Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,3,Mod(577,1014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1014, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1014.577");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.f (of order \(4\), 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: | \(27.6294988061\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - x^{2} + 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 78) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 775.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.775 |
Dual form | 1014.3.f.d.577.2 |
$q$-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 \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | − | 1.00000i | −0.500000 | − | 0.500000i | ||||
\(3\) | 1.73205 | 0.577350 | ||||||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | 1.26795 | + | 1.26795i | 0.253590 | + | 0.253590i | 0.822441 | − | 0.568851i | \(-0.192612\pi\) |
−0.568851 | + | 0.822441i | \(0.692612\pi\) | |||||||
\(6\) | −1.73205 | − | 1.73205i | −0.288675 | − | 0.288675i | ||||
\(7\) | 6.83013 | − | 6.83013i | 0.975732 | − | 0.975732i | −0.0239800 | − | 0.999712i | \(-0.507634\pi\) |
0.999712 | + | 0.0239800i | \(0.00763381\pi\) | |||||||
\(8\) | 2.00000 | − | 2.00000i | 0.250000 | − | 0.250000i | ||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | − | 2.53590i | − | 0.253590i | ||||||
\(11\) | 7.26795 | − | 7.26795i | 0.660723 | − | 0.660723i | −0.294828 | − | 0.955550i | \(-0.595262\pi\) |
0.955550 | + | 0.294828i | \(0.0952623\pi\) | |||||||
\(12\) | 3.46410i | 0.288675i | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −13.6603 | −0.975732 | ||||||||
\(15\) | 2.19615 | + | 2.19615i | 0.146410 | + | 0.146410i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | − | 18.9282i | − | 1.11342i | −0.830706 | − | 0.556712i | \(-0.812063\pi\) | ||
0.830706 | − | 0.556712i | \(-0.187937\pi\) | |||||||
\(18\) | −3.00000 | − | 3.00000i | −0.166667 | − | 0.166667i | ||||
\(19\) | 23.3923 | + | 23.3923i | 1.23117 | + | 1.23117i | 0.963513 | + | 0.267661i | \(0.0862506\pi\) |
0.267661 | + | 0.963513i | \(0.413749\pi\) | |||||||
\(20\) | −2.53590 | + | 2.53590i | −0.126795 | + | 0.126795i | ||||
\(21\) | 11.8301 | − | 11.8301i | 0.563339 | − | 0.563339i | ||||
\(22\) | −14.5359 | −0.660723 | ||||||||
\(23\) | − | 4.14359i | − | 0.180156i | −0.995935 | − | 0.0900781i | \(-0.971288\pi\) | ||
0.995935 | − | 0.0900781i | \(-0.0287117\pi\) | |||||||
\(24\) | 3.46410 | − | 3.46410i | 0.144338 | − | 0.144338i | ||||
\(25\) | − | 21.7846i | − | 0.871384i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | 13.6603 | + | 13.6603i | 0.487866 | + | 0.487866i | ||||
\(29\) | −17.3205 | −0.597259 | −0.298629 | − | 0.954369i | \(-0.596529\pi\) | ||||
−0.298629 | + | 0.954369i | \(0.596529\pi\) | |||||||
\(30\) | − | 4.39230i | − | 0.146410i | ||||||
\(31\) | −22.1699 | − | 22.1699i | −0.715157 | − | 0.715157i | 0.252452 | − | 0.967609i | \(-0.418763\pi\) |
−0.967609 | + | 0.252452i | \(0.918763\pi\) | |||||||
\(32\) | 4.00000 | + | 4.00000i | 0.125000 | + | 0.125000i | ||||
\(33\) | 12.5885 | − | 12.5885i | 0.381468 | − | 0.381468i | ||||
\(34\) | −18.9282 | + | 18.9282i | −0.556712 | + | 0.556712i | ||||
\(35\) | 17.3205 | 0.494872 | ||||||||
\(36\) | 6.00000i | 0.166667i | ||||||||
\(37\) | −26.1769 | + | 26.1769i | −0.707484 | + | 0.707484i | −0.966006 | − | 0.258521i | \(-0.916765\pi\) |
0.258521 | + | 0.966006i | \(0.416765\pi\) | |||||||
\(38\) | − | 46.7846i | − | 1.23117i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.07180 | 0.126795 | ||||||||
\(41\) | 18.2487 | + | 18.2487i | 0.445091 | + | 0.445091i | 0.893719 | − | 0.448628i | \(-0.148087\pi\) |
−0.448628 | + | 0.893719i | \(0.648087\pi\) | |||||||
\(42\) | −23.6603 | −0.563339 | ||||||||
\(43\) | 15.3397i | 0.356738i | 0.983964 | + | 0.178369i | \(0.0570821\pi\) | ||||
−0.983964 | + | 0.178369i | \(0.942918\pi\) | |||||||
\(44\) | 14.5359 | + | 14.5359i | 0.330361 | + | 0.330361i | ||||
\(45\) | 3.80385 | + | 3.80385i | 0.0845299 | + | 0.0845299i | ||||
\(46\) | −4.14359 | + | 4.14359i | −0.0900781 | + | 0.0900781i | ||||
\(47\) | −7.01924 | + | 7.01924i | −0.149345 | + | 0.149345i | −0.777826 | − | 0.628480i | \(-0.783677\pi\) |
0.628480 | + | 0.777826i | \(0.283677\pi\) | |||||||
\(48\) | −6.92820 | −0.144338 | ||||||||
\(49\) | − | 44.3013i | − | 0.904108i | ||||||
\(50\) | −21.7846 | + | 21.7846i | −0.435692 | + | 0.435692i | ||||
\(51\) | − | 32.7846i | − | 0.642835i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −61.6743 | −1.16367 | −0.581833 | − | 0.813308i | \(-0.697664\pi\) | ||||
−0.581833 | + | 0.813308i | \(0.697664\pi\) | |||||||
\(54\) | −5.19615 | − | 5.19615i | −0.0962250 | − | 0.0962250i | ||||
\(55\) | 18.4308 | 0.335105 | ||||||||
\(56\) | − | 27.3205i | − | 0.487866i | ||||||
\(57\) | 40.5167 | + | 40.5167i | 0.710819 | + | 0.710819i | ||||
\(58\) | 17.3205 | + | 17.3205i | 0.298629 | + | 0.298629i | ||||
\(59\) | 46.7321 | − | 46.7321i | 0.792069 | − | 0.792069i | −0.189762 | − | 0.981830i | \(-0.560771\pi\) |
0.981830 | + | 0.189762i | \(0.0607715\pi\) | |||||||
\(60\) | −4.39230 | + | 4.39230i | −0.0732051 | + | 0.0732051i | ||||
\(61\) | −7.30127 | −0.119693 | −0.0598465 | − | 0.998208i | \(-0.519061\pi\) | ||||
−0.0598465 | + | 0.998208i | \(0.519061\pi\) | |||||||
\(62\) | 44.3397i | 0.715157i | ||||||||
\(63\) | 20.4904 | − | 20.4904i | 0.325244 | − | 0.325244i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −25.1769 | −0.381468 | ||||||||
\(67\) | 27.7391 | + | 27.7391i | 0.414016 | + | 0.414016i | 0.883135 | − | 0.469119i | \(-0.155428\pi\) |
−0.469119 | + | 0.883135i | \(0.655428\pi\) | |||||||
\(68\) | 37.8564 | 0.556712 | ||||||||
\(69\) | − | 7.17691i | − | 0.104013i | ||||||
\(70\) | −17.3205 | − | 17.3205i | −0.247436 | − | 0.247436i | ||||
\(71\) | 76.0526 | + | 76.0526i | 1.07116 | + | 1.07116i | 0.997266 | + | 0.0738969i | \(0.0235436\pi\) |
0.0738969 | + | 0.997266i | \(0.476456\pi\) | |||||||
\(72\) | 6.00000 | − | 6.00000i | 0.0833333 | − | 0.0833333i | ||||
\(73\) | 67.4186 | − | 67.4186i | 0.923542 | − | 0.923542i | −0.0737356 | − | 0.997278i | \(-0.523492\pi\) |
0.997278 | + | 0.0737356i | \(0.0234921\pi\) | |||||||
\(74\) | 52.3538 | 0.707484 | ||||||||
\(75\) | − | 37.7321i | − | 0.503094i | ||||||
\(76\) | −46.7846 | + | 46.7846i | −0.615587 | + | 0.615587i | ||||
\(77\) | − | 99.2820i | − | 1.28938i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.8756 | 0.150325 | 0.0751623 | − | 0.997171i | \(-0.476053\pi\) | ||||
0.0751623 | + | 0.997171i | \(0.476053\pi\) | |||||||
\(80\) | −5.07180 | − | 5.07180i | −0.0633975 | − | 0.0633975i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | − | 36.4974i | − | 0.445091i | ||||||
\(83\) | −111.033 | − | 111.033i | −1.33775 | − | 1.33775i | −0.898235 | − | 0.439516i | \(-0.855150\pi\) |
−0.439516 | − | 0.898235i | \(-0.644850\pi\) | |||||||
\(84\) | 23.6603 | + | 23.6603i | 0.281670 | + | 0.281670i | ||||
\(85\) | 24.0000 | − | 24.0000i | 0.282353 | − | 0.282353i | ||||
\(86\) | 15.3397 | − | 15.3397i | 0.178369 | − | 0.178369i | ||||
\(87\) | −30.0000 | −0.344828 | ||||||||
\(88\) | − | 29.0718i | − | 0.330361i | ||||||
\(89\) | 118.641 | − | 118.641i | 1.33305 | − | 1.33305i | 0.430413 | − | 0.902632i | \(-0.358368\pi\) |
0.902632 | − | 0.430413i | \(-0.141632\pi\) | |||||||
\(90\) | − | 7.60770i | − | 0.0845299i | ||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.28719 | 0.0900781 | ||||||||
\(93\) | −38.3993 | − | 38.3993i | −0.412896 | − | 0.412896i | ||||
\(94\) | 14.0385 | 0.149345 | ||||||||
\(95\) | 59.3205i | 0.624426i | ||||||||
\(96\) | 6.92820 | + | 6.92820i | 0.0721688 | + | 0.0721688i | ||||
\(97\) | 109.988 | + | 109.988i | 1.13389 | + | 1.13389i | 0.989524 | + | 0.144371i | \(0.0461160\pi\) |
0.144371 | + | 0.989524i | \(0.453884\pi\) | |||||||
\(98\) | −44.3013 | + | 44.3013i | −0.452054 | + | 0.452054i | ||||
\(99\) | 21.8038 | − | 21.8038i | 0.220241 | − | 0.220241i | ||||
\(100\) | 43.5692 | 0.435692 | ||||||||
\(101\) | − | 186.813i | − | 1.84963i | −0.380415 | − | 0.924816i | \(-0.624219\pi\) | ||
0.380415 | − | 0.924816i | \(-0.375781\pi\) | |||||||
\(102\) | −32.7846 | + | 32.7846i | −0.321418 | + | 0.321418i | ||||
\(103\) | 83.2628i | 0.808377i | 0.914676 | + | 0.404188i | \(0.132446\pi\) | ||||
−0.914676 | + | 0.404188i | \(0.867554\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 30.0000 | 0.285714 | ||||||||
\(106\) | 61.6743 | + | 61.6743i | 0.581833 | + | 0.581833i | ||||
\(107\) | 102.497 | 0.957920 | 0.478960 | − | 0.877837i | \(-0.341014\pi\) | ||||
0.478960 | + | 0.877837i | \(0.341014\pi\) | |||||||
\(108\) | 10.3923i | 0.0962250i | ||||||||
\(109\) | −48.1891 | − | 48.1891i | −0.442102 | − | 0.442102i | 0.450616 | − | 0.892718i | \(-0.351204\pi\) |
−0.892718 | + | 0.450616i | \(0.851204\pi\) | |||||||
\(110\) | −18.4308 | − | 18.4308i | −0.167553 | − | 0.167553i | ||||
\(111\) | −45.3397 | + | 45.3397i | −0.408466 | + | 0.408466i | ||||
\(112\) | −27.3205 | + | 27.3205i | −0.243933 | + | 0.243933i | ||||
\(113\) | −45.2154 | −0.400136 | −0.200068 | − | 0.979782i | \(-0.564116\pi\) | ||||
−0.200068 | + | 0.979782i | \(0.564116\pi\) | |||||||
\(114\) | − | 81.0333i | − | 0.710819i | ||||||
\(115\) | 5.25387 | − | 5.25387i | 0.0456858 | − | 0.0456858i | ||||
\(116\) | − | 34.6410i | − | 0.298629i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −93.4641 | −0.792069 | ||||||||
\(119\) | −129.282 | − | 129.282i | −1.08640 | − | 1.08640i | ||||
\(120\) | 8.78461 | 0.0732051 | ||||||||
\(121\) | 15.3538i | 0.126891i | ||||||||
\(122\) | 7.30127 | + | 7.30127i | 0.0598465 | + | 0.0598465i | ||||
\(123\) | 31.6077 | + | 31.6077i | 0.256973 | + | 0.256973i | ||||
\(124\) | 44.3397 | − | 44.3397i | 0.357579 | − | 0.357579i | ||||
\(125\) | 59.3205 | − | 59.3205i | 0.474564 | − | 0.474564i | ||||
\(126\) | −40.9808 | −0.325244 | ||||||||
\(127\) | 236.846i | 1.86493i | 0.361260 | + | 0.932465i | \(0.382347\pi\) | ||||
−0.361260 | + | 0.932465i | \(0.617653\pi\) | |||||||
\(128\) | −8.00000 | + | 8.00000i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 26.5692i | 0.205963i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −209.636 | −1.60027 | −0.800137 | − | 0.599817i | \(-0.795240\pi\) | ||||
−0.800137 | + | 0.599817i | \(0.795240\pi\) | |||||||
\(132\) | 25.1769 | + | 25.1769i | 0.190734 | + | 0.190734i | ||||
\(133\) | 319.545 | 2.40259 | ||||||||
\(134\) | − | 55.4782i | − | 0.414016i | ||||||
\(135\) | 6.58846 | + | 6.58846i | 0.0488034 | + | 0.0488034i | ||||
\(136\) | −37.8564 | − | 37.8564i | −0.278356 | − | 0.278356i | ||||
\(137\) | −80.5359 | + | 80.5359i | −0.587853 | + | 0.587853i | −0.937050 | − | 0.349196i | \(-0.886455\pi\) |
0.349196 | + | 0.937050i | \(0.386455\pi\) | |||||||
\(138\) | −7.17691 | + | 7.17691i | −0.0520066 | + | 0.0520066i | ||||
\(139\) | −95.7077 | −0.688544 | −0.344272 | − | 0.938870i | \(-0.611874\pi\) | ||||
−0.344272 | + | 0.938870i | \(0.611874\pi\) | |||||||
\(140\) | 34.6410i | 0.247436i | ||||||||
\(141\) | −12.1577 | + | 12.1577i | −0.0862247 | + | 0.0862247i | ||||
\(142\) | − | 152.105i | − | 1.07116i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | −21.9615 | − | 21.9615i | −0.151459 | − | 0.151459i | ||||
\(146\) | −134.837 | −0.923542 | ||||||||
\(147\) | − | 76.7321i | − | 0.521987i | ||||||
\(148\) | −52.3538 | − | 52.3538i | −0.353742 | − | 0.353742i | ||||
\(149\) | −40.2102 | − | 40.2102i | −0.269867 | − | 0.269867i | 0.559179 | − | 0.829047i | \(-0.311116\pi\) |
−0.829047 | + | 0.559179i | \(0.811116\pi\) | |||||||
\(150\) | −37.7321 | + | 37.7321i | −0.251547 | + | 0.251547i | ||||
\(151\) | 55.0385 | − | 55.0385i | 0.364493 | − | 0.364493i | −0.500971 | − | 0.865464i | \(-0.667024\pi\) |
0.865464 | + | 0.500971i | \(0.167024\pi\) | |||||||
\(152\) | 93.5692 | 0.615587 | ||||||||
\(153\) | − | 56.7846i | − | 0.371141i | ||||||
\(154\) | −99.2820 | + | 99.2820i | −0.644689 | + | 0.644689i | ||||
\(155\) | − | 56.2205i | − | 0.362713i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 55.4308 | 0.353062 | 0.176531 | − | 0.984295i | \(-0.443512\pi\) | ||||
0.176531 | + | 0.984295i | \(0.443512\pi\) | |||||||
\(158\) | −11.8756 | − | 11.8756i | −0.0751623 | − | 0.0751623i | ||||
\(159\) | −106.823 | −0.671843 | ||||||||
\(160\) | 10.1436i | 0.0633975i | ||||||||
\(161\) | −28.3013 | − | 28.3013i | −0.175784 | − | 0.175784i | ||||
\(162\) | −9.00000 | − | 9.00000i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | 144.653 | − | 144.653i | 0.887443 | − | 0.887443i | −0.106834 | − | 0.994277i | \(-0.534071\pi\) |
0.994277 | + | 0.106834i | \(0.0340713\pi\) | |||||||
\(164\) | −36.4974 | + | 36.4974i | −0.222545 | + | 0.222545i | ||||
\(165\) | 31.9230 | 0.193473 | ||||||||
\(166\) | 222.067i | 1.33775i | ||||||||
\(167\) | −114.431 | + | 114.431i | −0.685214 | + | 0.685214i | −0.961170 | − | 0.275956i | \(-0.911006\pi\) |
0.275956 | + | 0.961170i | \(0.411006\pi\) | |||||||
\(168\) | − | 47.3205i | − | 0.281670i | ||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −48.0000 | −0.282353 | ||||||||
\(171\) | 70.1769 | + | 70.1769i | 0.410391 | + | 0.410391i | ||||
\(172\) | −30.6795 | −0.178369 | ||||||||
\(173\) | − | 268.459i | − | 1.55179i | −0.630865 | − | 0.775893i | \(-0.717300\pi\) | ||
0.630865 | − | 0.775893i | \(-0.282700\pi\) | |||||||
\(174\) | 30.0000 | + | 30.0000i | 0.172414 | + | 0.172414i | ||||
\(175\) | −148.792 | − | 148.792i | −0.850238 | − | 0.850238i | ||||
\(176\) | −29.0718 | + | 29.0718i | −0.165181 | + | 0.165181i | ||||
\(177\) | 80.9423 | − | 80.9423i | 0.457301 | − | 0.457301i | ||||
\(178\) | −237.282 | −1.33305 | ||||||||
\(179\) | − | 285.779i | − | 1.59653i | −0.602304 | − | 0.798267i | \(-0.705751\pi\) | ||
0.602304 | − | 0.798267i | \(-0.294249\pi\) | |||||||
\(180\) | −7.60770 | + | 7.60770i | −0.0422650 | + | 0.0422650i | ||||
\(181\) | 177.646i | 0.981471i | 0.871309 | + | 0.490735i | \(0.163272\pi\) | ||||
−0.871309 | + | 0.490735i | \(0.836728\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.6462 | −0.0691048 | ||||||||
\(184\) | −8.28719 | − | 8.28719i | −0.0450391 | − | 0.0450391i | ||||
\(185\) | −66.3820 | −0.358822 | ||||||||
\(186\) | 76.7987i | 0.412896i | ||||||||
\(187\) | −137.569 | − | 137.569i | −0.735664 | − | 0.735664i | ||||
\(188\) | −14.0385 | − | 14.0385i | −0.0746727 | − | 0.0746727i | ||||
\(189\) | 35.4904 | − | 35.4904i | 0.187780 | − | 0.187780i | ||||
\(190\) | 59.3205 | − | 59.3205i | 0.312213 | − | 0.312213i | ||||
\(191\) | 197.321 | 1.03309 | 0.516546 | − | 0.856260i | \(-0.327218\pi\) | ||||
0.516546 | + | 0.856260i | \(0.327218\pi\) | |||||||
\(192\) | − | 13.8564i | − | 0.0721688i | ||||||
\(193\) | −14.8494 | + | 14.8494i | −0.0769397 | + | 0.0769397i | −0.744529 | − | 0.667590i | \(-0.767326\pi\) |
0.667590 | + | 0.744529i | \(0.267326\pi\) | |||||||
\(194\) | − | 219.976i | − | 1.13389i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 88.6025 | 0.452054 | ||||||||
\(197\) | −106.956 | − | 106.956i | −0.542926 | − | 0.542926i | 0.381460 | − | 0.924385i | \(-0.375421\pi\) |
−0.924385 | + | 0.381460i | \(0.875421\pi\) | |||||||
\(198\) | −43.6077 | −0.220241 | ||||||||
\(199\) | − | 22.2154i | − | 0.111635i | −0.998441 | − | 0.0558176i | \(-0.982223\pi\) | ||
0.998441 | − | 0.0558176i | \(-0.0177765\pi\) | |||||||
\(200\) | −43.5692 | − | 43.5692i | −0.217846 | − | 0.217846i | ||||
\(201\) | 48.0455 | + | 48.0455i | 0.239032 | + | 0.239032i | ||||
\(202\) | −186.813 | + | 186.813i | −0.924816 | + | 0.924816i | ||||
\(203\) | −118.301 | + | 118.301i | −0.582765 | + | 0.582765i | ||||
\(204\) | 65.5692 | 0.321418 | ||||||||
\(205\) | 46.2769i | 0.225741i | ||||||||
\(206\) | 83.2628 | − | 83.2628i | 0.404188 | − | 0.404188i | ||||
\(207\) | − | 12.4308i | − | 0.0600521i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 340.028 | 1.62693 | ||||||||
\(210\) | −30.0000 | − | 30.0000i | −0.142857 | − | 0.142857i | ||||
\(211\) | 64.2013 | 0.304272 | 0.152136 | − | 0.988360i | \(-0.451385\pi\) | ||||
0.152136 | + | 0.988360i | \(0.451385\pi\) | |||||||
\(212\) | − | 123.349i | − | 0.581833i | ||||||
\(213\) | 131.727 | + | 131.727i | 0.618436 | + | 0.618436i | ||||
\(214\) | −102.497 | − | 102.497i | −0.478960 | − | 0.478960i | ||||
\(215\) | −19.4500 | + | 19.4500i | −0.0904652 | + | 0.0904652i | ||||
\(216\) | 10.3923 | − | 10.3923i | 0.0481125 | − | 0.0481125i | ||||
\(217\) | −302.846 | −1.39560 | ||||||||
\(218\) | 96.3782i | 0.442102i | ||||||||
\(219\) | 116.772 | − | 116.772i | 0.533207 | − | 0.533207i | ||||
\(220\) | 36.8616i | 0.167553i | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 90.6795 | 0.408466 | ||||||||
\(223\) | 154.531 | + | 154.531i | 0.692963 | + | 0.692963i | 0.962883 | − | 0.269920i | \(-0.0869972\pi\) |
−0.269920 | + | 0.962883i | \(0.586997\pi\) | |||||||
\(224\) | 54.6410 | 0.243933 | ||||||||
\(225\) | − | 65.3538i | − | 0.290461i | ||||||
\(226\) | 45.2154 | + | 45.2154i | 0.200068 | + | 0.200068i | ||||
\(227\) | 45.7128 | + | 45.7128i | 0.201378 | + | 0.201378i | 0.800590 | − | 0.599212i | \(-0.204519\pi\) |
−0.599212 | + | 0.800590i | \(0.704519\pi\) | |||||||
\(228\) | −81.0333 | + | 81.0333i | −0.355409 | + | 0.355409i | ||||
\(229\) | −58.6846 | + | 58.6846i | −0.256265 | + | 0.256265i | −0.823533 | − | 0.567268i | \(-0.808000\pi\) |
0.567268 | + | 0.823533i | \(0.308000\pi\) | |||||||
\(230\) | −10.5077 | −0.0456858 | ||||||||
\(231\) | − | 171.962i | − | 0.744422i | ||||||
\(232\) | −34.6410 | + | 34.6410i | −0.149315 | + | 0.149315i | ||||
\(233\) | 380.669i | 1.63377i | 0.576798 | + | 0.816887i | \(0.304302\pi\) | ||||
−0.576798 | + | 0.816887i | \(0.695698\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.8001 | −0.0757450 | ||||||||
\(236\) | 93.4641 | + | 93.4641i | 0.396034 | + | 0.396034i | ||||
\(237\) | 20.5692 | 0.0867900 | ||||||||
\(238\) | 258.564i | 1.08640i | ||||||||
\(239\) | 167.138 | + | 167.138i | 0.699324 | + | 0.699324i | 0.964265 | − | 0.264941i | \(-0.0853524\pi\) |
−0.264941 | + | 0.964265i | \(0.585352\pi\) | |||||||
\(240\) | −8.78461 | − | 8.78461i | −0.0366025 | − | 0.0366025i | ||||
\(241\) | −2.17691 | + | 2.17691i | −0.00903284 | + | 0.00903284i | −0.711609 | − | 0.702576i | \(-0.752033\pi\) |
0.702576 | + | 0.711609i | \(0.252033\pi\) | |||||||
\(242\) | 15.3538 | − | 15.3538i | 0.0634456 | − | 0.0634456i | ||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | − | 14.6025i | − | 0.0598465i | ||||||
\(245\) | 56.1718 | − | 56.1718i | 0.229272 | − | 0.229272i | ||||
\(246\) | − | 63.2154i | − | 0.256973i | ||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −88.6795 | −0.357579 | ||||||||
\(249\) | −192.315 | − | 192.315i | −0.772351 | − | 0.772351i | ||||
\(250\) | −118.641 | −0.474564 | ||||||||
\(251\) | 208.708i | 0.831505i | 0.909478 | + | 0.415752i | \(0.136482\pi\) | ||||
−0.909478 | + | 0.415752i | \(0.863518\pi\) | |||||||
\(252\) | 40.9808 | + | 40.9808i | 0.162622 | + | 0.162622i | ||||
\(253\) | −30.1154 | − | 30.1154i | −0.119033 | − | 0.119033i | ||||
\(254\) | 236.846 | − | 236.846i | 0.932465 | − | 0.932465i | ||||
\(255\) | 41.5692 | − | 41.5692i | 0.163017 | − | 0.163017i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 74.2205i | 0.288796i | 0.989520 | + | 0.144398i | \(0.0461245\pi\) | ||||
−0.989520 | + | 0.144398i | \(0.953875\pi\) | |||||||
\(258\) | 26.5692 | − | 26.5692i | 0.102981 | − | 0.102981i | ||||
\(259\) | 357.583i | 1.38063i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −51.9615 | −0.199086 | ||||||||
\(262\) | 209.636 | + | 209.636i | 0.800137 | + | 0.800137i | ||||
\(263\) | −24.3641 | −0.0926393 | −0.0463197 | − | 0.998927i | \(-0.514749\pi\) | ||||
−0.0463197 | + | 0.998927i | \(0.514749\pi\) | |||||||
\(264\) | − | 50.3538i | − | 0.190734i | ||||||
\(265\) | −78.1999 | − | 78.1999i | −0.295094 | − | 0.295094i | ||||
\(266\) | −319.545 | − | 319.545i | −1.20130 | − | 1.20130i | ||||
\(267\) | 205.492 | − | 205.492i | 0.769634 | − | 0.769634i | ||||
\(268\) | −55.4782 | + | 55.4782i | −0.207008 | + | 0.207008i | ||||
\(269\) | −175.741 | −0.653312 | −0.326656 | − | 0.945143i | \(-0.605922\pi\) | ||||
−0.326656 | + | 0.945143i | \(0.605922\pi\) | |||||||
\(270\) | − | 13.1769i | − | 0.0488034i | ||||||
\(271\) | 197.046 | − | 197.046i | 0.727105 | − | 0.727105i | −0.242937 | − | 0.970042i | \(-0.578111\pi\) |
0.970042 | + | 0.242937i | \(0.0781108\pi\) | |||||||
\(272\) | 75.7128i | 0.278356i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 161.072 | 0.587853 | ||||||||
\(275\) | −158.329 | − | 158.329i | −0.575743 | − | 0.575743i | ||||
\(276\) | 14.3538 | 0.0520066 | ||||||||
\(277\) | 446.985i | 1.61366i | 0.590782 | + | 0.806831i | \(0.298819\pi\) | ||||
−0.590782 | + | 0.806831i | \(0.701181\pi\) | |||||||
\(278\) | 95.7077 | + | 95.7077i | 0.344272 | + | 0.344272i | ||||
\(279\) | −66.5096 | − | 66.5096i | −0.238386 | − | 0.238386i | ||||
\(280\) | 34.6410 | − | 34.6410i | 0.123718 | − | 0.123718i | ||||
\(281\) | 5.54483 | − | 5.54483i | 0.0197325 | − | 0.0197325i | −0.697172 | − | 0.716904i | \(-0.745558\pi\) |
0.716904 | + | 0.697172i | \(0.245558\pi\) | |||||||
\(282\) | 24.3154 | 0.0862247 | ||||||||
\(283\) | 16.6462i | 0.0588204i | 0.999567 | + | 0.0294102i | \(0.00936291\pi\) | ||||
−0.999567 | + | 0.0294102i | \(0.990637\pi\) | |||||||
\(284\) | −152.105 | + | 152.105i | −0.535581 | + | 0.535581i | ||||
\(285\) | 102.746i | 0.360513i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 249.282 | 0.868579 | ||||||||
\(288\) | 12.0000 | + | 12.0000i | 0.0416667 | + | 0.0416667i | ||||
\(289\) | −69.2769 | −0.239712 | ||||||||
\(290\) | 43.9230i | 0.151459i | ||||||||
\(291\) | 190.504 | + | 190.504i | 0.654655 | + | 0.654655i | ||||
\(292\) | 134.837 | + | 134.837i | 0.461771 | + | 0.461771i | ||||
\(293\) | −132.473 | + | 132.473i | −0.452126 | + | 0.452126i | −0.896060 | − | 0.443933i | \(-0.853583\pi\) |
0.443933 | + | 0.896060i | \(0.353583\pi\) | |||||||
\(294\) | −76.7321 | + | 76.7321i | −0.260993 | + | 0.260993i | ||||
\(295\) | 118.508 | 0.401721 | ||||||||
\(296\) | 104.708i | 0.353742i | ||||||||
\(297\) | 37.7654 | − | 37.7654i | 0.127156 | − | 0.127156i | ||||
\(298\) | 80.4205i | 0.269867i | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 75.4641 | 0.251547 | ||||||||
\(301\) | 104.772 | + | 104.772i | 0.348081 | + | 0.348081i | ||||
\(302\) | −110.077 | −0.364493 | ||||||||
\(303\) | − | 323.569i | − | 1.06789i | ||||||
\(304\) | −93.5692 | − | 93.5692i | −0.307793 | − | 0.307793i | ||||
\(305\) | −9.25764 | − | 9.25764i | −0.0303529 | − | 0.0303529i | ||||
\(306\) | −56.7846 | + | 56.7846i | −0.185571 | + | 0.185571i | ||||
\(307\) | −375.069 | + | 375.069i | −1.22172 | + | 1.22172i | −0.254702 | + | 0.967020i | \(0.581977\pi\) |
−0.967020 | + | 0.254702i | \(0.918023\pi\) | |||||||
\(308\) | 198.564 | 0.644689 | ||||||||
\(309\) | 144.215i | 0.466716i | ||||||||
\(310\) | −56.2205 | + | 56.2205i | −0.181357 | + | 0.181357i | ||||
\(311\) | − | 296.238i | − | 0.952535i | −0.879300 | − | 0.476268i | \(-0.841989\pi\) | ||
0.879300 | − | 0.476268i | \(-0.158011\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 118.286 | 0.377910 | 0.188955 | − | 0.981986i | \(-0.439490\pi\) | ||||
0.188955 | + | 0.981986i | \(0.439490\pi\) | |||||||
\(314\) | −55.4308 | − | 55.4308i | −0.176531 | − | 0.176531i | ||||
\(315\) | 51.9615 | 0.164957 | ||||||||
\(316\) | 23.7513i | 0.0751623i | ||||||||
\(317\) | 280.708 | + | 280.708i | 0.885513 | + | 0.885513i | 0.994088 | − | 0.108575i | \(-0.0346288\pi\) |
−0.108575 | + | 0.994088i | \(0.534629\pi\) | |||||||
\(318\) | 106.823 | + | 106.823i | 0.335922 | + | 0.335922i | ||||
\(319\) | −125.885 | + | 125.885i | −0.394622 | + | 0.394622i | ||||
\(320\) | 10.1436 | − | 10.1436i | 0.0316987 | − | 0.0316987i | ||||
\(321\) | 177.531 | 0.553055 | ||||||||
\(322\) | 56.6025i | 0.175784i | ||||||||
\(323\) | 442.774 | − | 442.774i | 1.37082 | − | 1.37082i | ||||
\(324\) | 18.0000i | 0.0555556i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −289.306 | −0.887443 | ||||||||
\(327\) | −83.4660 | − | 83.4660i | −0.255248 | − | 0.255248i | ||||
\(328\) | 72.9948 | 0.222545 | ||||||||
\(329\) | 95.8846i | 0.291442i | ||||||||
\(330\) | −31.9230 | − | 31.9230i | −0.0967365 | − | 0.0967365i | ||||
\(331\) | −100.624 | − | 100.624i | −0.303999 | − | 0.303999i | 0.538577 | − | 0.842576i | \(-0.318962\pi\) |
−0.842576 | + | 0.538577i | \(0.818962\pi\) | |||||||
\(332\) | 222.067 | − | 222.067i | 0.668875 | − | 0.668875i | ||||
\(333\) | −78.5307 | + | 78.5307i | −0.235828 | + | 0.235828i | ||||
\(334\) | 228.862 | 0.685214 | ||||||||
\(335\) | 70.3435i | 0.209981i | ||||||||
\(336\) | −47.3205 | + | 47.3205i | −0.140835 | + | 0.140835i | ||||
\(337\) | 347.508i | 1.03118i | 0.856835 | + | 0.515590i | \(0.172427\pi\) | ||||
−0.856835 | + | 0.515590i | \(0.827573\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −78.3154 | −0.231019 | ||||||||
\(340\) | 48.0000 | + | 48.0000i | 0.141176 | + | 0.141176i | ||||
\(341\) | −322.259 | −0.945041 | ||||||||
\(342\) | − | 140.354i | − | 0.410391i | ||||||
\(343\) | 32.0929 | + | 32.0929i | 0.0935654 | + | 0.0935654i | ||||
\(344\) | 30.6795 | + | 30.6795i | 0.0891846 | + | 0.0891846i | ||||
\(345\) | 9.09996 | − | 9.09996i | 0.0263767 | − | 0.0263767i | ||||
\(346\) | −268.459 | + | 268.459i | −0.775893 | + | 0.775893i | ||||
\(347\) | 437.703 | 1.26139 | 0.630695 | − | 0.776031i | \(-0.282770\pi\) | ||||
0.630695 | + | 0.776031i | \(0.282770\pi\) | |||||||
\(348\) | − | 60.0000i | − | 0.172414i | ||||||
\(349\) | −316.897 | + | 316.897i | −0.908014 | + | 0.908014i | −0.996112 | − | 0.0880981i | \(-0.971921\pi\) |
0.0880981 | + | 0.996112i | \(0.471921\pi\) | |||||||
\(350\) | 297.583i | 0.850238i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 58.1436 | 0.165181 | ||||||||
\(353\) | 415.037 | + | 415.037i | 1.17574 | + | 1.17574i | 0.980818 | + | 0.194924i | \(0.0624461\pi\) |
0.194924 | + | 0.980818i | \(0.437554\pi\) | |||||||
\(354\) | −161.885 | −0.457301 | ||||||||
\(355\) | 192.862i | 0.543272i | ||||||||
\(356\) | 237.282 | + | 237.282i | 0.666523 | + | 0.666523i | ||||
\(357\) | −223.923 | − | 223.923i | −0.627235 | − | 0.627235i | ||||
\(358\) | −285.779 | + | 285.779i | −0.798267 | + | 0.798267i | ||||
\(359\) | −64.2769 | + | 64.2769i | −0.179044 | + | 0.179044i | −0.790939 | − | 0.611895i | \(-0.790408\pi\) |
0.611895 | + | 0.790939i | \(0.290408\pi\) | |||||||
\(360\) | 15.2154 | 0.0422650 | ||||||||
\(361\) | 733.400i | 2.03158i | ||||||||
\(362\) | 177.646 | − | 177.646i | 0.490735 | − | 0.490735i | ||||
\(363\) | 26.5936i | 0.0732606i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 170.967 | 0.468402 | ||||||||
\(366\) | 12.6462 | + | 12.6462i | 0.0345524 | + | 0.0345524i | ||||
\(367\) | −217.785 | −0.593419 | −0.296709 | − | 0.954968i | \(-0.595889\pi\) | ||||
−0.296709 | + | 0.954968i | \(0.595889\pi\) | |||||||
\(368\) | 16.5744i | 0.0450391i | ||||||||
\(369\) | 54.7461 | + | 54.7461i | 0.148364 | + | 0.148364i | ||||
\(370\) | 66.3820 | + | 66.3820i | 0.179411 | + | 0.179411i | ||||
\(371\) | −421.244 | + | 421.244i | −1.13543 | + | 1.13543i | ||||
\(372\) | 76.7987 | − | 76.7987i | 0.206448 | − | 0.206448i | ||||
\(373\) | −219.606 | −0.588757 | −0.294378 | − | 0.955689i | \(-0.595113\pi\) | ||||
−0.294378 | + | 0.955689i | \(0.595113\pi\) | |||||||
\(374\) | 275.138i | 0.735664i | ||||||||
\(375\) | 102.746 | − | 102.746i | 0.273990 | − | 0.273990i | ||||
\(376\) | 28.0770i | 0.0746727i | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −70.9808 | −0.187780 | ||||||||
\(379\) | −137.107 | − | 137.107i | −0.361760 | − | 0.361760i | 0.502701 | − | 0.864461i | \(-0.332340\pi\) |
−0.864461 | + | 0.502701i | \(0.832340\pi\) | |||||||
\(380\) | −118.641 | −0.312213 | ||||||||
\(381\) | 410.229i | 1.07672i | ||||||||
\(382\) | −197.321 | − | 197.321i | −0.516546 | − | 0.516546i | ||||
\(383\) | 137.751 | + | 137.751i | 0.359664 | + | 0.359664i | 0.863689 | − | 0.504025i | \(-0.168148\pi\) |
−0.504025 | + | 0.863689i | \(0.668148\pi\) | |||||||
\(384\) | −13.8564 | + | 13.8564i | −0.0360844 | + | 0.0360844i | ||||
\(385\) | 125.885 | − | 125.885i | 0.326973 | − | 0.326973i | ||||
\(386\) | 29.6987 | 0.0769397 | ||||||||
\(387\) | 46.0192i | 0.118913i | ||||||||
\(388\) | −219.976 | + | 219.976i | −0.566947 | + | 0.566947i | ||||
\(389\) | − | 17.7513i | − | 0.0456331i | −0.999740 | − | 0.0228166i | \(-0.992737\pi\) | ||
0.999740 | − | 0.0228166i | \(-0.00726337\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −78.4308 | −0.200590 | ||||||||
\(392\) | −88.6025 | − | 88.6025i | −0.226027 | − | 0.226027i | ||||
\(393\) | −363.100 | −0.923918 | ||||||||
\(394\) | 213.913i | 0.542926i | ||||||||
\(395\) | 15.0577 | + | 15.0577i | 0.0381208 | + | 0.0381208i | ||||
\(396\) | 43.6077 | + | 43.6077i | 0.110120 | + | 0.110120i | ||||
\(397\) | 238.643 | − | 238.643i | 0.601116 | − | 0.601116i | −0.339493 | − | 0.940609i | \(-0.610255\pi\) |
0.940609 | + | 0.339493i | \(0.110255\pi\) | |||||||
\(398\) | −22.2154 | + | 22.2154i | −0.0558176 | + | 0.0558176i | ||||
\(399\) | 553.468 | 1.38714 | ||||||||
\(400\) | 87.1384i | 0.217846i | ||||||||
\(401\) | −363.415 | + | 363.415i | −0.906273 | + | 0.906273i | −0.995969 | − | 0.0896965i | \(-0.971410\pi\) |
0.0896965 | + | 0.995969i | \(0.471410\pi\) | |||||||
\(402\) | − | 96.0910i | − | 0.239032i | ||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 373.626 | 0.924816 | ||||||||
\(405\) | 11.4115 | + | 11.4115i | 0.0281766 | + | 0.0281766i | ||||
\(406\) | 236.603 | 0.582765 | ||||||||
\(407\) | 380.505i | 0.934902i | ||||||||
\(408\) | −65.5692 | − | 65.5692i | −0.160709 | − | 0.160709i | ||||
\(409\) | −412.026 | − | 412.026i | −1.00740 | − | 1.00740i | −0.999972 | − | 0.00742680i | \(-0.997636\pi\) |
−0.00742680 | − | 0.999972i | \(-0.502364\pi\) | |||||||
\(410\) | 46.2769 | − | 46.2769i | 0.112870 | − | 0.112870i | ||||
\(411\) | −139.492 | + | 139.492i | −0.339397 | + | 0.339397i | ||||
\(412\) | −166.526 | −0.404188 | ||||||||
\(413\) | − | 638.372i | − | 1.54569i | ||||||
\(414\) | −12.4308 | + | 12.4308i | −0.0300260 | + | 0.0300260i | ||||
\(415\) | − | 281.569i | − | 0.678480i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −165.771 | −0.397531 | ||||||||
\(418\) | −340.028 | − | 340.028i | −0.813465 | − | 0.813465i | ||||
\(419\) | −782.354 | −1.86719 | −0.933596 | − | 0.358326i | \(-0.883348\pi\) | ||||
−0.933596 | + | 0.358326i | \(0.883348\pi\) | |||||||
\(420\) | 60.0000i | 0.142857i | ||||||||
\(421\) | 27.0352 | + | 27.0352i | 0.0642166 | + | 0.0642166i | 0.738486 | − | 0.674269i | \(-0.235541\pi\) |
−0.674269 | + | 0.738486i | \(0.735541\pi\) | |||||||
\(422\) | −64.2013 | − | 64.2013i | −0.152136 | − | 0.152136i | ||||
\(423\) | −21.0577 | + | 21.0577i | −0.0497818 | + | 0.0497818i | ||||
\(424\) | −123.349 | + | 123.349i | −0.290917 | + | 0.290917i | ||||
\(425\) | −412.344 | −0.970220 | ||||||||
\(426\) | − | 263.454i | − | 0.618436i | ||||||
\(427\) | −49.8686 | + | 49.8686i | −0.116788 | + | 0.116788i | ||||
\(428\) | 204.995i | 0.478960i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 38.9000 | 0.0904652 | ||||||||
\(431\) | −445.310 | − | 445.310i | −1.03320 | − | 1.03320i | −0.999430 | − | 0.0337728i | \(-0.989248\pi\) |
−0.0337728 | − | 0.999430i | \(-0.510752\pi\) | |||||||
\(432\) | −20.7846 | −0.0481125 | ||||||||
\(433\) | 237.785i | 0.549156i | 0.961565 | + | 0.274578i | \(0.0885382\pi\) | ||||
−0.961565 | + | 0.274578i | \(0.911462\pi\) | |||||||
\(434\) | 302.846 | + | 302.846i | 0.697802 | + | 0.697802i | ||||
\(435\) | −38.0385 | − | 38.0385i | −0.0874448 | − | 0.0874448i | ||||
\(436\) | 96.3782 | − | 96.3782i | 0.221051 | − | 0.221051i | ||||
\(437\) | 96.9282 | − | 96.9282i | 0.221804 | − | 0.221804i | ||||
\(438\) | −233.545 | −0.533207 | ||||||||
\(439\) | 689.463i | 1.57053i | 0.619160 | + | 0.785265i | \(0.287473\pi\) | ||||
−0.619160 | + | 0.785265i | \(0.712527\pi\) | |||||||
\(440\) | 36.8616 | − | 36.8616i | 0.0837763 | − | 0.0837763i | ||||
\(441\) | − | 132.904i | − | 0.301369i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −304.028 | −0.686294 | −0.343147 | − | 0.939282i | \(-0.611493\pi\) | ||||
−0.343147 | + | 0.939282i | \(0.611493\pi\) | |||||||
\(444\) | −90.6795 | − | 90.6795i | −0.204233 | − | 0.204233i | ||||
\(445\) | 300.862 | 0.676093 | ||||||||
\(446\) | − | 309.061i | − | 0.692963i | ||||||
\(447\) | −69.6462 | − | 69.6462i | −0.155808 | − | 0.155808i | ||||
\(448\) | −54.6410 | − | 54.6410i | −0.121967 | − | 0.121967i | ||||
\(449\) | 200.694 | − | 200.694i | 0.446979 | − | 0.446979i | −0.447370 | − | 0.894349i | \(-0.647639\pi\) |
0.894349 | + | 0.447370i | \(0.147639\pi\) | |||||||
\(450\) | −65.3538 | + | 65.3538i | −0.145231 | + | 0.145231i | ||||
\(451\) | 265.261 | 0.588163 | ||||||||
\(452\) | − | 90.4308i | − | 0.200068i | ||||||
\(453\) | 95.3294 | − | 95.3294i | 0.210440 | − | 0.210440i | ||||
\(454\) | − | 91.4256i | − | 0.201378i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 162.067 | 0.355409 | ||||||||
\(457\) | 101.519 | + | 101.519i | 0.222141 | + | 0.222141i | 0.809400 | − | 0.587258i | \(-0.199793\pi\) |
−0.587258 | + | 0.809400i | \(0.699793\pi\) | |||||||
\(458\) | 117.369 | 0.256265 | ||||||||
\(459\) | − | 98.3538i | − | 0.214278i | ||||||
\(460\) | 10.5077 | + | 10.5077i | 0.0228429 | + | 0.0228429i | ||||
\(461\) | 416.123 | + | 416.123i | 0.902653 | + | 0.902653i | 0.995665 | − | 0.0930121i | \(-0.0296495\pi\) |
−0.0930121 | + | 0.995665i | \(0.529650\pi\) | |||||||
\(462\) | −171.962 | + | 171.962i | −0.372211 | + | 0.372211i | ||||
\(463\) | 169.599 | − | 169.599i | 0.366305 | − | 0.366305i | −0.499823 | − | 0.866128i | \(-0.666601\pi\) |
0.866128 | + | 0.499823i | \(0.166601\pi\) | |||||||
\(464\) | 69.2820 | 0.149315 | ||||||||
\(465\) | − | 97.3768i | − | 0.209413i | ||||||
\(466\) | 380.669 | − | 380.669i | 0.816887 | − | 0.816887i | ||||
\(467\) | 732.649i | 1.56884i | 0.620230 | + | 0.784420i | \(0.287039\pi\) | ||||
−0.620230 | + | 0.784420i | \(0.712961\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 378.923 | 0.807938 | ||||||||
\(470\) | 17.8001 | + | 17.8001i | 0.0378725 | + | 0.0378725i | ||||
\(471\) | 96.0089 | 0.203841 | ||||||||
\(472\) | − | 186.928i | − | 0.396034i | ||||||
\(473\) | 111.488 | + | 111.488i | 0.235705 | + | 0.235705i | ||||
\(474\) | −20.5692 | − | 20.5692i | −0.0433950 | − | 0.0433950i | ||||
\(475\) | 509.592 | − | 509.592i | 1.07283 | − | 1.07283i | ||||
\(476\) | 258.564 | − | 258.564i | 0.543202 | − | 0.543202i | ||||
\(477\) | −185.023 | −0.387889 | ||||||||
\(478\) | − | 334.277i | − | 0.699324i | ||||||
\(479\) | −261.464 | + | 261.464i | −0.545854 | + | 0.545854i | −0.925239 | − | 0.379385i | \(-0.876136\pi\) |
0.379385 | + | 0.925239i | \(0.376136\pi\) | |||||||
\(480\) | 17.5692i | 0.0366025i | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 4.35383 | 0.00903284 | ||||||||
\(483\) | −49.0192 | − | 49.0192i | −0.101489 | − | 0.101489i | ||||
\(484\) | −30.7077 | −0.0634456 | ||||||||
\(485\) | 278.918i | 0.575088i | ||||||||
\(486\) | −15.5885 | − | 15.5885i | −0.0320750 | − | 0.0320750i | ||||
\(487\) | 137.000 | + | 137.000i | 0.281314 | + | 0.281314i | 0.833633 | − | 0.552319i | \(-0.186257\pi\) |
−0.552319 | + | 0.833633i | \(0.686257\pi\) | |||||||
\(488\) | −14.6025 | + | 14.6025i | −0.0299232 | + | 0.0299232i | ||||
\(489\) | 250.547 | − | 250.547i | 0.512365 | − | 0.512365i | ||||
\(490\) | −112.344 | −0.229272 | ||||||||
\(491\) | − | 36.9282i | − | 0.0752102i | −0.999293 | − | 0.0376051i | \(-0.988027\pi\) | ||
0.999293 | − | 0.0376051i | \(-0.0119729\pi\) | |||||||
\(492\) | −63.2154 | + | 63.2154i | −0.128487 | + | 0.128487i | ||||
\(493\) | 327.846i | 0.665002i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 55.2923 | 0.111702 | ||||||||
\(496\) | 88.6795 | + | 88.6795i | 0.178789 | + | 0.178789i | ||||
\(497\) | 1038.90 | 2.09034 | ||||||||
\(498\) | 384.631i | 0.772351i | ||||||||
\(499\) | −462.769 | − | 462.769i | −0.927393 | − | 0.927393i | 0.0701438 | − | 0.997537i | \(-0.477654\pi\) |
−0.997537 | + | 0.0701438i | \(0.977654\pi\) | |||||||
\(500\) | 118.641 | + | 118.641i | 0.237282 | + | 0.237282i | ||||
\(501\) | −198.200 | + | 198.200i | −0.395609 | + | 0.395609i | ||||
\(502\) | 208.708 | − | 208.708i | 0.415752 | − | 0.415752i | ||||
\(503\) | −358.756 | −0.713233 | −0.356617 | − | 0.934251i | \(-0.616070\pi\) | ||||
−0.356617 | + | 0.934251i | \(0.616070\pi\) | |||||||
\(504\) | − | 81.9615i | − | 0.162622i | ||||||
\(505\) | 236.869 | − | 236.869i | 0.469048 | − | 0.469048i | ||||
\(506\) | 60.2309i | 0.119033i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −473.692 | −0.932465 | ||||||||
\(509\) | 521.745 | + | 521.745i | 1.02504 | + | 1.02504i | 0.999678 | + | 0.0253604i | \(0.00807334\pi\) |
0.0253604 | + | 0.999678i | \(0.491927\pi\) | |||||||
\(510\) | −83.1384 | −0.163017 | ||||||||
\(511\) | − | 920.955i | − | 1.80226i | ||||||
\(512\) | −16.0000 | − | 16.0000i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 121.550 | + | 121.550i | 0.236940 | + | 0.236940i | ||||
\(514\) | 74.2205 | − | 74.2205i | 0.144398 | − | 0.144398i | ||||
\(515\) | −105.573 | + | 105.573i | −0.204996 | + | 0.204996i | ||||
\(516\) | −53.1384 | −0.102981 | ||||||||
\(517\) | 102.031i | 0.197352i | ||||||||
\(518\) | 357.583 | − | 357.583i | 0.690315 | − | 0.690315i | ||||
\(519\) | − | 464.985i | − | 0.895924i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 156.049 | 0.299518 | 0.149759 | − | 0.988723i | \(-0.452150\pi\) | ||||
0.149759 | + | 0.988723i | \(0.452150\pi\) | |||||||
\(522\) | 51.9615 | + | 51.9615i | 0.0995431 | + | 0.0995431i | ||||
\(523\) | 41.9230 | 0.0801588 | 0.0400794 | − | 0.999196i | \(-0.487239\pi\) | ||||
0.0400794 | + | 0.999196i | \(0.487239\pi\) | |||||||
\(524\) | − | 419.272i | − | 0.800137i | ||||||
\(525\) | −257.715 | − | 257.715i | −0.490885 | − | 0.490885i | ||||
\(526\) | 24.3641 | + | 24.3641i | 0.0463197 | + | 0.0463197i | ||||
\(527\) | −419.636 | + | 419.636i | −0.796273 | + | 0.796273i | ||||
\(528\) | −50.3538 | + | 50.3538i | −0.0953671 | + | 0.0953671i | ||||
\(529\) | 511.831 | 0.967544 | ||||||||
\(530\) | 156.400i | 0.295094i | ||||||||
\(531\) | 140.196 | − | 140.196i | 0.264023 | − | 0.264023i | ||||
\(532\) | 639.090i | 1.20130i | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −410.985 | −0.769634 | ||||||||
\(535\) | 129.962 | + | 129.962i | 0.242919 | + | 0.242919i | ||||
\(536\) | 110.956 | 0.207008 | ||||||||
\(537\) | − | 494.985i | − | 0.921759i | ||||||
\(538\) | 175.741 | + | 175.741i | 0.326656 | + | 0.326656i | ||||
\(539\) | −321.979 | − | 321.979i | −0.597364 | − | 0.597364i | ||||
\(540\) | −13.1769 | + | 13.1769i | −0.0244017 | + | 0.0244017i | ||||
\(541\) | 4.44298 | − | 4.44298i | 0.00821253 | − | 0.00821253i | −0.702989 | − | 0.711201i | \(-0.748152\pi\) |
0.711201 | + | 0.702989i | \(0.248152\pi\) | |||||||
\(542\) | −394.091 | −0.727105 | ||||||||
\(543\) | 307.692i | 0.566652i | ||||||||
\(544\) | 75.7128 | − | 75.7128i | 0.139178 | − | 0.139178i | ||||
\(545\) | − | 122.203i | − | 0.224225i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −101.508 | −0.185572 | −0.0927859 | − | 0.995686i | \(-0.529577\pi\) | ||||
−0.0927859 | + | 0.995686i | \(0.529577\pi\) | |||||||
\(548\) | −161.072 | − | 161.072i | −0.293927 | − | 0.293927i | ||||
\(549\) | −21.9038 | −0.0398977 | ||||||||
\(550\) | 316.659i | 0.575743i | ||||||||
\(551\) | −405.167 | − | 405.167i | −0.735330 | − | 0.735330i | ||||
\(552\) | −14.3538 | − | 14.3538i | −0.0260033 | − | 0.0260033i | ||||
\(553\) | 81.1122 | − | 81.1122i | 0.146677 | − | 0.146677i | ||||
\(554\) | 446.985 | − | 446.985i | 0.806831 | − | 0.806831i | ||||
\(555\) | −114.977 | −0.207166 | ||||||||
\(556\) | − | 191.415i | − | 0.344272i | ||||||
\(557\) | −465.846 | + | 465.846i | −0.836348 | + | 0.836348i | −0.988376 | − | 0.152028i | \(-0.951420\pi\) |
0.152028 | + | 0.988376i | \(0.451420\pi\) | |||||||
\(558\) | 133.019i | 0.238386i | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −69.2820 | −0.123718 | ||||||||
\(561\) | −238.277 | − | 238.277i | −0.424736 | − | 0.424736i | ||||
\(562\) | −11.0897 | −0.0197325 | ||||||||
\(563\) | − | 88.7255i | − | 0.157594i | −0.996891 | − | 0.0787971i | \(-0.974892\pi\) | ||
0.996891 | − | 0.0787971i | \(-0.0251079\pi\) | |||||||
\(564\) | −24.3154 | − | 24.3154i | −0.0431123 | − | 0.0431123i | ||||
\(565\) | −57.3308 | − | 57.3308i | −0.101470 | − | 0.101470i | ||||
\(566\) | 16.6462 | − | 16.6462i | 0.0294102 | − | 0.0294102i | ||||
\(567\) | 61.4711 | − | 61.4711i | 0.108415 | − | 0.108415i | ||||
\(568\) | 304.210 | 0.535581 | ||||||||
\(569\) | − | 431.569i | − | 0.758470i | −0.925300 | − | 0.379235i | \(-0.876187\pi\) | ||
0.925300 | − | 0.379235i | \(-0.123813\pi\) | |||||||
\(570\) | 102.746 | − | 102.746i | 0.180256 | − | 0.180256i | ||||
\(571\) | − | 959.892i | − | 1.68107i | −0.541756 | − | 0.840536i | \(-0.682240\pi\) | ||
0.541756 | − | 0.840536i | \(-0.317760\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 341.769 | 0.596456 | ||||||||
\(574\) | −249.282 | − | 249.282i | −0.434289 | − | 0.434289i | ||||
\(575\) | −90.2666 | −0.156985 | ||||||||
\(576\) | − | 24.0000i | − | 0.0416667i | ||||||
\(577\) | 313.669 | + | 313.669i | 0.543621 | + | 0.543621i | 0.924588 | − | 0.380968i | \(-0.124409\pi\) |
−0.380968 | + | 0.924588i | \(0.624409\pi\) | |||||||
\(578\) | 69.2769 | + | 69.2769i | 0.119856 | + | 0.119856i | ||||
\(579\) | −25.7199 | + | 25.7199i | −0.0444212 | + | 0.0444212i | ||||
\(580\) | 43.9230 | − | 43.9230i | 0.0757294 | − | 0.0757294i | ||||
\(581\) | −1516.74 | −2.61057 | ||||||||
\(582\) | − | 381.009i | − | 0.654655i | ||||||
\(583\) | −448.246 | + | 448.246i | −0.768861 | + | 0.768861i | ||||
\(584\) | − | 269.674i | − | 0.461771i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 264.946 | 0.452126 | ||||||||
\(587\) | 160.004 | + | 160.004i | 0.272579 | + | 0.272579i | 0.830138 | − | 0.557559i | \(-0.188262\pi\) |
−0.557559 | + | 0.830138i | \(0.688262\pi\) | |||||||
\(588\) | 153.464 | 0.260993 | ||||||||
\(589\) | − | 1037.21i | − | 1.76097i | ||||||
\(590\) | −118.508 | − | 118.508i | −0.200861 | − | 0.200861i | ||||
\(591\) | −185.254 | − | 185.254i | −0.313458 | − | 0.313458i | ||||
\(592\) | 104.708 | − | 104.708i | 0.176871 | − | 0.176871i | ||||
\(593\) | −335.229 | + | 335.229i | −0.565311 | + | 0.565311i | −0.930811 | − | 0.365500i | \(-0.880898\pi\) |
0.365500 | + | 0.930811i | \(0.380898\pi\) | |||||||
\(594\) | −75.5307 | −0.127156 | ||||||||
\(595\) | − | 327.846i | − | 0.551002i | ||||||
\(596\) | 80.4205 | − | 80.4205i | 0.134934 | − | 0.134934i | ||||
\(597\) | − | 38.4782i | − | 0.0644526i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 136.908 | 0.228560 | 0.114280 | − | 0.993449i | \(-0.463544\pi\) | ||||
0.114280 | + | 0.993449i | \(0.463544\pi\) | |||||||
\(600\) | −75.4641 | − | 75.4641i | −0.125774 | − | 0.125774i | ||||
\(601\) | −17.5692 | −0.0292333 | −0.0146167 | − | 0.999893i | \(-0.504653\pi\) | ||||
−0.0146167 | + | 0.999893i | \(0.504653\pi\) | |||||||
\(602\) | − | 209.545i | − | 0.348081i | ||||||
\(603\) | 83.2173 | + | 83.2173i | 0.138005 | + | 0.138005i | ||||
\(604\) | 110.077 | + | 110.077i | 0.182247 | + | 0.182247i | ||||
\(605\) | −19.4679 | + | 19.4679i | −0.0321783 | + | 0.0321783i | ||||
\(606\) | −323.569 | + | 323.569i | −0.533943 | + | 0.533943i | ||||
\(607\) | 844.600 | 1.39143 | 0.695716 | − | 0.718317i | \(-0.255087\pi\) | ||||
0.695716 | + | 0.718317i | \(0.255087\pi\) | |||||||
\(608\) | 187.138i | 0.307793i | ||||||||
\(609\) | −204.904 | + | 204.904i | −0.336459 | + | 0.336459i | ||||
\(610\) | 18.5153i | 0.0303529i | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 113.569 | 0.185571 | ||||||||
\(613\) | 445.757 | + | 445.757i | 0.727173 | + | 0.727173i | 0.970056 | − | 0.242883i | \(-0.0780930\pi\) |
−0.242883 | + | 0.970056i | \(0.578093\pi\) | |||||||
\(614\) | 750.137 | 1.22172 | ||||||||
\(615\) | 80.1539i | 0.130332i | ||||||||
\(616\) | −198.564 | − | 198.564i | −0.322344 | − | 0.322344i | ||||
\(617\) | 78.3397 | + | 78.3397i | 0.126969 | + | 0.126969i | 0.767736 | − | 0.640767i | \(-0.221383\pi\) |
−0.640767 | + | 0.767736i | \(0.721383\pi\) | |||||||
\(618\) | 144.215 | − | 144.215i | 0.233358 | − | 0.233358i | ||||
\(619\) | 111.970 | − | 111.970i | 0.180888 | − | 0.180888i | −0.610854 | − | 0.791743i | \(-0.709174\pi\) |
0.791743 | + | 0.610854i | \(0.209174\pi\) | |||||||
\(620\) | 112.441 | 0.181357 | ||||||||
\(621\) | − | 21.5307i | − | 0.0346711i | ||||||
\(622\) | −296.238 | + | 296.238i | −0.476268 | + | 0.476268i | ||||
\(623\) | − | 1620.67i | − | 2.60139i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −394.184 | −0.630695 | ||||||||
\(626\) | −118.286 | − | 118.286i | −0.188955 | − | 0.188955i | ||||
\(627\) | 588.946 | 0.939308 | ||||||||
\(628\) | 110.862i | 0.176531i | ||||||||
\(629\) | 495.482 | + | 495.482i | 0.787730 | + | 0.787730i | ||||
\(630\) | −51.9615 | − | 51.9615i | −0.0824786 | − | 0.0824786i | ||||
\(631\) | −773.445 | + | 773.445i | −1.22575 | + | 1.22575i | −0.260187 | + | 0.965558i | \(0.583784\pi\) |
−0.965558 | + | 0.260187i | \(0.916216\pi\) | |||||||
\(632\) | 23.7513 | − | 23.7513i | 0.0375812 | − | 0.0375812i | ||||
\(633\) | 111.200 | 0.175671 | ||||||||
\(634\) | − | 561.415i | − | 0.885513i | ||||||
\(635\) | −300.309 | + | 300.309i | −0.472927 | + | 0.472927i | ||||
\(636\) | − | 213.646i | − | 0.335922i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 251.769 | 0.394622 | ||||||||
\(639\) | 228.158 | + | 228.158i | 0.357054 | + | 0.357054i | ||||
\(640\) | −20.2872 | −0.0316987 | ||||||||
\(641\) | 408.613i | 0.637462i | 0.947845 | + | 0.318731i | \(0.103257\pi\) | ||||
−0.947845 | + | 0.318731i | \(0.896743\pi\) | |||||||
\(642\) | −177.531 | − | 177.531i | −0.276528 | − | 0.276528i | ||||
\(643\) | −316.730 | − | 316.730i | −0.492582 | − | 0.492582i | 0.416537 | − | 0.909119i | \(-0.363244\pi\) |
−0.909119 | + | 0.416537i | \(0.863244\pi\) | |||||||
\(644\) | 56.6025 | − | 56.6025i | 0.0878921 | − | 0.0878921i | ||||
\(645\) | −33.6884 | + | 33.6884i | −0.0522301 | + | 0.0522301i | ||||
\(646\) | −885.549 | −1.37082 | ||||||||
\(647\) | − | 322.841i | − | 0.498981i | −0.968377 | − | 0.249491i | \(-0.919737\pi\) | ||
0.968377 | − | 0.249491i | \(-0.0802632\pi\) | |||||||
\(648\) | 18.0000 | − | 18.0000i | 0.0277778 | − | 0.0277778i | ||||
\(649\) | − | 679.292i | − | 1.04668i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −524.545 | −0.805752 | ||||||||
\(652\) | 289.306 | + | 289.306i | 0.443722 | + | 0.443722i | ||||
\(653\) | −1020.85 | −1.56332 | −0.781660 | − | 0.623704i | \(-0.785627\pi\) | ||||
−0.781660 | + | 0.623704i | \(0.785627\pi\) | |||||||
\(654\) | 166.932i | 0.255248i | ||||||||
\(655\) | −265.808 | − | 265.808i | −0.405813 | − | 0.405813i | ||||
\(656\) | −72.9948 | − | 72.9948i | −0.111273 | − | 0.111273i | ||||
\(657\) | 202.256 | − | 202.256i | 0.307847 | − | 0.307847i | ||||
\(658\) | 95.8846 | − | 95.8846i | 0.145721 | − | 0.145721i | ||||
\(659\) | 227.685 | 0.345500 | 0.172750 | − | 0.984966i | \(-0.444735\pi\) | ||||
0.172750 | + | 0.984966i | \(0.444735\pi\) | |||||||
\(660\) | 63.8461i | 0.0967365i | ||||||||
\(661\) | 107.012 | − | 107.012i | 0.161894 | − | 0.161894i | −0.621511 | − | 0.783405i | \(-0.713481\pi\) |
0.783405 | + | 0.621511i | \(0.213481\pi\) | |||||||
\(662\) | 201.247i | 0.303999i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −444.133 | −0.668875 | ||||||||
\(665\) | 405.167 | + | 405.167i | 0.609273 | + | 0.609273i | ||||
\(666\) | 157.061 | 0.235828 | ||||||||
\(667\) | 71.7691i | 0.107600i | ||||||||
\(668\) | −228.862 | − | 228.862i | −0.342607 | − | 0.342607i | ||||
\(669\) | 267.655 | + | 267.655i | 0.400082 | + | 0.400082i | ||||
\(670\) | 70.3435 | − | 70.3435i | 0.104990 | − | 0.104990i | ||||
\(671\) | −53.0653 | + | 53.0653i | −0.0790838 | + | 0.0790838i | ||||
\(672\) | 94.6410 | 0.140835 | ||||||||
\(673\) | − | 707.991i | − | 1.05199i | −0.850487 | − | 0.525996i | \(-0.823693\pi\) | ||
0.850487 | − | 0.525996i | \(-0.176307\pi\) | |||||||
\(674\) | 347.508 | − | 347.508i | 0.515590 | − | 0.515590i | ||||
\(675\) | − | 113.196i | − | 0.167698i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −754.592 | −1.11461 | −0.557306 | − | 0.830307i | \(-0.688165\pi\) | ||||
−0.557306 | + | 0.830307i | \(0.688165\pi\) | |||||||
\(678\) | 78.3154 | + | 78.3154i | 0.115509 | + | 0.115509i | ||||
\(679\) | 1502.46 | 2.21276 | ||||||||
\(680\) | − | 96.0000i | − | 0.141176i | ||||||
\(681\) | 79.1769 | + | 79.1769i | 0.116266 | + | 0.116266i | ||||
\(682\) | 322.259 | + | 322.259i | 0.472521 | + | 0.472521i | ||||
\(683\) | 101.678 | − | 101.678i | 0.148870 | − | 0.148870i | −0.628743 | − | 0.777613i | \(-0.716430\pi\) |
0.777613 | + | 0.628743i | \(0.216430\pi\) | |||||||
\(684\) | −140.354 | + | 140.354i | −0.205196 | + | 0.205196i | ||||
\(685\) | −204.231 | −0.298147 | ||||||||
\(686\) | − | 64.1858i | − | 0.0935654i | ||||||
\(687\) | −101.645 | + | 101.645i | −0.147955 | + | 0.147955i | ||||
\(688\) | − | 61.3590i | − | 0.0891846i | ||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −18.1999 | −0.0263767 | ||||||||
\(691\) | −385.030 | − | 385.030i | −0.557207 | − | 0.557207i | 0.371304 | − | 0.928511i | \(-0.378911\pi\) |
−0.928511 | + | 0.371304i | \(0.878911\pi\) | |||||||
\(692\) | 536.918 | 0.775893 | ||||||||
\(693\) | − | 297.846i | − | 0.429792i | ||||||
\(694\) | −437.703 | − | 437.703i | −0.630695 | − | 0.630695i | ||||
\(695\) | −121.352 | − | 121.352i | −0.174608 | − | 0.174608i | ||||
\(696\) | −60.0000 | + | 60.0000i | −0.0862069 | + | 0.0862069i | ||||
\(697\) | 345.415 | − | 345.415i | 0.495574 | − | 0.495574i | ||||
\(698\) | 633.794 | 0.908014 | ||||||||
\(699\) | 659.338i | 0.943259i | ||||||||
\(700\) | 297.583 | − | 297.583i | 0.425119 | − | 0.425119i | ||||
\(701\) | − | 568.344i | − | 0.810761i | −0.914148 | − | 0.405381i | \(-0.867139\pi\) | ||
0.914148 | − | 0.405381i | \(-0.132861\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1224.68 | −1.74207 | ||||||||
\(704\) | −58.1436 | − | 58.1436i | −0.0825903 | − | 0.0825903i | ||||
\(705\) | −30.8306 | −0.0437314 | ||||||||
\(706\) | − | 830.074i | − | 1.17574i | ||||||
\(707\) | −1275.95 | − | 1275.95i | −1.80475 | − | 1.80475i | ||||
\(708\) | 161.885 | + | 161.885i | 0.228651 | + | 0.228651i | ||||
\(709\) | −259.419 | + | 259.419i | −0.365894 | + | 0.365894i | −0.865977 | − | 0.500084i | \(-0.833303\pi\) |
0.500084 | + | 0.865977i | \(0.333303\pi\) | |||||||
\(710\) | 192.862 | − | 192.862i | 0.271636 | − | 0.271636i | ||||
\(711\) | 35.6269 | 0.0501082 | ||||||||
\(712\) | − | 474.564i | − | 0.666523i | ||||||
\(713\) | −91.8629 | + | 91.8629i | −0.128840 | + | 0.128840i | ||||
\(714\) | 447.846i | 0.627235i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 571.559 | 0.798267 | ||||||||
\(717\) | 289.492 | + | 289.492i | 0.403755 | + | 0.403755i | ||||
\(718\) | 128.554 | 0.179044 | ||||||||
\(719\) | − | 263.520i | − | 0.366510i | −0.983065 | − | 0.183255i | \(-0.941337\pi\) | ||
0.983065 | − | 0.183255i | \(-0.0586633\pi\) | |||||||
\(720\) | −15.2154 | − | 15.2154i | −0.0211325 | − | 0.0211325i | ||||
\(721\) | 568.695 | + | 568.695i | 0.788759 | + | 0.788759i | ||||
\(722\) | 733.400 | − | 733.400i | 1.01579 | − | 1.01579i | ||||
\(723\) | −3.77053 | + | 3.77053i | −0.00521511 | + | 0.00521511i | ||||
\(724\) | −355.292 | −0.490735 | ||||||||
\(725\) | 377.321i | 0.520442i | ||||||||
\(726\) | 26.5936 | − | 26.5936i | 0.0366303 | − | 0.0366303i | ||||
\(727\) | − | 878.415i | − | 1.20827i | −0.796880 | − | 0.604137i | \(-0.793518\pi\) | ||
0.796880 | − | 0.604137i | \(-0.206482\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | −170.967 | − | 170.967i | −0.234201 | − | 0.234201i | ||||
\(731\) | 290.354 | 0.397201 | ||||||||
\(732\) | − | 25.2923i | − | 0.0345524i | ||||||
\(733\) | 146.627 | + | 146.627i | 0.200037 | + | 0.200037i | 0.800016 | − | 0.599979i | \(-0.204824\pi\) |
−0.599979 | + | 0.800016i | \(0.704824\pi\) | |||||||
\(734\) | 217.785 | + | 217.785i | 0.296709 | + | 0.296709i | ||||
\(735\) | 97.2923 | − | 97.2923i | 0.132371 | − | 0.132371i | ||||
\(736\) | 16.5744 | − | 16.5744i | 0.0225195 | − | 0.0225195i | ||||
\(737\) | 403.213 | 0.547100 | ||||||||
\(738\) | − | 109.492i | − | 0.148364i | ||||||
\(739\) | 455.161 | − | 455.161i | 0.615915 | − | 0.615915i | −0.328566 | − | 0.944481i | \(-0.606565\pi\) |
0.944481 | + | 0.328566i | \(0.106565\pi\) | |||||||
\(740\) | − | 132.764i | − | 0.179411i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 842.487 | 1.13543 | ||||||||
\(743\) | 9.63963 | + | 9.63963i | 0.0129739 | + | 0.0129739i | 0.713564 | − | 0.700590i | \(-0.247080\pi\) |
−0.700590 | + | 0.713564i | \(0.747080\pi\) | |||||||
\(744\) | −153.597 | −0.206448 | ||||||||
\(745\) | − | 101.969i | − | 0.136871i | ||||||
\(746\) | 219.606 | + | 219.606i | 0.294378 | + | 0.294378i | ||||
\(747\) | −333.100 | − | 333.100i | −0.445917 | − | 0.445917i | ||||
\(748\) | 275.138 | − | 275.138i | 0.367832 | − | 0.367832i | ||||
\(749\) | 700.070 | − | 700.070i | 0.934673 | − | 0.934673i | ||||
\(750\) | −205.492 | −0.273990 | ||||||||
\(751\) | − | 160.077i | − | 0.213152i | −0.994305 | − | 0.106576i | \(-0.966011\pi\) | ||
0.994305 | − | 0.106576i | \(-0.0339887\pi\) | |||||||
\(752\) | 28.0770 | − | 28.0770i | 0.0373364 | − | 0.0373364i | ||||
\(753\) | 361.492i | 0.480069i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 139.572 | 0.184864 | ||||||||
\(756\) | 70.9808 | + | 70.9808i | 0.0938899 | + | 0.0938899i | ||||
\(757\) | −1467.38 | −1.93842 | −0.969210 | − | 0.246234i | \(-0.920807\pi\) | ||||
−0.969210 | + | 0.246234i | \(0.920807\pi\) | |||||||
\(758\) | 274.214i | 0.361760i | ||||||||
\(759\) | −52.1615 | − | 52.1615i | −0.0687239 | − | 0.0687239i | ||||
\(760\) | 118.641 | + | 118.641i | 0.156107 | + | 0.156107i | ||||
\(761\) | −129.367 | + | 129.367i | −0.169995 | + | 0.169995i | −0.786977 | − | 0.616982i | \(-0.788355\pi\) |
0.616982 | + | 0.786977i | \(0.288355\pi\) | |||||||
\(762\) | 410.229 | − | 410.229i | 0.538359 | − | 0.538359i | ||||
\(763\) | −658.275 | −0.862746 | ||||||||
\(764\) | 394.641i | 0.516546i | ||||||||
\(765\) | 72.0000 | − | 72.0000i | 0.0941176 | − | 0.0941176i | ||||
\(766\) | − | 275.503i | − | 0.359664i | ||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 27.7128 | 0.0360844 | ||||||||
\(769\) | −961.315 | − | 961.315i | −1.25008 | − | 1.25008i | −0.955681 | − | 0.294404i | \(-0.904879\pi\) |
−0.294404 | − | 0.955681i | \(-0.595121\pi\) | |||||||
\(770\) | −251.769 | −0.326973 | ||||||||
\(771\) | 128.554i | 0.166736i | ||||||||
\(772\) | −29.6987 | − | 29.6987i | −0.0384699 | − | 0.0384699i | ||||
\(773\) | 692.232 | + | 692.232i | 0.895513 | + | 0.895513i | 0.995035 | − | 0.0995220i | \(-0.0317314\pi\) |
−0.0995220 | + | 0.995035i | \(0.531731\pi\) | |||||||
\(774\) | 46.0192 | − | 46.0192i | 0.0594564 | − | 0.0594564i | ||||
\(775\) | −482.962 | + | 482.962i | −0.623177 | + | 0.623177i | ||||
\(776\) | 439.951 | 0.566947 | ||||||||
\(777\) | 619.352i | 0.797107i | ||||||||
\(778\) | −17.7513 | + | 17.7513i | −0.0228166 | + | 0.0228166i | ||||
\(779\) | 853.759i | 1.09597i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1105.49 | 1.41548 | ||||||||
\(782\) | 78.4308 | + | 78.4308i | 0.100295 | + | 0.100295i | ||||
\(783\) | −90.0000 | −0.114943 | ||||||||
\(784\) | 177.205i | 0.226027i | ||||||||
\(785\) | 70.2834 | + | 70.2834i | 0.0895330 | + | 0.0895330i | ||||
\(786\) | 363.100 | + | 363.100i | 0.461959 | + | 0.461959i | ||||
\(787\) | −83.4533 | + | 83.4533i | −0.106040 | + | 0.106040i | −0.758136 | − | 0.652096i | \(-0.773890\pi\) |
0.652096 | + | 0.758136i | \(0.273890\pi\) | |||||||
\(788\) | 213.913 | − | 213.913i | 0.271463 | − | 0.271463i | ||||
\(789\) | −42.1999 | −0.0534853 | ||||||||
\(790\) | − | 30.1154i | − | 0.0381208i | ||||||
\(791\) | −308.827 | + | 308.827i | −0.390426 | + | 0.390426i | ||||
\(792\) | − | 87.2154i | − | 0.110120i | ||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −477.286 | −0.601116 | ||||||||
\(795\) | −135.446 | − | 135.446i | −0.170373 | − | 0.170373i | ||||
\(796\) | 44.4308 | 0.0558176 | ||||||||
\(797\) | − | 567.118i | − | 0.711566i | −0.934569 | − | 0.355783i | \(-0.884214\pi\) | ||
0.934569 | − | 0.355783i | \(-0.115786\pi\) | |||||||
\(798\) | −553.468 | − | 553.468i | −0.693569 | − | 0.693569i | ||||
\(799\) | 132.862 | + | 132.862i | 0.166285 | + | 0.166285i | ||||
\(800\) | 87.1384 | − | 87.1384i | 0.108923 | − | 0.108923i | ||||
\(801\) | 355.923 | − | 355.923i | 0.444348 | − | 0.444348i | ||||
\(802\) | 726.831 | 0.906273 | ||||||||
\(803\) | − | 979.990i | − | 1.22041i | ||||||
\(804\) | −96.0910 | + | 96.0910i | −0.119516 | + | 0.119516i | ||||
\(805\) | − | 71.7691i | − | 0.0891542i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −304.392 | −0.377190 | ||||||||
\(808\) | −373.626 | − | 373.626i | −0.462408 | − | 0.462408i | ||||
\(809\) | 87.4462 | 0.108092 | 0.0540459 | − | 0.998538i | \(-0.482788\pi\) | ||||
0.0540459 | + | 0.998538i | \(0.482788\pi\) | |||||||
\(810\) | − | 22.8231i | − | 0.0281766i | ||||||
\(811\) | 519.193 | + | 519.193i | 0.640189 | + | 0.640189i | 0.950602 | − | 0.310413i | \(-0.100467\pi\) |
−0.310413 | + | 0.950602i | \(0.600467\pi\) | |||||||
\(812\) | −236.603 | − | 236.603i | −0.291382 | − | 0.291382i | ||||
\(813\) | 341.293 | − | 341.293i | 0.419794 | − | 0.419794i | ||||
\(814\) | 380.505 | − | 380.505i | 0.467451 | − | 0.467451i | ||||
\(815\) | 366.826 | 0.450093 | ||||||||
\(816\) | 131.138i | 0.160709i | ||||||||
\(817\) | −358.832 | + | 358.832i | −0.439207 | + | 0.439207i | ||||
\(818\) | 824.053i | 1.00740i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −92.5538 | −0.112870 | ||||||||
\(821\) | −406.750 | − | 406.750i | −0.495432 | − | 0.495432i | 0.414580 | − | 0.910013i | \(-0.363928\pi\) |
−0.910013 | + | 0.414580i | \(0.863928\pi\) | |||||||
\(822\) | 278.985 | 0.339397 | ||||||||
\(823\) | 329.169i | 0.399963i | 0.979800 | + | 0.199981i | \(0.0640882\pi\) | ||||
−0.979800 | + | 0.199981i | \(0.935912\pi\) | |||||||
\(824\) | 166.526 | + | 166.526i | 0.202094 | + | 0.202094i | ||||
\(825\) | −274.235 | − | 274.235i | −0.332406 | − | 0.332406i | ||||
\(826\) | −638.372 | + | 638.372i | −0.772847 | + | 0.772847i | ||||
\(827\) | −514.410 | + | 514.410i | −0.622020 | + | 0.622020i | −0.946048 | − | 0.324028i | \(-0.894963\pi\) |
0.324028 | + | 0.946048i | \(0.394963\pi\) | |||||||
\(828\) | 24.8616 | 0.0300260 | ||||||||
\(829\) | − | 943.092i | − | 1.13763i | −0.822467 | − | 0.568813i | \(-0.807403\pi\) | ||
0.822467 | − | 0.568813i | \(-0.192597\pi\) | |||||||
\(830\) | −281.569 | + | 281.569i | −0.339240 | + | 0.339240i | ||||
\(831\) | 774.200i | 0.931649i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −838.543 | −1.00665 | ||||||||
\(834\) | 165.771 | + | 165.771i | 0.198766 | + | 0.198766i | ||||
\(835\) | −290.185 | −0.347527 | ||||||||
\(836\) | 680.056i | 0.813465i | ||||||||
\(837\) | −115.198 | − | 115.198i | −0.137632 | − | 0.137632i | ||||
\(838\) | 782.354 | + | 782.354i | 0.933596 | + | 0.933596i | ||||
\(839\) | 556.070 | − | 556.070i | 0.662778 | − | 0.662778i | −0.293256 | − | 0.956034i | \(-0.594739\pi\) |
0.956034 | + | 0.293256i | \(0.0947389\pi\) | |||||||
\(840\) | 60.0000 | − | 60.0000i | 0.0714286 | − | 0.0714286i | ||||
\(841\) | −541.000 | −0.643282 | ||||||||
\(842\) | − | 54.0704i | − | 0.0642166i | ||||||
\(843\) | 9.60392 | − | 9.60392i | 0.0113926 | − | 0.0113926i | ||||
\(844\) | 128.403i | 0.152136i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 42.1154 | 0.0497818 | ||||||||
\(847\) | 104.869 | + | 104.869i | 0.123812 | + | 0.123812i | ||||
\(848\) | 246.697 | 0.290917 | ||||||||
\(849\) | 28.8320i | 0.0339600i | ||||||||
\(850\) | 412.344 | + | 412.344i | 0.485110 | + | 0.485110i | ||||
\(851\) | 108.466 | + | 108.466i | 0.127458 | + | 0.127458i | ||||
\(852\) | −263.454 | + | 263.454i | −0.309218 | + | 0.309218i | ||||
\(853\) | −472.527 | + | 472.527i | −0.553960 | + | 0.553960i | −0.927581 | − | 0.373622i | \(-0.878116\pi\) |
0.373622 | + | 0.927581i | \(0.378116\pi\) | |||||||
\(854\) | 99.7372 | 0.116788 | ||||||||
\(855\) | 177.962i | 0.208142i | ||||||||
\(856\) | 204.995 | − | 204.995i | 0.239480 | − | 0.239480i | ||||
\(857\) | − | 436.543i | − | 0.509386i | −0.967022 | − | 0.254693i | \(-0.918026\pi\) | ||
0.967022 | − | 0.254693i | \(-0.0819743\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1238.40 | −1.44167 | −0.720837 | − | 0.693104i | \(-0.756243\pi\) | ||||
−0.720837 | + | 0.693104i | \(0.756243\pi\) | |||||||
\(860\) | −38.9000 | − | 38.9000i | −0.0452326 | − | 0.0452326i | ||||
\(861\) | 431.769 | 0.501474 | ||||||||
\(862\) | 890.620i | 1.03320i | ||||||||
\(863\) | −729.373 | − | 729.373i | −0.845160 | − | 0.845160i | 0.144365 | − | 0.989525i | \(-0.453886\pi\) |
−0.989525 | + | 0.144365i | \(0.953886\pi\) | |||||||
\(864\) | 20.7846 | + | 20.7846i | 0.0240563 | + | 0.0240563i | ||||
\(865\) | 340.392 | − | 340.392i | 0.393517 | − | 0.393517i | ||||
\(866\) | 237.785 | − | 237.785i | 0.274578 | − | 0.274578i | ||||
\(867\) | −119.991 | −0.138398 | ||||||||
\(868\) | − | 605.692i | − | 0.697802i | ||||||
\(869\) | 86.3116 | − | 86.3116i | 0.0993229 | − | 0.0993229i | ||||
\(870\) | 76.0770i | 0.0874448i | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −192.756 | −0.221051 | ||||||||
\(873\) | 329.963 | + | 329.963i | 0.377965 | + | 0.377965i | ||||
\(874\) | −193.856 | −0.221804 | ||||||||
\(875\) | − | 810.333i | − | 0.926095i | ||||||
\(876\) | 233.545 | + | 233.545i | 0.266604 | + | 0.266604i | ||||
\(877\) | 962.069 | + | 962.069i | 1.09700 | + | 1.09700i | 0.994760 | + | 0.102240i | \(0.0326011\pi\) |
0.102240 | + | 0.994760i | \(0.467399\pi\) | |||||||
\(878\) | 689.463 | − | 689.463i | 0.785265 | − | 0.785265i | ||||
\(879\) | −229.450 | + | 229.450i | −0.261035 | + | 0.261035i | ||||
\(880\) | −73.7231 | −0.0837763 | ||||||||
\(881\) | 1563.66i | 1.77487i | 0.460929 | + | 0.887437i | \(0.347516\pi\) | ||||
−0.460929 | + | 0.887437i | \(0.652484\pi\) | |||||||
\(882\) | −132.904 | + | 132.904i | −0.150685 | + | 0.150685i | ||||
\(883\) | − | 452.723i | − | 0.512710i | −0.966583 | − | 0.256355i | \(-0.917478\pi\) | ||
0.966583 | − | 0.256355i | \(-0.0825216\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 205.261 | 0.231934 | ||||||||
\(886\) | 304.028 | + | 304.028i | 0.343147 | + | 0.343147i | ||||
\(887\) | 910.939 | 1.02699 | 0.513494 | − | 0.858093i | \(-0.328351\pi\) | ||||
0.513494 | + | 0.858093i | \(0.328351\pi\) | |||||||
\(888\) | 181.359i | 0.204233i | ||||||||
\(889\) | 1617.69 | + | 1617.69i | 1.81967 | + | 1.81967i | ||||
\(890\) | −300.862 | − | 300.862i | −0.338047 | − | 0.338047i | ||||
\(891\) | 65.4115 | − | 65.4115i | 0.0734136 | − | 0.0734136i | ||||
\(892\) | −309.061 | + | 309.061i | −0.346481 | + | 0.346481i | ||||
\(893\) | −328.392 | −0.367741 | ||||||||
\(894\) | 139.292i | 0.155808i | ||||||||
\(895\) | 362.354 | − | 362.354i | 0.404865 | − | 0.404865i | ||||
\(896\) | 109.282i | 0.121967i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −401.387 | −0.446979 | ||||||||
\(899\) | 383.993 | + | 383.993i | 0.427134 | + | 0.427134i | ||||
\(900\) | 130.708 | 0.145231 | ||||||||
\(901\) | 1167.38i | 1.29565i | ||||||||
\(902\) | −265.261 | − | 265.261i | −0.294081 | − | 0.294081i | ||||
\(903\) | 181.471 | + | 181.471i | 0.200965 | + | 0.200965i | ||||
\(904\) | −90.4308 | + | 90.4308i | −0.100034 | + | 0.100034i | ||||
\(905\) | −225.246 | + | 225.246i | −0.248891 | + | 0.248891i | ||||
\(906\) | −190.659 | −0.210440 | ||||||||
\(907\) | 445.138i | 0.490781i | 0.969424 | + | 0.245391i | \(0.0789162\pi\) | ||||
−0.969424 | + | 0.245391i | \(0.921084\pi\) | |||||||
\(908\) | −91.4256 | + | 91.4256i | −0.100689 | + | 0.100689i | ||||
\(909\) | − | 560.438i | − | 0.616544i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 717.233 | 0.787303 | 0.393652 | − | 0.919260i | \(-0.371212\pi\) | ||||
0.393652 | + | 0.919260i | \(0.371212\pi\) | |||||||
\(912\) | −162.067 | − | 162.067i | −0.177705 | − | 0.177705i | ||||
\(913\) | −1613.97 | −1.76776 | ||||||||
\(914\) | − | 203.037i | − | 0.222141i | ||||||
\(915\) | −16.0347 | − | 16.0347i | −0.0175243 | − | 0.0175243i | ||||
\(916\) | −117.369 | − | 117.369i | −0.128132 | − | 0.128132i | ||||
\(917\) | −1431.84 | + | 1431.84i | −1.56144 | + | 1.56144i | ||||
\(918\) | −98.3538 | + | 98.3538i | −0.107139 | + | 0.107139i | ||||
\(919\) | 743.138 | 0.808638 | 0.404319 | − | 0.914618i | \(-0.367509\pi\) | ||||
0.404319 | + | 0.914618i | \(0.367509\pi\) | |||||||
\(920\) | − | 21.0155i | − | 0.0228429i | ||||||
\(921\) | −649.638 | + | 649.638i | −0.705361 | + | 0.705361i | ||||
\(922\) | − | 832.246i | − | 0.902653i | ||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 343.923 | 0.372211 | ||||||||
\(925\) | 570.254 | + | 570.254i | 0.616491 | + | 0.616491i | ||||
\(926\) | −339.199 | −0.366305 | ||||||||
\(927\) | 249.788i | 0.269459i | ||||||||
\(928\) | −69.2820 | − | 69.2820i | −0.0746574 | − | 0.0746574i | ||||
\(929\) | 1042.54 | + | 1042.54i | 1.12222 | + | 1.12222i | 0.991407 | + | 0.130814i | \(0.0417592\pi\) |
0.130814 | + | 0.991407i | \(0.458241\pi\) | |||||||
\(930\) | −97.3768 | + | 97.3768i | −0.104706 | + | 0.104706i | ||||
\(931\) | 1036.31 | − | 1036.31i | 1.11311 | − | 1.11311i | ||||
\(932\) | −761.338 | −0.816887 | ||||||||
\(933\) | − | 513.100i | − | 0.549946i | ||||||
\(934\) | 732.649 | − | 732.649i | 0.784420 | − | 0.784420i | ||||
\(935\) | − | 348.862i | − | 0.373114i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −172.477 | −0.184073 | −0.0920367 | − | 0.995756i | \(-0.529338\pi\) | ||||
−0.0920367 | + | 0.995756i | \(0.529338\pi\) | |||||||
\(938\) | −378.923 | − | 378.923i | −0.403969 | − | 0.403969i | ||||
\(939\) | 204.877 | 0.218186 | ||||||||
\(940\) | − | 35.6001i | − | 0.0378725i | ||||||
\(941\) | −145.055 | − | 145.055i | −0.154150 | − | 0.154150i | 0.625819 | − | 0.779969i | \(-0.284765\pi\) |
−0.779969 | + | 0.625819i | \(0.784765\pi\) | |||||||
\(942\) | −96.0089 | − | 96.0089i | −0.101920 | − | 0.101920i | ||||
\(943\) | 75.6152 | − | 75.6152i | 0.0801858 | − | 0.0801858i | ||||
\(944\) | −186.928 | + | 186.928i | −0.198017 | + | 0.198017i | ||||
\(945\) | 90.0000 | 0.0952381 | ||||||||
\(946\) | − | 222.977i | − | 0.235705i | ||||||
\(947\) | −487.474 | + | 487.474i | −0.514757 | + | 0.514757i | −0.915980 | − | 0.401224i | \(-0.868585\pi\) |
0.401224 | + | 0.915980i | \(0.368585\pi\) | |||||||
\(948\) | 41.1384i | 0.0433950i | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −1019.18 | −1.07283 | ||||||||
\(951\) | 486.200 | + | 486.200i | 0.511251 | + | 0.511251i | ||||
\(952\) | −517.128 | −0.543202 | ||||||||
\(953\) | 1206.62i | 1.26613i | 0.774100 | + | 0.633063i | \(0.218203\pi\) | ||||
−0.774100 | + | 0.633063i | \(0.781797\pi\) | |||||||
\(954\) | 185.023 | + | 185.023i | 0.193944 | + | 0.193944i | ||||
\(955\) | 250.192 | + | 250.192i | 0.261982 | + | 0.261982i | ||||
\(956\) | −334.277 | + | 334.277i | −0.349662 | + | 0.349662i | ||||
\(957\) | −218.038 | + | 218.038i | −0.227835 | + | 0.227835i | ||||
\(958\) | 522.928 | 0.545854 | ||||||||
\(959\) | 1100.14i | 1.14718i | ||||||||
\(960\) | 17.5692 | − | 17.5692i | 0.0183013 | − | 0.0183013i | ||||
\(961\) | 22.0065i | 0.0228996i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 307.492 | 0.319307 | ||||||||
\(964\) | −4.35383 | − | 4.35383i | −0.00451642 | − | 0.00451642i | ||||
\(965\) | −37.6565 | −0.0390223 | ||||||||
\(966\) | 98.0385i | 0.101489i | ||||||||
\(967\) | 169.831 | + | 169.831i | 0.175626 | + | 0.175626i | 0.789446 | − | 0.613820i | \(-0.210368\pi\) |
−0.613820 | + | 0.789446i | \(0.710368\pi\) | |||||||
\(968\) | 30.7077 | + | 30.7077i | 0.0317228 | + | 0.0317228i | ||||
\(969\) | 766.908 | − | 766.908i | 0.791442 | − | 0.791442i | ||||
\(970\) | 278.918 | − | 278.918i | 0.287544 | − | 0.287544i | ||||
\(971\) | 747.700 | 0.770031 | 0.385015 | − | 0.922910i | \(-0.374196\pi\) | ||||
0.385015 | + | 0.922910i | \(0.374196\pi\) | |||||||
\(972\) | 31.1769i | 0.0320750i | ||||||||
\(973\) | −653.695 | + | 653.695i | −0.671835 | + | 0.671835i | ||||
\(974\) | − | 274.000i | − | 0.281314i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 29.2051 | 0.0299232 | ||||||||
\(977\) | 152.967 | + | 152.967i | 0.156568 | + | 0.156568i | 0.781044 | − | 0.624476i | \(-0.214687\pi\) |
−0.624476 | + | 0.781044i | \(0.714687\pi\) | |||||||
\(978\) | −501.093 | −0.512365 | ||||||||
\(979\) | − | 1724.55i | − | 1.76155i | ||||||
\(980\) | 112.344 | + | 112.344i | 0.114636 | + | 0.114636i | ||||
\(981\) | −144.567 | − | 144.567i | −0.147367 | − | 0.147367i | ||||
\(982\) | −36.9282 | + | 36.9282i | −0.0376051 | + | 0.0376051i | ||||
\(983\) | −1367.93 | + | 1367.93i | −1.39158 | + | 1.39158i | −0.569801 | + | 0.821783i | \(0.692980\pi\) |
−0.821783 | + | 0.569801i | \(0.807020\pi\) | |||||||
\(984\) | 126.431 | 0.128487 | ||||||||
\(985\) | − | 271.230i | − | 0.275361i | ||||||
\(986\) | 327.846 | − | 327.846i | 0.332501 | − | 0.332501i | ||||
\(987\) | 166.077i | 0.168264i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 63.5617 | 0.0642686 | ||||||||
\(990\) | −55.2923 | − | 55.2923i | −0.0558509 | − | 0.0558509i | ||||
\(991\) | −1871.26 | −1.88826 | −0.944128 | − | 0.329579i | \(-0.893093\pi\) | ||||
−0.944128 | + | 0.329579i | \(0.893093\pi\) | |||||||
\(992\) | − | 177.359i | − | 0.178789i | ||||||
\(993\) | −174.285 | − | 174.285i | −0.175514 | − | 0.175514i | ||||
\(994\) | −1038.90 | − | 1038.90i | −1.04517 | − | 1.04517i | ||||
\(995\) | 28.1680 | − | 28.1680i | 0.0283095 | − | 0.0283095i | ||||
\(996\) | 384.631 | − | 384.631i | 0.386175 | − | 0.386175i | ||||
\(997\) | 1537.17 | 1.54179 | 0.770897 | − | 0.636960i | \(-0.219808\pi\) | ||||
0.770897 | + | 0.636960i | \(0.219808\pi\) | |||||||
\(998\) | 925.538i | 0.927393i | ||||||||
\(999\) | −136.019 | + | 136.019i | −0.136155 | + | 0.136155i |
(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 | 1014.3.f.d.775.2 | 4 | ||
13.4 | even | 6 | 78.3.l.a.37.1 | yes | 4 | ||
13.5 | odd | 4 | inner | 1014.3.f.d.577.2 | 4 | ||
13.8 | odd | 4 | 1014.3.f.e.577.2 | 4 | |||
13.11 | odd | 12 | 78.3.l.a.19.1 | ✓ | 4 | ||
13.12 | even | 2 | 1014.3.f.e.775.2 | 4 | |||
39.11 | even | 12 | 234.3.bb.c.19.1 | 4 | |||
39.17 | odd | 6 | 234.3.bb.c.37.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
78.3.l.a.19.1 | ✓ | 4 | 13.11 | odd | 12 | ||
78.3.l.a.37.1 | yes | 4 | 13.4 | even | 6 | ||
234.3.bb.c.19.1 | 4 | 39.11 | even | 12 | |||
234.3.bb.c.37.1 | 4 | 39.17 | odd | 6 | |||
1014.3.f.d.577.2 | 4 | 13.5 | odd | 4 | inner | ||
1014.3.f.d.775.2 | 4 | 1.1 | even | 1 | trivial | ||
1014.3.f.e.577.2 | 4 | 13.8 | odd | 4 | |||
1014.3.f.e.775.2 | 4 | 13.12 | even | 2 |