Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [114,4,Mod(7,114)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(114, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("114.7");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 114 = 2 \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 114.e (of order \(3\), 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: | \(6.72621774065\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.627014547.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 26x^{4} + 169x^{2} + 147 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 7.3 | ||
Root | \(1.01248i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 114.7 |
Dual form | 114.4.e.d.49.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/114\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(97\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.73205i | −0.353553 | − | 0.612372i | ||||
\(3\) | 1.50000 | + | 2.59808i | 0.288675 | + | 0.500000i | ||||
\(4\) | −2.00000 | + | 3.46410i | −0.250000 | + | 0.433013i | ||||
\(5\) | 4.22121 | + | 7.31135i | 0.377556 | + | 0.653947i | 0.990706 | − | 0.136020i | \(-0.0434311\pi\) |
−0.613150 | + | 0.789967i | \(0.710098\pi\) | |||||||
\(6\) | 3.00000 | − | 5.19615i | 0.204124 | − | 0.353553i | ||||
\(7\) | −9.44242 | −0.509843 | −0.254921 | − | 0.966962i | \(-0.582050\pi\) | ||||
−0.254921 | + | 0.966962i | \(0.582050\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | −4.50000 | + | 7.79423i | −0.166667 | + | 0.288675i | ||||
\(10\) | 8.44242 | − | 14.6227i | 0.266973 | − | 0.462410i | ||||
\(11\) | −47.4865 | −1.30161 | −0.650805 | − | 0.759245i | \(-0.725568\pi\) | ||||
−0.650805 | + | 0.759245i | \(0.725568\pi\) | |||||||
\(12\) | −12.0000 | −0.288675 | ||||||||
\(13\) | −33.8272 | + | 58.5905i | −0.721692 | + | 1.25001i | 0.238630 | + | 0.971111i | \(0.423302\pi\) |
−0.960321 | + | 0.278896i | \(0.910032\pi\) | |||||||
\(14\) | 9.44242 | + | 16.3547i | 0.180257 | + | 0.312214i | ||||
\(15\) | −12.6636 | + | 21.9340i | −0.217982 | + | 0.377556i | ||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | 38.8052 | + | 67.2126i | 0.553626 | + | 0.958909i | 0.998009 | + | 0.0630719i | \(0.0200898\pi\) |
−0.444383 | + | 0.895837i | \(0.646577\pi\) | |||||||
\(18\) | 18.0000 | 0.235702 | ||||||||
\(19\) | 53.6901 | − | 63.0585i | 0.648281 | − | 0.761401i | ||||
\(20\) | −33.7697 | −0.377556 | ||||||||
\(21\) | −14.1636 | − | 24.5321i | −0.147179 | − | 0.254921i | ||||
\(22\) | 47.4865 | + | 82.2490i | 0.460189 | + | 0.797070i | ||||
\(23\) | −85.4773 | + | 148.051i | −0.774924 | + | 1.34221i | 0.159913 | + | 0.987131i | \(0.448879\pi\) |
−0.934837 | + | 0.355077i | \(0.884455\pi\) | |||||||
\(24\) | 12.0000 | + | 20.7846i | 0.102062 | + | 0.176777i | ||||
\(25\) | 26.8628 | − | 46.5277i | 0.214902 | − | 0.372222i | ||||
\(26\) | 135.309 | 1.02063 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 18.8848 | − | 32.7095i | 0.127461 | − | 0.220768i | ||||
\(29\) | −120.061 | + | 207.952i | −0.768787 | + | 1.33158i | 0.169433 | + | 0.985542i | \(0.445806\pi\) |
−0.938221 | + | 0.346037i | \(0.887527\pi\) | |||||||
\(30\) | 50.6545 | 0.308273 | ||||||||
\(31\) | 279.104 | 1.61705 | 0.808526 | − | 0.588460i | \(-0.200265\pi\) | ||||
0.808526 | + | 0.588460i | \(0.200265\pi\) | |||||||
\(32\) | −16.0000 | + | 27.7128i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −71.2297 | − | 123.373i | −0.375742 | − | 0.650805i | ||||
\(34\) | 77.6104 | − | 134.425i | 0.391473 | − | 0.678051i | ||||
\(35\) | −39.8584 | − | 69.0368i | −0.192494 | − | 0.333410i | ||||
\(36\) | −18.0000 | − | 31.1769i | −0.0833333 | − | 0.144338i | ||||
\(37\) | −20.0617 | −0.0891383 | −0.0445692 | − | 0.999006i | \(-0.514192\pi\) | ||||
−0.0445692 | + | 0.999006i | \(0.514192\pi\) | |||||||
\(38\) | −162.911 | − | 29.9354i | −0.695463 | − | 0.127794i | ||||
\(39\) | −202.963 | −0.833338 | ||||||||
\(40\) | 33.7697 | + | 58.4908i | 0.133486 | + | 0.231205i | ||||
\(41\) | −35.9106 | − | 62.1990i | −0.136788 | − | 0.236923i | 0.789491 | − | 0.613762i | \(-0.210345\pi\) |
−0.926279 | + | 0.376839i | \(0.877011\pi\) | |||||||
\(42\) | −28.3272 | + | 49.0642i | −0.104071 | + | 0.180257i | ||||
\(43\) | −73.6589 | − | 127.581i | −0.261230 | − | 0.452463i | 0.705339 | − | 0.708870i | \(-0.250795\pi\) |
−0.966569 | + | 0.256407i | \(0.917461\pi\) | |||||||
\(44\) | 94.9729 | − | 164.498i | 0.325402 | − | 0.563614i | ||||
\(45\) | −75.9817 | −0.251704 | ||||||||
\(46\) | 341.909 | 1.09591 | ||||||||
\(47\) | 103.671 | − | 179.564i | 0.321746 | − | 0.557280i | −0.659103 | − | 0.752053i | \(-0.729064\pi\) |
0.980848 | + | 0.194773i | \(0.0623971\pi\) | |||||||
\(48\) | 24.0000 | − | 41.5692i | 0.0721688 | − | 0.125000i | ||||
\(49\) | −253.841 | −0.740061 | ||||||||
\(50\) | −107.451 | −0.303918 | ||||||||
\(51\) | −116.416 | + | 201.638i | −0.319636 | + | 0.553626i | ||||
\(52\) | −135.309 | − | 234.362i | −0.360846 | − | 0.625003i | ||||
\(53\) | 130.761 | − | 226.486i | 0.338896 | − | 0.586985i | −0.645330 | − | 0.763904i | \(-0.723280\pi\) |
0.984225 | + | 0.176920i | \(0.0566133\pi\) | |||||||
\(54\) | 27.0000 | + | 46.7654i | 0.0680414 | + | 0.117851i | ||||
\(55\) | −200.450 | − | 347.190i | −0.491431 | − | 0.851184i | ||||
\(56\) | −75.5393 | −0.180257 | ||||||||
\(57\) | 244.366 | + | 44.9031i | 0.567843 | + | 0.104343i | ||||
\(58\) | 480.245 | 1.08723 | ||||||||
\(59\) | 10.9909 | + | 19.0367i | 0.0242524 | + | 0.0420063i | 0.877897 | − | 0.478850i | \(-0.158946\pi\) |
−0.853644 | + | 0.520856i | \(0.825613\pi\) | |||||||
\(60\) | −50.6545 | − | 87.7362i | −0.108991 | − | 0.188778i | ||||
\(61\) | 326.552 | − | 565.604i | 0.685420 | − | 1.18718i | −0.287884 | − | 0.957665i | \(-0.592952\pi\) |
0.973304 | − | 0.229518i | \(-0.0737149\pi\) | |||||||
\(62\) | −279.104 | − | 483.423i | −0.571715 | − | 0.990239i | ||||
\(63\) | 42.4909 | − | 73.5963i | 0.0849738 | − | 0.147179i | ||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −571.167 | −1.08992 | ||||||||
\(66\) | −142.459 | + | 246.747i | −0.265690 | + | 0.460189i | ||||
\(67\) | 206.898 | − | 358.357i | 0.377262 | − | 0.653438i | −0.613400 | − | 0.789772i | \(-0.710199\pi\) |
0.990663 | + | 0.136334i | \(0.0435322\pi\) | |||||||
\(68\) | −310.442 | −0.553626 | ||||||||
\(69\) | −512.864 | −0.894805 | ||||||||
\(70\) | −79.7168 | + | 138.074i | −0.136114 | + | 0.235756i | ||||
\(71\) | 78.9726 | + | 136.785i | 0.132005 | + | 0.228639i | 0.924449 | − | 0.381305i | \(-0.124525\pi\) |
−0.792445 | + | 0.609944i | \(0.791192\pi\) | |||||||
\(72\) | −36.0000 | + | 62.3538i | −0.0589256 | + | 0.102062i | ||||
\(73\) | 551.073 | + | 954.486i | 0.883537 | + | 1.53033i | 0.847382 | + | 0.530984i | \(0.178178\pi\) |
0.0361550 | + | 0.999346i | \(0.488489\pi\) | |||||||
\(74\) | 20.0617 | + | 34.7478i | 0.0315151 | + | 0.0545858i | ||||
\(75\) | 161.177 | 0.248148 | ||||||||
\(76\) | 111.061 | + | 312.105i | 0.167626 | + | 0.471064i | ||||
\(77\) | 448.387 | 0.663616 | ||||||||
\(78\) | 202.963 | + | 351.543i | 0.294629 | + | 0.510313i | ||||
\(79\) | 208.907 | + | 361.837i | 0.297517 | + | 0.515314i | 0.975567 | − | 0.219701i | \(-0.0705083\pi\) |
−0.678050 | + | 0.735015i | \(0.737175\pi\) | |||||||
\(80\) | 67.5393 | − | 116.982i | 0.0943891 | − | 0.163487i | ||||
\(81\) | −40.5000 | − | 70.1481i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −71.8213 | + | 124.398i | −0.0967236 | + | 0.167530i | ||||
\(83\) | 1431.80 | 1.89350 | 0.946751 | − | 0.321967i | \(-0.104344\pi\) | ||||
0.946751 | + | 0.321967i | \(0.104344\pi\) | |||||||
\(84\) | 113.309 | 0.147179 | ||||||||
\(85\) | −327.610 | + | 567.437i | −0.418050 | + | 0.724084i | ||||
\(86\) | −147.318 | + | 255.162i | −0.184717 | + | 0.319940i | ||||
\(87\) | −720.368 | −0.887719 | ||||||||
\(88\) | −379.892 | −0.460189 | ||||||||
\(89\) | −644.697 | + | 1116.65i | −0.767839 | + | 1.32994i | 0.170893 | + | 0.985290i | \(0.445335\pi\) |
−0.938732 | + | 0.344647i | \(0.887999\pi\) | |||||||
\(90\) | 75.9817 | + | 131.604i | 0.0889909 | + | 0.154137i | ||||
\(91\) | 319.411 | − | 553.236i | 0.367949 | − | 0.637306i | ||||
\(92\) | −341.909 | − | 592.204i | −0.387462 | − | 0.671104i | ||||
\(93\) | 418.657 | + | 725.135i | 0.466803 | + | 0.808526i | ||||
\(94\) | −414.686 | −0.455017 | ||||||||
\(95\) | 687.680 | + | 126.363i | 0.742678 | + | 0.136470i | ||||
\(96\) | −96.0000 | −0.102062 | ||||||||
\(97\) | −69.3811 | − | 120.172i | −0.0726245 | − | 0.125789i | 0.827426 | − | 0.561574i | \(-0.189804\pi\) |
−0.900051 | + | 0.435785i | \(0.856471\pi\) | |||||||
\(98\) | 253.841 | + | 439.665i | 0.261651 | + | 0.453193i | ||||
\(99\) | 213.689 | − | 370.120i | 0.216935 | − | 0.375742i | ||||
\(100\) | 107.451 | + | 186.111i | 0.107451 | + | 0.186111i | ||||
\(101\) | 34.8153 | − | 60.3018i | 0.0342995 | − | 0.0594085i | −0.848366 | − | 0.529410i | \(-0.822413\pi\) |
0.882666 | + | 0.470002i | \(0.155747\pi\) | |||||||
\(102\) | 465.663 | 0.452034 | ||||||||
\(103\) | −644.346 | −0.616401 | −0.308201 | − | 0.951321i | \(-0.599727\pi\) | ||||
−0.308201 | + | 0.951321i | \(0.599727\pi\) | |||||||
\(104\) | −270.618 | + | 468.724i | −0.255157 | + | 0.441944i | ||||
\(105\) | 119.575 | − | 207.110i | 0.111137 | − | 0.192494i | ||||
\(106\) | −523.046 | −0.479271 | ||||||||
\(107\) | −189.454 | −0.171171 | −0.0855853 | − | 0.996331i | \(-0.527276\pi\) | ||||
−0.0855853 | + | 0.996331i | \(0.527276\pi\) | |||||||
\(108\) | 54.0000 | − | 93.5307i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | 119.576 | + | 207.112i | 0.105076 | + | 0.181998i | 0.913769 | − | 0.406233i | \(-0.133158\pi\) |
−0.808693 | + | 0.588231i | \(0.799825\pi\) | |||||||
\(110\) | −400.901 | + | 694.380i | −0.347494 | + | 0.601878i | ||||
\(111\) | −30.0925 | − | 52.1217i | −0.0257320 | − | 0.0445692i | ||||
\(112\) | 75.5393 | + | 130.838i | 0.0637303 | + | 0.110384i | ||||
\(113\) | 162.743 | 0.135483 | 0.0677413 | − | 0.997703i | \(-0.478421\pi\) | ||||
0.0677413 | + | 0.997703i | \(0.478421\pi\) | |||||||
\(114\) | −166.592 | − | 468.157i | −0.136866 | − | 0.384622i | ||||
\(115\) | −1443.27 | −1.17031 | ||||||||
\(116\) | −480.245 | − | 831.809i | −0.384394 | − | 0.665789i | ||||
\(117\) | −304.445 | − | 527.315i | −0.240564 | − | 0.416669i | ||||
\(118\) | 21.9817 | − | 38.0735i | 0.0171490 | − | 0.0297030i | ||||
\(119\) | −366.415 | − | 634.649i | −0.282262 | − | 0.488893i | ||||
\(120\) | −101.309 | + | 175.472i | −0.0770684 | + | 0.133486i | ||||
\(121\) | 923.965 | 0.694188 | ||||||||
\(122\) | −1306.21 | −0.969331 | ||||||||
\(123\) | 107.732 | − | 186.597i | 0.0789745 | − | 0.136788i | ||||
\(124\) | −558.209 | + | 966.846i | −0.404263 | + | 0.700204i | ||||
\(125\) | 1508.88 | 1.07966 | ||||||||
\(126\) | −169.963 | −0.120171 | ||||||||
\(127\) | 48.6891 | − | 84.3320i | 0.0340194 | − | 0.0589233i | −0.848514 | − | 0.529172i | \(-0.822503\pi\) |
0.882534 | + | 0.470249i | \(0.155836\pi\) | |||||||
\(128\) | −64.0000 | − | 110.851i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 220.977 | − | 382.743i | 0.150821 | − | 0.261230i | ||||
\(130\) | 571.167 | + | 989.291i | 0.385344 | + | 0.667435i | ||||
\(131\) | −189.699 | − | 328.568i | −0.126520 | − | 0.219138i | 0.795806 | − | 0.605551i | \(-0.207047\pi\) |
−0.922326 | + | 0.386413i | \(0.873714\pi\) | |||||||
\(132\) | 569.838 | 0.375742 | ||||||||
\(133\) | −506.964 | + | 595.425i | −0.330521 | + | 0.388195i | ||||
\(134\) | −827.591 | −0.533530 | ||||||||
\(135\) | −113.973 | − | 197.406i | −0.0726607 | − | 0.125852i | ||||
\(136\) | 310.442 | + | 537.701i | 0.195736 | + | 0.339026i | ||||
\(137\) | −1206.84 | + | 2090.31i | −0.752609 | + | 1.30356i | 0.193945 | + | 0.981012i | \(0.437872\pi\) |
−0.946554 | + | 0.322545i | \(0.895462\pi\) | |||||||
\(138\) | 512.864 | + | 888.307i | 0.316362 | + | 0.547954i | ||||
\(139\) | 1554.52 | − | 2692.51i | 0.948582 | − | 1.64299i | 0.200166 | − | 0.979762i | \(-0.435852\pi\) |
0.748416 | − | 0.663230i | \(-0.230815\pi\) | |||||||
\(140\) | 318.867 | 0.192494 | ||||||||
\(141\) | 622.029 | 0.371520 | ||||||||
\(142\) | 157.945 | − | 273.569i | 0.0933414 | − | 0.161672i | ||||
\(143\) | 1606.34 | − | 2782.26i | 0.939361 | − | 1.62702i | ||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | −2027.22 | −1.16104 | ||||||||
\(146\) | 1102.15 | − | 1908.97i | 0.624755 | − | 1.08211i | ||||
\(147\) | −380.761 | − | 659.498i | −0.213637 | − | 0.370030i | ||||
\(148\) | 40.1233 | − | 69.4956i | 0.0222846 | − | 0.0385980i | ||||
\(149\) | 1459.55 | + | 2528.02i | 0.802491 | + | 1.38995i | 0.917972 | + | 0.396645i | \(0.129826\pi\) |
−0.115481 | + | 0.993310i | \(0.536841\pi\) | |||||||
\(150\) | −161.177 | − | 279.166i | −0.0877336 | − | 0.151959i | ||||
\(151\) | −1915.72 | −1.03244 | −0.516221 | − | 0.856455i | \(-0.672662\pi\) | ||||
−0.516221 | + | 0.856455i | \(0.672662\pi\) | |||||||
\(152\) | 429.520 | − | 504.468i | 0.229202 | − | 0.269196i | ||||
\(153\) | −698.494 | −0.369084 | ||||||||
\(154\) | −448.387 | − | 776.629i | −0.234624 | − | 0.406380i | ||||
\(155\) | 1178.16 | + | 2040.63i | 0.610529 | + | 1.05747i | ||||
\(156\) | 405.927 | − | 703.086i | 0.208334 | − | 0.360846i | ||||
\(157\) | 1268.34 | + | 2196.84i | 0.644744 | + | 1.11673i | 0.984361 | + | 0.176166i | \(0.0563694\pi\) |
−0.339616 | + | 0.940564i | \(0.610297\pi\) | |||||||
\(158\) | 417.813 | − | 723.673i | 0.210376 | − | 0.364382i | ||||
\(159\) | 784.569 | 0.391323 | ||||||||
\(160\) | −270.157 | −0.133486 | ||||||||
\(161\) | 807.113 | − | 1397.96i | 0.395089 | − | 0.684315i | ||||
\(162\) | −81.0000 | + | 140.296i | −0.0392837 | + | 0.0680414i | ||||
\(163\) | −1731.52 | −0.832044 | −0.416022 | − | 0.909355i | \(-0.636576\pi\) | ||||
−0.416022 | + | 0.909355i | \(0.636576\pi\) | |||||||
\(164\) | 287.285 | 0.136788 | ||||||||
\(165\) | 601.351 | − | 1041.57i | 0.283728 | − | 0.491431i | ||||
\(166\) | −1431.80 | − | 2479.95i | −0.669454 | − | 1.15953i | ||||
\(167\) | 715.062 | − | 1238.52i | 0.331336 | − | 0.573891i | −0.651438 | − | 0.758702i | \(-0.725834\pi\) |
0.982774 | + | 0.184811i | \(0.0591672\pi\) | |||||||
\(168\) | −113.309 | − | 196.257i | −0.0520356 | − | 0.0901283i | ||||
\(169\) | −1190.07 | − | 2061.25i | −0.541677 | − | 0.938213i | ||||
\(170\) | 1310.44 | 0.591212 | ||||||||
\(171\) | 249.887 | + | 702.236i | 0.111751 | + | 0.314043i | ||||
\(172\) | 589.271 | 0.261230 | ||||||||
\(173\) | −146.662 | − | 254.027i | −0.0644539 | − | 0.111638i | 0.831998 | − | 0.554779i | \(-0.187197\pi\) |
−0.896452 | + | 0.443142i | \(0.853864\pi\) | |||||||
\(174\) | 720.368 | + | 1247.71i | 0.313856 | + | 0.543615i | ||||
\(175\) | −253.650 | + | 439.334i | −0.109566 | + | 0.189775i | ||||
\(176\) | 379.892 | + | 657.992i | 0.162701 | + | 0.281807i | ||||
\(177\) | −32.9726 | + | 57.1102i | −0.0140021 | + | 0.0242524i | ||||
\(178\) | 2578.79 | 1.08589 | ||||||||
\(179\) | −3843.52 | −1.60490 | −0.802452 | − | 0.596716i | \(-0.796472\pi\) | ||||
−0.802452 | + | 0.596716i | \(0.796472\pi\) | |||||||
\(180\) | 151.963 | − | 263.208i | 0.0629261 | − | 0.108991i | ||||
\(181\) | −884.639 | + | 1532.24i | −0.363286 | + | 0.629229i | −0.988499 | − | 0.151224i | \(-0.951678\pi\) |
0.625214 | + | 0.780454i | \(0.285012\pi\) | |||||||
\(182\) | −1277.64 | −0.520359 | ||||||||
\(183\) | 1959.31 | 0.791455 | ||||||||
\(184\) | −683.819 | + | 1184.41i | −0.273977 | + | 0.474542i | ||||
\(185\) | −84.6845 | − | 146.678i | −0.0336547 | − | 0.0582917i | ||||
\(186\) | 837.313 | − | 1450.27i | 0.330080 | − | 0.571715i | ||||
\(187\) | −1842.72 | − | 3191.69i | −0.720606 | − | 1.24813i | ||||
\(188\) | 414.686 | + | 718.257i | 0.160873 | + | 0.278640i | ||||
\(189\) | 254.945 | 0.0981192 | ||||||||
\(190\) | −468.812 | − | 1317.46i | −0.179006 | − | 0.503045i | ||||
\(191\) | −504.006 | −0.190935 | −0.0954676 | − | 0.995433i | \(-0.530435\pi\) | ||||
−0.0954676 | + | 0.995433i | \(0.530435\pi\) | |||||||
\(192\) | 96.0000 | + | 166.277i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | 1083.79 | + | 1877.19i | 0.404213 | + | 0.700118i | 0.994230 | − | 0.107273i | \(-0.0342120\pi\) |
−0.590016 | + | 0.807391i | \(0.700879\pi\) | |||||||
\(194\) | −138.762 | + | 240.343i | −0.0513533 | + | 0.0889465i | ||||
\(195\) | −856.751 | − | 1483.94i | −0.314632 | − | 0.544958i | ||||
\(196\) | 507.682 | − | 879.330i | 0.185015 | − | 0.320456i | ||||
\(197\) | 2111.10 | 0.763501 | 0.381750 | − | 0.924265i | \(-0.375321\pi\) | ||||
0.381750 | + | 0.924265i | \(0.375321\pi\) | |||||||
\(198\) | −854.756 | −0.306792 | ||||||||
\(199\) | −1069.30 | + | 1852.08i | −0.380907 | + | 0.659750i | −0.991192 | − | 0.132432i | \(-0.957722\pi\) |
0.610285 | + | 0.792182i | \(0.291055\pi\) | |||||||
\(200\) | 214.902 | − | 372.222i | 0.0759795 | − | 0.131600i | ||||
\(201\) | 1241.39 | 0.435625 | ||||||||
\(202\) | −139.261 | −0.0485068 | ||||||||
\(203\) | 1133.67 | − | 1963.57i | 0.391961 | − | 0.678896i | ||||
\(204\) | −465.663 | − | 806.551i | −0.159818 | − | 0.276813i | ||||
\(205\) | 303.172 | − | 525.110i | 0.103290 | − | 0.178904i | ||||
\(206\) | 644.346 | + | 1116.04i | 0.217931 | + | 0.377467i | ||||
\(207\) | −769.296 | − | 1332.46i | −0.258308 | − | 0.447403i | ||||
\(208\) | 1082.47 | 0.360846 | ||||||||
\(209\) | −2549.55 | + | 2994.43i | −0.843809 | + | 0.991047i | ||||
\(210\) | −478.301 | −0.157171 | ||||||||
\(211\) | 487.977 | + | 845.200i | 0.159212 | + | 0.275763i | 0.934585 | − | 0.355741i | \(-0.115771\pi\) |
−0.775373 | + | 0.631504i | \(0.782438\pi\) | |||||||
\(212\) | 523.046 | + | 905.942i | 0.169448 | + | 0.293492i | ||||
\(213\) | −236.918 | + | 410.354i | −0.0762129 | + | 0.132005i | ||||
\(214\) | 189.454 | + | 328.145i | 0.0605179 | + | 0.104820i | ||||
\(215\) | 621.859 | − | 1077.09i | 0.197258 | − | 0.341661i | ||||
\(216\) | −216.000 | −0.0680414 | ||||||||
\(217\) | −2635.42 | −0.824442 | ||||||||
\(218\) | 239.152 | − | 414.224i | 0.0743002 | − | 0.128692i | ||||
\(219\) | −1653.22 | + | 2863.46i | −0.510110 | + | 0.883537i | ||||
\(220\) | 1603.60 | 0.491431 | ||||||||
\(221\) | −5250.70 | −1.59819 | ||||||||
\(222\) | −60.1850 | + | 104.243i | −0.0181953 | + | 0.0315151i | ||||
\(223\) | 1787.73 | + | 3096.43i | 0.536839 | + | 0.929832i | 0.999072 | + | 0.0430737i | \(0.0137150\pi\) |
−0.462233 | + | 0.886758i | \(0.652952\pi\) | |||||||
\(224\) | 151.079 | − | 261.676i | 0.0450641 | − | 0.0780534i | ||||
\(225\) | 241.765 | + | 418.750i | 0.0716341 | + | 0.124074i | ||||
\(226\) | −162.743 | − | 281.878i | −0.0479003 | − | 0.0829658i | ||||
\(227\) | −86.5237 | −0.0252986 | −0.0126493 | − | 0.999920i | \(-0.504027\pi\) | ||||
−0.0126493 | + | 0.999920i | \(0.504027\pi\) | |||||||
\(228\) | −644.281 | + | 756.702i | −0.187143 | + | 0.219798i | ||||
\(229\) | −3928.05 | −1.13351 | −0.566753 | − | 0.823888i | \(-0.691801\pi\) | ||||
−0.566753 | + | 0.823888i | \(0.691801\pi\) | |||||||
\(230\) | 1443.27 | + | 2499.82i | 0.413767 | + | 0.716666i | ||||
\(231\) | 672.581 | + | 1164.94i | 0.191569 | + | 0.331808i | ||||
\(232\) | −960.491 | + | 1663.62i | −0.271807 | + | 0.470784i | ||||
\(233\) | −510.013 | − | 883.368i | −0.143399 | − | 0.248375i | 0.785375 | − | 0.619020i | \(-0.212470\pi\) |
−0.928775 | + | 0.370645i | \(0.879137\pi\) | |||||||
\(234\) | −608.890 | + | 1054.63i | −0.170104 | + | 0.294629i | ||||
\(235\) | 1750.48 | 0.485908 | ||||||||
\(236\) | −87.9270 | −0.0242524 | ||||||||
\(237\) | −626.720 | + | 1085.51i | −0.171771 | + | 0.297517i | ||||
\(238\) | −732.830 | + | 1269.30i | −0.199590 | + | 0.345699i | ||||
\(239\) | 264.681 | 0.0716351 | 0.0358175 | − | 0.999358i | \(-0.488596\pi\) | ||||
0.0358175 | + | 0.999358i | \(0.488596\pi\) | |||||||
\(240\) | 405.236 | 0.108991 | ||||||||
\(241\) | 86.1935 | − | 149.292i | 0.0230382 | − | 0.0399034i | −0.854276 | − | 0.519819i | \(-0.825999\pi\) |
0.877315 | + | 0.479916i | \(0.159333\pi\) | |||||||
\(242\) | −923.965 | − | 1600.35i | −0.245433 | − | 0.425102i | ||||
\(243\) | 121.500 | − | 210.444i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 1306.21 | + | 2262.42i | 0.342710 | + | 0.593592i | ||||
\(245\) | −1071.51 | − | 1855.92i | −0.279415 | − | 0.483960i | ||||
\(246\) | −430.928 | −0.111687 | ||||||||
\(247\) | 1878.44 | + | 5278.82i | 0.483897 | + | 1.35985i | ||||
\(248\) | 2232.84 | 0.571715 | ||||||||
\(249\) | 2147.70 | + | 3719.93i | 0.546607 | + | 0.946751i | ||||
\(250\) | −1508.88 | − | 2613.45i | −0.381719 | − | 0.661156i | ||||
\(251\) | 2442.43 | − | 4230.42i | 0.614203 | − | 1.06383i | −0.376321 | − | 0.926490i | \(-0.622811\pi\) |
0.990524 | − | 0.137342i | \(-0.0438558\pi\) | |||||||
\(252\) | 169.963 | + | 294.385i | 0.0424869 | + | 0.0735894i | ||||
\(253\) | 4059.02 | − | 7030.42i | 1.00865 | − | 1.74703i | ||||
\(254\) | −194.757 | −0.0481107 | ||||||||
\(255\) | −1965.66 | −0.482723 | ||||||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −2011.32 | + | 3483.71i | −0.488181 | + | 0.845555i | −0.999908 | − | 0.0135936i | \(-0.995673\pi\) |
0.511726 | + | 0.859149i | \(0.329006\pi\) | |||||||
\(258\) | −883.907 | −0.213293 | ||||||||
\(259\) | 189.431 | 0.0454465 | ||||||||
\(260\) | 1142.33 | − | 1978.58i | 0.272479 | − | 0.471948i | ||||
\(261\) | −1080.55 | − | 1871.57i | −0.256262 | − | 0.443860i | ||||
\(262\) | −379.398 | + | 657.136i | −0.0894629 | + | 0.154954i | ||||
\(263\) | 3571.06 | + | 6185.26i | 0.837266 | + | 1.45019i | 0.892172 | + | 0.451695i | \(0.149181\pi\) |
−0.0549063 | + | 0.998492i | \(0.517486\pi\) | |||||||
\(264\) | −569.838 | − | 986.988i | −0.132845 | − | 0.230094i | ||||
\(265\) | 2207.89 | 0.511809 | ||||||||
\(266\) | 1538.27 | + | 282.662i | 0.354577 | + | 0.0651546i | ||||
\(267\) | −3868.18 | −0.886625 | ||||||||
\(268\) | 827.591 | + | 1433.43i | 0.188631 | + | 0.326719i | ||||
\(269\) | −2540.63 | − | 4400.50i | −0.575855 | − | 0.997410i | −0.995948 | − | 0.0899291i | \(-0.971336\pi\) |
0.420093 | − | 0.907481i | \(-0.361997\pi\) | |||||||
\(270\) | −227.945 | + | 394.813i | −0.0513789 | + | 0.0889909i | ||||
\(271\) | 1486.90 | + | 2575.39i | 0.333295 | + | 0.577284i | 0.983156 | − | 0.182770i | \(-0.0585062\pi\) |
−0.649861 | + | 0.760053i | \(0.725173\pi\) | |||||||
\(272\) | 620.884 | − | 1075.40i | 0.138407 | − | 0.239727i | ||||
\(273\) | 1916.47 | 0.424871 | ||||||||
\(274\) | 4827.37 | 1.06435 | ||||||||
\(275\) | −1275.62 | + | 2209.44i | −0.279719 | + | 0.484488i | ||||
\(276\) | 1025.73 | − | 1776.61i | 0.223701 | − | 0.387462i | ||||
\(277\) | 7778.48 | 1.68723 | 0.843617 | − | 0.536946i | \(-0.180422\pi\) | ||||
0.843617 | + | 0.536946i | \(0.180422\pi\) | |||||||
\(278\) | −6218.09 | −1.34150 | ||||||||
\(279\) | −1255.97 | + | 2175.40i | −0.269509 | + | 0.466803i | ||||
\(280\) | −318.867 | − | 552.294i | −0.0680570 | − | 0.117878i | ||||
\(281\) | −1110.34 | + | 1923.16i | −0.235720 | + | 0.408279i | −0.959482 | − | 0.281771i | \(-0.909078\pi\) |
0.723762 | + | 0.690050i | \(0.242411\pi\) | |||||||
\(282\) | −622.029 | − | 1077.39i | −0.131352 | − | 0.227508i | ||||
\(283\) | 3808.17 | + | 6595.95i | 0.799902 | + | 1.38547i | 0.919679 | + | 0.392671i | \(0.128449\pi\) |
−0.119777 | + | 0.992801i | \(0.538218\pi\) | |||||||
\(284\) | −631.781 | −0.132005 | ||||||||
\(285\) | 703.218 | + | 1976.19i | 0.146158 | + | 0.410735i | ||||
\(286\) | −6425.35 | −1.32846 | ||||||||
\(287\) | 339.083 | + | 587.309i | 0.0697402 | + | 0.120794i | ||||
\(288\) | −144.000 | − | 249.415i | −0.0294628 | − | 0.0510310i | ||||
\(289\) | −555.190 | + | 961.618i | −0.113004 | + | 0.195729i | ||||
\(290\) | 2027.22 | + | 3511.24i | 0.410490 | + | 0.710990i | ||||
\(291\) | 208.143 | − | 360.515i | 0.0419298 | − | 0.0726245i | ||||
\(292\) | −4408.58 | −0.883537 | ||||||||
\(293\) | −9036.61 | −1.80179 | −0.900894 | − | 0.434038i | \(-0.857088\pi\) | ||||
−0.900894 | + | 0.434038i | \(0.857088\pi\) | |||||||
\(294\) | −761.522 | + | 1319.00i | −0.151064 | + | 0.261651i | ||||
\(295\) | −92.7895 | + | 160.716i | −0.0183133 | + | 0.0317195i | ||||
\(296\) | −160.493 | −0.0315151 | ||||||||
\(297\) | 1282.13 | 0.250495 | ||||||||
\(298\) | 2919.10 | − | 5056.03i | 0.567447 | − | 0.982846i | ||||
\(299\) | −5782.93 | − | 10016.3i | −1.11851 | − | 1.93732i | ||||
\(300\) | −322.354 | + | 558.333i | −0.0620370 | + | 0.107451i | ||||
\(301\) | 695.518 | + | 1204.67i | 0.133186 | + | 0.230685i | ||||
\(302\) | 1915.72 | + | 3318.12i | 0.365023 | + | 0.632239i | ||||
\(303\) | 208.892 | 0.0396057 | ||||||||
\(304\) | −1303.29 | − | 239.483i | −0.245883 | − | 0.0451819i | ||||
\(305\) | 5513.77 | 1.03514 | ||||||||
\(306\) | 698.494 | + | 1209.83i | 0.130491 | + | 0.226017i | ||||
\(307\) | −3898.58 | − | 6752.55i | −0.724769 | − | 1.25534i | −0.959069 | − | 0.283172i | \(-0.908613\pi\) |
0.234300 | − | 0.972164i | \(-0.424720\pi\) | |||||||
\(308\) | −896.774 | + | 1553.26i | −0.165904 | + | 0.287354i | ||||
\(309\) | −966.519 | − | 1674.06i | −0.177940 | − | 0.308201i | ||||
\(310\) | 2356.32 | − | 4081.26i | 0.431709 | − | 0.747742i | ||||
\(311\) | 2737.49 | 0.499128 | 0.249564 | − | 0.968358i | \(-0.419713\pi\) | ||||
0.249564 | + | 0.968358i | \(0.419713\pi\) | |||||||
\(312\) | −1623.71 | −0.294629 | ||||||||
\(313\) | 3823.08 | − | 6621.76i | 0.690393 | − | 1.19580i | −0.281316 | − | 0.959615i | \(-0.590771\pi\) |
0.971709 | − | 0.236181i | \(-0.0758957\pi\) | |||||||
\(314\) | 2536.69 | − | 4393.67i | 0.455903 | − | 0.789647i | ||||
\(315\) | 717.451 | 0.128330 | ||||||||
\(316\) | −1671.25 | −0.297517 | ||||||||
\(317\) | 3210.19 | − | 5560.22i | 0.568777 | − | 0.985152i | −0.427910 | − | 0.903821i | \(-0.640750\pi\) |
0.996687 | − | 0.0813300i | \(-0.0259168\pi\) | |||||||
\(318\) | −784.569 | − | 1358.91i | −0.138354 | − | 0.239635i | ||||
\(319\) | 5701.29 | − | 9874.92i | 1.00066 | − | 1.73320i | ||||
\(320\) | 270.157 | + | 467.926i | 0.0471945 | + | 0.0817433i | ||||
\(321\) | −284.182 | − | 492.217i | −0.0494127 | − | 0.0855853i | ||||
\(322\) | −3228.45 | −0.558741 | ||||||||
\(323\) | 6321.78 | + | 1161.65i | 1.08902 | + | 0.200111i | ||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | 1817.39 | + | 3147.81i | 0.310187 | + | 0.537259i | ||||
\(326\) | 1731.52 | + | 2999.08i | 0.294172 | + | 0.509521i | ||||
\(327\) | −358.728 | + | 621.336i | −0.0606658 | + | 0.105076i | ||||
\(328\) | −287.285 | − | 497.592i | −0.0483618 | − | 0.0837651i | ||||
\(329\) | −978.909 | + | 1695.52i | −0.164040 | + | 0.284125i | ||||
\(330\) | −2405.40 | −0.401252 | ||||||||
\(331\) | −4594.77 | −0.762996 | −0.381498 | − | 0.924370i | \(-0.624592\pi\) | ||||
−0.381498 | + | 0.924370i | \(0.624592\pi\) | |||||||
\(332\) | −2863.60 | + | 4959.91i | −0.473375 | + | 0.819910i | ||||
\(333\) | 90.2775 | − | 156.365i | 0.0148564 | − | 0.0257320i | ||||
\(334\) | −2860.25 | −0.468580 | ||||||||
\(335\) | 3493.43 | 0.569751 | ||||||||
\(336\) | −226.618 | + | 392.514i | −0.0367947 | + | 0.0637303i | ||||
\(337\) | −3305.63 | − | 5725.53i | −0.534331 | − | 0.925488i | −0.999195 | − | 0.0401060i | \(-0.987230\pi\) |
0.464865 | − | 0.885382i | \(-0.346103\pi\) | |||||||
\(338\) | −2380.13 | + | 4122.51i | −0.383024 | + | 0.663417i | ||||
\(339\) | 244.114 | + | 422.818i | 0.0391105 | + | 0.0677413i | ||||
\(340\) | −1310.44 | − | 2269.75i | −0.209025 | − | 0.362042i | ||||
\(341\) | −13253.7 | −2.10477 | ||||||||
\(342\) | 966.421 | − | 1135.05i | 0.152801 | − | 0.179464i | ||||
\(343\) | 5635.62 | 0.887157 | ||||||||
\(344\) | −589.271 | − | 1020.65i | −0.0923586 | − | 0.159970i | ||||
\(345\) | −2164.91 | − | 3749.73i | −0.337839 | − | 0.585155i | ||||
\(346\) | −293.325 | + | 508.053i | −0.0455758 | + | 0.0789396i | ||||
\(347\) | 1249.31 | + | 2163.88i | 0.193276 | + | 0.334764i | 0.946334 | − | 0.323190i | \(-0.104755\pi\) |
−0.753058 | + | 0.657954i | \(0.771422\pi\) | |||||||
\(348\) | 1440.74 | − | 2495.43i | 0.221930 | − | 0.384394i | ||||
\(349\) | 10330.5 | 1.58447 | 0.792235 | − | 0.610216i | \(-0.208917\pi\) | ||||
0.792235 | + | 0.610216i | \(0.208917\pi\) | |||||||
\(350\) | 1014.60 | 0.154950 | ||||||||
\(351\) | 913.336 | − | 1581.94i | 0.138890 | − | 0.240564i | ||||
\(352\) | 759.784 | − | 1315.98i | 0.115047 | − | 0.199268i | ||||
\(353\) | 2608.83 | 0.393354 | 0.196677 | − | 0.980468i | \(-0.436985\pi\) | ||||
0.196677 | + | 0.980468i | \(0.436985\pi\) | |||||||
\(354\) | 131.890 | 0.0198020 | ||||||||
\(355\) | −666.720 | + | 1154.79i | −0.0996783 | + | 0.172648i | ||||
\(356\) | −2578.79 | − | 4466.59i | −0.383920 | − | 0.664968i | ||||
\(357\) | 1099.25 | − | 1903.95i | 0.162964 | − | 0.282262i | ||||
\(358\) | 3843.52 | + | 6657.16i | 0.567419 | + | 0.982799i | ||||
\(359\) | −2075.16 | − | 3594.29i | −0.305078 | − | 0.528410i | 0.672201 | − | 0.740369i | \(-0.265349\pi\) |
−0.977279 | + | 0.211958i | \(0.932016\pi\) | |||||||
\(360\) | −607.854 | −0.0889909 | ||||||||
\(361\) | −1093.76 | − | 6771.23i | −0.159463 | − | 0.987204i | ||||
\(362\) | 3538.56 | 0.513764 | ||||||||
\(363\) | 1385.95 | + | 2400.53i | 0.200395 | + | 0.347094i | ||||
\(364\) | 1277.64 | + | 2212.94i | 0.183975 | + | 0.318653i | ||||
\(365\) | −4652.38 | + | 8058.17i | −0.667170 | + | 1.15557i | ||||
\(366\) | −1959.31 | − | 3393.62i | −0.279822 | − | 0.484665i | ||||
\(367\) | 3685.24 | − | 6383.02i | 0.524163 | − | 0.907878i | −0.475441 | − | 0.879748i | \(-0.657711\pi\) |
0.999604 | − | 0.0281300i | \(-0.00895523\pi\) | |||||||
\(368\) | 2735.27 | 0.387462 | ||||||||
\(369\) | 646.391 | 0.0911918 | ||||||||
\(370\) | −169.369 | + | 293.356i | −0.0237975 | + | 0.0412185i | ||||
\(371\) | −1234.70 | + | 2138.57i | −0.172783 | + | 0.299270i | ||||
\(372\) | −3349.25 | −0.466803 | ||||||||
\(373\) | 13166.5 | 1.82772 | 0.913858 | − | 0.406035i | \(-0.133089\pi\) | ||||
0.913858 | + | 0.406035i | \(0.133089\pi\) | |||||||
\(374\) | −3685.45 | + | 6383.38i | −0.509545 | + | 0.882558i | ||||
\(375\) | 2263.31 | + | 3920.17i | 0.311672 | + | 0.539832i | ||||
\(376\) | 829.372 | − | 1436.51i | 0.113754 | − | 0.197028i | ||||
\(377\) | −8122.69 | − | 14068.9i | −1.10965 | − | 1.92198i | ||||
\(378\) | −254.945 | − | 441.578i | −0.0346904 | − | 0.0600855i | ||||
\(379\) | −14284.2 | −1.93596 | −0.967978 | − | 0.251034i | \(-0.919230\pi\) | ||||
−0.967978 | + | 0.251034i | \(0.919230\pi\) | |||||||
\(380\) | −1813.10 | + | 2129.47i | −0.244763 | + | 0.287472i | ||||
\(381\) | 292.135 | 0.0392822 | ||||||||
\(382\) | 504.006 | + | 872.965i | 0.0675058 | + | 0.116923i | ||||
\(383\) | 4729.31 | + | 8191.40i | 0.630957 | + | 1.09285i | 0.987357 | + | 0.158515i | \(0.0506708\pi\) |
−0.356400 | + | 0.934334i | \(0.615996\pi\) | |||||||
\(384\) | 192.000 | − | 332.554i | 0.0255155 | − | 0.0441942i | ||||
\(385\) | 1892.73 | + | 3278.31i | 0.250552 | + | 0.433970i | ||||
\(386\) | 2167.59 | − | 3754.37i | 0.285822 | − | 0.495058i | ||||
\(387\) | 1325.86 | 0.174153 | ||||||||
\(388\) | 555.048 | 0.0726245 | ||||||||
\(389\) | 3550.48 | − | 6149.61i | 0.462767 | − | 0.801536i | −0.536330 | − | 0.844008i | \(-0.680190\pi\) |
0.999098 | + | 0.0424717i | \(0.0135232\pi\) | |||||||
\(390\) | −1713.50 | + | 2967.87i | −0.222478 | + | 0.385344i | ||||
\(391\) | −13267.9 | −1.71607 | ||||||||
\(392\) | −2030.73 | −0.261651 | ||||||||
\(393\) | 569.097 | − | 985.704i | 0.0730461 | − | 0.126520i | ||||
\(394\) | −2111.10 | − | 3656.53i | −0.269938 | − | 0.467547i | ||||
\(395\) | −1763.68 | + | 3054.78i | −0.224659 | + | 0.389120i | ||||
\(396\) | 854.756 | + | 1480.48i | 0.108467 | + | 0.187871i | ||||
\(397\) | −958.081 | − | 1659.44i | −0.121120 | − | 0.209786i | 0.799090 | − | 0.601212i | \(-0.205315\pi\) |
−0.920210 | + | 0.391426i | \(0.871982\pi\) | |||||||
\(398\) | 4277.19 | 0.538684 | ||||||||
\(399\) | −2307.40 | − | 423.993i | −0.289511 | − | 0.0531985i | ||||
\(400\) | −859.610 | −0.107451 | ||||||||
\(401\) | 2784.34 | + | 4822.63i | 0.346742 | + | 0.600575i | 0.985669 | − | 0.168693i | \(-0.0539546\pi\) |
−0.638927 | + | 0.769268i | \(0.720621\pi\) | |||||||
\(402\) | −1241.39 | − | 2150.14i | −0.154017 | − | 0.266765i | ||||
\(403\) | −9441.34 | + | 16352.9i | −1.16701 | + | 2.02133i | ||||
\(404\) | 139.261 | + | 241.207i | 0.0171498 | + | 0.0297042i | ||||
\(405\) | 341.918 | − | 592.219i | 0.0419507 | − | 0.0726607i | ||||
\(406\) | −4534.68 | −0.554316 | ||||||||
\(407\) | 952.658 | 0.116023 | ||||||||
\(408\) | −931.325 | + | 1613.10i | −0.113009 | + | 0.195736i | ||||
\(409\) | −36.3567 | + | 62.9716i | −0.00439541 | + | 0.00761307i | −0.868215 | − | 0.496189i | \(-0.834732\pi\) |
0.863819 | + | 0.503802i | \(0.168066\pi\) | |||||||
\(410\) | −1212.69 | −0.146074 | ||||||||
\(411\) | −7241.05 | −0.869038 | ||||||||
\(412\) | 1288.69 | − | 2232.08i | 0.154100 | − | 0.266910i | ||||
\(413\) | −103.780 | − | 179.753i | −0.0123649 | − | 0.0214166i | ||||
\(414\) | −1538.59 | + | 2664.92i | −0.182651 | + | 0.316362i | ||||
\(415\) | 6043.93 | + | 10468.4i | 0.714904 | + | 1.23825i | ||||
\(416\) | −1082.47 | − | 1874.90i | −0.127578 | − | 0.220972i | ||||
\(417\) | 9327.13 | 1.09533 | ||||||||
\(418\) | 7736.05 | + | 1421.53i | 0.905222 | + | 0.166337i | ||||
\(419\) | 340.170 | 0.0396620 | 0.0198310 | − | 0.999803i | \(-0.493687\pi\) | ||||
0.0198310 | + | 0.999803i | \(0.493687\pi\) | |||||||
\(420\) | 478.301 | + | 828.441i | 0.0555683 | + | 0.0962471i | ||||
\(421\) | −738.497 | − | 1279.11i | −0.0854920 | − | 0.148077i | 0.820109 | − | 0.572208i | \(-0.193913\pi\) |
−0.905601 | + | 0.424131i | \(0.860580\pi\) | |||||||
\(422\) | 975.953 | − | 1690.40i | 0.112580 | − | 0.194994i | ||||
\(423\) | 933.043 | + | 1616.08i | 0.107249 | + | 0.185760i | ||||
\(424\) | 1046.09 | − | 1811.88i | 0.119818 | − | 0.207530i | ||||
\(425\) | 4169.67 | 0.475903 | ||||||||
\(426\) | 947.672 | 0.107781 | ||||||||
\(427\) | −3083.44 | + | 5340.67i | −0.349457 | + | 0.605276i | ||||
\(428\) | 378.909 | − | 656.289i | 0.0427926 | − | 0.0741190i | ||||
\(429\) | 9638.02 | 1.08468 | ||||||||
\(430\) | −2487.44 | −0.278965 | ||||||||
\(431\) | 6139.52 | − | 10634.0i | 0.686149 | − | 1.18844i | −0.286925 | − | 0.957953i | \(-0.592633\pi\) |
0.973074 | − | 0.230492i | \(-0.0740335\pi\) | |||||||
\(432\) | 216.000 | + | 374.123i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | −3105.77 | + | 5379.35i | −0.344697 | + | 0.597032i | −0.985299 | − | 0.170841i | \(-0.945352\pi\) |
0.640602 | + | 0.767873i | \(0.278685\pi\) | |||||||
\(434\) | 2635.42 | + | 4564.68i | 0.291484 | + | 0.504866i | ||||
\(435\) | −3040.82 | − | 5266.86i | −0.335164 | − | 0.580521i | ||||
\(436\) | −956.609 | −0.105076 | ||||||||
\(437\) | 4746.60 | + | 13338.9i | 0.519590 | + | 1.46016i | ||||
\(438\) | 6612.87 | 0.721405 | ||||||||
\(439\) | 6734.49 | + | 11664.5i | 0.732164 | + | 1.26814i | 0.955957 | + | 0.293508i | \(0.0948228\pi\) |
−0.223793 | + | 0.974637i | \(0.571844\pi\) | |||||||
\(440\) | −1603.60 | − | 2777.52i | −0.173747 | − | 0.300939i | ||||
\(441\) | 1142.28 | − | 1978.49i | 0.123343 | − | 0.213637i | ||||
\(442\) | 5250.70 | + | 9094.47i | 0.565046 | + | 0.978688i | ||||
\(443\) | −3705.54 | + | 6418.19i | −0.397417 | + | 0.688346i | −0.993406 | − | 0.114646i | \(-0.963427\pi\) |
0.595989 | + | 0.802992i | \(0.296760\pi\) | |||||||
\(444\) | 240.740 | 0.0257320 | ||||||||
\(445\) | −10885.6 | −1.15961 | ||||||||
\(446\) | 3575.45 | − | 6192.87i | 0.379602 | − | 0.657491i | ||||
\(447\) | −4378.65 | + | 7584.05i | −0.463318 | + | 0.802491i | ||||
\(448\) | −604.315 | −0.0637303 | ||||||||
\(449\) | −3345.93 | −0.351680 | −0.175840 | − | 0.984419i | \(-0.556264\pi\) | ||||
−0.175840 | + | 0.984419i | \(0.556264\pi\) | |||||||
\(450\) | 483.530 | − | 837.499i | 0.0506530 | − | 0.0877336i | ||||
\(451\) | 1705.27 | + | 2953.61i | 0.178044 | + | 0.308382i | ||||
\(452\) | −325.485 | + | 563.757i | −0.0338706 | + | 0.0586657i | ||||
\(453\) | −2873.57 | − | 4977.17i | −0.298040 | − | 0.516221i | ||||
\(454\) | 86.5237 | + | 149.864i | 0.00894441 | + | 0.0154922i | ||||
\(455\) | 5393.20 | 0.555686 | ||||||||
\(456\) | 1954.93 | + | 359.224i | 0.200763 | + | 0.0368908i | ||||
\(457\) | −542.238 | −0.0555029 | −0.0277515 | − | 0.999615i | \(-0.508835\pi\) | ||||
−0.0277515 | + | 0.999615i | \(0.508835\pi\) | |||||||
\(458\) | 3928.05 | + | 6803.59i | 0.400755 | + | 0.694128i | ||||
\(459\) | −1047.74 | − | 1814.74i | −0.106545 | − | 0.184542i | ||||
\(460\) | 2886.54 | − | 4999.64i | 0.292578 | − | 0.506759i | ||||
\(461\) | −1911.72 | − | 3311.19i | −0.193140 | − | 0.334528i | 0.753149 | − | 0.657850i | \(-0.228534\pi\) |
−0.946289 | + | 0.323322i | \(0.895200\pi\) | |||||||
\(462\) | 1345.16 | − | 2329.89i | 0.135460 | − | 0.234624i | ||||
\(463\) | −3750.37 | −0.376445 | −0.188223 | − | 0.982126i | \(-0.560273\pi\) | ||||
−0.188223 | + | 0.982126i | \(0.560273\pi\) | |||||||
\(464\) | 3841.96 | 0.384394 | ||||||||
\(465\) | −3534.47 | + | 6121.89i | −0.352489 | + | 0.610529i | ||||
\(466\) | −1020.03 | + | 1766.74i | −0.101399 | + | 0.175628i | ||||
\(467\) | −2981.61 | −0.295444 | −0.147722 | − | 0.989029i | \(-0.547194\pi\) | ||||
−0.147722 | + | 0.989029i | \(0.547194\pi\) | |||||||
\(468\) | 2435.56 | 0.240564 | ||||||||
\(469\) | −1953.61 | + | 3383.76i | −0.192344 | + | 0.333150i | ||||
\(470\) | −1750.48 | − | 3031.91i | −0.171795 | − | 0.297557i | ||||
\(471\) | −3805.03 | + | 6590.51i | −0.372243 | + | 0.644744i | ||||
\(472\) | 87.9270 | + | 152.294i | 0.00857451 | + | 0.0148515i | ||||
\(473\) | 3497.80 | + | 6058.37i | 0.340019 | + | 0.588930i | ||||
\(474\) | 2506.88 | 0.242921 | ||||||||
\(475\) | −1491.71 | − | 4192.01i | −0.144093 | − | 0.404931i | ||||
\(476\) | 2931.32 | 0.282262 | ||||||||
\(477\) | 1176.85 | + | 2038.37i | 0.112965 | + | 0.195662i | ||||
\(478\) | −264.681 | − | 458.441i | −0.0253268 | − | 0.0438674i | ||||
\(479\) | −7677.92 | + | 13298.6i | −0.732387 | + | 1.26853i | 0.223474 | + | 0.974710i | \(0.428260\pi\) |
−0.955860 | + | 0.293821i | \(0.905073\pi\) | |||||||
\(480\) | −405.236 | − | 701.889i | −0.0385342 | − | 0.0667432i | ||||
\(481\) | 678.631 | − | 1175.42i | 0.0643304 | − | 0.111423i | ||||
\(482\) | −344.774 | −0.0325810 | ||||||||
\(483\) | 4842.68 | 0.456210 | ||||||||
\(484\) | −1847.93 | + | 3200.71i | −0.173547 | + | 0.300592i | ||||
\(485\) | 585.744 | − | 1014.54i | 0.0548397 | − | 0.0949851i | ||||
\(486\) | −486.000 | −0.0453609 | ||||||||
\(487\) | 439.463 | 0.0408911 | 0.0204455 | − | 0.999791i | \(-0.493492\pi\) | ||||
0.0204455 | + | 0.999791i | \(0.493492\pi\) | |||||||
\(488\) | 2612.41 | − | 4524.83i | 0.242333 | − | 0.419733i | ||||
\(489\) | −2597.28 | − | 4498.62i | −0.240190 | − | 0.416022i | ||||
\(490\) | −2143.03 | + | 3711.84i | −0.197576 | + | 0.342212i | ||||
\(491\) | −9882.91 | − | 17117.7i | −0.908370 | − | 1.57334i | −0.816329 | − | 0.577587i | \(-0.803994\pi\) |
−0.0920410 | − | 0.995755i | \(-0.529339\pi\) | |||||||
\(492\) | 430.928 | + | 746.388i | 0.0394872 | + | 0.0683939i | ||||
\(493\) | −18636.0 | −1.70248 | ||||||||
\(494\) | 7264.75 | − | 8532.39i | 0.661653 | − | 0.777106i | ||||
\(495\) | 3608.10 | 0.327621 | ||||||||
\(496\) | −2232.84 | − | 3867.38i | −0.202132 | − | 0.350102i | ||||
\(497\) | −745.692 | − | 1291.58i | −0.0673016 | − | 0.116570i | ||||
\(498\) | 4295.41 | − | 7439.86i | 0.386509 | − | 0.669454i | ||||
\(499\) | −4079.86 | − | 7066.53i | −0.366011 | − | 0.633950i | 0.622926 | − | 0.782280i | \(-0.285944\pi\) |
−0.988938 | + | 0.148330i | \(0.952610\pi\) | |||||||
\(500\) | −3017.75 | + | 5226.90i | −0.269916 | + | 0.467508i | ||||
\(501\) | 4290.37 | 0.382594 | ||||||||
\(502\) | −9769.73 | −0.868614 | ||||||||
\(503\) | 9837.15 | − | 17038.4i | 0.872002 | − | 1.51035i | 0.0120790 | − | 0.999927i | \(-0.496155\pi\) |
0.859923 | − | 0.510424i | \(-0.170512\pi\) | |||||||
\(504\) | 339.927 | − | 588.771i | 0.0300428 | − | 0.0520356i | ||||
\(505\) | 587.850 | 0.0518000 | ||||||||
\(506\) | −16236.1 | −1.42645 | ||||||||
\(507\) | 3570.20 | − | 6183.76i | 0.312738 | − | 0.541677i | ||||
\(508\) | 194.757 | + | 337.328i | 0.0170097 | + | 0.0294616i | ||||
\(509\) | 3427.87 | − | 5937.25i | 0.298502 | − | 0.517021i | −0.677291 | − | 0.735715i | \(-0.736846\pi\) |
0.975794 | + | 0.218694i | \(0.0701796\pi\) | |||||||
\(510\) | 1965.66 | + | 3404.62i | 0.170668 | + | 0.295606i | ||||
\(511\) | −5203.46 | − | 9012.65i | −0.450465 | − | 0.780228i | ||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | −1449.63 | + | 1702.58i | −0.124762 | + | 0.146532i | ||||
\(514\) | 8045.28 | 0.690393 | ||||||||
\(515\) | −2719.92 | − | 4711.04i | −0.232726 | − | 0.403093i | ||||
\(516\) | 883.907 | + | 1530.97i | 0.0754105 | + | 0.130615i | ||||
\(517\) | −4922.99 | + | 8526.87i | −0.418787 | + | 0.725361i | ||||
\(518\) | −189.431 | − | 328.103i | −0.0160678 | − | 0.0278302i | ||||
\(519\) | 439.987 | − | 762.080i | 0.0372125 | − | 0.0644539i | ||||
\(520\) | −4569.34 | −0.385344 | ||||||||
\(521\) | −12666.6 | −1.06513 | −0.532567 | − | 0.846388i | \(-0.678773\pi\) | ||||
−0.532567 | + | 0.846388i | \(0.678773\pi\) | |||||||
\(522\) | −2161.10 | + | 3743.14i | −0.181205 | + | 0.313856i | ||||
\(523\) | −2358.62 | + | 4085.24i | −0.197199 | + | 0.341559i | −0.947619 | − | 0.319402i | \(-0.896518\pi\) |
0.750420 | + | 0.660961i | \(0.229851\pi\) | |||||||
\(524\) | 1517.59 | 0.126520 | ||||||||
\(525\) | −1521.90 | −0.126516 | ||||||||
\(526\) | 7142.12 | − | 12370.5i | 0.592036 | − | 1.02544i | ||||
\(527\) | 10830.7 | + | 18759.3i | 0.895243 | + | 1.55061i | ||||
\(528\) | −1139.68 | + | 1973.98i | −0.0939356 | + | 0.162701i | ||||
\(529\) | −8529.25 | − | 14773.1i | −0.701015 | − | 1.21419i | ||||
\(530\) | −2207.89 | − | 3824.17i | −0.180952 | − | 0.313418i | ||||
\(531\) | −197.836 | −0.0161682 | ||||||||
\(532\) | −1048.68 | − | 2947.02i | −0.0854629 | − | 0.240169i | ||||
\(533\) | 4859.03 | 0.394874 | ||||||||
\(534\) | 3868.18 | + | 6699.88i | 0.313469 | + | 0.542944i | ||||
\(535\) | −799.726 | − | 1385.17i | −0.0646265 | − | 0.111936i | ||||
\(536\) | 1655.18 | − | 2866.86i | 0.133382 | − | 0.231025i | ||||
\(537\) | −5765.27 | − | 9985.75i | −0.463296 | − | 0.802452i | ||||
\(538\) | −5081.26 | + | 8801.00i | −0.407191 | + | 0.705275i | ||||
\(539\) | 12054.0 | 0.963270 | ||||||||
\(540\) | 911.781 | 0.0726607 | ||||||||
\(541\) | −5870.58 | + | 10168.1i | −0.466536 | + | 0.808064i | −0.999269 | − | 0.0382192i | \(-0.987831\pi\) |
0.532733 | + | 0.846283i | \(0.321165\pi\) | |||||||
\(542\) | 2973.80 | − | 5150.78i | 0.235675 | − | 0.408201i | ||||
\(543\) | −5307.83 | −0.419486 | ||||||||
\(544\) | −2483.53 | −0.195736 | ||||||||
\(545\) | −1009.51 | + | 1748.53i | −0.0793445 | + | 0.137429i | ||||
\(546\) | −1916.47 | − | 3319.42i | −0.150215 | − | 0.260179i | ||||
\(547\) | 11131.1 | − | 19279.6i | 0.870073 | − | 1.50701i | 0.00815327 | − | 0.999967i | \(-0.497405\pi\) |
0.861920 | − | 0.507044i | \(-0.169262\pi\) | |||||||
\(548\) | −4827.37 | − | 8361.24i | −0.376305 | − | 0.651779i | ||||
\(549\) | 2938.96 | + | 5090.44i | 0.228473 | + | 0.395728i | ||||
\(550\) | 5102.48 | 0.395583 | ||||||||
\(551\) | 6667.07 | + | 18735.9i | 0.515475 | + | 1.44859i | ||||
\(552\) | −4102.91 | −0.316362 | ||||||||
\(553\) | −1972.58 | − | 3416.61i | −0.151687 | − | 0.262729i | ||||
\(554\) | −7778.48 | − | 13472.7i | −0.596527 | − | 1.03322i | ||||
\(555\) | 254.053 | − | 440.033i | 0.0194306 | − | 0.0336547i | ||||
\(556\) | 6218.09 | + | 10770.0i | 0.474291 | + | 0.821496i | ||||
\(557\) | 9813.87 | − | 16998.1i | 0.746548 | − | 1.29306i | −0.202920 | − | 0.979195i | \(-0.565043\pi\) |
0.949468 | − | 0.313864i | \(-0.101623\pi\) | |||||||
\(558\) | 5023.88 | 0.381143 | ||||||||
\(559\) | 9966.71 | 0.754109 | ||||||||
\(560\) | −637.734 | + | 1104.59i | −0.0481236 | + | 0.0833525i | ||||
\(561\) | 5528.17 | − | 9575.07i | 0.416042 | − | 0.720606i | ||||
\(562\) | 4441.36 | 0.333358 | ||||||||
\(563\) | 9810.37 | 0.734384 | 0.367192 | − | 0.930145i | \(-0.380319\pi\) | ||||
0.367192 | + | 0.930145i | \(0.380319\pi\) | |||||||
\(564\) | −1244.06 | + | 2154.77i | −0.0928799 | + | 0.160873i | ||||
\(565\) | 686.970 | + | 1189.87i | 0.0511523 | + | 0.0885984i | ||||
\(566\) | 7616.34 | − | 13191.9i | 0.565616 | − | 0.979676i | ||||
\(567\) | 382.418 | + | 662.367i | 0.0283246 | + | 0.0490596i | ||||
\(568\) | 631.781 | + | 1094.28i | 0.0466707 | + | 0.0808360i | ||||
\(569\) | 2528.37 | 0.186282 | 0.0931412 | − | 0.995653i | \(-0.470309\pi\) | ||||
0.0931412 | + | 0.995653i | \(0.470309\pi\) | |||||||
\(570\) | 2719.64 | − | 3194.20i | 0.199848 | − | 0.234720i | ||||
\(571\) | −21892.0 | −1.60447 | −0.802233 | − | 0.597011i | \(-0.796355\pi\) | ||||
−0.802233 | + | 0.597011i | \(0.796355\pi\) | |||||||
\(572\) | 6425.35 | + | 11129.0i | 0.469680 | + | 0.813510i | ||||
\(573\) | −756.009 | − | 1309.45i | −0.0551182 | − | 0.0954676i | ||||
\(574\) | 678.166 | − | 1174.62i | 0.0493138 | − | 0.0854140i | ||||
\(575\) | 4592.32 | + | 7954.14i | 0.333066 | + | 0.576888i | ||||
\(576\) | −288.000 | + | 498.831i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −4002.61 | −0.288788 | −0.144394 | − | 0.989520i | \(-0.546123\pi\) | ||||
−0.144394 | + | 0.989520i | \(0.546123\pi\) | |||||||
\(578\) | 2220.76 | 0.159812 | ||||||||
\(579\) | −3251.38 | + | 5631.56i | −0.233373 | + | 0.404213i | ||||
\(580\) | 4054.43 | − | 7022.48i | 0.290261 | − | 0.502746i | ||||
\(581\) | −13519.7 | −0.965388 | ||||||||
\(582\) | −832.573 | −0.0592977 | ||||||||
\(583\) | −6209.40 | + | 10755.0i | −0.441110 | + | 0.764025i | ||||
\(584\) | 4408.58 | + | 7635.89i | 0.312377 | + | 0.541054i | ||||
\(585\) | 2570.25 | − | 4451.81i | 0.181653 | − | 0.314632i | ||||
\(586\) | 9036.61 | + | 15651.9i | 0.637029 | + | 1.10337i | ||||
\(587\) | −12259.2 | − | 21233.6i | −0.861998 | − | 1.49302i | −0.869997 | − | 0.493056i | \(-0.835880\pi\) |
0.00799928 | − | 0.999968i | \(-0.497454\pi\) | |||||||
\(588\) | 3046.09 | 0.213637 | ||||||||
\(589\) | 14985.1 | − | 17599.9i | 1.04831 | − | 1.23123i | ||||
\(590\) | 371.158 | 0.0258989 | ||||||||
\(591\) | 3166.65 | + | 5484.80i | 0.220404 | + | 0.381750i | ||||
\(592\) | 160.493 | + | 277.983i | 0.0111423 | + | 0.0192990i | ||||
\(593\) | 8849.35 | − | 15327.5i | 0.612815 | − | 1.06143i | −0.377948 | − | 0.925827i | \(-0.623370\pi\) |
0.990764 | − | 0.135600i | \(-0.0432963\pi\) | |||||||
\(594\) | −1282.13 | − | 2220.72i | −0.0885633 | − | 0.153396i | ||||
\(595\) | 3093.43 | − | 5357.97i | 0.213140 | − | 0.369169i | ||||
\(596\) | −11676.4 | −0.802491 | ||||||||
\(597\) | −6415.78 | −0.439833 | ||||||||
\(598\) | −11565.9 | + | 20032.6i | −0.790908 | + | 1.36989i | ||||
\(599\) | −1804.00 | + | 3124.63i | −0.123054 | + | 0.213137i | −0.920971 | − | 0.389632i | \(-0.872602\pi\) |
0.797916 | + | 0.602768i | \(0.205936\pi\) | |||||||
\(600\) | 1289.41 | 0.0877336 | ||||||||
\(601\) | 23195.0 | 1.57429 | 0.787143 | − | 0.616771i | \(-0.211559\pi\) | ||||
0.787143 | + | 0.616771i | \(0.211559\pi\) | |||||||
\(602\) | 1391.04 | − | 2409.34i | 0.0941767 | − | 0.163119i | ||||
\(603\) | 1862.08 | + | 3225.22i | 0.125754 | + | 0.217813i | ||||
\(604\) | 3831.43 | − | 6636.23i | 0.258110 | − | 0.447060i | ||||
\(605\) | 3900.25 | + | 6755.43i | 0.262095 | + | 0.453962i | ||||
\(606\) | −208.892 | − | 361.811i | −0.0140027 | − | 0.0242534i | ||||
\(607\) | −3485.49 | −0.233067 | −0.116534 | − | 0.993187i | \(-0.537178\pi\) | ||||
−0.116534 | + | 0.993187i | \(0.537178\pi\) | |||||||
\(608\) | 888.488 | + | 2496.84i | 0.0592647 | + | 0.166546i | ||||
\(609\) | 6802.02 | 0.452597 | ||||||||
\(610\) | −5513.77 | − | 9550.13i | −0.365977 | − | 0.633891i | ||||
\(611\) | 7013.84 | + | 12148.3i | 0.464402 | + | 0.804368i | ||||
\(612\) | 1396.99 | − | 2419.65i | 0.0922711 | − | 0.159818i | ||||
\(613\) | 5476.62 | + | 9485.79i | 0.360846 | + | 0.625004i | 0.988100 | − | 0.153811i | \(-0.0491546\pi\) |
−0.627254 | + | 0.778815i | \(0.715821\pi\) | |||||||
\(614\) | −7797.17 | + | 13505.1i | −0.512489 | + | 0.887657i | ||||
\(615\) | 1819.03 | 0.119269 | ||||||||
\(616\) | 3587.10 | 0.234624 | ||||||||
\(617\) | −3504.76 | + | 6070.42i | −0.228681 | + | 0.396088i | −0.957418 | − | 0.288707i | \(-0.906775\pi\) |
0.728736 | + | 0.684794i | \(0.240108\pi\) | |||||||
\(618\) | −1933.04 | + | 3348.12i | −0.125822 | + | 0.217931i | ||||
\(619\) | 24225.1 | 1.57301 | 0.786503 | − | 0.617587i | \(-0.211890\pi\) | ||||
0.786503 | + | 0.617587i | \(0.211890\pi\) | |||||||
\(620\) | −9425.26 | −0.610529 | ||||||||
\(621\) | 2307.89 | − | 3997.38i | 0.149134 | − | 0.258308i | ||||
\(622\) | −2737.49 | − | 4741.47i | −0.176468 | − | 0.305652i | ||||
\(623\) | 6087.49 | − | 10543.8i | 0.391477 | − | 0.678058i | ||||
\(624\) | 1623.71 | + | 2812.34i | 0.104167 | + | 0.180423i | ||||
\(625\) | 3011.43 | + | 5215.95i | 0.192731 | + | 0.333821i | ||||
\(626\) | −15292.3 | −0.976363 | ||||||||
\(627\) | −11604.1 | − | 2132.29i | −0.739110 | − | 0.135814i | ||||
\(628\) | −10146.7 | −0.644744 | ||||||||
\(629\) | −778.497 | − | 1348.40i | −0.0493493 | − | 0.0854755i | ||||
\(630\) | −717.451 | − | 1242.66i | −0.0453713 | − | 0.0785855i | ||||
\(631\) | −7452.24 | + | 12907.7i | −0.470157 | + | 0.814336i | −0.999418 | − | 0.0341235i | \(-0.989136\pi\) |
0.529261 | + | 0.848459i | \(0.322469\pi\) | |||||||
\(632\) | 1671.25 | + | 2894.69i | 0.105188 | + | 0.182191i | ||||
\(633\) | −1463.93 | + | 2535.60i | −0.0919210 | + | 0.159212i | ||||
\(634\) | −12840.8 | −0.804373 | ||||||||
\(635\) | 822.108 | 0.0513769 | ||||||||
\(636\) | −1569.14 | + | 2717.83i | −0.0978308 | + | 0.169448i | ||||
\(637\) | 8586.74 | − | 14872.7i | 0.534095 | − | 0.925081i | ||||
\(638\) | −22805.2 | −1.41515 | ||||||||
\(639\) | −1421.51 | −0.0880031 | ||||||||
\(640\) | 540.315 | − | 935.852i | 0.0333716 | − | 0.0578013i | ||||
\(641\) | 8374.53 | + | 14505.1i | 0.516028 | + | 0.893787i | 0.999827 | + | 0.0186079i | \(0.00592342\pi\) |
−0.483799 | + | 0.875179i | \(0.660743\pi\) | |||||||
\(642\) | −568.363 | + | 984.434i | −0.0349400 | + | 0.0605179i | ||||
\(643\) | 3554.81 | + | 6157.10i | 0.218022 | + | 0.377624i | 0.954203 | − | 0.299160i | \(-0.0967064\pi\) |
−0.736181 | + | 0.676784i | \(0.763373\pi\) | |||||||
\(644\) | 3228.45 | + | 5591.84i | 0.197545 | + | 0.342157i | ||||
\(645\) | 3731.15 | 0.227774 | ||||||||
\(646\) | −4309.75 | − | 12111.3i | −0.262484 | − | 0.737636i | ||||
\(647\) | 6637.82 | 0.403338 | 0.201669 | − | 0.979454i | \(-0.435363\pi\) | ||||
0.201669 | + | 0.979454i | \(0.435363\pi\) | |||||||
\(648\) | −324.000 | − | 561.184i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | −521.918 | − | 903.988i | −0.0315671 | − | 0.0546759i | ||||
\(650\) | 3634.78 | − | 6295.62i | 0.219335 | − | 0.379899i | ||||
\(651\) | −3953.13 | − | 6847.02i | −0.237996 | − | 0.412221i | ||||
\(652\) | 3463.04 | − | 5998.16i | 0.208011 | − | 0.360285i | ||||
\(653\) | −18762.0 | −1.12437 | −0.562184 | − | 0.827012i | \(-0.690039\pi\) | ||||
−0.562184 | + | 0.827012i | \(0.690039\pi\) | |||||||
\(654\) | 1434.91 | 0.0857944 | ||||||||
\(655\) | 1601.52 | − | 2773.91i | 0.0955365 | − | 0.165474i | ||||
\(656\) | −574.570 | + | 995.185i | −0.0341969 | + | 0.0592308i | ||||
\(657\) | −9919.31 | −0.589024 | ||||||||
\(658\) | 3915.64 | 0.231987 | ||||||||
\(659\) | −3078.28 | + | 5331.74i | −0.181962 | + | 0.315167i | −0.942549 | − | 0.334069i | \(-0.891578\pi\) |
0.760587 | + | 0.649236i | \(0.224911\pi\) | |||||||
\(660\) | 2405.40 | + | 4166.28i | 0.141864 | + | 0.245716i | ||||
\(661\) | −13082.6 | + | 22659.7i | −0.769824 | + | 1.33337i | 0.167835 | + | 0.985815i | \(0.446322\pi\) |
−0.937658 | + | 0.347558i | \(0.887011\pi\) | |||||||
\(662\) | 4594.77 | + | 7958.38i | 0.269760 | + | 0.467238i | ||||
\(663\) | −7876.04 | − | 13641.7i | −0.461358 | − | 0.799095i | ||||
\(664\) | 11454.4 | 0.669454 | ||||||||
\(665\) | −6493.36 | − | 1193.18i | −0.378649 | − | 0.0695780i | ||||
\(666\) | −361.110 | −0.0210101 | ||||||||
\(667\) | −20525.1 | − | 35550.4i | −1.19150 | − | 2.06375i | ||||
\(668\) | 2860.25 | + | 4954.09i | 0.165668 | + | 0.286946i | ||||
\(669\) | −5363.18 | + | 9289.30i | −0.309944 | + | 0.536839i | ||||
\(670\) | −3493.43 | − | 6050.80i | −0.201437 | − | 0.348900i | ||||
\(671\) | −15506.8 | + | 26858.5i | −0.892150 | + | 1.54525i | ||||
\(672\) | 906.472 | 0.0520356 | ||||||||
\(673\) | 31028.8 | 1.77723 | 0.888613 | − | 0.458657i | \(-0.151669\pi\) | ||||
0.888613 | + | 0.458657i | \(0.151669\pi\) | |||||||
\(674\) | −6611.27 | + | 11451.1i | −0.377829 | + | 0.654419i | ||||
\(675\) | −725.296 | + | 1256.25i | −0.0413580 | + | 0.0716341i | ||||
\(676\) | 9520.52 | 0.541677 | ||||||||
\(677\) | −4341.55 | −0.246469 | −0.123234 | − | 0.992378i | \(-0.539327\pi\) | ||||
−0.123234 | + | 0.992378i | \(0.539327\pi\) | |||||||
\(678\) | 488.228 | − | 845.635i | 0.0276553 | − | 0.0479003i | ||||
\(679\) | 655.125 | + | 1134.71i | 0.0370271 | + | 0.0641328i | ||||
\(680\) | −2620.88 | + | 4539.49i | −0.147803 | + | 0.256002i | ||||
\(681\) | −129.786 | − | 224.795i | −0.00730308 | − | 0.0126493i | ||||
\(682\) | 13253.7 | + | 22956.1i | 0.744149 | + | 1.28890i | ||||
\(683\) | 16457.2 | 0.921986 | 0.460993 | − | 0.887404i | \(-0.347493\pi\) | ||||
0.460993 | + | 0.887404i | \(0.347493\pi\) | |||||||
\(684\) | −2932.39 | − | 538.837i | −0.163922 | − | 0.0301213i | ||||
\(685\) | −20377.3 | −1.13661 | ||||||||
\(686\) | −5635.62 | − | 9761.18i | −0.313657 | − | 0.543270i | ||||
\(687\) | −5892.08 | − | 10205.4i | −0.327215 | − | 0.566753i | ||||
\(688\) | −1178.54 | + | 2041.30i | −0.0653074 | + | 0.113116i | ||||
\(689\) | 8846.60 | + | 15322.8i | 0.489156 | + | 0.847244i | ||||
\(690\) | −4329.81 | + | 7499.45i | −0.238889 | + | 0.413767i | ||||
\(691\) | 2522.21 | 0.138856 | 0.0694280 | − | 0.997587i | \(-0.477883\pi\) | ||||
0.0694280 | + | 0.997587i | \(0.477883\pi\) | |||||||
\(692\) | 1173.30 | 0.0644539 | ||||||||
\(693\) | −2017.74 | + | 3494.83i | −0.110603 | + | 0.191569i | ||||
\(694\) | 2498.63 | − | 4327.75i | 0.136667 | − | 0.236714i | ||||
\(695\) | 26247.8 | 1.43257 | ||||||||
\(696\) | −5762.95 | −0.313856 | ||||||||
\(697\) | 2787.04 | − | 4827.29i | 0.151459 | − | 0.262334i | ||||
\(698\) | −10330.5 | − | 17893.0i | −0.560195 | − | 0.970286i | ||||
\(699\) | 1530.04 | − | 2650.10i | 0.0827917 | − | 0.143399i | ||||
\(700\) | −1014.60 | − | 1757.34i | −0.0547832 | − | 0.0948873i | ||||
\(701\) | −2009.91 | − | 3481.27i | −0.108293 | − | 0.187569i | 0.806786 | − | 0.590844i | \(-0.201205\pi\) |
−0.915079 | + | 0.403275i | \(0.867872\pi\) | |||||||
\(702\) | −3653.34 | −0.196420 | ||||||||
\(703\) | −1077.11 | + | 1265.06i | −0.0577867 | + | 0.0678700i | ||||
\(704\) | −3039.13 | −0.162701 | ||||||||
\(705\) | 2625.71 | + | 4547.87i | 0.140270 | + | 0.242954i | ||||
\(706\) | −2608.83 | − | 4518.62i | −0.139072 | − | 0.240879i | ||||
\(707\) | −328.740 | + | 569.395i | −0.0174874 | + | 0.0302890i | ||||
\(708\) | −131.890 | − | 228.441i | −0.00700106 | − | 0.0121262i | ||||
\(709\) | 5026.45 | − | 8706.07i | 0.266252 | − | 0.461161i | −0.701639 | − | 0.712533i | \(-0.747548\pi\) |
0.967891 | + | 0.251371i | \(0.0808814\pi\) | |||||||
\(710\) | 2666.88 | 0.140966 | ||||||||
\(711\) | −3760.32 | −0.198344 | ||||||||
\(712\) | −5157.57 | + | 8933.18i | −0.271472 | + | 0.470204i | ||||
\(713\) | −23857.1 | + | 41321.7i | −1.25309 | + | 2.17042i | ||||
\(714\) | −4396.98 | −0.230466 | ||||||||
\(715\) | 27122.7 | 1.41865 | ||||||||
\(716\) | 7687.03 | − | 13314.3i | 0.401226 | − | 0.694944i | ||||
\(717\) | 397.021 | + | 687.661i | 0.0206793 | + | 0.0358175i | ||||
\(718\) | −4150.33 | + | 7188.58i | −0.215723 | + | 0.373643i | ||||
\(719\) | −5215.18 | − | 9032.95i | −0.270505 | − | 0.468529i | 0.698486 | − | 0.715624i | \(-0.253857\pi\) |
−0.968991 | + | 0.247095i | \(0.920524\pi\) | |||||||
\(720\) | 607.854 | + | 1052.83i | 0.0314630 | + | 0.0544956i | ||||
\(721\) | 6084.18 | 0.314268 | ||||||||
\(722\) | −10634.4 | + | 8665.67i | −0.548158 | + | 0.446680i | ||||
\(723\) | 517.161 | 0.0266022 | ||||||||
\(724\) | −3538.56 | − | 6128.96i | −0.181643 | − | 0.314615i | ||||
\(725\) | 6450.37 | + | 11172.4i | 0.330429 | + | 0.572319i | ||||
\(726\) | 2771.89 | − | 4801.06i | 0.141701 | − | 0.245433i | ||||
\(727\) | 10846.7 | + | 18787.1i | 0.553346 | + | 0.958424i | 0.998030 | + | 0.0627365i | \(0.0199828\pi\) |
−0.444684 | + | 0.895688i | \(0.646684\pi\) | |||||||
\(728\) | 2555.29 | − | 4425.89i | 0.130090 | − | 0.225322i | ||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 18609.5 | 0.943520 | ||||||||
\(731\) | 5716.70 | − | 9901.61i | 0.289247 | − | 0.500991i | ||||
\(732\) | −3918.62 | + | 6787.25i | −0.197864 | + | 0.342710i | ||||
\(733\) | −3382.86 | −0.170462 | −0.0852310 | − | 0.996361i | \(-0.527163\pi\) | ||||
−0.0852310 | + | 0.996361i | \(0.527163\pi\) | |||||||
\(734\) | −14741.0 | −0.741279 | ||||||||
\(735\) | 3214.54 | − | 5567.75i | 0.161320 | − | 0.279415i | ||||
\(736\) | −2735.27 | − | 4737.64i | −0.136989 | − | 0.237271i | ||||
\(737\) | −9824.84 | + | 17017.1i | −0.491048 | + | 0.850521i | ||||
\(738\) | −646.391 | − | 1119.58i | −0.0322412 | − | 0.0558434i | ||||
\(739\) | −4008.94 | − | 6943.69i | −0.199555 | − | 0.345640i | 0.748829 | − | 0.662763i | \(-0.230616\pi\) |
−0.948384 | + | 0.317123i | \(0.897283\pi\) | |||||||
\(740\) | 677.476 | 0.0336547 | ||||||||
\(741\) | −10897.1 | + | 12798.6i | −0.540237 | + | 0.634504i | ||||
\(742\) | 4938.82 | 0.244353 | ||||||||
\(743\) | −4678.96 | − | 8104.19i | −0.231029 | − | 0.400153i | 0.727082 | − | 0.686550i | \(-0.240876\pi\) |
−0.958111 | + | 0.286397i | \(0.907542\pi\) | |||||||
\(744\) | 3349.25 | + | 5801.08i | 0.165040 | + | 0.285857i | ||||
\(745\) | −12322.1 | + | 21342.6i | −0.605971 | + | 1.04957i | ||||
\(746\) | −13166.5 | − | 22805.1i | −0.646195 | − | 1.11924i | ||||
\(747\) | −6443.11 | + | 11159.8i | −0.315584 | + | 0.546607i | ||||
\(748\) | 14741.8 | 0.720606 | ||||||||
\(749\) | 1788.91 | 0.0872700 | ||||||||
\(750\) | 4526.63 | − | 7840.35i | 0.220385 | − | 0.381719i | ||||
\(751\) | 6483.64 | − | 11230.0i | 0.315035 | − | 0.545657i | −0.664410 | − | 0.747368i | \(-0.731317\pi\) |
0.979445 | + | 0.201712i | \(0.0646504\pi\) | |||||||
\(752\) | −3317.49 | −0.160873 | ||||||||
\(753\) | 14654.6 | 0.709221 | ||||||||
\(754\) | −16245.4 | + | 28137.8i | −0.784644 | + | 1.35904i | ||||
\(755\) | −8086.63 | − | 14006.5i | −0.389805 | − | 0.675162i | ||||
\(756\) | −509.890 | + | 883.156i | −0.0245298 | + | 0.0424869i | ||||
\(757\) | −13890.7 | − | 24059.4i | −0.666931 | − | 1.15516i | −0.978758 | − | 0.205019i | \(-0.934274\pi\) |
0.311827 | − | 0.950139i | \(-0.399059\pi\) | |||||||
\(758\) | 14284.2 | + | 24740.9i | 0.684464 | + | 1.18553i | ||||
\(759\) | 24354.1 | 1.16469 | ||||||||
\(760\) | 5501.44 | + | 1010.91i | 0.262576 | + | 0.0482493i | ||||
\(761\) | 26066.1 | 1.24165 | 0.620825 | − | 0.783949i | \(-0.286798\pi\) | ||||
0.620825 | + | 0.783949i | \(0.286798\pi\) | |||||||
\(762\) | −292.135 | − | 505.992i | −0.0138884 | − | 0.0240553i | ||||
\(763\) | −1129.09 | − | 1955.64i | −0.0535724 | − | 0.0927901i | ||||
\(764\) | 1008.01 | − | 1745.93i | 0.0477338 | − | 0.0826774i | ||||
\(765\) | −2948.49 | − | 5106.93i | −0.139350 | − | 0.241361i | ||||
\(766\) | 9458.62 | − | 16382.8i | 0.446154 | − | 0.772761i | ||||
\(767\) | −1487.16 | −0.0700109 | ||||||||
\(768\) | −768.000 | −0.0360844 | ||||||||
\(769\) | 18417.7 | − | 31900.4i | 0.863665 | − | 1.49591i | −0.00470099 | − | 0.999989i | \(-0.501496\pi\) |
0.868366 | − | 0.495923i | \(-0.165170\pi\) | |||||||
\(770\) | 3785.47 | − | 6556.63i | 0.177167 | − | 0.306863i | ||||
\(771\) | −12067.9 | −0.563703 | ||||||||
\(772\) | −8670.35 | −0.404213 | ||||||||
\(773\) | −5604.20 | + | 9706.76i | −0.260762 | + | 0.451653i | −0.966445 | − | 0.256875i | \(-0.917307\pi\) |
0.705683 | + | 0.708528i | \(0.250640\pi\) | |||||||
\(774\) | −1325.86 | − | 2296.46i | −0.0615724 | − | 0.106647i | ||||
\(775\) | 7497.53 | − | 12986.1i | 0.347509 | − | 0.601903i | ||||
\(776\) | −555.048 | − | 961.372i | −0.0256766 | − | 0.0444733i | ||||
\(777\) | 284.146 | + | 492.155i | 0.0131193 | + | 0.0227233i | ||||
\(778\) | −14201.9 | −0.654452 | ||||||||
\(779\) | −5850.22 | − | 1075.00i | −0.269071 | − | 0.0494426i | ||||
\(780\) | 6854.01 | 0.314632 | ||||||||
\(781\) | −3750.13 | − | 6495.42i | −0.171819 | − | 0.297598i | ||||
\(782\) | 13267.9 | + | 22980.6i | 0.606724 | + | 1.05088i | ||||
\(783\) | 3241.66 | − | 5614.71i | 0.147953 | − | 0.256262i | ||||
\(784\) | 2030.73 | + | 3517.32i | 0.0925076 | + | 0.160228i | ||||
\(785\) | −10707.9 | + | 18546.6i | −0.486854 | + | 0.843257i | ||||
\(786\) | −2276.39 | −0.103303 | ||||||||
\(787\) | −25466.9 | −1.15349 | −0.576745 | − | 0.816924i | \(-0.695677\pi\) | ||||
−0.576745 | + | 0.816924i | \(0.695677\pi\) | |||||||
\(788\) | −4222.20 | + | 7313.07i | −0.190875 | + | 0.330606i | ||||
\(789\) | −10713.2 | + | 18555.8i | −0.483396 | + | 0.837266i | ||||
\(790\) | 7054.70 | 0.317715 | ||||||||
\(791\) | −1536.68 | −0.0690748 | ||||||||
\(792\) | 1709.51 | − | 2960.96i | 0.0766981 | − | 0.132845i | ||||
\(793\) | 22092.7 | + | 38265.7i | 0.989324 | + | 1.71356i | ||||
\(794\) | −1916.16 | + | 3318.89i | −0.0856449 | + | 0.148341i | ||||
\(795\) | 3311.83 | + | 5736.26i | 0.147746 | + | 0.255904i | ||||
\(796\) | −4277.19 | − | 7408.31i | −0.190453 | − | 0.329875i | ||||
\(797\) | 31745.4 | 1.41089 | 0.705446 | − | 0.708764i | \(-0.250747\pi\) | ||||
0.705446 | + | 0.708764i | \(0.250747\pi\) | |||||||
\(798\) | 1573.03 | + | 4420.54i | 0.0697801 | + | 0.196097i | ||||
\(799\) | 16092.0 | 0.712507 | ||||||||
\(800\) | 859.610 | + | 1488.89i | 0.0379897 | + | 0.0658002i | ||||
\(801\) | −5802.27 | − | 10049.8i | −0.255946 | − | 0.443312i | ||||
\(802\) | 5568.69 | − | 9645.25i | 0.245184 | − | 0.424670i | ||||
\(803\) | −26168.5 | − | 45325.2i | −1.15002 | − | 1.99189i | ||||
\(804\) | −2482.77 | + | 4300.29i | −0.108906 | + | 0.188631i | ||||
\(805\) | 13628.0 | 0.596674 | ||||||||
\(806\) | 37765.3 | 1.65041 | ||||||||
\(807\) | 7621.89 | − | 13201.5i | 0.332470 | − | 0.575855i | ||||
\(808\) | 278.522 | − | 482.415i | 0.0121267 | − | 0.0210041i | ||||
\(809\) | −14106.2 | −0.613040 | −0.306520 | − | 0.951864i | \(-0.599165\pi\) | ||||
−0.306520 | + | 0.951864i | \(0.599165\pi\) | |||||||
\(810\) | −1367.67 | −0.0593273 | ||||||||
\(811\) | −21337.7 | + | 36958.0i | −0.923882 | + | 1.60021i | −0.130532 | + | 0.991444i | \(0.541669\pi\) |
−0.793350 | + | 0.608766i | \(0.791665\pi\) | |||||||
\(812\) | 4534.68 | + | 7854.29i | 0.195980 | + | 0.339448i | ||||
\(813\) | −4460.71 | + | 7726.17i | −0.192428 | + | 0.333295i | ||||
\(814\) | −952.658 | − | 1650.05i | −0.0410204 | − | 0.0710495i | ||||
\(815\) | −7309.11 | − | 12659.7i | −0.314143 | − | 0.544112i | ||||
\(816\) | 3725.30 | 0.159818 | ||||||||
\(817\) | −11999.8 | − | 2205.01i | −0.513856 | − | 0.0944228i | ||||
\(818\) | 145.427 | 0.00621604 | ||||||||
\(819\) | 2874.70 | + | 4979.12i | 0.122650 | + | 0.212435i | ||||
\(820\) | 1212.69 | + | 2100.44i | 0.0516451 | + | 0.0894519i | ||||
\(821\) | 9719.65 | − | 16834.9i | 0.413177 | − | 0.715643i | −0.582058 | − | 0.813147i | \(-0.697752\pi\) |
0.995235 | + | 0.0975038i | \(0.0310858\pi\) | |||||||
\(822\) | 7241.05 | + | 12541.9i | 0.307251 | + | 0.532175i | ||||
\(823\) | 12511.7 | − | 21670.9i | 0.529928 | − | 0.917863i | −0.469462 | − | 0.882953i | \(-0.655552\pi\) |
0.999390 | − | 0.0349103i | \(-0.0111145\pi\) | |||||||
\(824\) | −5154.77 | −0.217931 | ||||||||
\(825\) | −7653.72 | −0.322992 | ||||||||
\(826\) | −207.561 | + | 359.506i | −0.00874330 | + | 0.0151438i | ||||
\(827\) | 16772.9 | − | 29051.5i | 0.705260 | − | 1.22155i | −0.261338 | − | 0.965247i | \(-0.584164\pi\) |
0.966598 | − | 0.256298i | \(-0.0825029\pi\) | |||||||
\(828\) | 6154.37 | 0.258308 | ||||||||
\(829\) | 5555.52 | 0.232752 | 0.116376 | − | 0.993205i | \(-0.462872\pi\) | ||||
0.116376 | + | 0.993205i | \(0.462872\pi\) | |||||||
\(830\) | 12087.9 | − | 20936.8i | 0.505513 | − | 0.875575i | ||||
\(831\) | 11667.7 | + | 20209.1i | 0.487062 | + | 0.843617i | ||||
\(832\) | −2164.94 | + | 3749.79i | −0.0902114 | + | 0.156251i | ||||
\(833\) | −9850.35 | − | 17061.3i | −0.409717 | − | 0.709651i | ||||
\(834\) | −9327.13 | − | 16155.1i | −0.387257 | − | 0.670749i | ||||
\(835\) | 12073.7 | 0.500392 | ||||||||
\(836\) | −5273.90 | − | 14820.8i | −0.218184 | − | 0.613142i | ||||
\(837\) | −7535.82 | −0.311202 | ||||||||
\(838\) | −340.170 | − | 589.192i | −0.0140227 | − | 0.0242879i | ||||
\(839\) | −20491.2 | − | 35491.8i | −0.843188 | − | 1.46044i | −0.887185 | − | 0.461413i | \(-0.847343\pi\) |
0.0439970 | − | 0.999032i | \(-0.485991\pi\) | |||||||
\(840\) | 956.602 | − | 1656.88i | 0.0392927 | − | 0.0680570i | ||||
\(841\) | −16635.0 | − | 28812.6i | −0.682068 | − | 1.18138i | ||||
\(842\) | −1476.99 | + | 2558.23i | −0.0604520 | + | 0.104706i | ||||
\(843\) | −6662.04 | −0.272186 | ||||||||
\(844\) | −3903.81 | −0.159212 | ||||||||
\(845\) | 10047.0 | − | 17402.0i | 0.409028 | − | 0.708456i | ||||
\(846\) | 1866.09 | − | 3232.16i | 0.0758362 | − | 0.131352i | ||||
\(847\) | −8724.46 | −0.353927 | ||||||||
\(848\) | −4184.37 | −0.169448 | ||||||||
\(849\) | −11424.5 | + | 19787.8i | −0.461824 | + | 0.799902i | ||||
\(850\) | −4169.67 | − | 7222.08i | −0.168257 | − | 0.291430i | ||||
\(851\) | 1714.82 | − | 2970.15i | 0.0690754 | − | 0.119642i | ||||
\(852\) | −947.672 | − | 1641.42i | −0.0381064 | − | 0.0660023i | ||||
\(853\) | 15804.6 | + | 27374.4i | 0.634397 | + | 1.09881i | 0.986643 | + | 0.162900i | \(0.0520849\pi\) |
−0.352245 | + | 0.935908i | \(0.614582\pi\) | |||||||
\(854\) | 12333.7 | 0.494206 | ||||||||
\(855\) | −4079.46 | + | 4791.30i | −0.163175 | + | 0.191648i | ||||
\(856\) | −1515.63 | −0.0605179 | ||||||||
\(857\) | −10481.8 | − | 18155.1i | −0.417798 | − | 0.723647i | 0.577920 | − | 0.816094i | \(-0.303865\pi\) |
−0.995718 | + | 0.0924465i | \(0.970531\pi\) | |||||||
\(858\) | −9638.02 | − | 16693.5i | −0.383492 | − | 0.664228i | ||||
\(859\) | −1948.32 | + | 3374.59i | −0.0773875 | + | 0.134039i | −0.902122 | − | 0.431481i | \(-0.857991\pi\) |
0.824735 | + | 0.565520i | \(0.191325\pi\) | |||||||
\(860\) | 2487.44 | + | 4308.37i | 0.0986289 | + | 0.170830i | ||||
\(861\) | −1017.25 | + | 1761.93i | −0.0402645 | + | 0.0697402i | ||||
\(862\) | −24558.1 | −0.970361 | ||||||||
\(863\) | 2630.83 | 0.103771 | 0.0518856 | − | 0.998653i | \(-0.483477\pi\) | ||||
0.0518856 | + | 0.998653i | \(0.483477\pi\) | |||||||
\(864\) | 432.000 | − | 748.246i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | 1238.18 | − | 2144.60i | 0.0486700 | − | 0.0842989i | ||||
\(866\) | 12423.1 | 0.487475 | ||||||||
\(867\) | −3331.14 | −0.130486 | ||||||||
\(868\) | 5270.84 | − | 9129.36i | 0.206111 | − | 0.356994i | ||||
\(869\) | −9920.23 | − | 17182.3i | −0.387251 | − | 0.670738i | ||||
\(870\) | −6081.65 | + | 10533.7i | −0.236997 | + | 0.410490i | ||||
\(871\) | 13997.6 | + | 24244.5i | 0.544534 | + | 0.943161i | ||||
\(872\) | 956.609 | + | 1656.90i | 0.0371501 | + | 0.0643458i | ||||
\(873\) | 1248.86 | 0.0484164 | ||||||||
\(874\) | 18357.1 | − | 21560.3i | 0.710457 | − | 0.834426i | ||||
\(875\) | −14247.4 | −0.550459 | ||||||||
\(876\) | −6612.87 | − | 11453.8i | −0.255055 | − | 0.441768i | ||||
\(877\) | 18288.7 | + | 31676.9i | 0.704178 | + | 1.21967i | 0.966987 | + | 0.254825i | \(0.0820178\pi\) |
−0.262809 | + | 0.964848i | \(0.584649\pi\) | |||||||
\(878\) | 13469.0 | − | 23329.0i | 0.517718 | − | 0.896714i | ||||
\(879\) | −13554.9 | − | 23477.8i | −0.520132 | − | 0.900894i | ||||
\(880\) | −3207.20 | + | 5555.04i | −0.122858 | + | 0.212796i | ||||
\(881\) | 6389.06 | 0.244328 | 0.122164 | − | 0.992510i | \(-0.461017\pi\) | ||||
0.122164 | + | 0.992510i | \(0.461017\pi\) | |||||||
\(882\) | −4569.13 | −0.174434 | ||||||||
\(883\) | 8868.92 | − | 15361.4i | 0.338010 | − | 0.585451i | −0.646048 | − | 0.763297i | \(-0.723580\pi\) |
0.984058 | + | 0.177846i | \(0.0569129\pi\) | |||||||
\(884\) | 10501.4 | − | 18188.9i | 0.399548 | − | 0.692037i | ||||
\(885\) | −556.737 | −0.0211463 | ||||||||
\(886\) | 14822.2 | 0.562033 | ||||||||
\(887\) | −14810.5 | + | 25652.6i | −0.560641 | + | 0.971058i | 0.436800 | + | 0.899559i | \(0.356112\pi\) |
−0.997441 | + | 0.0714994i | \(0.977222\pi\) | |||||||
\(888\) | −240.740 | − | 416.974i | −0.00909764 | − | 0.0157576i | ||||
\(889\) | −459.743 | + | 796.298i | −0.0173445 | + | 0.0300416i | ||||
\(890\) | 10885.6 | + | 18854.4i | 0.409984 | + | 0.710114i | ||||
\(891\) | 1923.20 | + | 3331.08i | 0.0723117 | + | 0.125247i | ||||
\(892\) | −14301.8 | −0.536839 | ||||||||
\(893\) | −5756.93 | − | 16178.2i | −0.215732 | − | 0.606251i | ||||
\(894\) | 17514.6 | 0.655231 | ||||||||
\(895\) | −16224.3 | − | 28101.3i | −0.605942 | − | 1.04952i | ||||
\(896\) | 604.315 | + | 1046.70i | 0.0225321 | + | 0.0390267i | ||||
\(897\) | 17348.8 | − | 30049.0i | 0.645774 | − | 1.11851i | ||||
\(898\) | 3345.93 | + | 5795.33i | 0.124338 | + | 0.215359i | ||||
\(899\) | −33509.7 | + | 58040.4i | −1.24317 | + | 2.15323i | ||||
\(900\) | −1934.12 | −0.0716341 | ||||||||
\(901\) | 20296.9 | 0.750486 | ||||||||
\(902\) | 3410.54 | − | 5907.23i | 0.125896 | − | 0.218059i | ||||
\(903\) | −2086.55 | + | 3614.02i | −0.0768950 | + | 0.133186i | ||||
\(904\) | 1301.94 | 0.0479003 | ||||||||
\(905\) | −14937.0 | −0.548643 | ||||||||
\(906\) | −5747.15 | + | 9954.35i | −0.210746 | + | 0.365023i | ||||
\(907\) | −7176.13 | − | 12429.4i | −0.262712 | − | 0.455030i | 0.704250 | − | 0.709952i | \(-0.251283\pi\) |
−0.966962 | + | 0.254922i | \(0.917950\pi\) | |||||||
\(908\) | 173.047 | − | 299.727i | 0.00632465 | − | 0.0109546i | ||||
\(909\) | 313.338 | + | 542.717i | 0.0114332 | + | 0.0198028i | ||||
\(910\) | −5393.20 | − | 9341.30i | −0.196465 | − | 0.340287i | ||||
\(911\) | 50.5532 | 0.00183853 | 0.000919266 | − | 1.00000i | \(-0.499707\pi\) | ||||
0.000919266 | 1.00000i | \(0.499707\pi\) | ||||||||
\(912\) | −1332.73 | − | 3745.26i | −0.0483895 | − | 0.135985i | ||||
\(913\) | −67991.2 | −2.46460 | ||||||||
\(914\) | 542.238 | + | 939.184i | 0.0196232 | + | 0.0339885i | ||||
\(915\) | 8270.65 | + | 14325.2i | 0.298819 | + | 0.517570i | ||||
\(916\) | 7856.10 | − | 13607.2i | 0.283377 | − | 0.490823i | ||||
\(917\) | 1791.22 | + | 3102.48i | 0.0645051 | + | 0.111726i | ||||
\(918\) | −2095.48 | + | 3629.48i | −0.0753390 | + | 0.130491i | ||||
\(919\) | −38362.9 | −1.37701 | −0.688507 | − | 0.725230i | \(-0.741734\pi\) | ||||
−0.688507 | + | 0.725230i | \(0.741734\pi\) | |||||||
\(920\) | −11546.2 | −0.413767 | ||||||||
\(921\) | 11695.8 | − | 20257.6i | 0.418445 | − | 0.724769i | ||||
\(922\) | −3823.43 | + | 6622.38i | −0.136571 | + | 0.236547i | ||||
\(923\) | −10685.7 | −0.381066 | ||||||||
\(924\) | −5380.64 | −0.191569 | ||||||||
\(925\) | −538.913 | + | 933.424i | −0.0191560 | + | 0.0331792i | ||||
\(926\) | 3750.37 | + | 6495.82i | 0.133094 | + | 0.230525i | ||||
\(927\) | 2899.56 | − | 5022.18i | 0.102734 | − | 0.177940i | ||||
\(928\) | −3841.96 | − | 6654.48i | −0.135904 | − | 0.235392i | ||||
\(929\) | 19043.5 | + | 32984.3i | 0.672548 | + | 1.16489i | 0.977179 | + | 0.212417i | \(0.0681335\pi\) |
−0.304631 | + | 0.952470i | \(0.598533\pi\) | |||||||
\(930\) | 14137.9 | 0.498494 | ||||||||
\(931\) | −13628.7 | + | 16006.8i | −0.479767 | + | 0.563483i | ||||
\(932\) | 4080.10 | 0.143399 | ||||||||
\(933\) | 4106.24 | + | 7112.21i | 0.144086 | + | 0.249564i | ||||
\(934\) | 2981.61 | + | 5164.30i | 0.104455 | + | 0.180922i | ||||
\(935\) | 15557.0 | − | 26945.6i | 0.544138 | − | 0.942475i | ||||
\(936\) | −2435.56 | − | 4218.52i | −0.0850522 | − | 0.147315i | ||||
\(937\) | −22120.0 | + | 38313.0i | −0.771217 | + | 1.33579i | 0.165680 | + | 0.986180i | \(0.447018\pi\) |
−0.936897 | + | 0.349607i | \(0.886315\pi\) | |||||||
\(938\) | 7814.46 | 0.272016 | ||||||||
\(939\) | 22938.5 | 0.797197 | ||||||||
\(940\) | −3500.95 | + | 6063.83i | −0.121477 | + | 0.210404i | ||||
\(941\) | −12104.5 | + | 20965.7i | −0.419338 | + | 0.726314i | −0.995873 | − | 0.0907581i | \(-0.971071\pi\) |
0.576535 | + | 0.817072i | \(0.304404\pi\) | |||||||
\(942\) | 15220.1 | 0.526431 | ||||||||
\(943\) | 12278.2 | 0.424001 | ||||||||
\(944\) | 175.854 | − | 304.588i | 0.00606309 | − | 0.0105016i | ||||
\(945\) | 1076.18 | + | 1863.99i | 0.0370455 | + | 0.0641648i | ||||
\(946\) | 6995.60 | − | 12116.7i | 0.240430 | − | 0.416437i | ||||
\(947\) | 10262.4 | + | 17774.9i | 0.352146 | + | 0.609935i | 0.986625 | − | 0.163005i | \(-0.0521187\pi\) |
−0.634479 | + | 0.772940i | \(0.718785\pi\) | |||||||
\(948\) | −2506.88 | − | 4342.04i | −0.0858857 | − | 0.148758i | ||||
\(949\) | −74565.1 | −2.55056 | ||||||||
\(950\) | −5769.06 | + | 6775.72i | −0.197024 | + | 0.231403i | ||||
\(951\) | 19261.2 | 0.656768 | ||||||||
\(952\) | −2931.32 | − | 5077.20i | −0.0997948 | − | 0.172850i | ||||
\(953\) | 2455.68 | + | 4253.36i | 0.0834703 | + | 0.144575i | 0.904738 | − | 0.425968i | \(-0.140066\pi\) |
−0.821268 | + | 0.570543i | \(0.806733\pi\) | |||||||
\(954\) | 2353.71 | − | 4076.74i | 0.0798785 | − | 0.138354i | ||||
\(955\) | −2127.52 | − | 3684.96i | −0.0720888 | − | 0.124861i | ||||
\(956\) | −529.362 | + | 916.882i | −0.0179088 | + | 0.0310189i | ||||
\(957\) | 34207.7 | 1.15546 | ||||||||
\(958\) | 30711.7 | 1.03575 | ||||||||
\(959\) | 11395.5 | − | 19737.6i | 0.383712 | − | 0.664609i | ||||
\(960\) | −810.472 | + | 1403.78i | −0.0272478 | + | 0.0471945i | ||||
\(961\) | 48108.3 | 1.61486 | ||||||||
\(962\) | −2714.52 | −0.0909769 | ||||||||
\(963\) | 852.545 | − | 1476.65i | 0.0285284 | − | 0.0494127i | ||||
\(964\) | 344.774 | + | 597.166i | 0.0115191 | + | 0.0199517i | ||||
\(965\) | −9149.84 | + | 15848.0i | −0.305227 | + | 0.528668i | ||||
\(966\) | −4842.68 | − | 8387.76i | −0.161295 | − | 0.279370i | ||||
\(967\) | 20197.3 | + | 34982.8i | 0.671668 | + | 1.16336i | 0.977431 | + | 0.211255i | \(0.0677551\pi\) |
−0.305763 | + | 0.952108i | \(0.598912\pi\) | |||||||
\(968\) | 7391.72 | 0.245433 | ||||||||
\(969\) | 6464.62 | + | 18166.9i | 0.214317 | + | 0.602277i | ||||
\(970\) | −2342.98 | −0.0775550 | ||||||||
\(971\) | 13395.9 | + | 23202.4i | 0.442735 | + | 0.766840i | 0.997891 | − | 0.0649061i | \(-0.0206748\pi\) |
−0.555156 | + | 0.831746i | \(0.687341\pi\) | |||||||
\(972\) | 486.000 | + | 841.777i | 0.0160375 | + | 0.0277778i | ||||
\(973\) | −14678.4 | + | 25423.8i | −0.483627 | + | 0.837667i | ||||
\(974\) | −439.463 | − | 761.172i | −0.0144572 | − | 0.0250406i | ||||
\(975\) | −5452.17 | + | 9443.43i | −0.179086 | + | 0.310187i | ||||
\(976\) | −10449.7 | −0.342710 | ||||||||
\(977\) | −8122.31 | −0.265973 | −0.132987 | − | 0.991118i | \(-0.542457\pi\) | ||||
−0.132987 | + | 0.991118i | \(0.542457\pi\) | |||||||
\(978\) | −5194.56 | + | 8997.24i | −0.169840 | + | 0.294172i | ||||
\(979\) | 30614.4 | − | 53025.6i | 0.999427 | − | 1.73106i | ||||
\(980\) | 8572.12 | 0.279415 | ||||||||
\(981\) | −2152.37 | −0.0700509 | ||||||||
\(982\) | −19765.8 | + | 34235.4i | −0.642314 | + | 1.11252i | ||||
\(983\) | 16459.0 | + | 28507.9i | 0.534041 | + | 0.924986i | 0.999209 | + | 0.0397634i | \(0.0126604\pi\) |
−0.465168 | + | 0.885222i | \(0.654006\pi\) | |||||||
\(984\) | 861.855 | − | 1492.78i | 0.0279217 | − | 0.0483618i | ||||
\(985\) | 8911.39 | + | 15435.0i | 0.288265 | + | 0.499289i | ||||
\(986\) | 18636.0 | + | 32278.6i | 0.601919 | + | 1.04255i | ||||
\(987\) | −5873.46 | −0.189417 | ||||||||
\(988\) | −22043.3 | − | 4050.52i | −0.709808 | − | 0.130430i | ||||
\(989\) | 25184.7 | 0.809733 | ||||||||
\(990\) | −3608.10 | − | 6249.42i | −0.115831 | − | 0.200626i | ||||
\(991\) | 15885.1 | + | 27513.7i | 0.509189 | + | 0.881941i | 0.999943 | + | 0.0106428i | \(0.00338777\pi\) |
−0.490755 | + | 0.871298i | \(0.663279\pi\) | |||||||
\(992\) | −4465.67 | + | 7734.77i | −0.142929 | + | 0.247560i | ||||
\(993\) | −6892.16 | − | 11937.6i | −0.220258 | − | 0.381498i | ||||
\(994\) | −1491.38 | + | 2583.15i | −0.0475894 | + | 0.0824272i | ||||
\(995\) | −18054.9 | −0.575255 | ||||||||
\(996\) | −17181.6 | −0.546607 | ||||||||
\(997\) | −7753.26 | + | 13429.0i | −0.246287 | + | 0.426582i | −0.962493 | − | 0.271308i | \(-0.912544\pi\) |
0.716206 | + | 0.697889i | \(0.245877\pi\) | |||||||
\(998\) | −8159.72 | + | 14133.1i | −0.258809 | + | 0.448271i | ||||
\(999\) | 541.665 | 0.0171547 |
(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 | 114.4.e.d.7.3 | ✓ | 6 | |
3.2 | odd | 2 | 342.4.g.h.235.1 | 6 | |||
19.7 | even | 3 | 2166.4.a.u.1.1 | 3 | |||
19.11 | even | 3 | inner | 114.4.e.d.49.3 | yes | 6 | |
19.12 | odd | 6 | 2166.4.a.t.1.1 | 3 | |||
57.11 | odd | 6 | 342.4.g.h.163.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.4.e.d.7.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
114.4.e.d.49.3 | yes | 6 | 19.11 | even | 3 | inner | |
342.4.g.h.163.1 | 6 | 57.11 | odd | 6 | |||
342.4.g.h.235.1 | 6 | 3.2 | odd | 2 | |||
2166.4.a.t.1.1 | 3 | 19.12 | odd | 6 | |||
2166.4.a.u.1.1 | 3 | 19.7 | even | 3 |