Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [168,4,Mod(125,168)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(168, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("168.125");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 168 = 2^{3} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 168.i (of order \(2\), degree \(1\), 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: | \(9.91232088096\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 125.69 | ||
Character | \(\chi\) | \(=\) | 168.125 |
Dual form | 168.4.i.c.125.71 |
$q$-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 \(\left(\mathbb{Z}/168\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(85\) | \(113\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.60932 | − | 1.09154i | 0.922533 | − | 0.385918i | ||||
\(3\) | −4.05635 | − | 3.24747i | −0.780644 | − | 0.624976i | ||||
\(4\) | 5.61708 | − | 5.69635i | 0.702135 | − | 0.712044i | ||||
\(5\) | − | 13.2397i | − | 1.18419i | −0.805868 | − | 0.592095i | \(-0.798301\pi\) | ||
0.805868 | − | 0.592095i | \(-0.201699\pi\) | |||||||
\(6\) | −14.1290 | − | 4.04602i | −0.961359 | − | 0.275297i | ||||
\(7\) | 18.4748 | − | 1.29729i | 0.997544 | − | 0.0700470i | ||||
\(8\) | 8.43895 | − | 20.9949i | 0.372953 | − | 0.927850i | ||||
\(9\) | 5.90788 | + | 26.3457i | 0.218810 | + | 0.975767i | ||||
\(10\) | −14.4516 | − | 34.5465i | −0.457000 | − | 1.09246i | ||||
\(11\) | −49.5250 | −1.35749 | −0.678743 | − | 0.734376i | \(-0.737475\pi\) | ||||
−0.678743 | + | 0.734376i | \(0.737475\pi\) | |||||||
\(12\) | −41.2835 | + | 4.86507i | −0.993128 | + | 0.117035i | ||||
\(13\) | 28.7924 | 0.614276 | 0.307138 | − | 0.951665i | \(-0.400629\pi\) | ||||
0.307138 | + | 0.951665i | \(0.400629\pi\) | |||||||
\(14\) | 46.7905 | − | 23.5510i | 0.893235 | − | 0.449590i | ||||
\(15\) | −42.9954 | + | 53.7046i | −0.740091 | + | 0.924432i | ||||
\(16\) | −0.896814 | − | 63.9937i | −0.0140127 | − | 0.999902i | ||||
\(17\) | −69.2560 | −0.988061 | −0.494031 | − | 0.869445i | \(-0.664477\pi\) | ||||
−0.494031 | + | 0.869445i | \(0.664477\pi\) | |||||||
\(18\) | 44.1730 | + | 62.2957i | 0.578426 | + | 0.815735i | ||||
\(19\) | −24.7890 | −0.299315 | −0.149658 | − | 0.988738i | \(-0.547817\pi\) | ||||
−0.149658 | + | 0.988738i | \(0.547817\pi\) | |||||||
\(20\) | −75.4177 | − | 74.3682i | −0.843196 | − | 0.831462i | ||||
\(21\) | −79.1529 | − | 54.7340i | −0.822504 | − | 0.568759i | ||||
\(22\) | −129.227 | + | 54.0585i | −1.25233 | + | 0.523878i | ||||
\(23\) | − | 85.5006i | − | 0.775135i | −0.921841 | − | 0.387568i | \(-0.873315\pi\) | ||
0.921841 | − | 0.387568i | \(-0.126685\pi\) | |||||||
\(24\) | −102.411 | + | 57.7572i | −0.871027 | + | 0.491235i | ||||
\(25\) | −50.2885 | −0.402308 | ||||||||
\(26\) | 75.1286 | − | 31.4281i | 0.566690 | − | 0.237060i | ||||
\(27\) | 61.5925 | − | 126.053i | 0.439018 | − | 0.898478i | ||||
\(28\) | 96.3845 | − | 112.526i | 0.650534 | − | 0.759477i | ||||
\(29\) | 111.594 | 0.714569 | 0.357284 | − | 0.933996i | \(-0.383703\pi\) | ||||
0.357284 | + | 0.933996i | \(0.383703\pi\) | |||||||
\(30\) | −53.5679 | + | 187.064i | −0.326004 | + | 1.13843i | ||||
\(31\) | 236.812i | 1.37202i | 0.727592 | + | 0.686010i | \(0.240640\pi\) | ||||
−0.727592 | + | 0.686010i | \(0.759360\pi\) | |||||||
\(32\) | −72.1918 | − | 166.001i | −0.398807 | − | 0.917035i | ||||
\(33\) | 200.891 | + | 160.831i | 1.05971 | + | 0.848396i | ||||
\(34\) | −180.711 | + | 75.5957i | −0.911519 | + | 0.381310i | ||||
\(35\) | −17.1756 | − | 244.600i | −0.0829490 | − | 1.18128i | ||||
\(36\) | 183.260 | + | 114.333i | 0.848424 | + | 0.529318i | ||||
\(37\) | − | 261.434i | − | 1.16161i | −0.814044 | − | 0.580804i | \(-0.802738\pi\) | ||
0.814044 | − | 0.580804i | \(-0.197262\pi\) | |||||||
\(38\) | −64.6825 | + | 27.0582i | −0.276128 | + | 0.115511i | ||||
\(39\) | −116.792 | − | 93.5026i | −0.479531 | − | 0.383908i | ||||
\(40\) | −277.965 | − | 111.729i | −1.09875 | − | 0.441647i | ||||
\(41\) | 471.089 | 1.79443 | 0.897217 | − | 0.441590i | \(-0.145585\pi\) | ||||
0.897217 | + | 0.441590i | \(0.145585\pi\) | |||||||
\(42\) | −266.280 | − | 56.4198i | −0.978282 | − | 0.207280i | ||||
\(43\) | 261.133i | 0.926101i | 0.886332 | + | 0.463051i | \(0.153245\pi\) | ||||
−0.886332 | + | 0.463051i | \(0.846755\pi\) | |||||||
\(44\) | −278.186 | + | 282.112i | −0.953139 | + | 0.966590i | ||||
\(45\) | 348.808 | − | 78.2183i | 1.15549 | − | 0.259113i | ||||
\(46\) | −93.3274 | − | 223.098i | −0.299138 | − | 0.715088i | ||||
\(47\) | −217.418 | −0.674757 | −0.337379 | − | 0.941369i | \(-0.609540\pi\) | ||||
−0.337379 | + | 0.941369i | \(0.609540\pi\) | |||||||
\(48\) | −204.180 | + | 262.493i | −0.613975 | + | 0.789325i | ||||
\(49\) | 339.634 | − | 47.9342i | 0.990187 | − | 0.139750i | ||||
\(50\) | −131.219 | + | 54.8919i | −0.371142 | + | 0.155258i | ||||
\(51\) | 280.926 | + | 224.907i | 0.771324 | + | 0.617514i | ||||
\(52\) | 161.729 | − | 164.012i | 0.431305 | − | 0.437391i | ||||
\(53\) | 11.8711 | 0.0307665 | 0.0153832 | − | 0.999882i | \(-0.495103\pi\) | ||||
0.0153832 | + | 0.999882i | \(0.495103\pi\) | |||||||
\(54\) | 23.1225 | − | 396.143i | 0.0582699 | − | 0.998301i | ||||
\(55\) | 655.694i | 1.60752i | ||||||||
\(56\) | 128.671 | − | 398.823i | 0.307043 | − | 0.951696i | ||||
\(57\) | 100.553 | + | 80.5016i | 0.233659 | + | 0.187065i | ||||
\(58\) | 291.184 | − | 121.809i | 0.659213 | − | 0.275765i | ||||
\(59\) | 236.528i | 0.521921i | 0.965350 | + | 0.260960i | \(0.0840392\pi\) | ||||
−0.965350 | + | 0.260960i | \(0.915961\pi\) | |||||||
\(60\) | 64.4118 | + | 546.580i | 0.138592 | + | 1.17605i | ||||
\(61\) | 754.519 | 1.58371 | 0.791855 | − | 0.610709i | \(-0.209116\pi\) | ||||
0.791855 | + | 0.610709i | \(0.209116\pi\) | |||||||
\(62\) | 258.490 | + | 617.917i | 0.529487 | + | 1.26573i | ||||
\(63\) | 143.325 | + | 479.067i | 0.286623 | + | 0.958044i | ||||
\(64\) | −369.568 | − | 354.349i | −0.721813 | − | 0.692088i | ||||
\(65\) | − | 381.202i | − | 0.727420i | ||||||
\(66\) | 699.741 | + | 200.379i | 1.30503 | + | 0.373711i | ||||
\(67\) | − | 163.127i | − | 0.297449i | −0.988879 | − | 0.148725i | \(-0.952483\pi\) | ||
0.988879 | − | 0.148725i | \(-0.0475168\pi\) | |||||||
\(68\) | −389.016 | + | 394.506i | −0.693752 | + | 0.703543i | ||||
\(69\) | −277.661 | + | 346.820i | −0.484441 | + | 0.605105i | ||||
\(70\) | −311.807 | − | 619.490i | −0.532401 | − | 1.05776i | ||||
\(71\) | − | 478.338i | − | 0.799554i | −0.916613 | − | 0.399777i | \(-0.869088\pi\) | ||
0.916613 | − | 0.399777i | \(-0.130912\pi\) | |||||||
\(72\) | 602.981 | + | 98.2952i | 0.986972 | + | 0.160892i | ||||
\(73\) | − | 1038.37i | − | 1.66482i | −0.554157 | − | 0.832412i | \(-0.686959\pi\) | ||
0.554157 | − | 0.832412i | \(-0.313041\pi\) | |||||||
\(74\) | −285.366 | − | 682.164i | −0.448285 | − | 1.07162i | ||||
\(75\) | 203.988 | + | 163.310i | 0.314059 | + | 0.251433i | ||||
\(76\) | −139.242 | + | 141.207i | −0.210160 | + | 0.213126i | ||||
\(77\) | −914.963 | + | 64.2482i | −1.35415 | + | 0.0950878i | ||||
\(78\) | −406.810 | − | 116.495i | −0.590540 | − | 0.169108i | ||||
\(79\) | −148.084 | −0.210895 | −0.105448 | − | 0.994425i | \(-0.533628\pi\) | ||||
−0.105448 | + | 0.994425i | \(0.533628\pi\) | |||||||
\(80\) | −847.255 | + | 11.8735i | −1.18407 | + | 0.0165937i | ||||
\(81\) | −659.194 | + | 311.295i | −0.904244 | + | 0.427016i | ||||
\(82\) | 1229.22 | − | 514.213i | 1.65542 | − | 0.692504i | ||||
\(83\) | − | 739.797i | − | 0.978353i | −0.872185 | − | 0.489176i | \(-0.837297\pi\) | ||
0.872185 | − | 0.489176i | \(-0.162703\pi\) | |||||||
\(84\) | −756.393 | + | 143.438i | −0.982490 | + | 0.186313i | ||||
\(85\) | 916.925i | 1.17005i | ||||||||
\(86\) | 285.037 | + | 681.378i | 0.357399 | + | 0.854359i | ||||
\(87\) | −452.664 | − | 362.398i | −0.557824 | − | 0.446588i | ||||
\(88\) | −417.939 | + | 1039.77i | −0.506278 | + | 1.25954i | ||||
\(89\) | 1347.82 | 1.60527 | 0.802635 | − | 0.596470i | \(-0.203431\pi\) | ||||
0.802635 | + | 0.596470i | \(0.203431\pi\) | |||||||
\(90\) | 824.773 | − | 584.835i | 0.965986 | − | 0.684967i | ||||
\(91\) | 531.934 | − | 37.3521i | 0.612767 | − | 0.0430282i | ||||
\(92\) | −487.042 | − | 480.264i | −0.551930 | − | 0.544250i | ||||
\(93\) | 769.039 | − | 960.590i | 0.857480 | − | 1.07106i | ||||
\(94\) | −567.311 | + | 237.320i | −0.622486 | + | 0.260401i | ||||
\(95\) | 328.198i | 0.354447i | ||||||||
\(96\) | −246.249 | + | 907.798i | −0.261798 | + | 0.965123i | ||||
\(97\) | 183.115i | 0.191675i | 0.995397 | + | 0.0958375i | \(0.0305529\pi\) | ||||
−0.995397 | + | 0.0958375i | \(0.969447\pi\) | |||||||
\(98\) | 833.891 | − | 495.800i | 0.859548 | − | 0.511054i | ||||
\(99\) | −292.588 | − | 1304.77i | −0.297032 | − | 1.32459i | ||||
\(100\) | −282.475 | + | 286.461i | −0.282475 | + | 0.286461i | ||||
\(101\) | 857.904i | 0.845194i | 0.906318 | + | 0.422597i | \(0.138882\pi\) | ||||
−0.906318 | + | 0.422597i | \(0.861118\pi\) | |||||||
\(102\) | 978.520 | + | 280.211i | 0.949882 | + | 0.272010i | ||||
\(103\) | 493.737i | 0.472324i | 0.971714 | + | 0.236162i | \(0.0758896\pi\) | ||||
−0.971714 | + | 0.236162i | \(0.924110\pi\) | |||||||
\(104\) | 242.978 | − | 604.493i | 0.229096 | − | 0.569956i | ||||
\(105\) | −724.659 | + | 1047.96i | −0.673519 | + | 0.974002i | ||||
\(106\) | 30.9755 | − | 12.9578i | 0.0283831 | − | 0.0118733i | ||||
\(107\) | 583.614 | 0.527290 | 0.263645 | − | 0.964620i | \(-0.415075\pi\) | ||||
0.263645 | + | 0.964620i | \(0.415075\pi\) | |||||||
\(108\) | −372.072 | − | 1058.90i | −0.331506 | − | 0.943453i | ||||
\(109\) | 1856.22i | 1.63113i | 0.578665 | + | 0.815565i | \(0.303574\pi\) | ||||
−0.578665 | + | 0.815565i | \(0.696426\pi\) | |||||||
\(110\) | 715.716 | + | 1710.91i | 0.620372 | + | 1.48299i | ||||
\(111\) | −848.999 | + | 1060.47i | −0.725976 | + | 0.906802i | ||||
\(112\) | −99.5867 | − | 1181.11i | −0.0840184 | − | 0.996464i | ||||
\(113\) | − | 951.492i | − | 0.792114i | −0.918226 | − | 0.396057i | \(-0.870378\pi\) | ||
0.918226 | − | 0.396057i | \(-0.129622\pi\) | |||||||
\(114\) | 350.245 | + | 100.297i | 0.287750 | + | 0.0824005i | ||||
\(115\) | −1132.00 | −0.917908 | ||||||||
\(116\) | 626.833 | − | 635.679i | 0.501724 | − | 0.508804i | ||||
\(117\) | 170.102 | + | 758.558i | 0.134410 | + | 0.599390i | ||||
\(118\) | 258.180 | + | 617.177i | 0.201418 | + | 0.481489i | ||||
\(119\) | −1279.49 | + | 89.8449i | −0.985634 | + | 0.0692107i | ||||
\(120\) | 764.685 | + | 1355.89i | 0.581716 | + | 1.03146i | ||||
\(121\) | 1121.73 | 0.842770 | ||||||||
\(122\) | 1968.78 | − | 823.588i | 1.46102 | − | 0.611182i | ||||
\(123\) | −1910.90 | − | 1529.85i | −1.40081 | − | 1.12148i | ||||
\(124\) | 1348.96 | + | 1330.19i | 0.976939 | + | 0.963344i | ||||
\(125\) | − | 989.155i | − | 0.707781i | ||||||
\(126\) | 896.900 | + | 1093.59i | 0.634145 | + | 0.773214i | ||||
\(127\) | 2550.61 | 1.78213 | 0.891065 | − | 0.453876i | \(-0.149959\pi\) | ||||
0.891065 | + | 0.453876i | \(0.149959\pi\) | |||||||
\(128\) | −1351.11 | − | 521.212i | −0.932985 | − | 0.359914i | ||||
\(129\) | 848.020 | − | 1059.24i | 0.578791 | − | 0.722956i | ||||
\(130\) | −416.097 | − | 994.677i | −0.280724 | − | 0.671069i | ||||
\(131\) | 439.670i | 0.293238i | 0.989193 | + | 0.146619i | \(0.0468391\pi\) | ||||
−0.989193 | + | 0.146619i | \(0.953161\pi\) | |||||||
\(132\) | 2044.57 | − | 240.943i | 1.34816 | − | 0.158874i | ||||
\(133\) | −457.972 | + | 32.1585i | −0.298580 | + | 0.0209661i | ||||
\(134\) | −178.059 | − | 425.650i | −0.114791 | − | 0.274407i | ||||
\(135\) | −1668.90 | − | 815.464i | −1.06397 | − | 0.519881i | ||||
\(136\) | −584.448 | + | 1454.02i | −0.368500 | + | 0.916773i | ||||
\(137\) | 1126.88i | 0.702745i | 0.936236 | + | 0.351373i | \(0.114285\pi\) | ||||
−0.936236 | + | 0.351373i | \(0.885715\pi\) | |||||||
\(138\) | −345.937 | + | 1208.04i | −0.213392 | + | 0.745184i | ||||
\(139\) | −2419.55 | −1.47643 | −0.738215 | − | 0.674565i | \(-0.764331\pi\) | ||||
−0.738215 | + | 0.674565i | \(0.764331\pi\) | |||||||
\(140\) | −1489.80 | − | 1276.10i | −0.899366 | − | 0.770356i | ||||
\(141\) | 881.921 | + | 706.057i | 0.526745 | + | 0.421707i | ||||
\(142\) | −522.125 | − | 1248.14i | −0.308562 | − | 0.737615i | ||||
\(143\) | −1425.95 | −0.833871 | ||||||||
\(144\) | 1680.66 | − | 401.695i | 0.972605 | − | 0.232462i | ||||
\(145\) | − | 1477.47i | − | 0.846186i | ||||||
\(146\) | −1133.42 | − | 2709.44i | −0.642485 | − | 1.53586i | ||||
\(147\) | −1533.34 | − | 908.514i | −0.860324 | − | 0.509748i | ||||
\(148\) | −1489.22 | − | 1468.50i | −0.827115 | − | 0.815605i | ||||
\(149\) | −2049.54 | −1.12688 | −0.563439 | − | 0.826158i | \(-0.690522\pi\) | ||||
−0.563439 | + | 0.826158i | \(0.690522\pi\) | |||||||
\(150\) | 710.528 | + | 203.468i | 0.386762 | + | 0.110754i | ||||
\(151\) | 288.181 | 0.155310 | 0.0776551 | − | 0.996980i | \(-0.475257\pi\) | ||||
0.0776551 | + | 0.996980i | \(0.475257\pi\) | |||||||
\(152\) | −209.193 | + | 520.442i | −0.111630 | + | 0.277720i | ||||
\(153\) | −409.156 | − | 1824.60i | −0.216198 | − | 0.964118i | ||||
\(154\) | −2317.30 | + | 1166.36i | −1.21255 | + | 0.610313i | ||||
\(155\) | 3135.31 | 1.62473 | ||||||||
\(156\) | −1188.65 | + | 140.077i | −0.610054 | + | 0.0718920i | ||||
\(157\) | −2088.48 | −1.06165 | −0.530824 | − | 0.847482i | \(-0.678117\pi\) | ||||
−0.530824 | + | 0.847482i | \(0.678117\pi\) | |||||||
\(158\) | −386.398 | + | 161.639i | −0.194558 | + | 0.0813883i | ||||
\(159\) | −48.1534 | − | 38.5511i | −0.0240177 | − | 0.0192283i | ||||
\(160\) | −2197.80 | + | 955.794i | −1.08594 | + | 0.472264i | ||||
\(161\) | −110.919 | − | 1579.60i | −0.0542959 | − | 0.773231i | ||||
\(162\) | −1380.26 | + | 1531.80i | −0.669402 | + | 0.742900i | ||||
\(163\) | 4111.75i | 1.97581i | 0.155057 | + | 0.987906i | \(0.450444\pi\) | ||||
−0.155057 | + | 0.987906i | \(0.549556\pi\) | |||||||
\(164\) | 2646.15 | − | 2683.49i | 1.25993 | − | 1.27772i | ||||
\(165\) | 2129.35 | − | 2659.72i | 1.00466 | − | 1.25490i | ||||
\(166\) | −807.518 | − | 1930.37i | −0.377564 | − | 0.902563i | ||||
\(167\) | −1224.94 | −0.567598 | −0.283799 | − | 0.958884i | \(-0.591595\pi\) | ||||
−0.283799 | + | 0.958884i | \(0.591595\pi\) | |||||||
\(168\) | −1817.10 | + | 1199.91i | −0.834478 | + | 0.551041i | ||||
\(169\) | −1368.00 | −0.622665 | ||||||||
\(170\) | 1000.86 | + | 2392.55i | 0.451544 | + | 1.07941i | ||||
\(171\) | −146.451 | − | 653.085i | −0.0654934 | − | 0.292062i | ||||
\(172\) | 1487.50 | + | 1466.80i | 0.659425 | + | 0.650248i | ||||
\(173\) | 2451.51i | 1.07737i | 0.842508 | + | 0.538685i | \(0.181079\pi\) | ||||
−0.842508 | + | 0.538685i | \(0.818921\pi\) | |||||||
\(174\) | −1576.72 | − | 451.511i | −0.686957 | − | 0.196718i | ||||
\(175\) | −929.068 | + | 65.2386i | −0.401320 | + | 0.0281804i | ||||
\(176\) | 44.4147 | + | 3169.29i | 0.0190221 | + | 1.35735i | ||||
\(177\) | 768.118 | − | 959.439i | 0.326188 | − | 0.407434i | ||||
\(178\) | 3516.90 | − | 1471.20i | 1.48091 | − | 0.619502i | ||||
\(179\) | −926.214 | −0.386751 | −0.193376 | − | 0.981125i | \(-0.561944\pi\) | ||||
−0.193376 | + | 0.981125i | \(0.561944\pi\) | |||||||
\(180\) | 1513.72 | − | 2426.29i | 0.626813 | − | 1.00470i | ||||
\(181\) | −876.720 | −0.360034 | −0.180017 | − | 0.983664i | \(-0.557615\pi\) | ||||
−0.180017 | + | 0.983664i | \(0.557615\pi\) | |||||||
\(182\) | 1347.21 | − | 678.090i | 0.548693 | − | 0.276173i | ||||
\(183\) | −3060.59 | − | 2450.28i | −1.23631 | − | 0.989780i | ||||
\(184\) | −1795.07 | − | 721.536i | −0.719210 | − | 0.289089i | ||||
\(185\) | −3461.29 | −1.37556 | ||||||||
\(186\) | 958.144 | − | 3345.92i | 0.377713 | − | 1.31901i | ||||
\(187\) | 3429.90 | 1.34128 | ||||||||
\(188\) | −1221.25 | + | 1238.49i | −0.473771 | + | 0.480457i | ||||
\(189\) | 974.380 | − | 2408.70i | 0.375004 | − | 0.927023i | ||||
\(190\) | 358.242 | + | 856.374i | 0.136787 | + | 0.326989i | ||||
\(191\) | 2476.56i | 0.938208i | 0.883143 | + | 0.469104i | \(0.155423\pi\) | ||||
−0.883143 | + | 0.469104i | \(0.844577\pi\) | |||||||
\(192\) | 348.358 | + | 2637.52i | 0.130940 | + | 0.991390i | ||||
\(193\) | 3130.49 | 1.16755 | 0.583776 | − | 0.811915i | \(-0.301575\pi\) | ||||
0.583776 | + | 0.811915i | \(0.301575\pi\) | |||||||
\(194\) | 199.877 | + | 477.804i | 0.0739708 | + | 0.176827i | ||||
\(195\) | −1237.94 | + | 1546.29i | −0.454620 | + | 0.567856i | ||||
\(196\) | 1634.70 | − | 2203.92i | 0.595737 | − | 0.803180i | ||||
\(197\) | −85.4470 | −0.0309028 | −0.0154514 | − | 0.999881i | \(-0.504919\pi\) | ||||
−0.0154514 | + | 0.999881i | \(0.504919\pi\) | |||||||
\(198\) | −2187.67 | − | 3085.19i | −0.785205 | − | 1.10735i | ||||
\(199\) | − | 3536.74i | − | 1.25986i | −0.776650 | − | 0.629932i | \(-0.783083\pi\) | ||
0.776650 | − | 0.629932i | \(-0.216917\pi\) | |||||||
\(200\) | −424.382 | + | 1055.80i | −0.150042 | + | 0.373282i | ||||
\(201\) | −529.749 | + | 661.699i | −0.185899 | + | 0.232202i | ||||
\(202\) | 936.437 | + | 2238.54i | 0.326176 | + | 0.779720i | ||||
\(203\) | 2061.67 | − | 144.770i | 0.712814 | − | 0.0500534i | ||||
\(204\) | 2859.13 | − | 336.935i | 0.981271 | − | 0.115638i | ||||
\(205\) | − | 6237.06i | − | 2.12495i | ||||||
\(206\) | 538.934 | + | 1288.32i | 0.182278 | + | 0.435735i | ||||
\(207\) | 2252.58 | − | 505.128i | 0.756352 | − | 0.169608i | ||||
\(208\) | −25.8215 | − | 1842.54i | −0.00860767 | − | 0.614216i | ||||
\(209\) | 1227.68 | 0.406317 | ||||||||
\(210\) | −746.979 | + | 3525.45i | −0.245459 | + | 1.15847i | ||||
\(211\) | − | 1696.15i | − | 0.553403i | −0.960956 | − | 0.276701i | \(-0.910759\pi\) | ||
0.960956 | − | 0.276701i | \(-0.0892413\pi\) | |||||||
\(212\) | 66.6810 | − | 67.6221i | 0.0216022 | − | 0.0219071i | ||||
\(213\) | −1553.39 | + | 1940.31i | −0.499702 | + | 0.624167i | ||||
\(214\) | 1522.83 | − | 637.038i | 0.486443 | − | 0.203491i | ||||
\(215\) | 3457.31 | 1.09668 | ||||||||
\(216\) | −2126.69 | − | 2356.88i | −0.669921 | − | 0.742433i | ||||
\(217\) | 307.213 | + | 4375.04i | 0.0961059 | + | 1.36865i | ||||
\(218\) | 2026.13 | + | 4843.46i | 0.629482 | + | 1.50477i | ||||
\(219\) | −3372.08 | + | 4211.99i | −1.04047 | + | 1.29964i | ||||
\(220\) | 3735.06 | + | 3683.09i | 1.14463 | + | 1.12870i | ||||
\(221\) | −1994.05 | −0.606942 | ||||||||
\(222\) | −1057.77 | + | 3693.81i | −0.319786 | + | 1.11672i | ||||
\(223\) | − | 3936.51i | − | 1.18210i | −0.806635 | − | 0.591050i | \(-0.798714\pi\) | ||
0.806635 | − | 0.591050i | \(-0.201286\pi\) | |||||||
\(224\) | −1549.08 | − | 2973.18i | −0.462063 | − | 0.886847i | ||||
\(225\) | −297.099 | − | 1324.89i | −0.0880292 | − | 0.392559i | ||||
\(226\) | −1038.59 | − | 2482.75i | −0.305691 | − | 0.730751i | ||||
\(227\) | 6229.85i | 1.82154i | 0.412912 | + | 0.910771i | \(0.364512\pi\) | ||||
−0.412912 | + | 0.910771i | \(0.635488\pi\) | |||||||
\(228\) | 1023.38 | − | 120.600i | 0.297258 | − | 0.0350305i | ||||
\(229\) | 3973.83 | 1.14672 | 0.573359 | − | 0.819304i | \(-0.305640\pi\) | ||||
0.573359 | + | 0.819304i | \(0.305640\pi\) | |||||||
\(230\) | −2953.75 | + | 1235.62i | −0.846801 | + | 0.354237i | ||||
\(231\) | 3920.05 | + | 2710.70i | 1.11654 | + | 0.772083i | ||||
\(232\) | 941.737 | − | 2342.90i | 0.266500 | − | 0.663013i | ||||
\(233\) | 3401.07i | 0.956273i | 0.878285 | + | 0.478137i | \(0.158688\pi\) | ||||
−0.878285 | + | 0.478137i | \(0.841312\pi\) | |||||||
\(234\) | 1271.85 | + | 1793.64i | 0.355313 | + | 0.501086i | ||||
\(235\) | 2878.53i | 0.799042i | ||||||||
\(236\) | 1347.35 | + | 1328.60i | 0.371630 | + | 0.366459i | ||||
\(237\) | 600.679 | + | 480.898i | 0.164634 | + | 0.131804i | ||||
\(238\) | −3240.52 | + | 1631.05i | −0.882571 | + | 0.444223i | ||||
\(239\) | 4477.57i | 1.21184i | 0.795525 | + | 0.605920i | \(0.207195\pi\) | ||||
−0.795525 | + | 0.605920i | \(0.792805\pi\) | |||||||
\(240\) | 3475.32 | + | 2703.27i | 0.934712 | + | 0.727064i | ||||
\(241\) | 2312.70i | 0.618151i | 0.951037 | + | 0.309076i | \(0.100020\pi\) | ||||
−0.951037 | + | 0.309076i | \(0.899980\pi\) | |||||||
\(242\) | 2926.94 | − | 1224.41i | 0.777483 | − | 0.325240i | ||||
\(243\) | 3684.84 | + | 877.992i | 0.972768 | + | 0.231783i | ||||
\(244\) | 4238.20 | − | 4298.01i | 1.11198 | − | 1.12767i | ||||
\(245\) | −634.632 | − | 4496.64i | −0.165490 | − | 1.17257i | ||||
\(246\) | −6656.04 | − | 1906.04i | −1.72510 | − | 0.494001i | ||||
\(247\) | −713.737 | −0.183862 | ||||||||
\(248\) | 4971.83 | + | 1998.44i | 1.27303 | + | 0.511699i | ||||
\(249\) | −2402.47 | + | 3000.87i | −0.611447 | + | 0.763745i | ||||
\(250\) | −1079.70 | − | 2581.02i | −0.273145 | − | 0.652952i | ||||
\(251\) | − | 4493.21i | − | 1.12992i | −0.825119 | − | 0.564958i | \(-0.808892\pi\) | ||
0.825119 | − | 0.564958i | \(-0.191108\pi\) | |||||||
\(252\) | 3534.00 | + | 1874.53i | 0.883417 | + | 0.468588i | ||||
\(253\) | 4234.42i | 1.05224i | ||||||||
\(254\) | 6655.36 | − | 2784.10i | 1.64407 | − | 0.687755i | ||||
\(255\) | 2977.69 | − | 3719.37i | 0.731255 | − | 0.913395i | ||||
\(256\) | −4094.39 | + | 114.781i | −0.999607 | + | 0.0280227i | ||||
\(257\) | 1431.96 | 0.347562 | 0.173781 | − | 0.984784i | \(-0.444402\pi\) | ||||
0.173781 | + | 0.984784i | \(0.444402\pi\) | |||||||
\(258\) | 1056.55 | − | 3689.55i | 0.254953 | − | 0.890316i | ||||
\(259\) | −339.155 | − | 4829.93i | −0.0813670 | − | 1.15875i | ||||
\(260\) | −2171.46 | − | 2141.24i | −0.517955 | − | 0.510747i | ||||
\(261\) | 659.285 | + | 2940.03i | 0.156355 | + | 0.697253i | ||||
\(262\) | 479.917 | + | 1147.24i | 0.113166 | + | 0.270521i | ||||
\(263\) | − | 902.626i | − | 0.211629i | −0.994386 | − | 0.105814i | \(-0.966255\pi\) | ||
0.994386 | − | 0.105814i | \(-0.0337449\pi\) | |||||||
\(264\) | 5071.93 | − | 2860.42i | 1.18241 | − | 0.666844i | ||||
\(265\) | − | 157.170i | − | 0.0364334i | ||||||
\(266\) | −1159.89 | + | 583.806i | −0.267359 | + | 0.134569i | ||||
\(267\) | −5467.24 | − | 4377.02i | −1.25314 | − | 1.00325i | ||||
\(268\) | −929.227 | − | 916.296i | −0.211797 | − | 0.208850i | ||||
\(269\) | 1889.72i | 0.428321i | 0.976798 | + | 0.214160i | \(0.0687015\pi\) | ||||
−0.976798 | + | 0.214160i | \(0.931298\pi\) | |||||||
\(270\) | −5244.80 | − | 306.134i | −1.18218 | − | 0.0690027i | ||||
\(271\) | 7620.90i | 1.70825i | 0.520065 | + | 0.854127i | \(0.325908\pi\) | ||||
−0.520065 | + | 0.854127i | \(0.674092\pi\) | |||||||
\(272\) | 62.1097 | + | 4431.95i | 0.0138454 | + | 0.987964i | ||||
\(273\) | −2279.01 | − | 1575.93i | −0.505245 | − | 0.349375i | ||||
\(274\) | 1230.04 | + | 2940.40i | 0.271202 | + | 0.648306i | ||||
\(275\) | 2490.54 | 0.546128 | ||||||||
\(276\) | 415.967 | + | 3529.77i | 0.0907183 | + | 0.769809i | ||||
\(277\) | 2983.80i | 0.647218i | 0.946191 | + | 0.323609i | \(0.104896\pi\) | ||||
−0.946191 | + | 0.323609i | \(0.895104\pi\) | |||||||
\(278\) | −6313.38 | + | 2641.04i | −1.36206 | + | 0.569781i | ||||
\(279\) | −6238.98 | + | 1399.06i | −1.33877 | + | 0.300213i | ||||
\(280\) | −5280.28 | − | 1703.56i | −1.12699 | − | 0.363598i | ||||
\(281\) | 2988.80i | 0.634508i | 0.948341 | + | 0.317254i | \(0.102761\pi\) | ||||
−0.948341 | + | 0.317254i | \(0.897239\pi\) | |||||||
\(282\) | 3071.90 | + | 879.675i | 0.648684 | + | 0.185758i | ||||
\(283\) | 3150.99 | 0.661861 | 0.330930 | − | 0.943655i | \(-0.392637\pi\) | ||||
0.330930 | + | 0.943655i | \(0.392637\pi\) | |||||||
\(284\) | −2724.78 | − | 2686.86i | −0.569317 | − | 0.561395i | ||||
\(285\) | 1065.81 | − | 1331.29i | 0.221521 | − | 0.276697i | ||||
\(286\) | −3720.75 | + | 1556.48i | −0.769274 | + | 0.321806i | ||||
\(287\) | 8703.27 | − | 611.138i | 1.79003 | − | 0.125695i | ||||
\(288\) | 3946.92 | − | 2882.66i | 0.807550 | − | 0.589800i | ||||
\(289\) | −116.610 | −0.0237350 | ||||||||
\(290\) | −1612.71 | − | 3855.18i | −0.326558 | − | 0.780635i | ||||
\(291\) | 594.659 | − | 742.776i | 0.119792 | − | 0.149630i | ||||
\(292\) | −5914.93 | − | 5832.62i | −1.18543 | − | 1.16893i | ||||
\(293\) | − | 1635.98i | − | 0.326194i | −0.986610 | − | 0.163097i | \(-0.947852\pi\) | ||
0.986610 | − | 0.163097i | \(-0.0521484\pi\) | |||||||
\(294\) | −4992.65 | − | 696.901i | −0.990398 | − | 0.138245i | ||||
\(295\) | 3131.55 | 0.618054 | ||||||||
\(296\) | −5488.77 | − | 2206.23i | −1.07780 | − | 0.433224i | ||||
\(297\) | −3050.37 | + | 6242.78i | −0.595961 | + | 1.21967i | ||||
\(298\) | −5347.90 | + | 2237.15i | −1.03958 | + | 0.434882i | ||||
\(299\) | − | 2461.77i | − | 0.476147i | ||||||
\(300\) | 2076.09 | − | 244.657i | 0.399543 | − | 0.0470843i | ||||
\(301\) | 338.764 | + | 4824.37i | 0.0648706 | + | 0.923827i | ||||
\(302\) | 751.956 | − | 314.561i | 0.143279 | − | 0.0599369i | ||||
\(303\) | 2786.02 | − | 3479.96i | 0.528226 | − | 0.659796i | ||||
\(304\) | 22.2311 | + | 1586.34i | 0.00419422 | + | 0.299286i | ||||
\(305\) | − | 9989.58i | − | 1.87541i | ||||||
\(306\) | −3059.24 | − | 4314.35i | −0.571520 | − | 0.805996i | ||||
\(307\) | 3788.51 | 0.704305 | 0.352152 | − | 0.935943i | \(-0.385450\pi\) | ||||
0.352152 | + | 0.935943i | \(0.385450\pi\) | |||||||
\(308\) | −4773.44 | + | 5572.84i | −0.883091 | + | 1.03098i | ||||
\(309\) | 1603.40 | − | 2002.77i | 0.295191 | − | 0.368717i | ||||
\(310\) | 8181.01 | − | 3422.31i | 1.49887 | − | 0.627014i | ||||
\(311\) | 4998.37 | 0.911356 | 0.455678 | − | 0.890145i | \(-0.349397\pi\) | ||||
0.455678 | + | 0.890145i | \(0.349397\pi\) | |||||||
\(312\) | −2948.68 | + | 1662.97i | −0.535051 | + | 0.301754i | ||||
\(313\) | 1152.65i | 0.208152i | 0.994569 | + | 0.104076i | \(0.0331885\pi\) | ||||
−0.994569 | + | 0.104076i | \(0.966812\pi\) | |||||||
\(314\) | −5449.50 | + | 2279.66i | −0.979406 | + | 0.409709i | ||||
\(315\) | 6342.68 | − | 1897.57i | 1.13451 | − | 0.339416i | ||||
\(316\) | −831.799 | + | 843.537i | −0.148077 | + | 0.150167i | ||||
\(317\) | 2738.80 | 0.485256 | 0.242628 | − | 0.970119i | \(-0.421991\pi\) | ||||
0.242628 | + | 0.970119i | \(0.421991\pi\) | |||||||
\(318\) | −167.728 | − | 48.0308i | −0.0295777 | − | 0.00846991i | ||||
\(319\) | −5526.70 | −0.970018 | ||||||||
\(320\) | −4691.46 | + | 4892.95i | −0.819565 | + | 0.854764i | ||||
\(321\) | −2367.34 | − | 1895.27i | −0.411626 | − | 0.329544i | ||||
\(322\) | −2013.62 | − | 4000.62i | −0.348493 | − | 0.692378i | ||||
\(323\) | 1716.79 | 0.295742 | ||||||||
\(324\) | −1929.50 | + | 5503.57i | −0.330847 | + | 0.943684i | ||||
\(325\) | −1447.93 | −0.247128 | ||||||||
\(326\) | 4488.14 | + | 10728.9i | 0.762500 | + | 1.82275i | ||||
\(327\) | 6028.01 | − | 7529.46i | 1.01942 | − | 1.27333i | ||||
\(328\) | 3975.50 | − | 9890.45i | 0.669239 | − | 1.66497i | ||||
\(329\) | −4016.74 | + | 282.053i | −0.673100 | + | 0.0472647i | ||||
\(330\) | 2652.95 | − | 9264.33i | 0.442546 | − | 1.54541i | ||||
\(331\) | − | 5222.20i | − | 0.867184i | −0.901109 | − | 0.433592i | \(-0.857246\pi\) | ||
0.901109 | − | 0.433592i | \(-0.142754\pi\) | |||||||
\(332\) | −4214.14 | − | 4155.50i | −0.696630 | − | 0.686936i | ||||
\(333\) | 6887.66 | − | 1544.52i | 1.13346 | − | 0.254172i | ||||
\(334\) | −3196.26 | + | 1337.07i | −0.523628 | + | 0.219046i | ||||
\(335\) | −2159.74 | −0.352237 | ||||||||
\(336\) | −3431.65 | + | 5114.38i | −0.557178 | + | 0.830393i | ||||
\(337\) | −2898.62 | −0.468540 | −0.234270 | − | 0.972172i | \(-0.575270\pi\) | ||||
−0.234270 | + | 0.972172i | \(0.575270\pi\) | |||||||
\(338\) | −3569.53 | + | 1493.22i | −0.574429 | + | 0.240297i | ||||
\(339\) | −3089.94 | + | 3859.58i | −0.495052 | + | 0.618359i | ||||
\(340\) | 5223.13 | + | 5150.44i | 0.833129 | + | 0.821535i | ||||
\(341\) | − | 11728.1i | − | 1.86250i | ||||||
\(342\) | −1095.00 | − | 1544.25i | −0.173132 | − | 0.244162i | ||||
\(343\) | 6212.48 | − | 1326.18i | 0.977966 | − | 0.208766i | ||||
\(344\) | 5482.44 | + | 2203.69i | 0.859284 | + | 0.345392i | ||||
\(345\) | 4591.78 | + | 3676.13i | 0.716560 | + | 0.573670i | ||||
\(346\) | 2675.92 | + | 6396.77i | 0.415776 | + | 0.993909i | ||||
\(347\) | 10559.0 | 1.63353 | 0.816765 | − | 0.576970i | \(-0.195765\pi\) | ||||
0.816765 | + | 0.576970i | \(0.195765\pi\) | |||||||
\(348\) | −4607.00 | + | 542.913i | −0.709658 | + | 0.0836298i | ||||
\(349\) | −4344.86 | −0.666404 | −0.333202 | − | 0.942855i | \(-0.608129\pi\) | ||||
−0.333202 | + | 0.942855i | \(0.608129\pi\) | |||||||
\(350\) | −2353.02 | + | 1184.34i | −0.359355 | + | 0.180874i | ||||
\(351\) | 1773.40 | − | 3629.37i | 0.269678 | − | 0.551914i | ||||
\(352\) | 3575.30 | + | 8221.20i | 0.541375 | + | 1.24486i | ||||
\(353\) | −9819.24 | −1.48053 | −0.740263 | − | 0.672318i | \(-0.765299\pi\) | ||||
−0.740263 | + | 0.672318i | \(0.765299\pi\) | |||||||
\(354\) | 956.996 | − | 3341.91i | 0.143683 | − | 0.501753i | ||||
\(355\) | −6333.03 | −0.946824 | ||||||||
\(356\) | 7570.83 | − | 7677.68i | 1.12712 | − | 1.14302i | ||||
\(357\) | 5481.81 | + | 3790.66i | 0.812685 | + | 0.561969i | ||||
\(358\) | −2416.79 | + | 1011.00i | −0.356791 | + | 0.149254i | ||||
\(359\) | 728.937i | 0.107164i | 0.998563 | + | 0.0535820i | \(0.0170638\pi\) | ||||
−0.998563 | + | 0.0535820i | \(0.982936\pi\) | |||||||
\(360\) | 1301.39 | − | 7983.26i | 0.190526 | − | 1.16876i | ||||
\(361\) | −6244.50 | −0.910410 | ||||||||
\(362\) | −2287.64 | + | 956.975i | −0.332143 | + | 0.138943i | ||||
\(363\) | −4550.11 | − | 3642.77i | −0.657903 | − | 0.526711i | ||||
\(364\) | 2775.14 | − | 3239.89i | 0.399607 | − | 0.466529i | ||||
\(365\) | −13747.7 | −1.97147 | ||||||||
\(366\) | −10660.6 | − | 3052.80i | −1.52251 | − | 0.435990i | ||||
\(367\) | − | 8207.43i | − | 1.16737i | −0.811981 | − | 0.583685i | \(-0.801610\pi\) | ||
0.811981 | − | 0.583685i | \(-0.198390\pi\) | |||||||
\(368\) | −5471.50 | + | 76.6782i | −0.775059 | + | 0.0108618i | ||||
\(369\) | 2783.14 | + | 12411.2i | 0.392641 | + | 1.75095i | ||||
\(370\) | −9031.62 | + | 3778.14i | −1.26900 | + | 0.530855i | ||||
\(371\) | 219.316 | − | 15.4003i | 0.0306909 | − | 0.00215510i | ||||
\(372\) | −1152.11 | − | 9776.43i | −0.160575 | − | 1.36259i | ||||
\(373\) | − | 6620.48i | − | 0.919023i | −0.888172 | − | 0.459511i | \(-0.848025\pi\) | ||
0.888172 | − | 0.459511i | \(-0.151975\pi\) | |||||||
\(374\) | 8949.71 | − | 3743.88i | 1.23738 | − | 0.517624i | ||||
\(375\) | −3212.25 | + | 4012.35i | −0.442346 | + | 0.552525i | ||||
\(376\) | −1834.78 | + | 4564.65i | −0.251653 | + | 0.626074i | ||||
\(377\) | 3213.07 | 0.438942 | ||||||||
\(378\) | −86.7287 | − | 7348.65i | −0.0118012 | − | 0.999930i | ||||
\(379\) | 2808.73i | 0.380672i | 0.981719 | + | 0.190336i | \(0.0609578\pi\) | ||||
−0.981719 | + | 0.190336i | \(0.939042\pi\) | |||||||
\(380\) | 1869.53 | + | 1843.52i | 0.252382 | + | 0.248869i | ||||
\(381\) | −10346.2 | − | 8283.04i | −1.39121 | − | 1.11379i | ||||
\(382\) | 2703.27 | + | 6462.13i | 0.362071 | + | 0.865528i | ||||
\(383\) | −2395.34 | −0.319573 | −0.159786 | − | 0.987152i | \(-0.551081\pi\) | ||||
−0.159786 | + | 0.987152i | \(0.551081\pi\) | |||||||
\(384\) | 3787.94 | + | 6501.89i | 0.503392 | + | 0.864058i | ||||
\(385\) | 850.624 | + | 12113.8i | 0.112602 | + | 1.60357i | ||||
\(386\) | 8168.44 | − | 3417.05i | 1.07711 | − | 0.450579i | ||||
\(387\) | −6879.73 | + | 1542.74i | −0.903660 | + | 0.202641i | ||||
\(388\) | 1043.09 | + | 1028.57i | 0.136481 | + | 0.134582i | ||||
\(389\) | −12078.7 | −1.57432 | −0.787162 | − | 0.616746i | \(-0.788450\pi\) | ||||
−0.787162 | + | 0.616746i | \(0.788450\pi\) | |||||||
\(390\) | −1542.35 | + | 5386.02i | −0.200256 | + | 0.699312i | ||||
\(391\) | 5921.43i | 0.765881i | ||||||||
\(392\) | 1859.79 | − | 7535.08i | 0.239626 | − | 0.970865i | ||||
\(393\) | 1427.81 | − | 1783.45i | 0.183266 | − | 0.228914i | ||||
\(394\) | −222.958 | + | 93.2688i | −0.0285088 | + | 0.0119259i | ||||
\(395\) | 1960.58i | 0.249740i | ||||||||
\(396\) | −9075.93 | − | 5662.33i | −1.15172 | − | 0.718542i | ||||
\(397\) | 5240.22 | 0.662466 | 0.331233 | − | 0.943549i | \(-0.392535\pi\) | ||||
0.331233 | + | 0.943549i | \(0.392535\pi\) | |||||||
\(398\) | −3860.50 | − | 9228.48i | −0.486204 | − | 1.16227i | ||||
\(399\) | 1962.12 | + | 1356.80i | 0.246188 | + | 0.170238i | ||||
\(400\) | 45.0994 | + | 3218.15i | 0.00563743 | + | 0.402268i | ||||
\(401\) | − | 10649.8i | − | 1.32625i | −0.748509 | − | 0.663125i | \(-0.769230\pi\) | ||
0.748509 | − | 0.663125i | \(-0.230770\pi\) | |||||||
\(402\) | −660.014 | + | 2304.82i | −0.0818868 | + | 0.285956i | ||||
\(403\) | 6818.39i | 0.842799i | ||||||||
\(404\) | 4886.92 | + | 4818.92i | 0.601815 | + | 0.593441i | ||||
\(405\) | 4121.44 | + | 8727.50i | 0.505669 | + | 1.07080i | ||||
\(406\) | 5221.54 | − | 2628.15i | 0.638278 | − | 0.321263i | ||||
\(407\) | 12947.5i | 1.57687i | ||||||||
\(408\) | 7092.61 | − | 4000.03i | 0.860628 | − | 0.485370i | ||||
\(409\) | − | 10197.5i | − | 1.23284i | −0.787416 | − | 0.616421i | \(-0.788582\pi\) | ||
0.787416 | − | 0.616421i | \(-0.211418\pi\) | |||||||
\(410\) | −6808.00 | − | 16274.5i | −0.820057 | − | 1.96034i | ||||
\(411\) | 3659.52 | − | 4571.03i | 0.439199 | − | 0.548594i | ||||
\(412\) | 2812.50 | + | 2773.36i | 0.336315 | + | 0.331635i | ||||
\(413\) | 306.845 | + | 4369.80i | 0.0365590 | + | 0.520639i | ||||
\(414\) | 5326.32 | − | 3776.82i | 0.632305 | − | 0.448358i | ||||
\(415\) | −9794.66 | −1.15856 | ||||||||
\(416\) | −2078.58 | − | 4779.58i | −0.244978 | − | 0.563312i | ||||
\(417\) | 9814.54 | + | 7857.43i | 1.15257 | + | 0.922733i | ||||
\(418\) | 3203.40 | − | 1340.06i | 0.374841 | − | 0.156805i | ||||
\(419\) | 9402.75i | 1.09631i | 0.836376 | + | 0.548155i | \(0.184670\pi\) | ||||
−0.836376 | + | 0.548155i | \(0.815330\pi\) | |||||||
\(420\) | 1899.07 | + | 10014.4i | 0.220631 | + | 1.16346i | ||||
\(421\) | − | 1525.15i | − | 0.176559i | −0.996096 | − | 0.0882793i | \(-0.971863\pi\) | ||
0.996096 | − | 0.0882793i | \(-0.0281368\pi\) | |||||||
\(422\) | −1851.42 | − | 4425.80i | −0.213568 | − | 0.510532i | ||||
\(423\) | −1284.48 | − | 5728.02i | −0.147644 | − | 0.658406i | ||||
\(424\) | 100.180 | − | 249.233i | 0.0114744 | − | 0.0285467i | ||||
\(425\) | 3482.78 | 0.397505 | ||||||||
\(426\) | −1935.36 | + | 6758.46i | −0.220114 | + | 0.768658i | ||||
\(427\) | 13939.6 | − | 978.829i | 1.57982 | − | 0.110934i | ||||
\(428\) | 3278.20 | − | 3324.47i | 0.370229 | − | 0.375454i | ||||
\(429\) | 5784.13 | + | 4630.72i | 0.650957 | + | 0.521149i | ||||
\(430\) | 9021.21 | − | 3773.79i | 1.01172 | − | 0.423229i | ||||
\(431\) | − | 7819.69i | − | 0.873924i | −0.899480 | − | 0.436962i | \(-0.856054\pi\) | ||
0.899480 | − | 0.436962i | \(-0.143946\pi\) | |||||||
\(432\) | −8121.84 | − | 3828.49i | −0.904542 | − | 0.426385i | ||||
\(433\) | − | 11246.6i | − | 1.24821i | −0.781340 | − | 0.624106i | \(-0.785464\pi\) | ||
0.781340 | − | 0.624106i | \(-0.214536\pi\) | |||||||
\(434\) | 5577.15 | + | 11080.5i | 0.616847 | + | 1.22554i | ||||
\(435\) | −4798.03 | + | 5993.12i | −0.528846 | + | 0.660570i | ||||
\(436\) | 10573.7 | + | 10426.5i | 1.16144 | + | 1.14527i | ||||
\(437\) | 2119.48i | 0.232010i | ||||||||
\(438\) | −4201.27 | + | 14671.2i | −0.458320 | + | 1.60049i | ||||
\(439\) | 5899.62i | 0.641397i | 0.947181 | + | 0.320698i | \(0.103918\pi\) | ||||
−0.947181 | + | 0.320698i | \(0.896082\pi\) | |||||||
\(440\) | 13766.2 | + | 5533.37i | 1.49154 | + | 0.599530i | ||||
\(441\) | 3269.38 | + | 8664.71i | 0.353027 | + | 0.935613i | ||||
\(442\) | −5203.11 | + | 2176.58i | −0.559924 | + | 0.234230i | ||||
\(443\) | −991.808 | −0.106371 | −0.0531854 | − | 0.998585i | \(-0.516937\pi\) | ||||
−0.0531854 | + | 0.998585i | \(0.516937\pi\) | |||||||
\(444\) | 1271.89 | + | 10792.9i | 0.135949 | + | 1.15362i | ||||
\(445\) | − | 17844.7i | − | 1.90095i | ||||||
\(446\) | −4296.86 | − | 10271.6i | −0.456193 | − | 1.09053i | ||||
\(447\) | 8313.64 | + | 6655.81i | 0.879690 | + | 0.704271i | ||||
\(448\) | −7287.38 | − | 6067.08i | −0.768518 | − | 0.639828i | ||||
\(449\) | 13929.7i | 1.46411i | 0.681248 | + | 0.732053i | \(0.261438\pi\) | ||||
−0.681248 | + | 0.732053i | \(0.738562\pi\) | |||||||
\(450\) | −2221.39 | − | 3132.76i | −0.232705 | − | 0.328177i | ||||
\(451\) | −23330.7 | −2.43592 | ||||||||
\(452\) | −5420.03 | − | 5344.61i | −0.564020 | − | 0.556171i | ||||
\(453\) | −1168.96 | − | 935.859i | −0.121242 | − | 0.0970651i | ||||
\(454\) | 6800.14 | + | 16255.7i | 0.702965 | + | 1.68043i | ||||
\(455\) | −494.529 | − | 7042.62i | −0.0509535 | − | 0.725633i | ||||
\(456\) | 2538.68 | − | 1431.74i | 0.260712 | − | 0.147034i | ||||
\(457\) | −10005.2 | −1.02412 | −0.512060 | − | 0.858950i | \(-0.671117\pi\) | ||||
−0.512060 | + | 0.858950i | \(0.671117\pi\) | |||||||
\(458\) | 10369.0 | − | 4337.60i | 1.05789 | − | 0.442539i | ||||
\(459\) | −4265.65 | + | 8729.92i | −0.433777 | + | 0.887752i | ||||
\(460\) | −6358.53 | + | 6448.26i | −0.644496 | + | 0.653591i | ||||
\(461\) | 15566.9i | 1.57272i | 0.617770 | + | 0.786359i | \(0.288036\pi\) | ||||
−0.617770 | + | 0.786359i | \(0.711964\pi\) | |||||||
\(462\) | 13187.5 | + | 2794.19i | 1.32800 | + | 0.281380i | ||||
\(463\) | −10866.3 | −1.09071 | −0.545357 | − | 0.838204i | \(-0.683606\pi\) | ||||
−0.545357 | + | 0.838204i | \(0.683606\pi\) | |||||||
\(464\) | −100.079 | − | 7141.32i | −0.0100131 | − | 0.714499i | ||||
\(465\) | −12717.9 | − | 10181.8i | −1.26834 | − | 1.01542i | ||||
\(466\) | 3712.41 | + | 8874.48i | 0.369043 | + | 0.882194i | ||||
\(467\) | − | 2184.04i | − | 0.216414i | −0.994128 | − | 0.108207i | \(-0.965489\pi\) | ||
0.994128 | − | 0.108207i | \(-0.0345109\pi\) | |||||||
\(468\) | 5276.49 | + | 3291.92i | 0.521166 | + | 0.325147i | ||||
\(469\) | −211.622 | − | 3013.73i | −0.0208354 | − | 0.296719i | ||||
\(470\) | 3142.03 | + | 7511.01i | 0.308364 | + | 0.737142i | ||||
\(471\) | 8471.59 | + | 6782.27i | 0.828769 | + | 0.663504i | ||||
\(472\) | 4965.87 | + | 1996.05i | 0.484264 | + | 0.194652i | ||||
\(473\) | − | 12932.6i | − | 1.25717i | ||||||
\(474\) | 2092.28 | + | 599.150i | 0.202746 | + | 0.0580588i | ||||
\(475\) | 1246.60 | 0.120417 | ||||||||
\(476\) | −6675.20 | + | 7793.08i | −0.642767 | + | 0.750410i | ||||
\(477\) | 70.1332 | + | 312.753i | 0.00673203 | + | 0.0300209i | ||||
\(478\) | 4887.45 | + | 11683.4i | 0.467671 | + | 1.11796i | ||||
\(479\) | −7028.43 | −0.670433 | −0.335216 | − | 0.942141i | \(-0.608809\pi\) | ||||
−0.335216 | + | 0.942141i | \(0.608809\pi\) | |||||||
\(480\) | 12018.9 | + | 3260.25i | 1.14289 | + | 0.310019i | ||||
\(481\) | − | 7527.32i | − | 0.713547i | ||||||
\(482\) | 2524.41 | + | 6034.58i | 0.238555 | + | 0.570265i | ||||
\(483\) | −4679.79 | + | 6767.63i | −0.440865 | + | 0.637552i | ||||
\(484\) | 6300.83 | − | 6389.75i | 0.591738 | − | 0.600089i | ||||
\(485\) | 2424.37 | 0.226980 | ||||||||
\(486\) | 10573.3 | − | 1731.19i | 0.986859 | − | 0.161581i | ||||
\(487\) | 3566.36 | 0.331842 | 0.165921 | − | 0.986139i | \(-0.446940\pi\) | ||||
0.165921 | + | 0.986139i | \(0.446940\pi\) | |||||||
\(488\) | 6367.35 | − | 15841.0i | 0.590649 | − | 1.46945i | ||||
\(489\) | 13352.8 | − | 16678.7i | 1.23483 | − | 1.54241i | ||||
\(490\) | −6564.22 | − | 11040.4i | −0.605186 | − | 1.01787i | ||||
\(491\) | 2231.72 | 0.205124 | 0.102562 | − | 0.994727i | \(-0.467296\pi\) | ||||
0.102562 | + | 0.994727i | \(0.467296\pi\) | |||||||
\(492\) | −19448.2 | + | 2291.88i | −1.78210 | + | 0.210012i | ||||
\(493\) | −7728.56 | −0.706038 | ||||||||
\(494\) | −1862.37 | + | 779.072i | −0.169619 | + | 0.0709557i | ||||
\(495\) | −17274.7 | + | 3873.76i | −1.56857 | + | 0.351743i | ||||
\(496\) | 15154.5 | − | 212.376i | 1.37189 | − | 0.0192257i | ||||
\(497\) | −620.542 | − | 8837.19i | −0.0560063 | − | 0.797590i | ||||
\(498\) | −2993.23 | + | 10452.6i | −0.269337 | + | 0.940548i | ||||
\(499\) | − | 20669.1i | − | 1.85426i | −0.374743 | − | 0.927129i | \(-0.622269\pi\) | ||
0.374743 | − | 0.927129i | \(-0.377731\pi\) | |||||||
\(500\) | −5634.57 | − | 5556.16i | −0.503971 | − | 0.496958i | ||||
\(501\) | 4968.79 | + | 3977.96i | 0.443092 | + | 0.354735i | ||||
\(502\) | −4904.52 | − | 11724.2i | −0.436055 | − | 1.04239i | ||||
\(503\) | −17146.1 | −1.51990 | −0.759948 | − | 0.649984i | \(-0.774775\pi\) | ||||
−0.759948 | + | 0.649984i | \(0.774775\pi\) | |||||||
\(504\) | 11267.5 | + | 1033.74i | 0.995818 | + | 0.0913620i | ||||
\(505\) | 11358.4 | 1.00087 | ||||||||
\(506\) | 4622.04 | + | 11048.9i | 0.406076 | + | 0.970723i | ||||
\(507\) | 5549.06 | + | 4442.52i | 0.486080 | + | 0.389151i | ||||
\(508\) | 14327.0 | − | 14529.2i | 1.25130 | − | 1.26895i | ||||
\(509\) | 7036.98i | 0.612787i | 0.951905 | + | 0.306393i | \(0.0991223\pi\) | ||||
−0.951905 | + | 0.306393i | \(0.900878\pi\) | |||||||
\(510\) | 3709.89 | − | 12955.3i | 0.322112 | − | 1.12484i | ||||
\(511\) | −1347.07 | − | 19183.7i | −0.116616 | − | 1.66074i | ||||
\(512\) | −10558.3 | + | 4768.69i | −0.911356 | + | 0.411618i | ||||
\(513\) | −1526.82 | + | 3124.73i | −0.131405 | + | 0.268928i | ||||
\(514\) | 3736.44 | − | 1563.04i | 0.320637 | − | 0.134130i | ||||
\(515\) | 6536.91 | 0.559322 | ||||||||
\(516\) | −1270.43 | − | 10780.5i | −0.108387 | − | 0.919737i | ||||
\(517\) | 10767.6 | 0.915974 | ||||||||
\(518\) | −6157.03 | − | 12232.6i | −0.522247 | − | 1.03759i | ||||
\(519\) | 7961.20 | − | 9944.17i | 0.673330 | − | 0.841042i | ||||
\(520\) | −8003.28 | − | 3216.95i | −0.674937 | − | 0.271293i | ||||
\(521\) | −5554.16 | −0.467048 | −0.233524 | − | 0.972351i | \(-0.575026\pi\) | ||||
−0.233524 | + | 0.972351i | \(0.575026\pi\) | |||||||
\(522\) | 4929.44 | + | 6951.83i | 0.413325 | + | 0.582899i | ||||
\(523\) | 1129.07 | 0.0943994 | 0.0471997 | − | 0.998885i | \(-0.484970\pi\) | ||||
0.0471997 | + | 0.998885i | \(0.484970\pi\) | |||||||
\(524\) | 2504.51 | + | 2469.66i | 0.208798 | + | 0.205892i | ||||
\(525\) | 3980.48 | + | 2752.49i | 0.330900 | + | 0.228816i | ||||
\(526\) | −985.253 | − | 2355.24i | −0.0816712 | − | 0.195234i | ||||
\(527\) | − | 16400.6i | − | 1.35564i | ||||||
\(528\) | 10112.0 | − | 13000.0i | 0.833464 | − | 1.07150i | ||||
\(529\) | 4856.64 | 0.399165 | ||||||||
\(530\) | −171.557 | − | 410.105i | −0.0140603 | − | 0.0336110i | ||||
\(531\) | −6231.50 | + | 1397.38i | −0.509273 | + | 0.114202i | ||||
\(532\) | −2389.28 | + | 2789.40i | −0.194715 | + | 0.227323i | ||||
\(533\) | 13563.8 | 1.10228 | ||||||||
\(534\) | −19043.5 | − | 5453.32i | −1.54324 | − | 0.441925i | ||||
\(535\) | − | 7726.84i | − | 0.624412i | ||||||
\(536\) | −3424.82 | − | 1376.62i | −0.275989 | − | 0.110935i | ||||
\(537\) | 3757.04 | + | 3007.85i | 0.301915 | + | 0.241710i | ||||
\(538\) | 2062.71 | + | 4930.88i | 0.165297 | + | 0.395140i | ||||
\(539\) | −16820.4 | + | 2373.94i | −1.34417 | + | 0.189708i | ||||
\(540\) | −14019.5 | + | 4926.11i | −1.11723 | + | 0.392566i | ||||
\(541\) | 13088.7i | 1.04016i | 0.854118 | + | 0.520079i | \(0.174097\pi\) | ||||
−0.854118 | + | 0.520079i | \(0.825903\pi\) | |||||||
\(542\) | 8318.52 | + | 19885.4i | 0.659245 | + | 1.57592i | ||||
\(543\) | 3556.28 | + | 2847.12i | 0.281058 | + | 0.225012i | ||||
\(544\) | 4999.71 | + | 11496.6i | 0.394046 | + | 0.906087i | ||||
\(545\) | 24575.7 | 1.93157 | ||||||||
\(546\) | −7666.84 | − | 1624.46i | −0.600935 | − | 0.127327i | ||||
\(547\) | − | 134.806i | − | 0.0105373i | −0.999986 | − | 0.00526863i | \(-0.998323\pi\) | ||
0.999986 | − | 0.00526863i | \(-0.00167706\pi\) | |||||||
\(548\) | 6419.12 | + | 6329.79i | 0.500385 | + | 0.493422i | ||||
\(549\) | 4457.61 | + | 19878.4i | 0.346532 | + | 1.54533i | ||||
\(550\) | 6498.61 | − | 2718.52i | 0.503821 | − | 0.210760i | ||||
\(551\) | −2766.31 | −0.213881 | ||||||||
\(552\) | 4938.27 | + | 8756.25i | 0.380773 | + | 0.675164i | ||||
\(553\) | −2735.81 | + | 192.107i | −0.210377 | + | 0.0147726i | ||||
\(554\) | 3256.94 | + | 7785.69i | 0.249773 | + | 0.597080i | ||||
\(555\) | 14040.2 | + | 11240.4i | 1.07383 | + | 0.859695i | ||||
\(556\) | −13590.8 | + | 13782.6i | −1.03665 | + | 1.05128i | ||||
\(557\) | −949.790 | −0.0722512 | −0.0361256 | − | 0.999347i | \(-0.511502\pi\) | ||||
−0.0361256 | + | 0.999347i | \(0.511502\pi\) | |||||||
\(558\) | −14752.3 | + | 10460.7i | −1.11921 | + | 0.793612i | ||||
\(559\) | 7518.65i | 0.568882i | ||||||||
\(560\) | −15637.4 | + | 1318.49i | −1.18000 | + | 0.0994938i | ||||
\(561\) | −13912.9 | − | 11138.5i | −1.04706 | − | 0.838267i | ||||
\(562\) | 3262.40 | + | 7798.73i | 0.244868 | + | 0.585355i | ||||
\(563\) | 3122.65i | 0.233755i | 0.993146 | + | 0.116877i | \(0.0372884\pi\) | ||||
−0.993146 | + | 0.116877i | \(0.962712\pi\) | |||||||
\(564\) | 8975.77 | − | 1057.75i | 0.670120 | − | 0.0789705i | ||||
\(565\) | −12597.4 | −0.938014 | ||||||||
\(566\) | 8221.92 | − | 3439.43i | 0.610589 | − | 0.255424i | ||||
\(567\) | −11774.6 | + | 6606.26i | −0.872112 | + | 0.489307i | ||||
\(568\) | −10042.6 | − | 4036.67i | −0.741866 | − | 0.298196i | ||||
\(569\) | 15497.7i | 1.14182i | 0.821011 | + | 0.570912i | \(0.193410\pi\) | ||||
−0.821011 | + | 0.570912i | \(0.806590\pi\) | |||||||
\(570\) | 1327.90 | − | 4637.13i | 0.0975779 | − | 0.340751i | ||||
\(571\) | − | 11912.4i | − | 0.873063i | −0.899689 | − | 0.436531i | \(-0.856207\pi\) | ||
0.899689 | − | 0.436531i | \(-0.143793\pi\) | |||||||
\(572\) | −8009.65 | + | 8122.69i | −0.585490 | + | 0.593753i | ||||
\(573\) | 8042.56 | − | 10045.8i | 0.586357 | − | 0.732406i | ||||
\(574\) | 22042.5 | − | 11094.6i | 1.60285 | − | 0.806760i | ||||
\(575\) | 4299.70i | 0.311843i | ||||||||
\(576\) | 7152.22 | − | 11830.0i | 0.517377 | − | 0.855757i | ||||
\(577\) | 5650.41i | 0.407677i | 0.979005 | + | 0.203838i | \(0.0653417\pi\) | ||||
−0.979005 | + | 0.203838i | \(0.934658\pi\) | |||||||
\(578\) | −304.273 | + | 127.285i | −0.0218963 | + | 0.00915977i | ||||
\(579\) | −12698.3 | − | 10166.2i | −0.911443 | − | 0.729692i | ||||
\(580\) | −8416.17 | − | 8299.05i | −0.602521 | − | 0.594137i | ||||
\(581\) | −959.729 | − | 13667.6i | −0.0685306 | − | 0.975949i | ||||
\(582\) | 740.885 | − | 2587.23i | 0.0527675 | − | 0.184269i | ||||
\(583\) | −587.917 | −0.0417651 | ||||||||
\(584\) | −21800.5 | − | 8762.77i | −1.54471 | − | 0.620901i | ||||
\(585\) | 10043.0 | − | 2252.10i | 0.709793 | − | 0.159167i | ||||
\(586\) | −1785.74 | − | 4268.79i | −0.125884 | − | 0.300925i | ||||
\(587\) | − | 9396.05i | − | 0.660675i | −0.943863 | − | 0.330338i | \(-0.892837\pi\) | ||
0.943863 | − | 0.330338i | \(-0.107163\pi\) | |||||||
\(588\) | −13788.1 | + | 3631.24i | −0.967026 | + | 0.254676i | ||||
\(589\) | − | 5870.33i | − | 0.410667i | ||||||
\(590\) | 8171.21 | − | 3418.21i | 0.570175 | − | 0.238518i | ||||
\(591\) | 346.603 | + | 277.487i | 0.0241241 | + | 0.0193135i | ||||
\(592\) | −16730.1 | + | 234.458i | −1.16149 | + | 0.0162773i | ||||
\(593\) | 5680.51 | 0.393374 | 0.196687 | − | 0.980466i | \(-0.436982\pi\) | ||||
0.196687 | + | 0.980466i | \(0.436982\pi\) | |||||||
\(594\) | −1145.14 | + | 19619.0i | −0.0791006 | + | 1.35518i | ||||
\(595\) | 1189.52 | + | 16940.0i | 0.0819587 | + | 1.16718i | ||||
\(596\) | −11512.4 | + | 11674.9i | −0.791220 | + | 0.802386i | ||||
\(597\) | −11485.5 | + | 14346.2i | −0.787385 | + | 0.983506i | ||||
\(598\) | −2687.12 | − | 6423.55i | −0.183754 | − | 0.439261i | ||||
\(599\) | 11213.1i | 0.764866i | 0.923983 | + | 0.382433i | \(0.124914\pi\) | ||||
−0.923983 | + | 0.382433i | \(0.875086\pi\) | |||||||
\(600\) | 5150.12 | − | 2904.52i | 0.350421 | − | 0.197628i | ||||
\(601\) | 4599.55i | 0.312179i | 0.987743 | + | 0.156089i | \(0.0498888\pi\) | ||||
−0.987743 | + | 0.156089i | \(0.950111\pi\) | |||||||
\(602\) | 6149.93 | + | 12218.5i | 0.416366 | + | 0.827226i | ||||
\(603\) | 4297.69 | − | 963.734i | 0.290241 | − | 0.0650850i | ||||
\(604\) | 1618.74 | − | 1641.58i | 0.109049 | − | 0.110588i | ||||
\(605\) | − | 14851.3i | − | 0.998000i | ||||||
\(606\) | 3471.09 | − | 12121.4i | 0.232679 | − | 0.812536i | ||||
\(607\) | 27115.8i | 1.81318i | 0.422017 | + | 0.906588i | \(0.361322\pi\) | ||||
−0.422017 | + | 0.906588i | \(0.638678\pi\) | |||||||
\(608\) | 1789.56 | + | 4115.00i | 0.119369 | + | 0.274483i | ||||
\(609\) | −8833.00 | − | 6107.99i | −0.587736 | − | 0.406417i | ||||
\(610\) | −10904.0 | − | 26066.0i | −0.723756 | − | 1.73013i | ||||
\(611\) | −6259.98 | −0.414487 | ||||||||
\(612\) | −12691.8 | − | 7918.22i | −0.838294 | − | 0.522998i | ||||
\(613\) | 2010.26i | 0.132453i | 0.997805 | + | 0.0662263i | \(0.0210959\pi\) | ||||
−0.997805 | + | 0.0662263i | \(0.978904\pi\) | |||||||
\(614\) | 9885.42 | − | 4135.31i | 0.649745 | − | 0.271804i | ||||
\(615\) | −20254.7 | + | 25299.7i | −1.32804 | + | 1.65883i | ||||
\(616\) | −6372.45 | + | 19751.7i | −0.416807 | + | 1.29191i | ||||
\(617\) | − | 15659.8i | − | 1.02178i | −0.859646 | − | 0.510891i | \(-0.829316\pi\) | ||
0.859646 | − | 0.510891i | \(-0.170684\pi\) | |||||||
\(618\) | 1997.67 | − | 6976.03i | 0.130029 | − | 0.454073i | ||||
\(619\) | 27135.8 | 1.76200 | 0.881001 | − | 0.473115i | \(-0.156870\pi\) | ||||
0.881001 | + | 0.473115i | \(0.156870\pi\) | |||||||
\(620\) | 17611.3 | − | 17859.8i | 1.14078 | − | 1.15688i | ||||
\(621\) | −10777.6 | − | 5266.20i | −0.696442 | − | 0.340298i | ||||
\(622\) | 13042.3 | − | 5455.92i | 0.840756 | − | 0.351708i | ||||
\(623\) | 24900.7 | − | 1748.52i | 1.60133 | − | 0.112444i | ||||
\(624\) | −5878.84 | + | 7557.82i | −0.377150 | + | 0.484863i | ||||
\(625\) | −19382.1 | −1.24046 | ||||||||
\(626\) | 1258.16 | + | 3007.62i | 0.0803294 | + | 0.192027i | ||||
\(627\) | −4979.88 | − | 3986.84i | −0.317189 | − | 0.253938i | ||||
\(628\) | −11731.2 | + | 11896.7i | −0.745420 | + | 0.755940i | ||||
\(629\) | 18105.9i | 1.14774i | ||||||||
\(630\) | 14478.8 | − | 11874.7i | 0.915633 | − | 0.750948i | ||||
\(631\) | 854.200 | 0.0538909 | 0.0269455 | − | 0.999637i | \(-0.491422\pi\) | ||||
0.0269455 | + | 0.999637i | \(0.491422\pi\) | |||||||
\(632\) | −1249.67 | + | 3109.00i | −0.0786540 | + | 0.195679i | ||||
\(633\) | −5508.20 | + | 6880.18i | −0.345863 | + | 0.432011i | ||||
\(634\) | 7146.39 | − | 2989.51i | 0.447665 | − | 0.187269i | ||||
\(635\) | − | 33769.3i | − | 2.11038i | ||||||
\(636\) | −490.082 | + | 57.7538i | −0.0305551 | + | 0.00360077i | ||||
\(637\) | 9778.89 | − | 1380.14i | 0.608248 | − | 0.0858449i | ||||
\(638\) | −14420.9 | + | 6032.61i | −0.894873 | + | 0.374347i | ||||
\(639\) | 12602.2 | − | 2825.97i | 0.780178 | − | 0.174951i | ||||
\(640\) | −6900.66 | + | 17888.2i | −0.426207 | + | 1.10483i | ||||
\(641\) | 29337.9i | 1.80777i | 0.427779 | + | 0.903884i | \(0.359296\pi\) | ||||
−0.427779 | + | 0.903884i | \(0.640704\pi\) | |||||||
\(642\) | −8245.90 | − | 2361.31i | −0.506915 | − | 0.145161i | ||||
\(643\) | −24076.1 | −1.47662 | −0.738310 | − | 0.674461i | \(-0.764376\pi\) | ||||
−0.738310 | + | 0.674461i | \(0.764376\pi\) | |||||||
\(644\) | −9621.02 | − | 8240.93i | −0.588698 | − | 0.504252i | ||||
\(645\) | −14024.0 | − | 11227.5i | −0.856117 | − | 0.685399i | ||||
\(646\) | 4479.65 | − | 1873.94i | 0.272832 | − | 0.114132i | ||||
\(647\) | 9606.99 | 0.583755 | 0.291878 | − | 0.956456i | \(-0.405720\pi\) | ||||
0.291878 | + | 0.956456i | \(0.405720\pi\) | |||||||
\(648\) | 972.685 | + | 16466.7i | 0.0589671 | + | 0.998260i | ||||
\(649\) | − | 11714.1i | − | 0.708500i | ||||||
\(650\) | −3778.11 | + | 1580.47i | −0.227984 | + | 0.0953711i | ||||
\(651\) | 12961.7 | − | 18744.3i | 0.780349 | − | 1.12849i | ||||
\(652\) | 23422.0 | + | 23096.0i | 1.40686 | + | 1.38729i | ||||
\(653\) | −5450.16 | −0.326618 | −0.163309 | − | 0.986575i | \(-0.552217\pi\) | ||||
−0.163309 | + | 0.986575i | \(0.552217\pi\) | |||||||
\(654\) | 7510.28 | − | 26226.6i | 0.449045 | − | 1.56810i | ||||
\(655\) | 5821.08 | 0.347249 | ||||||||
\(656\) | −422.479 | − | 30146.8i | −0.0251449 | − | 1.79426i | ||||
\(657\) | 27356.6 | − | 6134.58i | 1.62448 | − | 0.364281i | ||||
\(658\) | −10173.1 | + | 5120.40i | −0.602717 | + | 0.303364i | ||||
\(659\) | 15534.8 | 0.918287 | 0.459144 | − | 0.888362i | \(-0.348156\pi\) | ||||
0.459144 | + | 0.888362i | \(0.348156\pi\) | |||||||
\(660\) | −3190.00 | − | 27069.4i | −0.188137 | − | 1.59648i | ||||
\(661\) | −10381.1 | −0.610858 | −0.305429 | − | 0.952215i | \(-0.598800\pi\) | ||||
−0.305429 | + | 0.952215i | \(0.598800\pi\) | |||||||
\(662\) | −5700.24 | − | 13626.4i | −0.334662 | − | 0.800006i | ||||
\(663\) | 8088.55 | + | 6475.61i | 0.473806 | + | 0.379324i | ||||
\(664\) | −15531.9 | − | 6243.11i | −0.907765 | − | 0.364879i | ||||
\(665\) | 425.768 | + | 6063.39i | 0.0248279 | + | 0.353576i | ||||
\(666\) | 16286.2 | − | 11548.3i | 0.947564 | − | 0.671904i | ||||
\(667\) | − | 9541.36i | − | 0.553888i | ||||||
\(668\) | −6880.59 | + | 6977.69i | −0.398530 | + | 0.404154i | ||||
\(669\) | −12783.7 | + | 15967.9i | −0.738784 | + | 0.922799i | ||||
\(670\) | −5635.46 | + | 2357.45i | −0.324950 | + | 0.135934i | ||||
\(671\) | −37367.6 | −2.14986 | ||||||||
\(672\) | −3371.71 | + | 17090.8i | −0.193551 | + | 0.981090i | ||||
\(673\) | 29748.6 | 1.70390 | 0.851948 | − | 0.523626i | \(-0.175421\pi\) | ||||
0.851948 | + | 0.523626i | \(0.175421\pi\) | |||||||
\(674\) | −7563.42 | + | 3163.96i | −0.432244 | + | 0.180818i | ||||
\(675\) | −3097.39 | + | 6339.02i | −0.176620 | + | 0.361465i | ||||
\(676\) | −7684.14 | + | 7792.58i | −0.437195 | + | 0.443365i | ||||
\(677\) | − | 6845.80i | − | 0.388634i | −0.980939 | − | 0.194317i | \(-0.937751\pi\) | ||
0.980939 | − | 0.194317i | \(-0.0622491\pi\) | |||||||
\(678\) | −3849.75 | + | 13443.7i | −0.218066 | + | 0.761506i | ||||
\(679\) | 237.552 | + | 3383.00i | 0.0134262 | + | 0.191204i | ||||
\(680\) | 19250.7 | + | 7737.89i | 1.08563 | + | 0.436374i | ||||
\(681\) | 20231.3 | − | 25270.4i | 1.13842 | − | 1.42198i | ||||
\(682\) | −12801.7 | − | 30602.4i | −0.718772 | − | 1.71822i | ||||
\(683\) | −13901.9 | −0.778833 | −0.389417 | − | 0.921062i | \(-0.627323\pi\) | ||||
−0.389417 | + | 0.921062i | \(0.627323\pi\) | |||||||
\(684\) | −4542.83 | − | 2834.20i | −0.253946 | − | 0.158433i | ||||
\(685\) | 14919.5 | 0.832184 | ||||||||
\(686\) | 14762.8 | − | 10241.6i | 0.821639 | − | 0.570008i | ||||
\(687\) | −16119.2 | − | 12904.9i | −0.895178 | − | 0.716671i | ||||
\(688\) | 16710.9 | − | 234.187i | 0.926011 | − | 0.0129772i | ||||
\(689\) | 341.799 | 0.0188991 | ||||||||
\(690\) | 15994.1 | + | 4580.09i | 0.882440 | + | 0.252697i | ||||
\(691\) | −7713.20 | −0.424637 | −0.212318 | − | 0.977201i | \(-0.568101\pi\) | ||||
−0.212318 | + | 0.977201i | \(0.568101\pi\) | |||||||
\(692\) | 13964.7 | + | 13770.3i | 0.767134 | + | 0.756459i | ||||
\(693\) | −7098.16 | − | 23725.8i | −0.389086 | − | 1.30053i | ||||
\(694\) | 27551.7 | − | 11525.5i | 1.50699 | − | 0.630408i | ||||
\(695\) | 32034.1i | 1.74838i | ||||||||
\(696\) | −11428.5 | + | 6445.36i | −0.622409 | + | 0.351021i | ||||
\(697\) | −32625.7 | −1.77301 | ||||||||
\(698\) | −11337.1 | + | 4742.59i | −0.614780 | + | 0.257177i | ||||
\(699\) | 11044.9 | − | 13795.9i | 0.597648 | − | 0.746509i | ||||
\(700\) | −4847.03 | + | 5658.75i | −0.261715 | + | 0.305544i | ||||
\(701\) | 28716.9 | 1.54725 | 0.773626 | − | 0.633643i | \(-0.218441\pi\) | ||||
0.773626 | + | 0.633643i | \(0.218441\pi\) | |||||||
\(702\) | 665.753 | − | 11405.9i | 0.0357938 | − | 0.613232i | ||||
\(703\) | 6480.69i | 0.347687i | ||||||||
\(704\) | 18302.9 | + | 17549.2i | 0.979851 | + | 0.939501i | ||||
\(705\) | 9347.95 | − | 11676.3i | 0.499382 | − | 0.623767i | ||||
\(706\) | −25621.5 | + | 10718.1i | −1.36583 | + | 0.571361i | ||||
\(707\) | 1112.95 | + | 15849.6i | 0.0592033 | + | 0.843118i | ||||
\(708\) | −1150.73 | − | 9764.72i | −0.0610832 | − | 0.518334i | ||||
\(709\) | 6971.08i | 0.369259i | 0.982808 | + | 0.184629i | \(0.0591085\pi\) | ||||
−0.982808 | + | 0.184629i | \(0.940892\pi\) | |||||||
\(710\) | −16524.9 | + | 6912.76i | −0.873477 | + | 0.365396i | ||||
\(711\) | −874.862 | − | 3901.38i | −0.0461461 | − | 0.205785i | ||||
\(712\) | 11374.2 | − | 28297.4i | 0.598690 | − | 1.48945i | ||||
\(713\) | 20247.6 | 1.06350 | ||||||||
\(714\) | 18441.5 | + | 3907.41i | 0.966602 | + | 0.204805i | ||||
\(715\) | 18879.0i | 0.987463i | ||||||||
\(716\) | −5202.62 | + | 5276.04i | −0.271552 | + | 0.275384i | ||||
\(717\) | 14540.8 | − | 18162.6i | 0.757371 | − | 0.946016i | ||||
\(718\) | 795.664 | + | 1902.03i | 0.0413565 | + | 0.0988623i | ||||
\(719\) | −19292.8 | −1.00070 | −0.500348 | − | 0.865825i | \(-0.666795\pi\) | ||||
−0.500348 | + | 0.865825i | \(0.666795\pi\) | |||||||
\(720\) | −5318.30 | − | 22251.4i | −0.275280 | − | 1.15175i | ||||
\(721\) | 640.519 | + | 9121.68i | 0.0330849 | + | 0.471164i | ||||
\(722\) | −16293.9 | + | 6816.13i | −0.839884 | + | 0.351343i | ||||
\(723\) | 7510.44 | − | 9381.13i | 0.386329 | − | 0.482556i | ||||
\(724\) | −4924.61 | + | 4994.10i | −0.252792 | + | 0.256360i | ||||
\(725\) | −5611.90 | −0.287477 | ||||||||
\(726\) | −15848.9 | − | 4538.53i | −0.810205 | − | 0.232012i | ||||
\(727\) | 12461.6i | 0.635732i | 0.948136 | + | 0.317866i | \(0.102966\pi\) | ||||
−0.948136 | + | 0.317866i | \(0.897034\pi\) | |||||||
\(728\) | 3704.76 | − | 11483.1i | 0.188609 | − | 0.584604i | ||||
\(729\) | −12095.7 | − | 15527.8i | −0.614527 | − | 0.788896i | ||||
\(730\) | −35872.1 | + | 15006.1i | −1.81875 | + | 0.760825i | ||||
\(731\) | − | 18085.0i | − | 0.915045i | ||||||
\(732\) | −31149.2 | + | 3670.79i | −1.57283 | + | 0.185350i | ||||
\(733\) | 26437.4 | 1.33218 | 0.666090 | − | 0.745872i | \(-0.267967\pi\) | ||||
0.666090 | + | 0.745872i | \(0.267967\pi\) | |||||||
\(734\) | −8958.74 | − | 21415.8i | −0.450508 | − | 1.07694i | ||||
\(735\) | −12028.4 | + | 20300.9i | −0.603639 | + | 1.01879i | ||||
\(736\) | −14193.2 | + | 6172.44i | −0.710826 | + | 0.309129i | ||||
\(737\) | 8078.86i | 0.403784i | ||||||||
\(738\) | 20809.4 | + | 29346.8i | 1.03795 | + | 1.46378i | ||||
\(739\) | − | 24642.5i | − | 1.22664i | −0.789834 | − | 0.613321i | \(-0.789833\pi\) | ||
0.789834 | − | 0.613321i | \(-0.210167\pi\) | |||||||
\(740\) | −19442.4 | + | 19716.7i | −0.965832 | + | 0.979462i | ||||
\(741\) | 2895.16 | + | 2317.84i | 0.143531 | + | 0.114909i | ||||
\(742\) | 555.456 | − | 279.577i | 0.0274817 | − | 0.0138323i | ||||
\(743\) | − | 29736.2i | − | 1.46826i | −0.679012 | − | 0.734128i | \(-0.737591\pi\) | ||
0.679012 | − | 0.734128i | \(-0.262409\pi\) | |||||||
\(744\) | −13677.6 | − | 24252.2i | −0.673984 | − | 1.19507i | ||||
\(745\) | 27135.2i | 1.33444i | ||||||||
\(746\) | −7226.52 | − | 17274.9i | −0.354667 | − | 0.847829i | ||||
\(747\) | 19490.5 | − | 4370.63i | 0.954645 | − | 0.214074i | ||||
\(748\) | 19266.0 | − | 19537.9i | 0.941760 | − | 0.955050i | ||||
\(749\) | 10782.1 | − | 757.115i | 0.525995 | − | 0.0369351i | ||||
\(750\) | −4002.14 | + | 13975.8i | −0.194850 | + | 0.680432i | ||||
\(751\) | 8068.95 | 0.392064 | 0.196032 | − | 0.980597i | \(-0.437194\pi\) | ||||
0.196032 | + | 0.980597i | \(0.437194\pi\) | |||||||
\(752\) | 194.983 | + | 13913.4i | 0.00945519 | + | 0.674691i | ||||
\(753\) | −14591.6 | + | 18226.0i | −0.706171 | + | 0.882063i | ||||
\(754\) | 8383.91 | − | 3507.19i | 0.404939 | − | 0.169396i | ||||
\(755\) | − | 3815.42i | − | 0.183917i | ||||||
\(756\) | −8247.65 | − | 19080.3i | −0.396778 | − | 0.917915i | ||||
\(757\) | 10634.4i | 0.510587i | 0.966864 | + | 0.255293i | \(0.0821720\pi\) | ||||
−0.966864 | + | 0.255293i | \(0.917828\pi\) | |||||||
\(758\) | 3065.84 | + | 7328.87i | 0.146908 | + | 0.351183i | ||||
\(759\) | 13751.1 | − | 17176.3i | 0.657622 | − | 0.821422i | ||||
\(760\) | 6890.48 | + | 2769.65i | 0.328873 | + | 0.132192i | ||||
\(761\) | −3296.31 | −0.157019 | −0.0785094 | − | 0.996913i | \(-0.525016\pi\) | ||||
−0.0785094 | + | 0.996913i | \(0.525016\pi\) | |||||||
\(762\) | −36037.7 | − | 10319.8i | −1.71327 | − | 0.490614i | ||||
\(763\) | 2408.05 | + | 34293.2i | 0.114256 | + | 1.62712i | ||||
\(764\) | 14107.4 | + | 13911.0i | 0.668045 | + | 0.658748i | ||||
\(765\) | −24157.1 | + | 5417.09i | −1.14170 | + | 0.256020i | ||||
\(766\) | −6250.21 | + | 2614.61i | −0.294816 | + | 0.123329i | ||||
\(767\) | 6810.22i | 0.320603i | ||||||||
\(768\) | 16981.0 | + | 12830.8i | 0.797851 | + | 0.602855i | ||||
\(769\) | − | 29295.6i | − | 1.37376i | −0.726769 | − | 0.686882i | \(-0.758979\pi\) | ||
0.726769 | − | 0.686882i | \(-0.241021\pi\) | |||||||
\(770\) | 15442.2 | + | 30680.3i | 0.722727 | + | 1.43590i | ||||
\(771\) | −5808.53 | − | 4650.25i | −0.271322 | − | 0.217218i | ||||
\(772\) | 17584.2 | − | 17832.4i | 0.819779 | − | 0.831348i | ||||
\(773\) | − | 3337.03i | − | 0.155271i | −0.996982 | − | 0.0776356i | \(-0.975263\pi\) | ||
0.996982 | − | 0.0776356i | \(-0.0247371\pi\) | |||||||
\(774\) | −16267.4 | + | 11535.0i | −0.755453 | + | 0.535681i | ||||
\(775\) | − | 11908.9i | − | 0.551975i | ||||||
\(776\) | 3844.47 | + | 1545.30i | 0.177846 | + | 0.0714857i | ||||
\(777\) | −14309.3 | + | 20693.3i | −0.660674 | + | 0.955427i | ||||
\(778\) | −31517.0 | + | 13184.3i | −1.45237 | + | 0.607559i | ||||
\(779\) | −11677.8 | −0.537102 | ||||||||
\(780\) | 1854.57 | + | 15737.4i | 0.0851339 | + | 0.722421i | ||||
\(781\) | 23689.7i | 1.08538i | ||||||||
\(782\) | 6463.48 | + | 15450.9i | 0.295567 | + | 0.706551i | ||||
\(783\) | 6873.36 | − | 14066.8i | 0.313709 | − | 0.642025i | ||||
\(784\) | −3372.07 | − | 21691.5i | −0.153611 | − | 0.988131i | ||||
\(785\) | 27650.7i | 1.25719i | ||||||||
\(786\) | 1778.91 | − | 6212.11i | 0.0807273 | − | 0.281907i | ||||
\(787\) | 643.131 | 0.0291298 | 0.0145649 | − | 0.999894i | \(-0.495364\pi\) | ||||
0.0145649 | + | 0.999894i | \(0.495364\pi\) | |||||||
\(788\) | −479.963 | + | 486.736i | −0.0216979 | + | 0.0220041i | ||||
\(789\) | −2931.25 | + | 3661.37i | −0.132263 | + | 0.165207i | ||||
\(790\) | 2140.05 | + | 5115.77i | 0.0963792 | + | 0.230394i | ||||
\(791\) | −1234.36 | − | 17578.6i | −0.0554851 | − | 0.790168i | ||||
\(792\) | −29862.6 | − | 4868.07i | −1.33980 | − | 0.218408i | ||||
\(793\) | 21724.5 | 0.972835 | ||||||||
\(794\) | 13673.4 | − | 5719.91i | 0.611147 | − | 0.255657i | ||||
\(795\) | −510.403 | + | 637.534i | −0.0227700 | + | 0.0284415i | ||||
\(796\) | −20146.5 | − | 19866.2i | −0.897079 | − | 0.884595i | ||||
\(797\) | 12470.7i | 0.554248i | 0.960834 | + | 0.277124i | \(0.0893813\pi\) | ||||
−0.960834 | + | 0.277124i | \(0.910619\pi\) | |||||||
\(798\) | 6600.81 | + | 1398.59i | 0.292815 | + | 0.0620421i | ||||
\(799\) | 15057.5 | 0.666702 | ||||||||
\(800\) | 3630.42 | + | 8347.94i | 0.160443 | + | 0.368930i | ||||
\(801\) | 7962.79 | + | 35509.4i | 0.351250 | + | 1.56637i | ||||
\(802\) | −11624.7 | − | 27788.7i | −0.511823 | − | 1.22351i | ||||
\(803\) | 51425.4i | 2.25998i | ||||||||
\(804\) | 793.623 | + | 6734.45i | 0.0348121 | + | 0.295405i | ||||
\(805\) | −20913.4 | + | 1468.53i | −0.915654 | + | 0.0642967i | ||||
\(806\) | 7442.54 | + | 17791.3i | 0.325251 | + | 0.777510i | ||||
\(807\) | 6136.81 | − | 7665.36i | 0.267690 | − | 0.334366i | ||||
\(808\) | 18011.6 | + | 7239.81i | 0.784214 | + | 0.315217i | ||||
\(809\) | − | 36823.8i | − | 1.60032i | −0.599789 | − | 0.800158i | \(-0.704749\pi\) | ||
0.599789 | − | 0.800158i | \(-0.295251\pi\) | |||||||
\(810\) | 20280.6 | + | 18274.1i | 0.879736 | + | 0.792700i | ||||
\(811\) | 28331.7 | 1.22671 | 0.613354 | − | 0.789808i | \(-0.289820\pi\) | ||||
0.613354 | + | 0.789808i | \(0.289820\pi\) | |||||||
\(812\) | 10755.9 | − | 12557.2i | 0.464851 | − | 0.542699i | ||||
\(813\) | 24748.6 | − | 30913.0i | 1.06762 | − | 1.33354i | ||||
\(814\) | 14132.7 | + | 33784.2i | 0.608541 | + | 1.45471i | ||||
\(815\) | 54438.2 | 2.33974 | ||||||||
\(816\) | 14140.7 | − | 18179.2i | 0.606645 | − | 0.779902i | ||||
\(817\) | − | 6473.23i | − | 0.277196i | ||||||
\(818\) | −11131.0 | − | 26608.5i | −0.475776 | − | 1.13734i | ||||
\(819\) | 4126.67 | + | 13793.5i | 0.176065 | + | 0.588503i | ||||
\(820\) | −35528.5 | − | 35034.1i | −1.51306 | − | 1.49200i | ||||
\(821\) | 24314.1 | 1.03358 | 0.516789 | − | 0.856113i | \(-0.327127\pi\) | ||||
0.516789 | + | 0.856113i | \(0.327127\pi\) | |||||||
\(822\) | 4559.39 | − | 15921.8i | 0.193463 | − | 0.675591i | ||||
\(823\) | −7780.71 | −0.329549 | −0.164774 | − | 0.986331i | \(-0.552690\pi\) | ||||
−0.164774 | + | 0.986331i | \(0.552690\pi\) | |||||||
\(824\) | 10365.9 | + | 4166.63i | 0.438246 | + | 0.176154i | ||||
\(825\) | −10102.5 | − | 8087.95i | −0.426331 | − | 0.341317i | ||||
\(826\) | 5570.47 | + | 11067.3i | 0.234651 | + | 0.466198i | ||||
\(827\) | −9658.38 | −0.406112 | −0.203056 | − | 0.979167i | \(-0.565087\pi\) | ||||
−0.203056 | + | 0.979167i | \(0.565087\pi\) | |||||||
\(828\) | 9775.51 | − | 15668.8i | 0.410293 | − | 0.657643i | ||||
\(829\) | −4178.46 | −0.175059 | −0.0875296 | − | 0.996162i | \(-0.527897\pi\) | ||||
−0.0875296 | + | 0.996162i | \(0.527897\pi\) | |||||||
\(830\) | −25557.4 | + | 10691.3i | −1.06881 | + | 0.447107i | ||||
\(831\) | 9689.81 | − | 12103.3i | 0.404496 | − | 0.505247i | ||||
\(832\) | −10640.8 | − | 10202.6i | −0.443392 | − | 0.425133i | ||||
\(833\) | −23521.7 | + | 3319.73i | −0.978365 | + | 0.138081i | ||||
\(834\) | 34186.0 | + | 9789.55i | 1.41938 | + | 0.406456i | ||||
\(835\) | 16217.8i | 0.672144i | ||||||||
\(836\) | 6895.96 | − | 6993.28i | 0.285289 | − | 0.289315i | ||||
\(837\) | 29850.8 | + | 14585.8i | 1.23273 | + | 0.602342i | ||||
\(838\) | 10263.5 | + | 24534.8i | 0.423086 | + | 1.01138i | ||||
\(839\) | 937.651 | 0.0385832 | 0.0192916 | − | 0.999814i | \(-0.493859\pi\) | ||||
0.0192916 | + | 0.999814i | \(0.493859\pi\) | |||||||
\(840\) | 15886.4 | + | 24057.8i | 0.652537 | + | 0.988182i | ||||
\(841\) | −11935.8 | −0.489391 | ||||||||
\(842\) | −1664.76 | − | 3979.60i | −0.0681371 | − | 0.162881i | ||||
\(843\) | 9706.04 | − | 12123.6i | 0.396552 | − | 0.495325i | ||||
\(844\) | −9661.88 | − | 9527.43i | −0.394047 | − | 0.388563i | ||||
\(845\) | 18111.8i | 0.737354i | ||||||||
\(846\) | −9603.97 | − | 13544.2i | −0.390297 | − | 0.550423i | ||||
\(847\) | 20723.6 | − | 1455.20i | 0.840700 | − | 0.0590335i | ||||
\(848\) | −10.6462 | − | 759.677i | −0.000431122 | − | 0.0307635i | ||||
\(849\) | −12781.5 | − | 10232.7i | −0.516678 | − | 0.413647i | ||||
\(850\) | 9087.68 | − | 3801.59i | 0.366711 | − | 0.153404i | ||||
\(851\) | −22352.8 | −0.900403 | ||||||||
\(852\) | 2327.15 | + | 19747.5i | 0.0935761 | + | 0.794059i | ||||
\(853\) | 5791.89 | 0.232486 | 0.116243 | − | 0.993221i | \(-0.462915\pi\) | ||||
0.116243 | + | 0.993221i | \(0.462915\pi\) | |||||||
\(854\) | 35304.3 | − | 17769.7i | 1.41462 | − | 0.712021i | ||||
\(855\) | −8646.62 | + | 1938.96i | −0.345857 | + | 0.0775566i | ||||
\(856\) | 4925.09 | − | 12252.9i | 0.196654 | − | 0.489246i | ||||
\(857\) | −1880.84 | −0.0749687 | −0.0374843 | − | 0.999297i | \(-0.511934\pi\) | ||||
−0.0374843 | + | 0.999297i | \(0.511934\pi\) | |||||||
\(858\) | 20147.2 | + | 5769.40i | 0.801650 | + | 0.229562i | ||||
\(859\) | −9503.79 | −0.377491 | −0.188746 | − | 0.982026i | \(-0.560442\pi\) | ||||
−0.188746 | + | 0.982026i | \(0.560442\pi\) | |||||||
\(860\) | 19420.0 | − | 19694.0i | 0.770018 | − | 0.780885i | ||||
\(861\) | −37288.1 | − | 25784.6i | −1.47593 | − | 1.02060i | ||||
\(862\) | −8535.51 | − | 20404.1i | −0.337263 | − | 0.806224i | ||||
\(863\) | − | 5322.63i | − | 0.209947i | −0.994475 | − | 0.104974i | \(-0.966524\pi\) | ||
0.994475 | − | 0.104974i | \(-0.0334758\pi\) | |||||||
\(864\) | −25371.4 | − | 1124.43i | −0.999019 | − | 0.0442753i | ||||
\(865\) | 32457.2 | 1.27581 | ||||||||
\(866\) | −12276.1 | − | 29345.9i | −0.481707 | − | 1.15152i | ||||
\(867\) | 473.011 | + | 378.688i | 0.0185286 | + | 0.0148338i | ||||
\(868\) | 26647.4 | + | 22825.0i | 1.04202 | + | 0.892546i | ||||
\(869\) | 7333.85 | 0.286288 | ||||||||
\(870\) | −5977.86 | + | 20875.2i | −0.232952 | + | 0.813489i | ||||
\(871\) | − | 4696.82i | − | 0.182716i | ||||||
\(872\) | 38971.0 | + | 15664.5i | 1.51345 | + | 0.608335i | ||||
\(873\) | −4824.29 | + | 1081.82i | −0.187030 | + | 0.0419405i | ||||
\(874\) | 2313.49 | + | 5530.39i | 0.0895368 | + | 0.214037i | ||||
\(875\) | −1283.22 | − | 18274.4i | −0.0495779 | − | 0.706043i | ||||
\(876\) | 5051.75 | + | 42867.7i | 0.194843 | + | 1.65338i | ||||
\(877\) | − | 15099.1i | − | 0.581369i | −0.956819 | − | 0.290684i | \(-0.906117\pi\) | ||
0.956819 | − | 0.290684i | \(-0.0938829\pi\) | |||||||
\(878\) | 6439.67 | + | 15394.0i | 0.247526 | + | 0.591710i | ||||
\(879\) | −5312.79 | + | 6636.09i | −0.203863 | + | 0.254641i | ||||
\(880\) | 41960.3 | − | 588.036i | 1.60737 | − | 0.0225258i | ||||
\(881\) | −25460.6 | −0.973654 | −0.486827 | − | 0.873498i | \(-0.661846\pi\) | ||||
−0.486827 | + | 0.873498i | \(0.661846\pi\) | |||||||
\(882\) | 17988.7 | + | 19040.3i | 0.686748 | + | 0.726895i | ||||
\(883\) | 29492.7i | 1.12402i | 0.827131 | + | 0.562009i | \(0.189972\pi\) | ||||
−0.827131 | + | 0.562009i | \(0.810028\pi\) | |||||||
\(884\) | −11200.7 | + | 11358.8i | −0.426155 | + | 0.432169i | ||||
\(885\) | −12702.6 | − | 10169.6i | −0.482480 | − | 0.386269i | ||||
\(886\) | −2587.94 | + | 1082.60i | −0.0981305 | + | 0.0410504i | ||||
\(887\) | 11558.8 | 0.437550 | 0.218775 | − | 0.975775i | \(-0.429794\pi\) | ||||
0.218775 | + | 0.975775i | \(0.429794\pi\) | |||||||
\(888\) | 15099.7 | + | 26773.8i | 0.570622 | + | 1.01179i | ||||
\(889\) | 47122.0 | − | 3308.88i | 1.77775 | − | 0.124833i | ||||
\(890\) | −19478.2 | − | 46562.6i | −0.733609 | − | 1.75369i | ||||
\(891\) | 32646.6 | − | 15416.9i | 1.22750 | − | 0.579669i | ||||
\(892\) | −22423.7 | − | 22111.7i | −0.841707 | − | 0.829994i | ||||
\(893\) | 5389.57 | 0.201965 | ||||||||
\(894\) | 28958.0 | + | 8292.47i | 1.08333 | + | 0.310225i | ||||
\(895\) | 12262.8i | 0.457987i | ||||||||
\(896\) | −25637.6 | − | 7876.49i | −0.955905 | − | 0.293677i | ||||
\(897\) | −7994.53 | + | 9985.80i | −0.297580 | + | 0.371701i | ||||
\(898\) | 15204.8 | + | 36347.0i | 0.565024 | + | 1.35069i | ||||
\(899\) | 26426.8i | 0.980403i | ||||||||
\(900\) | −9215.84 | − | 5749.62i | −0.341328 | − | 0.212949i | ||||
\(901\) | −822.146 | −0.0303992 | ||||||||
\(902\) | −60877.2 | + | 25466.4i | −2.24722 | + | 0.940065i | ||||
\(903\) | 14292.8 | − | 20669.4i | 0.526728 | − | 0.761722i | ||||
\(904\) | −19976.4 | − | 8029.60i | −0.734963 | − | 0.295421i | ||||
\(905\) | 11607.5i | 0.426348i | ||||||||
\(906\) | −4071.72 | − | 1165.98i | −0.149309 | − | 0.0427563i | ||||
\(907\) | − | 10190.2i | − | 0.373053i | −0.982450 | − | 0.186527i | \(-0.940277\pi\) | ||
0.982450 | − | 0.186527i | \(-0.0597231\pi\) | |||||||
\(908\) | 35487.4 | + | 34993.6i | 1.29702 | + | 1.27897i | ||||
\(909\) | −22602.1 | + | 5068.40i | −0.824713 | + | 0.184937i | ||||
\(910\) | −8977.68 | − | 17836.6i | −0.327041 | − | 0.649757i | ||||
\(911\) | 33432.8i | 1.21589i | 0.793978 | + | 0.607947i | \(0.208007\pi\) | ||||
−0.793978 | + | 0.607947i | \(0.791993\pi\) | |||||||
\(912\) | 5061.42 | − | 6506.95i | 0.183772 | − | 0.236257i | ||||
\(913\) | 36638.5i | 1.32810i | ||||||||
\(914\) | −26106.7 | + | 10921.1i | −0.944784 | + | 0.395226i | ||||
\(915\) | −32440.8 | + | 40521.2i | −1.17209 | + | 1.46403i | ||||
\(916\) | 22321.3 | − | 22636.3i | 0.805151 | − | 0.816513i | ||||
\(917\) | 570.378 | + | 8122.80i | 0.0205404 | + | 0.292517i | ||||
\(918\) | −1601.37 | + | 27435.3i | −0.0575742 | + | 0.986382i | ||||
\(919\) | −38879.2 | −1.39554 | −0.697772 | − | 0.716320i | \(-0.745825\pi\) | ||||
−0.697772 | + | 0.716320i | \(0.745825\pi\) | |||||||
\(920\) | −9552.89 | + | 23766.2i | −0.342336 | + | 0.851682i | ||||
\(921\) | −15367.5 | − | 12303.1i | −0.549812 | − | 0.440174i | ||||
\(922\) | 16991.9 | + | 40619.0i | 0.606940 | + | 1.45088i | ||||
\(923\) | − | 13772.5i | − | 0.491146i | ||||||
\(924\) | 37460.3 | − | 7103.75i | 1.33372 | − | 0.252918i | ||||
\(925\) | 13147.1i | 0.467324i | ||||||||
\(926\) | −28353.7 | + | 11861.0i | −1.00622 | + | 0.420926i | ||||
\(927\) | −13007.9 | + | 2916.94i | −0.460878 | + | 0.103349i | ||||
\(928\) | −8056.17 | − | 18524.7i | −0.284975 | − | 0.655285i | ||||
\(929\) | −19916.3 | −0.703370 | −0.351685 | − | 0.936118i | \(-0.614391\pi\) | ||||
−0.351685 | + | 0.936118i | \(0.614391\pi\) | |||||||
\(930\) | −44298.9 | − | 12685.5i | −1.56195 | − | 0.447284i | ||||
\(931\) | −8419.20 | + | 1188.24i | −0.296378 | + | 0.0418293i | ||||
\(932\) | 19373.7 | + | 19104.1i | 0.680908 | + | 0.671433i | ||||
\(933\) | −20275.1 | − | 16232.1i | −0.711444 | − | 0.569575i | ||||
\(934\) | −2383.97 | − | 5698.86i | −0.0835180 | − | 0.199649i | ||||
\(935\) | − | 45410.7i | − | 1.58833i | ||||||
\(936\) | 17361.3 | + | 2830.16i | 0.606273 | + | 0.0988318i | ||||
\(937\) | − | 27614.4i | − | 0.962779i | −0.876507 | − | 0.481390i | \(-0.840132\pi\) | ||
0.876507 | − | 0.481390i | \(-0.159868\pi\) | |||||||
\(938\) | −3841.80 | − | 7632.78i | −0.133730 | − | 0.265692i | ||||
\(939\) | 3743.19 | − | 4675.54i | 0.130090 | − | 0.162492i | ||||
\(940\) | 16397.1 | + | 16169.0i | 0.568953 | + | 0.561035i | ||||
\(941\) | − | 33189.4i | − | 1.14978i | −0.818231 | − | 0.574890i | \(-0.805045\pi\) | ||
0.818231 | − | 0.574890i | \(-0.194955\pi\) | |||||||
\(942\) | 29508.2 | + | 8450.02i | 1.02063 | + | 0.292268i | ||||
\(943\) | − | 40278.4i | − | 1.39093i | ||||||
\(944\) | 15136.3 | − | 212.122i | 0.521870 | − | 0.00731353i | ||||
\(945\) | −31890.4 | − | 12900.5i | −1.09777 | − | 0.444076i | ||||
\(946\) | −14116.5 | − | 33745.3i | −0.485164 | − | 1.15978i | ||||
\(947\) | 6141.76 | 0.210750 | 0.105375 | − | 0.994433i | \(-0.466396\pi\) | ||||
0.105375 | + | 0.994433i | \(0.466396\pi\) | |||||||
\(948\) | 6113.43 | − | 720.438i | 0.209446 | − | 0.0246822i | ||||
\(949\) | − | 29897.2i | − | 1.02266i | ||||||
\(950\) | 3252.78 | − | 1360.72i | 0.111089 | − | 0.0464710i | ||||
\(951\) | −11109.5 | − | 8894.16i | −0.378812 | − | 0.303273i | ||||
\(952\) | −8911.26 | + | 27620.9i | −0.303378 | + | 0.940333i | ||||
\(953\) | − | 7097.85i | − | 0.241261i | −0.992697 | − | 0.120631i | \(-0.961508\pi\) | ||
0.992697 | − | 0.120631i | \(-0.0384916\pi\) | |||||||
\(954\) | 524.383 | + | 739.519i | 0.0177961 | + | 0.0250973i | ||||
\(955\) | 32788.8 | 1.11102 | ||||||||
\(956\) | 25505.8 | + | 25150.9i | 0.862883 | + | 0.850876i | ||||
\(957\) | 22418.2 | + | 17947.8i | 0.757239 | + | 0.606238i | ||||
\(958\) | −18339.4 | + | 7671.82i | −0.618497 | + | 0.258732i | ||||
\(959\) | 1461.89 | + | 20818.9i | 0.0492252 | + | 0.701019i | ||||
\(960\) | 34919.9 | − | 4612.13i | 1.17400 | − | 0.155058i | ||||
\(961\) | −26288.8 | −0.882441 | ||||||||
\(962\) | −8216.37 | − | 19641.2i | −0.275371 | − | 0.658271i | ||||
\(963\) | 3447.92 | + | 15375.7i | 0.115377 | + | 0.514513i | ||||
\(964\) | 13174.0 | + | 12990.6i | 0.440151 | + | 0.434026i | ||||
\(965\) | − | 41446.6i | − | 1.38260i | ||||||
\(966\) | −4823.93 | + | 22767.1i | −0.160670 | + | 0.758301i | ||||
\(967\) | 10526.5 | 0.350063 | 0.175031 | − | 0.984563i | \(-0.443997\pi\) | ||||
0.175031 | + | 0.984563i | \(0.443997\pi\) | |||||||
\(968\) | 9466.20 | − | 23550.5i | 0.314313 | − | 0.781964i | ||||
\(969\) | −6963.89 | − | 5575.22i | −0.230869 | − | 0.184832i | ||||
\(970\) | 6325.96 | − | 2646.30i | 0.209396 | − | 0.0875955i | ||||
\(971\) | 10918.3i | 0.360848i | 0.983589 | + | 0.180424i | \(0.0577470\pi\) | ||||
−0.983589 | + | 0.180424i | \(0.942253\pi\) | |||||||
\(972\) | 25699.4 | − | 16058.4i | 0.848054 | − | 0.529910i | ||||
\(973\) | −44700.7 | + | 3138.86i | −1.47280 | + | 0.103419i | ||||
\(974\) | 9305.75 | − | 3892.82i | 0.306135 | − | 0.128064i | ||||
\(975\) | 5873.30 | + | 4702.10i | 0.192919 | + | 0.154449i | ||||
\(976\) | −676.663 | − | 48284.5i | −0.0221921 | − | 1.58355i | ||||
\(977\) | 23312.8i | 0.763400i | 0.924286 | + | 0.381700i | \(0.124661\pi\) | ||||
−0.924286 | + | 0.381700i | \(0.875339\pi\) | |||||||
\(978\) | 16636.2 | − | 58095.1i | 0.543934 | − | 1.89946i | ||||
\(979\) | −66751.0 | −2.17913 | ||||||||
\(980\) | −29179.2 | − | 21642.9i | −0.951118 | − | 0.705466i | ||||
\(981\) | −48903.4 | + | 10966.3i | −1.59160 | + | 0.356909i | ||||
\(982\) | 5823.26 | − | 2436.01i | 0.189234 | − | 0.0791611i | ||||
\(983\) | 17319.7 | 0.561965 | 0.280982 | − | 0.959713i | \(-0.409340\pi\) | ||||
0.280982 | + | 0.959713i | \(0.409340\pi\) | |||||||
\(984\) | −48245.0 | + | 27208.8i | −1.56300 | + | 0.881488i | ||||
\(985\) | 1131.29i | 0.0365948i | ||||||||
\(986\) | −20166.3 | + | 8436.03i | −0.651343 | + | 0.272472i | ||||
\(987\) | 17209.2 | + | 11900.1i | 0.554991 | + | 0.383774i | ||||
\(988\) | −4009.12 | + | 4065.69i | −0.129096 | + | 0.130918i | ||||
\(989\) | 22327.0 | 0.717854 | ||||||||
\(990\) | −40846.9 | + | 28963.9i | −1.31131 | + | 0.929833i | ||||
\(991\) | 20423.3 | 0.654660 | 0.327330 | − | 0.944910i | \(-0.393851\pi\) | ||||
0.327330 | + | 0.944910i | \(0.393851\pi\) | |||||||
\(992\) | 39311.0 | − | 17095.9i | 1.25819 | − | 0.547172i | ||||
\(993\) | −16958.9 | + | 21183.0i | −0.541969 | + | 0.676962i | ||||
\(994\) | −11265.3 | − | 22381.7i | −0.359472 | − | 0.714189i | ||||
\(995\) | −46825.2 | −1.49192 | ||||||||
\(996\) | 3599.16 | + | 30541.4i | 0.114502 | + | 0.971629i | ||||
\(997\) | 47651.1 | 1.51367 | 0.756833 | − | 0.653608i | \(-0.226745\pi\) | ||||
0.756833 | + | 0.653608i | \(0.226745\pi\) | |||||||
\(998\) | −22561.1 | − | 53932.2i | −0.715591 | − | 1.71061i | ||||
\(999\) | −32954.5 | − | 16102.4i | −1.04368 | − | 0.509966i |
(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 | 168.4.i.c.125.69 | yes | 80 | |
3.2 | odd | 2 | inner | 168.4.i.c.125.11 | yes | 80 | |
4.3 | odd | 2 | 672.4.i.c.209.63 | 80 | |||
7.6 | odd | 2 | inner | 168.4.i.c.125.70 | yes | 80 | |
8.3 | odd | 2 | 672.4.i.c.209.18 | 80 | |||
8.5 | even | 2 | inner | 168.4.i.c.125.10 | yes | 80 | |
12.11 | even | 2 | 672.4.i.c.209.62 | 80 | |||
21.20 | even | 2 | inner | 168.4.i.c.125.12 | yes | 80 | |
24.5 | odd | 2 | inner | 168.4.i.c.125.72 | yes | 80 | |
24.11 | even | 2 | 672.4.i.c.209.19 | 80 | |||
28.27 | even | 2 | 672.4.i.c.209.17 | 80 | |||
56.13 | odd | 2 | inner | 168.4.i.c.125.9 | ✓ | 80 | |
56.27 | even | 2 | 672.4.i.c.209.64 | 80 | |||
84.83 | odd | 2 | 672.4.i.c.209.20 | 80 | |||
168.83 | odd | 2 | 672.4.i.c.209.61 | 80 | |||
168.125 | even | 2 | inner | 168.4.i.c.125.71 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.4.i.c.125.9 | ✓ | 80 | 56.13 | odd | 2 | inner | |
168.4.i.c.125.10 | yes | 80 | 8.5 | even | 2 | inner | |
168.4.i.c.125.11 | yes | 80 | 3.2 | odd | 2 | inner | |
168.4.i.c.125.12 | yes | 80 | 21.20 | even | 2 | inner | |
168.4.i.c.125.69 | yes | 80 | 1.1 | even | 1 | trivial | |
168.4.i.c.125.70 | yes | 80 | 7.6 | odd | 2 | inner | |
168.4.i.c.125.71 | yes | 80 | 168.125 | even | 2 | inner | |
168.4.i.c.125.72 | yes | 80 | 24.5 | odd | 2 | inner | |
672.4.i.c.209.17 | 80 | 28.27 | even | 2 | |||
672.4.i.c.209.18 | 80 | 8.3 | odd | 2 | |||
672.4.i.c.209.19 | 80 | 24.11 | even | 2 | |||
672.4.i.c.209.20 | 80 | 84.83 | odd | 2 | |||
672.4.i.c.209.61 | 80 | 168.83 | odd | 2 | |||
672.4.i.c.209.62 | 80 | 12.11 | even | 2 | |||
672.4.i.c.209.63 | 80 | 4.3 | odd | 2 | |||
672.4.i.c.209.64 | 80 | 56.27 | even | 2 |