Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(121,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.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: | \(8.86339462436\) |
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 | 211.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1110.211 |
Dual form | 1110.2.i.f.121.1 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.00000 | + | 1.73205i | −0.377964 | + | 0.654654i | −0.990766 | − | 0.135583i | \(-0.956709\pi\) |
0.612801 | + | 0.790237i | \(0.290043\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −5.00000 | −1.50756 | −0.753778 | − | 0.657129i | \(-0.771771\pi\) | ||||
−0.753778 | + | 0.657129i | \(0.771771\pi\) | |||||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | −2.50000 | + | 4.33013i | −0.693375 | + | 1.20096i | 0.277350 | + | 0.960769i | \(0.410544\pi\) |
−0.970725 | + | 0.240192i | \(0.922790\pi\) | |||||||
\(14\) | −2.00000 | −0.534522 | ||||||||
\(15\) | −0.500000 | − | 0.866025i | −0.129099 | − | 0.223607i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 2.50000 | + | 4.33013i | 0.606339 | + | 1.05021i | 0.991838 | + | 0.127502i | \(0.0406959\pi\) |
−0.385499 | + | 0.922708i | \(0.625971\pi\) | |||||||
\(18\) | 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 | \(0.240348\pi\) | |||||||
\(20\) | 0.500000 | + | 0.866025i | 0.111803 | + | 0.193649i | ||||
\(21\) | 1.00000 | + | 1.73205i | 0.218218 | + | 0.377964i | ||||
\(22\) | −2.50000 | − | 4.33013i | −0.533002 | − | 0.923186i | ||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −5.00000 | −0.980581 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.00000 | − | 1.73205i | −0.188982 | − | 0.327327i | ||||
\(29\) | −9.00000 | −1.67126 | −0.835629 | − | 0.549294i | \(-0.814897\pi\) | ||||
−0.835629 | + | 0.549294i | \(0.814897\pi\) | |||||||
\(30\) | 0.500000 | − | 0.866025i | 0.0912871 | − | 0.158114i | ||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −2.50000 | + | 4.33013i | −0.435194 | + | 0.753778i | ||||
\(34\) | −2.50000 | + | 4.33013i | −0.428746 | + | 0.742611i | ||||
\(35\) | 1.00000 | + | 1.73205i | 0.169031 | + | 0.292770i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.500000 | + | 6.06218i | 0.0821995 | + | 0.996616i | ||||
\(38\) | −2.00000 | −0.324443 | ||||||||
\(39\) | 2.50000 | + | 4.33013i | 0.400320 | + | 0.693375i | ||||
\(40\) | −0.500000 | + | 0.866025i | −0.0790569 | + | 0.136931i | ||||
\(41\) | −3.00000 | + | 5.19615i | −0.468521 | + | 0.811503i | −0.999353 | − | 0.0359748i | \(-0.988546\pi\) |
0.530831 | + | 0.847477i | \(0.321880\pi\) | |||||||
\(42\) | −1.00000 | + | 1.73205i | −0.154303 | + | 0.267261i | ||||
\(43\) | 4.00000 | 0.609994 | 0.304997 | − | 0.952353i | \(-0.401344\pi\) | ||||
0.304997 | + | 0.952353i | \(0.401344\pi\) | |||||||
\(44\) | 2.50000 | − | 4.33013i | 0.376889 | − | 0.652791i | ||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.00000 | 1.31278 | 0.656392 | − | 0.754420i | \(-0.272082\pi\) | ||||
0.656392 | + | 0.754420i | \(0.272082\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.50000 | + | 2.59808i | 0.214286 | + | 0.371154i | ||||
\(50\) | 0.500000 | − | 0.866025i | 0.0707107 | − | 0.122474i | ||||
\(51\) | 5.00000 | 0.700140 | ||||||||
\(52\) | −2.50000 | − | 4.33013i | −0.346688 | − | 0.600481i | ||||
\(53\) | −3.00000 | − | 5.19615i | −0.412082 | − | 0.713746i | 0.583036 | − | 0.812447i | \(-0.301865\pi\) |
−0.995117 | + | 0.0987002i | \(0.968532\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | −2.50000 | + | 4.33013i | −0.337100 | + | 0.583874i | ||||
\(56\) | 1.00000 | − | 1.73205i | 0.133631 | − | 0.231455i | ||||
\(57\) | 1.00000 | + | 1.73205i | 0.132453 | + | 0.229416i | ||||
\(58\) | −4.50000 | − | 7.79423i | −0.590879 | − | 1.02343i | ||||
\(59\) | −1.50000 | − | 2.59808i | −0.195283 | − | 0.338241i | 0.751710 | − | 0.659494i | \(-0.229229\pi\) |
−0.946993 | + | 0.321253i | \(0.895896\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(62\) | 2.00000 | + | 3.46410i | 0.254000 | + | 0.439941i | ||||
\(63\) | 2.00000 | 0.251976 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.50000 | + | 4.33013i | 0.310087 | + | 0.537086i | ||||
\(66\) | −5.00000 | −0.615457 | ||||||||
\(67\) | 4.50000 | − | 7.79423i | 0.549762 | − | 0.952217i | −0.448528 | − | 0.893769i | \(-0.648052\pi\) |
0.998290 | − | 0.0584478i | \(-0.0186151\pi\) | |||||||
\(68\) | −5.00000 | −0.606339 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.00000 | + | 1.73205i | −0.119523 | + | 0.207020i | ||||
\(71\) | 6.00000 | − | 10.3923i | 0.712069 | − | 1.23334i | −0.252010 | − | 0.967725i | \(-0.581092\pi\) |
0.964079 | − | 0.265615i | \(-0.0855750\pi\) | |||||||
\(72\) | 0.500000 | + | 0.866025i | 0.0589256 | + | 0.102062i | ||||
\(73\) | −12.0000 | −1.40449 | −0.702247 | − | 0.711934i | \(-0.747820\pi\) | ||||
−0.702247 | + | 0.711934i | \(0.747820\pi\) | |||||||
\(74\) | −5.00000 | + | 3.46410i | −0.581238 | + | 0.402694i | ||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −1.00000 | − | 1.73205i | −0.114708 | − | 0.198680i | ||||
\(77\) | 5.00000 | − | 8.66025i | 0.569803 | − | 0.986928i | ||||
\(78\) | −2.50000 | + | 4.33013i | −0.283069 | + | 0.490290i | ||||
\(79\) | −8.00000 | + | 13.8564i | −0.900070 | + | 1.55897i | −0.0726692 | + | 0.997356i | \(0.523152\pi\) |
−0.827401 | + | 0.561611i | \(0.810182\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −6.00000 | −0.662589 | ||||||||
\(83\) | 1.00000 | + | 1.73205i | 0.109764 | + | 0.190117i | 0.915675 | − | 0.401920i | \(-0.131657\pi\) |
−0.805910 | + | 0.592037i | \(0.798324\pi\) | |||||||
\(84\) | −2.00000 | −0.218218 | ||||||||
\(85\) | 5.00000 | 0.542326 | ||||||||
\(86\) | 2.00000 | + | 3.46410i | 0.215666 | + | 0.373544i | ||||
\(87\) | −4.50000 | + | 7.79423i | −0.482451 | + | 0.835629i | ||||
\(88\) | 5.00000 | 0.533002 | ||||||||
\(89\) | 7.00000 | + | 12.1244i | 0.741999 | + | 1.28518i | 0.951584 | + | 0.307389i | \(0.0994552\pi\) |
−0.209585 | + | 0.977790i | \(0.567211\pi\) | |||||||
\(90\) | −0.500000 | − | 0.866025i | −0.0527046 | − | 0.0912871i | ||||
\(91\) | −5.00000 | − | 8.66025i | −0.524142 | − | 0.907841i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.00000 | − | 3.46410i | 0.207390 | − | 0.359211i | ||||
\(94\) | 4.50000 | + | 7.79423i | 0.464140 | + | 0.803913i | ||||
\(95\) | 1.00000 | + | 1.73205i | 0.102598 | + | 0.177705i | ||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | −18.0000 | −1.82762 | −0.913812 | − | 0.406138i | \(-0.866875\pi\) | ||||
−0.913812 | + | 0.406138i | \(0.866875\pi\) | |||||||
\(98\) | −1.50000 | + | 2.59808i | −0.151523 | + | 0.262445i | ||||
\(99\) | 2.50000 | + | 4.33013i | 0.251259 | + | 0.435194i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 5.00000 | 0.497519 | 0.248759 | − | 0.968565i | \(-0.419977\pi\) | ||||
0.248759 | + | 0.968565i | \(0.419977\pi\) | |||||||
\(102\) | 2.50000 | + | 4.33013i | 0.247537 | + | 0.428746i | ||||
\(103\) | −4.00000 | −0.394132 | −0.197066 | − | 0.980390i | \(-0.563141\pi\) | ||||
−0.197066 | + | 0.980390i | \(0.563141\pi\) | |||||||
\(104\) | 2.50000 | − | 4.33013i | 0.245145 | − | 0.424604i | ||||
\(105\) | 2.00000 | 0.195180 | ||||||||
\(106\) | 3.00000 | − | 5.19615i | 0.291386 | − | 0.504695i | ||||
\(107\) | 1.00000 | − | 1.73205i | 0.0966736 | − | 0.167444i | −0.813632 | − | 0.581380i | \(-0.802513\pi\) |
0.910306 | + | 0.413936i | \(0.135846\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | −7.00000 | − | 12.1244i | −0.670478 | − | 1.16130i | −0.977769 | − | 0.209687i | \(-0.932756\pi\) |
0.307290 | − | 0.951616i | \(-0.400578\pi\) | |||||||
\(110\) | −5.00000 | −0.476731 | ||||||||
\(111\) | 5.50000 | + | 2.59808i | 0.522037 | + | 0.246598i | ||||
\(112\) | 2.00000 | 0.188982 | ||||||||
\(113\) | −7.50000 | − | 12.9904i | −0.705541 | − | 1.22203i | −0.966496 | − | 0.256681i | \(-0.917371\pi\) |
0.260955 | − | 0.965351i | \(-0.415962\pi\) | |||||||
\(114\) | −1.00000 | + | 1.73205i | −0.0936586 | + | 0.162221i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.50000 | − | 7.79423i | 0.417815 | − | 0.723676i | ||||
\(117\) | 5.00000 | 0.462250 | ||||||||
\(118\) | 1.50000 | − | 2.59808i | 0.138086 | − | 0.239172i | ||||
\(119\) | −10.0000 | −0.916698 | ||||||||
\(120\) | 0.500000 | + | 0.866025i | 0.0456435 | + | 0.0790569i | ||||
\(121\) | 14.0000 | 1.27273 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.00000 | + | 5.19615i | 0.270501 | + | 0.468521i | ||||
\(124\) | −2.00000 | + | 3.46410i | −0.179605 | + | 0.311086i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 1.00000 | + | 1.73205i | 0.0890871 | + | 0.154303i | ||||
\(127\) | 1.00000 | + | 1.73205i | 0.0887357 | + | 0.153695i | 0.906977 | − | 0.421180i | \(-0.138384\pi\) |
−0.818241 | + | 0.574875i | \(0.805051\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 2.00000 | − | 3.46410i | 0.176090 | − | 0.304997i | ||||
\(130\) | −2.50000 | + | 4.33013i | −0.219265 | + | 0.379777i | ||||
\(131\) | −5.50000 | − | 9.52628i | −0.480537 | − | 0.832315i | 0.519213 | − | 0.854645i | \(-0.326225\pi\) |
−0.999751 | + | 0.0223297i | \(0.992892\pi\) | |||||||
\(132\) | −2.50000 | − | 4.33013i | −0.217597 | − | 0.376889i | ||||
\(133\) | −2.00000 | − | 3.46410i | −0.173422 | − | 0.300376i | ||||
\(134\) | 9.00000 | 0.777482 | ||||||||
\(135\) | −0.500000 | + | 0.866025i | −0.0430331 | + | 0.0745356i | ||||
\(136\) | −2.50000 | − | 4.33013i | −0.214373 | − | 0.371305i | ||||
\(137\) | −3.00000 | −0.256307 | −0.128154 | − | 0.991754i | \(-0.540905\pi\) | ||||
−0.128154 | + | 0.991754i | \(0.540905\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.00000 | + | 13.8564i | 0.678551 | + | 1.17529i | 0.975417 | + | 0.220366i | \(0.0707252\pi\) |
−0.296866 | + | 0.954919i | \(0.595942\pi\) | |||||||
\(140\) | −2.00000 | −0.169031 | ||||||||
\(141\) | 4.50000 | − | 7.79423i | 0.378968 | − | 0.656392i | ||||
\(142\) | 12.0000 | 1.00702 | ||||||||
\(143\) | 12.5000 | − | 21.6506i | 1.04530 | − | 1.81052i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | −4.50000 | + | 7.79423i | −0.373705 | + | 0.647275i | ||||
\(146\) | −6.00000 | − | 10.3923i | −0.496564 | − | 0.860073i | ||||
\(147\) | 3.00000 | 0.247436 | ||||||||
\(148\) | −5.50000 | − | 2.59808i | −0.452097 | − | 0.213561i | ||||
\(149\) | 15.0000 | 1.22885 | 0.614424 | − | 0.788976i | \(-0.289388\pi\) | ||||
0.614424 | + | 0.788976i | \(0.289388\pi\) | |||||||
\(150\) | −0.500000 | − | 0.866025i | −0.0408248 | − | 0.0707107i | ||||
\(151\) | −4.00000 | + | 6.92820i | −0.325515 | + | 0.563809i | −0.981617 | − | 0.190864i | \(-0.938871\pi\) |
0.656101 | + | 0.754673i | \(0.272204\pi\) | |||||||
\(152\) | 1.00000 | − | 1.73205i | 0.0811107 | − | 0.140488i | ||||
\(153\) | 2.50000 | − | 4.33013i | 0.202113 | − | 0.350070i | ||||
\(154\) | 10.0000 | 0.805823 | ||||||||
\(155\) | 2.00000 | − | 3.46410i | 0.160644 | − | 0.278243i | ||||
\(156\) | −5.00000 | −0.400320 | ||||||||
\(157\) | 6.50000 | + | 11.2583i | 0.518756 | + | 0.898513i | 0.999762 | + | 0.0217953i | \(0.00693820\pi\) |
−0.481006 | + | 0.876717i | \(0.659728\pi\) | |||||||
\(158\) | −16.0000 | −1.27289 | ||||||||
\(159\) | −6.00000 | −0.475831 | ||||||||
\(160\) | −0.500000 | − | 0.866025i | −0.0395285 | − | 0.0684653i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 4.50000 | + | 7.79423i | 0.352467 | + | 0.610491i | 0.986681 | − | 0.162667i | \(-0.0520095\pi\) |
−0.634214 | + | 0.773158i | \(0.718676\pi\) | |||||||
\(164\) | −3.00000 | − | 5.19615i | −0.234261 | − | 0.405751i | ||||
\(165\) | 2.50000 | + | 4.33013i | 0.194625 | + | 0.337100i | ||||
\(166\) | −1.00000 | + | 1.73205i | −0.0776151 | + | 0.134433i | ||||
\(167\) | 8.50000 | − | 14.7224i | 0.657750 | − | 1.13926i | −0.323447 | − | 0.946246i | \(-0.604842\pi\) |
0.981197 | − | 0.193010i | \(-0.0618249\pi\) | |||||||
\(168\) | −1.00000 | − | 1.73205i | −0.0771517 | − | 0.133631i | ||||
\(169\) | −6.00000 | − | 10.3923i | −0.461538 | − | 0.799408i | ||||
\(170\) | 2.50000 | + | 4.33013i | 0.191741 | + | 0.332106i | ||||
\(171\) | 2.00000 | 0.152944 | ||||||||
\(172\) | −2.00000 | + | 3.46410i | −0.152499 | + | 0.264135i | ||||
\(173\) | −7.00000 | − | 12.1244i | −0.532200 | − | 0.921798i | −0.999293 | − | 0.0375896i | \(-0.988032\pi\) |
0.467093 | − | 0.884208i | \(-0.345301\pi\) | |||||||
\(174\) | −9.00000 | −0.682288 | ||||||||
\(175\) | 2.00000 | 0.151186 | ||||||||
\(176\) | 2.50000 | + | 4.33013i | 0.188445 | + | 0.326396i | ||||
\(177\) | −3.00000 | −0.225494 | ||||||||
\(178\) | −7.00000 | + | 12.1244i | −0.524672 | + | 0.908759i | ||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 0.500000 | − | 0.866025i | 0.0372678 | − | 0.0645497i | ||||
\(181\) | −7.00000 | + | 12.1244i | −0.520306 | + | 0.901196i | 0.479415 | + | 0.877588i | \(0.340849\pi\) |
−0.999721 | + | 0.0236082i | \(0.992485\pi\) | |||||||
\(182\) | 5.00000 | − | 8.66025i | 0.370625 | − | 0.641941i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.50000 | + | 2.59808i | 0.404368 | + | 0.191014i | ||||
\(186\) | 4.00000 | 0.293294 | ||||||||
\(187\) | −12.5000 | − | 21.6506i | −0.914091 | − | 1.58325i | ||||
\(188\) | −4.50000 | + | 7.79423i | −0.328196 | + | 0.568453i | ||||
\(189\) | 1.00000 | − | 1.73205i | 0.0727393 | − | 0.125988i | ||||
\(190\) | −1.00000 | + | 1.73205i | −0.0725476 | + | 0.125656i | ||||
\(191\) | 18.0000 | 1.30243 | 0.651217 | − | 0.758891i | \(-0.274259\pi\) | ||||
0.651217 | + | 0.758891i | \(0.274259\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | 26.0000 | 1.87152 | 0.935760 | − | 0.352636i | \(-0.114715\pi\) | ||||
0.935760 | + | 0.352636i | \(0.114715\pi\) | |||||||
\(194\) | −9.00000 | − | 15.5885i | −0.646162 | − | 1.11919i | ||||
\(195\) | 5.00000 | 0.358057 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | 5.00000 | + | 8.66025i | 0.356235 | + | 0.617018i | 0.987329 | − | 0.158689i | \(-0.0507268\pi\) |
−0.631093 | + | 0.775707i | \(0.717394\pi\) | |||||||
\(198\) | −2.50000 | + | 4.33013i | −0.177667 | + | 0.307729i | ||||
\(199\) | 7.00000 | 0.496217 | 0.248108 | − | 0.968732i | \(-0.420191\pi\) | ||||
0.248108 | + | 0.968732i | \(0.420191\pi\) | |||||||
\(200\) | 0.500000 | + | 0.866025i | 0.0353553 | + | 0.0612372i | ||||
\(201\) | −4.50000 | − | 7.79423i | −0.317406 | − | 0.549762i | ||||
\(202\) | 2.50000 | + | 4.33013i | 0.175899 | + | 0.304667i | ||||
\(203\) | 9.00000 | − | 15.5885i | 0.631676 | − | 1.09410i | ||||
\(204\) | −2.50000 | + | 4.33013i | −0.175035 | + | 0.303170i | ||||
\(205\) | 3.00000 | + | 5.19615i | 0.209529 | + | 0.362915i | ||||
\(206\) | −2.00000 | − | 3.46410i | −0.139347 | − | 0.241355i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.00000 | 0.346688 | ||||||||
\(209\) | 5.00000 | − | 8.66025i | 0.345857 | − | 0.599042i | ||||
\(210\) | 1.00000 | + | 1.73205i | 0.0690066 | + | 0.119523i | ||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | 6.00000 | 0.412082 | ||||||||
\(213\) | −6.00000 | − | 10.3923i | −0.411113 | − | 0.712069i | ||||
\(214\) | 2.00000 | 0.136717 | ||||||||
\(215\) | 2.00000 | − | 3.46410i | 0.136399 | − | 0.236250i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −4.00000 | + | 6.92820i | −0.271538 | + | 0.470317i | ||||
\(218\) | 7.00000 | − | 12.1244i | 0.474100 | − | 0.821165i | ||||
\(219\) | −6.00000 | + | 10.3923i | −0.405442 | + | 0.702247i | ||||
\(220\) | −2.50000 | − | 4.33013i | −0.168550 | − | 0.291937i | ||||
\(221\) | −25.0000 | −1.68168 | ||||||||
\(222\) | 0.500000 | + | 6.06218i | 0.0335578 | + | 0.406867i | ||||
\(223\) | 12.0000 | 0.803579 | 0.401790 | − | 0.915732i | \(-0.368388\pi\) | ||||
0.401790 | + | 0.915732i | \(0.368388\pi\) | |||||||
\(224\) | 1.00000 | + | 1.73205i | 0.0668153 | + | 0.115728i | ||||
\(225\) | −0.500000 | + | 0.866025i | −0.0333333 | + | 0.0577350i | ||||
\(226\) | 7.50000 | − | 12.9904i | 0.498893 | − | 0.864107i | ||||
\(227\) | −9.00000 | + | 15.5885i | −0.597351 | + | 1.03464i | 0.395860 | + | 0.918311i | \(0.370447\pi\) |
−0.993210 | + | 0.116331i | \(0.962887\pi\) | |||||||
\(228\) | −2.00000 | −0.132453 | ||||||||
\(229\) | 2.00000 | − | 3.46410i | 0.132164 | − | 0.228914i | −0.792347 | − | 0.610071i | \(-0.791141\pi\) |
0.924510 | + | 0.381157i | \(0.124474\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.00000 | − | 8.66025i | −0.328976 | − | 0.569803i | ||||
\(232\) | 9.00000 | 0.590879 | ||||||||
\(233\) | 18.0000 | 1.17922 | 0.589610 | − | 0.807688i | \(-0.299282\pi\) | ||||
0.589610 | + | 0.807688i | \(0.299282\pi\) | |||||||
\(234\) | 2.50000 | + | 4.33013i | 0.163430 | + | 0.283069i | ||||
\(235\) | 4.50000 | − | 7.79423i | 0.293548 | − | 0.508439i | ||||
\(236\) | 3.00000 | 0.195283 | ||||||||
\(237\) | 8.00000 | + | 13.8564i | 0.519656 | + | 0.900070i | ||||
\(238\) | −5.00000 | − | 8.66025i | −0.324102 | − | 0.561361i | ||||
\(239\) | 10.0000 | + | 17.3205i | 0.646846 | + | 1.12037i | 0.983872 | + | 0.178875i | \(0.0572458\pi\) |
−0.337026 | + | 0.941495i | \(0.609421\pi\) | |||||||
\(240\) | −0.500000 | + | 0.866025i | −0.0322749 | + | 0.0559017i | ||||
\(241\) | −12.5000 | + | 21.6506i | −0.805196 | + | 1.39464i | 0.110963 | + | 0.993825i | \(0.464606\pi\) |
−0.916159 | + | 0.400815i | \(0.868727\pi\) | |||||||
\(242\) | 7.00000 | + | 12.1244i | 0.449977 | + | 0.779383i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.00000 | 0.191663 | ||||||||
\(246\) | −3.00000 | + | 5.19615i | −0.191273 | + | 0.331295i | ||||
\(247\) | −5.00000 | − | 8.66025i | −0.318142 | − | 0.551039i | ||||
\(248\) | −4.00000 | −0.254000 | ||||||||
\(249\) | 2.00000 | 0.126745 | ||||||||
\(250\) | −0.500000 | − | 0.866025i | −0.0316228 | − | 0.0547723i | ||||
\(251\) | −7.00000 | −0.441836 | −0.220918 | − | 0.975292i | \(-0.570905\pi\) | ||||
−0.220918 | + | 0.975292i | \(0.570905\pi\) | |||||||
\(252\) | −1.00000 | + | 1.73205i | −0.0629941 | + | 0.109109i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −1.00000 | + | 1.73205i | −0.0627456 | + | 0.108679i | ||||
\(255\) | 2.50000 | − | 4.33013i | 0.156556 | − | 0.271163i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 6.50000 | + | 11.2583i | 0.405459 | + | 0.702275i | 0.994375 | − | 0.105919i | \(-0.0337784\pi\) |
−0.588916 | + | 0.808194i | \(0.700445\pi\) | |||||||
\(258\) | 4.00000 | 0.249029 | ||||||||
\(259\) | −11.0000 | − | 5.19615i | −0.683507 | − | 0.322873i | ||||
\(260\) | −5.00000 | −0.310087 | ||||||||
\(261\) | 4.50000 | + | 7.79423i | 0.278543 | + | 0.482451i | ||||
\(262\) | 5.50000 | − | 9.52628i | 0.339791 | − | 0.588536i | ||||
\(263\) | 14.0000 | − | 24.2487i | 0.863277 | − | 1.49524i | −0.00547092 | − | 0.999985i | \(-0.501741\pi\) |
0.868748 | − | 0.495255i | \(-0.164925\pi\) | |||||||
\(264\) | 2.50000 | − | 4.33013i | 0.153864 | − | 0.266501i | ||||
\(265\) | −6.00000 | −0.368577 | ||||||||
\(266\) | 2.00000 | − | 3.46410i | 0.122628 | − | 0.212398i | ||||
\(267\) | 14.0000 | 0.856786 | ||||||||
\(268\) | 4.50000 | + | 7.79423i | 0.274881 | + | 0.476108i | ||||
\(269\) | 6.00000 | 0.365826 | 0.182913 | − | 0.983129i | \(-0.441447\pi\) | ||||
0.182913 | + | 0.983129i | \(0.441447\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | 0.500000 | + | 0.866025i | 0.0303728 | + | 0.0526073i | 0.880812 | − | 0.473466i | \(-0.156997\pi\) |
−0.850439 | + | 0.526073i | \(0.823664\pi\) | |||||||
\(272\) | 2.50000 | − | 4.33013i | 0.151585 | − | 0.262553i | ||||
\(273\) | −10.0000 | −0.605228 | ||||||||
\(274\) | −1.50000 | − | 2.59808i | −0.0906183 | − | 0.156956i | ||||
\(275\) | 2.50000 | + | 4.33013i | 0.150756 | + | 0.261116i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.500000 | − | 0.866025i | 0.0300421 | − | 0.0520344i | −0.850613 | − | 0.525792i | \(-0.823769\pi\) |
0.880656 | + | 0.473757i | \(0.157103\pi\) | |||||||
\(278\) | −8.00000 | + | 13.8564i | −0.479808 | + | 0.831052i | ||||
\(279\) | −2.00000 | − | 3.46410i | −0.119737 | − | 0.207390i | ||||
\(280\) | −1.00000 | − | 1.73205i | −0.0597614 | − | 0.103510i | ||||
\(281\) | −5.00000 | − | 8.66025i | −0.298275 | − | 0.516627i | 0.677466 | − | 0.735554i | \(-0.263078\pi\) |
−0.975741 | + | 0.218926i | \(0.929745\pi\) | |||||||
\(282\) | 9.00000 | 0.535942 | ||||||||
\(283\) | 7.50000 | − | 12.9904i | 0.445829 | − | 0.772198i | −0.552281 | − | 0.833658i | \(-0.686242\pi\) |
0.998110 | + | 0.0614601i | \(0.0195757\pi\) | |||||||
\(284\) | 6.00000 | + | 10.3923i | 0.356034 | + | 0.616670i | ||||
\(285\) | 2.00000 | 0.118470 | ||||||||
\(286\) | 25.0000 | 1.47828 | ||||||||
\(287\) | −6.00000 | − | 10.3923i | −0.354169 | − | 0.613438i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −4.00000 | + | 6.92820i | −0.235294 | + | 0.407541i | ||||
\(290\) | −9.00000 | −0.528498 | ||||||||
\(291\) | −9.00000 | + | 15.5885i | −0.527589 | + | 0.913812i | ||||
\(292\) | 6.00000 | − | 10.3923i | 0.351123 | − | 0.608164i | ||||
\(293\) | −5.00000 | + | 8.66025i | −0.292103 | + | 0.505937i | −0.974307 | − | 0.225225i | \(-0.927688\pi\) |
0.682204 | + | 0.731162i | \(0.261022\pi\) | |||||||
\(294\) | 1.50000 | + | 2.59808i | 0.0874818 | + | 0.151523i | ||||
\(295\) | −3.00000 | −0.174667 | ||||||||
\(296\) | −0.500000 | − | 6.06218i | −0.0290619 | − | 0.352357i | ||||
\(297\) | 5.00000 | 0.290129 | ||||||||
\(298\) | 7.50000 | + | 12.9904i | 0.434463 | + | 0.752513i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.500000 | − | 0.866025i | 0.0288675 | − | 0.0500000i | ||||
\(301\) | −4.00000 | + | 6.92820i | −0.230556 | + | 0.399335i | ||||
\(302\) | −8.00000 | −0.460348 | ||||||||
\(303\) | 2.50000 | − | 4.33013i | 0.143621 | − | 0.248759i | ||||
\(304\) | 2.00000 | 0.114708 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 5.00000 | 0.285831 | ||||||||
\(307\) | −16.0000 | −0.913168 | −0.456584 | − | 0.889680i | \(-0.650927\pi\) | ||||
−0.456584 | + | 0.889680i | \(0.650927\pi\) | |||||||
\(308\) | 5.00000 | + | 8.66025i | 0.284901 | + | 0.493464i | ||||
\(309\) | −2.00000 | + | 3.46410i | −0.113776 | + | 0.197066i | ||||
\(310\) | 4.00000 | 0.227185 | ||||||||
\(311\) | 12.0000 | + | 20.7846i | 0.680458 | + | 1.17859i | 0.974841 | + | 0.222900i | \(0.0715523\pi\) |
−0.294384 | + | 0.955687i | \(0.595114\pi\) | |||||||
\(312\) | −2.50000 | − | 4.33013i | −0.141535 | − | 0.245145i | ||||
\(313\) | 7.00000 | + | 12.1244i | 0.395663 | + | 0.685309i | 0.993186 | − | 0.116543i | \(-0.0371814\pi\) |
−0.597522 | + | 0.801852i | \(0.703848\pi\) | |||||||
\(314\) | −6.50000 | + | 11.2583i | −0.366816 | + | 0.635344i | ||||
\(315\) | 1.00000 | − | 1.73205i | 0.0563436 | − | 0.0975900i | ||||
\(316\) | −8.00000 | − | 13.8564i | −0.450035 | − | 0.779484i | ||||
\(317\) | −9.00000 | − | 15.5885i | −0.505490 | − | 0.875535i | −0.999980 | − | 0.00635137i | \(-0.997978\pi\) |
0.494489 | − | 0.869184i | \(-0.335355\pi\) | |||||||
\(318\) | −3.00000 | − | 5.19615i | −0.168232 | − | 0.291386i | ||||
\(319\) | 45.0000 | 2.51952 | ||||||||
\(320\) | 0.500000 | − | 0.866025i | 0.0279508 | − | 0.0484123i | ||||
\(321\) | −1.00000 | − | 1.73205i | −0.0558146 | − | 0.0966736i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.0000 | −0.556415 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 5.00000 | 0.277350 | ||||||||
\(326\) | −4.50000 | + | 7.79423i | −0.249232 | + | 0.431682i | ||||
\(327\) | −14.0000 | −0.774202 | ||||||||
\(328\) | 3.00000 | − | 5.19615i | 0.165647 | − | 0.286910i | ||||
\(329\) | −9.00000 | + | 15.5885i | −0.496186 | + | 0.859419i | ||||
\(330\) | −2.50000 | + | 4.33013i | −0.137620 | + | 0.238366i | ||||
\(331\) | −14.0000 | − | 24.2487i | −0.769510 | − | 1.33283i | −0.937829 | − | 0.347097i | \(-0.887167\pi\) |
0.168320 | − | 0.985732i | \(-0.446166\pi\) | |||||||
\(332\) | −2.00000 | −0.109764 | ||||||||
\(333\) | 5.00000 | − | 3.46410i | 0.273998 | − | 0.189832i | ||||
\(334\) | 17.0000 | 0.930199 | ||||||||
\(335\) | −4.50000 | − | 7.79423i | −0.245861 | − | 0.425844i | ||||
\(336\) | 1.00000 | − | 1.73205i | 0.0545545 | − | 0.0944911i | ||||
\(337\) | −7.00000 | + | 12.1244i | −0.381314 | + | 0.660456i | −0.991250 | − | 0.131995i | \(-0.957862\pi\) |
0.609936 | + | 0.792451i | \(0.291195\pi\) | |||||||
\(338\) | 6.00000 | − | 10.3923i | 0.326357 | − | 0.565267i | ||||
\(339\) | −15.0000 | −0.814688 | ||||||||
\(340\) | −2.50000 | + | 4.33013i | −0.135582 | + | 0.234834i | ||||
\(341\) | −20.0000 | −1.08306 | ||||||||
\(342\) | 1.00000 | + | 1.73205i | 0.0540738 | + | 0.0936586i | ||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | −4.00000 | −0.215666 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.00000 | − | 12.1244i | 0.376322 | − | 0.651809i | ||||
\(347\) | 18.0000 | 0.966291 | 0.483145 | − | 0.875540i | \(-0.339494\pi\) | ||||
0.483145 | + | 0.875540i | \(0.339494\pi\) | |||||||
\(348\) | −4.50000 | − | 7.79423i | −0.241225 | − | 0.417815i | ||||
\(349\) | 10.0000 | + | 17.3205i | 0.535288 | + | 0.927146i | 0.999149 | + | 0.0412379i | \(0.0131301\pi\) |
−0.463862 | + | 0.885908i | \(0.653537\pi\) | |||||||
\(350\) | 1.00000 | + | 1.73205i | 0.0534522 | + | 0.0925820i | ||||
\(351\) | 2.50000 | − | 4.33013i | 0.133440 | − | 0.231125i | ||||
\(352\) | −2.50000 | + | 4.33013i | −0.133250 | + | 0.230797i | ||||
\(353\) | 1.00000 | + | 1.73205i | 0.0532246 | + | 0.0921878i | 0.891410 | − | 0.453197i | \(-0.149717\pi\) |
−0.838186 | + | 0.545385i | \(0.816383\pi\) | |||||||
\(354\) | −1.50000 | − | 2.59808i | −0.0797241 | − | 0.138086i | ||||
\(355\) | −6.00000 | − | 10.3923i | −0.318447 | − | 0.551566i | ||||
\(356\) | −14.0000 | −0.741999 | ||||||||
\(357\) | −5.00000 | + | 8.66025i | −0.264628 | + | 0.458349i | ||||
\(358\) | −6.00000 | − | 10.3923i | −0.317110 | − | 0.549250i | ||||
\(359\) | −18.0000 | −0.950004 | −0.475002 | − | 0.879985i | \(-0.657553\pi\) | ||||
−0.475002 | + | 0.879985i | \(0.657553\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | 7.50000 | + | 12.9904i | 0.394737 | + | 0.683704i | ||||
\(362\) | −14.0000 | −0.735824 | ||||||||
\(363\) | 7.00000 | − | 12.1244i | 0.367405 | − | 0.636364i | ||||
\(364\) | 10.0000 | 0.524142 | ||||||||
\(365\) | −6.00000 | + | 10.3923i | −0.314054 | + | 0.543958i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.00000 | − | 3.46410i | 0.104399 | − | 0.180825i | −0.809093 | − | 0.587680i | \(-0.800041\pi\) |
0.913493 | + | 0.406855i | \(0.133375\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.00000 | 0.312348 | ||||||||
\(370\) | 0.500000 | + | 6.06218i | 0.0259938 | + | 0.315158i | ||||
\(371\) | 12.0000 | 0.623009 | ||||||||
\(372\) | 2.00000 | + | 3.46410i | 0.103695 | + | 0.179605i | ||||
\(373\) | −5.00000 | + | 8.66025i | −0.258890 | + | 0.448411i | −0.965945 | − | 0.258748i | \(-0.916690\pi\) |
0.707055 | + | 0.707159i | \(0.250023\pi\) | |||||||
\(374\) | 12.5000 | − | 21.6506i | 0.646360 | − | 1.11953i | ||||
\(375\) | −0.500000 | + | 0.866025i | −0.0258199 | + | 0.0447214i | ||||
\(376\) | −9.00000 | −0.464140 | ||||||||
\(377\) | 22.5000 | − | 38.9711i | 1.15881 | − | 2.00712i | ||||
\(378\) | 2.00000 | 0.102869 | ||||||||
\(379\) | 3.00000 | + | 5.19615i | 0.154100 | + | 0.266908i | 0.932731 | − | 0.360573i | \(-0.117419\pi\) |
−0.778631 | + | 0.627482i | \(0.784086\pi\) | |||||||
\(380\) | −2.00000 | −0.102598 | ||||||||
\(381\) | 2.00000 | 0.102463 | ||||||||
\(382\) | 9.00000 | + | 15.5885i | 0.460480 | + | 0.797575i | ||||
\(383\) | 7.50000 | − | 12.9904i | 0.383232 | − | 0.663777i | −0.608290 | − | 0.793715i | \(-0.708144\pi\) |
0.991522 | + | 0.129937i | \(0.0414776\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −5.00000 | − | 8.66025i | −0.254824 | − | 0.441367i | ||||
\(386\) | 13.0000 | + | 22.5167i | 0.661683 | + | 1.14607i | ||||
\(387\) | −2.00000 | − | 3.46410i | −0.101666 | − | 0.176090i | ||||
\(388\) | 9.00000 | − | 15.5885i | 0.456906 | − | 0.791384i | ||||
\(389\) | 7.00000 | − | 12.1244i | 0.354914 | − | 0.614729i | −0.632189 | − | 0.774814i | \(-0.717843\pi\) |
0.987103 | + | 0.160085i | \(0.0511768\pi\) | |||||||
\(390\) | 2.50000 | + | 4.33013i | 0.126592 | + | 0.219265i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −1.50000 | − | 2.59808i | −0.0757614 | − | 0.131223i | ||||
\(393\) | −11.0000 | −0.554877 | ||||||||
\(394\) | −5.00000 | + | 8.66025i | −0.251896 | + | 0.436297i | ||||
\(395\) | 8.00000 | + | 13.8564i | 0.402524 | + | 0.697191i | ||||
\(396\) | −5.00000 | −0.251259 | ||||||||
\(397\) | −23.0000 | −1.15434 | −0.577168 | − | 0.816625i | \(-0.695842\pi\) | ||||
−0.577168 | + | 0.816625i | \(0.695842\pi\) | |||||||
\(398\) | 3.50000 | + | 6.06218i | 0.175439 | + | 0.303870i | ||||
\(399\) | −4.00000 | −0.200250 | ||||||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | −30.0000 | −1.49813 | −0.749064 | − | 0.662497i | \(-0.769497\pi\) | ||||
−0.749064 | + | 0.662497i | \(0.769497\pi\) | |||||||
\(402\) | 4.50000 | − | 7.79423i | 0.224440 | − | 0.388741i | ||||
\(403\) | −10.0000 | + | 17.3205i | −0.498135 | + | 0.862796i | ||||
\(404\) | −2.50000 | + | 4.33013i | −0.124380 | + | 0.215432i | ||||
\(405\) | 0.500000 | + | 0.866025i | 0.0248452 | + | 0.0430331i | ||||
\(406\) | 18.0000 | 0.893325 | ||||||||
\(407\) | −2.50000 | − | 30.3109i | −0.123920 | − | 1.50245i | ||||
\(408\) | −5.00000 | −0.247537 | ||||||||
\(409\) | 12.5000 | + | 21.6506i | 0.618085 | + | 1.07056i | 0.989835 | + | 0.142222i | \(0.0454247\pi\) |
−0.371750 | + | 0.928333i | \(0.621242\pi\) | |||||||
\(410\) | −3.00000 | + | 5.19615i | −0.148159 | + | 0.256620i | ||||
\(411\) | −1.50000 | + | 2.59808i | −0.0739895 | + | 0.128154i | ||||
\(412\) | 2.00000 | − | 3.46410i | 0.0985329 | − | 0.170664i | ||||
\(413\) | 6.00000 | 0.295241 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.00000 | 0.0981761 | ||||||||
\(416\) | 2.50000 | + | 4.33013i | 0.122573 | + | 0.212302i | ||||
\(417\) | 16.0000 | 0.783523 | ||||||||
\(418\) | 10.0000 | 0.489116 | ||||||||
\(419\) | 18.0000 | + | 31.1769i | 0.879358 | + | 1.52309i | 0.852047 | + | 0.523465i | \(0.175361\pi\) |
0.0273103 | + | 0.999627i | \(0.491306\pi\) | |||||||
\(420\) | −1.00000 | + | 1.73205i | −0.0487950 | + | 0.0845154i | ||||
\(421\) | 20.0000 | 0.974740 | 0.487370 | − | 0.873195i | \(-0.337956\pi\) | ||||
0.487370 | + | 0.873195i | \(0.337956\pi\) | |||||||
\(422\) | 2.00000 | + | 3.46410i | 0.0973585 | + | 0.168630i | ||||
\(423\) | −4.50000 | − | 7.79423i | −0.218797 | − | 0.378968i | ||||
\(424\) | 3.00000 | + | 5.19615i | 0.145693 | + | 0.252347i | ||||
\(425\) | 2.50000 | − | 4.33013i | 0.121268 | − | 0.210042i | ||||
\(426\) | 6.00000 | − | 10.3923i | 0.290701 | − | 0.503509i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.00000 | + | 1.73205i | 0.0483368 | + | 0.0837218i | ||||
\(429\) | −12.5000 | − | 21.6506i | −0.603506 | − | 1.04530i | ||||
\(430\) | 4.00000 | 0.192897 | ||||||||
\(431\) | −18.0000 | + | 31.1769i | −0.867029 | + | 1.50174i | −0.00201168 | + | 0.999998i | \(0.500640\pi\) |
−0.865018 | + | 0.501741i | \(0.832693\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | 24.0000 | 1.15337 | 0.576683 | − | 0.816968i | \(-0.304347\pi\) | ||||
0.576683 | + | 0.816968i | \(0.304347\pi\) | |||||||
\(434\) | −8.00000 | −0.384012 | ||||||||
\(435\) | 4.50000 | + | 7.79423i | 0.215758 | + | 0.373705i | ||||
\(436\) | 14.0000 | 0.670478 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −12.0000 | −0.573382 | ||||||||
\(439\) | −0.500000 | + | 0.866025i | −0.0238637 | + | 0.0413331i | −0.877711 | − | 0.479191i | \(-0.840930\pi\) |
0.853847 | + | 0.520524i | \(0.174263\pi\) | |||||||
\(440\) | 2.50000 | − | 4.33013i | 0.119183 | − | 0.206431i | ||||
\(441\) | 1.50000 | − | 2.59808i | 0.0714286 | − | 0.123718i | ||||
\(442\) | −12.5000 | − | 21.6506i | −0.594564 | − | 1.02982i | ||||
\(443\) | −10.0000 | −0.475114 | −0.237557 | − | 0.971374i | \(-0.576347\pi\) | ||||
−0.237557 | + | 0.971374i | \(0.576347\pi\) | |||||||
\(444\) | −5.00000 | + | 3.46410i | −0.237289 | + | 0.164399i | ||||
\(445\) | 14.0000 | 0.663664 | ||||||||
\(446\) | 6.00000 | + | 10.3923i | 0.284108 | + | 0.492090i | ||||
\(447\) | 7.50000 | − | 12.9904i | 0.354738 | − | 0.614424i | ||||
\(448\) | −1.00000 | + | 1.73205i | −0.0472456 | + | 0.0818317i | ||||
\(449\) | −10.0000 | + | 17.3205i | −0.471929 | + | 0.817405i | −0.999484 | − | 0.0321156i | \(-0.989776\pi\) |
0.527555 | + | 0.849521i | \(0.323109\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | 15.0000 | − | 25.9808i | 0.706322 | − | 1.22339i | ||||
\(452\) | 15.0000 | 0.705541 | ||||||||
\(453\) | 4.00000 | + | 6.92820i | 0.187936 | + | 0.325515i | ||||
\(454\) | −18.0000 | −0.844782 | ||||||||
\(455\) | −10.0000 | −0.468807 | ||||||||
\(456\) | −1.00000 | − | 1.73205i | −0.0468293 | − | 0.0811107i | ||||
\(457\) | −16.0000 | + | 27.7128i | −0.748448 | + | 1.29635i | 0.200118 | + | 0.979772i | \(0.435868\pi\) |
−0.948566 | + | 0.316579i | \(0.897466\pi\) | |||||||
\(458\) | 4.00000 | 0.186908 | ||||||||
\(459\) | −2.50000 | − | 4.33013i | −0.116690 | − | 0.202113i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.50000 | − | 6.06218i | −0.163011 | − | 0.282344i | 0.772936 | − | 0.634484i | \(-0.218787\pi\) |
−0.935947 | + | 0.352140i | \(0.885454\pi\) | |||||||
\(462\) | 5.00000 | − | 8.66025i | 0.232621 | − | 0.402911i | ||||
\(463\) | 13.0000 | − | 22.5167i | 0.604161 | − | 1.04644i | −0.388022 | − | 0.921650i | \(-0.626842\pi\) |
0.992183 | − | 0.124788i | \(-0.0398251\pi\) | |||||||
\(464\) | 4.50000 | + | 7.79423i | 0.208907 | + | 0.361838i | ||||
\(465\) | −2.00000 | − | 3.46410i | −0.0927478 | − | 0.160644i | ||||
\(466\) | 9.00000 | + | 15.5885i | 0.416917 | + | 0.722121i | ||||
\(467\) | 18.0000 | 0.832941 | 0.416470 | − | 0.909149i | \(-0.363267\pi\) | ||||
0.416470 | + | 0.909149i | \(0.363267\pi\) | |||||||
\(468\) | −2.50000 | + | 4.33013i | −0.115563 | + | 0.200160i | ||||
\(469\) | 9.00000 | + | 15.5885i | 0.415581 | + | 0.719808i | ||||
\(470\) | 9.00000 | 0.415139 | ||||||||
\(471\) | 13.0000 | 0.599008 | ||||||||
\(472\) | 1.50000 | + | 2.59808i | 0.0690431 | + | 0.119586i | ||||
\(473\) | −20.0000 | −0.919601 | ||||||||
\(474\) | −8.00000 | + | 13.8564i | −0.367452 | + | 0.636446i | ||||
\(475\) | 2.00000 | 0.0917663 | ||||||||
\(476\) | 5.00000 | − | 8.66025i | 0.229175 | − | 0.396942i | ||||
\(477\) | −3.00000 | + | 5.19615i | −0.137361 | + | 0.237915i | ||||
\(478\) | −10.0000 | + | 17.3205i | −0.457389 | + | 0.792222i | ||||
\(479\) | 15.0000 | + | 25.9808i | 0.685367 | + | 1.18709i | 0.973321 | + | 0.229447i | \(0.0736918\pi\) |
−0.287954 | + | 0.957644i | \(0.592975\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | −27.5000 | − | 12.9904i | −1.25389 | − | 0.592310i | ||||
\(482\) | −25.0000 | −1.13872 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.00000 | + | 12.1244i | −0.318182 | + | 0.551107i | ||||
\(485\) | −9.00000 | + | 15.5885i | −0.408669 | + | 0.707835i | ||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | 26.0000 | 1.17817 | 0.589086 | − | 0.808070i | \(-0.299488\pi\) | ||||
0.589086 | + | 0.808070i | \(0.299488\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.00000 | 0.406994 | ||||||||
\(490\) | 1.50000 | + | 2.59808i | 0.0677631 | + | 0.117369i | ||||
\(491\) | −36.0000 | −1.62466 | −0.812329 | − | 0.583200i | \(-0.801800\pi\) | ||||
−0.812329 | + | 0.583200i | \(0.801800\pi\) | |||||||
\(492\) | −6.00000 | −0.270501 | ||||||||
\(493\) | −22.5000 | − | 38.9711i | −1.01335 | − | 1.75517i | ||||
\(494\) | 5.00000 | − | 8.66025i | 0.224961 | − | 0.389643i | ||||
\(495\) | 5.00000 | 0.224733 | ||||||||
\(496\) | −2.00000 | − | 3.46410i | −0.0898027 | − | 0.155543i | ||||
\(497\) | 12.0000 | + | 20.7846i | 0.538274 | + | 0.932317i | ||||
\(498\) | 1.00000 | + | 1.73205i | 0.0448111 | + | 0.0776151i | ||||
\(499\) | −16.0000 | + | 27.7128i | −0.716258 | + | 1.24060i | 0.246214 | + | 0.969216i | \(0.420813\pi\) |
−0.962472 | + | 0.271380i | \(0.912520\pi\) | |||||||
\(500\) | 0.500000 | − | 0.866025i | 0.0223607 | − | 0.0387298i | ||||
\(501\) | −8.50000 | − | 14.7224i | −0.379752 | − | 0.657750i | ||||
\(502\) | −3.50000 | − | 6.06218i | −0.156213 | − | 0.270568i | ||||
\(503\) | −2.50000 | − | 4.33013i | −0.111469 | − | 0.193071i | 0.804893 | − | 0.593419i | \(-0.202222\pi\) |
−0.916363 | + | 0.400349i | \(0.868889\pi\) | |||||||
\(504\) | −2.00000 | −0.0890871 | ||||||||
\(505\) | 2.50000 | − | 4.33013i | 0.111249 | − | 0.192688i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.0000 | −0.532939 | ||||||||
\(508\) | −2.00000 | −0.0887357 | ||||||||
\(509\) | −13.0000 | − | 22.5167i | −0.576215 | − | 0.998033i | −0.995908 | − | 0.0903676i | \(-0.971196\pi\) |
0.419694 | − | 0.907666i | \(-0.362138\pi\) | |||||||
\(510\) | 5.00000 | 0.221404 | ||||||||
\(511\) | 12.0000 | − | 20.7846i | 0.530849 | − | 0.919457i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.00000 | − | 1.73205i | 0.0441511 | − | 0.0764719i | ||||
\(514\) | −6.50000 | + | 11.2583i | −0.286703 | + | 0.496584i | ||||
\(515\) | −2.00000 | + | 3.46410i | −0.0881305 | + | 0.152647i | ||||
\(516\) | 2.00000 | + | 3.46410i | 0.0880451 | + | 0.152499i | ||||
\(517\) | −45.0000 | −1.97910 | ||||||||
\(518\) | −1.00000 | − | 12.1244i | −0.0439375 | − | 0.532714i | ||||
\(519\) | −14.0000 | −0.614532 | ||||||||
\(520\) | −2.50000 | − | 4.33013i | −0.109632 | − | 0.189889i | ||||
\(521\) | 10.0000 | − | 17.3205i | 0.438108 | − | 0.758825i | −0.559436 | − | 0.828874i | \(-0.688982\pi\) |
0.997544 | + | 0.0700486i | \(0.0223154\pi\) | |||||||
\(522\) | −4.50000 | + | 7.79423i | −0.196960 | + | 0.341144i | ||||
\(523\) | 14.0000 | − | 24.2487i | 0.612177 | − | 1.06032i | −0.378695 | − | 0.925521i | \(-0.623627\pi\) |
0.990873 | − | 0.134801i | \(-0.0430394\pi\) | |||||||
\(524\) | 11.0000 | 0.480537 | ||||||||
\(525\) | 1.00000 | − | 1.73205i | 0.0436436 | − | 0.0755929i | ||||
\(526\) | 28.0000 | 1.22086 | ||||||||
\(527\) | 10.0000 | + | 17.3205i | 0.435607 | + | 0.754493i | ||||
\(528\) | 5.00000 | 0.217597 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | −3.00000 | − | 5.19615i | −0.130312 | − | 0.225706i | ||||
\(531\) | −1.50000 | + | 2.59808i | −0.0650945 | + | 0.112747i | ||||
\(532\) | 4.00000 | 0.173422 | ||||||||
\(533\) | −15.0000 | − | 25.9808i | −0.649722 | − | 1.12535i | ||||
\(534\) | 7.00000 | + | 12.1244i | 0.302920 | + | 0.524672i | ||||
\(535\) | −1.00000 | − | 1.73205i | −0.0432338 | − | 0.0748831i | ||||
\(536\) | −4.50000 | + | 7.79423i | −0.194370 | + | 0.336659i | ||||
\(537\) | −6.00000 | + | 10.3923i | −0.258919 | + | 0.448461i | ||||
\(538\) | 3.00000 | + | 5.19615i | 0.129339 | + | 0.224022i | ||||
\(539\) | −7.50000 | − | 12.9904i | −0.323048 | − | 0.559535i | ||||
\(540\) | −0.500000 | − | 0.866025i | −0.0215166 | − | 0.0372678i | ||||
\(541\) | −32.0000 | −1.37579 | −0.687894 | − | 0.725811i | \(-0.741464\pi\) | ||||
−0.687894 | + | 0.725811i | \(0.741464\pi\) | |||||||
\(542\) | −0.500000 | + | 0.866025i | −0.0214768 | + | 0.0371990i | ||||
\(543\) | 7.00000 | + | 12.1244i | 0.300399 | + | 0.520306i | ||||
\(544\) | 5.00000 | 0.214373 | ||||||||
\(545\) | −14.0000 | −0.599694 | ||||||||
\(546\) | −5.00000 | − | 8.66025i | −0.213980 | − | 0.370625i | ||||
\(547\) | −44.0000 | −1.88130 | −0.940652 | − | 0.339372i | \(-0.889785\pi\) | ||||
−0.940652 | + | 0.339372i | \(0.889785\pi\) | |||||||
\(548\) | 1.50000 | − | 2.59808i | 0.0640768 | − | 0.110984i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.50000 | + | 4.33013i | −0.106600 | + | 0.184637i | ||||
\(551\) | 9.00000 | − | 15.5885i | 0.383413 | − | 0.664091i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.0000 | − | 27.7128i | −0.680389 | − | 1.17847i | ||||
\(554\) | 1.00000 | 0.0424859 | ||||||||
\(555\) | 5.00000 | − | 3.46410i | 0.212238 | − | 0.147043i | ||||
\(556\) | −16.0000 | −0.678551 | ||||||||
\(557\) | −7.00000 | − | 12.1244i | −0.296600 | − | 0.513725i | 0.678756 | − | 0.734364i | \(-0.262519\pi\) |
−0.975356 | + | 0.220638i | \(0.929186\pi\) | |||||||
\(558\) | 2.00000 | − | 3.46410i | 0.0846668 | − | 0.146647i | ||||
\(559\) | −10.0000 | + | 17.3205i | −0.422955 | + | 0.732579i | ||||
\(560\) | 1.00000 | − | 1.73205i | 0.0422577 | − | 0.0731925i | ||||
\(561\) | −25.0000 | −1.05550 | ||||||||
\(562\) | 5.00000 | − | 8.66025i | 0.210912 | − | 0.365311i | ||||
\(563\) | 24.0000 | 1.01148 | 0.505740 | − | 0.862686i | \(-0.331220\pi\) | ||||
0.505740 | + | 0.862686i | \(0.331220\pi\) | |||||||
\(564\) | 4.50000 | + | 7.79423i | 0.189484 | + | 0.328196i | ||||
\(565\) | −15.0000 | −0.631055 | ||||||||
\(566\) | 15.0000 | 0.630497 | ||||||||
\(567\) | −1.00000 | − | 1.73205i | −0.0419961 | − | 0.0727393i | ||||
\(568\) | −6.00000 | + | 10.3923i | −0.251754 | + | 0.436051i | ||||
\(569\) | −30.0000 | −1.25767 | −0.628833 | − | 0.777541i | \(-0.716467\pi\) | ||||
−0.628833 | + | 0.777541i | \(0.716467\pi\) | |||||||
\(570\) | 1.00000 | + | 1.73205i | 0.0418854 | + | 0.0725476i | ||||
\(571\) | −1.00000 | − | 1.73205i | −0.0418487 | − | 0.0724841i | 0.844342 | − | 0.535804i | \(-0.179991\pi\) |
−0.886191 | + | 0.463320i | \(0.846658\pi\) | |||||||
\(572\) | 12.5000 | + | 21.6506i | 0.522651 | + | 0.905259i | ||||
\(573\) | 9.00000 | − | 15.5885i | 0.375980 | − | 0.651217i | ||||
\(574\) | 6.00000 | − | 10.3923i | 0.250435 | − | 0.433766i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −6.00000 | − | 10.3923i | −0.249783 | − | 0.432637i | 0.713682 | − | 0.700470i | \(-0.247026\pi\) |
−0.963466 | + | 0.267832i | \(0.913693\pi\) | |||||||
\(578\) | −8.00000 | −0.332756 | ||||||||
\(579\) | 13.0000 | − | 22.5167i | 0.540262 | − | 0.935760i | ||||
\(580\) | −4.50000 | − | 7.79423i | −0.186852 | − | 0.323638i | ||||
\(581\) | −4.00000 | −0.165948 | ||||||||
\(582\) | −18.0000 | −0.746124 | ||||||||
\(583\) | 15.0000 | + | 25.9808i | 0.621237 | + | 1.07601i | ||||
\(584\) | 12.0000 | 0.496564 | ||||||||
\(585\) | 2.50000 | − | 4.33013i | 0.103362 | − | 0.179029i | ||||
\(586\) | −10.0000 | −0.413096 | ||||||||
\(587\) | −21.0000 | + | 36.3731i | −0.866763 | + | 1.50128i | −0.00147660 | + | 0.999999i | \(0.500470\pi\) |
−0.865286 | + | 0.501278i | \(0.832863\pi\) | |||||||
\(588\) | −1.50000 | + | 2.59808i | −0.0618590 | + | 0.107143i | ||||
\(589\) | −4.00000 | + | 6.92820i | −0.164817 | + | 0.285472i | ||||
\(590\) | −1.50000 | − | 2.59808i | −0.0617540 | − | 0.106961i | ||||
\(591\) | 10.0000 | 0.411345 | ||||||||
\(592\) | 5.00000 | − | 3.46410i | 0.205499 | − | 0.142374i | ||||
\(593\) | 11.0000 | 0.451716 | 0.225858 | − | 0.974160i | \(-0.427481\pi\) | ||||
0.225858 | + | 0.974160i | \(0.427481\pi\) | |||||||
\(594\) | 2.50000 | + | 4.33013i | 0.102576 | + | 0.177667i | ||||
\(595\) | −5.00000 | + | 8.66025i | −0.204980 | + | 0.355036i | ||||
\(596\) | −7.50000 | + | 12.9904i | −0.307212 | + | 0.532107i | ||||
\(597\) | 3.50000 | − | 6.06218i | 0.143245 | − | 0.248108i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.00000 | − | 8.66025i | 0.204294 | − | 0.353848i | −0.745613 | − | 0.666379i | \(-0.767843\pi\) |
0.949908 | + | 0.312531i | \(0.101177\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | −6.50000 | − | 11.2583i | −0.265141 | − | 0.459237i | 0.702460 | − | 0.711723i | \(-0.252085\pi\) |
−0.967600 | + | 0.252486i | \(0.918752\pi\) | |||||||
\(602\) | −8.00000 | −0.326056 | ||||||||
\(603\) | −9.00000 | −0.366508 | ||||||||
\(604\) | −4.00000 | − | 6.92820i | −0.162758 | − | 0.281905i | ||||
\(605\) | 7.00000 | − | 12.1244i | 0.284590 | − | 0.492925i | ||||
\(606\) | 5.00000 | 0.203111 | ||||||||
\(607\) | −17.0000 | − | 29.4449i | −0.690009 | − | 1.19513i | −0.971834 | − | 0.235665i | \(-0.924273\pi\) |
0.281826 | − | 0.959466i | \(-0.409060\pi\) | |||||||
\(608\) | 1.00000 | + | 1.73205i | 0.0405554 | + | 0.0702439i | ||||
\(609\) | −9.00000 | − | 15.5885i | −0.364698 | − | 0.631676i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22.5000 | + | 38.9711i | −0.910253 | + | 1.57660i | ||||
\(612\) | 2.50000 | + | 4.33013i | 0.101057 | + | 0.175035i | ||||
\(613\) | 21.5000 | + | 37.2391i | 0.868377 | + | 1.50407i | 0.863655 | + | 0.504084i | \(0.168170\pi\) |
0.00472215 | + | 0.999989i | \(0.498497\pi\) | |||||||
\(614\) | −8.00000 | − | 13.8564i | −0.322854 | − | 0.559199i | ||||
\(615\) | 6.00000 | 0.241943 | ||||||||
\(616\) | −5.00000 | + | 8.66025i | −0.201456 | + | 0.348932i | ||||
\(617\) | 1.50000 | + | 2.59808i | 0.0603877 | + | 0.104595i | 0.894639 | − | 0.446790i | \(-0.147433\pi\) |
−0.834251 | + | 0.551385i | \(0.814100\pi\) | |||||||
\(618\) | −4.00000 | −0.160904 | ||||||||
\(619\) | 10.0000 | 0.401934 | 0.200967 | − | 0.979598i | \(-0.435592\pi\) | ||||
0.200967 | + | 0.979598i | \(0.435592\pi\) | |||||||
\(620\) | 2.00000 | + | 3.46410i | 0.0803219 | + | 0.139122i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12.0000 | + | 20.7846i | −0.481156 | + | 0.833387i | ||||
\(623\) | −28.0000 | −1.12180 | ||||||||
\(624\) | 2.50000 | − | 4.33013i | 0.100080 | − | 0.173344i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −7.00000 | + | 12.1244i | −0.279776 | + | 0.484587i | ||||
\(627\) | −5.00000 | − | 8.66025i | −0.199681 | − | 0.345857i | ||||
\(628\) | −13.0000 | −0.518756 | ||||||||
\(629\) | −25.0000 | + | 17.3205i | −0.996815 | + | 0.690614i | ||||
\(630\) | 2.00000 | 0.0796819 | ||||||||
\(631\) | −12.5000 | − | 21.6506i | −0.497617 | − | 0.861898i | 0.502379 | − | 0.864647i | \(-0.332458\pi\) |
−0.999996 | + | 0.00274930i | \(0.999125\pi\) | |||||||
\(632\) | 8.00000 | − | 13.8564i | 0.318223 | − | 0.551178i | ||||
\(633\) | 2.00000 | − | 3.46410i | 0.0794929 | − | 0.137686i | ||||
\(634\) | 9.00000 | − | 15.5885i | 0.357436 | − | 0.619097i | ||||
\(635\) | 2.00000 | 0.0793676 | ||||||||
\(636\) | 3.00000 | − | 5.19615i | 0.118958 | − | 0.206041i | ||||
\(637\) | −15.0000 | −0.594322 | ||||||||
\(638\) | 22.5000 | + | 38.9711i | 0.890784 | + | 1.54288i | ||||
\(639\) | −12.0000 | −0.474713 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(642\) | 1.00000 | − | 1.73205i | 0.0394669 | − | 0.0683586i | ||||
\(643\) | 19.0000 | 0.749287 | 0.374643 | − | 0.927169i | \(-0.377765\pi\) | ||||
0.374643 | + | 0.927169i | \(0.377765\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.00000 | − | 3.46410i | −0.0787499 | − | 0.136399i | ||||
\(646\) | −5.00000 | − | 8.66025i | −0.196722 | − | 0.340733i | ||||
\(647\) | −9.50000 | + | 16.4545i | −0.373484 | + | 0.646892i | −0.990099 | − | 0.140372i | \(-0.955170\pi\) |
0.616615 | + | 0.787265i | \(0.288503\pi\) | |||||||
\(648\) | 0.500000 | − | 0.866025i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | 7.50000 | + | 12.9904i | 0.294401 | + | 0.509917i | ||||
\(650\) | 2.50000 | + | 4.33013i | 0.0980581 | + | 0.169842i | ||||
\(651\) | 4.00000 | + | 6.92820i | 0.156772 | + | 0.271538i | ||||
\(652\) | −9.00000 | −0.352467 | ||||||||
\(653\) | −14.0000 | + | 24.2487i | −0.547862 | + | 0.948925i | 0.450558 | + | 0.892747i | \(0.351225\pi\) |
−0.998421 | + | 0.0561784i | \(0.982108\pi\) | |||||||
\(654\) | −7.00000 | − | 12.1244i | −0.273722 | − | 0.474100i | ||||
\(655\) | −11.0000 | −0.429806 | ||||||||
\(656\) | 6.00000 | 0.234261 | ||||||||
\(657\) | 6.00000 | + | 10.3923i | 0.234082 | + | 0.405442i | ||||
\(658\) | −18.0000 | −0.701713 | ||||||||
\(659\) | 13.5000 | − | 23.3827i | 0.525885 | − | 0.910860i | −0.473660 | − | 0.880708i | \(-0.657067\pi\) |
0.999545 | − | 0.0301523i | \(-0.00959924\pi\) | |||||||
\(660\) | −5.00000 | −0.194625 | ||||||||
\(661\) | −16.0000 | + | 27.7128i | −0.622328 | + | 1.07790i | 0.366723 | + | 0.930330i | \(0.380480\pi\) |
−0.989051 | + | 0.147573i | \(0.952854\pi\) | |||||||
\(662\) | 14.0000 | − | 24.2487i | 0.544125 | − | 0.942453i | ||||
\(663\) | −12.5000 | + | 21.6506i | −0.485460 | + | 0.840841i | ||||
\(664\) | −1.00000 | − | 1.73205i | −0.0388075 | − | 0.0672166i | ||||
\(665\) | −4.00000 | −0.155113 | ||||||||
\(666\) | 5.50000 | + | 2.59808i | 0.213121 | + | 0.100673i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 8.50000 | + | 14.7224i | 0.328875 | + | 0.569628i | ||||
\(669\) | 6.00000 | − | 10.3923i | 0.231973 | − | 0.401790i | ||||
\(670\) | 4.50000 | − | 7.79423i | 0.173850 | − | 0.301117i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 2.00000 | 0.0771517 | ||||||||
\(673\) | −3.00000 | + | 5.19615i | −0.115642 | + | 0.200297i | −0.918036 | − | 0.396497i | \(-0.870226\pi\) |
0.802395 | + | 0.596794i | \(0.203559\pi\) | |||||||
\(674\) | −14.0000 | −0.539260 | ||||||||
\(675\) | 0.500000 | + | 0.866025i | 0.0192450 | + | 0.0333333i | ||||
\(676\) | 12.0000 | 0.461538 | ||||||||
\(677\) | −20.0000 | −0.768662 | −0.384331 | − | 0.923195i | \(-0.625568\pi\) | ||||
−0.384331 | + | 0.923195i | \(0.625568\pi\) | |||||||
\(678\) | −7.50000 | − | 12.9904i | −0.288036 | − | 0.498893i | ||||
\(679\) | 18.0000 | − | 31.1769i | 0.690777 | − | 1.19646i | ||||
\(680\) | −5.00000 | −0.191741 | ||||||||
\(681\) | 9.00000 | + | 15.5885i | 0.344881 | + | 0.597351i | ||||
\(682\) | −10.0000 | − | 17.3205i | −0.382920 | − | 0.663237i | ||||
\(683\) | 17.0000 | + | 29.4449i | 0.650487 | + | 1.12668i | 0.983005 | + | 0.183579i | \(0.0587685\pi\) |
−0.332518 | + | 0.943097i | \(0.607898\pi\) | |||||||
\(684\) | −1.00000 | + | 1.73205i | −0.0382360 | + | 0.0662266i | ||||
\(685\) | −1.50000 | + | 2.59808i | −0.0573121 | + | 0.0992674i | ||||
\(686\) | −10.0000 | − | 17.3205i | −0.381802 | − | 0.661300i | ||||
\(687\) | −2.00000 | − | 3.46410i | −0.0763048 | − | 0.132164i | ||||
\(688\) | −2.00000 | − | 3.46410i | −0.0762493 | − | 0.132068i | ||||
\(689\) | 30.0000 | 1.14291 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.00000 | + | 8.66025i | 0.190209 | + | 0.329452i | 0.945319 | − | 0.326146i | \(-0.105750\pi\) |
−0.755110 | + | 0.655598i | \(0.772417\pi\) | |||||||
\(692\) | 14.0000 | 0.532200 | ||||||||
\(693\) | −10.0000 | −0.379869 | ||||||||
\(694\) | 9.00000 | + | 15.5885i | 0.341635 | + | 0.591730i | ||||
\(695\) | 16.0000 | 0.606915 | ||||||||
\(696\) | 4.50000 | − | 7.79423i | 0.170572 | − | 0.295439i | ||||
\(697\) | −30.0000 | −1.13633 | ||||||||
\(698\) | −10.0000 | + | 17.3205i | −0.378506 | + | 0.655591i | ||||
\(699\) | 9.00000 | − | 15.5885i | 0.340411 | − | 0.589610i | ||||
\(700\) | −1.00000 | + | 1.73205i | −0.0377964 | + | 0.0654654i | ||||
\(701\) | 2.50000 | + | 4.33013i | 0.0944237 | + | 0.163547i | 0.909368 | − | 0.415993i | \(-0.136566\pi\) |
−0.814944 | + | 0.579539i | \(0.803232\pi\) | |||||||
\(702\) | 5.00000 | 0.188713 | ||||||||
\(703\) | −11.0000 | − | 5.19615i | −0.414873 | − | 0.195977i | ||||
\(704\) | −5.00000 | −0.188445 | ||||||||
\(705\) | −4.50000 | − | 7.79423i | −0.169480 | − | 0.293548i | ||||
\(706\) | −1.00000 | + | 1.73205i | −0.0376355 | + | 0.0651866i | ||||
\(707\) | −5.00000 | + | 8.66025i | −0.188044 | + | 0.325702i | ||||
\(708\) | 1.50000 | − | 2.59808i | 0.0563735 | − | 0.0976417i | ||||
\(709\) | 24.0000 | 0.901339 | 0.450669 | − | 0.892691i | \(-0.351185\pi\) | ||||
0.450669 | + | 0.892691i | \(0.351185\pi\) | |||||||
\(710\) | 6.00000 | − | 10.3923i | 0.225176 | − | 0.390016i | ||||
\(711\) | 16.0000 | 0.600047 | ||||||||
\(712\) | −7.00000 | − | 12.1244i | −0.262336 | − | 0.454379i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −10.0000 | −0.374241 | ||||||||
\(715\) | −12.5000 | − | 21.6506i | −0.467473 | − | 0.809688i | ||||
\(716\) | 6.00000 | − | 10.3923i | 0.224231 | − | 0.388379i | ||||
\(717\) | 20.0000 | 0.746914 | ||||||||
\(718\) | −9.00000 | − | 15.5885i | −0.335877 | − | 0.581756i | ||||
\(719\) | −3.00000 | − | 5.19615i | −0.111881 | − | 0.193784i | 0.804648 | − | 0.593753i | \(-0.202354\pi\) |
−0.916529 | + | 0.399969i | \(0.869021\pi\) | |||||||
\(720\) | 0.500000 | + | 0.866025i | 0.0186339 | + | 0.0322749i | ||||
\(721\) | 4.00000 | − | 6.92820i | 0.148968 | − | 0.258020i | ||||
\(722\) | −7.50000 | + | 12.9904i | −0.279121 | + | 0.483452i | ||||
\(723\) | 12.5000 | + | 21.6506i | 0.464880 | + | 0.805196i | ||||
\(724\) | −7.00000 | − | 12.1244i | −0.260153 | − | 0.450598i | ||||
\(725\) | 4.50000 | + | 7.79423i | 0.167126 | + | 0.289470i | ||||
\(726\) | 14.0000 | 0.519589 | ||||||||
\(727\) | 14.0000 | − | 24.2487i | 0.519231 | − | 0.899335i | −0.480519 | − | 0.876984i | \(-0.659552\pi\) |
0.999750 | − | 0.0223506i | \(-0.00711500\pi\) | |||||||
\(728\) | 5.00000 | + | 8.66025i | 0.185312 | + | 0.320970i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −12.0000 | −0.444140 | ||||||||
\(731\) | 10.0000 | + | 17.3205i | 0.369863 | + | 0.640622i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.5000 | − | 28.5788i | 0.609441 | − | 1.05558i | −0.381891 | − | 0.924207i | \(-0.624727\pi\) |
0.991333 | − | 0.131376i | \(-0.0419396\pi\) | |||||||
\(734\) | 4.00000 | 0.147643 | ||||||||
\(735\) | 1.50000 | − | 2.59808i | 0.0553283 | − | 0.0958315i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22.5000 | + | 38.9711i | −0.828798 | + | 1.43552i | ||||
\(738\) | 3.00000 | + | 5.19615i | 0.110432 | + | 0.191273i | ||||
\(739\) | 10.0000 | 0.367856 | 0.183928 | − | 0.982940i | \(-0.441119\pi\) | ||||
0.183928 | + | 0.982940i | \(0.441119\pi\) | |||||||
\(740\) | −5.00000 | + | 3.46410i | −0.183804 | + | 0.127343i | ||||
\(741\) | −10.0000 | −0.367359 | ||||||||
\(742\) | 6.00000 | + | 10.3923i | 0.220267 | + | 0.381514i | ||||
\(743\) | −13.5000 | + | 23.3827i | −0.495267 | + | 0.857828i | −0.999985 | − | 0.00545664i | \(-0.998263\pi\) |
0.504718 | + | 0.863284i | \(0.331596\pi\) | |||||||
\(744\) | −2.00000 | + | 3.46410i | −0.0733236 | + | 0.127000i | ||||
\(745\) | 7.50000 | − | 12.9904i | 0.274779 | − | 0.475931i | ||||
\(746\) | −10.0000 | −0.366126 | ||||||||
\(747\) | 1.00000 | − | 1.73205i | 0.0365881 | − | 0.0633724i | ||||
\(748\) | 25.0000 | 0.914091 | ||||||||
\(749\) | 2.00000 | + | 3.46410i | 0.0730784 | + | 0.126576i | ||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 3.00000 | 0.109472 | 0.0547358 | − | 0.998501i | \(-0.482568\pi\) | ||||
0.0547358 | + | 0.998501i | \(0.482568\pi\) | |||||||
\(752\) | −4.50000 | − | 7.79423i | −0.164098 | − | 0.284226i | ||||
\(753\) | −3.50000 | + | 6.06218i | −0.127547 | + | 0.220918i | ||||
\(754\) | 45.0000 | 1.63880 | ||||||||
\(755\) | 4.00000 | + | 6.92820i | 0.145575 | + | 0.252143i | ||||
\(756\) | 1.00000 | + | 1.73205i | 0.0363696 | + | 0.0629941i | ||||
\(757\) | −11.0000 | − | 19.0526i | −0.399802 | − | 0.692477i | 0.593899 | − | 0.804539i | \(-0.297588\pi\) |
−0.993701 | + | 0.112062i | \(0.964254\pi\) | |||||||
\(758\) | −3.00000 | + | 5.19615i | −0.108965 | + | 0.188733i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.00000 | − | 1.73205i | −0.0362738 | − | 0.0628281i | ||||
\(761\) | 24.0000 | + | 41.5692i | 0.869999 | + | 1.50688i | 0.861996 | + | 0.506915i | \(0.169214\pi\) |
0.00800331 | + | 0.999968i | \(0.497452\pi\) | |||||||
\(762\) | 1.00000 | + | 1.73205i | 0.0362262 | + | 0.0627456i | ||||
\(763\) | 28.0000 | 1.01367 | ||||||||
\(764\) | −9.00000 | + | 15.5885i | −0.325609 | + | 0.563971i | ||||
\(765\) | −2.50000 | − | 4.33013i | −0.0903877 | − | 0.156556i | ||||
\(766\) | 15.0000 | 0.541972 | ||||||||
\(767\) | 15.0000 | 0.541619 | ||||||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | 15.0000 | 0.540914 | 0.270457 | − | 0.962732i | \(-0.412825\pi\) | ||||
0.270457 | + | 0.962732i | \(0.412825\pi\) | |||||||
\(770\) | 5.00000 | − | 8.66025i | 0.180187 | − | 0.312094i | ||||
\(771\) | 13.0000 | 0.468184 | ||||||||
\(772\) | −13.0000 | + | 22.5167i | −0.467880 | + | 0.810392i | ||||
\(773\) | 3.00000 | − | 5.19615i | 0.107903 | − | 0.186893i | −0.807018 | − | 0.590527i | \(-0.798920\pi\) |
0.914920 | + | 0.403634i | \(0.132253\pi\) | |||||||
\(774\) | 2.00000 | − | 3.46410i | 0.0718885 | − | 0.124515i | ||||
\(775\) | −2.00000 | − | 3.46410i | −0.0718421 | − | 0.124434i | ||||
\(776\) | 18.0000 | 0.646162 | ||||||||
\(777\) | −10.0000 | + | 6.92820i | −0.358748 | + | 0.248548i | ||||
\(778\) | 14.0000 | 0.501924 | ||||||||
\(779\) | −6.00000 | − | 10.3923i | −0.214972 | − | 0.372343i | ||||
\(780\) | −2.50000 | + | 4.33013i | −0.0895144 | + | 0.155043i | ||||
\(781\) | −30.0000 | + | 51.9615i | −1.07348 | + | 1.85933i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.00000 | 0.321634 | ||||||||
\(784\) | 1.50000 | − | 2.59808i | 0.0535714 | − | 0.0927884i | ||||
\(785\) | 13.0000 | 0.463990 | ||||||||
\(786\) | −5.50000 | − | 9.52628i | −0.196179 | − | 0.339791i | ||||
\(787\) | −7.00000 | −0.249523 | −0.124762 | − | 0.992187i | \(-0.539817\pi\) | ||||
−0.124762 | + | 0.992187i | \(0.539817\pi\) | |||||||
\(788\) | −10.0000 | −0.356235 | ||||||||
\(789\) | −14.0000 | − | 24.2487i | −0.498413 | − | 0.863277i | ||||
\(790\) | −8.00000 | + | 13.8564i | −0.284627 | + | 0.492989i | ||||
\(791\) | 30.0000 | 1.06668 | ||||||||
\(792\) | −2.50000 | − | 4.33013i | −0.0888336 | − | 0.153864i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −11.5000 | − | 19.9186i | −0.408120 | − | 0.706884i | ||||
\(795\) | −3.00000 | + | 5.19615i | −0.106399 | + | 0.184289i | ||||
\(796\) | −3.50000 | + | 6.06218i | −0.124054 | + | 0.214868i | ||||
\(797\) | −16.0000 | − | 27.7128i | −0.566749 | − | 0.981638i | −0.996885 | − | 0.0788739i | \(-0.974868\pi\) |
0.430136 | − | 0.902764i | \(-0.358466\pi\) | |||||||
\(798\) | −2.00000 | − | 3.46410i | −0.0707992 | − | 0.122628i | ||||
\(799\) | 22.5000 | + | 38.9711i | 0.795993 | + | 1.37870i | ||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 7.00000 | − | 12.1244i | 0.247333 | − | 0.428393i | ||||
\(802\) | −15.0000 | − | 25.9808i | −0.529668 | − | 0.917413i | ||||
\(803\) | 60.0000 | 2.11735 | ||||||||
\(804\) | 9.00000 | 0.317406 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −20.0000 | −0.704470 | ||||||||
\(807\) | 3.00000 | − | 5.19615i | 0.105605 | − | 0.182913i | ||||
\(808\) | −5.00000 | −0.175899 | ||||||||
\(809\) | −25.0000 | + | 43.3013i | −0.878953 | + | 1.52239i | −0.0264621 | + | 0.999650i | \(0.508424\pi\) |
−0.852491 | + | 0.522742i | \(0.824909\pi\) | |||||||
\(810\) | −0.500000 | + | 0.866025i | −0.0175682 | + | 0.0304290i | ||||
\(811\) | 8.00000 | − | 13.8564i | 0.280918 | − | 0.486564i | −0.690693 | − | 0.723148i | \(-0.742694\pi\) |
0.971611 | + | 0.236584i | \(0.0760278\pi\) | |||||||
\(812\) | 9.00000 | + | 15.5885i | 0.315838 | + | 0.547048i | ||||
\(813\) | 1.00000 | 0.0350715 | ||||||||
\(814\) | 25.0000 | − | 17.3205i | 0.876250 | − | 0.607083i | ||||
\(815\) | 9.00000 | 0.315256 | ||||||||
\(816\) | −2.50000 | − | 4.33013i | −0.0875175 | − | 0.151585i | ||||
\(817\) | −4.00000 | + | 6.92820i | −0.139942 | + | 0.242387i | ||||
\(818\) | −12.5000 | + | 21.6506i | −0.437052 | + | 0.756997i | ||||
\(819\) | −5.00000 | + | 8.66025i | −0.174714 | + | 0.302614i | ||||
\(820\) | −6.00000 | −0.209529 | ||||||||
\(821\) | 16.5000 | − | 28.5788i | 0.575854 | − | 0.997408i | −0.420094 | − | 0.907480i | \(-0.638003\pi\) |
0.995948 | − | 0.0899279i | \(-0.0286637\pi\) | |||||||
\(822\) | −3.00000 | −0.104637 | ||||||||
\(823\) | −17.0000 | − | 29.4449i | −0.592583 | − | 1.02638i | −0.993883 | − | 0.110437i | \(-0.964775\pi\) |
0.401300 | − | 0.915947i | \(-0.368558\pi\) | |||||||
\(824\) | 4.00000 | 0.139347 | ||||||||
\(825\) | 5.00000 | 0.174078 | ||||||||
\(826\) | 3.00000 | + | 5.19615i | 0.104383 | + | 0.180797i | ||||
\(827\) | −11.0000 | + | 19.0526i | −0.382507 | + | 0.662522i | −0.991420 | − | 0.130715i | \(-0.958273\pi\) |
0.608913 | + | 0.793237i | \(0.291606\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.0000 | − | 22.5167i | −0.451509 | − | 0.782036i | 0.546971 | − | 0.837151i | \(-0.315781\pi\) |
−0.998480 | + | 0.0551154i | \(0.982447\pi\) | |||||||
\(830\) | 1.00000 | + | 1.73205i | 0.0347105 | + | 0.0601204i | ||||
\(831\) | −0.500000 | − | 0.866025i | −0.0173448 | − | 0.0300421i | ||||
\(832\) | −2.50000 | + | 4.33013i | −0.0866719 | + | 0.150120i | ||||
\(833\) | −7.50000 | + | 12.9904i | −0.259860 | + | 0.450090i | ||||
\(834\) | 8.00000 | + | 13.8564i | 0.277017 | + | 0.479808i | ||||
\(835\) | −8.50000 | − | 14.7224i | −0.294155 | − | 0.509491i | ||||
\(836\) | 5.00000 | + | 8.66025i | 0.172929 | + | 0.299521i | ||||
\(837\) | −4.00000 | −0.138260 | ||||||||
\(838\) | −18.0000 | + | 31.1769i | −0.621800 | + | 1.07699i | ||||
\(839\) | −2.00000 | − | 3.46410i | −0.0690477 | − | 0.119594i | 0.829435 | − | 0.558604i | \(-0.188663\pi\) |
−0.898482 | + | 0.439010i | \(0.855329\pi\) | |||||||
\(840\) | −2.00000 | −0.0690066 | ||||||||
\(841\) | 52.0000 | 1.79310 | ||||||||
\(842\) | 10.0000 | + | 17.3205i | 0.344623 | + | 0.596904i | ||||
\(843\) | −10.0000 | −0.344418 | ||||||||
\(844\) | −2.00000 | + | 3.46410i | −0.0688428 | + | 0.119239i | ||||
\(845\) | −12.0000 | −0.412813 | ||||||||
\(846\) | 4.50000 | − | 7.79423i | 0.154713 | − | 0.267971i | ||||
\(847\) | −14.0000 | + | 24.2487i | −0.481046 | + | 0.833196i | ||||
\(848\) | −3.00000 | + | 5.19615i | −0.103020 | + | 0.178437i | ||||
\(849\) | −7.50000 | − | 12.9904i | −0.257399 | − | 0.445829i | ||||
\(850\) | 5.00000 | 0.171499 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 12.0000 | 0.411113 | ||||||||
\(853\) | 23.5000 | + | 40.7032i | 0.804625 | + | 1.39365i | 0.916544 | + | 0.399934i | \(0.130967\pi\) |
−0.111919 | + | 0.993717i | \(0.535700\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.00000 | − | 1.73205i | 0.0341993 | − | 0.0592349i | ||||
\(856\) | −1.00000 | + | 1.73205i | −0.0341793 | + | 0.0592003i | ||||
\(857\) | 43.0000 | 1.46885 | 0.734426 | − | 0.678689i | \(-0.237451\pi\) | ||||
0.734426 | + | 0.678689i | \(0.237451\pi\) | |||||||
\(858\) | 12.5000 | − | 21.6506i | 0.426743 | − | 0.739140i | ||||
\(859\) | 10.0000 | 0.341196 | 0.170598 | − | 0.985341i | \(-0.445430\pi\) | ||||
0.170598 | + | 0.985341i | \(0.445430\pi\) | |||||||
\(860\) | 2.00000 | + | 3.46410i | 0.0681994 | + | 0.118125i | ||||
\(861\) | −12.0000 | −0.408959 | ||||||||
\(862\) | −36.0000 | −1.22616 | ||||||||
\(863\) | −10.5000 | − | 18.1865i | −0.357424 | − | 0.619077i | 0.630106 | − | 0.776509i | \(-0.283012\pi\) |
−0.987530 | + | 0.157433i | \(0.949678\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | −14.0000 | −0.476014 | ||||||||
\(866\) | 12.0000 | + | 20.7846i | 0.407777 | + | 0.706290i | ||||
\(867\) | 4.00000 | + | 6.92820i | 0.135847 | + | 0.235294i | ||||
\(868\) | −4.00000 | − | 6.92820i | −0.135769 | − | 0.235159i | ||||
\(869\) | 40.0000 | − | 69.2820i | 1.35691 | − | 2.35023i | ||||
\(870\) | −4.50000 | + | 7.79423i | −0.152564 | + | 0.264249i | ||||
\(871\) | 22.5000 | + | 38.9711i | 0.762383 | + | 1.32049i | ||||
\(872\) | 7.00000 | + | 12.1244i | 0.237050 | + | 0.410582i | ||||
\(873\) | 9.00000 | + | 15.5885i | 0.304604 | + | 0.527589i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | − | 1.73205i | 0.0338062 | − | 0.0585540i | ||||
\(876\) | −6.00000 | − | 10.3923i | −0.202721 | − | 0.351123i | ||||
\(877\) | 43.0000 | 1.45201 | 0.726003 | − | 0.687691i | \(-0.241376\pi\) | ||||
0.726003 | + | 0.687691i | \(0.241376\pi\) | |||||||
\(878\) | −1.00000 | −0.0337484 | ||||||||
\(879\) | 5.00000 | + | 8.66025i | 0.168646 | + | 0.292103i | ||||
\(880\) | 5.00000 | 0.168550 | ||||||||
\(881\) | 16.0000 | − | 27.7128i | 0.539054 | − | 0.933668i | −0.459902 | − | 0.887970i | \(-0.652115\pi\) |
0.998955 | − | 0.0456985i | \(-0.0145514\pi\) | |||||||
\(882\) | 3.00000 | 0.101015 | ||||||||
\(883\) | −23.5000 | + | 40.7032i | −0.790838 | + | 1.36977i | 0.134611 | + | 0.990899i | \(0.457022\pi\) |
−0.925449 | + | 0.378873i | \(0.876312\pi\) | |||||||
\(884\) | 12.5000 | − | 21.6506i | 0.420420 | − | 0.728190i | ||||
\(885\) | −1.50000 | + | 2.59808i | −0.0504219 | + | 0.0873334i | ||||
\(886\) | −5.00000 | − | 8.66025i | −0.167978 | − | 0.290947i | ||||
\(887\) | 8.00000 | 0.268614 | 0.134307 | − | 0.990940i | \(-0.457119\pi\) | ||||
0.134307 | + | 0.990940i | \(0.457119\pi\) | |||||||
\(888\) | −5.50000 | − | 2.59808i | −0.184568 | − | 0.0871857i | ||||
\(889\) | −4.00000 | −0.134156 | ||||||||
\(890\) | 7.00000 | + | 12.1244i | 0.234641 | + | 0.406409i | ||||
\(891\) | 2.50000 | − | 4.33013i | 0.0837532 | − | 0.145065i | ||||
\(892\) | −6.00000 | + | 10.3923i | −0.200895 | + | 0.347960i | ||||
\(893\) | −9.00000 | + | 15.5885i | −0.301174 | + | 0.521648i | ||||
\(894\) | 15.0000 | 0.501675 | ||||||||
\(895\) | −6.00000 | + | 10.3923i | −0.200558 | + | 0.347376i | ||||
\(896\) | −2.00000 | −0.0668153 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −20.0000 | −0.667409 | ||||||||
\(899\) | −36.0000 | −1.20067 | ||||||||
\(900\) | −0.500000 | − | 0.866025i | −0.0166667 | − | 0.0288675i | ||||
\(901\) | 15.0000 | − | 25.9808i | 0.499722 | − | 0.865545i | ||||
\(902\) | 30.0000 | 0.998891 | ||||||||
\(903\) | 4.00000 | + | 6.92820i | 0.133112 | + | 0.230556i | ||||
\(904\) | 7.50000 | + | 12.9904i | 0.249446 | + | 0.432054i | ||||
\(905\) | 7.00000 | + | 12.1244i | 0.232688 | + | 0.403027i | ||||
\(906\) | −4.00000 | + | 6.92820i | −0.132891 | + | 0.230174i | ||||
\(907\) | 2.00000 | − | 3.46410i | 0.0664089 | − | 0.115024i | −0.830909 | − | 0.556408i | \(-0.812179\pi\) |
0.897318 | + | 0.441384i | \(0.145512\pi\) | |||||||
\(908\) | −9.00000 | − | 15.5885i | −0.298675 | − | 0.517321i | ||||
\(909\) | −2.50000 | − | 4.33013i | −0.0829198 | − | 0.143621i | ||||
\(910\) | −5.00000 | − | 8.66025i | −0.165748 | − | 0.287085i | ||||
\(911\) | −34.0000 | −1.12647 | −0.563235 | − | 0.826297i | \(-0.690443\pi\) | ||||
−0.563235 | + | 0.826297i | \(0.690443\pi\) | |||||||
\(912\) | 1.00000 | − | 1.73205i | 0.0331133 | − | 0.0573539i | ||||
\(913\) | −5.00000 | − | 8.66025i | −0.165476 | − | 0.286613i | ||||
\(914\) | −32.0000 | −1.05847 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.00000 | + | 3.46410i | 0.0660819 | + | 0.114457i | ||||
\(917\) | 22.0000 | 0.726504 | ||||||||
\(918\) | 2.50000 | − | 4.33013i | 0.0825123 | − | 0.142915i | ||||
\(919\) | −25.0000 | −0.824674 | −0.412337 | − | 0.911031i | \(-0.635287\pi\) | ||||
−0.412337 | + | 0.911031i | \(0.635287\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.00000 | + | 13.8564i | −0.263609 | + | 0.456584i | ||||
\(922\) | 3.50000 | − | 6.06218i | 0.115266 | − | 0.199647i | ||||
\(923\) | 30.0000 | + | 51.9615i | 0.987462 | + | 1.71033i | ||||
\(924\) | 10.0000 | 0.328976 | ||||||||
\(925\) | 5.00000 | − | 3.46410i | 0.164399 | − | 0.113899i | ||||
\(926\) | 26.0000 | 0.854413 | ||||||||
\(927\) | 2.00000 | + | 3.46410i | 0.0656886 | + | 0.113776i | ||||
\(928\) | −4.50000 | + | 7.79423i | −0.147720 | + | 0.255858i | ||||
\(929\) | 2.00000 | − | 3.46410i | 0.0656179 | − | 0.113653i | −0.831350 | − | 0.555749i | \(-0.812431\pi\) |
0.896968 | + | 0.442096i | \(0.145765\pi\) | |||||||
\(930\) | 2.00000 | − | 3.46410i | 0.0655826 | − | 0.113592i | ||||
\(931\) | −6.00000 | −0.196642 | ||||||||
\(932\) | −9.00000 | + | 15.5885i | −0.294805 | + | 0.510617i | ||||
\(933\) | 24.0000 | 0.785725 | ||||||||
\(934\) | 9.00000 | + | 15.5885i | 0.294489 | + | 0.510070i | ||||
\(935\) | −25.0000 | −0.817587 | ||||||||
\(936\) | −5.00000 | −0.163430 | ||||||||
\(937\) | 17.0000 | + | 29.4449i | 0.555366 | + | 0.961922i | 0.997875 | + | 0.0651578i | \(0.0207551\pi\) |
−0.442509 | + | 0.896764i | \(0.645912\pi\) | |||||||
\(938\) | −9.00000 | + | 15.5885i | −0.293860 | + | 0.508981i | ||||
\(939\) | 14.0000 | 0.456873 | ||||||||
\(940\) | 4.50000 | + | 7.79423i | 0.146774 | + | 0.254220i | ||||
\(941\) | −7.00000 | − | 12.1244i | −0.228193 | − | 0.395243i | 0.729079 | − | 0.684429i | \(-0.239949\pi\) |
−0.957273 | + | 0.289187i | \(0.906615\pi\) | |||||||
\(942\) | 6.50000 | + | 11.2583i | 0.211781 | + | 0.366816i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −1.50000 | + | 2.59808i | −0.0488208 | + | 0.0845602i | ||||
\(945\) | −1.00000 | − | 1.73205i | −0.0325300 | − | 0.0563436i | ||||
\(946\) | −10.0000 | − | 17.3205i | −0.325128 | − | 0.563138i | ||||
\(947\) | 3.00000 | + | 5.19615i | 0.0974869 | + | 0.168852i | 0.910644 | − | 0.413192i | \(-0.135586\pi\) |
−0.813157 | + | 0.582045i | \(0.802253\pi\) | |||||||
\(948\) | −16.0000 | −0.519656 | ||||||||
\(949\) | 30.0000 | − | 51.9615i | 0.973841 | − | 1.68674i | ||||
\(950\) | 1.00000 | + | 1.73205i | 0.0324443 | + | 0.0561951i | ||||
\(951\) | −18.0000 | −0.583690 | ||||||||
\(952\) | 10.0000 | 0.324102 | ||||||||
\(953\) | 15.5000 | + | 26.8468i | 0.502094 | + | 0.869653i | 0.999997 | + | 0.00241992i | \(0.000770286\pi\) |
−0.497903 | + | 0.867233i | \(0.665896\pi\) | |||||||
\(954\) | −6.00000 | −0.194257 | ||||||||
\(955\) | 9.00000 | − | 15.5885i | 0.291233 | − | 0.504431i | ||||
\(956\) | −20.0000 | −0.646846 | ||||||||
\(957\) | 22.5000 | − | 38.9711i | 0.727322 | − | 1.25976i | ||||
\(958\) | −15.0000 | + | 25.9808i | −0.484628 | + | 0.839400i | ||||
\(959\) | 3.00000 | − | 5.19615i | 0.0968751 | − | 0.167793i | ||||
\(960\) | −0.500000 | − | 0.866025i | −0.0161374 | − | 0.0279508i | ||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | −2.50000 | − | 30.3109i | −0.0806032 | − | 0.977262i | ||||
\(963\) | −2.00000 | −0.0644491 | ||||||||
\(964\) | −12.5000 | − | 21.6506i | −0.402598 | − | 0.697320i | ||||
\(965\) | 13.0000 | − | 22.5167i | 0.418485 | − | 0.724837i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.00000 | − | 5.19615i | 0.0964735 | − | 0.167097i | −0.813749 | − | 0.581216i | \(-0.802577\pi\) |
0.910223 | + | 0.414119i | \(0.135910\pi\) | |||||||
\(968\) | −14.0000 | −0.449977 | ||||||||
\(969\) | −5.00000 | + | 8.66025i | −0.160623 | + | 0.278207i | ||||
\(970\) | −18.0000 | −0.577945 | ||||||||
\(971\) | −26.0000 | − | 45.0333i | −0.834380 | − | 1.44519i | −0.894534 | − | 0.446999i | \(-0.852493\pi\) |
0.0601548 | − | 0.998189i | \(-0.480841\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −32.0000 | −1.02587 | ||||||||
\(974\) | 13.0000 | + | 22.5167i | 0.416547 | + | 0.721480i | ||||
\(975\) | 2.50000 | − | 4.33013i | 0.0800641 | − | 0.138675i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.5000 | + | 35.5070i | 0.655853 | + | 1.13597i | 0.981679 | + | 0.190541i | \(0.0610243\pi\) |
−0.325826 | + | 0.945430i | \(0.605642\pi\) | |||||||
\(978\) | 4.50000 | + | 7.79423i | 0.143894 | + | 0.249232i | ||||
\(979\) | −35.0000 | − | 60.6218i | −1.11860 | − | 1.93748i | ||||
\(980\) | −1.50000 | + | 2.59808i | −0.0479157 | + | 0.0829925i | ||||
\(981\) | −7.00000 | + | 12.1244i | −0.223493 | + | 0.387101i | ||||
\(982\) | −18.0000 | − | 31.1769i | −0.574403 | − | 0.994895i | ||||
\(983\) | −24.0000 | − | 41.5692i | −0.765481 | − | 1.32585i | −0.939992 | − | 0.341197i | \(-0.889168\pi\) |
0.174511 | − | 0.984655i | \(-0.444166\pi\) | |||||||
\(984\) | −3.00000 | − | 5.19615i | −0.0956365 | − | 0.165647i | ||||
\(985\) | 10.0000 | 0.318626 | ||||||||
\(986\) | 22.5000 | − | 38.9711i | 0.716546 | − | 1.24109i | ||||
\(987\) | 9.00000 | + | 15.5885i | 0.286473 | + | 0.496186i | ||||
\(988\) | 10.0000 | 0.318142 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 2.50000 | + | 4.33013i | 0.0794552 | + | 0.137620i | ||||
\(991\) | −3.00000 | −0.0952981 | −0.0476491 | − | 0.998864i | \(-0.515173\pi\) | ||||
−0.0476491 | + | 0.998864i | \(0.515173\pi\) | |||||||
\(992\) | 2.00000 | − | 3.46410i | 0.0635001 | − | 0.109985i | ||||
\(993\) | −28.0000 | −0.888553 | ||||||||
\(994\) | −12.0000 | + | 20.7846i | −0.380617 | + | 0.659248i | ||||
\(995\) | 3.50000 | − | 6.06218i | 0.110957 | − | 0.192184i | ||||
\(996\) | −1.00000 | + | 1.73205i | −0.0316862 | + | 0.0548821i | ||||
\(997\) | −1.50000 | − | 2.59808i | −0.0475055 | − | 0.0822819i | 0.841295 | − | 0.540576i | \(-0.181794\pi\) |
−0.888800 | + | 0.458295i | \(0.848460\pi\) | |||||||
\(998\) | −32.0000 | −1.01294 | ||||||||
\(999\) | −0.500000 | − | 6.06218i | −0.0158193 | − | 0.191799i |
(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 | 1110.2.i.f.211.1 | yes | 2 | |
37.10 | even | 3 | inner | 1110.2.i.f.121.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.i.f.121.1 | ✓ | 2 | 37.10 | even | 3 | inner | |
1110.2.i.f.211.1 | yes | 2 | 1.1 | even | 1 | trivial |