Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(161,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 5, 8]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.ba (of order \(10\), degree \(4\), 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: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 161.14 | ||
Character | \(\chi\) | \(=\) | 900.161 |
Dual form | 900.3.ba.a.341.14 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.65177 | + | 4.23888i | 0.530353 | + | 0.847777i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.40455 | 0.914935 | 0.457468 | − | 0.889226i | \(-0.348757\pi\) | ||||
0.457468 | + | 0.889226i | \(0.348757\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7.63768 | + | 10.5124i | 0.694335 | + | 0.955670i | 0.999994 | + | 0.00352896i | \(0.00112331\pi\) |
−0.305659 | + | 0.952141i | \(0.598877\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.47722 | − | 1.79980i | −0.190555 | − | 0.138446i | 0.488417 | − | 0.872610i | \(-0.337574\pi\) |
−0.678972 | + | 0.734164i | \(0.737574\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 27.0399 | − | 8.78580i | 1.59058 | − | 0.516812i | 0.625828 | − | 0.779961i | \(-0.284761\pi\) |
0.964755 | + | 0.263149i | \(0.0847611\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.60900 | − | 4.95199i | −0.0846842 | − | 0.260631i | 0.899744 | − | 0.436418i | \(-0.143753\pi\) |
−0.984428 | + | 0.175787i | \(0.943753\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.08886 | − | 1.49868i | −0.0473416 | − | 0.0651601i | 0.784690 | − | 0.619888i | \(-0.212822\pi\) |
−0.832031 | + | 0.554728i | \(0.812822\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −10.9363 | + | 22.4811i | −0.437451 | + | 0.899242i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −18.8359 | − | 6.12014i | −0.649512 | − | 0.211039i | −0.0343133 | − | 0.999411i | \(-0.510924\pi\) |
−0.615199 | + | 0.788372i | \(0.710924\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.41047 | + | 4.34098i | 0.0454991 | + | 0.140032i | 0.971225 | − | 0.238163i | \(-0.0765451\pi\) |
−0.925726 | + | 0.378194i | \(0.876545\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 16.9834 | + | 27.1481i | 0.485239 | + | 0.775661i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 27.4084 | + | 19.9134i | 0.740767 | + | 0.538199i | 0.892951 | − | 0.450153i | \(-0.148631\pi\) |
−0.152184 | + | 0.988352i | \(0.548631\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.14508 | + | 7.08160i | −0.125490 | + | 0.172722i | −0.867139 | − | 0.498066i | \(-0.834044\pi\) |
0.741649 | + | 0.670788i | \(0.234044\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −29.6940 | −0.690559 | −0.345279 | − | 0.938500i | \(-0.612216\pi\) | ||||
−0.345279 | + | 0.938500i | \(0.612216\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 13.2827 | + | 4.31580i | 0.282610 | + | 0.0918256i | 0.446892 | − | 0.894588i | \(-0.352531\pi\) |
−0.164282 | + | 0.986413i | \(0.552531\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.98180 | −0.162894 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 36.9022 | + | 11.9903i | 0.696268 | + | 0.226231i | 0.635704 | − | 0.771933i | \(-0.280710\pi\) |
0.0605645 | + | 0.998164i | \(0.480710\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −24.3074 | + | 60.2516i | −0.441952 | + | 1.09548i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 42.2369 | − | 58.1341i | 0.715879 | − | 0.985323i | −0.283771 | − | 0.958892i | \(-0.591586\pi\) |
0.999651 | − | 0.0264314i | \(-0.00841436\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.46094 | − | 4.69414i | 0.105917 | − | 0.0769532i | −0.533566 | − | 0.845758i | \(-0.679148\pi\) |
0.639483 | + | 0.768805i | \(0.279148\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.06016 | − | 15.2733i | 0.0163101 | − | 0.234974i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.6107 | − | 41.8895i | −0.203145 | − | 0.625217i | −0.999784 | − | 0.0207616i | \(-0.993391\pi\) |
0.796639 | − | 0.604455i | \(-0.206609\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 40.2562 | + | 13.0800i | 0.566989 | + | 0.184226i | 0.578464 | − | 0.815708i | \(-0.303652\pi\) |
−0.0114744 | + | 0.999934i | \(0.503652\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −88.0786 | + | 63.9928i | −1.20656 | + | 0.876614i | −0.994913 | − | 0.100733i | \(-0.967881\pi\) |
−0.211642 | + | 0.977347i | \(0.567881\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 48.9159 | + | 67.3270i | 0.635271 | + | 0.874376i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −35.0562 | + | 107.892i | −0.443750 | + | 1.36572i | 0.440099 | + | 0.897949i | \(0.354943\pi\) |
−0.883849 | + | 0.467772i | \(0.845057\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 68.7223 | − | 22.3292i | 0.827980 | − | 0.269027i | 0.135786 | − | 0.990738i | \(-0.456644\pi\) |
0.692194 | + | 0.721711i | \(0.256644\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 108.946 | + | 91.3212i | 1.28171 | + | 1.07437i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 76.6686 | + | 105.525i | 0.861445 | + | 1.18568i | 0.981223 | + | 0.192877i | \(0.0617818\pi\) |
−0.119778 | + | 0.992801i | \(0.538218\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.8654 | − | 11.5269i | −0.174346 | − | 0.126669i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 16.7242 | − | 19.9519i | 0.176045 | − | 0.210020i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −24.5643 | + | 75.6012i | −0.253240 | + | 0.779394i | 0.740931 | + | 0.671581i | \(0.234385\pi\) |
−0.994171 | + | 0.107813i | \(0.965615\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 15.1877i | − | 0.150374i | −0.997169 | − | 0.0751869i | \(-0.976045\pi\) | ||
0.997169 | − | 0.0751869i | \(-0.0239553\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.88425 | + | 8.87682i | −0.0280025 | + | 0.0861827i | −0.964081 | − | 0.265608i | \(-0.914427\pi\) |
0.936079 | + | 0.351791i | \(0.114427\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 82.2087i | 0.768306i | 0.923269 | + | 0.384153i | \(0.125506\pi\) | ||||
−0.923269 | + | 0.384153i | \(0.874494\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −43.0799 | − | 31.2994i | −0.395228 | − | 0.287150i | 0.372366 | − | 0.928086i | \(-0.378546\pi\) |
−0.767595 | + | 0.640936i | \(0.778546\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.54996 | + | 3.50973i | −0.0225661 | + | 0.0310595i | −0.820151 | − | 0.572147i | \(-0.806111\pi\) |
0.797585 | + | 0.603207i | \(0.206111\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.46535 | − | 8.58969i | 0.0301334 | − | 0.0746929i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 173.178 | − | 56.2691i | 1.45528 | − | 0.472849i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14.7847 | + | 45.5025i | −0.122187 | + | 0.376054i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −124.295 | + | 13.2569i | −0.994360 | + | 0.106055i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 121.599 | − | 88.3467i | 0.957471 | − | 0.695644i | 0.00490920 | − | 0.999988i | \(-0.498437\pi\) |
0.952562 | + | 0.304344i | \(0.0984373\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 185.356 | − | 60.2260i | 1.41493 | − | 0.459740i | 0.500946 | − | 0.865479i | \(-0.332986\pi\) |
0.913989 | + | 0.405739i | \(0.132986\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.3049 | − | 31.7153i | −0.0774806 | − | 0.238461i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −20.9414 | + | 28.8233i | −0.152857 | + | 0.210389i | −0.878577 | − | 0.477601i | \(-0.841507\pi\) |
0.725720 | + | 0.687990i | \(0.241507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 201.595 | − | 146.467i | 1.45032 | − | 1.05372i | 0.464570 | − | 0.885537i | \(-0.346209\pi\) |
0.985755 | − | 0.168186i | \(-0.0537909\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 39.7878i | − | 0.278236i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −24.0057 | − | 96.0722i | −0.165557 | − | 0.662567i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 269.977i | 1.81193i | 0.423357 | + | 0.905963i | \(0.360852\pi\) | ||||
−0.423357 | + | 0.905963i | \(0.639148\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −138.115 | −0.914667 | −0.457333 | − | 0.889295i | \(-0.651195\pi\) | ||||
−0.457333 | + | 0.889295i | \(0.651195\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.6607 | + | 17.4901i | −0.0945851 | + | 0.112839i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −92.5578 | −0.589540 | −0.294770 | − | 0.955568i | \(-0.595243\pi\) | ||||
−0.294770 | + | 0.955568i | \(0.595243\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.97363 | − | 9.59837i | −0.0433144 | − | 0.0596172i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 210.578 | + | 152.994i | 1.29189 | + | 0.938615i | 0.999842 | − | 0.0177879i | \(-0.00566236\pi\) |
0.292051 | + | 0.956403i | \(0.405662\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −78.7484 | + | 25.5869i | −0.471547 | + | 0.153215i | −0.535144 | − | 0.844761i | \(-0.679743\pi\) |
0.0635972 | + | 0.997976i | \(0.479743\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −49.3266 | − | 151.812i | −0.291873 | − | 0.898293i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −183.908 | − | 253.128i | −1.06305 | − | 1.46317i | −0.876917 | − | 0.480641i | \(-0.840404\pi\) |
−0.186135 | − | 0.982524i | \(-0.559596\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −70.0418 | + | 143.981i | −0.400239 | + | 0.822748i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −155.165 | − | 50.4161i | −0.866842 | − | 0.281654i | −0.158359 | − | 0.987382i | \(-0.550620\pi\) |
−0.708483 | + | 0.705727i | \(0.750620\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −33.3697 | − | 102.702i | −0.184363 | − | 0.567412i | 0.815574 | − | 0.578653i | \(-0.196422\pi\) |
−0.999937 | + | 0.0112417i | \(0.996422\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.7298 | + | 168.987i | −0.0634042 | + | 0.913441i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 298.882 | + | 217.150i | 1.59830 | + | 1.16123i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 127.267 | − | 175.168i | 0.666318 | − | 0.917108i | −0.333352 | − | 0.942803i | \(-0.608180\pi\) |
0.999670 | + | 0.0256942i | \(0.00817962\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −188.553 | −0.976959 | −0.488480 | − | 0.872575i | \(-0.662448\pi\) | ||||
−0.488480 | + | 0.872575i | \(0.662448\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.70553 | + | 2.17876i | 0.0340382 | + | 0.0110597i | 0.325987 | − | 0.945374i | \(-0.394304\pi\) |
−0.291948 | + | 0.956434i | \(0.594304\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −57.3828 | −0.288356 | −0.144178 | − | 0.989552i | \(-0.546054\pi\) | ||||
−0.144178 | + | 0.989552i | \(0.546054\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −120.635 | − | 39.1967i | −0.594262 | − | 0.193087i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −43.6616 | − | 3.03066i | −0.212984 | − | 0.0147837i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 39.7682 | − | 54.7362i | 0.190278 | − | 0.261896i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −129.694 | + | 94.2282i | −0.614663 | + | 0.446579i | −0.851053 | − | 0.525079i | \(-0.824036\pi\) |
0.236390 | + | 0.971658i | \(0.424036\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −78.7416 | − | 125.870i | −0.366240 | − | 0.585440i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.03343 | + | 27.8020i | 0.0416287 | + | 0.128120i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −82.7965 | − | 26.9022i | −0.374645 | − | 0.121729i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −245.569 | + | 178.417i | −1.10121 | + | 0.800074i | −0.981257 | − | 0.192706i | \(-0.938274\pi\) |
−0.119951 | + | 0.992780i | \(0.538274\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −88.9964 | − | 122.493i | −0.392055 | − | 0.539617i | 0.566673 | − | 0.823943i | \(-0.308230\pi\) |
−0.958728 | + | 0.284326i | \(0.908230\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 135.756 | − | 417.815i | 0.592822 | − | 1.82452i | 0.0275404 | − | 0.999621i | \(-0.491233\pi\) |
0.565282 | − | 0.824898i | \(-0.308767\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −145.800 | + | 47.3732i | −0.625749 | + | 0.203318i | −0.604691 | − | 0.796460i | \(-0.706703\pi\) |
−0.0210581 | + | 0.999778i | \(0.506703\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.9284 | + | 67.7482i | 0.0720356 | + | 0.288290i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.24102 | − | 3.08449i | −0.00937664 | − | 0.0129058i | 0.804303 | − | 0.594219i | \(-0.202539\pi\) |
−0.813680 | + | 0.581314i | \(0.802539\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −376.999 | − | 273.906i | −1.56431 | − | 1.13654i | −0.932360 | − | 0.361531i | \(-0.882254\pi\) |
−0.631951 | − | 0.775008i | \(-0.717746\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −21.1659 | − | 33.8339i | −0.0863913 | − | 0.138098i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.92677 | + | 15.1630i | −0.0199464 | + | 0.0613888i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 170.159i | − | 0.677926i | −0.940800 | − | 0.338963i | \(-0.889924\pi\) | ||
0.940800 | − | 0.338963i | \(-0.110076\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.43836 | − | 22.8929i | 0.0294006 | − | 0.0904858i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 192.347i | 0.748431i | 0.927342 | + | 0.374215i | \(0.122088\pi\) | ||||
−0.927342 | + | 0.374215i | \(0.877912\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 175.538 | + | 127.536i | 0.677754 | + | 0.492417i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −78.2994 | + | 107.770i | −0.297716 | + | 0.409772i | −0.931501 | − | 0.363738i | \(-0.881500\pi\) |
0.633785 | + | 0.773509i | \(0.281500\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 47.0308 | + | 188.220i | 0.177475 | + | 0.710263i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 211.418 | − | 68.6939i | 0.785941 | − | 0.255368i | 0.111566 | − | 0.993757i | \(-0.464413\pi\) |
0.674375 | + | 0.738389i | \(0.264413\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 154.476 | − | 475.427i | 0.570020 | − | 1.75434i | −0.0825210 | − | 0.996589i | \(-0.526297\pi\) |
0.652541 | − | 0.757753i | \(-0.273703\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −319.857 | + | 56.7371i | −1.16312 | + | 0.206317i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 277.946 | − | 201.940i | 1.00342 | − | 0.729024i | 0.0405977 | − | 0.999176i | \(-0.487074\pi\) |
0.962818 | + | 0.270151i | \(0.0870738\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −252.490 | + | 82.0390i | −0.898542 | + | 0.291954i | −0.721635 | − | 0.692274i | \(-0.756609\pi\) |
−0.176907 | + | 0.984228i | \(0.556609\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.6616 | + | 32.8131i | 0.0376736 | + | 0.115947i | 0.968125 | − | 0.250469i | \(-0.0805847\pi\) |
−0.930451 | + | 0.366416i | \(0.880585\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −32.9519 | + | 45.3544i | −0.114815 | + | 0.158029i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 420.161 | − | 305.265i | 1.45384 | − | 1.05628i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 118.927i | 0.405893i | 0.979190 | + | 0.202946i | \(0.0650517\pi\) | ||||
−0.979190 | + | 0.202946i | \(0.934948\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 358.426 | + | 24.8792i | 1.21500 | + | 0.0843364i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.67229i | 0.0189709i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −190.177 | −0.631816 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 37.0308 | + | 14.9394i | 0.121413 | + | 0.0489816i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 559.101 | 1.82118 | 0.910589 | − | 0.413314i | \(-0.135629\pi\) | ||||
0.910589 | + | 0.413314i | \(0.135629\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −287.409 | − | 395.585i | −0.924146 | − | 1.27198i | −0.962100 | − | 0.272698i | \(-0.912084\pi\) |
0.0379540 | − | 0.999279i | \(-0.487916\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −206.023 | − | 149.685i | −0.658221 | − | 0.478226i | 0.207840 | − | 0.978163i | \(-0.433357\pi\) |
−0.866062 | + | 0.499937i | \(0.833357\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −550.719 | + | 178.939i | −1.73728 | + | 0.564478i | −0.994470 | − | 0.105021i | \(-0.966509\pi\) |
−0.742813 | + | 0.669499i | \(0.766509\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −79.5252 | − | 244.753i | −0.249295 | − | 0.767252i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −87.0145 | − | 119.765i | −0.269395 | − | 0.370790i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 67.5530 | − | 36.0073i | 0.207855 | − | 0.110792i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 85.0695 | + | 27.6408i | 0.258570 | + | 0.0840145i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −136.030 | − | 418.657i | −0.410966 | − | 1.26482i | −0.915809 | − | 0.401613i | \(-0.868450\pi\) |
0.504843 | − | 0.863211i | \(-0.331550\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 141.472 | − | 168.775i | 0.422305 | − | 0.503807i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −95.4850 | − | 69.3739i | −0.283338 | − | 0.205857i | 0.437034 | − | 0.899445i | \(-0.356029\pi\) |
−0.720372 | + | 0.693588i | \(0.756029\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −34.8613 | + | 47.9825i | −0.102233 | + | 0.140711i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −364.943 | −1.06397 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 326.505 | + | 106.088i | 0.940935 | + | 0.305728i | 0.739027 | − | 0.673676i | \(-0.235286\pi\) |
0.201908 | + | 0.979404i | \(0.435286\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −293.247 | −0.840249 | −0.420125 | − | 0.907466i | \(-0.638014\pi\) | ||||
−0.420125 | + | 0.907466i | \(0.638014\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −499.906 | − | 162.429i | −1.41616 | − | 0.460139i | −0.501782 | − | 0.864994i | \(-0.667322\pi\) |
−0.914381 | + | 0.404855i | \(0.867322\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 51.3053 | + | 205.327i | 0.144522 | + | 0.578385i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 84.2923 | − | 116.018i | 0.234797 | − | 0.323171i | −0.675317 | − | 0.737527i | \(-0.735993\pi\) |
0.910115 | + | 0.414356i | \(0.135993\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 270.122 | − | 196.255i | 0.748260 | − | 0.543643i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −504.822 | − | 203.661i | −1.38307 | − | 0.557975i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 46.5084 | + | 143.138i | 0.126726 | + | 0.390022i | 0.994212 | − | 0.107440i | \(-0.0342654\pi\) |
−0.867486 | + | 0.497462i | \(0.834265\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 236.342 | + | 76.7922i | 0.637040 | + | 0.206987i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −353.068 | + | 256.519i | −0.946563 | + | 0.687718i | −0.949991 | − | 0.312276i | \(-0.898909\pi\) |
0.00342873 | + | 0.999994i | \(0.498909\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 35.6455 | + | 49.0618i | 0.0945503 | + | 0.130137i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 202.259 | − | 622.489i | 0.533665 | − | 1.64245i | −0.212852 | − | 0.977084i | \(-0.568275\pi\) |
0.746517 | − | 0.665367i | \(-0.231725\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 298.099 | − | 96.8583i | 0.778327 | − | 0.252894i | 0.107201 | − | 0.994237i | \(-0.465811\pi\) |
0.671126 | + | 0.741344i | \(0.265811\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −155.678 | + | 385.884i | −0.404357 | + | 1.00230i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.3414 | − | 32.1267i | −0.0600037 | − | 0.0825880i | 0.777961 | − | 0.628313i | \(-0.216254\pi\) |
−0.837964 | + | 0.545725i | \(0.816254\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −42.6097 | − | 30.9577i | −0.108976 | − | 0.0791758i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −550.302 | + | 137.505i | −1.39317 | + | 0.348114i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 181.148 | − | 557.515i | 0.456291 | − | 1.40432i | −0.413322 | − | 0.910585i | \(-0.635632\pi\) |
0.869613 | − | 0.493734i | \(-0.164368\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 240.627i | − | 0.600067i | −0.953929 | − | 0.300034i | \(-0.903002\pi\) | ||
0.953929 | − | 0.300034i | \(-0.0969979\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.31887 | − | 13.2921i | 0.0107168 | − | 0.0329829i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 440.219i | 1.08162i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 278.080 | + | 202.037i | 0.679902 | + | 0.493977i | 0.873325 | − | 0.487138i | \(-0.161959\pi\) |
−0.193423 | + | 0.981115i | \(0.561959\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 270.508 | − | 372.322i | 0.654983 | − | 0.901507i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 276.887 | + | 232.094i | 0.667197 | + | 0.559263i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −181.855 | + | 59.0884i | −0.434023 | + | 0.141023i | −0.517876 | − | 0.855456i | \(-0.673277\pi\) |
0.0838535 | + | 0.996478i | \(0.473277\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −170.176 | + | 523.749i | −0.404219 | + | 1.24406i | 0.517326 | + | 0.855788i | \(0.326927\pi\) |
−0.921545 | + | 0.388270i | \(0.873073\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −98.2017 | + | 703.970i | −0.231063 | + | 1.65640i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 41.3794 | − | 30.0639i | 0.0969072 | − | 0.0704072i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 523.416 | − | 170.068i | 1.21442 | − | 0.394589i | 0.369374 | − | 0.929281i | \(-0.379572\pi\) |
0.845047 | + | 0.534691i | \(0.179572\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 69.2362 | + | 213.087i | 0.159899 | + | 0.492118i | 0.998624 | − | 0.0524365i | \(-0.0166987\pi\) |
−0.838725 | + | 0.544555i | \(0.816699\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.66949 | + | 7.80338i | −0.0129737 | + | 0.0178567i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −381.341 | + | 277.061i | −0.868659 | + | 0.631118i | −0.930227 | − | 0.366985i | \(-0.880390\pi\) |
0.0615676 | + | 0.998103i | \(0.480390\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 627.722i | − | 1.41698i | −0.705721 | − | 0.708490i | \(-0.749377\pi\) | ||
0.705721 | − | 0.708490i | \(-0.250623\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −244.002 | + | 604.818i | −0.548320 | + | 1.35914i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 361.286i | 0.804646i | 0.915498 | + | 0.402323i | \(0.131797\pi\) | ||||
−0.915498 | + | 0.402323i | \(0.868203\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −113.741 | −0.252197 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.78982 | − | 97.8185i | 0.0149227 | − | 0.214986i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 346.134 | 0.757404 | 0.378702 | − | 0.925519i | \(-0.376370\pi\) | ||||
0.378702 | + | 0.925519i | \(0.376370\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 434.514 | + | 598.058i | 0.942547 | + | 1.29730i | 0.954759 | + | 0.297379i | \(0.0961126\pi\) |
−0.0122123 | + | 0.999925i | \(0.503887\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −139.715 | − | 101.509i | −0.301761 | − | 0.219242i | 0.426592 | − | 0.904444i | \(-0.359714\pi\) |
−0.728353 | + | 0.685202i | \(0.759714\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 256.382 | − | 83.3037i | 0.548999 | − | 0.178381i | −0.0213664 | − | 0.999772i | \(-0.506802\pi\) |
0.570365 | + | 0.821391i | \(0.306802\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −87.1705 | − | 268.283i | −0.185865 | − | 0.572033i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −226.794 | − | 312.155i | −0.479479 | − | 0.659946i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 128.923 | + | 17.9843i | 0.271416 | + | 0.0378617i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 833.189 | + | 270.720i | 1.73943 | + | 0.565177i | 0.994759 | − | 0.102250i | \(-0.0326041\pi\) |
0.744676 | + | 0.667426i | \(0.232604\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −32.0564 | − | 98.6594i | −0.0666453 | − | 0.205113i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −385.604 | + | 96.3515i | −0.795059 | + | 0.198663i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 270.570 | + | 196.580i | 0.555585 | + | 0.403656i | 0.829840 | − | 0.558001i | \(-0.188431\pi\) |
−0.274256 | + | 0.961657i | \(0.588431\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 344.800 | − | 474.576i | 0.702240 | − | 0.966550i | −0.297690 | − | 0.954663i | \(-0.596216\pi\) |
0.999929 | − | 0.0118873i | \(-0.00378392\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −563.090 | −1.14217 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 257.823 | + | 83.7717i | 0.518758 | + | 0.168555i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −459.281 | −0.920403 | −0.460202 | − | 0.887814i | \(-0.652223\pi\) | ||||
−0.460202 | + | 0.887814i | \(0.652223\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −526.878 | − | 171.193i | −1.04747 | − | 0.340344i | −0.265795 | − | 0.964029i | \(-0.585635\pi\) |
−0.781675 | + | 0.623686i | \(0.785635\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 64.3791 | − | 40.2743i | 0.127483 | − | 0.0797512i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.7591 | − | 24.4433i | 0.0348901 | − | 0.0480221i | −0.791216 | − | 0.611537i | \(-0.790551\pi\) |
0.826106 | + | 0.563515i | \(0.190551\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −564.103 | + | 409.845i | −1.10392 | + | 0.802045i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −45.2762 | + | 11.3132i | −0.0879149 | + | 0.0219674i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 56.0796 | + | 172.595i | 0.108471 | + | 0.333840i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.6889 | + | 12.5708i | 0.0742590 | + | 0.0241282i | 0.345911 | − | 0.938267i | \(-0.387570\pi\) |
−0.271652 | + | 0.962396i | \(0.587570\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 432.450 | − | 314.193i | 0.826864 | − | 0.600752i | −0.0918065 | − | 0.995777i | \(-0.529264\pi\) |
0.918670 | + | 0.395025i | \(0.129264\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 76.2780 | + | 104.988i | 0.144740 | + | 0.199218i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 162.410 | − | 499.845i | 0.307012 | − | 0.944887i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 25.4910 | − | 8.28252i | 0.0478255 | − | 0.0155394i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −348.473 | + | 217.998i | −0.651352 | + | 0.407474i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −60.9624 | − | 83.9076i | −0.113103 | − | 0.155673i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.6592 | + | 20.8221i | 0.0529745 | + | 0.0384882i | 0.613957 | − | 0.789339i | \(-0.289577\pi\) |
−0.560983 | + | 0.827827i | \(0.689577\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.4366 | − | 265.609i | 0.0338286 | − | 0.487356i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −111.187 | + | 342.199i | −0.203267 | + | 0.625592i | 0.796513 | + | 0.604622i | \(0.206676\pi\) |
−0.999780 | + | 0.0209707i | \(0.993324\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 103.122i | 0.187155i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −224.519 | + | 690.999i | −0.406002 | + | 1.24955i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 581.028i | 1.04314i | 0.853209 | + | 0.521569i | \(0.174653\pi\) | ||||
−0.853209 | + | 0.521569i | \(0.825347\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 73.5585 | + | 53.4434i | 0.131590 | + | 0.0956054i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 497.947 | − | 685.366i | 0.884454 | − | 1.21735i | −0.0907139 | − | 0.995877i | \(-0.528915\pi\) |
0.975167 | − | 0.221469i | \(-0.0710851\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.6392 | − | 1.50203i | −0.0382995 | − | 0.00265846i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 195.245 | − | 63.4390i | 0.343137 | − | 0.111492i | −0.132379 | − | 0.991199i | \(-0.542261\pi\) |
0.475516 | + | 0.879707i | \(0.342261\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 154.235 | − | 474.686i | 0.270113 | − | 0.831323i | −0.720358 | − | 0.693603i | \(-0.756022\pi\) |
0.990471 | − | 0.137721i | \(-0.0439776\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 45.6000 | − | 8.08864i | 0.0793043 | − | 0.0140672i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 281.175 | − | 204.285i | 0.487304 | − | 0.354047i | −0.316842 | − | 0.948478i | \(-0.602623\pi\) |
0.804147 | + | 0.594431i | \(0.202623\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 440.135 | − | 143.009i | 0.757548 | − | 0.246142i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 155.802 | + | 479.508i | 0.267241 | + | 0.822483i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −222.988 | + | 306.916i | −0.379877 | + | 0.522856i | −0.955552 | − | 0.294823i | \(-0.904739\pi\) |
0.575675 | + | 0.817679i | \(0.304739\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.2271 | − | 13.9693i | 0.0326436 | − | 0.0237170i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1032.11i | 1.74049i | 0.492615 | + | 0.870247i | \(0.336041\pi\) | ||||
−0.492615 | + | 0.870247i | \(0.663959\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 697.747 | + | 584.871i | 1.17268 | + | 0.982976i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 473.462i | 0.790421i | 0.918591 | + | 0.395210i | \(0.129328\pi\) | ||||
−0.918591 | + | 0.395210i | \(0.870672\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −282.810 | −0.470566 | −0.235283 | − | 0.971927i | \(-0.575602\pi\) | ||||
−0.235283 | + | 0.971927i | \(0.575602\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −232.085 | + | 57.9916i | −0.383612 | + | 0.0958538i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 426.439 | 0.702535 | 0.351268 | − | 0.936275i | \(-0.385751\pi\) | ||||
0.351268 | + | 0.936275i | \(0.385751\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −25.1365 | − | 34.5974i | −0.0411399 | − | 0.0566242i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −141.691 | − | 102.944i | −0.231143 | − | 0.167935i | 0.466185 | − | 0.884687i | \(-0.345628\pi\) |
−0.697328 | + | 0.716752i | \(0.745628\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 137.680 | − | 44.7349i | 0.223144 | − | 0.0725039i | −0.195311 | − | 0.980741i | \(-0.562572\pi\) |
0.418455 | + | 0.908237i | \(0.362572\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 81.4074 | + | 250.546i | 0.131514 | + | 0.404760i | 0.995032 | − | 0.0995598i | \(-0.0317434\pi\) |
−0.863517 | + | 0.504319i | \(0.831743\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 491.028 | + | 675.842i | 0.788167 | + | 1.08482i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −385.796 | − | 491.718i | −0.617274 | − | 0.786749i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 916.075 | + | 297.651i | 1.45640 | + | 0.473213i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −119.477 | − | 367.713i | −0.189346 | − | 0.582747i | 0.810650 | − | 0.585531i | \(-0.199114\pi\) |
−0.999996 | + | 0.00278376i | \(0.999114\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 696.943 | + | 281.168i | 1.09755 | + | 0.442785i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.7726 | + | 14.3657i | 0.0310403 | + | 0.0225521i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 126.177 | − | 173.667i | 0.196843 | − | 0.270932i | −0.699173 | − | 0.714952i | \(-0.746448\pi\) |
0.896017 | + | 0.444021i | \(0.146448\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −548.794 | −0.853490 | −0.426745 | − | 0.904372i | \(-0.640340\pi\) | ||||
−0.426745 | + | 0.904372i | \(0.640340\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −111.627 | − | 36.2697i | −0.172530 | − | 0.0560583i | 0.221478 | − | 0.975165i | \(-0.428912\pi\) |
−0.394008 | + | 0.919107i | \(0.628912\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 933.719 | 1.43870 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.65171 | − | 1.18651i | −0.00559220 | − | 0.00181702i | 0.306220 | − | 0.951961i | \(-0.400936\pi\) |
−0.311812 | + | 0.950144i | \(0.600936\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 746.813 | + | 625.999i | 1.14017 | + | 0.955724i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 575.488 | − | 792.091i | 0.873274 | − | 1.20196i | −0.104965 | − | 0.994476i | \(-0.533473\pi\) |
0.978239 | − | 0.207483i | \(-0.0665270\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 345.603 | − | 251.095i | 0.522849 | − | 0.379872i | −0.294827 | − | 0.955551i | \(-0.595262\pi\) |
0.817676 | + | 0.575679i | \(0.195262\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 107.111 | − | 127.783i | 0.161069 | − | 0.192155i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.3374 | + | 34.8929i | 0.0169976 | + | 0.0523132i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 98.6932 | + | 32.0674i | 0.147084 | + | 0.0477904i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −581.966 | + | 422.823i | −0.864733 | + | 0.628266i | −0.929169 | − | 0.369656i | \(-0.879475\pi\) |
0.0644352 | + | 0.997922i | \(0.479475\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 406.648 | + | 559.703i | 0.600662 | + | 0.826740i | 0.995769 | − | 0.0918952i | \(-0.0292925\pi\) |
−0.395107 | + | 0.918635i | \(0.629292\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −157.323 | + | 484.191i | −0.231699 | + | 0.713095i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 412.828 | − | 134.136i | 0.604434 | − | 0.196392i | 0.00921688 | − | 0.999958i | \(-0.497066\pi\) |
0.595217 | + | 0.803565i | \(0.297066\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −177.710 | − | 12.3353i | −0.259431 | − | 0.0180078i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −69.8347 | − | 96.1192i | −0.101357 | − | 0.139505i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −460.520 | − | 334.588i | −0.666455 | − | 0.484208i | 0.202382 | − | 0.979307i | \(-0.435132\pi\) |
−0.868837 | + | 0.495099i | \(0.835132\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1155.44 | + | 466.141i | 1.66251 | + | 0.670706i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −76.9051 | + | 236.690i | −0.110337 | + | 0.339583i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 269.426i | − | 0.384345i | −0.981361 | − | 0.192173i | \(-0.938447\pi\) | ||
0.981361 | − | 0.192173i | \(-0.0615534\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 54.5107 | − | 167.767i | 0.0775402 | − | 0.238644i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 97.2706i | − | 0.137582i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −433.936 | − | 315.273i | −0.612040 | − | 0.444673i | 0.238092 | − | 0.971243i | \(-0.423478\pi\) |
−0.850132 | + | 0.526569i | \(0.823478\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.96995 | − | 6.84055i | 0.00697048 | − | 0.00959404i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 168.656 | − | 105.508i | 0.235882 | − | 0.147563i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −90.4529 | + | 29.3899i | −0.125804 | + | 0.0408761i | −0.371242 | − | 0.928536i | \(-0.621068\pi\) |
0.245438 | + | 0.969412i | \(0.421068\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.4723 | + | 56.8520i | −0.0256204 | + | 0.0788516i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 343.581 | − | 356.519i | 0.473905 | − | 0.491750i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −892.381 | + | 648.353i | −1.22748 | + | 0.891819i | −0.996699 | − | 0.0811855i | \(-0.974129\pi\) |
−0.230785 | + | 0.973005i | \(0.574129\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −802.924 | + | 260.886i | −1.09839 | + | 0.356889i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 443.580 | + | 1365.20i | 0.605157 | + | 1.86248i | 0.495705 | + | 0.868491i | \(0.334910\pi\) |
0.109453 | + | 0.993992i | \(0.465090\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 336.404 | − | 463.020i | 0.456450 | − | 0.628250i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 843.208 | − | 612.626i | 1.14101 | − | 0.828994i | 0.153752 | − | 0.988109i | \(-0.450864\pi\) |
0.987260 | + | 0.159116i | \(0.0508643\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1006.03i | 1.35401i | 0.735977 | + | 0.677006i | \(0.236723\pi\) | ||||
−0.735977 | + | 0.677006i | \(0.763277\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1144.40 | + | 715.916i | −1.53611 | + | 0.960961i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 526.510i | 0.702950i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −698.284 | −0.929806 | −0.464903 | − | 0.885362i | \(-0.653911\pi\) | ||||
−0.464903 | + | 0.885362i | \(0.653911\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −366.248 | − | 585.452i | −0.485097 | − | 0.775433i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −240.559 | −0.317779 | −0.158889 | − | 0.987296i | \(-0.550791\pi\) | ||||
−0.158889 | + | 0.987296i | \(0.550791\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −449.802 | − | 619.099i | −0.591067 | − | 0.813534i | 0.403787 | − | 0.914853i | \(-0.367694\pi\) |
−0.994854 | + | 0.101319i | \(0.967694\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −275.907 | − | 200.458i | −0.361608 | − | 0.262724i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −209.260 | + | 67.9926i | −0.272829 | + | 0.0886475i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.2844 | − | 47.0405i | −0.0198757 | − | 0.0611710i | 0.940627 | − | 0.339443i | \(-0.110238\pi\) |
−0.960502 | + | 0.278272i | \(0.910238\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 65.8162 | + | 90.5883i | 0.0851439 | + | 0.117191i | 0.849464 | − | 0.527646i | \(-0.176925\pi\) |
−0.764320 | + | 0.644837i | \(0.776925\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −113.015 | − | 15.7653i | −0.145826 | − | 0.0203423i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 43.3465 | + | 14.0841i | 0.0556438 | + | 0.0180798i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 169.962 | + | 523.090i | 0.217621 | + | 0.669769i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −245.442 | − | 392.342i | −0.312664 | − | 0.499798i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 815.520 | + | 592.510i | 1.03624 | + | 0.752872i | 0.969548 | − | 0.244902i | \(-0.0787558\pi\) |
0.0666911 | + | 0.997774i | \(0.478756\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.3314 | + | 22.4782i | −0.0206465 | + | 0.0284174i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.4537 | −0.0308369 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30.3919 | + | 9.87494i | 0.0381329 | + | 0.0123901i | 0.328021 | − | 0.944670i | \(-0.393618\pi\) |
−0.289888 | + | 0.957060i | \(0.593618\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 397.080 | 0.496971 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1345.43 | − | 437.158i | −1.67551 | − | 0.544405i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 22.1940 | − | 55.0130i | 0.0275701 | − | 0.0683392i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 104.062 | − | 143.229i | 0.128631 | − | 0.177045i | −0.739844 | − | 0.672778i | \(-0.765101\pi\) |
0.868475 | + | 0.495734i | \(0.165101\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −700.534 | + | 508.968i | −0.863790 | + | 0.627580i | −0.928913 | − | 0.370297i | \(-0.879256\pi\) |
0.0651233 | + | 0.997877i | \(0.479256\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −90.1198 | + | 1298.32i | −0.110576 | + | 1.59303i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 47.7777 | + | 147.045i | 0.0584794 | + | 0.179981i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 168.994 | + | 54.9095i | 0.205839 | + | 0.0668813i | 0.410122 | − | 0.912031i | \(-0.365486\pi\) |
−0.204283 | + | 0.978912i | \(0.565486\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 512.628 | − | 372.446i | 0.622877 | − | 0.452546i | −0.231048 | − | 0.972942i | \(-0.574216\pi\) |
0.853925 | + | 0.520396i | \(0.174216\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −493.072 | − | 678.656i | −0.596218 | − | 0.820623i | 0.399138 | − | 0.916891i | \(-0.369310\pi\) |
−0.995355 | + | 0.0962675i | \(0.969310\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −235.221 | + | 723.936i | −0.283741 | + | 0.873264i | 0.703032 | + | 0.711158i | \(0.251829\pi\) |
−0.986773 | + | 0.162107i | \(0.948171\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −215.827 | + | 70.1265i | −0.259096 | + | 0.0841854i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −317.282 | − | 265.955i | −0.379979 | − | 0.318509i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −369.544 | − | 508.633i | −0.440457 | − | 0.606238i | 0.529856 | − | 0.848087i | \(-0.322246\pi\) |
−0.970314 | + | 0.241850i | \(0.922246\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −363.050 | − | 263.771i | −0.431688 | − | 0.313640i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 512.709 | − | 611.658i | 0.606756 | − | 0.723856i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −94.6890 | + | 291.423i | −0.111793 | + | 0.344065i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 62.7592i | − | 0.0737476i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 140.866 | − | 433.541i | 0.165142 | − | 0.508254i | −0.833905 | − | 0.551908i | \(-0.813900\pi\) |
0.999047 | + | 0.0436539i | \(0.0138999\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1558.32i | − | 1.81834i | −0.416423 | − | 0.909171i | \(-0.636717\pi\) | ||
0.416423 | − | 0.909171i | \(-0.363283\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −788.279 | − | 572.718i | −0.917670 | − | 0.666726i | 0.0252728 | − | 0.999681i | \(-0.491955\pi\) |
−0.942943 | + | 0.332954i | \(0.891955\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 188.167 | − | 258.990i | 0.218039 | − | 0.300105i | −0.685960 | − | 0.727639i | \(-0.740618\pi\) |
0.903999 | + | 0.427534i | \(0.140618\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 585.298 | − | 1450.80i | 0.676645 | − | 1.67723i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1401.95 | + | 455.521i | −1.61329 | + | 0.524190i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −41.6762 | + | 128.266i | −0.0478486 | + | 0.147263i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −796.053 | + | 84.9046i | −0.909775 | + | 0.0970339i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 957.827 | − | 695.902i | 1.09216 | − | 0.793503i | 0.112400 | − | 0.993663i | \(-0.464146\pi\) |
0.979763 | + | 0.200160i | \(0.0641461\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 711.158 | − | 231.069i | 0.807216 | − | 0.262281i | 0.123798 | − | 0.992307i | \(-0.460492\pi\) |
0.683418 | + | 0.730027i | \(0.260492\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −243.167 | − | 748.390i | −0.275387 | − | 0.847554i | −0.989117 | − | 0.147133i | \(-0.952996\pi\) |
0.713730 | − | 0.700421i | \(-0.247004\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −647.316 | + | 890.955i | −0.729782 | + | 1.00446i | 0.269360 | + | 0.963040i | \(0.413188\pi\) |
−0.999142 | + | 0.0414189i | \(0.986812\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 778.785 | − | 565.821i | 0.876024 | − | 0.636469i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 72.7199i | − | 0.0814332i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −197.753 | − | 791.417i | −0.220953 | − | 0.884265i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 90.3984i | − | 0.100554i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1103.18 | 1.22439 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 346.851 | − | 413.791i | 0.383261 | − | 0.457228i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1028.21 | −1.13364 | −0.566822 | − | 0.823841i | \(-0.691827\pi\) | ||||
−0.566822 | + | 0.823841i | \(0.691827\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 535.454 | + | 736.989i | 0.587765 | + | 0.808989i | 0.994520 | − | 0.104549i | \(-0.0333398\pi\) |
−0.406755 | + | 0.913537i | \(0.633340\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 759.613 | + | 551.891i | 0.831997 | + | 0.604481i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1187.12 | − | 385.720i | 1.29457 | − | 0.420632i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −353.826 | − | 1088.96i | −0.385012 | − | 1.18494i | −0.936472 | − | 0.350743i | \(-0.885929\pi\) |
0.551460 | − | 0.834201i | \(-0.314071\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −76.1819 | − | 104.855i | −0.0825373 | − | 0.113603i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −747.419 | + | 398.392i | −0.808021 | + | 0.430694i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 308.060 | + | 100.095i | 0.331604 | + | 0.107745i | 0.470087 | − | 0.882620i | \(-0.344223\pi\) |
−0.138483 | + | 0.990365i | \(0.544223\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.8427 | + | 39.5258i | 0.0137945 | + | 0.0424552i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −127.910 | + | 1842.76i | −0.136803 | + | 1.97086i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −611.800 | − | 444.498i | −0.652935 | − | 0.474385i | 0.211335 | − | 0.977414i | \(-0.432219\pi\) |
−0.864270 | + | 0.503029i | \(0.832219\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −720.045 | + | 991.057i | −0.765192 | + | 1.05320i | 0.231573 | + | 0.972818i | \(0.425613\pi\) |
−0.996764 | + | 0.0803784i | \(0.974387\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.2153 | 0.0171955 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1395.84 | − | 453.537i | −1.47396 | − | 0.478919i | −0.541660 | − | 0.840598i | \(-0.682204\pi\) |
−0.932303 | + | 0.361678i | \(0.882204\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 333.364 | 0.351280 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1439.40 | − | 467.690i | −1.51039 | − | 0.490756i | −0.567362 | − | 0.823468i | \(-0.692036\pi\) |
−0.943028 | + | 0.332713i | \(0.892036\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1080.00 | + | 74.9653i | 1.13089 | + | 0.0784977i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −134.120 | + | 184.600i | −0.139854 | + | 0.192492i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 760.611 | − | 552.616i | 0.791478 | − | 0.575043i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −499.999 | − | 799.255i | −0.518134 | − | 0.828244i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.92221 | + | 8.99364i | 0.00302194 | + | 0.00930056i | 0.952556 | − | 0.304363i | \(-0.0984436\pi\) |
−0.949534 | + | 0.313664i | \(0.898444\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −606.110 | − | 196.937i | −0.624212 | − | 0.202819i | −0.0202027 | − | 0.999796i | \(-0.506431\pi\) |
−0.604010 | + | 0.796977i | \(0.706431\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1291.13 | − | 938.057i | 1.32695 | − | 0.964088i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 919.151 | + | 1265.10i | 0.940790 | + | 1.29489i | 0.955499 | + | 0.294994i | \(0.0953176\pi\) |
−0.0147096 | + | 0.999892i | \(0.504682\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −523.750 | + | 1611.94i | −0.534985 | + | 1.64651i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1332.38 | − | 432.918i | 1.35543 | − | 0.440405i | 0.460912 | − | 0.887446i | \(-0.347522\pi\) |
0.894513 | + | 0.447041i | \(0.147522\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.54600 | + | 34.2015i | 0.00867614 | + | 0.0347224i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.3325 | + | 44.5019i | 0.0326921 | + | 0.0449968i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 791.863 | + | 575.322i | 0.799055 | + | 0.580547i | 0.910637 | − | 0.413208i | \(-0.135592\pi\) |
−0.111582 | + | 0.993755i | \(0.535592\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −152.166 | − | 243.239i | −0.152930 | − | 0.244461i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 339.802 | − | 1045.80i | 0.340825 | − | 1.04895i | −0.622957 | − | 0.782256i | \(-0.714069\pi\) |
0.963781 | − | 0.266694i | \(-0.0859312\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 900.3.ba.a.161.14 | yes | 80 | |
3.2 | odd | 2 | inner | 900.3.ba.a.161.7 | ✓ | 80 | |
25.16 | even | 5 | inner | 900.3.ba.a.341.7 | yes | 80 | |
75.41 | odd | 10 | inner | 900.3.ba.a.341.14 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
900.3.ba.a.161.7 | ✓ | 80 | 3.2 | odd | 2 | inner | |
900.3.ba.a.161.14 | yes | 80 | 1.1 | even | 1 | trivial | |
900.3.ba.a.341.7 | yes | 80 | 25.16 | even | 5 | inner | |
900.3.ba.a.341.14 | yes | 80 | 75.41 | odd | 10 | inner |