Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [960,2,Mod(671,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 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("960.671");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.66563859404\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 671.1 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 960.671 |
Dual form | 960.2.b.a.671.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/960\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(577\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −1.41421 | − | 1.00000i | −0.816497 | − | 0.577350i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.00000i | − | 0.755929i | −0.925820 | − | 0.377964i | \(-0.876624\pi\) | ||
0.925820 | − | 0.377964i | \(-0.123376\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | + | 2.82843i | 0.333333 | + | 0.942809i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000i | 0.603023i | 0.953463 | + | 0.301511i | \(0.0974911\pi\) | ||||
−0.953463 | + | 0.301511i | \(0.902509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.82843i | 0.784465i | 0.919866 | + | 0.392232i | \(0.128297\pi\) | ||||
−0.919866 | + | 0.392232i | \(0.871703\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.41421 | + | 1.00000i | 0.365148 | + | 0.258199i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.82843i | 0.685994i | 0.939336 | + | 0.342997i | \(0.111442\pi\) | ||||
−0.939336 | + | 0.342997i | \(0.888558\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.65685 | −1.29777 | −0.648886 | − | 0.760886i | \(-0.724765\pi\) | ||||
−0.648886 | + | 0.760886i | \(0.724765\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | + | 2.82843i | −0.436436 | + | 0.617213i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.48528 | 1.76930 | 0.884652 | − | 0.466252i | \(-0.154396\pi\) | ||||
0.884652 | + | 0.466252i | \(0.154396\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.41421 | − | 5.00000i | 0.272166 | − | 0.962250i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.00000i | − | 1.07763i | −0.842424 | − | 0.538816i | \(-0.818872\pi\) | ||
0.842424 | − | 0.538816i | \(-0.181128\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.00000 | − | 2.82843i | 0.348155 | − | 0.492366i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.00000i | 0.338062i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.82843i | − | 0.464991i | −0.972598 | − | 0.232495i | \(-0.925311\pi\) | ||
0.972598 | − | 0.232495i | \(-0.0746890\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.82843 | − | 4.00000i | 0.452911 | − | 0.640513i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.3137i | 1.76690i | 0.468521 | + | 0.883452i | \(0.344787\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.48528 | 1.29399 | 0.646997 | − | 0.762493i | \(-0.276025\pi\) | ||||
0.646997 | + | 0.762493i | \(0.276025\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | − | 2.82843i | −0.149071 | − | 0.421637i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.82843 | 0.412568 | 0.206284 | − | 0.978492i | \(-0.433863\pi\) | ||||
0.206284 | + | 0.978492i | \(0.433863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.82843 | − | 4.00000i | 0.396059 | − | 0.560112i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.0000 | 1.37361 | 0.686803 | − | 0.726844i | \(-0.259014\pi\) | ||||
0.686803 | + | 0.726844i | \(0.259014\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.00000i | − | 0.269680i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.00000 | + | 5.65685i | 1.05963 | + | 0.749269i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.0000i | 1.30189i | 0.759125 | + | 0.650945i | \(0.225627\pi\) | ||||
−0.759125 | + | 0.650945i | \(0.774373\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.65685 | − | 2.00000i | 0.712697 | − | 0.251976i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 2.82843i | − | 0.350823i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.82843 | 0.345547 | 0.172774 | − | 0.984962i | \(-0.444727\pi\) | ||||
0.172774 | + | 0.984962i | \(0.444727\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12.0000 | − | 8.48528i | −1.44463 | − | 1.02151i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.65685 | −0.671345 | −0.335673 | − | 0.941979i | \(-0.608964\pi\) | ||||
−0.335673 | + | 0.941979i | \(0.608964\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.0000 | 1.17041 | 0.585206 | − | 0.810885i | \(-0.301014\pi\) | ||||
0.585206 | + | 0.810885i | \(0.301014\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.41421 | − | 1.00000i | −0.163299 | − | 0.115470i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.00000 | 0.455842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000i | 0.225018i | 0.993651 | + | 0.112509i | \(0.0358886\pi\) | ||||
−0.993651 | + | 0.112509i | \(0.964111\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | + | 5.65685i | −0.777778 | + | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 2.00000i | − | 0.219529i | −0.993958 | − | 0.109764i | \(-0.964990\pi\) | ||
0.993958 | − | 0.109764i | \(-0.0350096\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 2.82843i | − | 0.306786i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.82843 | − | 2.00000i | −0.303239 | − | 0.214423i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.65685i | 0.599625i | 0.953998 | + | 0.299813i | \(0.0969242\pi\) | ||||
−0.953998 | + | 0.299813i | \(0.903076\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.65685 | 0.592999 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.00000 | + | 8.48528i | −0.622171 | + | 0.879883i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.65685 | 0.580381 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.0000 | −1.42148 | −0.710742 | − | 0.703452i | \(-0.751641\pi\) | ||||
−0.710742 | + | 0.703452i | \(0.751641\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.65685 | + | 2.00000i | −0.568535 | + | 0.201008i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.0000 | 1.79107 | 0.895533 | − | 0.444994i | \(-0.146794\pi\) | ||||
0.895533 | + | 0.444994i | \(0.146794\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.00000i | 0.591198i | 0.955312 | + | 0.295599i | \(0.0955191\pi\) | ||||
−0.955312 | + | 0.295599i | \(0.904481\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.00000 | − | 2.82843i | 0.195180 | − | 0.276026i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.0000i | 1.35343i | 0.736245 | + | 0.676716i | \(0.236597\pi\) | ||||
−0.736245 | + | 0.676716i | \(0.763403\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 16.9706i | − | 1.62549i | −0.582623 | − | 0.812743i | \(-0.697974\pi\) | ||
0.582623 | − | 0.812743i | \(-0.302026\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.82843 | + | 4.00000i | −0.268462 | + | 0.379663i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 14.1421i | − | 1.33038i | −0.746674 | − | 0.665190i | \(-0.768350\pi\) | ||
0.746674 | − | 0.665190i | \(-0.231650\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.48528 | −0.791257 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.00000 | + | 2.82843i | −0.739600 | + | 0.261488i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.65685 | 0.518563 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.3137 | − | 16.0000i | 1.02012 | − | 1.44267i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.00000i | − | 0.177471i | −0.996055 | − | 0.0887357i | \(-0.971717\pi\) | ||
0.996055 | − | 0.0887357i | \(-0.0282826\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.0000 | − | 8.48528i | −1.05654 | − | 0.747087i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 6.00000i | − | 0.524222i | −0.965038 | − | 0.262111i | \(-0.915581\pi\) | ||
0.965038 | − | 0.262111i | \(-0.0844187\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.3137i | 0.981023i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.41421 | + | 5.00000i | −0.121716 | + | 0.430331i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.82843i | 0.241649i | 0.992674 | + | 0.120824i | \(0.0385538\pi\) | ||||
−0.992674 | + | 0.120824i | \(0.961446\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.9706 | −1.43942 | −0.719712 | − | 0.694273i | \(-0.755726\pi\) | ||||
−0.719712 | + | 0.694273i | \(0.755726\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.00000 | − | 2.82843i | −0.336861 | − | 0.238197i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.65685 | −0.473050 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00000 | −0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.24264 | − | 3.00000i | −0.349927 | − | 0.247436i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.0000 | −1.14692 | −0.573462 | − | 0.819232i | \(-0.694400\pi\) | ||||
−0.573462 | + | 0.819232i | \(0.694400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.00000i | 0.162758i | 0.996683 | + | 0.0813788i | \(0.0259324\pi\) | ||||
−0.996683 | + | 0.0813788i | \(0.974068\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.00000 | + | 2.82843i | −0.646762 | + | 0.228665i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.00000i | 0.481932i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.7990i | 1.58013i | 0.613022 | + | 0.790066i | \(0.289954\pi\) | ||||
−0.613022 | + | 0.790066i | \(0.710046\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.1421 | − | 10.0000i | −1.12154 | − | 0.793052i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 16.9706i | − | 1.33747i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.48528 | 0.664619 | 0.332309 | − | 0.943170i | \(-0.392172\pi\) | ||||
0.332309 | + | 0.943170i | \(0.392172\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.00000 | + | 2.82843i | −0.155700 | + | 0.220193i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.7990 | −1.53209 | −0.766046 | − | 0.642786i | \(-0.777779\pi\) | ||||
−0.766046 | + | 0.642786i | \(0.777779\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.65685 | − | 16.0000i | −0.432590 | − | 1.22355i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.0000 | 1.36851 | 0.684257 | − | 0.729241i | \(-0.260127\pi\) | ||||
0.684257 | + | 0.729241i | \(0.260127\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 2.00000i | − | 0.151186i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.0000 | − | 14.1421i | 0.751646 | − | 1.06299i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.0000i | 1.34538i | 0.739923 | + | 0.672692i | \(0.234862\pi\) | ||||
−0.739923 | + | 0.672692i | \(0.765138\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.6274i | 1.68188i | 0.541126 | + | 0.840941i | \(0.317998\pi\) | ||||
−0.541126 | + | 0.840941i | \(0.682002\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.82843i | 0.207950i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.65685 | −0.413670 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −10.0000 | − | 2.82843i | −0.727393 | − | 0.205738i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.65685 | −0.409316 | −0.204658 | − | 0.978834i | \(-0.565608\pi\) | ||||
−0.204658 | + | 0.978834i | \(0.565608\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.0000 | −1.00774 | −0.503871 | − | 0.863779i | \(-0.668091\pi\) | ||||
−0.503871 | + | 0.863779i | \(0.668091\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.82843 | + | 4.00000i | −0.202548 | + | 0.286446i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.0000 | 0.712470 | 0.356235 | − | 0.934396i | \(-0.384060\pi\) | ||||
0.356235 | + | 0.934396i | \(0.384060\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.0000i | 1.84309i | 0.388270 | + | 0.921546i | \(0.373073\pi\) | ||||
−0.388270 | + | 0.921546i | \(0.626927\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.00000 | − | 2.82843i | −0.282138 | − | 0.199502i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 4.00000i | − | 0.280745i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 11.3137i | − | 0.790184i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.48528 | + | 24.0000i | 0.589768 | + | 1.66812i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 11.3137i | − | 0.782586i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.3137 | 0.778868 | 0.389434 | − | 0.921054i | \(-0.372671\pi\) | ||||
0.389434 | + | 0.921054i | \(0.372671\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.00000 | + | 5.65685i | 0.548151 | + | 0.387601i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.48528 | −0.578691 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.0000 | −0.814613 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −14.1421 | − | 10.0000i | −0.955637 | − | 0.675737i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.00000 | −0.538138 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.0000i | 0.937509i | 0.883328 | + | 0.468755i | \(0.155297\pi\) | ||||
−0.883328 | + | 0.468755i | \(0.844703\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | + | 2.82843i | 0.0666667 | + | 0.188562i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 10.0000i | − | 0.663723i | −0.943328 | − | 0.331862i | \(-0.892323\pi\) | ||
0.943328 | − | 0.331862i | \(-0.107677\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 28.2843i | − | 1.86908i | −0.355862 | − | 0.934539i | \(-0.615813\pi\) | ||
0.355862 | − | 0.934539i | \(-0.384187\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.65685 | − | 4.00000i | −0.372194 | − | 0.263181i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.48528i | 0.555889i | 0.960597 | + | 0.277945i | \(0.0896532\pi\) | ||||
−0.960597 | + | 0.277945i | \(0.910347\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.82843 | −0.184506 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.00000 | − | 2.82843i | 0.129914 | − | 0.183726i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.6274 | −1.46365 | −0.731823 | − | 0.681495i | \(-0.761330\pi\) | ||||
−0.731823 | + | 0.681495i | \(0.761330\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.0000 | −0.901819 | −0.450910 | − | 0.892570i | \(-0.648900\pi\) | ||||
−0.450910 | + | 0.892570i | \(0.648900\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5563 | − | 1.00000i | 0.997940 | − | 0.0641500i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.00000 | −0.191663 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 16.0000i | − | 1.01806i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.00000 | + | 2.82843i | −0.126745 | + | 0.179244i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.0000i | 1.13615i | 0.822977 | + | 0.568075i | \(0.192312\pi\) | ||||
−0.822977 | + | 0.568075i | \(0.807688\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.9706i | 1.06693i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.82843 | + | 4.00000i | −0.177123 | + | 0.250490i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 19.7990i | − | 1.23503i | −0.786560 | − | 0.617514i | \(-0.788140\pi\) | ||
0.786560 | − | 0.617514i | \(-0.211860\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.65685 | −0.351500 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | + | 5.65685i | 0.123797 | + | 0.350150i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.1421 | −0.872041 | −0.436021 | − | 0.899937i | \(-0.643613\pi\) | ||||
−0.436021 | + | 0.899937i | \(0.643613\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.0000 | −0.614295 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.65685 | − | 8.00000i | 0.346194 | − | 0.489592i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.00000 | −0.365826 | −0.182913 | − | 0.983129i | \(-0.558553\pi\) | ||||
−0.182913 | + | 0.983129i | \(0.558553\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.0000i | 0.607457i | 0.952759 | + | 0.303728i | \(0.0982315\pi\) | ||||
−0.952759 | + | 0.303728i | \(0.901768\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.00000 | − | 5.65685i | −0.484182 | − | 0.342368i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.00000i | 0.120605i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 25.4558i | − | 1.52949i | −0.644331 | − | 0.764747i | \(-0.722864\pi\) | ||
0.644331 | − | 0.764747i | \(-0.277136\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 16.9706 | − | 6.00000i | 1.01600 | − | 0.359211i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 11.3137i | − | 0.674919i | −0.941340 | − | 0.337460i | \(-0.890432\pi\) | ||
0.941340 | − | 0.337460i | \(-0.109568\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.48528 | 0.504398 | 0.252199 | − | 0.967675i | \(-0.418846\pi\) | ||||
0.252199 | + | 0.967675i | \(0.418846\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.00000 | − | 5.65685i | −0.473879 | − | 0.335083i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 22.6274 | 1.33565 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.00000 | 0.529412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 19.7990 | + | 14.0000i | 1.16064 | + | 0.820695i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.00000 | −0.350524 | −0.175262 | − | 0.984522i | \(-0.556077\pi\) | ||||
−0.175262 | + | 0.984522i | \(0.556077\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 10.0000i | − | 0.582223i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 10.0000 | + | 2.82843i | 0.580259 | + | 0.164122i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 24.0000i | 1.38796i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 16.9706i | − | 0.978167i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −25.4558 | − | 18.0000i | −1.46240 | − | 1.03407i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.1421 | 0.807134 | 0.403567 | − | 0.914950i | \(-0.367770\pi\) | ||||
0.403567 | + | 0.914950i | \(0.367770\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.00000 | − | 8.48528i | 0.341328 | − | 0.482711i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.2843 | 1.60385 | 0.801927 | − | 0.597422i | \(-0.203808\pi\) | ||||
0.801927 | + | 0.597422i | \(0.203808\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.0000 | 0.565233 | 0.282617 | − | 0.959233i | \(-0.408798\pi\) | ||||
0.282617 | + | 0.959233i | \(0.408798\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.65685 | + | 2.00000i | −0.318728 | + | 0.112687i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.0000 | 1.01098 | 0.505490 | − | 0.862832i | \(-0.331312\pi\) | ||||
0.505490 | + | 0.862832i | \(0.331312\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.00000i | 0.223957i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.0000 | − | 19.7990i | 0.781404 | − | 1.10507i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 16.0000i | − | 0.890264i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.82843i | 0.156893i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.9706 | + | 24.0000i | −0.938474 | + | 1.32720i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 5.65685i | − | 0.311872i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.00000 | − | 2.82843i | 0.438397 | − | 0.154997i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.82843 | −0.154533 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.0000 | −0.762629 | −0.381314 | − | 0.924445i | \(-0.624528\pi\) | ||||
−0.381314 | + | 0.924445i | \(0.624528\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.1421 | + | 20.0000i | −0.768095 | + | 1.08625i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.0000 | 0.649836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 20.0000i | − | 1.07990i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.0000 | + | 8.48528i | 0.646058 | + | 0.456832i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 18.0000i | − | 0.966291i | −0.875540 | − | 0.483145i | \(-0.839494\pi\) | ||
0.875540 | − | 0.483145i | \(-0.160506\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.65685i | 0.302804i | 0.988472 | + | 0.151402i | \(0.0483789\pi\) | ||||
−0.988472 | + | 0.151402i | \(0.951621\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.1421 | + | 4.00000i | 0.754851 | + | 0.213504i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 31.1127i | 1.65596i | 0.560756 | + | 0.827981i | \(0.310510\pi\) | ||||
−0.560756 | + | 0.827981i | \(0.689490\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.65685 | 0.300235 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.00000 | − | 5.65685i | −0.423405 | − | 0.299392i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.3137 | 0.597115 | 0.298557 | − | 0.954392i | \(-0.403495\pi\) | ||||
0.298557 | + | 0.954392i | \(0.403495\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | 0.684211 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.89949 | − | 7.00000i | −0.519589 | − | 0.367405i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.0000 | −0.523424 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 26.0000i | − | 1.35719i | −0.734513 | − | 0.678594i | \(-0.762589\pi\) | ||
0.734513 | − | 0.678594i | \(-0.237411\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −32.0000 | + | 11.3137i | −1.66585 | + | 0.588968i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 20.0000i | − | 1.03835i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.1421i | 0.732252i | 0.930565 | + | 0.366126i | \(0.119316\pi\) | ||||
−0.930565 | + | 0.366126i | \(0.880684\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.41421 | + | 1.00000i | 0.0730297 | + | 0.0516398i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.65685i | 0.291343i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.9706 | −0.871719 | −0.435860 | − | 0.900015i | \(-0.643556\pi\) | ||||
−0.435860 | + | 0.900015i | \(0.643556\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.00000 | + | 2.82843i | −0.102463 | + | 0.144905i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.1421 | −0.722629 | −0.361315 | − | 0.932444i | \(-0.617672\pi\) | ||||
−0.361315 | + | 0.932444i | \(0.617672\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.00000 | −0.203859 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.48528 | + | 24.0000i | 0.431331 | + | 1.21999i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.00000 | −0.304212 | −0.152106 | − | 0.988364i | \(-0.548606\pi\) | ||||
−0.152106 | + | 0.988364i | \(0.548606\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000i | 1.21373i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.00000 | + | 8.48528i | −0.302660 | + | 0.428026i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 2.00000i | − | 0.100631i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.48528i | 0.425864i | 0.977067 | + | 0.212932i | \(0.0683013\pi\) | ||||
−0.977067 | + | 0.212932i | \(0.931699\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.3137 | − | 16.0000i | 0.566394 | − | 0.801002i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.3137i | 0.564980i | 0.959270 | + | 0.282490i | \(0.0911603\pi\) | ||||
−0.959270 | + | 0.282490i | \(0.908840\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.9706 | 0.845364 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.00000 | − | 5.65685i | 0.347833 | − | 0.281091i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.65685 | 0.280400 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.0000 | 1.28562 | 0.642809 | − | 0.766027i | \(-0.277769\pi\) | ||||
0.642809 | + | 0.766027i | \(0.277769\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.82843 | − | 4.00000i | 0.139516 | − | 0.197305i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 20.0000 | 0.984136 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.00000i | 0.0981761i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 24.0000 | + | 16.9706i | 1.17529 | + | 0.831052i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 30.0000i | − | 1.46560i | −0.680446 | − | 0.732798i | \(-0.738214\pi\) | ||
0.680446 | − | 0.732798i | \(-0.261786\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.6274i | 1.10279i | 0.834243 | + | 0.551396i | \(0.185905\pi\) | ||||
−0.834243 | + | 0.551396i | \(0.814095\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.82843 | + | 8.00000i | 0.137523 | + | 0.388973i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.82843i | 0.137199i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.00000 | + | 5.65685i | 0.386244 | + | 0.273115i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.65685 | 0.272481 | 0.136241 | − | 0.990676i | \(-0.456498\pi\) | ||||
0.136241 | + | 0.990676i | \(0.456498\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.0000 | 0.865025 | 0.432512 | − | 0.901628i | \(-0.357627\pi\) | ||||
0.432512 | + | 0.901628i | \(0.357627\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.82843 | + | 2.00000i | 0.135613 | + | 0.0958927i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −48.0000 | −2.29615 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 6.00000i | − | 0.286364i | −0.989696 | − | 0.143182i | \(-0.954267\pi\) | ||
0.989696 | − | 0.143182i | \(-0.0457335\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.00000 | + | 8.48528i | 0.142857 | + | 0.404061i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.0000i | 0.665160i | 0.943075 | + | 0.332580i | \(0.107919\pi\) | ||||
−0.943075 | + | 0.332580i | \(0.892081\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 5.65685i | − | 0.268161i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 19.7990 | + | 14.0000i | 0.936460 | + | 0.662177i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.65685i | 0.266963i | 0.991051 | + | 0.133482i | \(0.0426157\pi\) | ||||
−0.991051 | + | 0.133482i | \(0.957384\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.6274 | −1.06548 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.00000 | − | 2.82843i | 0.0939682 | − | 0.132891i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.65685 | −0.265197 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.00000 | −0.280668 | −0.140334 | − | 0.990104i | \(-0.544818\pi\) | ||||
−0.140334 | + | 0.990104i | \(0.544818\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14.1421 | + | 4.00000i | 0.660098 | + | 0.186704i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.0000 | −0.652045 | −0.326023 | − | 0.945362i | \(-0.605709\pi\) | ||||
−0.326023 | + | 0.945362i | \(0.605709\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.00000i | 0.278844i | 0.990233 | + | 0.139422i | \(0.0445244\pi\) | ||||
−0.990233 | + | 0.139422i | \(0.955476\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.00000 | − | 8.48528i | 0.278243 | − | 0.393496i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 2.00000i | − | 0.0925490i | −0.998929 | − | 0.0462745i | \(-0.985265\pi\) | ||
0.998929 | − | 0.0462745i | \(-0.0147349\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 5.65685i | − | 0.261209i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.7990 | − | 28.0000i | 0.912289 | − | 1.29017i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16.9706i | 0.780307i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.65685 | −0.259554 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.0000 | + | 28.2843i | 0.457869 | + | 1.29505i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.6274 | 1.03387 | 0.516937 | − | 0.856024i | \(-0.327072\pi\) | ||||
0.516937 | + | 0.856024i | \(0.327072\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.00000 | 0.364769 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −16.9706 | + | 24.0000i | −0.772187 | + | 1.09204i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.0000 | 0.635707 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 26.0000i | − | 1.17817i | −0.808070 | − | 0.589086i | \(-0.799488\pi\) | ||
0.808070 | − | 0.589086i | \(-0.200512\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.0000 | − | 8.48528i | −0.542659 | − | 0.383718i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 30.0000i | − | 1.35388i | −0.736038 | − | 0.676941i | \(-0.763305\pi\) | ||
0.736038 | − | 0.676941i | \(-0.236695\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.65685i | 0.254772i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.65685 | − | 2.00000i | 0.254257 | − | 0.0898933i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.3137i | 0.507489i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.9706 | −0.759707 | −0.379853 | − | 0.925047i | \(-0.624026\pi\) | ||||
−0.379853 | + | 0.925047i | \(0.624026\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 28.0000 | + | 19.7990i | 1.25095 | + | 0.884554i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.7990 | 0.882793 | 0.441397 | − | 0.897312i | \(-0.354483\pi\) | ||||
0.441397 | + | 0.897312i | \(0.354483\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.0000 | −0.800989 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.07107 | − | 5.00000i | −0.314037 | − | 0.222058i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.0000 | −0.975133 | −0.487566 | − | 0.873086i | \(-0.662115\pi\) | ||||
−0.487566 | + | 0.873086i | \(0.662115\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 20.0000i | − | 0.884748i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.00000 | + | 28.2843i | −0.353209 | + | 1.24878i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 6.00000i | − | 0.264392i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.65685i | 0.248788i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −25.4558 | − | 18.0000i | −1.11739 | − | 0.790112i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.82843 | −0.123678 | −0.0618392 | − | 0.998086i | \(-0.519697\pi\) | ||||
−0.0618392 | + | 0.998086i | \(0.519697\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.00000 | + | 2.82843i | −0.0872872 | + | 0.123443i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.9706 | 0.739249 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 49.0000 | 2.13043 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −28.2843 | + | 10.0000i | −1.22743 | + | 0.433963i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −32.0000 | −1.38607 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 14.0000i | − | 0.605273i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.0000 | − | 25.4558i | 0.776757 | − | 1.09850i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.00000i | 0.258438i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 33.9411i | − | 1.45924i | −0.683851 | − | 0.729621i | \(-0.739696\pi\) | ||
0.683851 | − | 0.729621i | \(-0.260304\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 22.6274 | − | 32.0000i | 0.971035 | − | 1.37325i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.9706i | 0.726939i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.7990 | −0.846544 | −0.423272 | − | 0.906003i | \(-0.639118\pi\) | ||||
−0.423272 | + | 0.906003i | \(0.639118\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.3137 | −0.481980 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.00000 | 0.170097 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.82843 | − | 4.00000i | 0.120060 | − | 0.169791i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.00000 | 0.0847427 | 0.0423714 | − | 0.999102i | \(-0.486509\pi\) | ||||
0.0423714 | + | 0.999102i | \(0.486509\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.0000i | 1.01509i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.00000 | + | 5.65685i | 0.337760 | + | 0.238833i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 42.0000i | − | 1.77009i | −0.465506 | − | 0.885044i | \(-0.654128\pi\) | ||
0.465506 | − | 0.885044i | \(-0.345872\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.1421i | 0.594964i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11.3137 | + | 14.0000i | 0.475131 | + | 0.587945i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.9706i | 0.711443i | 0.934592 | + | 0.355722i | \(0.115765\pi\) | ||||
−0.934592 | + | 0.355722i | \(0.884235\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.6274 | 0.946928 | 0.473464 | − | 0.880813i | \(-0.343003\pi\) | ||||
0.473464 | + | 0.880813i | \(0.343003\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.00000 | + | 5.65685i | 0.334205 | + | 0.236318i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.48528 | 0.353861 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.00000 | 0.0832611 | 0.0416305 | − | 0.999133i | \(-0.486745\pi\) | ||||
0.0416305 | + | 0.999133i | \(0.486745\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.7990 | + | 14.0000i | 0.822818 | + | 0.581820i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.00000 | −0.165948 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.0000i | 0.828315i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.00000 | − | 2.82843i | 0.330759 | − | 0.116941i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.0000i | 1.23823i | 0.785299 | + | 0.619116i | \(0.212509\pi\) | ||||
−0.785299 | + | 0.619116i | \(0.787491\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 33.9411i | 1.39852i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.1421 | − | 10.0000i | −0.581730 | − | 0.411345i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 25.4558i | − | 1.04535i | −0.852533 | − | 0.522673i | \(-0.824935\pi\) | ||
0.852533 | − | 0.522673i | \(-0.175065\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.65685 | −0.231908 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 26.0000 | − | 36.7696i | 1.06411 | − | 1.50488i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.6274 | 0.924531 | 0.462266 | − | 0.886742i | \(-0.347037\pi\) | ||||
0.462266 | + | 0.886742i | \(0.347037\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.0000 | −0.571072 | −0.285536 | − | 0.958368i | \(-0.592172\pi\) | ||||
−0.285536 | + | 0.958368i | \(0.592172\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.82843 | + | 8.00000i | 0.115182 | + | 0.325785i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.00000 | −0.284590 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 26.0000i | − | 1.05531i | −0.849460 | − | 0.527654i | \(-0.823072\pi\) | ||
0.849460 | − | 0.527654i | \(-0.176928\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.00000 | + | 5.65685i | −0.162088 | + | 0.229227i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.00000i | 0.323645i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 42.4264i | − | 1.71359i | −0.515660 | − | 0.856793i | \(-0.672453\pi\) | ||
0.515660 | − | 0.856793i | \(-0.327547\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −11.3137 | + | 16.0000i | −0.456213 | + | 0.645182i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.82843i | 0.113868i | 0.998378 | + | 0.0569341i | \(0.0181325\pi\) | ||||
−0.998378 | + | 0.0569341i | \(0.981868\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 39.5980 | 1.59158 | 0.795789 | − | 0.605575i | \(-0.207057\pi\) | ||||
0.795789 | + | 0.605575i | \(0.207057\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.0000 | − | 42.4264i | 0.481543 | − | 1.70251i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.3137 | 0.453274 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11.3137 | + | 16.0000i | −0.451826 | + | 0.638978i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.00000 | 0.318981 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.00000i | 0.0796187i | 0.999207 | + | 0.0398094i | \(0.0126751\pi\) | ||||
−0.999207 | + | 0.0398094i | \(0.987325\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.0000 | − | 11.3137i | −0.635943 | − | 0.449680i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.00000i | 0.0793676i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.48528i | 0.336199i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.65685 | − | 16.0000i | −0.223782 | − | 0.632950i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.6274i | 0.893729i | 0.894602 | + | 0.446865i | \(0.147459\pi\) | ||||
−0.894602 | + | 0.446865i | \(0.852541\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.1421 | −0.557711 | −0.278856 | − | 0.960333i | \(-0.589955\pi\) | ||||
−0.278856 | + | 0.960333i | \(0.589955\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.0000 | + | 8.48528i | 0.472500 | + | 0.334108i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.7990 | −0.778379 | −0.389189 | − | 0.921158i | \(-0.627245\pi\) | ||||
−0.389189 | + | 0.921158i | \(0.627245\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.0000 | −0.785069 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.9706 | + | 12.0000i | 0.665129 | + | 0.470317i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −46.0000 | −1.80012 | −0.900060 | − | 0.435767i | \(-0.856477\pi\) | ||||
−0.900060 | + | 0.435767i | \(0.856477\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.00000i | 0.234439i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.0000 | + | 28.2843i | 0.390137 | + | 1.10347i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 30.0000i | − | 1.16863i | −0.811525 | − | 0.584317i | \(-0.801362\pi\) | ||
0.811525 | − | 0.584317i | \(-0.198638\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.3137i | 0.440052i | 0.975494 | + | 0.220026i | \(0.0706143\pi\) | ||||
−0.975494 | + | 0.220026i | \(0.929386\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.3137 | + | 8.00000i | 0.439388 | + | 0.310694i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 11.3137i | − | 0.438727i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.9706 | 0.657103 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.0000 | − | 19.7990i | 0.541271 | − | 0.765473i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.0000 | 0.693849 | 0.346925 | − | 0.937893i | \(-0.387226\pi\) | ||||
0.346925 | + | 0.937893i | \(0.387226\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.41421 | − | 5.00000i | 0.0544331 | − | 0.192450i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.00000 | −0.230599 | −0.115299 | − | 0.993331i | \(-0.536783\pi\) | ||||
−0.115299 | + | 0.993331i | \(0.536783\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 28.0000i | 1.07454i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.0000 | + | 14.1421i | −0.383201 | + | 0.541928i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.0000i | 0.841807i | 0.907106 | + | 0.420903i | \(0.138287\pi\) | ||||
−0.907106 | + | 0.420903i | \(0.861713\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 2.82843i | − | 0.108069i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −28.2843 | + | 40.0000i | −1.07911 | + | 1.52610i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 28.2843i | 1.07754i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.3137 | 0.430394 | 0.215197 | − | 0.976571i | \(-0.430961\pi\) | ||||
0.215197 | + | 0.976571i | \(0.430961\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.00000 | + | 11.3137i | 0.151947 | + | 0.429772i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.9706 | 0.643730 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −32.0000 | −1.21209 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.48528 | − | 12.0000i | 0.320943 | − | 0.453882i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.0000 | −1.13308 | −0.566542 | − | 0.824033i | \(-0.691719\pi\) | ||||
−0.566542 | + | 0.824033i | \(0.691719\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.0000i | 0.603451i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.00000 | + | 2.82843i | 0.150649 | + | 0.106525i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 36.0000i | − | 1.35392i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 5.65685i | − | 0.212448i | −0.994342 | − | 0.106224i | \(-0.966124\pi\) | ||
0.994342 | − | 0.106224i | \(-0.0338760\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.65685 | + | 2.00000i | −0.212149 | + | 0.0750059i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 50.9117i | − | 1.90666i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.65685 | 0.211554 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 32.0000 | + | 22.6274i | 1.19506 | + | 0.845036i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −33.9411 | −1.26579 | −0.632895 | − | 0.774237i | \(-0.718134\pi\) | ||||
−0.632895 | + | 0.774237i | \(0.718134\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.0000 | 0.446903 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 19.7990 | + | 14.0000i | 0.736332 | + | 0.520666i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.00000 | 0.0742781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 26.0000i | − | 0.964287i | −0.876092 | − | 0.482143i | \(-0.839858\pi\) | ||
0.876092 | − | 0.482143i | \(-0.160142\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.0000 | − | 14.1421i | −0.851852 | − | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.0000i | 0.887672i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 42.4264i | − | 1.56706i | −0.621357 | − | 0.783528i | \(-0.713418\pi\) | ||
0.621357 | − | 0.783528i | \(-0.286582\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.24264 | + | 3.00000i | 0.156492 | + | 0.110657i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.65685i | 0.208373i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 39.5980 | 1.45664 | 0.728318 | − | 0.685240i | \(-0.240303\pi\) | ||||
0.728318 | + | 0.685240i | \(0.240303\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.0000 | + | 22.6274i | −0.587775 | + | 0.831239i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.82843 | −0.103765 | −0.0518825 | − | 0.998653i | \(-0.516522\pi\) | ||||
−0.0518825 | + | 0.998653i | \(0.516522\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.0000 | 0.512920 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.65685 | − | 2.00000i | 0.206973 | − | 0.0731762i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 28.0000 | 1.02310 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.0000i | 0.364905i | 0.983215 | + | 0.182453i | \(0.0584036\pi\) | ||||
−0.983215 | + | 0.182453i | \(0.941596\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18.0000 | − | 25.4558i | 0.655956 | − | 0.927663i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 2.00000i | − | 0.0727875i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 14.1421i | − | 0.514005i | −0.966411 | − | 0.257002i | \(-0.917265\pi\) | ||
0.966411 | − | 0.257002i | \(-0.0827348\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 16.9706 | − | 24.0000i | 0.615992 | − | 0.871145i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 33.9411i | − | 1.23036i | −0.788385 | − | 0.615182i | \(-0.789082\pi\) | ||
0.788385 | − | 0.615182i | \(-0.210918\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −33.9411 | −1.22875 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.00000 | − | 2.82843i | 0.289241 | − | 0.102262i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −28.2843 | −1.02129 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.0000 | 0.649097 | 0.324548 | − | 0.945869i | \(-0.394788\pi\) | ||||
0.324548 | + | 0.945869i | \(0.394788\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.7990 | + | 28.0000i | −0.713043 | + | 1.00840i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.0000 | 0.935155 | 0.467578 | − | 0.883952i | \(-0.345127\pi\) | ||||
0.467578 | + | 0.883952i | \(0.345127\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 6.00000i | − | 0.215526i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.00000 | + | 5.65685i | 0.286998 | + | 0.202939i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 64.0000i | − | 2.29304i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 11.3137i | − | 0.404836i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.82843 | − | 10.0000i | 0.101080 | − | 0.357371i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 19.7990i | − | 0.706656i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.7990 | −0.705758 | −0.352879 | − | 0.935669i | \(-0.614797\pi\) | ||||
−0.352879 | + | 0.935669i | \(0.614797\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20.0000 | + | 14.1421i | 0.712019 | + | 0.503473i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −28.2843 | −1.00567 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 14.1421 | + | 10.0000i | 0.501570 | + | 0.354663i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.00000 | 0.0708436 | 0.0354218 | − | 0.999372i | \(-0.488723\pi\) | ||||
0.0354218 | + | 0.999372i | \(0.488723\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.00000i | 0.283020i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.0000 | + | 5.65685i | −0.565332 | + | 0.199875i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.0000i | 0.705785i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.9706i | 0.598134i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.48528 | + | 6.00000i | 0.298696 | + | 0.211210i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 28.2843i | − | 0.994422i | −0.867630 | − | 0.497211i | \(-0.834357\pi\) | ||
0.867630 | − | 0.497211i | \(-0.165643\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.6274 | −0.794556 | −0.397278 | − | 0.917698i | \(-0.630045\pi\) | ||||
−0.397278 | + | 0.917698i | \(0.630045\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.0000 | − | 14.1421i | 0.350715 | − | 0.495986i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.48528 | −0.297226 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −48.0000 | −1.67931 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.65685 | + | 16.0000i | 0.197666 | + | 0.559085i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.00000 | 0.0698005 | 0.0349002 | − | 0.999391i | \(-0.488889\pi\) | ||||
0.0349002 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 26.0000i | − | 0.906303i | −0.891434 | − | 0.453152i | \(-0.850300\pi\) | ||
0.891434 | − | 0.453152i | \(-0.149700\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.00000 | − | 2.82843i | 0.0696311 | − | 0.0984732i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.00000i | 0.208640i | 0.994544 | + | 0.104320i | \(0.0332667\pi\) | ||||
−0.994544 | + | 0.104320i | \(0.966733\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39.5980i | 1.37529i | 0.726045 | + | 0.687647i | \(0.241356\pi\) | ||||
−0.726045 | + | 0.687647i | \(0.758644\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.4558 | + | 36.0000i | −0.883053 | + | 1.24883i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.48528i | 0.293998i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.7990 | 0.685172 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −30.0000 | − | 8.48528i | −1.03695 | − | 0.293294i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −45.2548 | −1.56237 | −0.781185 | − | 0.624299i | \(-0.785385\pi\) | ||||
−0.781185 | + | 0.624299i | \(0.785385\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.3137 | + | 16.0000i | −0.389665 | + | 0.551069i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.00000 | −0.172005 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 14.0000i | − | 0.481046i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.0000 | − | 8.48528i | −0.411839 | − | 0.291214i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 24.0000i | − | 0.822709i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 19.7990i | − | 0.677905i | −0.940804 | − | 0.338952i | \(-0.889927\pi\) | ||
0.940804 | − | 0.338952i | \(-0.110073\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.65685 | + | 16.0000i | 0.193460 | + | 0.547188i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 19.7990i | − | 0.676321i | −0.941089 | − | 0.338160i | \(-0.890195\pi\) | ||
0.941089 | − | 0.338160i | \(-0.109805\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.9706 | 0.579028 | 0.289514 | − | 0.957174i | \(-0.406506\pi\) | ||||
0.289514 | + | 0.957174i | \(0.406506\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −32.0000 | − | 22.6274i | −1.09056 | − | 0.771140i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.7990 | 0.673965 | 0.336983 | − | 0.941511i | \(-0.390594\pi\) | ||||
0.336983 | + | 0.941511i | \(0.390594\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.0000 | −0.612018 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.7279 | − | 9.00000i | −0.432263 | − | 0.305656i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.00000 | −0.135691 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.00000i | 0.271070i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.0000 | − | 39.5980i | −0.473828 | − | 1.34019i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.00000i | 0.0676123i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.48528i | 0.286528i | 0.989685 | + | 0.143264i | \(0.0457597\pi\) | ||||
−0.989685 | + | 0.143264i | \(0.954240\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.48528 | + | 6.00000i | 0.286201 | + | 0.202375i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45.2548i | 1.52467i | 0.647180 | + | 0.762337i | \(0.275948\pi\) | ||||
−0.647180 | + | 0.762337i | \(0.724052\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.4558 | −0.856657 | −0.428329 | − | 0.903623i | \(-0.640897\pi\) | ||||
−0.428329 | + | 0.903623i | \(0.640897\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.0000 | + | 14.1421i | −0.336146 | + | 0.475383i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.1421 | 0.474846 | 0.237423 | − | 0.971406i | \(-0.423697\pi\) | ||||
0.237423 | + | 0.971406i | \(0.423697\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.00000 | −0.134156 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.3137 | − | 14.0000i | −0.379023 | − | 0.469018i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16.0000 | −0.535420 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 18.0000i | − | 0.601674i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 24.0000 | − | 33.9411i | 0.801337 | − | 1.13326i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 12.0000i | − | 0.400222i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.2843i | 0.942286i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −16.9706 | + | 24.0000i | −0.564745 | + | 0.798670i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 22.6274i | − | 0.752161i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.1421 | 0.469582 | 0.234791 | − | 0.972046i | \(-0.424559\pi\) | ||||
0.234791 | + | 0.972046i | \(0.424559\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.0000 | + | 50.9117i | 0.597022 | + | 1.68863i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.65685 | −0.187420 | −0.0937100 | − | 0.995600i | \(-0.529873\pi\) | ||||
−0.0937100 | + | 0.995600i | \(0.529873\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.00000 | 0.132381 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.0000 | −0.396275 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.0000i | 0.857661i | 0.903385 | + | 0.428830i | \(0.141074\pi\) | ||||
−0.903385 | + | 0.428830i | \(0.858926\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.0000 | − | 14.1421i | −0.659022 | − | 0.465999i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 16.0000i | − | 0.526646i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 2.82843i | − | 0.0929981i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.9706 | + | 6.00000i | −0.557386 | + | 0.197066i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 39.5980i | − | 1.29917i | −0.760290 | − | 0.649584i | \(-0.774943\pi\) | ||
0.760290 | − | 0.649584i | \(-0.225057\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.9706 | −0.556188 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −40.0000 | − | 28.2843i | −1.30954 | − | 0.925985i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.65685 | 0.184999 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.0000 | −1.24141 | −0.620703 | − | 0.784046i | \(-0.713153\pi\) | ||||
−0.620703 | + | 0.784046i | \(0.713153\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.1421 | − | 10.0000i | −0.461511 | − | 0.326338i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −54.0000 | −1.76035 | −0.880175 | − | 0.474650i | \(-0.842575\pi\) | ||||
−0.880175 | + | 0.474650i | \(0.842575\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 96.0000i | 3.12619i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 10.0000 | + | 2.82843i | 0.325300 | + | 0.0920087i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 2.00000i | − | 0.0649913i | −0.999472 | − | 0.0324956i | \(-0.989654\pi\) | ||
0.999472 | − | 0.0324956i | \(-0.0103455\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28.2843i | 0.918146i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25.4558 | − | 18.0000i | −0.825462 | − | 0.583690i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 14.1421i | − | 0.458109i | −0.973414 | − | 0.229054i | \(-0.926437\pi\) | ||
0.973414 | − | 0.229054i | \(-0.0735634\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.65685 | 0.183052 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.00000 | − | 5.65685i | 0.129302 | − | 0.182860i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.65685 | 0.182669 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.00000 | −0.161290 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −39.5980 | + | 14.0000i | −1.27603 | + | 0.451144i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.0000 | 0.450676 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.0000i | 1.73652i | 0.496107 | + | 0.868261i | \(0.334762\pi\) | ||||
−0.496107 | + | 0.868261i | \(0.665238\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −16.0000 | + | 22.6274i | −0.513994 | + | 0.726897i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34.0000i | 1.09111i | 0.838074 | + | 0.545556i | \(0.183681\pi\) | ||||
−0.838074 | + | 0.545556i | \(0.816319\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 33.9411i | 1.08810i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.82843 | − | 4.00000i | 0.0905822 | − | 0.128103i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 36.7696i | 1.17636i | 0.808729 | + | 0.588181i | \(0.200156\pi\) | ||||
−0.808729 | + | 0.588181i | \(0.799844\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.3137 | −0.361588 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 48.0000 | − | 16.9706i | 1.53252 | − | 0.541828i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.48528 | 0.270638 | 0.135319 | − | 0.990802i | \(-0.456794\pi\) | ||||
0.135319 | + | 0.990802i | \(0.456794\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.0000 | −0.318626 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.65685 | + | 8.00000i | −0.180060 | + | 0.254643i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 72.0000 | 2.28947 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 54.0000i | − | 1.71537i | −0.514178 | − | 0.857683i | \(-0.671903\pi\) | ||
0.514178 | − | 0.857683i | \(-0.328097\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 26.0000i | − | 0.824255i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 25.4558i | − | 0.806195i | −0.915157 | − | 0.403097i | \(-0.867934\pi\) | ||
0.915157 | − | 0.403097i | \(-0.132066\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −14.1421 | − | 4.00000i | −0.447437 | − | 0.126554i |
(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 | 960.2.b.a.671.1 | ✓ | 4 | |
3.2 | odd | 2 | 960.2.b.b.671.2 | yes | 4 | ||
4.3 | odd | 2 | inner | 960.2.b.a.671.4 | yes | 4 | |
8.3 | odd | 2 | 960.2.b.b.671.1 | yes | 4 | ||
8.5 | even | 2 | 960.2.b.b.671.4 | yes | 4 | ||
12.11 | even | 2 | 960.2.b.b.671.3 | yes | 4 | ||
24.5 | odd | 2 | inner | 960.2.b.a.671.3 | yes | 4 | |
24.11 | even | 2 | inner | 960.2.b.a.671.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
960.2.b.a.671.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
960.2.b.a.671.2 | yes | 4 | 24.11 | even | 2 | inner | |
960.2.b.a.671.3 | yes | 4 | 24.5 | odd | 2 | inner | |
960.2.b.a.671.4 | yes | 4 | 4.3 | odd | 2 | inner | |
960.2.b.b.671.1 | yes | 4 | 8.3 | odd | 2 | ||
960.2.b.b.671.2 | yes | 4 | 3.2 | odd | 2 | ||
960.2.b.b.671.3 | yes | 4 | 12.11 | even | 2 | ||
960.2.b.b.671.4 | yes | 4 | 8.5 | even | 2 |