Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(271,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.271");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.bf (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: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 271.5 | ||
Character | \(\chi\) | \(=\) | 756.271 |
Dual form | 756.2.bf.b.703.5 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.953127 | + | 1.04477i | −0.673963 | + | 0.738765i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.183097 | − | 1.99160i | −0.0915486 | − | 0.995801i | ||||
\(5\) | 0.703801 | + | 0.406340i | 0.314749 | + | 0.181721i | 0.649050 | − | 0.760746i | \(-0.275167\pi\) |
−0.334300 | + | 0.942467i | \(0.608500\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.60258 | + | 0.476010i | −0.983682 | + | 0.179915i | ||||
\(8\) | 2.25528 | + | 1.70695i | 0.797363 | + | 0.603500i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.09534 | + | 0.348018i | −0.346378 | + | 0.110053i | ||||
\(11\) | 1.86129 | − | 1.07462i | 0.561200 | − | 0.324009i | −0.192427 | − | 0.981311i | \(-0.561636\pi\) |
0.753627 | + | 0.657302i | \(0.228303\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.14045i | − | 1.42570i | −0.701315 | − | 0.712852i | \(-0.747403\pi\) | ||
0.701315 | − | 0.712852i | \(-0.252597\pi\) | |||||||
\(14\) | 1.98327 | − | 3.17280i | 0.530050 | − | 0.847966i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.93295 | + | 0.729313i | −0.983238 | + | 0.182328i | ||||
\(17\) | 1.78009 | − | 1.02773i | 0.431735 | − | 0.249262i | −0.268351 | − | 0.963321i | \(-0.586479\pi\) |
0.700085 | + | 0.714059i | \(0.253145\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.57359 | + | 2.72553i | −0.361005 | + | 0.625280i | −0.988127 | − | 0.153642i | \(-0.950900\pi\) |
0.627121 | + | 0.778922i | \(0.284233\pi\) | |||||||
\(20\) | 0.680403 | − | 1.47609i | 0.152143 | − | 0.330064i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.651317 | + | 2.96887i | −0.138861 | + | 0.632965i | ||||
\(23\) | −1.64186 | − | 0.947931i | −0.342352 | − | 0.197657i | 0.318959 | − | 0.947768i | \(-0.396667\pi\) |
−0.661312 | + | 0.750111i | \(0.730000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.16978 | − | 3.75816i | −0.433955 | − | 0.751632i | ||||
\(26\) | 5.37059 | + | 4.89950i | 1.05326 | + | 0.960871i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.42455 | + | 5.09614i | 0.269214 | + | 0.963080i | ||||
\(29\) | 7.65207 | 1.42095 | 0.710477 | − | 0.703721i | \(-0.248479\pi\) | ||||
0.710477 | + | 0.703721i | \(0.248479\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.513811 | + | 0.889946i | 0.0922831 | + | 0.159839i | 0.908471 | − | 0.417947i | \(-0.137250\pi\) |
−0.816188 | + | 0.577786i | \(0.803917\pi\) | |||||||
\(32\) | 2.98664 | − | 4.80417i | 0.527968 | − | 0.849264i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.622902 | + | 2.83935i | −0.106827 | + | 0.486944i | ||||
\(35\) | −2.02512 | − | 0.722515i | −0.342308 | − | 0.122127i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.94725 | − | 5.10478i | 0.484524 | − | 0.839221i | −0.515318 | − | 0.856999i | \(-0.672326\pi\) |
0.999842 | + | 0.0177786i | \(0.00565939\pi\) | |||||||
\(38\) | −1.34773 | − | 4.24182i | −0.218631 | − | 0.688113i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.893668 | + | 2.11777i | 0.141301 | + | 0.334849i | ||||
\(41\) | − | 2.55145i | − | 0.398469i | −0.979952 | − | 0.199235i | \(-0.936154\pi\) | ||
0.979952 | − | 0.199235i | \(-0.0638456\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 10.2817i | − | 1.56795i | −0.620793 | − | 0.783974i | \(-0.713189\pi\) | ||
0.620793 | − | 0.783974i | \(-0.286811\pi\) | |||||||
\(44\) | −2.48100 | − | 3.51019i | −0.374025 | − | 0.529181i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.55528 | − | 0.811875i | 0.376755 | − | 0.119704i | ||||
\(47\) | 1.06224 | − | 1.83986i | 0.154944 | − | 0.268371i | −0.778095 | − | 0.628147i | \(-0.783814\pi\) |
0.933039 | + | 0.359776i | \(0.117147\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.54683 | − | 2.47771i | 0.935261 | − | 0.353958i | ||||
\(50\) | 5.99450 | + | 1.31509i | 0.847750 | + | 0.185981i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −10.2377 | + | 0.941201i | −1.41972 | + | 0.130521i | ||||
\(53\) | 3.32185 | + | 5.75361i | 0.456291 | + | 0.790319i | 0.998761 | − | 0.0497559i | \(-0.0158443\pi\) |
−0.542471 | + | 0.840075i | \(0.682511\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.74664 | 0.235516 | ||||||||
\(56\) | −6.68208 | − | 3.36894i | −0.892931 | − | 0.450194i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.29339 | + | 7.99467i | −0.957670 | + | 1.04975i | ||||
\(59\) | −6.32614 | − | 10.9572i | −0.823593 | − | 1.42651i | −0.902990 | − | 0.429662i | \(-0.858633\pi\) |
0.0793963 | − | 0.996843i | \(-0.474701\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.15384 | + | 2.97557i | 0.659882 | + | 0.380983i | 0.792232 | − | 0.610220i | \(-0.208919\pi\) |
−0.132350 | + | 0.991203i | \(0.542252\pi\) | |||||||
\(62\) | −1.41952 | − | 0.311417i | −0.180279 | − | 0.0395500i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.17261 | + | 7.69933i | 0.271577 | + | 0.962417i | ||||
\(65\) | 2.08877 | − | 3.61785i | 0.259080 | − | 0.448739i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.91842 | − | 3.99435i | 0.845220 | − | 0.487988i | −0.0138151 | − | 0.999905i | \(-0.504398\pi\) |
0.859035 | + | 0.511917i | \(0.171064\pi\) | |||||||
\(68\) | −2.37277 | − | 3.35705i | −0.287740 | − | 0.407102i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.68506 | − | 1.42714i | 0.320926 | − | 0.170576i | ||||
\(71\) | 11.0579i | 1.31234i | 0.754615 | + | 0.656168i | \(0.227824\pi\) | ||||
−0.754615 | + | 0.656168i | \(0.772176\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.64340 | − | 4.99027i | 1.01163 | − | 0.584067i | 0.0999643 | − | 0.994991i | \(-0.468127\pi\) |
0.911670 | + | 0.410924i | \(0.134794\pi\) | |||||||
\(74\) | 2.52423 | + | 7.94470i | 0.293436 | + | 0.923553i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.71629 | + | 2.63492i | 0.655703 | + | 0.302246i | ||||
\(77\) | −4.33262 | + | 3.68277i | −0.493748 | + | 0.419690i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.82469 | − | 3.94024i | −0.767837 | − | 0.443311i | 0.0642652 | − | 0.997933i | \(-0.479530\pi\) |
−0.832103 | + | 0.554622i | \(0.812863\pi\) | |||||||
\(80\) | −3.06436 | − | 1.08482i | −0.342606 | − | 0.121287i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.66568 | + | 2.43185i | 0.294375 | + | 0.268553i | ||||
\(83\) | 17.5056 | 1.92148 | 0.960742 | − | 0.277443i | \(-0.0894869\pi\) | ||||
0.960742 | + | 0.277443i | \(0.0894869\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.67044 | 0.181184 | ||||||||
\(86\) | 10.7421 | + | 9.79979i | 1.15835 | + | 1.05674i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.03206 | + | 0.753572i | 0.643020 | + | 0.0803311i | ||||
\(89\) | 0.484920 | + | 0.279969i | 0.0514014 | + | 0.0296766i | 0.525480 | − | 0.850806i | \(-0.323886\pi\) |
−0.474079 | + | 0.880482i | \(0.657219\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.44690 | + | 13.3784i | 0.256505 | + | 1.40244i | ||||
\(92\) | −1.58728 | + | 3.44350i | −0.165485 | + | 0.359010i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.909781 | + | 2.86342i | 0.0938368 | + | 0.295340i | ||||
\(95\) | −2.21498 | + | 1.27882i | −0.227252 | + | 0.131204i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.84737i | − | 0.187572i | −0.995592 | − | 0.0937859i | \(-0.970103\pi\) | ||
0.995592 | − | 0.0937859i | \(-0.0298969\pi\) | |||||||
\(98\) | −3.65132 | + | 9.20151i | −0.368839 | + | 0.929493i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.08748 | + | 5.00944i | −0.708748 | + | 0.500944i | ||||
\(101\) | −14.1467 | + | 8.16763i | −1.40765 | + | 0.812709i | −0.995162 | − | 0.0982519i | \(-0.968675\pi\) |
−0.412492 | + | 0.910961i | \(0.635342\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.38508 | + | 4.13108i | −0.235009 | + | 0.407048i | −0.959275 | − | 0.282473i | \(-0.908845\pi\) |
0.724266 | + | 0.689520i | \(0.242179\pi\) | |||||||
\(104\) | 8.77451 | − | 11.5932i | 0.860411 | − | 1.13680i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.17735 | − | 2.01335i | −0.891383 | − | 0.195554i | ||||
\(107\) | 4.05383 | + | 2.34048i | 0.391898 | + | 0.226263i | 0.682982 | − | 0.730435i | \(-0.260683\pi\) |
−0.291084 | + | 0.956697i | \(0.594016\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.19616 | − | 7.26796i | −0.401919 | − | 0.696144i | 0.592038 | − | 0.805910i | \(-0.298323\pi\) |
−0.993958 | + | 0.109765i | \(0.964990\pi\) | |||||||
\(110\) | −1.66477 | + | 1.82484i | −0.158729 | + | 0.173991i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 9.88865 | − | 3.77022i | 0.934390 | − | 0.356252i | ||||
\(113\) | 2.60313 | 0.244882 | 0.122441 | − | 0.992476i | \(-0.460928\pi\) | ||||
0.122441 | + | 0.992476i | \(0.460928\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.770364 | − | 1.33431i | −0.0718368 | − | 0.124425i | ||||
\(116\) | −1.40107 | − | 15.2399i | −0.130086 | − | 1.41499i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 17.4774 | + | 3.83423i | 1.60892 | + | 0.352969i | ||||
\(119\) | −4.14361 | + | 3.52210i | −0.379844 | + | 0.322870i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.19040 | + | 5.52594i | −0.290036 | + | 0.502358i | ||||
\(122\) | −8.02106 | + | 2.54849i | −0.726193 | + | 0.230730i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.67834 | − | 1.18625i | 0.150719 | − | 0.106529i | ||||
\(125\) | − | 7.59006i | − | 0.678876i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.70221i | − | 0.594725i | −0.954765 | − | 0.297363i | \(-0.903893\pi\) | ||
0.954765 | − | 0.297363i | \(-0.0961070\pi\) | |||||||
\(128\) | −10.1148 | − | 5.06856i | −0.894033 | − | 0.448002i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.78897 | + | 5.63056i | 0.156903 | + | 0.493833i | ||||
\(131\) | −7.37529 | + | 12.7744i | −0.644382 | + | 1.11610i | 0.340062 | + | 0.940403i | \(0.389552\pi\) |
−0.984444 | + | 0.175699i | \(0.943781\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.79800 | − | 7.84245i | 0.242617 | − | 0.680027i | ||||
\(134\) | −2.42095 | + | 11.0353i | −0.209138 | + | 0.953305i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.76890 | + | 0.720697i | 0.494679 | + | 0.0617992i | ||||
\(137\) | −10.0957 | − | 17.4863i | −0.862534 | − | 1.49395i | −0.869475 | − | 0.493977i | \(-0.835543\pi\) |
0.00694033 | − | 0.999976i | \(-0.497791\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.5005 | −1.90847 | −0.954235 | − | 0.299058i | \(-0.903327\pi\) | ||||
−0.954235 | + | 0.299058i | \(0.903327\pi\) | |||||||
\(140\) | −1.06817 | + | 4.16552i | −0.0902766 | + | 0.352051i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −11.5530 | − | 10.5396i | −0.969509 | − | 0.884466i | ||||
\(143\) | −5.52401 | − | 9.56786i | −0.461941 | − | 0.800105i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.38553 | + | 3.10934i | 0.447244 | + | 0.258217i | ||||
\(146\) | −3.02457 | + | 13.7868i | −0.250315 | + | 1.14100i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.7063 | − | 4.93507i | −0.880054 | − | 0.405660i | ||||
\(149\) | −5.94705 | + | 10.3006i | −0.487201 | + | 0.843857i | −0.999892 | − | 0.0147163i | \(-0.995315\pi\) |
0.512691 | + | 0.858573i | \(0.328649\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.34848 | − | 4.82000i | 0.679390 | − | 0.392246i | −0.120235 | − | 0.992745i | \(-0.538365\pi\) |
0.799625 | + | 0.600499i | \(0.205032\pi\) | |||||||
\(152\) | −8.20124 | + | 3.46081i | −0.665208 | + | 0.280709i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.281892 | − | 8.03675i | 0.0227155 | − | 0.647620i | ||||
\(155\) | 0.835127i | 0.0670790i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.18117 | − | 2.99135i | 0.413503 | − | 0.238736i | −0.278791 | − | 0.960352i | \(-0.589934\pi\) |
0.692294 | + | 0.721616i | \(0.256600\pi\) | |||||||
\(158\) | 10.6214 | − | 3.37470i | 0.844997 | − | 0.268477i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.05412 | − | 2.16759i | 0.320506 | − | 0.171363i | ||||
\(161\) | 4.72430 | + | 1.68552i | 0.372327 | + | 0.132838i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.53520 | + | 4.92780i | 0.668528 | + | 0.385975i | 0.795519 | − | 0.605929i | \(-0.207198\pi\) |
−0.126990 | + | 0.991904i | \(0.540532\pi\) | |||||||
\(164\) | −5.08147 | + | 0.467163i | −0.396796 | + | 0.0364793i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.6850 | + | 18.2893i | −1.29501 | + | 1.41953i | ||||
\(167\) | −20.4794 | −1.58474 | −0.792371 | − | 0.610040i | \(-0.791153\pi\) | ||||
−0.792371 | + | 0.610040i | \(0.791153\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.4242 | −1.03263 | ||||||||
\(170\) | −1.59214 | + | 1.74523i | −0.122112 | + | 0.133853i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −20.4771 | + | 1.88256i | −1.56136 | + | 0.143543i | ||||
\(173\) | −3.46120 | − | 1.99833i | −0.263150 | − | 0.151930i | 0.362620 | − | 0.931937i | \(-0.381882\pi\) |
−0.625771 | + | 0.780007i | \(0.715215\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.43594 | + | 8.74808i | 0.562104 | + | 0.661292i | ||||
\(176\) | −6.53663 | + | 5.58388i | −0.492717 | + | 0.420900i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.754694 | + | 0.239785i | −0.0565667 | + | 0.0179726i | ||||
\(179\) | 15.9493 | − | 9.20832i | 1.19211 | − | 0.688262i | 0.233322 | − | 0.972400i | \(-0.425041\pi\) |
0.958784 | + | 0.284137i | \(0.0917072\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.77700i | 0.652389i | 0.945303 | + | 0.326195i | \(0.105767\pi\) | ||||
−0.945303 | + | 0.326195i | \(0.894233\pi\) | |||||||
\(182\) | −16.3096 | − | 10.1949i | −1.20895 | − | 0.755694i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.08480 | − | 4.94044i | −0.153693 | − | 0.364214i | ||||
\(185\) | 4.14855 | − | 2.39517i | 0.305007 | − | 0.176096i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.20884 | − | 3.82582i | 0.161526 | − | 0.279772i | ||||
\(188\) | −3.85876 | − | 1.77869i | −0.281429 | − | 0.129725i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.775084 | − | 3.53303i | 0.0562305 | − | 0.256313i | ||||
\(191\) | 19.0198 | + | 10.9811i | 1.37623 | + | 0.794565i | 0.991703 | − | 0.128551i | \(-0.0410324\pi\) |
0.384523 | + | 0.923115i | \(0.374366\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.350671 | − | 0.607379i | −0.0252418 | − | 0.0437201i | 0.853129 | − | 0.521701i | \(-0.174702\pi\) |
−0.878370 | + | 0.477981i | \(0.841369\pi\) | |||||||
\(194\) | 1.93008 | + | 1.76078i | 0.138572 | + | 0.126416i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.13331 | − | 12.5850i | −0.438094 | − | 0.898929i | ||||
\(197\) | −23.9596 | −1.70705 | −0.853524 | − | 0.521053i | \(-0.825539\pi\) | ||||
−0.853524 | + | 0.521053i | \(0.825539\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.09676 | + | 1.89965i | 0.0777473 | + | 0.134662i | 0.902278 | − | 0.431155i | \(-0.141894\pi\) |
−0.824530 | + | 0.565818i | \(0.808561\pi\) | |||||||
\(200\) | 1.52155 | − | 12.1794i | 0.107590 | − | 0.861216i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.95034 | − | 22.5649i | 0.348305 | − | 1.58766i | ||||
\(203\) | −19.9151 | + | 3.64246i | −1.39777 | + | 0.255651i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.03675 | − | 1.79571i | 0.0724101 | − | 0.125418i | ||||
\(206\) | −2.04275 | − | 6.42931i | −0.142325 | − | 0.447951i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.74899 | + | 20.2171i | 0.259946 | + | 1.40181i | ||||
\(209\) | 6.76400i | 0.467876i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 11.0443i | − | 0.760320i | −0.924921 | − | 0.380160i | \(-0.875869\pi\) | ||
0.924921 | − | 0.380160i | \(-0.124131\pi\) | |||||||
\(212\) | 10.8507 | − | 7.66926i | 0.745227 | − | 0.526727i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.30908 | + | 2.00455i | −0.431280 | + | 0.137028i | ||||
\(215\) | 4.17787 | − | 7.23629i | 0.284929 | − | 0.493511i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.76086 | − | 2.07158i | −0.119535 | − | 0.140628i | ||||
\(218\) | 11.5928 | + | 2.54326i | 0.785166 | + | 0.172251i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.319804 | − | 3.47860i | −0.0215612 | − | 0.234527i | ||||
\(221\) | −5.28301 | − | 9.15045i | −0.355374 | − | 0.615526i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.4097 | −1.36673 | −0.683367 | − | 0.730075i | \(-0.739485\pi\) | ||||
−0.683367 | + | 0.730075i | \(0.739485\pi\) | |||||||
\(224\) | −5.48612 | + | 13.9249i | −0.366557 | + | 0.930396i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.48111 | + | 2.71968i | −0.165041 | + | 0.180910i | ||||
\(227\) | 2.20721 | + | 3.82300i | 0.146498 | + | 0.253742i | 0.929931 | − | 0.367735i | \(-0.119867\pi\) |
−0.783433 | + | 0.621476i | \(0.786533\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.5530 | − | 9.55686i | −1.09385 | − | 0.631535i | −0.159252 | − | 0.987238i | \(-0.550908\pi\) |
−0.934599 | + | 0.355703i | \(0.884241\pi\) | |||||||
\(230\) | 2.12830 | + | 0.466912i | 0.140336 | + | 0.0307873i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 17.2576 | + | 13.0617i | 1.13302 | + | 0.857545i | ||||
\(233\) | 7.20579 | − | 12.4808i | 0.472067 | − | 0.817644i | −0.527422 | − | 0.849603i | \(-0.676841\pi\) |
0.999489 | + | 0.0319592i | \(0.0101747\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.49522 | − | 0.863264i | 0.0975372 | − | 0.0563131i | ||||
\(236\) | −20.6641 | + | 14.6054i | −1.34512 | + | 0.950729i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.269594 | − | 7.68614i | 0.0174752 | − | 0.498218i | ||||
\(239\) | 13.3320i | 0.862375i | 0.902262 | + | 0.431187i | \(0.141905\pi\) | ||||
−0.902262 | + | 0.431187i | \(0.858095\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.3015 | + | 12.2984i | −1.37215 | + | 0.792210i | −0.991198 | − | 0.132386i | \(-0.957736\pi\) |
−0.380950 | + | 0.924596i | \(0.624403\pi\) | |||||||
\(242\) | −2.73249 | − | 8.60016i | −0.175651 | − | 0.552839i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.98250 | − | 10.8092i | 0.318972 | − | 0.691989i | ||||
\(245\) | 5.61446 | + | 0.916424i | 0.358694 | + | 0.0585482i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.0104 | + | 8.08893i | 0.891463 | + | 0.514687i | ||||
\(248\) | −0.360309 | + | 2.88413i | −0.0228796 | + | 0.183143i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.92989 | + | 7.23430i | 0.501530 | + | 0.457537i | ||||
\(251\) | 1.47312 | 0.0929824 | 0.0464912 | − | 0.998919i | \(-0.485196\pi\) | ||||
0.0464912 | + | 0.998919i | \(0.485196\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.07465 | −0.256171 | ||||||||
\(254\) | 7.00228 | + | 6.38806i | 0.439362 | + | 0.400823i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.9362 | − | 5.73670i | 0.933513 | − | 0.358544i | ||||
\(257\) | 9.23212 | + | 5.33017i | 0.575884 | + | 0.332487i | 0.759496 | − | 0.650512i | \(-0.225446\pi\) |
−0.183612 | + | 0.982999i | \(0.558779\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.24051 | + | 14.6885i | −0.325630 | + | 0.912700i | ||||
\(260\) | −7.58777 | − | 3.49757i | −0.470573 | − | 0.216910i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.31672 | − | 19.8811i | −0.390248 | − | 1.22826i | ||||
\(263\) | 23.1783 | − | 13.3820i | 1.42924 | − | 0.825170i | 0.432175 | − | 0.901790i | \(-0.357746\pi\) |
0.997060 | + | 0.0766200i | \(0.0244128\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.39919i | 0.331670i | ||||||||
\(266\) | 5.52672 | + | 10.3981i | 0.338865 | + | 0.637550i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.22190 | − | 13.0474i | −0.563317 | − | 0.796996i | ||||
\(269\) | −17.3592 | + | 10.0223i | −1.05841 | + | 0.611073i | −0.924992 | − | 0.379987i | \(-0.875929\pi\) |
−0.133418 | + | 0.991060i | \(0.542595\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.36814 | − | 7.56584i | 0.265346 | − | 0.459592i | −0.702309 | − | 0.711873i | \(-0.747847\pi\) |
0.967654 | + | 0.252281i | \(0.0811806\pi\) | |||||||
\(272\) | −6.25146 | + | 5.34027i | −0.379051 | + | 0.323802i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 27.8917 | + | 6.11893i | 1.68500 | + | 0.369658i | ||||
\(275\) | −8.07716 | − | 4.66335i | −0.487071 | − | 0.281211i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.73771 | + | 9.93800i | 0.344746 | + | 0.597117i | 0.985308 | − | 0.170790i | \(-0.0546319\pi\) |
−0.640562 | + | 0.767906i | \(0.721299\pi\) | |||||||
\(278\) | 21.4459 | − | 23.5079i | 1.28624 | − | 1.40991i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.33392 | − | 5.08626i | −0.199240 | − | 0.303962i | ||||
\(281\) | 19.6940 | 1.17484 | 0.587422 | − | 0.809281i | \(-0.300143\pi\) | ||||
0.587422 | + | 0.809281i | \(0.300143\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.80656 | + | 3.12905i | 0.107389 | + | 0.186003i | 0.914712 | − | 0.404107i | \(-0.132418\pi\) |
−0.807323 | + | 0.590110i | \(0.799084\pi\) | |||||||
\(284\) | 22.0230 | − | 2.02468i | 1.30683 | − | 0.120143i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.2613 | + | 3.34806i | 0.902420 | + | 0.197975i | ||||
\(287\) | 1.21452 | + | 6.64034i | 0.0716906 | + | 0.391967i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.38752 | + | 11.0635i | −0.375737 | + | 0.650795i | ||||
\(290\) | −8.38165 | + | 2.66306i | −0.492188 | + | 0.156380i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −11.5212 | − | 16.3005i | −0.674228 | − | 0.953915i | ||||
\(293\) | 26.8845i | 1.57061i | 0.619110 | + | 0.785304i | \(0.287494\pi\) | ||||
−0.619110 | + | 0.785304i | \(0.712506\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 10.2822i | − | 0.598656i | ||||||
\(296\) | 15.3605 | − | 6.48191i | 0.892811 | − | 0.376754i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.09347 | − | 16.0311i | −0.295057 | − | 0.928656i | ||||
\(299\) | −4.87279 | + | 8.43991i | −0.281800 | + | 0.488093i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.89421 | + | 26.7590i | 0.282097 | + | 1.54236i | ||||
\(302\) | −2.92137 | + | 13.3163i | −0.168106 | + | 0.766269i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.20107 | − | 11.8670i | 0.240948 | − | 0.680620i | ||||
\(305\) | 2.41819 | + | 4.18842i | 0.138465 | + | 0.239828i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.99662 | −0.570537 | −0.285269 | − | 0.958448i | \(-0.592083\pi\) | ||||
−0.285269 | + | 0.958448i | \(0.592083\pi\) | |||||||
\(308\) | 8.12789 | + | 7.95456i | 0.463130 | + | 0.453253i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.872517 | − | 0.795982i | −0.0495556 | − | 0.0452087i | ||||
\(311\) | −9.81325 | − | 16.9970i | −0.556458 | − | 0.963814i | −0.997788 | − | 0.0664690i | \(-0.978827\pi\) |
0.441330 | − | 0.897345i | \(-0.354507\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.3657 | + | 11.1808i | 1.09462 | + | 0.631977i | 0.934802 | − | 0.355171i | \(-0.115577\pi\) |
0.159814 | + | 0.987147i | \(0.448911\pi\) | |||||||
\(314\) | −1.81304 | + | 8.26428i | −0.102316 | + | 0.466380i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.59780 | + | 14.3135i | −0.371155 | + | 0.805197i | ||||
\(317\) | −1.16986 | + | 2.02626i | −0.0657061 | + | 0.113806i | −0.897007 | − | 0.442016i | \(-0.854263\pi\) |
0.831301 | + | 0.555823i | \(0.187597\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.2427 | − | 8.22304i | 0.797439 | − | 0.460402i | ||||
\(320\) | −1.59946 | + | 6.30162i | −0.0894125 | + | 0.352271i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.26385 | + | 3.32931i | −0.349071 | + | 0.185535i | ||||
\(323\) | 6.46892i | 0.359940i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −19.3186 | + | 11.1536i | −1.07160 | + | 0.618691i | ||||
\(326\) | −13.2836 | + | 4.22052i | −0.735708 | + | 0.233753i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.35521 | − | 5.75424i | 0.240476 | − | 0.317725i | ||||
\(329\) | −1.88878 | + | 5.29402i | −0.104132 | + | 0.291869i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.7526 | + | 14.8683i | 1.41549 | + | 0.817234i | 0.995898 | − | 0.0904788i | \(-0.0288397\pi\) |
0.419592 | + | 0.907713i | \(0.362173\pi\) | |||||||
\(332\) | −3.20522 | − | 34.8641i | −0.175909 | − | 1.91342i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 19.5194 | − | 21.3963i | 1.06806 | − | 1.17075i | ||||
\(335\) | 6.49226 | 0.354710 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.92824 | −0.105038 | −0.0525191 | − | 0.998620i | \(-0.516725\pi\) | ||||
−0.0525191 | + | 0.998620i | \(0.516725\pi\) | |||||||
\(338\) | 12.7950 | − | 14.0252i | 0.695954 | − | 0.762871i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.305852 | − | 3.32685i | −0.0165872 | − | 0.180424i | ||||
\(341\) | 1.91270 | + | 1.10430i | 0.103579 | + | 0.0598011i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.8592 | + | 9.56478i | −0.856317 | + | 0.516450i | ||||
\(344\) | 17.5504 | − | 23.1882i | 0.946256 | − | 1.25022i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.38676 | − | 1.71151i | 0.289594 | − | 0.0920113i | ||||
\(347\) | −11.6827 | + | 6.74504i | −0.627163 | + | 0.362093i | −0.779652 | − | 0.626212i | \(-0.784604\pi\) |
0.152490 | + | 0.988305i | \(0.451271\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.7410i | 1.21730i | 0.793439 | + | 0.608650i | \(0.208288\pi\) | ||||
−0.793439 | + | 0.608650i | \(0.791712\pi\) | |||||||
\(350\) | −16.2271 | − | 0.569172i | −0.867377 | − | 0.0304235i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.396363 | − | 12.1514i | 0.0211262 | − | 0.647673i | ||||
\(353\) | 22.4215 | − | 12.9450i | 1.19337 | − | 0.688995i | 0.234304 | − | 0.972163i | \(-0.424719\pi\) |
0.959070 | + | 0.283169i | \(0.0913856\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.49328 | + | 7.78259i | −0.238479 | + | 0.413057i | ||||
\(356\) | 0.468798 | − | 1.01703i | 0.0248463 | − | 0.0539024i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.58110 | + | 25.4401i | −0.294970 | + | 1.34455i | ||||
\(359\) | −0.384185 | − | 0.221809i | −0.0202765 | − | 0.0117066i | 0.489827 | − | 0.871819i | \(-0.337060\pi\) |
−0.510104 | + | 0.860113i | \(0.670393\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.54765 | + | 7.87677i | 0.239350 | + | 0.414567i | ||||
\(362\) | −9.16997 | − | 8.36560i | −0.481963 | − | 0.439686i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 26.1964 | − | 7.32281i | 1.37307 | − | 0.383819i | ||||
\(365\) | 8.11098 | 0.424548 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.6052 | + | 23.5650i | 0.710188 | + | 1.23008i | 0.964786 | + | 0.263035i | \(0.0847233\pi\) |
−0.254599 | + | 0.967047i | \(0.581943\pi\) | |||||||
\(368\) | 7.14871 | + | 2.53073i | 0.372652 | + | 0.131924i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.45169 | + | 6.61719i | −0.0754699 | + | 0.344011i | ||||
\(371\) | −11.3841 | − | 13.3930i | −0.591035 | − | 0.695329i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.63311 | + | 14.9530i | −0.447005 | + | 0.774236i | −0.998189 | − | 0.0601476i | \(-0.980843\pi\) |
0.551184 | + | 0.834384i | \(0.314176\pi\) | |||||||
\(374\) | 1.89181 | + | 5.95423i | 0.0978231 | + | 0.307886i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.53622 | − | 2.33621i | 0.285509 | − | 0.120481i | ||||
\(377\) | − | 39.3350i | − | 2.02586i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 30.0266i | − | 1.54236i | −0.636616 | − | 0.771181i | \(-0.719666\pi\) | ||
0.636616 | − | 0.771181i | \(-0.280334\pi\) | |||||||
\(380\) | 2.95246 | + | 4.17721i | 0.151458 | + | 0.214287i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −29.6011 | + | 9.40500i | −1.51452 | + | 0.481201i | ||||
\(383\) | 10.5011 | − | 18.1884i | 0.536581 | − | 0.929386i | −0.462504 | − | 0.886617i | \(-0.653049\pi\) |
0.999085 | − | 0.0427689i | \(-0.0136179\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.54576 | + | 0.831417i | −0.231673 | + | 0.0423729i | ||||
\(386\) | 0.968807 | + | 0.212539i | 0.0493110 | + | 0.0108179i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.67922 | + | 0.338248i | −0.186784 | + | 0.0171719i | ||||
\(389\) | 4.55328 | + | 7.88652i | 0.230861 | + | 0.399862i | 0.958062 | − | 0.286562i | \(-0.0925125\pi\) |
−0.727201 | + | 0.686425i | \(0.759179\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.89688 | −0.197074 | ||||||||
\(392\) | 18.9943 | + | 5.58720i | 0.959357 | + | 0.282196i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 22.8365 | − | 25.0323i | 1.15049 | − | 1.26111i | ||||
\(395\) | −3.20215 | − | 5.54628i | −0.161118 | − | 0.279064i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.92841 | − | 2.26807i | −0.197161 | − | 0.113831i | 0.398169 | − | 0.917312i | \(-0.369646\pi\) |
−0.595331 | + | 0.803481i | \(0.702979\pi\) | |||||||
\(398\) | −3.03005 | − | 0.664739i | −0.151883 | − | 0.0333203i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11.2745 | + | 13.1982i | 0.563725 | + | 0.659911i | ||||
\(401\) | 12.5118 | − | 21.6711i | 0.624810 | − | 1.08220i | −0.363767 | − | 0.931490i | \(-0.618510\pi\) |
0.988577 | − | 0.150714i | \(-0.0481571\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.57472 | − | 2.64122i | 0.227883 | − | 0.131568i | ||||
\(404\) | 18.8569 | + | 26.6792i | 0.938165 | + | 1.32734i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 15.1761 | − | 24.2785i | 0.753177 | − | 1.20492i | ||||
\(407\) | − | 12.6686i | − | 0.627961i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.37147 | − | 1.94652i | 0.166708 | − | 0.0962490i | −0.414325 | − | 0.910129i | \(-0.635982\pi\) |
0.581033 | + | 0.813880i | \(0.302649\pi\) | |||||||
\(410\) | 0.887951 | + | 2.79471i | 0.0438527 | + | 0.138021i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.66417 | + | 3.99374i | 0.426853 | + | 0.196758i | ||||
\(413\) | 21.6800 | + | 25.5057i | 1.06680 | + | 1.25505i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.3204 | + | 7.11320i | 0.604786 | + | 0.349173i | ||||
\(416\) | −24.6956 | − | 15.3526i | −1.21080 | − | 0.752725i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.06684 | − | 6.44696i | −0.345651 | − | 0.315331i | ||||
\(419\) | 11.4873 | 0.561192 | 0.280596 | − | 0.959826i | \(-0.409468\pi\) | ||||
0.280596 | + | 0.959826i | \(0.409468\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.14186 | −0.348073 | −0.174037 | − | 0.984739i | \(-0.555681\pi\) | ||||
−0.174037 | + | 0.984739i | \(0.555681\pi\) | |||||||
\(422\) | 11.5388 | + | 10.5266i | 0.561698 | + | 0.512428i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.32944 | + | 18.6463i | −0.113128 | + | 0.905543i | ||||
\(425\) | −7.72479 | − | 4.45991i | −0.374707 | − | 0.216337i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.8297 | − | 5.29088i | −0.717659 | − | 0.256044i | ||||
\(428\) | 3.91905 | − | 8.50214i | 0.189435 | − | 0.410967i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.57823 | + | 11.2620i | 0.172558 | + | 0.543103i | ||||
\(431\) | 17.9137 | − | 10.3425i | 0.862873 | − | 0.498180i | −0.00210056 | − | 0.999998i | \(-0.500669\pi\) |
0.864973 | + | 0.501818i | \(0.167335\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.4701i | 0.695389i | 0.937608 | + | 0.347695i | \(0.113035\pi\) | ||||
−0.937608 | + | 0.347695i | \(0.886965\pi\) | |||||||
\(434\) | 3.84264 | + | 0.134782i | 0.184453 | + | 0.00646974i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.7066 | + | 9.68782i | −0.656426 | + | 0.463962i | ||||
\(437\) | 5.16723 | − | 2.98330i | 0.247182 | − | 0.142711i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.54215 | − | 4.40313i | 0.121330 | − | 0.210150i | −0.798962 | − | 0.601381i | \(-0.794617\pi\) |
0.920292 | + | 0.391231i | \(0.127951\pi\) | |||||||
\(440\) | 3.93916 | + | 2.98143i | 0.187792 | + | 0.142134i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 14.5955 | + | 3.20200i | 0.694238 | + | 0.152303i | ||||
\(443\) | 4.97946 | + | 2.87489i | 0.236581 | + | 0.136590i | 0.613605 | − | 0.789614i | \(-0.289719\pi\) |
−0.377023 | + | 0.926204i | \(0.623052\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.227525 | + | 0.394084i | 0.0107857 | + | 0.0186814i | ||||
\(446\) | 19.4530 | − | 21.3235i | 0.921128 | − | 1.00970i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −9.31936 | − | 19.0039i | −0.440298 | − | 0.897852i | ||||
\(449\) | 18.3848 | 0.867630 | 0.433815 | − | 0.901002i | \(-0.357167\pi\) | ||||
0.433815 | + | 0.901002i | \(0.357167\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.74183 | − | 4.74898i | −0.129108 | − | 0.223621i | ||||
\(452\) | −0.476626 | − | 5.18440i | −0.0224186 | − | 0.243854i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.09792 | − | 1.33777i | −0.286190 | − | 0.0627849i | ||||
\(455\) | −3.71405 | + | 10.4100i | −0.174117 | + | 0.488029i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.5364 | − | 25.1777i | 0.679982 | − | 1.17776i | −0.295003 | − | 0.955496i | \(-0.595321\pi\) |
0.974986 | − | 0.222268i | \(-0.0713459\pi\) | |||||||
\(458\) | 25.7618 | − | 8.18517i | 1.20377 | − | 0.382468i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.51636 | + | 1.77857i | −0.117326 | + | 0.0829261i | ||||
\(461\) | 27.4011i | 1.27620i | 0.769954 | + | 0.638099i | \(0.220279\pi\) | ||||
−0.769954 | + | 0.638099i | \(0.779721\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 33.6619i | − | 1.56440i | −0.623027 | − | 0.782200i | \(-0.714097\pi\) | ||
0.623027 | − | 0.782200i | \(-0.285903\pi\) | |||||||
\(464\) | −30.0952 | + | 5.58075i | −1.39714 | + | 0.259080i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.17155 | + | 19.4242i | 0.285892 | + | 0.899809i | ||||
\(467\) | −7.28260 | + | 12.6138i | −0.336998 | + | 0.583698i | −0.983867 | − | 0.178903i | \(-0.942745\pi\) |
0.646868 | + | 0.762602i | \(0.276078\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.1044 | + | 13.6889i | −0.743632 | + | 0.632093i | ||||
\(470\) | −0.523218 | + | 2.38496i | −0.0241342 | + | 0.110010i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.43619 | − | 35.5100i | 0.204192 | − | 1.63448i | ||||
\(473\) | −11.0489 | − | 19.1373i | −0.508029 | − | 0.879933i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.6573 | 0.626641 | ||||||||
\(476\) | 7.77330 | + | 7.60753i | 0.356289 | + | 0.348691i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −13.9289 | − | 12.7071i | −0.637093 | − | 0.581209i | ||||
\(479\) | −3.36750 | − | 5.83269i | −0.153865 | − | 0.266502i | 0.778780 | − | 0.627297i | \(-0.215839\pi\) |
−0.932645 | + | 0.360795i | \(0.882505\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.2408 | − | 15.1502i | −1.19648 | − | 0.690788i | ||||
\(482\) | 7.45398 | − | 33.9771i | 0.339519 | − | 1.54762i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.5896 | + | 5.34222i | 0.526801 | + | 0.242828i | ||||
\(485\) | 0.750659 | − | 1.30018i | 0.0340857 | − | 0.0590381i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.48186 | − | 2.58760i | 0.203093 | − | 0.117256i | −0.395005 | − | 0.918679i | \(-0.629257\pi\) |
0.598097 | + | 0.801424i | \(0.295924\pi\) | |||||||
\(488\) | 6.54421 | + | 15.5081i | 0.296243 | + | 0.702021i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.30874 | + | 4.99236i | −0.285000 | + | 0.225532i | ||||
\(491\) | − | 4.23104i | − | 0.190944i | −0.995432 | − | 0.0954720i | \(-0.969564\pi\) | ||
0.995432 | − | 0.0954720i | \(-0.0304360\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.6214 | − | 7.86430i | 0.613475 | − | 0.354190i | ||||
\(494\) | −21.8048 | + | 6.92794i | −0.981046 | + | 0.311703i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.66984 | − | 3.12539i | −0.119879 | − | 0.140334i | ||||
\(497\) | −5.26369 | − | 28.7792i | −0.236109 | − | 1.29092i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.9498 | + | 14.4048i | 1.11691 | + | 0.644846i | 0.940609 | − | 0.339491i | \(-0.110255\pi\) |
0.176297 | + | 0.984337i | \(0.443588\pi\) | |||||||
\(500\) | −15.1164 | + | 1.38972i | −0.676025 | + | 0.0621501i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.40407 | + | 1.53907i | −0.0626667 | + | 0.0686922i | ||||
\(503\) | −33.0972 | −1.47573 | −0.737865 | − | 0.674948i | \(-0.764166\pi\) | ||||
−0.737865 | + | 0.674948i | \(0.764166\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.2753 | −0.590744 | ||||||||
\(506\) | 3.88366 | − | 4.25708i | 0.172650 | − | 0.189250i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −13.3481 | + | 1.22716i | −0.592228 | + | 0.0544462i | ||||
\(509\) | 16.1832 | + | 9.34337i | 0.717308 | + | 0.414138i | 0.813761 | − | 0.581200i | \(-0.197416\pi\) |
−0.0964533 | + | 0.995338i | \(0.530750\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20.1197 | + | 17.1019i | −0.890044 | + | 0.756544i | ||||
\(512\) | −8.24255 | + | 21.0727i | −0.364273 | + | 0.931292i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −14.3682 | + | 4.56513i | −0.633754 | + | 0.201359i | ||||
\(515\) | −3.35725 | + | 1.93831i | −0.147938 | + | 0.0854120i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 4.56602i | − | 0.200813i | ||||||
\(518\) | −10.3513 | − | 19.4752i | −0.454809 | − | 0.855689i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10.8863 | − | 4.59385i | 0.477395 | − | 0.201454i | ||||
\(521\) | −17.4125 | + | 10.0531i | −0.762855 | + | 0.440435i | −0.830320 | − | 0.557287i | \(-0.811842\pi\) |
0.0674646 | + | 0.997722i | \(0.478509\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.3935 | − | 18.0021i | 0.454476 | − | 0.787175i | −0.544182 | − | 0.838967i | \(-0.683160\pi\) |
0.998658 | + | 0.0517922i | \(0.0164933\pi\) | |||||||
\(524\) | 26.7919 | + | 12.3497i | 1.17041 | + | 0.539499i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.11073 | + | 36.9708i | −0.353645 | + | 1.61200i | ||||
\(527\) | 1.82926 | + | 1.05612i | 0.0796837 | + | 0.0460054i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.70286 | − | 16.8058i | −0.421863 | − | 0.730689i | ||||
\(530\) | −5.64093 | − | 5.14612i | −0.245026 | − | 0.223533i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −16.1313 | − | 4.13657i | −0.699382 | − | 0.179343i | ||||
\(533\) | −13.1156 | −0.568099 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.90206 | + | 3.29446i | 0.0822332 | + | 0.142432i | ||||
\(536\) | 22.4212 | + | 2.80103i | 0.968448 | + | 0.120986i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.07447 | − | 27.6890i | 0.261889 | − | 1.19376i | ||||
\(539\) | 9.52296 | − | 11.6471i | 0.410183 | − | 0.501674i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.1843 | − | 26.3000i | 0.652824 | − | 1.13072i | −0.329611 | − | 0.944117i | \(-0.606917\pi\) |
0.982435 | − | 0.186607i | \(-0.0597492\pi\) | |||||||
\(542\) | 3.74118 | + | 11.7749i | 0.160698 | + | 0.505776i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.379071 | − | 11.6213i | 0.0162525 | − | 0.498260i | ||||
\(545\) | − | 6.82026i | − | 0.292148i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.2770i | 0.567685i | 0.958871 | + | 0.283842i | \(0.0916092\pi\) | ||||
−0.958871 | + | 0.283842i | \(0.908391\pi\) | |||||||
\(548\) | −32.9772 | + | 23.3083i | −1.40872 | + | 0.995682i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 12.5707 | − | 3.99403i | 0.536017 | − | 0.170306i | ||||
\(551\) | −12.0412 | + | 20.8560i | −0.512972 | + | 0.888493i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.6374 | + | 7.00615i | 0.835066 | + | 0.297932i | ||||
\(554\) | −15.8517 | − | 3.47758i | −0.673475 | − | 0.147748i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.11978 | + | 44.8121i | 0.174718 | + | 1.90046i | ||||
\(557\) | 15.4608 | + | 26.7788i | 0.655093 | + | 1.13465i | 0.981870 | + | 0.189553i | \(0.0607040\pi\) |
−0.326777 | + | 0.945101i | \(0.605963\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −52.8527 | −2.23543 | ||||||||
\(560\) | 8.49163 | + | 1.36467i | 0.358837 | + | 0.0576678i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −18.7709 | + | 20.5757i | −0.791801 | + | 0.867934i | ||||
\(563\) | 11.6019 | + | 20.0950i | 0.488960 | + | 0.846904i | 0.999919 | − | 0.0127010i | \(-0.00404296\pi\) |
−0.510959 | + | 0.859605i | \(0.670710\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.83209 | + | 1.05776i | 0.0770764 | + | 0.0445001i | ||||
\(566\) | −4.99102 | − | 1.09494i | −0.209788 | − | 0.0460238i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −18.8754 | + | 24.9388i | −0.791994 | + | 1.04641i | ||||
\(569\) | −6.30064 | + | 10.9130i | −0.264137 | + | 0.457498i | −0.967337 | − | 0.253494i | \(-0.918420\pi\) |
0.703200 | + | 0.710992i | \(0.251754\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.0513 | + | 20.8142i | −1.50870 | + | 0.871049i | −0.508752 | + | 0.860913i | \(0.669893\pi\) |
−0.999949 | + | 0.0101362i | \(0.996774\pi\) | |||||||
\(572\) | −18.0439 | + | 12.7535i | −0.754455 | + | 0.533249i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.09523 | − | 5.06020i | −0.337888 | − | 0.211209i | ||||
\(575\) | 8.22719i | 0.343097i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.5101 | − | 11.2642i | 0.812218 | − | 0.468934i | −0.0355075 | − | 0.999369i | \(-0.511305\pi\) |
0.847726 | + | 0.530435i | \(0.177971\pi\) | |||||||
\(578\) | −5.47073 | − | 17.2184i | −0.227552 | − | 0.716193i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.20649 | − | 11.2951i | 0.216188 | − | 0.469006i | ||||
\(581\) | −45.5596 | + | 8.33282i | −1.89013 | + | 0.345704i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.3658 | + | 7.13942i | 0.512141 | + | 0.295685i | ||||
\(584\) | 28.0115 | + | 3.49942i | 1.15912 | + | 0.144807i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28.0882 | − | 25.6243i | −1.16031 | − | 1.05853i | ||||
\(587\) | 8.49214 | 0.350508 | 0.175254 | − | 0.984523i | \(-0.443925\pi\) | ||||
0.175254 | + | 0.984523i | \(0.443925\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.23410 | −0.133259 | ||||||||
\(590\) | 10.7426 | + | 9.80029i | 0.442266 | + | 0.403472i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.86839 | + | 22.2263i | −0.323389 | + | 0.913496i | ||||
\(593\) | 0.699256 | + | 0.403715i | 0.0287150 | + | 0.0165786i | 0.514289 | − | 0.857617i | \(-0.328056\pi\) |
−0.485574 | + | 0.874196i | \(0.661389\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.34745 | + | 0.795145i | −0.178228 | + | 0.0325978i | ||||
\(596\) | 21.6036 | + | 9.95814i | 0.884916 | + | 0.407901i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.17340 | − | 13.1353i | −0.170663 | − | 0.537141i | ||||
\(599\) | 27.9459 | − | 16.1346i | 1.14184 | − | 0.659240i | 0.194953 | − | 0.980813i | \(-0.437545\pi\) |
0.946885 | + | 0.321572i | \(0.104211\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.37514i | 0.0968838i | 0.998826 | + | 0.0484419i | \(0.0154256\pi\) | ||||
−0.998826 | + | 0.0484419i | \(0.984574\pi\) | |||||||
\(602\) | −32.6219 | − | 20.3914i | −1.32957 | − | 0.831092i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11.1281 | − | 15.7443i | −0.452796 | − | 0.640627i | ||||
\(605\) | −4.49082 | + | 2.59277i | −0.182578 | + | 0.105411i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.99848 | − | 15.5858i | 0.365237 | − | 0.632609i | −0.623577 | − | 0.781762i | \(-0.714321\pi\) |
0.988814 | + | 0.149153i | \(0.0476545\pi\) | |||||||
\(608\) | 8.39417 | + | 15.6999i | 0.340429 | + | 0.636717i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.68079 | − | 1.46565i | −0.270497 | − | 0.0593423i | ||||
\(611\) | −9.45770 | − | 5.46041i | −0.382618 | − | 0.220904i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.95667 | + | 15.5134i | 0.361757 | + | 0.626581i | 0.988250 | − | 0.152846i | \(-0.0488438\pi\) |
−0.626493 | + | 0.779427i | \(0.715510\pi\) | |||||||
\(614\) | 9.52805 | − | 10.4442i | 0.384521 | − | 0.421493i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −16.0576 | + | 0.910090i | −0.646980 | + | 0.0366686i | ||||
\(617\) | −7.48143 | −0.301191 | −0.150596 | − | 0.988595i | \(-0.548119\pi\) | ||||
−0.150596 | + | 0.988595i | \(0.548119\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.6007 | + | 25.2892i | 0.586852 | + | 1.01646i | 0.994642 | + | 0.103381i | \(0.0329662\pi\) |
−0.407790 | + | 0.913076i | \(0.633700\pi\) | |||||||
\(620\) | 1.66324 | − | 0.152909i | 0.0667973 | − | 0.00614099i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 27.1113 | + | 5.94774i | 1.08706 | + | 0.238482i | ||||
\(623\) | −1.39531 | − | 0.497814i | −0.0559019 | − | 0.0199445i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.76474 | + | 13.4489i | −0.310589 | + | 0.537957i | ||||
\(626\) | −30.1394 | + | 9.57604i | −1.20461 | + | 0.382735i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.90624 | − | 9.77112i | −0.275589 | − | 0.389910i | ||||
\(629\) | − | 12.1159i | − | 0.483094i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 3.89890i | − | 0.155213i | −0.996984 | − | 0.0776063i | \(-0.975272\pi\) | ||
0.996984 | − | 0.0776063i | \(-0.0247277\pi\) | |||||||
\(632\) | −8.66581 | − | 20.5358i | −0.344707 | − | 0.816870i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.00195 | − | 3.15353i | −0.0397927 | − | 0.125243i | ||||
\(635\) | 2.72338 | − | 4.71702i | 0.108074 | − | 0.187189i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.7365 | − | 33.6536i | −0.504639 | − | 1.33341i | ||||
\(638\) | −4.98392 | + | 22.7180i | −0.197315 | + | 0.899414i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −5.05927 | − | 7.67731i | −0.199985 | − | 0.303472i | ||||
\(641\) | 1.10624 | + | 1.91606i | 0.0436938 | + | 0.0756799i | 0.887045 | − | 0.461683i | \(-0.152754\pi\) |
−0.843351 | + | 0.537362i | \(0.819421\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −32.8438 | −1.29523 | −0.647616 | − | 0.761967i | \(-0.724234\pi\) | ||||
−0.647616 | + | 0.761967i | \(0.724234\pi\) | |||||||
\(644\) | 2.49188 | − | 9.71754i | 0.0981937 | − | 0.382925i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.75854 | − | 6.16570i | −0.265911 | − | 0.242586i | ||||
\(647\) | 16.0315 | + | 27.7674i | 0.630263 | + | 1.09165i | 0.987498 | + | 0.157633i | \(0.0503864\pi\) |
−0.357234 | + | 0.934015i | \(0.616280\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23.5496 | − | 13.5963i | −0.924401 | − | 0.533703i | ||||
\(650\) | 6.76013 | − | 30.8144i | 0.265154 | − | 1.20864i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.25144 | − | 17.9010i | 0.323151 | − | 0.701056i | ||||
\(653\) | −15.9326 | + | 27.5961i | −0.623491 | + | 1.07992i | 0.365340 | + | 0.930874i | \(0.380953\pi\) |
−0.988831 | + | 0.149044i | \(0.952380\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.3815 | + | 5.99375i | −0.405638 | + | 0.234195i | ||||
\(656\) | 1.86080 | + | 10.0347i | 0.0726522 | + | 0.391790i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.73080 | − | 7.01922i | −0.145442 | − | 0.273638i | ||||
\(659\) | 16.2660i | 0.633634i | 0.948487 | + | 0.316817i | \(0.102614\pi\) | ||||
−0.948487 | + | 0.316817i | \(0.897386\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.3471 | − | 21.5624i | 1.45263 | − | 0.838679i | 0.454004 | − | 0.891000i | \(-0.349995\pi\) |
0.998630 | + | 0.0523206i | \(0.0166618\pi\) | |||||||
\(662\) | −40.0794 | + | 12.7342i | −1.55773 | + | 0.494930i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 39.4800 | + | 29.8812i | 1.53212 | + | 1.15961i | ||||
\(665\) | 5.15594 | − | 4.38259i | 0.199939 | − | 0.169949i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.5637 | − | 7.25363i | −0.486467 | − | 0.280862i | ||||
\(668\) | 3.74971 | + | 40.7867i | 0.145081 | + | 1.57809i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.18795 | + | 6.78293i | −0.239061 | + | 0.262048i | ||||
\(671\) | 12.7904 | 0.493768 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.3814 | 0.785645 | 0.392822 | − | 0.919614i | \(-0.371499\pi\) | ||||
0.392822 | + | 0.919614i | \(0.371499\pi\) | |||||||
\(674\) | 1.83786 | − | 2.01458i | 0.0707918 | − | 0.0775986i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.45793 | + | 26.7356i | 0.0945358 | + | 1.02829i | ||||
\(677\) | −31.8523 | − | 18.3900i | −1.22419 | − | 0.706784i | −0.258378 | − | 0.966044i | \(-0.583188\pi\) |
−0.965807 | + | 0.259260i | \(0.916521\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.879366 | + | 4.80792i | 0.0337470 | + | 0.184511i | ||||
\(680\) | 3.76731 | + | 2.85136i | 0.144470 | + | 0.109345i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.97679 | + | 0.945800i | −0.113987 | + | 0.0362165i | ||||
\(683\) | −29.7576 | + | 17.1805i | −1.13864 | + | 0.657395i | −0.946094 | − | 0.323892i | \(-0.895008\pi\) |
−0.192548 | + | 0.981288i | \(0.561675\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 16.4091i | − | 0.626961i | ||||||
\(686\) | 5.12283 | − | 25.6857i | 0.195591 | − | 0.980686i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.49860 | + | 40.4375i | 0.285881 | + | 1.54167i | ||||
\(689\) | 29.5761 | − | 17.0758i | 1.12676 | − | 0.650535i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.0149 | − | 41.5950i | 0.913568 | − | 1.58235i | 0.104584 | − | 0.994516i | \(-0.466649\pi\) |
0.808984 | − | 0.587830i | \(-0.200018\pi\) | |||||||
\(692\) | −3.34613 | + | 7.25923i | −0.127201 | + | 0.275954i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.08812 | − | 18.6347i | 0.155183 | − | 0.707363i | ||||
\(695\) | −15.8359 | − | 9.14286i | −0.600690 | − | 0.346808i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.62221 | − | 4.54180i | −0.0993234 | − | 0.172033i | ||||
\(698\) | −23.7592 | − | 21.6751i | −0.899298 | − | 0.820414i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 16.0612 | − | 16.4112i | 0.607056 | − | 0.620284i | ||||
\(701\) | 1.33206 | 0.0503111 | 0.0251555 | − | 0.999684i | \(-0.491992\pi\) | ||||
0.0251555 | + | 0.999684i | \(0.491992\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.27549 | + | 16.0656i | 0.349832 | + | 0.605926i | ||||
\(704\) | 12.3177 | + | 11.9960i | 0.464240 | + | 0.452115i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.84589 | + | 35.7636i | −0.295284 | + | 1.34598i | ||||
\(707\) | 32.9301 | − | 27.9909i | 1.23847 | − | 1.05271i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.9986 | − | 27.7104i | 0.600840 | − | 1.04068i | −0.391855 | − | 0.920027i | \(-0.628166\pi\) |
0.992694 | − | 0.120658i | \(-0.0385003\pi\) | |||||||
\(710\) | −3.84837 | − | 12.1123i | −0.144427 | − | 0.454565i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.615738 | + | 1.45915i | 0.0230758 | + | 0.0546838i | ||||
\(713\) | − | 1.94823i | − | 0.0729617i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 8.97849i | − | 0.335777i | ||||||
\(716\) | −21.2596 | − | 30.0786i | −0.794507 | − | 1.12409i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.597917 | − | 0.189973i | 0.0223141 | − | 0.00708973i | ||||
\(719\) | −1.60377 | + | 2.77780i | −0.0598104 | + | 0.103595i | −0.894380 | − | 0.447308i | \(-0.852383\pi\) |
0.834570 | + | 0.550902i | \(0.185716\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.24092 | − | 11.8868i | 0.157940 | − | 0.442687i | ||||
\(722\) | −12.5639 | − | 2.75630i | −0.467581 | − | 0.102579i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 17.4803 | − | 1.60704i | 0.649650 | − | 0.0597253i | ||||
\(725\) | −16.6033 | − | 28.7577i | −0.616630 | − | 1.06803i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −50.4852 | −1.87239 | −0.936197 | − | 0.351477i | \(-0.885680\pi\) | ||||
−0.936197 | + | 0.351477i | \(0.885680\pi\) | |||||||
\(728\) | −17.3179 | + | 34.3489i | −0.641843 | + | 1.27305i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7.73080 | + | 8.47413i | −0.286130 | + | 0.313642i | ||||
\(731\) | −10.5669 | − | 18.3024i | −0.390830 | − | 0.676938i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.98706 | − | 2.87928i | −0.184201 | − | 0.106349i | 0.405064 | − | 0.914288i | \(-0.367249\pi\) |
−0.589265 | + | 0.807940i | \(0.700583\pi\) | |||||||
\(734\) | −37.5875 | − | 8.24604i | −1.38738 | − | 0.304367i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.45767 | + | 5.05666i | −0.348614 | + | 0.186391i | ||||
\(737\) | 8.58479 | − | 14.8693i | 0.316225 | − | 0.547718i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.7520 | − | 13.1359i | 0.836945 | − | 0.483210i | −0.0192796 | − | 0.999814i | \(-0.506137\pi\) |
0.856225 | + | 0.516604i | \(0.172804\pi\) | |||||||
\(740\) | −5.52980 | − | 7.82371i | −0.203280 | − | 0.287605i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 24.8432 | + | 0.871382i | 0.912021 | + | 0.0319894i | ||||
\(743\) | − | 1.42155i | − | 0.0521516i | −0.999660 | − | 0.0260758i | \(-0.991699\pi\) | ||
0.999660 | − | 0.0260758i | \(-0.00830112\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.37108 | + | 4.83304i | −0.306693 | + | 0.177069i | ||||
\(746\) | −7.39401 | − | 23.2717i | −0.270714 | − | 0.852038i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.02395 | − | 3.69863i | −0.293385 | − | 0.135235i | ||||
\(749\) | −11.6645 | − | 4.16162i | −0.426211 | − | 0.152062i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.4368 | + | 23.9235i | 1.51205 | + | 0.872982i | 0.999901 | + | 0.0140857i | \(0.00448377\pi\) |
0.512149 | + | 0.858897i | \(0.328850\pi\) | |||||||
\(752\) | −2.83592 | + | 8.01079i | −0.103415 | + | 0.292123i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 41.0962 | + | 37.4913i | 1.49663 | + | 1.36535i | ||||
\(755\) | 7.83423 | 0.285117 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.0162 | 1.12730 | 0.563651 | − | 0.826013i | \(-0.309396\pi\) | ||||
0.563651 | + | 0.826013i | \(0.309396\pi\) | |||||||
\(758\) | 31.3709 | + | 28.6191i | 1.13944 | + | 1.03949i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.17831 | − | 0.896771i | −0.260385 | − | 0.0325293i | ||||
\(761\) | −10.0676 | − | 5.81256i | −0.364952 | − | 0.210705i | 0.306299 | − | 0.951935i | \(-0.400909\pi\) |
−0.671251 | + | 0.741230i | \(0.734243\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.3805 | + | 16.9180i | 0.520607 | + | 0.612473i | ||||
\(764\) | 18.3875 | − | 39.8905i | 0.665236 | − | 1.44319i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.99389 | + | 28.3072i | 0.324963 | + | 1.02278i | ||||
\(767\) | −56.3249 | + | 32.5192i | −2.03377 | + | 1.17420i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 27.9395i | − | 1.00752i | −0.863843 | − | 0.503762i | \(-0.831949\pi\) | ||
0.863843 | − | 0.503762i | \(-0.168051\pi\) | |||||||
\(770\) | 3.46405 | − | 5.54173i | 0.124836 | − | 0.199710i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.14545 | + | 0.809605i | −0.0412257 | + | 0.0291383i | ||||
\(773\) | −46.4286 | + | 26.8056i | −1.66992 | + | 0.964129i | −0.702243 | + | 0.711938i | \(0.747818\pi\) |
−0.967677 | + | 0.252191i | \(0.918849\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.22971 | − | 3.86197i | 0.0800935 | − | 0.138726i | ||||
\(776\) | 3.15337 | − | 4.16634i | 0.113200 | − | 0.149563i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −12.5795 | − | 2.75971i | −0.450996 | − | 0.0989404i | ||||
\(779\) | 6.95405 | + | 4.01492i | 0.249155 | + | 0.143850i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.8830 | + | 20.5820i | 0.425209 | + | 0.736483i | ||||
\(782\) | 3.71423 | − | 4.07136i | 0.132820 | − | 0.145591i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −23.9413 | + | 14.5194i | −0.855048 | + | 0.518550i | ||||
\(785\) | 4.86202 | 0.173533 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.7021 | − | 35.8571i | −0.737950 | − | 1.27817i | −0.953417 | − | 0.301656i | \(-0.902461\pi\) |
0.215467 | − | 0.976511i | \(-0.430873\pi\) | |||||||
\(788\) | 4.38693 | + | 47.7179i | 0.156278 | + | 1.69988i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.84666 | + | 1.94080i | 0.314750 | + | 0.0690505i | ||||
\(791\) | −6.77485 | + | 1.23912i | −0.240886 | + | 0.0440579i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.2958 | − | 26.4931i | 0.543169 | − | 0.940796i | ||||
\(794\) | 6.11389 | − | 1.94254i | 0.216974 | − | 0.0689380i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.58252 | − | 2.53213i | 0.126979 | − | 0.0897490i | ||||
\(797\) | 10.5390i | 0.373311i | 0.982425 | + | 0.186656i | \(0.0597648\pi\) | ||||
−0.982425 | + | 0.186656i | \(0.940235\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 4.36682i | − | 0.154487i | ||||||
\(800\) | −24.5352 | − | 0.800303i | −0.867449 | − | 0.0282950i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 10.7160 | + | 33.7273i | 0.378396 | + | 1.19095i | ||||
\(803\) | 10.7253 | − | 18.5767i | 0.378486 | − | 0.655557i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.64008 | + | 3.10594i | 0.0930505 | + | 0.109470i | ||||
\(806\) | −1.60082 | + | 7.29695i | −0.0563865 | + | 0.257024i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −45.8467 | − | 5.72753i | −1.61288 | − | 0.201494i | ||||
\(809\) | 19.6904 | + | 34.1047i | 0.692276 | + | 1.19906i | 0.971090 | + | 0.238712i | \(0.0767252\pi\) |
−0.278814 | + | 0.960345i | \(0.589941\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.44942 | 0.191355 | 0.0956775 | − | 0.995412i | \(-0.469498\pi\) | ||||
0.0956775 | + | 0.995412i | \(0.469498\pi\) | |||||||
\(812\) | 10.9007 | + | 38.9960i | 0.382541 | + | 1.36849i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 13.2358 | + | 12.0748i | 0.463916 | + | 0.423222i | ||||
\(815\) | 4.00472 | + | 6.93638i | 0.140279 | + | 0.242971i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28.0232 | + | 16.1792i | 0.980407 | + | 0.566038i | ||||
\(818\) | −1.17977 | + | 5.37769i | −0.0412497 | + | 0.188027i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.76617 | − | 1.73601i | −0.131520 | − | 0.0606242i | ||||
\(821\) | −16.0464 | + | 27.7932i | −0.560024 | + | 0.969990i | 0.437469 | + | 0.899233i | \(0.355875\pi\) |
−0.997494 | + | 0.0707570i | \(0.977459\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.0465 | − | 16.1927i | 0.977640 | − | 0.564440i | 0.0760829 | − | 0.997101i | \(-0.475759\pi\) |
0.901557 | + | 0.432661i | \(0.142425\pi\) | |||||||
\(824\) | −12.4306 | + | 5.24554i | −0.433041 | + | 0.182737i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −47.3114 | − | 1.65946i | −1.64617 | − | 0.0577401i | ||||
\(827\) | 15.1100i | 0.525426i | 0.964874 | + | 0.262713i | \(0.0846173\pi\) | ||||
−0.964874 | + | 0.262713i | \(0.915383\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.0615 | + | 15.0466i | −0.905153 | + | 0.522590i | −0.878868 | − | 0.477064i | \(-0.841701\pi\) |
−0.0262843 | + | 0.999655i | \(0.508368\pi\) | |||||||
\(830\) | −19.1746 | + | 6.09225i | −0.665561 | + | 0.211465i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 39.5780 | − | 11.1682i | 1.37212 | − | 0.387188i | ||||
\(833\) | 9.10751 | − | 11.1389i | 0.315557 | − | 0.385941i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.4134 | − | 8.32158i | −0.498796 | − | 0.287980i | ||||
\(836\) | 13.4712 | − | 1.23847i | 0.465911 | − | 0.0428334i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −10.9489 | + | 12.0016i | −0.378222 | + | 0.414589i | ||||
\(839\) | −14.7609 | −0.509602 | −0.254801 | − | 0.966993i | \(-0.582010\pi\) | ||||
−0.254801 | + | 0.966993i | \(0.582010\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.5542 | 1.01911 | ||||||||
\(842\) | 6.80710 | − | 7.46162i | 0.234588 | − | 0.257144i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −21.9958 | + | 2.02218i | −0.757128 | + | 0.0696063i | ||||
\(845\) | −9.44796 | − | 5.45478i | −0.325020 | − | 0.187650i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.67287 | − | 15.9003i | 0.194922 | − | 0.546342i | ||||
\(848\) | −17.2608 | − | 20.2060i | −0.592740 | − | 0.693877i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 12.0223 | − | 3.81978i | 0.412361 | − | 0.131017i | ||||
\(851\) | −9.67795 | + | 5.58757i | −0.331756 | + | 0.191539i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.60254i | 0.226067i | 0.993591 | + | 0.113033i | \(0.0360567\pi\) | ||||
−0.993591 | + | 0.113033i | \(0.963943\pi\) | |||||||
\(854\) | 19.6623 | − | 10.4508i | 0.672831 | − | 0.357618i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.14744 | + | 12.1981i | 0.175936 | + | 0.416924i | ||||
\(857\) | 2.44768 | − | 1.41317i | 0.0836111 | − | 0.0482729i | −0.457612 | − | 0.889152i | \(-0.651295\pi\) |
0.541223 | + | 0.840879i | \(0.317962\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.29006 | + | 14.3588i | −0.282853 | + | 0.489916i | −0.972086 | − | 0.234624i | \(-0.924614\pi\) |
0.689233 | + | 0.724540i | \(0.257948\pi\) | |||||||
\(860\) | −15.1768 | − | 6.99572i | −0.517523 | − | 0.238552i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.26850 | + | 28.5734i | −0.213506 | + | 0.973215i | ||||
\(863\) | −3.90041 | − | 2.25190i | −0.132771 | − | 0.0766557i | 0.432143 | − | 0.901805i | \(-0.357758\pi\) |
−0.564915 | + | 0.825149i | \(0.691091\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.62400 | − | 2.81285i | −0.0552176 | − | 0.0956397i | ||||
\(866\) | −15.1180 | − | 13.7919i | −0.513729 | − | 0.468666i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.80334 | + | 3.88622i | −0.129094 | + | 0.131907i | ||||
\(869\) | −16.9370 | −0.574547 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.5328 | − | 35.5638i | −0.695726 | − | 1.20503i | ||||
\(872\) | 2.94255 | − | 23.5540i | 0.0996472 | − | 0.797638i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.80816 | + | 8.24204i | −0.0611618 | + | 0.278791i | ||||
\(875\) | 3.61295 | + | 19.7537i | 0.122140 | + | 0.667798i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.22271 | + | 2.11780i | −0.0412880 | + | 0.0715130i | −0.885931 | − | 0.463817i | \(-0.846479\pi\) |
0.844643 | + | 0.535330i | \(0.179813\pi\) | |||||||
\(878\) | 2.17727 | + | 6.85270i | 0.0734795 | + | 0.231268i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.86944 | + | 1.27385i | −0.231569 | + | 0.0429413i | ||||
\(881\) | − | 46.1550i | − | 1.55500i | −0.628883 | − | 0.777500i | \(-0.716487\pi\) | ||
0.628883 | − | 0.777500i | \(-0.283513\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.58454i | 0.221587i | 0.993843 | + | 0.110794i | \(0.0353393\pi\) | ||||
−0.993843 | + | 0.110794i | \(0.964661\pi\) | |||||||
\(884\) | −17.2567 | + | 12.1971i | −0.580407 | + | 0.410232i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.74967 | + | 2.46226i | −0.260355 | + | 0.0827214i | ||||
\(887\) | −3.75381 | + | 6.50180i | −0.126041 | + | 0.218309i | −0.922139 | − | 0.386858i | \(-0.873560\pi\) |
0.796099 | + | 0.605167i | \(0.206894\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.19032 | + | 17.4430i | 0.107000 | + | 0.585021i | ||||
\(890\) | −0.628589 | − | 0.137901i | −0.0210703 | − | 0.00462246i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.73696 | + | 40.6480i | 0.125123 | + | 1.36100i | ||||
\(893\) | 3.34306 | + | 5.79036i | 0.111871 | + | 0.193767i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.9668 | 0.500286 | ||||||||
\(896\) | 28.7373 | + | 8.37657i | 0.960046 | + | 0.279841i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −17.5230 | + | 19.2079i | −0.584750 | + | 0.640975i | ||||
\(899\) | 3.93171 | + | 6.80993i | 0.131130 | + | 0.227124i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.8264 | + | 6.82796i | 0.393993 | + | 0.227472i | ||||
\(902\) | 7.57492 | + | 1.66180i | 0.252217 | + | 0.0553319i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.87080 | + | 4.44343i | 0.195260 | + | 0.147786i | ||||
\(905\) | −3.56645 | + | 6.17726i | −0.118553 | + | 0.205339i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.8284 | − | 13.1800i | 0.758005 | − | 0.437634i | −0.0705742 | − | 0.997507i | \(-0.522483\pi\) |
0.828579 | + | 0.559872i | \(0.189150\pi\) | |||||||
\(908\) | 7.20976 | − | 5.09587i | 0.239264 | − | 0.169112i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.33614 | − | 13.8024i | −0.243191 | − | 0.457545i | ||||
\(911\) | − | 41.7614i | − | 1.38362i | −0.722081 | − | 0.691808i | \(-0.756814\pi\) | ||
0.722081 | − | 0.691808i | \(-0.243186\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.5829 | − | 18.8118i | 1.07834 | − | 0.622578i | ||||
\(914\) | 12.4500 | + | 39.1848i | 0.411809 | + | 1.29612i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.0026 | + | 34.7167i | −0.528742 | + | 1.14707i | ||||
\(917\) | 13.1140 | − | 36.7570i | 0.433064 | − | 1.21382i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.1773 | + | 9.91735i | 0.566628 | + | 0.327143i | 0.755802 | − | 0.654801i | \(-0.227247\pi\) |
−0.189173 | + | 0.981944i | \(0.560581\pi\) | |||||||
\(920\) | 0.540216 | − | 4.32422i | 0.0178104 | − | 0.142565i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −28.6280 | − | 26.1168i | −0.942811 | − | 0.860110i | ||||
\(923\) | 56.8428 | 1.87100 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.5795 | −0.841047 | ||||||||
\(926\) | 35.1690 | + | 32.0840i | 1.15572 | + | 1.05435i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 22.8539 | − | 36.7618i | 0.750218 | − | 1.20677i | ||||
\(929\) | 48.7429 | + | 28.1417i | 1.59920 | + | 0.923301i | 0.991641 | + | 0.129029i | \(0.0411862\pi\) |
0.607563 | + | 0.794271i | \(0.292147\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.54893 | + | 21.7425i | −0.116311 | + | 0.712581i | ||||
\(932\) | −26.1761 | − | 12.0659i | −0.857428 | − | 0.395231i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.23733 | − | 19.6312i | −0.204092 | − | 0.642354i | ||||
\(935\) | 3.10917 | − | 1.79508i | 0.101681 | − | 0.0587054i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.78557i | − | 0.0910006i | −0.998964 | − | 0.0455003i | \(-0.985512\pi\) | ||
0.998964 | − | 0.0455003i | \(-0.0144882\pi\) | |||||||
\(938\) | 1.04779 | − | 29.8726i | 0.0342116 | − | 0.975376i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.99305 | − | 2.81981i | −0.0650060 | − | 0.0919722i | ||||
\(941\) | 42.7539 | − | 24.6840i | 1.39374 | − | 0.804674i | 0.400009 | − | 0.916511i | \(-0.369007\pi\) |
0.993727 | + | 0.111837i | \(0.0356735\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.41860 | + | 4.18913i | −0.0787603 | + | 0.136417i | ||||
\(944\) | 32.8716 | + | 38.4804i | 1.06988 | + | 1.25243i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 30.5251 | + | 6.69666i | 0.992457 | + | 0.217727i | ||||
\(947\) | −42.7332 | − | 24.6720i | −1.38864 | − | 0.801734i | −0.395481 | − | 0.918474i | \(-0.629422\pi\) |
−0.993162 | + | 0.116740i | \(0.962755\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.6522 | − | 44.4310i | −0.832706 | − | 1.44229i | ||||
\(950\) | −13.0172 | + | 14.2688i | −0.422332 | + | 0.462940i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −15.3571 | + | 0.870386i | −0.497726 | + | 0.0282094i | ||||
\(953\) | −34.4944 | −1.11738 | −0.558691 | − | 0.829376i | \(-0.688696\pi\) | ||||
−0.558691 | + | 0.829376i | \(0.688696\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.92412 | + | 15.4570i | 0.288778 | + | 0.500178i | ||||
\(956\) | 26.5520 | − | 2.44105i | 0.858753 | − | 0.0789492i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.30349 | + | 2.04102i | 0.300582 | + | 0.0659423i | ||||
\(959\) | 34.5985 | + | 40.7037i | 1.11724 | + | 1.31439i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.9720 | − | 25.9323i | 0.482968 | − | 0.836525i | ||||
\(962\) | 40.8393 | − | 12.9757i | 1.31671 | − | 0.418353i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 28.3938 | + | 40.1722i | 0.914502 | + | 1.29386i | ||||
\(965\) | − | 0.569966i | − | 0.0183478i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 5.11586i | − | 0.164515i | −0.996611 | − | 0.0822575i | \(-0.973787\pi\) | ||
0.996611 | − | 0.0822575i | \(-0.0262130\pi\) | |||||||
\(968\) | −16.6278 | + | 7.01669i | −0.534437 | + | 0.225525i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.642918 | + | 2.02350i | 0.0206429 | + | 0.0649708i | ||||
\(971\) | 21.5432 | − | 37.3139i | 0.691354 | − | 1.19746i | −0.280040 | − | 0.959988i | \(-0.590348\pi\) |
0.971394 | − | 0.237472i | \(-0.0763189\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 58.5594 | − | 10.7105i | 1.87733 | − | 0.343362i | ||||
\(974\) | −1.56833 | + | 7.14884i | −0.0502525 | + | 0.229064i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −22.4399 | − | 7.94402i | −0.718285 | − | 0.254282i | ||||
\(977\) | −11.9965 | − | 20.7786i | −0.383803 | − | 0.664766i | 0.607800 | − | 0.794090i | \(-0.292052\pi\) |
−0.991602 | + | 0.129325i | \(0.958719\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.20344 | 0.0384620 | ||||||||
\(980\) | 0.797159 | − | 11.3496i | 0.0254643 | − | 0.362548i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.42047 | + | 4.03272i | 0.141063 | + | 0.128689i | ||||
\(983\) | 17.1303 | + | 29.6706i | 0.546372 | + | 0.946344i | 0.998519 | + | 0.0544009i | \(0.0173249\pi\) |
−0.452147 | + | 0.891943i | \(0.649342\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.8628 | − | 9.73572i | −0.537292 | − | 0.310206i | ||||
\(986\) | −4.76649 | + | 21.7269i | −0.151796 | + | 0.691925i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 13.5447 | − | 29.3843i | 0.430913 | − | 0.934839i | ||||
\(989\) | −9.74636 | + | 16.8812i | −0.309916 | + | 0.536791i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.24015 | + | 1.29335i | −0.0711608 | + | 0.0410847i | −0.535158 | − | 0.844752i | \(-0.679748\pi\) |
0.463997 | + | 0.885837i | \(0.346415\pi\) | |||||||
\(992\) | 5.81001 | + | 0.189514i | 0.184468 | + | 0.00601709i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 35.0846 | + | 21.9308i | 1.11282 | + | 0.695604i | ||||
\(995\) | 1.78263i | 0.0565132i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.1394 | + | 9.89541i | −0.542809 | + | 0.313391i | −0.746217 | − | 0.665703i | \(-0.768132\pi\) |
0.203408 | + | 0.979094i | \(0.434798\pi\) | |||||||
\(998\) | −38.8300 | + | 12.3373i | −1.22914 | + | 0.390529i | ||||
\(999\) | 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 | 756.2.bf.b.271.5 | ✓ | 32 | |
3.2 | odd | 2 | 756.2.bf.c.271.12 | yes | 32 | ||
4.3 | odd | 2 | 756.2.bf.c.271.7 | yes | 32 | ||
7.3 | odd | 6 | 756.2.bf.c.703.7 | yes | 32 | ||
12.11 | even | 2 | inner | 756.2.bf.b.271.10 | yes | 32 | |
21.17 | even | 6 | inner | 756.2.bf.b.703.10 | yes | 32 | |
28.3 | even | 6 | inner | 756.2.bf.b.703.5 | yes | 32 | |
84.59 | odd | 6 | 756.2.bf.c.703.12 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.bf.b.271.5 | ✓ | 32 | 1.1 | even | 1 | trivial | |
756.2.bf.b.271.10 | yes | 32 | 12.11 | even | 2 | inner | |
756.2.bf.b.703.5 | yes | 32 | 28.3 | even | 6 | inner | |
756.2.bf.b.703.10 | yes | 32 | 21.17 | even | 6 | inner | |
756.2.bf.c.271.7 | yes | 32 | 4.3 | odd | 2 | ||
756.2.bf.c.271.12 | yes | 32 | 3.2 | odd | 2 | ||
756.2.bf.c.703.7 | yes | 32 | 7.3 | odd | 6 | ||
756.2.bf.c.703.12 | yes | 32 | 84.59 | odd | 6 |