Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2940,2,Mod(1469,2940)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2940, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2940.1469");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2940.f (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: | \(23.4760181943\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1469.6 | ||
Character | \(\chi\) | \(=\) | 2940.1469 |
Dual form | 2940.2.f.b.1469.8 |
$q$-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 \(\left(\mathbb{Z}/2940\mathbb{Z}\right)^\times\).
\(n\) | \(1081\) | \(1177\) | \(1471\) | \(1961\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.57897 | − | 0.711939i | −0.911618 | − | 0.411038i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.16481 | − | 0.559982i | 0.968134 | − | 0.250432i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.98629 | + | 2.24826i | 0.662095 | + | 0.749420i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.19829i | 0.662810i | 0.943489 | + | 0.331405i | \(0.107523\pi\) | ||||
−0.943489 | + | 0.331405i | \(0.892477\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.07095 | −1.40643 | −0.703215 | − | 0.710978i | \(-0.748253\pi\) | ||||
−0.703215 | + | 0.710978i | \(0.748253\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.81685 | − | 0.657022i | −0.985506 | − | 0.169642i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.90787i | 0.705262i | 0.935762 | + | 0.352631i | \(0.114713\pi\) | ||||
−0.935762 | + | 0.352631i | \(0.885287\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.155105i | 0.0355834i | 0.999842 | + | 0.0177917i | \(0.00566358\pi\) | ||||
−0.999842 | + | 0.0177917i | \(0.994336\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.63484 | −0.757916 | −0.378958 | − | 0.925414i | \(-0.623718\pi\) | ||||
−0.378958 | + | 0.925414i | \(0.623718\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.37284 | − | 2.42451i | 0.874568 | − | 0.484903i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.53566 | − | 4.96405i | −0.295538 | − | 0.955331i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.88854i | − | 0.722084i | −0.932549 | − | 0.361042i | \(-0.882421\pi\) | ||
0.932549 | − | 0.361042i | \(-0.117579\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 9.79837i | − | 1.75984i | −0.475122 | − | 0.879920i | \(-0.657596\pi\) | ||
0.475122 | − | 0.879920i | \(-0.342404\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.56505 | − | 3.47103i | 0.272440 | − | 0.604229i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.01287i | 0.659712i | 0.944031 | + | 0.329856i | \(0.107000\pi\) | ||||
−0.944031 | + | 0.329856i | \(0.893000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.00688 | + | 3.61021i | 1.28213 | + | 0.578096i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.97945 | −1.24618 | −0.623090 | − | 0.782150i | \(-0.714123\pi\) | ||||
−0.623090 | + | 0.782150i | \(0.714123\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.59370i | − | 0.395536i | −0.980249 | − | 0.197768i | \(-0.936631\pi\) | ||
0.980249 | − | 0.197768i | \(-0.0633692\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.55892 | + | 3.75478i | 0.828675 | + | 0.559730i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 12.2525i | − | 1.78722i | −0.448848 | − | 0.893608i | \(-0.648166\pi\) | ||
0.448848 | − | 0.893608i | \(-0.351834\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.07023 | − | 4.59144i | 0.289890 | − | 0.642930i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.42504 | 1.29463 | 0.647314 | − | 0.762223i | \(-0.275892\pi\) | ||||
0.647314 | + | 0.762223i | \(0.275892\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.23100 | + | 4.75889i | 0.165988 | + | 0.641689i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.110425 | − | 0.244905i | 0.0146261 | − | 0.0324385i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.80649 | 0.886129 | 0.443064 | − | 0.896490i | \(-0.353891\pi\) | ||||
0.443064 | + | 0.896490i | \(0.353891\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.97180i | − | 0.892647i | −0.894872 | − | 0.446324i | \(-0.852733\pi\) | ||
0.894872 | − | 0.446324i | \(-0.147267\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.9777 | + | 2.83964i | −1.36161 | + | 0.352214i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 6.51121i | − | 0.795471i | −0.917500 | − | 0.397736i | \(-0.869796\pi\) | ||
0.917500 | − | 0.397736i | \(-0.130204\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.73930 | + | 2.58778i | 0.690930 | + | 0.311533i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.22868i | − | 0.264495i | −0.991217 | − | 0.132248i | \(-0.957781\pi\) | ||
0.991217 | − | 0.132248i | \(-0.0422194\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.0608 | 1.52865 | 0.764325 | − | 0.644831i | \(-0.223072\pi\) | ||||
0.764325 | + | 0.644831i | \(0.223072\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.63069 | + | 0.715035i | −0.996586 | + | 0.0825652i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.68597 | −0.414705 | −0.207352 | − | 0.978266i | \(-0.566485\pi\) | ||||
−0.207352 | + | 0.978266i | \(0.566485\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.10934 | + | 8.93137i | −0.123260 | + | 0.992374i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 13.6861i | − | 1.50225i | −0.660162 | − | 0.751123i | \(-0.729512\pi\) | ||
0.660162 | − | 0.751123i | \(-0.270488\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.62836 | + | 6.29500i | 0.176620 | + | 0.682789i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.76841 | + | 6.13989i | −0.296804 | + | 0.658265i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.3301 | 1.20098 | 0.600492 | − | 0.799631i | \(-0.294971\pi\) | ||||
0.600492 | + | 0.799631i | \(0.294971\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.97585 | + | 15.4713i | −0.723362 | + | 1.60430i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.0868557 | + | 0.335772i | 0.00891121 | + | 0.0344495i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.73455 | 0.176117 | 0.0880586 | − | 0.996115i | \(-0.471934\pi\) | ||||
0.0880586 | + | 0.996115i | \(0.471934\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.94233 | + | 4.36643i | −0.496723 | + | 0.438843i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.6985 | −1.36305 | −0.681524 | − | 0.731796i | \(-0.738683\pi\) | ||||
−0.681524 | + | 0.731796i | \(0.738683\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.45213 | −0.931346 | −0.465673 | − | 0.884957i | \(-0.654188\pi\) | ||||
−0.465673 | + | 0.884957i | \(0.654188\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.87241 | −0.181013 | −0.0905065 | − | 0.995896i | \(-0.528849\pi\) | ||||
−0.0905065 | + | 0.995896i | \(0.528849\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.67338 | −0.734976 | −0.367488 | − | 0.930028i | \(-0.619782\pi\) | ||||
−0.367488 | + | 0.930028i | \(0.619782\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.85692 | − | 6.33619i | 0.271167 | − | 0.601405i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.38523 | −0.318455 | −0.159228 | − | 0.987242i | \(-0.550900\pi\) | ||||
−0.159228 | + | 0.987242i | \(0.550900\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.86875 | + | 2.03544i | −0.733765 | + | 0.189806i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.0724 | − | 11.4008i | −0.931190 | − | 1.05401i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.16751 | 0.560683 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12.5993 | + | 5.68088i | 1.13604 | + | 0.512228i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.10870 | − | 7.69733i | 0.725264 | − | 0.688470i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.6585i | 1.03452i | 0.855827 | + | 0.517262i | \(0.173049\pi\) | ||||
−0.855827 | + | 0.517262i | \(0.826951\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.84656 | + | 4.09537i | −0.162580 | + | 0.360577i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.0471 | 0.877821 | 0.438911 | − | 0.898531i | \(-0.355364\pi\) | ||||
0.438911 | + | 0.898531i | \(0.355364\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.10419 | − | 9.88630i | −0.525365 | − | 0.850877i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.4230 | 1.65942 | 0.829708 | − | 0.558198i | \(-0.188507\pi\) | ||||
0.829708 | + | 0.558198i | \(0.188507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.71667i | 0.400063i | 0.979789 | + | 0.200031i | \(0.0641044\pi\) | ||||
−0.979789 | + | 0.200031i | \(0.935896\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.72306 | + | 19.3464i | −0.734614 | + | 1.62926i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 11.1474i | − | 0.932195i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.17751 | − | 8.41797i | −0.180833 | − | 0.699075i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 2.56445i | − | 0.210088i | −0.994468 | − | 0.105044i | \(-0.966502\pi\) | ||
0.994468 | − | 0.105044i | \(-0.0334983\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.38227 | −0.438003 | −0.219001 | − | 0.975725i | \(-0.570280\pi\) | ||||
−0.219001 | + | 0.975725i | \(0.570280\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.53765 | + | 5.77586i | −0.528538 | + | 0.466951i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.48691 | − | 21.2117i | −0.440719 | − | 1.70376i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.74803 | −0.458742 | −0.229371 | − | 0.973339i | \(-0.573667\pi\) | ||||
−0.229371 | + | 0.973339i | \(0.573667\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.8818 | − | 6.71005i | −1.18021 | − | 0.532142i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.31538i | 0.181355i | 0.995880 | + | 0.0906774i | \(0.0289032\pi\) | ||||
−0.995880 | + | 0.0906774i | \(0.971097\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.44433 | − | 8.39054i | 0.112441 | − | 0.653203i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 20.3572i | − | 1.57529i | −0.616132 | − | 0.787643i | \(-0.711301\pi\) | ||
0.616132 | − | 0.787643i | \(-0.288699\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.7146 | 0.978043 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.348715 | + | 0.308082i | −0.0266669 | + | 0.0235596i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 21.7254i | − | 1.65175i | −0.563850 | − | 0.825877i | \(-0.690681\pi\) | ||
0.563850 | − | 0.825877i | \(-0.309319\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.7472 | − | 4.84580i | −0.807811 | − | 0.364233i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 16.9273i | − | 1.26521i | −0.774475 | − | 0.632604i | \(-0.781986\pi\) | ||
0.774475 | − | 0.632604i | \(-0.218014\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 24.5548i | − | 1.82515i | −0.408912 | − | 0.912574i | \(-0.634092\pi\) | ||
0.408912 | − | 0.912574i | \(-0.365908\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.96350 | + | 11.0083i | −0.366912 | + | 0.813753i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.24713 | + | 8.68712i | 0.165213 | + | 0.638689i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.39235 | −0.467455 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 18.6786i | − | 1.35154i | −0.737113 | − | 0.675770i | \(-0.763811\pi\) | ||
0.737113 | − | 0.675770i | \(-0.236189\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.2568i | 1.31415i | 0.753824 | + | 0.657076i | \(0.228207\pi\) | ||||
−0.753824 | + | 0.657076i | \(0.771793\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 19.3551 | + | 3.33173i | 1.38604 | + | 0.238590i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.28939 | 0.376853 | 0.188427 | − | 0.982087i | \(-0.439661\pi\) | ||||
0.188427 | + | 0.982087i | \(0.439661\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.33067i | 0.377881i | 0.981988 | + | 0.188941i | \(0.0605054\pi\) | ||||
−0.981988 | + | 0.188941i | \(0.939495\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.63559 | + | 10.2810i | −0.326969 | + | 0.725166i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.2740 | + | 4.46835i | −1.20647 | + | 0.312083i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.21983 | − | 8.17206i | −0.501813 | − | 0.567998i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.340965 | −0.0235850 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.2924 | −1.39698 | −0.698492 | − | 0.715618i | \(-0.746145\pi\) | ||||
−0.698492 | + | 0.715618i | \(0.746145\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.58668 | + | 3.51901i | −0.108718 | + | 0.241119i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.45243 | − | 5.61488i | −0.0990546 | − | 0.382932i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −20.6226 | − | 9.29849i | −1.39355 | − | 0.628334i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 14.7457i | − | 0.991901i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −27.4665 | −1.83929 | −0.919645 | − | 0.392750i | \(-0.871524\pi\) | ||||
−0.919645 | + | 0.392750i | \(0.871524\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.1366 | + | 5.01550i | 0.942443 | + | 0.334367i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 5.40469i | − | 0.358722i | −0.983783 | − | 0.179361i | \(-0.942597\pi\) | ||
0.983783 | − | 0.179361i | \(-0.0574029\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.74357i | 0.313464i | 0.987641 | + | 0.156732i | \(0.0500958\pi\) | ||||
−0.987641 | + | 0.156732i | \(0.949904\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.81595 | −0.118967 | −0.0594834 | − | 0.998229i | \(-0.518945\pi\) | ||||
−0.0594834 | + | 0.998229i | \(0.518945\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.86120 | − | 26.5245i | −0.447575 | − | 1.73027i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.82004 | + | 2.62419i | 0.378052 | + | 0.170459i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 16.5077i | − | 1.06779i | −0.845549 | − | 0.533897i | \(-0.820727\pi\) | ||
0.845549 | − | 0.533897i | \(-0.179273\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.6532i | 1.00831i | 0.863612 | + | 0.504156i | \(0.168196\pi\) | ||||
−0.863612 | + | 0.504156i | \(0.831804\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.11021 | − | 13.3126i | 0.520270 | − | 0.854002i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 0.786528i | − | 0.0500456i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.74368 | + | 21.6100i | −0.617481 | + | 1.36948i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.9733 | −1.45006 | −0.725031 | − | 0.688716i | \(-0.758175\pi\) | ||||
−0.725031 | + | 0.688716i | \(0.758175\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 7.99044i | − | 0.502354i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.91053 | − | 11.0989i | 0.119642 | − | 0.695040i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.08162i | 0.566496i | 0.959047 | + | 0.283248i | \(0.0914120\pi\) | ||||
−0.959047 | + | 0.283248i | \(0.908588\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.74246 | − | 7.72376i | 0.541144 | − | 0.478089i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.1174 | 1.11717 | 0.558584 | − | 0.829448i | \(-0.311345\pi\) | ||||
0.558584 | + | 0.829448i | \(0.311345\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.4035 | − | 5.27785i | 1.25337 | − | 0.324216i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −17.8898 | − | 8.06632i | −1.09484 | − | 0.493650i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.7746 | −1.14471 | −0.572353 | − | 0.820007i | \(-0.693969\pi\) | ||||
−0.572353 | + | 0.820007i | \(0.693969\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.5534i | 1.06629i | 0.846022 | + | 0.533147i | \(0.178991\pi\) | ||||
−0.846022 | + | 0.533147i | \(0.821009\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.32979 | + | 9.61278i | 0.321398 | + | 0.579672i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 19.2815i | − | 1.15851i | −0.815145 | − | 0.579257i | \(-0.803343\pi\) | ||
0.815145 | − | 0.579257i | \(-0.196657\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 22.0293 | − | 19.4624i | 1.31886 | − | 1.16518i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6.16244i | − | 0.367620i | −0.982962 | − | 0.183810i | \(-0.941157\pi\) | ||
0.982962 | − | 0.183810i | \(-0.0588432\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.2606 | 1.38270 | 0.691350 | − | 0.722520i | \(-0.257016\pi\) | ||||
0.691350 | + | 0.722520i | \(0.257016\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.101907 | − | 0.592010i | 0.00603645 | − | 0.0350677i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.54429 | 0.502605 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.73880 | − | 1.23490i | −0.160552 | − | 0.0723909i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 30.1092i | 1.75900i | 0.475900 | + | 0.879499i | \(0.342122\pi\) | ||||
−0.475900 | + | 0.879499i | \(0.657878\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.7348 | − | 3.81151i | 0.857892 | − | 0.221915i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 10.9124 | − | 3.37583i | 0.633203 | − | 0.195885i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 18.4321 | 1.06596 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 21.6294 | + | 9.75247i | 1.24258 | + | 0.560265i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.90408 | − | 15.0926i | −0.223547 | − | 0.864203i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.575026 | 0.0328185 | 0.0164092 | − | 0.999865i | \(-0.494777\pi\) | ||||
0.0164092 | + | 0.999865i | \(0.494777\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.9246 | + | 6.72934i | 0.849032 | + | 0.382819i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.04265 | −0.399352 | −0.199676 | − | 0.979862i | \(-0.563989\pi\) | ||||
−0.199676 | + | 0.979862i | \(0.563989\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.21607 | 0.464400 | 0.232200 | − | 0.972668i | \(-0.425408\pi\) | ||||
0.232200 | + | 0.972668i | \(0.425408\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −29.0153 | −1.62966 | −0.814832 | − | 0.579698i | \(-0.803171\pi\) | ||||
−0.814832 | + | 0.579698i | \(0.803171\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.54815 | 0.478605 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.95648 | + | 1.33304i | 0.165015 | + | 0.0744033i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.451024 | −0.0250956 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −22.1745 | + | 12.2946i | −1.23002 | + | 0.681981i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.1160 | + | 5.46298i | 0.670018 | + | 0.302103i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.92177 | 0.105630 | 0.0528150 | − | 0.998604i | \(-0.483181\pi\) | ||||
0.0528150 | + | 0.998604i | \(0.483181\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.02197 | + | 7.97070i | −0.494401 | + | 0.436792i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.64616 | − | 14.0956i | −0.199211 | − | 0.770123i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 23.9897i | − | 1.30680i | −0.757011 | − | 0.653402i | \(-0.773341\pi\) | ||
0.757011 | − | 0.653402i | \(-0.226659\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.34517 | + | 2.41007i | 0.290310 | + | 0.130897i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.5397 | 1.16644 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 13.8736 | + | 2.38817i | 0.746931 | + | 0.128575i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.5388 | −0.995213 | −0.497606 | − | 0.867403i | \(-0.665788\pi\) | ||||
−0.497606 | + | 0.867403i | \(0.665788\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.7711i | 1.37949i | 0.724051 | + | 0.689747i | \(0.242278\pi\) | ||||
−0.724051 | + | 0.689747i | \(0.757722\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.78725 | + | 25.1724i | 0.415653 | + | 1.34361i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.1537i | 0.646874i | 0.946250 | + | 0.323437i | \(0.104838\pi\) | ||||
−0.946250 | + | 0.323437i | \(0.895162\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.24802 | − | 4.82467i | −0.0662379 | − | 0.256067i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.0223i | 1.10952i | 0.832011 | + | 0.554759i | \(0.187189\pi\) | ||||
−0.832011 | + | 0.554759i | \(0.812811\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9759 | 0.998734 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.73831 | − | 4.39089i | −0.511129 | − | 0.230462i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 28.2742 | − | 7.31381i | 1.47994 | − | 0.382822i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.5306 | −1.22829 | −0.614145 | − | 0.789194i | \(-0.710499\pi\) | ||||
−0.614145 | + | 0.789194i | \(0.710499\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −15.8495 | − | 17.9399i | −0.825090 | − | 0.933913i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 35.8517i | 1.85633i | 0.372166 | + | 0.928166i | \(0.378615\pi\) | ||||
−0.372166 | + | 0.928166i | \(0.621385\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −18.2834 | + | 6.38095i | −0.944152 | + | 0.329511i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19.7186i | 1.01556i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.3860 | −0.636227 | −0.318114 | − | 0.948053i | \(-0.603049\pi\) | ||||
−0.318114 | + | 0.948053i | \(0.603049\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.30013 | − | 18.4084i | 0.425229 | − | 0.943090i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.7586i | 0.805226i | 0.915370 | + | 0.402613i | \(0.131898\pi\) | ||||
−0.915370 | + | 0.402613i | \(0.868102\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.83131 | − | 5.15183i | 0.296422 | − | 0.261882i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 13.9576i | − | 0.707681i | −0.935306 | − | 0.353840i | \(-0.884876\pi\) | ||
0.935306 | − | 0.353840i | \(-0.115124\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 10.5696i | − | 0.534530i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.8641 | − | 7.15294i | −0.800238 | − | 0.360818i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.97945 | + | 2.06408i | −0.401490 | + | 0.103855i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.75124 | −0.188269 | −0.0941347 | − | 0.995559i | \(-0.530008\pi\) | ||||
−0.0941347 | + | 0.995559i | \(0.530008\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 7.09180i | − | 0.354147i | −0.984198 | − | 0.177074i | \(-0.943337\pi\) | ||
0.984198 | − | 0.177074i | \(-0.0566631\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 49.6871i | 2.47509i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.59989 | + | 19.9560i | 0.129189 | + | 0.991620i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.82146 | −0.437263 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 13.3712i | − | 0.661163i | −0.943777 | − | 0.330582i | \(-0.892755\pi\) | ||
0.943777 | − | 0.330582i | \(-0.107245\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −30.6683 | − | 13.8280i | −1.51275 | − | 0.682084i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.66398 | − | 29.6279i | −0.376210 | − | 1.45438i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.35798 | − | 7.44748i | 0.164441 | − | 0.364705i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.5013 | −1.00155 | −0.500777 | − | 0.865576i | \(-0.666952\pi\) | ||||
−0.500777 | + | 0.865576i | \(0.666952\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.45042 | −0.411848 | −0.205924 | − | 0.978568i | \(-0.566020\pi\) | ||||
−0.205924 | + | 0.978568i | \(0.566020\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 27.5469 | − | 24.3370i | 1.33938 | − | 1.18331i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.05017 | + | 12.7157i | 0.341984 | + | 0.616800i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.93629 | + | 17.6014i | −0.383168 | + | 0.849806i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.9646i | 0.720820i | 0.932794 | + | 0.360410i | \(0.117363\pi\) | ||||
−0.932794 | + | 0.360410i | \(0.882637\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.78058 | −0.0855692 | −0.0427846 | − | 0.999084i | \(-0.513623\pi\) | ||||
−0.0427846 | + | 0.999084i | \(0.513623\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.55486 | + | 14.8420i | −0.122496 | + | 0.711618i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 0.563780i | − | 0.0269693i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 33.2628i | 1.58755i | 0.608213 | + | 0.793774i | \(0.291887\pi\) | ||||
−0.608213 | + | 0.793774i | \(0.708113\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 35.4666 | 1.68507 | 0.842535 | − | 0.538641i | \(-0.181062\pi\) | ||||
0.842535 | + | 0.538641i | \(0.181062\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 24.5275 | − | 6.34463i | 1.16271 | − | 0.300764i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.82573 | + | 4.04918i | −0.0863541 | + | 0.191520i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 22.2177i | − | 1.04852i | −0.851559 | − | 0.524258i | \(-0.824343\pi\) | ||
0.851559 | − | 0.524258i | \(-0.175657\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 17.5412i | − | 0.825981i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.49843 | + | 3.83185i | 0.399291 | + | 0.180036i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 38.6337i | − | 1.80721i | −0.428368 | − | 0.903604i | \(-0.640911\pi\) | ||
0.428368 | − | 0.903604i | \(-0.359089\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14.4348 | − | 4.46550i | 0.673759 | − | 0.208432i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.3198 | −1.31898 | −0.659491 | − | 0.751712i | \(-0.729228\pi\) | ||||
−0.659491 | + | 0.751712i | \(0.729228\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 0.569792i | − | 0.0264805i | −0.999912 | − | 0.0132402i | \(-0.995785\pi\) | ||
0.999912 | − | 0.0132402i | \(-0.00421462\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.43775 | + | 37.3989i | −0.298543 | + | 1.73433i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 32.2741i | 1.49347i | 0.665123 | + | 0.746734i | \(0.268379\pi\) | ||||
−0.665123 | + | 0.746734i | \(0.731621\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.07595 | + | 4.09224i | 0.418198 | + | 0.188561i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.70171 | 0.262165 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.376053 | + | 0.678247i | 0.0172545 | + | 0.0311201i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.7208 | + | 21.1899i | 0.857167 | + | 0.970220i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 42.9641 | 1.96308 | 0.981541 | − | 0.191253i | \(-0.0612552\pi\) | ||||
0.981541 | + | 0.191253i | \(0.0612552\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 20.3491i | − | 0.927838i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.75498 | − | 0.971318i | 0.170505 | − | 0.0441053i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.3089i | 0.920284i | 0.887845 | + | 0.460142i | \(0.152201\pi\) | ||||
−0.887845 | + | 0.460142i | \(0.847799\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.64841 | − | 3.65592i | 0.0745438 | − | 0.165326i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 27.4781i | − | 1.24007i | −0.784574 | − | 0.620036i | \(-0.787118\pi\) | ||
0.784574 | − | 0.620036i | \(-0.212882\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.3074 | 0.509259 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.25410 | + | 12.2201i | −0.370994 | + | 0.549254i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.6767 | 1.64188 | 0.820938 | − | 0.571017i | \(-0.193451\pi\) | ||||
0.820938 | + | 0.571017i | \(0.193451\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.4931 | + | 32.1433i | −0.647503 | + | 1.43606i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.23782i | 0.144367i | 0.997391 | + | 0.0721837i | \(0.0229968\pi\) | ||||
−0.997391 | + | 0.0721837i | \(0.977003\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −29.6546 | + | 7.67089i | −1.31961 | + | 0.341350i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −20.0759 | − | 9.05199i | −0.891602 | − | 0.402013i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.0171 | −0.576975 | −0.288487 | − | 0.957484i | \(-0.593152\pi\) | ||||
−0.288487 | + | 0.957484i | \(0.593152\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.769946 | − | 0.238188i | 0.0339939 | − | 0.0105162i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −20.4621 | + | 5.29302i | −0.901668 | + | 0.233239i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26.9346 | 1.18458 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.4672 | + | 34.3038i | −0.678934 | + | 1.50577i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.53166 | −0.373779 | −0.186889 | − | 0.982381i | \(-0.559841\pi\) | ||||
−0.186889 | + | 0.982381i | \(0.559841\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.3558 | 1.19618 | 0.598092 | − | 0.801427i | \(-0.295926\pi\) | ||||
0.598092 | + | 0.801427i | \(0.295926\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28.4924 | 1.24115 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.78794 | −0.425563 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.5196 | + | 15.3027i | 0.586702 | + | 0.664083i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 40.4634 | 1.75267 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.05343 | + | 1.04852i | −0.175245 | + | 0.0453314i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.0512 | + | 26.7277i | −0.520049 | + | 1.15339i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.53907 | −0.238143 | −0.119072 | − | 0.992886i | \(-0.537992\pi\) | ||||
−0.119072 | + | 0.992886i | \(0.537992\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17.4816 | + | 38.7713i | −0.750205 | + | 1.66384i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.6114 | + | 4.29695i | −0.711556 | + | 0.184061i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.1333i | 1.16014i | 0.814568 | + | 0.580068i | \(0.196974\pi\) | ||||
−0.814568 | + | 0.580068i | \(0.803026\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.6744 | − | 13.8480i | 0.668968 | − | 0.591017i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.603131 | 0.0256942 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.63654 | − | 15.3165i | 0.111915 | − | 0.650150i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −36.8859 | −1.56291 | −0.781453 | − | 0.623964i | \(-0.785521\pi\) | ||||
−0.781453 | + | 0.623964i | \(0.785521\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.1525i | 0.556293i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.0933 | + | 4.55096i | 0.426140 | + | 0.192142i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 32.8085i | − | 1.38271i | −0.722513 | − | 0.691357i | \(-0.757013\pi\) | ||
0.722513 | − | 0.691357i | \(-0.242987\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.32838 | + | 1.89567i | −0.308307 | + | 0.0797512i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 14.2653i | − | 0.598032i | −0.954248 | − | 0.299016i | \(-0.903342\pi\) | ||
0.954248 | − | 0.299016i | \(-0.0966584\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.8302 | −0.453229 | −0.226614 | − | 0.973985i | \(-0.572766\pi\) | ||||
−0.226614 | + | 0.973985i | \(0.572766\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.2981 | + | 29.4930i | −0.555534 | + | 1.23209i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15.8946 | + | 8.81272i | −0.662849 | + | 0.367516i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.4905 | 1.10281 | 0.551407 | − | 0.834236i | \(-0.314091\pi\) | ||||
0.551407 | + | 0.834236i | \(0.314091\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.9977 | − | 28.8269i | 0.540167 | − | 1.19800i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.7190i | 0.858092i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −28.1890 | − | 19.0403i | −1.16547 | − | 0.787220i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 18.9901i | − | 0.783804i | −0.920007 | − | 0.391902i | \(-0.871817\pi\) | ||
0.920007 | − | 0.391902i | \(-0.128183\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.51977 | 0.0626211 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.35178 | − | 3.76572i | −0.343546 | − | 0.154901i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 31.5973i | 1.29754i | 0.760983 | + | 0.648772i | \(0.224717\pi\) | ||||
−0.760983 | + | 0.648772i | \(0.775283\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.79512 | − | 8.41697i | 0.155324 | − | 0.344484i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.72344i | 0.0704178i | 0.999380 | + | 0.0352089i | \(0.0112097\pi\) | ||||
−0.999380 | + | 0.0352089i | \(0.988790\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.9659i | 1.71183i | 0.517120 | + | 0.855913i | \(0.327004\pi\) | ||||
−0.517120 | + | 0.855913i | \(0.672996\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.6389 | − | 12.9331i | 0.596142 | − | 0.526678i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.3515 | − | 3.45370i | 0.542817 | − | 0.140413i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.99600 | 0.324548 | 0.162274 | − | 0.986746i | \(-0.448117\pi\) | ||||
0.162274 | + | 0.986746i | \(0.448117\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 62.1320i | 2.51359i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 35.9232i | 1.45092i | 0.688262 | + | 0.725462i | \(0.258374\pi\) | ||||
−0.688262 | + | 0.725462i | \(0.741626\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 30.4563 | + | 5.24267i | 1.22812 | + | 0.211405i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.5615 | 0.586225 | 0.293112 | − | 0.956078i | \(-0.405309\pi\) | ||||
0.293112 | + | 0.956078i | \(0.405309\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.7421i | 1.07486i | 0.843309 | + | 0.537429i | \(0.180604\pi\) | ||||
−0.843309 | + | 0.537429i | \(0.819396\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.58187 | + | 18.0435i | 0.223993 | + | 0.724061i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.2435 | − | 21.2040i | 0.529739 | − | 0.848161i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.538373 | + | 0.242746i | 0.0215005 | + | 0.00969435i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11.6689 | −0.465270 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.0412 | 1.19592 | 0.597961 | − | 0.801525i | \(-0.295978\pi\) | ||||
0.597961 | + | 0.801525i | \(0.295978\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 32.0410 | + | 14.4469i | 1.27352 | + | 0.574214i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.52854 | + | 25.2384i | 0.259077 | + | 1.00156i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.01064 | − | 4.42679i | 0.198218 | − | 0.175121i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 38.9572i | − | 1.53872i | −0.638818 | − | 0.769358i | \(-0.720576\pi\) | ||
0.638818 | − | 0.769358i | \(-0.279424\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −33.9814 | −1.34010 | −0.670049 | − | 0.742317i | \(-0.733727\pi\) | ||||
−0.670049 | + | 0.742317i | \(0.733727\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.70412 | + | 9.89976i | −0.0670996 | + | 0.389803i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.1558i | 0.438579i | 0.975660 | + | 0.219289i | \(0.0703738\pi\) | ||||
−0.975660 | + | 0.219289i | \(0.929626\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.9626i | 0.587335i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.4880 | 0.919157 | 0.459579 | − | 0.888137i | \(-0.348000\pi\) | ||||
0.459579 | + | 0.888137i | \(0.348000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.7502 | − | 5.62621i | 0.849849 | − | 0.219834i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 25.9425 | + | 29.3641i | 1.01211 | + | 1.14560i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 8.07402i | − | 0.314519i | −0.987557 | − | 0.157259i | \(-0.949734\pi\) | ||
0.987557 | − | 0.157259i | \(-0.0502659\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 15.4885i | − | 0.602433i | −0.953556 | − | 0.301217i | \(-0.902607\pi\) | ||
0.953556 | − | 0.301217i | \(-0.0973927\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.4980 | + | 23.2830i | −0.407709 | + | 0.904235i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.1342i | 0.547280i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 43.3687 | + | 19.5545i | 1.67673 | + | 0.756019i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.3260 | 0.591655 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.4028i | 0.593735i | 0.954919 | + | 0.296867i | \(0.0959419\pi\) | ||||
−0.954919 | + | 0.296867i | \(0.904058\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −18.7506 | − | 17.9838i | −0.721710 | − | 0.692195i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.1263i | 0.773518i | 0.922181 | + | 0.386759i | \(0.126405\pi\) | ||||
−0.922181 | + | 0.386759i | \(0.873595\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.84781 | + | 8.53383i | −0.147448 | + | 0.327017i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.80121 | 0.336769 | 0.168384 | − | 0.985721i | \(-0.446145\pi\) | ||||
0.168384 | + | 0.985721i | \(0.446145\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 42.0471 | − | 10.8765i | 1.60654 | − | 0.415570i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.37713 | − | 7.48994i | 0.128846 | − | 0.285759i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −47.7939 | −1.82080 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 36.3368i | − | 1.38232i | −0.722703 | − | 0.691159i | \(-0.757100\pi\) | ||
0.722703 | − | 0.691159i | \(-0.242900\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.64125 | + | 10.2107i | 0.100188 | + | 0.387315i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 23.2032i | − | 0.878884i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.86733 | + | 1.29285i | 0.108452 | + | 0.0488999i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.52551i | 0.284235i | 0.989850 | + | 0.142117i | \(0.0453910\pi\) | ||||
−0.989850 | + | 0.142117i | \(0.954609\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.622414 | −0.0234748 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.05018 | + | 46.7661i | −0.303187 | + | 1.76131i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.9451 | −0.411051 | −0.205525 | − | 0.978652i | \(-0.565890\pi\) | ||||
−0.205525 | + | 0.978652i | \(0.565890\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.32140 | − | 8.28703i | −0.274574 | − | 0.310788i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 35.6155i | 1.33381i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.24236 | − | 24.1321i | −0.233451 | − | 0.902490i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.7525 | + | 26.0652i | −0.438905 | + | 0.973421i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.4203 | 0.612373 | 0.306186 | − | 0.951972i | \(-0.400947\pi\) | ||||
0.306186 | + | 0.951972i | \(0.400947\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.1441 | − | 24.7160i | 0.414455 | − | 0.919196i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.42783 | − | 17.0040i | −0.350141 | − | 0.631512i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.1583 | 1.11851 | 0.559254 | − | 0.828996i | \(-0.311088\pi\) | ||||
0.559254 | + | 0.828996i | \(0.311088\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.2835 | + | 15.2462i | −0.825315 | + | 0.564673i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.54215 | 0.278956 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.2975 | 1.52536 | 0.762680 | − | 0.646776i | \(-0.223883\pi\) | ||||
0.762680 | + | 0.646776i | \(0.223883\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.3135 | 0.527246 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −48.0567 | −1.76779 | −0.883897 | − | 0.467682i | \(-0.845089\pi\) | ||||
−0.883897 | + | 0.467682i | \(0.845089\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.559960 | + | 1.24190i | −0.0205706 | + | 0.0456224i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.1299 | −0.921927 | −0.460964 | − | 0.887419i | \(-0.652496\pi\) | ||||
−0.460964 | + | 0.887419i | \(0.652496\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.43604 | − | 5.55155i | −0.0526126 | − | 0.203393i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 30.7699 | − | 27.1845i | 1.12581 | − | 0.994630i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.37050 | −0.0865008 | −0.0432504 | − | 0.999064i | \(-0.513771\pi\) | ||||
−0.0432504 | + | 0.999064i | \(0.513771\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 36.2741 | + | 16.3556i | 1.32190 | + | 0.596031i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.6516 | + | 3.01397i | −0.424045 | + | 0.109690i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 43.4331i | − | 1.57860i | −0.614006 | − | 0.789301i | \(-0.710443\pi\) | ||
0.614006 | − | 0.789301i | \(-0.289557\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.68870 | + | 12.6166i | −0.206487 | + | 0.457955i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.7460 | −1.11454 | −0.557271 | − | 0.830331i | \(-0.688152\pi\) | ||||
−0.557271 | + | 0.830331i | \(0.688152\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.9184 | + | 16.1646i | −0.394756 | + | 0.584433i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −34.5154 | −1.24628 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 22.3354i | − | 0.805435i | −0.915324 | − | 0.402717i | \(-0.868066\pi\) | ||
0.915324 | − | 0.402717i | \(-0.131934\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.46556 | − | 14.3396i | 0.232852 | − | 0.516428i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 29.0010i | − | 1.04309i | −0.853222 | − | 0.521547i | \(-0.825355\pi\) | ||
0.853222 | − | 0.521547i | \(-0.174645\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −23.7563 | − | 42.8467i | −0.853351 | − | 1.53910i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 1.23765i | − | 0.0443434i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.89928 | 0.175310 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −19.3029 | + | 5.97148i | −0.689830 | + | 0.213403i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.4434 | + | 3.21879i | −0.444124 | + | 0.114884i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.8511 | −0.957140 | −0.478570 | − | 0.878050i | \(-0.658845\pi\) | ||||
−0.478570 | + | 0.878050i | \(0.658845\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −28.6068 | − | 12.8985i | −1.01843 | − | 0.459198i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 35.3537i | 1.25545i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −35.9739 | − | 6.19246i | −1.27586 | − | 0.219624i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.6894i | 0.449480i | 0.974419 | + | 0.224740i | \(0.0721533\pi\) | ||||
−0.974419 | + | 0.224740i | \(0.927847\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 35.6288 | 1.26046 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 22.5047 | + | 25.4729i | 0.795166 | + | 0.900041i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 28.7114i | 1.01320i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 29.6445 | + | 13.3664i | 1.04353 | + | 0.470518i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.38958i | 0.0840133i | 0.999117 | + | 0.0420067i | \(0.0133751\pi\) | ||||
−0.999117 | + | 0.0420067i | \(0.986625\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 26.9826i | − | 0.947486i | −0.880663 | − | 0.473743i | \(-0.842903\pi\) | ||
0.880663 | − | 0.473743i | \(-0.157097\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.4970 | − | 27.7163i | 0.438288 | − | 0.972054i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.29657 | + | 5.01237i | 0.0454170 | + | 0.175576i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.402295 | 0.0140745 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 31.1133i | − | 1.08586i | −0.839778 | − | 0.542930i | \(-0.817315\pi\) | ||
0.839778 | − | 0.542930i | \(-0.182685\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.4887i | 0.609616i | 0.952414 | + | 0.304808i | \(0.0985923\pi\) | ||||
−0.952414 | + | 0.304808i | \(0.901408\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.57186 | − | 18.9728i | −0.0547250 | − | 0.660547i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.1404 | 0.839445 | 0.419722 | − | 0.907653i | \(-0.362127\pi\) | ||||
0.419722 | + | 0.907653i | \(0.362127\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 23.2654i | − | 0.808042i | −0.914750 | − | 0.404021i | \(-0.867612\pi\) | ||
0.914750 | − | 0.404021i | \(-0.132388\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.7273 | + | 30.4449i | −0.476193 | + | 1.05612i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.3996 | − | 44.0695i | −0.394501 | − | 1.52509i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −48.6396 | + | 15.0470i | −1.68123 | + | 0.520099i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.2640 | −0.699593 | −0.349796 | − | 0.936826i | \(-0.613749\pi\) | ||||
−0.349796 | + | 0.936826i | \(0.613749\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.8792 | 0.478594 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.38728 | + | 9.73030i | −0.151106 | + | 0.335129i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 27.5247 | − | 7.11993i | 0.946877 | − | 0.244933i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −36.7278 | − | 16.5601i | −1.26049 | − | 0.568343i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 14.5861i | − | 0.500006i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.3638 | −0.560288 | −0.280144 | − | 0.959958i | \(-0.590382\pi\) | ||||
−0.280144 | + | 0.959958i | \(0.590382\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.582383 | + | 0.862214i | −0.0199171 | + | 0.0294871i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30.8994i | 1.05550i | 0.849398 | + | 0.527752i | \(0.176965\pi\) | ||||
−0.849398 | + | 0.527752i | \(0.823035\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 49.7980i | 1.69909i | 0.527520 | + | 0.849543i | \(0.323122\pi\) | ||||
−0.527520 | + | 0.849543i | \(0.676878\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.00483 | −0.0682451 | −0.0341225 | − | 0.999418i | \(-0.510864\pi\) | ||||
−0.0341225 | + | 0.999418i | \(0.510864\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.1658 | − | 47.0315i | −0.413651 | − | 1.59912i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.4912 | − | 6.08301i | −0.458184 | − | 0.206590i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 8.10285i | − | 0.274870i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.0180i | 1.11877i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.44532 | + | 3.89972i | 0.116606 | + | 0.131986i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 37.4955i | − | 1.26613i | −0.774097 | − | 0.633067i | \(-0.781796\pi\) | ||
0.774097 | − | 0.633067i | \(-0.218204\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 21.4359 | − | 47.5415i | 0.723016 | − | 1.60354i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.7858 | 1.50887 | 0.754436 | − | 0.656374i | \(-0.227911\pi\) | ||||
0.754436 | + | 0.656374i | \(0.227911\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 5.59317i | − | 0.188225i | −0.995562 | − | 0.0941127i | \(-0.969999\pi\) | ||
0.995562 | − | 0.0941127i | \(-0.0300014\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −25.9793 | − | 4.47201i | −0.873285 | − | 0.150325i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 12.4118i | − | 0.416748i | −0.978049 | − | 0.208374i | \(-0.933183\pi\) | ||
0.978049 | − | 0.208374i | \(-0.0668171\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −19.6338 | − | 2.43866i | −0.657756 | − | 0.0816981i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.90042 | 0.0635952 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.47900 | − | 36.6445i | −0.316848 | − | 1.22489i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −29.1037 | − | 13.1225i | −0.971745 | − | 0.438149i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −38.1014 | −1.27075 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.4068i | 0.913052i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.7503 | − | 53.1567i | −0.457074 | − | 1.76699i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 39.7981i | − | 1.32147i | −0.750617 | − | 0.660737i | \(-0.770244\pi\) | ||
0.750617 | − | 0.660737i | \(-0.229756\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −27.2091 | − | 30.7977i | −0.902467 | − | 1.02150i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 32.2818i | − | 1.06954i | −0.844996 | − | 0.534772i | \(-0.820398\pi\) | ||
0.844996 | − | 0.534772i | \(-0.179602\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30.0861 | 0.995704 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.58062 | + | 26.6103i | −0.151431 | + | 0.879709i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.6592 | 0.714471 | 0.357235 | − | 0.934014i | \(-0.383719\pi\) | ||||
0.357235 | + | 0.934014i | \(0.383719\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.907948 | − | 0.409384i | −0.0299179 | − | 0.0134896i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.3015i | 0.371994i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.72926 | + | 17.5476i | 0.319896 | + | 0.576963i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −18.7746 | − | 21.2509i | −0.616640 | − | 0.697970i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −36.8987 | −1.21061 | −0.605303 | − | 0.795995i | \(-0.706948\pi\) | ||||
−0.605303 | + | 0.795995i | \(0.706948\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.1201 | + | 5.01394i | 0.364057 | + | 0.164149i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13.8382 | + | 3.57960i | −0.452559 | + | 0.117065i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39.9185 | −1.30408 | −0.652041 | − | 0.758184i | \(-0.726087\pi\) | ||||
−0.652041 | + | 0.758184i | \(0.726087\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.9729 | − | 5.84934i | −0.423355 | − | 0.190886i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 50.6169 | 1.65006 | 0.825032 | − | 0.565086i | \(-0.191157\pi\) | ||||
0.825032 | + | 0.565086i | \(0.191157\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29.0040 | 0.944501 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 31.8954 | 1.03646 | 0.518230 | − | 0.855241i | \(-0.326591\pi\) | ||||
0.518230 | + | 0.855241i | \(0.326591\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −66.2307 | −2.14994 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 45.8143 | + | 20.6572i | 1.48563 | + | 0.669854i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.68959 | 0.119518 | 0.0597588 | − | 0.998213i | \(-0.480967\pi\) | ||||
0.0597588 | + | 0.998213i | \(0.480967\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.4597 | − | 40.4358i | −0.338468 | − | 1.30847i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −13.4973 | − | 6.08577i | −0.436305 | − | 0.196725i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −65.0081 | −2.09704 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.71915 | − | 4.20967i | −0.119848 | − | 0.135655i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.2235 | + | 39.5226i | 0.329105 | + | 1.27228i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.8775i | 1.41100i | 0.708708 | + | 0.705502i | \(0.249279\pi\) | ||||
−0.708708 | + | 0.705502i | \(0.750721\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.712153 | + | 0.321102i | 0.0228776 | + | 0.0103153i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.6348 | 0.886842 | 0.443421 | − | 0.896313i | \(-0.353765\pi\) | ||||
0.443421 | + | 0.896313i | \(0.353765\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 43.7658 | − | 3.62591i | 1.40163 | − | 0.116122i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 48.8293 | 1.56219 | 0.781094 | − | 0.624413i | \(-0.214662\pi\) | ||||
0.781094 | + | 0.624413i | \(0.214662\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.9068i | 0.796024i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.2415 | − | 17.2517i | −0.486624 | − | 0.550806i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 20.9766i | − | 0.669050i | −0.942387 | − | 0.334525i | \(-0.891424\pi\) | ||
0.942387 | − | 0.334525i | \(-0.108576\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.4505 | − | 2.96196i | 0.364845 | − | 0.0943760i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.42769i | 0.299783i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.7338 | 0.912759 | 0.456379 | − | 0.889785i | \(-0.349146\pi\) | ||||
0.456379 | + | 0.889785i | \(0.349146\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.03442 | − | 1.36818i | −0.0962943 | − | 0.0434180i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.98508 | + | 11.5399i | 0.0946334 | + | 0.365840i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.2318 | −0.482395 | −0.241198 | − | 0.970476i | \(-0.577540\pi\) | ||||
−0.241198 | + | 0.970476i | \(0.577540\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 19.9201 | − | 6.16240i | 0.630243 | − | 0.194970i |
(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 | 2940.2.f.b.1469.6 | yes | 48 | |
3.2 | odd | 2 | inner | 2940.2.f.b.1469.7 | yes | 48 | |
5.4 | even | 2 | inner | 2940.2.f.b.1469.44 | yes | 48 | |
7.6 | odd | 2 | inner | 2940.2.f.b.1469.43 | yes | 48 | |
15.14 | odd | 2 | inner | 2940.2.f.b.1469.41 | yes | 48 | |
21.20 | even | 2 | inner | 2940.2.f.b.1469.42 | yes | 48 | |
35.34 | odd | 2 | inner | 2940.2.f.b.1469.5 | ✓ | 48 | |
105.104 | even | 2 | inner | 2940.2.f.b.1469.8 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2940.2.f.b.1469.5 | ✓ | 48 | 35.34 | odd | 2 | inner | |
2940.2.f.b.1469.6 | yes | 48 | 1.1 | even | 1 | trivial | |
2940.2.f.b.1469.7 | yes | 48 | 3.2 | odd | 2 | inner | |
2940.2.f.b.1469.8 | yes | 48 | 105.104 | even | 2 | inner | |
2940.2.f.b.1469.41 | yes | 48 | 15.14 | odd | 2 | inner | |
2940.2.f.b.1469.42 | yes | 48 | 21.20 | even | 2 | inner | |
2940.2.f.b.1469.43 | yes | 48 | 7.6 | odd | 2 | inner | |
2940.2.f.b.1469.44 | yes | 48 | 5.4 | even | 2 | inner |