Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(307,1050)]
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, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.307");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.m (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: | \(8.38429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
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 | 643.1 | ||
Root | \(-0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.643 |
Dual form | 1050.2.m.d.307.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | −2.63896 | + | 0.189469i | −0.997433 | + | 0.0716124i | ||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.46410 | −1.64749 | −0.823744 | − | 0.566961i | \(-0.808119\pi\) | ||||
−0.823744 | + | 0.566961i | \(0.808119\pi\) | |||||||
\(12\) | 0.707107 | + | 0.707107i | 0.204124 | + | 0.204124i | ||||
\(13\) | −2.63896 | + | 2.63896i | −0.731915 | + | 0.731915i | −0.970999 | − | 0.239084i | \(-0.923153\pi\) |
0.239084 | + | 0.970999i | \(0.423153\pi\) | |||||||
\(14\) | 1.73205 | − | 2.00000i | 0.462910 | − | 0.534522i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 3.53553 | + | 3.53553i | 0.857493 | + | 0.857493i | 0.991042 | − | 0.133549i | \(-0.0426374\pi\) |
−0.133549 | + | 0.991042i | \(0.542637\pi\) | |||||||
\(18\) | 0.707107 | + | 0.707107i | 0.166667 | + | 0.166667i | ||||
\(19\) | 7.46410 | 1.71238 | 0.856191 | − | 0.516659i | \(-0.172825\pi\) | ||||
0.856191 | + | 0.516659i | \(0.172825\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.73205 | − | 2.00000i | 0.377964 | − | 0.436436i | ||||
\(22\) | 3.86370 | − | 3.86370i | 0.823744 | − | 0.823744i | ||||
\(23\) | −0.707107 | − | 0.707107i | −0.147442 | − | 0.147442i | 0.629532 | − | 0.776974i | \(-0.283247\pi\) |
−0.776974 | + | 0.629532i | \(0.783247\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 3.73205i | − | 0.731915i | ||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0.189469 | + | 2.63896i | 0.0358062 | + | 0.498716i | ||||
\(29\) | − | 7.73205i | − | 1.43581i | −0.696143 | − | 0.717903i | \(-0.745102\pi\) | ||
0.696143 | − | 0.717903i | \(-0.254898\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.92820i | − | 1.42395i | −0.702206 | − | 0.711974i | \(-0.747802\pi\) | ||
0.702206 | − | 0.711974i | \(-0.252198\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | 3.86370 | − | 3.86370i | 0.672584 | − | 0.672584i | ||||
\(34\) | −5.00000 | −0.857493 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 4.89898 | − | 4.89898i | 0.805387 | − | 0.805387i | −0.178545 | − | 0.983932i | \(-0.557139\pi\) |
0.983932 | + | 0.178545i | \(0.0571389\pi\) | |||||||
\(38\) | −5.27792 | + | 5.27792i | −0.856191 | + | 0.856191i | ||||
\(39\) | − | 3.73205i | − | 0.597606i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.73205i | 0.895196i | 0.894235 | + | 0.447598i | \(0.147720\pi\) | ||||
−0.894235 | + | 0.447598i | \(0.852280\pi\) | |||||||
\(42\) | 0.189469 | + | 2.63896i | 0.0292357 | + | 0.407200i | ||||
\(43\) | −2.63896 | − | 2.63896i | −0.402437 | − | 0.402437i | 0.476654 | − | 0.879091i | \(-0.341850\pi\) |
−0.879091 | + | 0.476654i | \(0.841850\pi\) | |||||||
\(44\) | 5.46410i | 0.823744i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −5.93426 | − | 5.93426i | −0.865600 | − | 0.865600i | 0.126382 | − | 0.991982i | \(-0.459664\pi\) |
−0.991982 | + | 0.126382i | \(0.959664\pi\) | |||||||
\(48\) | 0.707107 | − | 0.707107i | 0.102062 | − | 0.102062i | ||||
\(49\) | 6.92820 | − | 1.00000i | 0.989743 | − | 0.142857i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.00000 | −0.700140 | ||||||||
\(52\) | 2.63896 | + | 2.63896i | 0.365958 | + | 0.365958i | ||||
\(53\) | −2.50026 | − | 2.50026i | −0.343437 | − | 0.343437i | 0.514221 | − | 0.857658i | \(-0.328081\pi\) |
−0.857658 | + | 0.514221i | \(0.828081\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.00000 | − | 1.73205i | −0.267261 | − | 0.231455i | ||||
\(57\) | −5.27792 | + | 5.27792i | −0.699077 | + | 0.699077i | ||||
\(58\) | 5.46739 | + | 5.46739i | 0.717903 | + | 0.717903i | ||||
\(59\) | 7.19615 | 0.936859 | 0.468430 | − | 0.883501i | \(-0.344820\pi\) | ||||
0.468430 | + | 0.883501i | \(0.344820\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 2.46410i | − | 0.315496i | −0.987479 | − | 0.157748i | \(-0.949577\pi\) | ||
0.987479 | − | 0.157748i | \(-0.0504233\pi\) | |||||||
\(62\) | 5.60609 | + | 5.60609i | 0.711974 | + | 0.711974i | ||||
\(63\) | 0.189469 | + | 2.63896i | 0.0238708 | + | 0.332478i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.46410i | 0.672584i | ||||||||
\(67\) | 4.52004 | − | 4.52004i | 0.552211 | − | 0.552211i | −0.374867 | − | 0.927078i | \(-0.622312\pi\) |
0.927078 | + | 0.374867i | \(0.122312\pi\) | |||||||
\(68\) | 3.53553 | − | 3.53553i | 0.428746 | − | 0.428746i | ||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.4641 | −1.36054 | −0.680269 | − | 0.732962i | \(-0.738137\pi\) | ||||
−0.680269 | + | 0.732962i | \(0.738137\pi\) | |||||||
\(72\) | 0.707107 | − | 0.707107i | 0.0833333 | − | 0.0833333i | ||||
\(73\) | 8.76268 | − | 8.76268i | 1.02559 | − | 1.02559i | 0.0259307 | − | 0.999664i | \(-0.491745\pi\) |
0.999664 | − | 0.0259307i | \(-0.00825492\pi\) | |||||||
\(74\) | 6.92820i | 0.805387i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 7.46410i | − | 0.856191i | ||||||
\(77\) | 14.4195 | − | 1.03528i | 1.64326 | − | 0.117981i | ||||
\(78\) | 2.63896 | + | 2.63896i | 0.298803 | + | 0.298803i | ||||
\(79\) | − | 12.3923i | − | 1.39424i | −0.716953 | − | 0.697122i | \(-0.754464\pi\) | ||
0.716953 | − | 0.697122i | \(-0.245536\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −4.05317 | − | 4.05317i | −0.447598 | − | 0.447598i | ||||
\(83\) | −0.328169 | + | 0.328169i | −0.0360213 | + | 0.0360213i | −0.724888 | − | 0.688867i | \(-0.758109\pi\) |
0.688867 | + | 0.724888i | \(0.258109\pi\) | |||||||
\(84\) | −2.00000 | − | 1.73205i | −0.218218 | − | 0.188982i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.73205 | 0.402437 | ||||||||
\(87\) | 5.46739 | + | 5.46739i | 0.586165 | + | 0.586165i | ||||
\(88\) | −3.86370 | − | 3.86370i | −0.411872 | − | 0.411872i | ||||
\(89\) | 12.0000 | 1.27200 | 0.635999 | − | 0.771690i | \(-0.280588\pi\) | ||||
0.635999 | + | 0.771690i | \(0.280588\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.46410 | − | 7.46410i | 0.677622 | − | 0.782450i | ||||
\(92\) | −0.707107 | + | 0.707107i | −0.0737210 | + | 0.0737210i | ||||
\(93\) | 5.60609 | + | 5.60609i | 0.581324 | + | 0.581324i | ||||
\(94\) | 8.39230 | 0.865600 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | −2.17209 | − | 2.17209i | −0.220542 | − | 0.220542i | 0.588185 | − | 0.808727i | \(-0.299843\pi\) |
−0.808727 | + | 0.588185i | \(0.799843\pi\) | |||||||
\(98\) | −4.19187 | + | 5.60609i | −0.423443 | + | 0.566300i | ||||
\(99\) | 5.46410i | 0.549163i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.53590i | 0.650346i | 0.945655 | + | 0.325173i | \(0.105423\pi\) | ||||
−0.945655 | + | 0.325173i | \(0.894577\pi\) | |||||||
\(102\) | 3.53553 | − | 3.53553i | 0.350070 | − | 0.350070i | ||||
\(103\) | 2.91636 | − | 2.91636i | 0.287357 | − | 0.287357i | −0.548677 | − | 0.836034i | \(-0.684868\pi\) |
0.836034 | + | 0.548677i | \(0.184868\pi\) | |||||||
\(104\) | −3.73205 | −0.365958 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.53590 | 0.343437 | ||||||||
\(107\) | −6.31319 | + | 6.31319i | −0.610319 | + | 0.610319i | −0.943029 | − | 0.332710i | \(-0.892037\pi\) |
0.332710 | + | 0.943029i | \(0.392037\pi\) | |||||||
\(108\) | 0.707107 | − | 0.707107i | 0.0680414 | − | 0.0680414i | ||||
\(109\) | 12.3923i | 1.18697i | 0.804846 | + | 0.593484i | \(0.202248\pi\) | ||||
−0.804846 | + | 0.593484i | \(0.797752\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.92820i | 0.657596i | ||||||||
\(112\) | 2.63896 | − | 0.189469i | 0.249358 | − | 0.0179031i | ||||
\(113\) | −1.79315 | − | 1.79315i | −0.168685 | − | 0.168685i | 0.617716 | − | 0.786401i | \(-0.288058\pi\) |
−0.786401 | + | 0.617716i | \(0.788058\pi\) | |||||||
\(114\) | − | 7.46410i | − | 0.699077i | ||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.73205 | −0.717903 | ||||||||
\(117\) | 2.63896 | + | 2.63896i | 0.243972 | + | 0.243972i | ||||
\(118\) | −5.08845 | + | 5.08845i | −0.468430 | + | 0.468430i | ||||
\(119\) | −10.0000 | − | 8.66025i | −0.916698 | − | 0.793884i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.8564 | 1.71422 | ||||||||
\(122\) | 1.74238 | + | 1.74238i | 0.157748 | + | 0.157748i | ||||
\(123\) | −4.05317 | − | 4.05317i | −0.365462 | − | 0.365462i | ||||
\(124\) | −7.92820 | −0.711974 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.00000 | − | 1.73205i | −0.178174 | − | 0.154303i | ||||
\(127\) | 5.27792 | − | 5.27792i | 0.468339 | − | 0.468339i | −0.433037 | − | 0.901376i | \(-0.642558\pi\) |
0.901376 | + | 0.433037i | \(0.142558\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 3.73205 | 0.328589 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.3923i | 1.25746i | 0.777623 | + | 0.628731i | \(0.216425\pi\) | ||||
−0.777623 | + | 0.628731i | \(0.783575\pi\) | |||||||
\(132\) | −3.86370 | − | 3.86370i | −0.336292 | − | 0.336292i | ||||
\(133\) | −19.6975 | + | 1.41421i | −1.70799 | + | 0.122628i | ||||
\(134\) | 6.39230i | 0.552211i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.00000i | 0.428746i | ||||||||
\(137\) | −5.55532 | + | 5.55532i | −0.474623 | + | 0.474623i | −0.903407 | − | 0.428784i | \(-0.858942\pi\) |
0.428784 | + | 0.903407i | \(0.358942\pi\) | |||||||
\(138\) | −0.707107 | + | 0.707107i | −0.0601929 | + | 0.0601929i | ||||
\(139\) | −19.8564 | −1.68420 | −0.842099 | − | 0.539323i | \(-0.818680\pi\) | ||||
−0.842099 | + | 0.539323i | \(0.818680\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.39230 | 0.706760 | ||||||||
\(142\) | 8.10634 | − | 8.10634i | 0.680269 | − | 0.680269i | ||||
\(143\) | 14.4195 | − | 14.4195i | 1.20582 | − | 1.20582i | ||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 12.3923i | 1.02559i | ||||||||
\(147\) | −4.19187 | + | 5.60609i | −0.345740 | + | 0.462382i | ||||
\(148\) | −4.89898 | − | 4.89898i | −0.402694 | − | 0.402694i | ||||
\(149\) | 7.73205i | 0.633434i | 0.948520 | + | 0.316717i | \(0.102581\pi\) | ||||
−0.948520 | + | 0.316717i | \(0.897419\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.0000 | 1.30206 | 0.651031 | − | 0.759051i | \(-0.274337\pi\) | ||||
0.651031 | + | 0.759051i | \(0.274337\pi\) | |||||||
\(152\) | 5.27792 | + | 5.27792i | 0.428096 | + | 0.428096i | ||||
\(153\) | 3.53553 | − | 3.53553i | 0.285831 | − | 0.285831i | ||||
\(154\) | −9.46410 | + | 10.9282i | −0.762639 | + | 0.880620i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.73205 | −0.298803 | ||||||||
\(157\) | −5.65685 | − | 5.65685i | −0.451466 | − | 0.451466i | 0.444375 | − | 0.895841i | \(-0.353426\pi\) |
−0.895841 | + | 0.444375i | \(0.853426\pi\) | |||||||
\(158\) | 8.76268 | + | 8.76268i | 0.697122 | + | 0.697122i | ||||
\(159\) | 3.53590 | 0.280415 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.00000 | + | 1.73205i | 0.157622 | + | 0.136505i | ||||
\(162\) | 0.707107 | − | 0.707107i | 0.0555556 | − | 0.0555556i | ||||
\(163\) | 0.568406 | + | 0.568406i | 0.0445210 | + | 0.0445210i | 0.729017 | − | 0.684496i | \(-0.239978\pi\) |
−0.684496 | + | 0.729017i | \(0.739978\pi\) | |||||||
\(164\) | 5.73205 | 0.447598 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 0.464102i | − | 0.0360213i | ||||||
\(167\) | −10.9348 | − | 10.9348i | −0.846158 | − | 0.846158i | 0.143493 | − | 0.989651i | \(-0.454166\pi\) |
−0.989651 | + | 0.143493i | \(0.954166\pi\) | |||||||
\(168\) | 2.63896 | − | 0.189469i | 0.203600 | − | 0.0146178i | ||||
\(169\) | − | 0.928203i | − | 0.0714002i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 7.46410i | − | 0.570794i | ||||||
\(172\) | −2.63896 | + | 2.63896i | −0.201219 | + | 0.201219i | ||||
\(173\) | 6.59059 | − | 6.59059i | 0.501074 | − | 0.501074i | −0.410698 | − | 0.911771i | \(-0.634715\pi\) |
0.911771 | + | 0.410698i | \(0.134715\pi\) | |||||||
\(174\) | −7.73205 | −0.586165 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.46410 | 0.411872 | ||||||||
\(177\) | −5.08845 | + | 5.08845i | −0.382471 | + | 0.382471i | ||||
\(178\) | −8.48528 | + | 8.48528i | −0.635999 | + | 0.635999i | ||||
\(179\) | − | 13.8564i | − | 1.03568i | −0.855479 | − | 0.517838i | \(-0.826737\pi\) | ||
0.855479 | − | 0.517838i | \(-0.173263\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.00000i | − | 0.148659i | −0.997234 | − | 0.0743294i | \(-0.976318\pi\) | ||
0.997234 | − | 0.0743294i | \(-0.0236816\pi\) | |||||||
\(182\) | 0.707107 | + | 9.84873i | 0.0524142 | + | 0.730036i | ||||
\(183\) | 1.74238 | + | 1.74238i | 0.128801 | + | 0.128801i | ||||
\(184\) | − | 1.00000i | − | 0.0737210i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −7.92820 | −0.581324 | ||||||||
\(187\) | −19.3185 | − | 19.3185i | −1.41271 | − | 1.41271i | ||||
\(188\) | −5.93426 | + | 5.93426i | −0.432800 | + | 0.432800i | ||||
\(189\) | −2.00000 | − | 1.73205i | −0.145479 | − | 0.125988i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.26795 | 0.453533 | 0.226766 | − | 0.973949i | \(-0.427185\pi\) | ||||
0.226766 | + | 0.973949i | \(0.427185\pi\) | |||||||
\(192\) | −0.707107 | − | 0.707107i | −0.0510310 | − | 0.0510310i | ||||
\(193\) | −12.6264 | − | 12.6264i | −0.908867 | − | 0.908867i | 0.0873137 | − | 0.996181i | \(-0.472172\pi\) |
−0.996181 | + | 0.0873137i | \(0.972172\pi\) | |||||||
\(194\) | 3.07180 | 0.220542 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.00000 | − | 6.92820i | −0.0714286 | − | 0.494872i | ||||
\(197\) | −5.22715 | + | 5.22715i | −0.372419 | + | 0.372419i | −0.868358 | − | 0.495939i | \(-0.834824\pi\) |
0.495939 | + | 0.868358i | \(0.334824\pi\) | |||||||
\(198\) | −3.86370 | − | 3.86370i | −0.274581 | − | 0.274581i | ||||
\(199\) | 16.0000 | 1.13421 | 0.567105 | − | 0.823646i | \(-0.308063\pi\) | ||||
0.567105 | + | 0.823646i | \(0.308063\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.39230i | 0.450878i | ||||||||
\(202\) | −4.62158 | − | 4.62158i | −0.325173 | − | 0.325173i | ||||
\(203\) | 1.46498 | + | 20.4046i | 0.102822 | + | 1.43212i | ||||
\(204\) | 5.00000i | 0.350070i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.12436i | 0.287357i | ||||||||
\(207\) | −0.707107 | + | 0.707107i | −0.0491473 | + | 0.0491473i | ||||
\(208\) | 2.63896 | − | 2.63896i | 0.182979 | − | 0.182979i | ||||
\(209\) | −40.7846 | −2.82113 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.3205 | −0.710493 | −0.355247 | − | 0.934773i | \(-0.615603\pi\) | ||||
−0.355247 | + | 0.934773i | \(0.615603\pi\) | |||||||
\(212\) | −2.50026 | + | 2.50026i | −0.171718 | + | 0.171718i | ||||
\(213\) | 8.10634 | − | 8.10634i | 0.555438 | − | 0.555438i | ||||
\(214\) | − | 8.92820i | − | 0.610319i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 1.50215 | + | 20.9222i | 0.101972 | + | 1.42029i | ||||
\(218\) | −8.76268 | − | 8.76268i | −0.593484 | − | 0.593484i | ||||
\(219\) | 12.3923i | 0.837394i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.6603 | −1.25522 | ||||||||
\(222\) | −4.89898 | − | 4.89898i | −0.328798 | − | 0.328798i | ||||
\(223\) | −8.19428 | + | 8.19428i | −0.548729 | + | 0.548729i | −0.926073 | − | 0.377344i | \(-0.876837\pi\) |
0.377344 | + | 0.926073i | \(0.376837\pi\) | |||||||
\(224\) | −1.73205 | + | 2.00000i | −0.115728 | + | 0.133631i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.53590 | 0.168685 | ||||||||
\(227\) | −0.984508 | − | 0.984508i | −0.0653441 | − | 0.0653441i | 0.673680 | − | 0.739024i | \(-0.264713\pi\) |
−0.739024 | + | 0.673680i | \(0.764713\pi\) | |||||||
\(228\) | 5.27792 | + | 5.27792i | 0.349539 | + | 0.349539i | ||||
\(229\) | 15.0718 | 0.995972 | 0.497986 | − | 0.867185i | \(-0.334073\pi\) | ||||
0.497986 | + | 0.867185i | \(0.334073\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.46410 | + | 10.9282i | −0.622692 | + | 0.719023i | ||||
\(232\) | 5.46739 | − | 5.46739i | 0.358951 | − | 0.358951i | ||||
\(233\) | −7.34847 | − | 7.34847i | −0.481414 | − | 0.481414i | 0.424169 | − | 0.905583i | \(-0.360566\pi\) |
−0.905583 | + | 0.424169i | \(0.860566\pi\) | |||||||
\(234\) | −3.73205 | −0.243972 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 7.19615i | − | 0.468430i | ||||||
\(237\) | 8.76268 | + | 8.76268i | 0.569197 | + | 0.569197i | ||||
\(238\) | 13.1948 | − | 0.947343i | 0.855291 | − | 0.0614072i | ||||
\(239\) | 8.53590i | 0.552141i | 0.961137 | + | 0.276071i | \(0.0890324\pi\) | ||||
−0.961137 | + | 0.276071i | \(0.910968\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 0.928203i | − | 0.0597908i | −0.999553 | − | 0.0298954i | \(-0.990483\pi\) | ||
0.999553 | − | 0.0298954i | \(-0.00951742\pi\) | |||||||
\(242\) | −13.3335 | + | 13.3335i | −0.857109 | + | 0.857109i | ||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | −2.46410 | −0.157748 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.73205 | 0.365462 | ||||||||
\(247\) | −19.6975 | + | 19.6975i | −1.25332 | + | 1.25332i | ||||
\(248\) | 5.60609 | − | 5.60609i | 0.355987 | − | 0.355987i | ||||
\(249\) | − | 0.464102i | − | 0.0294112i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 20.2679i | − | 1.27930i | −0.768666 | − | 0.639651i | \(-0.779079\pi\) | ||
0.768666 | − | 0.639651i | \(-0.220921\pi\) | |||||||
\(252\) | 2.63896 | − | 0.189469i | 0.166239 | − | 0.0119354i | ||||
\(253\) | 3.86370 | + | 3.86370i | 0.242909 | + | 0.242909i | ||||
\(254\) | 7.46410i | 0.468339i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −16.9198 | − | 16.9198i | −1.05543 | − | 1.05543i | −0.998371 | − | 0.0570569i | \(-0.981828\pi\) |
−0.0570569 | − | 0.998371i | \(-0.518172\pi\) | |||||||
\(258\) | −2.63896 | + | 2.63896i | −0.164294 | + | 0.164294i | ||||
\(259\) | −12.0000 | + | 13.8564i | −0.745644 | + | 0.860995i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.73205 | −0.478602 | ||||||||
\(262\) | −10.1769 | − | 10.1769i | −0.628731 | − | 0.628731i | ||||
\(263\) | 4.94975 | + | 4.94975i | 0.305215 | + | 0.305215i | 0.843050 | − | 0.537835i | \(-0.180758\pi\) |
−0.537835 | + | 0.843050i | \(0.680758\pi\) | |||||||
\(264\) | 5.46410 | 0.336292 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 12.9282 | − | 14.9282i | 0.792679 | − | 0.915307i | ||||
\(267\) | −8.48528 | + | 8.48528i | −0.519291 | + | 0.519291i | ||||
\(268\) | −4.52004 | − | 4.52004i | −0.276106 | − | 0.276106i | ||||
\(269\) | −21.8564 | −1.33261 | −0.666304 | − | 0.745680i | \(-0.732125\pi\) | ||||
−0.666304 | + | 0.745680i | \(0.732125\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.92820i | 0.177876i | 0.996037 | + | 0.0889378i | \(0.0283472\pi\) | ||||
−0.996037 | + | 0.0889378i | \(0.971653\pi\) | |||||||
\(272\) | −3.53553 | − | 3.53553i | −0.214373 | − | 0.214373i | ||||
\(273\) | 0.707107 | + | 9.84873i | 0.0427960 | + | 0.596072i | ||||
\(274\) | − | 7.85641i | − | 0.474623i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 1.00000i | − | 0.0601929i | ||||||
\(277\) | 5.93426 | − | 5.93426i | 0.356555 | − | 0.356555i | −0.505987 | − | 0.862541i | \(-0.668871\pi\) |
0.862541 | + | 0.505987i | \(0.168871\pi\) | |||||||
\(278\) | 14.0406 | − | 14.0406i | 0.842099 | − | 0.842099i | ||||
\(279\) | −7.92820 | −0.474649 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.8564 | 0.826604 | 0.413302 | − | 0.910594i | \(-0.364375\pi\) | ||||
0.413302 | + | 0.910594i | \(0.364375\pi\) | |||||||
\(282\) | −5.93426 | + | 5.93426i | −0.353380 | + | 0.353380i | ||||
\(283\) | −16.1112 | + | 16.1112i | −0.957709 | + | 0.957709i | −0.999141 | − | 0.0414327i | \(-0.986808\pi\) |
0.0414327 | + | 0.999141i | \(0.486808\pi\) | |||||||
\(284\) | 11.4641i | 0.680269i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 20.3923i | 1.20582i | ||||||||
\(287\) | −1.08604 | − | 15.1266i | −0.0641072 | − | 0.892898i | ||||
\(288\) | −0.707107 | − | 0.707107i | −0.0416667 | − | 0.0416667i | ||||
\(289\) | 8.00000i | 0.470588i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.07180 | 0.180072 | ||||||||
\(292\) | −8.76268 | − | 8.76268i | −0.512797 | − | 0.512797i | ||||
\(293\) | −1.31268 | + | 1.31268i | −0.0766874 | + | 0.0766874i | −0.744410 | − | 0.667723i | \(-0.767269\pi\) |
0.667723 | + | 0.744410i | \(0.267269\pi\) | |||||||
\(294\) | −1.00000 | − | 6.92820i | −0.0583212 | − | 0.404061i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.92820 | 0.402694 | ||||||||
\(297\) | −3.86370 | − | 3.86370i | −0.224195 | − | 0.224195i | ||||
\(298\) | −5.46739 | − | 5.46739i | −0.316717 | − | 0.316717i | ||||
\(299\) | 3.73205 | 0.215830 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.46410 | + | 6.46410i | 0.430224 | + | 0.372585i | ||||
\(302\) | −11.3137 | + | 11.3137i | −0.651031 | + | 0.651031i | ||||
\(303\) | −4.62158 | − | 4.62158i | −0.265503 | − | 0.265503i | ||||
\(304\) | −7.46410 | −0.428096 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 5.00000i | 0.285831i | ||||||||
\(307\) | −3.58630 | − | 3.58630i | −0.204681 | − | 0.204681i | 0.597321 | − | 0.802002i | \(-0.296232\pi\) |
−0.802002 | + | 0.597321i | \(0.796232\pi\) | |||||||
\(308\) | −1.03528 | − | 14.4195i | −0.0589903 | − | 0.821629i | ||||
\(309\) | 4.12436i | 0.234626i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 25.8564i | − | 1.46618i | −0.680130 | − | 0.733091i | \(-0.738077\pi\) | ||
0.680130 | − | 0.733091i | \(-0.261923\pi\) | |||||||
\(312\) | 2.63896 | − | 2.63896i | 0.149402 | − | 0.149402i | ||||
\(313\) | 21.3891 | − | 21.3891i | 1.20898 | − | 1.20898i | 0.237625 | − | 0.971357i | \(-0.423631\pi\) |
0.971357 | − | 0.237625i | \(-0.0763688\pi\) | |||||||
\(314\) | 8.00000 | 0.451466 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.3923 | −0.697122 | ||||||||
\(317\) | 19.3693 | − | 19.3693i | 1.08789 | − | 1.08789i | 0.0921415 | − | 0.995746i | \(-0.470629\pi\) |
0.995746 | − | 0.0921415i | \(-0.0293712\pi\) | |||||||
\(318\) | −2.50026 | + | 2.50026i | −0.140207 | + | 0.140207i | ||||
\(319\) | 42.2487i | 2.36547i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 8.92820i | − | 0.498324i | ||||||
\(322\) | −2.63896 | + | 0.189469i | −0.147063 | + | 0.0105587i | ||||
\(323\) | 26.3896 | + | 26.3896i | 1.46836 | + | 1.46836i | ||||
\(324\) | 1.00000i | 0.0555556i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.803848 | −0.0445210 | ||||||||
\(327\) | −8.76268 | − | 8.76268i | −0.484577 | − | 0.484577i | ||||
\(328\) | −4.05317 | + | 4.05317i | −0.223799 | + | 0.223799i | ||||
\(329\) | 16.7846 | + | 14.5359i | 0.925365 | + | 0.801390i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.3205 | −1.66657 | −0.833283 | − | 0.552847i | \(-0.813541\pi\) | ||||
−0.833283 | + | 0.552847i | \(0.813541\pi\) | |||||||
\(332\) | 0.328169 | + | 0.328169i | 0.0180106 | + | 0.0180106i | ||||
\(333\) | −4.89898 | − | 4.89898i | −0.268462 | − | 0.268462i | ||||
\(334\) | 15.4641 | 0.846158 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.73205 | + | 2.00000i | −0.0944911 | + | 0.109109i | ||||
\(337\) | 15.7458 | − | 15.7458i | 0.857729 | − | 0.857729i | −0.133341 | − | 0.991070i | \(-0.542571\pi\) |
0.991070 | + | 0.133341i | \(0.0425705\pi\) | |||||||
\(338\) | 0.656339 | + | 0.656339i | 0.0357001 | + | 0.0357001i | ||||
\(339\) | 2.53590 | 0.137731 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 43.3205i | 2.34594i | ||||||||
\(342\) | 5.27792 | + | 5.27792i | 0.285397 | + | 0.285397i | ||||
\(343\) | −18.0938 | + | 3.95164i | −0.976972 | + | 0.213368i | ||||
\(344\) | − | 3.73205i | − | 0.201219i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.32051i | 0.501074i | ||||||||
\(347\) | 3.20736 | − | 3.20736i | 0.172180 | − | 0.172180i | −0.615756 | − | 0.787937i | \(-0.711149\pi\) |
0.787937 | + | 0.615756i | \(0.211149\pi\) | |||||||
\(348\) | 5.46739 | − | 5.46739i | 0.293083 | − | 0.293083i | ||||
\(349\) | −4.60770 | −0.246644 | −0.123322 | − | 0.992367i | \(-0.539355\pi\) | ||||
−0.123322 | + | 0.992367i | \(0.539355\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.73205 | −0.199202 | ||||||||
\(352\) | −3.86370 | + | 3.86370i | −0.205936 | + | 0.205936i | ||||
\(353\) | −9.14162 | + | 9.14162i | −0.486559 | + | 0.486559i | −0.907219 | − | 0.420659i | \(-0.861799\pi\) |
0.420659 | + | 0.907219i | \(0.361799\pi\) | |||||||
\(354\) | − | 7.19615i | − | 0.382471i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 12.0000i | − | 0.635999i | ||||||
\(357\) | 13.1948 | − | 0.947343i | 0.698342 | − | 0.0501387i | ||||
\(358\) | 9.79796 | + | 9.79796i | 0.517838 | + | 0.517838i | ||||
\(359\) | − | 36.1244i | − | 1.90657i | −0.302071 | − | 0.953285i | \(-0.597678\pi\) | ||
0.302071 | − | 0.953285i | \(-0.402322\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 36.7128 | 1.93225 | ||||||||
\(362\) | 1.41421 | + | 1.41421i | 0.0743294 | + | 0.0743294i | ||||
\(363\) | −13.3335 | + | 13.3335i | −0.699827 | + | 0.699827i | ||||
\(364\) | −7.46410 | − | 6.46410i | −0.391225 | − | 0.338811i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.46410 | −0.128801 | ||||||||
\(367\) | 7.63947 | + | 7.63947i | 0.398777 | + | 0.398777i | 0.877802 | − | 0.479024i | \(-0.159009\pi\) |
−0.479024 | + | 0.877802i | \(0.659009\pi\) | |||||||
\(368\) | 0.707107 | + | 0.707107i | 0.0368605 | + | 0.0368605i | ||||
\(369\) | 5.73205 | 0.298399 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.07180 | + | 6.12436i | 0.367149 | + | 0.317961i | ||||
\(372\) | 5.60609 | − | 5.60609i | 0.290662 | − | 0.290662i | ||||
\(373\) | 10.8332 | + | 10.8332i | 0.560924 | + | 0.560924i | 0.929570 | − | 0.368646i | \(-0.120179\pi\) |
−0.368646 | + | 0.929570i | \(0.620179\pi\) | |||||||
\(374\) | 27.3205 | 1.41271 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 8.39230i | − | 0.432800i | ||||||
\(377\) | 20.4046 | + | 20.4046i | 1.05089 | + | 1.05089i | ||||
\(378\) | 2.63896 | − | 0.189469i | 0.135733 | − | 0.00974522i | ||||
\(379\) | − | 19.3923i | − | 0.996116i | −0.867144 | − | 0.498058i | \(-0.834047\pi\) | ||
0.867144 | − | 0.498058i | \(-0.165953\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.46410i | 0.382398i | ||||||||
\(382\) | −4.43211 | + | 4.43211i | −0.226766 | + | 0.226766i | ||||
\(383\) | 21.0101 | − | 21.0101i | 1.07357 | − | 1.07357i | 0.0764978 | − | 0.997070i | \(-0.475626\pi\) |
0.997070 | − | 0.0764978i | \(-0.0243738\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.8564 | 0.908867 | ||||||||
\(387\) | −2.63896 | + | 2.63896i | −0.134146 | + | 0.134146i | ||||
\(388\) | −2.17209 | + | 2.17209i | −0.110271 | + | 0.110271i | ||||
\(389\) | − | 26.9282i | − | 1.36531i | −0.730739 | − | 0.682657i | \(-0.760824\pi\) | ||
0.730739 | − | 0.682657i | \(-0.239176\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 5.00000i | − | 0.252861i | ||||||
\(392\) | 5.60609 | + | 4.19187i | 0.283150 | + | 0.211722i | ||||
\(393\) | −10.1769 | − | 10.1769i | −0.513357 | − | 0.513357i | ||||
\(394\) | − | 7.39230i | − | 0.372419i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.46410 | 0.274581 | ||||||||
\(397\) | 7.15900 | + | 7.15900i | 0.359300 | + | 0.359300i | 0.863555 | − | 0.504255i | \(-0.168233\pi\) |
−0.504255 | + | 0.863555i | \(0.668233\pi\) | |||||||
\(398\) | −11.3137 | + | 11.3137i | −0.567105 | + | 0.567105i | ||||
\(399\) | 12.9282 | − | 14.9282i | 0.647220 | − | 0.747345i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.3205 | −0.665194 | −0.332597 | − | 0.943069i | \(-0.607925\pi\) | ||||
−0.332597 | + | 0.943069i | \(0.607925\pi\) | |||||||
\(402\) | −4.52004 | − | 4.52004i | −0.225439 | − | 0.225439i | ||||
\(403\) | 20.9222 | + | 20.9222i | 1.04221 | + | 1.04221i | ||||
\(404\) | 6.53590 | 0.325173 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.4641 | − | 13.3923i | −0.767470 | − | 0.664649i | ||||
\(407\) | −26.7685 | + | 26.7685i | −1.32687 | + | 1.32687i | ||||
\(408\) | −3.53553 | − | 3.53553i | −0.175035 | − | 0.175035i | ||||
\(409\) | −20.3923 | −1.00833 | −0.504167 | − | 0.863606i | \(-0.668201\pi\) | ||||
−0.504167 | + | 0.863606i | \(0.668201\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 7.85641i | − | 0.387528i | ||||||
\(412\) | −2.91636 | − | 2.91636i | −0.143679 | − | 0.143679i | ||||
\(413\) | −18.9903 | + | 1.36345i | −0.934454 | + | 0.0670908i | ||||
\(414\) | − | 1.00000i | − | 0.0491473i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.73205i | 0.182979i | ||||||||
\(417\) | 14.0406 | − | 14.0406i | 0.687571 | − | 0.687571i | ||||
\(418\) | 28.8391 | − | 28.8391i | 1.41057 | − | 1.41057i | ||||
\(419\) | −17.3397 | −0.847102 | −0.423551 | − | 0.905872i | \(-0.639217\pi\) | ||||
−0.423551 | + | 0.905872i | \(0.639217\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.3205 | −1.42899 | −0.714497 | − | 0.699638i | \(-0.753344\pi\) | ||||
−0.714497 | + | 0.699638i | \(0.753344\pi\) | |||||||
\(422\) | 7.29770 | − | 7.29770i | 0.355247 | − | 0.355247i | ||||
\(423\) | −5.93426 | + | 5.93426i | −0.288533 | + | 0.288533i | ||||
\(424\) | − | 3.53590i | − | 0.171718i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 11.4641i | 0.555438i | ||||||||
\(427\) | 0.466870 | + | 6.50266i | 0.0225934 | + | 0.314686i | ||||
\(428\) | 6.31319 | + | 6.31319i | 0.305160 | + | 0.305160i | ||||
\(429\) | 20.3923i | 0.984550i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.80385 | −0.327730 | −0.163865 | − | 0.986483i | \(-0.552396\pi\) | ||||
−0.163865 | + | 0.986483i | \(0.552396\pi\) | |||||||
\(432\) | −0.707107 | − | 0.707107i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | 0.378937 | − | 0.378937i | 0.0182106 | − | 0.0182106i | −0.697943 | − | 0.716153i | \(-0.745901\pi\) |
0.716153 | + | 0.697943i | \(0.245901\pi\) | |||||||
\(434\) | −15.8564 | − | 13.7321i | −0.761132 | − | 0.659160i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12.3923 | 0.593484 | ||||||||
\(437\) | −5.27792 | − | 5.27792i | −0.252477 | − | 0.252477i | ||||
\(438\) | −8.76268 | − | 8.76268i | −0.418697 | − | 0.418697i | ||||
\(439\) | 39.7846 | 1.89882 | 0.949408 | − | 0.314046i | \(-0.101684\pi\) | ||||
0.949408 | + | 0.314046i | \(0.101684\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00000 | − | 6.92820i | −0.0476190 | − | 0.329914i | ||||
\(442\) | 13.1948 | − | 13.1948i | 0.627612 | − | 0.627612i | ||||
\(443\) | −7.24693 | − | 7.24693i | −0.344312 | − | 0.344312i | 0.513674 | − | 0.857986i | \(-0.328284\pi\) |
−0.857986 | + | 0.513674i | \(0.828284\pi\) | |||||||
\(444\) | 6.92820 | 0.328798 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 11.5885i | − | 0.548729i | ||||||
\(447\) | −5.46739 | − | 5.46739i | −0.258598 | − | 0.258598i | ||||
\(448\) | −0.189469 | − | 2.63896i | −0.00895155 | − | 0.124679i | ||||
\(449\) | 30.7846i | 1.45282i | 0.687264 | + | 0.726408i | \(0.258812\pi\) | ||||
−0.687264 | + | 0.726408i | \(0.741188\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 31.3205i | − | 1.47483i | ||||||
\(452\) | −1.79315 | + | 1.79315i | −0.0843427 | + | 0.0843427i | ||||
\(453\) | −11.3137 | + | 11.3137i | −0.531564 | + | 0.531564i | ||||
\(454\) | 1.39230 | 0.0653441 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.46410 | −0.349539 | ||||||||
\(457\) | 16.1248 | − | 16.1248i | 0.754284 | − | 0.754284i | −0.220991 | − | 0.975276i | \(-0.570929\pi\) |
0.975276 | + | 0.220991i | \(0.0709293\pi\) | |||||||
\(458\) | −10.6574 | + | 10.6574i | −0.497986 | + | 0.497986i | ||||
\(459\) | 5.00000i | 0.233380i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.6077i | 0.540624i | 0.962773 | + | 0.270312i | \(0.0871269\pi\) | ||||
−0.962773 | + | 0.270312i | \(0.912873\pi\) | |||||||
\(462\) | −1.03528 | − | 14.4195i | −0.0481654 | − | 0.670858i | ||||
\(463\) | −15.0759 | − | 15.0759i | −0.700635 | − | 0.700635i | 0.263912 | − | 0.964547i | \(-0.414987\pi\) |
−0.964547 | + | 0.263912i | \(0.914987\pi\) | |||||||
\(464\) | 7.73205i | 0.358951i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.3923 | 0.481414 | ||||||||
\(467\) | 15.2282 | + | 15.2282i | 0.704676 | + | 0.704676i | 0.965411 | − | 0.260734i | \(-0.0839647\pi\) |
−0.260734 | + | 0.965411i | \(0.583965\pi\) | |||||||
\(468\) | 2.63896 | − | 2.63896i | 0.121986 | − | 0.121986i | ||||
\(469\) | −11.0718 | + | 12.7846i | −0.511248 | + | 0.590338i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.00000 | 0.368621 | ||||||||
\(472\) | 5.08845 | + | 5.08845i | 0.234215 | + | 0.234215i | ||||
\(473\) | 14.4195 | + | 14.4195i | 0.663011 | + | 0.663011i | ||||
\(474\) | −12.3923 | −0.569197 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.66025 | + | 10.0000i | −0.396942 | + | 0.458349i | ||||
\(477\) | −2.50026 | + | 2.50026i | −0.114479 | + | 0.114479i | ||||
\(478\) | −6.03579 | − | 6.03579i | −0.276071 | − | 0.276071i | ||||
\(479\) | −0.928203 | −0.0424107 | −0.0212053 | − | 0.999775i | \(-0.506750\pi\) | ||||
−0.0212053 | + | 0.999775i | \(0.506750\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.8564i | 1.17895i | ||||||||
\(482\) | 0.656339 | + | 0.656339i | 0.0298954 | + | 0.0298954i | ||||
\(483\) | −2.63896 | + | 0.189469i | −0.120077 | + | 0.00862112i | ||||
\(484\) | − | 18.8564i | − | 0.857109i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | −26.8701 | + | 26.8701i | −1.21760 | + | 1.21760i | −0.249128 | + | 0.968471i | \(0.580144\pi\) |
−0.968471 | + | 0.249128i | \(0.919856\pi\) | |||||||
\(488\) | 1.74238 | − | 1.74238i | 0.0788740 | − | 0.0788740i | ||||
\(489\) | −0.803848 | −0.0363512 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.32051 | 0.420629 | 0.210314 | − | 0.977634i | \(-0.432551\pi\) | ||||
0.210314 | + | 0.977634i | \(0.432551\pi\) | |||||||
\(492\) | −4.05317 | + | 4.05317i | −0.182731 | + | 0.182731i | ||||
\(493\) | 27.3369 | − | 27.3369i | 1.23119 | − | 1.23119i | ||||
\(494\) | − | 27.8564i | − | 1.25332i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.92820i | 0.355987i | ||||||||
\(497\) | 30.2533 | − | 2.17209i | 1.35705 | − | 0.0974315i | ||||
\(498\) | 0.328169 | + | 0.328169i | 0.0147056 | + | 0.0147056i | ||||
\(499\) | 3.39230i | 0.151860i | 0.997113 | + | 0.0759302i | \(0.0241926\pi\) | ||||
−0.997113 | + | 0.0759302i | \(0.975807\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.4641 | 0.690885 | ||||||||
\(502\) | 14.3316 | + | 14.3316i | 0.639651 | + | 0.639651i | ||||
\(503\) | −20.0764 | + | 20.0764i | −0.895162 | + | 0.895162i | −0.995003 | − | 0.0998413i | \(-0.968166\pi\) |
0.0998413 | + | 0.995003i | \(0.468166\pi\) | |||||||
\(504\) | −1.73205 | + | 2.00000i | −0.0771517 | + | 0.0890871i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.46410 | −0.242909 | ||||||||
\(507\) | 0.656339 | + | 0.656339i | 0.0291490 | + | 0.0291490i | ||||
\(508\) | −5.27792 | − | 5.27792i | −0.234170 | − | 0.234170i | ||||
\(509\) | 19.8564 | 0.880120 | 0.440060 | − | 0.897968i | \(-0.354957\pi\) | ||||
0.440060 | + | 0.897968i | \(0.354957\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −21.4641 | + | 24.7846i | −0.949516 | + | 1.09641i | ||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 5.27792 | + | 5.27792i | 0.233026 | + | 0.233026i | ||||
\(514\) | 23.9282 | 1.05543 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 3.73205i | − | 0.164294i | ||||||
\(517\) | 32.4254 | + | 32.4254i | 1.42607 | + | 1.42607i | ||||
\(518\) | −1.31268 | − | 18.2832i | −0.0576757 | − | 0.803319i | ||||
\(519\) | 9.32051i | 0.409125i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 11.5885i | − | 0.507700i | −0.967244 | − | 0.253850i | \(-0.918303\pi\) | ||
0.967244 | − | 0.253850i | \(-0.0816969\pi\) | |||||||
\(522\) | 5.46739 | − | 5.46739i | 0.239301 | − | 0.239301i | ||||
\(523\) | −22.9048 | + | 22.9048i | −1.00156 | + | 1.00156i | −0.00155899 | + | 0.999999i | \(0.500496\pi\) |
−0.999999 | + | 0.00155899i | \(0.999504\pi\) | |||||||
\(524\) | 14.3923 | 0.628731 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.00000 | −0.305215 | ||||||||
\(527\) | 28.0304 | − | 28.0304i | 1.22102 | − | 1.22102i | ||||
\(528\) | −3.86370 | + | 3.86370i | −0.168146 | + | 0.168146i | ||||
\(529\) | − | 22.0000i | − | 0.956522i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 7.19615i | − | 0.312286i | ||||||
\(532\) | 1.41421 | + | 19.6975i | 0.0613139 | + | 0.853993i | ||||
\(533\) | −15.1266 | − | 15.1266i | −0.655208 | − | 0.655208i | ||||
\(534\) | − | 12.0000i | − | 0.519291i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.39230 | 0.276106 | ||||||||
\(537\) | 9.79796 | + | 9.79796i | 0.422813 | + | 0.422813i | ||||
\(538\) | 15.4548 | − | 15.4548i | 0.666304 | − | 0.666304i | ||||
\(539\) | −37.8564 | + | 5.46410i | −1.63059 | + | 0.235356i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.32051 | 0.228747 | 0.114373 | − | 0.993438i | \(-0.463514\pi\) | ||||
0.114373 | + | 0.993438i | \(0.463514\pi\) | |||||||
\(542\) | −2.07055 | − | 2.07055i | −0.0889378 | − | 0.0889378i | ||||
\(543\) | 1.41421 | + | 1.41421i | 0.0606897 | + | 0.0606897i | ||||
\(544\) | 5.00000 | 0.214373 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −7.46410 | − | 6.46410i | −0.319434 | − | 0.276638i | ||||
\(547\) | 28.0948 | − | 28.0948i | 1.20125 | − | 1.20125i | 0.227459 | − | 0.973788i | \(-0.426958\pi\) |
0.973788 | − | 0.227459i | \(-0.0730419\pi\) | |||||||
\(548\) | 5.55532 | + | 5.55532i | 0.237311 | + | 0.237311i | ||||
\(549\) | −2.46410 | −0.105165 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 57.7128i | − | 2.45865i | ||||||
\(552\) | 0.707107 | + | 0.707107i | 0.0300965 | + | 0.0300965i | ||||
\(553\) | 2.34795 | + | 32.7028i | 0.0998452 | + | 1.39066i | ||||
\(554\) | 8.39230i | 0.356555i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 19.8564i | 0.842099i | ||||||||
\(557\) | 11.4152 | − | 11.4152i | 0.483679 | − | 0.483679i | −0.422625 | − | 0.906305i | \(-0.638891\pi\) |
0.906305 | + | 0.422625i | \(0.138891\pi\) | |||||||
\(558\) | 5.60609 | − | 5.60609i | 0.237325 | − | 0.237325i | ||||
\(559\) | 13.9282 | 0.589100 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 27.3205 | 1.15347 | ||||||||
\(562\) | −9.79796 | + | 9.79796i | −0.413302 | + | 0.413302i | ||||
\(563\) | 24.3698 | − | 24.3698i | 1.02706 | − | 1.02706i | 0.0274412 | − | 0.999623i | \(-0.491264\pi\) |
0.999623 | − | 0.0274412i | \(-0.00873590\pi\) | |||||||
\(564\) | − | 8.39230i | − | 0.353380i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 22.7846i | − | 0.957709i | ||||||
\(567\) | 2.63896 | − | 0.189469i | 0.110826 | − | 0.00795694i | ||||
\(568\) | −8.10634 | − | 8.10634i | −0.340135 | − | 0.340135i | ||||
\(569\) | − | 11.6077i | − | 0.486620i | −0.969949 | − | 0.243310i | \(-0.921767\pi\) | ||
0.969949 | − | 0.243310i | \(-0.0782332\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −42.4641 | −1.77707 | −0.888534 | − | 0.458811i | \(-0.848275\pi\) | ||||
−0.888534 | + | 0.458811i | \(0.848275\pi\) | |||||||
\(572\) | −14.4195 | − | 14.4195i | −0.602911 | − | 0.602911i | ||||
\(573\) | −4.43211 | + | 4.43211i | −0.185154 | + | 0.185154i | ||||
\(574\) | 11.4641 | + | 9.92820i | 0.478502 | + | 0.414395i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 16.5916 | + | 16.5916i | 0.690718 | + | 0.690718i | 0.962390 | − | 0.271672i | \(-0.0875765\pi\) |
−0.271672 | + | 0.962390i | \(0.587576\pi\) | |||||||
\(578\) | −5.65685 | − | 5.65685i | −0.235294 | − | 0.235294i | ||||
\(579\) | 17.8564 | 0.742087 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.803848 | − | 0.928203i | 0.0333492 | − | 0.0385084i | ||||
\(582\) | −2.17209 | + | 2.17209i | −0.0900360 | + | 0.0900360i | ||||
\(583\) | 13.6617 | + | 13.6617i | 0.565808 | + | 0.565808i | ||||
\(584\) | 12.3923 | 0.512797 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 1.85641i | − | 0.0766874i | ||||||
\(587\) | 25.6825 | + | 25.6825i | 1.06003 | + | 1.06003i | 0.998079 | + | 0.0619500i | \(0.0197319\pi\) |
0.0619500 | + | 0.998079i | \(0.480268\pi\) | |||||||
\(588\) | 5.60609 | + | 4.19187i | 0.231191 | + | 0.172870i | ||||
\(589\) | − | 59.1769i | − | 2.43834i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 7.39230i | − | 0.304079i | ||||||
\(592\) | −4.89898 | + | 4.89898i | −0.201347 | + | 0.201347i | ||||
\(593\) | −7.07107 | + | 7.07107i | −0.290374 | + | 0.290374i | −0.837228 | − | 0.546854i | \(-0.815825\pi\) |
0.546854 | + | 0.837228i | \(0.315825\pi\) | |||||||
\(594\) | 5.46410 | 0.224195 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.73205 | 0.316717 | ||||||||
\(597\) | −11.3137 | + | 11.3137i | −0.463039 | + | 0.463039i | ||||
\(598\) | −2.63896 | + | 2.63896i | −0.107915 | + | 0.107915i | ||||
\(599\) | − | 14.5167i | − | 0.593135i | −0.955012 | − | 0.296567i | \(-0.904158\pi\) | ||
0.955012 | − | 0.296567i | \(-0.0958419\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 25.3205i | − | 1.03285i | −0.856334 | − | 0.516423i | \(-0.827263\pi\) | ||
0.856334 | − | 0.516423i | \(-0.172737\pi\) | |||||||
\(602\) | −9.84873 | + | 0.707107i | −0.401404 | + | 0.0288195i | ||||
\(603\) | −4.52004 | − | 4.52004i | −0.184070 | − | 0.184070i | ||||
\(604\) | − | 16.0000i | − | 0.651031i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 6.53590 | 0.265503 | ||||||||
\(607\) | 9.62209 | + | 9.62209i | 0.390549 | + | 0.390549i | 0.874883 | − | 0.484334i | \(-0.160938\pi\) |
−0.484334 | + | 0.874883i | \(0.660938\pi\) | |||||||
\(608\) | 5.27792 | − | 5.27792i | 0.214048 | − | 0.214048i | ||||
\(609\) | −15.4641 | − | 13.3923i | −0.626637 | − | 0.542684i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 31.3205 | 1.26709 | ||||||||
\(612\) | −3.53553 | − | 3.53553i | −0.142915 | − | 0.142915i | ||||
\(613\) | 3.20736 | + | 3.20736i | 0.129544 | + | 0.129544i | 0.768906 | − | 0.639362i | \(-0.220801\pi\) |
−0.639362 | + | 0.768906i | \(0.720801\pi\) | |||||||
\(614\) | 5.07180 | 0.204681 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.9282 | + | 9.46410i | 0.440310 | + | 0.381320i | ||||
\(617\) | 32.2223 | − | 32.2223i | 1.29722 | − | 1.29722i | 0.367000 | − | 0.930221i | \(-0.380385\pi\) |
0.930221 | − | 0.367000i | \(-0.119615\pi\) | |||||||
\(618\) | −2.91636 | − | 2.91636i | −0.117313 | − | 0.117313i | ||||
\(619\) | −10.0000 | −0.401934 | −0.200967 | − | 0.979598i | \(-0.564408\pi\) | ||||
−0.200967 | + | 0.979598i | \(0.564408\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 1.00000i | − | 0.0401286i | ||||||
\(622\) | 18.2832 | + | 18.2832i | 0.733091 | + | 0.733091i | ||||
\(623\) | −31.6675 | + | 2.27362i | −1.26873 | + | 0.0910908i | ||||
\(624\) | 3.73205i | 0.149402i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 30.2487i | 1.20898i | ||||||||
\(627\) | 28.8391 | − | 28.8391i | 1.15172 | − | 1.15172i | ||||
\(628\) | −5.65685 | + | 5.65685i | −0.225733 | + | 0.225733i | ||||
\(629\) | 34.6410 | 1.38123 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.00000 | −0.0796187 | −0.0398094 | − | 0.999207i | \(-0.512675\pi\) | ||||
−0.0398094 | + | 0.999207i | \(0.512675\pi\) | |||||||
\(632\) | 8.76268 | − | 8.76268i | 0.348561 | − | 0.348561i | ||||
\(633\) | 7.29770 | − | 7.29770i | 0.290058 | − | 0.290058i | ||||
\(634\) | 27.3923i | 1.08789i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 3.53590i | − | 0.140207i | ||||||
\(637\) | −15.6443 | + | 20.9222i | −0.619849 | + | 0.828968i | ||||
\(638\) | −29.8744 | − | 29.8744i | −1.18274 | − | 1.18274i | ||||
\(639\) | 11.4641i | 0.453513i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.9282 | −0.589629 | −0.294814 | − | 0.955555i | \(-0.595258\pi\) | ||||
−0.294814 | + | 0.955555i | \(0.595258\pi\) | |||||||
\(642\) | 6.31319 | + | 6.31319i | 0.249162 | + | 0.249162i | ||||
\(643\) | −4.41851 | + | 4.41851i | −0.174249 | + | 0.174249i | −0.788843 | − | 0.614594i | \(-0.789320\pi\) |
0.614594 | + | 0.788843i | \(0.289320\pi\) | |||||||
\(644\) | 1.73205 | − | 2.00000i | 0.0682524 | − | 0.0788110i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −37.3205 | −1.46836 | ||||||||
\(647\) | −27.8038 | − | 27.8038i | −1.09308 | − | 1.09308i | −0.995198 | − | 0.0978821i | \(-0.968793\pi\) |
−0.0978821 | − | 0.995198i | \(-0.531207\pi\) | |||||||
\(648\) | −0.707107 | − | 0.707107i | −0.0277778 | − | 0.0277778i | ||||
\(649\) | −39.3205 | −1.54346 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.8564 | − | 13.7321i | −0.621462 | − | 0.538202i | ||||
\(652\) | 0.568406 | − | 0.568406i | 0.0222605 | − | 0.0222605i | ||||
\(653\) | −16.3142 | − | 16.3142i | −0.638425 | − | 0.638425i | 0.311742 | − | 0.950167i | \(-0.399088\pi\) |
−0.950167 | + | 0.311742i | \(0.899088\pi\) | |||||||
\(654\) | 12.3923 | 0.484577 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 5.73205i | − | 0.223799i | ||||||
\(657\) | −8.76268 | − | 8.76268i | −0.341865 | − | 0.341865i | ||||
\(658\) | −22.1469 | + | 1.59008i | −0.863378 | + | 0.0619877i | ||||
\(659\) | 7.85641i | 0.306042i | 0.988223 | + | 0.153021i | \(0.0489002\pi\) | ||||
−0.988223 | + | 0.153021i | \(0.951100\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 4.92820i | − | 0.191685i | −0.995397 | − | 0.0958424i | \(-0.969446\pi\) | ||
0.995397 | − | 0.0958424i | \(-0.0305545\pi\) | |||||||
\(662\) | 21.4398 | − | 21.4398i | 0.833283 | − | 0.833283i | ||||
\(663\) | 13.1948 | − | 13.1948i | 0.512443 | − | 0.512443i | ||||
\(664\) | −0.464102 | −0.0180106 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.92820 | 0.268462 | ||||||||
\(667\) | −5.46739 | + | 5.46739i | −0.211698 | + | 0.211698i | ||||
\(668\) | −10.9348 | + | 10.9348i | −0.423079 | + | 0.423079i | ||||
\(669\) | − | 11.5885i | − | 0.448036i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.4641i | 0.519776i | ||||||||
\(672\) | −0.189469 | − | 2.63896i | −0.00730891 | − | 0.101800i | ||||
\(673\) | 28.3722 | + | 28.3722i | 1.09367 | + | 1.09367i | 0.995134 | + | 0.0985345i | \(0.0314155\pi\) |
0.0985345 | + | 0.995134i | \(0.468585\pi\) | |||||||
\(674\) | 22.2679i | 0.857729i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.928203 | −0.0357001 | ||||||||
\(677\) | −20.7327 | − | 20.7327i | −0.796824 | − | 0.796824i | 0.185770 | − | 0.982593i | \(-0.440522\pi\) |
−0.982593 | + | 0.185770i | \(0.940522\pi\) | |||||||
\(678\) | −1.79315 | + | 1.79315i | −0.0688655 | + | 0.0688655i | ||||
\(679\) | 6.14359 | + | 5.32051i | 0.235769 | + | 0.204182i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.39230 | 0.0533532 | ||||||||
\(682\) | −30.6322 | − | 30.6322i | −1.17297 | − | 1.17297i | ||||
\(683\) | 24.6980 | + | 24.6980i | 0.945042 | + | 0.945042i | 0.998567 | − | 0.0535250i | \(-0.0170457\pi\) |
−0.0535250 | + | 0.998567i | \(0.517046\pi\) | |||||||
\(684\) | −7.46410 | −0.285397 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 10.0000 | − | 15.5885i | 0.381802 | − | 0.595170i | ||||
\(687\) | −10.6574 | + | 10.6574i | −0.406604 | + | 0.406604i | ||||
\(688\) | 2.63896 | + | 2.63896i | 0.100609 | + | 0.100609i | ||||
\(689\) | 13.1962 | 0.502733 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 51.1769i | 1.94686i | 0.228981 | + | 0.973431i | \(0.426460\pi\) | ||||
−0.228981 | + | 0.973431i | \(0.573540\pi\) | |||||||
\(692\) | −6.59059 | − | 6.59059i | −0.250537 | − | 0.250537i | ||||
\(693\) | −1.03528 | − | 14.4195i | −0.0393269 | − | 0.547753i | ||||
\(694\) | 4.53590i | 0.172180i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7.73205i | 0.293083i | ||||||||
\(697\) | −20.2659 | + | 20.2659i | −0.767624 | + | 0.767624i | ||||
\(698\) | 3.25813 | − | 3.25813i | 0.123322 | − | 0.123322i | ||||
\(699\) | 10.3923 | 0.393073 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.9808 | −0.754663 | −0.377331 | − | 0.926078i | \(-0.623158\pi\) | ||||
−0.377331 | + | 0.926078i | \(0.623158\pi\) | |||||||
\(702\) | 2.63896 | − | 2.63896i | 0.0996011 | − | 0.0996011i | ||||
\(703\) | 36.5665 | − | 36.5665i | 1.37913 | − | 1.37913i | ||||
\(704\) | − | 5.46410i | − | 0.205936i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 12.9282i | − | 0.486559i | ||||||
\(707\) | −1.23835 | − | 17.2480i | −0.0465729 | − | 0.648676i | ||||
\(708\) | 5.08845 | + | 5.08845i | 0.191236 | + | 0.191236i | ||||
\(709\) | 15.0718i | 0.566033i | 0.959115 | + | 0.283017i | \(0.0913352\pi\) | ||||
−0.959115 | + | 0.283017i | \(0.908665\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.3923 | −0.464748 | ||||||||
\(712\) | 8.48528 | + | 8.48528i | 0.317999 | + | 0.317999i | ||||
\(713\) | −5.60609 | + | 5.60609i | −0.209950 | + | 0.209950i | ||||
\(714\) | −8.66025 | + | 10.0000i | −0.324102 | + | 0.374241i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −13.8564 | −0.517838 | ||||||||
\(717\) | −6.03579 | − | 6.03579i | −0.225411 | − | 0.225411i | ||||
\(718\) | 25.5438 | + | 25.5438i | 0.953285 | + | 0.953285i | ||||
\(719\) | 19.3205 | 0.720533 | 0.360267 | − | 0.932849i | \(-0.382686\pi\) | ||||
0.360267 | + | 0.932849i | \(0.382686\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.14359 | + | 8.24871i | −0.266041 | + | 0.307198i | ||||
\(722\) | −25.9599 | + | 25.9599i | −0.966127 | + | 0.966127i | ||||
\(723\) | 0.656339 | + | 0.656339i | 0.0244095 | + | 0.0244095i | ||||
\(724\) | −2.00000 | −0.0743294 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | − | 18.8564i | − | 0.699827i | ||||||
\(727\) | 3.49837 | + | 3.49837i | 0.129747 | + | 0.129747i | 0.768998 | − | 0.639251i | \(-0.220755\pi\) |
−0.639251 | + | 0.768998i | \(0.720755\pi\) | |||||||
\(728\) | 9.84873 | − | 0.707107i | 0.365018 | − | 0.0262071i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 18.6603i | − | 0.690174i | ||||||
\(732\) | 1.74238 | − | 1.74238i | 0.0644003 | − | 0.0644003i | ||||
\(733\) | −0.189469 | + | 0.189469i | −0.00699819 | + | 0.00699819i | −0.710597 | − | 0.703599i | \(-0.751575\pi\) |
0.703599 | + | 0.710597i | \(0.251575\pi\) | |||||||
\(734\) | −10.8038 | −0.398777 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −24.6980 | + | 24.6980i | −0.909761 | + | 0.909761i | ||||
\(738\) | −4.05317 | + | 4.05317i | −0.149199 | + | 0.149199i | ||||
\(739\) | 12.3205i | 0.453217i | 0.973986 | + | 0.226609i | \(0.0727638\pi\) | ||||
−0.973986 | + | 0.226609i | \(0.927236\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 27.8564i | − | 1.02333i | ||||||
\(742\) | −9.33109 | + | 0.669942i | −0.342555 | + | 0.0245943i | ||||
\(743\) | 25.2020 | + | 25.2020i | 0.924572 | + | 0.924572i | 0.997348 | − | 0.0727764i | \(-0.0231860\pi\) |
−0.0727764 | + | 0.997348i | \(0.523186\pi\) | |||||||
\(744\) | 7.92820i | 0.290662i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −15.3205 | −0.560924 | ||||||||
\(747\) | 0.328169 | + | 0.328169i | 0.0120071 | + | 0.0120071i | ||||
\(748\) | −19.3185 | + | 19.3185i | −0.706355 | + | 0.706355i | ||||
\(749\) | 15.4641 | − | 17.8564i | 0.565046 | − | 0.652459i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.1769 | −1.35660 | −0.678302 | − | 0.734783i | \(-0.737284\pi\) | ||||
−0.678302 | + | 0.734783i | \(0.737284\pi\) | |||||||
\(752\) | 5.93426 | + | 5.93426i | 0.216400 | + | 0.216400i | ||||
\(753\) | 14.3316 | + | 14.3316i | 0.522273 | + | 0.522273i | ||||
\(754\) | −28.8564 | −1.05089 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.73205 | + | 2.00000i | −0.0629941 | + | 0.0727393i | ||||
\(757\) | −25.5302 | + | 25.5302i | −0.927910 | + | 0.927910i | −0.997571 | − | 0.0696608i | \(-0.977808\pi\) |
0.0696608 | + | 0.997571i | \(0.477808\pi\) | |||||||
\(758\) | 13.7124 | + | 13.7124i | 0.498058 | + | 0.498058i | ||||
\(759\) | −5.46410 | −0.198334 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.8564i | 0.502294i | 0.967949 | + | 0.251147i | \(0.0808078\pi\) | ||||
−0.967949 | + | 0.251147i | \(0.919192\pi\) | |||||||
\(762\) | −5.27792 | − | 5.27792i | −0.191199 | − | 0.191199i | ||||
\(763\) | −2.34795 | − | 32.7028i | −0.0850016 | − | 1.18392i | ||||
\(764\) | − | 6.26795i | − | 0.226766i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 29.7128i | 1.07357i | ||||||||
\(767\) | −18.9903 | + | 18.9903i | −0.685702 | + | 0.685702i | ||||
\(768\) | −0.707107 | + | 0.707107i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | 15.3205 | 0.552472 | 0.276236 | − | 0.961090i | \(-0.410913\pi\) | ||||
0.276236 | + | 0.961090i | \(0.410913\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.9282 | 0.861753 | ||||||||
\(772\) | −12.6264 | + | 12.6264i | −0.454434 | + | 0.454434i | ||||
\(773\) | 5.37945 | − | 5.37945i | 0.193485 | − | 0.193485i | −0.603715 | − | 0.797200i | \(-0.706313\pi\) |
0.797200 | + | 0.603715i | \(0.206313\pi\) | |||||||
\(774\) | − | 3.73205i | − | 0.134146i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 3.07180i | − | 0.110271i | ||||||
\(777\) | −1.31268 | − | 18.2832i | −0.0470920 | − | 0.655908i | ||||
\(778\) | 19.0411 | + | 19.0411i | 0.682657 | + | 0.682657i | ||||
\(779\) | 42.7846i | 1.53292i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 62.6410 | 2.24147 | ||||||||
\(782\) | 3.53553 | + | 3.53553i | 0.126430 | + | 0.126430i | ||||
\(783\) | 5.46739 | − | 5.46739i | 0.195388 | − | 0.195388i | ||||
\(784\) | −6.92820 | + | 1.00000i | −0.247436 | + | 0.0357143i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 14.3923 | 0.513357 | ||||||||
\(787\) | 13.0053 | + | 13.0053i | 0.463590 | + | 0.463590i | 0.899830 | − | 0.436240i | \(-0.143690\pi\) |
−0.436240 | + | 0.899830i | \(0.643690\pi\) | |||||||
\(788\) | 5.22715 | + | 5.22715i | 0.186209 | + | 0.186209i | ||||
\(789\) | −7.00000 | −0.249207 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.07180 | + | 4.39230i | 0.180332 | + | 0.156172i | ||||
\(792\) | −3.86370 | + | 3.86370i | −0.137291 | + | 0.137291i | ||||
\(793\) | 6.50266 | + | 6.50266i | 0.230916 | + | 0.230916i | ||||
\(794\) | −10.1244 | −0.359300 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 16.0000i | − | 0.567105i | ||||||
\(797\) | −27.8038 | − | 27.8038i | −0.984861 | − | 0.984861i | 0.0150261 | − | 0.999887i | \(-0.495217\pi\) |
−0.999887 | + | 0.0150261i | \(0.995217\pi\) | |||||||
\(798\) | 1.41421 | + | 19.6975i | 0.0500626 | + | 0.697282i | ||||
\(799\) | − | 41.9615i | − | 1.48449i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 12.0000i | − | 0.423999i | ||||||
\(802\) | 9.41902 | − | 9.41902i | 0.332597 | − | 0.332597i | ||||
\(803\) | −47.8802 | + | 47.8802i | −1.68966 | + | 1.68966i | ||||
\(804\) | 6.39230 | 0.225439 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −29.5885 | −1.04221 | ||||||||
\(807\) | 15.4548 | − | 15.4548i | 0.544035 | − | 0.544035i | ||||
\(808\) | −4.62158 | + | 4.62158i | −0.162587 | + | 0.162587i | ||||
\(809\) | − | 2.53590i | − | 0.0891574i | −0.999006 | − | 0.0445787i | \(-0.985805\pi\) | ||
0.999006 | − | 0.0445787i | \(-0.0141946\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 6.53590i | − | 0.229506i | −0.993394 | − | 0.114753i | \(-0.963392\pi\) | ||
0.993394 | − | 0.114753i | \(-0.0366077\pi\) | |||||||
\(812\) | 20.4046 | − | 1.46498i | 0.716060 | − | 0.0514108i | ||||
\(813\) | −2.07055 | − | 2.07055i | −0.0726174 | − | 0.0726174i | ||||
\(814\) | − | 37.8564i | − | 1.32687i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5.00000 | 0.175035 | ||||||||
\(817\) | −19.6975 | − | 19.6975i | −0.689127 | − | 0.689127i | ||||
\(818\) | 14.4195 | − | 14.4195i | 0.504167 | − | 0.504167i | ||||
\(819\) | −7.46410 | − | 6.46410i | −0.260817 | − | 0.225874i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.784610 | −0.0273831 | −0.0136915 | − | 0.999906i | \(-0.504358\pi\) | ||||
−0.0136915 | + | 0.999906i | \(0.504358\pi\) | |||||||
\(822\) | 5.55532 | + | 5.55532i | 0.193764 | + | 0.193764i | ||||
\(823\) | −32.9058 | − | 32.9058i | −1.14703 | − | 1.14703i | −0.987135 | − | 0.159891i | \(-0.948886\pi\) |
−0.159891 | − | 0.987135i | \(-0.551114\pi\) | |||||||
\(824\) | 4.12436 | 0.143679 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.4641 | − | 14.3923i | 0.433682 | − | 0.500772i | ||||
\(827\) | −7.17260 | + | 7.17260i | −0.249416 | + | 0.249416i | −0.820731 | − | 0.571315i | \(-0.806433\pi\) |
0.571315 | + | 0.820731i | \(0.306433\pi\) | |||||||
\(828\) | 0.707107 | + | 0.707107i | 0.0245737 | + | 0.0245737i | ||||
\(829\) | −12.1769 | −0.422922 | −0.211461 | − | 0.977386i | \(-0.567822\pi\) | ||||
−0.211461 | + | 0.977386i | \(0.567822\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.39230i | 0.291126i | ||||||||
\(832\) | −2.63896 | − | 2.63896i | −0.0914894 | − | 0.0914894i | ||||
\(833\) | 28.0304 | + | 20.9594i | 0.971197 | + | 0.726199i | ||||
\(834\) | 19.8564i | 0.687571i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 40.7846i | 1.41057i | ||||||||
\(837\) | 5.60609 | − | 5.60609i | 0.193775 | − | 0.193775i | ||||
\(838\) | 12.2611 | − | 12.2611i | 0.423551 | − | 0.423551i | ||||
\(839\) | 18.6795 | 0.644888 | 0.322444 | − | 0.946589i | \(-0.395496\pi\) | ||||
0.322444 | + | 0.946589i | \(0.395496\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −30.7846 | −1.06154 | ||||||||
\(842\) | 20.7327 | − | 20.7327i | 0.714497 | − | 0.714497i | ||||
\(843\) | −9.79796 | + | 9.79796i | −0.337460 | + | 0.337460i | ||||
\(844\) | 10.3205i | 0.355247i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 8.39230i | − | 0.288533i | ||||||
\(847\) | −49.7613 | + | 3.57270i | −1.70982 | + | 0.122759i | ||||
\(848\) | 2.50026 | + | 2.50026i | 0.0858592 | + | 0.0858592i | ||||
\(849\) | − | 22.7846i | − | 0.781966i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.92820 | −0.237496 | ||||||||
\(852\) | −8.10634 | − | 8.10634i | −0.277719 | − | 0.277719i | ||||
\(853\) | −12.2611 | + | 12.2611i | −0.419810 | + | 0.419810i | −0.885138 | − | 0.465328i | \(-0.845936\pi\) |
0.465328 | + | 0.885138i | \(0.345936\pi\) | |||||||
\(854\) | −4.92820 | − | 4.26795i | −0.168640 | − | 0.146046i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.92820 | −0.305160 | ||||||||
\(857\) | 9.69642 | + | 9.69642i | 0.331224 | + | 0.331224i | 0.853051 | − | 0.521828i | \(-0.174750\pi\) |
−0.521828 | + | 0.853051i | \(0.674750\pi\) | |||||||
\(858\) | −14.4195 | − | 14.4195i | −0.492275 | − | 0.492275i | ||||
\(859\) | 46.6410 | 1.59137 | 0.795685 | − | 0.605710i | \(-0.207111\pi\) | ||||
0.795685 | + | 0.605710i | \(0.207111\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.4641 | + | 9.92820i | 0.390696 | + | 0.338352i | ||||
\(862\) | 4.81105 | − | 4.81105i | 0.163865 | − | 0.163865i | ||||
\(863\) | −31.4644 | − | 31.4644i | −1.07106 | − | 1.07106i | −0.997274 | − | 0.0737877i | \(-0.976491\pi\) |
−0.0737877 | − | 0.997274i | \(-0.523509\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.535898i | 0.0182106i | ||||||||
\(867\) | −5.65685 | − | 5.65685i | −0.192117 | − | 0.192117i | ||||
\(868\) | 20.9222 | − | 1.50215i | 0.710146 | − | 0.0509862i | ||||
\(869\) | 67.7128i | 2.29700i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.8564i | 0.808343i | ||||||||
\(872\) | −8.76268 | + | 8.76268i | −0.296742 | + | 0.296742i | ||||
\(873\) | −2.17209 | + | 2.17209i | −0.0735141 | + | 0.0735141i | ||||
\(874\) | 7.46410 | 0.252477 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.3923 | 0.418697 | ||||||||
\(877\) | 16.9706 | − | 16.9706i | 0.573055 | − | 0.573055i | −0.359926 | − | 0.932981i | \(-0.617198\pi\) |
0.932981 | + | 0.359926i | \(0.117198\pi\) | |||||||
\(878\) | −28.1320 | + | 28.1320i | −0.949408 | + | 0.949408i | ||||
\(879\) | − | 1.85641i | − | 0.0626150i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 6.51666i | − | 0.219552i | −0.993956 | − | 0.109776i | \(-0.964987\pi\) | ||
0.993956 | − | 0.109776i | \(-0.0350133\pi\) | |||||||
\(882\) | 5.60609 | + | 4.19187i | 0.188767 | + | 0.141148i | ||||
\(883\) | 13.5737 | + | 13.5737i | 0.456792 | + | 0.456792i | 0.897601 | − | 0.440809i | \(-0.145308\pi\) |
−0.440809 | + | 0.897601i | \(0.645308\pi\) | |||||||
\(884\) | 18.6603i | 0.627612i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.2487 | 0.344312 | ||||||||
\(887\) | 4.89898 | + | 4.89898i | 0.164492 | + | 0.164492i | 0.784553 | − | 0.620062i | \(-0.212892\pi\) |
−0.620062 | + | 0.784553i | \(0.712892\pi\) | |||||||
\(888\) | −4.89898 | + | 4.89898i | −0.164399 | + | 0.164399i | ||||
\(889\) | −12.9282 | + | 14.9282i | −0.433598 | + | 0.500676i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.46410 | 0.183054 | ||||||||
\(892\) | 8.19428 | + | 8.19428i | 0.274365 | + | 0.274365i | ||||
\(893\) | −44.2939 | − | 44.2939i | −1.48224 | − | 1.48224i | ||||
\(894\) | 7.73205 | 0.258598 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.00000 | + | 1.73205i | 0.0668153 | + | 0.0578638i | ||||
\(897\) | −2.63896 | + | 2.63896i | −0.0881123 | + | 0.0881123i | ||||
\(898\) | −21.7680 | − | 21.7680i | −0.726408 | − | 0.726408i | ||||
\(899\) | −61.3013 | −2.04451 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 17.6795i | − | 0.588989i | ||||||
\(902\) | 22.1469 | + | 22.1469i | 0.737413 | + | 0.737413i | ||||
\(903\) | −9.84873 | + | 0.707107i | −0.327745 | + | 0.0235310i | ||||
\(904\) | − | 2.53590i | − | 0.0843427i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | − | 16.0000i | − | 0.531564i | ||||||
\(907\) | −22.9928 | + | 22.9928i | −0.763462 | + | 0.763462i | −0.976946 | − | 0.213485i | \(-0.931519\pi\) |
0.213485 | + | 0.976946i | \(0.431519\pi\) | |||||||
\(908\) | −0.984508 | + | 0.984508i | −0.0326721 | + | 0.0326721i | ||||
\(909\) | 6.53590 | 0.216782 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.5167 | 0.746010 | 0.373005 | − | 0.927829i | \(-0.378327\pi\) | ||||
0.373005 | + | 0.927829i | \(0.378327\pi\) | |||||||
\(912\) | 5.27792 | − | 5.27792i | 0.174769 | − | 0.174769i | ||||
\(913\) | 1.79315 | − | 1.79315i | 0.0593446 | − | 0.0593446i | ||||
\(914\) | 22.8038i | 0.754284i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 15.0718i | − | 0.497986i | ||||||
\(917\) | −2.72689 | − | 37.9807i | −0.0900499 | − | 1.25423i | ||||
\(918\) | −3.53553 | − | 3.53553i | −0.116690 | − | 0.116690i | ||||
\(919\) | 1.60770i | 0.0530330i | 0.999648 | + | 0.0265165i | \(0.00844145\pi\) | ||||
−0.999648 | + | 0.0265165i | \(0.991559\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.07180 | 0.167121 | ||||||||
\(922\) | −8.20788 | − | 8.20788i | −0.270312 | − | 0.270312i | ||||
\(923\) | 30.2533 | − | 30.2533i | 0.995799 | − | 0.995799i | ||||
\(924\) | 10.9282 | + | 9.46410i | 0.359511 | + | 0.311346i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 21.3205 | 0.700635 | ||||||||
\(927\) | −2.91636 | − | 2.91636i | −0.0957858 | − | 0.0957858i | ||||
\(928\) | −5.46739 | − | 5.46739i | −0.179476 | − | 0.179476i | ||||
\(929\) | −16.9090 | −0.554765 | −0.277383 | − | 0.960760i | \(-0.589467\pi\) | ||||
−0.277383 | + | 0.960760i | \(0.589467\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 51.7128 | − | 7.46410i | 1.69482 | − | 0.244626i | ||||
\(932\) | −7.34847 | + | 7.34847i | −0.240707 | + | 0.240707i | ||||
\(933\) | 18.2832 | + | 18.2832i | 0.598566 | + | 0.598566i | ||||
\(934\) | −21.5359 | −0.704676 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.73205i | 0.121986i | ||||||||
\(937\) | 19.7990 | + | 19.7990i | 0.646805 | + | 0.646805i | 0.952219 | − | 0.305415i | \(-0.0987951\pi\) |
−0.305415 | + | 0.952219i | \(0.598795\pi\) | |||||||
\(938\) | −1.21114 | − | 16.8690i | −0.0395452 | − | 0.550793i | ||||
\(939\) | 30.2487i | 0.987129i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.0718i | 0.426128i | 0.977038 | + | 0.213064i | \(0.0683443\pi\) | ||||
−0.977038 | + | 0.213064i | \(0.931656\pi\) | |||||||
\(942\) | −5.65685 | + | 5.65685i | −0.184310 | + | 0.184310i | ||||
\(943\) | 4.05317 | − | 4.05317i | 0.131989 | − | 0.131989i | ||||
\(944\) | −7.19615 | −0.234215 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −20.3923 | −0.663011 | ||||||||
\(947\) | −42.3992 | + | 42.3992i | −1.37779 | + | 1.37779i | −0.529444 | + | 0.848345i | \(0.677599\pi\) |
−0.848345 | + | 0.529444i | \(0.822401\pi\) | |||||||
\(948\) | 8.76268 | − | 8.76268i | 0.284599 | − | 0.284599i | ||||
\(949\) | 46.2487i | 1.50130i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 27.3923i | 0.888256i | ||||||||
\(952\) | −0.947343 | − | 13.1948i | −0.0307036 | − | 0.427646i | ||||
\(953\) | −31.1127 | − | 31.1127i | −1.00784 | − | 1.00784i | −0.999969 | − | 0.00787013i | \(-0.997495\pi\) |
−0.00787013 | − | 0.999969i | \(-0.502505\pi\) | |||||||
\(954\) | − | 3.53590i | − | 0.114479i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 8.53590 | 0.276071 | ||||||||
\(957\) | −29.8744 | − | 29.8744i | −0.965701 | − | 0.965701i | ||||
\(958\) | 0.656339 | − | 0.656339i | 0.0212053 | − | 0.0212053i | ||||
\(959\) | 13.6077 | − | 15.7128i | 0.439415 | − | 0.507393i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.8564 | −1.02763 | ||||||||
\(962\) | −18.2832 | − | 18.2832i | −0.589475 | − | 0.589475i | ||||
\(963\) | 6.31319 | + | 6.31319i | 0.203440 | + | 0.203440i | ||||
\(964\) | −0.928203 | −0.0298954 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.73205 | − | 2.00000i | 0.0557278 | − | 0.0643489i | ||||
\(967\) | 10.6574 | − | 10.6574i | 0.342718 | − | 0.342718i | −0.514670 | − | 0.857388i | \(-0.672086\pi\) |
0.857388 | + | 0.514670i | \(0.172086\pi\) | |||||||
\(968\) | 13.3335 | + | 13.3335i | 0.428555 | + | 0.428555i | ||||
\(969\) | −37.3205 | −1.19891 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 11.4641i | − | 0.367901i | −0.982936 | − | 0.183950i | \(-0.941111\pi\) | ||
0.982936 | − | 0.183950i | \(-0.0588885\pi\) | |||||||
\(972\) | −0.707107 | − | 0.707107i | −0.0226805 | − | 0.0226805i | ||||
\(973\) | 52.4002 | − | 3.76217i | 1.67987 | − | 0.120610i | ||||
\(974\) | − | 38.0000i | − | 1.21760i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.46410i | 0.0788740i | ||||||||
\(977\) | −23.1822 | + | 23.1822i | −0.741665 | + | 0.741665i | −0.972898 | − | 0.231233i | \(-0.925724\pi\) |
0.231233 | + | 0.972898i | \(0.425724\pi\) | |||||||
\(978\) | 0.568406 | − | 0.568406i | 0.0181756 | − | 0.0181756i | ||||
\(979\) | −65.5692 | −2.09560 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.3923 | 0.395656 | ||||||||
\(982\) | −6.59059 | + | 6.59059i | −0.210314 | + | 0.210314i | ||||
\(983\) | −5.10205 | + | 5.10205i | −0.162730 | + | 0.162730i | −0.783775 | − | 0.621045i | \(-0.786708\pi\) |
0.621045 | + | 0.783775i | \(0.286708\pi\) | |||||||
\(984\) | − | 5.73205i | − | 0.182731i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 38.6603i | 1.23119i | ||||||||
\(987\) | −22.1469 | + | 1.59008i | −0.704945 | + | 0.0506128i | ||||
\(988\) | 19.6975 | + | 19.6975i | 0.626659 | + | 0.626659i | ||||
\(989\) | 3.73205i | 0.118672i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.3205 | 0.486672 | 0.243336 | − | 0.969942i | \(-0.421758\pi\) | ||||
0.243336 | + | 0.969942i | \(0.421758\pi\) | |||||||
\(992\) | −5.60609 | − | 5.60609i | −0.177993 | − | 0.177993i | ||||
\(993\) | 21.4398 | − | 21.4398i | 0.680373 | − | 0.680373i | ||||
\(994\) | −19.8564 | + | 22.9282i | −0.629807 | + | 0.727238i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.464102 | −0.0147056 | ||||||||
\(997\) | −16.9706 | − | 16.9706i | −0.537463 | − | 0.537463i | 0.385320 | − | 0.922783i | \(-0.374091\pi\) |
−0.922783 | + | 0.385320i | \(0.874091\pi\) | |||||||
\(998\) | −2.39872 | − | 2.39872i | −0.0759302 | − | 0.0759302i | ||||
\(999\) | 6.92820 | 0.219199 |
(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 | 1050.2.m.d.643.1 | yes | 8 | |
5.2 | odd | 4 | 1050.2.m.c.307.2 | ✓ | 8 | ||
5.3 | odd | 4 | 1050.2.m.c.307.3 | yes | 8 | ||
5.4 | even | 2 | inner | 1050.2.m.d.643.4 | yes | 8 | |
7.6 | odd | 2 | 1050.2.m.c.643.2 | yes | 8 | ||
35.13 | even | 4 | inner | 1050.2.m.d.307.4 | yes | 8 | |
35.27 | even | 4 | inner | 1050.2.m.d.307.1 | yes | 8 | |
35.34 | odd | 2 | 1050.2.m.c.643.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.2.m.c.307.2 | ✓ | 8 | 5.2 | odd | 4 | ||
1050.2.m.c.307.3 | yes | 8 | 5.3 | odd | 4 | ||
1050.2.m.c.643.2 | yes | 8 | 7.6 | odd | 2 | ||
1050.2.m.c.643.3 | yes | 8 | 35.34 | odd | 2 | ||
1050.2.m.d.307.1 | yes | 8 | 35.27 | even | 4 | inner | |
1050.2.m.d.307.4 | yes | 8 | 35.13 | even | 4 | inner | |
1050.2.m.d.643.1 | yes | 8 | 1.1 | even | 1 | trivial | |
1050.2.m.d.643.4 | yes | 8 | 5.4 | even | 2 | inner |