Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [350,4,Mod(149,350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(350, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("350.149");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.j (of order \(6\), 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: | \(20.6506685020\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 249.2 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 350.249 |
Dual form | 350.4.j.b.149.2 |
$q$-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 \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.73205 | − | 1.00000i | 0.612372 | − | 0.353553i | ||||
\(3\) | −4.33013 | − | 2.50000i | −0.833333 | − | 0.481125i | 0.0216593 | − | 0.999765i | \(-0.493105\pi\) |
−0.854993 | + | 0.518640i | \(0.826438\pi\) | |||||||
\(4\) | 2.00000 | − | 3.46410i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −10.0000 | −0.680414 | ||||||||
\(7\) | −12.1244 | − | 14.0000i | −0.654654 | − | 0.755929i | ||||
\(8\) | − | 8.00000i | − | 0.353553i | ||||||
\(9\) | −1.00000 | − | 1.73205i | −0.0370370 | − | 0.0641500i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 28.5000 | − | 49.3634i | 0.781188 | − | 1.35306i | −0.150061 | − | 0.988677i | \(-0.547947\pi\) |
0.931250 | − | 0.364381i | \(-0.118720\pi\) | |||||||
\(12\) | −17.3205 | + | 10.0000i | −0.416667 | + | 0.240563i | ||||
\(13\) | 70.0000i | 1.49342i | 0.665148 | + | 0.746712i | \(0.268369\pi\) | ||||
−0.665148 | + | 0.746712i | \(0.731631\pi\) | |||||||
\(14\) | −35.0000 | − | 12.1244i | −0.668153 | − | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | −44.1673 | − | 25.5000i | −0.630126 | − | 0.363803i | 0.150675 | − | 0.988583i | \(-0.451855\pi\) |
−0.780801 | + | 0.624780i | \(0.785189\pi\) | |||||||
\(18\) | −3.46410 | − | 2.00000i | −0.0453609 | − | 0.0261891i | ||||
\(19\) | 2.50000 | + | 4.33013i | 0.0301863 | + | 0.0522842i | 0.880724 | − | 0.473630i | \(-0.157057\pi\) |
−0.850538 | + | 0.525914i | \(0.823723\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 17.5000 | + | 90.9327i | 0.181848 | + | 0.944911i | ||||
\(22\) | − | 114.000i | − | 1.10477i | ||||||
\(23\) | −59.7558 | + | 34.5000i | −0.541736 | + | 0.312772i | −0.745782 | − | 0.666190i | \(-0.767924\pi\) |
0.204046 | + | 0.978961i | \(0.434591\pi\) | |||||||
\(24\) | −20.0000 | + | 34.6410i | −0.170103 | + | 0.294628i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 70.0000 | + | 121.244i | 0.528005 | + | 0.914531i | ||||
\(27\) | 145.000i | 1.03353i | ||||||||
\(28\) | −72.7461 | + | 14.0000i | −0.490990 | + | 0.0944911i | ||||
\(29\) | −114.000 | −0.729975 | −0.364987 | − | 0.931012i | \(-0.618927\pi\) | ||||
−0.364987 | + | 0.931012i | \(0.618927\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −11.5000 | + | 19.9186i | −0.0666278 | + | 0.115403i | −0.897415 | − | 0.441188i | \(-0.854557\pi\) |
0.830787 | + | 0.556590i | \(0.187891\pi\) | |||||||
\(32\) | −27.7128 | − | 16.0000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | −246.817 | + | 142.500i | −1.30198 | + | 0.751699i | ||||
\(34\) | −102.000 | −0.514496 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −8.00000 | −0.0370370 | ||||||||
\(37\) | −219.104 | + | 126.500i | −0.973528 | + | 0.562067i | −0.900310 | − | 0.435249i | \(-0.856660\pi\) |
−0.0732182 | + | 0.997316i | \(0.523327\pi\) | |||||||
\(38\) | 8.66025 | + | 5.00000i | 0.0369705 | + | 0.0213449i | ||||
\(39\) | 175.000 | − | 303.109i | 0.718524 | − | 1.24452i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −42.0000 | −0.159983 | −0.0799914 | − | 0.996796i | \(-0.525489\pi\) | ||||
−0.0799914 | + | 0.996796i | \(0.525489\pi\) | |||||||
\(42\) | 121.244 | + | 140.000i | 0.445435 | + | 0.514344i | ||||
\(43\) | 124.000i | 0.439763i | 0.975527 | + | 0.219882i | \(0.0705671\pi\) | ||||
−0.975527 | + | 0.219882i | \(0.929433\pi\) | |||||||
\(44\) | −114.000 | − | 197.454i | −0.390594 | − | 0.676529i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −69.0000 | + | 119.512i | −0.221163 | + | 0.383065i | ||||
\(47\) | 174.071 | − | 100.500i | 0.540231 | − | 0.311903i | −0.204941 | − | 0.978774i | \(-0.565700\pi\) |
0.745173 | + | 0.666871i | \(0.232367\pi\) | |||||||
\(48\) | 80.0000i | 0.240563i | ||||||||
\(49\) | −49.0000 | + | 339.482i | −0.142857 | + | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 127.500 | + | 220.836i | 0.350070 | + | 0.606339i | ||||
\(52\) | 242.487 | + | 140.000i | 0.646671 | + | 0.373356i | ||||
\(53\) | −340.348 | − | 196.500i | −0.882083 | − | 0.509271i | −0.0107383 | − | 0.999942i | \(-0.503418\pi\) |
−0.871345 | + | 0.490672i | \(0.836751\pi\) | |||||||
\(54\) | 145.000 | + | 251.147i | 0.365407 | + | 0.632904i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −112.000 | + | 96.9948i | −0.267261 | + | 0.231455i | ||||
\(57\) | − | 25.0000i | − | 0.0580935i | ||||||
\(58\) | −197.454 | + | 114.000i | −0.447016 | + | 0.258085i | ||||
\(59\) | 109.500 | − | 189.660i | 0.241622 | − | 0.418501i | −0.719555 | − | 0.694436i | \(-0.755654\pi\) |
0.961176 | + | 0.275935i | \(0.0889873\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 354.500 | + | 614.012i | 0.744083 | + | 1.28879i | 0.950622 | + | 0.310351i | \(0.100447\pi\) |
−0.206539 | + | 0.978438i | \(0.566220\pi\) | |||||||
\(62\) | 46.0000i | 0.0942259i | ||||||||
\(63\) | −12.1244 | + | 35.0000i | −0.0242464 | + | 0.0699934i | ||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −285.000 | + | 493.634i | −0.531531 | + | 0.920639i | ||||
\(67\) | −362.865 | − | 209.500i | −0.661656 | − | 0.382007i | 0.131251 | − | 0.991349i | \(-0.458100\pi\) |
−0.792908 | + | 0.609342i | \(0.791434\pi\) | |||||||
\(68\) | −176.669 | + | 102.000i | −0.315063 | + | 0.181902i | ||||
\(69\) | 345.000 | 0.601929 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −96.0000 | −0.160466 | −0.0802331 | − | 0.996776i | \(-0.525566\pi\) | ||||
−0.0802331 | + | 0.996776i | \(0.525566\pi\) | |||||||
\(72\) | −13.8564 | + | 8.00000i | −0.0226805 | + | 0.0130946i | ||||
\(73\) | −271.066 | − | 156.500i | −0.434601 | − | 0.250917i | 0.266704 | − | 0.963779i | \(-0.414065\pi\) |
−0.701305 | + | 0.712862i | \(0.747399\pi\) | |||||||
\(74\) | −253.000 | + | 438.209i | −0.397441 | + | 0.688388i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 20.0000 | 0.0301863 | ||||||||
\(77\) | −1036.63 | + | 199.500i | −1.53422 | + | 0.295261i | ||||
\(78\) | − | 700.000i | − | 1.01615i | ||||||
\(79\) | 230.500 | + | 399.238i | 0.328269 | + | 0.568579i | 0.982169 | − | 0.188003i | \(-0.0602013\pi\) |
−0.653899 | + | 0.756582i | \(0.726868\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 335.500 | − | 581.103i | 0.460219 | − | 0.797124i | ||||
\(82\) | −72.7461 | + | 42.0000i | −0.0979691 | + | 0.0565625i | ||||
\(83\) | 588.000i | 0.777607i | 0.921321 | + | 0.388804i | \(0.127112\pi\) | ||||
−0.921321 | + | 0.388804i | \(0.872888\pi\) | |||||||
\(84\) | 350.000 | + | 121.244i | 0.454621 | + | 0.157485i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 124.000 | + | 214.774i | 0.155480 | + | 0.269299i | ||||
\(87\) | 493.634 | + | 285.000i | 0.608312 | + | 0.351209i | ||||
\(88\) | −394.908 | − | 228.000i | −0.478378 | − | 0.276192i | ||||
\(89\) | −508.500 | − | 880.748i | −0.605628 | − | 1.04898i | −0.991952 | − | 0.126615i | \(-0.959589\pi\) |
0.386324 | − | 0.922363i | \(-0.373745\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 980.000 | − | 848.705i | 1.12892 | − | 0.977675i | ||||
\(92\) | 276.000i | 0.312772i | ||||||||
\(93\) | 99.5929 | − | 57.5000i | 0.111046 | − | 0.0641126i | ||||
\(94\) | 201.000 | − | 348.142i | 0.220549 | − | 0.382001i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 80.0000 | + | 138.564i | 0.0850517 | + | 0.147314i | ||||
\(97\) | − | 1834.00i | − | 1.91974i | −0.280451 | − | 0.959868i | \(-0.590484\pi\) | ||
0.280451 | − | 0.959868i | \(-0.409516\pi\) | |||||||
\(98\) | 254.611 | + | 637.000i | 0.262445 | + | 0.656599i | ||||
\(99\) | −114.000 | −0.115732 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 142.500 | − | 246.817i | 0.140389 | − | 0.243161i | −0.787254 | − | 0.616629i | \(-0.788498\pi\) |
0.927643 | + | 0.373468i | \(0.121831\pi\) | |||||||
\(102\) | 441.673 | + | 255.000i | 0.428746 | + | 0.247537i | ||||
\(103\) | 432.147 | − | 249.500i | 0.413405 | − | 0.238679i | −0.278847 | − | 0.960336i | \(-0.589952\pi\) |
0.692252 | + | 0.721656i | \(0.256619\pi\) | |||||||
\(104\) | 560.000 | 0.528005 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −786.000 | −0.720218 | ||||||||
\(107\) | −958.690 | + | 553.500i | −0.866169 | + | 0.500083i | −0.866073 | − | 0.499917i | \(-0.833364\pi\) |
−9.56665e−5 | 1.00000i | \(0.500030\pi\) | ||||||||
\(108\) | 502.295 | + | 290.000i | 0.447531 | + | 0.258382i | ||||
\(109\) | 461.500 | − | 799.341i | 0.405538 | − | 0.702413i | −0.588846 | − | 0.808246i | \(-0.700417\pi\) |
0.994384 | + | 0.105832i | \(0.0337507\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1265.00 | 1.08170 | ||||||||
\(112\) | −96.9948 | + | 280.000i | −0.0818317 | + | 0.236228i | ||||
\(113\) | − | 1542.00i | − | 1.28371i | −0.766826 | − | 0.641855i | \(-0.778165\pi\) | ||
0.766826 | − | 0.641855i | \(-0.221835\pi\) | |||||||
\(114\) | −25.0000 | − | 43.3013i | −0.0205392 | − | 0.0355749i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −228.000 | + | 394.908i | −0.182494 | + | 0.316088i | ||||
\(117\) | 121.244 | − | 70.0000i | 0.0958032 | − | 0.0553120i | ||||
\(118\) | − | 438.000i | − | 0.341705i | ||||||
\(119\) | 178.500 | + | 927.513i | 0.137505 | + | 0.714496i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −959.000 | − | 1661.04i | −0.720511 | − | 1.24796i | ||||
\(122\) | 1228.02 | + | 709.000i | 0.911312 | + | 0.526146i | ||||
\(123\) | 181.865 | + | 105.000i | 0.133319 | + | 0.0769718i | ||||
\(124\) | 46.0000 | + | 79.6743i | 0.0333139 | + | 0.0577013i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 14.0000 | + | 72.7461i | 0.00989856 | + | 0.0514344i | ||||
\(127\) | − | 2056.00i | − | 1.43654i | −0.695765 | − | 0.718270i | \(-0.744934\pi\) | ||
0.695765 | − | 0.718270i | \(-0.255066\pi\) | |||||||
\(128\) | −110.851 | + | 64.0000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 310.000 | − | 536.936i | 0.211581 | − | 0.366469i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1024.50 | − | 1774.49i | −0.683290 | − | 1.18349i | −0.973971 | − | 0.226673i | \(-0.927215\pi\) |
0.290681 | − | 0.956820i | \(-0.406118\pi\) | |||||||
\(132\) | 1140.00i | 0.751699i | ||||||||
\(133\) | 30.3109 | − | 87.5000i | 0.0197616 | − | 0.0570467i | ||||
\(134\) | −838.000 | −0.540240 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −204.000 | + | 353.338i | −0.128624 | + | 0.222783i | ||||
\(137\) | 122.110 | + | 70.5000i | 0.0761498 | + | 0.0439651i | 0.537591 | − | 0.843205i | \(-0.319334\pi\) |
−0.461442 | + | 0.887171i | \(0.652668\pi\) | |||||||
\(138\) | 597.558 | − | 345.000i | 0.368605 | − | 0.212814i | ||||
\(139\) | −1484.00 | −0.905548 | −0.452774 | − | 0.891625i | \(-0.649566\pi\) | ||||
−0.452774 | + | 0.891625i | \(0.649566\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1005.00 | −0.600257 | ||||||||
\(142\) | −166.277 | + | 96.0000i | −0.0982651 | + | 0.0567334i | ||||
\(143\) | 3455.44 | + | 1995.00i | 2.02069 | + | 1.16665i | ||||
\(144\) | −16.0000 | + | 27.7128i | −0.00925926 | + | 0.0160375i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −626.000 | −0.354850 | ||||||||
\(147\) | 1060.88 | − | 1347.50i | 0.595238 | − | 0.756054i | ||||
\(148\) | 1012.00i | 0.562067i | ||||||||
\(149\) | −28.5000 | − | 49.3634i | −0.0156699 | − | 0.0271410i | 0.858084 | − | 0.513509i | \(-0.171655\pi\) |
−0.873754 | + | 0.486368i | \(0.838321\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −419.500 | + | 726.595i | −0.226082 | + | 0.391586i | −0.956644 | − | 0.291261i | \(-0.905925\pi\) |
0.730561 | + | 0.682847i | \(0.239258\pi\) | |||||||
\(152\) | 34.6410 | − | 20.0000i | 0.0184852 | − | 0.0106725i | ||||
\(153\) | 102.000i | 0.0538968i | ||||||||
\(154\) | −1596.00 | + | 1382.18i | −0.835126 | + | 0.723240i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −700.000 | − | 1212.44i | −0.359262 | − | 0.622260i | ||||
\(157\) | 2453.45 | + | 1416.50i | 1.24718 | + | 0.720057i | 0.970545 | − | 0.240919i | \(-0.0774488\pi\) |
0.276631 | + | 0.960976i | \(0.410782\pi\) | |||||||
\(158\) | 798.475 | + | 461.000i | 0.402046 | + | 0.232121i | ||||
\(159\) | 982.500 | + | 1701.74i | 0.490046 | + | 0.848785i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1207.50 | + | 418.290i | 0.591083 | + | 0.204757i | ||||
\(162\) | − | 1342.00i | − | 0.650849i | ||||||
\(163\) | 2001.38 | − | 1155.50i | 0.961721 | − | 0.555250i | 0.0650188 | − | 0.997884i | \(-0.479289\pi\) |
0.896702 | + | 0.442634i | \(0.145956\pi\) | |||||||
\(164\) | −84.0000 | + | 145.492i | −0.0399957 | + | 0.0692746i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 588.000 | + | 1018.45i | 0.274926 | + | 0.476185i | ||||
\(167\) | 1260.00i | 0.583843i | 0.956442 | + | 0.291921i | \(0.0942945\pi\) | ||||
−0.956442 | + | 0.291921i | \(0.905705\pi\) | |||||||
\(168\) | 727.461 | − | 140.000i | 0.334077 | − | 0.0642931i | ||||
\(169\) | −2703.00 | −1.23031 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.00000 | − | 8.66025i | 0.00223602 | − | 0.00387290i | ||||
\(172\) | 429.549 | + | 248.000i | 0.190423 | + | 0.109941i | ||||
\(173\) | −2829.30 | + | 1633.50i | −1.24340 | + | 0.717877i | −0.969785 | − | 0.243962i | \(-0.921553\pi\) |
−0.273615 | + | 0.961839i | \(0.588219\pi\) | |||||||
\(174\) | 1140.00 | 0.496685 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −912.000 | −0.390594 | ||||||||
\(177\) | −948.298 | + | 547.500i | −0.402703 | + | 0.232501i | ||||
\(178\) | −1761.50 | − | 1017.00i | −0.741740 | − | 0.428244i | ||||
\(179\) | 643.500 | − | 1114.57i | 0.268701 | − | 0.465403i | −0.699826 | − | 0.714314i | \(-0.746739\pi\) |
0.968527 | + | 0.248910i | \(0.0800724\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2674.00 | −1.09810 | −0.549052 | − | 0.835788i | \(-0.685011\pi\) | ||||
−0.549052 | + | 0.835788i | \(0.685011\pi\) | |||||||
\(182\) | 848.705 | − | 2450.00i | 0.345660 | − | 0.997836i | ||||
\(183\) | − | 3545.00i | − | 1.43199i | ||||||
\(184\) | 276.000 | + | 478.046i | 0.110581 | + | 0.191533i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 115.000 | − | 199.186i | 0.0453345 | − | 0.0785216i | ||||
\(187\) | −2517.54 | + | 1453.50i | −0.984494 | + | 0.568398i | ||||
\(188\) | − | 804.000i | − | 0.311903i | ||||||
\(189\) | 2030.00 | − | 1758.03i | 0.781274 | − | 0.676603i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2092.50 | − | 3624.32i | −0.792712 | − | 1.37302i | −0.924282 | − | 0.381711i | \(-0.875335\pi\) |
0.131570 | − | 0.991307i | \(-0.457998\pi\) | |||||||
\(192\) | 277.128 | + | 160.000i | 0.104167 | + | 0.0601407i | ||||
\(193\) | −73.6122 | − | 42.5000i | −0.0274545 | − | 0.0158509i | 0.486210 | − | 0.873842i | \(-0.338379\pi\) |
−0.513664 | + | 0.857991i | \(0.671712\pi\) | |||||||
\(194\) | −1834.00 | − | 3176.58i | −0.678730 | − | 1.17559i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1078.00 | + | 848.705i | 0.392857 | + | 0.309295i | ||||
\(197\) | − | 390.000i | − | 0.141047i | −0.997510 | − | 0.0705237i | \(-0.977533\pi\) | ||
0.997510 | − | 0.0705237i | \(-0.0224671\pi\) | |||||||
\(198\) | −197.454 | + | 114.000i | −0.0708709 | + | 0.0409173i | ||||
\(199\) | −1416.50 | + | 2453.45i | −0.504588 | + | 0.873972i | 0.495398 | + | 0.868666i | \(0.335022\pi\) |
−0.999986 | + | 0.00530596i | \(0.998311\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1047.50 | + | 1814.32i | 0.367587 | + | 0.636679i | ||||
\(202\) | − | 570.000i | − | 0.198540i | ||||||
\(203\) | 1382.18 | + | 1596.00i | 0.477881 | + | 0.551809i | ||||
\(204\) | 1020.00 | 0.350070 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 499.000 | − | 864.293i | 0.168772 | − | 0.292321i | ||||
\(207\) | 119.512 | + | 69.0000i | 0.0401286 | + | 0.0231683i | ||||
\(208\) | 969.948 | − | 560.000i | 0.323336 | − | 0.186678i | ||||
\(209\) | 285.000 | 0.0943247 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −124.000 | −0.0404574 | −0.0202287 | − | 0.999795i | \(-0.506439\pi\) | ||||
−0.0202287 | + | 0.999795i | \(0.506439\pi\) | |||||||
\(212\) | −1361.39 | + | 786.000i | −0.441041 | + | 0.254635i | ||||
\(213\) | 415.692 | + | 240.000i | 0.133722 | + | 0.0772044i | ||||
\(214\) | −1107.00 | + | 1917.38i | −0.353612 | + | 0.612474i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1160.00 | 0.365407 | ||||||||
\(217\) | 418.290 | − | 80.5000i | 0.130854 | − | 0.0251829i | ||||
\(218\) | − | 1846.00i | − | 0.573518i | ||||||
\(219\) | 782.500 | + | 1355.33i | 0.241445 | + | 0.418195i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1785.00 | − | 3091.71i | 0.543313 | − | 0.941045i | ||||
\(222\) | 2191.04 | − | 1265.00i | 0.662402 | − | 0.382438i | ||||
\(223\) | − | 56.0000i | − | 0.0168163i | −0.999965 | − | 0.00840816i | \(-0.997324\pi\) | ||
0.999965 | − | 0.00840816i | \(-0.00267643\pi\) | |||||||
\(224\) | 112.000 | + | 581.969i | 0.0334077 | + | 0.173591i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1542.00 | − | 2670.82i | −0.453860 | − | 0.786108i | ||||
\(227\) | 2647.44 | + | 1528.50i | 0.774083 | + | 0.446917i | 0.834329 | − | 0.551267i | \(-0.185855\pi\) |
−0.0602465 | + | 0.998184i | \(0.519189\pi\) | |||||||
\(228\) | −86.6025 | − | 50.0000i | −0.0251552 | − | 0.0145234i | ||||
\(229\) | −480.500 | − | 832.250i | −0.138656 | − | 0.240160i | 0.788332 | − | 0.615250i | \(-0.210945\pi\) |
−0.926988 | + | 0.375090i | \(0.877612\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4987.50 | + | 1727.72i | 1.42058 | + | 0.492102i | ||||
\(232\) | 912.000i | 0.258085i | ||||||||
\(233\) | 2449.99 | − | 1414.50i | 0.688858 | − | 0.397712i | −0.114326 | − | 0.993443i | \(-0.536471\pi\) |
0.803184 | + | 0.595731i | \(0.203138\pi\) | |||||||
\(234\) | 140.000 | − | 242.487i | 0.0391115 | − | 0.0677431i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −438.000 | − | 758.638i | −0.120811 | − | 0.209251i | ||||
\(237\) | − | 2305.00i | − | 0.631755i | ||||||
\(238\) | 1236.68 | + | 1428.00i | 0.336817 | + | 0.388922i | ||||
\(239\) | 3540.00 | 0.958090 | 0.479045 | − | 0.877790i | \(-0.340983\pi\) | ||||
0.479045 | + | 0.877790i | \(0.340983\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2615.50 | + | 4530.18i | −0.699084 | + | 1.21085i | 0.269701 | + | 0.962944i | \(0.413075\pi\) |
−0.968785 | + | 0.247904i | \(0.920258\pi\) | |||||||
\(242\) | −3322.07 | − | 1918.00i | −0.882442 | − | 0.509478i | ||||
\(243\) | 484.974 | − | 280.000i | 0.128029 | − | 0.0739177i | ||||
\(244\) | 2836.00 | 0.744083 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 420.000 | 0.108855 | ||||||||
\(247\) | −303.109 | + | 175.000i | −0.0780824 | + | 0.0450809i | ||||
\(248\) | 159.349 | + | 92.0000i | 0.0408010 | + | 0.0235565i | ||||
\(249\) | 1470.00 | − | 2546.11i | 0.374126 | − | 0.648006i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5040.00 | 1.26742 | 0.633709 | − | 0.773571i | \(-0.281532\pi\) | ||||
0.633709 | + | 0.773571i | \(0.281532\pi\) | |||||||
\(252\) | 96.9948 | + | 112.000i | 0.0242464 | + | 0.0279974i | ||||
\(253\) | 3933.00i | 0.977334i | ||||||||
\(254\) | −2056.00 | − | 3561.10i | −0.507893 | − | 0.879697i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −1244.48 | + | 718.500i | −0.302056 | + | 0.174392i | −0.643366 | − | 0.765559i | \(-0.722463\pi\) |
0.341310 | + | 0.939951i | \(0.389129\pi\) | |||||||
\(258\) | − | 1240.00i | − | 0.299221i | ||||||
\(259\) | 4427.50 | + | 1533.73i | 1.06221 | + | 0.367959i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 114.000 | + | 197.454i | 0.0270361 | + | 0.0468279i | ||||
\(262\) | −3548.97 | − | 2049.00i | −0.836856 | − | 0.483159i | ||||
\(263\) | −2013.51 | − | 1162.50i | −0.472085 | − | 0.272558i | 0.245027 | − | 0.969516i | \(-0.421203\pi\) |
−0.717112 | + | 0.696958i | \(0.754536\pi\) | |||||||
\(264\) | 1140.00 | + | 1974.54i | 0.265766 | + | 0.460320i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −35.0000 | − | 181.865i | −0.00806762 | − | 0.0419206i | ||||
\(267\) | 5085.00i | 1.16553i | ||||||||
\(268\) | −1451.46 | + | 838.000i | −0.330828 | + | 0.191004i | ||||
\(269\) | −1192.50 | + | 2065.47i | −0.270290 | + | 0.468156i | −0.968936 | − | 0.247311i | \(-0.920453\pi\) |
0.698646 | + | 0.715467i | \(0.253786\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 165.500 | + | 286.654i | 0.0370975 | + | 0.0642547i | 0.883978 | − | 0.467528i | \(-0.154855\pi\) |
−0.846881 | + | 0.531783i | \(0.821522\pi\) | |||||||
\(272\) | 816.000i | 0.181902i | ||||||||
\(273\) | −6365.29 | + | 1225.00i | −1.41115 | + | 0.271576i | ||||
\(274\) | 282.000 | 0.0621761 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 690.000 | − | 1195.12i | 0.150482 | − | 0.260643i | ||||
\(277\) | −4218.41 | − | 2435.50i | −0.915017 | − | 0.528285i | −0.0329750 | − | 0.999456i | \(-0.510498\pi\) |
−0.882042 | + | 0.471171i | \(0.843831\pi\) | |||||||
\(278\) | −2570.36 | + | 1484.00i | −0.554533 | + | 0.320160i | ||||
\(279\) | 46.0000 | 0.00987078 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7026.00 | −1.49159 | −0.745794 | − | 0.666177i | \(-0.767930\pi\) | ||||
−0.745794 | + | 0.666177i | \(0.767930\pi\) | |||||||
\(282\) | −1740.71 | + | 1005.00i | −0.367581 | + | 0.212223i | ||||
\(283\) | −4635.83 | − | 2676.50i | −0.973752 | − | 0.562196i | −0.0733738 | − | 0.997305i | \(-0.523377\pi\) |
−0.900378 | + | 0.435109i | \(0.856710\pi\) | |||||||
\(284\) | −192.000 | + | 332.554i | −0.0401166 | + | 0.0694839i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7980.00 | 1.64989 | ||||||||
\(287\) | 509.223 | + | 588.000i | 0.104733 | + | 0.120936i | ||||
\(288\) | 64.0000i | 0.0130946i | ||||||||
\(289\) | −1156.00 | − | 2002.25i | −0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4585.00 | + | 7941.45i | −0.923634 | + | 1.59978i | ||||
\(292\) | −1084.26 | + | 626.000i | −0.217300 | + | 0.125458i | ||||
\(293\) | − | 4158.00i | − | 0.829054i | −0.910037 | − | 0.414527i | \(-0.863947\pi\) | ||
0.910037 | − | 0.414527i | \(-0.136053\pi\) | |||||||
\(294\) | 490.000 | − | 3394.82i | 0.0972020 | − | 0.673435i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1012.00 | + | 1752.84i | 0.198721 | + | 0.344194i | ||||
\(297\) | 7157.70 | + | 4132.50i | 1.39842 | + | 0.807380i | ||||
\(298\) | −98.7269 | − | 57.0000i | −0.0191916 | − | 0.0110803i | ||||
\(299\) | −2415.00 | − | 4182.90i | −0.467101 | − | 0.809042i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1736.00 | − | 1503.42i | 0.332430 | − | 0.287893i | ||||
\(302\) | 1678.00i | 0.319729i | ||||||||
\(303\) | −1234.09 | + | 712.500i | −0.233982 | + | 0.135089i | ||||
\(304\) | 40.0000 | − | 69.2820i | 0.00754657 | − | 0.0130710i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 102.000 | + | 176.669i | 0.0190554 | + | 0.0330049i | ||||
\(307\) | − | 9604.00i | − | 1.78544i | −0.450615 | − | 0.892719i | \(-0.648795\pi\) | ||
0.450615 | − | 0.892719i | \(-0.351205\pi\) | |||||||
\(308\) | −1382.18 | + | 3990.00i | −0.255704 | + | 0.738154i | ||||
\(309\) | −2495.00 | −0.459338 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5065.50 | + | 8773.70i | −0.923595 | + | 1.59971i | −0.129791 | + | 0.991541i | \(0.541430\pi\) |
−0.793805 | + | 0.608173i | \(0.791903\pi\) | |||||||
\(312\) | −2424.87 | − | 1400.00i | −0.440004 | − | 0.254037i | ||||
\(313\) | −9352.21 | + | 5399.50i | −1.68888 | + | 0.975073i | −0.733495 | + | 0.679695i | \(0.762112\pi\) |
−0.955380 | + | 0.295378i | \(0.904554\pi\) | |||||||
\(314\) | 5666.00 | 1.01831 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1844.00 | 0.328269 | ||||||||
\(317\) | 459.859 | − | 265.500i | 0.0814772 | − | 0.0470409i | −0.458708 | − | 0.888587i | \(-0.651688\pi\) |
0.540185 | + | 0.841546i | \(0.318354\pi\) | |||||||
\(318\) | 3403.48 | + | 1965.00i | 0.600181 | + | 0.346515i | ||||
\(319\) | −3249.00 | + | 5627.43i | −0.570248 | + | 0.987698i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5535.00 | 0.962410 | ||||||||
\(322\) | 2509.74 | − | 483.000i | 0.434355 | − | 0.0835917i | ||||
\(323\) | − | 255.000i | − | 0.0439275i | ||||||
\(324\) | −1342.00 | − | 2324.41i | −0.230110 | − | 0.398562i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2311.00 | − | 4002.77i | 0.392621 | − | 0.680040i | ||||
\(327\) | −3996.71 | + | 2307.50i | −0.675897 | + | 0.390229i | ||||
\(328\) | 336.000i | 0.0565625i | ||||||||
\(329\) | −3517.50 | − | 1218.50i | −0.589441 | − | 0.204188i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3507.50 | + | 6075.17i | 0.582446 | + | 1.00883i | 0.995189 | + | 0.0979784i | \(0.0312376\pi\) |
−0.412743 | + | 0.910848i | \(0.635429\pi\) | |||||||
\(332\) | 2036.89 | + | 1176.00i | 0.336714 | + | 0.194402i | ||||
\(333\) | 438.209 | + | 253.000i | 0.0721132 | + | 0.0416346i | ||||
\(334\) | 1260.00 | + | 2182.38i | 0.206420 | + | 0.357529i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1120.00 | − | 969.948i | 0.181848 | − | 0.157485i | ||||
\(337\) | 8990.00i | 1.45316i | 0.687079 | + | 0.726582i | \(0.258892\pi\) | ||||
−0.687079 | + | 0.726582i | \(0.741108\pi\) | |||||||
\(338\) | −4681.73 | + | 2703.00i | −0.753410 | + | 0.434982i | ||||
\(339\) | −3855.00 | + | 6677.06i | −0.617625 | + | 1.06976i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 655.500 | + | 1135.36i | 0.104098 | + | 0.180303i | ||||
\(342\) | − | 20.0000i | − | 0.00316221i | ||||||
\(343\) | 5346.84 | − | 3430.00i | 0.841698 | − | 0.539949i | ||||
\(344\) | 992.000 | 0.155480 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3267.00 | + | 5658.61i | −0.507616 | + | 0.879216i | ||||
\(347\) | 7542.22 | + | 4354.50i | 1.16682 | + | 0.673665i | 0.952929 | − | 0.303192i | \(-0.0980523\pi\) |
0.213893 | + | 0.976857i | \(0.431386\pi\) | |||||||
\(348\) | 1974.54 | − | 1140.00i | 0.304156 | − | 0.175605i | ||||
\(349\) | −6482.00 | −0.994193 | −0.497097 | − | 0.867695i | \(-0.665601\pi\) | ||||
−0.497097 | + | 0.867695i | \(0.665601\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10150.0 | −1.54350 | ||||||||
\(352\) | −1579.63 | + | 912.000i | −0.239189 | + | 0.138096i | ||||
\(353\) | −1847.23 | − | 1066.50i | −0.278522 | − | 0.160805i | 0.354232 | − | 0.935158i | \(-0.384742\pi\) |
−0.632754 | + | 0.774353i | \(0.718076\pi\) | |||||||
\(354\) | −1095.00 | + | 1896.60i | −0.164403 | + | 0.284754i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4068.00 | −0.605628 | ||||||||
\(357\) | 1545.86 | − | 4462.50i | 0.229175 | − | 0.661570i | ||||
\(358\) | − | 2574.00i | − | 0.380000i | ||||||
\(359\) | 1924.50 | + | 3333.33i | 0.282928 | + | 0.490046i | 0.972105 | − | 0.234548i | \(-0.0753608\pi\) |
−0.689176 | + | 0.724594i | \(0.742028\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3417.00 | − | 5918.42i | 0.498178 | − | 0.862869i | ||||
\(362\) | −4631.50 | + | 2674.00i | −0.672449 | + | 0.388238i | ||||
\(363\) | 9590.00i | 1.38662i | ||||||||
\(364\) | −980.000 | − | 5092.23i | −0.141115 | − | 0.733256i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3545.00 | − | 6140.12i | −0.506284 | − | 0.876910i | ||||
\(367\) | −5621.37 | − | 3245.50i | −0.799545 | − | 0.461618i | 0.0437668 | − | 0.999042i | \(-0.486064\pi\) |
−0.843312 | + | 0.537424i | \(0.819397\pi\) | |||||||
\(368\) | 956.092 | + | 552.000i | 0.135434 | + | 0.0781929i | ||||
\(369\) | 42.0000 | + | 72.7461i | 0.00592529 | + | 0.0102629i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1375.50 | + | 7147.31i | 0.192486 | + | 1.00019i | ||||
\(372\) | − | 460.000i | − | 0.0641126i | ||||||
\(373\) | −799.341 | + | 461.500i | −0.110961 | + | 0.0640632i | −0.554453 | − | 0.832215i | \(-0.687073\pi\) |
0.443493 | + | 0.896278i | \(0.353739\pi\) | |||||||
\(374\) | −2907.00 | + | 5035.07i | −0.401918 | + | 0.696143i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −804.000 | − | 1392.57i | −0.110274 | − | 0.191001i | ||||
\(377\) | − | 7980.00i | − | 1.09016i | ||||||
\(378\) | 1758.03 | − | 5075.00i | 0.239215 | − | 0.690555i | ||||
\(379\) | −6344.00 | −0.859814 | −0.429907 | − | 0.902873i | \(-0.641454\pi\) | ||||
−0.429907 | + | 0.902873i | \(0.641454\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5140.00 | + | 8902.74i | −0.691155 | + | 1.19712i | ||||
\(382\) | −7248.63 | − | 4185.00i | −0.970870 | − | 0.560532i | ||||
\(383\) | 4336.19 | − | 2503.50i | 0.578509 | − | 0.334002i | −0.182032 | − | 0.983293i | \(-0.558267\pi\) |
0.760541 | + | 0.649290i | \(0.224934\pi\) | |||||||
\(384\) | 640.000 | 0.0850517 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −170.000 | −0.0224165 | ||||||||
\(387\) | 214.774 | − | 124.000i | 0.0282108 | − | 0.0162875i | ||||
\(388\) | −6353.16 | − | 3668.00i | −0.831270 | − | 0.479934i | ||||
\(389\) | 6145.50 | − | 10644.3i | 0.801001 | − | 1.38737i | −0.117958 | − | 0.993019i | \(-0.537635\pi\) |
0.918958 | − | 0.394355i | \(-0.129032\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3519.00 | 0.455150 | ||||||||
\(392\) | 2715.86 | + | 392.000i | 0.349927 | + | 0.0505076i | ||||
\(393\) | 10245.0i | 1.31499i | ||||||||
\(394\) | −390.000 | − | 675.500i | −0.0498678 | − | 0.0863736i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −228.000 | + | 394.908i | −0.0289329 | + | 0.0501133i | ||||
\(397\) | 768.165 | − | 443.500i | 0.0971110 | − | 0.0560671i | −0.450658 | − | 0.892697i | \(-0.648811\pi\) |
0.547769 | + | 0.836630i | \(0.315477\pi\) | |||||||
\(398\) | 5666.00i | 0.713595i | ||||||||
\(399\) | −350.000 | + | 303.109i | −0.0439146 | + | 0.0380311i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5977.50 | − | 10353.3i | −0.744394 | − | 1.28933i | −0.950477 | − | 0.310794i | \(-0.899405\pi\) |
0.206083 | − | 0.978535i | \(-0.433928\pi\) | |||||||
\(402\) | 3628.65 | + | 2095.00i | 0.450200 | + | 0.259923i | ||||
\(403\) | −1394.30 | − | 805.000i | −0.172345 | − | 0.0995035i | ||||
\(404\) | −570.000 | − | 987.269i | −0.0701945 | − | 0.121580i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3990.00 | + | 1382.18i | 0.487735 | + | 0.168956i | ||||
\(407\) | 14421.0i | 1.75632i | ||||||||
\(408\) | 1766.69 | − | 1020.00i | 0.214373 | − | 0.123768i | ||||
\(409\) | −1710.50 | + | 2962.67i | −0.206794 | + | 0.358178i | −0.950703 | − | 0.310103i | \(-0.899636\pi\) |
0.743909 | + | 0.668281i | \(0.232970\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −352.500 | − | 610.548i | −0.0423055 | − | 0.0732752i | ||||
\(412\) | − | 1996.00i | − | 0.238679i | ||||||
\(413\) | −3982.85 | + | 766.500i | −0.474536 | + | 0.0913245i | ||||
\(414\) | 276.000 | 0.0327649 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1120.00 | − | 1939.90i | 0.132001 | − | 0.228633i | ||||
\(417\) | 6425.91 | + | 3710.00i | 0.754624 | + | 0.435682i | ||||
\(418\) | 493.634 | − | 285.000i | 0.0577618 | − | 0.0333488i | ||||
\(419\) | 5460.00 | 0.636607 | 0.318304 | − | 0.947989i | \(-0.396887\pi\) | ||||
0.318304 | + | 0.947989i | \(0.396887\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7730.00 | 0.894863 | 0.447431 | − | 0.894318i | \(-0.352339\pi\) | ||||
0.447431 | + | 0.894318i | \(0.352339\pi\) | |||||||
\(422\) | −214.774 | + | 124.000i | −0.0247750 | + | 0.0143039i | ||||
\(423\) | −348.142 | − | 201.000i | −0.0400171 | − | 0.0231039i | ||||
\(424\) | −1572.00 | + | 2722.78i | −0.180054 | + | 0.311863i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 960.000 | 0.109183 | ||||||||
\(427\) | 4298.08 | − | 12407.5i | 0.487117 | − | 1.40619i | ||||
\(428\) | 4428.00i | 0.500083i | ||||||||
\(429\) | −9975.00 | − | 17277.2i | −1.12260 | − | 1.94441i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5656.50 | − | 9797.35i | 0.632167 | − | 1.09495i | −0.354941 | − | 0.934889i | \(-0.615499\pi\) |
0.987108 | − | 0.160057i | \(-0.0511677\pi\) | |||||||
\(432\) | 2009.18 | − | 1160.00i | 0.223765 | − | 0.129191i | ||||
\(433\) | − | 4214.00i | − | 0.467695i | −0.972273 | − | 0.233847i | \(-0.924868\pi\) | ||
0.972273 | − | 0.233847i | \(-0.0751316\pi\) | |||||||
\(434\) | 644.000 | − | 557.720i | 0.0712281 | − | 0.0616853i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1846.00 | − | 3197.37i | −0.202769 | − | 0.351207i | ||||
\(437\) | −298.779 | − | 172.500i | −0.0327060 | − | 0.0188828i | ||||
\(438\) | 2710.66 | + | 1565.00i | 0.295708 | + | 0.170727i | ||||
\(439\) | 8276.50 | + | 14335.3i | 0.899808 | + | 1.55851i | 0.827739 | + | 0.561114i | \(0.189627\pi\) |
0.0720696 | + | 0.997400i | \(0.477040\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 637.000 | − | 254.611i | 0.0687831 | − | 0.0274929i | ||||
\(442\) | − | 7140.00i | − | 0.768360i | ||||||
\(443\) | 14198.5 | − | 8197.50i | 1.52278 | − | 0.879176i | 0.523140 | − | 0.852247i | \(-0.324760\pi\) |
0.999637 | − | 0.0269294i | \(-0.00857293\pi\) | |||||||
\(444\) | 2530.00 | − | 4382.09i | 0.270425 | − | 0.468389i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −56.0000 | − | 96.9948i | −0.00594546 | − | 0.0102978i | ||||
\(447\) | 285.000i | 0.0301567i | ||||||||
\(448\) | 775.959 | + | 896.000i | 0.0818317 | + | 0.0944911i | ||||
\(449\) | 15090.0 | 1.58606 | 0.793030 | − | 0.609182i | \(-0.208502\pi\) | ||||
0.793030 | + | 0.609182i | \(0.208502\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1197.00 | + | 2073.26i | −0.124977 | + | 0.216466i | ||||
\(452\) | −5341.64 | − | 3084.00i | −0.555862 | − | 0.320927i | ||||
\(453\) | 3632.98 | − | 2097.50i | 0.376804 | − | 0.217548i | ||||
\(454\) | 6114.00 | 0.632036 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −200.000 | −0.0205392 | ||||||||
\(457\) | −12804.2 | + | 7392.50i | −1.31062 | + | 0.756688i | −0.982199 | − | 0.187842i | \(-0.939851\pi\) |
−0.328423 | + | 0.944531i | \(0.606517\pi\) | |||||||
\(458\) | −1664.50 | − | 961.000i | −0.169819 | − | 0.0980449i | ||||
\(459\) | 3697.50 | − | 6404.26i | 0.376001 | − | 0.651253i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2898.00 | 0.292784 | 0.146392 | − | 0.989227i | \(-0.453234\pi\) | ||||
0.146392 | + | 0.989227i | \(0.453234\pi\) | |||||||
\(462\) | 10366.3 | − | 1995.00i | 1.04391 | − | 0.200900i | ||||
\(463\) | − | 464.000i | − | 0.0465743i | −0.999729 | − | 0.0232872i | \(-0.992587\pi\) | ||
0.999729 | − | 0.0232872i | \(-0.00741320\pi\) | |||||||
\(464\) | 912.000 | + | 1579.63i | 0.0912468 | + | 0.158044i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2829.00 | − | 4899.97i | 0.281225 | − | 0.487096i | ||||
\(467\) | 3665.89 | − | 2116.50i | 0.363248 | − | 0.209721i | −0.307256 | − | 0.951627i | \(-0.599411\pi\) |
0.670505 | + | 0.741905i | \(0.266078\pi\) | |||||||
\(468\) | − | 560.000i | − | 0.0553120i | ||||||
\(469\) | 1466.50 | + | 7620.16i | 0.144385 | + | 0.750248i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7082.50 | − | 12267.2i | −0.692876 | − | 1.20010i | ||||
\(472\) | −1517.28 | − | 876.000i | −0.147963 | − | 0.0854262i | ||||
\(473\) | 6121.07 | + | 3534.00i | 0.595025 | + | 0.343538i | ||||
\(474\) | −2305.00 | − | 3992.38i | −0.223359 | − | 0.386869i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3570.00 | + | 1236.68i | 0.343762 | + | 0.119083i | ||||
\(477\) | 786.000i | 0.0754475i | ||||||||
\(478\) | 6131.46 | − | 3540.00i | 0.586708 | − | 0.338736i | ||||
\(479\) | 1369.50 | − | 2372.04i | 0.130635 | − | 0.226266i | −0.793287 | − | 0.608848i | \(-0.791632\pi\) |
0.923921 | + | 0.382582i | \(0.124965\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8855.00 | − | 15337.3i | −0.839404 | − | 1.45389i | ||||
\(482\) | 10462.0i | 0.988654i | ||||||||
\(483\) | −4182.90 | − | 4830.00i | −0.394055 | − | 0.455016i | ||||
\(484\) | −7672.00 | −0.720511 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 560.000 | − | 969.948i | 0.0522677 | − | 0.0905304i | ||||
\(487\) | −14766.6 | − | 8525.50i | −1.37400 | − | 0.793280i | −0.382572 | − | 0.923926i | \(-0.624962\pi\) |
−0.991429 | + | 0.130646i | \(0.958295\pi\) | |||||||
\(488\) | 4912.10 | − | 2836.00i | 0.455656 | − | 0.263073i | ||||
\(489\) | −11555.0 | −1.06858 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4296.00 | −0.394859 | −0.197429 | − | 0.980317i | \(-0.563259\pi\) | ||||
−0.197429 | + | 0.980317i | \(0.563259\pi\) | |||||||
\(492\) | 727.461 | − | 420.000i | 0.0666595 | − | 0.0384859i | ||||
\(493\) | 5035.07 | + | 2907.00i | 0.459976 | + | 0.265567i | ||||
\(494\) | −350.000 | + | 606.218i | −0.0318770 | + | 0.0552126i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 368.000 | 0.0333139 | ||||||||
\(497\) | 1163.94 | + | 1344.00i | 0.105050 | + | 0.121301i | ||||
\(498\) | − | 5880.00i | − | 0.529095i | ||||||
\(499\) | 1700.50 | + | 2945.35i | 0.152555 | + | 0.264233i | 0.932166 | − | 0.362031i | \(-0.117917\pi\) |
−0.779611 | + | 0.626264i | \(0.784583\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3150.00 | − | 5455.96i | 0.280901 | − | 0.486536i | ||||
\(502\) | 8729.54 | − | 5040.00i | 0.776132 | − | 0.448100i | ||||
\(503\) | − | 16800.0i | − | 1.48921i | −0.667503 | − | 0.744607i | \(-0.732637\pi\) | ||
0.667503 | − | 0.744607i | \(-0.267363\pi\) | |||||||
\(504\) | 280.000 | + | 96.9948i | 0.0247464 | + | 0.00857241i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3933.00 | + | 6812.16i | 0.345540 | + | 0.598493i | ||||
\(507\) | 11704.3 | + | 6757.50i | 1.02526 | + | 0.591935i | ||||
\(508\) | −7122.19 | − | 4112.00i | −0.622040 | − | 0.359135i | ||||
\(509\) | 919.500 | + | 1592.62i | 0.0800710 | + | 0.138687i | 0.903280 | − | 0.429051i | \(-0.141152\pi\) |
−0.823209 | + | 0.567738i | \(0.807819\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1095.50 | + | 5692.38i | 0.0948377 | + | 0.492791i | ||||
\(512\) | 512.000i | 0.0441942i | ||||||||
\(513\) | −627.868 | + | 362.500i | −0.0540372 | + | 0.0311984i | ||||
\(514\) | −1437.00 | + | 2488.96i | −0.123314 | + | 0.213586i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1240.00 | − | 2147.74i | −0.105791 | − | 0.183235i | ||||
\(517\) | − | 11457.0i | − | 0.974620i | ||||||
\(518\) | 9202.39 | − | 1771.00i | 0.780559 | − | 0.150219i | ||||
\(519\) | 16335.0 | 1.38155 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −151.500 | + | 262.406i | −0.0127396 | + | 0.0220656i | −0.872325 | − | 0.488927i | \(-0.837389\pi\) |
0.859585 | + | 0.510992i | \(0.170722\pi\) | |||||||
\(522\) | 394.908 | + | 228.000i | 0.0331123 | + | 0.0191174i | ||||
\(523\) | 18764.2 | − | 10833.5i | 1.56883 | − | 0.905767i | 0.572528 | − | 0.819885i | \(-0.305963\pi\) |
0.996305 | − | 0.0858815i | \(-0.0273706\pi\) | |||||||
\(524\) | −8196.00 | −0.683290 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4650.00 | −0.385456 | ||||||||
\(527\) | 1015.85 | − | 586.500i | 0.0839678 | − | 0.0484788i | ||||
\(528\) | 3949.08 | + | 2280.00i | 0.325495 | + | 0.187925i | ||||
\(529\) | −3703.00 | + | 6413.78i | −0.304348 | + | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −438.000 | −0.0357958 | ||||||||
\(532\) | −242.487 | − | 280.000i | −0.0197616 | − | 0.0228187i | ||||
\(533\) | − | 2940.00i | − | 0.238922i | ||||||
\(534\) | 5085.00 | + | 8807.48i | 0.412078 | + | 0.713739i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1676.00 | + | 2902.92i | −0.135060 | + | 0.233931i | ||||
\(537\) | −5572.87 | + | 3217.50i | −0.447835 | + | 0.258557i | ||||
\(538\) | 4770.00i | 0.382248i | ||||||||
\(539\) | 15361.5 | + | 12094.0i | 1.22758 | + | 0.966470i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2519.50 | − | 4363.90i | −0.200225 | − | 0.346800i | 0.748376 | − | 0.663275i | \(-0.230834\pi\) |
−0.948601 | + | 0.316475i | \(0.897501\pi\) | |||||||
\(542\) | 573.309 | + | 331.000i | 0.0454349 | + | 0.0262319i | ||||
\(543\) | 11578.8 | + | 6685.00i | 0.915087 | + | 0.528326i | ||||
\(544\) | 816.000 | + | 1413.35i | 0.0643120 | + | 0.111392i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −9800.00 | + | 8487.05i | −0.768134 | + | 0.665224i | ||||
\(547\) | − | 2392.00i | − | 0.186974i | −0.995621 | − | 0.0934868i | \(-0.970199\pi\) | ||
0.995621 | − | 0.0934868i | \(-0.0298013\pi\) | |||||||
\(548\) | 488.438 | − | 282.000i | 0.0380749 | − | 0.0219826i | ||||
\(549\) | 709.000 | − | 1228.02i | 0.0551173 | − | 0.0954659i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −285.000 | − | 493.634i | −0.0220352 | − | 0.0381661i | ||||
\(552\) | − | 2760.00i | − | 0.212814i | ||||||
\(553\) | 2794.66 | − | 8067.50i | 0.214903 | − | 0.620371i | ||||
\(554\) | −9742.00 | −0.747108 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2968.00 | + | 5140.73i | −0.226387 | + | 0.392114i | ||||
\(557\) | 19181.6 | + | 11074.5i | 1.45916 | + | 0.842445i | 0.998970 | − | 0.0453775i | \(-0.0144491\pi\) |
0.460187 | + | 0.887822i | \(0.347782\pi\) | |||||||
\(558\) | 79.6743 | − | 46.0000i | 0.00604459 | − | 0.00348985i | ||||
\(559\) | −8680.00 | −0.656753 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14535.0 | 1.09388 | ||||||||
\(562\) | −12169.4 | + | 7026.00i | −0.913407 | + | 0.527356i | ||||
\(563\) | −7230.45 | − | 4174.50i | −0.541256 | − | 0.312494i | 0.204332 | − | 0.978902i | \(-0.434498\pi\) |
−0.745588 | + | 0.666408i | \(0.767831\pi\) | |||||||
\(564\) | −2010.00 | + | 3481.42i | −0.150064 | + | 0.259919i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −10706.0 | −0.795065 | ||||||||
\(567\) | −12203.2 | + | 2348.50i | −0.903853 | + | 0.173947i | ||||
\(568\) | 768.000i | 0.0567334i | ||||||||
\(569\) | −7672.50 | − | 13289.2i | −0.565286 | − | 0.979105i | −0.997023 | − | 0.0771050i | \(-0.975432\pi\) |
0.431737 | − | 0.902000i | \(-0.357901\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5796.50 | − | 10039.8i | 0.424827 | − | 0.735821i | −0.571578 | − | 0.820548i | \(-0.693668\pi\) |
0.996404 | + | 0.0847268i | \(0.0270017\pi\) | |||||||
\(572\) | 13821.8 | − | 7980.00i | 1.01034 | − | 0.583323i | ||||
\(573\) | 20925.0i | 1.52557i | ||||||||
\(574\) | 1470.00 | + | 509.223i | 0.106893 | + | 0.0370288i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 64.0000 | + | 110.851i | 0.00462963 | + | 0.00801875i | ||||
\(577\) | 12637.9 | + | 7296.50i | 0.911825 | + | 0.526442i | 0.881018 | − | 0.473083i | \(-0.156859\pi\) |
0.0308071 | + | 0.999525i | \(0.490192\pi\) | |||||||
\(578\) | −4004.50 | − | 2312.00i | −0.288175 | − | 0.166378i | ||||
\(579\) | 212.500 | + | 368.061i | 0.0152525 | + | 0.0264181i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8232.00 | − | 7129.12i | 0.587816 | − | 0.509063i | ||||
\(582\) | 18340.0i | 1.30622i | ||||||||
\(583\) | −19399.8 | + | 11200.5i | −1.37815 | + | 0.795673i | ||||
\(584\) | −1252.00 | + | 2168.53i | −0.0887125 | + | 0.153655i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4158.00 | − | 7201.87i | −0.293115 | − | 0.507690i | ||||
\(587\) | − | 15372.0i | − | 1.08087i | −0.841386 | − | 0.540435i | \(-0.818260\pi\) | ||
0.841386 | − | 0.540435i | \(-0.181740\pi\) | |||||||
\(588\) | −2546.11 | − | 6370.00i | −0.178571 | − | 0.446759i | ||||
\(589\) | −115.000 | −0.00804498 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −975.000 | + | 1688.75i | −0.0678615 | + | 0.117540i | ||||
\(592\) | 3505.67 | + | 2024.00i | 0.243382 | + | 0.140517i | ||||
\(593\) | 12447.4 | − | 7186.50i | 0.861978 | − | 0.497663i | −0.00269639 | − | 0.999996i | \(-0.500858\pi\) |
0.864674 | + | 0.502333i | \(0.167525\pi\) | |||||||
\(594\) | 16530.0 | 1.14181 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −228.000 | −0.0156699 | ||||||||
\(597\) | 12267.2 | − | 7082.50i | 0.840980 | − | 0.485540i | ||||
\(598\) | −8365.81 | − | 4830.00i | −0.572079 | − | 0.330290i | ||||
\(599\) | 1273.50 | − | 2205.77i | 0.0868678 | − | 0.150459i | −0.819318 | − | 0.573340i | \(-0.805648\pi\) |
0.906186 | + | 0.422880i | \(0.138981\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7042.00 | −0.477952 | −0.238976 | − | 0.971025i | \(-0.576812\pi\) | ||||
−0.238976 | + | 0.971025i | \(0.576812\pi\) | |||||||
\(602\) | 1503.42 | − | 4340.00i | 0.101785 | − | 0.293829i | ||||
\(603\) | 838.000i | 0.0565937i | ||||||||
\(604\) | 1678.00 | + | 2906.38i | 0.113041 | + | 0.195793i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1425.00 | + | 2468.17i | −0.0955226 | + | 0.165450i | ||||
\(607\) | −19564.4 | + | 11295.5i | −1.30823 | + | 0.755305i | −0.981800 | − | 0.189917i | \(-0.939178\pi\) |
−0.326427 | + | 0.945223i | \(0.605845\pi\) | |||||||
\(608\) | − | 160.000i | − | 0.0106725i | ||||||
\(609\) | −1995.00 | − | 10366.3i | −0.132745 | − | 0.689761i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7035.00 | + | 12185.0i | 0.465803 | + | 0.806794i | ||||
\(612\) | 353.338 | + | 204.000i | 0.0233380 | + | 0.0134742i | ||||
\(613\) | −7348.23 | − | 4242.50i | −0.484163 | − | 0.279532i | 0.237987 | − | 0.971268i | \(-0.423513\pi\) |
−0.722150 | + | 0.691737i | \(0.756846\pi\) | |||||||
\(614\) | −9604.00 | − | 16634.6i | −0.631247 | − | 1.09335i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1596.00 | + | 8293.06i | 0.104391 | + | 0.542430i | ||||
\(617\) | − | 18282.0i | − | 1.19288i | −0.802658 | − | 0.596439i | \(-0.796582\pi\) | ||
0.802658 | − | 0.596439i | \(-0.203418\pi\) | |||||||
\(618\) | −4321.47 | + | 2495.00i | −0.281286 | + | 0.162401i | ||||
\(619\) | 1145.50 | − | 1984.06i | 0.0743805 | − | 0.128831i | −0.826436 | − | 0.563030i | \(-0.809635\pi\) |
0.900817 | + | 0.434200i | \(0.142969\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5002.50 | − | 8664.58i | −0.323258 | − | 0.559900i | ||||
\(622\) | 20262.0i | 1.30616i | ||||||||
\(623\) | −6165.23 | + | 17797.5i | −0.396477 | + | 1.14453i | ||||
\(624\) | −5600.00 | −0.359262 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −10799.0 | + | 18704.4i | −0.689481 | + | 1.19422i | ||||
\(627\) | −1234.09 | − | 712.500i | −0.0786039 | − | 0.0453820i | ||||
\(628\) | 9813.80 | − | 5666.00i | 0.623588 | − | 0.360029i | ||||
\(629\) | 12903.0 | 0.817927 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6928.00 | −0.437083 | −0.218541 | − | 0.975828i | \(-0.570130\pi\) | ||||
−0.218541 | + | 0.975828i | \(0.570130\pi\) | |||||||
\(632\) | 3193.90 | − | 1844.00i | 0.201023 | − | 0.116061i | ||||
\(633\) | 536.936 | + | 310.000i | 0.0337145 | + | 0.0194651i | ||||
\(634\) | 531.000 | − | 919.719i | 0.0332629 | − | 0.0576131i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 7860.00 | 0.490046 | ||||||||
\(637\) | −23763.7 | − | 3430.00i | −1.47811 | − | 0.213346i | ||||
\(638\) | 12996.0i | 0.806452i | ||||||||
\(639\) | 96.0000 | + | 166.277i | 0.00594319 | + | 0.0102939i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12487.5 | + | 21629.0i | −0.769464 | + | 1.33275i | 0.168390 | + | 0.985721i | \(0.446143\pi\) |
−0.937854 | + | 0.347031i | \(0.887190\pi\) | |||||||
\(642\) | 9586.90 | − | 5535.00i | 0.589353 | − | 0.340263i | ||||
\(643\) | − | 9548.00i | − | 0.585593i | −0.956175 | − | 0.292797i | \(-0.905414\pi\) | ||
0.956175 | − | 0.292797i | \(-0.0945859\pi\) | |||||||
\(644\) | 3864.00 | − | 3346.32i | 0.236433 | − | 0.204757i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −255.000 | − | 441.673i | −0.0155307 | − | 0.0269000i | ||||
\(647\) | −8773.70 | − | 5065.50i | −0.533122 | − | 0.307798i | 0.209165 | − | 0.977880i | \(-0.432925\pi\) |
−0.742287 | + | 0.670082i | \(0.766259\pi\) | |||||||
\(648\) | −4648.82 | − | 2684.00i | −0.281826 | − | 0.162712i | ||||
\(649\) | −6241.50 | − | 10810.6i | −0.377504 | − | 0.653857i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2012.50 | − | 697.150i | −0.121161 | − | 0.0419716i | ||||
\(652\) | − | 9244.00i | − | 0.555250i | ||||||
\(653\) | −14427.1 | + | 8329.50i | −0.864589 | + | 0.499171i | −0.865546 | − | 0.500829i | \(-0.833029\pi\) |
0.000957229 | 1.00000i | \(0.499695\pi\) | ||||||||
\(654\) | −4615.00 | + | 7993.41i | −0.275934 | + | 0.477932i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 336.000 | + | 581.969i | 0.0199979 | + | 0.0346373i | ||||
\(657\) | 626.000i | 0.0371729i | ||||||||
\(658\) | −7310.99 | + | 1407.00i | −0.433149 | + | 0.0833595i | ||||
\(659\) | −29556.0 | −1.74710 | −0.873550 | − | 0.486735i | \(-0.838188\pi\) | ||||
−0.873550 | + | 0.486735i | \(0.838188\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −95.5000 | + | 165.411i | −0.00561955 | + | 0.00973334i | −0.868822 | − | 0.495125i | \(-0.835122\pi\) |
0.863202 | + | 0.504859i | \(0.168455\pi\) | |||||||
\(662\) | 12150.3 | + | 7015.00i | 0.713348 | + | 0.411852i | ||||
\(663\) | −15458.6 | + | 8925.00i | −0.905521 | + | 0.522803i | ||||
\(664\) | 4704.00 | 0.274926 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1012.00 | 0.0588802 | ||||||||
\(667\) | 6812.16 | − | 3933.00i | 0.395454 | − | 0.228315i | ||||
\(668\) | 4364.77 | + | 2520.00i | 0.252811 | + | 0.145961i | ||||
\(669\) | −140.000 | + | 242.487i | −0.00809075 | + | 0.0140136i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 40413.0 | 2.32508 | ||||||||
\(672\) | 969.948 | − | 2800.00i | 0.0556794 | − | 0.160733i | ||||
\(673\) | − | 2606.00i | − | 0.149263i | −0.997211 | − | 0.0746314i | \(-0.976222\pi\) | ||
0.997211 | − | 0.0746314i | \(-0.0237780\pi\) | |||||||
\(674\) | 8990.00 | + | 15571.1i | 0.513771 | + | 0.889878i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5406.00 | + | 9363.47i | −0.307579 | + | 0.532742i | ||||
\(677\) | −3645.10 | + | 2104.50i | −0.206931 | + | 0.119472i | −0.599885 | − | 0.800087i | \(-0.704787\pi\) |
0.392953 | + | 0.919559i | \(0.371453\pi\) | |||||||
\(678\) | 15420.0i | 0.873454i | ||||||||
\(679\) | −25676.0 | + | 22236.1i | −1.45118 | + | 1.25676i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7642.50 | − | 13237.2i | −0.430046 | − | 0.744861i | ||||
\(682\) | 2270.72 | + | 1311.00i | 0.127493 | + | 0.0736082i | ||||
\(683\) | 21047.0 | + | 12151.5i | 1.17912 | + | 0.680768i | 0.955812 | − | 0.293979i | \(-0.0949797\pi\) |
0.223312 | + | 0.974747i | \(0.428313\pi\) | |||||||
\(684\) | −20.0000 | − | 34.6410i | −0.00111801 | − | 0.00193645i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 5831.00 | − | 11287.8i | 0.324532 | − | 0.628235i | ||||
\(687\) | 4805.00i | 0.266845i | ||||||||
\(688\) | 1718.19 | − | 992.000i | 0.0952116 | − | 0.0549704i | ||||
\(689\) | 13755.0 | − | 23824.4i | 0.760557 | − | 1.31732i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7520.50 | − | 13025.9i | −0.414028 | − | 0.717117i | 0.581298 | − | 0.813691i | \(-0.302545\pi\) |
−0.995326 | + | 0.0965734i | \(0.969212\pi\) | |||||||
\(692\) | 13068.0i | 0.717877i | ||||||||
\(693\) | 1382.18 | + | 1596.00i | 0.0757641 | + | 0.0874849i | ||||
\(694\) | 17418.0 | 0.952706 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2280.00 | − | 3949.08i | 0.124171 | − | 0.215071i | ||||
\(697\) | 1855.03 | + | 1071.00i | 0.100809 | + | 0.0582023i | ||||
\(698\) | −11227.2 | + | 6482.00i | −0.608817 | + | 0.351500i | ||||
\(699\) | −14145.0 | −0.765398 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24726.0 | 1.33222 | 0.666111 | − | 0.745852i | \(-0.267958\pi\) | ||||
0.666111 | + | 0.745852i | \(0.267958\pi\) | |||||||
\(702\) | −17580.3 | + | 10150.0i | −0.945194 | + | 0.545708i | ||||
\(703\) | −1095.52 | − | 632.500i | −0.0587744 | − | 0.0339334i | ||||
\(704\) | −1824.00 | + | 3159.26i | −0.0976486 | + | 0.169132i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4266.00 | −0.227412 | ||||||||
\(707\) | −5183.16 | + | 997.500i | −0.275718 | + | 0.0530620i | ||||
\(708\) | 4380.00i | 0.232501i | ||||||||
\(709\) | −2478.50 | − | 4292.89i | −0.131286 | − | 0.227395i | 0.792886 | − | 0.609370i | \(-0.208577\pi\) |
−0.924173 | + | 0.381975i | \(0.875244\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 461.000 | − | 798.475i | 0.0243162 | − | 0.0421170i | ||||
\(712\) | −7045.98 | + | 4068.00i | −0.370870 | + | 0.214122i | ||||
\(713\) | − | 1587.00i | − | 0.0833571i | ||||||
\(714\) | −1785.00 | − | 9275.13i | −0.0935601 | − | 0.486153i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2574.00 | − | 4458.30i | −0.134350 | − | 0.232702i | ||||
\(717\) | −15328.6 | − | 8850.00i | −0.798409 | − | 0.460961i | ||||
\(718\) | 6666.66 | + | 3849.00i | 0.346515 | + | 0.200060i | ||||
\(719\) | 13834.5 | + | 23962.1i | 0.717580 | + | 1.24288i | 0.961956 | + | 0.273204i | \(0.0880834\pi\) |
−0.244376 | + | 0.969680i | \(0.578583\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8732.50 | − | 3025.03i | −0.451061 | − | 0.156252i | ||||
\(722\) | − | 13668.0i | − | 0.704529i | ||||||
\(723\) | 22650.9 | − | 13077.5i | 1.16514 | − | 0.672694i | ||||
\(724\) | −5348.00 | + | 9263.01i | −0.274526 | + | 0.475493i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 9590.00 | + | 16610.4i | 0.490246 | + | 0.849130i | ||||
\(727\) | − | 13888.0i | − | 0.708497i | −0.935151 | − | 0.354249i | \(-0.884737\pi\) | ||
0.935151 | − | 0.354249i | \(-0.115263\pi\) | |||||||
\(728\) | −6789.64 | − | 7840.00i | −0.345660 | − | 0.399134i | ||||
\(729\) | −20917.0 | −1.06269 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3162.00 | − | 5476.74i | 0.159987 | − | 0.277106i | ||||
\(732\) | −12280.2 | − | 7090.00i | −0.620069 | − | 0.357997i | ||||
\(733\) | −12334.8 | + | 7121.50i | −0.621550 | + | 0.358852i | −0.777472 | − | 0.628917i | \(-0.783498\pi\) |
0.155922 | + | 0.987769i | \(0.450165\pi\) | |||||||
\(734\) | −12982.0 | −0.652826 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2208.00 | 0.110581 | ||||||||
\(737\) | −20683.3 | + | 11941.5i | −1.03376 | + | 0.596840i | ||||
\(738\) | 145.492 | + | 84.0000i | 0.00725697 | + | 0.00418981i | ||||
\(739\) | 18479.5 | − | 32007.4i | 0.919864 | − | 1.59325i | 0.120244 | − | 0.992744i | \(-0.461632\pi\) |
0.799620 | − | 0.600507i | \(-0.205034\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1750.00 | 0.0867582 | ||||||||
\(742\) | 9529.74 | + | 11004.0i | 0.471493 | + | 0.544433i | ||||
\(743\) | 12528.0i | 0.618584i | 0.950967 | + | 0.309292i | \(0.100092\pi\) | ||||
−0.950967 | + | 0.309292i | \(0.899908\pi\) | |||||||
\(744\) | −460.000 | − | 796.743i | −0.0226672 | − | 0.0392608i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −923.000 | + | 1598.68i | −0.0452995 | + | 0.0784610i | ||||
\(747\) | 1018.45 | − | 588.000i | 0.0498835 | − | 0.0288003i | ||||
\(748\) | 11628.0i | 0.568398i | ||||||||
\(749\) | 19372.5 | + | 6710.83i | 0.945068 | + | 0.327381i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8883.50 | + | 15386.7i | 0.431643 | + | 0.747627i | 0.997015 | − | 0.0772090i | \(-0.0246009\pi\) |
−0.565372 | + | 0.824836i | \(0.691268\pi\) | |||||||
\(752\) | −2785.14 | − | 1608.00i | −0.135058 | − | 0.0779757i | ||||
\(753\) | −21823.8 | − | 12600.0i | −1.05618 | − | 0.609787i | ||||
\(754\) | −7980.00 | − | 13821.8i | −0.385430 | − | 0.667585i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2030.00 | − | 10548.2i | −0.0976592 | − | 0.507452i | ||||
\(757\) | − | 28726.0i | − | 1.37921i | −0.724184 | − | 0.689606i | \(-0.757784\pi\) | ||
0.724184 | − | 0.689606i | \(-0.242216\pi\) | |||||||
\(758\) | −10988.1 | + | 6344.00i | −0.526526 | + | 0.303990i | ||||
\(759\) | 9832.50 | − | 17030.4i | 0.470220 | − | 0.814445i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13234.5 | + | 22922.8i | 0.630421 | + | 1.09192i | 0.987466 | + | 0.157834i | \(0.0504510\pi\) |
−0.357045 | + | 0.934087i | \(0.616216\pi\) | |||||||
\(762\) | 20560.0i | 0.977441i | ||||||||
\(763\) | −16786.2 | + | 3230.50i | −0.796462 | + | 0.153279i | ||||
\(764\) | −16740.0 | −0.792712 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5007.00 | − | 8672.38i | 0.236175 | − | 0.409068i | ||||
\(767\) | 13276.2 | + | 7665.00i | 0.625000 | + | 0.360844i | ||||
\(768\) | 1108.51 | − | 640.000i | 0.0520833 | − | 0.0300703i | ||||
\(769\) | −5054.00 | −0.236999 | −0.118499 | − | 0.992954i | \(-0.537808\pi\) | ||||
−0.118499 | + | 0.992954i | \(0.537808\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7185.00 | 0.335618 | ||||||||
\(772\) | −294.449 | + | 170.000i | −0.0137273 | + | 0.00792543i | ||||
\(773\) | −30800.2 | − | 17782.5i | −1.43313 | − | 0.827415i | −0.435767 | − | 0.900059i | \(-0.643523\pi\) |
−0.997358 | + | 0.0726439i | \(0.976856\pi\) | |||||||
\(774\) | 248.000 | − | 429.549i | 0.0115170 | − | 0.0199481i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −14672.0 | −0.678730 | ||||||||
\(777\) | −15337.3 | − | 17710.0i | −0.708138 | − | 0.817687i | ||||
\(778\) | − | 24582.0i | − | 1.13279i | ||||||
\(779\) | −105.000 | − | 181.865i | −0.00482929 | − | 0.00836457i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2736.00 | + | 4738.89i | −0.125354 | + | 0.217120i | ||||
\(782\) | 6095.09 | − | 3519.00i | 0.278721 | − | 0.160920i | ||||
\(783\) | − | 16530.0i | − | 0.754450i | ||||||
\(784\) | 5096.00 | − | 2036.89i | 0.232143 | − | 0.0927884i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 10245.0 | + | 17744.9i | 0.464920 | + | 0.805265i | ||||
\(787\) | 7472.93 | + | 4314.50i | 0.338477 | + | 0.195420i | 0.659598 | − | 0.751618i | \(-0.270726\pi\) |
−0.321121 | + | 0.947038i | \(0.604060\pi\) | |||||||
\(788\) | −1351.00 | − | 780.000i | −0.0610753 | − | 0.0352619i | ||||
\(789\) | 5812.50 | + | 10067.5i | 0.262269 | + | 0.454264i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21588.0 | + | 18695.8i | −0.970393 | + | 0.840385i | ||||
\(792\) | 912.000i | 0.0409173i | ||||||||
\(793\) | −42980.8 | + | 24815.0i | −1.92471 | + | 1.11123i | ||||
\(794\) | 887.000 | − | 1536.33i | 0.0396454 | − | 0.0686679i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5666.00 | + | 9813.80i | 0.252294 | + | 0.436986i | ||||
\(797\) | 20706.0i | 0.920256i | 0.887853 | + | 0.460128i | \(0.152197\pi\) | ||||
−0.887853 | + | 0.460128i | \(0.847803\pi\) | |||||||
\(798\) | −303.109 | + | 875.000i | −0.0134460 | + | 0.0388154i | ||||
\(799\) | −10251.0 | −0.453885 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1017.00 | + | 1761.50i | −0.0448613 | + | 0.0777021i | ||||
\(802\) | −20706.7 | − | 11955.0i | −0.911693 | − | 0.526366i | ||||
\(803\) | −15450.8 | + | 8920.50i | −0.679011 | + | 0.392027i | ||||
\(804\) | 8380.00 | 0.367587 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3220.00 | −0.140719 | ||||||||
\(807\) | 10327.4 | − | 5962.50i | 0.450483 | − | 0.260087i | ||||
\(808\) | −1974.54 | − | 1140.00i | −0.0859703 | − | 0.0496350i | ||||
\(809\) | −8092.50 | + | 14016.6i | −0.351690 | + | 0.609145i | −0.986546 | − | 0.163486i | \(-0.947726\pi\) |
0.634856 | + | 0.772631i | \(0.281060\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11788.0 | −0.510398 | −0.255199 | − | 0.966889i | \(-0.582141\pi\) | ||||
−0.255199 | + | 0.966889i | \(0.582141\pi\) | |||||||
\(812\) | 8293.06 | − | 1596.00i | 0.358411 | − | 0.0689761i | ||||
\(813\) | − | 1655.00i | − | 0.0713941i | ||||||
\(814\) | 14421.0 | + | 24977.9i | 0.620953 | + | 1.07552i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2040.00 | − | 3533.38i | 0.0875175 | − | 0.151585i | ||||
\(817\) | −536.936 | + | 310.000i | −0.0229927 | + | 0.0132748i | ||||
\(818\) | 6842.00i | 0.292451i | ||||||||
\(819\) | −2450.00 | − | 848.705i | −0.104530 | − | 0.0362102i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14896.5 | + | 25801.5i | 0.633242 | + | 1.09681i | 0.986885 | + | 0.161426i | \(0.0516094\pi\) |
−0.353643 | + | 0.935380i | \(0.615057\pi\) | |||||||
\(822\) | −1221.10 | − | 705.000i | −0.0518134 | − | 0.0299145i | ||||
\(823\) | 26260.5 | + | 15161.5i | 1.11225 | + | 0.642159i | 0.939412 | − | 0.342791i | \(-0.111372\pi\) |
0.172840 | + | 0.984950i | \(0.444706\pi\) | |||||||
\(824\) | −1996.00 | − | 3457.17i | −0.0843859 | − | 0.146161i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6132.00 | + | 5310.47i | −0.258305 | + | 0.223698i | ||||
\(827\) | 21156.0i | 0.889560i | 0.895640 | + | 0.444780i | \(0.146718\pi\) | ||||
−0.895640 | + | 0.444780i | \(0.853282\pi\) | |||||||
\(828\) | 478.046 | − | 276.000i | 0.0200643 | − | 0.0115841i | ||||
\(829\) | −2634.50 | + | 4563.09i | −0.110374 | + | 0.191173i | −0.915921 | − | 0.401358i | \(-0.868538\pi\) |
0.805547 | + | 0.592532i | \(0.201871\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12177.5 | + | 21092.0i | 0.508343 | + | 0.880475i | ||||
\(832\) | − | 4480.00i | − | 0.186678i | ||||||
\(833\) | 10821.0 | − | 13744.5i | 0.450090 | − | 0.571691i | ||||
\(834\) | 14840.0 | 0.616148 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 570.000 | − | 987.269i | 0.0235812 | − | 0.0408438i | ||||
\(837\) | −2888.19 | − | 1667.50i | −0.119272 | − | 0.0688617i | ||||
\(838\) | 9457.00 | − | 5460.00i | 0.389841 | − | 0.225075i | ||||
\(839\) | 39816.0 | 1.63838 | 0.819190 | − | 0.573522i | \(-0.194423\pi\) | ||||
0.819190 | + | 0.573522i | \(0.194423\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11393.0 | −0.467137 | ||||||||
\(842\) | 13388.8 | − | 7730.00i | 0.547989 | − | 0.316382i | ||||
\(843\) | 30423.5 | + | 17565.0i | 1.24299 | + | 0.717640i | ||||
\(844\) | −248.000 | + | 429.549i | −0.0101144 | + | 0.0175186i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −804.000 | −0.0326739 | ||||||||
\(847\) | −11627.3 | + | 33565.0i | −0.471685 | + | 1.36164i | ||||
\(848\) | 6288.00i | 0.254635i | ||||||||
\(849\) | 13382.5 | + | 23179.2i | 0.540973 | + | 0.936993i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8728.50 | − | 15118.2i | 0.351597 | − | 0.608984i | ||||
\(852\) | 1662.77 | − | 960.000i | 0.0668609 | − | 0.0386022i | ||||
\(853\) | − | 14546.0i | − | 0.583875i | −0.956437 | − | 0.291938i | \(-0.905700\pi\) | ||
0.956437 | − | 0.291938i | \(-0.0943000\pi\) | |||||||
\(854\) | −4963.00 | − | 25788.5i | −0.198865 | − | 1.03333i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4428.00 | + | 7669.52i | 0.176806 | + | 0.306237i | ||||
\(857\) | 27235.6 | + | 15724.5i | 1.08559 | + | 0.626766i | 0.932399 | − | 0.361430i | \(-0.117711\pi\) |
0.153192 | + | 0.988196i | \(0.451045\pi\) | |||||||
\(858\) | −34554.4 | − | 19950.0i | −1.37490 | − | 0.793802i | ||||
\(859\) | −12261.5 | − | 21237.5i | −0.487028 | − | 0.843557i | 0.512861 | − | 0.858472i | \(-0.328586\pi\) |
−0.999889 | + | 0.0149147i | \(0.995252\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −735.000 | − | 3819.17i | −0.0290926 | − | 0.151170i | ||||
\(862\) | − | 22626.0i | − | 0.894019i | ||||||
\(863\) | 7069.37 | − | 4081.50i | 0.278846 | − | 0.160992i | −0.354055 | − | 0.935225i | \(-0.615197\pi\) |
0.632901 | + | 0.774233i | \(0.281864\pi\) | |||||||
\(864\) | 2320.00 | − | 4018.36i | 0.0913519 | − | 0.158226i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −4214.00 | − | 7298.86i | −0.165355 | − | 0.286403i | ||||
\(867\) | 11560.0i | 0.452824i | ||||||||
\(868\) | 557.720 | − | 1610.00i | 0.0218091 | − | 0.0629573i | ||||
\(869\) | 26277.0 | 1.02576 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14665.0 | − | 25400.5i | 0.570499 | − | 0.988133i | ||||
\(872\) | −6394.73 | − | 3692.00i | −0.248341 | − | 0.143379i | ||||
\(873\) | −3176.58 | + | 1834.00i | −0.123151 | + | 0.0711014i | ||||
\(874\) | −690.000 | −0.0267043 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6260.00 | 0.241445 | ||||||||
\(877\) | 3781.93 | − | 2183.50i | 0.145618 | − | 0.0840725i | −0.425421 | − | 0.904996i | \(-0.639874\pi\) |
0.571039 | + | 0.820923i | \(0.306541\pi\) | |||||||
\(878\) | 28670.6 | + | 16553.0i | 1.10204 | + | 0.636260i | ||||
\(879\) | −10395.0 | + | 18004.7i | −0.398879 | + | 0.690879i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −50190.0 | −1.91935 | −0.959673 | − | 0.281118i | \(-0.909295\pi\) | ||||
−0.959673 | + | 0.281118i | \(0.909295\pi\) | |||||||
\(882\) | 848.705 | − | 1078.00i | 0.0324007 | − | 0.0411544i | ||||
\(883\) | − | 12308.0i | − | 0.469079i | −0.972107 | − | 0.234540i | \(-0.924642\pi\) | ||
0.972107 | − | 0.234540i | \(-0.0753583\pi\) | |||||||
\(884\) | −7140.00 | − | 12366.8i | −0.271656 | − | 0.470523i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16395.0 | − | 28397.0i | 0.621671 | − | 1.07677i | ||||
\(887\) | 27381.1 | − | 15808.5i | 1.03649 | − | 0.598419i | 0.117654 | − | 0.993055i | \(-0.462463\pi\) |
0.918838 | + | 0.394636i | \(0.129129\pi\) | |||||||
\(888\) | − | 10120.0i | − | 0.382438i | ||||||
\(889\) | −28784.0 | + | 24927.7i | −1.08592 | + | 0.940436i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −19123.5 | − | 33122.9i | −0.719036 | − | 1.24541i | ||||
\(892\) | −193.990 | − | 112.000i | −0.00728168 | − | 0.00420408i | ||||
\(893\) | 870.356 | + | 502.500i | 0.0326152 | + | 0.0188304i | ||||
\(894\) | 285.000 | + | 493.634i | 0.0106620 | + | 0.0184671i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2240.00 | + | 775.959i | 0.0835191 | + | 0.0289319i | ||||
\(897\) | 24150.0i | 0.898935i | ||||||||
\(898\) | 26136.6 | − | 15090.0i | 0.971260 | − | 0.560757i | ||||
\(899\) | 1311.00 | − | 2270.72i | 0.0486366 | − | 0.0842411i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10021.5 | + | 17357.7i | 0.370549 | + | 0.641810i | ||||
\(902\) | 4788.00i | 0.176744i | ||||||||
\(903\) | −11275.7 | + | 2170.00i | −0.415537 | + | 0.0799702i | ||||
\(904\) | −12336.0 | −0.453860 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4195.00 | − | 7265.95i | 0.153830 | − | 0.266441i | ||||
\(907\) | 11713.0 | + | 6762.50i | 0.428802 | + | 0.247569i | 0.698836 | − | 0.715282i | \(-0.253702\pi\) |
−0.270034 | + | 0.962851i | \(0.587035\pi\) | |||||||
\(908\) | 10589.8 | − | 6114.00i | 0.387041 | − | 0.223458i | ||||
\(909\) | −570.000 | −0.0207984 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19248.0 | −0.700016 | −0.350008 | − | 0.936747i | \(-0.613821\pi\) | ||||
−0.350008 | + | 0.936747i | \(0.613821\pi\) | |||||||
\(912\) | −346.410 | + | 200.000i | −0.0125776 | + | 0.00726169i | ||||
\(913\) | 29025.7 | + | 16758.0i | 1.05215 | + | 0.607458i | ||||
\(914\) | −14785.0 | + | 25608.4i | −0.535059 | + | 0.926750i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3844.00 | −0.138656 | ||||||||
\(917\) | −12421.4 | + | 35857.5i | −0.447318 | + | 1.29130i | ||||
\(918\) | − | 14790.0i | − | 0.531746i | ||||||
\(919\) | −4347.50 | − | 7530.09i | −0.156051 | − | 0.270288i | 0.777390 | − | 0.629019i | \(-0.216543\pi\) |
−0.933441 | + | 0.358730i | \(0.883210\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24010.0 | + | 41586.5i | −0.859019 | + | 1.48786i | ||||
\(922\) | 5019.48 | − | 2898.00i | 0.179293 | − | 0.103515i | ||||
\(923\) | − | 6720.00i | − | 0.239644i | ||||||
\(924\) | 15960.0 | − | 13821.8i | 0.568231 | − | 0.492102i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −464.000 | − | 803.672i | −0.0164665 | − | 0.0285208i | ||||
\(927\) | −864.293 | − | 499.000i | −0.0306226 | − | 0.0176799i | ||||
\(928\) | 3159.26 | + | 1824.00i | 0.111754 | + | 0.0645213i | ||||
\(929\) | 9739.50 | + | 16869.3i | 0.343964 | + | 0.595763i | 0.985165 | − | 0.171610i | \(-0.0548968\pi\) |
−0.641201 | + | 0.767373i | \(0.721563\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1592.50 | + | 636.529i | −0.0560602 | + | 0.0224075i | ||||
\(932\) | − | 11316.0i | − | 0.397712i | ||||||
\(933\) | 43868.5 | − | 25327.5i | 1.53933 | − | 0.888730i | ||||
\(934\) | 4233.00 | − | 7331.77i | 0.148295 | − | 0.256855i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −560.000 | − | 969.948i | −0.0195557 | − | 0.0338715i | ||||
\(937\) | − | 12502.0i | − | 0.435883i | −0.975962 | − | 0.217942i | \(-0.930066\pi\) | ||
0.975962 | − | 0.217942i | \(-0.0699342\pi\) | |||||||
\(938\) | 10160.2 | + | 11732.0i | 0.353670 | + | 0.408383i | ||||
\(939\) | 53995.0 | 1.87653 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7996.50 | − | 13850.3i | 0.277023 | − | 0.479818i | −0.693621 | − | 0.720340i | \(-0.743986\pi\) |
0.970643 | + | 0.240523i | \(0.0773189\pi\) | |||||||
\(942\) | −24534.5 | − | 14165.0i | −0.848596 | − | 0.489937i | ||||
\(943\) | 2509.74 | − | 1449.00i | 0.0866685 | − | 0.0500381i | ||||
\(944\) | −3504.00 | −0.120811 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14136.0 | 0.485836 | ||||||||
\(947\) | 38106.0 | − | 22000.5i | 1.30758 | − | 0.754932i | 0.325888 | − | 0.945408i | \(-0.394337\pi\) |
0.981692 | + | 0.190477i | \(0.0610034\pi\) | |||||||
\(948\) | −7984.75 | − | 4610.00i | −0.273558 | − | 0.157939i | ||||
\(949\) | 10955.0 | − | 18974.6i | 0.374725 | − | 0.649043i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2655.00 | −0.0905303 | ||||||||
\(952\) | 7420.11 | − | 1428.00i | 0.252612 | − | 0.0486153i | ||||
\(953\) | 4002.00i | 0.136031i | 0.997684 | + | 0.0680155i | \(0.0216667\pi\) | ||||
−0.997684 | + | 0.0680155i | \(0.978333\pi\) | |||||||
\(954\) | 786.000 | + | 1361.39i | 0.0266747 | + | 0.0462020i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 7080.00 | − | 12262.9i | 0.239523 | − | 0.414865i | ||||
\(957\) | 28137.2 | − | 16245.0i | 0.950413 | − | 0.548721i | ||||
\(958\) | − | 5478.00i | − | 0.184745i | ||||||
\(959\) | −493.500 | − | 2564.30i | −0.0166173 | − | 0.0863458i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14631.0 | + | 25341.6i | 0.491121 | + | 0.850647i | ||||
\(962\) | −30674.6 | − | 17710.0i | −1.02806 | − | 0.593548i | ||||
\(963\) | 1917.38 | + | 1107.00i | 0.0641607 | + | 0.0370432i | ||||
\(964\) | 10462.0 | + | 18120.7i | 0.349542 | + | 0.605424i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −12075.0 | − | 4182.90i | −0.402181 | − | 0.139320i | ||||
\(967\) | 10544.0i | 0.350643i | 0.984511 | + | 0.175322i | \(0.0560966\pi\) | ||||
−0.984511 | + | 0.175322i | \(0.943903\pi\) | |||||||
\(968\) | −13288.3 | + | 7672.00i | −0.441221 | + | 0.254739i | ||||
\(969\) | −637.500 | + | 1104.18i | −0.0211346 | + | 0.0366062i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3091.50 | + | 5354.64i | 0.102174 | + | 0.176971i | 0.912580 | − | 0.408898i | \(-0.134087\pi\) |
−0.810406 | + | 0.585869i | \(0.800753\pi\) | |||||||
\(972\) | − | 2240.00i | − | 0.0739177i | ||||||
\(973\) | 17992.5 | + | 20776.0i | 0.592821 | + | 0.684530i | ||||
\(974\) | −34102.0 | −1.12187 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5672.00 | − | 9824.19i | 0.186021 | − | 0.322197i | ||||
\(977\) | −3224.21 | − | 1861.50i | −0.105580 | − | 0.0609567i | 0.446280 | − | 0.894893i | \(-0.352748\pi\) |
−0.551860 | + | 0.833937i | \(0.686082\pi\) | |||||||
\(978\) | −20013.8 | + | 11555.0i | −0.654368 | + | 0.377800i | ||||
\(979\) | −57969.0 | −1.89244 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1846.00 | −0.0600798 | ||||||||
\(982\) | −7440.89 | + | 4296.00i | −0.241801 | + | 0.139604i | ||||
\(983\) | −39748.0 | − | 22948.5i | −1.28969 | − | 0.744602i | −0.311089 | − | 0.950381i | \(-0.600694\pi\) |
−0.978599 | + | 0.205779i | \(0.934027\pi\) | |||||||
\(984\) | 840.000 | − | 1454.92i | 0.0272136 | − | 0.0471354i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 11628.0 | 0.375569 | ||||||||
\(987\) | 12185.0 | + | 14070.0i | 0.392961 | + | 0.453752i | ||||
\(988\) | 1400.00i | 0.0450809i | ||||||||
\(989\) | −4278.00 | − | 7409.71i | −0.137545 | − | 0.238236i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3233.50 | + | 5600.59i | −0.103648 | + | 0.179524i | −0.913185 | − | 0.407545i | \(-0.866385\pi\) |
0.809537 | + | 0.587069i | \(0.199718\pi\) | |||||||
\(992\) | 637.395 | − | 368.000i | 0.0204005 | − | 0.0117782i | ||||
\(993\) | − | 35075.0i | − | 1.12092i | ||||||
\(994\) | 3360.00 | + | 1163.94i | 0.107216 | + | 0.0371407i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −5880.00 | − | 10184.5i | −0.187063 | − | 0.324003i | ||||
\(997\) | −19952.4 | − | 11519.5i | −0.633799 | − | 0.365924i | 0.148423 | − | 0.988924i | \(-0.452580\pi\) |
−0.782222 | + | 0.623000i | \(0.785914\pi\) | |||||||
\(998\) | 5890.70 | + | 3401.00i | 0.186841 | + | 0.107873i | ||||
\(999\) | −18342.5 | − | 31770.1i | −0.580912 | − | 1.00617i |
(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 | 350.4.j.b.249.2 | 4 | ||
5.2 | odd | 4 | 350.4.e.e.151.1 | 2 | |||
5.3 | odd | 4 | 14.4.c.a.11.1 | yes | 2 | ||
5.4 | even | 2 | inner | 350.4.j.b.249.1 | 4 | ||
7.2 | even | 3 | inner | 350.4.j.b.149.1 | 4 | ||
15.8 | even | 4 | 126.4.g.d.109.1 | 2 | |||
20.3 | even | 4 | 112.4.i.a.81.1 | 2 | |||
35.2 | odd | 12 | 350.4.e.e.51.1 | 2 | |||
35.3 | even | 12 | 98.4.a.f.1.1 | 1 | |||
35.9 | even | 6 | inner | 350.4.j.b.149.2 | 4 | ||
35.13 | even | 4 | 98.4.c.a.67.1 | 2 | |||
35.17 | even | 12 | 2450.4.a.d.1.1 | 1 | |||
35.18 | odd | 12 | 98.4.a.d.1.1 | 1 | |||
35.23 | odd | 12 | 14.4.c.a.9.1 | ✓ | 2 | ||
35.32 | odd | 12 | 2450.4.a.q.1.1 | 1 | |||
35.33 | even | 12 | 98.4.c.a.79.1 | 2 | |||
40.3 | even | 4 | 448.4.i.e.193.1 | 2 | |||
40.13 | odd | 4 | 448.4.i.b.193.1 | 2 | |||
105.23 | even | 12 | 126.4.g.d.37.1 | 2 | |||
105.38 | odd | 12 | 882.4.a.c.1.1 | 1 | |||
105.53 | even | 12 | 882.4.a.f.1.1 | 1 | |||
105.68 | odd | 12 | 882.4.g.u.667.1 | 2 | |||
105.83 | odd | 4 | 882.4.g.u.361.1 | 2 | |||
140.3 | odd | 12 | 784.4.a.c.1.1 | 1 | |||
140.23 | even | 12 | 112.4.i.a.65.1 | 2 | |||
140.123 | even | 12 | 784.4.a.p.1.1 | 1 | |||
280.93 | odd | 12 | 448.4.i.b.65.1 | 2 | |||
280.163 | even | 12 | 448.4.i.e.65.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.4.c.a.9.1 | ✓ | 2 | 35.23 | odd | 12 | ||
14.4.c.a.11.1 | yes | 2 | 5.3 | odd | 4 | ||
98.4.a.d.1.1 | 1 | 35.18 | odd | 12 | |||
98.4.a.f.1.1 | 1 | 35.3 | even | 12 | |||
98.4.c.a.67.1 | 2 | 35.13 | even | 4 | |||
98.4.c.a.79.1 | 2 | 35.33 | even | 12 | |||
112.4.i.a.65.1 | 2 | 140.23 | even | 12 | |||
112.4.i.a.81.1 | 2 | 20.3 | even | 4 | |||
126.4.g.d.37.1 | 2 | 105.23 | even | 12 | |||
126.4.g.d.109.1 | 2 | 15.8 | even | 4 | |||
350.4.e.e.51.1 | 2 | 35.2 | odd | 12 | |||
350.4.e.e.151.1 | 2 | 5.2 | odd | 4 | |||
350.4.j.b.149.1 | 4 | 7.2 | even | 3 | inner | ||
350.4.j.b.149.2 | 4 | 35.9 | even | 6 | inner | ||
350.4.j.b.249.1 | 4 | 5.4 | even | 2 | inner | ||
350.4.j.b.249.2 | 4 | 1.1 | even | 1 | trivial | ||
448.4.i.b.65.1 | 2 | 280.93 | odd | 12 | |||
448.4.i.b.193.1 | 2 | 40.13 | odd | 4 | |||
448.4.i.e.65.1 | 2 | 280.163 | even | 12 | |||
448.4.i.e.193.1 | 2 | 40.3 | even | 4 | |||
784.4.a.c.1.1 | 1 | 140.3 | odd | 12 | |||
784.4.a.p.1.1 | 1 | 140.123 | even | 12 | |||
882.4.a.c.1.1 | 1 | 105.38 | odd | 12 | |||
882.4.a.f.1.1 | 1 | 105.53 | even | 12 | |||
882.4.g.u.361.1 | 2 | 105.83 | odd | 4 | |||
882.4.g.u.667.1 | 2 | 105.68 | odd | 12 | |||
2450.4.a.d.1.1 | 1 | 35.17 | even | 12 | |||
2450.4.a.q.1.1 | 1 | 35.32 | odd | 12 |