Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [200,4,Mod(149,200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("200.149");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 200 = 2^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 200.f (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: | \(11.8003820011\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{11} + 7x^{10} - 12x^{9} + 21x^{8} - 68x^{6} + 336x^{4} - 768x^{3} + 1792x^{2} - 4096x + 4096 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{15} \) |
Twist minimal: | no (minimal twist has level 40) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 149.4 | ||
Root | \(-1.86176 + 0.730647i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 200.149 |
Dual form | 200.4.f.c.149.3 |
$q$-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 \(\left(\mathbb{Z}/200\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(177\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.13111 | + | 2.59241i | −0.399910 | + | 0.916555i | ||||
\(3\) | 6.25785 | 1.20432 | 0.602161 | − | 0.798374i | \(-0.294306\pi\) | ||||
0.602161 | + | 0.798374i | \(0.294306\pi\) | |||||||
\(4\) | −5.44116 | − | 5.86462i | −0.680145 | − | 0.733078i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −7.07834 | + | 16.2229i | −0.481620 | + | 1.10383i | ||||
\(7\) | 34.6280i | 1.86973i | 0.354998 | + | 0.934867i | \(0.384482\pi\) | ||||
−0.354998 | + | 0.934867i | \(0.615518\pi\) | |||||||
\(8\) | 21.3581 | − | 7.47214i | 0.943902 | − | 0.330225i | ||||
\(9\) | 12.1606 | 0.450394 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 7.91595i | − | 0.216977i | −0.994098 | − | 0.108489i | \(-0.965399\pi\) | ||
0.994098 | − | 0.108489i | \(-0.0346011\pi\) | |||||||
\(12\) | −34.0499 | − | 36.6999i | −0.819114 | − | 0.882862i | ||||
\(13\) | 11.0346 | 0.235420 | 0.117710 | − | 0.993048i | \(-0.462445\pi\) | ||||
0.117710 | + | 0.993048i | \(0.462445\pi\) | |||||||
\(14\) | −89.7698 | − | 39.1682i | −1.71371 | − | 0.747725i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.78760 | + | 63.8207i | −0.0748062 | + | 0.997198i | ||||
\(17\) | − | 57.6152i | − | 0.821985i | −0.911639 | − | 0.410992i | \(-0.865182\pi\) | ||
0.911639 | − | 0.410992i | \(-0.134818\pi\) | |||||||
\(18\) | −13.7551 | + | 31.5253i | −0.180117 | + | 0.412810i | ||||
\(19\) | 141.133i | 1.70411i | 0.523453 | + | 0.852055i | \(0.324644\pi\) | ||||
−0.523453 | + | 0.852055i | \(0.675356\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 216.696i | 2.25176i | ||||||||
\(22\) | 20.5214 | + | 8.95385i | 0.198871 | + | 0.0867712i | ||||
\(23\) | 129.328i | 1.17247i | 0.810143 | + | 0.586233i | \(0.199390\pi\) | ||||
−0.810143 | + | 0.586233i | \(0.800610\pi\) | |||||||
\(24\) | 133.655 | − | 46.7595i | 1.13676 | − | 0.397698i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −12.4814 | + | 28.6062i | −0.0941465 | + | 0.215775i | ||||
\(27\) | −92.8625 | −0.661903 | ||||||||
\(28\) | 203.080 | − | 188.416i | 1.37066 | − | 1.27169i | ||||
\(29\) | 89.1664i | 0.570958i | 0.958385 | + | 0.285479i | \(0.0921527\pi\) | ||||
−0.958385 | + | 0.285479i | \(0.907847\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −78.3307 | −0.453826 | −0.226913 | − | 0.973915i | \(-0.572863\pi\) | ||||
−0.226913 | + | 0.973915i | \(0.572863\pi\) | |||||||
\(32\) | −160.034 | − | 84.5999i | −0.884071 | − | 0.467353i | ||||
\(33\) | − | 49.5368i | − | 0.261310i | ||||||
\(34\) | 149.362 | + | 65.1694i | 0.753394 | + | 0.328720i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −66.1679 | − | 71.3175i | −0.306333 | − | 0.330174i | ||||
\(37\) | 249.332 | 1.10783 | 0.553917 | − | 0.832572i | \(-0.313132\pi\) | ||||
0.553917 | + | 0.832572i | \(0.313132\pi\) | |||||||
\(38\) | −365.874 | − | 159.637i | −1.56191 | − | 0.681489i | ||||
\(39\) | 69.0530 | 0.283521 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 91.8705 | 0.349946 | 0.174973 | − | 0.984573i | \(-0.444016\pi\) | ||||
0.174973 | + | 0.984573i | \(0.444016\pi\) | |||||||
\(42\) | −561.766 | − | 245.109i | −2.06386 | − | 0.900502i | ||||
\(43\) | −194.184 | −0.688668 | −0.344334 | − | 0.938847i | \(-0.611895\pi\) | ||||
−0.344334 | + | 0.938847i | \(0.611895\pi\) | |||||||
\(44\) | −46.4240 | + | 43.0719i | −0.159061 | + | 0.147576i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −335.270 | − | 146.285i | −1.07463 | − | 0.468880i | ||||
\(47\) | 72.6149i | 0.225361i | 0.993631 | + | 0.112680i | \(0.0359437\pi\) | ||||
−0.993631 | + | 0.112680i | \(0.964056\pi\) | |||||||
\(48\) | −29.9600 | + | 399.380i | −0.0900908 | + | 1.20095i | ||||
\(49\) | −856.096 | −2.49591 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 360.547i | − | 0.989935i | ||||||
\(52\) | −60.0411 | − | 64.7139i | −0.160119 | − | 0.172581i | ||||
\(53\) | 456.782 | 1.18385 | 0.591923 | − | 0.805995i | \(-0.298369\pi\) | ||||
0.591923 | + | 0.805995i | \(0.298369\pi\) | |||||||
\(54\) | 105.038 | − | 240.737i | 0.264701 | − | 0.606671i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 258.745 | + | 739.586i | 0.617433 | + | 1.76485i | ||||
\(57\) | 883.187i | 2.05230i | ||||||||
\(58\) | −231.156 | − | 100.857i | −0.523314 | − | 0.228331i | ||||
\(59\) | − | 341.098i | − | 0.752664i | −0.926485 | − | 0.376332i | \(-0.877185\pi\) | ||
0.926485 | − | 0.376332i | \(-0.122815\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 217.067i | − | 0.455616i | −0.973706 | − | 0.227808i | \(-0.926844\pi\) | ||
0.973706 | − | 0.227808i | \(-0.0731559\pi\) | |||||||
\(62\) | 88.6011 | − | 203.065i | 0.181489 | − | 0.415957i | ||||
\(63\) | 421.098i | 0.842117i | ||||||||
\(64\) | 400.334 | − | 319.181i | 0.781903 | − | 0.623400i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 128.420 | + | 56.0318i | 0.239505 | + | 0.104501i | ||||
\(67\) | 529.237 | 0.965024 | 0.482512 | − | 0.875889i | \(-0.339724\pi\) | ||||
0.482512 | + | 0.875889i | \(0.339724\pi\) | |||||||
\(68\) | −337.892 | + | 313.494i | −0.602579 | + | 0.559069i | ||||
\(69\) | 809.314i | 1.41203i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 381.540 | 0.637754 | 0.318877 | − | 0.947796i | \(-0.396694\pi\) | ||||
0.318877 | + | 0.947796i | \(0.396694\pi\) | |||||||
\(72\) | 259.728 | − | 90.8659i | 0.425128 | − | 0.148731i | ||||
\(73\) | − | 876.902i | − | 1.40594i | −0.711220 | − | 0.702970i | \(-0.751857\pi\) | ||
0.711220 | − | 0.702970i | \(-0.248143\pi\) | |||||||
\(74\) | −282.023 | + | 646.370i | −0.443034 | + | 1.01539i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 827.690 | − | 767.926i | 1.24924 | − | 1.15904i | ||||
\(77\) | 274.113 | 0.405690 | ||||||||
\(78\) | −78.1069 | + | 179.013i | −0.113383 | + | 0.259863i | ||||
\(79\) | 203.950 | 0.290458 | 0.145229 | − | 0.989398i | \(-0.453608\pi\) | ||||
0.145229 | + | 0.989398i | \(0.453608\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −909.456 | −1.24754 | ||||||||
\(82\) | −103.916 | + | 238.166i | −0.139947 | + | 0.320744i | ||||
\(83\) | 996.654 | 1.31804 | 0.659018 | − | 0.752127i | \(-0.270972\pi\) | ||||
0.659018 | + | 0.752127i | \(0.270972\pi\) | |||||||
\(84\) | 1270.84 | − | 1179.08i | 1.65072 | − | 1.53153i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 219.644 | − | 503.403i | 0.275405 | − | 0.631202i | ||||
\(87\) | 557.989i | 0.687618i | ||||||||
\(88\) | −59.1491 | − | 169.069i | −0.0716513 | − | 0.204805i | ||||
\(89\) | −172.456 | −0.205396 | −0.102698 | − | 0.994713i | \(-0.532748\pi\) | ||||
−0.102698 | + | 0.994713i | \(0.532748\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 382.107i | 0.440172i | ||||||||
\(92\) | 758.459 | − | 703.693i | 0.859509 | − | 0.797447i | ||||
\(93\) | −490.182 | −0.546553 | ||||||||
\(94\) | −188.247 | − | 82.1358i | −0.206556 | − | 0.0901240i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1001.47 | − | 529.413i | −1.06471 | − | 0.562844i | ||||
\(97\) | − | 1058.49i | − | 1.10797i | −0.832527 | − | 0.553984i | \(-0.813107\pi\) | ||
0.832527 | − | 0.553984i | \(-0.186893\pi\) | |||||||
\(98\) | 968.343 | − | 2219.35i | 0.998137 | − | 2.28763i | ||||
\(99\) | − | 96.2629i | − | 0.0977251i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 689.992i | − | 0.679770i | −0.940467 | − | 0.339885i | \(-0.889612\pi\) | ||
0.940467 | − | 0.339885i | \(-0.110388\pi\) | |||||||
\(102\) | 934.685 | + | 407.820i | 0.907330 | + | 0.395885i | ||||
\(103\) | 1289.96i | 1.23402i | 0.786956 | + | 0.617009i | \(0.211656\pi\) | ||||
−0.786956 | + | 0.617009i | \(0.788344\pi\) | |||||||
\(104\) | 235.678 | − | 82.4523i | 0.222213 | − | 0.0777414i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −516.673 | + | 1184.16i | −0.473431 | + | 1.08506i | ||||
\(107\) | 1843.74 | 1.66580 | 0.832902 | − | 0.553420i | \(-0.186678\pi\) | ||||
0.832902 | + | 0.553420i | \(0.186678\pi\) | |||||||
\(108\) | 505.279 | + | 544.603i | 0.450190 | + | 0.485227i | ||||
\(109\) | − | 340.598i | − | 0.299297i | −0.988739 | − | 0.149648i | \(-0.952186\pi\) | ||
0.988739 | − | 0.149648i | \(-0.0478142\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1560.28 | 1.33419 | ||||||||
\(112\) | −2209.98 | − | 165.785i | −1.86450 | − | 0.139868i | ||||
\(113\) | 157.831i | 0.131393i | 0.997840 | + | 0.0656967i | \(0.0209270\pi\) | ||||
−0.997840 | + | 0.0656967i | \(0.979073\pi\) | |||||||
\(114\) | −2289.58 | − | 998.986i | −1.88104 | − | 0.820733i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 522.927 | − | 485.168i | 0.418557 | − | 0.388334i | ||||
\(117\) | 134.188 | 0.106031 | ||||||||
\(118\) | 884.265 | + | 385.821i | 0.689858 | + | 0.300997i | ||||
\(119\) | 1995.10 | 1.53689 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1268.34 | 0.952921 | ||||||||
\(122\) | 562.727 | + | 245.528i | 0.417597 | + | 0.182205i | ||||
\(123\) | 574.912 | 0.421447 | ||||||||
\(124\) | 426.210 | + | 459.380i | 0.308668 | + | 0.332690i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1091.66 | − | 476.310i | −0.771846 | − | 0.336770i | ||||
\(127\) | − | 494.704i | − | 0.345652i | −0.984952 | − | 0.172826i | \(-0.944710\pi\) | ||
0.984952 | − | 0.172826i | \(-0.0552899\pi\) | |||||||
\(128\) | 374.623 | + | 1398.86i | 0.258690 | + | 0.965960i | ||||
\(129\) | −1215.17 | −0.829379 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 488.783i | − | 0.325993i | −0.986627 | − | 0.162997i | \(-0.947884\pi\) | ||
0.986627 | − | 0.162997i | \(-0.0521160\pi\) | |||||||
\(132\) | −290.514 | + | 269.537i | −0.191561 | + | 0.177729i | ||||
\(133\) | −4887.14 | −3.18623 | ||||||||
\(134\) | −598.628 | + | 1372.00i | −0.385922 | + | 0.884498i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −430.509 | − | 1230.55i | −0.271440 | − | 0.775873i | ||||
\(137\) | 1532.13i | 0.955464i | 0.878506 | + | 0.477732i | \(0.158541\pi\) | ||||
−0.878506 | + | 0.477732i | \(0.841459\pi\) | |||||||
\(138\) | −2098.07 | − | 915.427i | −1.29420 | − | 0.564683i | ||||
\(139\) | − | 755.095i | − | 0.460765i | −0.973100 | − | 0.230382i | \(-0.926002\pi\) | ||
0.973100 | − | 0.230382i | \(-0.0739977\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 454.413i | 0.271407i | ||||||||
\(142\) | −431.566 | + | 989.108i | −0.255044 | + | 0.584536i | ||||
\(143\) | − | 87.3495i | − | 0.0510807i | ||||||
\(144\) | −58.2202 | + | 776.100i | −0.0336922 | + | 0.449132i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2273.29 | + | 991.877i | 1.28862 | + | 0.562249i | ||||
\(147\) | −5357.32 | −3.00588 | ||||||||
\(148\) | −1356.65 | − | 1462.24i | −0.753488 | − | 0.812129i | ||||
\(149\) | 1446.67i | 0.795410i | 0.917513 | + | 0.397705i | \(0.130193\pi\) | ||||
−0.917513 | + | 0.397705i | \(0.869807\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1230.20 | −0.662998 | −0.331499 | − | 0.943456i | \(-0.607554\pi\) | ||||
−0.331499 | + | 0.943456i | \(0.607554\pi\) | |||||||
\(152\) | 1054.56 | + | 3014.32i | 0.562739 | + | 1.60851i | ||||
\(153\) | − | 700.637i | − | 0.370217i | ||||||
\(154\) | −310.053 | + | 710.613i | −0.162239 | + | 0.371837i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −375.728 | − | 404.970i | −0.192835 | − | 0.207843i | ||||
\(157\) | −1773.74 | −0.901657 | −0.450828 | − | 0.892611i | \(-0.648871\pi\) | ||||
−0.450828 | + | 0.892611i | \(0.648871\pi\) | |||||||
\(158\) | −230.691 | + | 528.722i | −0.116157 | + | 0.266221i | ||||
\(159\) | 2858.47 | 1.42573 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4478.36 | −2.19220 | ||||||||
\(162\) | 1028.70 | − | 2357.68i | 0.498903 | − | 1.14344i | ||||
\(163\) | 1711.28 | 0.822319 | 0.411159 | − | 0.911563i | \(-0.365124\pi\) | ||||
0.411159 | + | 0.911563i | \(0.365124\pi\) | |||||||
\(164\) | −499.882 | − | 538.786i | −0.238014 | − | 0.256537i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1127.33 | + | 2583.73i | −0.527095 | + | 1.20805i | ||||
\(167\) | − | 3913.26i | − | 1.81328i | −0.421909 | − | 0.906638i | \(-0.638640\pi\) | ||
0.421909 | − | 0.906638i | \(-0.361360\pi\) | |||||||
\(168\) | 1619.19 | + | 4628.22i | 0.743589 | + | 2.12544i | ||||
\(169\) | −2075.24 | −0.944578 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1716.26i | 0.767520i | ||||||||
\(172\) | 1056.58 | + | 1138.81i | 0.468394 | + | 0.504847i | ||||
\(173\) | 3985.34 | 1.75144 | 0.875722 | − | 0.482815i | \(-0.160386\pi\) | ||||
0.875722 | + | 0.482815i | \(0.160386\pi\) | |||||||
\(174\) | −1446.54 | − | 631.150i | −0.630239 | − | 0.274985i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 505.201 | + | 37.8984i | 0.216369 | + | 0.0162312i | ||||
\(177\) | − | 2134.54i | − | 0.906450i | ||||||
\(178\) | 195.067 | − | 447.076i | 0.0821400 | − | 0.188257i | ||||
\(179\) | − | 884.734i | − | 0.369431i | −0.982792 | − | 0.184715i | \(-0.940864\pi\) | ||
0.982792 | − | 0.184715i | \(-0.0591363\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2810.77i | 1.15427i | 0.816649 | + | 0.577134i | \(0.195829\pi\) | ||||
−0.816649 | + | 0.577134i | \(0.804171\pi\) | |||||||
\(182\) | −990.576 | − | 432.206i | −0.403442 | − | 0.176029i | ||||
\(183\) | − | 1358.37i | − | 0.548709i | ||||||
\(184\) | 966.356 | + | 2762.19i | 0.387178 | + | 1.10669i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 554.452 | − | 1270.75i | 0.218572 | − | 0.500946i | ||||
\(187\) | −456.079 | −0.178352 | ||||||||
\(188\) | 425.859 | − | 395.109i | 0.165207 | − | 0.153278i | ||||
\(189\) | − | 3215.64i | − | 1.23758i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −749.321 | −0.283869 | −0.141935 | − | 0.989876i | \(-0.545332\pi\) | ||||
−0.141935 | + | 0.989876i | \(0.545332\pi\) | |||||||
\(192\) | 2505.23 | − | 1997.39i | 0.941663 | − | 0.750775i | ||||
\(193\) | − | 3969.83i | − | 1.48060i | −0.672279 | − | 0.740298i | \(-0.734685\pi\) | ||
0.672279 | − | 0.740298i | \(-0.265315\pi\) | |||||||
\(194\) | 2744.03 | + | 1197.27i | 1.01551 | + | 0.443087i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4658.15 | + | 5020.68i | 1.69758 | + | 1.82969i | ||||
\(197\) | −2243.20 | −0.811275 | −0.405638 | − | 0.914034i | \(-0.632951\pi\) | ||||
−0.405638 | + | 0.914034i | \(0.632951\pi\) | |||||||
\(198\) | 249.553 | + | 108.884i | 0.0895704 | + | 0.0390812i | ||||
\(199\) | 672.030 | 0.239392 | 0.119696 | − | 0.992811i | \(-0.461808\pi\) | ||||
0.119696 | + | 0.992811i | \(0.461808\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3311.89 | 1.16220 | ||||||||
\(202\) | 1788.74 | + | 780.460i | 0.623046 | + | 0.271846i | ||||
\(203\) | −3087.65 | −1.06754 | ||||||||
\(204\) | −2114.47 | + | 1961.79i | −0.725700 | + | 0.673299i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3344.11 | − | 1459.10i | −1.13104 | − | 0.493495i | ||||
\(207\) | 1572.71i | 0.528071i | ||||||||
\(208\) | −52.8293 | + | 704.237i | −0.0176108 | + | 0.234760i | ||||
\(209\) | 1117.20 | 0.369753 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 1935.07i | − | 0.631356i | −0.948866 | − | 0.315678i | \(-0.897768\pi\) | ||
0.948866 | − | 0.315678i | \(-0.102232\pi\) | |||||||
\(212\) | −2485.42 | − | 2678.85i | −0.805186 | − | 0.867851i | ||||
\(213\) | 2387.62 | 0.768061 | ||||||||
\(214\) | −2085.48 | + | 4779.73i | −0.666171 | + | 1.52680i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1983.36 | + | 693.882i | −0.624772 | + | 0.218577i | ||||
\(217\) | − | 2712.43i | − | 0.848535i | ||||||
\(218\) | 882.968 | + | 385.255i | 0.274322 | + | 0.119692i | ||||
\(219\) | − | 5487.52i | − | 1.69321i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 635.762i | − | 0.193511i | ||||||
\(222\) | −1764.86 | + | 4044.88i | −0.533556 | + | 1.22286i | ||||
\(223\) | 2492.56i | 0.748494i | 0.927329 | + | 0.374247i | \(0.122099\pi\) | ||||
−0.927329 | + | 0.374247i | \(0.877901\pi\) | |||||||
\(224\) | 2929.52 | − | 5541.65i | 0.873826 | − | 1.65298i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −409.161 | − | 178.524i | −0.120429 | − | 0.0525455i | ||||
\(227\) | 3155.27 | 0.922567 | 0.461283 | − | 0.887253i | \(-0.347389\pi\) | ||||
0.461283 | + | 0.887253i | \(0.347389\pi\) | |||||||
\(228\) | 5179.56 | − | 4805.56i | 1.50449 | − | 1.39586i | ||||
\(229\) | 2299.43i | 0.663539i | 0.943360 | + | 0.331770i | \(0.107646\pi\) | ||||
−0.943360 | + | 0.331770i | \(0.892354\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1715.36 | 0.488581 | ||||||||
\(232\) | 666.264 | + | 1904.42i | 0.188545 | + | 0.538928i | ||||
\(233\) | 741.991i | 0.208624i | 0.994545 | + | 0.104312i | \(0.0332641\pi\) | ||||
−0.994545 | + | 0.104312i | \(0.966736\pi\) | |||||||
\(234\) | −151.782 | + | 347.870i | −0.0424030 | + | 0.0971836i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2000.41 | + | 1855.97i | −0.551761 | + | 0.511920i | ||||
\(237\) | 1276.29 | 0.349806 | ||||||||
\(238\) | −2256.68 | + | 5172.11i | −0.614618 | + | 1.40865i | ||||
\(239\) | −5786.01 | −1.56597 | −0.782984 | − | 0.622042i | \(-0.786303\pi\) | ||||
−0.782984 | + | 0.622042i | \(0.786303\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 265.054 | 0.0708449 | 0.0354224 | − | 0.999372i | \(-0.488722\pi\) | ||||
0.0354224 | + | 0.999372i | \(0.488722\pi\) | |||||||
\(242\) | −1434.64 | + | 3288.05i | −0.381082 | + | 0.873404i | ||||
\(243\) | −3183.95 | −0.840537 | ||||||||
\(244\) | −1273.02 | + | 1181.10i | −0.334002 | + | 0.309885i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −650.291 | + | 1490.41i | −0.168541 | + | 0.386280i | ||||
\(247\) | 1557.35i | 0.401181i | ||||||||
\(248\) | −1672.99 | + | 585.298i | −0.428368 | + | 0.149865i | ||||
\(249\) | 6236.91 | 1.58734 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1762.02i | 0.443098i | 0.975149 | + | 0.221549i | \(0.0711113\pi\) | ||||
−0.975149 | + | 0.221549i | \(0.928889\pi\) | |||||||
\(252\) | 2469.58 | − | 2291.26i | 0.617337 | − | 0.572761i | ||||
\(253\) | 1023.75 | 0.254398 | ||||||||
\(254\) | 1282.47 | + | 559.567i | 0.316809 | + | 0.138230i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4050.16 | − | 611.095i | −0.988808 | − | 0.149193i | ||||
\(257\) | 1507.84i | 0.365980i | 0.983115 | + | 0.182990i | \(0.0585775\pi\) | ||||
−0.983115 | + | 0.182990i | \(0.941422\pi\) | |||||||
\(258\) | 1374.50 | − | 3150.22i | 0.331677 | − | 0.760171i | ||||
\(259\) | 8633.85i | 2.07136i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1084.32i | 0.257156i | ||||||||
\(262\) | 1267.12 | + | 552.869i | 0.298791 | + | 0.130368i | ||||
\(263\) | 2772.54i | 0.650046i | 0.945706 | + | 0.325023i | \(0.105372\pi\) | ||||
−0.945706 | + | 0.325023i | \(0.894628\pi\) | |||||||
\(264\) | −370.146 | − | 1058.01i | −0.0862913 | − | 0.246652i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5527.92 | − | 12669.5i | 1.27420 | − | 2.92035i | ||||
\(267\) | −1079.20 | −0.247364 | ||||||||
\(268\) | −2879.66 | − | 3103.78i | −0.656356 | − | 0.707438i | ||||
\(269\) | − | 5166.61i | − | 1.17106i | −0.810652 | − | 0.585528i | \(-0.800887\pi\) | ||
0.810652 | − | 0.585528i | \(-0.199113\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1458.79 | −0.326994 | −0.163497 | − | 0.986544i | \(-0.552277\pi\) | ||||
−0.163497 | + | 0.986544i | \(0.552277\pi\) | |||||||
\(272\) | 3677.04 | + | 275.838i | 0.819682 | + | 0.0614896i | ||||
\(273\) | 2391.16i | 0.530109i | ||||||||
\(274\) | −3971.90 | − | 1733.01i | −0.875735 | − | 0.382099i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4746.32 | − | 4403.60i | 1.03513 | − | 0.960383i | ||||
\(277\) | 1994.60 | 0.432650 | 0.216325 | − | 0.976321i | \(-0.430593\pi\) | ||||
0.216325 | + | 0.976321i | \(0.430593\pi\) | |||||||
\(278\) | 1957.51 | + | 854.099i | 0.422316 | + | 0.184264i | ||||
\(279\) | −952.551 | −0.204400 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −311.583 | −0.0661477 | −0.0330739 | − | 0.999453i | \(-0.510530\pi\) | ||||
−0.0330739 | + | 0.999453i | \(0.510530\pi\) | |||||||
\(282\) | −1178.02 | − | 513.993i | −0.248760 | − | 0.108538i | ||||
\(283\) | −6072.33 | −1.27549 | −0.637743 | − | 0.770249i | \(-0.720132\pi\) | ||||
−0.637743 | + | 0.770249i | \(0.720132\pi\) | |||||||
\(284\) | −2076.02 | − | 2237.59i | −0.433765 | − | 0.467523i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 226.446 | + | 98.8023i | 0.0468182 | + | 0.0204276i | ||||
\(287\) | 3181.29i | 0.654305i | ||||||||
\(288\) | −1946.11 | − | 1028.79i | −0.398180 | − | 0.210493i | ||||
\(289\) | 1593.49 | 0.324341 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 6623.84i | − | 1.33435i | ||||||
\(292\) | −5142.70 | + | 4771.36i | −1.03066 | + | 0.956243i | ||||
\(293\) | −2321.06 | −0.462791 | −0.231395 | − | 0.972860i | \(-0.574329\pi\) | ||||
−0.231395 | + | 0.972860i | \(0.574329\pi\) | |||||||
\(294\) | 6059.74 | − | 13888.3i | 1.20208 | − | 2.75505i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5325.24 | − | 1863.04i | 1.04569 | − | 0.365835i | ||||
\(297\) | 735.095i | 0.143618i | ||||||||
\(298\) | −3750.37 | − | 1636.35i | −0.729037 | − | 0.318092i | ||||
\(299\) | 1427.08i | 0.276021i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 6724.19i | − | 1.28763i | ||||||
\(302\) | 1391.50 | − | 3189.19i | 0.265139 | − | 0.607674i | ||||
\(303\) | − | 4317.86i | − | 0.818662i | ||||||
\(304\) | −9007.19 | − | 675.686i | −1.69933 | − | 0.127478i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1816.34 | + | 792.501i | 0.339324 | + | 0.148053i | ||||
\(307\) | 2499.43 | 0.464658 | 0.232329 | − | 0.972637i | \(-0.425365\pi\) | ||||
0.232329 | + | 0.972637i | \(0.425365\pi\) | |||||||
\(308\) | −1491.49 | − | 1607.57i | −0.275928 | − | 0.297402i | ||||
\(309\) | 8072.39i | 1.48616i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3052.83 | −0.556624 | −0.278312 | − | 0.960491i | \(-0.589775\pi\) | ||||
−0.278312 | + | 0.960491i | \(0.589775\pi\) | |||||||
\(312\) | 1474.84 | − | 515.974i | 0.267616 | − | 0.0936258i | ||||
\(313\) | 6179.23i | 1.11588i | 0.829881 | + | 0.557941i | \(0.188408\pi\) | ||||
−0.829881 | + | 0.557941i | \(0.811592\pi\) | |||||||
\(314\) | 2006.31 | − | 4598.27i | 0.360581 | − | 0.826418i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1109.73 | − | 1196.09i | −0.197554 | − | 0.212929i | ||||
\(317\) | 3116.20 | 0.552124 | 0.276062 | − | 0.961140i | \(-0.410971\pi\) | ||||
0.276062 | + | 0.961140i | \(0.410971\pi\) | |||||||
\(318\) | −3233.26 | + | 7410.32i | −0.570164 | + | 1.30676i | ||||
\(319\) | 705.836 | 0.123885 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11537.8 | 2.00617 | ||||||||
\(322\) | 5065.54 | − | 11609.7i | 0.876682 | − | 2.00927i | ||||
\(323\) | 8131.39 | 1.40075 | ||||||||
\(324\) | 4948.49 | + | 5333.62i | 0.848507 | + | 0.914543i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1935.66 | + | 4436.34i | −0.328853 | + | 0.753700i | ||||
\(327\) | − | 2131.41i | − | 0.360450i | ||||||
\(328\) | 1962.18 | − | 686.469i | 0.330314 | − | 0.115561i | ||||
\(329\) | −2514.51 | −0.421365 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 4157.26i | − | 0.690343i | −0.938540 | − | 0.345171i | \(-0.887821\pi\) | ||
0.938540 | − | 0.345171i | \(-0.112179\pi\) | |||||||
\(332\) | −5422.95 | − | 5845.00i | −0.896455 | − | 0.966223i | ||||
\(333\) | 3032.03 | 0.498962 | ||||||||
\(334\) | 10144.8 | + | 4426.35i | 1.66197 | + | 0.725146i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −13829.7 | − | 1037.45i | −2.24545 | − | 0.168446i | ||||
\(337\) | 8123.42i | 1.31309i | 0.754287 | + | 0.656544i | \(0.227983\pi\) | ||||
−0.754287 | + | 0.656544i | \(0.772017\pi\) | |||||||
\(338\) | 2347.33 | − | 5379.86i | 0.377746 | − | 0.865757i | ||||
\(339\) | 987.679i | 0.158240i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 620.062i | 0.0984699i | ||||||||
\(342\) | −4449.25 | − | 1941.29i | −0.703474 | − | 0.306939i | ||||
\(343\) | − | 17767.5i | − | 2.79695i | ||||||
\(344\) | −4147.39 | + | 1450.97i | −0.650035 | + | 0.227416i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4507.88 | + | 10331.6i | −0.700419 | + | 1.60529i | ||||
\(347\) | 4620.55 | 0.714824 | 0.357412 | − | 0.933947i | \(-0.383659\pi\) | ||||
0.357412 | + | 0.933947i | \(0.383659\pi\) | |||||||
\(348\) | 3272.40 | − | 3036.11i | 0.504077 | − | 0.467680i | ||||
\(349\) | − | 5560.98i | − | 0.852929i | −0.904504 | − | 0.426465i | \(-0.859759\pi\) | ||
0.904504 | − | 0.426465i | \(-0.140241\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1024.70 | −0.155825 | ||||||||
\(352\) | −669.689 | + | 1266.82i | −0.101405 | + | 0.191823i | ||||
\(353\) | 12031.8i | 1.81413i | 0.420989 | + | 0.907066i | \(0.361683\pi\) | ||||
−0.420989 | + | 0.907066i | \(0.638317\pi\) | |||||||
\(354\) | 5533.59 | + | 2414.41i | 0.830811 | + | 0.362498i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 938.359 | + | 1011.39i | 0.139699 | + | 0.150572i | ||||
\(357\) | 12485.0 | 1.85092 | ||||||||
\(358\) | 2293.59 | + | 1000.74i | 0.338603 | + | 0.147739i | ||||
\(359\) | −1533.24 | −0.225408 | −0.112704 | − | 0.993629i | \(-0.535951\pi\) | ||||
−0.112704 | + | 0.993629i | \(0.535951\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13059.5 | −1.90399 | ||||||||
\(362\) | −7286.66 | − | 3179.30i | −1.05795 | − | 0.461603i | ||||
\(363\) | 7937.06 | 1.14762 | ||||||||
\(364\) | 2240.91 | − | 2079.10i | 0.322680 | − | 0.299381i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3521.46 | + | 1536.48i | 0.502922 | + | 0.219434i | ||||
\(367\) | 5480.04i | 0.779444i | 0.920933 | + | 0.389722i | \(0.127429\pi\) | ||||
−0.920933 | + | 0.389722i | \(0.872571\pi\) | |||||||
\(368\) | −8253.79 | − | 619.169i | −1.16918 | − | 0.0877077i | ||||
\(369\) | 1117.20 | 0.157613 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15817.4i | 2.21348i | ||||||||
\(372\) | 2667.16 | + | 2874.73i | 0.371735 | + | 0.400666i | ||||
\(373\) | −6225.70 | −0.864221 | −0.432111 | − | 0.901821i | \(-0.642231\pi\) | ||||
−0.432111 | + | 0.901821i | \(0.642231\pi\) | |||||||
\(374\) | 515.878 | − | 1182.34i | 0.0713246 | − | 0.163469i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 542.588 | + | 1550.91i | 0.0744198 | + | 0.212719i | ||||
\(377\) | 983.917i | 0.134415i | ||||||||
\(378\) | 8336.25 | + | 3637.26i | 1.13431 | + | 0.494921i | ||||
\(379\) | 11172.0i | 1.51416i | 0.653325 | + | 0.757078i | \(0.273374\pi\) | ||||
−0.653325 | + | 0.757078i | \(0.726626\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 3095.78i | − | 0.416277i | ||||||
\(382\) | 847.569 | − | 1942.55i | 0.113522 | − | 0.260182i | ||||
\(383\) | 7621.03i | 1.01675i | 0.861135 | + | 0.508376i | \(0.169754\pi\) | ||||
−0.861135 | + | 0.508376i | \(0.830246\pi\) | |||||||
\(384\) | 2344.33 | + | 8753.85i | 0.311546 | + | 1.16333i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10291.4 | + | 4490.34i | 1.35705 | + | 0.592104i | ||||
\(387\) | −2361.40 | −0.310172 | ||||||||
\(388\) | −6207.62 | + | 5759.39i | −0.812227 | + | 0.753579i | ||||
\(389\) | − | 5546.31i | − | 0.722903i | −0.932391 | − | 0.361451i | \(-0.882281\pi\) | ||
0.932391 | − | 0.361451i | \(-0.117719\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7451.25 | 0.963749 | ||||||||
\(392\) | −18284.6 | + | 6396.87i | −2.35589 | + | 0.824211i | ||||
\(393\) | − | 3058.73i | − | 0.392601i | ||||||
\(394\) | 2537.31 | − | 5815.28i | 0.324437 | − | 0.743578i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −564.546 | + | 523.782i | −0.0716401 | + | 0.0664672i | ||||
\(397\) | −11025.2 | −1.39380 | −0.696900 | − | 0.717169i | \(-0.745438\pi\) | ||||
−0.696900 | + | 0.717169i | \(0.745438\pi\) | |||||||
\(398\) | −760.143 | + | 1742.18i | −0.0957350 | + | 0.219416i | ||||
\(399\) | −30583.0 | −3.83725 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10522.3 | 1.31037 | 0.655186 | − | 0.755467i | \(-0.272590\pi\) | ||||
0.655186 | + | 0.755467i | \(0.272590\pi\) | |||||||
\(402\) | −3746.12 | + | 8585.76i | −0.464775 | + | 1.06522i | ||||
\(403\) | −864.350 | −0.106840 | ||||||||
\(404\) | −4046.54 | + | 3754.35i | −0.498324 | + | 0.462342i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3492.49 | − | 8004.45i | 0.426919 | − | 0.978458i | ||||
\(407\) | − | 1973.70i | − | 0.240375i | ||||||
\(408\) | −2694.06 | − | 7700.59i | −0.326901 | − | 0.934402i | ||||
\(409\) | −2320.17 | −0.280502 | −0.140251 | − | 0.990116i | \(-0.544791\pi\) | ||||
−0.140251 | + | 0.990116i | \(0.544791\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9587.82i | 1.15069i | ||||||||
\(412\) | 7565.14 | − | 7018.89i | 0.904631 | − | 0.839310i | ||||
\(413\) | 11811.5 | 1.40728 | ||||||||
\(414\) | −4077.10 | − | 1778.91i | −0.484006 | − | 0.211181i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1765.91 | − | 933.528i | −0.208128 | − | 0.110024i | ||||
\(417\) | − | 4725.27i | − | 0.554910i | ||||||
\(418\) | −1263.68 | + | 2896.24i | −0.147868 | + | 0.338898i | ||||
\(419\) | − | 9212.17i | − | 1.07409i | −0.843554 | − | 0.537045i | \(-0.819541\pi\) | ||
0.843554 | − | 0.537045i | \(-0.180459\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6967.70i | 0.806615i | 0.915064 | + | 0.403308i | \(0.132140\pi\) | ||||
−0.915064 | + | 0.403308i | \(0.867860\pi\) | |||||||
\(422\) | 5016.50 | + | 2188.79i | 0.578672 | + | 0.252485i | ||||
\(423\) | 883.042i | 0.101501i | ||||||||
\(424\) | 9755.98 | − | 3413.14i | 1.11743 | − | 0.390935i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2700.67 | + | 6189.69i | −0.307155 | + | 0.703970i | ||||
\(427\) | 7516.59 | 0.851882 | ||||||||
\(428\) | −10032.1 | − | 10812.8i | −1.13299 | − | 1.22116i | ||||
\(429\) | − | 546.620i | − | 0.0615176i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11247.1 | −1.25697 | −0.628486 | − | 0.777821i | \(-0.716325\pi\) | ||||
−0.628486 | + | 0.777821i | \(0.716325\pi\) | |||||||
\(432\) | 444.588 | − | 5926.55i | 0.0495145 | − | 0.660049i | ||||
\(433\) | 2589.27i | 0.287372i | 0.989623 | + | 0.143686i | \(0.0458956\pi\) | ||||
−0.989623 | + | 0.143686i | \(0.954104\pi\) | |||||||
\(434\) | 7031.74 | + | 3068.07i | 0.777728 | + | 0.339337i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1997.48 | + | 1853.25i | −0.219408 | + | 0.203565i | ||||
\(437\) | −18252.4 | −1.99801 | ||||||||
\(438\) | 14225.9 | + | 6207.01i | 1.55192 | + | 0.677129i | ||||
\(439\) | −4220.01 | −0.458793 | −0.229396 | − | 0.973333i | \(-0.573675\pi\) | ||||
−0.229396 | + | 0.973333i | \(0.573675\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10410.7 | −1.12414 | ||||||||
\(442\) | 1648.16 | + | 719.120i | 0.177364 | + | 0.0773870i | ||||
\(443\) | 9764.04 | 1.04719 | 0.523593 | − | 0.851969i | \(-0.324591\pi\) | ||||
0.523593 | + | 0.851969i | \(0.324591\pi\) | |||||||
\(444\) | −8489.73 | − | 9150.45i | −0.907443 | − | 0.978066i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6461.73 | − | 2819.37i | −0.686035 | − | 0.299330i | ||||
\(447\) | 9053.06i | 0.957931i | ||||||||
\(448\) | 11052.6 | + | 13862.8i | 1.16559 | + | 1.46195i | ||||
\(449\) | 17159.3 | 1.80355 | 0.901777 | − | 0.432202i | \(-0.142263\pi\) | ||||
0.901777 | + | 0.432202i | \(0.142263\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 727.242i | − | 0.0759302i | ||||||
\(452\) | 925.617 | − | 858.781i | 0.0963216 | − | 0.0893665i | ||||
\(453\) | −7698.43 | −0.798463 | ||||||||
\(454\) | −3568.97 | + | 8179.75i | −0.368943 | + | 0.845583i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6599.30 | + | 18863.2i | 0.677720 | + | 1.93717i | ||||
\(457\) | − | 13027.3i | − | 1.33346i | −0.745299 | − | 0.666730i | \(-0.767693\pi\) | ||
0.745299 | − | 0.666730i | \(-0.232307\pi\) | |||||||
\(458\) | −5961.05 | − | 2600.92i | −0.608170 | − | 0.265356i | ||||
\(459\) | 5350.29i | 0.544075i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 313.396i | − | 0.0316623i | −0.999875 | − | 0.0158312i | \(-0.994961\pi\) | ||
0.999875 | − | 0.0158312i | \(-0.00503943\pi\) | |||||||
\(462\) | −1940.27 | + | 4446.91i | −0.195388 | + | 0.447811i | ||||
\(463\) | − | 12166.5i | − | 1.22123i | −0.791930 | − | 0.610613i | \(-0.790923\pi\) | ||
0.791930 | − | 0.610613i | \(-0.209077\pi\) | |||||||
\(464\) | −5690.66 | − | 426.892i | −0.569358 | − | 0.0427112i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1923.54 | − | 839.277i | −0.191216 | − | 0.0834308i | ||||
\(467\) | −1844.42 | −0.182761 | −0.0913806 | − | 0.995816i | \(-0.529128\pi\) | ||||
−0.0913806 | + | 0.995816i | \(0.529128\pi\) | |||||||
\(468\) | −730.138 | − | 786.962i | −0.0721168 | − | 0.0777293i | ||||
\(469\) | 18326.4i | 1.80434i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11099.8 | −1.08589 | ||||||||
\(472\) | −2548.73 | − | 7285.19i | −0.248548 | − | 0.710441i | ||||
\(473\) | 1537.15i | 0.149425i | ||||||||
\(474\) | −1443.63 | + | 3308.66i | −0.139891 | + | 0.320616i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −10855.6 | − | 11700.5i | −1.04531 | − | 1.12666i | ||||
\(477\) | 5554.75 | 0.533196 | ||||||||
\(478\) | 6544.65 | − | 14999.7i | 0.626245 | − | 1.43529i | ||||
\(479\) | 16355.9 | 1.56017 | 0.780084 | − | 0.625675i | \(-0.215176\pi\) | ||||
0.780084 | + | 0.625675i | \(0.215176\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2751.28 | 0.260806 | ||||||||
\(482\) | −299.806 | + | 687.128i | −0.0283315 | + | 0.0649332i | ||||
\(483\) | −28024.9 | −2.64012 | ||||||||
\(484\) | −6901.23 | − | 7438.32i | −0.648124 | − | 0.698565i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 3601.41 | − | 8254.09i | 0.336139 | − | 0.770398i | ||||
\(487\) | − | 11824.6i | − | 1.10025i | −0.835082 | − | 0.550126i | \(-0.814580\pi\) | ||
0.835082 | − | 0.550126i | \(-0.185420\pi\) | |||||||
\(488\) | −1621.96 | − | 4636.13i | −0.150456 | − | 0.430057i | ||||
\(489\) | 10708.9 | 0.990337 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 7931.40i | − | 0.729000i | −0.931203 | − | 0.364500i | \(-0.881240\pi\) | ||
0.931203 | − | 0.364500i | \(-0.118760\pi\) | |||||||
\(492\) | −3128.18 | − | 3371.64i | −0.286645 | − | 0.308954i | ||||
\(493\) | 5137.34 | 0.469319 | ||||||||
\(494\) | −4037.28 | − | 1761.54i | −0.367704 | − | 0.160436i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 375.016 | − | 4999.12i | 0.0339490 | − | 0.452555i | ||||
\(497\) | 13212.0i | 1.19243i | ||||||||
\(498\) | −7054.66 | + | 16168.6i | −0.634793 | + | 1.45488i | ||||
\(499\) | − | 2734.69i | − | 0.245333i | −0.992448 | − | 0.122667i | \(-0.960855\pi\) | ||
0.992448 | − | 0.122667i | \(-0.0391446\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 24488.6i | − | 2.18377i | ||||||
\(502\) | −4567.87 | − | 1993.05i | −0.406124 | − | 0.177199i | ||||
\(503\) | 7297.64i | 0.646890i | 0.946247 | + | 0.323445i | \(0.104841\pi\) | ||||
−0.946247 | + | 0.323445i | \(0.895159\pi\) | |||||||
\(504\) | 3146.50 | + | 8993.84i | 0.278088 | + | 0.794876i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1157.98 | + | 2653.98i | −0.101736 | + | 0.233170i | ||||
\(507\) | −12986.5 | −1.13758 | ||||||||
\(508\) | −2901.25 | + | 2691.76i | −0.253390 | + | 0.235094i | ||||
\(509\) | − | 10972.4i | − | 0.955486i | −0.878500 | − | 0.477743i | \(-0.841455\pi\) | ||
0.878500 | − | 0.477743i | \(-0.158545\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30365.3 | 2.62873 | ||||||||
\(512\) | 6165.40 | − | 9808.44i | 0.532177 | − | 0.846633i | ||||
\(513\) | − | 13105.9i | − | 1.12796i | ||||||
\(514\) | −3908.95 | − | 1705.55i | −0.335440 | − | 0.146359i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 6611.94 | + | 7126.52i | 0.564098 | + | 0.607999i | ||||
\(517\) | 574.815 | 0.0488982 | ||||||||
\(518\) | −22382.5 | − | 9765.88i | −1.89851 | − | 0.828355i | ||||
\(519\) | 24939.7 | 2.10931 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7693.43 | 0.646939 | 0.323470 | − | 0.946239i | \(-0.395151\pi\) | ||||
0.323470 | + | 0.946239i | \(0.395151\pi\) | |||||||
\(522\) | −2811.00 | − | 1226.49i | −0.235697 | − | 0.102839i | ||||
\(523\) | −14535.3 | −1.21527 | −0.607634 | − | 0.794217i | \(-0.707881\pi\) | ||||
−0.607634 | + | 0.794217i | \(0.707881\pi\) | |||||||
\(524\) | −2866.53 | + | 2659.54i | −0.238979 | + | 0.221723i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7187.55 | − | 3136.06i | −0.595802 | − | 0.259959i | ||||
\(527\) | 4513.04i | 0.373038i | ||||||||
\(528\) | 3161.47 | + | 237.162i | 0.260578 | + | 0.0195476i | ||||
\(529\) | −4558.69 | −0.374676 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 4147.97i | − | 0.338995i | ||||||
\(532\) | 26591.7 | + | 28661.2i | 2.16710 | + | 2.33576i | ||||
\(533\) | 1013.76 | 0.0823840 | ||||||||
\(534\) | 1220.70 | − | 2797.73i | 0.0989230 | − | 0.226722i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 11303.5 | − | 3954.54i | 0.910889 | − | 0.318675i | ||||
\(537\) | − | 5536.53i | − | 0.444914i | ||||||
\(538\) | 13394.0 | + | 5844.03i | 1.07334 | + | 0.468316i | ||||
\(539\) | 6776.81i | 0.541555i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19131.8i | 1.52040i | 0.649686 | + | 0.760202i | \(0.274900\pi\) | ||||
−0.649686 | + | 0.760202i | \(0.725100\pi\) | |||||||
\(542\) | 1650.06 | − | 3781.78i | 0.130768 | − | 0.299708i | ||||
\(543\) | 17589.3i | 1.39011i | ||||||||
\(544\) | −4874.24 | + | 9220.39i | −0.384157 | + | 0.726693i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −6198.87 | − | 2704.68i | −0.485874 | − | 0.211996i | ||||
\(547\) | 7142.78 | 0.558324 | 0.279162 | − | 0.960244i | \(-0.409943\pi\) | ||||
0.279162 | + | 0.960244i | \(0.409943\pi\) | |||||||
\(548\) | 8985.36 | − | 8336.55i | 0.700430 | − | 0.649854i | ||||
\(549\) | − | 2639.67i | − | 0.205207i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12584.3 | −0.972974 | ||||||||
\(552\) | 6047.30 | + | 17285.4i | 0.466287 | + | 1.33282i | ||||
\(553\) | 7062.39i | 0.543080i | ||||||||
\(554\) | −2256.12 | + | 5170.82i | −0.173021 | + | 0.396547i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4428.35 | + | 4108.59i | −0.337777 | + | 0.313387i | ||||
\(557\) | 11347.8 | 0.863236 | 0.431618 | − | 0.902057i | \(-0.357943\pi\) | ||||
0.431618 | + | 0.902057i | \(0.357943\pi\) | |||||||
\(558\) | 1077.44 | − | 2469.40i | 0.0817417 | − | 0.187344i | ||||
\(559\) | −2142.74 | −0.162126 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2854.07 | −0.214793 | ||||||||
\(562\) | 352.437 | − | 807.751i | 0.0264531 | − | 0.0606280i | ||||
\(563\) | 8802.19 | 0.658913 | 0.329456 | − | 0.944171i | \(-0.393135\pi\) | ||||
0.329456 | + | 0.944171i | \(0.393135\pi\) | |||||||
\(564\) | 2664.96 | − | 2472.53i | 0.198963 | − | 0.184596i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6868.51 | − | 15742.0i | 0.510079 | − | 1.16905i | ||||
\(567\) | − | 31492.6i | − | 2.33257i | ||||||
\(568\) | 8148.96 | − | 2850.92i | 0.601977 | − | 0.210602i | ||||
\(569\) | −16714.7 | −1.23149 | −0.615744 | − | 0.787946i | \(-0.711145\pi\) | ||||
−0.615744 | + | 0.787946i | \(0.711145\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 17386.8i | − | 1.27428i | −0.770746 | − | 0.637142i | \(-0.780116\pi\) | ||
0.770746 | − | 0.637142i | \(-0.219884\pi\) | |||||||
\(572\) | −512.272 | + | 475.283i | −0.0374461 | + | 0.0347422i | ||||
\(573\) | −4689.14 | −0.341870 | ||||||||
\(574\) | −8247.20 | − | 3598.40i | −0.599706 | − | 0.261663i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4868.32 | − | 3881.44i | 0.352164 | − | 0.280776i | ||||
\(577\) | − | 2260.52i | − | 0.163097i | −0.996669 | − | 0.0815483i | \(-0.974014\pi\) | ||
0.996669 | − | 0.0815483i | \(-0.0259865\pi\) | |||||||
\(578\) | −1802.42 | + | 4130.97i | −0.129707 | + | 0.297276i | ||||
\(579\) | − | 24842.6i | − | 1.78311i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 34512.1i | 2.46438i | ||||||||
\(582\) | 17171.7 | + | 7492.32i | 1.22301 | + | 0.533620i | ||||
\(583\) | − | 3615.86i | − | 0.256867i | ||||||
\(584\) | −6552.33 | − | 18728.9i | −0.464276 | − | 1.32707i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2625.38 | − | 6017.13i | 0.185074 | − | 0.424173i | ||||
\(587\) | −25591.0 | −1.79941 | −0.899705 | − | 0.436498i | \(-0.856219\pi\) | ||||
−0.899705 | + | 0.436498i | \(0.856219\pi\) | |||||||
\(588\) | 29150.0 | + | 31418.6i | 2.04443 | + | 2.20354i | ||||
\(589\) | − | 11055.0i | − | 0.773369i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14037.6 | −0.977037 | ||||||||
\(592\) | −1193.70 | + | 15912.5i | −0.0828729 | + | 1.10473i | ||||
\(593\) | − | 10053.7i | − | 0.696218i | −0.937454 | − | 0.348109i | \(-0.886824\pi\) | ||
0.937454 | − | 0.348109i | \(-0.113176\pi\) | |||||||
\(594\) | −1905.67 | − | 831.476i | −0.131634 | − | 0.0574342i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8484.20 | − | 7871.58i | 0.583098 | − | 0.540994i | ||||
\(597\) | 4205.46 | 0.288305 | ||||||||
\(598\) | −3699.58 | − | 1614.20i | −0.252989 | − | 0.110384i | ||||
\(599\) | 7086.68 | 0.483395 | 0.241698 | − | 0.970352i | \(-0.422296\pi\) | ||||
0.241698 | + | 0.970352i | \(0.422296\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6673.11 | 0.452915 | 0.226458 | − | 0.974021i | \(-0.427286\pi\) | ||||
0.226458 | + | 0.974021i | \(0.427286\pi\) | |||||||
\(602\) | 17431.8 | + | 7605.83i | 1.18018 | + | 0.514934i | ||||
\(603\) | 6435.86 | 0.434641 | ||||||||
\(604\) | 6693.74 | + | 7214.69i | 0.450934 | + | 0.486029i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 11193.7 | + | 4884.00i | 0.750348 | + | 0.327391i | ||||
\(607\) | 15205.6i | 1.01677i | 0.861131 | + | 0.508383i | \(0.169757\pi\) | ||||
−0.861131 | + | 0.508383i | \(0.830243\pi\) | |||||||
\(608\) | 11939.8 | − | 22586.0i | 0.796420 | − | 1.50655i | ||||
\(609\) | −19322.0 | −1.28566 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 801.278i | 0.0530544i | ||||||||
\(612\) | −4108.97 | + | 3812.28i | −0.271398 | + | 0.251801i | ||||
\(613\) | 8147.64 | 0.536836 | 0.268418 | − | 0.963303i | \(-0.413499\pi\) | ||||
0.268418 | + | 0.963303i | \(0.413499\pi\) | |||||||
\(614\) | −2827.14 | + | 6479.55i | −0.185821 | + | 0.425885i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5854.53 | − | 2048.21i | 0.382931 | − | 0.133969i | ||||
\(617\) | − | 449.110i | − | 0.0293039i | −0.999893 | − | 0.0146519i | \(-0.995336\pi\) | ||
0.999893 | − | 0.0146519i | \(-0.00466402\pi\) | |||||||
\(618\) | −20926.9 | − | 9130.80i | −1.36214 | − | 0.594328i | ||||
\(619\) | − | 27800.4i | − | 1.80516i | −0.430524 | − | 0.902579i | \(-0.641671\pi\) | ||
0.430524 | − | 0.902579i | \(-0.358329\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 12009.7i | − | 0.776059i | ||||||
\(622\) | 3453.10 | − | 7914.18i | 0.222599 | − | 0.510176i | ||||
\(623\) | − | 5971.79i | − | 0.384037i | ||||||
\(624\) | −330.598 | + | 4407.01i | −0.0212091 | + | 0.282727i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −16019.1 | − | 6989.42i | −1.02277 | − | 0.446252i | ||||
\(627\) | 6991.26 | 0.445302 | ||||||||
\(628\) | 9651.22 | + | 10402.3i | 0.613257 | + | 0.660984i | ||||
\(629\) | − | 14365.3i | − | 0.910623i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14793.5 | 0.933315 | 0.466657 | − | 0.884438i | \(-0.345458\pi\) | ||||
0.466657 | + | 0.884438i | \(0.345458\pi\) | |||||||
\(632\) | 4355.99 | − | 1523.95i | 0.274164 | − | 0.0959166i | ||||
\(633\) | − | 12109.4i | − | 0.760356i | ||||||
\(634\) | −3524.78 | + | 8078.46i | −0.220800 | + | 0.506052i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −15553.4 | − | 16763.8i | −0.969704 | − | 1.04517i | ||||
\(637\) | −9446.70 | −0.587585 | ||||||||
\(638\) | −798.382 | + | 1829.82i | −0.0495427 | + | 0.113547i | ||||
\(639\) | 4639.77 | 0.287240 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13853.8 | −0.853655 | −0.426828 | − | 0.904333i | \(-0.640369\pi\) | ||||
−0.426828 | + | 0.904333i | \(0.640369\pi\) | |||||||
\(642\) | −13050.6 | + | 29910.8i | −0.802285 | + | 1.83876i | ||||
\(643\) | 4978.60 | 0.305345 | 0.152672 | − | 0.988277i | \(-0.451212\pi\) | ||||
0.152672 | + | 0.988277i | \(0.451212\pi\) | |||||||
\(644\) | 24367.5 | + | 26263.9i | 1.49101 | + | 1.60705i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9197.54 | + | 21079.9i | −0.560174 | + | 1.28387i | ||||
\(647\) | 1903.39i | 0.115657i | 0.998327 | + | 0.0578284i | \(0.0184176\pi\) | ||||
−0.998327 | + | 0.0578284i | \(0.981582\pi\) | |||||||
\(648\) | −19424.2 | + | 6795.58i | −1.17756 | + | 0.411969i | ||||
\(649\) | −2700.11 | −0.163311 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 16974.0i | − | 1.02191i | ||||||
\(652\) | −9311.36 | − | 10036.0i | −0.559296 | − | 0.602824i | ||||
\(653\) | −10877.0 | −0.651839 | −0.325920 | − | 0.945397i | \(-0.605674\pi\) | ||||
−0.325920 | + | 0.945397i | \(0.605674\pi\) | |||||||
\(654\) | 5525.48 | + | 2410.87i | 0.330372 | + | 0.144147i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −439.839 | + | 5863.24i | −0.0261781 | + | 0.348965i | ||||
\(657\) | − | 10663.7i | − | 0.633226i | ||||||
\(658\) | 2844.19 | − | 6518.62i | 0.168508 | − | 0.386204i | ||||
\(659\) | 30611.3i | 1.80948i | 0.425965 | + | 0.904739i | \(0.359935\pi\) | ||||
−0.425965 | + | 0.904739i | \(0.640065\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 16098.8i | − | 0.947310i | −0.880710 | − | 0.473655i | \(-0.842934\pi\) | ||
0.880710 | − | 0.473655i | \(-0.157066\pi\) | |||||||
\(662\) | 10777.3 | + | 4702.34i | 0.632737 | + | 0.276075i | ||||
\(663\) | − | 3978.50i | − | 0.233050i | ||||||
\(664\) | 21286.6 | − | 7447.14i | 1.24410 | − | 0.435249i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3429.57 | + | 7860.26i | −0.199540 | + | 0.457326i | ||||
\(667\) | −11531.7 | −0.669429 | ||||||||
\(668\) | −22949.8 | + | 21292.7i | −1.32927 | + | 1.23329i | ||||
\(669\) | 15598.0i | 0.901428i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1718.29 | −0.0988583 | ||||||||
\(672\) | 18332.5 | − | 34678.8i | 1.05237 | − | 1.99072i | ||||
\(673\) | − | 23837.8i | − | 1.36535i | −0.730724 | − | 0.682673i | \(-0.760817\pi\) | ||
0.730724 | − | 0.682673i | \(-0.239183\pi\) | |||||||
\(674\) | −21059.2 | − | 9188.52i | −1.20352 | − | 0.525117i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11291.7 | + | 12170.5i | 0.642450 | + | 0.692449i | ||||
\(677\) | 25235.3 | 1.43260 | 0.716302 | − | 0.697791i | \(-0.245833\pi\) | ||||
0.716302 | + | 0.697791i | \(0.245833\pi\) | |||||||
\(678\) | −2560.47 | − | 1117.18i | −0.145036 | − | 0.0632817i | ||||
\(679\) | 36653.2 | 2.07161 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19745.2 | 1.11107 | ||||||||
\(682\) | −1607.45 | − | 701.361i | −0.0902531 | − | 0.0393791i | ||||
\(683\) | 19975.3 | 1.11909 | 0.559543 | − | 0.828802i | \(-0.310977\pi\) | ||||
0.559543 | + | 0.828802i | \(0.310977\pi\) | |||||||
\(684\) | 10065.2 | − | 9338.46i | 0.562652 | − | 0.522025i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 46060.5 | + | 20097.0i | 2.56356 | + | 1.11853i | ||||
\(687\) | 14389.5i | 0.799115i | ||||||||
\(688\) | 929.673 | − | 12392.9i | 0.0515166 | − | 0.686739i | ||||
\(689\) | 5040.42 | 0.278700 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13772.3i | 0.758209i | 0.925354 | + | 0.379104i | \(0.123768\pi\) | ||||
−0.925354 | + | 0.379104i | \(0.876232\pi\) | |||||||
\(692\) | −21684.9 | − | 23372.5i | −1.19124 | − | 1.28395i | ||||
\(693\) | 3333.39 | 0.182720 | ||||||||
\(694\) | −5226.37 | + | 11978.3i | −0.285865 | + | 0.655175i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4169.37 | + | 11917.6i | 0.227069 | + | 0.649044i | ||||
\(697\) | − | 5293.14i | − | 0.287650i | ||||||
\(698\) | 14416.3 | + | 6290.10i | 0.781756 | + | 0.341095i | ||||
\(699\) | 4643.26i | 0.251251i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 6347.90i | − | 0.342021i | −0.985269 | − | 0.171011i | \(-0.945297\pi\) | ||
0.985269 | − | 0.171011i | \(-0.0547032\pi\) | |||||||
\(702\) | 1159.06 | − | 2656.45i | 0.0623159 | − | 0.142822i | ||||
\(703\) | 35188.9i | 1.88787i | ||||||||
\(704\) | −2526.62 | − | 3169.02i | −0.135264 | − | 0.169655i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −31191.4 | − | 13609.4i | −1.66275 | − | 0.725488i | ||||
\(707\) | 23893.0 | 1.27099 | ||||||||
\(708\) | −12518.3 | + | 11614.4i | −0.664499 | + | 0.616517i | ||||
\(709\) | − | 17910.5i | − | 0.948719i | −0.880331 | − | 0.474360i | \(-0.842680\pi\) | ||
0.880331 | − | 0.474360i | \(-0.157320\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2480.16 | 0.130821 | ||||||||
\(712\) | −3683.32 | + | 1288.61i | −0.193874 | + | 0.0678270i | ||||
\(713\) | − | 10130.3i | − | 0.532096i | ||||||
\(714\) | −14122.0 | + | 32366.3i | −0.740199 | + | 1.69647i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5188.63 | + | 4813.98i | −0.270821 | + | 0.251266i | ||||
\(717\) | −36208.0 | −1.88593 | ||||||||
\(718\) | 1734.27 | − | 3974.78i | 0.0901426 | − | 0.206598i | ||||
\(719\) | −36601.6 | −1.89849 | −0.949243 | − | 0.314545i | \(-0.898148\pi\) | ||||
−0.949243 | + | 0.314545i | \(0.898148\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −44668.8 | −2.30728 | ||||||||
\(722\) | 14771.7 | − | 33855.4i | 0.761423 | − | 1.74511i | ||||
\(723\) | 1658.67 | 0.0853201 | ||||||||
\(724\) | 16484.1 | − | 15293.8i | 0.846169 | − | 0.785070i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −8977.73 | + | 20576.1i | −0.458946 | + | 1.05186i | ||||
\(727\) | − | 2644.18i | − | 0.134893i | −0.997723 | − | 0.0674466i | \(-0.978515\pi\) | ||
0.997723 | − | 0.0674466i | \(-0.0214852\pi\) | |||||||
\(728\) | 2855.15 | + | 8161.06i | 0.145356 | + | 0.415479i | ||||
\(729\) | 4630.66 | 0.235262 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11187.9i | 0.566075i | ||||||||
\(732\) | −7966.34 | + | 7391.12i | −0.402247 | + | 0.373202i | ||||
\(733\) | −33452.1 | −1.68565 | −0.842825 | − | 0.538188i | \(-0.819109\pi\) | ||||
−0.842825 | + | 0.538188i | \(0.819109\pi\) | |||||||
\(734\) | −14206.5 | − | 6198.56i | −0.714403 | − | 0.311707i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10941.1 | − | 20696.8i | 0.547955 | − | 1.03654i | ||||
\(737\) | − | 4189.42i | − | 0.209388i | ||||||
\(738\) | −1263.69 | + | 2896.25i | −0.0630310 | + | 0.144461i | ||||
\(739\) | − | 25834.9i | − | 1.28600i | −0.765867 | − | 0.642999i | \(-0.777690\pi\) | ||
0.765867 | − | 0.642999i | \(-0.222310\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9745.64i | 0.483151i | ||||||||
\(742\) | −41005.2 | − | 17891.3i | −2.02877 | − | 0.885190i | ||||
\(743\) | 7625.09i | 0.376497i | 0.982121 | + | 0.188249i | \(0.0602811\pi\) | ||||
−0.982121 | + | 0.188249i | \(0.939719\pi\) | |||||||
\(744\) | −10469.3 | + | 3662.71i | −0.515893 | + | 0.180486i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7041.98 | − | 16139.6i | 0.345610 | − | 0.792106i | ||||
\(747\) | 12119.9 | 0.593635 | ||||||||
\(748\) | 2481.60 | + | 2674.73i | 0.121305 | + | 0.130746i | ||||
\(749\) | 63845.0i | 3.11461i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25362.7 | 1.23235 | 0.616177 | − | 0.787607i | \(-0.288680\pi\) | ||||
0.616177 | + | 0.787607i | \(0.288680\pi\) | |||||||
\(752\) | −4634.33 | − | 347.651i | −0.224730 | − | 0.0168584i | ||||
\(753\) | 11026.4i | 0.533633i | ||||||||
\(754\) | −2550.72 | − | 1112.92i | −0.123198 | − | 0.0537537i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −18858.5 | + | 17496.8i | −0.907245 | + | 0.841736i | ||||
\(757\) | −38948.0 | −1.87000 | −0.935000 | − | 0.354648i | \(-0.884601\pi\) | ||||
−0.935000 | + | 0.354648i | \(0.884601\pi\) | |||||||
\(758\) | −28962.3 | − | 12636.8i | −1.38781 | − | 0.605525i | ||||
\(759\) | 6406.48 | 0.306378 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13722.2 | −0.653654 | −0.326827 | − | 0.945084i | \(-0.605979\pi\) | ||||
−0.326827 | + | 0.945084i | \(0.605979\pi\) | |||||||
\(762\) | 8025.52 | + | 3501.68i | 0.381541 | + | 0.166473i | ||||
\(763\) | 11794.2 | 0.559606 | ||||||||
\(764\) | 4077.18 | + | 4394.49i | 0.193072 | + | 0.208098i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19756.8 | − | 8620.26i | −0.931909 | − | 0.406609i | ||||
\(767\) | − | 3763.89i | − | 0.177192i | ||||||
\(768\) | −25345.3 | − | 3824.14i | −1.19084 | − | 0.179677i | ||||
\(769\) | −18689.5 | −0.876414 | −0.438207 | − | 0.898874i | \(-0.644386\pi\) | ||||
−0.438207 | + | 0.898874i | \(0.644386\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9435.86i | 0.440758i | ||||||||
\(772\) | −23281.6 | + | 21600.5i | −1.08539 | + | 1.00702i | ||||
\(773\) | −6386.49 | −0.297162 | −0.148581 | − | 0.988900i | \(-0.547471\pi\) | ||||
−0.148581 | + | 0.988900i | \(0.547471\pi\) | |||||||
\(774\) | 2671.01 | − | 6121.70i | 0.124041 | − | 0.284289i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7909.15 | − | 22607.2i | −0.365879 | − | 1.04581i | ||||
\(777\) | 54029.3i | 2.49458i | ||||||||
\(778\) | 14378.3 | + | 6273.52i | 0.662580 | + | 0.289096i | ||||
\(779\) | 12965.9i | 0.596345i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 3020.25i | − | 0.138378i | ||||||
\(782\) | −8428.22 | + | 19316.7i | −0.385413 | + | 0.883329i | ||||
\(783\) | − | 8280.21i | − | 0.377919i | ||||||
\(784\) | 4098.64 | − | 54636.6i | 0.186709 | − | 2.48891i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 7929.47 | + | 3459.77i | 0.359841 | + | 0.157005i | ||||
\(787\) | −19410.3 | −0.879167 | −0.439583 | − | 0.898202i | \(-0.644874\pi\) | ||||
−0.439583 | + | 0.898202i | \(0.644874\pi\) | |||||||
\(788\) | 12205.6 | + | 13155.5i | 0.551785 | + | 0.594728i | ||||
\(789\) | 17350.1i | 0.782865i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5465.35 | −0.245671 | ||||||||
\(792\) | −719.290 | − | 2055.99i | −0.0322713 | − | 0.0922429i | ||||
\(793\) | − | 2395.25i | − | 0.107261i | ||||||
\(794\) | 12470.8 | − | 28581.8i | 0.557394 | − | 1.27749i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3656.62 | − | 3941.20i | −0.162821 | − | 0.175493i | ||||
\(797\) | 30740.8 | 1.36624 | 0.683121 | − | 0.730305i | \(-0.260622\pi\) | ||||
0.683121 | + | 0.730305i | \(0.260622\pi\) | |||||||
\(798\) | 34592.8 | − | 79283.5i | 1.53455 | − | 3.51705i | ||||
\(799\) | 4183.72 | 0.185243 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2097.17 | −0.0925092 | ||||||||
\(802\) | −11902.0 | + | 27278.1i | −0.524031 | + | 1.20103i | ||||
\(803\) | −6941.51 | −0.305057 | ||||||||
\(804\) | −18020.5 | − | 19423.0i | −0.790465 | − | 0.851984i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 977.679 | − | 2240.75i | 0.0427262 | − | 0.0979243i | ||||
\(807\) | − | 32331.9i | − | 1.41033i | ||||||
\(808\) | −5155.71 | − | 14736.9i | −0.224477 | − | 0.641636i | ||||
\(809\) | −31805.5 | −1.38223 | −0.691114 | − | 0.722746i | \(-0.742880\pi\) | ||||
−0.691114 | + | 0.722746i | \(0.742880\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31014.7i | 1.34288i | 0.741060 | + | 0.671439i | \(0.234323\pi\) | ||||
−0.741060 | + | 0.671439i | \(0.765677\pi\) | |||||||
\(812\) | 16800.4 | + | 18107.9i | 0.726081 | + | 0.782590i | ||||
\(813\) | −9128.90 | −0.393806 | ||||||||
\(814\) | 5116.63 | + | 2232.48i | 0.220317 | + | 0.0961281i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 23010.4 | + | 1726.15i | 0.987162 | + | 0.0740533i | ||||
\(817\) | − | 27405.7i | − | 1.17357i | ||||||
\(818\) | 2624.38 | − | 6014.84i | 0.112175 | − | 0.257095i | ||||
\(819\) | 4646.66i | 0.198251i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 12021.4i | − | 0.511021i | −0.966806 | − | 0.255511i | \(-0.917756\pi\) | ||
0.966806 | − | 0.255511i | \(-0.0822436\pi\) | |||||||
\(822\) | −24855.6 | − | 10844.9i | −1.05467 | − | 0.460171i | ||||
\(823\) | 15489.0i | 0.656032i | 0.944672 | + | 0.328016i | \(0.106380\pi\) | ||||
−0.944672 | + | 0.328016i | \(0.893620\pi\) | |||||||
\(824\) | 9638.78 | + | 27551.1i | 0.407503 | + | 1.16479i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13360.2 | + | 30620.3i | −0.562785 | + | 1.28985i | ||||
\(827\) | 17097.2 | 0.718898 | 0.359449 | − | 0.933165i | \(-0.382965\pi\) | ||||
0.359449 | + | 0.933165i | \(0.382965\pi\) | |||||||
\(828\) | 9223.34 | − | 8557.35i | 0.387117 | − | 0.359165i | ||||
\(829\) | 9885.97i | 0.414178i | 0.978322 | + | 0.207089i | \(0.0663990\pi\) | ||||
−0.978322 | + | 0.207089i | \(0.933601\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12481.9 | 0.521050 | ||||||||
\(832\) | 4417.54 | − | 3522.04i | 0.184075 | − | 0.146761i | ||||
\(833\) | 49324.2i | 2.05160i | ||||||||
\(834\) | 12249.8 | + | 5344.82i | 0.508605 | + | 0.221914i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6078.86 | − | 6551.95i | −0.251485 | − | 0.271057i | ||||
\(837\) | 7273.99 | 0.300389 | ||||||||
\(838\) | 23881.7 | + | 10420.0i | 0.984462 | + | 0.429539i | ||||
\(839\) | 39204.3 | 1.61321 | 0.806606 | − | 0.591090i | \(-0.201302\pi\) | ||||
0.806606 | + | 0.591090i | \(0.201302\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16438.4 | 0.674007 | ||||||||
\(842\) | −18063.1 | − | 7881.27i | −0.739307 | − | 0.322573i | ||||
\(843\) | −1949.84 | −0.0796632 | ||||||||
\(844\) | −11348.5 | + | 10529.0i | −0.462833 | + | 0.429413i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2289.21 | − | 998.822i | −0.0930314 | − | 0.0405913i | ||||
\(847\) | 43920.0i | 1.78171i | ||||||||
\(848\) | −2186.89 | + | 29152.1i | −0.0885589 | + | 1.18053i | ||||
\(849\) | −37999.7 | −1.53610 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 32245.5i | 1.29890i | ||||||||
\(852\) | −12991.4 | − | 14002.5i | −0.522393 | − | 0.563049i | ||||
\(853\) | 45054.1 | 1.80847 | 0.904234 | − | 0.427038i | \(-0.140443\pi\) | ||||
0.904234 | + | 0.427038i | \(0.140443\pi\) | |||||||
\(854\) | −8502.13 | + | 19486.1i | −0.340676 | + | 0.780796i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 39378.7 | − | 13776.7i | 1.57236 | − | 0.550090i | ||||
\(857\) | 48464.2i | 1.93174i | 0.259021 | + | 0.965872i | \(0.416600\pi\) | ||||
−0.259021 | + | 0.965872i | \(0.583400\pi\) | |||||||
\(858\) | 1417.06 | + | 618.290i | 0.0563842 | + | 0.0246015i | ||||
\(859\) | − | 1000.76i | − | 0.0397503i | −0.999802 | − | 0.0198751i | \(-0.993673\pi\) | ||
0.999802 | − | 0.0198751i | \(-0.00632687\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 19908.0i | 0.787995i | ||||||||
\(862\) | 12721.8 | − | 29157.1i | 0.502675 | − | 1.15208i | ||||
\(863\) | 22485.5i | 0.886922i | 0.896294 | + | 0.443461i | \(0.146250\pi\) | ||||
−0.896294 | + | 0.443461i | \(0.853750\pi\) | |||||||
\(864\) | 14861.1 | + | 7856.16i | 0.585170 | + | 0.309343i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −6712.44 | − | 2928.76i | −0.263392 | − | 0.114923i | ||||
\(867\) | 9971.79 | 0.390611 | ||||||||
\(868\) | −15907.4 | + | 14758.8i | −0.622042 | + | 0.577126i | ||||
\(869\) | − | 1614.46i | − | 0.0630228i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5839.94 | 0.227186 | ||||||||
\(872\) | −2544.99 | − | 7274.51i | −0.0988353 | − | 0.282507i | ||||
\(873\) | − | 12871.9i | − | 0.499022i | ||||||
\(874\) | 20645.6 | − | 47317.6i | 0.799023 | − | 1.83129i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −32182.2 | + | 29858.4i | −1.24125 | + | 1.15162i | ||||
\(877\) | 43726.2 | 1.68361 | 0.841806 | − | 0.539780i | \(-0.181493\pi\) | ||||
0.841806 | + | 0.539780i | \(0.181493\pi\) | |||||||
\(878\) | 4773.32 | − | 10940.0i | 0.183476 | − | 0.420509i | ||||
\(879\) | −14524.8 | −0.557349 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20290.0 | 0.775923 | 0.387962 | − | 0.921675i | \(-0.373179\pi\) | ||||
0.387962 | + | 0.921675i | \(0.373179\pi\) | |||||||
\(882\) | 11775.7 | − | 26988.7i | 0.449554 | − | 1.03034i | ||||
\(883\) | 14887.3 | 0.567382 | 0.283691 | − | 0.958916i | \(-0.408441\pi\) | ||||
0.283691 | + | 0.958916i | \(0.408441\pi\) | |||||||
\(884\) | −3728.51 | + | 3459.28i | −0.141859 | + | 0.131616i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11044.2 | + | 25312.4i | −0.418780 | + | 0.959803i | ||||
\(887\) | − | 34359.3i | − | 1.30065i | −0.759658 | − | 0.650323i | \(-0.774633\pi\) | ||
0.759658 | − | 0.650323i | \(-0.225367\pi\) | |||||||
\(888\) | 33324.6 | − | 11658.6i | 1.25935 | − | 0.440583i | ||||
\(889\) | 17130.6 | 0.646278 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7199.21i | 0.270687i | ||||||||
\(892\) | 14617.9 | − | 13562.4i | 0.548704 | − | 0.509084i | ||||
\(893\) | −10248.3 | −0.384040 | ||||||||
\(894\) | −23469.2 | − | 10240.1i | −0.877996 | − | 0.383086i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −48439.7 | + | 12972.4i | −1.80609 | + | 0.483682i | ||||
\(897\) | 8930.47i | 0.332419i | ||||||||
\(898\) | −19409.1 | + | 44483.8i | −0.721258 | + | 1.65306i | ||||
\(899\) | − | 6984.47i | − | 0.259116i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 26317.6i | − | 0.973103i | ||||||
\(902\) | 1885.31 | + | 822.595i | 0.0695941 | + | 0.0303652i | ||||
\(903\) | − | 42078.9i | − | 1.55072i | ||||||
\(904\) | 1179.33 | + | 3370.96i | 0.0433894 | + | 0.124022i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 8707.81 | − | 19957.5i | 0.319313 | − | 0.731835i | ||||
\(907\) | 53363.9 | 1.95360 | 0.976802 | − | 0.214144i | \(-0.0686963\pi\) | ||||
0.976802 | + | 0.214144i | \(0.0686963\pi\) | |||||||
\(908\) | −17168.3 | − | 18504.5i | −0.627479 | − | 0.676313i | ||||
\(909\) | − | 8390.73i | − | 0.306164i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25213.9 | −0.916984 | −0.458492 | − | 0.888699i | \(-0.651610\pi\) | ||||
−0.458492 | + | 0.888699i | \(0.651610\pi\) | |||||||
\(912\) | −56365.6 | − | 4228.34i | −2.04655 | − | 0.153525i | ||||
\(913\) | − | 7889.46i | − | 0.285984i | ||||||
\(914\) | 33772.1 | + | 14735.4i | 1.22219 | + | 0.533264i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13485.3 | − | 12511.6i | 0.486426 | − | 0.451303i | ||||
\(917\) | 16925.5 | 0.609521 | ||||||||
\(918\) | −13870.1 | − | 6051.80i | −0.498674 | − | 0.217581i | ||||
\(919\) | −3747.02 | −0.134497 | −0.0672485 | − | 0.997736i | \(-0.521422\pi\) | ||||
−0.0672485 | + | 0.997736i | \(0.521422\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15641.1 | 0.559599 | ||||||||
\(922\) | 812.452 | + | 354.487i | 0.0290202 | + | 0.0126621i | ||||
\(923\) | 4210.15 | 0.150140 | ||||||||
\(924\) | −9333.53 | − | 10059.9i | −0.332306 | − | 0.358168i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 31540.6 | + | 13761.8i | 1.11932 | + | 0.488380i | ||||
\(927\) | 15686.8i | 0.555794i | ||||||||
\(928\) | 7543.47 | − | 14269.6i | 0.266839 | − | 0.504767i | ||||
\(929\) | 27726.7 | 0.979209 | 0.489604 | − | 0.871945i | \(-0.337141\pi\) | ||||
0.489604 | + | 0.871945i | \(0.337141\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 120823.i | − | 4.25330i | ||||||
\(932\) | 4351.50 | − | 4037.29i | 0.152938 | − | 0.141895i | ||||
\(933\) | −19104.1 | −0.670355 | ||||||||
\(934\) | 2086.25 | − | 4781.48i | 0.0730879 | − | 0.167511i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2866.00 | − | 1002.67i | 0.100083 | − | 0.0350143i | ||||
\(937\) | − | 29333.2i | − | 1.02270i | −0.859371 | − | 0.511352i | \(-0.829145\pi\) | ||
0.859371 | − | 0.511352i | \(-0.170855\pi\) | |||||||
\(938\) | −47509.5 | − | 20729.3i | −1.65378 | − | 0.721572i | ||||
\(939\) | 38668.7i | 1.34388i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24218.4i | 0.838998i | 0.907756 | + | 0.419499i | \(0.137794\pi\) | ||||
−0.907756 | + | 0.419499i | \(0.862206\pi\) | |||||||
\(942\) | 12555.2 | − | 28775.2i | 0.434256 | − | 0.995274i | ||||
\(943\) | 11881.4i | 0.410299i | ||||||||
\(944\) | 21769.1 | + | 1633.04i | 0.750555 | + | 0.0563039i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3984.91 | − | 1738.69i | −0.136956 | − | 0.0597566i | ||||
\(947\) | −50824.6 | −1.74401 | −0.872005 | − | 0.489497i | \(-0.837180\pi\) | ||||
−0.872005 | + | 0.489497i | \(0.837180\pi\) | |||||||
\(948\) | −6944.49 | − | 7484.96i | −0.237918 | − | 0.256435i | ||||
\(949\) | − | 9676.28i | − | 0.330986i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19500.7 | 0.664935 | ||||||||
\(952\) | 42611.4 | − | 14907.7i | 1.45068 | − | 0.507521i | ||||
\(953\) | − | 10155.1i | − | 0.345180i | −0.984994 | − | 0.172590i | \(-0.944786\pi\) | ||
0.984994 | − | 0.172590i | \(-0.0552136\pi\) | |||||||
\(954\) | −6283.06 | + | 14400.2i | −0.213230 | + | 0.488704i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 31482.6 | + | 33932.8i | 1.06508 | + | 1.14798i | ||||
\(957\) | 4417.01 | 0.149197 | ||||||||
\(958\) | −18500.4 | + | 42401.2i | −0.623926 | + | 1.42998i | ||||
\(959\) | −53054.5 | −1.78646 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23655.3 | −0.794042 | ||||||||
\(962\) | −3112.02 | + | 7132.45i | −0.104299 | + | 0.239043i | ||||
\(963\) | 22421.0 | 0.750268 | ||||||||
\(964\) | −1442.20 | − | 1554.44i | −0.0481848 | − | 0.0519348i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 31699.4 | − | 72651.9i | 1.05581 | − | 2.41981i | ||||
\(967\) | 28225.7i | 0.938652i | 0.883025 | + | 0.469326i | \(0.155503\pi\) | ||||
−0.883025 | + | 0.469326i | \(0.844497\pi\) | |||||||
\(968\) | 27089.2 | − | 9477.20i | 0.899464 | − | 0.314678i | ||||
\(969\) | 50885.0 | 1.68696 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 47631.4i | − | 1.57422i | −0.616814 | − | 0.787109i | \(-0.711577\pi\) | ||
0.616814 | − | 0.787109i | \(-0.288423\pi\) | |||||||
\(972\) | 17324.4 | + | 18672.7i | 0.571687 | + | 0.616179i | ||||
\(973\) | 26147.4 | 0.861508 | ||||||||
\(974\) | 30654.1 | + | 13375.0i | 1.00844 | + | 0.440001i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13853.4 | + | 1039.23i | 0.454340 | + | 0.0340829i | ||||
\(977\) | − | 13542.4i | − | 0.443460i | −0.975108 | − | 0.221730i | \(-0.928830\pi\) | ||
0.975108 | − | 0.221730i | \(-0.0711703\pi\) | |||||||
\(978\) | −12113.0 | + | 27761.9i | −0.396045 | + | 0.907698i | ||||
\(979\) | 1365.15i | 0.0445663i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 4141.88i | − | 0.134801i | ||||||
\(982\) | 20561.4 | + | 8971.32i | 0.668168 | + | 0.291534i | ||||
\(983\) | − | 35108.5i | − | 1.13915i | −0.821938 | − | 0.569576i | \(-0.807107\pi\) | ||
0.821938 | − | 0.569576i | \(-0.192893\pi\) | |||||||
\(984\) | 12279.0 | − | 4295.82i | 0.397805 | − | 0.139172i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5810.92 | + | 13318.1i | −0.187685 | + | 0.430156i | ||||
\(987\) | −15735.4 | −0.507460 | ||||||||
\(988\) | 9133.25 | − | 8473.77i | 0.294097 | − | 0.272861i | ||||
\(989\) | − | 25113.4i | − | 0.807440i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42816.1 | −1.37245 | −0.686225 | − | 0.727390i | \(-0.740733\pi\) | ||||
−0.686225 | + | 0.727390i | \(0.740733\pi\) | |||||||
\(992\) | 12535.6 | + | 6626.77i | 0.401215 | + | 0.212097i | ||||
\(993\) | − | 26015.5i | − | 0.831396i | ||||||
\(994\) | −34250.8 | − | 14944.2i | −1.09293 | − | 0.476864i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −33936.0 | − | 36577.1i | −1.07962 | − | 1.16364i | ||||
\(997\) | −13029.0 | −0.413873 | −0.206936 | − | 0.978354i | \(-0.566349\pi\) | ||||
−0.206936 | + | 0.978354i | \(0.566349\pi\) | |||||||
\(998\) | 7089.42 | + | 3093.24i | 0.224861 | + | 0.0981111i | ||||
\(999\) | −23153.6 | −0.733280 |
(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 | 200.4.f.c.149.4 | 12 | ||
4.3 | odd | 2 | 800.4.f.b.49.3 | 12 | |||
5.2 | odd | 4 | 40.4.d.a.21.1 | ✓ | 12 | ||
5.3 | odd | 4 | 200.4.d.b.101.12 | 12 | |||
5.4 | even | 2 | 200.4.f.b.149.9 | 12 | |||
8.3 | odd | 2 | 800.4.f.c.49.9 | 12 | |||
8.5 | even | 2 | 200.4.f.b.149.10 | 12 | |||
15.2 | even | 4 | 360.4.k.c.181.12 | 12 | |||
20.3 | even | 4 | 800.4.d.d.401.3 | 12 | |||
20.7 | even | 4 | 160.4.d.a.81.10 | 12 | |||
20.19 | odd | 2 | 800.4.f.c.49.10 | 12 | |||
40.3 | even | 4 | 800.4.d.d.401.10 | 12 | |||
40.13 | odd | 4 | 200.4.d.b.101.11 | 12 | |||
40.19 | odd | 2 | 800.4.f.b.49.4 | 12 | |||
40.27 | even | 4 | 160.4.d.a.81.3 | 12 | |||
40.29 | even | 2 | inner | 200.4.f.c.149.3 | 12 | ||
40.37 | odd | 4 | 40.4.d.a.21.2 | yes | 12 | ||
60.47 | odd | 4 | 1440.4.k.c.721.12 | 12 | |||
80.27 | even | 4 | 1280.4.a.bd.1.5 | 6 | |||
80.37 | odd | 4 | 1280.4.a.bb.1.2 | 6 | |||
80.67 | even | 4 | 1280.4.a.ba.1.2 | 6 | |||
80.77 | odd | 4 | 1280.4.a.bc.1.5 | 6 | |||
120.77 | even | 4 | 360.4.k.c.181.11 | 12 | |||
120.107 | odd | 4 | 1440.4.k.c.721.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.4.d.a.21.1 | ✓ | 12 | 5.2 | odd | 4 | ||
40.4.d.a.21.2 | yes | 12 | 40.37 | odd | 4 | ||
160.4.d.a.81.3 | 12 | 40.27 | even | 4 | |||
160.4.d.a.81.10 | 12 | 20.7 | even | 4 | |||
200.4.d.b.101.11 | 12 | 40.13 | odd | 4 | |||
200.4.d.b.101.12 | 12 | 5.3 | odd | 4 | |||
200.4.f.b.149.9 | 12 | 5.4 | even | 2 | |||
200.4.f.b.149.10 | 12 | 8.5 | even | 2 | |||
200.4.f.c.149.3 | 12 | 40.29 | even | 2 | inner | ||
200.4.f.c.149.4 | 12 | 1.1 | even | 1 | trivial | ||
360.4.k.c.181.11 | 12 | 120.77 | even | 4 | |||
360.4.k.c.181.12 | 12 | 15.2 | even | 4 | |||
800.4.d.d.401.3 | 12 | 20.3 | even | 4 | |||
800.4.d.d.401.10 | 12 | 40.3 | even | 4 | |||
800.4.f.b.49.3 | 12 | 4.3 | odd | 2 | |||
800.4.f.b.49.4 | 12 | 40.19 | odd | 2 | |||
800.4.f.c.49.9 | 12 | 8.3 | odd | 2 | |||
800.4.f.c.49.10 | 12 | 20.19 | odd | 2 | |||
1280.4.a.ba.1.2 | 6 | 80.67 | even | 4 | |||
1280.4.a.bb.1.2 | 6 | 80.37 | odd | 4 | |||
1280.4.a.bc.1.5 | 6 | 80.77 | odd | 4 | |||
1280.4.a.bd.1.5 | 6 | 80.27 | even | 4 | |||
1440.4.k.c.721.6 | 12 | 120.107 | odd | 4 | |||
1440.4.k.c.721.12 | 12 | 60.47 | odd | 4 |