Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(121,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 121.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.121 |
Dual form | 570.2.i.a.391.1 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | −1.00000 | −0.377964 | −0.188982 | − | 0.981981i | \(-0.560519\pi\) | ||||
−0.188982 | + | 0.981981i | \(0.560519\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0.500000 | − | 0.866025i | 0.158114 | − | 0.273861i | ||||
\(11\) | −3.00000 | −0.904534 | −0.452267 | − | 0.891883i | \(-0.649385\pi\) | ||||
−0.452267 | + | 0.891883i | \(0.649385\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −1.00000 | + | 1.73205i | −0.277350 | + | 0.480384i | −0.970725 | − | 0.240192i | \(-0.922790\pi\) |
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | 0.500000 | + | 0.866025i | 0.133631 | + | 0.231455i | ||||
\(15\) | 0.500000 | − | 0.866025i | 0.129099 | − | 0.223607i | ||||
\(16\) | −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 | \(0.573966\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −3.50000 | − | 2.59808i | −0.802955 | − | 0.596040i | ||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0.500000 | + | 0.866025i | 0.109109 | + | 0.188982i | ||||
\(22\) | 1.50000 | + | 2.59808i | 0.319801 | + | 0.553912i | ||||
\(23\) | −4.50000 | + | 7.79423i | −0.938315 | + | 1.62521i | −0.169701 | + | 0.985496i | \(0.554280\pi\) |
−0.768613 | + | 0.639713i | \(0.779053\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.500000 | − | 0.866025i | 0.0944911 | − | 0.163663i | ||||
\(29\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 1.50000 | + | 2.59808i | 0.261116 | + | 0.452267i | ||||
\(34\) | 3.00000 | − | 5.19615i | 0.514496 | − | 0.891133i | ||||
\(35\) | −0.500000 | − | 0.866025i | −0.0845154 | − | 0.146385i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | 5.00000 | 0.821995 | 0.410997 | − | 0.911636i | \(-0.365181\pi\) | ||||
0.410997 | + | 0.911636i | \(0.365181\pi\) | |||||||
\(38\) | −0.500000 | + | 4.33013i | −0.0811107 | + | 0.702439i | ||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 0.500000 | + | 0.866025i | 0.0790569 | + | 0.136931i | ||||
\(41\) | 1.50000 | + | 2.59808i | 0.234261 | + | 0.405751i | 0.959058 | − | 0.283211i | \(-0.0913998\pi\) |
−0.724797 | + | 0.688963i | \(0.758066\pi\) | |||||||
\(42\) | 0.500000 | − | 0.866025i | 0.0771517 | − | 0.133631i | ||||
\(43\) | 5.00000 | + | 8.66025i | 0.762493 | + | 1.32068i | 0.941562 | + | 0.336840i | \(0.109358\pi\) |
−0.179069 | + | 0.983836i | \(0.557309\pi\) | |||||||
\(44\) | 1.50000 | − | 2.59808i | 0.226134 | − | 0.391675i | ||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 9.00000 | 1.32698 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | −0.500000 | + | 0.866025i | −0.0721688 | + | 0.125000i | ||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 3.00000 | − | 5.19615i | 0.420084 | − | 0.727607i | ||||
\(52\) | −1.00000 | − | 1.73205i | −0.138675 | − | 0.240192i | ||||
\(53\) | −1.50000 | + | 2.59808i | −0.206041 | + | 0.356873i | −0.950464 | − | 0.310835i | \(-0.899391\pi\) |
0.744423 | + | 0.667708i | \(0.232725\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | −1.50000 | − | 2.59808i | −0.202260 | − | 0.350325i | ||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −0.500000 | + | 4.33013i | −0.0662266 | + | 0.573539i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.00000 | + | 10.3923i | 0.781133 | + | 1.35296i | 0.931282 | + | 0.364299i | \(0.118692\pi\) |
−0.150148 | + | 0.988663i | \(0.547975\pi\) | |||||||
\(60\) | 0.500000 | + | 0.866025i | 0.0645497 | + | 0.111803i | ||||
\(61\) | 5.00000 | − | 8.66025i | 0.640184 | − | 1.10883i | −0.345207 | − | 0.938527i | \(-0.612191\pi\) |
0.985391 | − | 0.170305i | \(-0.0544754\pi\) | |||||||
\(62\) | 2.00000 | + | 3.46410i | 0.254000 | + | 0.439941i | ||||
\(63\) | 0.500000 | − | 0.866025i | 0.0629941 | − | 0.109109i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.00000 | −0.248069 | ||||||||
\(66\) | 1.50000 | − | 2.59808i | 0.184637 | − | 0.319801i | ||||
\(67\) | 5.00000 | − | 8.66025i | 0.610847 | − | 1.05802i | −0.380251 | − | 0.924883i | \(-0.624162\pi\) |
0.991098 | − | 0.133135i | \(-0.0425044\pi\) | |||||||
\(68\) | −6.00000 | −0.727607 | ||||||||
\(69\) | 9.00000 | 1.08347 | ||||||||
\(70\) | −0.500000 | + | 0.866025i | −0.0597614 | + | 0.103510i | ||||
\(71\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | 2.00000 | + | 3.46410i | 0.234082 | + | 0.405442i | 0.959006 | − | 0.283387i | \(-0.0914581\pi\) |
−0.724923 | + | 0.688830i | \(0.758125\pi\) | |||||||
\(74\) | −2.50000 | − | 4.33013i | −0.290619 | − | 0.503367i | ||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 4.00000 | − | 1.73205i | 0.458831 | − | 0.198680i | ||||
\(77\) | 3.00000 | 0.341882 | ||||||||
\(78\) | −1.00000 | − | 1.73205i | −0.113228 | − | 0.196116i | ||||
\(79\) | −7.00000 | − | 12.1244i | −0.787562 | − | 1.36410i | −0.927457 | − | 0.373930i | \(-0.878010\pi\) |
0.139895 | − | 0.990166i | \(-0.455323\pi\) | |||||||
\(80\) | 0.500000 | − | 0.866025i | 0.0559017 | − | 0.0968246i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 1.50000 | − | 2.59808i | 0.165647 | − | 0.286910i | ||||
\(83\) | −18.0000 | −1.97576 | −0.987878 | − | 0.155230i | \(-0.950388\pi\) | ||||
−0.987878 | + | 0.155230i | \(0.950388\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | −3.00000 | + | 5.19615i | −0.325396 | + | 0.563602i | ||||
\(86\) | 5.00000 | − | 8.66025i | 0.539164 | − | 0.933859i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.00000 | −0.319801 | ||||||||
\(89\) | −7.50000 | + | 12.9904i | −0.794998 | + | 1.37698i | 0.127842 | + | 0.991795i | \(0.459195\pi\) |
−0.922840 | + | 0.385183i | \(0.874138\pi\) | |||||||
\(90\) | 0.500000 | + | 0.866025i | 0.0527046 | + | 0.0912871i | ||||
\(91\) | 1.00000 | − | 1.73205i | 0.104828 | − | 0.181568i | ||||
\(92\) | −4.50000 | − | 7.79423i | −0.469157 | − | 0.812605i | ||||
\(93\) | 2.00000 | + | 3.46410i | 0.207390 | + | 0.359211i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.500000 | − | 4.33013i | 0.0512989 | − | 0.444262i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −4.00000 | − | 6.92820i | −0.406138 | − | 0.703452i | 0.588315 | − | 0.808632i | \(-0.299792\pi\) |
−0.994453 | + | 0.105180i | \(0.966458\pi\) | |||||||
\(98\) | 3.00000 | + | 5.19615i | 0.303046 | + | 0.524891i | ||||
\(99\) | 1.50000 | − | 2.59808i | 0.150756 | − | 0.261116i | ||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | −3.00000 | + | 5.19615i | −0.298511 | + | 0.517036i | −0.975796 | − | 0.218685i | \(-0.929823\pi\) |
0.677284 | + | 0.735721i | \(0.263157\pi\) | |||||||
\(102\) | −6.00000 | −0.594089 | ||||||||
\(103\) | −1.00000 | −0.0985329 | −0.0492665 | − | 0.998786i | \(-0.515688\pi\) | ||||
−0.0492665 | + | 0.998786i | \(0.515688\pi\) | |||||||
\(104\) | −1.00000 | + | 1.73205i | −0.0980581 | + | 0.169842i | ||||
\(105\) | −0.500000 | + | 0.866025i | −0.0487950 | + | 0.0845154i | ||||
\(106\) | 3.00000 | 0.291386 | ||||||||
\(107\) | 6.00000 | 0.580042 | 0.290021 | − | 0.957020i | \(-0.406338\pi\) | ||||
0.290021 | + | 0.957020i | \(0.406338\pi\) | |||||||
\(108\) | −0.500000 | + | 0.866025i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | −1.00000 | − | 1.73205i | −0.0957826 | − | 0.165900i | 0.814152 | − | 0.580651i | \(-0.197202\pi\) |
−0.909935 | + | 0.414751i | \(0.863869\pi\) | |||||||
\(110\) | −1.50000 | + | 2.59808i | −0.143019 | + | 0.247717i | ||||
\(111\) | −2.50000 | − | 4.33013i | −0.237289 | − | 0.410997i | ||||
\(112\) | 0.500000 | + | 0.866025i | 0.0472456 | + | 0.0818317i | ||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | 4.00000 | − | 1.73205i | 0.374634 | − | 0.162221i | ||||
\(115\) | −9.00000 | −0.839254 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | − | 1.73205i | −0.0924500 | − | 0.160128i | ||||
\(118\) | 6.00000 | − | 10.3923i | 0.552345 | − | 0.956689i | ||||
\(119\) | −3.00000 | − | 5.19615i | −0.275010 | − | 0.476331i | ||||
\(120\) | 0.500000 | − | 0.866025i | 0.0456435 | − | 0.0790569i | ||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | −10.0000 | −0.905357 | ||||||||
\(123\) | 1.50000 | − | 2.59808i | 0.135250 | − | 0.234261i | ||||
\(124\) | 2.00000 | − | 3.46410i | 0.179605 | − | 0.311086i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −1.00000 | −0.0890871 | ||||||||
\(127\) | −5.50000 | + | 9.52628i | −0.488046 | + | 0.845321i | −0.999905 | − | 0.0137486i | \(-0.995624\pi\) |
0.511859 | + | 0.859069i | \(0.328957\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 5.00000 | − | 8.66025i | 0.440225 | − | 0.762493i | ||||
\(130\) | 1.00000 | + | 1.73205i | 0.0877058 | + | 0.151911i | ||||
\(131\) | −4.50000 | − | 7.79423i | −0.393167 | − | 0.680985i | 0.599699 | − | 0.800226i | \(-0.295287\pi\) |
−0.992865 | + | 0.119241i | \(0.961954\pi\) | |||||||
\(132\) | −3.00000 | −0.261116 | ||||||||
\(133\) | 3.50000 | + | 2.59808i | 0.303488 | + | 0.225282i | ||||
\(134\) | −10.0000 | −0.863868 | ||||||||
\(135\) | 0.500000 | + | 0.866025i | 0.0430331 | + | 0.0745356i | ||||
\(136\) | 3.00000 | + | 5.19615i | 0.257248 | + | 0.445566i | ||||
\(137\) | 6.00000 | − | 10.3923i | 0.512615 | − | 0.887875i | −0.487278 | − | 0.873247i | \(-0.662010\pi\) |
0.999893 | − | 0.0146279i | \(-0.00465636\pi\) | |||||||
\(138\) | −4.50000 | − | 7.79423i | −0.383065 | − | 0.663489i | ||||
\(139\) | 2.00000 | − | 3.46410i | 0.169638 | − | 0.293821i | −0.768655 | − | 0.639664i | \(-0.779074\pi\) |
0.938293 | + | 0.345843i | \(0.112407\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.00000 | − | 5.19615i | 0.250873 | − | 0.434524i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.00000 | − | 3.46410i | 0.165521 | − | 0.286691i | ||||
\(147\) | 3.00000 | + | 5.19615i | 0.247436 | + | 0.428571i | ||||
\(148\) | −2.50000 | + | 4.33013i | −0.205499 | + | 0.355934i | ||||
\(149\) | −9.00000 | − | 15.5885i | −0.737309 | − | 1.27706i | −0.953703 | − | 0.300750i | \(-0.902763\pi\) |
0.216394 | − | 0.976306i | \(-0.430570\pi\) | |||||||
\(150\) | −0.500000 | − | 0.866025i | −0.0408248 | − | 0.0707107i | ||||
\(151\) | −10.0000 | −0.813788 | −0.406894 | − | 0.913475i | \(-0.633388\pi\) | ||||
−0.406894 | + | 0.913475i | \(0.633388\pi\) | |||||||
\(152\) | −3.50000 | − | 2.59808i | −0.283887 | − | 0.210732i | ||||
\(153\) | −6.00000 | −0.485071 | ||||||||
\(154\) | −1.50000 | − | 2.59808i | −0.120873 | − | 0.209359i | ||||
\(155\) | −2.00000 | − | 3.46410i | −0.160644 | − | 0.278243i | ||||
\(156\) | −1.00000 | + | 1.73205i | −0.0800641 | + | 0.138675i | ||||
\(157\) | 6.50000 | + | 11.2583i | 0.518756 | + | 0.898513i | 0.999762 | + | 0.0217953i | \(0.00693820\pi\) |
−0.481006 | + | 0.876717i | \(0.659728\pi\) | |||||||
\(158\) | −7.00000 | + | 12.1244i | −0.556890 | + | 0.964562i | ||||
\(159\) | 3.00000 | 0.237915 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 4.50000 | − | 7.79423i | 0.354650 | − | 0.614271i | ||||
\(162\) | −0.500000 | + | 0.866025i | −0.0392837 | + | 0.0680414i | ||||
\(163\) | −22.0000 | −1.72317 | −0.861586 | − | 0.507611i | \(-0.830529\pi\) | ||||
−0.861586 | + | 0.507611i | \(0.830529\pi\) | |||||||
\(164\) | −3.00000 | −0.234261 | ||||||||
\(165\) | −1.50000 | + | 2.59808i | −0.116775 | + | 0.202260i | ||||
\(166\) | 9.00000 | + | 15.5885i | 0.698535 | + | 1.20990i | ||||
\(167\) | 10.5000 | − | 18.1865i | 0.812514 | − | 1.40732i | −0.0985846 | − | 0.995129i | \(-0.531432\pi\) |
0.911099 | − | 0.412188i | \(-0.135235\pi\) | |||||||
\(168\) | 0.500000 | + | 0.866025i | 0.0385758 | + | 0.0668153i | ||||
\(169\) | 4.50000 | + | 7.79423i | 0.346154 | + | 0.599556i | ||||
\(170\) | 6.00000 | 0.460179 | ||||||||
\(171\) | 4.00000 | − | 1.73205i | 0.305888 | − | 0.132453i | ||||
\(172\) | −10.0000 | −0.762493 | ||||||||
\(173\) | 10.5000 | + | 18.1865i | 0.798300 | + | 1.38270i | 0.920722 | + | 0.390218i | \(0.127601\pi\) |
−0.122422 | + | 0.992478i | \(0.539066\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.500000 | − | 0.866025i | 0.0377964 | − | 0.0654654i | ||||
\(176\) | 1.50000 | + | 2.59808i | 0.113067 | + | 0.195837i | ||||
\(177\) | 6.00000 | − | 10.3923i | 0.450988 | − | 0.781133i | ||||
\(178\) | 15.0000 | 1.12430 | ||||||||
\(179\) | 15.0000 | 1.12115 | 0.560576 | − | 0.828103i | \(-0.310580\pi\) | ||||
0.560576 | + | 0.828103i | \(0.310580\pi\) | |||||||
\(180\) | 0.500000 | − | 0.866025i | 0.0372678 | − | 0.0645497i | ||||
\(181\) | 8.00000 | − | 13.8564i | 0.594635 | − | 1.02994i | −0.398963 | − | 0.916967i | \(-0.630630\pi\) |
0.993598 | − | 0.112972i | \(-0.0360369\pi\) | |||||||
\(182\) | −2.00000 | −0.148250 | ||||||||
\(183\) | −10.0000 | −0.739221 | ||||||||
\(184\) | −4.50000 | + | 7.79423i | −0.331744 | + | 0.574598i | ||||
\(185\) | 2.50000 | + | 4.33013i | 0.183804 | + | 0.318357i | ||||
\(186\) | 2.00000 | − | 3.46410i | 0.146647 | − | 0.254000i | ||||
\(187\) | −9.00000 | − | 15.5885i | −0.658145 | − | 1.13994i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −4.00000 | + | 1.73205i | −0.290191 | + | 0.125656i | ||||
\(191\) | 6.00000 | 0.434145 | 0.217072 | − | 0.976156i | \(-0.430349\pi\) | ||||
0.217072 | + | 0.976156i | \(0.430349\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 5.00000 | + | 8.66025i | 0.359908 | + | 0.623379i | 0.987945 | − | 0.154805i | \(-0.0494748\pi\) |
−0.628037 | + | 0.778183i | \(0.716141\pi\) | |||||||
\(194\) | −4.00000 | + | 6.92820i | −0.287183 | + | 0.497416i | ||||
\(195\) | 1.00000 | + | 1.73205i | 0.0716115 | + | 0.124035i | ||||
\(196\) | 3.00000 | − | 5.19615i | 0.214286 | − | 0.371154i | ||||
\(197\) | −3.00000 | −0.213741 | −0.106871 | − | 0.994273i | \(-0.534083\pi\) | ||||
−0.106871 | + | 0.994273i | \(0.534083\pi\) | |||||||
\(198\) | −3.00000 | −0.213201 | ||||||||
\(199\) | 5.00000 | − | 8.66025i | 0.354441 | − | 0.613909i | −0.632581 | − | 0.774494i | \(-0.718005\pi\) |
0.987022 | + | 0.160585i | \(0.0513380\pi\) | |||||||
\(200\) | −0.500000 | + | 0.866025i | −0.0353553 | + | 0.0612372i | ||||
\(201\) | −10.0000 | −0.705346 | ||||||||
\(202\) | 6.00000 | 0.422159 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.00000 | + | 5.19615i | 0.210042 | + | 0.363803i | ||||
\(205\) | −1.50000 | + | 2.59808i | −0.104765 | + | 0.181458i | ||||
\(206\) | 0.500000 | + | 0.866025i | 0.0348367 | + | 0.0603388i | ||||
\(207\) | −4.50000 | − | 7.79423i | −0.312772 | − | 0.541736i | ||||
\(208\) | 2.00000 | 0.138675 | ||||||||
\(209\) | 10.5000 | + | 7.79423i | 0.726300 | + | 0.539138i | ||||
\(210\) | 1.00000 | 0.0690066 | ||||||||
\(211\) | 12.5000 | + | 21.6506i | 0.860535 | + | 1.49049i | 0.871413 | + | 0.490550i | \(0.163204\pi\) |
−0.0108774 | + | 0.999941i | \(0.503462\pi\) | |||||||
\(212\) | −1.50000 | − | 2.59808i | −0.103020 | − | 0.178437i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.00000 | − | 5.19615i | −0.205076 | − | 0.355202i | ||||
\(215\) | −5.00000 | + | 8.66025i | −0.340997 | + | 0.590624i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 4.00000 | 0.271538 | ||||||||
\(218\) | −1.00000 | + | 1.73205i | −0.0677285 | + | 0.117309i | ||||
\(219\) | 2.00000 | − | 3.46410i | 0.135147 | − | 0.234082i | ||||
\(220\) | 3.00000 | 0.202260 | ||||||||
\(221\) | −12.0000 | −0.807207 | ||||||||
\(222\) | −2.50000 | + | 4.33013i | −0.167789 | + | 0.290619i | ||||
\(223\) | 0.500000 | + | 0.866025i | 0.0334825 | + | 0.0579934i | 0.882281 | − | 0.470723i | \(-0.156007\pi\) |
−0.848799 | + | 0.528716i | \(0.822674\pi\) | |||||||
\(224\) | 0.500000 | − | 0.866025i | 0.0334077 | − | 0.0578638i | ||||
\(225\) | −0.500000 | − | 0.866025i | −0.0333333 | − | 0.0577350i | ||||
\(226\) | 3.00000 | + | 5.19615i | 0.199557 | + | 0.345643i | ||||
\(227\) | 12.0000 | 0.796468 | 0.398234 | − | 0.917284i | \(-0.369623\pi\) | ||||
0.398234 | + | 0.917284i | \(0.369623\pi\) | |||||||
\(228\) | −3.50000 | − | 2.59808i | −0.231793 | − | 0.172062i | ||||
\(229\) | −10.0000 | −0.660819 | −0.330409 | − | 0.943838i | \(-0.607187\pi\) | ||||
−0.330409 | + | 0.943838i | \(0.607187\pi\) | |||||||
\(230\) | 4.50000 | + | 7.79423i | 0.296721 | + | 0.513936i | ||||
\(231\) | −1.50000 | − | 2.59808i | −0.0986928 | − | 0.170941i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.00000 | − | 5.19615i | −0.196537 | − | 0.340411i | 0.750867 | − | 0.660454i | \(-0.229636\pi\) |
−0.947403 | + | 0.320043i | \(0.896303\pi\) | |||||||
\(234\) | −1.00000 | + | 1.73205i | −0.0653720 | + | 0.113228i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −12.0000 | −0.781133 | ||||||||
\(237\) | −7.00000 | + | 12.1244i | −0.454699 | + | 0.787562i | ||||
\(238\) | −3.00000 | + | 5.19615i | −0.194461 | + | 0.336817i | ||||
\(239\) | 12.0000 | 0.776215 | 0.388108 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388108 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | 5.00000 | − | 8.66025i | 0.322078 | − | 0.557856i | −0.658838 | − | 0.752285i | \(-0.728952\pi\) |
0.980917 | + | 0.194429i | \(0.0622852\pi\) | |||||||
\(242\) | 1.00000 | + | 1.73205i | 0.0642824 | + | 0.111340i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 5.00000 | + | 8.66025i | 0.320092 | + | 0.554416i | ||||
\(245\) | −3.00000 | − | 5.19615i | −0.191663 | − | 0.331970i | ||||
\(246\) | −3.00000 | −0.191273 | ||||||||
\(247\) | 8.00000 | − | 3.46410i | 0.509028 | − | 0.220416i | ||||
\(248\) | −4.00000 | −0.254000 | ||||||||
\(249\) | 9.00000 | + | 15.5885i | 0.570352 | + | 0.987878i | ||||
\(250\) | 0.500000 | + | 0.866025i | 0.0316228 | + | 0.0547723i | ||||
\(251\) | 6.00000 | − | 10.3923i | 0.378717 | − | 0.655956i | −0.612159 | − | 0.790735i | \(-0.709699\pi\) |
0.990876 | + | 0.134778i | \(0.0430322\pi\) | |||||||
\(252\) | 0.500000 | + | 0.866025i | 0.0314970 | + | 0.0545545i | ||||
\(253\) | 13.5000 | − | 23.3827i | 0.848738 | − | 1.47006i | ||||
\(254\) | 11.0000 | 0.690201 | ||||||||
\(255\) | 6.00000 | 0.375735 | ||||||||
\(256\) | −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 | \(0.106747\pi\) | |||||||
\(258\) | −10.0000 | −0.622573 | ||||||||
\(259\) | −5.00000 | −0.310685 | ||||||||
\(260\) | 1.00000 | − | 1.73205i | 0.0620174 | − | 0.107417i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.50000 | + | 7.79423i | −0.278011 | + | 0.481529i | ||||
\(263\) | −7.50000 | − | 12.9904i | −0.462470 | − | 0.801021i | 0.536614 | − | 0.843828i | \(-0.319703\pi\) |
−0.999083 | + | 0.0428069i | \(0.986370\pi\) | |||||||
\(264\) | 1.50000 | + | 2.59808i | 0.0923186 | + | 0.159901i | ||||
\(265\) | −3.00000 | −0.184289 | ||||||||
\(266\) | 0.500000 | − | 4.33013i | 0.0306570 | − | 0.265497i | ||||
\(267\) | 15.0000 | 0.917985 | ||||||||
\(268\) | 5.00000 | + | 8.66025i | 0.305424 | + | 0.529009i | ||||
\(269\) | 15.0000 | + | 25.9808i | 0.914566 | + | 1.58408i | 0.807535 | + | 0.589819i | \(0.200801\pi\) |
0.107031 | + | 0.994256i | \(0.465866\pi\) | |||||||
\(270\) | 0.500000 | − | 0.866025i | 0.0304290 | − | 0.0527046i | ||||
\(271\) | −1.00000 | − | 1.73205i | −0.0607457 | − | 0.105215i | 0.834053 | − | 0.551684i | \(-0.186015\pi\) |
−0.894799 | + | 0.446469i | \(0.852681\pi\) | |||||||
\(272\) | 3.00000 | − | 5.19615i | 0.181902 | − | 0.315063i | ||||
\(273\) | −2.00000 | −0.121046 | ||||||||
\(274\) | −12.0000 | −0.724947 | ||||||||
\(275\) | 1.50000 | − | 2.59808i | 0.0904534 | − | 0.156670i | ||||
\(276\) | −4.50000 | + | 7.79423i | −0.270868 | + | 0.469157i | ||||
\(277\) | −10.0000 | −0.600842 | −0.300421 | − | 0.953807i | \(-0.597127\pi\) | ||||
−0.300421 | + | 0.953807i | \(0.597127\pi\) | |||||||
\(278\) | −4.00000 | −0.239904 | ||||||||
\(279\) | 2.00000 | − | 3.46410i | 0.119737 | − | 0.207390i | ||||
\(280\) | −0.500000 | − | 0.866025i | −0.0298807 | − | 0.0517549i | ||||
\(281\) | −7.50000 | + | 12.9904i | −0.447412 | + | 0.774941i | −0.998217 | − | 0.0596933i | \(-0.980988\pi\) |
0.550804 | + | 0.834634i | \(0.314321\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.0000 | + | 19.0526i | 0.653882 | + | 1.13256i | 0.982173 | + | 0.187980i | \(0.0601941\pi\) |
−0.328291 | + | 0.944577i | \(0.606473\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.00000 | + | 1.73205i | −0.236940 | + | 0.102598i | ||||
\(286\) | −6.00000 | −0.354787 | ||||||||
\(287\) | −1.50000 | − | 2.59808i | −0.0885422 | − | 0.153360i | ||||
\(288\) | −0.500000 | − | 0.866025i | −0.0294628 | − | 0.0510310i | ||||
\(289\) | −9.50000 | + | 16.4545i | −0.558824 | + | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.00000 | + | 6.92820i | −0.234484 | + | 0.406138i | ||||
\(292\) | −4.00000 | −0.234082 | ||||||||
\(293\) | 9.00000 | 0.525786 | 0.262893 | − | 0.964825i | \(-0.415323\pi\) | ||||
0.262893 | + | 0.964825i | \(0.415323\pi\) | |||||||
\(294\) | 3.00000 | − | 5.19615i | 0.174964 | − | 0.303046i | ||||
\(295\) | −6.00000 | + | 10.3923i | −0.349334 | + | 0.605063i | ||||
\(296\) | 5.00000 | 0.290619 | ||||||||
\(297\) | −3.00000 | −0.174078 | ||||||||
\(298\) | −9.00000 | + | 15.5885i | −0.521356 | + | 0.903015i | ||||
\(299\) | −9.00000 | − | 15.5885i | −0.520483 | − | 0.901504i | ||||
\(300\) | −0.500000 | + | 0.866025i | −0.0288675 | + | 0.0500000i | ||||
\(301\) | −5.00000 | − | 8.66025i | −0.288195 | − | 0.499169i | ||||
\(302\) | 5.00000 | + | 8.66025i | 0.287718 | + | 0.498342i | ||||
\(303\) | 6.00000 | 0.344691 | ||||||||
\(304\) | −0.500000 | + | 4.33013i | −0.0286770 | + | 0.248350i | ||||
\(305\) | 10.0000 | 0.572598 | ||||||||
\(306\) | 3.00000 | + | 5.19615i | 0.171499 | + | 0.297044i | ||||
\(307\) | 8.00000 | + | 13.8564i | 0.456584 | + | 0.790827i | 0.998778 | − | 0.0494267i | \(-0.0157394\pi\) |
−0.542194 | + | 0.840254i | \(0.682406\pi\) | |||||||
\(308\) | −1.50000 | + | 2.59808i | −0.0854704 | + | 0.148039i | ||||
\(309\) | 0.500000 | + | 0.866025i | 0.0284440 | + | 0.0492665i | ||||
\(310\) | −2.00000 | + | 3.46410i | −0.113592 | + | 0.196748i | ||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 2.00000 | 0.113228 | ||||||||
\(313\) | −4.00000 | + | 6.92820i | −0.226093 | + | 0.391605i | −0.956647 | − | 0.291250i | \(-0.905929\pi\) |
0.730554 | + | 0.682855i | \(0.239262\pi\) | |||||||
\(314\) | 6.50000 | − | 11.2583i | 0.366816 | − | 0.635344i | ||||
\(315\) | 1.00000 | 0.0563436 | ||||||||
\(316\) | 14.0000 | 0.787562 | ||||||||
\(317\) | −7.50000 | + | 12.9904i | −0.421242 | + | 0.729612i | −0.996061 | − | 0.0886679i | \(-0.971739\pi\) |
0.574819 | + | 0.818280i | \(0.305072\pi\) | |||||||
\(318\) | −1.50000 | − | 2.59808i | −0.0841158 | − | 0.145693i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.500000 | + | 0.866025i | 0.0279508 | + | 0.0484123i | ||||
\(321\) | −3.00000 | − | 5.19615i | −0.167444 | − | 0.290021i | ||||
\(322\) | −9.00000 | −0.501550 | ||||||||
\(323\) | 3.00000 | − | 25.9808i | 0.166924 | − | 1.44561i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −1.00000 | − | 1.73205i | −0.0554700 | − | 0.0960769i | ||||
\(326\) | 11.0000 | + | 19.0526i | 0.609234 | + | 1.05522i | ||||
\(327\) | −1.00000 | + | 1.73205i | −0.0553001 | + | 0.0957826i | ||||
\(328\) | 1.50000 | + | 2.59808i | 0.0828236 | + | 0.143455i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3.00000 | 0.165145 | ||||||||
\(331\) | 5.00000 | 0.274825 | 0.137412 | − | 0.990514i | \(-0.456121\pi\) | ||||
0.137412 | + | 0.990514i | \(0.456121\pi\) | |||||||
\(332\) | 9.00000 | − | 15.5885i | 0.493939 | − | 0.855528i | ||||
\(333\) | −2.50000 | + | 4.33013i | −0.136999 | + | 0.237289i | ||||
\(334\) | −21.0000 | −1.14907 | ||||||||
\(335\) | 10.0000 | 0.546358 | ||||||||
\(336\) | 0.500000 | − | 0.866025i | 0.0272772 | − | 0.0472456i | ||||
\(337\) | 11.0000 | + | 19.0526i | 0.599208 | + | 1.03786i | 0.992938 | + | 0.118633i | \(0.0378512\pi\) |
−0.393730 | + | 0.919226i | \(0.628816\pi\) | |||||||
\(338\) | 4.50000 | − | 7.79423i | 0.244768 | − | 0.423950i | ||||
\(339\) | 3.00000 | + | 5.19615i | 0.162938 | + | 0.282216i | ||||
\(340\) | −3.00000 | − | 5.19615i | −0.162698 | − | 0.281801i | ||||
\(341\) | 12.0000 | 0.649836 | ||||||||
\(342\) | −3.50000 | − | 2.59808i | −0.189258 | − | 0.140488i | ||||
\(343\) | 13.0000 | 0.701934 | ||||||||
\(344\) | 5.00000 | + | 8.66025i | 0.269582 | + | 0.466930i | ||||
\(345\) | 4.50000 | + | 7.79423i | 0.242272 | + | 0.419627i | ||||
\(346\) | 10.5000 | − | 18.1865i | 0.564483 | − | 0.977714i | ||||
\(347\) | 15.0000 | + | 25.9808i | 0.805242 | + | 1.39472i | 0.916127 | + | 0.400887i | \(0.131298\pi\) |
−0.110885 | + | 0.993833i | \(0.535369\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.00000 | 0.107058 | 0.0535288 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535288 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | −1.00000 | + | 1.73205i | −0.0533761 | + | 0.0924500i | ||||
\(352\) | 1.50000 | − | 2.59808i | 0.0799503 | − | 0.138478i | ||||
\(353\) | −6.00000 | −0.319348 | −0.159674 | − | 0.987170i | \(-0.551044\pi\) | ||||
−0.159674 | + | 0.987170i | \(0.551044\pi\) | |||||||
\(354\) | −12.0000 | −0.637793 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.50000 | − | 12.9904i | −0.397499 | − | 0.688489i | ||||
\(357\) | −3.00000 | + | 5.19615i | −0.158777 | + | 0.275010i | ||||
\(358\) | −7.50000 | − | 12.9904i | −0.396387 | − | 0.686563i | ||||
\(359\) | 6.00000 | + | 10.3923i | 0.316668 | + | 0.548485i | 0.979791 | − | 0.200026i | \(-0.0641026\pi\) |
−0.663123 | + | 0.748511i | \(0.730769\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | 5.50000 | + | 18.1865i | 0.289474 | + | 0.957186i | ||||
\(362\) | −16.0000 | −0.840941 | ||||||||
\(363\) | 1.00000 | + | 1.73205i | 0.0524864 | + | 0.0909091i | ||||
\(364\) | 1.00000 | + | 1.73205i | 0.0524142 | + | 0.0907841i | ||||
\(365\) | −2.00000 | + | 3.46410i | −0.104685 | + | 0.181319i | ||||
\(366\) | 5.00000 | + | 8.66025i | 0.261354 | + | 0.452679i | ||||
\(367\) | −4.00000 | + | 6.92820i | −0.208798 | + | 0.361649i | −0.951336 | − | 0.308155i | \(-0.900289\pi\) |
0.742538 | + | 0.669804i | \(0.233622\pi\) | |||||||
\(368\) | 9.00000 | 0.469157 | ||||||||
\(369\) | −3.00000 | −0.156174 | ||||||||
\(370\) | 2.50000 | − | 4.33013i | 0.129969 | − | 0.225113i | ||||
\(371\) | 1.50000 | − | 2.59808i | 0.0778761 | − | 0.134885i | ||||
\(372\) | −4.00000 | −0.207390 | ||||||||
\(373\) | 23.0000 | 1.19089 | 0.595447 | − | 0.803394i | \(-0.296975\pi\) | ||||
0.595447 | + | 0.803394i | \(0.296975\pi\) | |||||||
\(374\) | −9.00000 | + | 15.5885i | −0.465379 | + | 0.806060i | ||||
\(375\) | 0.500000 | + | 0.866025i | 0.0258199 | + | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.500000 | + | 0.866025i | 0.0257172 | + | 0.0445435i | ||||
\(379\) | −16.0000 | −0.821865 | −0.410932 | − | 0.911666i | \(-0.634797\pi\) | ||||
−0.410932 | + | 0.911666i | \(0.634797\pi\) | |||||||
\(380\) | 3.50000 | + | 2.59808i | 0.179546 | + | 0.133278i | ||||
\(381\) | 11.0000 | 0.563547 | ||||||||
\(382\) | −3.00000 | − | 5.19615i | −0.153493 | − | 0.265858i | ||||
\(383\) | −12.0000 | − | 20.7846i | −0.613171 | − | 1.06204i | −0.990702 | − | 0.136047i | \(-0.956560\pi\) |
0.377531 | − | 0.925997i | \(-0.376773\pi\) | |||||||
\(384\) | −0.500000 | + | 0.866025i | −0.0255155 | + | 0.0441942i | ||||
\(385\) | 1.50000 | + | 2.59808i | 0.0764471 | + | 0.132410i | ||||
\(386\) | 5.00000 | − | 8.66025i | 0.254493 | − | 0.440795i | ||||
\(387\) | −10.0000 | −0.508329 | ||||||||
\(388\) | 8.00000 | 0.406138 | ||||||||
\(389\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(390\) | 1.00000 | − | 1.73205i | 0.0506370 | − | 0.0877058i | ||||
\(391\) | −54.0000 | −2.73090 | ||||||||
\(392\) | −6.00000 | −0.303046 | ||||||||
\(393\) | −4.50000 | + | 7.79423i | −0.226995 | + | 0.393167i | ||||
\(394\) | 1.50000 | + | 2.59808i | 0.0755689 | + | 0.130889i | ||||
\(395\) | 7.00000 | − | 12.1244i | 0.352208 | − | 0.610043i | ||||
\(396\) | 1.50000 | + | 2.59808i | 0.0753778 | + | 0.130558i | ||||
\(397\) | −14.5000 | − | 25.1147i | −0.727734 | − | 1.26047i | −0.957839 | − | 0.287307i | \(-0.907240\pi\) |
0.230105 | − | 0.973166i | \(-0.426093\pi\) | |||||||
\(398\) | −10.0000 | −0.501255 | ||||||||
\(399\) | 0.500000 | − | 4.33013i | 0.0250313 | − | 0.216777i | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 9.00000 | + | 15.5885i | 0.449439 | + | 0.778450i | 0.998350 | − | 0.0574304i | \(-0.0182907\pi\) |
−0.548911 | + | 0.835881i | \(0.684957\pi\) | |||||||
\(402\) | 5.00000 | + | 8.66025i | 0.249377 | + | 0.431934i | ||||
\(403\) | 4.00000 | − | 6.92820i | 0.199254 | − | 0.345118i | ||||
\(404\) | −3.00000 | − | 5.19615i | −0.149256 | − | 0.258518i | ||||
\(405\) | 0.500000 | − | 0.866025i | 0.0248452 | − | 0.0430331i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.0000 | −0.743522 | ||||||||
\(408\) | 3.00000 | − | 5.19615i | 0.148522 | − | 0.257248i | ||||
\(409\) | −2.50000 | + | 4.33013i | −0.123617 | + | 0.214111i | −0.921192 | − | 0.389109i | \(-0.872783\pi\) |
0.797574 | + | 0.603220i | \(0.206116\pi\) | |||||||
\(410\) | 3.00000 | 0.148159 | ||||||||
\(411\) | −12.0000 | −0.591916 | ||||||||
\(412\) | 0.500000 | − | 0.866025i | 0.0246332 | − | 0.0426660i | ||||
\(413\) | −6.00000 | − | 10.3923i | −0.295241 | − | 0.511372i | ||||
\(414\) | −4.50000 | + | 7.79423i | −0.221163 | + | 0.383065i | ||||
\(415\) | −9.00000 | − | 15.5885i | −0.441793 | − | 0.765207i | ||||
\(416\) | −1.00000 | − | 1.73205i | −0.0490290 | − | 0.0849208i | ||||
\(417\) | −4.00000 | −0.195881 | ||||||||
\(418\) | 1.50000 | − | 12.9904i | 0.0733674 | − | 0.635380i | ||||
\(419\) | 21.0000 | 1.02592 | 0.512959 | − | 0.858413i | \(-0.328549\pi\) | ||||
0.512959 | + | 0.858413i | \(0.328549\pi\) | |||||||
\(420\) | −0.500000 | − | 0.866025i | −0.0243975 | − | 0.0422577i | ||||
\(421\) | −13.0000 | − | 22.5167i | −0.633581 | − | 1.09739i | −0.986814 | − | 0.161859i | \(-0.948251\pi\) |
0.353233 | − | 0.935536i | \(-0.385082\pi\) | |||||||
\(422\) | 12.5000 | − | 21.6506i | 0.608490 | − | 1.05394i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.50000 | + | 2.59808i | −0.0728464 | + | 0.126174i | ||||
\(425\) | −6.00000 | −0.291043 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.00000 | + | 8.66025i | −0.241967 | + | 0.419099i | ||||
\(428\) | −3.00000 | + | 5.19615i | −0.145010 | + | 0.251166i | ||||
\(429\) | −6.00000 | −0.289683 | ||||||||
\(430\) | 10.0000 | 0.482243 | ||||||||
\(431\) | −15.0000 | + | 25.9808i | −0.722525 | + | 1.25145i | 0.237460 | + | 0.971397i | \(0.423685\pi\) |
−0.959985 | + | 0.280052i | \(0.909648\pi\) | |||||||
\(432\) | −0.500000 | − | 0.866025i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | 8.00000 | − | 13.8564i | 0.384455 | − | 0.665896i | −0.607238 | − | 0.794520i | \(-0.707723\pi\) |
0.991693 | + | 0.128624i | \(0.0410559\pi\) | |||||||
\(434\) | −2.00000 | − | 3.46410i | −0.0960031 | − | 0.166282i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | 0.0957826 | ||||||||
\(437\) | 36.0000 | − | 15.5885i | 1.72211 | − | 0.745697i | ||||
\(438\) | −4.00000 | −0.191127 | ||||||||
\(439\) | −7.00000 | − | 12.1244i | −0.334092 | − | 0.578664i | 0.649218 | − | 0.760602i | \(-0.275096\pi\) |
−0.983310 | + | 0.181938i | \(0.941763\pi\) | |||||||
\(440\) | −1.50000 | − | 2.59808i | −0.0715097 | − | 0.123858i | ||||
\(441\) | 3.00000 | − | 5.19615i | 0.142857 | − | 0.247436i | ||||
\(442\) | 6.00000 | + | 10.3923i | 0.285391 | + | 0.494312i | ||||
\(443\) | 9.00000 | − | 15.5885i | 0.427603 | − | 0.740630i | −0.569057 | − | 0.822298i | \(-0.692691\pi\) |
0.996660 | + | 0.0816684i | \(0.0260248\pi\) | |||||||
\(444\) | 5.00000 | 0.237289 | ||||||||
\(445\) | −15.0000 | −0.711068 | ||||||||
\(446\) | 0.500000 | − | 0.866025i | 0.0236757 | − | 0.0410075i | ||||
\(447\) | −9.00000 | + | 15.5885i | −0.425685 | + | 0.737309i | ||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 3.00000 | 0.141579 | 0.0707894 | − | 0.997491i | \(-0.477448\pi\) | ||||
0.0707894 | + | 0.997491i | \(0.477448\pi\) | |||||||
\(450\) | −0.500000 | + | 0.866025i | −0.0235702 | + | 0.0408248i | ||||
\(451\) | −4.50000 | − | 7.79423i | −0.211897 | − | 0.367016i | ||||
\(452\) | 3.00000 | − | 5.19615i | 0.141108 | − | 0.244406i | ||||
\(453\) | 5.00000 | + | 8.66025i | 0.234920 | + | 0.406894i | ||||
\(454\) | −6.00000 | − | 10.3923i | −0.281594 | − | 0.487735i | ||||
\(455\) | 2.00000 | 0.0937614 | ||||||||
\(456\) | −0.500000 | + | 4.33013i | −0.0234146 | + | 0.202777i | ||||
\(457\) | 38.0000 | 1.77757 | 0.888783 | − | 0.458329i | \(-0.151552\pi\) | ||||
0.888783 | + | 0.458329i | \(0.151552\pi\) | |||||||
\(458\) | 5.00000 | + | 8.66025i | 0.233635 | + | 0.404667i | ||||
\(459\) | 3.00000 | + | 5.19615i | 0.140028 | + | 0.242536i | ||||
\(460\) | 4.50000 | − | 7.79423i | 0.209814 | − | 0.363408i | ||||
\(461\) | −15.0000 | − | 25.9808i | −0.698620 | − | 1.21004i | −0.968945 | − | 0.247276i | \(-0.920465\pi\) |
0.270326 | − | 0.962769i | \(-0.412869\pi\) | |||||||
\(462\) | −1.50000 | + | 2.59808i | −0.0697863 | + | 0.120873i | ||||
\(463\) | 11.0000 | 0.511213 | 0.255607 | − | 0.966781i | \(-0.417725\pi\) | ||||
0.255607 | + | 0.966781i | \(0.417725\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.00000 | + | 3.46410i | −0.0927478 | + | 0.160644i | ||||
\(466\) | −3.00000 | + | 5.19615i | −0.138972 | + | 0.240707i | ||||
\(467\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(468\) | 2.00000 | 0.0924500 | ||||||||
\(469\) | −5.00000 | + | 8.66025i | −0.230879 | + | 0.399893i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.50000 | − | 11.2583i | 0.299504 | − | 0.518756i | ||||
\(472\) | 6.00000 | + | 10.3923i | 0.276172 | + | 0.478345i | ||||
\(473\) | −15.0000 | − | 25.9808i | −0.689701 | − | 1.19460i | ||||
\(474\) | 14.0000 | 0.643041 | ||||||||
\(475\) | 4.00000 | − | 1.73205i | 0.183533 | − | 0.0794719i | ||||
\(476\) | 6.00000 | 0.275010 | ||||||||
\(477\) | −1.50000 | − | 2.59808i | −0.0686803 | − | 0.118958i | ||||
\(478\) | −6.00000 | − | 10.3923i | −0.274434 | − | 0.475333i | ||||
\(479\) | −6.00000 | + | 10.3923i | −0.274147 | + | 0.474837i | −0.969920 | − | 0.243426i | \(-0.921729\pi\) |
0.695773 | + | 0.718262i | \(0.255062\pi\) | |||||||
\(480\) | 0.500000 | + | 0.866025i | 0.0228218 | + | 0.0395285i | ||||
\(481\) | −5.00000 | + | 8.66025i | −0.227980 | + | 0.394874i | ||||
\(482\) | −10.0000 | −0.455488 | ||||||||
\(483\) | −9.00000 | −0.409514 | ||||||||
\(484\) | 1.00000 | − | 1.73205i | 0.0454545 | − | 0.0787296i | ||||
\(485\) | 4.00000 | − | 6.92820i | 0.181631 | − | 0.314594i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 11.0000 | 0.498458 | 0.249229 | − | 0.968445i | \(-0.419823\pi\) | ||||
0.249229 | + | 0.968445i | \(0.419823\pi\) | |||||||
\(488\) | 5.00000 | − | 8.66025i | 0.226339 | − | 0.392031i | ||||
\(489\) | 11.0000 | + | 19.0526i | 0.497437 | + | 0.861586i | ||||
\(490\) | −3.00000 | + | 5.19615i | −0.135526 | + | 0.234738i | ||||
\(491\) | −1.50000 | − | 2.59808i | −0.0676941 | − | 0.117250i | 0.830192 | − | 0.557478i | \(-0.188231\pi\) |
−0.897886 | + | 0.440228i | \(0.854898\pi\) | |||||||
\(492\) | 1.50000 | + | 2.59808i | 0.0676252 | + | 0.117130i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −7.00000 | − | 5.19615i | −0.314945 | − | 0.233786i | ||||
\(495\) | 3.00000 | 0.134840 | ||||||||
\(496\) | 2.00000 | + | 3.46410i | 0.0898027 | + | 0.155543i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 9.00000 | − | 15.5885i | 0.403300 | − | 0.698535i | ||||
\(499\) | 12.5000 | + | 21.6506i | 0.559577 | + | 0.969216i | 0.997532 | + | 0.0702185i | \(0.0223697\pi\) |
−0.437955 | + | 0.898997i | \(0.644297\pi\) | |||||||
\(500\) | 0.500000 | − | 0.866025i | 0.0223607 | − | 0.0387298i | ||||
\(501\) | −21.0000 | −0.938211 | ||||||||
\(502\) | −12.0000 | −0.535586 | ||||||||
\(503\) | −19.5000 | + | 33.7750i | −0.869462 | + | 1.50595i | −0.00691465 | + | 0.999976i | \(0.502201\pi\) |
−0.862547 | + | 0.505976i | \(0.831132\pi\) | |||||||
\(504\) | 0.500000 | − | 0.866025i | 0.0222718 | − | 0.0385758i | ||||
\(505\) | −6.00000 | −0.266996 | ||||||||
\(506\) | −27.0000 | −1.20030 | ||||||||
\(507\) | 4.50000 | − | 7.79423i | 0.199852 | − | 0.346154i | ||||
\(508\) | −5.50000 | − | 9.52628i | −0.244023 | − | 0.422660i | ||||
\(509\) | 9.00000 | − | 15.5885i | 0.398918 | − | 0.690946i | −0.594675 | − | 0.803966i | \(-0.702719\pi\) |
0.993593 | + | 0.113020i | \(0.0360525\pi\) | |||||||
\(510\) | −3.00000 | − | 5.19615i | −0.132842 | − | 0.230089i | ||||
\(511\) | −2.00000 | − | 3.46410i | −0.0884748 | − | 0.153243i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −3.50000 | − | 2.59808i | −0.154529 | − | 0.114708i | ||||
\(514\) | −6.00000 | −0.264649 | ||||||||
\(515\) | −0.500000 | − | 0.866025i | −0.0220326 | − | 0.0381616i | ||||
\(516\) | 5.00000 | + | 8.66025i | 0.220113 | + | 0.381246i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 2.50000 | + | 4.33013i | 0.109844 | + | 0.190255i | ||||
\(519\) | 10.5000 | − | 18.1865i | 0.460899 | − | 0.798300i | ||||
\(520\) | −2.00000 | −0.0877058 | ||||||||
\(521\) | −42.0000 | −1.84005 | −0.920027 | − | 0.391856i | \(-0.871833\pi\) | ||||
−0.920027 | + | 0.391856i | \(0.871833\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.00000 | − | 13.8564i | 0.349816 | − | 0.605898i | −0.636401 | − | 0.771358i | \(-0.719578\pi\) |
0.986216 | + | 0.165460i | \(0.0529109\pi\) | |||||||
\(524\) | 9.00000 | 0.393167 | ||||||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | −7.50000 | + | 12.9904i | −0.327016 | + | 0.566408i | ||||
\(527\) | −12.0000 | − | 20.7846i | −0.522728 | − | 0.905392i | ||||
\(528\) | 1.50000 | − | 2.59808i | 0.0652791 | − | 0.113067i | ||||
\(529\) | −29.0000 | − | 50.2295i | −1.26087 | − | 2.18389i | ||||
\(530\) | 1.50000 | + | 2.59808i | 0.0651558 | + | 0.112853i | ||||
\(531\) | −12.0000 | −0.520756 | ||||||||
\(532\) | −4.00000 | + | 1.73205i | −0.173422 | + | 0.0750939i | ||||
\(533\) | −6.00000 | −0.259889 | ||||||||
\(534\) | −7.50000 | − | 12.9904i | −0.324557 | − | 0.562149i | ||||
\(535\) | 3.00000 | + | 5.19615i | 0.129701 | + | 0.224649i | ||||
\(536\) | 5.00000 | − | 8.66025i | 0.215967 | − | 0.374066i | ||||
\(537\) | −7.50000 | − | 12.9904i | −0.323649 | − | 0.560576i | ||||
\(538\) | 15.0000 | − | 25.9808i | 0.646696 | − | 1.12011i | ||||
\(539\) | 18.0000 | 0.775315 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | 2.00000 | − | 3.46410i | 0.0859867 | − | 0.148933i | −0.819825 | − | 0.572615i | \(-0.805929\pi\) |
0.905811 | + | 0.423681i | \(0.139262\pi\) | |||||||
\(542\) | −1.00000 | + | 1.73205i | −0.0429537 | + | 0.0743980i | ||||
\(543\) | −16.0000 | −0.686626 | ||||||||
\(544\) | −6.00000 | −0.257248 | ||||||||
\(545\) | 1.00000 | − | 1.73205i | 0.0428353 | − | 0.0741929i | ||||
\(546\) | 1.00000 | + | 1.73205i | 0.0427960 | + | 0.0741249i | ||||
\(547\) | −13.0000 | + | 22.5167i | −0.555840 | + | 0.962743i | 0.441998 | + | 0.897016i | \(0.354270\pi\) |
−0.997838 | + | 0.0657267i | \(0.979063\pi\) | |||||||
\(548\) | 6.00000 | + | 10.3923i | 0.256307 | + | 0.443937i | ||||
\(549\) | 5.00000 | + | 8.66025i | 0.213395 | + | 0.369611i | ||||
\(550\) | −3.00000 | −0.127920 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 9.00000 | 0.383065 | ||||||||
\(553\) | 7.00000 | + | 12.1244i | 0.297670 | + | 0.515580i | ||||
\(554\) | 5.00000 | + | 8.66025i | 0.212430 | + | 0.367939i | ||||
\(555\) | 2.50000 | − | 4.33013i | 0.106119 | − | 0.183804i | ||||
\(556\) | 2.00000 | + | 3.46410i | 0.0848189 | + | 0.146911i | ||||
\(557\) | −16.5000 | + | 28.5788i | −0.699127 | + | 1.21092i | 0.269642 | + | 0.962961i | \(0.413095\pi\) |
−0.968769 | + | 0.247964i | \(0.920239\pi\) | |||||||
\(558\) | −4.00000 | −0.169334 | ||||||||
\(559\) | −20.0000 | −0.845910 | ||||||||
\(560\) | −0.500000 | + | 0.866025i | −0.0211289 | + | 0.0365963i | ||||
\(561\) | −9.00000 | + | 15.5885i | −0.379980 | + | 0.658145i | ||||
\(562\) | 15.0000 | 0.632737 | ||||||||
\(563\) | 12.0000 | 0.505740 | 0.252870 | − | 0.967500i | \(-0.418626\pi\) | ||||
0.252870 | + | 0.967500i | \(0.418626\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.00000 | − | 5.19615i | −0.126211 | − | 0.218604i | ||||
\(566\) | 11.0000 | − | 19.0526i | 0.462364 | − | 0.800839i | ||||
\(567\) | 0.500000 | + | 0.866025i | 0.0209980 | + | 0.0363696i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −45.0000 | −1.88650 | −0.943249 | − | 0.332086i | \(-0.892248\pi\) | ||||
−0.943249 | + | 0.332086i | \(0.892248\pi\) | |||||||
\(570\) | 3.50000 | + | 2.59808i | 0.146599 | + | 0.108821i | ||||
\(571\) | 44.0000 | 1.84134 | 0.920671 | − | 0.390339i | \(-0.127642\pi\) | ||||
0.920671 | + | 0.390339i | \(0.127642\pi\) | |||||||
\(572\) | 3.00000 | + | 5.19615i | 0.125436 | + | 0.217262i | ||||
\(573\) | −3.00000 | − | 5.19615i | −0.125327 | − | 0.217072i | ||||
\(574\) | −1.50000 | + | 2.59808i | −0.0626088 | + | 0.108442i | ||||
\(575\) | −4.50000 | − | 7.79423i | −0.187663 | − | 0.325042i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 2.00000 | 0.0832611 | 0.0416305 | − | 0.999133i | \(-0.486745\pi\) | ||||
0.0416305 | + | 0.999133i | \(0.486745\pi\) | |||||||
\(578\) | 19.0000 | 0.790296 | ||||||||
\(579\) | 5.00000 | − | 8.66025i | 0.207793 | − | 0.359908i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.0000 | 0.746766 | ||||||||
\(582\) | 8.00000 | 0.331611 | ||||||||
\(583\) | 4.50000 | − | 7.79423i | 0.186371 | − | 0.322804i | ||||
\(584\) | 2.00000 | + | 3.46410i | 0.0827606 | + | 0.143346i | ||||
\(585\) | 1.00000 | − | 1.73205i | 0.0413449 | − | 0.0716115i | ||||
\(586\) | −4.50000 | − | 7.79423i | −0.185893 | − | 0.321977i | ||||
\(587\) | 6.00000 | + | 10.3923i | 0.247647 | + | 0.428936i | 0.962872 | − | 0.269957i | \(-0.0870095\pi\) |
−0.715226 | + | 0.698893i | \(0.753676\pi\) | |||||||
\(588\) | −6.00000 | −0.247436 | ||||||||
\(589\) | 14.0000 | + | 10.3923i | 0.576860 | + | 0.428207i | ||||
\(590\) | 12.0000 | 0.494032 | ||||||||
\(591\) | 1.50000 | + | 2.59808i | 0.0617018 | + | 0.106871i | ||||
\(592\) | −2.50000 | − | 4.33013i | −0.102749 | − | 0.177967i | ||||
\(593\) | 6.00000 | − | 10.3923i | 0.246390 | − | 0.426761i | −0.716131 | − | 0.697966i | \(-0.754089\pi\) |
0.962522 | + | 0.271205i | \(0.0874221\pi\) | |||||||
\(594\) | 1.50000 | + | 2.59808i | 0.0615457 | + | 0.106600i | ||||
\(595\) | 3.00000 | − | 5.19615i | 0.122988 | − | 0.213021i | ||||
\(596\) | 18.0000 | 0.737309 | ||||||||
\(597\) | −10.0000 | −0.409273 | ||||||||
\(598\) | −9.00000 | + | 15.5885i | −0.368037 | + | 0.637459i | ||||
\(599\) | 15.0000 | − | 25.9808i | 0.612883 | − | 1.06155i | −0.377869 | − | 0.925859i | \(-0.623343\pi\) |
0.990752 | − | 0.135686i | \(-0.0433238\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | 17.0000 | 0.693444 | 0.346722 | − | 0.937968i | \(-0.387295\pi\) | ||||
0.346722 | + | 0.937968i | \(0.387295\pi\) | |||||||
\(602\) | −5.00000 | + | 8.66025i | −0.203785 | + | 0.352966i | ||||
\(603\) | 5.00000 | + | 8.66025i | 0.203616 | + | 0.352673i | ||||
\(604\) | 5.00000 | − | 8.66025i | 0.203447 | − | 0.352381i | ||||
\(605\) | −1.00000 | − | 1.73205i | −0.0406558 | − | 0.0704179i | ||||
\(606\) | −3.00000 | − | 5.19615i | −0.121867 | − | 0.211079i | ||||
\(607\) | −49.0000 | −1.98885 | −0.994424 | − | 0.105453i | \(-0.966371\pi\) | ||||
−0.994424 | + | 0.105453i | \(0.966371\pi\) | |||||||
\(608\) | 4.00000 | − | 1.73205i | 0.162221 | − | 0.0702439i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.00000 | − | 8.66025i | −0.202444 | − | 0.350643i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 3.00000 | − | 5.19615i | 0.121268 | − | 0.210042i | ||||
\(613\) | 3.50000 | + | 6.06218i | 0.141364 | + | 0.244849i | 0.928010 | − | 0.372554i | \(-0.121518\pi\) |
−0.786647 | + | 0.617403i | \(0.788185\pi\) | |||||||
\(614\) | 8.00000 | − | 13.8564i | 0.322854 | − | 0.559199i | ||||
\(615\) | 3.00000 | 0.120972 | ||||||||
\(616\) | 3.00000 | 0.120873 | ||||||||
\(617\) | −12.0000 | + | 20.7846i | −0.483102 | + | 0.836757i | −0.999812 | − | 0.0194037i | \(-0.993823\pi\) |
0.516710 | + | 0.856161i | \(0.327157\pi\) | |||||||
\(618\) | 0.500000 | − | 0.866025i | 0.0201129 | − | 0.0348367i | ||||
\(619\) | −19.0000 | −0.763674 | −0.381837 | − | 0.924230i | \(-0.624709\pi\) | ||||
−0.381837 | + | 0.924230i | \(0.624709\pi\) | |||||||
\(620\) | 4.00000 | 0.160644 | ||||||||
\(621\) | −4.50000 | + | 7.79423i | −0.180579 | + | 0.312772i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.50000 | − | 12.9904i | 0.300481 | − | 0.520449i | ||||
\(624\) | −1.00000 | − | 1.73205i | −0.0400320 | − | 0.0693375i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 8.00000 | 0.319744 | ||||||||
\(627\) | 1.50000 | − | 12.9904i | 0.0599042 | − | 0.518786i | ||||
\(628\) | −13.0000 | −0.518756 | ||||||||
\(629\) | 15.0000 | + | 25.9808i | 0.598089 | + | 1.03592i | ||||
\(630\) | −0.500000 | − | 0.866025i | −0.0199205 | − | 0.0345033i | ||||
\(631\) | −16.0000 | + | 27.7128i | −0.636950 | + | 1.10323i | 0.349148 | + | 0.937067i | \(0.386471\pi\) |
−0.986098 | + | 0.166162i | \(0.946862\pi\) | |||||||
\(632\) | −7.00000 | − | 12.1244i | −0.278445 | − | 0.482281i | ||||
\(633\) | 12.5000 | − | 21.6506i | 0.496830 | − | 0.860535i | ||||
\(634\) | 15.0000 | 0.595726 | ||||||||
\(635\) | −11.0000 | −0.436522 | ||||||||
\(636\) | −1.50000 | + | 2.59808i | −0.0594789 | + | 0.103020i | ||||
\(637\) | 6.00000 | − | 10.3923i | 0.237729 | − | 0.411758i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.500000 | − | 0.866025i | 0.0197642 | − | 0.0342327i | ||||
\(641\) | 3.00000 | + | 5.19615i | 0.118493 | + | 0.205236i | 0.919171 | − | 0.393860i | \(-0.128860\pi\) |
−0.800678 | + | 0.599095i | \(0.795527\pi\) | |||||||
\(642\) | −3.00000 | + | 5.19615i | −0.118401 | + | 0.205076i | ||||
\(643\) | 17.0000 | + | 29.4449i | 0.670415 | + | 1.16119i | 0.977787 | + | 0.209603i | \(0.0672170\pi\) |
−0.307372 | + | 0.951589i | \(0.599450\pi\) | |||||||
\(644\) | 4.50000 | + | 7.79423i | 0.177325 | + | 0.307136i | ||||
\(645\) | 10.0000 | 0.393750 | ||||||||
\(646\) | −24.0000 | + | 10.3923i | −0.944267 | + | 0.408880i | ||||
\(647\) | −39.0000 | −1.53325 | −0.766624 | − | 0.642096i | \(-0.778065\pi\) | ||||
−0.766624 | + | 0.642096i | \(0.778065\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | −18.0000 | − | 31.1769i | −0.706562 | − | 1.22380i | ||||
\(650\) | −1.00000 | + | 1.73205i | −0.0392232 | + | 0.0679366i | ||||
\(651\) | −2.00000 | − | 3.46410i | −0.0783862 | − | 0.135769i | ||||
\(652\) | 11.0000 | − | 19.0526i | 0.430793 | − | 0.746156i | ||||
\(653\) | −15.0000 | −0.586995 | −0.293498 | − | 0.955960i | \(-0.594819\pi\) | ||||
−0.293498 | + | 0.955960i | \(0.594819\pi\) | |||||||
\(654\) | 2.00000 | 0.0782062 | ||||||||
\(655\) | 4.50000 | − | 7.79423i | 0.175830 | − | 0.304546i | ||||
\(656\) | 1.50000 | − | 2.59808i | 0.0585652 | − | 0.101438i | ||||
\(657\) | −4.00000 | −0.156055 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.5000 | − | 23.3827i | 0.525885 | − | 0.910860i | −0.473660 | − | 0.880708i | \(-0.657067\pi\) |
0.999545 | − | 0.0301523i | \(-0.00959924\pi\) | |||||||
\(660\) | −1.50000 | − | 2.59808i | −0.0583874 | − | 0.101130i | ||||
\(661\) | 2.00000 | − | 3.46410i | 0.0777910 | − | 0.134738i | −0.824506 | − | 0.565854i | \(-0.808547\pi\) |
0.902297 | + | 0.431116i | \(0.141880\pi\) | |||||||
\(662\) | −2.50000 | − | 4.33013i | −0.0971653 | − | 0.168295i | ||||
\(663\) | 6.00000 | + | 10.3923i | 0.233021 | + | 0.403604i | ||||
\(664\) | −18.0000 | −0.698535 | ||||||||
\(665\) | −0.500000 | + | 4.33013i | −0.0193892 | + | 0.167915i | ||||
\(666\) | 5.00000 | 0.193746 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 10.5000 | + | 18.1865i | 0.406257 | + | 0.703658i | ||||
\(669\) | 0.500000 | − | 0.866025i | 0.0193311 | − | 0.0334825i | ||||
\(670\) | −5.00000 | − | 8.66025i | −0.193167 | − | 0.334575i | ||||
\(671\) | −15.0000 | + | 25.9808i | −0.579069 | + | 1.00298i | ||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | 32.0000 | 1.23351 | 0.616755 | − | 0.787155i | \(-0.288447\pi\) | ||||
0.616755 | + | 0.787155i | \(0.288447\pi\) | |||||||
\(674\) | 11.0000 | − | 19.0526i | 0.423704 | − | 0.733877i | ||||
\(675\) | −0.500000 | + | 0.866025i | −0.0192450 | + | 0.0333333i | ||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | 33.0000 | 1.26829 | 0.634147 | − | 0.773213i | \(-0.281352\pi\) | ||||
0.634147 | + | 0.773213i | \(0.281352\pi\) | |||||||
\(678\) | 3.00000 | − | 5.19615i | 0.115214 | − | 0.199557i | ||||
\(679\) | 4.00000 | + | 6.92820i | 0.153506 | + | 0.265880i | ||||
\(680\) | −3.00000 | + | 5.19615i | −0.115045 | + | 0.199263i | ||||
\(681\) | −6.00000 | − | 10.3923i | −0.229920 | − | 0.398234i | ||||
\(682\) | −6.00000 | − | 10.3923i | −0.229752 | − | 0.397942i | ||||
\(683\) | 30.0000 | 1.14792 | 0.573959 | − | 0.818884i | \(-0.305407\pi\) | ||||
0.573959 | + | 0.818884i | \(0.305407\pi\) | |||||||
\(684\) | −0.500000 | + | 4.33013i | −0.0191180 | + | 0.165567i | ||||
\(685\) | 12.0000 | 0.458496 | ||||||||
\(686\) | −6.50000 | − | 11.2583i | −0.248171 | − | 0.429845i | ||||
\(687\) | 5.00000 | + | 8.66025i | 0.190762 | + | 0.330409i | ||||
\(688\) | 5.00000 | − | 8.66025i | 0.190623 | − | 0.330169i | ||||
\(689\) | −3.00000 | − | 5.19615i | −0.114291 | − | 0.197958i | ||||
\(690\) | 4.50000 | − | 7.79423i | 0.171312 | − | 0.296721i | ||||
\(691\) | −1.00000 | −0.0380418 | −0.0190209 | − | 0.999819i | \(-0.506055\pi\) | ||||
−0.0190209 | + | 0.999819i | \(0.506055\pi\) | |||||||
\(692\) | −21.0000 | −0.798300 | ||||||||
\(693\) | −1.50000 | + | 2.59808i | −0.0569803 | + | 0.0986928i | ||||
\(694\) | 15.0000 | − | 25.9808i | 0.569392 | − | 0.986216i | ||||
\(695\) | 4.00000 | 0.151729 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.00000 | + | 15.5885i | −0.340899 | + | 0.590455i | ||||
\(698\) | −1.00000 | − | 1.73205i | −0.0378506 | − | 0.0655591i | ||||
\(699\) | −3.00000 | + | 5.19615i | −0.113470 | + | 0.196537i | ||||
\(700\) | 0.500000 | + | 0.866025i | 0.0188982 | + | 0.0327327i | ||||
\(701\) | 21.0000 | + | 36.3731i | 0.793159 | + | 1.37379i | 0.924002 | + | 0.382389i | \(0.124898\pi\) |
−0.130843 | + | 0.991403i | \(0.541768\pi\) | |||||||
\(702\) | 2.00000 | 0.0754851 | ||||||||
\(703\) | −17.5000 | − | 12.9904i | −0.660025 | − | 0.489942i | ||||
\(704\) | −3.00000 | −0.113067 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.00000 | + | 5.19615i | 0.112906 | + | 0.195560i | ||||
\(707\) | 3.00000 | − | 5.19615i | 0.112827 | − | 0.195421i | ||||
\(708\) | 6.00000 | + | 10.3923i | 0.225494 | + | 0.390567i | ||||
\(709\) | −7.00000 | + | 12.1244i | −0.262891 | + | 0.455340i | −0.967009 | − | 0.254743i | \(-0.918009\pi\) |
0.704118 | + | 0.710083i | \(0.251342\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.0000 | 0.525041 | ||||||||
\(712\) | −7.50000 | + | 12.9904i | −0.281074 | + | 0.486835i | ||||
\(713\) | 18.0000 | − | 31.1769i | 0.674105 | − | 1.16758i | ||||
\(714\) | 6.00000 | 0.224544 | ||||||||
\(715\) | 6.00000 | 0.224387 | ||||||||
\(716\) | −7.50000 | + | 12.9904i | −0.280288 | + | 0.485473i | ||||
\(717\) | −6.00000 | − | 10.3923i | −0.224074 | − | 0.388108i | ||||
\(718\) | 6.00000 | − | 10.3923i | 0.223918 | − | 0.387837i | ||||
\(719\) | −18.0000 | − | 31.1769i | −0.671287 | − | 1.16270i | −0.977539 | − | 0.210752i | \(-0.932409\pi\) |
0.306253 | − | 0.951950i | \(-0.400925\pi\) | |||||||
\(720\) | 0.500000 | + | 0.866025i | 0.0186339 | + | 0.0322749i | ||||
\(721\) | 1.00000 | 0.0372419 | ||||||||
\(722\) | 13.0000 | − | 13.8564i | 0.483810 | − | 0.515682i | ||||
\(723\) | −10.0000 | −0.371904 | ||||||||
\(724\) | 8.00000 | + | 13.8564i | 0.297318 | + | 0.514969i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.00000 | − | 1.73205i | 0.0371135 | − | 0.0642824i | ||||
\(727\) | 20.0000 | + | 34.6410i | 0.741759 | + | 1.28476i | 0.951694 | + | 0.307049i | \(0.0993415\pi\) |
−0.209935 | + | 0.977715i | \(0.567325\pi\) | |||||||
\(728\) | 1.00000 | − | 1.73205i | 0.0370625 | − | 0.0641941i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 4.00000 | 0.148047 | ||||||||
\(731\) | −30.0000 | + | 51.9615i | −1.10959 | + | 1.92187i | ||||
\(732\) | 5.00000 | − | 8.66025i | 0.184805 | − | 0.320092i | ||||
\(733\) | 41.0000 | 1.51437 | 0.757185 | − | 0.653201i | \(-0.226574\pi\) | ||||
0.757185 | + | 0.653201i | \(0.226574\pi\) | |||||||
\(734\) | 8.00000 | 0.295285 | ||||||||
\(735\) | −3.00000 | + | 5.19615i | −0.110657 | + | 0.191663i | ||||
\(736\) | −4.50000 | − | 7.79423i | −0.165872 | − | 0.287299i | ||||
\(737\) | −15.0000 | + | 25.9808i | −0.552532 | + | 0.957014i | ||||
\(738\) | 1.50000 | + | 2.59808i | 0.0552158 | + | 0.0956365i | ||||
\(739\) | 24.5000 | + | 42.4352i | 0.901247 | + | 1.56101i | 0.825877 | + | 0.563850i | \(0.190680\pi\) |
0.0753699 | + | 0.997156i | \(0.475986\pi\) | |||||||
\(740\) | −5.00000 | −0.183804 | ||||||||
\(741\) | −7.00000 | − | 5.19615i | −0.257151 | − | 0.190885i | ||||
\(742\) | −3.00000 | −0.110133 | ||||||||
\(743\) | 19.5000 | + | 33.7750i | 0.715386 | + | 1.23908i | 0.962811 | + | 0.270177i | \(0.0870823\pi\) |
−0.247425 | + | 0.968907i | \(0.579584\pi\) | |||||||
\(744\) | 2.00000 | + | 3.46410i | 0.0733236 | + | 0.127000i | ||||
\(745\) | 9.00000 | − | 15.5885i | 0.329734 | − | 0.571117i | ||||
\(746\) | −11.5000 | − | 19.9186i | −0.421045 | − | 0.729271i | ||||
\(747\) | 9.00000 | − | 15.5885i | 0.329293 | − | 0.570352i | ||||
\(748\) | 18.0000 | 0.658145 | ||||||||
\(749\) | −6.00000 | −0.219235 | ||||||||
\(750\) | 0.500000 | − | 0.866025i | 0.0182574 | − | 0.0316228i | ||||
\(751\) | −4.00000 | + | 6.92820i | −0.145962 | + | 0.252814i | −0.929731 | − | 0.368238i | \(-0.879961\pi\) |
0.783769 | + | 0.621052i | \(0.213294\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.0000 | −0.437304 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.00000 | − | 8.66025i | −0.181969 | − | 0.315179i | ||||
\(756\) | 0.500000 | − | 0.866025i | 0.0181848 | − | 0.0314970i | ||||
\(757\) | 3.50000 | + | 6.06218i | 0.127210 | + | 0.220334i | 0.922595 | − | 0.385771i | \(-0.126065\pi\) |
−0.795385 | + | 0.606105i | \(0.792731\pi\) | |||||||
\(758\) | 8.00000 | + | 13.8564i | 0.290573 | + | 0.503287i | ||||
\(759\) | −27.0000 | −0.980038 | ||||||||
\(760\) | 0.500000 | − | 4.33013i | 0.0181369 | − | 0.157070i | ||||
\(761\) | 15.0000 | 0.543750 | 0.271875 | − | 0.962333i | \(-0.412356\pi\) | ||||
0.271875 | + | 0.962333i | \(0.412356\pi\) | |||||||
\(762\) | −5.50000 | − | 9.52628i | −0.199244 | − | 0.345101i | ||||
\(763\) | 1.00000 | + | 1.73205i | 0.0362024 | + | 0.0627044i | ||||
\(764\) | −3.00000 | + | 5.19615i | −0.108536 | + | 0.187990i | ||||
\(765\) | −3.00000 | − | 5.19615i | −0.108465 | − | 0.187867i | ||||
\(766\) | −12.0000 | + | 20.7846i | −0.433578 | + | 0.750978i | ||||
\(767\) | −24.0000 | −0.866590 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −1.00000 | + | 1.73205i | −0.0360609 | + | 0.0624593i | −0.883493 | − | 0.468445i | \(-0.844814\pi\) |
0.847432 | + | 0.530904i | \(0.178148\pi\) | |||||||
\(770\) | 1.50000 | − | 2.59808i | 0.0540562 | − | 0.0936282i | ||||
\(771\) | −6.00000 | −0.216085 | ||||||||
\(772\) | −10.0000 | −0.359908 | ||||||||
\(773\) | 10.5000 | − | 18.1865i | 0.377659 | − | 0.654124i | −0.613062 | − | 0.790034i | \(-0.710063\pi\) |
0.990721 | + | 0.135910i | \(0.0433959\pi\) | |||||||
\(774\) | 5.00000 | + | 8.66025i | 0.179721 | + | 0.311286i | ||||
\(775\) | 2.00000 | − | 3.46410i | 0.0718421 | − | 0.124434i | ||||
\(776\) | −4.00000 | − | 6.92820i | −0.143592 | − | 0.248708i | ||||
\(777\) | 2.50000 | + | 4.33013i | 0.0896870 | + | 0.155342i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.50000 | − | 12.9904i | 0.0537431 | − | 0.465429i | ||||
\(780\) | −2.00000 | −0.0716115 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 27.0000 | + | 46.7654i | 0.965518 | + | 1.67233i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.00000 | + | 5.19615i | 0.107143 | + | 0.185577i | ||||
\(785\) | −6.50000 | + | 11.2583i | −0.231995 | + | 0.401827i | ||||
\(786\) | 9.00000 | 0.321019 | ||||||||
\(787\) | 32.0000 | 1.14068 | 0.570338 | − | 0.821410i | \(-0.306812\pi\) | ||||
0.570338 | + | 0.821410i | \(0.306812\pi\) | |||||||
\(788\) | 1.50000 | − | 2.59808i | 0.0534353 | − | 0.0925526i | ||||
\(789\) | −7.50000 | + | 12.9904i | −0.267007 | + | 0.462470i | ||||
\(790\) | −14.0000 | −0.498098 | ||||||||
\(791\) | 6.00000 | 0.213335 | ||||||||
\(792\) | 1.50000 | − | 2.59808i | 0.0533002 | − | 0.0923186i | ||||
\(793\) | 10.0000 | + | 17.3205i | 0.355110 | + | 0.615069i | ||||
\(794\) | −14.5000 | + | 25.1147i | −0.514586 | + | 0.891289i | ||||
\(795\) | 1.50000 | + | 2.59808i | 0.0531995 | + | 0.0921443i | ||||
\(796\) | 5.00000 | + | 8.66025i | 0.177220 | + | 0.306955i | ||||
\(797\) | −33.0000 | −1.16892 | −0.584460 | − | 0.811423i | \(-0.698694\pi\) | ||||
−0.584460 | + | 0.811423i | \(0.698694\pi\) | |||||||
\(798\) | −4.00000 | + | 1.73205i | −0.141598 | + | 0.0613139i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.500000 | − | 0.866025i | −0.0176777 | − | 0.0306186i | ||||
\(801\) | −7.50000 | − | 12.9904i | −0.264999 | − | 0.458993i | ||||
\(802\) | 9.00000 | − | 15.5885i | 0.317801 | − | 0.550448i | ||||
\(803\) | −6.00000 | − | 10.3923i | −0.211735 | − | 0.366736i | ||||
\(804\) | 5.00000 | − | 8.66025i | 0.176336 | − | 0.305424i | ||||
\(805\) | 9.00000 | 0.317208 | ||||||||
\(806\) | −8.00000 | −0.281788 | ||||||||
\(807\) | 15.0000 | − | 25.9808i | 0.528025 | − | 0.914566i | ||||
\(808\) | −3.00000 | + | 5.19615i | −0.105540 | + | 0.182800i | ||||
\(809\) | −30.0000 | −1.05474 | −0.527372 | − | 0.849635i | \(-0.676823\pi\) | ||||
−0.527372 | + | 0.849635i | \(0.676823\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 21.5000 | − | 37.2391i | 0.754967 | − | 1.30764i | −0.190424 | − | 0.981702i | \(-0.560986\pi\) |
0.945391 | − | 0.325939i | \(-0.105681\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.00000 | + | 1.73205i | −0.0350715 | + | 0.0607457i | ||||
\(814\) | 7.50000 | + | 12.9904i | 0.262875 | + | 0.455313i | ||||
\(815\) | −11.0000 | − | 19.0526i | −0.385313 | − | 0.667382i | ||||
\(816\) | −6.00000 | −0.210042 | ||||||||
\(817\) | 5.00000 | − | 43.3013i | 0.174928 | − | 1.51492i | ||||
\(818\) | 5.00000 | 0.174821 | ||||||||
\(819\) | 1.00000 | + | 1.73205i | 0.0349428 | + | 0.0605228i | ||||
\(820\) | −1.50000 | − | 2.59808i | −0.0523823 | − | 0.0907288i | ||||
\(821\) | −15.0000 | + | 25.9808i | −0.523504 | + | 0.906735i | 0.476122 | + | 0.879379i | \(0.342042\pi\) |
−0.999626 | + | 0.0273557i | \(0.991291\pi\) | |||||||
\(822\) | 6.00000 | + | 10.3923i | 0.209274 | + | 0.362473i | ||||
\(823\) | −20.5000 | + | 35.5070i | −0.714585 | + | 1.23770i | 0.248534 | + | 0.968623i | \(0.420051\pi\) |
−0.963119 | + | 0.269075i | \(0.913282\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | −3.00000 | −0.104447 | ||||||||
\(826\) | −6.00000 | + | 10.3923i | −0.208767 | + | 0.361595i | ||||
\(827\) | −24.0000 | + | 41.5692i | −0.834562 | + | 1.44550i | 0.0598250 | + | 0.998209i | \(0.480946\pi\) |
−0.894387 | + | 0.447295i | \(0.852388\pi\) | |||||||
\(828\) | 9.00000 | 0.312772 | ||||||||
\(829\) | 8.00000 | 0.277851 | 0.138926 | − | 0.990303i | \(-0.455635\pi\) | ||||
0.138926 | + | 0.990303i | \(0.455635\pi\) | |||||||
\(830\) | −9.00000 | + | 15.5885i | −0.312395 | + | 0.541083i | ||||
\(831\) | 5.00000 | + | 8.66025i | 0.173448 | + | 0.300421i | ||||
\(832\) | −1.00000 | + | 1.73205i | −0.0346688 | + | 0.0600481i | ||||
\(833\) | −18.0000 | − | 31.1769i | −0.623663 | − | 1.08022i | ||||
\(834\) | 2.00000 | + | 3.46410i | 0.0692543 | + | 0.119952i | ||||
\(835\) | 21.0000 | 0.726735 | ||||||||
\(836\) | −12.0000 | + | 5.19615i | −0.415029 | + | 0.179713i | ||||
\(837\) | −4.00000 | −0.138260 | ||||||||
\(838\) | −10.5000 | − | 18.1865i | −0.362716 | − | 0.628243i | ||||
\(839\) | 15.0000 | + | 25.9808i | 0.517858 | + | 0.896956i | 0.999785 | + | 0.0207443i | \(0.00660359\pi\) |
−0.481927 | + | 0.876211i | \(0.660063\pi\) | |||||||
\(840\) | −0.500000 | + | 0.866025i | −0.0172516 | + | 0.0298807i | ||||
\(841\) | 14.5000 | + | 25.1147i | 0.500000 | + | 0.866025i | ||||
\(842\) | −13.0000 | + | 22.5167i | −0.448010 | + | 0.775975i | ||||
\(843\) | 15.0000 | 0.516627 | ||||||||
\(844\) | −25.0000 | −0.860535 | ||||||||
\(845\) | −4.50000 | + | 7.79423i | −0.154805 | + | 0.268130i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.00000 | 0.0687208 | ||||||||
\(848\) | 3.00000 | 0.103020 | ||||||||
\(849\) | 11.0000 | − | 19.0526i | 0.377519 | − | 0.653882i | ||||
\(850\) | 3.00000 | + | 5.19615i | 0.102899 | + | 0.178227i | ||||
\(851\) | −22.5000 | + | 38.9711i | −0.771290 | + | 1.33591i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.0000 | − | 32.9090i | −0.650548 | − | 1.12678i | −0.982990 | − | 0.183658i | \(-0.941206\pi\) |
0.332443 | − | 0.943123i | \(-0.392127\pi\) | |||||||
\(854\) | 10.0000 | 0.342193 | ||||||||
\(855\) | 3.50000 | + | 2.59808i | 0.119697 | + | 0.0888523i | ||||
\(856\) | 6.00000 | 0.205076 | ||||||||
\(857\) | −12.0000 | − | 20.7846i | −0.409912 | − | 0.709989i | 0.584967 | − | 0.811057i | \(-0.301107\pi\) |
−0.994880 | + | 0.101068i | \(0.967774\pi\) | |||||||
\(858\) | 3.00000 | + | 5.19615i | 0.102418 | + | 0.177394i | ||||
\(859\) | −8.50000 | + | 14.7224i | −0.290016 | + | 0.502323i | −0.973813 | − | 0.227349i | \(-0.926994\pi\) |
0.683797 | + | 0.729672i | \(0.260327\pi\) | |||||||
\(860\) | −5.00000 | − | 8.66025i | −0.170499 | − | 0.295312i | ||||
\(861\) | −1.50000 | + | 2.59808i | −0.0511199 | + | 0.0885422i | ||||
\(862\) | 30.0000 | 1.02180 | ||||||||
\(863\) | −39.0000 | −1.32758 | −0.663788 | − | 0.747921i | \(-0.731052\pi\) | ||||
−0.663788 | + | 0.747921i | \(0.731052\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | −10.5000 | + | 18.1865i | −0.357011 | + | 0.618361i | ||||
\(866\) | −16.0000 | −0.543702 | ||||||||
\(867\) | 19.0000 | 0.645274 | ||||||||
\(868\) | −2.00000 | + | 3.46410i | −0.0678844 | + | 0.117579i | ||||
\(869\) | 21.0000 | + | 36.3731i | 0.712376 | + | 1.23387i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.0000 | + | 17.3205i | 0.338837 | + | 0.586883i | ||||
\(872\) | −1.00000 | − | 1.73205i | −0.0338643 | − | 0.0586546i | ||||
\(873\) | 8.00000 | 0.270759 | ||||||||
\(874\) | −31.5000 | − | 23.3827i | −1.06550 | − | 0.790931i | ||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 2.00000 | + | 3.46410i | 0.0675737 | + | 0.117041i | ||||
\(877\) | −17.5000 | − | 30.3109i | −0.590933 | − | 1.02353i | −0.994107 | − | 0.108403i | \(-0.965426\pi\) |
0.403174 | − | 0.915123i | \(-0.367907\pi\) | |||||||
\(878\) | −7.00000 | + | 12.1244i | −0.236239 | + | 0.409177i | ||||
\(879\) | −4.50000 | − | 7.79423i | −0.151781 | − | 0.262893i | ||||
\(880\) | −1.50000 | + | 2.59808i | −0.0505650 | + | 0.0875811i | ||||
\(881\) | 39.0000 | 1.31394 | 0.656972 | − | 0.753915i | \(-0.271837\pi\) | ||||
0.656972 | + | 0.753915i | \(0.271837\pi\) | |||||||
\(882\) | −6.00000 | −0.202031 | ||||||||
\(883\) | −13.0000 | + | 22.5167i | −0.437485 | + | 0.757746i | −0.997495 | − | 0.0707399i | \(-0.977464\pi\) |
0.560010 | + | 0.828486i | \(0.310797\pi\) | |||||||
\(884\) | 6.00000 | − | 10.3923i | 0.201802 | − | 0.349531i | ||||
\(885\) | 12.0000 | 0.403376 | ||||||||
\(886\) | −18.0000 | −0.604722 | ||||||||
\(887\) | −18.0000 | + | 31.1769i | −0.604381 | + | 1.04682i | 0.387768 | + | 0.921757i | \(0.373246\pi\) |
−0.992149 | + | 0.125061i | \(0.960087\pi\) | |||||||
\(888\) | −2.50000 | − | 4.33013i | −0.0838945 | − | 0.145310i | ||||
\(889\) | 5.50000 | − | 9.52628i | 0.184464 | − | 0.319501i | ||||
\(890\) | 7.50000 | + | 12.9904i | 0.251401 | + | 0.435439i | ||||
\(891\) | 1.50000 | + | 2.59808i | 0.0502519 | + | 0.0870388i | ||||
\(892\) | −1.00000 | −0.0334825 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 18.0000 | 0.602010 | ||||||||
\(895\) | 7.50000 | + | 12.9904i | 0.250697 | + | 0.434221i | ||||
\(896\) | 0.500000 | + | 0.866025i | 0.0167038 | + | 0.0289319i | ||||
\(897\) | −9.00000 | + | 15.5885i | −0.300501 | + | 0.520483i | ||||
\(898\) | −1.50000 | − | 2.59808i | −0.0500556 | − | 0.0866989i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −18.0000 | −0.599667 | ||||||||
\(902\) | −4.50000 | + | 7.79423i | −0.149834 | + | 0.259519i | ||||
\(903\) | −5.00000 | + | 8.66025i | −0.166390 | + | 0.288195i | ||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | 16.0000 | 0.531858 | ||||||||
\(906\) | 5.00000 | − | 8.66025i | 0.166114 | − | 0.287718i | ||||
\(907\) | 5.00000 | + | 8.66025i | 0.166022 | + | 0.287559i | 0.937018 | − | 0.349281i | \(-0.113574\pi\) |
−0.770996 | + | 0.636841i | \(0.780241\pi\) | |||||||
\(908\) | −6.00000 | + | 10.3923i | −0.199117 | + | 0.344881i | ||||
\(909\) | −3.00000 | − | 5.19615i | −0.0995037 | − | 0.172345i | ||||
\(910\) | −1.00000 | − | 1.73205i | −0.0331497 | − | 0.0574169i | ||||
\(911\) | 30.0000 | 0.993944 | 0.496972 | − | 0.867766i | \(-0.334445\pi\) | ||||
0.496972 | + | 0.867766i | \(0.334445\pi\) | |||||||
\(912\) | 4.00000 | − | 1.73205i | 0.132453 | − | 0.0573539i | ||||
\(913\) | 54.0000 | 1.78714 | ||||||||
\(914\) | −19.0000 | − | 32.9090i | −0.628464 | − | 1.08853i | ||||
\(915\) | −5.00000 | − | 8.66025i | −0.165295 | − | 0.286299i | ||||
\(916\) | 5.00000 | − | 8.66025i | 0.165205 | − | 0.286143i | ||||
\(917\) | 4.50000 | + | 7.79423i | 0.148603 | + | 0.257388i | ||||
\(918\) | 3.00000 | − | 5.19615i | 0.0990148 | − | 0.171499i | ||||
\(919\) | 8.00000 | 0.263896 | 0.131948 | − | 0.991257i | \(-0.457877\pi\) | ||||
0.131948 | + | 0.991257i | \(0.457877\pi\) | |||||||
\(920\) | −9.00000 | −0.296721 | ||||||||
\(921\) | 8.00000 | − | 13.8564i | 0.263609 | − | 0.456584i | ||||
\(922\) | −15.0000 | + | 25.9808i | −0.493999 | + | 0.855631i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 3.00000 | 0.0986928 | ||||||||
\(925\) | −2.50000 | + | 4.33013i | −0.0821995 | + | 0.142374i | ||||
\(926\) | −5.50000 | − | 9.52628i | −0.180741 | − | 0.313053i | ||||
\(927\) | 0.500000 | − | 0.866025i | 0.0164222 | − | 0.0284440i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.5000 | − | 23.3827i | −0.442921 | − | 0.767161i | 0.554984 | − | 0.831861i | \(-0.312724\pi\) |
−0.997905 | + | 0.0646999i | \(0.979391\pi\) | |||||||
\(930\) | 4.00000 | 0.131165 | ||||||||
\(931\) | 21.0000 | + | 15.5885i | 0.688247 | + | 0.510891i | ||||
\(932\) | 6.00000 | 0.196537 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.00000 | − | 15.5885i | 0.294331 | − | 0.509797i | ||||
\(936\) | −1.00000 | − | 1.73205i | −0.0326860 | − | 0.0566139i | ||||
\(937\) | 2.00000 | − | 3.46410i | 0.0653372 | − | 0.113167i | −0.831506 | − | 0.555515i | \(-0.812521\pi\) |
0.896843 | + | 0.442348i | \(0.145854\pi\) | |||||||
\(938\) | 10.0000 | 0.326512 | ||||||||
\(939\) | 8.00000 | 0.261070 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.0000 | − | 20.7846i | 0.391189 | − | 0.677559i | −0.601418 | − | 0.798935i | \(-0.705397\pi\) |
0.992607 | + | 0.121376i | \(0.0387306\pi\) | |||||||
\(942\) | −13.0000 | −0.423563 | ||||||||
\(943\) | −27.0000 | −0.879241 | ||||||||
\(944\) | 6.00000 | − | 10.3923i | 0.195283 | − | 0.338241i | ||||
\(945\) | −0.500000 | − | 0.866025i | −0.0162650 | − | 0.0281718i | ||||
\(946\) | −15.0000 | + | 25.9808i | −0.487692 | + | 0.844707i | ||||
\(947\) | −9.00000 | − | 15.5885i | −0.292461 | − | 0.506557i | 0.681930 | − | 0.731417i | \(-0.261141\pi\) |
−0.974391 | + | 0.224860i | \(0.927807\pi\) | |||||||
\(948\) | −7.00000 | − | 12.1244i | −0.227349 | − | 0.393781i | ||||
\(949\) | −8.00000 | −0.259691 | ||||||||
\(950\) | −3.50000 | − | 2.59808i | −0.113555 | − | 0.0842927i | ||||
\(951\) | 15.0000 | 0.486408 | ||||||||
\(952\) | −3.00000 | − | 5.19615i | −0.0972306 | − | 0.168408i | ||||
\(953\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(954\) | −1.50000 | + | 2.59808i | −0.0485643 | + | 0.0841158i | ||||
\(955\) | 3.00000 | + | 5.19615i | 0.0970777 | + | 0.168144i | ||||
\(956\) | −6.00000 | + | 10.3923i | −0.194054 | + | 0.336111i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.0000 | 0.387702 | ||||||||
\(959\) | −6.00000 | + | 10.3923i | −0.193750 | + | 0.335585i | ||||
\(960\) | 0.500000 | − | 0.866025i | 0.0161374 | − | 0.0279508i | ||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 10.0000 | 0.322413 | ||||||||
\(963\) | −3.00000 | + | 5.19615i | −0.0966736 | + | 0.167444i | ||||
\(964\) | 5.00000 | + | 8.66025i | 0.161039 | + | 0.278928i | ||||
\(965\) | −5.00000 | + | 8.66025i | −0.160956 | + | 0.278783i | ||||
\(966\) | 4.50000 | + | 7.79423i | 0.144785 | + | 0.250775i | ||||
\(967\) | −22.0000 | − | 38.1051i | −0.707472 | − | 1.22538i | −0.965792 | − | 0.259318i | \(-0.916502\pi\) |
0.258320 | − | 0.966060i | \(-0.416831\pi\) | |||||||
\(968\) | −2.00000 | −0.0642824 | ||||||||
\(969\) | −24.0000 | + | 10.3923i | −0.770991 | + | 0.333849i | ||||
\(970\) | −8.00000 | −0.256865 | ||||||||
\(971\) | −6.00000 | − | 10.3923i | −0.192549 | − | 0.333505i | 0.753545 | − | 0.657396i | \(-0.228342\pi\) |
−0.946094 | + | 0.323891i | \(0.895009\pi\) | |||||||
\(972\) | −0.500000 | − | 0.866025i | −0.0160375 | − | 0.0277778i | ||||
\(973\) | −2.00000 | + | 3.46410i | −0.0641171 | + | 0.111054i | ||||
\(974\) | −5.50000 | − | 9.52628i | −0.176231 | − | 0.305242i | ||||
\(975\) | −1.00000 | + | 1.73205i | −0.0320256 | + | 0.0554700i | ||||
\(976\) | −10.0000 | −0.320092 | ||||||||
\(977\) | −24.0000 | −0.767828 | −0.383914 | − | 0.923369i | \(-0.625424\pi\) | ||||
−0.383914 | + | 0.923369i | \(0.625424\pi\) | |||||||
\(978\) | 11.0000 | − | 19.0526i | 0.351741 | − | 0.609234i | ||||
\(979\) | 22.5000 | − | 38.9711i | 0.719103 | − | 1.24552i | ||||
\(980\) | 6.00000 | 0.191663 | ||||||||
\(981\) | 2.00000 | 0.0638551 | ||||||||
\(982\) | −1.50000 | + | 2.59808i | −0.0478669 | + | 0.0829079i | ||||
\(983\) | −4.50000 | − | 7.79423i | −0.143528 | − | 0.248597i | 0.785295 | − | 0.619122i | \(-0.212511\pi\) |
−0.928823 | + | 0.370525i | \(0.879178\pi\) | |||||||
\(984\) | 1.50000 | − | 2.59808i | 0.0478183 | − | 0.0828236i | ||||
\(985\) | −1.50000 | − | 2.59808i | −0.0477940 | − | 0.0827816i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.00000 | + | 8.66025i | −0.0318142 | + | 0.275519i | ||||
\(989\) | −90.0000 | −2.86183 | ||||||||
\(990\) | −1.50000 | − | 2.59808i | −0.0476731 | − | 0.0825723i | ||||
\(991\) | 26.0000 | + | 45.0333i | 0.825917 | + | 1.43053i | 0.901216 | + | 0.433370i | \(0.142676\pi\) |
−0.0752991 | + | 0.997161i | \(0.523991\pi\) | |||||||
\(992\) | 2.00000 | − | 3.46410i | 0.0635001 | − | 0.109985i | ||||
\(993\) | −2.50000 | − | 4.33013i | −0.0793351 | − | 0.137412i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.0000 | 0.317021 | ||||||||
\(996\) | −18.0000 | −0.570352 | ||||||||
\(997\) | 24.5000 | − | 42.4352i | 0.775923 | − | 1.34394i | −0.158352 | − | 0.987383i | \(-0.550618\pi\) |
0.934274 | − | 0.356555i | \(-0.116049\pi\) | |||||||
\(998\) | 12.5000 | − | 21.6506i | 0.395681 | − | 0.685339i | ||||
\(999\) | 5.00000 | 0.158193 |
(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 | 570.2.i.a.121.1 | ✓ | 2 | |
3.2 | odd | 2 | 1710.2.l.g.1261.1 | 2 | |||
19.11 | even | 3 | inner | 570.2.i.a.391.1 | yes | 2 | |
57.11 | odd | 6 | 1710.2.l.g.1531.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.i.a.121.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
570.2.i.a.391.1 | yes | 2 | 19.11 | even | 3 | inner | |
1710.2.l.g.1261.1 | 2 | 3.2 | odd | 2 | |||
1710.2.l.g.1531.1 | 2 | 57.11 | odd | 6 |