Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,3,Mod(99,392)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(392, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("392.99");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.g (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: | \(10.6812263629\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.15582448.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 13x^{4} - 21x^{3} + 20x^{2} - 10x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.4 | ||
Root | \(0.500000 + 0.759064i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 392.99 |
Dual form | 392.3.g.j.99.3 |
$q$-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 \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(297\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.789608 | + | 1.83753i | −0.394804 | + | 0.918765i | ||||
\(3\) | 5.33225 | 1.77742 | 0.888709 | − | 0.458472i | \(-0.151603\pi\) | ||||
0.888709 | + | 0.458472i | \(0.151603\pi\) | |||||||
\(4\) | −2.75304 | − | 2.90186i | −0.688259 | − | 0.725465i | ||||
\(5\) | − | 2.15693i | − | 0.431386i | −0.976461 | − | 0.215693i | \(-0.930799\pi\) | ||
0.976461 | − | 0.215693i | \(-0.0692011\pi\) | |||||||
\(6\) | −4.21039 | + | 9.79818i | −0.701732 | + | 1.63303i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 7.50608 | − | 2.76746i | 0.938259 | − | 0.345932i | ||||
\(9\) | 19.4329 | 2.15921 | ||||||||
\(10\) | 3.96343 | + | 1.70313i | 0.396343 | + | 0.170313i | ||||
\(11\) | 5.25911 | 0.478101 | 0.239051 | − | 0.971007i | \(-0.423164\pi\) | ||||
0.239051 | + | 0.971007i | \(0.423164\pi\) | |||||||
\(12\) | −14.6799 | − | 15.4734i | −1.22332 | − | 1.28945i | ||||
\(13\) | − | 21.4116i | − | 1.64704i | −0.567285 | − | 0.823522i | \(-0.692006\pi\) | ||
0.567285 | − | 0.823522i | \(-0.307994\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 11.5013i | − | 0.766754i | ||||||
\(16\) | −0.841567 | + | 15.9779i | −0.0525979 | + | 0.998616i | ||||
\(17\) | 0.926859 | 0.0545211 | 0.0272606 | − | 0.999628i | \(-0.491322\pi\) | ||||
0.0272606 | + | 0.999628i | \(0.491322\pi\) | |||||||
\(18\) | −15.3444 | + | 35.7086i | −0.852467 | + | 1.98381i | ||||
\(19\) | −5.93010 | −0.312110 | −0.156055 | − | 0.987748i | \(-0.549878\pi\) | ||||
−0.156055 | + | 0.987748i | \(0.549878\pi\) | |||||||
\(20\) | −6.25911 | + | 5.93812i | −0.312956 | + | 0.296906i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.15264 | + | 9.66378i | −0.188756 | + | 0.439263i | ||||
\(23\) | − | 8.68920i | − | 0.377791i | −0.981997 | − | 0.188896i | \(-0.939509\pi\) | ||
0.981997 | − | 0.188896i | \(-0.0604908\pi\) | |||||||
\(24\) | 40.0243 | − | 14.7568i | 1.66768 | − | 0.614867i | ||||
\(25\) | 20.3476 | 0.813906 | ||||||||
\(26\) | 39.3444 | + | 16.9067i | 1.51325 | + | 0.650260i | ||||
\(27\) | 55.6311 | 2.06041 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.42223i | 0.324904i | 0.986716 | + | 0.162452i | \(0.0519403\pi\) | ||||
−0.986716 | + | 0.162452i | \(0.948060\pi\) | |||||||
\(30\) | 21.1340 | + | 9.08153i | 0.704467 | + | 0.302718i | ||||
\(31\) | 34.5039i | 1.11303i | 0.830837 | + | 0.556515i | \(0.187862\pi\) | ||||
−0.830837 | + | 0.556515i | \(0.812138\pi\) | |||||||
\(32\) | −28.6953 | − | 14.1626i | −0.896728 | − | 0.442583i | ||||
\(33\) | 28.0429 | 0.849786 | ||||||||
\(34\) | −0.731855 | + | 1.70313i | −0.0215252 | + | 0.0500921i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −53.4996 | − | 56.3916i | −1.48610 | − | 1.56643i | ||||
\(37\) | 12.8002i | 0.345952i | 0.984926 | + | 0.172976i | \(0.0553383\pi\) | ||||
−0.984926 | + | 0.172976i | \(0.944662\pi\) | |||||||
\(38\) | 4.68245 | − | 10.8967i | 0.123222 | − | 0.286756i | ||||
\(39\) | − | 114.172i | − | 2.92748i | ||||||
\(40\) | −5.96922 | − | 16.1901i | −0.149231 | − | 0.404752i | ||||
\(41\) | 43.1339 | 1.05205 | 0.526023 | − | 0.850470i | \(-0.323683\pi\) | ||||
0.526023 | + | 0.850470i | \(0.323683\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −41.7382 | −0.970656 | −0.485328 | − | 0.874332i | \(-0.661300\pi\) | ||||
−0.485328 | + | 0.874332i | \(0.661300\pi\) | |||||||
\(44\) | −14.4785 | − | 15.2612i | −0.329058 | − | 0.346846i | ||||
\(45\) | − | 41.9155i | − | 0.931456i | ||||||
\(46\) | 15.9667 | + | 6.86106i | 0.347101 | + | 0.149154i | ||||
\(47\) | − | 45.9983i | − | 0.978686i | −0.872091 | − | 0.489343i | \(-0.837237\pi\) | ||
0.872091 | − | 0.489343i | \(-0.162763\pi\) | |||||||
\(48\) | −4.48745 | + | 85.1980i | −0.0934885 | + | 1.77496i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −16.0667 | + | 37.3894i | −0.321333 | + | 0.747788i | ||||
\(51\) | 4.94225 | 0.0969068 | ||||||||
\(52\) | −62.1333 | + | 58.9468i | −1.19487 | + | 1.13359i | ||||
\(53\) | 74.4818i | 1.40532i | 0.711528 | + | 0.702658i | \(0.248004\pi\) | ||||
−0.711528 | + | 0.702658i | \(0.751996\pi\) | |||||||
\(54\) | −43.9267 | + | 102.224i | −0.813458 | + | 1.89303i | ||||
\(55\) | − | 11.3436i | − | 0.206246i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −31.6208 | −0.554751 | ||||||||
\(58\) | −17.3136 | − | 7.43987i | −0.298511 | − | 0.128274i | ||||
\(59\) | 53.6734 | 0.909719 | 0.454860 | − | 0.890563i | \(-0.349689\pi\) | ||||
0.454860 | + | 0.890563i | \(0.349689\pi\) | |||||||
\(60\) | −33.3752 | + | 31.6635i | −0.556253 | + | 0.527726i | ||||
\(61\) | 27.8160i | 0.456000i | 0.973661 | + | 0.228000i | \(0.0732186\pi\) | ||||
−0.973661 | + | 0.228000i | \(0.926781\pi\) | |||||||
\(62\) | −63.4020 | − | 27.2446i | −1.02261 | − | 0.439429i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 48.6823 | − | 41.5455i | 0.760661 | − | 0.649149i | ||||
\(65\) | −46.1833 | −0.710512 | ||||||||
\(66\) | −22.1429 | + | 51.5297i | −0.335499 | + | 0.780754i | ||||
\(67\) | −78.4907 | −1.17150 | −0.585751 | − | 0.810491i | \(-0.699201\pi\) | ||||
−0.585751 | + | 0.810491i | \(0.699201\pi\) | |||||||
\(68\) | −2.55168 | − | 2.68961i | −0.0375247 | − | 0.0395531i | ||||
\(69\) | − | 46.3330i | − | 0.671493i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 74.5100i | 1.04944i | 0.851276 | + | 0.524719i | \(0.175829\pi\) | ||||
−0.851276 | + | 0.524719i | \(0.824171\pi\) | |||||||
\(72\) | 145.865 | − | 53.7799i | 2.02590 | − | 0.746943i | ||||
\(73\) | 33.6041 | 0.460330 | 0.230165 | − | 0.973152i | \(-0.426073\pi\) | ||||
0.230165 | + | 0.973152i | \(0.426073\pi\) | |||||||
\(74\) | −23.5208 | − | 10.1072i | −0.317848 | − | 0.136583i | ||||
\(75\) | 108.499 | 1.44665 | ||||||||
\(76\) | 16.3258 | + | 17.2083i | 0.214813 | + | 0.226425i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 209.794 | + | 90.1511i | 2.68967 | + | 1.15578i | ||||
\(79\) | 30.2118i | 0.382428i | 0.981548 | + | 0.191214i | \(0.0612424\pi\) | ||||
−0.981548 | + | 0.191214i | \(0.938758\pi\) | |||||||
\(80\) | 34.4631 | + | 1.81520i | 0.430789 | + | 0.0226900i | ||||
\(81\) | 121.743 | 1.50299 | ||||||||
\(82\) | −34.0589 | + | 79.2599i | −0.415352 | + | 0.966584i | ||||
\(83\) | −72.9274 | −0.878644 | −0.439322 | − | 0.898330i | \(-0.644781\pi\) | ||||
−0.439322 | + | 0.898330i | \(0.644781\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 1.99917i | − | 0.0235197i | ||||||
\(86\) | 32.9568 | − | 76.6952i | 0.383219 | − | 0.891805i | ||||
\(87\) | 50.2417i | 0.577491i | ||||||||
\(88\) | 39.4753 | − | 14.5544i | 0.448583 | − | 0.165391i | ||||
\(89\) | −54.8396 | −0.616176 | −0.308088 | − | 0.951358i | \(-0.599689\pi\) | ||||
−0.308088 | + | 0.951358i | \(0.599689\pi\) | |||||||
\(90\) | 77.0211 | + | 33.0968i | 0.855790 | + | 0.367743i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −25.2148 | + | 23.9217i | −0.274074 | + | 0.260018i | ||||
\(93\) | 183.984i | 1.97832i | ||||||||
\(94\) | 84.5232 | + | 36.3206i | 0.899183 | + | 0.386389i | ||||
\(95\) | 12.7908i | 0.134640i | ||||||||
\(96\) | −153.011 | − | 75.5188i | −1.59386 | − | 0.786655i | ||||
\(97\) | −53.7125 | −0.553738 | −0.276869 | − | 0.960908i | \(-0.589297\pi\) | ||||
−0.276869 | + | 0.960908i | \(0.589297\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 102.200 | 1.03232 | ||||||||
\(100\) | −56.0178 | − | 59.0460i | −0.560178 | − | 0.590460i | ||||
\(101\) | − | 90.3019i | − | 0.894078i | −0.894515 | − | 0.447039i | \(-0.852479\pi\) | ||
0.894515 | − | 0.447039i | \(-0.147521\pi\) | |||||||
\(102\) | −3.90244 | + | 9.08153i | −0.0382592 | + | 0.0890346i | ||||
\(103\) | 112.812i | 1.09526i | 0.836720 | + | 0.547631i | \(0.184470\pi\) | ||||
−0.836720 | + | 0.547631i | \(0.815530\pi\) | |||||||
\(104\) | −59.2556 | − | 160.717i | −0.569766 | − | 1.54535i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −136.863 | − | 58.8114i | −1.29116 | − | 0.554825i | ||||
\(107\) | −143.990 | −1.34570 | −0.672851 | − | 0.739778i | \(-0.734930\pi\) | ||||
−0.672851 | + | 0.739778i | \(0.734930\pi\) | |||||||
\(108\) | −153.154 | − | 161.433i | −1.41810 | − | 1.49475i | ||||
\(109\) | − | 66.6813i | − | 0.611755i | −0.952071 | − | 0.305877i | \(-0.901050\pi\) | ||
0.952071 | − | 0.305877i | \(-0.0989498\pi\) | |||||||
\(110\) | 20.8441 | + | 8.95696i | 0.189492 | + | 0.0814269i | ||||
\(111\) | 68.2540i | 0.614901i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.16467 | 0.0634042 | 0.0317021 | − | 0.999497i | \(-0.489907\pi\) | ||||
0.0317021 | + | 0.999497i | \(0.489907\pi\) | |||||||
\(114\) | 24.9680 | − | 58.1042i | 0.219018 | − | 0.509686i | ||||
\(115\) | −18.7420 | −0.162974 | ||||||||
\(116\) | 27.3420 | − | 25.9397i | 0.235707 | − | 0.223618i | ||||
\(117\) | − | 416.090i | − | 3.55632i | ||||||
\(118\) | −42.3810 | + | 98.6266i | −0.359161 | + | 0.835818i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −31.8294 | − | 86.3297i | −0.265245 | − | 0.719414i | ||||
\(121\) | −93.3417 | −0.771419 | ||||||||
\(122\) | −51.1127 | − | 21.9637i | −0.418957 | − | 0.180031i | ||||
\(123\) | 230.001 | 1.86993 | ||||||||
\(124\) | 100.126 | − | 94.9906i | 0.807464 | − | 0.766054i | ||||
\(125\) | − | 97.8118i | − | 0.782494i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 131.492i | 1.03537i | 0.855572 | + | 0.517684i | \(0.173206\pi\) | ||||
−0.855572 | + | 0.517684i | \(0.826794\pi\) | |||||||
\(128\) | 37.9012 | + | 122.260i | 0.296103 | + | 0.955156i | ||||
\(129\) | −222.559 | −1.72526 | ||||||||
\(130\) | 36.4667 | − | 84.8632i | 0.280513 | − | 0.652794i | ||||
\(131\) | −8.76120 | −0.0668794 | −0.0334397 | − | 0.999441i | \(-0.510646\pi\) | ||||
−0.0334397 | + | 0.999441i | \(0.510646\pi\) | |||||||
\(132\) | −77.2032 | − | 81.3766i | −0.584873 | − | 0.616489i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 61.9769 | − | 144.229i | 0.462514 | − | 1.07634i | ||||
\(135\) | − | 119.992i | − | 0.888833i | ||||||
\(136\) | 6.95707 | − | 2.56504i | 0.0511549 | − | 0.0188606i | ||||
\(137\) | −236.841 | −1.72876 | −0.864381 | − | 0.502837i | \(-0.832290\pi\) | ||||
−0.864381 | + | 0.502837i | \(0.832290\pi\) | |||||||
\(138\) | 85.1383 | + | 36.5849i | 0.616944 | + | 0.265108i | ||||
\(139\) | 172.122 | 1.23828 | 0.619142 | − | 0.785279i | \(-0.287480\pi\) | ||||
0.619142 | + | 0.785279i | \(0.287480\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 245.274i | − | 1.73954i | ||||||
\(142\) | −136.914 | − | 58.8337i | −0.964186 | − | 0.414322i | ||||
\(143\) | − | 112.606i | − | 0.787453i | ||||||
\(144\) | −16.3541 | + | 310.497i | −0.113570 | + | 2.15623i | ||||
\(145\) | 20.3231 | 0.140159 | ||||||||
\(146\) | −26.5341 | + | 61.7485i | −0.181740 | + | 0.422935i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 37.1444 | − | 35.2395i | 0.250976 | − | 0.238105i | ||||
\(149\) | − | 230.707i | − | 1.54837i | −0.632959 | − | 0.774186i | \(-0.718160\pi\) | ||
0.632959 | − | 0.774186i | \(-0.281840\pi\) | |||||||
\(150\) | −85.6715 | + | 199.370i | −0.571144 | + | 1.32913i | ||||
\(151\) | 147.890i | 0.979406i | 0.871889 | + | 0.489703i | \(0.162895\pi\) | ||||
−0.871889 | + | 0.489703i | \(0.837105\pi\) | |||||||
\(152\) | −44.5118 | + | 16.4113i | −0.292840 | + | 0.107969i | ||||
\(153\) | 18.0116 | 0.117723 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 74.4227 | 0.480146 | ||||||||
\(156\) | −331.311 | + | 314.320i | −2.12379 | + | 2.01487i | ||||
\(157\) | − | 114.829i | − | 0.731396i | −0.930734 | − | 0.365698i | \(-0.880830\pi\) | ||
0.930734 | − | 0.365698i | \(-0.119170\pi\) | |||||||
\(158\) | −55.5151 | − | 23.8555i | −0.351361 | − | 0.150984i | ||||
\(159\) | 397.156i | 2.49783i | ||||||||
\(160\) | −30.5479 | + | 61.8938i | −0.190924 | + | 0.386836i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −96.1289 | + | 223.706i | −0.593388 | + | 1.38090i | ||||
\(163\) | 49.3091 | 0.302510 | 0.151255 | − | 0.988495i | \(-0.451669\pi\) | ||||
0.151255 | + | 0.988495i | \(0.451669\pi\) | |||||||
\(164\) | −118.749 | − | 125.168i | −0.724081 | − | 0.763222i | ||||
\(165\) | − | 60.4867i | − | 0.366586i | ||||||
\(166\) | 57.5841 | − | 134.006i | 0.346892 | − | 0.807267i | ||||
\(167\) | − | 241.457i | − | 1.44585i | −0.690926 | − | 0.722926i | \(-0.742797\pi\) | ||
0.690926 | − | 0.722926i | \(-0.257203\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −289.455 | −1.71275 | ||||||||
\(170\) | 3.67354 | + | 1.57856i | 0.0216091 | + | 0.00928566i | ||||
\(171\) | −115.239 | −0.673913 | ||||||||
\(172\) | 114.907 | + | 121.118i | 0.668063 | + | 0.704177i | ||||
\(173\) | − | 54.4211i | − | 0.314573i | −0.987553 | − | 0.157286i | \(-0.949725\pi\) | ||
0.987553 | − | 0.157286i | \(-0.0502746\pi\) | |||||||
\(174\) | −92.3207 | − | 39.6713i | −0.530579 | − | 0.227996i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.42590 | + | 84.0293i | −0.0251471 | + | 0.477439i | ||||
\(177\) | 286.200 | 1.61695 | ||||||||
\(178\) | 43.3018 | − | 100.770i | 0.243269 | − | 0.566121i | ||||
\(179\) | −127.020 | −0.709609 | −0.354805 | − | 0.934940i | \(-0.615453\pi\) | ||||
−0.354805 | + | 0.934940i | \(0.615453\pi\) | |||||||
\(180\) | −121.633 | + | 115.395i | −0.675739 | + | 0.641083i | ||||
\(181\) | 212.704i | 1.17516i | 0.809165 | + | 0.587581i | \(0.199920\pi\) | ||||
−0.809165 | + | 0.587581i | \(0.800080\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 148.322i | 0.810502i | ||||||||
\(184\) | −24.0470 | − | 65.2218i | −0.130690 | − | 0.354466i | ||||
\(185\) | 27.6092 | 0.149239 | ||||||||
\(186\) | −338.076 | − | 145.275i | −1.81761 | − | 0.781049i | ||||
\(187\) | 4.87446 | 0.0260666 | ||||||||
\(188\) | −133.480 | + | 126.635i | −0.710002 | + | 0.673590i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −23.5035 | − | 10.0997i | −0.123703 | − | 0.0531565i | ||||
\(191\) | − | 40.5347i | − | 0.212224i | −0.994354 | − | 0.106112i | \(-0.966160\pi\) | ||
0.994354 | − | 0.106112i | \(-0.0338402\pi\) | |||||||
\(192\) | 259.587 | − | 221.531i | 1.35201 | − | 1.15381i | ||||
\(193\) | 282.307 | 1.46273 | 0.731364 | − | 0.681987i | \(-0.238884\pi\) | ||||
0.731364 | + | 0.681987i | \(0.238884\pi\) | |||||||
\(194\) | 42.4119 | − | 98.6985i | 0.218618 | − | 0.508755i | ||||
\(195\) | −246.261 | −1.26288 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 261.806i | − | 1.32896i | −0.747304 | − | 0.664482i | \(-0.768652\pi\) | ||
0.747304 | − | 0.664482i | \(-0.231348\pi\) | |||||||
\(198\) | −80.6980 | + | 187.796i | −0.407565 | + | 0.948463i | ||||
\(199\) | 322.124i | 1.61871i | 0.587317 | + | 0.809357i | \(0.300184\pi\) | ||||
−0.587317 | + | 0.809357i | \(0.699816\pi\) | |||||||
\(200\) | 152.731 | − | 56.3113i | 0.763655 | − | 0.281556i | ||||
\(201\) | −418.532 | −2.08225 | ||||||||
\(202\) | 165.932 | + | 71.3031i | 0.821448 | + | 0.352986i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −13.6062 | − | 14.3417i | −0.0666970 | − | 0.0703025i | ||||
\(205\) | − | 93.0369i | − | 0.453839i | ||||||
\(206\) | −207.295 | − | 89.0773i | −1.00629 | − | 0.432414i | ||||
\(207\) | − | 168.857i | − | 0.815732i | ||||||
\(208\) | 342.111 | + | 18.0193i | 1.64476 | + | 0.0866311i | ||||
\(209\) | −31.1870 | −0.149220 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 169.792 | 0.804702 | 0.402351 | − | 0.915485i | \(-0.368193\pi\) | ||||
0.402351 | + | 0.915485i | \(0.368193\pi\) | |||||||
\(212\) | 216.136 | − | 205.051i | 1.01951 | − | 0.967222i | ||||
\(213\) | 397.306i | 1.86529i | ||||||||
\(214\) | 113.696 | − | 264.586i | 0.531288 | − | 1.23638i | ||||
\(215\) | 90.0265i | 0.418728i | ||||||||
\(216\) | 417.571 | − | 153.957i | 1.93320 | − | 0.712763i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 122.529 | + | 52.6521i | 0.562059 | + | 0.241523i | ||||
\(219\) | 179.185 | 0.818199 | ||||||||
\(220\) | −32.9174 | + | 31.2292i | −0.149624 | + | 0.141951i | ||||
\(221\) | − | 19.8455i | − | 0.0897986i | ||||||
\(222\) | −125.419 | − | 53.8939i | −0.564950 | − | 0.242765i | ||||
\(223\) | 45.4626i | 0.203868i | 0.994791 | + | 0.101934i | \(0.0325031\pi\) | ||||
−0.994791 | + | 0.101934i | \(0.967497\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 395.414 | 1.75740 | ||||||||
\(226\) | −5.65728 | + | 13.1653i | −0.0250322 | + | 0.0582536i | ||||
\(227\) | 185.131 | 0.815554 | 0.407777 | − | 0.913082i | \(-0.366304\pi\) | ||||
0.407777 | + | 0.913082i | \(0.366304\pi\) | |||||||
\(228\) | 87.0532 | + | 91.7590i | 0.381812 | + | 0.402452i | ||||
\(229\) | 184.952i | 0.807650i | 0.914836 | + | 0.403825i | \(0.132320\pi\) | ||||
−0.914836 | + | 0.403825i | \(0.867680\pi\) | |||||||
\(230\) | 14.7988 | − | 34.4390i | 0.0643428 | − | 0.149735i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 26.0756 | + | 70.7239i | 0.112395 | + | 0.304845i | ||||
\(233\) | 96.7007 | 0.415025 | 0.207512 | − | 0.978232i | \(-0.433463\pi\) | ||||
0.207512 | + | 0.978232i | \(0.433463\pi\) | |||||||
\(234\) | 764.577 | + | 328.548i | 3.26742 | + | 1.40405i | ||||
\(235\) | −99.2151 | −0.422192 | ||||||||
\(236\) | −147.765 | − | 155.753i | −0.626123 | − | 0.659969i | ||||
\(237\) | 161.097i | 0.679734i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 163.185i | 0.682782i | 0.939921 | + | 0.341391i | \(0.110898\pi\) | ||||
−0.939921 | + | 0.341391i | \(0.889102\pi\) | |||||||
\(240\) | 183.766 | + | 9.67913i | 0.765693 | + | 0.0403297i | ||||
\(241\) | 205.491 | 0.852659 | 0.426330 | − | 0.904568i | \(-0.359806\pi\) | ||||
0.426330 | + | 0.904568i | \(0.359806\pi\) | |||||||
\(242\) | 73.7034 | − | 171.518i | 0.304559 | − | 0.708753i | ||||
\(243\) | 148.483 | 0.611039 | ||||||||
\(244\) | 80.7180 | − | 76.5784i | 0.330812 | − | 0.313846i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −181.611 | + | 422.634i | −0.738254 | + | 1.71802i | ||||
\(247\) | 126.973i | 0.514059i | ||||||||
\(248\) | 95.4882 | + | 258.989i | 0.385033 | + | 1.04431i | ||||
\(249\) | −388.868 | −1.56172 | ||||||||
\(250\) | 179.732 | + | 77.2330i | 0.718929 | + | 0.308932i | ||||
\(251\) | −159.299 | −0.634658 | −0.317329 | − | 0.948316i | \(-0.602786\pi\) | ||||
−0.317329 | + | 0.948316i | \(0.602786\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 45.6975i | − | 0.180622i | ||||||
\(254\) | −241.620 | − | 103.827i | −0.951260 | − | 0.408767i | ||||
\(255\) | − | 10.6601i | − | 0.0418043i | ||||||
\(256\) | −254.584 | − | 26.8929i | −0.994467 | − | 0.105050i | ||||
\(257\) | 215.777 | 0.839599 | 0.419800 | − | 0.907617i | \(-0.362100\pi\) | ||||
0.419800 | + | 0.907617i | \(0.362100\pi\) | |||||||
\(258\) | 175.734 | − | 408.959i | 0.681140 | − | 1.58511i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 127.144 | + | 134.017i | 0.489017 | + | 0.515452i | ||||
\(261\) | 183.101i | 0.701538i | ||||||||
\(262\) | 6.91792 | − | 16.0990i | 0.0264043 | − | 0.0614465i | ||||
\(263\) | 329.157i | 1.25155i | 0.780004 | + | 0.625775i | \(0.215217\pi\) | ||||
−0.780004 | + | 0.625775i | \(0.784783\pi\) | |||||||
\(264\) | 210.492 | − | 77.6077i | 0.797319 | − | 0.293968i | ||||
\(265\) | 160.652 | 0.606234 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −292.419 | −1.09520 | ||||||||
\(268\) | 216.088 | + | 227.769i | 0.806298 | + | 0.849884i | ||||
\(269\) | − | 293.067i | − | 1.08947i | −0.838609 | − | 0.544734i | \(-0.816631\pi\) | ||
0.838609 | − | 0.544734i | \(-0.183369\pi\) | |||||||
\(270\) | 220.490 | + | 94.7470i | 0.816629 | + | 0.350915i | ||||
\(271\) | 26.8502i | 0.0990782i | 0.998772 | + | 0.0495391i | \(0.0157752\pi\) | ||||
−0.998772 | + | 0.0495391i | \(0.984225\pi\) | |||||||
\(272\) | −0.780014 | + | 14.8092i | −0.00286770 | + | 0.0544456i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 187.011 | − | 435.202i | 0.682523 | − | 1.58833i | ||||
\(275\) | 107.011 | 0.389129 | ||||||||
\(276\) | −134.452 | + | 127.557i | −0.487144 | + | 0.462161i | ||||
\(277\) | 334.777i | 1.20858i | 0.796764 | + | 0.604291i | \(0.206543\pi\) | ||||
−0.796764 | + | 0.604291i | \(0.793457\pi\) | |||||||
\(278\) | −135.909 | + | 316.279i | −0.488880 | + | 1.13769i | ||||
\(279\) | 670.513i | 2.40327i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −123.357 | −0.438994 | −0.219497 | − | 0.975613i | \(-0.570442\pi\) | ||||
−0.219497 | + | 0.975613i | \(0.570442\pi\) | |||||||
\(282\) | 450.699 | + | 193.671i | 1.59822 | + | 0.686776i | ||||
\(283\) | −0.618906 | −0.00218695 | −0.00109347 | − | 0.999999i | \(-0.500348\pi\) | ||||
−0.00109347 | + | 0.999999i | \(0.500348\pi\) | |||||||
\(284\) | 216.218 | − | 205.129i | 0.761330 | − | 0.722285i | ||||
\(285\) | 68.2039i | 0.239312i | ||||||||
\(286\) | 206.917 | + | 88.9145i | 0.723485 | + | 0.310890i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −557.634 | − | 275.222i | −1.93623 | − | 0.955631i | ||||
\(289\) | −288.141 | −0.997027 | ||||||||
\(290\) | −16.0473 | + | 37.3443i | −0.0553355 | + | 0.128774i | ||||
\(291\) | −286.409 | −0.984223 | ||||||||
\(292\) | −92.5133 | − | 97.5143i | −0.316826 | − | 0.333953i | ||||
\(293\) | 28.2794i | 0.0965169i | 0.998835 | + | 0.0482584i | \(0.0153671\pi\) | ||||
−0.998835 | + | 0.0482584i | \(0.984633\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 115.770i | − | 0.392440i | ||||||
\(296\) | 35.4241 | + | 96.0794i | 0.119676 | + | 0.324592i | ||||
\(297\) | 292.570 | 0.985084 | ||||||||
\(298\) | 423.932 | + | 182.168i | 1.42259 | + | 0.611303i | ||||
\(299\) | −186.049 | −0.622239 | ||||||||
\(300\) | −298.701 | − | 314.848i | −0.995671 | − | 1.04949i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −271.753 | − | 116.775i | −0.899844 | − | 0.386674i | ||||
\(303\) | − | 481.512i | − | 1.58915i | ||||||
\(304\) | 4.99057 | − | 94.7502i | 0.0164164 | − | 0.311678i | ||||
\(305\) | 59.9972 | 0.196712 | ||||||||
\(306\) | −14.2221 | + | 33.0968i | −0.0464774 | + | 0.108160i | ||||
\(307\) | 400.893 | 1.30584 | 0.652921 | − | 0.757426i | \(-0.273543\pi\) | ||||
0.652921 | + | 0.757426i | \(0.273543\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 601.542i | 1.94674i | ||||||||
\(310\) | −58.7647 | + | 136.754i | −0.189564 | + | 0.441142i | ||||
\(311\) | − | 162.226i | − | 0.521628i | −0.965389 | − | 0.260814i | \(-0.916009\pi\) | ||
0.965389 | − | 0.260814i | \(-0.0839910\pi\) | |||||||
\(312\) | −315.966 | − | 856.983i | −1.01271 | − | 2.74674i | ||||
\(313\) | −266.246 | −0.850626 | −0.425313 | − | 0.905046i | \(-0.639836\pi\) | ||||
−0.425313 | + | 0.905046i | \(0.639836\pi\) | |||||||
\(314\) | 211.002 | + | 90.6700i | 0.671981 | + | 0.288758i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 87.6704 | − | 83.1742i | 0.277438 | − | 0.263210i | ||||
\(317\) | 432.855i | 1.36547i | 0.730664 | + | 0.682737i | \(0.239211\pi\) | ||||
−0.730664 | + | 0.682737i | \(0.760789\pi\) | |||||||
\(318\) | −729.786 | − | 313.597i | −2.29492 | − | 0.986155i | ||||
\(319\) | 49.5525i | 0.155337i | ||||||||
\(320\) | −89.6109 | − | 105.005i | −0.280034 | − | 0.328139i | ||||
\(321\) | −767.792 | −2.39187 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.49636 | −0.0170166 | ||||||||
\(324\) | −335.162 | − | 353.280i | −1.03445 | − | 1.09037i | ||||
\(325\) | − | 435.675i | − | 1.34054i | ||||||
\(326\) | −38.9349 | + | 90.6069i | −0.119432 | + | 0.277935i | ||||
\(327\) | − | 355.562i | − | 1.08734i | ||||||
\(328\) | 323.766 | − | 119.371i | 0.987092 | − | 0.363937i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 111.146 | + | 47.7608i | 0.336807 | + | 0.144730i | ||||
\(331\) | 81.2529 | 0.245477 | 0.122738 | − | 0.992439i | \(-0.460832\pi\) | ||||
0.122738 | + | 0.992439i | \(0.460832\pi\) | |||||||
\(332\) | 200.772 | + | 211.625i | 0.604735 | + | 0.637425i | ||||
\(333\) | 248.746i | 0.746984i | ||||||||
\(334\) | 443.685 | + | 190.657i | 1.32840 | + | 0.570828i | ||||
\(335\) | 169.299i | 0.505370i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −69.4941 | −0.206214 | −0.103107 | − | 0.994670i | \(-0.532878\pi\) | ||||
−0.103107 | + | 0.994670i | \(0.532878\pi\) | |||||||
\(338\) | 228.556 | − | 531.883i | 0.676202 | − | 1.57362i | ||||
\(339\) | 38.2038 | 0.112696 | ||||||||
\(340\) | −5.80131 | + | 5.50380i | −0.0170627 | + | 0.0161876i | ||||
\(341\) | 181.460i | 0.532141i | ||||||||
\(342\) | 90.9938 | − | 211.756i | 0.266064 | − | 0.619168i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −313.290 | + | 115.509i | −0.910727 | + | 0.335781i | ||||
\(345\) | −99.9372 | −0.289673 | ||||||||
\(346\) | 100.000 | + | 42.9713i | 0.289018 | + | 0.124195i | ||||
\(347\) | −349.353 | −1.00678 | −0.503391 | − | 0.864059i | \(-0.667915\pi\) | ||||
−0.503391 | + | 0.864059i | \(0.667915\pi\) | |||||||
\(348\) | 145.794 | − | 138.317i | 0.418949 | − | 0.397463i | ||||
\(349\) | − | 165.836i | − | 0.475174i | −0.971366 | − | 0.237587i | \(-0.923643\pi\) | ||
0.971366 | − | 0.237587i | \(-0.0763566\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 1191.15i | − | 3.39358i | ||||||
\(352\) | −150.912 | − | 74.4830i | −0.428727 | − | 0.211599i | ||||
\(353\) | −471.717 | −1.33631 | −0.668154 | − | 0.744023i | \(-0.732915\pi\) | ||||
−0.668154 | + | 0.744023i | \(0.732915\pi\) | |||||||
\(354\) | −225.986 | + | 525.902i | −0.638379 | + | 1.48560i | ||||
\(355\) | 160.713 | 0.452713 | ||||||||
\(356\) | 150.976 | + | 159.137i | 0.424089 | + | 0.447014i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 100.296 | − | 233.403i | 0.280157 | − | 0.651964i | ||||
\(359\) | 656.986i | 1.83004i | 0.403403 | + | 0.915022i | \(0.367827\pi\) | ||||
−0.403403 | + | 0.915022i | \(0.632173\pi\) | |||||||
\(360\) | −116.000 | − | 314.621i | −0.322221 | − | 0.873947i | ||||
\(361\) | −325.834 | −0.902587 | ||||||||
\(362\) | −390.851 | − | 167.953i | −1.07970 | − | 0.463959i | ||||
\(363\) | −497.722 | −1.37113 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 72.4817i | − | 0.198580i | ||||||
\(366\) | −272.546 | − | 117.116i | −0.744661 | − | 0.319990i | ||||
\(367\) | 355.475i | 0.968596i | 0.874903 | + | 0.484298i | \(0.160925\pi\) | ||||
−0.874903 | + | 0.484298i | \(0.839075\pi\) | |||||||
\(368\) | 138.835 | + | 7.31254i | 0.377268 | + | 0.0198710i | ||||
\(369\) | 838.218 | 2.27159 | ||||||||
\(370\) | −21.8004 | + | 50.7327i | −0.0589201 | + | 0.137116i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 533.895 | − | 506.514i | 1.43520 | − | 1.36160i | ||||
\(373\) | − | 315.998i | − | 0.847180i | −0.905854 | − | 0.423590i | \(-0.860770\pi\) | ||
0.905854 | − | 0.423590i | \(-0.139230\pi\) | |||||||
\(374\) | −3.84891 | + | 8.95696i | −0.0102912 | + | 0.0239491i | ||||
\(375\) | − | 521.557i | − | 1.39082i | ||||||
\(376\) | −127.298 | − | 345.266i | −0.338559 | − | 0.918262i | ||||
\(377\) | 201.745 | 0.535132 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −178.404 | −0.470723 | −0.235361 | − | 0.971908i | \(-0.575627\pi\) | ||||
−0.235361 | + | 0.971908i | \(0.575627\pi\) | |||||||
\(380\) | 37.1171 | − | 35.2136i | 0.0976767 | − | 0.0926674i | ||||
\(381\) | 701.147i | 1.84028i | ||||||||
\(382\) | 74.4838 | + | 32.0066i | 0.194984 | + | 0.0837868i | ||||
\(383\) | − | 698.400i | − | 1.82350i | −0.410746 | − | 0.911750i | \(-0.634732\pi\) | ||
0.410746 | − | 0.911750i | \(-0.365268\pi\) | |||||||
\(384\) | 202.099 | + | 651.921i | 0.526299 | + | 1.69771i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −222.912 | + | 518.747i | −0.577491 | + | 1.34390i | ||||
\(387\) | −811.096 | −2.09586 | ||||||||
\(388\) | 147.873 | + | 155.866i | 0.381115 | + | 0.401717i | ||||
\(389\) | 175.358i | 0.450792i | 0.974267 | + | 0.225396i | \(0.0723676\pi\) | ||||
−0.974267 | + | 0.225396i | \(0.927632\pi\) | |||||||
\(390\) | 194.450 | − | 452.512i | 0.498589 | − | 1.16029i | ||||
\(391\) | − | 8.05366i | − | 0.0205976i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −46.7170 | −0.118873 | ||||||||
\(394\) | 481.077 | + | 206.724i | 1.22101 | + | 0.524681i | ||||
\(395\) | 65.1648 | 0.164974 | ||||||||
\(396\) | −281.360 | − | 296.570i | −0.710506 | − | 0.748914i | ||||
\(397\) | 385.708i | 0.971557i | 0.874082 | + | 0.485778i | \(0.161464\pi\) | ||||
−0.874082 | + | 0.485778i | \(0.838536\pi\) | |||||||
\(398\) | −591.913 | − | 254.352i | −1.48722 | − | 0.639075i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −17.1239 | + | 325.112i | −0.0428098 | + | 0.812779i | ||||
\(401\) | 527.096 | 1.31446 | 0.657228 | − | 0.753692i | \(-0.271729\pi\) | ||||
0.657228 | + | 0.753692i | \(0.271729\pi\) | |||||||
\(402\) | 330.477 | − | 769.066i | 0.822081 | − | 1.91310i | ||||
\(403\) | 738.783 | 1.83321 | ||||||||
\(404\) | −262.043 | + | 248.604i | −0.648622 | + | 0.615357i | ||||
\(405\) | − | 262.590i | − | 0.648371i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 67.3178i | 0.165400i | ||||||||
\(408\) | 37.0969 | − | 13.6775i | 0.0909237 | − | 0.0335232i | ||||
\(409\) | −423.744 | −1.03605 | −0.518025 | − | 0.855366i | \(-0.673333\pi\) | ||||
−0.518025 | + | 0.855366i | \(0.673333\pi\) | |||||||
\(410\) | 170.958 | + | 73.4627i | 0.416971 | + | 0.179177i | ||||
\(411\) | −1262.89 | −3.07273 | ||||||||
\(412\) | 327.364 | − | 310.576i | 0.794574 | − | 0.753824i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 310.279 | + | 133.331i | 0.749467 | + | 0.322055i | ||||
\(415\) | 157.300i | 0.379035i | ||||||||
\(416\) | −303.244 | + | 614.411i | −0.728953 | + | 1.47695i | ||||
\(417\) | 917.796 | 2.20095 | ||||||||
\(418\) | 24.6255 | − | 57.3072i | 0.0589128 | − | 0.137098i | ||||
\(419\) | 295.598 | 0.705485 | 0.352742 | − | 0.935721i | \(-0.385249\pi\) | ||||
0.352742 | + | 0.935721i | \(0.385249\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 126.260i | 0.299904i | 0.988693 | + | 0.149952i | \(0.0479119\pi\) | ||||
−0.988693 | + | 0.149952i | \(0.952088\pi\) | |||||||
\(422\) | −134.069 | + | 311.998i | −0.317700 | + | 0.739332i | ||||
\(423\) | − | 893.881i | − | 2.11319i | ||||||
\(424\) | 206.125 | + | 559.066i | 0.486144 | + | 1.31855i | ||||
\(425\) | 18.8594 | 0.0443750 | ||||||||
\(426\) | −730.063 | − | 313.716i | −1.71376 | − | 0.736424i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 396.410 | + | 417.839i | 0.926192 | + | 0.976259i | ||||
\(429\) | − | 600.443i | − | 1.39963i | ||||||
\(430\) | −165.426 | − | 71.0857i | −0.384713 | − | 0.165316i | ||||
\(431\) | − | 254.263i | − | 0.589937i | −0.955507 | − | 0.294968i | \(-0.904691\pi\) | ||
0.955507 | − | 0.294968i | \(-0.0953091\pi\) | |||||||
\(432\) | −46.8173 | + | 888.865i | −0.108373 | + | 2.05756i | ||||
\(433\) | 546.301 | 1.26167 | 0.630833 | − | 0.775919i | \(-0.282713\pi\) | ||||
0.630833 | + | 0.775919i | \(0.282713\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 108.368 | 0.249122 | ||||||||
\(436\) | −193.500 | + | 183.576i | −0.443807 | + | 0.421046i | ||||
\(437\) | 51.5278i | 0.117913i | ||||||||
\(438\) | −141.486 | + | 329.259i | −0.323028 | + | 0.751733i | ||||
\(439\) | − | 273.335i | − | 0.622631i | −0.950307 | − | 0.311315i | \(-0.899230\pi\) | ||
0.950307 | − | 0.311315i | \(-0.100770\pi\) | |||||||
\(440\) | −31.3928 | − | 85.1456i | −0.0713473 | − | 0.193513i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 36.4667 | + | 15.6702i | 0.0825039 | + | 0.0354529i | ||||
\(443\) | 474.770 | 1.07172 | 0.535858 | − | 0.844308i | \(-0.319988\pi\) | ||||
0.535858 | + | 0.844308i | \(0.319988\pi\) | |||||||
\(444\) | 198.063 | − | 187.906i | 0.446089 | − | 0.423211i | ||||
\(445\) | 118.285i | 0.265810i | ||||||||
\(446\) | −83.5390 | − | 35.8977i | −0.187307 | − | 0.0804881i | ||||
\(447\) | − | 1230.19i | − | 2.75210i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 782.101 | 1.74187 | 0.870936 | − | 0.491396i | \(-0.163513\pi\) | ||||
0.870936 | + | 0.491396i | \(0.163513\pi\) | |||||||
\(450\) | −312.222 | + | 726.586i | −0.693828 | + | 1.61464i | ||||
\(451\) | 226.846 | 0.502985 | ||||||||
\(452\) | −19.7246 | − | 20.7909i | −0.0436385 | − | 0.0459975i | ||||
\(453\) | 788.589i | 1.74081i | ||||||||
\(454\) | −146.181 | + | 340.183i | −0.321984 | + | 0.749302i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −237.348 | + | 87.5092i | −0.520500 | + | 0.191906i | ||||
\(457\) | −189.559 | −0.414789 | −0.207395 | − | 0.978257i | \(-0.566498\pi\) | ||||
−0.207395 | + | 0.978257i | \(0.566498\pi\) | |||||||
\(458\) | −339.855 | − | 146.040i | −0.742041 | − | 0.318864i | ||||
\(459\) | 51.5621 | 0.112336 | ||||||||
\(460\) | 51.5975 | + | 54.3867i | 0.112168 | + | 0.118232i | ||||
\(461\) | 202.533i | 0.439335i | 0.975575 | + | 0.219667i | \(0.0704972\pi\) | ||||
−0.975575 | + | 0.219667i | \(0.929503\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 652.927i | 1.41021i | 0.709103 | + | 0.705105i | \(0.249100\pi\) | ||||
−0.709103 | + | 0.705105i | \(0.750900\pi\) | |||||||
\(464\) | −150.547 | − | 7.92943i | −0.324455 | − | 0.0170893i | ||||
\(465\) | 396.841 | 0.853420 | ||||||||
\(466\) | −76.3557 | + | 177.691i | −0.163853 | + | 0.381310i | ||||
\(467\) | 545.449 | 1.16799 | 0.583993 | − | 0.811759i | \(-0.301490\pi\) | ||||
0.583993 | + | 0.811759i | \(0.301490\pi\) | |||||||
\(468\) | −1207.43 | + | 1145.51i | −2.57998 | + | 2.44767i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 78.3411 | − | 182.311i | 0.166683 | − | 0.387895i | ||||
\(471\) | − | 612.298i | − | 1.30000i | ||||||
\(472\) | 402.877 | − | 148.539i | 0.853552 | − | 0.314701i | ||||
\(473\) | −219.506 | −0.464072 | ||||||||
\(474\) | −296.021 | − | 127.204i | −0.624516 | − | 0.268362i | ||||
\(475\) | −120.663 | −0.254028 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1447.40i | 3.03438i | ||||||||
\(478\) | −299.857 | − | 128.852i | −0.627316 | − | 0.269565i | ||||
\(479\) | 108.897i | 0.227343i | 0.993518 | + | 0.113672i | \(0.0362612\pi\) | ||||
−0.993518 | + | 0.113672i | \(0.963739\pi\) | |||||||
\(480\) | −162.889 | + | 330.033i | −0.339352 | + | 0.687570i | ||||
\(481\) | 274.073 | 0.569797 | ||||||||
\(482\) | −162.257 | + | 377.596i | −0.336633 | + | 0.783394i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 256.973 | + | 270.865i | 0.530937 | + | 0.559637i | ||||
\(485\) | 115.854i | 0.238875i | ||||||||
\(486\) | −117.243 | + | 272.841i | −0.241241 | + | 0.561402i | ||||
\(487\) | − | 429.353i | − | 0.881629i | −0.897598 | − | 0.440814i | \(-0.854690\pi\) | ||
0.897598 | − | 0.440814i | \(-0.145310\pi\) | |||||||
\(488\) | 76.9796 | + | 208.789i | 0.157745 | + | 0.427846i | ||||
\(489\) | 262.929 | 0.537686 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 453.887 | 0.924413 | 0.462206 | − | 0.886772i | \(-0.347058\pi\) | ||||
0.462206 | + | 0.886772i | \(0.347058\pi\) | |||||||
\(492\) | −633.201 | − | 667.430i | −1.28699 | − | 1.35657i | ||||
\(493\) | 8.73307i | 0.0177141i | ||||||||
\(494\) | −233.316 | − | 100.259i | −0.472300 | − | 0.202953i | ||||
\(495\) | − | 220.438i | − | 0.445330i | ||||||
\(496\) | −551.299 | − | 29.0374i | −1.11149 | − | 0.0585431i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 307.053 | − | 714.556i | 0.616572 | − | 1.43485i | ||||
\(499\) | 333.396 | 0.668129 | 0.334064 | − | 0.942550i | \(-0.391580\pi\) | ||||
0.334064 | + | 0.942550i | \(0.391580\pi\) | |||||||
\(500\) | −283.836 | + | 269.280i | −0.567672 | + | 0.538559i | ||||
\(501\) | − | 1287.51i | − | 2.56988i | ||||||
\(502\) | 125.784 | − | 292.717i | 0.250566 | − | 0.583102i | ||||
\(503\) | − | 580.170i | − | 1.15342i | −0.816949 | − | 0.576710i | \(-0.804336\pi\) | ||
0.816949 | − | 0.576710i | \(-0.195664\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −194.775 | −0.385693 | ||||||||
\(506\) | 83.9705 | + | 36.0831i | 0.165950 | + | 0.0713105i | ||||
\(507\) | −1543.45 | −3.04428 | ||||||||
\(508\) | 381.570 | − | 362.002i | 0.751123 | − | 0.712601i | ||||
\(509\) | − | 307.463i | − | 0.604054i | −0.953299 | − | 0.302027i | \(-0.902337\pi\) | ||
0.953299 | − | 0.302027i | \(-0.0976632\pi\) | |||||||
\(510\) | 19.5882 | + | 8.41730i | 0.0384083 | + | 0.0165045i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 250.438 | − | 446.570i | 0.489136 | − | 0.872207i | ||||
\(513\) | −329.898 | −0.643075 | ||||||||
\(514\) | −170.379 | + | 396.497i | −0.331477 | + | 0.771395i | ||||
\(515\) | 243.328 | 0.472481 | ||||||||
\(516\) | 612.713 | + | 645.834i | 1.18743 | + | 1.25162i | ||||
\(517\) | − | 241.910i | − | 0.467911i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 290.187i | − | 0.559127i | ||||||
\(520\) | −346.655 | + | 127.810i | −0.666645 | + | 0.245789i | ||||
\(521\) | 720.959 | 1.38380 | 0.691899 | − | 0.721994i | \(-0.256774\pi\) | ||||
0.691899 | + | 0.721994i | \(0.256774\pi\) | |||||||
\(522\) | −336.455 | − | 144.578i | −0.644549 | − | 0.276970i | ||||
\(523\) | −269.977 | −0.516208 | −0.258104 | − | 0.966117i | \(-0.583098\pi\) | ||||
−0.258104 | + | 0.966117i | \(0.583098\pi\) | |||||||
\(524\) | 24.1199 | + | 25.4238i | 0.0460304 | + | 0.0485186i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −604.837 | − | 259.905i | −1.14988 | − | 0.494117i | ||||
\(527\) | 31.9803i | 0.0606836i | ||||||||
\(528\) | −23.6000 | + | 448.066i | −0.0446970 | + | 0.848609i | ||||
\(529\) | 453.498 | 0.857274 | ||||||||
\(530\) | −126.852 | + | 295.203i | −0.239344 | + | 0.556987i | ||||
\(531\) | 1043.03 | 1.96428 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 923.564i | − | 1.73277i | ||||||
\(534\) | 230.896 | − | 537.329i | 0.432390 | − | 1.00623i | ||||
\(535\) | 310.577i | 0.580517i | ||||||||
\(536\) | −589.157 | + | 217.220i | −1.09917 | + | 0.405261i | ||||
\(537\) | −677.303 | −1.26127 | ||||||||
\(538\) | 538.520 | + | 231.408i | 1.00097 | + | 0.430127i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −348.201 | + | 330.344i | −0.644817 | + | 0.611748i | ||||
\(541\) | − | 907.242i | − | 1.67697i | −0.544922 | − | 0.838486i | \(-0.683441\pi\) | ||
0.544922 | − | 0.838486i | \(-0.316559\pi\) | |||||||
\(542\) | −49.3380 | − | 21.2011i | −0.0910296 | − | 0.0391165i | ||||
\(543\) | 1134.19i | 2.08875i | ||||||||
\(544\) | −26.5965 | − | 13.1268i | −0.0488906 | − | 0.0241301i | ||||
\(545\) | −143.827 | −0.263903 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −557.327 | −1.01888 | −0.509439 | − | 0.860506i | \(-0.670147\pi\) | ||||
−0.509439 | + | 0.860506i | \(0.670147\pi\) | |||||||
\(548\) | 652.031 | + | 687.278i | 1.18984 | + | 1.25416i | ||||
\(549\) | 540.546i | 0.984601i | ||||||||
\(550\) | −84.4964 | + | 196.635i | −0.153630 | + | 0.357518i | ||||
\(551\) | − | 55.8747i | − | 0.101406i | ||||||
\(552\) | −128.225 | − | 347.779i | −0.232291 | − | 0.630035i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −615.163 | − | 264.343i | −1.11040 | − | 0.477153i | ||||
\(555\) | 147.219 | 0.265260 | ||||||||
\(556\) | −473.857 | − | 499.472i | −0.852261 | − | 0.898331i | ||||
\(557\) | − | 856.668i | − | 1.53800i | −0.639246 | − | 0.769002i | \(-0.720754\pi\) | ||
0.639246 | − | 0.769002i | \(-0.279246\pi\) | |||||||
\(558\) | −1232.09 | − | 529.442i | −2.20804 | − | 0.948821i | ||||
\(559\) | 893.680i | 1.59871i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 25.9918 | 0.0463313 | ||||||||
\(562\) | 97.4039 | − | 226.673i | 0.173317 | − | 0.403332i | ||||
\(563\) | 13.6887 | 0.0243139 | 0.0121569 | − | 0.999926i | \(-0.496130\pi\) | ||||
0.0121569 | + | 0.999926i | \(0.496130\pi\) | |||||||
\(564\) | −711.752 | + | 675.250i | −1.26197 | + | 1.19725i | ||||
\(565\) | − | 15.4537i | − | 0.0273517i | ||||||
\(566\) | 0.488693 | − | 1.13726i | 0.000863416 | − | 0.00200929i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 206.204 | + | 559.278i | 0.363034 | + | 0.984644i | ||||
\(569\) | −1091.98 | −1.91913 | −0.959563 | − | 0.281495i | \(-0.909170\pi\) | ||||
−0.959563 | + | 0.281495i | \(0.909170\pi\) | |||||||
\(570\) | −125.327 | − | 53.8544i | −0.219871 | − | 0.0944813i | ||||
\(571\) | 719.098 | 1.25937 | 0.629683 | − | 0.776852i | \(-0.283185\pi\) | ||||
0.629683 | + | 0.776852i | \(0.283185\pi\) | |||||||
\(572\) | −326.766 | + | 310.008i | −0.571270 | + | 0.541972i | ||||
\(573\) | − | 216.142i | − | 0.377210i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 176.805i | − | 0.307486i | ||||||
\(576\) | 946.041 | − | 807.351i | 1.64243 | − | 1.40165i | ||||
\(577\) | −1031.12 | −1.78704 | −0.893518 | − | 0.449027i | \(-0.851771\pi\) | ||||
−0.893518 | + | 0.449027i | \(0.851771\pi\) | |||||||
\(578\) | 227.518 | − | 529.468i | 0.393631 | − | 0.916034i | ||||
\(579\) | 1505.33 | 2.59988 | ||||||||
\(580\) | −55.9503 | − | 58.9748i | −0.0964660 | − | 0.101681i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 226.151 | − | 526.285i | 0.388575 | − | 0.904270i | ||||
\(583\) | 391.708i | 0.671883i | ||||||||
\(584\) | 252.235 | − | 92.9979i | 0.431909 | − | 0.159243i | ||||
\(585\) | −897.477 | −1.53415 | ||||||||
\(586\) | −51.9643 | − | 22.3297i | −0.0886764 | − | 0.0381053i | ||||
\(587\) | −671.907 | −1.14464 | −0.572322 | − | 0.820029i | \(-0.693957\pi\) | ||||
−0.572322 | + | 0.820029i | \(0.693957\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 204.612i | − | 0.347388i | ||||||
\(590\) | 212.731 | + | 91.4129i | 0.360561 | + | 0.154937i | ||||
\(591\) | − | 1396.02i | − | 2.36213i | ||||||
\(592\) | −204.520 | − | 10.7722i | −0.345473 | − | 0.0181963i | ||||
\(593\) | 353.998 | 0.596962 | 0.298481 | − | 0.954416i | \(-0.403520\pi\) | ||||
0.298481 | + | 0.954416i | \(0.403520\pi\) | |||||||
\(594\) | −231.016 | + | 537.606i | −0.388915 | + | 0.905061i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −669.480 | + | 635.146i | −1.12329 | + | 1.06568i | ||||
\(597\) | 1717.65i | 2.87713i | ||||||||
\(598\) | 146.906 | − | 341.871i | 0.245662 | − | 0.571691i | ||||
\(599\) | 1136.14i | 1.89672i | 0.317193 | + | 0.948361i | \(0.397260\pi\) | ||||
−0.317193 | + | 0.948361i | \(0.602740\pi\) | |||||||
\(600\) | 814.400 | − | 300.266i | 1.35733 | − | 0.500443i | ||||
\(601\) | −6.80783 | −0.0113275 | −0.00566375 | − | 0.999984i | \(-0.501803\pi\) | ||||
−0.00566375 | + | 0.999984i | \(0.501803\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1525.30 | −2.52953 | ||||||||
\(604\) | 429.157 | − | 407.148i | 0.710524 | − | 0.674085i | ||||
\(605\) | 201.332i | 0.332780i | ||||||||
\(606\) | 884.794 | + | 380.206i | 1.46006 | + | 0.627403i | ||||
\(607\) | 446.439i | 0.735484i | 0.929928 | + | 0.367742i | \(0.119869\pi\) | ||||
−0.929928 | + | 0.367742i | \(0.880131\pi\) | |||||||
\(608\) | 170.166 | + | 83.9859i | 0.279878 | + | 0.138135i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −47.3743 | + | 110.247i | −0.0776627 | + | 0.180732i | ||||
\(611\) | −984.895 | −1.61194 | ||||||||
\(612\) | −49.5866 | − | 52.2671i | −0.0810238 | − | 0.0854037i | ||||
\(613\) | − | 641.609i | − | 1.04667i | −0.852127 | − | 0.523335i | \(-0.824688\pi\) | ||
0.852127 | − | 0.523335i | \(-0.175312\pi\) | |||||||
\(614\) | −316.549 | + | 736.654i | −0.515552 | + | 1.19976i | ||||
\(615\) | − | 496.096i | − | 0.806661i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −502.890 | −0.815057 | −0.407528 | − | 0.913193i | \(-0.633609\pi\) | ||||
−0.407528 | + | 0.913193i | \(0.633609\pi\) | |||||||
\(618\) | −1105.35 | − | 474.983i | −1.78860 | − | 0.768580i | ||||
\(619\) | 432.989 | 0.699498 | 0.349749 | − | 0.936843i | \(-0.386267\pi\) | ||||
0.349749 | + | 0.936843i | \(0.386267\pi\) | |||||||
\(620\) | −204.888 | − | 215.964i | −0.330465 | − | 0.348329i | ||||
\(621\) | − | 483.389i | − | 0.778405i | ||||||
\(622\) | 298.096 | + | 128.095i | 0.479254 | + | 0.205941i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1824.22 | + | 96.0833i | 2.92343 | + | 0.153980i | ||||
\(625\) | 297.718 | 0.476348 | ||||||||
\(626\) | 210.230 | − | 489.235i | 0.335831 | − | 0.781526i | ||||
\(627\) | −166.297 | −0.265227 | ||||||||
\(628\) | −333.218 | + | 316.129i | −0.530602 | + | 0.503390i | ||||
\(629\) | 11.8640i | 0.0188617i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 238.957i | − | 0.378695i | −0.981910 | − | 0.189348i | \(-0.939363\pi\) | ||
0.981910 | − | 0.189348i | \(-0.0606373\pi\) | |||||||
\(632\) | 83.6099 | + | 226.772i | 0.132294 | + | 0.358817i | ||||
\(633\) | 905.375 | 1.43029 | ||||||||
\(634\) | −795.385 | − | 341.786i | −1.25455 | − | 0.539095i | ||||
\(635\) | 283.619 | 0.446644 | ||||||||
\(636\) | 1152.49 | − | 1093.38i | 1.81209 | − | 1.71916i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −91.0543 | − | 39.1271i | −0.142718 | − | 0.0613277i | ||||
\(639\) | 1447.95i | 2.26596i | ||||||||
\(640\) | 263.706 | − | 81.7503i | 0.412041 | − | 0.127735i | ||||
\(641\) | −7.96130 | −0.0124201 | −0.00621006 | − | 0.999981i | \(-0.501977\pi\) | ||||
−0.00621006 | + | 0.999981i | \(0.501977\pi\) | |||||||
\(642\) | 606.255 | − | 1410.84i | 0.944322 | − | 2.19757i | ||||
\(643\) | −584.919 | −0.909672 | −0.454836 | − | 0.890575i | \(-0.650302\pi\) | ||||
−0.454836 | + | 0.890575i | \(0.650302\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 480.044i | 0.744255i | ||||||||
\(646\) | 4.33997 | − | 10.0997i | 0.00671822 | − | 0.0156343i | ||||
\(647\) | 335.680i | 0.518825i | 0.965767 | + | 0.259413i | \(0.0835289\pi\) | ||||
−0.965767 | + | 0.259413i | \(0.916471\pi\) | |||||||
\(648\) | 913.809 | − | 336.918i | 1.41020 | − | 0.519934i | ||||
\(649\) | 282.275 | 0.434938 | ||||||||
\(650\) | 800.566 | + | 344.012i | 1.23164 | + | 0.529250i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −135.750 | − | 143.088i | −0.208205 | − | 0.219460i | ||||
\(653\) | 48.5265i | 0.0743132i | 0.999309 | + | 0.0371566i | \(0.0118300\pi\) | ||||
−0.999309 | + | 0.0371566i | \(0.988170\pi\) | |||||||
\(654\) | 653.355 | + | 280.754i | 0.999014 | + | 0.429288i | ||||
\(655\) | 18.8973i | 0.0288509i | ||||||||
\(656\) | −36.3001 | + | 689.187i | −0.0553355 | + | 1.05059i | ||||
\(657\) | 653.026 | 0.993951 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1224.65 | 1.85835 | 0.929176 | − | 0.369638i | \(-0.120518\pi\) | ||||
0.929176 | + | 0.369638i | \(0.120518\pi\) | |||||||
\(660\) | −175.524 | + | 166.522i | −0.265945 | + | 0.252306i | ||||
\(661\) | − | 838.042i | − | 1.26784i | −0.773399 | − | 0.633919i | \(-0.781445\pi\) | ||
0.773399 | − | 0.633919i | \(-0.218555\pi\) | |||||||
\(662\) | −64.1579 | + | 149.305i | −0.0969153 | + | 0.225536i | ||||
\(663\) | − | 105.821i | − | 0.159610i | ||||||
\(664\) | −547.399 | + | 201.824i | −0.824396 | + | 0.303951i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −457.078 | − | 196.412i | −0.686303 | − | 0.294912i | ||||
\(667\) | 81.8716 | 0.122746 | ||||||||
\(668\) | −700.674 | + | 664.741i | −1.04891 | + | 0.995121i | ||||
\(669\) | 242.418i | 0.362359i | ||||||||
\(670\) | −311.092 | − | 133.680i | −0.464317 | − | 0.199522i | ||||
\(671\) | 146.287i | 0.218014i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 147.714 | 0.219486 | 0.109743 | − | 0.993960i | \(-0.464997\pi\) | ||||
0.109743 | + | 0.993960i | \(0.464997\pi\) | |||||||
\(674\) | 54.8731 | − | 127.698i | 0.0814141 | − | 0.189462i | ||||
\(675\) | 1131.96 | 1.67698 | ||||||||
\(676\) | 796.881 | + | 839.958i | 1.17882 | + | 1.24254i | ||||
\(677\) | − | 837.185i | − | 1.23661i | −0.785938 | − | 0.618305i | \(-0.787820\pi\) | ||
0.785938 | − | 0.618305i | \(-0.212180\pi\) | |||||||
\(678\) | −30.1661 | + | 70.2007i | −0.0444927 | + | 0.103541i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −5.53263 | − | 15.0059i | −0.00813622 | − | 0.0220676i | ||||
\(681\) | 987.164 | 1.44958 | ||||||||
\(682\) | −333.438 | − | 143.282i | −0.488913 | − | 0.210091i | ||||
\(683\) | −64.4377 | −0.0943451 | −0.0471725 | − | 0.998887i | \(-0.515021\pi\) | ||||
−0.0471725 | + | 0.998887i | \(0.515021\pi\) | |||||||
\(684\) | 317.258 | + | 334.408i | 0.463827 | + | 0.488900i | ||||
\(685\) | 510.849i | 0.745765i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 986.210i | 1.43553i | ||||||||
\(688\) | 35.1255 | − | 666.887i | 0.0510545 | − | 0.969312i | ||||
\(689\) | 1594.77 | 2.31462 | ||||||||
\(690\) | 78.9112 | − | 183.638i | 0.114364 | − | 0.266141i | ||||
\(691\) | −526.747 | −0.762297 | −0.381149 | − | 0.924514i | \(-0.624471\pi\) | ||||
−0.381149 | + | 0.924514i | \(0.624471\pi\) | |||||||
\(692\) | −157.922 | + | 149.823i | −0.228211 | + | 0.216508i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 275.852 | − | 641.948i | 0.397482 | − | 0.924997i | ||||
\(695\) | − | 371.254i | − | 0.534179i | ||||||
\(696\) | 139.042 | + | 377.118i | 0.199773 | + | 0.541836i | ||||
\(697\) | 39.9790 | 0.0573587 | ||||||||
\(698\) | 304.728 | + | 130.945i | 0.436574 | + | 0.187601i | ||||
\(699\) | 515.633 | 0.737672 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 695.486i | − | 0.992134i | −0.868284 | − | 0.496067i | \(-0.834777\pi\) | ||
0.868284 | − | 0.496067i | \(-0.165223\pi\) | |||||||
\(702\) | 2188.77 | + | 940.540i | 3.11791 | + | 1.33980i | ||||
\(703\) | − | 75.9065i | − | 0.107975i | ||||||
\(704\) | 256.026 | − | 218.493i | 0.363673 | − | 0.310359i | ||||
\(705\) | −529.040 | −0.750412 | ||||||||
\(706\) | 372.471 | − | 866.794i | 0.527580 | − | 1.22775i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −787.920 | − | 830.513i | −1.11288 | − | 1.17304i | ||||
\(709\) | − | 927.410i | − | 1.30805i | −0.756471 | − | 0.654027i | \(-0.773078\pi\) | ||
0.756471 | − | 0.654027i | \(-0.226922\pi\) | |||||||
\(710\) | −126.900 | + | 295.315i | −0.178733 | + | 0.415937i | ||||
\(711\) | 587.104i | 0.825744i | ||||||||
\(712\) | −411.630 | + | 151.766i | −0.578133 | + | 0.213155i | ||||
\(713\) | 299.812 | 0.420493 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −242.883 | −0.339697 | ||||||||
\(716\) | 349.691 | + | 368.594i | 0.488395 | + | 0.514796i | ||||
\(717\) | 870.143i | 1.21359i | ||||||||
\(718\) | −1207.23 | − | 518.762i | −1.68138 | − | 0.722509i | ||||
\(719\) | − | 1328.34i | − | 1.84748i | −0.383022 | − | 0.923739i | \(-0.625117\pi\) | ||
0.383022 | − | 0.923739i | \(-0.374883\pi\) | |||||||
\(720\) | 669.720 | + | 35.2747i | 0.930167 | + | 0.0489927i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 257.281 | − | 598.730i | 0.356345 | − | 0.829266i | ||||
\(723\) | 1095.73 | 1.51553 | ||||||||
\(724\) | 617.238 | − | 585.583i | 0.852539 | − | 0.808817i | ||||
\(725\) | 191.720i | 0.264441i | ||||||||
\(726\) | 393.005 | − | 914.579i | 0.541330 | − | 1.25975i | ||||
\(727\) | − | 539.401i | − | 0.741954i | −0.928642 | − | 0.370977i | \(-0.879023\pi\) | ||
0.928642 | − | 0.370977i | \(-0.120977\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −303.936 | −0.416922 | ||||||||
\(730\) | 133.187 | + | 57.2322i | 0.182448 | + | 0.0784002i | ||||
\(731\) | −38.6854 | −0.0529212 | ||||||||
\(732\) | 430.409 | − | 408.336i | 0.587991 | − | 0.557836i | ||||
\(733\) | − | 442.088i | − | 0.603121i | −0.953447 | − | 0.301561i | \(-0.902492\pi\) | ||
0.953447 | − | 0.301561i | \(-0.0975076\pi\) | |||||||
\(734\) | −653.196 | − | 280.686i | −0.889913 | − | 0.382406i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −123.062 | + | 249.339i | −0.167204 | + | 0.338776i | ||||
\(737\) | −412.791 | −0.560097 | ||||||||
\(738\) | −661.864 | + | 1540.25i | −0.896835 | + | 2.08706i | ||||
\(739\) | −1148.23 | −1.55376 | −0.776882 | − | 0.629646i | \(-0.783200\pi\) | ||||
−0.776882 | + | 0.629646i | \(0.783200\pi\) | |||||||
\(740\) | −76.0091 | − | 80.1180i | −0.102715 | − | 0.108268i | ||||
\(741\) | 677.050i | 0.913698i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 588.688i | − | 0.792313i | −0.918183 | − | 0.396156i | \(-0.870344\pi\) | ||
0.918183 | − | 0.396156i | \(-0.129656\pi\) | |||||||
\(744\) | 509.168 | + | 1381.00i | 0.684365 | + | 1.85618i | ||||
\(745\) | −497.620 | −0.667946 | ||||||||
\(746\) | 580.656 | + | 249.515i | 0.778360 | + | 0.334470i | ||||
\(747\) | −1417.19 | −1.89718 | ||||||||
\(748\) | −13.4196 | − | 14.1450i | −0.0179406 | − | 0.0189104i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 958.378 | + | 411.826i | 1.27784 | + | 0.549101i | ||||
\(751\) | 818.399i | 1.08975i | 0.838519 | + | 0.544873i | \(0.183422\pi\) | ||||
−0.838519 | + | 0.544873i | \(0.816578\pi\) | |||||||
\(752\) | 734.953 | + | 38.7106i | 0.977332 | + | 0.0514769i | ||||
\(753\) | −849.423 | −1.12805 | ||||||||
\(754\) | −159.299 | + | 370.712i | −0.211272 | + | 0.491660i | ||||
\(755\) | 318.989 | 0.422503 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 105.101i | 0.138838i | 0.997588 | + | 0.0694192i | \(0.0221146\pi\) | ||||
−0.997588 | + | 0.0694192i | \(0.977885\pi\) | |||||||
\(758\) | 140.869 | − | 327.823i | 0.185843 | − | 0.432484i | ||||
\(759\) | − | 243.671i | − | 0.321042i | ||||||
\(760\) | 35.3981 | + | 96.0088i | 0.0465764 | + | 0.126327i | ||||
\(761\) | 1014.23 | 1.33276 | 0.666382 | − | 0.745610i | \(-0.267842\pi\) | ||||
0.666382 | + | 0.745610i | \(0.267842\pi\) | |||||||
\(762\) | −1288.38 | − | 553.631i | −1.69079 | − | 0.726550i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −117.626 | + | 111.594i | −0.153961 | + | 0.146065i | ||||
\(765\) | − | 38.8498i | − | 0.0507840i | ||||||
\(766\) | 1283.33 | + | 551.463i | 1.67537 | + | 0.719925i | ||||
\(767\) | − | 1149.23i | − | 1.49835i | ||||||
\(768\) | −1357.50 | − | 143.400i | −1.76758 | − | 0.186718i | ||||
\(769\) | −1183.99 | −1.53964 | −0.769822 | − | 0.638258i | \(-0.779655\pi\) | ||||
−0.769822 | + | 0.638258i | \(0.779655\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1150.58 | 1.49232 | ||||||||
\(772\) | −777.201 | − | 819.214i | −1.00674 | − | 1.06116i | ||||
\(773\) | 324.311i | 0.419549i | 0.977750 | + | 0.209774i | \(0.0672730\pi\) | ||||
−0.977750 | + | 0.209774i | \(0.932727\pi\) | |||||||
\(774\) | 640.448 | − | 1490.41i | 0.827452 | − | 1.92560i | ||||
\(775\) | 702.074i | 0.905902i | ||||||||
\(776\) | −403.170 | + | 148.647i | −0.519550 | + | 0.191556i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −322.226 | − | 138.464i | −0.414172 | − | 0.177975i | ||||
\(779\) | −255.788 | −0.328355 | ||||||||
\(780\) | 677.966 | + | 714.615i | 0.869187 | + | 0.916173i | ||||
\(781\) | 391.857i | 0.501737i | ||||||||
\(782\) | 14.7988 | + | 6.35924i | 0.0189244 | + | 0.00813202i | ||||
\(783\) | 524.168i | 0.669436i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −247.679 | −0.315514 | ||||||||
\(786\) | 36.8881 | − | 85.8438i | 0.0469314 | − | 0.109216i | ||||
\(787\) | 268.536 | 0.341214 | 0.170607 | − | 0.985339i | \(-0.445427\pi\) | ||||
0.170607 | + | 0.985339i | \(0.445427\pi\) | |||||||
\(788\) | −759.724 | + | 720.762i | −0.964117 | + | 0.914673i | ||||
\(789\) | 1755.15i | 2.22453i | ||||||||
\(790\) | −51.4547 | + | 119.742i | −0.0651325 | + | 0.151573i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 767.121 | − | 282.834i | 0.968587 | − | 0.357114i | ||||
\(793\) | 595.584 | 0.751051 | ||||||||
\(794\) | −708.750 | − | 304.558i | −0.892633 | − | 0.383575i | ||||
\(795\) | 856.638 | 1.07753 | ||||||||
\(796\) | 934.759 | − | 886.820i | 1.17432 | − | 1.11410i | ||||
\(797\) | 1502.06i | 1.88465i | 0.334705 | + | 0.942323i | \(0.391363\pi\) | ||||
−0.334705 | + | 0.942323i | \(0.608637\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 42.6339i | − | 0.0533591i | ||||||
\(800\) | −583.881 | − | 288.177i | −0.729852 | − | 0.360221i | ||||
\(801\) | −1065.70 | −1.33046 | ||||||||
\(802\) | −416.200 | + | 968.556i | −0.518952 | + | 1.20768i | ||||
\(803\) | 176.728 | 0.220084 | ||||||||
\(804\) | 1152.24 | + | 1214.52i | 1.43313 | + | 1.51060i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −583.349 | + | 1357.54i | −0.723758 | + | 1.68429i | ||||
\(807\) | − | 1562.71i | − | 1.93644i | ||||||
\(808\) | −249.907 | − | 677.812i | −0.309290 | − | 0.838877i | ||||
\(809\) | 70.7587 | 0.0874644 | 0.0437322 | − | 0.999043i | \(-0.486075\pi\) | ||||
0.0437322 | + | 0.999043i | \(0.486075\pi\) | |||||||
\(810\) | 482.518 | + | 207.344i | 0.595701 | + | 0.255980i | ||||
\(811\) | 5.94522 | 0.00733072 | 0.00366536 | − | 0.999993i | \(-0.498833\pi\) | ||||
0.00366536 | + | 0.999993i | \(0.498833\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 143.172i | 0.176103i | ||||||||
\(814\) | −123.698 | − | 53.1547i | −0.151964 | − | 0.0653006i | ||||
\(815\) | − | 106.356i | − | 0.130499i | ||||||
\(816\) | −4.15923 | + | 78.9665i | −0.00509710 | + | 0.0967727i | ||||
\(817\) | 247.512 | 0.302952 | ||||||||
\(818\) | 334.592 | − | 778.643i | 0.409037 | − | 0.951886i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −269.980 | + | 256.134i | −0.329244 | + | 0.312359i | ||||
\(821\) | 15.1449i | 0.0184469i | 0.999957 | + | 0.00922344i | \(0.00293595\pi\) | ||||
−0.999957 | + | 0.00922344i | \(0.997064\pi\) | |||||||
\(822\) | 997.191 | − | 2320.61i | 1.21313 | − | 2.82312i | ||||
\(823\) | − | 1482.76i | − | 1.80165i | −0.434185 | − | 0.900824i | \(-0.642964\pi\) | ||
0.434185 | − | 0.900824i | \(-0.357036\pi\) | |||||||
\(824\) | 312.203 | + | 846.775i | 0.378887 | + | 1.02764i | ||||
\(825\) | 570.607 | 0.691645 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −74.3070 | −0.0898513 | −0.0449257 | − | 0.998990i | \(-0.514305\pi\) | ||||
−0.0449257 | + | 0.998990i | \(0.514305\pi\) | |||||||
\(828\) | −489.998 | + | 464.869i | −0.591785 | + | 0.561436i | ||||
\(829\) | 142.862i | 0.172331i | 0.996281 | + | 0.0861654i | \(0.0274613\pi\) | ||||
−0.996281 | + | 0.0861654i | \(0.972539\pi\) | |||||||
\(830\) | −289.043 | − | 124.205i | −0.348244 | − | 0.149645i | ||||
\(831\) | 1785.12i | 2.14815i | ||||||||
\(832\) | −889.555 | − | 1042.36i | −1.06918 | − | 1.25284i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −724.699 | + | 1686.48i | −0.868944 | + | 2.02216i | ||||
\(835\) | −520.807 | −0.623721 | ||||||||
\(836\) | 85.8591 | + | 90.5004i | 0.102702 | + | 0.108254i | ||||
\(837\) | 1919.49i | 2.29330i | ||||||||
\(838\) | −233.407 | + | 543.170i | −0.278528 | + | 0.648175i | ||||
\(839\) | 16.7454i | 0.0199588i | 0.999950 | + | 0.00997940i | \(0.00317659\pi\) | ||||
−0.999950 | + | 0.00997940i | \(0.996823\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 752.222 | 0.894437 | ||||||||
\(842\) | −232.006 | − | 99.6955i | −0.275541 | − | 0.118403i | ||||
\(843\) | −657.773 | −0.780276 | ||||||||
\(844\) | −467.444 | − | 492.713i | −0.553844 | − | 0.583783i | ||||
\(845\) | 624.335i | 0.738858i | ||||||||
\(846\) | 1642.53 | + | 705.816i | 1.94153 | + | 0.834298i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1190.06 | − | 62.6814i | −1.40337 | − | 0.0739167i | ||||
\(849\) | −3.30017 | −0.00388712 | ||||||||
\(850\) | −14.8915 | + | 34.6547i | −0.0175194 | + | 0.0407703i | ||||
\(851\) | 111.224 | 0.130698 | ||||||||
\(852\) | 1152.93 | − | 1093.80i | 1.35320 | − | 1.28380i | ||||
\(853\) | − | 1299.38i | − | 1.52331i | −0.647984 | − | 0.761654i | \(-0.724388\pi\) | ||
0.647984 | − | 0.761654i | \(-0.275612\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 248.563i | 0.290717i | ||||||||
\(856\) | −1080.80 | + | 398.487i | −1.26262 | + | 0.465522i | ||||
\(857\) | −1195.34 | −1.39479 | −0.697396 | − | 0.716686i | \(-0.745658\pi\) | ||||
−0.697396 | + | 0.716686i | \(0.745658\pi\) | |||||||
\(858\) | 1103.33 | + | 474.115i | 1.28594 | + | 0.552581i | ||||
\(859\) | −341.769 | −0.397869 | −0.198934 | − | 0.980013i | \(-0.563748\pi\) | ||||
−0.198934 | + | 0.980013i | \(0.563748\pi\) | |||||||
\(860\) | 261.244 | − | 247.846i | 0.303772 | − | 0.288193i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 467.216 | + | 200.768i | 0.542014 | + | 0.232909i | ||||
\(863\) | − | 974.986i | − | 1.12976i | −0.825172 | − | 0.564882i | \(-0.808922\pi\) | ||
0.825172 | − | 0.564882i | \(-0.191078\pi\) | |||||||
\(864\) | −1596.35 | − | 787.883i | −1.84763 | − | 0.911902i | ||||
\(865\) | −117.383 | −0.135702 | ||||||||
\(866\) | −431.364 | + | 1003.85i | −0.498111 | + | 1.15917i | ||||
\(867\) | −1536.44 | −1.77213 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 158.887i | 0.182839i | ||||||||
\(870\) | −85.5682 | + | 199.129i | −0.0983543 | + | 0.228884i | ||||
\(871\) | 1680.61i | 1.92952i | ||||||||
\(872\) | −184.538 | − | 500.515i | −0.211626 | − | 0.573985i | ||||
\(873\) | −1043.79 | −1.19564 | ||||||||
\(874\) | −94.6839 | − | 40.6868i | −0.108334 | − | 0.0465524i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −493.304 | − | 519.971i | −0.563133 | − | 0.593574i | ||||
\(877\) | 316.570i | 0.360970i | 0.983578 | + | 0.180485i | \(0.0577667\pi\) | ||||
−0.983578 | + | 0.180485i | \(0.942233\pi\) | |||||||
\(878\) | 502.261 | + | 215.828i | 0.572052 | + | 0.245817i | ||||
\(879\) | 150.793i | 0.171551i | ||||||||
\(880\) | 181.246 | + | 9.54636i | 0.205961 | + | 0.0108481i | ||||
\(881\) | −464.977 | −0.527783 | −0.263891 | − | 0.964552i | \(-0.585006\pi\) | ||||
−0.263891 | + | 0.964552i | \(0.585006\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 69.4594 | 0.0786630 | 0.0393315 | − | 0.999226i | \(-0.487477\pi\) | ||||
0.0393315 | + | 0.999226i | \(0.487477\pi\) | |||||||
\(884\) | −57.5888 | + | 54.6354i | −0.0651457 | + | 0.0618048i | ||||
\(885\) | − | 617.315i | − | 0.697531i | ||||||
\(886\) | −374.882 | + | 872.405i | −0.423118 | + | 0.984655i | ||||
\(887\) | 10.9320i | 0.0123247i | 0.999981 | + | 0.00616235i | \(0.00196155\pi\) | ||||
−0.999981 | + | 0.00616235i | \(0.998038\pi\) | |||||||
\(888\) | 188.890 | + | 512.320i | 0.212714 | + | 0.576936i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −217.353 | − | 93.3991i | −0.244217 | − | 0.104943i | ||||
\(891\) | 640.258 | 0.718583 | ||||||||
\(892\) | 131.926 | − | 125.160i | 0.147899 | − | 0.140314i | ||||
\(893\) | 272.774i | 0.305458i | ||||||||
\(894\) | 2260.51 | + | 971.368i | 2.52854 | + | 1.08654i | ||||
\(895\) | 273.974i | 0.306116i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −992.062 | −1.10598 | ||||||||
\(898\) | −617.553 | + | 1437.13i | −0.687698 | + | 1.60037i | ||||
\(899\) | −325.104 | −0.361628 | ||||||||
\(900\) | −1088.59 | − | 1147.44i | −1.20955 | − | 1.27493i | ||||
\(901\) | 69.0341i | 0.0766194i | ||||||||
\(902\) | −179.119 | + | 416.837i | −0.198580 | + | 0.462125i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 53.7786 | − | 19.8279i | 0.0594896 | − | 0.0219336i | ||||
\(905\) | 458.789 | 0.506949 | ||||||||
\(906\) | −1449.06 | − | 622.676i | −1.59940 | − | 0.687280i | ||||
\(907\) | −22.7176 | −0.0250469 | −0.0125235 | − | 0.999922i | \(-0.503986\pi\) | ||||
−0.0125235 | + | 0.999922i | \(0.503986\pi\) | |||||||
\(908\) | −509.672 | − | 537.223i | −0.561312 | − | 0.591655i | ||||
\(909\) | − | 1754.83i | − | 1.93051i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 721.866i | − | 0.792389i | −0.918167 | − | 0.396194i | \(-0.870331\pi\) | ||
0.918167 | − | 0.396194i | \(-0.129669\pi\) | |||||||
\(912\) | 26.6110 | − | 505.232i | 0.0291787 | − | 0.553983i | ||||
\(913\) | −383.534 | −0.420081 | ||||||||
\(914\) | 149.677 | − | 348.320i | 0.163760 | − | 0.381094i | ||||
\(915\) | 319.920 | 0.349640 | ||||||||
\(916\) | 536.704 | − | 509.179i | 0.585922 | − | 0.555873i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −40.7139 | + | 94.7470i | −0.0443506 | + | 0.103210i | ||||
\(919\) | 130.722i | 0.142244i | 0.997468 | + | 0.0711221i | \(0.0226580\pi\) | ||||
−0.997468 | + | 0.0711221i | \(0.977342\pi\) | |||||||
\(920\) | −140.679 | + | 51.8678i | −0.152912 | + | 0.0563780i | ||||
\(921\) | 2137.67 | 2.32103 | ||||||||
\(922\) | −372.161 | − | 159.922i | −0.403646 | − | 0.173451i | ||||
\(923\) | 1595.38 | 1.72847 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 260.454i | 0.281572i | ||||||||
\(926\) | −1199.77 | − | 515.557i | −1.29565 | − | 0.556757i | ||||
\(927\) | 2192.27i | 2.36491i | ||||||||
\(928\) | 133.444 | − | 270.373i | 0.143797 | − | 0.291351i | ||||
\(929\) | −455.285 | −0.490081 | −0.245041 | − | 0.969513i | \(-0.578801\pi\) | ||||
−0.245041 | + | 0.969513i | \(0.578801\pi\) | |||||||
\(930\) | −313.349 | + | 729.207i | −0.336934 | + | 0.784093i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −266.221 | − | 280.612i | −0.285645 | − | 0.301086i | ||||
\(933\) | − | 865.032i | − | 0.927152i | ||||||
\(934\) | −430.691 | + | 1002.28i | −0.461125 | + | 1.07310i | ||||
\(935\) | − | 10.5139i | − | 0.0112448i | ||||||
\(936\) | −1151.51 | − | 3123.20i | −1.23025 | − | 3.33675i | ||||
\(937\) | −1242.79 | −1.32635 | −0.663176 | − | 0.748464i | \(-0.730792\pi\) | ||||
−0.663176 | + | 0.748464i | \(0.730792\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1419.69 | −1.51192 | ||||||||
\(940\) | 273.143 | + | 287.908i | 0.290578 | + | 0.306285i | ||||
\(941\) | − | 1137.11i | − | 1.20841i | −0.796830 | − | 0.604204i | \(-0.793491\pi\) | ||
0.796830 | − | 0.604204i | \(-0.206509\pi\) | |||||||
\(942\) | 1125.12 | + | 483.476i | 1.19439 | + | 0.513244i | ||||
\(943\) | − | 374.799i | − | 0.397454i | ||||||
\(944\) | −45.1698 | + | 857.586i | −0.0478493 | + | 0.908460i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 173.324 | − | 403.349i | 0.183217 | − | 0.426373i | ||||
\(947\) | 704.842 | 0.744289 | 0.372145 | − | 0.928175i | \(-0.378623\pi\) | ||||
0.372145 | + | 0.928175i | \(0.378623\pi\) | |||||||
\(948\) | 467.481 | − | 443.506i | 0.493123 | − | 0.467833i | ||||
\(949\) | − | 719.516i | − | 0.758183i | ||||||
\(950\) | 95.2769 | − | 221.723i | 0.100291 | − | 0.233392i | ||||
\(951\) | 2308.09i | 2.42702i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 765.039 | 0.802769 | 0.401384 | − | 0.915910i | \(-0.368529\pi\) | ||||
0.401384 | + | 0.915910i | \(0.368529\pi\) | |||||||
\(954\) | −2659.64 | − | 1142.88i | −2.78788 | − | 1.19799i | ||||
\(955\) | −87.4307 | −0.0915505 | ||||||||
\(956\) | 473.539 | − | 449.254i | 0.495334 | − | 0.469931i | ||||
\(957\) | 264.227i | 0.276099i | ||||||||
\(958\) | −200.102 | − | 85.9863i | −0.208875 | − | 0.0897561i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −477.828 | − | 559.911i | −0.497737 | − | 0.583240i | ||||
\(961\) | −229.522 | −0.238836 | ||||||||
\(962\) | −216.410 | + | 503.617i | −0.224958 | + | 0.523510i | ||||
\(963\) | −2798.15 | −2.90566 | ||||||||
\(964\) | −565.724 | − | 596.305i | −0.586851 | − | 0.618574i | ||||
\(965\) | − | 608.916i | − | 0.631001i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 771.494i | − | 0.797822i | −0.916990 | − | 0.398911i | \(-0.869388\pi\) | ||
0.916990 | − | 0.398911i | \(-0.130612\pi\) | |||||||
\(968\) | −700.630 | + | 258.319i | −0.723791 | + | 0.266859i | ||||
\(969\) | −29.3080 | −0.0302456 | ||||||||
\(970\) | −212.886 | − | 91.4795i | −0.219470 | − | 0.0943088i | ||||
\(971\) | 917.509 | 0.944911 | 0.472456 | − | 0.881354i | \(-0.343368\pi\) | ||||
0.472456 | + | 0.881354i | \(0.343368\pi\) | |||||||
\(972\) | −408.778 | − | 430.875i | −0.420554 | − | 0.443287i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 788.949 | + | 339.021i | 0.810010 | + | 0.348071i | ||||
\(975\) | − | 2323.13i | − | 2.38270i | ||||||
\(976\) | −444.440 | − | 23.4090i | −0.455368 | − | 0.0239846i | ||||
\(977\) | 266.601 | 0.272877 | 0.136439 | − | 0.990649i | \(-0.456434\pi\) | ||||
0.136439 | + | 0.990649i | \(0.456434\pi\) | |||||||
\(978\) | −207.611 | + | 483.139i | −0.212281 | + | 0.494007i | ||||
\(979\) | −288.408 | −0.294594 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 1295.81i | − | 1.32091i | ||||||
\(982\) | −358.393 | + | 834.031i | −0.364962 | + | 0.849318i | ||||
\(983\) | − | 1849.77i | − | 1.88176i | −0.338743 | − | 0.940879i | \(-0.610002\pi\) | ||
0.338743 | − | 0.940879i | \(-0.389998\pi\) | |||||||
\(984\) | 1726.40 | − | 636.518i | 1.75448 | − | 0.646868i | ||||
\(985\) | −564.698 | −0.573297 | ||||||||
\(986\) | −16.0473 | − | 6.89571i | −0.0162751 | − | 0.00699362i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 368.457 | − | 349.560i | 0.372932 | − | 0.353806i | ||||
\(989\) | 362.672i | 0.366705i | ||||||||
\(990\) | 405.062 | + | 174.060i | 0.409154 | + | 0.175818i | ||||
\(991\) | 350.359i | 0.353541i | 0.984252 | + | 0.176770i | \(0.0565650\pi\) | ||||
−0.984252 | + | 0.176770i | \(0.943435\pi\) | |||||||
\(992\) | 488.667 | − | 990.100i | 0.492608 | − | 0.998085i | ||||
\(993\) | 433.261 | 0.436315 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 694.800 | 0.698291 | ||||||||
\(996\) | 1070.57 | + | 1128.44i | 1.07487 | + | 1.13297i | ||||
\(997\) | − | 525.961i | − | 0.527543i | −0.964585 | − | 0.263772i | \(-0.915033\pi\) | ||
0.964585 | − | 0.263772i | \(-0.0849666\pi\) | |||||||
\(998\) | −263.252 | + | 612.626i | −0.263780 | + | 0.613854i | ||||
\(999\) | 712.089i | 0.712802i |
(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 | 392.3.g.j.99.4 | 6 | ||
4.3 | odd | 2 | 1568.3.g.j.687.1 | 6 | |||
7.2 | even | 3 | 56.3.k.d.11.6 | yes | 12 | ||
7.3 | odd | 6 | 392.3.k.l.275.2 | 12 | |||
7.4 | even | 3 | 56.3.k.d.51.2 | yes | 12 | ||
7.5 | odd | 6 | 392.3.k.l.67.6 | 12 | |||
7.6 | odd | 2 | 392.3.g.i.99.4 | 6 | |||
8.3 | odd | 2 | inner | 392.3.g.j.99.3 | 6 | ||
8.5 | even | 2 | 1568.3.g.j.687.2 | 6 | |||
28.11 | odd | 6 | 224.3.o.d.79.6 | 12 | |||
28.23 | odd | 6 | 224.3.o.d.207.5 | 12 | |||
28.27 | even | 2 | 1568.3.g.l.687.6 | 6 | |||
56.3 | even | 6 | 392.3.k.l.275.6 | 12 | |||
56.11 | odd | 6 | 56.3.k.d.51.6 | yes | 12 | ||
56.13 | odd | 2 | 1568.3.g.l.687.5 | 6 | |||
56.19 | even | 6 | 392.3.k.l.67.2 | 12 | |||
56.27 | even | 2 | 392.3.g.i.99.3 | 6 | |||
56.37 | even | 6 | 224.3.o.d.207.6 | 12 | |||
56.51 | odd | 6 | 56.3.k.d.11.2 | ✓ | 12 | ||
56.53 | even | 6 | 224.3.o.d.79.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.k.d.11.2 | ✓ | 12 | 56.51 | odd | 6 | ||
56.3.k.d.11.6 | yes | 12 | 7.2 | even | 3 | ||
56.3.k.d.51.2 | yes | 12 | 7.4 | even | 3 | ||
56.3.k.d.51.6 | yes | 12 | 56.11 | odd | 6 | ||
224.3.o.d.79.5 | 12 | 56.53 | even | 6 | |||
224.3.o.d.79.6 | 12 | 28.11 | odd | 6 | |||
224.3.o.d.207.5 | 12 | 28.23 | odd | 6 | |||
224.3.o.d.207.6 | 12 | 56.37 | even | 6 | |||
392.3.g.i.99.3 | 6 | 56.27 | even | 2 | |||
392.3.g.i.99.4 | 6 | 7.6 | odd | 2 | |||
392.3.g.j.99.3 | 6 | 8.3 | odd | 2 | inner | ||
392.3.g.j.99.4 | 6 | 1.1 | even | 1 | trivial | ||
392.3.k.l.67.2 | 12 | 56.19 | even | 6 | |||
392.3.k.l.67.6 | 12 | 7.5 | odd | 6 | |||
392.3.k.l.275.2 | 12 | 7.3 | odd | 6 | |||
392.3.k.l.275.6 | 12 | 56.3 | even | 6 | |||
1568.3.g.j.687.1 | 6 | 4.3 | odd | 2 | |||
1568.3.g.j.687.2 | 6 | 8.5 | even | 2 | |||
1568.3.g.l.687.5 | 6 | 56.13 | odd | 2 | |||
1568.3.g.l.687.6 | 6 | 28.27 | even | 2 |