Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,4,Mod(116,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("245.116");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.e (of order \(3\), degree \(2\), not 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: | \(14.4554679514\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 27 x^{10} + 22 x^{9} + 399 x^{8} + 492 x^{7} + 4046 x^{6} + 8784 x^{5} + 22536 x^{4} + 22736 x^{3} + 18792 x^{2} + 4256 x + 784 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 226.5 | ||
Root | \(2.14754 + 3.71965i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.226 |
Dual form | 245.4.e.p.116.5 |
$q$-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 \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.44043 | − | 2.49490i | 0.509270 | − | 0.882082i | −0.490672 | − | 0.871344i | \(-0.663249\pi\) |
0.999942 | − | 0.0107374i | \(-0.00341790\pi\) | |||||||
\(3\) | 1.44526 | + | 2.50327i | 0.278141 | + | 0.481754i | 0.970923 | − | 0.239393i | \(-0.0769485\pi\) |
−0.692782 | + | 0.721147i | \(0.743615\pi\) | |||||||
\(4\) | −0.149696 | − | 0.259281i | −0.0187120 | − | 0.0324102i | ||||
\(5\) | 2.50000 | − | 4.33013i | 0.223607 | − | 0.387298i | ||||
\(6\) | 8.32721 | 0.566595 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 22.1844 | 0.980422 | ||||||||
\(9\) | 9.32244 | − | 16.1469i | 0.345275 | − | 0.598035i | ||||
\(10\) | −7.20217 | − | 12.4745i | −0.227753 | − | 0.394479i | ||||
\(11\) | 23.2440 | + | 40.2598i | 0.637122 | + | 1.10353i | 0.986061 | + | 0.166382i | \(0.0532085\pi\) |
−0.348940 | + | 0.937145i | \(0.613458\pi\) | |||||||
\(12\) | 0.432700 | − | 0.749459i | 0.0104092 | − | 0.0180292i | ||||
\(13\) | −31.0537 | −0.662519 | −0.331260 | − | 0.943540i | \(-0.607474\pi\) | ||||
−0.331260 | + | 0.943540i | \(0.607474\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 14.4526 | 0.248777 | ||||||||
\(16\) | 33.1528 | − | 57.4223i | 0.518012 | − | 0.897223i | ||||
\(17\) | 30.9258 | + | 53.5651i | 0.441212 | + | 0.764202i | 0.997780 | − | 0.0666002i | \(-0.0212152\pi\) |
−0.556567 | + | 0.830803i | \(0.687882\pi\) | |||||||
\(18\) | −26.8567 | − | 46.5172i | −0.351677 | − | 0.609122i | ||||
\(19\) | −12.3107 | + | 21.3227i | −0.148645 | + | 0.257461i | −0.930727 | − | 0.365715i | \(-0.880825\pi\) |
0.782082 | + | 0.623176i | \(0.214158\pi\) | |||||||
\(20\) | −1.49696 | −0.0167365 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 133.926 | 1.29787 | ||||||||
\(23\) | 77.4708 | − | 134.183i | 0.702339 | − | 1.21649i | −0.265305 | − | 0.964165i | \(-0.585473\pi\) |
0.967643 | − | 0.252322i | \(-0.0811941\pi\) | |||||||
\(24\) | 32.0623 | + | 55.5335i | 0.272695 | + | 0.472322i | ||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | −44.7308 | + | 77.4760i | −0.337401 | + | 0.584396i | ||||
\(27\) | 131.938 | 0.940422 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 200.436 | 1.28345 | 0.641724 | − | 0.766936i | \(-0.278219\pi\) | ||||
0.641724 | + | 0.766936i | \(0.278219\pi\) | |||||||
\(30\) | 20.8180 | − | 36.0579i | 0.126694 | − | 0.219441i | ||||
\(31\) | −64.6273 | − | 111.938i | −0.374432 | − | 0.648536i | 0.615810 | − | 0.787895i | \(-0.288829\pi\) |
−0.990242 | + | 0.139359i | \(0.955496\pi\) | |||||||
\(32\) | −6.77096 | − | 11.7277i | −0.0374046 | − | 0.0647867i | ||||
\(33\) | −67.1874 | + | 116.372i | −0.354419 | + | 0.613872i | ||||
\(34\) | 178.186 | 0.898785 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.58213 | −0.0258432 | ||||||||
\(37\) | 38.9831 | − | 67.5207i | 0.173210 | − | 0.300009i | −0.766330 | − | 0.642447i | \(-0.777919\pi\) |
0.939540 | + | 0.342438i | \(0.111253\pi\) | |||||||
\(38\) | 35.4654 | + | 61.4279i | 0.151401 | + | 0.262235i | ||||
\(39\) | −44.8808 | − | 77.7357i | −0.184274 | − | 0.319171i | ||||
\(40\) | 55.4611 | − | 96.0614i | 0.219229 | − | 0.379716i | ||||
\(41\) | 235.479 | 0.896967 | 0.448483 | − | 0.893791i | \(-0.351964\pi\) | ||||
0.448483 | + | 0.893791i | \(0.351964\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −278.388 | −0.987296 | −0.493648 | − | 0.869662i | \(-0.664337\pi\) | ||||
−0.493648 | + | 0.869662i | \(0.664337\pi\) | |||||||
\(44\) | 6.95909 | − | 12.0535i | 0.0238437 | − | 0.0412985i | ||||
\(45\) | −46.6122 | − | 80.7347i | −0.154412 | − | 0.267449i | ||||
\(46\) | −223.183 | − | 386.565i | −0.715360 | − | 1.23904i | ||||
\(47\) | −184.042 | + | 318.771i | −0.571177 | + | 0.989308i | 0.425268 | + | 0.905067i | \(0.360180\pi\) |
−0.996445 | + | 0.0842404i | \(0.973154\pi\) | |||||||
\(48\) | 191.658 | 0.576321 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −72.0217 | −0.203708 | ||||||||
\(51\) | −89.3918 | + | 154.831i | −0.245438 | + | 0.425112i | ||||
\(52\) | 4.64862 | + | 8.05165i | 0.0123971 | + | 0.0214724i | ||||
\(53\) | 84.7920 | + | 146.864i | 0.219756 | + | 0.380629i | 0.954733 | − | 0.297463i | \(-0.0961405\pi\) |
−0.734977 | + | 0.678092i | \(0.762807\pi\) | |||||||
\(54\) | 190.047 | − | 329.172i | 0.478929 | − | 0.829529i | ||||
\(55\) | 232.440 | 0.569859 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −71.1686 | −0.165377 | ||||||||
\(58\) | 288.714 | − | 500.068i | 0.653622 | − | 1.13211i | ||||
\(59\) | −345.745 | − | 598.847i | −0.762918 | − | 1.32141i | −0.941341 | − | 0.337458i | \(-0.890433\pi\) |
0.178423 | − | 0.983954i | \(-0.442900\pi\) | |||||||
\(60\) | −2.16350 | − | 3.74730i | −0.00465511 | − | 0.00806290i | ||||
\(61\) | −348.286 | + | 603.249i | −0.731041 | + | 1.26620i | 0.225398 | + | 0.974267i | \(0.427632\pi\) |
−0.956439 | + | 0.291933i | \(0.905702\pi\) | |||||||
\(62\) | −372.365 | −0.762749 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 491.432 | 0.959827 | ||||||||
\(65\) | −77.6343 | + | 134.467i | −0.148144 | + | 0.256593i | ||||
\(66\) | 193.558 | + | 335.252i | 0.360990 | + | 0.625253i | ||||
\(67\) | −1.16656 | − | 2.02054i | −0.00212713 | − | 0.00368430i | 0.864960 | − | 0.501841i | \(-0.167344\pi\) |
−0.867087 | + | 0.498157i | \(0.834010\pi\) | |||||||
\(68\) | 9.25895 | − | 16.0370i | 0.0165120 | − | 0.0285995i | ||||
\(69\) | 447.863 | 0.781396 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −866.599 | −1.44854 | −0.724270 | − | 0.689516i | \(-0.757823\pi\) | ||||
−0.724270 | + | 0.689516i | \(0.757823\pi\) | |||||||
\(72\) | 206.813 | − | 358.210i | 0.338516 | − | 0.586326i | ||||
\(73\) | −376.222 | − | 651.635i | −0.603197 | − | 1.04477i | −0.992334 | − | 0.123588i | \(-0.960560\pi\) |
0.389136 | − | 0.921180i | \(-0.372774\pi\) | |||||||
\(74\) | −112.305 | − | 194.518i | −0.176422 | − | 0.305571i | ||||
\(75\) | 36.1315 | − | 62.5817i | 0.0556281 | − | 0.0963508i | ||||
\(76\) | 7.37145 | 0.0111258 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −258.591 | −0.375380 | ||||||||
\(79\) | −421.391 | + | 729.871i | −0.600130 | + | 1.03945i | 0.392671 | + | 0.919679i | \(0.371551\pi\) |
−0.992801 | + | 0.119776i | \(0.961782\pi\) | |||||||
\(80\) | −165.764 | − | 287.111i | −0.231662 | − | 0.401250i | ||||
\(81\) | −61.0215 | − | 105.692i | −0.0837058 | − | 0.144983i | ||||
\(82\) | 339.192 | − | 587.497i | 0.456798 | − | 0.791198i | ||||
\(83\) | −1443.44 | −1.90890 | −0.954450 | − | 0.298372i | \(-0.903556\pi\) | ||||
−0.954450 | + | 0.298372i | \(0.903556\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 309.258 | 0.394632 | ||||||||
\(86\) | −400.999 | + | 694.550i | −0.502800 | + | 0.870875i | ||||
\(87\) | 289.682 | + | 501.744i | 0.356979 | + | 0.618306i | ||||
\(88\) | 515.655 | + | 893.141i | 0.624648 | + | 1.08192i | ||||
\(89\) | 719.031 | − | 1245.40i | 0.856372 | − | 1.48328i | −0.0189949 | − | 0.999820i | \(-0.506047\pi\) |
0.875367 | − | 0.483460i | \(-0.160620\pi\) | |||||||
\(90\) | −268.567 | −0.314549 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −46.3884 | −0.0525687 | ||||||||
\(93\) | 186.807 | − | 323.559i | 0.208290 | − | 0.360768i | ||||
\(94\) | 530.201 | + | 918.335i | 0.581767 | + | 1.00765i | ||||
\(95\) | 61.5534 | + | 106.614i | 0.0664763 | + | 0.115140i | ||||
\(96\) | 19.5716 | − | 33.8990i | 0.0208075 | − | 0.0360397i | ||||
\(97\) | 23.4509 | 0.0245472 | 0.0122736 | − | 0.999925i | \(-0.496093\pi\) | ||||
0.0122736 | + | 0.999925i | \(0.496093\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 866.764 | 0.879930 | ||||||||
\(100\) | −3.74241 | + | 6.48204i | −0.00374241 | + | 0.00648204i | ||||
\(101\) | 738.207 | + | 1278.61i | 0.727271 | + | 1.25967i | 0.958032 | + | 0.286660i | \(0.0925450\pi\) |
−0.230761 | + | 0.973010i | \(0.574122\pi\) | |||||||
\(102\) | 257.526 | + | 446.048i | 0.249989 | + | 0.432993i | ||||
\(103\) | −504.721 | + | 874.202i | −0.482831 | + | 0.836289i | −0.999806 | − | 0.0197124i | \(-0.993725\pi\) |
0.516974 | + | 0.856001i | \(0.327058\pi\) | |||||||
\(104\) | −688.909 | −0.649549 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 488.549 | 0.447661 | ||||||||
\(107\) | −709.253 | + | 1228.46i | −0.640805 | + | 1.10991i | 0.344449 | + | 0.938805i | \(0.388066\pi\) |
−0.985253 | + | 0.171101i | \(0.945267\pi\) | |||||||
\(108\) | −19.7506 | − | 34.2090i | −0.0175972 | − | 0.0304793i | ||||
\(109\) | 438.930 | + | 760.249i | 0.385705 | + | 0.668061i | 0.991867 | − | 0.127281i | \(-0.0406249\pi\) |
−0.606162 | + | 0.795341i | \(0.707292\pi\) | |||||||
\(110\) | 334.815 | − | 579.916i | 0.290212 | − | 0.502662i | ||||
\(111\) | 225.363 | 0.192707 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1500.11 | −1.24884 | −0.624419 | − | 0.781090i | \(-0.714664\pi\) | ||||
−0.624419 | + | 0.781090i | \(0.714664\pi\) | |||||||
\(114\) | −102.514 | + | 177.559i | −0.0842218 | + | 0.145876i | ||||
\(115\) | −387.354 | − | 670.917i | −0.314095 | − | 0.544029i | ||||
\(116\) | −30.0045 | − | 51.9693i | −0.0240159 | − | 0.0415968i | ||||
\(117\) | −289.496 | + | 501.422i | −0.228752 | + | 0.396210i | ||||
\(118\) | −1992.09 | −1.55412 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 320.623 | 0.243906 | ||||||||
\(121\) | −415.070 | + | 718.922i | −0.311848 | + | 0.540137i | ||||
\(122\) | 1003.37 | + | 1737.88i | 0.744594 | + | 1.28968i | ||||
\(123\) | 340.329 | + | 589.467i | 0.249483 | + | 0.432117i | ||||
\(124\) | −19.3489 | + | 33.5133i | −0.0140128 | + | 0.0242708i | ||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 416.639 | 0.291108 | 0.145554 | − | 0.989350i | \(-0.453503\pi\) | ||||
0.145554 | + | 0.989350i | \(0.453503\pi\) | |||||||
\(128\) | 762.042 | − | 1319.90i | 0.526216 | − | 0.911433i | ||||
\(129\) | −402.343 | − | 696.878i | −0.274607 | − | 0.475634i | ||||
\(130\) | 223.654 | + | 387.380i | 0.150890 | + | 0.261350i | ||||
\(131\) | 205.248 | − | 355.500i | 0.136890 | − | 0.237101i | −0.789428 | − | 0.613843i | \(-0.789623\pi\) |
0.926318 | + | 0.376743i | \(0.122956\pi\) | |||||||
\(132\) | 40.2308 | 0.0265276 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −6.72139 | −0.00433313 | ||||||||
\(135\) | 329.844 | − | 571.306i | 0.210285 | − | 0.364224i | ||||
\(136\) | 686.071 | + | 1188.31i | 0.432574 | + | 0.749241i | ||||
\(137\) | −880.987 | − | 1525.91i | −0.549400 | − | 0.951589i | −0.998316 | − | 0.0580146i | \(-0.981523\pi\) |
0.448916 | − | 0.893574i | \(-0.351810\pi\) | |||||||
\(138\) | 645.116 | − | 1117.37i | 0.397942 | − | 0.689255i | ||||
\(139\) | 865.719 | 0.528268 | 0.264134 | − | 0.964486i | \(-0.414914\pi\) | ||||
0.264134 | + | 0.964486i | \(0.414914\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1063.96 | −0.635470 | ||||||||
\(142\) | −1248.28 | + | 2162.08i | −0.737698 | + | 1.27773i | ||||
\(143\) | −721.814 | − | 1250.22i | −0.422106 | − | 0.731108i | ||||
\(144\) | −618.129 | − | 1070.63i | −0.357713 | − | 0.619578i | ||||
\(145\) | 501.089 | − | 867.912i | 0.286988 | − | 0.497077i | ||||
\(146\) | −2167.69 | −1.22876 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −23.3425 | −0.0129645 | ||||||||
\(149\) | −1509.62 | + | 2614.73i | −0.830018 | + | 1.43763i | 0.0680059 | + | 0.997685i | \(0.478336\pi\) |
−0.898023 | + | 0.439948i | \(0.854997\pi\) | |||||||
\(150\) | −104.090 | − | 180.289i | −0.0566595 | − | 0.0981371i | ||||
\(151\) | −270.948 | − | 469.296i | −0.146023 | − | 0.252919i | 0.783731 | − | 0.621100i | \(-0.213314\pi\) |
−0.929754 | + | 0.368181i | \(0.879981\pi\) | |||||||
\(152\) | −273.105 | + | 473.032i | −0.145735 | + | 0.252421i | ||||
\(153\) | 1153.22 | 0.609359 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −646.273 | −0.334902 | ||||||||
\(156\) | −13.4370 | + | 23.2735i | −0.00689627 | + | 0.0119447i | ||||
\(157\) | −1293.04 | − | 2239.62i | −0.657300 | − | 1.13848i | −0.981312 | − | 0.192424i | \(-0.938365\pi\) |
0.324012 | − | 0.946053i | \(-0.394968\pi\) | |||||||
\(158\) | 1213.97 | + | 2102.66i | 0.611256 | + | 1.05873i | ||||
\(159\) | −245.093 | + | 424.514i | −0.122246 | + | 0.211737i | ||||
\(160\) | −67.7096 | −0.0334557 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −351.590 | −0.170515 | ||||||||
\(163\) | 1233.07 | − | 2135.74i | 0.592525 | − | 1.02628i | −0.401366 | − | 0.915918i | \(-0.631464\pi\) |
0.993891 | − | 0.110366i | \(-0.0352024\pi\) | |||||||
\(164\) | −35.2503 | − | 61.0553i | −0.0167841 | − | 0.0290709i | ||||
\(165\) | 335.937 | + | 581.860i | 0.158501 | + | 0.274532i | ||||
\(166\) | −2079.19 | + | 3601.26i | −0.972145 | + | 1.68381i | ||||
\(167\) | 459.020 | 0.212695 | 0.106347 | − | 0.994329i | \(-0.466084\pi\) | ||||
0.106347 | + | 0.994329i | \(0.466084\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1232.67 | −0.561068 | ||||||||
\(170\) | 445.466 | − | 771.569i | 0.200974 | − | 0.348098i | ||||
\(171\) | 229.531 | + | 397.560i | 0.102647 | + | 0.177790i | ||||
\(172\) | 41.6736 | + | 72.1807i | 0.0184743 | + | 0.0319984i | ||||
\(173\) | 2250.73 | − | 3898.38i | 0.989132 | − | 1.71323i | 0.367233 | − | 0.930129i | \(-0.380305\pi\) |
0.621899 | − | 0.783097i | \(-0.286361\pi\) | |||||||
\(174\) | 1669.07 | 0.727195 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3082.41 | 1.32015 | ||||||||
\(177\) | 999.383 | − | 1730.98i | 0.424397 | − | 0.735077i | ||||
\(178\) | −2071.43 | − | 3587.82i | −0.872249 | − | 1.51078i | ||||
\(179\) | −980.055 | − | 1697.51i | −0.409233 | − | 0.708813i | 0.585571 | − | 0.810621i | \(-0.300870\pi\) |
−0.994804 | + | 0.101808i | \(0.967537\pi\) | |||||||
\(180\) | −13.9553 | + | 24.1714i | −0.00577872 | + | 0.0100090i | ||||
\(181\) | 3645.47 | 1.49705 | 0.748524 | − | 0.663108i | \(-0.230763\pi\) | ||||
0.748524 | + | 0.663108i | \(0.230763\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2013.46 | −0.813329 | ||||||||
\(184\) | 1718.65 | − | 2976.78i | 0.688588 | − | 1.19267i | ||||
\(185\) | −194.915 | − | 337.604i | −0.0774620 | − | 0.134168i | ||||
\(186\) | −538.165 | − | 932.129i | −0.212151 | − | 0.367457i | ||||
\(187\) | −1437.68 | + | 2490.14i | −0.562212 | + | 0.973780i | ||||
\(188\) | 110.202 | 0.0427515 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 354.654 | 0.135417 | ||||||||
\(191\) | −1257.22 | + | 2177.57i | −0.476280 | + | 0.824941i | −0.999631 | − | 0.0271763i | \(-0.991348\pi\) |
0.523351 | + | 0.852117i | \(0.324682\pi\) | |||||||
\(192\) | 710.247 | + | 1230.18i | 0.266967 | + | 0.462400i | ||||
\(193\) | −1094.68 | − | 1896.05i | −0.408274 | − | 0.707152i | 0.586422 | − | 0.810006i | \(-0.300536\pi\) |
−0.994697 | + | 0.102854i | \(0.967203\pi\) | |||||||
\(194\) | 33.7795 | − | 58.5078i | 0.0125012 | − | 0.0216526i | ||||
\(195\) | −448.808 | −0.164819 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3886.50 | −1.40559 | −0.702795 | − | 0.711392i | \(-0.748065\pi\) | ||||
−0.702795 | + | 0.711392i | \(0.748065\pi\) | |||||||
\(198\) | 1248.52 | − | 2162.49i | 0.448122 | − | 0.776170i | ||||
\(199\) | −484.680 | − | 839.491i | −0.172654 | − | 0.299045i | 0.766693 | − | 0.642014i | \(-0.221901\pi\) |
−0.939347 | + | 0.342969i | \(0.888567\pi\) | |||||||
\(200\) | −277.305 | − | 480.307i | −0.0980422 | − | 0.169814i | ||||
\(201\) | 3.37196 | − | 5.84041i | 0.00118328 | − | 0.00204951i | ||||
\(202\) | 4253.35 | 1.48151 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 53.5264 | 0.0183706 | ||||||||
\(205\) | 588.697 | − | 1019.65i | 0.200568 | − | 0.347394i | ||||
\(206\) | 1454.03 | + | 2518.46i | 0.491783 | + | 0.851794i | ||||
\(207\) | −1444.43 | − | 2501.83i | −0.485001 | − | 0.840046i | ||||
\(208\) | −1029.52 | + | 1783.17i | −0.343193 | + | 0.594427i | ||||
\(209\) | −1144.60 | −0.378821 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3079.69 | 1.00481 | 0.502404 | − | 0.864633i | \(-0.332449\pi\) | ||||
0.502404 | + | 0.864633i | \(0.332449\pi\) | |||||||
\(212\) | 25.3861 | − | 43.9700i | 0.00822417 | − | 0.0142447i | ||||
\(213\) | −1252.46 | − | 2169.33i | −0.402898 | − | 0.697840i | ||||
\(214\) | 2043.26 | + | 3539.04i | 0.652685 | + | 1.13048i | ||||
\(215\) | −695.969 | + | 1205.45i | −0.220766 | + | 0.382378i | ||||
\(216\) | 2926.96 | 0.922011 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2529.00 | 0.785712 | ||||||||
\(219\) | 1087.48 | − | 1883.57i | 0.335547 | − | 0.581185i | ||||
\(220\) | −34.7954 | − | 60.2675i | −0.0106632 | − | 0.0184692i | ||||
\(221\) | −960.362 | − | 1663.40i | −0.292312 | − | 0.506299i | ||||
\(222\) | 324.621 | − | 562.259i | 0.0981401 | − | 0.169984i | ||||
\(223\) | −162.003 | −0.0486480 | −0.0243240 | − | 0.999704i | \(-0.507743\pi\) | ||||
−0.0243240 | + | 0.999704i | \(0.507743\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −466.122 | −0.138110 | ||||||||
\(226\) | −2160.81 | + | 3742.63i | −0.635995 | + | 1.10158i | ||||
\(227\) | 189.976 | + | 329.048i | 0.0555470 | + | 0.0962101i | 0.892462 | − | 0.451123i | \(-0.148976\pi\) |
−0.836915 | + | 0.547333i | \(0.815643\pi\) | |||||||
\(228\) | 10.6537 | + | 18.4527i | 0.00309455 | + | 0.00535991i | ||||
\(229\) | −2390.75 | + | 4140.90i | −0.689892 | + | 1.19493i | 0.281980 | + | 0.959420i | \(0.409009\pi\) |
−0.971872 | + | 0.235508i | \(0.924325\pi\) | |||||||
\(230\) | −2231.83 | −0.639838 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4446.55 | 1.25832 | ||||||||
\(233\) | 1262.27 | − | 2186.31i | 0.354910 | − | 0.614722i | −0.632193 | − | 0.774811i | \(-0.717845\pi\) |
0.987103 | + | 0.160090i | \(0.0511783\pi\) | |||||||
\(234\) | 834.000 | + | 1444.53i | 0.232993 | + | 0.403555i | ||||
\(235\) | 920.211 | + | 1593.85i | 0.255438 | + | 0.442432i | ||||
\(236\) | −103.513 | + | 179.290i | −0.0285515 | + | 0.0494526i | ||||
\(237\) | −2436.08 | −0.667682 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 113.452 | 0.0307053 | 0.0153527 | − | 0.999882i | \(-0.495113\pi\) | ||||
0.0153527 | + | 0.999882i | \(0.495113\pi\) | |||||||
\(240\) | 479.144 | − | 829.902i | 0.128869 | − | 0.223208i | ||||
\(241\) | 3362.67 | + | 5824.32i | 0.898791 | + | 1.55675i | 0.829041 | + | 0.559187i | \(0.188887\pi\) |
0.0697499 | + | 0.997565i | \(0.477780\pi\) | |||||||
\(242\) | 1195.76 | + | 2071.12i | 0.317630 | + | 0.550151i | ||||
\(243\) | 1957.54 | − | 3390.56i | 0.516775 | − | 0.895081i | ||||
\(244\) | 208.549 | 0.0547170 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1960.88 | 0.508217 | ||||||||
\(247\) | 382.292 | − | 662.150i | 0.0984805 | − | 0.170573i | ||||
\(248\) | −1433.72 | − | 2483.27i | −0.367102 | − | 0.635839i | ||||
\(249\) | −2086.16 | − | 3613.33i | −0.530943 | − | 0.919620i | ||||
\(250\) | −180.054 | + | 311.863i | −0.0455505 | + | 0.0788958i | ||||
\(251\) | 3815.00 | 0.959366 | 0.479683 | − | 0.877442i | \(-0.340752\pi\) | ||||
0.479683 | + | 0.877442i | \(0.340752\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7202.94 | 1.78990 | ||||||||
\(254\) | 600.141 | − | 1039.48i | 0.148253 | − | 0.256781i | ||||
\(255\) | 446.959 | + | 774.156i | 0.109763 | + | 0.190116i | ||||
\(256\) | −229.615 | − | 397.705i | −0.0560584 | − | 0.0970961i | ||||
\(257\) | 1100.95 | − | 1906.90i | 0.267220 | − | 0.462838i | −0.700923 | − | 0.713237i | \(-0.747228\pi\) |
0.968143 | + | 0.250399i | \(0.0805617\pi\) | |||||||
\(258\) | −2318.19 | −0.559397 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 46.4862 | 0.0110883 | ||||||||
\(261\) | 1868.55 | − | 3236.42i | 0.443143 | − | 0.767546i | ||||
\(262\) | −591.292 | − | 1024.15i | −0.139428 | − | 0.241496i | ||||
\(263\) | 602.090 | + | 1042.85i | 0.141165 | + | 0.244505i | 0.927936 | − | 0.372740i | \(-0.121582\pi\) |
−0.786770 | + | 0.617246i | \(0.788248\pi\) | |||||||
\(264\) | −1490.51 | + | 2581.65i | −0.347480 | + | 0.601853i | ||||
\(265\) | 847.920 | 0.196556 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4156.75 | 0.952767 | ||||||||
\(268\) | −0.349258 | + | 0.604933i | −7.96058e−5 | + | 0.000137881i | ||||
\(269\) | 2564.49 | + | 4441.83i | 0.581263 | + | 1.00678i | 0.995330 | + | 0.0965307i | \(0.0307746\pi\) |
−0.414067 | + | 0.910246i | \(0.635892\pi\) | |||||||
\(270\) | −950.236 | − | 1645.86i | −0.214183 | − | 0.370977i | ||||
\(271\) | 404.196 | − | 700.087i | 0.0906020 | − | 0.156927i | −0.817163 | − | 0.576407i | \(-0.804454\pi\) |
0.907765 | + | 0.419480i | \(0.137788\pi\) | |||||||
\(272\) | 4101.10 | 0.914213 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5076.01 | −1.11917 | ||||||||
\(275\) | 581.101 | − | 1006.50i | 0.127424 | − | 0.220705i | ||||
\(276\) | −67.0433 | − | 116.122i | −0.0146215 | − | 0.0253252i | ||||
\(277\) | −90.1326 | − | 156.114i | −0.0195507 | − | 0.0338628i | 0.856085 | − | 0.516836i | \(-0.172890\pi\) |
−0.875635 | + | 0.482973i | \(0.839557\pi\) | |||||||
\(278\) | 1247.01 | − | 2159.88i | 0.269031 | − | 0.465976i | ||||
\(279\) | −2409.93 | −0.517129 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3068.29 | −0.651384 | −0.325692 | − | 0.945476i | \(-0.605597\pi\) | ||||
−0.325692 | + | 0.945476i | \(0.605597\pi\) | |||||||
\(282\) | −1532.56 | + | 2654.47i | −0.323626 | + | 0.560537i | ||||
\(283\) | −1934.09 | − | 3349.94i | −0.406253 | − | 0.703651i | 0.588214 | − | 0.808706i | \(-0.299831\pi\) |
−0.994466 | + | 0.105055i | \(0.966498\pi\) | |||||||
\(284\) | 129.727 | + | 224.693i | 0.0271051 | + | 0.0469475i | ||||
\(285\) | −177.922 | + | 308.169i | −0.0369795 | + | 0.0640504i | ||||
\(286\) | −4158.90 | −0.859863 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −252.488 | −0.0516596 | ||||||||
\(289\) | 543.688 | − | 941.696i | 0.110663 | − | 0.191674i | ||||
\(290\) | −1443.57 | − | 2500.34i | −0.292308 | − | 0.506293i | ||||
\(291\) | 33.8927 | + | 58.7039i | 0.00682758 | + | 0.0118257i | ||||
\(292\) | −112.638 | + | 195.095i | −0.0225741 | + | 0.0390995i | ||||
\(293\) | 1967.79 | 0.392353 | 0.196176 | − | 0.980569i | \(-0.437147\pi\) | ||||
0.196176 | + | 0.980569i | \(0.437147\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3457.45 | −0.682374 | ||||||||
\(296\) | 864.817 | − | 1497.91i | 0.169819 | − | 0.294136i | ||||
\(297\) | 3066.76 | + | 5311.79i | 0.599163 | + | 1.03778i | ||||
\(298\) | 4349.00 | + | 7532.70i | 0.845406 | + | 1.46429i | ||||
\(299\) | −2405.76 | + | 4166.90i | −0.465313 | + | 0.805946i | ||||
\(300\) | −21.6350 | −0.00416366 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1561.13 | −0.297460 | ||||||||
\(303\) | −2133.81 | + | 3695.86i | −0.404567 | + | 0.700731i | ||||
\(304\) | 816.266 | + | 1413.81i | 0.154000 | + | 0.266736i | ||||
\(305\) | 1741.43 | + | 3016.25i | 0.326931 | + | 0.566262i | ||||
\(306\) | 1661.13 | − | 2877.16i | 0.310328 | − | 0.537505i | ||||
\(307\) | −5487.54 | −1.02016 | −0.510082 | − | 0.860126i | \(-0.670385\pi\) | ||||
−0.510082 | + | 0.860126i | \(0.670385\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2917.82 | −0.537180 | ||||||||
\(310\) | −930.913 | + | 1612.39i | −0.170556 | + | 0.295411i | ||||
\(311\) | −2586.40 | − | 4479.77i | −0.471579 | − | 0.816799i | 0.527892 | − | 0.849312i | \(-0.322983\pi\) |
−0.999471 | + | 0.0325121i | \(0.989649\pi\) | |||||||
\(312\) | −995.654 | − | 1724.52i | −0.180666 | − | 0.312923i | ||||
\(313\) | 2881.46 | − | 4990.83i | 0.520351 | − | 0.901274i | −0.479370 | − | 0.877613i | \(-0.659135\pi\) |
0.999720 | − | 0.0236604i | \(-0.00753204\pi\) | |||||||
\(314\) | −7450.17 | −1.33897 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 252.323 | 0.0449186 | ||||||||
\(317\) | −1590.44 | + | 2754.72i | −0.281792 | + | 0.488077i | −0.971826 | − | 0.235699i | \(-0.924262\pi\) |
0.690035 | + | 0.723776i | \(0.257595\pi\) | |||||||
\(318\) | 706.081 | + | 1222.97i | 0.124513 | + | 0.215662i | ||||
\(319\) | 4658.94 | + | 8069.51i | 0.817713 | + | 1.41632i | ||||
\(320\) | 1228.58 | − | 2127.96i | 0.214624 | − | 0.371739i | ||||
\(321\) | −4100.23 | −0.712936 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1522.87 | −0.262337 | ||||||||
\(324\) | −18.2694 | + | 31.6435i | −0.00313261 | + | 0.00542584i | ||||
\(325\) | 388.172 | + | 672.333i | 0.0662519 | + | 0.114752i | ||||
\(326\) | −3552.32 | − | 6152.79i | −0.603511 | − | 1.04531i | ||||
\(327\) | −1268.74 | + | 2197.52i | −0.214561 | + | 0.371630i | ||||
\(328\) | 5223.97 | 0.879406 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1935.58 | 0.322879 | ||||||||
\(331\) | −4616.51 | + | 7996.03i | −0.766606 | + | 1.32780i | 0.172788 | + | 0.984959i | \(0.444722\pi\) |
−0.939394 | + | 0.342841i | \(0.888611\pi\) | |||||||
\(332\) | 216.078 | + | 374.258i | 0.0357194 | + | 0.0618678i | ||||
\(333\) | −726.835 | − | 1258.92i | −0.119611 | − | 0.207172i | ||||
\(334\) | 661.188 | − | 1145.21i | 0.108319 | − | 0.187614i | ||||
\(335\) | −11.6656 | −0.00190256 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3259.50 | −0.526874 | −0.263437 | − | 0.964677i | \(-0.584856\pi\) | ||||
−0.263437 | + | 0.964677i | \(0.584856\pi\) | |||||||
\(338\) | −1775.57 | + | 3075.38i | −0.285735 | + | 0.494908i | ||||
\(339\) | −2168.05 | − | 3755.18i | −0.347353 | − | 0.601632i | ||||
\(340\) | −46.2948 | − | 80.1849i | −0.00738437 | − | 0.0127901i | ||||
\(341\) | 3004.40 | − | 5203.77i | 0.477118 | − | 0.826392i | ||||
\(342\) | 1322.50 | 0.209101 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −6175.87 | −0.967967 | ||||||||
\(345\) | 1119.66 | − | 1939.30i | 0.174725 | − | 0.302633i | ||||
\(346\) | −6484.05 | − | 11230.7i | −1.00747 | − | 1.74499i | ||||
\(347\) | −925.566 | − | 1603.13i | −0.143190 | − | 0.248013i | 0.785506 | − | 0.618854i | \(-0.212403\pi\) |
−0.928696 | + | 0.370841i | \(0.879069\pi\) | |||||||
\(348\) | 86.7286 | − | 150.218i | 0.0133596 | − | 0.0231395i | ||||
\(349\) | −1102.14 | −0.169043 | −0.0845216 | − | 0.996422i | \(-0.526936\pi\) | ||||
−0.0845216 | + | 0.996422i | \(0.526936\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4097.15 | −0.623048 | ||||||||
\(352\) | 314.769 | − | 545.196i | 0.0476626 | − | 0.0825541i | ||||
\(353\) | 1335.12 | + | 2312.50i | 0.201307 | + | 0.348674i | 0.948950 | − | 0.315427i | \(-0.102148\pi\) |
−0.747643 | + | 0.664101i | \(0.768814\pi\) | |||||||
\(354\) | −2879.09 | − | 4986.73i | −0.432265 | − | 0.748705i | ||||
\(355\) | −2166.50 | + | 3752.48i | −0.323904 | + | 0.561017i | ||||
\(356\) | −430.545 | −0.0640978 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5646.82 | −0.833641 | ||||||||
\(359\) | −217.726 | + | 377.113i | −0.0320088 | + | 0.0554409i | −0.881586 | − | 0.472023i | \(-0.843524\pi\) |
0.849577 | + | 0.527464i | \(0.176857\pi\) | |||||||
\(360\) | −1034.06 | − | 1791.05i | −0.151389 | − | 0.262213i | ||||
\(361\) | 3126.39 | + | 5415.07i | 0.455809 | + | 0.789484i | ||||
\(362\) | 5251.06 | − | 9095.10i | 0.762402 | − | 1.32052i | ||||
\(363\) | −2399.54 | −0.346951 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3762.22 | −0.539516 | ||||||||
\(366\) | −2900.25 | + | 5023.39i | −0.414204 | + | 0.717422i | ||||
\(367\) | −1237.33 | − | 2143.11i | −0.175989 | − | 0.304822i | 0.764514 | − | 0.644607i | \(-0.222979\pi\) |
−0.940503 | + | 0.339785i | \(0.889646\pi\) | |||||||
\(368\) | −5136.74 | − | 8897.10i | −0.727639 | − | 1.26031i | ||||
\(369\) | 2195.24 | − | 3802.26i | 0.309701 | − | 0.536417i | ||||
\(370\) | −1123.05 | −0.157796 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −111.857 | −0.0155901 | ||||||||
\(373\) | −2719.09 | + | 4709.61i | −0.377451 | + | 0.653764i | −0.990691 | − | 0.136133i | \(-0.956533\pi\) |
0.613240 | + | 0.789897i | \(0.289866\pi\) | |||||||
\(374\) | 4141.77 | + | 7173.75i | 0.572636 | + | 0.991834i | ||||
\(375\) | −180.658 | − | 312.908i | −0.0248777 | − | 0.0430894i | ||||
\(376\) | −4082.87 | + | 7071.74i | −0.559995 | + | 0.969939i | ||||
\(377\) | −6224.28 | −0.850309 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10597.1 | 1.43624 | 0.718122 | − | 0.695917i | \(-0.245002\pi\) | ||||
0.718122 | + | 0.695917i | \(0.245002\pi\) | |||||||
\(380\) | 18.4286 | − | 31.9193i | 0.00248781 | − | 0.00430902i | ||||
\(381\) | 602.153 | + | 1042.96i | 0.0809691 | + | 0.140243i | ||||
\(382\) | 3621.89 | + | 6273.30i | 0.485110 | + | 0.840236i | ||||
\(383\) | −2335.68 | + | 4045.52i | −0.311613 | + | 0.539729i | −0.978712 | − | 0.205240i | \(-0.934203\pi\) |
0.667099 | + | 0.744969i | \(0.267536\pi\) | |||||||
\(384\) | 4405.40 | 0.585448 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6307.27 | −0.831688 | ||||||||
\(387\) | −2595.25 | + | 4495.11i | −0.340889 | + | 0.590437i | ||||
\(388\) | −3.51051 | − | 6.08039i | −0.000459328 | − | 0.000795580i | ||||
\(389\) | −1778.84 | − | 3081.05i | −0.231853 | − | 0.401582i | 0.726500 | − | 0.687166i | \(-0.241146\pi\) |
−0.958354 | + | 0.285585i | \(0.907812\pi\) | |||||||
\(390\) | −646.477 | + | 1119.73i | −0.0839376 | + | 0.145384i | ||||
\(391\) | 9583.40 | 1.23952 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1186.55 | 0.152299 | ||||||||
\(394\) | −5598.24 | + | 9696.43i | −0.715825 | + | 1.23985i | ||||
\(395\) | 2106.96 | + | 3649.36i | 0.268386 | + | 0.464858i | ||||
\(396\) | −129.751 | − | 224.736i | −0.0164653 | − | 0.0285187i | ||||
\(397\) | −4592.28 | + | 7954.07i | −0.580554 | + | 1.00555i | 0.414859 | + | 0.909886i | \(0.363831\pi\) |
−0.995414 | + | 0.0956642i | \(0.969503\pi\) | |||||||
\(398\) | −2792.60 | −0.351709 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1657.64 | −0.207205 | ||||||||
\(401\) | 4603.26 | − | 7973.08i | 0.573256 | − | 0.992909i | −0.422972 | − | 0.906143i | \(-0.639013\pi\) |
0.996229 | − | 0.0867664i | \(-0.0276534\pi\) | |||||||
\(402\) | −9.71417 | − | 16.8254i | −0.00120522 | − | 0.00208750i | ||||
\(403\) | 2006.92 | + | 3476.08i | 0.248069 | + | 0.429668i | ||||
\(404\) | 221.014 | − | 382.807i | 0.0272174 | − | 0.0471420i | ||||
\(405\) | −610.215 | −0.0748687 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3624.50 | 0.441424 | ||||||||
\(408\) | −1983.11 | + | 3434.84i | −0.240633 | + | 0.416789i | ||||
\(409\) | −3826.83 | − | 6628.26i | −0.462652 | − | 0.801336i | 0.536441 | − | 0.843938i | \(-0.319769\pi\) |
−0.999092 | + | 0.0426020i | \(0.986435\pi\) | |||||||
\(410\) | −1695.96 | − | 2937.49i | −0.204286 | − | 0.353834i | ||||
\(411\) | 2546.51 | − | 4410.69i | 0.305621 | − | 0.529351i | ||||
\(412\) | 302.219 | 0.0361390 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −8322.44 | −0.987985 | ||||||||
\(415\) | −3608.61 | + | 6250.30i | −0.426843 | + | 0.739314i | ||||
\(416\) | 210.264 | + | 364.187i | 0.0247813 | + | 0.0429225i | ||||
\(417\) | 1251.19 | + | 2167.12i | 0.146933 | + | 0.254495i | ||||
\(418\) | −1648.72 | + | 2855.66i | −0.192922 | + | 0.334151i | ||||
\(419\) | 370.864 | 0.0432408 | 0.0216204 | − | 0.999766i | \(-0.493117\pi\) | ||||
0.0216204 | + | 0.999766i | \(0.493117\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1221.96 | 0.141460 | 0.0707302 | − | 0.997495i | \(-0.477467\pi\) | ||||
0.0707302 | + | 0.997495i | \(0.477467\pi\) | |||||||
\(422\) | 4436.09 | − | 7683.53i | 0.511719 | − | 0.886323i | ||||
\(423\) | 3431.44 | + | 5943.44i | 0.394427 | + | 0.683167i | ||||
\(424\) | 1881.06 | + | 3258.09i | 0.215454 | + | 0.373177i | ||||
\(425\) | 773.145 | − | 1339.13i | 0.0882425 | − | 0.152840i | ||||
\(426\) | −7216.35 | −0.820736 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 424.690 | 0.0479630 | ||||||||
\(429\) | 2086.42 | − | 3613.78i | 0.234809 | − | 0.406702i | ||||
\(430\) | 2004.99 | + | 3472.75i | 0.224859 | + | 0.389467i | ||||
\(431\) | 7464.46 | + | 12928.8i | 0.834224 | + | 1.44492i | 0.894661 | + | 0.446746i | \(0.147417\pi\) |
−0.0604373 | + | 0.998172i | \(0.519250\pi\) | |||||||
\(432\) | 4374.09 | − | 7576.15i | 0.487150 | − | 0.843768i | ||||
\(433\) | −4544.42 | −0.504367 | −0.252184 | − | 0.967679i | \(-0.581149\pi\) | ||||
−0.252184 | + | 0.967679i | \(0.581149\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2896.82 | 0.319292 | ||||||||
\(436\) | 131.412 | − | 227.613i | 0.0144346 | − | 0.0250015i | ||||
\(437\) | 1907.44 | + | 3303.78i | 0.208799 | + | 0.361650i | ||||
\(438\) | −3132.88 | − | 5426.30i | −0.341769 | − | 0.591961i | ||||
\(439\) | 4715.94 | − | 8168.25i | 0.512710 | − | 0.888040i | −0.487181 | − | 0.873301i | \(-0.661975\pi\) |
0.999891 | − | 0.0147389i | \(-0.00469170\pi\) | |||||||
\(440\) | 5156.55 | 0.558702 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5533.35 | −0.595463 | ||||||||
\(443\) | 2771.30 | − | 4800.04i | 0.297220 | − | 0.514801i | −0.678279 | − | 0.734805i | \(-0.737274\pi\) |
0.975499 | + | 0.220004i | \(0.0706071\pi\) | |||||||
\(444\) | −33.7360 | − | 58.4325i | −0.00360595 | − | 0.00624568i | ||||
\(445\) | −3595.15 | − | 6226.99i | −0.382981 | − | 0.663343i | ||||
\(446\) | −233.354 | + | 404.181i | −0.0247750 | + | 0.0429115i | ||||
\(447\) | −8727.16 | −0.923447 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16311.6 | 1.71446 | 0.857229 | − | 0.514936i | \(-0.172184\pi\) | ||||
0.857229 | + | 0.514936i | \(0.172184\pi\) | |||||||
\(450\) | −671.417 | + | 1162.93i | −0.0703354 | + | 0.121824i | ||||
\(451\) | 5473.48 | + | 9480.35i | 0.571477 | + | 0.989827i | ||||
\(452\) | 224.561 | + | 388.951i | 0.0233683 | + | 0.0404750i | ||||
\(453\) | 783.181 | − | 1356.51i | 0.0812297 | − | 0.140694i | ||||
\(454\) | 1094.59 | 0.113154 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1578.83 | −0.162140 | ||||||||
\(457\) | 7115.54 | − | 12324.5i | 0.728339 | − | 1.26152i | −0.229246 | − | 0.973368i | \(-0.573626\pi\) |
0.957585 | − | 0.288151i | \(-0.0930405\pi\) | |||||||
\(458\) | 6887.44 | + | 11929.4i | 0.702683 | + | 1.21708i | ||||
\(459\) | 4080.28 | + | 7067.25i | 0.414926 | + | 0.718673i | ||||
\(460\) | −115.971 | + | 200.868i | −0.0117547 | + | 0.0203598i | ||||
\(461\) | 4960.94 | 0.501202 | 0.250601 | − | 0.968090i | \(-0.419372\pi\) | ||||
0.250601 | + | 0.968090i | \(0.419372\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15479.5 | 1.55377 | 0.776885 | − | 0.629642i | \(-0.216799\pi\) | ||||
0.776885 | + | 0.629642i | \(0.216799\pi\) | |||||||
\(464\) | 6645.00 | − | 11509.5i | 0.664841 | − | 1.15154i | ||||
\(465\) | −934.033 | − | 1617.79i | −0.0931500 | − | 0.161341i | ||||
\(466\) | −3636.43 | − | 6298.48i | −0.361490 | − | 0.626119i | ||||
\(467\) | −7407.82 | + | 12830.7i | −0.734033 | + | 1.27138i | 0.221114 | + | 0.975248i | \(0.429031\pi\) |
−0.955146 | + | 0.296134i | \(0.904303\pi\) | |||||||
\(468\) | 173.346 | 0.0171216 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5302.01 | 0.520348 | ||||||||
\(471\) | 3737.57 | − | 6473.67i | 0.365644 | − | 0.633314i | ||||
\(472\) | −7670.15 | − | 13285.1i | −0.747981 | − | 1.29554i | ||||
\(473\) | −6470.85 | − | 11207.8i | −0.629027 | − | 1.08951i | ||||
\(474\) | −3509.02 | + | 6077.79i | −0.340030 | + | 0.588950i | ||||
\(475\) | 615.534 | 0.0594582 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3161.87 | 0.303506 | ||||||||
\(478\) | 163.419 | − | 283.051i | 0.0156373 | − | 0.0270846i | ||||
\(479\) | −4549.48 | − | 7879.93i | −0.433969 | − | 0.751656i | 0.563242 | − | 0.826292i | \(-0.309554\pi\) |
−0.997211 | + | 0.0746358i | \(0.976221\pi\) | |||||||
\(480\) | −97.8581 | − | 169.495i | −0.00930540 | − | 0.0161174i | ||||
\(481\) | −1210.57 | + | 2096.77i | −0.114755 | + | 0.198762i | ||||
\(482\) | 19374.8 | 1.83091 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 248.538 | 0.0233412 | ||||||||
\(485\) | 58.6273 | − | 101.545i | 0.00548892 | − | 0.00950710i | ||||
\(486\) | −5639.42 | − | 9767.75i | −0.526356 | − | 0.911676i | ||||
\(487\) | 7495.72 | + | 12983.0i | 0.697461 | + | 1.20804i | 0.969344 | + | 0.245707i | \(0.0790202\pi\) |
−0.271883 | + | 0.962330i | \(0.587646\pi\) | |||||||
\(488\) | −7726.53 | + | 13382.7i | −0.716729 | + | 1.24141i | ||||
\(489\) | 7128.45 | 0.659222 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8243.61 | 0.757697 | 0.378848 | − | 0.925459i | \(-0.376320\pi\) | ||||
0.378848 | + | 0.925459i | \(0.376320\pi\) | |||||||
\(492\) | 101.892 | − | 176.482i | 0.00933667 | − | 0.0161716i | ||||
\(493\) | 6198.64 | + | 10736.4i | 0.566273 | + | 0.980814i | ||||
\(494\) | −1101.33 | − | 1907.57i | −0.100306 | − | 0.173736i | ||||
\(495\) | 2166.91 | − | 3753.20i | 0.196758 | − | 0.340795i | ||||
\(496\) | −8570.29 | −0.775841 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −12019.9 | −1.08157 | ||||||||
\(499\) | −4613.74 | + | 7991.24i | −0.413907 | + | 0.716908i | −0.995313 | − | 0.0967057i | \(-0.969169\pi\) |
0.581406 | + | 0.813614i | \(0.302503\pi\) | |||||||
\(500\) | 18.7120 | + | 32.4102i | 0.00167365 | + | 0.00289885i | ||||
\(501\) | 663.405 | + | 1149.05i | 0.0591591 | + | 0.102467i | ||||
\(502\) | 5495.26 | − | 9518.06i | 0.488576 | − | 0.846239i | ||||
\(503\) | 13750.9 | 1.21893 | 0.609465 | − | 0.792813i | \(-0.291384\pi\) | ||||
0.609465 | + | 0.792813i | \(0.291384\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7382.07 | 0.650491 | ||||||||
\(506\) | 10375.4 | − | 17970.6i | 0.911543 | − | 1.57884i | ||||
\(507\) | −1781.53 | − | 3085.69i | −0.156056 | − | 0.270297i | ||||
\(508\) | −62.3693 | − | 108.027i | −0.00544723 | − | 0.00943488i | ||||
\(509\) | 7771.98 | − | 13461.5i | 0.676792 | − | 1.17224i | −0.299150 | − | 0.954206i | \(-0.596703\pi\) |
0.975942 | − | 0.218032i | \(-0.0699637\pi\) | |||||||
\(510\) | 2575.26 | 0.223597 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 10869.7 | 0.938236 | ||||||||
\(513\) | −1624.24 | + | 2813.27i | −0.139789 | + | 0.242122i | ||||
\(514\) | −3171.69 | − | 5493.53i | −0.272174 | − | 0.471419i | ||||
\(515\) | 2523.61 | + | 4371.01i | 0.215929 | + | 0.374000i | ||||
\(516\) | −120.458 | + | 208.640i | −0.0102769 | + | 0.0178001i | ||||
\(517\) | −17111.5 | −1.45564 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13011.6 | 1.10047 | ||||||||
\(520\) | −1722.27 | + | 2983.06i | −0.145244 | + | 0.251569i | ||||
\(521\) | −7623.86 | − | 13204.9i | −0.641089 | − | 1.11040i | −0.985190 | − | 0.171466i | \(-0.945150\pi\) |
0.344101 | − | 0.938933i | \(-0.388184\pi\) | |||||||
\(522\) | −5383.04 | − | 9323.71i | −0.451359 | − | 0.781777i | ||||
\(523\) | −11108.1 | + | 19239.8i | −0.928723 | + | 1.60860i | −0.143263 | + | 0.989685i | \(0.545759\pi\) |
−0.785461 | + | 0.618912i | \(0.787574\pi\) | |||||||
\(524\) | −122.899 | −0.0102460 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3469.08 | 0.287565 | ||||||||
\(527\) | 3997.30 | − | 6923.53i | 0.330408 | − | 0.572284i | ||||
\(528\) | 4454.89 | + | 7716.10i | 0.367186 | + | 0.635985i | ||||
\(529\) | −5919.96 | − | 10253.7i | −0.486559 | − | 0.842745i | ||||
\(530\) | 1221.37 | − | 2115.48i | 0.100100 | − | 0.173378i | ||||
\(531\) | −12892.7 | −1.05367 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7312.50 | −0.594258 | ||||||||
\(534\) | 5987.52 | − | 10370.7i | 0.485216 | − | 0.840419i | ||||
\(535\) | 3546.27 | + | 6142.31i | 0.286577 | + | 0.496365i | ||||
\(536\) | −25.8794 | − | 44.8244i | −0.00208548 | − | 0.00361217i | ||||
\(537\) | 2832.87 | − | 4906.68i | 0.227649 | − | 0.394299i | ||||
\(538\) | 14775.9 | 1.18408 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −197.506 | −0.0157394 | ||||||||
\(541\) | 6492.65 | − | 11245.6i | 0.515972 | − | 0.893690i | −0.483856 | − | 0.875148i | \(-0.660764\pi\) |
0.999828 | − | 0.0185424i | \(-0.00590258\pi\) | |||||||
\(542\) | −1164.43 | − | 2016.86i | −0.0922818 | − | 0.159837i | ||||
\(543\) | 5268.66 | + | 9125.58i | 0.416390 | + | 0.721208i | ||||
\(544\) | 418.795 | − | 725.374i | 0.0330068 | − | 0.0571694i | ||||
\(545\) | 4389.30 | 0.344985 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8226.94 | −0.643069 | −0.321534 | − | 0.946898i | \(-0.604199\pi\) | ||||
−0.321534 | + | 0.946898i | \(0.604199\pi\) | |||||||
\(548\) | −263.761 | + | 456.847i | −0.0205608 | + | 0.0356123i | ||||
\(549\) | 6493.75 | + | 11247.5i | 0.504821 | + | 0.874375i | ||||
\(550\) | −1674.07 | − | 2899.58i | −0.129787 | − | 0.224797i | ||||
\(551\) | −2467.50 | + | 4273.84i | −0.190779 | + | 0.330438i | ||||
\(552\) | 9935.57 | 0.766098 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −519.320 | −0.0398263 | ||||||||
\(555\) | 563.408 | − | 975.851i | 0.0430907 | − | 0.0746352i | ||||
\(556\) | −129.595 | − | 224.465i | −0.00988497 | − | 0.0171213i | ||||
\(557\) | −8920.63 | − | 15451.0i | −0.678599 | − | 1.17537i | −0.975403 | − | 0.220429i | \(-0.929254\pi\) |
0.296804 | − | 0.954938i | \(-0.404079\pi\) | |||||||
\(558\) | −3471.35 | + | 6012.56i | −0.263358 | + | 0.456150i | ||||
\(559\) | 8644.97 | 0.654103 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8311.30 | −0.625496 | ||||||||
\(562\) | −4419.67 | + | 7655.09i | −0.331731 | + | 0.574574i | ||||
\(563\) | 539.199 | + | 933.919i | 0.0403633 | + | 0.0699112i | 0.885501 | − | 0.464637i | \(-0.153815\pi\) |
−0.845138 | + | 0.534548i | \(0.820482\pi\) | |||||||
\(564\) | 159.270 | + | 275.864i | 0.0118909 | + | 0.0205957i | ||||
\(565\) | −3750.28 | + | 6495.67i | −0.279248 | + | 0.483673i | ||||
\(566\) | −11143.7 | −0.827570 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −19225.0 | −1.42018 | ||||||||
\(569\) | −8493.24 | + | 14710.7i | −0.625756 | + | 1.08384i | 0.362638 | + | 0.931930i | \(0.381876\pi\) |
−0.988394 | + | 0.151911i | \(0.951457\pi\) | |||||||
\(570\) | 512.568 | + | 887.794i | 0.0376651 | + | 0.0652379i | ||||
\(571\) | 6131.49 | + | 10620.1i | 0.449378 | + | 0.778346i | 0.998346 | − | 0.0574980i | \(-0.0183123\pi\) |
−0.548968 | + | 0.835844i | \(0.684979\pi\) | |||||||
\(572\) | −216.106 | + | 374.306i | −0.0157969 | + | 0.0273610i | ||||
\(573\) | −7268.07 | −0.529891 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3873.54 | −0.280935 | ||||||||
\(576\) | 4581.34 | − | 7935.11i | 0.331405 | − | 0.574010i | ||||
\(577\) | −3525.25 | − | 6105.92i | −0.254347 | − | 0.440542i | 0.710371 | − | 0.703827i | \(-0.248527\pi\) |
−0.964718 | + | 0.263286i | \(0.915194\pi\) | |||||||
\(578\) | −1566.29 | − | 2712.90i | −0.112715 | − | 0.195228i | ||||
\(579\) | 3164.21 | − | 5480.56i | 0.227116 | − | 0.393376i | ||||
\(580\) | −300.045 | −0.0214805 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 195.281 | 0.0139083 | ||||||||
\(583\) | −3941.82 | + | 6827.42i | −0.280023 | + | 0.485014i | ||||
\(584\) | −8346.26 | − | 14456.1i | −0.591388 | − | 1.02431i | ||||
\(585\) | 1447.48 | + | 2507.11i | 0.102301 | + | 0.177190i | ||||
\(586\) | 2834.47 | − | 4909.44i | 0.199814 | − | 0.346087i | ||||
\(587\) | 20085.3 | 1.41228 | 0.706141 | − | 0.708071i | \(-0.250434\pi\) | ||||
0.706141 | + | 0.708071i | \(0.250434\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3182.42 | 0.222631 | ||||||||
\(590\) | −4980.22 | + | 8626.00i | −0.347513 | + | 0.601910i | ||||
\(591\) | −5617.00 | − | 9728.94i | −0.390952 | − | 0.677149i | ||||
\(592\) | −2584.79 | − | 4476.99i | −0.179450 | − | 0.310816i | ||||
\(593\) | −9487.17 | + | 16432.3i | −0.656984 | + | 1.13793i | 0.324409 | + | 0.945917i | \(0.394835\pi\) |
−0.981392 | + | 0.192013i | \(0.938499\pi\) | |||||||
\(594\) | 17669.9 | 1.22054 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 903.936 | 0.0621252 | ||||||||
\(597\) | 1400.98 | − | 2426.57i | 0.0960440 | − | 0.166353i | ||||
\(598\) | 6930.67 | + | 12004.3i | 0.473940 | + | 0.820888i | ||||
\(599\) | −8397.87 | − | 14545.5i | −0.572834 | − | 0.992178i | −0.996273 | − | 0.0862537i | \(-0.972510\pi\) |
0.423439 | − | 0.905925i | \(-0.360823\pi\) | |||||||
\(600\) | 801.557 | − | 1388.34i | 0.0545391 | − | 0.0944644i | ||||
\(601\) | 13624.3 | 0.924702 | 0.462351 | − | 0.886697i | \(-0.347006\pi\) | ||||
0.462351 | + | 0.886697i | \(0.347006\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −43.5006 | −0.00293778 | ||||||||
\(604\) | −81.1198 | + | 140.504i | −0.00546476 | + | 0.00946525i | ||||
\(605\) | 2075.35 | + | 3594.61i | 0.139463 | + | 0.241556i | ||||
\(606\) | 6147.21 | + | 10647.3i | 0.412068 | + | 0.713723i | ||||
\(607\) | −4199.75 | + | 7274.19i | −0.280828 | + | 0.486409i | −0.971589 | − | 0.236675i | \(-0.923942\pi\) |
0.690761 | + | 0.723083i | \(0.257276\pi\) | |||||||
\(608\) | 333.421 | 0.0222401 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10033.7 | 0.665985 | ||||||||
\(611\) | 5715.20 | − | 9899.01i | 0.378416 | − | 0.655436i | ||||
\(612\) | −172.632 | − | 299.007i | −0.0114023 | − | 0.0197494i | ||||
\(613\) | −7760.21 | − | 13441.1i | −0.511308 | − | 0.885612i | −0.999914 | − | 0.0131070i | \(-0.995828\pi\) |
0.488606 | − | 0.872505i | \(-0.337506\pi\) | |||||||
\(614\) | −7904.43 | + | 13690.9i | −0.519539 | + | 0.899868i | ||||
\(615\) | 3403.29 | 0.223144 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26665.1 | −1.73987 | −0.869933 | − | 0.493169i | \(-0.835838\pi\) | ||||
−0.869933 | + | 0.493169i | \(0.835838\pi\) | |||||||
\(618\) | −4202.92 | + | 7279.67i | −0.273570 | + | 0.473837i | ||||
\(619\) | −6115.78 | − | 10592.8i | −0.397114 | − | 0.687822i | 0.596254 | − | 0.802796i | \(-0.296655\pi\) |
−0.993369 | + | 0.114973i | \(0.963322\pi\) | |||||||
\(620\) | 96.7446 | + | 167.567i | 0.00626670 | + | 0.0108542i | ||||
\(621\) | 10221.3 | − | 17703.8i | 0.660495 | − | 1.14401i | ||||
\(622\) | −14902.1 | −0.960645 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −5951.68 | −0.381824 | ||||||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −8301.10 | − | 14377.9i | −0.529998 | − | 0.917983i | ||||
\(627\) | −1654.25 | − | 2865.24i | −0.105366 | − | 0.182498i | ||||
\(628\) | −387.128 | + | 670.525i | −0.0245988 | + | 0.0426064i | ||||
\(629\) | 4822.34 | 0.305690 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7237.27 | −0.456595 | −0.228297 | − | 0.973591i | \(-0.573316\pi\) | ||||
−0.228297 | + | 0.973591i | \(0.573316\pi\) | |||||||
\(632\) | −9348.33 | + | 16191.8i | −0.588380 | + | 1.01910i | ||||
\(633\) | 4450.96 | + | 7709.29i | 0.279478 | + | 0.484071i | ||||
\(634\) | 4581.84 | + | 7935.98i | 0.287016 | + | 0.497126i | ||||
\(635\) | 1041.60 | − | 1804.10i | 0.0650938 | − | 0.112746i | ||||
\(636\) | 146.758 | 0.00914990 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 26843.5 | 1.66575 | ||||||||
\(639\) | −8078.82 | + | 13992.9i | −0.500146 | + | 0.866278i | ||||
\(640\) | −3810.21 | − | 6599.48i | −0.235331 | − | 0.407605i | ||||
\(641\) | −2452.42 | − | 4247.71i | −0.151115 | − | 0.261739i | 0.780523 | − | 0.625127i | \(-0.214953\pi\) |
−0.931638 | + | 0.363389i | \(0.881620\pi\) | |||||||
\(642\) | −5906.10 | + | 10229.7i | −0.363077 | + | 0.628867i | ||||
\(643\) | 8394.46 | 0.514845 | 0.257422 | − | 0.966299i | \(-0.417127\pi\) | ||||
0.257422 | + | 0.966299i | \(0.417127\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4023.43 | −0.245616 | ||||||||
\(646\) | −2193.59 | + | 3799.42i | −0.133600 | + | 0.231403i | ||||
\(647\) | 4763.22 | + | 8250.15i | 0.289431 | + | 0.501309i | 0.973674 | − | 0.227945i | \(-0.0732007\pi\) |
−0.684243 | + | 0.729254i | \(0.739867\pi\) | |||||||
\(648\) | −1353.73 | − | 2344.72i | −0.0820670 | − | 0.142144i | ||||
\(649\) | 16073.0 | − | 27839.3i | 0.972143 | − | 1.68380i | ||||
\(650\) | 2236.54 | 0.134961 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −738.345 | −0.0443494 | ||||||||
\(653\) | −7975.03 | + | 13813.2i | −0.477928 | + | 0.827796i | −0.999680 | − | 0.0253017i | \(-0.991945\pi\) |
0.521752 | + | 0.853097i | \(0.325279\pi\) | |||||||
\(654\) | 3655.06 | + | 6330.75i | 0.218539 | + | 0.378520i | ||||
\(655\) | −1026.24 | − | 1777.50i | −0.0612191 | − | 0.106035i | ||||
\(656\) | 7806.78 | − | 13521.7i | 0.464639 | − | 0.804779i | ||||
\(657\) | −14029.2 | −0.833077 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3370.65 | −0.199244 | −0.0996221 | − | 0.995025i | \(-0.531763\pi\) | ||||
−0.0996221 | + | 0.995025i | \(0.531763\pi\) | |||||||
\(660\) | 100.577 | − | 174.204i | 0.00593175 | − | 0.0102741i | ||||
\(661\) | 12127.0 | + | 21004.6i | 0.713594 | + | 1.23598i | 0.963499 | + | 0.267710i | \(0.0862671\pi\) |
−0.249906 | + | 0.968270i | \(0.580400\pi\) | |||||||
\(662\) | 13299.6 | + | 23035.5i | 0.780819 | + | 1.35242i | ||||
\(663\) | 2775.95 | − | 4808.08i | 0.162608 | − | 0.281645i | ||||
\(664\) | −32022.0 | −1.87153 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4187.83 | −0.243656 | ||||||||
\(667\) | 15527.9 | − | 26895.2i | 0.901415 | − | 1.56130i | ||||
\(668\) | −68.7136 | − | 119.015i | −0.00397995 | − | 0.00689348i | ||||
\(669\) | −234.136 | − | 405.536i | −0.0135310 | − | 0.0234364i | ||||
\(670\) | −16.8035 | + | 29.1045i | −0.000968918 | + | 0.00167821i | ||||
\(671\) | −32382.3 | −1.86305 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3510.41 | −0.201064 | −0.100532 | − | 0.994934i | \(-0.532055\pi\) | ||||
−0.100532 | + | 0.994934i | \(0.532055\pi\) | |||||||
\(674\) | −4695.10 | + | 8132.15i | −0.268321 | + | 0.464746i | ||||
\(675\) | −1649.22 | − | 2856.53i | −0.0940422 | − | 0.162886i | ||||
\(676\) | 184.525 | + | 319.607i | 0.0104987 | + | 0.0181843i | ||||
\(677\) | 4525.59 | − | 7838.56i | 0.256917 | − | 0.444993i | −0.708498 | − | 0.705713i | \(-0.750627\pi\) |
0.965414 | + | 0.260720i | \(0.0839600\pi\) | |||||||
\(678\) | −12491.7 | −0.707585 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6860.71 | 0.386906 | ||||||||
\(681\) | −549.130 | + | 951.122i | −0.0308997 | + | 0.0535199i | ||||
\(682\) | −8655.27 | − | 14991.4i | −0.485964 | − | 0.841714i | ||||
\(683\) | −3552.86 | − | 6153.74i | −0.199043 | − | 0.344753i | 0.749175 | − | 0.662372i | \(-0.230450\pi\) |
−0.948219 | + | 0.317619i | \(0.897117\pi\) | |||||||
\(684\) | 68.7199 | − | 119.026i | 0.00384148 | − | 0.00665363i | ||||
\(685\) | −8809.87 | −0.491398 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13821.0 | −0.767548 | ||||||||
\(688\) | −9229.32 | + | 15985.6i | −0.511431 | + | 0.885824i | ||||
\(689\) | −2633.11 | − | 4560.68i | −0.145593 | − | 0.252174i | ||||
\(690\) | −3225.58 | − | 5586.87i | −0.177965 | − | 0.308244i | ||||
\(691\) | −6314.70 | + | 10937.4i | −0.347645 | + | 0.602138i | −0.985831 | − | 0.167744i | \(-0.946352\pi\) |
0.638186 | + | 0.769882i | \(0.279685\pi\) | |||||||
\(692\) | −1347.70 | −0.0740346 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5332.86 | −0.291690 | ||||||||
\(695\) | 2164.30 | − | 3748.67i | 0.118124 | − | 0.204597i | ||||
\(696\) | 6426.43 | + | 11130.9i | 0.349990 | + | 0.606201i | ||||
\(697\) | 7282.38 | + | 12613.5i | 0.395753 | + | 0.685464i | ||||
\(698\) | −1587.56 | + | 2749.73i | −0.0860887 | + | 0.149110i | ||||
\(699\) | 7297.23 | 0.394859 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −912.952 | −0.0491893 | −0.0245947 | − | 0.999698i | \(-0.507830\pi\) | ||||
−0.0245947 | + | 0.999698i | \(0.507830\pi\) | |||||||
\(702\) | −5901.68 | + | 10222.0i | −0.317300 | + | 0.549579i | ||||
\(703\) | 959.817 | + | 1662.45i | 0.0514939 | + | 0.0891900i | ||||
\(704\) | 11422.8 | + | 19785.0i | 0.611527 | + | 1.05920i | ||||
\(705\) | −2659.89 | + | 4607.07i | −0.142096 | + | 0.246117i | ||||
\(706\) | 7692.63 | 0.410079 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −598.416 | −0.0317653 | ||||||||
\(709\) | 10355.2 | − | 17935.8i | 0.548518 | − | 0.950061i | −0.449858 | − | 0.893100i | \(-0.648525\pi\) |
0.998376 | − | 0.0569613i | \(-0.0181412\pi\) | |||||||
\(710\) | 6241.39 | + | 10810.4i | 0.329909 | + | 0.571419i | ||||
\(711\) | 7856.79 | + | 13608.4i | 0.414420 | + | 0.717797i | ||||
\(712\) | 15951.3 | − | 27628.4i | 0.839606 | − | 1.45424i | ||||
\(713\) | −20026.9 | −1.05191 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7218.14 | −0.377543 | ||||||||
\(716\) | −293.421 | + | 508.220i | −0.0153152 | + | 0.0265266i | ||||
\(717\) | 163.967 | + | 283.999i | 0.00854040 | + | 0.0147924i | ||||
\(718\) | 627.241 | + | 1086.41i | 0.0326023 | + | 0.0564688i | ||||
\(719\) | 1234.88 | − | 2138.88i | 0.0640518 | − | 0.110941i | −0.832221 | − | 0.554444i | \(-0.812931\pi\) |
0.896273 | + | 0.443503i | \(0.146264\pi\) | |||||||
\(720\) | −6181.29 | −0.319949 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 18013.4 | 0.928520 | ||||||||
\(723\) | −9719.88 | + | 16835.3i | −0.499981 | + | 0.865992i | ||||
\(724\) | −545.713 | − | 945.203i | −0.0280128 | − | 0.0485196i | ||||
\(725\) | −2505.45 | − | 4339.56i | −0.128345 | − | 0.222300i | ||||
\(726\) | −3456.37 | + | 5986.62i | −0.176692 | + | 0.306039i | ||||
\(727\) | −10893.4 | −0.555729 | −0.277865 | − | 0.960620i | \(-0.589627\pi\) | ||||
−0.277865 | + | 0.960620i | \(0.589627\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8021.48 | 0.407533 | ||||||||
\(730\) | −5419.22 | + | 9386.37i | −0.274759 | + | 0.475897i | ||||
\(731\) | −8609.36 | − | 14911.9i | −0.435607 | − | 0.754494i | ||||
\(732\) | 301.407 | + | 522.053i | 0.0152190 | + | 0.0263601i | ||||
\(733\) | 13130.0 | − | 22741.8i | 0.661619 | − | 1.14596i | −0.318571 | − | 0.947899i | \(-0.603203\pi\) |
0.980190 | − | 0.198059i | \(-0.0634636\pi\) | |||||||
\(734\) | −7129.14 | −0.358503 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2098.21 | −0.105083 | ||||||||
\(737\) | 54.2310 | − | 93.9308i | 0.00271048 | − | 0.00469469i | ||||
\(738\) | −6324.19 | − | 10953.8i | −0.315443 | − | 0.546363i | ||||
\(739\) | 920.414 | + | 1594.20i | 0.0458160 | + | 0.0793556i | 0.888024 | − | 0.459797i | \(-0.152078\pi\) |
−0.842208 | + | 0.539153i | \(0.818745\pi\) | |||||||
\(740\) | −58.3562 | + | 101.076i | −0.00289894 | + | 0.00502112i | ||||
\(741\) | 2210.05 | 0.109566 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4022.25 | 0.198603 | 0.0993015 | − | 0.995057i | \(-0.468339\pi\) | ||||
0.0993015 | + | 0.995057i | \(0.468339\pi\) | |||||||
\(744\) | 4144.20 | − | 7177.96i | 0.204212 | − | 0.353705i | ||||
\(745\) | 7548.08 | + | 13073.7i | 0.371195 | + | 0.642929i | ||||
\(746\) | 7833.34 | + | 13567.7i | 0.384449 | + | 0.665885i | ||||
\(747\) | −13456.4 | + | 23307.2i | −0.659096 | + | 1.14159i | ||||
\(748\) | 860.862 | 0.0420805 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1040.90 | −0.0506778 | ||||||||
\(751\) | −12862.6 | + | 22278.7i | −0.624986 | + | 1.08251i | 0.363558 | + | 0.931572i | \(0.381562\pi\) |
−0.988544 | + | 0.150936i | \(0.951771\pi\) | |||||||
\(752\) | 12203.0 | + | 21136.2i | 0.591753 | + | 1.02495i | ||||
\(753\) | 5513.68 | + | 9549.97i | 0.266839 | + | 0.462178i | ||||
\(754\) | −8965.66 | + | 15529.0i | −0.433037 | + | 0.750042i | ||||
\(755\) | −2709.48 | −0.130607 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11359.2 | 0.545385 | 0.272692 | − | 0.962101i | \(-0.412086\pi\) | ||||
0.272692 | + | 0.962101i | \(0.412086\pi\) | |||||||
\(758\) | 15264.4 | − | 26438.7i | 0.731436 | − | 1.26688i | ||||
\(759\) | 10410.1 | + | 18030.9i | 0.497844 | + | 0.862292i | ||||
\(760\) | 1365.53 | + | 2365.16i | 0.0651748 | + | 0.112886i | ||||
\(761\) | 3921.69 | − | 6792.56i | 0.186808 | − | 0.323561i | −0.757376 | − | 0.652979i | \(-0.773519\pi\) |
0.944184 | + | 0.329418i | \(0.106852\pi\) | |||||||
\(762\) | 3469.45 | 0.164941 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 752.806 | 0.0356487 | ||||||||
\(765\) | 2883.04 | − | 4993.57i | 0.136257 | − | 0.236004i | ||||
\(766\) | 6728.79 | + | 11654.6i | 0.317390 | + | 0.549736i | ||||
\(767\) | 10736.7 | + | 18596.4i | 0.505448 | + | 0.875461i | ||||
\(768\) | 663.709 | − | 1149.58i | 0.0311843 | − | 0.0540127i | ||||
\(769\) | −29007.8 | −1.36027 | −0.680136 | − | 0.733086i | \(-0.738079\pi\) | ||||
−0.680136 | + | 0.733086i | \(0.738079\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6364.65 | 0.297299 | ||||||||
\(772\) | −327.740 | + | 567.662i | −0.0152793 | + | 0.0264645i | ||||
\(773\) | −339.580 | − | 588.170i | −0.0158006 | − | 0.0273674i | 0.858017 | − | 0.513621i | \(-0.171696\pi\) |
−0.873818 | + | 0.486254i | \(0.838363\pi\) | |||||||
\(774\) | 7476.57 | + | 12949.8i | 0.347209 | + | 0.601384i | ||||
\(775\) | −1615.68 | + | 2798.44i | −0.0748865 | + | 0.129707i | ||||
\(776\) | 520.245 | 0.0240666 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10249.2 | −0.472304 | ||||||||
\(779\) | −2898.91 | + | 5021.05i | −0.133330 | + | 0.230934i | ||||
\(780\) | 67.1848 | + | 116.367i | 0.00308410 | + | 0.00534183i | ||||
\(781\) | −20143.3 | − | 34889.1i | −0.922897 | − | 1.59850i | ||||
\(782\) | 13804.2 | − | 23909.6i | 0.631252 | − | 1.09336i | ||||
\(783\) | 26445.0 | 1.20698 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12930.4 | −0.587907 | ||||||||
\(786\) | 1709.14 | − | 2960.32i | 0.0775612 | − | 0.134340i | ||||
\(787\) | −12164.5 | − | 21069.6i | −0.550976 | − | 0.954318i | −0.998204 | − | 0.0598987i | \(-0.980922\pi\) |
0.447228 | − | 0.894420i | \(-0.352411\pi\) | |||||||
\(788\) | 581.794 | + | 1007.70i | 0.0263015 | + | 0.0455554i | ||||
\(789\) | −1740.35 | + | 3014.38i | −0.0785276 | + | 0.136014i | ||||
\(790\) | 12139.7 | 0.546724 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 19228.7 | 0.862703 | ||||||||
\(793\) | 10815.6 | − | 18733.1i | 0.484329 | − | 0.838882i | ||||
\(794\) | 13229.8 | + | 22914.6i | 0.591318 | + | 1.02419i | ||||
\(795\) | 1225.47 | + | 2122.57i | 0.0546702 | + | 0.0946916i | ||||
\(796\) | −145.110 | + | 251.337i | −0.00646140 | + | 0.0111915i | ||||
\(797\) | −2791.24 | −0.124054 | −0.0620269 | − | 0.998074i | \(-0.519756\pi\) | ||||
−0.0620269 | + | 0.998074i | \(0.519756\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22766.6 | −1.00804 | ||||||||
\(800\) | −169.274 | + | 293.191i | −0.00748093 | + | 0.0129573i | ||||
\(801\) | −13406.2 | − | 23220.3i | −0.591368 | − | 1.02428i | ||||
\(802\) | −13261.4 | − | 22969.4i | −0.583885 | − | 1.01132i | ||||
\(803\) | 17489.8 | − | 30293.2i | 0.768620 | − | 1.33129i | ||||
\(804\) | −2.01908 | −8.85664e−5 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11563.3 | 0.505336 | ||||||||
\(807\) | −7412.72 | + | 12839.2i | −0.323346 | + | 0.560051i | ||||
\(808\) | 16376.7 | + | 28365.3i | 0.713033 | + | 1.23501i | ||||
\(809\) | −7847.97 | − | 13593.1i | −0.341063 | − | 0.590739i | 0.643567 | − | 0.765390i | \(-0.277454\pi\) |
−0.984630 | + | 0.174651i | \(0.944120\pi\) | |||||||
\(810\) | −878.974 | + | 1522.43i | −0.0381284 | + | 0.0660403i | ||||
\(811\) | 9580.84 | 0.414832 | 0.207416 | − | 0.978253i | \(-0.433495\pi\) | ||||
0.207416 | + | 0.978253i | \(0.433495\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2336.67 | 0.100800 | ||||||||
\(814\) | 5220.85 | − | 9042.77i | 0.224804 | − | 0.389372i | ||||
\(815\) | −6165.36 | − | 10678.7i | −0.264985 | − | 0.458968i | ||||
\(816\) | 5927.17 | + | 10266.2i | 0.254280 | + | 0.440426i | ||||
\(817\) | 3427.14 | − | 5935.98i | 0.146757 | − | 0.254191i | ||||
\(818\) | −22049.2 | −0.942458 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −352.503 | −0.0150121 | ||||||||
\(821\) | −13770.5 | + | 23851.2i | −0.585376 | + | 1.01390i | 0.409452 | + | 0.912332i | \(0.365720\pi\) |
−0.994828 | + | 0.101570i | \(0.967614\pi\) | |||||||
\(822\) | −7336.16 | − | 12706.6i | −0.311287 | − | 0.539165i | ||||
\(823\) | 5873.23 | + | 10172.7i | 0.248758 | + | 0.430862i | 0.963182 | − | 0.268852i | \(-0.0866442\pi\) |
−0.714423 | + | 0.699714i | \(0.753311\pi\) | |||||||
\(824\) | −11196.9 | + | 19393.7i | −0.473379 | + | 0.819916i | ||||
\(825\) | 3359.37 | 0.141768 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20831.7 | −0.875924 | −0.437962 | − | 0.898994i | \(-0.644300\pi\) | ||||
−0.437962 | + | 0.898994i | \(0.644300\pi\) | |||||||
\(828\) | −432.453 | + | 749.030i | −0.0181507 | + | 0.0314379i | ||||
\(829\) | −1795.00 | − | 3109.03i | −0.0752027 | − | 0.130255i | 0.825972 | − | 0.563712i | \(-0.190627\pi\) |
−0.901174 | + | 0.433457i | \(0.857294\pi\) | |||||||
\(830\) | 10395.9 | + | 18006.3i | 0.434757 | + | 0.753021i | ||||
\(831\) | 260.530 | − | 451.252i | 0.0108757 | − | 0.0188372i | ||||
\(832\) | −15260.8 | −0.635904 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 7209.02 | 0.299314 | ||||||||
\(835\) | 1147.55 | − | 1987.62i | 0.0475600 | − | 0.0823764i | ||||
\(836\) | 171.342 | + | 296.773i | 0.00708851 | + | 0.0122777i | ||||
\(837\) | −8526.77 | − | 14768.8i | −0.352124 | − | 0.609897i | ||||
\(838\) | 534.205 | − | 925.271i | 0.0220213 | − | 0.0381419i | ||||
\(839\) | −10917.2 | −0.449229 | −0.224614 | − | 0.974448i | \(-0.572112\pi\) | ||||
−0.224614 | + | 0.974448i | \(0.572112\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15785.5 | 0.647239 | ||||||||
\(842\) | 1760.16 | − | 3048.68i | 0.0720416 | − | 0.124780i | ||||
\(843\) | −4434.49 | − | 7680.75i | −0.181177 | − | 0.313807i | ||||
\(844\) | −461.018 | − | 798.507i | −0.0188020 | − | 0.0325660i | ||||
\(845\) | −3081.67 | + | 5337.60i | −0.125459 | + | 0.217301i | ||||
\(846\) | 19771.1 | 0.803479 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 11244.4 | 0.455345 | ||||||||
\(849\) | 5590.52 | − | 9683.07i | 0.225991 | − | 0.391428i | ||||
\(850\) | −2227.33 | − | 3857.85i | −0.0898785 | − | 0.155674i | ||||
\(851\) | −6040.11 | − | 10461.8i | −0.243305 | − | 0.421416i | ||||
\(852\) | −374.978 | + | 649.481i | −0.0150781 | + | 0.0261160i | ||||
\(853\) | 35912.9 | 1.44154 | 0.720770 | − | 0.693175i | \(-0.243789\pi\) | ||||
0.720770 | + | 0.693175i | \(0.243789\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2295.31 | 0.0918105 | ||||||||
\(856\) | −15734.4 | + | 27252.7i | −0.628259 | + | 1.08818i | ||||
\(857\) | 19676.6 | + | 34080.9i | 0.784295 | + | 1.35844i | 0.929419 | + | 0.369025i | \(0.120308\pi\) |
−0.145124 | + | 0.989413i | \(0.546358\pi\) | |||||||
\(858\) | −6010.70 | − | 10410.8i | −0.239163 | − | 0.414242i | ||||
\(859\) | −16117.4 | + | 27916.1i | −0.640183 | + | 1.10883i | 0.345208 | + | 0.938526i | \(0.387808\pi\) |
−0.985392 | + | 0.170304i | \(0.945525\pi\) | |||||||
\(860\) | 416.736 | 0.0165239 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 43008.2 | 1.69938 | ||||||||
\(863\) | −21905.7 | + | 37941.7i | −0.864053 | + | 1.49658i | 0.00393116 | + | 0.999992i | \(0.498749\pi\) |
−0.867984 | + | 0.496592i | \(0.834585\pi\) | |||||||
\(864\) | −893.344 | − | 1547.32i | −0.0351761 | − | 0.0609269i | ||||
\(865\) | −11253.6 | − | 19491.9i | −0.442353 | − | 0.766178i | ||||
\(866\) | −6545.94 | + | 11337.9i | −0.256859 | + | 0.444893i | ||||
\(867\) | 3143.09 | 0.123120 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −39179.3 | −1.52942 | ||||||||
\(870\) | 4172.68 | − | 7227.29i | 0.162606 | − | 0.281641i | ||||
\(871\) | 36.2259 | + | 62.7452i | 0.00140926 | + | 0.00244092i | ||||
\(872\) | 9737.41 | + | 16865.7i | 0.378154 | + | 0.654982i | ||||
\(873\) | 218.620 | − | 378.660i | 0.00847555 | − | 0.0146801i | ||||
\(874\) | 10990.1 | 0.425340 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −651.165 | −0.0251151 | ||||||||
\(877\) | 4570.34 | − | 7916.06i | 0.175974 | − | 0.304796i | −0.764524 | − | 0.644596i | \(-0.777026\pi\) |
0.940498 | + | 0.339799i | \(0.110359\pi\) | |||||||
\(878\) | −13586.0 | − | 23531.6i | −0.522216 | − | 0.904504i | ||||
\(879\) | 2843.97 | + | 4925.90i | 0.109129 | + | 0.189017i | ||||
\(880\) | 7706.04 | − | 13347.2i | 0.295194 | − | 0.511290i | ||||
\(881\) | 23013.1 | 0.880058 | 0.440029 | − | 0.897984i | \(-0.354968\pi\) | ||||
0.440029 | + | 0.897984i | \(0.354968\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7448.15 | 0.283862 | 0.141931 | − | 0.989877i | \(-0.454669\pi\) | ||||
0.141931 | + | 0.989877i | \(0.454669\pi\) | |||||||
\(884\) | −287.525 | + | 498.008i | −0.0109395 | + | 0.0189478i | ||||
\(885\) | −4996.92 | − | 8654.91i | −0.189796 | − | 0.328736i | ||||
\(886\) | −7983.76 | − | 13828.3i | −0.302731 | − | 0.524345i | ||||
\(887\) | −23030.5 | + | 39890.0i | −0.871803 | + | 1.51001i | −0.0116736 | + | 0.999932i | \(0.503716\pi\) |
−0.860130 | + | 0.510076i | \(0.829617\pi\) | |||||||
\(888\) | 4999.55 | 0.188935 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −20714.3 | −0.780163 | ||||||||
\(891\) | 2836.77 | − | 4913.43i | 0.106662 | − | 0.184743i | ||||
\(892\) | 24.2512 | + | 42.0043i | 0.000910303 | + | 0.00157669i | ||||
\(893\) | −4531.37 | − | 7848.56i | −0.169806 | − | 0.294112i | ||||
\(894\) | −12570.9 | + | 21773.4i | −0.470284 | + | 0.814555i | ||||
\(895\) | −9800.55 | −0.366029 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −13907.8 | −0.517690 | ||||||||
\(898\) | 23495.8 | − | 40695.8i | 0.873122 | − | 1.51229i | ||||
\(899\) | −12953.6 | − | 22436.3i | −0.480564 | − | 0.832362i | ||||
\(900\) | 69.7767 | + | 120.857i | 0.00258432 | + | 0.00447618i | ||||
\(901\) | −5244.52 | + | 9083.78i | −0.193918 | + | 0.335876i | ||||
\(902\) | 31536.7 | 1.16414 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −33279.1 | −1.22439 | ||||||||
\(905\) | 9113.67 | − | 15785.3i | 0.334750 | − | 0.579804i | ||||
\(906\) | −2256.24 | − | 3907.92i | −0.0827358 | − | 0.143303i | ||||
\(907\) | −19248.0 | − | 33338.6i | −0.704653 | − | 1.22050i | −0.966817 | − | 0.255472i | \(-0.917769\pi\) |
0.262163 | − | 0.965024i | \(-0.415564\pi\) | |||||||
\(908\) | 56.8774 | − | 98.5146i | 0.00207879 | − | 0.00360057i | ||||
\(909\) | 27527.6 | 1.00444 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18329.1 | −0.666596 | −0.333298 | − | 0.942822i | \(-0.608162\pi\) | ||||
−0.333298 | + | 0.942822i | \(0.608162\pi\) | |||||||
\(912\) | −2359.44 | + | 4086.66i | −0.0856674 | + | 0.148380i | ||||
\(913\) | −33551.5 | − | 58112.9i | −1.21620 | − | 2.10652i | ||||
\(914\) | −20498.9 | − | 35505.2i | −0.741842 | − | 1.28491i | ||||
\(915\) | −5033.65 | + | 8718.53i | −0.181866 | + | 0.315001i | ||||
\(916\) | 1431.55 | 0.0516371 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 23509.5 | 0.845237 | ||||||||
\(919\) | 18724.2 | − | 32431.3i | 0.672094 | − | 1.16410i | −0.305216 | − | 0.952283i | \(-0.598729\pi\) |
0.977309 | − | 0.211817i | \(-0.0679381\pi\) | |||||||
\(920\) | −8593.23 | − | 14883.9i | −0.307946 | − | 0.533378i | ||||
\(921\) | −7930.93 | − | 13736.8i | −0.283749 | − | 0.491468i | ||||
\(922\) | 7145.91 | − | 12377.1i | 0.255247 | − | 0.442101i | ||||
\(923\) | 26911.1 | 0.959686 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1949.15 | −0.0692841 | ||||||||
\(926\) | 22297.3 | − | 38620.0i | 0.791289 | − | 1.37055i | ||||
\(927\) | 9410.46 | + | 16299.4i | 0.333420 | + | 0.577500i | ||||
\(928\) | −1357.14 | − | 2350.64i | −0.0480069 | − | 0.0831504i | ||||
\(929\) | 1473.17 | − | 2551.61i | 0.0520271 | − | 0.0901136i | −0.838839 | − | 0.544380i | \(-0.816765\pi\) |
0.890866 | + | 0.454266i | \(0.150098\pi\) | |||||||
\(930\) | −5381.65 | −0.189754 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −755.827 | −0.0265643 | ||||||||
\(933\) | 7476.04 | − | 12948.9i | 0.262331 | − | 0.454370i | ||||
\(934\) | 21341.0 | + | 36963.6i | 0.747642 | + | 1.29495i | ||||
\(935\) | 7188.41 | + | 12450.7i | 0.251429 | + | 0.435488i | ||||
\(936\) | −6422.31 | + | 11123.8i | −0.224273 | + | 0.388453i | ||||
\(937\) | 48870.0 | 1.70386 | 0.851928 | − | 0.523659i | \(-0.175434\pi\) | ||||
0.851928 | + | 0.523659i | \(0.175434\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16657.9 | 0.578923 | ||||||||
\(940\) | 275.504 | − | 477.187i | 0.00955953 | − | 0.0165576i | ||||
\(941\) | −10330.5 | − | 17892.9i | −0.357879 | − | 0.619864i | 0.629727 | − | 0.776816i | \(-0.283167\pi\) |
−0.987606 | + | 0.156952i | \(0.949833\pi\) | |||||||
\(942\) | −10767.5 | − | 18649.8i | −0.372423 | − | 0.645056i | ||||
\(943\) | 18242.8 | − | 31597.4i | 0.629974 | − | 1.09115i | ||||
\(944\) | −45849.6 | −1.58080 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −37283.3 | −1.28138 | ||||||||
\(947\) | −6565.16 | + | 11371.2i | −0.225279 | + | 0.390194i | −0.956403 | − | 0.292050i | \(-0.905663\pi\) |
0.731124 | + | 0.682244i | \(0.238996\pi\) | |||||||
\(948\) | 364.672 | + | 631.631i | 0.0124937 | + | 0.0216397i | ||||
\(949\) | 11683.1 | + | 20235.7i | 0.399630 | + | 0.692179i | ||||
\(950\) | 886.636 | − | 1535.70i | 0.0302803 | − | 0.0524470i | ||||
\(951\) | −9194.40 | −0.313511 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16098.9 | 0.547214 | 0.273607 | − | 0.961842i | \(-0.411783\pi\) | ||||
0.273607 | + | 0.961842i | \(0.411783\pi\) | |||||||
\(954\) | 4554.47 | − | 7888.57i | 0.154566 | − | 0.267717i | ||||
\(955\) | 6286.12 | + | 10887.9i | 0.212999 | + | 0.368925i | ||||
\(956\) | −16.9833 | − | 29.4159i | −0.000574559 | − | 0.000995165i | ||||
\(957\) | −13466.8 | + | 23325.1i | −0.454878 | + | 0.787872i | ||||
\(958\) | −26212.9 | −0.884030 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 7102.47 | 0.238783 | ||||||||
\(961\) | 6542.13 | − | 11331.3i | 0.219601 | − | 0.380360i | ||||
\(962\) | 3487.49 | + | 6040.51i | 0.116883 | + | 0.202447i | ||||
\(963\) | 13223.9 | + | 22904.5i | 0.442508 | + | 0.766447i | ||||
\(964\) | 1006.76 | − | 1743.76i | 0.0336364 | − | 0.0582600i | ||||
\(965\) | −10946.8 | −0.365172 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15916.9 | 0.529320 | 0.264660 | − | 0.964342i | \(-0.414740\pi\) | ||||
0.264660 | + | 0.964342i | \(0.414740\pi\) | |||||||
\(968\) | −9208.08 | + | 15948.9i | −0.305743 | + | 0.529562i | ||||
\(969\) | −2200.95 | − | 3812.15i | −0.0729666 | − | 0.126382i | ||||
\(970\) | −168.897 | − | 292.539i | −0.00559069 | − | 0.00968336i | ||||
\(971\) | 337.954 | − | 585.354i | 0.0111694 | − | 0.0193459i | −0.860387 | − | 0.509642i | \(-0.829778\pi\) |
0.871556 | + | 0.490296i | \(0.163111\pi\) | |||||||
\(972\) | −1172.15 | −0.0386796 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 43188.3 | 1.42078 | ||||||||
\(975\) | −1122.02 | + | 1943.39i | −0.0368547 | + | 0.0638343i | ||||
\(976\) | 23093.3 | + | 39998.8i | 0.757375 | + | 1.31181i | ||||
\(977\) | 23084.7 | + | 39983.8i | 0.755931 | + | 1.30931i | 0.944910 | + | 0.327329i | \(0.106149\pi\) |
−0.188980 | + | 0.981981i | \(0.560518\pi\) | |||||||
\(978\) | 10268.1 | − | 17784.8i | 0.335722 | − | 0.581487i | ||||
\(979\) | 66852.7 | 2.18245 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16367.6 | 0.532698 | ||||||||
\(982\) | 11874.4 | − | 20567.0i | 0.385872 | − | 0.668350i | ||||
\(983\) | −25168.1 | − | 43592.4i | −0.816620 | − | 1.41443i | −0.908159 | − | 0.418626i | \(-0.862512\pi\) |
0.0915383 | − | 0.995802i | \(-0.470822\pi\) | |||||||
\(984\) | 7550.00 | + | 13077.0i | 0.244599 | + | 0.423657i | ||||
\(985\) | −9716.24 | + | 16829.0i | −0.314300 | + | 0.544383i | ||||
\(986\) | 35714.9 | 1.15354 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −228.911 | −0.00737108 | ||||||||
\(989\) | −21566.9 | + | 37355.0i | −0.693416 | + | 1.20103i | ||||
\(990\) | −6242.58 | − | 10812.5i | −0.200406 | − | 0.347114i | ||||
\(991\) | −20093.5 | − | 34802.9i | −0.644087 | − | 1.11559i | −0.984512 | − | 0.175319i | \(-0.943904\pi\) |
0.340425 | − | 0.940272i | \(-0.389429\pi\) | |||||||
\(992\) | −875.178 | + | 1515.85i | −0.0280110 | + | 0.0485165i | ||||
\(993\) | −26688.3 | −0.852897 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4846.80 | −0.154426 | ||||||||
\(996\) | −624.579 | + | 1081.80i | −0.0198700 | + | 0.0344159i | ||||
\(997\) | 8875.10 | + | 15372.1i | 0.281923 | + | 0.488305i | 0.971858 | − | 0.235566i | \(-0.0756944\pi\) |
−0.689935 | + | 0.723871i | \(0.742361\pi\) | |||||||
\(998\) | 13291.6 | + | 23021.7i | 0.421581 | + | 0.730199i | ||||
\(999\) | 5143.34 | − | 8908.52i | 0.162891 | − | 0.282135i |
(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 | 245.4.e.p.226.5 | 12 | ||
7.2 | even | 3 | 245.4.a.p.1.2 | yes | 6 | ||
7.3 | odd | 6 | 245.4.e.q.116.5 | 12 | |||
7.4 | even | 3 | inner | 245.4.e.p.116.5 | 12 | ||
7.5 | odd | 6 | 245.4.a.o.1.2 | ✓ | 6 | ||
7.6 | odd | 2 | 245.4.e.q.226.5 | 12 | |||
21.2 | odd | 6 | 2205.4.a.ca.1.5 | 6 | |||
21.5 | even | 6 | 2205.4.a.bz.1.5 | 6 | |||
35.9 | even | 6 | 1225.4.a.bi.1.5 | 6 | |||
35.19 | odd | 6 | 1225.4.a.bj.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
245.4.a.o.1.2 | ✓ | 6 | 7.5 | odd | 6 | ||
245.4.a.p.1.2 | yes | 6 | 7.2 | even | 3 | ||
245.4.e.p.116.5 | 12 | 7.4 | even | 3 | inner | ||
245.4.e.p.226.5 | 12 | 1.1 | even | 1 | trivial | ||
245.4.e.q.116.5 | 12 | 7.3 | odd | 6 | |||
245.4.e.q.226.5 | 12 | 7.6 | odd | 2 | |||
1225.4.a.bi.1.5 | 6 | 35.9 | even | 6 | |||
1225.4.a.bj.1.5 | 6 | 35.19 | odd | 6 | |||
2205.4.a.bz.1.5 | 6 | 21.5 | even | 6 | |||
2205.4.a.ca.1.5 | 6 | 21.2 | odd | 6 |