Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(43,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.43");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.l (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: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.12745506816.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 23x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.2 | ||
Root | \(-1.54779 + 1.54779i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.43 |
Dual form | 1050.3.l.e.757.2 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.00000i | 0.500000 | − | 0.500000i | ||||
\(3\) | −1.22474 | − | 1.22474i | −0.408248 | − | 0.408248i | ||||
\(4\) | − | 2.00000i | − | 0.500000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.44949 | −0.408248 | ||||||||
\(7\) | 1.87083 | − | 1.87083i | 0.267261 | − | 0.267261i | ||||
\(8\) | −2.00000 | − | 2.00000i | −0.250000 | − | 0.250000i | ||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.18939 | 0.380853 | 0.190427 | − | 0.981701i | \(-0.439013\pi\) | ||||
0.190427 | + | 0.981701i | \(0.439013\pi\) | |||||||
\(12\) | −2.44949 | + | 2.44949i | −0.204124 | + | 0.204124i | ||||
\(13\) | 12.9946 | + | 12.9946i | 0.999581 | + | 0.999581i | 1.00000 | 0.000418908i | \(-0.000133343\pi\) | |
−0.000418908 | 1.00000i | \(0.500133\pi\) | ||||||||
\(14\) | − | 3.74166i | − | 0.267261i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −23.0622 | + | 23.0622i | −1.35660 | + | 1.35660i | −0.478528 | + | 0.878072i | \(0.658829\pi\) |
−0.878072 | + | 0.478528i | \(0.841171\pi\) | |||||||
\(18\) | 3.00000 | + | 3.00000i | 0.166667 | + | 0.166667i | ||||
\(19\) | 32.6732i | 1.71964i | 0.510597 | + | 0.859820i | \(0.329424\pi\) | ||||
−0.510597 | + | 0.859820i | \(0.670576\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.58258 | −0.218218 | ||||||||
\(22\) | 4.18939 | − | 4.18939i | 0.190427 | − | 0.190427i | ||||
\(23\) | −13.5097 | − | 13.5097i | −0.587379 | − | 0.587379i | 0.349542 | − | 0.936921i | \(-0.386337\pi\) |
−0.936921 | + | 0.349542i | \(0.886337\pi\) | |||||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 25.9891 | 0.999581 | ||||||||
\(27\) | 3.67423 | − | 3.67423i | 0.136083 | − | 0.136083i | ||||
\(28\) | −3.74166 | − | 3.74166i | −0.133631 | − | 0.133631i | ||||
\(29\) | 23.2944i | 0.803255i | 0.915803 | + | 0.401627i | \(0.131555\pi\) | ||||
−0.915803 | + | 0.401627i | \(0.868445\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 32.2818 | 1.04135 | 0.520675 | − | 0.853755i | \(-0.325680\pi\) | ||||
0.520675 | + | 0.853755i | \(0.325680\pi\) | |||||||
\(32\) | −4.00000 | + | 4.00000i | −0.125000 | + | 0.125000i | ||||
\(33\) | −5.13093 | − | 5.13093i | −0.155483 | − | 0.155483i | ||||
\(34\) | 46.1244i | 1.35660i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | −21.0196 | + | 21.0196i | −0.568098 | + | 0.568098i | −0.931595 | − | 0.363497i | \(-0.881583\pi\) |
0.363497 | + | 0.931595i | \(0.381583\pi\) | |||||||
\(38\) | 32.6732 | + | 32.6732i | 0.859820 | + | 0.859820i | ||||
\(39\) | − | 31.8300i | − | 0.816154i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −51.9782 | −1.26776 | −0.633881 | − | 0.773431i | \(-0.718539\pi\) | ||||
−0.633881 | + | 0.773431i | \(0.718539\pi\) | |||||||
\(42\) | −4.58258 | + | 4.58258i | −0.109109 | + | 0.109109i | ||||
\(43\) | −24.7626 | − | 24.7626i | −0.575874 | − | 0.575874i | 0.357889 | − | 0.933764i | \(-0.383496\pi\) |
−0.933764 | + | 0.357889i | \(0.883496\pi\) | |||||||
\(44\) | − | 8.37878i | − | 0.190427i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −27.0194 | −0.587379 | ||||||||
\(47\) | 52.0691 | − | 52.0691i | 1.10785 | − | 1.10785i | 0.114420 | − | 0.993432i | \(-0.463499\pi\) |
0.993432 | − | 0.114420i | \(-0.0365009\pi\) | |||||||
\(48\) | 4.89898 | + | 4.89898i | 0.102062 | + | 0.102062i | ||||
\(49\) | − | 7.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 56.4906 | 1.10766 | ||||||||
\(52\) | 25.9891 | − | 25.9891i | 0.499791 | − | 0.499791i | ||||
\(53\) | 26.3788 | + | 26.3788i | 0.497713 | + | 0.497713i | 0.910725 | − | 0.413013i | \(-0.135523\pi\) |
−0.413013 | + | 0.910725i | \(0.635523\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.48331 | −0.133631 | ||||||||
\(57\) | 40.0163 | − | 40.0163i | 0.702040 | − | 0.702040i | ||||
\(58\) | 23.2944 | + | 23.2944i | 0.401627 | + | 0.401627i | ||||
\(59\) | 103.106i | 1.74757i | 0.486316 | + | 0.873783i | \(0.338341\pi\) | ||||
−0.486316 | + | 0.873783i | \(0.661659\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 119.719 | 1.96261 | 0.981303 | − | 0.192470i | \(-0.0616497\pi\) | ||||
0.981303 | + | 0.192470i | \(0.0616497\pi\) | |||||||
\(62\) | 32.2818 | − | 32.2818i | 0.520675 | − | 0.520675i | ||||
\(63\) | 5.61249 | + | 5.61249i | 0.0890871 | + | 0.0890871i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −10.2619 | −0.155483 | ||||||||
\(67\) | −49.4740 | + | 49.4740i | −0.738417 | + | 0.738417i | −0.972272 | − | 0.233854i | \(-0.924866\pi\) |
0.233854 | + | 0.972272i | \(0.424866\pi\) | |||||||
\(68\) | 46.1244 | + | 46.1244i | 0.678300 | + | 0.678300i | ||||
\(69\) | 33.0919i | 0.479593i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 94.0594 | 1.32478 | 0.662390 | − | 0.749159i | \(-0.269542\pi\) | ||||
0.662390 | + | 0.749159i | \(0.269542\pi\) | |||||||
\(72\) | 6.00000 | − | 6.00000i | 0.0833333 | − | 0.0833333i | ||||
\(73\) | −15.0771 | − | 15.0771i | −0.206535 | − | 0.206535i | 0.596258 | − | 0.802793i | \(-0.296654\pi\) |
−0.802793 | + | 0.596258i | \(0.796654\pi\) | |||||||
\(74\) | 42.0393i | 0.568098i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 65.3463 | 0.859820 | ||||||||
\(77\) | 7.83763 | − | 7.83763i | 0.101787 | − | 0.101787i | ||||
\(78\) | −31.8300 | − | 31.8300i | −0.408077 | − | 0.408077i | ||||
\(79\) | 112.890i | 1.42899i | 0.699642 | + | 0.714494i | \(0.253343\pi\) | ||||
−0.699642 | + | 0.714494i | \(0.746657\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | −51.9782 | + | 51.9782i | −0.633881 | + | 0.633881i | ||||
\(83\) | 13.6666 | + | 13.6666i | 0.164658 | + | 0.164658i | 0.784627 | − | 0.619968i | \(-0.212855\pi\) |
−0.619968 | + | 0.784627i | \(0.712855\pi\) | |||||||
\(84\) | 9.16515i | 0.109109i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −49.5252 | −0.575874 | ||||||||
\(87\) | 28.5297 | − | 28.5297i | 0.327927 | − | 0.327927i | ||||
\(88\) | −8.37878 | − | 8.37878i | −0.0952134 | − | 0.0952134i | ||||
\(89\) | − | 35.6390i | − | 0.400438i | −0.979751 | − | 0.200219i | \(-0.935835\pi\) | ||
0.979751 | − | 0.200219i | \(-0.0641654\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 48.6212 | 0.534299 | ||||||||
\(92\) | −27.0194 | + | 27.0194i | −0.293689 | + | 0.293689i | ||||
\(93\) | −39.5370 | − | 39.5370i | −0.425129 | − | 0.425129i | ||||
\(94\) | − | 104.138i | − | 1.10785i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9.79796 | 0.102062 | ||||||||
\(97\) | 72.1545 | − | 72.1545i | 0.743861 | − | 0.743861i | −0.229458 | − | 0.973319i | \(-0.573695\pi\) |
0.973319 | + | 0.229458i | \(0.0736953\pi\) | |||||||
\(98\) | −7.00000 | − | 7.00000i | −0.0714286 | − | 0.0714286i | ||||
\(99\) | 12.5682i | 0.126951i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 27.1945 | 0.269253 | 0.134626 | − | 0.990896i | \(-0.457017\pi\) | ||||
0.134626 | + | 0.990896i | \(0.457017\pi\) | |||||||
\(102\) | 56.4906 | − | 56.4906i | 0.553830 | − | 0.553830i | ||||
\(103\) | −42.1649 | − | 42.1649i | −0.409368 | − | 0.409368i | 0.472150 | − | 0.881518i | \(-0.343478\pi\) |
−0.881518 | + | 0.472150i | \(0.843478\pi\) | |||||||
\(104\) | − | 51.9782i | − | 0.499791i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 52.7576 | 0.497713 | ||||||||
\(107\) | 78.0442 | − | 78.0442i | 0.729385 | − | 0.729385i | −0.241112 | − | 0.970497i | \(-0.577512\pi\) |
0.970497 | + | 0.241112i | \(0.0775121\pi\) | |||||||
\(108\) | −7.34847 | − | 7.34847i | −0.0680414 | − | 0.0680414i | ||||
\(109\) | 115.318i | 1.05796i | 0.848634 | + | 0.528981i | \(0.177426\pi\) | ||||
−0.848634 | + | 0.528981i | \(0.822574\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 51.4874 | 0.463850 | ||||||||
\(112\) | −7.48331 | + | 7.48331i | −0.0668153 | + | 0.0668153i | ||||
\(113\) | −70.2690 | − | 70.2690i | −0.621849 | − | 0.621849i | 0.324155 | − | 0.946004i | \(-0.394920\pi\) |
−0.946004 | + | 0.324155i | \(0.894920\pi\) | |||||||
\(114\) | − | 80.0326i | − | 0.702040i | ||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 46.5888 | 0.401627 | ||||||||
\(117\) | −38.9837 | + | 38.9837i | −0.333194 | + | 0.333194i | ||||
\(118\) | 103.106 | + | 103.106i | 0.873783 | + | 0.873783i | ||||
\(119\) | 86.2909i | 0.725133i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −103.449 | −0.854951 | ||||||||
\(122\) | 119.719 | − | 119.719i | 0.981303 | − | 0.981303i | ||||
\(123\) | 63.6600 | + | 63.6600i | 0.517561 | + | 0.517561i | ||||
\(124\) | − | 64.5637i | − | 0.520675i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 11.2250 | 0.0890871 | ||||||||
\(127\) | 15.4063 | − | 15.4063i | 0.121309 | − | 0.121309i | −0.643846 | − | 0.765155i | \(-0.722662\pi\) |
0.765155 | + | 0.643846i | \(0.222662\pi\) | |||||||
\(128\) | 8.00000 | + | 8.00000i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 60.6557i | 0.470200i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −237.306 | −1.81150 | −0.905750 | − | 0.423812i | \(-0.860692\pi\) | ||||
−0.905750 | + | 0.423812i | \(0.860692\pi\) | |||||||
\(132\) | −10.2619 | + | 10.2619i | −0.0777414 | + | 0.0777414i | ||||
\(133\) | 61.1259 | + | 61.1259i | 0.459593 | + | 0.459593i | ||||
\(134\) | 98.9479i | 0.738417i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 92.2488 | 0.678300 | ||||||||
\(137\) | −48.4157 | + | 48.4157i | −0.353399 | + | 0.353399i | −0.861373 | − | 0.507973i | \(-0.830395\pi\) |
0.507973 | + | 0.861373i | \(0.330395\pi\) | |||||||
\(138\) | 33.0919 | + | 33.0919i | 0.239796 | + | 0.239796i | ||||
\(139\) | − | 106.547i | − | 0.766523i | −0.923640 | − | 0.383262i | \(-0.874801\pi\) | ||
0.923640 | − | 0.383262i | \(-0.125199\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −127.543 | −0.904558 | ||||||||
\(142\) | 94.0594 | − | 94.0594i | 0.662390 | − | 0.662390i | ||||
\(143\) | 54.4392 | + | 54.4392i | 0.380694 | + | 0.380694i | ||||
\(144\) | − | 12.0000i | − | 0.0833333i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −30.1541 | −0.206535 | ||||||||
\(147\) | −8.57321 | + | 8.57321i | −0.0583212 | + | 0.0583212i | ||||
\(148\) | 42.0393 | + | 42.0393i | 0.284049 | + | 0.284049i | ||||
\(149\) | 30.2575i | 0.203070i | 0.994832 | + | 0.101535i | \(0.0323755\pi\) | ||||
−0.994832 | + | 0.101535i | \(0.967625\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 181.315 | 1.20076 | 0.600379 | − | 0.799715i | \(-0.295016\pi\) | ||||
0.600379 | + | 0.799715i | \(0.295016\pi\) | |||||||
\(152\) | 65.3463 | − | 65.3463i | 0.429910 | − | 0.429910i | ||||
\(153\) | −69.1866 | − | 69.1866i | −0.452200 | − | 0.452200i | ||||
\(154\) | − | 15.6753i | − | 0.101787i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −63.6600 | −0.408077 | ||||||||
\(157\) | −8.53019 | + | 8.53019i | −0.0543324 | + | 0.0543324i | −0.733751 | − | 0.679419i | \(-0.762232\pi\) |
0.679419 | + | 0.733751i | \(0.262232\pi\) | |||||||
\(158\) | 112.890 | + | 112.890i | 0.714494 | + | 0.714494i | ||||
\(159\) | − | 64.6145i | − | 0.406381i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −50.5487 | −0.313967 | ||||||||
\(162\) | −9.00000 | + | 9.00000i | −0.0555556 | + | 0.0555556i | ||||
\(163\) | 60.3100 | + | 60.3100i | 0.370000 | + | 0.370000i | 0.867477 | − | 0.497477i | \(-0.165740\pi\) |
−0.497477 | + | 0.867477i | \(0.665740\pi\) | |||||||
\(164\) | 103.956i | 0.633881i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 27.3333 | 0.164658 | ||||||||
\(167\) | 131.125 | − | 131.125i | 0.785181 | − | 0.785181i | −0.195519 | − | 0.980700i | \(-0.562639\pi\) |
0.980700 | + | 0.195519i | \(0.0626390\pi\) | |||||||
\(168\) | 9.16515 | + | 9.16515i | 0.0545545 | + | 0.0545545i | ||||
\(169\) | 168.717i | 0.998324i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −98.0195 | −0.573213 | ||||||||
\(172\) | −49.5252 | + | 49.5252i | −0.287937 | + | 0.287937i | ||||
\(173\) | −78.0609 | − | 78.0609i | −0.451219 | − | 0.451219i | 0.444540 | − | 0.895759i | \(-0.353367\pi\) |
−0.895759 | + | 0.444540i | \(0.853367\pi\) | |||||||
\(174\) | − | 57.0593i | − | 0.327927i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −16.7576 | −0.0952134 | ||||||||
\(177\) | 126.279 | − | 126.279i | 0.713441 | − | 0.713441i | ||||
\(178\) | −35.6390 | − | 35.6390i | −0.200219 | − | 0.200219i | ||||
\(179\) | − | 116.492i | − | 0.650796i | −0.945577 | − | 0.325398i | \(-0.894502\pi\) | ||
0.945577 | − | 0.325398i | \(-0.105498\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 256.478 | 1.41701 | 0.708503 | − | 0.705708i | \(-0.249371\pi\) | ||||
0.708503 | + | 0.705708i | \(0.249371\pi\) | |||||||
\(182\) | 48.6212 | − | 48.6212i | 0.267149 | − | 0.267149i | ||||
\(183\) | −146.625 | − | 146.625i | −0.801231 | − | 0.801231i | ||||
\(184\) | 54.0388i | 0.293689i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −79.0740 | −0.425129 | ||||||||
\(187\) | −96.6165 | + | 96.6165i | −0.516666 | + | 0.516666i | ||||
\(188\) | −104.138 | − | 104.138i | −0.553926 | − | 0.553926i | ||||
\(189\) | − | 13.7477i | − | 0.0727393i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −134.669 | −0.705072 | −0.352536 | − | 0.935798i | \(-0.614681\pi\) | ||||
−0.352536 | + | 0.935798i | \(0.614681\pi\) | |||||||
\(192\) | 9.79796 | − | 9.79796i | 0.0510310 | − | 0.0510310i | ||||
\(193\) | −194.945 | − | 194.945i | −1.01008 | − | 1.01008i | −0.999949 | − | 0.0101307i | \(-0.996775\pi\) |
−0.0101307 | − | 0.999949i | \(-0.503225\pi\) | |||||||
\(194\) | − | 144.309i | − | 0.743861i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | −69.6888 | + | 69.6888i | −0.353750 | + | 0.353750i | −0.861503 | − | 0.507753i | \(-0.830476\pi\) |
0.507753 | + | 0.861503i | \(0.330476\pi\) | |||||||
\(198\) | 12.5682 | + | 12.5682i | 0.0634756 | + | 0.0634756i | ||||
\(199\) | 346.988i | 1.74366i | 0.489809 | + | 0.871830i | \(0.337066\pi\) | ||||
−0.489809 | + | 0.871830i | \(0.662934\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 121.186 | 0.602915 | ||||||||
\(202\) | 27.1945 | − | 27.1945i | 0.134626 | − | 0.134626i | ||||
\(203\) | 43.5798 | + | 43.5798i | 0.214679 | + | 0.214679i | ||||
\(204\) | − | 112.981i | − | 0.553830i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −84.3298 | −0.409368 | ||||||||
\(207\) | 40.5291 | − | 40.5291i | 0.195793 | − | 0.195793i | ||||
\(208\) | −51.9782 | − | 51.9782i | −0.249895 | − | 0.249895i | ||||
\(209\) | 136.881i | 0.654931i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −59.3269 | −0.281170 | −0.140585 | − | 0.990069i | \(-0.544898\pi\) | ||||
−0.140585 | + | 0.990069i | \(0.544898\pi\) | |||||||
\(212\) | 52.7576 | − | 52.7576i | 0.248856 | − | 0.248856i | ||||
\(213\) | −115.199 | − | 115.199i | −0.540839 | − | 0.540839i | ||||
\(214\) | − | 156.088i | − | 0.729385i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −14.6969 | −0.0680414 | ||||||||
\(217\) | 60.3938 | − | 60.3938i | 0.278312 | − | 0.278312i | ||||
\(218\) | 115.318 | + | 115.318i | 0.528981 | + | 0.528981i | ||||
\(219\) | 36.9311i | 0.168635i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −599.366 | −2.71206 | ||||||||
\(222\) | 51.4874 | − | 51.4874i | 0.231925 | − | 0.231925i | ||||
\(223\) | 12.0682 | + | 12.0682i | 0.0541173 | + | 0.0541173i | 0.733648 | − | 0.679530i | \(-0.237816\pi\) |
−0.679530 | + | 0.733648i | \(0.737816\pi\) | |||||||
\(224\) | 14.9666i | 0.0668153i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −140.538 | −0.621849 | ||||||||
\(227\) | −239.151 | + | 239.151i | −1.05353 | + | 1.05353i | −0.0550464 | + | 0.998484i | \(0.517531\pi\) |
−0.998484 | + | 0.0550464i | \(0.982469\pi\) | |||||||
\(228\) | −80.0326 | − | 80.0326i | −0.351020 | − | 0.351020i | ||||
\(229\) | − | 85.4596i | − | 0.373186i | −0.982437 | − | 0.186593i | \(-0.940255\pi\) | ||
0.982437 | − | 0.186593i | \(-0.0597446\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −19.1982 | −0.0831090 | ||||||||
\(232\) | 46.5888 | − | 46.5888i | 0.200814 | − | 0.200814i | ||||
\(233\) | 72.0103 | + | 72.0103i | 0.309057 | + | 0.309057i | 0.844544 | − | 0.535487i | \(-0.179872\pi\) |
−0.535487 | + | 0.844544i | \(0.679872\pi\) | |||||||
\(234\) | 77.9673i | 0.333194i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 206.213 | 0.873783 | ||||||||
\(237\) | 138.261 | − | 138.261i | 0.583382 | − | 0.583382i | ||||
\(238\) | 86.2909 | + | 86.2909i | 0.362567 | + | 0.362567i | ||||
\(239\) | 260.366i | 1.08940i | 0.838632 | + | 0.544699i | \(0.183356\pi\) | ||||
−0.838632 | + | 0.544699i | \(0.816644\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 69.8087 | 0.289663 | 0.144831 | − | 0.989456i | \(-0.453736\pi\) | ||||
0.144831 | + | 0.989456i | \(0.453736\pi\) | |||||||
\(242\) | −103.449 | + | 103.449i | −0.427475 | + | 0.427475i | ||||
\(243\) | 11.0227 | + | 11.0227i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | − | 239.438i | − | 0.981303i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 127.320 | 0.517561 | ||||||||
\(247\) | −424.573 | + | 424.573i | −1.71892 | + | 1.71892i | ||||
\(248\) | −64.5637 | − | 64.5637i | −0.260337 | − | 0.260337i | ||||
\(249\) | − | 33.4763i | − | 0.134443i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −39.4536 | −0.157186 | −0.0785928 | − | 0.996907i | \(-0.525043\pi\) | ||||
−0.0785928 | + | 0.996907i | \(0.525043\pi\) | |||||||
\(252\) | 11.2250 | − | 11.2250i | 0.0445435 | − | 0.0445435i | ||||
\(253\) | −56.5974 | − | 56.5974i | −0.223705 | − | 0.223705i | ||||
\(254\) | − | 30.8126i | − | 0.121309i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −43.4383 | + | 43.4383i | −0.169021 | + | 0.169021i | −0.786549 | − | 0.617528i | \(-0.788134\pi\) |
0.617528 | + | 0.786549i | \(0.288134\pi\) | |||||||
\(258\) | 60.6557 | + | 60.6557i | 0.235100 | + | 0.235100i | ||||
\(259\) | 78.6483i | 0.303661i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −69.8831 | −0.267752 | ||||||||
\(262\) | −237.306 | + | 237.306i | −0.905750 | + | 0.905750i | ||||
\(263\) | −186.173 | − | 186.173i | −0.707881 | − | 0.707881i | 0.258208 | − | 0.966089i | \(-0.416868\pi\) |
−0.966089 | + | 0.258208i | \(0.916868\pi\) | |||||||
\(264\) | 20.5237i | 0.0777414i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 122.252 | 0.459593 | ||||||||
\(267\) | −43.6487 | + | 43.6487i | −0.163478 | + | 0.163478i | ||||
\(268\) | 98.9479 | + | 98.9479i | 0.369209 | + | 0.369209i | ||||
\(269\) | − | 166.391i | − | 0.618555i | −0.950972 | − | 0.309278i | \(-0.899913\pi\) | ||
0.950972 | − | 0.309278i | \(-0.100087\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 335.279 | 1.23719 | 0.618597 | − | 0.785709i | \(-0.287702\pi\) | ||||
0.618597 | + | 0.785709i | \(0.287702\pi\) | |||||||
\(272\) | 92.2488 | − | 92.2488i | 0.339150 | − | 0.339150i | ||||
\(273\) | −59.5485 | − | 59.5485i | −0.218126 | − | 0.218126i | ||||
\(274\) | 96.8314i | 0.353399i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 66.1838 | 0.239796 | ||||||||
\(277\) | −233.563 | + | 233.563i | −0.843188 | + | 0.843188i | −0.989272 | − | 0.146084i | \(-0.953333\pi\) |
0.146084 | + | 0.989272i | \(0.453333\pi\) | |||||||
\(278\) | −106.547 | − | 106.547i | −0.383262 | − | 0.383262i | ||||
\(279\) | 96.8455i | 0.347116i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −333.559 | −1.18704 | −0.593522 | − | 0.804818i | \(-0.702263\pi\) | ||||
−0.593522 | + | 0.804818i | \(0.702263\pi\) | |||||||
\(282\) | −127.543 | + | 127.543i | −0.452279 | + | 0.452279i | ||||
\(283\) | 298.203 | + | 298.203i | 1.05372 | + | 1.05372i | 0.998473 | + | 0.0552481i | \(0.0175950\pi\) |
0.0552481 | + | 0.998473i | \(0.482405\pi\) | |||||||
\(284\) | − | 188.119i | − | 0.662390i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 108.878 | 0.380694 | ||||||||
\(287\) | −97.2423 | + | 97.2423i | −0.338823 | + | 0.338823i | ||||
\(288\) | −12.0000 | − | 12.0000i | −0.0416667 | − | 0.0416667i | ||||
\(289\) | − | 774.730i | − | 2.68073i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −176.742 | −0.607360 | ||||||||
\(292\) | −30.1541 | + | 30.1541i | −0.103268 | + | 0.103268i | ||||
\(293\) | 27.0786 | + | 27.0786i | 0.0924186 | + | 0.0924186i | 0.751805 | − | 0.659386i | \(-0.229184\pi\) |
−0.659386 | + | 0.751805i | \(0.729184\pi\) | |||||||
\(294\) | 17.1464i | 0.0583212i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 84.0786 | 0.284049 | ||||||||
\(297\) | 15.3928 | − | 15.3928i | 0.0518276 | − | 0.0518276i | ||||
\(298\) | 30.2575 | + | 30.2575i | 0.101535 | + | 0.101535i | ||||
\(299\) | − | 351.105i | − | 1.17426i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −92.6532 | −0.307818 | ||||||||
\(302\) | 181.315 | − | 181.315i | 0.600379 | − | 0.600379i | ||||
\(303\) | −33.3064 | − | 33.3064i | −0.109922 | − | 0.109922i | ||||
\(304\) | − | 130.693i | − | 0.429910i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −138.373 | −0.452200 | ||||||||
\(307\) | 51.6680 | − | 51.6680i | 0.168300 | − | 0.168300i | −0.617932 | − | 0.786232i | \(-0.712029\pi\) |
0.786232 | + | 0.617932i | \(0.212029\pi\) | |||||||
\(308\) | −15.6753 | − | 15.6753i | −0.0508937 | − | 0.0508937i | ||||
\(309\) | 103.282i | 0.334247i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 190.936 | 0.613942 | 0.306971 | − | 0.951719i | \(-0.400685\pi\) | ||||
0.306971 | + | 0.951719i | \(0.400685\pi\) | |||||||
\(312\) | −63.6600 | + | 63.6600i | −0.204039 | + | 0.204039i | ||||
\(313\) | 417.438 | + | 417.438i | 1.33367 | + | 1.33367i | 0.902064 | + | 0.431602i | \(0.142052\pi\) |
0.431602 | + | 0.902064i | \(0.357948\pi\) | |||||||
\(314\) | 17.0604i | 0.0543324i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 225.780 | 0.714494 | ||||||||
\(317\) | 91.5155 | − | 91.5155i | 0.288692 | − | 0.288692i | −0.547871 | − | 0.836563i | \(-0.684561\pi\) |
0.836563 | + | 0.547871i | \(0.184561\pi\) | |||||||
\(318\) | −64.6145 | − | 64.6145i | −0.203190 | − | 0.203190i | ||||
\(319\) | 97.5892i | 0.305922i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −191.169 | −0.595541 | ||||||||
\(322\) | −50.5487 | + | 50.5487i | −0.156984 | + | 0.156984i | ||||
\(323\) | −753.515 | − | 753.515i | −2.33286 | − | 2.33286i | ||||
\(324\) | 18.0000i | 0.0555556i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 120.620 | 0.370000 | ||||||||
\(327\) | 141.235 | − | 141.235i | 0.431911 | − | 0.431911i | ||||
\(328\) | 103.956 | + | 103.956i | 0.316940 | + | 0.316940i | ||||
\(329\) | − | 194.825i | − | 0.592172i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 172.125 | 0.520016 | 0.260008 | − | 0.965606i | \(-0.416275\pi\) | ||||
0.260008 | + | 0.965606i | \(0.416275\pi\) | |||||||
\(332\) | 27.3333 | − | 27.3333i | 0.0823291 | − | 0.0823291i | ||||
\(333\) | −63.0589 | − | 63.0589i | −0.189366 | − | 0.189366i | ||||
\(334\) | − | 262.251i | − | 0.785181i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 18.3303 | 0.0545545 | ||||||||
\(337\) | −283.042 | + | 283.042i | −0.839888 | + | 0.839888i | −0.988844 | − | 0.148956i | \(-0.952409\pi\) |
0.148956 | + | 0.988844i | \(0.452409\pi\) | |||||||
\(338\) | 168.717 | + | 168.717i | 0.499162 | + | 0.499162i | ||||
\(339\) | 172.123i | 0.507738i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 135.241 | 0.396601 | ||||||||
\(342\) | −98.0195 | + | 98.0195i | −0.286607 | + | 0.286607i | ||||
\(343\) | −13.0958 | − | 13.0958i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | 99.0504i | 0.287937i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −156.122 | −0.451219 | ||||||||
\(347\) | −379.546 | + | 379.546i | −1.09379 | + | 1.09379i | −0.0986739 | + | 0.995120i | \(0.531460\pi\) |
−0.995120 | + | 0.0986739i | \(0.968540\pi\) | |||||||
\(348\) | −57.0593 | − | 57.0593i | −0.163964 | − | 0.163964i | ||||
\(349\) | 112.412i | 0.322097i | 0.986947 | + | 0.161048i | \(0.0514875\pi\) | ||||
−0.986947 | + | 0.161048i | \(0.948513\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 95.4901 | 0.272051 | ||||||||
\(352\) | −16.7576 | + | 16.7576i | −0.0476067 | + | 0.0476067i | ||||
\(353\) | −125.437 | − | 125.437i | −0.355346 | − | 0.355346i | 0.506748 | − | 0.862094i | \(-0.330847\pi\) |
−0.862094 | + | 0.506748i | \(0.830847\pi\) | |||||||
\(354\) | − | 252.558i | − | 0.713441i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −71.2780 | −0.200219 | ||||||||
\(357\) | 105.684 | − | 105.684i | 0.296034 | − | 0.296034i | ||||
\(358\) | −116.492 | − | 116.492i | −0.325398 | − | 0.325398i | ||||
\(359\) | − | 427.225i | − | 1.19004i | −0.803710 | − | 0.595021i | \(-0.797144\pi\) | ||
0.803710 | − | 0.595021i | \(-0.202856\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −706.535 | −1.95716 | ||||||||
\(362\) | 256.478 | − | 256.478i | 0.708503 | − | 0.708503i | ||||
\(363\) | 126.699 | + | 126.699i | 0.349032 | + | 0.349032i | ||||
\(364\) | − | 97.2423i | − | 0.267149i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −293.250 | −0.801231 | ||||||||
\(367\) | −311.079 | + | 311.079i | −0.847627 | + | 0.847627i | −0.989837 | − | 0.142210i | \(-0.954579\pi\) |
0.142210 | + | 0.989837i | \(0.454579\pi\) | |||||||
\(368\) | 54.0388 | + | 54.0388i | 0.146845 | + | 0.146845i | ||||
\(369\) | − | 155.935i | − | 0.422587i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 98.7003 | 0.266039 | ||||||||
\(372\) | −79.0740 | + | 79.0740i | −0.212565 | + | 0.212565i | ||||
\(373\) | −176.246 | − | 176.246i | −0.472508 | − | 0.472508i | 0.430217 | − | 0.902725i | \(-0.358437\pi\) |
−0.902725 | + | 0.430217i | \(0.858437\pi\) | |||||||
\(374\) | 193.233i | 0.516666i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −208.276 | −0.553926 | ||||||||
\(377\) | −302.700 | + | 302.700i | −0.802918 | + | 0.802918i | ||||
\(378\) | −13.7477 | − | 13.7477i | −0.0363696 | − | 0.0363696i | ||||
\(379\) | 486.127i | 1.28266i | 0.767266 | + | 0.641329i | \(0.221617\pi\) | ||||
−0.767266 | + | 0.641329i | \(0.778383\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −37.7376 | −0.0990488 | ||||||||
\(382\) | −134.669 | + | 134.669i | −0.352536 | + | 0.352536i | ||||
\(383\) | 78.0432 | + | 78.0432i | 0.203768 | + | 0.203768i | 0.801612 | − | 0.597844i | \(-0.203976\pi\) |
−0.597844 | + | 0.801612i | \(0.703976\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −389.891 | −1.01008 | ||||||||
\(387\) | 74.2878 | − | 74.2878i | 0.191958 | − | 0.191958i | ||||
\(388\) | −144.309 | − | 144.309i | −0.371930 | − | 0.371930i | ||||
\(389\) | − | 283.465i | − | 0.728702i | −0.931262 | − | 0.364351i | \(-0.881291\pi\) | ||
0.931262 | − | 0.364351i | \(-0.118709\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 623.127 | 1.59368 | ||||||||
\(392\) | −14.0000 | + | 14.0000i | −0.0357143 | + | 0.0357143i | ||||
\(393\) | 290.640 | + | 290.640i | 0.739542 | + | 0.739542i | ||||
\(394\) | 139.378i | 0.353750i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 25.1363 | 0.0634756 | ||||||||
\(397\) | −242.573 | + | 242.573i | −0.611015 | + | 0.611015i | −0.943210 | − | 0.332196i | \(-0.892211\pi\) |
0.332196 | + | 0.943210i | \(0.392211\pi\) | |||||||
\(398\) | 346.988 | + | 346.988i | 0.871830 | + | 0.871830i | ||||
\(399\) | − | 149.727i | − | 0.375256i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 263.635 | 0.657445 | 0.328723 | − | 0.944427i | \(-0.393382\pi\) | ||||
0.328723 | + | 0.944427i | \(0.393382\pi\) | |||||||
\(402\) | 121.186 | − | 121.186i | 0.301458 | − | 0.301458i | ||||
\(403\) | 419.488 | + | 419.488i | 1.04091 | + | 1.04091i | ||||
\(404\) | − | 54.3890i | − | 0.134626i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 87.1596 | 0.214679 | ||||||||
\(407\) | −88.0594 | + | 88.0594i | −0.216362 | + | 0.216362i | ||||
\(408\) | −112.981 | − | 112.981i | −0.276915 | − | 0.276915i | ||||
\(409\) | 202.287i | 0.494590i | 0.968940 | + | 0.247295i | \(0.0795417\pi\) | ||||
−0.968940 | + | 0.247295i | \(0.920458\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 118.594 | 0.288549 | ||||||||
\(412\) | −84.3298 | + | 84.3298i | −0.204684 | + | 0.204684i | ||||
\(413\) | 192.894 | + | 192.894i | 0.467057 | + | 0.467057i | ||||
\(414\) | − | 81.0582i | − | 0.195793i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −103.956 | −0.249895 | ||||||||
\(417\) | −130.493 | + | 130.493i | −0.312932 | + | 0.312932i | ||||
\(418\) | 136.881 | + | 136.881i | 0.327465 | + | 0.327465i | ||||
\(419\) | − | 498.267i | − | 1.18918i | −0.804029 | − | 0.594591i | \(-0.797314\pi\) | ||
0.804029 | − | 0.594591i | \(-0.202686\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 662.760 | 1.57425 | 0.787126 | − | 0.616793i | \(-0.211568\pi\) | ||||
0.787126 | + | 0.616793i | \(0.211568\pi\) | |||||||
\(422\) | −59.3269 | + | 59.3269i | −0.140585 | + | 0.140585i | ||||
\(423\) | 156.207 | + | 156.207i | 0.369284 | + | 0.369284i | ||||
\(424\) | − | 105.515i | − | 0.248856i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −230.398 | −0.540839 | ||||||||
\(427\) | 223.974 | − | 223.974i | 0.524528 | − | 0.524528i | ||||
\(428\) | −156.088 | − | 156.088i | −0.364693 | − | 0.364693i | ||||
\(429\) | − | 133.348i | − | 0.310835i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 73.7144 | 0.171031 | 0.0855155 | − | 0.996337i | \(-0.472746\pi\) | ||||
0.0855155 | + | 0.996337i | \(0.472746\pi\) | |||||||
\(432\) | −14.6969 | + | 14.6969i | −0.0340207 | + | 0.0340207i | ||||
\(433\) | −254.779 | − | 254.779i | −0.588405 | − | 0.588405i | 0.348794 | − | 0.937199i | \(-0.386591\pi\) |
−0.937199 | + | 0.348794i | \(0.886591\pi\) | |||||||
\(434\) | − | 120.788i | − | 0.278312i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 230.636 | 0.528981 | ||||||||
\(437\) | 441.405 | − | 441.405i | 1.01008 | − | 1.01008i | ||||
\(438\) | 36.9311 | + | 36.9311i | 0.0843176 | + | 0.0843176i | ||||
\(439\) | − | 596.437i | − | 1.35863i | −0.733848 | − | 0.679314i | \(-0.762278\pi\) | ||
0.733848 | − | 0.679314i | \(-0.237722\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 21.0000 | 0.0476190 | ||||||||
\(442\) | −599.366 | + | 599.366i | −1.35603 | + | 1.35603i | ||||
\(443\) | 169.240 | + | 169.240i | 0.382031 | + | 0.382031i | 0.871833 | − | 0.489802i | \(-0.162931\pi\) |
−0.489802 | + | 0.871833i | \(0.662931\pi\) | |||||||
\(444\) | − | 102.975i | − | 0.231925i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 24.1363 | 0.0541173 | ||||||||
\(447\) | 37.0577 | − | 37.0577i | 0.0829032 | − | 0.0829032i | ||||
\(448\) | 14.9666 | + | 14.9666i | 0.0334077 | + | 0.0334077i | ||||
\(449\) | − | 286.986i | − | 0.639167i | −0.947558 | − | 0.319583i | \(-0.896457\pi\) | ||
0.947558 | − | 0.319583i | \(-0.103543\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −217.757 | −0.482831 | ||||||||
\(452\) | −140.538 | + | 140.538i | −0.310925 | + | 0.310925i | ||||
\(453\) | −222.064 | − | 222.064i | −0.490208 | − | 0.490208i | ||||
\(454\) | 478.303i | 1.05353i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −160.065 | −0.351020 | ||||||||
\(457\) | 546.344 | − | 546.344i | 1.19550 | − | 1.19550i | 0.220001 | − | 0.975500i | \(-0.429394\pi\) |
0.975500 | − | 0.220001i | \(-0.0706060\pi\) | |||||||
\(458\) | −85.4596 | − | 85.4596i | −0.186593 | − | 0.186593i | ||||
\(459\) | 169.472i | 0.369220i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −208.632 | −0.452565 | −0.226282 | − | 0.974062i | \(-0.572657\pi\) | ||||
−0.226282 | + | 0.974062i | \(0.572657\pi\) | |||||||
\(462\) | −19.1982 | + | 19.1982i | −0.0415545 | + | 0.0415545i | ||||
\(463\) | 140.594 | + | 140.594i | 0.303659 | + | 0.303659i | 0.842443 | − | 0.538785i | \(-0.181116\pi\) |
−0.538785 | + | 0.842443i | \(0.681116\pi\) | |||||||
\(464\) | − | 93.1775i | − | 0.200814i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 144.021 | 0.309057 | ||||||||
\(467\) | −0.0661206 | + | 0.0661206i | −0.000141586 | + | 0.000141586i | −0.707178 | − | 0.707036i | \(-0.750032\pi\) |
0.707036 | + | 0.707178i | \(0.250032\pi\) | |||||||
\(468\) | 77.9673 | + | 77.9673i | 0.166597 | + | 0.166597i | ||||
\(469\) | 185.115i | 0.394701i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 20.8946 | 0.0443622 | ||||||||
\(472\) | 206.213 | − | 206.213i | 0.436892 | − | 0.436892i | ||||
\(473\) | −103.740 | − | 103.740i | −0.219324 | − | 0.219324i | ||||
\(474\) | − | 276.523i | − | 0.583382i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 172.582 | 0.362567 | ||||||||
\(477\) | −79.1363 | + | 79.1363i | −0.165904 | + | 0.165904i | ||||
\(478\) | 260.366 | + | 260.366i | 0.544699 | + | 0.544699i | ||||
\(479\) | 539.039i | 1.12534i | 0.826681 | + | 0.562672i | \(0.190226\pi\) | ||||
−0.826681 | + | 0.562672i | \(0.809774\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −546.282 | −1.13572 | ||||||||
\(482\) | 69.8087 | − | 69.8087i | 0.144831 | − | 0.144831i | ||||
\(483\) | 61.9093 | + | 61.9093i | 0.128177 | + | 0.128177i | ||||
\(484\) | 206.898i | 0.427475i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 22.0454 | 0.0453609 | ||||||||
\(487\) | 61.8493 | − | 61.8493i | 0.127001 | − | 0.127001i | −0.640749 | − | 0.767750i | \(-0.721376\pi\) |
0.767750 | + | 0.640749i | \(0.221376\pi\) | |||||||
\(488\) | −239.438 | − | 239.438i | −0.490651 | − | 0.490651i | ||||
\(489\) | − | 147.729i | − | 0.302104i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 191.070 | 0.389145 | 0.194573 | − | 0.980888i | \(-0.437668\pi\) | ||||
0.194573 | + | 0.980888i | \(0.437668\pi\) | |||||||
\(492\) | 127.320 | − | 127.320i | 0.258781 | − | 0.258781i | ||||
\(493\) | −537.220 | − | 537.220i | −1.08970 | − | 1.08970i | ||||
\(494\) | 849.146i | 1.71892i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −129.127 | −0.260337 | ||||||||
\(497\) | 175.969 | − | 175.969i | 0.354063 | − | 0.354063i | ||||
\(498\) | −33.4763 | − | 33.4763i | −0.0672214 | − | 0.0672214i | ||||
\(499\) | 190.849i | 0.382463i | 0.981545 | + | 0.191232i | \(0.0612481\pi\) | ||||
−0.981545 | + | 0.191232i | \(0.938752\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −321.190 | −0.641098 | ||||||||
\(502\) | −39.4536 | + | 39.4536i | −0.0785928 | + | 0.0785928i | ||||
\(503\) | 527.972 | + | 527.972i | 1.04965 | + | 1.04965i | 0.998701 | + | 0.0509448i | \(0.0162233\pi\) |
0.0509448 | + | 0.998701i | \(0.483777\pi\) | |||||||
\(504\) | − | 22.4499i | − | 0.0445435i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −113.195 | −0.223705 | ||||||||
\(507\) | 206.635 | − | 206.635i | 0.407564 | − | 0.407564i | ||||
\(508\) | −30.8126 | − | 30.8126i | −0.0606547 | − | 0.0606547i | ||||
\(509\) | − | 861.064i | − | 1.69168i | −0.533438 | − | 0.845839i | \(-0.679100\pi\) | ||
0.533438 | − | 0.845839i | \(-0.320900\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −56.4132 | −0.110398 | ||||||||
\(512\) | 16.0000 | − | 16.0000i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 120.049 | + | 120.049i | 0.234013 | + | 0.234013i | ||||
\(514\) | 86.8766i | 0.169021i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 121.311 | 0.235100 | ||||||||
\(517\) | 218.137 | − | 218.137i | 0.421929 | − | 0.421929i | ||||
\(518\) | 78.6483 | + | 78.6483i | 0.151831 | + | 0.151831i | ||||
\(519\) | 191.209i | 0.368419i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −550.681 | −1.05697 | −0.528485 | − | 0.848943i | \(-0.677240\pi\) | ||||
−0.528485 | + | 0.848943i | \(0.677240\pi\) | |||||||
\(522\) | −69.8831 | + | 69.8831i | −0.133876 | + | 0.133876i | ||||
\(523\) | 493.771 | + | 493.771i | 0.944112 | + | 0.944112i | 0.998519 | − | 0.0544065i | \(-0.0173267\pi\) |
−0.0544065 | + | 0.998519i | \(0.517327\pi\) | |||||||
\(524\) | 474.613i | 0.905750i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −372.345 | −0.707881 | ||||||||
\(527\) | −744.490 | + | 744.490i | −1.41269 | + | 1.41269i | ||||
\(528\) | 20.5237 | + | 20.5237i | 0.0388707 | + | 0.0388707i | ||||
\(529\) | − | 163.976i | − | 0.309973i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −309.319 | −0.582522 | ||||||||
\(532\) | 122.252 | − | 122.252i | 0.229797 | − | 0.229797i | ||||
\(533\) | −675.434 | − | 675.434i | −1.26723 | − | 1.26723i | ||||
\(534\) | 87.2974i | 0.163478i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 197.896 | 0.369209 | ||||||||
\(537\) | −142.673 | + | 142.673i | −0.265686 | + | 0.265686i | ||||
\(538\) | −166.391 | − | 166.391i | −0.309278 | − | 0.309278i | ||||
\(539\) | − | 29.3257i | − | 0.0544076i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 278.337 | 0.514486 | 0.257243 | − | 0.966347i | \(-0.417186\pi\) | ||||
0.257243 | + | 0.966347i | \(0.417186\pi\) | |||||||
\(542\) | 335.279 | − | 335.279i | 0.618597 | − | 0.618597i | ||||
\(543\) | −314.120 | − | 314.120i | −0.578490 | − | 0.578490i | ||||
\(544\) | − | 184.498i | − | 0.339150i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −119.097 | −0.218126 | ||||||||
\(547\) | −111.170 | + | 111.170i | −0.203236 | + | 0.203236i | −0.801385 | − | 0.598149i | \(-0.795903\pi\) |
0.598149 | + | 0.801385i | \(0.295903\pi\) | |||||||
\(548\) | 96.8314 | + | 96.8314i | 0.176700 | + | 0.176700i | ||||
\(549\) | 359.157i | 0.654202i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −761.101 | −1.38131 | ||||||||
\(552\) | 66.1838 | − | 66.1838i | 0.119898 | − | 0.119898i | ||||
\(553\) | 211.198 | + | 211.198i | 0.381913 | + | 0.381913i | ||||
\(554\) | 467.126i | 0.843188i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −213.093 | −0.383262 | ||||||||
\(557\) | 159.846 | − | 159.846i | 0.286977 | − | 0.286977i | −0.548907 | − | 0.835884i | \(-0.684956\pi\) |
0.835884 | + | 0.548907i | \(0.184956\pi\) | |||||||
\(558\) | 96.8455 | + | 96.8455i | 0.173558 | + | 0.173558i | ||||
\(559\) | − | 643.558i | − | 1.15127i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 236.661 | 0.421856 | ||||||||
\(562\) | −333.559 | + | 333.559i | −0.593522 | + | 0.593522i | ||||
\(563\) | −39.8174 | − | 39.8174i | −0.0707237 | − | 0.0707237i | 0.670860 | − | 0.741584i | \(-0.265925\pi\) |
−0.741584 | + | 0.670860i | \(0.765925\pi\) | |||||||
\(564\) | 255.085i | 0.452279i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 596.406 | 1.05372 | ||||||||
\(567\) | −16.8375 | + | 16.8375i | −0.0296957 | + | 0.0296957i | ||||
\(568\) | −188.119 | − | 188.119i | −0.331195 | − | 0.331195i | ||||
\(569\) | 166.511i | 0.292638i | 0.989237 | + | 0.146319i | \(0.0467426\pi\) | ||||
−0.989237 | + | 0.146319i | \(0.953257\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 602.196 | 1.05463 | 0.527317 | − | 0.849668i | \(-0.323198\pi\) | ||||
0.527317 | + | 0.849668i | \(0.323198\pi\) | |||||||
\(572\) | 108.878 | − | 108.878i | 0.190347 | − | 0.190347i | ||||
\(573\) | 164.935 | + | 164.935i | 0.287844 | + | 0.287844i | ||||
\(574\) | 194.485i | 0.338823i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | −644.862 | + | 644.862i | −1.11761 | + | 1.11761i | −0.125521 | + | 0.992091i | \(0.540060\pi\) |
−0.992091 | + | 0.125521i | \(0.959940\pi\) | |||||||
\(578\) | −774.730 | − | 774.730i | −1.34036 | − | 1.34036i | ||||
\(579\) | 477.517i | 0.824726i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 51.1359 | 0.0880135 | ||||||||
\(582\) | −176.742 | + | 176.742i | −0.303680 | + | 0.303680i | ||||
\(583\) | 110.511 | + | 110.511i | 0.189556 | + | 0.189556i | ||||
\(584\) | 60.3083i | 0.103268i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 54.1573 | 0.0924186 | ||||||||
\(587\) | 666.493 | − | 666.493i | 1.13542 | − | 1.13542i | 0.146162 | − | 0.989261i | \(-0.453308\pi\) |
0.989261 | − | 0.146162i | \(-0.0466920\pi\) | |||||||
\(588\) | 17.1464 | + | 17.1464i | 0.0291606 | + | 0.0291606i | ||||
\(589\) | 1054.75i | 1.79075i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 170.702 | 0.288836 | ||||||||
\(592\) | 84.0786 | − | 84.0786i | 0.142025 | − | 0.142025i | ||||
\(593\) | 526.020 | + | 526.020i | 0.887049 | + | 0.887049i | 0.994239 | − | 0.107190i | \(-0.0341853\pi\) |
−0.107190 | + | 0.994239i | \(0.534185\pi\) | |||||||
\(594\) | − | 30.7856i | − | 0.0518276i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 60.5150 | 0.101535 | ||||||||
\(597\) | 424.972 | − | 424.972i | 0.711846 | − | 0.711846i | ||||
\(598\) | −351.105 | − | 351.105i | −0.587132 | − | 0.587132i | ||||
\(599\) | − | 637.374i | − | 1.06406i | −0.846724 | − | 0.532032i | \(-0.821429\pi\) | ||
0.846724 | − | 0.532032i | \(-0.178571\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 203.010 | 0.337786 | 0.168893 | − | 0.985634i | \(-0.445981\pi\) | ||||
0.168893 | + | 0.985634i | \(0.445981\pi\) | |||||||
\(602\) | −92.6532 | + | 92.6532i | −0.153909 | + | 0.153909i | ||||
\(603\) | −148.422 | − | 148.422i | −0.246139 | − | 0.246139i | ||||
\(604\) | − | 362.629i | − | 0.600379i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −66.6127 | −0.109922 | ||||||||
\(607\) | 347.828 | − | 347.828i | 0.573028 | − | 0.573028i | −0.359945 | − | 0.932973i | \(-0.617205\pi\) |
0.932973 | + | 0.359945i | \(0.117205\pi\) | |||||||
\(608\) | −130.693 | − | 130.693i | −0.214955 | − | 0.214955i | ||||
\(609\) | − | 106.748i | − | 0.175285i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1353.23 | 2.21478 | ||||||||
\(612\) | −138.373 | + | 138.373i | −0.226100 | + | 0.226100i | ||||
\(613\) | −216.062 | − | 216.062i | −0.352467 | − | 0.352467i | 0.508560 | − | 0.861027i | \(-0.330178\pi\) |
−0.861027 | + | 0.508560i | \(0.830178\pi\) | |||||||
\(614\) | − | 103.336i | − | 0.168300i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −31.3505 | −0.0508937 | ||||||||
\(617\) | 432.131 | − | 432.131i | 0.700375 | − | 0.700375i | −0.264116 | − | 0.964491i | \(-0.585080\pi\) |
0.964491 | + | 0.264116i | \(0.0850802\pi\) | |||||||
\(618\) | 103.282 | + | 103.282i | 0.167124 | + | 0.167124i | ||||
\(619\) | 134.611i | 0.217465i | 0.994071 | + | 0.108732i | \(0.0346792\pi\) | ||||
−0.994071 | + | 0.108732i | \(0.965321\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −99.2757 | −0.159864 | ||||||||
\(622\) | 190.936 | − | 190.936i | 0.306971 | − | 0.306971i | ||||
\(623\) | −66.6745 | − | 66.6745i | −0.107022 | − | 0.107022i | ||||
\(624\) | 127.320i | 0.204039i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 834.875 | 1.33367 | ||||||||
\(627\) | 167.644 | − | 167.644i | 0.267374 | − | 0.267374i | ||||
\(628\) | 17.0604 | + | 17.0604i | 0.0271662 | + | 0.0271662i | ||||
\(629\) | − | 969.518i | − | 1.54136i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −911.796 | −1.44500 | −0.722500 | − | 0.691370i | \(-0.757007\pi\) | ||||
−0.722500 | + | 0.691370i | \(0.757007\pi\) | |||||||
\(632\) | 225.780 | − | 225.780i | 0.357247 | − | 0.357247i | ||||
\(633\) | 72.6603 | + | 72.6603i | 0.114787 | + | 0.114787i | ||||
\(634\) | − | 183.031i | − | 0.288692i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −129.229 | −0.203190 | ||||||||
\(637\) | 90.9619 | − | 90.9619i | 0.142797 | − | 0.142797i | ||||
\(638\) | 97.5892 | + | 97.5892i | 0.152961 | + | 0.152961i | ||||
\(639\) | 282.178i | 0.441594i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 277.395 | 0.432754 | 0.216377 | − | 0.976310i | \(-0.430576\pi\) | ||||
0.216377 | + | 0.976310i | \(0.430576\pi\) | |||||||
\(642\) | −191.169 | + | 191.169i | −0.297770 | + | 0.297770i | ||||
\(643\) | 303.972 | + | 303.972i | 0.472741 | + | 0.472741i | 0.902800 | − | 0.430060i | \(-0.141508\pi\) |
−0.430060 | + | 0.902800i | \(0.641508\pi\) | |||||||
\(644\) | 101.097i | 0.156984i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1507.03 | −2.33286 | ||||||||
\(647\) | −88.7310 | + | 88.7310i | −0.137142 | + | 0.137142i | −0.772345 | − | 0.635203i | \(-0.780916\pi\) |
0.635203 | + | 0.772345i | \(0.280916\pi\) | |||||||
\(648\) | 18.0000 | + | 18.0000i | 0.0277778 | + | 0.0277778i | ||||
\(649\) | 431.953i | 0.665567i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −147.934 | −0.227241 | ||||||||
\(652\) | 120.620 | − | 120.620i | 0.185000 | − | 0.185000i | ||||
\(653\) | −370.166 | − | 370.166i | −0.566869 | − | 0.566869i | 0.364381 | − | 0.931250i | \(-0.381281\pi\) |
−0.931250 | + | 0.364381i | \(0.881281\pi\) | |||||||
\(654\) | − | 282.470i | − | 0.431911i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 207.913 | 0.316940 | ||||||||
\(657\) | 45.2312 | − | 45.2312i | 0.0688451 | − | 0.0688451i | ||||
\(658\) | −194.825 | − | 194.825i | −0.296086 | − | 0.296086i | ||||
\(659\) | 89.6092i | 0.135978i | 0.997686 | + | 0.0679888i | \(0.0216582\pi\) | ||||
−0.997686 | + | 0.0679888i | \(0.978342\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −179.575 | −0.271671 | −0.135836 | − | 0.990731i | \(-0.543372\pi\) | ||||
−0.135836 | + | 0.990731i | \(0.543372\pi\) | |||||||
\(662\) | 172.125 | − | 172.125i | 0.260008 | − | 0.260008i | ||||
\(663\) | 734.070 | + | 734.070i | 1.10720 | + | 1.10720i | ||||
\(664\) | − | 54.6665i | − | 0.0823291i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −126.118 | −0.189366 | ||||||||
\(667\) | 314.700 | − | 314.700i | 0.471814 | − | 0.471814i | ||||
\(668\) | −262.251 | − | 262.251i | −0.392591 | − | 0.392591i | ||||
\(669\) | − | 29.5608i | − | 0.0441866i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 501.549 | 0.747465 | ||||||||
\(672\) | 18.3303 | − | 18.3303i | 0.0272772 | − | 0.0272772i | ||||
\(673\) | −875.881 | − | 875.881i | −1.30146 | − | 1.30146i | −0.927409 | − | 0.374049i | \(-0.877969\pi\) |
−0.374049 | − | 0.927409i | \(-0.622031\pi\) | |||||||
\(674\) | 566.085i | 0.839888i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 337.434 | 0.499162 | ||||||||
\(677\) | 893.879 | − | 893.879i | 1.32035 | − | 1.32035i | 0.406865 | − | 0.913488i | \(-0.366622\pi\) |
0.913488 | − | 0.406865i | \(-0.133378\pi\) | |||||||
\(678\) | 172.123 | + | 172.123i | 0.253869 | + | 0.253869i | ||||
\(679\) | − | 269.977i | − | 0.397610i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 585.799 | 0.860204 | ||||||||
\(682\) | 135.241 | − | 135.241i | 0.198301 | − | 0.198301i | ||||
\(683\) | −25.2004 | − | 25.2004i | −0.0368966 | − | 0.0368966i | 0.688418 | − | 0.725314i | \(-0.258306\pi\) |
−0.725314 | + | 0.688418i | \(0.758306\pi\) | |||||||
\(684\) | 196.039i | 0.286607i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −26.1916 | −0.0381802 | ||||||||
\(687\) | −104.666 | + | 104.666i | −0.152353 | + | 0.152353i | ||||
\(688\) | 99.0504 | + | 99.0504i | 0.143969 | + | 0.143969i | ||||
\(689\) | 685.561i | 0.995008i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 301.682 | 0.436588 | 0.218294 | − | 0.975883i | \(-0.429951\pi\) | ||||
0.218294 | + | 0.975883i | \(0.429951\pi\) | |||||||
\(692\) | −156.122 | + | 156.122i | −0.225610 | + | 0.225610i | ||||
\(693\) | 23.5129 | + | 23.5129i | 0.0339291 | + | 0.0339291i | ||||
\(694\) | 759.093i | 1.09379i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −114.119 | −0.163964 | ||||||||
\(697\) | 1198.73 | − | 1198.73i | 1.71985 | − | 1.71985i | ||||
\(698\) | 112.412 | + | 112.412i | 0.161048 | + | 0.161048i | ||||
\(699\) | − | 176.389i | − | 0.252344i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1292.71 | −1.84409 | −0.922045 | − | 0.387084i | \(-0.873483\pi\) | ||||
−0.922045 | + | 0.387084i | \(0.873483\pi\) | |||||||
\(702\) | 95.4901 | − | 95.4901i | 0.136026 | − | 0.136026i | ||||
\(703\) | −686.778 | − | 686.778i | −0.976925 | − | 0.976925i | ||||
\(704\) | 33.5151i | 0.0476067i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −250.874 | −0.355346 | ||||||||
\(707\) | 50.8763 | − | 50.8763i | 0.0719608 | − | 0.0719608i | ||||
\(708\) | −252.558 | − | 252.558i | −0.356720 | − | 0.356720i | ||||
\(709\) | − | 137.796i | − | 0.194353i | −0.995267 | − | 0.0971764i | \(-0.969019\pi\) | ||
0.995267 | − | 0.0971764i | \(-0.0309811\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −338.670 | −0.476329 | ||||||||
\(712\) | −71.2780 | + | 71.2780i | −0.100110 | + | 0.100110i | ||||
\(713\) | −436.118 | − | 436.118i | −0.611666 | − | 0.611666i | ||||
\(714\) | − | 211.369i | − | 0.296034i | ||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −232.985 | −0.325398 | ||||||||
\(717\) | 318.882 | − | 318.882i | 0.444745 | − | 0.444745i | ||||
\(718\) | −427.225 | − | 427.225i | −0.595021 | − | 0.595021i | ||||
\(719\) | 848.625i | 1.18028i | 0.807299 | + | 0.590142i | \(0.200928\pi\) | ||||
−0.807299 | + | 0.590142i | \(0.799072\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −157.767 | −0.218816 | ||||||||
\(722\) | −706.535 | + | 706.535i | −0.978581 | + | 0.978581i | ||||
\(723\) | −85.4978 | − | 85.4978i | −0.118254 | − | 0.118254i | ||||
\(724\) | − | 512.956i | − | 0.708503i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 253.397 | 0.349032 | ||||||||
\(727\) | 140.883 | − | 140.883i | 0.193786 | − | 0.193786i | −0.603544 | − | 0.797330i | \(-0.706245\pi\) |
0.797330 | + | 0.603544i | \(0.206245\pi\) | |||||||
\(728\) | −97.2423 | − | 97.2423i | −0.133575 | − | 0.133575i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1142.16 | 1.56246 | ||||||||
\(732\) | −293.250 | + | 293.250i | −0.400615 | + | 0.400615i | ||||
\(733\) | 527.284 | + | 527.284i | 0.719351 | + | 0.719351i | 0.968472 | − | 0.249122i | \(-0.0801419\pi\) |
−0.249122 | + | 0.968472i | \(0.580142\pi\) | |||||||
\(734\) | 622.158i | 0.847627i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 108.078 | 0.146845 | ||||||||
\(737\) | −207.266 | + | 207.266i | −0.281229 | + | 0.281229i | ||||
\(738\) | −155.935 | − | 155.935i | −0.211294 | − | 0.211294i | ||||
\(739\) | 546.536i | 0.739562i | 0.929119 | + | 0.369781i | \(0.120567\pi\) | ||||
−0.929119 | + | 0.369781i | \(0.879433\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1039.99 | 1.40349 | ||||||||
\(742\) | 98.7003 | − | 98.7003i | 0.133019 | − | 0.133019i | ||||
\(743\) | 369.606 | + | 369.606i | 0.497451 | + | 0.497451i | 0.910644 | − | 0.413192i | \(-0.135586\pi\) |
−0.413192 | + | 0.910644i | \(0.635586\pi\) | |||||||
\(744\) | 158.148i | 0.212565i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −352.491 | −0.472508 | ||||||||
\(747\) | −40.9999 | + | 40.9999i | −0.0548861 | + | 0.0548861i | ||||
\(748\) | 193.233 | + | 193.233i | 0.258333 | + | 0.258333i | ||||
\(749\) | − | 292.015i | − | 0.389873i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 300.340 | 0.399920 | 0.199960 | − | 0.979804i | \(-0.435919\pi\) | ||||
0.199960 | + | 0.979804i | \(0.435919\pi\) | |||||||
\(752\) | −208.276 | + | 208.276i | −0.276963 | + | 0.276963i | ||||
\(753\) | 48.3206 | + | 48.3206i | 0.0641708 | + | 0.0641708i | ||||
\(754\) | 605.400i | 0.802918i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −27.4955 | −0.0363696 | ||||||||
\(757\) | 873.112 | − | 873.112i | 1.15338 | − | 1.15338i | 0.167515 | − | 0.985870i | \(-0.446426\pi\) |
0.985870 | − | 0.167515i | \(-0.0535743\pi\) | |||||||
\(758\) | 486.127 | + | 486.127i | 0.641329 | + | 0.641329i | ||||
\(759\) | 138.635i | 0.182654i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −928.459 | −1.22005 | −0.610026 | − | 0.792382i | \(-0.708841\pi\) | ||||
−0.610026 | + | 0.792382i | \(0.708841\pi\) | |||||||
\(762\) | −37.7376 | + | 37.7376i | −0.0495244 | + | 0.0495244i | ||||
\(763\) | 215.740 | + | 215.740i | 0.282752 | + | 0.282752i | ||||
\(764\) | 269.337i | 0.352536i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 156.086 | 0.203768 | ||||||||
\(767\) | −1339.82 | + | 1339.82i | −1.74683 | + | 1.74683i | ||||
\(768\) | −19.5959 | − | 19.5959i | −0.0255155 | − | 0.0255155i | ||||
\(769\) | 978.370i | 1.27226i | 0.771581 | + | 0.636131i | \(0.219466\pi\) | ||||
−0.771581 | + | 0.636131i | \(0.780534\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 106.402 | 0.138005 | ||||||||
\(772\) | −389.891 | + | 389.891i | −0.505040 | + | 0.505040i | ||||
\(773\) | 576.310 | + | 576.310i | 0.745550 | + | 0.745550i | 0.973640 | − | 0.228090i | \(-0.0732482\pi\) |
−0.228090 | + | 0.973640i | \(0.573248\pi\) | |||||||
\(774\) | − | 148.576i | − | 0.191958i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −288.618 | −0.371930 | ||||||||
\(777\) | 96.3241 | − | 96.3241i | 0.123969 | − | 0.123969i | ||||
\(778\) | −283.465 | − | 283.465i | −0.364351 | − | 0.364351i | ||||
\(779\) | − | 1698.29i | − | 2.18009i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 394.051 | 0.504547 | ||||||||
\(782\) | 623.127 | − | 623.127i | 0.796838 | − | 0.796838i | ||||
\(783\) | 85.5890 | + | 85.5890i | 0.109309 | + | 0.109309i | ||||
\(784\) | 28.0000i | 0.0357143i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 581.280 | 0.739542 | ||||||||
\(787\) | −107.845 | + | 107.845i | −0.137033 | + | 0.137033i | −0.772296 | − | 0.635263i | \(-0.780892\pi\) |
0.635263 | + | 0.772296i | \(0.280892\pi\) | |||||||
\(788\) | 139.378 | + | 139.378i | 0.176875 | + | 0.176875i | ||||
\(789\) | 456.028i | 0.577982i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −262.922 | −0.332392 | ||||||||
\(792\) | 25.1363 | − | 25.1363i | 0.0317378 | − | 0.0317378i | ||||
\(793\) | 1555.69 | + | 1555.69i | 1.96178 | + | 1.96178i | ||||
\(794\) | 485.146i | 0.611015i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 693.976 | 0.871830 | ||||||||
\(797\) | 1071.74 | − | 1071.74i | 1.34472 | − | 1.34472i | 0.453426 | − | 0.891294i | \(-0.350202\pi\) |
0.891294 | − | 0.453426i | \(-0.149798\pi\) | |||||||
\(798\) | −149.727 | − | 149.727i | −0.187628 | − | 0.187628i | ||||
\(799\) | 2401.65i | 3.00583i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 106.917 | 0.133479 | ||||||||
\(802\) | 263.635 | − | 263.635i | 0.328723 | − | 0.328723i | ||||
\(803\) | −63.1637 | − | 63.1637i | −0.0786596 | − | 0.0786596i | ||||
\(804\) | − | 242.372i | − | 0.301458i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 838.976 | 1.04091 | ||||||||
\(807\) | −203.787 | + | 203.787i | −0.252524 | + | 0.252524i | ||||
\(808\) | −54.3890 | − | 54.3890i | −0.0673132 | − | 0.0673132i | ||||
\(809\) | 1544.59i | 1.90926i | 0.297790 | + | 0.954631i | \(0.403750\pi\) | ||||
−0.297790 | + | 0.954631i | \(0.596250\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 664.090 | 0.818853 | 0.409426 | − | 0.912343i | \(-0.365729\pi\) | ||||
0.409426 | + | 0.912343i | \(0.365729\pi\) | |||||||
\(812\) | 87.1596 | − | 87.1596i | 0.107339 | − | 0.107339i | ||||
\(813\) | −410.632 | − | 410.632i | −0.505082 | − | 0.505082i | ||||
\(814\) | 176.119i | 0.216362i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −225.963 | −0.276915 | ||||||||
\(817\) | 809.072 | − | 809.072i | 0.990297 | − | 0.990297i | ||||
\(818\) | 202.287 | + | 202.287i | 0.247295 | + | 0.247295i | ||||
\(819\) | 145.863i | 0.178100i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 300.711 | 0.366274 | 0.183137 | − | 0.983087i | \(-0.441375\pi\) | ||||
0.183137 | + | 0.983087i | \(0.441375\pi\) | |||||||
\(822\) | 118.594 | − | 118.594i | 0.144275 | − | 0.144275i | ||||
\(823\) | −398.146 | − | 398.146i | −0.483774 | − | 0.483774i | 0.422560 | − | 0.906335i | \(-0.361131\pi\) |
−0.906335 | + | 0.422560i | \(0.861131\pi\) | |||||||
\(824\) | 168.660i | 0.204684i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 385.789 | 0.467057 | ||||||||
\(827\) | −699.014 | + | 699.014i | −0.845240 | + | 0.845240i | −0.989535 | − | 0.144294i | \(-0.953909\pi\) |
0.144294 | + | 0.989535i | \(0.453909\pi\) | |||||||
\(828\) | −81.0582 | − | 81.0582i | −0.0978964 | − | 0.0978964i | ||||
\(829\) | − | 1480.53i | − | 1.78593i | −0.450128 | − | 0.892964i | \(-0.648622\pi\) | ||
0.450128 | − | 0.892964i | \(-0.351378\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 572.110 | 0.688460 | ||||||||
\(832\) | −103.956 | + | 103.956i | −0.124948 | + | 0.124948i | ||||
\(833\) | 161.435 | + | 161.435i | 0.193800 | + | 0.193800i | ||||
\(834\) | 260.985i | 0.312932i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 273.761 | 0.327465 | ||||||||
\(837\) | 118.611 | − | 118.611i | 0.141710 | − | 0.141710i | ||||
\(838\) | −498.267 | − | 498.267i | −0.594591 | − | 0.594591i | ||||
\(839\) | − | 925.220i | − | 1.10277i | −0.834252 | − | 0.551383i | \(-0.814100\pi\) | ||
0.834252 | − | 0.551383i | \(-0.185900\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 298.372 | 0.354782 | ||||||||
\(842\) | 662.760 | − | 662.760i | 0.787126 | − | 0.787126i | ||||
\(843\) | 408.525 | + | 408.525i | 0.484609 | + | 0.484609i | ||||
\(844\) | 118.654i | 0.140585i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 312.414 | 0.369284 | ||||||||
\(847\) | −193.535 | + | 193.535i | −0.228495 | + | 0.228495i | ||||
\(848\) | −105.515 | − | 105.515i | −0.124428 | − | 0.124428i | ||||
\(849\) | − | 730.445i | − | 0.860359i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 567.938 | 0.667378 | ||||||||
\(852\) | −230.398 | + | 230.398i | −0.270420 | + | 0.270420i | ||||
\(853\) | 806.088 | + | 806.088i | 0.945004 | + | 0.945004i | 0.998565 | − | 0.0535608i | \(-0.0170571\pi\) |
−0.0535608 | + | 0.998565i | \(0.517057\pi\) | |||||||
\(854\) | − | 447.947i | − | 0.524528i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −312.177 | −0.364693 | ||||||||
\(857\) | −1114.29 | + | 1114.29i | −1.30023 | + | 1.30023i | −0.371990 | + | 0.928237i | \(0.621325\pi\) |
−0.928237 | + | 0.371990i | \(0.878675\pi\) | |||||||
\(858\) | −133.348 | − | 133.348i | −0.155418 | − | 0.155418i | ||||
\(859\) | − | 1548.40i | − | 1.80257i | −0.433231 | − | 0.901283i | \(-0.642627\pi\) | ||
0.433231 | − | 0.901283i | \(-0.357373\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 238.194 | 0.276648 | ||||||||
\(862\) | 73.7144 | − | 73.7144i | 0.0855155 | − | 0.0855155i | ||||
\(863\) | −276.765 | − | 276.765i | −0.320701 | − | 0.320701i | 0.528335 | − | 0.849036i | \(-0.322816\pi\) |
−0.849036 | + | 0.528335i | \(0.822816\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −509.559 | −0.588405 | ||||||||
\(867\) | −948.847 | + | 948.847i | −1.09440 | + | 1.09440i | ||||
\(868\) | −120.788 | − | 120.788i | −0.139156 | − | 0.139156i | ||||
\(869\) | 472.940i | 0.544235i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1285.78 | −1.47622 | ||||||||
\(872\) | 230.636 | − | 230.636i | 0.264490 | − | 0.264490i | ||||
\(873\) | 216.463 | + | 216.463i | 0.247954 | + | 0.247954i | ||||
\(874\) | − | 882.809i | − | 1.01008i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 73.8623 | 0.0843176 | ||||||||
\(877\) | −11.6377 | + | 11.6377i | −0.0132699 | + | 0.0132699i | −0.713711 | − | 0.700441i | \(-0.752987\pi\) |
0.700441 | + | 0.713711i | \(0.252987\pi\) | |||||||
\(878\) | −596.437 | − | 596.437i | −0.679314 | − | 0.679314i | ||||
\(879\) | − | 66.3289i | − | 0.0754594i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −745.486 | −0.846182 | −0.423091 | − | 0.906087i | \(-0.639055\pi\) | ||||
−0.423091 | + | 0.906087i | \(0.639055\pi\) | |||||||
\(882\) | 21.0000 | − | 21.0000i | 0.0238095 | − | 0.0238095i | ||||
\(883\) | 411.268 | + | 411.268i | 0.465762 | + | 0.465762i | 0.900538 | − | 0.434777i | \(-0.143173\pi\) |
−0.434777 | + | 0.900538i | \(0.643173\pi\) | |||||||
\(884\) | 1198.73i | 1.35603i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 338.480 | 0.382031 | ||||||||
\(887\) | 278.003 | − | 278.003i | 0.313419 | − | 0.313419i | −0.532813 | − | 0.846233i | \(-0.678865\pi\) |
0.846233 | + | 0.532813i | \(0.178865\pi\) | |||||||
\(888\) | −102.975 | − | 102.975i | −0.115963 | − | 0.115963i | ||||
\(889\) | − | 57.6451i | − | 0.0648426i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −37.7045 | −0.0423170 | ||||||||
\(892\) | 24.1363 | − | 24.1363i | 0.0270586 | − | 0.0270586i | ||||
\(893\) | 1701.26 | + | 1701.26i | 1.90511 | + | 1.90511i | ||||
\(894\) | − | 74.1154i | − | 0.0829032i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 29.9333 | 0.0334077 | ||||||||
\(897\) | −430.014 | + | 430.014i | −0.479392 | + | 0.479392i | ||||
\(898\) | −286.986 | − | 286.986i | −0.319583 | − | 0.319583i | ||||
\(899\) | 751.985i | 0.836469i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1216.71 | −1.35039 | ||||||||
\(902\) | −217.757 | + | 217.757i | −0.241416 | + | 0.241416i | ||||
\(903\) | 113.476 | + | 113.476i | 0.125666 | + | 0.125666i | ||||
\(904\) | 281.076i | 0.310925i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −444.128 | −0.490208 | ||||||||
\(907\) | 737.439 | − | 737.439i | 0.813053 | − | 0.813053i | −0.172038 | − | 0.985090i | \(-0.555035\pi\) |
0.985090 | + | 0.172038i | \(0.0550351\pi\) | |||||||
\(908\) | 478.303 | + | 478.303i | 0.526765 | + | 0.526765i | ||||
\(909\) | 81.5836i | 0.0897509i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1367.27 | 1.50084 | 0.750422 | − | 0.660959i | \(-0.229850\pi\) | ||||
0.750422 | + | 0.660959i | \(0.229850\pi\) | |||||||
\(912\) | −160.065 | + | 160.065i | −0.175510 | + | 0.175510i | ||||
\(913\) | 57.2548 | + | 57.2548i | 0.0627106 | + | 0.0627106i | ||||
\(914\) | − | 1092.69i | − | 1.19550i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −170.919 | −0.186593 | ||||||||
\(917\) | −443.960 | + | 443.960i | −0.484144 | + | 0.484144i | ||||
\(918\) | 169.472 | + | 169.472i | 0.184610 | + | 0.184610i | ||||
\(919\) | − | 1127.32i | − | 1.22668i | −0.789819 | − | 0.613340i | \(-0.789826\pi\) | ||
0.789819 | − | 0.613340i | \(-0.210174\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −126.560 | −0.137416 | ||||||||
\(922\) | −208.632 | + | 208.632i | −0.226282 | + | 0.226282i | ||||
\(923\) | 1222.26 | + | 1222.26i | 1.32423 | + | 1.32423i | ||||
\(924\) | 38.3964i | 0.0415545i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 281.188 | 0.303659 | ||||||||
\(927\) | 126.495 | − | 126.495i | 0.136456 | − | 0.136456i | ||||
\(928\) | −93.1775 | − | 93.1775i | −0.100407 | − | 0.100407i | ||||
\(929\) | 533.383i | 0.574147i | 0.957909 | + | 0.287074i | \(0.0926824\pi\) | ||||
−0.957909 | + | 0.287074i | \(0.907318\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 228.712 | 0.245663 | ||||||||
\(932\) | 144.021 | − | 144.021i | 0.154529 | − | 0.154529i | ||||
\(933\) | −233.848 | − | 233.848i | −0.250641 | − | 0.250641i | ||||
\(934\) | 0.132241i | 0.000141586i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 155.935 | 0.166597 | ||||||||
\(937\) | 1173.01 | − | 1173.01i | 1.25188 | − | 1.25188i | 0.297008 | − | 0.954875i | \(-0.404011\pi\) |
0.954875 | − | 0.297008i | \(-0.0959889\pi\) | |||||||
\(938\) | 185.115 | + | 185.115i | 0.197350 | + | 0.197350i | ||||
\(939\) | − | 1022.51i | − | 1.08893i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −704.024 | −0.748166 | −0.374083 | − | 0.927395i | \(-0.622042\pi\) | ||||
−0.374083 | + | 0.927395i | \(0.622042\pi\) | |||||||
\(942\) | 20.8946 | − | 20.8946i | 0.0221811 | − | 0.0221811i | ||||
\(943\) | 702.210 | + | 702.210i | 0.744656 | + | 0.744656i | ||||
\(944\) | − | 412.426i | − | 0.436892i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −207.480 | −0.219324 | ||||||||
\(947\) | 591.011 | − | 591.011i | 0.624088 | − | 0.624088i | −0.322486 | − | 0.946574i | \(-0.604519\pi\) |
0.946574 | + | 0.322486i | \(0.104519\pi\) | |||||||
\(948\) | −276.523 | − | 276.523i | −0.291691 | − | 0.291691i | ||||
\(949\) | − | 391.840i | − | 0.412897i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −224.166 | −0.235716 | ||||||||
\(952\) | 172.582 | − | 172.582i | 0.181283 | − | 0.181283i | ||||
\(953\) | −761.334 | − | 761.334i | −0.798881 | − | 0.798881i | 0.184038 | − | 0.982919i | \(-0.441083\pi\) |
−0.982919 | + | 0.184038i | \(0.941083\pi\) | |||||||
\(954\) | 158.273i | 0.165904i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 520.732 | 0.544699 | ||||||||
\(957\) | 119.522 | − | 119.522i | 0.124892 | − | 0.124892i | ||||
\(958\) | 539.039 | + | 539.039i | 0.562672 | + | 0.562672i | ||||
\(959\) | 181.155i | 0.188900i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 81.1166 | 0.0844085 | ||||||||
\(962\) | −546.282 | + | 546.282i | −0.567860 | + | 0.567860i | ||||
\(963\) | 234.133 | + | 234.133i | 0.243128 | + | 0.243128i | ||||
\(964\) | − | 139.617i | − | 0.144831i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 123.819 | 0.128177 | ||||||||
\(967\) | −310.712 | + | 310.712i | −0.321316 | + | 0.321316i | −0.849272 | − | 0.527956i | \(-0.822959\pi\) |
0.527956 | + | 0.849272i | \(0.322959\pi\) | |||||||
\(968\) | 206.898 | + | 206.898i | 0.213738 | + | 0.213738i | ||||
\(969\) | 1845.73i | 1.90478i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 198.336 | 0.204259 | 0.102130 | − | 0.994771i | \(-0.467434\pi\) | ||||
0.102130 | + | 0.994771i | \(0.467434\pi\) | |||||||
\(972\) | 22.0454 | − | 22.0454i | 0.0226805 | − | 0.0226805i | ||||
\(973\) | −199.331 | − | 199.331i | −0.204862 | − | 0.204862i | ||||
\(974\) | − | 123.699i | − | 0.127001i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −478.876 | −0.490651 | ||||||||
\(977\) | 38.5224 | − | 38.5224i | 0.0394293 | − | 0.0394293i | −0.687117 | − | 0.726547i | \(-0.741124\pi\) |
0.726547 | + | 0.687117i | \(0.241124\pi\) | |||||||
\(978\) | −147.729 | − | 147.729i | −0.151052 | − | 0.151052i | ||||
\(979\) | − | 149.306i | − | 0.152508i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −345.954 | −0.352654 | ||||||||
\(982\) | 191.070 | − | 191.070i | 0.194573 | − | 0.194573i | ||||
\(983\) | −183.804 | − | 183.804i | −0.186983 | − | 0.186983i | 0.607407 | − | 0.794391i | \(-0.292210\pi\) |
−0.794391 | + | 0.607407i | \(0.792210\pi\) | |||||||
\(984\) | − | 254.640i | − | 0.258781i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1074.44 | −1.08970 | ||||||||
\(987\) | −238.610 | + | 238.610i | −0.241753 | + | 0.241753i | ||||
\(988\) | 849.146 | + | 849.146i | 0.859460 | + | 0.859460i | ||||
\(989\) | 669.071i | 0.676513i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1218.07 | −1.22913 | −0.614567 | − | 0.788865i | \(-0.710669\pi\) | ||||
−0.614567 | + | 0.788865i | \(0.710669\pi\) | |||||||
\(992\) | −129.127 | + | 129.127i | −0.130169 | + | 0.130169i | ||||
\(993\) | −210.810 | − | 210.810i | −0.212296 | − | 0.212296i | ||||
\(994\) | − | 351.938i | − | 0.354063i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −66.9526 | −0.0672214 | ||||||||
\(997\) | 696.062 | − | 696.062i | 0.698156 | − | 0.698156i | −0.265856 | − | 0.964013i | \(-0.585655\pi\) |
0.964013 | + | 0.265856i | \(0.0856547\pi\) | |||||||
\(998\) | 190.849 | + | 190.849i | 0.191232 | + | 0.191232i | ||||
\(999\) | 154.462i | 0.154617i |
(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 | 1050.3.l.e.43.2 | yes | 8 | |
5.2 | odd | 4 | inner | 1050.3.l.e.757.2 | yes | 8 | |
5.3 | odd | 4 | 1050.3.l.a.757.3 | yes | 8 | ||
5.4 | even | 2 | 1050.3.l.a.43.3 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.3.l.a.43.3 | ✓ | 8 | 5.4 | even | 2 | ||
1050.3.l.a.757.3 | yes | 8 | 5.3 | odd | 4 | ||
1050.3.l.e.43.2 | yes | 8 | 1.1 | even | 1 | trivial | |
1050.3.l.e.757.2 | yes | 8 | 5.2 | odd | 4 | inner |