Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,2,Mod(67,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1078.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.e (of order \(3\), 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: | \(8.60787333789\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 154) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1078.67 |
Dual form | 1078.2.e.d.177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(981\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | −0.684819 | − | 0.728714i | \(-0.740119\pi\) |
0.973494 | + | 0.228714i | \(0.0734519\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | + | 1.73205i | 0.333333 | + | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | ||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | −5.00000 | −1.38675 | −0.693375 | − | 0.720577i | \(-0.743877\pi\) | ||||
−0.693375 | + | 0.720577i | \(0.743877\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 3.00000 | − | 5.19615i | 0.727607 | − | 1.26025i | −0.230285 | − | 0.973123i | \(-0.573966\pi\) |
0.957892 | − | 0.287129i | \(-0.0927008\pi\) | |||||||
\(18\) | 1.00000 | − | 1.73205i | 0.235702 | − | 0.408248i | ||||
\(19\) | 1.00000 | + | 1.73205i | 0.229416 | + | 0.397360i | 0.957635 | − | 0.287984i | \(-0.0929851\pi\) |
−0.728219 | + | 0.685344i | \(0.759652\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −3.00000 | − | 5.19615i | −0.625543 | − | 1.08347i | −0.988436 | − | 0.151642i | \(-0.951544\pi\) |
0.362892 | − | 0.931831i | \(-0.381789\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | 2.50000 | − | 4.33013i | 0.500000 | − | 0.866025i | ||||
\(26\) | 2.50000 | + | 4.33013i | 0.490290 | + | 0.849208i | ||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | − | 6.92820i | 0.718421 | − | 1.24434i | −0.243204 | − | 0.969975i | \(-0.578198\pi\) |
0.961625 | − | 0.274367i | \(-0.0884683\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −0.500000 | − | 0.866025i | −0.0870388 | − | 0.150756i | ||||
\(34\) | −6.00000 | −1.02899 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.00000 | −0.333333 | ||||||||
\(37\) | −1.00000 | − | 1.73205i | −0.164399 | − | 0.284747i | 0.772043 | − | 0.635571i | \(-0.219235\pi\) |
−0.936442 | + | 0.350823i | \(0.885902\pi\) | |||||||
\(38\) | 1.00000 | − | 1.73205i | 0.162221 | − | 0.280976i | ||||
\(39\) | −2.50000 | + | 4.33013i | −0.400320 | + | 0.693375i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0.500000 | + | 0.866025i | 0.0753778 | + | 0.130558i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.00000 | + | 5.19615i | −0.442326 | + | 0.766131i | ||||
\(47\) | 3.00000 | + | 5.19615i | 0.437595 | + | 0.757937i | 0.997503 | − | 0.0706177i | \(-0.0224970\pi\) |
−0.559908 | + | 0.828554i | \(0.689164\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.00000 | −0.707107 | ||||||||
\(51\) | −3.00000 | − | 5.19615i | −0.420084 | − | 0.727607i | ||||
\(52\) | 2.50000 | − | 4.33013i | 0.346688 | − | 0.600481i | ||||
\(53\) | 6.00000 | − | 10.3923i | 0.824163 | − | 1.42749i | −0.0783936 | − | 0.996922i | \(-0.524979\pi\) |
0.902557 | − | 0.430570i | \(-0.141688\pi\) | |||||||
\(54\) | −2.50000 | − | 4.33013i | −0.340207 | − | 0.589256i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.00000 | 0.264906 | ||||||||
\(58\) | −1.50000 | − | 2.59808i | −0.196960 | − | 0.341144i | ||||
\(59\) | −1.50000 | + | 2.59808i | −0.195283 | + | 0.338241i | −0.946993 | − | 0.321253i | \(-0.895896\pi\) |
0.751710 | + | 0.659494i | \(0.229229\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.50000 | − | 6.06218i | −0.448129 | − | 0.776182i | 0.550135 | − | 0.835076i | \(-0.314576\pi\) |
−0.998264 | + | 0.0588933i | \(0.981243\pi\) | |||||||
\(62\) | −8.00000 | −1.01600 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.500000 | + | 0.866025i | −0.0615457 | + | 0.106600i | ||||
\(67\) | 6.50000 | − | 11.2583i | 0.794101 | − | 1.37542i | −0.129307 | − | 0.991605i | \(-0.541275\pi\) |
0.923408 | − | 0.383819i | \(-0.125391\pi\) | |||||||
\(68\) | 3.00000 | + | 5.19615i | 0.363803 | + | 0.630126i | ||||
\(69\) | −6.00000 | −0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.0000 | −1.42414 | −0.712069 | − | 0.702109i | \(-0.752242\pi\) | ||||
−0.712069 | + | 0.702109i | \(0.752242\pi\) | |||||||
\(72\) | 1.00000 | + | 1.73205i | 0.117851 | + | 0.204124i | ||||
\(73\) | −5.00000 | + | 8.66025i | −0.585206 | + | 1.01361i | 0.409644 | + | 0.912245i | \(0.365653\pi\) |
−0.994850 | + | 0.101361i | \(0.967680\pi\) | |||||||
\(74\) | −1.00000 | + | 1.73205i | −0.116248 | + | 0.201347i | ||||
\(75\) | −2.50000 | − | 4.33013i | −0.288675 | − | 0.500000i | ||||
\(76\) | −2.00000 | −0.229416 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.00000 | 0.566139 | ||||||||
\(79\) | 0.500000 | + | 0.866025i | 0.0562544 | + | 0.0974355i | 0.892781 | − | 0.450490i | \(-0.148751\pi\) |
−0.836527 | + | 0.547926i | \(0.815418\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −3.00000 | − | 5.19615i | −0.331295 | − | 0.573819i | ||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.00000 | + | 3.46410i | 0.215666 | + | 0.373544i | ||||
\(87\) | 1.50000 | − | 2.59808i | 0.160817 | − | 0.278543i | ||||
\(88\) | 0.500000 | − | 0.866025i | 0.0533002 | − | 0.0923186i | ||||
\(89\) | 3.00000 | + | 5.19615i | 0.317999 | + | 0.550791i | 0.980071 | − | 0.198650i | \(-0.0636557\pi\) |
−0.662071 | + | 0.749441i | \(0.730322\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 6.00000 | 0.625543 | ||||||||
\(93\) | −4.00000 | − | 6.92820i | −0.414781 | − | 0.718421i | ||||
\(94\) | 3.00000 | − | 5.19615i | 0.309426 | − | 0.535942i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.500000 | + | 0.866025i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | 13.0000 | 1.31995 | 0.659975 | − | 0.751288i | \(-0.270567\pi\) | ||||
0.659975 | + | 0.751288i | \(0.270567\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | 2.50000 | + | 4.33013i | 0.250000 | + | 0.433013i | ||||
\(101\) | 1.50000 | − | 2.59808i | 0.149256 | − | 0.258518i | −0.781697 | − | 0.623658i | \(-0.785646\pi\) |
0.930953 | + | 0.365140i | \(0.118979\pi\) | |||||||
\(102\) | −3.00000 | + | 5.19615i | −0.297044 | + | 0.514496i | ||||
\(103\) | −2.00000 | − | 3.46410i | −0.197066 | − | 0.341328i | 0.750510 | − | 0.660859i | \(-0.229808\pi\) |
−0.947576 | + | 0.319531i | \(0.896475\pi\) | |||||||
\(104\) | −5.00000 | −0.490290 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.0000 | −1.16554 | ||||||||
\(107\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(108\) | −2.50000 | + | 4.33013i | −0.240563 | + | 0.416667i | ||||
\(109\) | −7.00000 | + | 12.1244i | −0.670478 | + | 1.16130i | 0.307290 | + | 0.951616i | \(0.400578\pi\) |
−0.977769 | + | 0.209687i | \(0.932756\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.00000 | −0.189832 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.00000 | 0.846649 | 0.423324 | − | 0.905978i | \(-0.360863\pi\) | ||||
0.423324 | + | 0.905978i | \(0.360863\pi\) | |||||||
\(114\) | −1.00000 | − | 1.73205i | −0.0936586 | − | 0.162221i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.50000 | + | 2.59808i | −0.139272 | + | 0.241225i | ||||
\(117\) | −5.00000 | − | 8.66025i | −0.462250 | − | 0.800641i | ||||
\(118\) | 3.00000 | 0.276172 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | −3.50000 | + | 6.06218i | −0.316875 | + | 0.548844i | ||||
\(123\) | 3.00000 | − | 5.19615i | 0.270501 | − | 0.468521i | ||||
\(124\) | 4.00000 | + | 6.92820i | 0.359211 | + | 0.622171i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.0000 | −1.15356 | −0.576782 | − | 0.816898i | \(-0.695692\pi\) | ||||
−0.576782 | + | 0.816898i | \(0.695692\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | −2.00000 | + | 3.46410i | −0.176090 | + | 0.304997i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.00000 | + | 5.19615i | 0.262111 | + | 0.453990i | 0.966803 | − | 0.255524i | \(-0.0822479\pi\) |
−0.704692 | + | 0.709514i | \(0.748915\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −13.0000 | −1.12303 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.00000 | − | 5.19615i | 0.257248 | − | 0.445566i | ||||
\(137\) | −7.50000 | + | 12.9904i | −0.640768 | + | 1.10984i | 0.344493 | + | 0.938789i | \(0.388051\pi\) |
−0.985262 | + | 0.171054i | \(0.945283\pi\) | |||||||
\(138\) | 3.00000 | + | 5.19615i | 0.255377 | + | 0.442326i | ||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | 6.00000 | + | 10.3923i | 0.503509 | + | 0.872103i | ||||
\(143\) | −2.50000 | + | 4.33013i | −0.209061 | + | 0.362103i | ||||
\(144\) | 1.00000 | − | 1.73205i | 0.0833333 | − | 0.144338i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.0000 | 0.827606 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.00000 | 0.164399 | ||||||||
\(149\) | 3.00000 | + | 5.19615i | 0.245770 | + | 0.425685i | 0.962348 | − | 0.271821i | \(-0.0876260\pi\) |
−0.716578 | + | 0.697507i | \(0.754293\pi\) | |||||||
\(150\) | −2.50000 | + | 4.33013i | −0.204124 | + | 0.353553i | ||||
\(151\) | 0.500000 | − | 0.866025i | 0.0406894 | − | 0.0704761i | −0.844963 | − | 0.534824i | \(-0.820378\pi\) |
0.885653 | + | 0.464348i | \(0.153711\pi\) | |||||||
\(152\) | 1.00000 | + | 1.73205i | 0.0811107 | + | 0.140488i | ||||
\(153\) | 12.0000 | 0.970143 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.50000 | − | 4.33013i | −0.200160 | − | 0.346688i | ||||
\(157\) | −2.00000 | + | 3.46410i | −0.159617 | + | 0.276465i | −0.934731 | − | 0.355357i | \(-0.884359\pi\) |
0.775113 | + | 0.631822i | \(0.217693\pi\) | |||||||
\(158\) | 0.500000 | − | 0.866025i | 0.0397779 | − | 0.0688973i | ||||
\(159\) | −6.00000 | − | 10.3923i | −0.475831 | − | 0.824163i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −8.50000 | − | 14.7224i | −0.665771 | − | 1.15315i | −0.979076 | − | 0.203497i | \(-0.934769\pi\) |
0.313304 | − | 0.949653i | \(-0.398564\pi\) | |||||||
\(164\) | −3.00000 | + | 5.19615i | −0.234261 | + | 0.405751i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.00000 | + | 5.19615i | 0.232845 | + | 0.403300i | ||||
\(167\) | −9.00000 | −0.696441 | −0.348220 | − | 0.937413i | \(-0.613214\pi\) | ||||
−0.348220 | + | 0.937413i | \(0.613214\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.00000 | + | 3.46410i | −0.152944 | + | 0.264906i | ||||
\(172\) | 2.00000 | − | 3.46410i | 0.152499 | − | 0.264135i | ||||
\(173\) | −7.50000 | − | 12.9904i | −0.570214 | − | 0.987640i | −0.996544 | − | 0.0830722i | \(-0.973527\pi\) |
0.426329 | − | 0.904568i | \(-0.359807\pi\) | |||||||
\(174\) | −3.00000 | −0.227429 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 1.50000 | + | 2.59808i | 0.112747 | + | 0.195283i | ||||
\(178\) | 3.00000 | − | 5.19615i | 0.224860 | − | 0.389468i | ||||
\(179\) | −4.50000 | + | 7.79423i | −0.336346 | + | 0.582568i | −0.983742 | − | 0.179585i | \(-0.942524\pi\) |
0.647397 | + | 0.762153i | \(0.275858\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0000 | 0.743294 | 0.371647 | − | 0.928374i | \(-0.378793\pi\) | ||||
0.371647 | + | 0.928374i | \(0.378793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.00000 | −0.517455 | ||||||||
\(184\) | −3.00000 | − | 5.19615i | −0.221163 | − | 0.383065i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.00000 | + | 6.92820i | −0.293294 | + | 0.508001i | ||||
\(187\) | −3.00000 | − | 5.19615i | −0.219382 | − | 0.379980i | ||||
\(188\) | −6.00000 | −0.437595 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.00000 | + | 15.5885i | 0.651217 | + | 1.12794i | 0.982828 | + | 0.184525i | \(0.0590746\pi\) |
−0.331611 | + | 0.943416i | \(0.607592\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | 11.0000 | − | 19.0526i | 0.791797 | − | 1.37143i | −0.133056 | − | 0.991109i | \(-0.542479\pi\) |
0.924853 | − | 0.380325i | \(-0.124188\pi\) | |||||||
\(194\) | −6.50000 | − | 11.2583i | −0.466673 | − | 0.808301i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.00000 | −0.641223 | −0.320612 | − | 0.947211i | \(-0.603888\pi\) | ||||
−0.320612 | + | 0.947211i | \(0.603888\pi\) | |||||||
\(198\) | −1.00000 | − | 1.73205i | −0.0710669 | − | 0.123091i | ||||
\(199\) | 7.00000 | − | 12.1244i | 0.496217 | − | 0.859473i | −0.503774 | − | 0.863836i | \(-0.668055\pi\) |
0.999990 | + | 0.00436292i | \(0.00138876\pi\) | |||||||
\(200\) | 2.50000 | − | 4.33013i | 0.176777 | − | 0.306186i | ||||
\(201\) | −6.50000 | − | 11.2583i | −0.458475 | − | 0.794101i | ||||
\(202\) | −3.00000 | −0.211079 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 6.00000 | 0.420084 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.00000 | + | 3.46410i | −0.139347 | + | 0.241355i | ||||
\(207\) | 6.00000 | − | 10.3923i | 0.417029 | − | 0.722315i | ||||
\(208\) | 2.50000 | + | 4.33013i | 0.173344 | + | 0.300240i | ||||
\(209\) | 2.00000 | 0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.0000 | 1.78991 | 0.894957 | − | 0.446153i | \(-0.147206\pi\) | ||||
0.894957 | + | 0.446153i | \(0.147206\pi\) | |||||||
\(212\) | 6.00000 | + | 10.3923i | 0.412082 | + | 0.713746i | ||||
\(213\) | −6.00000 | + | 10.3923i | −0.411113 | + | 0.712069i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.00000 | 0.340207 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 14.0000 | 0.948200 | ||||||||
\(219\) | 5.00000 | + | 8.66025i | 0.337869 | + | 0.585206i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.0000 | + | 25.9808i | −1.00901 | + | 1.74766i | ||||
\(222\) | 1.00000 | + | 1.73205i | 0.0671156 | + | 0.116248i | ||||
\(223\) | 10.0000 | 0.669650 | 0.334825 | − | 0.942280i | \(-0.391323\pi\) | ||||
0.334825 | + | 0.942280i | \(0.391323\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.0000 | 0.666667 | ||||||||
\(226\) | −4.50000 | − | 7.79423i | −0.299336 | − | 0.518464i | ||||
\(227\) | −3.00000 | + | 5.19615i | −0.199117 | + | 0.344881i | −0.948242 | − | 0.317547i | \(-0.897141\pi\) |
0.749125 | + | 0.662428i | \(0.230474\pi\) | |||||||
\(228\) | −1.00000 | + | 1.73205i | −0.0662266 | + | 0.114708i | ||||
\(229\) | 10.0000 | + | 17.3205i | 0.660819 | + | 1.14457i | 0.980401 | + | 0.197013i | \(0.0631241\pi\) |
−0.319582 | + | 0.947559i | \(0.603543\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.00000 | 0.196960 | ||||||||
\(233\) | 15.0000 | + | 25.9808i | 0.982683 | + | 1.70206i | 0.651813 | + | 0.758380i | \(0.274009\pi\) |
0.330870 | + | 0.943676i | \(0.392658\pi\) | |||||||
\(234\) | −5.00000 | + | 8.66025i | −0.326860 | + | 0.566139i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.50000 | − | 2.59808i | −0.0976417 | − | 0.169120i | ||||
\(237\) | 1.00000 | 0.0649570 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.0000 | 1.35838 | 0.679189 | − | 0.733964i | \(-0.262332\pi\) | ||||
0.679189 | + | 0.733964i | \(0.262332\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.00000 | + | 8.66025i | −0.322078 | + | 0.557856i | −0.980917 | − | 0.194429i | \(-0.937715\pi\) |
0.658838 | + | 0.752285i | \(0.271048\pi\) | |||||||
\(242\) | −0.500000 | + | 0.866025i | −0.0321412 | + | 0.0556702i | ||||
\(243\) | 8.00000 | + | 13.8564i | 0.513200 | + | 0.888889i | ||||
\(244\) | 7.00000 | 0.448129 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.00000 | −0.382546 | ||||||||
\(247\) | −5.00000 | − | 8.66025i | −0.318142 | − | 0.551039i | ||||
\(248\) | 4.00000 | − | 6.92820i | 0.254000 | − | 0.439941i | ||||
\(249\) | −3.00000 | + | 5.19615i | −0.190117 | + | 0.329293i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.00000 | −0.377217 | ||||||||
\(254\) | 6.50000 | + | 11.2583i | 0.407846 | + | 0.706410i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 13.5000 | + | 23.3827i | 0.842107 | + | 1.45857i | 0.888110 | + | 0.459631i | \(0.152018\pi\) |
−0.0460033 | + | 0.998941i | \(0.514648\pi\) | |||||||
\(258\) | 4.00000 | 0.249029 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.00000 | + | 5.19615i | 0.185695 | + | 0.321634i | ||||
\(262\) | 3.00000 | − | 5.19615i | 0.185341 | − | 0.321019i | ||||
\(263\) | 1.50000 | − | 2.59808i | 0.0924940 | − | 0.160204i | −0.816066 | − | 0.577959i | \(-0.803849\pi\) |
0.908560 | + | 0.417755i | \(0.137183\pi\) | |||||||
\(264\) | −0.500000 | − | 0.866025i | −0.0307729 | − | 0.0533002i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.00000 | 0.367194 | ||||||||
\(268\) | 6.50000 | + | 11.2583i | 0.397051 | + | 0.687712i | ||||
\(269\) | −12.0000 | + | 20.7846i | −0.731653 | + | 1.26726i | 0.224523 | + | 0.974469i | \(0.427917\pi\) |
−0.956176 | + | 0.292791i | \(0.905416\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.5000 | − | 21.6506i | −0.759321 | − | 1.31518i | −0.943197 | − | 0.332233i | \(-0.892198\pi\) |
0.183876 | − | 0.982949i | \(-0.441135\pi\) | |||||||
\(272\) | −6.00000 | −0.363803 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.0000 | 0.906183 | ||||||||
\(275\) | −2.50000 | − | 4.33013i | −0.150756 | − | 0.261116i | ||||
\(276\) | 3.00000 | − | 5.19615i | 0.180579 | − | 0.312772i | ||||
\(277\) | 0.500000 | − | 0.866025i | 0.0300421 | − | 0.0520344i | −0.850613 | − | 0.525792i | \(-0.823769\pi\) |
0.880656 | + | 0.473757i | \(0.157103\pi\) | |||||||
\(278\) | −2.00000 | − | 3.46410i | −0.119952 | − | 0.207763i | ||||
\(279\) | 16.0000 | 0.957895 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | −3.00000 | − | 5.19615i | −0.178647 | − | 0.309426i | ||||
\(283\) | −11.0000 | + | 19.0526i | −0.653882 | + | 1.13256i | 0.328291 | + | 0.944577i | \(0.393527\pi\) |
−0.982173 | + | 0.187980i | \(0.939806\pi\) | |||||||
\(284\) | 6.00000 | − | 10.3923i | 0.356034 | − | 0.616670i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.00000 | 0.295656 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.00000 | −0.117851 | ||||||||
\(289\) | −9.50000 | − | 16.4545i | −0.558824 | − | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.50000 | − | 11.2583i | 0.381037 | − | 0.659975i | ||||
\(292\) | −5.00000 | − | 8.66025i | −0.292603 | − | 0.506803i | ||||
\(293\) | 18.0000 | 1.05157 | 0.525786 | − | 0.850617i | \(-0.323771\pi\) | ||||
0.525786 | + | 0.850617i | \(0.323771\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.00000 | − | 1.73205i | −0.0581238 | − | 0.100673i | ||||
\(297\) | 2.50000 | − | 4.33013i | 0.145065 | − | 0.251259i | ||||
\(298\) | 3.00000 | − | 5.19615i | 0.173785 | − | 0.301005i | ||||
\(299\) | 15.0000 | + | 25.9808i | 0.867472 | + | 1.50251i | ||||
\(300\) | 5.00000 | 0.288675 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.00000 | −0.0575435 | ||||||||
\(303\) | −1.50000 | − | 2.59808i | −0.0861727 | − | 0.149256i | ||||
\(304\) | 1.00000 | − | 1.73205i | 0.0573539 | − | 0.0993399i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6.00000 | − | 10.3923i | −0.342997 | − | 0.594089i | ||||
\(307\) | −32.0000 | −1.82634 | −0.913168 | − | 0.407583i | \(-0.866372\pi\) | ||||
−0.913168 | + | 0.407583i | \(0.866372\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.00000 | −0.227552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | − | 20.7846i | 0.680458 | − | 1.17859i | −0.294384 | − | 0.955687i | \(-0.595114\pi\) |
0.974841 | − | 0.222900i | \(-0.0715523\pi\) | |||||||
\(312\) | −2.50000 | + | 4.33013i | −0.141535 | + | 0.245145i | ||||
\(313\) | −3.50000 | − | 6.06218i | −0.197832 | − | 0.342655i | 0.749993 | − | 0.661445i | \(-0.230057\pi\) |
−0.947825 | + | 0.318791i | \(0.896723\pi\) | |||||||
\(314\) | 4.00000 | 0.225733 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.00000 | −0.0562544 | ||||||||
\(317\) | 12.0000 | + | 20.7846i | 0.673987 | + | 1.16738i | 0.976764 | + | 0.214318i | \(0.0687530\pi\) |
−0.302777 | + | 0.953062i | \(0.597914\pi\) | |||||||
\(318\) | −6.00000 | + | 10.3923i | −0.336463 | + | 0.582772i | ||||
\(319\) | 1.50000 | − | 2.59808i | 0.0839839 | − | 0.145464i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.0000 | 0.667698 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | −12.5000 | + | 21.6506i | −0.693375 | + | 1.20096i | ||||
\(326\) | −8.50000 | + | 14.7224i | −0.470771 | + | 0.815400i | ||||
\(327\) | 7.00000 | + | 12.1244i | 0.387101 | + | 0.670478i | ||||
\(328\) | 6.00000 | 0.331295 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.50000 | + | 11.2583i | 0.357272 | + | 0.618814i | 0.987504 | − | 0.157593i | \(-0.0503735\pi\) |
−0.630232 | + | 0.776407i | \(0.717040\pi\) | |||||||
\(332\) | 3.00000 | − | 5.19615i | 0.164646 | − | 0.285176i | ||||
\(333\) | 2.00000 | − | 3.46410i | 0.109599 | − | 0.189832i | ||||
\(334\) | 4.50000 | + | 7.79423i | 0.246229 | + | 0.426481i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.0000 | −1.19842 | −0.599208 | − | 0.800593i | \(-0.704518\pi\) | ||||
−0.599208 | + | 0.800593i | \(0.704518\pi\) | |||||||
\(338\) | −6.00000 | − | 10.3923i | −0.326357 | − | 0.565267i | ||||
\(339\) | 4.50000 | − | 7.79423i | 0.244406 | − | 0.423324i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.00000 | − | 6.92820i | −0.216612 | − | 0.375183i | ||||
\(342\) | 4.00000 | 0.216295 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −4.00000 | −0.215666 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.50000 | + | 12.9904i | −0.403202 | + | 0.698367i | ||||
\(347\) | −6.00000 | + | 10.3923i | −0.322097 | + | 0.557888i | −0.980921 | − | 0.194409i | \(-0.937721\pi\) |
0.658824 | + | 0.752297i | \(0.271054\pi\) | |||||||
\(348\) | 1.50000 | + | 2.59808i | 0.0804084 | + | 0.139272i | ||||
\(349\) | 34.0000 | 1.81998 | 0.909989 | − | 0.414632i | \(-0.136090\pi\) | ||||
0.909989 | + | 0.414632i | \(0.136090\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −25.0000 | −1.33440 | ||||||||
\(352\) | 0.500000 | + | 0.866025i | 0.0266501 | + | 0.0461593i | ||||
\(353\) | 15.0000 | − | 25.9808i | 0.798369 | − | 1.38282i | −0.122308 | − | 0.992492i | \(-0.539030\pi\) |
0.920677 | − | 0.390324i | \(-0.127637\pi\) | |||||||
\(354\) | 1.50000 | − | 2.59808i | 0.0797241 | − | 0.138086i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.00000 | 0.475665 | ||||||||
\(359\) | 4.50000 | + | 7.79423i | 0.237501 | + | 0.411364i | 0.959997 | − | 0.280012i | \(-0.0903384\pi\) |
−0.722496 | + | 0.691375i | \(0.757005\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | − | 12.9904i | 0.394737 | − | 0.683704i | ||||
\(362\) | −5.00000 | − | 8.66025i | −0.262794 | − | 0.455173i | ||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.50000 | + | 6.06218i | 0.182948 | + | 0.316875i | ||||
\(367\) | 19.0000 | − | 32.9090i | 0.991792 | − | 1.71783i | 0.385164 | − | 0.922848i | \(-0.374145\pi\) |
0.606628 | − | 0.794986i | \(-0.292522\pi\) | |||||||
\(368\) | −3.00000 | + | 5.19615i | −0.156386 | + | 0.270868i | ||||
\(369\) | 6.00000 | + | 10.3923i | 0.312348 | + | 0.541002i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 8.00000 | 0.414781 | ||||||||
\(373\) | −5.50000 | − | 9.52628i | −0.284779 | − | 0.493252i | 0.687776 | − | 0.725923i | \(-0.258587\pi\) |
−0.972556 | + | 0.232671i | \(0.925254\pi\) | |||||||
\(374\) | −3.00000 | + | 5.19615i | −0.155126 | + | 0.268687i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.00000 | + | 5.19615i | 0.154713 | + | 0.267971i | ||||
\(377\) | −15.0000 | −0.772539 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.0000 | −1.28416 | −0.642082 | − | 0.766636i | \(-0.721929\pi\) | ||||
−0.642082 | + | 0.766636i | \(0.721929\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.50000 | + | 11.2583i | −0.333005 | + | 0.576782i | ||||
\(382\) | 9.00000 | − | 15.5885i | 0.460480 | − | 0.797575i | ||||
\(383\) | 6.00000 | + | 10.3923i | 0.306586 | + | 0.531022i | 0.977613 | − | 0.210411i | \(-0.0674801\pi\) |
−0.671027 | + | 0.741433i | \(0.734147\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −22.0000 | −1.11977 | ||||||||
\(387\) | −4.00000 | − | 6.92820i | −0.203331 | − | 0.352180i | ||||
\(388\) | −6.50000 | + | 11.2583i | −0.329988 | + | 0.571555i | ||||
\(389\) | −6.00000 | + | 10.3923i | −0.304212 | + | 0.526911i | −0.977086 | − | 0.212847i | \(-0.931726\pi\) |
0.672874 | + | 0.739758i | \(0.265060\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −36.0000 | −1.82060 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.00000 | 0.302660 | ||||||||
\(394\) | 4.50000 | + | 7.79423i | 0.226707 | + | 0.392668i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.00000 | + | 1.73205i | −0.0502519 | + | 0.0870388i | ||||
\(397\) | 1.00000 | + | 1.73205i | 0.0501886 | + | 0.0869291i | 0.890028 | − | 0.455905i | \(-0.150684\pi\) |
−0.839840 | + | 0.542834i | \(0.817351\pi\) | |||||||
\(398\) | −14.0000 | −0.701757 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.00000 | −0.250000 | ||||||||
\(401\) | 4.50000 | + | 7.79423i | 0.224719 | + | 0.389225i | 0.956235 | − | 0.292599i | \(-0.0945202\pi\) |
−0.731516 | + | 0.681824i | \(0.761187\pi\) | |||||||
\(402\) | −6.50000 | + | 11.2583i | −0.324191 | + | 0.561514i | ||||
\(403\) | −20.0000 | + | 34.6410i | −0.996271 | + | 1.72559i | ||||
\(404\) | 1.50000 | + | 2.59808i | 0.0746278 | + | 0.129259i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.00000 | −0.0991363 | ||||||||
\(408\) | −3.00000 | − | 5.19615i | −0.148522 | − | 0.257248i | ||||
\(409\) | −2.00000 | + | 3.46410i | −0.0988936 | + | 0.171289i | −0.911227 | − | 0.411905i | \(-0.864864\pi\) |
0.812333 | + | 0.583193i | \(0.198197\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.50000 | + | 12.9904i | 0.369948 | + | 0.640768i | ||||
\(412\) | 4.00000 | 0.197066 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −12.0000 | −0.589768 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.50000 | − | 4.33013i | 0.122573 | − | 0.212302i | ||||
\(417\) | 2.00000 | − | 3.46410i | 0.0979404 | − | 0.169638i | ||||
\(418\) | −1.00000 | − | 1.73205i | −0.0489116 | − | 0.0847174i | ||||
\(419\) | −12.0000 | −0.586238 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.0000 | −0.779792 | −0.389896 | − | 0.920859i | \(-0.627489\pi\) | ||||
−0.389896 | + | 0.920859i | \(0.627489\pi\) | |||||||
\(422\) | −13.0000 | − | 22.5167i | −0.632830 | − | 1.09609i | ||||
\(423\) | −6.00000 | + | 10.3923i | −0.291730 | + | 0.505291i | ||||
\(424\) | 6.00000 | − | 10.3923i | 0.291386 | − | 0.504695i | ||||
\(425\) | −15.0000 | − | 25.9808i | −0.727607 | − | 1.26025i | ||||
\(426\) | 12.0000 | 0.581402 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.50000 | + | 4.33013i | 0.120701 | + | 0.209061i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.50000 | + | 12.9904i | −0.361262 | + | 0.625725i | −0.988169 | − | 0.153370i | \(-0.950987\pi\) |
0.626907 | + | 0.779094i | \(0.284321\pi\) | |||||||
\(432\) | −2.50000 | − | 4.33013i | −0.120281 | − | 0.208333i | ||||
\(433\) | −14.0000 | −0.672797 | −0.336399 | − | 0.941720i | \(-0.609209\pi\) | ||||
−0.336399 | + | 0.941720i | \(0.609209\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.00000 | − | 12.1244i | −0.335239 | − | 0.580651i | ||||
\(437\) | 6.00000 | − | 10.3923i | 0.287019 | − | 0.497131i | ||||
\(438\) | 5.00000 | − | 8.66025i | 0.238909 | − | 0.413803i | ||||
\(439\) | −9.50000 | − | 16.4545i | −0.453410 | − | 0.785330i | 0.545185 | − | 0.838316i | \(-0.316459\pi\) |
−0.998595 | + | 0.0529862i | \(0.983126\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 30.0000 | 1.42695 | ||||||||
\(443\) | −6.00000 | − | 10.3923i | −0.285069 | − | 0.493753i | 0.687557 | − | 0.726130i | \(-0.258683\pi\) |
−0.972626 | + | 0.232377i | \(0.925350\pi\) | |||||||
\(444\) | 1.00000 | − | 1.73205i | 0.0474579 | − | 0.0821995i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.00000 | − | 8.66025i | −0.236757 | − | 0.410075i | ||||
\(447\) | 6.00000 | 0.283790 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.0000 | 1.41579 | 0.707894 | − | 0.706319i | \(-0.249646\pi\) | ||||
0.707894 | + | 0.706319i | \(0.249646\pi\) | |||||||
\(450\) | −5.00000 | − | 8.66025i | −0.235702 | − | 0.408248i | ||||
\(451\) | 3.00000 | − | 5.19615i | 0.141264 | − | 0.244677i | ||||
\(452\) | −4.50000 | + | 7.79423i | −0.211662 | + | 0.366610i | ||||
\(453\) | −0.500000 | − | 0.866025i | −0.0234920 | − | 0.0406894i | ||||
\(454\) | 6.00000 | 0.281594 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.00000 | 0.0936586 | ||||||||
\(457\) | 11.0000 | + | 19.0526i | 0.514558 | + | 0.891241i | 0.999857 | + | 0.0168929i | \(0.00537742\pi\) |
−0.485299 | + | 0.874348i | \(0.661289\pi\) | |||||||
\(458\) | 10.0000 | − | 17.3205i | 0.467269 | − | 0.809334i | ||||
\(459\) | 15.0000 | − | 25.9808i | 0.700140 | − | 1.21268i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −39.0000 | −1.81641 | −0.908206 | − | 0.418524i | \(-0.862547\pi\) | ||||
−0.908206 | + | 0.418524i | \(0.862547\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.0000 | 1.20832 | 0.604161 | − | 0.796862i | \(-0.293508\pi\) | ||||
0.604161 | + | 0.796862i | \(0.293508\pi\) | |||||||
\(464\) | −1.50000 | − | 2.59808i | −0.0696358 | − | 0.120613i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15.0000 | − | 25.9808i | 0.694862 | − | 1.20354i | ||||
\(467\) | −6.00000 | − | 10.3923i | −0.277647 | − | 0.480899i | 0.693153 | − | 0.720791i | \(-0.256221\pi\) |
−0.970799 | + | 0.239892i | \(0.922888\pi\) | |||||||
\(468\) | 10.0000 | 0.462250 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.00000 | + | 3.46410i | 0.0921551 | + | 0.159617i | ||||
\(472\) | −1.50000 | + | 2.59808i | −0.0690431 | + | 0.119586i | ||||
\(473\) | −2.00000 | + | 3.46410i | −0.0919601 | + | 0.159280i | ||||
\(474\) | −0.500000 | − | 0.866025i | −0.0229658 | − | 0.0397779i | ||||
\(475\) | 10.0000 | 0.458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 24.0000 | 1.09888 | ||||||||
\(478\) | −10.5000 | − | 18.1865i | −0.480259 | − | 0.831833i | ||||
\(479\) | −1.50000 | + | 2.59808i | −0.0685367 | + | 0.118709i | −0.898257 | − | 0.439470i | \(-0.855166\pi\) |
0.829721 | + | 0.558179i | \(0.188500\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.00000 | + | 8.66025i | 0.227980 | + | 0.394874i | ||||
\(482\) | 10.0000 | 0.455488 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 8.00000 | − | 13.8564i | 0.362887 | − | 0.628539i | ||||
\(487\) | 2.00000 | − | 3.46410i | 0.0906287 | − | 0.156973i | −0.817147 | − | 0.576429i | \(-0.804446\pi\) |
0.907776 | + | 0.419456i | \(0.137779\pi\) | |||||||
\(488\) | −3.50000 | − | 6.06218i | −0.158438 | − | 0.274422i | ||||
\(489\) | −17.0000 | −0.768767 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.0000 | −1.35388 | −0.676941 | − | 0.736038i | \(-0.736695\pi\) | ||||
−0.676941 | + | 0.736038i | \(0.736695\pi\) | |||||||
\(492\) | 3.00000 | + | 5.19615i | 0.135250 | + | 0.234261i | ||||
\(493\) | 9.00000 | − | 15.5885i | 0.405340 | − | 0.702069i | ||||
\(494\) | −5.00000 | + | 8.66025i | −0.224961 | + | 0.389643i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.00000 | −0.359211 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 6.00000 | 0.268866 | ||||||||
\(499\) | −4.00000 | − | 6.92820i | −0.179065 | − | 0.310149i | 0.762496 | − | 0.646993i | \(-0.223974\pi\) |
−0.941560 | + | 0.336844i | \(0.890640\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.50000 | + | 7.79423i | −0.201045 | + | 0.348220i | ||||
\(502\) | 6.00000 | + | 10.3923i | 0.267793 | + | 0.463831i | ||||
\(503\) | −21.0000 | −0.936344 | −0.468172 | − | 0.883637i | \(-0.655087\pi\) | ||||
−0.468172 | + | 0.883637i | \(0.655087\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.00000 | + | 5.19615i | 0.133366 | + | 0.230997i | ||||
\(507\) | 6.00000 | − | 10.3923i | 0.266469 | − | 0.461538i | ||||
\(508\) | 6.50000 | − | 11.2583i | 0.288391 | − | 0.499508i | ||||
\(509\) | 3.00000 | + | 5.19615i | 0.132973 | + | 0.230315i | 0.924821 | − | 0.380402i | \(-0.124214\pi\) |
−0.791849 | + | 0.610718i | \(0.790881\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 5.00000 | + | 8.66025i | 0.220755 | + | 0.382360i | ||||
\(514\) | 13.5000 | − | 23.3827i | 0.595459 | − | 1.03137i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.00000 | − | 3.46410i | −0.0880451 | − | 0.152499i | ||||
\(517\) | 6.00000 | 0.263880 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.0000 | −0.658427 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.00000 | + | 15.5885i | −0.394297 | + | 0.682943i | −0.993011 | − | 0.118020i | \(-0.962345\pi\) |
0.598714 | + | 0.800963i | \(0.295679\pi\) | |||||||
\(522\) | 3.00000 | − | 5.19615i | 0.131306 | − | 0.227429i | ||||
\(523\) | −8.00000 | − | 13.8564i | −0.349816 | − | 0.605898i | 0.636401 | − | 0.771358i | \(-0.280422\pi\) |
−0.986216 | + | 0.165460i | \(0.947089\pi\) | |||||||
\(524\) | −6.00000 | −0.262111 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.00000 | −0.130806 | ||||||||
\(527\) | −24.0000 | − | 41.5692i | −1.04546 | − | 1.81078i | ||||
\(528\) | −0.500000 | + | 0.866025i | −0.0217597 | + | 0.0376889i | ||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.00000 | −0.260378 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −30.0000 | −1.29944 | ||||||||
\(534\) | −3.00000 | − | 5.19615i | −0.129823 | − | 0.224860i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.50000 | − | 11.2583i | 0.280757 | − | 0.486286i | ||||
\(537\) | 4.50000 | + | 7.79423i | 0.194189 | + | 0.336346i | ||||
\(538\) | 24.0000 | 1.03471 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.50000 | − | 4.33013i | −0.107483 | − | 0.186167i | 0.807267 | − | 0.590187i | \(-0.200946\pi\) |
−0.914750 | + | 0.404020i | \(0.867613\pi\) | |||||||
\(542\) | −12.5000 | + | 21.6506i | −0.536921 | + | 0.929974i | ||||
\(543\) | 5.00000 | − | 8.66025i | 0.214571 | − | 0.371647i | ||||
\(544\) | 3.00000 | + | 5.19615i | 0.128624 | + | 0.222783i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | −7.50000 | − | 12.9904i | −0.320384 | − | 0.554922i | ||||
\(549\) | 7.00000 | − | 12.1244i | 0.298753 | − | 0.517455i | ||||
\(550\) | −2.50000 | + | 4.33013i | −0.106600 | + | 0.184637i | ||||
\(551\) | 3.00000 | + | 5.19615i | 0.127804 | + | 0.221364i | ||||
\(552\) | −6.00000 | −0.255377 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.00000 | −0.0424859 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.00000 | + | 3.46410i | −0.0848189 | + | 0.146911i | ||||
\(557\) | 3.00000 | − | 5.19615i | 0.127114 | − | 0.220168i | −0.795443 | − | 0.606028i | \(-0.792762\pi\) |
0.922557 | + | 0.385860i | \(0.126095\pi\) | |||||||
\(558\) | −8.00000 | − | 13.8564i | −0.338667 | − | 0.586588i | ||||
\(559\) | 20.0000 | 0.845910 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.00000 | −0.253320 | ||||||||
\(562\) | 3.00000 | + | 5.19615i | 0.126547 | + | 0.219186i | ||||
\(563\) | 9.00000 | − | 15.5885i | 0.379305 | − | 0.656975i | −0.611656 | − | 0.791123i | \(-0.709497\pi\) |
0.990961 | + | 0.134148i | \(0.0428299\pi\) | |||||||
\(564\) | −3.00000 | + | 5.19615i | −0.126323 | + | 0.218797i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 22.0000 | 0.924729 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.0000 | −0.503509 | ||||||||
\(569\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | + | 17.3205i | −0.418487 | + | 0.724841i | −0.995788 | − | 0.0916910i | \(-0.970773\pi\) |
0.577301 | + | 0.816532i | \(0.304106\pi\) | |||||||
\(572\) | −2.50000 | − | 4.33013i | −0.104530 | − | 0.181052i | ||||
\(573\) | 18.0000 | 0.751961 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −30.0000 | −1.25109 | ||||||||
\(576\) | 1.00000 | + | 1.73205i | 0.0416667 | + | 0.0721688i | ||||
\(577\) | −3.50000 | + | 6.06218i | −0.145707 | + | 0.252372i | −0.929636 | − | 0.368478i | \(-0.879879\pi\) |
0.783930 | + | 0.620850i | \(0.213212\pi\) | |||||||
\(578\) | −9.50000 | + | 16.4545i | −0.395148 | + | 0.684416i | ||||
\(579\) | −11.0000 | − | 19.0526i | −0.457144 | − | 0.791797i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −13.0000 | −0.538867 | ||||||||
\(583\) | −6.00000 | − | 10.3923i | −0.248495 | − | 0.430405i | ||||
\(584\) | −5.00000 | + | 8.66025i | −0.206901 | + | 0.358364i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.00000 | − | 15.5885i | −0.371787 | − | 0.643953i | ||||
\(587\) | −9.00000 | −0.371470 | −0.185735 | − | 0.982600i | \(-0.559467\pi\) | ||||
−0.185735 | + | 0.982600i | \(0.559467\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.0000 | 0.659269 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.50000 | + | 7.79423i | −0.185105 | + | 0.320612i | ||||
\(592\) | −1.00000 | + | 1.73205i | −0.0410997 | + | 0.0711868i | ||||
\(593\) | 12.0000 | + | 20.7846i | 0.492781 | + | 0.853522i | 0.999965 | − | 0.00831589i | \(-0.00264706\pi\) |
−0.507184 | + | 0.861838i | \(0.669314\pi\) | |||||||
\(594\) | −5.00000 | −0.205152 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | −7.00000 | − | 12.1244i | −0.286491 | − | 0.496217i | ||||
\(598\) | 15.0000 | − | 25.9808i | 0.613396 | − | 1.06243i | ||||
\(599\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(600\) | −2.50000 | − | 4.33013i | −0.102062 | − | 0.176777i | ||||
\(601\) | 10.0000 | 0.407909 | 0.203954 | − | 0.978980i | \(-0.434621\pi\) | ||||
0.203954 | + | 0.978980i | \(0.434621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 26.0000 | 1.05880 | ||||||||
\(604\) | 0.500000 | + | 0.866025i | 0.0203447 | + | 0.0352381i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.50000 | + | 2.59808i | −0.0609333 | + | 0.105540i | ||||
\(607\) | 4.00000 | + | 6.92820i | 0.162355 | + | 0.281207i | 0.935713 | − | 0.352763i | \(-0.114758\pi\) |
−0.773358 | + | 0.633970i | \(0.781424\pi\) | |||||||
\(608\) | −2.00000 | −0.0811107 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.0000 | − | 25.9808i | −0.606835 | − | 1.05107i | ||||
\(612\) | −6.00000 | + | 10.3923i | −0.242536 | + | 0.420084i | ||||
\(613\) | −13.0000 | + | 22.5167i | −0.525065 | + | 0.909439i | 0.474509 | + | 0.880251i | \(0.342626\pi\) |
−0.999574 | + | 0.0291886i | \(0.990708\pi\) | |||||||
\(614\) | 16.0000 | + | 27.7128i | 0.645707 | + | 1.11840i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.0000 | 0.845428 | 0.422714 | − | 0.906263i | \(-0.361077\pi\) | ||||
0.422714 | + | 0.906263i | \(0.361077\pi\) | |||||||
\(618\) | 2.00000 | + | 3.46410i | 0.0804518 | + | 0.139347i | ||||
\(619\) | 22.0000 | − | 38.1051i | 0.884255 | − | 1.53157i | 0.0376891 | − | 0.999290i | \(-0.488000\pi\) |
0.846566 | − | 0.532284i | \(-0.178666\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −15.0000 | − | 25.9808i | −0.601929 | − | 1.04257i | ||||
\(622\) | −24.0000 | −0.962312 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.00000 | 0.200160 | ||||||||
\(625\) | −12.5000 | − | 21.6506i | −0.500000 | − | 0.866025i | ||||
\(626\) | −3.50000 | + | 6.06218i | −0.139888 | + | 0.242293i | ||||
\(627\) | 1.00000 | − | 1.73205i | 0.0399362 | − | 0.0691714i | ||||
\(628\) | −2.00000 | − | 3.46410i | −0.0798087 | − | 0.138233i | ||||
\(629\) | −12.0000 | −0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0000 | −0.636950 | −0.318475 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(632\) | 0.500000 | + | 0.866025i | 0.0198889 | + | 0.0344486i | ||||
\(633\) | 13.0000 | − | 22.5167i | 0.516704 | − | 0.894957i | ||||
\(634\) | 12.0000 | − | 20.7846i | 0.476581 | − | 0.825462i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 12.0000 | 0.475831 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −3.00000 | −0.118771 | ||||||||
\(639\) | −12.0000 | − | 20.7846i | −0.474713 | − | 0.822226i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.50000 | + | 7.79423i | −0.177739 | + | 0.307854i | −0.941106 | − | 0.338112i | \(-0.890212\pi\) |
0.763367 | + | 0.645966i | \(0.223545\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.0000 | 0.749287 | 0.374643 | − | 0.927169i | \(-0.377765\pi\) | ||||
0.374643 | + | 0.927169i | \(0.377765\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.00000 | − | 10.3923i | −0.236067 | − | 0.408880i | ||||
\(647\) | 18.0000 | − | 31.1769i | 0.707653 | − | 1.22569i | −0.258073 | − | 0.966126i | \(-0.583087\pi\) |
0.965726 | − | 0.259565i | \(-0.0835793\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | 1.50000 | + | 2.59808i | 0.0588802 | + | 0.101983i | ||||
\(650\) | 25.0000 | 0.980581 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.0000 | 0.665771 | ||||||||
\(653\) | 15.0000 | + | 25.9808i | 0.586995 | + | 1.01671i | 0.994623 | + | 0.103558i | \(0.0330227\pi\) |
−0.407628 | + | 0.913148i | \(0.633644\pi\) | |||||||
\(654\) | 7.00000 | − | 12.1244i | 0.273722 | − | 0.474100i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.00000 | − | 5.19615i | −0.117130 | − | 0.202876i | ||||
\(657\) | −20.0000 | −0.780274 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.0000 | −0.467454 | −0.233727 | − | 0.972302i | \(-0.575092\pi\) | ||||
−0.233727 | + | 0.972302i | \(0.575092\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.0000 | + | 29.4449i | −0.661223 | + | 1.14527i | 0.319071 | + | 0.947731i | \(0.396629\pi\) |
−0.980294 | + | 0.197542i | \(0.936704\pi\) | |||||||
\(662\) | 6.50000 | − | 11.2583i | 0.252630 | − | 0.437567i | ||||
\(663\) | 15.0000 | + | 25.9808i | 0.582552 | + | 1.00901i | ||||
\(664\) | −6.00000 | −0.232845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.00000 | −0.154997 | ||||||||
\(667\) | −9.00000 | − | 15.5885i | −0.348481 | − | 0.603587i | ||||
\(668\) | 4.50000 | − | 7.79423i | 0.174110 | − | 0.301568i | ||||
\(669\) | 5.00000 | − | 8.66025i | 0.193311 | − | 0.334825i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.00000 | −0.270232 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.00000 | −0.154189 | −0.0770943 | − | 0.997024i | \(-0.524564\pi\) | ||||
−0.0770943 | + | 0.997024i | \(0.524564\pi\) | |||||||
\(674\) | 11.0000 | + | 19.0526i | 0.423704 | + | 0.733877i | ||||
\(675\) | 12.5000 | − | 21.6506i | 0.481125 | − | 0.833333i | ||||
\(676\) | −6.00000 | + | 10.3923i | −0.230769 | + | 0.399704i | ||||
\(677\) | 21.0000 | + | 36.3731i | 0.807096 | + | 1.39793i | 0.914867 | + | 0.403755i | \(0.132295\pi\) |
−0.107772 | + | 0.994176i | \(0.534372\pi\) | |||||||
\(678\) | −9.00000 | −0.345643 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.00000 | + | 5.19615i | 0.114960 | + | 0.199117i | ||||
\(682\) | −4.00000 | + | 6.92820i | −0.153168 | + | 0.265295i | ||||
\(683\) | 22.5000 | − | 38.9711i | 0.860939 | − | 1.49119i | −0.0100856 | − | 0.999949i | \(-0.503210\pi\) |
0.871024 | − | 0.491240i | \(-0.163456\pi\) | |||||||
\(684\) | −2.00000 | − | 3.46410i | −0.0764719 | − | 0.132453i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.0000 | 0.763048 | ||||||||
\(688\) | 2.00000 | + | 3.46410i | 0.0762493 | + | 0.132068i | ||||
\(689\) | −30.0000 | + | 51.9615i | −1.14291 | + | 1.97958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.5000 | + | 30.3109i | 0.665731 | + | 1.15308i | 0.979086 | + | 0.203445i | \(0.0652137\pi\) |
−0.313355 | + | 0.949636i | \(0.601453\pi\) | |||||||
\(692\) | 15.0000 | 0.570214 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.0000 | 0.455514 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.50000 | − | 2.59808i | 0.0568574 | − | 0.0984798i | ||||
\(697\) | 18.0000 | − | 31.1769i | 0.681799 | − | 1.18091i | ||||
\(698\) | −17.0000 | − | 29.4449i | −0.643459 | − | 1.11450i | ||||
\(699\) | 30.0000 | 1.13470 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.00000 | −0.113308 | −0.0566542 | − | 0.998394i | \(-0.518043\pi\) | ||||
−0.0566542 | + | 0.998394i | \(0.518043\pi\) | |||||||
\(702\) | 12.5000 | + | 21.6506i | 0.471782 | + | 0.817151i | ||||
\(703\) | 2.00000 | − | 3.46410i | 0.0754314 | − | 0.130651i | ||||
\(704\) | 0.500000 | − | 0.866025i | 0.0188445 | − | 0.0326396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −30.0000 | −1.12906 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −3.00000 | −0.112747 | ||||||||
\(709\) | 5.00000 | + | 8.66025i | 0.187779 | + | 0.325243i | 0.944509 | − | 0.328484i | \(-0.106538\pi\) |
−0.756730 | + | 0.653727i | \(0.773204\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.00000 | + | 1.73205i | −0.0375029 | + | 0.0649570i | ||||
\(712\) | 3.00000 | + | 5.19615i | 0.112430 | + | 0.194734i | ||||
\(713\) | −48.0000 | −1.79761 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.50000 | − | 7.79423i | −0.168173 | − | 0.291284i | ||||
\(717\) | 10.5000 | − | 18.1865i | 0.392130 | − | 0.679189i | ||||
\(718\) | 4.50000 | − | 7.79423i | 0.167939 | − | 0.290878i | ||||
\(719\) | −3.00000 | − | 5.19615i | −0.111881 | − | 0.193784i | 0.804648 | − | 0.593753i | \(-0.202354\pi\) |
−0.916529 | + | 0.399969i | \(0.869021\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −15.0000 | −0.558242 | ||||||||
\(723\) | 5.00000 | + | 8.66025i | 0.185952 | + | 0.322078i | ||||
\(724\) | −5.00000 | + | 8.66025i | −0.185824 | + | 0.321856i | ||||
\(725\) | 7.50000 | − | 12.9904i | 0.278543 | − | 0.482451i | ||||
\(726\) | 0.500000 | + | 0.866025i | 0.0185567 | + | 0.0321412i | ||||
\(727\) | −50.0000 | −1.85440 | −0.927199 | − | 0.374570i | \(-0.877790\pi\) | ||||
−0.927199 | + | 0.374570i | \(0.877790\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.0000 | + | 20.7846i | −0.443836 | + | 0.768747i | ||||
\(732\) | 3.50000 | − | 6.06218i | 0.129364 | − | 0.224065i | ||||
\(733\) | −21.5000 | − | 37.2391i | −0.794121 | − | 1.37546i | −0.923396 | − | 0.383849i | \(-0.874598\pi\) |
0.129275 | − | 0.991609i | \(-0.458735\pi\) | |||||||
\(734\) | −38.0000 | −1.40261 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.00000 | 0.221163 | ||||||||
\(737\) | −6.50000 | − | 11.2583i | −0.239431 | − | 0.414706i | ||||
\(738\) | 6.00000 | − | 10.3923i | 0.220863 | − | 0.382546i | ||||
\(739\) | −1.00000 | + | 1.73205i | −0.0367856 | + | 0.0637145i | −0.883832 | − | 0.467804i | \(-0.845045\pi\) |
0.847046 | + | 0.531519i | \(0.178379\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.0000 | −0.367359 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36.0000 | −1.32071 | −0.660356 | − | 0.750953i | \(-0.729595\pi\) | ||||
−0.660356 | + | 0.750953i | \(0.729595\pi\) | |||||||
\(744\) | −4.00000 | − | 6.92820i | −0.146647 | − | 0.254000i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −5.50000 | + | 9.52628i | −0.201369 | + | 0.348782i | ||||
\(747\) | −6.00000 | − | 10.3923i | −0.219529 | − | 0.380235i | ||||
\(748\) | 6.00000 | 0.219382 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.00000 | + | 13.8564i | 0.291924 | + | 0.505627i | 0.974265 | − | 0.225407i | \(-0.0723712\pi\) |
−0.682341 | + | 0.731034i | \(0.739038\pi\) | |||||||
\(752\) | 3.00000 | − | 5.19615i | 0.109399 | − | 0.189484i | ||||
\(753\) | −6.00000 | + | 10.3923i | −0.218652 | + | 0.378717i | ||||
\(754\) | 7.50000 | + | 12.9904i | 0.273134 | + | 0.473082i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.0000 | −0.363456 | −0.181728 | − | 0.983349i | \(-0.558169\pi\) | ||||
−0.181728 | + | 0.983349i | \(0.558169\pi\) | |||||||
\(758\) | 12.5000 | + | 21.6506i | 0.454020 | + | 0.786386i | ||||
\(759\) | −3.00000 | + | 5.19615i | −0.108893 | + | 0.188608i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.0000 | + | 25.9808i | 0.543750 | + | 0.941802i | 0.998684 | + | 0.0512772i | \(0.0163292\pi\) |
−0.454935 | + | 0.890525i | \(0.650337\pi\) | |||||||
\(762\) | 13.0000 | 0.470940 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −18.0000 | −0.651217 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.00000 | − | 10.3923i | 0.216789 | − | 0.375489i | ||||
\(767\) | 7.50000 | − | 12.9904i | 0.270809 | − | 0.469055i | ||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | −2.00000 | −0.0721218 | −0.0360609 | − | 0.999350i | \(-0.511481\pi\) | ||||
−0.0360609 | + | 0.999350i | \(0.511481\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.0000 | 0.972381 | ||||||||
\(772\) | 11.0000 | + | 19.0526i | 0.395899 | + | 0.685717i | ||||
\(773\) | −12.0000 | + | 20.7846i | −0.431610 | + | 0.747570i | −0.997012 | − | 0.0772449i | \(-0.975388\pi\) |
0.565402 | + | 0.824815i | \(0.308721\pi\) | |||||||
\(774\) | −4.00000 | + | 6.92820i | −0.143777 | + | 0.249029i | ||||
\(775\) | −20.0000 | − | 34.6410i | −0.718421 | − | 1.24434i | ||||
\(776\) | 13.0000 | 0.466673 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12.0000 | 0.430221 | ||||||||
\(779\) | 6.00000 | + | 10.3923i | 0.214972 | + | 0.372343i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.00000 | + | 10.3923i | −0.214697 | + | 0.371866i | ||||
\(782\) | 18.0000 | + | 31.1769i | 0.643679 | + | 1.11488i | ||||
\(783\) | 15.0000 | 0.536056 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.00000 | − | 5.19615i | −0.107006 | − | 0.185341i | ||||
\(787\) | 7.00000 | − | 12.1244i | 0.249523 | − | 0.432187i | −0.713871 | − | 0.700278i | \(-0.753059\pi\) |
0.963394 | + | 0.268091i | \(0.0863928\pi\) | |||||||
\(788\) | 4.50000 | − | 7.79423i | 0.160306 | − | 0.277658i | ||||
\(789\) | −1.50000 | − | 2.59808i | −0.0534014 | − | 0.0924940i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.00000 | 0.0710669 | ||||||||
\(793\) | 17.5000 | + | 30.3109i | 0.621443 | + | 1.07637i | ||||
\(794\) | 1.00000 | − | 1.73205i | 0.0354887 | − | 0.0614682i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.00000 | + | 12.1244i | 0.248108 | + | 0.429736i | ||||
\(797\) | −6.00000 | −0.212531 | −0.106265 | − | 0.994338i | \(-0.533889\pi\) | ||||
−0.106265 | + | 0.994338i | \(0.533889\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.0000 | 1.27359 | ||||||||
\(800\) | 2.50000 | + | 4.33013i | 0.0883883 | + | 0.153093i | ||||
\(801\) | −6.00000 | + | 10.3923i | −0.212000 | + | 0.367194i | ||||
\(802\) | 4.50000 | − | 7.79423i | 0.158901 | − | 0.275224i | ||||
\(803\) | 5.00000 | + | 8.66025i | 0.176446 | + | 0.305614i | ||||
\(804\) | 13.0000 | 0.458475 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 40.0000 | 1.40894 | ||||||||
\(807\) | 12.0000 | + | 20.7846i | 0.422420 | + | 0.731653i | ||||
\(808\) | 1.50000 | − | 2.59808i | 0.0527698 | − | 0.0914000i | ||||
\(809\) | −18.0000 | + | 31.1769i | −0.632846 | + | 1.09612i | 0.354121 | + | 0.935200i | \(0.384780\pi\) |
−0.986967 | + | 0.160922i | \(0.948553\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.0000 | 0.561836 | 0.280918 | − | 0.959732i | \(-0.409361\pi\) | ||||
0.280918 | + | 0.959732i | \(0.409361\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −25.0000 | −0.876788 | ||||||||
\(814\) | 1.00000 | + | 1.73205i | 0.0350500 | + | 0.0607083i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.00000 | + | 5.19615i | −0.105021 | + | 0.181902i | ||||
\(817\) | −4.00000 | − | 6.92820i | −0.139942 | − | 0.242387i | ||||
\(818\) | 4.00000 | 0.139857 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.5000 | − | 23.3827i | −0.471153 | − | 0.816061i | 0.528302 | − | 0.849056i | \(-0.322829\pi\) |
−0.999456 | + | 0.0329950i | \(0.989495\pi\) | |||||||
\(822\) | 7.50000 | − | 12.9904i | 0.261593 | − | 0.453092i | ||||
\(823\) | −13.0000 | + | 22.5167i | −0.453152 | + | 0.784881i | −0.998580 | − | 0.0532760i | \(-0.983034\pi\) |
0.545428 | + | 0.838157i | \(0.316367\pi\) | |||||||
\(824\) | −2.00000 | − | 3.46410i | −0.0696733 | − | 0.120678i | ||||
\(825\) | −5.00000 | −0.174078 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 42.0000 | 1.46048 | 0.730242 | − | 0.683189i | \(-0.239408\pi\) | ||||
0.730242 | + | 0.683189i | \(0.239408\pi\) | |||||||
\(828\) | 6.00000 | + | 10.3923i | 0.208514 | + | 0.361158i | ||||
\(829\) | −8.00000 | + | 13.8564i | −0.277851 | + | 0.481253i | −0.970851 | − | 0.239686i | \(-0.922956\pi\) |
0.692999 | + | 0.720938i | \(0.256289\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.500000 | − | 0.866025i | −0.0173448 | − | 0.0300421i | ||||
\(832\) | −5.00000 | −0.173344 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −4.00000 | −0.138509 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.00000 | + | 1.73205i | −0.0345857 | + | 0.0599042i | ||||
\(837\) | 20.0000 | − | 34.6410i | 0.691301 | − | 1.19737i | ||||
\(838\) | 6.00000 | + | 10.3923i | 0.207267 | + | 0.358996i | ||||
\(839\) | −30.0000 | −1.03572 | −0.517858 | − | 0.855467i | \(-0.673270\pi\) | ||||
−0.517858 | + | 0.855467i | \(0.673270\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 8.00000 | + | 13.8564i | 0.275698 | + | 0.477523i | ||||
\(843\) | −3.00000 | + | 5.19615i | −0.103325 | + | 0.178965i | ||||
\(844\) | −13.0000 | + | 22.5167i | −0.447478 | + | 0.775055i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 12.0000 | 0.412568 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −12.0000 | −0.412082 | ||||||||
\(849\) | 11.0000 | + | 19.0526i | 0.377519 | + | 0.653882i | ||||
\(850\) | −15.0000 | + | 25.9808i | −0.514496 | + | 0.891133i | ||||
\(851\) | −6.00000 | + | 10.3923i | −0.205677 | + | 0.356244i | ||||
\(852\) | −6.00000 | − | 10.3923i | −0.205557 | − | 0.356034i | ||||
\(853\) | 58.0000 | 1.98588 | 0.992941 | − | 0.118609i | \(-0.0378434\pi\) | ||||
0.992941 | + | 0.118609i | \(0.0378434\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.0000 | − | 41.5692i | 0.819824 | − | 1.41998i | −0.0859870 | − | 0.996296i | \(-0.527404\pi\) |
0.905811 | − | 0.423681i | \(-0.139262\pi\) | |||||||
\(858\) | 2.50000 | − | 4.33013i | 0.0853486 | − | 0.147828i | ||||
\(859\) | 17.5000 | + | 30.3109i | 0.597092 | + | 1.03419i | 0.993248 | + | 0.116011i | \(0.0370107\pi\) |
−0.396156 | + | 0.918183i | \(0.629656\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.0000 | 0.510902 | ||||||||
\(863\) | −3.00000 | − | 5.19615i | −0.102121 | − | 0.176879i | 0.810437 | − | 0.585826i | \(-0.199230\pi\) |
−0.912558 | + | 0.408946i | \(0.865896\pi\) | |||||||
\(864\) | −2.50000 | + | 4.33013i | −0.0850517 | + | 0.147314i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 7.00000 | + | 12.1244i | 0.237870 | + | 0.412002i | ||||
\(867\) | −19.0000 | −0.645274 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.00000 | 0.0339227 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32.5000 | + | 56.2917i | −1.10122 | + | 1.90737i | ||||
\(872\) | −7.00000 | + | 12.1244i | −0.237050 | + | 0.410582i | ||||
\(873\) | 13.0000 | + | 22.5167i | 0.439983 | + | 0.762073i | ||||
\(874\) | −12.0000 | −0.405906 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.0000 | −0.337869 | ||||||||
\(877\) | 18.5000 | + | 32.0429i | 0.624701 | + | 1.08201i | 0.988599 | + | 0.150574i | \(0.0481123\pi\) |
−0.363898 | + | 0.931439i | \(0.618554\pi\) | |||||||
\(878\) | −9.50000 | + | 16.4545i | −0.320609 | + | 0.555312i | ||||
\(879\) | 9.00000 | − | 15.5885i | 0.303562 | − | 0.525786i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.0000 | 0.505363 | 0.252681 | − | 0.967550i | \(-0.418688\pi\) | ||||
0.252681 | + | 0.967550i | \(0.418688\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.0000 | −0.639401 | −0.319700 | − | 0.947519i | \(-0.603582\pi\) | ||||
−0.319700 | + | 0.947519i | \(0.603582\pi\) | |||||||
\(884\) | −15.0000 | − | 25.9808i | −0.504505 | − | 0.873828i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.00000 | + | 10.3923i | −0.201574 | + | 0.349136i | ||||
\(887\) | 28.5000 | + | 49.3634i | 0.956936 | + | 1.65746i | 0.729873 | + | 0.683582i | \(0.239579\pi\) |
0.227063 | + | 0.973880i | \(0.427088\pi\) | |||||||
\(888\) | −2.00000 | −0.0671156 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.500000 | + | 0.866025i | 0.0167506 | + | 0.0290129i | ||||
\(892\) | −5.00000 | + | 8.66025i | −0.167412 | + | 0.289967i | ||||
\(893\) | −6.00000 | + | 10.3923i | −0.200782 | + | 0.347765i | ||||
\(894\) | −3.00000 | − | 5.19615i | −0.100335 | − | 0.173785i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 30.0000 | 1.00167 | ||||||||
\(898\) | −15.0000 | − | 25.9808i | −0.500556 | − | 0.866989i | ||||
\(899\) | 12.0000 | − | 20.7846i | 0.400222 | − | 0.693206i | ||||
\(900\) | −5.00000 | + | 8.66025i | −0.166667 | + | 0.288675i | ||||
\(901\) | −36.0000 | − | 62.3538i | −1.19933 | − | 2.07731i | ||||
\(902\) | −6.00000 | −0.199778 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.00000 | 0.299336 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.500000 | + | 0.866025i | −0.0166114 | + | 0.0287718i | ||||
\(907\) | −22.0000 | + | 38.1051i | −0.730498 | + | 1.26526i | 0.226173 | + | 0.974087i | \(0.427379\pi\) |
−0.956671 | + | 0.291172i | \(0.905955\pi\) | |||||||
\(908\) | −3.00000 | − | 5.19615i | −0.0995585 | − | 0.172440i | ||||
\(909\) | 6.00000 | 0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.0000 | 0.993944 | 0.496972 | − | 0.867766i | \(-0.334445\pi\) | ||||
0.496972 | + | 0.867766i | \(0.334445\pi\) | |||||||
\(912\) | −1.00000 | − | 1.73205i | −0.0331133 | − | 0.0573539i | ||||
\(913\) | −3.00000 | + | 5.19615i | −0.0992855 | + | 0.171968i | ||||
\(914\) | 11.0000 | − | 19.0526i | 0.363848 | − | 0.630203i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −20.0000 | −0.660819 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −30.0000 | −0.990148 | ||||||||
\(919\) | 8.00000 | + | 13.8564i | 0.263896 | + | 0.457081i | 0.967274 | − | 0.253735i | \(-0.0816592\pi\) |
−0.703378 | + | 0.710816i | \(0.748326\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.0000 | + | 27.7128i | −0.527218 | + | 0.913168i | ||||
\(922\) | 19.5000 | + | 33.7750i | 0.642198 | + | 1.11232i | ||||
\(923\) | 60.0000 | 1.97492 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.0000 | −0.328798 | ||||||||
\(926\) | −13.0000 | − | 22.5167i | −0.427207 | − | 0.739943i | ||||
\(927\) | 4.00000 | − | 6.92820i | 0.131377 | − | 0.227552i | ||||
\(928\) | −1.50000 | + | 2.59808i | −0.0492399 | + | 0.0852860i | ||||
\(929\) | 7.50000 | + | 12.9904i | 0.246067 | + | 0.426201i | 0.962431 | − | 0.271526i | \(-0.0875283\pi\) |
−0.716364 | + | 0.697727i | \(0.754195\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −30.0000 | −0.982683 | ||||||||
\(933\) | −12.0000 | − | 20.7846i | −0.392862 | − | 0.680458i | ||||
\(934\) | −6.00000 | + | 10.3923i | −0.196326 | + | 0.340047i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.00000 | − | 8.66025i | −0.163430 | − | 0.283069i | ||||
\(937\) | 52.0000 | 1.69877 | 0.849383 | − | 0.527777i | \(-0.176974\pi\) | ||||
0.849383 | + | 0.527777i | \(0.176974\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.00000 | −0.228436 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.5000 | + | 23.3827i | −0.440087 | + | 0.762254i | −0.997695 | − | 0.0678506i | \(-0.978386\pi\) |
0.557608 | + | 0.830104i | \(0.311719\pi\) | |||||||
\(942\) | 2.00000 | − | 3.46410i | 0.0651635 | − | 0.112867i | ||||
\(943\) | −18.0000 | − | 31.1769i | −0.586161 | − | 1.01526i | ||||
\(944\) | 3.00000 | 0.0976417 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.00000 | 0.130051 | ||||||||
\(947\) | 12.0000 | + | 20.7846i | 0.389948 | + | 0.675409i | 0.992442 | − | 0.122714i | \(-0.0391598\pi\) |
−0.602494 | + | 0.798123i | \(0.705826\pi\) | |||||||
\(948\) | −0.500000 | + | 0.866025i | −0.0162392 | + | 0.0281272i | ||||
\(949\) | 25.0000 | − | 43.3013i | 0.811534 | − | 1.40562i | ||||
\(950\) | −5.00000 | − | 8.66025i | −0.162221 | − | 0.280976i | ||||
\(951\) | 24.0000 | 0.778253 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.0000 | 0.777436 | 0.388718 | − | 0.921357i | \(-0.372918\pi\) | ||||
0.388718 | + | 0.921357i | \(0.372918\pi\) | |||||||
\(954\) | −12.0000 | − | 20.7846i | −0.388514 | − | 0.672927i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −10.5000 | + | 18.1865i | −0.339594 | + | 0.588195i | ||||
\(957\) | −1.50000 | − | 2.59808i | −0.0484881 | − | 0.0839839i | ||||
\(958\) | 3.00000 | 0.0969256 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5000 | − | 28.5788i | −0.532258 | − | 0.921898i | ||||
\(962\) | 5.00000 | − | 8.66025i | 0.161206 | − | 0.279218i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.00000 | − | 8.66025i | −0.161039 | − | 0.278928i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.0000 | 1.02905 | 0.514525 | − | 0.857475i | \(-0.327968\pi\) | ||||
0.514525 | + | 0.857475i | \(0.327968\pi\) | |||||||
\(968\) | −0.500000 | − | 0.866025i | −0.0160706 | − | 0.0278351i | ||||
\(969\) | 6.00000 | − | 10.3923i | 0.192748 | − | 0.333849i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.5000 | − | 28.5788i | −0.529510 | − | 0.917139i | −0.999408 | − | 0.0344175i | \(-0.989042\pi\) |
0.469897 | − | 0.882721i | \(-0.344291\pi\) | |||||||
\(972\) | −16.0000 | −0.513200 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −4.00000 | −0.128168 | ||||||||
\(975\) | 12.5000 | + | 21.6506i | 0.400320 | + | 0.693375i | ||||
\(976\) | −3.50000 | + | 6.06218i | −0.112032 | + | 0.194046i | ||||
\(977\) | 9.00000 | − | 15.5885i | 0.287936 | − | 0.498719i | −0.685381 | − | 0.728184i | \(-0.740364\pi\) |
0.973317 | + | 0.229465i | \(0.0736978\pi\) | |||||||
\(978\) | 8.50000 | + | 14.7224i | 0.271800 | + | 0.470771i | ||||
\(979\) | 6.00000 | 0.191761 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −28.0000 | −0.893971 | ||||||||
\(982\) | 15.0000 | + | 25.9808i | 0.478669 | + | 0.829079i | ||||
\(983\) | −3.00000 | + | 5.19615i | −0.0956851 | + | 0.165732i | −0.909894 | − | 0.414840i | \(-0.863838\pi\) |
0.814209 | + | 0.580572i | \(0.197171\pi\) | |||||||
\(984\) | 3.00000 | − | 5.19615i | 0.0956365 | − | 0.165647i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −18.0000 | −0.573237 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.0000 | 0.318142 | ||||||||
\(989\) | 12.0000 | + | 20.7846i | 0.381578 | + | 0.660912i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.00000 | − | 13.8564i | 0.254128 | − | 0.440163i | −0.710530 | − | 0.703667i | \(-0.751545\pi\) |
0.964658 | + | 0.263504i | \(0.0848781\pi\) | |||||||
\(992\) | 4.00000 | + | 6.92820i | 0.127000 | + | 0.219971i | ||||
\(993\) | 13.0000 | 0.412543 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.00000 | − | 5.19615i | −0.0950586 | − | 0.164646i | ||||
\(997\) | −23.0000 | + | 39.8372i | −0.728417 | + | 1.26166i | 0.229135 | + | 0.973395i | \(0.426410\pi\) |
−0.957552 | + | 0.288261i | \(0.906923\pi\) | |||||||
\(998\) | −4.00000 | + | 6.92820i | −0.126618 | + | 0.219308i | ||||
\(999\) | −5.00000 | − | 8.66025i | −0.158193 | − | 0.273998i |
(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 | 1078.2.e.d.67.1 | 2 | ||
7.2 | even | 3 | inner | 1078.2.e.d.177.1 | 2 | ||
7.3 | odd | 6 | 1078.2.a.k.1.1 | 1 | |||
7.4 | even | 3 | 1078.2.a.i.1.1 | 1 | |||
7.5 | odd | 6 | 154.2.e.b.23.1 | ✓ | 2 | ||
7.6 | odd | 2 | 154.2.e.b.67.1 | yes | 2 | ||
21.5 | even | 6 | 1386.2.k.n.793.1 | 2 | |||
21.11 | odd | 6 | 9702.2.a.l.1.1 | 1 | |||
21.17 | even | 6 | 9702.2.a.o.1.1 | 1 | |||
21.20 | even | 2 | 1386.2.k.n.991.1 | 2 | |||
28.3 | even | 6 | 8624.2.a.l.1.1 | 1 | |||
28.11 | odd | 6 | 8624.2.a.t.1.1 | 1 | |||
28.19 | even | 6 | 1232.2.q.c.177.1 | 2 | |||
28.27 | even | 2 | 1232.2.q.c.529.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.e.b.23.1 | ✓ | 2 | 7.5 | odd | 6 | ||
154.2.e.b.67.1 | yes | 2 | 7.6 | odd | 2 | ||
1078.2.a.i.1.1 | 1 | 7.4 | even | 3 | |||
1078.2.a.k.1.1 | 1 | 7.3 | odd | 6 | |||
1078.2.e.d.67.1 | 2 | 1.1 | even | 1 | trivial | ||
1078.2.e.d.177.1 | 2 | 7.2 | even | 3 | inner | ||
1232.2.q.c.177.1 | 2 | 28.19 | even | 6 | |||
1232.2.q.c.529.1 | 2 | 28.27 | even | 2 | |||
1386.2.k.n.793.1 | 2 | 21.5 | even | 6 | |||
1386.2.k.n.991.1 | 2 | 21.20 | even | 2 | |||
8624.2.a.l.1.1 | 1 | 28.3 | even | 6 | |||
8624.2.a.t.1.1 | 1 | 28.11 | odd | 6 | |||
9702.2.a.l.1.1 | 1 | 21.11 | odd | 6 | |||
9702.2.a.o.1.1 | 1 | 21.17 | even | 6 |