Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [39,4,Mod(25,39)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(39, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("39.25");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 39 = 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 39.b (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: | \(2.30107449022\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.1362828.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 23x^{2} + 48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 25.4 | ||
Root | \(4.54739i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 39.25 |
Dual form | 39.4.b.b.25.1 |
$q$-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 \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).
\(n\) | \(14\) | \(28\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.54739i | 1.60775i | 0.594801 | + | 0.803873i | \(0.297231\pi\) | ||||
−0.594801 | + | 0.803873i | \(0.702769\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | −12.6788 | −1.58485 | ||||||||
\(5\) | 12.9118i | 1.15487i | 0.816437 | + | 0.577434i | \(0.195946\pi\) | ||||
−0.816437 | + | 0.577434i | \(0.804054\pi\) | |||||||
\(6\) | 13.6422i | 0.928233i | ||||||||
\(7\) | − | 16.7289i | − | 0.903273i | −0.892202 | − | 0.451637i | \(-0.850840\pi\) | ||
0.892202 | − | 0.451637i | \(-0.149160\pi\) | |||||||
\(8\) | − | 21.2762i | − | 0.940286i | ||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −58.7151 | −1.85674 | ||||||||
\(11\) | − | 24.9280i | − | 0.683280i | −0.939831 | − | 0.341640i | \(-0.889018\pi\) | ||
0.939831 | − | 0.341640i | \(-0.110982\pi\) | |||||||
\(12\) | −38.0363 | −0.915012 | ||||||||
\(13\) | 33.7151 | + | 32.5621i | 0.719299 | + | 0.694700i | ||||
\(14\) | 76.0727 | 1.45223 | ||||||||
\(15\) | 38.7355i | 0.666764i | ||||||||
\(16\) | −4.67878 | −0.0731059 | ||||||||
\(17\) | 134.145 | 1.91383 | 0.956913 | − | 0.290376i | \(-0.0937804\pi\) | ||||
0.956913 | + | 0.290376i | \(0.0937804\pi\) | |||||||
\(18\) | 40.9265i | 0.535915i | ||||||||
\(19\) | − | 14.9376i | − | 0.180365i | −0.995925 | − | 0.0901824i | \(-0.971255\pi\) | ||
0.995925 | − | 0.0901824i | \(-0.0287450\pi\) | |||||||
\(20\) | − | 163.706i | − | 1.83029i | ||||||
\(21\) | − | 50.1866i | − | 0.521505i | ||||||
\(22\) | 113.358 | 1.09854 | ||||||||
\(23\) | −72.0000 | −0.652741 | −0.326370 | − | 0.945242i | \(-0.605826\pi\) | ||||
−0.326370 | + | 0.945242i | \(0.605826\pi\) | |||||||
\(24\) | − | 63.8287i | − | 0.542875i | ||||||
\(25\) | −41.7151 | −0.333721 | ||||||||
\(26\) | −148.073 | + | 153.316i | −1.11690 | + | 1.15645i | ||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 212.101i | 1.43155i | ||||||||
\(29\) | −206.145 | −1.32001 | −0.660004 | − | 0.751262i | \(-0.729445\pi\) | ||||
−0.660004 | + | 0.751262i | \(0.729445\pi\) | |||||||
\(30\) | −176.145 | −1.07199 | ||||||||
\(31\) | − | 249.142i | − | 1.44346i | −0.692176 | − | 0.721728i | \(-0.743348\pi\) | ||
0.692176 | − | 0.721728i | \(-0.256652\pi\) | |||||||
\(32\) | − | 191.486i | − | 1.05782i | ||||||
\(33\) | − | 74.7841i | − | 0.394492i | ||||||
\(34\) | 610.012i | 3.07694i | ||||||||
\(35\) | 216.000 | 1.04316 | ||||||||
\(36\) | −114.109 | −0.528282 | ||||||||
\(37\) | − | 293.955i | − | 1.30610i | −0.757313 | − | 0.653052i | \(-0.773488\pi\) | ||
0.757313 | − | 0.653052i | \(-0.226512\pi\) | |||||||
\(38\) | 67.9273 | 0.289981 | ||||||||
\(39\) | 101.145 | + | 97.6863i | 0.415288 | + | 0.401085i | ||||
\(40\) | 274.715 | 1.08591 | ||||||||
\(41\) | 250.506i | 0.954208i | 0.878847 | + | 0.477104i | \(0.158314\pi\) | ||||
−0.878847 | + | 0.477104i | \(0.841686\pi\) | |||||||
\(42\) | 228.218 | 0.838448 | ||||||||
\(43\) | −432.145 | −1.53259 | −0.766297 | − | 0.642486i | \(-0.777903\pi\) | ||||
−0.766297 | + | 0.642486i | \(0.777903\pi\) | |||||||
\(44\) | 316.057i | 1.08290i | ||||||||
\(45\) | 116.206i | 0.384956i | ||||||||
\(46\) | − | 327.412i | − | 1.04944i | ||||||
\(47\) | 159.889i | 0.496217i | 0.968732 | + | 0.248109i | \(0.0798090\pi\) | ||||
−0.968732 | + | 0.248109i | \(0.920191\pi\) | |||||||
\(48\) | −14.0363 | −0.0422077 | ||||||||
\(49\) | 63.1454 | 0.184097 | ||||||||
\(50\) | − | 189.695i | − | 0.536539i | ||||||
\(51\) | 402.436 | 1.10495 | ||||||||
\(52\) | −427.467 | − | 412.848i | −1.13998 | − | 1.10099i | ||||
\(53\) | −194.581 | −0.504298 | −0.252149 | − | 0.967688i | \(-0.581137\pi\) | ||||
−0.252149 | + | 0.967688i | \(0.581137\pi\) | |||||||
\(54\) | 122.780i | 0.309411i | ||||||||
\(55\) | 321.866 | 0.789099 | ||||||||
\(56\) | −355.927 | −0.849336 | ||||||||
\(57\) | − | 44.8129i | − | 0.104134i | ||||||
\(58\) | − | 937.424i | − | 2.12224i | ||||||
\(59\) | − | 232.647i | − | 0.513358i | −0.966497 | − | 0.256679i | \(-0.917372\pi\) | ||
0.966497 | − | 0.256679i | \(-0.0826283\pi\) | |||||||
\(60\) | − | 491.118i | − | 1.05672i | ||||||
\(61\) | −185.006 | −0.388321 | −0.194160 | − | 0.980970i | \(-0.562198\pi\) | ||||
−0.194160 | + | 0.980970i | \(0.562198\pi\) | |||||||
\(62\) | 1132.94 | 2.32071 | ||||||||
\(63\) | − | 150.560i | − | 0.301091i | ||||||
\(64\) | 833.333 | 1.62760 | ||||||||
\(65\) | −420.436 | + | 435.324i | −0.802287 | + | 0.830696i | ||||
\(66\) | 340.073 | 0.634243 | ||||||||
\(67\) | − | 39.4393i | − | 0.0719145i | −0.999353 | − | 0.0359573i | \(-0.988552\pi\) | ||
0.999353 | − | 0.0359573i | \(-0.0114480\pi\) | |||||||
\(68\) | −1700.80 | −3.03312 | ||||||||
\(69\) | −216.000 | −0.376860 | ||||||||
\(70\) | 982.237i | 1.67714i | ||||||||
\(71\) | 920.460i | 1.53857i | 0.638905 | + | 0.769286i | \(0.279388\pi\) | ||||
−0.638905 | + | 0.769286i | \(0.720612\pi\) | |||||||
\(72\) | − | 191.486i | − | 0.313429i | ||||||
\(73\) | 549.078i | 0.880338i | 0.897915 | + | 0.440169i | \(0.145082\pi\) | ||||
−0.897915 | + | 0.440169i | \(0.854918\pi\) | |||||||
\(74\) | 1336.73 | 2.09988 | ||||||||
\(75\) | −125.145 | −0.192674 | ||||||||
\(76\) | 189.391i | 0.285851i | ||||||||
\(77\) | −417.018 | −0.617189 | ||||||||
\(78\) | −444.218 | + | 459.948i | −0.644843 | + | 0.667677i | ||||
\(79\) | 933.140 | 1.32894 | 0.664471 | − | 0.747314i | \(-0.268657\pi\) | ||||
0.664471 | + | 0.747314i | \(0.268657\pi\) | |||||||
\(80\) | − | 60.4116i | − | 0.0844277i | ||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −1139.15 | −1.53412 | ||||||||
\(83\) | − | 1095.38i | − | 1.44860i | −0.689484 | − | 0.724301i | \(-0.742163\pi\) | ||
0.689484 | − | 0.724301i | \(-0.257837\pi\) | |||||||
\(84\) | 636.304i | 0.826506i | ||||||||
\(85\) | 1732.06i | 2.21022i | ||||||||
\(86\) | − | 1965.13i | − | 2.46402i | ||||||
\(87\) | −618.436 | −0.762107 | ||||||||
\(88\) | −530.375 | −0.642479 | ||||||||
\(89\) | 532.114i | 0.633753i | 0.948467 | + | 0.316876i | \(0.102634\pi\) | ||||
−0.948467 | + | 0.316876i | \(0.897366\pi\) | |||||||
\(90\) | −528.436 | −0.618912 | ||||||||
\(91\) | 544.727 | − | 564.015i | 0.627504 | − | 0.649724i | ||||
\(92\) | 912.872 | 1.03449 | ||||||||
\(93\) | − | 747.425i | − | 0.833380i | ||||||
\(94\) | −727.079 | −0.797792 | ||||||||
\(95\) | 192.872 | 0.208298 | ||||||||
\(96\) | − | 574.459i | − | 0.610734i | ||||||
\(97\) | − | 362.661i | − | 0.379615i | −0.981821 | − | 0.189808i | \(-0.939214\pi\) | ||
0.981821 | − | 0.189808i | \(-0.0607864\pi\) | |||||||
\(98\) | 287.147i | 0.295982i | ||||||||
\(99\) | − | 224.352i | − | 0.227760i | ||||||
\(100\) | 528.897 | 0.528897 | ||||||||
\(101\) | −1490.58 | −1.46850 | −0.734249 | − | 0.678880i | \(-0.762466\pi\) | ||||
−0.734249 | + | 0.678880i | \(0.762466\pi\) | |||||||
\(102\) | 1830.03i | 1.77648i | ||||||||
\(103\) | −628.436 | −0.601181 | −0.300591 | − | 0.953753i | \(-0.597184\pi\) | ||||
−0.300591 | + | 0.953753i | \(0.597184\pi\) | |||||||
\(104\) | 692.799 | − | 717.331i | 0.653217 | − | 0.676347i | ||||
\(105\) | 648.000 | 0.602270 | ||||||||
\(106\) | − | 884.838i | − | 0.810784i | ||||||
\(107\) | 477.454 | 0.431376 | 0.215688 | − | 0.976462i | \(-0.430801\pi\) | ||||
0.215688 | + | 0.976462i | \(0.430801\pi\) | |||||||
\(108\) | −342.327 | −0.305004 | ||||||||
\(109\) | − | 378.207i | − | 0.332345i | −0.986097 | − | 0.166173i | \(-0.946859\pi\) | ||
0.986097 | − | 0.166173i | \(-0.0531409\pi\) | |||||||
\(110\) | 1463.65i | 1.26867i | ||||||||
\(111\) | − | 881.864i | − | 0.754079i | ||||||
\(112\) | 78.2706i | 0.0660346i | ||||||||
\(113\) | 13.2732 | 0.0110499 | 0.00552495 | − | 0.999985i | \(-0.498241\pi\) | ||||
0.00552495 | + | 0.999985i | \(0.498241\pi\) | |||||||
\(114\) | 203.782 | 0.167420 | ||||||||
\(115\) | − | 929.651i | − | 0.753830i | ||||||
\(116\) | 2613.67 | 2.09201 | ||||||||
\(117\) | 303.436 | + | 293.059i | 0.239766 | + | 0.231567i | ||||
\(118\) | 1057.94 | 0.825349 | ||||||||
\(119\) | − | 2244.10i | − | 1.72871i | ||||||
\(120\) | 824.145 | 0.626949 | ||||||||
\(121\) | 709.593 | 0.533128 | ||||||||
\(122\) | − | 841.294i | − | 0.624321i | ||||||
\(123\) | 751.519i | 0.550912i | ||||||||
\(124\) | 3158.81i | 2.28766i | ||||||||
\(125\) | 1075.36i | 0.769465i | ||||||||
\(126\) | 684.654 | 0.484078 | ||||||||
\(127\) | −145.988 | −0.102003 | −0.0510015 | − | 0.998699i | \(-0.516241\pi\) | ||||
−0.0510015 | + | 0.998699i | \(0.516241\pi\) | |||||||
\(128\) | 2257.60i | 1.55895i | ||||||||
\(129\) | −1296.44 | −0.884844 | ||||||||
\(130\) | −1979.59 | − | 1911.89i | −1.33555 | − | 1.28987i | ||||
\(131\) | 317.163 | 0.211532 | 0.105766 | − | 0.994391i | \(-0.466271\pi\) | ||||
0.105766 | + | 0.994391i | \(0.466271\pi\) | |||||||
\(132\) | 948.171i | 0.625210i | ||||||||
\(133\) | −249.890 | −0.162919 | ||||||||
\(134\) | 179.346 | 0.115620 | ||||||||
\(135\) | 348.619i | 0.222255i | ||||||||
\(136\) | − | 2854.11i | − | 1.79954i | ||||||
\(137\) | − | 443.149i | − | 0.276356i | −0.990407 | − | 0.138178i | \(-0.955875\pi\) | ||
0.990407 | − | 0.138178i | \(-0.0441247\pi\) | |||||||
\(138\) | − | 982.237i | − | 0.605895i | ||||||
\(139\) | 785.018 | 0.479024 | 0.239512 | − | 0.970893i | \(-0.423013\pi\) | ||||
0.239512 | + | 0.970893i | \(0.423013\pi\) | |||||||
\(140\) | −2738.62 | −1.65325 | ||||||||
\(141\) | 479.667i | 0.286491i | ||||||||
\(142\) | −4185.69 | −2.47363 | ||||||||
\(143\) | 811.709 | − | 840.452i | 0.474675 | − | 0.491483i | ||||
\(144\) | −42.1090 | −0.0243686 | ||||||||
\(145\) | − | 2661.71i | − | 1.52444i | ||||||
\(146\) | −2496.87 | −1.41536 | ||||||||
\(147\) | 189.436 | 0.106289 | ||||||||
\(148\) | 3726.99i | 2.06997i | ||||||||
\(149\) | 135.420i | 0.0744566i | 0.999307 | + | 0.0372283i | \(0.0118529\pi\) | ||||
−0.999307 | + | 0.0372283i | \(0.988147\pi\) | |||||||
\(150\) | − | 569.085i | − | 0.309771i | ||||||
\(151\) | 2373.74i | 1.27929i | 0.768672 | + | 0.639643i | \(0.220918\pi\) | ||||
−0.768672 | + | 0.639643i | \(0.779082\pi\) | |||||||
\(152\) | −317.817 | −0.169594 | ||||||||
\(153\) | 1207.31 | 0.637942 | ||||||||
\(154\) | − | 1896.34i | − | 0.992283i | ||||||
\(155\) | 3216.87 | 1.66700 | ||||||||
\(156\) | −1282.40 | − | 1238.54i | −0.658168 | − | 0.635659i | ||||
\(157\) | −1166.73 | −0.593089 | −0.296544 | − | 0.955019i | \(-0.595834\pi\) | ||||
−0.296544 | + | 0.955019i | \(0.595834\pi\) | |||||||
\(158\) | 4243.35i | 2.13660i | ||||||||
\(159\) | −583.744 | −0.291157 | ||||||||
\(160\) | 2472.44 | 1.22165 | ||||||||
\(161\) | 1204.48i | 0.589603i | ||||||||
\(162\) | 368.339i | 0.178638i | ||||||||
\(163\) | 2309.19i | 1.10963i | 0.831974 | + | 0.554815i | \(0.187211\pi\) | ||||
−0.831974 | + | 0.554815i | \(0.812789\pi\) | |||||||
\(164\) | − | 3176.12i | − | 1.51227i | ||||||
\(165\) | 965.599 | 0.455587 | ||||||||
\(166\) | 4981.14 | 2.32898 | ||||||||
\(167\) | 600.788i | 0.278386i | 0.990265 | + | 0.139193i | \(0.0444508\pi\) | ||||
−0.990265 | + | 0.139193i | \(0.955549\pi\) | |||||||
\(168\) | −1067.78 | −0.490364 | ||||||||
\(169\) | 76.4186 | + | 2195.67i | 0.0347831 | + | 0.999395i | ||||
\(170\) | −7876.36 | −3.55347 | ||||||||
\(171\) | − | 134.439i | − | 0.0601216i | ||||||
\(172\) | 5479.08 | 2.42893 | ||||||||
\(173\) | −3430.36 | −1.50755 | −0.753773 | − | 0.657135i | \(-0.771768\pi\) | ||||
−0.753773 | + | 0.657135i | \(0.771768\pi\) | |||||||
\(174\) | − | 2812.27i | − | 1.22527i | ||||||
\(175\) | 697.846i | 0.301441i | ||||||||
\(176\) | 116.633i | 0.0499519i | ||||||||
\(177\) | − | 697.942i | − | 0.296387i | ||||||
\(178\) | −2419.73 | −1.01891 | ||||||||
\(179\) | −978.837 | −0.408725 | −0.204362 | − | 0.978895i | \(-0.565512\pi\) | ||||
−0.204362 | + | 0.978895i | \(0.565512\pi\) | |||||||
\(180\) | − | 1473.36i | − | 0.610097i | ||||||
\(181\) | 3839.09 | 1.57656 | 0.788279 | − | 0.615318i | \(-0.210972\pi\) | ||||
0.788279 | + | 0.615318i | \(0.210972\pi\) | |||||||
\(182\) | 2564.80 | + | 2477.09i | 1.04459 | + | 1.00887i | ||||
\(183\) | −555.018 | −0.224197 | ||||||||
\(184\) | 1531.89i | 0.613763i | ||||||||
\(185\) | 3795.49 | 1.50838 | ||||||||
\(186\) | 3398.83 | 1.33986 | ||||||||
\(187\) | − | 3343.98i | − | 1.30768i | ||||||
\(188\) | − | 2027.20i | − | 0.786429i | ||||||
\(189\) | − | 451.679i | − | 0.173835i | ||||||
\(190\) | 877.065i | 0.334890i | ||||||||
\(191\) | −487.709 | −0.184761 | −0.0923806 | − | 0.995724i | \(-0.529448\pi\) | ||||
−0.0923806 | + | 0.995724i | \(0.529448\pi\) | |||||||
\(192\) | 2500.00 | 0.939697 | ||||||||
\(193\) | − | 4245.61i | − | 1.58345i | −0.610878 | − | 0.791725i | \(-0.709183\pi\) | ||
0.610878 | − | 0.791725i | \(-0.290817\pi\) | |||||||
\(194\) | 1649.16 | 0.610325 | ||||||||
\(195\) | −1261.31 | + | 1305.97i | −0.463201 | + | 0.479603i | ||||
\(196\) | −800.606 | −0.291766 | ||||||||
\(197\) | − | 2712.71i | − | 0.981079i | −0.871419 | − | 0.490539i | \(-0.836800\pi\) | ||
0.871419 | − | 0.490539i | \(-0.163200\pi\) | |||||||
\(198\) | 1020.22 | 0.366180 | ||||||||
\(199\) | −3116.90 | −1.11031 | −0.555153 | − | 0.831748i | \(-0.687340\pi\) | ||||
−0.555153 | + | 0.831748i | \(0.687340\pi\) | |||||||
\(200\) | 887.541i | 0.313793i | ||||||||
\(201\) | − | 118.318i | − | 0.0415199i | ||||||
\(202\) | − | 6778.26i | − | 2.36097i | ||||||
\(203\) | 3448.58i | 1.19233i | ||||||||
\(204\) | −5102.40 | −1.75117 | ||||||||
\(205\) | −3234.49 | −1.10198 | ||||||||
\(206\) | − | 2857.75i | − | 0.966546i | ||||||
\(207\) | −648.000 | −0.217580 | ||||||||
\(208\) | −157.746 | − | 152.351i | −0.0525851 | − | 0.0507867i | ||||
\(209\) | −372.366 | −0.123240 | ||||||||
\(210\) | 2946.71i | 0.968297i | ||||||||
\(211\) | −1051.22 | −0.342981 | −0.171491 | − | 0.985186i | \(-0.554858\pi\) | ||||
−0.171491 | + | 0.985186i | \(0.554858\pi\) | |||||||
\(212\) | 2467.06 | 0.799236 | ||||||||
\(213\) | 2761.38i | 0.888294i | ||||||||
\(214\) | 2171.17i | 0.693542i | ||||||||
\(215\) | − | 5579.78i | − | 1.76994i | ||||||
\(216\) | − | 574.459i | − | 0.180958i | ||||||
\(217\) | −4167.85 | −1.30384 | ||||||||
\(218\) | 1719.85 | 0.534327 | ||||||||
\(219\) | 1647.23i | 0.508264i | ||||||||
\(220\) | −4080.87 | −1.25060 | ||||||||
\(221\) | 4522.73 | + | 4368.06i | 1.37661 | + | 1.32953i | ||||
\(222\) | 4010.18 | 1.21237 | ||||||||
\(223\) | 5496.12i | 1.65044i | 0.564814 | + | 0.825218i | \(0.308948\pi\) | ||||
−0.564814 | + | 0.825218i | \(0.691052\pi\) | |||||||
\(224\) | −3203.35 | −0.955502 | ||||||||
\(225\) | −375.436 | −0.111240 | ||||||||
\(226\) | 60.3585i | 0.0177654i | ||||||||
\(227\) | − | 921.570i | − | 0.269457i | −0.990883 | − | 0.134729i | \(-0.956984\pi\) | ||
0.990883 | − | 0.134729i | \(-0.0430162\pi\) | |||||||
\(228\) | 568.173i | 0.165036i | ||||||||
\(229\) | − | 192.941i | − | 0.0556764i | −0.999612 | − | 0.0278382i | \(-0.991138\pi\) | ||
0.999612 | − | 0.0278382i | \(-0.00886232\pi\) | |||||||
\(230\) | 4227.49 | 1.21197 | ||||||||
\(231\) | −1251.05 | −0.356334 | ||||||||
\(232\) | 4386.00i | 1.24119i | ||||||||
\(233\) | −913.779 | −0.256926 | −0.128463 | − | 0.991714i | \(-0.541004\pi\) | ||||
−0.128463 | + | 0.991714i | \(0.541004\pi\) | |||||||
\(234\) | −1332.65 | + | 1379.84i | −0.372301 | + | 0.385484i | ||||
\(235\) | −2064.46 | −0.573066 | ||||||||
\(236\) | 2949.68i | 0.813594i | ||||||||
\(237\) | 2799.42 | 0.767265 | ||||||||
\(238\) | 10204.8 | 2.77932 | ||||||||
\(239\) | − | 1976.86i | − | 0.535032i | −0.963553 | − | 0.267516i | \(-0.913797\pi\) | ||
0.963553 | − | 0.267516i | \(-0.0862028\pi\) | |||||||
\(240\) | − | 181.235i | − | 0.0487444i | ||||||
\(241\) | − | 3904.45i | − | 1.04360i | −0.853068 | − | 0.521800i | \(-0.825261\pi\) | ||
0.853068 | − | 0.521800i | \(-0.174739\pi\) | |||||||
\(242\) | 3226.80i | 0.857134i | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 2345.65 | 0.615429 | ||||||||
\(245\) | 815.322i | 0.212608i | ||||||||
\(246\) | −3417.45 | −0.885727 | ||||||||
\(247\) | 486.401 | − | 503.624i | 0.125299 | − | 0.129736i | ||||
\(248\) | −5300.80 | −1.35726 | ||||||||
\(249\) | − | 3286.15i | − | 0.836350i | ||||||
\(250\) | −4890.08 | −1.23710 | ||||||||
\(251\) | 942.035 | 0.236895 | 0.118448 | − | 0.992960i | \(-0.462208\pi\) | ||||
0.118448 | + | 0.992960i | \(0.462208\pi\) | |||||||
\(252\) | 1908.91i | 0.477183i | ||||||||
\(253\) | 1794.82i | 0.446005i | ||||||||
\(254\) | − | 663.866i | − | 0.163995i | ||||||
\(255\) | 5196.18i | 1.27607i | ||||||||
\(256\) | −3599.54 | −0.878794 | ||||||||
\(257\) | 812.616 | 0.197236 | 0.0986179 | − | 0.995125i | \(-0.468558\pi\) | ||||
0.0986179 | + | 0.995125i | \(0.468558\pi\) | |||||||
\(258\) | − | 5895.40i | − | 1.42260i | ||||||
\(259\) | −4917.52 | −1.17977 | ||||||||
\(260\) | 5330.62 | − | 5519.37i | 1.27150 | − | 1.31653i | ||||
\(261\) | −1855.31 | −0.440003 | ||||||||
\(262\) | 1442.26i | 0.340089i | ||||||||
\(263\) | −2608.29 | −0.611536 | −0.305768 | − | 0.952106i | \(-0.598913\pi\) | ||||
−0.305768 | + | 0.952106i | \(0.598913\pi\) | |||||||
\(264\) | −1591.13 | −0.370936 | ||||||||
\(265\) | − | 2512.40i | − | 0.582398i | ||||||
\(266\) | − | 1136.35i | − | 0.261932i | ||||||
\(267\) | 1596.34i | 0.365897i | ||||||||
\(268\) | 500.042i | 0.113974i | ||||||||
\(269\) | −4791.02 | −1.08592 | −0.542962 | − | 0.839757i | \(-0.682697\pi\) | ||||
−0.542962 | + | 0.839757i | \(0.682697\pi\) | |||||||
\(270\) | −1585.31 | −0.357329 | ||||||||
\(271\) | 3663.62i | 0.821214i | 0.911812 | + | 0.410607i | \(0.134683\pi\) | ||||
−0.911812 | + | 0.410607i | \(0.865317\pi\) | |||||||
\(272\) | −627.637 | −0.139912 | ||||||||
\(273\) | 1634.18 | − | 1692.05i | 0.362290 | − | 0.375118i | ||||
\(274\) | 2015.17 | 0.444311 | ||||||||
\(275\) | 1039.88i | 0.228025i | ||||||||
\(276\) | 2738.62 | 0.597266 | ||||||||
\(277\) | 624.326 | 0.135423 | 0.0677114 | − | 0.997705i | \(-0.478430\pi\) | ||||
0.0677114 | + | 0.997705i | \(0.478430\pi\) | |||||||
\(278\) | 3569.78i | 0.770149i | ||||||||
\(279\) | − | 2242.27i | − | 0.481152i | ||||||
\(280\) | − | 4595.67i | − | 0.980871i | ||||||
\(281\) | − | 5535.12i | − | 1.17508i | −0.809195 | − | 0.587540i | \(-0.800096\pi\) | ||
0.809195 | − | 0.587540i | \(-0.199904\pi\) | |||||||
\(282\) | −2181.24 | −0.460605 | ||||||||
\(283\) | −175.151 | −0.0367903 | −0.0183952 | − | 0.999831i | \(-0.505856\pi\) | ||||
−0.0183952 | + | 0.999831i | \(0.505856\pi\) | |||||||
\(284\) | − | 11670.3i | − | 2.43840i | ||||||
\(285\) | 578.616 | 0.120261 | ||||||||
\(286\) | 3821.86 | + | 3691.16i | 0.790180 | + | 0.763157i | ||||
\(287\) | 4190.69 | 0.861911 | ||||||||
\(288\) | − | 1723.38i | − | 0.352607i | ||||||
\(289\) | 13082.0 | 2.66273 | ||||||||
\(290\) | 12103.8 | 2.45091 | ||||||||
\(291\) | − | 1087.98i | − | 0.219171i | ||||||
\(292\) | − | 6961.64i | − | 1.39520i | ||||||
\(293\) | 7774.33i | 1.55011i | 0.631895 | + | 0.775054i | \(0.282277\pi\) | ||||
−0.631895 | + | 0.775054i | \(0.717723\pi\) | |||||||
\(294\) | 861.440i | 0.170885i | ||||||||
\(295\) | 3003.90 | 0.592861 | ||||||||
\(296\) | −6254.25 | −1.22811 | ||||||||
\(297\) | − | 673.057i | − | 0.131497i | ||||||
\(298\) | −615.808 | −0.119707 | ||||||||
\(299\) | −2427.49 | − | 2344.47i | −0.469516 | − | 0.453459i | ||||
\(300\) | 1586.69 | 0.305359 | ||||||||
\(301\) | 7229.30i | 1.38435i | ||||||||
\(302\) | −10794.3 | −2.05677 | ||||||||
\(303\) | −4471.74 | −0.847838 | ||||||||
\(304\) | 69.8899i | 0.0131857i | ||||||||
\(305\) | − | 2388.76i | − | 0.448459i | ||||||
\(306\) | 5490.10i | 1.02565i | ||||||||
\(307\) | − | 8022.85i | − | 1.49149i | −0.666230 | − | 0.745746i | \(-0.732093\pi\) | ||
0.666230 | − | 0.745746i | \(-0.267907\pi\) | |||||||
\(308\) | 5287.27 | 0.978150 | ||||||||
\(309\) | −1885.31 | −0.347092 | ||||||||
\(310\) | 14628.4i | 2.68012i | ||||||||
\(311\) | 9264.87 | 1.68927 | 0.844635 | − | 0.535343i | \(-0.179818\pi\) | ||||
0.844635 | + | 0.535343i | \(0.179818\pi\) | |||||||
\(312\) | 2078.40 | − | 2151.99i | 0.377135 | − | 0.390489i | ||||
\(313\) | 7423.57 | 1.34059 | 0.670296 | − | 0.742094i | \(-0.266167\pi\) | ||||
0.670296 | + | 0.742094i | \(0.266167\pi\) | |||||||
\(314\) | − | 5305.56i | − | 0.953536i | ||||||
\(315\) | 1944.00 | 0.347721 | ||||||||
\(316\) | −11831.1 | −2.10617 | ||||||||
\(317\) | 2641.04i | 0.467935i | 0.972244 | + | 0.233968i | \(0.0751710\pi\) | ||||
−0.972244 | + | 0.233968i | \(0.924829\pi\) | |||||||
\(318\) | − | 2654.51i | − | 0.468106i | ||||||
\(319\) | 5138.80i | 0.901936i | ||||||||
\(320\) | 10759.8i | 1.87967i | ||||||||
\(321\) | 1432.36 | 0.249055 | ||||||||
\(322\) | −5477.23 | −0.947932 | ||||||||
\(323\) | − | 2003.82i | − | 0.345187i | ||||||
\(324\) | −1026.98 | −0.176094 | ||||||||
\(325\) | −1406.43 | − | 1358.33i | −0.240045 | − | 0.231836i | ||||
\(326\) | −10500.8 | −1.78400 | ||||||||
\(327\) | − | 1134.62i | − | 0.191880i | ||||||
\(328\) | 5329.84 | 0.897229 | ||||||||
\(329\) | 2674.76 | 0.448220 | ||||||||
\(330\) | 4390.96i | 0.732467i | ||||||||
\(331\) | 10779.5i | 1.79001i | 0.446052 | + | 0.895007i | \(0.352830\pi\) | ||||
−0.446052 | + | 0.895007i | \(0.647170\pi\) | |||||||
\(332\) | 13888.1i | 2.29581i | ||||||||
\(333\) | − | 2645.59i | − | 0.435368i | ||||||
\(334\) | −2732.02 | −0.447573 | ||||||||
\(335\) | 509.233 | 0.0830518 | ||||||||
\(336\) | 234.812i | 0.0381251i | ||||||||
\(337\) | 313.465 | 0.0506693 | 0.0253346 | − | 0.999679i | \(-0.491935\pi\) | ||||
0.0253346 | + | 0.999679i | \(0.491935\pi\) | |||||||
\(338\) | −9984.58 | + | 347.505i | −1.60677 | + | 0.0559225i | ||||
\(339\) | 39.8196 | 0.00637966 | ||||||||
\(340\) | − | 21960.4i | − | 3.50286i | ||||||
\(341\) | −6210.61 | −0.986286 | ||||||||
\(342\) | 611.346 | 0.0966602 | ||||||||
\(343\) | − | 6794.35i | − | 1.06956i | ||||||
\(344\) | 9194.43i | 1.44108i | ||||||||
\(345\) | − | 2788.95i | − | 0.435224i | ||||||
\(346\) | − | 15599.2i | − | 2.42375i | ||||||
\(347\) | −2849.23 | −0.440792 | −0.220396 | − | 0.975410i | \(-0.570735\pi\) | ||||
−0.220396 | + | 0.975410i | \(0.570735\pi\) | |||||||
\(348\) | 7841.01 | 1.20782 | ||||||||
\(349\) | − | 6466.94i | − | 0.991883i | −0.868356 | − | 0.495941i | \(-0.834823\pi\) | ||
0.868356 | − | 0.495941i | \(-0.165177\pi\) | |||||||
\(350\) | −3173.38 | −0.484641 | ||||||||
\(351\) | 910.308 | + | 879.177i | 0.138429 | + | 0.133695i | ||||
\(352\) | −4773.38 | −0.722789 | ||||||||
\(353\) | − | 2773.10i | − | 0.418122i | −0.977903 | − | 0.209061i | \(-0.932959\pi\) | ||
0.977903 | − | 0.209061i | \(-0.0670408\pi\) | |||||||
\(354\) | 3173.82 | 0.476515 | ||||||||
\(355\) | −11884.8 | −1.77685 | ||||||||
\(356\) | − | 6746.56i | − | 1.00440i | ||||||
\(357\) | − | 6732.30i | − | 0.998070i | ||||||
\(358\) | − | 4451.16i | − | 0.657126i | ||||||
\(359\) | 1467.11i | 0.215685i | 0.994168 | + | 0.107843i | \(0.0343942\pi\) | ||||
−0.994168 | + | 0.107843i | \(0.965606\pi\) | |||||||
\(360\) | 2472.44 | 0.361969 | ||||||||
\(361\) | 6635.87 | 0.967469 | ||||||||
\(362\) | 17457.8i | 2.53471i | ||||||||
\(363\) | 2128.78 | 0.307801 | ||||||||
\(364\) | −6906.47 | + | 7151.03i | −0.994498 | + | 1.02971i | ||||
\(365\) | −7089.59 | −1.01667 | ||||||||
\(366\) | − | 2523.88i | − | 0.360452i | ||||||
\(367\) | 4648.22 | 0.661130 | 0.330565 | − | 0.943783i | \(-0.392761\pi\) | ||||
0.330565 | + | 0.943783i | \(0.392761\pi\) | |||||||
\(368\) | 336.872 | 0.0477192 | ||||||||
\(369\) | 2254.56i | 0.318069i | ||||||||
\(370\) | 17259.6i | 2.42509i | ||||||||
\(371\) | 3255.12i | 0.455519i | ||||||||
\(372\) | 9476.44i | 1.32078i | ||||||||
\(373\) | 1763.72 | 0.244831 | 0.122416 | − | 0.992479i | \(-0.460936\pi\) | ||||
0.122416 | + | 0.992479i | \(0.460936\pi\) | |||||||
\(374\) | 15206.4 | 2.10242 | ||||||||
\(375\) | 3226.08i | 0.444251i | ||||||||
\(376\) | 3401.84 | 0.466586 | ||||||||
\(377\) | −6950.22 | − | 6712.53i | −0.949481 | − | 0.917010i | ||||
\(378\) | 2053.96 | 0.279483 | ||||||||
\(379\) | 1930.47i | 0.261640i | 0.991406 | + | 0.130820i | \(0.0417611\pi\) | ||||
−0.991406 | + | 0.130820i | \(0.958239\pi\) | |||||||
\(380\) | −2445.38 | −0.330120 | ||||||||
\(381\) | −437.965 | −0.0588914 | ||||||||
\(382\) | − | 2217.81i | − | 0.297049i | ||||||
\(383\) | − | 8845.93i | − | 1.18017i | −0.807340 | − | 0.590086i | \(-0.799094\pi\) | ||
0.807340 | − | 0.590086i | \(-0.200906\pi\) | |||||||
\(384\) | 6772.81i | 0.900061i | ||||||||
\(385\) | − | 5384.46i | − | 0.712772i | ||||||
\(386\) | 19306.5 | 2.54579 | ||||||||
\(387\) | −3889.31 | −0.510865 | ||||||||
\(388\) | 4598.10i | 0.601632i | ||||||||
\(389\) | 1598.08 | 0.208292 | 0.104146 | − | 0.994562i | \(-0.466789\pi\) | ||||
0.104146 | + | 0.994562i | \(0.466789\pi\) | |||||||
\(390\) | −5938.76 | − | 5735.66i | −0.771079 | − | 0.744709i | ||||
\(391\) | −9658.47 | −1.24923 | ||||||||
\(392\) | − | 1343.50i | − | 0.173104i | ||||||
\(393\) | 951.489 | 0.122128 | ||||||||
\(394\) | 12335.8 | 1.57733 | ||||||||
\(395\) | 12048.5i | 1.53475i | ||||||||
\(396\) | 2844.51i | 0.360965i | ||||||||
\(397\) | − | 3578.82i | − | 0.452433i | −0.974077 | − | 0.226217i | \(-0.927364\pi\) | ||
0.974077 | − | 0.226217i | \(-0.0726357\pi\) | |||||||
\(398\) | − | 14173.7i | − | 1.78509i | ||||||
\(399\) | −749.669 | −0.0940611 | ||||||||
\(400\) | 195.176 | 0.0243970 | ||||||||
\(401\) | 3485.99i | 0.434120i | 0.976158 | + | 0.217060i | \(0.0696467\pi\) | ||||
−0.976158 | + | 0.217060i | \(0.930353\pi\) | |||||||
\(402\) | 538.038 | 0.0667534 | ||||||||
\(403\) | 8112.58 | − | 8399.84i | 1.00277 | − | 1.03828i | ||||
\(404\) | 18898.8 | 2.32735 | ||||||||
\(405\) | 1045.86i | 0.128319i | ||||||||
\(406\) | −15682.0 | −1.91696 | ||||||||
\(407\) | −7327.71 | −0.892435 | ||||||||
\(408\) | − | 8562.33i | − | 1.03897i | ||||||
\(409\) | 14709.1i | 1.77828i | 0.457637 | + | 0.889139i | \(0.348696\pi\) | ||||
−0.457637 | + | 0.889139i | \(0.651304\pi\) | |||||||
\(410\) | − | 14708.5i | − | 1.77171i | ||||||
\(411\) | − | 1329.45i | − | 0.159554i | ||||||
\(412\) | 7967.80 | 0.952780 | ||||||||
\(413\) | −3891.92 | −0.463702 | ||||||||
\(414\) | − | 2946.71i | − | 0.349814i | ||||||
\(415\) | 14143.4 | 1.67294 | ||||||||
\(416\) | 6235.20 | − | 6455.98i | 0.734869 | − | 0.760891i | ||||
\(417\) | 2355.05 | 0.276565 | ||||||||
\(418\) | − | 1693.29i | − | 0.198138i | ||||||
\(419\) | 3709.01 | 0.432451 | 0.216226 | − | 0.976343i | \(-0.430625\pi\) | ||||
0.216226 | + | 0.976343i | \(0.430625\pi\) | |||||||
\(420\) | −8215.85 | −0.954506 | ||||||||
\(421\) | 794.029i | 0.0919207i | 0.998943 | + | 0.0459603i | \(0.0146348\pi\) | ||||
−0.998943 | + | 0.0459603i | \(0.985365\pi\) | |||||||
\(422\) | − | 4780.32i | − | 0.551427i | ||||||
\(423\) | 1439.00i | 0.165406i | ||||||||
\(424\) | 4139.96i | 0.474185i | ||||||||
\(425\) | −5595.89 | −0.638684 | ||||||||
\(426\) | −12557.1 | −1.42815 | ||||||||
\(427\) | 3094.94i | 0.350760i | ||||||||
\(428\) | −6053.53 | −0.683664 | ||||||||
\(429\) | 2435.13 | − | 2521.35i | 0.274054 | − | 0.283758i | ||||
\(430\) | 25373.5 | 2.84562 | ||||||||
\(431\) | 2891.52i | 0.323155i | 0.986860 | + | 0.161577i | \(0.0516582\pi\) | ||||
−0.986860 | + | 0.161577i | \(0.948342\pi\) | |||||||
\(432\) | −126.327 | −0.0140692 | ||||||||
\(433\) | −5560.94 | −0.617186 | −0.308593 | − | 0.951194i | \(-0.599858\pi\) | ||||
−0.308593 | + | 0.951194i | \(0.599858\pi\) | |||||||
\(434\) | − | 18952.9i | − | 2.09624i | ||||||
\(435\) | − | 7985.14i | − | 0.880133i | ||||||
\(436\) | 4795.20i | 0.526717i | ||||||||
\(437\) | 1075.51i | 0.117731i | ||||||||
\(438\) | −7490.62 | −0.817159 | ||||||||
\(439\) | −15127.2 | −1.64460 | −0.822302 | − | 0.569051i | \(-0.807311\pi\) | ||||
−0.822302 | + | 0.569051i | \(0.807311\pi\) | |||||||
\(440\) | − | 6848.11i | − | 0.741979i | ||||||
\(441\) | 568.308 | 0.0613658 | ||||||||
\(442\) | −19863.3 | + | 20566.6i | −2.13755 | + | 2.21324i | ||||
\(443\) | 2357.89 | 0.252883 | 0.126441 | − | 0.991974i | \(-0.459644\pi\) | ||||
0.126441 | + | 0.991974i | \(0.459644\pi\) | |||||||
\(444\) | 11181.0i | 1.19510i | ||||||||
\(445\) | −6870.56 | −0.731901 | ||||||||
\(446\) | −24993.0 | −2.65348 | ||||||||
\(447\) | 406.260i | 0.0429876i | ||||||||
\(448\) | − | 13940.7i | − | 1.47017i | ||||||
\(449\) | 7165.06i | 0.753096i | 0.926397 | + | 0.376548i | \(0.122889\pi\) | ||||
−0.926397 | + | 0.376548i | \(0.877111\pi\) | |||||||
\(450\) | − | 1707.26i | − | 0.178846i | ||||||
\(451\) | 6244.63 | 0.651992 | ||||||||
\(452\) | −168.288 | −0.0175124 | ||||||||
\(453\) | 7121.22i | 0.738596i | ||||||||
\(454\) | 4190.74 | 0.433219 | ||||||||
\(455\) | 7282.47 | + | 7033.41i | 0.750346 | + | 0.724685i | ||||
\(456\) | −953.451 | −0.0979154 | ||||||||
\(457\) | 8020.96i | 0.821017i | 0.911857 | + | 0.410508i | \(0.134649\pi\) | ||||
−0.911857 | + | 0.410508i | \(0.865351\pi\) | |||||||
\(458\) | 877.378 | 0.0895135 | ||||||||
\(459\) | 3621.92 | 0.368316 | ||||||||
\(460\) | 11786.8i | 1.19471i | ||||||||
\(461\) | − | 4146.59i | − | 0.418928i | −0.977816 | − | 0.209464i | \(-0.932828\pi\) | ||
0.977816 | − | 0.209464i | \(-0.0671720\pi\) | |||||||
\(462\) | − | 5689.03i | − | 0.572895i | ||||||
\(463\) | − | 7118.21i | − | 0.714495i | −0.934010 | − | 0.357248i | \(-0.883715\pi\) | ||
0.934010 | − | 0.357248i | \(-0.116285\pi\) | |||||||
\(464\) | 964.509 | 0.0965004 | ||||||||
\(465\) | 9650.62 | 0.962444 | ||||||||
\(466\) | − | 4155.31i | − | 0.413071i | ||||||
\(467\) | 2128.22 | 0.210883 | 0.105441 | − | 0.994426i | \(-0.466374\pi\) | ||||
0.105441 | + | 0.994426i | \(0.466374\pi\) | |||||||
\(468\) | −3847.20 | − | 3715.63i | −0.379993 | − | 0.366998i | ||||
\(469\) | −659.774 | −0.0649585 | ||||||||
\(470\) | − | 9387.91i | − | 0.921344i | ||||||
\(471\) | −3500.18 | −0.342420 | ||||||||
\(472\) | −4949.86 | −0.482703 | ||||||||
\(473\) | 10772.5i | 1.04719i | ||||||||
\(474\) | 12730.1i | 1.23357i | ||||||||
\(475\) | 623.125i | 0.0601915i | ||||||||
\(476\) | 28452.4i | 2.73974i | ||||||||
\(477\) | −1751.23 | −0.168099 | ||||||||
\(478\) | 8989.57 | 0.860196 | ||||||||
\(479\) | 3715.30i | 0.354397i | 0.984175 | + | 0.177199i | \(0.0567035\pi\) | ||||
−0.984175 | + | 0.177199i | \(0.943296\pi\) | |||||||
\(480\) | 7417.31 | 0.705317 | ||||||||
\(481\) | 9571.78 | − | 9910.71i | 0.907350 | − | 0.939479i | ||||
\(482\) | 17755.0 | 1.67784 | ||||||||
\(483\) | 3613.43i | 0.340408i | ||||||||
\(484\) | −8996.77 | −0.844926 | ||||||||
\(485\) | 4682.62 | 0.438405 | ||||||||
\(486\) | 1105.02i | 0.103137i | ||||||||
\(487\) | − | 8139.28i | − | 0.757343i | −0.925531 | − | 0.378671i | \(-0.876381\pi\) | ||
0.925531 | − | 0.378671i | \(-0.123619\pi\) | |||||||
\(488\) | 3936.23i | 0.365133i | ||||||||
\(489\) | 6927.57i | 0.640645i | ||||||||
\(490\) | −3707.59 | −0.341820 | ||||||||
\(491\) | −18081.7 | −1.66194 | −0.830972 | − | 0.556315i | \(-0.812215\pi\) | ||||
−0.830972 | + | 0.556315i | \(0.812215\pi\) | |||||||
\(492\) | − | 9528.35i | − | 0.873112i | ||||||
\(493\) | −27653.4 | −2.52626 | ||||||||
\(494\) | 2290.18 | + | 2211.86i | 0.208583 | + | 0.201450i | ||||
\(495\) | 2896.80 | 0.263033 | ||||||||
\(496\) | 1165.68i | 0.105525i | ||||||||
\(497\) | 15398.3 | 1.38975 | ||||||||
\(498\) | 14943.4 | 1.34464 | ||||||||
\(499\) | 11031.5i | 0.989659i | 0.868990 | + | 0.494829i | \(0.164769\pi\) | ||||
−0.868990 | + | 0.494829i | \(0.835231\pi\) | |||||||
\(500\) | − | 13634.2i | − | 1.21948i | ||||||
\(501\) | 1802.37i | 0.160726i | ||||||||
\(502\) | 4283.80i | 0.380868i | ||||||||
\(503\) | 8016.14 | 0.710581 | 0.355290 | − | 0.934756i | \(-0.384382\pi\) | ||||
0.355290 | + | 0.934756i | \(0.384382\pi\) | |||||||
\(504\) | −3203.35 | −0.283112 | ||||||||
\(505\) | − | 19246.1i | − | 1.69592i | ||||||
\(506\) | −8161.74 | −0.717063 | ||||||||
\(507\) | 229.256 | + | 6587.01i | 0.0200821 | + | 0.577001i | ||||
\(508\) | 1850.95 | 0.161659 | ||||||||
\(509\) | 20173.9i | 1.75676i | 0.477959 | + | 0.878382i | \(0.341377\pi\) | ||||
−0.477959 | + | 0.878382i | \(0.658623\pi\) | |||||||
\(510\) | −23629.1 | −2.05159 | ||||||||
\(511\) | 9185.44 | 0.795186 | ||||||||
\(512\) | 1692.30i | 0.146074i | ||||||||
\(513\) | − | 403.316i | − | 0.0347112i | ||||||
\(514\) | 3695.29i | 0.317105i | ||||||||
\(515\) | − | 8114.25i | − | 0.694285i | ||||||
\(516\) | 16437.2 | 1.40234 | ||||||||
\(517\) | 3985.72 | 0.339056 | ||||||||
\(518\) | − | 22361.9i | − | 1.89677i | ||||||
\(519\) | −10291.1 | −0.870382 | ||||||||
\(520\) | 9262.05 | + | 8945.30i | 0.781092 | + | 0.754380i | ||||
\(521\) | 9746.95 | 0.819619 | 0.409810 | − | 0.912171i | \(-0.365595\pi\) | ||||
0.409810 | + | 0.912171i | \(0.365595\pi\) | |||||||
\(522\) | − | 8436.81i | − | 0.707413i | ||||||
\(523\) | −18929.3 | −1.58264 | −0.791320 | − | 0.611402i | \(-0.790606\pi\) | ||||
−0.791320 | + | 0.611402i | \(0.790606\pi\) | |||||||
\(524\) | −4021.24 | −0.335245 | ||||||||
\(525\) | 2093.54i | 0.174037i | ||||||||
\(526\) | − | 11860.9i | − | 0.983195i | ||||||
\(527\) | − | 33421.2i | − | 2.76252i | ||||||
\(528\) | 349.898i | 0.0288397i | ||||||||
\(529\) | −6983.00 | −0.573929 | ||||||||
\(530\) | 11424.9 | 0.936349 | ||||||||
\(531\) | − | 2093.83i | − | 0.171119i | ||||||
\(532\) | 3168.30 | 0.258201 | ||||||||
\(533\) | −8157.02 | + | 8445.85i | −0.662889 | + | 0.686361i | ||||
\(534\) | −7259.20 | −0.588270 | ||||||||
\(535\) | 6164.80i | 0.498182i | ||||||||
\(536\) | −839.120 | −0.0676203 | ||||||||
\(537\) | −2936.51 | −0.235977 | ||||||||
\(538\) | − | 21786.6i | − | 1.74589i | ||||||
\(539\) | − | 1574.09i | − | 0.125790i | ||||||
\(540\) | − | 4420.07i | − | 0.352240i | ||||||
\(541\) | 11366.8i | 0.903321i | 0.892190 | + | 0.451661i | \(0.149168\pi\) | ||||
−0.892190 | + | 0.451661i | \(0.850832\pi\) | |||||||
\(542\) | −16659.9 | −1.32030 | ||||||||
\(543\) | 11517.3 | 0.910227 | ||||||||
\(544\) | − | 25687.0i | − | 2.02449i | ||||||
\(545\) | 4883.34 | 0.383815 | ||||||||
\(546\) | 7694.40 | + | 7431.26i | 0.603095 | + | 0.582470i | ||||
\(547\) | 17495.4 | 1.36755 | 0.683775 | − | 0.729693i | \(-0.260337\pi\) | ||||
0.683775 | + | 0.729693i | \(0.260337\pi\) | |||||||
\(548\) | 5618.59i | 0.437983i | ||||||||
\(549\) | −1665.05 | −0.129440 | ||||||||
\(550\) | −4728.72 | −0.366606 | ||||||||
\(551\) | 3079.33i | 0.238083i | ||||||||
\(552\) | 4595.67i | 0.354356i | ||||||||
\(553\) | − | 15610.4i | − | 1.20040i | ||||||
\(554\) | 2839.05i | 0.217725i | ||||||||
\(555\) | 11386.5 | 0.870862 | ||||||||
\(556\) | −9953.06 | −0.759180 | ||||||||
\(557\) | 11873.1i | 0.903192i | 0.892223 | + | 0.451596i | \(0.149145\pi\) | ||||
−0.892223 | + | 0.451596i | \(0.850855\pi\) | |||||||
\(558\) | 10196.5 | 0.773571 | ||||||||
\(559\) | −14569.8 | − | 14071.6i | −1.10239 | − | 1.06469i | ||||
\(560\) | −1010.62 | −0.0762613 | ||||||||
\(561\) | − | 10031.9i | − | 0.754989i | ||||||
\(562\) | 25170.4 | 1.88923 | ||||||||
\(563\) | 2829.31 | 0.211796 | 0.105898 | − | 0.994377i | \(-0.466228\pi\) | ||||
0.105898 | + | 0.994377i | \(0.466228\pi\) | |||||||
\(564\) | − | 6081.60i | − | 0.454045i | ||||||
\(565\) | 171.381i | 0.0127612i | ||||||||
\(566\) | − | 796.481i | − | 0.0591495i | ||||||
\(567\) | − | 1355.04i | − | 0.100364i | ||||||
\(568\) | 19583.9 | 1.44670 | ||||||||
\(569\) | −16136.8 | −1.18891 | −0.594453 | − | 0.804130i | \(-0.702632\pi\) | ||||
−0.594453 | + | 0.804130i | \(0.702632\pi\) | |||||||
\(570\) | 2631.20i | 0.193349i | ||||||||
\(571\) | 17840.5 | 1.30754 | 0.653769 | − | 0.756695i | \(-0.273187\pi\) | ||||
0.653769 | + | 0.756695i | \(0.273187\pi\) | |||||||
\(572\) | −10291.5 | + | 10655.9i | −0.752288 | + | 0.778926i | ||||
\(573\) | −1463.13 | −0.106672 | ||||||||
\(574\) | 19056.7i | 1.38573i | ||||||||
\(575\) | 3003.49 | 0.217833 | ||||||||
\(576\) | 7500.00 | 0.542534 | ||||||||
\(577\) | 8516.17i | 0.614442i | 0.951638 | + | 0.307221i | \(0.0993990\pi\) | ||||
−0.951638 | + | 0.307221i | \(0.900601\pi\) | |||||||
\(578\) | 59488.9i | 4.28099i | ||||||||
\(579\) | − | 12736.8i | − | 0.914205i | ||||||
\(580\) | 33747.3i | 2.41600i | ||||||||
\(581\) | −18324.5 | −1.30848 | ||||||||
\(582\) | 4947.49 | 0.352371 | ||||||||
\(583\) | 4850.53i | 0.344577i | ||||||||
\(584\) | 11682.3 | 0.827770 | ||||||||
\(585\) | −3783.92 | + | 3917.91i | −0.267429 | + | 0.276899i | ||||
\(586\) | −35352.9 | −2.49218 | ||||||||
\(587\) | − | 20688.3i | − | 1.45468i | −0.686277 | − | 0.727340i | \(-0.740756\pi\) | ||
0.686277 | − | 0.727340i | \(-0.259244\pi\) | |||||||
\(588\) | −2401.82 | −0.168451 | ||||||||
\(589\) | −3721.59 | −0.260349 | ||||||||
\(590\) | 13659.9i | 0.953169i | ||||||||
\(591\) | − | 8138.13i | − | 0.566426i | ||||||
\(592\) | 1375.35i | 0.0954839i | ||||||||
\(593\) | − | 11435.9i | − | 0.791933i | −0.918265 | − | 0.395966i | \(-0.870410\pi\) | ||
0.918265 | − | 0.395966i | \(-0.129590\pi\) | |||||||
\(594\) | 3060.65 | 0.211414 | ||||||||
\(595\) | 28975.4 | 1.99643 | ||||||||
\(596\) | − | 1716.96i | − | 0.118002i | ||||||
\(597\) | −9350.69 | −0.641035 | ||||||||
\(598\) | 10661.2 | − | 11038.7i | 0.729047 | − | 0.754863i | ||||
\(599\) | 1260.80 | 0.0860016 | 0.0430008 | − | 0.999075i | \(-0.486308\pi\) | ||||
0.0430008 | + | 0.999075i | \(0.486308\pi\) | |||||||
\(600\) | 2662.62i | 0.181169i | ||||||||
\(601\) | 6261.10 | 0.424951 | 0.212476 | − | 0.977166i | \(-0.431847\pi\) | ||||
0.212476 | + | 0.977166i | \(0.431847\pi\) | |||||||
\(602\) | −32874.5 | −2.22569 | ||||||||
\(603\) | − | 354.954i | − | 0.0239715i | ||||||
\(604\) | − | 30096.1i | − | 2.02747i | ||||||
\(605\) | 9162.14i | 0.615692i | ||||||||
\(606\) | − | 20334.8i | − | 1.36311i | ||||||
\(607\) | 3230.33 | 0.216005 | 0.108003 | − | 0.994151i | \(-0.465555\pi\) | ||||
0.108003 | + | 0.994151i | \(0.465555\pi\) | |||||||
\(608\) | −2860.35 | −0.190794 | ||||||||
\(609\) | 10345.7i | 0.688391i | ||||||||
\(610\) | 10862.6 | 0.721009 | ||||||||
\(611\) | −5206.33 | + | 5390.68i | −0.344722 | + | 0.356929i | ||||
\(612\) | −15307.2 | −1.01104 | ||||||||
\(613\) | 14868.5i | 0.979660i | 0.871818 | + | 0.489830i | \(0.162941\pi\) | ||||
−0.871818 | + | 0.489830i | \(0.837059\pi\) | |||||||
\(614\) | 36483.0 | 2.39794 | ||||||||
\(615\) | −9703.48 | −0.636231 | ||||||||
\(616\) | 8872.57i | 0.580334i | ||||||||
\(617\) | − | 19952.8i | − | 1.30190i | −0.759121 | − | 0.650949i | \(-0.774371\pi\) | ||
0.759121 | − | 0.650949i | \(-0.225629\pi\) | |||||||
\(618\) | − | 8573.24i | − | 0.558036i | ||||||
\(619\) | − | 8316.48i | − | 0.540012i | −0.962859 | − | 0.270006i | \(-0.912974\pi\) | ||
0.962859 | − | 0.270006i | \(-0.0870257\pi\) | |||||||
\(620\) | −40786.0 | −2.64194 | ||||||||
\(621\) | −1944.00 | −0.125620 | ||||||||
\(622\) | 42131.0i | 2.71592i | ||||||||
\(623\) | 8901.66 | 0.572452 | ||||||||
\(624\) | −473.237 | − | 457.053i | −0.0303600 | − | 0.0293217i | ||||
\(625\) | −19099.2 | −1.22235 | ||||||||
\(626\) | 33757.9i | 2.15533i | ||||||||
\(627\) | −1117.10 | −0.0711525 | ||||||||
\(628\) | 14792.7 | 0.939955 | ||||||||
\(629\) | − | 39432.6i | − | 2.49965i | ||||||
\(630\) | 8840.13i | 0.559046i | ||||||||
\(631\) | 12605.9i | 0.795299i | 0.917537 | + | 0.397649i | \(0.130174\pi\) | ||||
−0.917537 | + | 0.397649i | \(0.869826\pi\) | |||||||
\(632\) | − | 19853.7i | − | 1.24959i | ||||||
\(633\) | −3153.66 | −0.198020 | ||||||||
\(634\) | −12009.8 | −0.752321 | ||||||||
\(635\) | − | 1884.98i | − | 0.117800i | ||||||
\(636\) | 7401.17 | 0.461439 | ||||||||
\(637\) | 2128.95 | + | 2056.15i | 0.132421 | + | 0.127892i | ||||
\(638\) | −23368.1 | −1.45008 | ||||||||
\(639\) | 8284.14i | 0.512857i | ||||||||
\(640\) | −29149.8 | −1.80038 | ||||||||
\(641\) | 9224.04 | 0.568374 | 0.284187 | − | 0.958769i | \(-0.408276\pi\) | ||||
0.284187 | + | 0.958769i | \(0.408276\pi\) | |||||||
\(642\) | 6513.51i | 0.400417i | ||||||||
\(643\) | 4439.16i | 0.272260i | 0.990691 | + | 0.136130i | \(0.0434665\pi\) | ||||
−0.990691 | + | 0.136130i | \(0.956533\pi\) | |||||||
\(644\) | − | 15271.3i | − | 0.934431i | ||||||
\(645\) | − | 16739.4i | − | 1.02188i | ||||||
\(646\) | 9112.13 | 0.554972 | ||||||||
\(647\) | 9601.15 | 0.583401 | 0.291700 | − | 0.956510i | \(-0.405779\pi\) | ||||
0.291700 | + | 0.956510i | \(0.405779\pi\) | |||||||
\(648\) | − | 1723.38i | − | 0.104476i | ||||||
\(649\) | −5799.44 | −0.350767 | ||||||||
\(650\) | 6176.87 | − | 6395.59i | 0.372733 | − | 0.385932i | ||||
\(651\) | −12503.6 | −0.752770 | ||||||||
\(652\) | − | 29277.7i | − | 1.75859i | ||||||
\(653\) | 27112.8 | 1.62482 | 0.812410 | − | 0.583087i | \(-0.198155\pi\) | ||||
0.812410 | + | 0.583087i | \(0.198155\pi\) | |||||||
\(654\) | 5159.56 | 0.308494 | ||||||||
\(655\) | 4095.15i | 0.244291i | ||||||||
\(656\) | − | 1172.06i | − | 0.0697583i | ||||||
\(657\) | 4941.70i | 0.293446i | ||||||||
\(658\) | 12163.2i | 0.720624i | ||||||||
\(659\) | 5587.26 | 0.330271 | 0.165136 | − | 0.986271i | \(-0.447194\pi\) | ||||
0.165136 | + | 0.986271i | \(0.447194\pi\) | |||||||
\(660\) | −12242.6 | −0.722035 | ||||||||
\(661\) | 3060.13i | 0.180069i | 0.995939 | + | 0.0900343i | \(0.0286977\pi\) | ||||
−0.995939 | + | 0.0900343i | \(0.971302\pi\) | |||||||
\(662\) | −49018.6 | −2.87789 | ||||||||
\(663\) | 13568.2 | + | 13104.2i | 0.794788 | + | 0.767607i | ||||
\(664\) | −23305.6 | −1.36210 | ||||||||
\(665\) | − | 3226.53i | − | 0.188150i | ||||||
\(666\) | 12030.5 | 0.699961 | ||||||||
\(667\) | 14842.5 | 0.861623 | ||||||||
\(668\) | − | 7617.26i | − | 0.441199i | ||||||
\(669\) | 16488.4i | 0.952880i | ||||||||
\(670\) | 2315.68i | 0.133526i | ||||||||
\(671\) | 4611.83i | 0.265332i | ||||||||
\(672\) | −9610.04 | −0.551660 | ||||||||
\(673\) | −4121.55 | −0.236069 | −0.118034 | − | 0.993010i | \(-0.537659\pi\) | ||||
−0.118034 | + | 0.993010i | \(0.537659\pi\) | |||||||
\(674\) | 1425.45i | 0.0814633i | ||||||||
\(675\) | −1126.31 | −0.0642246 | ||||||||
\(676\) | −968.894 | − | 27838.4i | −0.0551260 | − | 1.58389i | ||||
\(677\) | 22889.5 | 1.29943 | 0.649715 | − | 0.760178i | \(-0.274888\pi\) | ||||
0.649715 | + | 0.760178i | \(0.274888\pi\) | |||||||
\(678\) | 181.075i | 0.0102569i | ||||||||
\(679\) | −6066.91 | −0.342896 | ||||||||
\(680\) | 36851.8 | 2.07824 | ||||||||
\(681\) | − | 2764.71i | − | 0.155571i | ||||||
\(682\) | − | 28242.1i | − | 1.58570i | ||||||
\(683\) | 19297.9i | 1.08113i | 0.841301 | + | 0.540566i | \(0.181790\pi\) | ||||
−0.841301 | + | 0.540566i | \(0.818210\pi\) | |||||||
\(684\) | 1704.52i | 0.0952835i | ||||||||
\(685\) | 5721.87 | 0.319155 | ||||||||
\(686\) | 30896.6 | 1.71959 | ||||||||
\(687\) | − | 578.823i | − | 0.0321448i | ||||||
\(688\) | 2021.91 | 0.112042 | ||||||||
\(689\) | −6560.34 | − | 6335.98i | −0.362742 | − | 0.350336i | ||||
\(690\) | 12682.5 | 0.699729 | ||||||||
\(691\) | − | 30317.8i | − | 1.66910i | −0.550935 | − | 0.834548i | \(-0.685729\pi\) | ||
0.550935 | − | 0.834548i | \(-0.314271\pi\) | |||||||
\(692\) | 43492.8 | 2.38923 | ||||||||
\(693\) | −3753.16 | −0.205730 | ||||||||
\(694\) | − | 12956.6i | − | 0.708682i | ||||||
\(695\) | 10136.0i | 0.553210i | ||||||||
\(696\) | 13158.0i | 0.716599i | ||||||||
\(697\) | 33604.3i | 1.82619i | ||||||||
\(698\) | 29407.7 | 1.59470 | ||||||||
\(699\) | −2741.34 | −0.148336 | ||||||||
\(700\) | − | 8847.84i | − | 0.477738i | ||||||
\(701\) | −9606.16 | −0.517574 | −0.258787 | − | 0.965934i | \(-0.583323\pi\) | ||||
−0.258787 | + | 0.965934i | \(0.583323\pi\) | |||||||
\(702\) | −3997.96 | + | 4139.53i | −0.214948 | + | 0.222559i | ||||
\(703\) | −4390.99 | −0.235575 | ||||||||
\(704\) | − | 20773.4i | − | 1.11211i | ||||||
\(705\) | −6193.38 | −0.330860 | ||||||||
\(706\) | 12610.4 | 0.672235 | ||||||||
\(707\) | 24935.7i | 1.32646i | ||||||||
\(708\) | 8849.05i | 0.469729i | ||||||||
\(709\) | 23398.8i | 1.23944i | 0.784825 | + | 0.619718i | \(0.212753\pi\) | ||||
−0.784825 | + | 0.619718i | \(0.787247\pi\) | |||||||
\(710\) | − | 54044.9i | − | 2.85672i | ||||||
\(711\) | 8398.26 | 0.442981 | ||||||||
\(712\) | 11321.4 | 0.595909 | ||||||||
\(713\) | 17938.2i | 0.942203i | ||||||||
\(714\) | 30614.4 | 1.60464 | ||||||||
\(715\) | 10851.8 | + | 10480.6i | 0.567598 | + | 0.548187i | ||||
\(716\) | 12410.5 | 0.647766 | ||||||||
\(717\) | − | 5930.59i | − | 0.308901i | ||||||
\(718\) | −6671.51 | −0.346767 | ||||||||
\(719\) | 23588.7 | 1.22352 | 0.611758 | − | 0.791045i | \(-0.290463\pi\) | ||||
0.611758 | + | 0.791045i | \(0.290463\pi\) | |||||||
\(720\) | − | 543.704i | − | 0.0281426i | ||||||
\(721\) | 10513.0i | 0.543031i | ||||||||
\(722\) | 30175.9i | 1.55544i | ||||||||
\(723\) | − | 11713.3i | − | 0.602522i | ||||||
\(724\) | −48674.9 | −2.49861 | ||||||||
\(725\) | 8599.38 | 0.440514 | ||||||||
\(726\) | 9680.40i | 0.494867i | ||||||||
\(727\) | −15733.5 | −0.802644 | −0.401322 | − | 0.915937i | \(-0.631449\pi\) | ||||
−0.401322 | + | 0.915937i | \(0.631449\pi\) | |||||||
\(728\) | −12000.1 | − | 11589.7i | −0.610926 | − | 0.590034i | ||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | − | 32239.2i | − | 1.63455i | ||||||
\(731\) | −57970.3 | −2.93312 | ||||||||
\(732\) | 7036.94 | 0.355318 | ||||||||
\(733\) | − | 17297.1i | − | 0.871598i | −0.900044 | − | 0.435799i | \(-0.856466\pi\) | ||
0.900044 | − | 0.435799i | \(-0.143534\pi\) | |||||||
\(734\) | 21137.3i | 1.06293i | ||||||||
\(735\) | 2445.96i | 0.122749i | ||||||||
\(736\) | 13787.0i | 0.690484i | ||||||||
\(737\) | −983.144 | −0.0491378 | ||||||||
\(738\) | −10252.4 | −0.511375 | ||||||||
\(739\) | − | 38749.2i | − | 1.92884i | −0.264377 | − | 0.964419i | \(-0.585166\pi\) | ||
0.264377 | − | 0.964419i | \(-0.414834\pi\) | |||||||
\(740\) | −48122.2 | −2.39055 | ||||||||
\(741\) | 1459.20 | − | 1510.87i | 0.0723417 | − | 0.0749033i | ||||
\(742\) | −14802.3 | −0.732359 | ||||||||
\(743\) | − | 3139.76i | − | 0.155029i | −0.996991 | − | 0.0775144i | \(-0.975302\pi\) | ||
0.996991 | − | 0.0775144i | \(-0.0246984\pi\) | |||||||
\(744\) | −15902.4 | −0.783616 | ||||||||
\(745\) | −1748.52 | −0.0859876 | ||||||||
\(746\) | 8020.33i | 0.393626i | ||||||||
\(747\) | − | 9858.45i | − | 0.482867i | ||||||
\(748\) | 42397.6i | 2.07247i | ||||||||
\(749\) | − | 7987.25i | − | 0.389650i | ||||||
\(750\) | −14670.2 | −0.714242 | ||||||||
\(751\) | −40628.6 | −1.97411 | −0.987055 | − | 0.160380i | \(-0.948728\pi\) | ||||
−0.987055 | + | 0.160380i | \(0.948728\pi\) | |||||||
\(752\) | − | 748.086i | − | 0.0362764i | ||||||
\(753\) | 2826.11 | 0.136772 | ||||||||
\(754\) | 30524.5 | − | 31605.4i | 1.47432 | − | 1.52652i | ||||
\(755\) | −30649.3 | −1.47741 | ||||||||
\(756\) | 5726.74i | 0.275502i | ||||||||
\(757\) | 24004.9 | 1.15254 | 0.576271 | − | 0.817259i | \(-0.304507\pi\) | ||||
0.576271 | + | 0.817259i | \(0.304507\pi\) | |||||||
\(758\) | −8778.62 | −0.420651 | ||||||||
\(759\) | 5384.46i | 0.257501i | ||||||||
\(760\) | − | 4103.60i | − | 0.195859i | ||||||
\(761\) | − | 29540.1i | − | 1.40713i | −0.710630 | − | 0.703566i | \(-0.751590\pi\) | ||
0.710630 | − | 0.703566i | \(-0.248410\pi\) | |||||||
\(762\) | − | 1991.60i | − | 0.0946824i | ||||||
\(763\) | −6326.97 | −0.300199 | ||||||||
\(764\) | 6183.56 | 0.292818 | ||||||||
\(765\) | 15588.5i | 0.736739i | ||||||||
\(766\) | 40225.9 | 1.89742 | ||||||||
\(767\) | 7575.49 | − | 7843.73i | 0.356630 | − | 0.369258i | ||||
\(768\) | −10798.6 | −0.507372 | ||||||||
\(769\) | 7585.63i | 0.355715i | 0.984056 | + | 0.177857i | \(0.0569166\pi\) | ||||
−0.984056 | + | 0.177857i | \(0.943083\pi\) | |||||||
\(770\) | 24485.2 | 1.14596 | ||||||||
\(771\) | 2437.85 | 0.113874 | ||||||||
\(772\) | 53829.2i | 2.50953i | ||||||||
\(773\) | 3284.29i | 0.152817i | 0.997077 | + | 0.0764086i | \(0.0243453\pi\) | ||||
−0.997077 | + | 0.0764086i | \(0.975655\pi\) | |||||||
\(774\) | − | 17686.2i | − | 0.821341i | ||||||
\(775\) | 10393.0i | 0.481712i | ||||||||
\(776\) | −7716.07 | −0.356947 | ||||||||
\(777\) | −14752.6 | −0.681140 | ||||||||
\(778\) | 7267.08i | 0.334881i | ||||||||
\(779\) | 3741.98 | 0.172106 | ||||||||
\(780\) | 15991.8 | − | 16558.1i | 0.734103 | − | 0.760097i | ||||
\(781\) | 22945.3 | 1.05128 | ||||||||
\(782\) | − | 43920.8i | − | 2.00845i | ||||||
\(783\) | −5565.92 | −0.254036 | ||||||||
\(784\) | −295.443 | −0.0134586 | ||||||||
\(785\) | − | 15064.6i | − | 0.684939i | ||||||
\(786\) | 4326.79i | 0.196351i | ||||||||
\(787\) | 41624.1i | 1.88531i | 0.333772 | + | 0.942654i | \(0.391679\pi\) | ||||
−0.333772 | + | 0.942654i | \(0.608321\pi\) | |||||||
\(788\) | 34393.8i | 1.55486i | ||||||||
\(789\) | −7824.87 | −0.353071 | ||||||||
\(790\) | −54789.4 | −2.46749 | ||||||||
\(791\) | − | 222.046i | − | 0.00998108i | ||||||
\(792\) | −4773.38 | −0.214160 | ||||||||
\(793\) | −6237.49 | − | 6024.18i | −0.279319 | − | 0.269767i | ||||
\(794\) | 16274.3 | 0.727398 | ||||||||
\(795\) | − | 7537.20i | − | 0.336248i | ||||||
\(796\) | 39518.4 | 1.75967 | ||||||||
\(797\) | 30333.3 | 1.34813 | 0.674066 | − | 0.738671i | \(-0.264546\pi\) | ||||
0.674066 | + | 0.738671i | \(0.264546\pi\) | |||||||
\(798\) | − | 3409.04i | − | 0.151226i | ||||||
\(799\) | 21448.4i | 0.949674i | ||||||||
\(800\) | 7987.87i | 0.353017i | ||||||||
\(801\) | 4789.03i | 0.211251i | ||||||||
\(802\) | −15852.2 | −0.697954 | ||||||||
\(803\) | 13687.4 | 0.601518 | ||||||||
\(804\) | 1500.13i | 0.0658027i | ||||||||
\(805\) | −15552.0 | −0.680914 | ||||||||
\(806\) | 38197.4 | + | 36891.1i | 1.66929 | + | 1.61220i | ||||
\(807\) | −14373.1 | −0.626958 | ||||||||
\(808\) | 31714.0i | 1.38081i | ||||||||
\(809\) | −24853.9 | −1.08012 | −0.540060 | − | 0.841627i | \(-0.681598\pi\) | ||||
−0.540060 | + | 0.841627i | \(0.681598\pi\) | |||||||
\(810\) | −4755.92 | −0.206304 | ||||||||
\(811\) | − | 17383.5i | − | 0.752674i | −0.926483 | − | 0.376337i | \(-0.877184\pi\) | ||
0.926483 | − | 0.376337i | \(-0.122816\pi\) | |||||||
\(812\) | − | 43723.7i | − | 1.88966i | ||||||
\(813\) | 10990.9i | 0.474128i | ||||||||
\(814\) | − | 33322.0i | − | 1.43481i | ||||||
\(815\) | −29815.8 | −1.28148 | ||||||||
\(816\) | −1882.91 | −0.0807782 | ||||||||
\(817\) | 6455.23i | 0.276426i | ||||||||
\(818\) | −66887.8 | −2.85902 | ||||||||
\(819\) | 4902.54 | − | 5076.14i | 0.209168 | − | 0.216575i | ||||
\(820\) | 41009.4 | 1.74648 | ||||||||
\(821\) | − | 31169.4i | − | 1.32499i | −0.749065 | − | 0.662496i | \(-0.769497\pi\) | ||
0.749065 | − | 0.662496i | \(-0.230503\pi\) | |||||||
\(822\) | 6045.52 | 0.256523 | ||||||||
\(823\) | −5512.79 | −0.233492 | −0.116746 | − | 0.993162i | \(-0.537246\pi\) | ||||
−0.116746 | + | 0.993162i | \(0.537246\pi\) | |||||||
\(824\) | 13370.8i | 0.565282i | ||||||||
\(825\) | 3119.63i | 0.131650i | ||||||||
\(826\) | − | 17698.1i | − | 0.745516i | ||||||
\(827\) | 13335.8i | 0.560738i | 0.959892 | + | 0.280369i | \(0.0904568\pi\) | ||||
−0.959892 | + | 0.280369i | \(0.909543\pi\) | |||||||
\(828\) | 8215.85 | 0.344832 | ||||||||
\(829\) | 28338.5 | 1.18726 | 0.593628 | − | 0.804739i | \(-0.297695\pi\) | ||||
0.593628 | + | 0.804739i | \(0.297695\pi\) | |||||||
\(830\) | 64315.5i | 2.68967i | ||||||||
\(831\) | 1872.98 | 0.0781864 | ||||||||
\(832\) | 28095.9 | + | 27135.1i | 1.17073 | + | 1.13070i | ||||
\(833\) | 8470.66 | 0.352330 | ||||||||
\(834\) | 10709.3i | 0.444646i | ||||||||
\(835\) | −7757.27 | −0.321499 | ||||||||
\(836\) | 4721.15 | 0.195316 | ||||||||
\(837\) | − | 6726.82i | − | 0.277793i | ||||||
\(838\) | 16866.3i | 0.695272i | ||||||||
\(839\) | 27149.5i | 1.11717i | 0.829447 | + | 0.558585i | \(0.188656\pi\) | ||||
−0.829447 | + | 0.558585i | \(0.811344\pi\) | |||||||
\(840\) | − | 13787.0i | − | 0.566306i | ||||||
\(841\) | 18106.9 | 0.742421 | ||||||||
\(842\) | −3610.76 | −0.147785 | ||||||||
\(843\) | − | 16605.4i | − | 0.678433i | ||||||
\(844\) | 13328.2 | 0.543573 | ||||||||
\(845\) | −28350.1 | + | 986.703i | −1.15417 | + | 0.0401700i | ||||
\(846\) | −6543.71 | −0.265931 | ||||||||
\(847\) | − | 11870.7i | − | 0.481560i | ||||||
\(848\) | 910.404 | 0.0368672 | ||||||||
\(849\) | −525.454 | −0.0212409 | ||||||||
\(850\) | − | 25446.7i | − | 1.02684i | ||||||
\(851\) | 21164.7i | 0.852547i | ||||||||
\(852\) | − | 35010.9i | − | 1.40781i | ||||||
\(853\) | − | 7978.22i | − | 0.320245i | −0.987097 | − | 0.160123i | \(-0.948811\pi\) | ||
0.987097 | − | 0.160123i | \(-0.0511889\pi\) | |||||||
\(854\) | −14073.9 | −0.563933 | ||||||||
\(855\) | 1735.85 | 0.0694325 | ||||||||
\(856\) | − | 10158.4i | − | 0.405616i | ||||||
\(857\) | 13614.4 | 0.542657 | 0.271329 | − | 0.962487i | \(-0.412537\pi\) | ||||
0.271329 | + | 0.962487i | \(0.412537\pi\) | |||||||
\(858\) | 11465.6 | + | 11073.5i | 0.456211 | + | 0.440609i | ||||
\(859\) | −35007.7 | −1.39051 | −0.695255 | − | 0.718763i | \(-0.744709\pi\) | ||||
−0.695255 | + | 0.718763i | \(0.744709\pi\) | |||||||
\(860\) | 70744.8i | 2.80509i | ||||||||
\(861\) | 12572.1 | 0.497624 | ||||||||
\(862\) | −13148.9 | −0.519551 | ||||||||
\(863\) | − | 24461.5i | − | 0.964867i | −0.875933 | − | 0.482434i | \(-0.839753\pi\) | ||
0.875933 | − | 0.482434i | \(-0.160247\pi\) | |||||||
\(864\) | − | 5170.13i | − | 0.203578i | ||||||
\(865\) | − | 44292.2i | − | 1.74102i | ||||||
\(866\) | − | 25287.8i | − | 0.992278i | ||||||
\(867\) | 39245.9 | 1.53733 | ||||||||
\(868\) | 52843.3 | 2.06638 | ||||||||
\(869\) | − | 23261.3i | − | 0.908040i | ||||||
\(870\) | 36311.5 | 1.41503 | ||||||||
\(871\) | 1284.23 | − | 1329.70i | 0.0499591 | − | 0.0517281i | ||||
\(872\) | −8046.82 | −0.312500 | ||||||||
\(873\) | − | 3263.95i | − | 0.126538i | ||||||
\(874\) | −4890.77 | −0.189282 | ||||||||
\(875\) | 17989.5 | 0.695037 | ||||||||
\(876\) | − | 20884.9i | − | 0.805520i | ||||||
\(877\) | − | 43121.6i | − | 1.66034i | −0.557514 | − | 0.830168i | \(-0.688245\pi\) | ||
0.557514 | − | 0.830168i | \(-0.311755\pi\) | |||||||
\(878\) | − | 68789.3i | − | 2.64411i | ||||||
\(879\) | 23323.0i | 0.894955i | ||||||||
\(880\) | −1505.94 | −0.0576878 | ||||||||
\(881\) | 40824.5 | 1.56120 | 0.780598 | − | 0.625034i | \(-0.214915\pi\) | ||||
0.780598 | + | 0.625034i | \(0.214915\pi\) | |||||||
\(882\) | 2584.32i | 0.0986605i | ||||||||
\(883\) | −8262.14 | −0.314885 | −0.157442 | − | 0.987528i | \(-0.550325\pi\) | ||||
−0.157442 | + | 0.987528i | \(0.550325\pi\) | |||||||
\(884\) | −57342.7 | − | 55381.6i | −2.18172 | − | 2.10711i | ||||
\(885\) | 9011.70 | 0.342288 | ||||||||
\(886\) | 10722.3i | 0.406571i | ||||||||
\(887\) | −40858.6 | −1.54667 | −0.773336 | − | 0.633997i | \(-0.781413\pi\) | ||||
−0.773336 | + | 0.633997i | \(0.781413\pi\) | |||||||
\(888\) | −18762.8 | −0.709050 | ||||||||
\(889\) | 2442.22i | 0.0921365i | ||||||||
\(890\) | − | 31243.2i | − | 1.17671i | ||||||
\(891\) | − | 2019.17i | − | 0.0759201i | ||||||
\(892\) | − | 69684.1i | − | 2.61569i | ||||||
\(893\) | 2388.37 | 0.0895001 | ||||||||
\(894\) | −1847.42 | −0.0691131 | ||||||||
\(895\) | − | 12638.6i | − | 0.472023i | ||||||
\(896\) | 37767.1 | 1.40816 | ||||||||
\(897\) | −7282.47 | − | 7033.41i | −0.271075 | − | 0.261805i | ||||
\(898\) | −32582.3 | −1.21079 | ||||||||
\(899\) | 51359.4i | 1.90537i | ||||||||
\(900\) | 4760.07 | 0.176299 | ||||||||
\(901\) | −26102.2 | −0.965139 | ||||||||
\(902\) | 28396.8i | 1.04824i | ||||||||
\(903\) | 21687.9i | 0.799256i | ||||||||
\(904\) | − | 282.404i | − | 0.0103901i | ||||||
\(905\) | 49569.6i | 1.82072i | ||||||||
\(906\) | −32383.0 | −1.18747 | ||||||||
\(907\) | 32729.3 | 1.19819 | 0.599095 | − | 0.800678i | \(-0.295527\pi\) | ||||
0.599095 | + | 0.800678i | \(0.295527\pi\) | |||||||
\(908\) | 11684.4i | 0.427048i | ||||||||
\(909\) | −13415.2 | −0.489500 | ||||||||
\(910\) | −31983.7 | + | 33116.2i | −1.16511 | + | 1.20637i | ||||
\(911\) | 11065.9 | 0.402447 | 0.201223 | − | 0.979545i | \(-0.435508\pi\) | ||||
0.201223 | + | 0.979545i | \(0.435508\pi\) | |||||||
\(912\) | 209.670i | 0.00761279i | ||||||||
\(913\) | −27305.7 | −0.989801 | ||||||||
\(914\) | −36474.5 | −1.31999 | ||||||||
\(915\) | − | 7166.29i | − | 0.258918i | ||||||
\(916\) | 2446.26i | 0.0882386i | ||||||||
\(917\) | − | 5305.77i | − | 0.191071i | ||||||
\(918\) | 16470.3i | 0.592158i | ||||||||
\(919\) | 50682.2 | 1.81921 | 0.909604 | − | 0.415477i | \(-0.136385\pi\) | ||||
0.909604 | + | 0.415477i | \(0.136385\pi\) | |||||||
\(920\) | −19779.5 | −0.708816 | ||||||||
\(921\) | − | 24068.5i | − | 0.861114i | ||||||
\(922\) | 18856.2 | 0.673531 | ||||||||
\(923\) | −29972.1 | + | 31033.4i | −1.06885 | + | 1.10669i | ||||
\(924\) | 15861.8 | 0.564735 | ||||||||
\(925\) | 12262.3i | 0.435874i | ||||||||
\(926\) | 32369.3 | 1.14873 | ||||||||
\(927\) | −5655.92 | −0.200394 | ||||||||
\(928\) | 39474.0i | 1.39633i | ||||||||
\(929\) | 41045.5i | 1.44958i | 0.688970 | + | 0.724790i | \(0.258063\pi\) | ||||
−0.688970 | + | 0.724790i | \(0.741937\pi\) | |||||||
\(930\) | 43885.1i | 1.54737i | ||||||||
\(931\) | − | 943.243i | − | 0.0332047i | ||||||
\(932\) | 11585.6 | 0.407188 | ||||||||
\(933\) | 27794.6 | 0.975300 | ||||||||
\(934\) | 9677.86i | 0.339046i | ||||||||
\(935\) | 43176.9 | 1.51020 | ||||||||
\(936\) | 6235.20 | − | 6455.98i | 0.217739 | − | 0.225449i | ||||
\(937\) | −788.985 | −0.0275080 | −0.0137540 | − | 0.999905i | \(-0.504378\pi\) | ||||
−0.0137540 | + | 0.999905i | \(0.504378\pi\) | |||||||
\(938\) | − | 3000.25i | − | 0.104437i | ||||||
\(939\) | 22270.7 | 0.773991 | ||||||||
\(940\) | 26174.8 | 0.908222 | ||||||||
\(941\) | − | 25676.2i | − | 0.889499i | −0.895655 | − | 0.444750i | \(-0.853293\pi\) | ||
0.895655 | − | 0.444750i | \(-0.146707\pi\) | |||||||
\(942\) | − | 15916.7i | − | 0.550524i | ||||||
\(943\) | − | 18036.5i | − | 0.622851i | ||||||
\(944\) | 1088.51i | 0.0375295i | ||||||||
\(945\) | 5832.00 | 0.200757 | ||||||||
\(946\) | −48986.9 | −1.68362 | ||||||||
\(947\) | 679.352i | 0.0233115i | 0.999932 | + | 0.0116557i | \(0.00371022\pi\) | ||||
−0.999932 | + | 0.0116557i | \(0.996290\pi\) | |||||||
\(948\) | −35493.2 | −1.21600 | ||||||||
\(949\) | −17879.1 | + | 18512.2i | −0.611571 | + | 0.633227i | ||||
\(950\) | −2833.60 | −0.0967726 | ||||||||
\(951\) | 7923.12i | 0.270163i | ||||||||
\(952\) | −47746.0 | −1.62548 | ||||||||
\(953\) | 20238.4 | 0.687917 | 0.343958 | − | 0.938985i | \(-0.388232\pi\) | ||||
0.343958 | + | 0.938985i | \(0.388232\pi\) | |||||||
\(954\) | − | 7963.54i | − | 0.270261i | ||||||
\(955\) | − | 6297.21i | − | 0.213375i | ||||||
\(956\) | 25064.2i | 0.847944i | ||||||||
\(957\) | 15416.4i | 0.520733i | ||||||||
\(958\) | −16894.9 | −0.569781 | ||||||||
\(959\) | −7413.38 | −0.249625 | ||||||||
\(960\) | 32279.5i | 1.08523i | ||||||||
\(961\) | −32280.6 | −1.08357 | ||||||||
\(962\) | 45067.9 | + | 43526.6i | 1.51044 | + | 1.45879i | ||||
\(963\) | 4297.08 | 0.143792 | ||||||||
\(964\) | 49503.6i | 1.65395i | ||||||||
\(965\) | 54818.6 | 1.82868 | ||||||||
\(966\) | −16431.7 | −0.547289 | ||||||||
\(967\) | − | 6161.63i | − | 0.204906i | −0.994738 | − | 0.102453i | \(-0.967331\pi\) | ||
0.994738 | − | 0.102453i | \(-0.0326692\pi\) | |||||||
\(968\) | − | 15097.5i | − | 0.501293i | ||||||
\(969\) | − | 6011.45i | − | 0.199294i | ||||||
\(970\) | 21293.7i | 0.704845i | ||||||||
\(971\) | −48569.5 | −1.60522 | −0.802610 | − | 0.596504i | \(-0.796556\pi\) | ||||
−0.802610 | + | 0.596504i | \(0.796556\pi\) | |||||||
\(972\) | −3080.94 | −0.101668 | ||||||||
\(973\) | − | 13132.4i | − | 0.432689i | ||||||
\(974\) | 37012.5 | 1.21761 | ||||||||
\(975\) | −4219.29 | − | 4075.00i | −0.138590 | − | 0.133851i | ||||
\(976\) | 865.602 | 0.0283886 | ||||||||
\(977\) | − | 44595.8i | − | 1.46033i | −0.683269 | − | 0.730167i | \(-0.739442\pi\) | ||
0.683269 | − | 0.730167i | \(-0.260558\pi\) | |||||||
\(978\) | −31502.4 | −1.03000 | ||||||||
\(979\) | 13264.6 | 0.433031 | ||||||||
\(980\) | − | 10337.3i | − | 0.336951i | ||||||
\(981\) | − | 3403.86i | − | 0.110782i | ||||||
\(982\) | − | 82224.4i | − | 2.67198i | ||||||
\(983\) | 29599.0i | 0.960389i | 0.877162 | + | 0.480195i | \(0.159434\pi\) | ||||
−0.877162 | + | 0.480195i | \(0.840566\pi\) | |||||||
\(984\) | 15989.5 | 0.518015 | ||||||||
\(985\) | 35026.0 | 1.13302 | ||||||||
\(986\) | − | 125751.i | − | 4.06159i | ||||||
\(987\) | 8024.29 | 0.258780 | ||||||||
\(988\) | −6166.97 | + | 6385.34i | −0.198580 | + | 0.205612i | ||||
\(989\) | 31114.5 | 1.00039 | ||||||||
\(990\) | 13172.9i | 0.422890i | ||||||||
\(991\) | 5718.45 | 0.183302 | 0.0916511 | − | 0.995791i | \(-0.470786\pi\) | ||||
0.0916511 | + | 0.995791i | \(0.470786\pi\) | |||||||
\(992\) | −47707.2 | −1.52692 | ||||||||
\(993\) | 32338.5i | 1.03347i | ||||||||
\(994\) | 70021.9i | 2.23437i | ||||||||
\(995\) | − | 40244.8i | − | 1.28226i | ||||||
\(996\) | 41664.4i | 1.32549i | ||||||||
\(997\) | −1491.44 | −0.0473766 | −0.0236883 | − | 0.999719i | \(-0.507541\pi\) | ||||
−0.0236883 | + | 0.999719i | \(0.507541\pi\) | |||||||
\(998\) | −50164.8 | −1.59112 | ||||||||
\(999\) | − | 7936.77i | − | 0.251360i |
(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 | 39.4.b.b.25.4 | yes | 4 | |
3.2 | odd | 2 | 117.4.b.e.64.1 | 4 | |||
4.3 | odd | 2 | 624.4.c.c.337.4 | 4 | |||
13.5 | odd | 4 | 507.4.a.l.1.4 | 4 | |||
13.8 | odd | 4 | 507.4.a.l.1.1 | 4 | |||
13.12 | even | 2 | inner | 39.4.b.b.25.1 | ✓ | 4 | |
39.5 | even | 4 | 1521.4.a.w.1.1 | 4 | |||
39.8 | even | 4 | 1521.4.a.w.1.4 | 4 | |||
39.38 | odd | 2 | 117.4.b.e.64.4 | 4 | |||
52.51 | odd | 2 | 624.4.c.c.337.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.b.b.25.1 | ✓ | 4 | 13.12 | even | 2 | inner | |
39.4.b.b.25.4 | yes | 4 | 1.1 | even | 1 | trivial | |
117.4.b.e.64.1 | 4 | 3.2 | odd | 2 | |||
117.4.b.e.64.4 | 4 | 39.38 | odd | 2 | |||
507.4.a.l.1.1 | 4 | 13.8 | odd | 4 | |||
507.4.a.l.1.4 | 4 | 13.5 | odd | 4 | |||
624.4.c.c.337.1 | 4 | 52.51 | odd | 2 | |||
624.4.c.c.337.4 | 4 | 4.3 | odd | 2 | |||
1521.4.a.w.1.1 | 4 | 39.5 | even | 4 | |||
1521.4.a.w.1.4 | 4 | 39.8 | even | 4 |