618937i | ||||||
\(116\) | − | 309621.i | − | 0.198361i | ||||||
\(117\) | 287917. | 0.179767 | ||||||||
\(118\) | − | 142383.i | − | 0.0866585i | ||||||
\(119\) | − | 506010.i | − | 0.300275i | ||||||
\(120\) | 1.64828e6i | 0.953864i | ||||||||
\(121\) | −1.52371e6 | −0.860092 | ||||||||
\(122\) | 249582. | 0.137447 | ||||||||
\(123\) | − | 1.72624e6i | − | 0.927655i | ||||||
\(124\) | 350316. | 0.183736 | ||||||||
\(125\) | − | 1.25038e6i | − | 0.640197i | ||||||
\(126\) | 152010. | 0.0759908 | ||||||||
\(127\) | −1.48723e6 | −0.726050 | −0.363025 | − | 0.931779i | \(-0.618256\pi\) | ||||
−0.363025 | + | 0.931779i | \(0.618256\pi\) | |||||||
\(128\) | 1.24408e6i | 0.593225i | ||||||||
\(129\) | −164484. | − | 1.56256e6i | −0.0766221 | − | 0.727894i | ||||
\(130\) | −921370. | −0.419377 | ||||||||
\(131\) | − | 1.22120e6i | − | 0.543216i | −0.962408 | − | 0.271608i | \(-0.912445\pi\) | ||
0.962408 | − | 0.271608i | \(-0.0875554\pi\) | |||||||
\(132\) | 127938.i | 0.0556259i | ||||||||
\(133\) | −719856. | −0.305978 | ||||||||
\(134\) | 2.14166e6i | 0.890094i | ||||||||
\(135\) | −3.19968e6 | −1.30048 | ||||||||
\(136\) | 4.42447e6i | 1.75891i | ||||||||
\(137\) | 4.63396e6i | 1.80215i | 0.433663 | + | 0.901075i | \(0.357221\pi\) | ||||
−0.433663 | + | 0.901075i | \(0.642779\pi\) | |||||||
\(138\) | −875809. | −0.333252 | ||||||||
\(139\) | 4.40785e6 | 1.64128 | 0.820640 | − | 0.571445i | \(-0.193617\pi\) | ||||
0.820640 | + | 0.571445i | \(0.193617\pi\) | |||||||
\(140\) | 124045. | 0.0452057 | ||||||||
\(141\) | 770799.i | 0.274969i | ||||||||
\(142\) | −2.58761e6 | −0.903718 | ||||||||
\(143\) | −423488. | −0.144822 | ||||||||
\(144\) | −1.04746e6 | −0.350791 | ||||||||
\(145\) | −3.61144e6 | −1.18461 | ||||||||
\(146\) | −642355. | −0.206403 | ||||||||
\(147\) | − | 2.24679e6i | − | 0.707310i | ||||||
\(148\) | − | 306748.i | − | 0.0946231i | ||||||
\(149\) | 285992.i | 0.0864560i | 0.999065 | + | 0.0432280i | \(0.0137642\pi\) | ||||
−0.999065 | + | 0.0432280i | \(0.986236\pi\) | |||||||
\(150\) | 1.04167e6 | 0.308642 | ||||||||
\(151\) | 663208.i | 0.192628i | 0.995351 | + | 0.0963139i | \(0.0307053\pi\) | ||||
−0.995351 | + | 0.0963139i | \(0.969295\pi\) | |||||||
\(152\) | 6.29430e6 | 1.79233 | ||||||||
\(153\) | −2.72336e6 | −0.760381 | ||||||||
\(154\) | −223587. | −0.0612188 | ||||||||
\(155\) | − | 4.08610e6i | − | 1.09727i | ||||||
\(156\) | − | 218596.i | − | 0.0575795i | ||||||
\(157\) | − | 5.29376e6i | − | 1.36793i | −0.729513 | − | 0.683967i | \(-0.760253\pi\) | ||
0.729513 | − | 0.683967i | \(-0.239747\pi\) | |||||||
\(158\) | − | 3.10159e6i | − | 0.786346i | ||||||
\(159\) | 3.52096e6i | 0.875931i | ||||||||
\(160\) | −1.98609e6 | −0.484884 | ||||||||
\(161\) | 390297.i | 0.0935229i | ||||||||
\(162\) | 1.21492e6i | 0.285760i | ||||||||
\(163\) | − | 3.06833e6i | − | 0.708499i | −0.935151 | − | 0.354250i | \(-0.884736\pi\) | ||
0.935151 | − | 0.354250i | \(-0.115264\pi\) | |||||||
\(164\) | 1.13593e6 | 0.257525 | ||||||||
\(165\) | 1.49227e6 | 0.332198 | ||||||||
\(166\) | − | 4.72942e6i | − | 1.03391i | ||||||
\(167\) | 3.30726e6 | 0.710100 | 0.355050 | − | 0.934847i | \(-0.384464\pi\) | ||||
0.355050 | + | 0.934847i | \(0.384464\pi\) | |||||||
\(168\) | − | 683416.i | − | 0.144131i | ||||||
\(169\) | −4.10323e6 | −0.850092 | ||||||||
\(170\) | 8.71510e6 | 1.77389 | ||||||||
\(171\) | 3.87429e6i | 0.774825i | ||||||||
\(172\) | 1.02822e6 | − | 108236.i | 0.202070 | − | 0.0212710i | ||||
\(173\) | 4.04583e6 | 0.781393 | 0.390696 | − | 0.920520i | \(-0.372234\pi\) | ||||
0.390696 | + | 0.920520i | \(0.372234\pi\) | |||||||
\(174\) | 3.36008e6i | 0.637825i | ||||||||
\(175\) | − | 464210.i | − | 0.0866165i | ||||||
\(176\) | 1.54067e6 | 0.282600 | ||||||||
\(177\) | − | 394016.i | − | 0.0710549i | ||||||
\(178\) | 9.00557e6 | 1.59680 | ||||||||
\(179\) | 1.00806e7i | 1.75763i | 0.477160 | + | 0.878816i | \(0.341666\pi\) | ||||
−0.477160 | + | 0.878816i | \(0.658334\pi\) | |||||||
\(180\) | − | 667612.i | − | 0.114474i | ||||||
\(181\) | −7.62117e6 | −1.28524 | −0.642622 | − | 0.766183i | \(-0.722154\pi\) | ||||
−0.642622 | + | 0.766183i | \(0.722154\pi\) | |||||||
\(182\) | 382023. | 0.0633688 | ||||||||
\(183\) | 690669. | 0.112698 | ||||||||
\(184\) | − | 3.41270e6i | − | 0.547828i | ||||||
\(185\) | −3.57793e6 | −0.565088 | ||||||||
\(186\) | −3.80171e6 | −0.590800 | ||||||||
\(187\) | 4.00571e6 | 0.612569 | ||||||||
\(188\) | −507213. | −0.0763339 | ||||||||
\(189\) | 1.32667e6 | 0.196506 | ||||||||
\(190\) | − | 1.23982e7i | − | 1.80758i | ||||||
\(191\) | 9.84078e6i | 1.41231i | 0.708058 | + | 0.706154i | \(0.249571\pi\) | ||||
−0.708058 | + | 0.706154i | \(0.750429\pi\) | |||||||
\(192\) | 5.76181e6i | 0.814058i | ||||||||
\(193\) | 2.29302e6 | 0.318960 | 0.159480 | − | 0.987201i | \(-0.449018\pi\) | ||||
0.159480 | + | 0.987201i | \(0.449018\pi\) | |||||||
\(194\) | − | 598224.i | − | 0.0819329i | ||||||
\(195\) | −2.54971e6 | −0.343864 | ||||||||
\(196\) | 1.47847e6 | 0.196356 | ||||||||
\(197\) | 3.50465e6 | 0.458401 | 0.229201 | − | 0.973379i | \(-0.426389\pi\) | ||||
0.229201 | + | 0.973379i | \(0.426389\pi\) | |||||||
\(198\) | 1.20335e6i | 0.155024i | ||||||||
\(199\) | 7.63511e6i | 0.968849i | 0.874833 | + | 0.484425i | \(0.160971\pi\) | ||||
−0.874833 | + | 0.484425i | \(0.839029\pi\) | |||||||
\(200\) | 4.05898e6i | 0.507372i | ||||||||
\(201\) | 5.92662e6i | 0.729825i | ||||||||
\(202\) | − | 8.55811e6i | − | 1.03830i | ||||||
\(203\) | 1.49739e6 | 0.178998 | ||||||||
\(204\) | 2.06766e6i | 0.243551i | ||||||||
\(205\) | − | 1.32495e7i | − | 1.53794i | ||||||
\(206\) | − | 5.26406e6i | − | 0.602170i | ||||||
\(207\) | 2.10059e6 | 0.236827 | ||||||||
\(208\) | −2.63241e6 | −0.292525 | ||||||||
\(209\) | − | 5.69857e6i | − | 0.624205i | ||||||
\(210\) | −1.34616e6 | −0.145358 | ||||||||
\(211\) | 1.06028e7i | 1.12869i | 0.825540 | + | 0.564344i | \(0.190871\pi\) | ||||
−0.825540 | + | 0.564344i | \(0.809129\pi\) | |||||||
\(212\) | −2.31692e6 | −0.243166 | ||||||||
\(213\) | −7.16069e6 | −0.740996 | ||||||||
\(214\) | 4.31950e6i | 0.440750i | ||||||||
\(215\) | −1.26247e6 | − | 1.19932e7i | −0.127030 | − | 1.20676i | ||||
\(216\) | −1.16001e7 | −1.15107 | ||||||||
\(217\) | 1.69420e6i | 0.165800i | ||||||||
\(218\) | 7.85282e6i | 0.757978i | ||||||||
\(219\) | −1.77759e6 | −0.169238 | ||||||||
\(220\) | 981969.i | 0.0922210i | ||||||||
\(221\) | −6.84419e6 | −0.634082 | ||||||||
\(222\) | 3.32890e6i | 0.304258i | ||||||||
\(223\) | − | 6.78272e6i | − | 0.611631i | −0.952091 | − | 0.305815i | \(-0.901071\pi\) | ||
0.952091 | − | 0.305815i | \(-0.0989290\pi\) | |||||||
\(224\) | 823481. | 0.0732671 | ||||||||
\(225\) | −2.49839e6 | −0.219338 | ||||||||
\(226\) | 3.88157e6 | 0.336265 | ||||||||
\(227\) | − | 2.30718e6i | − | 0.197244i | −0.995125 | − | 0.0986220i | \(-0.968557\pi\) | ||
0.995125 | − | 0.0986220i | \(-0.0314435\pi\) | |||||||
\(228\) | 2.94148e6 | 0.248177 | ||||||||
\(229\) | −3.28542e6 | −0.273580 | −0.136790 | − | 0.990600i | \(-0.543679\pi\) | ||||
−0.136790 | + | 0.990600i | \(0.543679\pi\) | |||||||
\(230\) | −6.72215e6 | −0.552491 | ||||||||
\(231\) | −618733. | −0.0501958 | ||||||||
\(232\) | −1.30930e7 | −1.04851 | ||||||||
\(233\) | − | 1.01559e6i | − | 0.0802878i | −0.999194 | − | 0.0401439i | \(-0.987218\pi\) | ||
0.999194 | − | 0.0401439i | \(-0.0127816\pi\) | |||||||
\(234\) | − | 2.05606e6i | − | 0.160468i | ||||||
\(235\) | 5.91616e6i | 0.455865i | ||||||||
\(236\) | 259277. | 0.0197255 | ||||||||
\(237\) | − | 8.58304e6i | − | 0.644757i | ||||||
\(238\) | −3.61350e6 | −0.268038 | ||||||||
\(239\) | 1.27984e7 | 0.937479 | 0.468740 | − | 0.883336i | \(-0.344708\pi\) | ||||
0.468740 | + | 0.883336i | \(0.344708\pi\) | |||||||
\(240\) | 9.27598e6 | 0.671005 | ||||||||
\(241\) | 7.77825e6i | 0.555688i | 0.960626 | + | 0.277844i | \(0.0896198\pi\) | ||||
−0.960626 | + | 0.277844i | \(0.910380\pi\) | |||||||
\(242\) | 1.08810e7i | 0.767756i | ||||||||
\(243\) | − | 1.20163e7i | − | 0.837438i | ||||||
\(244\) | 454485.i | 0.0312860i | ||||||||
\(245\) | − | 1.72449e7i | − | 1.17263i | ||||||
\(246\) | −1.23274e7 | −0.828066 | ||||||||
\(247\) | 9.73662e6i | 0.646127i | ||||||||
\(248\) | − | 1.48138e7i | − | 0.971207i | ||||||
\(249\) | − | 1.30877e7i | − | 0.847746i | ||||||
\(250\) | −8.92919e6 | −0.571468 | ||||||||
\(251\) | 1.19067e7 | 0.752956 | 0.376478 | − | 0.926425i | \(-0.377135\pi\) | ||||
0.376478 | + | 0.926425i | \(0.377135\pi\) | |||||||
\(252\) | 276808.i | 0.0172973i | ||||||||
\(253\) | −3.08970e6 | −0.190789 | ||||||||
\(254\) | 1.06205e7i | 0.648104i | ||||||||
\(255\) | 2.41173e7 | 1.45448 | ||||||||
\(256\) | −9.77590e6 | −0.582689 | ||||||||
\(257\) | − | 6.20650e6i | − | 0.365635i | −0.983147 | − | 0.182817i | \(-0.941478\pi\) | ||
0.983147 | − | 0.182817i | \(-0.0585217\pi\) | |||||||
\(258\) | −1.11585e7 | + | 1.17460e6i | −0.649750 | + | 0.0683963i | ||||
\(259\) | 1.48350e6 | 0.0853861 | ||||||||
\(260\) | − | 1.67780e6i | − | 0.0954598i | ||||||
\(261\) | − | 8.05901e6i | − | 0.453273i | ||||||
\(262\) | −8.72076e6 | −0.484898 | ||||||||
\(263\) | 1.56294e7i | 0.859162i | 0.903028 | + | 0.429581i | \(0.141339\pi\) | ||||
−0.903028 | + | 0.429581i | \(0.858661\pi\) | |||||||
\(264\) | 5.41010e6 | 0.294032 | ||||||||
\(265\) | 2.70247e7i | 1.45219i | ||||||||
\(266\) | 5.14060e6i | 0.273130i | ||||||||
\(267\) | 2.49211e7 | 1.30928 | ||||||||
\(268\) | −3.89993e6 | −0.202606 | ||||||||
\(269\) | −2.69821e7 | −1.38618 | −0.693090 | − | 0.720851i | \(-0.743751\pi\) | ||||
−0.693090 | + | 0.720851i | \(0.743751\pi\) | |||||||
\(270\) | 2.28494e7i | 1.16087i | ||||||||
\(271\) | 2.23391e7 | 1.12243 | 0.561213 | − | 0.827672i | \(-0.310335\pi\) | ||||
0.561213 | + | 0.827672i | \(0.310335\pi\) | |||||||
\(272\) | 2.48995e7 | 1.23733 | ||||||||
\(273\) | 1.05717e6 | 0.0519587 | ||||||||
\(274\) | 3.30919e7 | 1.60868 | ||||||||
\(275\) | 3.67481e6 | 0.176700 | ||||||||
\(276\) | − | 1.59484e6i | − | 0.0758558i | ||||||
\(277\) | 3.66692e7i | 1.72529i | 0.505812 | + | 0.862644i | \(0.331193\pi\) | ||||
−0.505812 | + | 0.862644i | \(0.668807\pi\) | |||||||
\(278\) | − | 3.14772e7i | − | 1.46508i | ||||||
\(279\) | 9.11824e6 | 0.419854 | ||||||||
\(280\) | − | 5.24547e6i | − | 0.238952i | ||||||
\(281\) | −3.37401e7 | −1.52065 | −0.760323 | − | 0.649546i | \(-0.774959\pi\) | ||||
−0.760323 | + | 0.649546i | \(0.774959\pi\) | |||||||
\(282\) | 5.50439e6 | 0.245449 | ||||||||
\(283\) | −1.38133e7 | −0.609448 | −0.304724 | − | 0.952441i | \(-0.598564\pi\) | ||||
−0.304724 | + | 0.952441i | \(0.598564\pi\) | |||||||
\(284\) | − | 4.71199e6i | − | 0.205707i | ||||||
\(285\) | − | 3.43096e7i | − | 1.48211i | ||||||
\(286\) | 3.02420e6i | 0.129274i | ||||||||
\(287\) | 5.49359e6i | 0.232386i | ||||||||
\(288\) | − | 4.43200e6i | − | 0.185533i | ||||||
\(289\) | 4.06006e7 | 1.68205 | ||||||||
\(290\) | 2.57898e7i | 1.05744i | ||||||||
\(291\) | − | 1.65547e6i | − | 0.0671802i | ||||||
\(292\) | − | 1.16972e6i | − | 0.0469821i | ||||||
\(293\) | 3.07684e7 | 1.22321 | 0.611605 | − | 0.791163i | \(-0.290524\pi\) | ||||
0.611605 | + | 0.791163i | \(0.290524\pi\) | |||||||
\(294\) | −1.60447e7 | −0.631377 | ||||||||
\(295\) | − | 3.02421e6i | − | 0.117800i | ||||||
\(296\) | −1.29715e7 | −0.500165 | ||||||||
\(297\) | 1.05022e7i | 0.400878i | ||||||||
\(298\) | 2.04231e6 | 0.0771744 | ||||||||
\(299\) | 5.27908e6 | 0.197490 | ||||||||
\(300\) | 1.89686e6i | 0.0702540i | ||||||||
\(301\) | 523453. | + | 4.97269e6i | 0.0191946 | + | 0.182344i | ||||
\(302\) | 4.73607e6 | 0.171948 | ||||||||
\(303\) | − | 2.36829e7i | − | 0.851347i | ||||||
\(304\) | − | 3.54223e7i | − | 1.26083i | ||||||
\(305\) | 5.30114e6 | 0.186840 | ||||||||
\(306\) | 1.94480e7i | 0.678750i | ||||||||
\(307\) | 1.70554e7 | 0.589450 | 0.294725 | − | 0.955582i | \(-0.404772\pi\) | ||||
0.294725 | + | 0.955582i | \(0.404772\pi\) | |||||||
\(308\) | − | 407149.i | − | 0.0139348i | ||||||
\(309\) | − | 1.45672e7i | − | 0.493744i | ||||||
\(310\) | −2.91795e7 | −0.979474 | ||||||||
\(311\) | −1.62947e7 | −0.541709 | −0.270855 | − | 0.962620i | \(-0.587306\pi\) | ||||
−0.270855 | + | 0.962620i | \(0.587306\pi\) | |||||||
\(312\) | −9.24375e6 | −0.304358 | ||||||||
\(313\) | 3.82726e7i | 1.24811i | 0.781379 | + | 0.624057i | \(0.214517\pi\) | ||||
−0.781379 | + | 0.624057i | \(0.785483\pi\) | |||||||
\(314\) | −3.78035e7 | −1.22108 | ||||||||
\(315\) | 3.22870e6 | 0.103299 | ||||||||
\(316\) | 5.64795e6 | 0.178990 | ||||||||
\(317\) | −3.73589e7 | −1.17278 | −0.586390 | − | 0.810029i | \(-0.699452\pi\) | ||||
−0.586390 | + | 0.810029i | \(0.699452\pi\) | |||||||
\(318\) | 2.51437e7 | 0.781895 | ||||||||
\(319\) | 1.18538e7i | 0.365160i | ||||||||
\(320\) | 4.42240e7i | 1.34961i | ||||||||
\(321\) | 1.19534e7i | 0.361389i | ||||||||
\(322\) | 2.78717e6 | 0.0834826 | ||||||||
\(323\) | − | 9.20972e7i | − | 2.73300i | ||||||
\(324\) | −2.21234e6 | −0.0650455 | ||||||||
\(325\) | −6.27881e6 | −0.182906 | ||||||||
\(326\) | −2.19114e7 | −0.632438 | ||||||||
\(327\) | 2.17311e7i | 0.621497i | ||||||||
\(328\) | − | 4.80350e7i | − | 1.36125i | ||||||
\(329\) | − | 2.45299e6i | − | 0.0688823i | ||||||
\(330\) | − | 1.06565e7i | − | 0.296534i | ||||||
\(331\) | − | 5.23966e7i | − | 1.44484i | −0.691455 | − | 0.722419i | \(-0.743030\pi\) | ||
0.691455 | − | 0.722419i | \(-0.256970\pi\) | |||||||
\(332\) | 8.61219e6 | 0.235342 | ||||||||
\(333\) | − | 7.98423e6i | − | 0.216222i | ||||||
\(334\) | − | 2.36177e7i | − | 0.633866i | ||||||
\(335\) | 4.54889e7i | 1.20996i | ||||||||
\(336\) | −3.84605e6 | −0.101390 | ||||||||
\(337\) | −1.79657e7 | −0.469413 | −0.234706 | − | 0.972066i | \(-0.575413\pi\) | ||||
−0.234706 | + | 0.972066i | \(0.575413\pi\) | |||||||
\(338\) | 2.93018e7i | 0.758830i | ||||||||
\(339\) | 1.07415e7 | 0.275718 | ||||||||
\(340\) | 1.58701e7i | 0.403777i | ||||||||
\(341\) | −1.34117e7 | −0.338238 | ||||||||
\(342\) | 2.76669e7 | 0.691643 | ||||||||
\(343\) | 1.45491e7i | 0.360540i | ||||||||
\(344\) | −4.57699e6 | − | 4.34804e7i | −0.112436 | − | 1.06812i | ||||
\(345\) | −1.86022e7 | −0.453010 | ||||||||
\(346\) | − | 2.88919e7i | − | 0.697506i | ||||||
\(347\) | 1.42201e7i | 0.340342i | 0.985415 | + | 0.170171i | \(0.0544319\pi\) | ||||
−0.985415 | + | 0.170171i | \(0.945568\pi\) | |||||||
\(348\) | −6.11865e6 | −0.145184 | ||||||||
\(349\) | 5.94543e7i | 1.39864i | 0.714807 | + | 0.699322i | \(0.246515\pi\) | ||||
−0.714807 | + | 0.699322i | \(0.753485\pi\) | |||||||
\(350\) | −3.31500e6 | −0.0773177 | ||||||||
\(351\) | − | 1.79442e7i | − | 0.414957i | ||||||
\(352\) | 6.51889e6i | 0.149467i | ||||||||
\(353\) | −4.22812e7 | −0.961222 | −0.480611 | − | 0.876934i | \(-0.659585\pi\) | ||||
−0.480611 | + | 0.876934i | \(0.659585\pi\) | |||||||
\(354\) | −2.81373e6 | −0.0634267 | ||||||||
\(355\) | −5.49609e7 | −1.22848 | ||||||||
\(356\) | 1.63990e7i | 0.363469i | ||||||||
\(357\) | −9.99964e6 | −0.219776 | ||||||||
\(358\) | 7.19873e7 | 1.56894 | ||||||||
\(359\) | −4.65626e6 | −0.100636 | −0.0503181 | − | 0.998733i | \(-0.516024\pi\) | ||||
−0.0503181 | + | 0.998733i | \(0.516024\pi\) | |||||||
\(360\) | −2.82313e7 | −0.605094 | ||||||||
\(361\) | −8.39726e7 | −1.78491 | ||||||||
\(362\) | 5.44239e7i | 1.14727i | ||||||||
\(363\) | 3.01110e7i | 0.629515i | ||||||||
\(364\) | 695658.i | 0.0144242i | ||||||||
\(365\) | −1.36436e7 | −0.280577 | ||||||||
\(366\) | − | 4.93218e6i | − | 0.100599i | ||||||
\(367\) | 8.70497e7 | 1.76104 | 0.880519 | − | 0.474010i | \(-0.157194\pi\) | ||||
0.880519 | + | 0.474010i | \(0.157194\pi\) | |||||||
\(368\) | −1.92056e7 | −0.385375 | ||||||||
\(369\) | 2.95667e7 | 0.588469 | ||||||||
\(370\) | 2.55505e7i | 0.504423i | ||||||||
\(371\) | − | 1.12051e7i | − | 0.219429i | ||||||
\(372\) | − | 6.92285e6i | − | 0.134480i | ||||||
\(373\) | 7.31787e7i | 1.41013i | 0.709144 | + | 0.705064i | \(0.249082\pi\) | ||||
−0.709144 | + | 0.705064i | \(0.750918\pi\) | |||||||
\(374\) | − | 2.86054e7i | − | 0.546806i | ||||||
\(375\) | −2.47098e7 | −0.468570 | ||||||||
\(376\) | 2.14485e7i | 0.403491i | ||||||||
\(377\) | − | 2.02534e7i | − | 0.377985i | ||||||
\(378\) | − | 9.47392e6i | − | 0.175410i | ||||||
\(379\) | 6.34098e7 | 1.16477 | 0.582383 | − | 0.812914i | \(-0.302120\pi\) | ||||
0.582383 | + | 0.812914i | \(0.302120\pi\) | |||||||
\(380\) | 2.25769e7 | 0.411447 | ||||||||
\(381\) | 2.93902e7i | 0.531407i | ||||||||
\(382\) | 7.02745e7 | 1.26069 | ||||||||
\(383\) | 3.12303e7i | 0.555878i | 0.960599 | + | 0.277939i | \(0.0896514\pi\) | ||||
−0.960599 | + | 0.277939i | \(0.910349\pi\) | |||||||
\(384\) | 2.45852e7 | 0.434191 | ||||||||
\(385\) | −4.74900e6 | −0.0832186 | ||||||||
\(386\) | − | 1.63748e7i | − | 0.284718i | ||||||
\(387\) | 2.67632e7 | − | 2.81724e6i | 0.461748 | − | 0.0486061i | ||||
\(388\) | 1.08936e6 | 0.0186498 | ||||||||
\(389\) | − | 8.33816e7i | − | 1.41652i | −0.705954 | − | 0.708258i | \(-0.749481\pi\) | ||
0.705954 | − | 0.708258i | \(-0.250519\pi\) | |||||||
\(390\) | 1.82079e7i | 0.306948i | ||||||||
\(391\) | −4.99340e7 | −0.835346 | ||||||||
\(392\) | − | 6.25199e7i | − | 1.03791i | ||||||
\(393\) | −2.41330e7 | −0.397588 | ||||||||
\(394\) | − | 2.50272e7i | − | 0.409189i | ||||||
\(395\) | − | 6.58780e7i | − | 1.06893i | ||||||
\(396\) | −2.19129e6 | −0.0352869 | ||||||||
\(397\) | 5.18629e7 | 0.828868 | 0.414434 | − | 0.910079i | \(-0.363980\pi\) | ||||
0.414434 | + | 0.910079i | \(0.363980\pi\) | |||||||
\(398\) | 5.45235e7 | 0.864838 | ||||||||
\(399\) | 1.42256e7i | 0.223950i | ||||||||
\(400\) | 2.28426e7 | 0.356916 | ||||||||
\(401\) | −7.16633e7 | −1.11138 | −0.555692 | − | 0.831389i | \(-0.687546\pi\) | ||||
−0.555692 | + | 0.831389i | \(0.687546\pi\) | |||||||
\(402\) | 4.23229e7 | 0.651474 | ||||||||
\(403\) | 2.29154e7 | 0.350117 | ||||||||
\(404\) | 1.55842e7 | 0.236342 | ||||||||
\(405\) | 2.58049e7i | 0.388451i | ||||||||
\(406\) | − | 1.06931e7i | − | 0.159781i | ||||||
\(407\) | 1.17438e7i | 0.174190i | ||||||||
\(408\) | 8.74352e7 | 1.28738 | ||||||||
\(409\) | − | 7.67014e7i | − | 1.12107i | −0.828130 | − | 0.560536i | \(-0.810595\pi\) | ||
0.828130 | − | 0.560536i | \(-0.189405\pi\) | |||||||
\(410\) | −9.46170e7 | −1.37283 | ||||||||
\(411\) | 9.15751e7 | 1.31902 | ||||||||
\(412\) | 9.58577e6 | 0.137068 | ||||||||
\(413\) | 1.25391e6i | 0.0177999i | ||||||||
\(414\) | − | 1.50007e7i | − | 0.211402i | ||||||
\(415\) | − | 1.00453e8i | − | 1.40546i | ||||||
\(416\) | − | 1.11382e7i | − | 0.154716i | ||||||
\(417\) | − | 8.71068e7i | − | 1.20128i | ||||||
\(418\) | −4.06944e7 | −0.557193 | ||||||||
\(419\) | 1.21037e8i | 1.64542i | 0.568463 | + | 0.822709i | \(0.307538\pi\) | ||||
−0.568463 | + | 0.822709i | \(0.692462\pi\) | |||||||
\(420\) | − | 2.45133e6i | − | 0.0330868i | ||||||
\(421\) | − | 9.79470e7i | − | 1.31264i | −0.754484 | − | 0.656319i | \(-0.772113\pi\) | ||
0.754484 | − | 0.656319i | \(-0.227887\pi\) | |||||||
\(422\) | 7.57163e7 | 1.00752 | ||||||||
\(423\) | −1.32021e7 | −0.174430 | ||||||||
\(424\) | 9.79755e7i | 1.28535i | ||||||||
\(425\) | 5.93903e7 | 0.773658 | ||||||||
\(426\) | 5.11356e7i | 0.661446i | ||||||||
\(427\) | −2.19798e6 | −0.0282319 | ||||||||
\(428\) | −7.86574e6 | −0.100325 | ||||||||
\(429\) | 8.36886e6i | 0.105997i | ||||||||
\(430\) | −8.56455e7 | + | 9.01551e6i | −1.07721 | + | 0.113393i | ||||
\(431\) | −1.07153e8 | −1.33836 | −0.669180 | − | 0.743100i | \(-0.733355\pi\) | ||||
−0.669180 | + | 0.743100i | \(0.733355\pi\) | |||||||
\(432\) | 6.52820e7i | 0.809733i | ||||||||
\(433\) | 6.76798e7i | 0.833672i | 0.908982 | + | 0.416836i | \(0.136861\pi\) | ||||
−0.908982 | + | 0.416836i | \(0.863139\pi\) | |||||||
\(434\) | 1.20985e7 | 0.148001 | ||||||||
\(435\) | 7.13683e7i | 0.867036i | ||||||||
\(436\) | −1.42999e7 | −0.172533 | ||||||||
\(437\) | 7.10367e7i | 0.851213i | ||||||||
\(438\) | 1.26940e7i | 0.151070i | ||||||||
\(439\) | −4.94825e7 | −0.584868 | −0.292434 | − | 0.956286i | \(-0.594465\pi\) | ||||
−0.292434 | + | 0.956286i | \(0.594465\pi\) | |||||||
\(440\) | 4.15245e7 | 0.487468 | ||||||||
\(441\) | 3.84824e7 | 0.448690 | ||||||||
\(442\) | 4.88754e7i | 0.566010i | ||||||||
\(443\) | −1.18835e8 | −1.36689 | −0.683446 | − | 0.730001i | \(-0.739520\pi\) | ||||
−0.683446 | + | 0.730001i | \(0.739520\pi\) | |||||||
\(444\) | −6.06188e6 | −0.0692561 | ||||||||
\(445\) | 1.91279e8 | 2.17063 | ||||||||
\(446\) | −4.84365e7 | −0.545969 | ||||||||
\(447\) | 5.65170e6 | 0.0632785 | ||||||||
\(448\) | − | 1.83364e7i | − | 0.203929i | ||||||
\(449\) | 4.56263e7i | 0.504054i | 0.967720 | + | 0.252027i | \(0.0810971\pi\) | ||||
−0.967720 | + | 0.252027i | \(0.918903\pi\) | |||||||
\(450\) | 1.78414e7i | 0.195791i | ||||||||
\(451\) | −4.34887e7 | −0.474075 | ||||||||
\(452\) | 7.06828e6i | 0.0765418i | ||||||||
\(453\) | 1.31061e7 | 0.140987 | ||||||||
\(454\) | −1.64759e7 | −0.176069 | ||||||||
\(455\) | 8.11419e6 | 0.0861412 | ||||||||
\(456\) | − | 1.24386e8i | − | 1.31183i | ||||||
\(457\) | − | 1.21404e8i | − | 1.27199i | −0.771693 | − | 0.635996i | \(-0.780590\pi\) | ||
0.771693 | − | 0.635996i | \(-0.219410\pi\) | |||||||
\(458\) | 2.34617e7i | 0.244209i | ||||||||
\(459\) | 1.69732e8i | 1.75519i | ||||||||
\(460\) | − | 1.22409e7i | − | 0.125760i | ||||||
\(461\) | −1.90871e8 | −1.94821 | −0.974106 | − | 0.226093i | \(-0.927405\pi\) | ||||
−0.974106 | + | 0.226093i | \(0.927405\pi\) | |||||||
\(462\) | 4.41847e6i | 0.0448070i | ||||||||
\(463\) | − | 8.17525e6i | − | 0.0823680i | −0.999152 | − | 0.0411840i | \(-0.986887\pi\) | ||
0.999152 | − | 0.0411840i | \(-0.0131130\pi\) | |||||||
\(464\) | 7.36830e7i | 0.737587i | ||||||||
\(465\) | −8.07485e7 | −0.803111 | ||||||||
\(466\) | −7.25247e6 | −0.0716684 | ||||||||
\(467\) | − | 1.86571e8i | − | 1.83186i | −0.401334 | − | 0.915932i | \(-0.631453\pi\) | ||
0.401334 | − | 0.915932i | \(-0.368547\pi\) | |||||||
\(468\) | 3.74405e6 | 0.0365262 | ||||||||
\(469\) | − | 1.88608e7i | − | 0.182828i | ||||||
\(470\) | 4.22482e7 | 0.406925 | ||||||||
\(471\) | −1.04614e8 | −1.00121 | ||||||||
\(472\) | − | 1.09640e7i | − | 0.104266i | ||||||
\(473\) | −3.93652e7 | + | 4.14379e6i | −0.371988 | + | 0.0391574i | ||||
\(474\) | −6.12928e7 | −0.575539 | ||||||||
\(475\) | − | 8.44893e7i | − | 0.788353i | ||||||
\(476\) | − | 6.58012e6i | − | 0.0610117i | ||||||
\(477\) | −6.03062e7 | −0.555657 | ||||||||
\(478\) | − | 9.13952e7i | − | 0.836835i | ||||||
\(479\) | 1.51306e8 | 1.37673 | 0.688365 | − | 0.725364i | \(-0.258329\pi\) | ||||
0.688365 | + | 0.725364i | \(0.258329\pi\) | |||||||
\(480\) | 3.92485e7i | 0.354894i | ||||||||
\(481\) | − | 2.00655e7i | − | 0.180308i | ||||||
\(482\) | 5.55457e7 | 0.496031 | ||||||||
\(483\) | 7.71295e6 | 0.0684509 | ||||||||
\(484\) | −1.98142e7 | −0.174759 | ||||||||
\(485\) | − | 1.27063e7i | − | 0.111377i | ||||||
\(486\) | −8.58103e7 | −0.747534 | ||||||||
\(487\) | 1.17577e8 | 1.01797 | 0.508984 | − | 0.860776i | \(-0.330021\pi\) | ||||
0.508984 | + | 0.860776i | \(0.330021\pi\) | |||||||
\(488\) | 1.92188e7 | 0.165374 | ||||||||
\(489\) | −6.06355e7 | −0.518562 | ||||||||
\(490\) | −1.23149e8 | −1.04675 | ||||||||
\(491\) | 1.63911e7i | 0.138472i | 0.997600 | + | 0.0692362i | \(0.0220562\pi\) | ||||
−0.997600 | + | 0.0692362i | \(0.977944\pi\) | |||||||
\(492\) | − | 2.24479e7i | − | 0.188487i | ||||||
\(493\) | 1.91574e8i | 1.59881i | ||||||||
\(494\) | 6.95307e7 | 0.576761 | ||||||||
\(495\) | 2.55593e7i | 0.210733i | ||||||||
\(496\) | −8.33675e7 | −0.683206 | ||||||||
\(497\) | 2.27881e7 | 0.185626 | ||||||||
\(498\) | −9.34614e7 | −0.756736 | ||||||||
\(499\) | − | 1.32763e8i | − | 1.06850i | −0.845325 | − | 0.534252i | \(-0.820593\pi\) | ||
0.845325 | − | 0.534252i | \(-0.179407\pi\) | |||||||
\(500\) | − | 1.62599e7i | − | 0.130079i | ||||||
\(501\) | − | 6.53572e7i | − | 0.519733i | ||||||
\(502\) | − | 8.50275e7i | − | 0.672122i | ||||||
\(503\) | 2.13319e8i | 1.67620i | 0.545518 | + | 0.838099i | \(0.316333\pi\) | ||||
−0.545518 | + | 0.838099i | \(0.683667\pi\) | |||||||
\(504\) | 1.17054e7 | 0.0914312 | ||||||||
\(505\) | − | 1.81775e8i | − | 1.41143i | ||||||
\(506\) | 2.20640e7i | 0.170307i | ||||||||
\(507\) | 8.10870e7i | 0.622196i | ||||||||
\(508\) | −1.93398e7 | −0.147523 | ||||||||
\(509\) | 2.22706e8 | 1.68880 | 0.844400 | − | 0.535713i | \(-0.179957\pi\) | ||||
0.844400 | + | 0.535713i | \(0.179957\pi\) | |||||||
\(510\) | − | 1.72225e8i | − | 1.29834i | ||||||
\(511\) | 5.65699e6 | 0.0423958 | ||||||||
\(512\) | 1.49433e8i | 1.11336i | ||||||||
\(513\) | 2.41462e8 | 1.78853 | ||||||||
\(514\) | −4.43216e7 | −0.326382 | ||||||||
\(515\) | − | 1.11809e8i | − | 0.818568i | ||||||
\(516\) | −2.13894e6 | − | 2.03195e7i | −0.0155686 | − | 0.147898i | ||||
\(517\) | 1.94185e7 | 0.140522 | ||||||||
\(518\) | − | 1.05939e7i | − | 0.0762194i | ||||||
\(519\) | − | 7.99526e7i | − | 0.571914i | ||||||
\(520\) | −7.09491e7 | −0.504588 | ||||||||
\(521\) | − | 8.01608e7i | − | 0.566825i | −0.958998 | − | 0.283412i | \(-0.908533\pi\) | ||
0.958998 | − | 0.283412i | \(-0.0914665\pi\) | |||||||
\(522\) | −5.75506e7 | −0.404612 | ||||||||
\(523\) | 1.76645e8i | 1.23480i | 0.786650 | + | 0.617400i | \(0.211814\pi\) | ||||
−0.786650 | + | 0.617400i | \(0.788186\pi\) | |||||||
\(524\) | − | 1.58804e7i | − | 0.110374i | ||||||
\(525\) | −9.17359e6 | −0.0633960 | ||||||||
\(526\) | 1.11612e8 | 0.766926 | ||||||||
\(527\) | −2.16753e8 | −1.48093 | ||||||||
\(528\) | − | 3.04464e7i | − | 0.206840i | ||||||
\(529\) | −1.09521e8 | −0.739825 | ||||||||
\(530\) | 1.92987e8 | 1.29629 | ||||||||
\(531\) | 6.74861e6 | 0.0450745 | ||||||||
\(532\) | −9.36095e6 | −0.0621706 | ||||||||
\(533\) | 7.43052e7 | 0.490724 | ||||||||
\(534\) | − | 1.77966e8i | − | 1.16872i | ||||||
\(535\) | 9.17464e7i | 0.599139i | ||||||||
\(536\) | 1.64916e8i | 1.07095i | ||||||||
\(537\) | 1.99210e8 | 1.28644 | ||||||||
\(538\) | 1.92684e8i | 1.23736i | ||||||||
\(539\) | −5.66026e7 | −0.361468 | ||||||||
\(540\) | −4.16084e7 | −0.264241 | ||||||||
\(541\) | −6.68009e7 | −0.421882 | −0.210941 | − | 0.977499i | \(-0.567653\pi\) | ||||
−0.210941 | + | 0.977499i | \(0.567653\pi\) | |||||||
\(542\) | − | 1.59527e8i | − | 1.00193i | ||||||
\(543\) | 1.50607e8i | 0.940691i | ||||||||
\(544\) | 1.05355e8i | 0.654422i | ||||||||
\(545\) | 1.66794e8i | 1.03037i | ||||||||
\(546\) | − | 7.54944e6i | − | 0.0463806i | ||||||
\(547\) | 1.50528e8 | 0.919718 | 0.459859 | − | 0.887992i | \(-0.347900\pi\) | ||||
0.459859 | + | 0.887992i | \(0.347900\pi\) | |||||||
\(548\) | 6.02598e7i | 0.366172i | ||||||||
\(549\) | 1.18296e7i | 0.0714914i | ||||||||
\(550\) | − | 2.62424e7i | − | 0.157730i | ||||||
\(551\) | 2.72535e8 | 1.62918 | ||||||||
\(552\) | −6.74408e7 | −0.400964 | ||||||||
\(553\) | 2.73146e7i | 0.161518i | ||||||||
\(554\) | 2.61860e8 | 1.54007 | ||||||||
\(555\) | 7.07060e7i | 0.413597i | ||||||||
\(556\) | 5.73194e7 | 0.333486 | ||||||||
\(557\) | 2.12922e8 | 1.23213 | 0.616063 | − | 0.787697i | \(-0.288727\pi\) | ||||
0.616063 | + | 0.787697i | \(0.288727\pi\) | |||||||
\(558\) | − | 6.51148e7i | − | 0.374780i | ||||||
\(559\) | 6.72596e7 | − | 7.08012e6i | 0.385052 | − | 0.0405326i | ||||
\(560\) | −2.95198e7 | −0.168093 | ||||||||
\(561\) | − | 7.91598e7i | − | 0.448349i | ||||||
\(562\) | 2.40943e8i | 1.35739i | ||||||||
\(563\) | −2.20517e8 | −1.23571 | −0.617854 | − | 0.786293i | \(-0.711998\pi\) | ||||
−0.617854 | + | 0.786293i | \(0.711998\pi\) | |||||||
\(564\) | 1.00234e7i | 0.0558700i | ||||||||
\(565\) | 8.24447e7 | 0.457107 | ||||||||
\(566\) | 9.86426e7i | 0.544021i | ||||||||
\(567\) | − | 1.06993e7i | − | 0.0586959i | ||||||
\(568\) | −1.99256e8 | −1.08734 | ||||||||
\(569\) | −7.04114e7 | −0.382214 | −0.191107 | − | 0.981569i | \(-0.561208\pi\) | ||||
−0.191107 | + | 0.981569i | \(0.561208\pi\) | |||||||
\(570\) | −2.45010e8 | −1.32300 | ||||||||
\(571\) | − | 1.62010e8i | − | 0.870230i | −0.900375 | − | 0.435115i | \(-0.856708\pi\) | ||
0.900375 | − | 0.435115i | \(-0.143292\pi\) | |||||||
\(572\) | −5.50701e6 | −0.0294258 | ||||||||
\(573\) | 1.94471e8 | 1.03369 | ||||||||
\(574\) | 3.92306e7 | 0.207438 | ||||||||
\(575\) | −4.58091e7 | −0.240962 | ||||||||
\(576\) | −9.86869e7 | −0.516407 | ||||||||
\(577\) | 1.10893e8i | 0.577267i | 0.957440 | + | 0.288633i | \(0.0932009\pi\) | ||||
−0.957440 | + | 0.288633i | \(0.906799\pi\) | |||||||
\(578\) | − | 2.89935e8i | − | 1.50147i | ||||||
\(579\) | − | 4.53140e7i | − | 0.233452i | ||||||
\(580\) | −4.69629e7 | −0.240697 | ||||||||
\(581\) | 4.16503e7i | 0.212368i | ||||||||
\(582\) | −1.18219e7 | −0.0599680 | ||||||||
\(583\) | 8.87025e7 | 0.447641 | ||||||||
\(584\) | −4.94638e7 | −0.248341 | ||||||||
\(585\) | − | 4.36708e7i | − | 0.218134i | ||||||
\(586\) | − | 2.19722e8i | − | 1.09189i | ||||||
\(587\) | − | 3.50946e8i | − | 1.73510i | −0.497346 | − | 0.867552i | \(-0.665692\pi\) | ||
0.497346 | − | 0.867552i | \(-0.334308\pi\) | |||||||
\(588\) | − | 2.92171e7i | − | 0.143716i | ||||||
\(589\) | 3.08356e8i | 1.50906i | ||||||||
\(590\) | −2.15964e7 | −0.105154 | ||||||||
\(591\) | − | 6.92579e7i | − | 0.335511i | ||||||
\(592\) | 7.29993e7i | 0.351847i | ||||||||
\(593\) | − | 2.22461e8i | − | 1.06682i | −0.845857 | − | 0.533409i | \(-0.820911\pi\) | ||
0.845857 | − | 0.533409i | \(-0.179089\pi\) | |||||||
\(594\) | 7.49981e7 | 0.357842 | ||||||||
\(595\) | −7.67508e7 | −0.364361 | ||||||||
\(596\) | 3.71902e6i | 0.0175667i | ||||||||
\(597\) | 1.50883e8 | 0.709116 | ||||||||
\(598\) | − | 3.76987e7i | − | 0.176288i | ||||||
\(599\) | −1.33213e8 | −0.619818 | −0.309909 | − | 0.950766i | \(-0.600299\pi\) | ||||
−0.309909 | + | 0.950766i | \(0.600299\pi\) | |||||||
\(600\) | 8.02124e7 | 0.371354 | ||||||||
\(601\) | 2.01869e8i | 0.929923i | 0.885331 | + | 0.464961i | \(0.153932\pi\) | ||||
−0.885331 | + | 0.464961i | \(0.846068\pi\) | |||||||
\(602\) | 3.55108e7 | − | 3.73806e6i | 0.162769 | − | 0.0171339i | ||||
\(603\) | −1.01510e8 | −0.462973 | ||||||||
\(604\) | 8.62432e6i | 0.0391394i | ||||||||
\(605\) | 2.31113e8i | 1.04366i | ||||||||
\(606\) | −1.69123e8 | −0.759950 | ||||||||
\(607\) | − | 2.22303e8i | − | 0.993984i | −0.867755 | − | 0.496992i | \(-0.834438\pi\) | ||
0.867755 | − | 0.496992i | \(-0.165562\pi\) | |||||||
\(608\) | 1.49879e8 | 0.666853 | ||||||||
\(609\) | − | 2.95911e7i | − | 0.131011i | ||||||
\(610\) | − | 3.78562e7i | − | 0.166782i | ||||||
\(611\) | −3.31786e7 | −0.145457 | ||||||||
\(612\) | −3.54144e7 | −0.154499 | ||||||||
\(613\) | −1.59462e8 | −0.692272 | −0.346136 | − | 0.938184i | \(-0.612506\pi\) | ||||
−0.346136 | + | 0.938184i | \(0.612506\pi\) | |||||||
\(614\) | − | 1.21795e8i | − | 0.526169i | ||||||
\(615\) | −2.61834e8 | −1.12564 | ||||||||
\(616\) | −1.72171e7 | −0.0736576 | ||||||||
\(617\) | 2.02638e8 | 0.862710 | 0.431355 | − | 0.902182i | \(-0.358036\pi\) | ||||
0.431355 | + | 0.902182i | \(0.358036\pi\) | |||||||
\(618\) | −1.04027e8 | −0.440738 | ||||||||
\(619\) | −3.11733e8 | −1.31435 | −0.657176 | − | 0.753737i | \(-0.728249\pi\) | ||||
−0.657176 | + | 0.753737i | \(0.728249\pi\) | |||||||
\(620\) | − | 5.31354e7i | − | 0.222951i | ||||||
\(621\) | − | 1.30918e8i | − | 0.546668i | ||||||
\(622\) | 1.16363e8i | 0.483554i | ||||||||
\(623\) | −7.93089e7 | −0.327988 | ||||||||
\(624\) | 5.20209e7i | 0.214104i | ||||||||
\(625\) | −3.04990e8 | −1.24924 | ||||||||
\(626\) | 2.73310e8 | 1.11412 | ||||||||
\(627\) | −1.12614e8 | −0.456865 | ||||||||
\(628\) | − | 6.88397e7i | − | 0.277946i | ||||||
\(629\) | 1.89796e8i | 0.762668i | ||||||||
\(630\) | − | 2.30567e7i | − | 0.0922094i | ||||||
\(631\) | 5.37251e7i | 0.213840i | 0.994268 | + | 0.106920i | \(0.0340989\pi\) | ||||
−0.994268 | + | 0.106920i | \(0.965901\pi\) | |||||||
\(632\) | − | 2.38835e8i | − | 0.946120i | ||||||
\(633\) | 2.09530e8 | 0.826105 | ||||||||
\(634\) | 2.66786e8i | 1.04688i | ||||||||
\(635\) | 2.25580e8i | 0.881008i | ||||||||
\(636\) | 4.57863e7i | 0.177977i | ||||||||
\(637\) | 9.67117e7 | 0.374163 | ||||||||
\(638\) | 8.46495e7 | 0.325958 | ||||||||
\(639\) | − | 1.22647e8i | − | 0.470059i | ||||||
\(640\) | 1.88701e8 | 0.719836 | ||||||||
\(641\) | − | 2.85462e8i | − | 1.08386i | −0.840423 | − | 0.541932i | \(-0.817693\pi\) | ||
0.840423 | − | 0.541932i | \(-0.182307\pi\) | |||||||
\(642\) | 8.53608e7 | 0.322592 | ||||||||
\(643\) | 1.02329e7 | 0.0384917 | 0.0192458 | − | 0.999815i | \(-0.493873\pi\) | ||||
0.0192458 | + | 0.999815i | \(0.493873\pi\) | |||||||
\(644\) | 5.07540e6i | 0.0190026i | ||||||||
\(645\) | −2.37007e8 | + | 2.49486e7i | −0.883247 | + | 0.0929754i | ||||
\(646\) | −6.57680e8 | −2.43959 | ||||||||
\(647\) | 3.72540e8i | 1.37550i | 0.725948 | + | 0.687750i | \(0.241401\pi\) | ||||
−0.725948 | + | 0.687750i | \(0.758599\pi\) | |||||||
\(648\) | 9.35532e7i | 0.343822i | ||||||||
\(649\) | −9.92632e6 | −0.0363123 | ||||||||
\(650\) | 4.48380e7i | 0.163270i | ||||||||
\(651\) | 3.34803e7 | 0.121352 | ||||||||
\(652\) | − | 3.99004e7i | − | 0.143957i | ||||||
\(653\) | 4.26942e7i | 0.153331i | 0.997057 | + | 0.0766653i | \(0.0244273\pi\) | ||||
−0.997057 | + | 0.0766653i | \(0.975573\pi\) | |||||||
\(654\) | 1.55185e8 | 0.554776 | ||||||||
\(655\) | −1.85229e8 | −0.659153 | ||||||||
\(656\) | −2.70326e8 | −0.957583 | ||||||||
\(657\) | − | 3.04461e7i | − | 0.107358i | ||||||
\(658\) | −1.75172e7 | −0.0614874 | ||||||||
\(659\) | 5.08637e8 | 1.77726 | 0.888632 | − | 0.458621i | \(-0.151656\pi\) | ||||
0.888632 | + | 0.458621i | \(0.151656\pi\) | |||||||
\(660\) | 1.94054e7 | 0.0674980 | ||||||||
\(661\) | −2.03116e7 | −0.0703299 | −0.0351650 | − | 0.999382i | \(-0.511196\pi\) | ||||
−0.0351650 | + | 0.999382i | \(0.511196\pi\) | |||||||
\(662\) | −3.74172e8 | −1.28973 | ||||||||
\(663\) | 1.35253e8i | 0.464095i | ||||||||
\(664\) | − | 3.64184e8i | − | 1.24399i | ||||||
\(665\) | 1.09187e8i | 0.371282i | ||||||||
\(666\) | −5.70166e7 | −0.193009 | ||||||||
\(667\) | − | 1.47765e8i | − | 0.497961i | ||||||
\(668\) | 4.30074e7 | 0.144283 | ||||||||
\(669\) | −1.34038e8 | −0.447662 | ||||||||
\(670\) | 3.24843e8 | 1.08006 | ||||||||
\(671\) | − | 1.73998e7i | − | 0.0575940i | ||||||
\(672\) | − | 1.62734e7i | − | 0.0536254i | ||||||
\(673\) | 1.75373e8i | 0.575329i | 0.957731 | + | 0.287665i | \(0.0928789\pi\) | ||||
−0.957731 | + | 0.287665i | \(0.907121\pi\) | |||||||
\(674\) | 1.28296e8i | 0.419018i | ||||||||
\(675\) | 1.55710e8i | 0.506298i | ||||||||
\(676\) | −5.33582e7 | −0.172727 | ||||||||
\(677\) | − | 5.93350e8i | − | 1.91225i | −0.292956 | − | 0.956126i | \(-0.594639\pi\) | ||
0.292956 | − | 0.956126i | \(-0.405361\pi\) | |||||||
\(678\) | − | 7.67065e7i | − | 0.246118i | ||||||
\(679\) | 5.26835e6i | 0.0168293i | ||||||||
\(680\) | 6.71097e8 | 2.13432 | ||||||||
\(681\) | −4.55939e7 | −0.144366 | ||||||||
\(682\) | 9.57753e7i | 0.301926i | ||||||||
\(683\) | −3.53734e8 | −1.11024 | −0.555118 | − | 0.831772i | \(-0.687327\pi\) | ||||
−0.555118 | + | 0.831772i | \(0.687327\pi\) | |||||||
\(684\) | 5.03810e7i | 0.157434i | ||||||||
\(685\) | 7.02872e8 | 2.18678 | ||||||||
\(686\) | 1.03897e8 | 0.321834 | ||||||||
\(687\) | 6.49255e7i | 0.200237i | ||||||||
\(688\) | −2.44694e8 | + | 2.57578e7i | −0.751377 | + | 0.0790941i | ||||
\(689\) | −1.51558e8 | −0.463362 | ||||||||
\(690\) | 1.32841e8i | 0.404377i | ||||||||
\(691\) | 8.65200e7i | 0.262230i | 0.991367 | + | 0.131115i | \(0.0418557\pi\) | ||||
−0.991367 | + | 0.131115i | \(0.958144\pi\) | |||||||
\(692\) | 5.26117e7 | 0.158768 | ||||||||
\(693\) | − | 1.05975e7i | − | 0.0318423i | ||||||
\(694\) | 1.01548e8 | 0.303804 | ||||||||
\(695\) | − | 6.68576e8i | − | 1.99158i | ||||||
\(696\) | 2.58739e8i | 0.767423i | ||||||||
\(697\) | −7.02841e8 | −2.07567 | ||||||||
\(698\) | 4.24573e8 | 1.24849 | ||||||||
\(699\) | −2.00698e7 | −0.0587639 | ||||||||
\(700\) | − | 6.03656e6i | − | 0.0175993i | ||||||
\(701\) | 1.50201e8 | 0.436032 | 0.218016 | − | 0.975945i | \(-0.430042\pi\) | ||||
0.218016 | + | 0.975945i | \(0.430042\pi\) | |||||||
\(702\) | −1.28142e8 | −0.370409 | ||||||||
\(703\) | 2.70006e8 | 0.777155 | ||||||||
\(704\) | 1.45155e8 | 0.416021 | ||||||||
\(705\) | 1.16914e8 | 0.333655 | ||||||||
\(706\) | 3.01937e8i | 0.858029i | ||||||||
\(707\) | 7.53683e7i | 0.213270i | ||||||||
\(708\) | − | 5.12375e6i | − | 0.0144374i | ||||||
\(709\) | 7.03450e8 | 1.97376 | 0.986880 | − | 0.161454i | \(-0.0516184\pi\) | ||||
0.986880 | + | 0.161454i | \(0.0516184\pi\) | |||||||
\(710\) | 3.92484e8i | 1.09660i | ||||||||
\(711\) | 1.47008e8 | 0.409009 | ||||||||
\(712\) | 6.93464e8 | 1.92125 | ||||||||
\(713\) | 1.67187e8 | 0.461247 | ||||||||
\(714\) | 7.14090e7i | 0.196181i | ||||||||
\(715\) | 6.42341e7i | 0.175731i | ||||||||
\(716\) | 1.31088e8i | 0.357127i | ||||||||
\(717\) | − | 2.52918e8i | − | 0.686156i | ||||||
\(718\) | 3.32511e7i | 0.0898323i | ||||||||
\(719\) | −6.87823e8 | −1.85050 | −0.925252 | − | 0.379354i | \(-0.876146\pi\) | ||||
−0.925252 | + | 0.379354i | \(0.876146\pi\) | |||||||
\(720\) | 1.58877e8i | 0.425660i | ||||||||
\(721\) | 4.63587e7i | 0.123688i | ||||||||
\(722\) | 5.99661e8i | 1.59329i | ||||||||
\(723\) | 1.53712e8 | 0.406717 | ||||||||
\(724\) | −9.91052e7 | −0.261144 | ||||||||
\(725\) | 1.75749e8i | 0.461188i | ||||||||
\(726\) | 2.15028e8 | 0.561933 | ||||||||
\(727\) | − | 4.47696e8i | − | 1.16514i | −0.812779 | − | 0.582572i | \(-0.802046\pi\) | ||
0.812779 | − | 0.582572i | \(-0.197954\pi\) | |||||||
\(728\) | 2.94173e7 | 0.0762445 | ||||||||
\(729\) | −3.61487e8 | −0.933061 | ||||||||
\(730\) | 9.74313e7i | 0.250455i | ||||||||
\(731\) | −6.36199e8 | + | 6.69697e7i | −1.62870 | + | 0.171446i | ||||
\(732\) | 8.98142e6 | 0.0228987 | ||||||||
\(733\) | − | 5.04366e8i | − | 1.28066i | −0.768100 | − | 0.640330i | \(-0.778798\pi\) | ||
0.768100 | − | 0.640330i | \(-0.221202\pi\) | |||||||
\(734\) | − | 6.21635e8i | − | 1.57198i | ||||||
\(735\) | −3.40789e8 | −0.858270 | ||||||||
\(736\) | − | 8.12626e7i | − | 0.203825i | ||||||
\(737\) | 1.49307e8 | 0.372974 | ||||||||
\(738\) | − | 2.11140e8i | − | 0.525293i | ||||||
\(739\) | − | 2.26091e8i | − | 0.560209i | −0.959970 | − | 0.280104i | \(-0.909631\pi\) | ||
0.959970 | − | 0.280104i | \(-0.0903691\pi\) | |||||||
\(740\) | −4.65271e7 | −0.114818 | ||||||||
\(741\) | 1.92413e8 | 0.472910 | ||||||||
\(742\) | −8.00173e7 | −0.195872 | ||||||||
\(743\) | 2.00268e8i | 0.488252i | 0.969743 | + | 0.244126i | \(0.0785011\pi\) | ||||
−0.969743 | + | 0.244126i | \(0.921499\pi\) | |||||||
\(744\) | −2.92747e8 | −0.710842 | ||||||||
\(745\) | 4.33788e7 | 0.104908 | ||||||||
\(746\) | 5.22580e8 | 1.25874 | ||||||||
\(747\) | 2.24163e8 | 0.537778 | ||||||||
\(748\) | 5.20900e7 | 0.124466 | ||||||||
\(749\) | − | 3.80403e7i | − | 0.0905313i | ||||||
\(750\) | 1.76456e8i | 0.418267i | ||||||||
\(751\) | − | 7.41639e8i | − | 1.75095i | −0.483267 | − | 0.875473i | \(-0.660550\pi\) | ||
0.483267 | − | 0.875473i | \(-0.339450\pi\) | |||||||
\(752\) | 1.20706e8 | 0.283840 | ||||||||
\(753\) | − | 2.35297e8i | − | 0.551101i | ||||||
\(754\) | −1.44633e8 | −0.337406 | ||||||||
\(755\) | 1.00594e8 | 0.233740 | ||||||||
\(756\) | 1.72519e7 | 0.0399274 | ||||||||
\(757\) | 4.49947e8i | 1.03723i | 0.855009 | + | 0.518614i | \(0.173552\pi\) | ||||
−0.855009 | + | 0.518614i | \(0.826448\pi\) | |||||||
\(758\) | − | 4.52819e8i | − | 1.03972i | ||||||
\(759\) | 6.10577e7i | 0.139642i | ||||||||
\(760\) | − | 9.54710e8i | − | 2.17486i | ||||||
\(761\) | 3.06930e8i | 0.696442i | 0.937412 | + | 0.348221i | \(0.113214\pi\) | ||||
−0.937412 | + | 0.348221i | \(0.886786\pi\) | |||||||
\(762\) | 2.09880e8 | 0.474358 | ||||||||
\(763\) | − | 6.91571e7i | − | 0.155691i | ||||||
\(764\) | 1.27969e8i | 0.286962i | ||||||||
\(765\) | 4.13076e8i | 0.922667i | ||||||||
\(766\) | 2.23020e8 | 0.496201 | ||||||||
\(767\) | 1.69602e7 | 0.0375876 | ||||||||
\(768\) | 1.93189e8i | 0.426480i | ||||||||
\(769\) | 5.68563e8 | 1.25026 | 0.625129 | − | 0.780522i | \(-0.285046\pi\) | ||||
0.625129 | + | 0.780522i | \(0.285046\pi\) | |||||||
\(770\) | 3.39134e7i | 0.0742846i | ||||||||
\(771\) | −1.22651e8 | −0.267614 | ||||||||
\(772\) | 2.98183e7 | 0.0648083 | ||||||||
\(773\) | − | 1.80822e8i | − | 0.391483i | −0.980656 | − | 0.195741i | \(-0.937289\pi\) | ||
0.980656 | − | 0.195741i | \(-0.0627113\pi\) | |||||||
\(774\) | −2.01183e7 | − | 1.91120e8i | −0.0433880 | − | 0.412177i | ||||
\(775\) | −1.98848e8 | −0.427185 | ||||||||
\(776\) | − | 4.60656e7i | − | 0.0985806i | ||||||
\(777\) | − | 2.93165e7i | − | 0.0624955i | ||||||
\(778\) | −5.95441e8 | −1.26444 | ||||||||
\(779\) | 9.99870e8i | 2.11510i | ||||||||
\(780\) | −3.31563e7 | −0.0698685 | ||||||||
\(781\) | 1.80397e8i | 0.378683i | ||||||||
\(782\) | 3.56587e8i | 0.745667i | ||||||||
\(783\) | −5.02272e8 | −1.04629 | ||||||||
\(784\) | −3.51842e8 | −0.730130 | ||||||||
\(785\) | −8.02949e8 | −1.65989 | ||||||||
\(786\) | 1.72337e8i | 0.354905i | ||||||||
\(787\) | −7.97430e8 | −1.63594 | −0.817972 | − | 0.575258i | \(-0.804902\pi\) | ||||
−0.817972 | + | 0.575258i | \(0.804902\pi\) | |||||||
\(788\) | 4.55742e7 | 0.0931409 | ||||||||
\(789\) | 3.08864e8 | 0.628834 | ||||||||
\(790\) | −4.70445e8 | −0.954173 | ||||||||
\(791\) | −3.41836e7 | −0.0690699 | ||||||||
\(792\) | 9.26630e7i | 0.186522i | ||||||||
\(793\) | 2.97295e7i | 0.0596167i | ||||||||
\(794\) | − | 3.70361e8i | − | 0.739884i | ||||||
\(795\) | 5.34054e8 | 1.06288 | ||||||||
\(796\) | 9.92865e7i | 0.196857i | ||||||||
\(797\) | −6.23204e8 | −1.23099 | −0.615496 | − | 0.788140i | \(-0.711044\pi\) | ||||
−0.615496 | + | 0.788140i | \(0.711044\pi\) | |||||||
\(798\) | 1.01587e8 | 0.199908 | ||||||||
\(799\) | 3.13831e8 | 0.615256 | ||||||||
\(800\) | 9.66517e7i | 0.188773i | ||||||||
\(801\) | 4.26843e8i | 0.830559i | ||||||||
\(802\) | 5.11759e8i | 0.992070i | ||||||||
\(803\) | 4.47823e7i | 0.0864887i | ||||||||
\(804\) | 7.70693e7i | 0.148290i | ||||||||
\(805\) | 5.91997e7 | 0.113483 | ||||||||
\(806\) | − | 1.63643e8i | − | 0.312529i | ||||||
\(807\) | 5.33214e8i | 1.01457i | ||||||||
\(808\) | − | 6.59008e8i | − | 1.24927i | ||||||
\(809\) | −7.50640e7 | −0.141771 | −0.0708853 | − | 0.997484i | \(-0.522582\pi\) | ||||
−0.0708853 | + | 0.997484i | \(0.522582\pi\) | |||||||
\(810\) | 1.84276e8 | 0.346749 | ||||||||
\(811\) | 7.34418e8i | 1.37683i | 0.725317 | + | 0.688415i | \(0.241693\pi\) | ||||
−0.725317 | + | 0.688415i | \(0.758307\pi\) | |||||||
\(812\) | 1.94720e7 | 0.0363699 | ||||||||
\(813\) | − | 4.41459e8i | − | 0.821521i | ||||||
\(814\) | 8.38640e7 | 0.155490 | ||||||||
\(815\) | −4.65400e8 | −0.859712 | ||||||||
\(816\) | − | 4.92058e8i | − | 0.905619i | ||||||
\(817\) | 9.52719e7 | + | 9.05063e8i | 0.174702 | + | 1.65964i | ||||
\(818\) | −5.47736e8 | −1.00072 | ||||||||
\(819\) | 1.81070e7i | 0.0329606i | ||||||||
\(820\) | − | 1.72296e8i | − | 0.312488i | ||||||
\(821\) | 2.55907e8 | 0.462436 | 0.231218 | − | 0.972902i | \(-0.425729\pi\) | ||||
0.231218 | + | 0.972902i | \(0.425729\pi\) | |||||||
\(822\) | − | 6.53952e8i | − | 1.17742i | ||||||
\(823\) | 2.70463e7 | 0.0485186 | 0.0242593 | − | 0.999706i | \(-0.492277\pi\) | ||||
0.0242593 | + | 0.999706i | \(0.492277\pi\) | |||||||
\(824\) | − | 4.05353e8i | − | 0.724523i | ||||||
\(825\) | − | 7.26206e7i | − | 0.129330i | ||||||
\(826\) | 8.95439e6 | 0.0158890 | ||||||||
\(827\) | 7.15059e8 | 1.26423 | 0.632114 | − | 0.774876i | \(-0.282188\pi\) | ||||
0.632114 | + | 0.774876i | \(0.282188\pi\) | |||||||
\(828\) | 2.73160e7 | 0.0481200 | ||||||||
\(829\) | − | 4.42063e8i | − | 0.775927i | −0.921675 | − | 0.387964i | \(-0.873179\pi\) | ||
0.921675 | − | 0.387964i | \(-0.126821\pi\) | |||||||
\(830\) | −7.17350e8 | −1.25458 | ||||||||
\(831\) | 7.24646e8 | 1.26277 | ||||||||
\(832\) | −2.48014e8 | −0.430632 | ||||||||
\(833\) | −9.14782e8 | −1.58264 | ||||||||
\(834\) | −6.22043e8 | −1.07232 | ||||||||
\(835\) | − | 5.01641e8i | − | 0.861655i | ||||||
\(836\) | − | 7.41038e7i | − | 0.126830i | ||||||
\(837\) | − | 5.68287e8i | − | 0.969151i | ||||||
\(838\) | 8.64344e8 | 1.46877 | ||||||||
\(839\) | 9.68041e7i | 0.163911i | 0.996636 | + | 0.0819555i | \(0.0261165\pi\) | ||||
−0.996636 | + | 0.0819555i | \(0.973883\pi\) | |||||||
\(840\) | −1.03660e8 | −0.174893 | ||||||||
\(841\) | 2.79153e7 | 0.0469303 | ||||||||
\(842\) | −6.99455e8 | −1.17172 | ||||||||
\(843\) | 6.66763e8i | 1.11298i | ||||||||
\(844\) | 1.37878e8i | 0.229334i | ||||||||
\(845\) | 6.22372e8i | 1.03153i | ||||||||
\(846\) | 9.42779e7i | 0.155704i | ||||||||
\(847\) | − | 9.58253e7i | − | 0.157699i | ||||||
\(848\) | 5.51375e8 | 0.904190 | ||||||||
\(849\) | 2.72974e8i | 0.446065i | ||||||||
\(850\) | − | 4.24115e8i | − | 0.690601i | ||||||
\(851\) | − | 1.46394e8i | − | 0.237539i | ||||||
\(852\) | −9.31171e7 | −0.150560 | ||||||||
\(853\) | 2.63624e8 | 0.424754 | 0.212377 | − | 0.977188i | \(-0.431879\pi\) | ||||
0.212377 | + | 0.977188i | \(0.431879\pi\) | |||||||
\(854\) | 1.56961e7i | 0.0252011i | ||||||||
\(855\) | 5.87646e8 | 0.940193 | ||||||||
\(856\) | 3.32618e8i | 0.530304i | ||||||||
\(857\) | 3.79690e8 | 0.603235 | 0.301617 | − | 0.953429i | \(-0.402474\pi\) | ||||
0.301617 | + | 0.953429i | \(0.402474\pi\) | |||||||
\(858\) | 5.97633e7 | 0.0946178 | ||||||||
\(859\) | 5.37277e7i | 0.0847654i | 0.999101 | + | 0.0423827i | \(0.0134949\pi\) | ||||
−0.999101 | + | 0.0423827i | \(0.986505\pi\) | |||||||
\(860\) | −1.64171e7 | − | 1.55959e8i | −0.0258108 | − | 0.245197i | ||||
\(861\) | 1.08563e8 | 0.170087 | ||||||||
\(862\) | 7.65197e8i | 1.19468i | ||||||||
\(863\) | − | 1.15271e9i | − | 1.79345i | −0.442593 | − | 0.896723i | \(-0.645941\pi\) | ||
0.442593 | − | 0.896723i | \(-0.354059\pi\) | |||||||
\(864\) | −2.76221e8 | −0.428268 | ||||||||
\(865\) | − | 6.13665e8i | − | 0.948163i | ||||||
\(866\) | 4.83312e8 | 0.744172 | ||||||||
\(867\) | − | 8.02338e8i | − | 1.23112i | ||||||
\(868\) | 2.20313e7i | 0.0336884i | ||||||||
\(869\) | −2.16230e8 | −0.329501 | ||||||||
\(870\) | 5.09652e8 | 0.773955 | ||||||||
\(871\) | −2.55108e8 | −0.386073 | ||||||||
\(872\) | 6.04698e8i | 0.911988i | ||||||||
\(873\) | 2.83544e7 | 0.0426165 | ||||||||
\(874\) | 5.07284e8 | 0.759830 | ||||||||
\(875\) | 7.86362e7 | 0.117381 | ||||||||
\(876\) | −2.31156e7 | −0.0343870 | ||||||||
\(877\) | −6.96046e8 | −1.03190 | −0.515952 | − | 0.856617i | \(-0.672562\pi\) | ||||
−0.515952 | + | 0.856617i | \(0.672562\pi\) | |||||||
\(878\) | 3.53362e8i | 0.522079i | ||||||||
\(879\) | − | 6.08036e8i | − | 0.895287i | ||||||
\(880\) | − | 2.33687e8i | − | 0.342915i | ||||||
\(881\) | −8.69205e7 | −0.127114 | −0.0635572 | − | 0.997978i | \(-0.520245\pi\) | ||||
−0.0635572 | + | 0.997978i | \(0.520245\pi\) | |||||||
\(882\) | − | 2.74809e8i | − | 0.400521i | ||||||
\(883\) | 3.48995e8 | 0.506918 | 0.253459 | − | 0.967346i | \(-0.418432\pi\) | ||||
0.253459 | + | 0.967346i | \(0.418432\pi\) | |||||||
\(884\) | −8.90014e7 | −0.128837 | ||||||||
\(885\) | −5.97637e7 | −0.0862199 | ||||||||
\(886\) | 8.48621e8i | 1.22015i | ||||||||
\(887\) | 1.18586e9i | 1.69927i | 0.527374 | + | 0.849633i | \(0.323177\pi\) | ||||
−0.527374 | + | 0.849633i | \(0.676823\pi\) | |||||||
\(888\) | 2.56338e8i | 0.366079i | ||||||||
\(889\) | − | 9.35312e7i | − | 0.133122i | ||||||
\(890\) | − | 1.36595e9i | − | 1.93760i | ||||||
\(891\) | 8.46988e7 | 0.119741 | ||||||||
\(892\) | − | 8.82020e7i | − | 0.124275i | ||||||
\(893\) | − | 4.46460e8i | − | 0.626943i | ||||||
\(894\) | − | 4.03596e7i | − | 0.0564852i | ||||||
\(895\) | 1.52901e9 | 2.13276 | ||||||||
\(896\) | −7.82400e7 | −0.108769 | ||||||||
\(897\) | − | 1.04324e8i | − | 0.144546i | ||||||
\(898\) | 3.25825e8 | 0.449940 | ||||||||
\(899\) | − | 6.41419e8i | − | 0.882801i | ||||||
\(900\) | −3.24889e7 | −0.0445664 | ||||||||
\(901\) | 1.43356e9 | 1.95994 | ||||||||
\(902\) | 3.10560e8i | 0.423180i | ||||||||
\(903\) | 9.82690e7 | − | 1.03443e7i | 0.133461 | − | 0.0140488i | ||||
\(904\) | 2.98896e8 | 0.404590 | ||||||||
\(905\) | 1.15597e9i | 1.55955i | ||||||||
\(906\) | − | 9.35930e7i | − | 0.125852i | ||||||
\(907\) | −3.44670e8 | −0.461936 | −0.230968 | − | 0.972961i | \(-0.574189\pi\) | ||||
−0.230968 | + | 0.972961i | \(0.574189\pi\) | |||||||
\(908\) | − | 3.00024e7i | − | 0.0400773i | ||||||
\(909\) | 4.05635e8 | 0.540062 | ||||||||
\(910\) | − | 5.79447e7i | − | 0.0768934i | ||||||
\(911\) | − | 2.34712e8i | − | 0.310441i | −0.987880 | − | 0.155221i | \(-0.950391\pi\) | ||
0.987880 | − | 0.155221i | \(-0.0496088\pi\) | |||||||
\(912\) | −7.00007e8 | −0.922822 | ||||||||
\(913\) | −3.29715e8 | −0.433238 | ||||||||
\(914\) | −8.66964e8 | −1.13544 | ||||||||
\(915\) | − | 1.04760e8i | − | 0.136751i | ||||||
\(916\) | −4.27233e7 | −0.0555877 | ||||||||
\(917\) | 7.68007e7 | 0.0995995 | ||||||||
\(918\) | 1.21208e9 | 1.56676 | ||||||||
\(919\) | 2.29468e8 | 0.295648 | 0.147824 | − | 0.989014i | \(-0.452773\pi\) | ||||
0.147824 | + | 0.989014i | \(0.452773\pi\) | |||||||
\(920\) | −5.17632e8 | −0.664749 | ||||||||
\(921\) | − | 3.37045e8i | − | 0.431428i | ||||||
\(922\) | 1.36304e9i | 1.73906i | ||||||||
\(923\) | − | 3.08228e8i | − | 0.391983i | ||||||
\(924\) | −8.04597e6 | −0.0101991 | ||||||||
\(925\) | 1.74118e8i | 0.219997i | ||||||||
\(926\) | −5.83807e7 | −0.0735253 | ||||||||
\(927\) | 2.49504e8 | 0.313212 | ||||||||
\(928\) | −3.11767e8 | −0.390110 | ||||||||
\(929\) | 7.55756e8i | 0.942615i | 0.881969 | + | 0.471308i | \(0.156218\pi\) | ||||
−0.881969 | + | 0.471308i | \(0.843782\pi\) | |||||||
\(930\) | 5.76637e8i | 0.716892i | ||||||||
\(931\) | 1.30138e9i | 1.61270i | ||||||||
\(932\) | − | 1.32066e7i | − | 0.0163134i | ||||||
\(933\) | 3.22012e8i | 0.396486i | ||||||||
\(934\) | −1.33233e9 | −1.63520 | ||||||||
\(935\) | − | 6.07580e8i | − | 0.743308i | ||||||
\(936\) | − | 1.58325e8i | − | 0.193073i | ||||||
\(937\) | − | 7.08819e8i | − | 0.861622i | −0.902442 | − | 0.430811i | \(-0.858228\pi\) | ||
0.902442 | − | 0.430811i | \(-0.141772\pi\) | |||||||
\(938\) | −1.34688e8 | −0.163200 | ||||||||
\(939\) | 7.56332e8 | 0.913515 | ||||||||
\(940\) | 7.69333e7i | 0.0926256i | ||||||||
\(941\) | 1.27658e9 | 1.53207 | 0.766034 | − | 0.642800i | \(-0.222227\pi\) | ||||
0.766034 | + | 0.642800i | \(0.222227\pi\) | |||||||
\(942\) | 7.47063e8i | 0.893727i | ||||||||
\(943\) | 5.42117e8 | 0.646485 | ||||||||
\(944\) | −6.17021e7 | −0.0733472 | ||||||||
\(945\) | − | 2.01227e8i | − | 0.238446i | ||||||
\(946\) | 2.95914e7 | + | 2.81113e8i | 0.0349537 | + | 0.332053i | ||||
\(947\) | −1.28977e9 | −1.51866 | −0.759332 | − | 0.650703i | \(-0.774474\pi\) | ||||
−0.759332 | + | 0.650703i | \(0.774474\pi\) | |||||||
\(948\) | − | 1.11613e8i | − | 0.131006i | ||||||
\(949\) | − | 7.65153e7i | − | 0.0895261i | ||||||
\(950\) | −6.03351e8 | −0.703719 | ||||||||
\(951\) | 7.38277e8i | 0.858377i | ||||||||
\(952\) | −2.78253e8 | −0.322500 | ||||||||
\(953\) | − | 1.85601e8i | − | 0.214438i | −0.994235 | − | 0.107219i | \(-0.965805\pi\) | ||
0.994235 | − | 0.107219i | \(-0.0341946\pi\) | |||||||
\(954\) | 4.30656e8i | 0.496004i | ||||||||
\(955\) | 1.49263e9 | 1.71373 | ||||||||
\(956\) | 1.66429e8 | 0.190483 | ||||||||
\(957\) | 2.34251e8 | 0.267267 | ||||||||
\(958\) | − | 1.08050e9i | − | 1.22893i | ||||||
\(959\) | −2.91428e8 | −0.330427 | ||||||||
\(960\) | 8.73942e8 | 0.987800 | ||||||||
\(961\) | −1.61780e8 | −0.182286 | ||||||||
\(962\) | −1.43291e8 | −0.160951 | ||||||||
\(963\) | −2.04734e8 | −0.229251 | ||||||||
\(964\) | 1.01148e8i | 0.112908i | ||||||||
\(965\) | − | 3.47802e8i | − | 0.387035i | ||||||
\(966\) | − | 5.50793e7i | − | 0.0611023i | ||||||
\(967\) | −1.18105e9 | −1.30614 | −0.653069 | − | 0.757299i | \(-0.726519\pi\) | ||||
−0.653069 | + | 0.757299i | \(0.726519\pi\) | |||||||
\(968\) | 8.37881e8i | 0.923754i | ||||||||
\(969\) | −1.82000e9 | −2.00032 | ||||||||
\(970\) | −9.07377e7 | −0.0994197 | ||||||||
\(971\) | −6.52107e8 | −0.712297 | −0.356149 | − | 0.934429i | \(-0.615910\pi\) | ||||
−0.356149 | + | 0.934429i | \(0.615910\pi\) | |||||||
\(972\) | − | 1.56259e8i | − | 0.170156i | ||||||
\(973\) | 2.77208e8i | 0.300932i | ||||||||
\(974\) | − | 8.39632e8i | − | 0.908682i | ||||||
\(975\) | 1.24080e8i | 0.133872i | ||||||||
\(976\) | − | 1.08157e8i | − | 0.116334i | ||||||
\(977\) | −9.78836e8 | −1.04961 | −0.524803 | − | 0.851224i | \(-0.675861\pi\) | ||||
−0.524803 | + | 0.851224i | \(0.675861\pi\) | |||||||
\(978\) | 4.33008e8i | 0.462891i | ||||||||
\(979\) | − | 6.27830e8i | − | 0.669105i | ||||||
\(980\) | − | 2.24252e8i | − | 0.238263i | ||||||
\(981\) | −3.72206e8 | −0.394254 | ||||||||
\(982\) | 1.17051e8 | 0.123607 | ||||||||
\(983\) | 2.69098e8i | 0.283303i | 0.989917 | + | 0.141651i | \(0.0452412\pi\) | ||||
−0.989917 | + | 0.141651i | \(0.954759\pi\) | |||||||
\(984\) | −9.49256e8 | −0.996318 | ||||||||
\(985\) | − | 5.31580e8i | − | 0.556237i | ||||||
\(986\) | 1.36806e9 | 1.42716 | ||||||||
\(987\) | −4.84753e7 | −0.0504160 | ||||||||
\(988\) | 1.26614e8i | 0.131284i | ||||||||
\(989\) | 4.90714e8 | − | 5.16553e7i | 0.507271 | − | 0.0533981i | ||||
\(990\) | 1.82523e8 | 0.188110 | ||||||||
\(991\) | − | 8.36450e6i | − | 0.00859447i | −0.999991 | − | 0.00429723i | \(-0.998632\pi\) | ||
0.999991 | − | 0.00429723i | \(-0.00136786\pi\) | |||||||
\(992\) | − | 3.52744e8i | − | 0.361347i | ||||||
\(993\) | −1.03545e9 | −1.05750 | ||||||||
\(994\) | − | 1.62734e8i | − | 0.165698i | ||||||
\(995\) | 1.15808e9 | 1.17563 | ||||||||
\(996\) | − | 1.70192e8i | − | 0.172251i | ||||||
\(997\) | − | 1.20623e9i | − | 1.21715i | −0.793497 | − | 0.608574i | \(-0.791742\pi\) | ||
0.793497 | − | 0.608574i | \(-0.208258\pi\) | |||||||
\(998\) | −9.48082e8 | −0.953794 | ||||||||
\(999\) | −4.97611e8 | −0.499107 |
(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 | 43.7.b.b.42.7 | ✓ | 20 | |
43.42 | odd | 2 | inner | 43.7.b.b.42.14 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.7.b.b.42.7 | ✓ | 20 | 1.1 | even | 1 | trivial | |
43.7.b.b.42.14 | yes | 20 | 43.42 | odd | 2 | inner |