Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(101,546)]
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, 1, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.bn (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 | 101.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.101 |
Dual form | 546.2.bn.d.173.1 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||
\(5\) | 1.50000 | − | 0.866025i | 0.670820 | − | 0.387298i | −0.125567 | − | 0.992085i | \(-0.540075\pi\) |
0.796387 | + | 0.604787i | \(0.206742\pi\) | |||||||
\(6\) | − | 1.73205i | − | 0.707107i | ||||||
\(7\) | 0.500000 | − | 2.59808i | 0.188982 | − | 0.981981i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(10\) | − | 1.73205i | − | 0.547723i | ||||||
\(11\) | −3.00000 | −0.904534 | −0.452267 | − | 0.891883i | \(-0.649385\pi\) | ||||
−0.452267 | + | 0.891883i | \(0.649385\pi\) | |||||||
\(12\) | −1.50000 | − | 0.866025i | −0.433013 | − | 0.250000i | ||||
\(13\) | 1.00000 | + | 3.46410i | 0.277350 | + | 0.960769i | ||||
\(14\) | −2.00000 | − | 1.73205i | −0.534522 | − | 0.462910i | ||||
\(15\) | 1.50000 | − | 2.59808i | 0.387298 | − | 0.670820i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 3.00000 | + | 5.19615i | 0.727607 | + | 1.26025i | 0.957892 | + | 0.287129i | \(0.0927008\pi\) |
−0.230285 | + | 0.973123i | \(0.573966\pi\) | |||||||
\(18\) | −1.50000 | − | 2.59808i | −0.353553 | − | 0.612372i | ||||
\(19\) | −7.00000 | −1.60591 | −0.802955 | − | 0.596040i | \(-0.796740\pi\) | ||||
−0.802955 | + | 0.596040i | \(0.796740\pi\) | |||||||
\(20\) | −1.50000 | − | 0.866025i | −0.335410 | − | 0.193649i | ||||
\(21\) | −1.50000 | − | 4.33013i | −0.327327 | − | 0.944911i | ||||
\(22\) | −1.50000 | + | 2.59808i | −0.319801 | + | 0.553912i | ||||
\(23\) | 3.00000 | + | 1.73205i | 0.625543 | + | 0.361158i | 0.779024 | − | 0.626994i | \(-0.215715\pi\) |
−0.153481 | + | 0.988152i | \(0.549048\pi\) | |||||||
\(24\) | −1.50000 | + | 0.866025i | −0.306186 | + | 0.176777i | ||||
\(25\) | −1.00000 | + | 1.73205i | −0.200000 | + | 0.346410i | ||||
\(26\) | 3.50000 | + | 0.866025i | 0.686406 | + | 0.169842i | ||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | −2.50000 | + | 0.866025i | −0.472456 | + | 0.163663i | ||||
\(29\) | 7.50000 | − | 4.33013i | 1.39272 | − | 0.804084i | 0.399100 | − | 0.916907i | \(-0.369323\pi\) |
0.993615 | + | 0.112823i | \(0.0359893\pi\) | |||||||
\(30\) | −1.50000 | − | 2.59808i | −0.273861 | − | 0.474342i | ||||
\(31\) | −0.500000 | + | 0.866025i | −0.0898027 | + | 0.155543i | −0.907428 | − | 0.420208i | \(-0.861957\pi\) |
0.817625 | + | 0.575751i | \(0.195290\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −4.50000 | + | 2.59808i | −0.783349 | + | 0.452267i | ||||
\(34\) | 6.00000 | 1.02899 | ||||||||
\(35\) | −1.50000 | − | 4.33013i | −0.253546 | − | 0.731925i | ||||
\(36\) | −3.00000 | −0.500000 | ||||||||
\(37\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(38\) | −3.50000 | + | 6.06218i | −0.567775 | + | 0.983415i | ||||
\(39\) | 4.50000 | + | 4.33013i | 0.720577 | + | 0.693375i | ||||
\(40\) | −1.50000 | + | 0.866025i | −0.237171 | + | 0.136931i | ||||
\(41\) | 4.50000 | − | 2.59808i | 0.702782 | − | 0.405751i | −0.105601 | − | 0.994409i | \(-0.533677\pi\) |
0.808383 | + | 0.588657i | \(0.200343\pi\) | |||||||
\(42\) | −4.50000 | − | 0.866025i | −0.694365 | − | 0.133631i | ||||
\(43\) | −0.500000 | + | 0.866025i | −0.0762493 | + | 0.132068i | −0.901629 | − | 0.432511i | \(-0.857628\pi\) |
0.825380 | + | 0.564578i | \(0.190961\pi\) | |||||||
\(44\) | 1.50000 | + | 2.59808i | 0.226134 | + | 0.391675i | ||||
\(45\) | − | 5.19615i | − | 0.774597i | ||||||
\(46\) | 3.00000 | − | 1.73205i | 0.442326 | − | 0.255377i | ||||
\(47\) | −1.50000 | + | 0.866025i | −0.218797 | + | 0.126323i | −0.605393 | − | 0.795926i | \(-0.706984\pi\) |
0.386596 | + | 0.922249i | \(0.373651\pi\) | |||||||
\(48\) | 1.73205i | 0.250000i | ||||||||
\(49\) | −6.50000 | − | 2.59808i | −0.928571 | − | 0.371154i | ||||
\(50\) | 1.00000 | + | 1.73205i | 0.141421 | + | 0.244949i | ||||
\(51\) | 9.00000 | + | 5.19615i | 1.26025 | + | 0.727607i | ||||
\(52\) | 2.50000 | − | 2.59808i | 0.346688 | − | 0.360288i | ||||
\(53\) | −1.50000 | − | 0.866025i | −0.206041 | − | 0.118958i | 0.393429 | − | 0.919355i | \(-0.371289\pi\) |
−0.599470 | + | 0.800397i | \(0.704622\pi\) | |||||||
\(54\) | −4.50000 | − | 2.59808i | −0.612372 | − | 0.353553i | ||||
\(55\) | −4.50000 | + | 2.59808i | −0.606780 | + | 0.350325i | ||||
\(56\) | −0.500000 | + | 2.59808i | −0.0668153 | + | 0.347183i | ||||
\(57\) | −10.5000 | + | 6.06218i | −1.39076 | + | 0.802955i | ||||
\(58\) | − | 8.66025i | − | 1.13715i | ||||||
\(59\) | 9.00000 | − | 5.19615i | 1.17170 | − | 0.676481i | 0.217620 | − | 0.976034i | \(-0.430171\pi\) |
0.954080 | + | 0.299552i | \(0.0968372\pi\) | |||||||
\(60\) | −3.00000 | −0.387298 | ||||||||
\(61\) | − | 1.73205i | − | 0.221766i | −0.993833 | − | 0.110883i | \(-0.964632\pi\) | ||
0.993833 | − | 0.110883i | \(-0.0353679\pi\) | |||||||
\(62\) | 0.500000 | + | 0.866025i | 0.0635001 | + | 0.109985i | ||||
\(63\) | −6.00000 | − | 5.19615i | −0.755929 | − | 0.654654i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.50000 | + | 4.33013i | 0.558156 | + | 0.537086i | ||||
\(66\) | 5.19615i | 0.639602i | ||||||||
\(67\) | 1.73205i | 0.211604i | 0.994387 | + | 0.105802i | \(0.0337409\pi\) | ||||
−0.994387 | + | 0.105802i | \(0.966259\pi\) | |||||||
\(68\) | 3.00000 | − | 5.19615i | 0.363803 | − | 0.630126i | ||||
\(69\) | 6.00000 | 0.722315 | ||||||||
\(70\) | −4.50000 | − | 0.866025i | −0.537853 | − | 0.103510i | ||||
\(71\) | −4.50000 | + | 7.79423i | −0.534052 | + | 0.925005i | 0.465157 | + | 0.885228i | \(0.345998\pi\) |
−0.999209 | + | 0.0397765i | \(0.987335\pi\) | |||||||
\(72\) | −1.50000 | + | 2.59808i | −0.176777 | + | 0.306186i | ||||
\(73\) | −6.50000 | + | 11.2583i | −0.760767 | + | 1.31769i | 0.181688 | + | 0.983356i | \(0.441844\pi\) |
−0.942455 | + | 0.334332i | \(0.891489\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.46410i | 0.400000i | ||||||||
\(76\) | 3.50000 | + | 6.06218i | 0.401478 | + | 0.695379i | ||||
\(77\) | −1.50000 | + | 7.79423i | −0.170941 | + | 0.888235i | ||||
\(78\) | 6.00000 | − | 1.73205i | 0.679366 | − | 0.196116i | ||||
\(79\) | −0.500000 | − | 0.866025i | −0.0562544 | − | 0.0974355i | 0.836527 | − | 0.547926i | \(-0.184582\pi\) |
−0.892781 | + | 0.450490i | \(0.851249\pi\) | |||||||
\(80\) | 1.73205i | 0.193649i | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | − | 5.19615i | − | 0.573819i | ||||||
\(83\) | 3.46410i | 0.380235i | 0.981761 | + | 0.190117i | \(0.0608868\pi\) | ||||
−0.981761 | + | 0.190117i | \(0.939113\pi\) | |||||||
\(84\) | −3.00000 | + | 3.46410i | −0.327327 | + | 0.377964i | ||||
\(85\) | 9.00000 | + | 5.19615i | 0.976187 | + | 0.563602i | ||||
\(86\) | 0.500000 | + | 0.866025i | 0.0539164 | + | 0.0933859i | ||||
\(87\) | 7.50000 | − | 12.9904i | 0.804084 | − | 1.39272i | ||||
\(88\) | 3.00000 | 0.319801 | ||||||||
\(89\) | 6.00000 | + | 3.46410i | 0.635999 | + | 0.367194i | 0.783072 | − | 0.621932i | \(-0.213652\pi\) |
−0.147073 | + | 0.989126i | \(0.546985\pi\) | |||||||
\(90\) | −4.50000 | − | 2.59808i | −0.474342 | − | 0.273861i | ||||
\(91\) | 9.50000 | − | 0.866025i | 0.995871 | − | 0.0907841i | ||||
\(92\) | − | 3.46410i | − | 0.361158i | ||||||
\(93\) | 1.73205i | 0.179605i | ||||||||
\(94\) | 1.73205i | 0.178647i | ||||||||
\(95\) | −10.5000 | + | 6.06218i | −1.07728 | + | 0.621966i | ||||
\(96\) | 1.50000 | + | 0.866025i | 0.153093 | + | 0.0883883i | ||||
\(97\) | 9.50000 | − | 16.4545i | 0.964579 | − | 1.67070i | 0.253837 | − | 0.967247i | \(-0.418307\pi\) |
0.710742 | − | 0.703452i | \(-0.248359\pi\) | |||||||
\(98\) | −5.50000 | + | 4.33013i | −0.555584 | + | 0.437409i | ||||
\(99\) | −4.50000 | + | 7.79423i | −0.452267 | + | 0.783349i | ||||
\(100\) | 2.00000 | 0.200000 | ||||||||
\(101\) | 9.00000 | 0.895533 | 0.447767 | − | 0.894150i | \(-0.352219\pi\) | ||||
0.447767 | + | 0.894150i | \(0.352219\pi\) | |||||||
\(102\) | 9.00000 | − | 5.19615i | 0.891133 | − | 0.514496i | ||||
\(103\) | −7.50000 | + | 4.33013i | −0.738997 | + | 0.426660i | −0.821705 | − | 0.569914i | \(-0.806977\pi\) |
0.0827075 | + | 0.996574i | \(0.473643\pi\) | |||||||
\(104\) | −1.00000 | − | 3.46410i | −0.0980581 | − | 0.339683i | ||||
\(105\) | −6.00000 | − | 5.19615i | −0.585540 | − | 0.507093i | ||||
\(106\) | −1.50000 | + | 0.866025i | −0.145693 | + | 0.0841158i | ||||
\(107\) | −9.00000 | − | 5.19615i | −0.870063 | − | 0.502331i | −0.00269372 | − | 0.999996i | \(-0.500857\pi\) |
−0.867369 | + | 0.497665i | \(0.834191\pi\) | |||||||
\(108\) | −4.50000 | + | 2.59808i | −0.433013 | + | 0.250000i | ||||
\(109\) | −7.50000 | − | 4.33013i | −0.718370 | − | 0.414751i | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) |
−0.814152 | + | 0.580651i | \(0.802798\pi\) | |||||||
\(110\) | 5.19615i | 0.495434i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.00000 | + | 1.73205i | 0.188982 | + | 0.163663i | ||||
\(113\) | 1.50000 | + | 0.866025i | 0.141108 | + | 0.0814688i | 0.568892 | − | 0.822412i | \(-0.307372\pi\) |
−0.427784 | + | 0.903881i | \(0.640706\pi\) | |||||||
\(114\) | 12.1244i | 1.13555i | ||||||||
\(115\) | 6.00000 | 0.559503 | ||||||||
\(116\) | −7.50000 | − | 4.33013i | −0.696358 | − | 0.402042i | ||||
\(117\) | 10.5000 | + | 2.59808i | 0.970725 | + | 0.240192i | ||||
\(118\) | − | 10.3923i | − | 0.956689i | ||||||
\(119\) | 15.0000 | − | 5.19615i | 1.37505 | − | 0.476331i | ||||
\(120\) | −1.50000 | + | 2.59808i | −0.136931 | + | 0.237171i | ||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | −1.50000 | − | 0.866025i | −0.135804 | − | 0.0784063i | ||||
\(123\) | 4.50000 | − | 7.79423i | 0.405751 | − | 0.702782i | ||||
\(124\) | 1.00000 | 0.0898027 | ||||||||
\(125\) | 12.1244i | 1.08444i | ||||||||
\(126\) | −7.50000 | + | 2.59808i | −0.668153 | + | 0.231455i | ||||
\(127\) | 8.50000 | + | 14.7224i | 0.754253 | + | 1.30640i | 0.945745 | + | 0.324910i | \(0.105334\pi\) |
−0.191492 | + | 0.981494i | \(0.561333\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 1.73205i | 0.152499i | ||||||||
\(130\) | 6.00000 | − | 1.73205i | 0.526235 | − | 0.151911i | ||||
\(131\) | −1.50000 | − | 2.59808i | −0.131056 | − | 0.226995i | 0.793028 | − | 0.609185i | \(-0.208503\pi\) |
−0.924084 | + | 0.382190i | \(0.875170\pi\) | |||||||
\(132\) | 4.50000 | + | 2.59808i | 0.391675 | + | 0.226134i | ||||
\(133\) | −3.50000 | + | 18.1865i | −0.303488 | + | 1.57697i | ||||
\(134\) | 1.50000 | + | 0.866025i | 0.129580 | + | 0.0748132i | ||||
\(135\) | −4.50000 | − | 7.79423i | −0.387298 | − | 0.670820i | ||||
\(136\) | −3.00000 | − | 5.19615i | −0.257248 | − | 0.445566i | ||||
\(137\) | 3.00000 | + | 5.19615i | 0.256307 | + | 0.443937i | 0.965250 | − | 0.261329i | \(-0.0841608\pi\) |
−0.708942 | + | 0.705266i | \(0.750827\pi\) | |||||||
\(138\) | 3.00000 | − | 5.19615i | 0.255377 | − | 0.442326i | ||||
\(139\) | 19.5000 | + | 11.2583i | 1.65397 | + | 0.954919i | 0.975417 | + | 0.220366i | \(0.0707252\pi\) |
0.678551 | + | 0.734553i | \(0.262608\pi\) | |||||||
\(140\) | −3.00000 | + | 3.46410i | −0.253546 | + | 0.292770i | ||||
\(141\) | −1.50000 | + | 2.59808i | −0.126323 | + | 0.218797i | ||||
\(142\) | 4.50000 | + | 7.79423i | 0.377632 | + | 0.654077i | ||||
\(143\) | −3.00000 | − | 10.3923i | −0.250873 | − | 0.869048i | ||||
\(144\) | 1.50000 | + | 2.59808i | 0.125000 | + | 0.216506i | ||||
\(145\) | 7.50000 | − | 12.9904i | 0.622841 | − | 1.07879i | ||||
\(146\) | 6.50000 | + | 11.2583i | 0.537944 | + | 0.931746i | ||||
\(147\) | −12.0000 | + | 1.73205i | −0.989743 | + | 0.142857i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −21.0000 | −1.72039 | −0.860194 | − | 0.509968i | \(-0.829657\pi\) | ||||
−0.860194 | + | 0.509968i | \(0.829657\pi\) | |||||||
\(150\) | 3.00000 | + | 1.73205i | 0.244949 | + | 0.141421i | ||||
\(151\) | −19.5000 | − | 11.2583i | −1.58689 | − | 0.916190i | −0.993816 | − | 0.111040i | \(-0.964582\pi\) |
−0.593072 | − | 0.805150i | \(-0.702085\pi\) | |||||||
\(152\) | 7.00000 | 0.567775 | ||||||||
\(153\) | 18.0000 | 1.45521 | ||||||||
\(154\) | 6.00000 | + | 5.19615i | 0.483494 | + | 0.418718i | ||||
\(155\) | 1.73205i | 0.139122i | ||||||||
\(156\) | 1.50000 | − | 6.06218i | 0.120096 | − | 0.485363i | ||||
\(157\) | 1.50000 | + | 0.866025i | 0.119713 | + | 0.0691164i | 0.558661 | − | 0.829396i | \(-0.311315\pi\) |
−0.438948 | + | 0.898513i | \(0.644649\pi\) | |||||||
\(158\) | −1.00000 | −0.0795557 | ||||||||
\(159\) | −3.00000 | −0.237915 | ||||||||
\(160\) | 1.50000 | + | 0.866025i | 0.118585 | + | 0.0684653i | ||||
\(161\) | 6.00000 | − | 6.92820i | 0.472866 | − | 0.546019i | ||||
\(162\) | −9.00000 | −0.707107 | ||||||||
\(163\) | − | 5.19615i | − | 0.406994i | −0.979076 | − | 0.203497i | \(-0.934769\pi\) | ||
0.979076 | − | 0.203497i | \(-0.0652307\pi\) | |||||||
\(164\) | −4.50000 | − | 2.59808i | −0.351391 | − | 0.202876i | ||||
\(165\) | −4.50000 | + | 7.79423i | −0.350325 | + | 0.606780i | ||||
\(166\) | 3.00000 | + | 1.73205i | 0.232845 | + | 0.134433i | ||||
\(167\) | −7.50000 | + | 4.33013i | −0.580367 | + | 0.335075i | −0.761279 | − | 0.648424i | \(-0.775428\pi\) |
0.180912 | + | 0.983499i | \(0.442095\pi\) | |||||||
\(168\) | 1.50000 | + | 4.33013i | 0.115728 | + | 0.334077i | ||||
\(169\) | −11.0000 | + | 6.92820i | −0.846154 | + | 0.532939i | ||||
\(170\) | 9.00000 | − | 5.19615i | 0.690268 | − | 0.398527i | ||||
\(171\) | −10.5000 | + | 18.1865i | −0.802955 | + | 1.39076i | ||||
\(172\) | 1.00000 | 0.0762493 | ||||||||
\(173\) | 9.00000 | 0.684257 | 0.342129 | − | 0.939653i | \(-0.388852\pi\) | ||||
0.342129 | + | 0.939653i | \(0.388852\pi\) | |||||||
\(174\) | −7.50000 | − | 12.9904i | −0.568574 | − | 0.984798i | ||||
\(175\) | 4.00000 | + | 3.46410i | 0.302372 | + | 0.261861i | ||||
\(176\) | 1.50000 | − | 2.59808i | 0.113067 | − | 0.195837i | ||||
\(177\) | 9.00000 | − | 15.5885i | 0.676481 | − | 1.17170i | ||||
\(178\) | 6.00000 | − | 3.46410i | 0.449719 | − | 0.259645i | ||||
\(179\) | − | 19.0526i | − | 1.42406i | −0.702152 | − | 0.712028i | \(-0.747777\pi\) | ||
0.702152 | − | 0.712028i | \(-0.252223\pi\) | |||||||
\(180\) | −4.50000 | + | 2.59808i | −0.335410 | + | 0.193649i | ||||
\(181\) | 13.8564i | 1.02994i | 0.857209 | + | 0.514969i | \(0.172197\pi\) | ||||
−0.857209 | + | 0.514969i | \(0.827803\pi\) | |||||||
\(182\) | 4.00000 | − | 8.66025i | 0.296500 | − | 0.641941i | ||||
\(183\) | −1.50000 | − | 2.59808i | −0.110883 | − | 0.192055i | ||||
\(184\) | −3.00000 | − | 1.73205i | −0.221163 | − | 0.127688i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.50000 | + | 0.866025i | 0.109985 | + | 0.0635001i | ||||
\(187\) | −9.00000 | − | 15.5885i | −0.658145 | − | 1.13994i | ||||
\(188\) | 1.50000 | + | 0.866025i | 0.109399 | + | 0.0631614i | ||||
\(189\) | −13.5000 | − | 2.59808i | −0.981981 | − | 0.188982i | ||||
\(190\) | 12.1244i | 0.879593i | ||||||||
\(191\) | 15.5885i | 1.12794i | 0.825795 | + | 0.563971i | \(0.190727\pi\) | ||||
−0.825795 | + | 0.563971i | \(0.809273\pi\) | |||||||
\(192\) | 1.50000 | − | 0.866025i | 0.108253 | − | 0.0625000i | ||||
\(193\) | 12.1244i | 0.872730i | 0.899770 | + | 0.436365i | \(0.143734\pi\) | ||||
−0.899770 | + | 0.436365i | \(0.856266\pi\) | |||||||
\(194\) | −9.50000 | − | 16.4545i | −0.682060 | − | 1.18136i | ||||
\(195\) | 10.5000 | + | 2.59808i | 0.751921 | + | 0.186052i | ||||
\(196\) | 1.00000 | + | 6.92820i | 0.0714286 | + | 0.494872i | ||||
\(197\) | 10.5000 | + | 18.1865i | 0.748094 | + | 1.29574i | 0.948735 | + | 0.316072i | \(0.102364\pi\) |
−0.200641 | + | 0.979665i | \(0.564303\pi\) | |||||||
\(198\) | 4.50000 | + | 7.79423i | 0.319801 | + | 0.553912i | ||||
\(199\) | −3.00000 | + | 1.73205i | −0.212664 | + | 0.122782i | −0.602549 | − | 0.798082i | \(-0.705848\pi\) |
0.389885 | + | 0.920864i | \(0.372515\pi\) | |||||||
\(200\) | 1.00000 | − | 1.73205i | 0.0707107 | − | 0.122474i | ||||
\(201\) | 1.50000 | + | 2.59808i | 0.105802 | + | 0.183254i | ||||
\(202\) | 4.50000 | − | 7.79423i | 0.316619 | − | 0.548400i | ||||
\(203\) | −7.50000 | − | 21.6506i | −0.526397 | − | 1.51958i | ||||
\(204\) | − | 10.3923i | − | 0.727607i | ||||||
\(205\) | 4.50000 | − | 7.79423i | 0.314294 | − | 0.544373i | ||||
\(206\) | 8.66025i | 0.603388i | ||||||||
\(207\) | 9.00000 | − | 5.19615i | 0.625543 | − | 0.361158i | ||||
\(208\) | −3.50000 | − | 0.866025i | −0.242681 | − | 0.0600481i | ||||
\(209\) | 21.0000 | 1.45260 | ||||||||
\(210\) | −7.50000 | + | 2.59808i | −0.517549 | + | 0.179284i | ||||
\(211\) | 0.500000 | + | 0.866025i | 0.0344214 | + | 0.0596196i | 0.882723 | − | 0.469894i | \(-0.155708\pi\) |
−0.848301 | + | 0.529514i | \(0.822374\pi\) | |||||||
\(212\) | 1.73205i | 0.118958i | ||||||||
\(213\) | 15.5885i | 1.06810i | ||||||||
\(214\) | −9.00000 | + | 5.19615i | −0.615227 | + | 0.355202i | ||||
\(215\) | 1.73205i | 0.118125i | ||||||||
\(216\) | 5.19615i | 0.353553i | ||||||||
\(217\) | 2.00000 | + | 1.73205i | 0.135769 | + | 0.117579i | ||||
\(218\) | −7.50000 | + | 4.33013i | −0.507964 | + | 0.293273i | ||||
\(219\) | 22.5167i | 1.52153i | ||||||||
\(220\) | 4.50000 | + | 2.59808i | 0.303390 | + | 0.175162i | ||||
\(221\) | −15.0000 | + | 15.5885i | −1.00901 | + | 1.04859i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.5000 | − | 25.1147i | −0.970992 | − | 1.68181i | −0.692574 | − | 0.721347i | \(-0.743523\pi\) |
−0.278418 | − | 0.960460i | \(-0.589810\pi\) | |||||||
\(224\) | 2.50000 | − | 0.866025i | 0.167038 | − | 0.0578638i | ||||
\(225\) | 3.00000 | + | 5.19615i | 0.200000 | + | 0.346410i | ||||
\(226\) | 1.50000 | − | 0.866025i | 0.0997785 | − | 0.0576072i | ||||
\(227\) | 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 | ||||
\(229\) | −12.5000 | − | 21.6506i | −0.826023 | − | 1.43071i | −0.901135 | − | 0.433539i | \(-0.857265\pi\) |
0.0751115 | − | 0.997175i | \(-0.476069\pi\) | |||||||
\(230\) | 3.00000 | − | 5.19615i | 0.197814 | − | 0.342624i | ||||
\(231\) | 4.50000 | + | 12.9904i | 0.296078 | + | 0.854704i | ||||
\(232\) | −7.50000 | + | 4.33013i | −0.492399 | + | 0.284287i | ||||
\(233\) | −19.5000 | + | 11.2583i | −1.27749 | + | 0.737558i | −0.976386 | − | 0.216034i | \(-0.930688\pi\) |
−0.301102 | + | 0.953592i | \(0.597354\pi\) | |||||||
\(234\) | 7.50000 | − | 7.79423i | 0.490290 | − | 0.509525i | ||||
\(235\) | −1.50000 | + | 2.59808i | −0.0978492 | + | 0.169480i | ||||
\(236\) | −9.00000 | − | 5.19615i | −0.585850 | − | 0.338241i | ||||
\(237\) | −1.50000 | − | 0.866025i | −0.0974355 | − | 0.0562544i | ||||
\(238\) | 3.00000 | − | 15.5885i | 0.194461 | − | 1.01045i | ||||
\(239\) | −12.0000 | −0.776215 | −0.388108 | − | 0.921614i | \(-0.626871\pi\) | ||||
−0.388108 | + | 0.921614i | \(0.626871\pi\) | |||||||
\(240\) | 1.50000 | + | 2.59808i | 0.0968246 | + | 0.167705i | ||||
\(241\) | −5.00000 | − | 8.66025i | −0.322078 | − | 0.557856i | 0.658838 | − | 0.752285i | \(-0.271048\pi\) |
−0.980917 | + | 0.194429i | \(0.937715\pi\) | |||||||
\(242\) | −1.00000 | + | 1.73205i | −0.0642824 | + | 0.111340i | ||||
\(243\) | −13.5000 | − | 7.79423i | −0.866025 | − | 0.500000i | ||||
\(244\) | −1.50000 | + | 0.866025i | −0.0960277 | + | 0.0554416i | ||||
\(245\) | −12.0000 | + | 1.73205i | −0.766652 | + | 0.110657i | ||||
\(246\) | −4.50000 | − | 7.79423i | −0.286910 | − | 0.496942i | ||||
\(247\) | −7.00000 | − | 24.2487i | −0.445399 | − | 1.54291i | ||||
\(248\) | 0.500000 | − | 0.866025i | 0.0317500 | − | 0.0549927i | ||||
\(249\) | 3.00000 | + | 5.19615i | 0.190117 | + | 0.329293i | ||||
\(250\) | 10.5000 | + | 6.06218i | 0.664078 | + | 0.383406i | ||||
\(251\) | −7.50000 | + | 12.9904i | −0.473396 | + | 0.819946i | −0.999536 | − | 0.0304521i | \(-0.990305\pi\) |
0.526140 | + | 0.850398i | \(0.323639\pi\) | |||||||
\(252\) | −1.50000 | + | 7.79423i | −0.0944911 | + | 0.490990i | ||||
\(253\) | −9.00000 | − | 5.19615i | −0.565825 | − | 0.326679i | ||||
\(254\) | 17.0000 | 1.06667 | ||||||||
\(255\) | 18.0000 | 1.12720 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 3.00000 | − | 5.19615i | 0.187135 | − | 0.324127i | −0.757159 | − | 0.653231i | \(-0.773413\pi\) |
0.944294 | + | 0.329104i | \(0.106747\pi\) | |||||||
\(258\) | 1.50000 | + | 0.866025i | 0.0933859 | + | 0.0539164i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.50000 | − | 6.06218i | 0.0930261 | − | 0.375960i | ||||
\(261\) | − | 25.9808i | − | 1.60817i | ||||||
\(262\) | −3.00000 | −0.185341 | ||||||||
\(263\) | 8.66025i | 0.534014i | 0.963695 | + | 0.267007i | \(0.0860347\pi\) | ||||
−0.963695 | + | 0.267007i | \(0.913965\pi\) | |||||||
\(264\) | 4.50000 | − | 2.59808i | 0.276956 | − | 0.159901i | ||||
\(265\) | −3.00000 | −0.184289 | ||||||||
\(266\) | 14.0000 | + | 12.1244i | 0.858395 | + | 0.743392i | ||||
\(267\) | 12.0000 | 0.734388 | ||||||||
\(268\) | 1.50000 | − | 0.866025i | 0.0916271 | − | 0.0529009i | ||||
\(269\) | −15.0000 | − | 25.9808i | −0.914566 | − | 1.58408i | −0.807535 | − | 0.589819i | \(-0.799199\pi\) |
−0.107031 | − | 0.994256i | \(-0.534134\pi\) | |||||||
\(270\) | −9.00000 | −0.547723 | ||||||||
\(271\) | 8.00000 | − | 13.8564i | 0.485965 | − | 0.841717i | −0.513905 | − | 0.857847i | \(-0.671801\pi\) |
0.999870 | + | 0.0161307i | \(0.00513477\pi\) | |||||||
\(272\) | −6.00000 | −0.363803 | ||||||||
\(273\) | 13.5000 | − | 9.52628i | 0.817057 | − | 0.576557i | ||||
\(274\) | 6.00000 | 0.362473 | ||||||||
\(275\) | 3.00000 | − | 5.19615i | 0.180907 | − | 0.313340i | ||||
\(276\) | −3.00000 | − | 5.19615i | −0.180579 | − | 0.312772i | ||||
\(277\) | 5.00000 | + | 8.66025i | 0.300421 | + | 0.520344i | 0.976231 | − | 0.216731i | \(-0.0695395\pi\) |
−0.675810 | + | 0.737075i | \(0.736206\pi\) | |||||||
\(278\) | 19.5000 | − | 11.2583i | 1.16953 | − | 0.675230i | ||||
\(279\) | 1.50000 | + | 2.59808i | 0.0898027 | + | 0.155543i | ||||
\(280\) | 1.50000 | + | 4.33013i | 0.0896421 | + | 0.258775i | ||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 1.50000 | + | 2.59808i | 0.0893237 | + | 0.154713i | ||||
\(283\) | − | 22.5167i | − | 1.33848i | −0.743048 | − | 0.669238i | \(-0.766621\pi\) | ||
0.743048 | − | 0.669238i | \(-0.233379\pi\) | |||||||
\(284\) | 9.00000 | 0.534052 | ||||||||
\(285\) | −10.5000 | + | 18.1865i | −0.621966 | + | 1.07728i | ||||
\(286\) | −10.5000 | − | 2.59808i | −0.620878 | − | 0.153627i | ||||
\(287\) | −4.50000 | − | 12.9904i | −0.265627 | − | 0.766798i | ||||
\(288\) | 3.00000 | 0.176777 | ||||||||
\(289\) | −9.50000 | + | 16.4545i | −0.558824 | + | 0.967911i | ||||
\(290\) | −7.50000 | − | 12.9904i | −0.440415 | − | 0.762821i | ||||
\(291\) | − | 32.9090i | − | 1.92916i | ||||||
\(292\) | 13.0000 | 0.760767 | ||||||||
\(293\) | −25.5000 | − | 14.7224i | −1.48973 | − | 0.860094i | −0.489795 | − | 0.871838i | \(-0.662928\pi\) |
−0.999931 | + | 0.0117441i | \(0.996262\pi\) | |||||||
\(294\) | −4.50000 | + | 11.2583i | −0.262445 | + | 0.656599i | ||||
\(295\) | 9.00000 | − | 15.5885i | 0.524000 | − | 0.907595i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 15.5885i | 0.904534i | ||||||||
\(298\) | −10.5000 | + | 18.1865i | −0.608249 | + | 1.05352i | ||||
\(299\) | −3.00000 | + | 12.1244i | −0.173494 | + | 0.701170i | ||||
\(300\) | 3.00000 | − | 1.73205i | 0.173205 | − | 0.100000i | ||||
\(301\) | 2.00000 | + | 1.73205i | 0.115278 | + | 0.0998337i | ||||
\(302\) | −19.5000 | + | 11.2583i | −1.12210 | + | 0.647844i | ||||
\(303\) | 13.5000 | − | 7.79423i | 0.775555 | − | 0.447767i | ||||
\(304\) | 3.50000 | − | 6.06218i | 0.200739 | − | 0.347690i | ||||
\(305\) | −1.50000 | − | 2.59808i | −0.0858898 | − | 0.148765i | ||||
\(306\) | 9.00000 | − | 15.5885i | 0.514496 | − | 0.891133i | ||||
\(307\) | 4.00000 | 0.228292 | 0.114146 | − | 0.993464i | \(-0.463587\pi\) | ||||
0.114146 | + | 0.993464i | \(0.463587\pi\) | |||||||
\(308\) | 7.50000 | − | 2.59808i | 0.427352 | − | 0.148039i | ||||
\(309\) | −7.50000 | + | 12.9904i | −0.426660 | + | 0.738997i | ||||
\(310\) | 1.50000 | + | 0.866025i | 0.0851943 | + | 0.0491869i | ||||
\(311\) | 1.50000 | − | 2.59808i | 0.0850572 | − | 0.147323i | −0.820358 | − | 0.571850i | \(-0.806226\pi\) |
0.905416 | + | 0.424526i | \(0.139559\pi\) | |||||||
\(312\) | −4.50000 | − | 4.33013i | −0.254762 | − | 0.245145i | ||||
\(313\) | −4.50000 | + | 2.59808i | −0.254355 | + | 0.146852i | −0.621757 | − | 0.783210i | \(-0.713581\pi\) |
0.367402 | + | 0.930062i | \(0.380247\pi\) | |||||||
\(314\) | 1.50000 | − | 0.866025i | 0.0846499 | − | 0.0488726i | ||||
\(315\) | −13.5000 | − | 2.59808i | −0.760639 | − | 0.146385i | ||||
\(316\) | −0.500000 | + | 0.866025i | −0.0281272 | + | 0.0487177i | ||||
\(317\) | −1.50000 | − | 2.59808i | −0.0842484 | − | 0.145922i | 0.820822 | − | 0.571184i | \(-0.193516\pi\) |
−0.905071 | + | 0.425261i | \(0.860182\pi\) | |||||||
\(318\) | −1.50000 | + | 2.59808i | −0.0841158 | + | 0.145693i | ||||
\(319\) | −22.5000 | + | 12.9904i | −1.25976 | + | 0.727322i | ||||
\(320\) | 1.50000 | − | 0.866025i | 0.0838525 | − | 0.0484123i | ||||
\(321\) | −18.0000 | −1.00466 | ||||||||
\(322\) | −3.00000 | − | 8.66025i | −0.167183 | − | 0.482617i | ||||
\(323\) | −21.0000 | − | 36.3731i | −1.16847 | − | 2.02385i | ||||
\(324\) | −4.50000 | + | 7.79423i | −0.250000 | + | 0.433013i | ||||
\(325\) | −7.00000 | − | 1.73205i | −0.388290 | − | 0.0960769i | ||||
\(326\) | −4.50000 | − | 2.59808i | −0.249232 | − | 0.143894i | ||||
\(327\) | −15.0000 | −0.829502 | ||||||||
\(328\) | −4.50000 | + | 2.59808i | −0.248471 | + | 0.143455i | ||||
\(329\) | 1.50000 | + | 4.33013i | 0.0826977 | + | 0.238728i | ||||
\(330\) | 4.50000 | + | 7.79423i | 0.247717 | + | 0.429058i | ||||
\(331\) | − | 25.9808i | − | 1.42803i | −0.700129 | − | 0.714016i | \(-0.746874\pi\) | ||
0.700129 | − | 0.714016i | \(-0.253126\pi\) | |||||||
\(332\) | 3.00000 | − | 1.73205i | 0.164646 | − | 0.0950586i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.66025i | 0.473868i | ||||||||
\(335\) | 1.50000 | + | 2.59808i | 0.0819538 | + | 0.141948i | ||||
\(336\) | 4.50000 | + | 0.866025i | 0.245495 | + | 0.0472456i | ||||
\(337\) | −10.0000 | −0.544735 | −0.272367 | − | 0.962193i | \(-0.587807\pi\) | ||||
−0.272367 | + | 0.962193i | \(0.587807\pi\) | |||||||
\(338\) | 0.500000 | + | 12.9904i | 0.0271964 | + | 0.706584i | ||||
\(339\) | 3.00000 | 0.162938 | ||||||||
\(340\) | − | 10.3923i | − | 0.563602i | ||||||
\(341\) | 1.50000 | − | 2.59808i | 0.0812296 | − | 0.140694i | ||||
\(342\) | 10.5000 | + | 18.1865i | 0.567775 | + | 0.983415i | ||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 0.500000 | − | 0.866025i | 0.0269582 | − | 0.0466930i | ||||
\(345\) | 9.00000 | − | 5.19615i | 0.484544 | − | 0.279751i | ||||
\(346\) | 4.50000 | − | 7.79423i | 0.241921 | − | 0.419020i | ||||
\(347\) | 9.00000 | − | 5.19615i | 0.483145 | − | 0.278944i | −0.238581 | − | 0.971123i | \(-0.576682\pi\) |
0.721726 | + | 0.692179i | \(0.243349\pi\) | |||||||
\(348\) | −15.0000 | −0.804084 | ||||||||
\(349\) | 17.5000 | + | 30.3109i | 0.936754 | + | 1.62250i | 0.771477 | + | 0.636257i | \(0.219518\pi\) |
0.165277 | + | 0.986247i | \(0.447148\pi\) | |||||||
\(350\) | 5.00000 | − | 1.73205i | 0.267261 | − | 0.0925820i | ||||
\(351\) | 18.0000 | − | 5.19615i | 0.960769 | − | 0.277350i | ||||
\(352\) | −1.50000 | − | 2.59808i | −0.0799503 | − | 0.138478i | ||||
\(353\) | − | 25.9808i | − | 1.38282i | −0.722464 | − | 0.691408i | \(-0.756991\pi\) | ||
0.722464 | − | 0.691408i | \(-0.243009\pi\) | |||||||
\(354\) | −9.00000 | − | 15.5885i | −0.478345 | − | 0.828517i | ||||
\(355\) | 15.5885i | 0.827349i | ||||||||
\(356\) | − | 6.92820i | − | 0.367194i | ||||||
\(357\) | 18.0000 | − | 20.7846i | 0.952661 | − | 1.10004i | ||||
\(358\) | −16.5000 | − | 9.52628i | −0.872052 | − | 0.503480i | ||||
\(359\) | 1.50000 | + | 2.59808i | 0.0791670 | + | 0.137121i | 0.902891 | − | 0.429870i | \(-0.141441\pi\) |
−0.823724 | + | 0.566991i | \(0.808107\pi\) | |||||||
\(360\) | 5.19615i | 0.273861i | ||||||||
\(361\) | 30.0000 | 1.57895 | ||||||||
\(362\) | 12.0000 | + | 6.92820i | 0.630706 | + | 0.364138i | ||||
\(363\) | −3.00000 | + | 1.73205i | −0.157459 | + | 0.0909091i | ||||
\(364\) | −5.50000 | − | 7.79423i | −0.288278 | − | 0.408529i | ||||
\(365\) | 22.5167i | 1.17858i | ||||||||
\(366\) | −3.00000 | −0.156813 | ||||||||
\(367\) | − | 15.5885i | − | 0.813711i | −0.913493 | − | 0.406855i | \(-0.866625\pi\) | ||
0.913493 | − | 0.406855i | \(-0.133375\pi\) | |||||||
\(368\) | −3.00000 | + | 1.73205i | −0.156386 | + | 0.0902894i | ||||
\(369\) | − | 15.5885i | − | 0.811503i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.00000 | + | 3.46410i | −0.155752 | + | 0.179847i | ||||
\(372\) | 1.50000 | − | 0.866025i | 0.0777714 | − | 0.0449013i | ||||
\(373\) | −29.0000 | −1.50156 | −0.750782 | − | 0.660551i | \(-0.770323\pi\) | ||||
−0.750782 | + | 0.660551i | \(0.770323\pi\) | |||||||
\(374\) | −18.0000 | −0.930758 | ||||||||
\(375\) | 10.5000 | + | 18.1865i | 0.542218 | + | 0.939149i | ||||
\(376\) | 1.50000 | − | 0.866025i | 0.0773566 | − | 0.0446619i | ||||
\(377\) | 22.5000 | + | 21.6506i | 1.15881 | + | 1.11506i | ||||
\(378\) | −9.00000 | + | 10.3923i | −0.462910 | + | 0.534522i | ||||
\(379\) | −16.5000 | + | 9.52628i | −0.847548 | + | 0.489332i | −0.859823 | − | 0.510593i | \(-0.829426\pi\) |
0.0122747 | + | 0.999925i | \(0.496093\pi\) | |||||||
\(380\) | 10.5000 | + | 6.06218i | 0.538639 | + | 0.310983i | ||||
\(381\) | 25.5000 | + | 14.7224i | 1.30640 | + | 0.754253i | ||||
\(382\) | 13.5000 | + | 7.79423i | 0.690720 | + | 0.398787i | ||||
\(383\) | 5.19615i | 0.265511i | 0.991149 | + | 0.132755i | \(0.0423825\pi\) | ||||
−0.991149 | + | 0.132755i | \(0.957617\pi\) | |||||||
\(384\) | − | 1.73205i | − | 0.0883883i | ||||||
\(385\) | 4.50000 | + | 12.9904i | 0.229341 | + | 0.662051i | ||||
\(386\) | 10.5000 | + | 6.06218i | 0.534436 | + | 0.308557i | ||||
\(387\) | 1.50000 | + | 2.59808i | 0.0762493 | + | 0.132068i | ||||
\(388\) | −19.0000 | −0.964579 | ||||||||
\(389\) | 4.50000 | + | 2.59808i | 0.228159 | + | 0.131728i | 0.609722 | − | 0.792615i | \(-0.291281\pi\) |
−0.381563 | + | 0.924343i | \(0.624614\pi\) | |||||||
\(390\) | 7.50000 | − | 7.79423i | 0.379777 | − | 0.394676i | ||||
\(391\) | 20.7846i | 1.05112i | ||||||||
\(392\) | 6.50000 | + | 2.59808i | 0.328300 | + | 0.131223i | ||||
\(393\) | −4.50000 | − | 2.59808i | −0.226995 | − | 0.131056i | ||||
\(394\) | 21.0000 | 1.05796 | ||||||||
\(395\) | −1.50000 | − | 0.866025i | −0.0754732 | − | 0.0435745i | ||||
\(396\) | 9.00000 | 0.452267 | ||||||||
\(397\) | 29.0000 | 1.45547 | 0.727734 | − | 0.685859i | \(-0.240573\pi\) | ||||
0.727734 | + | 0.685859i | \(0.240573\pi\) | |||||||
\(398\) | 3.46410i | 0.173640i | ||||||||
\(399\) | 10.5000 | + | 30.3109i | 0.525657 | + | 1.51744i | ||||
\(400\) | −1.00000 | − | 1.73205i | −0.0500000 | − | 0.0866025i | ||||
\(401\) | 9.00000 | − | 15.5885i | 0.449439 | − | 0.778450i | −0.548911 | − | 0.835881i | \(-0.684957\pi\) |
0.998350 | + | 0.0574304i | \(0.0182907\pi\) | |||||||
\(402\) | 3.00000 | 0.149626 | ||||||||
\(403\) | −3.50000 | − | 0.866025i | −0.174347 | − | 0.0431398i | ||||
\(404\) | −4.50000 | − | 7.79423i | −0.223883 | − | 0.387777i | ||||
\(405\) | −13.5000 | − | 7.79423i | −0.670820 | − | 0.387298i | ||||
\(406\) | −22.5000 | − | 4.33013i | −1.11666 | − | 0.214901i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −9.00000 | − | 5.19615i | −0.445566 | − | 0.257248i | ||||
\(409\) | 11.0000 | + | 19.0526i | 0.543915 | + | 0.942088i | 0.998674 | + | 0.0514740i | \(0.0163919\pi\) |
−0.454759 | + | 0.890614i | \(0.650275\pi\) | |||||||
\(410\) | −4.50000 | − | 7.79423i | −0.222239 | − | 0.384930i | ||||
\(411\) | 9.00000 | + | 5.19615i | 0.443937 | + | 0.256307i | ||||
\(412\) | 7.50000 | + | 4.33013i | 0.369498 | + | 0.213330i | ||||
\(413\) | −9.00000 | − | 25.9808i | −0.442861 | − | 1.27843i | ||||
\(414\) | − | 10.3923i | − | 0.510754i | ||||||
\(415\) | 3.00000 | + | 5.19615i | 0.147264 | + | 0.255069i | ||||
\(416\) | −2.50000 | + | 2.59808i | −0.122573 | + | 0.127381i | ||||
\(417\) | 39.0000 | 1.90984 | ||||||||
\(418\) | 10.5000 | − | 18.1865i | 0.513572 | − | 0.889532i | ||||
\(419\) | −16.5000 | − | 28.5788i | −0.806078 | − | 1.39617i | −0.915561 | − | 0.402179i | \(-0.868253\pi\) |
0.109483 | − | 0.993989i | \(-0.465080\pi\) | |||||||
\(420\) | −1.50000 | + | 7.79423i | −0.0731925 | + | 0.380319i | ||||
\(421\) | 13.8564i | 0.675320i | 0.941268 | + | 0.337660i | \(0.109635\pi\) | ||||
−0.941268 | + | 0.337660i | \(0.890365\pi\) | |||||||
\(422\) | 1.00000 | 0.0486792 | ||||||||
\(423\) | 5.19615i | 0.252646i | ||||||||
\(424\) | 1.50000 | + | 0.866025i | 0.0728464 | + | 0.0420579i | ||||
\(425\) | −12.0000 | −0.582086 | ||||||||
\(426\) | 13.5000 | + | 7.79423i | 0.654077 | + | 0.377632i | ||||
\(427\) | −4.50000 | − | 0.866025i | −0.217770 | − | 0.0419099i | ||||
\(428\) | 10.3923i | 0.502331i | ||||||||
\(429\) | −13.5000 | − | 12.9904i | −0.651786 | − | 0.627182i | ||||
\(430\) | 1.50000 | + | 0.866025i | 0.0723364 | + | 0.0417635i | ||||
\(431\) | 21.0000 | 1.01153 | 0.505767 | − | 0.862670i | \(-0.331209\pi\) | ||||
0.505767 | + | 0.862670i | \(0.331209\pi\) | |||||||
\(432\) | 4.50000 | + | 2.59808i | 0.216506 | + | 0.125000i | ||||
\(433\) | 4.50000 | + | 2.59808i | 0.216256 | + | 0.124856i | 0.604216 | − | 0.796821i | \(-0.293487\pi\) |
−0.387959 | + | 0.921676i | \(0.626820\pi\) | |||||||
\(434\) | 2.50000 | − | 0.866025i | 0.120004 | − | 0.0415705i | ||||
\(435\) | − | 25.9808i | − | 1.24568i | ||||||
\(436\) | 8.66025i | 0.414751i | ||||||||
\(437\) | −21.0000 | − | 12.1244i | −1.00457 | − | 0.579987i | ||||
\(438\) | 19.5000 | + | 11.2583i | 0.931746 | + | 0.537944i | ||||
\(439\) | −3.00000 | − | 1.73205i | −0.143182 | − | 0.0826663i | 0.426698 | − | 0.904394i | \(-0.359677\pi\) |
−0.569880 | + | 0.821728i | \(0.693010\pi\) | |||||||
\(440\) | 4.50000 | − | 2.59808i | 0.214529 | − | 0.123858i | ||||
\(441\) | −16.5000 | + | 12.9904i | −0.785714 | + | 0.618590i | ||||
\(442\) | 6.00000 | + | 20.7846i | 0.285391 | + | 0.988623i | ||||
\(443\) | −10.5000 | + | 6.06218i | −0.498870 | + | 0.288023i | −0.728247 | − | 0.685315i | \(-0.759665\pi\) |
0.229377 | + | 0.973338i | \(0.426331\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.0000 | 0.568855 | ||||||||
\(446\) | −29.0000 | −1.37319 | ||||||||
\(447\) | −31.5000 | + | 18.1865i | −1.48990 | + | 0.860194i | ||||
\(448\) | 0.500000 | − | 2.59808i | 0.0236228 | − | 0.122748i | ||||
\(449\) | −7.50000 | + | 12.9904i | −0.353947 | + | 0.613054i | −0.986937 | − | 0.161106i | \(-0.948494\pi\) |
0.632990 | + | 0.774160i | \(0.281827\pi\) | |||||||
\(450\) | 6.00000 | 0.282843 | ||||||||
\(451\) | −13.5000 | + | 7.79423i | −0.635690 | + | 0.367016i | ||||
\(452\) | − | 1.73205i | − | 0.0814688i | ||||||
\(453\) | −39.0000 | −1.83238 | ||||||||
\(454\) | − | 10.3923i | − | 0.487735i | ||||||
\(455\) | 13.5000 | − | 9.52628i | 0.632890 | − | 0.446599i | ||||
\(456\) | 10.5000 | − | 6.06218i | 0.491708 | − | 0.283887i | ||||
\(457\) | 18.0000 | + | 10.3923i | 0.842004 | + | 0.486132i | 0.857945 | − | 0.513741i | \(-0.171741\pi\) |
−0.0159406 | + | 0.999873i | \(0.505074\pi\) | |||||||
\(458\) | −25.0000 | −1.16817 | ||||||||
\(459\) | 27.0000 | − | 15.5885i | 1.26025 | − | 0.727607i | ||||
\(460\) | −3.00000 | − | 5.19615i | −0.139876 | − | 0.242272i | ||||
\(461\) | 22.5000 | + | 12.9904i | 1.04793 | + | 0.605022i | 0.922069 | − | 0.387026i | \(-0.126497\pi\) |
0.125860 | + | 0.992048i | \(0.459831\pi\) | |||||||
\(462\) | 13.5000 | + | 2.59808i | 0.628077 | + | 0.120873i | ||||
\(463\) | − | 31.1769i | − | 1.44891i | −0.689320 | − | 0.724457i | \(-0.742091\pi\) | ||
0.689320 | − | 0.724457i | \(-0.257909\pi\) | |||||||
\(464\) | 8.66025i | 0.402042i | ||||||||
\(465\) | 1.50000 | + | 2.59808i | 0.0695608 | + | 0.120483i | ||||
\(466\) | 22.5167i | 1.04306i | ||||||||
\(467\) | 4.50000 | + | 7.79423i | 0.208235 | + | 0.360674i | 0.951159 | − | 0.308702i | \(-0.0998947\pi\) |
−0.742923 | + | 0.669376i | \(0.766561\pi\) | |||||||
\(468\) | −3.00000 | − | 10.3923i | −0.138675 | − | 0.480384i | ||||
\(469\) | 4.50000 | + | 0.866025i | 0.207791 | + | 0.0399893i | ||||
\(470\) | 1.50000 | + | 2.59808i | 0.0691898 | + | 0.119840i | ||||
\(471\) | 3.00000 | 0.138233 | ||||||||
\(472\) | −9.00000 | + | 5.19615i | −0.414259 | + | 0.239172i | ||||
\(473\) | 1.50000 | − | 2.59808i | 0.0689701 | − | 0.119460i | ||||
\(474\) | −1.50000 | + | 0.866025i | −0.0688973 | + | 0.0397779i | ||||
\(475\) | 7.00000 | − | 12.1244i | 0.321182 | − | 0.556304i | ||||
\(476\) | −12.0000 | − | 10.3923i | −0.550019 | − | 0.476331i | ||||
\(477\) | −4.50000 | + | 2.59808i | −0.206041 | + | 0.118958i | ||||
\(478\) | −6.00000 | + | 10.3923i | −0.274434 | + | 0.475333i | ||||
\(479\) | 19.0526i | 0.870534i | 0.900302 | + | 0.435267i | \(0.143346\pi\) | ||||
−0.900302 | + | 0.435267i | \(0.856654\pi\) | |||||||
\(480\) | 3.00000 | 0.136931 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −10.0000 | −0.455488 | ||||||||
\(483\) | 3.00000 | − | 15.5885i | 0.136505 | − | 0.709299i | ||||
\(484\) | 1.00000 | + | 1.73205i | 0.0454545 | + | 0.0787296i | ||||
\(485\) | − | 32.9090i | − | 1.49432i | ||||||
\(486\) | −13.5000 | + | 7.79423i | −0.612372 | + | 0.353553i | ||||
\(487\) | −3.00000 | + | 1.73205i | −0.135943 | + | 0.0784867i | −0.566429 | − | 0.824110i | \(-0.691675\pi\) |
0.430486 | + | 0.902597i | \(0.358342\pi\) | |||||||
\(488\) | 1.73205i | 0.0784063i | ||||||||
\(489\) | −4.50000 | − | 7.79423i | −0.203497 | − | 0.352467i | ||||
\(490\) | −4.50000 | + | 11.2583i | −0.203289 | + | 0.508600i | ||||
\(491\) | 31.5000 | − | 18.1865i | 1.42158 | − | 0.820747i | 0.425141 | − | 0.905127i | \(-0.360224\pi\) |
0.996434 | + | 0.0843802i | \(0.0268910\pi\) | |||||||
\(492\) | −9.00000 | −0.405751 | ||||||||
\(493\) | 45.0000 | + | 25.9808i | 2.02670 | + | 1.17011i | ||||
\(494\) | −24.5000 | − | 6.06218i | −1.10231 | − | 0.272750i | ||||
\(495\) | 15.5885i | 0.700649i | ||||||||
\(496\) | −0.500000 | − | 0.866025i | −0.0224507 | − | 0.0388857i | ||||
\(497\) | 18.0000 | + | 15.5885i | 0.807410 | + | 0.699238i | ||||
\(498\) | 6.00000 | 0.268866 | ||||||||
\(499\) | −28.5000 | + | 16.4545i | −1.27584 | + | 0.736604i | −0.976080 | − | 0.217412i | \(-0.930238\pi\) |
−0.299755 | + | 0.954016i | \(0.596905\pi\) | |||||||
\(500\) | 10.5000 | − | 6.06218i | 0.469574 | − | 0.271109i | ||||
\(501\) | −7.50000 | + | 12.9904i | −0.335075 | + | 0.580367i | ||||
\(502\) | 7.50000 | + | 12.9904i | 0.334741 | + | 0.579789i | ||||
\(503\) | −13.5000 | + | 23.3827i | −0.601935 | + | 1.04258i | 0.390593 | + | 0.920564i | \(0.372270\pi\) |
−0.992528 | + | 0.122019i | \(0.961063\pi\) | |||||||
\(504\) | 6.00000 | + | 5.19615i | 0.267261 | + | 0.231455i | ||||
\(505\) | 13.5000 | − | 7.79423i | 0.600742 | − | 0.346839i | ||||
\(506\) | −9.00000 | + | 5.19615i | −0.400099 | + | 0.230997i | ||||
\(507\) | −10.5000 | + | 19.9186i | −0.466321 | + | 0.884615i | ||||
\(508\) | 8.50000 | − | 14.7224i | 0.377127 | − | 0.653202i | ||||
\(509\) | 6.00000 | + | 3.46410i | 0.265945 | + | 0.153544i | 0.627044 | − | 0.778984i | \(-0.284265\pi\) |
−0.361098 | + | 0.932528i | \(0.617598\pi\) | |||||||
\(510\) | 9.00000 | − | 15.5885i | 0.398527 | − | 0.690268i | ||||
\(511\) | 26.0000 | + | 22.5167i | 1.15017 | + | 0.996078i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 36.3731i | 1.60591i | ||||||||
\(514\) | −3.00000 | − | 5.19615i | −0.132324 | − | 0.229192i | ||||
\(515\) | −7.50000 | + | 12.9904i | −0.330489 | + | 0.572425i | ||||
\(516\) | 1.50000 | − | 0.866025i | 0.0660338 | − | 0.0381246i | ||||
\(517\) | 4.50000 | − | 2.59808i | 0.197910 | − | 0.114263i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.5000 | − | 7.79423i | 0.592584 | − | 0.342129i | ||||
\(520\) | −4.50000 | − | 4.33013i | −0.197338 | − | 0.189889i | ||||
\(521\) | 7.50000 | − | 12.9904i | 0.328581 | − | 0.569119i | −0.653650 | − | 0.756797i | \(-0.726763\pi\) |
0.982231 | + | 0.187678i | \(0.0600963\pi\) | |||||||
\(522\) | −22.5000 | − | 12.9904i | −0.984798 | − | 0.568574i | ||||
\(523\) | 27.0000 | + | 15.5885i | 1.18063 | + | 0.681636i | 0.956160 | − | 0.292846i | \(-0.0946023\pi\) |
0.224468 | + | 0.974481i | \(0.427936\pi\) | |||||||
\(524\) | −1.50000 | + | 2.59808i | −0.0655278 | + | 0.113497i | ||||
\(525\) | 9.00000 | + | 1.73205i | 0.392792 | + | 0.0755929i | ||||
\(526\) | 7.50000 | + | 4.33013i | 0.327016 | + | 0.188803i | ||||
\(527\) | −6.00000 | −0.261364 | ||||||||
\(528\) | − | 5.19615i | − | 0.226134i | ||||||
\(529\) | −5.50000 | − | 9.52628i | −0.239130 | − | 0.414186i | ||||
\(530\) | −1.50000 | + | 2.59808i | −0.0651558 | + | 0.112853i | ||||
\(531\) | − | 31.1769i | − | 1.35296i | ||||||
\(532\) | 17.5000 | − | 6.06218i | 0.758721 | − | 0.262829i | ||||
\(533\) | 13.5000 | + | 12.9904i | 0.584750 | + | 0.562676i | ||||
\(534\) | 6.00000 | − | 10.3923i | 0.259645 | − | 0.449719i | ||||
\(535\) | −18.0000 | −0.778208 | ||||||||
\(536\) | − | 1.73205i | − | 0.0748132i | ||||||
\(537\) | −16.5000 | − | 28.5788i | −0.712028 | − | 1.23327i | ||||
\(538\) | −30.0000 | −1.29339 | ||||||||
\(539\) | 19.5000 | + | 7.79423i | 0.839924 | + | 0.335721i | ||||
\(540\) | −4.50000 | + | 7.79423i | −0.193649 | + | 0.335410i | ||||
\(541\) | −13.5000 | + | 7.79423i | −0.580410 | + | 0.335100i | −0.761296 | − | 0.648404i | \(-0.775437\pi\) |
0.180886 | + | 0.983504i | \(0.442103\pi\) | |||||||
\(542\) | −8.00000 | − | 13.8564i | −0.343629 | − | 0.595184i | ||||
\(543\) | 12.0000 | + | 20.7846i | 0.514969 | + | 0.891953i | ||||
\(544\) | −3.00000 | + | 5.19615i | −0.128624 | + | 0.222783i | ||||
\(545\) | −15.0000 | −0.642529 | ||||||||
\(546\) | −1.50000 | − | 16.4545i | −0.0641941 | − | 0.704187i | ||||
\(547\) | 44.0000 | 1.88130 | 0.940652 | − | 0.339372i | \(-0.110215\pi\) | ||||
0.940652 | + | 0.339372i | \(0.110215\pi\) | |||||||
\(548\) | 3.00000 | − | 5.19615i | 0.128154 | − | 0.221969i | ||||
\(549\) | −4.50000 | − | 2.59808i | −0.192055 | − | 0.110883i | ||||
\(550\) | −3.00000 | − | 5.19615i | −0.127920 | − | 0.221565i | ||||
\(551\) | −52.5000 | + | 30.3109i | −2.23658 | + | 1.29129i | ||||
\(552\) | −6.00000 | −0.255377 | ||||||||
\(553\) | −2.50000 | + | 0.866025i | −0.106311 | + | 0.0368271i | ||||
\(554\) | 10.0000 | 0.424859 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 22.5167i | − | 0.954919i | ||||||
\(557\) | −33.0000 | −1.39825 | −0.699127 | − | 0.714997i | \(-0.746428\pi\) | ||||
−0.699127 | + | 0.714997i | \(0.746428\pi\) | |||||||
\(558\) | 3.00000 | 0.127000 | ||||||||
\(559\) | −3.50000 | − | 0.866025i | −0.148034 | − | 0.0366290i | ||||
\(560\) | 4.50000 | + | 0.866025i | 0.190160 | + | 0.0365963i | ||||
\(561\) | −27.0000 | − | 15.5885i | −1.13994 | − | 0.658145i | ||||
\(562\) | 3.00000 | − | 5.19615i | 0.126547 | − | 0.219186i | ||||
\(563\) | 6.00000 | + | 10.3923i | 0.252870 | + | 0.437983i | 0.964315 | − | 0.264758i | \(-0.0852922\pi\) |
−0.711445 | + | 0.702742i | \(0.751959\pi\) | |||||||
\(564\) | 3.00000 | 0.126323 | ||||||||
\(565\) | 3.00000 | 0.126211 | ||||||||
\(566\) | −19.5000 | − | 11.2583i | −0.819646 | − | 0.473223i | ||||
\(567\) | −22.5000 | + | 7.79423i | −0.944911 | + | 0.327327i | ||||
\(568\) | 4.50000 | − | 7.79423i | 0.188816 | − | 0.327039i | ||||
\(569\) | −12.0000 | − | 6.92820i | −0.503066 | − | 0.290445i | 0.226913 | − | 0.973915i | \(-0.427137\pi\) |
−0.729979 | + | 0.683470i | \(0.760470\pi\) | |||||||
\(570\) | 10.5000 | + | 18.1865i | 0.439797 | + | 0.761750i | ||||
\(571\) | 2.50000 | − | 4.33013i | 0.104622 | − | 0.181210i | −0.808962 | − | 0.587861i | \(-0.799970\pi\) |
0.913584 | + | 0.406651i | \(0.133303\pi\) | |||||||
\(572\) | −7.50000 | + | 7.79423i | −0.313591 | + | 0.325893i | ||||
\(573\) | 13.5000 | + | 23.3827i | 0.563971 | + | 0.976826i | ||||
\(574\) | −13.5000 | − | 2.59808i | −0.563479 | − | 0.108442i | ||||
\(575\) | −6.00000 | + | 3.46410i | −0.250217 | + | 0.144463i | ||||
\(576\) | 1.50000 | − | 2.59808i | 0.0625000 | − | 0.108253i | ||||
\(577\) | 3.50000 | − | 6.06218i | 0.145707 | − | 0.252372i | −0.783930 | − | 0.620850i | \(-0.786788\pi\) |
0.929636 | + | 0.368478i | \(0.120121\pi\) | |||||||
\(578\) | 9.50000 | + | 16.4545i | 0.395148 | + | 0.684416i | ||||
\(579\) | 10.5000 | + | 18.1865i | 0.436365 | + | 0.755807i | ||||
\(580\) | −15.0000 | −0.622841 | ||||||||
\(581\) | 9.00000 | + | 1.73205i | 0.373383 | + | 0.0718576i | ||||
\(582\) | −28.5000 | − | 16.4545i | −1.18136 | − | 0.682060i | ||||
\(583\) | 4.50000 | + | 2.59808i | 0.186371 | + | 0.107601i | ||||
\(584\) | 6.50000 | − | 11.2583i | 0.268972 | − | 0.465873i | ||||
\(585\) | 18.0000 | − | 5.19615i | 0.744208 | − | 0.214834i | ||||
\(586\) | −25.5000 | + | 14.7224i | −1.05340 | + | 0.608178i | ||||
\(587\) | 28.5000 | − | 16.4545i | 1.17632 | − | 0.679149i | 0.221160 | − | 0.975237i | \(-0.429016\pi\) |
0.955161 | + | 0.296088i | \(0.0956823\pi\) | |||||||
\(588\) | 7.50000 | + | 9.52628i | 0.309295 | + | 0.392857i | ||||
\(589\) | 3.50000 | − | 6.06218i | 0.144215 | − | 0.249788i | ||||
\(590\) | −9.00000 | − | 15.5885i | −0.370524 | − | 0.641767i | ||||
\(591\) | 31.5000 | + | 18.1865i | 1.29574 | + | 0.748094i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.50000 | − | 4.33013i | 0.307988 | − | 0.177817i | −0.338038 | − | 0.941133i | \(-0.609763\pi\) |
0.646026 | + | 0.763316i | \(0.276430\pi\) | |||||||
\(594\) | 13.5000 | + | 7.79423i | 0.553912 | + | 0.319801i | ||||
\(595\) | 18.0000 | − | 20.7846i | 0.737928 | − | 0.852086i | ||||
\(596\) | 10.5000 | + | 18.1865i | 0.430097 | + | 0.744949i | ||||
\(597\) | −3.00000 | + | 5.19615i | −0.122782 | + | 0.212664i | ||||
\(598\) | 9.00000 | + | 8.66025i | 0.368037 | + | 0.354144i | ||||
\(599\) | −25.5000 | − | 14.7224i | −1.04190 | − | 0.601542i | −0.121530 | − | 0.992588i | \(-0.538780\pi\) |
−0.920371 | + | 0.391045i | \(0.872114\pi\) | |||||||
\(600\) | − | 3.46410i | − | 0.141421i | ||||||
\(601\) | −19.5000 | + | 11.2583i | −0.795422 | + | 0.459237i | −0.841868 | − | 0.539684i | \(-0.818544\pi\) |
0.0464461 | + | 0.998921i | \(0.485210\pi\) | |||||||
\(602\) | 2.50000 | − | 0.866025i | 0.101892 | − | 0.0352966i | ||||
\(603\) | 4.50000 | + | 2.59808i | 0.183254 | + | 0.105802i | ||||
\(604\) | 22.5167i | 0.916190i | ||||||||
\(605\) | −3.00000 | + | 1.73205i | −0.121967 | + | 0.0704179i | ||||
\(606\) | − | 15.5885i | − | 0.633238i | ||||||
\(607\) | 19.0526i | 0.773320i | 0.922222 | + | 0.386660i | \(0.126371\pi\) | ||||
−0.922222 | + | 0.386660i | \(0.873629\pi\) | |||||||
\(608\) | −3.50000 | − | 6.06218i | −0.141944 | − | 0.245854i | ||||
\(609\) | −30.0000 | − | 25.9808i | −1.21566 | − | 1.05279i | ||||
\(610\) | −3.00000 | −0.121466 | ||||||||
\(611\) | −4.50000 | − | 4.33013i | −0.182051 | − | 0.175178i | ||||
\(612\) | −9.00000 | − | 15.5885i | −0.363803 | − | 0.630126i | ||||
\(613\) | − | 22.5167i | − | 0.909439i | −0.890635 | − | 0.454720i | \(-0.849739\pi\) | ||
0.890635 | − | 0.454720i | \(-0.150261\pi\) | |||||||
\(614\) | 2.00000 | − | 3.46410i | 0.0807134 | − | 0.139800i | ||||
\(615\) | − | 15.5885i | − | 0.628587i | ||||||
\(616\) | 1.50000 | − | 7.79423i | 0.0604367 | − | 0.314038i | ||||
\(617\) | 4.50000 | − | 7.79423i | 0.181163 | − | 0.313784i | −0.761114 | − | 0.648618i | \(-0.775347\pi\) |
0.942277 | + | 0.334835i | \(0.108680\pi\) | |||||||
\(618\) | 7.50000 | + | 12.9904i | 0.301694 | + | 0.522550i | ||||
\(619\) | −2.50000 | + | 4.33013i | −0.100483 | + | 0.174042i | −0.911884 | − | 0.410448i | \(-0.865372\pi\) |
0.811400 | + | 0.584491i | \(0.198706\pi\) | |||||||
\(620\) | 1.50000 | − | 0.866025i | 0.0602414 | − | 0.0347804i | ||||
\(621\) | 9.00000 | − | 15.5885i | 0.361158 | − | 0.625543i | ||||
\(622\) | −1.50000 | − | 2.59808i | −0.0601445 | − | 0.104173i | ||||
\(623\) | 12.0000 | − | 13.8564i | 0.480770 | − | 0.555145i | ||||
\(624\) | −6.00000 | + | 1.73205i | −0.240192 | + | 0.0693375i | ||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | 5.19615i | 0.207680i | ||||||||
\(627\) | 31.5000 | − | 18.1865i | 1.25799 | − | 0.726300i | ||||
\(628\) | − | 1.73205i | − | 0.0691164i | ||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −9.00000 | + | 10.3923i | −0.358569 | + | 0.414039i | ||||
\(631\) | −1.50000 | − | 0.866025i | −0.0597141 | − | 0.0344759i | 0.469846 | − | 0.882749i | \(-0.344310\pi\) |
−0.529560 | + | 0.848273i | \(0.677643\pi\) | |||||||
\(632\) | 0.500000 | + | 0.866025i | 0.0198889 | + | 0.0344486i | ||||
\(633\) | 1.50000 | + | 0.866025i | 0.0596196 | + | 0.0344214i | ||||
\(634\) | −3.00000 | −0.119145 | ||||||||
\(635\) | 25.5000 | + | 14.7224i | 1.01194 | + | 0.584242i | ||||
\(636\) | 1.50000 | + | 2.59808i | 0.0594789 | + | 0.103020i | ||||
\(637\) | 2.50000 | − | 25.1147i | 0.0990536 | − | 0.995082i | ||||
\(638\) | 25.9808i | 1.02859i | ||||||||
\(639\) | 13.5000 | + | 23.3827i | 0.534052 | + | 0.925005i | ||||
\(640\) | − | 1.73205i | − | 0.0684653i | ||||||
\(641\) | −30.0000 | + | 17.3205i | −1.18493 | + | 0.684119i | −0.957150 | − | 0.289594i | \(-0.906480\pi\) |
−0.227779 | + | 0.973713i | \(0.573146\pi\) | |||||||
\(642\) | −9.00000 | + | 15.5885i | −0.355202 | + | 0.615227i | ||||
\(643\) | 14.5000 | − | 25.1147i | 0.571824 | − | 0.990429i | −0.424555 | − | 0.905402i | \(-0.639569\pi\) |
0.996379 | − | 0.0850262i | \(-0.0270974\pi\) | |||||||
\(644\) | −9.00000 | − | 1.73205i | −0.354650 | − | 0.0682524i | ||||
\(645\) | 1.50000 | + | 2.59808i | 0.0590624 | + | 0.102299i | ||||
\(646\) | −42.0000 | −1.65247 | ||||||||
\(647\) | 3.00000 | 0.117942 | 0.0589711 | − | 0.998260i | \(-0.481218\pi\) | ||||
0.0589711 | + | 0.998260i | \(0.481218\pi\) | |||||||
\(648\) | 4.50000 | + | 7.79423i | 0.176777 | + | 0.306186i | ||||
\(649\) | −27.0000 | + | 15.5885i | −1.05984 | + | 0.611900i | ||||
\(650\) | −5.00000 | + | 5.19615i | −0.196116 | + | 0.203810i | ||||
\(651\) | 4.50000 | + | 0.866025i | 0.176369 | + | 0.0339422i | ||||
\(652\) | −4.50000 | + | 2.59808i | −0.176234 | + | 0.101749i | ||||
\(653\) | 36.0000 | + | 20.7846i | 1.40879 | + | 0.813365i | 0.995272 | − | 0.0971316i | \(-0.0309668\pi\) |
0.413517 | + | 0.910496i | \(0.364300\pi\) | |||||||
\(654\) | −7.50000 | + | 12.9904i | −0.293273 | + | 0.507964i | ||||
\(655\) | −4.50000 | − | 2.59808i | −0.175830 | − | 0.101515i | ||||
\(656\) | 5.19615i | 0.202876i | ||||||||
\(657\) | 19.5000 | + | 33.7750i | 0.760767 | + | 1.31769i | ||||
\(658\) | 4.50000 | + | 0.866025i | 0.175428 | + | 0.0337612i | ||||
\(659\) | 34.5000 | + | 19.9186i | 1.34393 | + | 0.775918i | 0.987382 | − | 0.158359i | \(-0.0506204\pi\) |
0.356548 | + | 0.934277i | \(0.383954\pi\) | |||||||
\(660\) | 9.00000 | 0.350325 | ||||||||
\(661\) | 13.0000 | 0.505641 | 0.252821 | − | 0.967513i | \(-0.418642\pi\) | ||||
0.252821 | + | 0.967513i | \(0.418642\pi\) | |||||||
\(662\) | −22.5000 | − | 12.9904i | −0.874487 | − | 0.504885i | ||||
\(663\) | −9.00000 | + | 36.3731i | −0.349531 | + | 1.41261i | ||||
\(664\) | − | 3.46410i | − | 0.134433i | ||||||
\(665\) | 10.5000 | + | 30.3109i | 0.407173 | + | 1.17541i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30.0000 | 1.16160 | ||||||||
\(668\) | 7.50000 | + | 4.33013i | 0.290184 | + | 0.167538i | ||||
\(669\) | −43.5000 | − | 25.1147i | −1.68181 | − | 0.970992i | ||||
\(670\) | 3.00000 | 0.115900 | ||||||||
\(671\) | 5.19615i | 0.200595i | ||||||||
\(672\) | 3.00000 | − | 3.46410i | 0.115728 | − | 0.133631i | ||||
\(673\) | −3.50000 | − | 6.06218i | −0.134915 | − | 0.233680i | 0.790650 | − | 0.612268i | \(-0.209743\pi\) |
−0.925565 | + | 0.378589i | \(0.876409\pi\) | |||||||
\(674\) | −5.00000 | + | 8.66025i | −0.192593 | + | 0.333581i | ||||
\(675\) | 9.00000 | + | 5.19615i | 0.346410 | + | 0.200000i | ||||
\(676\) | 11.5000 | + | 6.06218i | 0.442308 | + | 0.233161i | ||||
\(677\) | 13.5000 | + | 23.3827i | 0.518847 | + | 0.898670i | 0.999760 | + | 0.0219013i | \(0.00697196\pi\) |
−0.480913 | + | 0.876768i | \(0.659695\pi\) | |||||||
\(678\) | 1.50000 | − | 2.59808i | 0.0576072 | − | 0.0997785i | ||||
\(679\) | −38.0000 | − | 32.9090i | −1.45831 | − | 1.26293i | ||||
\(680\) | −9.00000 | − | 5.19615i | −0.345134 | − | 0.199263i | ||||
\(681\) | 9.00000 | − | 15.5885i | 0.344881 | − | 0.597351i | ||||
\(682\) | −1.50000 | − | 2.59808i | −0.0574380 | − | 0.0994855i | ||||
\(683\) | 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 | ||||||||
\(685\) | 9.00000 | + | 5.19615i | 0.343872 | + | 0.198535i | ||||
\(686\) | 8.50000 | + | 16.4545i | 0.324532 | + | 0.628235i | ||||
\(687\) | −37.5000 | − | 21.6506i | −1.43071 | − | 0.826023i | ||||
\(688\) | −0.500000 | − | 0.866025i | −0.0190623 | − | 0.0330169i | ||||
\(689\) | 1.50000 | − | 6.06218i | 0.0571454 | − | 0.230951i | ||||
\(690\) | − | 10.3923i | − | 0.395628i | ||||||
\(691\) | −22.0000 | + | 38.1051i | −0.836919 | + | 1.44959i | 0.0555386 | + | 0.998457i | \(0.482312\pi\) |
−0.892458 | + | 0.451130i | \(0.851021\pi\) | |||||||
\(692\) | −4.50000 | − | 7.79423i | −0.171064 | − | 0.296292i | ||||
\(693\) | 18.0000 | + | 15.5885i | 0.683763 | + | 0.592157i | ||||
\(694\) | − | 10.3923i | − | 0.394486i | ||||||
\(695\) | 39.0000 | 1.47935 | ||||||||
\(696\) | −7.50000 | + | 12.9904i | −0.284287 | + | 0.492399i | ||||
\(697\) | 27.0000 | + | 15.5885i | 1.02270 | + | 0.590455i | ||||
\(698\) | 35.0000 | 1.32477 | ||||||||
\(699\) | −19.5000 | + | 33.7750i | −0.737558 | + | 1.27749i | ||||
\(700\) | 1.00000 | − | 5.19615i | 0.0377964 | − | 0.196396i | ||||
\(701\) | − | 27.7128i | − | 1.04670i | −0.852118 | − | 0.523349i | \(-0.824682\pi\) | ||
0.852118 | − | 0.523349i | \(-0.175318\pi\) | |||||||
\(702\) | 4.50000 | − | 18.1865i | 0.169842 | − | 0.686406i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −3.00000 | −0.113067 | ||||||||
\(705\) | 5.19615i | 0.195698i | ||||||||
\(706\) | −22.5000 | − | 12.9904i | −0.846799 | − | 0.488899i | ||||
\(707\) | 4.50000 | − | 23.3827i | 0.169240 | − | 0.879396i | ||||
\(708\) | −18.0000 | −0.676481 | ||||||||
\(709\) | − | 25.9808i | − | 0.975728i | −0.872920 | − | 0.487864i | \(-0.837776\pi\) | ||
0.872920 | − | 0.487864i | \(-0.162224\pi\) | |||||||
\(710\) | 13.5000 | + | 7.79423i | 0.506646 | + | 0.292512i | ||||
\(711\) | −3.00000 | −0.112509 | ||||||||
\(712\) | −6.00000 | − | 3.46410i | −0.224860 | − | 0.129823i | ||||
\(713\) | −3.00000 | + | 1.73205i | −0.112351 | + | 0.0648658i | ||||
\(714\) | −9.00000 | − | 25.9808i | −0.336817 | − | 0.972306i | ||||
\(715\) | −13.5000 | − | 12.9904i | −0.504871 | − | 0.485813i | ||||
\(716\) | −16.5000 | + | 9.52628i | −0.616634 | + | 0.356014i | ||||
\(717\) | −18.0000 | + | 10.3923i | −0.672222 | + | 0.388108i | ||||
\(718\) | 3.00000 | 0.111959 | ||||||||
\(719\) | −3.00000 | −0.111881 | −0.0559406 | − | 0.998434i | \(-0.517816\pi\) | ||||
−0.0559406 | + | 0.998434i | \(0.517816\pi\) | |||||||
\(720\) | 4.50000 | + | 2.59808i | 0.167705 | + | 0.0968246i | ||||
\(721\) | 7.50000 | + | 21.6506i | 0.279315 | + | 0.806312i | ||||
\(722\) | 15.0000 | − | 25.9808i | 0.558242 | − | 0.966904i | ||||
\(723\) | −15.0000 | − | 8.66025i | −0.557856 | − | 0.322078i | ||||
\(724\) | 12.0000 | − | 6.92820i | 0.445976 | − | 0.257485i | ||||
\(725\) | 17.3205i | 0.643268i | ||||||||
\(726\) | 3.46410i | 0.128565i | ||||||||
\(727\) | − | 10.3923i | − | 0.385429i | −0.981255 | − | 0.192715i | \(-0.938271\pi\) | ||
0.981255 | − | 0.192715i | \(-0.0617292\pi\) | |||||||
\(728\) | −9.50000 | + | 0.866025i | −0.352093 | + | 0.0320970i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 19.5000 | + | 11.2583i | 0.721727 | + | 0.416689i | ||||
\(731\) | −6.00000 | −0.221918 | ||||||||
\(732\) | −1.50000 | + | 2.59808i | −0.0554416 | + | 0.0960277i | ||||
\(733\) | −18.5000 | − | 32.0429i | −0.683313 | − | 1.18353i | −0.973964 | − | 0.226704i | \(-0.927205\pi\) |
0.290651 | − | 0.956829i | \(-0.406128\pi\) | |||||||
\(734\) | −13.5000 | − | 7.79423i | −0.498294 | − | 0.287690i | ||||
\(735\) | −16.5000 | + | 12.9904i | −0.608612 | + | 0.479157i | ||||
\(736\) | 3.46410i | 0.127688i | ||||||||
\(737\) | − | 5.19615i | − | 0.191403i | ||||||
\(738\) | −13.5000 | − | 7.79423i | −0.496942 | − | 0.286910i | ||||
\(739\) | − | 19.0526i | − | 0.700860i | −0.936589 | − | 0.350430i | \(-0.886036\pi\) | ||
0.936589 | − | 0.350430i | \(-0.113964\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −31.5000 | − | 30.3109i | −1.15718 | − | 1.11350i | ||||
\(742\) | 1.50000 | + | 4.33013i | 0.0550667 | + | 0.158964i | ||||
\(743\) | 4.50000 | + | 7.79423i | 0.165089 | + | 0.285943i | 0.936687 | − | 0.350168i | \(-0.113876\pi\) |
−0.771598 | + | 0.636111i | \(0.780542\pi\) | |||||||
\(744\) | − | 1.73205i | − | 0.0635001i | ||||||
\(745\) | −31.5000 | + | 18.1865i | −1.15407 | + | 0.666303i | ||||
\(746\) | −14.5000 | + | 25.1147i | −0.530883 | + | 0.919516i | ||||
\(747\) | 9.00000 | + | 5.19615i | 0.329293 | + | 0.190117i | ||||
\(748\) | −9.00000 | + | 15.5885i | −0.329073 | + | 0.569970i | ||||
\(749\) | −18.0000 | + | 20.7846i | −0.657706 | + | 0.759453i | ||||
\(750\) | 21.0000 | 0.766812 | ||||||||
\(751\) | −2.00000 | + | 3.46410i | −0.0729810 | + | 0.126407i | −0.900207 | − | 0.435463i | \(-0.856585\pi\) |
0.827225 | + | 0.561870i | \(0.189918\pi\) | |||||||
\(752\) | − | 1.73205i | − | 0.0631614i | ||||||
\(753\) | 25.9808i | 0.946792i | ||||||||
\(754\) | 30.0000 | − | 8.66025i | 1.09254 | − | 0.315388i | ||||
\(755\) | −39.0000 | −1.41936 | ||||||||
\(756\) | 4.50000 | + | 12.9904i | 0.163663 | + | 0.472456i | ||||
\(757\) | −23.5000 | − | 40.7032i | −0.854122 | − | 1.47938i | −0.877457 | − | 0.479655i | \(-0.840762\pi\) |
0.0233351 | − | 0.999728i | \(-0.492572\pi\) | |||||||
\(758\) | 19.0526i | 0.692020i | ||||||||
\(759\) | −18.0000 | −0.653359 | ||||||||
\(760\) | 10.5000 | − | 6.06218i | 0.380875 | − | 0.219898i | ||||
\(761\) | − | 29.4449i | − | 1.06738i | −0.845682 | − | 0.533688i | \(-0.820806\pi\) | ||
0.845682 | − | 0.533688i | \(-0.179194\pi\) | |||||||
\(762\) | 25.5000 | − | 14.7224i | 0.923768 | − | 0.533337i | ||||
\(763\) | −15.0000 | + | 17.3205i | −0.543036 | + | 0.627044i | ||||
\(764\) | 13.5000 | − | 7.79423i | 0.488413 | − | 0.281985i | ||||
\(765\) | 27.0000 | − | 15.5885i | 0.976187 | − | 0.563602i | ||||
\(766\) | 4.50000 | + | 2.59808i | 0.162592 | + | 0.0938723i | ||||
\(767\) | 27.0000 | + | 25.9808i | 0.974913 | + | 0.938111i | ||||
\(768\) | −1.50000 | − | 0.866025i | −0.0541266 | − | 0.0312500i | ||||
\(769\) | −6.50000 | − | 11.2583i | −0.234396 | − | 0.405986i | 0.724701 | − | 0.689063i | \(-0.241978\pi\) |
−0.959097 | + | 0.283078i | \(0.908645\pi\) | |||||||
\(770\) | 13.5000 | + | 2.59808i | 0.486506 | + | 0.0936282i | ||||
\(771\) | − | 10.3923i | − | 0.374270i | ||||||
\(772\) | 10.5000 | − | 6.06218i | 0.377903 | − | 0.218183i | ||||
\(773\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(774\) | 3.00000 | 0.107833 | ||||||||
\(775\) | −1.00000 | − | 1.73205i | −0.0359211 | − | 0.0622171i | ||||
\(776\) | −9.50000 | + | 16.4545i | −0.341030 | + | 0.590682i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.50000 | − | 2.59808i | 0.161333 | − | 0.0931455i | ||||
\(779\) | −31.5000 | + | 18.1865i | −1.12860 | + | 0.651600i | ||||
\(780\) | −3.00000 | − | 10.3923i | −0.107417 | − | 0.372104i | ||||
\(781\) | 13.5000 | − | 23.3827i | 0.483068 | − | 0.836698i | ||||
\(782\) | 18.0000 | + | 10.3923i | 0.643679 | + | 0.371628i | ||||
\(783\) | −22.5000 | − | 38.9711i | −0.804084 | − | 1.39272i | ||||
\(784\) | 5.50000 | − | 4.33013i | 0.196429 | − | 0.154647i | ||||
\(785\) | 3.00000 | 0.107075 | ||||||||
\(786\) | −4.50000 | + | 2.59808i | −0.160510 | + | 0.0926703i | ||||
\(787\) | 2.00000 | + | 3.46410i | 0.0712923 | + | 0.123482i | 0.899468 | − | 0.436987i | \(-0.143954\pi\) |
−0.828176 | + | 0.560469i | \(0.810621\pi\) | |||||||
\(788\) | 10.5000 | − | 18.1865i | 0.374047 | − | 0.647868i | ||||
\(789\) | 7.50000 | + | 12.9904i | 0.267007 | + | 0.462470i | ||||
\(790\) | −1.50000 | + | 0.866025i | −0.0533676 | + | 0.0308118i | ||||
\(791\) | 3.00000 | − | 3.46410i | 0.106668 | − | 0.123169i | ||||
\(792\) | 4.50000 | − | 7.79423i | 0.159901 | − | 0.276956i | ||||
\(793\) | 6.00000 | − | 1.73205i | 0.213066 | − | 0.0615069i | ||||
\(794\) | 14.5000 | − | 25.1147i | 0.514586 | − | 0.891289i | ||||
\(795\) | −4.50000 | + | 2.59808i | −0.159599 | + | 0.0921443i | ||||
\(796\) | 3.00000 | + | 1.73205i | 0.106332 | + | 0.0613909i | ||||
\(797\) | 19.5000 | − | 33.7750i | 0.690725 | − | 1.19637i | −0.280875 | − | 0.959744i | \(-0.590625\pi\) |
0.971601 | − | 0.236627i | \(-0.0760420\pi\) | |||||||
\(798\) | 31.5000 | + | 6.06218i | 1.11509 | + | 0.214599i | ||||
\(799\) | −9.00000 | − | 5.19615i | −0.318397 | − | 0.183827i | ||||
\(800\) | −2.00000 | −0.0707107 | ||||||||
\(801\) | 18.0000 | − | 10.3923i | 0.635999 | − | 0.367194i | ||||
\(802\) | −9.00000 | − | 15.5885i | −0.317801 | − | 0.550448i | ||||
\(803\) | 19.5000 | − | 33.7750i | 0.688140 | − | 1.19189i | ||||
\(804\) | 1.50000 | − | 2.59808i | 0.0529009 | − | 0.0916271i | ||||
\(805\) | 3.00000 | − | 15.5885i | 0.105736 | − | 0.549421i | ||||
\(806\) | −2.50000 | + | 2.59808i | −0.0880587 | + | 0.0915133i | ||||
\(807\) | −45.0000 | − | 25.9808i | −1.58408 | − | 0.914566i | ||||
\(808\) | −9.00000 | −0.316619 | ||||||||
\(809\) | − | 50.2295i | − | 1.76597i | −0.469397 | − | 0.882987i | \(-0.655529\pi\) | ||
0.469397 | − | 0.882987i | \(-0.344471\pi\) | |||||||
\(810\) | −13.5000 | + | 7.79423i | −0.474342 | + | 0.273861i | ||||
\(811\) | 28.0000 | 0.983213 | 0.491606 | − | 0.870817i | \(-0.336410\pi\) | ||||
0.491606 | + | 0.870817i | \(0.336410\pi\) | |||||||
\(812\) | −15.0000 | + | 17.3205i | −0.526397 | + | 0.607831i | ||||
\(813\) | − | 27.7128i | − | 0.971931i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.50000 | − | 7.79423i | −0.157628 | − | 0.273020i | ||||
\(816\) | −9.00000 | + | 5.19615i | −0.315063 | + | 0.181902i | ||||
\(817\) | 3.50000 | − | 6.06218i | 0.122449 | − | 0.212089i | ||||
\(818\) | 22.0000 | 0.769212 | ||||||||
\(819\) | 12.0000 | − | 25.9808i | 0.419314 | − | 0.907841i | ||||
\(820\) | −9.00000 | −0.314294 | ||||||||
\(821\) | 3.00000 | − | 5.19615i | 0.104701 | − | 0.181347i | −0.808915 | − | 0.587925i | \(-0.799945\pi\) |
0.913616 | + | 0.406578i | \(0.133278\pi\) | |||||||
\(822\) | 9.00000 | − | 5.19615i | 0.313911 | − | 0.181237i | ||||
\(823\) | 8.00000 | + | 13.8564i | 0.278862 | + | 0.483004i | 0.971102 | − | 0.238664i | \(-0.0767093\pi\) |
−0.692240 | + | 0.721668i | \(0.743376\pi\) | |||||||
\(824\) | 7.50000 | − | 4.33013i | 0.261275 | − | 0.150847i | ||||
\(825\) | − | 10.3923i | − | 0.361814i | ||||||
\(826\) | −27.0000 | − | 5.19615i | −0.939450 | − | 0.180797i | ||||
\(827\) | 36.0000 | 1.25184 | 0.625921 | − | 0.779886i | \(-0.284723\pi\) | ||||
0.625921 | + | 0.779886i | \(0.284723\pi\) | |||||||
\(828\) | −9.00000 | − | 5.19615i | −0.312772 | − | 0.180579i | ||||
\(829\) | 15.5885i | 0.541409i | 0.962662 | + | 0.270705i | \(0.0872567\pi\) | ||||
−0.962662 | + | 0.270705i | \(0.912743\pi\) | |||||||
\(830\) | 6.00000 | 0.208263 | ||||||||
\(831\) | 15.0000 | + | 8.66025i | 0.520344 | + | 0.300421i | ||||
\(832\) | 1.00000 | + | 3.46410i | 0.0346688 | + | 0.120096i | ||||
\(833\) | −6.00000 | − | 41.5692i | −0.207888 | − | 1.44029i | ||||
\(834\) | 19.5000 | − | 33.7750i | 0.675230 | − | 1.16953i | ||||
\(835\) | −7.50000 | + | 12.9904i | −0.259548 | + | 0.449551i | ||||
\(836\) | −10.5000 | − | 18.1865i | −0.363150 | − | 0.628994i | ||||
\(837\) | 4.50000 | + | 2.59808i | 0.155543 | + | 0.0898027i | ||||
\(838\) | −33.0000 | −1.13997 | ||||||||
\(839\) | −4.50000 | − | 2.59808i | −0.155357 | − | 0.0896956i | 0.420306 | − | 0.907382i | \(-0.361923\pi\) |
−0.575663 | + | 0.817687i | \(0.695256\pi\) | |||||||
\(840\) | 6.00000 | + | 5.19615i | 0.207020 | + | 0.179284i | ||||
\(841\) | 23.0000 | − | 39.8372i | 0.793103 | − | 1.37370i | ||||
\(842\) | 12.0000 | + | 6.92820i | 0.413547 | + | 0.238762i | ||||
\(843\) | 9.00000 | − | 5.19615i | 0.309976 | − | 0.178965i | ||||
\(844\) | 0.500000 | − | 0.866025i | 0.0172107 | − | 0.0298098i | ||||
\(845\) | −10.5000 | + | 19.9186i | −0.361211 | + | 0.685220i | ||||
\(846\) | 4.50000 | + | 2.59808i | 0.154713 | + | 0.0893237i | ||||
\(847\) | −1.00000 | + | 5.19615i | −0.0343604 | + | 0.178542i | ||||
\(848\) | 1.50000 | − | 0.866025i | 0.0515102 | − | 0.0297394i | ||||
\(849\) | −19.5000 | − | 33.7750i | −0.669238 | − | 1.15915i | ||||
\(850\) | −6.00000 | + | 10.3923i | −0.205798 | + | 0.356453i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 13.5000 | − | 7.79423i | 0.462502 | − | 0.267026i | ||||
\(853\) | −10.0000 | −0.342393 | −0.171197 | − | 0.985237i | \(-0.554763\pi\) | ||||
−0.171197 | + | 0.985237i | \(0.554763\pi\) | |||||||
\(854\) | −3.00000 | + | 3.46410i | −0.102658 | + | 0.118539i | ||||
\(855\) | 36.3731i | 1.24393i | ||||||||
\(856\) | 9.00000 | + | 5.19615i | 0.307614 | + | 0.177601i | ||||
\(857\) | 19.5000 | − | 33.7750i | 0.666107 | − | 1.15373i | −0.312877 | − | 0.949794i | \(-0.601293\pi\) |
0.978984 | − | 0.203938i | \(-0.0653741\pi\) | |||||||
\(858\) | −18.0000 | + | 5.19615i | −0.614510 | + | 0.177394i | ||||
\(859\) | 4.50000 | − | 2.59808i | 0.153538 | − | 0.0886452i | −0.421263 | − | 0.906939i | \(-0.638413\pi\) |
0.574801 | + | 0.818293i | \(0.305080\pi\) | |||||||
\(860\) | 1.50000 | − | 0.866025i | 0.0511496 | − | 0.0295312i | ||||
\(861\) | −18.0000 | − | 15.5885i | −0.613438 | − | 0.531253i | ||||
\(862\) | 10.5000 | − | 18.1865i | 0.357631 | − | 0.619436i | ||||
\(863\) | 19.5000 | + | 33.7750i | 0.663788 | + | 1.14971i | 0.979612 | + | 0.200897i | \(0.0643855\pi\) |
−0.315825 | + | 0.948818i | \(0.602281\pi\) | |||||||
\(864\) | 4.50000 | − | 2.59808i | 0.153093 | − | 0.0883883i | ||||
\(865\) | 13.5000 | − | 7.79423i | 0.459014 | − | 0.265012i | ||||
\(866\) | 4.50000 | − | 2.59808i | 0.152916 | − | 0.0882862i | ||||
\(867\) | 32.9090i | 1.11765i | ||||||||
\(868\) | 0.500000 | − | 2.59808i | 0.0169711 | − | 0.0881845i | ||||
\(869\) | 1.50000 | + | 2.59808i | 0.0508840 | + | 0.0881337i | ||||
\(870\) | −22.5000 | − | 12.9904i | −0.762821 | − | 0.440415i | ||||
\(871\) | −6.00000 | + | 1.73205i | −0.203302 | + | 0.0586883i | ||||
\(872\) | 7.50000 | + | 4.33013i | 0.253982 | + | 0.146637i | ||||
\(873\) | −28.5000 | − | 49.3634i | −0.964579 | − | 1.67070i | ||||
\(874\) | −21.0000 | + | 12.1244i | −0.710336 | + | 0.410112i | ||||
\(875\) | 31.5000 | + | 6.06218i | 1.06489 | + | 0.204939i | ||||
\(876\) | 19.5000 | − | 11.2583i | 0.658844 | − | 0.380384i | ||||
\(877\) | − | 12.1244i | − | 0.409410i | −0.978824 | − | 0.204705i | \(-0.934376\pi\) | ||
0.978824 | − | 0.204705i | \(-0.0656236\pi\) | |||||||
\(878\) | −3.00000 | + | 1.73205i | −0.101245 | + | 0.0584539i | ||||
\(879\) | −51.0000 | −1.72019 | ||||||||
\(880\) | − | 5.19615i | − | 0.175162i | ||||||
\(881\) | −28.5000 | − | 49.3634i | −0.960189 | − | 1.66310i | −0.722019 | − | 0.691873i | \(-0.756786\pi\) |
−0.238171 | − | 0.971223i | \(-0.576548\pi\) | |||||||
\(882\) | 3.00000 | + | 20.7846i | 0.101015 | + | 0.699854i | ||||
\(883\) | −52.0000 | −1.74994 | −0.874970 | − | 0.484178i | \(-0.839119\pi\) | ||||
−0.874970 | + | 0.484178i | \(0.839119\pi\) | |||||||
\(884\) | 21.0000 | + | 5.19615i | 0.706306 | + | 0.174766i | ||||
\(885\) | − | 31.1769i | − | 1.04800i | ||||||
\(886\) | 12.1244i | 0.407326i | ||||||||
\(887\) | −12.0000 | + | 20.7846i | −0.402921 | + | 0.697879i | −0.994077 | − | 0.108678i | \(-0.965338\pi\) |
0.591156 | + | 0.806557i | \(0.298672\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 42.5000 | − | 14.7224i | 1.42540 | − | 0.493775i | ||||
\(890\) | 6.00000 | − | 10.3923i | 0.201120 | − | 0.348351i | ||||
\(891\) | 13.5000 | + | 23.3827i | 0.452267 | + | 0.783349i | ||||
\(892\) | −14.5000 | + | 25.1147i | −0.485496 | + | 0.840904i | ||||
\(893\) | 10.5000 | − | 6.06218i | 0.351369 | − | 0.202863i | ||||
\(894\) | 36.3731i | 1.21650i | ||||||||
\(895\) | −16.5000 | − | 28.5788i | −0.551534 | − | 0.955285i | ||||
\(896\) | −2.00000 | − | 1.73205i | −0.0668153 | − | 0.0578638i | ||||
\(897\) | 6.00000 | + | 20.7846i | 0.200334 | + | 0.693978i | ||||
\(898\) | 7.50000 | + | 12.9904i | 0.250278 | + | 0.433495i | ||||
\(899\) | 8.66025i | 0.288836i | ||||||||
\(900\) | 3.00000 | − | 5.19615i | 0.100000 | − | 0.173205i | ||||
\(901\) | − | 10.3923i | − | 0.346218i | ||||||
\(902\) | 15.5885i | 0.519039i | ||||||||
\(903\) | 4.50000 | + | 0.866025i | 0.149751 | + | 0.0288195i | ||||
\(904\) | −1.50000 | − | 0.866025i | −0.0498893 | − | 0.0288036i | ||||
\(905\) | 12.0000 | + | 20.7846i | 0.398893 | + | 0.690904i | ||||
\(906\) | −19.5000 | + | 33.7750i | −0.647844 | + | 1.12210i | ||||
\(907\) | −7.00000 | −0.232431 | −0.116216 | − | 0.993224i | \(-0.537076\pi\) | ||||
−0.116216 | + | 0.993224i | \(0.537076\pi\) | |||||||
\(908\) | −9.00000 | − | 5.19615i | −0.298675 | − | 0.172440i | ||||
\(909\) | 13.5000 | − | 23.3827i | 0.447767 | − | 0.775555i | ||||
\(910\) | −1.50000 | − | 16.4545i | −0.0497245 | − | 0.545461i | ||||
\(911\) | 24.2487i | 0.803396i | 0.915772 | + | 0.401698i | \(0.131580\pi\) | ||||
−0.915772 | + | 0.401698i | \(0.868420\pi\) | |||||||
\(912\) | − | 12.1244i | − | 0.401478i | ||||||
\(913\) | − | 10.3923i | − | 0.343935i | ||||||
\(914\) | 18.0000 | − | 10.3923i | 0.595387 | − | 0.343747i | ||||
\(915\) | −4.50000 | − | 2.59808i | −0.148765 | − | 0.0858898i | ||||
\(916\) | −12.5000 | + | 21.6506i | −0.413012 | + | 0.715357i | ||||
\(917\) | −7.50000 | + | 2.59808i | −0.247672 | + | 0.0857960i | ||||
\(918\) | − | 31.1769i | − | 1.02899i | ||||||
\(919\) | −37.0000 | −1.22052 | −0.610259 | − | 0.792202i | \(-0.708935\pi\) | ||||
−0.610259 | + | 0.792202i | \(0.708935\pi\) | |||||||
\(920\) | −6.00000 | −0.197814 | ||||||||
\(921\) | 6.00000 | − | 3.46410i | 0.197707 | − | 0.114146i | ||||
\(922\) | 22.5000 | − | 12.9904i | 0.740998 | − | 0.427815i | ||||
\(923\) | −31.5000 | − | 7.79423i | −1.03684 | − | 0.256550i | ||||
\(924\) | 9.00000 | − | 10.3923i | 0.296078 | − | 0.341882i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −27.0000 | − | 15.5885i | −0.887275 | − | 0.512268i | ||||
\(927\) | 25.9808i | 0.853320i | ||||||||
\(928\) | 7.50000 | + | 4.33013i | 0.246200 | + | 0.142143i | ||||
\(929\) | − | 8.66025i | − | 0.284134i | −0.989857 | − | 0.142067i | \(-0.954625\pi\) | ||
0.989857 | − | 0.142067i | \(-0.0453748\pi\) | |||||||
\(930\) | 3.00000 | 0.0983739 | ||||||||
\(931\) | 45.5000 | + | 18.1865i | 1.49120 | + | 0.596040i | ||||
\(932\) | 19.5000 | + | 11.2583i | 0.638744 | + | 0.368779i | ||||
\(933\) | − | 5.19615i | − | 0.170114i | ||||||
\(934\) | 9.00000 | 0.294489 | ||||||||
\(935\) | −27.0000 | − | 15.5885i | −0.882994 | − | 0.509797i | ||||
\(936\) | −10.5000 | − | 2.59808i | −0.343203 | − | 0.0849208i | ||||
\(937\) | 20.7846i | 0.679004i | 0.940605 | + | 0.339502i | \(0.110258\pi\) | ||||
−0.940605 | + | 0.339502i | \(0.889742\pi\) | |||||||
\(938\) | 3.00000 | − | 3.46410i | 0.0979535 | − | 0.113107i | ||||
\(939\) | −4.50000 | + | 7.79423i | −0.146852 | + | 0.254355i | ||||
\(940\) | 3.00000 | 0.0978492 | ||||||||
\(941\) | −16.5000 | − | 9.52628i | −0.537885 | − | 0.310548i | 0.206337 | − | 0.978481i | \(-0.433846\pi\) |
−0.744221 | + | 0.667933i | \(0.767179\pi\) | |||||||
\(942\) | 1.50000 | − | 2.59808i | 0.0488726 | − | 0.0846499i | ||||
\(943\) | 18.0000 | 0.586161 | ||||||||
\(944\) | 10.3923i | 0.338241i | ||||||||
\(945\) | −22.5000 | + | 7.79423i | −0.731925 | + | 0.253546i | ||||
\(946\) | −1.50000 | − | 2.59808i | −0.0487692 | − | 0.0844707i | ||||
\(947\) | −6.00000 | + | 10.3923i | −0.194974 | + | 0.337705i | −0.946892 | − | 0.321552i | \(-0.895796\pi\) |
0.751918 | + | 0.659256i | \(0.229129\pi\) | |||||||
\(948\) | 1.73205i | 0.0562544i | ||||||||
\(949\) | −45.5000 | − | 11.2583i | −1.47699 | − | 0.365461i | ||||
\(950\) | −7.00000 | − | 12.1244i | −0.227110 | − | 0.393366i | ||||
\(951\) | −4.50000 | − | 2.59808i | −0.145922 | − | 0.0842484i | ||||
\(952\) | −15.0000 | + | 5.19615i | −0.486153 | + | 0.168408i | ||||
\(953\) | 25.5000 | + | 14.7224i | 0.826026 | + | 0.476906i | 0.852490 | − | 0.522743i | \(-0.175091\pi\) |
−0.0264640 | + | 0.999650i | \(0.508425\pi\) | |||||||
\(954\) | 5.19615i | 0.168232i | ||||||||
\(955\) | 13.5000 | + | 23.3827i | 0.436850 | + | 0.756646i | ||||
\(956\) | 6.00000 | + | 10.3923i | 0.194054 | + | 0.336111i | ||||
\(957\) | −22.5000 | + | 38.9711i | −0.727322 | + | 1.25976i | ||||
\(958\) | 16.5000 | + | 9.52628i | 0.533091 | + | 0.307780i | ||||
\(959\) | 15.0000 | − | 5.19615i | 0.484375 | − | 0.167793i | ||||
\(960\) | 1.50000 | − | 2.59808i | 0.0484123 | − | 0.0838525i | ||||
\(961\) | 15.0000 | + | 25.9808i | 0.483871 | + | 0.838089i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −27.0000 | + | 15.5885i | −0.870063 | + | 0.502331i | ||||
\(964\) | −5.00000 | + | 8.66025i | −0.161039 | + | 0.278928i | ||||
\(965\) | 10.5000 | + | 18.1865i | 0.338007 | + | 0.585445i | ||||
\(966\) | −12.0000 | − | 10.3923i | −0.386094 | − | 0.334367i | ||||
\(967\) | 10.3923i | 0.334194i | 0.985940 | + | 0.167097i | \(0.0534393\pi\) | ||||
−0.985940 | + | 0.167097i | \(0.946561\pi\) | |||||||
\(968\) | 2.00000 | 0.0642824 | ||||||||
\(969\) | −63.0000 | − | 36.3731i | −2.02385 | − | 1.16847i | ||||
\(970\) | −28.5000 | − | 16.4545i | −0.915080 | − | 0.528322i | ||||
\(971\) | 33.0000 | 1.05902 | 0.529510 | − | 0.848304i | \(-0.322376\pi\) | ||||
0.529510 | + | 0.848304i | \(0.322376\pi\) | |||||||
\(972\) | 15.5885i | 0.500000i | ||||||||
\(973\) | 39.0000 | − | 45.0333i | 1.25028 | − | 1.44370i | ||||
\(974\) | 3.46410i | 0.110997i | ||||||||
\(975\) | −12.0000 | + | 3.46410i | −0.384308 | + | 0.110940i | ||||
\(976\) | 1.50000 | + | 0.866025i | 0.0480138 | + | 0.0277208i | ||||
\(977\) | 3.00000 | 0.0959785 | 0.0479893 | − | 0.998848i | \(-0.484719\pi\) | ||||
0.0479893 | + | 0.998848i | \(0.484719\pi\) | |||||||
\(978\) | −9.00000 | −0.287788 | ||||||||
\(979\) | −18.0000 | − | 10.3923i | −0.575282 | − | 0.332140i | ||||
\(980\) | 7.50000 | + | 9.52628i | 0.239579 | + | 0.304306i | ||||
\(981\) | −22.5000 | + | 12.9904i | −0.718370 | + | 0.414751i | ||||
\(982\) | − | 36.3731i | − | 1.16071i | ||||||
\(983\) | 25.5000 | + | 14.7224i | 0.813324 | + | 0.469573i | 0.848109 | − | 0.529822i | \(-0.177741\pi\) |
−0.0347851 | + | 0.999395i | \(0.511075\pi\) | |||||||
\(984\) | −4.50000 | + | 7.79423i | −0.143455 | + | 0.248471i | ||||
\(985\) | 31.5000 | + | 18.1865i | 1.00367 | + | 0.579471i | ||||
\(986\) | 45.0000 | − | 25.9808i | 1.43309 | − | 0.827396i | ||||
\(987\) | 6.00000 | + | 5.19615i | 0.190982 | + | 0.165395i | ||||
\(988\) | −17.5000 | + | 18.1865i | −0.556749 | + | 0.578591i | ||||
\(989\) | −3.00000 | + | 1.73205i | −0.0953945 | + | 0.0550760i | ||||
\(990\) | 13.5000 | + | 7.79423i | 0.429058 | + | 0.247717i | ||||
\(991\) | 25.0000 | 0.794151 | 0.397076 | − | 0.917786i | \(-0.370025\pi\) | ||||
0.397076 | + | 0.917786i | \(0.370025\pi\) | |||||||
\(992\) | −1.00000 | −0.0317500 | ||||||||
\(993\) | −22.5000 | − | 38.9711i | −0.714016 | − | 1.23671i | ||||
\(994\) | 22.5000 | − | 7.79423i | 0.713657 | − | 0.247218i | ||||
\(995\) | −3.00000 | + | 5.19615i | −0.0951064 | + | 0.164729i | ||||
\(996\) | 3.00000 | − | 5.19615i | 0.0950586 | − | 0.164646i | ||||
\(997\) | 24.0000 | − | 13.8564i | 0.760088 | − | 0.438837i | −0.0692396 | − | 0.997600i | \(-0.522057\pi\) |
0.829327 | + | 0.558763i | \(0.188724\pi\) | |||||||
\(998\) | 32.9090i | 1.04172i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 546.2.bn.d.101.1 | yes | 2 | |
3.2 | odd | 2 | 546.2.bn.a.101.1 | yes | 2 | ||
7.5 | odd | 6 | 546.2.bi.b.257.1 | yes | 2 | ||
13.4 | even | 6 | 546.2.bi.d.17.1 | yes | 2 | ||
21.5 | even | 6 | 546.2.bi.d.257.1 | yes | 2 | ||
39.17 | odd | 6 | 546.2.bi.b.17.1 | ✓ | 2 | ||
91.82 | odd | 6 | 546.2.bn.a.173.1 | yes | 2 | ||
273.173 | even | 6 | inner | 546.2.bn.d.173.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.bi.b.17.1 | ✓ | 2 | 39.17 | odd | 6 | ||
546.2.bi.b.257.1 | yes | 2 | 7.5 | odd | 6 | ||
546.2.bi.d.17.1 | yes | 2 | 13.4 | even | 6 | ||
546.2.bi.d.257.1 | yes | 2 | 21.5 | even | 6 | ||
546.2.bn.a.101.1 | yes | 2 | 3.2 | odd | 2 | ||
546.2.bn.a.173.1 | yes | 2 | 91.82 | odd | 6 | ||
546.2.bn.d.101.1 | yes | 2 | 1.1 | even | 1 | trivial | |
546.2.bn.d.173.1 | yes | 2 | 273.173 | even | 6 | inner |