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: | \(1\) |
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 | 173.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.173 |
Dual form | 546.2.bn.a.101.1 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||
\(5\) | −1.50000 | − | 0.866025i | −0.670820 | − | 0.387298i | 0.125567 | − | 0.992085i | \(-0.459925\pi\) |
−0.796387 | + | 0.604787i | \(0.793258\pi\) | |||||||
\(6\) | 1.50000 | + | 0.866025i | 0.612372 | + | 0.353553i | ||||
\(7\) | 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 | \(-0.350615\pi\) | ||||
0.452267 | + | 0.891883i | \(0.350615\pi\) | |||||||
\(12\) | − | 1.73205i | − | 0.500000i | ||||||
\(13\) | 1.00000 | − | 3.46410i | 0.277350 | − | 0.960769i | ||||
\(14\) | 2.00000 | − | 1.73205i | 0.534522 | − | 0.462910i | ||||
\(15\) | 3.00000 | 0.774597 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −3.00000 | + | 5.19615i | −0.727607 | + | 1.26025i | 0.230285 | + | 0.973123i | \(0.426034\pi\) |
−0.957892 | + | 0.287129i | \(0.907299\pi\) | |||||||
\(18\) | −3.00000 | −0.707107 | ||||||||
\(19\) | −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 | ||||
\(21\) | −3.00000 | − | 3.46410i | −0.654654 | − | 0.755929i | ||||
\(22\) | −1.50000 | − | 2.59808i | −0.319801 | − | 0.553912i | ||||
\(23\) | −3.00000 | + | 1.73205i | −0.625543 | + | 0.361158i | −0.779024 | − | 0.626994i | \(-0.784285\pi\) |
0.153481 | + | 0.988152i | \(0.450952\pi\) | |||||||
\(24\) | −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 | \(-0.630677\pi\) |
−0.993615 | + | 0.112823i | \(0.964011\pi\) | |||||||
\(30\) | −1.50000 | − | 2.59808i | −0.273861 | − | 0.474342i | ||||
\(31\) | −0.500000 | − | 0.866025i | −0.0898027 | − | 0.155543i | 0.817625 | − | 0.575751i | \(-0.195290\pi\) |
−0.907428 | + | 0.420208i | \(0.861957\pi\) | |||||||
\(32\) | −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 | ||||
\(36\) | 1.50000 | + | 2.59808i | 0.250000 | + | 0.433013i | ||||
\(37\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(38\) | 3.50000 | + | 6.06218i | 0.567775 | + | 0.983415i | ||||
\(39\) | 1.50000 | + | 6.06218i | 0.240192 | + | 0.970725i | ||||
\(40\) | −1.50000 | − | 0.866025i | −0.237171 | − | 0.136931i | ||||
\(41\) | −4.50000 | − | 2.59808i | −0.702782 | − | 0.405751i | 0.105601 | − | 0.994409i | \(-0.466323\pi\) |
−0.808383 | + | 0.588657i | \(0.799657\pi\) | |||||||
\(42\) | −1.50000 | + | 4.33013i | −0.231455 | + | 0.668153i | ||||
\(43\) | −0.500000 | − | 0.866025i | −0.0762493 | − | 0.132068i | 0.825380 | − | 0.564578i | \(-0.190961\pi\) |
−0.901629 | + | 0.432511i | \(0.857628\pi\) | |||||||
\(44\) | −1.50000 | + | 2.59808i | −0.226134 | + | 0.391675i | ||||
\(45\) | −4.50000 | + | 2.59808i | −0.670820 | + | 0.387298i | ||||
\(46\) | 3.00000 | + | 1.73205i | 0.442326 | + | 0.255377i | ||||
\(47\) | 1.50000 | + | 0.866025i | 0.218797 | + | 0.126323i | 0.605393 | − | 0.795926i | \(-0.293016\pi\) |
−0.386596 | + | 0.922249i | \(0.626349\pi\) | |||||||
\(48\) | 1.50000 | + | 0.866025i | 0.216506 | + | 0.125000i | ||||
\(49\) | −6.50000 | + | 2.59808i | −0.928571 | + | 0.371154i | ||||
\(50\) | −1.00000 | + | 1.73205i | −0.141421 | + | 0.244949i | ||||
\(51\) | − | 10.3923i | − | 1.45521i | ||||||
\(52\) | 2.50000 | + | 2.59808i | 0.346688 | + | 0.360288i | ||||
\(53\) | 1.50000 | − | 0.866025i | 0.206041 | − | 0.118958i | −0.393429 | − | 0.919355i | \(-0.628711\pi\) |
0.599470 | + | 0.800397i | \(0.295378\pi\) | |||||||
\(54\) | 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 | \(-0.569829\pi\) |
−0.954080 | + | 0.299552i | \(0.903163\pi\) | |||||||
\(60\) | −1.50000 | + | 2.59808i | −0.193649 | + | 0.335410i | ||||
\(61\) | 1.73205i | 0.221766i | 0.993833 | + | 0.110883i | \(0.0353679\pi\) | ||||
−0.993833 | + | 0.110883i | \(0.964632\pi\) | |||||||
\(62\) | −0.500000 | + | 0.866025i | −0.0635001 | + | 0.109985i | ||||
\(63\) | 7.50000 | + | 2.59808i | 0.944911 | + | 0.327327i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.50000 | + | 4.33013i | −0.558156 | + | 0.537086i | ||||
\(66\) | 4.50000 | + | 2.59808i | 0.553912 | + | 0.319801i | ||||
\(67\) | − | 1.73205i | − | 0.211604i | −0.994387 | − | 0.105802i | \(-0.966259\pi\) | ||
0.994387 | − | 0.105802i | \(-0.0337409\pi\) | |||||||
\(68\) | −3.00000 | − | 5.19615i | −0.363803 | − | 0.630126i | ||||
\(69\) | 3.00000 | − | 5.19615i | 0.361158 | − | 0.625543i | ||||
\(70\) | −4.50000 | + | 0.866025i | −0.537853 | + | 0.103510i | ||||
\(71\) | 4.50000 | + | 7.79423i | 0.534052 | + | 0.925005i | 0.999209 | + | 0.0397765i | \(0.0126646\pi\) |
−0.465157 | + | 0.885228i | \(0.654002\pi\) | |||||||
\(72\) | 1.50000 | − | 2.59808i | 0.176777 | − | 0.306186i | ||||
\(73\) | −6.50000 | − | 11.2583i | −0.760767 | − | 1.31769i | −0.942455 | − | 0.334332i | \(-0.891489\pi\) |
0.181688 | − | 0.983356i | \(-0.441844\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.00000 | + | 1.73205i | 0.346410 | + | 0.200000i | ||||
\(76\) | 3.50000 | − | 6.06218i | 0.401478 | − | 0.695379i | ||||
\(77\) | 1.50000 | + | 7.79423i | 0.170941 | + | 0.888235i | ||||
\(78\) | 4.50000 | − | 4.33013i | 0.509525 | − | 0.490290i | ||||
\(79\) | −0.500000 | + | 0.866025i | −0.0562544 | + | 0.0974355i | −0.892781 | − | 0.450490i | \(-0.851249\pi\) |
0.836527 | + | 0.547926i | \(0.184582\pi\) | |||||||
\(80\) | 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 | \(0.939113\pi\) | |||||||
\(84\) | 4.50000 | − | 0.866025i | 0.490990 | − | 0.0944911i | ||||
\(85\) | 9.00000 | − | 5.19615i | 0.976187 | − | 0.563602i | ||||
\(86\) | −0.500000 | + | 0.866025i | −0.0539164 | + | 0.0933859i | ||||
\(87\) | 15.0000 | 1.60817 | ||||||||
\(88\) | 3.00000 | 0.319801 | ||||||||
\(89\) | −6.00000 | + | 3.46410i | −0.635999 | + | 0.367194i | −0.783072 | − | 0.621932i | \(-0.786348\pi\) |
0.147073 | + | 0.989126i | \(0.453015\pi\) | |||||||
\(90\) | 4.50000 | + | 2.59808i | 0.474342 | + | 0.273861i | ||||
\(91\) | 9.50000 | + | 0.866025i | 0.995871 | + | 0.0907841i | ||||
\(92\) | − | 3.46410i | − | 0.361158i | ||||||
\(93\) | 1.50000 | + | 0.866025i | 0.155543 | + | 0.0898027i | ||||
\(94\) | − | 1.73205i | − | 0.178647i | ||||||
\(95\) | 10.5000 | + | 6.06218i | 1.07728 | + | 0.621966i | ||||
\(96\) | − | 1.73205i | − | 0.176777i | ||||||
\(97\) | 9.50000 | + | 16.4545i | 0.964579 | + | 1.67070i | 0.710742 | + | 0.703452i | \(0.248359\pi\) |
0.253837 | + | 0.967247i | \(0.418307\pi\) | |||||||
\(98\) | 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 | \(-0.647781\pi\) | ||||
−0.447767 | + | 0.894150i | \(0.647781\pi\) | |||||||
\(102\) | −9.00000 | + | 5.19615i | −0.891133 | + | 0.514496i | ||||
\(103\) | −7.50000 | − | 4.33013i | −0.738997 | − | 0.426660i | 0.0827075 | − | 0.996574i | \(-0.473643\pi\) |
−0.821705 | + | 0.569914i | \(0.806977\pi\) | |||||||
\(104\) | 1.00000 | − | 3.46410i | 0.0980581 | − | 0.339683i | ||||
\(105\) | 1.50000 | + | 7.79423i | 0.146385 | + | 0.760639i | ||||
\(106\) | −1.50000 | − | 0.866025i | −0.145693 | − | 0.0841158i | ||||
\(107\) | 9.00000 | − | 5.19615i | 0.870063 | − | 0.502331i | 0.00269372 | − | 0.999996i | \(-0.499143\pi\) |
0.867369 | + | 0.497665i | \(0.165809\pi\) | |||||||
\(108\) | −4.50000 | − | 2.59808i | −0.433013 | − | 0.250000i | ||||
\(109\) | −7.50000 | + | 4.33013i | −0.718370 | + | 0.414751i | −0.814152 | − | 0.580651i | \(-0.802798\pi\) |
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 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 | \(-0.692628\pi\) |
0.427784 | + | 0.903881i | \(0.359294\pi\) | |||||||
\(114\) | −10.5000 | − | 6.06218i | −0.983415 | − | 0.567775i | ||||
\(115\) | 6.00000 | 0.559503 | ||||||||
\(116\) | 7.50000 | − | 4.33013i | 0.696358 | − | 0.402042i | ||||
\(117\) | −7.50000 | − | 7.79423i | −0.693375 | − | 0.720577i | ||||
\(118\) | 10.3923i | 0.956689i | ||||||||
\(119\) | −15.0000 | − | 5.19615i | −1.37505 | − | 0.476331i | ||||
\(120\) | 3.00000 | 0.273861 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | 1.50000 | − | 0.866025i | 0.135804 | − | 0.0784063i | ||||
\(123\) | 9.00000 | 0.811503 | ||||||||
\(124\) | 1.00000 | 0.0898027 | ||||||||
\(125\) | 12.1244i | 1.08444i | ||||||||
\(126\) | −1.50000 | − | 7.79423i | −0.133631 | − | 0.694365i | ||||
\(127\) | 8.50000 | − | 14.7224i | 0.754253 | − | 1.30640i | −0.191492 | − | 0.981494i | \(-0.561333\pi\) |
0.945745 | − | 0.324910i | \(-0.105334\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 1.50000 | + | 0.866025i | 0.132068 | + | 0.0762493i | ||||
\(130\) | 6.00000 | + | 1.73205i | 0.526235 | + | 0.151911i | ||||
\(131\) | 1.50000 | − | 2.59808i | 0.131056 | − | 0.226995i | −0.793028 | − | 0.609185i | \(-0.791497\pi\) |
0.924084 | + | 0.382190i | \(0.124830\pi\) | |||||||
\(132\) | − | 5.19615i | − | 0.452267i | ||||||
\(133\) | −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 | \(-0.915839\pi\) |
0.708942 | + | 0.705266i | \(0.249173\pi\) | |||||||
\(138\) | −6.00000 | −0.510754 | ||||||||
\(139\) | 19.5000 | − | 11.2583i | 1.65397 | − | 0.954919i | 0.678551 | − | 0.734553i | \(-0.262608\pi\) |
0.975417 | − | 0.220366i | \(-0.0707252\pi\) | |||||||
\(140\) | 3.00000 | + | 3.46410i | 0.253546 | + | 0.292770i | ||||
\(141\) | −3.00000 | −0.252646 | ||||||||
\(142\) | 4.50000 | − | 7.79423i | 0.377632 | − | 0.654077i | ||||
\(143\) | 3.00000 | − | 10.3923i | 0.250873 | − | 0.869048i | ||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | 7.50000 | + | 12.9904i | 0.622841 | + | 1.07879i | ||||
\(146\) | −6.50000 | + | 11.2583i | −0.537944 | + | 0.931746i | ||||
\(147\) | 7.50000 | − | 9.52628i | 0.618590 | − | 0.785714i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 21.0000 | 1.72039 | 0.860194 | − | 0.509968i | \(-0.170343\pi\) | ||||
0.860194 | + | 0.509968i | \(0.170343\pi\) | |||||||
\(150\) | − | 3.46410i | − | 0.282843i | ||||||
\(151\) | −19.5000 | + | 11.2583i | −1.58689 | + | 0.916190i | −0.593072 | + | 0.805150i | \(0.702085\pi\) |
−0.993816 | + | 0.111040i | \(0.964582\pi\) | |||||||
\(152\) | −7.00000 | −0.567775 | ||||||||
\(153\) | 9.00000 | + | 15.5885i | 0.727607 | + | 1.26025i | ||||
\(154\) | 6.00000 | − | 5.19615i | 0.483494 | − | 0.418718i | ||||
\(155\) | 1.73205i | 0.139122i | ||||||||
\(156\) | −6.00000 | − | 1.73205i | −0.480384 | − | 0.138675i | ||||
\(157\) | 1.50000 | − | 0.866025i | 0.119713 | − | 0.0691164i | −0.438948 | − | 0.898513i | \(-0.644649\pi\) |
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | 1.00000 | 0.0795557 | ||||||||
\(159\) | −1.50000 | + | 2.59808i | −0.118958 | + | 0.206041i | ||||
\(160\) | 1.50000 | − | 0.866025i | 0.118585 | − | 0.0684653i | ||||
\(161\) | −6.00000 | − | 6.92820i | −0.472866 | − | 0.546019i | ||||
\(162\) | −4.50000 | + | 7.79423i | −0.353553 | + | 0.612372i | ||||
\(163\) | 5.19615i | 0.406994i | 0.979076 | + | 0.203497i | \(0.0652307\pi\) | ||||
−0.979076 | + | 0.203497i | \(0.934769\pi\) | |||||||
\(164\) | 4.50000 | − | 2.59808i | 0.351391 | − | 0.202876i | ||||
\(165\) | 9.00000 | 0.700649 | ||||||||
\(166\) | 3.00000 | − | 1.73205i | 0.232845 | − | 0.134433i | ||||
\(167\) | 7.50000 | + | 4.33013i | 0.580367 | + | 0.335075i | 0.761279 | − | 0.648424i | \(-0.224572\pi\) |
−0.180912 | + | 0.983499i | \(0.557905\pi\) | |||||||
\(168\) | −3.00000 | − | 3.46410i | −0.231455 | − | 0.267261i | ||||
\(169\) | −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 | \(-0.611148\pi\) | ||||
−0.342129 | + | 0.939653i | \(0.611148\pi\) | |||||||
\(174\) | −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 | ||||
\(177\) | 18.0000 | 1.35296 | ||||||||
\(178\) | 6.00000 | + | 3.46410i | 0.449719 | + | 0.259645i | ||||
\(179\) | − | 19.0526i | − | 1.42406i | −0.702152 | − | 0.712028i | \(-0.747777\pi\) | ||
0.702152 | − | 0.712028i | \(-0.252223\pi\) | |||||||
\(180\) | − | 5.19615i | − | 0.387298i | ||||||
\(181\) | − | 13.8564i | − | 1.02994i | −0.857209 | − | 0.514969i | \(-0.827803\pi\) | ||
0.857209 | − | 0.514969i | \(-0.172197\pi\) | |||||||
\(182\) | −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 | ||||||||
\(186\) | − | 1.73205i | − | 0.127000i | ||||||
\(187\) | −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 | \(-0.856266\pi\) | ||
0.899770 | − | 0.436365i | \(-0.143734\pi\) | |||||||
\(194\) | 9.50000 | − | 16.4545i | 0.682060 | − | 1.18136i | ||||
\(195\) | 3.00000 | − | 10.3923i | 0.214834 | − | 0.744208i | ||||
\(196\) | 1.00000 | − | 6.92820i | 0.0714286 | − | 0.494872i | ||||
\(197\) | −10.5000 | + | 18.1865i | −0.748094 | + | 1.29574i | 0.200641 | + | 0.979665i | \(0.435697\pi\) |
−0.948735 | + | 0.316072i | \(0.897636\pi\) | |||||||
\(198\) | −9.00000 | −0.639602 | ||||||||
\(199\) | −3.00000 | − | 1.73205i | −0.212664 | − | 0.122782i | 0.389885 | − | 0.920864i | \(-0.372515\pi\) |
−0.602549 | + | 0.798082i | \(0.705848\pi\) | |||||||
\(200\) | −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 | ||||
\(204\) | 9.00000 | + | 5.19615i | 0.630126 | + | 0.363803i | ||||
\(205\) | 4.50000 | + | 7.79423i | 0.314294 | + | 0.544373i | ||||
\(206\) | 8.66025i | 0.603388i | ||||||||
\(207\) | 10.3923i | 0.722315i | ||||||||
\(208\) | −3.50000 | + | 0.866025i | −0.242681 | + | 0.0600481i | ||||
\(209\) | −21.0000 | −1.45260 | ||||||||
\(210\) | 6.00000 | − | 5.19615i | 0.414039 | − | 0.358569i | ||||
\(211\) | 0.500000 | − | 0.866025i | 0.0344214 | − | 0.0596196i | −0.848301 | − | 0.529514i | \(-0.822374\pi\) |
0.882723 | + | 0.469894i | \(0.155708\pi\) | |||||||
\(212\) | 1.73205i | 0.118958i | ||||||||
\(213\) | −13.5000 | − | 7.79423i | −0.925005 | − | 0.534052i | ||||
\(214\) | −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 | ||||
\(219\) | 19.5000 | + | 11.2583i | 1.31769 | + | 0.760767i | ||||
\(220\) | 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 | −0.278418 | + | 0.960460i | \(0.589810\pi\) |
−0.692574 | + | 0.721347i | \(0.743523\pi\) | |||||||
\(224\) | −2.50000 | − | 0.866025i | −0.167038 | − | 0.0578638i | ||||
\(225\) | −6.00000 | −0.400000 | ||||||||
\(226\) | 1.50000 | + | 0.866025i | 0.0997785 | + | 0.0576072i | ||||
\(227\) | −9.00000 | − | 5.19615i | −0.597351 | − | 0.344881i | 0.170648 | − | 0.985332i | \(-0.445414\pi\) |
−0.767999 | + | 0.640451i | \(0.778747\pi\) | |||||||
\(228\) | 12.1244i | 0.802955i | ||||||||
\(229\) | −12.5000 | + | 21.6506i | −0.826023 | + | 1.43071i | 0.0751115 | + | 0.997175i | \(0.476069\pi\) |
−0.901135 | + | 0.433539i | \(0.857265\pi\) | |||||||
\(230\) | −3.00000 | − | 5.19615i | −0.197814 | − | 0.342624i | ||||
\(231\) | −9.00000 | − | 10.3923i | −0.592157 | − | 0.683763i | ||||
\(232\) | −7.50000 | − | 4.33013i | −0.492399 | − | 0.284287i | ||||
\(233\) | 19.5000 | + | 11.2583i | 1.27749 | + | 0.737558i | 0.976386 | − | 0.216034i | \(-0.0693123\pi\) |
0.301102 | + | 0.953592i | \(0.402646\pi\) | |||||||
\(234\) | −3.00000 | + | 10.3923i | −0.196116 | + | 0.679366i | ||||
\(235\) | −1.50000 | − | 2.59808i | −0.0978492 | − | 0.169480i | ||||
\(236\) | 9.00000 | − | 5.19615i | 0.585850 | − | 0.338241i | ||||
\(237\) | − | 1.73205i | − | 0.112509i | ||||||
\(238\) | 3.00000 | + | 15.5885i | 0.194461 | + | 1.01045i | ||||
\(239\) | 12.0000 | 0.776215 | 0.388108 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388108 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(240\) | −1.50000 | − | 2.59808i | −0.0968246 | − | 0.167705i | ||||
\(241\) | −5.00000 | + | 8.66025i | −0.322078 | + | 0.557856i | −0.980917 | − | 0.194429i | \(-0.937715\pi\) |
0.658838 | + | 0.752285i | \(0.271048\pi\) | |||||||
\(242\) | 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 | \(-0.00969471\pi\) |
−0.526140 | + | 0.850398i | \(0.676361\pi\) | |||||||
\(252\) | −6.00000 | + | 5.19615i | −0.377964 | + | 0.327327i | ||||
\(253\) | −9.00000 | + | 5.19615i | −0.565825 | + | 0.326679i | ||||
\(254\) | −17.0000 | −1.06667 | ||||||||
\(255\) | −9.00000 | + | 15.5885i | −0.563602 | + | 0.976187i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −3.00000 | − | 5.19615i | −0.187135 | − | 0.324127i | 0.757159 | − | 0.653231i | \(-0.226587\pi\) |
−0.944294 | + | 0.329104i | \(0.893253\pi\) | |||||||
\(258\) | − | 1.73205i | − | 0.107833i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.50000 | − | 6.06218i | −0.0930261 | − | 0.375960i | ||||
\(261\) | −22.5000 | + | 12.9904i | −1.39272 | + | 0.804084i | ||||
\(262\) | −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 | ||||
\(267\) | 6.00000 | − | 10.3923i | 0.367194 | − | 0.635999i | ||||
\(268\) | 1.50000 | + | 0.866025i | 0.0916271 | + | 0.0529009i | ||||
\(269\) | 15.0000 | − | 25.9808i | 0.914566 | − | 1.58408i | 0.107031 | − | 0.994256i | \(-0.465866\pi\) |
0.807535 | − | 0.589819i | \(-0.200801\pi\) | |||||||
\(270\) | −9.00000 | −0.547723 | ||||||||
\(271\) | 8.00000 | + | 13.8564i | 0.485965 | + | 0.841717i | 0.999870 | − | 0.0161307i | \(-0.00513477\pi\) |
−0.513905 | + | 0.857847i | \(0.671801\pi\) | |||||||
\(272\) | 6.00000 | 0.363803 | ||||||||
\(273\) | −15.0000 | + | 6.92820i | −0.907841 | + | 0.419314i | ||||
\(274\) | 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 | −0.675810 | − | 0.737075i | \(-0.736206\pi\) |
0.976231 | + | 0.216731i | \(0.0695395\pi\) | |||||||
\(278\) | −19.5000 | − | 11.2583i | −1.16953 | − | 0.675230i | ||||
\(279\) | −3.00000 | −0.179605 | ||||||||
\(280\) | 1.50000 | − | 4.33013i | 0.0896421 | − | 0.258775i | ||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 1.50000 | + | 2.59808i | 0.0893237 | + | 0.154713i | ||||
\(283\) | 22.5167i | 1.33848i | 0.743048 | + | 0.669238i | \(0.233379\pi\) | ||||
−0.743048 | + | 0.669238i | \(0.766621\pi\) | |||||||
\(284\) | −9.00000 | −0.534052 | ||||||||
\(285\) | −21.0000 | −1.24393 | ||||||||
\(286\) | −10.5000 | + | 2.59808i | −0.620878 | + | 0.153627i | ||||
\(287\) | 4.50000 | − | 12.9904i | 0.265627 | − | 0.766798i | ||||
\(288\) | 1.50000 | + | 2.59808i | 0.0883883 | + | 0.153093i | ||||
\(289\) | −9.50000 | − | 16.4545i | −0.558824 | − | 0.967911i | ||||
\(290\) | 7.50000 | − | 12.9904i | 0.440415 | − | 0.762821i | ||||
\(291\) | −28.5000 | − | 16.4545i | −1.67070 | − | 0.964579i | ||||
\(292\) | 13.0000 | 0.760767 | ||||||||
\(293\) | 25.5000 | − | 14.7224i | 1.48973 | − | 0.860094i | 0.489795 | − | 0.871838i | \(-0.337072\pi\) |
0.999931 | + | 0.0117441i | \(0.00373833\pi\) | |||||||
\(294\) | −12.0000 | − | 1.73205i | −0.699854 | − | 0.101015i | ||||
\(295\) | 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 | ||||
\(309\) | 15.0000 | 0.853320 | ||||||||
\(310\) | 1.50000 | − | 0.866025i | 0.0851943 | − | 0.0491869i | ||||
\(311\) | −1.50000 | − | 2.59808i | −0.0850572 | − | 0.147323i | 0.820358 | − | 0.571850i | \(-0.193774\pi\) |
−0.905416 | + | 0.424526i | \(0.860441\pi\) | |||||||
\(312\) | 1.50000 | + | 6.06218i | 0.0849208 | + | 0.343203i | ||||
\(313\) | −4.50000 | − | 2.59808i | −0.254355 | − | 0.146852i | 0.367402 | − | 0.930062i | \(-0.380247\pi\) |
−0.621757 | + | 0.783210i | \(0.713581\pi\) | |||||||
\(314\) | −1.50000 | − | 0.866025i | −0.0846499 | − | 0.0488726i | ||||
\(315\) | −9.00000 | − | 10.3923i | −0.507093 | − | 0.585540i | ||||
\(316\) | −0.500000 | − | 0.866025i | −0.0281272 | − | 0.0487177i | ||||
\(317\) | 1.50000 | − | 2.59808i | 0.0842484 | − | 0.145922i | −0.820822 | − | 0.571184i | \(-0.806484\pi\) |
0.905071 | + | 0.425261i | \(0.139818\pi\) | |||||||
\(318\) | 3.00000 | 0.168232 | ||||||||
\(319\) | −22.5000 | − | 12.9904i | −1.25976 | − | 0.727322i | ||||
\(320\) | −1.50000 | − | 0.866025i | −0.0838525 | − | 0.0484123i | ||||
\(321\) | −9.00000 | + | 15.5885i | −0.502331 | + | 0.870063i | ||||
\(322\) | −3.00000 | + | 8.66025i | −0.167183 | + | 0.482617i | ||||
\(323\) | 21.0000 | − | 36.3731i | 1.16847 | − | 2.02385i | ||||
\(324\) | 9.00000 | 0.500000 | ||||||||
\(325\) | −7.00000 | + | 1.73205i | −0.388290 | + | 0.0960769i | ||||
\(326\) | 4.50000 | − | 2.59808i | 0.249232 | − | 0.143894i | ||||
\(327\) | 7.50000 | − | 12.9904i | 0.414751 | − | 0.718370i | ||||
\(328\) | −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 | \(0.253126\pi\) | ||||
−0.700129 | + | 0.714016i | \(0.746874\pi\) | |||||||
\(332\) | −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 | ||||
\(336\) | −1.50000 | + | 4.33013i | −0.0818317 | + | 0.236228i | ||||
\(337\) | −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 | ||||
\(339\) | 1.50000 | − | 2.59808i | 0.0814688 | − | 0.141108i | ||||
\(340\) | 10.3923i | 0.563602i | ||||||||
\(341\) | −1.50000 | − | 2.59808i | −0.0812296 | − | 0.140694i | ||||
\(342\) | 21.0000 | 1.13555 | ||||||||
\(343\) | −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 | \(-0.423318\pi\) |
−0.721726 | + | 0.692179i | \(0.756651\pi\) | |||||||
\(348\) | −7.50000 | + | 12.9904i | −0.402042 | + | 0.696358i | ||||
\(349\) | 17.5000 | − | 30.3109i | 0.936754 | − | 1.62250i | 0.165277 | − | 0.986247i | \(-0.447148\pi\) |
0.771477 | − | 0.636257i | \(-0.219518\pi\) | |||||||
\(350\) | −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 | ||||||
\(357\) | 27.0000 | − | 5.19615i | 1.42899 | − | 0.275010i | ||||
\(358\) | −16.5000 | + | 9.52628i | −0.872052 | + | 0.503480i | ||||
\(359\) | −1.50000 | + | 2.59808i | −0.0791670 | + | 0.137121i | −0.902891 | − | 0.429870i | \(-0.858559\pi\) |
0.823724 | + | 0.566991i | \(0.191893\pi\) | |||||||
\(360\) | −4.50000 | + | 2.59808i | −0.237171 | + | 0.136931i | ||||
\(361\) | 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 | ||||||||
\(366\) | −1.50000 | + | 2.59808i | −0.0784063 | + | 0.135804i | ||||
\(367\) | 15.5885i | 0.813711i | 0.913493 | + | 0.406855i | \(0.133375\pi\) | ||||
−0.913493 | + | 0.406855i | \(0.866625\pi\) | |||||||
\(368\) | 3.00000 | + | 1.73205i | 0.156386 | + | 0.0902894i | ||||
\(369\) | −13.5000 | + | 7.79423i | −0.702782 | + | 0.405751i | ||||
\(370\) | 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 | 0.0122747 | − | 0.999925i | \(-0.496093\pi\) |
−0.859823 | + | 0.510593i | \(0.829426\pi\) | |||||||
\(380\) | −10.5000 | + | 6.06218i | −0.538639 | + | 0.310983i | ||||
\(381\) | 29.4449i | 1.50851i | ||||||||
\(382\) | 13.5000 | − | 7.79423i | 0.690720 | − | 0.398787i | ||||
\(383\) | 5.19615i | 0.265511i | 0.991149 | + | 0.132755i | \(0.0423825\pi\) | ||||
−0.991149 | + | 0.132755i | \(0.957617\pi\) | |||||||
\(384\) | 1.50000 | + | 0.866025i | 0.0765466 | + | 0.0441942i | ||||
\(385\) | 4.50000 | − | 12.9904i | 0.229341 | − | 0.662051i | ||||
\(386\) | −10.5000 | + | 6.06218i | −0.534436 | + | 0.308557i | ||||
\(387\) | −3.00000 | −0.152499 | ||||||||
\(388\) | −19.0000 | −0.964579 | ||||||||
\(389\) | −4.50000 | + | 2.59808i | −0.228159 | + | 0.131728i | −0.609722 | − | 0.792615i | \(-0.708719\pi\) |
0.381563 | + | 0.924343i | \(0.375386\pi\) | |||||||
\(390\) | −10.5000 | + | 2.59808i | −0.531688 | + | 0.131559i | ||||
\(391\) | − | 20.7846i | − | 1.05112i | ||||||
\(392\) | −6.50000 | + | 2.59808i | −0.328300 | + | 0.131223i | ||||
\(393\) | 5.19615i | 0.262111i | ||||||||
\(394\) | 21.0000 | 1.05796 | ||||||||
\(395\) | 1.50000 | − | 0.866025i | 0.0754732 | − | 0.0435745i | ||||
\(396\) | 4.50000 | + | 7.79423i | 0.226134 | + | 0.391675i | ||||
\(397\) | 29.0000 | 1.45547 | 0.727734 | − | 0.685859i | \(-0.240573\pi\) | ||||
0.727734 | + | 0.685859i | \(0.240573\pi\) | |||||||
\(398\) | 3.46410i | 0.173640i | ||||||||
\(399\) | 21.0000 | + | 24.2487i | 1.05131 | + | 1.21395i | ||||
\(400\) | −1.00000 | + | 1.73205i | −0.0500000 | + | 0.0866025i | ||||
\(401\) | −9.00000 | − | 15.5885i | −0.449439 | − | 0.778450i | 0.548911 | − | 0.835881i | \(-0.315043\pi\) |
−0.998350 | + | 0.0574304i | \(0.981709\pi\) | |||||||
\(402\) | 1.50000 | − | 2.59808i | 0.0748132 | − | 0.129580i | ||||
\(403\) | −3.50000 | + | 0.866025i | −0.174347 | + | 0.0431398i | ||||
\(404\) | 4.50000 | − | 7.79423i | 0.223883 | − | 0.387777i | ||||
\(405\) | 15.5885i | 0.774597i | ||||||||
\(406\) | −22.5000 | + | 4.33013i | −1.11666 | + | 0.214901i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | − | 10.3923i | − | 0.514496i | ||||||
\(409\) | 11.0000 | − | 19.0526i | 0.543915 | − | 0.942088i | −0.454759 | − | 0.890614i | \(-0.650275\pi\) |
0.998674 | − | 0.0514740i | \(-0.0163919\pi\) | |||||||
\(410\) | 4.50000 | − | 7.79423i | 0.222239 | − | 0.384930i | ||||
\(411\) | − | 10.3923i | − | 0.512615i | ||||||
\(412\) | 7.50000 | − | 4.33013i | 0.369498 | − | 0.213330i | ||||
\(413\) | 9.00000 | − | 25.9808i | 0.442861 | − | 1.27843i | ||||
\(414\) | 9.00000 | − | 5.19615i | 0.442326 | − | 0.255377i | ||||
\(415\) | 3.00000 | − | 5.19615i | 0.147264 | − | 0.255069i | ||||
\(416\) | 2.50000 | + | 2.59808i | 0.122573 | + | 0.127381i | ||||
\(417\) | −19.5000 | + | 33.7750i | −0.954919 | + | 1.65397i | ||||
\(418\) | 10.5000 | + | 18.1865i | 0.513572 | + | 0.889532i | ||||
\(419\) | 16.5000 | − | 28.5788i | 0.806078 | − | 1.39617i | −0.109483 | − | 0.993989i | \(-0.534920\pi\) |
0.915561 | − | 0.402179i | \(-0.131747\pi\) | |||||||
\(420\) | −7.50000 | − | 2.59808i | −0.365963 | − | 0.126773i | ||||
\(421\) | − | 13.8564i | − | 0.675320i | −0.941268 | − | 0.337660i | \(-0.890365\pi\) | ||
0.941268 | − | 0.337660i | \(-0.109635\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | 4.50000 | − | 2.59808i | 0.218797 | − | 0.126323i | ||||
\(424\) | 1.50000 | − | 0.866025i | 0.0728464 | − | 0.0420579i | ||||
\(425\) | 12.0000 | 0.582086 | ||||||||
\(426\) | 15.5885i | 0.755263i | ||||||||
\(427\) | −4.50000 | + | 0.866025i | −0.217770 | + | 0.0419099i | ||||
\(428\) | 10.3923i | 0.502331i | ||||||||
\(429\) | 4.50000 | + | 18.1865i | 0.217262 | + | 0.878054i | ||||
\(430\) | 1.50000 | − | 0.866025i | 0.0723364 | − | 0.0417635i | ||||
\(431\) | −21.0000 | −1.01153 | −0.505767 | − | 0.862670i | \(-0.668791\pi\) | ||||
−0.505767 | + | 0.862670i | \(0.668791\pi\) | |||||||
\(432\) | 4.50000 | − | 2.59808i | 0.216506 | − | 0.125000i | ||||
\(433\) | 4.50000 | − | 2.59808i | 0.216256 | − | 0.124856i | −0.387959 | − | 0.921676i | \(-0.626820\pi\) |
0.604216 | + | 0.796821i | \(0.293487\pi\) | |||||||
\(434\) | −2.50000 | − | 0.866025i | −0.120004 | − | 0.0415705i | ||||
\(435\) | −22.5000 | − | 12.9904i | −1.07879 | − | 0.622841i | ||||
\(436\) | − | 8.66025i | − | 0.414751i | ||||||
\(437\) | 21.0000 | − | 12.1244i | 1.00457 | − | 0.579987i | ||||
\(438\) | − | 22.5167i | − | 1.07589i | ||||||
\(439\) | −3.00000 | + | 1.73205i | −0.143182 | + | 0.0826663i | −0.569880 | − | 0.821728i | \(-0.693010\pi\) |
0.426698 | + | 0.904394i | \(0.359677\pi\) | |||||||
\(440\) | −4.50000 | − | 2.59808i | −0.214529 | − | 0.123858i | ||||
\(441\) | −3.00000 | + | 20.7846i | −0.142857 | + | 0.989743i | ||||
\(442\) | 6.00000 | − | 20.7846i | 0.285391 | − | 0.988623i | ||||
\(443\) | 10.5000 | + | 6.06218i | 0.498870 | + | 0.288023i | 0.728247 | − | 0.685315i | \(-0.240335\pi\) |
−0.229377 | + | 0.973338i | \(0.573669\pi\) | |||||||
\(444\) | 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 | \(-0.0515060\pi\) |
−0.632990 | + | 0.774160i | \(0.718173\pi\) | |||||||
\(450\) | 3.00000 | + | 5.19615i | 0.141421 | + | 0.244949i | ||||
\(451\) | −13.5000 | − | 7.79423i | −0.635690 | − | 0.367016i | ||||
\(452\) | − | 1.73205i | − | 0.0814688i | ||||||
\(453\) | 19.5000 | − | 33.7750i | 0.916190 | − | 1.58689i | ||||
\(454\) | 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 | −0.0159406 | − | 0.999873i | \(-0.505074\pi\) |
0.857945 | + | 0.513741i | \(0.171741\pi\) | |||||||
\(458\) | 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 | \(-0.873503\pi\) |
−0.125860 | + | 0.992048i | \(0.540169\pi\) | |||||||
\(462\) | −4.50000 | + | 12.9904i | −0.209359 | + | 0.604367i | ||||
\(463\) | 31.1769i | 1.44891i | 0.689320 | + | 0.724457i | \(0.257909\pi\) | ||||
−0.689320 | + | 0.724457i | \(0.742091\pi\) | |||||||
\(464\) | 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 | \(-0.900105\pi\) |
0.742923 | + | 0.669376i | \(0.233439\pi\) | |||||||
\(468\) | 10.5000 | − | 2.59808i | 0.485363 | − | 0.120096i | ||||
\(469\) | 4.50000 | − | 0.866025i | 0.207791 | − | 0.0399893i | ||||
\(470\) | −1.50000 | + | 2.59808i | −0.0691898 | + | 0.119840i | ||||
\(471\) | −1.50000 | + | 2.59808i | −0.0691164 | + | 0.119713i | ||||
\(472\) | −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 | ||||
\(477\) | − | 5.19615i | − | 0.237915i | ||||||
\(478\) | −6.00000 | − | 10.3923i | −0.274434 | − | 0.475333i | ||||
\(479\) | 19.0526i | 0.870534i | 0.900302 | + | 0.435267i | \(0.143346\pi\) | ||||
−0.900302 | + | 0.435267i | \(0.856654\pi\) | |||||||
\(480\) | −1.50000 | + | 2.59808i | −0.0684653 | + | 0.118585i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 10.0000 | 0.455488 | ||||||||
\(483\) | 15.0000 | + | 5.19615i | 0.682524 | + | 0.236433i | ||||
\(484\) | 1.00000 | − | 1.73205i | 0.0454545 | − | 0.0787296i | ||||
\(485\) | − | 32.9090i | − | 1.49432i | ||||||
\(486\) | − | 15.5885i | − | 0.707107i | ||||||
\(487\) | −3.00000 | − | 1.73205i | −0.135943 | − | 0.0784867i | 0.430486 | − | 0.902597i | \(-0.358342\pi\) |
−0.566429 | + | 0.824110i | \(0.691675\pi\) | |||||||
\(488\) | 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 | \(-0.639776\pi\) |
−0.996434 | + | 0.0843802i | \(0.973109\pi\) | |||||||
\(492\) | −4.50000 | + | 7.79423i | −0.202876 | + | 0.351391i | ||||
\(493\) | 45.0000 | − | 25.9808i | 2.02670 | − | 1.17011i | ||||
\(494\) | 24.5000 | − | 6.06218i | 1.10231 | − | 0.272750i | ||||
\(495\) | −13.5000 | + | 7.79423i | −0.606780 | + | 0.350325i | ||||
\(496\) | −0.500000 | + | 0.866025i | −0.0224507 | + | 0.0388857i | ||||
\(497\) | −18.0000 | + | 15.5885i | −0.807410 | + | 0.699238i | ||||
\(498\) | −3.00000 | + | 5.19615i | −0.134433 | + | 0.232845i | ||||
\(499\) | −28.5000 | − | 16.4545i | −1.27584 | − | 0.736604i | −0.299755 | − | 0.954016i | \(-0.596905\pi\) |
−0.976080 | + | 0.217412i | \(0.930238\pi\) | |||||||
\(500\) | −10.5000 | − | 6.06218i | −0.469574 | − | 0.271109i | ||||
\(501\) | −15.0000 | −0.670151 | ||||||||
\(502\) | 7.50000 | − | 12.9904i | 0.334741 | − | 0.579789i | ||||
\(503\) | 13.5000 | + | 23.3827i | 0.601935 | + | 1.04258i | 0.992528 | + | 0.122019i | \(0.0389368\pi\) |
−0.390593 | + | 0.920564i | \(0.627730\pi\) | |||||||
\(504\) | 7.50000 | + | 2.59808i | 0.334077 | + | 0.115728i | ||||
\(505\) | 13.5000 | + | 7.79423i | 0.600742 | + | 0.346839i | ||||
\(506\) | 9.00000 | + | 5.19615i | 0.400099 | + | 0.230997i | ||||
\(507\) | 22.5000 | + | 0.866025i | 0.999260 | + | 0.0384615i | ||||
\(508\) | 8.50000 | + | 14.7224i | 0.377127 | + | 0.653202i | ||||
\(509\) | −6.00000 | + | 3.46410i | −0.265945 | + | 0.153544i | −0.627044 | − | 0.778984i | \(-0.715735\pi\) |
0.361098 | + | 0.932528i | \(0.382402\pi\) | |||||||
\(510\) | 18.0000 | 0.797053 | ||||||||
\(511\) | 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 | \(-0.273237\pi\) |
−0.982231 | + | 0.187678i | \(0.939904\pi\) | |||||||
\(522\) | 22.5000 | + | 12.9904i | 0.984798 | + | 0.568574i | ||||
\(523\) | 27.0000 | − | 15.5885i | 1.18063 | − | 0.681636i | 0.224468 | − | 0.974481i | \(-0.427936\pi\) |
0.956160 | + | 0.292846i | \(0.0946023\pi\) | |||||||
\(524\) | 1.50000 | + | 2.59808i | 0.0655278 | + | 0.113497i | ||||
\(525\) | −3.00000 | + | 8.66025i | −0.130931 | + | 0.377964i | ||||
\(526\) | 7.50000 | − | 4.33013i | 0.327016 | − | 0.188803i | ||||
\(527\) | 6.00000 | 0.261364 | ||||||||
\(528\) | 4.50000 | + | 2.59808i | 0.195837 | + | 0.113067i | ||||
\(529\) | −5.50000 | + | 9.52628i | −0.239130 | + | 0.414186i | ||||
\(530\) | 1.50000 | + | 2.59808i | 0.0651558 | + | 0.112853i | ||||
\(531\) | −27.0000 | + | 15.5885i | −1.17170 | + | 0.676481i | ||||
\(532\) | 17.5000 | + | 6.06218i | 0.758721 | + | 0.262829i | ||||
\(533\) | −13.5000 | + | 12.9904i | −0.584750 | + | 0.562676i | ||||
\(534\) | −12.0000 | −0.519291 | ||||||||
\(535\) | −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 | 0.180886 | − | 0.983504i | \(-0.442103\pi\) |
−0.761296 | + | 0.648404i | \(0.775437\pi\) | |||||||
\(542\) | 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 | ||||||||
\(546\) | 13.5000 | + | 9.52628i | 0.577747 | + | 0.407687i | ||||
\(547\) | 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 | ||||
\(552\) | 3.00000 | − | 5.19615i | 0.127688 | − | 0.221163i | ||||
\(553\) | −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 | \(-0.253572\pi\) | ||||
0.699127 | + | 0.714997i | \(0.253572\pi\) | |||||||
\(558\) | 1.50000 | + | 2.59808i | 0.0635001 | + | 0.109985i | ||||
\(559\) | −3.50000 | + | 0.866025i | −0.148034 | + | 0.0366290i | ||||
\(560\) | −4.50000 | + | 0.866025i | −0.190160 | + | 0.0365963i | ||||
\(561\) | − | 31.1769i | − | 1.31629i | ||||||
\(562\) | 3.00000 | + | 5.19615i | 0.126547 | + | 0.219186i | ||||
\(563\) | −6.00000 | + | 10.3923i | −0.252870 | + | 0.437983i | −0.964315 | − | 0.264758i | \(-0.914708\pi\) |
0.711445 | + | 0.702742i | \(0.248041\pi\) | |||||||
\(564\) | 1.50000 | − | 2.59808i | 0.0631614 | − | 0.109399i | ||||
\(565\) | 3.00000 | 0.126211 | ||||||||
\(566\) | 19.5000 | − | 11.2583i | 0.819646 | − | 0.473223i | ||||
\(567\) | 18.0000 | − | 15.5885i | 0.755929 | − | 0.654654i | ||||
\(568\) | 4.50000 | + | 7.79423i | 0.188816 | + | 0.327039i | ||||
\(569\) | 12.0000 | − | 6.92820i | 0.503066 | − | 0.290445i | −0.226913 | − | 0.973915i | \(-0.572863\pi\) |
0.729979 | + | 0.683470i | \(0.239530\pi\) | |||||||
\(570\) | 10.5000 | + | 18.1865i | 0.439797 | + | 0.761750i | ||||
\(571\) | 2.50000 | + | 4.33013i | 0.104622 | + | 0.181210i | 0.913584 | − | 0.406651i | \(-0.133303\pi\) |
−0.808962 | + | 0.587861i | \(0.799970\pi\) | |||||||
\(572\) | 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 | 0.929636 | − | 0.368478i | \(-0.120121\pi\) |
−0.783930 | + | 0.620850i | \(0.786788\pi\) | |||||||
\(578\) | −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 | ||||
\(582\) | 32.9090i | 1.36412i | ||||||||
\(583\) | 4.50000 | − | 2.59808i | 0.186371 | − | 0.107601i | ||||
\(584\) | −6.50000 | − | 11.2583i | −0.268972 | − | 0.465873i | ||||
\(585\) | 4.50000 | + | 18.1865i | 0.186052 | + | 0.751921i | ||||
\(586\) | −25.5000 | − | 14.7224i | −1.05340 | − | 0.608178i | ||||
\(587\) | −28.5000 | − | 16.4545i | −1.17632 | − | 0.679149i | −0.221160 | − | 0.975237i | \(-0.570984\pi\) |
−0.955161 | + | 0.296088i | \(0.904318\pi\) | |||||||
\(588\) | 4.50000 | + | 11.2583i | 0.185577 | + | 0.464286i | ||||
\(589\) | 3.50000 | + | 6.06218i | 0.144215 | + | 0.249788i | ||||
\(590\) | 9.00000 | − | 15.5885i | 0.370524 | − | 0.641767i | ||||
\(591\) | − | 36.3731i | − | 1.49619i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.50000 | − | 4.33013i | −0.307988 | − | 0.177817i | 0.338038 | − | 0.941133i | \(-0.390237\pi\) |
−0.646026 | + | 0.763316i | \(0.723570\pi\) | |||||||
\(594\) | 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 | ||||
\(597\) | 6.00000 | 0.245564 | ||||||||
\(598\) | 9.00000 | − | 8.66025i | 0.368037 | − | 0.354144i | ||||
\(599\) | 25.5000 | − | 14.7224i | 1.04190 | − | 0.601542i | 0.121530 | − | 0.992588i | \(-0.461220\pi\) |
0.920371 | + | 0.391045i | \(0.127886\pi\) | |||||||
\(600\) | 3.00000 | + | 1.73205i | 0.122474 | + | 0.0707107i | ||||
\(601\) | −19.5000 | − | 11.2583i | −0.795422 | − | 0.459237i | 0.0464461 | − | 0.998921i | \(-0.485210\pi\) |
−0.841868 | + | 0.539684i | \(0.818544\pi\) | |||||||
\(602\) | −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 | ||||
\(606\) | −13.5000 | − | 7.79423i | −0.548400 | − | 0.316619i | ||||
\(607\) | − | 19.0526i | − | 0.773320i | −0.922222 | − | 0.386660i | \(-0.873629\pi\) | ||
0.922222 | − | 0.386660i | \(-0.126371\pi\) | |||||||
\(608\) | 3.50000 | − | 6.06218i | 0.141944 | − | 0.245854i | ||||
\(609\) | 7.50000 | + | 38.9711i | 0.303915 | + | 1.57919i | ||||
\(610\) | −3.00000 | −0.121466 | ||||||||
\(611\) | 4.50000 | − | 4.33013i | 0.182051 | − | 0.175178i | ||||
\(612\) | −18.0000 | −0.727607 | ||||||||
\(613\) | 22.5167i | 0.909439i | 0.890635 | + | 0.454720i | \(0.150261\pi\) | ||||
−0.890635 | + | 0.454720i | \(0.849739\pi\) | |||||||
\(614\) | −2.00000 | − | 3.46410i | −0.0807134 | − | 0.139800i | ||||
\(615\) | −13.5000 | − | 7.79423i | −0.544373 | − | 0.314294i | ||||
\(616\) | 1.50000 | + | 7.79423i | 0.0604367 | + | 0.314038i | ||||
\(617\) | −4.50000 | − | 7.79423i | −0.181163 | − | 0.313784i | 0.761114 | − | 0.648618i | \(-0.224653\pi\) |
−0.942277 | + | 0.334835i | \(0.891320\pi\) | |||||||
\(618\) | −7.50000 | − | 12.9904i | −0.301694 | − | 0.522550i | ||||
\(619\) | −2.50000 | − | 4.33013i | −0.100483 | − | 0.174042i | 0.811400 | − | 0.584491i | \(-0.198706\pi\) |
−0.911884 | + | 0.410448i | \(0.865372\pi\) | |||||||
\(620\) | −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 | ||||
\(624\) | 4.50000 | − | 4.33013i | 0.180144 | − | 0.173344i | ||||
\(625\) | 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 | ||||||||
\(630\) | −4.50000 | + | 12.9904i | −0.179284 | + | 0.517549i | ||||
\(631\) | −1.50000 | + | 0.866025i | −0.0597141 | + | 0.0344759i | −0.529560 | − | 0.848273i | \(-0.677643\pi\) |
0.469846 | + | 0.882749i | \(0.344310\pi\) | |||||||
\(632\) | −0.500000 | + | 0.866025i | −0.0198889 | + | 0.0344486i | ||||
\(633\) | 1.73205i | 0.0688428i | ||||||||
\(634\) | −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 | ||||||||
\(639\) | 27.0000 | 1.06810 | ||||||||
\(640\) | 1.73205i | 0.0684653i | ||||||||
\(641\) | 30.0000 | + | 17.3205i | 1.18493 | + | 0.684119i | 0.957150 | − | 0.289594i | \(-0.0935202\pi\) |
0.227779 | + | 0.973713i | \(0.426854\pi\) | |||||||
\(642\) | 18.0000 | 0.710403 | ||||||||
\(643\) | 14.5000 | + | 25.1147i | 0.571824 | + | 0.990429i | 0.996379 | + | 0.0850262i | \(0.0270974\pi\) |
−0.424555 | + | 0.905402i | \(0.639569\pi\) | |||||||
\(644\) | 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 | \(-0.518782\pi\) | ||||
−0.0589711 | + | 0.998260i | \(0.518782\pi\) | |||||||
\(648\) | −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 | ||||
\(651\) | −1.50000 | + | 4.33013i | −0.0587896 | + | 0.169711i | ||||
\(652\) | −4.50000 | − | 2.59808i | −0.176234 | − | 0.101749i | ||||
\(653\) | −36.0000 | + | 20.7846i | −1.40879 | + | 0.813365i | −0.995272 | − | 0.0971316i | \(-0.969033\pi\) |
−0.413517 | + | 0.910496i | \(0.635700\pi\) | |||||||
\(654\) | −15.0000 | −0.586546 | ||||||||
\(655\) | −4.50000 | + | 2.59808i | −0.175830 | + | 0.101515i | ||||
\(656\) | 5.19615i | 0.202876i | ||||||||
\(657\) | −39.0000 | −1.52153 | ||||||||
\(658\) | 4.50000 | − | 0.866025i | 0.175428 | − | 0.0337612i | ||||
\(659\) | −34.5000 | + | 19.9186i | −1.34393 | + | 0.775918i | −0.987382 | − | 0.158359i | \(-0.949380\pi\) |
−0.356548 | + | 0.934277i | \(0.616046\pi\) | |||||||
\(660\) | −4.50000 | + | 7.79423i | −0.175162 | + | 0.303390i | ||||
\(661\) | 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 | ||||
\(663\) | −36.0000 | − | 10.3923i | −1.39812 | − | 0.403604i | ||||
\(664\) | 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 | ||||
\(669\) | − | 50.2295i | − | 1.94198i | ||||||
\(670\) | 3.00000 | 0.115900 | ||||||||
\(671\) | 5.19615i | 0.200595i | ||||||||
\(672\) | 4.50000 | − | 0.866025i | 0.173591 | − | 0.0334077i | ||||
\(673\) | −3.50000 | + | 6.06218i | −0.134915 | + | 0.233680i | −0.925565 | − | 0.378589i | \(-0.876409\pi\) |
0.790650 | + | 0.612268i | \(0.209743\pi\) | |||||||
\(674\) | 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 | 0.480913 | + | 0.876768i | \(0.340305\pi\) |
−0.999760 | + | 0.0219013i | \(0.993028\pi\) | |||||||
\(678\) | −3.00000 | −0.115214 | ||||||||
\(679\) | −38.0000 | + | 32.9090i | −1.45831 | + | 1.26293i | ||||
\(680\) | 9.00000 | − | 5.19615i | 0.345134 | − | 0.199263i | ||||
\(681\) | 18.0000 | 0.689761 | ||||||||
\(682\) | −1.50000 | + | 2.59808i | −0.0574380 | + | 0.0994855i | ||||
\(683\) | −6.00000 | + | 10.3923i | −0.229584 | + | 0.397650i | −0.957685 | − | 0.287819i | \(-0.907070\pi\) |
0.728101 | + | 0.685470i | \(0.240403\pi\) | |||||||
\(684\) | −10.5000 | − | 18.1865i | −0.401478 | − | 0.695379i | ||||
\(685\) | 9.00000 | − | 5.19615i | 0.343872 | − | 0.198535i | ||||
\(686\) | −8.50000 | + | 16.4545i | −0.324532 | + | 0.628235i | ||||
\(687\) | − | 43.3013i | − | 1.65205i | ||||||
\(688\) | −0.500000 | + | 0.866025i | −0.0190623 | + | 0.0330169i | ||||
\(689\) | −1.50000 | − | 6.06218i | −0.0571454 | − | 0.230951i | ||||
\(690\) | 9.00000 | + | 5.19615i | 0.342624 | + | 0.197814i | ||||
\(691\) | −22.0000 | − | 38.1051i | −0.836919 | − | 1.44959i | −0.892458 | − | 0.451130i | \(-0.851021\pi\) |
0.0555386 | − | 0.998457i | \(-0.482312\pi\) | |||||||
\(692\) | 4.50000 | − | 7.79423i | 0.171064 | − | 0.296292i | ||||
\(693\) | 22.5000 | + | 7.79423i | 0.854704 | + | 0.296078i | ||||
\(694\) | 10.3923i | 0.394486i | ||||||||
\(695\) | −39.0000 | −1.47935 | ||||||||
\(696\) | 15.0000 | 0.568574 | ||||||||
\(697\) | 27.0000 | − | 15.5885i | 1.02270 | − | 0.590455i | ||||
\(698\) | −35.0000 | −1.32477 | ||||||||
\(699\) | −39.0000 | −1.47512 | ||||||||
\(700\) | 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 | ||||||||
\(705\) | 4.50000 | + | 2.59808i | 0.169480 | + | 0.0978492i | ||||
\(706\) | −22.5000 | + | 12.9904i | −0.846799 | + | 0.488899i | ||||
\(707\) | −4.50000 | − | 23.3827i | −0.169240 | − | 0.879396i | ||||
\(708\) | −9.00000 | + | 15.5885i | −0.338241 | + | 0.585850i | ||||
\(709\) | 25.9808i | 0.975728i | 0.872920 | + | 0.487864i | \(0.162224\pi\) | ||||
−0.872920 | + | 0.487864i | \(0.837776\pi\) | |||||||
\(710\) | −13.5000 | + | 7.79423i | −0.506646 | + | 0.292512i | ||||
\(711\) | 1.50000 | + | 2.59808i | 0.0562544 | + | 0.0974355i | ||||
\(712\) | −6.00000 | + | 3.46410i | −0.224860 | + | 0.129823i | ||||
\(713\) | 3.00000 | + | 1.73205i | 0.112351 | + | 0.0648658i | ||||
\(714\) | −18.0000 | − | 20.7846i | −0.673633 | − | 0.777844i | ||||
\(715\) | −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 | \(-0.482184\pi\) | ||||
0.0559406 | + | 0.998434i | \(0.482184\pi\) | |||||||
\(720\) | 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 | ||||
\(723\) | − | 17.3205i | − | 0.644157i | ||||||
\(724\) | 12.0000 | + | 6.92820i | 0.445976 | + | 0.257485i | ||||
\(725\) | 17.3205i | 0.643268i | ||||||||
\(726\) | −3.00000 | − | 1.73205i | −0.111340 | − | 0.0642824i | ||||
\(727\) | 10.3923i | 0.385429i | 0.981255 | + | 0.192715i | \(0.0617292\pi\) | ||||
−0.981255 | + | 0.192715i | \(0.938271\pi\) | |||||||
\(728\) | 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 | ||||||||
\(732\) | 3.00000 | 0.110883 | ||||||||
\(733\) | −18.5000 | + | 32.0429i | −0.683313 | + | 1.18353i | 0.290651 | + | 0.956829i | \(0.406128\pi\) |
−0.973964 | + | 0.226704i | \(0.927205\pi\) | |||||||
\(734\) | 13.5000 | − | 7.79423i | 0.498294 | − | 0.287690i | ||||
\(735\) | −19.5000 | + | 7.79423i | −0.719268 | + | 0.287494i | ||||
\(736\) | − | 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 | \(0.113964\pi\) | ||||
−0.936589 | + | 0.350430i | \(0.886036\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.5000 | − | 42.4352i | −0.385727 | − | 1.55890i | ||||
\(742\) | 1.50000 | − | 4.33013i | 0.0550667 | − | 0.158964i | ||||
\(743\) | −4.50000 | + | 7.79423i | −0.165089 | + | 0.285943i | −0.936687 | − | 0.350168i | \(-0.886124\pi\) |
0.771598 | + | 0.636111i | \(0.219458\pi\) | |||||||
\(744\) | 1.50000 | + | 0.866025i | 0.0549927 | + | 0.0317500i | ||||
\(745\) | −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 | ||||
\(750\) | −10.5000 | + | 18.1865i | −0.383406 | + | 0.664078i | ||||
\(751\) | −2.00000 | − | 3.46410i | −0.0729810 | − | 0.126407i | 0.827225 | − | 0.561870i | \(-0.189918\pi\) |
−0.900207 | + | 0.435463i | \(0.856585\pi\) | |||||||
\(752\) | − | 1.73205i | − | 0.0631614i | ||||||
\(753\) | −22.5000 | − | 12.9904i | −0.819946 | − | 0.473396i | ||||
\(754\) | 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 | 0.0233351 | + | 0.999728i | \(0.492572\pi\) |
−0.877457 | + | 0.479655i | \(0.840762\pi\) | |||||||
\(758\) | 19.0526i | 0.692020i | ||||||||
\(759\) | 9.00000 | − | 15.5885i | 0.326679 | − | 0.565825i | ||||
\(760\) | 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 | ||||
\(765\) | − | 31.1769i | − | 1.12720i | ||||||
\(766\) | 4.50000 | − | 2.59808i | 0.162592 | − | 0.0938723i | ||||
\(767\) | −27.0000 | + | 25.9808i | −0.974913 | + | 0.938111i | ||||
\(768\) | − | 1.73205i | − | 0.0625000i | ||||||
\(769\) | −6.50000 | + | 11.2583i | −0.234396 | + | 0.405986i | −0.959097 | − | 0.283078i | \(-0.908645\pi\) |
0.724701 | + | 0.689063i | \(0.241978\pi\) | |||||||
\(770\) | −13.5000 | + | 2.59808i | −0.486506 | + | 0.0936282i | ||||
\(771\) | 9.00000 | + | 5.19615i | 0.324127 | + | 0.187135i | ||||
\(772\) | 10.5000 | + | 6.06218i | 0.377903 | + | 0.218183i | ||||
\(773\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(774\) | 1.50000 | + | 2.59808i | 0.0539164 | + | 0.0933859i | ||||
\(775\) | −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 | ||||
\(780\) | 7.50000 | + | 7.79423i | 0.268543 | + | 0.279078i | ||||
\(781\) | 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 | −0.828176 | − | 0.560469i | \(-0.810621\pi\) |
0.899468 | + | 0.436987i | \(0.143954\pi\) | |||||||
\(788\) | −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 | −0.971601 | − | 0.236627i | \(-0.923958\pi\) |
0.280875 | − | 0.959744i | \(-0.409375\pi\) | |||||||
\(798\) | 10.5000 | − | 30.3109i | 0.371696 | − | 1.07299i | ||||
\(799\) | −9.00000 | + | 5.19615i | −0.318397 | + | 0.183827i | ||||
\(800\) | 2.00000 | 0.0707107 | ||||||||
\(801\) | 20.7846i | 0.734388i | ||||||||
\(802\) | −9.00000 | + | 15.5885i | −0.317801 | + | 0.550448i | ||||
\(803\) | −19.5000 | − | 33.7750i | −0.688140 | − | 1.19189i | ||||
\(804\) | −3.00000 | −0.105802 | ||||||||
\(805\) | 3.00000 | + | 15.5885i | 0.105736 | + | 0.549421i | ||||
\(806\) | 2.50000 | + | 2.59808i | 0.0880587 | + | 0.0915133i | ||||
\(807\) | 51.9615i | 1.82913i | ||||||||
\(808\) | −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 | ||||
\(813\) | −24.0000 | − | 13.8564i | −0.841717 | − | 0.485965i | ||||
\(814\) | 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 | ||||||||
\(819\) | 16.5000 | − | 23.3827i | 0.576557 | − | 0.817057i | ||||
\(820\) | −9.00000 | −0.314294 | ||||||||
\(821\) | −3.00000 | − | 5.19615i | −0.104701 | − | 0.181347i | 0.808915 | − | 0.587925i | \(-0.200055\pi\) |
−0.913616 | + | 0.406578i | \(0.866722\pi\) | |||||||
\(822\) | −9.00000 | + | 5.19615i | −0.313911 | + | 0.181237i | ||||
\(823\) | 8.00000 | − | 13.8564i | 0.278862 | − | 0.483004i | −0.692240 | − | 0.721668i | \(-0.743376\pi\) |
0.971102 | + | 0.238664i | \(0.0767093\pi\) | |||||||
\(824\) | −7.50000 | − | 4.33013i | −0.261275 | − | 0.150847i | ||||
\(825\) | 9.00000 | + | 5.19615i | 0.313340 | + | 0.180907i | ||||
\(826\) | −27.0000 | + | 5.19615i | −0.939450 | + | 0.180797i | ||||
\(827\) | −36.0000 | −1.25184 | −0.625921 | − | 0.779886i | \(-0.715277\pi\) | ||||
−0.625921 | + | 0.779886i | \(0.715277\pi\) | |||||||
\(828\) | −9.00000 | − | 5.19615i | −0.312772 | − | 0.180579i | ||||
\(829\) | − | 15.5885i | − | 0.541409i | −0.962662 | − | 0.270705i | \(-0.912743\pi\) | ||
0.962662 | − | 0.270705i | \(-0.0872567\pi\) | |||||||
\(830\) | −6.00000 | −0.208263 | ||||||||
\(831\) | 17.3205i | 0.600842i | ||||||||
\(832\) | 1.00000 | − | 3.46410i | 0.0346688 | − | 0.120096i | ||||
\(833\) | 6.00000 | − | 41.5692i | 0.207888 | − | 1.44029i | ||||
\(834\) | 39.0000 | 1.35046 | ||||||||
\(835\) | −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 | \(-0.638077\pi\) |
0.575663 | + | 0.817687i | \(0.304744\pi\) | |||||||
\(840\) | 1.50000 | + | 7.79423i | 0.0517549 | + | 0.268926i | ||||
\(841\) | 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 | ||||
\(855\) | 31.5000 | − | 18.1865i | 1.07728 | − | 0.621966i | ||||
\(856\) | 9.00000 | − | 5.19615i | 0.307614 | − | 0.177601i | ||||
\(857\) | −19.5000 | − | 33.7750i | −0.666107 | − | 1.15373i | −0.978984 | − | 0.203938i | \(-0.934626\pi\) |
0.312877 | − | 0.949794i | \(-0.398707\pi\) | |||||||
\(858\) | 13.5000 | − | 12.9904i | 0.460882 | − | 0.443484i | ||||
\(859\) | 4.50000 | + | 2.59808i | 0.153538 | + | 0.0886452i | 0.574801 | − | 0.818293i | \(-0.305080\pi\) |
−0.421263 | + | 0.906939i | \(0.638413\pi\) | |||||||
\(860\) | −1.50000 | − | 0.866025i | −0.0511496 | − | 0.0295312i | ||||
\(861\) | 4.50000 | + | 23.3827i | 0.153360 | + | 0.796880i | ||||
\(862\) | 10.5000 | + | 18.1865i | 0.357631 | + | 0.619436i | ||||
\(863\) | −19.5000 | + | 33.7750i | −0.663788 | + | 1.14971i | 0.315825 | + | 0.948818i | \(0.397719\pi\) |
−0.979612 | + | 0.200897i | \(0.935615\pi\) | |||||||
\(864\) | −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 | ||||
\(867\) | 28.5000 | + | 16.4545i | 0.967911 | + | 0.558824i | ||||
\(868\) | 0.500000 | + | 2.59808i | 0.0169711 | + | 0.0881845i | ||||
\(869\) | −1.50000 | + | 2.59808i | −0.0508840 | + | 0.0881337i | ||||
\(870\) | 25.9808i | 0.880830i | ||||||||
\(871\) | −6.00000 | − | 1.73205i | −0.203302 | − | 0.0586883i | ||||
\(872\) | −7.50000 | + | 4.33013i | −0.253982 | + | 0.146637i | ||||
\(873\) | 57.0000 | 1.92916 | ||||||||
\(874\) | −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 | \(0.0656236\pi\) | ||||
−0.978824 | + | 0.204705i | \(0.934376\pi\) | |||||||
\(878\) | 3.00000 | + | 1.73205i | 0.101245 | + | 0.0584539i | ||||
\(879\) | −25.5000 | + | 44.1673i | −0.860094 | + | 1.48973i | ||||
\(880\) | 5.19615i | 0.175162i | ||||||||
\(881\) | 28.5000 | − | 49.3634i | 0.960189 | − | 1.66310i | 0.238171 | − | 0.971223i | \(-0.423452\pi\) |
0.722019 | − | 0.691873i | \(-0.243214\pi\) | |||||||
\(882\) | 19.5000 | − | 7.79423i | 0.656599 | − | 0.262445i | ||||
\(883\) | −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 | ||||
\(885\) | −27.0000 | − | 15.5885i | −0.907595 | − | 0.524000i | ||||
\(886\) | − | 12.1244i | − | 0.407326i | ||||||
\(887\) | 12.0000 | + | 20.7846i | 0.402921 | + | 0.697879i | 0.994077 | − | 0.108678i | \(-0.0346618\pi\) |
−0.591156 | + | 0.806557i | \(0.701328\pi\) | |||||||
\(888\) | 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 | ||||
\(894\) | 31.5000 | + | 18.1865i | 1.05352 | + | 0.608249i | ||||
\(895\) | −16.5000 | + | 28.5788i | −0.551534 | + | 0.955285i | ||||
\(896\) | 2.00000 | − | 1.73205i | 0.0668153 | − | 0.0578638i | ||||
\(897\) | −15.0000 | − | 15.5885i | −0.500835 | − | 0.520483i | ||||
\(898\) | 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 | ||||||||
\(903\) | −1.50000 | + | 4.33013i | −0.0499169 | + | 0.144098i | ||||
\(904\) | −1.50000 | + | 0.866025i | −0.0498893 | + | 0.0288036i | ||||
\(905\) | −12.0000 | + | 20.7846i | −0.398893 | + | 0.690904i | ||||
\(906\) | −39.0000 | −1.29569 | ||||||||
\(907\) | −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 | \(0.868420\pi\) | |||||||
\(912\) | −10.5000 | − | 6.06218i | −0.347690 | − | 0.200739i | ||||
\(913\) | 10.3923i | 0.343935i | ||||||||
\(914\) | −18.0000 | − | 10.3923i | −0.595387 | − | 0.343747i | ||||
\(915\) | 5.19615i | 0.171780i | ||||||||
\(916\) | −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 | ||||
\(924\) | 13.5000 | − | 2.59808i | 0.444117 | − | 0.0854704i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 27.0000 | − | 15.5885i | 0.887275 | − | 0.512268i | ||||
\(927\) | −22.5000 | + | 12.9904i | −0.738997 | + | 0.426660i | ||||
\(928\) | 7.50000 | − | 4.33013i | 0.246200 | − | 0.142143i | ||||
\(929\) | − | 8.66025i | − | 0.284134i | −0.989857 | − | 0.142067i | \(-0.954625\pi\) | ||
0.989857 | − | 0.142067i | \(-0.0453748\pi\) | |||||||
\(930\) | −1.50000 | + | 2.59808i | −0.0491869 | + | 0.0851943i | ||||
\(931\) | 45.5000 | − | 18.1865i | 1.49120 | − | 0.596040i | ||||
\(932\) | −19.5000 | + | 11.2583i | −0.638744 | + | 0.368779i | ||||
\(933\) | 4.50000 | + | 2.59808i | 0.147323 | + | 0.0850572i | ||||
\(934\) | 9.00000 | 0.294489 | ||||||||
\(935\) | 27.0000 | − | 15.5885i | 0.882994 | − | 0.509797i | ||||
\(936\) | −7.50000 | − | 7.79423i | −0.245145 | − | 0.254762i | ||||
\(937\) | − | 20.7846i | − | 0.679004i | −0.940605 | − | 0.339502i | \(-0.889742\pi\) | ||
0.940605 | − | 0.339502i | \(-0.110258\pi\) | |||||||
\(938\) | −3.00000 | − | 3.46410i | −0.0979535 | − | 0.113107i | ||||
\(939\) | 9.00000 | 0.293704 | ||||||||
\(940\) | 3.00000 | 0.0978492 | ||||||||
\(941\) | 16.5000 | − | 9.52628i | 0.537885 | − | 0.310548i | −0.206337 | − | 0.978481i | \(-0.566154\pi\) |
0.744221 | + | 0.667933i | \(0.232821\pi\) | |||||||
\(942\) | 3.00000 | 0.0977453 | ||||||||
\(943\) | 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 | \(-0.104204\pi\) |
−0.751918 | + | 0.659256i | \(0.770871\pi\) | |||||||
\(948\) | 1.50000 | + | 0.866025i | 0.0487177 | + | 0.0281272i | ||||
\(949\) | −45.5000 | + | 11.2583i | −1.47699 | + | 0.365461i | ||||
\(950\) | 7.00000 | − | 12.1244i | 0.227110 | − | 0.393366i | ||||
\(951\) | 5.19615i | 0.168497i | ||||||||
\(952\) | −15.0000 | − | 5.19615i | −0.486153 | − | 0.168408i | ||||
\(953\) | −25.5000 | + | 14.7224i | −0.826026 | + | 0.476906i | −0.852490 | − | 0.522743i | \(-0.824909\pi\) |
0.0264640 | + | 0.999650i | \(0.491575\pi\) | |||||||
\(954\) | −4.50000 | + | 2.59808i | −0.145693 | + | 0.0841158i | ||||
\(955\) | 13.5000 | − | 23.3827i | 0.436850 | − | 0.756646i | ||||
\(956\) | −6.00000 | + | 10.3923i | −0.194054 | + | 0.336111i | ||||
\(957\) | 45.0000 | 1.45464 | ||||||||
\(958\) | 16.5000 | − | 9.52628i | 0.533091 | − | 0.307780i | ||||
\(959\) | −15.0000 | − | 5.19615i | −0.484375 | − | 0.167793i | ||||
\(960\) | 3.00000 | 0.0968246 | ||||||||
\(961\) | 15.0000 | − | 25.9808i | 0.483871 | − | 0.838089i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 31.1769i | − | 1.00466i | ||||||
\(964\) | −5.00000 | − | 8.66025i | −0.161039 | − | 0.278928i | ||||
\(965\) | −10.5000 | + | 18.1865i | −0.338007 | + | 0.585445i | ||||
\(966\) | −3.00000 | − | 15.5885i | −0.0965234 | − | 0.501550i | ||||
\(967\) | − | 10.3923i | − | 0.334194i | −0.985940 | − | 0.167097i | \(-0.946561\pi\) | ||
0.985940 | − | 0.167097i | \(-0.0534393\pi\) | |||||||
\(968\) | −2.00000 | −0.0642824 | ||||||||
\(969\) | 72.7461i | 2.33694i | ||||||||
\(970\) | −28.5000 | + | 16.4545i | −0.915080 | + | 0.528322i | ||||
\(971\) | −33.0000 | −1.05902 | −0.529510 | − | 0.848304i | \(-0.677624\pi\) | ||||
−0.529510 | + | 0.848304i | \(0.677624\pi\) | |||||||
\(972\) | −13.5000 | + | 7.79423i | −0.433013 | + | 0.250000i | ||||
\(973\) | 39.0000 | + | 45.0333i | 1.25028 | + | 1.44370i | ||||
\(974\) | 3.46410i | 0.110997i | ||||||||
\(975\) | 9.00000 | − | 8.66025i | 0.288231 | − | 0.277350i | ||||
\(976\) | 1.50000 | − | 0.866025i | 0.0480138 | − | 0.0277208i | ||||
\(977\) | −3.00000 | −0.0959785 | −0.0479893 | − | 0.998848i | \(-0.515281\pi\) | ||||
−0.0479893 | + | 0.998848i | \(0.515281\pi\) | |||||||
\(978\) | −4.50000 | + | 7.79423i | −0.143894 | + | 0.249232i | ||||
\(979\) | −18.0000 | + | 10.3923i | −0.575282 | + | 0.332140i | ||||
\(980\) | −7.50000 | + | 9.52628i | −0.239579 | + | 0.304306i | ||||
\(981\) | 25.9808i | 0.829502i | ||||||||
\(982\) | 36.3731i | 1.16071i | ||||||||
\(983\) | −25.5000 | + | 14.7224i | −0.813324 | + | 0.469573i | −0.848109 | − | 0.529822i | \(-0.822259\pi\) |
0.0347851 | + | 0.999395i | \(0.488925\pi\) | |||||||
\(984\) | 9.00000 | 0.286910 | ||||||||
\(985\) | 31.5000 | − | 18.1865i | 1.00367 | − | 0.579471i | ||||
\(986\) | −45.0000 | − | 25.9808i | −1.43309 | − | 0.827396i | ||||
\(987\) | −1.50000 | − | 7.79423i | −0.0477455 | − | 0.248093i | ||||
\(988\) | −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 | ||||
\(996\) | 6.00000 | 0.190117 | ||||||||
\(997\) | 24.0000 | + | 13.8564i | 0.760088 | + | 0.438837i | 0.829327 | − | 0.558763i | \(-0.188724\pi\) |
−0.0692396 | + | 0.997600i | \(0.522057\pi\) | |||||||
\(998\) | 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.a.173.1 | yes | 2 | |
3.2 | odd | 2 | 546.2.bn.d.173.1 | yes | 2 | ||
7.3 | odd | 6 | 546.2.bi.d.17.1 | yes | 2 | ||
13.10 | even | 6 | 546.2.bi.b.257.1 | yes | 2 | ||
21.17 | even | 6 | 546.2.bi.b.17.1 | ✓ | 2 | ||
39.23 | odd | 6 | 546.2.bi.d.257.1 | yes | 2 | ||
91.10 | odd | 6 | 546.2.bn.d.101.1 | yes | 2 | ||
273.101 | even | 6 | inner | 546.2.bn.a.101.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.bi.b.17.1 | ✓ | 2 | 21.17 | even | 6 | ||
546.2.bi.b.257.1 | yes | 2 | 13.10 | even | 6 | ||
546.2.bi.d.17.1 | yes | 2 | 7.3 | odd | 6 | ||
546.2.bi.d.257.1 | yes | 2 | 39.23 | odd | 6 | ||
546.2.bn.a.101.1 | yes | 2 | 273.101 | even | 6 | inner | |
546.2.bn.a.173.1 | yes | 2 | 1.1 | even | 1 | trivial | |
546.2.bn.d.101.1 | yes | 2 | 91.10 | odd | 6 | ||
546.2.bn.d.173.1 | yes | 2 | 3.2 | odd | 2 |