Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [775,2,Mod(249,775)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(775, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("775.249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 775 = 5^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 775.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: | \(6.18840615665\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{5} + 28x^{4} - 12x^{3} + 2x^{2} + 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 155) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 249.1 | ||
Root | \(-0.520627 + 0.520627i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 775.249 |
Dual form | 775.2.b.e.249.8 |
$q$-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 \(\left(\mathbb{Z}/775\mathbb{Z}\right)^\times\).
\(n\) | \(251\) | \(652\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.80027i | − 1.98009i | −0.140746 | − | 0.990046i | \(-0.544950\pi\) | ||||
0.140746 | − | 0.990046i | \(-0.455050\pi\) | |||||||
\(3\) | 0.342376i | 0.197671i | 0.995104 | + | 0.0988355i | \(0.0315118\pi\) | ||||
−0.995104 | + | 0.0988355i | \(0.968488\pi\) | |||||||
\(4\) | −5.84153 | −2.92076 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.958747 | 0.391407 | ||||||||
\(7\) | 1.04125i | 0.393557i | 0.980448 | + | 0.196778i | \(0.0630479\pi\) | ||||
−0.980448 | + | 0.196778i | \(0.936952\pi\) | |||||||
\(8\) | 10.7573i | 3.80329i | ||||||||
\(9\) | 2.88278 | 0.960926 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.64180 | 1.39955 | 0.699777 | − | 0.714361i | \(-0.253283\pi\) | ||||
0.699777 | + | 0.714361i | \(0.253283\pi\) | |||||||
\(12\) | − 2.00000i | − 0.577350i | ||||||||
\(13\) | − 2.95875i | − 0.820609i | −0.911949 | − | 0.410304i | \(-0.865422\pi\) | ||||
0.911949 | − | 0.410304i | \(-0.134578\pi\) | |||||||
\(14\) | 2.91579 | 0.779278 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 18.4404 | 4.61009 | ||||||||
\(17\) | 6.29942i | 1.52783i | 0.645314 | + | 0.763917i | \(0.276726\pi\) | ||||
−0.645314 | + | 0.763917i | \(0.723274\pi\) | |||||||
\(18\) | − 8.07256i | − 1.90272i | ||||||||
\(19\) | 1.11552 | 0.255918 | 0.127959 | − | 0.991779i | \(-0.459157\pi\) | ||||
0.127959 | + | 0.991779i | \(0.459157\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.356500 | −0.0777948 | ||||||||
\(22\) | − 12.9983i | − 2.77125i | ||||||||
\(23\) | − 3.87454i | − 0.807897i | −0.914782 | − | 0.403949i | \(-0.867637\pi\) | ||||
0.914782 | − | 0.403949i | \(-0.132363\pi\) | |||||||
\(24\) | −3.68305 | −0.751800 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −8.28530 | −1.62488 | ||||||||
\(27\) | 2.01412i | 0.387618i | ||||||||
\(28\) | − 6.08251i | − 1.14949i | ||||||||
\(29\) | −2.35650 | −0.437591 | −0.218796 | − | 0.975771i | \(-0.570213\pi\) | ||||
−0.218796 | + | 0.975771i | \(0.570213\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | − 30.1234i | − 5.32512i | ||||||||
\(33\) | 1.58924i | 0.276651i | ||||||||
\(34\) | 17.6401 | 3.02525 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −16.8398 | −2.80664 | ||||||||
\(37\) | 1.30112i | 0.213903i | 0.994264 | + | 0.106952i | \(0.0341090\pi\) | ||||
−0.994264 | + | 0.106952i | \(0.965891\pi\) | |||||||
\(38\) | − 3.12376i | − 0.506741i | ||||||||
\(39\) | 1.01300 | 0.162211 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.92573 | 0.300749 | 0.150375 | − | 0.988629i | \(-0.451952\pi\) | ||||
0.150375 | + | 0.988629i | \(0.451952\pi\) | |||||||
\(42\) | 0.998298i | 0.154041i | ||||||||
\(43\) | 4.29942i | 0.655656i | 0.944737 | + | 0.327828i | \(0.106317\pi\) | ||||
−0.944737 | + | 0.327828i | \(0.893683\pi\) | |||||||
\(44\) | −27.1152 | −4.08777 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10.8498 | −1.59971 | ||||||||
\(47\) | − 3.31525i | − 0.483579i | −0.970329 | − | 0.241789i | \(-0.922266\pi\) | ||||
0.970329 | − | 0.241789i | \(-0.0777343\pi\) | |||||||
\(48\) | 6.31355i | 0.911282i | ||||||||
\(49\) | 5.91579 | 0.845113 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.15677 | −0.302009 | ||||||||
\(52\) | 17.2836i | 2.39680i | ||||||||
\(53\) | − 5.10964i | − 0.701862i | −0.936401 | − | 0.350931i | \(-0.885865\pi\) | ||||
0.936401 | − | 0.350931i | \(-0.114135\pi\) | |||||||
\(54\) | 5.64010 | 0.767520 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −11.2011 | −1.49681 | ||||||||
\(57\) | 0.381928i | 0.0505875i | ||||||||
\(58\) | 6.59884i | 0.866471i | ||||||||
\(59\) | 5.07256 | 0.660392 | 0.330196 | − | 0.943912i | \(-0.392885\pi\) | ||||
0.330196 | + | 0.943912i | \(0.392885\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.31525 | 0.680548 | 0.340274 | − | 0.940326i | \(-0.389480\pi\) | ||||
0.340274 | + | 0.940326i | \(0.389480\pi\) | |||||||
\(62\) | − 2.80027i | − 0.355635i | ||||||||
\(63\) | 3.00170i | 0.378179i | ||||||||
\(64\) | −47.4730 | −5.93413 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.45031 | 0.547795 | ||||||||
\(67\) | − 8.64180i | − 1.05576i | −0.849318 | − | 0.527882i | \(-0.822986\pi\) | ||||
0.849318 | − | 0.527882i | \(-0.177014\pi\) | |||||||
\(68\) | − 36.7982i | − 4.46244i | ||||||||
\(69\) | 1.32655 | 0.159698 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.88278 | −0.460801 | −0.230401 | − | 0.973096i | \(-0.574004\pi\) | ||||
−0.230401 | + | 0.973096i | \(0.574004\pi\) | |||||||
\(72\) | 31.0110i | 3.65468i | ||||||||
\(73\) | − 12.1740i | − 1.42485i | −0.701746 | − | 0.712427i | \(-0.747596\pi\) | ||||
0.701746 | − | 0.712427i | \(-0.252404\pi\) | |||||||
\(74\) | 3.64350 | 0.423548 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.51634 | −0.747475 | ||||||||
\(77\) | 4.83329i | 0.550804i | ||||||||
\(78\) | − 2.83669i | − 0.321192i | ||||||||
\(79\) | 7.12376 | 0.801486 | 0.400743 | − | 0.916191i | \(-0.368752\pi\) | ||||
0.400743 | + | 0.916191i | \(0.368752\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.95875 | 0.884305 | ||||||||
\(82\) | − 5.39258i | − 0.595511i | ||||||||
\(83\) | 7.46614i | 0.819515i | 0.912195 | + | 0.409757i | \(0.134387\pi\) | ||||
−0.912195 | + | 0.409757i | \(0.865613\pi\) | |||||||
\(84\) | 2.08251 | 0.227220 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 12.0396 | 1.29826 | ||||||||
\(87\) | − 0.806810i | − 0.0864991i | ||||||||
\(88\) | 49.9333i | 5.32291i | ||||||||
\(89\) | 12.1598 | 1.28894 | 0.644470 | − | 0.764630i | \(-0.277078\pi\) | ||||
0.644470 | + | 0.764630i | \(0.277078\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.08080 | 0.322956 | ||||||||
\(92\) | 22.6332i | 2.35968i | ||||||||
\(93\) | 0.342376i | 0.0355028i | ||||||||
\(94\) | −9.28360 | −0.957530 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 10.3135 | 1.05262 | ||||||||
\(97\) | − 0.915792i | − 0.0929846i | −0.998919 | − | 0.0464923i | \(-0.985196\pi\) | ||||
0.998919 | − | 0.0464923i | \(-0.0148043\pi\) | |||||||
\(98\) | − 16.5658i | − 1.67340i | ||||||||
\(99\) | 13.3813 | 1.34487 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.11382 | −0.409340 | −0.204670 | − | 0.978831i | \(-0.565612\pi\) | ||||
−0.204670 | + | 0.978831i | \(0.565612\pi\) | |||||||
\(102\) | 6.03955i | 0.598005i | ||||||||
\(103\) | 16.9983i | 1.67489i | 0.546520 | + | 0.837446i | \(0.315952\pi\) | ||||
−0.546520 | + | 0.837446i | \(0.684048\pi\) | |||||||
\(104\) | 31.8282 | 3.12101 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.3084 | −1.38975 | ||||||||
\(107\) | 4.84976i | 0.468844i | 0.972135 | + | 0.234422i | \(0.0753198\pi\) | ||||
−0.972135 | + | 0.234422i | \(0.924680\pi\) | |||||||
\(108\) | − 11.7656i | − 1.13214i | ||||||||
\(109\) | −9.19803 | −0.881011 | −0.440506 | − | 0.897750i | \(-0.645201\pi\) | ||||
−0.440506 | + | 0.897750i | \(0.645201\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.445474 | −0.0422825 | ||||||||
\(112\) | 19.2011i | 1.81433i | ||||||||
\(113\) | − 3.47508i | − 0.326908i | −0.986551 | − | 0.163454i | \(-0.947736\pi\) | ||||
0.986551 | − | 0.163454i | \(-0.0522636\pi\) | |||||||
\(114\) | 1.06950 | 0.100168 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 13.7656 | 1.27810 | ||||||||
\(117\) | − 8.52941i | − 0.788544i | ||||||||
\(118\) | − 14.2046i | − 1.30764i | ||||||||
\(119\) | −6.55929 | −0.601289 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.5463 | 0.958753 | ||||||||
\(122\) | − 14.8841i | − 1.34755i | ||||||||
\(123\) | 0.659325i | 0.0594494i | ||||||||
\(124\) | −5.84153 | −0.524584 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 8.40558 | 0.748829 | ||||||||
\(127\) | 12.8728i | 1.14228i | 0.820853 | + | 0.571140i | \(0.193499\pi\) | ||||
−0.820853 | + | 0.571140i | \(0.806501\pi\) | |||||||
\(128\) | 72.6906i | 6.42500i | ||||||||
\(129\) | −1.47202 | −0.129604 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.4668 | 1.35134 | 0.675672 | − | 0.737202i | \(-0.263853\pi\) | ||||
0.675672 | + | 0.737202i | \(0.263853\pi\) | |||||||
\(132\) | − 9.28360i | − 0.808033i | ||||||||
\(133\) | 1.16154i | 0.100718i | ||||||||
\(134\) | −24.1994 | −2.09051 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −67.7649 | −5.81079 | ||||||||
\(137\) | − 16.5734i | − 1.41596i | −0.706231 | − | 0.707981i | \(-0.749606\pi\) | ||||
0.706231 | − | 0.707981i | \(-0.250394\pi\) | |||||||
\(138\) | − 3.71470i | − 0.316216i | ||||||||
\(139\) | −21.5259 | −1.82581 | −0.912903 | − | 0.408176i | \(-0.866165\pi\) | ||||
−0.912903 | + | 0.408176i | \(0.866165\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.13506 | 0.0955895 | ||||||||
\(142\) | 10.8728i | 0.912428i | ||||||||
\(143\) | − 13.7339i | − 1.14849i | ||||||||
\(144\) | 53.1595 | 4.42996 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −34.0904 | −2.82134 | ||||||||
\(147\) | 2.02543i | 0.167054i | ||||||||
\(148\) | − 7.60054i | − 0.624761i | ||||||||
\(149\) | −20.7556 | −1.70037 | −0.850183 | − | 0.526487i | \(-0.823509\pi\) | ||||
−0.850183 | + | 0.526487i | \(0.823509\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.4451 | −1.50104 | −0.750522 | − | 0.660846i | \(-0.770198\pi\) | ||||
−0.750522 | + | 0.660846i | \(0.770198\pi\) | |||||||
\(152\) | 12.0000i | 0.973329i | ||||||||
\(153\) | 18.1598i | 1.46814i | ||||||||
\(154\) | 13.5345 | 1.09064 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.91749 | −0.473779 | ||||||||
\(157\) | 5.64350i | 0.450400i | 0.974313 | + | 0.225200i | \(0.0723036\pi\) | ||||
−0.974313 | + | 0.225200i | \(0.927696\pi\) | |||||||
\(158\) | − 19.9485i | − 1.58701i | ||||||||
\(159\) | 1.74942 | 0.138738 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.03438 | 0.317953 | ||||||||
\(162\) | − 22.2867i | − 1.75101i | ||||||||
\(163\) | 16.1994i | 1.26883i | 0.772991 | + | 0.634417i | \(0.218760\pi\) | ||||
−0.772991 | + | 0.634417i | \(0.781240\pi\) | |||||||
\(164\) | −11.2492 | −0.878417 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 20.9072 | 1.62271 | ||||||||
\(167\) | 5.14919i | 0.398456i | 0.979953 | + | 0.199228i | \(0.0638434\pi\) | ||||
−0.979953 | + | 0.199228i | \(0.936157\pi\) | |||||||
\(168\) | − 3.83499i | − 0.295876i | ||||||||
\(169\) | 4.24582 | 0.326601 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.21580 | 0.245918 | ||||||||
\(172\) | − 25.1152i | − 1.91501i | ||||||||
\(173\) | − 10.7621i | − 0.818226i | −0.912484 | − | 0.409113i | \(-0.865838\pi\) | ||||
0.912484 | − | 0.409113i | \(-0.134162\pi\) | |||||||
\(174\) | −2.25929 | −0.171276 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 85.5965 | 6.45208 | ||||||||
\(177\) | 1.73673i | 0.130540i | ||||||||
\(178\) | − 34.0509i | − 2.55222i | ||||||||
\(179\) | 10.2740 | 0.767914 | 0.383957 | − | 0.923351i | \(-0.374561\pi\) | ||||
0.383957 | + | 0.923351i | \(0.374561\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.53622 | 0.188516 | 0.0942578 | − | 0.995548i | \(-0.469952\pi\) | ||||
0.0942578 | + | 0.995548i | \(0.469952\pi\) | |||||||
\(182\) | − 8.62709i | − 0.639483i | ||||||||
\(183\) | 1.81981i | 0.134525i | ||||||||
\(184\) | 41.6796 | 3.07266 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.958747 | 0.0702987 | ||||||||
\(187\) | 29.2406i | 2.13829i | ||||||||
\(188\) | 19.3661i | 1.41242i | ||||||||
\(189\) | −2.09721 | −0.152550 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.45031 | −0.322013 | −0.161007 | − | 0.986953i | \(-0.551474\pi\) | ||||
−0.161007 | + | 0.986953i | \(0.551474\pi\) | |||||||
\(192\) | − 16.2536i | − 1.17301i | ||||||||
\(193\) | 2.71300i | 0.195286i | 0.995222 | + | 0.0976430i | \(0.0311303\pi\) | ||||
−0.995222 | + | 0.0976430i | \(0.968870\pi\) | |||||||
\(194\) | −2.56447 | −0.184118 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −34.5573 | −2.46838 | ||||||||
\(197\) | − 5.04125i | − 0.359174i | −0.983742 | − | 0.179587i | \(-0.942524\pi\) | ||||
0.983742 | − | 0.179587i | \(-0.0574762\pi\) | |||||||
\(198\) | − 37.4712i | − 2.66296i | ||||||||
\(199\) | 14.3531 | 1.01746 | 0.508732 | − | 0.860925i | \(-0.330114\pi\) | ||||
0.508732 | + | 0.860925i | \(0.330114\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.95875 | 0.208694 | ||||||||
\(202\) | 11.5198i | 0.810531i | ||||||||
\(203\) | − 2.45371i | − 0.172217i | ||||||||
\(204\) | 12.5988 | 0.882095 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 47.5999 | 3.31644 | ||||||||
\(207\) | − 11.1694i | − 0.776330i | ||||||||
\(208\) | − 54.5604i | − 3.78308i | ||||||||
\(209\) | 5.17802 | 0.358171 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.6288 | −0.800559 | −0.400280 | − | 0.916393i | \(-0.631087\pi\) | ||||
−0.400280 | + | 0.916393i | \(0.631087\pi\) | |||||||
\(212\) | 29.8481i | 2.04997i | ||||||||
\(213\) | − 1.32937i | − 0.0910870i | ||||||||
\(214\) | 13.5807 | 0.928355 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −21.6666 | −1.47422 | ||||||||
\(217\) | 1.04125i | 0.0706849i | ||||||||
\(218\) | 25.7570i | 1.74448i | ||||||||
\(219\) | 4.16808 | 0.281652 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.6384 | 1.25375 | ||||||||
\(222\) | 1.24745i | 0.0837232i | ||||||||
\(223\) | − 5.45483i | − 0.365283i | −0.983180 | − | 0.182641i | \(-0.941535\pi\) | ||||
0.983180 | − | 0.182641i | \(-0.0584647\pi\) | |||||||
\(224\) | 31.3661 | 2.09574 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.73118 | −0.647309 | ||||||||
\(227\) | − 7.97352i | − 0.529221i | −0.964355 | − | 0.264611i | \(-0.914757\pi\) | ||||
0.964355 | − | 0.264611i | \(-0.0852434\pi\) | |||||||
\(228\) | − 2.23104i | − 0.147754i | ||||||||
\(229\) | −22.0197 | −1.45510 | −0.727550 | − | 0.686054i | \(-0.759341\pi\) | ||||
−0.727550 | + | 0.686054i | \(0.759341\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.65480 | −0.108878 | ||||||||
\(232\) | − 25.3496i | − 1.66428i | ||||||||
\(233\) | 17.2723i | 1.13155i | 0.824561 | + | 0.565773i | \(0.191422\pi\) | ||||
−0.824561 | + | 0.565773i | \(0.808578\pi\) | |||||||
\(234\) | −23.8847 | −1.56139 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −29.6315 | −1.92885 | ||||||||
\(237\) | 2.43901i | 0.158430i | ||||||||
\(238\) | 18.3678i | 1.19061i | ||||||||
\(239\) | 21.3462 | 1.38077 | 0.690386 | − | 0.723441i | \(-0.257441\pi\) | ||||
0.690386 | + | 0.723441i | \(0.257441\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.15984 | −0.267959 | −0.133979 | − | 0.990984i | \(-0.542776\pi\) | ||||
−0.133979 | + | 0.990984i | \(0.542776\pi\) | |||||||
\(242\) | − 29.5325i | − 1.89842i | ||||||||
\(243\) | 8.76726i | 0.562420i | ||||||||
\(244\) | −31.0492 | −1.98772 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.84629 | 0.117715 | ||||||||
\(247\) | − 3.30054i | − 0.210008i | ||||||||
\(248\) | 10.7573i | 0.683090i | ||||||||
\(249\) | −2.55623 | −0.161994 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.76896 | 0.364134 | 0.182067 | − | 0.983286i | \(-0.441721\pi\) | ||||
0.182067 | + | 0.983286i | \(0.441721\pi\) | |||||||
\(252\) | − 17.5345i | − 1.10457i | ||||||||
\(253\) | − 17.9848i | − 1.13070i | ||||||||
\(254\) | 36.0475 | 2.26182 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 108.607 | 6.78796 | ||||||||
\(257\) | − 22.4417i | − 1.39988i | −0.714203 | − | 0.699938i | \(-0.753211\pi\) | ||||
0.714203 | − | 0.699938i | \(-0.246789\pi\) | |||||||
\(258\) | 4.12206i | 0.256628i | ||||||||
\(259\) | −1.35480 | −0.0841831 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.79327 | −0.420493 | ||||||||
\(262\) | − 43.3114i | − 2.67579i | ||||||||
\(263\) | − 10.1904i | − 0.628369i | −0.949362 | − | 0.314185i | \(-0.898269\pi\) | ||||
0.949362 | − | 0.314185i | \(-0.101731\pi\) | |||||||
\(264\) | −17.0960 | −1.05218 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.25262 | 0.199431 | ||||||||
\(267\) | 4.16324i | 0.254786i | ||||||||
\(268\) | 50.4813i | 3.08364i | ||||||||
\(269\) | −28.0904 | −1.71270 | −0.856351 | − | 0.516394i | \(-0.827274\pi\) | ||||
−0.856351 | + | 0.516394i | \(0.827274\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.0429548 | 0.00260932 | 0.00130466 | − | 0.999999i | \(-0.499585\pi\) | ||||
0.00130466 | + | 0.999999i | \(0.499585\pi\) | |||||||
\(272\) | 116.164i | 7.04346i | ||||||||
\(273\) | 1.05479i | 0.0638391i | ||||||||
\(274\) | −46.4101 | −2.80374 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −7.74908 | −0.466440 | ||||||||
\(277\) | − 21.8288i | − 1.31156i | −0.754951 | − | 0.655782i | \(-0.772339\pi\) | ||||
0.754951 | − | 0.655782i | \(-0.227661\pi\) | |||||||
\(278\) | 60.2785i | 3.61526i | ||||||||
\(279\) | 2.88278 | 0.172587 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.20415 | −0.549074 | −0.274537 | − | 0.961577i | \(-0.588525\pi\) | ||||
−0.274537 | + | 0.961577i | \(0.588525\pi\) | |||||||
\(282\) | − 3.17848i | − 0.189276i | ||||||||
\(283\) | 6.85317i | 0.407379i | 0.979036 | + | 0.203689i | \(0.0652932\pi\) | ||||
−0.979036 | + | 0.203689i | \(0.934707\pi\) | |||||||
\(284\) | 22.6813 | 1.34589 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −38.4587 | −2.27411 | ||||||||
\(287\) | 2.00518i | 0.118362i | ||||||||
\(288\) | − 86.8391i | − 5.11705i | ||||||||
\(289\) | −22.6827 | −1.33428 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.313546 | 0.0183804 | ||||||||
\(292\) | 71.1145i | 4.16166i | ||||||||
\(293\) | 16.6101i | 0.970375i | 0.874410 | + | 0.485188i | \(0.161249\pi\) | ||||
−0.874410 | + | 0.485188i | \(0.838751\pi\) | |||||||
\(294\) | 5.67175 | 0.330783 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −13.9966 | −0.813536 | ||||||||
\(297\) | 9.34916i | 0.542493i | ||||||||
\(298\) | 58.1214i | 3.36688i | ||||||||
\(299\) | −11.4638 | −0.662968 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.47679 | −0.258038 | ||||||||
\(302\) | 51.6514i | 2.97220i | ||||||||
\(303\) | − 1.40847i | − 0.0809147i | ||||||||
\(304\) | 20.5706 | 1.17980 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 50.8525 | 2.90704 | ||||||||
\(307\) | 16.9553i | 0.967693i | 0.875153 | + | 0.483846i | \(0.160761\pi\) | ||||
−0.875153 | + | 0.483846i | \(0.839239\pi\) | |||||||
\(308\) | − 28.2338i | − 1.60877i | ||||||||
\(309\) | −5.81981 | −0.331078 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.638734 | −0.0362193 | −0.0181096 | − | 0.999836i | \(-0.505765\pi\) | ||||
−0.0181096 | + | 0.999836i | \(0.505765\pi\) | |||||||
\(312\) | 10.8972i | 0.616933i | ||||||||
\(313\) | 18.1141i | 1.02387i | 0.859025 | + | 0.511934i | \(0.171071\pi\) | ||||
−0.859025 | + | 0.511934i | \(0.828929\pi\) | |||||||
\(314\) | 15.8033 | 0.891834 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −41.6136 | −2.34095 | ||||||||
\(317\) | − 5.06433i | − 0.284441i | −0.989835 | − | 0.142220i | \(-0.954576\pi\) | ||||
0.989835 | − | 0.142220i | \(-0.0454242\pi\) | |||||||
\(318\) | − 4.89885i | − 0.274714i | ||||||||
\(319\) | −10.9384 | −0.612433 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.66044 | −0.0926770 | ||||||||
\(322\) | − 11.2974i | − 0.629577i | ||||||||
\(323\) | 7.02713i | 0.391000i | ||||||||
\(324\) | −46.4912 | −2.58285 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 45.3627 | 2.51241 | ||||||||
\(327\) | − 3.14919i | − 0.174150i | ||||||||
\(328\) | 20.7157i | 1.14383i | ||||||||
\(329\) | 3.45201 | 0.190316 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.0344 | −1.10119 | −0.550594 | − | 0.834773i | \(-0.685599\pi\) | ||||
−0.550594 | + | 0.834773i | \(0.685599\pi\) | |||||||
\(332\) | − 43.6136i | − 2.39361i | ||||||||
\(333\) | 3.75085i | 0.205545i | ||||||||
\(334\) | 14.4191 | 0.788979 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −6.57400 | −0.358641 | ||||||||
\(337\) | − 4.86729i | − 0.265138i | −0.991174 | − | 0.132569i | \(-0.957677\pi\) | ||||
0.991174 | − | 0.132569i | \(-0.0423227\pi\) | |||||||
\(338\) | − 11.8894i | − 0.646700i | ||||||||
\(339\) | 1.18979 | 0.0646203 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.64180 | 0.251367 | ||||||||
\(342\) | − 9.00511i | − 0.486940i | ||||||||
\(343\) | 13.4486i | 0.726157i | ||||||||
\(344\) | −46.2502 | −2.49365 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −30.1368 | −1.62016 | ||||||||
\(347\) | − 10.1221i | − 0.543381i | −0.962385 | − | 0.271690i | \(-0.912417\pi\) | ||||
0.962385 | − | 0.271690i | \(-0.0875826\pi\) | |||||||
\(348\) | 4.71300i | 0.252643i | ||||||||
\(349\) | 18.3245 | 0.980888 | 0.490444 | − | 0.871473i | \(-0.336835\pi\) | ||||
0.490444 | + | 0.871473i | \(0.336835\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.95928 | 0.318083 | ||||||||
\(352\) | − 139.827i | − 7.45279i | ||||||||
\(353\) | 14.3248i | 0.762435i | 0.924485 | + | 0.381217i | \(0.124495\pi\) | ||||
−0.924485 | + | 0.381217i | \(0.875505\pi\) | |||||||
\(354\) | 4.86331 | 0.258482 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −71.0320 | −3.76469 | ||||||||
\(357\) | − 2.24575i | − 0.118857i | ||||||||
\(358\) | − 28.7700i | − 1.52054i | ||||||||
\(359\) | −12.3197 | −0.650207 | −0.325104 | − | 0.945678i | \(-0.605399\pi\) | ||||
−0.325104 | + | 0.945678i | \(0.605399\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7556 | −0.934506 | ||||||||
\(362\) | − 7.10210i | − 0.373278i | ||||||||
\(363\) | 3.61080i | 0.189518i | ||||||||
\(364\) | −17.9966 | −0.943278 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5.09598 | 0.266371 | ||||||||
\(367\) | 24.4706i | 1.27735i | 0.769475 | + | 0.638676i | \(0.220518\pi\) | ||||
−0.769475 | + | 0.638676i | \(0.779482\pi\) | |||||||
\(368\) | − 71.4479i | − 3.72448i | ||||||||
\(369\) | 5.55146 | 0.288998 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.32042 | 0.276223 | ||||||||
\(372\) | − 2.00000i | − 0.103695i | ||||||||
\(373\) | − 26.5276i | − 1.37355i | −0.726870 | − | 0.686775i | \(-0.759026\pi\) | ||||
0.726870 | − | 0.686775i | \(-0.240974\pi\) | |||||||
\(374\) | 81.8818 | 4.23400 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 35.6632 | 1.83919 | ||||||||
\(377\) | 6.97229i | 0.359091i | ||||||||
\(378\) | 5.87277i | 0.302063i | ||||||||
\(379\) | −12.5528 | −0.644795 | −0.322398 | − | 0.946604i | \(-0.604489\pi\) | ||||
−0.322398 | + | 0.946604i | \(0.604489\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.40735 | −0.225796 | ||||||||
\(382\) | 12.4621i | 0.637615i | ||||||||
\(383\) | − 11.5882i | − 0.592129i | −0.955168 | − | 0.296064i | \(-0.904326\pi\) | ||||
0.955168 | − | 0.296064i | \(-0.0956743\pi\) | |||||||
\(384\) | −24.8875 | −1.27004 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.59714 | 0.386684 | ||||||||
\(387\) | 12.3943i | 0.630037i | ||||||||
\(388\) | 5.34962i | 0.271586i | ||||||||
\(389\) | −32.5790 | −1.65182 | −0.825909 | − | 0.563803i | \(-0.809338\pi\) | ||||
−0.825909 | + | 0.563803i | \(0.809338\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.4074 | 1.23433 | ||||||||
\(392\) | 63.6381i | 3.21421i | ||||||||
\(393\) | 5.29548i | 0.267122i | ||||||||
\(394\) | −14.1169 | −0.711198 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −78.1671 | −3.92804 | ||||||||
\(397\) | 29.8508i | 1.49817i | 0.662475 | + | 0.749084i | \(0.269506\pi\) | ||||
−0.662475 | + | 0.749084i | \(0.730494\pi\) | |||||||
\(398\) | − 40.1926i | − 2.01467i | ||||||||
\(399\) | −0.397683 | −0.0199091 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.9176 | −1.24432 | −0.622162 | − | 0.782889i | \(-0.713745\pi\) | ||||
−0.622162 | + | 0.782889i | \(0.713745\pi\) | |||||||
\(402\) | − 8.28530i | − 0.413233i | ||||||||
\(403\) | − 2.95875i | − 0.147386i | ||||||||
\(404\) | 24.0310 | 1.19559 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.87107 | −0.341005 | ||||||||
\(407\) | 6.03955i | 0.299369i | ||||||||
\(408\) | − 23.2011i | − 1.14863i | ||||||||
\(409\) | −13.8085 | −0.682787 | −0.341393 | − | 0.939920i | \(-0.610899\pi\) | ||||
−0.341393 | + | 0.939920i | \(0.610899\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.67435 | 0.279895 | ||||||||
\(412\) | − 99.2960i | − 4.89196i | ||||||||
\(413\) | 5.28182i | 0.259902i | ||||||||
\(414\) | −31.2775 | −1.53720 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −89.1276 | −4.36984 | ||||||||
\(417\) | − 7.36997i | − 0.360909i | ||||||||
\(418\) | − 14.4999i | − 0.709211i | ||||||||
\(419\) | 21.7799 | 1.06402 | 0.532009 | − | 0.846738i | \(-0.321437\pi\) | ||||
0.532009 | + | 0.846738i | \(0.321437\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.23758 | 0.157790 | 0.0788949 | − | 0.996883i | \(-0.474861\pi\) | ||||
0.0788949 | + | 0.996883i | \(0.474861\pi\) | |||||||
\(422\) | 32.5638i | 1.58518i | ||||||||
\(423\) | − 9.55712i | − 0.464683i | ||||||||
\(424\) | 54.9660 | 2.66938 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.72260 | −0.180361 | ||||||||
\(427\) | 5.53452i | 0.267834i | ||||||||
\(428\) | − 28.3300i | − 1.36938i | ||||||||
\(429\) | 4.70216 | 0.227023 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.6466 | −0.609167 | −0.304583 | − | 0.952486i | \(-0.598517\pi\) | ||||
−0.304583 | + | 0.952486i | \(0.598517\pi\) | |||||||
\(432\) | 37.1412i | 1.78696i | ||||||||
\(433\) | − 31.9914i | − 1.53741i | −0.639604 | − | 0.768705i | \(-0.720902\pi\) | ||||
0.639604 | − | 0.768705i | \(-0.279098\pi\) | |||||||
\(434\) | 2.91579 | 0.139963 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 53.7305 | 2.57322 | ||||||||
\(437\) | − 4.32212i | − 0.206755i | ||||||||
\(438\) | − 11.6717i | − 0.557698i | ||||||||
\(439\) | 13.8432 | 0.660701 | 0.330351 | − | 0.943858i | \(-0.392833\pi\) | ||||
0.330351 | + | 0.943858i | \(0.392833\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.0539 | 0.812091 | ||||||||
\(442\) | − 52.1926i | − 2.48255i | ||||||||
\(443\) | 20.3479i | 0.966759i | 0.875411 | + | 0.483379i | \(0.160591\pi\) | ||||
−0.875411 | + | 0.483379i | \(0.839409\pi\) | |||||||
\(444\) | 2.60225 | 0.123497 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −15.2750 | −0.723293 | ||||||||
\(447\) | − 7.10623i | − 0.336113i | ||||||||
\(448\) | − 49.4314i | − 2.33542i | ||||||||
\(449\) | −8.71640 | −0.411353 | −0.205676 | − | 0.978620i | \(-0.565939\pi\) | ||||
−0.205676 | + | 0.978620i | \(0.565939\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.93886 | 0.420915 | ||||||||
\(452\) | 20.2998i | 0.954822i | ||||||||
\(453\) | − 6.31518i | − 0.296713i | ||||||||
\(454\) | −22.3280 | −1.04791 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.10852 | −0.192399 | ||||||||
\(457\) | − 0.0311855i | − 0.00145879i | −1.00000 | 0.000729397i | \(-0.999768\pi\) | |||||
1.00000 | 0.000729397i | \(-0.000232174\pi\) | ||||||||
\(458\) | 61.6611i | 2.88123i | ||||||||
\(459\) | −12.6878 | −0.592217 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.4882 | −1.37340 | −0.686700 | − | 0.726941i | \(-0.740941\pi\) | ||||
−0.686700 | + | 0.726941i | \(0.740941\pi\) | |||||||
\(462\) | 4.63390i | 0.215588i | ||||||||
\(463\) | 19.1547i | 0.890196i | 0.895482 | + | 0.445098i | \(0.146831\pi\) | ||||
−0.895482 | + | 0.445098i | \(0.853169\pi\) | |||||||
\(464\) | −43.4547 | −2.01734 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 48.3671 | 2.24056 | ||||||||
\(467\) | − 23.9367i | − 1.10766i | −0.832630 | − | 0.553829i | \(-0.813166\pi\) | ||||
0.832630 | − | 0.553829i | \(-0.186834\pi\) | |||||||
\(468\) | 49.8248i | 2.30315i | ||||||||
\(469\) | 8.99830 | 0.415503 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.93220 | −0.0890311 | ||||||||
\(472\) | 54.5672i | 2.51166i | ||||||||
\(473\) | 19.9570i | 0.917626i | ||||||||
\(474\) | 6.82988 | 0.313707 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 38.3163 | 1.75622 | ||||||||
\(477\) | − 14.7299i | − 0.674438i | ||||||||
\(478\) | − 59.7752i | − 2.73406i | ||||||||
\(479\) | −21.4039 | −0.977968 | −0.488984 | − | 0.872293i | \(-0.662632\pi\) | ||||
−0.488984 | + | 0.872293i | \(0.662632\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.84969 | 0.175531 | ||||||||
\(482\) | 11.6487i | 0.530583i | ||||||||
\(483\) | 1.38127i | 0.0628502i | ||||||||
\(484\) | −61.6064 | −2.80029 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 24.5507 | 1.11364 | ||||||||
\(487\) | 26.0763i | 1.18163i | 0.806807 | + | 0.590815i | \(0.201194\pi\) | ||||
−0.806807 | + | 0.590815i | \(0.798806\pi\) | |||||||
\(488\) | 57.1778i | 2.58832i | ||||||||
\(489\) | −5.54629 | −0.250812 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.9367 | −0.538696 | −0.269348 | − | 0.963043i | \(-0.586808\pi\) | ||||
−0.269348 | + | 0.963043i | \(0.586808\pi\) | |||||||
\(492\) | − 3.85147i | − 0.173638i | ||||||||
\(493\) | − 14.8446i | − 0.668567i | ||||||||
\(494\) | −9.24241 | −0.415836 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 18.4404 | 0.827997 | ||||||||
\(497\) | − 4.04295i | − 0.181351i | ||||||||
\(498\) | 7.15813i | 0.320764i | ||||||||
\(499\) | −16.5394 | −0.740406 | −0.370203 | − | 0.928951i | \(-0.620712\pi\) | ||||
−0.370203 | + | 0.928951i | \(0.620712\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.76296 | −0.0787632 | ||||||||
\(502\) | − 16.1547i | − 0.721018i | ||||||||
\(503\) | − 16.6418i | − 0.742021i | −0.928629 | − | 0.371011i | \(-0.879011\pi\) | ||||
0.928629 | − | 0.371011i | \(-0.120989\pi\) | |||||||
\(504\) | −32.2903 | −1.43832 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −50.3624 | −2.23888 | ||||||||
\(507\) | 1.45367i | 0.0645596i | ||||||||
\(508\) | − 75.1970i | − 3.33633i | ||||||||
\(509\) | 43.0388 | 1.90766 | 0.953831 | − | 0.300345i | \(-0.0971018\pi\) | ||||
0.953831 | + | 0.300345i | \(0.0971018\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.6762 | 0.560761 | ||||||||
\(512\) | − 158.749i | − 7.01579i | ||||||||
\(513\) | 2.24680i | 0.0991984i | ||||||||
\(514\) | −62.8430 | −2.77188 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 8.59884 | 0.378543 | ||||||||
\(517\) | − 15.3887i | − 0.676795i | ||||||||
\(518\) | 3.79381i | 0.166690i | ||||||||
\(519\) | 3.68468 | 0.161740 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.2138 | 1.63037 | 0.815184 | − | 0.579203i | \(-0.196636\pi\) | ||||
0.815184 | + | 0.579203i | \(0.196636\pi\) | |||||||
\(522\) | 19.0230i | 0.832614i | ||||||||
\(523\) | 23.4085i | 1.02358i | 0.859110 | + | 0.511791i | \(0.171018\pi\) | ||||
−0.859110 | + | 0.511791i | \(0.828982\pi\) | |||||||
\(524\) | −90.3500 | −3.94696 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −28.5360 | −1.24423 | ||||||||
\(527\) | 6.29942i | 0.274407i | ||||||||
\(528\) | 29.3062i | 1.27539i | ||||||||
\(529\) | 7.98795 | 0.347302 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.6231 | 0.634588 | ||||||||
\(532\) | − 6.78516i | − 0.294174i | ||||||||
\(533\) | − 5.69776i | − 0.246797i | ||||||||
\(534\) | 11.6582 | 0.504500 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 92.9626 | 4.01537 | ||||||||
\(537\) | 3.51757i | 0.151794i | ||||||||
\(538\) | 78.6608i | 3.39131i | ||||||||
\(539\) | 27.4599 | 1.18278 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.38298 | 0.102452 | 0.0512261 | − | 0.998687i | \(-0.483687\pi\) | ||||
0.0512261 | + | 0.998687i | \(0.483687\pi\) | |||||||
\(542\) | − 0.120285i | − 0.00516669i | ||||||||
\(543\) | 0.868341i | 0.0372641i | ||||||||
\(544\) | 189.760 | 8.13590 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.95371 | 0.126407 | ||||||||
\(547\) | − 21.4400i | − 0.916709i | −0.888769 | − | 0.458355i | \(-0.848439\pi\) | ||||
0.888769 | − | 0.458355i | \(-0.151561\pi\) | |||||||
\(548\) | 96.8140i | 4.13569i | ||||||||
\(549\) | 15.3227 | 0.653956 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.62872 | −0.111987 | ||||||||
\(552\) | 14.2701i | 0.607377i | ||||||||
\(553\) | 7.41764i | 0.315430i | ||||||||
\(554\) | −61.1265 | −2.59702 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 125.744 | 5.33275 | ||||||||
\(557\) | − 12.5276i | − 0.530813i | −0.964137 | − | 0.265407i | \(-0.914494\pi\) | ||||
0.964137 | − | 0.265407i | \(-0.0855062\pi\) | |||||||
\(558\) | − 8.07256i | − 0.341739i | ||||||||
\(559\) | 12.7209 | 0.538037 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.0113 | −0.422678 | ||||||||
\(562\) | 25.7741i | 1.08722i | ||||||||
\(563\) | − 10.7361i | − 0.452472i | −0.974073 | − | 0.226236i | \(-0.927358\pi\) | ||||
0.974073 | − | 0.226236i | \(-0.0726420\pi\) | |||||||
\(564\) | −6.63049 | −0.279194 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 19.1907 | 0.806647 | ||||||||
\(567\) | 8.28707i | 0.348024i | ||||||||
\(568\) | − 41.7683i | − 1.75256i | ||||||||
\(569\) | −1.00783 | −0.0422504 | −0.0211252 | − | 0.999777i | \(-0.506725\pi\) | ||||
−0.0211252 | + | 0.999777i | \(0.506725\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.88631 | −0.413729 | −0.206865 | − | 0.978370i | \(-0.566326\pi\) | ||||
−0.206865 | + | 0.978370i | \(0.566326\pi\) | |||||||
\(572\) | 80.2270i | 3.35446i | ||||||||
\(573\) | − 1.52368i | − 0.0636527i | ||||||||
\(574\) | 5.61504 | 0.234367 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −136.854 | −5.70226 | ||||||||
\(577\) | 22.1564i | 0.922384i | 0.887300 | + | 0.461192i | \(0.152578\pi\) | ||||
−0.887300 | + | 0.461192i | \(0.847422\pi\) | |||||||
\(578\) | 63.5178i | 2.64199i | ||||||||
\(579\) | −0.928867 | −0.0386024 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.77414 | −0.322526 | ||||||||
\(582\) | − 0.878013i | − 0.0363948i | ||||||||
\(583\) | − 23.7179i | − 0.982295i | ||||||||
\(584\) | 130.959 | 5.41913 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 46.5129 | 1.92143 | ||||||||
\(587\) | 16.7526i | 0.691452i | 0.938336 | + | 0.345726i | \(0.112367\pi\) | ||||
−0.938336 | + | 0.345726i | \(0.887633\pi\) | |||||||
\(588\) | − 11.8316i | − 0.487926i | ||||||||
\(589\) | 1.11552 | 0.0459642 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.72601 | 0.0709984 | ||||||||
\(592\) | 23.9932i | 0.986114i | ||||||||
\(593\) | 21.0526i | 0.864525i | 0.901748 | + | 0.432262i | \(0.142285\pi\) | ||||
−0.901748 | + | 0.432262i | \(0.857715\pi\) | |||||||
\(594\) | 26.1802 | 1.07419 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 121.244 | 4.96637 | ||||||||
\(597\) | 4.91416i | 0.201123i | ||||||||
\(598\) | 32.1017i | 1.31274i | ||||||||
\(599\) | 24.1994 | 0.988760 | 0.494380 | − | 0.869246i | \(-0.335395\pi\) | ||||
0.494380 | + | 0.869246i | \(0.335395\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.0275 | −1.51038 | −0.755192 | − | 0.655504i | \(-0.772456\pi\) | ||||
−0.755192 | + | 0.655504i | \(0.772456\pi\) | |||||||
\(602\) | 12.5362i | 0.510938i | ||||||||
\(603\) | − 24.9124i | − 1.01451i | ||||||||
\(604\) | 107.748 | 4.38419 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.94411 | −0.160219 | ||||||||
\(607\) | − 10.9011i | − 0.442461i | −0.975222 | − | 0.221231i | \(-0.928993\pi\) | ||||
0.975222 | − | 0.221231i | \(-0.0710074\pi\) | |||||||
\(608\) | − 33.6033i | − 1.36279i | ||||||||
\(609\) | 0.840093 | 0.0340423 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.80898 | −0.396829 | ||||||||
\(612\) | − 106.081i | − 4.28808i | ||||||||
\(613\) | − 17.8882i | − 0.722497i | −0.932469 | − | 0.361249i | \(-0.882351\pi\) | ||||
0.932469 | − | 0.361249i | \(-0.117649\pi\) | |||||||
\(614\) | 47.4796 | 1.91612 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −51.9932 | −2.09487 | ||||||||
\(617\) | − 39.3548i | − 1.58436i | −0.610285 | − | 0.792182i | \(-0.708945\pi\) | ||||
0.610285 | − | 0.792182i | \(-0.291055\pi\) | |||||||
\(618\) | 16.2971i | 0.655564i | ||||||||
\(619\) | −19.5429 | −0.785495 | −0.392747 | − | 0.919646i | \(-0.628475\pi\) | ||||
−0.392747 | + | 0.919646i | \(0.628475\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.80380 | 0.313156 | ||||||||
\(622\) | 1.78863i | 0.0717175i | ||||||||
\(623\) | 12.6615i | 0.507271i | ||||||||
\(624\) | 18.6802 | 0.747806 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 50.7243 | 2.02735 | ||||||||
\(627\) | 1.77283i | 0.0708000i | ||||||||
\(628\) | − 32.9666i | − 1.31551i | ||||||||
\(629\) | −8.19632 | −0.326809 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.4486 | −1.33157 | −0.665784 | − | 0.746145i | \(-0.731903\pi\) | ||||
−0.665784 | + | 0.746145i | \(0.731903\pi\) | |||||||
\(632\) | 76.6325i | 3.04828i | ||||||||
\(633\) | − 3.98142i | − 0.158247i | ||||||||
\(634\) | −14.1815 | −0.563219 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −10.2193 | −0.405220 | ||||||||
\(637\) | − 17.5033i | − 0.693507i | ||||||||
\(638\) | 30.6305i | 1.21267i | ||||||||
\(639\) | −11.1932 | −0.442796 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.13506 | 0.281818 | 0.140909 | − | 0.990023i | \(-0.454998\pi\) | ||||
0.140909 | + | 0.990023i | \(0.454998\pi\) | |||||||
\(642\) | 4.64970i | 0.183509i | ||||||||
\(643\) | − 21.1141i | − 0.832660i | −0.909214 | − | 0.416330i | \(-0.863316\pi\) | ||||
0.909214 | − | 0.416330i | \(-0.136684\pi\) | |||||||
\(644\) | −23.5669 | −0.928666 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 19.6779 | 0.774216 | ||||||||
\(647\) | − 1.08185i | − 0.0425320i | −0.999774 | − | 0.0212660i | \(-0.993230\pi\) | ||||
0.999774 | − | 0.0212660i | \(-0.00676969\pi\) | |||||||
\(648\) | 85.6148i | 3.36327i | ||||||||
\(649\) | 23.5458 | 0.924254 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.356500 | −0.0139724 | ||||||||
\(652\) | − 94.6291i | − 3.70596i | ||||||||
\(653\) | − 47.5112i | − 1.85926i | −0.368497 | − | 0.929629i | \(-0.620127\pi\) | ||||
0.368497 | − | 0.929629i | \(-0.379873\pi\) | |||||||
\(654\) | −8.81858 | −0.344834 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 35.5112 | 1.38648 | ||||||||
\(657\) | − 35.0948i | − 1.36918i | ||||||||
\(658\) | − 9.66657i | − 0.376842i | ||||||||
\(659\) | 24.3048 | 0.946782 | 0.473391 | − | 0.880852i | \(-0.343030\pi\) | ||||
0.473391 | + | 0.880852i | \(0.343030\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.23308 | 0.0479613 | 0.0239806 | − | 0.999712i | \(-0.492366\pi\) | ||||
0.0239806 | + | 0.999712i | \(0.492366\pi\) | |||||||
\(662\) | 56.1017i | 2.18045i | ||||||||
\(663\) | 6.38134i | 0.247831i | ||||||||
\(664\) | −80.3156 | −3.11685 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.5034 | 0.406999 | ||||||||
\(667\) | 9.13035i | 0.353529i | ||||||||
\(668\) | − 30.0791i | − 1.16380i | ||||||||
\(669\) | 1.86761 | 0.0722058 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.6723 | 0.952464 | ||||||||
\(672\) | 10.7390i | 0.414266i | ||||||||
\(673\) | 11.0242i | 0.424951i | 0.977166 | + | 0.212476i | \(0.0681526\pi\) | ||||
−0.977166 | + | 0.212476i | \(0.931847\pi\) | |||||||
\(674\) | −13.6297 | −0.524998 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −24.8020 | −0.953925 | ||||||||
\(677\) | − 39.3994i | − 1.51424i | −0.653274 | − | 0.757122i | \(-0.726605\pi\) | ||||
0.653274 | − | 0.757122i | \(-0.273395\pi\) | |||||||
\(678\) | − 3.33173i | − 0.127954i | ||||||||
\(679\) | 0.953571 | 0.0365947 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.72995 | 0.104612 | ||||||||
\(682\) | − 12.9983i | − 0.497731i | ||||||||
\(683\) | − 42.8213i | − 1.63851i | −0.573428 | − | 0.819256i | \(-0.694387\pi\) | ||||
0.573428 | − | 0.819256i | \(-0.305613\pi\) | |||||||
\(684\) | −18.7852 | −0.718268 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 37.6598 | 1.43786 | ||||||||
\(687\) | − 7.53901i | − 0.287631i | ||||||||
\(688\) | 79.2829i | 3.02263i | ||||||||
\(689\) | −15.1181 | −0.575954 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.1911 | −1.30069 | −0.650346 | − | 0.759638i | \(-0.725376\pi\) | ||||
−0.650346 | + | 0.759638i | \(0.725376\pi\) | |||||||
\(692\) | 62.8670i | 2.38984i | ||||||||
\(693\) | 13.9333i | 0.529282i | ||||||||
\(694\) | −28.3445 | −1.07594 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.67911 | 0.328981 | ||||||||
\(697\) | 12.1310i | 0.459495i | ||||||||
\(698\) | − 51.3136i | − 1.94225i | ||||||||
\(699\) | −5.91362 | −0.223674 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.6598 | −1.19577 | −0.597886 | − | 0.801581i | \(-0.703993\pi\) | ||||
−0.597886 | + | 0.801581i | \(0.703993\pi\) | |||||||
\(702\) | − 16.6876i | − 0.629834i | ||||||||
\(703\) | 1.45143i | 0.0547417i | ||||||||
\(704\) | −220.360 | −8.30514 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 40.1135 | 1.50969 | ||||||||
\(707\) | − 4.28353i | − 0.161099i | ||||||||
\(708\) | − 10.1451i | − 0.381277i | ||||||||
\(709\) | 19.8198 | 0.744349 | 0.372174 | − | 0.928163i | \(-0.378612\pi\) | ||||
0.372174 | + | 0.928163i | \(0.378612\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20.5362 | 0.770168 | ||||||||
\(712\) | 130.807i | 4.90221i | ||||||||
\(713\) | − 3.87454i | − 0.145103i | ||||||||
\(714\) | −6.28870 | −0.235349 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −60.0158 | −2.24290 | ||||||||
\(717\) | 7.30844i | 0.272939i | ||||||||
\(718\) | 34.4984i | 1.28747i | ||||||||
\(719\) | −25.7339 | −0.959713 | −0.479856 | − | 0.877347i | \(-0.659311\pi\) | ||||
−0.479856 | + | 0.877347i | \(0.659311\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.6995 | −0.659165 | ||||||||
\(722\) | 49.7206i | 1.85041i | ||||||||
\(723\) | − 1.42423i | − 0.0529677i | ||||||||
\(724\) | −14.8154 | −0.550610 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 10.1112 | 0.375263 | ||||||||
\(727\) | 24.6909i | 0.915734i | 0.889021 | + | 0.457867i | \(0.151386\pi\) | ||||
−0.889021 | + | 0.457867i | \(0.848614\pi\) | |||||||
\(728\) | 33.1412i | 1.22829i | ||||||||
\(729\) | 20.8745 | 0.773131 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −27.0839 | −1.00173 | ||||||||
\(732\) | − 10.6305i | − 0.392914i | ||||||||
\(733\) | − 23.0265i | − 0.850505i | −0.905075 | − | 0.425252i | \(-0.860185\pi\) | ||||
0.905075 | − | 0.425252i | \(-0.139815\pi\) | |||||||
\(734\) | 68.5242 | 2.52928 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −116.714 | −4.30215 | ||||||||
\(737\) | − 40.1135i | − 1.47760i | ||||||||
\(738\) | − 15.5456i | − 0.572242i | ||||||||
\(739\) | 27.2176 | 1.00121 | 0.500607 | − | 0.865675i | \(-0.333110\pi\) | ||||
0.500607 | + | 0.865675i | \(0.333110\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.13003 | 0.0415126 | ||||||||
\(742\) | − 14.8986i | − 0.546946i | ||||||||
\(743\) | 23.0434i | 0.845380i | 0.906274 | + | 0.422690i | \(0.138914\pi\) | ||||
−0.906274 | + | 0.422690i | \(0.861086\pi\) | |||||||
\(744\) | −3.68305 | −0.135027 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −74.2846 | −2.71975 | ||||||||
\(747\) | 21.5232i | 0.787493i | ||||||||
\(748\) | − 170.810i | − 6.24543i | ||||||||
\(749\) | −5.04983 | −0.184517 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.5480 | −0.457883 | −0.228941 | − | 0.973440i | \(-0.573526\pi\) | ||||
−0.228941 | + | 0.973440i | \(0.573526\pi\) | |||||||
\(752\) | − 61.1344i | − 2.22934i | ||||||||
\(753\) | 1.97516i | 0.0719787i | ||||||||
\(754\) | 19.5243 | 0.711033 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 12.2509 | 0.445562 | ||||||||
\(757\) | − 0.441361i | − 0.0160415i | −0.999968 | − | 0.00802077i | \(-0.997447\pi\) | ||||
0.999968 | − | 0.00802077i | \(-0.00255312\pi\) | |||||||
\(758\) | 35.1513i | 1.27675i | ||||||||
\(759\) | 6.15758 | 0.223506 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.0903 | −0.837024 | −0.418512 | − | 0.908211i | \(-0.637448\pi\) | ||||
−0.418512 | + | 0.908211i | \(0.637448\pi\) | |||||||
\(762\) | 12.3418i | 0.447096i | ||||||||
\(763\) | − 9.57747i | − 0.346728i | ||||||||
\(764\) | 25.9966 | 0.940524 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −32.4501 | −1.17247 | ||||||||
\(767\) | − 15.0084i | − 0.541923i | ||||||||
\(768\) | 37.1846i | 1.34178i | ||||||||
\(769\) | 16.5906 | 0.598272 | 0.299136 | − | 0.954210i | \(-0.403301\pi\) | ||||
0.299136 | + | 0.954210i | \(0.403301\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.68352 | 0.276715 | ||||||||
\(772\) | − 15.8481i | − 0.570384i | ||||||||
\(773\) | − 50.6033i | − 1.82008i | −0.414525 | − | 0.910038i | \(-0.636052\pi\) | ||||
0.414525 | − | 0.910038i | \(-0.363948\pi\) | |||||||
\(774\) | 34.7074 | 1.24753 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.85147 | 0.353647 | ||||||||
\(777\) | − 0.463851i | − 0.0166406i | ||||||||
\(778\) | 91.2300i | 3.27075i | ||||||||
\(779\) | 2.14819 | 0.0769670 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.0231 | −0.644916 | ||||||||
\(782\) | − 68.3472i | − 2.44409i | ||||||||
\(783\) | − 4.74628i | − 0.169618i | ||||||||
\(784\) | 109.089 | 3.89605 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 14.8288 | 0.528925 | ||||||||
\(787\) | 42.9038i | 1.52936i | 0.644413 | + | 0.764678i | \(0.277102\pi\) | ||||
−0.644413 | + | 0.764678i | \(0.722898\pi\) | |||||||
\(788\) | 29.4486i | 1.04906i | ||||||||
\(789\) | 3.48897 | 0.124210 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.61844 | 0.128657 | ||||||||
\(792\) | 143.947i | 5.11492i | ||||||||
\(793\) | − 15.7265i | − 0.558463i | ||||||||
\(794\) | 83.5903 | 2.96651 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −83.8440 | −2.97177 | ||||||||
\(797\) | − 33.5707i | − 1.18913i | −0.804046 | − | 0.594567i | \(-0.797324\pi\) | ||||
0.804046 | − | 0.594567i | \(-0.202676\pi\) | |||||||
\(798\) | 1.11362i | 0.0394218i | ||||||||
\(799\) | 20.8841 | 0.738828 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 35.0541 | 1.23858 | ||||||||
\(802\) | 69.7760i | 2.46388i | ||||||||
\(803\) | − 56.5091i | − 1.99416i | ||||||||
\(804\) | −17.2836 | −0.609545 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.28530 | −0.291837 | ||||||||
\(807\) | − 9.61749i | − 0.338552i | ||||||||
\(808\) | − 44.2536i | − 1.55684i | ||||||||
\(809\) | −35.3774 | −1.24380 | −0.621902 | − | 0.783095i | \(-0.713640\pi\) | ||||
−0.621902 | + | 0.783095i | \(0.713640\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 54.9833 | 1.93072 | 0.965362 | − | 0.260916i | \(-0.0840245\pi\) | ||||
0.965362 | + | 0.260916i | \(0.0840245\pi\) | |||||||
\(812\) | 14.3334i | 0.503005i | ||||||||
\(813\) | 0.0147067i | 0 0.000515787i | ||||||||
\(814\) | 16.9124 | 0.592779 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −39.7717 | −1.39229 | ||||||||
\(817\) | 4.79609i | 0.167794i | ||||||||
\(818\) | 38.6676i | 1.35198i | ||||||||
\(819\) | 8.88128 | 0.310337 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 47.1995 | 1.64727 | 0.823636 | − | 0.567118i | \(-0.191942\pi\) | ||||
0.823636 | + | 0.567118i | \(0.191942\pi\) | |||||||
\(822\) | − 15.8897i | − 0.554217i | ||||||||
\(823\) | 31.1661i | 1.08638i | 0.839609 | + | 0.543192i | \(0.182784\pi\) | ||||
−0.839609 | + | 0.543192i | \(0.817216\pi\) | |||||||
\(824\) | −182.856 | −6.37009 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.7905 | 0.514629 | ||||||||
\(827\) | 2.62427i | 0.0912548i | 0.998959 | + | 0.0456274i | \(0.0145287\pi\) | ||||
−0.998959 | + | 0.0456274i | \(0.985471\pi\) | |||||||
\(828\) | 65.2466i | 2.26747i | ||||||||
\(829\) | −30.1876 | −1.04846 | −0.524230 | − | 0.851577i | \(-0.675647\pi\) | ||||
−0.524230 | + | 0.851577i | \(0.675647\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.47365 | 0.259258 | ||||||||
\(832\) | 140.461i | 4.86960i | ||||||||
\(833\) | 37.2661i | 1.29119i | ||||||||
\(834\) | −20.6379 | −0.714633 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −30.2475 | −1.04613 | ||||||||
\(837\) | 2.01412i | 0.0696183i | ||||||||
\(838\) | − 60.9897i | − 2.10685i | ||||||||
\(839\) | 9.75555 | 0.336799 | 0.168399 | − | 0.985719i | \(-0.446140\pi\) | ||||
0.168399 | + | 0.985719i | \(0.446140\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.4469 | −0.808514 | ||||||||
\(842\) | − 9.06610i | − 0.312438i | ||||||||
\(843\) | − 3.15128i | − 0.108536i | ||||||||
\(844\) | 67.9299 | 2.33824 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −26.7625 | −0.920115 | ||||||||
\(847\) | 10.9814i | 0.377324i | ||||||||
\(848\) | − 94.2236i | − 3.23565i | ||||||||
\(849\) | −2.34636 | −0.0805270 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.04125 | 0.172812 | ||||||||
\(852\) | 7.76556i | 0.266044i | ||||||||
\(853\) | − 39.4547i | − 1.35090i | −0.737404 | − | 0.675452i | \(-0.763948\pi\) | ||||
0.737404 | − | 0.675452i | \(-0.236052\pi\) | |||||||
\(854\) | 15.4982 | 0.530336 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −52.1705 | −1.78315 | ||||||||
\(857\) | − 10.6006i | − 0.362110i | −0.983473 | − | 0.181055i | \(-0.942049\pi\) | ||||
0.983473 | − | 0.181055i | \(-0.0579512\pi\) | |||||||
\(858\) | − 13.1673i | − 0.449526i | ||||||||
\(859\) | 30.1660 | 1.02925 | 0.514625 | − | 0.857416i | \(-0.327931\pi\) | ||||
0.514625 | + | 0.857416i | \(0.327931\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.686525 | −0.0233967 | ||||||||
\(862\) | 35.4140i | 1.20621i | ||||||||
\(863\) | − 11.7962i | − 0.401546i | −0.979638 | − | 0.200773i | \(-0.935655\pi\) | ||||
0.979638 | − | 0.200773i | \(-0.0643454\pi\) | |||||||
\(864\) | 60.6723 | 2.06411 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −89.5847 | −3.04421 | ||||||||
\(867\) | − 7.76602i | − 0.263748i | ||||||||
\(868\) | − 6.08251i | − 0.206454i | ||||||||
\(869\) | 33.0670 | 1.12172 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.5689 | −0.866369 | ||||||||
\(872\) | − 98.9461i | − 3.35074i | ||||||||
\(873\) | − 2.64003i | − 0.0893513i | ||||||||
\(874\) | −12.1031 | −0.409394 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −24.3479 | −0.822640 | ||||||||
\(877\) | 12.3531i | 0.417134i | 0.978008 | + | 0.208567i | \(0.0668800\pi\) | ||||
−0.978008 | + | 0.208567i | \(0.933120\pi\) | |||||||
\(878\) | − 38.7648i | − 1.30825i | ||||||||
\(879\) | −5.68692 | −0.191815 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.2740 | 0.952575 | 0.476288 | − | 0.879290i | \(-0.341982\pi\) | ||||
0.476288 | + | 0.879290i | \(0.341982\pi\) | |||||||
\(882\) | − 47.7556i | − 1.60802i | ||||||||
\(883\) | − 14.7328i | − 0.495798i | −0.968786 | − | 0.247899i | \(-0.920260\pi\) | ||||
0.968786 | − | 0.247899i | \(-0.0797401\pi\) | |||||||
\(884\) | −108.877 | −3.66192 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 56.9797 | 1.91427 | ||||||||
\(887\) | 26.9237i | 0.904009i | 0.892016 | + | 0.452005i | \(0.149291\pi\) | ||||
−0.892016 | + | 0.452005i | \(0.850709\pi\) | |||||||
\(888\) | − 4.79210i | − 0.160812i | ||||||||
\(889\) | −13.4039 | −0.449552 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 36.9429 | 1.23763 | ||||||||
\(892\) | 31.8645i | 1.06690i | ||||||||
\(893\) | − 3.69822i | − 0.123756i | ||||||||
\(894\) | −19.8994 | −0.665535 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −75.6893 | −2.52860 | ||||||||
\(897\) | − 3.92493i | − 0.131050i | ||||||||
\(898\) | 24.4083i | 0.814516i | ||||||||
\(899\) | −2.35650 | −0.0785937 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.1877 | 1.07233 | ||||||||
\(902\) | − 25.0313i | − 0.833450i | ||||||||
\(903\) | − 1.53275i | − 0.0510066i | ||||||||
\(904\) | 37.3826 | 1.24333 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −17.6842 | −0.587519 | ||||||||
\(907\) | − 25.7869i | − 0.856239i | −0.903722 | − | 0.428119i | \(-0.859176\pi\) | ||||
0.903722 | − | 0.428119i | \(-0.140824\pi\) | |||||||
\(908\) | 46.5775i | 1.54573i | ||||||||
\(909\) | −11.8592 | −0.393346 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.4130 | 0.808839 | 0.404419 | − | 0.914574i | \(-0.367474\pi\) | ||||
0.404419 | + | 0.914574i | \(0.367474\pi\) | |||||||
\(912\) | 7.04288i | 0.233213i | ||||||||
\(913\) | 34.6563i | 1.14696i | ||||||||
\(914\) | −0.0873278 | −0.00288855 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 128.628 | 4.25000 | ||||||||
\(917\) | 16.1049i | 0.531831i | ||||||||
\(918\) | 35.5293i | 1.17264i | ||||||||
\(919\) | 6.86800 | 0.226554 | 0.113277 | − | 0.993563i | \(-0.463865\pi\) | ||||
0.113277 | + | 0.993563i | \(0.463865\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.80511 | −0.191285 | ||||||||
\(922\) | 82.5749i | 2.71946i | ||||||||
\(923\) | 11.4882i | 0.378137i | ||||||||
\(924\) | 9.66657 | 0.318007 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 53.6385 | 1.76267 | ||||||||
\(927\) | 49.0023i | 1.60945i | ||||||||
\(928\) | 70.9858i | 2.33022i | ||||||||
\(929\) | −12.6470 | −0.414934 | −0.207467 | − | 0.978242i | \(-0.566522\pi\) | ||||
−0.207467 | + | 0.978242i | \(0.566522\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.59918 | 0.216279 | ||||||||
\(932\) | − 100.897i | − 3.30498i | ||||||||
\(933\) | − 0.218687i | − 0.00715950i | ||||||||
\(934\) | −67.0293 | −2.19326 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 91.7536 | 2.99906 | ||||||||
\(937\) | 42.8873i | 1.40107i | 0.713619 | + | 0.700534i | \(0.247055\pi\) | ||||
−0.713619 | + | 0.700534i | \(0.752945\pi\) | |||||||
\(938\) | − 25.1977i | − 0.822734i | ||||||||
\(939\) | −6.20183 | −0.202389 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.2254 | 0.789725 | 0.394863 | − | 0.918740i | \(-0.370792\pi\) | ||||
0.394863 | + | 0.918740i | \(0.370792\pi\) | |||||||
\(942\) | 5.41069i | 0.176290i | ||||||||
\(943\) | − 7.46133i | − 0.242974i | ||||||||
\(944\) | 93.5400 | 3.04447 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 55.8852 | 1.81698 | ||||||||
\(947\) | − 16.2682i | − 0.528647i | −0.964434 | − | 0.264323i | \(-0.914851\pi\) | ||||
0.964434 | − | 0.264323i | \(-0.0851486\pi\) | |||||||
\(948\) | − 14.2475i | − 0.462738i | ||||||||
\(949\) | −36.0197 | −1.16925 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.73391 | 0.0562257 | ||||||||
\(952\) | − 70.5604i | − 2.28688i | ||||||||
\(953\) | − 19.2891i | − 0.624837i | −0.949945 | − | 0.312418i | \(-0.898861\pi\) | ||||
0.949945 | − | 0.312418i | \(-0.101139\pi\) | |||||||
\(954\) | −41.2479 | −1.33545 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −124.694 | −4.03291 | ||||||||
\(957\) | − 3.74505i | − 0.121060i | ||||||||
\(958\) | 59.9367i | 1.93647i | ||||||||
\(959\) | 17.2571 | 0.557261 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | − 10.7802i | − 0.347567i | ||||||||
\(963\) | 13.9808i | 0.450525i | ||||||||
\(964\) | 24.2998 | 0.782644 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.86795 | 0.124449 | ||||||||
\(967\) | 20.9745i | 0.674496i | 0.941416 | + | 0.337248i | \(0.109496\pi\) | ||||
−0.941416 | + | 0.337248i | \(0.890504\pi\) | |||||||
\(968\) | 113.450i | 3.64641i | ||||||||
\(969\) | −2.40592 | −0.0772894 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.2572 | −0.521718 | −0.260859 | − | 0.965377i | \(-0.584006\pi\) | ||||
−0.260859 | + | 0.965377i | \(0.584006\pi\) | |||||||
\(972\) | − 51.2142i | − 1.64270i | ||||||||
\(973\) | − 22.4139i | − 0.718558i | ||||||||
\(974\) | 73.0207 | 2.33973 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 98.0151 | 3.13739 | ||||||||
\(977\) | 12.3649i | 0.395587i | 0.980244 | + | 0.197794i | \(0.0633776\pi\) | ||||
−0.980244 | + | 0.197794i | \(0.936622\pi\) | |||||||
\(978\) | 15.5311i | 0.496630i | ||||||||
\(979\) | 56.4435 | 1.80394 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −26.5159 | −0.846587 | ||||||||
\(982\) | 33.4260i | 1.06667i | ||||||||
\(983\) | − 39.4586i | − 1.25853i | −0.777189 | − | 0.629267i | \(-0.783355\pi\) | ||||
0.777189 | − | 0.629267i | \(-0.216645\pi\) | |||||||
\(984\) | −7.09257 | −0.226103 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −41.5689 | −1.32382 | ||||||||
\(987\) | 1.18189i | 0.0376199i | ||||||||
\(988\) | 19.2802i | 0.613385i | ||||||||
\(989\) | 16.6583 | 0.529702 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −55.5390 | −1.76425 | −0.882127 | − | 0.471011i | \(-0.843889\pi\) | ||||
−0.882127 | + | 0.471011i | \(0.843889\pi\) | |||||||
\(992\) | − 30.1234i | − 0.956420i | ||||||||
\(993\) | − 6.85930i | − 0.217673i | ||||||||
\(994\) | −11.3214 | −0.359092 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 14.9323 | 0.473147 | ||||||||
\(997\) | 13.4120i | 0.424762i | 0.977187 | + | 0.212381i | \(0.0681218\pi\) | ||||
−0.977187 | + | 0.212381i | \(0.931878\pi\) | |||||||
\(998\) | 46.3149i | 1.46607i | ||||||||
\(999\) | −2.62062 | −0.0829129 |
(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 | 775.2.b.e.249.1 | 8 | ||
5.2 | odd | 4 | 775.2.a.g.1.4 | 4 | |||
5.3 | odd | 4 | 155.2.a.d.1.1 | ✓ | 4 | ||
5.4 | even | 2 | inner | 775.2.b.e.249.8 | 8 | ||
15.2 | even | 4 | 6975.2.a.bj.1.1 | 4 | |||
15.8 | even | 4 | 1395.2.a.m.1.4 | 4 | |||
20.3 | even | 4 | 2480.2.a.z.1.2 | 4 | |||
35.13 | even | 4 | 7595.2.a.q.1.1 | 4 | |||
40.3 | even | 4 | 9920.2.a.cd.1.3 | 4 | |||
40.13 | odd | 4 | 9920.2.a.ch.1.2 | 4 | |||
155.123 | even | 4 | 4805.2.a.j.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
155.2.a.d.1.1 | ✓ | 4 | 5.3 | odd | 4 | ||
775.2.a.g.1.4 | 4 | 5.2 | odd | 4 | |||
775.2.b.e.249.1 | 8 | 1.1 | even | 1 | trivial | ||
775.2.b.e.249.8 | 8 | 5.4 | even | 2 | inner | ||
1395.2.a.m.1.4 | 4 | 15.8 | even | 4 | |||
2480.2.a.z.1.2 | 4 | 20.3 | even | 4 | |||
4805.2.a.j.1.1 | 4 | 155.123 | even | 4 | |||
6975.2.a.bj.1.1 | 4 | 15.2 | even | 4 | |||
7595.2.a.q.1.1 | 4 | 35.13 | even | 4 | |||
9920.2.a.cd.1.3 | 4 | 40.3 | even | 4 | |||
9920.2.a.ch.1.2 | 4 | 40.13 | odd | 4 |