Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [760,2,Mod(609,760)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(760, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("760.609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 760 = 2^{3} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 760.d (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: | \(6.06863055362\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 609.1 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 760.609 |
Dual form | 760.2.d.d.609.4 |
$q$-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 \(\left(\mathbb{Z}/760\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(381\) | \(401\) | \(457\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.41421i | − | 0.816497i | −0.912871 | − | 0.408248i | \(-0.866140\pi\) | ||
0.912871 | − | 0.408248i | \(-0.133860\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | − | 2.00000i | 0.447214 | − | 0.894427i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.82843i | 1.82497i | 0.409106 | + | 0.912487i | \(0.365841\pi\) | ||||
−0.409106 | + | 0.912487i | \(0.634159\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.82843 | 1.45583 | 0.727913 | − | 0.685670i | \(-0.240491\pi\) | ||||
0.727913 | + | 0.685670i | \(0.240491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 0.585786i | − | 0.162468i | −0.996695 | − | 0.0812340i | \(-0.974114\pi\) | ||
0.996695 | − | 0.0812340i | \(-0.0258861\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.82843 | − | 1.41421i | −0.730297 | − | 0.365148i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.82843i | 0.685994i | 0.939336 | + | 0.342997i | \(0.111442\pi\) | ||||
−0.939336 | + | 0.342997i | \(0.888558\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.82843 | 1.49008 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.65685i | 1.59656i | 0.602284 | + | 0.798282i | \(0.294258\pi\) | ||||
−0.602284 | + | 0.798282i | \(0.705742\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.00000 | − | 4.00000i | −0.600000 | − | 0.800000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.65685i | − | 1.08866i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.65685 | −0.679061 | −0.339530 | − | 0.940595i | \(-0.610268\pi\) | ||||
−0.339530 | + | 0.940595i | \(0.610268\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.82843 | 1.22642 | 0.613211 | − | 0.789919i | \(-0.289878\pi\) | ||||
0.613211 | + | 0.789919i | \(0.289878\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 6.82843i | − | 1.18868i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.65685 | + | 4.82843i | 1.63231 | + | 0.816153i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 0.585786i | − | 0.0963027i | −0.998840 | − | 0.0481513i | \(-0.984667\pi\) | ||
0.998840 | − | 0.0481513i | \(-0.0153330\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.828427 | −0.132655 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.828427 | 0.129379 | 0.0646893 | − | 0.997905i | \(-0.479394\pi\) | ||||
0.0646893 | + | 0.997905i | \(0.479394\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.82843i | − | 1.34632i | −0.739496 | − | 0.673161i | \(-0.764936\pi\) | ||
0.739496 | − | 0.673161i | \(-0.235064\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | − | 2.00000i | 0.149071 | − | 0.298142i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 0.828427i | − | 0.120839i | −0.998173 | − | 0.0604193i | \(-0.980756\pi\) | ||
0.998173 | − | 0.0604193i | \(-0.0192438\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −16.3137 | −2.33053 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.00000 | 0.560112 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 11.8995i | − | 1.63452i | −0.576268 | − | 0.817261i | \(-0.695492\pi\) | ||
0.576268 | − | 0.817261i | \(-0.304508\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.82843 | − | 9.65685i | 0.651065 | − | 1.30213i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.41421i | − | 0.187317i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.82843 | 0.888985 | 0.444493 | − | 0.895782i | \(-0.353384\pi\) | ||||
0.444493 | + | 0.895782i | \(0.353384\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.65685 | −0.724286 | −0.362143 | − | 0.932123i | \(-0.617955\pi\) | ||||
−0.362143 | + | 0.932123i | \(0.617955\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.82843i | 0.608325i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.17157 | − | 0.585786i | −0.145316 | − | 0.0726579i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 9.89949i | − | 1.20942i | −0.796447 | − | 0.604708i | \(-0.793290\pi\) | ||
0.796447 | − | 0.604708i | \(-0.206710\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.8284 | 1.30359 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.48528 | −1.00702 | −0.503509 | − | 0.863990i | \(-0.667958\pi\) | ||||
−0.503509 | + | 0.863990i | \(0.667958\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.17157i | − | 0.137122i | −0.997647 | − | 0.0685611i | \(-0.978159\pi\) | ||
0.997647 | − | 0.0685611i | \(-0.0218408\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.65685 | + | 4.24264i | −0.653197 | + | 0.489898i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 23.3137i | 2.65684i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.48528 | −0.954669 | −0.477334 | − | 0.878722i | \(-0.658397\pi\) | ||||
−0.477334 | + | 0.878722i | \(0.658397\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.6569i | 1.71856i | 0.511503 | + | 0.859282i | \(0.329089\pi\) | ||||
−0.511503 | + | 0.859282i | \(0.670911\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.65685 | + | 2.82843i | 0.613572 | + | 0.306786i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.17157i | 0.554451i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.3137 | 1.41125 | 0.705625 | − | 0.708585i | \(-0.250666\pi\) | ||||
0.705625 | + | 0.708585i | \(0.250666\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.82843 | 0.296500 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 9.65685i | − | 1.00137i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00000 | − | 2.00000i | 0.102598 | − | 0.205196i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.07107i | − | 0.108750i | −0.998521 | − | 0.0543752i | \(-0.982683\pi\) | ||
0.998521 | − | 0.0543752i | \(-0.0173167\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.82843 | 0.485275 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.00000 | −0.796030 | −0.398015 | − | 0.917379i | \(-0.630301\pi\) | ||||
−0.398015 | + | 0.917379i | \(0.630301\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.89949i | 0.975426i | 0.873004 | + | 0.487713i | \(0.162169\pi\) | ||||
−0.873004 | + | 0.487713i | \(0.837831\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.82843 | − | 13.6569i | 0.666386 | − | 1.33277i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.2426i | 1.57024i | 0.619347 | + | 0.785118i | \(0.287398\pi\) | ||||
−0.619347 | + | 0.785118i | \(0.712602\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.4853 | 1.00431 | 0.502154 | − | 0.864778i | \(-0.332541\pi\) | ||||
0.502154 | + | 0.864778i | \(0.332541\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.828427 | −0.0786308 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 11.4142i | − | 1.07376i | −0.843659 | − | 0.536879i | \(-0.819603\pi\) | ||
0.843659 | − | 0.536879i | \(-0.180397\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.3137 | + | 7.65685i | 1.42801 | + | 0.714005i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 0.585786i | − | 0.0541560i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13.6569 | −1.25192 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.3137 | 1.11943 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 1.17157i | − | 0.105637i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.0000 | + | 2.00000i | −0.983870 | + | 0.178885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.7279i | 1.12942i | 0.825289 | + | 0.564710i | \(0.191012\pi\) | ||||
−0.825289 | + | 0.564710i | \(0.808988\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.4853 | −1.09927 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.6569 | −1.54269 | −0.771343 | − | 0.636419i | \(-0.780415\pi\) | ||||
−0.771343 | + | 0.636419i | \(0.780415\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.82843i | 0.418678i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.3137 | − | 5.65685i | −0.973729 | − | 0.486864i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.82843i | 0.241649i | 0.992674 | + | 0.120824i | \(0.0385538\pi\) | ||||
−0.992674 | + | 0.120824i | \(0.961446\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.1716 | −1.28684 | −0.643418 | − | 0.765515i | \(-0.722484\pi\) | ||||
−0.643418 | + | 0.765515i | \(0.722484\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.17157 | −0.0986642 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 2.82843i | − | 0.236525i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.65685 | + | 7.31371i | −0.303685 | + | 0.607370i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 23.0711i | 1.90287i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.00000 | −0.327693 | −0.163846 | − | 0.986486i | \(-0.552390\pi\) | ||||
−0.163846 | + | 0.986486i | \(0.552390\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.34315 | −0.190682 | −0.0953412 | − | 0.995445i | \(-0.530394\pi\) | ||||
−0.0953412 | + | 0.995445i | \(0.530394\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.82843i | 0.228665i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.82843 | − | 13.6569i | 0.548472 | − | 1.09694i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 4.48528i | − | 0.357964i | −0.983852 | − | 0.178982i | \(-0.942720\pi\) | ||
0.983852 | − | 0.178982i | \(-0.0572805\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −16.8284 | −1.33458 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −36.9706 | −2.91369 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 14.4853i | − | 1.13457i | −0.823520 | − | 0.567287i | \(-0.807993\pi\) | ||
0.823520 | − | 0.567287i | \(-0.192007\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −13.6569 | − | 6.82843i | −1.06318 | − | 0.531592i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 3.07107i | − | 0.237646i | −0.992915 | − | 0.118823i | \(-0.962088\pi\) | ||
0.992915 | − | 0.118823i | \(-0.0379122\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.6569 | 0.973604 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.58579i | 0.652765i | 0.945238 | + | 0.326383i | \(0.105830\pi\) | ||||
−0.945238 | + | 0.326383i | \(0.894170\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 19.3137 | − | 14.4853i | 1.45998 | − | 1.09498i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 9.65685i | − | 0.725854i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.8284 | −1.70628 | −0.853138 | − | 0.521685i | \(-0.825304\pi\) | ||||
−0.853138 | + | 0.521685i | \(0.825304\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.68629 | 0.199670 | 0.0998352 | − | 0.995004i | \(-0.468168\pi\) | ||||
0.0998352 | + | 0.995004i | \(0.468168\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.00000i | 0.591377i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.17157 | − | 0.585786i | −0.0861358 | − | 0.0430679i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.6569i | 0.998688i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 27.3137 | 1.98678 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.3137 | 1.39749 | 0.698745 | − | 0.715370i | \(-0.253742\pi\) | ||||
0.698745 | + | 0.715370i | \(0.253742\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.07107i | 0.0770971i | 0.999257 | + | 0.0385486i | \(0.0122734\pi\) | ||||
−0.999257 | + | 0.0385486i | \(0.987727\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.828427 | + | 1.65685i | −0.0593249 | + | 0.118650i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.3431i | 0.736919i | 0.929644 | + | 0.368459i | \(0.120115\pi\) | ||||
−0.929644 | + | 0.368459i | \(0.879885\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.3137 | 0.802008 | 0.401004 | − | 0.916076i | \(-0.368661\pi\) | ||||
0.401004 | + | 0.916076i | \(0.368661\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.0000 | −0.987484 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 17.6569i | − | 1.23927i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.828427 | − | 1.65685i | 0.0578599 | − | 0.115720i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.65685i | 0.532188i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.82843 | 0.333989 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.6274 | −1.55774 | −0.778868 | − | 0.627188i | \(-0.784206\pi\) | ||||
−0.778868 | + | 0.627188i | \(0.784206\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.0000i | 0.822226i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.6569 | − | 8.82843i | −1.20419 | − | 0.602094i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 32.9706i | 2.23819i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.65685 | −0.111960 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.65685 | 0.111452 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 9.89949i | − | 0.662919i | −0.943469 | − | 0.331460i | \(-0.892459\pi\) | ||
0.943469 | − | 0.331460i | \(-0.107541\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00000 | − | 4.00000i | −0.200000 | − | 0.266667i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.92893i | 0.327145i | 0.986531 | + | 0.163572i | \(0.0523017\pi\) | ||||
−0.986531 | + | 0.163572i | \(0.947698\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.31371 | −0.218976 | −0.109488 | − | 0.993988i | \(-0.534921\pi\) | ||||
−0.109488 | + | 0.993988i | \(0.534921\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 32.9706 | 2.16930 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 28.9706i | − | 1.89792i | −0.315389 | − | 0.948962i | \(-0.602135\pi\) | ||
0.315389 | − | 0.948962i | \(-0.397865\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.65685 | − | 0.828427i | −0.108081 | − | 0.0540406i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.0000i | 0.779484i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.97056 | 0.580257 | 0.290129 | − | 0.956988i | \(-0.406302\pi\) | ||||
0.290129 | + | 0.956988i | \(0.406302\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.17157 | 0.204299 | 0.102149 | − | 0.994769i | \(-0.467428\pi\) | ||||
0.102149 | + | 0.994769i | \(0.467428\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 9.89949i | − | 0.635053i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −16.3137 | + | 32.6274i | −1.04224 | + | 2.08449i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 0.585786i | − | 0.0372727i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 22.1421 | 1.40320 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.00000 | 0.252478 | 0.126239 | − | 0.992000i | \(-0.459709\pi\) | ||||
0.126239 | + | 0.992000i | \(0.459709\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 36.9706i | 2.32432i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.00000 | − | 8.00000i | 0.250490 | − | 0.500979i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 10.2426i | − | 0.638918i | −0.947600 | − | 0.319459i | \(-0.896499\pi\) | ||
0.947600 | − | 0.319459i | \(-0.103501\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.82843 | 0.175750 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.65685 | −0.226354 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.31371i | 0.327657i | 0.986489 | + | 0.163829i | \(0.0523844\pi\) | ||||
−0.986489 | + | 0.163829i | \(0.947616\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −23.7990 | − | 11.8995i | −1.46196 | − | 0.730980i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 18.8284i | − | 1.15228i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −20.1421 | −1.22809 | −0.614044 | − | 0.789272i | \(-0.710458\pi\) | ||||
−0.614044 | + | 0.789272i | \(0.710458\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.1716 | 1.16459 | 0.582295 | − | 0.812978i | \(-0.302155\pi\) | ||||
0.582295 | + | 0.812978i | \(0.302155\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 4.00000i | − | 0.242091i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.4853 | − | 19.3137i | −0.873495 | − | 1.16466i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.17157i | 0.551066i | 0.961292 | + | 0.275533i | \(0.0888544\pi\) | ||||
−0.961292 | + | 0.275533i | \(0.911146\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.82843 | 0.408807 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.4853 | −1.34136 | −0.670680 | − | 0.741747i | \(-0.733997\pi\) | ||||
−0.670680 | + | 0.741747i | \(0.733997\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.97056i | 0.176582i | 0.996095 | + | 0.0882908i | \(0.0281405\pi\) | ||||
−0.996095 | + | 0.0882908i | \(0.971860\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.82843 | − | 1.41421i | −0.167542 | − | 0.0837708i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.00000i | 0.236113i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.00000 | 0.529412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.51472 | −0.0887944 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.75736i | 0.570031i | 0.958523 | + | 0.285016i | \(0.0919988\pi\) | ||||
−0.958523 | + | 0.285016i | \(0.908001\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.82843 | − | 13.6569i | 0.397566 | − | 0.795133i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 27.3137i | − | 1.58490i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.48528 | 0.259391 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 42.6274 | 2.45700 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.3137i | 0.649956i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.65685 | + | 11.3137i | −0.323911 | + | 0.647821i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.58579i | 0.147579i | 0.997274 | + | 0.0737893i | \(0.0235092\pi\) | ||||
−0.997274 | + | 0.0737893i | \(0.976491\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.0000 | 0.796432 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.1716 | −1.31394 | −0.656970 | − | 0.753917i | \(-0.728162\pi\) | ||||
−0.656970 | + | 0.753917i | \(0.728162\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 20.9706i | − | 1.18533i | −0.805450 | − | 0.592663i | \(-0.798077\pi\) | ||
0.805450 | − | 0.592663i | \(-0.201923\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.65685 | + | 4.82843i | 0.544102 | + | 0.272051i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 10.7279i | − | 0.602540i | −0.953539 | − | 0.301270i | \(-0.902589\pi\) | ||
0.953539 | − | 0.301270i | \(-0.0974106\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −17.6569 | −0.988594 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 22.9706 | 1.28209 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.82843i | 0.157378i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.34315 | + | 1.75736i | −0.129974 | + | 0.0974808i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 14.8284i | − | 0.820014i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.00000 | 0.220527 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.6569 | −0.750649 | −0.375324 | − | 0.926894i | \(-0.622469\pi\) | ||||
−0.375324 | + | 0.926894i | \(0.622469\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 0.585786i | − | 0.0321009i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.7990 | − | 9.89949i | −1.08173 | − | 0.540867i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 15.8995i | − | 0.866101i | −0.901370 | − | 0.433050i | \(-0.857437\pi\) | ||
0.901370 | − | 0.433050i | \(-0.142563\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.1421 | −0.876720 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 32.9706 | 1.78546 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 44.9706i | − | 2.42818i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10.8284 | − | 21.6569i | 0.582983 | − | 1.16597i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 18.0000i | − | 0.966291i | −0.875540 | − | 0.483145i | \(-0.839494\pi\) | ||
0.875540 | − | 0.483145i | \(-0.160506\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.6274 | −1.53239 | −0.766195 | − | 0.642608i | \(-0.777852\pi\) | ||||
−0.766195 | + | 0.642608i | \(0.777852\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.31371 | −0.176873 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.1421i | 0.752710i | 0.926476 | + | 0.376355i | \(0.122823\pi\) | ||||
−0.926476 | + | 0.376355i | \(0.877177\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.48528 | + | 16.9706i | −0.450352 | + | 0.900704i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 19.3137i | 1.02219i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.4853 | 0.553392 | 0.276696 | − | 0.960958i | \(-0.410761\pi\) | ||||
0.276696 | + | 0.960958i | \(0.410761\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 17.4142i | − | 0.914009i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.34315 | − | 1.17157i | −0.122646 | − | 0.0613229i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.1421i | 1.05141i | 0.850667 | + | 0.525705i | \(0.176199\pi\) | ||||
−0.850667 | + | 0.525705i | \(0.823801\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.828427 | 0.0431262 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 57.4558 | 2.98296 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 27.8995i | − | 1.44458i | −0.691590 | − | 0.722291i | \(-0.743089\pi\) | ||
0.691590 | − | 0.722291i | \(-0.256911\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.82843 | + | 15.5563i | 0.146059 | + | 0.803326i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.14214i | 0.110326i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.3137 | 1.19754 | 0.598772 | − | 0.800919i | \(-0.295655\pi\) | ||||
0.598772 | + | 0.800919i | \(0.295655\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.0000 | 0.922168 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.4142i | 0.685434i | 0.939439 | + | 0.342717i | \(0.111347\pi\) | ||||
−0.939439 | + | 0.342717i | \(0.888653\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 46.6274 | + | 23.3137i | 2.37635 | + | 1.18818i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 8.82843i | − | 0.448774i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.31371 | 0.472224 | 0.236112 | − | 0.971726i | \(-0.424127\pi\) | ||||
0.236112 | + | 0.971726i | \(0.424127\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.6569 | −1.09523 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 24.9706i | 1.25960i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.48528 | + | 16.9706i | −0.426941 | + | 0.853882i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.1716i | 0.661062i | 0.943795 | + | 0.330531i | \(0.107228\pi\) | ||||
−0.943795 | + | 0.330531i | \(0.892772\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.82843 | 0.341849 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.9706 | −1.34685 | −0.673423 | − | 0.739258i | \(-0.735177\pi\) | ||||
−0.673423 | + | 0.739258i | \(0.735177\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 4.00000i | − | 0.199254i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.00000 | + | 10.0000i | −0.248452 | + | 0.496904i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.82843i | − | 0.140200i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 36.8284 | 1.82105 | 0.910524 | − | 0.413456i | \(-0.135678\pi\) | ||||
0.910524 | + | 0.413456i | \(0.135678\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.00000 | 0.197305 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 32.9706i | 1.62238i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 31.3137 | + | 15.6569i | 1.53713 | + | 0.768565i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 21.4558i | 1.05070i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.6274 | 0.519183 | 0.259592 | − | 0.965718i | \(-0.416412\pi\) | ||||
0.259592 | + | 0.965718i | \(0.416412\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.79899 | −0.0876774 | −0.0438387 | − | 0.999039i | \(-0.513959\pi\) | ||||
−0.0438387 | + | 0.999039i | \(0.513959\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 0.828427i | − | 0.0402795i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.3137 | − | 8.48528i | 0.548795 | − | 0.411597i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 27.3137i | − | 1.32180i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.00000 | −0.193122 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.9411 | −1.44221 | −0.721107 | − | 0.692824i | \(-0.756366\pi\) | ||||
−0.721107 | + | 0.692824i | \(0.756366\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.5563i | 1.80484i | 0.430854 | + | 0.902421i | \(0.358212\pi\) | ||||
−0.430854 | + | 0.902421i | \(0.641788\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.3431 | + | 5.17157i | 0.495916 | + | 0.247958i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.65685i | 0.366277i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −28.4853 | −1.35953 | −0.679764 | − | 0.733431i | \(-0.737918\pi\) | ||||
−0.679764 | + | 0.733431i | \(0.737918\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.3137 | −0.776843 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 16.6274i | − | 0.789992i | −0.918683 | − | 0.394996i | \(-0.870746\pi\) | ||
0.918683 | − | 0.394996i | \(-0.129254\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.3137 | − | 26.6274i | 0.631130 | − | 1.26226i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.65685i | 0.267560i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.4853 | 1.24992 | 0.624959 | − | 0.780658i | \(-0.285116\pi\) | ||||
0.624959 | + | 0.780658i | \(0.285116\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.00000 | 0.188353 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.31371i | 0.155692i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.82843 | − | 5.65685i | 0.132599 | − | 0.265197i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 8.97056i | − | 0.419625i | −0.977742 | − | 0.209813i | \(-0.932715\pi\) | ||
0.977742 | − | 0.209813i | \(-0.0672854\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 16.0000 | 0.746816 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.31371 | −0.247484 | −0.123742 | − | 0.992314i | \(-0.539490\pi\) | ||||
−0.123742 | + | 0.992314i | \(0.539490\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 30.9706i | − | 1.43932i | −0.694325 | − | 0.719662i | \(-0.744297\pi\) | ||
0.694325 | − | 0.719662i | \(-0.255703\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −19.3137 | − | 9.65685i | −0.895652 | − | 0.447826i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.6569i | 0.909611i | 0.890591 | + | 0.454805i | \(0.150291\pi\) | ||||
−0.890591 | + | 0.454805i | \(0.849709\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 47.7990 | 2.20715 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.34315 | −0.292277 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 42.6274i | − | 1.96001i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.00000 | − | 4.00000i | −0.137649 | − | 0.183533i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 11.8995i | − | 0.544840i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.8284 | 0.586146 | 0.293073 | − | 0.956090i | \(-0.405322\pi\) | ||||
0.293073 | + | 0.956090i | \(0.405322\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.343146 | −0.0156461 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 52.2843i | 2.37902i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.14214 | − | 1.07107i | −0.0972694 | − | 0.0486347i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 7.27208i | − | 0.329529i | −0.986333 | − | 0.164765i | \(-0.947314\pi\) | ||
0.986333 | − | 0.164765i | \(-0.0526865\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −20.4853 | −0.926376 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.34315 | 0.286262 | 0.143131 | − | 0.989704i | \(-0.454283\pi\) | ||||
0.143131 | + | 0.989704i | \(0.454283\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 10.3431i | − | 0.465832i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.82843 | − | 9.65685i | 0.217022 | − | 0.434043i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 40.9706i | − | 1.83778i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.4558 | −0.691899 | −0.345949 | − | 0.938253i | \(-0.612443\pi\) | ||||
−0.345949 | + | 0.938253i | \(0.612443\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.34315 | −0.194037 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.0000i | 1.15928i | 0.814872 | + | 0.579641i | \(0.196807\pi\) | ||||
−0.814872 | + | 0.579641i | \(0.803193\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.00000 | + | 16.0000i | −0.355995 | + | 0.711991i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 17.8995i | − | 0.794944i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 43.9411 | 1.94766 | 0.973828 | − | 0.227286i | \(-0.0729852\pi\) | ||||
0.973828 | + | 0.227286i | \(0.0729852\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.65685 | 0.250244 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 5.65685i | − | 0.249756i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 19.7990 | + | 9.89949i | 0.872448 | + | 0.436224i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 4.00000i | − | 0.175920i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.1421 | 0.532981 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.3431 | −1.06649 | −0.533246 | − | 0.845960i | \(-0.679028\pi\) | ||||
−0.533246 | + | 0.845960i | \(0.679028\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 34.5858i | − | 1.51233i | −0.654381 | − | 0.756165i | \(-0.727071\pi\) | ||
0.654381 | − | 0.756165i | \(-0.272929\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −20.4853 | − | 27.3137i | −0.894051 | − | 1.19207i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19.3137i | 0.841318i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −35.6274 | −1.54902 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.82843 | 0.296328 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 0.485281i | − | 0.0210199i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 32.4853 | + | 16.2426i | 1.40446 | + | 0.702231i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 32.2843i | 1.39317i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −78.7696 | −3.39284 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.00000 | 0.171973 | 0.0859867 | − | 0.996296i | \(-0.472596\pi\) | ||||
0.0859867 | + | 0.996296i | \(0.472596\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 3.79899i | − | 0.163030i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.4853 | − | 20.9706i | 0.449140 | − | 0.898280i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 8.24264i | − | 0.352430i | −0.984352 | − | 0.176215i | \(-0.943615\pi\) | ||
0.984352 | − | 0.176215i | \(-0.0563854\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.65685 | −0.241429 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.65685 | −0.155787 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 40.9706i | − | 1.74225i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.828427 | + | 1.65685i | −0.0351648 | + | 0.0703295i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.8284i | 0.628301i | 0.949373 | + | 0.314150i | \(0.101720\pi\) | ||||
−0.949373 | + | 0.314150i | \(0.898280\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.17157 | −0.218734 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19.3137 | 0.815425 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 45.4142i | 1.91398i | 0.290119 | + | 0.956990i | \(0.406305\pi\) | ||||
−0.290119 | + | 0.956990i | \(0.593695\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.8284 | − | 11.4142i | −0.960399 | − | 0.480200i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 24.1421i | − | 1.01387i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.4558 | −0.480254 | −0.240127 | − | 0.970741i | \(-0.577189\pi\) | ||||
−0.240127 | + | 0.970741i | \(0.577189\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −47.4558 | −1.98597 | −0.992983 | − | 0.118260i | \(-0.962268\pi\) | ||||
−0.992983 | + | 0.118260i | \(0.962268\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 27.3137i | − | 1.14105i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 30.6274 | − | 22.9706i | 1.27725 | − | 0.957939i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.34315i | 0.264069i | 0.991245 | + | 0.132034i | \(0.0421509\pi\) | ||||
−0.991245 | + | 0.132034i | \(0.957849\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.51472 | 0.0629496 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −75.5980 | −3.13633 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 57.4558i | − | 2.37958i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.17157 | − | 0.585786i | −0.0484386 | − | 0.0242193i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.0000i | 0.742940i | 0.928445 | + | 0.371470i | \(0.121146\pi\) | ||||
−0.928445 | + | 0.371470i | \(0.878854\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.82843 | 0.281360 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.6274 | 0.601692 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.6274i | 0.600676i | 0.953833 | + | 0.300338i | \(0.0970995\pi\) | ||||
−0.953833 | + | 0.300338i | \(0.902901\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.6569 | + | 27.3137i | −0.559876 | + | 1.11975i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 16.0000i | − | 0.654836i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −45.4558 | −1.85728 | −0.928638 | − | 0.370988i | \(-0.879019\pi\) | ||||
−0.928638 | + | 0.370988i | \(0.879019\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.8579 | −0.483692 | −0.241846 | − | 0.970315i | \(-0.577753\pi\) | ||||
−0.241846 | + | 0.970315i | \(0.577753\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 9.89949i | − | 0.403139i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.3137 | − | 24.6274i | 0.500623 | − | 1.00125i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 41.2132i | − | 1.67279i | −0.548125 | − | 0.836396i | \(-0.684658\pi\) | ||
0.548125 | − | 0.836396i | \(-0.315342\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −24.9706 | −1.01186 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.485281 | −0.0196324 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.4853i | 0.988951i | 0.869192 | + | 0.494476i | \(0.164640\pi\) | ||||
−0.869192 | + | 0.494476i | \(0.835360\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.34315 | − | 1.17157i | −0.0944848 | − | 0.0472424i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 6.82843i | − | 0.274902i | −0.990509 | − | 0.137451i | \(-0.956109\pi\) | ||
0.990509 | − | 0.137451i | \(-0.0438910\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.1716 | −1.25289 | −0.626446 | − | 0.779465i | \(-0.715491\pi\) | ||||
−0.626446 | + | 0.779465i | \(0.715491\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 43.3137 | 1.73812 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 64.2843i | 2.57549i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 6.82843i | − | 0.272701i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.65685 | 0.0660631 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.7990 | −0.867804 | −0.433902 | − | 0.900960i | \(-0.642864\pi\) | ||||
−0.433902 | + | 0.900960i | \(0.642864\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 32.0000i | 1.27189i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 25.4558 | + | 12.7279i | 1.01018 | + | 0.505092i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.55635i | 0.378636i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.48528 | −0.335673 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.8579 | −0.468357 | −0.234179 | − | 0.972194i | \(-0.575240\pi\) | ||||
−0.234179 | + | 0.972194i | \(0.575240\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 10.9706i | − | 0.432637i | −0.976323 | − | 0.216318i | \(-0.930595\pi\) | ||
0.976323 | − | 0.216318i | \(-0.0694049\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.4853 | + | 24.9706i | −0.491607 | + | 0.983215i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.2843i | 0.404316i | 0.979353 | + | 0.202158i | \(0.0647955\pi\) | ||||
−0.979353 | + | 0.202158i | \(0.935204\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32.9706 | 1.29421 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 46.6274 | 1.82747 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.82843i | 0.110685i | 0.998467 | + | 0.0553425i | \(0.0176251\pi\) | ||||
−0.998467 | + | 0.0553425i | \(0.982375\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.6569 | + | 35.3137i | −0.689910 | + | 1.37982i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 1.17157i | − | 0.0457074i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.4853 | 1.26545 | 0.632723 | − | 0.774378i | \(-0.281937\pi\) | ||||
0.632723 | + | 0.774378i | \(0.281937\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.4558 | 1.06791 | 0.533954 | − | 0.845513i | \(-0.320705\pi\) | ||||
0.533954 | + | 0.845513i | \(0.320705\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 2.34315i | − | 0.0910002i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.65685 | + | 4.82843i | 0.374477 | + | 0.187238i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 28.0000i | − | 1.08416i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.0000 | −0.541271 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −27.3137 | −1.05443 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.7574i | 0.838685i | 0.907828 | + | 0.419342i | \(0.137739\pi\) | ||||
−0.907828 | + | 0.419342i | \(0.862261\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −22.6274 | + | 16.9706i | −0.870930 | + | 0.653197i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 12.1005i | − | 0.465060i | −0.972589 | − | 0.232530i | \(-0.925300\pi\) | ||
0.972589 | − | 0.232530i | \(-0.0747004\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.17157 | 0.198467 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.97056 | 0.267113 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.0711i | 1.34196i | 0.741477 | + | 0.670979i | \(0.234126\pi\) | ||||
−0.741477 | + | 0.670979i | \(0.765874\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.65685 | + | 2.82843i | 0.216137 | + | 0.108069i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.68629i | 0.178793i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.97056 | −0.265557 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 38.7696 | 1.47486 | 0.737432 | − | 0.675422i | \(-0.236038\pi\) | ||||
0.737432 | + | 0.675422i | \(0.236038\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 23.3137i | 0.885615i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.1716 | + | 30.3431i | −0.575491 | + | 1.15098i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.34315i | 0.0887530i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −40.9706 | −1.54965 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.3137 | 1.18270 | 0.591351 | − | 0.806414i | \(-0.298595\pi\) | ||||
0.591351 | + | 0.806414i | \(0.298595\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.585786i | − | 0.0220934i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.17157 | + | 2.34315i | −0.0441240 | + | 0.0882480i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 38.6274i | − | 1.45273i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33.3137 | −1.25112 | −0.625561 | − | 0.780175i | \(-0.715130\pi\) | ||||
−0.625561 | + | 0.780175i | \(0.715130\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.48528 | −0.318223 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 52.2843i | 1.95806i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.65685 | − | 2.82843i | −0.211554 | − | 0.105777i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 12.6863i | − | 0.473778i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.48528 | −0.0926854 | −0.0463427 | − | 0.998926i | \(-0.514757\pi\) | ||||
−0.0463427 | + | 0.998926i | \(0.514757\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −47.7990 | −1.78013 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 4.48528i | − | 0.166809i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.9706 | + | 14.6274i | 0.407436 | + | 0.543249i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.4558i | 1.16663i | 0.812245 | + | 0.583316i | \(0.198245\pi\) | ||||
−0.812245 | + | 0.583316i | \(0.801755\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.0000 | −1.07407 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.9706 | 0.923570 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 12.6863i | − | 0.468579i | −0.972167 | − | 0.234289i | \(-0.924724\pi\) | ||
0.972167 | − | 0.234289i | \(-0.0752763\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 46.1421 | + | 23.0711i | 1.70198 | + | 0.850989i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 47.7990i | − | 1.76070i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.0000 | 0.441427 | 0.220714 | − | 0.975339i | \(-0.429161\pi\) | ||||
0.220714 | + | 0.975339i | \(0.429161\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.828427 | −0.0304330 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 2.10051i | − | 0.0770601i | −0.999257 | − | 0.0385300i | \(-0.987732\pi\) | ||
0.999257 | − | 0.0385300i | \(-0.0122675\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.00000 | + | 8.00000i | −0.146549 | + | 0.293097i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15.6569i | 0.572854i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −78.4264 | −2.86564 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.5980 | 1.59091 | 0.795456 | − | 0.606011i | \(-0.207231\pi\) | ||||
0.795456 | + | 0.606011i | \(0.207231\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 5.65685i | − | 0.206147i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.34315 | + | 4.68629i | −0.0852758 | + | 0.170552i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 38.6274i | − | 1.40394i | −0.712208 | − | 0.701969i | \(-0.752305\pi\) | ||
0.712208 | − | 0.701969i | \(-0.247695\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 52.2843 | 1.89780 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.2843 | −0.880304 | −0.440152 | − | 0.897923i | \(-0.645075\pi\) | ||||
−0.440152 | + | 0.897923i | \(0.645075\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 50.6274i | 1.83284i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.65685 | + | 2.82843i | 0.204524 | + | 0.102262i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 4.00000i | − | 0.144432i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.2843 | 1.30844 | 0.654222 | − | 0.756302i | \(-0.272996\pi\) | ||||
0.654222 | + | 0.756302i | \(0.272996\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.4853 | −0.521675 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.0711i | 0.470134i | 0.971979 | + | 0.235067i | \(0.0755309\pi\) | ||||
−0.971979 | + | 0.235067i | \(0.924469\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −20.4853 | − | 27.3137i | −0.735853 | − | 0.981137i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 4.00000i | − | 0.143499i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.828427 | 0.0296815 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −40.9706 | −1.46604 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 20.6863i | 0.739268i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.97056 | − | 4.48528i | −0.320173 | − | 0.160087i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 28.5269i | − | 1.01687i | −0.861099 | − | 0.508437i | \(-0.830223\pi\) | ||
0.861099 | − | 0.508437i | \(-0.169777\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.51472 | 0.267531 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 55.1127 | 1.95958 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.31371i | 0.117673i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −16.8284 | + | 33.6569i | −0.596843 | + | 1.19369i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 38.0416i | − | 1.34750i | −0.738958 | − | 0.673752i | \(-0.764682\pi\) | ||
0.738958 | − | 0.673752i | \(-0.235318\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.34315 | 0.0828945 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.3137 | 0.470417 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 5.65685i | − | 0.199626i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −36.9706 | + | 73.9411i | −1.30304 | + | 2.60608i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 28.4853i | 1.00273i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 35.2548 | 1.23949 | 0.619747 | − | 0.784802i | \(-0.287235\pi\) | ||||
0.619747 | + | 0.784802i | \(0.287235\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26.8284 | −0.942073 | −0.471037 | − | 0.882114i | \(-0.656120\pi\) | ||||
−0.471037 | + | 0.882114i | \(0.656120\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 27.1127i | − | 0.950884i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −28.9706 | − | 14.4853i | −1.01479 | − | 0.507397i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 8.82843i | − | 0.308868i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.82843 | 0.0988332 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.02944 | 0.175529 | 0.0877643 | − | 0.996141i | \(-0.472028\pi\) | ||||
0.0877643 | + | 0.996141i | \(0.472028\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 26.4853i | − | 0.923219i | −0.887083 | − | 0.461609i | \(-0.847272\pi\) | ||
0.887083 | − | 0.461609i | \(-0.152728\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −27.3137 | + | 20.4853i | −0.950941 | + | 0.713206i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 33.4142i | − | 1.16193i | −0.813930 | − | 0.580963i | \(-0.802676\pi\) | ||
0.813930 | − | 0.580963i | \(-0.197324\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.4853 | −1.05880 | −0.529399 | − | 0.848373i | \(-0.677582\pi\) | ||||
−0.529399 | + | 0.848373i | \(0.677582\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.9706 | 0.449944 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 46.1421i | − | 1.59873i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.14214 | − | 3.07107i | −0.212557 | − | 0.106279i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 38.6274i | − | 1.33516i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.48528 | −0.292944 | −0.146472 | − | 0.989215i | \(-0.546792\pi\) | ||||
−0.146472 | + | 0.989215i | \(0.546792\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.6274 | −0.538876 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 31.7990i | 1.09522i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.6569 | − | 25.3137i | 0.435409 | − | 0.870818i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 59.4558i | 2.04293i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.20101 | 0.144178 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.48528 | 0.153753 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 47.3137i | − | 1.61999i | −0.586436 | − | 0.809995i | \(-0.699470\pi\) | ||
0.586436 | − | 0.809995i | \(-0.300530\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.00000 | − | 2.00000i | 0.0341993 | − | 0.0683986i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 56.6690i | 1.93578i | 0.251378 | + | 0.967889i | \(0.419116\pi\) | ||||
−0.251378 | + | 0.967889i | \(0.580884\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.9411 | 0.475665 | 0.237833 | − | 0.971306i | \(-0.423563\pi\) | ||||
0.237833 | + | 0.971306i | \(0.423563\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.65685 | 0.192785 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 4.04163i | − | 0.137579i | −0.997631 | − | 0.0687894i | \(-0.978086\pi\) | ||
0.997631 | − | 0.0687894i | \(-0.0219136\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.1716 | + | 8.58579i | 0.583851 | + | 0.291925i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 12.7279i | − | 0.432263i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −40.9706 | −1.38983 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.79899 | −0.196491 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 1.07107i | − | 0.0362502i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.65685 | − | 53.1127i | −0.326461 | − | 1.79554i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.1838i | 0.816628i | 0.912842 | + | 0.408314i | \(0.133883\pi\) | ||||
−0.912842 | + | 0.408314i | \(0.866117\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.7990 | 0.465428 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.2843 | 0.683394 | 0.341697 | − | 0.939810i | \(-0.388998\pi\) | ||||
0.341697 | + | 0.939810i | \(0.388998\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.7696i | 1.43931i | 0.694332 | + | 0.719655i | \(0.255700\pi\) | ||||
−0.694332 | + | 0.719655i | \(0.744300\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −19.3137 | − | 9.65685i | −0.649223 | − | 0.324612i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 0.443651i | − | 0.0148963i | −0.999972 | − | 0.00744817i | \(-0.997629\pi\) | ||
0.999972 | − | 0.00744817i | \(-0.00237085\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −61.4558 | −2.06116 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −24.1421 | −0.808792 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 0.828427i | − | 0.0277223i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.8284 | + | 45.6569i | −0.763070 | + | 1.52614i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 6.34315i | − | 0.211791i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24.9706 | −0.832815 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33.6569 | 1.12127 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 60.2843i | − | 2.00613i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.68629 | − | 5.37258i | 0.0892954 | − | 0.178591i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 3.07107i | − | 0.101973i | −0.998699 | − | 0.0509866i | \(-0.983763\pi\) | ||
0.998699 | − | 0.0509866i | \(-0.0162366\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.00000 | −0.265343 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.3431 | 0.740261 | 0.370131 | − | 0.928980i | \(-0.379313\pi\) | ||||
0.370131 | + | 0.928980i | \(0.379313\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 75.5980i | 2.50193i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 16.0000 | + | 8.00000i | 0.528944 | + | 0.264472i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 85.2548i | − | 2.81536i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.0000 | 0.527791 | 0.263896 | − | 0.964551i | \(-0.414993\pi\) | ||||
0.263896 | + | 0.964551i | \(0.414993\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.65685 | 0.120497 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.97056i | 0.163608i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.34315 | + | 1.75736i | −0.0770422 | + | 0.0577816i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.89949i | 0.325142i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.0000 | 0.459325 | 0.229663 | − | 0.973270i | \(-0.426238\pi\) | ||||
0.229663 | + | 0.973270i | \(0.426238\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.3137 | −0.534660 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 32.7696i | 1.07283i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 27.3137 | + | 13.6569i | 0.893254 | + | 0.446627i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.14214i | − | 0.0699805i | −0.999388 | − | 0.0349903i | \(-0.988860\pi\) | ||
0.999388 | − | 0.0349903i | \(-0.0111400\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −29.6569 | −0.967815 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.9411 | 1.04125 | 0.520625 | − | 0.853785i | \(-0.325699\pi\) | ||||
0.520625 | + | 0.853785i | \(0.325699\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.34315i | 0.206561i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 27.3137 | − | 54.6274i | 0.888515 | − | 1.77703i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.3137i | 1.34252i | 0.741224 | + | 0.671258i | \(0.234246\pi\) | ||||
−0.741224 | + | 0.671258i | \(0.765754\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.686292 | −0.0222780 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.1716 | −0.491972 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 44.3848i | − | 1.43776i | −0.695132 | − | 0.718882i | \(-0.744654\pi\) | ||
0.695132 | − | 0.718882i | \(-0.255346\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.3137 | − | 38.6274i | 0.624977 | − | 1.24995i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 24.9706i | 0.807184i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −13.6569 | −0.441003 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.6274 | 0.504110 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.2426i | 0.523412i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.14214 | + | 1.07107i | 0.0689578 | + | 0.0344789i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 28.3431i | − | 0.911454i | −0.890120 | − | 0.455727i | \(-0.849379\pi\) | ||
0.890120 | − | 0.455727i | \(-0.150621\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.00000 | 0.128499 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.5147 | 0.626257 | 0.313129 | − | 0.949711i | \(-0.398623\pi\) | ||||
0.313129 | + | 0.949711i | \(0.398623\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 73.2548i | − | 2.34844i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.48528 | + | 3.31371i | 0.0795927 | + | 0.106124i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 17.0711i | − | 0.546152i | −0.961992 | − | 0.273076i | \(-0.911959\pi\) | ||
0.961992 | − | 0.273076i | \(-0.0880410\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 64.2843 | 2.05453 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.4853 | 0.334769 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 4.52691i | − | 0.144386i | −0.997391 | − | 0.0721930i | \(-0.977000\pi\) | ||
0.997391 | − | 0.0721930i | \(-0.0229998\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20.6863 | + | 10.3431i | 0.659120 | + | 0.329560i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 5.65685i | − | 0.180060i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 67.5980 | 2.14949 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.2843 | −0.644351 | −0.322176 | − | 0.946680i | \(-0.604414\pi\) | ||||
−0.322176 | + | 0.946680i | \(0.604414\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.3137i | 0.612902i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.3137 | − | 22.6274i | 0.358669 | − | 0.717337i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.45584i | 0.172788i | 0.996261 | + | 0.0863942i | \(0.0275344\pi\) | ||||
−0.996261 | + | 0.0863942i | \(0.972466\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.31371 | −0.104841 |
(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 | 760.2.d.d.609.1 | ✓ | 4 | |
4.3 | odd | 2 | 1520.2.d.g.609.3 | 4 | |||
5.2 | odd | 4 | 3800.2.a.m.1.1 | 2 | |||
5.3 | odd | 4 | 3800.2.a.o.1.2 | 2 | |||
5.4 | even | 2 | inner | 760.2.d.d.609.4 | yes | 4 | |
20.3 | even | 4 | 7600.2.a.z.1.1 | 2 | |||
20.7 | even | 4 | 7600.2.a.bb.1.2 | 2 | |||
20.19 | odd | 2 | 1520.2.d.g.609.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
760.2.d.d.609.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
760.2.d.d.609.4 | yes | 4 | 5.4 | even | 2 | inner | |
1520.2.d.g.609.2 | 4 | 20.19 | odd | 2 | |||
1520.2.d.g.609.3 | 4 | 4.3 | odd | 2 | |||
3800.2.a.m.1.1 | 2 | 5.2 | odd | 4 | |||
3800.2.a.o.1.2 | 2 | 5.3 | odd | 4 | |||
7600.2.a.z.1.1 | 2 | 20.3 | even | 4 | |||
7600.2.a.bb.1.2 | 2 | 20.7 | even | 4 |