Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [378,4,Mod(215,378)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(378, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("378.215");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.k (of order \(6\), degree \(2\), 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: | \(22.3027219822\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} + 2 x^{18} - 32 x^{17} - 669 x^{16} + 1752 x^{15} - 1654 x^{14} + 13878 x^{13} + 494085 x^{12} - 780096 x^{11} + 556152 x^{10} - 2898760 x^{9} + \cdots + 2458624 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{18}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 269.2 | ||
Root | \(-4.83258 + 1.29489i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 378.269 |
Dual form | 378.4.k.d.215.2 |
$q$-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 \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.73205 | + | 1.00000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | − | 3.46410i | 0.250000 | − | 0.433013i | ||||
\(5\) | −3.43124 | − | 5.94308i | −0.306899 | − | 0.531565i | 0.670783 | − | 0.741654i | \(-0.265958\pi\) |
−0.977682 | + | 0.210088i | \(0.932625\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −18.5152 | − | 0.434813i | −0.999724 | − | 0.0234777i | ||||
\(8\) | 8.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 11.8862 | + | 6.86248i | 0.375873 | + | 0.217011i | ||||
\(11\) | 28.6032 | + | 16.5141i | 0.784017 | + | 0.452652i | 0.837852 | − | 0.545898i | \(-0.183811\pi\) |
−0.0538351 | + | 0.998550i | \(0.517145\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 65.9110i | 1.40619i | 0.711097 | + | 0.703093i | \(0.248198\pi\) | ||||
−0.711097 | + | 0.703093i | \(0.751802\pi\) | |||||||
\(14\) | 32.5040 | − | 17.7620i | 0.620504 | − | 0.339079i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | −7.20650 | + | 12.4820i | −0.102814 | + | 0.178078i | −0.912843 | − | 0.408311i | \(-0.866118\pi\) |
0.810029 | + | 0.586390i | \(0.199451\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −44.9254 | + | 25.9377i | −0.542452 | + | 0.313185i | −0.746072 | − | 0.665865i | \(-0.768063\pi\) |
0.203620 | + | 0.979050i | \(0.434729\pi\) | |||||||
\(20\) | −27.4499 | −0.306899 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −66.0562 | −0.640147 | ||||||||
\(23\) | 174.131 | − | 100.535i | 1.57865 | − | 0.911433i | 0.583600 | − | 0.812041i | \(-0.301644\pi\) |
0.995048 | − | 0.0993915i | \(-0.0316896\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 38.9532 | − | 67.4689i | 0.311626 | − | 0.539752i | ||||
\(26\) | −65.9110 | − | 114.161i | −0.497162 | − | 0.861110i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −38.5365 | + | 63.2688i | −0.260097 | + | 0.427024i | ||||
\(29\) | − | 227.304i | − | 1.45549i | −0.685847 | − | 0.727746i | \(-0.740568\pi\) | ||
0.685847 | − | 0.727746i | \(-0.259432\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −24.5744 | − | 14.1881i | −0.142377 | − | 0.0822017i | 0.427119 | − | 0.904195i | \(-0.359528\pi\) |
−0.569497 | + | 0.821994i | \(0.692862\pi\) | |||||||
\(32\) | 27.7128 | + | 16.0000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 28.8260i | − | 0.145400i | ||||||
\(35\) | 60.9458 | + | 111.529i | 0.294335 | + | 0.538624i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −101.081 | − | 175.078i | −0.449126 | − | 0.777910i | 0.549203 | − | 0.835689i | \(-0.314931\pi\) |
−0.998329 | + | 0.0577792i | \(0.981598\pi\) | |||||||
\(38\) | 51.8754 | − | 89.8508i | 0.221455 | − | 0.383572i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 47.5446 | − | 27.4499i | 0.187937 | − | 0.108505i | ||||
\(41\) | 34.6120 | 0.131841 | 0.0659206 | − | 0.997825i | \(-0.479002\pi\) | ||||
0.0659206 | + | 0.997825i | \(0.479002\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −483.052 | −1.71313 | −0.856566 | − | 0.516038i | \(-0.827406\pi\) | ||||
−0.856566 | + | 0.516038i | \(0.827406\pi\) | |||||||
\(44\) | 114.413 | − | 66.0562i | 0.392008 | − | 0.226326i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −201.070 | + | 348.263i | −0.644480 | + | 1.11627i | ||||
\(47\) | −95.7687 | − | 165.876i | −0.297219 | − | 0.514799i | 0.678280 | − | 0.734804i | \(-0.262726\pi\) |
−0.975499 | + | 0.220005i | \(0.929393\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 342.622 | + | 16.1012i | 0.998898 | + | 0.0469424i | ||||
\(50\) | 155.813i | 0.440705i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 228.322 | + | 131.822i | 0.608897 | + | 0.351547i | ||||
\(53\) | −75.4532 | − | 43.5629i | −0.195553 | − | 0.112902i | 0.399027 | − | 0.916939i | \(-0.369348\pi\) |
−0.594579 | + | 0.804037i | \(0.702681\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 226.655i | − | 0.555675i | ||||||
\(56\) | 3.47850 | − | 148.121i | 0.00830061 | − | 0.353456i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 227.304 | + | 393.702i | 0.514594 | + | 0.891303i | ||||
\(59\) | 292.449 | − | 506.536i | 0.645315 | − | 1.11772i | −0.338913 | − | 0.940818i | \(-0.610059\pi\) |
0.984229 | − | 0.176901i | \(-0.0566073\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 303.713 | − | 175.349i | 0.637483 | − | 0.368051i | −0.146162 | − | 0.989261i | \(-0.546692\pi\) |
0.783644 | + | 0.621210i | \(0.213359\pi\) | |||||||
\(62\) | 56.7523 | 0.116251 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 391.714 | − | 226.156i | 0.747480 | − | 0.431558i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 315.762 | − | 546.916i | 0.575768 | − | 0.997260i | −0.420190 | − | 0.907436i | \(-0.638036\pi\) |
0.995958 | − | 0.0898233i | \(-0.0286302\pi\) | |||||||
\(68\) | 28.8260 | + | 49.9281i | 0.0514068 | + | 0.0890392i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −217.090 | − | 132.228i | −0.370675 | − | 0.225775i | ||||
\(71\) | − | 932.935i | − | 1.55942i | −0.626139 | − | 0.779712i | \(-0.715366\pi\) | ||
0.626139 | − | 0.779712i | \(-0.284634\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 191.352 | + | 110.477i | 0.306795 | + | 0.177128i | 0.645491 | − | 0.763768i | \(-0.276653\pi\) |
−0.338697 | + | 0.940896i | \(0.609986\pi\) | |||||||
\(74\) | 350.156 | + | 202.163i | 0.550065 | + | 0.317580i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 207.501i | 0.313185i | ||||||||
\(77\) | −522.412 | − | 318.197i | −0.773174 | − | 0.470934i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 228.057 | + | 395.007i | 0.324790 | + | 0.562553i | 0.981470 | − | 0.191616i | \(-0.0613729\pi\) |
−0.656680 | + | 0.754170i | \(0.728040\pi\) | |||||||
\(80\) | −54.8998 | + | 95.0893i | −0.0767248 | + | 0.132891i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −59.9498 | + | 34.6120i | −0.0807360 | + | 0.0466129i | ||||
\(83\) | 1363.85 | 1.80364 | 0.901822 | − | 0.432107i | \(-0.142230\pi\) | ||||
0.901822 | + | 0.432107i | \(0.142230\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 98.9088 | 0.126214 | ||||||||
\(86\) | 836.670 | − | 483.052i | 1.04907 | − | 0.605684i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −132.112 | + | 228.825i | −0.160037 | + | 0.277192i | ||||
\(89\) | 358.658 | + | 621.215i | 0.427165 | + | 0.739872i | 0.996620 | − | 0.0821507i | \(-0.0261789\pi\) |
−0.569455 | + | 0.822023i | \(0.692846\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 28.6589 | − | 1220.35i | 0.0330140 | − | 1.40580i | ||||
\(92\) | − | 804.279i | − | 0.911433i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 331.752 | + | 191.537i | 0.364018 | + | 0.210166i | ||||
\(95\) | 308.299 | + | 177.997i | 0.332956 | + | 0.192232i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 9.90916i | − | 0.0103724i | −0.999987 | − | 0.00518620i | \(-0.998349\pi\) | ||
0.999987 | − | 0.00518620i | \(-0.00165083\pi\) | |||||||
\(98\) | −609.540 | + | 314.734i | −0.628294 | + | 0.324417i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −155.813 | − | 269.876i | −0.155813 | − | 0.269876i | ||||
\(101\) | −47.7022 | + | 82.6226i | −0.0469955 | + | 0.0813985i | −0.888566 | − | 0.458748i | \(-0.848298\pi\) |
0.841571 | + | 0.540147i | \(0.181631\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 983.832 | − | 568.016i | 0.941163 | − | 0.543381i | 0.0508385 | − | 0.998707i | \(-0.483811\pi\) |
0.890325 | + | 0.455326i | \(0.150477\pi\) | |||||||
\(104\) | −527.288 | −0.497162 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 174.252 | 0.159668 | ||||||||
\(107\) | −1799.33 | + | 1038.84i | −1.62568 | + | 0.938584i | −0.640313 | + | 0.768114i | \(0.721195\pi\) |
−0.985363 | + | 0.170470i | \(0.945471\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 59.1994 | − | 102.536i | 0.0520208 | − | 0.0901027i | −0.838842 | − | 0.544374i | \(-0.816767\pi\) |
0.890863 | + | 0.454272i | \(0.150100\pi\) | |||||||
\(110\) | 226.655 | + | 392.577i | 0.196461 | + | 0.340280i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 142.096 | + | 260.032i | 0.119882 | + | 0.219381i | ||||
\(113\) | 112.853i | 0.0939496i | 0.998896 | + | 0.0469748i | \(0.0149580\pi\) | ||||
−0.998896 | + | 0.0469748i | \(0.985042\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1194.97 | − | 689.918i | −0.968972 | − | 0.559436i | ||||
\(116\) | −787.403 | − | 454.608i | −0.630246 | − | 0.363873i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1169.80i | 0.912614i | ||||||||
\(119\) | 138.857 | − | 227.973i | 0.106966 | − | 0.175616i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −120.072 | − | 207.970i | −0.0902117 | − | 0.156251i | ||||
\(122\) | −350.697 | + | 607.426i | −0.260251 | + | 0.450768i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −98.2978 | + | 56.7523i | −0.0711887 | + | 0.0411008i | ||||
\(125\) | −1392.44 | −0.996349 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −857.420 | −0.599084 | −0.299542 | − | 0.954083i | \(-0.596834\pi\) | ||||
−0.299542 | + | 0.954083i | \(0.596834\pi\) | |||||||
\(128\) | 110.851 | − | 64.0000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −452.313 | + | 783.429i | −0.305157 | + | 0.528548i | ||||
\(131\) | 357.900 | + | 619.902i | 0.238702 | + | 0.413443i | 0.960342 | − | 0.278825i | \(-0.0899449\pi\) |
−0.721640 | + | 0.692268i | \(0.756612\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 843.078 | − | 460.706i | 0.549655 | − | 0.300363i | ||||
\(134\) | 1263.05i | 0.814259i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −99.8562 | − | 57.6520i | −0.0629603 | − | 0.0363501i | ||||
\(137\) | 114.971 | + | 66.3786i | 0.0716982 | + | 0.0413950i | 0.535421 | − | 0.844586i | \(-0.320153\pi\) |
−0.463722 | + | 0.885981i | \(0.653486\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2907.60i | − | 1.77424i | −0.461540 | − | 0.887119i | \(-0.652703\pi\) | ||
0.461540 | − | 0.887119i | \(-0.347297\pi\) | |||||||
\(140\) | 508.239 | + | 11.9356i | 0.306815 | + | 0.00720528i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 932.935 | + | 1615.89i | 0.551339 | + | 0.954948i | ||||
\(143\) | −1088.46 | + | 1885.27i | −0.636514 | + | 1.10247i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1350.88 | + | 779.933i | −0.773688 | + | 0.446689i | ||||
\(146\) | −441.908 | −0.250497 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −808.651 | −0.449126 | ||||||||
\(149\) | 2517.63 | − | 1453.55i | 1.38424 | − | 0.799192i | 0.391583 | − | 0.920143i | \(-0.371928\pi\) |
0.992659 | + | 0.120951i | \(0.0385943\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −451.859 | + | 782.642i | −0.243521 | + | 0.421791i | −0.961715 | − | 0.274052i | \(-0.911636\pi\) |
0.718193 | + | 0.695843i | \(0.244969\pi\) | |||||||
\(152\) | −207.501 | − | 359.403i | −0.110728 | − | 0.191786i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1223.04 | + | 28.7221i | 0.639971 | + | 0.0150292i | ||||
\(155\) | 194.730i | 0.100911i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2157.41 | + | 1245.58i | 1.09669 | + | 0.633174i | 0.935350 | − | 0.353725i | \(-0.115085\pi\) |
0.161340 | + | 0.986899i | \(0.448418\pi\) | |||||||
\(158\) | −790.013 | − | 456.114i | −0.397785 | − | 0.229661i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 219.599i | − | 0.108505i | ||||||
\(161\) | −3267.78 | + | 1785.70i | −1.59961 | + | 0.874119i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 727.153 | + | 1259.47i | 0.349417 | + | 0.605208i | 0.986146 | − | 0.165879i | \(-0.0530463\pi\) |
−0.636729 | + | 0.771088i | \(0.719713\pi\) | |||||||
\(164\) | 69.2241 | − | 119.900i | 0.0329603 | − | 0.0570890i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2362.27 | + | 1363.85i | −1.10450 | + | 0.637685i | ||||
\(167\) | −1402.20 | −0.649733 | −0.324866 | − | 0.945760i | \(-0.605319\pi\) | ||||
−0.324866 | + | 0.945760i | \(0.605319\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2147.26 | −0.977362 | ||||||||
\(170\) | −171.315 | + | 98.9088i | −0.0772898 | + | 0.0446233i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −966.103 | + | 1673.34i | −0.428283 | + | 0.741808i | ||||
\(173\) | 1458.60 | + | 2526.36i | 0.641012 | + | 1.11027i | 0.985207 | + | 0.171367i | \(0.0548185\pi\) |
−0.344195 | + | 0.938898i | \(0.611848\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −750.561 | + | 1232.26i | −0.324212 | + | 0.532287i | ||||
\(176\) | − | 528.450i | − | 0.226326i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1242.43 | − | 717.317i | −0.523169 | − | 0.302052i | ||||
\(179\) | −2921.84 | − | 1686.93i | −1.22005 | − | 0.704396i | −0.255121 | − | 0.966909i | \(-0.582115\pi\) |
−0.964928 | + | 0.262513i | \(0.915449\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3857.00i | − | 1.58392i | −0.610576 | − | 0.791958i | \(-0.709062\pi\) | ||
0.610576 | − | 0.791958i | \(-0.290938\pi\) | |||||||
\(182\) | 1170.71 | + | 2142.37i | 0.476808 | + | 0.872545i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 804.279 | + | 1393.05i | 0.322240 | + | 0.558136i | ||||
\(185\) | −693.669 | + | 1201.47i | −0.275673 | + | 0.477480i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −412.258 | + | 238.017i | −0.161215 | + | 0.0930777i | ||||
\(188\) | −766.149 | −0.297219 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −711.987 | −0.271858 | ||||||||
\(191\) | 1849.52 | − | 1067.82i | 0.700662 | − | 0.404527i | −0.106932 | − | 0.994266i | \(-0.534103\pi\) |
0.807594 | + | 0.589739i | \(0.200769\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 566.229 | − | 980.737i | 0.211182 | − | 0.365777i | −0.740903 | − | 0.671612i | \(-0.765602\pi\) |
0.952085 | + | 0.305835i | \(0.0989355\pi\) | |||||||
\(194\) | 9.90916 | + | 17.1632i | 0.00366720 | + | 0.00635177i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 741.020 | − | 1154.67i | 0.270051 | − | 0.420800i | ||||
\(197\) | 1972.82i | 0.713490i | 0.934202 | + | 0.356745i | \(0.116114\pi\) | ||||
−0.934202 | + | 0.356745i | \(0.883886\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1006.36 | + | 581.025i | 0.358489 | + | 0.206974i | 0.668418 | − | 0.743786i | \(-0.266972\pi\) |
−0.309929 | + | 0.950760i | \(0.600305\pi\) | |||||||
\(200\) | 539.752 | + | 311.626i | 0.190831 | + | 0.110176i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 190.809i | − | 0.0664616i | ||||||
\(203\) | −98.8346 | + | 4208.56i | −0.0341716 | + | 1.45509i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −118.762 | − | 205.702i | −0.0404620 | − | 0.0700822i | ||||
\(206\) | −1136.03 | + | 1967.66i | −0.384228 | + | 0.665503i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 913.290 | − | 527.288i | 0.304448 | − | 0.175773i | ||||
\(209\) | −1713.35 | −0.567055 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3561.70 | −1.16207 | −0.581037 | − | 0.813877i | \(-0.697353\pi\) | ||||
−0.581037 | + | 0.813877i | \(0.697353\pi\) | |||||||
\(212\) | −301.813 | + | 174.252i | −0.0977764 | + | 0.0564512i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2077.68 | − | 3598.65i | 0.663679 | − | 1.14953i | ||||
\(215\) | 1657.46 | + | 2870.81i | 0.525759 | + | 0.910641i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 448.831 | + | 273.379i | 0.140408 | + | 0.0855217i | ||||
\(218\) | 236.797i | 0.0735686i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −785.155 | − | 453.309i | −0.240614 | − | 0.138919i | ||||
\(221\) | −822.703 | − | 474.988i | −0.250412 | − | 0.144575i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 479.700i | 0.144050i | 0.997403 | + | 0.0720249i | \(0.0229461\pi\) | ||||
−0.997403 | + | 0.0720249i | \(0.977054\pi\) | |||||||
\(224\) | −506.150 | − | 308.292i | −0.150976 | − | 0.0919583i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −112.853 | − | 195.467i | −0.0332162 | − | 0.0575321i | ||||
\(227\) | 2054.69 | − | 3558.83i | 0.600769 | − | 1.04056i | −0.391935 | − | 0.919993i | \(-0.628194\pi\) |
0.992705 | − | 0.120570i | \(-0.0384724\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1965.47 | + | 1134.77i | −0.567170 | + | 0.327456i | −0.756018 | − | 0.654550i | \(-0.772858\pi\) |
0.188848 | + | 0.982006i | \(0.439525\pi\) | |||||||
\(230\) | 2759.67 | 0.791162 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1818.43 | 0.514594 | ||||||||
\(233\) | −292.043 | + | 168.611i | −0.0821133 | + | 0.0474081i | −0.540494 | − | 0.841348i | \(-0.681763\pi\) |
0.458381 | + | 0.888756i | \(0.348429\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −657.210 | + | 1138.32i | −0.182433 | + | 0.315983i | ||||
\(236\) | −1169.80 | − | 2026.15i | −0.322658 | − | 0.558859i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −12.5339 | + | 533.718i | −0.00341367 | + | 0.145360i | ||||
\(239\) | − | 1119.50i | − | 0.302990i | −0.988458 | − | 0.151495i | \(-0.951591\pi\) | ||
0.988458 | − | 0.151495i | \(-0.0484088\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3778.92 | + | 2181.76i | 1.01005 | + | 0.583152i | 0.911206 | − | 0.411951i | \(-0.135153\pi\) |
0.0988426 | + | 0.995103i | \(0.468486\pi\) | |||||||
\(242\) | 415.941 | + | 240.144i | 0.110486 | + | 0.0637893i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 1402.79i | − | 0.368051i | ||||||
\(245\) | −1079.93 | − | 2091.48i | −0.281608 | − | 0.545386i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1709.58 | − | 2961.08i | −0.440396 | − | 0.762789i | ||||
\(248\) | 113.505 | − | 196.596i | 0.0290627 | − | 0.0503380i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2411.78 | − | 1392.44i | 0.610137 | − | 0.352263i | ||||
\(251\) | −3878.06 | −0.975222 | −0.487611 | − | 0.873061i | \(-0.662132\pi\) | ||||
−0.487611 | + | 0.873061i | \(0.662132\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6640.95 | 1.65025 | ||||||||
\(254\) | 1485.09 | − | 857.420i | 0.366863 | − | 0.211808i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 300.225 | + | 520.005i | 0.0728698 | + | 0.126214i | 0.900158 | − | 0.435564i | \(-0.143451\pi\) |
−0.827288 | + | 0.561778i | \(0.810118\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1795.41 | + | 3285.55i | 0.430739 | + | 0.788240i | ||||
\(260\) | − | 1809.25i | − | 0.431558i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1239.80 | − | 715.801i | −0.292349 | − | 0.168788i | ||||
\(263\) | −3050.60 | − | 1761.27i | −0.715240 | − | 0.412944i | 0.0977581 | − | 0.995210i | \(-0.468833\pi\) |
−0.812998 | + | 0.582266i | \(0.802166\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 597.899i | 0.138599i | ||||||||
\(266\) | −999.549 | + | 1641.04i | −0.230399 | + | 0.378267i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1263.05 | − | 2187.66i | −0.287884 | − | 0.498630i | ||||
\(269\) | 2938.40 | − | 5089.46i | 0.666012 | − | 1.15357i | −0.312998 | − | 0.949754i | \(-0.601333\pi\) |
0.979010 | − | 0.203813i | \(-0.0653335\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2902.80 | − | 1675.93i | 0.650673 | − | 0.375666i | −0.138041 | − | 0.990427i | \(-0.544080\pi\) |
0.788714 | + | 0.614760i | \(0.210747\pi\) | |||||||
\(272\) | 230.608 | 0.0514068 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −265.515 | −0.0585413 | ||||||||
\(275\) | 2228.37 | − | 1286.55i | 0.488640 | − | 0.282116i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2396.31 | + | 4150.53i | −0.519785 | + | 0.900293i | 0.479951 | + | 0.877295i | \(0.340654\pi\) |
−0.999736 | + | 0.0229980i | \(0.992679\pi\) | |||||||
\(278\) | 2907.60 | + | 5036.11i | 0.627288 | + | 1.08649i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −892.232 | + | 487.566i | −0.190432 | + | 0.104063i | ||||
\(281\) | − | 6132.70i | − | 1.30194i | −0.759102 | − | 0.650971i | \(-0.774362\pi\) | ||
0.759102 | − | 0.650971i | \(-0.225638\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2487.31 | − | 1436.05i | −0.522458 | − | 0.301641i | 0.215482 | − | 0.976508i | \(-0.430868\pi\) |
−0.737940 | + | 0.674867i | \(0.764201\pi\) | |||||||
\(284\) | −3231.78 | − | 1865.87i | −0.675250 | − | 0.389856i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 4353.83i | − | 0.900166i | ||||||
\(287\) | −640.847 | − | 15.0498i | −0.131805 | − | 0.00309533i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2352.63 | + | 4074.88i | 0.478859 | + | 0.829408i | ||||
\(290\) | 1559.87 | − | 2701.77i | 0.315857 | − | 0.547080i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 765.407 | − | 441.908i | 0.153397 | − | 0.0885640i | ||||
\(293\) | 4741.31 | 0.945360 | 0.472680 | − | 0.881234i | \(-0.343287\pi\) | ||||
0.472680 | + | 0.881234i | \(0.343287\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4013.85 | −0.792187 | ||||||||
\(296\) | 1400.62 | − | 808.651i | 0.275033 | − | 0.158790i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2907.10 | + | 5035.25i | −0.565114 | + | 0.978806i | ||||
\(299\) | 6626.35 | + | 11477.2i | 1.28165 | + | 2.21987i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8943.77 | + | 210.037i | 1.71266 | + | 0.0402204i | ||||
\(302\) | − | 1807.43i | − | 0.344391i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 718.806 | + | 415.003i | 0.135613 | + | 0.0782962i | ||||
\(305\) | −2084.22 | − | 1203.33i | −0.391286 | − | 0.225909i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 6632.39i | − | 1.23300i | −0.787355 | − | 0.616499i | \(-0.788550\pi\) | ||
0.787355 | − | 0.616499i | \(-0.211450\pi\) | |||||||
\(308\) | −2147.09 | + | 1173.29i | −0.397214 | + | 0.217060i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −194.730 | − | 337.283i | −0.0356773 | − | 0.0617948i | ||||
\(311\) | 3785.11 | − | 6556.00i | 0.690140 | − | 1.19536i | −0.281651 | − | 0.959517i | \(-0.590882\pi\) |
0.971792 | − | 0.235841i | \(-0.0757846\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5933.44 | + | 3425.67i | −1.07150 | + | 0.618628i | −0.928590 | − | 0.371108i | \(-0.878978\pi\) |
−0.142906 | + | 0.989736i | \(0.545645\pi\) | |||||||
\(314\) | −4982.33 | −0.895443 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1824.46 | 0.324790 | ||||||||
\(317\) | 4568.52 | − | 2637.63i | 0.809443 | − | 0.467332i | −0.0373193 | − | 0.999303i | \(-0.511882\pi\) |
0.846762 | + | 0.531971i | \(0.178549\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3753.71 | − | 6501.61i | 0.658832 | − | 1.14113i | ||||
\(320\) | 219.599 | + | 380.357i | 0.0383624 | + | 0.0664456i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3874.26 | − | 6360.71i | 0.670510 | − | 1.10083i | ||||
\(323\) | − | 747.679i | − | 0.128799i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4446.95 | + | 2567.45i | 0.758992 | + | 0.438204i | ||||
\(326\) | −2518.93 | − | 1454.31i | −0.427947 | − | 0.247075i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 276.896i | 0.0466129i | ||||||||
\(329\) | 1701.05 | + | 3112.87i | 0.285051 | + | 0.521635i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3089.55 | + | 5351.25i | 0.513042 | + | 0.888614i | 0.999886 | + | 0.0151252i | \(0.00481468\pi\) |
−0.486844 | + | 0.873489i | \(0.661852\pi\) | |||||||
\(332\) | 2727.71 | − | 4724.53i | 0.450911 | − | 0.781001i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2428.68 | − | 1402.20i | 0.397878 | − | 0.229715i | ||||
\(335\) | −4333.82 | −0.706811 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3792.02 | −0.612951 | −0.306475 | − | 0.951879i | \(-0.599150\pi\) | ||||
−0.306475 | + | 0.951879i | \(0.599150\pi\) | |||||||
\(338\) | 3719.17 | − | 2147.26i | 0.598509 | − | 0.345550i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 197.818 | − | 342.630i | 0.0315534 | − | 0.0546522i | ||||
\(341\) | −468.605 | − | 811.648i | −0.0744175 | − | 0.128895i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6336.70 | − | 447.093i | −0.997520 | − | 0.0703813i | ||||
\(344\) | − | 3864.41i | − | 0.605684i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5052.73 | − | 2917.19i | −0.785076 | − | 0.453264i | ||||
\(347\) | −6380.27 | − | 3683.65i | −0.987062 | − | 0.569881i | −0.0826675 | − | 0.996577i | \(-0.526344\pi\) |
−0.904395 | + | 0.426696i | \(0.859677\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9408.31i | 1.44302i | 0.692402 | + | 0.721512i | \(0.256553\pi\) | ||||
−0.692402 | + | 0.721512i | \(0.743447\pi\) | |||||||
\(350\) | 67.7494 | − | 2884.90i | 0.0103467 | − | 0.440584i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 528.450 | + | 915.302i | 0.0800184 | + | 0.138596i | ||||
\(353\) | −1411.89 | + | 2445.47i | −0.212883 | + | 0.368723i | −0.952615 | − | 0.304177i | \(-0.901619\pi\) |
0.739733 | + | 0.672901i | \(0.234952\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5544.51 | + | 3201.12i | −0.828935 | + | 0.478586i | ||||
\(356\) | 2869.27 | 0.427165 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6747.71 | 0.996167 | ||||||||
\(359\) | 9971.93 | − | 5757.30i | 1.46601 | − | 0.846402i | 0.466734 | − | 0.884398i | \(-0.345431\pi\) |
0.999278 | + | 0.0379953i | \(0.0120972\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2083.97 | + | 3609.55i | −0.303830 | + | 0.526250i | ||||
\(362\) | 3857.00 | + | 6680.52i | 0.559999 | + | 0.969946i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4170.11 | − | 2539.98i | −0.600475 | − | 0.365745i | ||||
\(365\) | − | 1516.29i | − | 0.217442i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7817.42 | − | 4513.39i | −1.11190 | − | 0.641954i | −0.172577 | − | 0.984996i | \(-0.555209\pi\) |
−0.939320 | + | 0.343042i | \(0.888543\pi\) | |||||||
\(368\) | −2786.10 | − | 1608.56i | −0.394662 | − | 0.227858i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 2774.67i | − | 0.389861i | ||||||
\(371\) | 1378.09 | + | 839.382i | 0.192848 | + | 0.117462i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1982.76 | + | 3434.23i | 0.275236 | + | 0.476723i | 0.970195 | − | 0.242327i | \(-0.0779105\pi\) |
−0.694958 | + | 0.719050i | \(0.744577\pi\) | |||||||
\(374\) | 476.034 | − | 824.515i | 0.0658159 | − | 0.113996i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1327.01 | − | 766.149i | 0.182009 | − | 0.105083i | ||||
\(377\) | 14981.8 | 2.04669 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12103.7 | −1.64044 | −0.820221 | − | 0.572047i | \(-0.806149\pi\) | ||||
−0.820221 | + | 0.572047i | \(0.806149\pi\) | |||||||
\(380\) | 1233.20 | − | 711.987i | 0.166478 | − | 0.0961162i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2135.64 | + | 3699.03i | −0.286044 | + | 0.495443i | ||||
\(383\) | −2263.10 | − | 3919.81i | −0.301930 | − | 0.522958i | 0.674643 | − | 0.738144i | \(-0.264297\pi\) |
−0.976573 | + | 0.215186i | \(0.930964\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −98.5523 | + | 4196.55i | −0.0130459 | + | 0.555521i | ||||
\(386\) | 2264.92i | 0.298656i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −34.3263 | − | 19.8183i | −0.00449138 | − | 0.00259310i | ||||
\(389\) | −2027.54 | − | 1170.60i | −0.264268 | − | 0.152575i | 0.362012 | − | 0.932173i | \(-0.382090\pi\) |
−0.626280 | + | 0.779598i | \(0.715423\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2898.02i | 0.374831i | ||||||||
\(392\) | −128.810 | + | 2740.98i | −0.0165966 | + | 0.353164i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1972.82 | − | 3417.02i | −0.252257 | − | 0.436922i | ||||
\(395\) | 1565.04 | − | 2710.72i | 0.199356 | − | 0.345294i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9683.92 | − | 5591.01i | 1.22424 | − | 0.706813i | 0.258418 | − | 0.966033i | \(-0.416799\pi\) |
0.965818 | + | 0.259220i | \(0.0834655\pi\) | |||||||
\(398\) | −2324.10 | −0.292705 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1246.50 | −0.155813 | ||||||||
\(401\) | 9808.28 | − | 5662.81i | 1.22145 | − | 0.705205i | 0.256224 | − | 0.966617i | \(-0.417521\pi\) |
0.965227 | + | 0.261412i | \(0.0841881\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 935.150 | − | 1619.73i | 0.115591 | − | 0.200209i | ||||
\(404\) | 190.809 | + | 330.490i | 0.0234977 | + | 0.0406993i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4037.38 | − | 7388.28i | −0.493526 | − | 0.903139i | ||||
\(407\) | − | 6677.06i | − | 0.813193i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9068.41 | + | 5235.65i | 1.09634 | + | 0.632974i | 0.935258 | − | 0.353967i | \(-0.115168\pi\) |
0.161084 | + | 0.986941i | \(0.448501\pi\) | |||||||
\(410\) | 411.404 | + | 237.524i | 0.0495556 | + | 0.0286109i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 4544.12i | − | 0.543381i | ||||||
\(413\) | −5634.98 | + | 9251.44i | −0.671379 | + | 1.10226i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4679.71 | − | 8105.50i | −0.553537 | − | 0.958755i | ||||
\(416\) | −1054.58 | + | 1826.58i | −0.124291 | + | 0.215278i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2967.60 | − | 1713.35i | 0.347249 | − | 0.200484i | ||||
\(419\) | −10355.8 | −1.20743 | −0.603717 | − | 0.797199i | \(-0.706314\pi\) | ||||
−0.603717 | + | 0.797199i | \(0.706314\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2613.96 | 0.302604 | 0.151302 | − | 0.988488i | \(-0.451653\pi\) | ||||
0.151302 | + | 0.988488i | \(0.451653\pi\) | |||||||
\(422\) | 6169.05 | − | 3561.70i | 0.711623 | − | 0.410855i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 348.503 | − | 603.626i | 0.0399170 | − | 0.0691383i | ||||
\(425\) | 561.432 | + | 972.430i | 0.0640788 | + | 0.110988i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5699.53 | + | 3114.55i | −0.645948 | + | 0.352983i | ||||
\(428\) | 8310.73i | 0.938584i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5741.63 | − | 3314.93i | −0.643920 | − | 0.371768i | ||||
\(431\) | −3344.94 | − | 1931.20i | −0.373829 | − | 0.215830i | 0.301301 | − | 0.953529i | \(-0.402579\pi\) |
−0.675130 | + | 0.737699i | \(0.735912\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17569.5i | 1.94997i | 0.222280 | + | 0.974983i | \(0.428650\pi\) | ||||
−0.222280 | + | 0.974983i | \(0.571350\pi\) | |||||||
\(434\) | −1050.78 | − | 24.6766i | −0.116219 | − | 0.00272930i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −236.797 | − | 410.145i | −0.0260104 | − | 0.0450514i | ||||
\(437\) | −5215.28 | + | 9033.13i | −0.570894 | + | 0.988817i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9969.18 | + | 5755.71i | −1.08383 | + | 0.625752i | −0.931928 | − | 0.362643i | \(-0.881874\pi\) |
−0.151906 | + | 0.988395i | \(0.548541\pi\) | |||||||
\(440\) | 1813.24 | 0.196461 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1899.95 | 0.204460 | ||||||||
\(443\) | 6386.93 | − | 3687.49i | 0.684993 | − | 0.395481i | −0.116740 | − | 0.993162i | \(-0.537245\pi\) |
0.801734 | + | 0.597681i | \(0.203911\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2461.28 | − | 4263.07i | 0.262193 | − | 0.454132i | ||||
\(446\) | −479.700 | − | 830.865i | −0.0509293 | − | 0.0882121i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1184.97 | + | 27.8280i | 0.124966 | + | 0.00293471i | ||||
\(449\) | − | 10388.6i | − | 1.09192i | −0.837813 | − | 0.545958i | \(-0.816166\pi\) | ||
0.837813 | − | 0.545958i | \(-0.183834\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 990.015 | + | 571.585i | 0.103366 | + | 0.0596783i | ||||
\(452\) | 390.934 | + | 225.706i | 0.0406814 | + | 0.0234874i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8218.77i | 0.849616i | ||||||||
\(455\) | −7350.99 | + | 4017.00i | −0.757406 | + | 0.413890i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1264.70 | − | 2190.53i | −0.129454 | − | 0.224220i | 0.794011 | − | 0.607903i | \(-0.207989\pi\) |
−0.923465 | + | 0.383683i | \(0.874656\pi\) | |||||||
\(458\) | 2269.53 | − | 3930.94i | 0.231546 | − | 0.401050i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4779.89 | + | 2759.67i | −0.484486 | + | 0.279718i | ||||
\(461\) | −19385.0 | −1.95845 | −0.979227 | − | 0.202767i | \(-0.935007\pi\) | ||||
−0.979227 | + | 0.202767i | \(0.935007\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7386.83 | 0.741458 | 0.370729 | − | 0.928741i | \(-0.379108\pi\) | ||||
0.370729 | + | 0.928741i | \(0.379108\pi\) | |||||||
\(464\) | −3149.61 | + | 1818.43i | −0.315123 | + | 0.181936i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 337.223 | − | 584.087i | 0.0335226 | − | 0.0580629i | ||||
\(467\) | 6019.62 | + | 10426.3i | 0.596477 | + | 1.03313i | 0.993337 | + | 0.115249i | \(0.0367667\pi\) |
−0.396860 | + | 0.917879i | \(0.629900\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6084.19 | + | 9988.93i | −0.599023 | + | 0.983467i | ||||
\(470\) | − | 2628.84i | − | 0.257999i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4052.29 | + | 2339.59i | 0.395173 | + | 0.228153i | ||||
\(473\) | −13816.8 | − | 7977.14i | −1.34312 | − | 0.775453i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4041.42i | 0.390386i | ||||||||
\(476\) | −512.008 | − | 936.960i | −0.0493022 | − | 0.0902216i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1119.50 | + | 1939.04i | 0.107123 | + | 0.185543i | ||||
\(479\) | −7469.93 | + | 12938.3i | −0.712546 | + | 1.23417i | 0.251352 | + | 0.967896i | \(0.419125\pi\) |
−0.963898 | + | 0.266271i | \(0.914208\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11539.6 | − | 6662.38i | 1.09389 | − | 0.631556i | ||||
\(482\) | −8727.04 | −0.824701 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −960.574 | −0.0902117 | ||||||||
\(485\) | −58.8909 | + | 34.0007i | −0.00551360 | + | 0.00318328i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2645.81 | − | 4582.68i | 0.246187 | − | 0.426409i | −0.716278 | − | 0.697815i | \(-0.754156\pi\) |
0.962465 | + | 0.271407i | \(0.0874889\pi\) | |||||||
\(488\) | 1402.79 | + | 2429.70i | 0.130126 | + | 0.225384i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3961.96 | + | 2542.62i | 0.365272 | + | 0.234416i | ||||
\(491\) | 14095.0i | 1.29552i | 0.761845 | + | 0.647759i | \(0.224294\pi\) | ||||
−0.761845 | + | 0.647759i | \(0.775706\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2837.21 | + | 1638.06i | 0.259192 | + | 0.149644i | ||||
\(494\) | 5922.16 | + | 3419.16i | 0.539373 | + | 0.311407i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 454.018i | 0.0411008i | ||||||||
\(497\) | −405.652 | + | 17273.4i | −0.0366116 | + | 1.55899i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4303.22 | − | 7453.40i | −0.386050 | − | 0.668658i | 0.605865 | − | 0.795568i | \(-0.292827\pi\) |
−0.991914 | + | 0.126910i | \(0.959494\pi\) | |||||||
\(500\) | −2784.88 | + | 4823.56i | −0.249087 | + | 0.431432i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6716.99 | − | 3878.06i | 0.597199 | − | 0.344793i | ||||
\(503\) | 9541.90 | 0.845830 | 0.422915 | − | 0.906169i | \(-0.361007\pi\) | ||||
0.422915 | + | 0.906169i | \(0.361007\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 654.710 | 0.0576915 | ||||||||
\(506\) | −11502.5 | + | 6640.95i | −1.01057 | + | 0.583451i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1714.84 | + | 2970.19i | −0.149771 | + | 0.259411i | ||||
\(509\) | 4949.39 | + | 8572.60i | 0.430998 | + | 0.746510i | 0.996960 | − | 0.0779213i | \(-0.0248283\pi\) |
−0.565962 | + | 0.824432i | \(0.691495\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3494.87 | − | 2128.70i | −0.302552 | − | 0.184282i | ||||
\(512\) | − | 512.000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1040.01 | − | 600.450i | −0.0892469 | − | 0.0515267i | ||||
\(515\) | −6751.52 | − | 3897.99i | −0.577685 | − | 0.333526i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 6326.12i | − | 0.538148i | ||||||
\(518\) | −6395.29 | − | 3895.33i | −0.542458 | − | 0.330407i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1809.25 | + | 3133.72i | 0.152579 | + | 0.264274i | ||||
\(521\) | 4465.58 | − | 7734.61i | 0.375510 | − | 0.650402i | −0.614893 | − | 0.788610i | \(-0.710801\pi\) |
0.990403 | + | 0.138208i | \(0.0441343\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7532.64 | + | 4348.97i | −0.629789 | + | 0.363609i | −0.780670 | − | 0.624943i | \(-0.785122\pi\) |
0.150882 | + | 0.988552i | \(0.451789\pi\) | |||||||
\(524\) | 2863.20 | 0.238702 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7045.06 | 0.583991 | ||||||||
\(527\) | 354.191 | − | 204.492i | 0.0292767 | − | 0.0169029i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14131.0 | − | 24475.6i | 1.16142 | − | 2.01164i | ||||
\(530\) | −597.899 | − | 1035.59i | −0.0490020 | − | 0.0848740i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 90.2243 | − | 3841.92i | 0.00735285 | − | 0.313099i | ||||
\(533\) | 2281.32i | 0.185393i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12347.8 | + | 7129.02i | 0.997837 | + | 0.576102i | ||||
\(536\) | 4375.33 | + | 2526.10i | 0.352585 | + | 0.203565i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 11753.6i | 0.941884i | ||||||||
\(539\) | 9534.18 | + | 6118.62i | 0.761904 | + | 0.488957i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3981.40 | − | 6895.99i | −0.316402 | − | 0.548025i | 0.663332 | − | 0.748325i | \(-0.269142\pi\) |
−0.979735 | + | 0.200300i | \(0.935808\pi\) | |||||||
\(542\) | −3351.86 | + | 5805.60i | −0.265636 | + | 0.460096i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −399.425 | + | 230.608i | −0.0314801 | + | 0.0181751i | ||||
\(545\) | −812.508 | −0.0638606 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10238.1 | −0.800276 | −0.400138 | − | 0.916455i | \(-0.631038\pi\) | ||||
−0.400138 | + | 0.916455i | \(0.631038\pi\) | |||||||
\(548\) | 459.885 | − | 265.515i | 0.0358491 | − | 0.0206975i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2573.10 | + | 4456.74i | −0.199486 | + | 0.345520i | ||||
\(551\) | 5895.73 | + | 10211.7i | 0.455838 | + | 0.789534i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4050.76 | − | 7412.77i | −0.311493 | − | 0.570024i | ||||
\(554\) | − | 9585.24i | − | 0.735086i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10072.2 | − | 5815.19i | −0.768268 | − | 0.443560i | ||||
\(557\) | 2902.01 | + | 1675.47i | 0.220758 | + | 0.127454i | 0.606301 | − | 0.795235i | \(-0.292653\pi\) |
−0.385543 | + | 0.922690i | \(0.625986\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 31838.4i | − | 2.40898i | ||||||
\(560\) | 1057.82 | − | 1736.72i | 0.0798236 | − | 0.131053i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6132.70 | + | 10622.1i | 0.460306 | + | 0.797274i | ||||
\(563\) | 1477.19 | − | 2558.58i | 0.110580 | − | 0.191529i | −0.805425 | − | 0.592698i | \(-0.798063\pi\) |
0.916004 | + | 0.401169i | \(0.131396\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 670.693 | − | 387.225i | 0.0499403 | − | 0.0288331i | ||||
\(566\) | 5744.21 | 0.426585 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7463.48 | 0.551339 | ||||||||
\(569\) | −10620.5 | + | 6131.74i | −0.782485 | + | 0.451768i | −0.837310 | − | 0.546728i | \(-0.815873\pi\) |
0.0548252 | + | 0.998496i | \(0.482540\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6836.24 | − | 11840.7i | 0.501029 | − | 0.867808i | −0.498970 | − | 0.866619i | \(-0.666288\pi\) |
0.999999 | − | 0.00118894i | \(-0.000378452\pi\) | |||||||
\(572\) | 4353.83 | + | 7541.06i | 0.318257 | + | 0.551237i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1125.03 | − | 614.780i | 0.0818081 | − | 0.0447046i | ||||
\(575\) | − | 15664.6i | − | 1.13610i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21055.8 | + | 12156.6i | 1.51918 | + | 0.877096i | 0.999745 | + | 0.0225837i | \(0.00718923\pi\) |
0.519431 | + | 0.854513i | \(0.326144\pi\) | |||||||
\(578\) | −8149.76 | − | 4705.27i | −0.586480 | − | 0.338604i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6239.47i | 0.446689i | ||||||||
\(581\) | −25252.0 | − | 593.021i | −1.80315 | − | 0.0423454i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1438.80 | − | 2492.08i | −0.102211 | − | 0.177035i | ||||
\(584\) | −883.815 | + | 1530.81i | −0.0626242 | + | 0.108468i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8212.19 | + | 4741.31i | −0.578912 | + | 0.334235i | ||||
\(587\) | −20911.9 | −1.47040 | −0.735200 | − | 0.677851i | \(-0.762912\pi\) | ||||
−0.735200 | + | 0.677851i | \(0.762912\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1472.02 | 0.102977 | ||||||||
\(590\) | 6952.19 | − | 4013.85i | 0.485114 | − | 0.280080i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1617.30 | + | 2801.25i | −0.112282 | + | 0.194477i | ||||
\(593\) | 2269.12 | + | 3930.24i | 0.157136 | + | 0.272168i | 0.933835 | − | 0.357705i | \(-0.116441\pi\) |
−0.776699 | + | 0.629872i | \(0.783107\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1831.31 | − | 43.0068i | −0.126179 | − | 0.00296321i | ||||
\(596\) | − | 11628.4i | − | 0.799192i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −22954.4 | − | 13252.7i | −1.56969 | − | 0.906260i | ||||
\(599\) | 19553.9 | + | 11289.4i | 1.33380 | + | 0.770072i | 0.985880 | − | 0.167451i | \(-0.0535535\pi\) |
0.347924 | + | 0.937523i | \(0.386887\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3449.47i | 0.234121i | 0.993125 | + | 0.117061i | \(0.0373471\pi\) | ||||
−0.993125 | + | 0.117061i | \(0.962653\pi\) | |||||||
\(602\) | −15701.1 | + | 8579.98i | −1.06301 | + | 0.580887i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1807.43 | + | 3130.57i | 0.121761 | + | 0.210896i | ||||
\(605\) | −823.990 | + | 1427.19i | −0.0553718 | + | 0.0959068i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4570.23 | − | 2638.63i | 0.305601 | − | 0.176439i | −0.339355 | − | 0.940658i | \(-0.610209\pi\) |
0.644956 | + | 0.764219i | \(0.276875\pi\) | |||||||
\(608\) | −1660.01 | −0.110728 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4813.30 | 0.319484 | ||||||||
\(611\) | 10933.1 | − | 6312.21i | 0.723903 | − | 0.417946i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5405.00 | + | 9361.73i | −0.356127 | + | 0.616830i | −0.987310 | − | 0.158804i | \(-0.949236\pi\) |
0.631183 | + | 0.775634i | \(0.282570\pi\) | |||||||
\(614\) | 6632.39 | + | 11487.6i | 0.435931 | + | 0.755054i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2545.58 | − | 4179.30i | 0.166500 | − | 0.273358i | ||||
\(617\) | 19744.4i | 1.28830i | 0.764900 | + | 0.644149i | \(0.222788\pi\) | ||||
−0.764900 | + | 0.644149i | \(0.777212\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 948.715 | + | 547.741i | 0.0616027 | + | 0.0355664i | 0.530485 | − | 0.847694i | \(-0.322010\pi\) |
−0.468882 | + | 0.883261i | \(0.655343\pi\) | |||||||
\(620\) | 674.566 | + | 389.461i | 0.0436955 | + | 0.0252276i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15140.4i | 0.976006i | ||||||||
\(623\) | −6370.50 | − | 11657.8i | −0.409677 | − | 0.749697i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −91.3572 | − | 158.235i | −0.00584686 | − | 0.0101271i | ||||
\(626\) | 6851.35 | − | 11866.9i | 0.437436 | − | 0.757662i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8629.65 | − | 4982.33i | 0.548345 | − | 0.316587i | ||||
\(629\) | 2913.77 | 0.184705 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4564.95 | 0.287999 | 0.144000 | − | 0.989578i | \(-0.454004\pi\) | ||||
0.144000 | + | 0.989578i | \(0.454004\pi\) | |||||||
\(632\) | −3160.05 | + | 1824.46i | −0.198893 | + | 0.114831i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5275.27 | + | 9137.03i | −0.330454 | + | 0.572363i | ||||
\(635\) | 2942.01 | + | 5095.71i | 0.183859 | + | 0.318452i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1061.25 | + | 22582.6i | −0.0660098 | + | 1.40464i | ||||
\(638\) | 15014.8i | 0.931729i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −760.714 | − | 439.198i | −0.0469842 | − | 0.0271263i | ||||
\(641\) | 4810.24 | + | 2777.20i | 0.296401 | + | 0.171127i | 0.640825 | − | 0.767687i | \(-0.278592\pi\) |
−0.344424 | + | 0.938814i | \(0.611926\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27961.1i | 1.71490i | 0.514570 | + | 0.857449i | \(0.327952\pi\) | ||||
−0.514570 | + | 0.857449i | \(0.672048\pi\) | |||||||
\(644\) | −349.710 | + | 14891.3i | −0.0213983 | + | 0.911182i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 747.679 | + | 1295.02i | 0.0455372 | + | 0.0788728i | ||||
\(647\) | −10177.2 | + | 17627.5i | −0.618406 | + | 1.07111i | 0.371371 | + | 0.928485i | \(0.378888\pi\) |
−0.989777 | + | 0.142626i | \(0.954445\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16729.9 | − | 9659.03i | 1.01188 | − | 0.584207i | ||||
\(650\) | −10269.8 | −0.619714 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5817.22 | 0.349417 | ||||||||
\(653\) | 10991.1 | − | 6345.71i | 0.658674 | − | 0.380286i | −0.133097 | − | 0.991103i | \(-0.542492\pi\) |
0.791772 | + | 0.610817i | \(0.209159\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2456.08 | − | 4254.06i | 0.146515 | − | 0.253771i | ||||
\(656\) | −276.896 | − | 479.599i | −0.0164802 | − | 0.0285445i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6059.17 | − | 3690.59i | −0.358983 | − | 0.218654i | ||||
\(659\) | − | 19546.6i | − | 1.15543i | −0.816239 | − | 0.577714i | \(-0.803945\pi\) | ||
0.816239 | − | 0.577714i | \(-0.196055\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22849.3 | − | 13192.0i | −1.34453 | − | 0.776264i | −0.357060 | − | 0.934081i | \(-0.616221\pi\) |
−0.987468 | + | 0.157818i | \(0.949554\pi\) | |||||||
\(662\) | −10702.5 | − | 6179.09i | −0.628345 | − | 0.362775i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10910.8i | 0.637685i | ||||||||
\(665\) | −5630.82 | − | 3429.69i | −0.328351 | − | 0.199996i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22851.9 | − | 39580.7i | −1.32658 | − | 2.29771i | ||||
\(668\) | −2804.40 | + | 4857.36i | −0.162433 | + | 0.281343i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7506.39 | − | 4333.82i | 0.432832 | − | 0.249896i | ||||
\(671\) | 11582.9 | 0.666396 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 829.227 | 0.0474953 | 0.0237477 | − | 0.999718i | \(-0.492440\pi\) | ||||
0.0237477 | + | 0.999718i | \(0.492440\pi\) | |||||||
\(674\) | 6567.97 | − | 3792.02i | 0.375354 | − | 0.216711i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4294.53 | + | 7438.34i | −0.244340 | + | 0.423210i | ||||
\(677\) | 745.967 | + | 1292.05i | 0.0423484 | + | 0.0733495i | 0.886423 | − | 0.462877i | \(-0.153183\pi\) |
−0.844074 | + | 0.536226i | \(0.819849\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.30863 | + | 183.470i | −0.000243520 | + | 0.0103695i | ||||
\(680\) | 791.271i | 0.0446233i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1623.30 | + | 937.210i | 0.0911425 | + | 0.0526212i | ||||
\(683\) | −6008.93 | − | 3469.26i | −0.336640 | − | 0.194359i | 0.322145 | − | 0.946690i | \(-0.395596\pi\) |
−0.658785 | + | 0.752331i | \(0.728929\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 911.044i | − | 0.0508163i | ||||||
\(686\) | 11422.6 | − | 5562.31i | 0.635737 | − | 0.309577i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3864.41 | + | 6693.36i | 0.214141 | + | 0.370904i | ||||
\(689\) | 2871.28 | − | 4973.20i | 0.158762 | − | 0.274984i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −150.567 | + | 86.9299i | −0.00828921 | + | 0.00478578i | −0.504139 | − | 0.863623i | \(-0.668190\pi\) |
0.495850 | + | 0.868408i | \(0.334857\pi\) | |||||||
\(692\) | 11668.8 | 0.641012 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14734.6 | 0.805933 | ||||||||
\(695\) | −17280.1 | + | 9976.66i | −0.943123 | + | 0.544513i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −249.432 | + | 432.028i | −0.0135551 | + | 0.0234781i | ||||
\(698\) | −9408.31 | − | 16295.7i | −0.510186 | − | 0.883668i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2767.55 | + | 5064.54i | 0.149434 | + | 0.273460i | ||||
\(701\) | 13902.8i | 0.749076i | 0.927211 | + | 0.374538i | \(0.122199\pi\) | ||||
−0.927211 | + | 0.374538i | \(0.877801\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9082.24 | + | 5243.63i | 0.487259 | + | 0.281319i | ||||
\(704\) | −1830.60 | − | 1056.90i | −0.0980021 | − | 0.0565815i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 5647.58i | − | 0.301061i | ||||||
\(707\) | 919.138 | − | 1509.03i | 0.0488936 | − | 0.0802728i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1902.55 | − | 3295.32i | −0.100778 | − | 0.174553i | 0.811227 | − | 0.584731i | \(-0.198800\pi\) |
−0.912006 | + | 0.410178i | \(0.865467\pi\) | |||||||
\(710\) | 6402.25 | − | 11089.0i | 0.338411 | − | 0.586146i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4969.72 | + | 2869.27i | −0.261584 | + | 0.151026i | ||||
\(713\) | −5705.58 | −0.299685 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14939.0 | 0.781382 | ||||||||
\(716\) | −11687.4 | + | 6747.71i | −0.610025 | + | 0.352198i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −11514.6 | + | 19943.9i | −0.598497 | + | 1.03663i | ||||
\(719\) | −15869.0 | − | 27485.9i | −0.823107 | − | 1.42566i | −0.903358 | − | 0.428888i | \(-0.858906\pi\) |
0.0802513 | − | 0.996775i | \(-0.474428\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18462.8 | + | 10089.1i | −0.953661 | + | 0.521135i | ||||
\(722\) | − | 8335.89i | − | 0.429681i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −13361.0 | − | 7714.01i | −0.685856 | − | 0.395979i | ||||
\(725\) | −15335.9 | − | 8854.21i | −0.785604 | − | 0.453569i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 3362.88i | − | 0.171558i | −0.996314 | − | 0.0857789i | \(-0.972662\pi\) | ||
0.996314 | − | 0.0857789i | \(-0.0273379\pi\) | |||||||
\(728\) | 9762.82 | + | 229.272i | 0.497025 | + | 0.0116722i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1516.29 | + | 2626.29i | 0.0768773 | + | 0.133155i | ||||
\(731\) | 3481.11 | − | 6029.46i | 0.176133 | − | 0.305072i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26902.9 | + | 15532.4i | −1.35564 | + | 0.782676i | −0.989032 | − | 0.147701i | \(-0.952813\pi\) |
−0.366603 | + | 0.930377i | \(0.619479\pi\) | |||||||
\(734\) | 18053.6 | 0.907860 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6434.23 | 0.322240 | ||||||||
\(737\) | 18063.6 | − | 10429.0i | 0.902824 | − | 0.521246i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −222.377 | + | 385.168i | −0.0110694 | + | 0.0191727i | −0.871507 | − | 0.490383i | \(-0.836857\pi\) |
0.860438 | + | 0.509556i | \(0.170190\pi\) | |||||||
\(740\) | 2774.67 | + | 4805.88i | 0.137837 | + | 0.238740i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3226.30 | − | 75.7669i | −0.159624 | − | 0.00374864i | ||||
\(743\) | − | 9748.08i | − | 0.481322i | −0.970609 | − | 0.240661i | \(-0.922636\pi\) | ||
0.970609 | − | 0.240661i | \(-0.0773643\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17277.1 | − | 9974.97i | −0.849645 | − | 0.490543i | ||||
\(746\) | −6868.47 | − | 3965.51i | −0.337094 | − | 0.194622i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1904.14i | 0.0930777i | ||||||||
\(749\) | 33766.5 | − | 18451.9i | 1.64726 | − | 0.900159i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8765.46 | − | 15182.2i | −0.425907 | − | 0.737693i | 0.570598 | − | 0.821230i | \(-0.306712\pi\) |
−0.996505 | + | 0.0835371i | \(0.973378\pi\) | |||||||
\(752\) | −1532.30 | + | 2654.02i | −0.0743048 | + | 0.128700i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −25949.3 | + | 14981.8i | −1.25334 | + | 0.723615i | ||||
\(755\) | 6201.74 | 0.298946 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4717.30 | 0.226490 | 0.113245 | − | 0.993567i | \(-0.463875\pi\) | ||||
0.113245 | + | 0.993567i | \(0.463875\pi\) | |||||||
\(758\) | 20964.3 | − | 12103.7i | 1.00456 | − | 0.579984i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1423.97 | + | 2466.39i | −0.0679644 | + | 0.117718i | ||||
\(761\) | −16185.3 | − | 28033.8i | −0.770983 | − | 1.33538i | −0.937025 | − | 0.349262i | \(-0.886432\pi\) |
0.166042 | − | 0.986119i | \(-0.446901\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1140.67 | + | 1872.73i | −0.0541219 | + | 0.0888565i | ||||
\(764\) | − | 8542.55i | − | 0.404527i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7839.62 | + | 4526.20i | 0.369787 | + | 0.213497i | ||||
\(767\) | 33386.3 | + | 19275.6i | 1.57172 | + | 0.907434i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 15910.1i | − | 0.746076i | −0.927816 | − | 0.373038i | \(-0.878316\pi\) | ||
0.927816 | − | 0.373038i | \(-0.121684\pi\) | |||||||
\(770\) | −4025.85 | − | 7367.18i | −0.188418 | − | 0.344798i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2264.92 | − | 3922.95i | −0.105591 | − | 0.182889i | ||||
\(773\) | 7751.27 | − | 13425.6i | 0.360665 | − | 0.624690i | −0.627406 | − | 0.778693i | \(-0.715883\pi\) |
0.988070 | + | 0.154003i | \(0.0492165\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1914.51 | + | 1105.34i | −0.0887369 | + | 0.0512323i | ||||
\(776\) | 79.2732 | 0.00366720 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4682.40 | 0.215774 | ||||||||
\(779\) | −1554.96 | + | 897.756i | −0.0715176 | + | 0.0412907i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15406.5 | − | 26684.9i | 0.705877 | − | 1.22261i | ||||
\(782\) | −2898.02 | − | 5019.51i | −0.132523 | − | 0.229536i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2517.87 | − | 4876.32i | −0.114699 | − | 0.222135i | ||||
\(785\) | − | 17095.6i | − | 0.777283i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25807.5 | − | 14899.9i | −1.16892 | − | 0.674874i | −0.215491 | − | 0.976506i | \(-0.569135\pi\) |
−0.953424 | + | 0.301632i | \(0.902469\pi\) | |||||||
\(788\) | 6834.05 | + | 3945.64i | 0.308950 | + | 0.178373i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6260.15i | 0.281932i | ||||||||
\(791\) | 49.0699 | − | 2089.49i | 0.00220572 | − | 0.0939237i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11557.4 | + | 20018.0i | 0.517548 | + | 0.896420i | ||||
\(794\) | −11182.0 | + | 19367.8i | −0.499792 | + | 0.865666i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4025.46 | − | 2324.10i | 0.179244 | − | 0.103487i | ||||
\(797\) | 34495.2 | 1.53310 | 0.766550 | − | 0.642184i | \(-0.221972\pi\) | ||||
0.766550 | + | 0.642184i | \(0.221972\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2760.63 | 0.122233 | ||||||||
\(800\) | 2159.01 | − | 1246.50i | 0.0954155 | − | 0.0550882i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −11325.6 | + | 19616.6i | −0.498655 | + | 0.863697i | ||||
\(803\) | 3648.84 | + | 6319.98i | 0.160355 | + | 0.277743i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21825.1 | + | 13293.5i | 0.955571 | + | 0.582031i | ||||
\(806\) | 3740.60i | 0.163470i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −660.980 | − | 381.617i | −0.0287787 | − | 0.0166154i | ||||
\(809\) | −8073.09 | − | 4661.00i | −0.350846 | − | 0.202561i | 0.314212 | − | 0.949353i | \(-0.398260\pi\) |
−0.665058 | + | 0.746792i | \(0.731593\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 13684.8i | − | 0.592524i | −0.955107 | − | 0.296262i | \(-0.904260\pi\) | ||
0.955107 | − | 0.296262i | \(-0.0957401\pi\) | |||||||
\(812\) | 14381.2 | + | 8759.50i | 0.621530 | + | 0.378569i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6677.06 | + | 11565.0i | 0.287507 | + | 0.497977i | ||||
\(815\) | 4990.07 | − | 8643.05i | 0.214472 | − | 0.371476i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21701.3 | − | 12529.2i | 0.929292 | − | 0.536527i | ||||
\(818\) | −20942.6 | −0.895160 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −950.097 | −0.0404620 | ||||||||
\(821\) | 34689.6 | − | 20028.1i | 1.47464 | − | 0.851381i | 0.475044 | − | 0.879962i | \(-0.342432\pi\) |
0.999591 | + | 0.0285809i | \(0.00909884\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3961.13 | − | 6860.88i | 0.167772 | − | 0.290589i | −0.769864 | − | 0.638208i | \(-0.779676\pi\) |
0.937636 | + | 0.347618i | \(0.113009\pi\) | |||||||
\(824\) | 4544.12 | + | 7870.65i | 0.192114 | + | 0.332751i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 508.642 | − | 21658.9i | 0.0214260 | − | 0.912362i | ||||
\(827\) | 15771.5i | 0.663155i | 0.943428 | + | 0.331577i | \(0.107581\pi\) | ||||
−0.943428 | + | 0.331577i | \(0.892419\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30793.3 | + | 17778.5i | 1.29010 | + | 0.744840i | 0.978672 | − | 0.205429i | \(-0.0658589\pi\) |
0.311429 | + | 0.950269i | \(0.399192\pi\) | |||||||
\(830\) | 16211.0 | + | 9359.42i | 0.677942 | + | 0.391410i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 4218.31i | − | 0.175773i | ||||||
\(833\) | −2670.08 | + | 4160.58i | −0.111060 | + | 0.173056i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4811.28 | + | 8333.38i | 0.199403 | + | 0.345375i | ||||
\(836\) | −3426.69 | + | 5935.20i | −0.141764 | + | 0.245542i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 17936.8 | − | 10355.8i | 0.739399 | − | 0.426892i | ||||
\(839\) | −24413.9 | −1.00460 | −0.502301 | − | 0.864693i | \(-0.667513\pi\) | ||||
−0.502301 | + | 0.864693i | \(0.667513\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27278.0 | −1.11846 | ||||||||
\(842\) | −4527.50 | + | 2613.96i | −0.185307 | + | 0.106987i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7123.41 | + | 12338.1i | −0.290519 | + | 0.503193i | ||||
\(845\) | 7367.77 | + | 12761.4i | 0.299952 | + | 0.519531i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2132.72 | + | 3902.81i | 0.0865184 | + | 0.158326i | ||||
\(848\) | 1394.01i | 0.0564512i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1944.86 | − | 1122.86i | −0.0784801 | − | 0.0453105i | ||||
\(851\) | −35202.9 | − | 20324.4i | −1.41803 | − | 0.818697i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 32086.8i | − | 1.28796i | −0.765041 | − | 0.643981i | \(-0.777281\pi\) | ||
0.765041 | − | 0.643981i | \(-0.222719\pi\) | |||||||
\(854\) | 6757.33 | − | 11094.1i | 0.270762 | − | 0.444534i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8310.73 | − | 14394.6i | −0.331840 | − | 0.574763i | ||||
\(857\) | 6399.64 | − | 11084.5i | 0.255085 | − | 0.441820i | −0.709834 | − | 0.704369i | \(-0.751230\pi\) |
0.964919 | + | 0.262549i | \(0.0845633\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −42677.2 | + | 24639.7i | −1.69514 | + | 0.978690i | −0.744899 | + | 0.667177i | \(0.767502\pi\) |
−0.950242 | + | 0.311513i | \(0.899164\pi\) | |||||||
\(860\) | 13259.7 | 0.525759 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7724.82 | 0.305230 | ||||||||
\(863\) | −10317.0 | + | 5956.55i | −0.406948 | + | 0.234952i | −0.689478 | − | 0.724307i | \(-0.742160\pi\) |
0.282529 | + | 0.959259i | \(0.408826\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10009.6 | − | 17337.1i | 0.393452 | − | 0.681479i | ||||
\(866\) | −17569.5 | − | 30431.2i | −0.689417 | − | 1.19411i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1844.68 | − | 1008.04i | 0.0721341 | − | 0.0394182i | ||||
\(869\) | 15064.6i | 0.588069i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 36047.8 | + | 20812.2i | 1.40233 | + | 0.809638i | ||||
\(872\) | 820.290 | + | 473.595i | 0.0318561 | + | 0.0183921i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 20861.1i | − | 0.807366i | ||||||
\(875\) | 25781.2 | + | 605.451i | 0.996075 | + | 0.0233920i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8249.14 | − | 14287.9i | −0.317621 | − | 0.550136i | 0.662370 | − | 0.749177i | \(-0.269551\pi\) |
−0.979991 | + | 0.199041i | \(0.936217\pi\) | |||||||
\(878\) | 11511.4 | − | 19938.4i | 0.442473 | − | 0.766386i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3140.62 | + | 1813.24i | −0.120307 | + | 0.0694593i | ||||
\(881\) | −21721.2 | −0.830655 | −0.415327 | − | 0.909672i | \(-0.636333\pi\) | ||||
−0.415327 | + | 0.909672i | \(0.636333\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30605.7 | −1.16644 | −0.583219 | − | 0.812315i | \(-0.698207\pi\) | ||||
−0.583219 | + | 0.812315i | \(0.698207\pi\) | |||||||
\(884\) | −3290.81 | + | 1899.95i | −0.125206 | + | 0.0722876i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7374.99 | + | 12773.9i | −0.279647 | + | 0.484363i | ||||
\(887\) | 2826.08 | + | 4894.91i | 0.106979 | + | 0.185293i | 0.914545 | − | 0.404484i | \(-0.132549\pi\) |
−0.807566 | + | 0.589777i | \(0.799216\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15875.3 | + | 372.817i | 0.598919 | + | 0.0140651i | ||||
\(890\) | 9845.14i | 0.370798i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1661.73 | + | 959.400i | 0.0623754 | + | 0.0360124i | ||||
\(893\) | 8604.89 | + | 4968.04i | 0.322454 | + | 0.186169i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23153.0i | 0.864715i | ||||||||
\(896\) | −2080.26 | + | 1136.77i | −0.0775630 | + | 0.0423849i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10388.6 | + | 17993.7i | 0.386051 | + | 0.668659i | ||||
\(899\) | −3225.00 | + | 5585.86i | −0.119644 | + | 0.207229i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1087.51 | − | 627.872i | 0.0402110 | − | 0.0232158i | ||||
\(902\) | −2286.34 | −0.0843978 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −902.823 | −0.0332162 | ||||||||
\(905\) | −22922.5 | + | 13234.3i | −0.841954 | + | 0.486103i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17938.9 | − | 31071.2i | 0.656728 | − | 1.13749i | −0.324729 | − | 0.945807i | \(-0.605273\pi\) |
0.981458 | − | 0.191680i | \(-0.0613935\pi\) | |||||||
\(908\) | −8218.77 | − | 14235.3i | −0.300385 | − | 0.520282i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 8715.29 | − | 14308.6i | 0.317482 | − | 0.521238i | ||||
\(911\) | − | 45908.2i | − | 1.66960i | −0.550554 | − | 0.834800i | \(-0.685583\pi\) | ||
0.550554 | − | 0.834800i | \(-0.314417\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 39010.6 | + | 22522.8i | 1.41409 | + | 0.816424i | ||||
\(914\) | 4381.06 | + | 2529.40i | 0.158548 | + | 0.0915375i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9078.12i | 0.327456i | ||||||||
\(917\) | −6357.04 | − | 11633.2i | −0.228929 | − | 0.418933i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21716.4 | + | 37613.9i | 0.779498 | + | 1.35013i | 0.932231 | + | 0.361862i | \(0.117859\pi\) |
−0.152734 | + | 0.988267i | \(0.548808\pi\) | |||||||
\(920\) | 5519.34 | − | 9559.78i | 0.197791 | − | 0.342583i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 33575.7 | − | 19385.0i | 1.19930 | − | 0.692418i | ||||
\(923\) | 61490.7 | 2.19284 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15749.8 | −0.559837 | ||||||||
\(926\) | −12794.4 | + | 7386.83i | −0.454048 | + | 0.262145i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3636.86 | − | 6299.23i | 0.128648 | − | 0.222826i | ||||
\(929\) | 19732.4 | + | 34177.5i | 0.696877 | + | 1.20703i | 0.969544 | + | 0.244917i | \(0.0787608\pi\) |
−0.272667 | + | 0.962108i | \(0.587906\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15810.0 | + | 8163.46i | −0.556556 | + | 0.287376i | ||||
\(932\) | 1348.89i | 0.0474081i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −20852.6 | − | 12039.2i | −0.730532 | − | 0.421773i | ||||
\(935\) | 2829.11 | + | 1633.39i | 0.0989537 | + | 0.0571309i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28000.6i | 0.976242i | 0.872776 | + | 0.488121i | \(0.162318\pi\) | ||||
−0.872776 | + | 0.488121i | \(0.837682\pi\) | |||||||
\(938\) | 549.189 | − | 23385.5i | 0.0191169 | − | 0.814035i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2628.84 | + | 4553.29i | 0.0912163 | + | 0.157991i | ||||
\(941\) | 22909.8 | − | 39680.9i | 0.793664 | − | 1.37467i | −0.130019 | − | 0.991511i | \(-0.541504\pi\) |
0.923684 | − | 0.383156i | \(-0.125163\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6027.04 | − | 3479.72i | 0.208131 | − | 0.120164i | ||||
\(944\) | −9358.36 | −0.322658 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 31908.6 | 1.09666 | ||||||||
\(947\) | −21397.3 | + | 12353.7i | −0.734234 | + | 0.423910i | −0.819969 | − | 0.572408i | \(-0.806009\pi\) |
0.0857353 | + | 0.996318i | \(0.472676\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7281.65 | + | 12612.2i | −0.249075 | + | 0.431411i | ||||
\(950\) | −4041.42 | − | 6999.95i | −0.138022 | − | 0.239062i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1823.78 | + | 1110.85i | 0.0620895 | + | 0.0378183i | ||||
\(953\) | 48776.9i | 1.65796i | 0.559275 | + | 0.828982i | \(0.311080\pi\) | ||||
−0.559275 | + | 0.828982i | \(0.688920\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12692.3 | − | 7327.88i | −0.430065 | − | 0.248298i | ||||
\(956\) | −3878.08 | − | 2239.01i | −0.131199 | − | 0.0757476i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 29879.7i | − | 1.00769i | ||||||
\(959\) | −2099.85 | − | 1279.00i | −0.0707066 | − | 0.0430669i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14492.9 | − | 25102.4i | −0.486486 | − | 0.842618i | ||||
\(962\) | −13324.8 | + | 23079.2i | −0.446577 | + | 0.773495i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 15115.7 | − | 8727.04i | 0.505024 | − | 0.291576i | ||||
\(965\) | −7771.47 | −0.259246 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1312.29 | 0.0436406 | 0.0218203 | − | 0.999762i | \(-0.493054\pi\) | ||||
0.0218203 | + | 0.999762i | \(0.493054\pi\) | |||||||
\(968\) | 1663.76 | − | 960.574i | 0.0552432 | − | 0.0318947i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 68.0013 | − | 117.782i | 0.00225092 | − | 0.00389871i | ||||
\(971\) | −20988.7 | − | 36353.5i | −0.693676 | − | 1.20148i | −0.970625 | − | 0.240597i | \(-0.922657\pi\) |
0.276949 | − | 0.960885i | \(-0.410677\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1264.26 | + | 53834.6i | −0.0416550 | + | 1.77375i | ||||
\(974\) | 10583.2i | 0.348161i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4859.40 | − | 2805.58i | −0.159371 | − | 0.0920127i | ||||
\(977\) | 48936.5 | + | 28253.5i | 1.60247 | + | 0.925188i | 0.990991 | + | 0.133931i | \(0.0427599\pi\) |
0.611483 | + | 0.791258i | \(0.290573\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23691.6i | 0.773430i | ||||||||
\(980\) | −9404.94 | − | 441.978i | −0.306561 | − | 0.0144066i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −14095.0 | − | 24413.3i | −0.458035 | − | 0.793340i | ||||
\(983\) | −11084.9 | + | 19199.5i | −0.359667 | + | 0.622961i | −0.987905 | − | 0.155060i | \(-0.950443\pi\) |
0.628238 | + | 0.778021i | \(0.283776\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11724.6 | − | 6769.21i | 0.379267 | − | 0.218970i | ||||
\(986\) | −6552.26 | −0.211629 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −13676.6 | −0.440396 | ||||||||
\(989\) | −84114.4 | + | 48563.5i | −2.70443 | + | 1.56140i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17799.4 | − | 30829.4i | 0.570550 | − | 0.988222i | −0.425959 | − | 0.904742i | \(-0.640063\pi\) |
0.996509 | − | 0.0834796i | \(-0.0266033\pi\) | |||||||
\(992\) | −454.018 | − | 786.382i | −0.0145313 | − | 0.0251690i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −16570.8 | − | 30324.1i | −0.528767 | − | 0.967629i | ||||
\(995\) | − | 7974.54i | − | 0.254080i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16868.4 | − | 9738.99i | −0.535836 | − | 0.309365i | 0.207554 | − | 0.978224i | \(-0.433450\pi\) |
−0.743390 | + | 0.668859i | \(0.766783\pi\) | |||||||
\(998\) | 14906.8 | + | 8606.45i | 0.472812 | + | 0.272978i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 378.4.k.d.269.2 | yes | 20 | |
3.2 | odd | 2 | inner | 378.4.k.d.269.9 | yes | 20 | |
7.5 | odd | 6 | inner | 378.4.k.d.215.9 | yes | 20 | |
21.5 | even | 6 | inner | 378.4.k.d.215.2 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.4.k.d.215.2 | ✓ | 20 | 21.5 | even | 6 | inner | |
378.4.k.d.215.9 | yes | 20 | 7.5 | odd | 6 | inner | |
378.4.k.d.269.2 | yes | 20 | 1.1 | even | 1 | trivial | |
378.4.k.d.269.9 | yes | 20 | 3.2 | odd | 2 | inner |