Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(2015,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.2015");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 12x^{10} + 47x^{8} - 44x^{6} + 81x^{4} + 848x^{2} + 1600 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2015.9 | ||
Root | \(0.366740 + 1.25423i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.2015 |
Dual form | 2736.2.d.a.2015.4 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.09425i | 0.489365i | 0.969603 | + | 0.244682i | \(0.0786837\pi\) | ||||
−0.969603 | + | 0.244682i | \(0.921316\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.25511i | − 0.474385i | −0.971463 | − | 0.237193i | \(-0.923773\pi\) | ||||
0.971463 | − | 0.237193i | \(-0.0762272\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.92198 | −0.881011 | −0.440506 | − | 0.897750i | \(-0.645201\pi\) | ||||
−0.440506 | + | 0.897750i | \(0.645201\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.58480 | −1.27160 | −0.635798 | − | 0.771856i | \(-0.719329\pi\) | ||||
−0.635798 | + | 0.771856i | \(0.719329\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.680734i | 0.165102i | 0.996587 | + | 0.0825511i | \(0.0263068\pi\) | ||||
−0.996587 | + | 0.0825511i | \(0.973693\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000i | 0.229416i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.07037 | 1.26576 | 0.632880 | − | 0.774250i | \(-0.281873\pi\) | ||||
0.632880 | + | 0.774250i | \(0.281873\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.80261 | 0.760522 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.82773i | 0.339401i | 0.985496 | + | 0.169701i | \(0.0542801\pi\) | ||||
−0.985496 | + | 0.169701i | \(0.945720\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 8.58480i | − 1.54188i | −0.636910 | − | 0.770938i | \(-0.719788\pi\) | ||||
0.636910 | − | 0.770938i | \(-0.280212\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.37340 | 0.232147 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.510210 | −0.0838780 | −0.0419390 | − | 0.999120i | \(-0.513354\pi\) | ||||
−0.0419390 | + | 0.999120i | \(0.513354\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.18920i | 0.498069i | 0.968495 | + | 0.249035i | \(0.0801133\pi\) | ||||
−0.968495 | + | 0.249035i | \(0.919887\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 5.38741i | − 0.821573i | −0.911732 | − | 0.410787i | \(-0.865254\pi\) | ||||
0.911732 | − | 0.410787i | \(-0.134746\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.9937 | 1.60360 | 0.801801 | − | 0.597591i | \(-0.203875\pi\) | ||||
0.801801 | + | 0.597591i | \(0.203875\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.42471 | 0.774959 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 9.03317i | − 1.24080i | −0.784285 | − | 0.620401i | \(-0.786970\pi\) | ||||
0.784285 | − | 0.620401i | \(-0.213030\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 3.19739i | − 0.431136i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.54997 | 0.462167 | 0.231084 | − | 0.972934i | \(-0.425773\pi\) | ||||
0.231084 | + | 0.972934i | \(0.425773\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.29240 | 0.549586 | 0.274793 | − | 0.961503i | \(-0.411391\pi\) | ||||
0.274793 | + | 0.961503i | \(0.411391\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 5.01693i | − 0.622274i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 11.0950i | − 1.35547i | −0.735306 | − | 0.677736i | \(-0.762961\pi\) | ||||
0.735306 | − | 0.677736i | \(-0.237039\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.1407 | 1.44084 | 0.720421 | − | 0.693537i | \(-0.243949\pi\) | ||||
0.720421 | + | 0.693537i | \(0.243949\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.25511 | −0.615064 | −0.307532 | − | 0.951538i | \(-0.599503\pi\) | ||||
−0.307532 | + | 0.951538i | \(0.599503\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.66740i | 0.417939i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.26462i | 0.929842i | 0.885352 | + | 0.464921i | \(0.153917\pi\) | ||||
−0.885352 | + | 0.464921i | \(0.846083\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.07037 | 0.666310 | 0.333155 | − | 0.942872i | \(-0.391887\pi\) | ||||
0.333155 | + | 0.942872i | \(0.391887\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.744895 | −0.0807952 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 13.9685i | − 1.48066i | −0.672246 | − | 0.740328i | \(-0.734670\pi\) | ||||
0.672246 | − | 0.740328i | \(-0.265330\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.75441i | 0.603226i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.09425 | −0.112268 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.67982 | −0.779767 | −0.389884 | − | 0.920864i | \(-0.627485\pi\) | ||||
−0.389884 | + | 0.920864i | \(0.627485\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.96280i | 0.294809i | 0.989076 | + | 0.147405i | \(0.0470919\pi\) | ||||
−0.989076 | + | 0.147405i | \(0.952908\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 14.6594i | − 1.44443i | −0.691667 | − | 0.722217i | \(-0.743123\pi\) | ||||
0.691667 | − | 0.722217i | \(-0.256877\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.84397 | −0.564958 | −0.282479 | − | 0.959274i | \(-0.591157\pi\) | ||||
−0.282479 | + | 0.959274i | \(0.591157\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.02042 | −0.480869 | −0.240435 | − | 0.970665i | \(-0.577290\pi\) | ||||
−0.240435 | + | 0.970665i | \(0.577290\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.1400i | 1.04797i | 0.851728 | + | 0.523984i | \(0.175555\pi\) | ||||
−0.851728 | + | 0.523984i | \(0.824445\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.64252i | 0.619418i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.854393 | 0.0783221 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.46201 | −0.223819 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.63228i | 0.861537i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 0.320184i | − 0.0284117i | −0.999899 | − | 0.0142059i | \(-0.995478\pi\) | ||||
0.999899 | − | 0.0142059i | \(-0.00452201\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.2877 | 1.16096 | 0.580478 | − | 0.814276i | \(-0.302866\pi\) | ||||
0.580478 | + | 0.814276i | \(0.302866\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.25511 | 0.108831 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.9074i | 1.87167i | 0.352432 | + | 0.935837i | \(0.385355\pi\) | ||||
−0.352432 | + | 0.935837i | \(0.614645\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.25511i | 0.106457i | 0.998582 | + | 0.0532283i | \(0.0169511\pi\) | ||||
−0.998582 | + | 0.0532283i | \(0.983049\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.3967 | 1.12029 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00000 | −0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 17.3040i | − 1.41760i | −0.705411 | − | 0.708799i | \(-0.749237\pi\) | ||||
0.705411 | − | 0.708799i | \(-0.250763\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.39394 | 0.754540 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.67982 | −0.134064 | −0.0670320 | − | 0.997751i | \(-0.521353\pi\) | ||||
−0.0670320 | + | 0.997751i | \(0.521353\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 7.61896i | − 0.600458i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 19.3596i | − 1.51636i | −0.652043 | − | 0.758182i | \(-0.726088\pi\) | ||||
0.652043 | − | 0.758182i | \(-0.273912\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 25.0847 | 1.94111 | 0.970555 | − | 0.240881i | \(-0.0774364\pi\) | ||||
0.970555 | + | 0.240881i | \(0.0774364\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.02042 | 0.616955 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 9.59147i | − 0.729226i | −0.931159 | − | 0.364613i | \(-0.881201\pi\) | ||||
0.931159 | − | 0.364613i | \(-0.118799\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 4.77268i | − 0.360780i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.39394 | −0.702136 | −0.351068 | − | 0.936350i | \(-0.614181\pi\) | ||||
−0.351068 | + | 0.936350i | \(0.614181\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.7748 | 0.800887 | 0.400443 | − | 0.916322i | \(-0.368856\pi\) | ||||
0.400443 | + | 0.916322i | \(0.368856\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 0.558299i | − 0.0410469i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 1.98909i | − 0.145457i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.89380 | 0.281746 | 0.140873 | − | 0.990028i | \(-0.455009\pi\) | ||||
0.140873 | + | 0.990028i | \(0.455009\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.8494 | 0.780959 | 0.390479 | − | 0.920612i | \(-0.372309\pi\) | ||||
0.390479 | + | 0.920612i | \(0.372309\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.61965i | 0.614125i | 0.951689 | + | 0.307062i | \(0.0993460\pi\) | ||||
−0.951689 | + | 0.307062i | \(0.900654\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 10.4078i | − 0.737792i | −0.929471 | − | 0.368896i | \(-0.879736\pi\) | ||||
0.929471 | − | 0.368896i | \(-0.120264\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.29400 | 0.161007 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.48979 | −0.243738 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 2.92198i | − 0.202118i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 16.1154i | − 1.10943i | −0.832040 | − | 0.554716i | \(-0.812827\pi\) | ||||
0.832040 | − | 0.554716i | \(-0.187173\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.89519 | 0.402049 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.7748 | −0.731443 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 3.12103i | − 0.209943i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.26462i | 0.553440i | 0.960951 | + | 0.276720i | \(0.0892474\pi\) | ||||
−0.960951 | + | 0.276720i | \(0.910753\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.74680 | 0.182312 | 0.0911559 | − | 0.995837i | \(-0.470944\pi\) | ||||
0.0911559 | + | 0.995837i | \(0.470944\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.1622 | 1.33236 | 0.666179 | − | 0.745792i | \(-0.267929\pi\) | ||||
0.666179 | + | 0.745792i | \(0.267929\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.33759i | 0.415189i | 0.978215 | + | 0.207595i | \(0.0665635\pi\) | ||||
−0.978215 | + | 0.207595i | \(0.933437\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.0299i | 0.784746i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.40298 | 0.155436 | 0.0777178 | − | 0.996975i | \(-0.475237\pi\) | ||||
0.0777178 | + | 0.996975i | \(0.475237\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.0746 | −0.906624 | −0.453312 | − | 0.891352i | \(-0.649758\pi\) | ||||
−0.453312 | + | 0.891352i | \(0.649758\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.93600i | 0.379237i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 4.58480i | − 0.291724i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.92477 | −0.437087 | −0.218544 | − | 0.975827i | \(-0.570131\pi\) | ||||
−0.218544 | + | 0.975827i | \(0.570131\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.7375 | −1.11515 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 12.3960i | − 0.773243i | −0.922238 | − | 0.386621i | \(-0.873642\pi\) | ||||
0.922238 | − | 0.386621i | \(-0.126358\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.640367i | 0.0397905i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.0219 | −0.617979 | −0.308989 | − | 0.951065i | \(-0.599991\pi\) | ||||
−0.308989 | + | 0.951065i | \(0.599991\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.88457 | 0.607204 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.76304i | 0.412350i | 0.978515 | + | 0.206175i | \(0.0661016\pi\) | ||||
−0.978515 | + | 0.206175i | \(0.933898\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 27.9444i | − 1.69750i | −0.528791 | − | 0.848752i | \(-0.677355\pi\) | ||||
0.528791 | − | 0.848752i | \(-0.322645\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −11.1112 | −0.670029 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.5774 | 0.935958 | 0.467979 | − | 0.883740i | \(-0.344982\pi\) | ||||
0.467979 | + | 0.883740i | \(0.344982\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.20613i | 0.489537i | 0.969582 | + | 0.244768i | \(0.0787119\pi\) | ||||
−0.969582 | + | 0.244768i | \(0.921288\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.5570i | 1.34088i | 0.741966 | + | 0.670438i | \(0.233894\pi\) | ||||
−0.741966 | + | 0.670438i | \(0.766106\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.00278 | 0.236277 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.5366 | 0.972741 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.3946i | 0.607261i | 0.952790 | + | 0.303631i | \(0.0981989\pi\) | ||||
−0.952790 | + | 0.303631i | \(0.901801\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.88457i | 0.226168i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −27.8315 | −1.60954 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.76177 | −0.389742 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.69697i | 0.268948i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 5.02042i | − 0.286531i | −0.989684 | − | 0.143265i | \(-0.954240\pi\) | ||||
0.989684 | − | 0.143265i | \(-0.0457602\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.40298 | 0.136260 | 0.0681301 | − | 0.997676i | \(-0.478297\pi\) | ||||
0.0681301 | + | 0.997676i | \(0.478297\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.67982 | 0.321042 | 0.160521 | − | 0.987032i | \(-0.448683\pi\) | ||||
0.160521 | + | 0.987032i | \(0.448683\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 27.3652i | − 1.53698i | −0.639860 | − | 0.768491i | \(-0.721008\pi\) | ||||
0.639860 | − | 0.768491i | \(-0.278992\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 5.34060i | − 0.299016i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.680734 | −0.0378771 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17.4342 | −0.967077 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 13.7983i | − 0.760725i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.0746i | 1.43319i | 0.697490 | + | 0.716595i | \(0.254300\pi\) | ||||
−0.697490 | + | 0.716595i | \(0.745700\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.1407 | 0.663320 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −31.0394 | −1.69083 | −0.845413 | − | 0.534113i | \(-0.820646\pi\) | ||||
−0.845413 | + | 0.534113i | \(0.820646\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.0847i | 1.35841i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 15.5943i | − 0.842014i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.2877 | −0.713323 | −0.356662 | − | 0.934234i | \(-0.616085\pi\) | ||||
−0.356662 | + | 0.934234i | \(0.616085\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.21426 | 0.0649981 | 0.0324991 | − | 0.999472i | \(-0.489653\pi\) | ||||
0.0324991 | + | 0.999472i | \(0.489653\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 19.3751i | − 1.03123i | −0.856820 | − | 0.515615i | \(-0.827563\pi\) | ||||
0.856820 | − | 0.515615i | \(-0.172437\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.2850i | 0.705097i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −36.0784 | −1.90415 | −0.952073 | − | 0.305872i | \(-0.901052\pi\) | ||||
−0.952073 | + | 0.305872i | \(0.901052\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 5.75041i | − 0.300990i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 5.75441i | − 0.300378i | −0.988657 | − | 0.150189i | \(-0.952012\pi\) | ||||
0.988657 | − | 0.150189i | \(-0.0479882\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.3376 | −0.588618 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.58480 | 0.133836 | 0.0669180 | − | 0.997758i | \(-0.478683\pi\) | ||||
0.0669180 | + | 0.997758i | \(0.478683\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 8.37979i | − 0.431581i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.53063i | 0.386822i | 0.981118 | + | 0.193411i | \(0.0619552\pi\) | ||||
−0.981118 | + | 0.193411i | \(0.938045\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.5755 | 1.35794 | 0.678972 | − | 0.734164i | \(-0.262426\pi\) | ||||
0.678972 | + | 0.734164i | \(0.262426\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.01306 | −0.204524 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.61743i | 0.386219i | 0.981177 | + | 0.193110i | \(0.0618573\pi\) | ||||
−0.981177 | + | 0.193110i | \(0.938143\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.13231i | 0.208980i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.04358 | −0.455032 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.7245 | 0.588435 | 0.294217 | − | 0.955739i | \(-0.404941\pi\) | ||||
0.294217 | + | 0.955739i | \(0.404941\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.73778i | 0.236594i | 0.992978 | + | 0.118297i | \(0.0377434\pi\) | ||||
−0.992978 | + | 0.118297i | \(0.962257\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 39.3596i | 1.96064i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.49083 | 0.0738975 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.7544 | −1.27347 | −0.636737 | − | 0.771081i | \(-0.719716\pi\) | ||||
−0.636737 | + | 0.771081i | \(0.719716\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 4.45559i | − 0.219245i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.64252i | 0.326068i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.0732 | −0.492106 | −0.246053 | − | 0.969256i | \(-0.579134\pi\) | ||||
−0.246053 | + | 0.969256i | \(0.579134\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.77483 | −0.135237 | −0.0676185 | − | 0.997711i | \(-0.521540\pi\) | ||||
−0.0676185 | + | 0.997711i | \(0.521540\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.58857i | 0.125564i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 5.38741i | − 0.260715i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.5347 | 1.03729 | 0.518645 | − | 0.854990i | \(-0.326437\pi\) | ||||
0.518645 | + | 0.854990i | \(0.326437\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.3055 | 1.16805 | 0.584023 | − | 0.811737i | \(-0.301478\pi\) | ||||
0.584023 | + | 0.811737i | \(0.301478\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.07037i | 0.290385i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.39478i | 0.305206i | 0.988288 | + | 0.152603i | \(0.0487656\pi\) | ||||
−0.988288 | + | 0.152603i | \(0.951234\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.5873 | −1.12067 | −0.560333 | − | 0.828267i | \(-0.689327\pi\) | ||||
−0.560333 | + | 0.828267i | \(0.689327\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.2850 | 0.724580 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.57314i | 0.121434i | 0.998155 | + | 0.0607171i | \(0.0193387\pi\) | ||||
−0.998155 | + | 0.0607171i | \(0.980661\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 9.31879i | − 0.438805i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.29678 | −0.295197 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.06508 | −0.330490 | −0.165245 | − | 0.986253i | \(-0.552842\pi\) | ||||
−0.165245 | + | 0.986253i | \(0.552842\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.0425i | 1.07319i | 0.843839 | + | 0.536597i | \(0.180290\pi\) | ||||
−0.843839 | + | 0.536597i | \(0.819710\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 27.5774i | − 1.28163i | −0.767694 | − | 0.640816i | \(-0.778596\pi\) | ||||
0.767694 | − | 0.640816i | \(-0.221404\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.5128 | 0.532747 | 0.266373 | − | 0.963870i | \(-0.414175\pi\) | ||||
0.266373 | + | 0.963870i | \(0.414175\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.9254 | −0.643016 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.7419i | 0.723815i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.80261i | 0.174476i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.52040 | −0.115160 | −0.0575800 | − | 0.998341i | \(-0.518338\pi\) | ||||
−0.0575800 | + | 0.998341i | \(0.518338\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.33921 | 0.106659 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 8.40366i | − 0.381590i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.4546i | 0.473745i | 0.971541 | + | 0.236873i | \(0.0761224\pi\) | ||||
−0.971541 | + | 0.236873i | \(0.923878\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −41.0018 | −1.85038 | −0.925192 | − | 0.379499i | \(-0.876096\pi\) | ||||
−0.925192 | + | 0.379499i | \(0.876096\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.24420 | −0.0560359 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 15.2379i | − 0.683514i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.0841i | 1.48105i | 0.672030 | + | 0.740524i | \(0.265423\pi\) | ||||
−0.672030 | + | 0.740524i | \(0.734577\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.6611 | −0.653708 | −0.326854 | − | 0.945075i | \(-0.605989\pi\) | ||||
−0.326854 | + | 0.945075i | \(0.605989\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.24205 | −0.144269 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 2.92351i | − 0.129582i | −0.997899 | − | 0.0647911i | \(-0.979362\pi\) | ||||
0.997899 | − | 0.0647911i | \(-0.0206381\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.59571i | 0.291777i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.0411 | 0.706854 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −32.1236 | −1.41279 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.91075i | 0.171333i | 0.996324 | + | 0.0856664i | \(0.0273019\pi\) | ||||
−0.996324 | + | 0.0856664i | \(0.972698\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.8290i | 0.517246i | 0.965978 | + | 0.258623i | \(0.0832688\pi\) | ||||
−0.965978 | + | 0.258623i | \(0.916731\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.84397 | 0.254567 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.8494 | 0.602149 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 14.6219i | − 0.633343i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 6.39478i | − 0.276470i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15.8509 | −0.682748 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 44.9948 | 1.93448 | 0.967239 | − | 0.253869i | \(-0.0817033\pi\) | ||||
0.967239 | + | 0.253869i | \(0.0817033\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 5.49361i | − 0.235320i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.4152i | 0.488079i | 0.969765 | + | 0.244039i | \(0.0784726\pi\) | ||||
−0.969765 | + | 0.244039i | \(0.921527\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.82773 | −0.0778640 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.3730 | 0.441103 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 39.6234i | − 1.67890i | −0.543440 | − | 0.839448i | \(-0.682878\pi\) | ||||
0.543440 | − | 0.839448i | \(-0.317122\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.7002i | 1.04471i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −27.8315 | −1.17296 | −0.586478 | − | 0.809965i | \(-0.699486\pi\) | ||||
−0.586478 | + | 0.809965i | \(0.699486\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.1900 | −0.512838 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.6523i | 1.45270i | 0.687326 | + | 0.726349i | \(0.258784\pi\) | ||||
−0.687326 | + | 0.726349i | \(0.741216\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.9444i | 1.16944i | 0.811236 | + | 0.584719i | \(0.198795\pi\) | ||||
−0.811236 | + | 0.584719i | \(0.801205\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 23.0833 | 0.962639 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.2924 | 0.678262 | 0.339131 | − | 0.940739i | \(-0.389867\pi\) | ||||
0.339131 | + | 0.940739i | \(0.389867\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 7.61896i | − 0.316088i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 26.3948i | 1.09316i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.01915 | 0.248437 | 0.124218 | − | 0.992255i | \(-0.460358\pi\) | ||||
0.124218 | + | 0.992255i | \(0.460358\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.58480 | 0.353731 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.52388i | 0.308969i | 0.987995 | + | 0.154484i | \(0.0493716\pi\) | ||||
−0.987995 | + | 0.154484i | \(0.950628\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.934921i | 0.0383280i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.1407 | −0.496057 | −0.248029 | − | 0.968753i | \(-0.579783\pi\) | ||||
−0.248029 | + | 0.968753i | \(0.579783\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.6256 | 1.16766 | 0.583832 | − | 0.811874i | \(-0.301553\pi\) | ||||
0.583832 | + | 0.811874i | \(0.301553\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 2.69406i | − 0.109529i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 30.7748i | − 1.24911i | −0.780980 | − | 0.624556i | \(-0.785280\pi\) | ||||
0.780980 | − | 0.624556i | \(-0.214720\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −50.4042 | −2.03913 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.14322 | 0.328901 | 0.164451 | − | 0.986385i | \(-0.447415\pi\) | ||||
0.164451 | + | 0.986385i | \(0.447415\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.93822i | 0.279322i | 0.990199 | + | 0.139661i | \(0.0446013\pi\) | ||||
−0.990199 | + | 0.139661i | \(0.955399\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 42.1900i | 1.69576i | 0.530188 | + | 0.847880i | \(0.322121\pi\) | ||||
−0.530188 | + | 0.847880i | \(0.677879\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.5319 | −0.702401 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.47291 | 0.338917 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 0.347317i | − 0.0138485i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 0.614738i | − 0.0244723i | −0.999925 | − | 0.0122362i | \(-0.996105\pi\) | ||||
0.999925 | − | 0.0122362i | \(-0.00389499\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.350362 | 0.0139037 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.8712 | −0.985434 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 41.0784i | − 1.62250i | −0.584700 | − | 0.811250i | \(-0.698788\pi\) | ||||
0.584700 | − | 0.811250i | \(-0.301212\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 17.5366i | − 0.691576i | −0.938313 | − | 0.345788i | \(-0.887612\pi\) | ||||
0.938313 | − | 0.345788i | \(-0.112388\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30.3006 | −1.19124 | −0.595621 | − | 0.803266i | \(-0.703094\pi\) | ||||
−0.595621 | + | 0.803266i | \(0.703094\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.3730 | −0.407175 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 36.6895i | 1.43577i | 0.696162 | + | 0.717885i | \(0.254889\pi\) | ||||
−0.696162 | + | 0.717885i | \(0.745111\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.5401i | 0.568130i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −40.7754 | −1.58838 | −0.794192 | − | 0.607667i | \(-0.792105\pi\) | ||||
−0.794192 | + | 0.607667i | \(0.792105\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.7748 | 0.808047 | 0.404024 | − | 0.914749i | \(-0.367611\pi\) | ||||
0.404024 | + | 0.914749i | \(0.367611\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.37340i | 0.0532582i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.0950i | 0.429601i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.5423 | −0.484191 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.394777 | 0.0152175 | 0.00760876 | − | 0.999971i | \(-0.497578\pi\) | ||||
0.00760876 | + | 0.999971i | \(0.497578\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.5579i | 0.790103i | 0.918659 | + | 0.395051i | \(0.129273\pi\) | ||||
−0.918659 | + | 0.395051i | \(0.870727\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.63898i | 0.369910i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.4403 | −0.858654 | −0.429327 | − | 0.903149i | \(-0.641249\pi\) | ||||
−0.429327 | + | 0.903149i | \(0.641249\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −23.9722 | −0.915931 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 41.4153i | 1.57780i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.1974i | 0.882470i | 0.897392 | + | 0.441235i | \(0.145460\pi\) | ||||
−0.897392 | + | 0.441235i | \(0.854540\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.37340 | −0.0520961 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.17100 | −0.0822324 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 45.3892i | 1.71433i | 0.515045 | + | 0.857163i | \(0.327775\pi\) | ||||
−0.515045 | + | 0.857163i | \(0.672225\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 0.510210i | − 0.0192429i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.71862 | 0.139853 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −40.8494 | −1.53413 | −0.767066 | − | 0.641568i | \(-0.778284\pi\) | ||||
−0.767066 | + | 0.641568i | \(0.778284\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 52.1130i | − 1.95165i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.6594i | 0.548230i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30.3006 | 1.13002 | 0.565012 | − | 0.825083i | \(-0.308872\pi\) | ||||
0.565012 | + | 0.825083i | \(0.308872\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.3991 | −0.685218 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.95015i | 0.258122i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.5366i | 0.650397i | 0.945646 | + | 0.325198i | \(0.105431\pi\) | ||||
−0.945646 | + | 0.325198i | \(0.894569\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.66740 | 0.135644 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.51021 | 0.240460 | 0.120230 | − | 0.992746i | \(-0.461637\pi\) | ||||
0.120230 | + | 0.992746i | \(0.461637\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 32.4195i | 1.19419i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 20.9349i | − 0.770104i | −0.922895 | − | 0.385052i | \(-0.874184\pi\) | ||||
0.922895 | − | 0.385052i | \(-0.125816\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.6935 | −0.722484 | −0.361242 | − | 0.932472i | \(-0.617647\pi\) | ||||
−0.361242 | + | 0.932472i | \(0.617647\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.9349 | 0.693722 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.33479i | 0.268008i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 34.3392i | − 1.25306i | −0.779399 | − | 0.626528i | \(-0.784475\pi\) | ||||
0.779399 | − | 0.626528i | \(-0.215525\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.2178 | −0.589446 | −0.294723 | − | 0.955583i | \(-0.595227\pi\) | ||||
−0.294723 | + | 0.955583i | \(0.595227\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 48.6038i | − 1.76189i | −0.473222 | − | 0.880943i | \(-0.656909\pi\) | ||||
0.473222 | − | 0.880943i | \(-0.343091\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.30115i | 0.228117i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −16.2759 | −0.587690 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −37.9912 | −1.37000 | −0.685000 | − | 0.728543i | \(-0.740198\pi\) | ||||
−0.685000 | + | 0.728543i | \(0.740198\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 6.36494i | − 0.228931i | −0.993427 | − | 0.114466i | \(-0.963484\pi\) | ||||
0.993427 | − | 0.114466i | \(-0.0365156\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 32.6447i | − 1.17263i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.18920 | −0.114265 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −35.4751 | −1.26940 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 1.83814i | − 0.0656061i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 28.9050i | − 1.03035i | −0.857085 | − | 0.515176i | \(-0.827727\pi\) | ||||
0.857085 | − | 0.515176i | \(-0.172273\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.9819 | 0.497140 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.6798 | −0.698851 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 33.7705i | − 1.19621i | −0.801417 | − | 0.598106i | \(-0.795920\pi\) | ||||
0.801417 | − | 0.598106i | \(-0.204080\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.48382i | 0.264758i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.3553 | 0.541878 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.33706 | 0.293843 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 39.5841i | − 1.39170i | −0.718186 | − | 0.695851i | \(-0.755027\pi\) | ||||
0.718186 | − | 0.695851i | \(-0.244973\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 19.0394i | − 0.668565i | −0.942473 | − | 0.334283i | \(-0.891506\pi\) | ||||
0.942473 | − | 0.334283i | \(-0.108494\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.1843 | 0.742055 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.38741 | 0.188482 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 24.8413i | − 0.866968i | −0.901161 | − | 0.433484i | \(-0.857284\pi\) | ||||
0.901161 | − | 0.433484i | \(-0.142716\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 1.25511i | − 0.0437502i | −0.999761 | − | 0.0218751i | \(-0.993036\pi\) | ||||
0.999761 | − | 0.0218751i | \(-0.00696362\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.4195 | 1.12733 | 0.563667 | − | 0.826002i | \(-0.309390\pi\) | ||||
0.563667 | + | 0.826002i | \(0.309390\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.90499 | 0.309283 | 0.154641 | − | 0.987971i | \(-0.450578\pi\) | ||||
0.154641 | + | 0.987971i | \(0.450578\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.69279i | 0.127947i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 27.4489i | 0.949910i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31.0311 | −1.07131 | −0.535656 | − | 0.844436i | \(-0.679936\pi\) | ||||
−0.535656 | + | 0.844436i | \(0.679936\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.6594 | 0.884807 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.77636i | 0.301916i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.09008i | 0.106176i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.09717 | −0.106169 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45.5088 | 1.55819 | 0.779096 | − | 0.626904i | \(-0.215678\pi\) | ||||
0.779096 | + | 0.626904i | \(0.215678\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30.4046i | 1.03860i | 0.854592 | + | 0.519301i | \(0.173808\pi\) | ||||
−0.854592 | + | 0.519301i | \(0.826192\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 52.1236i | − 1.77843i | −0.457487 | − | 0.889216i | \(-0.651250\pi\) | ||||
0.457487 | − | 0.889216i | \(-0.348750\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.6879 | −0.397862 | −0.198931 | − | 0.980013i | \(-0.563747\pi\) | ||||
−0.198931 | + | 0.980013i | \(0.563747\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.4955 | 0.356857 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 24.1491i | − 0.819202i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 50.8685i | 1.72361i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.0895 | 0.408700 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46.7939 | 1.58012 | 0.790058 | − | 0.613032i | \(-0.210050\pi\) | ||||
0.790058 | + | 0.613032i | \(0.210050\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.2550i | 1.45730i | 0.684888 | + | 0.728648i | \(0.259851\pi\) | ||||
−0.684888 | + | 0.728648i | \(0.740149\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 8.78574i | − 0.295664i | −0.989013 | − | 0.147832i | \(-0.952771\pi\) | ||||
0.989013 | − | 0.147832i | \(-0.0472294\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.68516 | −0.258042 | −0.129021 | − | 0.991642i | \(-0.541184\pi\) | ||||
−0.129021 | + | 0.991642i | \(0.541184\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.401864 | −0.0134781 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.9937i | 0.367892i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 10.2793i | − 0.343601i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.6907 | 0.523315 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.14919 | 0.204859 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.7904i | 0.391926i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 21.2295i | − 0.704913i | −0.935828 | − | 0.352457i | \(-0.885346\pi\) | ||||
0.935828 | − | 0.352457i | \(-0.114654\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.74958 | 0.223624 | 0.111812 | − | 0.993729i | \(-0.464335\pi\) | ||||
0.111812 | + | 0.993729i | \(0.464335\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.7375 | −0.587027 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 16.6775i | − 0.550740i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.83039i | 0.0933661i | 0.998910 | + | 0.0466830i | \(0.0148651\pi\) | ||||
−0.998910 | + | 0.0466830i | \(0.985135\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −55.6629 | −1.83217 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.94013 | −0.0637911 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.7323i | 1.30358i | 0.758401 | + | 0.651788i | \(0.225981\pi\) | ||||
−0.758401 | + | 0.651788i | \(0.774019\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.42471i | 0.177788i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.17657 | 0.0711815 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.7245 | −0.513696 | −0.256848 | − | 0.966452i | \(-0.582684\pi\) | ||||
−0.256848 | + | 0.966452i | \(0.582684\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 44.1756i | − 1.44008i | −0.693931 | − | 0.720041i | \(-0.744123\pi\) | ||||
0.693931 | − | 0.720041i | \(-0.255877\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.3596i | 0.630436i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.1703 | 0.427978 | 0.213989 | − | 0.976836i | \(-0.431354\pi\) | ||||
0.213989 | + | 0.976836i | \(0.431354\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.0936 | 0.782112 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 9.88407i | − 0.320177i | −0.987103 | − | 0.160088i | \(-0.948822\pi\) | ||||
0.987103 | − | 0.160088i | \(-0.0511779\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.26080i | 0.137876i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 27.4961 | 0.887895 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −42.6988 | −1.37738 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.8720i | 0.382173i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 31.5088i | − 1.01326i | −0.862165 | − | 0.506628i | \(-0.830892\pi\) | ||||
0.862165 | − | 0.506628i | \(-0.169108\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35.5166 | −1.13978 | −0.569891 | − | 0.821720i | \(-0.693015\pi\) | ||||
−0.569891 | + | 0.821720i | \(0.693015\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.57529 | 0.0505014 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.4790i | 0.463226i | 0.972808 | + | 0.231613i | \(0.0744002\pi\) | ||||
−0.972808 | + | 0.231613i | \(0.925600\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 40.8157i | 1.30447i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.6907 | 0.500456 | 0.250228 | − | 0.968187i | \(-0.419494\pi\) | ||||
0.250228 | + | 0.968187i | \(0.419494\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.43207 | −0.300531 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 32.7036i | − 1.03991i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.0950i | 0.352445i | 0.984350 | + | 0.176222i | \(0.0563878\pi\) | ||||
−0.984350 | + | 0.176222i | \(0.943612\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.3888 | 0.361049 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.8772 | 0.787869 | 0.393934 | − | 0.919139i | \(-0.371114\pi\) | ||||
0.393934 | + | 0.919139i | \(0.371114\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 2736.2.d.a.2015.9 | yes | 12 | |
3.2 | odd | 2 | inner | 2736.2.d.a.2015.3 | ✓ | 12 | |
4.3 | odd | 2 | inner | 2736.2.d.a.2015.10 | yes | 12 | |
12.11 | even | 2 | inner | 2736.2.d.a.2015.4 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2736.2.d.a.2015.3 | ✓ | 12 | 3.2 | odd | 2 | inner | |
2736.2.d.a.2015.4 | yes | 12 | 12.11 | even | 2 | inner | |
2736.2.d.a.2015.9 | yes | 12 | 1.1 | even | 1 | trivial | |
2736.2.d.a.2015.10 | yes | 12 | 4.3 | odd | 2 | inner |