Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(251,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.251");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.q (of order \(6\), 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: | \(4.35983195036\) |
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: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 251.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.251 |
Dual form | 546.2.q.d.335.1 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 1.50000 | + | 0.866025i | 0.866025 | + | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | − | 3.46410i | − | 1.54919i | −0.632456 | − | 0.774597i | \(-0.717953\pi\) | ||
0.632456 | − | 0.774597i | \(-0.282047\pi\) | |||||||
\(6\) | 1.50000 | − | 0.866025i | 0.612372 | − | 0.353553i | ||||
\(7\) | 2.50000 | + | 0.866025i | 0.944911 | + | 0.327327i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.50000 | + | 2.59808i | 0.500000 | + | 0.866025i | ||||
\(10\) | −3.00000 | − | 1.73205i | −0.948683 | − | 0.547723i | ||||
\(11\) | −1.50000 | + | 2.59808i | −0.452267 | + | 0.783349i | −0.998526 | − | 0.0542666i | \(-0.982718\pi\) |
0.546259 | + | 0.837616i | \(0.316051\pi\) | |||||||
\(12\) | − | 1.73205i | − | 0.500000i | ||||||
\(13\) | 3.50000 | − | 0.866025i | 0.970725 | − | 0.240192i | ||||
\(14\) | 2.00000 | − | 1.73205i | 0.534522 | − | 0.462910i | ||||
\(15\) | 3.00000 | − | 5.19615i | 0.774597 | − | 1.34164i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.50000 | − | 2.59808i | −0.363803 | − | 0.630126i | 0.624780 | − | 0.780801i | \(-0.285189\pi\) |
−0.988583 | + | 0.150675i | \(0.951855\pi\) | |||||||
\(18\) | 3.00000 | 0.707107 | ||||||||
\(19\) | −3.50000 | − | 6.06218i | −0.802955 | − | 1.39076i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) |
0.114708 | − | 0.993399i | \(-0.463407\pi\) | |||||||
\(20\) | −3.00000 | + | 1.73205i | −0.670820 | + | 0.387298i | ||||
\(21\) | 3.00000 | + | 3.46410i | 0.654654 | + | 0.755929i | ||||
\(22\) | 1.50000 | + | 2.59808i | 0.319801 | + | 0.553912i | ||||
\(23\) | 6.00000 | + | 3.46410i | 1.25109 | + | 0.722315i | 0.971325 | − | 0.237754i | \(-0.0764114\pi\) |
0.279761 | + | 0.960070i | \(0.409745\pi\) | |||||||
\(24\) | −1.50000 | − | 0.866025i | −0.306186 | − | 0.176777i | ||||
\(25\) | −7.00000 | −1.40000 | ||||||||
\(26\) | 1.00000 | − | 3.46410i | 0.196116 | − | 0.679366i | ||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | −0.500000 | − | 2.59808i | −0.0944911 | − | 0.490990i | ||||
\(29\) | −1.50000 | − | 0.866025i | −0.278543 | − | 0.160817i | 0.354221 | − | 0.935162i | \(-0.384746\pi\) |
−0.632764 | + | 0.774345i | \(0.718080\pi\) | |||||||
\(30\) | −3.00000 | − | 5.19615i | −0.547723 | − | 0.948683i | ||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −4.50000 | + | 2.59808i | −0.783349 | + | 0.452267i | ||||
\(34\) | −3.00000 | −0.514496 | ||||||||
\(35\) | 3.00000 | − | 8.66025i | 0.507093 | − | 1.46385i | ||||
\(36\) | 1.50000 | − | 2.59808i | 0.250000 | − | 0.433013i | ||||
\(37\) | −6.00000 | − | 3.46410i | −0.986394 | − | 0.569495i | −0.0821995 | − | 0.996616i | \(-0.526194\pi\) |
−0.904194 | + | 0.427121i | \(0.859528\pi\) | |||||||
\(38\) | −7.00000 | −1.13555 | ||||||||
\(39\) | 6.00000 | + | 1.73205i | 0.960769 | + | 0.277350i | ||||
\(40\) | 3.46410i | 0.547723i | ||||||||
\(41\) | −4.50000 | − | 2.59808i | −0.702782 | − | 0.405751i | 0.105601 | − | 0.994409i | \(-0.466323\pi\) |
−0.808383 | + | 0.588657i | \(0.799657\pi\) | |||||||
\(42\) | 4.50000 | − | 0.866025i | 0.694365 | − | 0.133631i | ||||
\(43\) | 4.00000 | + | 6.92820i | 0.609994 | + | 1.05654i | 0.991241 | + | 0.132068i | \(0.0421616\pi\) |
−0.381246 | + | 0.924473i | \(0.624505\pi\) | |||||||
\(44\) | 3.00000 | 0.452267 | ||||||||
\(45\) | 9.00000 | − | 5.19615i | 1.34164 | − | 0.774597i | ||||
\(46\) | 6.00000 | − | 3.46410i | 0.884652 | − | 0.510754i | ||||
\(47\) | 8.66025i | 1.26323i | 0.775283 | + | 0.631614i | \(0.217607\pi\) | ||||
−0.775283 | + | 0.631614i | \(0.782393\pi\) | |||||||
\(48\) | −1.50000 | + | 0.866025i | −0.216506 | + | 0.125000i | ||||
\(49\) | 5.50000 | + | 4.33013i | 0.785714 | + | 0.618590i | ||||
\(50\) | −3.50000 | + | 6.06218i | −0.494975 | + | 0.857321i | ||||
\(51\) | − | 5.19615i | − | 0.727607i | ||||||
\(52\) | −2.50000 | − | 2.59808i | −0.346688 | − | 0.360288i | ||||
\(53\) | 8.66025i | 1.18958i | 0.803882 | + | 0.594789i | \(0.202764\pi\) | ||||
−0.803882 | + | 0.594789i | \(0.797236\pi\) | |||||||
\(54\) | 4.50000 | + | 2.59808i | 0.612372 | + | 0.353553i | ||||
\(55\) | 9.00000 | + | 5.19615i | 1.21356 | + | 0.700649i | ||||
\(56\) | −2.50000 | − | 0.866025i | −0.334077 | − | 0.115728i | ||||
\(57\) | − | 12.1244i | − | 1.60591i | ||||||
\(58\) | −1.50000 | + | 0.866025i | −0.196960 | + | 0.113715i | ||||
\(59\) | 9.00000 | − | 5.19615i | 1.17170 | − | 0.676481i | 0.217620 | − | 0.976034i | \(-0.430171\pi\) |
0.954080 | + | 0.299552i | \(0.0968372\pi\) | |||||||
\(60\) | −6.00000 | −0.774597 | ||||||||
\(61\) | 4.50000 | − | 2.59808i | 0.576166 | − | 0.332650i | −0.183442 | − | 0.983030i | \(-0.558724\pi\) |
0.759608 | + | 0.650381i | \(0.225391\pi\) | |||||||
\(62\) | −2.00000 | + | 3.46410i | −0.254000 | + | 0.439941i | ||||
\(63\) | 1.50000 | + | 7.79423i | 0.188982 | + | 0.981981i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.00000 | − | 12.1244i | −0.372104 | − | 1.50384i | ||||
\(66\) | 5.19615i | 0.639602i | ||||||||
\(67\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(68\) | −1.50000 | + | 2.59808i | −0.181902 | + | 0.315063i | ||||
\(69\) | 6.00000 | + | 10.3923i | 0.722315 | + | 1.25109i | ||||
\(70\) | −6.00000 | − | 6.92820i | −0.717137 | − | 0.828079i | ||||
\(71\) | 3.00000 | + | 5.19615i | 0.356034 | + | 0.616670i | 0.987294 | − | 0.158901i | \(-0.0507952\pi\) |
−0.631260 | + | 0.775571i | \(0.717462\pi\) | |||||||
\(72\) | −1.50000 | − | 2.59808i | −0.176777 | − | 0.306186i | ||||
\(73\) | −4.00000 | −0.468165 | −0.234082 | − | 0.972217i | \(-0.575209\pi\) | ||||
−0.234082 | + | 0.972217i | \(0.575209\pi\) | |||||||
\(74\) | −6.00000 | + | 3.46410i | −0.697486 | + | 0.402694i | ||||
\(75\) | −10.5000 | − | 6.06218i | −1.21244 | − | 0.700000i | ||||
\(76\) | −3.50000 | + | 6.06218i | −0.401478 | + | 0.695379i | ||||
\(77\) | −6.00000 | + | 5.19615i | −0.683763 | + | 0.592157i | ||||
\(78\) | 4.50000 | − | 4.33013i | 0.509525 | − | 0.490290i | ||||
\(79\) | −11.0000 | −1.23760 | −0.618798 | − | 0.785550i | \(-0.712380\pi\) | ||||
−0.618798 | + | 0.785550i | \(0.712380\pi\) | |||||||
\(80\) | 3.00000 | + | 1.73205i | 0.335410 | + | 0.193649i | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | −4.50000 | + | 2.59808i | −0.496942 | + | 0.286910i | ||||
\(83\) | 13.8564i | 1.52094i | 0.649374 | + | 0.760469i | \(0.275031\pi\) | ||||
−0.649374 | + | 0.760469i | \(0.724969\pi\) | |||||||
\(84\) | 1.50000 | − | 4.33013i | 0.163663 | − | 0.472456i | ||||
\(85\) | −9.00000 | + | 5.19615i | −0.976187 | + | 0.563602i | ||||
\(86\) | 8.00000 | 0.862662 | ||||||||
\(87\) | −1.50000 | − | 2.59808i | −0.160817 | − | 0.278543i | ||||
\(88\) | 1.50000 | − | 2.59808i | 0.159901 | − | 0.276956i | ||||
\(89\) | −7.50000 | − | 4.33013i | −0.794998 | − | 0.458993i | 0.0467209 | − | 0.998908i | \(-0.485123\pi\) |
−0.841719 | + | 0.539915i | \(0.818456\pi\) | |||||||
\(90\) | − | 10.3923i | − | 1.09545i | ||||||
\(91\) | 9.50000 | + | 0.866025i | 0.995871 | + | 0.0907841i | ||||
\(92\) | − | 6.92820i | − | 0.722315i | ||||||
\(93\) | −6.00000 | − | 3.46410i | −0.622171 | − | 0.359211i | ||||
\(94\) | 7.50000 | + | 4.33013i | 0.773566 | + | 0.446619i | ||||
\(95\) | −21.0000 | + | 12.1244i | −2.15455 | + | 1.24393i | ||||
\(96\) | 1.73205i | 0.176777i | ||||||||
\(97\) | 1.00000 | + | 1.73205i | 0.101535 | + | 0.175863i | 0.912317 | − | 0.409484i | \(-0.134291\pi\) |
−0.810782 | + | 0.585348i | \(0.800958\pi\) | |||||||
\(98\) | 6.50000 | − | 2.59808i | 0.656599 | − | 0.262445i | ||||
\(99\) | −9.00000 | −0.904534 | ||||||||
\(100\) | 3.50000 | + | 6.06218i | 0.350000 | + | 0.606218i | ||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | −4.50000 | − | 2.59808i | −0.445566 | − | 0.257248i | ||||
\(103\) | 3.46410i | 0.341328i | 0.985329 | + | 0.170664i | \(0.0545913\pi\) | ||||
−0.985329 | + | 0.170664i | \(0.945409\pi\) | |||||||
\(104\) | −3.50000 | + | 0.866025i | −0.343203 | + | 0.0849208i | ||||
\(105\) | 12.0000 | − | 10.3923i | 1.17108 | − | 1.01419i | ||||
\(106\) | 7.50000 | + | 4.33013i | 0.728464 | + | 0.420579i | ||||
\(107\) | −4.50000 | − | 2.59808i | −0.435031 | − | 0.251166i | 0.266456 | − | 0.963847i | \(-0.414147\pi\) |
−0.701488 | + | 0.712681i | \(0.747481\pi\) | |||||||
\(108\) | 4.50000 | − | 2.59808i | 0.433013 | − | 0.250000i | ||||
\(109\) | 3.46410i | 0.331801i | 0.986143 | + | 0.165900i | \(0.0530530\pi\) | ||||
−0.986143 | + | 0.165900i | \(0.946947\pi\) | |||||||
\(110\) | 9.00000 | − | 5.19615i | 0.858116 | − | 0.495434i | ||||
\(111\) | −6.00000 | − | 10.3923i | −0.569495 | − | 0.986394i | ||||
\(112\) | −2.00000 | + | 1.73205i | −0.188982 | + | 0.163663i | ||||
\(113\) | −12.0000 | + | 6.92820i | −1.12887 | + | 0.651751i | −0.943649 | − | 0.330947i | \(-0.892632\pi\) |
−0.185216 | + | 0.982698i | \(0.559298\pi\) | |||||||
\(114\) | −10.5000 | − | 6.06218i | −0.983415 | − | 0.567775i | ||||
\(115\) | 12.0000 | − | 20.7846i | 1.11901 | − | 1.93817i | ||||
\(116\) | 1.73205i | 0.160817i | ||||||||
\(117\) | 7.50000 | + | 7.79423i | 0.693375 | + | 0.720577i | ||||
\(118\) | − | 10.3923i | − | 0.956689i | ||||||
\(119\) | −1.50000 | − | 7.79423i | −0.137505 | − | 0.714496i | ||||
\(120\) | −3.00000 | + | 5.19615i | −0.273861 | + | 0.474342i | ||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | − | 5.19615i | − | 0.470438i | ||||||
\(123\) | −4.50000 | − | 7.79423i | −0.405751 | − | 0.702782i | ||||
\(124\) | 2.00000 | + | 3.46410i | 0.179605 | + | 0.311086i | ||||
\(125\) | 6.92820i | 0.619677i | ||||||||
\(126\) | 7.50000 | + | 2.59808i | 0.668153 | + | 0.231455i | ||||
\(127\) | 4.00000 | − | 6.92820i | 0.354943 | − | 0.614779i | −0.632166 | − | 0.774833i | \(-0.717834\pi\) |
0.987108 | + | 0.160055i | \(0.0511671\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 13.8564i | 1.21999i | ||||||||
\(130\) | −12.0000 | − | 3.46410i | −1.05247 | − | 0.303822i | ||||
\(131\) | 6.00000 | 0.524222 | 0.262111 | − | 0.965038i | \(-0.415581\pi\) | ||||
0.262111 | + | 0.965038i | \(0.415581\pi\) | |||||||
\(132\) | 4.50000 | + | 2.59808i | 0.391675 | + | 0.226134i | ||||
\(133\) | −3.50000 | − | 18.1865i | −0.303488 | − | 1.57697i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 18.0000 | 1.54919 | ||||||||
\(136\) | 1.50000 | + | 2.59808i | 0.128624 | + | 0.222783i | ||||
\(137\) | 6.00000 | + | 10.3923i | 0.512615 | + | 0.887875i | 0.999893 | + | 0.0146279i | \(0.00465636\pi\) |
−0.487278 | + | 0.873247i | \(0.662010\pi\) | |||||||
\(138\) | 12.0000 | 1.02151 | ||||||||
\(139\) | −4.50000 | + | 2.59808i | −0.381685 | + | 0.220366i | −0.678551 | − | 0.734553i | \(-0.737392\pi\) |
0.296866 | + | 0.954919i | \(0.404058\pi\) | |||||||
\(140\) | −9.00000 | + | 1.73205i | −0.760639 | + | 0.146385i | ||||
\(141\) | −7.50000 | + | 12.9904i | −0.631614 | + | 1.09399i | ||||
\(142\) | 6.00000 | 0.503509 | ||||||||
\(143\) | −3.00000 | + | 10.3923i | −0.250873 | + | 0.869048i | ||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | −3.00000 | + | 5.19615i | −0.249136 | + | 0.431517i | ||||
\(146\) | −2.00000 | + | 3.46410i | −0.165521 | + | 0.286691i | ||||
\(147\) | 4.50000 | + | 11.2583i | 0.371154 | + | 0.928571i | ||||
\(148\) | 6.92820i | 0.569495i | ||||||||
\(149\) | −3.00000 | − | 5.19615i | −0.245770 | − | 0.425685i | 0.716578 | − | 0.697507i | \(-0.245707\pi\) |
−0.962348 | + | 0.271821i | \(0.912374\pi\) | |||||||
\(150\) | −10.5000 | + | 6.06218i | −0.857321 | + | 0.494975i | ||||
\(151\) | − | 8.66025i | − | 0.704761i | −0.935857 | − | 0.352381i | \(-0.885372\pi\) | ||
0.935857 | − | 0.352381i | \(-0.114628\pi\) | |||||||
\(152\) | 3.50000 | + | 6.06218i | 0.283887 | + | 0.491708i | ||||
\(153\) | 4.50000 | − | 7.79423i | 0.363803 | − | 0.630126i | ||||
\(154\) | 1.50000 | + | 7.79423i | 0.120873 | + | 0.628077i | ||||
\(155\) | 13.8564i | 1.11297i | ||||||||
\(156\) | −1.50000 | − | 6.06218i | −0.120096 | − | 0.485363i | ||||
\(157\) | 13.8564i | 1.10586i | 0.833227 | + | 0.552931i | \(0.186491\pi\) | ||||
−0.833227 | + | 0.552931i | \(0.813509\pi\) | |||||||
\(158\) | −5.50000 | + | 9.52628i | −0.437557 | + | 0.757870i | ||||
\(159\) | −7.50000 | + | 12.9904i | −0.594789 | + | 1.03020i | ||||
\(160\) | 3.00000 | − | 1.73205i | 0.237171 | − | 0.136931i | ||||
\(161\) | 12.0000 | + | 13.8564i | 0.945732 | + | 1.09204i | ||||
\(162\) | 4.50000 | + | 7.79423i | 0.353553 | + | 0.612372i | ||||
\(163\) | 21.0000 | − | 12.1244i | 1.64485 | − | 0.949653i | 0.665771 | − | 0.746156i | \(-0.268103\pi\) |
0.979076 | − | 0.203497i | \(-0.0652307\pi\) | |||||||
\(164\) | 5.19615i | 0.405751i | ||||||||
\(165\) | 9.00000 | + | 15.5885i | 0.700649 | + | 1.21356i | ||||
\(166\) | 12.0000 | + | 6.92820i | 0.931381 | + | 0.537733i | ||||
\(167\) | −15.0000 | − | 8.66025i | −1.16073 | − | 0.670151i | −0.209255 | − | 0.977861i | \(-0.567104\pi\) |
−0.951480 | + | 0.307711i | \(0.900437\pi\) | |||||||
\(168\) | −3.00000 | − | 3.46410i | −0.231455 | − | 0.267261i | ||||
\(169\) | 11.5000 | − | 6.06218i | 0.884615 | − | 0.466321i | ||||
\(170\) | 10.3923i | 0.797053i | ||||||||
\(171\) | 10.5000 | − | 18.1865i | 0.802955 | − | 1.39076i | ||||
\(172\) | 4.00000 | − | 6.92820i | 0.304997 | − | 0.528271i | ||||
\(173\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(174\) | −3.00000 | −0.227429 | ||||||||
\(175\) | −17.5000 | − | 6.06218i | −1.32288 | − | 0.458258i | ||||
\(176\) | −1.50000 | − | 2.59808i | −0.113067 | − | 0.195837i | ||||
\(177\) | 18.0000 | 1.35296 | ||||||||
\(178\) | −7.50000 | + | 4.33013i | −0.562149 | + | 0.324557i | ||||
\(179\) | −21.0000 | − | 12.1244i | −1.56961 | − | 0.906217i | −0.996213 | − | 0.0869415i | \(-0.972291\pi\) |
−0.573400 | − | 0.819275i | \(-0.694376\pi\) | |||||||
\(180\) | −9.00000 | − | 5.19615i | −0.670820 | − | 0.387298i | ||||
\(181\) | − | 1.73205i | − | 0.128742i | −0.997926 | − | 0.0643712i | \(-0.979496\pi\) | ||
0.997926 | − | 0.0643712i | \(-0.0205042\pi\) | |||||||
\(182\) | 5.50000 | − | 7.79423i | 0.407687 | − | 0.577747i | ||||
\(183\) | 9.00000 | 0.665299 | ||||||||
\(184\) | −6.00000 | − | 3.46410i | −0.442326 | − | 0.255377i | ||||
\(185\) | −12.0000 | + | 20.7846i | −0.882258 | + | 1.52811i | ||||
\(186\) | −6.00000 | + | 3.46410i | −0.439941 | + | 0.254000i | ||||
\(187\) | 9.00000 | 0.658145 | ||||||||
\(188\) | 7.50000 | − | 4.33013i | 0.546994 | − | 0.315807i | ||||
\(189\) | −4.50000 | + | 12.9904i | −0.327327 | + | 0.944911i | ||||
\(190\) | 24.2487i | 1.75919i | ||||||||
\(191\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(192\) | 1.50000 | + | 0.866025i | 0.108253 | + | 0.0625000i | ||||
\(193\) | −10.5000 | − | 6.06218i | −0.755807 | − | 0.436365i | 0.0719816 | − | 0.997406i | \(-0.477068\pi\) |
−0.827788 | + | 0.561041i | \(0.810401\pi\) | |||||||
\(194\) | 2.00000 | 0.143592 | ||||||||
\(195\) | 6.00000 | − | 20.7846i | 0.429669 | − | 1.48842i | ||||
\(196\) | 1.00000 | − | 6.92820i | 0.0714286 | − | 0.494872i | ||||
\(197\) | 13.5000 | − | 23.3827i | 0.961835 | − | 1.66595i | 0.243947 | − | 0.969788i | \(-0.421558\pi\) |
0.717888 | − | 0.696159i | \(-0.245109\pi\) | |||||||
\(198\) | −4.50000 | + | 7.79423i | −0.319801 | + | 0.553912i | ||||
\(199\) | −9.00000 | + | 5.19615i | −0.637993 | + | 0.368345i | −0.783841 | − | 0.620962i | \(-0.786742\pi\) |
0.145848 | + | 0.989307i | \(0.453409\pi\) | |||||||
\(200\) | 7.00000 | 0.494975 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.00000 | − | 3.46410i | −0.210559 | − | 0.243132i | ||||
\(204\) | −4.50000 | + | 2.59808i | −0.315063 | + | 0.181902i | ||||
\(205\) | −9.00000 | + | 15.5885i | −0.628587 | + | 1.08875i | ||||
\(206\) | 3.00000 | + | 1.73205i | 0.209020 | + | 0.120678i | ||||
\(207\) | 20.7846i | 1.44463i | ||||||||
\(208\) | −1.00000 | + | 3.46410i | −0.0693375 | + | 0.240192i | ||||
\(209\) | 21.0000 | 1.45260 | ||||||||
\(210\) | −3.00000 | − | 15.5885i | −0.207020 | − | 1.07571i | ||||
\(211\) | 11.0000 | − | 19.0526i | 0.757271 | − | 1.31163i | −0.186966 | − | 0.982366i | \(-0.559865\pi\) |
0.944237 | − | 0.329266i | \(-0.106801\pi\) | |||||||
\(212\) | 7.50000 | − | 4.33013i | 0.515102 | − | 0.297394i | ||||
\(213\) | 10.3923i | 0.712069i | ||||||||
\(214\) | −4.50000 | + | 2.59808i | −0.307614 | + | 0.177601i | ||||
\(215\) | 24.0000 | − | 13.8564i | 1.63679 | − | 0.944999i | ||||
\(216\) | − | 5.19615i | − | 0.353553i | ||||||
\(217\) | −10.0000 | − | 3.46410i | −0.678844 | − | 0.235159i | ||||
\(218\) | 3.00000 | + | 1.73205i | 0.203186 | + | 0.117309i | ||||
\(219\) | −6.00000 | − | 3.46410i | −0.405442 | − | 0.234082i | ||||
\(220\) | − | 10.3923i | − | 0.700649i | ||||||
\(221\) | −7.50000 | − | 7.79423i | −0.504505 | − | 0.524297i | ||||
\(222\) | −12.0000 | −0.805387 | ||||||||
\(223\) | −8.00000 | + | 13.8564i | −0.535720 | + | 0.927894i | 0.463409 | + | 0.886145i | \(0.346626\pi\) |
−0.999128 | + | 0.0417488i | \(0.986707\pi\) | |||||||
\(224\) | 0.500000 | + | 2.59808i | 0.0334077 | + | 0.173591i | ||||
\(225\) | −10.5000 | − | 18.1865i | −0.700000 | − | 1.21244i | ||||
\(226\) | 13.8564i | 0.921714i | ||||||||
\(227\) | 9.00000 | − | 5.19615i | 0.597351 | − | 0.344881i | −0.170648 | − | 0.985332i | \(-0.554586\pi\) |
0.767999 | + | 0.640451i | \(0.221253\pi\) | |||||||
\(228\) | −10.5000 | + | 6.06218i | −0.695379 | + | 0.401478i | ||||
\(229\) | −13.0000 | −0.859064 | −0.429532 | − | 0.903052i | \(-0.641321\pi\) | ||||
−0.429532 | + | 0.903052i | \(0.641321\pi\) | |||||||
\(230\) | −12.0000 | − | 20.7846i | −0.791257 | − | 1.37050i | ||||
\(231\) | −13.5000 | + | 2.59808i | −0.888235 | + | 0.170941i | ||||
\(232\) | 1.50000 | + | 0.866025i | 0.0984798 | + | 0.0568574i | ||||
\(233\) | 6.92820i | 0.453882i | 0.973909 | + | 0.226941i | \(0.0728724\pi\) | ||||
−0.973909 | + | 0.226941i | \(0.927128\pi\) | |||||||
\(234\) | 10.5000 | − | 2.59808i | 0.686406 | − | 0.169842i | ||||
\(235\) | 30.0000 | 1.95698 | ||||||||
\(236\) | −9.00000 | − | 5.19615i | −0.585850 | − | 0.338241i | ||||
\(237\) | −16.5000 | − | 9.52628i | −1.07179 | − | 0.618798i | ||||
\(238\) | −7.50000 | − | 2.59808i | −0.486153 | − | 0.168408i | ||||
\(239\) | 12.0000 | 0.776215 | 0.388108 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388108 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(240\) | 3.00000 | + | 5.19615i | 0.193649 | + | 0.335410i | ||||
\(241\) | 5.00000 | + | 8.66025i | 0.322078 | + | 0.557856i | 0.980917 | − | 0.194429i | \(-0.0622852\pi\) |
−0.658838 | + | 0.752285i | \(0.728952\pi\) | |||||||
\(242\) | 2.00000 | 0.128565 | ||||||||
\(243\) | −13.5000 | + | 7.79423i | −0.866025 | + | 0.500000i | ||||
\(244\) | −4.50000 | − | 2.59808i | −0.288083 | − | 0.166325i | ||||
\(245\) | 15.0000 | − | 19.0526i | 0.958315 | − | 1.21722i | ||||
\(246\) | −9.00000 | −0.573819 | ||||||||
\(247\) | −17.5000 | − | 18.1865i | −1.11350 | − | 1.15718i | ||||
\(248\) | 4.00000 | 0.254000 | ||||||||
\(249\) | −12.0000 | + | 20.7846i | −0.760469 | + | 1.31717i | ||||
\(250\) | 6.00000 | + | 3.46410i | 0.379473 | + | 0.219089i | ||||
\(251\) | −15.0000 | − | 25.9808i | −0.946792 | − | 1.63989i | −0.752124 | − | 0.659022i | \(-0.770970\pi\) |
−0.194668 | − | 0.980869i | \(-0.562363\pi\) | |||||||
\(252\) | 6.00000 | − | 5.19615i | 0.377964 | − | 0.327327i | ||||
\(253\) | −18.0000 | + | 10.3923i | −1.13165 | + | 0.653359i | ||||
\(254\) | −4.00000 | − | 6.92820i | −0.250982 | − | 0.434714i | ||||
\(255\) | −18.0000 | −1.12720 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 13.5000 | − | 23.3827i | 0.842107 | − | 1.45857i | −0.0460033 | − | 0.998941i | \(-0.514648\pi\) |
0.888110 | − | 0.459631i | \(-0.152018\pi\) | |||||||
\(258\) | 12.0000 | + | 6.92820i | 0.747087 | + | 0.431331i | ||||
\(259\) | −12.0000 | − | 13.8564i | −0.745644 | − | 0.860995i | ||||
\(260\) | −9.00000 | + | 8.66025i | −0.558156 | + | 0.537086i | ||||
\(261\) | − | 5.19615i | − | 0.321634i | ||||||
\(262\) | 3.00000 | − | 5.19615i | 0.185341 | − | 0.321019i | ||||
\(263\) | 21.0000 | + | 12.1244i | 1.29492 | + | 0.747620i | 0.979521 | − | 0.201341i | \(-0.0645299\pi\) |
0.315394 | + | 0.948961i | \(0.397863\pi\) | |||||||
\(264\) | 4.50000 | − | 2.59808i | 0.276956 | − | 0.159901i | ||||
\(265\) | 30.0000 | 1.84289 | ||||||||
\(266\) | −17.5000 | − | 6.06218i | −1.07299 | − | 0.371696i | ||||
\(267\) | −7.50000 | − | 12.9904i | −0.458993 | − | 0.794998i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.0000 | − | 20.7846i | −0.731653 | − | 1.26726i | −0.956176 | − | 0.292791i | \(-0.905416\pi\) |
0.224523 | − | 0.974469i | \(-0.427917\pi\) | |||||||
\(270\) | 9.00000 | − | 15.5885i | 0.547723 | − | 0.948683i | ||||
\(271\) | 4.00000 | − | 6.92820i | 0.242983 | − | 0.420858i | −0.718580 | − | 0.695444i | \(-0.755208\pi\) |
0.961563 | + | 0.274586i | \(0.0885408\pi\) | |||||||
\(272\) | 3.00000 | 0.181902 | ||||||||
\(273\) | 13.5000 | + | 9.52628i | 0.817057 | + | 0.576557i | ||||
\(274\) | 12.0000 | 0.724947 | ||||||||
\(275\) | 10.5000 | − | 18.1865i | 0.633174 | − | 1.09669i | ||||
\(276\) | 6.00000 | − | 10.3923i | 0.361158 | − | 0.625543i | ||||
\(277\) | 8.00000 | + | 13.8564i | 0.480673 | + | 0.832551i | 0.999754 | − | 0.0221745i | \(-0.00705893\pi\) |
−0.519081 | + | 0.854725i | \(0.673726\pi\) | |||||||
\(278\) | 5.19615i | 0.311645i | ||||||||
\(279\) | −6.00000 | − | 10.3923i | −0.359211 | − | 0.622171i | ||||
\(280\) | −3.00000 | + | 8.66025i | −0.179284 | + | 0.517549i | ||||
\(281\) | 12.0000 | 0.715860 | 0.357930 | − | 0.933748i | \(-0.383483\pi\) | ||||
0.357930 | + | 0.933748i | \(0.383483\pi\) | |||||||
\(282\) | 7.50000 | + | 12.9904i | 0.446619 | + | 0.773566i | ||||
\(283\) | 3.00000 | + | 1.73205i | 0.178331 | + | 0.102960i | 0.586509 | − | 0.809943i | \(-0.300502\pi\) |
−0.408177 | + | 0.912903i | \(0.633835\pi\) | |||||||
\(284\) | 3.00000 | − | 5.19615i | 0.178017 | − | 0.308335i | ||||
\(285\) | −42.0000 | −2.48787 | ||||||||
\(286\) | 7.50000 | + | 7.79423i | 0.443484 | + | 0.460882i | ||||
\(287\) | −9.00000 | − | 10.3923i | −0.531253 | − | 0.613438i | ||||
\(288\) | −1.50000 | + | 2.59808i | −0.0883883 | + | 0.153093i | ||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 3.00000 | + | 5.19615i | 0.176166 | + | 0.305129i | ||||
\(291\) | 3.46410i | 0.203069i | ||||||||
\(292\) | 2.00000 | + | 3.46410i | 0.117041 | + | 0.202721i | ||||
\(293\) | −6.00000 | + | 3.46410i | −0.350524 | + | 0.202375i | −0.664916 | − | 0.746918i | \(-0.731533\pi\) |
0.314392 | + | 0.949293i | \(0.398199\pi\) | |||||||
\(294\) | 12.0000 | + | 1.73205i | 0.699854 | + | 0.101015i | ||||
\(295\) | −18.0000 | − | 31.1769i | −1.04800 | − | 1.81519i | ||||
\(296\) | 6.00000 | + | 3.46410i | 0.348743 | + | 0.201347i | ||||
\(297\) | −13.5000 | − | 7.79423i | −0.783349 | − | 0.452267i | ||||
\(298\) | −6.00000 | −0.347571 | ||||||||
\(299\) | 24.0000 | + | 6.92820i | 1.38796 | + | 0.400668i | ||||
\(300\) | 12.1244i | 0.700000i | ||||||||
\(301\) | 4.00000 | + | 20.7846i | 0.230556 | + | 1.19800i | ||||
\(302\) | −7.50000 | − | 4.33013i | −0.431577 | − | 0.249171i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.00000 | 0.401478 | ||||||||
\(305\) | −9.00000 | − | 15.5885i | −0.515339 | − | 0.892592i | ||||
\(306\) | −4.50000 | − | 7.79423i | −0.257248 | − | 0.445566i | ||||
\(307\) | −7.00000 | −0.399511 | −0.199756 | − | 0.979846i | \(-0.564015\pi\) | ||||
−0.199756 | + | 0.979846i | \(0.564015\pi\) | |||||||
\(308\) | 7.50000 | + | 2.59808i | 0.427352 | + | 0.148039i | ||||
\(309\) | −3.00000 | + | 5.19615i | −0.170664 | + | 0.295599i | ||||
\(310\) | 12.0000 | + | 6.92820i | 0.681554 | + | 0.393496i | ||||
\(311\) | −3.00000 | −0.170114 | −0.0850572 | − | 0.996376i | \(-0.527107\pi\) | ||||
−0.0850572 | + | 0.996376i | \(0.527107\pi\) | |||||||
\(312\) | −6.00000 | − | 1.73205i | −0.339683 | − | 0.0980581i | ||||
\(313\) | − | 20.7846i | − | 1.17482i | −0.809291 | − | 0.587408i | \(-0.800148\pi\) | ||
0.809291 | − | 0.587408i | \(-0.199852\pi\) | |||||||
\(314\) | 12.0000 | + | 6.92820i | 0.677199 | + | 0.390981i | ||||
\(315\) | 27.0000 | − | 5.19615i | 1.52128 | − | 0.292770i | ||||
\(316\) | 5.50000 | + | 9.52628i | 0.309399 | + | 0.535895i | ||||
\(317\) | 18.0000 | 1.01098 | 0.505490 | − | 0.862832i | \(-0.331312\pi\) | ||||
0.505490 | + | 0.862832i | \(0.331312\pi\) | |||||||
\(318\) | 7.50000 | + | 12.9904i | 0.420579 | + | 0.728464i | ||||
\(319\) | 4.50000 | − | 2.59808i | 0.251952 | − | 0.145464i | ||||
\(320\) | − | 3.46410i | − | 0.193649i | ||||||
\(321\) | −4.50000 | − | 7.79423i | −0.251166 | − | 0.435031i | ||||
\(322\) | 18.0000 | − | 3.46410i | 1.00310 | − | 0.193047i | ||||
\(323\) | −10.5000 | + | 18.1865i | −0.584236 | + | 1.01193i | ||||
\(324\) | 9.00000 | 0.500000 | ||||||||
\(325\) | −24.5000 | + | 6.06218i | −1.35902 | + | 0.336269i | ||||
\(326\) | − | 24.2487i | − | 1.34301i | ||||||
\(327\) | −3.00000 | + | 5.19615i | −0.165900 | + | 0.287348i | ||||
\(328\) | 4.50000 | + | 2.59808i | 0.248471 | + | 0.143455i | ||||
\(329\) | −7.50000 | + | 21.6506i | −0.413488 | + | 1.19364i | ||||
\(330\) | 18.0000 | 0.990867 | ||||||||
\(331\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(332\) | 12.0000 | − | 6.92820i | 0.658586 | − | 0.380235i | ||||
\(333\) | − | 20.7846i | − | 1.13899i | ||||||
\(334\) | −15.0000 | + | 8.66025i | −0.820763 | + | 0.473868i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.50000 | + | 0.866025i | −0.245495 | + | 0.0472456i | ||||
\(337\) | −19.0000 | −1.03500 | −0.517498 | − | 0.855684i | \(-0.673136\pi\) | ||||
−0.517498 | + | 0.855684i | \(0.673136\pi\) | |||||||
\(338\) | 0.500000 | − | 12.9904i | 0.0271964 | − | 0.706584i | ||||
\(339\) | −24.0000 | −1.30350 | ||||||||
\(340\) | 9.00000 | + | 5.19615i | 0.488094 | + | 0.281801i | ||||
\(341\) | 6.00000 | − | 10.3923i | 0.324918 | − | 0.562775i | ||||
\(342\) | −10.5000 | − | 18.1865i | −0.567775 | − | 0.983415i | ||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | −4.00000 | − | 6.92820i | −0.215666 | − | 0.373544i | ||||
\(345\) | 36.0000 | − | 20.7846i | 1.93817 | − | 1.11901i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.5000 | − | 7.79423i | 0.724718 | − | 0.418416i | −0.0917687 | − | 0.995780i | \(-0.529252\pi\) |
0.816487 | + | 0.577364i | \(0.195919\pi\) | |||||||
\(348\) | −1.50000 | + | 2.59808i | −0.0804084 | + | 0.139272i | ||||
\(349\) | −1.00000 | + | 1.73205i | −0.0535288 | + | 0.0927146i | −0.891548 | − | 0.452926i | \(-0.850380\pi\) |
0.838019 | + | 0.545640i | \(0.183714\pi\) | |||||||
\(350\) | −14.0000 | + | 12.1244i | −0.748331 | + | 0.648074i | ||||
\(351\) | 4.50000 | + | 18.1865i | 0.240192 | + | 0.970725i | ||||
\(352\) | −3.00000 | −0.159901 | ||||||||
\(353\) | 18.0000 | + | 10.3923i | 0.958043 | + | 0.553127i | 0.895570 | − | 0.444920i | \(-0.146768\pi\) |
0.0624731 | + | 0.998047i | \(0.480101\pi\) | |||||||
\(354\) | 9.00000 | − | 15.5885i | 0.478345 | − | 0.828517i | ||||
\(355\) | 18.0000 | − | 10.3923i | 0.955341 | − | 0.551566i | ||||
\(356\) | 8.66025i | 0.458993i | ||||||||
\(357\) | 4.50000 | − | 12.9904i | 0.238165 | − | 0.687524i | ||||
\(358\) | −21.0000 | + | 12.1244i | −1.10988 | + | 0.640792i | ||||
\(359\) | −24.0000 | −1.26667 | −0.633336 | − | 0.773877i | \(-0.718315\pi\) | ||||
−0.633336 | + | 0.773877i | \(0.718315\pi\) | |||||||
\(360\) | −9.00000 | + | 5.19615i | −0.474342 | + | 0.273861i | ||||
\(361\) | −15.0000 | + | 25.9808i | −0.789474 | + | 1.36741i | ||||
\(362\) | −1.50000 | − | 0.866025i | −0.0788382 | − | 0.0455173i | ||||
\(363\) | 3.46410i | 0.181818i | ||||||||
\(364\) | −4.00000 | − | 8.66025i | −0.209657 | − | 0.453921i | ||||
\(365\) | 13.8564i | 0.725277i | ||||||||
\(366\) | 4.50000 | − | 7.79423i | 0.235219 | − | 0.407411i | ||||
\(367\) | −18.0000 | − | 10.3923i | −0.939592 | − | 0.542474i | −0.0497598 | − | 0.998761i | \(-0.515846\pi\) |
−0.889833 | + | 0.456287i | \(0.849179\pi\) | |||||||
\(368\) | −6.00000 | + | 3.46410i | −0.312772 | + | 0.180579i | ||||
\(369\) | − | 15.5885i | − | 0.811503i | ||||||
\(370\) | 12.0000 | + | 20.7846i | 0.623850 | + | 1.08054i | ||||
\(371\) | −7.50000 | + | 21.6506i | −0.389381 | + | 1.12404i | ||||
\(372\) | 6.92820i | 0.359211i | ||||||||
\(373\) | 10.0000 | + | 17.3205i | 0.517780 | + | 0.896822i | 0.999787 | + | 0.0206542i | \(0.00657489\pi\) |
−0.482006 | + | 0.876168i | \(0.660092\pi\) | |||||||
\(374\) | 4.50000 | − | 7.79423i | 0.232689 | − | 0.403030i | ||||
\(375\) | −6.00000 | + | 10.3923i | −0.309839 | + | 0.536656i | ||||
\(376\) | − | 8.66025i | − | 0.446619i | ||||||
\(377\) | −6.00000 | − | 1.73205i | −0.309016 | − | 0.0892052i | ||||
\(378\) | 9.00000 | + | 10.3923i | 0.462910 | + | 0.534522i | ||||
\(379\) | −9.00000 | − | 5.19615i | −0.462299 | − | 0.266908i | 0.250711 | − | 0.968062i | \(-0.419335\pi\) |
−0.713010 | + | 0.701153i | \(0.752669\pi\) | |||||||
\(380\) | 21.0000 | + | 12.1244i | 1.07728 | + | 0.621966i | ||||
\(381\) | 12.0000 | − | 6.92820i | 0.614779 | − | 0.354943i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.50000 | + | 2.59808i | −0.229939 | + | 0.132755i | −0.610544 | − | 0.791982i | \(-0.709049\pi\) |
0.380605 | + | 0.924738i | \(0.375716\pi\) | |||||||
\(384\) | 1.50000 | − | 0.866025i | 0.0765466 | − | 0.0441942i | ||||
\(385\) | 18.0000 | + | 20.7846i | 0.917365 | + | 1.05928i | ||||
\(386\) | −10.5000 | + | 6.06218i | −0.534436 | + | 0.308557i | ||||
\(387\) | −12.0000 | + | 20.7846i | −0.609994 | + | 1.05654i | ||||
\(388\) | 1.00000 | − | 1.73205i | 0.0507673 | − | 0.0879316i | ||||
\(389\) | 20.7846i | 1.05382i | 0.849921 | + | 0.526911i | \(0.176650\pi\) | ||||
−0.849921 | + | 0.526911i | \(0.823350\pi\) | |||||||
\(390\) | −15.0000 | − | 15.5885i | −0.759555 | − | 0.789352i | ||||
\(391\) | − | 20.7846i | − | 1.05112i | ||||||
\(392\) | −5.50000 | − | 4.33013i | −0.277792 | − | 0.218704i | ||||
\(393\) | 9.00000 | + | 5.19615i | 0.453990 | + | 0.262111i | ||||
\(394\) | −13.5000 | − | 23.3827i | −0.680120 | − | 1.17800i | ||||
\(395\) | 38.1051i | 1.91728i | ||||||||
\(396\) | 4.50000 | + | 7.79423i | 0.226134 | + | 0.391675i | ||||
\(397\) | −3.50000 | − | 6.06218i | −0.175660 | − | 0.304252i | 0.764730 | − | 0.644351i | \(-0.222873\pi\) |
−0.940389 | + | 0.340099i | \(0.889539\pi\) | |||||||
\(398\) | 10.3923i | 0.520919i | ||||||||
\(399\) | 10.5000 | − | 30.3109i | 0.525657 | − | 1.51744i | ||||
\(400\) | 3.50000 | − | 6.06218i | 0.175000 | − | 0.303109i | ||||
\(401\) | −9.00000 | + | 15.5885i | −0.449439 | + | 0.778450i | −0.998350 | − | 0.0574304i | \(-0.981709\pi\) |
0.548911 | + | 0.835881i | \(0.315043\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.0000 | + | 3.46410i | −0.697390 | + | 0.172559i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 27.0000 | + | 15.5885i | 1.34164 | + | 0.774597i | ||||
\(406\) | −4.50000 | + | 0.866025i | −0.223331 | + | 0.0429801i | ||||
\(407\) | 18.0000 | − | 10.3923i | 0.892227 | − | 0.515127i | ||||
\(408\) | 5.19615i | 0.257248i | ||||||||
\(409\) | −2.00000 | − | 3.46410i | −0.0988936 | − | 0.171289i | 0.812333 | − | 0.583193i | \(-0.198197\pi\) |
−0.911227 | + | 0.411905i | \(0.864864\pi\) | |||||||
\(410\) | 9.00000 | + | 15.5885i | 0.444478 | + | 0.769859i | ||||
\(411\) | 20.7846i | 1.02523i | ||||||||
\(412\) | 3.00000 | − | 1.73205i | 0.147799 | − | 0.0853320i | ||||
\(413\) | 27.0000 | − | 5.19615i | 1.32858 | − | 0.255686i | ||||
\(414\) | 18.0000 | + | 10.3923i | 0.884652 | + | 0.510754i | ||||
\(415\) | 48.0000 | 2.35623 | ||||||||
\(416\) | 2.50000 | + | 2.59808i | 0.122573 | + | 0.127381i | ||||
\(417\) | −9.00000 | −0.440732 | ||||||||
\(418\) | 10.5000 | − | 18.1865i | 0.513572 | − | 0.889532i | ||||
\(419\) | −6.00000 | + | 10.3923i | −0.293119 | + | 0.507697i | −0.974546 | − | 0.224189i | \(-0.928027\pi\) |
0.681426 | + | 0.731887i | \(0.261360\pi\) | |||||||
\(420\) | −15.0000 | − | 5.19615i | −0.731925 | − | 0.253546i | ||||
\(421\) | − | 24.2487i | − | 1.18181i | −0.806741 | − | 0.590905i | \(-0.798771\pi\) | ||
0.806741 | − | 0.590905i | \(-0.201229\pi\) | |||||||
\(422\) | −11.0000 | − | 19.0526i | −0.535472 | − | 0.927464i | ||||
\(423\) | −22.5000 | + | 12.9904i | −1.09399 | + | 0.631614i | ||||
\(424\) | − | 8.66025i | − | 0.420579i | ||||||
\(425\) | 10.5000 | + | 18.1865i | 0.509325 | + | 0.882176i | ||||
\(426\) | 9.00000 | + | 5.19615i | 0.436051 | + | 0.251754i | ||||
\(427\) | 13.5000 | − | 2.59808i | 0.653311 | − | 0.125730i | ||||
\(428\) | 5.19615i | 0.251166i | ||||||||
\(429\) | −13.5000 | + | 12.9904i | −0.651786 | + | 0.627182i | ||||
\(430\) | − | 27.7128i | − | 1.33643i | ||||||
\(431\) | 9.00000 | − | 15.5885i | 0.433515 | − | 0.750870i | −0.563658 | − | 0.826008i | \(-0.690607\pi\) |
0.997173 | + | 0.0751385i | \(0.0239399\pi\) | |||||||
\(432\) | −4.50000 | − | 2.59808i | −0.216506 | − | 0.125000i | ||||
\(433\) | −15.0000 | + | 8.66025i | −0.720854 | + | 0.416185i | −0.815067 | − | 0.579367i | \(-0.803300\pi\) |
0.0942129 | + | 0.995552i | \(0.469967\pi\) | |||||||
\(434\) | −8.00000 | + | 6.92820i | −0.384012 | + | 0.332564i | ||||
\(435\) | −9.00000 | + | 5.19615i | −0.431517 | + | 0.249136i | ||||
\(436\) | 3.00000 | − | 1.73205i | 0.143674 | − | 0.0829502i | ||||
\(437\) | − | 48.4974i | − | 2.31995i | ||||||
\(438\) | −6.00000 | + | 3.46410i | −0.286691 | + | 0.165521i | ||||
\(439\) | −3.00000 | − | 1.73205i | −0.143182 | − | 0.0826663i | 0.426698 | − | 0.904394i | \(-0.359677\pi\) |
−0.569880 | + | 0.821728i | \(0.693010\pi\) | |||||||
\(440\) | −9.00000 | − | 5.19615i | −0.429058 | − | 0.247717i | ||||
\(441\) | −3.00000 | + | 20.7846i | −0.142857 | + | 0.989743i | ||||
\(442\) | −10.5000 | + | 2.59808i | −0.499434 | + | 0.123578i | ||||
\(443\) | − | 29.4449i | − | 1.39897i | −0.714648 | − | 0.699484i | \(-0.753413\pi\) | ||
0.714648 | − | 0.699484i | \(-0.246587\pi\) | |||||||
\(444\) | −6.00000 | + | 10.3923i | −0.284747 | + | 0.493197i | ||||
\(445\) | −15.0000 | + | 25.9808i | −0.711068 | + | 1.23161i | ||||
\(446\) | 8.00000 | + | 13.8564i | 0.378811 | + | 0.656120i | ||||
\(447\) | − | 10.3923i | − | 0.491539i | ||||||
\(448\) | 2.50000 | + | 0.866025i | 0.118114 | + | 0.0409159i | ||||
\(449\) | −18.0000 | − | 31.1769i | −0.849473 | − | 1.47133i | −0.881680 | − | 0.471848i | \(-0.843587\pi\) |
0.0322072 | − | 0.999481i | \(-0.489746\pi\) | |||||||
\(450\) | −21.0000 | −0.989949 | ||||||||
\(451\) | 13.5000 | − | 7.79423i | 0.635690 | − | 0.367016i | ||||
\(452\) | 12.0000 | + | 6.92820i | 0.564433 | + | 0.325875i | ||||
\(453\) | 7.50000 | − | 12.9904i | 0.352381 | − | 0.610341i | ||||
\(454\) | − | 10.3923i | − | 0.487735i | ||||||
\(455\) | 3.00000 | − | 32.9090i | 0.140642 | − | 1.54280i | ||||
\(456\) | 12.1244i | 0.567775i | ||||||||
\(457\) | −6.00000 | − | 3.46410i | −0.280668 | − | 0.162044i | 0.353058 | − | 0.935602i | \(-0.385142\pi\) |
−0.633726 | + | 0.773558i | \(0.718475\pi\) | |||||||
\(458\) | −6.50000 | + | 11.2583i | −0.303725 | + | 0.526067i | ||||
\(459\) | 13.5000 | − | 7.79423i | 0.630126 | − | 0.363803i | ||||
\(460\) | −24.0000 | −1.11901 | ||||||||
\(461\) | −27.0000 | + | 15.5885i | −1.25752 | + | 0.726027i | −0.972591 | − | 0.232523i | \(-0.925302\pi\) |
−0.284925 | + | 0.958550i | \(0.591969\pi\) | |||||||
\(462\) | −4.50000 | + | 12.9904i | −0.209359 | + | 0.604367i | ||||
\(463\) | − | 36.3731i | − | 1.69040i | −0.534450 | − | 0.845200i | \(-0.679481\pi\) | ||
0.534450 | − | 0.845200i | \(-0.320519\pi\) | |||||||
\(464\) | 1.50000 | − | 0.866025i | 0.0696358 | − | 0.0402042i | ||||
\(465\) | −12.0000 | + | 20.7846i | −0.556487 | + | 0.963863i | ||||
\(466\) | 6.00000 | + | 3.46410i | 0.277945 | + | 0.160471i | ||||
\(467\) | 6.00000 | 0.277647 | 0.138823 | − | 0.990317i | \(-0.455668\pi\) | ||||
0.138823 | + | 0.990317i | \(0.455668\pi\) | |||||||
\(468\) | 3.00000 | − | 10.3923i | 0.138675 | − | 0.480384i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 15.0000 | − | 25.9808i | 0.691898 | − | 1.19840i | ||||
\(471\) | −12.0000 | + | 20.7846i | −0.552931 | + | 0.957704i | ||||
\(472\) | −9.00000 | + | 5.19615i | −0.414259 | + | 0.239172i | ||||
\(473\) | −24.0000 | −1.10352 | ||||||||
\(474\) | −16.5000 | + | 9.52628i | −0.757870 | + | 0.437557i | ||||
\(475\) | 24.5000 | + | 42.4352i | 1.12414 | + | 1.94706i | ||||
\(476\) | −6.00000 | + | 5.19615i | −0.275010 | + | 0.238165i | ||||
\(477\) | −22.5000 | + | 12.9904i | −1.03020 | + | 0.594789i | ||||
\(478\) | 6.00000 | − | 10.3923i | 0.274434 | − | 0.475333i | ||||
\(479\) | 28.5000 | + | 16.4545i | 1.30220 | + | 0.751825i | 0.980781 | − | 0.195113i | \(-0.0625074\pi\) |
0.321417 | + | 0.946938i | \(0.395841\pi\) | |||||||
\(480\) | 6.00000 | 0.273861 | ||||||||
\(481\) | −24.0000 | − | 6.92820i | −1.09431 | − | 0.315899i | ||||
\(482\) | 10.0000 | 0.455488 | ||||||||
\(483\) | 6.00000 | + | 31.1769i | 0.273009 | + | 1.41860i | ||||
\(484\) | 1.00000 | − | 1.73205i | 0.0454545 | − | 0.0787296i | ||||
\(485\) | 6.00000 | − | 3.46410i | 0.272446 | − | 0.157297i | ||||
\(486\) | 15.5885i | 0.707107i | ||||||||
\(487\) | 7.50000 | − | 4.33013i | 0.339857 | − | 0.196217i | −0.320352 | − | 0.947299i | \(-0.603801\pi\) |
0.660209 | + | 0.751082i | \(0.270468\pi\) | |||||||
\(488\) | −4.50000 | + | 2.59808i | −0.203705 | + | 0.117609i | ||||
\(489\) | 42.0000 | 1.89931 | ||||||||
\(490\) | −9.00000 | − | 22.5167i | −0.406579 | − | 1.01720i | ||||
\(491\) | 9.00000 | + | 5.19615i | 0.406164 | + | 0.234499i | 0.689140 | − | 0.724628i | \(-0.257988\pi\) |
−0.282976 | + | 0.959127i | \(0.591322\pi\) | |||||||
\(492\) | −4.50000 | + | 7.79423i | −0.202876 | + | 0.351391i | ||||
\(493\) | 5.19615i | 0.234023i | ||||||||
\(494\) | −24.5000 | + | 6.06218i | −1.10231 | + | 0.272750i | ||||
\(495\) | 31.1769i | 1.40130i | ||||||||
\(496\) | 2.00000 | − | 3.46410i | 0.0898027 | − | 0.155543i | ||||
\(497\) | 3.00000 | + | 15.5885i | 0.134568 | + | 0.699238i | ||||
\(498\) | 12.0000 | + | 20.7846i | 0.537733 | + | 0.931381i | ||||
\(499\) | 41.5692i | 1.86089i | 0.366427 | + | 0.930447i | \(0.380581\pi\) | ||||
−0.366427 | + | 0.930447i | \(0.619419\pi\) | |||||||
\(500\) | 6.00000 | − | 3.46410i | 0.268328 | − | 0.154919i | ||||
\(501\) | −15.0000 | − | 25.9808i | −0.670151 | − | 1.16073i | ||||
\(502\) | −30.0000 | −1.33897 | ||||||||
\(503\) | 6.00000 | + | 10.3923i | 0.267527 | + | 0.463370i | 0.968223 | − | 0.250090i | \(-0.0804603\pi\) |
−0.700696 | + | 0.713460i | \(0.747127\pi\) | |||||||
\(504\) | −1.50000 | − | 7.79423i | −0.0668153 | − | 0.347183i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 20.7846i | 0.923989i | ||||||||
\(507\) | 22.5000 | + | 0.866025i | 0.999260 | + | 0.0384615i | ||||
\(508\) | −8.00000 | −0.354943 | ||||||||
\(509\) | 24.0000 | + | 13.8564i | 1.06378 | + | 0.614174i | 0.926476 | − | 0.376354i | \(-0.122822\pi\) |
0.137305 | + | 0.990529i | \(0.456156\pi\) | |||||||
\(510\) | −9.00000 | + | 15.5885i | −0.398527 | + | 0.690268i | ||||
\(511\) | −10.0000 | − | 3.46410i | −0.442374 | − | 0.153243i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 31.5000 | − | 18.1865i | 1.39076 | − | 0.802955i | ||||
\(514\) | −13.5000 | − | 23.3827i | −0.595459 | − | 1.03137i | ||||
\(515\) | 12.0000 | 0.528783 | ||||||||
\(516\) | 12.0000 | − | 6.92820i | 0.528271 | − | 0.304997i | ||||
\(517\) | −22.5000 | − | 12.9904i | −0.989549 | − | 0.571316i | ||||
\(518\) | −18.0000 | + | 3.46410i | −0.790875 | + | 0.152204i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.00000 | + | 12.1244i | 0.131559 | + | 0.531688i | ||||
\(521\) | −3.00000 | −0.131432 | −0.0657162 | − | 0.997838i | \(-0.520933\pi\) | ||||
−0.0657162 | + | 0.997838i | \(0.520933\pi\) | |||||||
\(522\) | −4.50000 | − | 2.59808i | −0.196960 | − | 0.113715i | ||||
\(523\) | 28.5000 | + | 16.4545i | 1.24622 | + | 0.719504i | 0.970353 | − | 0.241692i | \(-0.0777024\pi\) |
0.275865 | + | 0.961196i | \(0.411036\pi\) | |||||||
\(524\) | −3.00000 | − | 5.19615i | −0.131056 | − | 0.226995i | ||||
\(525\) | −21.0000 | − | 24.2487i | −0.916515 | − | 1.05830i | ||||
\(526\) | 21.0000 | − | 12.1244i | 0.915644 | − | 0.528647i | ||||
\(527\) | 6.00000 | + | 10.3923i | 0.261364 | + | 0.452696i | ||||
\(528\) | − | 5.19615i | − | 0.226134i | ||||||
\(529\) | 12.5000 | + | 21.6506i | 0.543478 | + | 0.941332i | ||||
\(530\) | 15.0000 | − | 25.9808i | 0.651558 | − | 1.12853i | ||||
\(531\) | 27.0000 | + | 15.5885i | 1.17170 | + | 0.676481i | ||||
\(532\) | −14.0000 | + | 12.1244i | −0.606977 | + | 0.525657i | ||||
\(533\) | −18.0000 | − | 5.19615i | −0.779667 | − | 0.225070i | ||||
\(534\) | −15.0000 | −0.649113 | ||||||||
\(535\) | −9.00000 | + | 15.5885i | −0.389104 | + | 0.673948i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −21.0000 | − | 36.3731i | −0.906217 | − | 1.56961i | ||||
\(538\) | −24.0000 | −1.03471 | ||||||||
\(539\) | −19.5000 | + | 7.79423i | −0.839924 | + | 0.335721i | ||||
\(540\) | −9.00000 | − | 15.5885i | −0.387298 | − | 0.670820i | ||||
\(541\) | − | 31.1769i | − | 1.34040i | −0.742180 | − | 0.670200i | \(-0.766208\pi\) | ||
0.742180 | − | 0.670200i | \(-0.233792\pi\) | |||||||
\(542\) | −4.00000 | − | 6.92820i | −0.171815 | − | 0.297592i | ||||
\(543\) | 1.50000 | − | 2.59808i | 0.0643712 | − | 0.111494i | ||||
\(544\) | 1.50000 | − | 2.59808i | 0.0643120 | − | 0.111392i | ||||
\(545\) | 12.0000 | 0.514024 | ||||||||
\(546\) | 15.0000 | − | 6.92820i | 0.641941 | − | 0.296500i | ||||
\(547\) | 2.00000 | 0.0855138 | 0.0427569 | − | 0.999086i | \(-0.486386\pi\) | ||||
0.0427569 | + | 0.999086i | \(0.486386\pi\) | |||||||
\(548\) | 6.00000 | − | 10.3923i | 0.256307 | − | 0.443937i | ||||
\(549\) | 13.5000 | + | 7.79423i | 0.576166 | + | 0.332650i | ||||
\(550\) | −10.5000 | − | 18.1865i | −0.447722 | − | 0.775476i | ||||
\(551\) | 12.1244i | 0.516515i | ||||||||
\(552\) | −6.00000 | − | 10.3923i | −0.255377 | − | 0.442326i | ||||
\(553\) | −27.5000 | − | 9.52628i | −1.16942 | − | 0.405099i | ||||
\(554\) | 16.0000 | 0.679775 | ||||||||
\(555\) | −36.0000 | + | 20.7846i | −1.52811 | + | 0.882258i | ||||
\(556\) | 4.50000 | + | 2.59808i | 0.190843 | + | 0.110183i | ||||
\(557\) | −1.50000 | + | 2.59808i | −0.0635570 | + | 0.110084i | −0.896053 | − | 0.443947i | \(-0.853578\pi\) |
0.832496 | + | 0.554031i | \(0.186911\pi\) | |||||||
\(558\) | −12.0000 | −0.508001 | ||||||||
\(559\) | 20.0000 | + | 20.7846i | 0.845910 | + | 0.879095i | ||||
\(560\) | 6.00000 | + | 6.92820i | 0.253546 | + | 0.292770i | ||||
\(561\) | 13.5000 | + | 7.79423i | 0.569970 | + | 0.329073i | ||||
\(562\) | 6.00000 | − | 10.3923i | 0.253095 | − | 0.438373i | ||||
\(563\) | −12.0000 | − | 20.7846i | −0.505740 | − | 0.875967i | −0.999978 | − | 0.00664037i | \(-0.997886\pi\) |
0.494238 | − | 0.869326i | \(-0.335447\pi\) | |||||||
\(564\) | 15.0000 | 0.631614 | ||||||||
\(565\) | 24.0000 | + | 41.5692i | 1.00969 | + | 1.74883i | ||||
\(566\) | 3.00000 | − | 1.73205i | 0.126099 | − | 0.0728035i | ||||
\(567\) | −18.0000 | + | 15.5885i | −0.755929 | + | 0.654654i | ||||
\(568\) | −3.00000 | − | 5.19615i | −0.125877 | − | 0.218026i | ||||
\(569\) | −15.0000 | − | 8.66025i | −0.628833 | − | 0.363057i | 0.151467 | − | 0.988462i | \(-0.451600\pi\) |
−0.780300 | + | 0.625406i | \(0.784934\pi\) | |||||||
\(570\) | −21.0000 | + | 36.3731i | −0.879593 | + | 1.52350i | ||||
\(571\) | 40.0000 | 1.67395 | 0.836974 | − | 0.547243i | \(-0.184323\pi\) | ||||
0.836974 | + | 0.547243i | \(0.184323\pi\) | |||||||
\(572\) | 10.5000 | − | 2.59808i | 0.439027 | − | 0.108631i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −13.5000 | + | 2.59808i | −0.563479 | + | 0.108442i | ||||
\(575\) | −42.0000 | − | 24.2487i | −1.75152 | − | 1.01124i | ||||
\(576\) | 1.50000 | + | 2.59808i | 0.0625000 | + | 0.108253i | ||||
\(577\) | 10.0000 | 0.416305 | 0.208153 | − | 0.978096i | \(-0.433255\pi\) | ||||
0.208153 | + | 0.978096i | \(0.433255\pi\) | |||||||
\(578\) | −4.00000 | − | 6.92820i | −0.166378 | − | 0.288175i | ||||
\(579\) | −10.5000 | − | 18.1865i | −0.436365 | − | 0.755807i | ||||
\(580\) | 6.00000 | 0.249136 | ||||||||
\(581\) | −12.0000 | + | 34.6410i | −0.497844 | + | 1.43715i | ||||
\(582\) | 3.00000 | + | 1.73205i | 0.124354 | + | 0.0717958i | ||||
\(583\) | −22.5000 | − | 12.9904i | −0.931855 | − | 0.538007i | ||||
\(584\) | 4.00000 | 0.165521 | ||||||||
\(585\) | 27.0000 | − | 25.9808i | 1.11631 | − | 1.07417i | ||||
\(586\) | 6.92820i | 0.286201i | ||||||||
\(587\) | −15.0000 | − | 8.66025i | −0.619116 | − | 0.357447i | 0.157409 | − | 0.987534i | \(-0.449686\pi\) |
−0.776525 | + | 0.630087i | \(0.783019\pi\) | |||||||
\(588\) | 7.50000 | − | 9.52628i | 0.309295 | − | 0.392857i | ||||
\(589\) | 14.0000 | + | 24.2487i | 0.576860 | + | 0.999151i | ||||
\(590\) | −36.0000 | −1.48210 | ||||||||
\(591\) | 40.5000 | − | 23.3827i | 1.66595 | − | 0.961835i | ||||
\(592\) | 6.00000 | − | 3.46410i | 0.246598 | − | 0.142374i | ||||
\(593\) | 8.66025i | 0.355634i | 0.984064 | + | 0.177817i | \(0.0569035\pi\) | ||||
−0.984064 | + | 0.177817i | \(0.943096\pi\) | |||||||
\(594\) | −13.5000 | + | 7.79423i | −0.553912 | + | 0.319801i | ||||
\(595\) | −27.0000 | + | 5.19615i | −1.10689 | + | 0.213021i | ||||
\(596\) | −3.00000 | + | 5.19615i | −0.122885 | + | 0.212843i | ||||
\(597\) | −18.0000 | −0.736691 | ||||||||
\(598\) | 18.0000 | − | 17.3205i | 0.736075 | − | 0.708288i | ||||
\(599\) | − | 3.46410i | − | 0.141539i | −0.997493 | − | 0.0707697i | \(-0.977454\pi\) | ||
0.997493 | − | 0.0707697i | \(-0.0225455\pi\) | |||||||
\(600\) | 10.5000 | + | 6.06218i | 0.428661 | + | 0.247487i | ||||
\(601\) | −27.0000 | − | 15.5885i | −1.10135 | − | 0.635866i | −0.164777 | − | 0.986331i | \(-0.552690\pi\) |
−0.936576 | + | 0.350464i | \(0.886024\pi\) | |||||||
\(602\) | 20.0000 | + | 6.92820i | 0.815139 | + | 0.282372i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7.50000 | + | 4.33013i | −0.305171 | + | 0.176190i | ||||
\(605\) | 6.00000 | − | 3.46410i | 0.243935 | − | 0.140836i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.00000 | + | 3.46410i | −0.243532 | + | 0.140604i | −0.616799 | − | 0.787121i | \(-0.711571\pi\) |
0.373267 | + | 0.927724i | \(0.378238\pi\) | |||||||
\(608\) | 3.50000 | − | 6.06218i | 0.141944 | − | 0.245854i | ||||
\(609\) | −1.50000 | − | 7.79423i | −0.0607831 | − | 0.315838i | ||||
\(610\) | −18.0000 | −0.728799 | ||||||||
\(611\) | 7.50000 | + | 30.3109i | 0.303418 | + | 1.22625i | ||||
\(612\) | −9.00000 | −0.363803 | ||||||||
\(613\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(614\) | −3.50000 | + | 6.06218i | −0.141249 | + | 0.244650i | ||||
\(615\) | −27.0000 | + | 15.5885i | −1.08875 | + | 0.628587i | ||||
\(616\) | 6.00000 | − | 5.19615i | 0.241747 | − | 0.209359i | ||||
\(617\) | 3.00000 | + | 5.19615i | 0.120775 | + | 0.209189i | 0.920074 | − | 0.391745i | \(-0.128129\pi\) |
−0.799298 | + | 0.600935i | \(0.794795\pi\) | |||||||
\(618\) | 3.00000 | + | 5.19615i | 0.120678 | + | 0.209020i | ||||
\(619\) | 31.0000 | 1.24600 | 0.622998 | − | 0.782224i | \(-0.285915\pi\) | ||||
0.622998 | + | 0.782224i | \(0.285915\pi\) | |||||||
\(620\) | 12.0000 | − | 6.92820i | 0.481932 | − | 0.278243i | ||||
\(621\) | −18.0000 | + | 31.1769i | −0.722315 | + | 1.25109i | ||||
\(622\) | −1.50000 | + | 2.59808i | −0.0601445 | + | 0.104173i | ||||
\(623\) | −15.0000 | − | 17.3205i | −0.600962 | − | 0.693932i | ||||
\(624\) | −4.50000 | + | 4.33013i | −0.180144 | + | 0.173344i | ||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | −18.0000 | − | 10.3923i | −0.719425 | − | 0.415360i | ||||
\(627\) | 31.5000 | + | 18.1865i | 1.25799 | + | 0.726300i | ||||
\(628\) | 12.0000 | − | 6.92820i | 0.478852 | − | 0.276465i | ||||
\(629\) | 20.7846i | 0.828737i | ||||||||
\(630\) | 9.00000 | − | 25.9808i | 0.358569 | − | 1.03510i | ||||
\(631\) | −40.5000 | + | 23.3827i | −1.61228 | + | 0.930850i | −0.623439 | + | 0.781872i | \(0.714265\pi\) |
−0.988841 | + | 0.148978i | \(0.952402\pi\) | |||||||
\(632\) | 11.0000 | 0.437557 | ||||||||
\(633\) | 33.0000 | − | 19.0526i | 1.31163 | − | 0.757271i | ||||
\(634\) | 9.00000 | − | 15.5885i | 0.357436 | − | 0.619097i | ||||
\(635\) | −24.0000 | − | 13.8564i | −0.952411 | − | 0.549875i | ||||
\(636\) | 15.0000 | 0.594789 | ||||||||
\(637\) | 23.0000 | + | 10.3923i | 0.911293 | + | 0.411758i | ||||
\(638\) | − | 5.19615i | − | 0.205718i | ||||||
\(639\) | −9.00000 | + | 15.5885i | −0.356034 | + | 0.616670i | ||||
\(640\) | −3.00000 | − | 1.73205i | −0.118585 | − | 0.0684653i | ||||
\(641\) | 3.00000 | − | 1.73205i | 0.118493 | − | 0.0684119i | −0.439582 | − | 0.898202i | \(-0.644873\pi\) |
0.558075 | + | 0.829790i | \(0.311540\pi\) | |||||||
\(642\) | −9.00000 | −0.355202 | ||||||||
\(643\) | −23.5000 | − | 40.7032i | −0.926750 | − | 1.60518i | −0.788723 | − | 0.614749i | \(-0.789257\pi\) |
−0.138027 | − | 0.990429i | \(-0.544076\pi\) | |||||||
\(644\) | 6.00000 | − | 17.3205i | 0.236433 | − | 0.682524i | ||||
\(645\) | 48.0000 | 1.89000 | ||||||||
\(646\) | 10.5000 | + | 18.1865i | 0.413117 | + | 0.715540i | ||||
\(647\) | 10.5000 | − | 18.1865i | 0.412798 | − | 0.714986i | −0.582397 | − | 0.812905i | \(-0.697885\pi\) |
0.995194 | + | 0.0979182i | \(0.0312184\pi\) | |||||||
\(648\) | 4.50000 | − | 7.79423i | 0.176777 | − | 0.306186i | ||||
\(649\) | 31.1769i | 1.22380i | ||||||||
\(650\) | −7.00000 | + | 24.2487i | −0.274563 | + | 0.951113i | ||||
\(651\) | −12.0000 | − | 13.8564i | −0.470317 | − | 0.543075i | ||||
\(652\) | −21.0000 | − | 12.1244i | −0.822423 | − | 0.474826i | ||||
\(653\) | −4.50000 | − | 2.59808i | −0.176099 | − | 0.101671i | 0.409360 | − | 0.912373i | \(-0.365752\pi\) |
−0.585458 | + | 0.810702i | \(0.699085\pi\) | |||||||
\(654\) | 3.00000 | + | 5.19615i | 0.117309 | + | 0.203186i | ||||
\(655\) | − | 20.7846i | − | 0.812122i | ||||||
\(656\) | 4.50000 | − | 2.59808i | 0.175695 | − | 0.101438i | ||||
\(657\) | −6.00000 | − | 10.3923i | −0.234082 | − | 0.405442i | ||||
\(658\) | 15.0000 | + | 17.3205i | 0.584761 | + | 0.675224i | ||||
\(659\) | −1.50000 | + | 0.866025i | −0.0584317 | + | 0.0337356i | −0.528931 | − | 0.848665i | \(-0.677407\pi\) |
0.470500 | + | 0.882400i | \(0.344074\pi\) | |||||||
\(660\) | 9.00000 | − | 15.5885i | 0.350325 | − | 0.606780i | ||||
\(661\) | −7.00000 | + | 12.1244i | −0.272268 | + | 0.471583i | −0.969442 | − | 0.245319i | \(-0.921107\pi\) |
0.697174 | + | 0.716902i | \(0.254441\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.50000 | − | 18.1865i | −0.174766 | − | 0.706306i | ||||
\(664\) | − | 13.8564i | − | 0.537733i | ||||||
\(665\) | −63.0000 | + | 12.1244i | −2.44304 | + | 0.470162i | ||||
\(666\) | −18.0000 | − | 10.3923i | −0.697486 | − | 0.402694i | ||||
\(667\) | −6.00000 | − | 10.3923i | −0.232321 | − | 0.402392i | ||||
\(668\) | 17.3205i | 0.670151i | ||||||||
\(669\) | −24.0000 | + | 13.8564i | −0.927894 | + | 0.535720i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.5885i | 0.601786i | ||||||||
\(672\) | −1.50000 | + | 4.33013i | −0.0578638 | + | 0.167038i | ||||
\(673\) | 14.5000 | − | 25.1147i | 0.558934 | − | 0.968102i | −0.438652 | − | 0.898657i | \(-0.644544\pi\) |
0.997586 | − | 0.0694449i | \(-0.0221228\pi\) | |||||||
\(674\) | −9.50000 | + | 16.4545i | −0.365926 | + | 0.633803i | ||||
\(675\) | − | 36.3731i | − | 1.40000i | ||||||
\(676\) | −11.0000 | − | 6.92820i | −0.423077 | − | 0.266469i | ||||
\(677\) | 6.00000 | 0.230599 | 0.115299 | − | 0.993331i | \(-0.463217\pi\) | ||||
0.115299 | + | 0.993331i | \(0.463217\pi\) | |||||||
\(678\) | −12.0000 | + | 20.7846i | −0.460857 | + | 0.798228i | ||||
\(679\) | 1.00000 | + | 5.19615i | 0.0383765 | + | 0.199410i | ||||
\(680\) | 9.00000 | − | 5.19615i | 0.345134 | − | 0.199263i | ||||
\(681\) | 18.0000 | 0.689761 | ||||||||
\(682\) | −6.00000 | − | 10.3923i | −0.229752 | − | 0.397942i | ||||
\(683\) | 6.00000 | + | 10.3923i | 0.229584 | + | 0.397650i | 0.957685 | − | 0.287819i | \(-0.0929302\pi\) |
−0.728101 | + | 0.685470i | \(0.759597\pi\) | |||||||
\(684\) | −21.0000 | −0.802955 | ||||||||
\(685\) | 36.0000 | − | 20.7846i | 1.37549 | − | 0.794139i | ||||
\(686\) | 18.5000 | − | 0.866025i | 0.706333 | − | 0.0330650i | ||||
\(687\) | −19.5000 | − | 11.2583i | −0.743971 | − | 0.429532i | ||||
\(688\) | −8.00000 | −0.304997 | ||||||||
\(689\) | 7.50000 | + | 30.3109i | 0.285727 | + | 1.15475i | ||||
\(690\) | − | 41.5692i | − | 1.58251i | ||||||
\(691\) | 4.00000 | − | 6.92820i | 0.152167 | − | 0.263561i | −0.779857 | − | 0.625958i | \(-0.784708\pi\) |
0.932024 | + | 0.362397i | \(0.118041\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −22.5000 | − | 7.79423i | −0.854704 | − | 0.296078i | ||||
\(694\) | − | 15.5885i | − | 0.591730i | ||||||
\(695\) | 9.00000 | + | 15.5885i | 0.341389 | + | 0.591304i | ||||
\(696\) | 1.50000 | + | 2.59808i | 0.0568574 | + | 0.0984798i | ||||
\(697\) | 15.5885i | 0.590455i | ||||||||
\(698\) | 1.00000 | + | 1.73205i | 0.0378506 | + | 0.0655591i | ||||
\(699\) | −6.00000 | + | 10.3923i | −0.226941 | + | 0.393073i | ||||
\(700\) | 3.50000 | + | 18.1865i | 0.132288 | + | 0.687386i | ||||
\(701\) | 12.1244i | 0.457931i | 0.973435 | + | 0.228965i | \(0.0735342\pi\) | ||||
−0.973435 | + | 0.228965i | \(0.926466\pi\) | |||||||
\(702\) | 18.0000 | + | 5.19615i | 0.679366 | + | 0.196116i | ||||
\(703\) | 48.4974i | 1.82911i | ||||||||
\(704\) | −1.50000 | + | 2.59808i | −0.0565334 | + | 0.0979187i | ||||
\(705\) | 45.0000 | + | 25.9808i | 1.69480 | + | 0.978492i | ||||
\(706\) | 18.0000 | − | 10.3923i | 0.677439 | − | 0.391120i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −9.00000 | − | 15.5885i | −0.338241 | − | 0.585850i | ||||
\(709\) | 21.0000 | − | 12.1244i | 0.788672 | − | 0.455340i | −0.0508231 | − | 0.998708i | \(-0.516184\pi\) |
0.839495 | + | 0.543368i | \(0.182851\pi\) | |||||||
\(710\) | − | 20.7846i | − | 0.780033i | ||||||
\(711\) | −16.5000 | − | 28.5788i | −0.618798 | − | 1.07179i | ||||
\(712\) | 7.50000 | + | 4.33013i | 0.281074 | + | 0.162278i | ||||
\(713\) | −24.0000 | − | 13.8564i | −0.898807 | − | 0.518927i | ||||
\(714\) | −9.00000 | − | 10.3923i | −0.336817 | − | 0.388922i | ||||
\(715\) | 36.0000 | + | 10.3923i | 1.34632 | + | 0.388650i | ||||
\(716\) | 24.2487i | 0.906217i | ||||||||
\(717\) | 18.0000 | + | 10.3923i | 0.672222 | + | 0.388108i | ||||
\(718\) | −12.0000 | + | 20.7846i | −0.447836 | + | 0.775675i | ||||
\(719\) | 10.5000 | + | 18.1865i | 0.391584 | + | 0.678243i | 0.992659 | − | 0.120950i | \(-0.0385939\pi\) |
−0.601075 | + | 0.799193i | \(0.705261\pi\) | |||||||
\(720\) | 10.3923i | 0.387298i | ||||||||
\(721\) | −3.00000 | + | 8.66025i | −0.111726 | + | 0.322525i | ||||
\(722\) | 15.0000 | + | 25.9808i | 0.558242 | + | 0.966904i | ||||
\(723\) | 17.3205i | 0.644157i | ||||||||
\(724\) | −1.50000 | + | 0.866025i | −0.0557471 | + | 0.0321856i | ||||
\(725\) | 10.5000 | + | 6.06218i | 0.389960 | + | 0.225144i | ||||
\(726\) | 3.00000 | + | 1.73205i | 0.111340 | + | 0.0642824i | ||||
\(727\) | 34.6410i | 1.28476i | 0.766385 | + | 0.642382i | \(0.222054\pi\) | ||||
−0.766385 | + | 0.642382i | \(0.777946\pi\) | |||||||
\(728\) | −9.50000 | − | 0.866025i | −0.352093 | − | 0.0320970i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 12.0000 | + | 6.92820i | 0.444140 | + | 0.256424i | ||||
\(731\) | 12.0000 | − | 20.7846i | 0.443836 | − | 0.768747i | ||||
\(732\) | −4.50000 | − | 7.79423i | −0.166325 | − | 0.288083i | ||||
\(733\) | −13.0000 | −0.480166 | −0.240083 | − | 0.970752i | \(-0.577175\pi\) | ||||
−0.240083 | + | 0.970752i | \(0.577175\pi\) | |||||||
\(734\) | −18.0000 | + | 10.3923i | −0.664392 | + | 0.383587i | ||||
\(735\) | 39.0000 | − | 15.5885i | 1.43854 | − | 0.574989i | ||||
\(736\) | 6.92820i | 0.255377i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −13.5000 | − | 7.79423i | −0.496942 | − | 0.286910i | ||||
\(739\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(740\) | 24.0000 | 0.882258 | ||||||||
\(741\) | −10.5000 | − | 42.4352i | −0.385727 | − | 1.55890i | ||||
\(742\) | 15.0000 | + | 17.3205i | 0.550667 | + | 0.635856i | ||||
\(743\) | 3.00000 | − | 5.19615i | 0.110059 | − | 0.190628i | −0.805735 | − | 0.592277i | \(-0.798229\pi\) |
0.915794 | + | 0.401648i | \(0.131563\pi\) | |||||||
\(744\) | 6.00000 | + | 3.46410i | 0.219971 | + | 0.127000i | ||||
\(745\) | −18.0000 | + | 10.3923i | −0.659469 | + | 0.380745i | ||||
\(746\) | 20.0000 | 0.732252 | ||||||||
\(747\) | −36.0000 | + | 20.7846i | −1.31717 | + | 0.760469i | ||||
\(748\) | −4.50000 | − | 7.79423i | −0.164536 | − | 0.284985i | ||||
\(749\) | −9.00000 | − | 10.3923i | −0.328853 | − | 0.379727i | ||||
\(750\) | 6.00000 | + | 10.3923i | 0.219089 | + | 0.379473i | ||||
\(751\) | −15.5000 | + | 26.8468i | −0.565603 | + | 0.979653i | 0.431390 | + | 0.902165i | \(0.358023\pi\) |
−0.996993 | + | 0.0774878i | \(0.975310\pi\) | |||||||
\(752\) | −7.50000 | − | 4.33013i | −0.273497 | − | 0.157903i | ||||
\(753\) | − | 51.9615i | − | 1.89358i | ||||||
\(754\) | −4.50000 | + | 4.33013i | −0.163880 | + | 0.157694i | ||||
\(755\) | −30.0000 | −1.09181 | ||||||||
\(756\) | 13.5000 | − | 2.59808i | 0.490990 | − | 0.0944911i | ||||
\(757\) | −10.0000 | + | 17.3205i | −0.363456 | + | 0.629525i | −0.988527 | − | 0.151043i | \(-0.951737\pi\) |
0.625071 | + | 0.780568i | \(0.285070\pi\) | |||||||
\(758\) | −9.00000 | + | 5.19615i | −0.326895 | + | 0.188733i | ||||
\(759\) | −36.0000 | −1.30672 | ||||||||
\(760\) | 21.0000 | − | 12.1244i | 0.761750 | − | 0.439797i | ||||
\(761\) | 6.00000 | − | 3.46410i | 0.217500 | − | 0.125574i | −0.387292 | − | 0.921957i | \(-0.626590\pi\) |
0.604792 | + | 0.796383i | \(0.293256\pi\) | |||||||
\(762\) | − | 13.8564i | − | 0.501965i | ||||||
\(763\) | −3.00000 | + | 8.66025i | −0.108607 | + | 0.313522i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −27.0000 | − | 15.5885i | −0.976187 | − | 0.563602i | ||||
\(766\) | 5.19615i | 0.187745i | ||||||||
\(767\) | 27.0000 | − | 25.9808i | 0.974913 | − | 0.938111i | ||||
\(768\) | − | 1.73205i | − | 0.0625000i | ||||||
\(769\) | 20.0000 | − | 34.6410i | 0.721218 | − | 1.24919i | −0.239293 | − | 0.970947i | \(-0.576916\pi\) |
0.960512 | − | 0.278240i | \(-0.0897509\pi\) | |||||||
\(770\) | 27.0000 | − | 5.19615i | 0.973012 | − | 0.187256i | ||||
\(771\) | 40.5000 | − | 23.3827i | 1.45857 | − | 0.842107i | ||||
\(772\) | 12.1244i | 0.436365i | ||||||||
\(773\) | 9.00000 | − | 5.19615i | 0.323708 | − | 0.186893i | −0.329336 | − | 0.944213i | \(-0.606825\pi\) |
0.653044 | + | 0.757320i | \(0.273492\pi\) | |||||||
\(774\) | 12.0000 | + | 20.7846i | 0.431331 | + | 0.747087i | ||||
\(775\) | 28.0000 | 1.00579 | ||||||||
\(776\) | −1.00000 | − | 1.73205i | −0.0358979 | − | 0.0621770i | ||||
\(777\) | −6.00000 | − | 31.1769i | −0.215249 | − | 1.11847i | ||||
\(778\) | 18.0000 | + | 10.3923i | 0.645331 | + | 0.372582i | ||||
\(779\) | 36.3731i | 1.30320i | ||||||||
\(780\) | −21.0000 | + | 5.19615i | −0.751921 | + | 0.186052i | ||||
\(781\) | −18.0000 | −0.644091 | ||||||||
\(782\) | −18.0000 | − | 10.3923i | −0.643679 | − | 0.371628i | ||||
\(783\) | 4.50000 | − | 7.79423i | 0.160817 | − | 0.278543i | ||||
\(784\) | −6.50000 | + | 2.59808i | −0.232143 | + | 0.0927884i | ||||
\(785\) | 48.0000 | 1.71319 | ||||||||
\(786\) | 9.00000 | − | 5.19615i | 0.321019 | − | 0.185341i | ||||
\(787\) | 8.50000 | + | 14.7224i | 0.302992 | + | 0.524798i | 0.976812 | − | 0.214097i | \(-0.0686810\pi\) |
−0.673820 | + | 0.738896i | \(0.735348\pi\) | |||||||
\(788\) | −27.0000 | −0.961835 | ||||||||
\(789\) | 21.0000 | + | 36.3731i | 0.747620 | + | 1.29492i | ||||
\(790\) | 33.0000 | + | 19.0526i | 1.17409 | + | 0.677860i | ||||
\(791\) | −36.0000 | + | 6.92820i | −1.28001 | + | 0.246339i | ||||
\(792\) | 9.00000 | 0.319801 | ||||||||
\(793\) | 13.5000 | − | 12.9904i | 0.479399 | − | 0.461302i | ||||
\(794\) | −7.00000 | −0.248421 | ||||||||
\(795\) | 45.0000 | + | 25.9808i | 1.59599 | + | 0.921443i | ||||
\(796\) | 9.00000 | + | 5.19615i | 0.318997 | + | 0.184173i | ||||
\(797\) | 6.00000 | + | 10.3923i | 0.212531 | + | 0.368114i | 0.952506 | − | 0.304520i | \(-0.0984960\pi\) |
−0.739975 | + | 0.672634i | \(0.765163\pi\) | |||||||
\(798\) | −21.0000 | − | 24.2487i | −0.743392 | − | 0.858395i | ||||
\(799\) | 22.5000 | − | 12.9904i | 0.795993 | − | 0.459567i | ||||
\(800\) | −3.50000 | − | 6.06218i | −0.123744 | − | 0.214330i | ||||
\(801\) | − | 25.9808i | − | 0.917985i | ||||||
\(802\) | 9.00000 | + | 15.5885i | 0.317801 | + | 0.550448i | ||||
\(803\) | 6.00000 | − | 10.3923i | 0.211735 | − | 0.366736i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 48.0000 | − | 41.5692i | 1.69178 | − | 1.46512i | ||||
\(806\) | −4.00000 | + | 13.8564i | −0.140894 | + | 0.488071i | ||||
\(807\) | − | 41.5692i | − | 1.46331i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 42.0000 | + | 24.2487i | 1.47664 | + | 0.852539i | 0.999652 | − | 0.0263699i | \(-0.00839478\pi\) |
0.476989 | + | 0.878909i | \(0.341728\pi\) | |||||||
\(810\) | 27.0000 | − | 15.5885i | 0.948683 | − | 0.547723i | ||||
\(811\) | −28.0000 | −0.983213 | −0.491606 | − | 0.870817i | \(-0.663590\pi\) | ||||
−0.491606 | + | 0.870817i | \(0.663590\pi\) | |||||||
\(812\) | −1.50000 | + | 4.33013i | −0.0526397 | + | 0.151958i | ||||
\(813\) | 12.0000 | − | 6.92820i | 0.420858 | − | 0.242983i | ||||
\(814\) | − | 20.7846i | − | 0.728500i | ||||||
\(815\) | −42.0000 | − | 72.7461i | −1.47120 | − | 2.54819i | ||||
\(816\) | 4.50000 | + | 2.59808i | 0.157532 | + | 0.0909509i | ||||
\(817\) | 28.0000 | − | 48.4974i | 0.979596 | − | 1.69671i | ||||
\(818\) | −4.00000 | −0.139857 | ||||||||
\(819\) | 12.0000 | + | 25.9808i | 0.419314 | + | 0.907841i | ||||
\(820\) | 18.0000 | 0.628587 | ||||||||
\(821\) | 1.50000 | − | 2.59808i | 0.0523504 | − | 0.0906735i | −0.838663 | − | 0.544651i | \(-0.816662\pi\) |
0.891013 | + | 0.453978i | \(0.149995\pi\) | |||||||
\(822\) | 18.0000 | + | 10.3923i | 0.627822 | + | 0.362473i | ||||
\(823\) | 8.00000 | + | 13.8564i | 0.278862 | + | 0.483004i | 0.971102 | − | 0.238664i | \(-0.0767093\pi\) |
−0.692240 | + | 0.721668i | \(0.743376\pi\) | |||||||
\(824\) | − | 3.46410i | − | 0.120678i | ||||||
\(825\) | 31.5000 | − | 18.1865i | 1.09669 | − | 0.633174i | ||||
\(826\) | 9.00000 | − | 25.9808i | 0.313150 | − | 0.903986i | ||||
\(827\) | 12.0000 | 0.417281 | 0.208640 | − | 0.977992i | \(-0.433096\pi\) | ||||
0.208640 | + | 0.977992i | \(0.433096\pi\) | |||||||
\(828\) | 18.0000 | − | 10.3923i | 0.625543 | − | 0.361158i | ||||
\(829\) | 13.5000 | + | 7.79423i | 0.468874 | + | 0.270705i | 0.715768 | − | 0.698338i | \(-0.246077\pi\) |
−0.246894 | + | 0.969042i | \(0.579410\pi\) | |||||||
\(830\) | 24.0000 | − | 41.5692i | 0.833052 | − | 1.44289i | ||||
\(831\) | 27.7128i | 0.961347i | ||||||||
\(832\) | 3.50000 | − | 0.866025i | 0.121341 | − | 0.0300240i | ||||
\(833\) | 3.00000 | − | 20.7846i | 0.103944 | − | 0.720144i | ||||
\(834\) | −4.50000 | + | 7.79423i | −0.155822 | + | 0.269892i | ||||
\(835\) | −30.0000 | + | 51.9615i | −1.03819 | + | 1.79820i | ||||
\(836\) | −10.5000 | − | 18.1865i | −0.363150 | − | 0.628994i | ||||
\(837\) | − | 20.7846i | − | 0.718421i | ||||||
\(838\) | 6.00000 | + | 10.3923i | 0.207267 | + | 0.358996i | ||||
\(839\) | −27.0000 | + | 15.5885i | −0.932144 | + | 0.538173i | −0.887489 | − | 0.460829i | \(-0.847552\pi\) |
−0.0446547 | + | 0.999002i | \(0.514219\pi\) | |||||||
\(840\) | −12.0000 | + | 10.3923i | −0.414039 | + | 0.358569i | ||||
\(841\) | −13.0000 | − | 22.5167i | −0.448276 | − | 0.776437i | ||||
\(842\) | −21.0000 | − | 12.1244i | −0.723708 | − | 0.417833i | ||||
\(843\) | 18.0000 | + | 10.3923i | 0.619953 | + | 0.357930i | ||||
\(844\) | −22.0000 | −0.757271 | ||||||||
\(845\) | −21.0000 | − | 39.8372i | −0.722422 | − | 1.37044i | ||||
\(846\) | 25.9808i | 0.893237i | ||||||||
\(847\) | 1.00000 | + | 5.19615i | 0.0343604 | + | 0.178542i | ||||
\(848\) | −7.50000 | − | 4.33013i | −0.257551 | − | 0.148697i | ||||
\(849\) | 3.00000 | + | 5.19615i | 0.102960 | + | 0.178331i | ||||
\(850\) | 21.0000 | 0.720294 | ||||||||
\(851\) | −24.0000 | − | 41.5692i | −0.822709 | − | 1.42497i | ||||
\(852\) | 9.00000 | − | 5.19615i | 0.308335 | − | 0.178017i | ||||
\(853\) | −35.0000 | −1.19838 | −0.599189 | − | 0.800608i | \(-0.704510\pi\) | ||||
−0.599189 | + | 0.800608i | \(0.704510\pi\) | |||||||
\(854\) | 4.50000 | − | 12.9904i | 0.153987 | − | 0.444522i | ||||
\(855\) | −63.0000 | − | 36.3731i | −2.15455 | − | 1.24393i | ||||
\(856\) | 4.50000 | + | 2.59808i | 0.153807 | + | 0.0888004i | ||||
\(857\) | 18.0000 | 0.614868 | 0.307434 | − | 0.951569i | \(-0.400530\pi\) | ||||
0.307434 | + | 0.951569i | \(0.400530\pi\) | |||||||
\(858\) | 4.50000 | + | 18.1865i | 0.153627 | + | 0.620878i | ||||
\(859\) | 39.8372i | 1.35923i | 0.733571 | + | 0.679613i | \(0.237852\pi\) | ||||
−0.733571 | + | 0.679613i | \(0.762148\pi\) | |||||||
\(860\) | −24.0000 | − | 13.8564i | −0.818393 | − | 0.472500i | ||||
\(861\) | −4.50000 | − | 23.3827i | −0.153360 | − | 0.796880i | ||||
\(862\) | −9.00000 | − | 15.5885i | −0.306541 | − | 0.530945i | ||||
\(863\) | −24.0000 | −0.816970 | −0.408485 | − | 0.912765i | \(-0.633943\pi\) | ||||
−0.408485 | + | 0.912765i | \(0.633943\pi\) | |||||||
\(864\) | −4.50000 | + | 2.59808i | −0.153093 | + | 0.0883883i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 17.3205i | 0.588575i | ||||||||
\(867\) | 12.0000 | − | 6.92820i | 0.407541 | − | 0.235294i | ||||
\(868\) | 2.00000 | + | 10.3923i | 0.0678844 | + | 0.352738i | ||||
\(869\) | 16.5000 | − | 28.5788i | 0.559724 | − | 0.969471i | ||||
\(870\) | 10.3923i | 0.352332i | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | − | 3.46410i | − | 0.117309i | ||||||
\(873\) | −3.00000 | + | 5.19615i | −0.101535 | + | 0.175863i | ||||
\(874\) | −42.0000 | − | 24.2487i | −1.42067 | − | 0.820225i | ||||
\(875\) | −6.00000 | + | 17.3205i | −0.202837 | + | 0.585540i | ||||
\(876\) | 6.92820i | 0.234082i | ||||||||
\(877\) | 21.0000 | − | 12.1244i | 0.709120 | − | 0.409410i | −0.101615 | − | 0.994824i | \(-0.532401\pi\) |
0.810735 | + | 0.585413i | \(0.199068\pi\) | |||||||
\(878\) | −3.00000 | + | 1.73205i | −0.101245 | + | 0.0584539i | ||||
\(879\) | −12.0000 | −0.404750 | ||||||||
\(880\) | −9.00000 | + | 5.19615i | −0.303390 | + | 0.175162i | ||||
\(881\) | 15.0000 | − | 25.9808i | 0.505363 | − | 0.875314i | −0.494618 | − | 0.869111i | \(-0.664692\pi\) |
0.999981 | − | 0.00620358i | \(-0.00197467\pi\) | |||||||
\(882\) | 16.5000 | + | 12.9904i | 0.555584 | + | 0.437409i | ||||
\(883\) | 2.00000 | 0.0673054 | 0.0336527 | − | 0.999434i | \(-0.489286\pi\) | ||||
0.0336527 | + | 0.999434i | \(0.489286\pi\) | |||||||
\(884\) | −3.00000 | + | 10.3923i | −0.100901 | + | 0.349531i | ||||
\(885\) | − | 62.3538i | − | 2.09600i | ||||||
\(886\) | −25.5000 | − | 14.7224i | −0.856689 | − | 0.494610i | ||||
\(887\) | 13.5000 | − | 23.3827i | 0.453286 | − | 0.785114i | −0.545302 | − | 0.838240i | \(-0.683585\pi\) |
0.998588 | + | 0.0531258i | \(0.0169184\pi\) | |||||||
\(888\) | 6.00000 | + | 10.3923i | 0.201347 | + | 0.348743i | ||||
\(889\) | 16.0000 | − | 13.8564i | 0.536623 | − | 0.464729i | ||||
\(890\) | 15.0000 | + | 25.9808i | 0.502801 | + | 0.870877i | ||||
\(891\) | −13.5000 | − | 23.3827i | −0.452267 | − | 0.783349i | ||||
\(892\) | 16.0000 | 0.535720 | ||||||||
\(893\) | 52.5000 | − | 30.3109i | 1.75685 | − | 1.01432i | ||||
\(894\) | −9.00000 | − | 5.19615i | −0.301005 | − | 0.173785i | ||||
\(895\) | −42.0000 | + | 72.7461i | −1.40391 | + | 2.43164i | ||||
\(896\) | 2.00000 | − | 1.73205i | 0.0668153 | − | 0.0578638i | ||||
\(897\) | 30.0000 | + | 31.1769i | 1.00167 | + | 1.04097i | ||||
\(898\) | −36.0000 | −1.20134 | ||||||||
\(899\) | 6.00000 | + | 3.46410i | 0.200111 | + | 0.115534i | ||||
\(900\) | −10.5000 | + | 18.1865i | −0.350000 | + | 0.606218i | ||||
\(901\) | 22.5000 | − | 12.9904i | 0.749584 | − | 0.432772i | ||||
\(902\) | − | 15.5885i | − | 0.519039i | ||||||
\(903\) | −12.0000 | + | 34.6410i | −0.399335 | + | 1.15278i | ||||
\(904\) | 12.0000 | − | 6.92820i | 0.399114 | − | 0.230429i | ||||
\(905\) | −6.00000 | −0.199447 | ||||||||
\(906\) | −7.50000 | − | 12.9904i | −0.249171 | − | 0.431577i | ||||
\(907\) | 5.00000 | − | 8.66025i | 0.166022 | − | 0.287559i | −0.770996 | − | 0.636841i | \(-0.780241\pi\) |
0.937018 | + | 0.349281i | \(0.113574\pi\) | |||||||
\(908\) | −9.00000 | − | 5.19615i | −0.298675 | − | 0.172440i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −27.0000 | − | 19.0526i | −0.895041 | − | 0.631586i | ||||
\(911\) | 48.4974i | 1.60679i | 0.595446 | + | 0.803396i | \(0.296976\pi\) | ||||
−0.595446 | + | 0.803396i | \(0.703024\pi\) | |||||||
\(912\) | 10.5000 | + | 6.06218i | 0.347690 | + | 0.200739i | ||||
\(913\) | −36.0000 | − | 20.7846i | −1.19143 | − | 0.687870i | ||||
\(914\) | −6.00000 | + | 3.46410i | −0.198462 | + | 0.114582i | ||||
\(915\) | − | 31.1769i | − | 1.03068i | ||||||
\(916\) | 6.50000 | + | 11.2583i | 0.214766 | + | 0.371986i | ||||
\(917\) | 15.0000 | + | 5.19615i | 0.495344 | + | 0.171592i | ||||
\(918\) | − | 15.5885i | − | 0.514496i | ||||||
\(919\) | −14.5000 | − | 25.1147i | −0.478311 | − | 0.828459i | 0.521380 | − | 0.853325i | \(-0.325417\pi\) |
−0.999691 | + | 0.0248659i | \(0.992084\pi\) | |||||||
\(920\) | −12.0000 | + | 20.7846i | −0.395628 | + | 0.685248i | ||||
\(921\) | −10.5000 | − | 6.06218i | −0.345987 | − | 0.199756i | ||||
\(922\) | 31.1769i | 1.02676i | ||||||||
\(923\) | 15.0000 | + | 15.5885i | 0.493731 | + | 0.513100i | ||||
\(924\) | 9.00000 | + | 10.3923i | 0.296078 | + | 0.341882i | ||||
\(925\) | 42.0000 | + | 24.2487i | 1.38095 | + | 0.797293i | ||||
\(926\) | −31.5000 | − | 18.1865i | −1.03515 | − | 0.597647i | ||||
\(927\) | −9.00000 | + | 5.19615i | −0.295599 | + | 0.170664i | ||||
\(928\) | − | 1.73205i | − | 0.0568574i | ||||||
\(929\) | −25.5000 | + | 14.7224i | −0.836628 | + | 0.483027i | −0.856117 | − | 0.516783i | \(-0.827129\pi\) |
0.0194887 | + | 0.999810i | \(0.493796\pi\) | |||||||
\(930\) | 12.0000 | + | 20.7846i | 0.393496 | + | 0.681554i | ||||
\(931\) | 7.00000 | − | 48.4974i | 0.229416 | − | 1.58944i | ||||
\(932\) | 6.00000 | − | 3.46410i | 0.196537 | − | 0.113470i | ||||
\(933\) | −4.50000 | − | 2.59808i | −0.147323 | − | 0.0850572i | ||||
\(934\) | 3.00000 | − | 5.19615i | 0.0981630 | − | 0.170023i | ||||
\(935\) | − | 31.1769i | − | 1.01959i | ||||||
\(936\) | −7.50000 | − | 7.79423i | −0.245145 | − | 0.254762i | ||||
\(937\) | − | 38.1051i | − | 1.24484i | −0.782683 | − | 0.622420i | \(-0.786150\pi\) | ||
0.782683 | − | 0.622420i | \(-0.213850\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.0000 | − | 31.1769i | 0.587408 | − | 1.01742i | ||||
\(940\) | −15.0000 | − | 25.9808i | −0.489246 | − | 0.847399i | ||||
\(941\) | − | 38.1051i | − | 1.24219i | −0.783735 | − | 0.621096i | \(-0.786688\pi\) | ||
0.783735 | − | 0.621096i | \(-0.213312\pi\) | |||||||
\(942\) | 12.0000 | + | 20.7846i | 0.390981 | + | 0.677199i | ||||
\(943\) | −18.0000 | − | 31.1769i | −0.586161 | − | 1.01526i | ||||
\(944\) | 10.3923i | 0.338241i | ||||||||
\(945\) | 45.0000 | + | 15.5885i | 1.46385 | + | 0.507093i | ||||
\(946\) | −12.0000 | + | 20.7846i | −0.390154 | + | 0.675766i | ||||
\(947\) | 1.50000 | − | 2.59808i | 0.0487435 | − | 0.0844261i | −0.840624 | − | 0.541619i | \(-0.817812\pi\) |
0.889368 | + | 0.457193i | \(0.151145\pi\) | |||||||
\(948\) | 19.0526i | 0.618798i | ||||||||
\(949\) | −14.0000 | + | 3.46410i | −0.454459 | + | 0.112449i | ||||
\(950\) | 49.0000 | 1.58977 | ||||||||
\(951\) | 27.0000 | + | 15.5885i | 0.875535 | + | 0.505490i | ||||
\(952\) | 1.50000 | + | 7.79423i | 0.0486153 | + | 0.252612i | ||||
\(953\) | −33.0000 | + | 19.0526i | −1.06897 | + | 0.617173i | −0.927901 | − | 0.372826i | \(-0.878389\pi\) |
−0.141074 | + | 0.989999i | \(0.545055\pi\) | |||||||
\(954\) | 25.9808i | 0.841158i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6.00000 | − | 10.3923i | −0.194054 | − | 0.336111i | ||||
\(957\) | 9.00000 | 0.290929 | ||||||||
\(958\) | 28.5000 | − | 16.4545i | 0.920793 | − | 0.531620i | ||||
\(959\) | 6.00000 | + | 31.1769i | 0.193750 | + | 1.00676i | ||||
\(960\) | 3.00000 | − | 5.19615i | 0.0968246 | − | 0.167705i | ||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | −18.0000 | + | 17.3205i | −0.580343 | + | 0.558436i | ||||
\(963\) | − | 15.5885i | − | 0.502331i | ||||||
\(964\) | 5.00000 | − | 8.66025i | 0.161039 | − | 0.278928i | ||||
\(965\) | −21.0000 | + | 36.3731i | −0.676014 | + | 1.17089i | ||||
\(966\) | 30.0000 | + | 10.3923i | 0.965234 | + | 0.334367i | ||||
\(967\) | 24.2487i | 0.779786i | 0.920860 | + | 0.389893i | \(0.127488\pi\) | ||||
−0.920860 | + | 0.389893i | \(0.872512\pi\) | |||||||
\(968\) | −1.00000 | − | 1.73205i | −0.0321412 | − | 0.0556702i | ||||
\(969\) | −31.5000 | + | 18.1865i | −1.01193 | + | 0.584236i | ||||
\(970\) | − | 6.92820i | − | 0.222451i | ||||||
\(971\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(972\) | 13.5000 | + | 7.79423i | 0.433013 | + | 0.250000i | ||||
\(973\) | −13.5000 | + | 2.59808i | −0.432790 | + | 0.0832905i | ||||
\(974\) | − | 8.66025i | − | 0.277492i | ||||||
\(975\) | −42.0000 | − | 12.1244i | −1.34508 | − | 0.388290i | ||||
\(976\) | 5.19615i | 0.166325i | ||||||||
\(977\) | 9.00000 | − | 15.5885i | 0.287936 | − | 0.498719i | −0.685381 | − | 0.728184i | \(-0.740364\pi\) |
0.973317 | + | 0.229465i | \(0.0736978\pi\) | |||||||
\(978\) | 21.0000 | − | 36.3731i | 0.671506 | − | 1.16308i | ||||
\(979\) | 22.5000 | − | 12.9904i | 0.719103 | − | 0.415174i | ||||
\(980\) | −24.0000 | − | 3.46410i | −0.766652 | − | 0.110657i | ||||
\(981\) | −9.00000 | + | 5.19615i | −0.287348 | + | 0.165900i | ||||
\(982\) | 9.00000 | − | 5.19615i | 0.287202 | − | 0.165816i | ||||
\(983\) | 58.8897i | 1.87829i | 0.343520 | + | 0.939145i | \(0.388381\pi\) | ||||
−0.343520 | + | 0.939145i | \(0.611619\pi\) | |||||||
\(984\) | 4.50000 | + | 7.79423i | 0.143455 | + | 0.248471i | ||||
\(985\) | −81.0000 | − | 46.7654i | −2.58087 | − | 1.49007i | ||||
\(986\) | 4.50000 | + | 2.59808i | 0.143309 | + | 0.0827396i | ||||
\(987\) | −30.0000 | + | 25.9808i | −0.954911 | + | 0.826977i | ||||
\(988\) | −7.00000 | + | 24.2487i | −0.222700 | + | 0.771454i | ||||
\(989\) | 55.4256i | 1.76243i | ||||||||
\(990\) | 27.0000 | + | 15.5885i | 0.858116 | + | 0.495434i | ||||
\(991\) | 8.50000 | − | 14.7224i | 0.270011 | − | 0.467673i | −0.698853 | − | 0.715265i | \(-0.746306\pi\) |
0.968864 | + | 0.247592i | \(0.0796392\pi\) | |||||||
\(992\) | −2.00000 | − | 3.46410i | −0.0635001 | − | 0.109985i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 15.0000 | + | 5.19615i | 0.475771 | + | 0.164812i | ||||
\(995\) | 18.0000 | + | 31.1769i | 0.570638 | + | 0.988375i | ||||
\(996\) | 24.0000 | 0.760469 | ||||||||
\(997\) | −19.5000 | + | 11.2583i | −0.617571 | + | 0.356555i | −0.775923 | − | 0.630828i | \(-0.782715\pi\) |
0.158352 | + | 0.987383i | \(0.449382\pi\) | |||||||
\(998\) | 36.0000 | + | 20.7846i | 1.13956 | + | 0.657925i | ||||
\(999\) | 18.0000 | − | 31.1769i | 0.569495 | − | 0.986394i |
(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 | 546.2.q.d.251.1 | yes | 2 | |
3.2 | odd | 2 | 546.2.q.b.251.1 | yes | 2 | ||
7.6 | odd | 2 | 546.2.q.c.251.1 | yes | 2 | ||
13.10 | even | 6 | 546.2.q.a.335.1 | yes | 2 | ||
21.20 | even | 2 | 546.2.q.a.251.1 | ✓ | 2 | ||
39.23 | odd | 6 | 546.2.q.c.335.1 | yes | 2 | ||
91.62 | odd | 6 | 546.2.q.b.335.1 | yes | 2 | ||
273.62 | even | 6 | inner | 546.2.q.d.335.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.q.a.251.1 | ✓ | 2 | 21.20 | even | 2 | ||
546.2.q.a.335.1 | yes | 2 | 13.10 | even | 6 | ||
546.2.q.b.251.1 | yes | 2 | 3.2 | odd | 2 | ||
546.2.q.b.335.1 | yes | 2 | 91.62 | odd | 6 | ||
546.2.q.c.251.1 | yes | 2 | 7.6 | odd | 2 | ||
546.2.q.c.335.1 | yes | 2 | 39.23 | odd | 6 | ||
546.2.q.d.251.1 | yes | 2 | 1.1 | even | 1 | trivial | |
546.2.q.d.335.1 | yes | 2 | 273.62 | even | 6 | inner |