Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,3,Mod(151,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.151");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.17440793081\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.6080256576.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 7x^{6} - 12x^{5} + 12x^{4} - 48x^{3} + 112x^{2} - 192x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 151.1 | ||
Root | \(-1.51328 - 1.30766i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.151 |
Dual form | 300.3.c.f.151.2 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.88911 | − | 0.656712i | −0.944554 | − | 0.328356i | ||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 3.13746 | + | 2.48120i | 0.784365 | + | 0.620300i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.13746 | − | 3.27203i | 0.189576 | − | 0.545339i | ||||
\(7\) | − | 9.55505i | − | 1.36501i | −0.730882 | − | 0.682504i | \(-0.760891\pi\) | ||
0.730882 | − | 0.682504i | \(-0.239109\pi\) | |||||||
\(8\) | −4.29756 | − | 6.74766i | −0.537196 | − | 0.843458i | ||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 9.92480i | 0.902255i | 0.892460 | + | 0.451127i | \(0.148978\pi\) | ||||
−0.892460 | + | 0.451127i | \(0.851022\pi\) | |||||||
\(12\) | −4.29756 | + | 5.43424i | −0.358130 | + | 0.452853i | ||||
\(13\) | −7.55643 | −0.581264 | −0.290632 | − | 0.956835i | \(-0.593866\pi\) | ||||
−0.290632 | + | 0.956835i | \(0.593866\pi\) | |||||||
\(14\) | −6.27492 | + | 18.0505i | −0.448208 | + | 1.28932i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.68729 | + | 15.5693i | 0.230456 | + | 0.973083i | ||||
\(17\) | −17.1903 | −1.01119 | −0.505596 | − | 0.862770i | \(-0.668727\pi\) | ||||
−0.505596 | + | 0.862770i | \(0.668727\pi\) | |||||||
\(18\) | 5.66732 | + | 1.97014i | 0.314851 | + | 0.109452i | ||||
\(19\) | − | 26.1762i | − | 1.37770i | −0.724905 | − | 0.688849i | \(-0.758116\pi\) | ||
0.724905 | − | 0.688849i | \(-0.241884\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 16.5498 | 0.788087 | ||||||||
\(22\) | 6.51774 | − | 18.7490i | 0.296261 | − | 0.852228i | ||||
\(23\) | − | 1.67451i | − | 0.0728047i | −0.999337 | − | 0.0364023i | \(-0.988410\pi\) | ||
0.999337 | − | 0.0364023i | \(-0.0115898\pi\) | |||||||
\(24\) | 11.6873 | − | 7.44360i | 0.486971 | − | 0.310150i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 14.2749 | + | 4.96240i | 0.549035 | + | 0.190862i | ||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | 23.7080 | − | 29.9786i | 0.846714 | − | 1.07066i | ||||
\(29\) | 0.350497 | 0.0120861 | 0.00604305 | − | 0.999982i | \(-0.498076\pi\) | ||||
0.00604305 | + | 0.999982i | \(0.498076\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 46.0258i | − | 1.48470i | −0.670010 | − | 0.742352i | \(-0.733710\pi\) | ||
0.670010 | − | 0.742352i | \(-0.266290\pi\) | |||||||
\(32\) | 3.25887 | − | 31.8336i | 0.101840 | − | 0.994801i | ||||
\(33\) | −17.1903 | −0.520917 | ||||||||
\(34\) | 32.4743 | + | 11.2890i | 0.955125 | + | 0.332031i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −9.41238 | − | 7.44360i | −0.261455 | − | 0.206767i | ||||
\(37\) | −22.6693 | −0.612684 | −0.306342 | − | 0.951922i | \(-0.599105\pi\) | ||||
−0.306342 | + | 0.951922i | \(0.599105\pi\) | |||||||
\(38\) | −17.1903 | + | 49.4498i | −0.452375 | + | 1.30131i | ||||
\(39\) | − | 13.0881i | − | 0.335593i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −77.2990 | −1.88534 | −0.942671 | − | 0.333724i | \(-0.891695\pi\) | ||||
−0.942671 | + | 0.333724i | \(0.891695\pi\) | |||||||
\(42\) | −31.2644 | − | 10.8685i | −0.744391 | − | 0.258773i | ||||
\(43\) | − | 41.7994i | − | 0.972079i | −0.873937 | − | 0.486039i | \(-0.838441\pi\) | ||
0.873937 | − | 0.486039i | \(-0.161559\pi\) | |||||||
\(44\) | −24.6254 | + | 31.1386i | −0.559668 | + | 0.707697i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.09967 | + | 3.16332i | −0.0239058 | + | 0.0687679i | ||||
\(47\) | − | 14.0866i | − | 0.299715i | −0.988708 | − | 0.149857i | \(-0.952119\pi\) | ||
0.988708 | − | 0.149857i | \(-0.0478814\pi\) | |||||||
\(48\) | −26.9669 | + | 6.38658i | −0.561810 | + | 0.133054i | ||||
\(49\) | −42.2990 | −0.863245 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 29.7744i | − | 0.583812i | ||||||
\(52\) | −23.7080 | − | 18.7490i | −0.455923 | − | 0.360558i | ||||
\(53\) | 22.6693 | 0.427723 | 0.213861 | − | 0.976864i | \(-0.431396\pi\) | ||||
0.213861 | + | 0.976864i | \(0.431396\pi\) | |||||||
\(54\) | −3.41238 | + | 9.81609i | −0.0631921 | + | 0.181780i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −64.4743 | + | 41.0634i | −1.15133 | + | 0.733276i | ||||
\(57\) | 45.3386 | 0.795414 | ||||||||
\(58\) | −0.662126 | − | 0.230175i | −0.0114160 | − | 0.00396854i | ||||
\(59\) | − | 94.7802i | − | 1.60644i | −0.595680 | − | 0.803222i | \(-0.703117\pi\) | ||
0.595680 | − | 0.803222i | \(-0.296883\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 38.0000 | 0.622951 | 0.311475 | − | 0.950254i | \(-0.399177\pi\) | ||||
0.311475 | + | 0.950254i | \(0.399177\pi\) | |||||||
\(62\) | −30.2257 | + | 86.9478i | −0.487512 | + | 1.40238i | ||||
\(63\) | 28.6652i | 0.455002i | ||||||||
\(64\) | −27.0619 | + | 57.9970i | −0.422842 | + | 0.906203i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 32.4743 | + | 11.2890i | 0.492034 | + | 0.171046i | ||||
\(67\) | 29.8477i | 0.445488i | 0.974877 | + | 0.222744i | \(0.0715013\pi\) | ||||
−0.974877 | + | 0.222744i | \(0.928499\pi\) | |||||||
\(68\) | −53.9337 | − | 42.6525i | −0.793143 | − | 0.627242i | ||||
\(69\) | 2.90033 | 0.0420338 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.19630i | 0.101356i | 0.998715 | + | 0.0506782i | \(0.0161383\pi\) | ||||
−0.998715 | + | 0.0506782i | \(0.983862\pi\) | |||||||
\(72\) | 12.8927 | + | 20.2430i | 0.179065 | + | 0.281153i | ||||
\(73\) | 34.3805 | 0.470966 | 0.235483 | − | 0.971878i | \(-0.424333\pi\) | ||||
0.235483 | + | 0.971878i | \(0.424333\pi\) | |||||||
\(74\) | 42.8248 | + | 14.8872i | 0.578713 | + | 0.201178i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 64.9485 | − | 82.1269i | 0.854586 | − | 1.08062i | ||||
\(77\) | 94.8320 | 1.23158 | ||||||||
\(78\) | −8.59513 | + | 24.7249i | −0.110194 | + | 0.316986i | ||||
\(79\) | − | 46.0258i | − | 0.582606i | −0.956631 | − | 0.291303i | \(-0.905911\pi\) | ||
0.956631 | − | 0.291303i | \(-0.0940887\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 146.026 | + | 50.7632i | 1.78081 | + | 0.619063i | ||||
\(83\) | 24.1336i | 0.290767i | 0.989375 | + | 0.145383i | \(0.0464415\pi\) | ||||
−0.989375 | + | 0.145383i | \(0.953558\pi\) | |||||||
\(84\) | 51.9244 | + | 41.0634i | 0.618148 | + | 0.488851i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −27.4502 | + | 78.9636i | −0.319188 | + | 0.918181i | ||||
\(87\) | 0.607078i | 0.00697791i | ||||||||
\(88\) | 66.9692 | − | 42.6525i | 0.761014 | − | 0.484687i | ||||
\(89\) | −100.199 | −1.12584 | −0.562918 | − | 0.826513i | \(-0.690321\pi\) | ||||
−0.562918 | + | 0.826513i | \(0.690321\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 72.2021i | 0.793430i | ||||||||
\(92\) | 4.15479 | − | 5.25370i | 0.0451607 | − | 0.0571054i | ||||
\(93\) | 79.7191 | 0.857195 | ||||||||
\(94\) | −9.25083 | + | 26.6111i | −0.0984131 | + | 0.283097i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 55.1375 | + | 5.64452i | 0.574349 | + | 0.0587971i | ||||
\(97\) | −131.861 | −1.35939 | −0.679696 | − | 0.733494i | \(-0.737888\pi\) | ||||
−0.679696 | + | 0.733494i | \(0.737888\pi\) | |||||||
\(98\) | 79.9074 | + | 27.7783i | 0.815382 | + | 0.283452i | ||||
\(99\) | − | 29.7744i | − | 0.300752i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 29.4502 | 0.291586 | 0.145793 | − | 0.989315i | \(-0.453427\pi\) | ||||
0.145793 | + | 0.989315i | \(0.453427\pi\) | |||||||
\(102\) | −19.5532 | + | 56.2471i | −0.191698 | + | 0.551442i | ||||
\(103\) | 143.786i | 1.39598i | 0.716107 | + | 0.697991i | \(0.245922\pi\) | ||||
−0.716107 | + | 0.697991i | \(0.754078\pi\) | |||||||
\(104\) | 32.4743 | + | 50.9882i | 0.312252 | + | 0.490272i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −42.8248 | − | 14.8872i | −0.404007 | − | 0.140445i | ||||
\(107\) | 35.1014i | 0.328050i | 0.986456 | + | 0.164025i | \(0.0524478\pi\) | ||||
−0.986456 | + | 0.164025i | \(0.947552\pi\) | |||||||
\(108\) | 12.8927 | − | 16.3027i | 0.119377 | − | 0.150951i | ||||
\(109\) | 151.498 | 1.38989 | 0.694947 | − | 0.719061i | \(-0.255428\pi\) | ||||
0.694947 | + | 0.719061i | \(0.255428\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 39.2644i | − | 0.353733i | ||||||
\(112\) | 148.766 | − | 35.2323i | 1.32827 | − | 0.314574i | ||||
\(113\) | −32.3031 | −0.285868 | −0.142934 | − | 0.989732i | \(-0.545654\pi\) | ||||
−0.142934 | + | 0.989732i | \(0.545654\pi\) | |||||||
\(114\) | −85.6495 | − | 29.7744i | −0.751311 | − | 0.261179i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.09967 | + | 0.869652i | 0.00947990 | + | 0.00749700i | ||||
\(117\) | 22.6693 | 0.193755 | ||||||||
\(118\) | −62.2433 | + | 179.050i | −0.527486 | + | 1.51737i | ||||
\(119\) | 164.254i | 1.38028i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.4983 | 0.185937 | ||||||||
\(122\) | −71.7861 | − | 24.9551i | −0.588411 | − | 0.204550i | ||||
\(123\) | − | 133.886i | − | 1.08850i | ||||||
\(124\) | 114.199 | − | 144.404i | 0.920962 | − | 1.16455i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 18.8248 | − | 54.1516i | 0.149403 | − | 0.429774i | ||||
\(127\) | 192.053i | 1.51223i | 0.654438 | + | 0.756116i | \(0.272905\pi\) | ||||
−0.654438 | + | 0.756116i | \(0.727095\pi\) | |||||||
\(128\) | 89.2102 | − | 91.7908i | 0.696954 | − | 0.717115i | ||||
\(129\) | 72.3987 | 0.561230 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 42.4277i | 0.323876i | 0.986801 | + | 0.161938i | \(0.0517744\pi\) | ||||
−0.986801 | + | 0.161938i | \(0.948226\pi\) | |||||||
\(132\) | −53.9337 | − | 42.6525i | −0.408589 | − | 0.323125i | ||||
\(133\) | −250.115 | −1.88057 | ||||||||
\(134\) | 19.6013 | − | 56.3855i | 0.146279 | − | 0.420787i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 73.8762 | + | 115.994i | 0.543208 | + | 0.852897i | ||||
\(137\) | 206.854 | 1.50988 | 0.754942 | − | 0.655791i | \(-0.227665\pi\) | ||||
0.754942 | + | 0.655791i | \(0.227665\pi\) | |||||||
\(138\) | −5.47904 | − | 1.90468i | −0.0397032 | − | 0.0138020i | ||||
\(139\) | 46.0258i | 0.331121i | 0.986200 | + | 0.165561i | \(0.0529433\pi\) | ||||
−0.986200 | + | 0.165561i | \(0.947057\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 24.3987 | 0.173040 | ||||||||
\(142\) | 4.72590 | − | 13.5946i | 0.0332810 | − | 0.0957366i | ||||
\(143\) | − | 74.9961i | − | 0.524448i | ||||||
\(144\) | −11.0619 | − | 46.7080i | −0.0768186 | − | 0.324361i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −64.9485 | − | 22.5781i | −0.444853 | − | 0.154645i | ||||
\(147\) | − | 73.2640i | − | 0.498395i | ||||||
\(148\) | −71.1240 | − | 56.2471i | −0.480567 | − | 0.380048i | ||||
\(149\) | −11.6495 | −0.0781846 | −0.0390923 | − | 0.999236i | \(-0.512447\pi\) | ||||
−0.0390923 | + | 0.999236i | \(0.512447\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 125.424i | − | 0.830624i | −0.909679 | − | 0.415312i | \(-0.863672\pi\) | ||
0.909679 | − | 0.415312i | \(-0.136328\pi\) | |||||||
\(152\) | −176.628 | + | 112.494i | −1.16203 | + | 0.740093i | ||||
\(153\) | 51.5708 | 0.337064 | ||||||||
\(154\) | −179.148 | − | 62.2773i | −1.16330 | − | 0.404398i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 32.4743 | − | 41.0634i | 0.208168 | − | 0.263227i | ||||
\(157\) | −197.220 | −1.25618 | −0.628090 | − | 0.778140i | \(-0.716163\pi\) | ||||
−0.628090 | + | 0.778140i | \(0.716163\pi\) | |||||||
\(158\) | −30.2257 | + | 86.9478i | −0.191302 | + | 0.550303i | ||||
\(159\) | 39.2644i | 0.246946i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.0000 | −0.0993789 | ||||||||
\(162\) | −17.0020 | − | 5.91041i | −0.104950 | − | 0.0364840i | ||||
\(163\) | − | 18.4196i | − | 0.113004i | −0.998402 | − | 0.0565018i | \(-0.982005\pi\) | ||
0.998402 | − | 0.0565018i | \(-0.0179947\pi\) | |||||||
\(164\) | −242.522 | − | 191.794i | −1.47880 | − | 1.16948i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.8488 | − | 45.5910i | 0.0954749 | − | 0.274645i | ||||
\(167\) | − | 92.8920i | − | 0.556240i | −0.960546 | − | 0.278120i | \(-0.910289\pi\) | ||
0.960546 | − | 0.278120i | \(-0.0897112\pi\) | |||||||
\(168\) | −71.1240 | − | 111.673i | −0.423357 | − | 0.664718i | ||||
\(169\) | −111.900 | −0.662132 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 78.5287i | 0.459232i | ||||||||
\(172\) | 103.713 | − | 131.144i | 0.602981 | − | 0.762464i | ||||
\(173\) | 117.501 | 0.679198 | 0.339599 | − | 0.940570i | \(-0.389709\pi\) | ||||
0.339599 | + | 0.940570i | \(0.389709\pi\) | |||||||
\(174\) | 0.398675 | − | 1.14684i | 0.00229124 | − | 0.00659101i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −154.522 | + | 36.5956i | −0.877968 | + | 0.207930i | ||||
\(177\) | 164.164 | 0.927481 | ||||||||
\(178\) | 189.287 | + | 65.8021i | 1.06341 | + | 0.369675i | ||||
\(179\) | 231.988i | 1.29602i | 0.761631 | + | 0.648011i | \(0.224399\pi\) | ||||
−0.761631 | + | 0.648011i | \(0.775601\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −218.096 | −1.20495 | −0.602476 | − | 0.798137i | \(-0.705819\pi\) | ||||
−0.602476 | + | 0.798137i | \(0.705819\pi\) | |||||||
\(182\) | 47.4160 | − | 136.398i | 0.260527 | − | 0.749437i | ||||
\(183\) | 65.8179i | 0.359661i | ||||||||
\(184\) | −11.2990 | + | 7.19630i | −0.0614076 | + | 0.0391103i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −150.598 | − | 52.3525i | −0.809667 | − | 0.281465i | ||||
\(187\) | − | 170.610i | − | 0.912352i | ||||||
\(188\) | 34.9516 | − | 44.1961i | 0.185913 | − | 0.235085i | ||||
\(189\) | −49.6495 | −0.262696 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 137.208i | 0.718366i | 0.933267 | + | 0.359183i | \(0.116945\pi\) | ||||
−0.933267 | + | 0.359183i | \(0.883055\pi\) | |||||||
\(192\) | −100.454 | − | 46.8725i | −0.523197 | − | 0.244128i | ||||
\(193\) | 37.0290 | 0.191860 | 0.0959301 | − | 0.995388i | \(-0.469417\pi\) | ||||
0.0959301 | + | 0.995388i | \(0.469417\pi\) | |||||||
\(194\) | 249.100 | + | 86.5947i | 1.28402 | + | 0.446364i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −132.711 | − | 104.952i | −0.677099 | − | 0.535471i | ||||
\(197\) | −194.572 | −0.987674 | −0.493837 | − | 0.869554i | \(-0.664406\pi\) | ||||
−0.493837 | + | 0.869554i | \(0.664406\pi\) | |||||||
\(198\) | −19.5532 | + | 56.2471i | −0.0987536 | + | 0.284076i | ||||
\(199\) | 176.037i | 0.884610i | 0.896865 | + | 0.442305i | \(0.145839\pi\) | ||||
−0.896865 | + | 0.442305i | \(0.854161\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −51.6977 | −0.257202 | ||||||||
\(202\) | −55.6345 | − | 19.3403i | −0.275419 | − | 0.0957440i | ||||
\(203\) | − | 3.34901i | − | 0.0164976i | ||||||
\(204\) | 73.8762 | − | 93.4159i | 0.362138 | − | 0.457921i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 94.4261 | − | 271.628i | 0.458379 | − | 1.31858i | ||||
\(207\) | 5.02352i | 0.0242682i | ||||||||
\(208\) | −27.8628 | − | 117.649i | −0.133956 | − | 0.565618i | ||||
\(209\) | 259.794 | 1.24303 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.7193i | 0.0981955i | 0.998794 | + | 0.0490978i | \(0.0156346\pi\) | ||||
−0.998794 | + | 0.0490978i | \(0.984365\pi\) | |||||||
\(212\) | 71.1240 | + | 56.2471i | 0.335490 | + | 0.265316i | ||||
\(213\) | −12.4644 | −0.0585181 | ||||||||
\(214\) | 23.0515 | − | 66.3103i | 0.107717 | − | 0.309861i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −35.0619 | + | 22.3308i | −0.162324 | + | 0.103383i | ||||
\(217\) | −439.779 | −2.02663 | ||||||||
\(218\) | −286.197 | − | 99.4908i | −1.31283 | − | 0.456380i | ||||
\(219\) | 59.5488i | 0.271912i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 129.897 | 0.587769 | ||||||||
\(222\) | −25.7854 | + | 74.1746i | −0.116150 | + | 0.334120i | ||||
\(223\) | 97.0265i | 0.435096i | 0.976050 | + | 0.217548i | \(0.0698059\pi\) | ||||
−0.976050 | + | 0.217548i | \(0.930194\pi\) | |||||||
\(224\) | −304.172 | − | 31.1386i | −1.35791 | − | 0.139012i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 61.0241 | + | 21.2138i | 0.270018 | + | 0.0938666i | ||||
\(227\) | − | 407.256i | − | 1.79408i | −0.441948 | − | 0.897040i | \(-0.645713\pi\) | ||
0.441948 | − | 0.897040i | \(-0.354287\pi\) | |||||||
\(228\) | 142.248 | + | 112.494i | 0.623895 | + | 0.493395i | ||||
\(229\) | 7.89702 | 0.0344848 | 0.0172424 | − | 0.999851i | \(-0.494511\pi\) | ||||
0.0172424 | + | 0.999851i | \(0.494511\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 164.254i | 0.711055i | ||||||||
\(232\) | −1.50628 | − | 2.36503i | −0.00649260 | − | 0.0101941i | ||||
\(233\) | −28.1483 | −0.120808 | −0.0604042 | − | 0.998174i | \(-0.519239\pi\) | ||||
−0.0604042 | + | 0.998174i | \(0.519239\pi\) | |||||||
\(234\) | −42.8248 | − | 14.8872i | −0.183012 | − | 0.0636205i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 235.169 | − | 297.369i | 0.996477 | − | 1.26004i | ||||
\(237\) | 79.7191 | 0.336368 | ||||||||
\(238\) | 107.867 | − | 310.293i | 0.453225 | − | 1.30375i | ||||
\(239\) | − | 296.005i | − | 1.23851i | −0.785189 | − | 0.619257i | \(-0.787434\pi\) | ||
0.785189 | − | 0.619257i | \(-0.212566\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 465.794 | 1.93276 | 0.966378 | − | 0.257127i | \(-0.0827758\pi\) | ||||
0.966378 | + | 0.257127i | \(0.0827758\pi\) | |||||||
\(242\) | −42.5018 | − | 14.7749i | −0.175627 | − | 0.0610534i | ||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 119.223 | + | 94.2856i | 0.488621 | + | 0.386416i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −87.9244 | + | 252.925i | −0.357416 | + | 1.02815i | ||||
\(247\) | 197.799i | 0.800806i | ||||||||
\(248\) | −310.567 | + | 197.799i | −1.25229 | + | 0.797577i | ||||
\(249\) | −41.8007 | −0.167874 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 141.676i | − | 0.564445i | −0.959349 | − | 0.282223i | \(-0.908928\pi\) | ||
0.959349 | − | 0.282223i | \(-0.0910716\pi\) | |||||||
\(252\) | −71.1240 | + | 89.9357i | −0.282238 | + | 0.356888i | ||||
\(253\) | 16.6191 | 0.0656883 | ||||||||
\(254\) | 126.124 | − | 362.810i | 0.496550 | − | 1.42838i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −228.808 | + | 114.817i | −0.893780 | + | 0.448505i | ||||
\(257\) | 41.7549 | 0.162470 | 0.0812352 | − | 0.996695i | \(-0.474113\pi\) | ||||
0.0812352 | + | 0.996695i | \(0.474113\pi\) | |||||||
\(258\) | −136.769 | − | 47.5451i | −0.530112 | − | 0.184283i | ||||
\(259\) | 216.606i | 0.836318i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.05149 | −0.00402870 | ||||||||
\(262\) | 27.8628 | − | 80.1505i | 0.106346 | − | 0.305918i | ||||
\(263\) | − | 203.283i | − | 0.772939i | −0.922302 | − | 0.386469i | \(-0.873694\pi\) | ||
0.922302 | − | 0.386469i | \(-0.126306\pi\) | |||||||
\(264\) | 73.8762 | + | 115.994i | 0.279834 | + | 0.439371i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 472.495 | + | 164.254i | 1.77630 | + | 0.617495i | ||||
\(267\) | − | 173.550i | − | 0.650001i | ||||||
\(268\) | −74.0580 | + | 93.6458i | −0.276336 | + | 0.349425i | ||||
\(269\) | 244.048 | 0.907242 | 0.453621 | − | 0.891195i | \(-0.350132\pi\) | ||||
0.453621 | + | 0.891195i | \(0.350132\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 466.585i | 1.72172i | 0.508845 | + | 0.860858i | \(0.330073\pi\) | ||||
−0.508845 | + | 0.860858i | \(0.669927\pi\) | |||||||
\(272\) | −63.3855 | − | 267.641i | −0.233035 | − | 0.983973i | ||||
\(273\) | −125.058 | −0.458087 | ||||||||
\(274\) | −390.770 | − | 135.844i | −1.42617 | − | 0.495780i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 9.09967 | + | 7.19630i | 0.0329698 | + | 0.0260736i | ||||
\(277\) | 494.181 | 1.78405 | 0.892023 | − | 0.451990i | \(-0.149286\pi\) | ||||
0.892023 | + | 0.451990i | \(0.149286\pi\) | |||||||
\(278\) | 30.2257 | − | 86.9478i | 0.108726 | − | 0.312762i | ||||
\(279\) | 138.078i | 0.494902i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −43.4020 | −0.154455 | −0.0772277 | − | 0.997013i | \(-0.524607\pi\) | ||||
−0.0772277 | + | 0.997013i | \(0.524607\pi\) | |||||||
\(282\) | −46.0917 | − | 16.0229i | −0.163446 | − | 0.0568188i | ||||
\(283\) | − | 310.785i | − | 1.09818i | −0.835763 | − | 0.549090i | \(-0.814974\pi\) | ||
0.835763 | − | 0.549090i | \(-0.185026\pi\) | |||||||
\(284\) | −17.8555 | + | 22.5781i | −0.0628714 | + | 0.0795003i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −49.2508 | + | 141.676i | −0.172206 | + | 0.495370i | ||||
\(287\) | 738.596i | 2.57351i | ||||||||
\(288\) | −9.77660 | + | 95.5009i | −0.0339465 | + | 0.331600i | ||||
\(289\) | 6.50497 | 0.0225085 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 228.390i | − | 0.784845i | ||||||
\(292\) | 107.867 | + | 85.3049i | 0.369409 | + | 0.292140i | ||||
\(293\) | 245.207 | 0.836886 | 0.418443 | − | 0.908243i | \(-0.362576\pi\) | ||||
0.418443 | + | 0.908243i | \(0.362576\pi\) | |||||||
\(294\) | −48.1134 | + | 138.404i | −0.163651 | + | 0.470761i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 97.4228 | + | 152.965i | 0.329131 | + | 0.516773i | ||||
\(297\) | 51.5708 | 0.173639 | ||||||||
\(298\) | 22.0072 | + | 7.65037i | 0.0738496 | + | 0.0256724i | ||||
\(299\) | 12.6533i | 0.0423187i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −399.395 | −1.32689 | ||||||||
\(302\) | −82.3676 | + | 236.940i | −0.272740 | + | 0.784569i | ||||
\(303\) | 51.0092i | 0.168347i | ||||||||
\(304\) | 407.547 | − | 96.5195i | 1.34061 | − | 0.317498i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −97.4228 | − | 33.8671i | −0.318375 | − | 0.110677i | ||||
\(307\) | − | 337.514i | − | 1.09939i | −0.835364 | − | 0.549697i | \(-0.814743\pi\) | ||
0.835364 | − | 0.549697i | \(-0.185257\pi\) | |||||||
\(308\) | 297.531 | + | 235.297i | 0.966011 | + | 0.763952i | ||||
\(309\) | −249.045 | −0.805970 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 427.756i | − | 1.37542i | −0.725986 | − | 0.687710i | \(-0.758616\pi\) | ||
0.725986 | − | 0.687710i | \(-0.241384\pi\) | |||||||
\(312\) | −88.3142 | + | 56.2471i | −0.283058 | + | 0.180279i | ||||
\(313\) | −83.8739 | −0.267968 | −0.133984 | − | 0.990984i | \(-0.542777\pi\) | ||||
−0.133984 | + | 0.990984i | \(0.542777\pi\) | |||||||
\(314\) | 372.571 | + | 129.517i | 1.18653 | + | 0.412475i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 114.199 | − | 144.404i | 0.361390 | − | 0.456975i | ||||
\(317\) | 112.204 | 0.353957 | 0.176978 | − | 0.984215i | \(-0.443368\pi\) | ||||
0.176978 | + | 0.984215i | \(0.443368\pi\) | |||||||
\(318\) | 25.7854 | − | 74.1746i | 0.0810861 | − | 0.233254i | ||||
\(319\) | 3.47861i | 0.0109047i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −60.7974 | −0.189400 | ||||||||
\(322\) | 30.2257 | + | 10.5074i | 0.0938687 | + | 0.0326317i | ||||
\(323\) | 449.976i | 1.39312i | ||||||||
\(324\) | 28.2371 | + | 22.3308i | 0.0871516 | + | 0.0689222i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −12.0964 | + | 34.7966i | −0.0371054 | + | 0.106738i | ||||
\(327\) | 262.403i | 0.802455i | ||||||||
\(328\) | 332.197 | + | 521.588i | 1.01280 | + | 1.59021i | ||||
\(329\) | −134.598 | −0.409113 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 132.621i | − | 0.400666i | −0.979728 | − | 0.200333i | \(-0.935798\pi\) | ||
0.979728 | − | 0.200333i | \(-0.0642025\pi\) | |||||||
\(332\) | −59.8803 | + | 75.7182i | −0.180362 | + | 0.228067i | ||||
\(333\) | 68.0079 | 0.204228 | ||||||||
\(334\) | −61.0033 | + | 175.483i | −0.182645 | + | 0.525398i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 61.0241 | + | 257.670i | 0.181619 | + | 0.766874i | ||||
\(337\) | 20.7739 | 0.0616437 | 0.0308219 | − | 0.999525i | \(-0.490188\pi\) | ||||
0.0308219 | + | 0.999525i | \(0.490188\pi\) | |||||||
\(338\) | 211.392 | + | 73.4863i | 0.625420 | + | 0.217415i | ||||
\(339\) | − | 55.9506i | − | 0.165046i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 456.797 | 1.33958 | ||||||||
\(342\) | 51.5708 | − | 148.349i | 0.150792 | − | 0.433770i | ||||
\(343\) | − | 64.0283i | − | 0.186672i | ||||||
\(344\) | −282.048 | + | 179.636i | −0.819907 | + | 0.522196i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −221.973 | − | 77.1645i | −0.641539 | − | 0.223019i | ||||
\(347\) | − | 8.89616i | − | 0.0256374i | −0.999918 | − | 0.0128187i | \(-0.995920\pi\) | ||
0.999918 | − | 0.0128187i | \(-0.00408042\pi\) | |||||||
\(348\) | −1.50628 | + | 1.90468i | −0.00432840 | + | 0.00547323i | ||||
\(349\) | −19.4020 | −0.0555931 | −0.0277965 | − | 0.999614i | \(-0.508849\pi\) | ||||
−0.0277965 | + | 0.999614i | \(0.508849\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 39.2644i | 0.111864i | ||||||||
\(352\) | 315.942 | + | 32.3436i | 0.897564 | + | 0.0918853i | ||||
\(353\) | −80.2902 | −0.227451 | −0.113726 | − | 0.993512i | \(-0.536278\pi\) | ||||
−0.113726 | + | 0.993512i | \(0.536278\pi\) | |||||||
\(354\) | −310.124 | − | 107.809i | −0.876056 | − | 0.304544i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −314.371 | − | 248.615i | −0.883065 | − | 0.698356i | ||||
\(357\) | −284.496 | −0.796907 | ||||||||
\(358\) | 152.349 | − | 438.251i | 0.425557 | − | 1.22416i | ||||
\(359\) | − | 314.115i | − | 0.874972i | −0.899225 | − | 0.437486i | \(-0.855869\pi\) | ||
0.899225 | − | 0.437486i | \(-0.144131\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −324.196 | −0.898050 | ||||||||
\(362\) | 412.008 | + | 143.227i | 1.13814 | + | 0.395653i | ||||
\(363\) | 38.9683i | 0.107351i | ||||||||
\(364\) | −179.148 | + | 226.531i | −0.492164 | + | 0.622338i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 43.2234 | − | 124.337i | 0.118097 | − | 0.339719i | ||||
\(367\) | 476.800i | 1.29918i | 0.760283 | + | 0.649592i | \(0.225060\pi\) | ||||
−0.760283 | + | 0.649592i | \(0.774940\pi\) | |||||||
\(368\) | 26.0709 | − | 6.17440i | 0.0708450 | − | 0.0167783i | ||||
\(369\) | 231.897 | 0.628447 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 216.606i | − | 0.583844i | ||||||
\(372\) | 250.115 | + | 197.799i | 0.672353 | + | 0.531718i | ||||
\(373\) | 86.1333 | 0.230920 | 0.115460 | − | 0.993312i | \(-0.463166\pi\) | ||||
0.115460 | + | 0.993312i | \(0.463166\pi\) | |||||||
\(374\) | −112.042 | + | 322.300i | −0.299576 | + | 0.861766i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −95.0515 | + | 60.5380i | −0.252797 | + | 0.161005i | ||||
\(377\) | −2.64850 | −0.00702521 | ||||||||
\(378\) | 93.7933 | + | 32.6054i | 0.248130 | + | 0.0862577i | ||||
\(379\) | − | 638.035i | − | 1.68347i | −0.539891 | − | 0.841735i | \(-0.681534\pi\) | ||
0.539891 | − | 0.841735i | \(-0.318466\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −332.646 | −0.873087 | ||||||||
\(382\) | 90.1061 | − | 259.201i | 0.235880 | − | 0.678535i | ||||
\(383\) | 216.742i | 0.565907i | 0.959134 | + | 0.282953i | \(0.0913142\pi\) | ||||
−0.959134 | + | 0.282953i | \(0.908686\pi\) | |||||||
\(384\) | 158.986 | + | 154.517i | 0.414027 | + | 0.402387i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −69.9518 | − | 24.3174i | −0.181222 | − | 0.0629985i | ||||
\(387\) | 125.398i | 0.324026i | ||||||||
\(388\) | −413.708 | − | 327.174i | −1.06626 | − | 0.843231i | ||||
\(389\) | −476.640 | −1.22529 | −0.612647 | − | 0.790356i | \(-0.709895\pi\) | ||||
−0.612647 | + | 0.790356i | \(0.709895\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.7852i | 0.0736195i | ||||||||
\(392\) | 181.783 | + | 285.419i | 0.463731 | + | 0.728111i | ||||
\(393\) | −73.4869 | −0.186990 | ||||||||
\(394\) | 367.567 | + | 127.778i | 0.932912 | + | 0.324309i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 73.8762 | − | 93.4159i | 0.186556 | − | 0.235899i | ||||
\(397\) | 43.0792 | 0.108512 | 0.0542559 | − | 0.998527i | \(-0.482721\pi\) | ||||
0.0542559 | + | 0.998527i | \(0.482721\pi\) | |||||||
\(398\) | 115.606 | − | 332.554i | 0.290467 | − | 0.835562i | ||||
\(399\) | − | 433.213i | − | 1.08575i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −168.694 | −0.420684 | −0.210342 | − | 0.977628i | \(-0.567458\pi\) | ||||
−0.210342 | + | 0.977628i | \(0.567458\pi\) | |||||||
\(402\) | 97.6625 | + | 33.9505i | 0.242942 | + | 0.0844540i | ||||
\(403\) | 347.791i | 0.863005i | ||||||||
\(404\) | 92.3987 | + | 73.0718i | 0.228710 | + | 0.180871i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.19934 | + | 6.32665i | −0.00541709 | + | 0.0155829i | ||||
\(407\) | − | 224.988i | − | 0.552797i | ||||||
\(408\) | −200.908 | + | 127.957i | −0.492421 | + | 0.313621i | ||||
\(409\) | −373.890 | −0.914157 | −0.457079 | − | 0.889426i | \(-0.651104\pi\) | ||||
−0.457079 | + | 0.889426i | \(0.651104\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 358.282i | 0.871732i | ||||||||
\(412\) | −356.762 | + | 451.123i | −0.865927 | + | 1.09496i | ||||
\(413\) | −905.630 | −2.19281 | ||||||||
\(414\) | 3.29901 | − | 9.48997i | 0.00796862 | − | 0.0229226i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −24.6254 | + | 240.549i | −0.0591957 | + | 0.578242i | ||||
\(417\) | −79.7191 | −0.191173 | ||||||||
\(418\) | −490.779 | − | 170.610i | −1.17411 | − | 0.408158i | ||||
\(419\) | − | 87.5839i | − | 0.209031i | −0.994523 | − | 0.104515i | \(-0.966671\pi\) | ||
0.994523 | − | 0.104515i | \(-0.0333291\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 70.3023 | 0.166989 | 0.0834944 | − | 0.996508i | \(-0.473392\pi\) | ||||
0.0834944 | + | 0.996508i | \(0.473392\pi\) | |||||||
\(422\) | 13.6066 | − | 39.1409i | 0.0322431 | − | 0.0927510i | ||||
\(423\) | 42.2597i | 0.0999048i | ||||||||
\(424\) | −97.4228 | − | 152.965i | −0.229771 | − | 0.360766i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 23.5465 | + | 8.18550i | 0.0552735 | + | 0.0192148i | ||||
\(427\) | − | 363.092i | − | 0.850332i | ||||||
\(428\) | −87.0935 | + | 110.129i | −0.203490 | + | 0.257311i | ||||
\(429\) | 129.897 | 0.302790 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 247.370i | 0.573944i | 0.957939 | + | 0.286972i | \(0.0926487\pi\) | ||||
−0.957939 | + | 0.286972i | \(0.907351\pi\) | |||||||
\(432\) | 80.9006 | − | 19.1597i | 0.187270 | − | 0.0443512i | ||||
\(433\) | 636.247 | 1.46939 | 0.734696 | − | 0.678397i | \(-0.237325\pi\) | ||||
0.734696 | + | 0.678397i | \(0.237325\pi\) | |||||||
\(434\) | 830.791 | + | 288.808i | 1.91426 | + | 0.665457i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 475.320 | + | 375.898i | 1.09018 | + | 0.862151i | ||||
\(437\) | −43.8323 | −0.100303 | ||||||||
\(438\) | 39.1064 | − | 112.494i | 0.0892840 | − | 0.256836i | ||||
\(439\) | − | 769.786i | − | 1.75350i | −0.480947 | − | 0.876750i | \(-0.659707\pi\) | ||
0.480947 | − | 0.876750i | \(-0.340293\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 126.897 | 0.287748 | ||||||||
\(442\) | −245.390 | − | 85.3049i | −0.555180 | − | 0.192998i | ||||
\(443\) | − | 612.214i | − | 1.38197i | −0.722868 | − | 0.690986i | \(-0.757177\pi\) | ||
0.722868 | − | 0.690986i | \(-0.242823\pi\) | |||||||
\(444\) | 97.4228 | − | 123.190i | 0.219421 | − | 0.277456i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 63.7185 | − | 183.294i | 0.142867 | − | 0.410972i | ||||
\(447\) | − | 20.1775i | − | 0.0451399i | ||||||
\(448\) | 554.165 | + | 258.578i | 1.23697 | + | 0.577182i | ||||
\(449\) | −175.897 | −0.391753 | −0.195876 | − | 0.980629i | \(-0.562755\pi\) | ||||
−0.195876 | + | 0.980629i | \(0.562755\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 767.177i | − | 1.70106i | ||||||
\(452\) | −101.350 | − | 80.1505i | −0.224225 | − | 0.177324i | ||||
\(453\) | 217.241 | 0.479561 | ||||||||
\(454\) | −267.450 | + | 769.351i | −0.589097 | + | 1.69461i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −194.846 | − | 305.929i | −0.427293 | − | 0.670898i | ||||
\(457\) | 365.357 | 0.799469 | 0.399734 | − | 0.916631i | \(-0.369102\pi\) | ||||
0.399734 | + | 0.916631i | \(0.369102\pi\) | |||||||
\(458\) | −14.9183 | − | 5.18607i | −0.0325728 | − | 0.0113233i | ||||
\(459\) | 89.3232i | 0.194604i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 308.350 | 0.668873 | 0.334437 | − | 0.942418i | \(-0.391454\pi\) | ||||
0.334437 | + | 0.942418i | \(0.391454\pi\) | |||||||
\(462\) | 107.867 | − | 310.293i | 0.233479 | − | 0.671630i | ||||
\(463\) | − | 92.6302i | − | 0.200065i | −0.994984 | − | 0.100033i | \(-0.968105\pi\) | ||
0.994984 | − | 0.100033i | \(-0.0318947\pi\) | |||||||
\(464\) | 1.29238 | + | 5.45700i | 0.00278531 | + | 0.0117608i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 53.1752 | + | 18.4854i | 0.114110 | + | 0.0396681i | ||||
\(467\) | − | 606.103i | − | 1.29786i | −0.760846 | − | 0.648932i | \(-0.775216\pi\) | ||
0.760846 | − | 0.648932i | \(-0.224784\pi\) | |||||||
\(468\) | 71.1240 | + | 56.2471i | 0.151974 | + | 0.120186i | ||||
\(469\) | 285.196 | 0.608094 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 341.596i | − | 0.725256i | ||||||
\(472\) | −639.545 | + | 407.324i | −1.35497 | + | 0.862975i | ||||
\(473\) | 414.851 | 0.877063 | ||||||||
\(474\) | −150.598 | − | 52.3525i | −0.317717 | − | 0.110448i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −407.547 | + | 515.339i | −0.856190 | + | 1.08265i | ||||
\(477\) | −68.0079 | −0.142574 | ||||||||
\(478\) | −194.390 | + | 559.185i | −0.406673 | + | 1.16984i | ||||
\(479\) | 138.947i | 0.290078i | 0.989426 | + | 0.145039i | \(0.0463307\pi\) | ||||
−0.989426 | + | 0.145039i | \(0.953669\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 171.299 | 0.356131 | ||||||||
\(482\) | −879.935 | − | 305.893i | −1.82559 | − | 0.634632i | ||||
\(483\) | − | 27.7128i | − | 0.0573764i | ||||||
\(484\) | 70.5876 | + | 55.8229i | 0.145842 | + | 0.115337i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 10.2371 | − | 29.4483i | 0.0210640 | − | 0.0605932i | ||||
\(487\) | 201.243i | 0.413230i | 0.978422 | + | 0.206615i | \(0.0662447\pi\) | ||||
−0.978422 | + | 0.206615i | \(0.933755\pi\) | |||||||
\(488\) | −163.307 | − | 256.411i | −0.334646 | − | 0.525433i | ||||
\(489\) | 31.9036 | 0.0652426 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 347.368i | 0.707470i | 0.935346 | + | 0.353735i | \(0.115089\pi\) | ||||
−0.935346 | + | 0.353735i | \(0.884911\pi\) | |||||||
\(492\) | 332.197 | − | 420.061i | 0.675198 | − | 0.853783i | ||||
\(493\) | −6.02513 | −0.0122214 | ||||||||
\(494\) | 129.897 | − | 373.664i | 0.262949 | − | 0.756404i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 716.591 | − | 169.711i | 1.44474 | − | 0.342159i | ||||
\(497\) | 68.7610 | 0.138352 | ||||||||
\(498\) | 78.9660 | + | 27.4510i | 0.158566 | + | 0.0551225i | ||||
\(499\) | 672.277i | 1.34725i | 0.739074 | + | 0.673625i | \(0.235264\pi\) | ||||
−0.739074 | + | 0.673625i | \(0.764736\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 160.894 | 0.321145 | ||||||||
\(502\) | −93.0401 | + | 267.641i | −0.185339 | + | 0.533149i | ||||
\(503\) | 436.350i | 0.867496i | 0.901034 | + | 0.433748i | \(0.142809\pi\) | ||||
−0.901034 | + | 0.433748i | \(0.857191\pi\) | |||||||
\(504\) | 193.423 | − | 123.190i | 0.383775 | − | 0.244425i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −31.3954 | − | 10.9140i | −0.0620462 | − | 0.0215692i | ||||
\(507\) | − | 193.817i | − | 0.382282i | ||||||
\(508\) | −476.523 | + | 602.559i | −0.938037 | + | 1.18614i | ||||
\(509\) | 109.547 | 0.215219 | 0.107610 | − | 0.994193i | \(-0.465680\pi\) | ||||
0.107610 | + | 0.994193i | \(0.465680\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 328.508i | − | 0.642872i | ||||||
\(512\) | 507.644 | − | 66.6415i | 0.991493 | − | 0.130159i | ||||
\(513\) | −136.016 | −0.265138 | ||||||||
\(514\) | −78.8796 | − | 27.4210i | −0.153462 | − | 0.0533482i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 227.148 | + | 179.636i | 0.440209 | + | 0.348131i | ||||
\(517\) | 139.807 | 0.270419 | ||||||||
\(518\) | 142.248 | − | 409.193i | 0.274610 | − | 0.789947i | ||||
\(519\) | 203.518i | 0.392135i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −743.100 | −1.42629 | −0.713147 | − | 0.701014i | \(-0.752731\pi\) | ||||
−0.713147 | + | 0.701014i | \(0.752731\pi\) | |||||||
\(522\) | 1.98638 | + | 0.690526i | 0.00380532 | + | 0.00132285i | ||||
\(523\) | − | 366.211i | − | 0.700212i | −0.936710 | − | 0.350106i | \(-0.886146\pi\) | ||
0.936710 | − | 0.350106i | \(-0.113854\pi\) | |||||||
\(524\) | −105.272 | + | 133.115i | −0.200900 | + | 0.254037i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −133.498 | + | 384.023i | −0.253799 | + | 0.730083i | ||||
\(527\) | 791.196i | 1.50132i | ||||||||
\(528\) | −63.3855 | − | 267.641i | −0.120048 | − | 0.506895i | ||||
\(529\) | 526.196 | 0.994699 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 284.341i | 0.535481i | ||||||||
\(532\) | −784.727 | − | 620.586i | −1.47505 | − | 1.16652i | ||||
\(533\) | 584.105 | 1.09588 | ||||||||
\(534\) | −113.973 | + | 327.855i | −0.213432 | + | 0.613961i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 201.402 | − | 128.272i | 0.375750 | − | 0.239314i | ||||
\(537\) | −401.815 | −0.748259 | ||||||||
\(538\) | −461.033 | − | 160.269i | −0.856939 | − | 0.297898i | ||||
\(539\) | − | 419.809i | − | 0.778867i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 170.688 | 0.315504 | 0.157752 | − | 0.987479i | \(-0.449575\pi\) | ||||
0.157752 | + | 0.987479i | \(0.449575\pi\) | |||||||
\(542\) | 306.412 | − | 881.430i | 0.565336 | − | 1.62625i | ||||
\(543\) | − | 377.754i | − | 0.695680i | ||||||
\(544\) | −56.0208 | + | 547.228i | −0.102979 | + | 1.00593i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 236.248 | + | 82.1269i | 0.432688 | + | 0.150416i | ||||
\(547\) | − | 507.600i | − | 0.927971i | −0.885843 | − | 0.463986i | \(-0.846419\pi\) | ||
0.885843 | − | 0.463986i | \(-0.153581\pi\) | |||||||
\(548\) | 648.997 | + | 513.247i | 1.18430 | + | 0.936581i | ||||
\(549\) | −114.000 | −0.207650 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 9.17469i | − | 0.0166510i | ||||||
\(552\) | −12.4644 | − | 19.5705i | −0.0225804 | − | 0.0354537i | ||||
\(553\) | −439.779 | −0.795261 | ||||||||
\(554\) | −933.561 | − | 324.534i | −1.68513 | − | 0.585802i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −114.199 | + | 144.404i | −0.205394 | + | 0.259720i | ||||
\(557\) | −788.492 | −1.41561 | −0.707803 | − | 0.706410i | \(-0.750314\pi\) | ||||
−0.707803 | + | 0.706410i | \(0.750314\pi\) | |||||||
\(558\) | 90.6772 | − | 260.843i | 0.162504 | − | 0.467461i | ||||
\(559\) | 315.854i | 0.565035i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 295.505 | 0.526747 | ||||||||
\(562\) | 81.9910 | + | 28.5026i | 0.145892 | + | 0.0507164i | ||||
\(563\) | − | 936.102i | − | 1.66270i | −0.555747 | − | 0.831351i | \(-0.687568\pi\) | ||
0.555747 | − | 0.831351i | \(-0.312432\pi\) | |||||||
\(564\) | 76.5498 | + | 60.5380i | 0.135727 | + | 0.107337i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −204.096 | + | 587.107i | −0.360594 | + | 1.03729i | ||||
\(567\) | − | 85.9955i | − | 0.151667i | ||||||
\(568\) | 48.5582 | − | 30.9266i | 0.0854898 | − | 0.0544482i | ||||
\(569\) | 95.4983 | 0.167835 | 0.0839177 | − | 0.996473i | \(-0.473257\pi\) | ||||
0.0839177 | + | 0.996473i | \(0.473257\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 889.123i | 1.55713i | 0.627562 | + | 0.778566i | \(0.284053\pi\) | ||||
−0.627562 | + | 0.778566i | \(0.715947\pi\) | |||||||
\(572\) | 186.080 | − | 235.297i | 0.325315 | − | 0.411359i | ||||
\(573\) | −237.651 | −0.414749 | ||||||||
\(574\) | 485.045 | − | 1395.29i | 0.845026 | − | 2.43081i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 81.1856 | − | 173.991i | 0.140947 | − | 0.302068i | ||||
\(577\) | 522.147 | 0.904934 | 0.452467 | − | 0.891781i | \(-0.350544\pi\) | ||||
0.452467 | + | 0.891781i | \(0.350544\pi\) | |||||||
\(578\) | −12.2886 | − | 4.27189i | −0.0212605 | − | 0.00739081i | ||||
\(579\) | 64.1361i | 0.110771i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 230.598 | 0.396898 | ||||||||
\(582\) | −149.986 | + | 431.453i | −0.257709 | + | 0.741329i | ||||
\(583\) | 224.988i | 0.385915i | ||||||||
\(584\) | −147.752 | − | 231.988i | −0.253001 | − | 0.397240i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −463.223 | − | 161.031i | −0.790484 | − | 0.274796i | ||||
\(587\) | − | 95.8440i | − | 0.163278i | −0.996662 | − | 0.0816388i | \(-0.973985\pi\) | ||
0.996662 | − | 0.0816388i | \(-0.0260154\pi\) | |||||||
\(588\) | 181.783 | − | 229.863i | 0.309154 | − | 0.390923i | ||||
\(589\) | −1204.78 | −2.04547 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 337.008i | − | 0.570234i | ||||||
\(592\) | −83.5883 | − | 352.946i | −0.141197 | − | 0.596192i | ||||
\(593\) | −878.624 | −1.48166 | −0.740829 | − | 0.671693i | \(-0.765567\pi\) | ||||
−0.740829 | + | 0.671693i | \(0.765567\pi\) | |||||||
\(594\) | −97.4228 | − | 33.8671i | −0.164011 | − | 0.0570154i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −36.5498 | − | 28.9047i | −0.0613252 | − | 0.0484979i | ||||
\(597\) | −304.906 | −0.510730 | ||||||||
\(598\) | 8.30957 | − | 23.9034i | 0.0138956 | − | 0.0399723i | ||||
\(599\) | 967.652i | 1.61545i | 0.589563 | + | 0.807723i | \(0.299300\pi\) | ||||
−0.589563 | + | 0.807723i | \(0.700700\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 279.704 | 0.465398 | 0.232699 | − | 0.972549i | \(-0.425244\pi\) | ||||
0.232699 | + | 0.972549i | \(0.425244\pi\) | |||||||
\(602\) | 754.501 | + | 262.288i | 1.25332 | + | 0.435694i | ||||
\(603\) | − | 89.5430i | − | 0.148496i | ||||||
\(604\) | 311.203 | − | 393.513i | 0.515236 | − | 0.651512i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 33.4983 | − | 96.3619i | 0.0552778 | − | 0.159013i | ||||
\(607\) | − | 747.564i | − | 1.23157i | −0.787914 | − | 0.615786i | \(-0.788839\pi\) | ||
0.787914 | − | 0.615786i | \(-0.211161\pi\) | |||||||
\(608\) | −833.285 | − | 85.3049i | −1.37053 | − | 0.140304i | ||||
\(609\) | 5.80066 | 0.00952490 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 106.444i | 0.174213i | ||||||||
\(612\) | 161.801 | + | 127.957i | 0.264381 | + | 0.209081i | ||||
\(613\) | −457.152 | −0.745761 | −0.372881 | − | 0.927879i | \(-0.621630\pi\) | ||||
−0.372881 | + | 0.927879i | \(0.621630\pi\) | |||||||
\(614\) | −221.650 | + | 637.600i | −0.360993 | + | 1.03844i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −407.547 | − | 639.894i | −0.661601 | − | 1.03879i | ||||
\(617\) | −764.888 | −1.23969 | −0.619844 | − | 0.784725i | \(-0.712804\pi\) | ||||
−0.619844 | + | 0.784725i | \(0.712804\pi\) | |||||||
\(618\) | 470.473 | + | 163.551i | 0.761283 | + | 0.264645i | ||||
\(619\) | − | 365.359i | − | 0.590240i | −0.955460 | − | 0.295120i | \(-0.904640\pi\) | ||
0.955460 | − | 0.295120i | \(-0.0953597\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.70099 | −0.0140113 | ||||||||
\(622\) | −280.912 | + | 808.077i | −0.451627 | + | 1.29916i | ||||
\(623\) | 957.410i | 1.53677i | ||||||||
\(624\) | 203.773 | − | 48.2598i | 0.326560 | − | 0.0773393i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 158.447 | + | 55.0810i | 0.253110 | + | 0.0879888i | ||||
\(627\) | 449.976i | 0.717666i | ||||||||
\(628\) | −618.771 | − | 489.343i | −0.985304 | − | 0.779209i | ||||
\(629\) | 389.691 | 0.619541 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 62.1578i | − | 0.0985067i | −0.998786 | − | 0.0492534i | \(-0.984316\pi\) | ||
0.998786 | − | 0.0492534i | \(-0.0156842\pi\) | |||||||
\(632\) | −310.567 | + | 197.799i | −0.491403 | + | 0.312973i | ||||
\(633\) | −35.8868 | −0.0566932 | ||||||||
\(634\) | −211.966 | − | 73.6859i | −0.334331 | − | 0.116224i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −97.4228 | + | 123.190i | −0.153180 | + | 0.193696i | ||||
\(637\) | 319.630 | 0.501773 | ||||||||
\(638\) | 2.28444 | − | 6.57147i | 0.00358063 | − | 0.0103001i | ||||
\(639\) | − | 21.5889i | − | 0.0337855i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1111.69 | −1.73431 | −0.867154 | − | 0.498041i | \(-0.834053\pi\) | ||||
−0.867154 | + | 0.498041i | \(0.834053\pi\) | |||||||
\(642\) | 114.853 | + | 39.9264i | 0.178898 | + | 0.0621906i | ||||
\(643\) | 468.983i | 0.729367i | 0.931132 | + | 0.364683i | \(0.118823\pi\) | ||||
−0.931132 | + | 0.364683i | \(0.881177\pi\) | |||||||
\(644\) | −50.1993 | − | 39.6992i | −0.0779493 | − | 0.0616447i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 295.505 | − | 850.054i | 0.457438 | − | 1.31587i | ||||
\(647\) | 96.7647i | 0.149559i | 0.997200 | + | 0.0747795i | \(0.0238253\pi\) | ||||
−0.997200 | + | 0.0747795i | \(0.976175\pi\) | |||||||
\(648\) | −38.6781 | − | 60.7290i | −0.0596884 | − | 0.0937175i | ||||
\(649\) | 940.675 | 1.44942 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 761.720i | − | 1.17008i | ||||||
\(652\) | 45.7027 | − | 57.7907i | 0.0700961 | − | 0.0886360i | ||||
\(653\) | 920.353 | 1.40942 | 0.704712 | − | 0.709494i | \(-0.251076\pi\) | ||||
0.704712 | + | 0.709494i | \(0.251076\pi\) | |||||||
\(654\) | 172.323 | − | 495.707i | 0.263491 | − | 0.757962i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −285.024 | − | 1203.49i | −0.434488 | − | 1.83459i | ||||
\(657\) | −103.142 | −0.156989 | ||||||||
\(658\) | 254.270 | + | 88.3921i | 0.386429 | + | 0.134335i | ||||
\(659\) | − | 591.020i | − | 0.896844i | −0.893822 | − | 0.448422i | \(-0.851986\pi\) | ||
0.893822 | − | 0.448422i | \(-0.148014\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −306.193 | −0.463226 | −0.231613 | − | 0.972808i | \(-0.574400\pi\) | ||||
−0.231613 | + | 0.972808i | \(0.574400\pi\) | |||||||
\(662\) | −87.0935 | + | 250.535i | −0.131561 | + | 0.378451i | ||||
\(663\) | 224.988i | 0.339349i | ||||||||
\(664\) | 162.846 | − | 103.716i | 0.245249 | − | 0.156198i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −128.474 | − | 44.6616i | −0.192904 | − | 0.0670595i | ||||
\(667\) | − | 0.586909i | − | 0.000879924i | ||||||
\(668\) | 230.484 | − | 291.445i | 0.345035 | − | 0.436295i | ||||
\(669\) | −168.055 | −0.251203 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 377.142i | 0.562060i | ||||||||
\(672\) | 53.9337 | − | 526.841i | 0.0802585 | − | 0.783990i | ||||
\(673\) | 556.892 | 0.827476 | 0.413738 | − | 0.910396i | \(-0.364223\pi\) | ||||
0.413738 | + | 0.910396i | \(0.364223\pi\) | |||||||
\(674\) | −39.2442 | − | 13.6425i | −0.0582258 | − | 0.0202411i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −351.083 | − | 277.647i | −0.519353 | − | 0.410721i | ||||
\(677\) | −58.1920 | −0.0859557 | −0.0429779 | − | 0.999076i | \(-0.513684\pi\) | ||||
−0.0429779 | + | 0.999076i | \(0.513684\pi\) | |||||||
\(678\) | −36.7435 | + | 105.697i | −0.0541939 | + | 0.155895i | ||||
\(679\) | 1259.94i | 1.85558i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 705.389 | 1.03581 | ||||||||
\(682\) | −862.940 | − | 299.984i | −1.26531 | − | 0.439860i | ||||
\(683\) | − | 357.274i | − | 0.523096i | −0.965191 | − | 0.261548i | \(-0.915767\pi\) | ||
0.965191 | − | 0.261548i | \(-0.0842329\pi\) | |||||||
\(684\) | −194.846 | + | 246.381i | −0.284862 | + | 0.360206i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −42.0482 | + | 120.956i | −0.0612947 | + | 0.176321i | ||||
\(687\) | 13.6780i | 0.0199098i | ||||||||
\(688\) | 650.788 | − | 154.127i | 0.945913 | − | 0.224021i | ||||
\(689\) | −171.299 | −0.248620 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 614.707i | 0.889590i | 0.895632 | + | 0.444795i | \(0.146724\pi\) | ||||
−0.895632 | + | 0.444795i | \(0.853276\pi\) | |||||||
\(692\) | 368.655 | + | 291.544i | 0.532739 | + | 0.421307i | ||||
\(693\) | −284.496 | −0.410528 | ||||||||
\(694\) | −5.84222 | + | 16.8058i | −0.00841818 | + | 0.0242159i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.09636 | − | 2.60896i | 0.00588557 | − | 0.00374850i | ||||
\(697\) | 1328.79 | 1.90644 | ||||||||
\(698\) | 36.6524 | + | 12.7415i | 0.0525107 | + | 0.0182543i | ||||
\(699\) | − | 48.7543i | − | 0.0697487i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −886.028 | −1.26395 | −0.631975 | − | 0.774989i | \(-0.717755\pi\) | ||||
−0.631975 | + | 0.774989i | \(0.717755\pi\) | |||||||
\(702\) | 25.7854 | − | 74.1746i | 0.0367313 | − | 0.105662i | ||||
\(703\) | 593.397i | 0.844093i | ||||||||
\(704\) | −575.609 | − | 268.584i | −0.817626 | − | 0.381511i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 151.677 | + | 52.7276i | 0.214840 | + | 0.0746849i | ||||
\(707\) | − | 281.398i | − | 0.398017i | ||||||
\(708\) | 515.058 | + | 407.324i | 0.727483 | + | 0.575316i | ||||
\(709\) | 760.887 | 1.07318 | 0.536592 | − | 0.843842i | \(-0.319712\pi\) | ||||
0.536592 | + | 0.843842i | \(0.319712\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 138.078i | 0.194202i | ||||||||
\(712\) | 430.613 | + | 676.111i | 0.604794 | + | 0.949594i | ||||
\(713\) | −77.0706 | −0.108093 | ||||||||
\(714\) | 537.444 | + | 186.832i | 0.752722 | + | 0.261669i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −575.609 | + | 727.853i | −0.803923 | + | 1.01655i | ||||
\(717\) | 512.695 | 0.715056 | ||||||||
\(718\) | −206.283 | + | 593.397i | −0.287302 | + | 0.826458i | ||||
\(719\) | 575.877i | 0.800942i | 0.916309 | + | 0.400471i | \(0.131154\pi\) | ||||
−0.916309 | + | 0.400471i | \(0.868846\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1373.88 | 1.90553 | ||||||||
\(722\) | 612.441 | + | 212.903i | 0.848257 | + | 0.294880i | ||||
\(723\) | 806.779i | 1.11588i | ||||||||
\(724\) | −684.268 | − | 541.141i | −0.945122 | − | 0.747432i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 25.5909 | − | 73.6153i | 0.0352492 | − | 0.101398i | ||||
\(727\) | 327.332i | 0.450250i | 0.974330 | + | 0.225125i | \(0.0722790\pi\) | ||||
−0.974330 | + | 0.225125i | \(0.927721\pi\) | |||||||
\(728\) | 487.195 | − | 310.293i | 0.669224 | − | 0.426227i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 718.542i | 0.982958i | ||||||||
\(732\) | −163.307 | + | 206.501i | −0.223098 | + | 0.282105i | ||||
\(733\) | 947.567 | 1.29272 | 0.646362 | − | 0.763031i | \(-0.276290\pi\) | ||||
0.646362 | + | 0.763031i | \(0.276290\pi\) | |||||||
\(734\) | 313.120 | − | 900.727i | 0.426595 | − | 1.22715i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −53.3056 | − | 5.45700i | −0.0724261 | − | 0.00741440i | ||||
\(737\) | −296.232 | −0.401943 | ||||||||
\(738\) | −438.079 | − | 152.290i | −0.593602 | − | 0.206354i | ||||
\(739\) | − | 183.234i | − | 0.247948i | −0.992285 | − | 0.123974i | \(-0.960436\pi\) | ||
0.992285 | − | 0.123974i | \(-0.0395640\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −342.598 | −0.462345 | ||||||||
\(742\) | −142.248 | + | 409.193i | −0.191709 | + | 0.551473i | ||||
\(743\) | − | 183.712i | − | 0.247258i | −0.992329 | − | 0.123629i | \(-0.960547\pi\) | ||
0.992329 | − | 0.123629i | \(-0.0394532\pi\) | |||||||
\(744\) | −342.598 | − | 537.918i | −0.460481 | − | 0.723008i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −162.715 | − | 56.5648i | −0.218117 | − | 0.0758241i | ||||
\(747\) | − | 72.4009i | − | 0.0969222i | ||||||
\(748\) | 423.317 | − | 535.281i | 0.565932 | − | 0.715617i | ||||
\(749\) | 335.395 | 0.447791 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 345.748i | − | 0.460384i | −0.973145 | − | 0.230192i | \(-0.926065\pi\) | ||
0.973145 | − | 0.230192i | \(-0.0739354\pi\) | |||||||
\(752\) | 219.319 | − | 51.9414i | 0.291647 | − | 0.0690710i | ||||
\(753\) | 245.390 | 0.325882 | ||||||||
\(754\) | 5.00331 | + | 1.73930i | 0.00663569 | + | 0.00230677i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −155.773 | − | 123.190i | −0.206049 | − | 0.162950i | ||||
\(757\) | 549.335 | 0.725674 | 0.362837 | − | 0.931853i | \(-0.381808\pi\) | ||||
0.362837 | + | 0.931853i | \(0.381808\pi\) | |||||||
\(758\) | −419.005 | + | 1205.32i | −0.552778 | + | 1.59013i | ||||
\(759\) | 28.7852i | 0.0379252i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 251.485 | 0.330467 | 0.165233 | − | 0.986255i | \(-0.447162\pi\) | ||||
0.165233 | + | 0.986255i | \(0.447162\pi\) | |||||||
\(762\) | 628.405 | + | 218.453i | 0.824678 | + | 0.286683i | ||||
\(763\) | − | 1447.57i | − | 1.89721i | ||||||
\(764\) | −340.440 | + | 430.484i | −0.445602 | + | 0.563461i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 142.337 | − | 409.450i | 0.185819 | − | 0.534529i | ||||
\(767\) | 716.200i | 0.933768i | ||||||||
\(768\) | −198.869 | − | 396.307i | −0.258945 | − | 0.516024i | ||||
\(769\) | −583.691 | −0.759026 | −0.379513 | − | 0.925186i | \(-0.623908\pi\) | ||||
−0.379513 | + | 0.925186i | \(0.623908\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 72.3216i | 0.0938024i | ||||||||
\(772\) | 116.177 | + | 91.8764i | 0.150488 | + | 0.119011i | ||||
\(773\) | −1328.04 | −1.71803 | −0.859015 | − | 0.511951i | \(-0.828923\pi\) | ||||
−0.859015 | + | 0.511951i | \(0.828923\pi\) | |||||||
\(774\) | 82.3505 | − | 236.891i | 0.106396 | − | 0.306060i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 566.681 | + | 889.753i | 0.730259 | + | 1.14659i | ||||
\(777\) | −375.173 | −0.482848 | ||||||||
\(778\) | 900.424 | + | 313.015i | 1.15736 | + | 0.402333i | ||||
\(779\) | 2023.40i | 2.59743i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −71.4219 | −0.0914492 | ||||||||
\(782\) | 18.9036 | − | 54.3784i | 0.0241734 | − | 0.0695376i | ||||
\(783\) | − | 1.82123i | − | 0.00232597i | ||||||
\(784\) | −155.969 | − | 658.567i | −0.198940 | − | 0.840009i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 138.825 | + | 48.2598i | 0.176622 | + | 0.0613992i | ||||
\(787\) | 1318.83i | 1.67577i | 0.545850 | + | 0.837883i | \(0.316207\pi\) | ||||
−0.545850 | + | 0.837883i | \(0.683793\pi\) | |||||||
\(788\) | −610.461 | − | 482.772i | −0.774697 | − | 0.612654i | ||||
\(789\) | 352.096 | 0.446256 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 308.658i | 0.390212i | ||||||||
\(792\) | −200.908 | + | 127.957i | −0.253671 | + | 0.161562i | ||||
\(793\) | −287.144 | −0.362099 | ||||||||
\(794\) | −81.3812 | − | 28.2906i | −0.102495 | − | 0.0356305i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −436.784 | + | 552.310i | −0.548724 | + | 0.693857i | ||||
\(797\) | 1277.40 | 1.60276 | 0.801381 | − | 0.598154i | \(-0.204099\pi\) | ||||
0.801381 | + | 0.598154i | \(0.204099\pi\) | |||||||
\(798\) | −284.496 | + | 818.385i | −0.356511 | + | 1.02555i | ||||
\(799\) | 242.152i | 0.303069i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 300.598 | 0.375278 | ||||||||
\(802\) | 318.682 | + | 110.784i | 0.397359 | + | 0.138134i | ||||
\(803\) | 341.220i | 0.424931i | ||||||||
\(804\) | −162.199 | − | 128.272i | −0.201740 | − | 0.159543i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 228.399 | − | 657.015i | 0.283373 | − | 0.815155i | ||||
\(807\) | 422.704i | 0.523797i | ||||||||
\(808\) | −126.564 | − | 198.720i | −0.156639 | − | 0.245940i | ||||
\(809\) | −321.093 | −0.396901 | −0.198451 | − | 0.980111i | \(-0.563591\pi\) | ||||
−0.198451 | + | 0.980111i | \(0.563591\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 946.932i | − | 1.16761i | −0.811894 | − | 0.583805i | \(-0.801563\pi\) | ||
0.811894 | − | 0.583805i | \(-0.198437\pi\) | |||||||
\(812\) | 8.30957 | − | 10.5074i | 0.0102335 | − | 0.0129401i | ||||
\(813\) | −808.149 | −0.994033 | ||||||||
\(814\) | −147.752 | + | 425.027i | −0.181514 | + | 0.522146i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 463.567 | − | 109.787i | 0.568097 | − | 0.134543i | ||||
\(817\) | −1094.15 | −1.33923 | ||||||||
\(818\) | 706.319 | + | 245.538i | 0.863471 | + | 0.300169i | ||||
\(819\) | − | 216.606i | − | 0.264477i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1169.34 | 1.42429 | 0.712144 | − | 0.702033i | \(-0.247724\pi\) | ||||
0.712144 | + | 0.702033i | \(0.247724\pi\) | |||||||
\(822\) | 235.288 | − | 676.833i | 0.286239 | − | 0.823398i | ||||
\(823\) | − | 1251.71i | − | 1.52091i | −0.649389 | − | 0.760457i | \(-0.724975\pi\) | ||
0.649389 | − | 0.760457i | \(-0.275025\pi\) | |||||||
\(824\) | 970.220 | − | 617.930i | 1.17745 | − | 0.749915i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1710.83 | + | 594.738i | 2.07123 | + | 0.720022i | ||||
\(827\) | 892.104i | 1.07872i | 0.842074 | + | 0.539362i | \(0.181334\pi\) | ||||
−0.842074 | + | 0.539362i | \(0.818666\pi\) | |||||||
\(828\) | −12.4644 | + | 15.7611i | −0.0150536 | + | 0.0190351i | ||||
\(829\) | −998.688 | −1.20469 | −0.602345 | − | 0.798236i | \(-0.705767\pi\) | ||||
−0.602345 | + | 0.798236i | \(0.705767\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 855.946i | 1.03002i | ||||||||
\(832\) | 204.491 | − | 438.251i | 0.245783 | − | 0.526743i | ||||
\(833\) | 727.131 | 0.872906 | ||||||||
\(834\) | 150.598 | + | 52.3525i | 0.180573 | + | 0.0627728i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 815.093 | + | 644.601i | 0.974992 | + | 0.771054i | ||||
\(837\) | −239.157 | −0.285732 | ||||||||
\(838\) | −57.5174 | + | 165.455i | −0.0686365 | + | 0.197441i | ||||
\(839\) | − | 610.359i | − | 0.727484i | −0.931500 | − | 0.363742i | \(-0.881499\pi\) | ||
0.931500 | − | 0.363742i | \(-0.118501\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −840.877 | −0.999854 | ||||||||
\(842\) | −132.809 | − | 46.1684i | −0.157730 | − | 0.0548318i | ||||
\(843\) | − | 75.1744i | − | 0.0891749i | ||||||
\(844\) | −51.4086 | + | 65.0058i | −0.0609107 | + | 0.0770211i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 27.7525 | − | 79.8332i | 0.0328044 | − | 0.0943655i | ||||
\(847\) | − | 214.973i | − | 0.253805i | ||||||
\(848\) | 83.5883 | + | 352.946i | 0.0985712 | + | 0.416209i | ||||
\(849\) | 538.296 | 0.634035 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 37.9599i | 0.0446062i | ||||||||
\(852\) | −39.1064 | − | 30.9266i | −0.0458995 | − | 0.0362988i | ||||
\(853\) | 832.689 | 0.976189 | 0.488094 | − | 0.872791i | \(-0.337692\pi\) | ||||
0.488094 | + | 0.872791i | \(0.337692\pi\) | |||||||
\(854\) | −238.447 | + | 685.920i | −0.279212 | + | 0.803185i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 236.852 | − | 150.850i | 0.276696 | − | 0.176227i | ||||
\(857\) | −149.415 | −0.174347 | −0.0871735 | − | 0.996193i | \(-0.527783\pi\) | ||||
−0.0871735 | + | 0.996193i | \(0.527783\pi\) | |||||||
\(858\) | −245.390 | − | 85.3049i | −0.286002 | − | 0.0994230i | ||||
\(859\) | 394.144i | 0.458840i | 0.973327 | + | 0.229420i | \(0.0736830\pi\) | ||||
−0.973327 | + | 0.229420i | \(0.926317\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1279.29 | −1.48581 | ||||||||
\(862\) | 162.451 | − | 467.308i | 0.188458 | − | 0.542121i | ||||
\(863\) | 1409.58i | 1.63335i | 0.577095 | + | 0.816677i | \(0.304186\pi\) | ||||
−0.577095 | + | 0.816677i | \(0.695814\pi\) | |||||||
\(864\) | −165.412 | − | 16.9336i | −0.191450 | − | 0.0195990i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1201.94 | − | 417.831i | −1.38792 | − | 0.482484i | ||||
\(867\) | 11.2669i | 0.0129953i | ||||||||
\(868\) | −1379.79 | − | 1091.18i | −1.58962 | − | 1.25712i | ||||
\(869\) | 456.797 | 0.525659 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 225.542i | − | 0.258946i | ||||||
\(872\) | −651.074 | − | 1022.26i | −0.746644 | − | 1.17232i | ||||
\(873\) | 395.583 | 0.453131 | ||||||||
\(874\) | 82.8040 | + | 28.7852i | 0.0947414 | + | 0.0329350i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −147.752 | + | 186.832i | −0.168667 | + | 0.213278i | ||||
\(877\) | −872.780 | −0.995189 | −0.497594 | − | 0.867410i | \(-0.665783\pi\) | ||||
−0.497594 | + | 0.867410i | \(0.665783\pi\) | |||||||
\(878\) | −505.528 | + | 1454.21i | −0.575772 | + | 1.65627i | ||||
\(879\) | 424.712i | 0.483176i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1103.38 | 1.25241 | 0.626206 | − | 0.779657i | \(-0.284607\pi\) | ||||
0.626206 | + | 0.779657i | \(0.284607\pi\) | |||||||
\(882\) | −239.722 | − | 83.3348i | −0.271794 | − | 0.0944839i | ||||
\(883\) | 536.884i | 0.608023i | 0.952668 | + | 0.304011i | \(0.0983261\pi\) | ||||
−0.952668 | + | 0.304011i | \(0.901674\pi\) | |||||||
\(884\) | 407.547 | + | 322.300i | 0.461025 | + | 0.364593i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −402.048 | + | 1156.54i | −0.453779 | + | 1.30535i | ||||
\(887\) | − | 888.945i | − | 1.00219i | −0.865392 | − | 0.501096i | \(-0.832930\pi\) | ||
0.865392 | − | 0.501096i | \(-0.167070\pi\) | |||||||
\(888\) | −264.943 | + | 168.741i | −0.298359 | + | 0.190024i | ||||
\(889\) | 1835.08 | 2.06421 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 89.3232i | 0.100251i | ||||||||
\(892\) | −240.742 | + | 304.417i | −0.269890 | + | 0.341274i | ||||
\(893\) | −368.734 | −0.412916 | ||||||||
\(894\) | −13.2508 | + | 38.1175i | −0.0148220 | + | 0.0426371i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −877.066 | − | 852.408i | −0.978868 | − | 0.951348i | ||||
\(897\) | −21.9162 | −0.0244327 | ||||||||
\(898\) | 332.288 | + | 115.514i | 0.370032 | + | 0.128634i | ||||
\(899\) | − | 16.1319i | − | 0.0179443i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −389.691 | −0.432510 | ||||||||
\(902\) | −503.814 | + | 1449.28i | −0.558553 | + | 1.60674i | ||||
\(903\) | − | 691.773i | − | 0.766083i | ||||||
\(904\) | 138.825 | + | 217.971i | 0.153567 | + | 0.241118i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −410.392 | − | 142.665i | −0.452971 | − | 0.157467i | ||||
\(907\) | − | 1668.40i | − | 1.83947i | −0.392543 | − | 0.919734i | \(-0.628405\pi\) | ||
0.392543 | − | 0.919734i | \(-0.371595\pi\) | |||||||
\(908\) | 1010.48 | − | 1277.75i | 1.11287 | − | 1.40721i | ||||
\(909\) | −88.3505 | −0.0971953 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1498.13i | − | 1.64449i | −0.569131 | − | 0.822247i | \(-0.692720\pi\) | ||
0.569131 | − | 0.822247i | \(-0.307280\pi\) | |||||||
\(912\) | 167.177 | + | 705.891i | 0.183308 | + | 0.774004i | ||||
\(913\) | −239.521 | −0.262345 | ||||||||
\(914\) | −690.199 | − | 239.935i | −0.755142 | − | 0.262510i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 24.7766 | + | 19.5941i | 0.0270487 | + | 0.0213909i | ||||
\(917\) | 405.399 | 0.442093 | ||||||||
\(918\) | 58.6596 | − | 168.741i | 0.0638994 | − | 0.183814i | ||||
\(919\) | − | 1094.82i | − | 1.19131i | −0.803240 | − | 0.595656i | \(-0.796892\pi\) | ||
0.803240 | − | 0.595656i | \(-0.203108\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 584.591 | 0.634735 | ||||||||
\(922\) | −582.507 | − | 202.497i | −0.631787 | − | 0.219629i | ||||
\(923\) | − | 54.3784i | − | 0.0589148i | ||||||
\(924\) | −407.547 | + | 515.339i | −0.441068 | + | 0.557727i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −60.8314 | + | 174.988i | −0.0656926 | + | 0.188972i | ||||
\(927\) | − | 431.358i | − | 0.465327i | ||||||
\(928\) | 1.14222 | − | 11.1576i | 0.00123084 | − | 0.0120233i | ||||
\(929\) | −1145.90 | −1.23348 | −0.616740 | − | 0.787167i | \(-0.711547\pi\) | ||||
−0.616740 | + | 0.787167i | \(0.711547\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1107.23i | 1.18929i | ||||||||
\(932\) | −88.3142 | − | 69.8417i | −0.0947578 | − | 0.0749374i | ||||
\(933\) | 740.894 | 0.794099 | ||||||||
\(934\) | −398.035 | + | 1144.99i | −0.426162 | + | 1.22590i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −97.4228 | − | 152.965i | −0.104084 | − | 0.163424i | ||||
\(937\) | 1272.49 | 1.35805 | 0.679025 | − | 0.734115i | \(-0.262403\pi\) | ||||
0.679025 | + | 0.734115i | \(0.262403\pi\) | |||||||
\(938\) | −538.766 | − | 187.292i | −0.574378 | − | 0.199671i | ||||
\(939\) | − | 145.274i | − | 0.154711i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 707.360 | 0.751711 | 0.375856 | − | 0.926678i | \(-0.377349\pi\) | ||||
0.375856 | + | 0.926678i | \(0.377349\pi\) | |||||||
\(942\) | −224.330 | + | 645.311i | −0.238142 | + | 0.685044i | ||||
\(943\) | 129.438i | 0.137262i | ||||||||
\(944\) | 1475.66 | − | 349.482i | 1.56320 | − | 0.370214i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −783.698 | − | 272.437i | −0.828433 | − | 0.287989i | ||||
\(947\) | − | 284.977i | − | 0.300926i | −0.988616 | − | 0.150463i | \(-0.951924\pi\) | ||
0.988616 | − | 0.150463i | \(-0.0480765\pi\) | |||||||
\(948\) | 250.115 | + | 197.799i | 0.263835 | + | 0.208649i | ||||
\(949\) | −259.794 | −0.273756 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 194.343i | 0.204357i | ||||||||
\(952\) | 1108.33 | − | 705.891i | 1.16421 | − | 0.741482i | ||||
\(953\) | 295.247 | 0.309808 | 0.154904 | − | 0.987930i | \(-0.450493\pi\) | ||||
0.154904 | + | 0.987930i | \(0.450493\pi\) | |||||||
\(954\) | 128.474 | + | 44.6616i | 0.134669 | + | 0.0468151i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 734.447 | − | 928.702i | 0.768250 | − | 0.971446i | ||||
\(957\) | −6.02513 | −0.00629585 | ||||||||
\(958\) | 91.2483 | − | 262.486i | 0.0952487 | − | 0.273994i | ||||
\(959\) | − | 1976.50i | − | 2.06100i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1157.38 | −1.20435 | ||||||||
\(962\) | −323.602 | − | 112.494i | −0.336385 | − | 0.116938i | ||||
\(963\) | − | 105.304i | − | 0.109350i | ||||||
\(964\) | 1461.41 | + | 1155.73i | 1.51598 | + | 1.19889i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −18.1993 | + | 52.3525i | −0.0188399 | + | 0.0541951i | ||||
\(967\) | − | 348.013i | − | 0.359889i | −0.983677 | − | 0.179945i | \(-0.942408\pi\) | ||
0.983677 | − | 0.179945i | \(-0.0575918\pi\) | |||||||
\(968\) | −96.6881 | − | 151.811i | −0.0998844 | − | 0.156830i | ||||
\(969\) | −779.382 | −0.804316 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 798.691i | − | 0.822545i | −0.911513 | − | 0.411272i | \(-0.865085\pi\) | ||
0.911513 | − | 0.411272i | \(-0.134915\pi\) | |||||||
\(972\) | −38.6781 | + | 48.9081i | −0.0397923 | + | 0.0503170i | ||||
\(973\) | 439.779 | 0.451983 | ||||||||
\(974\) | 132.159 | − | 380.170i | 0.135687 | − | 0.390318i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 140.117 | + | 591.634i | 0.143563 | + | 0.606183i | ||||
\(977\) | 721.834 | 0.738827 | 0.369413 | − | 0.929265i | \(-0.379559\pi\) | ||||
0.369413 | + | 0.929265i | \(0.379559\pi\) | |||||||
\(978\) | −60.2694 | − | 20.9515i | −0.0616252 | − | 0.0214228i | ||||
\(979\) | − | 994.458i | − | 1.01579i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −454.495 | −0.463298 | ||||||||
\(982\) | 228.121 | − | 656.216i | 0.232302 | − | 0.668244i | ||||
\(983\) | − | 1717.25i | − | 1.74695i | −0.486870 | − | 0.873474i | \(-0.661861\pi\) | ||
0.486870 | − | 0.873474i | \(-0.338139\pi\) | |||||||
\(984\) | −903.416 | + | 575.383i | −0.918106 | + | 0.584739i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 11.3821 | + | 3.95677i | 0.0115437 | + | 0.00401296i | ||||
\(987\) | − | 233.131i | − | 0.236201i | ||||||
\(988\) | −490.779 | + | 620.586i | −0.496740 | + | 0.628124i | ||||
\(989\) | −69.9934 | −0.0707719 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 342.270i | 0.345378i | 0.984976 | + | 0.172689i | \(0.0552456\pi\) | ||||
−0.984976 | + | 0.172689i | \(0.944754\pi\) | |||||||
\(992\) | −1465.17 | − | 149.992i | −1.47699 | − | 0.151202i | ||||
\(993\) | 229.706 | 0.231325 | ||||||||
\(994\) | −129.897 | − | 45.1562i | −0.130681 | − | 0.0454288i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −131.148 | − | 103.716i | −0.131675 | − | 0.104132i | ||||
\(997\) | −1586.05 | −1.59082 | −0.795410 | − | 0.606072i | \(-0.792744\pi\) | ||||
−0.795410 | + | 0.606072i | \(0.792744\pi\) | |||||||
\(998\) | 441.493 | − | 1270.00i | 0.442377 | − | 1.27255i | ||||
\(999\) | 117.793i | 0.117911i |
(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 | 300.3.c.f.151.1 | 8 | ||
3.2 | odd | 2 | 900.3.c.r.451.8 | 8 | |||
4.3 | odd | 2 | inner | 300.3.c.f.151.2 | 8 | ||
5.2 | odd | 4 | 60.3.f.b.19.5 | yes | 8 | ||
5.3 | odd | 4 | 60.3.f.b.19.4 | yes | 8 | ||
5.4 | even | 2 | inner | 300.3.c.f.151.8 | 8 | ||
12.11 | even | 2 | 900.3.c.r.451.7 | 8 | |||
15.2 | even | 4 | 180.3.f.h.19.4 | 8 | |||
15.8 | even | 4 | 180.3.f.h.19.5 | 8 | |||
15.14 | odd | 2 | 900.3.c.r.451.1 | 8 | |||
20.3 | even | 4 | 60.3.f.b.19.6 | yes | 8 | ||
20.7 | even | 4 | 60.3.f.b.19.3 | ✓ | 8 | ||
20.19 | odd | 2 | inner | 300.3.c.f.151.7 | 8 | ||
40.3 | even | 4 | 960.3.j.e.319.3 | 8 | |||
40.13 | odd | 4 | 960.3.j.e.319.7 | 8 | |||
40.27 | even | 4 | 960.3.j.e.319.8 | 8 | |||
40.37 | odd | 4 | 960.3.j.e.319.4 | 8 | |||
60.23 | odd | 4 | 180.3.f.h.19.3 | 8 | |||
60.47 | odd | 4 | 180.3.f.h.19.6 | 8 | |||
60.59 | even | 2 | 900.3.c.r.451.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.3.f.b.19.3 | ✓ | 8 | 20.7 | even | 4 | ||
60.3.f.b.19.4 | yes | 8 | 5.3 | odd | 4 | ||
60.3.f.b.19.5 | yes | 8 | 5.2 | odd | 4 | ||
60.3.f.b.19.6 | yes | 8 | 20.3 | even | 4 | ||
180.3.f.h.19.3 | 8 | 60.23 | odd | 4 | |||
180.3.f.h.19.4 | 8 | 15.2 | even | 4 | |||
180.3.f.h.19.5 | 8 | 15.8 | even | 4 | |||
180.3.f.h.19.6 | 8 | 60.47 | odd | 4 | |||
300.3.c.f.151.1 | 8 | 1.1 | even | 1 | trivial | ||
300.3.c.f.151.2 | 8 | 4.3 | odd | 2 | inner | ||
300.3.c.f.151.7 | 8 | 20.19 | odd | 2 | inner | ||
300.3.c.f.151.8 | 8 | 5.4 | even | 2 | inner | ||
900.3.c.r.451.1 | 8 | 15.14 | odd | 2 | |||
900.3.c.r.451.2 | 8 | 60.59 | even | 2 | |||
900.3.c.r.451.7 | 8 | 12.11 | even | 2 | |||
900.3.c.r.451.8 | 8 | 3.2 | odd | 2 | |||
960.3.j.e.319.3 | 8 | 40.3 | even | 4 | |||
960.3.j.e.319.4 | 8 | 40.37 | odd | 4 | |||
960.3.j.e.319.7 | 8 | 40.13 | odd | 4 | |||
960.3.j.e.319.8 | 8 | 40.27 | even | 4 |