Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,2,Mod(649,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, 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("675.649");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.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: | \(5.38990213644\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{13})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 135) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.1 | ||
Root | \(-2.30278i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 675.649 |
Dual form | 675.2.b.i.649.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.30278i | − 1.62831i | −0.580649 | − | 0.814154i | \(-0.697201\pi\) | ||||
0.580649 | − | 0.814154i | \(-0.302799\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.30278 | −1.65139 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.60555i | − 0.984806i | −0.870367 | − | 0.492403i | \(-0.836119\pi\) | ||||
0.870367 | − | 0.492403i | \(-0.163881\pi\) | |||||||
\(8\) | 3.00000i | 1.06066i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.60555 | 1.38863 | 0.694313 | − | 0.719673i | \(-0.255708\pi\) | ||||
0.694313 | + | 0.719673i | \(0.255708\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 6.60555i | − 1.83205i | −0.401121 | − | 0.916025i | \(-0.631379\pi\) | ||||
0.401121 | − | 0.916025i | \(-0.368621\pi\) | |||||||
\(14\) | −6.00000 | −1.60357 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.302776 | 0.0756939 | ||||||||
\(17\) | 1.60555i | 0.389403i | 0.980863 | + | 0.194702i | \(0.0623739\pi\) | ||||
−0.980863 | + | 0.194702i | \(0.937626\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.60555 | −0.827170 | −0.413585 | − | 0.910465i | \(-0.635724\pi\) | ||||
−0.413585 | + | 0.910465i | \(0.635724\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 10.6056i | − 2.26111i | ||||||||
\(23\) | 3.00000i | 0.625543i | 0.949828 | + | 0.312772i | \(0.101257\pi\) | ||||
−0.949828 | + | 0.312772i | \(0.898743\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −15.2111 | −2.98314 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 8.60555i | 1.62630i | ||||||||
\(29\) | −1.39445 | −0.258943 | −0.129471 | − | 0.991583i | \(-0.541328\pi\) | ||||
−0.129471 | + | 0.991583i | \(0.541328\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.60555 | −1.00679 | −0.503393 | − | 0.864057i | \(-0.667915\pi\) | ||||
−0.503393 | + | 0.864057i | \(0.667915\pi\) | |||||||
\(32\) | 5.30278i | 0.937407i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.69722 | 0.634069 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000i | 0.328798i | 0.986394 | + | 0.164399i | \(0.0525685\pi\) | ||||
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(38\) | 8.30278i | 1.34689i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.60555 | −0.719266 | −0.359633 | − | 0.933094i | \(-0.617098\pi\) | ||||
−0.359633 | + | 0.933094i | \(0.617098\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 0.605551i | − 0.0923457i | −0.998933 | − | 0.0461729i | \(-0.985297\pi\) | ||||
0.998933 | − | 0.0461729i | \(-0.0147025\pi\) | |||||||
\(44\) | −15.2111 | −2.29316 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.90833 | 1.01858 | ||||||||
\(47\) | − 9.21110i | − 1.34358i | −0.740743 | − | 0.671789i | \(-0.765526\pi\) | ||||
0.740743 | − | 0.671789i | \(-0.234474\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.211103 | 0.0301575 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 21.8167i | 3.02543i | ||||||||
\(53\) | − 1.60555i | − 0.220539i | −0.993902 | − | 0.110270i | \(-0.964829\pi\) | ||||
0.993902 | − | 0.110270i | \(-0.0351715\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 7.81665 | 1.04454 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.21110i | 0.421638i | ||||||||
\(59\) | 1.39445 | 0.181542 | 0.0907709 | − | 0.995872i | \(-0.471067\pi\) | ||||
0.0907709 | + | 0.995872i | \(0.471067\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.21110 | −0.539176 | −0.269588 | − | 0.962976i | \(-0.586888\pi\) | ||||
−0.269588 | + | 0.962976i | \(0.586888\pi\) | |||||||
\(62\) | 12.9083i | 1.63936i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 12.8167 | 1.60208 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 0.788897i | − 0.0963792i | −0.998838 | − | 0.0481896i | \(-0.984655\pi\) | ||||
0.998838 | − | 0.0481896i | \(-0.0153452\pi\) | |||||||
\(68\) | − 5.30278i | − 0.643056i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.39445 | 0.877560 | 0.438780 | − | 0.898595i | \(-0.355411\pi\) | ||||
0.438780 | + | 0.898595i | \(0.355411\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 12.6056i | − 1.47537i | −0.675146 | − | 0.737684i | \(-0.735919\pi\) | ||||
0.675146 | − | 0.737684i | \(-0.264081\pi\) | |||||||
\(74\) | 4.60555 | 0.535384 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11.9083 | 1.36598 | ||||||||
\(77\) | − 12.0000i | − 1.36753i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.6056 | 1.30573 | 0.652863 | − | 0.757476i | \(-0.273568\pi\) | ||||
0.652863 | + | 0.757476i | \(0.273568\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10.6056i | 1.17119i | ||||||||
\(83\) | − 3.00000i | − 0.329293i | −0.986353 | − | 0.164646i | \(-0.947352\pi\) | ||||
0.986353 | − | 0.164646i | \(-0.0526483\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.39445 | −0.150367 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 13.8167i | 1.47286i | ||||||||
\(89\) | 13.8167 | 1.46456 | 0.732281 | − | 0.681002i | \(-0.238456\pi\) | ||||
0.732281 | + | 0.681002i | \(0.238456\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17.2111 | −1.80421 | ||||||||
\(92\) | − 9.90833i | − 1.03301i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −21.2111 | −2.18776 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.00000i | 0.812277i | 0.913812 | + | 0.406138i | \(0.133125\pi\) | ||||
−0.913812 | + | 0.406138i | \(0.866875\pi\) | |||||||
\(98\) | − 0.486122i | − 0.0491057i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.0000 | 1.19404 | 0.597022 | − | 0.802225i | \(-0.296350\pi\) | ||||
0.597022 | + | 0.802225i | \(0.296350\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.00000i | 0.394132i | 0.980390 | + | 0.197066i | \(0.0631413\pi\) | ||||
−0.980390 | + | 0.197066i | \(0.936859\pi\) | |||||||
\(104\) | 19.8167 | 1.94318 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.69722 | −0.359106 | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.00000 | 0.670478 | 0.335239 | − | 0.942133i | \(-0.391183\pi\) | ||||
0.335239 | + | 0.942133i | \(0.391183\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 0.788897i | − 0.0745438i | ||||||||
\(113\) | 15.2111i | 1.43094i | 0.698643 | + | 0.715470i | \(0.253787\pi\) | ||||
−0.698643 | + | 0.715470i | \(0.746213\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.60555 | 0.427615 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 3.21110i | − 0.295606i | ||||||||
\(119\) | 4.18335 | 0.383487 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.2111 | 0.928282 | ||||||||
\(122\) | 9.69722i | 0.877945i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 18.5139 | 1.66260 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 19.2111i | − 1.70471i | −0.522964 | − | 0.852355i | \(-0.675174\pi\) | ||||
0.522964 | − | 0.852355i | \(-0.324826\pi\) | |||||||
\(128\) | − 18.9083i | − 1.67128i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.00000 | 0.524222 | 0.262111 | − | 0.965038i | \(-0.415581\pi\) | ||||
0.262111 | + | 0.965038i | \(0.415581\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.39445i | 0.814602i | ||||||||
\(134\) | −1.81665 | −0.156935 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.81665 | −0.413025 | ||||||||
\(137\) | 16.8167i | 1.43674i | 0.695659 | + | 0.718372i | \(0.255112\pi\) | ||||
−0.695659 | + | 0.718372i | \(0.744888\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 17.0278i | − 1.42894i | ||||||||
\(143\) | − 30.4222i | − 2.54403i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −29.0278 | −2.40235 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 6.60555i | − 0.542973i | ||||||||
\(149\) | −23.0278 | −1.88651 | −0.943254 | − | 0.332073i | \(-0.892252\pi\) | ||||
−0.943254 | + | 0.332073i | \(0.892252\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.4222 | 1.17366 | 0.586831 | − | 0.809709i | \(-0.300375\pi\) | ||||
0.586831 | + | 0.809709i | \(0.300375\pi\) | |||||||
\(152\) | − 10.8167i | − 0.877346i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −27.6333 | −2.22676 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 17.8167i | − 1.42192i | −0.703231 | − | 0.710962i | \(-0.748260\pi\) | ||||
0.703231 | − | 0.710962i | \(-0.251740\pi\) | |||||||
\(158\) | − 26.7250i | − 2.12613i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.81665 | 0.616039 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 2.00000i | − 0.156652i | −0.996928 | − | 0.0783260i | \(-0.975042\pi\) | ||||
0.996928 | − | 0.0783260i | \(-0.0249575\pi\) | |||||||
\(164\) | 15.2111 | 1.18779 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.90833 | −0.536190 | ||||||||
\(167\) | − 3.00000i | − 0.232147i | −0.993241 | − | 0.116073i | \(-0.962969\pi\) | ||||
0.993241 | − | 0.116073i | \(-0.0370308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −30.6333 | −2.35641 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.00000i | 0.152499i | ||||||||
\(173\) | 10.8167i | 0.822375i | 0.911551 | + | 0.411187i | \(0.134886\pi\) | ||||
−0.911551 | + | 0.411187i | \(0.865114\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.39445 | 0.105111 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 31.8167i | − 2.38476i | ||||||||
\(179\) | 21.2111 | 1.58539 | 0.792696 | − | 0.609617i | \(-0.208677\pi\) | ||||
0.792696 | + | 0.609617i | \(0.208677\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.00000 | −0.520306 | −0.260153 | − | 0.965567i | \(-0.583773\pi\) | ||||
−0.260153 | + | 0.965567i | \(0.583773\pi\) | |||||||
\(182\) | 39.6333i | 2.93782i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −9.00000 | −0.663489 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.39445i | 0.540736i | ||||||||
\(188\) | 30.4222i | 2.21877i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.4222 | −0.898839 | −0.449420 | − | 0.893321i | \(-0.648369\pi\) | ||||
−0.449420 | + | 0.893321i | \(0.648369\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 0.183346i | − 0.0131975i | −0.999978 | − | 0.00659877i | \(-0.997900\pi\) | ||||
0.999978 | − | 0.00659877i | \(-0.00210047\pi\) | |||||||
\(194\) | 18.4222 | 1.32264 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.697224 | −0.0498017 | ||||||||
\(197\) | − 22.8167i | − 1.62562i | −0.582529 | − | 0.812810i | \(-0.697937\pi\) | ||||
0.582529 | − | 0.812810i | \(-0.302063\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.21110 | 0.0858528 | 0.0429264 | − | 0.999078i | \(-0.486332\pi\) | ||||
0.0429264 | + | 0.999078i | \(0.486332\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 27.6333i | − 1.94427i | ||||||||
\(203\) | 3.63331i | 0.255008i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 9.21110 | 0.641768 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 2.00000i | − 0.138675i | ||||||||
\(209\) | −16.6056 | −1.14863 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.81665 | −0.606963 | −0.303482 | − | 0.952837i | \(-0.598149\pi\) | ||||
−0.303482 | + | 0.952837i | \(0.598149\pi\) | |||||||
\(212\) | 5.30278i | 0.364196i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.6056i | 0.991489i | ||||||||
\(218\) | − 16.1194i | − 1.09175i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.6056 | 0.713407 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.0000i | 0.669650i | 0.942280 | + | 0.334825i | \(0.108677\pi\) | ||||
−0.942280 | + | 0.334825i | \(0.891323\pi\) | |||||||
\(224\) | 13.8167 | 0.923164 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 35.0278 | 2.33001 | ||||||||
\(227\) | − 11.7889i | − 0.782457i | −0.920294 | − | 0.391228i | \(-0.872050\pi\) | ||||
0.920294 | − | 0.391228i | \(-0.127950\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.21110 | −0.542605 | −0.271302 | − | 0.962494i | \(-0.587454\pi\) | ||||
−0.271302 | + | 0.962494i | \(0.587454\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 4.18335i | − 0.274650i | ||||||||
\(233\) | 18.0000i | 1.17922i | 0.807688 | + | 0.589610i | \(0.200718\pi\) | ||||
−0.807688 | + | 0.589610i | \(0.799282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.60555 | −0.299796 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 9.63331i | − 0.624435i | ||||||||
\(239\) | 15.2111 | 0.983924 | 0.491962 | − | 0.870617i | \(-0.336280\pi\) | ||||
0.491962 | + | 0.870617i | \(0.336280\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.7889 | 0.888221 | 0.444110 | − | 0.895972i | \(-0.353520\pi\) | ||||
0.444110 | + | 0.895972i | \(0.353520\pi\) | |||||||
\(242\) | − 23.5139i | − 1.51153i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 13.9083 | 0.890389 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.8167i | 1.51542i | ||||||||
\(248\) | − 16.8167i | − 1.06786i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.6333 | 1.74420 | 0.872099 | − | 0.489329i | \(-0.162758\pi\) | ||||
0.872099 | + | 0.489329i | \(0.162758\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.8167i | 0.868646i | ||||||||
\(254\) | −44.2389 | −2.77579 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −17.9083 | −1.11927 | ||||||||
\(257\) | 1.18335i | 0.0738151i | 0.999319 | + | 0.0369076i | \(0.0117507\pi\) | ||||
−0.999319 | + | 0.0369076i | \(0.988249\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.21110 | 0.323802 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 13.8167i | − 0.853596i | ||||||||
\(263\) | 2.78890i | 0.171971i | 0.996296 | + | 0.0859854i | \(0.0274038\pi\) | ||||
−0.996296 | + | 0.0859854i | \(0.972596\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 21.6333 | 1.32642 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.60555i | 0.159159i | ||||||||
\(269\) | 3.21110 | 0.195784 | 0.0978922 | − | 0.995197i | \(-0.468790\pi\) | ||||
0.0978922 | + | 0.995197i | \(0.468790\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.2389 | 1.89763 | 0.948813 | − | 0.315839i | \(-0.102286\pi\) | ||||
0.948813 | + | 0.315839i | \(0.102286\pi\) | |||||||
\(272\) | 0.486122i | 0.0294755i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 38.7250 | 2.33946 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.02776i | 0.422257i | 0.977458 | + | 0.211128i | \(0.0677138\pi\) | ||||
−0.977458 | + | 0.211128i | \(0.932286\pi\) | |||||||
\(278\) | − 9.21110i | − 0.552445i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.8167 | −1.18216 | −0.591081 | − | 0.806612i | \(-0.701299\pi\) | ||||
−0.591081 | + | 0.806612i | \(0.701299\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 3.39445i | − 0.201779i | −0.994898 | − | 0.100890i | \(-0.967831\pi\) | ||||
0.994898 | − | 0.100890i | \(-0.0321689\pi\) | |||||||
\(284\) | −24.4222 | −1.44919 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −70.0555 | −4.14247 | ||||||||
\(287\) | 12.0000i | 0.708338i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.4222 | 0.848365 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 41.6333i | 2.43641i | ||||||||
\(293\) | 7.18335i | 0.419656i | 0.977738 | + | 0.209828i | \(0.0672903\pi\) | ||||
−0.977738 | + | 0.209828i | \(0.932710\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.00000 | −0.348743 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 53.0278i | 3.07182i | ||||||||
\(299\) | 19.8167 | 1.14603 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.57779 | −0.0909426 | ||||||||
\(302\) | − 33.2111i | − 1.91108i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.09167 | −0.0626117 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.42221i | 0.480681i | 0.970689 | + | 0.240340i | \(0.0772590\pi\) | ||||
−0.970689 | + | 0.240340i | \(0.922741\pi\) | |||||||
\(308\) | 39.6333i | 2.25832i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.81665 | −0.443242 | −0.221621 | − | 0.975133i | \(-0.571135\pi\) | ||||
−0.221621 | + | 0.975133i | \(0.571135\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.6333i | 1.10974i | 0.831937 | + | 0.554870i | \(0.187232\pi\) | ||||
−0.831937 | + | 0.554870i | \(0.812768\pi\) | |||||||
\(314\) | −41.0278 | −2.31533 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −38.3305 | −2.15626 | ||||||||
\(317\) | − 7.60555i | − 0.427170i | −0.976924 | − | 0.213585i | \(-0.931486\pi\) | ||||
0.976924 | − | 0.213585i | \(-0.0685141\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.42221 | −0.359574 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − 18.0000i | − 1.00310i | ||||||||
\(323\) | − 5.78890i | − 0.322103i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.60555 | −0.255078 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 13.8167i | − 0.762897i | ||||||||
\(329\) | −24.0000 | −1.32316 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.2111 | 1.60559 | 0.802794 | − | 0.596257i | \(-0.203346\pi\) | ||||
0.802794 | + | 0.596257i | \(0.203346\pi\) | |||||||
\(332\) | 9.90833i | 0.543790i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.90833 | −0.378007 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.60555i | 0.359827i | 0.983682 | + | 0.179914i | \(0.0575818\pi\) | ||||
−0.983682 | + | 0.179914i | \(0.942418\pi\) | |||||||
\(338\) | 70.5416i | 3.83696i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −25.8167 | −1.39805 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 18.7889i | − 1.01451i | ||||||||
\(344\) | 1.81665 | 0.0979474 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 24.9083 | 1.33908 | ||||||||
\(347\) | 30.4222i | 1.63315i | 0.577240 | + | 0.816575i | \(0.304130\pi\) | ||||
−0.577240 | + | 0.816575i | \(0.695870\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.8444 | 1.70459 | 0.852296 | − | 0.523060i | \(-0.175209\pi\) | ||||
0.852296 | + | 0.523060i | \(0.175209\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 24.4222i | 1.30171i | ||||||||
\(353\) | − 21.6333i | − 1.15142i | −0.817652 | − | 0.575712i | \(-0.804725\pi\) | ||||
0.817652 | − | 0.575712i | \(-0.195275\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −45.6333 | −2.41856 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 48.8444i | − 2.58151i | ||||||||
\(359\) | 9.63331 | 0.508427 | 0.254213 | − | 0.967148i | \(-0.418183\pi\) | ||||
0.254213 | + | 0.967148i | \(0.418183\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.00000 | −0.315789 | ||||||||
\(362\) | 16.1194i | 0.847218i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 56.8444 | 2.97946 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 2.60555i | − 0.136009i | −0.997685 | − | 0.0680043i | \(-0.978337\pi\) | ||||
0.997685 | − | 0.0680043i | \(-0.0216632\pi\) | |||||||
\(368\) | 0.908327i | 0.0473498i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.18335 | −0.217189 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.2111i | 1.30538i | 0.757624 | + | 0.652691i | \(0.226360\pi\) | ||||
−0.757624 | + | 0.652691i | \(0.773640\pi\) | |||||||
\(374\) | 17.0278 | 0.880484 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 27.6333 | 1.42508 | ||||||||
\(377\) | 9.21110i | 0.474396i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.6056 | −1.10980 | −0.554901 | − | 0.831916i | \(-0.687244\pi\) | ||||
−0.554901 | + | 0.831916i | \(0.687244\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 28.6056i | 1.46359i | ||||||||
\(383\) | − 24.6333i | − 1.25870i | −0.777121 | − | 0.629352i | \(-0.783321\pi\) | ||||
0.777121 | − | 0.629352i | \(-0.216679\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.422205 | −0.0214897 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 26.4222i | − 1.34138i | ||||||||
\(389\) | −25.8167 | −1.30896 | −0.654478 | − | 0.756081i | \(-0.727112\pi\) | ||||
−0.654478 | + | 0.756081i | \(0.727112\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.81665 | −0.243589 | ||||||||
\(392\) | 0.633308i | 0.0319869i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −52.5416 | −2.64701 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 5.39445i | − 0.270740i | −0.990795 | − | 0.135370i | \(-0.956778\pi\) | ||||
0.990795 | − | 0.135370i | \(-0.0432222\pi\) | |||||||
\(398\) | − 2.78890i | − 0.139795i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.0000 | −1.49813 | −0.749064 | − | 0.662497i | \(-0.769497\pi\) | ||||
−0.749064 | + | 0.662497i | \(0.769497\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 37.0278i | 1.84448i | ||||||||
\(404\) | −39.6333 | −1.97183 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.36669 | 0.415232 | ||||||||
\(407\) | 9.21110i | 0.456577i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.00000 | −0.247234 | −0.123617 | − | 0.992330i | \(-0.539449\pi\) | ||||
−0.123617 | + | 0.992330i | \(0.539449\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 13.2111i | − 0.650864i | ||||||||
\(413\) | − 3.63331i | − 0.178783i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 35.0278 | 1.71738 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 38.2389i | 1.87032i | ||||||||
\(419\) | −23.0278 | −1.12498 | −0.562490 | − | 0.826804i | \(-0.690156\pi\) | ||||
−0.562490 | + | 0.826804i | \(0.690156\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.42221 | 0.264262 | 0.132131 | − | 0.991232i | \(-0.457818\pi\) | ||||
0.132131 | + | 0.991232i | \(0.457818\pi\) | |||||||
\(422\) | 20.3028i | 0.988324i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.81665 | 0.233917 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.9722i | 0.530984i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.18335 | 0.201505 | 0.100752 | − | 0.994912i | \(-0.467875\pi\) | ||||
0.100752 | + | 0.994912i | \(0.467875\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 22.2389i | − 1.06873i | −0.845253 | − | 0.534366i | \(-0.820551\pi\) | ||||
0.845253 | − | 0.534366i | \(-0.179449\pi\) | |||||||
\(434\) | 33.6333 | 1.61445 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −23.1194 | −1.10722 | ||||||||
\(437\) | − 10.8167i | − 0.517431i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.6056 | −1.31754 | −0.658771 | − | 0.752344i | \(-0.728923\pi\) | ||||
−0.658771 | + | 0.752344i | \(0.728923\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 24.4222i | − 1.16165i | ||||||||
\(443\) | 24.6333i | 1.17036i | 0.810902 | + | 0.585182i | \(0.198977\pi\) | ||||
−0.810902 | + | 0.585182i | \(0.801023\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 23.0278 | 1.09040 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 33.3944i | − 1.57774i | ||||||||
\(449\) | −38.2389 | −1.80460 | −0.902302 | − | 0.431105i | \(-0.858124\pi\) | ||||
−0.902302 | + | 0.431105i | \(0.858124\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.2111 | −0.998792 | ||||||||
\(452\) | − 50.2389i | − 2.36304i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −27.1472 | −1.27408 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 13.2111i | − 0.617989i | −0.951064 | − | 0.308995i | \(-0.900007\pi\) | ||||
0.951064 | − | 0.308995i | \(-0.0999925\pi\) | |||||||
\(458\) | 18.9083i | 0.883528i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.6333 | 1.00756 | 0.503782 | − | 0.863831i | \(-0.331942\pi\) | ||||
0.503782 | + | 0.863831i | \(0.331942\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.788897i | 0.0366632i | 0.999832 | + | 0.0183316i | \(0.00583545\pi\) | ||||
−0.999832 | + | 0.0183316i | \(0.994165\pi\) | |||||||
\(464\) | −0.422205 | −0.0196004 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 41.4500 | 1.92013 | ||||||||
\(467\) | 12.2111i | 0.565062i | 0.959258 | + | 0.282531i | \(0.0911741\pi\) | ||||
−0.959258 | + | 0.282531i | \(0.908826\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.05551 | −0.0949148 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.18335i | 0.192554i | ||||||||
\(473\) | − 2.78890i | − 0.128234i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −13.8167 | −0.633285 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − 35.0278i | − 1.60213i | ||||||||
\(479\) | 37.8167 | 1.72789 | 0.863944 | − | 0.503589i | \(-0.167987\pi\) | ||||
0.863944 | + | 0.503589i | \(0.167987\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.2111 | 0.602374 | ||||||||
\(482\) | − 31.7527i | − 1.44630i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −33.7250 | −1.53295 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 29.8167i | − 1.35112i | −0.737304 | − | 0.675561i | \(-0.763902\pi\) | ||||
0.737304 | − | 0.675561i | \(-0.236098\pi\) | |||||||
\(488\) | − 12.6333i | − 0.571883i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.2111 | 1.22802 | 0.614010 | − | 0.789298i | \(-0.289555\pi\) | ||||
0.614010 | + | 0.789298i | \(0.289555\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 2.23886i | − 0.100833i | ||||||||
\(494\) | 54.8444 | 2.46757 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.69722 | −0.0762076 | ||||||||
\(497\) | − 19.2666i | − 0.864226i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.3944 | 0.912981 | 0.456490 | − | 0.889728i | \(-0.349106\pi\) | ||||
0.456490 | + | 0.889728i | \(0.349106\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 63.6333i | − 2.84009i | ||||||||
\(503\) | − 2.57779i | − 0.114938i | −0.998347 | − | 0.0574691i | \(-0.981697\pi\) | ||||
0.998347 | − | 0.0574691i | \(-0.0183031\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 31.8167 | 1.41442 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 63.4500i | 2.81514i | ||||||||
\(509\) | 24.8444 | 1.10121 | 0.550605 | − | 0.834766i | \(-0.314397\pi\) | ||||
0.550605 | + | 0.834766i | \(0.314397\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −32.8444 | −1.45295 | ||||||||
\(512\) | 3.42221i | 0.151242i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.72498 | 0.120194 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 42.4222i | − 1.86573i | ||||||||
\(518\) | − 12.0000i | − 0.527250i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.6056 | −1.25323 | −0.626616 | − | 0.779328i | \(-0.715561\pi\) | ||||
−0.626616 | + | 0.779328i | \(0.715561\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 30.6056i | − 1.33829i | −0.743133 | − | 0.669144i | \(-0.766661\pi\) | ||||
0.743133 | − | 0.669144i | \(-0.233339\pi\) | |||||||
\(524\) | −19.8167 | −0.865695 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.42221 | 0.280021 | ||||||||
\(527\) | − 9.00000i | − 0.392046i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.0000 | 0.608696 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − 31.0278i | − 1.34522i | ||||||||
\(533\) | 30.4222i | 1.31773i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.36669 | 0.102226 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 7.39445i | − 0.318797i | ||||||||
\(539\) | 0.972244 | 0.0418775 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −40.4222 | −1.73789 | −0.868943 | − | 0.494912i | \(-0.835200\pi\) | ||||
−0.868943 | + | 0.494912i | \(0.835200\pi\) | |||||||
\(542\) | − 71.9361i | − 3.08992i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −8.51388 | −0.365030 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.605551i | 0.0258915i | 0.999916 | + | 0.0129458i | \(0.00412088\pi\) | ||||
−0.999916 | + | 0.0129458i | \(0.995879\pi\) | |||||||
\(548\) | − 55.5416i | − 2.37262i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.02776 | 0.214190 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 30.2389i | − 1.28589i | ||||||||
\(554\) | 16.1833 | 0.687564 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.2111 | −0.560276 | ||||||||
\(557\) | 9.63331i | 0.408176i | 0.978953 | + | 0.204088i | \(0.0654229\pi\) | ||||
−0.978953 | + | 0.204088i | \(0.934577\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.00000 | −0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 45.6333i | 1.92492i | ||||||||
\(563\) | − 24.0000i | − 1.01148i | −0.862686 | − | 0.505740i | \(-0.831220\pi\) | ||||
0.862686 | − | 0.505740i | \(-0.168780\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −7.81665 | −0.328558 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 22.1833i | 0.930793i | ||||||||
\(569\) | −16.1833 | −0.678441 | −0.339221 | − | 0.940707i | \(-0.610163\pi\) | ||||
−0.339221 | + | 0.940707i | \(0.610163\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.4500 | 1.19059 | 0.595297 | − | 0.803506i | \(-0.297034\pi\) | ||||
0.595297 | + | 0.803506i | \(0.297034\pi\) | |||||||
\(572\) | 100.478i | 4.20118i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 27.6333 | 1.15339 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.18335i | 0.257416i | 0.991683 | + | 0.128708i | \(0.0410830\pi\) | ||||
−0.991683 | + | 0.128708i | \(0.958917\pi\) | |||||||
\(578\) | − 33.2111i | − 1.38140i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.81665 | −0.324289 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 7.39445i | − 0.306247i | ||||||||
\(584\) | 37.8167 | 1.56486 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.5416 | 0.683329 | ||||||||
\(587\) | 21.0000i | 0.866763i | 0.901211 | + | 0.433381i | \(0.142680\pi\) | ||||
−0.901211 | + | 0.433381i | \(0.857320\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.2111 | 0.832784 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.605551i | 0.0248880i | ||||||||
\(593\) | 29.2389i | 1.20070i | 0.799739 | + | 0.600348i | \(0.204971\pi\) | ||||
−0.799739 | + | 0.600348i | \(0.795029\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 76.0555 | 3.11536 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 45.6333i | − 1.86608i | ||||||||
\(599\) | 22.6056 | 0.923638 | 0.461819 | − | 0.886974i | \(-0.347197\pi\) | ||||
0.461819 | + | 0.886974i | \(0.347197\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.6333 | −0.433742 | −0.216871 | − | 0.976200i | \(-0.569585\pi\) | ||||
−0.216871 | + | 0.976200i | \(0.569585\pi\) | |||||||
\(602\) | 3.63331i | 0.148083i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −47.6333 | −1.93817 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.6056i | 0.998709i | 0.866398 | + | 0.499354i | \(0.166429\pi\) | ||||
−0.866398 | + | 0.499354i | \(0.833571\pi\) | |||||||
\(608\) | − 19.1194i | − 0.775395i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −60.8444 | −2.46150 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.8444i | 1.16501i | 0.812825 | + | 0.582507i | \(0.197928\pi\) | ||||
−0.812825 | + | 0.582507i | \(0.802072\pi\) | |||||||
\(614\) | 19.3944 | 0.782696 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 36.0000 | 1.45048 | ||||||||
\(617\) | 38.4500i | 1.54794i | 0.633224 | + | 0.773969i | \(0.281731\pi\) | ||||
−0.633224 | + | 0.773969i | \(0.718269\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −35.6333 | −1.43222 | −0.716112 | − | 0.697986i | \(-0.754080\pi\) | ||||
−0.716112 | + | 0.697986i | \(0.754080\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 18.0000i | 0.721734i | ||||||||
\(623\) | − 36.0000i | − 1.44231i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 45.2111 | 1.80700 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 58.8444i | 2.34815i | ||||||||
\(629\) | −3.21110 | −0.128035 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.02776 | −0.239961 | −0.119981 | − | 0.992776i | \(-0.538283\pi\) | ||||
−0.119981 | + | 0.992776i | \(0.538283\pi\) | |||||||
\(632\) | 34.8167i | 1.38493i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −17.5139 | −0.695565 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1.39445i | − 0.0552501i | ||||||||
\(638\) | 14.7889i | 0.585498i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.0000 | −0.947943 | −0.473972 | − | 0.880540i | \(-0.657180\pi\) | ||||
−0.473972 | + | 0.880540i | \(0.657180\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 13.0278i | − 0.513765i | −0.966443 | − | 0.256882i | \(-0.917305\pi\) | ||||
0.966443 | − | 0.256882i | \(-0.0826953\pi\) | |||||||
\(644\) | −25.8167 | −1.01732 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13.3305 | −0.524483 | ||||||||
\(647\) | 23.7889i | 0.935238i | 0.883930 | + | 0.467619i | \(0.154888\pi\) | ||||
−0.883930 | + | 0.467619i | \(0.845112\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.42221 | 0.252094 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.60555i | 0.258693i | ||||||||
\(653\) | 23.2389i | 0.909407i | 0.890643 | + | 0.454703i | \(0.150255\pi\) | ||||
−0.890643 | + | 0.454703i | \(0.849745\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.39445 | −0.0544441 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 55.2666i | 2.15452i | ||||||||
\(659\) | 13.3944 | 0.521774 | 0.260887 | − | 0.965369i | \(-0.415985\pi\) | ||||
0.260887 | + | 0.965369i | \(0.415985\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.8444 | −1.35529 | −0.677645 | − | 0.735389i | \(-0.736999\pi\) | ||||
−0.677645 | + | 0.735389i | \(0.736999\pi\) | |||||||
\(662\) | − 67.2666i | − 2.61439i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.00000 | 0.349268 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 4.18335i | − 0.161980i | ||||||||
\(668\) | 9.90833i | 0.383365i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.3944 | −0.748714 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 25.0278i | − 0.964749i | −0.875965 | − | 0.482375i | \(-0.839774\pi\) | ||||
0.875965 | − | 0.482375i | \(-0.160226\pi\) | |||||||
\(674\) | 15.2111 | 0.585910 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 101.175 | 3.89134 | ||||||||
\(677\) | 21.6333i | 0.831436i | 0.909494 | + | 0.415718i | \(0.136470\pi\) | ||||
−0.909494 | + | 0.415718i | \(0.863530\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.8444 | 0.799935 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 59.4500i | 2.27646i | ||||||||
\(683\) | 9.00000i | 0.344375i | 0.985064 | + | 0.172188i | \(0.0550836\pi\) | ||||
−0.985064 | + | 0.172188i | \(0.944916\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −43.2666 | −1.65193 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 0.183346i | − 0.00699001i | ||||||||
\(689\) | −10.6056 | −0.404039 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.60555 | 0.365412 | 0.182706 | − | 0.983168i | \(-0.441514\pi\) | ||||
0.182706 | + | 0.983168i | \(0.441514\pi\) | |||||||
\(692\) | − 35.7250i | − 1.35806i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 70.0555 | 2.65927 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 7.39445i | − 0.280085i | ||||||||
\(698\) | − 73.3305i | − 2.77560i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.5778 | 0.437287 | 0.218644 | − | 0.975805i | \(-0.429837\pi\) | ||||
0.218644 | + | 0.975805i | \(0.429837\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 7.21110i | − 0.271972i | ||||||||
\(704\) | 59.0278 | 2.22469 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −49.8167 | −1.87487 | ||||||||
\(707\) | − 31.2666i | − 1.17590i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.8444 | 0.857940 | 0.428970 | − | 0.903319i | \(-0.358877\pi\) | ||||
0.428970 | + | 0.903319i | \(0.358877\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 41.4500i | 1.55340i | ||||||||
\(713\) | − 16.8167i | − 0.629789i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −70.0555 | −2.61810 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − 22.1833i | − 0.827875i | ||||||||
\(719\) | −37.2666 | −1.38981 | −0.694905 | − | 0.719101i | \(-0.744554\pi\) | ||||
−0.694905 | + | 0.719101i | \(0.744554\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.4222 | 0.388143 | ||||||||
\(722\) | 13.8167i | 0.514203i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 23.1194 | 0.859227 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.6333i | 1.32157i | 0.750577 | + | 0.660783i | \(0.229776\pi\) | ||||
−0.750577 | + | 0.660783i | \(0.770224\pi\) | |||||||
\(728\) | − 51.6333i | − 1.91366i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.972244 | 0.0359597 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 32.0000i | − 1.18195i | −0.806691 | − | 0.590973i | \(-0.798744\pi\) | ||||
0.806691 | − | 0.590973i | \(-0.201256\pi\) | |||||||
\(734\) | −6.00000 | −0.221464 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −15.9083 | −0.586389 | ||||||||
\(737\) | − 3.63331i | − 0.133835i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.02776 | 0.221735 | 0.110867 | − | 0.993835i | \(-0.464637\pi\) | ||||
0.110867 | + | 0.993835i | \(0.464637\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.63331i | 0.353650i | ||||||||
\(743\) | 5.57779i | 0.204629i | 0.994752 | + | 0.102315i | \(0.0326249\pi\) | ||||
−0.994752 | + | 0.102315i | \(0.967375\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 58.0555 | 2.12556 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 24.4222i | − 0.892964i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30.0278 | −1.09573 | −0.547864 | − | 0.836567i | \(-0.684559\pi\) | ||||
−0.547864 | + | 0.836567i | \(0.684559\pi\) | |||||||
\(752\) | − 2.78890i | − 0.101701i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 21.2111 | 0.772463 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.7889i | 0.610203i | 0.952320 | + | 0.305101i | \(0.0986904\pi\) | ||||
−0.952320 | + | 0.305101i | \(0.901310\pi\) | |||||||
\(758\) | 49.7527i | 1.80710i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.4500 | 0.415061 | 0.207530 | − | 0.978229i | \(-0.433457\pi\) | ||||
0.207530 | + | 0.978229i | \(0.433457\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 18.2389i | − 0.660291i | ||||||||
\(764\) | 41.0278 | 1.48433 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −56.7250 | −2.04956 | ||||||||
\(767\) | − 9.21110i | − 0.332594i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.0000 | −1.47850 | −0.739249 | − | 0.673432i | \(-0.764819\pi\) | ||||
−0.739249 | + | 0.673432i | \(0.764819\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.605551i | 0.0217943i | ||||||||
\(773\) | 4.81665i | 0.173243i | 0.996241 | + | 0.0866215i | \(0.0276071\pi\) | ||||
−0.996241 | + | 0.0866215i | \(0.972393\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −24.0000 | −0.861550 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 59.4500i | 2.13138i | ||||||||
\(779\) | 16.6056 | 0.594956 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34.0555 | 1.21860 | ||||||||
\(782\) | 11.0917i | 0.396637i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.0639167 | 0.00228274 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 39.0278i | − 1.39119i | −0.718434 | − | 0.695595i | \(-0.755141\pi\) | ||||
0.718434 | − | 0.695595i | \(-0.244859\pi\) | |||||||
\(788\) | 75.3583i | 2.68453i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 39.6333 | 1.40920 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.8167i | 0.987798i | ||||||||
\(794\) | −12.4222 | −0.440848 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.00000 | −0.141776 | ||||||||
\(797\) | 41.6611i | 1.47571i | 0.674959 | + | 0.737855i | \(0.264161\pi\) | ||||
−0.674959 | + | 0.737855i | \(0.735839\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.7889 | 0.523194 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 69.0833i | 2.43942i | ||||||||
\(803\) | − 58.0555i | − 2.04873i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 85.2666 | 3.00339 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 36.0000i | 1.26648i | ||||||||
\(809\) | −43.3944 | −1.52567 | −0.762834 | − | 0.646595i | \(-0.776193\pi\) | ||||
−0.762834 | + | 0.646595i | \(0.776193\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.5778 | 0.476781 | 0.238390 | − | 0.971169i | \(-0.423380\pi\) | ||||
0.238390 | + | 0.971169i | \(0.423380\pi\) | |||||||
\(812\) | − 12.0000i | − 0.421117i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 21.2111 | 0.743449 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.18335i | 0.0763856i | ||||||||
\(818\) | 11.5139i | 0.402573i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.0000 | 1.04701 | 0.523504 | − | 0.852023i | \(-0.324625\pi\) | ||||
0.523504 | + | 0.852023i | \(0.324625\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.8167i | 0.621050i | 0.950565 | + | 0.310525i | \(0.100505\pi\) | ||||
−0.950565 | + | 0.310525i | \(0.899495\pi\) | |||||||
\(824\) | −12.0000 | −0.418040 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.36669 | −0.291114 | ||||||||
\(827\) | − 48.2111i | − 1.67646i | −0.545314 | − | 0.838232i | \(-0.683589\pi\) | ||||
0.545314 | − | 0.838232i | \(-0.316411\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.7889 | 0.444177 | 0.222088 | − | 0.975027i | \(-0.428713\pi\) | ||||
0.222088 | + | 0.975027i | \(0.428713\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 84.6611i | − 2.93509i | ||||||||
\(833\) | 0.338936i | 0.0117434i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 54.8444 | 1.89683 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 53.0278i | 1.83181i | ||||||||
\(839\) | −33.2111 | −1.14657 | −0.573287 | − | 0.819354i | \(-0.694332\pi\) | ||||
−0.573287 | + | 0.819354i | \(0.694332\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0555 | −0.932949 | ||||||||
\(842\) | − 12.4861i | − 0.430300i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 29.1194 | 1.00233 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 26.6056i | − 0.914178i | ||||||||
\(848\) | − 0.486122i | − 0.0166935i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.00000 | −0.205677 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 29.2111i | − 1.00017i | −0.865977 | − | 0.500085i | \(-0.833302\pi\) | ||||
0.865977 | − | 0.500085i | \(-0.166698\pi\) | |||||||
\(854\) | 25.2666 | 0.864606 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.23886i | 0.178956i | 0.995989 | + | 0.0894780i | \(0.0285199\pi\) | ||||
−0.995989 | + | 0.0894780i | \(0.971480\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.0278 | 1.02453 | 0.512267 | − | 0.858826i | \(-0.328806\pi\) | ||||
0.512267 | + | 0.858826i | \(0.328806\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 9.63331i | − 0.328112i | ||||||||
\(863\) | − 30.2111i | − 1.02840i | −0.857671 | − | 0.514199i | \(-0.828089\pi\) | ||||
0.857671 | − | 0.514199i | \(-0.171911\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −51.2111 | −1.74022 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 48.2389i | − 1.63733i | ||||||||
\(869\) | 53.4500 | 1.81317 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.21110 | −0.176571 | ||||||||
\(872\) | 21.0000i | 0.711150i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −24.9083 | −0.842537 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.6611i | 0.765210i | 0.923912 | + | 0.382605i | \(0.124973\pi\) | ||||
−0.923912 | + | 0.382605i | \(0.875027\pi\) | |||||||
\(878\) | 63.5694i | 2.14536i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.3944 | −0.855561 | −0.427780 | − | 0.903883i | \(-0.640704\pi\) | ||||
−0.427780 | + | 0.903883i | \(0.640704\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 15.8167i | − 0.532273i | −0.963935 | − | 0.266136i | \(-0.914253\pi\) | ||||
0.963935 | − | 0.266136i | \(-0.0857472\pi\) | |||||||
\(884\) | −35.0278 | −1.17811 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 56.7250 | 1.90571 | ||||||||
\(887\) | − 30.6333i | − 1.02857i | −0.857621 | − | 0.514283i | \(-0.828058\pi\) | ||||
0.857621 | − | 0.514283i | \(-0.171942\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −50.0555 | −1.67881 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 33.0278i | − 1.10585i | ||||||||
\(893\) | 33.2111i | 1.11137i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −49.2666 | −1.64588 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 88.0555i | 2.93845i | ||||||||
\(899\) | 7.81665 | 0.260700 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.57779 | 0.0858788 | ||||||||
\(902\) | 48.8444i | 1.62634i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −45.6333 | −1.51774 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.57779i | 0.0523898i | 0.999657 | + | 0.0261949i | \(0.00833905\pi\) | ||||
−0.999657 | + | 0.0261949i | \(0.991661\pi\) | |||||||
\(908\) | 38.9361i | 1.29214i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.02776 | −0.166577 | −0.0832885 | − | 0.996525i | \(-0.526542\pi\) | ||||
−0.0832885 | + | 0.996525i | \(0.526542\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 13.8167i | − 0.457265i | ||||||||
\(914\) | −30.4222 | −1.00628 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 27.1194 | 0.896051 | ||||||||
\(917\) | − 15.6333i | − 0.516257i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.4222 | −0.871588 | −0.435794 | − | 0.900046i | \(-0.643532\pi\) | ||||
−0.435794 | + | 0.900046i | \(0.643532\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 49.8167i | − 1.64062i | ||||||||
\(923\) | − 48.8444i | − 1.60773i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.81665 | 0.0596989 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − 7.39445i | − 0.242735i | ||||||||
\(929\) | −19.3944 | −0.636311 | −0.318156 | − | 0.948039i | \(-0.603063\pi\) | ||||
−0.318156 | + | 0.948039i | \(0.603063\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.761141 | −0.0249454 | ||||||||
\(932\) | − 59.4500i | − 1.94735i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 28.1194 | 0.920096 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.2111i | 1.34631i | 0.739502 | + | 0.673154i | \(0.235061\pi\) | ||||
−0.739502 | + | 0.673154i | \(0.764939\pi\) | |||||||
\(938\) | 4.73338i | 0.154550i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.422205 | −0.0137635 | −0.00688175 | − | 0.999976i | \(-0.502191\pi\) | ||||
−0.00688175 | + | 0.999976i | \(0.502191\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 13.8167i | − 0.449932i | ||||||||
\(944\) | 0.422205 | 0.0137416 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.42221 | −0.208804 | ||||||||
\(947\) | 39.0000i | 1.26733i | 0.773608 | + | 0.633665i | \(0.218450\pi\) | ||||
−0.773608 | + | 0.633665i | \(0.781550\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −83.2666 | −2.70295 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 12.5500i | 0.406749i | ||||||||
\(953\) | 30.8444i | 0.999148i | 0.866271 | + | 0.499574i | \(0.166510\pi\) | ||||
−0.866271 | + | 0.499574i | \(0.833490\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −50.2389 | −1.62484 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 87.0833i | − 2.81353i | ||||||||
\(959\) | 43.8167 | 1.41491 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.422205 | 0.0136195 | ||||||||
\(962\) | − 30.4222i | − 0.980851i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −45.5416 | −1.46680 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.0000i | 1.60789i | 0.594703 | + | 0.803946i | \(0.297270\pi\) | ||||
−0.594703 | + | 0.803946i | \(0.702730\pi\) | |||||||
\(968\) | 30.6333i | 0.984592i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.0000 | −0.577647 | −0.288824 | − | 0.957382i | \(-0.593264\pi\) | ||||
−0.288824 | + | 0.957382i | \(0.593264\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 10.4222i | − 0.334121i | ||||||||
\(974\) | −68.6611 | −2.20004 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.27502 | −0.0408124 | ||||||||
\(977\) | − 15.2111i | − 0.486646i | −0.969945 | − | 0.243323i | \(-0.921762\pi\) | ||||
0.969945 | − | 0.243323i | \(-0.0782375\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 63.6333 | 2.03373 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 62.6611i | − 1.99959i | ||||||||
\(983\) | 42.6333i | 1.35979i | 0.733309 | + | 0.679896i | \(0.237975\pi\) | ||||
−0.733309 | + | 0.679896i | \(0.762025\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5.15559 | −0.164187 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 78.6611i | − 2.50254i | ||||||||
\(989\) | 1.81665 | 0.0577662 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.1833 | −0.927040 | −0.463520 | − | 0.886087i | \(-0.653414\pi\) | ||||
−0.463520 | + | 0.886087i | \(0.653414\pi\) | |||||||
\(992\) | − 29.7250i | − 0.943769i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −44.3667 | −1.40723 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 39.8722i | − 1.26276i | −0.775472 | − | 0.631382i | \(-0.782488\pi\) | ||||
0.775472 | − | 0.631382i | \(-0.217512\pi\) | |||||||
\(998\) | − 46.9638i | − 1.48661i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 675.2.b.i.649.1 | 4 | ||
3.2 | odd | 2 | 675.2.b.h.649.4 | 4 | |||
5.2 | odd | 4 | 675.2.a.p.1.2 | 2 | |||
5.3 | odd | 4 | 135.2.a.c.1.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 675.2.b.i.649.4 | 4 | ||
15.2 | even | 4 | 675.2.a.k.1.1 | 2 | |||
15.8 | even | 4 | 135.2.a.d.1.2 | yes | 2 | ||
15.14 | odd | 2 | 675.2.b.h.649.1 | 4 | |||
20.3 | even | 4 | 2160.2.a.ba.1.2 | 2 | |||
35.13 | even | 4 | 6615.2.a.p.1.1 | 2 | |||
40.3 | even | 4 | 8640.2.a.ck.1.2 | 2 | |||
40.13 | odd | 4 | 8640.2.a.cr.1.1 | 2 | |||
45.13 | odd | 12 | 405.2.e.k.136.2 | 4 | |||
45.23 | even | 12 | 405.2.e.j.136.1 | 4 | |||
45.38 | even | 12 | 405.2.e.j.271.1 | 4 | |||
45.43 | odd | 12 | 405.2.e.k.271.2 | 4 | |||
60.23 | odd | 4 | 2160.2.a.y.1.2 | 2 | |||
105.83 | odd | 4 | 6615.2.a.v.1.2 | 2 | |||
120.53 | even | 4 | 8640.2.a.df.1.1 | 2 | |||
120.83 | odd | 4 | 8640.2.a.cy.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.2.a.c.1.1 | ✓ | 2 | 5.3 | odd | 4 | ||
135.2.a.d.1.2 | yes | 2 | 15.8 | even | 4 | ||
405.2.e.j.136.1 | 4 | 45.23 | even | 12 | |||
405.2.e.j.271.1 | 4 | 45.38 | even | 12 | |||
405.2.e.k.136.2 | 4 | 45.13 | odd | 12 | |||
405.2.e.k.271.2 | 4 | 45.43 | odd | 12 | |||
675.2.a.k.1.1 | 2 | 15.2 | even | 4 | |||
675.2.a.p.1.2 | 2 | 5.2 | odd | 4 | |||
675.2.b.h.649.1 | 4 | 15.14 | odd | 2 | |||
675.2.b.h.649.4 | 4 | 3.2 | odd | 2 | |||
675.2.b.i.649.1 | 4 | 1.1 | even | 1 | trivial | ||
675.2.b.i.649.4 | 4 | 5.4 | even | 2 | inner | ||
2160.2.a.y.1.2 | 2 | 60.23 | odd | 4 | |||
2160.2.a.ba.1.2 | 2 | 20.3 | even | 4 | |||
6615.2.a.p.1.1 | 2 | 35.13 | even | 4 | |||
6615.2.a.v.1.2 | 2 | 105.83 | odd | 4 | |||
8640.2.a.ck.1.2 | 2 | 40.3 | even | 4 | |||
8640.2.a.cr.1.1 | 2 | 40.13 | odd | 4 | |||
8640.2.a.cy.1.2 | 2 | 120.83 | odd | 4 | |||
8640.2.a.df.1.1 | 2 | 120.53 | even | 4 |