Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,2,Mod(277,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("966.277");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.71354883526\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 415.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 966.415 |
Dual form | 966.2.i.f.277.1 |
$q$-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 \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(829\) | \(925\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −0.500000 | + | 2.59808i | −0.188982 | + | 0.981981i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.50000 | + | 2.59808i | 0.452267 | + | 0.783349i | 0.998526 | − | 0.0542666i | \(-0.0172821\pi\) |
−0.546259 | + | 0.837616i | \(0.683949\pi\) | |||||||
\(12\) | −0.500000 | + | 0.866025i | −0.144338 | + | 0.250000i | ||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 2.00000 | + | 1.73205i | 0.534522 | + | 0.462910i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.50000 | + | 2.59808i | 0.363803 | + | 0.630126i | 0.988583 | − | 0.150675i | \(-0.0481447\pi\) |
−0.624780 | + | 0.780801i | \(0.714811\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | −1.00000 | + | 1.73205i | −0.229416 | + | 0.397360i | −0.957635 | − | 0.287984i | \(-0.907015\pi\) |
0.728219 | + | 0.685344i | \(0.240348\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.50000 | − | 0.866025i | 0.545545 | − | 0.188982i | ||||
\(22\) | 3.00000 | 0.639602 | ||||||||
\(23\) | 0.500000 | − | 0.866025i | 0.104257 | − | 0.180579i | ||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | 2.50000 | + | 4.33013i | 0.500000 | + | 0.866025i | ||||
\(26\) | 1.00000 | − | 1.73205i | 0.196116 | − | 0.339683i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.50000 | − | 0.866025i | 0.472456 | − | 0.163663i | ||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | − | 1.73205i | −0.179605 | − | 0.311086i | 0.762140 | − | 0.647412i | \(-0.224149\pi\) |
−0.941745 | + | 0.336327i | \(0.890815\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 1.50000 | − | 2.59808i | 0.261116 | − | 0.452267i | ||||
\(34\) | 3.00000 | 0.514496 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −1.00000 | + | 1.73205i | −0.164399 | + | 0.284747i | −0.936442 | − | 0.350823i | \(-0.885902\pi\) |
0.772043 | + | 0.635571i | \(0.219235\pi\) | |||||||
\(38\) | 1.00000 | + | 1.73205i | 0.162221 | + | 0.280976i | ||||
\(39\) | −1.00000 | − | 1.73205i | −0.160128 | − | 0.277350i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0.500000 | − | 2.59808i | 0.0771517 | − | 0.400892i | ||||
\(43\) | 2.00000 | 0.304997 | 0.152499 | − | 0.988304i | \(-0.451268\pi\) | ||||
0.152499 | + | 0.988304i | \(0.451268\pi\) | |||||||
\(44\) | 1.50000 | − | 2.59808i | 0.226134 | − | 0.391675i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.500000 | − | 0.866025i | −0.0737210 | − | 0.127688i | ||||
\(47\) | 1.50000 | − | 2.59808i | 0.218797 | − | 0.378968i | −0.735643 | − | 0.677369i | \(-0.763120\pi\) |
0.954441 | + | 0.298401i | \(0.0964533\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −6.50000 | − | 2.59808i | −0.928571 | − | 0.371154i | ||||
\(50\) | 5.00000 | 0.707107 | ||||||||
\(51\) | 1.50000 | − | 2.59808i | 0.210042 | − | 0.363803i | ||||
\(52\) | −1.00000 | − | 1.73205i | −0.138675 | − | 0.240192i | ||||
\(53\) | 3.00000 | + | 5.19615i | 0.412082 | + | 0.713746i | 0.995117 | − | 0.0987002i | \(-0.0314685\pi\) |
−0.583036 | + | 0.812447i | \(0.698135\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.500000 | − | 2.59808i | 0.0668153 | − | 0.347183i | ||||
\(57\) | 2.00000 | 0.264906 | ||||||||
\(58\) | 1.50000 | − | 2.59808i | 0.196960 | − | 0.341144i | ||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | + | 1.73205i | −0.128037 | + | 0.221766i | −0.922916 | − | 0.385002i | \(-0.874201\pi\) |
0.794879 | + | 0.606768i | \(0.207534\pi\) | |||||||
\(62\) | −2.00000 | −0.254000 | ||||||||
\(63\) | −2.00000 | − | 1.73205i | −0.251976 | − | 0.218218i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.50000 | − | 2.59808i | −0.184637 | − | 0.319801i | ||||
\(67\) | −1.00000 | − | 1.73205i | −0.122169 | − | 0.211604i | 0.798454 | − | 0.602056i | \(-0.205652\pi\) |
−0.920623 | + | 0.390453i | \(0.872318\pi\) | |||||||
\(68\) | 1.50000 | − | 2.59808i | 0.181902 | − | 0.315063i | ||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.00000 | 0.356034 | 0.178017 | − | 0.984027i | \(-0.443032\pi\) | ||||
0.178017 | + | 0.984027i | \(0.443032\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | −5.50000 | − | 9.52628i | −0.643726 | − | 1.11497i | −0.984594 | − | 0.174855i | \(-0.944054\pi\) |
0.340868 | − | 0.940111i | \(-0.389279\pi\) | |||||||
\(74\) | 1.00000 | + | 1.73205i | 0.116248 | + | 0.201347i | ||||
\(75\) | 2.50000 | − | 4.33013i | 0.288675 | − | 0.500000i | ||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | −7.50000 | + | 2.59808i | −0.854704 | + | 0.296078i | ||||
\(78\) | −2.00000 | −0.226455 | ||||||||
\(79\) | −5.50000 | + | 9.52628i | −0.618798 | + | 1.07179i | 0.370907 | + | 0.928670i | \(0.379047\pi\) |
−0.989705 | + | 0.143120i | \(0.954286\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 3.00000 | − | 5.19615i | 0.331295 | − | 0.573819i | ||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | −2.00000 | − | 1.73205i | −0.218218 | − | 0.188982i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.00000 | − | 1.73205i | 0.107833 | − | 0.186772i | ||||
\(87\) | −1.50000 | − | 2.59808i | −0.160817 | − | 0.278543i | ||||
\(88\) | −1.50000 | − | 2.59808i | −0.159901 | − | 0.276956i | ||||
\(89\) | 3.00000 | − | 5.19615i | 0.317999 | − | 0.550791i | −0.662071 | − | 0.749441i | \(-0.730322\pi\) |
0.980071 | + | 0.198650i | \(0.0636557\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | + | 5.19615i | −0.104828 | + | 0.544705i | ||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | −1.00000 | + | 1.73205i | −0.103695 | + | 0.179605i | ||||
\(94\) | −1.50000 | − | 2.59808i | −0.154713 | − | 0.267971i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.500000 | − | 0.866025i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | 8.00000 | 0.812277 | 0.406138 | − | 0.913812i | \(-0.366875\pi\) | ||||
0.406138 | + | 0.913812i | \(0.366875\pi\) | |||||||
\(98\) | −5.50000 | + | 4.33013i | −0.555584 | + | 0.437409i | ||||
\(99\) | −3.00000 | −0.301511 | ||||||||
\(100\) | 2.50000 | − | 4.33013i | 0.250000 | − | 0.433013i | ||||
\(101\) | 1.50000 | + | 2.59808i | 0.149256 | + | 0.258518i | 0.930953 | − | 0.365140i | \(-0.118979\pi\) |
−0.781697 | + | 0.623658i | \(0.785646\pi\) | |||||||
\(102\) | −1.50000 | − | 2.59808i | −0.148522 | − | 0.257248i | ||||
\(103\) | −2.50000 | + | 4.33013i | −0.246332 | + | 0.426660i | −0.962505 | − | 0.271263i | \(-0.912559\pi\) |
0.716173 | + | 0.697923i | \(0.245892\pi\) | |||||||
\(104\) | −2.00000 | −0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | −6.00000 | + | 10.3923i | −0.580042 | + | 1.00466i | 0.415432 | + | 0.909624i | \(0.363630\pi\) |
−0.995474 | + | 0.0950377i | \(0.969703\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | 0.500000 | + | 0.866025i | 0.0478913 | + | 0.0829502i | 0.888977 | − | 0.457951i | \(-0.151417\pi\) |
−0.841086 | + | 0.540901i | \(0.818083\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.00000 | 0.189832 | ||||||||
\(112\) | −2.00000 | − | 1.73205i | −0.188982 | − | 0.163663i | ||||
\(113\) | 18.0000 | 1.69330 | 0.846649 | − | 0.532152i | \(-0.178617\pi\) | ||||
0.846649 | + | 0.532152i | \(0.178617\pi\) | |||||||
\(114\) | 1.00000 | − | 1.73205i | 0.0936586 | − | 0.162221i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.50000 | − | 2.59808i | −0.139272 | − | 0.241225i | ||||
\(117\) | −1.00000 | + | 1.73205i | −0.0924500 | + | 0.160128i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.50000 | + | 2.59808i | −0.687524 | + | 0.238165i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | 1.00000 | + | 1.73205i | 0.0905357 | + | 0.156813i | ||||
\(123\) | −3.00000 | − | 5.19615i | −0.270501 | − | 0.468521i | ||||
\(124\) | −1.00000 | + | 1.73205i | −0.0898027 | + | 0.155543i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.50000 | + | 0.866025i | −0.222718 | + | 0.0771517i | ||||
\(127\) | 2.00000 | 0.177471 | 0.0887357 | − | 0.996055i | \(-0.471717\pi\) | ||||
0.0887357 | + | 0.996055i | \(0.471717\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −1.00000 | − | 1.73205i | −0.0880451 | − | 0.152499i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(132\) | −3.00000 | −0.261116 | ||||||||
\(133\) | −4.00000 | − | 3.46410i | −0.346844 | − | 0.300376i | ||||
\(134\) | −2.00000 | −0.172774 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.50000 | − | 2.59808i | −0.128624 | − | 0.222783i | ||||
\(137\) | 10.5000 | + | 18.1865i | 0.897076 | + | 1.55378i | 0.831215 | + | 0.555952i | \(0.187646\pi\) |
0.0658609 | + | 0.997829i | \(0.479021\pi\) | |||||||
\(138\) | −0.500000 | + | 0.866025i | −0.0425628 | + | 0.0737210i | ||||
\(139\) | −13.0000 | −1.10265 | −0.551323 | − | 0.834292i | \(-0.685877\pi\) | ||||
−0.551323 | + | 0.834292i | \(0.685877\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.00000 | −0.252646 | ||||||||
\(142\) | 1.50000 | − | 2.59808i | 0.125877 | − | 0.218026i | ||||
\(143\) | 3.00000 | + | 5.19615i | 0.250873 | + | 0.434524i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −11.0000 | −0.910366 | ||||||||
\(147\) | 1.00000 | + | 6.92820i | 0.0824786 | + | 0.571429i | ||||
\(148\) | 2.00000 | 0.164399 | ||||||||
\(149\) | −6.00000 | + | 10.3923i | −0.491539 | + | 0.851371i | −0.999953 | − | 0.00974235i | \(-0.996899\pi\) |
0.508413 | + | 0.861113i | \(0.330232\pi\) | |||||||
\(150\) | −2.50000 | − | 4.33013i | −0.204124 | − | 0.353553i | ||||
\(151\) | 2.00000 | + | 3.46410i | 0.162758 | + | 0.281905i | 0.935857 | − | 0.352381i | \(-0.114628\pi\) |
−0.773099 | + | 0.634285i | \(0.781294\pi\) | |||||||
\(152\) | 1.00000 | − | 1.73205i | 0.0811107 | − | 0.140488i | ||||
\(153\) | −3.00000 | −0.242536 | ||||||||
\(154\) | −1.50000 | + | 7.79423i | −0.120873 | + | 0.628077i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.00000 | + | 1.73205i | −0.0800641 | + | 0.138675i | ||||
\(157\) | −11.5000 | − | 19.9186i | −0.917800 | − | 1.58968i | −0.802749 | − | 0.596316i | \(-0.796630\pi\) |
−0.115050 | − | 0.993360i | \(-0.536703\pi\) | |||||||
\(158\) | 5.50000 | + | 9.52628i | 0.437557 | + | 0.757870i | ||||
\(159\) | 3.00000 | − | 5.19615i | 0.237915 | − | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.00000 | + | 1.73205i | 0.157622 | + | 0.136505i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −11.5000 | + | 19.9186i | −0.900750 | + | 1.56014i | −0.0742262 | + | 0.997241i | \(0.523649\pi\) |
−0.826523 | + | 0.562902i | \(0.809685\pi\) | |||||||
\(164\) | −3.00000 | − | 5.19615i | −0.234261 | − | 0.405751i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | −2.50000 | + | 0.866025i | −0.192879 | + | 0.0668153i | ||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | − | 1.73205i | −0.0764719 | − | 0.132453i | ||||
\(172\) | −1.00000 | − | 1.73205i | −0.0762493 | − | 0.132068i | ||||
\(173\) | 7.50000 | − | 12.9904i | 0.570214 | − | 0.987640i | −0.426329 | − | 0.904568i | \(-0.640193\pi\) |
0.996544 | − | 0.0830722i | \(-0.0264732\pi\) | |||||||
\(174\) | −3.00000 | −0.227429 | ||||||||
\(175\) | −12.5000 | + | 4.33013i | −0.944911 | + | 0.327327i | ||||
\(176\) | −3.00000 | −0.226134 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.00000 | − | 5.19615i | −0.224860 | − | 0.389468i | ||||
\(179\) | −3.00000 | − | 5.19615i | −0.224231 | − | 0.388379i | 0.731858 | − | 0.681457i | \(-0.238654\pi\) |
−0.956088 | + | 0.293079i | \(0.905320\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.0000 | 0.817624 | 0.408812 | − | 0.912619i | \(-0.365943\pi\) | ||||
0.408812 | + | 0.912619i | \(0.365943\pi\) | |||||||
\(182\) | 4.00000 | + | 3.46410i | 0.296500 | + | 0.256776i | ||||
\(183\) | 2.00000 | 0.147844 | ||||||||
\(184\) | −0.500000 | + | 0.866025i | −0.0368605 | + | 0.0638442i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.00000 | + | 1.73205i | 0.0733236 | + | 0.127000i | ||||
\(187\) | −4.50000 | + | 7.79423i | −0.329073 | + | 0.569970i | ||||
\(188\) | −3.00000 | −0.218797 | ||||||||
\(189\) | −0.500000 | + | 2.59808i | −0.0363696 | + | 0.188982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.00000 | + | 10.3923i | −0.434145 | + | 0.751961i | −0.997225 | − | 0.0744412i | \(-0.976283\pi\) |
0.563081 | + | 0.826402i | \(0.309616\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | −7.00000 | − | 12.1244i | −0.503871 | − | 0.872730i | −0.999990 | − | 0.00447566i | \(-0.998575\pi\) |
0.496119 | − | 0.868255i | \(-0.334758\pi\) | |||||||
\(194\) | 4.00000 | − | 6.92820i | 0.287183 | − | 0.497416i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | + | 6.92820i | 0.0714286 | + | 0.494872i | ||||
\(197\) | 15.0000 | 1.06871 | 0.534353 | − | 0.845262i | \(-0.320555\pi\) | ||||
0.534353 | + | 0.845262i | \(0.320555\pi\) | |||||||
\(198\) | −1.50000 | + | 2.59808i | −0.106600 | + | 0.184637i | ||||
\(199\) | −8.50000 | − | 14.7224i | −0.602549 | − | 1.04365i | −0.992434 | − | 0.122782i | \(-0.960818\pi\) |
0.389885 | − | 0.920864i | \(-0.372515\pi\) | |||||||
\(200\) | −2.50000 | − | 4.33013i | −0.176777 | − | 0.306186i | ||||
\(201\) | −1.00000 | + | 1.73205i | −0.0705346 | + | 0.122169i | ||||
\(202\) | 3.00000 | 0.211079 | ||||||||
\(203\) | −1.50000 | + | 7.79423i | −0.105279 | + | 0.547048i | ||||
\(204\) | −3.00000 | −0.210042 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.50000 | + | 4.33013i | 0.174183 | + | 0.301694i | ||||
\(207\) | 0.500000 | + | 0.866025i | 0.0347524 | + | 0.0601929i | ||||
\(208\) | −1.00000 | + | 1.73205i | −0.0693375 | + | 0.120096i | ||||
\(209\) | −6.00000 | −0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.0000 | −1.30801 | −0.654007 | − | 0.756489i | \(-0.726913\pi\) | ||||
−0.654007 | + | 0.756489i | \(0.726913\pi\) | |||||||
\(212\) | 3.00000 | − | 5.19615i | 0.206041 | − | 0.356873i | ||||
\(213\) | −1.50000 | − | 2.59808i | −0.102778 | − | 0.178017i | ||||
\(214\) | 6.00000 | + | 10.3923i | 0.410152 | + | 0.710403i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 5.00000 | − | 1.73205i | 0.339422 | − | 0.117579i | ||||
\(218\) | 1.00000 | 0.0677285 | ||||||||
\(219\) | −5.50000 | + | 9.52628i | −0.371656 | + | 0.643726i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.00000 | + | 5.19615i | 0.201802 | + | 0.349531i | ||||
\(222\) | 1.00000 | − | 1.73205i | 0.0671156 | − | 0.116248i | ||||
\(223\) | −10.0000 | −0.669650 | −0.334825 | − | 0.942280i | \(-0.608677\pi\) | ||||
−0.334825 | + | 0.942280i | \(0.608677\pi\) | |||||||
\(224\) | −2.50000 | + | 0.866025i | −0.167038 | + | 0.0578638i | ||||
\(225\) | −5.00000 | −0.333333 | ||||||||
\(226\) | 9.00000 | − | 15.5885i | 0.598671 | − | 1.03693i | ||||
\(227\) | 1.50000 | + | 2.59808i | 0.0995585 | + | 0.172440i | 0.911502 | − | 0.411296i | \(-0.134924\pi\) |
−0.811943 | + | 0.583736i | \(0.801590\pi\) | |||||||
\(228\) | −1.00000 | − | 1.73205i | −0.0662266 | − | 0.114708i | ||||
\(229\) | 0.500000 | − | 0.866025i | 0.0330409 | − | 0.0572286i | −0.849032 | − | 0.528341i | \(-0.822814\pi\) |
0.882073 | + | 0.471113i | \(0.156147\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.00000 | + | 5.19615i | 0.394771 | + | 0.341882i | ||||
\(232\) | −3.00000 | −0.196960 | ||||||||
\(233\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(234\) | 1.00000 | + | 1.73205i | 0.0653720 | + | 0.113228i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.0000 | 0.714527 | ||||||||
\(238\) | −1.50000 | + | 7.79423i | −0.0972306 | + | 0.505225i | ||||
\(239\) | 15.0000 | 0.970269 | 0.485135 | − | 0.874439i | \(-0.338771\pi\) | ||||
0.485135 | + | 0.874439i | \(0.338771\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | − | 1.73205i | −0.0644157 | − | 0.111571i | 0.832019 | − | 0.554747i | \(-0.187185\pi\) |
−0.896435 | + | 0.443176i | \(0.853852\pi\) | |||||||
\(242\) | −1.00000 | − | 1.73205i | −0.0642824 | − | 0.111340i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 2.00000 | 0.128037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.00000 | −0.382546 | ||||||||
\(247\) | −2.00000 | + | 3.46410i | −0.127257 | + | 0.220416i | ||||
\(248\) | 1.00000 | + | 1.73205i | 0.0635001 | + | 0.109985i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.00000 | 0.189358 | 0.0946792 | − | 0.995508i | \(-0.469817\pi\) | ||||
0.0946792 | + | 0.995508i | \(0.469817\pi\) | |||||||
\(252\) | −0.500000 | + | 2.59808i | −0.0314970 | + | 0.163663i | ||||
\(253\) | 3.00000 | 0.188608 | ||||||||
\(254\) | 1.00000 | − | 1.73205i | 0.0627456 | − | 0.108679i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −3.00000 | + | 5.19615i | −0.187135 | + | 0.324127i | −0.944294 | − | 0.329104i | \(-0.893253\pi\) |
0.757159 | + | 0.653231i | \(0.226587\pi\) | |||||||
\(258\) | −2.00000 | −0.124515 | ||||||||
\(259\) | −4.00000 | − | 3.46410i | −0.248548 | − | 0.215249i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.50000 | + | 2.59808i | −0.0928477 | + | 0.160817i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.0000 | − | 20.7846i | −0.739952 | − | 1.28163i | −0.952517 | − | 0.304487i | \(-0.901515\pi\) |
0.212565 | − | 0.977147i | \(-0.431818\pi\) | |||||||
\(264\) | −1.50000 | + | 2.59808i | −0.0923186 | + | 0.159901i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5.00000 | + | 1.73205i | −0.306570 | + | 0.106199i | ||||
\(267\) | −6.00000 | −0.367194 | ||||||||
\(268\) | −1.00000 | + | 1.73205i | −0.0610847 | + | 0.105802i | ||||
\(269\) | −7.50000 | − | 12.9904i | −0.457283 | − | 0.792038i | 0.541533 | − | 0.840679i | \(-0.317844\pi\) |
−0.998816 | + | 0.0486418i | \(0.984511\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.0000 | − | 19.0526i | 0.668202 | − | 1.15736i | −0.310204 | − | 0.950670i | \(-0.600397\pi\) |
0.978406 | − | 0.206691i | \(-0.0662693\pi\) | |||||||
\(272\) | −3.00000 | −0.181902 | ||||||||
\(273\) | 5.00000 | − | 1.73205i | 0.302614 | − | 0.104828i | ||||
\(274\) | 21.0000 | 1.26866 | ||||||||
\(275\) | −7.50000 | + | 12.9904i | −0.452267 | + | 0.783349i | ||||
\(276\) | 0.500000 | + | 0.866025i | 0.0300965 | + | 0.0521286i | ||||
\(277\) | −4.00000 | − | 6.92820i | −0.240337 | − | 0.416275i | 0.720473 | − | 0.693482i | \(-0.243925\pi\) |
−0.960810 | + | 0.277207i | \(0.910591\pi\) | |||||||
\(278\) | −6.50000 | + | 11.2583i | −0.389844 | + | 0.675230i | ||||
\(279\) | 2.00000 | 0.119737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.00000 | −0.178965 | −0.0894825 | − | 0.995988i | \(-0.528521\pi\) | ||||
−0.0894825 | + | 0.995988i | \(0.528521\pi\) | |||||||
\(282\) | −1.50000 | + | 2.59808i | −0.0893237 | + | 0.154713i | ||||
\(283\) | −4.00000 | − | 6.92820i | −0.237775 | − | 0.411839i | 0.722300 | − | 0.691580i | \(-0.243085\pi\) |
−0.960076 | + | 0.279741i | \(0.909752\pi\) | |||||||
\(284\) | −1.50000 | − | 2.59808i | −0.0890086 | − | 0.154167i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.00000 | 0.354787 | ||||||||
\(287\) | −3.00000 | + | 15.5885i | −0.177084 | + | 0.920158i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.00000 | − | 6.92820i | −0.234484 | − | 0.406138i | ||||
\(292\) | −5.50000 | + | 9.52628i | −0.321863 | + | 0.557483i | ||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | 6.50000 | + | 2.59808i | 0.379088 | + | 0.151523i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.00000 | − | 1.73205i | 0.0581238 | − | 0.100673i | ||||
\(297\) | 1.50000 | + | 2.59808i | 0.0870388 | + | 0.150756i | ||||
\(298\) | 6.00000 | + | 10.3923i | 0.347571 | + | 0.602010i | ||||
\(299\) | 1.00000 | − | 1.73205i | 0.0578315 | − | 0.100167i | ||||
\(300\) | −5.00000 | −0.288675 | ||||||||
\(301\) | −1.00000 | + | 5.19615i | −0.0576390 | + | 0.299501i | ||||
\(302\) | 4.00000 | 0.230174 | ||||||||
\(303\) | 1.50000 | − | 2.59808i | 0.0861727 | − | 0.149256i | ||||
\(304\) | −1.00000 | − | 1.73205i | −0.0573539 | − | 0.0993399i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.50000 | + | 2.59808i | −0.0857493 | + | 0.148522i | ||||
\(307\) | 11.0000 | 0.627803 | 0.313902 | − | 0.949456i | \(-0.398364\pi\) | ||||
0.313902 | + | 0.949456i | \(0.398364\pi\) | |||||||
\(308\) | 6.00000 | + | 5.19615i | 0.341882 | + | 0.296078i | ||||
\(309\) | 5.00000 | 0.284440 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.50000 | + | 2.59808i | 0.0850572 | + | 0.147323i | 0.905416 | − | 0.424526i | \(-0.139559\pi\) |
−0.820358 | + | 0.571850i | \(0.806226\pi\) | |||||||
\(312\) | 1.00000 | + | 1.73205i | 0.0566139 | + | 0.0980581i | ||||
\(313\) | −4.00000 | + | 6.92820i | −0.226093 | + | 0.391605i | −0.956647 | − | 0.291250i | \(-0.905929\pi\) |
0.730554 | + | 0.682855i | \(0.239262\pi\) | |||||||
\(314\) | −23.0000 | −1.29797 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.0000 | 0.618798 | ||||||||
\(317\) | 9.00000 | − | 15.5885i | 0.505490 | − | 0.875535i | −0.494489 | − | 0.869184i | \(-0.664645\pi\) |
0.999980 | − | 0.00635137i | \(-0.00202172\pi\) | |||||||
\(318\) | −3.00000 | − | 5.19615i | −0.168232 | − | 0.291386i | ||||
\(319\) | 4.50000 | + | 7.79423i | 0.251952 | + | 0.436393i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.0000 | 0.669775 | ||||||||
\(322\) | 2.50000 | − | 0.866025i | 0.139320 | − | 0.0482617i | ||||
\(323\) | −6.00000 | −0.333849 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 5.00000 | + | 8.66025i | 0.277350 | + | 0.480384i | ||||
\(326\) | 11.5000 | + | 19.9186i | 0.636926 | + | 1.10319i | ||||
\(327\) | 0.500000 | − | 0.866025i | 0.0276501 | − | 0.0478913i | ||||
\(328\) | −6.00000 | −0.331295 | ||||||||
\(329\) | 6.00000 | + | 5.19615i | 0.330791 | + | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.00000 | + | 6.92820i | −0.219860 | + | 0.380808i | −0.954765 | − | 0.297361i | \(-0.903893\pi\) |
0.734905 | + | 0.678170i | \(0.237227\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.00000 | − | 1.73205i | −0.0547997 | − | 0.0949158i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.500000 | + | 2.59808i | −0.0272772 | + | 0.141737i | ||||
\(337\) | 14.0000 | 0.762629 | 0.381314 | − | 0.924445i | \(-0.375472\pi\) | ||||
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | −4.50000 | + | 7.79423i | −0.244768 | + | 0.423950i | ||||
\(339\) | −9.00000 | − | 15.5885i | −0.488813 | − | 0.846649i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.00000 | − | 5.19615i | 0.162459 | − | 0.281387i | ||||
\(342\) | −2.00000 | −0.108148 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | −2.00000 | −0.107833 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.50000 | − | 12.9904i | −0.403202 | − | 0.698367i | ||||
\(347\) | −3.00000 | − | 5.19615i | −0.161048 | − | 0.278944i | 0.774197 | − | 0.632945i | \(-0.218154\pi\) |
−0.935245 | + | 0.354001i | \(0.884821\pi\) | |||||||
\(348\) | −1.50000 | + | 2.59808i | −0.0804084 | + | 0.139272i | ||||
\(349\) | −22.0000 | −1.17763 | −0.588817 | − | 0.808267i | \(-0.700406\pi\) | ||||
−0.588817 | + | 0.808267i | \(0.700406\pi\) | |||||||
\(350\) | −2.50000 | + | 12.9904i | −0.133631 | + | 0.694365i | ||||
\(351\) | 2.00000 | 0.106752 | ||||||||
\(352\) | −1.50000 | + | 2.59808i | −0.0799503 | + | 0.138478i | ||||
\(353\) | 9.00000 | + | 15.5885i | 0.479022 | + | 0.829690i | 0.999711 | − | 0.0240566i | \(-0.00765819\pi\) |
−0.520689 | + | 0.853746i | \(0.674325\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 6.00000 | + | 5.19615i | 0.317554 | + | 0.275010i | ||||
\(358\) | −6.00000 | −0.317110 | ||||||||
\(359\) | 6.00000 | − | 10.3923i | 0.316668 | − | 0.548485i | −0.663123 | − | 0.748511i | \(-0.730769\pi\) |
0.979791 | + | 0.200026i | \(0.0641026\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | + | 12.9904i | 0.394737 | + | 0.683704i | ||||
\(362\) | 5.50000 | − | 9.52628i | 0.289074 | − | 0.500690i | ||||
\(363\) | −2.00000 | −0.104973 | ||||||||
\(364\) | 5.00000 | − | 1.73205i | 0.262071 | − | 0.0907841i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.00000 | − | 1.73205i | 0.0522708 | − | 0.0905357i | ||||
\(367\) | −4.00000 | − | 6.92820i | −0.208798 | − | 0.361649i | 0.742538 | − | 0.669804i | \(-0.233622\pi\) |
−0.951336 | + | 0.308155i | \(0.900289\pi\) | |||||||
\(368\) | 0.500000 | + | 0.866025i | 0.0260643 | + | 0.0451447i | ||||
\(369\) | −3.00000 | + | 5.19615i | −0.156174 | + | 0.270501i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −15.0000 | + | 5.19615i | −0.778761 | + | 0.269771i | ||||
\(372\) | 2.00000 | 0.103695 | ||||||||
\(373\) | 6.50000 | − | 11.2583i | 0.336557 | − | 0.582934i | −0.647225 | − | 0.762299i | \(-0.724071\pi\) |
0.983783 | + | 0.179364i | \(0.0574041\pi\) | |||||||
\(374\) | 4.50000 | + | 7.79423i | 0.232689 | + | 0.403030i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.50000 | + | 2.59808i | −0.0773566 | + | 0.133986i | ||||
\(377\) | 6.00000 | 0.309016 | ||||||||
\(378\) | 2.00000 | + | 1.73205i | 0.102869 | + | 0.0890871i | ||||
\(379\) | 20.0000 | 1.02733 | 0.513665 | − | 0.857991i | \(-0.328287\pi\) | ||||
0.513665 | + | 0.857991i | \(0.328287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.00000 | − | 1.73205i | −0.0512316 | − | 0.0887357i | ||||
\(382\) | 6.00000 | + | 10.3923i | 0.306987 | + | 0.531717i | ||||
\(383\) | 3.00000 | − | 5.19615i | 0.153293 | − | 0.265511i | −0.779143 | − | 0.626846i | \(-0.784346\pi\) |
0.932436 | + | 0.361335i | \(0.117679\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.0000 | −0.712581 | ||||||||
\(387\) | −1.00000 | + | 1.73205i | −0.0508329 | + | 0.0880451i | ||||
\(388\) | −4.00000 | − | 6.92820i | −0.203069 | − | 0.351726i | ||||
\(389\) | −12.0000 | − | 20.7846i | −0.608424 | − | 1.05382i | −0.991500 | − | 0.130105i | \(-0.958469\pi\) |
0.383076 | − | 0.923717i | \(-0.374865\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.00000 | 0.151717 | ||||||||
\(392\) | 6.50000 | + | 2.59808i | 0.328300 | + | 0.131223i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.50000 | − | 12.9904i | 0.377845 | − | 0.654446i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.50000 | + | 2.59808i | 0.0753778 | + | 0.130558i | ||||
\(397\) | 17.0000 | − | 29.4449i | 0.853206 | − | 1.47780i | −0.0250943 | − | 0.999685i | \(-0.507989\pi\) |
0.878300 | − | 0.478110i | \(-0.158678\pi\) | |||||||
\(398\) | −17.0000 | −0.852133 | ||||||||
\(399\) | −1.00000 | + | 5.19615i | −0.0500626 | + | 0.260133i | ||||
\(400\) | −5.00000 | −0.250000 | ||||||||
\(401\) | 7.50000 | − | 12.9904i | 0.374532 | − | 0.648709i | −0.615725 | − | 0.787961i | \(-0.711137\pi\) |
0.990257 | + | 0.139253i | \(0.0444700\pi\) | |||||||
\(402\) | 1.00000 | + | 1.73205i | 0.0498755 | + | 0.0863868i | ||||
\(403\) | −2.00000 | − | 3.46410i | −0.0996271 | − | 0.172559i | ||||
\(404\) | 1.50000 | − | 2.59808i | 0.0746278 | − | 0.129259i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.00000 | + | 5.19615i | 0.297775 | + | 0.257881i | ||||
\(407\) | −6.00000 | −0.297409 | ||||||||
\(408\) | −1.50000 | + | 2.59808i | −0.0742611 | + | 0.128624i | ||||
\(409\) | −14.5000 | − | 25.1147i | −0.716979 | − | 1.24184i | −0.962191 | − | 0.272374i | \(-0.912191\pi\) |
0.245212 | − | 0.969469i | \(-0.421142\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.5000 | − | 18.1865i | 0.517927 | − | 0.897076i | ||||
\(412\) | 5.00000 | 0.246332 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.00000 | + | 1.73205i | 0.0490290 | + | 0.0849208i | ||||
\(417\) | 6.50000 | + | 11.2583i | 0.318306 | + | 0.551323i | ||||
\(418\) | −3.00000 | + | 5.19615i | −0.146735 | + | 0.254152i | ||||
\(419\) | −21.0000 | −1.02592 | −0.512959 | − | 0.858413i | \(-0.671451\pi\) | ||||
−0.512959 | + | 0.858413i | \(0.671451\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.0000 | 0.828529 | 0.414265 | − | 0.910156i | \(-0.364039\pi\) | ||||
0.414265 | + | 0.910156i | \(0.364039\pi\) | |||||||
\(422\) | −9.50000 | + | 16.4545i | −0.462453 | + | 0.800992i | ||||
\(423\) | 1.50000 | + | 2.59808i | 0.0729325 | + | 0.126323i | ||||
\(424\) | −3.00000 | − | 5.19615i | −0.145693 | − | 0.252347i | ||||
\(425\) | −7.50000 | + | 12.9904i | −0.363803 | + | 0.630126i | ||||
\(426\) | −3.00000 | −0.145350 | ||||||||
\(427\) | −4.00000 | − | 3.46410i | −0.193574 | − | 0.167640i | ||||
\(428\) | 12.0000 | 0.580042 | ||||||||
\(429\) | 3.00000 | − | 5.19615i | 0.144841 | − | 0.250873i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.0000 | − | 25.9808i | −0.722525 | − | 1.25145i | −0.959985 | − | 0.280052i | \(-0.909648\pi\) |
0.237460 | − | 0.971397i | \(-0.423685\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | 2.00000 | 0.0961139 | 0.0480569 | − | 0.998845i | \(-0.484697\pi\) | ||||
0.0480569 | + | 0.998845i | \(0.484697\pi\) | |||||||
\(434\) | 1.00000 | − | 5.19615i | 0.0480015 | − | 0.249423i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.500000 | − | 0.866025i | 0.0239457 | − | 0.0414751i | ||||
\(437\) | 1.00000 | + | 1.73205i | 0.0478365 | + | 0.0828552i | ||||
\(438\) | 5.50000 | + | 9.52628i | 0.262800 | + | 0.455183i | ||||
\(439\) | −4.00000 | + | 6.92820i | −0.190910 | + | 0.330665i | −0.945552 | − | 0.325471i | \(-0.894477\pi\) |
0.754642 | + | 0.656136i | \(0.227810\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.50000 | − | 4.33013i | 0.261905 | − | 0.206197i | ||||
\(442\) | 6.00000 | 0.285391 | ||||||||
\(443\) | 12.0000 | − | 20.7846i | 0.570137 | − | 0.987507i | −0.426414 | − | 0.904528i | \(-0.640223\pi\) |
0.996551 | − | 0.0829786i | \(-0.0264433\pi\) | |||||||
\(444\) | −1.00000 | − | 1.73205i | −0.0474579 | − | 0.0821995i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.00000 | + | 8.66025i | −0.236757 | + | 0.410075i | ||||
\(447\) | 12.0000 | 0.567581 | ||||||||
\(448\) | −0.500000 | + | 2.59808i | −0.0236228 | + | 0.122748i | ||||
\(449\) | 12.0000 | 0.566315 | 0.283158 | − | 0.959073i | \(-0.408618\pi\) | ||||
0.283158 | + | 0.959073i | \(0.408618\pi\) | |||||||
\(450\) | −2.50000 | + | 4.33013i | −0.117851 | + | 0.204124i | ||||
\(451\) | 9.00000 | + | 15.5885i | 0.423793 | + | 0.734032i | ||||
\(452\) | −9.00000 | − | 15.5885i | −0.423324 | − | 0.733219i | ||||
\(453\) | 2.00000 | − | 3.46410i | 0.0939682 | − | 0.162758i | ||||
\(454\) | 3.00000 | 0.140797 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.00000 | −0.0936586 | ||||||||
\(457\) | −10.0000 | + | 17.3205i | −0.467780 | + | 0.810219i | −0.999322 | − | 0.0368128i | \(-0.988279\pi\) |
0.531542 | + | 0.847032i | \(0.321613\pi\) | |||||||
\(458\) | −0.500000 | − | 0.866025i | −0.0233635 | − | 0.0404667i | ||||
\(459\) | 1.50000 | + | 2.59808i | 0.0700140 | + | 0.121268i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.0000 | −1.39724 | −0.698620 | − | 0.715493i | \(-0.746202\pi\) | ||||
−0.698620 | + | 0.715493i | \(0.746202\pi\) | |||||||
\(462\) | 7.50000 | − | 2.59808i | 0.348932 | − | 0.120873i | ||||
\(463\) | 32.0000 | 1.48717 | 0.743583 | − | 0.668644i | \(-0.233125\pi\) | ||||
0.743583 | + | 0.668644i | \(0.233125\pi\) | |||||||
\(464\) | −1.50000 | + | 2.59808i | −0.0696358 | + | 0.120613i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.5000 | − | 18.1865i | 0.485882 | − | 0.841572i | −0.513986 | − | 0.857798i | \(-0.671832\pi\) |
0.999868 | + | 0.0162260i | \(0.00516512\pi\) | |||||||
\(468\) | 2.00000 | 0.0924500 | ||||||||
\(469\) | 5.00000 | − | 1.73205i | 0.230879 | − | 0.0799787i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.5000 | + | 19.9186i | −0.529892 | + | 0.917800i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.00000 | + | 5.19615i | 0.137940 | + | 0.238919i | ||||
\(474\) | 5.50000 | − | 9.52628i | 0.252623 | − | 0.437557i | ||||
\(475\) | −10.0000 | −0.458831 | ||||||||
\(476\) | 6.00000 | + | 5.19615i | 0.275010 | + | 0.238165i | ||||
\(477\) | −6.00000 | −0.274721 | ||||||||
\(478\) | 7.50000 | − | 12.9904i | 0.343042 | − | 0.594166i | ||||
\(479\) | −15.0000 | − | 25.9808i | −0.685367 | − | 1.18709i | −0.973321 | − | 0.229447i | \(-0.926308\pi\) |
0.287954 | − | 0.957644i | \(-0.407025\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.00000 | + | 3.46410i | −0.0911922 | + | 0.157949i | ||||
\(482\) | −2.00000 | −0.0910975 | ||||||||
\(483\) | 0.500000 | − | 2.59808i | 0.0227508 | − | 0.118217i | ||||
\(484\) | −2.00000 | −0.0909091 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.500000 | + | 0.866025i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | −1.00000 | − | 1.73205i | −0.0453143 | − | 0.0784867i | 0.842479 | − | 0.538730i | \(-0.181096\pi\) |
−0.887793 | + | 0.460243i | \(0.847762\pi\) | |||||||
\(488\) | 1.00000 | − | 1.73205i | 0.0452679 | − | 0.0784063i | ||||
\(489\) | 23.0000 | 1.04010 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | −3.00000 | + | 5.19615i | −0.135250 | + | 0.234261i | ||||
\(493\) | 4.50000 | + | 7.79423i | 0.202670 | + | 0.351034i | ||||
\(494\) | 2.00000 | + | 3.46410i | 0.0899843 | + | 0.155857i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | −1.50000 | + | 7.79423i | −0.0672842 | + | 0.349619i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.5000 | + | 30.3109i | −0.783408 | + | 1.35690i | 0.146538 | + | 0.989205i | \(0.453187\pi\) |
−0.929946 | + | 0.367697i | \(0.880146\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.50000 | − | 2.59808i | 0.0669483 | − | 0.115958i | ||||
\(503\) | 30.0000 | 1.33763 | 0.668817 | − | 0.743427i | \(-0.266801\pi\) | ||||
0.668817 | + | 0.743427i | \(0.266801\pi\) | |||||||
\(504\) | 2.00000 | + | 1.73205i | 0.0890871 | + | 0.0771517i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.50000 | − | 2.59808i | 0.0666831 | − | 0.115499i | ||||
\(507\) | 4.50000 | + | 7.79423i | 0.199852 | + | 0.346154i | ||||
\(508\) | −1.00000 | − | 1.73205i | −0.0443678 | − | 0.0768473i | ||||
\(509\) | 10.5000 | − | 18.1865i | 0.465404 | − | 0.806104i | −0.533815 | − | 0.845601i | \(-0.679242\pi\) |
0.999220 | + | 0.0394971i | \(0.0125756\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.5000 | − | 9.52628i | 1.21653 | − | 0.421418i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.00000 | + | 1.73205i | −0.0441511 | + | 0.0764719i | ||||
\(514\) | 3.00000 | + | 5.19615i | 0.132324 | + | 0.229192i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.00000 | + | 1.73205i | −0.0440225 | + | 0.0762493i | ||||
\(517\) | 9.00000 | 0.395820 | ||||||||
\(518\) | −5.00000 | + | 1.73205i | −0.219687 | + | 0.0761019i | ||||
\(519\) | −15.0000 | −0.658427 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.0000 | + | 36.3731i | 0.920027 | + | 1.59353i | 0.799370 | + | 0.600839i | \(0.205167\pi\) |
0.120656 | + | 0.992694i | \(0.461500\pi\) | |||||||
\(522\) | 1.50000 | + | 2.59808i | 0.0656532 | + | 0.113715i | ||||
\(523\) | 11.0000 | − | 19.0526i | 0.480996 | − | 0.833110i | −0.518766 | − | 0.854916i | \(-0.673608\pi\) |
0.999762 | + | 0.0218062i | \(0.00694167\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 10.0000 | + | 8.66025i | 0.436436 | + | 0.377964i | ||||
\(526\) | −24.0000 | −1.04645 | ||||||||
\(527\) | 3.00000 | − | 5.19615i | 0.130682 | − | 0.226348i | ||||
\(528\) | 1.50000 | + | 2.59808i | 0.0652791 | + | 0.113067i | ||||
\(529\) | −0.500000 | − | 0.866025i | −0.0217391 | − | 0.0376533i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.00000 | + | 5.19615i | −0.0433555 | + | 0.225282i | ||||
\(533\) | 12.0000 | 0.519778 | ||||||||
\(534\) | −3.00000 | + | 5.19615i | −0.129823 | + | 0.224860i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.00000 | + | 1.73205i | 0.0431934 | + | 0.0748132i | ||||
\(537\) | −3.00000 | + | 5.19615i | −0.129460 | + | 0.224231i | ||||
\(538\) | −15.0000 | −0.646696 | ||||||||
\(539\) | −3.00000 | − | 20.7846i | −0.129219 | − | 0.895257i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.0000 | + | 17.3205i | −0.429934 | + | 0.744667i | −0.996867 | − | 0.0790969i | \(-0.974796\pi\) |
0.566933 | + | 0.823764i | \(0.308130\pi\) | |||||||
\(542\) | −11.0000 | − | 19.0526i | −0.472490 | − | 0.818377i | ||||
\(543\) | −5.50000 | − | 9.52628i | −0.236028 | − | 0.408812i | ||||
\(544\) | −1.50000 | + | 2.59808i | −0.0643120 | + | 0.111392i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.00000 | − | 5.19615i | 0.0427960 | − | 0.222375i | ||||
\(547\) | 17.0000 | 0.726868 | 0.363434 | − | 0.931620i | \(-0.381604\pi\) | ||||
0.363434 | + | 0.931620i | \(0.381604\pi\) | |||||||
\(548\) | 10.5000 | − | 18.1865i | 0.448538 | − | 0.776890i | ||||
\(549\) | −1.00000 | − | 1.73205i | −0.0426790 | − | 0.0739221i | ||||
\(550\) | 7.50000 | + | 12.9904i | 0.319801 | + | 0.553912i | ||||
\(551\) | −3.00000 | + | 5.19615i | −0.127804 | + | 0.221364i | ||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | −22.0000 | − | 19.0526i | −0.935535 | − | 0.810197i | ||||
\(554\) | −8.00000 | −0.339887 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.50000 | + | 11.2583i | 0.275661 | + | 0.477460i | ||||
\(557\) | −15.0000 | − | 25.9808i | −0.635570 | − | 1.10084i | −0.986394 | − | 0.164399i | \(-0.947432\pi\) |
0.350824 | − | 0.936442i | \(-0.385902\pi\) | |||||||
\(558\) | 1.00000 | − | 1.73205i | 0.0423334 | − | 0.0733236i | ||||
\(559\) | 4.00000 | 0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.00000 | 0.379980 | ||||||||
\(562\) | −1.50000 | + | 2.59808i | −0.0632737 | + | 0.109593i | ||||
\(563\) | 4.50000 | + | 7.79423i | 0.189652 | + | 0.328488i | 0.945134 | − | 0.326682i | \(-0.105931\pi\) |
−0.755482 | + | 0.655169i | \(0.772597\pi\) | |||||||
\(564\) | 1.50000 | + | 2.59808i | 0.0631614 | + | 0.109399i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8.00000 | −0.336265 | ||||||||
\(567\) | 2.50000 | − | 0.866025i | 0.104990 | − | 0.0363696i | ||||
\(568\) | −3.00000 | −0.125877 | ||||||||
\(569\) | 3.00000 | − | 5.19615i | 0.125767 | − | 0.217834i | −0.796266 | − | 0.604947i | \(-0.793194\pi\) |
0.922032 | + | 0.387113i | \(0.126528\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.00000 | + | 3.46410i | 0.0836974 | + | 0.144968i | 0.904835 | − | 0.425762i | \(-0.139994\pi\) |
−0.821138 | + | 0.570730i | \(0.806660\pi\) | |||||||
\(572\) | 3.00000 | − | 5.19615i | 0.125436 | − | 0.217262i | ||||
\(573\) | 12.0000 | 0.501307 | ||||||||
\(574\) | 12.0000 | + | 10.3923i | 0.500870 | + | 0.433766i | ||||
\(575\) | 5.00000 | 0.208514 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 15.5000 | + | 26.8468i | 0.645273 | + | 1.11765i | 0.984238 | + | 0.176847i | \(0.0565899\pi\) |
−0.338965 | + | 0.940799i | \(0.610077\pi\) | |||||||
\(578\) | −4.00000 | − | 6.92820i | −0.166378 | − | 0.288175i | ||||
\(579\) | −7.00000 | + | 12.1244i | −0.290910 | + | 0.503871i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −8.00000 | −0.331611 | ||||||||
\(583\) | −9.00000 | + | 15.5885i | −0.372742 | + | 0.645608i | ||||
\(584\) | 5.50000 | + | 9.52628i | 0.227592 | + | 0.394200i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.0000 | −0.495293 | −0.247647 | − | 0.968850i | \(-0.579657\pi\) | ||||
−0.247647 | + | 0.968850i | \(0.579657\pi\) | |||||||
\(588\) | 5.50000 | − | 4.33013i | 0.226816 | − | 0.178571i | ||||
\(589\) | 4.00000 | 0.164817 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.50000 | − | 12.9904i | −0.308509 | − | 0.534353i | ||||
\(592\) | −1.00000 | − | 1.73205i | −0.0410997 | − | 0.0711868i | ||||
\(593\) | 21.0000 | − | 36.3731i | 0.862367 | − | 1.49366i | −0.00727173 | − | 0.999974i | \(-0.502315\pi\) |
0.869638 | − | 0.493689i | \(-0.164352\pi\) | |||||||
\(594\) | 3.00000 | 0.123091 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.0000 | 0.491539 | ||||||||
\(597\) | −8.50000 | + | 14.7224i | −0.347882 | + | 0.602549i | ||||
\(598\) | −1.00000 | − | 1.73205i | −0.0408930 | − | 0.0708288i | ||||
\(599\) | −7.50000 | − | 12.9904i | −0.306442 | − | 0.530773i | 0.671140 | − | 0.741331i | \(-0.265805\pi\) |
−0.977581 | + | 0.210558i | \(0.932472\pi\) | |||||||
\(600\) | −2.50000 | + | 4.33013i | −0.102062 | + | 0.176777i | ||||
\(601\) | 26.0000 | 1.06056 | 0.530281 | − | 0.847822i | \(-0.322086\pi\) | ||||
0.530281 | + | 0.847822i | \(0.322086\pi\) | |||||||
\(602\) | 4.00000 | + | 3.46410i | 0.163028 | + | 0.141186i | ||||
\(603\) | 2.00000 | 0.0814463 | ||||||||
\(604\) | 2.00000 | − | 3.46410i | 0.0813788 | − | 0.140952i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.50000 | − | 2.59808i | −0.0609333 | − | 0.105540i | ||||
\(607\) | −7.00000 | + | 12.1244i | −0.284121 | + | 0.492112i | −0.972396 | − | 0.233338i | \(-0.925035\pi\) |
0.688274 | + | 0.725450i | \(0.258368\pi\) | |||||||
\(608\) | −2.00000 | −0.0811107 | ||||||||
\(609\) | 7.50000 | − | 2.59808i | 0.303915 | − | 0.105279i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.00000 | − | 5.19615i | 0.121367 | − | 0.210214i | ||||
\(612\) | 1.50000 | + | 2.59808i | 0.0606339 | + | 0.105021i | ||||
\(613\) | −2.50000 | − | 4.33013i | −0.100974 | − | 0.174892i | 0.811112 | − | 0.584891i | \(-0.198863\pi\) |
−0.912086 | + | 0.409998i | \(0.865529\pi\) | |||||||
\(614\) | 5.50000 | − | 9.52628i | 0.221962 | − | 0.384449i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.50000 | − | 2.59808i | 0.302184 | − | 0.104679i | ||||
\(617\) | 33.0000 | 1.32853 | 0.664265 | − | 0.747497i | \(-0.268745\pi\) | ||||
0.664265 | + | 0.747497i | \(0.268745\pi\) | |||||||
\(618\) | 2.50000 | − | 4.33013i | 0.100565 | − | 0.174183i | ||||
\(619\) | −16.0000 | − | 27.7128i | −0.643094 | − | 1.11387i | −0.984738 | − | 0.174042i | \(-0.944317\pi\) |
0.341644 | − | 0.939829i | \(-0.389016\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.500000 | − | 0.866025i | 0.0200643 | − | 0.0347524i | ||||
\(622\) | 3.00000 | 0.120289 | ||||||||
\(623\) | 12.0000 | + | 10.3923i | 0.480770 | + | 0.416359i | ||||
\(624\) | 2.00000 | 0.0800641 | ||||||||
\(625\) | −12.5000 | + | 21.6506i | −0.500000 | + | 0.866025i | ||||
\(626\) | 4.00000 | + | 6.92820i | 0.159872 | + | 0.276907i | ||||
\(627\) | 3.00000 | + | 5.19615i | 0.119808 | + | 0.207514i | ||||
\(628\) | −11.5000 | + | 19.9186i | −0.458900 | + | 0.794838i | ||||
\(629\) | −6.00000 | −0.239236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.0000 | 0.676759 | 0.338380 | − | 0.941010i | \(-0.390121\pi\) | ||||
0.338380 | + | 0.941010i | \(0.390121\pi\) | |||||||
\(632\) | 5.50000 | − | 9.52628i | 0.218778 | − | 0.378935i | ||||
\(633\) | 9.50000 | + | 16.4545i | 0.377591 | + | 0.654007i | ||||
\(634\) | −9.00000 | − | 15.5885i | −0.357436 | − | 0.619097i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6.00000 | −0.237915 | ||||||||
\(637\) | −13.0000 | − | 5.19615i | −0.515079 | − | 0.205879i | ||||
\(638\) | 9.00000 | 0.356313 | ||||||||
\(639\) | −1.50000 | + | 2.59808i | −0.0593391 | + | 0.102778i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.50000 | + | 2.59808i | 0.0592464 | + | 0.102618i | 0.894127 | − | 0.447813i | \(-0.147797\pi\) |
−0.834881 | + | 0.550431i | \(0.814464\pi\) | |||||||
\(642\) | 6.00000 | − | 10.3923i | 0.236801 | − | 0.410152i | ||||
\(643\) | −28.0000 | −1.10421 | −0.552106 | − | 0.833774i | \(-0.686176\pi\) | ||||
−0.552106 | + | 0.833774i | \(0.686176\pi\) | |||||||
\(644\) | 0.500000 | − | 2.59808i | 0.0197028 | − | 0.102379i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.00000 | + | 5.19615i | −0.118033 | + | 0.204440i | ||||
\(647\) | 7.50000 | + | 12.9904i | 0.294855 | + | 0.510705i | 0.974951 | − | 0.222419i | \(-0.0713952\pi\) |
−0.680096 | + | 0.733123i | \(0.738062\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 10.0000 | 0.392232 | ||||||||
\(651\) | −4.00000 | − | 3.46410i | −0.156772 | − | 0.135769i | ||||
\(652\) | 23.0000 | 0.900750 | ||||||||
\(653\) | −1.50000 | + | 2.59808i | −0.0586995 | + | 0.101671i | −0.893882 | − | 0.448303i | \(-0.852029\pi\) |
0.835182 | + | 0.549973i | \(0.185362\pi\) | |||||||
\(654\) | −0.500000 | − | 0.866025i | −0.0195515 | − | 0.0338643i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.00000 | + | 5.19615i | −0.117130 | + | 0.202876i | ||||
\(657\) | 11.0000 | 0.429151 | ||||||||
\(658\) | 7.50000 | − | 2.59808i | 0.292380 | − | 0.101284i | ||||
\(659\) | 3.00000 | 0.116863 | 0.0584317 | − | 0.998291i | \(-0.481390\pi\) | ||||
0.0584317 | + | 0.998291i | \(0.481390\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.50000 | − | 4.33013i | −0.0972387 | − | 0.168422i | 0.813302 | − | 0.581842i | \(-0.197668\pi\) |
−0.910541 | + | 0.413419i | \(0.864334\pi\) | |||||||
\(662\) | 4.00000 | + | 6.92820i | 0.155464 | + | 0.269272i | ||||
\(663\) | 3.00000 | − | 5.19615i | 0.116510 | − | 0.201802i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.00000 | −0.0774984 | ||||||||
\(667\) | 1.50000 | − | 2.59808i | 0.0580802 | − | 0.100598i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.00000 | + | 8.66025i | 0.193311 | + | 0.334825i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.00000 | −0.231627 | ||||||||
\(672\) | 2.00000 | + | 1.73205i | 0.0771517 | + | 0.0668153i | ||||
\(673\) | −19.0000 | −0.732396 | −0.366198 | − | 0.930537i | \(-0.619341\pi\) | ||||
−0.366198 | + | 0.930537i | \(0.619341\pi\) | |||||||
\(674\) | 7.00000 | − | 12.1244i | 0.269630 | − | 0.467013i | ||||
\(675\) | 2.50000 | + | 4.33013i | 0.0962250 | + | 0.166667i | ||||
\(676\) | 4.50000 | + | 7.79423i | 0.173077 | + | 0.299778i | ||||
\(677\) | 9.00000 | − | 15.5885i | 0.345898 | − | 0.599113i | −0.639618 | − | 0.768693i | \(-0.720908\pi\) |
0.985517 | + | 0.169580i | \(0.0542410\pi\) | |||||||
\(678\) | −18.0000 | −0.691286 | ||||||||
\(679\) | −4.00000 | + | 20.7846i | −0.153506 | + | 0.797640i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.50000 | − | 2.59808i | 0.0574801 | − | 0.0995585i | ||||
\(682\) | −3.00000 | − | 5.19615i | −0.114876 | − | 0.198971i | ||||
\(683\) | −24.0000 | − | 41.5692i | −0.918334 | − | 1.59060i | −0.801945 | − | 0.597398i | \(-0.796201\pi\) |
−0.116390 | − | 0.993204i | \(-0.537132\pi\) | |||||||
\(684\) | −1.00000 | + | 1.73205i | −0.0382360 | + | 0.0662266i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.50000 | − | 16.4545i | −0.324532 | − | 0.628235i | ||||
\(687\) | −1.00000 | −0.0381524 | ||||||||
\(688\) | −1.00000 | + | 1.73205i | −0.0381246 | + | 0.0660338i | ||||
\(689\) | 6.00000 | + | 10.3923i | 0.228582 | + | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.50000 | + | 14.7224i | −0.323355 | + | 0.560068i | −0.981178 | − | 0.193105i | \(-0.938144\pi\) |
0.657823 | + | 0.753173i | \(0.271478\pi\) | |||||||
\(692\) | −15.0000 | −0.570214 | ||||||||
\(693\) | 1.50000 | − | 7.79423i | 0.0569803 | − | 0.296078i | ||||
\(694\) | −6.00000 | −0.227757 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.50000 | + | 2.59808i | 0.0568574 | + | 0.0984798i | ||||
\(697\) | 9.00000 | + | 15.5885i | 0.340899 | + | 0.590455i | ||||
\(698\) | −11.0000 | + | 19.0526i | −0.416356 | + | 0.721150i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 10.0000 | + | 8.66025i | 0.377964 | + | 0.327327i | ||||
\(701\) | −42.0000 | −1.58632 | −0.793159 | − | 0.609015i | \(-0.791565\pi\) | ||||
−0.793159 | + | 0.609015i | \(0.791565\pi\) | |||||||
\(702\) | 1.00000 | − | 1.73205i | 0.0377426 | − | 0.0653720i | ||||
\(703\) | −2.00000 | − | 3.46410i | −0.0754314 | − | 0.130651i | ||||
\(704\) | 1.50000 | + | 2.59808i | 0.0565334 | + | 0.0979187i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.0000 | 0.677439 | ||||||||
\(707\) | −7.50000 | + | 2.59808i | −0.282067 | + | 0.0977107i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.5000 | − | 26.8468i | 0.582115 | − | 1.00825i | −0.413114 | − | 0.910679i | \(-0.635559\pi\) |
0.995228 | − | 0.0975728i | \(-0.0311079\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.50000 | − | 9.52628i | −0.206266 | − | 0.357263i | ||||
\(712\) | −3.00000 | + | 5.19615i | −0.112430 | + | 0.194734i | ||||
\(713\) | −2.00000 | −0.0749006 | ||||||||
\(714\) | 7.50000 | − | 2.59808i | 0.280680 | − | 0.0972306i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.00000 | + | 5.19615i | −0.112115 | + | 0.194189i | ||||
\(717\) | −7.50000 | − | 12.9904i | −0.280093 | − | 0.485135i | ||||
\(718\) | −6.00000 | − | 10.3923i | −0.223918 | − | 0.387837i | ||||
\(719\) | 24.0000 | − | 41.5692i | 0.895049 | − | 1.55027i | 0.0613050 | − | 0.998119i | \(-0.480474\pi\) |
0.833744 | − | 0.552151i | \(-0.186193\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.0000 | − | 8.66025i | −0.372419 | − | 0.322525i | ||||
\(722\) | 15.0000 | 0.558242 | ||||||||
\(723\) | −1.00000 | + | 1.73205i | −0.0371904 | + | 0.0644157i | ||||
\(724\) | −5.50000 | − | 9.52628i | −0.204406 | − | 0.354041i | ||||
\(725\) | 7.50000 | + | 12.9904i | 0.278543 | + | 0.482451i | ||||
\(726\) | −1.00000 | + | 1.73205i | −0.0371135 | + | 0.0642824i | ||||
\(727\) | 23.0000 | 0.853023 | 0.426511 | − | 0.904482i | \(-0.359742\pi\) | ||||
0.426511 | + | 0.904482i | \(0.359742\pi\) | |||||||
\(728\) | 1.00000 | − | 5.19615i | 0.0370625 | − | 0.192582i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.00000 | + | 5.19615i | 0.110959 | + | 0.192187i | ||||
\(732\) | −1.00000 | − | 1.73205i | −0.0369611 | − | 0.0640184i | ||||
\(733\) | −20.5000 | + | 35.5070i | −0.757185 | + | 1.31148i | 0.187096 | + | 0.982342i | \(0.440092\pi\) |
−0.944281 | + | 0.329141i | \(0.893241\pi\) | |||||||
\(734\) | −8.00000 | −0.295285 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 3.00000 | − | 5.19615i | 0.110506 | − | 0.191403i | ||||
\(738\) | 3.00000 | + | 5.19615i | 0.110432 | + | 0.191273i | ||||
\(739\) | 12.5000 | + | 21.6506i | 0.459820 | + | 0.796431i | 0.998951 | − | 0.0457903i | \(-0.0145806\pi\) |
−0.539131 | + | 0.842222i | \(0.681247\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.00000 | 0.146944 | ||||||||
\(742\) | −3.00000 | + | 15.5885i | −0.110133 | + | 0.572270i | ||||
\(743\) | −12.0000 | −0.440237 | −0.220119 | − | 0.975473i | \(-0.570644\pi\) | ||||
−0.220119 | + | 0.975473i | \(0.570644\pi\) | |||||||
\(744\) | 1.00000 | − | 1.73205i | 0.0366618 | − | 0.0635001i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −6.50000 | − | 11.2583i | −0.237982 | − | 0.412197i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.00000 | 0.329073 | ||||||||
\(749\) | −24.0000 | − | 20.7846i | −0.876941 | − | 0.759453i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.0000 | + | 27.7128i | −0.583848 | + | 1.01125i | 0.411170 | + | 0.911559i | \(0.365120\pi\) |
−0.995018 | + | 0.0996961i | \(0.968213\pi\) | |||||||
\(752\) | 1.50000 | + | 2.59808i | 0.0546994 | + | 0.0947421i | ||||
\(753\) | −1.50000 | − | 2.59808i | −0.0546630 | − | 0.0946792i | ||||
\(754\) | 3.00000 | − | 5.19615i | 0.109254 | − | 0.189233i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.50000 | − | 0.866025i | 0.0909241 | − | 0.0314970i | ||||
\(757\) | 38.0000 | 1.38113 | 0.690567 | − | 0.723269i | \(-0.257361\pi\) | ||||
0.690567 | + | 0.723269i | \(0.257361\pi\) | |||||||
\(758\) | 10.0000 | − | 17.3205i | 0.363216 | − | 0.629109i | ||||
\(759\) | −1.50000 | − | 2.59808i | −0.0544466 | − | 0.0943042i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.0000 | + | 41.5692i | −0.869999 | + | 1.50688i | −0.00800331 | + | 0.999968i | \(0.502548\pi\) |
−0.861996 | + | 0.506915i | \(0.830786\pi\) | |||||||
\(762\) | −2.00000 | −0.0724524 | ||||||||
\(763\) | −2.50000 | + | 0.866025i | −0.0905061 | + | 0.0313522i | ||||
\(764\) | 12.0000 | 0.434145 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.00000 | − | 5.19615i | −0.108394 | − | 0.187745i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.500000 | + | 0.866025i | −0.0180422 | + | 0.0312500i | ||||
\(769\) | 14.0000 | 0.504853 | 0.252426 | − | 0.967616i | \(-0.418771\pi\) | ||||
0.252426 | + | 0.967616i | \(0.418771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.00000 | 0.216085 | ||||||||
\(772\) | −7.00000 | + | 12.1244i | −0.251936 | + | 0.436365i | ||||
\(773\) | 18.0000 | + | 31.1769i | 0.647415 | + | 1.12136i | 0.983738 | + | 0.179609i | \(0.0574833\pi\) |
−0.336323 | + | 0.941747i | \(0.609183\pi\) | |||||||
\(774\) | 1.00000 | + | 1.73205i | 0.0359443 | + | 0.0622573i | ||||
\(775\) | 5.00000 | − | 8.66025i | 0.179605 | − | 0.311086i | ||||
\(776\) | −8.00000 | −0.287183 | ||||||||
\(777\) | −1.00000 | + | 5.19615i | −0.0358748 | + | 0.186411i | ||||
\(778\) | −24.0000 | −0.860442 | ||||||||
\(779\) | −6.00000 | + | 10.3923i | −0.214972 | + | 0.372343i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.50000 | + | 7.79423i | 0.161023 | + | 0.278899i | ||||
\(782\) | 1.50000 | − | 2.59808i | 0.0536399 | − | 0.0929070i | ||||
\(783\) | 3.00000 | 0.107211 | ||||||||
\(784\) | 5.50000 | − | 4.33013i | 0.196429 | − | 0.154647i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.0000 | + | 34.6410i | 0.712923 | + | 1.23482i | 0.963755 | + | 0.266788i | \(0.0859624\pi\) |
−0.250832 | + | 0.968031i | \(0.580704\pi\) | |||||||
\(788\) | −7.50000 | − | 12.9904i | −0.267176 | − | 0.462763i | ||||
\(789\) | −12.0000 | + | 20.7846i | −0.427211 | + | 0.739952i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.00000 | + | 46.7654i | −0.320003 | + | 1.66279i | ||||
\(792\) | 3.00000 | 0.106600 | ||||||||
\(793\) | −2.00000 | + | 3.46410i | −0.0710221 | + | 0.123014i | ||||
\(794\) | −17.0000 | − | 29.4449i | −0.603307 | − | 1.04496i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.50000 | + | 14.7224i | −0.301275 | + | 0.521823i | ||||
\(797\) | 30.0000 | 1.06265 | 0.531327 | − | 0.847167i | \(-0.321693\pi\) | ||||
0.531327 | + | 0.847167i | \(0.321693\pi\) | |||||||
\(798\) | 4.00000 | + | 3.46410i | 0.141598 | + | 0.122628i | ||||
\(799\) | 9.00000 | 0.318397 | ||||||||
\(800\) | −2.50000 | + | 4.33013i | −0.0883883 | + | 0.153093i | ||||
\(801\) | 3.00000 | + | 5.19615i | 0.106000 | + | 0.183597i | ||||
\(802\) | −7.50000 | − | 12.9904i | −0.264834 | − | 0.458706i | ||||
\(803\) | 16.5000 | − | 28.5788i | 0.582272 | − | 1.00853i | ||||
\(804\) | 2.00000 | 0.0705346 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.00000 | −0.140894 | ||||||||
\(807\) | −7.50000 | + | 12.9904i | −0.264013 | + | 0.457283i | ||||
\(808\) | −1.50000 | − | 2.59808i | −0.0527698 | − | 0.0914000i | ||||
\(809\) | −15.0000 | − | 25.9808i | −0.527372 | − | 0.913435i | −0.999491 | − | 0.0319002i | \(-0.989844\pi\) |
0.472119 | − | 0.881535i | \(-0.343489\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.00000 | −0.245803 | −0.122902 | − | 0.992419i | \(-0.539220\pi\) | ||||
−0.122902 | + | 0.992419i | \(0.539220\pi\) | |||||||
\(812\) | 7.50000 | − | 2.59808i | 0.263198 | − | 0.0911746i | ||||
\(813\) | −22.0000 | −0.771574 | ||||||||
\(814\) | −3.00000 | + | 5.19615i | −0.105150 | + | 0.182125i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.50000 | + | 2.59808i | 0.0525105 | + | 0.0909509i | ||||
\(817\) | −2.00000 | + | 3.46410i | −0.0699711 | + | 0.121194i | ||||
\(818\) | −29.0000 | −1.01396 | ||||||||
\(819\) | −4.00000 | − | 3.46410i | −0.139771 | − | 0.121046i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.5000 | + | 28.5788i | −0.575854 | + | 0.997408i | 0.420094 | + | 0.907480i | \(0.361997\pi\) |
−0.995948 | + | 0.0899279i | \(0.971336\pi\) | |||||||
\(822\) | −10.5000 | − | 18.1865i | −0.366230 | − | 0.634328i | ||||
\(823\) | 11.0000 | + | 19.0526i | 0.383436 | + | 0.664130i | 0.991551 | − | 0.129719i | \(-0.0414074\pi\) |
−0.608115 | + | 0.793849i | \(0.708074\pi\) | |||||||
\(824\) | 2.50000 | − | 4.33013i | 0.0870916 | − | 0.150847i | ||||
\(825\) | 15.0000 | 0.522233 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21.0000 | −0.730242 | −0.365121 | − | 0.930960i | \(-0.618972\pi\) | ||||
−0.365121 | + | 0.930960i | \(0.618972\pi\) | |||||||
\(828\) | 0.500000 | − | 0.866025i | 0.0173762 | − | 0.0300965i | ||||
\(829\) | −19.0000 | − | 32.9090i | −0.659897 | − | 1.14298i | −0.980642 | − | 0.195810i | \(-0.937266\pi\) |
0.320745 | − | 0.947166i | \(-0.396067\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.00000 | + | 6.92820i | −0.138758 | + | 0.240337i | ||||
\(832\) | 2.00000 | 0.0693375 | ||||||||
\(833\) | −3.00000 | − | 20.7846i | −0.103944 | − | 0.720144i | ||||
\(834\) | 13.0000 | 0.450153 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.00000 | + | 5.19615i | 0.103757 | + | 0.179713i | ||||
\(837\) | −1.00000 | − | 1.73205i | −0.0345651 | − | 0.0598684i | ||||
\(838\) | −10.5000 | + | 18.1865i | −0.362716 | + | 0.628243i | ||||
\(839\) | −36.0000 | −1.24286 | −0.621429 | − | 0.783470i | \(-0.713448\pi\) | ||||
−0.621429 | + | 0.783470i | \(0.713448\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 8.50000 | − | 14.7224i | 0.292929 | − | 0.507369i | ||||
\(843\) | 1.50000 | + | 2.59808i | 0.0516627 | + | 0.0894825i | ||||
\(844\) | 9.50000 | + | 16.4545i | 0.327003 | + | 0.566387i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.00000 | 0.103142 | ||||||||
\(847\) | 4.00000 | + | 3.46410i | 0.137442 | + | 0.119028i | ||||
\(848\) | −6.00000 | −0.206041 | ||||||||
\(849\) | −4.00000 | + | 6.92820i | −0.137280 | + | 0.237775i | ||||
\(850\) | 7.50000 | + | 12.9904i | 0.257248 | + | 0.445566i | ||||
\(851\) | 1.00000 | + | 1.73205i | 0.0342796 | + | 0.0593739i | ||||
\(852\) | −1.50000 | + | 2.59808i | −0.0513892 | + | 0.0890086i | ||||
\(853\) | −46.0000 | −1.57501 | −0.787505 | − | 0.616308i | \(-0.788628\pi\) | ||||
−0.787505 | + | 0.616308i | \(0.788628\pi\) | |||||||
\(854\) | −5.00000 | + | 1.73205i | −0.171096 | + | 0.0592696i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.00000 | − | 10.3923i | 0.205076 | − | 0.355202i | ||||
\(857\) | 9.00000 | + | 15.5885i | 0.307434 | + | 0.532492i | 0.977800 | − | 0.209539i | \(-0.0671963\pi\) |
−0.670366 | + | 0.742030i | \(0.733863\pi\) | |||||||
\(858\) | −3.00000 | − | 5.19615i | −0.102418 | − | 0.177394i | ||||
\(859\) | −5.50000 | + | 9.52628i | −0.187658 | + | 0.325032i | −0.944469 | − | 0.328601i | \(-0.893423\pi\) |
0.756811 | + | 0.653633i | \(0.226756\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.0000 | − | 5.19615i | 0.511199 | − | 0.177084i | ||||
\(862\) | −30.0000 | −1.02180 | ||||||||
\(863\) | −1.50000 | + | 2.59808i | −0.0510606 | + | 0.0884395i | −0.890426 | − | 0.455128i | \(-0.849593\pi\) |
0.839365 | + | 0.543568i | \(0.182927\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.00000 | − | 1.73205i | 0.0339814 | − | 0.0588575i | ||||
\(867\) | −8.00000 | −0.271694 | ||||||||
\(868\) | −4.00000 | − | 3.46410i | −0.135769 | − | 0.117579i | ||||
\(869\) | −33.0000 | −1.11945 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.00000 | − | 3.46410i | −0.0677674 | − | 0.117377i | ||||
\(872\) | −0.500000 | − | 0.866025i | −0.0169321 | − | 0.0293273i | ||||
\(873\) | −4.00000 | + | 6.92820i | −0.135379 | + | 0.234484i | ||||
\(874\) | 2.00000 | 0.0676510 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 11.0000 | 0.371656 | ||||||||
\(877\) | 2.00000 | − | 3.46410i | 0.0675352 | − | 0.116974i | −0.830281 | − | 0.557346i | \(-0.811820\pi\) |
0.897816 | + | 0.440371i | \(0.145153\pi\) | |||||||
\(878\) | 4.00000 | + | 6.92820i | 0.134993 | + | 0.233816i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.0000 | −0.505363 | −0.252681 | − | 0.967550i | \(-0.581312\pi\) | ||||
−0.252681 | + | 0.967550i | \(0.581312\pi\) | |||||||
\(882\) | −1.00000 | − | 6.92820i | −0.0336718 | − | 0.233285i | ||||
\(883\) | 20.0000 | 0.673054 | 0.336527 | − | 0.941674i | \(-0.390748\pi\) | ||||
0.336527 | + | 0.941674i | \(0.390748\pi\) | |||||||
\(884\) | 3.00000 | − | 5.19615i | 0.100901 | − | 0.174766i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.0000 | − | 20.7846i | −0.403148 | − | 0.698273i | ||||
\(887\) | −13.5000 | + | 23.3827i | −0.453286 | + | 0.785114i | −0.998588 | − | 0.0531258i | \(-0.983082\pi\) |
0.545302 | + | 0.838240i | \(0.316415\pi\) | |||||||
\(888\) | −2.00000 | −0.0671156 | ||||||||
\(889\) | −1.00000 | + | 5.19615i | −0.0335389 | + | 0.174273i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.50000 | − | 2.59808i | 0.0502519 | − | 0.0870388i | ||||
\(892\) | 5.00000 | + | 8.66025i | 0.167412 | + | 0.289967i | ||||
\(893\) | 3.00000 | + | 5.19615i | 0.100391 | + | 0.173883i | ||||
\(894\) | 6.00000 | − | 10.3923i | 0.200670 | − | 0.347571i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.00000 | + | 1.73205i | 0.0668153 | + | 0.0578638i | ||||
\(897\) | −2.00000 | −0.0667781 | ||||||||
\(898\) | 6.00000 | − | 10.3923i | 0.200223 | − | 0.346796i | ||||
\(899\) | −3.00000 | − | 5.19615i | −0.100056 | − | 0.173301i | ||||
\(900\) | 2.50000 | + | 4.33013i | 0.0833333 | + | 0.144338i | ||||
\(901\) | −9.00000 | + | 15.5885i | −0.299833 | + | 0.519327i | ||||
\(902\) | 18.0000 | 0.599334 | ||||||||
\(903\) | 5.00000 | − | 1.73205i | 0.166390 | − | 0.0576390i | ||||
\(904\) | −18.0000 | −0.598671 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.00000 | − | 3.46410i | −0.0664455 | − | 0.115087i | ||||
\(907\) | −22.0000 | − | 38.1051i | −0.730498 | − | 1.26526i | −0.956671 | − | 0.291172i | \(-0.905955\pi\) |
0.226173 | − | 0.974087i | \(-0.427379\pi\) | |||||||
\(908\) | 1.50000 | − | 2.59808i | 0.0497792 | − | 0.0862202i | ||||
\(909\) | −3.00000 | −0.0995037 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.0000 | −0.795155 | −0.397578 | − | 0.917568i | \(-0.630149\pi\) | ||||
−0.397578 | + | 0.917568i | \(0.630149\pi\) | |||||||
\(912\) | −1.00000 | + | 1.73205i | −0.0331133 | + | 0.0573539i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 10.0000 | + | 17.3205i | 0.330771 | + | 0.572911i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.00000 | −0.0330409 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3.00000 | 0.0990148 | ||||||||
\(919\) | −14.5000 | + | 25.1147i | −0.478311 | + | 0.828459i | −0.999691 | − | 0.0248659i | \(-0.992084\pi\) |
0.521380 | + | 0.853325i | \(0.325417\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.50000 | − | 9.52628i | −0.181231 | − | 0.313902i | ||||
\(922\) | −15.0000 | + | 25.9808i | −0.493999 | + | 0.855631i | ||||
\(923\) | 6.00000 | 0.197492 | ||||||||
\(924\) | 1.50000 | − | 7.79423i | 0.0493464 | − | 0.256411i | ||||
\(925\) | −10.0000 | −0.328798 | ||||||||
\(926\) | 16.0000 | − | 27.7128i | 0.525793 | − | 0.910700i | ||||
\(927\) | −2.50000 | − | 4.33013i | −0.0821108 | − | 0.142220i | ||||
\(928\) | 1.50000 | + | 2.59808i | 0.0492399 | + | 0.0852860i | ||||
\(929\) | −21.0000 | + | 36.3731i | −0.688988 | + | 1.19336i | 0.283178 | + | 0.959067i | \(0.408611\pi\) |
−0.972166 | + | 0.234294i | \(0.924722\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.0000 | − | 8.66025i | 0.360510 | − | 0.283828i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.50000 | − | 2.59808i | 0.0491078 | − | 0.0850572i | ||||
\(934\) | −10.5000 | − | 18.1865i | −0.343570 | − | 0.595082i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.00000 | − | 1.73205i | 0.0326860 | − | 0.0566139i | ||||
\(937\) | 38.0000 | 1.24141 | 0.620703 | − | 0.784046i | \(-0.286847\pi\) | ||||
0.620703 | + | 0.784046i | \(0.286847\pi\) | |||||||
\(938\) | 1.00000 | − | 5.19615i | 0.0326512 | − | 0.169660i | ||||
\(939\) | 8.00000 | 0.261070 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.0000 | − | 46.7654i | −0.880175 | − | 1.52451i | −0.851146 | − | 0.524929i | \(-0.824092\pi\) |
−0.0290288 | − | 0.999579i | \(-0.509241\pi\) | |||||||
\(942\) | 11.5000 | + | 19.9186i | 0.374690 | + | 0.648983i | ||||
\(943\) | 3.00000 | − | 5.19615i | 0.0976934 | − | 0.169210i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.00000 | 0.195077 | ||||||||
\(947\) | 3.00000 | − | 5.19615i | 0.0974869 | − | 0.168852i | −0.813157 | − | 0.582045i | \(-0.802253\pi\) |
0.910644 | + | 0.413192i | \(0.135586\pi\) | |||||||
\(948\) | −5.50000 | − | 9.52628i | −0.178632 | − | 0.309399i | ||||
\(949\) | −11.0000 | − | 19.0526i | −0.357075 | − | 0.618472i | ||||
\(950\) | −5.00000 | + | 8.66025i | −0.162221 | + | 0.280976i | ||||
\(951\) | −18.0000 | −0.583690 | ||||||||
\(952\) | 7.50000 | − | 2.59808i | 0.243076 | − | 0.0842041i | ||||
\(953\) | 33.0000 | 1.06897 | 0.534487 | − | 0.845176i | \(-0.320505\pi\) | ||||
0.534487 | + | 0.845176i | \(0.320505\pi\) | |||||||
\(954\) | −3.00000 | + | 5.19615i | −0.0971286 | + | 0.168232i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −7.50000 | − | 12.9904i | −0.242567 | − | 0.420139i | ||||
\(957\) | 4.50000 | − | 7.79423i | 0.145464 | − | 0.251952i | ||||
\(958\) | −30.0000 | −0.969256 | ||||||||
\(959\) | −52.5000 | + | 18.1865i | −1.69531 | + | 0.587274i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | − | 23.3827i | 0.435484 | − | 0.754280i | ||||
\(962\) | 2.00000 | + | 3.46410i | 0.0644826 | + | 0.111687i | ||||
\(963\) | −6.00000 | − | 10.3923i | −0.193347 | − | 0.334887i | ||||
\(964\) | −1.00000 | + | 1.73205i | −0.0322078 | + | 0.0557856i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.00000 | − | 1.73205i | −0.0643489 | − | 0.0557278i | ||||
\(967\) | 14.0000 | 0.450210 | 0.225105 | − | 0.974335i | \(-0.427728\pi\) | ||||
0.225105 | + | 0.974335i | \(0.427728\pi\) | |||||||
\(968\) | −1.00000 | + | 1.73205i | −0.0321412 | + | 0.0556702i | ||||
\(969\) | 3.00000 | + | 5.19615i | 0.0963739 | + | 0.166924i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.5000 | + | 38.9711i | −0.722059 | + | 1.25064i | 0.238114 | + | 0.971237i | \(0.423471\pi\) |
−0.960173 | + | 0.279406i | \(0.909862\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 6.50000 | − | 33.7750i | 0.208380 | − | 1.08278i | ||||
\(974\) | −2.00000 | −0.0640841 | ||||||||
\(975\) | 5.00000 | − | 8.66025i | 0.160128 | − | 0.277350i | ||||
\(976\) | −1.00000 | − | 1.73205i | −0.0320092 | − | 0.0554416i | ||||
\(977\) | −9.00000 | − | 15.5885i | −0.287936 | − | 0.498719i | 0.685381 | − | 0.728184i | \(-0.259636\pi\) |
−0.973317 | + | 0.229465i | \(0.926302\pi\) | |||||||
\(978\) | 11.5000 | − | 19.9186i | 0.367729 | − | 0.636926i | ||||
\(979\) | 18.0000 | 0.575282 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.00000 | −0.0319275 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.00000 | + | 15.5885i | 0.287055 | + | 0.497195i | 0.973106 | − | 0.230360i | \(-0.0739903\pi\) |
−0.686050 | + | 0.727554i | \(0.740657\pi\) | |||||||
\(984\) | 3.00000 | + | 5.19615i | 0.0956365 | + | 0.165647i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 9.00000 | 0.286618 | ||||||||
\(987\) | 1.50000 | − | 7.79423i | 0.0477455 | − | 0.248093i | ||||
\(988\) | 4.00000 | 0.127257 | ||||||||
\(989\) | 1.00000 | − | 1.73205i | 0.0317982 | − | 0.0550760i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0000 | + | 34.6410i | 0.635321 | + | 1.10041i | 0.986447 | + | 0.164080i | \(0.0524655\pi\) |
−0.351126 | + | 0.936328i | \(0.614201\pi\) | |||||||
\(992\) | 1.00000 | − | 1.73205i | 0.0317500 | − | 0.0549927i | ||||
\(993\) | 8.00000 | 0.253872 | ||||||||
\(994\) | 6.00000 | + | 5.19615i | 0.190308 | + | 0.164812i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.0000 | + | 45.0333i | 0.823428 | + | 1.42622i | 0.903115 | + | 0.429400i | \(0.141275\pi\) |
−0.0796863 | + | 0.996820i | \(0.525392\pi\) | |||||||
\(998\) | 17.5000 | + | 30.3109i | 0.553953 | + | 0.959474i | ||||
\(999\) | −1.00000 | + | 1.73205i | −0.0316386 | + | 0.0547997i |
(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 | 966.2.i.f.415.1 | yes | 2 | |
7.2 | even | 3 | 6762.2.a.o.1.1 | 1 | |||
7.4 | even | 3 | inner | 966.2.i.f.277.1 | ✓ | 2 | |
7.5 | odd | 6 | 6762.2.a.e.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.i.f.277.1 | ✓ | 2 | 7.4 | even | 3 | inner | |
966.2.i.f.415.1 | yes | 2 | 1.1 | even | 1 | trivial | |
6762.2.a.e.1.1 | 1 | 7.5 | odd | 6 | |||
6762.2.a.o.1.1 | 1 | 7.2 | even | 3 |