Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(49,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 5, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.bx (of order \(10\), degree \(4\), not 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: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\Q(\zeta_{20})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(-0.587785 - 0.809017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.49 |
Dual form | 825.2.bx.c.724.2 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.53884 | − | 0.500000i | 1.08813 | − | 0.353553i | 0.290604 | − | 0.956844i | \(-0.406144\pi\) |
0.797522 | + | 0.603290i | \(0.206144\pi\) | |||||||
\(3\) | 0.587785 | − | 0.809017i | 0.339358 | − | 0.467086i | ||||
\(4\) | 0.500000 | − | 0.363271i | 0.250000 | − | 0.181636i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.500000 | − | 1.53884i | 0.204124 | − | 0.628230i | ||||
\(7\) | 3.07768 | + | 4.23607i | 1.16326 | + | 1.60108i | 0.698425 | + | 0.715683i | \(0.253885\pi\) |
0.464830 | + | 0.885400i | \(0.346115\pi\) | |||||||
\(8\) | −1.31433 | + | 1.80902i | −0.464685 | + | 0.639584i | ||||
\(9\) | −0.309017 | − | 0.951057i | −0.103006 | − | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.23607 | − | 3.07768i | −0.372689 | − | 0.927957i | ||||
\(12\) | − | 0.618034i | − | 0.178411i | ||||||
\(13\) | 3.07768 | − | 1.00000i | 0.853596 | − | 0.277350i | 0.150644 | − | 0.988588i | \(-0.451865\pi\) |
0.702951 | + | 0.711238i | \(0.251865\pi\) | |||||||
\(14\) | 6.85410 | + | 4.97980i | 1.83184 | + | 1.33091i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.50000 | + | 4.61653i | −0.375000 | + | 1.15413i | ||||
\(17\) | 1.90211 | + | 0.618034i | 0.461330 | + | 0.149895i | 0.530456 | − | 0.847713i | \(-0.322021\pi\) |
−0.0691254 | + | 0.997608i | \(0.522021\pi\) | |||||||
\(18\) | −0.951057 | − | 1.30902i | −0.224166 | − | 0.308538i | ||||
\(19\) | 4.04508 | + | 2.93893i | 0.928006 | + | 0.674236i | 0.945504 | − | 0.325611i | \(-0.105570\pi\) |
−0.0174977 | + | 0.999847i | \(0.505570\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.23607 | 1.14260 | ||||||||
\(22\) | −3.44095 | − | 4.11803i | −0.733614 | − | 0.877968i | ||||
\(23\) | − | 4.61803i | − | 0.962927i | −0.876466 | − | 0.481463i | \(-0.840105\pi\) | ||
0.876466 | − | 0.481463i | \(-0.159895\pi\) | |||||||
\(24\) | 0.690983 | + | 2.12663i | 0.141046 | + | 0.434096i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.23607 | − | 3.07768i | 0.830761 | − | 0.603583i | ||||
\(27\) | −0.951057 | − | 0.309017i | −0.183031 | − | 0.0594703i | ||||
\(28\) | 3.07768 | + | 1.00000i | 0.581628 | + | 0.188982i | ||||
\(29\) | 0.690983 | − | 0.502029i | 0.128312 | − | 0.0932244i | −0.521778 | − | 0.853081i | \(-0.674731\pi\) |
0.650090 | + | 0.759857i | \(0.274731\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.16312 | + | 6.65740i | 0.388508 | + | 1.19570i | 0.933904 | + | 0.357525i | \(0.116379\pi\) |
−0.545396 | + | 0.838179i | \(0.683621\pi\) | |||||||
\(32\) | 3.38197i | 0.597853i | ||||||||
\(33\) | −3.21644 | − | 0.809017i | −0.559910 | − | 0.140832i | ||||
\(34\) | 3.23607 | 0.554981 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.500000 | − | 0.363271i | −0.0833333 | − | 0.0605452i | ||||
\(37\) | −0.865300 | − | 1.19098i | −0.142254 | − | 0.195796i | 0.731945 | − | 0.681364i | \(-0.238613\pi\) |
−0.874199 | + | 0.485568i | \(0.838613\pi\) | |||||||
\(38\) | 7.69421 | + | 2.50000i | 1.24817 | + | 0.405554i | ||||
\(39\) | 1.00000 | − | 3.07768i | 0.160128 | − | 0.492824i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.28115 | − | 6.74315i | −1.44947 | − | 1.05310i | −0.985954 | − | 0.167016i | \(-0.946587\pi\) |
−0.463518 | − | 0.886087i | \(-0.653413\pi\) | |||||||
\(42\) | 8.05748 | − | 2.61803i | 1.24330 | − | 0.403971i | ||||
\(43\) | − | 9.09017i | − | 1.38624i | −0.720823 | − | 0.693119i | \(-0.756236\pi\) | ||
0.720823 | − | 0.693119i | \(-0.243764\pi\) | |||||||
\(44\) | −1.73607 | − | 1.08981i | −0.261722 | − | 0.164296i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.30902 | − | 7.10642i | −0.340446 | − | 1.04778i | ||||
\(47\) | −3.57971 | + | 4.92705i | −0.522155 | + | 0.718684i | −0.985910 | − | 0.167279i | \(-0.946502\pi\) |
0.463755 | + | 0.885964i | \(0.346502\pi\) | |||||||
\(48\) | 2.85317 | + | 3.92705i | 0.411820 | + | 0.566821i | ||||
\(49\) | −6.30902 | + | 19.4172i | −0.901288 | + | 2.77388i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.61803 | − | 1.17557i | 0.226570 | − | 0.164613i | ||||
\(52\) | 1.17557 | − | 1.61803i | 0.163022 | − | 0.224381i | ||||
\(53\) | −5.11855 | + | 1.66312i | −0.703087 | + | 0.228447i | −0.638675 | − | 0.769476i | \(-0.720517\pi\) |
−0.0644122 | + | 0.997923i | \(0.520517\pi\) | |||||||
\(54\) | −1.61803 | −0.220187 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −11.7082 | −1.56457 | ||||||||
\(57\) | 4.75528 | − | 1.54508i | 0.629853 | − | 0.204652i | ||||
\(58\) | 0.812299 | − | 1.11803i | 0.106660 | − | 0.146805i | ||||
\(59\) | 5.42705 | − | 3.94298i | 0.706542 | − | 0.513333i | −0.175514 | − | 0.984477i | \(-0.556159\pi\) |
0.882056 | + | 0.471144i | \(0.156159\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.16312 | − | 6.65740i | 0.276959 | − | 0.852392i | −0.711735 | − | 0.702448i | \(-0.752090\pi\) |
0.988694 | − | 0.149945i | \(-0.0479095\pi\) | |||||||
\(62\) | 6.65740 | + | 9.16312i | 0.845490 | + | 1.16372i | ||||
\(63\) | 3.07768 | − | 4.23607i | 0.387752 | − | 0.533694i | ||||
\(64\) | −1.30902 | − | 4.02874i | −0.163627 | − | 0.503593i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.35410 | + | 0.363271i | −0.659044 | + | 0.0447156i | ||||
\(67\) | − | 11.6180i | − | 1.41937i | −0.704520 | − | 0.709684i | \(-0.748838\pi\) | ||
0.704520 | − | 0.709684i | \(-0.251162\pi\) | |||||||
\(68\) | 1.17557 | − | 0.381966i | 0.142559 | − | 0.0463202i | ||||
\(69\) | −3.73607 | − | 2.71441i | −0.449770 | − | 0.326777i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.47214 | + | 7.60845i | −0.293389 | + | 0.902957i | 0.690369 | + | 0.723457i | \(0.257448\pi\) |
−0.983758 | + | 0.179500i | \(0.942552\pi\) | |||||||
\(72\) | 2.12663 | + | 0.690983i | 0.250625 | + | 0.0814331i | ||||
\(73\) | −2.66141 | − | 3.66312i | −0.311495 | − | 0.428736i | 0.624352 | − | 0.781143i | \(-0.285363\pi\) |
−0.935847 | + | 0.352408i | \(0.885363\pi\) | |||||||
\(74\) | −1.92705 | − | 1.40008i | −0.224015 | − | 0.162757i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.09017 | 0.354467 | ||||||||
\(77\) | 9.23305 | − | 14.7082i | 1.05220 | − | 1.67616i | ||||
\(78\) | − | 5.23607i | − | 0.592868i | ||||||
\(79\) | −0.954915 | − | 2.93893i | −0.107436 | − | 0.330655i | 0.882858 | − | 0.469640i | \(-0.155616\pi\) |
−0.990295 | + | 0.138985i | \(0.955616\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | −17.6538 | − | 5.73607i | −1.94954 | − | 0.633443i | ||||
\(83\) | −7.33094 | − | 2.38197i | −0.804675 | − | 0.261455i | −0.122334 | − | 0.992489i | \(-0.539038\pi\) |
−0.682341 | + | 0.731034i | \(0.739038\pi\) | |||||||
\(84\) | 2.61803 | − | 1.90211i | 0.285651 | − | 0.207538i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.54508 | − | 13.9883i | −0.490109 | − | 1.50840i | ||||
\(87\) | − | 0.854102i | − | 0.0915693i | ||||||
\(88\) | 7.19218 | + | 1.80902i | 0.766689 | + | 0.192842i | ||||
\(89\) | −4.14590 | −0.439464 | −0.219732 | − | 0.975560i | \(-0.570518\pi\) | ||||
−0.219732 | + | 0.975560i | \(0.570518\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.7082 | + | 9.95959i | 1.43701 | + | 1.04405i | ||||
\(92\) | −1.67760 | − | 2.30902i | −0.174902 | − | 0.240732i | ||||
\(93\) | 6.65740 | + | 2.16312i | 0.690340 | + | 0.224305i | ||||
\(94\) | −3.04508 | + | 9.37181i | −0.314077 | + | 0.966628i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.73607 | + | 1.98787i | 0.279249 | + | 0.202886i | ||||
\(97\) | −2.40414 | + | 0.781153i | −0.244104 | + | 0.0793141i | −0.428514 | − | 0.903535i | \(-0.640963\pi\) |
0.184410 | + | 0.982849i | \(0.440963\pi\) | |||||||
\(98\) | 33.0344i | 3.33698i | ||||||||
\(99\) | −2.54508 | + | 2.12663i | −0.255791 | + | 0.213734i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.04508 | + | 18.6049i | 0.601508 | + | 1.85125i | 0.519213 | + | 0.854645i | \(0.326225\pi\) |
0.0822950 | + | 0.996608i | \(0.473775\pi\) | |||||||
\(102\) | 1.90211 | − | 2.61803i | 0.188337 | − | 0.259224i | ||||
\(103\) | 2.71441 | + | 3.73607i | 0.267459 | + | 0.368126i | 0.921530 | − | 0.388308i | \(-0.126940\pi\) |
−0.654071 | + | 0.756433i | \(0.726940\pi\) | |||||||
\(104\) | −2.23607 | + | 6.88191i | −0.219265 | + | 0.674827i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.04508 | + | 5.11855i | −0.684279 | + | 0.497158i | ||||
\(107\) | −2.26538 | + | 3.11803i | −0.219003 | + | 0.301432i | −0.904356 | − | 0.426780i | \(-0.859648\pi\) |
0.685353 | + | 0.728211i | \(0.259648\pi\) | |||||||
\(108\) | −0.587785 | + | 0.190983i | −0.0565597 | + | 0.0183773i | ||||
\(109\) | −10.8541 | −1.03963 | −0.519817 | − | 0.854278i | \(-0.674000\pi\) | ||||
−0.519817 | + | 0.854278i | \(0.674000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.47214 | −0.139729 | ||||||||
\(112\) | −24.1724 | + | 7.85410i | −2.28408 | + | 0.742143i | ||||
\(113\) | 2.04087 | − | 2.80902i | 0.191989 | − | 0.264250i | −0.702161 | − | 0.712019i | \(-0.747781\pi\) |
0.894150 | + | 0.447769i | \(0.147781\pi\) | |||||||
\(114\) | 6.54508 | − | 4.75528i | 0.613003 | − | 0.445373i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.163119 | − | 0.502029i | 0.0151452 | − | 0.0466122i | ||||
\(117\) | −1.90211 | − | 2.61803i | −0.175850 | − | 0.242037i | ||||
\(118\) | 6.37988 | − | 8.78115i | 0.587316 | − | 0.808371i | ||||
\(119\) | 3.23607 | + | 9.95959i | 0.296650 | + | 0.912994i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.94427 | + | 7.60845i | −0.722207 | + | 0.691677i | ||||
\(122\) | − | 11.3262i | − | 1.02543i | ||||||
\(123\) | −10.9106 | + | 3.54508i | −0.983780 | + | 0.319650i | ||||
\(124\) | 3.50000 | + | 2.54290i | 0.314309 | + | 0.228359i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.61803 | − | 8.05748i | 0.233233 | − | 0.717817i | ||||
\(127\) | −1.84911 | − | 0.600813i | −0.164082 | − | 0.0533135i | 0.225824 | − | 0.974168i | \(-0.427493\pi\) |
−0.389906 | + | 0.920855i | \(0.627493\pi\) | |||||||
\(128\) | −8.00448 | − | 11.0172i | −0.707503 | − | 0.973794i | ||||
\(129\) | −7.35410 | − | 5.34307i | −0.647493 | − | 0.470431i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.18034 | −0.802090 | −0.401045 | − | 0.916058i | \(-0.631353\pi\) | ||||
−0.401045 | + | 0.916058i | \(0.631353\pi\) | |||||||
\(132\) | −1.90211 | + | 0.763932i | −0.165558 | + | 0.0664917i | ||||
\(133\) | 26.1803i | 2.27012i | ||||||||
\(134\) | −5.80902 | − | 17.8783i | −0.501823 | − | 1.54445i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.61803 | + | 2.62866i | −0.310244 | + | 0.225405i | ||||
\(137\) | 5.03280 | + | 1.63525i | 0.429981 | + | 0.139709i | 0.516008 | − | 0.856584i | \(-0.327417\pi\) |
−0.0860276 | + | 0.996293i | \(0.527417\pi\) | |||||||
\(138\) | −7.10642 | − | 2.30902i | −0.604939 | − | 0.196557i | ||||
\(139\) | −0.954915 | + | 0.693786i | −0.0809948 | + | 0.0588462i | −0.627546 | − | 0.778580i | \(-0.715940\pi\) |
0.546551 | + | 0.837426i | \(0.315940\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.88197 | + | 5.79210i | 0.158490 | + | 0.487782i | ||||
\(142\) | 12.9443i | 1.08626i | ||||||||
\(143\) | −6.88191 | − | 8.23607i | −0.575494 | − | 0.688735i | ||||
\(144\) | 4.85410 | 0.404508 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.92705 | − | 4.30625i | −0.490526 | − | 0.356388i | ||||
\(147\) | 12.0005 | + | 16.5172i | 0.989782 | + | 1.36232i | ||||
\(148\) | −0.865300 | − | 0.281153i | −0.0711272 | − | 0.0231106i | ||||
\(149\) | 6.21885 | − | 19.1396i | 0.509468 | − | 1.56798i | −0.283660 | − | 0.958925i | \(-0.591549\pi\) |
0.793127 | − | 0.609056i | \(-0.208451\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.3262 | + | 8.95554i | 1.00310 | + | 0.728791i | 0.962750 | − | 0.270395i | \(-0.0871542\pi\) |
0.0403454 | + | 0.999186i | \(0.487154\pi\) | |||||||
\(152\) | −10.6331 | + | 3.45492i | −0.862461 | + | 0.280231i | ||||
\(153\) | − | 2.00000i | − | 0.161690i | ||||||
\(154\) | 6.85410 | − | 27.2501i | 0.552319 | − | 2.19588i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.618034 | − | 1.90211i | −0.0494823 | − | 0.152291i | ||||
\(157\) | 7.24518 | − | 9.97214i | 0.578228 | − | 0.795863i | −0.415271 | − | 0.909698i | \(-0.636313\pi\) |
0.993500 | + | 0.113835i | \(0.0363134\pi\) | |||||||
\(158\) | −2.93893 | − | 4.04508i | −0.233808 | − | 0.321810i | ||||
\(159\) | −1.66312 | + | 5.11855i | −0.131894 | + | 0.405928i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 19.5623 | − | 14.2128i | 1.54173 | − | 1.12013i | ||||
\(162\) | −0.951057 | + | 1.30902i | −0.0747221 | + | 0.102846i | ||||
\(163\) | −6.24112 | + | 2.02786i | −0.488843 | + | 0.158835i | −0.543059 | − | 0.839695i | \(-0.682734\pi\) |
0.0542163 | + | 0.998529i | \(0.482734\pi\) | |||||||
\(164\) | −7.09017 | −0.553649 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.4721 | −0.968025 | ||||||||
\(167\) | −8.59226 | + | 2.79180i | −0.664889 | + | 0.216036i | −0.621968 | − | 0.783043i | \(-0.713667\pi\) |
−0.0429216 | + | 0.999078i | \(0.513667\pi\) | |||||||
\(168\) | −6.88191 | + | 9.47214i | −0.530951 | + | 0.730791i | ||||
\(169\) | −2.04508 | + | 1.48584i | −0.157314 | + | 0.114295i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.54508 | − | 4.75528i | 0.118156 | − | 0.363646i | ||||
\(172\) | −3.30220 | − | 4.54508i | −0.251790 | − | 0.346559i | ||||
\(173\) | 9.73508 | − | 13.3992i | 0.740144 | − | 1.01872i | −0.258466 | − | 0.966020i | \(-0.583217\pi\) |
0.998610 | − | 0.0527010i | \(-0.0167830\pi\) | |||||||
\(174\) | −0.427051 | − | 1.31433i | −0.0323747 | − | 0.0996389i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 16.0623 | − | 1.08981i | 1.21074 | − | 0.0821478i | ||||
\(177\) | − | 6.70820i | − | 0.504219i | ||||||
\(178\) | −6.37988 | + | 2.07295i | −0.478192 | + | 0.155374i | ||||
\(179\) | −8.51722 | − | 6.18812i | −0.636607 | − | 0.462522i | 0.222076 | − | 0.975029i | \(-0.428717\pi\) |
−0.858683 | + | 0.512507i | \(0.828717\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.236068 | + | 0.726543i | −0.0175468 | + | 0.0540035i | −0.959447 | − | 0.281891i | \(-0.909038\pi\) |
0.941900 | + | 0.335894i | \(0.109038\pi\) | |||||||
\(182\) | 26.0746 | + | 8.47214i | 1.93277 | + | 0.627996i | ||||
\(183\) | −4.11450 | − | 5.66312i | −0.304152 | − | 0.418630i | ||||
\(184\) | 8.35410 | + | 6.06961i | 0.615873 | + | 0.447458i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 11.3262 | 0.830480 | ||||||||
\(187\) | −0.449028 | − | 6.61803i | −0.0328362 | − | 0.483959i | ||||
\(188\) | 3.76393i | 0.274513i | ||||||||
\(189\) | −1.61803 | − | 4.97980i | −0.117695 | − | 0.362227i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.2812 | − | 9.64932i | 0.960991 | − | 0.698200i | 0.00760993 | − | 0.999971i | \(-0.497578\pi\) |
0.953381 | + | 0.301771i | \(0.0975777\pi\) | |||||||
\(192\) | −4.02874 | − | 1.30902i | −0.290749 | − | 0.0944702i | ||||
\(193\) | −7.64121 | − | 2.48278i | −0.550026 | − | 0.178714i | 0.0208024 | − | 0.999784i | \(-0.493378\pi\) |
−0.570829 | + | 0.821069i | \(0.693378\pi\) | |||||||
\(194\) | −3.30902 | + | 2.40414i | −0.237574 | + | 0.172607i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.89919 | + | 12.0005i | 0.278513 | + | 0.857176i | ||||
\(197\) | 9.76393i | 0.695651i | 0.937559 | + | 0.347826i | \(0.113080\pi\) | ||||
−0.937559 | + | 0.347826i | \(0.886920\pi\) | |||||||
\(198\) | −2.85317 | + | 4.54508i | −0.202766 | + | 0.323005i | ||||
\(199\) | 4.79837 | 0.340148 | 0.170074 | − | 0.985431i | \(-0.445599\pi\) | ||||
0.170074 | + | 0.985431i | \(0.445599\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.39919 | − | 6.82891i | −0.662968 | − | 0.481674i | ||||
\(202\) | 18.6049 | + | 25.6074i | 1.30903 | + | 1.80173i | ||||
\(203\) | 4.25325 | + | 1.38197i | 0.298520 | + | 0.0969950i | ||||
\(204\) | 0.381966 | − | 1.17557i | 0.0267430 | − | 0.0823064i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.04508 | + | 4.39201i | 0.421181 | + | 0.306006i | ||||
\(207\) | −4.39201 | + | 1.42705i | −0.305266 | + | 0.0991869i | ||||
\(208\) | 15.7082i | 1.08917i | ||||||||
\(209\) | 4.04508 | − | 16.0822i | 0.279804 | − | 1.11243i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.881966 | + | 2.71441i | 0.0607170 | + | 0.186868i | 0.976814 | − | 0.214088i | \(-0.0686780\pi\) |
−0.916097 | + | 0.400956i | \(0.868678\pi\) | |||||||
\(212\) | −1.95511 | + | 2.69098i | −0.134278 | + | 0.184817i | ||||
\(213\) | 4.70228 | + | 6.47214i | 0.322195 | + | 0.443463i | ||||
\(214\) | −1.92705 | + | 5.93085i | −0.131730 | + | 0.405425i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.80902 | − | 1.31433i | 0.123088 | − | 0.0894287i | ||||
\(217\) | −21.5438 | + | 29.6525i | −1.46249 | + | 2.01294i | ||||
\(218\) | −16.7027 | + | 5.42705i | −1.13125 | + | 0.367566i | ||||
\(219\) | −4.52786 | −0.305965 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.47214 | 0.435363 | ||||||||
\(222\) | −2.26538 | + | 0.736068i | −0.152043 | + | 0.0494016i | ||||
\(223\) | 12.3637 | − | 17.0172i | 0.827937 | − | 1.13956i | −0.160367 | − | 0.987058i | \(-0.551268\pi\) |
0.988303 | − | 0.152500i | \(-0.0487324\pi\) | |||||||
\(224\) | −14.3262 | + | 10.4086i | −0.957212 | + | 0.695455i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.73607 | − | 5.34307i | 0.115482 | − | 0.355416i | ||||
\(227\) | −4.73504 | − | 6.51722i | −0.314276 | − | 0.432563i | 0.622433 | − | 0.782673i | \(-0.286144\pi\) |
−0.936709 | + | 0.350110i | \(0.886144\pi\) | |||||||
\(228\) | 1.81636 | − | 2.50000i | 0.120291 | − | 0.165567i | ||||
\(229\) | −2.13525 | − | 6.57164i | −0.141102 | − | 0.434266i | 0.855387 | − | 0.517989i | \(-0.173319\pi\) |
−0.996489 | + | 0.0837225i | \(0.973319\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.47214 | − | 16.1150i | −0.425835 | − | 1.06029i | ||||
\(232\) | 1.90983i | 0.125386i | ||||||||
\(233\) | 9.76784 | − | 3.17376i | 0.639912 | − | 0.207920i | 0.0289512 | − | 0.999581i | \(-0.490783\pi\) |
0.610961 | + | 0.791661i | \(0.290783\pi\) | |||||||
\(234\) | −4.23607 | − | 3.07768i | −0.276920 | − | 0.201194i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.28115 | − | 3.94298i | 0.0833960 | − | 0.256666i | ||||
\(237\) | −2.93893 | − | 0.954915i | −0.190904 | − | 0.0620284i | ||||
\(238\) | 9.95959 | + | 13.7082i | 0.645585 | + | 0.888571i | ||||
\(239\) | 17.8262 | + | 12.9515i | 1.15308 | + | 0.837764i | 0.988888 | − | 0.148664i | \(-0.0474972\pi\) |
0.164196 | + | 0.986428i | \(0.447497\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.618034 | 0.0398111 | 0.0199055 | − | 0.999802i | \(-0.493663\pi\) | ||||
0.0199055 | + | 0.999802i | \(0.493663\pi\) | |||||||
\(242\) | −8.42075 | + | 15.6803i | −0.541306 | + | 1.00797i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −1.33688 | − | 4.11450i | −0.0855850 | − | 0.263404i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −15.0172 | + | 10.9106i | −0.957463 | + | 0.695638i | ||||
\(247\) | 15.3884 | + | 5.00000i | 0.979142 | + | 0.318142i | ||||
\(248\) | −14.8864 | − | 4.83688i | −0.945287 | − | 0.307142i | ||||
\(249\) | −6.23607 | + | 4.53077i | −0.395195 | + | 0.287126i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.09017 | + | 15.6659i | 0.321289 | + | 0.988825i | 0.973088 | + | 0.230433i | \(0.0740144\pi\) |
−0.651799 | + | 0.758391i | \(0.725986\pi\) | |||||||
\(252\) | − | 3.23607i | − | 0.203853i | ||||||
\(253\) | −14.2128 | + | 5.70820i | −0.893554 | + | 0.358872i | ||||
\(254\) | −3.14590 | −0.197391 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.9721 | − | 7.97172i | −0.685758 | − | 0.498233i | ||||
\(257\) | −5.62058 | − | 7.73607i | −0.350602 | − | 0.482563i | 0.596898 | − | 0.802317i | \(-0.296400\pi\) |
−0.947500 | + | 0.319754i | \(0.896400\pi\) | |||||||
\(258\) | −13.9883 | − | 4.54508i | −0.870876 | − | 0.282965i | ||||
\(259\) | 2.38197 | − | 7.33094i | 0.148008 | − | 0.455522i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.690983 | − | 0.502029i | −0.0427708 | − | 0.0310748i | ||||
\(262\) | −14.1271 | + | 4.59017i | −0.872775 | + | 0.283582i | ||||
\(263\) | − | 24.2148i | − | 1.49315i | −0.665303 | − | 0.746574i | \(-0.731698\pi\) | ||
0.665303 | − | 0.746574i | \(-0.268302\pi\) | |||||||
\(264\) | 5.69098 | − | 4.75528i | 0.350256 | − | 0.292667i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 13.0902 | + | 40.2874i | 0.802610 | + | 2.47018i | ||||
\(267\) | −2.43690 | + | 3.35410i | −0.149136 | + | 0.205268i | ||||
\(268\) | −4.22050 | − | 5.80902i | −0.257808 | − | 0.354842i | ||||
\(269\) | −0.263932 | + | 0.812299i | −0.0160922 | + | 0.0495268i | −0.958780 | − | 0.284149i | \(-0.908289\pi\) |
0.942688 | + | 0.333676i | \(0.108289\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.8713 | + | 10.8046i | −0.903369 | + | 0.656336i | −0.939329 | − | 0.343018i | \(-0.888551\pi\) |
0.0359605 | + | 0.999353i | \(0.488551\pi\) | |||||||
\(272\) | −5.70634 | + | 7.85410i | −0.345998 | + | 0.476225i | ||||
\(273\) | 16.1150 | − | 5.23607i | 0.975322 | − | 0.316901i | ||||
\(274\) | 8.56231 | 0.517268 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.85410 | −0.171797 | ||||||||
\(277\) | −21.5438 | + | 7.00000i | −1.29444 | + | 0.420589i | −0.873644 | − | 0.486566i | \(-0.838249\pi\) |
−0.420797 | + | 0.907155i | \(0.638249\pi\) | |||||||
\(278\) | −1.12257 | + | 1.54508i | −0.0673273 | + | 0.0926680i | ||||
\(279\) | 5.66312 | − | 4.11450i | 0.339042 | − | 0.246328i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.336881 | + | 1.03681i | −0.0200966 | + | 0.0618511i | −0.960602 | − | 0.277928i | \(-0.910352\pi\) |
0.940505 | + | 0.339779i | \(0.110352\pi\) | |||||||
\(282\) | 5.79210 | + | 7.97214i | 0.344914 | + | 0.474734i | ||||
\(283\) | 9.42481 | − | 12.9721i | 0.560247 | − | 0.771113i | −0.431111 | − | 0.902299i | \(-0.641878\pi\) |
0.991358 | + | 0.131185i | \(0.0418783\pi\) | |||||||
\(284\) | 1.52786 | + | 4.70228i | 0.0906621 | + | 0.279029i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −14.7082 | − | 9.23305i | −0.869714 | − | 0.545962i | ||||
\(287\) | − | 60.0689i | − | 3.54575i | ||||||
\(288\) | 3.21644 | − | 1.04508i | 0.189531 | − | 0.0615822i | ||||
\(289\) | −10.5172 | − | 7.64121i | −0.618660 | − | 0.449483i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.781153 | + | 2.40414i | −0.0457920 | + | 0.140933i | ||||
\(292\) | −2.66141 | − | 0.864745i | −0.155747 | − | 0.0506054i | ||||
\(293\) | 14.9721 | + | 20.6074i | 0.874682 | + | 1.20390i | 0.977866 | + | 0.209234i | \(0.0670971\pi\) |
−0.103183 | + | 0.994662i | \(0.532903\pi\) | |||||||
\(294\) | 26.7254 | + | 19.4172i | 1.55866 | + | 1.13243i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.29180 | 0.191332 | ||||||||
\(297\) | 0.224514 | + | 3.30902i | 0.0130276 | + | 0.192009i | ||||
\(298\) | − | 32.5623i | − | 1.88628i | ||||||
\(299\) | −4.61803 | − | 14.2128i | −0.267068 | − | 0.821950i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 38.5066 | − | 27.9767i | 2.21948 | − | 1.61255i | ||||
\(302\) | 23.4459 | + | 7.61803i | 1.34916 | + | 0.438369i | ||||
\(303\) | 18.6049 | + | 6.04508i | 1.06882 | + | 0.347281i | ||||
\(304\) | −19.6353 | + | 14.2658i | −1.12616 | + | 0.818202i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.00000 | − | 3.07768i | −0.0571662 | − | 0.175939i | ||||
\(307\) | − | 28.1246i | − | 1.60516i | −0.596547 | − | 0.802578i | \(-0.703461\pi\) | ||
0.596547 | − | 0.802578i | \(-0.296539\pi\) | |||||||
\(308\) | −0.726543 | − | 10.7082i | −0.0413986 | − | 0.610157i | ||||
\(309\) | 4.61803 | 0.262711 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.1353 | − | 7.36369i | −0.574718 | − | 0.417557i | 0.262098 | − | 0.965041i | \(-0.415586\pi\) |
−0.836816 | + | 0.547484i | \(0.815586\pi\) | |||||||
\(312\) | 4.25325 | + | 5.85410i | 0.240793 | + | 0.331423i | ||||
\(313\) | 8.05748 | + | 2.61803i | 0.455436 | + | 0.147980i | 0.527746 | − | 0.849402i | \(-0.323037\pi\) |
−0.0723104 | + | 0.997382i | \(0.523037\pi\) | |||||||
\(314\) | 6.16312 | − | 18.9681i | 0.347805 | − | 1.07043i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.54508 | − | 1.12257i | −0.0869178 | − | 0.0631495i | ||||
\(317\) | −3.40820 | + | 1.10739i | −0.191424 | + | 0.0621973i | −0.403160 | − | 0.915130i | \(-0.632088\pi\) |
0.211736 | + | 0.977327i | \(0.432088\pi\) | |||||||
\(318\) | 8.70820i | 0.488332i | ||||||||
\(319\) | −2.39919 | − | 1.50609i | −0.134329 | − | 0.0843246i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.19098 | + | 3.66547i | 0.0664742 | + | 0.204587i | ||||
\(322\) | 22.9969 | − | 31.6525i | 1.28157 | − | 1.76392i | ||||
\(323\) | 5.87785 | + | 8.09017i | 0.327052 | + | 0.450149i | ||||
\(324\) | −0.190983 | + | 0.587785i | −0.0106102 | + | 0.0326547i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.59017 | + | 6.24112i | −0.475766 | + | 0.345664i | ||||
\(327\) | −6.37988 | + | 8.78115i | −0.352808 | + | 0.485599i | ||||
\(328\) | 24.3970 | − | 7.92705i | 1.34710 | − | 0.437698i | ||||
\(329\) | −31.8885 | −1.75807 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.5967 | −1.51685 | −0.758427 | − | 0.651758i | \(-0.774032\pi\) | ||||
−0.758427 | + | 0.651758i | \(0.774032\pi\) | |||||||
\(332\) | −4.53077 | + | 1.47214i | −0.248658 | + | 0.0807940i | ||||
\(333\) | −0.865300 | + | 1.19098i | −0.0474181 | + | 0.0652655i | ||||
\(334\) | −11.8262 | + | 8.59226i | −0.647103 | + | 0.470148i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −7.85410 | + | 24.1724i | −0.428476 | + | 1.31871i | ||||
\(337\) | 16.9600 | + | 23.3435i | 0.923871 | + | 1.27160i | 0.962203 | + | 0.272334i | \(0.0877956\pi\) |
−0.0383318 | + | 0.999265i | \(0.512204\pi\) | |||||||
\(338\) | −2.40414 | + | 3.30902i | −0.130768 | + | 0.179987i | ||||
\(339\) | −1.07295 | − | 3.30220i | −0.0582746 | − | 0.179351i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.8156 | − | 14.8864i | 0.964769 | − | 0.806143i | ||||
\(342\) | − | 8.09017i | − | 0.437466i | ||||||
\(343\) | −66.8110 | + | 21.7082i | −3.60745 | + | 1.17213i | ||||
\(344\) | 16.4443 | + | 11.9475i | 0.886616 | + | 0.644164i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.28115 | − | 25.4868i | 0.445198 | − | 1.37018i | ||||
\(347\) | 26.8011 | + | 8.70820i | 1.43876 | + | 0.467481i | 0.921510 | − | 0.388355i | \(-0.126956\pi\) |
0.517248 | + | 0.855835i | \(0.326956\pi\) | |||||||
\(348\) | −0.310271 | − | 0.427051i | −0.0166323 | − | 0.0228923i | ||||
\(349\) | 26.0795 | + | 18.9479i | 1.39601 | + | 1.01426i | 0.995176 | + | 0.0981041i | \(0.0312778\pi\) |
0.400829 | + | 0.916153i | \(0.368722\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.23607 | −0.172729 | ||||||||
\(352\) | 10.4086 | − | 4.18034i | 0.554781 | − | 0.222813i | ||||
\(353\) | − | 17.8328i | − | 0.949145i | −0.880216 | − | 0.474573i | \(-0.842603\pi\) | ||
0.880216 | − | 0.474573i | \(-0.157397\pi\) | |||||||
\(354\) | −3.35410 | − | 10.3229i | −0.178269 | − | 0.548654i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.07295 | + | 1.50609i | −0.109866 | + | 0.0798224i | ||||
\(357\) | 9.95959 | + | 3.23607i | 0.527118 | + | 0.171271i | ||||
\(358\) | −16.2007 | − | 5.26393i | −0.856234 | − | 0.278207i | ||||
\(359\) | 2.66312 | − | 1.93487i | 0.140554 | − | 0.102118i | −0.515286 | − | 0.857018i | \(-0.672314\pi\) |
0.655840 | + | 0.754900i | \(0.272314\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.85410 | + | 5.70634i | 0.0975843 | + | 0.300334i | ||||
\(362\) | 1.23607i | 0.0649663i | ||||||||
\(363\) | 1.48584 | + | 10.8992i | 0.0779864 | + | 0.572059i | ||||
\(364\) | 10.4721 | 0.548889 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −9.16312 | − | 6.65740i | −0.478964 | − | 0.347988i | ||||
\(367\) | −13.0045 | − | 17.8992i | −0.678830 | − | 0.934330i | 0.321089 | − | 0.947049i | \(-0.395951\pi\) |
−0.999919 | + | 0.0127192i | \(0.995951\pi\) | |||||||
\(368\) | 21.3193 | + | 6.92705i | 1.11134 | + | 0.361097i | ||||
\(369\) | −3.54508 | + | 10.9106i | −0.184550 | + | 0.567986i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.7984 | − | 16.5640i | −1.18363 | − | 0.859959i | ||||
\(372\) | 4.11450 | − | 1.33688i | 0.213327 | − | 0.0693141i | ||||
\(373\) | 32.7426i | 1.69535i | 0.530516 | + | 0.847675i | \(0.321998\pi\) | ||||
−0.530516 | + | 0.847675i | \(0.678002\pi\) | |||||||
\(374\) | −4.00000 | − | 9.95959i | −0.206835 | − | 0.514998i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.20820 | − | 12.9515i | −0.217022 | − | 0.667924i | ||||
\(377\) | 1.62460 | − | 2.23607i | 0.0836711 | − | 0.115163i | ||||
\(378\) | −4.97980 | − | 6.85410i | −0.256133 | − | 0.352537i | ||||
\(379\) | 1.54508 | − | 4.75528i | 0.0793657 | − | 0.244262i | −0.903499 | − | 0.428590i | \(-0.859011\pi\) |
0.982865 | + | 0.184327i | \(0.0590106\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.57295 | + | 1.14281i | −0.0805846 | + | 0.0585482i | ||||
\(382\) | 15.6129 | − | 21.4894i | 0.798827 | − | 1.09949i | ||||
\(383\) | 12.7068 | − | 4.12868i | 0.649285 | − | 0.210966i | 0.0341862 | − | 0.999415i | \(-0.489116\pi\) |
0.615099 | + | 0.788450i | \(0.289116\pi\) | |||||||
\(384\) | −13.6180 | −0.694942 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.0000 | −0.661683 | ||||||||
\(387\) | −8.64527 | + | 2.80902i | −0.439464 | + | 0.142790i | ||||
\(388\) | −0.918300 | + | 1.26393i | −0.0466196 | + | 0.0641664i | ||||
\(389\) | −17.0344 | + | 12.3762i | −0.863680 | + | 0.627501i | −0.928884 | − | 0.370371i | \(-0.879230\pi\) |
0.0652033 | + | 0.997872i | \(0.479230\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.85410 | − | 8.78402i | 0.144338 | − | 0.444227i | ||||
\(392\) | −26.8339 | − | 36.9336i | −1.35531 | − | 1.86543i | ||||
\(393\) | −5.39607 | + | 7.42705i | −0.272196 | + | 0.374645i | ||||
\(394\) | 4.88197 | + | 15.0251i | 0.245950 | + | 0.756956i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.500000 | + | 1.98787i | −0.0251259 | + | 0.0998942i | ||||
\(397\) | 2.72949i | 0.136989i | 0.997651 | + | 0.0684946i | \(0.0218196\pi\) | ||||
−0.997651 | + | 0.0684946i | \(0.978180\pi\) | |||||||
\(398\) | 7.38394 | − | 2.39919i | 0.370123 | − | 0.120260i | ||||
\(399\) | 21.1803 | + | 15.3884i | 1.06034 | + | 0.770384i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.54508 | + | 29.3768i | −0.476659 | + | 1.46700i | 0.367049 | + | 0.930202i | \(0.380368\pi\) |
−0.843707 | + | 0.536803i | \(0.819632\pi\) | |||||||
\(402\) | −17.8783 | − | 5.80902i | −0.891689 | − | 0.289727i | ||||
\(403\) | 13.3148 | + | 18.3262i | 0.663257 | + | 0.912895i | ||||
\(404\) | 9.78115 | + | 7.10642i | 0.486631 | + | 0.353558i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.23607 | 0.359120 | ||||||||
\(407\) | −2.59590 | + | 4.13525i | −0.128674 | + | 0.204977i | ||||
\(408\) | 4.47214i | 0.221404i | ||||||||
\(409\) | 8.12868 | + | 25.0175i | 0.401937 | + | 1.23704i | 0.923426 | + | 0.383777i | \(0.125377\pi\) |
−0.521488 | + | 0.853258i | \(0.674623\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.28115 | − | 3.11044i | 0.211174 | − | 0.153427i | ||||
\(412\) | 2.71441 | + | 0.881966i | 0.133729 | + | 0.0434513i | ||||
\(413\) | 33.4055 | + | 10.8541i | 1.64378 | + | 0.534095i | ||||
\(414\) | −6.04508 | + | 4.39201i | −0.297100 | + | 0.215856i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.38197 | + | 10.4086i | 0.165815 | + | 0.510325i | ||||
\(417\) | 1.18034i | 0.0578015i | ||||||||
\(418\) | −1.81636 | − | 26.7705i | −0.0888409 | − | 1.30939i | ||||
\(419\) | 24.5967 | 1.20163 | 0.600815 | − | 0.799388i | \(-0.294843\pi\) | ||||
0.600815 | + | 0.799388i | \(0.294843\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.11803 | + | 2.26538i | 0.151964 | + | 0.110408i | 0.661169 | − | 0.750237i | \(-0.270061\pi\) |
−0.509205 | + | 0.860645i | \(0.670061\pi\) | |||||||
\(422\) | 2.71441 | + | 3.73607i | 0.132136 | + | 0.181869i | ||||
\(423\) | 5.79210 | + | 1.88197i | 0.281621 | + | 0.0915043i | ||||
\(424\) | 3.71885 | − | 11.4454i | 0.180603 | − | 0.555839i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10.4721 | + | 7.60845i | 0.507377 | + | 0.368631i | ||||
\(427\) | 34.8586 | − | 11.3262i | 1.68692 | − | 0.548115i | ||||
\(428\) | 2.38197i | 0.115137i | ||||||||
\(429\) | −10.7082 | + | 0.726543i | −0.516997 | + | 0.0350778i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.90983 | − | 15.1109i | −0.236498 | − | 0.727867i | −0.996919 | − | 0.0784361i | \(-0.975007\pi\) |
0.760421 | − | 0.649431i | \(-0.224993\pi\) | |||||||
\(432\) | 2.85317 | − | 3.92705i | 0.137273 | − | 0.188940i | ||||
\(433\) | −0.608030 | − | 0.836881i | −0.0292200 | − | 0.0402179i | 0.794157 | − | 0.607713i | \(-0.207913\pi\) |
−0.823377 | + | 0.567495i | \(0.807913\pi\) | |||||||
\(434\) | −18.3262 | + | 56.4024i | −0.879688 | + | 2.70740i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.42705 | + | 3.94298i | −0.259909 | + | 0.188835i | ||||
\(437\) | 13.5721 | − | 18.6803i | 0.649240 | − | 0.893602i | ||||
\(438\) | −6.96767 | + | 2.26393i | −0.332928 | + | 0.108175i | ||||
\(439\) | −25.3262 | −1.20876 | −0.604378 | − | 0.796698i | \(-0.706578\pi\) | ||||
−0.604378 | + | 0.796698i | \(0.706578\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.4164 | 0.972210 | ||||||||
\(442\) | 9.95959 | − | 3.23607i | 0.473730 | − | 0.153924i | ||||
\(443\) | 4.86128 | − | 6.69098i | 0.230967 | − | 0.317898i | −0.677766 | − | 0.735278i | \(-0.737052\pi\) |
0.908732 | + | 0.417380i | \(0.137052\pi\) | |||||||
\(444\) | −0.736068 | + | 0.534785i | −0.0349322 | + | 0.0253798i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.5172 | − | 32.3687i | 0.498005 | − | 1.53270i | ||||
\(447\) | −11.8290 | − | 16.2812i | −0.559490 | − | 0.770072i | ||||
\(448\) | 13.0373 | − | 17.9443i | 0.615953 | − | 0.847787i | ||||
\(449\) | 10.5902 | + | 32.5932i | 0.499781 | + | 1.53817i | 0.809371 | + | 0.587298i | \(0.199808\pi\) |
−0.309590 | + | 0.950870i | \(0.600192\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.28115 | + | 36.8994i | −0.437032 | + | 1.73753i | ||||
\(452\) | − | 2.14590i | − | 0.100935i | ||||||
\(453\) | 14.4904 | − | 4.70820i | 0.680817 | − | 0.221211i | ||||
\(454\) | −10.5451 | − | 7.66145i | −0.494905 | − | 0.359570i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.45492 | + | 10.6331i | −0.161791 | + | 0.497942i | ||||
\(457\) | −7.10642 | − | 2.30902i | −0.332424 | − | 0.108011i | 0.138049 | − | 0.990425i | \(-0.455917\pi\) |
−0.470473 | + | 0.882414i | \(0.655917\pi\) | |||||||
\(458\) | −6.57164 | − | 9.04508i | −0.307073 | − | 0.422649i | ||||
\(459\) | −1.61803 | − | 1.17557i | −0.0755234 | − | 0.0548709i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.05573 | 0.375193 | 0.187596 | − | 0.982246i | \(-0.439930\pi\) | ||||
0.187596 | + | 0.982246i | \(0.439930\pi\) | |||||||
\(462\) | −18.0171 | − | 21.5623i | −0.838230 | − | 1.00317i | ||||
\(463\) | − | 0.270510i | − | 0.0125717i | −0.999980 | − | 0.00628583i | \(-0.997999\pi\) | ||
0.999980 | − | 0.00628583i | \(-0.00200085\pi\) | |||||||
\(464\) | 1.28115 | + | 3.94298i | 0.0594760 | + | 0.183048i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 13.4443 | − | 9.76784i | 0.622794 | − | 0.452486i | ||||
\(467\) | −29.3768 | − | 9.54508i | −1.35939 | − | 0.441694i | −0.463553 | − | 0.886069i | \(-0.653426\pi\) |
−0.895841 | + | 0.444375i | \(0.853426\pi\) | |||||||
\(468\) | −1.90211 | − | 0.618034i | −0.0879252 | − | 0.0285686i | ||||
\(469\) | 49.2148 | − | 35.7566i | 2.27253 | − | 1.65109i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.80902 | − | 11.7229i | −0.175510 | − | 0.540165i | ||||
\(472\) | 15.0000i | 0.690431i | ||||||||
\(473\) | −27.9767 | + | 11.2361i | −1.28637 | + | 0.516635i | ||||
\(474\) | −5.00000 | −0.229658 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.23607 | + | 3.80423i | 0.239995 | + | 0.174366i | ||||
\(477\) | 3.16344 | + | 4.35410i | 0.144844 | + | 0.199361i | ||||
\(478\) | 33.9075 | + | 11.0172i | 1.55089 | + | 0.503916i | ||||
\(479\) | −2.03444 | + | 6.26137i | −0.0929560 | + | 0.286089i | −0.986716 | − | 0.162457i | \(-0.948058\pi\) |
0.893760 | + | 0.448546i | \(0.148058\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.85410 | − | 2.80017i | −0.175732 | − | 0.127677i | ||||
\(482\) | 0.951057 | − | 0.309017i | 0.0433194 | − | 0.0140753i | ||||
\(483\) | − | 24.1803i | − | 1.10024i | ||||||
\(484\) | −1.20820 | + | 6.69015i | −0.0549184 | + | 0.304098i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.500000 | + | 1.53884i | 0.0226805 | + | 0.0698033i | ||||
\(487\) | 4.80828 | − | 6.61803i | 0.217884 | − | 0.299892i | −0.686058 | − | 0.727547i | \(-0.740660\pi\) |
0.903942 | + | 0.427655i | \(0.140660\pi\) | |||||||
\(488\) | 9.20029 | + | 12.6631i | 0.416478 | + | 0.573232i | ||||
\(489\) | −2.02786 | + | 6.24112i | −0.0917032 | + | 0.282233i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.82624 | + | 4.23301i | −0.262934 | + | 0.191033i | −0.711440 | − | 0.702747i | \(-0.751957\pi\) |
0.448505 | + | 0.893780i | \(0.351957\pi\) | |||||||
\(492\) | −4.16750 | + | 5.73607i | −0.187885 | + | 0.258602i | ||||
\(493\) | 1.62460 | − | 0.527864i | 0.0731682 | − | 0.0237738i | ||||
\(494\) | 26.1803 | 1.17791 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −33.9787 | −1.52569 | ||||||||
\(497\) | −39.8384 | + | 12.9443i | −1.78700 | + | 0.580630i | ||||
\(498\) | −7.33094 | + | 10.0902i | −0.328507 | + | 0.452151i | ||||
\(499\) | 9.04508 | − | 6.57164i | 0.404914 | − | 0.294187i | −0.366626 | − | 0.930368i | \(-0.619487\pi\) |
0.771539 | + | 0.636182i | \(0.219487\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.79180 | + | 8.59226i | −0.124728 | + | 0.383874i | ||||
\(502\) | 15.6659 | + | 21.5623i | 0.699205 | + | 0.962373i | ||||
\(503\) | −8.16348 | + | 11.2361i | −0.363992 | + | 0.500992i | −0.951255 | − | 0.308404i | \(-0.900205\pi\) |
0.587264 | + | 0.809396i | \(0.300205\pi\) | |||||||
\(504\) | 3.61803 | + | 11.1352i | 0.161160 | + | 0.496000i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −19.0172 | + | 15.8904i | −0.845419 | + | 0.706416i | ||||
\(507\) | 2.52786i | 0.112266i | ||||||||
\(508\) | −1.14281 | + | 0.371323i | −0.0507042 | + | 0.0164748i | ||||
\(509\) | 7.66312 | + | 5.56758i | 0.339662 | + | 0.246779i | 0.744519 | − | 0.667601i | \(-0.232679\pi\) |
−0.404857 | + | 0.914380i | \(0.632679\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.32624 | − | 22.5478i | 0.324094 | − | 0.997458i | ||||
\(512\) | 5.03280 | + | 1.63525i | 0.222420 | + | 0.0722687i | ||||
\(513\) | −2.93893 | − | 4.04508i | −0.129757 | − | 0.178595i | ||||
\(514\) | −12.5172 | − | 9.09429i | −0.552111 | − | 0.401132i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.61803 | −0.247320 | ||||||||
\(517\) | 19.5887 | + | 4.92705i | 0.861509 | + | 0.216691i | ||||
\(518\) | − | 12.4721i | − | 0.547994i | ||||||
\(519\) | −5.11803 | − | 15.7517i | −0.224657 | − | 0.691422i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.7533 | + | 17.2578i | −1.04065 | + | 0.756077i | −0.970412 | − | 0.241453i | \(-0.922376\pi\) |
−0.0702381 | + | 0.997530i | \(0.522376\pi\) | |||||||
\(522\) | −1.31433 | − | 0.427051i | −0.0575266 | − | 0.0186915i | ||||
\(523\) | −3.57971 | − | 1.16312i | −0.156530 | − | 0.0508596i | 0.229704 | − | 0.973261i | \(-0.426224\pi\) |
−0.386234 | + | 0.922401i | \(0.626224\pi\) | |||||||
\(524\) | −4.59017 | + | 3.33495i | −0.200523 | + | 0.145688i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.1074 | − | 37.2627i | −0.527907 | − | 1.62473i | ||||
\(527\) | 14.0000i | 0.609850i | ||||||||
\(528\) | 8.55951 | − | 13.6353i | 0.372505 | − | 0.593398i | ||||
\(529\) | 1.67376 | 0.0727723 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.42705 | − | 3.94298i | −0.235514 | − | 0.171111i | ||||
\(532\) | 9.51057 | + | 13.0902i | 0.412335 | + | 0.567531i | ||||
\(533\) | −35.3076 | − | 11.4721i | −1.52934 | − | 0.496913i | ||||
\(534\) | −2.07295 | + | 6.37988i | −0.0897053 | + | 0.276084i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 21.0172 | + | 15.2699i | 0.907806 | + | 0.659559i | ||||
\(537\) | −10.0126 | + | 3.25329i | −0.432075 | + | 0.140390i | ||||
\(538\) | 1.38197i | 0.0595808i | ||||||||
\(539\) | 67.5582 | − | 4.58377i | 2.90994 | − | 0.197437i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.500000 | − | 1.53884i | −0.0214967 | − | 0.0661600i | 0.939733 | − | 0.341910i | \(-0.111074\pi\) |
−0.961229 | + | 0.275750i | \(0.911074\pi\) | |||||||
\(542\) | −17.4823 | + | 24.0623i | −0.750929 | + | 1.03356i | ||||
\(543\) | 0.449028 | + | 0.618034i | 0.0192696 | + | 0.0265224i | ||||
\(544\) | −2.09017 | + | 6.43288i | −0.0896153 | + | 0.275808i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 22.1803 | − | 16.1150i | 0.949231 | − | 0.689657i | ||||
\(547\) | 11.3799 | − | 15.6631i | 0.486570 | − | 0.669707i | −0.493181 | − | 0.869927i | \(-0.664166\pi\) |
0.979751 | + | 0.200220i | \(0.0641658\pi\) | |||||||
\(548\) | 3.11044 | − | 1.01064i | 0.132871 | − | 0.0431725i | ||||
\(549\) | −7.00000 | −0.298753 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.27051 | 0.181930 | ||||||||
\(552\) | 9.82084 | − | 3.19098i | 0.418003 | − | 0.135817i | ||||
\(553\) | 9.51057 | − | 13.0902i | 0.404430 | − | 0.556651i | ||||
\(554\) | −29.6525 | + | 21.5438i | −1.25981 | + | 0.915308i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.225425 | + | 0.693786i | −0.00956014 | + | 0.0294231i | ||||
\(557\) | 24.9192 | + | 34.2984i | 1.05586 | + | 1.45327i | 0.883615 | + | 0.468215i | \(0.155103\pi\) |
0.172247 | + | 0.985054i | \(0.444897\pi\) | |||||||
\(558\) | 6.65740 | − | 9.16312i | 0.281830 | − | 0.387906i | ||||
\(559\) | −9.09017 | − | 27.9767i | −0.384473 | − | 1.18329i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.61803 | − | 3.52671i | −0.237194 | − | 0.148898i | ||||
\(562\) | 1.76393i | 0.0744070i | ||||||||
\(563\) | 19.6619 | − | 6.38854i | 0.828651 | − | 0.269245i | 0.136174 | − | 0.990685i | \(-0.456519\pi\) |
0.692477 | + | 0.721440i | \(0.256519\pi\) | |||||||
\(564\) | 3.04508 | + | 2.21238i | 0.128221 | + | 0.0931582i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 8.01722 | − | 24.6745i | 0.336989 | − | 1.03715i | ||||
\(567\) | −4.97980 | − | 1.61803i | −0.209132 | − | 0.0679510i | ||||
\(568\) | −10.5146 | − | 14.4721i | −0.441184 | − | 0.607237i | ||||
\(569\) | −18.2533 | − | 13.2618i | −0.765218 | − | 0.555963i | 0.135289 | − | 0.990806i | \(-0.456804\pi\) |
−0.900506 | + | 0.434843i | \(0.856804\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.0902 | −0.464109 | −0.232055 | − | 0.972703i | \(-0.574545\pi\) | ||||
−0.232055 | + | 0.972703i | \(0.574545\pi\) | |||||||
\(572\) | −6.43288 | − | 1.61803i | −0.268972 | − | 0.0676534i | ||||
\(573\) | − | 16.4164i | − | 0.685805i | ||||||
\(574\) | −30.0344 | − | 92.4365i | −1.25361 | − | 3.85823i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.42705 | + | 2.48990i | −0.142794 | + | 0.103746i | ||||
\(577\) | 28.5442 | + | 9.27458i | 1.18831 | + | 0.386106i | 0.835448 | − | 0.549569i | \(-0.185208\pi\) |
0.352863 | + | 0.935675i | \(0.385208\pi\) | |||||||
\(578\) | −20.0049 | − | 6.50000i | −0.832096 | − | 0.270364i | ||||
\(579\) | −6.50000 | + | 4.72253i | −0.270131 | + | 0.196262i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.4721 | − | 38.3853i | −0.517431 | − | 1.59249i | ||||
\(582\) | 4.09017i | 0.169543i | ||||||||
\(583\) | 11.4454 | + | 13.6976i | 0.474021 | + | 0.567295i | ||||
\(584\) | 10.1246 | 0.418959 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 33.3435 | + | 24.2254i | 1.37741 | + | 1.00074i | ||||
\(587\) | 12.7068 | + | 17.4894i | 0.524464 | + | 0.721863i | 0.986274 | − | 0.165116i | \(-0.0527998\pi\) |
−0.461810 | + | 0.886979i | \(0.652800\pi\) | |||||||
\(588\) | 12.0005 | + | 3.89919i | 0.494891 | + | 0.160800i | ||||
\(589\) | −10.8156 | + | 33.2870i | −0.445649 | + | 1.37157i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.89919 | + | 5.73910i | 0.324929 | + | 0.236075i | ||||
\(592\) | 6.79615 | − | 2.20820i | 0.279320 | − | 0.0907566i | ||||
\(593\) | − | 3.11146i | − | 0.127772i | −0.997957 | − | 0.0638861i | \(-0.979651\pi\) | ||
0.997957 | − | 0.0638861i | \(-0.0203494\pi\) | |||||||
\(594\) | 2.00000 | + | 4.97980i | 0.0820610 | + | 0.204324i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.84346 | − | 11.8290i | −0.157434 | − | 0.484533i | ||||
\(597\) | 2.82041 | − | 3.88197i | 0.115432 | − | 0.158878i | ||||
\(598\) | −14.2128 | − | 19.5623i | −0.581207 | − | 0.799962i | ||||
\(599\) | 5.48936 | − | 16.8945i | 0.224289 | − | 0.690291i | −0.774074 | − | 0.633095i | \(-0.781784\pi\) |
0.998363 | − | 0.0571955i | \(-0.0182158\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.38197 | − | 6.08985i | 0.341908 | − | 0.248410i | −0.403559 | − | 0.914954i | \(-0.632227\pi\) |
0.745466 | + | 0.666543i | \(0.232227\pi\) | |||||||
\(602\) | 45.2672 | − | 62.3050i | 1.84495 | − | 2.53936i | ||||
\(603\) | −11.0494 | + | 3.59017i | −0.449967 | + | 0.146203i | ||||
\(604\) | 9.41641 | 0.383148 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 31.6525 | 1.28579 | ||||||||
\(607\) | 31.3849 | − | 10.1976i | 1.27387 | − | 0.413906i | 0.407454 | − | 0.913226i | \(-0.366417\pi\) |
0.866418 | + | 0.499319i | \(0.166417\pi\) | |||||||
\(608\) | −9.93935 | + | 13.6803i | −0.403094 | + | 0.554811i | ||||
\(609\) | 3.61803 | − | 2.62866i | 0.146610 | − | 0.106518i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.09017 | + | 18.7436i | −0.246382 | + | 0.758286i | ||||
\(612\) | −0.726543 | − | 1.00000i | −0.0293687 | − | 0.0404226i | ||||
\(613\) | −2.21238 | + | 3.04508i | −0.0893573 | + | 0.122990i | −0.851355 | − | 0.524590i | \(-0.824219\pi\) |
0.761998 | + | 0.647580i | \(0.224219\pi\) | |||||||
\(614\) | −14.0623 | − | 43.2793i | −0.567508 | − | 1.74661i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 14.4721 | + | 36.0341i | 0.583099 | + | 1.45186i | ||||
\(617\) | 42.2492i | 1.70089i | 0.526064 | + | 0.850445i | \(0.323667\pi\) | ||||
−0.526064 | + | 0.850445i | \(0.676333\pi\) | |||||||
\(618\) | 7.10642 | − | 2.30902i | 0.285862 | − | 0.0928823i | ||||
\(619\) | 34.6976 | + | 25.2093i | 1.39461 | + | 1.01325i | 0.995341 | + | 0.0964126i | \(0.0307368\pi\) |
0.399271 | + | 0.916833i | \(0.369263\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.42705 | + | 4.39201i | −0.0572656 | + | 0.176245i | ||||
\(622\) | −19.2784 | − | 6.26393i | −0.772993 | − | 0.251161i | ||||
\(623\) | −12.7598 | − | 17.5623i | −0.511209 | − | 0.703619i | ||||
\(624\) | 12.7082 | + | 9.23305i | 0.508735 | + | 0.369618i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 13.7082 | 0.547890 | ||||||||
\(627\) | −10.6331 | − | 12.7254i | −0.424647 | − | 0.508205i | ||||
\(628\) | − | 7.61803i | − | 0.303993i | ||||||
\(629\) | −0.909830 | − | 2.80017i | −0.0362773 | − | 0.111650i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.0623 | − | 23.2946i | 1.27638 | − | 0.927345i | 0.276943 | − | 0.960886i | \(-0.410679\pi\) |
0.999437 | + | 0.0335418i | \(0.0106787\pi\) | |||||||
\(632\) | 6.57164 | + | 2.13525i | 0.261406 | + | 0.0849359i | ||||
\(633\) | 2.71441 | + | 0.881966i | 0.107888 | + | 0.0350550i | ||||
\(634\) | −4.69098 | + | 3.40820i | −0.186303 | + | 0.135357i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.02786 | + | 3.16344i | 0.0407575 | + | 0.125439i | ||||
\(637\) | 66.0689i | 2.61774i | ||||||||
\(638\) | −4.44501 | − | 1.11803i | −0.175980 | − | 0.0442634i | ||||
\(639\) | 8.00000 | 0.316475 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.42705 | − | 2.48990i | −0.135360 | − | 0.0983451i | 0.518045 | − | 0.855354i | \(-0.326660\pi\) |
−0.653405 | + | 0.757009i | \(0.726660\pi\) | |||||||
\(642\) | 3.66547 | + | 5.04508i | 0.144665 | + | 0.199114i | ||||
\(643\) | 13.0045 | + | 4.22542i | 0.512848 | + | 0.166634i | 0.553997 | − | 0.832519i | \(-0.313102\pi\) |
−0.0411490 | + | 0.999153i | \(0.513102\pi\) | |||||||
\(644\) | 4.61803 | − | 14.2128i | 0.181976 | − | 0.560065i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13.0902 | + | 9.51057i | 0.515026 | + | 0.374188i | ||||
\(647\) | −30.0503 | + | 9.76393i | −1.18140 | + | 0.383860i | −0.832886 | − | 0.553444i | \(-0.813313\pi\) |
−0.348513 | + | 0.937304i | \(0.613313\pi\) | |||||||
\(648\) | − | 2.23607i | − | 0.0878410i | ||||||
\(649\) | −18.8435 | − | 11.8290i | −0.739670 | − | 0.464327i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.3262 | + | 34.8586i | 0.443910 | + | 1.36622i | ||||
\(652\) | −2.38390 | + | 3.28115i | −0.0933606 | + | 0.128500i | ||||
\(653\) | 25.6053 | + | 35.2426i | 1.00201 | + | 1.37915i | 0.924083 | + | 0.382192i | \(0.124831\pi\) |
0.0779293 | + | 0.996959i | \(0.475169\pi\) | |||||||
\(654\) | −5.42705 | + | 16.7027i | −0.212214 | + | 0.653129i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 45.0517 | − | 32.7319i | 1.75897 | − | 1.27797i | ||||
\(657\) | −2.66141 | + | 3.66312i | −0.103832 | + | 0.142912i | ||||
\(658\) | −49.0714 | + | 15.9443i | −1.91300 | + | 0.621572i | ||||
\(659\) | −42.0344 | −1.63743 | −0.818715 | − | 0.574201i | \(-0.805313\pi\) | ||||
−0.818715 | + | 0.574201i | \(0.805313\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.0902 | 0.586940 | 0.293470 | − | 0.955968i | \(-0.405190\pi\) | ||||
0.293470 | + | 0.955968i | \(0.405190\pi\) | |||||||
\(662\) | −42.4670 | + | 13.7984i | −1.65053 | + | 0.536289i | ||||
\(663\) | 3.80423 | − | 5.23607i | 0.147744 | − | 0.203352i | ||||
\(664\) | 13.9443 | − | 10.1311i | 0.541143 | − | 0.393163i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.736068 | + | 2.26538i | −0.0285221 | + | 0.0877819i | ||||
\(667\) | −2.31838 | − | 3.19098i | −0.0897682 | − | 0.123555i | ||||
\(668\) | −3.28195 | + | 4.51722i | −0.126983 | + | 0.174777i | ||||
\(669\) | −6.50000 | − | 20.0049i | −0.251305 | − | 0.773436i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −23.1631 | + | 1.57160i | −0.894202 | + | 0.0606709i | ||||
\(672\) | 17.7082i | 0.683109i | ||||||||
\(673\) | −33.5770 | + | 10.9098i | −1.29430 | + | 0.420543i | −0.873594 | − | 0.486655i | \(-0.838217\pi\) |
−0.420704 | + | 0.907198i | \(0.638217\pi\) | |||||||
\(674\) | 37.7705 | + | 27.4419i | 1.45487 | + | 1.05702i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.482779 | + | 1.48584i | −0.0185684 | + | 0.0571477i | ||||
\(677\) | 5.65334 | + | 1.83688i | 0.217275 | + | 0.0705971i | 0.415632 | − | 0.909533i | \(-0.363560\pi\) |
−0.198357 | + | 0.980130i | \(0.563560\pi\) | |||||||
\(678\) | −3.30220 | − | 4.54508i | −0.126820 | − | 0.174553i | ||||
\(679\) | −10.7082 | − | 7.77997i | −0.410943 | − | 0.298568i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.05573 | −0.308696 | ||||||||
\(682\) | 19.9722 | − | 31.8156i | 0.764775 | − | 1.21828i | ||||
\(683\) | 15.7082i | 0.601058i | 0.953773 | + | 0.300529i | \(0.0971632\pi\) | ||||
−0.953773 | + | 0.300529i | \(0.902837\pi\) | |||||||
\(684\) | −0.954915 | − | 2.93893i | −0.0365121 | − | 0.112373i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −91.9574 | + | 66.8110i | −3.51095 | + | 2.55086i | ||||
\(687\) | −6.57164 | − | 2.13525i | −0.250724 | − | 0.0814651i | ||||
\(688\) | 41.9650 | + | 13.6353i | 1.59990 | + | 0.519839i | ||||
\(689\) | −14.0902 | + | 10.2371i | −0.536793 | + | 0.390003i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.05573 | − | 27.8707i | −0.344496 | − | 1.06025i | −0.961853 | − | 0.273567i | \(-0.911797\pi\) |
0.617357 | − | 0.786683i | \(-0.288203\pi\) | |||||||
\(692\) | − | 10.2361i | − | 0.389117i | ||||||
\(693\) | −16.8415 | − | 4.23607i | −0.639756 | − | 0.160915i | ||||
\(694\) | 45.5967 | 1.73083 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.54508 | + | 1.12257i | 0.0585663 | + | 0.0425509i | ||||
\(697\) | −13.4863 | − | 18.5623i | −0.510830 | − | 0.703097i | ||||
\(698\) | 49.6062 | + | 16.1180i | 1.87762 | + | 0.610077i | ||||
\(699\) | 3.17376 | − | 9.76784i | 0.120043 | − | 0.369453i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.6976 | − | 23.7562i | −1.23497 | − | 0.897258i | −0.237717 | − | 0.971334i | \(-0.576399\pi\) |
−0.997253 | + | 0.0740763i | \(0.976399\pi\) | |||||||
\(702\) | −4.97980 | + | 1.61803i | −0.187950 | + | 0.0610688i | ||||
\(703\) | − | 7.36068i | − | 0.277613i | ||||||
\(704\) | −10.7812 | + | 9.00854i | −0.406330 | + | 0.339522i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.91641 | − | 27.4419i | −0.335573 | − | 1.03279i | ||||
\(707\) | −60.2066 | + | 82.8673i | −2.26430 | + | 3.11654i | ||||
\(708\) | −2.43690 | − | 3.35410i | −0.0915842 | − | 0.126055i | ||||
\(709\) | −5.81559 | + | 17.8986i | −0.218409 | + | 0.672195i | 0.780485 | + | 0.625175i | \(0.214972\pi\) |
−0.998894 | + | 0.0470197i | \(0.985028\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.50000 | + | 1.81636i | −0.0937573 | + | 0.0681187i | ||||
\(712\) | 5.44907 | − | 7.50000i | 0.204212 | − | 0.281074i | ||||
\(713\) | 30.7441 | − | 9.98936i | 1.15137 | − | 0.374104i | ||||
\(714\) | 16.9443 | 0.634123 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.50658 | −0.243162 | ||||||||
\(717\) | 20.9560 | − | 6.80902i | 0.782616 | − | 0.254287i | ||||
\(718\) | 3.13068 | − | 4.30902i | 0.116836 | − | 0.160811i | ||||
\(719\) | 21.7705 | − | 15.8172i | 0.811903 | − | 0.589882i | −0.102479 | − | 0.994735i | \(-0.532677\pi\) |
0.914382 | + | 0.404853i | \(0.132677\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.47214 | + | 22.9969i | −0.278277 | + | 0.856448i | ||||
\(722\) | 5.70634 | + | 7.85410i | 0.212368 | + | 0.292299i | ||||
\(723\) | 0.363271 | − | 0.500000i | 0.0135102 | − | 0.0185952i | ||||
\(724\) | 0.145898 | + | 0.449028i | 0.00542226 | + | 0.0166880i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.73607 | + | 16.0292i | 0.287112 | + | 0.594900i | ||||
\(727\) | 21.6738i | 0.803835i | 0.915676 | + | 0.401918i | \(0.131656\pi\) | ||||
−0.915676 | + | 0.401918i | \(0.868344\pi\) | |||||||
\(728\) | −36.0341 | + | 11.7082i | −1.33551 | + | 0.433935i | ||||
\(729\) | 0.809017 | + | 0.587785i | 0.0299636 | + | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.61803 | − | 17.2905i | 0.207790 | − | 0.639513i | ||||
\(732\) | −4.11450 | − | 1.33688i | −0.152076 | − | 0.0494125i | ||||
\(733\) | −2.85317 | − | 3.92705i | −0.105384 | − | 0.145049i | 0.753068 | − | 0.657943i | \(-0.228573\pi\) |
−0.858452 | + | 0.512894i | \(0.828573\pi\) | |||||||
\(734\) | −28.9615 | − | 21.0418i | −1.06899 | − | 0.776665i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15.6180 | 0.575688 | ||||||||
\(737\) | −35.7566 | + | 14.3607i | −1.31711 | + | 0.528982i | ||||
\(738\) | 18.5623i | 0.683288i | ||||||||
\(739\) | 6.18034 | + | 19.0211i | 0.227347 | + | 0.699704i | 0.998045 | + | 0.0625022i | \(0.0199080\pi\) |
−0.770697 | + | 0.637201i | \(0.780092\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.0902 | − | 9.51057i | 0.480879 | − | 0.349379i | ||||
\(742\) | −43.3651 | − | 14.0902i | −1.59198 | − | 0.517266i | ||||
\(743\) | −30.1033 | − | 9.78115i | −1.10438 | − | 0.358836i | −0.300595 | − | 0.953752i | \(-0.597185\pi\) |
−0.803788 | + | 0.594916i | \(0.797185\pi\) | |||||||
\(744\) | −12.6631 | + | 9.20029i | −0.464252 | + | 0.337299i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 16.3713 | + | 50.3858i | 0.599397 | + | 1.84475i | ||||
\(747\) | 7.70820i | 0.282028i | ||||||||
\(748\) | −2.62866 | − | 3.14590i | −0.0961132 | − | 0.115025i | ||||
\(749\) | −20.1803 | −0.737374 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.18034 | + | 5.94336i | 0.298505 | + | 0.216876i | 0.726948 | − | 0.686692i | \(-0.240938\pi\) |
−0.428444 | + | 0.903569i | \(0.640938\pi\) | |||||||
\(752\) | −17.3763 | − | 23.9164i | −0.633648 | − | 0.872142i | ||||
\(753\) | 15.6659 | + | 5.09017i | 0.570898 | + | 0.185496i | ||||
\(754\) | 1.38197 | − | 4.25325i | 0.0503282 | − | 0.154894i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.61803 | − | 1.90211i | −0.0952170 | − | 0.0691792i | ||||
\(757\) | 1.73060 | − | 0.562306i | 0.0628997 | − | 0.0204374i | −0.277398 | − | 0.960755i | \(-0.589472\pi\) |
0.340298 | + | 0.940318i | \(0.389472\pi\) | |||||||
\(758\) | − | 8.09017i | − | 0.293848i | ||||||
\(759\) | −3.73607 | + | 14.8536i | −0.135611 | + | 0.539153i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.07953 | + | 9.47781i | 0.111633 | + | 0.343570i | 0.991230 | − | 0.132149i | \(-0.0421878\pi\) |
−0.879597 | + | 0.475719i | \(0.842188\pi\) | |||||||
\(762\) | −1.84911 | + | 2.54508i | −0.0669863 | + | 0.0921987i | ||||
\(763\) | −33.4055 | − | 45.9787i | −1.20936 | − | 1.66454i | ||||
\(764\) | 3.13525 | − | 9.64932i | 0.113430 | − | 0.349100i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17.4894 | − | 12.7068i | 0.631916 | − | 0.459114i | ||||
\(767\) | 12.7598 | − | 17.5623i | 0.460728 | − | 0.634138i | ||||
\(768\) | −12.8985 | + | 4.19098i | −0.465435 | + | 0.151229i | ||||
\(769\) | −17.2361 | −0.621549 | −0.310774 | − | 0.950484i | \(-0.600588\pi\) | ||||
−0.310774 | + | 0.950484i | \(0.600588\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.56231 | −0.344378 | ||||||||
\(772\) | −4.72253 | + | 1.53444i | −0.169967 | + | 0.0552258i | ||||
\(773\) | −16.1680 | + | 22.2533i | −0.581521 | + | 0.800395i | −0.993861 | − | 0.110635i | \(-0.964712\pi\) |
0.412340 | + | 0.911030i | \(0.364712\pi\) | |||||||
\(774\) | −11.8992 | + | 8.64527i | −0.427707 | + | 0.310748i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.74671 | − | 5.37582i | 0.0627033 | − | 0.192981i | ||||
\(777\) | −4.53077 | − | 6.23607i | −0.162540 | − | 0.223718i | ||||
\(778\) | −20.0252 | + | 27.5623i | −0.717938 | + | 0.988157i | ||||
\(779\) | −17.7254 | − | 54.5532i | −0.635079 | − | 1.95457i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 26.4721 | − | 1.79611i | 0.947247 | − | 0.0642699i | ||||
\(782\) | − | 14.9443i | − | 0.534406i | ||||||
\(783\) | −0.812299 | + | 0.263932i | −0.0290292 | + | 0.00943216i | ||||
\(784\) | −80.1763 | − | 58.2515i | −2.86344 | − | 2.08041i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.59017 | + | 14.1271i | −0.163726 | + | 0.503897i | ||||
\(787\) | −31.1931 | − | 10.1353i | −1.11191 | − | 0.361283i | −0.305238 | − | 0.952276i | \(-0.598736\pi\) |
−0.806676 | + | 0.590993i | \(0.798736\pi\) | |||||||
\(788\) | 3.54696 | + | 4.88197i | 0.126355 | + | 0.173913i | ||||
\(789\) | −19.5902 | − | 14.2331i | −0.697429 | − | 0.506711i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.1803 | 0.646418 | ||||||||
\(792\) | −0.502029 | − | 7.39919i | −0.0178388 | − | 0.262919i | ||||
\(793\) | − | 22.6525i | − | 0.804413i | ||||||
\(794\) | 1.36475 | + | 4.20025i | 0.0484330 | + | 0.149061i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.39919 | − | 1.74311i | 0.0850369 | − | 0.0617829i | ||||
\(797\) | 14.5434 | + | 4.72542i | 0.515152 | + | 0.167383i | 0.555044 | − | 0.831821i | \(-0.312701\pi\) |
−0.0398919 | + | 0.999204i | \(0.512701\pi\) | |||||||
\(798\) | 40.2874 | + | 13.0902i | 1.42616 | + | 0.463387i | ||||
\(799\) | −9.85410 | + | 7.15942i | −0.348613 | + | 0.253282i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.28115 | + | 3.94298i | 0.0452673 | + | 0.139318i | ||||
\(802\) | 49.9787i | 1.76481i | ||||||||
\(803\) | −7.98424 | + | 12.7188i | −0.281758 | + | 0.448838i | ||||
\(804\) | −7.18034 | −0.253231 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 29.6525 | + | 21.5438i | 1.04446 | + | 0.758847i | ||||
\(807\) | 0.502029 | + | 0.690983i | 0.0176722 | + | 0.0243238i | ||||
\(808\) | −41.6017 | − | 13.5172i | −1.46354 | − | 0.475534i | ||||
\(809\) | −9.16970 | + | 28.2214i | −0.322389 | + | 0.992212i | 0.650216 | + | 0.759750i | \(0.274678\pi\) |
−0.972605 | + | 0.232463i | \(0.925322\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35.2984 | − | 25.6458i | −1.23949 | − | 0.900545i | −0.241929 | − | 0.970294i | \(-0.577780\pi\) |
−0.997565 | + | 0.0697492i | \(0.977780\pi\) | |||||||
\(812\) | 2.62866 | − | 0.854102i | 0.0922477 | − | 0.0299731i | ||||
\(813\) | 18.3820i | 0.644684i | ||||||||
\(814\) | −1.92705 | + | 7.66145i | −0.0675431 | + | 0.268534i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.00000 | + | 9.23305i | 0.105021 | + | 0.323221i | ||||
\(817\) | 26.7153 | − | 36.7705i | 0.934651 | − | 1.28644i | ||||
\(818\) | 25.0175 | + | 34.4336i | 0.874716 | + | 1.20394i | ||||
\(819\) | 5.23607 | − | 16.1150i | 0.182963 | − | 0.563102i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.8435 | + | 12.2375i | −0.587841 | + | 0.427091i | −0.841542 | − | 0.540191i | \(-0.818352\pi\) |
0.253702 | + | 0.967283i | \(0.418352\pi\) | |||||||
\(822\) | 5.03280 | − | 6.92705i | 0.175539 | − | 0.241609i | ||||
\(823\) | 15.7189 | − | 5.10739i | 0.547928 | − | 0.178032i | −0.0219545 | − | 0.999759i | \(-0.506989\pi\) |
0.569882 | + | 0.821727i | \(0.306989\pi\) | |||||||
\(824\) | −10.3262 | −0.359732 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 56.8328 | 1.97747 | ||||||||
\(827\) | 48.8999 | − | 15.8885i | 1.70042 | − | 0.552499i | 0.711724 | − | 0.702459i | \(-0.247914\pi\) |
0.988692 | + | 0.149960i | \(0.0479145\pi\) | |||||||
\(828\) | −1.67760 | + | 2.30902i | −0.0583006 | + | 0.0802439i | ||||
\(829\) | −26.6074 | + | 19.3314i | −0.924113 | + | 0.671407i | −0.944544 | − | 0.328384i | \(-0.893496\pi\) |
0.0204314 | + | 0.999791i | \(0.493496\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.00000 | + | 21.5438i | −0.242827 | + | 0.747346i | ||||
\(832\) | −8.05748 | − | 11.0902i | −0.279343 | − | 0.384482i | ||||
\(833\) | −24.0009 | + | 33.0344i | −0.831583 | + | 1.14458i | ||||
\(834\) | 0.590170 | + | 1.81636i | 0.0204359 | + | 0.0628953i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.81966 | − | 9.51057i | −0.132106 | − | 0.328930i | ||||
\(837\) | − | 7.00000i | − | 0.241955i | ||||||
\(838\) | 37.8505 | − | 12.2984i | 1.30752 | − | 0.424840i | ||||
\(839\) | 29.3713 | + | 21.3395i | 1.01401 | + | 0.736722i | 0.965047 | − | 0.262079i | \(-0.0844080\pi\) |
0.0489642 | + | 0.998801i | \(0.484408\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.73607 | + | 26.8869i | −0.301244 | + | 0.927133i | ||||
\(842\) | 5.93085 | + | 1.92705i | 0.204391 | + | 0.0664106i | ||||
\(843\) | 0.640786 | + | 0.881966i | 0.0220698 | + | 0.0303765i | ||||
\(844\) | 1.42705 | + | 1.03681i | 0.0491211 | + | 0.0356886i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.85410 | 0.338791 | ||||||||
\(847\) | −56.6799 | − | 10.2361i | −1.94754 | − | 0.351715i | ||||
\(848\) | − | 26.1246i | − | 0.897123i | ||||||
\(849\) | −4.95492 | − | 15.2497i | −0.170052 | − | 0.523367i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.50000 | + | 3.99598i | −0.188538 | + | 0.136981i | ||||
\(852\) | 4.70228 | + | 1.52786i | 0.161098 | + | 0.0523438i | ||||
\(853\) | −22.2173 | − | 7.21885i | −0.760707 | − | 0.247169i | −0.0971248 | − | 0.995272i | \(-0.530965\pi\) |
−0.663582 | + | 0.748104i | \(0.730965\pi\) | |||||||
\(854\) | 47.9787 | − | 34.8586i | 1.64180 | − | 1.19284i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.66312 | − | 8.19624i | −0.0910235 | − | 0.280142i | ||||
\(857\) | − | 41.0132i | − | 1.40098i | −0.713661 | − | 0.700491i | \(-0.752964\pi\) | ||
0.713661 | − | 0.700491i | \(-0.247036\pi\) | |||||||
\(858\) | −16.1150 | + | 6.47214i | −0.550156 | + | 0.220955i | ||||
\(859\) | 39.2705 | 1.33989 | 0.669946 | − | 0.742410i | \(-0.266317\pi\) | ||||
0.669946 | + | 0.742410i | \(0.266317\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −48.5967 | − | 35.3076i | −1.65617 | − | 1.20328i | ||||
\(862\) | −15.1109 | − | 20.7984i | −0.514679 | − | 0.708395i | ||||
\(863\) | −21.9071 | − | 7.11803i | −0.745725 | − | 0.242301i | −0.0885842 | − | 0.996069i | \(-0.528234\pi\) |
−0.657141 | + | 0.753768i | \(0.728234\pi\) | |||||||
\(864\) | 1.04508 | − | 3.21644i | 0.0355545 | − | 0.109426i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.35410 | − | 0.983813i | −0.0460143 | − | 0.0334313i | ||||
\(867\) | −12.3637 | + | 4.01722i | −0.419894 | + | 0.136432i | ||||
\(868\) | 22.6525i | 0.768875i | ||||||||
\(869\) | −7.86475 | + | 6.57164i | −0.266793 | + | 0.222928i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.6180 | − | 35.7566i | −0.393662 | − | 1.21157i | ||||
\(872\) | 14.2658 | − | 19.6353i | 0.483103 | − | 0.664934i | ||||
\(873\) | 1.48584 | + | 2.04508i | 0.0502881 | + | 0.0692156i | ||||
\(874\) | 11.5451 | − | 35.5321i | 0.390518 | − | 1.20189i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.26393 | + | 1.64484i | −0.0764912 | + | 0.0555741i | ||||
\(877\) | 4.42477 | − | 6.09017i | 0.149414 | − | 0.205650i | −0.727749 | − | 0.685844i | \(-0.759433\pi\) |
0.877163 | + | 0.480193i | \(0.159433\pi\) | |||||||
\(878\) | −38.9731 | + | 12.6631i | −1.31528 | + | 0.427360i | ||||
\(879\) | 25.4721 | 0.859154 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.1459 | −0.577660 | −0.288830 | − | 0.957380i | \(-0.593266\pi\) | ||||
−0.288830 | + | 0.957380i | \(0.593266\pi\) | |||||||
\(882\) | 31.4176 | − | 10.2082i | 1.05789 | − | 0.343728i | ||||
\(883\) | −13.6578 | + | 18.7984i | −0.459622 | + | 0.632616i | −0.974430 | − | 0.224690i | \(-0.927863\pi\) |
0.514808 | + | 0.857305i | \(0.327863\pi\) | |||||||
\(884\) | 3.23607 | − | 2.35114i | 0.108841 | − | 0.0790774i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.13525 | − | 12.7270i | 0.138927 | − | 0.427572i | ||||
\(887\) | −0.0982684 | − | 0.135255i | −0.00329953 | − | 0.00454142i | 0.807364 | − | 0.590054i | \(-0.200893\pi\) |
−0.810664 | + | 0.585512i | \(0.800893\pi\) | |||||||
\(888\) | 1.93487 | − | 2.66312i | 0.0649300 | − | 0.0893684i | ||||
\(889\) | −3.14590 | − | 9.68208i | −0.105510 | − | 0.324726i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.80902 | + | 1.76336i | 0.0941056 | + | 0.0590746i | ||||
\(892\) | − | 13.0000i | − | 0.435272i | ||||||
\(893\) | −28.9605 | + | 9.40983i | −0.969125 | + | 0.314888i | ||||
\(894\) | −26.3435 | − | 19.1396i | −0.881057 | − | 0.640125i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 22.0344 | − | 67.8150i | 0.736119 | − | 2.26554i | ||||
\(897\) | −14.2128 | − | 4.61803i | −0.474553 | − | 0.154192i | ||||
\(898\) | 32.5932 | + | 44.8607i | 1.08765 | + | 1.49702i | ||||
\(899\) | 4.83688 | + | 3.51420i | 0.161319 | + | 0.117205i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.7639 | −0.358599 | ||||||||
\(902\) | 4.16750 | + | 61.4230i | 0.138762 | + | 2.04516i | ||||
\(903\) | − | 47.5967i | − | 1.58392i | ||||||
\(904\) | 2.39919 | + | 7.38394i | 0.0797958 | + | 0.245586i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 19.9443 | − | 14.4904i | 0.662604 | − | 0.481410i | ||||
\(907\) | 42.6915 | + | 13.8713i | 1.41755 | + | 0.460590i | 0.914823 | − | 0.403856i | \(-0.132330\pi\) |
0.502727 | + | 0.864445i | \(0.332330\pi\) | |||||||
\(908\) | −4.73504 | − | 1.53851i | −0.157138 | − | 0.0510572i | ||||
\(909\) | 15.8262 | − | 11.4984i | 0.524923 | − | 0.381379i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.3475 | + | 50.3125i | 0.541618 | + | 1.66693i | 0.728899 | + | 0.684621i | \(0.240032\pi\) |
−0.187281 | + | 0.982306i | \(0.559968\pi\) | |||||||
\(912\) | 24.2705i | 0.803677i | ||||||||
\(913\) | 1.73060 | + | 25.5066i | 0.0572745 | + | 0.844145i | ||||
\(914\) | −12.0902 | −0.399907 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.45492 | − | 2.51014i | −0.114154 | − | 0.0829374i | ||||
\(917\) | −28.2542 | − | 38.8885i | −0.933035 | − | 1.28421i | ||||
\(918\) | −3.07768 | − | 1.00000i | −0.101579 | − | 0.0330049i | ||||
\(919\) | 6.87132 | − | 21.1478i | 0.226664 | − | 0.697600i | −0.771454 | − | 0.636285i | \(-0.780470\pi\) |
0.998118 | − | 0.0613155i | \(-0.0195296\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.7533 | − | 16.5312i | −0.749746 | − | 0.544723i | ||||
\(922\) | 12.3965 | − | 4.02786i | 0.408257 | − | 0.132651i | ||||
\(923\) | 25.8885i | 0.852132i | ||||||||
\(924\) | −9.09017 | − | 5.70634i | −0.299045 | − | 0.187725i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −0.135255 | − | 0.416272i | −0.00444475 | − | 0.0136795i | ||||
\(927\) | 2.71441 | − | 3.73607i | 0.0891530 | − | 0.122709i | ||||
\(928\) | 1.69784 | + | 2.33688i | 0.0557344 | + | 0.0767119i | ||||
\(929\) | 3.35410 | − | 10.3229i | 0.110045 | − | 0.338682i | −0.880837 | − | 0.473420i | \(-0.843019\pi\) |
0.990881 | + | 0.134738i | \(0.0430193\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −82.5861 | + | 60.0023i | −2.70665 | + | 1.96650i | ||||
\(932\) | 3.73098 | − | 5.13525i | 0.122212 | − | 0.168211i | ||||
\(933\) | −11.9147 | + | 3.87132i | −0.390070 | + | 0.126741i | ||||
\(934\) | −49.9787 | −1.63535 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.23607 | 0.236518 | ||||||||
\(937\) | −16.3597 | + | 5.31559i | −0.534449 | + | 0.173653i | −0.563793 | − | 0.825916i | \(-0.690658\pi\) |
0.0293438 | + | 0.999569i | \(0.490658\pi\) | |||||||
\(938\) | 57.8554 | − | 79.6312i | 1.88905 | − | 2.60005i | ||||
\(939\) | 6.85410 | − | 4.97980i | 0.223675 | − | 0.162510i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.00000 | + | 9.23305i | −0.0977972 | + | 0.300989i | −0.987973 | − | 0.154629i | \(-0.950582\pi\) |
0.890175 | + | 0.455618i | \(0.150582\pi\) | |||||||
\(942\) | −11.7229 | − | 16.1353i | −0.381954 | − | 0.525715i | ||||
\(943\) | −31.1401 | + | 42.8607i | −1.01406 | + | 1.39574i | ||||
\(944\) | 10.0623 | + | 30.9686i | 0.327500 | + | 1.00794i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −37.4336 | + | 31.2789i | −1.21707 | + | 1.01696i | ||||
\(947\) | 4.56231i | 0.148255i | 0.997249 | + | 0.0741275i | \(0.0236172\pi\) | ||||
−0.997249 | + | 0.0741275i | \(0.976383\pi\) | |||||||
\(948\) | −1.81636 | + | 0.590170i | −0.0589925 | + | 0.0191678i | ||||
\(949\) | −11.8541 | − | 8.61251i | −0.384800 | − | 0.279574i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.10739 | + | 3.40820i | −0.0359096 | + | 0.110518i | ||||
\(952\) | −22.2703 | − | 7.23607i | −0.721785 | − | 0.234522i | ||||
\(953\) | 28.8545 | + | 39.7148i | 0.934688 | + | 1.28649i | 0.958003 | + | 0.286760i | \(0.0925782\pi\) |
−0.0233143 | + | 0.999728i | \(0.507422\pi\) | |||||||
\(954\) | 7.04508 | + | 5.11855i | 0.228093 | + | 0.165719i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 13.6180 | 0.440439 | ||||||||
\(957\) | −2.62866 | + | 1.05573i | −0.0849724 | + | 0.0341268i | ||||
\(958\) | 10.6525i | 0.344166i | ||||||||
\(959\) | 8.56231 | + | 26.3521i | 0.276491 | + | 0.850953i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.5623 | + | 10.5801i | −0.469752 | + | 0.341295i | ||||
\(962\) | −7.33094 | − | 2.38197i | −0.236359 | − | 0.0767977i | ||||
\(963\) | 3.66547 | + | 1.19098i | 0.118118 | + | 0.0383789i | ||||
\(964\) | 0.309017 | − | 0.224514i | 0.00995277 | − | 0.00723111i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −12.0902 | − | 37.2097i | −0.388995 | − | 1.19720i | ||||
\(967\) | − | 32.6738i | − | 1.05072i | −0.850881 | − | 0.525359i | \(-0.823931\pi\) | ||
0.850881 | − | 0.525359i | \(-0.176069\pi\) | |||||||
\(968\) | −3.32244 | − | 24.3713i | −0.106787 | − | 0.783324i | ||||
\(969\) | 10.0000 | 0.321246 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.5172 | + | 18.5393i | 0.818887 | + | 0.594956i | 0.916393 | − | 0.400279i | \(-0.131087\pi\) |
−0.0975068 | + | 0.995235i | \(0.531087\pi\) | |||||||
\(972\) | 0.363271 | + | 0.500000i | 0.0116519 | + | 0.0160375i | ||||
\(973\) | −5.87785 | − | 1.90983i | −0.188435 | − | 0.0612263i | ||||
\(974\) | 4.09017 | − | 12.5882i | 0.131057 | − | 0.403354i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 27.4894 | + | 19.9722i | 0.879913 | + | 0.639294i | ||||
\(977\) | 43.8344 | − | 14.2426i | 1.40239 | − | 0.455663i | 0.492424 | − | 0.870356i | \(-0.336111\pi\) |
0.909961 | + | 0.414693i | \(0.136111\pi\) | |||||||
\(978\) | 10.6180i | 0.339527i | ||||||||
\(979\) | 5.12461 | + | 12.7598i | 0.163783 | + | 0.407804i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.35410 | + | 10.3229i | 0.107088 | + | 0.329584i | ||||
\(982\) | −6.84915 | + | 9.42705i | −0.218565 | + | 0.300829i | ||||
\(983\) | −11.1679 | − | 15.3713i | −0.356201 | − | 0.490269i | 0.592884 | − | 0.805288i | \(-0.297989\pi\) |
−0.949085 | + | 0.315019i | \(0.897989\pi\) | |||||||
\(984\) | 7.92705 | − | 24.3970i | 0.252705 | − | 0.777746i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.23607 | − | 1.62460i | 0.0712109 | − | 0.0517378i | ||||
\(987\) | −18.7436 | + | 25.7984i | −0.596616 | + | 0.821171i | ||||
\(988\) | 9.51057 | − | 3.09017i | 0.302571 | − | 0.0983114i | ||||
\(989\) | −41.9787 | −1.33485 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.00000 | −0.254128 | −0.127064 | − | 0.991894i | \(-0.540555\pi\) | ||||
−0.127064 | + | 0.991894i | \(0.540555\pi\) | |||||||
\(992\) | −22.5151 | + | 7.31559i | −0.714855 | + | 0.232270i | ||||
\(993\) | −16.2210 | + | 22.3262i | −0.514757 | + | 0.708502i | ||||
\(994\) | −54.8328 | + | 39.8384i | −1.73919 | + | 1.26360i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.47214 | + | 4.53077i | −0.0466464 | + | 0.143563i | ||||
\(997\) | 6.63715 | + | 9.13525i | 0.210201 | + | 0.289316i | 0.901079 | − | 0.433654i | \(-0.142776\pi\) |
−0.690879 | + | 0.722971i | \(0.742776\pi\) | |||||||
\(998\) | 10.6331 | − | 14.6353i | 0.336586 | − | 0.463271i | ||||
\(999\) | 0.454915 | + | 1.40008i | 0.0143929 | + | 0.0442967i |
(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 | 825.2.bx.c.49.2 | 8 | ||
5.2 | odd | 4 | 825.2.n.d.676.1 | yes | 4 | ||
5.3 | odd | 4 | 825.2.n.b.676.1 | yes | 4 | ||
5.4 | even | 2 | inner | 825.2.bx.c.49.1 | 8 | ||
11.9 | even | 5 | inner | 825.2.bx.c.724.1 | 8 | ||
55.3 | odd | 20 | 9075.2.a.z.1.1 | 2 | |||
55.8 | even | 20 | 9075.2.a.bt.1.2 | 2 | |||
55.9 | even | 10 | inner | 825.2.bx.c.724.2 | 8 | ||
55.42 | odd | 20 | 825.2.n.d.526.1 | yes | 4 | ||
55.47 | odd | 20 | 9075.2.a.by.1.2 | 2 | |||
55.52 | even | 20 | 9075.2.a.bc.1.1 | 2 | |||
55.53 | odd | 20 | 825.2.n.b.526.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.2.n.b.526.1 | ✓ | 4 | 55.53 | odd | 20 | ||
825.2.n.b.676.1 | yes | 4 | 5.3 | odd | 4 | ||
825.2.n.d.526.1 | yes | 4 | 55.42 | odd | 20 | ||
825.2.n.d.676.1 | yes | 4 | 5.2 | odd | 4 | ||
825.2.bx.c.49.1 | 8 | 5.4 | even | 2 | inner | ||
825.2.bx.c.49.2 | 8 | 1.1 | even | 1 | trivial | ||
825.2.bx.c.724.1 | 8 | 11.9 | even | 5 | inner | ||
825.2.bx.c.724.2 | 8 | 55.9 | even | 10 | inner | ||
9075.2.a.z.1.1 | 2 | 55.3 | odd | 20 | |||
9075.2.a.bc.1.1 | 2 | 55.52 | even | 20 | |||
9075.2.a.bt.1.2 | 2 | 55.8 | even | 20 | |||
9075.2.a.by.1.2 | 2 | 55.47 | odd | 20 |