Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [117,4,Mod(55,117)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(117, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("117.55");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 117.g (of order \(3\), 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: | \(6.90322347067\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 52 x^{14} + 1899 x^{12} + 33440 x^{10} + 424113 x^{8} + 2869882 x^{6} + 13705540 x^{4} + \cdots + 24920064 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 55.6 | ||
Root | \(1.37814 + 2.38701i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 117.55 |
Dual form | 117.4.g.f.100.6 |
$q$-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 \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(92\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.37814 | + | 2.38701i | 0.487246 | + | 0.843934i | 0.999892 | − | 0.0146655i | \(-0.00466834\pi\) |
−0.512647 | + | 0.858600i | \(0.671335\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.201468 | − | 0.348954i | 0.0251836 | − | 0.0436192i | ||||
\(5\) | −0.313209 | −0.0280143 | −0.0140071 | − | 0.999902i | \(-0.504459\pi\) | ||||
−0.0140071 | + | 0.999902i | \(0.504459\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −14.2830 | + | 24.7388i | −0.771208 | + | 1.33577i | 0.165693 | + | 0.986177i | \(0.447014\pi\) |
−0.936901 | + | 0.349595i | \(0.886319\pi\) | |||||||
\(8\) | 23.1608 | 1.02357 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.431646 | − | 0.747632i | −0.0136498 | − | 0.0236422i | ||||
\(11\) | 31.6086 | + | 54.7478i | 0.866397 | + | 1.50064i | 0.865654 | + | 0.500644i | \(0.166903\pi\) |
0.000743312 | 1.00000i | \(0.499763\pi\) | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.26982 | + | 46.8172i | −0.0484258 | + | 0.998827i | ||||
\(14\) | −78.7357 | −1.50307 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 30.3071 | + | 52.4934i | 0.473548 | + | 0.820209i | ||||
\(17\) | 49.4135 | − | 85.5867i | 0.704973 | − | 1.22105i | −0.261729 | − | 0.965142i | \(-0.584292\pi\) |
0.966701 | − | 0.255907i | \(-0.0823742\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.24486 | − | 12.5485i | 0.0874782 | − | 0.151517i | −0.818966 | − | 0.573842i | \(-0.805453\pi\) |
0.906445 | + | 0.422325i | \(0.138786\pi\) | |||||||
\(20\) | −0.0631018 | + | 0.109295i | −0.000705499 | + | 0.00122196i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −87.1222 | + | 150.900i | −0.844296 | + | 1.46236i | ||||
\(23\) | −7.19499 | − | 12.4621i | −0.0652286 | − | 0.112979i | 0.831567 | − | 0.555425i | \(-0.187444\pi\) |
−0.896795 | + | 0.442446i | \(0.854111\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −124.902 | −0.999215 | ||||||||
\(26\) | −114.881 | + | 59.1025i | −0.866539 | + | 0.445806i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.75514 | + | 9.96819i | 0.0388435 | + | 0.0672790i | ||||
\(29\) | −98.1415 | − | 169.986i | −0.628428 | − | 1.08847i | −0.987867 | − | 0.155301i | \(-0.950365\pi\) |
0.359439 | − | 0.933169i | \(-0.382968\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 118.691 | 0.687661 | 0.343830 | − | 0.939032i | \(-0.388276\pi\) | ||||
0.343830 | + | 0.939032i | \(0.388276\pi\) | |||||||
\(32\) | 9.10860 | − | 15.7766i | 0.0503184 | − | 0.0871540i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 272.395 | 1.37398 | ||||||||
\(35\) | 4.47356 | − | 7.74843i | 0.0216048 | − | 0.0374207i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −159.557 | − | 276.361i | −0.708947 | − | 1.22793i | −0.965248 | − | 0.261335i | \(-0.915837\pi\) |
0.256302 | − | 0.966597i | \(-0.417496\pi\) | |||||||
\(38\) | 39.9377 | 0.170493 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.25418 | −0.0286747 | ||||||||
\(41\) | 173.053 | + | 299.737i | 0.659180 | + | 1.14173i | 0.980828 | + | 0.194873i | \(0.0624296\pi\) |
−0.321649 | + | 0.946859i | \(0.604237\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 34.7427 | − | 60.1761i | 0.123214 | − | 0.213413i | −0.797819 | − | 0.602897i | \(-0.794013\pi\) |
0.921033 | + | 0.389483i | \(0.127346\pi\) | |||||||
\(44\) | 25.4726 | 0.0872758 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 19.8314 | − | 34.3490i | 0.0635647 | − | 0.110097i | ||||
\(47\) | 101.875 | 0.316170 | 0.158085 | − | 0.987426i | \(-0.449468\pi\) | ||||
0.158085 | + | 0.987426i | \(0.449468\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −236.507 | − | 409.642i | −0.689525 | − | 1.19429i | ||||
\(50\) | −172.132 | − | 298.142i | −0.486863 | − | 0.843272i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 15.8797 | + | 10.2242i | 0.0423485 | + | 0.0272663i | ||||
\(53\) | 594.823 | 1.54161 | 0.770804 | − | 0.637072i | \(-0.219855\pi\) | ||||
0.770804 | + | 0.637072i | \(0.219855\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.90012 | − | 17.1475i | −0.0242715 | − | 0.0420394i | ||||
\(56\) | −330.806 | + | 572.972i | −0.789388 | + | 1.36726i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 270.505 | − | 468.529i | 0.612398 | − | 1.06070i | ||||
\(59\) | −102.237 | + | 177.079i | −0.225595 | + | 0.390741i | −0.956498 | − | 0.291740i | \(-0.905766\pi\) |
0.730903 | + | 0.682481i | \(0.239099\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 107.989 | − | 187.043i | 0.226666 | − | 0.392596i | −0.730152 | − | 0.683285i | \(-0.760551\pi\) |
0.956818 | + | 0.290688i | \(0.0938842\pi\) | |||||||
\(62\) | 163.572 | + | 283.315i | 0.335060 | + | 0.580340i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 535.125 | 1.04517 | ||||||||
\(65\) | 0.710929 | − | 14.6636i | 0.00135661 | − | 0.0279814i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −34.3025 | − | 59.4136i | −0.0625480 | − | 0.108336i | 0.833056 | − | 0.553189i | \(-0.186589\pi\) |
−0.895604 | + | 0.444853i | \(0.853256\pi\) | |||||||
\(68\) | −19.9105 | − | 34.4860i | −0.0355074 | − | 0.0615007i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 24.6607 | 0.0421075 | ||||||||
\(71\) | 473.121 | − | 819.469i | 0.790832 | − | 1.36976i | −0.134620 | − | 0.990897i | \(-0.542981\pi\) |
0.925452 | − | 0.378864i | \(-0.123685\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −779.872 | −1.25037 | −0.625185 | − | 0.780476i | \(-0.714977\pi\) | ||||
−0.625185 | + | 0.780476i | \(0.714977\pi\) | |||||||
\(74\) | 439.784 | − | 761.727i | 0.690862 | − | 1.19661i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.91922 | − | 5.05624i | −0.00440602 | − | 0.00763145i | ||||
\(77\) | −1805.86 | −2.67269 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 240.022 | 0.341831 | 0.170915 | − | 0.985286i | \(-0.445328\pi\) | ||||
0.170915 | + | 0.985286i | \(0.445328\pi\) | |||||||
\(80\) | −9.49245 | − | 16.4414i | −0.0132661 | − | 0.0229776i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −476.982 | + | 826.158i | −0.642365 | + | 1.11261i | ||||
\(83\) | −855.576 | −1.13147 | −0.565733 | − | 0.824588i | \(-0.691407\pi\) | ||||
−0.565733 | + | 0.824588i | \(0.691407\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.4768 | + | 26.8065i | −0.0197493 | + | 0.0342068i | ||||
\(86\) | 191.521 | 0.240142 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 732.082 | + | 1268.00i | 0.886821 | + | 1.53602i | ||||
\(89\) | 632.029 | + | 1094.71i | 0.752753 | + | 1.30381i | 0.946484 | + | 0.322751i | \(0.104608\pi\) |
−0.193731 | + | 0.981055i | \(0.562059\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1125.78 | − | 724.842i | −1.29686 | − | 0.834989i | ||||
\(92\) | −5.79825 | −0.00657075 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 140.398 | + | 243.176i | 0.154052 | + | 0.266826i | ||||
\(95\) | −2.26916 | + | 3.93030i | −0.00245064 | + | 0.00424463i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −331.145 | + | 573.560i | −0.346625 | + | 0.600373i | −0.985648 | − | 0.168815i | \(-0.946006\pi\) |
0.639022 | + | 0.769188i | \(0.279339\pi\) | |||||||
\(98\) | 651.879 | − | 1129.09i | 0.671936 | − | 1.16383i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −25.1638 | + | 43.5850i | −0.0251638 | + | 0.0435850i | ||||
\(101\) | −396.785 | − | 687.252i | −0.390907 | − | 0.677071i | 0.601662 | − | 0.798751i | \(-0.294505\pi\) |
−0.992569 | + | 0.121680i | \(0.961172\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 980.791 | 0.938254 | 0.469127 | − | 0.883131i | \(-0.344569\pi\) | ||||
0.469127 | + | 0.883131i | \(0.344569\pi\) | |||||||
\(104\) | −52.5710 | + | 1084.32i | −0.0495674 | + | 1.02237i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 819.749 | + | 1419.85i | 0.751142 | + | 1.30102i | ||||
\(107\) | −402.972 | − | 697.968i | −0.364082 | − | 0.630609i | 0.624546 | − | 0.780988i | \(-0.285284\pi\) |
−0.988628 | + | 0.150379i | \(0.951951\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 845.184 | 0.742697 | 0.371348 | − | 0.928494i | \(-0.378896\pi\) | ||||
0.371348 | + | 0.928494i | \(0.378896\pi\) | |||||||
\(110\) | 27.2875 | − | 47.2633i | 0.0236523 | − | 0.0409671i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1731.50 | −1.46082 | ||||||||
\(113\) | 28.1887 | − | 48.8243i | 0.0234670 | − | 0.0406460i | −0.854053 | − | 0.520185i | \(-0.825863\pi\) |
0.877520 | + | 0.479539i | \(0.159196\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.25354 | + | 3.90324i | 0.00182733 | + | 0.00316503i | ||||
\(116\) | −79.0896 | −0.0633042 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −563.585 | −0.439680 | ||||||||
\(119\) | 1411.54 | + | 2444.87i | 1.08736 | + | 1.88337i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1332.71 | + | 2308.33i | −1.00129 | + | 1.73428i | ||||
\(122\) | 595.296 | 0.441767 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 23.9124 | − | 41.4175i | 0.0173177 | − | 0.0299952i | ||||
\(125\) | 78.2716 | 0.0560066 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −833.323 | − | 1443.36i | −0.582248 | − | 1.00848i | −0.995212 | − | 0.0977357i | \(-0.968840\pi\) |
0.412965 | − | 0.910747i | \(-0.364493\pi\) | |||||||
\(128\) | 664.607 | + | 1151.13i | 0.458934 | + | 0.794897i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 35.9818 | − | 18.5114i | 0.0242755 | − | 0.0124889i | ||||
\(131\) | 602.630 | 0.401924 | 0.200962 | − | 0.979599i | \(-0.435593\pi\) | ||||
0.200962 | + | 0.979599i | \(0.435593\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 206.956 | + | 358.459i | 0.134928 | + | 0.233702i | ||||
\(134\) | 94.5471 | − | 163.760i | 0.0609524 | − | 0.105573i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1144.46 | − | 1982.26i | 0.721591 | − | 1.24983i | ||||
\(137\) | 210.827 | − | 365.163i | 0.131476 | − | 0.227722i | −0.792770 | − | 0.609521i | \(-0.791362\pi\) |
0.924246 | + | 0.381799i | \(0.124695\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.5851 | + | 25.2622i | −0.00889995 | + | 0.0154152i | −0.870441 | − | 0.492273i | \(-0.836166\pi\) |
0.861541 | + | 0.507688i | \(0.169500\pi\) | |||||||
\(140\) | −1.80256 | − | 3.12213i | −0.00108817 | − | 0.00188477i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2608.10 | 1.54132 | ||||||||
\(143\) | −2634.88 | + | 1355.56i | −1.54084 | + | 0.792710i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 30.7388 | + | 53.2412i | 0.0176050 | + | 0.0304927i | ||||
\(146\) | −1074.77 | − | 1861.56i | −0.609238 | − | 1.05523i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −128.583 | −0.0714152 | ||||||||
\(149\) | 1070.90 | − | 1854.85i | 0.588802 | − | 1.01983i | −0.405588 | − | 0.914056i | \(-0.632933\pi\) |
0.994390 | − | 0.105778i | \(-0.0337334\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1459.30 | 0.786462 | 0.393231 | − | 0.919440i | \(-0.371357\pi\) | ||||
0.393231 | + | 0.919440i | \(0.371357\pi\) | |||||||
\(152\) | 167.797 | − | 290.633i | 0.0895403 | − | 0.155088i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2488.73 | − | 4310.60i | −1.30226 | − | 2.25557i | ||||
\(155\) | −37.1750 | −0.0192643 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2008.20 | 1.02084 | 0.510419 | − | 0.859926i | \(-0.329490\pi\) | ||||
0.510419 | + | 0.859926i | \(0.329490\pi\) | |||||||
\(158\) | 330.784 | + | 572.935i | 0.166555 | + | 0.288482i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.85290 | + | 4.94136i | −0.00140963 | + | 0.00244156i | ||||
\(161\) | 411.063 | 0.201219 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −274.248 | + | 475.011i | −0.131784 | + | 0.228256i | −0.924364 | − | 0.381511i | \(-0.875404\pi\) |
0.792581 | + | 0.609767i | \(0.208737\pi\) | |||||||
\(164\) | 139.459 | 0.0664019 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1179.10 | − | 2042.27i | −0.551302 | − | 0.954883i | ||||
\(167\) | −1981.29 | − | 3431.69i | −0.918064 | − | 1.59013i | −0.802352 | − | 0.596851i | \(-0.796418\pi\) |
−0.115712 | − | 0.993283i | \(-0.536915\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2186.70 | − | 212.533i | −0.995310 | − | 0.0967380i | ||||
\(170\) | −85.3165 | −0.0384910 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −13.9991 | − | 24.2472i | −0.00620594 | − | 0.0107490i | ||||
\(173\) | −864.771 | + | 1497.83i | −0.380042 | + | 0.658252i | −0.991068 | − | 0.133358i | \(-0.957424\pi\) |
0.611026 | + | 0.791611i | \(0.290757\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1783.97 | − | 3089.93i | 0.770603 | − | 1.33472i | ||||
\(176\) | −1915.93 | + | 3318.49i | −0.820561 | + | 1.42125i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1742.05 | + | 3017.32i | −0.733551 | + | 1.27055i | ||||
\(179\) | 726.456 | + | 1258.26i | 0.303340 | + | 0.525400i | 0.976890 | − | 0.213741i | \(-0.0685649\pi\) |
−0.673550 | + | 0.739141i | \(0.735232\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −550.329 | −0.225998 | −0.112999 | − | 0.993595i | \(-0.536046\pi\) | ||||
−0.112999 | + | 0.993595i | \(0.536046\pi\) | |||||||
\(182\) | 178.716 | − | 3686.18i | 0.0727875 | − | 1.50131i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −166.642 | − | 288.632i | −0.0667663 | − | 0.115643i | ||||
\(185\) | 49.9747 | + | 86.5588i | 0.0198606 | + | 0.0343996i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6247.58 | 2.44314 | ||||||||
\(188\) | 20.5246 | − | 35.5496i | 0.00796228 | − | 0.0137911i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −12.5089 | −0.00477625 | ||||||||
\(191\) | 934.340 | − | 1618.32i | 0.353960 | − | 0.613078i | −0.632979 | − | 0.774169i | \(-0.718168\pi\) |
0.986939 | + | 0.161091i | \(0.0515014\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2078.26 | − | 3599.66i | −0.775112 | − | 1.34253i | −0.934732 | − | 0.355354i | \(-0.884360\pi\) |
0.159620 | − | 0.987179i | \(-0.448973\pi\) | |||||||
\(194\) | −1825.45 | −0.675567 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −190.595 | −0.0694587 | ||||||||
\(197\) | −761.092 | − | 1318.25i | −0.275257 | − | 0.476758i | 0.694943 | − | 0.719065i | \(-0.255429\pi\) |
−0.970200 | + | 0.242306i | \(0.922096\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −404.065 | + | 699.861i | −0.143937 | + | 0.249306i | −0.928976 | − | 0.370141i | \(-0.879309\pi\) |
0.785039 | + | 0.619446i | \(0.212643\pi\) | |||||||
\(200\) | −2892.83 | −1.02277 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1093.65 | − | 1894.26i | 0.380935 | − | 0.659800i | ||||
\(203\) | 5607.01 | 1.93860 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −54.2018 | − | 93.8803i | −0.0184664 | − | 0.0319848i | ||||
\(206\) | 1351.67 | + | 2341.15i | 0.457160 | + | 0.791825i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2526.38 | + | 1299.74i | −0.842179 | + | 0.433273i | ||||
\(209\) | 916.001 | 0.303163 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2630.02 | + | 4555.32i | 0.858094 | + | 1.48626i | 0.873745 | + | 0.486384i | \(0.161685\pi\) |
−0.0156511 | + | 0.999878i | \(0.504982\pi\) | |||||||
\(212\) | 119.838 | − | 207.566i | 0.0388232 | − | 0.0672437i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1110.70 | − | 1923.79i | 0.354795 | − | 0.614523i | ||||
\(215\) | −10.8817 | + | 18.8477i | −0.00345176 | + | 0.00597862i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1695.26 | + | 2936.27i | −0.530330 | + | 0.918558i | ||||
\(218\) | 1164.78 | + | 2017.46i | 0.361876 | + | 0.626787i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −7.97824 | −0.00244497 | ||||||||
\(221\) | 3894.77 | + | 2507.67i | 1.18548 | + | 0.763276i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2345.36 | + | 4062.28i | 0.704290 | + | 1.21987i | 0.966947 | + | 0.254977i | \(0.0820678\pi\) |
−0.262657 | + | 0.964889i | \(0.584599\pi\) | |||||||
\(224\) | 260.196 | + | 450.672i | 0.0776119 | + | 0.134428i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 155.392 | 0.0457368 | ||||||||
\(227\) | −1780.31 | + | 3083.58i | −0.520542 | + | 0.901606i | 0.479172 | + | 0.877721i | \(0.340937\pi\) |
−0.999715 | + | 0.0238849i | \(0.992396\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3144.82 | −0.907490 | −0.453745 | − | 0.891131i | \(-0.649912\pi\) | ||||
−0.453745 | + | 0.891131i | \(0.649912\pi\) | |||||||
\(230\) | −6.21137 | + | 10.7584i | −0.00178072 | + | 0.00308430i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2273.04 | − | 3937.02i | −0.643242 | − | 1.11413i | ||||
\(233\) | −852.543 | −0.239708 | −0.119854 | − | 0.992792i | \(-0.538243\pi\) | ||||
−0.119854 | + | 0.992792i | \(0.538243\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −31.9081 | −0.00885727 | ||||||||
\(236\) | 41.1949 | + | 71.3517i | 0.0113625 | + | 0.0196805i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3890.61 | + | 6738.73i | −1.05962 | + | 1.83532i | ||||
\(239\) | 2189.33 | 0.592534 | 0.296267 | − | 0.955105i | \(-0.404258\pi\) | ||||
0.296267 | + | 0.955105i | \(0.404258\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3164.99 | + | 5481.92i | −0.845954 | + | 1.46523i | 0.0388369 | + | 0.999246i | \(0.487635\pi\) |
−0.884791 | + | 0.465989i | \(0.845699\pi\) | |||||||
\(242\) | −7346.65 | −1.95149 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −43.5128 | − | 75.3664i | −0.0114165 | − | 0.0197739i | ||||
\(245\) | 74.0762 | + | 128.304i | 0.0193165 | + | 0.0334572i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 571.039 | + | 367.667i | 0.147103 | + | 0.0947129i | ||||
\(248\) | 2748.97 | 0.703871 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 107.869 | + | 186.835i | 0.0272890 | + | 0.0472659i | ||||
\(251\) | 1801.49 | − | 3120.27i | 0.453023 | − | 0.784659i | −0.545549 | − | 0.838079i | \(-0.683679\pi\) |
0.998572 | + | 0.0534200i | \(0.0170122\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 454.848 | − | 787.819i | 0.113028 | − | 0.195770i | ||||
\(254\) | 2296.87 | − | 3978.29i | 0.567395 | − | 0.982757i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 308.657 | − | 534.610i | 0.0753558 | − | 0.130520i | ||||
\(257\) | −1536.32 | − | 2660.98i | −0.372891 | − | 0.645865i | 0.617118 | − | 0.786870i | \(-0.288300\pi\) |
−0.990009 | + | 0.141005i | \(0.954967\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9115.80 | 2.18698 | ||||||||
\(260\) | −4.97367 | − | 3.20233i | −0.00118636 | − | 0.000763846i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 830.507 | + | 1438.48i | 0.195836 | + | 0.339197i | ||||
\(263\) | 1771.60 | + | 3068.50i | 0.415367 | + | 0.719437i | 0.995467 | − | 0.0951084i | \(-0.0303198\pi\) |
−0.580100 | + | 0.814545i | \(0.696986\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −186.304 | −0.0431871 | ||||||||
\(266\) | −570.429 | + | 988.012i | −0.131486 | + | 0.227740i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −27.6435 | −0.00630072 | ||||||||
\(269\) | −2949.98 | + | 5109.52i | −0.668638 | + | 1.15811i | 0.309647 | + | 0.950852i | \(0.399789\pi\) |
−0.978285 | + | 0.207263i | \(0.933544\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1054.76 | + | 1826.90i | 0.236429 | + | 0.409507i | 0.959687 | − | 0.281071i | \(-0.0906896\pi\) |
−0.723258 | + | 0.690578i | \(0.757356\pi\) | |||||||
\(272\) | 5990.32 | 1.33535 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1162.19 | 0.256244 | ||||||||
\(275\) | −3947.98 | − | 6838.10i | −0.865717 | − | 1.49947i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3632.50 | + | 6291.67i | −0.787927 | + | 1.36473i | 0.139308 | + | 0.990249i | \(0.455512\pi\) |
−0.927235 | + | 0.374480i | \(0.877821\pi\) | |||||||
\(278\) | −80.4012 | −0.0173458 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 103.611 | − | 179.460i | 0.0221141 | − | 0.0383028i | ||||
\(281\) | −4771.36 | −1.01294 | −0.506469 | − | 0.862258i | \(-0.669049\pi\) | ||||
−0.506469 | + | 0.862258i | \(0.669049\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1018.13 | − | 1763.45i | −0.213857 | − | 0.370411i | 0.739061 | − | 0.673638i | \(-0.235269\pi\) |
−0.952918 | + | 0.303227i | \(0.901936\pi\) | |||||||
\(284\) | −190.638 | − | 330.194i | −0.0398319 | − | 0.0689909i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6866.96 | − | 4421.33i | −1.41976 | − | 0.914122i | ||||
\(287\) | −9886.86 | −2.03346 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2426.89 | − | 4203.50i | −0.493973 | − | 0.855587i | ||||
\(290\) | −84.7247 | + | 146.747i | −0.0171559 | + | 0.0297148i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −157.119 | + | 272.139i | −0.0314888 | + | 0.0545402i | ||||
\(293\) | 1859.51 | − | 3220.77i | 0.370764 | − | 0.642182i | −0.618920 | − | 0.785454i | \(-0.712429\pi\) |
0.989683 | + | 0.143273i | \(0.0457626\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 32.0215 | − | 55.4628i | 0.00631987 | − | 0.0109463i | ||||
\(296\) | −3695.47 | − | 6400.75i | −0.725659 | − | 1.25688i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5903.39 | 1.14756 | ||||||||
\(299\) | 599.771 | − | 308.562i | 0.116005 | − | 0.0596810i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 992.458 | + | 1718.99i | 0.190048 | + | 0.329172i | ||||
\(302\) | 2011.11 | + | 3483.35i | 0.383200 | + | 0.663722i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 878.282 | 0.165700 | ||||||||
\(305\) | −33.8232 | + | 58.5835i | −0.00634987 | + | 0.0109983i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7282.24 | −1.35381 | −0.676905 | − | 0.736070i | \(-0.736679\pi\) | ||||
−0.676905 | + | 0.736070i | \(0.736679\pi\) | |||||||
\(308\) | −363.824 | + | 630.162i | −0.0673078 | + | 0.116581i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −51.2323 | − | 88.7370i | −0.00938645 | − | 0.0162578i | ||||
\(311\) | 4569.28 | 0.833120 | 0.416560 | − | 0.909108i | \(-0.363236\pi\) | ||||
0.416560 | + | 0.909108i | \(0.363236\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.0294 | 0.00379761 | 0.00189880 | − | 0.999998i | \(-0.499396\pi\) | ||||
0.00189880 | + | 0.999998i | \(0.499396\pi\) | |||||||
\(314\) | 2767.57 | + | 4793.58i | 0.497399 | + | 0.861520i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 48.3569 | − | 83.7566i | 0.00860851 | − | 0.0149104i | ||||
\(317\) | 5159.17 | 0.914095 | 0.457047 | − | 0.889442i | \(-0.348907\pi\) | ||||
0.457047 | + | 0.889442i | \(0.348907\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6204.24 | − | 10746.1i | 1.08894 | − | 1.88609i | ||||
\(320\) | −167.606 | −0.0292796 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 566.502 | + | 981.211i | 0.0980433 | + | 0.169816i | ||||
\(323\) | −715.988 | − | 1240.13i | −0.123339 | − | 0.213630i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 283.505 | − | 5847.55i | 0.0483878 | − | 0.998043i | ||||
\(326\) | −1511.80 | −0.256844 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4008.05 | + | 6942.15i | 0.674719 | + | 1.16865i | ||||
\(329\) | −1455.08 | + | 2520.27i | −0.243833 | + | 0.422331i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3788.76 | − | 6562.33i | 0.629152 | − | 1.08972i | −0.358570 | − | 0.933503i | \(-0.616736\pi\) |
0.987722 | − | 0.156220i | \(-0.0499309\pi\) | |||||||
\(332\) | −172.372 | + | 298.556i | −0.0284943 | + | 0.0493536i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5460.98 | − | 9458.70i | 0.894645 | − | 1.54957i | ||||
\(335\) | 10.7438 | + | 18.6089i | 0.00175224 | + | 0.00303496i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2109.79 | −0.341032 | −0.170516 | − | 0.985355i | \(-0.554543\pi\) | ||||
−0.170516 | + | 0.985355i | \(0.554543\pi\) | |||||||
\(338\) | −2506.25 | − | 5512.56i | −0.403320 | − | 0.887111i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.23616 | + | 10.8013i | 0.000994715 | + | 0.00172290i | ||||
\(341\) | 3751.65 | + | 6498.05i | 0.595787 | + | 1.03193i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3713.98 | 0.584653 | ||||||||
\(344\) | 804.669 | − | 1393.73i | 0.126119 | − | 0.218444i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4767.09 | −0.740695 | ||||||||
\(347\) | −4053.95 | + | 7021.65i | −0.627169 | + | 1.08629i | 0.360948 | + | 0.932586i | \(0.382453\pi\) |
−0.988117 | + | 0.153703i | \(0.950880\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4343.19 | − | 7522.62i | −0.666148 | − | 1.15380i | −0.978973 | − | 0.203991i | \(-0.934609\pi\) |
0.312825 | − | 0.949811i | \(-0.398725\pi\) | |||||||
\(350\) | 9834.24 | 1.50189 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1151.64 | 0.174383 | ||||||||
\(353\) | −4525.12 | − | 7837.73i | −0.682288 | − | 1.18176i | −0.974281 | − | 0.225337i | \(-0.927652\pi\) |
0.291993 | − | 0.956421i | \(-0.405682\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −148.186 | + | 256.665i | −0.0221546 | + | 0.0383729i | ||||
\(356\) | 509.336 | 0.0758279 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2002.31 | + | 3468.11i | −0.295602 | + | 0.511998i | ||||
\(359\) | 7043.80 | 1.03554 | 0.517768 | − | 0.855521i | \(-0.326763\pi\) | ||||
0.517768 | + | 0.855521i | \(0.326763\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3324.52 | + | 5758.24i | 0.484695 | + | 0.839517i | ||||
\(362\) | −758.429 | − | 1313.64i | −0.110116 | − | 0.190727i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −479.746 | + | 246.813i | −0.0690811 | + | 0.0355399i | ||||
\(365\) | 244.263 | 0.0350282 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6912.55 | − | 11972.9i | −0.983194 | − | 1.70294i | −0.649703 | − | 0.760188i | \(-0.725107\pi\) |
−0.333491 | − | 0.942753i | \(-0.608227\pi\) | |||||||
\(368\) | 436.118 | − | 755.378i | 0.0617778 | − | 0.107002i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −137.744 | + | 238.580i | −0.0193540 | + | 0.0335221i | ||||
\(371\) | −8495.85 | + | 14715.2i | −1.18890 | + | 2.05924i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3184.09 | + | 5515.01i | −0.442000 | + | 0.765567i | −0.997838 | − | 0.0657238i | \(-0.979064\pi\) |
0.555837 | + | 0.831291i | \(0.312398\pi\) | |||||||
\(374\) | 8610.03 | + | 14913.0i | 1.19041 | + | 2.06185i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2359.51 | 0.323623 | ||||||||
\(377\) | 8181.03 | − | 4208.87i | 1.11762 | − | 0.574981i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1225.83 | − | 2123.20i | −0.166139 | − | 0.287761i | 0.770920 | − | 0.636932i | \(-0.219797\pi\) |
−0.937059 | + | 0.349171i | \(0.886463\pi\) | |||||||
\(380\) | 0.914327 | + | 1.58366i | 0.000123432 | + | 0.000213790i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5150.60 | 0.689863 | ||||||||
\(383\) | −5415.47 | + | 9379.87i | −0.722500 | + | 1.25141i | 0.237494 | + | 0.971389i | \(0.423674\pi\) |
−0.959995 | + | 0.280018i | \(0.909659\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 565.613 | 0.0748735 | ||||||||
\(386\) | 5728.27 | − | 9921.65i | 0.755340 | − | 1.30829i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 133.430 | + | 231.108i | 0.0174585 | + | 0.0302390i | ||||
\(389\) | −4978.07 | −0.648838 | −0.324419 | − | 0.945914i | \(-0.605169\pi\) | ||||
−0.324419 | + | 0.945914i | \(0.605169\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1422.12 | −0.183938 | ||||||||
\(392\) | −5477.70 | − | 9487.65i | −0.705779 | − | 1.22245i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2097.78 | − | 3633.46i | 0.268235 | − | 0.464597i | ||||
\(395\) | −75.1772 | −0.00957614 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4725.34 | + | 8184.52i | −0.597375 | + | 1.03468i | 0.395832 | + | 0.918323i | \(0.370456\pi\) |
−0.993207 | + | 0.116361i | \(0.962877\pi\) | |||||||
\(398\) | −2227.43 | −0.280530 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3785.41 | − | 6556.52i | −0.473176 | − | 0.819566i | ||||
\(401\) | −4388.39 | − | 7600.91i | −0.546498 | − | 0.946562i | −0.998511 | − | 0.0545506i | \(-0.982627\pi\) |
0.452013 | − | 0.892011i | \(-0.350706\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −269.407 | + | 5556.76i | −0.0333005 | + | 0.686854i | ||||
\(404\) | −319.759 | −0.0393777 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7727.24 | + | 13384.0i | 0.944572 | + | 1.63605i | ||||
\(407\) | 10086.8 | − | 17470.8i | 1.22846 | − | 2.12775i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2260.10 | − | 3914.60i | 0.273238 | − | 0.473263i | −0.696451 | − | 0.717605i | \(-0.745239\pi\) |
0.969689 | + | 0.244342i | \(0.0785719\pi\) | |||||||
\(410\) | 149.395 | − | 258.760i | 0.0179954 | − | 0.0311689i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 197.598 | − | 342.250i | 0.0236286 | − | 0.0409259i | ||||
\(413\) | −2920.49 | − | 5058.43i | −0.347961 | − | 0.602686i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 267.974 | 0.0316972 | ||||||||
\(416\) | 717.939 | + | 462.249i | 0.0846150 | + | 0.0544798i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1262.38 | + | 2186.50i | 0.147715 | + | 0.255850i | ||||
\(419\) | −6003.22 | − | 10397.9i | −0.699944 | − | 1.21234i | −0.968485 | − | 0.249070i | \(-0.919875\pi\) |
0.268541 | − | 0.963268i | \(-0.413458\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9731.52 | −1.12657 | −0.563284 | − | 0.826263i | \(-0.690462\pi\) | ||||
−0.563284 | + | 0.826263i | \(0.690462\pi\) | |||||||
\(422\) | −7249.05 | + | 12555.7i | −0.836205 | + | 1.44835i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 13776.6 | 1.57795 | ||||||||
\(425\) | −6171.84 | + | 10689.9i | −0.704420 | + | 1.22009i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3084.82 | + | 5343.06i | 0.349613 | + | 0.605547i | ||||
\(428\) | −324.745 | −0.0366755 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −59.9861 | −0.00672741 | ||||||||
\(431\) | 2055.51 | + | 3560.25i | 0.229723 | + | 0.397892i | 0.957726 | − | 0.287682i | \(-0.0928846\pi\) |
−0.728003 | + | 0.685574i | \(0.759551\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1453.03 | + | 2516.72i | −0.161266 | + | 0.279321i | −0.935323 | − | 0.353795i | \(-0.884891\pi\) |
0.774057 | + | 0.633116i | \(0.218224\pi\) | |||||||
\(434\) | −9345.19 | −1.03360 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 170.278 | − | 294.930i | 0.0187037 | − | 0.0323958i | ||||
\(437\) | −208.507 | −0.0228243 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4437.36 | − | 7685.73i | −0.482423 | − | 0.835581i | 0.517374 | − | 0.855760i | \(-0.326910\pi\) |
−0.999796 | + | 0.0201788i | \(0.993576\pi\) | |||||||
\(440\) | −229.295 | − | 397.150i | −0.0248436 | − | 0.0430305i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −618.288 | + | 12752.7i | −0.0665361 | + | 1.37237i | ||||
\(443\) | 12640.5 | 1.35569 | 0.677843 | − | 0.735207i | \(-0.262915\pi\) | ||||
0.677843 | + | 0.735207i | \(0.262915\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −197.957 | − | 342.872i | −0.0210878 | − | 0.0365252i | ||||
\(446\) | −6464.45 | + | 11196.8i | −0.686324 | + | 1.18875i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7643.18 | + | 13238.4i | −0.806041 | + | 1.39610i | ||||
\(449\) | 887.147 | − | 1536.58i | 0.0932451 | − | 0.161505i | −0.815630 | − | 0.578574i | \(-0.803609\pi\) |
0.908875 | + | 0.417069i | \(0.136943\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10940.0 | + | 18948.6i | −1.14222 | + | 1.97839i | ||||
\(452\) | −11.3583 | − | 19.6731i | −0.00118197 | − | 0.00204722i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9814.04 | −1.01453 | ||||||||
\(455\) | 352.606 | + | 227.027i | 0.0363306 | + | 0.0233916i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3084.41 | − | 5342.35i | −0.315717 | − | 0.546837i | 0.663873 | − | 0.747845i | \(-0.268912\pi\) |
−0.979590 | + | 0.201008i | \(0.935578\pi\) | |||||||
\(458\) | −4333.99 | − | 7506.69i | −0.442171 | − | 0.765862i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.81607 | 0.000184075 | ||||||||
\(461\) | 3727.69 | − | 6456.55i | 0.376607 | − | 0.652302i | −0.613959 | − | 0.789338i | \(-0.710424\pi\) |
0.990566 | + | 0.137036i | \(0.0437574\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5399.78 | 0.542006 | 0.271003 | − | 0.962578i | \(-0.412645\pi\) | ||||
0.271003 | + | 0.962578i | \(0.412645\pi\) | |||||||
\(464\) | 5948.76 | − | 10303.6i | 0.595182 | − | 1.03088i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1174.92 | − | 2035.03i | −0.116797 | − | 0.202298i | ||||
\(467\) | 3992.01 | 0.395564 | 0.197782 | − | 0.980246i | \(-0.436626\pi\) | ||||
0.197782 | + | 0.980246i | \(0.436626\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1959.77 | 0.192950 | ||||||||
\(470\) | −43.9738 | − | 76.1649i | −0.00431566 | − | 0.00747495i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2367.89 | + | 4101.30i | −0.230913 | + | 0.399952i | ||||
\(473\) | 4392.68 | 0.427009 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −904.897 | + | 1567.33i | −0.0874095 | + | 0.151398i | ||||
\(476\) | 1137.53 | 0.109535 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3017.19 | + | 5225.93i | 0.288710 | + | 0.500060i | ||||
\(479\) | −1575.81 | − | 2729.39i | −0.150315 | − | 0.260352i | 0.781029 | − | 0.624495i | \(-0.214695\pi\) |
−0.931343 | + | 0.364143i | \(0.881362\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13300.6 | − | 6842.72i | 1.26082 | − | 0.648651i | ||||
\(482\) | −17447.2 | −1.64875 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 536.999 | + | 930.110i | 0.0504319 | + | 0.0873507i | ||||
\(485\) | 103.718 | − | 179.644i | 0.00971046 | − | 0.0168190i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1954.59 | − | 3385.45i | 0.181870 | − | 0.315009i | −0.760647 | − | 0.649166i | \(-0.775118\pi\) |
0.942517 | + | 0.334157i | \(0.108452\pi\) | |||||||
\(488\) | 2501.12 | − | 4332.07i | 0.232009 | − | 0.401851i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −204.174 | + | 353.641i | −0.0188238 | + | 0.0326038i | ||||
\(491\) | −3322.57 | − | 5754.86i | −0.305388 | − | 0.528947i | 0.671960 | − | 0.740588i | \(-0.265453\pi\) |
−0.977348 | + | 0.211641i | \(0.932119\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19398.1 | −1.77210 | ||||||||
\(494\) | −90.6515 | + | 1869.77i | −0.00825628 | + | 0.170293i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3597.17 | + | 6230.48i | 0.325640 | + | 0.564026i | ||||
\(497\) | 13515.1 | + | 23408.9i | 1.21979 | + | 2.11274i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6111.83 | 0.548303 | 0.274151 | − | 0.961687i | \(-0.411603\pi\) | ||||
0.274151 | + | 0.961687i | \(0.411603\pi\) | |||||||
\(500\) | 15.7692 | − | 27.3131i | 0.00141044 | − | 0.00244296i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9930.79 | 0.882934 | ||||||||
\(503\) | −5477.03 | + | 9486.50i | −0.485505 | + | 0.840919i | −0.999861 | − | 0.0166575i | \(-0.994698\pi\) |
0.514356 | + | 0.857576i | \(0.328031\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 124.277 | + | 215.254i | 0.0109510 | + | 0.0189677i | ||||
\(506\) | 2507.37 | 0.220289 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −671.553 | −0.0586523 | ||||||||
\(509\) | 5560.57 | + | 9631.18i | 0.484220 | + | 0.838693i | 0.999836 | − | 0.0181268i | \(-0.00577025\pi\) |
−0.515616 | + | 0.856820i | \(0.672437\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11138.9 | − | 19293.1i | 0.964296 | − | 1.67021i | ||||
\(512\) | 12335.2 | 1.06473 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4234.52 | − | 7334.40i | 0.363379 | − | 0.629390i | ||||
\(515\) | −307.193 | −0.0262845 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3220.13 | + | 5577.42i | 0.273928 | + | 0.474458i | ||||
\(518\) | 12562.8 | + | 21759.5i | 1.06560 | + | 1.84567i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 16.4657 | − | 339.620i | 0.00138859 | − | 0.0286410i | ||||
\(521\) | 2403.33 | 0.202096 | 0.101048 | − | 0.994882i | \(-0.467780\pi\) | ||||
0.101048 | + | 0.994882i | \(0.467780\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2125.86 | − | 3682.10i | −0.177739 | − | 0.307853i | 0.763367 | − | 0.645965i | \(-0.223545\pi\) |
−0.941106 | + | 0.338113i | \(0.890212\pi\) | |||||||
\(524\) | 121.411 | − | 210.290i | 0.0101219 | − | 0.0175316i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4883.02 | + | 8457.64i | −0.404772 | + | 0.701085i | ||||
\(527\) | 5864.92 | − | 10158.3i | 0.484782 | − | 0.839667i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5979.96 | − | 10357.6i | 0.491490 | − | 0.851286i | ||||
\(530\) | −256.753 | − | 444.709i | −0.0210427 | − | 0.0364470i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 166.781 | 0.0135918 | ||||||||
\(533\) | −14425.6 | + | 7421.51i | −1.17231 | + | 0.603117i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 126.215 | + | 218.610i | 0.0101995 | + | 0.0176661i | ||||
\(536\) | −794.473 | − | 1376.07i | −0.0640224 | − | 0.110890i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −16261.9 | −1.30316 | ||||||||
\(539\) | 14951.3 | − | 25896.5i | 1.19480 | − | 2.06946i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8924.44 | −0.709227 | −0.354613 | − | 0.935013i | \(-0.615388\pi\) | ||||
−0.354613 | + | 0.935013i | \(0.615388\pi\) | |||||||
\(542\) | −2907.22 | + | 5035.45i | −0.230398 | + | 0.399061i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −900.176 | − | 1559.15i | −0.0709462 | − | 0.122882i | ||||
\(545\) | −264.719 | −0.0208061 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14696.0 | −1.14873 | −0.574367 | − | 0.818598i | \(-0.694752\pi\) | ||||
−0.574367 | + | 0.818598i | \(0.694752\pi\) | |||||||
\(548\) | −84.9499 | − | 147.138i | −0.00662204 | − | 0.0114697i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 10881.7 | − | 18847.7i | 0.843633 | − | 1.46122i | ||||
\(551\) | −2844.09 | −0.219895 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3428.23 | + | 5937.87i | −0.263623 | + | 0.456608i | ||||
\(554\) | −20024.3 | −1.53566 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.87688 | + | 10.1791i | 0.000448265 | + | 0.000776417i | ||||
\(557\) | −1232.01 | − | 2133.91i | −0.0937202 | − | 0.162328i | 0.815354 | − | 0.578963i | \(-0.196543\pi\) |
−0.909074 | + | 0.416635i | \(0.863209\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2738.41 | + | 1763.14i | 0.207196 | + | 0.133404i | ||||
\(560\) | 542.322 | 0.0409237 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6575.59 | − | 11389.3i | −0.493549 | − | 0.854852i | ||||
\(563\) | −9014.61 | + | 15613.8i | −0.674815 | + | 1.16881i | 0.301708 | + | 0.953400i | \(0.402443\pi\) |
−0.976523 | + | 0.215413i | \(0.930890\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.82897 | + | 15.2922i | −0.000657411 | + | 0.00113867i | ||||
\(566\) | 2806.25 | − | 4860.57i | 0.208402 | − | 0.360963i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10957.9 | − | 18979.6i | 0.809475 | − | 1.40205i | ||||
\(569\) | −5962.32 | − | 10327.0i | −0.439286 | − | 0.760865i | 0.558349 | − | 0.829606i | \(-0.311435\pi\) |
−0.997635 | + | 0.0687410i | \(0.978102\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5834.77 | 0.427632 | 0.213816 | − | 0.976874i | \(-0.431411\pi\) | ||||
0.213816 | + | 0.976874i | \(0.431411\pi\) | |||||||
\(572\) | −57.8182 | + | 1192.55i | −0.00422640 | + | 0.0871734i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −13625.5 | − | 23600.0i | −0.990794 | − | 1.71611i | ||||
\(575\) | 898.667 | + | 1556.54i | 0.0651774 | + | 0.112891i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15927.5 | 1.14917 | 0.574586 | − | 0.818444i | \(-0.305163\pi\) | ||||
0.574586 | + | 0.818444i | \(0.305163\pi\) | |||||||
\(578\) | 6689.19 | − | 11586.0i | 0.481373 | − | 0.833762i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 24.7716 | 0.00177342 | ||||||||
\(581\) | 12220.2 | − | 21166.0i | 0.872596 | − | 1.51138i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18801.6 | + | 32565.3i | 1.33564 | + | 2.31340i | ||||
\(584\) | −18062.5 | −1.27985 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10250.7 | 0.722612 | ||||||||
\(587\) | 6755.55 | + | 11701.0i | 0.475011 | + | 0.822743i | 0.999590 | − | 0.0286184i | \(-0.00911075\pi\) |
−0.524579 | + | 0.851362i | \(0.675777\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 859.898 | − | 1489.39i | 0.0601553 | − | 0.104192i | ||||
\(590\) | 176.520 | 0.0123173 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9671.42 | − | 16751.4i | 0.671441 | − | 1.16297i | ||||
\(593\) | 15830.4 | 1.09625 | 0.548126 | − | 0.836396i | \(-0.315341\pi\) | ||||
0.548126 | + | 0.836396i | \(0.315341\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −442.109 | − | 765.755i | −0.0304617 | − | 0.0527611i | ||||
\(596\) | −431.505 | − | 747.388i | −0.0296562 | − | 0.0513661i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1563.11 | + | 1006.42i | 0.106890 | + | 0.0688217i | ||||
\(599\) | −5914.12 | −0.403413 | −0.201706 | − | 0.979446i | \(-0.564649\pi\) | ||||
−0.201706 | + | 0.979446i | \(0.564649\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4946.10 | − | 8566.89i | −0.335700 | − | 0.581449i | 0.647919 | − | 0.761709i | \(-0.275639\pi\) |
−0.983619 | + | 0.180260i | \(0.942306\pi\) | |||||||
\(602\) | −2735.49 | + | 4738.01i | −0.185200 | + | 0.320775i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 294.002 | − | 509.226i | 0.0198059 | − | 0.0343048i | ||||
\(605\) | 417.418 | − | 722.989i | 0.0280503 | − | 0.0485846i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8391.16 | − | 14533.9i | 0.561098 | − | 0.971851i | −0.436302 | − | 0.899800i | \(-0.643712\pi\) |
0.997401 | − | 0.0720510i | \(-0.0229544\pi\) | |||||||
\(608\) | −131.981 | − | 228.598i | −0.00880352 | − | 0.0152481i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −186.452 | −0.0123758 | ||||||||
\(611\) | −231.238 | + | 4769.49i | −0.0153108 | + | 0.315799i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6122.83 | − | 10605.0i | −0.403424 | − | 0.698750i | 0.590713 | − | 0.806882i | \(-0.298847\pi\) |
−0.994137 | + | 0.108132i | \(0.965513\pi\) | |||||||
\(614\) | −10035.9 | − | 17382.8i | −0.659638 | − | 1.14253i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −41825.3 | −2.73569 | ||||||||
\(617\) | −5021.86 | + | 8698.12i | −0.327670 | + | 0.567542i | −0.982049 | − | 0.188625i | \(-0.939597\pi\) |
0.654379 | + | 0.756167i | \(0.272930\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9942.69 | −0.645607 | −0.322803 | − | 0.946466i | \(-0.604625\pi\) | ||||
−0.322803 | + | 0.946466i | \(0.604625\pi\) | |||||||
\(620\) | −7.48959 | + | 12.9724i | −0.000485144 | + | 0.000840294i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6297.10 | + | 10906.9i | 0.405934 | + | 0.703098i | ||||
\(623\) | −36109.1 | −2.32212 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15588.2 | 0.997646 | ||||||||
\(626\) | 28.9814 | + | 50.1973i | 0.00185037 | + | 0.00320493i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 404.588 | − | 700.767i | 0.0257083 | − | 0.0445281i | ||||
\(629\) | −31537.1 | −1.99915 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5134.31 | + | 8892.89i | −0.323920 | + | 0.561047i | −0.981293 | − | 0.192519i | \(-0.938334\pi\) |
0.657373 | + | 0.753566i | \(0.271668\pi\) | |||||||
\(632\) | 5559.11 | 0.349889 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7110.05 | + | 12315.0i | 0.445389 | + | 0.771436i | ||||
\(635\) | 261.004 | + | 452.073i | 0.0163113 | + | 0.0282519i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19715.1 | − | 10142.8i | 1.22628 | − | 0.630881i | ||||
\(638\) | 34201.2 | 2.12232 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −208.161 | − | 360.546i | −0.0128567 | − | 0.0222685i | ||||
\(641\) | 6828.72 | − | 11827.7i | 0.420777 | − | 0.728808i | −0.575238 | − | 0.817986i | \(-0.695091\pi\) |
0.996016 | + | 0.0891780i | \(0.0284240\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12335.8 | + | 21366.2i | −0.756572 | + | 1.31042i | 0.188017 | + | 0.982166i | \(0.439794\pi\) |
−0.944589 | + | 0.328256i | \(0.893539\pi\) | |||||||
\(644\) | 82.8163 | − | 143.442i | 0.00506742 | − | 0.00877703i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1973.46 | − | 3418.14i | 0.120193 | − | 0.208181i | ||||
\(647\) | 8256.13 | + | 14300.0i | 0.501672 | + | 0.868922i | 0.999998 | + | 0.00193194i | \(0.000614955\pi\) |
−0.498326 | + | 0.866990i | \(0.666052\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12926.3 | −0.781818 | ||||||||
\(650\) | 14348.9 | − | 7382.01i | 0.865859 | − | 0.445456i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 110.504 | + | 191.399i | 0.00663756 | + | 0.0114966i | ||||
\(653\) | −15297.4 | − | 26495.8i | −0.916742 | − | 1.58784i | −0.804330 | − | 0.594182i | \(-0.797476\pi\) |
−0.112412 | − | 0.993662i | \(-0.535858\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −188.749 | −0.0112596 | ||||||||
\(656\) | −10489.5 | + | 18168.3i | −0.624306 | + | 1.08133i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −8021.19 | −0.475226 | ||||||||
\(659\) | 1153.89 | − | 1998.60i | 0.0682084 | − | 0.118140i | −0.829904 | − | 0.557906i | \(-0.811605\pi\) |
0.898113 | + | 0.439765i | \(0.144938\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13811.2 | + | 23921.7i | 0.812700 | + | 1.40764i | 0.910968 | + | 0.412477i | \(0.135336\pi\) |
−0.0982684 | + | 0.995160i | \(0.531330\pi\) | |||||||
\(662\) | 20885.8 | 1.22621 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −19815.9 | −1.15814 | ||||||||
\(665\) | −64.8206 | − | 112.273i | −0.00377991 | − | 0.00654699i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1412.25 | + | 2446.09i | −0.0819830 | + | 0.141999i | ||||
\(668\) | −1596.67 | −0.0924805 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −29.6130 | + | 51.2913i | −0.00170754 | + | 0.00295754i | ||||
\(671\) | 13653.6 | 0.785530 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5652.94 | + | 9791.17i | 0.323781 | + | 0.560805i | 0.981265 | − | 0.192663i | \(-0.0617125\pi\) |
−0.657484 | + | 0.753469i | \(0.728379\pi\) | |||||||
\(674\) | −2907.58 | − | 5036.08i | −0.166166 | − | 0.287808i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −514.714 | + | 720.236i | −0.0292851 | + | 0.0409784i | ||||
\(677\) | 15455.8 | 0.877419 | 0.438710 | − | 0.898629i | \(-0.355436\pi\) | ||||
0.438710 | + | 0.898629i | \(0.355436\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9459.47 | − | 16384.3i | −0.534641 | − | 0.926025i | ||||
\(680\) | −358.455 | + | 620.862i | −0.0202149 | + | 0.0350132i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −10340.6 | + | 17910.4i | −0.580589 | + | 1.00561i | ||||
\(683\) | −8420.96 | + | 14585.5i | −0.471770 | + | 0.817130i | −0.999478 | − | 0.0322958i | \(-0.989718\pi\) |
0.527708 | + | 0.849426i | \(0.323051\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −66.0329 | + | 114.372i | −0.00368319 | + | 0.00637948i | ||||
\(686\) | 5118.37 | + | 8865.28i | 0.284869 | + | 0.493408i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4211.80 | 0.233391 | ||||||||
\(689\) | −1350.14 | + | 27847.9i | −0.0746537 | + | 1.53980i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12520.8 | + | 21686.6i | 0.689310 | + | 1.19392i | 0.972061 | + | 0.234727i | \(0.0754195\pi\) |
−0.282751 | + | 0.959193i | \(0.591247\pi\) | |||||||
\(692\) | 348.448 | + | 603.529i | 0.0191416 | + | 0.0331543i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −22347.6 | −1.22234 | ||||||||
\(695\) | 4.56819 | − | 7.91234i | 0.000249326 | − | 0.000431845i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34204.7 | 1.85881 | ||||||||
\(698\) | 11971.0 | − | 20734.4i | 0.649155 | − | 1.12437i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −718.828 | − | 1245.05i | −0.0388131 | − | 0.0672262i | ||||
\(701\) | −28309.0 | −1.52527 | −0.762635 | − | 0.646829i | \(-0.776095\pi\) | ||||
−0.762635 | + | 0.646829i | \(0.776095\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4623.88 | −0.248069 | ||||||||
\(704\) | 16914.6 | + | 29296.9i | 0.905528 | + | 1.56842i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12472.5 | − | 21603.0i | 0.664884 | − | 1.15161i | ||||
\(707\) | 22669.1 | 1.20588 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2520.59 | − | 4365.78i | 0.133516 | − | 0.231256i | −0.791514 | − | 0.611151i | \(-0.790707\pi\) |
0.925029 | + | 0.379895i | \(0.124040\pi\) | |||||||
\(710\) | −816.882 | −0.0431789 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 14638.3 | + | 25354.3i | 0.770498 | + | 1.33454i | ||||
\(713\) | −853.978 | − | 1479.13i | −0.0448552 | − | 0.0776914i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 825.269 | − | 424.574i | 0.0431655 | − | 0.0222072i | ||||
\(716\) | 585.431 | 0.0305567 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9707.33 | + | 16813.6i | 0.504560 | + | 0.873924i | ||||
\(719\) | −5919.62 | + | 10253.1i | −0.307044 | + | 0.531815i | −0.977714 | − | 0.209940i | \(-0.932673\pi\) |
0.670671 | + | 0.741755i | \(0.266006\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14008.6 | + | 24263.6i | −0.723590 | + | 1.25329i | ||||
\(722\) | −9163.31 | + | 15871.3i | −0.472331 | + | 0.818101i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −110.874 | + | 192.039i | −0.00569143 | + | 0.00985784i | ||||
\(725\) | 12258.1 | + | 21231.6i | 0.627935 | + | 1.08762i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31004.9 | −1.58172 | −0.790858 | − | 0.611999i | \(-0.790365\pi\) | ||||
−0.790858 | + | 0.611999i | \(0.790365\pi\) | |||||||
\(728\) | −26074.1 | − | 16787.9i | −1.32743 | − | 0.854673i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 336.628 | + | 583.057i | 0.0170674 | + | 0.0295615i | ||||
\(731\) | −3433.52 | − | 5947.02i | −0.173725 | − | 0.300901i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15666.0 | 0.789411 | 0.394706 | − | 0.918808i | \(-0.370847\pi\) | ||||
0.394706 | + | 0.918808i | \(0.370847\pi\) | |||||||
\(734\) | 19052.9 | − | 33000.6i | 0.958114 | − | 1.65950i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −262.145 | −0.0131288 | ||||||||
\(737\) | 2168.51 | − | 3755.97i | 0.108383 | − | 0.187724i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16669.7 | + | 28872.8i | 0.829777 | + | 1.43722i | 0.898213 | + | 0.439561i | \(0.144866\pi\) |
−0.0684357 | + | 0.997656i | \(0.521801\pi\) | |||||||
\(740\) | 40.2733 | 0.00200064 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −46833.8 | −2.31715 | ||||||||
\(743\) | −1013.07 | − | 1754.69i | −0.0500215 | − | 0.0866397i | 0.839931 | − | 0.542694i | \(-0.182596\pi\) |
−0.889952 | + | 0.456054i | \(0.849262\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −335.415 | + | 580.956i | −0.0164949 | + | 0.0285699i | ||||
\(746\) | −17552.5 | −0.861451 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1258.69 | − | 2180.11i | 0.0615271 | − | 0.106568i | ||||
\(749\) | 23022.6 | 1.12313 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17737.4 | − | 30722.0i | −0.861846 | − | 1.49276i | −0.870145 | − | 0.492795i | \(-0.835975\pi\) |
0.00829952 | − | 0.999966i | \(-0.497358\pi\) | |||||||
\(752\) | 3087.53 | + | 5347.76i | 0.149722 | + | 0.259325i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 21321.2 | + | 13727.8i | 1.02980 | + | 0.663044i | ||||
\(755\) | −457.065 | −0.0220322 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1199.29 | − | 2077.23i | −0.0575811 | − | 0.0997333i | 0.835798 | − | 0.549037i | \(-0.185005\pi\) |
−0.893379 | + | 0.449304i | \(0.851672\pi\) | |||||||
\(758\) | 3378.73 | − | 5852.13i | 0.161901 | − | 0.280421i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −52.5555 | + | 91.0289i | −0.00250841 | + | 0.00434469i | ||||
\(761\) | 2502.53 | − | 4334.52i | 0.119207 | − | 0.206473i | −0.800246 | − | 0.599671i | \(-0.795298\pi\) |
0.919454 | + | 0.393198i | \(0.128631\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12071.7 | + | 20908.9i | −0.572774 | + | 0.992074i | ||||
\(764\) | −376.480 | − | 652.082i | −0.0178280 | − | 0.0308789i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −29853.1 | −1.40814 | ||||||||
\(767\) | −8058.28 | − | 5188.37i | −0.379358 | − | 0.244252i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7054.78 | − | 12219.2i | −0.330822 | − | 0.573000i | 0.651851 | − | 0.758347i | \(-0.273993\pi\) |
−0.982673 | + | 0.185346i | \(0.940659\pi\) | |||||||
\(770\) | 779.493 | + | 1350.12i | 0.0364818 | + | 0.0631883i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1674.82 | −0.0780803 | ||||||||
\(773\) | 6366.85 | − | 11027.7i | 0.296248 | − | 0.513116i | −0.679027 | − | 0.734114i | \(-0.737598\pi\) |
0.975274 | + | 0.220997i | \(0.0709312\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14824.7 | −0.687121 | ||||||||
\(776\) | −7669.59 | + | 13284.1i | −0.354796 | + | 0.614526i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6860.46 | − | 11882.7i | −0.316143 | − | 0.547576i | ||||
\(779\) | 5014.98 | 0.230655 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 59818.8 | 2.74070 | ||||||||
\(782\) | −1959.88 | − | 3394.60i | −0.0896228 | − | 0.155231i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 14335.7 | − | 24830.1i | 0.653046 | − | 1.13111i | ||||
\(785\) | −628.986 | −0.0285980 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14214.7 | + | 24620.5i | −0.643834 | + | 1.11515i | 0.340735 | + | 0.940159i | \(0.389324\pi\) |
−0.984569 | + | 0.174994i | \(0.944009\pi\) | |||||||
\(788\) | −613.344 | −0.0277278 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −103.605 | − | 179.448i | −0.00466593 | − | 0.00808163i | ||||
\(791\) | 805.238 | + | 1394.71i | 0.0361959 | + | 0.0626932i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8511.70 | + | 5480.30i | 0.381159 | + | 0.245412i | ||||
\(794\) | −26048.7 | −1.16427 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 162.813 | + | 282.000i | 0.00724967 | + | 0.0125568i | ||||
\(797\) | −5963.36 | + | 10328.8i | −0.265035 | + | 0.459054i | −0.967573 | − | 0.252592i | \(-0.918717\pi\) |
0.702538 | + | 0.711646i | \(0.252050\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5034.00 | − | 8719.14i | 0.222891 | − | 0.386059i | ||||
\(800\) | −1137.68 | + | 1970.52i | −0.0502789 | + | 0.0870856i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12095.6 | − | 20950.2i | 0.532557 | − | 0.922416i | ||||
\(803\) | −24650.7 | − | 42696.2i | −1.08332 | − | 1.87636i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −128.749 | −0.00563702 | ||||||||
\(806\) | −13635.3 | + | 7014.91i | −0.595885 | + | 0.306563i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9189.87 | − | 15917.3i | −0.400122 | − | 0.693032i | ||||
\(809\) | −10002.8 | − | 17325.4i | −0.434710 | − | 0.752940i | 0.562562 | − | 0.826755i | \(-0.309816\pi\) |
−0.997272 | + | 0.0738150i | \(0.976483\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5933.84 | −0.256924 | −0.128462 | − | 0.991714i | \(-0.541004\pi\) | ||||
−0.128462 | + | 0.991714i | \(0.541004\pi\) | |||||||
\(812\) | 1129.64 | − | 1956.59i | 0.0488207 | − | 0.0845600i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 55603.8 | 2.39424 | ||||||||
\(815\) | 85.8968 | − | 148.778i | 0.00369182 | − | 0.00639442i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −503.412 | − | 871.935i | −0.0215571 | − | 0.0373380i | ||||
\(818\) | 12458.9 | 0.532537 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −43.6798 | −0.00186020 | ||||||||
\(821\) | 9228.51 | + | 15984.2i | 0.392299 | + | 0.679481i | 0.992752 | − | 0.120178i | \(-0.0383466\pi\) |
−0.600454 | + | 0.799660i | \(0.705013\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13260.1 | − | 22967.2i | 0.561627 | − | 0.972767i | −0.435727 | − | 0.900079i | \(-0.643509\pi\) |
0.997355 | − | 0.0726886i | \(-0.0231579\pi\) | |||||||
\(824\) | 22715.9 | 0.960372 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8049.68 | − | 13942.4i | 0.339085 | − | 0.587312i | ||||
\(827\) | −25664.8 | −1.07915 | −0.539573 | − | 0.841939i | \(-0.681414\pi\) | ||||
−0.539573 | + | 0.841939i | \(0.681414\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2181.34 | − | 3778.20i | −0.0913887 | − | 0.158290i | 0.816707 | − | 0.577053i | \(-0.195797\pi\) |
−0.908096 | + | 0.418763i | \(0.862464\pi\) | |||||||
\(830\) | 369.306 | + | 639.656i | 0.0154443 | + | 0.0267504i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1214.64 | + | 25053.0i | −0.0506130 | + | 1.04394i | ||||
\(833\) | −46746.6 | −1.94439 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 620.558 | + | 1074.84i | 0.0257189 | + | 0.0445465i | ||||
\(836\) | 184.545 | − | 319.642i | 0.00763473 | − | 0.0132237i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 16546.5 | − | 28659.4i | 0.682089 | − | 1.18141i | ||||
\(839\) | 17510.1 | − | 30328.4i | 0.720520 | − | 1.24798i | −0.240272 | − | 0.970706i | \(-0.577237\pi\) |
0.960792 | − | 0.277271i | \(-0.0894300\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7069.00 | + | 12243.9i | −0.289844 | + | 0.502024i | ||||
\(842\) | −13411.4 | − | 23229.2i | −0.548915 | − | 0.950749i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2119.46 | 0.0864394 | ||||||||
\(845\) | 684.893 | + | 66.5674i | 0.0278829 | + | 0.00271005i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −38070.2 | − | 65939.6i | −1.54440 | − | 2.67498i | ||||
\(848\) | 18027.4 | + | 31224.3i | 0.730026 | + | 1.26444i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −34022.6 | −1.37290 | ||||||||
\(851\) | −2296.02 | + | 3976.83i | −0.0924872 | + | 0.160193i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8318.36 | 0.333898 | 0.166949 | − | 0.985966i | \(-0.446608\pi\) | ||||
0.166949 | + | 0.985966i | \(0.446608\pi\) | |||||||
\(854\) | −8502.61 | + | 14726.9i | −0.340695 | + | 0.590100i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9333.17 | − | 16165.5i | −0.372665 | − | 0.645474i | ||||
\(857\) | 34832.3 | 1.38839 | 0.694193 | − | 0.719789i | \(-0.255761\pi\) | ||||
0.694193 | + | 0.719789i | \(0.255761\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12571.8 | −0.499353 | −0.249676 | − | 0.968329i | \(-0.580324\pi\) | ||||
−0.249676 | + | 0.968329i | \(0.580324\pi\) | |||||||
\(860\) | 4.38465 | + | 7.59443i | 0.000173855 | + | 0.000301126i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5665.57 | + | 9813.05i | −0.223863 | + | 0.387742i | ||||
\(863\) | 22474.2 | 0.886480 | 0.443240 | − | 0.896403i | \(-0.353829\pi\) | ||||
0.443240 | + | 0.896403i | \(0.353829\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 270.854 | − | 469.133i | 0.0106466 | − | 0.0184405i | ||||
\(866\) | −8009.90 | −0.314304 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 683.081 | + | 1183.13i | 0.0267112 | + | 0.0462651i | ||||
\(869\) | 7586.78 | + | 13140.7i | 0.296161 | + | 0.512966i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2859.44 | − | 1471.09i | 0.111238 | − | 0.0572283i | ||||
\(872\) | 19575.2 | 0.760205 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −287.351 | − | 497.707i | −0.0111210 | − | 0.0192622i | ||||
\(875\) | −1117.95 | + | 1936.35i | −0.0431927 | + | 0.0748120i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2692.60 | + | 4663.72i | −0.103675 | + | 0.179570i | −0.913196 | − | 0.407521i | \(-0.866393\pi\) |
0.809521 | + | 0.587090i | \(0.199727\pi\) | |||||||
\(878\) | 12230.6 | − | 21184.0i | 0.470117 | − | 0.814266i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 600.087 | − | 1039.38i | 0.0229874 | − | 0.0398154i | ||||
\(881\) | 14886.3 | + | 25783.9i | 0.569278 | + | 0.986018i | 0.996638 | + | 0.0819365i | \(0.0261105\pi\) |
−0.427360 | + | 0.904082i | \(0.640556\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27309.6 | −1.04082 | −0.520409 | − | 0.853917i | \(-0.674220\pi\) | ||||
−0.520409 | + | 0.853917i | \(0.674220\pi\) | |||||||
\(884\) | 1659.73 | − | 853.877i | 0.0631480 | − | 0.0324876i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 17420.4 | + | 30173.0i | 0.660552 | + | 1.14411i | ||||
\(887\) | 3264.98 | + | 5655.12i | 0.123594 | + | 0.214070i | 0.921182 | − | 0.389131i | \(-0.127225\pi\) |
−0.797589 | + | 0.603202i | \(0.793891\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 47609.3 | 1.79614 | ||||||||
\(890\) | 545.626 | − | 945.051i | 0.0205499 | − | 0.0355935i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1890.06 | 0.0709461 | ||||||||
\(893\) | 738.069 | − | 1278.37i | 0.0276579 | − | 0.0479050i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −227.533 | − | 394.098i | −0.00849785 | − | 0.0147187i | ||||
\(896\) | −37970.3 | −1.41573 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4890.45 | 0.181733 | ||||||||
\(899\) | −11648.5 | − | 20175.8i | −0.432145 | − | 0.748497i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 29392.3 | − | 50909.0i | 1.08679 | − | 1.88238i | ||||
\(902\) | −60307.1 | −2.22617 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 652.874 | − | 1130.81i | 0.0240202 | − | 0.0416042i | ||||
\(905\) | 172.368 | 0.00633116 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9718.71 | − | 16833.3i | −0.355793 | − | 0.616252i | 0.631460 | − | 0.775408i | \(-0.282456\pi\) |
−0.987253 | + | 0.159157i | \(0.949123\pi\) | |||||||
\(908\) | 717.351 | + | 1242.49i | 0.0262182 | + | 0.0454113i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −55.9755 | + | 1154.55i | −0.00203909 | + | 0.0420581i | ||||
\(911\) | 50234.6 | 1.82694 | 0.913472 | − | 0.406901i | \(-0.133391\pi\) | ||||
0.913472 | + | 0.406901i | \(0.133391\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27043.6 | − | 46840.9i | −0.980299 | − | 1.69793i | ||||
\(914\) | 8501.48 | − | 14725.0i | 0.307663 | − | 0.532888i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −633.581 | + | 1097.39i | −0.0228538 | + | 0.0395840i | ||||
\(917\) | −8607.35 | + | 14908.4i | −0.309967 | + | 0.536878i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6142.62 | + | 10639.3i | −0.220486 | + | 0.381892i | −0.954956 | − | 0.296749i | \(-0.904098\pi\) |
0.734470 | + | 0.678641i | \(0.237431\pi\) | |||||||
\(920\) | 52.1937 | + | 90.4022i | 0.00187041 | + | 0.00323964i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 20549.1 | 0.734000 | ||||||||
\(923\) | 37291.3 | + | 24010.2i | 1.32986 | + | 0.856236i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19929.0 | + | 34518.0i | 0.708390 | + | 1.22697i | ||||
\(926\) | 7441.64 | + | 12889.3i | 0.264090 | + | 0.457417i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3575.72 | −0.126486 | ||||||||
\(929\) | −12805.0 | + | 22178.9i | −0.452227 | + | 0.783280i | −0.998524 | − | 0.0543114i | \(-0.982704\pi\) |
0.546297 | + | 0.837591i | \(0.316037\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6853.84 | −0.241273 | ||||||||
\(932\) | −171.761 | + | 297.498i | −0.00603670 | + | 0.0104559i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5501.55 | + | 9528.96i | 0.192737 | + | 0.333830i | ||||
\(935\) | −1956.80 | −0.0684429 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29893.2 | −1.04223 | −0.521114 | − | 0.853487i | \(-0.674483\pi\) | ||||
−0.521114 | + | 0.853487i | \(0.674483\pi\) | |||||||
\(938\) | 2700.83 | + | 4677.97i | 0.0940140 | + | 0.162837i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.42848 | + | 11.1345i | −0.000223057 | + | 0.000386347i | ||||
\(941\) | 44960.3 | 1.55756 | 0.778780 | − | 0.627297i | \(-0.215839\pi\) | ||||
0.778780 | + | 0.627297i | \(0.215839\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2490.23 | − | 4313.21i | 0.0859947 | − | 0.148947i | ||||
\(944\) | −12394.0 | −0.427320 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6053.72 | + | 10485.3i | 0.208058 | + | 0.360368i | ||||
\(947\) | 16798.8 | + | 29096.4i | 0.576439 | + | 0.998422i | 0.995884 | + | 0.0906410i | \(0.0288916\pi\) |
−0.419444 | + | 0.907781i | \(0.637775\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1770.17 | − | 36511.4i | 0.0605502 | − | 1.24890i | ||||
\(950\) | −4988.29 | −0.170360 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 32692.5 | + | 56625.1i | 1.11299 | + | 1.92776i | ||||
\(953\) | 12925.1 | − | 22387.0i | 0.439335 | − | 0.760950i | −0.558303 | − | 0.829637i | \(-0.688547\pi\) |
0.997638 | + | 0.0686864i | \(0.0218808\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −292.644 | + | 506.874i | −0.00991595 | + | 0.0171749i | ||||
\(956\) | 441.080 | − | 763.973i | 0.0149221 | − | 0.0258459i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4343.37 | − | 7522.94i | 0.146480 | − | 0.253711i | ||||
\(959\) | 6022.47 | + | 10431.2i | 0.202790 | + | 0.351243i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15703.5 | −0.527123 | ||||||||
\(962\) | 34663.7 | + | 22318.4i | 1.16175 | + | 0.747998i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1275.29 | + | 2208.87i | 0.0426082 | + | 0.0737996i | ||||
\(965\) | 650.931 | + | 1127.45i | 0.0217142 | + | 0.0376101i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6296.49 | 0.209392 | 0.104696 | − | 0.994504i | \(-0.466613\pi\) | ||||
0.104696 | + | 0.994504i | \(0.466613\pi\) | |||||||
\(968\) | −30866.7 | + | 53462.7i | −1.02489 | + | 1.77516i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 571.749 | 0.0189255 | ||||||||
\(971\) | 3903.21 | − | 6760.56i | 0.129001 | − | 0.223436i | −0.794289 | − | 0.607540i | \(-0.792156\pi\) |
0.923290 | + | 0.384104i | \(0.125490\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −416.638 | − | 721.638i | −0.0137274 | − | 0.0237766i | ||||
\(974\) | 10774.8 | 0.354462 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13091.3 | 0.429348 | ||||||||
\(977\) | −27846.4 | − | 48231.4i | −0.911858 | − | 1.57938i | −0.811438 | − | 0.584438i | \(-0.801315\pi\) |
−0.100420 | − | 0.994945i | \(-0.532019\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −39955.2 | + | 69204.4i | −1.30437 | + | 2.25923i | ||||
\(980\) | 59.6960 | 0.00194584 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9157.92 | − | 15862.0i | 0.297598 | − | 0.515454i | ||||
\(983\) | −44635.5 | −1.44827 | −0.724135 | − | 0.689658i | \(-0.757761\pi\) | ||||
−0.724135 | + | 0.689658i | \(0.757761\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 238.381 | + | 412.888i | 0.00771112 | + | 0.0133560i | ||||
\(986\) | −26733.2 | − | 46303.3i | −0.863447 | − | 1.49553i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 243.345 | − | 125.193i | 0.00783587 | − | 0.00403129i | ||||
\(989\) | −999.892 | −0.0321484 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1942.16 | − | 3363.92i | −0.0622551 | − | 0.107829i | 0.833218 | − | 0.552945i | \(-0.186496\pi\) |
−0.895473 | + | 0.445116i | \(0.853163\pi\) | |||||||
\(992\) | 1081.11 | − | 1872.53i | 0.0346020 | − | 0.0599323i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −37251.5 | + | 64521.5i | −1.18868 | + | 2.05885i | ||||
\(995\) | 126.557 | − | 219.203i | 0.00403228 | − | 0.00698412i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9010.72 | − | 15607.0i | 0.286231 | − | 0.495767i | −0.686676 | − | 0.726964i | \(-0.740931\pi\) |
0.972907 | + | 0.231197i | \(0.0742642\pi\) | |||||||
\(998\) | 8422.95 | + | 14589.0i | 0.267158 | + | 0.462731i | ||||
\(999\) | 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 | 117.4.g.f.55.6 | yes | 16 | |
3.2 | odd | 2 | inner | 117.4.g.f.55.3 | ✓ | 16 | |
13.3 | even | 3 | 1521.4.a.bc.1.3 | 8 | |||
13.9 | even | 3 | inner | 117.4.g.f.100.6 | yes | 16 | |
13.10 | even | 6 | 1521.4.a.bd.1.6 | 8 | |||
39.23 | odd | 6 | 1521.4.a.bd.1.3 | 8 | |||
39.29 | odd | 6 | 1521.4.a.bc.1.6 | 8 | |||
39.35 | odd | 6 | inner | 117.4.g.f.100.3 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
117.4.g.f.55.3 | ✓ | 16 | 3.2 | odd | 2 | inner | |
117.4.g.f.55.6 | yes | 16 | 1.1 | even | 1 | trivial | |
117.4.g.f.100.3 | yes | 16 | 39.35 | odd | 6 | inner | |
117.4.g.f.100.6 | yes | 16 | 13.9 | even | 3 | inner | |
1521.4.a.bc.1.3 | 8 | 13.3 | even | 3 | |||
1521.4.a.bc.1.6 | 8 | 39.29 | odd | 6 | |||
1521.4.a.bd.1.3 | 8 | 39.23 | odd | 6 | |||
1521.4.a.bd.1.6 | 8 | 13.10 | even | 6 |