Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(97,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, 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("1470.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.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: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1273.2 | ||
Root | \(-0.923880 - 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.1273 |
Dual form | 1470.2.m.b.97.2 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 1.00000 | − | 2.00000i | 0.447214 | − | 0.894427i | ||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0.707107 | + | 2.12132i | 0.223607 | + | 0.670820i | ||||
\(11\) | 4.79271 | 1.44506 | 0.722528 | − | 0.691342i | \(-0.242980\pi\) | ||||
0.722528 | + | 0.691342i | \(0.242980\pi\) | |||||||
\(12\) | 0.707107 | + | 0.707107i | 0.204124 | + | 0.204124i | ||||
\(13\) | 4.37849 | − | 4.37849i | 1.21438 | − | 1.21438i | 0.244802 | − | 0.969573i | \(-0.421277\pi\) |
0.969573 | − | 0.244802i | \(-0.0787231\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.707107 | + | 2.12132i | 0.182574 | + | 0.547723i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −1.38896 | − | 1.38896i | −0.336871 | − | 0.336871i | 0.518317 | − | 0.855188i | \(-0.326559\pi\) |
−0.855188 | + | 0.518317i | \(0.826559\pi\) | |||||||
\(18\) | 0.707107 | + | 0.707107i | 0.166667 | + | 0.166667i | ||||
\(19\) | −3.41421 | −0.783274 | −0.391637 | − | 0.920120i | \(-0.628091\pi\) | ||||
−0.391637 | + | 0.920120i | \(0.628091\pi\) | |||||||
\(20\) | −2.00000 | − | 1.00000i | −0.447214 | − | 0.223607i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.38896 | + | 3.38896i | −0.722528 | + | 0.722528i | ||||
\(23\) | −3.00000 | − | 3.00000i | −0.625543 | − | 0.625543i | 0.321400 | − | 0.946943i | \(-0.395847\pi\) |
−0.946943 | + | 0.321400i | \(0.895847\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −3.00000 | − | 4.00000i | −0.600000 | − | 0.800000i | ||||
\(26\) | 6.19212i | 1.21438i | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.42901i | 0.265360i | 0.991159 | + | 0.132680i | \(0.0423583\pi\) | ||||
−0.991159 | + | 0.132680i | \(0.957642\pi\) | |||||||
\(30\) | −2.00000 | − | 1.00000i | −0.365148 | − | 0.182574i | ||||
\(31\) | − | 0.813631i | − | 0.146132i | −0.997327 | − | 0.0730662i | \(-0.976722\pi\) | ||
0.997327 | − | 0.0730662i | \(-0.0232784\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | −3.38896 | + | 3.38896i | −0.589941 | + | 0.589941i | ||||
\(34\) | 1.96428 | 0.336871 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | −6.18166 | + | 6.18166i | −1.01626 | + | 1.01626i | −0.0163933 | + | 0.999866i | \(0.505218\pi\) |
−0.999866 | + | 0.0163933i | \(0.994782\pi\) | |||||||
\(38\) | 2.41421 | − | 2.41421i | 0.391637 | − | 0.391637i | ||||
\(39\) | 6.19212i | 0.991533i | ||||||||
\(40\) | 2.12132 | − | 0.707107i | 0.335410 | − | 0.111803i | ||||
\(41\) | − | 1.92856i | − | 0.301190i | −0.988596 | − | 0.150595i | \(-0.951881\pi\) | ||
0.988596 | − | 0.150595i | \(-0.0481190\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.83889 | + | 5.83889i | 0.890422 | + | 0.890422i | 0.994563 | − | 0.104140i | \(-0.0332091\pi\) |
−0.104140 | + | 0.994563i | \(0.533209\pi\) | |||||||
\(44\) | − | 4.79271i | − | 0.722528i | ||||||
\(45\) | −2.00000 | − | 1.00000i | −0.298142 | − | 0.149071i | ||||
\(46\) | 4.24264 | 0.625543 | ||||||||
\(47\) | −6.59588 | − | 6.59588i | −0.962107 | − | 0.962107i | 0.0372006 | − | 0.999308i | \(-0.488156\pi\) |
−0.999308 | + | 0.0372006i | \(0.988156\pi\) | |||||||
\(48\) | 0.707107 | − | 0.707107i | 0.102062 | − | 0.102062i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.94975 | + | 0.707107i | 0.700000 | + | 0.100000i | ||||
\(51\) | 1.96428 | 0.275054 | ||||||||
\(52\) | −4.37849 | − | 4.37849i | −0.607188 | − | 0.607188i | ||||
\(53\) | −7.91376 | − | 7.91376i | −1.08704 | − | 1.08704i | −0.995832 | − | 0.0912069i | \(-0.970928\pi\) |
−0.0912069 | − | 0.995832i | \(-0.529072\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 4.79271 | − | 9.58541i | 0.646248 | − | 1.29250i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.41421 | − | 2.41421i | 0.319770 | − | 0.319770i | ||||
\(58\) | −1.01046 | − | 1.01046i | −0.132680 | − | 0.132680i | ||||
\(59\) | 5.36370 | 0.698294 | 0.349147 | − | 0.937068i | \(-0.386471\pi\) | ||||
0.349147 | + | 0.937068i | \(0.386471\pi\) | |||||||
\(60\) | 2.12132 | − | 0.707107i | 0.273861 | − | 0.0912871i | ||||
\(61\) | − | 9.58541i | − | 1.22729i | −0.789583 | − | 0.613643i | \(-0.789703\pi\) | ||
0.789583 | − | 0.613643i | \(-0.210297\pi\) | |||||||
\(62\) | 0.575324 | + | 0.575324i | 0.0730662 | + | 0.0730662i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −4.37849 | − | 13.1355i | −0.543085 | − | 1.62926i | ||||
\(66\) | − | 4.79271i | − | 0.589941i | ||||||
\(67\) | −6.36803 | + | 6.36803i | −0.777979 | + | 0.777979i | −0.979487 | − | 0.201508i | \(-0.935416\pi\) |
0.201508 | + | 0.979487i | \(0.435416\pi\) | |||||||
\(68\) | −1.38896 | + | 1.38896i | −0.168436 | + | 0.168436i | ||||
\(69\) | 4.24264 | 0.510754 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.9700 | 1.77662 | 0.888308 | − | 0.459248i | \(-0.151881\pi\) | ||||
0.888308 | + | 0.459248i | \(0.151881\pi\) | |||||||
\(72\) | 0.707107 | − | 0.707107i | 0.0833333 | − | 0.0833333i | ||||
\(73\) | 4.81363 | − | 4.81363i | 0.563393 | − | 0.563393i | −0.366877 | − | 0.930270i | \(-0.619573\pi\) |
0.930270 | + | 0.366877i | \(0.119573\pi\) | |||||||
\(74\) | − | 8.74219i | − | 1.01626i | ||||||
\(75\) | 4.94975 | + | 0.707107i | 0.571548 | + | 0.0816497i | ||||
\(76\) | 3.41421i | 0.391637i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.37849 | − | 4.37849i | −0.495767 | − | 0.495767i | ||||
\(79\) | 1.92856i | 0.216980i | 0.994098 | + | 0.108490i | \(0.0346015\pi\) | ||||
−0.994098 | + | 0.108490i | \(0.965398\pi\) | |||||||
\(80\) | −1.00000 | + | 2.00000i | −0.111803 | + | 0.223607i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 1.36370 | + | 1.36370i | 0.150595 | + | 0.150595i | ||||
\(83\) | 2.51434 | − | 2.51434i | 0.275985 | − | 0.275985i | −0.555519 | − | 0.831504i | \(-0.687480\pi\) |
0.831504 | + | 0.555519i | \(0.187480\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.16687 | + | 1.38896i | −0.451960 | + | 0.150653i | ||||
\(86\) | −8.25744 | −0.890422 | ||||||||
\(87\) | −1.01046 | − | 1.01046i | −0.108333 | − | 0.108333i | ||||
\(88\) | 3.38896 | + | 3.38896i | 0.361264 | + | 0.361264i | ||||
\(89\) | 9.97908 | 1.05778 | 0.528890 | − | 0.848690i | \(-0.322608\pi\) | ||||
0.528890 | + | 0.848690i | \(0.322608\pi\) | |||||||
\(90\) | 2.12132 | − | 0.707107i | 0.223607 | − | 0.0745356i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.00000 | + | 3.00000i | −0.312772 | + | 0.312772i | ||||
\(93\) | 0.575324 | + | 0.575324i | 0.0596583 | + | 0.0596583i | ||||
\(94\) | 9.32798 | 0.962107 | ||||||||
\(95\) | −3.41421 | + | 6.82843i | −0.350291 | + | 0.700582i | ||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | −11.2275 | − | 11.2275i | −1.13998 | − | 1.13998i | −0.988454 | − | 0.151523i | \(-0.951582\pi\) |
−0.151523 | − | 0.988454i | \(-0.548418\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 4.79271i | − | 0.481685i | ||||||
\(100\) | −4.00000 | + | 3.00000i | −0.400000 | + | 0.300000i | ||||
\(101\) | − | 12.9700i | − | 1.29057i | −0.763943 | − | 0.645283i | \(-0.776739\pi\) | ||
0.763943 | − | 0.645283i | \(-0.223261\pi\) | |||||||
\(102\) | −1.38896 | + | 1.38896i | −0.137527 | + | 0.137527i | ||||
\(103\) | −8.82843 | + | 8.82843i | −0.869891 | + | 0.869891i | −0.992460 | − | 0.122569i | \(-0.960887\pi\) |
0.122569 | + | 0.992460i | \(0.460887\pi\) | |||||||
\(104\) | 6.19212 | 0.607188 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.1918 | 1.08704 | ||||||||
\(107\) | 9.62113 | − | 9.62113i | 0.930110 | − | 0.930110i | −0.0676023 | − | 0.997712i | \(-0.521535\pi\) |
0.997712 | + | 0.0676023i | \(0.0215349\pi\) | |||||||
\(108\) | 0.707107 | − | 0.707107i | 0.0680414 | − | 0.0680414i | ||||
\(109\) | 14.4348i | 1.38260i | 0.722568 | + | 0.691300i | \(0.242962\pi\) | ||||
−0.722568 | + | 0.691300i | \(0.757038\pi\) | |||||||
\(110\) | 3.38896 | + | 10.1669i | 0.323124 | + | 0.969373i | ||||
\(111\) | − | 8.74219i | − | 0.829772i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.0209247 | − | 0.0209247i | −0.00196843 | − | 0.00196843i | 0.706122 | − | 0.708090i | \(-0.250443\pi\) |
−0.708090 | + | 0.706122i | \(0.750443\pi\) | |||||||
\(114\) | 3.41421i | 0.319770i | ||||||||
\(115\) | −9.00000 | + | 3.00000i | −0.839254 | + | 0.279751i | ||||
\(116\) | 1.42901 | 0.132680 | ||||||||
\(117\) | −4.37849 | − | 4.37849i | −0.404792 | − | 0.404792i | ||||
\(118\) | −3.79271 | + | 3.79271i | −0.349147 | + | 0.349147i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.00000 | + | 2.00000i | −0.0912871 | + | 0.182574i | ||||
\(121\) | 11.9700 | 1.08818 | ||||||||
\(122\) | 6.77791 | + | 6.77791i | 0.613643 | + | 0.613643i | ||||
\(123\) | 1.36370 | + | 1.36370i | 0.122960 | + | 0.122960i | ||||
\(124\) | −0.813631 | −0.0730662 | ||||||||
\(125\) | −11.0000 | + | 2.00000i | −0.983870 | + | 0.178885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.97003 | + | 8.97003i | −0.795962 | + | 0.795962i | −0.982456 | − | 0.186494i | \(-0.940287\pi\) |
0.186494 | + | 0.982456i | \(0.440287\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | −8.25744 | −0.727027 | ||||||||
\(130\) | 12.3842 | + | 6.19212i | 1.08617 | + | 0.543085i | ||||
\(131\) | 0.293157i | 0.0256133i | 0.999918 | + | 0.0128066i | \(0.00407659\pi\) | ||||
−0.999918 | + | 0.0128066i | \(0.995923\pi\) | |||||||
\(132\) | 3.38896 | + | 3.38896i | 0.294971 | + | 0.294971i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 9.00575i | − | 0.777979i | ||||||
\(135\) | 2.12132 | − | 0.707107i | 0.182574 | − | 0.0608581i | ||||
\(136\) | − | 1.96428i | − | 0.168436i | ||||||
\(137\) | 9.17733 | − | 9.17733i | 0.784072 | − | 0.784072i | −0.196443 | − | 0.980515i | \(-0.562939\pi\) |
0.980515 | + | 0.196443i | \(0.0629391\pi\) | |||||||
\(138\) | −3.00000 | + | 3.00000i | −0.255377 | + | 0.255377i | ||||
\(139\) | 18.6983 | 1.58597 | 0.792986 | − | 0.609240i | \(-0.208525\pi\) | ||||
0.792986 | + | 0.609240i | \(0.208525\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.32798 | 0.785557 | ||||||||
\(142\) | −10.5854 | + | 10.5854i | −0.888308 | + | 0.888308i | ||||
\(143\) | 20.9848 | − | 20.9848i | 1.75484 | − | 1.75484i | ||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | 2.85802 | + | 1.42901i | 0.237346 | + | 0.118673i | ||||
\(146\) | 6.80750i | 0.563393i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.18166 | + | 6.18166i | 0.508129 | + | 0.508129i | ||||
\(149\) | 1.86452i | 0.152748i | 0.997079 | + | 0.0763738i | \(0.0243342\pi\) | ||||
−0.997079 | + | 0.0763738i | \(0.975666\pi\) | |||||||
\(150\) | −4.00000 | + | 3.00000i | −0.326599 | + | 0.244949i | ||||
\(151\) | 8.15027 | 0.663260 | 0.331630 | − | 0.943410i | \(-0.392401\pi\) | ||||
0.331630 | + | 0.943410i | \(0.392401\pi\) | |||||||
\(152\) | −2.41421 | − | 2.41421i | −0.195819 | − | 0.195819i | ||||
\(153\) | −1.38896 | + | 1.38896i | −0.112290 | + | 0.112290i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.62726 | − | 0.813631i | −0.130705 | − | 0.0653524i | ||||
\(156\) | 6.19212 | 0.495767 | ||||||||
\(157\) | 13.0711 | + | 13.0711i | 1.04318 | + | 1.04318i | 0.999024 | + | 0.0441603i | \(0.0140612\pi\) |
0.0441603 | + | 0.999024i | \(0.485939\pi\) | |||||||
\(158\) | −1.36370 | − | 1.36370i | −0.108490 | − | 0.108490i | ||||
\(159\) | 11.1918 | 0.887564 | ||||||||
\(160\) | −0.707107 | − | 2.12132i | −0.0559017 | − | 0.167705i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.707107 | − | 0.707107i | 0.0555556 | − | 0.0555556i | ||||
\(163\) | 3.48909 | + | 3.48909i | 0.273286 | + | 0.273286i | 0.830422 | − | 0.557135i | \(-0.188100\pi\) |
−0.557135 | + | 0.830422i | \(0.688100\pi\) | |||||||
\(164\) | −1.92856 | −0.150595 | ||||||||
\(165\) | 3.38896 | + | 10.1669i | 0.263830 | + | 0.791489i | ||||
\(166\) | 3.55582i | 0.275985i | ||||||||
\(167\) | −12.0754 | − | 12.0754i | −0.934423 | − | 0.934423i | 0.0635557 | − | 0.997978i | \(-0.479756\pi\) |
−0.997978 | + | 0.0635557i | \(0.979756\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 25.3424i | − | 1.94942i | ||||||
\(170\) | 1.96428 | − | 3.92856i | 0.150653 | − | 0.301307i | ||||
\(171\) | 3.41421i | 0.261091i | ||||||||
\(172\) | 5.83889 | − | 5.83889i | 0.445211 | − | 0.445211i | ||||
\(173\) | 11.4638 | − | 11.4638i | 0.871579 | − | 0.871579i | −0.121066 | − | 0.992644i | \(-0.538631\pi\) |
0.992644 | + | 0.121066i | \(0.0386312\pi\) | |||||||
\(174\) | 1.42901 | 0.108333 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.79271 | −0.361264 | ||||||||
\(177\) | −3.79271 | + | 3.79271i | −0.285077 | + | 0.285077i | ||||
\(178\) | −7.05627 | + | 7.05627i | −0.528890 | + | 0.528890i | ||||
\(179\) | − | 15.9845i | − | 1.19473i | −0.801968 | − | 0.597367i | \(-0.796214\pi\) | ||
0.801968 | − | 0.597367i | \(-0.203786\pi\) | |||||||
\(180\) | −1.00000 | + | 2.00000i | −0.0745356 | + | 0.149071i | ||||
\(181\) | 10.3128i | 0.766545i | 0.923635 | + | 0.383272i | \(0.125203\pi\) | ||||
−0.923635 | + | 0.383272i | \(0.874797\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.77791 | + | 6.77791i | 0.501038 | + | 0.501038i | ||||
\(184\) | − | 4.24264i | − | 0.312772i | ||||||
\(185\) | 6.18166 | + | 18.5450i | 0.454485 | + | 1.36345i | ||||
\(186\) | −0.813631 | −0.0596583 | ||||||||
\(187\) | −6.65685 | − | 6.65685i | −0.486797 | − | 0.486797i | ||||
\(188\) | −6.59588 | + | 6.59588i | −0.481054 | + | 0.481054i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.41421 | − | 7.24264i | −0.175145 | − | 0.525436i | ||||
\(191\) | 14.5143 | 1.05022 | 0.525111 | − | 0.851034i | \(-0.324024\pi\) | ||||
0.525111 | + | 0.851034i | \(0.324024\pi\) | |||||||
\(192\) | −0.707107 | − | 0.707107i | −0.0510310 | − | 0.0510310i | ||||
\(193\) | −5.19212 | − | 5.19212i | −0.373737 | − | 0.373737i | 0.495099 | − | 0.868836i | \(-0.335132\pi\) |
−0.868836 | + | 0.495099i | \(0.835132\pi\) | |||||||
\(194\) | 15.8780 | 1.13998 | ||||||||
\(195\) | 12.3842 | + | 6.19212i | 0.886854 | + | 0.443427i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.7775 | + | 11.7775i | −0.839115 | + | 0.839115i | −0.988742 | − | 0.149628i | \(-0.952192\pi\) |
0.149628 | + | 0.988742i | \(0.452192\pi\) | |||||||
\(198\) | 3.38896 | + | 3.38896i | 0.240843 | + | 0.240843i | ||||
\(199\) | −2.12809 | −0.150856 | −0.0754280 | − | 0.997151i | \(-0.524032\pi\) | ||||
−0.0754280 | + | 0.997151i | \(0.524032\pi\) | |||||||
\(200\) | 0.707107 | − | 4.94975i | 0.0500000 | − | 0.350000i | ||||
\(201\) | − | 9.00575i | − | 0.635217i | ||||||
\(202\) | 9.17120 | + | 9.17120i | 0.645283 | + | 0.645283i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 1.96428i | − | 0.137527i | ||||||
\(205\) | −3.85712 | − | 1.92856i | −0.269393 | − | 0.134696i | ||||
\(206\) | − | 12.4853i | − | 0.869891i | ||||||
\(207\) | −3.00000 | + | 3.00000i | −0.208514 | + | 0.208514i | ||||
\(208\) | −4.37849 | + | 4.37849i | −0.303594 | + | 0.303594i | ||||
\(209\) | −16.3633 | −1.13187 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.6655 | −1.07846 | −0.539229 | − | 0.842159i | \(-0.681284\pi\) | ||||
−0.539229 | + | 0.842159i | \(0.681284\pi\) | |||||||
\(212\) | −7.91376 | + | 7.91376i | −0.543519 | + | 0.543519i | ||||
\(213\) | −10.5854 | + | 10.5854i | −0.725301 | + | 0.725301i | ||||
\(214\) | 13.6063i | 0.930110i | ||||||||
\(215\) | 17.5167 | − | 5.83889i | 1.19463 | − | 0.398209i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −10.2069 | − | 10.2069i | −0.691300 | − | 0.691300i | ||||
\(219\) | 6.80750i | 0.460008i | ||||||||
\(220\) | −9.58541 | − | 4.79271i | −0.646248 | − | 0.323124i | ||||
\(221\) | −12.1631 | −0.818176 | ||||||||
\(222\) | 6.18166 | + | 6.18166i | 0.414886 | + | 0.414886i | ||||
\(223\) | 8.76311 | − | 8.76311i | 0.586822 | − | 0.586822i | −0.349948 | − | 0.936769i | \(-0.613801\pi\) |
0.936769 | + | 0.349948i | \(0.113801\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.00000 | + | 3.00000i | −0.266667 | + | 0.200000i | ||||
\(226\) | 0.0295921 | 0.00196843 | ||||||||
\(227\) | 8.29316 | + | 8.29316i | 0.550436 | + | 0.550436i | 0.926567 | − | 0.376131i | \(-0.122746\pi\) |
−0.376131 | + | 0.926567i | \(0.622746\pi\) | |||||||
\(228\) | −2.41421 | − | 2.41421i | −0.159885 | − | 0.159885i | ||||
\(229\) | −19.1001 | −1.26217 | −0.631086 | − | 0.775713i | \(-0.717391\pi\) | ||||
−0.631086 | + | 0.775713i | \(0.717391\pi\) | |||||||
\(230\) | 4.24264 | − | 8.48528i | 0.279751 | − | 0.559503i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.01046 | + | 1.01046i | −0.0663401 | + | 0.0663401i | ||||
\(233\) | 10.5358 | + | 10.5358i | 0.690223 | + | 0.690223i | 0.962281 | − | 0.272058i | \(-0.0877042\pi\) |
−0.272058 | + | 0.962281i | \(0.587704\pi\) | |||||||
\(234\) | 6.19212 | 0.404792 | ||||||||
\(235\) | −19.7876 | + | 6.59588i | −1.29080 | + | 0.430267i | ||||
\(236\) | − | 5.36370i | − | 0.349147i | ||||||
\(237\) | −1.36370 | − | 1.36370i | −0.0885816 | − | 0.0885816i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 8.69833i | − | 0.562648i | −0.959613 | − | 0.281324i | \(-0.909226\pi\) | ||
0.959613 | − | 0.281324i | \(-0.0907736\pi\) | |||||||
\(240\) | −0.707107 | − | 2.12132i | −0.0456435 | − | 0.136931i | ||||
\(241\) | 6.79218i | 0.437523i | 0.975778 | + | 0.218761i | \(0.0702016\pi\) | ||||
−0.975778 | + | 0.218761i | \(0.929798\pi\) | |||||||
\(242\) | −8.46409 | + | 8.46409i | −0.544092 | + | 0.544092i | ||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | −9.58541 | −0.613643 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.92856 | −0.122960 | ||||||||
\(247\) | −14.9491 | + | 14.9491i | −0.951189 | + | 0.951189i | ||||
\(248\) | 0.575324 | − | 0.575324i | 0.0365331 | − | 0.0365331i | ||||
\(249\) | 3.55582i | 0.225341i | ||||||||
\(250\) | 6.36396 | − | 9.19239i | 0.402492 | − | 0.581378i | ||||
\(251\) | 9.34330i | 0.589744i | 0.955537 | + | 0.294872i | \(0.0952770\pi\) | ||||
−0.955537 | + | 0.294872i | \(0.904723\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.3781 | − | 14.3781i | −0.903945 | − | 0.903945i | ||||
\(254\) | − | 12.6855i | − | 0.795962i | ||||||
\(255\) | 1.96428 | − | 3.92856i | 0.123008 | − | 0.246016i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.67546 | + | 3.67546i | 0.229269 | + | 0.229269i | 0.812387 | − | 0.583118i | \(-0.198168\pi\) |
−0.583118 | + | 0.812387i | \(0.698168\pi\) | |||||||
\(258\) | 5.83889 | − | 5.83889i | 0.363513 | − | 0.363513i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −13.1355 | + | 4.37849i | −0.814628 | + | 0.271543i | ||||
\(261\) | 1.42901 | 0.0884535 | ||||||||
\(262\) | −0.207294 | − | 0.207294i | −0.0128066 | − | 0.0128066i | ||||
\(263\) | −8.79846 | − | 8.79846i | −0.542536 | − | 0.542536i | 0.381735 | − | 0.924272i | \(-0.375327\pi\) |
−0.924272 | + | 0.381735i | \(0.875327\pi\) | |||||||
\(264\) | −4.79271 | −0.294971 | ||||||||
\(265\) | −23.7413 | + | 7.91376i | −1.45842 | + | 0.486139i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.05627 | + | 7.05627i | −0.431837 | + | 0.431837i | ||||
\(268\) | 6.36803 | + | 6.36803i | 0.388989 | + | 0.388989i | ||||
\(269\) | −19.8982 | −1.21322 | −0.606608 | − | 0.795001i | \(-0.707470\pi\) | ||||
−0.606608 | + | 0.795001i | \(0.707470\pi\) | |||||||
\(270\) | −1.00000 | + | 2.00000i | −0.0608581 | + | 0.121716i | ||||
\(271\) | 19.6211i | 1.19190i | 0.803022 | + | 0.595949i | \(0.203224\pi\) | ||||
−0.803022 | + | 0.595949i | \(0.796776\pi\) | |||||||
\(272\) | 1.38896 | + | 1.38896i | 0.0842178 | + | 0.0842178i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.9787i | 0.784072i | ||||||||
\(275\) | −14.3781 | − | 19.1708i | −0.867033 | − | 1.15604i | ||||
\(276\) | − | 4.24264i | − | 0.255377i | ||||||
\(277\) | 11.3175 | − | 11.3175i | 0.680003 | − | 0.680003i | −0.279997 | − | 0.960001i | \(-0.590334\pi\) |
0.960001 | + | 0.279997i | \(0.0903336\pi\) | |||||||
\(278\) | −13.2217 | + | 13.2217i | −0.792986 | + | 0.792986i | ||||
\(279\) | −0.813631 | −0.0487108 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.4844 | 0.923721 | 0.461860 | − | 0.886953i | \(-0.347182\pi\) | ||||
0.461860 | + | 0.886953i | \(0.347182\pi\) | |||||||
\(282\) | −6.59588 | + | 6.59588i | −0.392779 | + | 0.392779i | ||||
\(283\) | 8.68645 | − | 8.68645i | 0.516356 | − | 0.516356i | −0.400111 | − | 0.916467i | \(-0.631028\pi\) |
0.916467 | + | 0.400111i | \(0.131028\pi\) | |||||||
\(284\) | − | 14.9700i | − | 0.888308i | ||||||
\(285\) | −2.41421 | − | 7.24264i | −0.143006 | − | 0.429017i | ||||
\(286\) | 29.6770i | 1.75484i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.707107 | − | 0.707107i | −0.0416667 | − | 0.0416667i | ||||
\(289\) | − | 13.1416i | − | 0.773036i | ||||||
\(290\) | −3.03139 | + | 1.01046i | −0.178009 | + | 0.0593364i | ||||
\(291\) | 15.8780 | 0.930787 | ||||||||
\(292\) | −4.81363 | − | 4.81363i | −0.281696 | − | 0.281696i | ||||
\(293\) | −21.7981 | + | 21.7981i | −1.27346 | + | 1.27346i | −0.329196 | + | 0.944261i | \(0.606778\pi\) |
−0.944261 | + | 0.329196i | \(0.893222\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.36370 | − | 10.7274i | 0.312286 | − | 0.624573i | ||||
\(296\) | −8.74219 | −0.508129 | ||||||||
\(297\) | 3.38896 | + | 3.38896i | 0.196647 | + | 0.196647i | ||||
\(298\) | −1.31842 | − | 1.31842i | −0.0763738 | − | 0.0763738i | ||||
\(299\) | −26.2710 | −1.51929 | ||||||||
\(300\) | 0.707107 | − | 4.94975i | 0.0408248 | − | 0.285774i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5.76311 | + | 5.76311i | −0.331630 | + | 0.331630i | ||||
\(303\) | 9.17120 | + | 9.17120i | 0.526872 | + | 0.526872i | ||||
\(304\) | 3.41421 | 0.195819 | ||||||||
\(305\) | −19.1708 | − | 9.58541i | −1.09772 | − | 0.548859i | ||||
\(306\) | − | 1.96428i | − | 0.112290i | ||||||
\(307\) | 3.10013 | + | 3.10013i | 0.176934 | + | 0.176934i | 0.790018 | − | 0.613084i | \(-0.210071\pi\) |
−0.613084 | + | 0.790018i | \(0.710071\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 12.4853i | − | 0.710263i | ||||||
\(310\) | 1.72597 | − | 0.575324i | 0.0980286 | − | 0.0326762i | ||||
\(311\) | 26.7180i | 1.51504i | 0.652813 | + | 0.757519i | \(0.273589\pi\) | ||||
−0.652813 | + | 0.757519i | \(0.726411\pi\) | |||||||
\(312\) | −4.37849 | + | 4.37849i | −0.247883 | + | 0.247883i | ||||
\(313\) | −3.39329 | + | 3.39329i | −0.191800 | + | 0.191800i | −0.796473 | − | 0.604673i | \(-0.793304\pi\) |
0.604673 | + | 0.796473i | \(0.293304\pi\) | |||||||
\(314\) | −18.4853 | −1.04318 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.92856 | 0.108490 | ||||||||
\(317\) | −19.3839 | + | 19.3839i | −1.08871 | + | 1.08871i | −0.0930449 | + | 0.995662i | \(0.529660\pi\) |
−0.995662 | + | 0.0930449i | \(0.970340\pi\) | |||||||
\(318\) | −7.91376 | + | 7.91376i | −0.443782 | + | 0.443782i | ||||
\(319\) | 6.84882i | 0.383460i | ||||||||
\(320\) | 2.00000 | + | 1.00000i | 0.111803 | + | 0.0559017i | ||||
\(321\) | 13.6063i | 0.759432i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.74219 | + | 4.74219i | 0.263862 | + | 0.263862i | ||||
\(324\) | 1.00000i | 0.0555556i | ||||||||
\(325\) | −30.6494 | − | 4.37849i | −1.70013 | − | 0.242875i | ||||
\(326\) | −4.93431 | −0.273286 | ||||||||
\(327\) | −10.2069 | − | 10.2069i | −0.564444 | − | 0.564444i | ||||
\(328\) | 1.36370 | − | 1.36370i | 0.0752976 | − | 0.0752976i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −9.58541 | − | 4.79271i | −0.527660 | − | 0.263830i | ||||
\(331\) | 33.6770 | 1.85106 | 0.925529 | − | 0.378678i | \(-0.123621\pi\) | ||||
0.925529 | + | 0.378678i | \(0.123621\pi\) | |||||||
\(332\) | −2.51434 | − | 2.51434i | −0.137993 | − | 0.137993i | ||||
\(333\) | 6.18166 | + | 6.18166i | 0.338753 | + | 0.338753i | ||||
\(334\) | 17.0772 | 0.934423 | ||||||||
\(335\) | 6.36803 | + | 19.1041i | 0.347923 | + | 1.04377i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.12158 | − | 6.12158i | 0.333464 | − | 0.333464i | −0.520436 | − | 0.853900i | \(-0.674231\pi\) |
0.853900 | + | 0.520436i | \(0.174231\pi\) | |||||||
\(338\) | 17.9198 | + | 17.9198i | 0.974708 | + | 0.974708i | ||||
\(339\) | 0.0295921 | 0.00160722 | ||||||||
\(340\) | 1.38896 | + | 4.16687i | 0.0753267 | + | 0.225980i | ||||
\(341\) | − | 3.89949i | − | 0.211169i | ||||||
\(342\) | −2.41421 | − | 2.41421i | −0.130546 | − | 0.130546i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 8.25744i | 0.445211i | ||||||||
\(345\) | 4.24264 | − | 8.48528i | 0.228416 | − | 0.456832i | ||||
\(346\) | 16.2123i | 0.871579i | ||||||||
\(347\) | 11.1622 | − | 11.1622i | 0.599216 | − | 0.599216i | −0.340888 | − | 0.940104i | \(-0.610728\pi\) |
0.940104 | + | 0.340888i | \(0.110728\pi\) | |||||||
\(348\) | −1.01046 | + | 1.01046i | −0.0541665 | + | 0.0541665i | ||||
\(349\) | 4.58631 | 0.245500 | 0.122750 | − | 0.992438i | \(-0.460829\pi\) | ||||
0.122750 | + | 0.992438i | \(0.460829\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.19212 | 0.330511 | ||||||||
\(352\) | 3.38896 | − | 3.38896i | 0.180632 | − | 0.180632i | ||||
\(353\) | −10.6016 | + | 10.6016i | −0.564268 | + | 0.564268i | −0.930517 | − | 0.366249i | \(-0.880642\pi\) |
0.366249 | + | 0.930517i | \(0.380642\pi\) | |||||||
\(354\) | − | 5.36370i | − | 0.285077i | ||||||
\(355\) | 14.9700 | − | 29.9401i | 0.794527 | − | 1.58905i | ||||
\(356\) | − | 9.97908i | − | 0.528890i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.3027 | + | 11.3027i | 0.597367 | + | 0.597367i | ||||
\(359\) | − | 25.4553i | − | 1.34348i | −0.740787 | − | 0.671740i | \(-0.765547\pi\) | ||
0.740787 | − | 0.671740i | \(-0.234453\pi\) | |||||||
\(360\) | −0.707107 | − | 2.12132i | −0.0372678 | − | 0.111803i | ||||
\(361\) | −7.34315 | −0.386481 | ||||||||
\(362\) | −7.29226 | − | 7.29226i | −0.383272 | − | 0.383272i | ||||
\(363\) | −8.46409 | + | 8.46409i | −0.444250 | + | 0.444250i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.81363 | − | 14.4409i | −0.251957 | − | 0.755871i | ||||
\(366\) | −9.58541 | −0.501038 | ||||||||
\(367\) | −3.27799 | − | 3.27799i | −0.171110 | − | 0.171110i | 0.616357 | − | 0.787467i | \(-0.288608\pi\) |
−0.787467 | + | 0.616357i | \(0.788608\pi\) | |||||||
\(368\) | 3.00000 | + | 3.00000i | 0.156386 | + | 0.156386i | ||||
\(369\) | −1.92856 | −0.100397 | ||||||||
\(370\) | −17.4844 | − | 8.74219i | −0.908970 | − | 0.454485i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.575324 | − | 0.575324i | 0.0298292 | − | 0.0298292i | ||||
\(373\) | 16.9596 | + | 16.9596i | 0.878133 | + | 0.878133i | 0.993341 | − | 0.115208i | \(-0.0367535\pi\) |
−0.115208 | + | 0.993341i | \(0.536753\pi\) | |||||||
\(374\) | 9.41421 | 0.486797 | ||||||||
\(375\) | 6.36396 | − | 9.19239i | 0.328634 | − | 0.474693i | ||||
\(376\) | − | 9.32798i | − | 0.481054i | ||||||
\(377\) | 6.25691 | + | 6.25691i | 0.322247 | + | 0.322247i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.7788i | 0.810503i | 0.914205 | + | 0.405252i | \(0.132816\pi\) | ||||
−0.914205 | + | 0.405252i | \(0.867184\pi\) | |||||||
\(380\) | 6.82843 | + | 3.41421i | 0.350291 | + | 0.175145i | ||||
\(381\) | − | 12.6855i | − | 0.649900i | ||||||
\(382\) | −10.2632 | + | 10.2632i | −0.525111 | + | 0.525111i | ||||
\(383\) | −7.68174 | + | 7.68174i | −0.392519 | + | 0.392519i | −0.875584 | − | 0.483066i | \(-0.839523\pi\) |
0.483066 | + | 0.875584i | \(0.339523\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.34277 | 0.373737 | ||||||||
\(387\) | 5.83889 | − | 5.83889i | 0.296807 | − | 0.296807i | ||||
\(388\) | −11.2275 | + | 11.2275i | −0.569988 | + | 0.569988i | ||||
\(389\) | − | 11.0657i | − | 0.561053i | −0.959846 | − | 0.280526i | \(-0.909491\pi\) | ||
0.959846 | − | 0.280526i | \(-0.0905090\pi\) | |||||||
\(390\) | −13.1355 | + | 4.37849i | −0.665141 | + | 0.221714i | ||||
\(391\) | 8.33373i | 0.421455i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.207294 | − | 0.207294i | −0.0104566 | − | 0.0104566i | ||||
\(394\) | − | 16.6560i | − | 0.839115i | ||||||
\(395\) | 3.85712 | + | 1.92856i | 0.194073 | + | 0.0970363i | ||||
\(396\) | −4.79271 | −0.240843 | ||||||||
\(397\) | 2.24264 | + | 2.24264i | 0.112555 | + | 0.112555i | 0.761141 | − | 0.648586i | \(-0.224639\pi\) |
−0.648586 | + | 0.761141i | \(0.724639\pi\) | |||||||
\(398\) | 1.50478 | − | 1.50478i | 0.0754280 | − | 0.0754280i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | + | 4.00000i | 0.150000 | + | 0.200000i | ||||
\(401\) | 30.3121 | 1.51371 | 0.756856 | − | 0.653582i | \(-0.226734\pi\) | ||||
0.756856 | + | 0.653582i | \(0.226734\pi\) | |||||||
\(402\) | 6.36803 | + | 6.36803i | 0.317608 | + | 0.317608i | ||||
\(403\) | −3.56248 | − | 3.56248i | −0.177460 | − | 0.177460i | ||||
\(404\) | −12.9700 | −0.645283 | ||||||||
\(405\) | −1.00000 | + | 2.00000i | −0.0496904 | + | 0.0993808i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −29.6269 | + | 29.6269i | −1.46855 | + | 1.46855i | ||||
\(408\) | 1.38896 | + | 1.38896i | 0.0687635 | + | 0.0687635i | ||||
\(409\) | −32.9343 | −1.62850 | −0.814248 | − | 0.580516i | \(-0.802851\pi\) | ||||
−0.814248 | + | 0.580516i | \(0.802851\pi\) | |||||||
\(410\) | 4.09109 | − | 1.36370i | 0.202045 | − | 0.0673482i | ||||
\(411\) | 12.9787i | 0.640192i | ||||||||
\(412\) | 8.82843 | + | 8.82843i | 0.434945 | + | 0.434945i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 4.24264i | − | 0.208514i | ||||||
\(415\) | −2.51434 | − | 7.54303i | −0.123424 | − | 0.370273i | ||||
\(416\) | − | 6.19212i | − | 0.303594i | ||||||
\(417\) | −13.2217 | + | 13.2217i | −0.647470 | + | 0.647470i | ||||
\(418\) | 11.5706 | − | 11.5706i | 0.565937 | − | 0.565937i | ||||
\(419\) | −2.34315 | −0.114470 | −0.0572351 | − | 0.998361i | \(-0.518228\pi\) | ||||
−0.0572351 | + | 0.998361i | \(0.518228\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.5654 | −1.09977 | −0.549885 | − | 0.835240i | \(-0.685328\pi\) | ||||
−0.549885 | + | 0.835240i | \(0.685328\pi\) | |||||||
\(422\) | 11.0772 | − | 11.0772i | 0.539229 | − | 0.539229i | ||||
\(423\) | −6.59588 | + | 6.59588i | −0.320702 | + | 0.320702i | ||||
\(424\) | − | 11.1918i | − | 0.543519i | ||||||
\(425\) | −1.38896 | + | 9.72269i | −0.0673742 | + | 0.471620i | ||||
\(426\) | − | 14.9700i | − | 0.725301i | ||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −9.62113 | − | 9.62113i | −0.465055 | − | 0.465055i | ||||
\(429\) | 29.6770i | 1.43282i | ||||||||
\(430\) | −8.25744 | + | 16.5149i | −0.398209 | + | 0.796418i | ||||
\(431\) | −2.72792 | −0.131399 | −0.0656997 | − | 0.997839i | \(-0.520928\pi\) | ||||
−0.0656997 | + | 0.997839i | \(0.520928\pi\) | |||||||
\(432\) | −0.707107 | − | 0.707107i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | 19.6211 | − | 19.6211i | 0.942931 | − | 0.942931i | −0.0555258 | − | 0.998457i | \(-0.517683\pi\) |
0.998457 | + | 0.0555258i | \(0.0176835\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.03139 | + | 1.01046i | −0.145344 | + | 0.0484480i | ||||
\(436\) | 14.4348 | 0.691300 | ||||||||
\(437\) | 10.2426 | + | 10.2426i | 0.489972 | + | 0.489972i | ||||
\(438\) | −4.81363 | − | 4.81363i | −0.230004 | − | 0.230004i | ||||
\(439\) | 26.8757 | 1.28271 | 0.641353 | − | 0.767246i | \(-0.278374\pi\) | ||||
0.641353 | + | 0.767246i | \(0.278374\pi\) | |||||||
\(440\) | 10.1669 | − | 3.38896i | 0.484686 | − | 0.161562i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.60058 | − | 8.60058i | 0.409088 | − | 0.409088i | ||||
\(443\) | −3.22209 | − | 3.22209i | −0.153086 | − | 0.153086i | 0.626409 | − | 0.779495i | \(-0.284524\pi\) |
−0.779495 | + | 0.626409i | \(0.784524\pi\) | |||||||
\(444\) | −8.74219 | −0.414886 | ||||||||
\(445\) | 9.97908 | − | 19.9582i | 0.473054 | − | 0.946107i | ||||
\(446\) | 12.3929i | 0.586822i | ||||||||
\(447\) | −1.31842 | − | 1.31842i | −0.0623589 | − | 0.0623589i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 5.12972i | − | 0.242087i | −0.992647 | − | 0.121043i | \(-0.961376\pi\) | ||
0.992647 | − | 0.121043i | \(-0.0386240\pi\) | |||||||
\(450\) | 0.707107 | − | 4.94975i | 0.0333333 | − | 0.233333i | ||||
\(451\) | − | 9.24301i | − | 0.435237i | ||||||
\(452\) | −0.0209247 | + | 0.0209247i | −0.000984217 | + | 0.000984217i | ||||
\(453\) | −5.76311 | + | 5.76311i | −0.270775 | + | 0.270775i | ||||
\(454\) | −11.7283 | −0.550436 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.41421 | 0.159885 | ||||||||
\(457\) | −0.908910 | + | 0.908910i | −0.0425170 | + | 0.0425170i | −0.728046 | − | 0.685529i | \(-0.759571\pi\) |
0.685529 | + | 0.728046i | \(0.259571\pi\) | |||||||
\(458\) | 13.5058 | − | 13.5058i | 0.631086 | − | 0.631086i | ||||
\(459\) | − | 1.96428i | − | 0.0916847i | ||||||
\(460\) | 3.00000 | + | 9.00000i | 0.139876 | + | 0.419627i | ||||
\(461\) | − | 18.0830i | − | 0.842207i | −0.907013 | − | 0.421104i | \(-0.861643\pi\) | ||
0.907013 | − | 0.421104i | \(-0.138357\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.20116 | + | 9.20116i | 0.427614 | + | 0.427614i | 0.887815 | − | 0.460201i | \(-0.152223\pi\) |
−0.460201 | + | 0.887815i | \(0.652223\pi\) | |||||||
\(464\) | − | 1.42901i | − | 0.0663401i | ||||||
\(465\) | 1.72597 | − | 0.575324i | 0.0800400 | − | 0.0266800i | ||||
\(466\) | −14.8999 | −0.690223 | ||||||||
\(467\) | −0.878944 | − | 0.878944i | −0.0406727 | − | 0.0406727i | 0.686478 | − | 0.727151i | \(-0.259156\pi\) |
−0.727151 | + | 0.686478i | \(0.759156\pi\) | |||||||
\(468\) | −4.37849 | + | 4.37849i | −0.202396 | + | 0.202396i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 9.32798 | − | 18.6560i | 0.430267 | − | 0.860535i | ||||
\(471\) | −18.4853 | −0.851757 | ||||||||
\(472\) | 3.79271 | + | 3.79271i | 0.174573 | + | 0.174573i | ||||
\(473\) | 27.9841 | + | 27.9841i | 1.28671 | + | 1.28671i | ||||
\(474\) | 1.92856 | 0.0885816 | ||||||||
\(475\) | 10.2426 | + | 13.6569i | 0.469965 | + | 0.626619i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.91376 | + | 7.91376i | −0.362346 | + | 0.362346i | ||||
\(478\) | 6.15065 | + | 6.15065i | 0.281324 | + | 0.281324i | ||||
\(479\) | −12.7065 | −0.580573 | −0.290287 | − | 0.956940i | \(-0.593751\pi\) | ||||
−0.290287 | + | 0.956940i | \(0.593751\pi\) | |||||||
\(480\) | 2.00000 | + | 1.00000i | 0.0912871 | + | 0.0456435i | ||||
\(481\) | 54.1327i | 2.46824i | ||||||||
\(482\) | −4.80280 | − | 4.80280i | −0.218761 | − | 0.218761i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 11.9700i | − | 0.544092i | ||||||
\(485\) | −33.6824 | + | 11.2275i | −1.52944 | + | 0.509813i | ||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 0.0923663 | − | 0.0923663i | 0.00418552 | − | 0.00418552i | −0.705011 | − | 0.709196i | \(-0.749058\pi\) |
0.709196 | + | 0.705011i | \(0.249058\pi\) | |||||||
\(488\) | 6.77791 | − | 6.77791i | 0.306822 | − | 0.306822i | ||||
\(489\) | −4.93431 | −0.223137 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.8138 | 1.52599 | 0.762997 | − | 0.646402i | \(-0.223727\pi\) | ||||
0.762997 | + | 0.646402i | \(0.223727\pi\) | |||||||
\(492\) | 1.36370 | − | 1.36370i | 0.0614802 | − | 0.0614802i | ||||
\(493\) | 1.98483 | − | 1.98483i | 0.0893923 | − | 0.0893923i | ||||
\(494\) | − | 21.1412i | − | 0.951189i | ||||||
\(495\) | −9.58541 | − | 4.79271i | −0.430832 | − | 0.215416i | ||||
\(496\) | 0.813631i | 0.0365331i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −2.51434 | − | 2.51434i | −0.112670 | − | 0.112670i | ||||
\(499\) | 5.20401i | 0.232963i | 0.993193 | + | 0.116482i | \(0.0371616\pi\) | ||||
−0.993193 | + | 0.116482i | \(0.962838\pi\) | |||||||
\(500\) | 2.00000 | + | 11.0000i | 0.0894427 | + | 0.491935i | ||||
\(501\) | 17.0772 | 0.762953 | ||||||||
\(502\) | −6.60671 | − | 6.60671i | −0.294872 | − | 0.294872i | ||||
\(503\) | −21.4748 | + | 21.4748i | −0.957515 | + | 0.957515i | −0.999134 | − | 0.0416187i | \(-0.986749\pi\) |
0.0416187 | + | 0.999134i | \(0.486749\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −25.9401 | − | 12.9700i | −1.15432 | − | 0.577159i | ||||
\(506\) | 20.3337 | 0.903945 | ||||||||
\(507\) | 17.9198 | + | 17.9198i | 0.795845 | + | 0.795845i | ||||
\(508\) | 8.97003 | + | 8.97003i | 0.397981 | + | 0.397981i | ||||
\(509\) | 11.0292 | 0.488862 | 0.244431 | − | 0.969667i | \(-0.421399\pi\) | ||||
0.244431 | + | 0.969667i | \(0.421399\pi\) | |||||||
\(510\) | 1.38896 | + | 4.16687i | 0.0615040 | + | 0.184512i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | −2.41421 | − | 2.41421i | −0.106590 | − | 0.106590i | ||||
\(514\) | −5.19788 | −0.229269 | ||||||||
\(515\) | 8.82843 | + | 26.4853i | 0.389027 | + | 1.16708i | ||||
\(516\) | 8.25744i | 0.363513i | ||||||||
\(517\) | −31.6121 | − | 31.6121i | −1.39030 | − | 1.39030i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.2123i | 0.711641i | ||||||||
\(520\) | 6.19212 | − | 12.3842i | 0.271543 | − | 0.543085i | ||||
\(521\) | − | 3.73696i | − | 0.163719i | −0.996644 | − | 0.0818597i | \(-0.973914\pi\) | ||
0.996644 | − | 0.0818597i | \(-0.0260859\pi\) | |||||||
\(522\) | −1.01046 | + | 1.01046i | −0.0442267 | + | 0.0442267i | ||||
\(523\) | −26.4849 | + | 26.4849i | −1.15810 | + | 1.15810i | −0.173221 | + | 0.984883i | \(0.555418\pi\) |
−0.984883 | + | 0.173221i | \(0.944582\pi\) | |||||||
\(524\) | 0.293157 | 0.0128066 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.4429 | 0.542536 | ||||||||
\(527\) | −1.13010 | + | 1.13010i | −0.0492278 | + | 0.0492278i | ||||
\(528\) | 3.38896 | − | 3.38896i | 0.147485 | − | 0.147485i | ||||
\(529\) | − | 5.00000i | − | 0.217391i | ||||||
\(530\) | 11.1918 | − | 22.3835i | 0.486139 | − | 0.972277i | ||||
\(531\) | − | 5.36370i | − | 0.232765i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.44418 | − | 8.44418i | −0.365758 | − | 0.365758i | ||||
\(534\) | − | 9.97908i | − | 0.431837i | ||||||
\(535\) | −9.62113 | − | 28.8634i | −0.415958 | − | 1.24787i | ||||
\(536\) | −9.00575 | −0.388989 | ||||||||
\(537\) | 11.3027 | + | 11.3027i | 0.487748 | + | 0.487748i | ||||
\(538\) | 14.0702 | − | 14.0702i | 0.606608 | − | 0.606608i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.707107 | − | 2.12132i | −0.0304290 | − | 0.0912871i | ||||
\(541\) | 29.0279 | 1.24801 | 0.624004 | − | 0.781421i | \(-0.285505\pi\) | ||||
0.624004 | + | 0.781421i | \(0.285505\pi\) | |||||||
\(542\) | −13.8742 | − | 13.8742i | −0.595949 | − | 0.595949i | ||||
\(543\) | −7.29226 | − | 7.29226i | −0.312941 | − | 0.312941i | ||||
\(544\) | −1.96428 | −0.0842178 | ||||||||
\(545\) | 28.8695 | + | 14.4348i | 1.23663 | + | 0.618317i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.6579 | − | 26.6579i | 1.13981 | − | 1.13981i | 0.151326 | − | 0.988484i | \(-0.451646\pi\) |
0.988484 | − | 0.151326i | \(-0.0483542\pi\) | |||||||
\(548\) | −9.17733 | − | 9.17733i | −0.392036 | − | 0.392036i | ||||
\(549\) | −9.58541 | −0.409095 | ||||||||
\(550\) | 23.7227 | + | 3.38896i | 1.01154 | + | 0.144506i | ||||
\(551\) | − | 4.87894i | − | 0.207850i | ||||||
\(552\) | 3.00000 | + | 3.00000i | 0.127688 | + | 0.127688i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 16.0054i | 0.680003i | ||||||||
\(555\) | −17.4844 | − | 8.74219i | −0.742171 | − | 0.371085i | ||||
\(556\) | − | 18.6983i | − | 0.792986i | ||||||
\(557\) | 14.7488 | − | 14.7488i | 0.624929 | − | 0.624929i | −0.321859 | − | 0.946788i | \(-0.604308\pi\) |
0.946788 | + | 0.321859i | \(0.104308\pi\) | |||||||
\(558\) | 0.575324 | − | 0.575324i | 0.0243554 | − | 0.0243554i | ||||
\(559\) | 51.1311 | 2.16261 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.41421 | 0.397468 | ||||||||
\(562\) | −10.9491 | + | 10.9491i | −0.461860 | + | 0.461860i | ||||
\(563\) | 12.8986 | − | 12.8986i | 0.543611 | − | 0.543611i | −0.380975 | − | 0.924585i | \(-0.624411\pi\) |
0.924585 | + | 0.380975i | \(0.124411\pi\) | |||||||
\(564\) | − | 9.32798i | − | 0.392779i | ||||||
\(565\) | −0.0627742 | + | 0.0209247i | −0.00264093 | + | 0.000880310i | ||||
\(566\) | 12.2845i | 0.516356i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.5854 | + | 10.5854i | 0.444154 | + | 0.444154i | ||||
\(569\) | 36.7562i | 1.54090i | 0.637499 | + | 0.770451i | \(0.279969\pi\) | ||||
−0.637499 | + | 0.770451i | \(0.720031\pi\) | |||||||
\(570\) | 6.82843 | + | 3.41421i | 0.286011 | + | 0.143006i | ||||
\(571\) | −24.8266 | −1.03896 | −0.519481 | − | 0.854482i | \(-0.673875\pi\) | ||||
−0.519481 | + | 0.854482i | \(0.673875\pi\) | |||||||
\(572\) | −20.9848 | − | 20.9848i | −0.877420 | − | 0.877420i | ||||
\(573\) | −10.2632 | + | 10.2632i | −0.428751 | + | 0.428751i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.00000 | + | 21.0000i | −0.125109 | + | 0.875761i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 13.4762 | + | 13.4762i | 0.561023 | + | 0.561023i | 0.929598 | − | 0.368575i | \(-0.120154\pi\) |
−0.368575 | + | 0.929598i | \(0.620154\pi\) | |||||||
\(578\) | 9.29252 | + | 9.29252i | 0.386518 | + | 0.386518i | ||||
\(579\) | 7.34277 | 0.305155 | ||||||||
\(580\) | 1.42901 | − | 2.85802i | 0.0593364 | − | 0.118673i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −11.2275 | + | 11.2275i | −0.465394 | + | 0.465394i | ||||
\(583\) | −37.9283 | − | 37.9283i | −1.57083 | − | 1.57083i | ||||
\(584\) | 6.80750 | 0.281696 | ||||||||
\(585\) | −13.1355 | + | 4.37849i | −0.543085 | + | 0.181028i | ||||
\(586\) | − | 30.8272i | − | 1.27346i | ||||||
\(587\) | 1.72777 | + | 1.72777i | 0.0713126 | + | 0.0713126i | 0.741864 | − | 0.670551i | \(-0.233942\pi\) |
−0.670551 | + | 0.741864i | \(0.733942\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.77791i | 0.114462i | ||||||||
\(590\) | 3.79271 | + | 11.3781i | 0.156143 | + | 0.468430i | ||||
\(591\) | − | 16.6560i | − | 0.685134i | ||||||
\(592\) | 6.18166 | − | 6.18166i | 0.254065 | − | 0.254065i | ||||
\(593\) | 6.64602 | − | 6.64602i | 0.272919 | − | 0.272919i | −0.557355 | − | 0.830274i | \(-0.688184\pi\) |
0.830274 | + | 0.557355i | \(0.188184\pi\) | |||||||
\(594\) | −4.79271 | −0.196647 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.86452 | 0.0763738 | ||||||||
\(597\) | 1.50478 | − | 1.50478i | 0.0615867 | − | 0.0615867i | ||||
\(598\) | 18.5764 | − | 18.5764i | 0.759644 | − | 0.759644i | ||||
\(599\) | 43.1818i | 1.76436i | 0.470912 | + | 0.882180i | \(0.343925\pi\) | ||||
−0.470912 | + | 0.882180i | \(0.656075\pi\) | |||||||
\(600\) | 3.00000 | + | 4.00000i | 0.122474 | + | 0.163299i | ||||
\(601\) | 40.8953i | 1.66815i | 0.551648 | + | 0.834077i | \(0.313999\pi\) | ||||
−0.551648 | + | 0.834077i | \(0.686001\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.36803 | + | 6.36803i | 0.259326 | + | 0.259326i | ||||
\(604\) | − | 8.15027i | − | 0.331630i | ||||||
\(605\) | 11.9700 | − | 23.9401i | 0.486651 | − | 0.973302i | ||||
\(606\) | −12.9700 | −0.526872 | ||||||||
\(607\) | 16.2569 | + | 16.2569i | 0.659848 | + | 0.659848i | 0.955344 | − | 0.295496i | \(-0.0954850\pi\) |
−0.295496 | + | 0.955344i | \(0.595485\pi\) | |||||||
\(608\) | −2.41421 | + | 2.41421i | −0.0979093 | + | 0.0979093i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 20.3337 | − | 6.77791i | 0.823289 | − | 0.274430i | ||||
\(611\) | −57.7600 | −2.33672 | ||||||||
\(612\) | 1.38896 | + | 1.38896i | 0.0561452 | + | 0.0561452i | ||||
\(613\) | −18.8228 | − | 18.8228i | −0.760246 | − | 0.760246i | 0.216120 | − | 0.976367i | \(-0.430660\pi\) |
−0.976367 | + | 0.216120i | \(0.930660\pi\) | |||||||
\(614\) | −4.38425 | −0.176934 | ||||||||
\(615\) | 4.09109 | − | 1.36370i | 0.164969 | − | 0.0549896i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.9343 | − | 23.9343i | 0.963559 | − | 0.963559i | −0.0357998 | − | 0.999359i | \(-0.511398\pi\) |
0.999359 | + | 0.0357998i | \(0.0113979\pi\) | |||||||
\(618\) | 8.82843 | + | 8.82843i | 0.355131 | + | 0.355131i | ||||
\(619\) | 41.9980 | 1.68804 | 0.844021 | − | 0.536311i | \(-0.180182\pi\) | ||||
0.844021 | + | 0.536311i | \(0.180182\pi\) | |||||||
\(620\) | −0.813631 | + | 1.62726i | −0.0326762 | + | 0.0653524i | ||||
\(621\) | − | 4.24264i | − | 0.170251i | ||||||
\(622\) | −18.8925 | − | 18.8925i | −0.757519 | − | 0.757519i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 6.19212i | − | 0.247883i | ||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | − | 4.79884i | − | 0.191800i | ||||||
\(627\) | 11.5706 | − | 11.5706i | 0.462086 | − | 0.462086i | ||||
\(628\) | 13.0711 | − | 13.0711i | 0.521592 | − | 0.521592i | ||||
\(629\) | 17.1721 | 0.684697 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.8053 | −1.58462 | −0.792312 | − | 0.610116i | \(-0.791123\pi\) | ||||
−0.792312 | + | 0.610116i | \(0.791123\pi\) | |||||||
\(632\) | −1.36370 | + | 1.36370i | −0.0542449 | + | 0.0542449i | ||||
\(633\) | 11.0772 | − | 11.0772i | 0.440279 | − | 0.440279i | ||||
\(634\) | − | 27.4129i | − | 1.08871i | ||||||
\(635\) | 8.97003 | + | 26.9101i | 0.355965 | + | 1.06789i | ||||
\(636\) | − | 11.1918i | − | 0.443782i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.84285 | − | 4.84285i | −0.191730 | − | 0.191730i | ||||
\(639\) | − | 14.9700i | − | 0.592205i | ||||||
\(640\) | −2.12132 | + | 0.707107i | −0.0838525 | + | 0.0279508i | ||||
\(641\) | 5.25452 | 0.207541 | 0.103771 | − | 0.994601i | \(-0.466909\pi\) | ||||
0.103771 | + | 0.994601i | \(0.466909\pi\) | |||||||
\(642\) | −9.62113 | − | 9.62113i | −0.379716 | − | 0.379716i | ||||
\(643\) | 10.6974 | − | 10.6974i | 0.421865 | − | 0.421865i | −0.463980 | − | 0.885846i | \(-0.653579\pi\) |
0.885846 | + | 0.463980i | \(0.153579\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.25744 | + | 16.5149i | −0.325136 | + | 0.650273i | ||||
\(646\) | −6.70647 | −0.263862 | ||||||||
\(647\) | 11.8180 | + | 11.8180i | 0.464612 | + | 0.464612i | 0.900164 | − | 0.435552i | \(-0.143447\pi\) |
−0.435552 | + | 0.900164i | \(0.643447\pi\) | |||||||
\(648\) | −0.707107 | − | 0.707107i | −0.0277778 | − | 0.0277778i | ||||
\(649\) | 25.7066 | 1.00907 | ||||||||
\(650\) | 24.7685 | − | 18.5764i | 0.971500 | − | 0.728625i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.48909 | − | 3.48909i | 0.136643 | − | 0.136643i | ||||
\(653\) | 17.2275 | + | 17.2275i | 0.674163 | + | 0.674163i | 0.958673 | − | 0.284510i | \(-0.0918309\pi\) |
−0.284510 | + | 0.958673i | \(0.591831\pi\) | |||||||
\(654\) | 14.4348 | 0.564444 | ||||||||
\(655\) | 0.586315 | + | 0.293157i | 0.0229092 | + | 0.0114546i | ||||
\(656\) | 1.92856i | 0.0752976i | ||||||||
\(657\) | −4.81363 | − | 4.81363i | −0.187798 | − | 0.187798i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.3904i | 0.872205i | 0.899897 | + | 0.436103i | \(0.143642\pi\) | ||||
−0.899897 | + | 0.436103i | \(0.856358\pi\) | |||||||
\(660\) | 10.1669 | − | 3.38896i | 0.395745 | − | 0.131915i | ||||
\(661\) | − | 1.18383i | − | 0.0460457i | −0.999735 | − | 0.0230228i | \(-0.992671\pi\) | ||
0.999735 | − | 0.0230228i | \(-0.00732904\pi\) | |||||||
\(662\) | −23.8133 | + | 23.8133i | −0.925529 | + | 0.925529i | ||||
\(663\) | 8.60058 | − | 8.60058i | 0.334019 | − | 0.334019i | ||||
\(664\) | 3.55582 | 0.137993 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.74219 | −0.338753 | ||||||||
\(667\) | 4.28703 | − | 4.28703i | 0.165994 | − | 0.165994i | ||||
\(668\) | −12.0754 | + | 12.0754i | −0.467211 | + | 0.467211i | ||||
\(669\) | 12.3929i | 0.479138i | ||||||||
\(670\) | −18.0115 | − | 9.00575i | −0.695845 | − | 0.347923i | ||||
\(671\) | − | 45.9401i | − | 1.77350i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.4257 | + | 24.4257i | 0.941542 | + | 0.941542i | 0.998383 | − | 0.0568408i | \(-0.0181027\pi\) |
−0.0568408 | + | 0.998383i | \(0.518103\pi\) | |||||||
\(674\) | 8.65723i | 0.333464i | ||||||||
\(675\) | 0.707107 | − | 4.94975i | 0.0272166 | − | 0.190516i | ||||
\(676\) | −25.3424 | −0.974708 | ||||||||
\(677\) | −8.12158 | − | 8.12158i | −0.312138 | − | 0.312138i | 0.533599 | − | 0.845737i | \(-0.320839\pi\) |
−0.845737 | + | 0.533599i | \(0.820839\pi\) | |||||||
\(678\) | −0.0209247 | + | 0.0209247i | −0.000803610 | + | 0.000803610i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.92856 | − | 1.96428i | −0.150653 | − | 0.0753267i | ||||
\(681\) | −11.7283 | −0.449429 | ||||||||
\(682\) | 2.75736 | + | 2.75736i | 0.105585 | + | 0.105585i | ||||
\(683\) | −3.42235 | − | 3.42235i | −0.130953 | − | 0.130953i | 0.638592 | − | 0.769545i | \(-0.279517\pi\) |
−0.769545 | + | 0.638592i | \(0.779517\pi\) | |||||||
\(684\) | 3.41421 | 0.130546 | ||||||||
\(685\) | −9.17733 | − | 27.5320i | −0.350648 | − | 1.05194i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.5058 | − | 13.5058i | 0.515280 | − | 0.515280i | ||||
\(688\) | −5.83889 | − | 5.83889i | −0.222606 | − | 0.222606i | ||||
\(689\) | −69.3007 | −2.64015 | ||||||||
\(690\) | 3.00000 | + | 9.00000i | 0.114208 | + | 0.342624i | ||||
\(691\) | − | 7.64587i | − | 0.290863i | −0.989368 | − | 0.145431i | \(-0.953543\pi\) | ||
0.989368 | − | 0.145431i | \(-0.0464570\pi\) | |||||||
\(692\) | −11.4638 | − | 11.4638i | −0.435789 | − | 0.435789i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.7857i | 0.599216i | ||||||||
\(695\) | 18.6983 | − | 37.3967i | 0.709268 | − | 1.41854i | ||||
\(696\) | − | 1.42901i | − | 0.0541665i | ||||||
\(697\) | −2.67868 | + | 2.67868i | −0.101462 | + | 0.101462i | ||||
\(698\) | −3.24301 | + | 3.24301i | −0.122750 | + | 0.122750i | ||||
\(699\) | −14.8999 | −0.563565 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.43752 | −0.243142 | −0.121571 | − | 0.992583i | \(-0.538793\pi\) | ||||
−0.121571 | + | 0.992583i | \(0.538793\pi\) | |||||||
\(702\) | −4.37849 | + | 4.37849i | −0.165256 | + | 0.165256i | ||||
\(703\) | 21.1055 | − | 21.1055i | 0.796009 | − | 0.796009i | ||||
\(704\) | 4.79271i | 0.180632i | ||||||||
\(705\) | 9.32798 | − | 18.6560i | 0.351312 | − | 0.702624i | ||||
\(706\) | − | 14.9930i | − | 0.564268i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 3.79271 | + | 3.79271i | 0.142539 | + | 0.142539i | ||||
\(709\) | − | 27.9610i | − | 1.05010i | −0.851072 | − | 0.525049i | \(-0.824047\pi\) | ||
0.851072 | − | 0.525049i | \(-0.175953\pi\) | |||||||
\(710\) | 10.5854 | + | 31.7562i | 0.397263 | + | 1.19179i | ||||
\(711\) | 1.92856 | 0.0723266 | ||||||||
\(712\) | 7.05627 | + | 7.05627i | 0.264445 | + | 0.264445i | ||||
\(713\) | −2.44089 | + | 2.44089i | −0.0914122 | + | 0.0914122i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −20.9848 | − | 62.9545i | −0.784788 | − | 2.35436i | ||||
\(716\) | −15.9845 | −0.597367 | ||||||||
\(717\) | 6.15065 | + | 6.15065i | 0.229700 | + | 0.229700i | ||||
\(718\) | 17.9996 | + | 17.9996i | 0.671740 | + | 0.671740i | ||||
\(719\) | −7.87879 | −0.293829 | −0.146915 | − | 0.989149i | \(-0.546934\pi\) | ||||
−0.146915 | + | 0.989149i | \(0.546934\pi\) | |||||||
\(720\) | 2.00000 | + | 1.00000i | 0.0745356 | + | 0.0372678i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 5.19239 | − | 5.19239i | 0.193241 | − | 0.193241i | ||||
\(723\) | −4.80280 | − | 4.80280i | −0.178618 | − | 0.178618i | ||||
\(724\) | 10.3128 | 0.383272 | ||||||||
\(725\) | 5.71604 | − | 4.28703i | 0.212288 | − | 0.159216i | ||||
\(726\) | − | 11.9700i | − | 0.444250i | ||||||
\(727\) | 18.9147 | + | 18.9147i | 0.701506 | + | 0.701506i | 0.964734 | − | 0.263228i | \(-0.0847870\pi\) |
−0.263228 | + | 0.964734i | \(0.584787\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 13.6150 | + | 6.80750i | 0.503914 | + | 0.251957i | ||||
\(731\) | − | 16.2199i | − | 0.599915i | ||||||
\(732\) | 6.77791 | − | 6.77791i | 0.250519 | − | 0.250519i | ||||
\(733\) | 8.42325 | − | 8.42325i | 0.311120 | − | 0.311120i | −0.534223 | − | 0.845343i | \(-0.679396\pi\) |
0.845343 | + | 0.534223i | \(0.179396\pi\) | |||||||
\(734\) | 4.63577 | 0.171110 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.24264 | −0.156386 | ||||||||
\(737\) | −30.5201 | + | 30.5201i | −1.12422 | + | 1.12422i | ||||
\(738\) | 1.36370 | − | 1.36370i | 0.0501984 | − | 0.0501984i | ||||
\(739\) | 41.5341i | 1.52786i | 0.645300 | + | 0.763929i | \(0.276732\pi\) | ||||
−0.645300 | + | 0.763929i | \(0.723268\pi\) | |||||||
\(740\) | 18.5450 | − | 6.18166i | 0.681727 | − | 0.227242i | ||||
\(741\) | − | 21.1412i | − | 0.776643i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.1412 | + | 13.1412i | 0.482105 | + | 0.482105i | 0.905803 | − | 0.423698i | \(-0.139268\pi\) |
−0.423698 | + | 0.905803i | \(0.639268\pi\) | |||||||
\(744\) | 0.813631i | 0.0298292i | ||||||||
\(745\) | 3.72904 | + | 1.86452i | 0.136622 | + | 0.0683108i | ||||
\(746\) | −23.9845 | −0.878133 | ||||||||
\(747\) | −2.51434 | − | 2.51434i | −0.0919951 | − | 0.0919951i | ||||
\(748\) | −6.65685 | + | 6.65685i | −0.243399 | + | 0.243399i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.00000 | + | 11.0000i | 0.0730297 | + | 0.401663i | ||||
\(751\) | −43.3038 | −1.58018 | −0.790088 | − | 0.612993i | \(-0.789965\pi\) | ||||
−0.790088 | + | 0.612993i | \(0.789965\pi\) | |||||||
\(752\) | 6.59588 | + | 6.59588i | 0.240527 | + | 0.240527i | ||||
\(753\) | −6.60671 | − | 6.60671i | −0.240762 | − | 0.240762i | ||||
\(754\) | −8.84860 | −0.322247 | ||||||||
\(755\) | 8.15027 | − | 16.3005i | 0.296619 | − | 0.593238i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.4945 | + | 22.4945i | −0.817575 | + | 0.817575i | −0.985756 | − | 0.168181i | \(-0.946211\pi\) |
0.168181 | + | 0.985756i | \(0.446211\pi\) | |||||||
\(758\) | −11.1573 | − | 11.1573i | −0.405252 | − | 0.405252i | ||||
\(759\) | 20.3337 | 0.738068 | ||||||||
\(760\) | −7.24264 | + | 2.41421i | −0.262718 | + | 0.0875727i | ||||
\(761\) | 37.7275i | 1.36762i | 0.729659 | + | 0.683811i | \(0.239679\pi\) | ||||
−0.729659 | + | 0.683811i | \(0.760321\pi\) | |||||||
\(762\) | 8.97003 | + | 8.97003i | 0.324950 | + | 0.324950i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 14.5143i | − | 0.525111i | ||||||
\(765\) | 1.38896 | + | 4.16687i | 0.0502178 | + | 0.150653i | ||||
\(766\) | − | 10.8636i | − | 0.392519i | ||||||
\(767\) | 23.4849 | − | 23.4849i | 0.847991 | − | 0.847991i | ||||
\(768\) | −0.707107 | + | 0.707107i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | −24.0564 | −0.867497 | −0.433748 | − | 0.901034i | \(-0.642809\pi\) | ||||
−0.433748 | + | 0.901034i | \(0.642809\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.19788 | −0.187197 | ||||||||
\(772\) | −5.19212 | + | 5.19212i | −0.186869 | + | 0.186869i | ||||
\(773\) | 13.5554 | − | 13.5554i | 0.487556 | − | 0.487556i | −0.419979 | − | 0.907534i | \(-0.637962\pi\) |
0.907534 | + | 0.419979i | \(0.137962\pi\) | |||||||
\(774\) | 8.25744i | 0.296807i | ||||||||
\(775\) | −3.25452 | + | 2.44089i | −0.116906 | + | 0.0876795i | ||||
\(776\) | − | 15.8780i | − | 0.569988i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.82462 | + | 7.82462i | 0.280526 | + | 0.280526i | ||||
\(779\) | 6.58451i | 0.235915i | ||||||||
\(780\) | 6.19212 | − | 12.3842i | 0.221714 | − | 0.443427i | ||||
\(781\) | 71.7470 | 2.56731 | ||||||||
\(782\) | −5.89284 | − | 5.89284i | −0.210727 | − | 0.210727i | ||||
\(783\) | −1.01046 | + | 1.01046i | −0.0361110 | + | 0.0361110i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 39.2132 | − | 13.0711i | 1.39958 | − | 0.466526i | ||||
\(786\) | 0.293157 | 0.0104566 | ||||||||
\(787\) | −7.95815 | − | 7.95815i | −0.283677 | − | 0.283677i | 0.550896 | − | 0.834574i | \(-0.314286\pi\) |
−0.834574 | + | 0.550896i | \(0.814286\pi\) | |||||||
\(788\) | 11.7775 | + | 11.7775i | 0.419557 | + | 0.419557i | ||||
\(789\) | 12.4429 | 0.442979 | ||||||||
\(790\) | −4.09109 | + | 1.36370i | −0.145554 | + | 0.0485182i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.38896 | − | 3.38896i | 0.120421 | − | 0.120421i | ||||
\(793\) | −41.9697 | − | 41.9697i | −1.49039 | − | 1.49039i | ||||
\(794\) | −3.17157 | −0.112555 | ||||||||
\(795\) | 11.1918 | − | 22.3835i | 0.396930 | − | 0.793861i | ||||
\(796\) | 2.12809i | 0.0754280i | ||||||||
\(797\) | 28.3339 | + | 28.3339i | 1.00364 | + | 1.00364i | 0.999993 | + | 0.00364437i | \(0.00116004\pi\) |
0.00364437 | + | 0.999993i | \(0.498840\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.3227i | 0.648212i | ||||||||
\(800\) | −4.94975 | − | 0.707107i | −0.175000 | − | 0.0250000i | ||||
\(801\) | − | 9.97908i | − | 0.352593i | ||||||
\(802\) | −21.4339 | + | 21.4339i | −0.756856 | + | 0.756856i | ||||
\(803\) | 23.0703 | − | 23.0703i | 0.814134 | − | 0.814134i | ||||
\(804\) | −9.00575 | −0.317608 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.03810 | 0.177460 | ||||||||
\(807\) | 14.0702 | − | 14.0702i | 0.495293 | − | 0.495293i | ||||
\(808\) | 9.17120 | − | 9.17120i | 0.322642 | − | 0.322642i | ||||
\(809\) | 54.0815i | 1.90140i | 0.310108 | + | 0.950701i | \(0.399635\pi\) | ||||
−0.310108 | + | 0.950701i | \(0.600365\pi\) | |||||||
\(810\) | −0.707107 | − | 2.12132i | −0.0248452 | − | 0.0745356i | ||||
\(811\) | − | 18.7583i | − | 0.658692i | −0.944209 | − | 0.329346i | \(-0.893172\pi\) | ||
0.944209 | − | 0.329346i | \(-0.106828\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.8742 | − | 13.8742i | −0.486591 | − | 0.486591i | ||||
\(814\) | − | 41.8987i | − | 1.46855i | ||||||
\(815\) | 10.4673 | − | 3.48909i | 0.366652 | − | 0.122217i | ||||
\(816\) | −1.96428 | −0.0687635 | ||||||||
\(817\) | −19.9352 | − | 19.9352i | −0.697445 | − | 0.697445i | ||||
\(818\) | 23.2881 | − | 23.2881i | 0.814248 | − | 0.814248i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.92856 | + | 3.85712i | −0.0673482 | + | 0.134696i | ||||
\(821\) | 5.32798 | 0.185948 | 0.0929738 | − | 0.995669i | \(-0.470363\pi\) | ||||
0.0929738 | + | 0.995669i | \(0.470363\pi\) | |||||||
\(822\) | −9.17733 | − | 9.17733i | −0.320096 | − | 0.320096i | ||||
\(823\) | 25.0206 | + | 25.0206i | 0.872162 | + | 0.872162i | 0.992708 | − | 0.120546i | \(-0.0384646\pi\) |
−0.120546 | + | 0.992708i | \(0.538465\pi\) | |||||||
\(824\) | −12.4853 | −0.434945 | ||||||||
\(825\) | 23.7227 | + | 3.38896i | 0.825918 | + | 0.117988i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.54969 | − | 1.54969i | 0.0538881 | − | 0.0538881i | −0.679649 | − | 0.733537i | \(-0.737868\pi\) |
0.733537 | + | 0.679649i | \(0.237868\pi\) | |||||||
\(828\) | 3.00000 | + | 3.00000i | 0.104257 | + | 0.104257i | ||||
\(829\) | 42.9402 | 1.49138 | 0.745688 | − | 0.666296i | \(-0.232121\pi\) | ||||
0.745688 | + | 0.666296i | \(0.232121\pi\) | |||||||
\(830\) | 7.11164 | + | 3.55582i | 0.246849 | + | 0.123424i | ||||
\(831\) | 16.0054i | 0.555221i | ||||||||
\(832\) | 4.37849 | + | 4.37849i | 0.151797 | + | 0.151797i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | − | 18.6983i | − | 0.647470i | ||||||
\(835\) | −36.2262 | + | 12.0754i | −1.25366 | + | 0.417886i | ||||
\(836\) | 16.3633i | 0.565937i | ||||||||
\(837\) | 0.575324 | − | 0.575324i | 0.0198861 | − | 0.0198861i | ||||
\(838\) | 1.65685 | − | 1.65685i | 0.0572351 | − | 0.0572351i | ||||
\(839\) | 21.9697 | 0.758477 | 0.379238 | − | 0.925299i | \(-0.376186\pi\) | ||||
0.379238 | + | 0.925299i | \(0.376186\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.9579 | 0.929584 | ||||||||
\(842\) | 15.9561 | − | 15.9561i | 0.549885 | − | 0.549885i | ||||
\(843\) | −10.9491 | + | 10.9491i | −0.377107 | + | 0.377107i | ||||
\(844\) | 15.6655i | 0.539229i | ||||||||
\(845\) | −50.6848 | − | 25.3424i | −1.74361 | − | 0.871805i | ||||
\(846\) | − | 9.32798i | − | 0.320702i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7.91376 | + | 7.91376i | 0.271760 | + | 0.271760i | ||||
\(849\) | 12.2845i | 0.421603i | ||||||||
\(850\) | −5.89284 | − | 7.85712i | −0.202123 | − | 0.269497i | ||||
\(851\) | 37.0900 | 1.27143 | ||||||||
\(852\) | 10.5854 | + | 10.5854i | 0.362650 | + | 0.362650i | ||||
\(853\) | −30.4644 | + | 30.4644i | −1.04308 | + | 1.04308i | −0.0440504 | + | 0.999029i | \(0.514026\pi\) |
−0.999029 | + | 0.0440504i | \(0.985974\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.82843 | + | 3.41421i | 0.233527 | + | 0.116764i | ||||
\(856\) | 13.6063 | 0.465055 | ||||||||
\(857\) | 13.2522 | + | 13.2522i | 0.452687 | + | 0.452687i | 0.896245 | − | 0.443559i | \(-0.146284\pi\) |
−0.443559 | + | 0.896245i | \(0.646284\pi\) | |||||||
\(858\) | −20.9848 | − | 20.9848i | −0.716410 | − | 0.716410i | ||||
\(859\) | −41.9283 | −1.43058 | −0.715288 | − | 0.698830i | \(-0.753705\pi\) | ||||
−0.715288 | + | 0.698830i | \(0.753705\pi\) | |||||||
\(860\) | −5.83889 | − | 17.5167i | −0.199104 | − | 0.597313i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.92893 | − | 1.92893i | 0.0656997 | − | 0.0656997i | ||||
\(863\) | 38.2419 | + | 38.2419i | 1.30177 | + | 1.30177i | 0.927198 | + | 0.374571i | \(0.122210\pi\) |
0.374571 | + | 0.927198i | \(0.377790\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −11.4638 | − | 34.3915i | −0.389782 | − | 1.16935i | ||||
\(866\) | 27.7485i | 0.942931i | ||||||||
\(867\) | 9.29252 | + | 9.29252i | 0.315591 | + | 0.315591i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.24301i | 0.313548i | ||||||||
\(870\) | 1.42901 | − | 2.85802i | 0.0484480 | − | 0.0968959i | ||||
\(871\) | 55.7648i | 1.88952i | ||||||||
\(872\) | −10.2069 | + | 10.2069i | −0.345650 | + | 0.345650i | ||||
\(873\) | −11.2275 | + | 11.2275i | −0.379992 | + | 0.379992i | ||||
\(874\) | −14.4853 | −0.489972 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.80750 | 0.230004 | ||||||||
\(877\) | 16.7669 | − | 16.7669i | 0.566179 | − | 0.566179i | −0.364877 | − | 0.931056i | \(-0.618889\pi\) |
0.931056 | + | 0.364877i | \(0.118889\pi\) | |||||||
\(878\) | −19.0040 | + | 19.0040i | −0.641353 | + | 0.641353i | ||||
\(879\) | − | 30.8272i | − | 1.03977i | ||||||
\(880\) | −4.79271 | + | 9.58541i | −0.161562 | + | 0.323124i | ||||
\(881\) | − | 18.7057i | − | 0.630212i | −0.949057 | − | 0.315106i | \(-0.897960\pi\) | ||
0.949057 | − | 0.315106i | \(-0.102040\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.4892 | + | 26.4892i | 0.891434 | + | 0.891434i | 0.994658 | − | 0.103224i | \(-0.0329159\pi\) |
−0.103224 | + | 0.994658i | \(0.532916\pi\) | |||||||
\(884\) | 12.1631i | 0.409088i | ||||||||
\(885\) | 3.79271 | + | 11.3781i | 0.127490 | + | 0.382471i | ||||
\(886\) | 4.55672 | 0.153086 | ||||||||
\(887\) | 16.2175 | + | 16.2175i | 0.544532 | + | 0.544532i | 0.924854 | − | 0.380322i | \(-0.124187\pi\) |
−0.380322 | + | 0.924854i | \(0.624187\pi\) | |||||||
\(888\) | 6.18166 | − | 6.18166i | 0.207443 | − | 0.207443i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 7.05627 | + | 21.1688i | 0.236527 | + | 0.709580i | ||||
\(891\) | −4.79271 | −0.160562 | ||||||||
\(892\) | −8.76311 | − | 8.76311i | −0.293411 | − | 0.293411i | ||||
\(893\) | 22.5197 | + | 22.5197i | 0.753594 | + | 0.753594i | ||||
\(894\) | 1.86452 | 0.0623589 | ||||||||
\(895\) | −31.9689 | − | 15.9845i | −1.06860 | − | 0.534301i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18.5764 | − | 18.5764i | 0.620247 | − | 0.620247i | ||||
\(898\) | 3.62726 | + | 3.62726i | 0.121043 | + | 0.121043i | ||||
\(899\) | 1.16269 | 0.0387778 | ||||||||
\(900\) | 3.00000 | + | 4.00000i | 0.100000 | + | 0.133333i | ||||
\(901\) | 21.9837i | 0.732384i | ||||||||
\(902\) | 6.53580 | + | 6.53580i | 0.217618 | + | 0.217618i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 0.0295921i | − | 0.000984217i | ||||||
\(905\) | 20.6256 | + | 10.3128i | 0.685619 | + | 0.342809i | ||||
\(906\) | − | 8.15027i | − | 0.270775i | ||||||
\(907\) | 22.2872 | − | 22.2872i | 0.740033 | − | 0.740033i | −0.232551 | − | 0.972584i | \(-0.574707\pi\) |
0.972584 | + | 0.232551i | \(0.0747072\pi\) | |||||||
\(908\) | 8.29316 | − | 8.29316i | 0.275218 | − | 0.275218i | ||||
\(909\) | −12.9700 | −0.430189 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39.2821 | −1.30147 | −0.650737 | − | 0.759303i | \(-0.725540\pi\) | ||||
−0.650737 | + | 0.759303i | \(0.725540\pi\) | |||||||
\(912\) | −2.41421 | + | 2.41421i | −0.0799426 | + | 0.0799426i | ||||
\(913\) | 12.0505 | − | 12.0505i | 0.398814 | − | 0.398814i | ||||
\(914\) | − | 1.28539i | − | 0.0425170i | ||||||
\(915\) | 20.3337 | − | 6.77791i | 0.672212 | − | 0.224071i | ||||
\(916\) | 19.1001i | 0.631086i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.38896 | + | 1.38896i | 0.0458424 | + | 0.0458424i | ||||
\(919\) | 6.33320i | 0.208913i | 0.994529 | + | 0.104457i | \(0.0333103\pi\) | ||||
−0.994529 | + | 0.104457i | \(0.966690\pi\) | |||||||
\(920\) | −8.48528 | − | 4.24264i | −0.279751 | − | 0.139876i | ||||
\(921\) | −4.38425 | −0.144466 | ||||||||
\(922\) | 12.7866 | + | 12.7866i | 0.421104 | + | 0.421104i | ||||
\(923\) | 65.5462 | − | 65.5462i | 2.15748 | − | 2.15748i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 43.2716 | + | 6.18166i | 1.42276 | + | 0.203252i | ||||
\(926\) | −13.0124 | −0.427614 | ||||||||
\(927\) | 8.82843 | + | 8.82843i | 0.289964 | + | 0.289964i | ||||
\(928\) | 1.01046 | + | 1.01046i | 0.0331701 | + | 0.0331701i | ||||
\(929\) | −13.8694 | −0.455039 | −0.227520 | − | 0.973773i | \(-0.573062\pi\) | ||||
−0.227520 | + | 0.973773i | \(0.573062\pi\) | |||||||
\(930\) | −0.813631 | + | 1.62726i | −0.0266800 | + | 0.0533600i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 10.5358 | − | 10.5358i | 0.345112 | − | 0.345112i | ||||
\(933\) | −18.8925 | − | 18.8925i | −0.618512 | − | 0.618512i | ||||
\(934\) | 1.24301 | 0.0406727 | ||||||||
\(935\) | −19.9706 | + | 6.65685i | −0.653107 | + | 0.217702i | ||||
\(936\) | − | 6.19212i | − | 0.202396i | ||||||
\(937\) | −41.3839 | − | 41.3839i | −1.35195 | − | 1.35195i | −0.883476 | − | 0.468476i | \(-0.844803\pi\) |
−0.468476 | − | 0.883476i | \(-0.655197\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 4.79884i | − | 0.156604i | ||||||
\(940\) | 6.59588 | + | 19.7876i | 0.215134 | + | 0.645401i | ||||
\(941\) | − | 29.0693i | − | 0.947631i | −0.880624 | − | 0.473815i | \(-0.842876\pi\) | ||
0.880624 | − | 0.473815i | \(-0.157124\pi\) | |||||||
\(942\) | 13.0711 | − | 13.0711i | 0.425878 | − | 0.425878i | ||||
\(943\) | −5.78568 | + | 5.78568i | −0.188408 | + | 0.188408i | ||||
\(944\) | −5.36370 | −0.174573 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −39.5755 | −1.28671 | ||||||||
\(947\) | −5.27261 | + | 5.27261i | −0.171337 | + | 0.171337i | −0.787566 | − | 0.616230i | \(-0.788659\pi\) |
0.616230 | + | 0.787566i | \(0.288659\pi\) | |||||||
\(948\) | −1.36370 | + | 1.36370i | −0.0442908 | + | 0.0442908i | ||||
\(949\) | − | 42.1529i | − | 1.36834i | ||||||
\(950\) | −16.8995 | − | 2.41421i | −0.548292 | − | 0.0783274i | ||||
\(951\) | − | 27.4129i | − | 0.888925i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.5493 | − | 23.5493i | −0.762837 | − | 0.762837i | 0.213997 | − | 0.976834i | \(-0.431352\pi\) |
−0.976834 | + | 0.213997i | \(0.931352\pi\) | |||||||
\(954\) | − | 11.1918i | − | 0.362346i | ||||||
\(955\) | 14.5143 | − | 29.0287i | 0.469673 | − | 0.939346i | ||||
\(956\) | −8.69833 | −0.281324 | ||||||||
\(957\) | −4.84285 | − | 4.84285i | −0.156547 | − | 0.156547i | ||||
\(958\) | 8.98483 | − | 8.98483i | 0.290287 | − | 0.290287i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2.12132 | + | 0.707107i | −0.0684653 | + | 0.0228218i | ||||
\(961\) | 30.3380 | 0.978645 | ||||||||
\(962\) | −38.2776 | − | 38.2776i | −1.23412 | − | 1.23412i | ||||
\(963\) | −9.62113 | − | 9.62113i | −0.310037 | − | 0.310037i | ||||
\(964\) | 6.79218 | 0.218761 | ||||||||
\(965\) | −15.5764 | + | 5.19212i | −0.501421 | + | 0.167140i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.2719 | + | 21.2719i | −0.684057 | + | 0.684057i | −0.960912 | − | 0.276855i | \(-0.910708\pi\) |
0.276855 | + | 0.960912i | \(0.410708\pi\) | |||||||
\(968\) | 8.46409 | + | 8.46409i | 0.272046 | + | 0.272046i | ||||
\(969\) | −6.70647 | −0.215443 | ||||||||
\(970\) | 15.8780 | − | 31.7561i | 0.509813 | − | 1.01963i | ||||
\(971\) | − | 8.07069i | − | 0.259001i | −0.991579 | − | 0.129500i | \(-0.958663\pi\) | ||
0.991579 | − | 0.129500i | \(-0.0413374\pi\) | |||||||
\(972\) | −0.707107 | − | 0.707107i | −0.0226805 | − | 0.0226805i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.130626i | 0.00418552i | ||||||||
\(975\) | 24.7685 | − | 18.5764i | 0.793227 | − | 0.594920i | ||||
\(976\) | 9.58541i | 0.306822i | ||||||||
\(977\) | −18.1531 | + | 18.1531i | −0.580770 | + | 0.580770i | −0.935115 | − | 0.354345i | \(-0.884704\pi\) |
0.354345 | + | 0.935115i | \(0.384704\pi\) | |||||||
\(978\) | 3.48909 | − | 3.48909i | 0.111569 | − | 0.111569i | ||||
\(979\) | 47.8268 | 1.52855 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.4348 | 0.460867 | ||||||||
\(982\) | −23.9100 | + | 23.9100i | −0.762997 | + | 0.762997i | ||||
\(983\) | −14.6311 | + | 14.6311i | −0.466659 | + | 0.466659i | −0.900830 | − | 0.434172i | \(-0.857041\pi\) |
0.434172 | + | 0.900830i | \(0.357041\pi\) | |||||||
\(984\) | 1.92856i | 0.0614802i | ||||||||
\(985\) | 11.7775 | + | 35.3326i | 0.375264 | + | 1.12579i | ||||
\(986\) | 2.80697i | 0.0893923i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 14.9491 | + | 14.9491i | 0.475595 | + | 0.475595i | ||||
\(989\) | − | 35.0333i | − | 1.11400i | ||||||
\(990\) | 10.1669 | − | 3.38896i | 0.323124 | − | 0.107708i | ||||
\(991\) | −54.1077 | −1.71879 | −0.859394 | − | 0.511315i | \(-0.829159\pi\) | ||||
−0.859394 | + | 0.511315i | \(0.829159\pi\) | |||||||
\(992\) | −0.575324 | − | 0.575324i | −0.0182666 | − | 0.0182666i | ||||
\(993\) | −23.8133 | + | 23.8133i | −0.755691 | + | 0.755691i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.12809 | + | 4.25617i | −0.0674649 | + | 0.134930i | ||||
\(996\) | 3.55582 | 0.112670 | ||||||||
\(997\) | −23.1318 | − | 23.1318i | −0.732592 | − | 0.732592i | 0.238541 | − | 0.971133i | \(-0.423331\pi\) |
−0.971133 | + | 0.238541i | \(0.923331\pi\) | |||||||
\(998\) | −3.67979 | − | 3.67979i | −0.116482 | − | 0.116482i | ||||
\(999\) | −8.74219 | −0.276591 |
(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 | 1470.2.m.b.1273.2 | yes | 8 | |
5.2 | odd | 4 | 1470.2.m.a.97.2 | ✓ | 8 | ||
7.6 | odd | 2 | 1470.2.m.a.1273.2 | yes | 8 | ||
35.27 | even | 4 | inner | 1470.2.m.b.97.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1470.2.m.a.97.2 | ✓ | 8 | 5.2 | odd | 4 | ||
1470.2.m.a.1273.2 | yes | 8 | 7.6 | odd | 2 | ||
1470.2.m.b.97.2 | yes | 8 | 35.27 | even | 4 | inner | |
1470.2.m.b.1273.2 | yes | 8 | 1.1 | even | 1 | trivial |