Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [38,4,Mod(7,38)]
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([2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("38.7");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 38.c (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: | \(2.24207258022\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 64x^{4} + 33x^{3} + 3984x^{2} - 945x + 225 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 11.1 | ||
Root | \(-3.78825 - 6.56144i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 38.11 |
Dual form | 38.4.c.c.7.1 |
$q$-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 \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).
\(n\) | \(21\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.73205i | 0.353553 | − | 0.612372i | ||||
\(3\) | −4.78825 | + | 8.29349i | −0.921499 | + | 1.59608i | −0.124402 | + | 0.992232i | \(0.539701\pi\) |
−0.797097 | + | 0.603851i | \(0.793632\pi\) | |||||||
\(4\) | −2.00000 | − | 3.46410i | −0.250000 | − | 0.433013i | ||||
\(5\) | −7.88908 | + | 13.6643i | −0.705620 | + | 1.22217i | 0.260847 | + | 0.965380i | \(0.415998\pi\) |
−0.966467 | + | 0.256790i | \(0.917335\pi\) | |||||||
\(6\) | 9.57650 | + | 16.5870i | 0.651598 | + | 1.12860i | ||||
\(7\) | 16.5765 | 0.895047 | 0.447523 | − | 0.894272i | \(-0.352306\pi\) | ||||
0.447523 | + | 0.894272i | \(0.352306\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | −32.3546 | − | 56.0399i | −1.19832 | − | 2.07555i | ||||
\(10\) | 15.7782 | + | 27.3286i | 0.498949 | + | 0.864205i | ||||
\(11\) | 16.0285 | 0.439342 | 0.219671 | − | 0.975574i | \(-0.429502\pi\) | ||||
0.219671 | + | 0.975574i | \(0.429502\pi\) | |||||||
\(12\) | 38.3060 | 0.921499 | ||||||||
\(13\) | 33.5522 | + | 58.1141i | 0.715823 | + | 1.23984i | 0.962641 | + | 0.270780i | \(0.0872815\pi\) |
−0.246818 | + | 0.969062i | \(0.579385\pi\) | |||||||
\(14\) | 16.5765 | − | 28.7113i | 0.316447 | − | 0.548102i | ||||
\(15\) | −75.5497 | − | 130.856i | −1.30046 | − | 2.25246i | ||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | −19.8025 | + | 34.2989i | −0.282518 | + | 0.489336i | −0.972004 | − | 0.234963i | \(-0.924503\pi\) |
0.689486 | + | 0.724299i | \(0.257836\pi\) | |||||||
\(18\) | −129.419 | −1.69468 | ||||||||
\(19\) | 14.7639 | − | 81.4925i | 0.178267 | − | 0.983982i | ||||
\(20\) | 63.1126 | 0.705620 | ||||||||
\(21\) | −79.3724 | + | 137.477i | −0.824785 | + | 1.42857i | ||||
\(22\) | 16.0285 | − | 27.7621i | 0.155331 | − | 0.269041i | ||||
\(23\) | 23.8404 | + | 41.2928i | 0.216133 | + | 0.374354i | 0.953623 | − | 0.301005i | \(-0.0973220\pi\) |
−0.737489 | + | 0.675359i | \(0.763989\pi\) | |||||||
\(24\) | 38.3060 | − | 66.3479i | 0.325799 | − | 0.564301i | ||||
\(25\) | −61.9750 | − | 107.344i | −0.495800 | − | 0.858751i | ||||
\(26\) | 134.209 | 1.01233 | ||||||||
\(27\) | 361.123 | 2.57401 | ||||||||
\(28\) | −33.1530 | − | 57.4227i | −0.223762 | − | 0.387567i | ||||
\(29\) | 59.2021 | + | 102.541i | 0.379088 | + | 0.656600i | 0.990930 | − | 0.134381i | \(-0.0429045\pi\) |
−0.611842 | + | 0.790980i | \(0.709571\pi\) | |||||||
\(30\) | −302.199 | −1.83912 | ||||||||
\(31\) | 120.050 | 0.695533 | 0.347767 | − | 0.937581i | \(-0.386940\pi\) | ||||
0.347767 | + | 0.937581i | \(0.386940\pi\) | |||||||
\(32\) | 16.0000 | + | 27.7128i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −76.7483 | + | 132.932i | −0.404853 | + | 0.701227i | ||||
\(34\) | 39.6050 | + | 68.5978i | 0.199770 | + | 0.346013i | ||||
\(35\) | −130.773 | + | 226.506i | −0.631563 | + | 1.09390i | ||||
\(36\) | −129.419 | + | 224.160i | −0.599160 | + | 1.03778i | ||||
\(37\) | 22.0924 | 0.0981614 | 0.0490807 | − | 0.998795i | \(-0.484371\pi\) | ||||
0.0490807 | + | 0.998795i | \(0.484371\pi\) | |||||||
\(38\) | −126.385 | − | 107.064i | −0.539537 | − | 0.457056i | ||||
\(39\) | −642.624 | −2.63852 | ||||||||
\(40\) | 63.1126 | − | 109.314i | 0.249474 | − | 0.432102i | ||||
\(41\) | −54.5508 | + | 94.4847i | −0.207790 | + | 0.359903i | −0.951018 | − | 0.309135i | \(-0.899960\pi\) |
0.743228 | + | 0.669038i | \(0.233294\pi\) | |||||||
\(42\) | 158.745 | + | 274.954i | 0.583211 | + | 1.01015i | ||||
\(43\) | 180.312 | − | 312.310i | 0.639473 | − | 1.10760i | −0.346075 | − | 0.938207i | \(-0.612486\pi\) |
0.985548 | − | 0.169394i | \(-0.0541809\pi\) | |||||||
\(44\) | −32.0569 | − | 55.5242i | −0.109836 | − | 0.190241i | ||||
\(45\) | 1020.99 | 3.38224 | ||||||||
\(46\) | 95.3617 | 0.305659 | ||||||||
\(47\) | −96.4726 | − | 167.095i | −0.299404 | − | 0.518582i | 0.676596 | − | 0.736354i | \(-0.263454\pi\) |
−0.976000 | + | 0.217772i | \(0.930121\pi\) | |||||||
\(48\) | −76.6120 | − | 132.696i | −0.230375 | − | 0.399021i | ||||
\(49\) | −68.2197 | −0.198891 | ||||||||
\(50\) | −247.900 | −0.701168 | ||||||||
\(51\) | −189.638 | − | 328.463i | −0.520680 | − | 0.901845i | ||||
\(52\) | 134.209 | − | 232.456i | 0.357911 | − | 0.619921i | ||||
\(53\) | −108.922 | − | 188.659i | −0.282294 | − | 0.488948i | 0.689655 | − | 0.724138i | \(-0.257762\pi\) |
−0.971949 | + | 0.235190i | \(0.924429\pi\) | |||||||
\(54\) | 361.123 | − | 625.483i | 0.910048 | − | 1.57625i | ||||
\(55\) | −126.450 | + | 219.017i | −0.310009 | + | 0.536951i | ||||
\(56\) | −132.612 | −0.316447 | ||||||||
\(57\) | 605.164 | + | 512.651i | 1.40624 | + | 1.19127i | ||||
\(58\) | 236.808 | 0.536111 | ||||||||
\(59\) | −211.595 | + | 366.493i | −0.466903 | + | 0.808701i | −0.999285 | − | 0.0378039i | \(-0.987964\pi\) |
0.532382 | + | 0.846504i | \(0.321297\pi\) | |||||||
\(60\) | −302.199 | + | 523.424i | −0.650228 | + | 1.12623i | ||||
\(61\) | −281.960 | − | 488.369i | −0.591824 | − | 1.02507i | −0.993987 | − | 0.109501i | \(-0.965075\pi\) |
0.402162 | − | 0.915568i | \(-0.368259\pi\) | |||||||
\(62\) | 120.050 | − | 207.932i | 0.245908 | − | 0.425925i | ||||
\(63\) | −536.327 | − | 928.945i | −1.07255 | − | 1.85772i | ||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −1058.78 | −2.02040 | ||||||||
\(66\) | 153.497 | + | 265.864i | 0.286275 | + | 0.495842i | ||||
\(67\) | 471.426 | + | 816.534i | 0.859610 | + | 1.48889i | 0.872302 | + | 0.488968i | \(0.162627\pi\) |
−0.0126922 | + | 0.999919i | \(0.504040\pi\) | |||||||
\(68\) | 158.420 | 0.282518 | ||||||||
\(69\) | −456.615 | −0.796667 | ||||||||
\(70\) | 261.546 | + | 453.012i | 0.446583 | + | 0.773504i | ||||
\(71\) | 332.873 | − | 576.552i | 0.556404 | − | 0.963721i | −0.441388 | − | 0.897316i | \(-0.645514\pi\) |
0.997793 | − | 0.0664045i | \(-0.0211528\pi\) | |||||||
\(72\) | 258.837 | + | 448.319i | 0.423670 | + | 0.733818i | ||||
\(73\) | 93.4728 | − | 161.900i | 0.149865 | − | 0.259574i | −0.781312 | − | 0.624140i | \(-0.785449\pi\) |
0.931178 | + | 0.364566i | \(0.118783\pi\) | |||||||
\(74\) | 22.0924 | − | 38.2652i | 0.0347053 | − | 0.0601113i | ||||
\(75\) | 1187.01 | 1.82752 | ||||||||
\(76\) | −311.826 | + | 111.841i | −0.470644 | + | 0.168804i | ||||
\(77\) | 265.696 | 0.393232 | ||||||||
\(78\) | −642.624 | + | 1113.06i | −0.932858 | + | 1.61576i | ||||
\(79\) | 438.177 | − | 758.945i | 0.624035 | − | 1.08086i | −0.364692 | − | 0.931128i | \(-0.618826\pi\) |
0.988727 | − | 0.149732i | \(-0.0478410\pi\) | |||||||
\(80\) | −126.225 | − | 218.628i | −0.176405 | − | 0.305543i | ||||
\(81\) | −855.571 | + | 1481.89i | −1.17362 | + | 2.03277i | ||||
\(82\) | 109.102 | + | 188.969i | 0.146930 | + | 0.254490i | ||||
\(83\) | −476.297 | −0.629885 | −0.314942 | − | 0.949111i | \(-0.601985\pi\) | ||||
−0.314942 | + | 0.949111i | \(0.601985\pi\) | |||||||
\(84\) | 634.979 | 0.824785 | ||||||||
\(85\) | −312.447 | − | 541.173i | −0.398701 | − | 0.690570i | ||||
\(86\) | −360.624 | − | 624.620i | −0.452176 | − | 0.783192i | ||||
\(87\) | −1133.90 | −1.39732 | ||||||||
\(88\) | −128.228 | −0.155331 | ||||||||
\(89\) | 482.370 | + | 835.489i | 0.574507 | + | 0.995075i | 0.996095 | + | 0.0882878i | \(0.0281395\pi\) |
−0.421588 | + | 0.906787i | \(0.638527\pi\) | |||||||
\(90\) | 1020.99 | − | 1768.41i | 1.19580 | − | 2.07119i | ||||
\(91\) | 556.177 | + | 963.328i | 0.640695 | + | 1.10972i | ||||
\(92\) | 95.3617 | − | 165.171i | 0.108067 | − | 0.187177i | ||||
\(93\) | −574.827 | + | 995.629i | −0.640933 | + | 1.11013i | ||||
\(94\) | −385.890 | −0.423421 | ||||||||
\(95\) | 997.063 | + | 844.639i | 1.07680 | + | 0.912191i | ||||
\(96\) | −306.448 | −0.325799 | ||||||||
\(97\) | 792.961 | − | 1373.45i | 0.830031 | − | 1.43766i | −0.0679822 | − | 0.997687i | \(-0.521656\pi\) |
0.898013 | − | 0.439969i | \(-0.145011\pi\) | |||||||
\(98\) | −68.2197 | + | 118.160i | −0.0703187 | + | 0.121796i | ||||
\(99\) | −518.595 | − | 898.234i | −0.526473 | − | 0.911878i | ||||
\(100\) | −247.900 | + | 429.376i | −0.247900 | + | 0.429376i | ||||
\(101\) | 521.913 | + | 903.980i | 0.514181 | + | 0.890588i | 0.999865 | + | 0.0164532i | \(0.00523746\pi\) |
−0.485683 | + | 0.874135i | \(0.661429\pi\) | |||||||
\(102\) | −758.554 | −0.736353 | ||||||||
\(103\) | 1427.83 | 1.36591 | 0.682954 | − | 0.730461i | \(-0.260695\pi\) | ||||
0.682954 | + | 0.730461i | \(0.260695\pi\) | |||||||
\(104\) | −268.417 | − | 464.912i | −0.253082 | − | 0.438350i | ||||
\(105\) | −1252.35 | − | 2169.13i | −1.16397 | − | 2.01605i | ||||
\(106\) | −435.688 | −0.399225 | ||||||||
\(107\) | 500.924 | 0.452581 | 0.226290 | − | 0.974060i | \(-0.427340\pi\) | ||||
0.226290 | + | 0.974060i | \(0.427340\pi\) | |||||||
\(108\) | −722.246 | − | 1250.97i | −0.643501 | − | 1.11458i | ||||
\(109\) | −606.462 | + | 1050.42i | −0.532922 | + | 0.923048i | 0.466339 | + | 0.884606i | \(0.345573\pi\) |
−0.999261 | + | 0.0384417i | \(0.987761\pi\) | |||||||
\(110\) | 252.900 | + | 438.035i | 0.219209 | + | 0.379682i | ||||
\(111\) | −105.784 | + | 183.223i | −0.0904556 | + | 0.156674i | ||||
\(112\) | −132.612 | + | 229.691i | −0.111881 | + | 0.193783i | ||||
\(113\) | 738.956 | 0.615178 | 0.307589 | − | 0.951519i | \(-0.400478\pi\) | ||||
0.307589 | + | 0.951519i | \(0.400478\pi\) | |||||||
\(114\) | 1493.10 | − | 535.524i | 1.22668 | − | 0.439968i | ||||
\(115\) | −752.315 | −0.610033 | ||||||||
\(116\) | 236.808 | − | 410.164i | 0.189544 | − | 0.328300i | ||||
\(117\) | 2171.14 | − | 3760.52i | 1.71557 | − | 2.97145i | ||||
\(118\) | 423.190 | + | 732.986i | 0.330151 | + | 0.571838i | ||||
\(119\) | −328.256 | + | 568.556i | −0.252867 | + | 0.437978i | ||||
\(120\) | 604.398 | + | 1046.85i | 0.459781 | + | 0.796364i | ||||
\(121\) | −1074.09 | −0.806978 | ||||||||
\(122\) | −1127.84 | −0.836966 | ||||||||
\(123\) | −522.405 | − | 904.832i | −0.382957 | − | 0.663301i | ||||
\(124\) | −240.099 | − | 415.864i | −0.173883 | − | 0.301175i | ||||
\(125\) | −16.5658 | −0.0118535 | ||||||||
\(126\) | −2145.31 | −1.51682 | ||||||||
\(127\) | −119.454 | − | 206.900i | −0.0834632 | − | 0.144563i | 0.821272 | − | 0.570537i | \(-0.193265\pi\) |
−0.904735 | + | 0.425974i | \(0.859931\pi\) | |||||||
\(128\) | 64.0000 | − | 110.851i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 1726.76 | + | 2990.84i | 1.17855 | + | 2.04131i | ||||
\(130\) | −1058.78 | + | 1833.86i | −0.714318 | + | 1.23724i | ||||
\(131\) | −132.624 | + | 229.712i | −0.0884537 | + | 0.153206i | −0.906858 | − | 0.421437i | \(-0.861526\pi\) |
0.818404 | + | 0.574643i | \(0.194859\pi\) | |||||||
\(132\) | 613.986 | 0.404853 | ||||||||
\(133\) | 244.734 | − | 1350.86i | 0.159557 | − | 0.880710i | ||||
\(134\) | 1885.70 | 1.21567 | ||||||||
\(135\) | −2848.93 | + | 4934.49i | −1.81627 | + | 3.14587i | ||||
\(136\) | 158.420 | − | 274.391i | 0.0998852 | − | 0.173006i | ||||
\(137\) | −1219.22 | − | 2111.76i | −0.760331 | − | 1.31693i | −0.942680 | − | 0.333698i | \(-0.891703\pi\) |
0.182349 | − | 0.983234i | \(-0.441630\pi\) | |||||||
\(138\) | −456.615 | + | 790.881i | −0.281664 | + | 0.487857i | ||||
\(139\) | 183.397 | + | 317.653i | 0.111910 | + | 0.193835i | 0.916541 | − | 0.399942i | \(-0.130970\pi\) |
−0.804630 | + | 0.593776i | \(0.797636\pi\) | |||||||
\(140\) | 1046.19 | 0.631563 | ||||||||
\(141\) | 1847.74 | 1.10360 | ||||||||
\(142\) | −665.745 | − | 1153.10i | −0.393437 | − | 0.681453i | ||||
\(143\) | 537.790 | + | 931.479i | 0.314491 | + | 0.544715i | ||||
\(144\) | 1035.35 | 0.599160 | ||||||||
\(145\) | −1868.20 | −1.06997 | ||||||||
\(146\) | −186.946 | − | 323.799i | −0.105971 | − | 0.183547i | ||||
\(147\) | 326.653 | − | 565.780i | 0.183278 | − | 0.317447i | ||||
\(148\) | −44.1848 | − | 76.5304i | −0.0245403 | − | 0.0425051i | ||||
\(149\) | 1120.88 | − | 1941.42i | 0.616281 | − | 1.06743i | −0.373877 | − | 0.927478i | \(-0.621972\pi\) |
0.990158 | − | 0.139952i | \(-0.0446949\pi\) | |||||||
\(150\) | 1187.01 | − | 2055.96i | 0.646125 | − | 1.11912i | ||||
\(151\) | −638.195 | −0.343944 | −0.171972 | − | 0.985102i | \(-0.555014\pi\) | ||||
−0.171972 | + | 0.985102i | \(0.555014\pi\) | |||||||
\(152\) | −118.111 | + | 651.940i | −0.0630269 | + | 0.347890i | ||||
\(153\) | 2562.81 | 1.35419 | ||||||||
\(154\) | 265.696 | − | 460.199i | 0.139028 | − | 0.240804i | ||||
\(155\) | −947.080 | + | 1640.39i | −0.490782 | + | 0.850060i | ||||
\(156\) | 1285.25 | + | 2226.12i | 0.659630 | + | 1.14251i | ||||
\(157\) | −1063.00 | + | 1841.16i | −0.540358 | + | 0.935928i | 0.458525 | + | 0.888682i | \(0.348378\pi\) |
−0.998883 | + | 0.0472466i | \(0.984955\pi\) | |||||||
\(158\) | −876.354 | − | 1517.89i | −0.441259 | − | 0.764283i | ||||
\(159\) | 2086.18 | 1.04054 | ||||||||
\(160\) | −504.901 | −0.249474 | ||||||||
\(161\) | 395.191 | + | 684.490i | 0.193450 | + | 0.335064i | ||||
\(162\) | 1711.14 | + | 2963.79i | 0.829877 | + | 1.43739i | ||||
\(163\) | −160.043 | −0.0769053 | −0.0384526 | − | 0.999260i | \(-0.512243\pi\) | ||||
−0.0384526 | + | 0.999260i | \(0.512243\pi\) | |||||||
\(164\) | 436.406 | 0.207790 | ||||||||
\(165\) | −1210.95 | − | 2097.42i | −0.571346 | − | 0.989600i | ||||
\(166\) | −476.297 | + | 824.971i | −0.222698 | + | 0.385724i | ||||
\(167\) | −1051.08 | − | 1820.52i | −0.487036 | − | 0.843571i | 0.512853 | − | 0.858476i | \(-0.328589\pi\) |
−0.999889 | + | 0.0149055i | \(0.995255\pi\) | |||||||
\(168\) | 634.979 | − | 1099.82i | 0.291605 | − | 0.505075i | ||||
\(169\) | −1153.00 | + | 1997.05i | −0.524805 | + | 0.908988i | ||||
\(170\) | −1249.79 | −0.563848 | ||||||||
\(171\) | −5044.51 | + | 1809.29i | −2.25593 | + | 0.809123i | ||||
\(172\) | −1442.50 | −0.639473 | ||||||||
\(173\) | 202.732 | − | 351.142i | 0.0890949 | − | 0.154317i | −0.818034 | − | 0.575170i | \(-0.804936\pi\) |
0.907129 | + | 0.420853i | \(0.138269\pi\) | |||||||
\(174\) | −1133.90 | + | 1963.97i | −0.494026 | + | 0.855678i | ||||
\(175\) | −1027.33 | − | 1779.39i | −0.443764 | − | 0.768623i | ||||
\(176\) | −128.228 | + | 222.097i | −0.0549178 | + | 0.0951204i | ||||
\(177\) | −2026.34 | − | 3509.72i | −0.860502 | − | 1.49043i | ||||
\(178\) | 1929.48 | 0.812476 | ||||||||
\(179\) | −1628.76 | −0.680107 | −0.340053 | − | 0.940406i | \(-0.610445\pi\) | ||||
−0.340053 | + | 0.940406i | \(0.610445\pi\) | |||||||
\(180\) | −2041.99 | − | 3536.82i | −0.845559 | − | 1.46455i | ||||
\(181\) | −1418.42 | − | 2456.77i | −0.582487 | − | 1.00890i | −0.995184 | − | 0.0980291i | \(-0.968746\pi\) |
0.412696 | − | 0.910869i | \(-0.364587\pi\) | |||||||
\(182\) | 2224.71 | 0.906079 | ||||||||
\(183\) | 5400.38 | 2.18146 | ||||||||
\(184\) | −190.723 | − | 330.342i | −0.0764147 | − | 0.132354i | ||||
\(185\) | −174.289 | + | 301.877i | −0.0692647 | + | 0.119970i | ||||
\(186\) | 1149.65 | + | 1991.26i | 0.453208 | + | 0.784979i | ||||
\(187\) | −317.403 | + | 549.759i | −0.124122 | + | 0.214986i | ||||
\(188\) | −385.890 | + | 668.382i | −0.149702 | + | 0.259291i | ||||
\(189\) | 5986.15 | 2.30386 | ||||||||
\(190\) | 2460.02 | − | 882.324i | 0.939308 | − | 0.336898i | ||||
\(191\) | 3521.85 | 1.33420 | 0.667099 | − | 0.744969i | \(-0.267536\pi\) | ||||
0.667099 | + | 0.744969i | \(0.267536\pi\) | |||||||
\(192\) | −306.448 | + | 530.783i | −0.115187 | + | 0.199510i | ||||
\(193\) | −2367.70 | + | 4100.97i | −0.883060 | + | 1.52950i | −0.0351378 | + | 0.999382i | \(0.511187\pi\) |
−0.847922 | + | 0.530121i | \(0.822146\pi\) | |||||||
\(194\) | −1585.92 | − | 2746.90i | −0.586920 | − | 1.01658i | ||||
\(195\) | 5069.71 | − | 8781.00i | 1.86179 | − | 3.22472i | ||||
\(196\) | 136.439 | + | 236.320i | 0.0497228 | + | 0.0861225i | ||||
\(197\) | 2357.30 | 0.852541 | 0.426270 | − | 0.904596i | \(-0.359827\pi\) | ||||
0.426270 | + | 0.904596i | \(0.359827\pi\) | |||||||
\(198\) | −2074.38 | −0.744545 | ||||||||
\(199\) | −342.578 | − | 593.362i | −0.122034 | − | 0.211369i | 0.798536 | − | 0.601947i | \(-0.205608\pi\) |
−0.920570 | + | 0.390579i | \(0.872275\pi\) | |||||||
\(200\) | 495.800 | + | 858.751i | 0.175292 | + | 0.303614i | ||||
\(201\) | −9029.22 | −3.16852 | ||||||||
\(202\) | 2087.65 | 0.727162 | ||||||||
\(203\) | 981.363 | + | 1699.77i | 0.339301 | + | 0.587687i | ||||
\(204\) | −758.554 | + | 1313.85i | −0.260340 | + | 0.450922i | ||||
\(205\) | −860.710 | − | 1490.79i | −0.293242 | − | 0.507910i | ||||
\(206\) | 1427.83 | − | 2473.08i | 0.482922 | − | 0.836445i | ||||
\(207\) | 1542.70 | − | 2672.03i | 0.517994 | − | 0.897192i | ||||
\(208\) | −1073.67 | −0.357911 | ||||||||
\(209\) | 236.643 | − | 1306.20i | 0.0783203 | − | 0.432305i | ||||
\(210\) | −5009.40 | −1.64610 | ||||||||
\(211\) | 265.510 | − | 459.876i | 0.0866277 | − | 0.150044i | −0.819456 | − | 0.573142i | \(-0.805724\pi\) |
0.906084 | + | 0.423099i | \(0.139058\pi\) | |||||||
\(212\) | −435.688 | + | 754.634i | −0.141147 | + | 0.244474i | ||||
\(213\) | 3187.75 | + | 5521.35i | 1.02545 | + | 1.77613i | ||||
\(214\) | 500.924 | − | 867.626i | 0.160012 | − | 0.277148i | ||||
\(215\) | 2844.99 | + | 4927.67i | 0.902451 | + | 1.56309i | ||||
\(216\) | −2888.98 | −0.910048 | ||||||||
\(217\) | 1990.00 | 0.622535 | ||||||||
\(218\) | 1212.92 | + | 2100.84i | 0.376833 | + | 0.652693i | ||||
\(219\) | 895.142 | + | 1550.43i | 0.276201 | + | 0.478395i | ||||
\(220\) | 1011.60 | 0.310009 | ||||||||
\(221\) | −2657.66 | −0.808932 | ||||||||
\(222\) | 211.568 | + | 366.446i | 0.0639618 | + | 0.110785i | ||||
\(223\) | −2425.86 | + | 4201.71i | −0.728463 | + | 1.26174i | 0.229069 | + | 0.973410i | \(0.426432\pi\) |
−0.957533 | + | 0.288325i | \(0.906902\pi\) | |||||||
\(224\) | 265.224 | + | 459.381i | 0.0791117 | + | 0.137025i | ||||
\(225\) | −4010.36 | + | 6946.15i | −1.18826 | + | 2.05812i | ||||
\(226\) | 738.956 | − | 1279.91i | 0.217498 | − | 0.376718i | ||||
\(227\) | −3971.88 | −1.16134 | −0.580668 | − | 0.814141i | \(-0.697208\pi\) | ||||
−0.580668 | + | 0.814141i | \(0.697208\pi\) | |||||||
\(228\) | 565.546 | − | 3121.65i | 0.164273 | − | 0.906738i | ||||
\(229\) | −78.9844 | −0.0227923 | −0.0113961 | − | 0.999935i | \(-0.503628\pi\) | ||||
−0.0113961 | + | 0.999935i | \(0.503628\pi\) | |||||||
\(230\) | −752.315 | + | 1303.05i | −0.215679 | + | 0.373567i | ||||
\(231\) | −1272.22 | + | 2203.55i | −0.362363 | + | 0.627631i | ||||
\(232\) | −473.617 | − | 820.328i | −0.134028 | − | 0.232143i | ||||
\(233\) | 821.646 | − | 1423.13i | 0.231021 | − | 0.400140i | −0.727088 | − | 0.686544i | \(-0.759127\pi\) |
0.958109 | + | 0.286405i | \(0.0924601\pi\) | |||||||
\(234\) | −4342.27 | − | 7521.04i | −1.21309 | − | 2.10114i | ||||
\(235\) | 3044.32 | 0.845061 | ||||||||
\(236\) | 1692.76 | 0.466903 | ||||||||
\(237\) | 4196.20 | + | 7268.03i | 1.15009 | + | 1.99202i | ||||
\(238\) | 656.512 | + | 1137.11i | 0.178804 | + | 0.309697i | ||||
\(239\) | −6316.74 | −1.70961 | −0.854803 | − | 0.518952i | \(-0.826322\pi\) | ||||
−0.854803 | + | 0.518952i | \(0.826322\pi\) | |||||||
\(240\) | 2417.59 | 0.650228 | ||||||||
\(241\) | 1747.33 | + | 3026.46i | 0.467034 | + | 0.808927i | 0.999291 | − | 0.0376561i | \(-0.0119891\pi\) |
−0.532257 | + | 0.846583i | \(0.678656\pi\) | |||||||
\(242\) | −1074.09 | + | 1860.38i | −0.285310 | + | 0.494171i | ||||
\(243\) | −3318.21 | − | 5747.32i | −0.875982 | − | 1.51724i | ||||
\(244\) | −1127.84 | + | 1953.48i | −0.295912 | + | 0.512535i | ||||
\(245\) | 538.191 | − | 932.174i | 0.140342 | − | 0.243079i | ||||
\(246\) | −2089.62 | −0.541583 | ||||||||
\(247\) | 5231.22 | − | 1876.26i | 1.34759 | − | 0.483334i | ||||
\(248\) | −960.396 | −0.245908 | ||||||||
\(249\) | 2280.63 | − | 3950.17i | 0.580438 | − | 1.00535i | ||||
\(250\) | −16.5658 | + | 28.6928i | −0.00419086 | + | 0.00725878i | ||||
\(251\) | −1815.19 | − | 3143.99i | −0.456468 | − | 0.790626i | 0.542303 | − | 0.840183i | \(-0.317552\pi\) |
−0.998771 | + | 0.0495570i | \(0.984219\pi\) | |||||||
\(252\) | −2145.31 | + | 3715.78i | −0.536276 | + | 0.928858i | ||||
\(253\) | 382.125 | + | 661.860i | 0.0949566 | + | 0.164470i | ||||
\(254\) | −477.816 | −0.118035 | ||||||||
\(255\) | 5984.29 | 1.46961 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 774.708 | + | 1341.83i | 0.188035 | + | 0.325686i | 0.944595 | − | 0.328238i | \(-0.106455\pi\) |
−0.756560 | + | 0.653924i | \(0.773122\pi\) | |||||||
\(258\) | 6907.04 | 1.66672 | ||||||||
\(259\) | 366.215 | 0.0878590 | ||||||||
\(260\) | 2117.56 | + | 3667.73i | 0.505099 | + | 0.874857i | ||||
\(261\) | 3830.92 | − | 6635.36i | 0.908538 | − | 1.57363i | ||||
\(262\) | 265.249 | + | 459.424i | 0.0625462 | + | 0.108333i | ||||
\(263\) | 1904.91 | − | 3299.39i | 0.446622 | − | 0.773571i | −0.551542 | − | 0.834147i | \(-0.685960\pi\) |
0.998164 | + | 0.0605757i | \(0.0192937\pi\) | |||||||
\(264\) | 613.986 | − | 1063.46i | 0.143137 | − | 0.247921i | ||||
\(265\) | 3437.18 | 0.796771 | ||||||||
\(266\) | −2095.02 | − | 1774.75i | −0.482910 | − | 0.409087i | ||||
\(267\) | −9238.83 | −2.11763 | ||||||||
\(268\) | 1885.70 | − | 3266.13i | 0.429805 | − | 0.744444i | ||||
\(269\) | 1688.20 | − | 2924.05i | 0.382644 | − | 0.662759i | −0.608795 | − | 0.793328i | \(-0.708347\pi\) |
0.991439 | + | 0.130568i | \(0.0416801\pi\) | |||||||
\(270\) | 5697.85 | + | 9868.97i | 1.28430 | + | 2.22447i | ||||
\(271\) | 1762.75 | − | 3053.17i | 0.395127 | − | 0.684380i | −0.597991 | − | 0.801503i | \(-0.704034\pi\) |
0.993117 | + | 0.117123i | \(0.0373673\pi\) | |||||||
\(272\) | −316.840 | − | 548.782i | −0.0706295 | − | 0.122334i | ||||
\(273\) | −10652.5 | −2.36160 | ||||||||
\(274\) | −4876.90 | −1.07527 | ||||||||
\(275\) | −993.365 | − | 1720.56i | −0.217826 | − | 0.377286i | ||||
\(276\) | 913.231 | + | 1581.76i | 0.199167 | + | 0.344967i | ||||
\(277\) | 6557.88 | 1.42247 | 0.711236 | − | 0.702953i | \(-0.248136\pi\) | ||||
0.711236 | + | 0.702953i | \(0.248136\pi\) | |||||||
\(278\) | 733.589 | 0.158265 | ||||||||
\(279\) | −3884.16 | − | 6727.56i | −0.833472 | − | 1.44362i | ||||
\(280\) | 1046.19 | − | 1812.05i | 0.223291 | − | 0.386752i | ||||
\(281\) | −3943.90 | − | 6831.04i | −0.837272 | − | 1.45020i | −0.892167 | − | 0.451705i | \(-0.850816\pi\) |
0.0548952 | − | 0.998492i | \(-0.482518\pi\) | |||||||
\(282\) | 1847.74 | − | 3200.38i | 0.390182 | − | 0.675815i | ||||
\(283\) | −1036.37 | + | 1795.04i | −0.217687 | + | 0.377046i | −0.954101 | − | 0.299486i | \(-0.903185\pi\) |
0.736413 | + | 0.676532i | \(0.236518\pi\) | |||||||
\(284\) | −2662.98 | −0.556404 | ||||||||
\(285\) | −11779.2 | + | 4224.79i | −2.44821 | + | 0.878087i | ||||
\(286\) | 2151.16 | 0.444758 | ||||||||
\(287\) | −904.261 | + | 1566.23i | −0.185982 | + | 0.322130i | ||||
\(288\) | 1035.35 | − | 1793.28i | 0.211835 | − | 0.366909i | ||||
\(289\) | 1672.22 | + | 2896.38i | 0.340367 | + | 0.589533i | ||||
\(290\) | −1868.20 | + | 3235.82i | −0.378291 | + | 0.655219i | ||||
\(291\) | 7593.79 | + | 13152.8i | 1.52974 | + | 2.64960i | ||||
\(292\) | −747.782 | −0.149865 | ||||||||
\(293\) | −7820.84 | −1.55938 | −0.779690 | − | 0.626165i | \(-0.784624\pi\) | ||||
−0.779690 | + | 0.626165i | \(0.784624\pi\) | |||||||
\(294\) | −653.306 | − | 1131.56i | −0.129597 | − | 0.224469i | ||||
\(295\) | −3338.58 | − | 5782.58i | −0.658913 | − | 1.14127i | ||||
\(296\) | −176.739 | −0.0347053 | ||||||||
\(297\) | 5788.25 | 1.13087 | ||||||||
\(298\) | −2241.76 | − | 3882.84i | −0.435777 | − | 0.754787i | ||||
\(299\) | −1599.80 | + | 2770.93i | −0.309427 | + | 0.535943i | ||||
\(300\) | −2374.02 | − | 4111.91i | −0.456879 | − | 0.791338i | ||||
\(301\) | 2988.95 | − | 5177.00i | 0.572359 | − | 0.991354i | ||||
\(302\) | −638.195 | + | 1105.39i | −0.121603 | + | 0.210622i | ||||
\(303\) | −9996.20 | −1.89527 | ||||||||
\(304\) | 1011.08 | + | 856.515i | 0.190755 | + | 0.161594i | ||||
\(305\) | 8897.62 | 1.67041 | ||||||||
\(306\) | 2562.81 | − | 4438.92i | 0.478778 | − | 0.829268i | ||||
\(307\) | 2968.90 | − | 5142.28i | 0.551934 | − | 0.955978i | −0.446201 | − | 0.894933i | \(-0.647223\pi\) |
0.998135 | − | 0.0610453i | \(-0.0194434\pi\) | |||||||
\(308\) | −531.392 | − | 920.397i | −0.0983080 | − | 0.170274i | ||||
\(309\) | −6836.82 | + | 11841.7i | −1.25868 | + | 2.18010i | ||||
\(310\) | 1894.16 | + | 3280.78i | 0.347036 | + | 0.601083i | ||||
\(311\) | 1832.63 | 0.334145 | 0.167073 | − | 0.985945i | \(-0.446569\pi\) | ||||
0.167073 | + | 0.985945i | \(0.446569\pi\) | |||||||
\(312\) | 5141.00 | 0.932858 | ||||||||
\(313\) | 469.166 | + | 812.619i | 0.0847247 | + | 0.146747i | 0.905274 | − | 0.424828i | \(-0.139666\pi\) |
−0.820549 | + | 0.571576i | \(0.806332\pi\) | |||||||
\(314\) | 2125.99 | + | 3682.32i | 0.382091 | + | 0.661801i | ||||
\(315\) | 16924.5 | 3.02726 | ||||||||
\(316\) | −3505.42 | −0.624035 | ||||||||
\(317\) | 3705.73 | + | 6418.51i | 0.656576 | + | 1.13722i | 0.981496 | + | 0.191481i | \(0.0613292\pi\) |
−0.324920 | + | 0.945741i | \(0.605337\pi\) | |||||||
\(318\) | 2086.18 | − | 3613.38i | 0.367885 | − | 0.637195i | ||||
\(319\) | 948.919 | + | 1643.58i | 0.166549 | + | 0.288472i | ||||
\(320\) | −504.901 | + | 874.514i | −0.0882026 | + | 0.152771i | ||||
\(321\) | −2398.55 | + | 4154.41i | −0.417053 | + | 0.722357i | ||||
\(322\) | 1580.76 | 0.273579 | ||||||||
\(323\) | 2502.74 | + | 2120.14i | 0.431134 | + | 0.365225i | ||||
\(324\) | 6844.57 | 1.17362 | ||||||||
\(325\) | 4158.79 | − | 7203.24i | 0.709810 | − | 1.22943i | ||||
\(326\) | −160.043 | + | 277.203i | −0.0271901 | + | 0.0470947i | ||||
\(327\) | −5807.78 | − | 10059.4i | −0.982174 | − | 1.70117i | ||||
\(328\) | 436.406 | − | 755.878i | 0.0734649 | − | 0.127245i | ||||
\(329\) | −1599.18 | − | 2769.86i | −0.267980 | − | 0.464155i | ||||
\(330\) | −4843.78 | −0.808005 | ||||||||
\(331\) | −5412.69 | −0.898817 | −0.449408 | − | 0.893326i | \(-0.648365\pi\) | ||||
−0.449408 | + | 0.893326i | \(0.648365\pi\) | |||||||
\(332\) | 952.595 | + | 1649.94i | 0.157471 | + | 0.272748i | ||||
\(333\) | −714.792 | − | 1238.06i | −0.117629 | − | 0.203739i | ||||
\(334\) | −4204.32 | −0.688773 | ||||||||
\(335\) | −14876.5 | −2.42623 | ||||||||
\(336\) | −1269.96 | − | 2199.63i | −0.206196 | − | 0.357142i | ||||
\(337\) | −4636.79 | + | 8031.15i | −0.749501 | + | 1.29817i | 0.198561 | + | 0.980088i | \(0.436373\pi\) |
−0.948062 | + | 0.318085i | \(0.896960\pi\) | |||||||
\(338\) | 2305.99 | + | 3994.09i | 0.371093 | + | 0.642752i | ||||
\(339\) | −3538.31 | + | 6128.52i | −0.566886 | + | 0.981875i | ||||
\(340\) | −1249.79 | + | 2164.69i | −0.199351 | + | 0.345285i | ||||
\(341\) | 1924.21 | 0.305577 | ||||||||
\(342\) | −1910.73 | + | 10546.6i | −0.302106 | + | 1.66754i | ||||
\(343\) | −6816.58 | −1.07306 | ||||||||
\(344\) | −1442.50 | + | 2498.48i | −0.226088 | + | 0.391596i | ||||
\(345\) | 3602.27 | − | 6239.32i | 0.562145 | − | 0.973663i | ||||
\(346\) | −405.464 | − | 702.284i | −0.0629996 | − | 0.109119i | ||||
\(347\) | 4837.24 | − | 8378.35i | 0.748348 | − | 1.29618i | −0.200266 | − | 0.979741i | \(-0.564181\pi\) |
0.948614 | − | 0.316435i | \(-0.102486\pi\) | |||||||
\(348\) | 2267.79 | + | 3927.93i | 0.349329 | + | 0.605056i | ||||
\(349\) | 1300.56 | 0.199477 | 0.0997387 | − | 0.995014i | \(-0.468199\pi\) | ||||
0.0997387 | + | 0.995014i | \(0.468199\pi\) | |||||||
\(350\) | −4109.32 | −0.627578 | ||||||||
\(351\) | 12116.5 | + | 20986.3i | 1.84253 | + | 3.19136i | ||||
\(352\) | 256.455 | + | 444.194i | 0.0388327 | + | 0.0672603i | ||||
\(353\) | 11985.4 | 1.80713 | 0.903564 | − | 0.428454i | \(-0.140942\pi\) | ||||
0.903564 | + | 0.428454i | \(0.140942\pi\) | |||||||
\(354\) | −8105.35 | −1.21693 | ||||||||
\(355\) | 5252.11 | + | 9096.93i | 0.785221 | + | 1.36004i | ||||
\(356\) | 1929.48 | − | 3341.96i | 0.287253 | − | 0.497538i | ||||
\(357\) | −3143.54 | − | 5444.77i | −0.466033 | − | 0.807193i | ||||
\(358\) | −1628.76 | + | 2821.09i | −0.240454 | + | 0.416478i | ||||
\(359\) | 2203.95 | − | 3817.35i | 0.324011 | − | 0.561204i | −0.657301 | − | 0.753628i | \(-0.728302\pi\) |
0.981312 | + | 0.192425i | \(0.0616352\pi\) | |||||||
\(360\) | −8167.95 | −1.19580 | ||||||||
\(361\) | −6423.05 | − | 2406.30i | −0.936442 | − | 0.350823i | ||||
\(362\) | −5673.68 | −0.823762 | ||||||||
\(363\) | 5143.00 | − | 8907.94i | 0.743630 | − | 1.28800i | ||||
\(364\) | 2224.71 | − | 3853.31i | 0.320347 | − | 0.554858i | ||||
\(365\) | 1474.83 | + | 2554.48i | 0.211496 | + | 0.366322i | ||||
\(366\) | 5400.38 | − | 9353.73i | 0.771263 | − | 1.33587i | ||||
\(367\) | −3130.04 | − | 5421.39i | −0.445196 | − | 0.771102i | 0.552870 | − | 0.833267i | \(-0.313533\pi\) |
−0.998066 | + | 0.0621658i | \(0.980199\pi\) | |||||||
\(368\) | −762.893 | −0.108067 | ||||||||
\(369\) | 7059.88 | 0.995997 | ||||||||
\(370\) | 348.577 | + | 603.754i | 0.0489775 | + | 0.0848315i | ||||
\(371\) | −1805.55 | − | 3127.30i | −0.252667 | − | 0.437631i | ||||
\(372\) | 4598.62 | 0.640933 | ||||||||
\(373\) | −2745.24 | −0.381081 | −0.190541 | − | 0.981679i | \(-0.561024\pi\) | ||||
−0.190541 | + | 0.981679i | \(0.561024\pi\) | |||||||
\(374\) | 634.807 | + | 1099.52i | 0.0877676 | + | 0.152018i | ||||
\(375\) | 79.3212 | − | 137.388i | 0.0109230 | − | 0.0189192i | ||||
\(376\) | 771.781 | + | 1336.76i | 0.105855 | + | 0.183347i | ||||
\(377\) | −3972.72 | + | 6880.95i | −0.542720 | + | 0.940018i | ||||
\(378\) | 5986.15 | − | 10368.3i | 0.814536 | − | 1.41082i | ||||
\(379\) | 10772.3 | 1.45998 | 0.729992 | − | 0.683455i | \(-0.239524\pi\) | ||||
0.729992 | + | 0.683455i | \(0.239524\pi\) | |||||||
\(380\) | 931.789 | − | 5143.20i | 0.125789 | − | 0.694318i | ||||
\(381\) | 2287.90 | 0.307645 | ||||||||
\(382\) | 3521.85 | − | 6100.02i | 0.471711 | − | 0.817027i | ||||
\(383\) | 1689.97 | − | 2927.12i | 0.225466 | − | 0.390519i | −0.730993 | − | 0.682385i | \(-0.760943\pi\) |
0.956459 | + | 0.291866i | \(0.0942761\pi\) | |||||||
\(384\) | 612.896 | + | 1061.57i | 0.0814498 | + | 0.141075i | ||||
\(385\) | −2096.09 | + | 3630.54i | −0.277472 | + | 0.480596i | ||||
\(386\) | 4735.39 | + | 8201.94i | 0.624417 | + | 1.08152i | ||||
\(387\) | −23335.8 | −3.06518 | ||||||||
\(388\) | −6343.69 | −0.830031 | ||||||||
\(389\) | −2351.28 | − | 4072.54i | −0.306464 | − | 0.530812i | 0.671122 | − | 0.741347i | \(-0.265813\pi\) |
−0.977586 | + | 0.210535i | \(0.932479\pi\) | |||||||
\(390\) | −10139.4 | − | 17562.0i | −1.31649 | − | 2.28022i | ||||
\(391\) | −1888.40 | −0.244246 | ||||||||
\(392\) | 545.758 | 0.0703187 | ||||||||
\(393\) | −1270.08 | − | 2199.84i | −0.163020 | − | 0.282359i | ||||
\(394\) | 2357.30 | − | 4082.96i | 0.301419 | − | 0.522073i | ||||
\(395\) | 6913.62 | + | 11974.7i | 0.880663 | + | 1.52535i | ||||
\(396\) | −2074.38 | + | 3592.93i | −0.263236 | + | 0.455939i | ||||
\(397\) | −125.749 | + | 217.804i | −0.0158972 | + | 0.0275347i | −0.873865 | − | 0.486169i | \(-0.838394\pi\) |
0.857967 | + | 0.513704i | \(0.171727\pi\) | |||||||
\(398\) | −1370.31 | −0.172582 | ||||||||
\(399\) | 10031.5 | + | 8497.95i | 1.25865 | + | 1.06624i | ||||
\(400\) | 1983.20 | 0.247900 | ||||||||
\(401\) | 3225.16 | − | 5586.15i | 0.401638 | − | 0.695658i | −0.592285 | − | 0.805728i | \(-0.701774\pi\) |
0.993924 | + | 0.110070i | \(0.0351075\pi\) | |||||||
\(402\) | −9029.22 | + | 15639.1i | −1.12024 | + | 1.94031i | ||||
\(403\) | 4027.92 | + | 6976.56i | 0.497879 | + | 0.862351i | ||||
\(404\) | 2087.65 | − | 3615.92i | 0.257091 | − | 0.445294i | ||||
\(405\) | −13499.3 | − | 23381.5i | −1.65626 | − | 2.86873i | ||||
\(406\) | 3925.45 | 0.479845 | ||||||||
\(407\) | 354.108 | 0.0431264 | ||||||||
\(408\) | 1517.11 | + | 2627.71i | 0.184088 | + | 0.318850i | ||||
\(409\) | −1007.96 | − | 1745.84i | −0.121859 | − | 0.211066i | 0.798642 | − | 0.601807i | \(-0.205552\pi\) |
−0.920501 | + | 0.390741i | \(0.872219\pi\) | |||||||
\(410\) | −3442.84 | −0.414707 | ||||||||
\(411\) | 23351.8 | 2.80258 | ||||||||
\(412\) | −2855.67 | − | 4946.16i | −0.341477 | − | 0.591456i | ||||
\(413\) | −3507.50 | + | 6075.17i | −0.417900 | + | 0.723825i | ||||
\(414\) | −3085.39 | − | 5344.06i | −0.366277 | − | 0.634411i | ||||
\(415\) | 3757.55 | − | 6508.26i | 0.444460 | − | 0.769827i | ||||
\(416\) | −1073.67 | + | 1859.65i | −0.126541 | + | 0.219175i | ||||
\(417\) | −3512.61 | −0.412501 | ||||||||
\(418\) | −2025.76 | − | 1716.08i | −0.237041 | − | 0.200804i | ||||
\(419\) | −10124.5 | −1.18046 | −0.590232 | − | 0.807234i | \(-0.700964\pi\) | ||||
−0.590232 | + | 0.807234i | \(0.700964\pi\) | |||||||
\(420\) | −5009.40 | + | 8676.53i | −0.581985 | + | 1.00803i | ||||
\(421\) | −1573.13 | + | 2724.75i | −0.182114 | + | 0.315430i | −0.942600 | − | 0.333924i | \(-0.891627\pi\) |
0.760487 | + | 0.649354i | \(0.224961\pi\) | |||||||
\(422\) | −531.020 | − | 919.753i | −0.0612550 | − | 0.106097i | ||||
\(423\) | −6242.67 | + | 10812.6i | −0.717563 | + | 1.24286i | ||||
\(424\) | 871.377 | + | 1509.27i | 0.0998061 | + | 0.172869i | ||||
\(425\) | 4909.04 | 0.560290 | ||||||||
\(426\) | 12751.0 | 1.45021 | ||||||||
\(427\) | −4673.91 | − | 8095.45i | −0.529710 | − | 0.917485i | ||||
\(428\) | −1001.85 | − | 1735.25i | −0.113145 | − | 0.195973i | ||||
\(429\) | −10300.3 | −1.15921 | ||||||||
\(430\) | 11380.0 | 1.27626 | ||||||||
\(431\) | −5831.16 | − | 10099.9i | −0.651687 | − | 1.12875i | −0.982713 | − | 0.185133i | \(-0.940728\pi\) |
0.331027 | − | 0.943621i | \(-0.392605\pi\) | |||||||
\(432\) | −2888.98 | + | 5003.87i | −0.321751 | + | 0.557289i | ||||
\(433\) | 4484.52 | + | 7767.42i | 0.497719 | + | 0.862074i | 0.999997 | − | 0.00263209i | \(-0.000837820\pi\) |
−0.502278 | + | 0.864706i | \(0.667504\pi\) | |||||||
\(434\) | 1990.00 | − | 3446.78i | 0.220099 | − | 0.381223i | ||||
\(435\) | 8945.40 | − | 15493.9i | 0.985975 | − | 1.70776i | ||||
\(436\) | 4851.69 | 0.532922 | ||||||||
\(437\) | 3717.03 | − | 1333.17i | 0.406887 | − | 0.145936i | ||||
\(438\) | 3580.57 | 0.390608 | ||||||||
\(439\) | −49.1536 | + | 85.1366i | −0.00534391 | + | 0.00925592i | −0.868685 | − | 0.495365i | \(-0.835034\pi\) |
0.863341 | + | 0.504621i | \(0.168368\pi\) | |||||||
\(440\) | 1011.60 | − | 1752.14i | 0.109605 | − | 0.189841i | ||||
\(441\) | 2207.23 | + | 3823.03i | 0.238336 | + | 0.412809i | ||||
\(442\) | −2657.66 | + | 4603.21i | −0.286000 | + | 0.495367i | ||||
\(443\) | 4660.23 | + | 8071.75i | 0.499806 | + | 0.865690i | 1.00000 | 0.000223670i | \(-7.11963e-5\pi\) | |
−0.500194 | + | 0.865914i | \(0.666738\pi\) | |||||||
\(444\) | 846.272 | 0.0904556 | ||||||||
\(445\) | −15221.8 | −1.62154 | ||||||||
\(446\) | 4851.71 | + | 8403.41i | 0.515101 | + | 0.892182i | ||||
\(447\) | 10734.1 | + | 18592.0i | 1.13580 | + | 1.96727i | ||||
\(448\) | 1060.90 | 0.111881 | ||||||||
\(449\) | 9992.53 | 1.05028 | 0.525141 | − | 0.851015i | \(-0.324013\pi\) | ||||
0.525141 | + | 0.851015i | \(0.324013\pi\) | |||||||
\(450\) | 8020.72 | + | 13892.3i | 0.840223 | + | 1.45531i | ||||
\(451\) | −874.365 | + | 1514.44i | −0.0912910 | + | 0.158121i | ||||
\(452\) | −1477.91 | − | 2559.82i | −0.153795 | − | 0.266380i | ||||
\(453\) | 3055.84 | − | 5292.86i | 0.316944 | − | 0.548963i | ||||
\(454\) | −3971.88 | + | 6879.50i | −0.410594 | + | 0.711170i | ||||
\(455\) | −17550.9 | −1.80835 | ||||||||
\(456\) | −4841.31 | − | 4101.21i | −0.497182 | − | 0.421177i | ||||
\(457\) | −1536.89 | −0.157314 | −0.0786572 | − | 0.996902i | \(-0.525063\pi\) | ||||
−0.0786572 | + | 0.996902i | \(0.525063\pi\) | |||||||
\(458\) | −78.9844 | + | 136.805i | −0.00805829 | + | 0.0139574i | ||||
\(459\) | −7151.13 | + | 12386.1i | −0.727203 | + | 1.25955i | ||||
\(460\) | 1504.63 | + | 2606.10i | 0.152508 | + | 0.264152i | ||||
\(461\) | 8312.46 | − | 14397.6i | 0.839804 | − | 1.45458i | −0.0502537 | − | 0.998736i | \(-0.516003\pi\) |
0.890058 | − | 0.455847i | \(-0.150664\pi\) | |||||||
\(462\) | 2544.44 | + | 4407.09i | 0.256229 | + | 0.443802i | ||||
\(463\) | 7191.48 | 0.721850 | 0.360925 | − | 0.932595i | \(-0.382461\pi\) | ||||
0.360925 | + | 0.932595i | \(0.382461\pi\) | |||||||
\(464\) | −1894.47 | −0.189544 | ||||||||
\(465\) | −9069.71 | − | 15709.2i | −0.904511 | − | 1.56666i | ||||
\(466\) | −1643.29 | − | 2846.27i | −0.163356 | − | 0.282942i | ||||
\(467\) | −7001.51 | −0.693772 | −0.346886 | − | 0.937907i | \(-0.612761\pi\) | ||||
−0.346886 | + | 0.937907i | \(0.612761\pi\) | |||||||
\(468\) | −17369.1 | −1.71557 | ||||||||
\(469\) | 7814.59 | + | 13535.3i | 0.769391 | + | 1.33262i | ||||
\(470\) | 3044.32 | − | 5272.91i | 0.298774 | − | 0.517492i | ||||
\(471\) | −10179.8 | − | 17631.9i | −0.995879 | − | 1.72491i | ||||
\(472\) | 1692.76 | − | 2931.94i | 0.165075 | − | 0.285919i | ||||
\(473\) | 2890.13 | − | 5005.85i | 0.280948 | − | 0.486616i | ||||
\(474\) | 16784.8 | 1.62648 | ||||||||
\(475\) | −9662.72 | + | 3465.68i | −0.933381 | + | 0.334772i | ||||
\(476\) | 2626.05 | 0.252867 | ||||||||
\(477\) | −7048.27 | + | 12208.0i | −0.676558 | + | 1.17183i | ||||
\(478\) | −6316.74 | + | 10940.9i | −0.604437 | + | 1.04692i | ||||
\(479\) | −955.918 | − | 1655.70i | −0.0911837 | − | 0.157935i | 0.816826 | − | 0.576884i | \(-0.195732\pi\) |
−0.908009 | + | 0.418950i | \(0.862398\pi\) | |||||||
\(480\) | 2417.59 | − | 4187.39i | 0.229890 | − | 0.398182i | ||||
\(481\) | 741.248 | + | 1283.88i | 0.0702661 | + | 0.121705i | ||||
\(482\) | 6989.31 | 0.660486 | ||||||||
\(483\) | −7569.08 | −0.713054 | ||||||||
\(484\) | 2148.18 | + | 3720.75i | 0.201745 | + | 0.349432i | ||||
\(485\) | 12511.5 | + | 21670.5i | 1.17137 | + | 2.02888i | ||||
\(486\) | −13272.9 | −1.23883 | ||||||||
\(487\) | −6061.32 | −0.563993 | −0.281997 | − | 0.959415i | \(-0.590997\pi\) | ||||
−0.281997 | + | 0.959415i | \(0.590997\pi\) | |||||||
\(488\) | 2255.68 | + | 3906.95i | 0.209241 | + | 0.362417i | ||||
\(489\) | 766.327 | − | 1327.32i | 0.0708681 | − | 0.122747i | ||||
\(490\) | −1076.38 | − | 1864.35i | −0.0992366 | − | 0.171883i | ||||
\(491\) | −3219.51 | + | 5576.36i | −0.295916 | + | 0.512541i | −0.975197 | − | 0.221337i | \(-0.928958\pi\) |
0.679282 | + | 0.733877i | \(0.262291\pi\) | |||||||
\(492\) | −2089.62 | + | 3619.33i | −0.191478 | + | 0.331650i | ||||
\(493\) | −4689.39 | −0.428397 | ||||||||
\(494\) | 1981.45 | − | 10937.0i | 0.180464 | − | 0.996111i | ||||
\(495\) | 16365.0 | 1.48596 | ||||||||
\(496\) | −960.396 | + | 1663.45i | −0.0869416 | + | 0.150587i | ||||
\(497\) | 5517.86 | − | 9557.22i | 0.498008 | − | 0.862575i | ||||
\(498\) | −4561.26 | − | 7900.34i | −0.410432 | − | 0.710889i | ||||
\(499\) | −8229.07 | + | 14253.2i | −0.738244 | + | 1.27868i | 0.215041 | + | 0.976605i | \(0.431011\pi\) |
−0.953285 | + | 0.302071i | \(0.902322\pi\) | |||||||
\(500\) | 33.1316 | + | 57.3857i | 0.00296338 | + | 0.00513273i | ||||
\(501\) | 20131.3 | 1.79521 | ||||||||
\(502\) | −7260.74 | −0.645543 | ||||||||
\(503\) | 1362.42 | + | 2359.78i | 0.120770 | + | 0.209179i | 0.920071 | − | 0.391751i | \(-0.128130\pi\) |
−0.799302 | + | 0.600930i | \(0.794797\pi\) | |||||||
\(504\) | 4290.61 | + | 7431.56i | 0.379205 | + | 0.656802i | ||||
\(505\) | −16469.7 | −1.45127 | ||||||||
\(506\) | 1528.50 | 0.134289 | ||||||||
\(507\) | −11041.7 | − | 19124.7i | −0.967214 | − | 1.67526i | ||||
\(508\) | −477.816 | + | 827.602i | −0.0417316 | + | 0.0722813i | ||||
\(509\) | −2730.41 | − | 4729.20i | −0.237767 | − | 0.411824i | 0.722307 | − | 0.691573i | \(-0.243082\pi\) |
−0.960073 | + | 0.279749i | \(0.909749\pi\) | |||||||
\(510\) | 5984.29 | − | 10365.1i | 0.519586 | − | 0.899949i | ||||
\(511\) | 1549.45 | − | 2683.73i | 0.134136 | − | 0.232331i | ||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 5331.59 | − | 29428.8i | 0.458861 | − | 2.53278i | ||||
\(514\) | 3098.83 | 0.265921 | ||||||||
\(515\) | −11264.3 | + | 19510.3i | −0.963813 | + | 1.66937i | ||||
\(516\) | 6907.04 | − | 11963.3i | 0.589274 | − | 1.02065i | ||||
\(517\) | −1546.31 | − | 2678.28i | −0.131541 | − | 0.227835i | ||||
\(518\) | 366.215 | − | 634.303i | 0.0310629 | − | 0.0538024i | ||||
\(519\) | 1941.46 | + | 3362.71i | 0.164202 | + | 0.284406i | ||||
\(520\) | 8470.26 | 0.714318 | ||||||||
\(521\) | 7411.04 | 0.623193 | 0.311596 | − | 0.950215i | \(-0.399136\pi\) | ||||
0.311596 | + | 0.950215i | \(0.399136\pi\) | |||||||
\(522\) | −7661.85 | − | 13270.7i | −0.642433 | − | 1.11273i | ||||
\(523\) | 399.710 | + | 692.318i | 0.0334189 | + | 0.0578833i | 0.882251 | − | 0.470779i | \(-0.156027\pi\) |
−0.848832 | + | 0.528662i | \(0.822694\pi\) | |||||||
\(524\) | 1060.99 | 0.0884537 | ||||||||
\(525\) | 19676.4 | 1.63571 | ||||||||
\(526\) | −3809.81 | − | 6598.79i | −0.315809 | − | 0.546998i | ||||
\(527\) | −2377.28 | + | 4117.57i | −0.196501 | + | 0.340349i | ||||
\(528\) | −1227.97 | − | 2126.91i | −0.101213 | − | 0.175307i | ||||
\(529\) | 4946.77 | − | 8568.06i | 0.406573 | − | 0.704204i | ||||
\(530\) | 3437.18 | − | 5953.37i | 0.281701 | − | 0.487920i | ||||
\(531\) | 27384.3 | 2.23800 | ||||||||
\(532\) | −5168.98 | + | 1853.94i | −0.421248 | + | 0.151087i | ||||
\(533\) | −7321.19 | −0.594964 | ||||||||
\(534\) | −9238.83 | + | 16002.1i | −0.748695 | + | 1.29678i | ||||
\(535\) | −3951.83 | + | 6844.77i | −0.319350 | + | 0.553131i | ||||
\(536\) | −3771.41 | − | 6532.27i | −0.303918 | − | 0.526401i | ||||
\(537\) | 7798.90 | − | 13508.1i | 0.626717 | − | 1.08551i | ||||
\(538\) | −3376.40 | − | 5848.09i | −0.270570 | − | 0.468642i | ||||
\(539\) | −1093.46 | −0.0873814 | ||||||||
\(540\) | 22791.4 | 1.81627 | ||||||||
\(541\) | −2947.56 | − | 5105.33i | −0.234243 | − | 0.405721i | 0.724809 | − | 0.688950i | \(-0.241928\pi\) |
−0.959052 | + | 0.283228i | \(0.908595\pi\) | |||||||
\(542\) | −3525.50 | − | 6106.34i | −0.279397 | − | 0.483930i | ||||
\(543\) | 27167.0 | 2.14705 | ||||||||
\(544\) | −1267.36 | −0.0998852 | ||||||||
\(545\) | −9568.84 | − | 16573.7i | −0.752081 | − | 1.30264i | ||||
\(546\) | −10652.5 | + | 18450.6i | −0.834951 | + | 1.44618i | ||||
\(547\) | −5745.64 | − | 9951.74i | −0.449115 | − | 0.777890i | 0.549214 | − | 0.835682i | \(-0.314927\pi\) |
−0.998329 | + | 0.0577920i | \(0.981594\pi\) | |||||||
\(548\) | −4876.90 | + | 8447.03i | −0.380166 | + | 0.658466i | ||||
\(549\) | −18245.4 | + | 31602.0i | −1.41839 | + | 2.45672i | ||||
\(550\) | −3973.46 | −0.308053 | ||||||||
\(551\) | 9230.38 | − | 3310.62i | 0.713661 | − | 0.255966i | ||||
\(552\) | 3652.92 | 0.281664 | ||||||||
\(553\) | 7263.44 | − | 12580.6i | 0.558540 | − | 0.967420i | ||||
\(554\) | 6557.88 | − | 11358.6i | 0.502920 | − | 0.871083i | ||||
\(555\) | −1669.08 | − | 2890.92i | −0.127655 | − | 0.221104i | ||||
\(556\) | 733.589 | − | 1270.61i | 0.0559552 | − | 0.0969173i | ||||
\(557\) | 1122.30 | + | 1943.88i | 0.0853740 | + | 0.147872i | 0.905551 | − | 0.424238i | \(-0.139458\pi\) |
−0.820176 | + | 0.572111i | \(0.806125\pi\) | |||||||
\(558\) | −15536.6 | −1.17871 | ||||||||
\(559\) | 24199.5 | 1.83100 | ||||||||
\(560\) | −2092.37 | − | 3624.09i | −0.157891 | − | 0.273475i | ||||
\(561\) | −3039.61 | − | 5264.76i | −0.228757 | − | 0.396218i | ||||
\(562\) | −15775.6 | −1.18408 | ||||||||
\(563\) | −19529.8 | −1.46196 | −0.730978 | − | 0.682401i | \(-0.760936\pi\) | ||||
−0.730978 | + | 0.682401i | \(0.760936\pi\) | |||||||
\(564\) | −3695.48 | − | 6400.76i | −0.275900 | − | 0.477873i | ||||
\(565\) | −5829.68 | + | 10097.3i | −0.434082 | + | 0.751853i | ||||
\(566\) | 2072.73 | + | 3590.08i | 0.153928 | + | 0.266612i | ||||
\(567\) | −14182.4 | + | 24564.6i | −1.05045 | + | 1.81943i | ||||
\(568\) | −2662.98 | + | 4612.42i | −0.196719 | + | 0.340727i | ||||
\(569\) | −3300.68 | −0.243184 | −0.121592 | − | 0.992580i | \(-0.538800\pi\) | ||||
−0.121592 | + | 0.992580i | \(0.538800\pi\) | |||||||
\(570\) | −4461.64 | + | 24626.9i | −0.327855 | + | 1.80966i | ||||
\(571\) | 3080.76 | 0.225789 | 0.112895 | − | 0.993607i | \(-0.463988\pi\) | ||||
0.112895 | + | 0.993607i | \(0.463988\pi\) | |||||||
\(572\) | 2151.16 | − | 3725.92i | 0.157246 | − | 0.272357i | ||||
\(573\) | −16863.5 | + | 29208.4i | −1.22946 | + | 2.12949i | ||||
\(574\) | 1808.52 | + | 3132.45i | 0.131509 | + | 0.227780i | ||||
\(575\) | 2955.02 | − | 5118.25i | 0.214318 | − | 0.371210i | ||||
\(576\) | −2070.70 | − | 3586.55i | −0.149790 | − | 0.259444i | ||||
\(577\) | 4946.52 | 0.356892 | 0.178446 | − | 0.983950i | \(-0.442893\pi\) | ||||
0.178446 | + | 0.983950i | \(0.442893\pi\) | |||||||
\(578\) | 6688.89 | 0.481352 | ||||||||
\(579\) | −22674.2 | − | 39272.9i | −1.62748 | − | 2.81887i | ||||
\(580\) | 3736.40 | + | 6471.63i | 0.267492 | + | 0.463310i | ||||
\(581\) | −7895.34 | −0.563776 | ||||||||
\(582\) | 30375.2 | 2.16339 | ||||||||
\(583\) | −1745.85 | − | 3023.91i | −0.124024 | − | 0.214816i | ||||
\(584\) | −747.782 | + | 1295.20i | −0.0529854 | + | 0.0917733i | ||||
\(585\) | 34256.5 | + | 59334.1i | 2.42108 | + | 4.19344i | ||||
\(586\) | −7820.84 | + | 13546.1i | −0.551324 | + | 0.954922i | ||||
\(587\) | −7278.01 | + | 12605.9i | −0.511748 | + | 0.886373i | 0.488160 | + | 0.872754i | \(0.337668\pi\) |
−0.999907 | + | 0.0136184i | \(0.995665\pi\) | |||||||
\(588\) | −2613.22 | −0.183278 | ||||||||
\(589\) | 1772.40 | − | 9783.13i | 0.123991 | − | 0.684392i | ||||
\(590\) | −13354.3 | −0.931844 | ||||||||
\(591\) | −11287.3 | + | 19550.2i | −0.785615 | + | 1.36073i | ||||
\(592\) | −176.739 | + | 306.121i | −0.0122702 | + | 0.0212526i | ||||
\(593\) | 10308.6 | + | 17855.1i | 0.713869 | + | 1.23646i | 0.963394 | + | 0.268089i | \(0.0863921\pi\) |
−0.249525 | + | 0.968368i | \(0.580275\pi\) | |||||||
\(594\) | 5788.25 | − | 10025.5i | 0.399823 | − | 0.692513i | ||||
\(595\) | −5179.27 | − | 8970.76i | −0.356856 | − | 0.618093i | ||||
\(596\) | −8967.02 | −0.616281 | ||||||||
\(597\) | 6561.39 | 0.449816 | ||||||||
\(598\) | 3199.59 | + | 5541.85i | 0.218798 | + | 0.378969i | ||||
\(599\) | −10652.2 | − | 18450.2i | −0.726608 | − | 1.25852i | −0.958309 | − | 0.285735i | \(-0.907762\pi\) |
0.231700 | − | 0.972787i | \(-0.425571\pi\) | |||||||
\(600\) | −9496.06 | −0.646125 | ||||||||
\(601\) | −26351.4 | −1.78852 | −0.894258 | − | 0.447553i | \(-0.852296\pi\) | ||||
−0.894258 | + | 0.447553i | \(0.852296\pi\) | |||||||
\(602\) | −5977.89 | − | 10354.0i | −0.404719 | − | 0.700993i | ||||
\(603\) | 30505.6 | − | 52837.3i | 2.06018 | − | 3.56833i | ||||
\(604\) | 1276.39 | + | 2210.77i | 0.0859860 | + | 0.148932i | ||||
\(605\) | 8473.56 | − | 14676.6i | 0.569420 | − | 0.986265i | ||||
\(606\) | −9996.20 | + | 17313.9i | −0.670079 | + | 1.16061i | ||||
\(607\) | 24027.8 | 1.60669 | 0.803344 | − | 0.595516i | \(-0.203052\pi\) | ||||
0.803344 | + | 0.595516i | \(0.203052\pi\) | |||||||
\(608\) | 2494.61 | − | 894.730i | 0.166398 | − | 0.0596811i | ||||
\(609\) | −18796.0 | −1.25066 | ||||||||
\(610\) | 8897.62 | − | 15411.1i | 0.590580 | − | 1.02292i | ||||
\(611\) | 6473.73 | − | 11212.8i | 0.428640 | − | 0.742426i | ||||
\(612\) | −5125.62 | − | 8877.83i | −0.338547 | − | 0.586381i | ||||
\(613\) | −7619.00 | + | 13196.5i | −0.502004 | + | 0.869497i | 0.497993 | + | 0.867181i | \(0.334070\pi\) |
−0.999997 | + | 0.00231571i | \(0.999263\pi\) | |||||||
\(614\) | −5937.79 | − | 10284.6i | −0.390276 | − | 0.675979i | ||||
\(615\) | 16485.2 | 1.08089 | ||||||||
\(616\) | −2125.57 | −0.139028 | ||||||||
\(617\) | 14065.4 | + | 24362.0i | 0.917751 | + | 1.58959i | 0.802822 | + | 0.596218i | \(0.203331\pi\) |
0.114929 | + | 0.993374i | \(0.463336\pi\) | |||||||
\(618\) | 13673.6 | + | 23683.4i | 0.890023 | + | 1.54157i | ||||
\(619\) | 9482.23 | 0.615708 | 0.307854 | − | 0.951434i | \(-0.400389\pi\) | ||||
0.307854 | + | 0.951434i | \(0.400389\pi\) | |||||||
\(620\) | 7576.64 | 0.490782 | ||||||||
\(621\) | 8609.32 | + | 14911.8i | 0.556329 | + | 0.963590i | ||||
\(622\) | 1832.63 | − | 3174.21i | 0.118138 | − | 0.204621i | ||||
\(623\) | 7996.01 | + | 13849.5i | 0.514211 | + | 0.890639i | ||||
\(624\) | 5141.00 | − | 8904.47i | 0.329815 | − | 0.571256i | ||||
\(625\) | 7877.57 | − | 13644.3i | 0.504164 | − | 0.873238i | ||||
\(626\) | 1876.66 | 0.119819 | ||||||||
\(627\) | 9699.85 | + | 8217.01i | 0.617822 | + | 0.523374i | ||||
\(628\) | 8503.96 | 0.540358 | ||||||||
\(629\) | −437.485 | + | 757.746i | −0.0277324 | + | 0.0480339i | ||||
\(630\) | 16924.5 | − | 29314.1i | 1.07030 | − | 1.85381i | ||||
\(631\) | 850.702 | + | 1473.46i | 0.0536702 | + | 0.0929595i | 0.891612 | − | 0.452800i | \(-0.149575\pi\) |
−0.837942 | + | 0.545759i | \(0.816241\pi\) | |||||||
\(632\) | −3505.42 | + | 6071.56i | −0.220630 | + | 0.382142i | ||||
\(633\) | 2542.65 | + | 4404.01i | 0.159655 | + | 0.276530i | ||||
\(634\) | 14822.9 | 0.928539 | ||||||||
\(635\) | 3769.53 | 0.235573 | ||||||||
\(636\) | −4172.37 | − | 7226.75i | −0.260134 | − | 0.450565i | ||||
\(637\) | −2288.92 | − | 3964.53i | −0.142371 | − | 0.246594i | ||||
\(638\) | 3795.67 | 0.235536 | ||||||||
\(639\) | −43079.9 | −2.66700 | ||||||||
\(640\) | 1009.80 | + | 1749.03i | 0.0623686 | + | 0.108026i | ||||
\(641\) | −10815.8 | + | 18733.5i | −0.666454 | + | 1.15433i | 0.312435 | + | 0.949939i | \(0.398855\pi\) |
−0.978889 | + | 0.204393i | \(0.934478\pi\) | |||||||
\(642\) | 4797.10 | + | 8308.82i | 0.294901 | + | 0.510783i | ||||
\(643\) | 2722.31 | − | 4715.17i | 0.166963 | − | 0.289189i | −0.770388 | − | 0.637576i | \(-0.779937\pi\) |
0.937351 | + | 0.348387i | \(0.113271\pi\) | |||||||
\(644\) | 1580.76 | − | 2737.96i | 0.0967248 | − | 0.167532i | ||||
\(645\) | −54490.2 | −3.32643 | ||||||||
\(646\) | 6174.93 | − | 2214.73i | 0.376083 | − | 0.134888i | ||||
\(647\) | 27393.8 | 1.66454 | 0.832272 | − | 0.554367i | \(-0.187040\pi\) | ||||
0.832272 | + | 0.554367i | \(0.187040\pi\) | |||||||
\(648\) | 6844.57 | − | 11855.1i | 0.414938 | − | 0.718694i | ||||
\(649\) | −3391.54 | + | 5874.32i | −0.205130 | + | 0.355296i | ||||
\(650\) | −8317.59 | − | 14406.5i | −0.501912 | − | 0.869337i | ||||
\(651\) | −9528.62 | + | 16504.0i | −0.573665 | + | 0.993617i | ||||
\(652\) | 320.087 | + | 554.406i | 0.0192263 | + | 0.0333010i | ||||
\(653\) | −23390.6 | −1.40175 | −0.700875 | − | 0.713284i | \(-0.747207\pi\) | ||||
−0.700875 | + | 0.713284i | \(0.747207\pi\) | |||||||
\(654\) | −23231.1 | −1.38900 | ||||||||
\(655\) | −2092.57 | − | 3624.43i | −0.124830 | − | 0.216211i | ||||
\(656\) | −872.812 | − | 1511.76i | −0.0519476 | − | 0.0899758i | ||||
\(657\) | −12097.1 | −0.718346 | ||||||||
\(658\) | −6396.71 | −0.378981 | ||||||||
\(659\) | 10029.5 | + | 17371.6i | 0.592860 | + | 1.02686i | 0.993845 | + | 0.110779i | \(0.0353345\pi\) |
−0.400985 | + | 0.916084i | \(0.631332\pi\) | |||||||
\(660\) | −4843.78 | + | 8389.68i | −0.285673 | + | 0.494800i | ||||
\(661\) | −11618.9 | − | 20124.5i | −0.683696 | − | 1.18420i | −0.973845 | − | 0.227214i | \(-0.927038\pi\) |
0.290149 | − | 0.956981i | \(-0.406295\pi\) | |||||||
\(662\) | −5412.69 | + | 9375.05i | −0.317780 | + | 0.550410i | ||||
\(663\) | 12725.6 | − | 22041.3i | 0.745430 | − | 1.29112i | ||||
\(664\) | 3810.38 | 0.222698 | ||||||||
\(665\) | 16527.8 | + | 14001.2i | 0.963791 | + | 0.816453i | ||||
\(666\) | −2859.17 | −0.166352 | ||||||||
\(667\) | −2822.80 | + | 4889.24i | −0.163867 | + | 0.283826i | ||||
\(668\) | −4204.32 | + | 7282.09i | −0.243518 | + | 0.421785i | ||||
\(669\) | −23231.2 | − | 40237.6i | −1.34256 | − | 2.32538i | ||||
\(670\) | −14876.5 | + | 25766.8i | −0.857803 | + | 1.48576i | ||||
\(671\) | −4519.39 | − | 7827.81i | −0.260013 | − | 0.450356i | ||||
\(672\) | −5079.83 | −0.291605 | ||||||||
\(673\) | −10185.3 | −0.583378 | −0.291689 | − | 0.956513i | \(-0.594217\pi\) | ||||
−0.291689 | + | 0.956513i | \(0.594217\pi\) | |||||||
\(674\) | 9273.57 | + | 16062.3i | 0.529977 | + | 0.917947i | ||||
\(675\) | −22380.6 | − | 38764.4i | −1.27619 | − | 2.21043i | ||||
\(676\) | 9223.97 | 0.524805 | ||||||||
\(677\) | 3202.89 | 0.181827 | 0.0909136 | − | 0.995859i | \(-0.471021\pi\) | ||||
0.0909136 | + | 0.995859i | \(0.471021\pi\) | |||||||
\(678\) | 7076.61 | + | 12257.0i | 0.400849 | + | 0.694291i | ||||
\(679\) | 13144.5 | − | 22767.0i | 0.742916 | − | 1.28677i | ||||
\(680\) | 2499.57 | + | 4329.39i | 0.140962 | + | 0.244154i | ||||
\(681\) | 19018.4 | − | 32940.8i | 1.07017 | − | 1.85359i | ||||
\(682\) | 1924.21 | − | 3332.83i | 0.108038 | − | 0.187127i | ||||
\(683\) | 1625.51 | 0.0910662 | 0.0455331 | − | 0.998963i | \(-0.485501\pi\) | ||||
0.0455331 | + | 0.998963i | \(0.485501\pi\) | |||||||
\(684\) | 16356.6 | + | 13856.1i | 0.914342 | + | 0.774564i | ||||
\(685\) | 38474.2 | 2.14602 | ||||||||
\(686\) | −6816.58 | + | 11806.7i | −0.379385 | + | 0.657115i | ||||
\(687\) | 378.197 | − | 655.056i | 0.0210031 | − | 0.0363784i | ||||
\(688\) | 2885.00 | + | 4996.96i | 0.159868 | + | 0.276900i | ||||
\(689\) | 7309.15 | − | 12659.8i | 0.404146 | − | 0.700001i | ||||
\(690\) | −7204.55 | − | 12478.6i | −0.397496 | − | 0.688484i | ||||
\(691\) | 839.130 | 0.0461968 | 0.0230984 | − | 0.999733i | \(-0.492647\pi\) | ||||
0.0230984 | + | 0.999733i | \(0.492647\pi\) | |||||||
\(692\) | −1621.85 | −0.0890949 | ||||||||
\(693\) | −8596.50 | − | 14889.6i | −0.471218 | − | 0.816173i | ||||
\(694\) | −9674.48 | − | 16756.7i | −0.529162 | − | 0.916535i | ||||
\(695\) | −5787.34 | −0.315865 | ||||||||
\(696\) | 9071.18 | 0.494026 | ||||||||
\(697\) | −2160.48 | − | 3742.06i | −0.117409 | − | 0.203358i | ||||
\(698\) | 1300.56 | − | 2252.64i | 0.0705259 | − | 0.122154i | ||||
\(699\) | 7868.49 | + | 13628.6i | 0.425771 | + | 0.737457i | ||||
\(700\) | −4109.32 | + | 7117.54i | −0.221882 | + | 0.384311i | ||||
\(701\) | 729.064 | − | 1262.78i | 0.0392816 | − | 0.0680377i | −0.845716 | − | 0.533633i | \(-0.820826\pi\) |
0.884998 | + | 0.465595i | \(0.154160\pi\) | |||||||
\(702\) | 48465.8 | 2.60573 | ||||||||
\(703\) | 326.171 | − | 1800.37i | 0.0174989 | − | 0.0965890i | ||||
\(704\) | 1025.82 | 0.0549178 | ||||||||
\(705\) | −14577.0 | + | 25248.0i | −0.778723 | + | 1.34879i | ||||
\(706\) | 11985.4 | − | 20759.2i | 0.638916 | − | 1.10663i | ||||
\(707\) | 8651.49 | + | 14984.8i | 0.460216 | + | 0.797118i | ||||
\(708\) | −8105.35 | + | 14038.9i | −0.430251 | + | 0.745217i | ||||
\(709\) | 16159.9 | + | 27989.8i | 0.855993 | + | 1.48262i | 0.875721 | + | 0.482818i | \(0.160387\pi\) |
−0.0197278 | + | 0.999805i | \(0.506280\pi\) | |||||||
\(710\) | 21008.5 | 1.11047 | ||||||||
\(711\) | −56708.2 | −2.99117 | ||||||||
\(712\) | −3858.96 | − | 6683.91i | −0.203119 | − | 0.351812i | ||||
\(713\) | 2862.03 | + | 4957.18i | 0.150328 | + | 0.260376i | ||||
\(714\) | −12574.2 | −0.659070 | ||||||||
\(715\) | −16970.7 | −0.887646 | ||||||||
\(716\) | 3257.52 | + | 5642.18i | 0.170027 | + | 0.294495i | ||||
\(717\) | 30246.1 | − | 52387.8i | 1.57540 | − | 2.72867i | ||||
\(718\) | −4407.90 | − | 7634.70i | −0.229110 | − | 0.396831i | ||||
\(719\) | 2885.84 | − | 4998.42i | 0.149685 | − | 0.259262i | −0.781426 | − | 0.623998i | \(-0.785507\pi\) |
0.931111 | + | 0.364736i | \(0.118841\pi\) | |||||||
\(720\) | −8167.95 | + | 14147.3i | −0.422780 | + | 0.732276i | ||||
\(721\) | 23668.5 | 1.22255 | ||||||||
\(722\) | −10590.9 | + | 8718.76i | −0.545917 | + | 0.449416i | ||||
\(723\) | −33466.6 | −1.72149 | ||||||||
\(724\) | −5673.68 | + | 9827.09i | −0.291244 | + | 0.504449i | ||||
\(725\) | 7338.10 | − | 12710.0i | 0.375904 | − | 0.651085i | ||||
\(726\) | −10286.0 | − | 17815.9i | −0.525826 | − | 0.910757i | ||||
\(727\) | −2726.16 | + | 4721.84i | −0.139075 | + | 0.240885i | −0.927147 | − | 0.374698i | \(-0.877746\pi\) |
0.788072 | + | 0.615583i | \(0.211080\pi\) | |||||||
\(728\) | −4449.42 | − | 7706.62i | −0.226520 | − | 0.392344i | ||||
\(729\) | 17352.9 | 0.881618 | ||||||||
\(730\) | 5899.31 | 0.299100 | ||||||||
\(731\) | 7141.26 | + | 12369.0i | 0.361326 | + | 0.625834i | ||||
\(732\) | −10800.8 | − | 18707.5i | −0.545365 | − | 0.944601i | ||||
\(733\) | 9558.30 | 0.481643 | 0.240821 | − | 0.970569i | \(-0.422583\pi\) | ||||
0.240821 | + | 0.970569i | \(0.422583\pi\) | |||||||
\(734\) | −12520.2 | −0.629602 | ||||||||
\(735\) | 5153.98 | + | 8926.96i | 0.258650 | + | 0.447994i | ||||
\(736\) | −762.893 | + | 1321.37i | −0.0382074 | + | 0.0661771i | ||||
\(737\) | 7556.23 | + | 13087.8i | 0.377663 | + | 0.654131i | ||||
\(738\) | 7059.88 | − | 12228.1i | 0.352138 | − | 0.609921i | ||||
\(739\) | −6476.74 | + | 11218.0i | −0.322396 | + | 0.558406i | −0.980982 | − | 0.194099i | \(-0.937822\pi\) |
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(740\) | 1394.31 | 0.0692647 | ||||||||
\(741\) | −9487.66 | + | 52369.1i | −0.470361 | + | 2.59626i | ||||
\(742\) | −7222.19 | −0.357325 | ||||||||
\(743\) | 91.9794 | − | 159.313i | 0.00454158 | − | 0.00786625i | −0.863746 | − | 0.503928i | \(-0.831888\pi\) |
0.868287 | + | 0.496062i | \(0.165221\pi\) | |||||||
\(744\) | 4598.62 | − | 7965.03i | 0.226604 | − | 0.392490i | ||||
\(745\) | 17685.4 | + | 30632.0i | 0.869721 | + | 1.50640i | ||||
\(746\) | −2745.24 | + | 4754.90i | −0.134733 | + | 0.233364i | ||||
\(747\) | 15410.4 | + | 26691.7i | 0.754804 | + | 1.30736i | ||||
\(748\) | 2539.23 | 0.124122 | ||||||||
\(749\) | 8303.57 | 0.405081 | ||||||||
\(750\) | −158.642 | − | 274.777i | −0.00772374 | − | 0.0133779i | ||||
\(751\) | −5247.19 | − | 9088.39i | −0.254957 | − | 0.441598i | 0.709927 | − | 0.704275i | \(-0.248728\pi\) |
−0.964884 | + | 0.262677i | \(0.915395\pi\) | |||||||
\(752\) | 3087.12 | 0.149702 | ||||||||
\(753\) | 34766.2 | 1.68254 | ||||||||
\(754\) | 7945.43 | + | 13761.9i | 0.383761 | + | 0.664693i | ||||
\(755\) | 5034.77 | − | 8720.47i | 0.242694 | − | 0.420358i | ||||
\(756\) | −11972.3 | − | 20736.6i | −0.575964 | − | 0.997599i | ||||
\(757\) | 4731.24 | − | 8194.75i | 0.227160 | − | 0.393452i | −0.729805 | − | 0.683655i | \(-0.760389\pi\) |
0.956965 | + | 0.290203i | \(0.0937227\pi\) | |||||||
\(758\) | 10772.3 | − | 18658.1i | 0.516183 | − | 0.894054i | ||||
\(759\) | −7318.84 | −0.350009 | ||||||||
\(760\) | −7976.50 | − | 6757.11i | −0.380708 | − | 0.322508i | ||||
\(761\) | −38400.1 | −1.82918 | −0.914588 | − | 0.404388i | \(-0.867485\pi\) | ||||
−0.914588 | + | 0.404388i | \(0.867485\pi\) | |||||||
\(762\) | 2287.90 | − | 3962.76i | 0.108769 | − | 0.188393i | ||||
\(763\) | −10053.0 | + | 17412.3i | −0.476990 | + | 0.826171i | ||||
\(764\) | −7043.70 | − | 12200.0i | −0.333550 | − | 0.577725i | ||||
\(765\) | −20218.2 | + | 35018.9i | −0.955543 | + | 1.65505i | ||||
\(766\) | −3379.95 | − | 5854.24i | −0.159429 | − | 0.276139i | ||||
\(767\) | −28397.9 | −1.33688 | ||||||||
\(768\) | 2451.58 | 0.115187 | ||||||||
\(769\) | 1535.93 | + | 2660.31i | 0.0720249 | + | 0.124751i | 0.899789 | − | 0.436326i | \(-0.143721\pi\) |
−0.827764 | + | 0.561077i | \(0.810387\pi\) | |||||||
\(770\) | 4192.19 | + | 7261.08i | 0.196203 | + | 0.339833i | ||||
\(771\) | −14838.0 | −0.693095 | ||||||||
\(772\) | 18941.6 | 0.883060 | ||||||||
\(773\) | −3588.67 | − | 6215.75i | −0.166980 | − | 0.289218i | 0.770377 | − | 0.637589i | \(-0.220068\pi\) |
−0.937357 | + | 0.348371i | \(0.886735\pi\) | |||||||
\(774\) | −23335.8 | + | 40418.7i | −1.08370 | + | 1.87703i | ||||
\(775\) | −7440.07 | − | 12886.6i | −0.344846 | − | 0.597290i | ||||
\(776\) | −6343.69 | + | 10987.6i | −0.293460 | + | 0.508288i | ||||
\(777\) | −1753.53 | + | 3037.20i | −0.0809620 | + | 0.140230i | ||||
\(778\) | −9405.12 | −0.433406 | ||||||||
\(779\) | 6894.41 | + | 5840.44i | 0.317096 | + | 0.268621i | ||||
\(780\) | −40557.7 | −1.86179 | ||||||||
\(781\) | 5335.44 | − | 9241.25i | 0.244452 | − | 0.423403i | ||||
\(782\) | −1888.40 | + | 3270.80i | −0.0863542 | + | 0.149570i | ||||
\(783\) | 21379.2 | + | 37029.9i | 0.975774 | + | 1.69009i | ||||
\(784\) | 545.758 | − | 945.280i | 0.0248614 | − | 0.0430612i | ||||
\(785\) | −16772.1 | − | 29050.1i | −0.762576 | − | 1.32082i | ||||
\(786\) | −5080.31 | −0.230545 | ||||||||
\(787\) | 40299.0 | 1.82529 | 0.912645 | − | 0.408754i | \(-0.134037\pi\) | ||||
0.912645 | + | 0.408754i | \(0.134037\pi\) | |||||||
\(788\) | −4714.60 | − | 8165.92i | −0.213135 | − | 0.369161i | ||||
\(789\) | 18242.3 | + | 31596.6i | 0.823123 | + | 1.42569i | ||||
\(790\) | 27654.5 | 1.24545 | ||||||||
\(791\) | 12249.3 | 0.550613 | ||||||||
\(792\) | 4148.76 | + | 7185.87i | 0.186136 | + | 0.322397i | ||||
\(793\) | 18920.7 | − | 32771.7i | 0.847283 | − | 1.46754i | ||||
\(794\) | 251.499 | + | 435.608i | 0.0112410 | + | 0.0194700i | ||||
\(795\) | −16458.1 | + | 28506.2i | −0.734223 | + | 1.27171i | ||||
\(796\) | −1370.31 | + | 2373.45i | −0.0610168 | + | 0.105684i | ||||
\(797\) | −33505.8 | −1.48913 | −0.744565 | − | 0.667550i | \(-0.767343\pi\) | ||||
−0.744565 | + | 0.667550i | \(0.767343\pi\) | |||||||
\(798\) | 24750.4 | − | 8877.11i | 1.09794 | − | 0.393792i | ||||
\(799\) | 7641.59 | 0.338348 | ||||||||
\(800\) | 1983.20 | − | 3435.01i | 0.0876459 | − | 0.151807i | ||||
\(801\) | 31213.8 | − | 54063.9i | 1.37689 | − | 2.38484i | ||||
\(802\) | −6450.33 | − | 11172.3i | −0.284001 | − | 0.491905i | ||||
\(803\) | 1498.23 | − | 2595.00i | 0.0658421 | − | 0.114042i | ||||
\(804\) | 18058.4 | + | 31278.1i | 0.792129 | + | 1.37201i | ||||
\(805\) | −12470.8 | −0.546008 | ||||||||
\(806\) | 16111.7 | 0.704107 | ||||||||
\(807\) | 16167.0 | + | 28002.1i | 0.705213 | + | 1.22146i | ||||
\(808\) | −4175.31 | − | 7231.84i | −0.181791 | − | 0.314870i | ||||
\(809\) | −20863.7 | −0.906710 | −0.453355 | − | 0.891330i | \(-0.649773\pi\) | ||||
−0.453355 | + | 0.891330i | \(0.649773\pi\) | |||||||
\(810\) | −53997.3 | −2.34231 | ||||||||
\(811\) | −8728.82 | − | 15118.8i | −0.377941 | − | 0.654613i | 0.612821 | − | 0.790221i | \(-0.290034\pi\) |
−0.990763 | + | 0.135608i | \(0.956701\pi\) | |||||||
\(812\) | 3925.45 | − | 6799.08i | 0.169651 | − | 0.293844i | ||||
\(813\) | 16881.0 | + | 29238.7i | 0.728218 | + | 1.26131i | ||||
\(814\) | 354.108 | − | 613.332i | 0.0152475 | − | 0.0264094i | ||||
\(815\) | 1262.59 | − | 2186.88i | 0.0542659 | − | 0.0939914i | ||||
\(816\) | 6068.43 | 0.260340 | ||||||||
\(817\) | −22788.8 | − | 19305.0i | −0.975862 | − | 0.826679i | ||||
\(818\) | −4031.84 | −0.172335 | ||||||||
\(819\) | 35989.8 | − | 62336.2i | 1.53552 | − | 2.65959i | ||||
\(820\) | −3442.84 | + | 5963.18i | −0.146621 | + | 0.253955i | ||||
\(821\) | −14635.8 | − | 25349.9i | −0.622158 | − | 1.07761i | −0.989083 | − | 0.147359i | \(-0.952923\pi\) |
0.366925 | − | 0.930251i | \(-0.380411\pi\) | |||||||
\(822\) | 23351.8 | − | 40446.5i | 0.990861 | − | 1.71622i | ||||
\(823\) | −19338.7 | − | 33495.5i | −0.819080 | − | 1.41869i | −0.906361 | − | 0.422505i | \(-0.861151\pi\) |
0.0872806 | − | 0.996184i | \(-0.472182\pi\) | |||||||
\(824\) | −11422.7 | −0.482922 | ||||||||
\(825\) | 19025.9 | 0.802906 | ||||||||
\(826\) | 7015.00 | + | 12150.3i | 0.295500 | + | 0.511821i | ||||
\(827\) | −2321.06 | − | 4020.19i | −0.0975951 | − | 0.169040i | 0.813094 | − | 0.582133i | \(-0.197782\pi\) |
−0.910689 | + | 0.413093i | \(0.864448\pi\) | |||||||
\(828\) | −12341.6 | −0.517994 | ||||||||
\(829\) | −7918.14 | −0.331735 | −0.165868 | − | 0.986148i | \(-0.553042\pi\) | ||||
−0.165868 | + | 0.986148i | \(0.553042\pi\) | |||||||
\(830\) | −7515.09 | − | 13016.5i | −0.314280 | − | 0.544350i | ||||
\(831\) | −31400.7 | + | 54387.7i | −1.31081 | + | 2.27038i | ||||
\(832\) | 2147.34 | + | 3719.30i | 0.0894779 | + | 0.154980i | ||||
\(833\) | 1350.92 | − | 2339.86i | 0.0561904 | − | 0.0973246i | ||||
\(834\) | −3512.61 | + | 6084.01i | −0.145841 | + | 0.252605i | ||||
\(835\) | 33168.2 | 1.37465 | ||||||||
\(836\) | −4998.09 | + | 1792.64i | −0.206774 | + | 0.0741626i | ||||
\(837\) | 43352.6 | 1.79031 | ||||||||
\(838\) | −10124.5 | + | 17536.1i | −0.417357 | + | 0.722883i | ||||
\(839\) | −4061.92 | + | 7035.45i | −0.167143 | + | 0.289500i | −0.937414 | − | 0.348216i | \(-0.886788\pi\) |
0.770271 | + | 0.637716i | \(0.220121\pi\) | |||||||
\(840\) | 10018.8 | + | 17353.1i | 0.411525 | + | 0.712783i | ||||
\(841\) | 5184.73 | − | 8980.21i | 0.212585 | − | 0.368207i | ||||
\(842\) | 3146.27 | + | 5449.49i | 0.128774 | + | 0.223043i | ||||
\(843\) | 75537.5 | 3.08618 | ||||||||
\(844\) | −2124.08 | −0.0866277 | ||||||||
\(845\) | −18192.1 | − | 31509.7i | −0.740626 | − | 1.28280i | ||||
\(846\) | 12485.3 | + | 21625.3i | 0.507394 | + | 0.878832i | ||||
\(847\) | −17804.6 | −0.722283 | ||||||||
\(848\) | 3485.51 | 0.141147 | ||||||||
\(849\) | −9924.75 | − | 17190.2i | −0.401198 | − | 0.694895i | ||||
\(850\) | 4909.04 | − | 8502.70i | 0.198093 | − | 0.343106i | ||||
\(851\) | 526.692 | + | 912.258i | 0.0212160 | + | 0.0367471i | ||||
\(852\) | 12751.0 | − | 22085.4i | 0.512726 | − | 0.888067i | ||||
\(853\) | −22594.4 | + | 39134.7i | −0.906938 | + | 1.57086i | −0.0886427 | + | 0.996063i | \(0.528253\pi\) |
−0.818295 | + | 0.574799i | \(0.805080\pi\) | |||||||
\(854\) | −18695.6 | −0.749124 | ||||||||
\(855\) | 15073.9 | − | 83203.3i | 0.602942 | − | 3.32806i | ||||
\(856\) | −4007.39 | −0.160012 | ||||||||
\(857\) | −15246.2 | + | 26407.1i | −0.607700 | + | 1.05257i | 0.383918 | + | 0.923367i | \(0.374574\pi\) |
−0.991618 | + | 0.129201i | \(0.958759\pi\) | |||||||
\(858\) | −10300.3 | + | 17840.6i | −0.409844 | + | 0.709870i | ||||
\(859\) | 19527.3 | + | 33822.2i | 0.775625 | + | 1.34342i | 0.934443 | + | 0.356113i | \(0.115898\pi\) |
−0.158818 | + | 0.987308i | \(0.550768\pi\) | |||||||
\(860\) | 11380.0 | − | 19710.7i | 0.451226 | − | 0.781545i | ||||
\(861\) | −8659.65 | − | 14999.0i | −0.342764 | − | 0.593685i | ||||
\(862\) | −23324.6 | −0.921624 | ||||||||
\(863\) | −21510.4 | −0.848461 | −0.424230 | − | 0.905554i | \(-0.639455\pi\) | ||||
−0.424230 | + | 0.905554i | \(0.639455\pi\) | |||||||
\(864\) | 5777.97 | + | 10007.7i | 0.227512 | + | 0.394063i | ||||
\(865\) | 3198.73 | + | 5540.37i | 0.125734 | + | 0.217778i | ||||
\(866\) | 17938.1 | 0.703881 | ||||||||
\(867\) | −32028.1 | −1.25459 | ||||||||
\(868\) | −3980.00 | − | 6893.56i | −0.155634 | − | 0.269565i | ||||
\(869\) | 7023.30 | − | 12164.7i | 0.274165 | − | 0.474867i | ||||
\(870\) | −17890.8 | − | 30987.8i | −0.697190 | − | 1.20757i | ||||
\(871\) | −31634.7 | + | 54792.9i | −1.23066 | + | 2.13156i | ||||
\(872\) | 4851.69 | − | 8403.38i | 0.188416 | − | 0.326347i | ||||
\(873\) | −102624. | −3.97857 | ||||||||
\(874\) | 1407.91 | − | 7771.26i | 0.0544889 | − | 0.300763i | ||||
\(875\) | −274.603 | −0.0106095 | ||||||||
\(876\) | 3580.57 | − | 6201.73i | 0.138101 | − | 0.239197i | ||||
\(877\) | −4199.45 | + | 7273.66i | −0.161694 | + | 0.280062i | −0.935476 | − | 0.353390i | \(-0.885029\pi\) |
0.773783 | + | 0.633451i | \(0.218362\pi\) | |||||||
\(878\) | 98.3073 | + | 170.273i | 0.00377871 | + | 0.00654492i | ||||
\(879\) | 37448.1 | − | 64862.1i | 1.43697 | − | 2.48890i | ||||
\(880\) | −2023.20 | − | 3504.28i | −0.0775022 | − | 0.134238i | ||||
\(881\) | −46320.2 | −1.77136 | −0.885679 | − | 0.464298i | \(-0.846307\pi\) | ||||
−0.885679 | + | 0.464298i | \(0.846307\pi\) | |||||||
\(882\) | 8828.90 | 0.337057 | ||||||||
\(883\) | −16002.0 | − | 27716.2i | −0.609863 | − | 1.05631i | −0.991262 | − | 0.131904i | \(-0.957891\pi\) |
0.381399 | − | 0.924411i | \(-0.375442\pi\) | |||||||
\(884\) | 5315.33 | + | 9206.42i | 0.202233 | + | 0.350278i | ||||
\(885\) | 63943.7 | 2.42875 | ||||||||
\(886\) | 18640.9 | 0.706833 | ||||||||
\(887\) | 16782.7 | + | 29068.6i | 0.635298 | + | 1.10037i | 0.986452 | + | 0.164051i | \(0.0524561\pi\) |
−0.351154 | + | 0.936318i | \(0.614211\pi\) | |||||||
\(888\) | 846.272 | − | 1465.79i | 0.0319809 | − | 0.0553925i | ||||
\(889\) | −1980.13 | − | 3429.68i | −0.0747035 | − | 0.129390i | ||||
\(890\) | −15221.8 | + | 26365.0i | −0.573299 | + | 0.992984i | ||||
\(891\) | −13713.5 | + | 23752.5i | −0.515622 | + | 0.893084i | ||||
\(892\) | 19406.8 | 0.728463 | ||||||||
\(893\) | −15041.3 | + | 5394.81i | −0.563650 | + | 0.202162i | ||||
\(894\) | 42936.3 | 1.60627 | ||||||||
\(895\) | 12849.4 | − | 22255.8i | 0.479897 | − | 0.831206i | ||||
\(896\) | 1060.90 | − | 1837.53i | 0.0395559 | − | 0.0685127i | ||||
\(897\) | −15320.4 | − | 26535.8i | −0.570272 | − | 0.987741i | ||||
\(898\) | 9992.53 | − | 17307.6i | 0.371331 | − | 0.643164i | ||||
\(899\) | 7107.18 | + | 12310.0i | 0.263668 | + | 0.456687i | ||||
\(900\) | 32082.9 | 1.18826 | ||||||||
\(901\) | 8627.71 | 0.319013 | ||||||||
\(902\) | 1748.73 | + | 3028.89i | 0.0645525 | + | 0.111808i | ||||
\(903\) | 28623.6 | + | 49577.6i | 1.05486 | + | 1.82706i | ||||
\(904\) | −5911.65 | −0.217498 | ||||||||
\(905\) | 44760.1 | 1.64406 | ||||||||
\(906\) | −6111.67 | − | 10585.7i | −0.224113 | − | 0.388176i | ||||
\(907\) | −19984.2 | + | 34613.7i | −0.731604 | + | 1.26718i | 0.224593 | + | 0.974453i | \(0.427895\pi\) |
−0.956197 | + | 0.292723i | \(0.905439\pi\) | |||||||
\(908\) | 7943.77 | + | 13759.0i | 0.290334 | + | 0.502873i | ||||
\(909\) | 33772.6 | − | 58495.9i | 1.23231 | − | 2.13442i | ||||
\(910\) | −17550.9 | + | 30399.1i | −0.639348 | + | 1.10738i | ||||
\(911\) | 38734.2 | 1.40869 | 0.704347 | − | 0.709855i | \(-0.251240\pi\) | ||||
0.704347 | + | 0.709855i | \(0.251240\pi\) | |||||||
\(912\) | −11944.8 | + | 4284.19i | −0.433697 | + | 0.155552i | ||||
\(913\) | −7634.32 | −0.276735 | ||||||||
\(914\) | −1536.89 | + | 2661.97i | −0.0556190 | + | 0.0963350i | ||||
\(915\) | −42604.0 | + | 73792.3i | −1.53928 | + | 2.66612i | ||||
\(916\) | 157.969 | + | 273.610i | 0.00569807 | + | 0.00986935i | ||||
\(917\) | −2198.45 | + | 3807.82i | −0.0791702 | + | 0.137127i | ||||
\(918\) | 14302.3 | + | 24772.2i | 0.514210 | + | 0.890638i | ||||
\(919\) | 7565.87 | 0.271572 | 0.135786 | − | 0.990738i | \(-0.456644\pi\) | ||||
0.135786 | + | 0.990738i | \(0.456644\pi\) | |||||||
\(920\) | 6018.52 | 0.215679 | ||||||||
\(921\) | 28431.6 | + | 49245.0i | 1.01721 | + | 1.76187i | ||||
\(922\) | −16624.9 | − | 28795.2i | −0.593831 | − | 1.02855i | ||||
\(923\) | 44674.4 | 1.59315 | ||||||||
\(924\) | 10177.7 | 0.362363 | ||||||||
\(925\) | −1369.18 | − | 2371.49i | −0.0486684 | − | 0.0842962i | ||||
\(926\) | 7191.48 | − | 12456.0i | 0.255212 | − | 0.442041i | ||||
\(927\) | −46197.0 | − | 80015.6i | −1.63680 | − | 2.83501i | ||||
\(928\) | −1894.47 | + | 3281.31i | −0.0670139 | + | 0.116071i | ||||
\(929\) | 11858.4 | − | 20539.3i | 0.418796 | − | 0.725376i | −0.577023 | − | 0.816728i | \(-0.695786\pi\) |
0.995819 | + | 0.0913524i | \(0.0291190\pi\) | |||||||
\(930\) | −36278.8 | −1.27917 | ||||||||
\(931\) | −1007.19 | + | 5559.40i | −0.0354558 | + | 0.195706i | ||||
\(932\) | −6573.17 | −0.231021 | ||||||||
\(933\) | −8775.11 | + | 15198.9i | −0.307914 | + | 0.533323i | ||||
\(934\) | −7001.51 | + | 12127.0i | −0.245285 | + | 0.424847i | ||||
\(935\) | −5008.04 | − | 8674.18i | −0.175166 | − | 0.303397i | ||||
\(936\) | −17369.1 | + | 30084.2i | −0.606546 | + | 1.05057i | ||||
\(937\) | −22291.9 | − | 38610.8i | −0.777210 | − | 1.34617i | −0.933544 | − | 0.358463i | \(-0.883301\pi\) |
0.156334 | − | 0.987704i | \(-0.450032\pi\) | |||||||
\(938\) | 31258.4 | 1.08808 | ||||||||
\(939\) | −8985.93 | −0.312295 | ||||||||
\(940\) | −6088.64 | − | 10545.8i | −0.211265 | − | 0.365922i | ||||
\(941\) | 20086.2 | + | 34790.3i | 0.695846 | + | 1.20524i | 0.969895 | + | 0.243525i | \(0.0783037\pi\) |
−0.274049 | + | 0.961716i | \(0.588363\pi\) | |||||||
\(942\) | −40719.1 | −1.40839 | ||||||||
\(943\) | −5202.05 | −0.179642 | ||||||||
\(944\) | −3385.52 | − | 5863.89i | −0.116726 | − | 0.202175i | ||||
\(945\) | −47225.2 | + | 81796.5i | −1.62565 | + | 2.81570i | ||||
\(946\) | −5780.26 | − | 10011.7i | −0.198660 | − | 0.344089i | ||||
\(947\) | 21487.4 | − | 37217.2i | 0.737324 | − | 1.27708i | −0.216372 | − | 0.976311i | \(-0.569423\pi\) |
0.953696 | − | 0.300772i | \(-0.0972442\pi\) | |||||||
\(948\) | 16784.8 | − | 29072.1i | 0.575047 | − | 0.996011i | ||||
\(949\) | 12544.9 | 0.429108 | ||||||||
\(950\) | −3659.98 | + | 20202.0i | −0.124995 | + | 0.689936i | ||||
\(951\) | −70975.8 | −2.42014 | ||||||||
\(952\) | 2626.05 | − | 4548.45i | 0.0894019 | − | 0.154849i | ||||
\(953\) | −16391.0 | + | 28390.0i | −0.557141 | + | 0.964997i | 0.440592 | + | 0.897707i | \(0.354769\pi\) |
−0.997733 | + | 0.0672898i | \(0.978565\pi\) | |||||||
\(954\) | 14096.5 | + | 24415.9i | 0.478399 | + | 0.828611i | ||||
\(955\) | −27784.1 | + | 48123.5i | −0.941438 | + | 1.63062i | ||||
\(956\) | 12633.5 | + | 21881.8i | 0.427402 | + | 0.740281i | ||||
\(957\) | −18174.6 | −0.613900 | ||||||||
\(958\) | −3823.67 | −0.128953 | ||||||||
\(959\) | −20210.5 | − | 35005.6i | −0.680532 | − | 1.17872i | ||||
\(960\) | −4835.18 | − | 8374.78i | −0.162557 | − | 0.281557i | ||||
\(961\) | −15379.1 | −0.516234 | ||||||||
\(962\) | 2964.99 | 0.0993713 | ||||||||
\(963\) | −16207.2 | − | 28071.7i | −0.542337 | − | 0.939355i | ||||
\(964\) | 6989.31 | − | 12105.8i | 0.233517 | − | 0.404464i | ||||
\(965\) | −37357.9 | − | 64705.7i | −1.24621 | − | 2.15850i | ||||
\(966\) | −7569.08 | + | 13110.0i | −0.252103 | + | 0.436655i | ||||
\(967\) | −9881.92 | + | 17116.0i | −0.328626 | + | 0.569196i | −0.982239 | − | 0.187632i | \(-0.939919\pi\) |
0.653614 | + | 0.756828i | \(0.273252\pi\) | |||||||
\(968\) | 8592.71 | 0.285310 | ||||||||
\(969\) | −29567.1 | + | 10604.7i | −0.980219 | + | 0.351571i | ||||
\(970\) | 50045.8 | 1.65657 | ||||||||
\(971\) | −6926.88 | + | 11997.7i | −0.228933 | + | 0.396524i | −0.957492 | − | 0.288459i | \(-0.906857\pi\) |
0.728559 | + | 0.684983i | \(0.240190\pi\) | |||||||
\(972\) | −13272.9 | + | 22989.3i | −0.437991 | + | 0.758622i | ||||
\(973\) | 3040.08 | + | 5265.58i | 0.100165 | + | 0.173491i | ||||
\(974\) | −6061.32 | + | 10498.5i | −0.199402 | + | 0.345374i | ||||
\(975\) | 39826.7 | + | 68981.8i | 1.30818 | + | 2.26583i | ||||
\(976\) | 9022.72 | 0.295912 | ||||||||
\(977\) | 53113.0 | 1.73924 | 0.869620 | − | 0.493722i | \(-0.164364\pi\) | ||||
0.869620 | + | 0.493722i | \(0.164364\pi\) | |||||||
\(978\) | −1532.65 | − | 2654.64i | −0.0501113 | − | 0.0867954i | ||||
\(979\) | 7731.65 | + | 13391.6i | 0.252405 | + | 0.437179i | ||||
\(980\) | −4305.53 | −0.140342 | ||||||||
\(981\) | 78487.4 | 2.55444 | ||||||||
\(982\) | 6439.02 | + | 11152.7i | 0.209244 | + | 0.362421i | ||||
\(983\) | 8672.89 | − | 15021.9i | 0.281406 | − | 0.487410i | −0.690325 | − | 0.723499i | \(-0.742533\pi\) |
0.971731 | + | 0.236090i | \(0.0758659\pi\) | |||||||
\(984\) | 4179.24 | + | 7238.66i | 0.135396 | + | 0.234512i | ||||
\(985\) | −18596.9 | + | 32210.8i | −0.601570 | + | 1.04195i | ||||
\(986\) | −4689.39 | + | 8122.27i | −0.151461 | + | 0.262338i | ||||
\(987\) | 30629.0 | 0.987774 | ||||||||
\(988\) | −16962.0 | − | 14369.0i | −0.546187 | − | 0.462690i | ||||
\(989\) | 17194.9 | 0.552847 | ||||||||
\(990\) | 16365.0 | − | 28344.9i | 0.525366 | − | 0.909961i | ||||
\(991\) | 3316.70 | − | 5744.69i | 0.106315 | − | 0.184143i | −0.807960 | − | 0.589238i | \(-0.799428\pi\) |
0.914275 | + | 0.405095i | \(0.132761\pi\) | |||||||
\(992\) | 1920.79 | + | 3326.91i | 0.0614770 | + | 0.106481i | ||||
\(993\) | 25917.3 | − | 44890.1i | 0.828258 | − | 1.43459i | ||||
\(994\) | −11035.7 | − | 19114.4i | −0.352145 | − | 0.609933i | ||||
\(995\) | 10810.5 | 0.344438 | ||||||||
\(996\) | −18245.0 | −0.580438 | ||||||||
\(997\) | 10306.3 | + | 17851.0i | 0.327386 | + | 0.567049i | 0.981992 | − | 0.188921i | \(-0.0604989\pi\) |
−0.654606 | + | 0.755970i | \(0.727166\pi\) | |||||||
\(998\) | 16458.1 | + | 28506.3i | 0.522017 | + | 0.904161i | ||||
\(999\) | 7978.08 | 0.252668 |
(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 | 38.4.c.c.11.1 | yes | 6 | |
3.2 | odd | 2 | 342.4.g.f.163.3 | 6 | |||
4.3 | odd | 2 | 304.4.i.e.49.3 | 6 | |||
19.7 | even | 3 | inner | 38.4.c.c.7.1 | ✓ | 6 | |
19.8 | odd | 6 | 722.4.a.k.1.1 | 3 | |||
19.11 | even | 3 | 722.4.a.j.1.3 | 3 | |||
57.26 | odd | 6 | 342.4.g.f.235.3 | 6 | |||
76.7 | odd | 6 | 304.4.i.e.273.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.4.c.c.7.1 | ✓ | 6 | 19.7 | even | 3 | inner | |
38.4.c.c.11.1 | yes | 6 | 1.1 | even | 1 | trivial | |
304.4.i.e.49.3 | 6 | 4.3 | odd | 2 | |||
304.4.i.e.273.3 | 6 | 76.7 | odd | 6 | |||
342.4.g.f.163.3 | 6 | 3.2 | odd | 2 | |||
342.4.g.f.235.3 | 6 | 57.26 | odd | 6 | |||
722.4.a.j.1.3 | 3 | 19.11 | even | 3 | |||
722.4.a.k.1.1 | 3 | 19.8 | odd | 6 |