Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,4,Mod(337,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.337");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(29.9139683729\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{18} + 112 x^{16} + 5026 x^{14} + 114847 x^{12} + 1397921 x^{10} + 8545747 x^{8} + 21033277 x^{6} + 6703200 x^{4} + 137781 x^{2} + 729 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 13^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.6 | ||
Root | \(-5.06791i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.337 |
Dual form | 507.4.b.k.337.13 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.82093i | − 0.997349i | −0.866789 | − | 0.498674i | \(-0.833820\pi\) | ||||
0.866789 | − | 0.498674i | \(-0.166180\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0.0423641 | 0.00529552 | ||||||||
\(5\) | − 3.41089i | − 0.305079i | −0.988297 | − | 0.152539i | \(-0.951255\pi\) | ||||
0.988297 | − | 0.152539i | \(-0.0487451\pi\) | |||||||
\(6\) | − 8.46278i | − 0.575820i | ||||||||
\(7\) | − 13.3442i | − 0.720518i | −0.932852 | − | 0.360259i | \(-0.882688\pi\) | ||||
0.932852 | − | 0.360259i | \(-0.117312\pi\) | |||||||
\(8\) | − 22.6869i | − 1.00263i | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −9.62187 | −0.304270 | ||||||||
\(11\) | − 35.4529i | − 0.971769i | −0.874023 | − | 0.485885i | \(-0.838498\pi\) | ||||
0.874023 | − | 0.485885i | \(-0.161502\pi\) | |||||||
\(12\) | 0.127092 | 0.00305737 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −37.6430 | −0.718607 | ||||||||
\(15\) | − 10.2327i | − 0.176137i | ||||||||
\(16\) | −63.6593 | −0.994676 | ||||||||
\(17\) | −69.6526 | −0.993720 | −0.496860 | − | 0.867831i | \(-0.665514\pi\) | ||||
−0.496860 | + | 0.867831i | \(0.665514\pi\) | |||||||
\(18\) | − 25.3884i | − 0.332450i | ||||||||
\(19\) | 12.4014i | 0.149740i | 0.997193 | + | 0.0748701i | \(0.0238542\pi\) | ||||
−0.997193 | + | 0.0748701i | \(0.976146\pi\) | |||||||
\(20\) | − 0.144499i | − 0.00161555i | ||||||||
\(21\) | − 40.0325i | − 0.415991i | ||||||||
\(22\) | −100.010 | −0.969193 | ||||||||
\(23\) | 126.251 | 1.14457 | 0.572287 | − | 0.820053i | \(-0.306056\pi\) | ||||
0.572287 | + | 0.820053i | \(0.306056\pi\) | |||||||
\(24\) | − 68.0608i | − 0.578869i | ||||||||
\(25\) | 113.366 | 0.906927 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | − 0.565314i | − 0.00381551i | ||||||||
\(29\) | −179.060 | −1.14657 | −0.573286 | − | 0.819356i | \(-0.694331\pi\) | ||||
−0.573286 | + | 0.819356i | \(0.694331\pi\) | |||||||
\(30\) | −28.8656 | −0.175670 | ||||||||
\(31\) | 255.935i | 1.48281i | 0.671055 | + | 0.741407i | \(0.265841\pi\) | ||||
−0.671055 | + | 0.741407i | \(0.734159\pi\) | |||||||
\(32\) | − 1.91716i | − 0.0105909i | ||||||||
\(33\) | − 106.359i | − 0.561051i | ||||||||
\(34\) | 196.485i | 0.991085i | ||||||||
\(35\) | −45.5155 | −0.219815 | ||||||||
\(36\) | 0.381277 | 0.00176517 | ||||||||
\(37\) | − 207.235i | − 0.920790i | −0.887714 | − | 0.460395i | \(-0.847708\pi\) | ||||
0.887714 | − | 0.460395i | \(-0.152292\pi\) | |||||||
\(38\) | 34.9833 | 0.149343 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −77.3825 | −0.305881 | ||||||||
\(41\) | − 117.701i | − 0.448337i | −0.974550 | − | 0.224169i | \(-0.928033\pi\) | ||||
0.974550 | − | 0.224169i | \(-0.0719666\pi\) | |||||||
\(42\) | −112.929 | −0.414888 | ||||||||
\(43\) | −553.224 | −1.96200 | −0.980998 | − | 0.194016i | \(-0.937849\pi\) | ||||
−0.980998 | + | 0.194016i | \(0.937849\pi\) | |||||||
\(44\) | − 1.50193i | − 0.00514602i | ||||||||
\(45\) | − 30.6980i | − 0.101693i | ||||||||
\(46\) | − 356.146i | − 1.14154i | ||||||||
\(47\) | − 62.9185i | − 0.195268i | −0.995222 | − | 0.0976341i | \(-0.968873\pi\) | ||||
0.995222 | − | 0.0976341i | \(-0.0311275\pi\) | |||||||
\(48\) | −190.978 | −0.574277 | ||||||||
\(49\) | 164.933 | 0.480854 | ||||||||
\(50\) | − 319.797i | − 0.904522i | ||||||||
\(51\) | −208.958 | −0.573724 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −147.031 | −0.381061 | −0.190531 | − | 0.981681i | \(-0.561021\pi\) | ||||
−0.190531 | + | 0.981681i | \(0.561021\pi\) | |||||||
\(54\) | − 76.1651i | − 0.191940i | ||||||||
\(55\) | −120.926 | −0.296466 | ||||||||
\(56\) | −302.738 | −0.722413 | ||||||||
\(57\) | 37.2041i | 0.0864526i | ||||||||
\(58\) | 505.115i | 1.14353i | ||||||||
\(59\) | − 274.087i | − 0.604798i | −0.953181 | − | 0.302399i | \(-0.902213\pi\) | ||||
0.953181 | − | 0.302399i | \(-0.0977875\pi\) | |||||||
\(60\) | − 0.433498i | 0 0.000932738i | ||||||||
\(61\) | 603.039 | 1.26576 | 0.632879 | − | 0.774251i | \(-0.281873\pi\) | ||||
0.632879 | + | 0.774251i | \(0.281873\pi\) | |||||||
\(62\) | 721.974 | 1.47888 | ||||||||
\(63\) | − 120.098i | − 0.240173i | ||||||||
\(64\) | −514.683 | −1.00524 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −300.031 | −0.559564 | ||||||||
\(67\) | − 741.019i | − 1.35119i | −0.737272 | − | 0.675596i | \(-0.763887\pi\) | ||||
0.737272 | − | 0.675596i | \(-0.236113\pi\) | |||||||
\(68\) | −2.95077 | −0.00526226 | ||||||||
\(69\) | 378.754 | 0.660820 | ||||||||
\(70\) | 128.396i | 0.219232i | ||||||||
\(71\) | 572.574i | 0.957071i | 0.878068 | + | 0.478536i | \(0.158832\pi\) | ||||
−0.878068 | + | 0.478536i | \(0.841168\pi\) | |||||||
\(72\) | − 204.182i | − 0.334210i | ||||||||
\(73\) | − 26.7155i | − 0.0428330i | −0.999771 | − | 0.0214165i | \(-0.993182\pi\) | ||||
0.999771 | − | 0.0214165i | \(-0.00681761\pi\) | |||||||
\(74\) | −584.595 | −0.918349 | ||||||||
\(75\) | 340.098 | 0.523614 | ||||||||
\(76\) | 0.525372i | 0 0.000792952i | ||||||||
\(77\) | −473.090 | −0.700177 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −207.798 | −0.295938 | −0.147969 | − | 0.988992i | \(-0.547274\pi\) | ||||
−0.147969 | + | 0.988992i | \(0.547274\pi\) | |||||||
\(80\) | 217.135i | 0.303455i | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −332.026 | −0.447149 | ||||||||
\(83\) | − 1031.37i | − 1.36395i | −0.731374 | − | 0.681976i | \(-0.761121\pi\) | ||||
0.731374 | − | 0.681976i | \(-0.238879\pi\) | |||||||
\(84\) | − 1.69594i | − 0.00220289i | ||||||||
\(85\) | 237.577i | 0.303163i | ||||||||
\(86\) | 1560.60i | 1.95679i | ||||||||
\(87\) | −537.179 | −0.661973 | ||||||||
\(88\) | −804.318 | −0.974325 | ||||||||
\(89\) | − 1229.66i | − 1.46453i | −0.681019 | − | 0.732266i | \(-0.738463\pi\) | ||||
0.681019 | − | 0.732266i | \(-0.261537\pi\) | |||||||
\(90\) | −86.5968 | −0.101423 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.34852 | 0.00606111 | ||||||||
\(93\) | 767.805i | 0.856103i | ||||||||
\(94\) | −177.488 | −0.194750 | ||||||||
\(95\) | 42.2996 | 0.0456826 | ||||||||
\(96\) | − 5.75148i | − 0.00611467i | ||||||||
\(97\) | 1795.12i | 1.87903i | 0.342502 | + | 0.939517i | \(0.388726\pi\) | ||||
−0.342502 | + | 0.939517i | \(0.611274\pi\) | |||||||
\(98\) | − 465.264i | − 0.479579i | ||||||||
\(99\) | − 319.076i | − 0.323923i | ||||||||
\(100\) | 4.80265 | 0.00480265 | ||||||||
\(101\) | 769.697 | 0.758295 | 0.379147 | − | 0.925336i | \(-0.376217\pi\) | ||||
0.379147 | + | 0.925336i | \(0.376217\pi\) | |||||||
\(102\) | 589.455i | 0.572203i | ||||||||
\(103\) | −1543.66 | −1.47671 | −0.738357 | − | 0.674410i | \(-0.764398\pi\) | ||||
−0.738357 | + | 0.674410i | \(0.764398\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −136.546 | −0.126910 | ||||||||
\(106\) | 414.764i | 0.380051i | ||||||||
\(107\) | 2027.64 | 1.83196 | 0.915978 | − | 0.401228i | \(-0.131417\pi\) | ||||
0.915978 | + | 0.401228i | \(0.131417\pi\) | |||||||
\(108\) | 1.14383 | 0.00101912 | ||||||||
\(109\) | 1644.97i | 1.44550i | 0.691108 | + | 0.722751i | \(0.257123\pi\) | ||||
−0.691108 | + | 0.722751i | \(0.742877\pi\) | |||||||
\(110\) | 341.123i | 0.295680i | ||||||||
\(111\) | − 621.705i | − 0.531618i | ||||||||
\(112\) | 849.481i | 0.716682i | ||||||||
\(113\) | −654.514 | −0.544880 | −0.272440 | − | 0.962173i | \(-0.587831\pi\) | ||||
−0.272440 | + | 0.962173i | \(0.587831\pi\) | |||||||
\(114\) | 104.950 | 0.0862234 | ||||||||
\(115\) | − 430.629i | − 0.349186i | ||||||||
\(116\) | −7.58571 | −0.00607169 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −773.179 | −0.603194 | ||||||||
\(119\) | 929.456i | 0.715993i | ||||||||
\(120\) | −232.148 | −0.176601 | ||||||||
\(121\) | 74.0896 | 0.0556646 | ||||||||
\(122\) | − 1701.13i | − 1.26240i | ||||||||
\(123\) | − 353.103i | − 0.258848i | ||||||||
\(124\) | 10.8425i | 0.00785227i | ||||||||
\(125\) | − 813.039i | − 0.581763i | ||||||||
\(126\) | −338.787 | −0.239536 | ||||||||
\(127\) | −1325.54 | −0.926161 | −0.463080 | − | 0.886316i | \(-0.653256\pi\) | ||||
−0.463080 | + | 0.886316i | \(0.653256\pi\) | |||||||
\(128\) | 1436.55i | 0.991983i | ||||||||
\(129\) | −1659.67 | −1.13276 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 930.114 | 0.620339 | 0.310170 | − | 0.950681i | \(-0.399614\pi\) | ||||
0.310170 | + | 0.950681i | \(0.399614\pi\) | |||||||
\(132\) | − 4.50580i | − 0.00297106i | ||||||||
\(133\) | 165.486 | 0.107891 | ||||||||
\(134\) | −2090.36 | −1.34761 | ||||||||
\(135\) | − 92.0939i | − 0.0587125i | ||||||||
\(136\) | 1580.20i | 0.996333i | ||||||||
\(137\) | 2751.03i | 1.71559i | 0.513989 | + | 0.857797i | \(0.328167\pi\) | ||||
−0.513989 | + | 0.857797i | \(0.671833\pi\) | |||||||
\(138\) | − 1068.44i | − 0.659068i | ||||||||
\(139\) | 2436.65 | 1.48686 | 0.743432 | − | 0.668812i | \(-0.233197\pi\) | ||||
0.743432 | + | 0.668812i | \(0.233197\pi\) | |||||||
\(140\) | −1.92822 | −0.00116403 | ||||||||
\(141\) | − 188.755i | − 0.112738i | ||||||||
\(142\) | 1615.19 | 0.954534 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −572.934 | −0.331559 | ||||||||
\(145\) | 610.753i | 0.349795i | ||||||||
\(146\) | −75.3624 | −0.0427194 | ||||||||
\(147\) | 494.799 | 0.277621 | ||||||||
\(148\) | − 8.77933i | − 0.00487606i | ||||||||
\(149\) | − 1517.58i | − 0.834397i | −0.908815 | − | 0.417198i | \(-0.863012\pi\) | ||||
0.908815 | − | 0.417198i | \(-0.136988\pi\) | |||||||
\(150\) | − 959.391i | − 0.522226i | ||||||||
\(151\) | − 583.642i | − 0.314544i | −0.987555 | − | 0.157272i | \(-0.949730\pi\) | ||||
0.987555 | − | 0.157272i | \(-0.0502699\pi\) | |||||||
\(152\) | 281.349 | 0.150134 | ||||||||
\(153\) | −626.873 | −0.331240 | ||||||||
\(154\) | 1334.55i | 0.698321i | ||||||||
\(155\) | 872.965 | 0.452376 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 26.0932 | 0.0132641 | 0.00663206 | − | 0.999978i | \(-0.497889\pi\) | ||||
0.00663206 | + | 0.999978i | \(0.497889\pi\) | |||||||
\(158\) | 586.184i | 0.295154i | ||||||||
\(159\) | −441.093 | −0.220006 | ||||||||
\(160\) | −6.53922 | −0.00323107 | ||||||||
\(161\) | − 1684.72i | − 0.824686i | ||||||||
\(162\) | − 228.495i | − 0.110817i | ||||||||
\(163\) | − 17.0905i | − 0.00821246i | −0.999992 | − | 0.00410623i | \(-0.998693\pi\) | ||||
0.999992 | − | 0.00410623i | \(-0.00130706\pi\) | |||||||
\(164\) | − 4.98631i | − 0.00237418i | ||||||||
\(165\) | −362.778 | −0.171165 | ||||||||
\(166\) | −2909.43 | −1.36034 | ||||||||
\(167\) | − 3919.48i | − 1.81616i | −0.418799 | − | 0.908079i | \(-0.637549\pi\) | ||||
0.418799 | − | 0.908079i | \(-0.362451\pi\) | |||||||
\(168\) | −908.215 | −0.417085 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 670.188 | 0.302359 | ||||||||
\(171\) | 111.612i | 0.0499134i | ||||||||
\(172\) | −23.4368 | −0.0103898 | ||||||||
\(173\) | 1976.35 | 0.868551 | 0.434276 | − | 0.900780i | \(-0.357004\pi\) | ||||
0.434276 | + | 0.900780i | \(0.357004\pi\) | |||||||
\(174\) | 1515.34i | 0.660218i | ||||||||
\(175\) | − 1512.77i | − 0.653457i | ||||||||
\(176\) | 2256.91i | 0.966596i | ||||||||
\(177\) | − 822.260i | − 0.349180i | ||||||||
\(178\) | −3468.77 | −1.46065 | ||||||||
\(179\) | 2784.34 | 1.16263 | 0.581316 | − | 0.813678i | \(-0.302538\pi\) | ||||
0.581316 | + | 0.813678i | \(0.302538\pi\) | |||||||
\(180\) | − 1.30049i | 0 0.000538517i | ||||||||
\(181\) | 1886.53 | 0.774723 | 0.387361 | − | 0.921928i | \(-0.373387\pi\) | ||||
0.387361 | + | 0.921928i | \(0.373387\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1809.12 | 0.730786 | ||||||||
\(184\) | − 2864.25i | − 1.14758i | ||||||||
\(185\) | −706.855 | −0.280914 | ||||||||
\(186\) | 2165.92 | 0.853834 | ||||||||
\(187\) | 2469.39i | 0.965666i | ||||||||
\(188\) | − 2.66549i | − 0.00103405i | ||||||||
\(189\) | − 360.293i | − 0.138664i | ||||||||
\(190\) | − 119.324i | − 0.0455615i | ||||||||
\(191\) | 2447.94 | 0.927364 | 0.463682 | − | 0.886002i | \(-0.346528\pi\) | ||||
0.463682 | + | 0.886002i | \(0.346528\pi\) | |||||||
\(192\) | −1544.05 | −0.580375 | ||||||||
\(193\) | 1925.66i | 0.718196i | 0.933300 | + | 0.359098i | \(0.116916\pi\) | ||||
−0.933300 | + | 0.359098i | \(0.883084\pi\) | |||||||
\(194\) | 5063.89 | 1.87405 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.98724 | 0.00254637 | ||||||||
\(197\) | − 1819.95i | − 0.658203i | −0.944294 | − | 0.329102i | \(-0.893254\pi\) | ||||
0.944294 | − | 0.329102i | \(-0.106746\pi\) | |||||||
\(198\) | −900.092 | −0.323064 | ||||||||
\(199\) | 1273.97 | 0.453816 | 0.226908 | − | 0.973916i | \(-0.427138\pi\) | ||||
0.226908 | + | 0.973916i | \(0.427138\pi\) | |||||||
\(200\) | − 2571.92i | − 0.909312i | ||||||||
\(201\) | − 2223.06i | − 0.780111i | ||||||||
\(202\) | − 2171.26i | − 0.756284i | ||||||||
\(203\) | 2389.40i | 0.826125i | ||||||||
\(204\) | −8.85231 | −0.00303817 | ||||||||
\(205\) | −401.465 | −0.136778 | ||||||||
\(206\) | 4354.56i | 1.47280i | ||||||||
\(207\) | 1136.26 | 0.381525 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 439.664 | 0.145513 | ||||||||
\(210\) | 385.188i | 0.126574i | ||||||||
\(211\) | −1319.44 | −0.430492 | −0.215246 | − | 0.976560i | \(-0.569055\pi\) | ||||
−0.215246 | + | 0.976560i | \(0.569055\pi\) | |||||||
\(212\) | −6.22884 | −0.00201792 | ||||||||
\(213\) | 1717.72i | 0.552565i | ||||||||
\(214\) | − 5719.83i | − 1.82710i | ||||||||
\(215\) | 1886.98i | 0.598564i | ||||||||
\(216\) | − 612.547i | − 0.192956i | ||||||||
\(217\) | 3415.24 | 1.06839 | ||||||||
\(218\) | 4640.35 | 1.44167 | ||||||||
\(219\) | − 80.1464i | − 0.0247296i | ||||||||
\(220\) | −5.12292 | −0.00156994 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1753.79 | −0.530209 | ||||||||
\(223\) | 1203.45i | 0.361384i | 0.983540 | + | 0.180692i | \(0.0578338\pi\) | ||||
−0.983540 | + | 0.180692i | \(0.942166\pi\) | |||||||
\(224\) | −25.5829 | −0.00763095 | ||||||||
\(225\) | 1020.29 | 0.302309 | ||||||||
\(226\) | 1846.34i | 0.543436i | ||||||||
\(227\) | − 4361.23i | − 1.27518i | −0.770377 | − | 0.637589i | \(-0.779932\pi\) | ||||
0.770377 | − | 0.637589i | \(-0.220068\pi\) | |||||||
\(228\) | 1.57612i | 0 0.000457811i | ||||||||
\(229\) | − 5384.29i | − 1.55373i | −0.629669 | − | 0.776864i | \(-0.716809\pi\) | ||||
0.629669 | − | 0.776864i | \(-0.283191\pi\) | |||||||
\(230\) | −1214.77 | −0.348260 | ||||||||
\(231\) | −1419.27 | −0.404247 | ||||||||
\(232\) | 4062.32i | 1.14959i | ||||||||
\(233\) | 4913.60 | 1.38155 | 0.690774 | − | 0.723070i | \(-0.257270\pi\) | ||||
0.690774 | + | 0.723070i | \(0.257270\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −214.608 | −0.0595722 | ||||||||
\(236\) | − 11.6114i | − 0.00320272i | ||||||||
\(237\) | −623.394 | −0.170860 | ||||||||
\(238\) | 2621.93 | 0.714094 | ||||||||
\(239\) | 963.718i | 0.260827i | 0.991460 | + | 0.130414i | \(0.0416306\pi\) | ||||
−0.991460 | + | 0.130414i | \(0.958369\pi\) | |||||||
\(240\) | 651.404i | 0.175200i | ||||||||
\(241\) | − 1544.48i | − 0.412817i | −0.978466 | − | 0.206409i | \(-0.933822\pi\) | ||||
0.978466 | − | 0.206409i | \(-0.0661776\pi\) | |||||||
\(242\) | − 209.001i | − 0.0555170i | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 25.5472 | 0.00670284 | ||||||||
\(245\) | − 562.568i | − 0.146698i | ||||||||
\(246\) | −996.079 | −0.258161 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 5806.38 | 1.48671 | ||||||||
\(249\) | − 3094.12i | − 0.787478i | ||||||||
\(250\) | −2293.52 | −0.580221 | ||||||||
\(251\) | −3768.17 | −0.947588 | −0.473794 | − | 0.880636i | \(-0.657116\pi\) | ||||
−0.473794 | + | 0.880636i | \(0.657116\pi\) | |||||||
\(252\) | − 5.08783i | − 0.00127184i | ||||||||
\(253\) | − 4475.98i | − 1.11226i | ||||||||
\(254\) | 3739.25i | 0.923705i | ||||||||
\(255\) | 712.731i | 0.175031i | ||||||||
\(256\) | −65.0695 | −0.0158861 | ||||||||
\(257\) | −1282.68 | −0.311327 | −0.155664 | − | 0.987810i | \(-0.549752\pi\) | ||||
−0.155664 | + | 0.987810i | \(0.549752\pi\) | |||||||
\(258\) | 4681.81i | 1.12976i | ||||||||
\(259\) | −2765.38 | −0.663445 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1611.54 | −0.382190 | ||||||||
\(262\) | − 2623.78i | − 0.618694i | ||||||||
\(263\) | 5029.74 | 1.17927 | 0.589633 | − | 0.807671i | \(-0.299272\pi\) | ||||
0.589633 | + | 0.807671i | \(0.299272\pi\) | |||||||
\(264\) | −2412.95 | −0.562527 | ||||||||
\(265\) | 501.506i | 0.116254i | ||||||||
\(266\) | − 466.824i | − 0.107604i | ||||||||
\(267\) | − 3688.97i | − 0.845548i | ||||||||
\(268\) | − 31.3926i | − 0.00715526i | ||||||||
\(269\) | 5628.46 | 1.27574 | 0.637868 | − | 0.770146i | \(-0.279816\pi\) | ||||
0.637868 | + | 0.770146i | \(0.279816\pi\) | |||||||
\(270\) | −259.790 | −0.0585568 | ||||||||
\(271\) | − 3368.39i | − 0.755037i | −0.926002 | − | 0.377518i | \(-0.876778\pi\) | ||||
0.926002 | − | 0.377518i | \(-0.123222\pi\) | |||||||
\(272\) | 4434.03 | 0.988429 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7760.45 | 1.71104 | ||||||||
\(275\) | − 4019.15i | − 0.881324i | ||||||||
\(276\) | 16.0456 | 0.00349938 | ||||||||
\(277\) | 6507.75 | 1.41160 | 0.705799 | − | 0.708412i | \(-0.250588\pi\) | ||||
0.705799 | + | 0.708412i | \(0.250588\pi\) | |||||||
\(278\) | − 6873.62i | − 1.48292i | ||||||||
\(279\) | 2303.41i | 0.494272i | ||||||||
\(280\) | 1032.61i | 0.220393i | ||||||||
\(281\) | 3625.51i | 0.769680i | 0.922983 | + | 0.384840i | \(0.125743\pi\) | ||||
−0.922983 | + | 0.384840i | \(0.874257\pi\) | |||||||
\(282\) | −532.465 | −0.112439 | ||||||||
\(283\) | 4635.41 | 0.973662 | 0.486831 | − | 0.873496i | \(-0.338153\pi\) | ||||
0.486831 | + | 0.873496i | \(0.338153\pi\) | |||||||
\(284\) | 24.2566i | 0.00506819i | ||||||||
\(285\) | 126.899 | 0.0263749 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1570.62 | −0.323035 | ||||||||
\(288\) | − 17.2545i | − 0.00353031i | ||||||||
\(289\) | −61.5178 | −0.0125214 | ||||||||
\(290\) | 1722.89 | 0.348867 | ||||||||
\(291\) | 5385.35i | 1.08486i | ||||||||
\(292\) | − 1.13178i | 0 0.000226823i | ||||||||
\(293\) | 2907.07i | 0.579634i | 0.957082 | + | 0.289817i | \(0.0935945\pi\) | ||||
−0.957082 | + | 0.289817i | \(0.906406\pi\) | |||||||
\(294\) | − 1395.79i | − 0.276885i | ||||||||
\(295\) | −934.879 | −0.184511 | ||||||||
\(296\) | −4701.53 | −0.923212 | ||||||||
\(297\) | − 957.229i | − 0.187017i | ||||||||
\(298\) | −4280.99 | −0.832185 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 14.4079 | 0.00277281 | ||||||||
\(301\) | 7382.32i | 1.41365i | ||||||||
\(302\) | −1646.41 | −0.313710 | ||||||||
\(303\) | 2309.09 | 0.437802 | ||||||||
\(304\) | − 789.461i | − 0.148943i | ||||||||
\(305\) | − 2056.90i | − 0.386156i | ||||||||
\(306\) | 1768.36i | 0.330362i | ||||||||
\(307\) | − 933.950i | − 0.173627i | −0.996225 | − | 0.0868133i | \(-0.972332\pi\) | ||||
0.996225 | − | 0.0868133i | \(-0.0276683\pi\) | |||||||
\(308\) | −20.0421 | −0.00370780 | ||||||||
\(309\) | −4630.98 | −0.852581 | ||||||||
\(310\) | − 2462.57i | − 0.451176i | ||||||||
\(311\) | 3633.55 | 0.662508 | 0.331254 | − | 0.943542i | \(-0.392528\pi\) | ||||
0.331254 | + | 0.943542i | \(0.392528\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7507.26 | −1.35570 | −0.677852 | − | 0.735198i | \(-0.737089\pi\) | ||||
−0.677852 | + | 0.735198i | \(0.737089\pi\) | |||||||
\(314\) | − 73.6071i | − 0.0132289i | ||||||||
\(315\) | −409.639 | −0.0732716 | ||||||||
\(316\) | −8.80319 | −0.00156715 | ||||||||
\(317\) | 1214.60i | 0.215202i | 0.994194 | + | 0.107601i | \(0.0343168\pi\) | ||||
−0.994194 | + | 0.107601i | \(0.965683\pi\) | |||||||
\(318\) | 1244.29i | 0.219423i | ||||||||
\(319\) | 6348.19i | 1.11420i | ||||||||
\(320\) | 1755.52i | 0.306677i | ||||||||
\(321\) | 6082.92 | 1.05768 | ||||||||
\(322\) | −4752.47 | −0.822500 | ||||||||
\(323\) | − 863.786i | − 0.148800i | ||||||||
\(324\) | 3.43149 | 0.000588391 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −48.2111 | −0.00819069 | ||||||||
\(327\) | 4934.92i | 0.834561i | ||||||||
\(328\) | −2670.28 | −0.449517 | ||||||||
\(329\) | −839.595 | −0.140694 | ||||||||
\(330\) | 1023.37i | 0.170711i | ||||||||
\(331\) | 2443.20i | 0.405712i | 0.979209 | + | 0.202856i | \(0.0650223\pi\) | ||||
−0.979209 | + | 0.202856i | \(0.934978\pi\) | |||||||
\(332\) | − 43.6933i | − 0.00722283i | ||||||||
\(333\) | − 1865.12i | − 0.306930i | ||||||||
\(334\) | −11056.6 | −1.81134 | ||||||||
\(335\) | −2527.53 | −0.412220 | ||||||||
\(336\) | 2548.44i | 0.413777i | ||||||||
\(337\) | −1890.96 | −0.305660 | −0.152830 | − | 0.988253i | \(-0.548839\pi\) | ||||
−0.152830 | + | 0.988253i | \(0.548839\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1963.54 | −0.314587 | ||||||||
\(340\) | 10.0647i | 0.00160540i | ||||||||
\(341\) | 9073.64 | 1.44095 | ||||||||
\(342\) | 314.850 | 0.0497811 | ||||||||
\(343\) | − 6777.95i | − 1.06698i | ||||||||
\(344\) | 12551.0i | 1.96716i | ||||||||
\(345\) | − 1291.89i | − 0.201602i | ||||||||
\(346\) | − 5575.15i | − 0.866248i | ||||||||
\(347\) | −2791.57 | −0.431872 | −0.215936 | − | 0.976408i | \(-0.569280\pi\) | ||||
−0.215936 | + | 0.976408i | \(0.569280\pi\) | |||||||
\(348\) | −22.7571 | −0.00350549 | ||||||||
\(349\) | 6917.33i | 1.06096i | 0.847696 | + | 0.530482i | \(0.177989\pi\) | ||||
−0.847696 | + | 0.530482i | \(0.822011\pi\) | |||||||
\(350\) | −4267.43 | −0.651724 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −67.9690 | −0.0102919 | ||||||||
\(353\) | 7638.37i | 1.15170i | 0.817556 | + | 0.575849i | \(0.195328\pi\) | ||||
−0.817556 | + | 0.575849i | \(0.804672\pi\) | |||||||
\(354\) | −2319.54 | −0.348254 | ||||||||
\(355\) | 1952.99 | 0.291982 | ||||||||
\(356\) | − 52.0933i | − 0.00775545i | ||||||||
\(357\) | 2788.37i | 0.413379i | ||||||||
\(358\) | − 7854.42i | − 1.15955i | ||||||||
\(359\) | 5490.97i | 0.807249i | 0.914925 | + | 0.403625i | \(0.132250\pi\) | ||||
−0.914925 | + | 0.403625i | \(0.867750\pi\) | |||||||
\(360\) | −696.443 | −0.101960 | ||||||||
\(361\) | 6705.21 | 0.977578 | ||||||||
\(362\) | − 5321.77i | − 0.772669i | ||||||||
\(363\) | 222.269 | 0.0321380 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −91.1234 | −0.0130674 | ||||||||
\(366\) | − 5103.39i | − 0.728848i | ||||||||
\(367\) | 6737.43 | 0.958287 | 0.479143 | − | 0.877737i | \(-0.340947\pi\) | ||||
0.479143 | + | 0.877737i | \(0.340947\pi\) | |||||||
\(368\) | −8037.07 | −1.13848 | ||||||||
\(369\) | − 1059.31i | − 0.149446i | ||||||||
\(370\) | 1993.99i | 0.280169i | ||||||||
\(371\) | 1962.01i | 0.274561i | ||||||||
\(372\) | 32.5274i | 0.00453351i | ||||||||
\(373\) | −3930.42 | −0.545602 | −0.272801 | − | 0.962070i | \(-0.587950\pi\) | ||||
−0.272801 | + | 0.962070i | \(0.587950\pi\) | |||||||
\(374\) | 6965.97 | 0.963106 | ||||||||
\(375\) | − 2439.12i | − 0.335881i | ||||||||
\(376\) | −1427.43 | −0.195782 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1016.36 | −0.138296 | ||||||||
\(379\) | 11897.7i | 1.61252i | 0.591563 | + | 0.806258i | \(0.298511\pi\) | ||||
−0.591563 | + | 0.806258i | \(0.701489\pi\) | |||||||
\(380\) | 1.79199 | 0.000241913 0 | ||||||||
\(381\) | −3976.61 | −0.534719 | ||||||||
\(382\) | − 6905.46i | − 0.924906i | ||||||||
\(383\) | 4748.31i | 0.633492i | 0.948510 | + | 0.316746i | \(0.102590\pi\) | ||||
−0.948510 | + | 0.316746i | \(0.897410\pi\) | |||||||
\(384\) | 4309.64i | 0.572722i | ||||||||
\(385\) | 1613.66i | 0.213609i | ||||||||
\(386\) | 5432.14 | 0.716292 | ||||||||
\(387\) | −4979.02 | −0.653999 | ||||||||
\(388\) | 76.0485i | 0.00995046i | ||||||||
\(389\) | −11299.5 | −1.47277 | −0.736386 | − | 0.676561i | \(-0.763469\pi\) | ||||
−0.736386 | + | 0.676561i | \(0.763469\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8793.73 | −1.13739 | ||||||||
\(392\) | − 3741.82i | − 0.482119i | ||||||||
\(393\) | 2790.34 | 0.358153 | ||||||||
\(394\) | −5133.95 | −0.656458 | ||||||||
\(395\) | 708.776i | 0.0902845i | ||||||||
\(396\) | − 13.5174i | − 0.00171534i | ||||||||
\(397\) | − 13853.0i | − 1.75129i | −0.482953 | − | 0.875646i | \(-0.660436\pi\) | ||||
0.482953 | − | 0.875646i | \(-0.339564\pi\) | |||||||
\(398\) | − 3593.78i | − 0.452613i | ||||||||
\(399\) | 496.457 | 0.0622906 | ||||||||
\(400\) | −7216.79 | −0.902099 | ||||||||
\(401\) | − 5434.64i | − 0.676790i | −0.941004 | − | 0.338395i | \(-0.890116\pi\) | ||||
0.941004 | − | 0.338395i | \(-0.109884\pi\) | |||||||
\(402\) | −6271.08 | −0.778042 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 32.6076 | 0.00401556 | ||||||||
\(405\) | − 276.282i | − 0.0338977i | ||||||||
\(406\) | 6740.34 | 0.823935 | ||||||||
\(407\) | −7347.09 | −0.894795 | ||||||||
\(408\) | 4740.61i | 0.575233i | ||||||||
\(409\) | − 3472.43i | − 0.419806i | −0.977722 | − | 0.209903i | \(-0.932685\pi\) | ||||
0.977722 | − | 0.209903i | \(-0.0673148\pi\) | |||||||
\(410\) | 1132.50i | 0.136416i | ||||||||
\(411\) | 8253.09i | 0.990498i | ||||||||
\(412\) | −65.3959 | −0.00781996 | ||||||||
\(413\) | −3657.46 | −0.435767 | ||||||||
\(414\) | − 3205.31i | − 0.380513i | ||||||||
\(415\) | −3517.90 | −0.416113 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7309.95 | 0.858441 | ||||||||
\(418\) | − 1240.26i | − 0.145127i | ||||||||
\(419\) | −4261.65 | −0.496886 | −0.248443 | − | 0.968647i | \(-0.579919\pi\) | ||||
−0.248443 | + | 0.968647i | \(0.579919\pi\) | |||||||
\(420\) | −5.78467 | −0.000672055 0 | ||||||||
\(421\) | 6235.06i | 0.721801i | 0.932604 | + | 0.360900i | \(0.117531\pi\) | ||||
−0.932604 | + | 0.360900i | \(0.882469\pi\) | |||||||
\(422\) | 3722.04i | 0.429351i | ||||||||
\(423\) | − 566.266i | − 0.0650894i | ||||||||
\(424\) | 3335.68i | 0.382064i | ||||||||
\(425\) | −7896.22 | −0.901231 | ||||||||
\(426\) | 4845.57 | 0.551100 | ||||||||
\(427\) | − 8047.06i | − 0.912001i | ||||||||
\(428\) | 85.8992 | 0.00970115 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5323.05 | 0.596977 | ||||||||
\(431\) | 2520.58i | 0.281698i | 0.990031 | + | 0.140849i | \(0.0449833\pi\) | ||||
−0.990031 | + | 0.140849i | \(0.955017\pi\) | |||||||
\(432\) | −1718.80 | −0.191426 | ||||||||
\(433\) | 1283.89 | 0.142494 | 0.0712468 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712468 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(434\) | − 9634.15i | − 1.06556i | ||||||||
\(435\) | 1832.26i | 0.201954i | ||||||||
\(436\) | 69.6878i | 0.00765468i | ||||||||
\(437\) | 1565.69i | 0.171389i | ||||||||
\(438\) | −226.087 | −0.0246641 | ||||||||
\(439\) | 16942.0 | 1.84190 | 0.920951 | − | 0.389677i | \(-0.127414\pi\) | ||||
0.920951 | + | 0.389677i | \(0.127414\pi\) | |||||||
\(440\) | 2743.44i | 0.297246i | ||||||||
\(441\) | 1484.40 | 0.160285 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2163.00 | −0.231980 | −0.115990 | − | 0.993250i | \(-0.537004\pi\) | ||||
−0.115990 | + | 0.993250i | \(0.537004\pi\) | |||||||
\(444\) | − 26.3380i | − 0.00281519i | ||||||||
\(445\) | −4194.22 | −0.446798 | ||||||||
\(446\) | 3394.83 | 0.360426 | ||||||||
\(447\) | − 4552.75i | − 0.481739i | ||||||||
\(448\) | 6868.01i | 0.724293i | ||||||||
\(449\) | 1673.35i | 0.175880i | 0.996126 | + | 0.0879400i | \(0.0280284\pi\) | ||||
−0.996126 | + | 0.0879400i | \(0.971972\pi\) | |||||||
\(450\) | − 2878.17i | − 0.301507i | ||||||||
\(451\) | −4172.85 | −0.435680 | ||||||||
\(452\) | −27.7279 | −0.00288542 | ||||||||
\(453\) | − 1750.92i | − 0.181602i | ||||||||
\(454\) | −12302.7 | −1.27180 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 844.046 | 0.0866800 | ||||||||
\(457\) | − 4652.38i | − 0.476212i | −0.971239 | − | 0.238106i | \(-0.923473\pi\) | ||||
0.971239 | − | 0.238106i | \(-0.0765266\pi\) | |||||||
\(458\) | −15188.7 | −1.54961 | ||||||||
\(459\) | −1880.62 | −0.191241 | ||||||||
\(460\) | − 18.2432i | − 0.00184912i | ||||||||
\(461\) | 3460.07i | 0.349570i | 0.984607 | + | 0.174785i | \(0.0559230\pi\) | ||||
−0.984607 | + | 0.174785i | \(0.944077\pi\) | |||||||
\(462\) | 4003.66i | 0.403176i | ||||||||
\(463\) | 2105.64i | 0.211355i | 0.994400 | + | 0.105677i | \(0.0337011\pi\) | ||||
−0.994400 | + | 0.105677i | \(0.966299\pi\) | |||||||
\(464\) | 11398.8 | 1.14047 | ||||||||
\(465\) | 2618.89 | 0.261179 | ||||||||
\(466\) | − 13860.9i | − 1.37789i | ||||||||
\(467\) | 1415.88 | 0.140298 | 0.0701489 | − | 0.997537i | \(-0.477653\pi\) | ||||
0.0701489 | + | 0.997537i | \(0.477653\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9888.28 | −0.973557 | ||||||||
\(470\) | 605.393i | 0.0594143i | ||||||||
\(471\) | 78.2797 | 0.00765804 | ||||||||
\(472\) | −6218.19 | −0.606388 | ||||||||
\(473\) | 19613.4i | 1.90661i | ||||||||
\(474\) | 1758.55i | 0.170407i | ||||||||
\(475\) | 1405.89i | 0.135803i | ||||||||
\(476\) | 39.3756i | 0.00379155i | ||||||||
\(477\) | −1323.28 | −0.127020 | ||||||||
\(478\) | 2718.58 | 0.260136 | ||||||||
\(479\) | 985.594i | 0.0940145i | 0.998895 | + | 0.0470073i | \(0.0149684\pi\) | ||||
−0.998895 | + | 0.0470073i | \(0.985032\pi\) | |||||||
\(480\) | −19.6177 | −0.00186546 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −4356.88 | −0.411723 | ||||||||
\(483\) | − 5054.16i | − 0.476133i | ||||||||
\(484\) | 3.13874 | 0.000294773 0 | ||||||||
\(485\) | 6122.93 | 0.573254 | ||||||||
\(486\) | − 685.486i | − 0.0639800i | ||||||||
\(487\) | 14724.7i | 1.37011i | 0.728494 | + | 0.685053i | \(0.240221\pi\) | ||||
−0.728494 | + | 0.685053i | \(0.759779\pi\) | |||||||
\(488\) | − 13681.1i | − 1.26909i | ||||||||
\(489\) | − 51.2715i | − 0.00474147i | ||||||||
\(490\) | −1586.96 | −0.146310 | ||||||||
\(491\) | 16301.2 | 1.49830 | 0.749149 | − | 0.662401i | \(-0.230463\pi\) | ||||
0.749149 | + | 0.662401i | \(0.230463\pi\) | |||||||
\(492\) | − 14.9589i | − 0.00137073i | ||||||||
\(493\) | 12472.0 | 1.13937 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1088.33 | −0.0988221 | ||||||||
\(496\) | − 16292.6i | − 1.47492i | ||||||||
\(497\) | 7640.53 | 0.689587 | ||||||||
\(498\) | −8728.30 | −0.785391 | ||||||||
\(499\) | 3230.42i | 0.289806i | 0.989446 | + | 0.144903i | \(0.0462870\pi\) | ||||
−0.989446 | + | 0.144903i | \(0.953713\pi\) | |||||||
\(500\) | − 34.4437i | − 0.00308074i | ||||||||
\(501\) | − 11758.4i | − 1.04856i | ||||||||
\(502\) | 10629.7i | 0.945076i | ||||||||
\(503\) | −3577.57 | −0.317129 | −0.158565 | − | 0.987349i | \(-0.550687\pi\) | ||||
−0.158565 | + | 0.987349i | \(0.550687\pi\) | |||||||
\(504\) | −2724.65 | −0.240804 | ||||||||
\(505\) | − 2625.35i | − 0.231340i | ||||||||
\(506\) | −12626.4 | −1.10931 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −56.1552 | −0.00490450 | ||||||||
\(509\) | − 13864.7i | − 1.20735i | −0.797231 | − | 0.603674i | \(-0.793703\pi\) | ||||
0.797231 | − | 0.603674i | \(-0.206297\pi\) | |||||||
\(510\) | 2010.56 | 0.174567 | ||||||||
\(511\) | −356.496 | −0.0308619 | ||||||||
\(512\) | 11675.9i | 1.00783i | ||||||||
\(513\) | 334.836i | 0.0288175i | ||||||||
\(514\) | 3618.34i | 0.310502i | ||||||||
\(515\) | 5265.25i | 0.450514i | ||||||||
\(516\) | −70.3105 | −0.00599854 | ||||||||
\(517\) | −2230.64 | −0.189756 | ||||||||
\(518\) | 7800.94i | 0.661686i | ||||||||
\(519\) | 5929.06 | 0.501458 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9554.66 | −0.803449 | −0.401725 | − | 0.915760i | \(-0.631589\pi\) | ||||
−0.401725 | + | 0.915760i | \(0.631589\pi\) | |||||||
\(522\) | 4546.03i | 0.381177i | ||||||||
\(523\) | −19809.1 | −1.65620 | −0.828098 | − | 0.560583i | \(-0.810577\pi\) | ||||
−0.828098 | + | 0.560583i | \(0.810577\pi\) | |||||||
\(524\) | 39.4035 | 0.00328502 | ||||||||
\(525\) | − 4538.32i | − 0.377274i | ||||||||
\(526\) | − 14188.5i | − 1.17614i | ||||||||
\(527\) | − 17826.5i | − 1.47350i | ||||||||
\(528\) | 6770.73i | 0.558064i | ||||||||
\(529\) | 3772.38 | 0.310050 | ||||||||
\(530\) | 1414.71 | 0.115946 | ||||||||
\(531\) | − 2466.78i | − 0.201599i | ||||||||
\(532\) | 7.01066 | 0.000571336 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −10406.3 | −0.843306 | ||||||||
\(535\) | − 6916.05i | − 0.558891i | ||||||||
\(536\) | −16811.4 | −1.35475 | ||||||||
\(537\) | 8353.02 | 0.671246 | ||||||||
\(538\) | − 15877.5i | − 1.27235i | ||||||||
\(539\) | − 5847.36i | − 0.467279i | ||||||||
\(540\) | − 3.90148i | 0 0.000310913i | ||||||||
\(541\) | 1011.14i | 0.0803551i | 0.999193 | + | 0.0401775i | \(0.0127923\pi\) | ||||
−0.999193 | + | 0.0401775i | \(0.987208\pi\) | |||||||
\(542\) | −9501.98 | −0.753035 | ||||||||
\(543\) | 5659.59 | 0.447286 | ||||||||
\(544\) | 133.535i | 0.0105244i | ||||||||
\(545\) | 5610.81 | 0.440992 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15745.2 | 1.23074 | 0.615372 | − | 0.788237i | \(-0.289006\pi\) | ||||
0.615372 | + | 0.788237i | \(0.289006\pi\) | |||||||
\(548\) | 116.545i | 0.00908495i | ||||||||
\(549\) | 5427.35 | 0.421919 | ||||||||
\(550\) | −11337.7 | −0.878987 | ||||||||
\(551\) | − 2220.58i | − 0.171688i | ||||||||
\(552\) | − 8592.76i | − 0.662558i | ||||||||
\(553\) | 2772.89i | 0.213229i | ||||||||
\(554\) | − 18357.9i | − 1.40785i | ||||||||
\(555\) | −2120.57 | −0.162186 | ||||||||
\(556\) | 103.227 | 0.00787371 | ||||||||
\(557\) | − 8510.94i | − 0.647433i | −0.946154 | − | 0.323716i | \(-0.895068\pi\) | ||||
0.946154 | − | 0.323716i | \(-0.104932\pi\) | |||||||
\(558\) | 6497.76 | 0.492961 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 2897.48 | 0.218645 | ||||||||
\(561\) | 7408.16i | 0.557528i | ||||||||
\(562\) | 10227.3 | 0.767639 | ||||||||
\(563\) | −16764.1 | −1.25493 | −0.627463 | − | 0.778646i | \(-0.715907\pi\) | ||||
−0.627463 | + | 0.778646i | \(0.715907\pi\) | |||||||
\(564\) | − 7.99646i | 0 0.000597006i | ||||||||
\(565\) | 2232.47i | 0.166232i | ||||||||
\(566\) | − 13076.1i | − 0.971080i | ||||||||
\(567\) | − 1080.88i | − 0.0800575i | ||||||||
\(568\) | 12990.0 | 0.959589 | ||||||||
\(569\) | −20755.4 | −1.52919 | −0.764597 | − | 0.644508i | \(-0.777062\pi\) | ||||
−0.764597 | + | 0.644508i | \(0.777062\pi\) | |||||||
\(570\) | − 357.972i | − 0.0263049i | ||||||||
\(571\) | 23408.6 | 1.71562 | 0.857810 | − | 0.513968i | \(-0.171825\pi\) | ||||
0.857810 | + | 0.513968i | \(0.171825\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7343.81 | 0.535414 | ||||||||
\(574\) | 4430.62i | 0.322179i | ||||||||
\(575\) | 14312.6 | 1.03805 | ||||||||
\(576\) | −4632.14 | −0.335080 | ||||||||
\(577\) | 10387.2i | 0.749436i | 0.927139 | + | 0.374718i | \(0.122261\pi\) | ||||
−0.927139 | + | 0.374718i | \(0.877739\pi\) | |||||||
\(578\) | 173.537i | 0.0124882i | ||||||||
\(579\) | 5776.97i | 0.414650i | ||||||||
\(580\) | 25.8740i | 0.00185234i | ||||||||
\(581\) | −13762.8 | −0.982752 | ||||||||
\(582\) | 15191.7 | 1.08198 | ||||||||
\(583\) | 5212.68i | 0.370304i | ||||||||
\(584\) | −606.092 | −0.0429457 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8200.63 | 0.578097 | ||||||||
\(587\) | − 2898.42i | − 0.203800i | −0.994795 | − | 0.101900i | \(-0.967508\pi\) | ||||
0.994795 | − | 0.101900i | \(-0.0324921\pi\) | |||||||
\(588\) | 20.9617 | 0.00147015 | ||||||||
\(589\) | −3173.94 | −0.222037 | ||||||||
\(590\) | 2637.23i | 0.184022i | ||||||||
\(591\) | − 5459.85i | − 0.380014i | ||||||||
\(592\) | 13192.4i | 0.915888i | ||||||||
\(593\) | − 8805.33i | − 0.609766i | −0.952390 | − | 0.304883i | \(-0.901383\pi\) | ||||
0.952390 | − | 0.304883i | \(-0.0986174\pi\) | |||||||
\(594\) | −2700.27 | −0.186521 | ||||||||
\(595\) | 3170.27 | 0.218434 | ||||||||
\(596\) | − 64.2910i | − 0.00441856i | ||||||||
\(597\) | 3821.91 | 0.262011 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20236.8 | −1.38039 | −0.690194 | − | 0.723624i | \(-0.742475\pi\) | ||||
−0.690194 | + | 0.723624i | \(0.742475\pi\) | |||||||
\(600\) | − 7715.77i | − 0.524992i | ||||||||
\(601\) | −9884.92 | −0.670906 | −0.335453 | − | 0.942057i | \(-0.608889\pi\) | ||||
−0.335453 | + | 0.942057i | \(0.608889\pi\) | |||||||
\(602\) | 20825.0 | 1.40991 | ||||||||
\(603\) | − 6669.17i | − 0.450397i | ||||||||
\(604\) | − 24.7255i | − 0.00166567i | ||||||||
\(605\) | − 252.711i | − 0.0169821i | ||||||||
\(606\) | − 6513.78i | − 0.436641i | ||||||||
\(607\) | 22919.3 | 1.53256 | 0.766281 | − | 0.642505i | \(-0.222105\pi\) | ||||
0.766281 | + | 0.642505i | \(0.222105\pi\) | |||||||
\(608\) | 23.7754 | 0.00158589 | ||||||||
\(609\) | 7168.21i | 0.476963i | ||||||||
\(610\) | −5802.36 | −0.385132 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −26.5569 | −0.00175409 | ||||||||
\(613\) | 916.052i | 0.0603572i | 0.999545 | + | 0.0301786i | \(0.00960761\pi\) | ||||
−0.999545 | + | 0.0301786i | \(0.990392\pi\) | |||||||
\(614\) | −2634.61 | −0.173166 | ||||||||
\(615\) | −1204.40 | −0.0789690 | ||||||||
\(616\) | 10733.0i | 0.702019i | ||||||||
\(617\) | − 30179.4i | − 1.96917i | −0.174915 | − | 0.984584i | \(-0.555965\pi\) | ||||
0.174915 | − | 0.984584i | \(-0.444035\pi\) | |||||||
\(618\) | 13063.7i | 0.850320i | ||||||||
\(619\) | − 5571.12i | − 0.361748i | −0.983506 | − | 0.180874i | \(-0.942107\pi\) | ||||
0.983506 | − | 0.180874i | \(-0.0578927\pi\) | |||||||
\(620\) | 36.9824 | 0.00239556 | ||||||||
\(621\) | 3408.78 | 0.220273 | ||||||||
\(622\) | − 10250.0i | − 0.660751i | ||||||||
\(623\) | −16408.8 | −1.05522 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11397.5 | 0.729443 | ||||||||
\(626\) | 21177.5i | 1.35211i | ||||||||
\(627\) | 1318.99 | 0.0840120 | ||||||||
\(628\) | 1.10542 | 7.02403e−5 0 | ||||||||
\(629\) | 14434.5i | 0.915007i | ||||||||
\(630\) | 1155.56i | 0.0730773i | ||||||||
\(631\) | 11360.1i | 0.716703i | 0.933587 | + | 0.358352i | \(0.116661\pi\) | ||||
−0.933587 | + | 0.358352i | \(0.883339\pi\) | |||||||
\(632\) | 4714.30i | 0.296717i | ||||||||
\(633\) | −3958.32 | −0.248545 | ||||||||
\(634\) | 3426.31 | 0.214631 | ||||||||
\(635\) | 4521.26i | 0.282552i | ||||||||
\(636\) | −18.6865 | −0.00116504 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 17907.8 | 1.11125 | ||||||||
\(639\) | 5153.17i | 0.319024i | ||||||||
\(640\) | 4899.89 | 0.302633 | ||||||||
\(641\) | 24709.8 | 1.52259 | 0.761293 | − | 0.648408i | \(-0.224565\pi\) | ||||
0.761293 | + | 0.648408i | \(0.224565\pi\) | |||||||
\(642\) | − 17159.5i | − 1.05488i | ||||||||
\(643\) | 15226.6i | 0.933869i | 0.884292 | + | 0.466934i | \(0.154642\pi\) | ||||
−0.884292 | + | 0.466934i | \(0.845358\pi\) | |||||||
\(644\) | − 71.3717i | − 0.00436714i | ||||||||
\(645\) | 5660.95i | 0.345581i | ||||||||
\(646\) | −2436.68 | −0.148405 | ||||||||
\(647\) | −16706.6 | −1.01515 | −0.507576 | − | 0.861607i | \(-0.669458\pi\) | ||||
−0.507576 | + | 0.861607i | \(0.669458\pi\) | |||||||
\(648\) | − 1837.64i | − 0.111403i | ||||||||
\(649\) | −9717.18 | −0.587724 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10245.7 | 0.616838 | ||||||||
\(652\) | − 0.724024i | 0 4.34892e-5i | ||||||||
\(653\) | −28205.8 | −1.69032 | −0.845158 | − | 0.534516i | \(-0.820494\pi\) | ||||
−0.845158 | + | 0.534516i | \(0.820494\pi\) | |||||||
\(654\) | 13921.0 | 0.832349 | ||||||||
\(655\) | − 3172.51i | − 0.189252i | ||||||||
\(656\) | 7492.77i | 0.445951i | ||||||||
\(657\) | − 240.439i | − 0.0142777i | ||||||||
\(658\) | 2368.44i | 0.140321i | ||||||||
\(659\) | −11424.2 | −0.675299 | −0.337649 | − | 0.941272i | \(-0.609632\pi\) | ||||
−0.337649 | + | 0.941272i | \(0.609632\pi\) | |||||||
\(660\) | −15.3688 | −0.000906407 0 | ||||||||
\(661\) | 26518.2i | 1.56042i | 0.625516 | + | 0.780211i | \(0.284888\pi\) | ||||
−0.625516 | + | 0.780211i | \(0.715112\pi\) | |||||||
\(662\) | 6892.10 | 0.404636 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −23398.7 | −1.36754 | ||||||||
\(665\) | − 564.453i | − 0.0329151i | ||||||||
\(666\) | −5261.36 | −0.306116 | ||||||||
\(667\) | −22606.5 | −1.31234 | ||||||||
\(668\) | − 166.045i | − 0.00961749i | ||||||||
\(669\) | 3610.34i | 0.208645i | ||||||||
\(670\) | 7129.98i | 0.411127i | ||||||||
\(671\) | − 21379.5i | − 1.23002i | ||||||||
\(672\) | −76.7488 | −0.00440573 | ||||||||
\(673\) | −22816.8 | −1.30687 | −0.653434 | − | 0.756984i | \(-0.726672\pi\) | ||||
−0.653434 | + | 0.756984i | \(0.726672\pi\) | |||||||
\(674\) | 5334.27i | 0.304849i | ||||||||
\(675\) | 3060.88 | 0.174538 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17737.6 | 1.00696 | 0.503478 | − | 0.864008i | \(-0.332053\pi\) | ||||
0.503478 | + | 0.864008i | \(0.332053\pi\) | |||||||
\(678\) | 5539.01i | 0.313753i | ||||||||
\(679\) | 23954.3 | 1.35388 | ||||||||
\(680\) | 5389.89 | 0.303960 | ||||||||
\(681\) | − 13083.7i | − 0.736224i | ||||||||
\(682\) | − 25596.1i | − 1.43713i | ||||||||
\(683\) | 18878.4i | 1.05763i | 0.848737 | + | 0.528816i | \(0.177364\pi\) | ||||
−0.848737 | + | 0.528816i | \(0.822636\pi\) | |||||||
\(684\) | 4.72835i | 0 0.000264317i | ||||||||
\(685\) | 9383.45 | 0.523391 | ||||||||
\(686\) | −19120.1 | −1.06415 | ||||||||
\(687\) | − 16152.9i | − 0.897045i | ||||||||
\(688\) | 35217.8 | 1.95155 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −3644.32 | −0.201068 | ||||||||
\(691\) | 11692.8i | 0.643726i | 0.946786 | + | 0.321863i | \(0.104309\pi\) | ||||
−0.946786 | + | 0.321863i | \(0.895691\pi\) | |||||||
\(692\) | 83.7265 | 0.00459943 | ||||||||
\(693\) | −4257.81 | −0.233392 | ||||||||
\(694\) | 7874.82i | 0.430726i | ||||||||
\(695\) | − 8311.14i | − 0.453611i | ||||||||
\(696\) | 12186.9i | 0.663714i | ||||||||
\(697\) | 8198.19i | 0.445522i | ||||||||
\(698\) | 19513.3 | 1.05815 | ||||||||
\(699\) | 14740.8 | 0.797638 | ||||||||
\(700\) | − 64.0873i | − 0.00346039i | ||||||||
\(701\) | −20658.1 | −1.11304 | −0.556522 | − | 0.830833i | \(-0.687865\pi\) | ||||
−0.556522 | + | 0.830833i | \(0.687865\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2569.99 | 0.137879 | ||||||||
\(704\) | 18247.0i | 0.976861i | ||||||||
\(705\) | −643.823 | −0.0343940 | ||||||||
\(706\) | 21547.3 | 1.14864 | ||||||||
\(707\) | − 10271.0i | − 0.546365i | ||||||||
\(708\) | − 34.8343i | − 0.00184909i | ||||||||
\(709\) | 20695.8i | 1.09626i | 0.836394 | + | 0.548128i | \(0.184659\pi\) | ||||
−0.836394 | + | 0.548128i | \(0.815341\pi\) | |||||||
\(710\) | − 5509.23i | − 0.291208i | ||||||||
\(711\) | −1870.18 | −0.0986461 | ||||||||
\(712\) | −27897.1 | −1.46838 | ||||||||
\(713\) | 32312.1i | 1.69719i | ||||||||
\(714\) | 7865.79 | 0.412283 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 117.956 | 0.00615674 | ||||||||
\(717\) | 2891.16i | 0.150589i | ||||||||
\(718\) | 15489.6 | 0.805109 | ||||||||
\(719\) | 26299.2 | 1.36411 | 0.682053 | − | 0.731302i | \(-0.261087\pi\) | ||||
0.682053 | + | 0.731302i | \(0.261087\pi\) | |||||||
\(720\) | 1954.21i | 0.101152i | ||||||||
\(721\) | 20598.9i | 1.06400i | ||||||||
\(722\) | − 18914.9i | − 0.974986i | ||||||||
\(723\) | − 4633.45i | − 0.238340i | ||||||||
\(724\) | 79.9213 | 0.00410256 | ||||||||
\(725\) | −20299.3 | −1.03986 | ||||||||
\(726\) | − 627.004i | − 0.0320528i | ||||||||
\(727\) | 16915.6 | 0.862952 | 0.431476 | − | 0.902125i | \(-0.357993\pi\) | ||||
0.431476 | + | 0.902125i | \(0.357993\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 257.053i | 0.0130328i | ||||||||
\(731\) | 38533.5 | 1.94967 | ||||||||
\(732\) | 76.6417 | 0.00386989 | ||||||||
\(733\) | − 13203.1i | − 0.665302i | −0.943050 | − | 0.332651i | \(-0.892057\pi\) | ||||
0.943050 | − | 0.332651i | \(-0.107943\pi\) | |||||||
\(734\) | − 19005.8i | − 0.955746i | ||||||||
\(735\) | − 1687.70i | − 0.0846964i | ||||||||
\(736\) | − 242.044i | − 0.0121221i | ||||||||
\(737\) | −26271.3 | −1.31305 | ||||||||
\(738\) | −2988.24 | −0.149050 | ||||||||
\(739\) | 16813.9i | 0.836954i | 0.908227 | + | 0.418477i | \(0.137436\pi\) | ||||
−0.908227 | + | 0.418477i | \(0.862564\pi\) | |||||||
\(740\) | −29.9453 | −0.00148758 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5534.68 | 0.273834 | ||||||||
\(743\) | − 32682.1i | − 1.61371i | −0.590747 | − | 0.806857i | \(-0.701167\pi\) | ||||
0.590747 | − | 0.806857i | \(-0.298833\pi\) | |||||||
\(744\) | 17419.1 | 0.858355 | ||||||||
\(745\) | −5176.30 | −0.254557 | ||||||||
\(746\) | 11087.4i | 0.544156i | ||||||||
\(747\) | − 9282.37i | − 0.454651i | ||||||||
\(748\) | 104.613i | 0.00511370i | ||||||||
\(749\) | − 27057.2i | − 1.31996i | ||||||||
\(750\) | −6880.57 | −0.334991 | ||||||||
\(751\) | −2157.76 | −0.104844 | −0.0524219 | − | 0.998625i | \(-0.516694\pi\) | ||||
−0.0524219 | + | 0.998625i | \(0.516694\pi\) | |||||||
\(752\) | 4005.35i | 0.194229i | ||||||||
\(753\) | −11304.5 | −0.547090 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1990.74 | −0.0959606 | ||||||||
\(756\) | − 15.2635i | 0 0.000734296i | ||||||||
\(757\) | 13769.6 | 0.661117 | 0.330558 | − | 0.943786i | \(-0.392763\pi\) | ||||
0.330558 | + | 0.943786i | \(0.392763\pi\) | |||||||
\(758\) | 33562.6 | 1.60824 | ||||||||
\(759\) | − 13427.9i | − 0.642165i | ||||||||
\(760\) | − 959.648i | − 0.0458028i | ||||||||
\(761\) | − 16905.2i | − 0.805272i | −0.915360 | − | 0.402636i | \(-0.868094\pi\) | ||||
0.915360 | − | 0.402636i | \(-0.131906\pi\) | |||||||
\(762\) | 11217.7i | 0.533302i | ||||||||
\(763\) | 21950.8 | 1.04151 | ||||||||
\(764\) | 103.705 | 0.00491087 | ||||||||
\(765\) | 2138.19i | 0.101054i | ||||||||
\(766\) | 13394.7 | 0.631813 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −195.208 | −0.00917185 | ||||||||
\(769\) | − 1153.35i | − 0.0540845i | −0.999634 | − | 0.0270422i | \(-0.991391\pi\) | ||||
0.999634 | − | 0.0270422i | \(-0.00860886\pi\) | |||||||
\(770\) | 4552.01 | 0.213043 | ||||||||
\(771\) | −3848.03 | −0.179745 | ||||||||
\(772\) | 81.5787i | 0.00380322i | ||||||||
\(773\) | 20713.9i | 0.963811i | 0.876223 | + | 0.481905i | \(0.160055\pi\) | ||||
−0.876223 | + | 0.481905i | \(0.839945\pi\) | |||||||
\(774\) | 14045.4i | 0.652265i | ||||||||
\(775\) | 29014.3i | 1.34480i | ||||||||
\(776\) | 40725.7 | 1.88398 | ||||||||
\(777\) | −8296.14 | −0.383040 | ||||||||
\(778\) | 31875.1i | 1.46887i | ||||||||
\(779\) | 1459.65 | 0.0671341 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20299.4 | 0.930053 | ||||||||
\(782\) | 24806.5i | 1.13437i | ||||||||
\(783\) | −4834.61 | −0.220658 | ||||||||
\(784\) | −10499.5 | −0.478294 | ||||||||
\(785\) | − 89.0010i | − 0.00404660i | ||||||||
\(786\) | − 7871.35i | − 0.357203i | ||||||||
\(787\) | 10870.2i | 0.492353i | 0.969225 | + | 0.246177i | \(0.0791743\pi\) | ||||
−0.969225 | + | 0.246177i | \(0.920826\pi\) | |||||||
\(788\) | − 77.1006i | − 0.00348553i | ||||||||
\(789\) | 15089.2 | 0.680850 | ||||||||
\(790\) | 1999.41 | 0.0900451 | ||||||||
\(791\) | 8733.95i | 0.392596i | ||||||||
\(792\) | −7238.86 | −0.324775 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −39078.4 | −1.74665 | ||||||||
\(795\) | 1504.52i | 0.0671192i | ||||||||
\(796\) | 53.9706 | 0.00240319 | ||||||||
\(797\) | −12026.6 | −0.534511 | −0.267255 | − | 0.963626i | \(-0.586117\pi\) | ||||
−0.267255 | + | 0.963626i | \(0.586117\pi\) | |||||||
\(798\) | − 1400.47i | − 0.0621255i | ||||||||
\(799\) | 4382.43i | 0.194042i | ||||||||
\(800\) | − 217.341i | − 0.00960519i | ||||||||
\(801\) | − 11066.9i | − 0.488177i | ||||||||
\(802\) | −15330.7 | −0.674996 | ||||||||
\(803\) | −947.142 | −0.0416238 | ||||||||
\(804\) | − 94.1778i | − 0.00413109i | ||||||||
\(805\) | −5746.39 | −0.251594 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16885.4 | 0.736547 | ||||||||
\(808\) | − 17462.1i | − 0.760289i | ||||||||
\(809\) | −32384.0 | −1.40737 | −0.703685 | − | 0.710512i | \(-0.748463\pi\) | ||||
−0.703685 | + | 0.710512i | \(0.748463\pi\) | |||||||
\(810\) | −779.371 | −0.0338078 | ||||||||
\(811\) | − 42506.8i | − 1.84046i | −0.391375 | − | 0.920231i | \(-0.628000\pi\) | ||||
0.391375 | − | 0.920231i | \(-0.372000\pi\) | |||||||
\(812\) | 101.225i | 0.00437476i | ||||||||
\(813\) | − 10105.2i | − 0.435921i | ||||||||
\(814\) | 20725.6i | 0.892423i | ||||||||
\(815\) | −58.2937 | −0.00250545 | ||||||||
\(816\) | 13302.1 | 0.570670 | ||||||||
\(817\) | − 6860.72i | − 0.293790i | ||||||||
\(818\) | −9795.47 | −0.418693 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −17.0077 | −0.000724312 0 | ||||||||
\(821\) | 20052.6i | 0.852427i | 0.904623 | + | 0.426213i | \(0.140153\pi\) | ||||
−0.904623 | + | 0.426213i | \(0.859847\pi\) | |||||||
\(822\) | 23281.4 | 0.987872 | ||||||||
\(823\) | 31625.5 | 1.33948 | 0.669742 | − | 0.742594i | \(-0.266405\pi\) | ||||
0.669742 | + | 0.742594i | \(0.266405\pi\) | |||||||
\(824\) | 35020.9i | 1.48060i | ||||||||
\(825\) | − 12057.5i | − 0.508832i | ||||||||
\(826\) | 10317.4i | 0.434612i | ||||||||
\(827\) | 5440.97i | 0.228780i | 0.993436 | + | 0.114390i | \(0.0364913\pi\) | ||||
−0.993436 | + | 0.114390i | \(0.963509\pi\) | |||||||
\(828\) | 48.1367 | 0.00202037 | ||||||||
\(829\) | 24845.8 | 1.04093 | 0.520465 | − | 0.853883i | \(-0.325759\pi\) | ||||
0.520465 | + | 0.853883i | \(0.325759\pi\) | |||||||
\(830\) | 9923.75i | 0.415010i | ||||||||
\(831\) | 19523.2 | 0.814986 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11488.0 | −0.477834 | ||||||||
\(834\) | − 20620.9i | − 0.856165i | ||||||||
\(835\) | −13368.9 | −0.554071 | ||||||||
\(836\) | 18.6260 | 0.000770566 0 | ||||||||
\(837\) | 6910.24i | 0.285368i | ||||||||
\(838\) | 12021.8i | 0.495568i | ||||||||
\(839\) | 45887.8i | 1.88823i | 0.329621 | + | 0.944113i | \(0.393079\pi\) | ||||
−0.329621 | + | 0.944113i | \(0.606921\pi\) | |||||||
\(840\) | 3097.82i | 0.127244i | ||||||||
\(841\) | 7673.40 | 0.314625 | ||||||||
\(842\) | 17588.7 | 0.719887 | ||||||||
\(843\) | 10876.5i | 0.444375i | ||||||||
\(844\) | −55.8969 | −0.00227968 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1597.40 | −0.0649168 | ||||||||
\(847\) | − 988.665i | − 0.0401073i | ||||||||
\(848\) | 9359.88 | 0.379033 | ||||||||
\(849\) | 13906.2 | 0.562144 | ||||||||
\(850\) | 22274.7i | 0.898842i | ||||||||
\(851\) | − 26163.7i | − 1.05391i | ||||||||
\(852\) | 72.7698i | 0.00292612i | ||||||||
\(853\) | − 33655.3i | − 1.35092i | −0.737397 | − | 0.675460i | \(-0.763945\pi\) | ||||
0.737397 | − | 0.675460i | \(-0.236055\pi\) | |||||||
\(854\) | −22700.2 | −0.909583 | ||||||||
\(855\) | 380.696 | 0.0152275 | ||||||||
\(856\) | − 46000.9i | − 1.83677i | ||||||||
\(857\) | −41365.6 | −1.64880 | −0.824399 | − | 0.566009i | \(-0.808487\pi\) | ||||
−0.824399 | + | 0.566009i | \(0.808487\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14866.0 | 0.590480 | 0.295240 | − | 0.955423i | \(-0.404600\pi\) | ||||
0.295240 | + | 0.955423i | \(0.404600\pi\) | |||||||
\(860\) | 79.9404i | 0.00316970i | ||||||||
\(861\) | −4711.87 | −0.186504 | ||||||||
\(862\) | 7110.37 | 0.280952 | ||||||||
\(863\) | − 15469.1i | − 0.610167i | −0.952326 | − | 0.305083i | \(-0.901316\pi\) | ||||
0.952326 | − | 0.305083i | \(-0.0986843\pi\) | |||||||
\(864\) | − 51.7634i | − 0.00203822i | ||||||||
\(865\) | − 6741.12i | − 0.264977i | ||||||||
\(866\) | − 3621.76i | − 0.142116i | ||||||||
\(867\) | −184.553 | −0.00722925 | ||||||||
\(868\) | 144.684 | 0.00565770 | ||||||||
\(869\) | 7367.05i | 0.287584i | ||||||||
\(870\) | 5168.67 | 0.201419 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 37319.4 | 1.44930 | ||||||||
\(873\) | 16156.0i | 0.626345i | ||||||||
\(874\) | 4416.69 | 0.170934 | ||||||||
\(875\) | −10849.3 | −0.419171 | ||||||||
\(876\) | − 3.39533i | 0 0.000130956i | ||||||||
\(877\) | − 38100.7i | − 1.46701i | −0.679684 | − | 0.733505i | \(-0.737883\pi\) | ||||
0.679684 | − | 0.733505i | \(-0.262117\pi\) | |||||||
\(878\) | − 47792.0i | − 1.83702i | ||||||||
\(879\) | 8721.21i | 0.334652i | ||||||||
\(880\) | 7698.06 | 0.294888 | ||||||||
\(881\) | −3879.84 | −0.148371 | −0.0741857 | − | 0.997244i | \(-0.523636\pi\) | ||||
−0.0741857 | + | 0.997244i | \(0.523636\pi\) | |||||||
\(882\) | − 4187.38i | − 0.159860i | ||||||||
\(883\) | −13046.5 | −0.497225 | −0.248613 | − | 0.968603i | \(-0.579975\pi\) | ||||
−0.248613 | + | 0.968603i | \(0.579975\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2804.64 | −0.106528 | ||||||||
\(886\) | 6101.66i | 0.231365i | ||||||||
\(887\) | −32833.2 | −1.24288 | −0.621438 | − | 0.783463i | \(-0.713451\pi\) | ||||
−0.621438 | + | 0.783463i | \(0.713451\pi\) | |||||||
\(888\) | −14104.6 | −0.533017 | ||||||||
\(889\) | 17688.2i | 0.667315i | ||||||||
\(890\) | 11831.6i | 0.445613i | ||||||||
\(891\) | − 2871.69i | − 0.107974i | ||||||||
\(892\) | 50.9829i | 0.00191372i | ||||||||
\(893\) | 780.274 | 0.0292395 | ||||||||
\(894\) | −12843.0 | −0.480462 | ||||||||
\(895\) | − 9497.06i | − 0.354695i | ||||||||
\(896\) | 19169.5 | 0.714741 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4720.39 | 0.175414 | ||||||||
\(899\) | − 45827.6i | − 1.70015i | ||||||||
\(900\) | 43.2238 | 0.00160088 | ||||||||
\(901\) | 10241.1 | 0.378668 | ||||||||
\(902\) | 11771.3i | 0.434525i | ||||||||
\(903\) | 22147.0i | 0.816173i | ||||||||
\(904\) | 14848.9i | 0.546314i | ||||||||
\(905\) | − 6434.74i | − 0.236352i | ||||||||
\(906\) | −4939.23 | −0.181120 | ||||||||
\(907\) | −21346.3 | −0.781468 | −0.390734 | − | 0.920504i | \(-0.627779\pi\) | ||||
−0.390734 | + | 0.920504i | \(0.627779\pi\) | |||||||
\(908\) | − 184.760i | − 0.00675272i | ||||||||
\(909\) | 6927.28 | 0.252765 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7792.71 | 0.283407 | 0.141704 | − | 0.989909i | \(-0.454742\pi\) | ||||
0.141704 | + | 0.989909i | \(0.454742\pi\) | |||||||
\(912\) | − 2368.38i | − 0.0859923i | ||||||||
\(913\) | −36565.2 | −1.32545 | ||||||||
\(914\) | −13124.0 | −0.474950 | ||||||||
\(915\) | − 6170.69i | − 0.222947i | ||||||||
\(916\) | − 228.101i | − 0.00822779i | ||||||||
\(917\) | − 12411.6i | − 0.446965i | ||||||||
\(918\) | 5305.09i | 0.190734i | ||||||||
\(919\) | −31352.0 | −1.12536 | −0.562681 | − | 0.826674i | \(-0.690230\pi\) | ||||
−0.562681 | + | 0.826674i | \(0.690230\pi\) | |||||||
\(920\) | −9769.64 | −0.350104 | ||||||||
\(921\) | − 2801.85i | − 0.100243i | ||||||||
\(922\) | 9760.61 | 0.348643 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −60.1262 | −0.00214070 | ||||||||
\(925\) | − 23493.4i | − 0.835089i | ||||||||
\(926\) | 5939.85 | 0.210794 | ||||||||
\(927\) | −13893.0 | −0.492238 | ||||||||
\(928\) | 343.286i | 0.0121432i | ||||||||
\(929\) | 12675.3i | 0.447646i | 0.974630 | + | 0.223823i | \(0.0718537\pi\) | ||||
−0.974630 | + | 0.223823i | \(0.928146\pi\) | |||||||
\(930\) | − 7387.71i | − 0.260487i | ||||||||
\(931\) | 2045.39i | 0.0720032i | ||||||||
\(932\) | 208.161 | 0.00731601 | ||||||||
\(933\) | 10900.7 | 0.382499 | ||||||||
\(934\) | − 3994.09i | − 0.139926i | ||||||||
\(935\) | 8422.80 | 0.294604 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12308.5 | −0.429138 | −0.214569 | − | 0.976709i | \(-0.568835\pi\) | ||||
−0.214569 | + | 0.976709i | \(0.568835\pi\) | |||||||
\(938\) | 27894.1i | 0.970976i | ||||||||
\(939\) | −22521.8 | −0.782717 | ||||||||
\(940\) | −9.09167 | −0.000315466 0 | ||||||||
\(941\) | 20465.2i | 0.708978i | 0.935060 | + | 0.354489i | \(0.115345\pi\) | ||||
−0.935060 | + | 0.354489i | \(0.884655\pi\) | |||||||
\(942\) | − 220.821i | − 0.00763774i | ||||||||
\(943\) | − 14859.9i | − 0.513155i | ||||||||
\(944\) | 17448.2i | 0.601578i | ||||||||
\(945\) | −1228.92 | −0.0423034 | ||||||||
\(946\) | 55328.0 | 1.90155 | ||||||||
\(947\) | − 11170.8i | − 0.383318i | −0.981462 | − | 0.191659i | \(-0.938613\pi\) | ||||
0.981462 | − | 0.191659i | \(-0.0613867\pi\) | |||||||
\(948\) | −26.4096 | −0.000904792 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 3965.91 | 0.135443 | ||||||||
\(951\) | 3643.81i | 0.124247i | ||||||||
\(952\) | 21086.5 | 0.717876 | ||||||||
\(953\) | −14109.4 | −0.479587 | −0.239794 | − | 0.970824i | \(-0.577080\pi\) | ||||
−0.239794 | + | 0.970824i | \(0.577080\pi\) | |||||||
\(954\) | 3732.87i | 0.126684i | ||||||||
\(955\) | − 8349.64i | − 0.282919i | ||||||||
\(956\) | 40.8271i | 0.00138122i | ||||||||
\(957\) | 19044.6i | 0.643285i | ||||||||
\(958\) | 2780.29 | 0.0937653 | ||||||||
\(959\) | 36710.2 | 1.23612 | ||||||||
\(960\) | 5266.57i | 0.177060i | ||||||||
\(961\) | −35711.6 | −1.19874 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18248.8 | 0.610652 | ||||||||
\(964\) | − 65.4307i | − 0.00218608i | ||||||||
\(965\) | 6568.19 | 0.219106 | ||||||||
\(966\) | −14257.4 | −0.474870 | ||||||||
\(967\) | − 40785.8i | − 1.35634i | −0.734904 | − | 0.678171i | \(-0.762773\pi\) | ||||
0.734904 | − | 0.678171i | \(-0.237227\pi\) | |||||||
\(968\) | − 1680.87i | − 0.0558110i | ||||||||
\(969\) | − 2591.36i | − 0.0859096i | ||||||||
\(970\) | − 17272.4i | − 0.571734i | ||||||||
\(971\) | 4230.29 | 0.139811 | 0.0699055 | − | 0.997554i | \(-0.477730\pi\) | ||||
0.0699055 | + | 0.997554i | \(0.477730\pi\) | |||||||
\(972\) | 10.2945 | 0.000339708 0 | ||||||||
\(973\) | − 32515.1i | − 1.07131i | ||||||||
\(974\) | 41537.4 | 1.36647 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −38389.0 | −1.25902 | ||||||||
\(977\) | − 59925.0i | − 1.96230i | −0.193242 | − | 0.981151i | \(-0.561900\pi\) | ||||
0.193242 | − | 0.981151i | \(-0.438100\pi\) | |||||||
\(978\) | −144.633 | −0.00472890 | ||||||||
\(979\) | −43594.9 | −1.42319 | ||||||||
\(980\) | − 23.8327i | 0 0.000776844i | ||||||||
\(981\) | 14804.8i | 0.481834i | ||||||||
\(982\) | − 45984.6i | − 1.49433i | ||||||||
\(983\) | 23333.3i | 0.757087i | 0.925584 | + | 0.378543i | \(0.123575\pi\) | ||||
−0.925584 | + | 0.378543i | \(0.876425\pi\) | |||||||
\(984\) | −8010.83 | −0.259528 | ||||||||
\(985\) | −6207.64 | −0.200804 | ||||||||
\(986\) | − 35182.5i | − 1.13635i | ||||||||
\(987\) | −2518.79 | −0.0812298 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −69845.2 | −2.24565 | ||||||||
\(990\) | 3070.11i | 0.0985601i | ||||||||
\(991\) | −32523.5 | −1.04253 | −0.521263 | − | 0.853396i | \(-0.674539\pi\) | ||||
−0.521263 | + | 0.853396i | \(0.674539\pi\) | |||||||
\(992\) | 490.668 | 0.0157044 | ||||||||
\(993\) | 7329.61i | 0.234238i | ||||||||
\(994\) | − 21553.4i | − 0.687759i | ||||||||
\(995\) | − 4345.37i | − 0.138450i | ||||||||
\(996\) | − 131.080i | − 0.00417010i | ||||||||
\(997\) | −7114.35 | −0.225992 | −0.112996 | − | 0.993595i | \(-0.536045\pi\) | ||||
−0.112996 | + | 0.993595i | \(0.536045\pi\) | |||||||
\(998\) | 9112.77 | 0.289038 | ||||||||
\(999\) | − 5595.35i | − 0.177206i |
(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 | 507.4.b.k.337.6 | 18 | ||
13.5 | odd | 4 | 507.4.a.p.1.3 | yes | 9 | ||
13.8 | odd | 4 | 507.4.a.o.1.7 | ✓ | 9 | ||
13.12 | even | 2 | inner | 507.4.b.k.337.13 | 18 | ||
39.5 | even | 4 | 1521.4.a.bf.1.7 | 9 | |||
39.8 | even | 4 | 1521.4.a.bi.1.3 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.4.a.o.1.7 | ✓ | 9 | 13.8 | odd | 4 | ||
507.4.a.p.1.3 | yes | 9 | 13.5 | odd | 4 | ||
507.4.b.k.337.6 | 18 | 1.1 | even | 1 | trivial | ||
507.4.b.k.337.13 | 18 | 13.12 | even | 2 | inner | ||
1521.4.a.bf.1.7 | 9 | 39.5 | even | 4 | |||
1521.4.a.bi.1.3 | 9 | 39.8 | even | 4 |