Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [42,5,Mod(19,42)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(42, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("42.19");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 42 = 2 \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 42.g (of order \(6\), degree \(2\), 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: | \(4.34153844952\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.2 | ||
Root | \(0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 42.31 |
Dual form | 42.5.g.a.19.2 |
$q$-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 \(\left(\mathbb{Z}/42\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(31\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | + | 2.44949i | 0.353553 | + | 0.612372i | ||||
\(3\) | −4.50000 | − | 2.59808i | −0.500000 | − | 0.288675i | ||||
\(4\) | −4.00000 | + | 6.92820i | −0.250000 | + | 0.433013i | ||||
\(5\) | −20.7426 | + | 11.9758i | −0.829706 | + | 0.479031i | −0.853752 | − | 0.520680i | \(-0.825678\pi\) |
0.0240462 | + | 0.999711i | \(0.492345\pi\) | |||||||
\(6\) | − | 14.6969i | − | 0.408248i | ||||||
\(7\) | −47.1985 | + | 13.1645i | −0.963234 | + | 0.268662i | ||||
\(8\) | −22.6274 | −0.353553 | ||||||||
\(9\) | 13.5000 | + | 23.3827i | 0.166667 | + | 0.288675i | ||||
\(10\) | −58.6690 | − | 33.8726i | −0.586690 | − | 0.338726i | ||||
\(11\) | −48.9853 | + | 84.8450i | −0.404837 | + | 0.701198i | −0.994302 | − | 0.106595i | \(-0.966005\pi\) |
0.589465 | + | 0.807794i | \(0.299338\pi\) | |||||||
\(12\) | 36.0000 | − | 20.7846i | 0.250000 | − | 0.144338i | ||||
\(13\) | − | 104.211i | − | 0.616636i | −0.951283 | − | 0.308318i | \(-0.900234\pi\) | ||
0.951283 | − | 0.308318i | \(-0.0997661\pi\) | |||||||
\(14\) | −98.9949 | − | 96.9948i | −0.505076 | − | 0.494872i | ||||
\(15\) | 124.456 | 0.553137 | ||||||||
\(16\) | −32.0000 | − | 55.4256i | −0.125000 | − | 0.216506i | ||||
\(17\) | 93.2498 | + | 53.8378i | 0.322664 | + | 0.186290i | 0.652579 | − | 0.757721i | \(-0.273687\pi\) |
−0.329916 | + | 0.944010i | \(0.607020\pi\) | |||||||
\(18\) | −38.1838 | + | 66.1362i | −0.117851 | + | 0.204124i | ||||
\(19\) | 33.2498 | − | 19.1968i | 0.0921047 | − | 0.0531767i | −0.453240 | − | 0.891388i | \(-0.649732\pi\) |
0.545345 | + | 0.838212i | \(0.316399\pi\) | |||||||
\(20\) | − | 191.612i | − | 0.479031i | ||||||
\(21\) | 246.595 | + | 63.3852i | 0.559173 | + | 0.143731i | ||||
\(22\) | −277.103 | −0.572526 | ||||||||
\(23\) | 510.749 | + | 884.644i | 0.965500 | + | 1.67229i | 0.708266 | + | 0.705945i | \(0.249478\pi\) |
0.257233 | + | 0.966349i | \(0.417189\pi\) | |||||||
\(24\) | 101.823 | + | 58.7878i | 0.176777 | + | 0.102062i | ||||
\(25\) | −25.6619 | + | 44.4477i | −0.0410590 | + | 0.0711164i | ||||
\(26\) | 255.265 | − | 147.377i | 0.377611 | − | 0.218014i | ||||
\(27\) | − | 140.296i | − | 0.192450i | ||||||
\(28\) | 97.5879 | − | 379.659i | 0.124474 | − | 0.484258i | ||||
\(29\) | 621.603 | 0.739124 | 0.369562 | − | 0.929206i | \(-0.379508\pi\) | ||||
0.369562 | + | 0.929206i | \(0.379508\pi\) | |||||||
\(30\) | 176.007 | + | 304.853i | 0.195563 | + | 0.338726i | ||||
\(31\) | −1315.61 | − | 759.568i | −1.36900 | − | 0.790393i | −0.378200 | − | 0.925724i | \(-0.623457\pi\) |
−0.990800 | + | 0.135331i | \(0.956790\pi\) | |||||||
\(32\) | 90.5097 | − | 156.767i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 440.868 | − | 254.535i | 0.404837 | − | 0.233733i | ||||
\(34\) | 304.553i | 0.263454i | ||||||||
\(35\) | 821.367 | − | 838.304i | 0.670503 | − | 0.684330i | ||||
\(36\) | −216.000 | −0.166667 | ||||||||
\(37\) | 281.118 | + | 486.910i | 0.205345 | + | 0.355669i | 0.950243 | − | 0.311511i | \(-0.100835\pi\) |
−0.744897 | + | 0.667179i | \(0.767502\pi\) | |||||||
\(38\) | 94.0446 | + | 54.2967i | 0.0651278 | + | 0.0376016i | ||||
\(39\) | −270.749 | + | 468.952i | −0.178007 | + | 0.308318i | ||||
\(40\) | 469.352 | − | 270.981i | 0.293345 | − | 0.169363i | ||||
\(41\) | − | 1023.20i | − | 0.608684i | −0.952563 | − | 0.304342i | \(-0.901563\pi\) | ||
0.952563 | − | 0.304342i | \(-0.0984365\pi\) | |||||||
\(42\) | 193.477 | + | 693.673i | 0.109681 | + | 0.393239i | ||||
\(43\) | −3382.41 | −1.82932 | −0.914658 | − | 0.404228i | \(-0.867540\pi\) | ||||
−0.914658 | + | 0.404228i | \(0.867540\pi\) | |||||||
\(44\) | −391.882 | − | 678.760i | −0.202419 | − | 0.350599i | ||||
\(45\) | −560.051 | − | 323.346i | −0.276569 | − | 0.159677i | ||||
\(46\) | −1444.62 | + | 2502.15i | −0.682711 | + | 1.18249i | ||||
\(47\) | −3416.50 | + | 1972.52i | −1.54663 | + | 0.892945i | −0.548231 | + | 0.836327i | \(0.684698\pi\) |
−0.998396 | + | 0.0566179i | \(0.981968\pi\) | |||||||
\(48\) | 332.554i | 0.144338i | ||||||||
\(49\) | 2054.39 | − | 1242.69i | 0.855641 | − | 0.517570i | ||||
\(50\) | −145.166 | −0.0580663 | ||||||||
\(51\) | −279.749 | − | 484.540i | −0.107555 | − | 0.186290i | ||||
\(52\) | 721.998 | + | 416.846i | 0.267011 | + | 0.154159i | ||||
\(53\) | −1095.30 | + | 1897.12i | −0.389925 | + | 0.675370i | −0.992439 | − | 0.122738i | \(-0.960833\pi\) |
0.602514 | + | 0.798108i | \(0.294166\pi\) | |||||||
\(54\) | 343.654 | − | 198.409i | 0.117851 | − | 0.0680414i | ||||
\(55\) | − | 2346.55i | − | 0.775718i | ||||||
\(56\) | 1067.98 | − | 297.878i | 0.340555 | − | 0.0949865i | ||||
\(57\) | −199.499 | −0.0614031 | ||||||||
\(58\) | 879.079 | + | 1522.61i | 0.261320 | + | 0.452619i | ||||
\(59\) | 2541.67 | + | 1467.44i | 0.730156 | + | 0.421556i | 0.818479 | − | 0.574536i | \(-0.194818\pi\) |
−0.0883234 | + | 0.996092i | \(0.528151\pi\) | |||||||
\(60\) | −497.823 | + | 862.255i | −0.138284 | + | 0.239515i | ||||
\(61\) | 576.207 | − | 332.673i | 0.154853 | − | 0.0894043i | −0.420571 | − | 0.907259i | \(-0.638170\pi\) |
0.575424 | + | 0.817855i | \(0.304837\pi\) | |||||||
\(62\) | − | 4296.76i | − | 1.11778i | ||||||
\(63\) | −945.000 | − | 925.907i | −0.238095 | − | 0.233285i | ||||
\(64\) | 512.000 | 0.125000 | ||||||||
\(65\) | 1248.01 | + | 2161.62i | 0.295388 | + | 0.511626i | ||||
\(66\) | 1246.96 | + | 719.934i | 0.286263 | + | 0.165274i | ||||
\(67\) | 2962.69 | − | 5131.53i | 0.659989 | − | 1.14314i | −0.320629 | − | 0.947205i | \(-0.603894\pi\) |
0.980618 | − | 0.195930i | \(-0.0627726\pi\) | |||||||
\(68\) | −745.998 | + | 430.702i | −0.161332 | + | 0.0931450i | ||||
\(69\) | − | 5307.86i | − | 1.11486i | ||||||
\(70\) | 3215.00 | + | 826.389i | 0.656123 | + | 0.168651i | ||||
\(71\) | −4494.41 | −0.891571 | −0.445785 | − | 0.895140i | \(-0.647076\pi\) | ||||
−0.445785 | + | 0.895140i | \(0.647076\pi\) | |||||||
\(72\) | −305.470 | − | 529.090i | −0.0589256 | − | 0.102062i | ||||
\(73\) | 7767.32 | + | 4484.46i | 1.45756 | + | 0.841521i | 0.998891 | − | 0.0470879i | \(-0.0149941\pi\) |
0.458666 | + | 0.888609i | \(0.348327\pi\) | |||||||
\(74\) | −795.121 | + | 1377.19i | −0.145201 | + | 0.251496i | ||||
\(75\) | 230.957 | − | 133.343i | 0.0410590 | − | 0.0237055i | ||||
\(76\) | 307.148i | 0.0531767i | ||||||||
\(77\) | 1195.09 | − | 4649.42i | 0.201567 | − | 0.784183i | ||||
\(78\) | −1531.59 | −0.251741 | ||||||||
\(79\) | 5223.41 | + | 9047.22i | 0.836951 | + | 1.44964i | 0.892432 | + | 0.451182i | \(0.148998\pi\) |
−0.0554805 | + | 0.998460i | \(0.517669\pi\) | |||||||
\(80\) | 1327.53 | + | 766.449i | 0.207426 | + | 0.119758i | ||||
\(81\) | −364.500 | + | 631.333i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 2506.31 | − | 1447.02i | 0.372741 | − | 0.215202i | ||||
\(83\) | 1269.28i | 0.184247i | 0.995748 | + | 0.0921234i | \(0.0293654\pi\) | ||||
−0.995748 | + | 0.0921234i | \(0.970635\pi\) | |||||||
\(84\) | −1425.53 | + | 1454.92i | −0.202031 | + | 0.206197i | ||||
\(85\) | −2579.00 | −0.356954 | ||||||||
\(86\) | −4783.45 | − | 8285.17i | −0.646761 | − | 1.12022i | ||||
\(87\) | −2797.21 | − | 1614.97i | −0.369562 | − | 0.213367i | ||||
\(88\) | 1108.41 | − | 1919.82i | 0.143132 | − | 0.247911i | ||||
\(89\) | −3121.46 | + | 1802.18i | −0.394074 | + | 0.227519i | −0.683924 | − | 0.729553i | \(-0.739728\pi\) |
0.289850 | + | 0.957072i | \(0.406395\pi\) | |||||||
\(90\) | − | 1829.12i | − | 0.225817i | ||||||
\(91\) | 1371.89 | + | 4918.62i | 0.165667 | + | 0.593965i | ||||
\(92\) | −8171.99 | −0.965500 | ||||||||
\(93\) | 3946.83 | + | 6836.11i | 0.456334 | + | 0.790393i | ||||
\(94\) | −9663.32 | − | 5579.12i | −1.09363 | − | 0.631408i | ||||
\(95\) | −459.792 | + | 796.383i | −0.0509465 | + | 0.0882419i | ||||
\(96\) | −814.587 | + | 470.302i | −0.0883883 | + | 0.0510310i | ||||
\(97\) | − | 1950.53i | − | 0.207304i | −0.994614 | − | 0.103652i | \(-0.966947\pi\) | ||
0.994614 | − | 0.103652i | \(-0.0330529\pi\) | |||||||
\(98\) | 5949.30 | + | 3274.79i | 0.619460 | + | 0.340982i | ||||
\(99\) | −2645.21 | −0.269891 | ||||||||
\(100\) | −205.295 | − | 355.582i | −0.0205295 | − | 0.0355582i | ||||
\(101\) | 9808.81 | + | 5663.12i | 0.961554 | + | 0.555153i | 0.896651 | − | 0.442738i | \(-0.145993\pi\) |
0.0649030 | + | 0.997892i | \(0.479326\pi\) | |||||||
\(102\) | 791.251 | − | 1370.49i | 0.0760525 | − | 0.131727i | ||||
\(103\) | −14141.2 | + | 8164.43i | −1.33294 | + | 0.769576i | −0.985750 | − | 0.168217i | \(-0.946199\pi\) |
−0.347195 | + | 0.937793i | \(0.612866\pi\) | |||||||
\(104\) | 2358.04i | 0.218014i | ||||||||
\(105\) | −5874.13 | + | 1638.39i | −0.532801 | + | 0.148607i | ||||
\(106\) | −6195.95 | −0.551438 | ||||||||
\(107\) | −2198.23 | − | 3807.45i | −0.192002 | − | 0.332557i | 0.753912 | − | 0.656976i | \(-0.228165\pi\) |
−0.945914 | + | 0.324419i | \(0.894831\pi\) | |||||||
\(108\) | 972.000 | + | 561.184i | 0.0833333 | + | 0.0481125i | ||||
\(109\) | 7348.89 | − | 12728.6i | 0.618541 | − | 1.07134i | −0.371211 | − | 0.928548i | \(-0.621057\pi\) |
0.989752 | − | 0.142796i | \(-0.0456093\pi\) | |||||||
\(110\) | 5747.84 | − | 3318.52i | 0.475028 | − | 0.274258i | ||||
\(111\) | − | 2921.46i | − | 0.237112i | ||||||
\(112\) | 2240.00 | + | 2194.74i | 0.178571 | + | 0.174964i | ||||
\(113\) | 2124.36 | 0.166368 | 0.0831842 | − | 0.996534i | \(-0.473491\pi\) | ||||
0.0831842 | + | 0.996534i | \(0.473491\pi\) | |||||||
\(114\) | −282.134 | − | 488.670i | −0.0217093 | − | 0.0376016i | ||||
\(115\) | −21188.6 | − | 12233.2i | −1.60216 | − | 0.925008i | ||||
\(116\) | −2486.41 | + | 4306.59i | −0.184781 | + | 0.320050i | ||||
\(117\) | 2436.74 | − | 1406.85i | 0.178007 | − | 0.102773i | ||||
\(118\) | 8301.07i | 0.596170i | ||||||||
\(119\) | −5109.99 | − | 1313.48i | −0.360850 | − | 0.0927533i | ||||
\(120\) | −2816.11 | −0.195563 | ||||||||
\(121\) | 2521.38 | + | 4367.17i | 0.172214 | + | 0.298283i | ||||
\(122\) | 1629.76 | + | 940.942i | 0.109497 | + | 0.0632184i | ||||
\(123\) | −2658.35 | + | 4604.39i | −0.175712 | + | 0.304342i | ||||
\(124\) | 10524.9 | − | 6076.54i | 0.684500 | − | 0.395196i | ||||
\(125\) | − | 16199.0i | − | 1.03674i | ||||||
\(126\) | 931.568 | − | 3624.20i | 0.0586778 | − | 0.228282i | ||||
\(127\) | 8498.07 | 0.526881 | 0.263441 | − | 0.964676i | \(-0.415143\pi\) | ||||
0.263441 | + | 0.964676i | \(0.415143\pi\) | |||||||
\(128\) | 724.077 | + | 1254.14i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 15220.8 | + | 8787.75i | 0.914658 | + | 0.528078i | ||||
\(130\) | −3529.91 | + | 6113.99i | −0.208871 | + | 0.361774i | ||||
\(131\) | 12533.4 | − | 7236.14i | 0.730340 | − | 0.421662i | −0.0882063 | − | 0.996102i | \(-0.528113\pi\) |
0.818547 | + | 0.574440i | \(0.194780\pi\) | |||||||
\(132\) | 4072.56i | 0.233733i | ||||||||
\(133\) | −1316.62 | + | 1343.77i | −0.0744318 | + | 0.0759666i | ||||
\(134\) | 16759.5 | 0.933366 | ||||||||
\(135\) | 1680.15 | + | 2910.11i | 0.0921895 | + | 0.159677i | ||||
\(136\) | −2110.00 | − | 1218.21i | −0.114079 | − | 0.0658634i | ||||
\(137\) | −6427.59 | + | 11132.9i | −0.342458 | + | 0.593154i | −0.984888 | − | 0.173190i | \(-0.944593\pi\) |
0.642431 | + | 0.766344i | \(0.277926\pi\) | |||||||
\(138\) | 13001.6 | − | 7506.45i | 0.682711 | − | 0.394164i | ||||
\(139\) | 5009.46i | 0.259275i | 0.991561 | + | 0.129638i | \(0.0413814\pi\) | ||||
−0.991561 | + | 0.129638i | \(0.958619\pi\) | |||||||
\(140\) | 2522.47 | + | 9043.81i | 0.128698 | + | 0.461419i | ||||
\(141\) | 20499.0 | 1.03108 | ||||||||
\(142\) | −6356.05 | − | 11009.0i | −0.315218 | − | 0.545973i | ||||
\(143\) | 8841.82 | + | 5104.83i | 0.432384 | + | 0.249637i | ||||
\(144\) | 864.000 | − | 1496.49i | 0.0416667 | − | 0.0721688i | ||||
\(145\) | −12893.7 | + | 7444.17i | −0.613255 | + | 0.354063i | ||||
\(146\) | 25368.0i | 1.19009i | ||||||||
\(147\) | −12473.4 | + | 254.611i | −0.577230 | + | 0.0117827i | ||||
\(148\) | −4497.88 | −0.205345 | ||||||||
\(149\) | −12699.5 | − | 21996.1i | −0.572022 | − | 0.990771i | −0.996358 | − | 0.0852664i | \(-0.972826\pi\) |
0.424336 | − | 0.905505i | \(-0.360507\pi\) | |||||||
\(150\) | 653.245 | + | 377.151i | 0.0290331 | + | 0.0167623i | ||||
\(151\) | 9154.39 | − | 15855.9i | 0.401491 | − | 0.695402i | −0.592415 | − | 0.805633i | \(-0.701826\pi\) |
0.993906 | + | 0.110230i | \(0.0351589\pi\) | |||||||
\(152\) | −752.357 | + | 434.373i | −0.0325639 | + | 0.0188008i | ||||
\(153\) | 2907.24i | 0.124193i | ||||||||
\(154\) | 13078.8 | − | 3647.91i | 0.551477 | − | 0.153816i | ||||
\(155\) | 36385.6 | 1.51449 | ||||||||
\(156\) | −2165.99 | − | 3751.61i | −0.0890037 | − | 0.154159i | ||||
\(157\) | −30522.6 | − | 17622.2i | −1.23829 | − | 0.714926i | −0.269544 | − | 0.962988i | \(-0.586873\pi\) |
−0.968744 | + | 0.248062i | \(0.920206\pi\) | |||||||
\(158\) | −14774.0 | + | 25589.4i | −0.591814 | + | 1.02505i | ||||
\(159\) | 9857.70 | − | 5691.35i | 0.389925 | − | 0.225123i | ||||
\(160\) | 4335.69i | 0.169363i | ||||||||
\(161\) | −35752.5 | − | 35030.1i | −1.37929 | − | 1.35142i | ||||
\(162\) | −2061.92 | −0.0785674 | ||||||||
\(163\) | −72.9693 | − | 126.386i | −0.00274641 | − | 0.00475691i | 0.864649 | − | 0.502377i | \(-0.167541\pi\) |
−0.867395 | + | 0.497620i | \(0.834208\pi\) | |||||||
\(164\) | 7088.92 | + | 4092.79i | 0.263568 | + | 0.152171i | ||||
\(165\) | −6096.50 | + | 10559.5i | −0.223930 | + | 0.387859i | ||||
\(166\) | −3109.08 | + | 1795.03i | −0.112828 | + | 0.0651411i | ||||
\(167\) | 31314.1i | 1.12281i | 0.827541 | + | 0.561405i | \(0.189739\pi\) | ||||
−0.827541 | + | 0.561405i | \(0.810261\pi\) | |||||||
\(168\) | −5579.82 | − | 1434.24i | −0.197698 | − | 0.0508164i | ||||
\(169\) | 17701.0 | 0.619760 | ||||||||
\(170\) | −3647.25 | − | 6317.22i | −0.126202 | − | 0.218589i | ||||
\(171\) | 897.744 | + | 518.313i | 0.0307016 | + | 0.0177256i | ||||
\(172\) | 13529.6 | − | 23434.0i | 0.457329 | − | 0.792117i | ||||
\(173\) | −34741.3 | + | 20057.9i | −1.16079 | + | 0.670183i | −0.951494 | − | 0.307669i | \(-0.900451\pi\) |
−0.209298 | + | 0.977852i | \(0.567118\pi\) | |||||||
\(174\) | − | 9135.66i | − | 0.301746i | ||||||
\(175\) | 626.073 | − | 2435.69i | 0.0204432 | − | 0.0795327i | ||||
\(176\) | 6270.12 | 0.202419 | ||||||||
\(177\) | −7625.02 | − | 13206.9i | −0.243385 | − | 0.421556i | ||||
\(178\) | −8828.83 | − | 5097.33i | −0.278653 | − | 0.160880i | ||||
\(179\) | 25077.2 | − | 43435.0i | 0.782661 | − | 1.35561i | −0.147726 | − | 0.989028i | \(-0.547195\pi\) |
0.930387 | − | 0.366580i | \(-0.119471\pi\) | |||||||
\(180\) | 4480.41 | − | 2586.77i | 0.138284 | − | 0.0798385i | ||||
\(181\) | 63974.3i | 1.95276i | 0.216069 | + | 0.976378i | \(0.430677\pi\) | ||||
−0.216069 | + | 0.976378i | \(0.569323\pi\) | |||||||
\(182\) | −10108.0 | + | 10316.4i | −0.305156 | + | 0.311448i | ||||
\(183\) | −3457.24 | −0.103235 | ||||||||
\(184\) | −11556.9 | − | 20017.2i | −0.341356 | − | 0.591245i | ||||
\(185\) | −11662.2 | − | 6733.20i | −0.340752 | − | 0.196733i | ||||
\(186\) | −11163.3 | + | 19335.4i | −0.322677 | + | 0.558892i | ||||
\(187\) | −9135.73 | + | 5274.52i | −0.261252 | + | 0.150834i | ||||
\(188\) | − | 31560.3i | − | 0.892945i | ||||||
\(189\) | 1846.92 | + | 6621.76i | 0.0517041 | + | 0.185375i | ||||
\(190\) | −2600.98 | −0.0720492 | ||||||||
\(191\) | 21384.4 | + | 37039.0i | 0.586180 | + | 1.01529i | 0.994727 | + | 0.102557i | \(0.0327024\pi\) |
−0.408547 | + | 0.912737i | \(0.633964\pi\) | |||||||
\(192\) | −2304.00 | − | 1330.22i | −0.0625000 | − | 0.0360844i | ||||
\(193\) | 4386.29 | − | 7597.28i | 0.117756 | − | 0.203959i | −0.801122 | − | 0.598501i | \(-0.795763\pi\) |
0.918878 | + | 0.394542i | \(0.129097\pi\) | |||||||
\(194\) | 4777.80 | − | 2758.46i | 0.126947 | − | 0.0732932i | ||||
\(195\) | − | 12969.7i | − | 0.341084i | ||||||
\(196\) | 392.000 | + | 19204.0i | 0.0102041 | + | 0.499896i | ||||
\(197\) | −32825.0 | −0.845808 | −0.422904 | − | 0.906174i | \(-0.638989\pi\) | ||||
−0.422904 | + | 0.906174i | \(0.638989\pi\) | |||||||
\(198\) | −3740.89 | − | 6479.40i | −0.0954210 | − | 0.165274i | ||||
\(199\) | −22918.7 | − | 13232.1i | −0.578740 | − | 0.334136i | 0.181893 | − | 0.983318i | \(-0.441778\pi\) |
−0.760632 | + | 0.649183i | \(0.775111\pi\) | |||||||
\(200\) | 580.663 | − | 1005.74i | 0.0145166 | − | 0.0251434i | ||||
\(201\) | −26664.2 | + | 15394.6i | −0.659989 | + | 0.381045i | ||||
\(202\) | 32035.4i | 0.785106i | ||||||||
\(203\) | −29338.7 | + | 8183.07i | −0.711949 | + | 0.198575i | ||||
\(204\) | 4475.99 | 0.107555 | ||||||||
\(205\) | 12253.6 | + | 21223.8i | 0.291578 | + | 0.505028i | ||||
\(206\) | −39997.4 | − | 23092.5i | −0.942534 | − | 0.544172i | ||||
\(207\) | −13790.2 | + | 23885.4i | −0.321833 | + | 0.557432i | ||||
\(208\) | −5775.99 | + | 3334.77i | −0.133506 | + | 0.0770795i | ||||
\(209\) | 3761.44i | 0.0861115i | ||||||||
\(210\) | −12320.5 | − | 12071.6i | −0.279376 | − | 0.273732i | ||||
\(211\) | 67056.3 | 1.50617 | 0.753087 | − | 0.657921i | \(-0.228564\pi\) | ||||
0.753087 | + | 0.657921i | \(0.228564\pi\) | |||||||
\(212\) | −8762.40 | − | 15176.9i | −0.194963 | − | 0.337685i | ||||
\(213\) | 20224.8 | + | 11676.8i | 0.445785 | + | 0.257374i | ||||
\(214\) | 6217.54 | − | 10769.1i | 0.135766 | − | 0.235154i | ||||
\(215\) | 70160.1 | − | 40506.9i | 1.51779 | − | 0.876299i | ||||
\(216\) | 3174.54i | 0.0680414i | ||||||||
\(217\) | 72094.1 | + | 18531.1i | 1.53102 | + | 0.393535i | ||||
\(218\) | 41571.6 | 0.874749 | ||||||||
\(219\) | −23302.0 | − | 40360.2i | −0.485852 | − | 0.841521i | ||||
\(220\) | 16257.3 | + | 9386.18i | 0.335896 | + | 0.193929i | ||||
\(221\) | 5610.52 | − | 9717.70i | 0.114873 | − | 0.198966i | ||||
\(222\) | 7156.09 | − | 4131.57i | 0.145201 | − | 0.0838319i | ||||
\(223\) | 56260.1i | 1.13133i | 0.824634 | + | 0.565666i | \(0.191381\pi\) | ||||
−0.824634 | + | 0.565666i | \(0.808619\pi\) | |||||||
\(224\) | −2208.16 | + | 8590.69i | −0.0440083 | + | 0.171211i | ||||
\(225\) | −1385.74 | −0.0273727 | ||||||||
\(226\) | 3004.30 | + | 5203.59i | 0.0588201 | + | 0.101879i | ||||
\(227\) | 52955.8 | + | 30574.1i | 1.02769 | + | 0.593337i | 0.916322 | − | 0.400442i | \(-0.131143\pi\) |
0.111368 | + | 0.993779i | \(0.464477\pi\) | |||||||
\(228\) | 797.995 | − | 1382.17i | 0.0153508 | − | 0.0265883i | ||||
\(229\) | 29274.9 | − | 16901.9i | 0.558244 | − | 0.322303i | −0.194196 | − | 0.980963i | \(-0.562210\pi\) |
0.752441 | + | 0.658660i | \(0.228877\pi\) | |||||||
\(230\) | − | 69201.6i | − | 1.30816i | ||||||
\(231\) | −17457.5 | + | 17817.4i | −0.327158 | + | 0.333904i | ||||
\(232\) | −14065.3 | −0.261320 | ||||||||
\(233\) | −4343.63 | − | 7523.39i | −0.0800094 | − | 0.138580i | 0.823244 | − | 0.567687i | \(-0.192162\pi\) |
−0.903254 | + | 0.429107i | \(0.858828\pi\) | |||||||
\(234\) | 6892.15 | + | 3979.19i | 0.125870 | + | 0.0726712i | ||||
\(235\) | 47244.8 | − | 81830.4i | 0.855496 | − | 1.48176i | ||||
\(236\) | −20333.4 | + | 11739.5i | −0.365078 | + | 0.210778i | ||||
\(237\) | − | 54283.3i | − | 0.966428i | ||||||
\(238\) | −4009.27 | − | 14374.4i | −0.0707801 | − | 0.253768i | ||||
\(239\) | −15715.0 | −0.275118 | −0.137559 | − | 0.990494i | \(-0.543926\pi\) | ||||
−0.137559 | + | 0.990494i | \(0.543926\pi\) | |||||||
\(240\) | −3982.59 | − | 6898.04i | −0.0691421 | − | 0.119758i | ||||
\(241\) | −4744.80 | − | 2739.41i | −0.0816928 | − | 0.0471654i | 0.458597 | − | 0.888644i | \(-0.348352\pi\) |
−0.540290 | + | 0.841479i | \(0.681685\pi\) | |||||||
\(242\) | −7131.55 | + | 12352.2i | −0.121774 | + | 0.210918i | ||||
\(243\) | 3280.50 | − | 1894.00i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | 5322.77i | 0.0894043i | ||||||||
\(245\) | −27731.4 | + | 50379.5i | −0.461998 | + | 0.839309i | ||||
\(246\) | −15037.9 | −0.248494 | ||||||||
\(247\) | −2000.52 | − | 3465.01i | −0.0327906 | − | 0.0567950i | ||||
\(248\) | 29768.9 | + | 17187.1i | 0.484015 | + | 0.279446i | ||||
\(249\) | 3297.68 | − | 5711.74i | 0.0531875 | − | 0.0921234i | ||||
\(250\) | 39679.3 | − | 22908.8i | 0.634868 | − | 0.366541i | ||||
\(251\) | − | 24350.9i | − | 0.386516i | −0.981148 | − | 0.193258i | \(-0.938095\pi\) | ||
0.981148 | − | 0.193258i | \(-0.0619054\pi\) | |||||||
\(252\) | 10194.9 | − | 2843.52i | 0.160539 | − | 0.0447771i | ||||
\(253\) | −100077. | −1.56348 | ||||||||
\(254\) | 12018.1 | + | 20815.9i | 0.186281 | + | 0.322647i | ||||
\(255\) | 11605.5 | + | 6700.43i | 0.178477 | + | 0.103044i | ||||
\(256\) | −2048.00 | + | 3547.24i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 10051.7 | − | 5803.37i | 0.152186 | − | 0.0878647i | −0.421973 | − | 0.906608i | \(-0.638662\pi\) |
0.574159 | + | 0.818744i | \(0.305329\pi\) | |||||||
\(258\) | 49711.0i | 0.746815i | ||||||||
\(259\) | −19678.2 | − | 19280.7i | −0.293350 | − | 0.287424i | ||||
\(260\) | −19968.2 | −0.295388 | ||||||||
\(261\) | 8391.64 | + | 14534.7i | 0.123187 | + | 0.213367i | ||||
\(262\) | 35449.7 | + | 20466.9i | 0.516429 | + | 0.298160i | ||||
\(263\) | −60333.8 | + | 104501.i | −0.872266 | + | 1.51081i | −0.0126200 | + | 0.999920i | \(0.504017\pi\) |
−0.859646 | + | 0.510889i | \(0.829316\pi\) | |||||||
\(264\) | −9975.69 | + | 5759.47i | −0.143132 | + | 0.0826370i | ||||
\(265\) | − | 52468.3i | − | 0.747145i | ||||||
\(266\) | −5153.55 | − | 1324.67i | −0.0728355 | − | 0.0187217i | ||||
\(267\) | 18728.8 | 0.262716 | ||||||||
\(268\) | 23701.5 | + | 41052.3i | 0.329995 | + | 0.571568i | ||||
\(269\) | −23596.3 | − | 13623.3i | −0.326091 | − | 0.188269i | 0.328013 | − | 0.944673i | \(-0.393621\pi\) |
−0.654104 | + | 0.756404i | \(0.726954\pi\) | |||||||
\(270\) | −4752.19 | + | 8231.04i | −0.0651878 | + | 0.112909i | ||||
\(271\) | −84041.9 | + | 48521.6i | −1.14435 | + | 0.660689i | −0.947503 | − | 0.319746i | \(-0.896402\pi\) |
−0.196843 | + | 0.980435i | \(0.563069\pi\) | |||||||
\(272\) | − | 6891.24i | − | 0.0931450i | ||||||
\(273\) | 6605.46 | − | 25698.1i | 0.0886294 | − | 0.344806i | ||||
\(274\) | −36359.9 | −0.484308 | ||||||||
\(275\) | −2514.11 | − | 4354.57i | −0.0332444 | − | 0.0575811i | ||||
\(276\) | 36774.0 | + | 21231.5i | 0.482750 | + | 0.278716i | ||||
\(277\) | −14876.4 | + | 25766.7i | −0.193882 | + | 0.335814i | −0.946534 | − | 0.322605i | \(-0.895441\pi\) |
0.752651 | + | 0.658419i | \(0.228775\pi\) | |||||||
\(278\) | −12270.6 | + | 7084.44i | −0.158773 | + | 0.0916676i | ||||
\(279\) | − | 41016.7i | − | 0.526929i | ||||||
\(280\) | −18585.4 | + | 18968.7i | −0.237059 | + | 0.241947i | ||||
\(281\) | −122275. | −1.54855 | −0.774276 | − | 0.632849i | \(-0.781886\pi\) | ||||
−0.774276 | + | 0.632849i | \(0.781886\pi\) | |||||||
\(282\) | 28989.9 | + | 50212.1i | 0.364543 | + | 0.631408i | ||||
\(283\) | −52568.4 | − | 30350.4i | −0.656374 | − | 0.378958i | 0.134520 | − | 0.990911i | \(-0.457051\pi\) |
−0.790894 | + | 0.611953i | \(0.790384\pi\) | |||||||
\(284\) | 17977.6 | − | 31138.2i | 0.222893 | − | 0.386062i | ||||
\(285\) | 4138.13 | − | 2389.15i | 0.0509465 | − | 0.0294140i | ||||
\(286\) | 28877.3i | 0.353040i | ||||||||
\(287\) | 13469.8 | + | 48293.4i | 0.163531 | + | 0.586305i | ||||
\(288\) | 4887.52 | 0.0589256 | ||||||||
\(289\) | −35963.5 | − | 62290.6i | −0.430592 | − | 0.745807i | ||||
\(290\) | −36468.9 | − | 21055.3i | −0.433637 | − | 0.250360i | ||||
\(291\) | −5067.62 | + | 8777.37i | −0.0598436 | + | 0.103652i | ||||
\(292\) | −62138.6 | + | 35875.7i | −0.728778 | + | 0.420760i | ||||
\(293\) | − | 29557.4i | − | 0.344296i | −0.985071 | − | 0.172148i | \(-0.944929\pi\) | ||
0.985071 | − | 0.172148i | \(-0.0550707\pi\) | |||||||
\(294\) | −18263.7 | − | 30193.3i | −0.211297 | − | 0.349314i | ||||
\(295\) | −70294.7 | −0.807752 | ||||||||
\(296\) | −6360.97 | − | 11017.5i | −0.0726005 | − | 0.125748i | ||||
\(297\) | 11903.4 | + | 6872.44i | 0.134946 | + | 0.0779109i | ||||
\(298\) | 35919.5 | − | 62214.4i | 0.404481 | − | 0.700581i | ||||
\(299\) | 92190.0 | − | 53225.9i | 1.03120 | − | 0.595362i | ||||
\(300\) | 2133.49i | 0.0237055i | ||||||||
\(301\) | 159644. | − | 44527.6i | 1.76206 | − | 0.491469i | ||||
\(302\) | 51785.0 | 0.567794 | ||||||||
\(303\) | −29426.4 | − | 50968.1i | −0.320518 | − | 0.555153i | ||||
\(304\) | −2127.99 | − | 1228.59i | −0.0230262 | − | 0.0132942i | ||||
\(305\) | −7968.04 | + | 13801.0i | −0.0856548 | + | 0.148358i | ||||
\(306\) | −7121.26 | + | 4111.46i | −0.0760525 | + | 0.0439090i | ||||
\(307\) | − | 107567.i | − | 1.14131i | −0.821191 | − | 0.570654i | \(-0.806690\pi\) | ||
0.821191 | − | 0.570654i | \(-0.193310\pi\) | |||||||
\(308\) | 27431.8 | + | 26877.5i | 0.289169 | + | 0.283327i | ||||
\(309\) | 84847.3 | 0.888630 | ||||||||
\(310\) | 51457.0 | + | 89126.2i | 0.535453 | + | 0.927432i | ||||
\(311\) | 37561.0 | + | 21685.9i | 0.388344 | + | 0.224211i | 0.681442 | − | 0.731872i | \(-0.261353\pi\) |
−0.293098 | + | 0.956082i | \(0.594686\pi\) | |||||||
\(312\) | 6126.36 | − | 10611.2i | 0.0629351 | − | 0.109007i | ||||
\(313\) | −93311.1 | + | 53873.2i | −0.952455 | + | 0.549900i | −0.893843 | − | 0.448381i | \(-0.852001\pi\) |
−0.0586125 | + | 0.998281i | \(0.518668\pi\) | |||||||
\(314\) | − | 99686.3i | − | 1.01106i | ||||||
\(315\) | 30690.2 | + | 7888.66i | 0.309300 | + | 0.0795027i | ||||
\(316\) | −83574.6 | −0.836951 | ||||||||
\(317\) | 77996.9 | + | 135095.i | 0.776174 | + | 1.34437i | 0.934133 | + | 0.356926i | \(0.116175\pi\) |
−0.157959 | + | 0.987446i | \(0.550491\pi\) | |||||||
\(318\) | 27881.8 | + | 16097.6i | 0.275719 | + | 0.159186i | ||||
\(319\) | −30449.4 | + | 52739.9i | −0.299225 | + | 0.518272i | ||||
\(320\) | −10620.2 | + | 6131.59i | −0.103713 | + | 0.0598788i | ||||
\(321\) | 22844.7i | 0.221705i | ||||||||
\(322\) | 35244.3 | − | 137115.i | 0.339920 | − | 1.32243i | ||||
\(323\) | 4134.05 | 0.0396251 | ||||||||
\(324\) | −2916.00 | − | 5050.66i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 4631.96 | + | 2674.26i | 0.0438529 | + | 0.0253185i | ||||
\(326\) | 206.388 | − | 357.475i | 0.00194200 | − | 0.00336365i | ||||
\(327\) | −66140.0 | + | 38185.9i | −0.618541 | + | 0.357115i | ||||
\(328\) | 23152.3i | 0.215202i | ||||||||
\(329\) | 135286. | − | 138076.i | 1.24986 | − | 1.27564i | ||||
\(330\) | −34487.0 | −0.316685 | ||||||||
\(331\) | −20109.4 | − | 34830.4i | −0.183545 | − | 0.317909i | 0.759540 | − | 0.650460i | \(-0.225424\pi\) |
−0.943085 | + | 0.332551i | \(0.892091\pi\) | |||||||
\(332\) | −8793.80 | − | 5077.10i | −0.0797812 | − | 0.0460617i | ||||
\(333\) | −7590.18 | + | 13146.6i | −0.0684484 | + | 0.118556i | ||||
\(334\) | −76703.5 | + | 44284.8i | −0.687578 | + | 0.396974i | ||||
\(335\) | 141922.i | 1.26462i | ||||||||
\(336\) | −4377.89 | − | 15696.0i | −0.0387781 | − | 0.139031i | ||||
\(337\) | 90476.4 | 0.796665 | 0.398332 | − | 0.917241i | \(-0.369589\pi\) | ||||
0.398332 | + | 0.917241i | \(0.369589\pi\) | |||||||
\(338\) | 25033.0 | + | 43358.3i | 0.219118 | + | 0.379524i | ||||
\(339\) | −9559.61 | − | 5519.25i | −0.0831842 | − | 0.0480264i | ||||
\(340\) | 10316.0 | − | 17867.8i | 0.0892386 | − | 0.154566i | ||||
\(341\) | 128891. | − | 74415.3i | 1.10844 | − | 0.639961i | ||||
\(342\) | 2932.02i | 0.0250677i | ||||||||
\(343\) | −80605.0 | + | 85697.8i | −0.685131 | + | 0.728420i | ||||
\(344\) | 76535.1 | 0.646761 | ||||||||
\(345\) | 63565.7 | + | 110099.i | 0.534054 | + | 0.925008i | ||||
\(346\) | −98263.3 | − | 56732.3i | −0.820803 | − | 0.473891i | ||||
\(347\) | −16037.2 | + | 27777.3i | −0.133190 | + | 0.230691i | −0.924904 | − | 0.380200i | \(-0.875855\pi\) |
0.791715 | + | 0.610891i | \(0.209189\pi\) | |||||||
\(348\) | 22377.7 | − | 12919.8i | 0.184781 | − | 0.106683i | ||||
\(349\) | − | 116783.i | − | 0.958805i | −0.877595 | − | 0.479402i | \(-0.840853\pi\) | ||
0.877595 | − | 0.479402i | \(-0.159147\pi\) | |||||||
\(350\) | 6851.60 | − | 1911.03i | 0.0559314 | − | 0.0156002i | ||||
\(351\) | −14620.5 | −0.118672 | ||||||||
\(352\) | 8867.28 | + | 15358.6i | 0.0715658 | + | 0.123956i | ||||
\(353\) | 107957. | + | 62329.1i | 0.866367 | + | 0.500197i | 0.866139 | − | 0.499803i | \(-0.166594\pi\) |
0.000227639 | 1.00000i | \(0.499928\pi\) | ||||||||
\(354\) | 21566.8 | − | 37354.8i | 0.172099 | − | 0.298085i | ||||
\(355\) | 93225.9 | − | 53824.0i | 0.739741 | − | 0.427090i | ||||
\(356\) | − | 28834.8i | − | 0.227519i | ||||||
\(357\) | 19582.5 | + | 19186.8i | 0.153649 | + | 0.150545i | ||||
\(358\) | 141858. | 1.10685 | ||||||||
\(359\) | −49721.0 | − | 86119.4i | −0.385790 | − | 0.668208i | 0.606088 | − | 0.795397i | \(-0.292738\pi\) |
−0.991878 | + | 0.127189i | \(0.959404\pi\) | |||||||
\(360\) | 12672.5 | + | 7316.48i | 0.0977817 | + | 0.0564543i | ||||
\(361\) | −64423.5 | + | 111585.i | −0.494344 | + | 0.856230i | ||||
\(362\) | −156704. | + | 90473.3i | −1.19581 | + | 0.690404i | ||||
\(363\) | − | 26203.0i | − | 0.198856i | ||||||
\(364\) | −39564.8 | − | 10169.8i | −0.298611 | − | 0.0767553i | ||||
\(365\) | −214820. | −1.61246 | ||||||||
\(366\) | −4889.28 | − | 8468.48i | −0.0364991 | − | 0.0632184i | ||||
\(367\) | 77002.3 | + | 44457.3i | 0.571704 | + | 0.330074i | 0.757830 | − | 0.652452i | \(-0.226260\pi\) |
−0.186126 | + | 0.982526i | \(0.559593\pi\) | |||||||
\(368\) | 32688.0 | − | 56617.2i | 0.241375 | − | 0.418074i | ||||
\(369\) | 23925.1 | − | 13813.2i | 0.175712 | − | 0.101447i | ||||
\(370\) | − | 38088.7i | − | 0.278223i | ||||||
\(371\) | 26722.0 | − | 103960.i | 0.194143 | − | 0.755298i | ||||
\(372\) | −63149.3 | −0.456334 | ||||||||
\(373\) | 45676.4 | + | 79113.9i | 0.328303 | + | 0.568637i | 0.982175 | − | 0.187968i | \(-0.0601900\pi\) |
−0.653872 | + | 0.756605i | \(0.726857\pi\) | |||||||
\(374\) | −25839.8 | − | 14918.6i | −0.184733 | − | 0.106656i | ||||
\(375\) | −42086.2 | + | 72895.5i | −0.299280 | + | 0.518368i | ||||
\(376\) | 77306.5 | − | 44632.9i | 0.546815 | − | 0.315704i | ||||
\(377\) | − | 64778.2i | − | 0.455770i | ||||||
\(378\) | −13608.0 | + | 13888.6i | −0.0952381 | + | 0.0972020i | ||||
\(379\) | 6328.51 | 0.0440578 | 0.0220289 | − | 0.999757i | \(-0.492987\pi\) | ||||
0.0220289 | + | 0.999757i | \(0.492987\pi\) | |||||||
\(380\) | −3678.34 | − | 6371.07i | −0.0254733 | − | 0.0441210i | ||||
\(381\) | −38241.3 | − | 22078.6i | −0.263441 | − | 0.152097i | ||||
\(382\) | −60484.4 | + | 104762.i | −0.414492 | + | 0.717922i | ||||
\(383\) | −11635.9 | + | 6717.98i | −0.0793235 | + | 0.0457974i | −0.539137 | − | 0.842218i | \(-0.681250\pi\) |
0.459814 | + | 0.888015i | \(0.347916\pi\) | |||||||
\(384\) | − | 7524.83i | − | 0.0510310i | ||||||
\(385\) | 30891.0 | + | 110753.i | 0.208406 | + | 0.747198i | ||||
\(386\) | 24812.6 | 0.166532 | ||||||||
\(387\) | −45662.5 | − | 79089.8i | −0.304886 | − | 0.528078i | ||||
\(388\) | 13513.6 | + | 7802.11i | 0.0897654 | + | 0.0518261i | ||||
\(389\) | −44148.1 | + | 76466.8i | −0.291752 | + | 0.505328i | −0.974224 | − | 0.225583i | \(-0.927571\pi\) |
0.682472 | + | 0.730911i | \(0.260905\pi\) | |||||||
\(390\) | 31769.2 | − | 18342.0i | 0.208871 | − | 0.120591i | ||||
\(391\) | 109990.i | 0.719451i | ||||||||
\(392\) | −46485.6 | + | 28118.8i | −0.302515 | + | 0.182989i | ||||
\(393\) | −75200.2 | −0.486894 | ||||||||
\(394\) | −46421.5 | − | 80404.4i | −0.299038 | − | 0.517950i | ||||
\(395\) | −216695. | − | 125109.i | −1.38885 | − | 0.801851i | ||||
\(396\) | 10580.8 | − | 18326.5i | 0.0674728 | − | 0.116866i | ||||
\(397\) | 187570. | − | 108294.i | 1.19010 | − | 0.687103i | 0.231769 | − | 0.972771i | \(-0.425549\pi\) |
0.958329 | + | 0.285668i | \(0.0922155\pi\) | |||||||
\(398\) | − | 74852.1i | − | 0.472539i | ||||||
\(399\) | 9416.04 | − | 2626.29i | 0.0591456 | − | 0.0164967i | ||||
\(400\) | 3284.72 | 0.0205295 | ||||||||
\(401\) | 2583.42 | + | 4474.61i | 0.0160659 | + | 0.0278270i | 0.873947 | − | 0.486022i | \(-0.161553\pi\) |
−0.857881 | + | 0.513849i | \(0.828219\pi\) | |||||||
\(402\) | −75417.8 | − | 43542.5i | −0.466683 | − | 0.269440i | ||||
\(403\) | −79155.7 | + | 137102.i | −0.487385 | + | 0.844175i | ||||
\(404\) | −78470.5 | + | 45305.0i | −0.480777 | + | 0.277577i | ||||
\(405\) | − | 17460.7i | − | 0.106451i | ||||||
\(406\) | −61535.6 | − | 60292.3i | −0.373314 | − | 0.365771i | ||||
\(407\) | −55082.5 | −0.332526 | ||||||||
\(408\) | 6330.01 | + | 10963.9i | 0.0380263 | + | 0.0658634i | ||||
\(409\) | 33697.7 | + | 19455.3i | 0.201443 | + | 0.116303i | 0.597329 | − | 0.801997i | \(-0.296229\pi\) |
−0.395885 | + | 0.918300i | \(0.629562\pi\) | |||||||
\(410\) | −34658.4 | + | 60030.0i | −0.206177 | + | 0.357109i | ||||
\(411\) | 57848.3 | − | 33398.7i | 0.342458 | − | 0.197718i | ||||
\(412\) | − | 130631.i | − | 0.769576i | ||||||
\(413\) | −139281. | − | 35801.0i | −0.816567 | − | 0.209891i | ||||
\(414\) | −78009.3 | −0.455141 | ||||||||
\(415\) | −15200.6 | − | 26328.1i | −0.0882599 | − | 0.152871i | ||||
\(416\) | −16337.0 | − | 9432.15i | −0.0944027 | − | 0.0545034i | ||||
\(417\) | 13015.0 | − | 22542.6i | 0.0748463 | − | 0.129638i | ||||
\(418\) | −9213.60 | + | 5319.48i | −0.0527323 | + | 0.0304450i | ||||
\(419\) | 263425.i | 1.50048i | 0.661167 | + | 0.750239i | \(0.270062\pi\) | ||||
−0.661167 | + | 0.750239i | \(0.729938\pi\) | |||||||
\(420\) | 12145.4 | − | 47250.7i | 0.0688514 | − | 0.267861i | ||||
\(421\) | −16375.1 | −0.0923889 | −0.0461944 | − | 0.998932i | \(-0.514709\pi\) | ||||
−0.0461944 | + | 0.998932i | \(0.514709\pi\) | |||||||
\(422\) | 94832.0 | + | 164254.i | 0.532513 | + | 0.922339i | ||||
\(423\) | −92245.4 | − | 53257.9i | −0.515542 | − | 0.297648i | ||||
\(424\) | 24783.8 | − | 42926.8i | 0.137859 | − | 0.238780i | ||||
\(425\) | −4785.93 | + | 2763.16i | −0.0264965 | + | 0.0152978i | ||||
\(426\) | 66054.0i | 0.363982i | ||||||||
\(427\) | −22816.6 | + | 23287.1i | −0.125140 | + | 0.127720i | ||||
\(428\) | 35171.7 | 0.192002 | ||||||||
\(429\) | −26525.5 | − | 45943.5i | −0.144128 | − | 0.249637i | ||||
\(430\) | 198443. | + | 114571.i | 1.07324 | + | 0.619637i | ||||
\(431\) | 125208. | − | 216867.i | 0.674028 | − | 1.16745i | −0.302724 | − | 0.953078i | \(-0.597896\pi\) |
0.976752 | − | 0.214373i | \(-0.0687708\pi\) | |||||||
\(432\) | −7776.00 | + | 4489.48i | −0.0416667 | + | 0.0240563i | ||||
\(433\) | − | 91495.1i | − | 0.488002i | −0.969775 | − | 0.244001i | \(-0.921540\pi\) | ||
0.969775 | − | 0.244001i | \(-0.0784601\pi\) | |||||||
\(434\) | 56564.6 | + | 202801.i | 0.300307 | + | 1.07669i | ||||
\(435\) | 77362.1 | 0.408837 | ||||||||
\(436\) | 58791.1 | + | 101829.i | 0.309270 | + | 0.535672i | ||||
\(437\) | 33964.6 | + | 19609.5i | 0.177854 | + | 0.102684i | ||||
\(438\) | 65907.9 | − | 114156.i | 0.343549 | − | 0.595045i | ||||
\(439\) | 7672.44 | − | 4429.69i | 0.0398111 | − | 0.0229850i | −0.479962 | − | 0.877289i | \(-0.659350\pi\) |
0.519773 | + | 0.854304i | \(0.326016\pi\) | |||||||
\(440\) | 53096.3i | 0.274258i | ||||||||
\(441\) | 56791.6 | + | 31261.0i | 0.292016 | + | 0.160741i | ||||
\(442\) | 31737.9 | 0.162455 | ||||||||
\(443\) | −150105. | − | 259989.i | −0.764868 | − | 1.32479i | −0.940316 | − | 0.340302i | \(-0.889471\pi\) |
0.175448 | − | 0.984489i | \(-0.443863\pi\) | |||||||
\(444\) | 20240.5 | + | 11685.8i | 0.102673 | + | 0.0592781i | ||||
\(445\) | 43164.9 | − | 74763.9i | 0.217977 | − | 0.377548i | ||||
\(446\) | −137808. | + | 79563.7i | −0.692797 | + | 0.399987i | ||||
\(447\) | 131977.i | 0.660514i | ||||||||
\(448\) | −24165.6 | + | 6740.20i | −0.120404 | + | 0.0335828i | ||||
\(449\) | 116866. | 0.579691 | 0.289846 | − | 0.957073i | \(-0.406396\pi\) | ||||
0.289846 | + | 0.957073i | \(0.406396\pi\) | |||||||
\(450\) | −1959.74 | − | 3394.36i | −0.00967771 | − | 0.0167623i | ||||
\(451\) | 86813.2 | + | 50121.6i | 0.426808 | + | 0.246418i | ||||
\(452\) | −8497.43 | + | 14718.0i | −0.0415921 | + | 0.0720396i | ||||
\(453\) | −82389.5 | + | 47567.6i | −0.401491 | + | 0.231801i | ||||
\(454\) | 172953.i | 0.839105i | ||||||||
\(455\) | −87360.9 | − | 85595.8i | −0.421982 | − | 0.413456i | ||||
\(456\) | 4514.14 | 0.0217093 | ||||||||
\(457\) | −36872.9 | − | 63865.7i | −0.176553 | − | 0.305798i | 0.764145 | − | 0.645045i | \(-0.223161\pi\) |
−0.940698 | + | 0.339246i | \(0.889828\pi\) | |||||||
\(458\) | 82801.9 | + | 47805.7i | 0.394738 | + | 0.227902i | ||||
\(459\) | 7553.23 | − | 13082.6i | 0.0358515 | − | 0.0620966i | ||||
\(460\) | 169509. | − | 97865.9i | 0.801081 | − | 0.462504i | ||||
\(461\) | − | 88219.1i | − | 0.415108i | −0.978224 | − | 0.207554i | \(-0.933450\pi\) | ||
0.978224 | − | 0.207554i | \(-0.0665502\pi\) | |||||||
\(462\) | −68332.2 | − | 17564.2i | −0.320141 | − | 0.0822895i | ||||
\(463\) | 297880. | 1.38957 | 0.694784 | − | 0.719219i | \(-0.255500\pi\) | ||||
0.694784 | + | 0.719219i | \(0.255500\pi\) | |||||||
\(464\) | −19891.3 | − | 34452.7i | −0.0923905 | − | 0.160025i | ||||
\(465\) | −163735. | − | 94532.6i | −0.757245 | − | 0.437196i | ||||
\(466\) | 12285.6 | − | 21279.4i | 0.0565752 | − | 0.0979911i | ||||
\(467\) | −162353. | + | 93734.8i | −0.744436 | + | 0.429801i | −0.823680 | − | 0.567055i | \(-0.808083\pi\) |
0.0792437 | + | 0.996855i | \(0.474749\pi\) | |||||||
\(468\) | 22509.7i | 0.102773i | ||||||||
\(469\) | −72280.7 | + | 281203.i | −0.328607 | + | 1.27842i | ||||
\(470\) | 267257. | 1.20985 | ||||||||
\(471\) | 91567.7 | + | 158600.i | 0.412763 | + | 0.714926i | ||||
\(472\) | −57511.5 | − | 33204.3i | −0.258149 | − | 0.149042i | ||||
\(473\) | 165688. | − | 286980.i | 0.740575 | − | 1.28271i | ||||
\(474\) | 132966. | − | 76768.2i | 0.591814 | − | 0.341684i | ||||
\(475\) | 1970.50i | 0.00873353i | ||||||||
\(476\) | 29540.0 | − | 30149.2i | 0.130376 | − | 0.133064i | ||||
\(477\) | −59146.2 | −0.259950 | ||||||||
\(478\) | −22224.4 | − | 38493.8i | −0.0972690 | − | 0.168475i | ||||
\(479\) | −104347. | − | 60244.5i | −0.454786 | − | 0.262571i | 0.255063 | − | 0.966924i | \(-0.417904\pi\) |
−0.709849 | + | 0.704354i | \(0.751237\pi\) | |||||||
\(480\) | 11264.5 | − | 19510.6i | 0.0488909 | − | 0.0846815i | ||||
\(481\) | 50741.6 | − | 29295.7i | 0.219318 | − | 0.126623i | ||||
\(482\) | − | 15496.4i | − | 0.0667019i | ||||||
\(483\) | 69875.2 | + | 250523.i | 0.299522 | + | 1.07387i | ||||
\(484\) | −40342.2 | −0.172214 | ||||||||
\(485\) | 23359.1 | + | 40459.1i | 0.0993052 | + | 0.172002i | ||||
\(486\) | 9278.66 | + | 5357.03i | 0.0392837 | + | 0.0226805i | ||||
\(487\) | 133697. | − | 231570.i | 0.563721 | − | 0.976393i | −0.433447 | − | 0.901179i | \(-0.642703\pi\) |
0.997167 | − | 0.0752136i | \(-0.0239639\pi\) | |||||||
\(488\) | −13038.1 | + | 7527.54i | −0.0547487 | + | 0.0316092i | ||||
\(489\) | 758.319i | 0.00317128i | ||||||||
\(490\) | −162622. | + | 3319.51i | −0.677311 | + | 0.0138255i | ||||
\(491\) | 178364. | 0.739851 | 0.369926 | − | 0.929061i | \(-0.379383\pi\) | ||||
0.369926 | + | 0.929061i | \(0.379383\pi\) | |||||||
\(492\) | −21266.8 | − | 36835.1i | −0.0878560 | − | 0.152171i | ||||
\(493\) | 57964.3 | + | 33465.7i | 0.238488 | + | 0.137691i | ||||
\(494\) | 5658.34 | − | 9800.53i | 0.0231865 | − | 0.0401602i | ||||
\(495\) | 54868.5 | − | 31678.4i | 0.223930 | − | 0.129286i | ||||
\(496\) | 97224.7i | 0.395196i | ||||||||
\(497\) | 212129. | − | 59166.5i | 0.858792 | − | 0.239532i | ||||
\(498\) | 18654.5 | 0.0752184 | ||||||||
\(499\) | −131873. | − | 228411.i | −0.529610 | − | 0.917311i | −0.999403 | − | 0.0345349i | \(-0.989005\pi\) |
0.469794 | − | 0.882776i | \(-0.344328\pi\) | |||||||
\(500\) | 112230. | + | 64796.0i | 0.448920 | + | 0.259184i | ||||
\(501\) | 81356.3 | − | 140913.i | 0.324128 | − | 0.561405i | ||||
\(502\) | 59647.2 | − | 34437.4i | 0.236692 | − | 0.136654i | ||||
\(503\) | 480056.i | 1.89739i | 0.316197 | + | 0.948694i | \(0.397594\pi\) | ||||
−0.316197 | + | 0.948694i | \(0.602406\pi\) | |||||||
\(504\) | 21382.9 | + | 20950.9i | 0.0841794 | + | 0.0824786i | ||||
\(505\) | −271281. | −1.06374 | ||||||||
\(506\) | −141530. | − | 245137.i | −0.552774 | − | 0.957432i | ||||
\(507\) | −79654.4 | − | 45988.5i | −0.309880 | − | 0.178909i | ||||
\(508\) | −33992.3 | + | 58876.3i | −0.131720 | + | 0.228146i | ||||
\(509\) | −52192.6 | + | 30133.4i | −0.201453 | + | 0.116309i | −0.597333 | − | 0.801993i | \(-0.703773\pi\) |
0.395880 | + | 0.918302i | \(0.370440\pi\) | |||||||
\(510\) | 37903.3i | 0.145726i | ||||||||
\(511\) | −425641. | − | 109407.i | −1.63005 | − | 0.418991i | ||||
\(512\) | −11585.2 | −0.0441942 | ||||||||
\(513\) | −2693.23 | − | 4664.82i | −0.0102339 | − | 0.0177256i | ||||
\(514\) | 28430.6 | + | 16414.4i | 0.107612 | + | 0.0621297i | ||||
\(515\) | 195551. | − | 338704.i | 0.737301 | − | 1.27704i | ||||
\(516\) | −121767. | + | 70302.0i | −0.457329 | + | 0.264039i | ||||
\(517\) | − | 386497.i | − | 1.44599i | ||||||
\(518\) | 19398.5 | − | 75468.6i | 0.0722952 | − | 0.281259i | ||||
\(519\) | 208448. | 0.773861 | ||||||||
\(520\) | −28239.3 | − | 48911.9i | −0.104435 | − | 0.180887i | ||||
\(521\) | 248823. | + | 143658.i | 0.916674 | + | 0.529242i | 0.882573 | − | 0.470176i | \(-0.155810\pi\) |
0.0341018 | + | 0.999418i | \(0.489143\pi\) | |||||||
\(522\) | −23735.1 | + | 41110.5i | −0.0871066 | + | 0.150873i | ||||
\(523\) | −239407. | + | 138222.i | −0.875254 | + | 0.505328i | −0.869091 | − | 0.494653i | \(-0.835295\pi\) |
−0.00616355 | + | 0.999981i | \(0.501962\pi\) | |||||||
\(524\) | 115778.i | 0.421662i | ||||||||
\(525\) | −9145.44 | + | 9334.02i | −0.0331807 | + | 0.0338649i | ||||
\(526\) | −341300. | −1.23357 | ||||||||
\(527\) | −81786.9 | − | 141659.i | −0.294484 | − | 0.510062i | ||||
\(528\) | −28215.5 | − | 16290.2i | −0.101209 | − | 0.0584332i | ||||
\(529\) | −381809. | + | 661313.i | −1.36438 | + | 2.36317i | ||||
\(530\) | 128520. | − | 74201.3i | 0.457531 | − | 0.264156i | ||||
\(531\) | 79241.5i | 0.281037i | ||||||||
\(532\) | −4043.44 | − | 14496.9i | −0.0142866 | − | 0.0512216i | ||||
\(533\) | −106629. | −0.375336 | ||||||||
\(534\) | 26486.5 | + | 45876.0i | 0.0928842 | + | 0.160880i | ||||
\(535\) | 91194.3 | + | 52651.0i | 0.318610 | + | 0.183950i | ||||
\(536\) | −67038.1 | + | 116113.i | −0.233341 | + | 0.404159i | ||||
\(537\) | −225695. | + | 130305.i | −0.782661 | + | 0.451869i | ||||
\(538\) | − | 77065.1i | − | 0.266252i | ||||||
\(539\) | 4800.56 | + | 235178.i | 0.0165240 | + | 0.809505i | ||||
\(540\) | −26882.5 | −0.0921895 | ||||||||
\(541\) | 29832.0 | + | 51670.6i | 0.101927 | + | 0.176542i | 0.912478 | − | 0.409125i | \(-0.134166\pi\) |
−0.810552 | + | 0.585667i | \(0.800833\pi\) | |||||||
\(542\) | −237707. | − | 137240.i | −0.809175 | − | 0.467177i | ||||
\(543\) | 166210. | − | 287884.i | 0.563712 | − | 0.976378i | ||||
\(544\) | 16880.0 | − | 9745.68i | 0.0570394 | − | 0.0329317i | ||||
\(545\) | 352034.i | 1.18520i | ||||||||
\(546\) | 72288.7 | − | 20162.6i | 0.242485 | − | 0.0676332i | ||||
\(547\) | 489585. | 1.63627 | 0.818133 | − | 0.575030i | \(-0.195010\pi\) | ||||
0.818133 | + | 0.575030i | \(0.195010\pi\) | |||||||
\(548\) | −51420.7 | − | 89063.3i | −0.171229 | − | 0.296577i | ||||
\(549\) | 15557.6 | + | 8982.18i | 0.0516176 | + | 0.0298014i | ||||
\(550\) | 7110.98 | − | 12316.6i | 0.0235074 | − | 0.0407160i | ||||
\(551\) | 20668.2 | − | 11932.8i | 0.0680767 | − | 0.0393041i | ||||
\(552\) | 120103.i | 0.394164i | ||||||||
\(553\) | −365639. | − | 358251.i | −1.19564 | − | 1.17149i | ||||
\(554\) | −84153.6 | −0.274191 | ||||||||
\(555\) | 34986.7 | + | 60598.8i | 0.113584 | + | 0.196733i | ||||
\(556\) | −34706.5 | − | 20037.8i | −0.112269 | − | 0.0648188i | ||||
\(557\) | −254267. | + | 440404.i | −0.819558 | + | 1.41952i | 0.0864495 | + | 0.996256i | \(0.472448\pi\) |
−0.906008 | + | 0.423261i | \(0.860885\pi\) | |||||||
\(558\) | 100470. | − | 58006.3i | 0.322677 | − | 0.186297i | ||||
\(559\) | 352486.i | 1.12802i | ||||||||
\(560\) | −72747.2 | − | 18699.0i | −0.231975 | − | 0.0596270i | ||||
\(561\) | 54814.4 | 0.174168 | ||||||||
\(562\) | −172923. | − | 299512.i | −0.547496 | − | 0.948290i | ||||
\(563\) | 103765. | + | 59908.5i | 0.327365 | + | 0.189004i | 0.654671 | − | 0.755914i | \(-0.272807\pi\) |
−0.327306 | + | 0.944919i | \(0.606141\pi\) | |||||||
\(564\) | −81995.9 | + | 142021.i | −0.257771 | + | 0.446473i | ||||
\(565\) | −44064.8 | + | 25440.8i | −0.138037 | + | 0.0796956i | ||||
\(566\) | − | 171688.i | − | 0.535927i | ||||||
\(567\) | 8892.70 | − | 34596.4i | 0.0276610 | − | 0.107613i | ||||
\(568\) | 101697. | 0.315218 | ||||||||
\(569\) | 48829.7 | + | 84575.5i | 0.150820 | + | 0.261228i | 0.931529 | − | 0.363667i | \(-0.118475\pi\) |
−0.780709 | + | 0.624895i | \(0.785142\pi\) | |||||||
\(570\) | 11704.4 | + | 6757.54i | 0.0360246 | + | 0.0207988i | ||||
\(571\) | −23825.7 | + | 41267.3i | −0.0730757 | + | 0.126571i | −0.900248 | − | 0.435378i | \(-0.856615\pi\) |
0.827172 | + | 0.561949i | \(0.189948\pi\) | |||||||
\(572\) | −70734.6 | + | 40838.6i | −0.216192 | + | 0.124819i | ||||
\(573\) | − | 222234.i | − | 0.676863i | ||||||
\(574\) | −99244.9 | + | 101291.i | −0.301220 | + | 0.307432i | ||||
\(575\) | −52427.2 | −0.158570 | ||||||||
\(576\) | 6912.00 | + | 11971.9i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | −113845. | − | 65728.4i | −0.341949 | − | 0.197425i | 0.319184 | − | 0.947693i | \(-0.396591\pi\) |
−0.661134 | + | 0.750268i | \(0.729924\pi\) | |||||||
\(578\) | 101720. | − | 176184.i | 0.304475 | − | 0.527366i | ||||
\(579\) | −39476.6 | + | 22791.8i | −0.117756 | + | 0.0679864i | ||||
\(580\) | − | 119107.i | − | 0.354063i | ||||||
\(581\) | −16709.3 | − | 59907.9i | −0.0495002 | − | 0.177473i | ||||
\(582\) | −28666.8 | −0.0846316 | ||||||||
\(583\) | −107307. | − | 185861.i | −0.315712 | − | 0.546830i | ||||
\(584\) | −175754. | − | 101472.i | −0.515324 | − | 0.297523i | ||||
\(585\) | −33696.3 | + | 58363.8i | −0.0984625 | + | 0.170542i | ||||
\(586\) | 72400.6 | − | 41800.5i | 0.210837 | − | 0.121727i | ||||
\(587\) | − | 135493.i | − | 0.393224i | −0.980481 | − | 0.196612i | \(-0.937006\pi\) | ||
0.980481 | − | 0.196612i | \(-0.0629940\pi\) | |||||||
\(588\) | 48129.5 | − | 87436.4i | 0.139205 | − | 0.252894i | ||||
\(589\) | −58325.0 | −0.168122 | ||||||||
\(590\) | −99411.7 | − | 172186.i | −0.285584 | − | 0.494645i | ||||
\(591\) | 147712. | + | 85281.8i | 0.422904 | + | 0.244164i | ||||
\(592\) | 17991.5 | − | 31162.3i | 0.0513363 | − | 0.0889171i | ||||
\(593\) | 162993. | − | 94104.0i | 0.463510 | − | 0.267608i | −0.250009 | − | 0.968244i | \(-0.580433\pi\) |
0.713519 | + | 0.700636i | \(0.247100\pi\) | |||||||
\(594\) | 38876.4i | 0.110183i | ||||||||
\(595\) | 121725. | − | 33951.1i | 0.343831 | − | 0.0959003i | ||||
\(596\) | 203191. | 0.572022 | ||||||||
\(597\) | 68756.0 | + | 119089.i | 0.192913 | + | 0.334136i | ||||
\(598\) | 260753. | + | 150546.i | 0.729166 | + | 0.420984i | ||||
\(599\) | 39202.4 | − | 67900.5i | 0.109259 | − | 0.189243i | −0.806211 | − | 0.591628i | \(-0.798485\pi\) |
0.915470 | + | 0.402385i | \(0.131819\pi\) | |||||||
\(600\) | −5225.96 | + | 3017.21i | −0.0145166 | + | 0.00838114i | ||||
\(601\) | − | 254898.i | − | 0.705695i | −0.935681 | − | 0.352848i | \(-0.885213\pi\) | ||
0.935681 | − | 0.352848i | \(-0.114787\pi\) | |||||||
\(602\) | 334841. | + | 328076.i | 0.923945 | + | 0.905277i | ||||
\(603\) | 159985. | 0.439993 | ||||||||
\(604\) | 73235.1 | + | 126847.i | 0.200745 | + | 0.347701i | ||||
\(605\) | −104600. | − | 60391.0i | −0.285774 | − | 0.164992i | ||||
\(606\) | 83230.5 | − | 144160.i | 0.226640 | − | 0.392553i | ||||
\(607\) | 489896. | − | 282842.i | 1.32962 | − | 0.767655i | 0.344378 | − | 0.938831i | \(-0.388090\pi\) |
0.985241 | + | 0.171176i | \(0.0547566\pi\) | |||||||
\(608\) | − | 6949.97i | − | 0.0188008i | ||||||
\(609\) | 153284. | + | 39400.4i | 0.413298 | + | 0.106235i | ||||
\(610\) | −45074.0 | −0.121134 | ||||||||
\(611\) | 205559. | + | 356038.i | 0.550622 | + | 0.953705i | ||||
\(612\) | −20142.0 | − | 11629.0i | −0.0537773 | − | 0.0310483i | ||||
\(613\) | 207111. | − | 358726.i | 0.551164 | − | 0.954645i | −0.447026 | − | 0.894521i | \(-0.647517\pi\) |
0.998191 | − | 0.0601241i | \(-0.0191496\pi\) | |||||||
\(614\) | 263485. | − | 152123.i | 0.698905 | − | 0.403513i | ||||
\(615\) | − | 127343.i | − | 0.336686i | ||||||
\(616\) | −27041.9 | + | 105204.i | −0.0712648 | + | 0.277251i | ||||
\(617\) | 22896.0 | 0.0601435 | 0.0300717 | − | 0.999548i | \(-0.490426\pi\) | ||||
0.0300717 | + | 0.999548i | \(0.490426\pi\) | |||||||
\(618\) | 119992. | + | 207832.i | 0.314178 | + | 0.544172i | ||||
\(619\) | 139564. | + | 80577.4i | 0.364244 | + | 0.210296i | 0.670941 | − | 0.741511i | \(-0.265890\pi\) |
−0.306697 | + | 0.951807i | \(0.599224\pi\) | |||||||
\(620\) | −145543. | + | 252087.i | −0.378623 | + | 0.655793i | ||||
\(621\) | 124112. | − | 71656.1i | 0.321833 | − | 0.185811i | ||||
\(622\) | 122674.i | 0.317082i | ||||||||
\(623\) | 123604. | − | 126152.i | 0.318460 | − | 0.325027i | ||||
\(624\) | 34655.9 | 0.0890037 | ||||||||
\(625\) | 177957. | + | 308230.i | 0.455569 | + | 0.789069i | ||||
\(626\) | −263924. | − | 152376.i | −0.673488 | − | 0.388838i | ||||
\(627\) | 9772.50 | − | 16926.5i | 0.0248583 | − | 0.0430558i | ||||
\(628\) | 244181. | − | 140978.i | 0.619144 | − | 0.357463i | ||||
\(629\) | 60539.0i | 0.153015i | ||||||||
\(630\) | 24079.4 | + | 86331.7i | 0.0606686 | + | 0.217515i | ||||
\(631\) | 489038. | 1.22824 | 0.614121 | − | 0.789212i | \(-0.289511\pi\) | ||||
0.614121 | + | 0.789212i | \(0.289511\pi\) | |||||||
\(632\) | −118192. | − | 204715.i | −0.295907 | − | 0.512526i | ||||
\(633\) | −301754. | − | 174217.i | −0.753087 | − | 0.434795i | ||||
\(634\) | −220609. | + | 382105.i | −0.548838 | + | 0.950615i | ||||
\(635\) | −176272. | + | 101771.i | −0.437156 | + | 0.252392i | ||||
\(636\) | 91061.5i | 0.225123i | ||||||||
\(637\) | −129502. | − | 214091.i | −0.319152 | − | 0.527619i | ||||
\(638\) | −172248. | −0.423168 | ||||||||
\(639\) | −60674.5 | − | 105091.i | −0.148595 | − | 0.257374i | ||||
\(640\) | −30038.6 | − | 17342.8i | −0.0733363 | − | 0.0423407i | ||||
\(641\) | −59669.8 | + | 103351.i | −0.145224 | + | 0.251536i | −0.929457 | − | 0.368932i | \(-0.879724\pi\) |
0.784232 | + | 0.620467i | \(0.213057\pi\) | |||||||
\(642\) | −55957.8 | + | 32307.3i | −0.135766 | + | 0.0783845i | ||||
\(643\) | − | 324224.i | − | 0.784194i | −0.919924 | − | 0.392097i | \(-0.871750\pi\) | ||
0.919924 | − | 0.392097i | \(-0.128250\pi\) | |||||||
\(644\) | 385706. | − | 107580.i | 0.930003 | − | 0.259394i | ||||
\(645\) | −420960. | −1.01186 | ||||||||
\(646\) | 5846.43 | + | 10126.3i | 0.0140096 | + | 0.0242653i | ||||
\(647\) | −399048. | − | 230391.i | −0.953272 | − | 0.550372i | −0.0591759 | − | 0.998248i | \(-0.518847\pi\) |
−0.894096 | + | 0.447876i | \(0.852181\pi\) | |||||||
\(648\) | 8247.69 | − | 14285.4i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | −249009. | + | 143765.i | −0.591188 | + | 0.341323i | ||||
\(650\) | 15127.9i | 0.0358057i | ||||||||
\(651\) | −276278. | − | 270696.i | −0.651905 | − | 0.638734i | ||||
\(652\) | 1167.51 | 0.00274641 | ||||||||
\(653\) | 279562. | + | 484216.i | 0.655620 | + | 1.13557i | 0.981738 | + | 0.190238i | \(0.0609260\pi\) |
−0.326118 | + | 0.945329i | \(0.605741\pi\) | |||||||
\(654\) | −187072. | − | 108006.i | −0.437375 | − | 0.252518i | ||||
\(655\) | −173317. | + | 300193.i | −0.403978 | + | 0.699711i | ||||
\(656\) | −56711.4 | + | 32742.3i | −0.131784 | + | 0.0760855i | ||||
\(657\) | 242161.i | 0.561014i | ||||||||
\(658\) | 529540. | + | 136114.i | 1.22306 | + | 0.314376i | ||||
\(659\) | −184372. | −0.424546 | −0.212273 | − | 0.977210i | \(-0.568087\pi\) | ||||
−0.212273 | + | 0.977210i | \(0.568087\pi\) | |||||||
\(660\) | −48772.0 | − | 84475.6i | −0.111965 | − | 0.193929i | ||||
\(661\) | 68612.1 | + | 39613.2i | 0.157035 | + | 0.0906645i | 0.576458 | − | 0.817126i | \(-0.304434\pi\) |
−0.419423 | + | 0.907791i | \(0.637768\pi\) | |||||||
\(662\) | 56877.9 | − | 98515.3i | 0.129786 | − | 0.224796i | ||||
\(663\) | −50494.6 | + | 29153.1i | −0.114873 | + | 0.0663220i | ||||
\(664\) | − | 28720.4i | − | 0.0651411i | ||||||
\(665\) | 11217.5 | − | 43641.0i | 0.0253661 | − | 0.0986851i | ||||
\(666\) | −42936.5 | −0.0968007 | ||||||||
\(667\) | 317483. | + | 549897.i | 0.713624 | + | 1.23603i | ||||
\(668\) | −216950. | − | 125256.i | −0.486191 | − | 0.280703i | ||||
\(669\) | 146168. | − | 253170.i | 0.326588 | − | 0.565666i | ||||
\(670\) | −347637. | + | 200708.i | −0.774419 | + | 0.447111i | ||||
\(671\) | 65184.4i | 0.144777i | ||||||||
\(672\) | 32256.0 | − | 32921.1i | 0.0714286 | − | 0.0729015i | ||||
\(673\) | −482896. | −1.06616 | −0.533082 | − | 0.846064i | \(-0.678966\pi\) | ||||
−0.533082 | + | 0.846064i | \(0.678966\pi\) | |||||||
\(674\) | 127953. | + | 221621.i | 0.281663 | + | 0.487855i | ||||
\(675\) | 6235.84 | + | 3600.27i | 0.0136863 | + | 0.00790182i | ||||
\(676\) | −70803.9 | + | 122636.i | −0.154940 | + | 0.268364i | ||||
\(677\) | −329375. | + | 190165.i | −0.718642 | + | 0.414908i | −0.814253 | − | 0.580511i | \(-0.802853\pi\) |
0.0956105 | + | 0.995419i | \(0.469520\pi\) | |||||||
\(678\) | − | 31221.6i | − | 0.0679196i | ||||||
\(679\) | 25677.6 | + | 92061.9i | 0.0556949 | + | 0.199683i | ||||
\(680\) | 58356.0 | 0.126202 | ||||||||
\(681\) | −158868. | − | 275167.i | −0.342563 | − | 0.593337i | ||||
\(682\) | 364559. | + | 210478.i | 0.783789 | + | 0.452521i | ||||
\(683\) | 171034. | − | 296240.i | 0.366642 | − | 0.635042i | −0.622396 | − | 0.782702i | \(-0.713841\pi\) |
0.989038 | + | 0.147660i | \(0.0471742\pi\) | |||||||
\(684\) | −7181.95 | + | 4146.50i | −0.0153508 | + | 0.00886278i | ||||
\(685\) | − | 307901.i | − | 0.656191i | ||||||
\(686\) | −323909. | − | 76246.1i | −0.688295 | − | 0.162020i | ||||
\(687\) | −175649. | −0.372163 | ||||||||
\(688\) | 108237. | + | 187472.i | 0.228665 | + | 0.396059i | ||||
\(689\) | 197701. | + | 114143.i | 0.416458 | + | 0.240442i | ||||
\(690\) | −179791. | + | 311407.i | −0.377633 | + | 0.654080i | ||||
\(691\) | 63274.0 | − | 36531.3i | 0.132516 | − | 0.0765084i | −0.432276 | − | 0.901741i | \(-0.642289\pi\) |
0.564793 | + | 0.825233i | \(0.308956\pi\) | |||||||
\(692\) | − | 320927.i | − | 0.670183i | ||||||
\(693\) | 124850. | − | 34822.7i | 0.259969 | − | 0.0725097i | ||||
\(694\) | −90720.3 | −0.188359 | ||||||||
\(695\) | −59992.1 | − | 103909.i | −0.124201 | − | 0.215122i | ||||
\(696\) | 63293.7 | + | 36542.6i | 0.130660 | + | 0.0754365i | ||||
\(697\) | 55086.7 | − | 95413.0i | 0.113392 | − | 0.196400i | ||||
\(698\) | 286060. | − | 165157.i | 0.587145 | − | 0.338989i | ||||
\(699\) | 45140.3i | 0.0923869i | ||||||||
\(700\) | 14370.7 | + | 14080.3i | 0.0293279 | + | 0.0287353i | ||||
\(701\) | −288287. | −0.586664 | −0.293332 | − | 0.956011i | \(-0.594764\pi\) | ||||
−0.293332 | + | 0.956011i | \(0.594764\pi\) | |||||||
\(702\) | −20676.5 | − | 35812.7i | −0.0419568 | − | 0.0726712i | ||||
\(703\) | 18694.2 | + | 10793.1i | 0.0378265 | + | 0.0218392i | ||||
\(704\) | −25080.5 | + | 43440.6i | −0.0506046 | + | 0.0876498i | ||||
\(705\) | −425203. | + | 245491.i | −0.855496 | + | 0.493921i | ||||
\(706\) | 352586.i | 0.707386i | ||||||||
\(707\) | −537513. | − | 138163.i | −1.07535 | − | 0.276409i | ||||
\(708\) | 122000. | 0.243385 | ||||||||
\(709\) | 155256. | + | 268911.i | 0.308856 | + | 0.534954i | 0.978112 | − | 0.208078i | \(-0.0667206\pi\) |
−0.669257 | + | 0.743031i | \(0.733387\pi\) | |||||||
\(710\) | 263683. | + | 152237.i | 0.523076 | + | 0.301998i | ||||
\(711\) | −141032. | + | 244275.i | −0.278984 | + | 0.483214i | ||||
\(712\) | 70630.7 | − | 40778.6i | 0.139326 | − | 0.0804401i | ||||
\(713\) | − | 1.55179e6i | − | 3.05250i | ||||||
\(714\) | −19304.1 | + | 75101.3i | −0.0378664 | + | 0.147316i | ||||
\(715\) | −244537. | −0.478335 | ||||||||
\(716\) | 200618. | + | 347480.i | 0.391330 | + | 0.677804i | ||||
\(717\) | 70717.6 | + | 40828.8i | 0.137559 | + | 0.0794198i | ||||
\(718\) | 140632. | − | 243582.i | 0.272795 | − | 0.472495i | ||||
\(719\) | 8733.60 | − | 5042.35i | 0.0168941 | − | 0.00975383i | −0.491529 | − | 0.870861i | \(-0.663562\pi\) |
0.508423 | + | 0.861107i | \(0.330229\pi\) | |||||||
\(720\) | 41388.3i | 0.0798385i | ||||||||
\(721\) | 559963. | − | 571510.i | 1.07718 | − | 1.09939i | ||||
\(722\) | −364434. | −0.699109 | ||||||||
\(723\) | 14234.4 | + | 24654.7i | 0.0272309 | + | 0.0471654i | ||||
\(724\) | −443227. | − | 255897.i | −0.845568 | − | 0.488189i | ||||
\(725\) | −15951.5 | + | 27628.8i | −0.0303477 | + | 0.0525638i | ||||
\(726\) | 64184.0 | − | 37056.6i | 0.121774 | − | 0.0703060i | ||||
\(727\) | − | 638552.i | − | 1.20817i | −0.796921 | − | 0.604084i | \(-0.793539\pi\) | ||
0.796921 | − | 0.604084i | \(-0.206461\pi\) | |||||||
\(728\) | −31042.3 | − | 111296.i | −0.0585721 | − | 0.209998i | ||||
\(729\) | −19683.0 | −0.0370370 | ||||||||
\(730\) | −303801. | − | 526199.i | −0.570090 | − | 0.987425i | ||||
\(731\) | −315409. | − | 182101.i | −0.590254 | − | 0.340783i | ||||
\(732\) | 13829.0 | − | 23952.5i | 0.0258088 | − | 0.0447021i | ||||
\(733\) | −715410. | + | 413042.i | −1.33152 | + | 0.768752i | −0.985532 | − | 0.169488i | \(-0.945789\pi\) |
−0.345985 | + | 0.938240i | \(0.612455\pi\) | |||||||
\(734\) | 251488.i | 0.466795i | ||||||||
\(735\) | 255681. | − | 154659.i | 0.473287 | − | 0.286287i | ||||
\(736\) | 184911. | 0.341356 | ||||||||
\(737\) | 290257. | + | 502739.i | 0.534376 | + | 0.925567i | ||||
\(738\) | 67670.4 | + | 39069.5i | 0.124247 | + | 0.0717341i | ||||
\(739\) | −384995. | + | 666831.i | −0.704962 | + | 1.22103i | 0.261743 | + | 0.965138i | \(0.415703\pi\) |
−0.966705 | + | 0.255893i | \(0.917630\pi\) | |||||||
\(740\) | 93298.0 | − | 53865.6i | 0.170376 | − | 0.0983667i | ||||
\(741\) | 20790.1i | 0.0378634i | ||||||||
\(742\) | 292440. | − | 81566.4i | 0.531164 | − | 0.148151i | ||||
\(743\) | −611777. | −1.10819 | −0.554097 | − | 0.832452i | \(-0.686936\pi\) | ||||
−0.554097 | + | 0.832452i | \(0.686936\pi\) | |||||||
\(744\) | −89306.6 | − | 154683.i | −0.161338 | − | 0.279446i | ||||
\(745\) | 526841. | + | 304172.i | 0.949220 | + | 0.548032i | ||||
\(746\) | −129193. | + | 223768.i | −0.232145 | + | 0.402087i | ||||
\(747\) | −29679.1 | + | 17135.2i | −0.0531875 | + | 0.0307078i | ||||
\(748\) | − | 84392.3i | − | 0.150834i | ||||||
\(749\) | 153876. | + | 150767.i | 0.274289 | + | 0.268747i | ||||
\(750\) | −238076. | −0.423246 | ||||||||
\(751\) | −185311. | − | 320968.i | −0.328565 | − | 0.569091i | 0.653663 | − | 0.756786i | \(-0.273232\pi\) |
−0.982227 | + | 0.187695i | \(0.939898\pi\) | |||||||
\(752\) | 218656. | + | 126241.i | 0.386657 | + | 0.223236i | ||||
\(753\) | −63265.5 | + | 109579.i | −0.111578 | + | 0.193258i | ||||
\(754\) | 158673. | − | 91610.2i | 0.279101 | − | 0.161139i | ||||
\(755\) | 438523.i | 0.769305i | ||||||||
\(756\) | −53264.6 | − | 13691.2i | −0.0931956 | − | 0.0239551i | ||||
\(757\) | 298778. | 0.521384 | 0.260692 | − | 0.965422i | \(-0.416049\pi\) | ||||
0.260692 | + | 0.965422i | \(0.416049\pi\) | |||||||
\(758\) | 8949.87 | + | 15501.6i | 0.0155768 | + | 0.0269798i | ||||
\(759\) | 450346. | + | 260007.i | 0.781740 | + | 0.451338i | ||||
\(760\) | 10403.9 | − | 18020.1i | 0.0180123 | − | 0.0311982i | ||||
\(761\) | 695541. | − | 401571.i | 1.20103 | − | 0.693414i | 0.240245 | − | 0.970712i | \(-0.422772\pi\) |
0.960784 | + | 0.277298i | \(0.0894389\pi\) | |||||||
\(762\) | − | 124896.i | − | 0.215098i | ||||||
\(763\) | −179291. | + | 697517.i | −0.307970 | + | 1.19813i | ||||
\(764\) | −342151. | −0.586180 | ||||||||
\(765\) | −34816.4 | − | 60303.8i | −0.0594924 | − | 0.103044i | ||||
\(766\) | −32911.2 | − | 19001.3i | −0.0560902 | − | 0.0323837i | ||||
\(767\) | 152924. | − | 264871.i | 0.259946 | − | 0.450240i | ||||
\(768\) | 18432.0 | − | 10641.7i | 0.0312500 | − | 0.0180422i | ||||
\(769\) | 452541.i | 0.765253i | 0.923903 | + | 0.382626i | \(0.124980\pi\) | ||||
−0.923903 | + | 0.382626i | \(0.875020\pi\) | |||||||
\(770\) | −227603. | + | 232296.i | −0.383881 | + | 0.391797i | ||||
\(771\) | −60310.4 | −0.101457 | ||||||||
\(772\) | 35090.3 | + | 60778.2i | 0.0588780 | + | 0.101980i | ||||
\(773\) | 908057. | + | 524267.i | 1.51969 | + | 0.877392i | 0.999731 | + | 0.0231996i | \(0.00738531\pi\) |
0.519957 | + | 0.854193i | \(0.325948\pi\) | |||||||
\(774\) | 129153. | − | 223700.i | 0.215587 | − | 0.373408i | ||||
\(775\) | 67522.1 | − | 38983.9i | 0.112420 | − | 0.0649056i | ||||
\(776\) | 44135.4i | 0.0732932i | ||||||||
\(777\) | 38459.5 | + | 137889.i | 0.0637032 | + | 0.228395i | ||||
\(778\) | −249740. | −0.412599 | ||||||||
\(779\) | −19642.1 | − | 34021.1i | −0.0323678 | − | 0.0560626i | ||||
\(780\) | 89856.9 | + | 51878.9i | 0.147694 | + | 0.0852711i | ||||
\(781\) | 220160. | − | 381328.i | 0.360941 | − | 0.625168i | ||||
\(782\) | −269421. | + | 155550.i | −0.440572 | + | 0.254365i | ||||
\(783\) | − | 87208.5i | − | 0.142244i | ||||||
\(784\) | −134617. | − | 74100.1i | −0.219012 | − | 0.120555i | ||||
\(785\) | 844159. | 1.36989 | ||||||||
\(786\) | −106349. | − | 184202.i | −0.172143 | − | 0.298160i | ||||
\(787\) | 169712. | + | 97983.5i | 0.274009 | + | 0.158199i | 0.630708 | − | 0.776020i | \(-0.282765\pi\) |
−0.356699 | + | 0.934219i | \(0.616098\pi\) | |||||||
\(788\) | 131300. | − | 227418.i | 0.211452 | − | 0.366246i | ||||
\(789\) | 543004. | − | 313504.i | 0.872266 | − | 0.503603i | ||||
\(790\) | − | 707722.i | − | 1.13399i | ||||||
\(791\) | −100266. | + | 27966.0i | −0.160252 | + | 0.0446970i | ||||
\(792\) | 59854.2 | 0.0954210 | ||||||||
\(793\) | −34668.4 | − | 60047.4i | −0.0551299 | − | 0.0954877i | ||||
\(794\) | 530528. | + | 306301.i | 0.841526 | + | 0.485855i | ||||
\(795\) | −136317. | + | 236107.i | −0.215682 | + | 0.373572i | ||||
\(796\) | 183349. | − | 105857.i | 0.289370 | − | 0.167068i | ||||
\(797\) | 66453.8i | 0.104617i | 0.998631 | + | 0.0523086i | \(0.0166579\pi\) | ||||
−0.998631 | + | 0.0523086i | \(0.983342\pi\) | |||||||
\(798\) | 19749.4 | + | 19350.3i | 0.0310133 | + | 0.0303867i | ||||
\(799\) | −424784. | −0.665387 | ||||||||
\(800\) | 4645.30 | + | 8045.90i | 0.00725828 | + | 0.0125717i | ||||
\(801\) | −84279.5 | − | 48658.8i | −0.131358 | − | 0.0758397i | ||||
\(802\) | −7307.01 | + | 12656.1i | −0.0113603 | + | 0.0196767i | ||||
\(803\) | −760969. | + | 439346.i | −1.18015 | + | 0.681358i | ||||
\(804\) | − | 246314.i | − | 0.381045i | ||||||
\(805\) | 1.16111e6 | + | 298454.i | 1.79177 | + | 0.460559i | ||||
\(806\) | −447772. | −0.689266 | ||||||||
\(807\) | 70788.8 | + | 122610.i | 0.108697 | + | 0.188269i | ||||
\(808\) | −221948. | − | 128142.i | −0.339961 | − | 0.196276i | ||||
\(809\) | −41152.3 | + | 71277.9i | −0.0628777 | + | 0.108907i | −0.895751 | − | 0.444557i | \(-0.853361\pi\) |
0.832873 | + | 0.553464i | \(0.186694\pi\) | |||||||
\(810\) | 42769.7 | − | 24693.1i | 0.0651878 | − | 0.0376362i | ||||
\(811\) | 469097.i | 0.713215i | 0.934254 | + | 0.356608i | \(0.116067\pi\) | ||||
−0.934254 | + | 0.356608i | \(0.883933\pi\) | |||||||
\(812\) | 60660.9 | − | 235997.i | 0.0920019 | − | 0.357927i | ||||
\(813\) | 504252. | 0.762898 | ||||||||
\(814\) | −77898.5 | − | 134924.i | −0.117566 | − | 0.203629i | ||||
\(815\) | 3027.15 | + | 1747.73i | 0.00455742 | + | 0.00263123i | ||||
\(816\) | −17904.0 | + | 31010.6i | −0.0268886 | + | 0.0465725i | ||||
\(817\) | −112464. | + | 64931.3i | −0.168489 | + | 0.0972769i | ||||
\(818\) | 110056.i | 0.164478i | ||||||||
\(819\) | −96490.1 | + | 98479.8i | −0.143852 | + | 0.146818i | ||||
\(820\) | −196057. | −0.291578 | ||||||||
\(821\) | 2689.76 | + | 4658.80i | 0.00399050 | + | 0.00691174i | 0.868014 | − | 0.496540i | \(-0.165396\pi\) |
−0.864023 | + | 0.503452i | \(0.832063\pi\) | |||||||
\(822\) | 163620. | + | 94465.8i | 0.242154 | + | 0.139808i | ||||
\(823\) | 484903. | − | 839877.i | 0.715905 | − | 1.23998i | −0.246704 | − | 0.969091i | \(-0.579348\pi\) |
0.962609 | − | 0.270893i | \(-0.0873190\pi\) | |||||||
\(824\) | 319979. | − | 184740.i | 0.471267 | − | 0.272086i | ||||
\(825\) | 26127.4i | 0.0383874i | ||||||||
\(826\) | −109279. | − | 391798.i | −0.160168 | − | 0.574251i | ||||
\(827\) | 838747. | 1.22637 | 0.613183 | − | 0.789941i | \(-0.289889\pi\) | ||||
0.613183 | + | 0.789941i | \(0.289889\pi\) | |||||||
\(828\) | −110322. | − | 191083.i | −0.160917 | − | 0.278716i | ||||
\(829\) | −765309. | − | 441852.i | −1.11360 | − | 0.642935i | −0.173838 | − | 0.984774i | \(-0.555617\pi\) |
−0.939759 | + | 0.341839i | \(0.888950\pi\) | |||||||
\(830\) | 42993.7 | − | 74467.2i | 0.0624091 | − | 0.108096i | ||||
\(831\) | 133888. | − | 77300.0i | 0.193882 | − | 0.111938i | ||||
\(832\) | − | 53356.3i | − | 0.0770795i | ||||||
\(833\) | 258475. | − | 5276.10i | 0.372502 | − | 0.00760367i | ||||
\(834\) | 73623.7 | 0.105849 | ||||||||
\(835\) | −375010. | − | 649536.i | −0.537861 | − | 0.931602i | ||||
\(836\) | −26060.0 | − | 15045.7i | −0.0372874 | − | 0.0215279i | ||||
\(837\) | −106564. | + | 184575.i | −0.152111 | + | 0.263464i | ||||
\(838\) | −645258. | + | 372540.i | −0.918852 | + | 0.530499i | ||||
\(839\) | − | 1.12626e6i | − | 1.59998i | −0.600011 | − | 0.799992i | \(-0.704837\pi\) | ||
0.600011 | − | 0.799992i | \(-0.295163\pi\) | |||||||
\(840\) | 132916. | − | 37072.6i | 0.188373 | − | 0.0525406i | ||||
\(841\) | −320891. | −0.453696 | ||||||||
\(842\) | −23157.9 | − | 40110.6i | −0.0326644 | − | 0.0565764i | ||||
\(843\) | 550238. | + | 317680.i | 0.774276 | + | 0.447028i | ||||
\(844\) | −268225. | + | 464580.i | −0.376543 | + | 0.652192i | ||||
\(845\) | −367165. | + | 211983.i | −0.514218 | + | 0.296884i | ||||
\(846\) | − | 301272.i | − | 0.420938i | ||||||
\(847\) | −176497. | − | 172931.i | −0.246020 | − | 0.241049i | ||||
\(848\) | 140198. | 0.194963 | ||||||||
\(849\) | 157705. | + | 273153.i | 0.218791 | + | 0.378958i | ||||
\(850\) | −13536.7 | − | 7815.40i | −0.0187359 | − | 0.0108172i | ||||
\(851\) | −287161. | + | 497378.i | −0.396522 | + | 0.686796i | ||||
\(852\) | −161799. | + | 93414.5i | −0.222893 | + | 0.128687i | ||||
\(853\) | 805486.i | 1.10703i | 0.832839 | + | 0.553516i | \(0.186714\pi\) | ||||
−0.832839 | + | 0.553516i | \(0.813286\pi\) | |||||||
\(854\) | −89309.2 | − | 22956.1i | −0.122456 | − | 0.0314762i | ||||
\(855\) | −24828.8 | −0.0339643 | ||||||||
\(856\) | 49740.3 | + | 86152.7i | 0.0678830 | + | 0.117577i | ||||
\(857\) | −849118. | − | 490238.i | −1.15613 | − | 0.667491i | −0.205756 | − | 0.978603i | \(-0.565965\pi\) |
−0.950373 | + | 0.311112i | \(0.899299\pi\) | |||||||
\(858\) | 75025.3 | − | 129948.i | 0.101914 | − | 0.176520i | ||||
\(859\) | −375665. | + | 216890.i | −0.509113 | + | 0.293936i | −0.732469 | − | 0.680800i | \(-0.761632\pi\) |
0.223356 | + | 0.974737i | \(0.428299\pi\) | |||||||
\(860\) | 648111.i | 0.876299i | ||||||||
\(861\) | 64855.6 | − | 252316.i | 0.0874865 | − | 0.340360i | ||||
\(862\) | 708284. | 0.953220 | ||||||||
\(863\) | 151578. | + | 262542.i | 0.203524 | + | 0.352514i | 0.949661 | − | 0.313278i | \(-0.101427\pi\) |
−0.746137 | + | 0.665792i | \(0.768094\pi\) | |||||||
\(864\) | −21993.8 | − | 12698.2i | −0.0294628 | − | 0.0170103i | ||||
\(865\) | 480418. | − | 832108.i | 0.642077 | − | 1.11211i | ||||
\(866\) | 224116. | − | 129394.i | 0.298839 | − | 0.172535i | ||||
\(867\) | 373744.i | 0.497205i | ||||||||
\(868\) | −416764. | + | 425358.i | −0.553160 | + | 0.564566i | ||||
\(869\) | −1.02348e6 | −1.35532 | ||||||||
\(870\) | 109407. | + | 189498.i | 0.144546 | + | 0.250360i | ||||
\(871\) | −534765. | − | 308747.i | −0.704898 | − | 0.406973i | ||||
\(872\) | −166286. | + | 288016.i | −0.218687 | + | 0.378777i | ||||
\(873\) | 45608.6 | − | 26332.1i | 0.0598436 | − | 0.0345507i | ||||
\(874\) | 110928.i | 0.145217i | ||||||||
\(875\) | 213251. | + | 764568.i | 0.278532 | + | 0.998619i | ||||
\(876\) | 372831. | 0.485852 | ||||||||
\(877\) | −177500. | − | 307439.i | −0.230781 | − | 0.399724i | 0.727257 | − | 0.686365i | \(-0.240795\pi\) |
−0.958038 | + | 0.286641i | \(0.907461\pi\) | |||||||
\(878\) | 21700.9 | + | 12529.0i | 0.0281507 | + | 0.0162528i | ||||
\(879\) | −76792.5 | + | 133008.i | −0.0993896 | + | 0.172148i | ||||
\(880\) | −130059. | + | 75089.5i | −0.167948 | + | 0.0969647i | ||||
\(881\) | − | 320002.i | − | 0.412288i | −0.978522 | − | 0.206144i | \(-0.933909\pi\) | ||
0.978522 | − | 0.206144i | \(-0.0660915\pi\) | |||||||
\(882\) | 3742.01 | + | 183320.i | 0.00481025 | + | 0.235653i | ||||
\(883\) | −1.08605e6 | −1.39293 | −0.696467 | − | 0.717589i | \(-0.745246\pi\) | ||||
−0.696467 | + | 0.717589i | \(0.745246\pi\) | |||||||
\(884\) | 44884.1 | + | 77741.6i | 0.0574365 | + | 0.0994830i | ||||
\(885\) | 316326. | + | 182631.i | 0.403876 | + | 0.233178i | ||||
\(886\) | 424560. | − | 735360.i | 0.540844 | − | 0.936769i | ||||
\(887\) | 1.11218e6 | − | 642117.i | 1.41360 | − | 0.816144i | 0.417878 | − | 0.908503i | \(-0.362774\pi\) |
0.995726 | + | 0.0923591i | \(0.0294408\pi\) | |||||||
\(888\) | 66105.1i | 0.0838319i | ||||||||
\(889\) | −401096. | + | 111872.i | −0.507510 | + | 0.141553i | ||||
\(890\) | 244178. | 0.308266 | ||||||||
\(891\) | −35710.3 | − | 61852.0i | −0.0449819 | − | 0.0779109i | ||||
\(892\) | −389781. | − | 225040.i | −0.489882 | − | 0.282833i | ||||
\(893\) | −75731.9 | + | 131171.i | −0.0949677 | + | 0.164489i | ||||
\(894\) | −323275. | + | 186643.i | −0.404481 | + | 0.233527i | ||||
\(895\) | 1.20128e6i | 1.49967i | ||||||||
\(896\) | −50685.4 | − | 49661.4i | −0.0631345 | − | 0.0618590i | ||||
\(897\) | −553140. | −0.687465 | ||||||||
\(898\) | 165274. | + | 286263.i | 0.204952 | + | 0.354987i | ||||
\(899\) | −817787. | − | 472150.i | −1.01186 | − | 0.584198i | ||||
\(900\) | 5542.97 | − | 9600.71i | 0.00684317 | − | 0.0118527i | ||||
\(901\) | −204273. | + | 117937.i | −0.251629 | + | 0.145278i | ||||
\(902\) | 283531.i | 0.348487i | ||||||||
\(903\) | −834086. | − | 214394.i | −1.02291 | − | 0.262929i | ||||
\(904\) | −48068.7 | −0.0588201 | ||||||||
\(905\) | −766141. | − | 1.32699e6i | −0.935430 | − | 1.62021i | ||||
\(906\) | −233033. | − | 134541.i | −0.283897 | − | 0.163908i | ||||
\(907\) | −24217.8 | + | 41946.4i | −0.0294388 | + | 0.0509894i | −0.880369 | − | 0.474289i | \(-0.842705\pi\) |
0.850931 | + | 0.525278i | \(0.176039\pi\) | |||||||
\(908\) | −423647. | + | 244593.i | −0.513845 | + | 0.296669i | ||||
\(909\) | 305808.i | 0.370102i | ||||||||
\(910\) | 86119.2 | − | 335040.i | 0.103996 | − | 0.404589i | ||||
\(911\) | 727675. | 0.876801 | 0.438400 | − | 0.898780i | \(-0.355545\pi\) | ||||
0.438400 | + | 0.898780i | \(0.355545\pi\) | |||||||
\(912\) | 6383.96 | + | 11057.3i | 0.00767539 | + | 0.0132942i | ||||
\(913\) | −107692. | − | 62175.8i | −0.129194 | − | 0.0745899i | ||||
\(914\) | 104292. | − | 180639.i | 0.124842 | − | 0.216232i | ||||
\(915\) | 71712.3 | − | 41403.1i | 0.0856548 | − | 0.0494528i | ||||
\(916\) | 270430.i | 0.322303i | ||||||||
\(917\) | −496296. | + | 506530.i | −0.590204 | + | 0.602375i | ||||
\(918\) | 42727.5 | 0.0507017 | ||||||||
\(919\) | −43858.0 | − | 75964.2i | −0.0519299 | − | 0.0899452i | 0.838892 | − | 0.544298i | \(-0.183204\pi\) |
−0.890822 | + | 0.454353i | \(0.849871\pi\) | |||||||
\(920\) | 479443. | + | 276806.i | 0.566449 | + | 0.327040i | ||||
\(921\) | −279468. | + | 484052.i | −0.329467 | + | 0.570654i | ||||
\(922\) | 216092. | − | 124761.i | 0.254201 | − | 0.146763i | ||||
\(923\) | 468369.i | 0.549775i | ||||||||
\(924\) | −53613.1 | − | 192219.i | −0.0627952 | − | 0.225139i | ||||
\(925\) | −28856.1 | −0.0337251 | ||||||||
\(926\) | 421266. | + | 729655.i | 0.491286 | + | 0.850933i | ||||
\(927\) | −381813. | − | 220440.i | −0.444315 | − | 0.256525i | ||||
\(928\) | 56261.1 | − | 97447.1i | 0.0653299 | − | 0.113155i | ||||
\(929\) | 781079. | − | 450956.i | 0.905032 | − | 0.522520i | 0.0262024 | − | 0.999657i | \(-0.491659\pi\) |
0.878829 | + | 0.477136i | \(0.158325\pi\) | |||||||
\(930\) | − | 534757.i | − | 0.618288i | ||||||
\(931\) | 44452.6 | − | 80756.7i | 0.0512859 | − | 0.0931707i | ||||
\(932\) | 69498.1 | 0.0800094 | ||||||||
\(933\) | −112683. | − | 195173.i | −0.129448 | − | 0.224211i | ||||
\(934\) | −459205. | − | 265122.i | −0.526396 | − | 0.303915i | ||||
\(935\) | 126333. | − | 218815.i | 0.144508 | − | 0.250296i | ||||
\(936\) | −55137.2 | + | 31833.5i | −0.0629351 | + | 0.0363356i | ||||
\(937\) | 1.24186e6i | 1.41447i | 0.706978 | + | 0.707236i | \(0.250058\pi\) | ||||
−0.706978 | + | 0.707236i | \(0.749942\pi\) | |||||||
\(938\) | −791024. | + | 220630.i | −0.899050 | + | 0.250760i | ||||
\(939\) | 559867. | 0.634970 | ||||||||
\(940\) | 377958. | + | 654643.i | 0.427748 | + | 0.740882i | ||||
\(941\) | 369139. | + | 213122.i | 0.416879 | + | 0.240685i | 0.693741 | − | 0.720224i | \(-0.255961\pi\) |
−0.276862 | + | 0.960910i | \(0.589294\pi\) | |||||||
\(942\) | −258993. | + | 448588.i | −0.291867 | + | 0.505529i | ||||
\(943\) | 905165. | − | 522598.i | 1.01790 | − | 0.587684i | ||||
\(944\) | − | 187832.i | − | 0.210778i | ||||||
\(945\) | −117611. | − | 115235.i | −0.131699 | − | 0.129038i | ||||
\(946\) | 937274. | 1.04733 | ||||||||
\(947\) | −13665.2 | − | 23668.9i | −0.0152376 | − | 0.0263923i | 0.858306 | − | 0.513138i | \(-0.171517\pi\) |
−0.873544 | + | 0.486746i | \(0.838184\pi\) | |||||||
\(948\) | 376086. | + | 217133.i | 0.418476 | + | 0.241607i | ||||
\(949\) | 467333. | − | 809444.i | 0.518912 | − | 0.898782i | ||||
\(950\) | −4826.73 | + | 2786.71i | −0.00534817 | + | 0.00308777i | ||||
\(951\) | − | 810568.i | − | 0.896248i | ||||||
\(952\) | 115626. | + | 29720.6i | 0.127580 | + | 0.0327932i | ||||
\(953\) | 1.30093e6 | 1.43242 | 0.716208 | − | 0.697887i | \(-0.245876\pi\) | ||||
0.716208 | + | 0.697887i | \(0.245876\pi\) | |||||||
\(954\) | −83645.4 | − | 144878.i | −0.0919063 | − | 0.159186i | ||||
\(955\) | −887140. | − | 512190.i | −0.972714 | − | 0.561597i | ||||
\(956\) | 62860.1 | − | 108877.i | 0.0687796 | − | 0.119130i | ||||
\(957\) | 274045. | − | 158220.i | 0.299225 | − | 0.172757i | ||||
\(958\) | − | 340794.i | − | 0.371331i | ||||||
\(959\) | 156814. | − | 610072.i | 0.170509 | − | 0.663352i | ||||
\(960\) | 63721.4 | 0.0691421 | ||||||||
\(961\) | 692125. | + | 1.19880e6i | 0.749442 | + | 1.29807i | ||||
\(962\) | 143519. | + | 82860.7i | 0.155081 | + | 0.0895362i | ||||
\(963\) | 59352.3 | − | 102801.i | 0.0640007 | − | 0.110852i | ||||
\(964\) | 37958.4 | − | 21915.3i | 0.0408464 | − | 0.0235827i | ||||
\(965\) | 210117.i | 0.225635i | ||||||||
\(966\) | −514835. | + | 525452.i | −0.551714 | + | 0.563091i | ||||
\(967\) | 463079. | 0.495225 | 0.247612 | − | 0.968859i | \(-0.420354\pi\) | ||||
0.247612 | + | 0.968859i | \(0.420354\pi\) | |||||||
\(968\) | −57052.4 | − | 98817.7i | −0.0608868 | − | 0.105459i | ||||
\(969\) | −18603.2 | − | 10740.6i | −0.0198125 | − | 0.0114388i | ||||
\(970\) | −66069.4 | + | 114436.i | −0.0702194 | + | 0.121623i | ||||
\(971\) | 54723.1 | − | 31594.4i | 0.0580406 | − | 0.0335098i | −0.470699 | − | 0.882294i | \(-0.655998\pi\) |
0.528739 | + | 0.848784i | \(0.322665\pi\) | |||||||
\(972\) | 30304.0i | 0.0320750i | ||||||||
\(973\) | −65946.8 | − | 236439.i | −0.0696575 | − | 0.249743i | ||||
\(974\) | 756305. | 0.797221 | ||||||||
\(975\) | −13895.9 | − | 24068.4i | −0.0146176 | − | 0.0253185i | ||||
\(976\) | −36877.2 | − | 21291.1i | −0.0387132 | − | 0.0223511i | ||||
\(977\) | −719497. | + | 1.24621e6i | −0.753772 | + | 1.30557i | 0.192210 | + | 0.981354i | \(0.438434\pi\) |
−0.945982 | + | 0.324218i | \(0.894899\pi\) | |||||||
\(978\) | −1857.49 | + | 1072.42i | −0.00194200 | + | 0.00112122i | ||||
\(979\) | − | 353121.i | − | 0.368432i | ||||||
\(980\) | −238114. | − | 393647.i | −0.247932 | − | 0.409878i | ||||
\(981\) | 396840. | 0.412361 | ||||||||
\(982\) | 252245. | + | 436901.i | 0.261577 | + | 0.453064i | ||||
\(983\) | 346926. | + | 200298.i | 0.359030 | + | 0.207286i | 0.668655 | − | 0.743573i | \(-0.266870\pi\) |
−0.309625 | + | 0.950859i | \(0.600204\pi\) | |||||||
\(984\) | 60151.5 | − | 104185.i | 0.0621235 | − | 0.107601i | ||||
\(985\) | 680877. | − | 393104.i | 0.701772 | − | 0.405168i | ||||
\(986\) | 189311.i | 0.194725i | ||||||||
\(987\) | −967521. | + | 269858.i | −0.993176 | + | 0.277014i | ||||
\(988\) | 32008.4 | 0.0327906 | ||||||||
\(989\) | −1.72756e6 | − | 2.99223e6i | −1.76620 | − | 3.05916i | ||||
\(990\) | 155192. | + | 89600.0i | 0.158343 | + | 0.0914192i | ||||
\(991\) | −99274.5 | + | 171949.i | −0.101086 | + | 0.175086i | −0.912132 | − | 0.409896i | \(-0.865565\pi\) |
0.811046 | + | 0.584982i | \(0.198898\pi\) | |||||||
\(992\) | −238151. | + | 137496.i | −0.242007 | + | 0.139723i | ||||
\(993\) | 208983.i | 0.211939i | ||||||||
\(994\) | 444924. | + | 435934.i | 0.450311 | + | 0.441213i | ||||
\(995\) | 633858. | 0.640245 | ||||||||
\(996\) | 26381.4 | + | 45693.9i | 0.0265937 | + | 0.0460617i | ||||
\(997\) | 792228. | + | 457393.i | 0.797003 | + | 0.460150i | 0.842422 | − | 0.538818i | \(-0.181129\pi\) |
−0.0454194 | + | 0.998968i | \(0.514462\pi\) | |||||||
\(998\) | 372994. | − | 646045.i | 0.374491 | − | 0.648637i | ||||
\(999\) | 68311.6 | − | 39439.7i | 0.0684484 | − | 0.0395187i |
(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 | 42.5.g.a.31.2 | yes | 4 | |
3.2 | odd | 2 | 126.5.n.b.73.1 | 4 | |||
4.3 | odd | 2 | 336.5.bh.d.241.1 | 4 | |||
7.2 | even | 3 | 294.5.g.c.19.2 | 4 | |||
7.3 | odd | 6 | 294.5.c.a.97.1 | 4 | |||
7.4 | even | 3 | 294.5.c.a.97.2 | 4 | |||
7.5 | odd | 6 | inner | 42.5.g.a.19.2 | ✓ | 4 | |
7.6 | odd | 2 | 294.5.g.c.31.2 | 4 | |||
21.5 | even | 6 | 126.5.n.b.19.1 | 4 | |||
21.11 | odd | 6 | 882.5.c.a.685.4 | 4 | |||
21.17 | even | 6 | 882.5.c.a.685.3 | 4 | |||
28.19 | even | 6 | 336.5.bh.d.145.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.5.g.a.19.2 | ✓ | 4 | 7.5 | odd | 6 | inner | |
42.5.g.a.31.2 | yes | 4 | 1.1 | even | 1 | trivial | |
126.5.n.b.19.1 | 4 | 21.5 | even | 6 | |||
126.5.n.b.73.1 | 4 | 3.2 | odd | 2 | |||
294.5.c.a.97.1 | 4 | 7.3 | odd | 6 | |||
294.5.c.a.97.2 | 4 | 7.4 | even | 3 | |||
294.5.g.c.19.2 | 4 | 7.2 | even | 3 | |||
294.5.g.c.31.2 | 4 | 7.6 | odd | 2 | |||
336.5.bh.d.145.1 | 4 | 28.19 | even | 6 | |||
336.5.bh.d.241.1 | 4 | 4.3 | odd | 2 | |||
882.5.c.a.685.3 | 4 | 21.17 | even | 6 | |||
882.5.c.a.685.4 | 4 | 21.11 | odd | 6 |