Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,2,Mod(1249,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1875.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.b (of order \(2\), degree \(1\), not 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: | \(14.9719503790\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 25x^{14} + 246x^{12} + 1220x^{10} + 3281x^{8} + 4880x^{6} + 3936x^{4} + 1600x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.10 | ||
Root | \(2.59716i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1249 |
Dual form | 1875.2.b.g.1249.7 |
$q$-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 \(\left(\mathbb{Z}/1875\mathbb{Z}\right)^\times\).
\(n\) | \(626\) | \(1252\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.770071i | 0.544523i | 0.962223 | + | 0.272261i | \(0.0877715\pi\) | ||||
−0.962223 | + | 0.272261i | \(0.912228\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 1.40699 | 0.703495 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.770071 | −0.314380 | ||||||||
\(7\) | − 3.98808i | − 1.50735i | −0.657246 | − | 0.753676i | \(-0.728279\pi\) | ||||
0.657246 | − | 0.753676i | \(-0.271721\pi\) | |||||||
\(8\) | 2.62363i | 0.927592i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.35014 | −1.91464 | −0.957319 | − | 0.289033i | \(-0.906666\pi\) | ||||
−0.957319 | + | 0.289033i | \(0.906666\pi\) | |||||||
\(12\) | 1.40699i | 0.406163i | ||||||||
\(13\) | 5.35433i | 1.48503i | 0.669832 | + | 0.742513i | \(0.266366\pi\) | ||||
−0.669832 | + | 0.742513i | \(0.733634\pi\) | |||||||
\(14\) | 3.07111 | 0.820787 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.793602 | 0.198400 | ||||||||
\(17\) | 3.45746i | 0.838557i | 0.907858 | + | 0.419279i | \(0.137717\pi\) | ||||
−0.907858 | + | 0.419279i | \(0.862283\pi\) | |||||||
\(18\) | − 0.770071i | − 0.181508i | ||||||||
\(19\) | −2.32026 | −0.532305 | −0.266152 | − | 0.963931i | \(-0.585752\pi\) | ||||
−0.266152 | + | 0.963931i | \(0.585752\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.98808 | 0.870270 | ||||||||
\(22\) | − 4.89006i | − 1.04256i | ||||||||
\(23\) | 0.955221i | 0.199177i | 0.995029 | + | 0.0995886i | \(0.0317527\pi\) | ||||
−0.995029 | + | 0.0995886i | \(0.968247\pi\) | |||||||
\(24\) | −2.62363 | −0.535545 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.12322 | −0.808630 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | − 5.61119i | − 1.06042i | ||||||||
\(29\) | −7.26630 | −1.34932 | −0.674659 | − | 0.738129i | \(-0.735709\pi\) | ||||
−0.674659 | + | 0.738129i | \(0.735709\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.40484 | 1.15034 | 0.575172 | − | 0.818033i | \(-0.304935\pi\) | ||||
0.575172 | + | 0.818033i | \(0.304935\pi\) | |||||||
\(32\) | 5.85838i | 1.03563i | ||||||||
\(33\) | − 6.35014i | − 1.10542i | ||||||||
\(34\) | −2.66249 | −0.456613 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.40699 | −0.234498 | ||||||||
\(37\) | 2.83348i | 0.465821i | 0.972498 | + | 0.232911i | \(0.0748249\pi\) | ||||
−0.972498 | + | 0.232911i | \(0.925175\pi\) | |||||||
\(38\) | − 1.78677i | − 0.289852i | ||||||||
\(39\) | −5.35433 | −0.857380 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.35164 | −0.835785 | −0.417893 | − | 0.908496i | \(-0.637231\pi\) | ||||
−0.417893 | + | 0.908496i | \(0.637231\pi\) | |||||||
\(42\) | 3.07111i | 0.473882i | ||||||||
\(43\) | 3.93593i | 0.600224i | 0.953904 | + | 0.300112i | \(0.0970241\pi\) | ||||
−0.953904 | + | 0.300112i | \(0.902976\pi\) | |||||||
\(44\) | −8.93458 | −1.34694 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.735588 | −0.108457 | ||||||||
\(47\) | − 2.48348i | − 0.362252i | −0.983460 | − | 0.181126i | \(-0.942026\pi\) | ||||
0.983460 | − | 0.181126i | \(-0.0579742\pi\) | |||||||
\(48\) | 0.793602i | 0.114547i | ||||||||
\(49\) | −8.90478 | −1.27211 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.45746 | −0.484141 | ||||||||
\(52\) | 7.53350i | 1.04471i | ||||||||
\(53\) | 3.95079i | 0.542682i | 0.962483 | + | 0.271341i | \(0.0874671\pi\) | ||||
−0.962483 | + | 0.271341i | \(0.912533\pi\) | |||||||
\(54\) | 0.770071 | 0.104793 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 10.4632 | 1.39821 | ||||||||
\(57\) | − 2.32026i | − 0.307326i | ||||||||
\(58\) | − 5.59557i | − 0.734735i | ||||||||
\(59\) | −0.0941232 | −0.0122538 | −0.00612690 | − | 0.999981i | \(-0.501950\pi\) | ||||
−0.00612690 | + | 0.999981i | \(0.501950\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.61174 | −0.846547 | −0.423273 | − | 0.906002i | \(-0.639119\pi\) | ||||
−0.423273 | + | 0.906002i | \(0.639119\pi\) | |||||||
\(62\) | 4.93218i | 0.626388i | ||||||||
\(63\) | 3.98808i | 0.502451i | ||||||||
\(64\) | −2.92417 | −0.365521 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.89006 | 0.601925 | ||||||||
\(67\) | 10.2811i | 1.25603i | 0.778201 | + | 0.628016i | \(0.216133\pi\) | ||||
−0.778201 | + | 0.628016i | \(0.783867\pi\) | |||||||
\(68\) | 4.86461i | 0.589921i | ||||||||
\(69\) | −0.955221 | −0.114995 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.81587 | −0.690217 | −0.345109 | − | 0.938563i | \(-0.612158\pi\) | ||||
−0.345109 | + | 0.938563i | \(0.612158\pi\) | |||||||
\(72\) | − 2.62363i | − 0.309197i | ||||||||
\(73\) | 3.79897i | 0.444635i | 0.974974 | + | 0.222318i | \(0.0713622\pi\) | ||||
−0.974974 | + | 0.222318i | \(0.928638\pi\) | |||||||
\(74\) | −2.18198 | −0.253650 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.26459 | −0.374474 | ||||||||
\(77\) | 25.3249i | 2.88603i | ||||||||
\(78\) | − 4.12322i | − 0.466863i | ||||||||
\(79\) | 5.44480 | 0.612587 | 0.306294 | − | 0.951937i | \(-0.400911\pi\) | ||||
0.306294 | + | 0.951937i | \(0.400911\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 4.12114i | − 0.455104i | ||||||||
\(83\) | 9.24696i | 1.01499i | 0.861656 | + | 0.507493i | \(0.169428\pi\) | ||||
−0.861656 | + | 0.507493i | \(0.830572\pi\) | |||||||
\(84\) | 5.61119 | 0.612231 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.03095 | −0.326836 | ||||||||
\(87\) | − 7.26630i | − 0.779030i | ||||||||
\(88\) | − 16.6604i | − 1.77600i | ||||||||
\(89\) | −10.1278 | −1.07355 | −0.536773 | − | 0.843727i | \(-0.680357\pi\) | ||||
−0.536773 | + | 0.843727i | \(0.680357\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 21.3535 | 2.23846 | ||||||||
\(92\) | 1.34399i | 0.140120i | ||||||||
\(93\) | 6.40484i | 0.664151i | ||||||||
\(94\) | 1.91245 | 0.197255 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.85838 | −0.597918 | ||||||||
\(97\) | − 7.89936i | − 0.802058i | −0.916065 | − | 0.401029i | \(-0.868653\pi\) | ||||
0.916065 | − | 0.401029i | \(-0.131347\pi\) | |||||||
\(98\) | − 6.85731i | − 0.692693i | ||||||||
\(99\) | 6.35014 | 0.638213 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.72974 | 0.868641 | 0.434321 | − | 0.900758i | \(-0.356989\pi\) | ||||
0.434321 | + | 0.900758i | \(0.356989\pi\) | |||||||
\(102\) | − 2.66249i | − 0.263626i | ||||||||
\(103\) | − 3.82390i | − 0.376780i | −0.982094 | − | 0.188390i | \(-0.939673\pi\) | ||||
0.982094 | − | 0.188390i | \(-0.0603268\pi\) | |||||||
\(104\) | −14.0478 | −1.37750 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.04239 | −0.295503 | ||||||||
\(107\) | − 14.1662i | − 1.36950i | −0.728780 | − | 0.684748i | \(-0.759912\pi\) | ||||
0.728780 | − | 0.684748i | \(-0.240088\pi\) | |||||||
\(108\) | − 1.40699i | − 0.135388i | ||||||||
\(109\) | −14.0557 | −1.34629 | −0.673145 | − | 0.739511i | \(-0.735057\pi\) | ||||
−0.673145 | + | 0.739511i | \(0.735057\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.83348 | −0.268942 | ||||||||
\(112\) | − 3.16495i | − 0.299059i | ||||||||
\(113\) | 9.26557i | 0.871632i | 0.900036 | + | 0.435816i | \(0.143540\pi\) | ||||
−0.900036 | + | 0.435816i | \(0.856460\pi\) | |||||||
\(114\) | 1.78677 | 0.167346 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −10.2236 | −0.949239 | ||||||||
\(117\) | − 5.35433i | − 0.495008i | ||||||||
\(118\) | − 0.0724815i | − 0.00667247i | ||||||||
\(119\) | 13.7886 | 1.26400 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 29.3242 | 2.66584 | ||||||||
\(122\) | − 5.09151i | − 0.460964i | ||||||||
\(123\) | − 5.35164i | − 0.482541i | ||||||||
\(124\) | 9.01155 | 0.809261 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.07111 | −0.273596 | ||||||||
\(127\) | − 6.91919i | − 0.613979i | −0.951713 | − | 0.306989i | \(-0.900678\pi\) | ||||
0.951713 | − | 0.306989i | \(-0.0993216\pi\) | |||||||
\(128\) | 9.46494i | 0.836591i | ||||||||
\(129\) | −3.93593 | −0.346540 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 22.0453 | 1.92611 | 0.963055 | − | 0.269305i | \(-0.0867938\pi\) | ||||
0.963055 | + | 0.269305i | \(0.0867938\pi\) | |||||||
\(132\) | − 8.93458i | − 0.777655i | ||||||||
\(133\) | 9.25339i | 0.802371i | ||||||||
\(134\) | −7.91715 | −0.683938 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.07108 | −0.777839 | ||||||||
\(137\) | − 1.29992i | − 0.111060i | −0.998457 | − | 0.0555299i | \(-0.982315\pi\) | ||||
0.998457 | − | 0.0555299i | \(-0.0176848\pi\) | |||||||
\(138\) | − 0.735588i | − 0.0626174i | ||||||||
\(139\) | −3.84419 | −0.326060 | −0.163030 | − | 0.986621i | \(-0.552127\pi\) | ||||
−0.163030 | + | 0.986621i | \(0.552127\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.48348 | 0.209146 | ||||||||
\(142\) | − 4.47864i | − 0.375839i | ||||||||
\(143\) | − 34.0008i | − 2.84329i | ||||||||
\(144\) | −0.793602 | −0.0661335 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.92547 | −0.242114 | ||||||||
\(147\) | − 8.90478i | − 0.734454i | ||||||||
\(148\) | 3.98668i | 0.327703i | ||||||||
\(149\) | −16.1035 | −1.31925 | −0.659623 | − | 0.751596i | \(-0.729284\pi\) | ||||
−0.659623 | + | 0.751596i | \(0.729284\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.8215 | −1.20616 | −0.603079 | − | 0.797682i | \(-0.706059\pi\) | ||||
−0.603079 | + | 0.797682i | \(0.706059\pi\) | |||||||
\(152\) | − 6.08750i | − 0.493761i | ||||||||
\(153\) | − 3.45746i | − 0.279519i | ||||||||
\(154\) | −19.5019 | −1.57151 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.53350 | −0.603162 | ||||||||
\(157\) | 5.29762i | 0.422796i | 0.977400 | + | 0.211398i | \(0.0678017\pi\) | ||||
−0.977400 | + | 0.211398i | \(0.932198\pi\) | |||||||
\(158\) | 4.19288i | 0.333568i | ||||||||
\(159\) | −3.95079 | −0.313318 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.80950 | 0.300230 | ||||||||
\(162\) | 0.770071i | 0.0605025i | ||||||||
\(163\) | − 2.86408i | − 0.224332i | −0.993689 | − | 0.112166i | \(-0.964221\pi\) | ||||
0.993689 | − | 0.112166i | \(-0.0357788\pi\) | |||||||
\(164\) | −7.52970 | −0.587971 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.12082 | −0.552683 | ||||||||
\(167\) | 2.57868i | 0.199544i | 0.995010 | + | 0.0997720i | \(0.0318113\pi\) | ||||
−0.995010 | + | 0.0997720i | \(0.968189\pi\) | |||||||
\(168\) | 10.4632i | 0.807255i | ||||||||
\(169\) | −15.6689 | −1.20530 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.32026 | 0.177435 | ||||||||
\(172\) | 5.53782i | 0.422255i | ||||||||
\(173\) | − 20.2272i | − 1.53784i | −0.639343 | − | 0.768921i | \(-0.720794\pi\) | ||||
0.639343 | − | 0.768921i | \(-0.279206\pi\) | |||||||
\(174\) | 5.59557 | 0.424199 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.03948 | −0.379865 | ||||||||
\(177\) | − 0.0941232i | − 0.00707473i | ||||||||
\(178\) | − 7.79913i | − 0.584570i | ||||||||
\(179\) | 26.2365 | 1.96101 | 0.980506 | − | 0.196491i | \(-0.0629546\pi\) | ||||
0.980506 | + | 0.196491i | \(0.0629546\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.37843 | 0.176787 | 0.0883936 | − | 0.996086i | \(-0.471827\pi\) | ||||
0.0883936 | + | 0.996086i | \(0.471827\pi\) | |||||||
\(182\) | 16.4437i | 1.21889i | ||||||||
\(183\) | − 6.61174i | − 0.488754i | ||||||||
\(184\) | −2.50614 | −0.184755 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.93218 | −0.361645 | ||||||||
\(187\) | − 21.9553i | − 1.60553i | ||||||||
\(188\) | − 3.49423i | − 0.254843i | ||||||||
\(189\) | −3.98808 | −0.290090 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.71292 | 0.413372 | 0.206686 | − | 0.978407i | \(-0.433732\pi\) | ||||
0.206686 | + | 0.978407i | \(0.433732\pi\) | |||||||
\(192\) | − 2.92417i | − 0.211034i | ||||||||
\(193\) | 4.18017i | 0.300895i | 0.988618 | + | 0.150448i | \(0.0480715\pi\) | ||||
−0.988618 | + | 0.150448i | \(0.951929\pi\) | |||||||
\(194\) | 6.08307 | 0.436739 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −12.5289 | −0.894924 | ||||||||
\(197\) | 14.6732i | 1.04542i | 0.852511 | + | 0.522710i | \(0.175079\pi\) | ||||
−0.852511 | + | 0.522710i | \(0.824921\pi\) | |||||||
\(198\) | 4.89006i | 0.347521i | ||||||||
\(199\) | −8.77623 | −0.622130 | −0.311065 | − | 0.950389i | \(-0.600686\pi\) | ||||
−0.311065 | + | 0.950389i | \(0.600686\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.2811 | −0.725170 | ||||||||
\(202\) | 6.72252i | 0.472995i | ||||||||
\(203\) | 28.9786i | 2.03390i | ||||||||
\(204\) | −4.86461 | −0.340591 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.94467 | 0.205165 | ||||||||
\(207\) | − 0.955221i | − 0.0663924i | ||||||||
\(208\) | 4.24921i | 0.294630i | ||||||||
\(209\) | 14.7340 | 1.01917 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.7411 | 1.29019 | 0.645095 | − | 0.764103i | \(-0.276818\pi\) | ||||
0.645095 | + | 0.764103i | \(0.276818\pi\) | |||||||
\(212\) | 5.55872i | 0.381774i | ||||||||
\(213\) | − 5.81587i | − 0.398497i | ||||||||
\(214\) | 10.9090 | 0.745722 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.62363 | 0.178515 | ||||||||
\(217\) | − 25.5430i | − 1.73397i | ||||||||
\(218\) | − 10.8239i | − 0.733085i | ||||||||
\(219\) | −3.79897 | −0.256710 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.5124 | −1.24528 | ||||||||
\(222\) | − 2.18198i | − 0.146445i | ||||||||
\(223\) | 16.5574i | 1.10877i | 0.832262 | + | 0.554383i | \(0.187046\pi\) | ||||
−0.832262 | + | 0.554383i | \(0.812954\pi\) | |||||||
\(224\) | 23.3637 | 1.56105 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.13515 | −0.474623 | ||||||||
\(227\) | 5.07350i | 0.336740i | 0.985724 | + | 0.168370i | \(0.0538504\pi\) | ||||
−0.985724 | + | 0.168370i | \(0.946150\pi\) | |||||||
\(228\) | − 3.26459i | − 0.216203i | ||||||||
\(229\) | 23.9323 | 1.58149 | 0.790744 | − | 0.612147i | \(-0.209694\pi\) | ||||
0.790744 | + | 0.612147i | \(0.209694\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −25.3249 | −1.66625 | ||||||||
\(232\) | − 19.0641i | − 1.25162i | ||||||||
\(233\) | − 18.5301i | − 1.21395i | −0.794722 | − | 0.606974i | \(-0.792383\pi\) | ||||
0.794722 | − | 0.606974i | \(-0.207617\pi\) | |||||||
\(234\) | 4.12322 | 0.269543 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.132430 | −0.00862048 | ||||||||
\(237\) | 5.44480i | 0.353678i | ||||||||
\(238\) | 10.6182i | 0.688277i | ||||||||
\(239\) | 14.5812 | 0.943179 | 0.471590 | − | 0.881818i | \(-0.343680\pi\) | ||||
0.471590 | + | 0.881818i | \(0.343680\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.0849630 | 0.00547295 | 0.00273647 | − | 0.999996i | \(-0.499129\pi\) | ||||
0.00273647 | + | 0.999996i | \(0.499129\pi\) | |||||||
\(242\) | 22.5818i | 1.45161i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −9.30266 | −0.595541 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.12114 | 0.262754 | ||||||||
\(247\) | − 12.4235i | − 0.790486i | ||||||||
\(248\) | 16.8039i | 1.06705i | ||||||||
\(249\) | −9.24696 | −0.586002 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.6190 | 1.30146 | 0.650729 | − | 0.759310i | \(-0.274463\pi\) | ||||
0.650729 | + | 0.759310i | \(0.274463\pi\) | |||||||
\(252\) | 5.61119i | 0.353472i | ||||||||
\(253\) | − 6.06578i | − 0.381352i | ||||||||
\(254\) | 5.32827 | 0.334325 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.1370 | −0.821063 | ||||||||
\(257\) | 12.1228i | 0.756199i | 0.925765 | + | 0.378100i | \(0.123422\pi\) | ||||
−0.925765 | + | 0.378100i | \(0.876578\pi\) | |||||||
\(258\) | − 3.03095i | − 0.188699i | ||||||||
\(259\) | 11.3001 | 0.702157 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.26630 | 0.449773 | ||||||||
\(262\) | 16.9765i | 1.04881i | ||||||||
\(263\) | − 7.25319i | − 0.447251i | −0.974675 | − | 0.223625i | \(-0.928211\pi\) | ||||
0.974675 | − | 0.223625i | \(-0.0717892\pi\) | |||||||
\(264\) | 16.6604 | 1.02538 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −7.12577 | −0.436909 | ||||||||
\(267\) | − 10.1278i | − 0.619812i | ||||||||
\(268\) | 14.4654i | 0.883612i | ||||||||
\(269\) | −10.3778 | −0.632744 | −0.316372 | − | 0.948635i | \(-0.602465\pi\) | ||||
−0.316372 | + | 0.948635i | \(0.602465\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −29.4681 | −1.79006 | −0.895031 | − | 0.446004i | \(-0.852847\pi\) | ||||
−0.895031 | + | 0.446004i | \(0.852847\pi\) | |||||||
\(272\) | 2.74385i | 0.166370i | ||||||||
\(273\) | 21.3535i | 1.29237i | ||||||||
\(274\) | 1.00103 | 0.0604745 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.34399 | −0.0808985 | ||||||||
\(277\) | − 17.4446i | − 1.04815i | −0.851673 | − | 0.524073i | \(-0.824412\pi\) | ||||
0.851673 | − | 0.524073i | \(-0.175588\pi\) | |||||||
\(278\) | − 2.96030i | − 0.177547i | ||||||||
\(279\) | −6.40484 | −0.383448 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.95212 | 0.534039 | 0.267019 | − | 0.963691i | \(-0.413961\pi\) | ||||
0.267019 | + | 0.963691i | \(0.413961\pi\) | |||||||
\(282\) | 1.91245i | 0.113885i | ||||||||
\(283\) | − 26.1417i | − 1.55396i | −0.629523 | − | 0.776982i | \(-0.716750\pi\) | ||||
0.629523 | − | 0.776982i | \(-0.283250\pi\) | |||||||
\(284\) | −8.18288 | −0.485564 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 26.1830 | 1.54823 | ||||||||
\(287\) | 21.3428i | 1.25982i | ||||||||
\(288\) | − 5.85838i | − 0.345208i | ||||||||
\(289\) | 5.04597 | 0.296822 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.89936 | 0.463069 | ||||||||
\(292\) | 5.34511i | 0.312799i | ||||||||
\(293\) | − 18.9520i | − 1.10719i | −0.832787 | − | 0.553594i | \(-0.813256\pi\) | ||||
0.832787 | − | 0.553594i | \(-0.186744\pi\) | |||||||
\(294\) | 6.85731 | 0.399927 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.43399 | −0.432092 | ||||||||
\(297\) | 6.35014i | 0.368472i | ||||||||
\(298\) | − 12.4008i | − 0.718360i | ||||||||
\(299\) | −5.11457 | −0.295783 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.6968 | 0.904749 | ||||||||
\(302\) | − 11.4136i | − 0.656780i | ||||||||
\(303\) | 8.72974i | 0.501510i | ||||||||
\(304\) | −1.84137 | −0.105610 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.66249 | 0.152204 | ||||||||
\(307\) | 6.75782i | 0.385689i | 0.981229 | + | 0.192845i | \(0.0617713\pi\) | ||||
−0.981229 | + | 0.192845i | \(0.938229\pi\) | |||||||
\(308\) | 35.6318i | 2.03031i | ||||||||
\(309\) | 3.82390 | 0.217534 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.0403 | 0.739445 | 0.369723 | − | 0.929142i | \(-0.379453\pi\) | ||||
0.369723 | + | 0.929142i | \(0.379453\pi\) | |||||||
\(312\) | − 14.0478i | − 0.795298i | ||||||||
\(313\) | 20.1274i | 1.13767i | 0.822453 | + | 0.568833i | \(0.192605\pi\) | ||||
−0.822453 | + | 0.568833i | \(0.807395\pi\) | |||||||
\(314\) | −4.07955 | −0.230222 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.66078 | 0.430952 | ||||||||
\(317\) | 12.7288i | 0.714921i | 0.933928 | + | 0.357460i | \(0.116357\pi\) | ||||
−0.933928 | + | 0.357460i | \(0.883643\pi\) | |||||||
\(318\) | − 3.04239i | − 0.170609i | ||||||||
\(319\) | 46.1420 | 2.58346 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.1662 | 0.790679 | ||||||||
\(322\) | 2.93358i | 0.163482i | ||||||||
\(323\) | − 8.02222i | − 0.446368i | ||||||||
\(324\) | 1.40699 | 0.0781661 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.20554 | 0.122154 | ||||||||
\(327\) | − 14.0557i | − 0.777281i | ||||||||
\(328\) | − 14.0407i | − 0.775267i | ||||||||
\(329\) | −9.90430 | −0.546042 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.3131 | −0.896649 | −0.448324 | − | 0.893871i | \(-0.647979\pi\) | ||||
−0.448324 | + | 0.893871i | \(0.647979\pi\) | |||||||
\(332\) | 13.0104i | 0.714038i | ||||||||
\(333\) | − 2.83348i | − 0.155274i | ||||||||
\(334\) | −1.98576 | −0.108656 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.16495 | 0.172662 | ||||||||
\(337\) | − 11.0359i | − 0.601166i | −0.953756 | − | 0.300583i | \(-0.902819\pi\) | ||||
0.953756 | − | 0.300583i | \(-0.0971812\pi\) | |||||||
\(338\) | − 12.0662i | − 0.656313i | ||||||||
\(339\) | −9.26557 | −0.503237 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −40.6716 | −2.20249 | ||||||||
\(342\) | 1.78677i | 0.0966173i | ||||||||
\(343\) | 7.59641i | 0.410168i | ||||||||
\(344\) | −10.3264 | −0.556763 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.5764 | 0.837390 | ||||||||
\(347\) | 30.3961i | 1.63175i | 0.578229 | + | 0.815875i | \(0.303744\pi\) | ||||
−0.578229 | + | 0.815875i | \(0.696256\pi\) | |||||||
\(348\) | − 10.2236i | − 0.548044i | ||||||||
\(349\) | 6.45842 | 0.345711 | 0.172856 | − | 0.984947i | \(-0.444701\pi\) | ||||
0.172856 | + | 0.984947i | \(0.444701\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.35433 | 0.285793 | ||||||||
\(352\) | − 37.2015i | − 1.98285i | ||||||||
\(353\) | 4.25227i | 0.226325i | 0.993576 | + | 0.113163i | \(0.0360981\pi\) | ||||
−0.993576 | + | 0.113163i | \(0.963902\pi\) | |||||||
\(354\) | 0.0724815 | 0.00385235 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −14.2497 | −0.755234 | ||||||||
\(357\) | 13.7886i | 0.729772i | ||||||||
\(358\) | 20.2040i | 1.06782i | ||||||||
\(359\) | 8.14893 | 0.430084 | 0.215042 | − | 0.976605i | \(-0.431011\pi\) | ||||
0.215042 | + | 0.976605i | \(0.431011\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.6164 | −0.716652 | ||||||||
\(362\) | 1.83156i | 0.0962646i | ||||||||
\(363\) | 29.3242i | 1.53912i | ||||||||
\(364\) | 30.0442 | 1.57474 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5.09151 | 0.266138 | ||||||||
\(367\) | − 7.18365i | − 0.374984i | −0.982266 | − | 0.187492i | \(-0.939964\pi\) | ||||
0.982266 | − | 0.187492i | \(-0.0600358\pi\) | |||||||
\(368\) | 0.758065i | 0.0395169i | ||||||||
\(369\) | 5.35164 | 0.278595 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.7561 | 0.818013 | ||||||||
\(372\) | 9.01155i | 0.467227i | ||||||||
\(373\) | − 7.23599i | − 0.374666i | −0.982297 | − | 0.187333i | \(-0.940016\pi\) | ||||
0.982297 | − | 0.187333i | \(-0.0599843\pi\) | |||||||
\(374\) | 16.9072 | 0.874250 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.51571 | 0.336022 | ||||||||
\(377\) | − 38.9062i | − 2.00377i | ||||||||
\(378\) | − 3.07111i | − 0.157961i | ||||||||
\(379\) | −1.57210 | −0.0807535 | −0.0403767 | − | 0.999185i | \(-0.512856\pi\) | ||||
−0.0403767 | + | 0.999185i | \(0.512856\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.91919 | 0.354481 | ||||||||
\(382\) | 4.39935i | 0.225090i | ||||||||
\(383\) | 28.4834i | 1.45543i | 0.685878 | + | 0.727717i | \(0.259419\pi\) | ||||
−0.685878 | + | 0.727717i | \(0.740581\pi\) | |||||||
\(384\) | −9.46494 | −0.483006 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.21903 | −0.163844 | ||||||||
\(387\) | − 3.93593i | − 0.200075i | ||||||||
\(388\) | − 11.1143i | − 0.564244i | ||||||||
\(389\) | −5.45707 | −0.276684 | −0.138342 | − | 0.990385i | \(-0.544177\pi\) | ||||
−0.138342 | + | 0.990385i | \(0.544177\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.30264 | −0.167022 | ||||||||
\(392\) | − 23.3628i | − 1.18000i | ||||||||
\(393\) | 22.0453i | 1.11204i | ||||||||
\(394\) | −11.2994 | −0.569255 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 8.93458 | 0.448980 | ||||||||
\(397\) | 13.6918i | 0.687172i | 0.939121 | + | 0.343586i | \(0.111642\pi\) | ||||
−0.939121 | + | 0.343586i | \(0.888358\pi\) | |||||||
\(398\) | − 6.75832i | − 0.338764i | ||||||||
\(399\) | −9.25339 | −0.463249 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.6255 | 0.530614 | 0.265307 | − | 0.964164i | \(-0.414527\pi\) | ||||
0.265307 | + | 0.964164i | \(0.414527\pi\) | |||||||
\(402\) | − 7.91715i | − 0.394872i | ||||||||
\(403\) | 34.2937i | 1.70829i | ||||||||
\(404\) | 12.2827 | 0.611085 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −22.3156 | −1.10750 | ||||||||
\(407\) | − 17.9930i | − 0.891879i | ||||||||
\(408\) | − 9.07108i | − 0.449085i | ||||||||
\(409\) | 20.5777 | 1.01750 | 0.508750 | − | 0.860914i | \(-0.330108\pi\) | ||||
0.508750 | + | 0.860914i | \(0.330108\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.29992 | 0.0641204 | ||||||||
\(412\) | − 5.38018i | − 0.265063i | ||||||||
\(413\) | 0.375371i | 0.0184708i | ||||||||
\(414\) | 0.735588 | 0.0361522 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −31.3677 | −1.53793 | ||||||||
\(417\) | − 3.84419i | − 0.188251i | ||||||||
\(418\) | 11.3462i | 0.554962i | ||||||||
\(419\) | −7.44362 | −0.363644 | −0.181822 | − | 0.983331i | \(-0.558200\pi\) | ||||
−0.181822 | + | 0.983331i | \(0.558200\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.2168 | 1.27773 | 0.638863 | − | 0.769320i | \(-0.279405\pi\) | ||||
0.638863 | + | 0.769320i | \(0.279405\pi\) | |||||||
\(422\) | 14.4320i | 0.702537i | ||||||||
\(423\) | 2.48348i | 0.120751i | ||||||||
\(424\) | −10.3654 | −0.503387 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.47864 | 0.216991 | ||||||||
\(427\) | 26.3682i | 1.27604i | ||||||||
\(428\) | − 19.9317i | − 0.963434i | ||||||||
\(429\) | 34.0008 | 1.64157 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.9859 | −1.10719 | −0.553597 | − | 0.832785i | \(-0.686745\pi\) | ||||
−0.553597 | + | 0.832785i | \(0.686745\pi\) | |||||||
\(432\) | − 0.793602i | − 0.0381822i | ||||||||
\(433\) | − 29.5347i | − 1.41934i | −0.704532 | − | 0.709672i | \(-0.748843\pi\) | ||||
0.704532 | − | 0.709672i | \(-0.251157\pi\) | |||||||
\(434\) | 19.6699 | 0.944188 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −19.7762 | −0.947108 | ||||||||
\(437\) | − 2.21636i | − 0.106023i | ||||||||
\(438\) | − 2.92547i | − 0.139785i | ||||||||
\(439\) | −23.4898 | −1.12111 | −0.560553 | − | 0.828119i | \(-0.689411\pi\) | ||||
−0.560553 | + | 0.828119i | \(0.689411\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.90478 | 0.424037 | ||||||||
\(442\) | − 14.2559i | − 0.678082i | ||||||||
\(443\) | 19.5349i | 0.928130i | 0.885801 | + | 0.464065i | \(0.153610\pi\) | ||||
−0.885801 | + | 0.464065i | \(0.846390\pi\) | |||||||
\(444\) | −3.98668 | −0.189199 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −12.7504 | −0.603748 | ||||||||
\(447\) | − 16.1035i | − 0.761667i | ||||||||
\(448\) | 11.6618i | 0.550969i | ||||||||
\(449\) | −1.18687 | −0.0560118 | −0.0280059 | − | 0.999608i | \(-0.508916\pi\) | ||||
−0.0280059 | + | 0.999608i | \(0.508916\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 33.9836 | 1.60023 | ||||||||
\(452\) | 13.0366i | 0.613189i | ||||||||
\(453\) | − 14.8215i | − 0.696375i | ||||||||
\(454\) | −3.90696 | −0.183363 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.08750 | 0.285073 | ||||||||
\(457\) | 23.4359i | 1.09629i | 0.836384 | + | 0.548144i | \(0.184665\pi\) | ||||
−0.836384 | + | 0.548144i | \(0.815335\pi\) | |||||||
\(458\) | 18.4295i | 0.861156i | ||||||||
\(459\) | 3.45746 | 0.161380 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 35.4249 | 1.64990 | 0.824950 | − | 0.565205i | \(-0.191203\pi\) | ||||
0.824950 | + | 0.565205i | \(0.191203\pi\) | |||||||
\(462\) | − 19.5019i | − 0.907312i | ||||||||
\(463\) | 9.44996i | 0.439177i | 0.975593 | + | 0.219588i | \(0.0704714\pi\) | ||||
−0.975593 | + | 0.219588i | \(0.929529\pi\) | |||||||
\(464\) | −5.76655 | −0.267706 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.2695 | 0.661022 | ||||||||
\(467\) | 0.0277734i | 0.00128520i | 1.00000 | 0.000642599i | \(0.000204546\pi\) | |||||
−1.00000 | 0.000642599i | \(0.999795\pi\) | ||||||||
\(468\) | − 7.53350i | − 0.348236i | ||||||||
\(469\) | 41.0017 | 1.89328 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.29762 | −0.244102 | ||||||||
\(472\) | − 0.246944i | − 0.0113665i | ||||||||
\(473\) | − 24.9937i | − 1.14921i | ||||||||
\(474\) | −4.19288 | −0.192585 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 19.4005 | 0.889219 | ||||||||
\(477\) | − 3.95079i | − 0.180894i | ||||||||
\(478\) | 11.2286i | 0.513583i | ||||||||
\(479\) | −9.30016 | −0.424935 | −0.212467 | − | 0.977168i | \(-0.568150\pi\) | ||||
−0.212467 | + | 0.977168i | \(0.568150\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.1714 | −0.691756 | ||||||||
\(482\) | 0.0654276i | 0.00298014i | ||||||||
\(483\) | 3.80950i | 0.173338i | ||||||||
\(484\) | 41.2589 | 1.87541 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.770071 | −0.0349311 | ||||||||
\(487\) | 32.5963i | 1.47708i | 0.674211 | + | 0.738539i | \(0.264484\pi\) | ||||
−0.674211 | + | 0.738539i | \(0.735516\pi\) | |||||||
\(488\) | − 17.3467i | − 0.785250i | ||||||||
\(489\) | 2.86408 | 0.129518 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.08119 | −0.0487932 | −0.0243966 | − | 0.999702i | \(-0.507766\pi\) | ||||
−0.0243966 | + | 0.999702i | \(0.507766\pi\) | |||||||
\(492\) | − 7.52970i | − 0.339465i | ||||||||
\(493\) | − 25.1230i | − 1.13148i | ||||||||
\(494\) | 9.56695 | 0.430437 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.08290 | 0.228229 | ||||||||
\(497\) | 23.1942i | 1.04040i | ||||||||
\(498\) | − 7.12082i | − 0.319092i | ||||||||
\(499\) | 43.9536 | 1.96763 | 0.983816 | − | 0.179181i | \(-0.0573449\pi\) | ||||
0.983816 | + | 0.179181i | \(0.0573449\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.57868 | −0.115207 | ||||||||
\(502\) | 15.8781i | 0.708673i | ||||||||
\(503\) | − 29.0142i | − 1.29368i | −0.762625 | − | 0.646841i | \(-0.776090\pi\) | ||||
0.762625 | − | 0.646841i | \(-0.223910\pi\) | |||||||
\(504\) | −10.4632 | −0.466069 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.67108 | 0.207655 | ||||||||
\(507\) | − 15.6689i | − 0.695880i | ||||||||
\(508\) | − 9.73523i | − 0.431931i | ||||||||
\(509\) | −5.13104 | −0.227429 | −0.113715 | − | 0.993513i | \(-0.536275\pi\) | ||||
−0.113715 | + | 0.993513i | \(0.536275\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.1506 | 0.670222 | ||||||||
\(512\) | 8.81345i | 0.389503i | ||||||||
\(513\) | 2.32026i | 0.102442i | ||||||||
\(514\) | −9.33541 | −0.411767 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.53782 | −0.243789 | ||||||||
\(517\) | 15.7704i | 0.693582i | ||||||||
\(518\) | 8.70191i | 0.382340i | ||||||||
\(519\) | 20.2272 | 0.887874 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.20068 | −0.359278 | −0.179639 | − | 0.983733i | \(-0.557493\pi\) | ||||
−0.179639 | + | 0.983733i | \(0.557493\pi\) | |||||||
\(522\) | 5.59557i | 0.244912i | ||||||||
\(523\) | 5.23806i | 0.229044i | 0.993421 | + | 0.114522i | \(0.0365337\pi\) | ||||
−0.993421 | + | 0.114522i | \(0.963466\pi\) | |||||||
\(524\) | 31.0176 | 1.35501 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.58547 | 0.243538 | ||||||||
\(527\) | 22.1445i | 0.964629i | ||||||||
\(528\) | − 5.03948i | − 0.219315i | ||||||||
\(529\) | 22.0876 | 0.960328 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.0941232 | 0.00408460 | ||||||||
\(532\) | 13.0194i | 0.564464i | ||||||||
\(533\) | − 28.6545i | − 1.24116i | ||||||||
\(534\) | 7.79913 | 0.337502 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −26.9737 | −1.16508 | ||||||||
\(537\) | 26.2365i | 1.13219i | ||||||||
\(538\) | − 7.99163i | − 0.344544i | ||||||||
\(539\) | 56.5466 | 2.43563 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.2888 | 0.571329 | 0.285664 | − | 0.958330i | \(-0.407786\pi\) | ||||
0.285664 | + | 0.958330i | \(0.407786\pi\) | |||||||
\(542\) | − 22.6926i | − 0.974729i | ||||||||
\(543\) | 2.37843i | 0.102068i | ||||||||
\(544\) | −20.2551 | −0.868431 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −16.4437 | −0.703726 | ||||||||
\(547\) | 40.1311i | 1.71588i | 0.513750 | + | 0.857940i | \(0.328256\pi\) | ||||
−0.513750 | + | 0.857940i | \(0.671744\pi\) | |||||||
\(548\) | − 1.82898i | − 0.0781300i | ||||||||
\(549\) | 6.61174 | 0.282182 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.8597 | 0.718249 | ||||||||
\(552\) | − 2.50614i | − 0.106668i | ||||||||
\(553\) | − 21.7143i | − 0.923385i | ||||||||
\(554\) | 13.4336 | 0.570740 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.40874 | −0.229382 | ||||||||
\(557\) | 45.6945i | 1.93614i | 0.250686 | + | 0.968069i | \(0.419344\pi\) | ||||
−0.250686 | + | 0.968069i | \(0.580656\pi\) | |||||||
\(558\) | − 4.93218i | − 0.208796i | ||||||||
\(559\) | −21.0743 | −0.891348 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.9553 | 0.926956 | ||||||||
\(562\) | 6.89377i | 0.290796i | ||||||||
\(563\) | 0.600201i | 0.0252955i | 0.999920 | + | 0.0126477i | \(0.00402601\pi\) | ||||
−0.999920 | + | 0.0126477i | \(0.995974\pi\) | |||||||
\(564\) | 3.49423 | 0.147134 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 20.1310 | 0.846168 | ||||||||
\(567\) | − 3.98808i | − 0.167484i | ||||||||
\(568\) | − 15.2587i | − 0.640240i | ||||||||
\(569\) | 11.9725 | 0.501914 | 0.250957 | − | 0.967998i | \(-0.419255\pi\) | ||||
0.250957 | + | 0.967998i | \(0.419255\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.4133 | −0.812422 | −0.406211 | − | 0.913779i | \(-0.633150\pi\) | ||||
−0.406211 | + | 0.913779i | \(0.633150\pi\) | |||||||
\(572\) | − 47.8387i | − 2.00024i | ||||||||
\(573\) | 5.71292i | 0.238660i | ||||||||
\(574\) | −16.4354 | −0.686002 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.92417 | 0.121840 | ||||||||
\(577\) | − 26.0641i | − 1.08506i | −0.840035 | − | 0.542532i | \(-0.817466\pi\) | ||||
0.840035 | − | 0.542532i | \(-0.182534\pi\) | |||||||
\(578\) | 3.88575i | 0.161626i | ||||||||
\(579\) | −4.18017 | −0.173722 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 36.8776 | 1.52994 | ||||||||
\(582\) | 6.08307i | 0.252151i | ||||||||
\(583\) | − 25.0880i | − 1.03904i | ||||||||
\(584\) | −9.96706 | −0.412440 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.5944 | 0.602888 | ||||||||
\(587\) | − 2.53968i | − 0.104824i | −0.998626 | − | 0.0524120i | \(-0.983309\pi\) | ||||
0.998626 | − | 0.0524120i | \(-0.0166909\pi\) | |||||||
\(588\) | − 12.5289i | − 0.516685i | ||||||||
\(589\) | −14.8609 | −0.612333 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.6732 | −0.603573 | ||||||||
\(592\) | 2.24865i | 0.0924191i | ||||||||
\(593\) | 4.27995i | 0.175757i | 0.996131 | + | 0.0878783i | \(0.0280087\pi\) | ||||
−0.996131 | + | 0.0878783i | \(0.971991\pi\) | |||||||
\(594\) | −4.89006 | −0.200642 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −22.6574 | −0.928084 | ||||||||
\(597\) | − 8.77623i | − 0.359187i | ||||||||
\(598\) | − 3.93858i | − 0.161061i | ||||||||
\(599\) | −27.1909 | −1.11099 | −0.555495 | − | 0.831520i | \(-0.687471\pi\) | ||||
−0.555495 | + | 0.831520i | \(0.687471\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −44.6772 | −1.82242 | −0.911211 | − | 0.411940i | \(-0.864851\pi\) | ||||
−0.911211 | + | 0.411940i | \(0.864851\pi\) | |||||||
\(602\) | 12.0877i | 0.492656i | ||||||||
\(603\) | − 10.2811i | − 0.418677i | ||||||||
\(604\) | −20.8537 | −0.848526 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.72252 | −0.273084 | ||||||||
\(607\) | − 3.48433i | − 0.141425i | −0.997497 | − | 0.0707123i | \(-0.977473\pi\) | ||||
0.997497 | − | 0.0707123i | \(-0.0225272\pi\) | |||||||
\(608\) | − 13.5930i | − 0.551268i | ||||||||
\(609\) | −28.9786 | −1.17427 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.2974 | 0.537954 | ||||||||
\(612\) | − 4.86461i | − 0.196640i | ||||||||
\(613\) | − 11.1118i | − 0.448803i | −0.974497 | − | 0.224402i | \(-0.927957\pi\) | ||||
0.974497 | − | 0.224402i | \(-0.0720427\pi\) | |||||||
\(614\) | −5.20400 | −0.210016 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −66.4429 | −2.67706 | ||||||||
\(617\) | 33.0355i | 1.32996i | 0.746861 | + | 0.664980i | \(0.231560\pi\) | ||||
−0.746861 | + | 0.664980i | \(0.768440\pi\) | |||||||
\(618\) | 2.94467i | 0.118452i | ||||||||
\(619\) | −17.0417 | −0.684964 | −0.342482 | − | 0.939524i | \(-0.611268\pi\) | ||||
−0.342482 | + | 0.939524i | \(0.611268\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.955221 | 0.0383317 | ||||||||
\(622\) | 10.0419i | 0.402645i | ||||||||
\(623\) | 40.3905i | 1.61821i | ||||||||
\(624\) | −4.24921 | −0.170105 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −15.4995 | −0.619485 | ||||||||
\(627\) | 14.7340i | 0.588419i | ||||||||
\(628\) | 7.45370i | 0.297435i | ||||||||
\(629\) | −9.79664 | −0.390618 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.72790 | 0.307643 | 0.153821 | − | 0.988099i | \(-0.450842\pi\) | ||||
0.153821 | + | 0.988099i | \(0.450842\pi\) | |||||||
\(632\) | 14.2851i | 0.568231i | ||||||||
\(633\) | 18.7411i | 0.744891i | ||||||||
\(634\) | −9.80208 | −0.389290 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −5.55872 | −0.220417 | ||||||||
\(637\) | − 47.6792i | − 1.88912i | ||||||||
\(638\) | 35.5327i | 1.40675i | ||||||||
\(639\) | 5.81587 | 0.230072 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.4910 | 0.572361 | 0.286181 | − | 0.958176i | \(-0.407614\pi\) | ||||
0.286181 | + | 0.958176i | \(0.407614\pi\) | |||||||
\(642\) | 10.9090i | 0.430543i | ||||||||
\(643\) | 42.5134i | 1.67656i | 0.545238 | + | 0.838282i | \(0.316439\pi\) | ||||
−0.545238 | + | 0.838282i | \(0.683561\pi\) | |||||||
\(644\) | 5.35992 | 0.211211 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.17768 | 0.243058 | ||||||||
\(647\) | 26.3343i | 1.03531i | 0.855590 | + | 0.517655i | \(0.173195\pi\) | ||||
−0.855590 | + | 0.517655i | \(0.826805\pi\) | |||||||
\(648\) | 2.62363i | 0.103066i | ||||||||
\(649\) | 0.597695 | 0.0234616 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 25.5430 | 1.00111 | ||||||||
\(652\) | − 4.02973i | − 0.157816i | ||||||||
\(653\) | 4.46840i | 0.174862i | 0.996171 | + | 0.0874310i | \(0.0278657\pi\) | ||||
−0.996171 | + | 0.0874310i | \(0.972134\pi\) | |||||||
\(654\) | 10.8239 | 0.423247 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.24707 | −0.165820 | ||||||||
\(657\) | − 3.79897i | − 0.148212i | ||||||||
\(658\) | − 7.62702i | − 0.297332i | ||||||||
\(659\) | −40.2092 | −1.56633 | −0.783165 | − | 0.621814i | \(-0.786396\pi\) | ||||
−0.783165 | + | 0.621814i | \(0.786396\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.0012 | −0.622374 | −0.311187 | − | 0.950349i | \(-0.600727\pi\) | ||||
−0.311187 | + | 0.950349i | \(0.600727\pi\) | |||||||
\(662\) | − 12.5622i | − 0.488246i | ||||||||
\(663\) | − 18.5124i | − 0.718962i | ||||||||
\(664\) | −24.2606 | −0.941492 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.18198 | 0.0845500 | ||||||||
\(667\) | − 6.94092i | − 0.268754i | ||||||||
\(668\) | 3.62817i | 0.140378i | ||||||||
\(669\) | −16.5574 | −0.640146 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 41.9855 | 1.62083 | ||||||||
\(672\) | 23.3637i | 0.901274i | ||||||||
\(673\) | − 10.6585i | − 0.410854i | −0.978672 | − | 0.205427i | \(-0.934142\pi\) | ||||
0.978672 | − | 0.205427i | \(-0.0658584\pi\) | |||||||
\(674\) | 8.49846 | 0.327349 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −22.0460 | −0.847922 | ||||||||
\(677\) | − 15.9650i | − 0.613585i | −0.951776 | − | 0.306793i | \(-0.900744\pi\) | ||||
0.951776 | − | 0.306793i | \(-0.0992558\pi\) | |||||||
\(678\) | − 7.13515i | − 0.274024i | ||||||||
\(679\) | −31.5033 | −1.20898 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.07350 | −0.194417 | ||||||||
\(682\) | − 31.3201i | − 1.19931i | ||||||||
\(683\) | 1.13294i | 0.0433508i | 0.999765 | + | 0.0216754i | \(0.00690004\pi\) | ||||
−0.999765 | + | 0.0216754i | \(0.993100\pi\) | |||||||
\(684\) | 3.26459 | 0.124825 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5.84978 | −0.223346 | ||||||||
\(687\) | 23.9323i | 0.913072i | ||||||||
\(688\) | 3.12356i | 0.119085i | ||||||||
\(689\) | −21.1538 | −0.805897 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.4786 | −0.436668 | −0.218334 | − | 0.975874i | \(-0.570062\pi\) | ||||
−0.218334 | + | 0.975874i | \(0.570062\pi\) | |||||||
\(692\) | − 28.4594i | − 1.08186i | ||||||||
\(693\) | − 25.3249i | − 0.962012i | ||||||||
\(694\) | −23.4072 | −0.888525 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 19.0641 | 0.722621 | ||||||||
\(697\) | − 18.5031i | − 0.700854i | ||||||||
\(698\) | 4.97344i | 0.188248i | ||||||||
\(699\) | 18.5301 | 0.700873 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.9382 | −1.05521 | −0.527605 | − | 0.849490i | \(-0.676910\pi\) | ||||
−0.527605 | + | 0.849490i | \(0.676910\pi\) | |||||||
\(702\) | 4.12322i | 0.155621i | ||||||||
\(703\) | − 6.57442i | − 0.247959i | ||||||||
\(704\) | 18.5689 | 0.699840 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.27455 | −0.123239 | ||||||||
\(707\) | − 34.8149i | − 1.30935i | ||||||||
\(708\) | − 0.132430i | − 0.00497704i | ||||||||
\(709\) | −26.2614 | −0.986266 | −0.493133 | − | 0.869954i | \(-0.664148\pi\) | ||||
−0.493133 | + | 0.869954i | \(0.664148\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.44480 | −0.204196 | ||||||||
\(712\) | − 26.5716i | − 0.995812i | ||||||||
\(713\) | 6.11804i | 0.229122i | ||||||||
\(714\) | −10.6182 | −0.397377 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 36.9146 | 1.37956 | ||||||||
\(717\) | 14.5812i | 0.544545i | ||||||||
\(718\) | 6.27526i | 0.234191i | ||||||||
\(719\) | 47.8778 | 1.78554 | 0.892771 | − | 0.450510i | \(-0.148758\pi\) | ||||
0.892771 | + | 0.450510i | \(0.148758\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.2500 | −0.567940 | ||||||||
\(722\) | − 10.4856i | − 0.390233i | ||||||||
\(723\) | 0.0849630i | 0.00315981i | ||||||||
\(724\) | 3.34642 | 0.124369 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −22.5818 | −0.838088 | ||||||||
\(727\) | 6.74514i | 0.250163i | 0.992146 | + | 0.125082i | \(0.0399193\pi\) | ||||
−0.992146 | + | 0.125082i | \(0.960081\pi\) | |||||||
\(728\) | 56.0236i | 2.07637i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.6083 | −0.503322 | ||||||||
\(732\) | − 9.30266i | − 0.343836i | ||||||||
\(733\) | 42.9974i | 1.58815i | 0.607822 | + | 0.794073i | \(0.292043\pi\) | ||||
−0.607822 | + | 0.794073i | \(0.707957\pi\) | |||||||
\(734\) | 5.53192 | 0.204187 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.59605 | −0.206273 | ||||||||
\(737\) | − 65.2862i | − 2.40485i | ||||||||
\(738\) | 4.12114i | 0.151701i | ||||||||
\(739\) | 17.0432 | 0.626943 | 0.313472 | − | 0.949598i | \(-0.398508\pi\) | ||||
0.313472 | + | 0.949598i | \(0.398508\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.4235 | 0.456387 | ||||||||
\(742\) | 12.1333i | 0.445427i | ||||||||
\(743\) | − 50.4068i | − 1.84925i | −0.380884 | − | 0.924623i | \(-0.624380\pi\) | ||||
0.380884 | − | 0.924623i | \(-0.375620\pi\) | |||||||
\(744\) | −16.8039 | −0.616061 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.57223 | 0.204014 | ||||||||
\(747\) | − 9.24696i | − 0.338329i | ||||||||
\(748\) | − 30.8910i | − 1.12949i | ||||||||
\(749\) | −56.4958 | −2.06431 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.00535 | −0.109667 | −0.0548334 | − | 0.998496i | \(-0.517463\pi\) | ||||
−0.0548334 | + | 0.998496i | \(0.517463\pi\) | |||||||
\(752\) | − 1.97089i | − 0.0718710i | ||||||||
\(753\) | 20.6190i | 0.751397i | ||||||||
\(754\) | 29.9606 | 1.09110 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5.61119 | −0.204077 | ||||||||
\(757\) | 8.74406i | 0.317808i | 0.987294 | + | 0.158904i | \(0.0507961\pi\) | ||||
−0.987294 | + | 0.158904i | \(0.949204\pi\) | |||||||
\(758\) | − 1.21063i | − 0.0439721i | ||||||||
\(759\) | 6.06578 | 0.220174 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.8086 | −1.15306 | −0.576530 | − | 0.817076i | \(-0.695594\pi\) | ||||
−0.576530 | + | 0.817076i | \(0.695594\pi\) | |||||||
\(762\) | 5.32827i | 0.193023i | ||||||||
\(763\) | 56.0551i | 2.02933i | ||||||||
\(764\) | 8.03802 | 0.290805 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −21.9342 | −0.792517 | ||||||||
\(767\) | − 0.503967i | − 0.0181972i | ||||||||
\(768\) | − 13.1370i | − 0.474041i | ||||||||
\(769\) | −28.7776 | −1.03775 | −0.518874 | − | 0.854851i | \(-0.673649\pi\) | ||||
−0.518874 | + | 0.854851i | \(0.673649\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.1228 | −0.436592 | ||||||||
\(772\) | 5.88146i | 0.211678i | ||||||||
\(773\) | 34.6320i | 1.24563i | 0.782370 | + | 0.622814i | \(0.214011\pi\) | ||||
−0.782370 | + | 0.622814i | \(0.785989\pi\) | |||||||
\(774\) | 3.03095 | 0.108945 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 20.7250 | 0.743983 | ||||||||
\(777\) | 11.3001i | 0.405390i | ||||||||
\(778\) | − 4.20233i | − 0.150661i | ||||||||
\(779\) | 12.4172 | 0.444893 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.9316 | 1.32152 | ||||||||
\(782\) | − 2.54327i | − 0.0909470i | ||||||||
\(783\) | 7.26630i | 0.259677i | ||||||||
\(784\) | −7.06685 | −0.252388 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −16.9765 | −0.605531 | ||||||||
\(787\) | 52.9281i | 1.88668i | 0.331821 | + | 0.943342i | \(0.392337\pi\) | ||||
−0.331821 | + | 0.943342i | \(0.607663\pi\) | |||||||
\(788\) | 20.6450i | 0.735448i | ||||||||
\(789\) | 7.25319 | 0.258220 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 36.9518 | 1.31386 | ||||||||
\(792\) | 16.6604i | 0.592001i | ||||||||
\(793\) | − 35.4015i | − 1.25714i | ||||||||
\(794\) | −10.5437 | −0.374181 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12.3481 | −0.437666 | ||||||||
\(797\) | − 32.9585i | − 1.16745i | −0.811952 | − | 0.583724i | \(-0.801595\pi\) | ||||
0.811952 | − | 0.583724i | \(-0.198405\pi\) | |||||||
\(798\) | − 7.12577i | − 0.252250i | ||||||||
\(799\) | 8.58652 | 0.303769 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.1278 | 0.357849 | ||||||||
\(802\) | 8.18242i | 0.288931i | ||||||||
\(803\) | − 24.1240i | − 0.851316i | ||||||||
\(804\) | −14.4654 | −0.510154 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −26.4086 | −0.930202 | ||||||||
\(807\) | − 10.3778i | − 0.365315i | ||||||||
\(808\) | 22.9036i | 0.805744i | ||||||||
\(809\) | 33.7389 | 1.18620 | 0.593098 | − | 0.805130i | \(-0.297905\pi\) | ||||
0.593098 | + | 0.805130i | \(0.297905\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.3207 | −0.818902 | −0.409451 | − | 0.912332i | \(-0.634280\pi\) | ||||
−0.409451 | + | 0.912332i | \(0.634280\pi\) | |||||||
\(812\) | 40.7726i | 1.43084i | ||||||||
\(813\) | − 29.4681i | − 1.03349i | ||||||||
\(814\) | 13.8559 | 0.485648 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.74385 | −0.0960539 | ||||||||
\(817\) | − 9.13240i | − 0.319502i | ||||||||
\(818\) | 15.8463i | 0.554052i | ||||||||
\(819\) | −21.3535 | −0.746152 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.9918 | 0.593018 | 0.296509 | − | 0.955030i | \(-0.404178\pi\) | ||||
0.296509 | + | 0.955030i | \(0.404178\pi\) | |||||||
\(822\) | 1.00103i | 0.0349150i | ||||||||
\(823\) | − 29.8674i | − 1.04111i | −0.853828 | − | 0.520555i | \(-0.825725\pi\) | ||||
0.853828 | − | 0.520555i | \(-0.174275\pi\) | |||||||
\(824\) | 10.0325 | 0.349498 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.289062 | −0.0100578 | ||||||||
\(827\) | 34.1803i | 1.18857i | 0.804256 | + | 0.594283i | \(0.202564\pi\) | ||||
−0.804256 | + | 0.594283i | \(0.797436\pi\) | |||||||
\(828\) | − 1.34399i | − 0.0467067i | ||||||||
\(829\) | −45.5662 | −1.58258 | −0.791289 | − | 0.611442i | \(-0.790590\pi\) | ||||
−0.791289 | + | 0.611442i | \(0.790590\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.4446 | 0.605148 | ||||||||
\(832\) | − 15.6570i | − 0.542808i | ||||||||
\(833\) | − 30.7879i | − 1.06674i | ||||||||
\(834\) | 2.96030 | 0.102507 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 20.7306 | 0.716982 | ||||||||
\(837\) | − 6.40484i | − 0.221384i | ||||||||
\(838\) | − 5.73212i | − 0.198013i | ||||||||
\(839\) | 5.10480 | 0.176237 | 0.0881186 | − | 0.996110i | \(-0.471915\pi\) | ||||
0.0881186 | + | 0.996110i | \(0.471915\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.7992 | 0.820661 | ||||||||
\(842\) | 20.1888i | 0.695751i | ||||||||
\(843\) | 8.95212i | 0.308328i | ||||||||
\(844\) | 26.3685 | 0.907642 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.91245 | −0.0657515 | ||||||||
\(847\) | − 116.947i | − 4.01836i | ||||||||
\(848\) | 3.13535i | 0.107668i | ||||||||
\(849\) | 26.1417 | 0.897181 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.70660 | −0.0927810 | ||||||||
\(852\) | − 8.18288i | − 0.280341i | ||||||||
\(853\) | 57.1027i | 1.95516i | 0.210564 | + | 0.977580i | \(0.432470\pi\) | ||||
−0.210564 | + | 0.977580i | \(0.567530\pi\) | |||||||
\(854\) | −20.3054 | −0.694835 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 37.1667 | 1.27033 | ||||||||
\(857\) | − 46.0057i | − 1.57153i | −0.618528 | − | 0.785763i | \(-0.712271\pi\) | ||||
0.618528 | − | 0.785763i | \(-0.287729\pi\) | |||||||
\(858\) | 26.1830i | 0.893873i | ||||||||
\(859\) | 39.1766 | 1.33669 | 0.668343 | − | 0.743853i | \(-0.267004\pi\) | ||||
0.668343 | + | 0.743853i | \(0.267004\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −21.3428 | −0.727359 | ||||||||
\(862\) | − 17.7008i | − 0.602892i | ||||||||
\(863\) | − 34.8513i | − 1.18635i | −0.805073 | − | 0.593175i | \(-0.797874\pi\) | ||||
0.805073 | − | 0.593175i | \(-0.202126\pi\) | |||||||
\(864\) | 5.85838 | 0.199306 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 22.7438 | 0.772865 | ||||||||
\(867\) | 5.04597i | 0.171370i | ||||||||
\(868\) | − 35.9388i | − 1.21984i | ||||||||
\(869\) | −34.5752 | −1.17288 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −55.0482 | −1.86524 | ||||||||
\(872\) | − 36.8768i | − 1.24881i | ||||||||
\(873\) | 7.89936i | 0.267353i | ||||||||
\(874\) | 1.70676 | 0.0577319 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.34511 | −0.180594 | ||||||||
\(877\) | − 24.0922i | − 0.813537i | −0.913531 | − | 0.406768i | \(-0.866656\pi\) | ||||
0.913531 | − | 0.406768i | \(-0.133344\pi\) | |||||||
\(878\) | − 18.0888i | − 0.610467i | ||||||||
\(879\) | 18.9520 | 0.639235 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.41163 | −0.0812499 | −0.0406250 | − | 0.999174i | \(-0.512935\pi\) | ||||
−0.0406250 | + | 0.999174i | \(0.512935\pi\) | |||||||
\(882\) | 6.85731i | 0.230898i | ||||||||
\(883\) | − 1.48748i | − 0.0500578i | −0.999687 | − | 0.0250289i | \(-0.992032\pi\) | ||||
0.999687 | − | 0.0250289i | \(-0.00796778\pi\) | |||||||
\(884\) | −26.0468 | −0.876047 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.0432 | −0.505388 | ||||||||
\(887\) | 20.1745i | 0.677392i | 0.940896 | + | 0.338696i | \(0.109986\pi\) | ||||
−0.940896 | + | 0.338696i | \(0.890014\pi\) | |||||||
\(888\) | − 7.43399i | − 0.249468i | ||||||||
\(889\) | −27.5943 | −0.925482 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.35014 | −0.212738 | ||||||||
\(892\) | 23.2961i | 0.780011i | ||||||||
\(893\) | 5.76232i | 0.192829i | ||||||||
\(894\) | 12.4008 | 0.414745 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 37.7470 | 1.26104 | ||||||||
\(897\) | − 5.11457i | − 0.170771i | ||||||||
\(898\) | − 0.913974i | − 0.0304997i | ||||||||
\(899\) | −46.5395 | −1.55218 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.6597 | −0.455070 | ||||||||
\(902\) | 26.1698i | 0.871360i | ||||||||
\(903\) | 15.6968i | 0.522357i | ||||||||
\(904\) | −24.3094 | −0.808518 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 11.4136 | 0.379192 | ||||||||
\(907\) | − 26.2850i | − 0.872778i | −0.899758 | − | 0.436389i | \(-0.856257\pi\) | ||||
0.899758 | − | 0.436389i | \(-0.143743\pi\) | |||||||
\(908\) | 7.13837i | 0.236895i | ||||||||
\(909\) | −8.72974 | −0.289547 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.8586 | −0.757340 | −0.378670 | − | 0.925532i | \(-0.623619\pi\) | ||||
−0.378670 | + | 0.925532i | \(0.623619\pi\) | |||||||
\(912\) | − 1.84137i | − 0.0609737i | ||||||||
\(913\) | − 58.7195i | − 1.94333i | ||||||||
\(914\) | −18.0473 | −0.596953 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 33.6724 | 1.11257 | ||||||||
\(917\) | − 87.9186i | − 2.90333i | ||||||||
\(918\) | 2.66249i | 0.0878753i | ||||||||
\(919\) | 15.7960 | 0.521061 | 0.260530 | − | 0.965466i | \(-0.416103\pi\) | ||||
0.260530 | + | 0.965466i | \(0.416103\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.75782 | −0.222678 | ||||||||
\(922\) | 27.2797i | 0.898408i | ||||||||
\(923\) | − 31.1401i | − 1.02499i | ||||||||
\(924\) | −35.6318 | −1.17220 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −7.27714 | −0.239142 | ||||||||
\(927\) | 3.82390i | 0.125593i | ||||||||
\(928\) | − 42.5688i | − 1.39739i | ||||||||
\(929\) | −48.5302 | −1.59222 | −0.796111 | − | 0.605150i | \(-0.793113\pi\) | ||||
−0.796111 | + | 0.605150i | \(0.793113\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.6614 | 0.677151 | ||||||||
\(932\) | − 26.0717i | − 0.854006i | ||||||||
\(933\) | 13.0403i | 0.426919i | ||||||||
\(934\) | −0.0213875 | −0.000699819 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 14.0478 | 0.459166 | ||||||||
\(937\) | 51.4725i | 1.68153i | 0.541397 | + | 0.840767i | \(0.317896\pi\) | ||||
−0.541397 | + | 0.840767i | \(0.682104\pi\) | |||||||
\(938\) | 31.5742i | 1.03094i | ||||||||
\(939\) | −20.1274 | −0.656832 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.4724 | −0.634782 | −0.317391 | − | 0.948295i | \(-0.602807\pi\) | ||||
−0.317391 | + | 0.948295i | \(0.602807\pi\) | |||||||
\(942\) | − 4.07955i | − 0.132919i | ||||||||
\(943\) | − 5.11199i | − 0.166469i | ||||||||
\(944\) | −0.0746963 | −0.00243116 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 19.2469 | 0.625772 | ||||||||
\(947\) | − 38.9572i | − 1.26594i | −0.774177 | − | 0.632970i | \(-0.781836\pi\) | ||||
0.774177 | − | 0.632970i | \(-0.218164\pi\) | |||||||
\(948\) | 7.66078i | 0.248810i | ||||||||
\(949\) | −20.3409 | −0.660295 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.7288 | −0.412760 | ||||||||
\(952\) | 36.1762i | 1.17248i | ||||||||
\(953\) | 0.532270i | 0.0172419i | 0.999963 | + | 0.00862095i | \(0.00274417\pi\) | ||||
−0.999963 | + | 0.00862095i | \(0.997256\pi\) | |||||||
\(954\) | 3.04239 | 0.0985009 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 20.5156 | 0.663522 | ||||||||
\(957\) | 46.1420i | 1.49156i | ||||||||
\(958\) | − 7.16178i | − 0.231387i | ||||||||
\(959\) | −5.18419 | −0.167406 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.0220 | 0.323290 | ||||||||
\(962\) | − 11.6831i | − 0.376677i | ||||||||
\(963\) | 14.1662i | 0.456499i | ||||||||
\(964\) | 0.119542 | 0.00385019 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.93358 | −0.0943865 | ||||||||
\(967\) | 36.8517i | 1.18507i | 0.805544 | + | 0.592536i | \(0.201873\pi\) | ||||
−0.805544 | + | 0.592536i | \(0.798127\pi\) | |||||||
\(968\) | 76.9358i | 2.47281i | ||||||||
\(969\) | 8.02222 | 0.257711 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.25064 | 0.136410 | 0.0682048 | − | 0.997671i | \(-0.478273\pi\) | ||||
0.0682048 | + | 0.997671i | \(0.478273\pi\) | |||||||
\(972\) | 1.40699i | 0.0451292i | ||||||||
\(973\) | 15.3310i | 0.491488i | ||||||||
\(974\) | −25.1014 | −0.804302 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.24709 | −0.167955 | ||||||||
\(977\) | − 31.6086i | − 1.01125i | −0.862754 | − | 0.505625i | \(-0.831262\pi\) | ||||
0.862754 | − | 0.505625i | \(-0.168738\pi\) | |||||||
\(978\) | 2.20554i | 0.0705255i | ||||||||
\(979\) | 64.3130 | 2.05545 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.0557 | 0.448763 | ||||||||
\(982\) | − 0.832590i | − 0.0265690i | ||||||||
\(983\) | − 45.3330i | − 1.44590i | −0.690901 | − | 0.722949i | \(-0.742786\pi\) | ||||
0.690901 | − | 0.722949i | \(-0.257214\pi\) | |||||||
\(984\) | 14.0407 | 0.447601 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 19.3465 | 0.616117 | ||||||||
\(987\) | − 9.90430i | − 0.315257i | ||||||||
\(988\) | − 17.4797i | − 0.556103i | ||||||||
\(989\) | −3.75968 | −0.119551 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.20124 | 0.292287 | 0.146143 | − | 0.989263i | \(-0.453314\pi\) | ||||
0.146143 | + | 0.989263i | \(0.453314\pi\) | |||||||
\(992\) | 37.5220i | 1.19132i | ||||||||
\(993\) | − 16.3131i | − 0.517680i | ||||||||
\(994\) | −17.8612 | −0.566522 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −13.0104 | −0.412250 | ||||||||
\(997\) | 13.1014i | 0.414924i | 0.978243 | + | 0.207462i | \(0.0665203\pi\) | ||||
−0.978243 | + | 0.207462i | \(0.933480\pi\) | |||||||
\(998\) | 33.8474i | 1.07142i | ||||||||
\(999\) | 2.83348 | 0.0896473 |
(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 | 1875.2.b.g.1249.10 | 16 | ||
5.2 | odd | 4 | 1875.2.a.o.1.4 | yes | 8 | ||
5.3 | odd | 4 | 1875.2.a.n.1.5 | ✓ | 8 | ||
5.4 | even | 2 | inner | 1875.2.b.g.1249.7 | 16 | ||
15.2 | even | 4 | 5625.2.a.u.1.5 | 8 | |||
15.8 | even | 4 | 5625.2.a.bc.1.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1875.2.a.n.1.5 | ✓ | 8 | 5.3 | odd | 4 | ||
1875.2.a.o.1.4 | yes | 8 | 5.2 | odd | 4 | ||
1875.2.b.g.1249.7 | 16 | 5.4 | even | 2 | inner | ||
1875.2.b.g.1249.10 | 16 | 1.1 | even | 1 | trivial | ||
5625.2.a.u.1.5 | 8 | 15.2 | even | 4 | |||
5625.2.a.bc.1.4 | 8 | 15.8 | even | 4 |