Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [38,5,Mod(27,38)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(38, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("38.27");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 38.d (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.92805859719\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 1024 x^{14} - 7028 x^{13} + 404698 x^{12} - 2337188 x^{11} + 77836288 x^{10} + \cdots + 23840536514409 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 27.1 | ||
Root | \(0.500000 + 17.6194i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 38.27 |
Dual form | 38.5.d.a.31.1 |
$q$-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 \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).
\(n\) | \(21\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.44949 | − | 1.41421i | −0.612372 | − | 0.353553i | ||||
\(3\) | −14.7841 | − | 8.53562i | −1.64268 | − | 0.948402i | −0.979875 | − | 0.199611i | \(-0.936032\pi\) |
−0.662806 | − | 0.748791i | \(-0.730635\pi\) | |||||||
\(4\) | 4.00000 | + | 6.92820i | 0.250000 | + | 0.433013i | ||||
\(5\) | −3.60911 | + | 6.25116i | −0.144364 | + | 0.250046i | −0.929136 | − | 0.369739i | \(-0.879447\pi\) |
0.784771 | + | 0.619785i | \(0.212780\pi\) | |||||||
\(6\) | 24.1424 | + | 41.8158i | 0.670622 | + | 1.16155i | ||||
\(7\) | 27.7970 | 0.567285 | 0.283642 | − | 0.958930i | \(-0.408457\pi\) | ||||
0.283642 | + | 0.958930i | \(0.408457\pi\) | |||||||
\(8\) | − | 22.6274i | − | 0.353553i | ||||||
\(9\) | 105.214 | + | 182.235i | 1.29893 | + | 2.24982i | ||||
\(10\) | 17.6809 | − | 10.2081i | 0.176809 | − | 0.102081i | ||||
\(11\) | 43.1224 | 0.356383 | 0.178192 | − | 0.983996i | \(-0.442975\pi\) | ||||
0.178192 | + | 0.983996i | \(0.442975\pi\) | |||||||
\(12\) | − | 136.570i | − | 0.948402i | ||||||
\(13\) | −274.840 | + | 158.679i | −1.62627 | + | 0.938928i | −0.641079 | + | 0.767475i | \(0.721513\pi\) |
−0.985192 | + | 0.171453i | \(0.945154\pi\) | |||||||
\(14\) | −68.0884 | − | 39.3108i | −0.347390 | − | 0.200565i | ||||
\(15\) | 106.715 | − | 61.6119i | 0.474289 | − | 0.273831i | ||||
\(16\) | −32.0000 | + | 55.4256i | −0.125000 | + | 0.216506i | ||||
\(17\) | 37.2748 | − | 64.5618i | 0.128979 | − | 0.223397i | −0.794303 | − | 0.607522i | \(-0.792164\pi\) |
0.923281 | + | 0.384125i | \(0.125497\pi\) | |||||||
\(18\) | − | 595.178i | − | 1.83697i | ||||||
\(19\) | 172.248 | + | 317.256i | 0.477142 | + | 0.878826i | ||||
\(20\) | −57.7457 | −0.144364 | ||||||||
\(21\) | −410.954 | − | 237.264i | −0.931868 | − | 0.538014i | ||||
\(22\) | −105.628 | − | 60.9843i | −0.218239 | − | 0.126001i | ||||
\(23\) | −48.8879 | − | 84.6764i | −0.0924158 | − | 0.160069i | 0.816111 | − | 0.577895i | \(-0.196126\pi\) |
−0.908527 | + | 0.417826i | \(0.862792\pi\) | |||||||
\(24\) | −193.139 | + | 334.527i | −0.335311 | + | 0.580775i | ||||
\(25\) | 286.449 | + | 496.144i | 0.458318 | + | 0.793830i | ||||
\(26\) | 897.623 | 1.32784 | ||||||||
\(27\) | − | 2209.49i | − | 3.03084i | ||||||
\(28\) | 111.188 | + | 192.583i | 0.141821 | + | 0.245642i | ||||
\(29\) | −1057.52 | + | 610.557i | −1.25745 | + | 0.725989i | −0.972578 | − | 0.232576i | \(-0.925284\pi\) |
−0.284872 | + | 0.958566i | \(0.591951\pi\) | |||||||
\(30\) | −348.530 | −0.387255 | ||||||||
\(31\) | 256.919i | 0.267346i | 0.991026 | + | 0.133673i | \(0.0426772\pi\) | ||||
−0.991026 | + | 0.133673i | \(0.957323\pi\) | |||||||
\(32\) | 156.767 | − | 90.5097i | 0.153093 | − | 0.0883883i | ||||
\(33\) | −637.527 | − | 368.076i | −0.585424 | − | 0.337995i | ||||
\(34\) | −182.608 | + | 105.429i | −0.157966 | + | 0.0912016i | ||||
\(35\) | −100.322 | + | 173.763i | −0.0818957 | + | 0.141847i | ||||
\(36\) | −841.709 | + | 1457.88i | −0.649467 | + | 1.12491i | ||||
\(37\) | 969.440i | 0.708138i | 0.935219 | + | 0.354069i | \(0.115202\pi\) | ||||
−0.935219 | + | 0.354069i | \(0.884798\pi\) | |||||||
\(38\) | 26.7480 | − | 1020.71i | 0.0185236 | − | 0.706864i | ||||
\(39\) | 5417.69 | 3.56193 | ||||||||
\(40\) | 141.448 | + | 81.6648i | 0.0884047 | + | 0.0510405i | ||||
\(41\) | 1666.06 | + | 961.900i | 0.991113 | + | 0.572219i | 0.905607 | − | 0.424118i | \(-0.139416\pi\) |
0.0855060 | + | 0.996338i | \(0.472749\pi\) | |||||||
\(42\) | 671.085 | + | 1162.35i | 0.380433 | + | 0.658930i | ||||
\(43\) | −1493.99 | + | 2587.67i | −0.807999 | + | 1.39949i | 0.106249 | + | 0.994340i | \(0.466116\pi\) |
−0.914248 | + | 0.405155i | \(0.867217\pi\) | |||||||
\(44\) | 172.490 | + | 298.761i | 0.0890959 | + | 0.154319i | ||||
\(45\) | −1518.91 | −0.750079 | ||||||||
\(46\) | 276.552i | 0.130696i | ||||||||
\(47\) | −1743.74 | − | 3020.25i | −0.789381 | − | 1.36725i | −0.926347 | − | 0.376672i | \(-0.877068\pi\) |
0.136966 | − | 0.990576i | \(-0.456265\pi\) | |||||||
\(48\) | 946.184 | − | 546.280i | 0.410670 | − | 0.237101i | ||||
\(49\) | −1628.33 | −0.678188 | ||||||||
\(50\) | − | 1620.40i | − | 0.648159i | ||||||
\(51\) | −1102.15 | + | 636.327i | −0.423741 | + | 0.244647i | ||||
\(52\) | −2198.72 | − | 1269.43i | −0.813136 | − | 0.469464i | ||||
\(53\) | 2526.15 | − | 1458.47i | 0.899306 | − | 0.519215i | 0.0223310 | − | 0.999751i | \(-0.492891\pi\) |
0.876975 | + | 0.480536i | \(0.159558\pi\) | |||||||
\(54\) | −3124.68 | + | 5412.11i | −1.07157 | + | 1.85601i | ||||
\(55\) | −155.633 | + | 269.565i | −0.0514490 | + | 0.0891123i | ||||
\(56\) | − | 628.973i | − | 0.200565i | ||||||
\(57\) | 161.440 | − | 6160.60i | 0.0496892 | − | 1.89615i | ||||
\(58\) | 3453.83 | 1.02670 | ||||||||
\(59\) | −2212.04 | − | 1277.12i | −0.635461 | − | 0.366883i | 0.147403 | − | 0.989077i | \(-0.452909\pi\) |
−0.782864 | + | 0.622193i | \(0.786242\pi\) | |||||||
\(60\) | 853.720 | + | 492.895i | 0.237144 | + | 0.136915i | ||||
\(61\) | −1683.62 | − | 2916.11i | −0.452464 | − | 0.783690i | 0.546075 | − | 0.837736i | \(-0.316121\pi\) |
−0.998538 | + | 0.0540463i | \(0.982788\pi\) | |||||||
\(62\) | 363.339 | − | 629.321i | 0.0945210 | − | 0.163715i | ||||
\(63\) | 2924.62 | + | 5065.59i | 0.736866 | + | 1.27629i | ||||
\(64\) | −512.000 | −0.125000 | ||||||||
\(65\) | − | 2290.76i | − | 0.542191i | ||||||
\(66\) | 1041.08 | + | 1803.20i | 0.238998 | + | 0.413958i | ||||
\(67\) | −388.431 | + | 224.261i | −0.0865295 | + | 0.0499579i | −0.542640 | − | 0.839965i | \(-0.682575\pi\) |
0.456111 | + | 0.889923i | \(0.349242\pi\) | |||||||
\(68\) | 596.397 | 0.128979 | ||||||||
\(69\) | 1669.16i | 0.350589i | ||||||||
\(70\) | 491.476 | − | 283.754i | 0.100301 | − | 0.0579090i | ||||
\(71\) | 3383.62 | + | 1953.54i | 0.671221 | + | 0.387530i | 0.796539 | − | 0.604587i | \(-0.206662\pi\) |
−0.125318 | + | 0.992117i | \(0.539995\pi\) | |||||||
\(72\) | 4123.52 | − | 2380.71i | 0.795431 | − | 0.459243i | ||||
\(73\) | −2338.04 | + | 4049.60i | −0.438738 | + | 0.759917i | −0.997592 | − | 0.0693489i | \(-0.977908\pi\) |
0.558854 | + | 0.829266i | \(0.311241\pi\) | |||||||
\(74\) | 1371.00 | − | 2374.63i | 0.250364 | − | 0.433644i | ||||
\(75\) | − | 9780.07i | − | 1.73868i | ||||||
\(76\) | −1509.02 | + | 2462.40i | −0.261258 | + | 0.426315i | ||||
\(77\) | 1198.67 | 0.202171 | ||||||||
\(78\) | −13270.6 | − | 7661.77i | −2.18123 | − | 1.25933i | ||||
\(79\) | 74.9327 | + | 43.2624i | 0.0120065 | + | 0.00693197i | 0.505991 | − | 0.862539i | \(-0.331127\pi\) |
−0.493985 | + | 0.869471i | \(0.664460\pi\) | |||||||
\(80\) | −230.983 | − | 400.074i | −0.0360911 | − | 0.0625116i | ||||
\(81\) | −10337.0 | + | 17904.2i | −1.57553 | + | 2.72889i | ||||
\(82\) | −2720.67 | − | 4712.33i | −0.404620 | − | 0.700822i | ||||
\(83\) | −2587.49 | −0.375598 | −0.187799 | − | 0.982208i | \(-0.560135\pi\) | ||||
−0.187799 | + | 0.982208i | \(0.560135\pi\) | |||||||
\(84\) | − | 3796.23i | − | 0.538014i | ||||||
\(85\) | 269.057 | + | 466.021i | 0.0372398 | + | 0.0645012i | ||||
\(86\) | 7319.02 | − | 4225.64i | 0.989592 | − | 0.571341i | ||||
\(87\) | 20845.9 | 2.75412 | ||||||||
\(88\) | − | 975.748i | − | 0.126001i | ||||||
\(89\) | −7551.95 | + | 4360.12i | −0.953409 | + | 0.550451i | −0.894138 | − | 0.447791i | \(-0.852211\pi\) |
−0.0592708 | + | 0.998242i | \(0.518878\pi\) | |||||||
\(90\) | 3720.55 | + | 2148.06i | 0.459328 | + | 0.265193i | ||||
\(91\) | −7639.71 | + | 4410.79i | −0.922559 | + | 0.532640i | ||||
\(92\) | 391.104 | − | 677.411i | 0.0462079 | − | 0.0800344i | ||||
\(93\) | 2192.97 | − | 3798.33i | 0.253551 | − | 0.439164i | ||||
\(94\) | 9864.10i | 1.11635i | ||||||||
\(95\) | −2604.88 | − | 68.2616i | −0.288629 | − | 0.00756361i | ||||
\(96\) | −3090.23 | −0.335311 | ||||||||
\(97\) | 9398.96 | + | 5426.49i | 0.998933 | + | 0.576734i | 0.907932 | − | 0.419117i | \(-0.137660\pi\) |
0.0910006 | + | 0.995851i | \(0.470993\pi\) | |||||||
\(98\) | 3988.58 | + | 2302.81i | 0.415304 | + | 0.239776i | ||||
\(99\) | 4537.07 | + | 7858.43i | 0.462919 | + | 0.801799i | ||||
\(100\) | −2291.59 | + | 3969.15i | −0.229159 | + | 0.396915i | ||||
\(101\) | 1844.63 | + | 3194.99i | 0.180828 | + | 0.313204i | 0.942163 | − | 0.335156i | \(-0.108789\pi\) |
−0.761335 | + | 0.648359i | \(0.775456\pi\) | |||||||
\(102\) | 3599.61 | 0.345983 | ||||||||
\(103\) | − | 7812.91i | − | 0.736441i | −0.929738 | − | 0.368221i | \(-0.879967\pi\) | ||
0.929738 | − | 0.368221i | \(-0.120033\pi\) | |||||||
\(104\) | 3590.49 | + | 6218.91i | 0.331961 | + | 0.574974i | ||||
\(105\) | 2966.35 | − | 1712.62i | 0.269057 | − | 0.155340i | ||||
\(106\) | −8250.37 | −0.734280 | ||||||||
\(107\) | 5256.06i | 0.459085i | 0.973299 | + | 0.229542i | \(0.0737230\pi\) | ||||
−0.973299 | + | 0.229542i | \(0.926277\pi\) | |||||||
\(108\) | 15307.8 | − | 8837.94i | 1.31239 | − | 0.757711i | ||||
\(109\) | 13867.3 | + | 8006.31i | 1.16719 | + | 0.673875i | 0.953016 | − | 0.302921i | \(-0.0979618\pi\) |
0.214171 | + | 0.976796i | \(0.431295\pi\) | |||||||
\(110\) | 762.444 | − | 440.198i | 0.0630119 | − | 0.0363800i | ||||
\(111\) | 8274.78 | − | 14332.3i | 0.671599 | − | 1.16324i | ||||
\(112\) | −889.502 | + | 1540.66i | −0.0709106 | + | 0.122821i | ||||
\(113\) | − | 1374.45i | − | 0.107640i | −0.998551 | − | 0.0538199i | \(-0.982860\pi\) | ||
0.998551 | − | 0.0538199i | \(-0.0171397\pi\) | |||||||
\(114\) | −9107.86 | + | 14862.0i | −0.700820 | + | 1.14358i | ||||
\(115\) | 705.767 | 0.0533661 | ||||||||
\(116\) | −8460.13 | − | 4884.46i | −0.628725 | − | 0.362995i | ||||
\(117\) | −57833.8 | − | 33390.4i | −4.22484 | − | 2.43921i | ||||
\(118\) | 3612.24 | + | 6256.59i | 0.259426 | + | 0.449339i | ||||
\(119\) | 1036.13 | − | 1794.62i | 0.0731676 | − | 0.126730i | ||||
\(120\) | −1394.12 | − | 2414.68i | −0.0968138 | − | 0.167686i | ||||
\(121\) | −12781.5 | −0.872991 | ||||||||
\(122\) | 9523.98i | 0.639880i | ||||||||
\(123\) | −16420.8 | − | 28441.7i | −1.08539 | − | 1.87995i | ||||
\(124\) | −1779.99 | + | 1027.68i | −0.115764 | + | 0.0668365i | ||||
\(125\) | −8646.68 | −0.553387 | ||||||||
\(126\) | − | 16544.1i | − | 1.04209i | ||||||
\(127\) | 6594.05 | − | 3807.08i | 0.408832 | − | 0.236039i | −0.281456 | − | 0.959574i | \(-0.590817\pi\) |
0.690288 | + | 0.723535i | \(0.257484\pi\) | |||||||
\(128\) | 1254.14 | + | 724.077i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 44174.7 | − | 25504.3i | 2.65457 | − | 1.53262i | ||||
\(130\) | −3239.62 | + | 5611.18i | −0.191693 | + | 0.332023i | ||||
\(131\) | −6095.42 | + | 10557.6i | −0.355190 | + | 0.615207i | −0.987150 | − | 0.159794i | \(-0.948917\pi\) |
0.631960 | + | 0.775001i | \(0.282250\pi\) | |||||||
\(132\) | − | 5889.22i | − | 0.337995i | ||||||
\(133\) | 4787.97 | + | 8818.76i | 0.270675 | + | 0.498545i | ||||
\(134\) | 1268.61 | 0.0706511 | ||||||||
\(135\) | 13811.8 | + | 7974.27i | 0.757851 | + | 0.437546i | ||||
\(136\) | −1460.87 | − | 843.432i | −0.0789829 | − | 0.0456008i | ||||
\(137\) | 9757.49 | + | 16900.5i | 0.519873 | + | 0.900446i | 0.999733 | + | 0.0231013i | \(0.00735404\pi\) |
−0.479860 | + | 0.877345i | \(0.659313\pi\) | |||||||
\(138\) | 2360.54 | − | 4088.58i | 0.123952 | − | 0.214691i | ||||
\(139\) | −12318.4 | − | 21336.2i | −0.637567 | − | 1.10430i | −0.985965 | − | 0.166952i | \(-0.946608\pi\) |
0.348398 | − | 0.937347i | \(-0.386726\pi\) | |||||||
\(140\) | −1605.15 | −0.0818957 | ||||||||
\(141\) | 59535.7i | 2.99460i | ||||||||
\(142\) | −5525.44 | − | 9570.34i | −0.274025 | − | 0.474625i | ||||
\(143\) | −11851.8 | + | 6842.61i | −0.579576 | + | 0.334618i | ||||
\(144\) | −13467.3 | −0.649467 | ||||||||
\(145\) | − | 8814.26i | − | 0.419228i | ||||||
\(146\) | 11454.0 | − | 6612.97i | 0.537343 | − | 0.310235i | ||||
\(147\) | 24073.4 | + | 13898.8i | 1.11405 | + | 0.643195i | ||||
\(148\) | −6716.48 | + | 3877.76i | −0.306633 | + | 0.177034i | ||||
\(149\) | 18434.1 | − | 31928.8i | 0.830328 | − | 1.43817i | −0.0674499 | − | 0.997723i | \(-0.521486\pi\) |
0.897778 | − | 0.440448i | \(-0.145180\pi\) | |||||||
\(150\) | −13831.1 | + | 23956.2i | −0.614716 | + | 1.06472i | ||||
\(151\) | 3708.22i | 0.162634i | 0.996688 | + | 0.0813171i | \(0.0259126\pi\) | ||||
−0.996688 | + | 0.0813171i | \(0.974087\pi\) | |||||||
\(152\) | 7178.69 | − | 3897.53i | 0.310712 | − | 0.168695i | ||||
\(153\) | 15687.3 | 0.670138 | ||||||||
\(154\) | −2936.13 | − | 1695.18i | −0.123804 | − | 0.0714782i | ||||
\(155\) | −1606.04 | − | 927.249i | −0.0668488 | − | 0.0385952i | ||||
\(156\) | 21670.8 | + | 37534.9i | 0.890482 | + | 1.54236i | ||||
\(157\) | −1832.48 | + | 3173.94i | −0.0743428 | + | 0.128766i | −0.900800 | − | 0.434234i | \(-0.857019\pi\) |
0.826457 | + | 0.562999i | \(0.190353\pi\) | |||||||
\(158\) | −122.365 | − | 211.942i | −0.00490164 | − | 0.00848989i | ||||
\(159\) | −49795.9 | −1.96970 | ||||||||
\(160\) | 1306.64i | 0.0510405i | ||||||||
\(161\) | −1358.94 | − | 2353.75i | −0.0524261 | − | 0.0908046i | ||||
\(162\) | 50640.9 | − | 29237.5i | 1.92962 | − | 1.11406i | ||||
\(163\) | 16538.3 | 0.622466 | 0.311233 | − | 0.950334i | \(-0.399258\pi\) | ||||
0.311233 | + | 0.950334i | \(0.399258\pi\) | |||||||
\(164\) | 15390.4i | 0.572219i | ||||||||
\(165\) | 4601.81 | − | 2656.85i | 0.169029 | − | 0.0975888i | ||||
\(166\) | 6338.03 | + | 3659.27i | 0.230006 | + | 0.132794i | ||||
\(167\) | −29352.3 | + | 16946.5i | −1.05247 | + | 0.607642i | −0.923339 | − | 0.383986i | \(-0.874551\pi\) |
−0.129128 | + | 0.991628i | \(0.541218\pi\) | |||||||
\(168\) | −5368.68 | + | 9298.82i | −0.190217 | + | 0.329465i | ||||
\(169\) | 36077.4 | − | 62488.0i | 1.26317 | − | 2.18788i | ||||
\(170\) | − | 1522.02i | − | 0.0526650i | ||||||
\(171\) | −39692.5 | + | 64769.4i | −1.35743 | + | 2.21502i | ||||
\(172\) | −23903.8 | −0.807999 | ||||||||
\(173\) | −25254.7 | − | 14580.8i | −0.843821 | − | 0.487180i | 0.0147405 | − | 0.999891i | \(-0.495308\pi\) |
−0.858561 | + | 0.512711i | \(0.828641\pi\) | |||||||
\(174\) | −51061.9 | − | 29480.6i | −1.68655 | − | 0.973728i | ||||
\(175\) | 7962.40 | + | 13791.3i | 0.259997 | + | 0.450328i | ||||
\(176\) | −1379.92 | + | 2390.09i | −0.0445479 | + | 0.0771593i | ||||
\(177\) | 21802.0 | + | 37762.3i | 0.695906 | + | 1.20534i | ||||
\(178\) | 24664.6 | 0.778455 | ||||||||
\(179\) | − | 11481.5i | − | 0.358336i | −0.983818 | − | 0.179168i | \(-0.942659\pi\) | ||
0.983818 | − | 0.179168i | \(-0.0573406\pi\) | |||||||
\(180\) | −6075.64 | − | 10523.3i | −0.187520 | − | 0.324794i | ||||
\(181\) | 17778.5 | − | 10264.4i | 0.542673 | − | 0.313312i | −0.203489 | − | 0.979077i | \(-0.565228\pi\) |
0.746161 | + | 0.665765i | \(0.231895\pi\) | |||||||
\(182\) | 24951.2 | 0.753266 | ||||||||
\(183\) | 57482.9i | 1.71647i | ||||||||
\(184\) | −1916.01 | + | 1106.21i | −0.0565929 | + | 0.0326739i | ||||
\(185\) | −6060.12 | − | 3498.81i | −0.177067 | − | 0.102230i | ||||
\(186\) | −10743.3 | + | 6202.65i | −0.310536 | + | 0.179288i | ||||
\(187\) | 1607.38 | − | 2784.06i | 0.0459658 | − | 0.0796151i | ||||
\(188\) | 13949.9 | − | 24162.0i | 0.394691 | − | 0.683624i | ||||
\(189\) | − | 61417.0i | − | 1.71935i | ||||||
\(190\) | 6284.09 | + | 3851.06i | 0.174075 | + | 0.106678i | ||||
\(191\) | 8170.94 | 0.223978 | 0.111989 | − | 0.993709i | \(-0.464278\pi\) | ||||
0.111989 | + | 0.993709i | \(0.464278\pi\) | |||||||
\(192\) | 7569.47 | + | 4370.24i | 0.205335 | + | 0.118550i | ||||
\(193\) | 30126.0 | + | 17393.2i | 0.808772 | + | 0.466945i | 0.846529 | − | 0.532342i | \(-0.178688\pi\) |
−0.0377570 | + | 0.999287i | \(0.512021\pi\) | |||||||
\(194\) | −15348.4 | − | 26584.3i | −0.407813 | − | 0.706352i | ||||
\(195\) | −19553.0 | + | 33866.8i | −0.514215 | + | 0.890646i | ||||
\(196\) | −6513.32 | − | 11281.4i | −0.169547 | − | 0.293664i | ||||
\(197\) | 14718.1 | 0.379243 | 0.189622 | − | 0.981857i | \(-0.439274\pi\) | ||||
0.189622 | + | 0.981857i | \(0.439274\pi\) | |||||||
\(198\) | − | 25665.5i | − | 0.654666i | ||||||
\(199\) | −11220.4 | − | 19434.2i | −0.283335 | − | 0.490751i | 0.688869 | − | 0.724886i | \(-0.258108\pi\) |
−0.972204 | + | 0.234135i | \(0.924774\pi\) | |||||||
\(200\) | 11226.5 | − | 6481.59i | 0.280661 | − | 0.162040i | ||||
\(201\) | 7656.82 | 0.189521 | ||||||||
\(202\) | − | 10434.8i | − | 0.255730i | ||||||
\(203\) | −29395.7 | + | 16971.6i | −0.713332 | + | 0.411843i | ||||
\(204\) | −8817.21 | − | 5090.62i | −0.211871 | − | 0.122324i | ||||
\(205\) | −12026.0 | + | 6943.20i | −0.286163 | + | 0.165216i | ||||
\(206\) | −11049.1 | + | 19137.6i | −0.260371 | + | 0.450976i | ||||
\(207\) | 10287.4 | − | 17818.2i | 0.240084 | − | 0.415838i | ||||
\(208\) | − | 20310.9i | − | 0.469464i | ||||||
\(209\) | 7427.75 | + | 13680.9i | 0.170045 | + | 0.313199i | ||||
\(210\) | −9688.07 | −0.219684 | ||||||||
\(211\) | −20300.9 | − | 11720.7i | −0.455984 | − | 0.263263i | 0.254370 | − | 0.967107i | \(-0.418132\pi\) |
−0.710354 | + | 0.703844i | \(0.751465\pi\) | |||||||
\(212\) | 20209.2 | + | 11667.8i | 0.449653 | + | 0.259607i | ||||
\(213\) | −33349.3 | − | 57762.7i | −0.735068 | − | 1.27318i | ||||
\(214\) | 7433.20 | − | 12874.7i | 0.162311 | − | 0.281131i | ||||
\(215\) | −10783.9 | − | 18678.3i | −0.233292 | − | 0.404074i | ||||
\(216\) | −49994.9 | −1.07157 | ||||||||
\(217\) | 7141.57i | 0.151661i | ||||||||
\(218\) | −22645.3 | − | 39222.8i | −0.476502 | − | 0.825325i | ||||
\(219\) | 69131.7 | − | 39913.2i | 1.44141 | − | 0.832201i | ||||
\(220\) | −2490.13 | −0.0514490 | ||||||||
\(221\) | 23658.9i | 0.484406i | ||||||||
\(222\) | −40538.0 | + | 23404.6i | −0.822538 | + | 0.474893i | ||||
\(223\) | −15209.0 | − | 8780.95i | −0.305839 | − | 0.176576i | 0.339224 | − | 0.940706i | \(-0.389835\pi\) |
−0.645063 | + | 0.764130i | \(0.723169\pi\) | |||||||
\(224\) | 4357.65 | − | 2515.89i | 0.0868474 | − | 0.0501414i | ||||
\(225\) | −60276.6 | + | 104402.i | −1.19065 | + | 2.06227i | ||||
\(226\) | −1943.77 | + | 3366.71i | −0.0380564 | + | 0.0659157i | ||||
\(227\) | − | 67121.7i | − | 1.30260i | −0.758820 | − | 0.651300i | \(-0.774224\pi\) | ||
0.758820 | − | 0.651300i | \(-0.225776\pi\) | |||||||
\(228\) | 43327.7 | − | 23523.9i | 0.833481 | − | 0.452522i | ||||
\(229\) | 47018.8 | 0.896604 | 0.448302 | − | 0.893882i | \(-0.352029\pi\) | ||||
0.448302 | + | 0.893882i | \(0.352029\pi\) | |||||||
\(230\) | −1728.77 | − | 998.106i | −0.0326800 | − | 0.0188678i | ||||
\(231\) | −17721.3 | − | 10231.4i | −0.332102 | − | 0.191739i | ||||
\(232\) | 13815.3 | + | 23928.8i | 0.256676 | + | 0.444576i | ||||
\(233\) | −24816.0 | + | 42982.6i | −0.457110 | + | 0.791737i | −0.998807 | − | 0.0488367i | \(-0.984449\pi\) |
0.541697 | + | 0.840574i | \(0.317782\pi\) | |||||||
\(234\) | 94442.2 | + | 163579.i | 1.72478 | + | 2.98741i | ||||
\(235\) | 25173.4 | 0.455834 | ||||||||
\(236\) | − | 20433.9i | − | 0.366883i | ||||||
\(237\) | −738.543 | − | 1279.19i | −0.0131486 | − | 0.0227740i | ||||
\(238\) | −5075.96 | + | 2930.61i | −0.0896116 | + | 0.0517373i | ||||
\(239\) | −41682.4 | −0.729721 | −0.364861 | − | 0.931062i | \(-0.618883\pi\) | ||||
−0.364861 | + | 0.931062i | \(0.618883\pi\) | |||||||
\(240\) | 7886.33i | 0.136915i | ||||||||
\(241\) | 43105.9 | − | 24887.2i | 0.742169 | − | 0.428492i | −0.0806884 | − | 0.996739i | \(-0.525712\pi\) |
0.822857 | + | 0.568248i | \(0.192379\pi\) | |||||||
\(242\) | 31308.1 | + | 18075.7i | 0.534596 | + | 0.308649i | ||||
\(243\) | 150657. | − | 86981.7i | 2.55138 | − | 1.47304i | ||||
\(244\) | 13468.9 | − | 23328.9i | 0.226232 | − | 0.391845i | ||||
\(245\) | 5876.81 | − | 10178.9i | 0.0979061 | − | 0.169578i | ||||
\(246\) | 92890.3i | 1.53497i | ||||||||
\(247\) | −97682.5 | − | 59862.5i | −1.60112 | − | 0.981208i | ||||
\(248\) | 5813.42 | 0.0945210 | ||||||||
\(249\) | 38253.8 | + | 22085.8i | 0.616987 | + | 0.356218i | ||||
\(250\) | 21180.0 | + | 12228.3i | 0.338879 | + | 0.195652i | ||||
\(251\) | 43512.0 | + | 75365.0i | 0.690656 | + | 1.19625i | 0.971623 | + | 0.236534i | \(0.0760114\pi\) |
−0.280967 | + | 0.959717i | \(0.590655\pi\) | |||||||
\(252\) | −23397.0 | + | 40524.7i | −0.368433 | + | 0.638144i | ||||
\(253\) | −2108.17 | − | 3651.45i | −0.0329354 | − | 0.0570459i | ||||
\(254\) | −21536.1 | −0.333810 | ||||||||
\(255\) | − | 9186.29i | − | 0.141273i | ||||||
\(256\) | −2048.00 | − | 3547.24i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −71993.9 | + | 41565.7i | −1.09001 | + | 0.629316i | −0.933578 | − | 0.358373i | \(-0.883331\pi\) |
−0.156429 | + | 0.987689i | \(0.549998\pi\) | |||||||
\(258\) | −144274. | −2.16745 | ||||||||
\(259\) | 26947.5i | 0.401716i | ||||||||
\(260\) | 15870.8 | − | 9163.02i | 0.234775 | − | 0.135548i | ||||
\(261\) | −222530. | − | 128478.i | −3.26669 | − | 1.88602i | ||||
\(262\) | 29861.3 | − | 17240.4i | 0.435017 | − | 0.251157i | ||||
\(263\) | −40829.3 | + | 70718.5i | −0.590284 | + | 1.02240i | 0.403910 | + | 0.914799i | \(0.367651\pi\) |
−0.994194 | + | 0.107603i | \(0.965683\pi\) | |||||||
\(264\) | −8328.62 | + | 14425.6i | −0.119499 | + | 0.206979i | ||||
\(265\) | 21055.1i | 0.299824i | ||||||||
\(266\) | 743.513 | − | 28372.7i | 0.0105081 | − | 0.400993i | ||||
\(267\) | 148865. | 2.08820 | ||||||||
\(268\) | −3107.45 | − | 1794.09i | −0.0432648 | − | 0.0249789i | ||||
\(269\) | 51027.6 | + | 29460.8i | 0.705181 | + | 0.407137i | 0.809274 | − | 0.587431i | \(-0.199861\pi\) |
−0.104093 | + | 0.994568i | \(0.533194\pi\) | |||||||
\(270\) | −22554.6 | − | 39065.8i | −0.309391 | − | 0.535882i | ||||
\(271\) | 44961.5 | − | 77875.7i | 0.612213 | − | 1.06038i | −0.378654 | − | 0.925538i | \(-0.623613\pi\) |
0.990867 | − | 0.134846i | \(-0.0430538\pi\) | |||||||
\(272\) | 2385.59 | + | 4131.96i | 0.0322446 | + | 0.0558493i | ||||
\(273\) | 150595. | 2.02063 | ||||||||
\(274\) | − | 55196.7i | − | 0.735211i | ||||||
\(275\) | 12352.4 | + | 21394.9i | 0.163337 | + | 0.282908i | ||||
\(276\) | −11564.3 | + | 6676.62i | −0.151810 | + | 0.0876473i | ||||
\(277\) | −9087.27 | −0.118433 | −0.0592166 | − | 0.998245i | \(-0.518860\pi\) | ||||
−0.0592166 | + | 0.998245i | \(0.518860\pi\) | |||||||
\(278\) | 69683.6i | 0.901656i | ||||||||
\(279\) | −46819.8 | + | 27031.4i | −0.601480 | + | 0.347265i | ||||
\(280\) | 3931.81 | + | 2270.03i | 0.0501506 | + | 0.0289545i | ||||
\(281\) | −47513.8 | + | 27432.1i | −0.601737 | + | 0.347413i | −0.769725 | − | 0.638376i | \(-0.779607\pi\) |
0.167987 | + | 0.985789i | \(0.446273\pi\) | |||||||
\(282\) | 84196.2 | − | 145832.i | 1.05875 | − | 1.83381i | ||||
\(283\) | −75890.2 | + | 131446.i | −0.947574 | + | 1.64125i | −0.197059 | + | 0.980392i | \(0.563139\pi\) |
−0.750515 | + | 0.660854i | \(0.770194\pi\) | |||||||
\(284\) | 31256.6i | 0.387530i | ||||||||
\(285\) | 37928.2 | + | 23243.5i | 0.466953 | + | 0.286161i | ||||
\(286\) | 38707.7 | 0.473222 | ||||||||
\(287\) | 46311.4 | + | 26737.9i | 0.562243 | + | 0.324611i | ||||
\(288\) | 32988.1 | + | 19045.7i | 0.397716 | + | 0.229621i | ||||
\(289\) | 38981.7 | + | 67518.2i | 0.466729 | + | 0.808398i | ||||
\(290\) | −12465.2 | + | 21590.4i | −0.148219 | + | 0.256723i | ||||
\(291\) | −92637.0 | − | 160452.i | −1.09395 | − | 1.89478i | ||||
\(292\) | −37408.6 | −0.438738 | ||||||||
\(293\) | − | 77275.4i | − | 0.900131i | −0.892996 | − | 0.450066i | \(-0.851401\pi\) | ||
0.892996 | − | 0.450066i | \(-0.148599\pi\) | |||||||
\(294\) | −39311.8 | − | 68090.0i | −0.454808 | − | 0.787750i | ||||
\(295\) | 15967.0 | − | 9218.53i | 0.183476 | − | 0.105930i | ||||
\(296\) | 21935.9 | 0.250364 | ||||||||
\(297\) | − | 95278.3i | − | 1.08014i | ||||||
\(298\) | −90308.4 | + | 52139.6i | −1.01694 | + | 0.587131i | ||||
\(299\) | 26872.7 | + | 15515.0i | 0.300586 | + | 0.173543i | ||||
\(300\) | 67758.3 | − | 39120.3i | 0.752870 | − | 0.434670i | ||||
\(301\) | −41528.4 | + | 71929.2i | −0.458365 | + | 0.793912i | ||||
\(302\) | 5244.22 | − | 9083.25i | 0.0574998 | − | 0.0995926i | ||||
\(303\) | − | 62980.2i | − | 0.685992i | ||||||
\(304\) | −23096.1 | − | 605.239i | −0.249914 | − | 0.00654907i | ||||
\(305\) | 24305.4 | 0.261278 | ||||||||
\(306\) | −38425.8 | − | 22185.2i | −0.410374 | − | 0.236930i | ||||
\(307\) | 54289.6 | + | 31344.1i | 0.576023 | + | 0.332567i | 0.759551 | − | 0.650447i | \(-0.225418\pi\) |
−0.183528 | + | 0.983014i | \(0.558752\pi\) | |||||||
\(308\) | 4794.68 | + | 8304.64i | 0.0505427 | + | 0.0875426i | ||||
\(309\) | −66688.0 | + | 115507.i | −0.698443 | + | 1.20974i | ||||
\(310\) | 2622.66 | + | 4542.58i | 0.0272909 | + | 0.0472693i | ||||
\(311\) | 85462.2 | 0.883596 | 0.441798 | − | 0.897115i | \(-0.354341\pi\) | ||||
0.441798 | + | 0.897115i | \(0.354341\pi\) | |||||||
\(312\) | − | 122588.i | − | 1.25933i | ||||||
\(313\) | −26593.0 | − | 46060.5i | −0.271443 | − | 0.470154i | 0.697788 | − | 0.716304i | \(-0.254168\pi\) |
−0.969232 | + | 0.246150i | \(0.920834\pi\) | |||||||
\(314\) | 8977.27 | − | 5183.03i | 0.0910510 | − | 0.0525683i | ||||
\(315\) | −42221.1 | −0.425508 | ||||||||
\(316\) | 692.199i | 0.00693197i | ||||||||
\(317\) | −11945.9 | + | 6896.97i | −0.118878 | + | 0.0686341i | −0.558260 | − | 0.829666i | \(-0.688531\pi\) |
0.439382 | + | 0.898300i | \(0.355197\pi\) | |||||||
\(318\) | 121975. | + | 70422.1i | 1.20619 | + | 0.696393i | ||||
\(319\) | −45602.6 | + | 26328.7i | −0.448134 | + | 0.258731i | ||||
\(320\) | 1847.86 | − | 3200.59i | 0.0180455 | − | 0.0312558i | ||||
\(321\) | 44863.8 | − | 77706.3i | 0.435397 | − | 0.754130i | ||||
\(322\) | 7687.30i | 0.0741416i | ||||||||
\(323\) | 26903.2 | + | 705.005i | 0.257869 | + | 0.00675751i | ||||
\(324\) | −165392. | −1.57553 | ||||||||
\(325\) | −157455. | − | 90906.7i | −1.49070 | − | 0.860655i | ||||
\(326\) | −40510.4 | − | 23388.7i | −0.381181 | − | 0.220075i | ||||
\(327\) | −136678. | − | 236733.i | −1.27821 | − | 2.21392i | ||||
\(328\) | 21765.3 | − | 37698.6i | 0.202310 | − | 0.350411i | ||||
\(329\) | −48470.7 | − | 83953.8i | −0.447804 | − | 0.775619i | ||||
\(330\) | −15029.4 | −0.138011 | ||||||||
\(331\) | 33630.8i | 0.306959i | 0.988152 | + | 0.153480i | \(0.0490480\pi\) | ||||
−0.988152 | + | 0.153480i | \(0.950952\pi\) | |||||||
\(332\) | −10350.0 | − | 17926.7i | −0.0938994 | − | 0.162639i | ||||
\(333\) | −176666. | + | 101998.i | −1.59318 | + | 0.919824i | ||||
\(334\) | 95864.1 | 0.859336 | ||||||||
\(335\) | − | 3237.52i | − | 0.0288485i | ||||||
\(336\) | 26301.0 | − | 15184.9i | 0.232967 | − | 0.134504i | ||||
\(337\) | 90344.3 | + | 52160.3i | 0.795502 | + | 0.459283i | 0.841896 | − | 0.539640i | \(-0.181440\pi\) |
−0.0463942 | + | 0.998923i | \(0.514773\pi\) | |||||||
\(338\) | −176743. | + | 102042.i | −1.54706 | + | 0.893197i | ||||
\(339\) | −11731.8 | + | 20320.1i | −0.102086 | + | 0.176818i | ||||
\(340\) | −2152.46 | + | 3728.17i | −0.0186199 | + | 0.0322506i | ||||
\(341\) | 11079.0i | 0.0952776i | ||||||||
\(342\) | 188824. | − | 102518.i | 1.61438 | − | 0.876495i | ||||
\(343\) | −112003. | −0.952010 | ||||||||
\(344\) | 58552.2 | + | 33805.1i | 0.494796 | + | 0.285671i | ||||
\(345\) | −10434.2 | − | 6024.16i | −0.0876635 | − | 0.0506126i | ||||
\(346\) | 41240.8 | + | 71431.1i | 0.344488 | + | 0.596671i | ||||
\(347\) | 25974.2 | − | 44988.7i | 0.215717 | − | 0.373632i | −0.737777 | − | 0.675044i | \(-0.764125\pi\) |
0.953494 | + | 0.301412i | \(0.0974579\pi\) | |||||||
\(348\) | 83383.7 | + | 144425.i | 0.688530 | + | 1.19257i | ||||
\(349\) | 150107. | 1.23239 | 0.616197 | − | 0.787592i | \(-0.288672\pi\) | ||||
0.616197 | + | 0.787592i | \(0.288672\pi\) | |||||||
\(350\) | − | 45042.1i | − | 0.367691i | ||||||
\(351\) | 350599. | + | 607254.i | 2.84574 | + | 4.92897i | ||||
\(352\) | 6760.18 | − | 3902.99i | 0.0545598 | − | 0.0315001i | ||||
\(353\) | 169193. | 1.35779 | 0.678894 | − | 0.734236i | \(-0.262459\pi\) | ||||
0.678894 | + | 0.734236i | \(0.262459\pi\) | |||||||
\(354\) | − | 123331.i | − | 0.984160i | ||||||
\(355\) | −24423.7 | + | 14101.0i | −0.193801 | + | 0.111891i | ||||
\(356\) | −60415.6 | − | 34881.0i | −0.476705 | − | 0.275225i | ||||
\(357\) | −30636.4 | + | 17688.0i | −0.240382 | + | 0.138785i | ||||
\(358\) | −16237.2 | + | 28123.7i | −0.126691 | + | 0.219435i | ||||
\(359\) | 52398.0 | − | 90756.0i | 0.406561 | − | 0.704185i | −0.587941 | − | 0.808904i | \(-0.700061\pi\) |
0.994502 | + | 0.104719i | \(0.0333944\pi\) | |||||||
\(360\) | 34369.0i | 0.265193i | ||||||||
\(361\) | −70982.1 | + | 109294.i | −0.544671 | + | 0.838650i | ||||
\(362\) | −58064.3 | −0.443090 | ||||||||
\(363\) | 188963. | + | 109098.i | 1.43405 | + | 0.827947i | ||||
\(364\) | −61117.7 | − | 35286.3i | −0.461279 | − | 0.266320i | ||||
\(365\) | −16876.4 | − | 29230.9i | −0.126676 | − | 0.219410i | ||||
\(366\) | 81293.1 | − | 140804.i | 0.606864 | − | 1.05112i | ||||
\(367\) | −14084.5 | − | 24395.0i | −0.104570 | − | 0.181121i | 0.808992 | − | 0.587819i | \(-0.200013\pi\) |
−0.913563 | + | 0.406698i | \(0.866680\pi\) | |||||||
\(368\) | 6257.66 | 0.0462079 | ||||||||
\(369\) | 404820.i | 2.97310i | ||||||||
\(370\) | 9896.14 | + | 17140.6i | 0.0722874 | + | 0.125205i | ||||
\(371\) | 70219.3 | − | 40541.1i | 0.510163 | − | 0.294542i | ||||
\(372\) | 35087.5 | 0.253551 | ||||||||
\(373\) | − | 15207.2i | − | 0.109303i | −0.998505 | − | 0.0546516i | \(-0.982595\pi\) | ||
0.998505 | − | 0.0546516i | \(-0.0174048\pi\) | |||||||
\(374\) | −7874.51 | + | 4546.35i | −0.0562964 | + | 0.0325027i | ||||
\(375\) | 127834. | + | 73804.8i | 0.909039 | + | 0.524834i | ||||
\(376\) | −68340.5 | + | 39456.4i | −0.483395 | + | 0.279088i | ||||
\(377\) | 193765. | − | 335611.i | 1.36330 | − | 2.36131i | ||||
\(378\) | −86856.7 | + | 150440.i | −0.607883 | + | 1.05288i | ||||
\(379\) | − | 47404.3i | − | 0.330019i | −0.986292 | − | 0.165010i | \(-0.947234\pi\) | ||
0.986292 | − | 0.165010i | \(-0.0527656\pi\) | |||||||
\(380\) | −9946.59 | − | 18320.2i | −0.0688822 | − | 0.126871i | ||||
\(381\) | −129983. | −0.895441 | ||||||||
\(382\) | −20014.6 | − | 11555.5i | −0.137158 | − | 0.0791882i | ||||
\(383\) | 24214.0 | + | 13979.9i | 0.165070 | + | 0.0953032i | 0.580259 | − | 0.814432i | \(-0.302951\pi\) |
−0.415189 | + | 0.909735i | \(0.636285\pi\) | |||||||
\(384\) | −12360.9 | − | 21409.7i | −0.0838277 | − | 0.145194i | ||||
\(385\) | −4326.13 | + | 7493.08i | −0.0291863 | + | 0.0505521i | ||||
\(386\) | −49195.5 | − | 85209.1i | −0.330180 | − | 0.571888i | ||||
\(387\) | −628752. | −4.19815 | ||||||||
\(388\) | 86823.9i | 0.576734i | ||||||||
\(389\) | −118471. | − | 205198.i | −0.782911 | − | 1.35604i | −0.930239 | − | 0.366954i | \(-0.880400\pi\) |
0.147328 | − | 0.989088i | \(-0.452933\pi\) | |||||||
\(390\) | 95789.8 | − | 55304.3i | 0.629782 | − | 0.363605i | ||||
\(391\) | −7289.15 | −0.0476786 | ||||||||
\(392\) | 36844.9i | 0.239776i | ||||||||
\(393\) | 180231. | − | 104056.i | 1.16693 | − | 0.673726i | ||||
\(394\) | −36051.7 | − | 20814.5i | −0.232238 | − | 0.134083i | ||||
\(395\) | −540.880 | + | 312.277i | −0.00346663 | + | 0.00200146i | ||||
\(396\) | −36296.5 | + | 62867.4i | −0.231459 | + | 0.400899i | ||||
\(397\) | 15150.7 | − | 26241.8i | 0.0961283 | − | 0.166499i | −0.813951 | − | 0.580934i | \(-0.802687\pi\) |
0.910079 | + | 0.414435i | \(0.136021\pi\) | |||||||
\(398\) | 63472.0i | 0.400697i | ||||||||
\(399\) | 4487.55 | − | 171246.i | 0.0281879 | − | 1.07566i | ||||
\(400\) | −36665.4 | −0.229159 | ||||||||
\(401\) | −156300. | − | 90239.9i | −0.972009 | − | 0.561190i | −0.0721608 | − | 0.997393i | \(-0.522989\pi\) |
−0.899848 | + | 0.436203i | \(0.856323\pi\) | |||||||
\(402\) | −18755.3 | − | 10828.4i | −0.116057 | − | 0.0670056i | ||||
\(403\) | −40767.7 | − | 70611.7i | −0.251018 | − | 0.434777i | ||||
\(404\) | −14757.0 | + | 25559.9i | −0.0904141 | + | 0.156602i | ||||
\(405\) | −74614.8 | − | 129237.i | −0.454899 | − | 0.787909i | ||||
\(406\) | 96006.0 | 0.582433 | ||||||||
\(407\) | 41804.6i | 0.252369i | ||||||||
\(408\) | 14398.4 | + | 24938.8i | 0.0864958 | + | 0.149815i | ||||
\(409\) | −185396. | + | 107039.i | −1.10829 | + | 0.639873i | −0.938386 | − | 0.345588i | \(-0.887680\pi\) |
−0.169905 | + | 0.985460i | \(0.554346\pi\) | |||||||
\(410\) | 39276.7 | 0.233651 | ||||||||
\(411\) | − | 333145.i | − | 1.97219i | ||||||
\(412\) | 54129.4 | − | 31251.6i | 0.318888 | − | 0.184110i | ||||
\(413\) | −61487.9 | − | 35500.1i | −0.360487 | − | 0.208127i | ||||
\(414\) | −50397.6 | + | 29097.0i | −0.294042 | + | 0.169765i | ||||
\(415\) | 9338.53 | − | 16174.8i | 0.0542229 | − | 0.0939168i | ||||
\(416\) | −28723.9 | + | 49751.3i | −0.165981 | + | 0.287487i | ||||
\(417\) | 420582.i | 2.41868i | ||||||||
\(418\) | 1153.44 | − | 44015.5i | 0.00660149 | − | 0.251915i | ||||
\(419\) | −58444.5 | −0.332901 | −0.166451 | − | 0.986050i | \(-0.553231\pi\) | ||||
−0.166451 | + | 0.986050i | \(0.553231\pi\) | |||||||
\(420\) | 23730.8 | + | 13701.0i | 0.134528 | + | 0.0776700i | ||||
\(421\) | 155922. | + | 90021.4i | 0.879716 | + | 0.507904i | 0.870565 | − | 0.492054i | \(-0.163754\pi\) |
0.00915094 | + | 0.999958i | \(0.497087\pi\) | |||||||
\(422\) | 33151.2 | + | 57419.6i | 0.186155 | + | 0.322430i | ||||
\(423\) | 366931. | − | 635543.i | 2.05071 | − | 3.55193i | ||||
\(424\) | −33001.5 | − | 57160.3i | −0.183570 | − | 0.317953i | ||||
\(425\) | 42709.3 | 0.236453 | ||||||||
\(426\) | 188652.i | 1.03954i | ||||||||
\(427\) | −46799.4 | − | 81059.0i | −0.256676 | − | 0.444575i | ||||
\(428\) | −36415.1 | + | 21024.3i | −0.198790 | + | 0.114771i | ||||
\(429\) | 233624. | 1.26941 | ||||||||
\(430\) | 61003.2i | 0.329925i | ||||||||
\(431\) | 320145. | − | 184836.i | 1.72343 | − | 0.995020i | 0.811875 | − | 0.583831i | \(-0.198447\pi\) |
0.911550 | − | 0.411189i | \(-0.134886\pi\) | |||||||
\(432\) | 122462. | + | 70703.5i | 0.656197 | + | 0.378856i | ||||
\(433\) | −255722. | + | 147641.i | −1.36393 | + | 0.787465i | −0.990144 | − | 0.140050i | \(-0.955274\pi\) |
−0.373785 | + | 0.927515i | \(0.621940\pi\) | |||||||
\(434\) | 10099.7 | − | 17493.2i | 0.0536203 | − | 0.0928731i | ||||
\(435\) | −75235.2 | + | 130311.i | −0.397596 | + | 0.688657i | ||||
\(436\) | 128101.i | 0.673875i | ||||||||
\(437\) | 18443.3 | − | 30095.4i | 0.0965773 | − | 0.157593i | ||||
\(438\) | −225783. | −1.17691 | ||||||||
\(439\) | 167735. | + | 96842.0i | 0.870353 | + | 0.502498i | 0.867465 | − | 0.497497i | \(-0.165748\pi\) |
0.00288733 | + | 0.999996i | \(0.499081\pi\) | |||||||
\(440\) | 6099.56 | + | 3521.58i | 0.0315060 | + | 0.0181900i | ||||
\(441\) | −171323. | − | 296739.i | −0.880922 | − | 1.52580i | ||||
\(442\) | 33458.7 | − | 57952.2i | 0.171263 | − | 0.296637i | ||||
\(443\) | 2155.55 | + | 3733.52i | 0.0109837 | + | 0.0190244i | 0.871465 | − | 0.490458i | \(-0.163170\pi\) |
−0.860481 | + | 0.509482i | \(0.829837\pi\) | |||||||
\(444\) | 132396. | 0.671599 | ||||||||
\(445\) | − | 62944.6i | − | 0.317862i | ||||||
\(446\) | 24836.3 | + | 43017.7i | 0.124858 | + | 0.216261i | ||||
\(447\) | −545065. | + | 314693.i | −2.72793 | + | 1.57497i | ||||
\(448\) | −14232.0 | −0.0709106 | ||||||||
\(449\) | 183388.i | 0.909657i | 0.890579 | + | 0.454829i | \(0.150299\pi\) | ||||
−0.890579 | + | 0.454829i | \(0.849701\pi\) | |||||||
\(450\) | 295294. | − | 170488.i | 1.45824 | − | 0.841916i | ||||
\(451\) | 71844.5 | + | 41479.5i | 0.353216 | + | 0.203929i | ||||
\(452\) | 9522.49 | − | 5497.81i | 0.0466094 | − | 0.0269100i | ||||
\(453\) | 31652.0 | − | 54822.8i | 0.154243 | − | 0.267156i | ||||
\(454\) | −94924.4 | + | 164414.i | −0.460539 | + | 0.797676i | ||||
\(455\) | − | 63676.0i | − | 0.307576i | ||||||
\(456\) | −139399. | − | 3652.98i | −0.670392 | − | 0.0175678i | ||||
\(457\) | 129953. | 0.622233 | 0.311116 | − | 0.950372i | \(-0.399297\pi\) | ||||
0.311116 | + | 0.950372i | \(0.399297\pi\) | |||||||
\(458\) | −115172. | − | 66494.6i | −0.549055 | − | 0.316997i | ||||
\(459\) | −142648. | − | 82358.1i | −0.677083 | − | 0.390914i | ||||
\(460\) | 2823.07 | + | 4889.70i | 0.0133415 | + | 0.0231082i | ||||
\(461\) | −96531.7 | + | 167198.i | −0.454222 | + | 0.786735i | −0.998643 | − | 0.0520766i | \(-0.983416\pi\) |
0.544421 | + | 0.838812i | \(0.316749\pi\) | |||||||
\(462\) | 28938.8 | + | 50123.4i | 0.135580 | + | 0.234832i | ||||
\(463\) | −62781.6 | −0.292867 | −0.146433 | − | 0.989221i | \(-0.546779\pi\) | ||||
−0.146433 | + | 0.989221i | \(0.546779\pi\) | |||||||
\(464\) | − | 78151.3i | − | 0.362995i | ||||||
\(465\) | 15829.3 | + | 27417.1i | 0.0732075 | + | 0.126799i | ||||
\(466\) | 121573. | − | 70190.3i | 0.559843 | − | 0.323225i | ||||
\(467\) | 287382. | 1.31773 | 0.658863 | − | 0.752263i | \(-0.271038\pi\) | ||||
0.658863 | + | 0.752263i | \(0.271038\pi\) | |||||||
\(468\) | − | 534246.i | − | 2.43921i | ||||||
\(469\) | −10797.2 | + | 6233.77i | −0.0490869 | + | 0.0283403i | ||||
\(470\) | −61662.0 | − | 35600.6i | −0.279140 | − | 0.161162i | ||||
\(471\) | 54183.1 | − | 31282.7i | 0.244243 | − | 0.141014i | ||||
\(472\) | −28898.0 | + | 50052.7i | −0.129713 | + | 0.224669i | ||||
\(473\) | −64424.4 | + | 111586.i | −0.287957 | + | 0.498757i | ||||
\(474\) | 4177.83i | 0.0185949i | ||||||||
\(475\) | −108064. | + | 176338.i | −0.478956 | + | 0.781551i | ||||
\(476\) | 16578.0 | 0.0731676 | ||||||||
\(477\) | 531571. | + | 306903.i | 2.33628 | + | 1.34885i | ||||
\(478\) | 102101. | + | 58947.8i | 0.446861 | + | 0.257995i | ||||
\(479\) | 180571. | + | 312758.i | 0.787005 | + | 1.36313i | 0.927794 | + | 0.373093i | \(0.121703\pi\) |
−0.140789 | + | 0.990040i | \(0.544964\pi\) | |||||||
\(480\) | 11153.0 | − | 19317.5i | 0.0484069 | − | 0.0838432i | ||||
\(481\) | −153830. | − | 266441.i | −0.664890 | − | 1.15162i | ||||
\(482\) | −140783. | −0.605979 | ||||||||
\(483\) | 46397.4i | 0.198884i | ||||||||
\(484\) | −51125.8 | − | 88552.5i | −0.218248 | − | 0.378016i | ||||
\(485\) | −67843.7 | + | 39169.6i | −0.288420 | + | 0.166520i | ||||
\(486\) | −492043. | −2.08320 | ||||||||
\(487\) | 172074.i | 0.725533i | 0.931880 | + | 0.362766i | \(0.118168\pi\) | ||||
−0.931880 | + | 0.362766i | \(0.881832\pi\) | |||||||
\(488\) | −65984.1 | + | 38095.9i | −0.277076 | + | 0.159970i | ||||
\(489\) | −244504. | − | 141165.i | −1.02251 | − | 0.590348i | ||||
\(490\) | −28790.4 | + | 16622.1i | −0.119910 | + | 0.0692301i | ||||
\(491\) | 56307.5 | − | 97527.5i | 0.233563 | − | 0.404543i | −0.725291 | − | 0.688442i | \(-0.758295\pi\) |
0.958854 | + | 0.283900i | \(0.0916282\pi\) | |||||||
\(492\) | 131367. | − | 227534.i | 0.542694 | − | 0.939974i | ||||
\(493\) | 91033.5i | 0.374548i | ||||||||
\(494\) | 154614. | + | 284777.i | 0.633570 | + | 1.16694i | ||||
\(495\) | −65499.0 | −0.267316 | ||||||||
\(496\) | −14239.9 | − | 8221.42i | −0.0578821 | − | 0.0334182i | ||||
\(497\) | 94054.5 | + | 54302.4i | 0.380773 | + | 0.219840i | ||||
\(498\) | −62468.2 | − | 108198.i | −0.251884 | − | 0.436276i | ||||
\(499\) | −65891.7 | + | 114128.i | −0.264624 | + | 0.458343i | −0.967465 | − | 0.253004i | \(-0.918581\pi\) |
0.702841 | + | 0.711347i | \(0.251915\pi\) | |||||||
\(500\) | −34586.7 | − | 59906.0i | −0.138347 | − | 0.239624i | ||||
\(501\) | 578597. | 2.30516 | ||||||||
\(502\) | − | 246141.i | − | 0.976735i | ||||||
\(503\) | 91727.9 | + | 158877.i | 0.362548 | + | 0.627951i | 0.988379 | − | 0.152007i | \(-0.0485736\pi\) |
−0.625832 | + | 0.779958i | \(0.715240\pi\) | |||||||
\(504\) | 114621. | − | 66176.6i | 0.451236 | − | 0.260521i | ||||
\(505\) | −26629.8 | −0.104421 | ||||||||
\(506\) | 11925.6i | 0.0465778i | ||||||||
\(507\) | −1.06675e6 | + | 615887.i | −4.14998 | + | 2.39599i | ||||
\(508\) | 52752.4 | + | 30456.6i | 0.204416 | + | 0.118020i | ||||
\(509\) | −98167.1 | + | 56676.8i | −0.378905 | + | 0.218761i | −0.677342 | − | 0.735669i | \(-0.736868\pi\) |
0.298437 | + | 0.954429i | \(0.403535\pi\) | |||||||
\(510\) | −12991.4 | + | 22501.7i | −0.0499476 | + | 0.0865118i | ||||
\(511\) | −64990.3 | + | 112566.i | −0.248890 | + | 0.431089i | ||||
\(512\) | 11585.2i | 0.0441942i | ||||||||
\(513\) | 700973. | − | 380580.i | 2.66359 | − | 1.44614i | ||||
\(514\) | 235131. | 0.889987 | ||||||||
\(515\) | 48839.7 | + | 28197.6i | 0.184144 | + | 0.106316i | ||||
\(516\) | 353397. | + | 204034.i | 1.32728 | + | 0.766308i | ||||
\(517\) | −75194.4 | − | 130240.i | −0.281322 | − | 0.487265i | ||||
\(518\) | 38109.5 | − | 66007.6i | 0.142028 | − | 0.246000i | ||||
\(519\) | 248913. | + | 431129.i | 0.924085 | + | 1.60056i | ||||
\(520\) | −51833.9 | −0.191693 | ||||||||
\(521\) | − | 107635.i | − | 0.396534i | −0.980148 | − | 0.198267i | \(-0.936469\pi\) | ||
0.980148 | − | 0.198267i | \(-0.0635312\pi\) | |||||||
\(522\) | 363390. | + | 629410.i | 1.33362 | + | 2.30990i | ||||
\(523\) | 219803. | − | 126903.i | 0.803583 | − | 0.463949i | −0.0411395 | − | 0.999153i | \(-0.513099\pi\) |
0.844722 | + | 0.535205i | \(0.179765\pi\) | |||||||
\(524\) | −97526.6 | −0.355190 | ||||||||
\(525\) | − | 271856.i | − | 0.986326i | ||||||
\(526\) | 200022. | − | 115483.i | 0.722947 | − | 0.417394i | ||||
\(527\) | 16587.2 | + | 9576.62i | 0.0597244 | + | 0.0344819i | ||||
\(528\) | 40801.7 | − | 23556.9i | 0.146356 | − | 0.0844987i | ||||
\(529\) | 135140. | − | 234070.i | 0.482919 | − | 0.836440i | ||||
\(530\) | 29776.5 | − | 51574.4i | 0.106004 | − | 0.183604i | ||||
\(531\) | − | 537482.i | − | 1.90623i | ||||||
\(532\) | −41946.3 | + | 68447.1i | −0.148207 | + | 0.241842i | ||||
\(533\) | −610533. | −2.14909 | ||||||||
\(534\) | −364644. | − | 210527.i | −1.27875 | − | 0.738289i | ||||
\(535\) | −32856.5 | − | 18969.7i | −0.114792 | − | 0.0662755i | ||||
\(536\) | 5074.44 | + | 8789.19i | 0.0176628 | + | 0.0305928i | ||||
\(537\) | −98001.3 | + | 169743.i | −0.339847 | + | 0.588632i | ||||
\(538\) | −83327.8 | − | 144328.i | −0.287889 | − | 0.498638i | ||||
\(539\) | −70217.5 | −0.241695 | ||||||||
\(540\) | 127588.i | 0.437546i | ||||||||
\(541\) | 89469.4 | + | 154965.i | 0.305689 | + | 0.529469i | 0.977414 | − | 0.211331i | \(-0.0677799\pi\) |
−0.671725 | + | 0.740800i | \(0.734447\pi\) | |||||||
\(542\) | −220266. | + | 127170.i | −0.749805 | + | 0.432900i | ||||
\(543\) | −350453. | −1.18858 | ||||||||
\(544\) | − | 13494.9i | − | 0.0456008i | ||||||
\(545\) | −100097. | + | 57791.3i | −0.337000 | + | 0.194567i | ||||
\(546\) | −368882. | − | 212974.i | −1.23738 | − | 0.714399i | ||||
\(547\) | −107864. | + | 62275.4i | −0.360498 | + | 0.208134i | −0.669299 | − | 0.742993i | \(-0.733406\pi\) |
0.308801 | + | 0.951127i | \(0.400072\pi\) | |||||||
\(548\) | −78060.0 | + | 135204.i | −0.259936 | + | 0.450223i | ||||
\(549\) | 354279. | − | 613629.i | 1.17544 | − | 2.03592i | ||||
\(550\) | − | 69875.5i | − | 0.230993i | ||||||
\(551\) | −375858. | − | 230336.i | −1.23800 | − | 0.758681i | ||||
\(552\) | 37768.7 | 0.123952 | ||||||||
\(553\) | 2082.90 | + | 1202.56i | 0.00681112 | + | 0.00393240i | ||||
\(554\) | 22259.2 | + | 12851.3i | 0.0725253 | + | 0.0418725i | ||||
\(555\) | 59729.1 | + | 103454.i | 0.193910 | + | 0.335862i | ||||
\(556\) | 98547.5 | − | 170689.i | 0.318784 | − | 0.552149i | ||||
\(557\) | 188555. | + | 326587.i | 0.607755 | + | 1.05266i | 0.991610 | + | 0.129269i | \(0.0412630\pi\) |
−0.383855 | + | 0.923394i | \(0.625404\pi\) | |||||||
\(558\) | 152913. | 0.491106 | ||||||||
\(559\) | − | 948258.i | − | 3.03461i | ||||||
\(560\) | −6420.62 | − | 11120.8i | −0.0204739 | − | 0.0354619i | ||||
\(561\) | −47527.4 | + | 27439.9i | −0.151014 | + | 0.0871882i | ||||
\(562\) | 155179. | 0.491316 | ||||||||
\(563\) | 417122.i | 1.31597i | 0.753030 | + | 0.657986i | \(0.228591\pi\) | ||||
−0.753030 | + | 0.657986i | \(0.771409\pi\) | |||||||
\(564\) | −412475. | + | 238143.i | −1.29670 | + | 0.748651i | ||||
\(565\) | 8591.93 | + | 4960.55i | 0.0269150 | + | 0.0155394i | ||||
\(566\) | 371785. | − | 214650.i | 1.16054 | − | 0.670036i | ||||
\(567\) | −287338. | + | 497684.i | −0.893772 | + | 1.54806i | ||||
\(568\) | 44203.5 | − | 76562.7i | 0.137012 | − | 0.237312i | ||||
\(569\) | − | 250904.i | − | 0.774966i | −0.921877 | − | 0.387483i | \(-0.873345\pi\) | ||
0.921877 | − | 0.387483i | \(-0.126655\pi\) | |||||||
\(570\) | −60033.6 | − | 110573.i | −0.184776 | − | 0.340330i | ||||
\(571\) | 528282. | 1.62029 | 0.810147 | − | 0.586227i | \(-0.199387\pi\) | ||||
0.810147 | + | 0.586227i | \(0.199387\pi\) | |||||||
\(572\) | −94814.0 | − | 54740.9i | −0.289788 | − | 0.167309i | ||||
\(573\) | −120800. | − | 69744.0i | −0.367924 | − | 0.212421i | ||||
\(574\) | −75626.2 | − | 130988.i | −0.229535 | − | 0.397566i | ||||
\(575\) | 28007.8 | − | 48510.9i | 0.0847116 | − | 0.146725i | ||||
\(576\) | −53869.4 | − | 93304.5i | −0.162367 | − | 0.281227i | ||||
\(577\) | 253777. | 0.762254 | 0.381127 | − | 0.924523i | \(-0.375536\pi\) | ||||
0.381127 | + | 0.924523i | \(0.375536\pi\) | |||||||
\(578\) | − | 220514.i | − | 0.660055i | ||||||
\(579\) | −296924. | − | 514288.i | −0.885703 | − | 1.53408i | ||||
\(580\) | 61067.0 | − | 35257.0i | 0.181531 | − | 0.104807i | ||||
\(581\) | −71924.4 | −0.213071 | ||||||||
\(582\) | 524034.i | 1.54708i | ||||||||
\(583\) | 108934. | − | 62892.9i | 0.320498 | − | 0.185039i | ||||
\(584\) | 91631.9 | + | 52903.7i | 0.268671 | + | 0.155117i | ||||
\(585\) | 417457. | − | 241019.i | 1.21983 | − | 0.704270i | ||||
\(586\) | −109284. | + | 189285.i | −0.318244 | + | 0.551216i | ||||
\(587\) | −210622. | + | 364808.i | −0.611262 | + | 1.05874i | 0.379766 | + | 0.925083i | \(0.376005\pi\) |
−0.991028 | + | 0.133655i | \(0.957329\pi\) | |||||||
\(588\) | 222381.i | 0.643195i | ||||||||
\(589\) | −81509.3 | + | 44253.9i | −0.234951 | + | 0.127562i | ||||
\(590\) | −52147.9 | −0.149807 | ||||||||
\(591\) | −217594. | − | 125628.i | −0.622976 | − | 0.359675i | ||||
\(592\) | −53731.8 | − | 31022.1i | −0.153316 | − | 0.0885172i | ||||
\(593\) | −71141.2 | − | 123220.i | −0.202307 | − | 0.350407i | 0.746964 | − | 0.664864i | \(-0.231511\pi\) |
−0.949271 | + | 0.314458i | \(0.898177\pi\) | |||||||
\(594\) | −134744. | + | 233383.i | −0.381888 | + | 0.661450i | ||||
\(595\) | 7478.98 | + | 12954.0i | 0.0211256 | + | 0.0365905i | ||||
\(596\) | 294946. | 0.830328 | ||||||||
\(597\) | 383091.i | 1.07486i | ||||||||
\(598\) | −43882.9 | − | 76007.5i | −0.122714 | − | 0.212547i | ||||
\(599\) | −213068. | + | 123015.i | −0.593833 | + | 0.342849i | −0.766612 | − | 0.642111i | \(-0.778059\pi\) |
0.172779 | + | 0.984961i | \(0.444725\pi\) | |||||||
\(600\) | −221298. | −0.614716 | ||||||||
\(601\) | 150238.i | 0.415939i | 0.978135 | + | 0.207969i | \(0.0666855\pi\) | ||||
−0.978135 | + | 0.207969i | \(0.933315\pi\) | |||||||
\(602\) | 203447. | − | 117460.i | 0.561381 | − | 0.324113i | ||||
\(603\) | −81736.5 | − | 47190.6i | −0.224792 | − | 0.129784i | ||||
\(604\) | −25691.3 | + | 14832.9i | −0.0704226 | + | 0.0406585i | ||||
\(605\) | 46129.7 | − | 79898.9i | 0.126029 | − | 0.218288i | ||||
\(606\) | −89067.4 | + | 154269.i | −0.242535 | + | 0.420082i | ||||
\(607\) | 61013.6i | 0.165596i | 0.996566 | + | 0.0827979i | \(0.0263856\pi\) | ||||
−0.996566 | + | 0.0827979i | \(0.973614\pi\) | |||||||
\(608\) | 55717.7 | + | 34145.3i | 0.150725 | + | 0.0923685i | ||||
\(609\) | 579453. | 1.56237 | ||||||||
\(610\) | −59535.9 | − | 34373.1i | −0.160000 | − | 0.0923759i | ||||
\(611\) | 958500. | + | 553390.i | 2.56749 | + | 1.48234i | ||||
\(612\) | 62749.1 | + | 108685.i | 0.167535 | + | 0.290178i | ||||
\(613\) | −38870.6 | + | 67325.8i | −0.103443 | + | 0.179168i | −0.913101 | − | 0.407734i | \(-0.866319\pi\) |
0.809658 | + | 0.586902i | \(0.199653\pi\) | |||||||
\(614\) | −88654.6 | − | 153554.i | −0.235161 | − | 0.407310i | ||||
\(615\) | 237058. | 0.626765 | ||||||||
\(616\) | − | 27122.8i | − | 0.0714782i | ||||||
\(617\) | −287267. | − | 497561.i | −0.754598 | − | 1.30700i | −0.945574 | − | 0.325408i | \(-0.894498\pi\) |
0.190976 | − | 0.981595i | \(-0.438835\pi\) | |||||||
\(618\) | 326703. | − | 188622.i | 0.855414 | − | 0.493874i | ||||
\(619\) | −127945. | −0.333921 | −0.166960 | − | 0.985964i | \(-0.553395\pi\) | ||||
−0.166960 | + | 0.985964i | \(0.553395\pi\) | |||||||
\(620\) | − | 14836.0i | − | 0.0385952i | ||||||
\(621\) | −187091. | + | 108017.i | −0.485144 | + | 0.280098i | ||||
\(622\) | −209339. | − | 120862.i | −0.541090 | − | 0.312398i | ||||
\(623\) | −209921. | + | 121198.i | −0.540854 | + | 0.312262i | ||||
\(624\) | −173366. | + | 300279.i | −0.445241 | + | 0.771180i | ||||
\(625\) | −147824. | + | 256038.i | −0.378429 | + | 0.655457i | ||||
\(626\) | 150433.i | 0.383879i | ||||||||
\(627\) | 6961.69 | − | 265660.i | 0.0177084 | − | 0.675758i | ||||
\(628\) | −29319.6 | −0.0743428 | ||||||||
\(629\) | 62588.9 | + | 36135.7i | 0.158196 | + | 0.0913346i | ||||
\(630\) | 103420. | + | 59709.6i | 0.260570 | + | 0.150440i | ||||
\(631\) | −299143. | − | 518131.i | −0.751312 | − | 1.30131i | −0.947187 | − | 0.320682i | \(-0.896088\pi\) |
0.195875 | − | 0.980629i | \(-0.437245\pi\) | |||||||
\(632\) | 978.917 | − | 1695.53i | 0.00245082 | − | 0.00424495i | ||||
\(633\) | 200087. | + | 346561.i | 0.499358 | + | 0.864913i | ||||
\(634\) | 39015.1 | 0.0970632 | ||||||||
\(635\) | 54960.6i | 0.136303i | ||||||||
\(636\) | −199184. | − | 344996.i | −0.492424 | − | 0.852904i | ||||
\(637\) | 447530. | − | 258381.i | 1.10292 | − | 0.636770i | ||||
\(638\) | 148938. | 0.365900 | ||||||||
\(639\) | 822155.i | 2.01350i | ||||||||
\(640\) | −9052.64 | + | 5226.54i | −0.0221012 | + | 0.0127601i | ||||
\(641\) | −554254. | − | 319999.i | −1.34894 | − | 0.778811i | −0.360841 | − | 0.932627i | \(-0.617510\pi\) |
−0.988099 | + | 0.153816i | \(0.950844\pi\) | |||||||
\(642\) | −219787. | + | 126894.i | −0.533251 | + | 0.307872i | ||||
\(643\) | 247974. | − | 429503.i | 0.599769 | − | 1.03883i | −0.393086 | − | 0.919502i | \(-0.628592\pi\) |
0.992855 | − | 0.119329i | \(-0.0380742\pi\) | |||||||
\(644\) | 10871.5 | − | 18830.0i | 0.0262130 | − | 0.0454023i | ||||
\(645\) | 368190.i | 0.885020i | ||||||||
\(646\) | −64902.0 | − | 39773.7i | −0.155522 | − | 0.0953084i | ||||
\(647\) | 191464. | 0.457383 | 0.228691 | − | 0.973499i | \(-0.426555\pi\) | ||||
0.228691 | + | 0.973499i | \(0.426555\pi\) | |||||||
\(648\) | 405127. | + | 233900.i | 0.964808 | + | 0.557032i | ||||
\(649\) | −95388.4 | − | 55072.5i | −0.226468 | − | 0.130751i | ||||
\(650\) | 257123. | + | 445350.i | 0.608575 | + | 1.05408i | ||||
\(651\) | 60957.8 | − | 105582.i | 0.143836 | − | 0.249131i | ||||
\(652\) | 66153.2 | + | 114581.i | 0.155616 | + | 0.269535i | ||||
\(653\) | −536161. | −1.25739 | −0.628693 | − | 0.777653i | \(-0.716410\pi\) | ||||
−0.628693 | + | 0.777653i | \(0.716410\pi\) | |||||||
\(654\) | 773166.i | 1.80766i | ||||||||
\(655\) | −43998.0 | − | 76206.8i | −0.102553 | − | 0.177628i | ||||
\(656\) | −106628. | + | 61561.6i | −0.247778 | + | 0.143055i | ||||
\(657\) | −983974. | −2.27957 | ||||||||
\(658\) | 274192.i | 0.633290i | ||||||||
\(659\) | 673164. | − | 388652.i | 1.55007 | − | 0.894931i | 0.551931 | − | 0.833890i | \(-0.313891\pi\) |
0.998135 | − | 0.0610412i | \(-0.0194421\pi\) | |||||||
\(660\) | 36814.5 | + | 21254.8i | 0.0845144 | + | 0.0487944i | ||||
\(661\) | 221097. | − | 127651.i | 0.506035 | − | 0.292159i | −0.225167 | − | 0.974320i | \(-0.572293\pi\) |
0.731202 | + | 0.682161i | \(0.238960\pi\) | |||||||
\(662\) | 47561.1 | − | 82378.3i | 0.108527 | − | 0.187973i | ||||
\(663\) | 201943. | − | 349776.i | 0.459412 | − | 0.795725i | ||||
\(664\) | 58548.2i | 0.132794i | ||||||||
\(665\) | −72407.8 | − | 1897.46i | −0.163735 | − | 0.00429072i | ||||
\(666\) | 576990. | 1.30083 | ||||||||
\(667\) | 103400. | + | 59697.7i | 0.232416 | + | 0.134186i | ||||
\(668\) | −234818. | − | 135572.i | −0.526234 | − | 0.303821i | ||||
\(669\) | 149902. | + | 259637.i | 0.334930 | + | 0.580116i | ||||
\(670\) | −4578.55 | + | 7930.28i | −0.0101995 | + | 0.0176660i | ||||
\(671\) | −72601.6 | − | 125750.i | −0.161251 | − | 0.279294i | ||||
\(672\) | −85898.8 | −0.190217 | ||||||||
\(673\) | − | 33852.4i | − | 0.0747412i | −0.999301 | − | 0.0373706i | \(-0.988102\pi\) | ||
0.999301 | − | 0.0373706i | \(-0.0118982\pi\) | |||||||
\(674\) | −147532. | − | 255532.i | −0.324762 | − | 0.562505i | ||||
\(675\) | 1.09622e6 | − | 632904.i | 2.40597 | − | 1.38909i | ||||
\(676\) | 577239. | 1.26317 | ||||||||
\(677\) | 5113.87i | 0.0111576i | 0.999984 | + | 0.00557882i | \(0.00177580\pi\) | ||||
−0.999984 | + | 0.00557882i | \(0.998224\pi\) | |||||||
\(678\) | 57473.9 | − | 33182.6i | 0.125029 | − | 0.0721856i | ||||
\(679\) | 261262. | + | 150840.i | 0.566680 | + | 0.327173i | ||||
\(680\) | 10544.9 | − | 6088.07i | 0.0228046 | − | 0.0131663i | ||||
\(681\) | −572925. | + | 992336.i | −1.23539 | + | 2.13976i | ||||
\(682\) | 15668.0 | − | 27137.8i | 0.0336857 | − | 0.0583454i | ||||
\(683\) | 654670.i | 1.40340i | 0.712473 | + | 0.701699i | \(0.247575\pi\) | ||||
−0.712473 | + | 0.701699i | \(0.752425\pi\) | |||||||
\(684\) | −607506. | − | 15919.8i | −1.29849 | − | 0.0340272i | ||||
\(685\) | −140863. | −0.300204 | ||||||||
\(686\) | 274350. | + | 158396.i | 0.582985 | + | 0.336587i | ||||
\(687\) | −695132. | − | 401335.i | −1.47283 | − | 0.850341i | ||||
\(688\) | −95615.3 | − | 165611.i | −0.202000 | − | 0.349874i | ||||
\(689\) | −462858. | + | 801693.i | −0.975010 | + | 1.68877i | ||||
\(690\) | 17038.9 | + | 29512.2i | 0.0357885 | + | 0.0619875i | ||||
\(691\) | −313533. | −0.656639 | −0.328319 | − | 0.944567i | \(-0.606482\pi\) | ||||
−0.328319 | + | 0.944567i | \(0.606482\pi\) | |||||||
\(692\) | − | 233293.i | − | 0.487180i | ||||||
\(693\) | 126117. | + | 218440.i | 0.262607 | + | 0.454848i | ||||
\(694\) | −127247. | + | 73466.3i | −0.264198 | + | 0.152535i | ||||
\(695\) | 177834. | 0.368168 | ||||||||
\(696\) | − | 471690.i | − | 0.973728i | ||||||
\(697\) | 124204. | − | 71709.3i | 0.255665 | − | 0.147608i | ||||
\(698\) | −367685. | − | 212283.i | −0.754685 | − | 0.435717i | ||||
\(699\) | 733767. | − | 423640.i | 1.50177 | − | 0.867048i | ||||
\(700\) | −63699.2 | + | 110330.i | −0.129998 | + | 0.225164i | ||||
\(701\) | 343918. | − | 595684.i | 0.699873 | − | 1.21222i | −0.268637 | − | 0.963241i | \(-0.586573\pi\) |
0.968510 | − | 0.248974i | \(-0.0800935\pi\) | |||||||
\(702\) | − | 1.98328e6i | − | 4.02449i | ||||||
\(703\) | −307561. | + | 166984.i | −0.622330 | + | 0.337882i | ||||
\(704\) | −22078.7 | −0.0445479 | ||||||||
\(705\) | −372167. | − | 214871.i | −0.748789 | − | 0.432314i | ||||
\(706\) | −414436. | − | 239275.i | −0.831472 | − | 0.480051i | ||||
\(707\) | 51275.0 | + | 88811.0i | 0.102581 | + | 0.177676i | ||||
\(708\) | −174416. | + | 302098.i | −0.347953 | + | 0.602672i | ||||
\(709\) | 192494. | + | 333410.i | 0.382935 | + | 0.663263i | 0.991480 | − | 0.130256i | \(-0.0415799\pi\) |
−0.608545 | + | 0.793519i | \(0.708247\pi\) | |||||||
\(710\) | 79767.6 | 0.158238 | ||||||||
\(711\) | 18207.2i | 0.0360167i | ||||||||
\(712\) | 98658.3 | + | 170881.i | 0.194614 | + | 0.337081i | ||||
\(713\) | 21755.0 | − | 12560.3i | 0.0427937 | − | 0.0247070i | ||||
\(714\) | 100058. | 0.196271 | ||||||||
\(715\) | − | 98782.9i | − | 0.193228i | ||||||
\(716\) | 79545.8 | − | 45925.8i | 0.155164 | − | 0.0895841i | ||||
\(717\) | 616238. | + | 355785.i | 1.19870 | + | 0.692069i | ||||
\(718\) | −256697. | + | 148204.i | −0.497934 | + | 0.287482i | ||||
\(719\) | 290675. | − | 503464.i | 0.562277 | − | 0.973892i | −0.435021 | − | 0.900421i | \(-0.643259\pi\) |
0.997297 | − | 0.0734714i | \(-0.0234078\pi\) | |||||||
\(720\) | 48605.1 | − | 84186.5i | 0.0937598 | − | 0.162397i | ||||
\(721\) | − | 217175.i | − | 0.417772i | ||||||
\(722\) | 328435. | − | 167330.i | 0.630049 | − | 0.320995i | ||||
\(723\) | −849711. | −1.62553 | ||||||||
\(724\) | 142228. | + | 82115.4i | 0.271336 | + | 0.156656i | ||||
\(725\) | −605848. | − | 349786.i | −1.15262 | − | 0.665468i | ||||
\(726\) | −308575. | − | 534467.i | −0.585447 | − | 1.01402i | ||||
\(727\) | 337400. | − | 584394.i | 0.638376 | − | 1.10570i | −0.347413 | − | 0.937712i | \(-0.612940\pi\) |
0.985789 | − | 0.167987i | \(-0.0537268\pi\) | |||||||
\(728\) | 99804.7 | + | 172867.i | 0.188317 | + | 0.326174i | ||||
\(729\) | −1.29517e6 | −2.43710 | ||||||||
\(730\) | 95467.6i | 0.179147i | ||||||||
\(731\) | 111376. | + | 192909.i | 0.208429 | + | 0.361010i | ||||
\(732\) | −398253. | + | 229932.i | −0.743254 | + | 0.429118i | ||||
\(733\) | 24253.2 | 0.0451400 | 0.0225700 | − | 0.999745i | \(-0.492815\pi\) | ||||
0.0225700 | + | 0.999745i | \(0.492815\pi\) | |||||||
\(734\) | 79673.8i | 0.147885i | ||||||||
\(735\) | −173767. | + | 100325.i | −0.321657 | + | 0.185709i | ||||
\(736\) | −15328.1 | − | 8849.66i | −0.0282964 | − | 0.0163370i | ||||
\(737\) | −16750.1 | + | 9670.66i | −0.0308377 | + | 0.0178042i | ||||
\(738\) | 572502. | − | 991603.i | 1.05115 | − | 1.82064i | ||||
\(739\) | −299357. | + | 518502.i | −0.548152 | + | 0.949427i | 0.450249 | + | 0.892903i | \(0.351335\pi\) |
−0.998401 | + | 0.0565243i | \(0.981998\pi\) | |||||||
\(740\) | − | 55981.0i | − | 0.102230i | ||||||
\(741\) | 933187. | + | 1.71880e6i | 1.69954 | + | 3.13031i | ||||
\(742\) | −229335. | −0.416546 | ||||||||
\(743\) | −934869. | − | 539747.i | −1.69345 | − | 0.977715i | −0.951694 | − | 0.307048i | \(-0.900659\pi\) |
−0.741759 | − | 0.670667i | \(-0.766008\pi\) | |||||||
\(744\) | −85946.4 | − | 49621.2i | −0.155268 | − | 0.0896440i | ||||
\(745\) | 133061. | + | 230469.i | 0.239739 | + | 0.415241i | ||||
\(746\) | −21506.3 | + | 37250.0i | −0.0386445 | + | 0.0669342i | ||||
\(747\) | −272239. | − | 471533.i | −0.487876 | − | 0.845027i | ||||
\(748\) | 25718.1 | 0.0459658 | ||||||||
\(749\) | 146103.i | 0.260432i | ||||||||
\(750\) | −208751. | − | 361568.i | −0.371114 | − | 0.642788i | ||||
\(751\) | −378044. | + | 218264.i | −0.670290 | + | 0.386992i | −0.796186 | − | 0.605051i | \(-0.793153\pi\) |
0.125897 | + | 0.992043i | \(0.459819\pi\) | |||||||
\(752\) | 223199. | 0.394691 | ||||||||
\(753\) | − | 1.48561e6i | − | 2.62008i | ||||||
\(754\) | −949250. | + | 548050.i | −1.66970 | + | 0.964001i | ||||
\(755\) | −23180.7 | − | 13383.4i | −0.0406660 | − | 0.0234786i | ||||
\(756\) | 425509. | − | 245668.i | 0.744501 | − | 0.429838i | ||||
\(757\) | −207037. | + | 358599.i | −0.361291 | + | 0.625774i | −0.988174 | − | 0.153340i | \(-0.950997\pi\) |
0.626883 | + | 0.779114i | \(0.284330\pi\) | |||||||
\(758\) | −67039.8 | + | 116116.i | −0.116680 | + | 0.202095i | ||||
\(759\) | 71978.0i | 0.124944i | ||||||||
\(760\) | −1544.58 | + | 58941.7i | −0.00267414 | + | 0.102046i | ||||
\(761\) | −165273. | −0.285386 | −0.142693 | − | 0.989767i | \(-0.545576\pi\) | ||||
−0.142693 | + | 0.989767i | \(0.545576\pi\) | |||||||
\(762\) | 318392. | + | 183824.i | 0.548343 | + | 0.316586i | ||||
\(763\) | 385470. | + | 222551.i | 0.662127 | + | 0.382279i | ||||
\(764\) | 32683.8 | + | 56609.9i | 0.0559945 | + | 0.0969853i | ||||
\(765\) | −56617.0 | + | 98063.6i | −0.0967441 | + | 0.167566i | ||||
\(766\) | −39541.2 | − | 68487.4i | −0.0673895 | − | 0.116722i | ||||
\(767\) | 810608. | 1.37791 | ||||||||
\(768\) | 69923.8i | 0.118550i | ||||||||
\(769\) | 32694.8 | + | 56629.0i | 0.0552873 | + | 0.0957604i | 0.892344 | − | 0.451355i | \(-0.149059\pi\) |
−0.837057 | + | 0.547115i | \(0.815726\pi\) | |||||||
\(770\) | 21193.6 | − | 12236.2i | 0.0357457 | − | 0.0206378i | ||||
\(771\) | 1.41916e6 | 2.38738 | ||||||||
\(772\) | 278292.i | 0.466945i | ||||||||
\(773\) | 423440. | − | 244473.i | 0.708652 | − | 0.409141i | −0.101910 | − | 0.994794i | \(-0.532495\pi\) |
0.810562 | + | 0.585653i | \(0.199162\pi\) | |||||||
\(774\) | 1.54012e6 | + | 889190.i | 2.57083 | + | 1.48427i | ||||
\(775\) | −127469. | + | 73594.2i | −0.212227 | + | 0.122529i | ||||
\(776\) | 122788. | − | 212674.i | 0.203906 | − | 0.353176i | ||||
\(777\) | 230014. | − | 398395.i | 0.380988 | − | 0.659891i | ||||
\(778\) | 670173.i | 1.10720i | ||||||||
\(779\) | −18193.1 | + | 694254.i | −0.0299800 | + | 1.14405i | ||||
\(780\) | −312848. | −0.514215 | ||||||||
\(781\) | 145910. | + | 84241.2i | 0.239212 | + | 0.138109i | ||||
\(782\) | 17854.7 | + | 10308.4i | 0.0291971 | + | 0.0168569i | ||||
\(783\) | 1.34902e6 | + | 2.33657e6i | 2.20036 | + | 3.81114i | ||||
\(784\) | 52106.5 | − | 90251.2i | 0.0847735 | − | 0.146832i | ||||
\(785\) | −13227.2 | − | 22910.2i | −0.0214649 | − | 0.0371783i | ||||
\(786\) | −588631. | −0.952793 | ||||||||
\(787\) | 377492.i | 0.609478i | 0.952436 | + | 0.304739i | \(0.0985693\pi\) | ||||
−0.952436 | + | 0.304739i | \(0.901431\pi\) | |||||||
\(788\) | 58872.2 | + | 101970.i | 0.0948109 | + | 0.164217i | ||||
\(789\) | 1.20725e6 | − | 697008.i | 1.93930 | − | 1.11965i | ||||
\(790\) | 1766.51 | 0.00283049 | ||||||||
\(791\) | − | 38205.6i | − | 0.0610625i | ||||||
\(792\) | 177816. | − | 102662.i | 0.283479 | − | 0.163666i | ||||
\(793\) | 925450. | + | 534309.i | 1.47166 | + | 0.849662i | ||||
\(794\) | −74222.9 | + | 42852.6i | −0.117733 | + | 0.0679730i | ||||
\(795\) | 179719. | − | 311282.i | 0.284354 | − | 0.492515i | ||||
\(796\) | 89762.9 | − | 155474.i | 0.141668 | − | 0.245376i | ||||
\(797\) | − | 981925.i | − | 1.54583i | −0.634509 | − | 0.772915i | \(-0.718798\pi\) | ||
0.634509 | − | 0.772915i | \(-0.281202\pi\) | |||||||
\(798\) | −253171. | + | 413119.i | −0.397564 | + | 0.648738i | ||||
\(799\) | −259991. | −0.407253 | ||||||||
\(800\) | 89811.6 | + | 51852.8i | 0.140331 | + | 0.0810199i | ||||
\(801\) | −1.58914e6 | − | 917489.i | −2.47683 | − | 1.43000i | ||||
\(802\) | 255237. | + | 442083.i | 0.396821 | + | 0.687314i | ||||
\(803\) | −100822. | + | 174628.i | −0.156359 | + | 0.270822i | ||||
\(804\) | 30627.3 | + | 53048.0i | 0.0473801 | + | 0.0820648i | ||||
\(805\) | 19618.2 | 0.0302738 | ||||||||
\(806\) | 230617.i | 0.354994i | ||||||||
\(807\) | −502933. | − | 871105.i | −0.772259 | − | 1.33759i | ||||
\(808\) | 72294.4 | − | 41739.2i | 0.110734 | − | 0.0639324i | ||||
\(809\) | −568713. | −0.868953 | −0.434477 | − | 0.900683i | \(-0.643067\pi\) | ||||
−0.434477 | + | 0.900683i | \(0.643067\pi\) | |||||||
\(810\) | 422085.i | 0.643325i | ||||||||
\(811\) | −413272. | + | 238603.i | −0.628340 | + | 0.362772i | −0.780109 | − | 0.625644i | \(-0.784836\pi\) |
0.151769 | + | 0.988416i | \(0.451503\pi\) | |||||||
\(812\) | −235166. | − | 135773.i | −0.356666 | − | 0.205921i | ||||
\(813\) | −1.32943e6 | + | 767549.i | −2.01134 | + | 1.16125i | ||||
\(814\) | 59120.6 | − | 102400.i | 0.0892258 | − | 0.154544i | ||||
\(815\) | −59688.4 | + | 103383.i | −0.0898618 | + | 0.155645i | ||||
\(816\) | − | 81449.9i | − | 0.122324i | ||||||
\(817\) | −1.07829e6 | − | 28256.9i | −1.61544 | − | 0.0423331i | ||||
\(818\) | 605501. | 0.904917 | ||||||||
\(819\) | −1.60760e6 | − | 928150.i | −2.39669 | − | 1.38373i | ||||
\(820\) | −96207.8 | − | 55545.6i | −0.143081 | − | 0.0826080i | ||||
\(821\) | −41062.7 | − | 71122.7i | −0.0609202 | − | 0.105517i | 0.833957 | − | 0.551830i | \(-0.186070\pi\) |
−0.894877 | + | 0.446313i | \(0.852737\pi\) | |||||||
\(822\) | −471138. | + | 816036.i | −0.697276 | + | 1.20772i | ||||
\(823\) | 224118. | + | 388185.i | 0.330886 | + | 0.573111i | 0.982686 | − | 0.185280i | \(-0.0593192\pi\) |
−0.651800 | + | 0.758391i | \(0.725986\pi\) | |||||||
\(824\) | −176786. | −0.260371 | ||||||||
\(825\) | − | 421740.i | − | 0.619636i | ||||||
\(826\) | 100409. | + | 173914.i | 0.147168 | + | 0.254903i | ||||
\(827\) | 132718. | − | 76624.6i | 0.194052 | − | 0.112036i | −0.399826 | − | 0.916591i | \(-0.630930\pi\) |
0.593878 | + | 0.804555i | \(0.297596\pi\) | |||||||
\(828\) | 164598. | 0.240084 | ||||||||
\(829\) | − | 260445.i | − | 0.378971i | −0.981884 | − | 0.189486i | \(-0.939318\pi\) | ||
0.981884 | − | 0.189486i | \(-0.0606820\pi\) | |||||||
\(830\) | −45749.3 | + | 26413.4i | −0.0664092 | + | 0.0383414i | ||||
\(831\) | 134347. | + | 77565.5i | 0.194548 | + | 0.112322i | ||||
\(832\) | 140718. | − | 81243.6i | 0.203284 | − | 0.117366i | ||||
\(833\) | −60695.6 | + | 105128.i | −0.0874717 | + | 0.151505i | ||||
\(834\) | 594793. | − | 1.03021e6i | 0.855133 | − | 1.48113i | ||||
\(835\) | − | 244647.i | − | 0.350887i | ||||||
\(836\) | −65072.7 | + | 106184.i | −0.0931079 | + | 0.151932i | ||||
\(837\) | 567659. | 0.810283 | ||||||||
\(838\) | 143159. | + | 82653.0i | 0.203860 | + | 0.117698i | ||||
\(839\) | −532352. | − | 307353.i | −0.756266 | − | 0.436630i | 0.0716874 | − | 0.997427i | \(-0.477162\pi\) |
−0.827954 | + | 0.560797i | \(0.810495\pi\) | |||||||
\(840\) | −38752.3 | − | 67120.9i | −0.0549210 | − | 0.0951260i | ||||
\(841\) | 391919. | − | 678824.i | 0.554121 | − | 0.959765i | ||||
\(842\) | −254619. | − | 441013.i | −0.359142 | − | 0.622053i | ||||
\(843\) | 936600. | 1.31795 | ||||||||
\(844\) | − | 187531.i | − | 0.263263i | ||||||
\(845\) | 260415. | + | 451051.i | 0.364714 | + | 0.631703i | ||||
\(846\) | −1.79759e6 | + | 1.03784e6i | −2.51159 | + | 1.45007i | ||||
\(847\) | −355286. | −0.495234 | ||||||||
\(848\) | 186685.i | 0.259607i | ||||||||
\(849\) | 2.24394e6 | − | 1.29554e6i | 3.11312 | − | 1.79736i | ||||
\(850\) | −104616. | − | 60400.0i | −0.144797 | − | 0.0835987i | ||||
\(851\) | 82088.7 | − | 47393.9i | 0.113351 | − | 0.0654431i | ||||
\(852\) | 266794. | − | 462101.i | 0.367534 | − | 0.636588i | ||||
\(853\) | −599487. | + | 1.03834e6i | −0.823914 | + | 1.42706i | 0.0788324 | + | 0.996888i | \(0.474881\pi\) |
−0.902746 | + | 0.430173i | \(0.858453\pi\) | |||||||
\(854\) | 264738.i | 0.362994i | ||||||||
\(855\) | −261629. | − | 481884.i | −0.357894 | − | 0.659189i | ||||
\(856\) | 118931. | 0.162311 | ||||||||
\(857\) | 1.04586e6 | + | 603829.i | 1.42401 | + | 0.822152i | 0.996639 | − | 0.0819247i | \(-0.0261067\pi\) |
0.427370 | + | 0.904077i | \(0.359440\pi\) | |||||||
\(858\) | −572259. | − | 330394.i | −0.777353 | − | 0.448805i | ||||
\(859\) | 362737. | + | 628279.i | 0.491593 | + | 0.851464i | 0.999953 | − | 0.00968062i | \(-0.00308148\pi\) |
−0.508360 | + | 0.861145i | \(0.669748\pi\) | |||||||
\(860\) | 86271.5 | − | 149427.i | 0.116646 | − | 0.202037i | ||||
\(861\) | −456449. | − | 790593.i | −0.615724 | − | 1.06647i | ||||
\(862\) | −1.04559e6 | −1.40717 | ||||||||
\(863\) | 392412.i | 0.526890i | 0.964674 | + | 0.263445i | \(0.0848588\pi\) | ||||
−0.964674 | + | 0.263445i | \(0.915141\pi\) | |||||||
\(864\) | −199980. | − | 346375.i | −0.267891 | − | 0.464001i | ||||
\(865\) | 182294. | − | 105247.i | 0.243635 | − | 0.140663i | ||||
\(866\) | 835184. | 1.11364 | ||||||||
\(867\) | − | 1.33093e6i | − | 1.77059i | ||||||
\(868\) | −49478.3 | + | 28566.3i | −0.0656712 | + | 0.0379153i | ||||
\(869\) | 3231.28 | + | 1865.58i | 0.00427893 | + | 0.00247044i | ||||
\(870\) | 368576. | − | 212797.i | 0.486954 | − | 0.281143i | ||||
\(871\) | 71170.9 | − | 123272.i | 0.0938137 | − | 0.162490i | ||||
\(872\) | 181162. | − | 313782.i | 0.238251 | − | 0.412663i | ||||
\(873\) | 2.28376e6i | 2.99656i | ||||||||
\(874\) | −87737.8 | + | 47635.6i | −0.114859 | + | 0.0623603i | ||||
\(875\) | −240351. | −0.313928 | ||||||||
\(876\) | 553053. | + | 319306.i | 0.720707 | + | 0.416100i | ||||
\(877\) | 206867. | + | 119435.i | 0.268962 | + | 0.155286i | 0.628416 | − | 0.777877i | \(-0.283704\pi\) |
−0.359454 | + | 0.933163i | \(0.617037\pi\) | |||||||
\(878\) | −273911. | − | 474427.i | −0.355320 | − | 0.615432i | ||||
\(879\) | −659593. | + | 1.14245e6i | −0.853687 | + | 1.47863i | ||||
\(880\) | −9960.53 | − | 17252.1i | −0.0128623 | − | 0.0222781i | ||||
\(881\) | −32790.7 | −0.0422472 | −0.0211236 | − | 0.999777i | \(-0.506724\pi\) | ||||
−0.0211236 | + | 0.999777i | \(0.506724\pi\) | |||||||
\(882\) | 969146.i | 1.24581i | ||||||||
\(883\) | −291560. | − | 504997.i | −0.373944 | − | 0.647691i | 0.616224 | − | 0.787571i | \(-0.288662\pi\) |
−0.990168 | + | 0.139880i | \(0.955328\pi\) | |||||||
\(884\) | −163914. | + | 94635.5i | −0.209754 | + | 0.121102i | ||||
\(885\) | −314744. | −0.401856 | ||||||||
\(886\) | − | 12193.6i | − | 0.0155334i | ||||||
\(887\) | 848389. | − | 489817.i | 1.07832 | − | 0.622568i | 0.147877 | − | 0.989006i | \(-0.452756\pi\) |
0.930443 | + | 0.366438i | \(0.119423\pi\) | |||||||
\(888\) | −324304. | − | 187237.i | −0.411269 | − | 0.237446i | ||||
\(889\) | 183295. | − | 105825.i | 0.231924 | − | 0.133901i | ||||
\(890\) | −89017.1 | + | 154182.i | −0.112381 | + | 0.194650i | ||||
\(891\) | −445757. | + | 772074.i | −0.561491 | + | 0.972531i | ||||
\(892\) | − | 140495.i | − | 0.176576i | ||||||
\(893\) | 657837. | − | 1.07345e6i | 0.824927 | − | 1.34610i | ||||
\(894\) | 1.78017e6 | 2.22734 | ||||||||
\(895\) | 71772.4 | + | 41437.8i | 0.0896007 | + | 0.0517310i | ||||
\(896\) | 34861.2 | + | 20127.1i | 0.0434237 | + | 0.0250707i | ||||
\(897\) | −264860. | − | 458750.i | −0.329178 | − | 0.570153i | ||||
\(898\) | 259350. | − | 449207.i | 0.321612 | − | 0.557049i | ||||
\(899\) | −156864. | − | 271696.i | −0.194090 | − | 0.336174i | ||||
\(900\) | −964426. | −1.19065 | ||||||||
\(901\) | − | 217457.i | − | 0.267870i | ||||||
\(902\) | −117322. | − | 203207.i | −0.144200 | − | 0.249762i | ||||
\(903\) | 1.22792e6 | − | 708941.i | 1.50590 | − | 0.869430i | ||||
\(904\) | −31100.3 | −0.0380564 | ||||||||
\(905\) | 148182.i | 0.180924i | ||||||||
\(906\) | −155062. | + | 89525.3i | −0.188908 | + | 0.109066i | ||||
\(907\) | 529497. | + | 305705.i | 0.643649 | + | 0.371611i | 0.786019 | − | 0.618202i | \(-0.212139\pi\) |
−0.142370 | + | 0.989814i | \(0.545472\pi\) | |||||||
\(908\) | 465033. | − | 268487.i | 0.564042 | − | 0.325650i | ||||
\(909\) | −388160. | + | 672313.i | −0.469768 | + | 0.813662i | ||||
\(910\) | −90051.5 | + | 155974.i | −0.108745 | + | 0.188351i | ||||
\(911\) | − | 992184.i | − | 1.19552i | −0.801676 | − | 0.597758i | \(-0.796058\pi\) | ||
0.801676 | − | 0.597758i | \(-0.203942\pi\) | |||||||
\(912\) | 336289. | + | 206087.i | 0.404318 | + | 0.247777i | ||||
\(913\) | −111579. | −0.133857 | ||||||||
\(914\) | −318318. | − | 183781.i | −0.381038 | − | 0.219992i | ||||
\(915\) | −359334. | − | 207462.i | −0.429197 | − | 0.247797i | ||||
\(916\) | 188075. | + | 325756.i | 0.224151 | + | 0.388241i | ||||
\(917\) | −169434. | + | 293468.i | −0.201494 | + | 0.348998i | ||||
\(918\) | 232944. | + | 403471.i | 0.276418 | + | 0.478770i | ||||
\(919\) | −1.24247e6 | −1.47115 | −0.735574 | − | 0.677444i | \(-0.763088\pi\) | ||||
−0.735574 | + | 0.677444i | \(0.763088\pi\) | |||||||
\(920\) | − | 15969.7i | − | 0.0188678i | ||||||
\(921\) | −535083. | − | 926792.i | −0.630815 | − | 1.09260i | ||||
\(922\) | 472907. | − | 273033.i | 0.556306 | − | 0.321183i | ||||
\(923\) | −1.23994e6 | −1.45545 | ||||||||
\(924\) | − | 163702.i | − | 0.191739i | ||||||
\(925\) | −480982. | + | 277695.i | −0.562141 | + | 0.324552i | ||||
\(926\) | 153783. | + | 88786.5i | 0.179344 | + | 0.103544i | ||||
\(927\) | 1.42379e6 | − | 822024.i | 1.65686 | − | 0.956589i | ||||
\(928\) | −110523. | + | 191431.i | −0.128338 | + | 0.222288i | ||||
\(929\) | −488587. | + | 846257.i | −0.566123 | + | 0.980553i | 0.430822 | + | 0.902437i | \(0.358224\pi\) |
−0.996944 | + | 0.0781159i | \(0.975110\pi\) | |||||||
\(930\) | − | 89544.0i | − | 0.103531i | ||||||
\(931\) | −280477. | − | 516598.i | −0.323592 | − | 0.596009i | ||||
\(932\) | −397056. | −0.457110 | ||||||||
\(933\) | −1.26348e6 | − | 729473.i | −1.45147 | − | 0.838004i | ||||
\(934\) | −703939. | − | 406419.i | −0.806940 | − | 0.465887i | ||||
\(935\) | 11602.4 | + | 20095.9i | 0.0132716 | + | 0.0229872i | ||||
\(936\) | −755538. | + | 1.30863e6i | −0.862391 | + | 1.49371i | ||||
\(937\) | −264931. | − | 458874.i | −0.301755 | − | 0.522655i | 0.674779 | − | 0.738020i | \(-0.264239\pi\) |
−0.976534 | + | 0.215366i | \(0.930906\pi\) | |||||||
\(938\) | 35263.5 | 0.0400793 | ||||||||
\(939\) | 907952.i | 1.02975i | ||||||||
\(940\) | 100694. | + | 174407.i | 0.113958 | + | 0.197382i | ||||
\(941\) | −212580. | + | 122733.i | −0.240073 | + | 0.138606i | −0.615210 | − | 0.788363i | \(-0.710929\pi\) |
0.375137 | + | 0.926969i | \(0.377596\pi\) | |||||||
\(942\) | −176961. | −0.199424 | ||||||||
\(943\) | − | 188101.i | − | 0.211528i | ||||||
\(944\) | 141570. | − | 81735.8i | 0.158865 | − | 0.0917209i | ||||
\(945\) | 383927. | + | 221660.i | 0.429917 | + | 0.248213i | ||||
\(946\) | 315614. | − | 182220.i | 0.352674 | − | 0.203617i | ||||
\(947\) | −630689. | + | 1.09239e6i | −0.703259 | + | 1.21808i | 0.264057 | + | 0.964507i | \(0.414939\pi\) |
−0.967316 | + | 0.253574i | \(0.918394\pi\) | |||||||
\(948\) | 5908.35 | − | 10233.6i | 0.00657430 | − | 0.0113870i | ||||
\(949\) | − | 1.48399e6i | − | 1.64777i | ||||||
\(950\) | 514082. | − | 279111.i | 0.569620 | − | 0.309264i | ||||
\(951\) | 235480. | 0.260371 | ||||||||
\(952\) | −40607.7 | − | 23444.8i | −0.0448058 | − | 0.0258686i | ||||
\(953\) | 1.01414e6 | + | 585517.i | 1.11664 | + | 0.644694i | 0.940542 | − | 0.339678i | \(-0.110318\pi\) |
0.176101 | + | 0.984372i | \(0.443652\pi\) | |||||||
\(954\) | −868052. | − | 1.50351e6i | −0.953782 | − | 1.65200i | ||||
\(955\) | −29489.8 | + | 51077.8i | −0.0323344 | + | 0.0560048i | ||||
\(956\) | −166730. | − | 288784.i | −0.182430 | − | 0.315979i | ||||
\(957\) | 898927. | 0.981523 | ||||||||
\(958\) | − | 1.02146e6i | − | 1.11299i | ||||||
\(959\) | 271229. | + | 469782.i | 0.294916 | + | 0.510809i | ||||
\(960\) | −54638.1 | + | 31545.3i | −0.0592861 | + | 0.0342289i | ||||
\(961\) | 857513. | 0.928526 | ||||||||
\(962\) | 870192.i | 0.940297i | ||||||||
\(963\) | −957841. | + | 553010.i | −1.03286 | + | 0.596321i | ||||
\(964\) | 344847. | + | 199098.i | 0.371085 | + | 0.214246i | ||||
\(965\) | −217456. | + | 125548.i | −0.233516 | + | 0.134820i | ||||
\(966\) | 65615.9 | − | 113650.i | 0.0703161 | − | 0.121791i | ||||
\(967\) | 545108. | − | 944154.i | 0.582947 | − | 1.00969i | −0.412181 | − | 0.911102i | \(-0.635233\pi\) |
0.995128 | − | 0.0985922i | \(-0.0314339\pi\) | |||||||
\(968\) | 289211.i | 0.308649i | ||||||||
\(969\) | −391722. | − | 240058.i | −0.417187 | − | 0.255664i | ||||
\(970\) | 221577. | 0.235494 | ||||||||
\(971\) | −384208. | − | 221823.i | −0.407500 | − | 0.235270i | 0.282215 | − | 0.959351i | \(-0.408931\pi\) |
−0.689715 | + | 0.724081i | \(0.742264\pi\) | |||||||
\(972\) | 1.20525e6 | + | 695853.i | 1.27569 | + | 0.736521i | ||||
\(973\) | −342415. | − | 593080.i | −0.361682 | − | 0.626452i | ||||
\(974\) | 243349. | − | 421493.i | 0.256515 | − | 0.444296i | ||||
\(975\) | 1.55189e6 | + | 2.68795e6i | 1.63249 | + | 2.82756i | ||||
\(976\) | 215503. | 0.226232 | ||||||||
\(977\) | − | 595953.i | − | 0.624343i | −0.950026 | − | 0.312171i | \(-0.898944\pi\) | ||
0.950026 | − | 0.312171i | \(-0.101056\pi\) | |||||||
\(978\) | 399274. | + | 691562.i | 0.417439 | + | 0.723025i | ||||
\(979\) | −325658. | + | 188019.i | −0.339779 | + | 0.196172i | ||||
\(980\) | 94029.0 | 0.0979061 | ||||||||
\(981\) | 3.36949e6i | 3.50128i | ||||||||
\(982\) | −275849. | + | 159262.i | −0.286055 | + | 0.165154i | ||||
\(983\) | −1.43473e6 | − | 828341.i | −1.48478 | − | 0.857239i | −0.484932 | − | 0.874552i | \(-0.661156\pi\) |
−0.999850 | + | 0.0173125i | \(0.994489\pi\) | |||||||
\(984\) | −643563. | + | 371561.i | −0.664662 | + | 0.383743i | ||||
\(985\) | −53119.0 | + | 92004.9i | −0.0547492 | + | 0.0948284i | ||||
\(986\) | 128741. | − | 222986.i | 0.132423 | − | 0.229363i | ||||
\(987\) | 1.65491e6i | 1.69879i | ||||||||
\(988\) | 24009.6 | − | 916214.i | 0.0245964 | − | 0.938606i | ||||
\(989\) | 292152. | 0.298687 | ||||||||
\(990\) | 160439. | + | 92629.6i | 0.163697 | + | 0.0945103i | ||||
\(991\) | 325512. | + | 187934.i | 0.331451 | + | 0.191363i | 0.656485 | − | 0.754339i | \(-0.272042\pi\) |
−0.325034 | + | 0.945702i | \(0.605376\pi\) | |||||||
\(992\) | 23253.7 | + | 40276.6i | 0.0236303 | + | 0.0409288i | ||||
\(993\) | 287060. | − | 497202.i | 0.291121 | − | 0.504236i | ||||
\(994\) | −153590. | − | 266026.i | −0.155450 | − | 0.269247i | ||||
\(995\) | 161982. | 0.163614 | ||||||||
\(996\) | 353374.i | 0.356218i | ||||||||
\(997\) | 900453. | + | 1.55963e6i | 0.905880 | + | 1.56903i | 0.819732 | + | 0.572747i | \(0.194122\pi\) |
0.0861476 | + | 0.996282i | \(0.472544\pi\) | |||||||
\(998\) | 322802. | − | 186370.i | 0.324097 | − | 0.187118i | ||||
\(999\) | 2.14196e6 | 2.14625 |
(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 | 38.5.d.a.27.1 | ✓ | 16 | |
3.2 | odd | 2 | 342.5.m.c.217.7 | 16 | |||
4.3 | odd | 2 | 304.5.r.c.65.8 | 16 | |||
19.12 | odd | 6 | inner | 38.5.d.a.31.1 | yes | 16 | |
57.50 | even | 6 | 342.5.m.c.145.7 | 16 | |||
76.31 | even | 6 | 304.5.r.c.145.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.5.d.a.27.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
38.5.d.a.31.1 | yes | 16 | 19.12 | odd | 6 | inner | |
304.5.r.c.65.8 | 16 | 4.3 | odd | 2 | |||
304.5.r.c.145.8 | 16 | 76.31 | even | 6 | |||
342.5.m.c.145.7 | 16 | 57.50 | even | 6 | |||
342.5.m.c.217.7 | 16 | 3.2 | odd | 2 |