Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [135,3,Mod(71,135)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(135, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("135.71");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 135 = 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 135.i (of order \(6\), degree \(2\), not 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: | \(3.67848356886\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 48x^{14} + 912x^{12} + 8704x^{10} + 43602x^{8} + 109032x^{6} + 117844x^{4} + 36000x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{6} \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 71.2 | ||
Root | \(2.82877i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 135.71 |
Dual form | 135.3.i.a.116.2 |
$q$-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 \(\left(\mathbb{Z}/135\mathbb{Z}\right)^\times\).
\(n\) | \(56\) | \(82\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.44978 | + | 1.41438i | −1.22489 | + | 0.707191i | −0.965957 | − | 0.258703i | \(-0.916705\pi\) |
−0.258935 | + | 0.965895i | \(0.583371\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00096 | − | 3.46576i | 0.500239 | − | 0.866440i | ||||
\(5\) | 1.93649 | + | 1.11803i | 0.387298 | + | 0.223607i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.97472 | − | 6.88441i | −0.567817 | − | 0.983488i | −0.996781 | − | 0.0801664i | \(-0.974455\pi\) |
0.428965 | − | 0.903321i | \(-0.358879\pi\) | |||||||
\(8\) | 0.00541780i | 0.000677225i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −6.32531 | −0.632531 | ||||||||
\(11\) | 0.0594938 | − | 0.0343488i | 0.00540853 | − | 0.00312262i | −0.497293 | − | 0.867582i | \(-0.665673\pi\) |
0.502702 | + | 0.864460i | \(0.332339\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.33957 | − | 7.51635i | 0.333813 | − | 0.578181i | −0.649443 | − | 0.760410i | \(-0.724998\pi\) |
0.983256 | + | 0.182229i | \(0.0583313\pi\) | |||||||
\(14\) | 19.4744 | + | 11.2435i | 1.39103 | + | 0.803110i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 7.99617 | + | 13.8498i | 0.499760 | + | 0.865611i | ||||
\(17\) | − | 26.5641i | − | 1.56260i | −0.624158 | − | 0.781298i | \(-0.714558\pi\) | ||
0.624158 | − | 0.781298i | \(-0.285442\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 26.6131 | 1.40069 | 0.700345 | − | 0.713805i | \(-0.253029\pi\) | ||||
0.700345 | + | 0.713805i | \(0.253029\pi\) | |||||||
\(20\) | 7.74968 | − | 4.47428i | 0.387484 | − | 0.223714i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.0971646 | + | 0.168294i | −0.00441657 | + | 0.00764973i | ||||
\(23\) | 25.6980 | + | 14.8368i | 1.11731 | + | 0.645077i | 0.940712 | − | 0.339207i | \(-0.110159\pi\) |
0.176594 | + | 0.984284i | \(0.443492\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.50000 | + | 4.33013i | 0.100000 | + | 0.173205i | ||||
\(26\) | 24.5512i | 0.944279i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −31.8130 | −1.13618 | ||||||||
\(29\) | 0.650245 | − | 0.375419i | 0.0224222 | − | 0.0129455i | −0.488747 | − | 0.872426i | \(-0.662546\pi\) |
0.511169 | + | 0.859480i | \(0.329213\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 17.3205 | − | 30.0000i | 0.558727 | − | 0.967743i | −0.438877 | − | 0.898547i | \(-0.644623\pi\) |
0.997603 | − | 0.0691954i | \(-0.0220432\pi\) | |||||||
\(32\) | −39.1965 | − | 22.6301i | −1.22489 | − | 0.707191i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 37.5719 | + | 65.0764i | 1.10505 | + | 1.91401i | ||||
\(35\) | − | 17.7755i | − | 0.507871i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −48.4411 | −1.30922 | −0.654609 | − | 0.755967i | \(-0.727167\pi\) | ||||
−0.654609 | + | 0.755967i | \(0.727167\pi\) | |||||||
\(38\) | −65.1963 | + | 37.6411i | −1.71569 | + | 0.990556i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.00605729 | + | 0.0104915i | −0.000151432 | + | 0.000262288i | ||||
\(41\) | −52.4148 | − | 30.2617i | −1.27841 | − | 0.738091i | −0.301855 | − | 0.953354i | \(-0.597606\pi\) |
−0.976556 | + | 0.215263i | \(0.930939\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −16.6490 | − | 28.8369i | −0.387186 | − | 0.670626i | 0.604884 | − | 0.796314i | \(-0.293220\pi\) |
−0.992070 | + | 0.125688i | \(0.959886\pi\) | |||||||
\(44\) | − | 0.274922i | − | 0.00624822i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −83.9395 | −1.82477 | ||||||||
\(47\) | 25.1252 | − | 14.5060i | 0.534578 | − | 0.308639i | −0.208301 | − | 0.978065i | \(-0.566793\pi\) |
0.742879 | + | 0.669426i | \(0.233460\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.09677 | + | 12.2920i | −0.144832 | + | 0.250856i | ||||
\(50\) | −12.2489 | − | 7.07191i | −0.244978 | − | 0.141438i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −17.3666 | − | 30.0798i | −0.333973 | − | 0.578458i | ||||
\(53\) | − | 6.99851i | − | 0.132047i | −0.997818 | − | 0.0660237i | \(-0.978969\pi\) | ||
0.997818 | − | 0.0660237i | \(-0.0210313\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.153612 | 0.00279295 | ||||||||
\(56\) | 0.0372984 | − | 0.0215342i | 0.000666043 | − | 0.000384540i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.06197 | + | 1.83939i | −0.0183099 | + | 0.0317136i | ||||
\(59\) | 57.1733 | + | 33.0090i | 0.969039 | + | 0.559475i | 0.898943 | − | 0.438065i | \(-0.144336\pi\) |
0.0700958 | + | 0.997540i | \(0.477669\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.50414 | + | 16.4617i | 0.155806 | + | 0.269863i | 0.933352 | − | 0.358962i | \(-0.116869\pi\) |
−0.777547 | + | 0.628825i | \(0.783536\pi\) | |||||||
\(62\) | 97.9914i | 1.58051i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0613 | 1.00096 | ||||||||
\(65\) | 16.8071 | − | 9.70357i | 0.258570 | − | 0.149286i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −51.2260 | + | 88.7261i | −0.764568 | + | 1.32427i | 0.175907 | + | 0.984407i | \(0.443714\pi\) |
−0.940475 | + | 0.339864i | \(0.889619\pi\) | |||||||
\(68\) | −92.0649 | − | 53.1537i | −1.35390 | − | 0.781672i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 25.1413 | + | 43.5461i | 0.359162 | + | 0.622087i | ||||
\(71\) | − | 11.3543i | − | 0.159919i | −0.996798 | − | 0.0799597i | \(-0.974521\pi\) | ||
0.996798 | − | 0.0799597i | \(-0.0254792\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 53.9568 | 0.739134 | 0.369567 | − | 0.929204i | \(-0.379506\pi\) | ||||
0.369567 | + | 0.929204i | \(0.379506\pi\) | |||||||
\(74\) | 118.670 | − | 68.5142i | 1.60365 | − | 0.925868i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 53.2517 | − | 92.2347i | 0.700680 | − | 1.21361i | ||||
\(77\) | −0.472942 | − | 0.273053i | −0.00614211 | − | 0.00354615i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −26.7351 | − | 46.3066i | −0.338419 | − | 0.586159i | 0.645717 | − | 0.763577i | \(-0.276559\pi\) |
−0.984136 | + | 0.177418i | \(0.943225\pi\) | |||||||
\(80\) | 35.7599i | 0.446999i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 171.207 | 2.08789 | ||||||||
\(83\) | −30.5050 | + | 17.6121i | −0.367530 | + | 0.212194i | −0.672379 | − | 0.740207i | \(-0.734727\pi\) |
0.304849 | + | 0.952401i | \(0.401394\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 29.6996 | − | 51.4412i | 0.349407 | − | 0.605191i | ||||
\(86\) | 81.5729 | + | 47.0961i | 0.948522 | + | 0.547629i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.000186095 | 0 | 0.000322326i | 2.11471e−6 | 0 | 3.66279e-6i | ||||
\(89\) | − | 74.9349i | − | 0.841965i | −0.907069 | − | 0.420983i | \(-0.861685\pi\) | ||
0.907069 | − | 0.420983i | \(-0.138315\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −68.9943 | −0.758179 | ||||||||
\(92\) | 102.841 | − | 59.3755i | 1.11784 | − | 0.645386i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −41.0341 | + | 71.0732i | −0.436533 | + | 0.756098i | ||||
\(95\) | 51.5361 | + | 29.7544i | 0.542485 | + | 0.313204i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −34.4893 | − | 59.7373i | −0.355560 | − | 0.615848i | 0.631653 | − | 0.775251i | \(-0.282377\pi\) |
−0.987214 | + | 0.159402i | \(0.949043\pi\) | |||||||
\(98\) | − | 40.1502i | − | 0.409696i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 20.0096 | 0.200096 | ||||||||
\(101\) | −15.7347 | + | 9.08446i | −0.155790 | + | 0.0899451i | −0.575868 | − | 0.817543i | \(-0.695336\pi\) |
0.420079 | + | 0.907488i | \(0.362003\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 23.8052 | − | 41.2318i | 0.231118 | − | 0.400309i | −0.727019 | − | 0.686617i | \(-0.759095\pi\) |
0.958137 | + | 0.286309i | \(0.0924282\pi\) | |||||||
\(104\) | 0.0407221 | + | 0.0235109i | 0.000391559 | + | 0.000226067i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.89857 | + | 17.1448i | 0.0933827 | + | 0.161744i | ||||
\(107\) | 149.680i | 1.39888i | 0.714693 | + | 0.699439i | \(0.246567\pi\) | ||||
−0.714693 | + | 0.699439i | \(0.753433\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −36.8532 | −0.338103 | −0.169051 | − | 0.985607i | \(-0.554070\pi\) | ||||
−0.169051 | + | 0.985607i | \(0.554070\pi\) | |||||||
\(110\) | −0.376317 | + | 0.217267i | −0.00342106 | + | 0.00197515i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 63.5650 | − | 110.098i | 0.567545 | − | 0.983017i | ||||
\(113\) | 53.1170 | + | 30.6671i | 0.470062 | + | 0.271390i | 0.716266 | − | 0.697828i | \(-0.245850\pi\) |
−0.246204 | + | 0.969218i | \(0.579183\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 33.1760 | + | 57.4626i | 0.288487 | + | 0.499674i | ||||
\(116\) | − | 3.00479i | − | 0.0259034i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −186.750 | −1.58262 | ||||||||
\(119\) | −182.879 | + | 105.585i | −1.53679 | + | 0.887269i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −60.4976 | + | 104.785i | −0.499980 | + | 0.865992i | ||||
\(122\) | −46.5662 | − | 26.8850i | −0.381690 | − | 0.220369i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −69.3153 | − | 120.058i | −0.558994 | − | 0.968206i | ||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 190.745 | 1.50193 | 0.750965 | − | 0.660342i | \(-0.229588\pi\) | ||||
0.750965 | + | 0.660342i | \(0.229588\pi\) | |||||||
\(128\) | −0.150143 | + | 0.0866848i | −0.00117299 | + | 0.000677225i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −27.4491 | + | 47.5433i | −0.211147 | + | 0.365718i | ||||
\(131\) | 24.8473 | + | 14.3456i | 0.189674 | + | 0.109508i | 0.591830 | − | 0.806063i | \(-0.298406\pi\) |
−0.402156 | + | 0.915571i | \(0.631739\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −105.780 | − | 183.216i | −0.795335 | − | 1.37756i | ||||
\(134\) | − | 289.813i | − | 2.16278i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.143919 | 0.00105823 | ||||||||
\(137\) | −101.630 | + | 58.6761i | −0.741825 | + | 0.428293i | −0.822732 | − | 0.568429i | \(-0.807551\pi\) |
0.0809076 | + | 0.996722i | \(0.474218\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.7198 | + | 27.2275i | −0.113092 | + | 0.195881i | −0.917015 | − | 0.398852i | \(-0.869409\pi\) |
0.803923 | + | 0.594733i | \(0.202742\pi\) | |||||||
\(140\) | −61.6056 | − | 35.5680i | −0.440040 | − | 0.254057i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 16.0593 | + | 27.8155i | 0.113094 | + | 0.195884i | ||||
\(143\) | − | 0.596235i | − | 0.00416948i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.67893 | 0.0115788 | ||||||||
\(146\) | −132.182 | + | 76.3156i | −0.905360 | + | 0.522710i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −96.9286 | + | 167.885i | −0.654923 | + | 1.13436i | ||||
\(149\) | −23.0951 | − | 13.3340i | −0.155001 | − | 0.0894896i | 0.420494 | − | 0.907296i | \(-0.361857\pi\) |
−0.575494 | + | 0.817806i | \(0.695190\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 50.6215 | + | 87.6791i | 0.335242 | + | 0.580656i | 0.983531 | − | 0.180738i | \(-0.0578486\pi\) |
−0.648289 | + | 0.761394i | \(0.724515\pi\) | |||||||
\(152\) | 0.144185i | 0.000948583i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.54481 | 0.0100312 | ||||||||
\(155\) | 67.0821 | − | 38.7299i | 0.432788 | − | 0.249870i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −139.688 | + | 241.946i | −0.889731 | + | 1.54106i | −0.0495387 | + | 0.998772i | \(0.515775\pi\) |
−0.840193 | + | 0.542288i | \(0.817558\pi\) | |||||||
\(158\) | 130.990 | + | 75.6273i | 0.829053 | + | 0.478654i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −50.6025 | − | 87.6461i | −0.316266 | − | 0.547788i | ||||
\(161\) | − | 235.888i | − | 1.46514i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 246.776 | 1.51396 | 0.756982 | − | 0.653436i | \(-0.226673\pi\) | ||||
0.756982 | + | 0.653436i | \(0.226673\pi\) | |||||||
\(164\) | −209.760 | + | 121.105i | −1.27902 | + | 0.738444i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 49.8204 | − | 86.2915i | 0.300123 | − | 0.519828i | ||||
\(167\) | −72.9485 | − | 42.1168i | −0.436817 | − | 0.252197i | 0.265429 | − | 0.964130i | \(-0.414486\pi\) |
−0.702247 | + | 0.711934i | \(0.747820\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 46.8363 | + | 81.1228i | 0.277138 | + | 0.480017i | ||||
\(170\) | 168.026i | 0.988391i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −133.256 | −0.774743 | ||||||||
\(173\) | 164.087 | − | 94.7357i | 0.948480 | − | 0.547605i | 0.0558715 | − | 0.998438i | \(-0.482206\pi\) |
0.892608 | + | 0.450833i | \(0.148873\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 19.8736 | − | 34.4221i | 0.113563 | − | 0.196698i | ||||
\(176\) | 0.951445 | + | 0.549317i | 0.00540594 | + | 0.00312112i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 105.987 | + | 183.574i | 0.595431 | + | 1.03132i | ||||
\(179\) | 111.227i | 0.621378i | 0.950512 | + | 0.310689i | \(0.100560\pi\) | ||||
−0.950512 | + | 0.310689i | \(0.899440\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 219.388 | 1.21209 | 0.606046 | − | 0.795430i | \(-0.292755\pi\) | ||||
0.606046 | + | 0.795430i | \(0.292755\pi\) | |||||||
\(182\) | 169.021 | − | 97.5843i | 0.928686 | − | 0.536177i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.0803827 | + | 0.139227i | −0.000436863 | + | 0.000756668i | ||||
\(185\) | −93.8058 | − | 54.1588i | −0.507058 | − | 0.292750i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.912445 | − | 1.58040i | −0.00487939 | − | 0.00845135i | ||||
\(188\) | − | 116.104i | − | 0.617573i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −168.336 | −0.885980 | ||||||||
\(191\) | 31.7265 | − | 18.3173i | 0.166107 | − | 0.0959020i | −0.414642 | − | 0.909985i | \(-0.636093\pi\) |
0.580749 | + | 0.814083i | \(0.302760\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −76.2245 | + | 132.025i | −0.394946 | + | 0.684066i | −0.993094 | − | 0.117319i | \(-0.962570\pi\) |
0.598149 | + | 0.801385i | \(0.295903\pi\) | |||||||
\(194\) | 168.983 | + | 97.5623i | 0.871045 | + | 0.502898i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 28.4007 | + | 49.1914i | 0.144901 | + | 0.250977i | ||||
\(197\) | 35.7863i | 0.181657i | 0.995867 | + | 0.0908283i | \(0.0289514\pi\) | ||||
−0.995867 | + | 0.0908283i | \(0.971049\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −104.576 | −0.525509 | −0.262754 | − | 0.964863i | \(-0.584631\pi\) | ||||
−0.262754 | + | 0.964863i | \(0.584631\pi\) | |||||||
\(200\) | −0.0234598 | + | 0.0135445i | −0.000117299 | + | 6.77225e-5i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 25.6978 | − | 44.5099i | 0.127217 | − | 0.220346i | ||||
\(203\) | −5.16908 | − | 2.98437i | −0.0254635 | − | 0.0147013i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −67.6673 | − | 117.203i | −0.330084 | − | 0.571723i | ||||
\(206\) | 134.679i | 0.653779i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 138.800 | 0.667306 | ||||||||
\(209\) | 1.58332 | − | 0.914128i | 0.00757567 | − | 0.00437382i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 54.4388 | − | 94.2907i | 0.258004 | − | 0.446875i | −0.707703 | − | 0.706510i | \(-0.750269\pi\) |
0.965707 | + | 0.259634i | \(0.0836020\pi\) | |||||||
\(212\) | −24.2552 | − | 14.0037i | −0.114411 | − | 0.0660553i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −211.705 | − | 366.683i | −0.989274 | − | 1.71347i | ||||
\(215\) | − | 74.4566i | − | 0.346310i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −275.377 | −1.26902 | ||||||||
\(218\) | 90.2823 | − | 52.1245i | 0.414139 | − | 0.239103i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.307372 | − | 0.532384i | 0.00139714 | − | 0.00241993i | ||||
\(221\) | −199.665 | − | 115.277i | −0.903464 | − | 0.521615i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 134.485 | + | 232.934i | 0.603070 | + | 1.04455i | 0.992353 | + | 0.123430i | \(0.0393895\pi\) |
−0.389283 | + | 0.921118i | \(0.627277\pi\) | |||||||
\(224\) | 359.793i | 1.60622i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −173.500 | −0.767700 | ||||||||
\(227\) | 71.7385 | − | 41.4183i | 0.316029 | − | 0.182459i | −0.333592 | − | 0.942717i | \(-0.608261\pi\) |
0.649621 | + | 0.760258i | \(0.274928\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 94.5387 | − | 163.746i | 0.412833 | − | 0.715047i | −0.582366 | − | 0.812927i | \(-0.697873\pi\) |
0.995198 | + | 0.0978799i | \(0.0312061\pi\) | |||||||
\(230\) | −162.548 | − | 93.8472i | −0.706731 | − | 0.408031i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.00203395 | + | 0.00352290i | 8.76701e−6 | + | 1.51849e-5i | ||||
\(233\) | 273.780i | 1.17502i | 0.809216 | + | 0.587512i | \(0.199892\pi\) | ||||
−0.809216 | + | 0.587512i | \(0.800108\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 64.8729 | 0.276055 | ||||||||
\(236\) | 228.803 | − | 132.099i | 0.969503 | − | 0.559743i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 298.675 | − | 517.320i | 1.25494 | − | 2.17362i | ||||
\(239\) | 44.2330 | + | 25.5379i | 0.185075 | + | 0.106853i | 0.589675 | − | 0.807641i | \(-0.299256\pi\) |
−0.404600 | + | 0.914494i | \(0.632589\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −95.5289 | − | 165.461i | −0.396385 | − | 0.686560i | 0.596892 | − | 0.802322i | \(-0.296402\pi\) |
−0.993277 | + | 0.115762i | \(0.963069\pi\) | |||||||
\(242\) | − | 342.267i | − | 1.41433i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 76.0695 | 0.311760 | ||||||||
\(245\) | −27.4857 | + | 15.8689i | −0.112186 | + | 0.0647709i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 115.489 | − | 200.034i | 0.467569 | − | 0.809852i | ||||
\(248\) | 0.162534 | + | 0.0938392i | 0.000655380 | + | 0.000378384i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −15.8133 | − | 27.3894i | −0.0632531 | − | 0.109558i | ||||
\(251\) | 169.083i | 0.673637i | 0.941570 | + | 0.336818i | \(0.109351\pi\) | ||||
−0.941570 | + | 0.336818i | \(0.890649\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.03850 | 0.00805731 | ||||||||
\(254\) | −467.284 | + | 269.787i | −1.83970 | + | 1.06215i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −127.877 | + | 221.490i | −0.499521 | + | 0.865195i | ||||
\(257\) | −247.257 | − | 142.754i | −0.962090 | − | 0.555463i | −0.0652745 | − | 0.997867i | \(-0.520792\pi\) |
−0.896816 | + | 0.442404i | \(0.854126\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 192.540 | + | 333.489i | 0.743396 | + | 1.28760i | ||||
\(260\) | − | 77.6657i | − | 0.298714i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −81.1606 | −0.309773 | ||||||||
\(263\) | −62.0090 | + | 35.8009i | −0.235776 | + | 0.136125i | −0.613234 | − | 0.789902i | \(-0.710132\pi\) |
0.377458 | + | 0.926027i | \(0.376798\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.82457 | − | 13.5526i | 0.0295267 | − | 0.0511417i | ||||
\(266\) | 518.274 | + | 299.226i | 1.94840 | + | 1.12491i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 205.002 | + | 355.074i | 0.764934 | + | 1.32490i | ||||
\(269\) | 39.6463i | 0.147384i | 0.997281 | + | 0.0736920i | \(0.0234782\pi\) | ||||
−0.997281 | + | 0.0736920i | \(0.976522\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 397.832 | 1.46801 | 0.734007 | − | 0.679142i | \(-0.237648\pi\) | ||||
0.734007 | + | 0.679142i | \(0.237648\pi\) | |||||||
\(272\) | 367.907 | − | 212.411i | 1.35260 | − | 0.780924i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 165.981 | − | 287.487i | 0.605770 | − | 1.04922i | ||||
\(275\) | 0.297469 | + | 0.171744i | 0.00108171 | + | 0.000624523i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −68.4595 | − | 118.575i | −0.247146 | − | 0.428070i | 0.715587 | − | 0.698524i | \(-0.246159\pi\) |
−0.962733 | + | 0.270454i | \(0.912826\pi\) | |||||||
\(278\) | − | 88.9352i | − | 0.319911i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.0963041 | 0.000343943 | ||||||||
\(281\) | 381.758 | − | 220.408i | 1.35857 | − | 0.784370i | 0.369137 | − | 0.929375i | \(-0.379653\pi\) |
0.989431 | + | 0.145005i | \(0.0463198\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −84.1670 | + | 145.782i | −0.297410 | + | 0.515129i | −0.975543 | − | 0.219810i | \(-0.929456\pi\) |
0.678133 | + | 0.734939i | \(0.262789\pi\) | |||||||
\(284\) | −39.3512 | − | 22.7194i | −0.138561 | − | 0.0799979i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.843305 | + | 1.46065i | 0.00294862 | + | 0.00510716i | ||||
\(287\) | 481.127i | 1.67640i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −416.653 | −1.44171 | ||||||||
\(290\) | −4.11300 | + | 2.37464i | −0.0141828 | + | 0.00818842i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 107.965 | − | 187.001i | 0.369744 | − | 0.640416i | ||||
\(293\) | 388.737 | + | 224.438i | 1.32675 | + | 0.765999i | 0.984795 | − | 0.173718i | \(-0.0555782\pi\) |
0.341953 | + | 0.939717i | \(0.388912\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 73.8104 | + | 127.843i | 0.250205 | + | 0.433367i | ||||
\(296\) | − | 0.262444i | − | 0.000886636i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 75.4373 | 0.253145 | ||||||||
\(299\) | 223.037 | − | 128.770i | 0.745943 | − | 0.430670i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −132.350 | + | 229.237i | −0.439702 | + | 0.761585i | ||||
\(302\) | −248.024 | − | 143.196i | −0.821270 | − | 0.474161i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 212.803 | + | 368.585i | 0.700010 | + | 1.21245i | ||||
\(305\) | 42.5038i | 0.139357i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −492.512 | −1.60427 | −0.802137 | − | 0.597140i | \(-0.796304\pi\) | ||||
−0.802137 | + | 0.597140i | \(0.796304\pi\) | |||||||
\(308\) | −1.89267 | + | 1.09274i | −0.00614505 | + | 0.00354785i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −109.558 | + | 189.760i | −0.353412 | + | 0.612128i | ||||
\(311\) | −71.5497 | − | 41.3092i | −0.230063 | − | 0.132827i | 0.380538 | − | 0.924765i | \(-0.375739\pi\) |
−0.610601 | + | 0.791938i | \(0.709072\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −96.1876 | − | 166.602i | −0.307308 | − | 0.532274i | 0.670464 | − | 0.741942i | \(-0.266095\pi\) |
−0.977773 | + | 0.209668i | \(0.932762\pi\) | |||||||
\(314\) | − | 790.288i | − | 2.51684i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −213.983 | −0.677162 | ||||||||
\(317\) | 31.6063 | − | 18.2479i | 0.0997043 | − | 0.0575643i | −0.449319 | − | 0.893372i | \(-0.648333\pi\) |
0.549023 | + | 0.835807i | \(0.315000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.0257904 | − | 0.0446702i | 8.08476e−5 | − | 0.000140032i | ||||
\(320\) | 124.054 | + | 71.6227i | 0.387669 | + | 0.223821i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 333.636 | + | 577.874i | 1.03614 | + | 1.79464i | ||||
\(323\) | − | 706.954i | − | 2.18871i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 43.3957 | 0.133525 | ||||||||
\(326\) | −604.548 | + | 349.036i | −1.85444 | + | 1.07066i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.163952 | − | 0.283973i | 0.000499854 | − | 0.000865772i | ||||
\(329\) | −199.731 | − | 115.315i | −0.607085 | − | 0.350501i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −142.388 | − | 246.624i | −0.430176 | − | 0.745087i | 0.566712 | − | 0.823916i | \(-0.308215\pi\) |
−0.996888 | + | 0.0788292i | \(0.974882\pi\) | |||||||
\(332\) | 140.964i | 0.424590i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 238.277 | 0.713405 | ||||||||
\(335\) | −198.398 | + | 114.545i | −0.592232 | + | 0.341925i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 122.391 | − | 211.988i | 0.363178 | − | 0.629043i | −0.625304 | − | 0.780381i | \(-0.715025\pi\) |
0.988482 | + | 0.151338i | \(0.0483583\pi\) | |||||||
\(338\) | −229.477 | − | 132.489i | −0.678927 | − | 0.391979i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −118.855 | − | 205.863i | −0.349574 | − | 0.605481i | ||||
\(341\) | − | 2.37975i | − | 0.00697875i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −276.692 | −0.806681 | ||||||||
\(344\) | 0.156233 | − | 0.0902010i | 0.000454165 | − | 0.000262212i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −267.985 | + | 464.164i | −0.774523 | + | 1.34151i | ||||
\(347\) | 219.275 | + | 126.599i | 0.631918 | + | 0.364838i | 0.781494 | − | 0.623912i | \(-0.214458\pi\) |
−0.149577 | + | 0.988750i | \(0.547791\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −259.518 | − | 449.498i | −0.743603 | − | 1.28796i | −0.950845 | − | 0.309669i | \(-0.899782\pi\) |
0.207241 | − | 0.978290i | \(-0.433551\pi\) | |||||||
\(350\) | 112.435i | 0.321244i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.10927 | −0.00883315 | ||||||||
\(353\) | −595.687 | + | 343.920i | −1.68750 | + | 0.974277i | −0.731072 | + | 0.682300i | \(0.760980\pi\) |
−0.956425 | + | 0.291977i | \(0.905687\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.6945 | − | 21.9875i | 0.0357590 | − | 0.0619365i | ||||
\(356\) | −259.706 | − | 149.942i | −0.729513 | − | 0.421184i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −157.317 | − | 272.481i | −0.439433 | − | 0.761121i | ||||
\(359\) | 340.488i | 0.948435i | 0.880408 | + | 0.474218i | \(0.157269\pi\) | ||||
−0.880408 | + | 0.474218i | \(0.842731\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 347.258 | 0.961933 | ||||||||
\(362\) | −537.454 | + | 310.299i | −1.48468 | + | 0.857180i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −138.055 | + | 239.118i | −0.379271 | + | 0.656916i | ||||
\(365\) | 104.487 | + | 60.3256i | 0.286266 | + | 0.165275i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 133.356 | + | 230.980i | 0.363368 | + | 0.629373i | 0.988513 | − | 0.151136i | \(-0.0482933\pi\) |
−0.625144 | + | 0.780509i | \(0.714960\pi\) | |||||||
\(368\) | 474.549i | 1.28954i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 306.405 | 0.828122 | ||||||||
\(371\) | −48.1806 | + | 27.8171i | −0.129867 | + | 0.0749787i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −140.463 | + | 243.288i | −0.376576 | + | 0.652248i | −0.990562 | − | 0.137069i | \(-0.956232\pi\) |
0.613986 | + | 0.789317i | \(0.289565\pi\) | |||||||
\(374\) | 4.47059 | + | 2.58109i | 0.0119534 | + | 0.00690132i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.0785908 | + | 0.136123i | 0.000209018 | + | 0.000362030i | ||||
\(377\) | − | 6.51663i | − | 0.0172855i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −532.151 | −1.40409 | −0.702046 | − | 0.712131i | \(-0.747730\pi\) | ||||
−0.702046 | + | 0.712131i | \(0.747730\pi\) | |||||||
\(380\) | 206.243 | − | 119.074i | 0.542745 | − | 0.313354i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −51.8153 | + | 89.7467i | −0.135642 | + | 0.234939i | ||||
\(383\) | −316.930 | − | 182.979i | −0.827493 | − | 0.477753i | 0.0255008 | − | 0.999675i | \(-0.491882\pi\) |
−0.852993 | + | 0.521922i | \(0.825215\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.610566 | − | 1.05753i | −0.00158589 | − | 0.00274683i | ||||
\(386\) | − | 431.242i | − | 1.11721i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −276.047 | −0.711461 | ||||||||
\(389\) | 82.2932 | − | 47.5120i | 0.211551 | − | 0.122139i | −0.390481 | − | 0.920611i | \(-0.627691\pi\) |
0.602032 | + | 0.798472i | \(0.294358\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 394.126 | − | 682.646i | 1.00799 | − | 1.74590i | ||||
\(392\) | −0.0665955 | − | 0.0384489i | −0.000169886 | − | 9.80839e-5i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −50.6156 | − | 87.6687i | −0.128466 | − | 0.222509i | ||||
\(395\) | − | 119.563i | − | 0.302691i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 691.691 | 1.74229 | 0.871147 | − | 0.491023i | \(-0.163377\pi\) | ||||
0.871147 | + | 0.491023i | \(0.163377\pi\) | |||||||
\(398\) | 256.189 | − | 147.911i | 0.643691 | − | 0.371635i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −39.9808 | + | 69.2488i | −0.0999521 | + | 0.173122i | ||||
\(401\) | −57.8355 | − | 33.3913i | −0.144228 | − | 0.0832701i | 0.426149 | − | 0.904653i | \(-0.359870\pi\) |
−0.570378 | + | 0.821383i | \(0.693203\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −150.327 | − | 260.374i | −0.373020 | − | 0.646090i | ||||
\(404\) | 72.7105i | 0.179976i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 16.8842 | 0.0415866 | ||||||||
\(407\) | −2.88195 | + | 1.66389i | −0.00708095 | + | 0.00408819i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −55.5485 | + | 96.2128i | −0.135815 | + | 0.235239i | −0.925909 | − | 0.377748i | \(-0.876699\pi\) |
0.790093 | + | 0.612987i | \(0.210032\pi\) | |||||||
\(410\) | 331.540 | + | 191.415i | 0.808635 | + | 0.466865i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −95.2663 | − | 165.006i | −0.231229 | − | 0.400500i | ||||
\(413\) | − | 524.806i | − | 1.27072i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −78.7635 | −0.189792 | ||||||||
\(416\) | −340.192 | + | 196.410i | −0.817769 | + | 0.472139i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.58585 | + | 4.47883i | −0.00618625 | + | 0.0107149i | ||||
\(419\) | 333.765 | + | 192.699i | 0.796576 | + | 0.459903i | 0.842272 | − | 0.539052i | \(-0.181217\pi\) |
−0.0456967 | + | 0.998955i | \(0.514551\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.4176 | + | 56.1490i | 0.0770015 | + | 0.133371i | 0.901955 | − | 0.431830i | \(-0.142132\pi\) |
−0.824953 | + | 0.565201i | \(0.808799\pi\) | |||||||
\(422\) | 307.989i | 0.729832i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.0379165 | 8.94258e−5 | ||||||||
\(425\) | 115.026 | − | 66.4103i | 0.270650 | − | 0.156260i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 75.5525 | − | 130.861i | 0.176938 | − | 0.306466i | ||||
\(428\) | 518.755 | + | 299.503i | 1.21204 | + | 0.699774i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 105.310 | + | 182.402i | 0.244907 | + | 0.424192i | ||||
\(431\) | − | 205.696i | − | 0.477253i | −0.971111 | − | 0.238626i | \(-0.923303\pi\) | ||
0.971111 | − | 0.238626i | \(-0.0766972\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −346.035 | −0.799156 | −0.399578 | − | 0.916699i | \(-0.630843\pi\) | ||||
−0.399578 | + | 0.916699i | \(0.630843\pi\) | |||||||
\(434\) | 674.613 | − | 389.488i | 1.55441 | − | 0.897438i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −73.7416 | + | 127.724i | −0.169132 | + | 0.292946i | ||||
\(437\) | 683.905 | + | 394.853i | 1.56500 | + | 0.903553i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 276.226 | + | 478.437i | 0.629216 | + | 1.08983i | 0.987709 | + | 0.156301i | \(0.0499571\pi\) |
−0.358494 | + | 0.933532i | \(0.616710\pi\) | |||||||
\(440\) | 0 | 0.000832242i | 0 | 1.89146e-6i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 652.183 | 1.47553 | ||||||||
\(443\) | −37.5855 | + | 21.7000i | −0.0848430 | + | 0.0489841i | −0.541821 | − | 0.840494i | \(-0.682265\pi\) |
0.456978 | + | 0.889478i | \(0.348932\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 83.7798 | − | 145.111i | 0.188269 | − | 0.326092i | ||||
\(446\) | −658.917 | − | 380.426i | −1.47739 | − | 0.852972i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −254.626 | − | 441.024i | −0.568361 | − | 0.984429i | ||||
\(449\) | − | 651.887i | − | 1.45186i | −0.687766 | − | 0.725932i | \(-0.741409\pi\) | ||
0.687766 | − | 0.725932i | \(-0.258591\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.15781 | −0.00921909 | ||||||||
\(452\) | 212.570 | − | 122.727i | 0.470287 | − | 0.271520i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −117.163 | + | 202.931i | −0.258067 | + | 0.446986i | ||||
\(455\) | −133.607 | − | 77.1379i | −0.293641 | − | 0.169534i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 230.589 | + | 399.393i | 0.504572 | + | 0.873945i | 0.999986 | + | 0.00528755i | \(0.00168309\pi\) |
−0.495414 | + | 0.868657i | \(0.664984\pi\) | |||||||
\(458\) | 534.856i | 1.16781i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 265.535 | 0.577251 | ||||||||
\(461\) | 632.194 | − | 364.998i | 1.37135 | − | 0.791752i | 0.380256 | − | 0.924881i | \(-0.375836\pi\) |
0.991099 | + | 0.133129i | \(0.0425026\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.69689 | − | 8.13525i | 0.0101445 | − | 0.0175707i | −0.860909 | − | 0.508760i | \(-0.830104\pi\) |
0.871053 | + | 0.491189i | \(0.163438\pi\) | |||||||
\(464\) | 10.3989 | + | 6.00383i | 0.0224115 | + | 0.0129393i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −387.230 | − | 670.703i | −0.830966 | − | 1.43928i | ||||
\(467\) | 56.2899i | 0.120535i | 0.998182 | + | 0.0602676i | \(0.0191954\pi\) | ||||
−0.998182 | + | 0.0602676i | \(0.980805\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 814.436 | 1.73654 | ||||||||
\(470\) | −158.925 | + | 91.7551i | −0.338137 | + | 0.195224i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.178836 | + | 0.309754i | −0.000378891 | + | 0.000656258i | ||||
\(473\) | −1.98102 | − | 1.14375i | −0.00418821 | − | 0.00241807i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 66.5328 | + | 115.238i | 0.140069 | + | 0.242607i | ||||
\(476\) | 845.084i | 1.77539i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −144.482 | −0.302263 | ||||||||
\(479\) | 649.023 | − | 374.714i | 1.35495 | − | 0.782283i | 0.366016 | − | 0.930609i | \(-0.380722\pi\) |
0.988939 | + | 0.148325i | \(0.0473882\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −210.213 | + | 364.100i | −0.437034 | + | 0.756965i | ||||
\(482\) | 468.050 | + | 270.229i | 0.971058 | + | 0.560641i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 242.106 | + | 419.341i | 0.500220 | + | 0.866406i | ||||
\(485\) | − | 154.241i | − | 0.318023i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −440.830 | −0.905196 | −0.452598 | − | 0.891715i | \(-0.649503\pi\) | ||||
−0.452598 | + | 0.891715i | \(0.649503\pi\) | |||||||
\(488\) | −0.0891860 | + | 0.0514916i | −0.000182758 | + | 0.000105515i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 44.8893 | − | 77.7505i | 0.0916108 | − | 0.158675i | ||||
\(491\) | 327.433 | + | 189.043i | 0.666869 | + | 0.385017i | 0.794889 | − | 0.606755i | \(-0.207529\pi\) |
−0.128020 | + | 0.991772i | \(0.540862\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.97268 | − | 17.2732i | −0.0202286 | − | 0.0350369i | ||||
\(494\) | 653.385i | 1.32264i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 553.991 | 1.11692 | ||||||||
\(497\) | −78.1675 | + | 45.1300i | −0.157279 | + | 0.0908049i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 286.566 | − | 496.347i | 0.574281 | − | 0.994684i | −0.421838 | − | 0.906671i | \(-0.638615\pi\) |
0.996119 | − | 0.0880128i | \(-0.0280516\pi\) | |||||||
\(500\) | 38.7484 | + | 22.3714i | 0.0774968 | + | 0.0447428i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −239.148 | − | 414.216i | −0.476390 | − | 0.825132i | ||||
\(503\) | 300.050i | 0.596522i | 0.954484 | + | 0.298261i | \(0.0964065\pi\) | ||||
−0.954484 | + | 0.298261i | \(0.903593\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −40.6269 | −0.0804494 | ||||||||
\(506\) | −4.99388 | + | 2.88322i | −0.00986933 | + | 0.00569806i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 381.673 | − | 661.077i | 0.751325 | − | 1.30133i | ||||
\(509\) | −643.429 | − | 371.484i | −1.26410 | − | 0.729831i | −0.290238 | − | 0.956954i | \(-0.593735\pi\) |
−0.973866 | + | 0.227124i | \(0.927068\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −214.463 | − | 371.461i | −0.419693 | − | 0.726930i | ||||
\(512\) | − | 724.164i | − | 1.41438i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 807.635 | 1.57127 | ||||||||
\(515\) | 92.1971 | − | 53.2300i | 0.179023 | − | 0.103359i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.996528 | − | 1.72604i | 0.00192752 | − | 0.00333856i | ||||
\(518\) | −943.361 | − | 544.650i | −1.82116 | − | 1.05145i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.0525720 | + | 0.0910574i | 0.000101100 | + | 0.000175110i | ||||
\(521\) | 682.606i | 1.31018i | 0.755549 | + | 0.655092i | \(0.227370\pi\) | ||||
−0.755549 | + | 0.655092i | \(0.772630\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 430.700 | 0.823518 | 0.411759 | − | 0.911293i | \(-0.364915\pi\) | ||||
0.411759 | + | 0.911293i | \(0.364915\pi\) | |||||||
\(524\) | 99.4367 | − | 57.4098i | 0.189765 | − | 0.109561i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 101.272 | − | 175.409i | 0.192533 | − | 0.333477i | ||||
\(527\) | −796.925 | − | 460.105i | −1.51219 | − | 0.873064i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 175.759 | + | 304.424i | 0.332249 | + | 0.575471i | ||||
\(530\) | 44.2678i | 0.0835241i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −846.642 | −1.59143 | ||||||||
\(533\) | −454.916 | + | 262.646i | −0.853500 | + | 0.492769i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −167.347 | + | 289.854i | −0.312798 | + | 0.541783i | ||||
\(536\) | −0.480701 | − | 0.277533i | −0.000896830 | − | 0.000517785i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −56.0751 | − | 97.1249i | −0.104229 | − | 0.180529i | ||||
\(539\) | 0.975061i | 0.00180902i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −297.028 | −0.549034 | −0.274517 | − | 0.961582i | \(-0.588518\pi\) | ||||
−0.274517 | + | 0.961582i | \(0.588518\pi\) | |||||||
\(542\) | −974.601 | + | 562.686i | −1.79816 | + | 1.03817i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −601.150 | + | 1041.22i | −1.10505 | + | 1.91401i | ||||
\(545\) | −71.3659 | − | 41.2031i | −0.130947 | − | 0.0756020i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −425.338 | − | 736.708i | −0.777584 | − | 1.34681i | −0.933331 | − | 0.359018i | \(-0.883112\pi\) |
0.155747 | − | 0.987797i | \(-0.450222\pi\) | |||||||
\(548\) | 469.634i | 0.856996i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.971646 | −0.00176663 | ||||||||
\(551\) | 17.3050 | − | 9.99107i | 0.0314066 | − | 0.0181326i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −212.529 | + | 368.111i | −0.384320 | + | 0.665662i | ||||
\(554\) | 335.422 | + | 193.656i | 0.605454 | + | 0.349559i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 62.9092 | + | 108.962i | 0.113146 | + | 0.195975i | ||||
\(557\) | − | 571.248i | − | 1.02558i | −0.858514 | − | 0.512790i | \(-0.828612\pi\) | ||
0.858514 | − | 0.512790i | \(-0.171388\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −288.998 | −0.516991 | ||||||||
\(560\) | 246.186 | − | 142.136i | 0.439618 | − | 0.253814i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −623.482 | + | 1079.90i | −1.10940 | + | 1.92154i | ||||
\(563\) | −451.760 | − | 260.824i | −0.802415 | − | 0.463275i | 0.0418998 | − | 0.999122i | \(-0.486659\pi\) |
−0.844315 | + | 0.535847i | \(0.819992\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 68.5737 | + | 118.773i | 0.121369 | + | 0.210218i | ||||
\(566\) | − | 476.177i | − | 0.841303i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.0615152 | 0.000108301 | ||||||||
\(569\) | −912.977 | + | 527.108i | −1.60453 | + | 0.926376i | −0.613964 | + | 0.789334i | \(0.710426\pi\) |
−0.990565 | + | 0.137042i | \(0.956240\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −182.461 | + | 316.032i | −0.319546 | + | 0.553470i | −0.980393 | − | 0.197050i | \(-0.936864\pi\) |
0.660847 | + | 0.750521i | \(0.270197\pi\) | |||||||
\(572\) | −2.06641 | − | 1.19304i | −0.00361260 | − | 0.00208574i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −680.498 | − | 1178.66i | −1.18554 | − | 2.05341i | ||||
\(575\) | 148.368i | 0.258031i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 77.3098 | 0.133986 | 0.0669929 | − | 0.997753i | \(-0.478660\pi\) | ||||
0.0669929 | + | 0.997753i | \(0.478660\pi\) | |||||||
\(578\) | 1020.71 | − | 589.307i | 1.76593 | − | 1.01956i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.35946 | − | 5.81875i | 0.00579217 | − | 0.0100323i | ||||
\(581\) | 242.497 | + | 140.006i | 0.417379 | + | 0.240974i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.240390 | − | 0.416368i | −0.000412333 | − | 0.000714182i | ||||
\(584\) | 0.292327i | 0.000500561i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1269.76 | −2.16683 | ||||||||
\(587\) | 113.472 | − | 65.5132i | 0.193309 | − | 0.111607i | −0.400222 | − | 0.916418i | \(-0.631067\pi\) |
0.593531 | + | 0.804811i | \(0.297734\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 460.953 | − | 798.394i | 0.782603 | − | 1.35551i | ||||
\(590\) | −361.639 | − | 208.792i | −0.612947 | − | 0.353885i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −387.343 | − | 670.898i | −0.654296 | − | 1.13327i | ||||
\(593\) | 525.116i | 0.885525i | 0.896639 | + | 0.442762i | \(0.146002\pi\) | ||||
−0.896639 | + | 0.442762i | \(0.853998\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −472.190 | −0.793597 | ||||||||
\(596\) | −92.4246 | + | 53.3614i | −0.155075 | + | 0.0895325i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −364.261 | + | 630.919i | −0.609132 | + | 1.05505i | ||||
\(599\) | 851.013 | + | 491.333i | 1.42072 | + | 0.820255i | 0.996361 | − | 0.0852374i | \(-0.0271649\pi\) |
0.424363 | + | 0.905492i | \(0.360498\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 415.553 | + | 719.759i | 0.691436 | + | 1.19760i | 0.971367 | + | 0.237582i | \(0.0763549\pi\) |
−0.279932 | + | 0.960020i | \(0.590312\pi\) | |||||||
\(602\) | − | 748.775i | − | 1.24381i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 405.166 | 0.670805 | ||||||||
\(605\) | −234.306 | + | 135.277i | −0.387283 | + | 0.223598i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 83.8988 | − | 145.317i | 0.138219 | − | 0.239402i | −0.788604 | − | 0.614902i | \(-0.789196\pi\) |
0.926822 | + | 0.375500i | \(0.122529\pi\) | |||||||
\(608\) | −1043.14 | − | 602.258i | −1.71569 | − | 0.990556i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −60.1166 | − | 104.125i | −0.0985519 | − | 0.170697i | ||||
\(611\) | − | 251.799i | − | 0.412110i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 833.750 | 1.36011 | 0.680057 | − | 0.733159i | \(-0.261955\pi\) | ||||
0.680057 | + | 0.733159i | \(0.261955\pi\) | |||||||
\(614\) | 1206.55 | − | 696.601i | 1.96506 | − | 1.13453i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.00147935 | − | 0.00256231i | 2.40154e−6 | − | 4.15959e-6i | ||||
\(617\) | 40.4387 | + | 23.3473i | 0.0655408 | + | 0.0378400i | 0.532412 | − | 0.846485i | \(-0.321286\pi\) |
−0.466872 | + | 0.884325i | \(0.654619\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 499.429 | + | 865.037i | 0.806833 | + | 1.39748i | 0.915047 | + | 0.403347i | \(0.132153\pi\) |
−0.108214 | + | 0.994128i | \(0.534513\pi\) | |||||||
\(620\) | − | 309.987i | − | 0.499979i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 233.708 | 0.375737 | ||||||||
\(623\) | −515.883 | + | 297.845i | −0.828063 | + | 0.478082i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5000 | + | 21.6506i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 471.277 | + | 272.092i | 0.752839 | + | 0.434652i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 559.019 | + | 968.249i | 0.890157 | + | 1.54180i | ||||
\(629\) | 1286.80i | 2.04578i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −676.922 | −1.07278 | −0.536388 | − | 0.843971i | \(-0.680212\pi\) | ||||
−0.536388 | + | 0.843971i | \(0.680212\pi\) | |||||||
\(632\) | 0.250880 | − | 0.144846i | 0.000396962 | − | 0.000229186i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −51.6190 | + | 89.4067i | −0.0814180 | + | 0.141020i | ||||
\(635\) | 369.377 | + | 213.260i | 0.581695 | + | 0.335842i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 61.5938 | + | 106.684i | 0.0966936 | + | 0.167478i | ||||
\(638\) | 0.145910i | 0.000228699i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.387666 | −0.000605729 | ||||||||
\(641\) | −620.711 | + | 358.367i | −0.968347 | + | 0.559076i | −0.898732 | − | 0.438498i | \(-0.855511\pi\) |
−0.0696153 | + | 0.997574i | \(0.522177\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 176.092 | − | 305.000i | 0.273860 | − | 0.474339i | −0.695987 | − | 0.718054i | \(-0.745033\pi\) |
0.969847 | + | 0.243715i | \(0.0783662\pi\) | |||||||
\(644\) | −817.531 | − | 472.002i | −1.26946 | − | 0.732922i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 999.904 | + | 1731.88i | 1.54784 | + | 2.68094i | ||||
\(647\) | − | 719.658i | − | 1.11230i | −0.831082 | − | 0.556150i | \(-0.812278\pi\) | ||
0.831082 | − | 0.556150i | \(-0.187722\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.53528 | 0.00698810 | ||||||||
\(650\) | −106.310 | + | 61.3781i | −0.163554 | + | 0.0944279i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 493.788 | − | 855.266i | 0.757344 | − | 1.31176i | ||||
\(653\) | 925.220 | + | 534.176i | 1.41688 | + | 0.818034i | 0.996023 | − | 0.0890951i | \(-0.0283975\pi\) |
0.420853 | + | 0.907129i | \(0.361731\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 32.0777 | + | 55.5602i | 0.0489736 | + | 0.0848248i | ||||
\(656\) | − | 967.911i | − | 1.47547i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 652.396 | 0.991484 | ||||||||
\(659\) | −896.771 | + | 517.751i | −1.36081 | + | 0.785662i | −0.989731 | − | 0.142941i | \(-0.954344\pi\) |
−0.371075 | + | 0.928603i | \(0.621011\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 559.316 | − | 968.764i | 0.846166 | − | 1.46560i | −0.0384381 | − | 0.999261i | \(-0.512238\pi\) |
0.884604 | − | 0.466342i | \(-0.154428\pi\) | |||||||
\(662\) | 697.641 | + | 402.783i | 1.05384 | + | 0.608434i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.0954187 | − | 0.165270i | −0.000143703 | − | 0.000248901i | ||||
\(665\) | − | 473.061i | − | 0.711370i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.2800 | 0.0334033 | ||||||||
\(668\) | −291.934 | + | 168.548i | −0.437026 | + | 0.252317i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 324.021 | − | 561.220i | 0.483613 | − | 0.837642i | ||||
\(671\) | 1.13087 | + | 0.652911i | 0.00168536 | + | 0.000973042i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 199.783 | + | 346.035i | 0.296855 | + | 0.514168i | 0.975415 | − | 0.220377i | \(-0.0707289\pi\) |
−0.678560 | + | 0.734545i | \(0.737396\pi\) | |||||||
\(674\) | 692.431i | 1.02735i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 374.870 | 0.554541 | ||||||||
\(677\) | −43.7403 | + | 25.2535i | −0.0646091 | + | 0.0373021i | −0.531957 | − | 0.846772i | \(-0.678543\pi\) |
0.467347 | + | 0.884074i | \(0.345210\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −274.171 | + | 474.878i | −0.403786 | + | 0.699378i | ||||
\(680\) | 0.278698 | + | 0.160907i | 0.000409851 | + | 0.000236627i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.36588 | + | 5.82988i | 0.00493531 | + | 0.00854821i | ||||
\(683\) | − | 857.907i | − | 1.25609i | −0.778179 | − | 0.628043i | \(-0.783856\pi\) | ||
0.778179 | − | 0.628043i | \(-0.216144\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −262.408 | −0.383077 | ||||||||
\(686\) | 677.835 | − | 391.348i | 0.988097 | − | 0.570478i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 266.256 | − | 461.170i | 0.387001 | − | 0.670305i | ||||
\(689\) | −52.6033 | − | 30.3705i | −0.0763473 | − | 0.0440791i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 106.360 | + | 184.220i | 0.153921 | + | 0.266599i | 0.932666 | − | 0.360742i | \(-0.117476\pi\) |
−0.778744 | + | 0.627341i | \(0.784143\pi\) | |||||||
\(692\) | − | 758.248i | − | 1.09573i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −716.236 | −1.03204 | ||||||||
\(695\) | −60.8824 | + | 35.1505i | −0.0876006 | + | 0.0505763i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −803.877 | + | 1392.36i | −1.15334 | + | 1.99764i | ||||
\(698\) | 1271.52 | + | 734.114i | 1.82167 | + | 1.05174i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −79.5324 | − | 137.754i | −0.113618 | − | 0.196792i | ||||
\(701\) | 991.279i | 1.41409i | 0.707167 | + | 0.707046i | \(0.249973\pi\) | ||||
−0.707167 | + | 0.707046i | \(0.750027\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1289.17 | −1.83381 | ||||||||
\(704\) | 3.81125 | − | 2.20043i | 0.00541371 | − | 0.00312560i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 972.869 | − | 1685.06i | 1.37800 | − | 2.38677i | ||||
\(707\) | 125.082 | + | 72.2163i | 0.176920 | + | 0.102145i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −403.573 | − | 699.009i | −0.569215 | − | 0.985909i | −0.996644 | − | 0.0818599i | \(-0.973914\pi\) |
0.427429 | − | 0.904049i | \(-0.359419\pi\) | |||||||
\(710\) | 71.8193i | 0.101154i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.405983 | 0.000570200 | ||||||||
\(713\) | 890.207 | − | 513.961i | 1.24854 | − | 0.720843i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.666611 | − | 1.15460i | 0.000932324 | − | 0.00161483i | ||||
\(716\) | 385.485 | + | 222.560i | 0.538387 | + | 0.310838i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −481.581 | − | 834.122i | −0.670725 | − | 1.16173i | ||||
\(719\) | − | 61.3194i | − | 0.0852843i | −0.999090 | − | 0.0426422i | \(-0.986422\pi\) | ||
0.999090 | − | 0.0426422i | \(-0.0135775\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −378.476 | −0.524931 | ||||||||
\(722\) | −850.706 | + | 491.155i | −1.17826 | + | 0.680270i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 438.987 | − | 760.348i | 0.606336 | − | 1.05020i | ||||
\(725\) | 3.25122 | + | 1.87710i | 0.00448445 | + | 0.00258910i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 227.024 | + | 393.217i | 0.312275 | + | 0.540876i | 0.978855 | − | 0.204558i | \(-0.0655756\pi\) |
−0.666579 | + | 0.745434i | \(0.732242\pi\) | |||||||
\(728\) | − | 0.373797i | − | 0.000513458i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −341.294 | −0.467526 | ||||||||
\(731\) | −766.028 | + | 442.266i | −1.04792 | + | 0.605015i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −146.499 | + | 253.744i | −0.199863 | + | 0.346172i | −0.948484 | − | 0.316826i | \(-0.897383\pi\) |
0.748621 | + | 0.662998i | \(0.230716\pi\) | |||||||
\(734\) | −653.388 | − | 377.234i | −0.890174 | − | 0.513942i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −671.516 | − | 1163.10i | −0.912386 | − | 1.58030i | ||||
\(737\) | 7.03821i | 0.00954981i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −228.122 | −0.308690 | −0.154345 | − | 0.988017i | \(-0.549327\pi\) | ||||
−0.154345 | + | 0.988017i | \(0.549327\pi\) | |||||||
\(740\) | −375.403 | + | 216.739i | −0.507301 | + | 0.292890i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 78.6881 | − | 136.292i | 0.106049 | − | 0.183682i | ||||
\(743\) | 177.764 | + | 102.632i | 0.239252 | + | 0.138132i | 0.614833 | − | 0.788657i | \(-0.289223\pi\) |
−0.375581 | + | 0.926790i | \(0.622557\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −29.8156 | − | 51.6422i | −0.0400210 | − | 0.0693184i | ||||
\(746\) | − | 794.672i | − | 1.06524i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7.30306 | −0.00976345 | ||||||||
\(749\) | 1030.46 | − | 594.935i | 1.37578 | − | 0.794306i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −96.3048 | + | 166.805i | −0.128235 | + | 0.222110i | −0.922993 | − | 0.384817i | \(-0.874265\pi\) |
0.794758 | + | 0.606927i | \(0.207598\pi\) | |||||||
\(752\) | 401.810 | + | 231.985i | 0.534322 | + | 0.308491i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9.21701 | + | 15.9643i | 0.0122241 | + | 0.0211728i | ||||
\(755\) | 226.386i | 0.299850i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 750.204 | 0.991023 | 0.495512 | − | 0.868601i | \(-0.334981\pi\) | ||||
0.495512 | + | 0.868601i | \(0.334981\pi\) | |||||||
\(758\) | 1303.65 | − | 752.665i | 1.71986 | − | 0.992962i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.161203 | + | 0.279212i | −0.000212110 | + | 0.000367385i | ||||
\(761\) | −897.102 | − | 517.942i | −1.17885 | − | 0.680607i | −0.223099 | − | 0.974796i | \(-0.571617\pi\) |
−0.955747 | + | 0.294188i | \(0.904951\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 146.481 | + | 253.713i | 0.191980 | + | 0.332520i | ||||
\(764\) | − | 146.608i | − | 0.191896i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1035.21 | 1.35145 | ||||||||
\(767\) | 496.215 | − | 286.490i | 0.646956 | − | 0.373520i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 92.5951 | − | 160.379i | 0.120410 | − | 0.208556i | −0.799520 | − | 0.600640i | \(-0.794912\pi\) |
0.919929 | + | 0.392084i | \(0.128246\pi\) | |||||||
\(770\) | 2.99151 | + | 1.72715i | 0.00388507 | + | 0.00224305i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 305.044 | + | 528.352i | 0.395135 | + | 0.684393i | ||||
\(773\) | 1178.69i | 1.52482i | 0.647093 | + | 0.762411i | \(0.275985\pi\) | ||||
−0.647093 | + | 0.762411i | \(0.724015\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 173.205 | 0.223491 | ||||||||
\(776\) | 0.323645 | − | 0.186857i | 0.000417068 | − | 0.000240794i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −134.400 | + | 232.788i | −0.172751 | + | 0.299214i | ||||
\(779\) | −1394.92 | − | 805.359i | −1.79066 | − | 1.03384i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.390005 | − | 0.675509i | −0.000499367 | − | 0.000864928i | ||||
\(782\) | 2229.78i | 2.85138i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −226.988 | −0.289525 | ||||||||
\(785\) | −541.009 | + | 312.351i | −0.689183 | + | 0.397900i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 57.1483 | − | 98.9837i | 0.0726153 | − | 0.125773i | −0.827431 | − | 0.561567i | \(-0.810199\pi\) |
0.900047 | + | 0.435793i | \(0.143532\pi\) | |||||||
\(788\) | 124.027 | + | 71.6069i | 0.157394 | + | 0.0908717i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 169.108 | + | 292.903i | 0.214061 | + | 0.370764i | ||||
\(791\) | − | 487.572i | − | 0.616400i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 164.975 | 0.208040 | ||||||||
\(794\) | −1694.49 | + | 978.315i | −2.13412 | + | 1.23214i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −209.253 | + | 362.436i | −0.262880 | + | 0.455322i | ||||
\(797\) | 942.410 | + | 544.101i | 1.18245 | + | 0.682686i | 0.956579 | − | 0.291472i | \(-0.0941449\pi\) |
0.225868 | + | 0.974158i | \(0.427478\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −385.340 | − | 667.428i | −0.482278 | − | 0.835330i | ||||
\(800\) | − | 226.301i | − | 0.282877i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 188.912 | 0.235552 | ||||||||
\(803\) | 3.21010 | − | 1.85335i | 0.00399763 | − | 0.00230803i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 263.731 | − | 456.795i | 0.327616 | − | 0.567447i | ||||
\(806\) | 736.538 | + | 425.240i | 0.913819 | + | 0.527594i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.0492178 | − | 0.0852478i | −6.09131e−5 | − | 0.000105505i | ||||
\(809\) | − | 1058.49i | − | 1.30840i | −0.756322 | − | 0.654199i | \(-0.773006\pi\) | ||
0.756322 | − | 0.654199i | \(-0.226994\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −325.951 | −0.401913 | −0.200956 | − | 0.979600i | \(-0.564405\pi\) | ||||
−0.200956 | + | 0.979600i | \(0.564405\pi\) | |||||||
\(812\) | −20.6862 | + | 11.9432i | −0.0254756 | + | 0.0147084i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.70676 | − | 8.15235i | 0.00578226 | − | 0.0100152i | ||||
\(815\) | 477.880 | + | 275.904i | 0.586355 | + | 0.338532i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −443.082 | − | 767.440i | −0.542328 | − | 0.939339i | ||||
\(818\) | − | 314.267i | − | 0.384190i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −541.597 | −0.660485 | ||||||||
\(821\) | 494.193 | − | 285.323i | 0.601941 | − | 0.347531i | −0.167864 | − | 0.985810i | \(-0.553687\pi\) |
0.769805 | + | 0.638280i | \(0.220354\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 580.756 | − | 1005.90i | 0.705658 | − | 1.22223i | −0.260796 | − | 0.965394i | \(-0.583985\pi\) |
0.966454 | − | 0.256841i | \(-0.0826817\pi\) | |||||||
\(824\) | 0.223386 | + | 0.128972i | 0.000271099 | + | 0.000156519i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 742.277 | + | 1285.66i | 0.898640 | + | 1.55649i | ||||
\(827\) | 422.843i | 0.511297i | 0.966770 | + | 0.255649i | \(0.0822890\pi\) | ||||
−0.966770 | + | 0.255649i | \(0.917711\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 455.988 | 0.550046 | 0.275023 | − | 0.961438i | \(-0.411315\pi\) | ||||
0.275023 | + | 0.961438i | \(0.411315\pi\) | |||||||
\(830\) | 192.954 | − | 111.402i | 0.232474 | − | 0.134219i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 277.998 | − | 481.507i | 0.334133 | − | 0.578735i | ||||
\(833\) | 326.525 | + | 188.520i | 0.391987 | + | 0.226314i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −94.1761 | − | 163.118i | −0.112786 | − | 0.195351i | ||||
\(836\) | − | 7.31652i | − | 0.00875182i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1090.20 | −1.30096 | ||||||||
\(839\) | 900.311 | − | 519.795i | 1.07308 | − | 0.619541i | 0.144056 | − | 0.989570i | \(-0.453985\pi\) |
0.929020 | + | 0.370029i | \(0.120652\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −420.218 | + | 727.839i | −0.499665 | + | 0.865445i | ||||
\(842\) | −158.832 | − | 91.7019i | −0.188637 | − | 0.108910i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −217.859 | − | 377.343i | −0.258127 | − | 0.447089i | ||||
\(845\) | 209.458i | 0.247880i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 961.844 | 1.13559 | ||||||||
\(848\) | 96.9277 | − | 55.9612i | 0.114302 | − | 0.0659920i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −187.859 | + | 325.382i | −0.221011 | + | 0.382802i | ||||
\(851\) | −1244.84 | − | 718.709i | −1.46280 | − | 0.844547i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 366.610 | + | 634.988i | 0.429789 | + | 0.744417i | 0.996854 | − | 0.0792562i | \(-0.0252545\pi\) |
−0.567065 | + | 0.823673i | \(0.691921\pi\) | |||||||
\(854\) | 427.441i | 0.500516i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.810936 | −0.000947355 | ||||||||
\(857\) | −163.543 | + | 94.4217i | −0.190832 | + | 0.110177i | −0.592372 | − | 0.805665i | \(-0.701808\pi\) |
0.401540 | + | 0.915842i | \(0.368475\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −626.637 | + | 1085.37i | −0.729496 | + | 1.26352i | 0.227600 | + | 0.973755i | \(0.426912\pi\) |
−0.957096 | + | 0.289770i | \(0.906421\pi\) | |||||||
\(860\) | −258.049 | − | 148.984i | −0.300057 | − | 0.173238i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 290.933 | + | 503.911i | 0.337509 | + | 0.584583i | ||||
\(863\) | − | 1407.42i | − | 1.63085i | −0.578865 | − | 0.815423i | \(-0.696504\pi\) | ||
0.578865 | − | 0.815423i | \(-0.303496\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 423.671 | 0.489793 | ||||||||
\(866\) | 847.710 | − | 489.426i | 0.978880 | − | 0.565156i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −551.017 | + | 954.390i | −0.634813 | + | 1.09953i | ||||
\(869\) | −3.18115 | − | 1.83664i | −0.00366070 | − | 0.00211350i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 444.598 | + | 770.066i | 0.510445 | + | 0.884117i | ||||
\(872\) | − | 0.199663i | − | 0.000228972i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2233.89 | −2.55594 | ||||||||
\(875\) | 76.9701 | − | 44.4387i | 0.0879658 | − | 0.0507871i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 387.079 | − | 670.440i | 0.441367 | − | 0.764470i | −0.556424 | − | 0.830898i | \(-0.687827\pi\) |
0.997791 | + | 0.0664286i | \(0.0211605\pi\) | |||||||
\(878\) | −1353.39 | − | 781.378i | −1.54144 | − | 0.889952i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.22831 | + | 2.12750i | 0.00139581 | + | 0.00241761i | ||||
\(881\) | 1442.00i | 1.63678i | 0.574662 | + | 0.818391i | \(0.305134\pi\) | ||||
−0.574662 | + | 0.818391i | \(0.694866\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1399.40 | 1.58483 | 0.792415 | − | 0.609983i | \(-0.208824\pi\) | ||||
0.792415 | + | 0.609983i | \(0.208824\pi\) | |||||||
\(884\) | −799.044 | + | 461.328i | −0.903896 | + | 0.521865i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 61.3841 | − | 106.320i | 0.0692823 | − | 0.120000i | ||||
\(887\) | −1215.08 | − | 701.524i | −1.36987 | − | 0.790895i | −0.378959 | − | 0.925413i | \(-0.623718\pi\) |
−0.990911 | + | 0.134518i | \(0.957051\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −758.158 | − | 1313.17i | −0.852822 | − | 1.47713i | ||||
\(890\) | 473.987i | 0.532569i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1076.39 | 1.20672 | ||||||||
\(893\) | 668.659 | − | 386.050i | 0.748778 | − | 0.432307i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −124.355 | + | 215.389i | −0.138944 | + | 0.240659i | ||||
\(896\) | 1.19355 | + | 0.689096i | 0.00133209 | + | 0.000769080i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 922.018 | + | 1596.98i | 1.02675 | + | 1.77838i | ||||
\(899\) | − | 26.0098i | − | 0.0289319i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −185.909 | −0.206337 | ||||||||
\(902\) | 10.1857 | − | 5.88074i | 0.0112924 | − | 0.00651966i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.166148 | + | 0.287777i | −0.000183792 | + | 0.000318338i | ||||
\(905\) | 424.844 | + | 245.284i | 0.469441 | + | 0.271032i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 456.415 | + | 790.534i | 0.503214 | + | 0.871592i | 0.999993 | + | 0.00371472i | \(0.00118244\pi\) |
−0.496780 | + | 0.867877i | \(0.665484\pi\) | |||||||
\(908\) | − | 331.505i | − | 0.365093i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 436.410 | 0.479572 | ||||||||
\(911\) | 757.008 | − | 437.059i | 0.830963 | − | 0.479757i | −0.0232190 | − | 0.999730i | \(-0.507391\pi\) |
0.854182 | + | 0.519973i | \(0.174058\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.20991 | + | 2.09562i | −0.00132520 | + | 0.00229531i | ||||
\(914\) | −1129.79 | − | 652.284i | −1.23609 | − | 0.713658i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −378.336 | − | 655.297i | −0.413030 | − | 0.715390i | ||||
\(917\) | − | 228.079i | − | 0.248723i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −234.165 | −0.254804 | −0.127402 | − | 0.991851i | \(-0.540664\pi\) | ||||
−0.127402 | + | 0.991851i | \(0.540664\pi\) | |||||||
\(920\) | −0.311321 | + | 0.179741i | −0.000338392 | + | 0.000195371i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1032.49 | + | 1788.33i | −1.11984 | + | 1.93962i | ||||
\(923\) | −85.3427 | − | 49.2726i | −0.0924623 | − | 0.0533831i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −121.103 | − | 209.756i | −0.130922 | − | 0.226763i | ||||
\(926\) | 26.5728i | 0.0286963i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −33.9831 | −0.0366197 | ||||||||
\(929\) | −200.544 | + | 115.784i | −0.215870 | + | 0.124633i | −0.604037 | − | 0.796957i | \(-0.706442\pi\) |
0.388166 | + | 0.921589i | \(0.373109\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −188.867 | + | 327.127i | −0.202865 | + | 0.351372i | ||||
\(932\) | 948.857 | + | 547.823i | 1.01809 | + | 0.587793i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −79.6155 | − | 137.898i | −0.0852414 | − | 0.147643i | ||||
\(935\) | − | 4.08058i | − | 0.00436426i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −140.899 | −0.150372 | −0.0751861 | − | 0.997170i | \(-0.523955\pi\) | ||||
−0.0751861 | + | 0.997170i | \(0.523955\pi\) | |||||||
\(938\) | −1995.19 | + | 1151.92i | −2.12707 | + | 1.22806i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 129.808 | − | 224.834i | 0.138094 | − | 0.239185i | ||||
\(941\) | 442.126 | + | 255.262i | 0.469847 | + | 0.271266i | 0.716176 | − | 0.697920i | \(-0.245891\pi\) |
−0.246329 | + | 0.969186i | \(0.579224\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −897.972 | − | 1555.33i | −0.952251 | − | 1.64935i | ||||
\(944\) | 1055.78i | 1.11841i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.47077 | 0.00684014 | ||||||||
\(947\) | 724.176 | − | 418.103i | 0.764706 | − | 0.441503i | −0.0662770 | − | 0.997801i | \(-0.521112\pi\) |
0.830983 | + | 0.556298i | \(0.187779\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 234.149 | − | 405.559i | 0.246733 | − | 0.427354i | ||||
\(950\) | −325.982 | − | 188.206i | −0.343139 | − | 0.198111i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.572039 | − | 0.990800i | −0.000600881 | − | 0.00104076i | ||||
\(953\) | − | 914.987i | − | 0.960112i | −0.877238 | − | 0.480056i | \(-0.840616\pi\) | ||
0.877238 | − | 0.480056i | \(-0.159384\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 81.9174 | 0.0857773 | ||||||||
\(956\) | 177.017 | − | 102.201i | 0.185164 | − | 0.106904i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1059.98 | + | 1835.93i | −1.10645 | + | 1.91642i | ||||
\(959\) | 807.901 | + | 466.442i | 0.842441 | + | 0.486384i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −119.501 | − | 206.982i | −0.124351 | − | 0.215382i | ||||
\(962\) | − | 1189.29i | − | 1.23627i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −764.597 | −0.793150 | ||||||||
\(965\) | −295.216 | + | 170.443i | −0.305924 | + | 0.176625i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 636.666 | − | 1102.74i | 0.658393 | − | 1.14037i | −0.322639 | − | 0.946522i | \(-0.604570\pi\) |
0.981032 | − | 0.193848i | \(-0.0620968\pi\) | |||||||
\(968\) | −0.567704 | − | 0.327764i | −0.000586472 | − | 0.000338600i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 218.156 | + | 377.857i | 0.224903 | + | 0.389543i | ||||
\(971\) | 1246.37i | 1.28360i | 0.766872 | + | 0.641800i | \(0.221812\pi\) | ||||
−0.766872 | + | 0.641800i | \(0.778188\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 249.927 | 0.256862 | ||||||||
\(974\) | 1079.94 | − | 623.503i | 1.10877 | − | 0.640147i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −151.993 | + | 263.260i | −0.155731 | + | 0.269734i | ||||
\(977\) | −1011.30 | − | 583.875i | −1.03511 | − | 0.597620i | −0.116665 | − | 0.993171i | \(-0.537220\pi\) |
−0.918444 | + | 0.395551i | \(0.870554\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.57392 | − | 4.45816i | −0.00262913 | − | 0.00455379i | ||||
\(980\) | 127.012i | 0.129604i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1069.52 | −1.08912 | ||||||||
\(983\) | 82.9062 | − | 47.8659i | 0.0843400 | − | 0.0486937i | −0.457237 | − | 0.889345i | \(-0.651161\pi\) |
0.541577 | + | 0.840651i | \(0.317828\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −40.0103 | + | 69.2999i | −0.0406196 | + | 0.0703553i | ||||
\(986\) | 48.8618 | + | 28.2104i | 0.0495556 | + | 0.0286109i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −462.179 | − | 800.517i | −0.467792 | − | 0.810240i | ||||
\(989\) | − | 988.069i | − | 0.999059i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1725.68 | −1.74135 | −0.870674 | − | 0.491860i | \(-0.836317\pi\) | ||||
−0.870674 | + | 0.491860i | \(0.836317\pi\) | |||||||
\(992\) | −1357.81 | + | 783.931i | −1.36876 | + | 0.790253i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 127.662 | − | 221.118i | 0.128433 | − | 0.222452i | ||||
\(995\) | −202.511 | − | 116.920i | −0.203529 | − | 0.117507i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −366.854 | − | 635.410i | −0.367958 | − | 0.637322i | 0.621288 | − | 0.783582i | \(-0.286610\pi\) |
−0.989246 | + | 0.146260i | \(0.953276\pi\) | |||||||
\(998\) | 1621.26i | 1.62451i | ||||||||
\(999\) | 0 | 0 |
(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 | 135.3.i.a.71.2 | 16 | ||
3.2 | odd | 2 | 45.3.i.a.41.7 | yes | 16 | ||
4.3 | odd | 2 | 2160.3.bs.c.881.8 | 16 | |||
5.2 | odd | 4 | 675.3.i.c.449.4 | 32 | |||
5.3 | odd | 4 | 675.3.i.c.449.13 | 32 | |||
5.4 | even | 2 | 675.3.j.b.476.7 | 16 | |||
9.2 | odd | 6 | inner | 135.3.i.a.116.2 | 16 | ||
9.4 | even | 3 | 405.3.c.a.161.4 | 16 | |||
9.5 | odd | 6 | 405.3.c.a.161.13 | 16 | |||
9.7 | even | 3 | 45.3.i.a.11.7 | ✓ | 16 | ||
12.11 | even | 2 | 720.3.bs.c.401.5 | 16 | |||
15.2 | even | 4 | 225.3.i.b.149.13 | 32 | |||
15.8 | even | 4 | 225.3.i.b.149.4 | 32 | |||
15.14 | odd | 2 | 225.3.j.b.176.2 | 16 | |||
36.7 | odd | 6 | 720.3.bs.c.641.5 | 16 | |||
36.11 | even | 6 | 2160.3.bs.c.1601.8 | 16 | |||
45.2 | even | 12 | 675.3.i.c.224.13 | 32 | |||
45.7 | odd | 12 | 225.3.i.b.74.4 | 32 | |||
45.29 | odd | 6 | 675.3.j.b.251.7 | 16 | |||
45.34 | even | 6 | 225.3.j.b.101.2 | 16 | |||
45.38 | even | 12 | 675.3.i.c.224.4 | 32 | |||
45.43 | odd | 12 | 225.3.i.b.74.13 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.3.i.a.11.7 | ✓ | 16 | 9.7 | even | 3 | ||
45.3.i.a.41.7 | yes | 16 | 3.2 | odd | 2 | ||
135.3.i.a.71.2 | 16 | 1.1 | even | 1 | trivial | ||
135.3.i.a.116.2 | 16 | 9.2 | odd | 6 | inner | ||
225.3.i.b.74.4 | 32 | 45.7 | odd | 12 | |||
225.3.i.b.74.13 | 32 | 45.43 | odd | 12 | |||
225.3.i.b.149.4 | 32 | 15.8 | even | 4 | |||
225.3.i.b.149.13 | 32 | 15.2 | even | 4 | |||
225.3.j.b.101.2 | 16 | 45.34 | even | 6 | |||
225.3.j.b.176.2 | 16 | 15.14 | odd | 2 | |||
405.3.c.a.161.4 | 16 | 9.4 | even | 3 | |||
405.3.c.a.161.13 | 16 | 9.5 | odd | 6 | |||
675.3.i.c.224.4 | 32 | 45.38 | even | 12 | |||
675.3.i.c.224.13 | 32 | 45.2 | even | 12 | |||
675.3.i.c.449.4 | 32 | 5.2 | odd | 4 | |||
675.3.i.c.449.13 | 32 | 5.3 | odd | 4 | |||
675.3.j.b.251.7 | 16 | 45.29 | odd | 6 | |||
675.3.j.b.476.7 | 16 | 5.4 | even | 2 | |||
720.3.bs.c.401.5 | 16 | 12.11 | even | 2 | |||
720.3.bs.c.641.5 | 16 | 36.7 | odd | 6 | |||
2160.3.bs.c.881.8 | 16 | 4.3 | odd | 2 | |||
2160.3.bs.c.1601.8 | 16 | 36.11 | even | 6 |