Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [867,2,Mod(688,867)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(867, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([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("867.688");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 867 = 3 \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 867.h (of order \(8\), 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: | \(6.92302985525\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{8})\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 51) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 688.1 | ||
Root | \(0.923880 + 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 867.688 |
Dual form | 867.2.h.c.712.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/867\mathbb{Z}\right)^\times\).
\(n\) | \(290\) | \(292\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{8}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(3\) | −0.382683 | + | 0.923880i | −0.220942 | + | 0.533402i | ||||
\(4\) | 2.00000i | 1.00000i | ||||||||
\(5\) | −2.77164 | − | 1.14805i | −1.23951 | − | 0.513424i | −0.335952 | − | 0.941879i | \(-0.609058\pi\) |
−0.903563 | + | 0.428456i | \(0.859058\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.69552 | − | 1.53073i | 1.39677 | − | 0.578563i | 0.447862 | − | 0.894103i | \(-0.352186\pi\) |
0.948912 | + | 0.315540i | \(0.102186\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.707107 | − | 0.707107i | −0.235702 | − | 0.235702i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.14805 | − | 2.77164i | −0.346150 | − | 0.835680i | −0.997067 | − | 0.0765316i | \(-0.975615\pi\) |
0.650917 | − | 0.759149i | \(-0.274385\pi\) | |||||||
\(12\) | −1.84776 | − | 0.765367i | −0.533402 | − | 0.220942i | ||||
\(13\) | − | 1.00000i | − | 0.277350i | −0.990338 | − | 0.138675i | \(-0.955716\pi\) | ||
0.990338 | − | 0.138675i | \(-0.0442844\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.12132 | − | 2.12132i | 0.547723 | − | 0.547723i | ||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.707107 | − | 0.707107i | 0.162221 | − | 0.162221i | −0.621329 | − | 0.783550i | \(-0.713407\pi\) |
0.783550 | + | 0.621329i | \(0.213407\pi\) | |||||||
\(20\) | 2.29610 | − | 5.54328i | 0.513424 | − | 1.23951i | ||||
\(21\) | 4.00000i | 0.872872i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.44415 | − | 8.31492i | −0.718155 | − | 1.73378i | −0.678538 | − | 0.734565i | \(-0.737386\pi\) |
−0.0396166 | − | 0.999215i | \(-0.512614\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.82843 | + | 2.82843i | 0.565685 | + | 0.565685i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.923880 | − | 0.382683i | 0.177801 | − | 0.0736475i | ||||
\(28\) | 3.06147 | + | 7.39104i | 0.578563 | + | 1.39677i | ||||
\(29\) | 5.54328 | + | 2.29610i | 1.02936 | + | 0.426375i | 0.832482 | − | 0.554053i | \(-0.186919\pi\) |
0.196879 | + | 0.980428i | \(0.436919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.765367 | − | 1.84776i | 0.137464 | − | 0.331867i | −0.840124 | − | 0.542394i | \(-0.817518\pi\) |
0.977588 | + | 0.210527i | \(0.0675179\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.00000 | 0.522233 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −12.0000 | −2.02837 | ||||||||
\(36\) | 1.41421 | − | 1.41421i | 0.235702 | − | 0.235702i | ||||
\(37\) | 1.53073 | − | 3.69552i | 0.251651 | − | 0.607539i | −0.746687 | − | 0.665176i | \(-0.768356\pi\) |
0.998338 | + | 0.0576366i | \(0.0183565\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.923880 | + | 0.382683i | 0.147939 | + | 0.0612784i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.77164 | − | 1.14805i | 0.432857 | − | 0.179295i | −0.155606 | − | 0.987819i | \(-0.549733\pi\) |
0.588463 | + | 0.808524i | \(0.299733\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.94975 | + | 4.94975i | 0.754829 | + | 0.754829i | 0.975376 | − | 0.220547i | \(-0.0707842\pi\) |
−0.220547 | + | 0.975376i | \(0.570784\pi\) | |||||||
\(44\) | 5.54328 | − | 2.29610i | 0.835680 | − | 0.346150i | ||||
\(45\) | 1.14805 | + | 2.77164i | 0.171141 | + | 0.413171i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 6.00000i | − | 0.875190i | −0.899172 | − | 0.437595i | \(-0.855830\pi\) | ||
0.899172 | − | 0.437595i | \(-0.144170\pi\) | |||||||
\(48\) | 1.53073 | − | 3.69552i | 0.220942 | − | 0.533402i | ||||
\(49\) | 6.36396 | − | 6.36396i | 0.909137 | − | 0.909137i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | 4.24264 | − | 4.24264i | 0.582772 | − | 0.582772i | −0.352892 | − | 0.935664i | \(-0.614802\pi\) |
0.935664 | + | 0.352892i | \(0.114802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.00000i | 1.21356i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.382683 | + | 0.923880i | 0.0506877 | + | 0.122371i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.24264 | + | 4.24264i | 0.552345 | + | 0.552345i | 0.927117 | − | 0.374772i | \(-0.122279\pi\) |
−0.374772 | + | 0.927117i | \(0.622279\pi\) | |||||||
\(60\) | 4.24264 | + | 4.24264i | 0.547723 | + | 0.547723i | ||||
\(61\) | 7.39104 | − | 3.06147i | 0.946325 | − | 0.391981i | 0.144477 | − | 0.989508i | \(-0.453850\pi\) |
0.801848 | + | 0.597527i | \(0.203850\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.69552 | − | 1.53073i | −0.465592 | − | 0.192854i | ||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | −1.14805 | + | 2.77164i | −0.142398 | + | 0.343779i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.00000 | 1.08347 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.59220 | + | 11.0866i | −0.544994 | + | 1.31573i | 0.376168 | + | 0.926552i | \(0.377242\pi\) |
−0.921162 | + | 0.389180i | \(0.872758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.84776 | − | 0.765367i | −0.216264 | − | 0.0895794i | 0.271921 | − | 0.962319i | \(-0.412341\pi\) |
−0.488185 | + | 0.872740i | \(0.662341\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.69552 | + | 1.53073i | −0.426722 | + | 0.176754i | ||||
\(76\) | 1.41421 | + | 1.41421i | 0.162221 | + | 0.162221i | ||||
\(77\) | −8.48528 | − | 8.48528i | −0.966988 | − | 0.966988i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.82683 | − | 9.23880i | −0.430552 | − | 1.03945i | −0.979110 | − | 0.203333i | \(-0.934823\pi\) |
0.548557 | − | 0.836113i | \(-0.315177\pi\) | |||||||
\(80\) | 11.0866 | + | 4.59220i | 1.23951 | + | 0.513424i | ||||
\(81\) | 1.00000i | 0.111111i | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.24264 | + | 4.24264i | −0.465690 | + | 0.465690i | −0.900515 | − | 0.434825i | \(-0.856810\pi\) |
0.434825 | + | 0.900515i | \(0.356810\pi\) | |||||||
\(84\) | −8.00000 | −0.872872 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.24264 | + | 4.24264i | −0.454859 | + | 0.454859i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.53073 | − | 3.69552i | −0.160464 | − | 0.387396i | ||||
\(92\) | 16.6298 | − | 6.88830i | 1.73378 | − | 0.718155i | ||||
\(93\) | 1.41421 | + | 1.41421i | 0.146647 | + | 0.146647i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.77164 | + | 1.14805i | −0.284364 | + | 0.117787i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.7821 | − | 6.12293i | −1.50089 | − | 0.621690i | −0.527238 | − | 0.849718i | \(-0.676772\pi\) |
−0.973655 | + | 0.228028i | \(0.926772\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.14805 | + | 2.77164i | −0.115383 | + | 0.278560i | ||||
\(100\) | −5.65685 | + | 5.65685i | −0.565685 | + | 0.565685i | ||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.00000 | 0.492665 | 0.246332 | − | 0.969185i | \(-0.420775\pi\) | ||||
0.246332 | + | 0.969185i | \(0.420775\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.59220 | − | 11.0866i | 0.448153 | − | 1.08194i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.31492 | − | 3.44415i | −0.803833 | − | 0.332959i | −0.0573426 | − | 0.998355i | \(-0.518263\pi\) |
−0.746491 | + | 0.665396i | \(0.768263\pi\) | |||||||
\(108\) | 0.765367 | + | 1.84776i | 0.0736475 | + | 0.177801i | ||||
\(109\) | −18.4776 | + | 7.65367i | −1.76983 | + | 0.733089i | −0.774953 | + | 0.632019i | \(0.782226\pi\) |
−0.994879 | + | 0.101069i | \(0.967774\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.82843 | + | 2.82843i | 0.268462 | + | 0.268462i | ||||
\(112\) | −14.7821 | + | 6.12293i | −1.39677 | + | 0.578563i | ||||
\(113\) | −3.44415 | − | 8.31492i | −0.323998 | − | 0.782201i | −0.999014 | − | 0.0443979i | \(-0.985863\pi\) |
0.675015 | − | 0.737804i | \(-0.264137\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 27.0000i | 2.51776i | ||||||||
\(116\) | −4.59220 | + | 11.0866i | −0.426375 | + | 1.02936i | ||||
\(117\) | −0.707107 | + | 0.707107i | −0.0653720 | + | 0.0653720i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.41421 | − | 1.41421i | 0.128565 | − | 0.128565i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.00000i | 0.270501i | ||||||||
\(124\) | 3.69552 | + | 1.53073i | 0.331867 | + | 0.137464i | ||||
\(125\) | 1.14805 | + | 2.77164i | 0.102685 | + | 0.247903i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.19239 | − | 9.19239i | −0.815693 | − | 0.815693i | 0.169788 | − | 0.985481i | \(-0.445692\pi\) |
−0.985481 | + | 0.169788i | \(0.945692\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.46716 | + | 2.67878i | −0.569401 | + | 0.235854i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.77164 | + | 1.14805i | 0.242159 | + | 0.100306i | 0.500462 | − | 0.865758i | \(-0.333163\pi\) |
−0.258303 | + | 0.966064i | \(0.583163\pi\) | |||||||
\(132\) | 6.00000i | 0.522233i | ||||||||
\(133\) | 1.53073 | − | 3.69552i | 0.132731 | − | 0.320442i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.00000 | −0.258199 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.00000 | −0.512615 | −0.256307 | − | 0.966595i | \(-0.582506\pi\) | ||||
−0.256307 | + | 0.966595i | \(0.582506\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.765367 | + | 1.84776i | −0.0649176 | + | 0.156725i | −0.953009 | − | 0.302942i | \(-0.902031\pi\) |
0.888091 | + | 0.459667i | \(0.152031\pi\) | |||||||
\(140\) | − | 24.0000i | − | 2.02837i | ||||||
\(141\) | 5.54328 | + | 2.29610i | 0.466828 | + | 0.193367i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.77164 | + | 1.14805i | −0.231776 | + | 0.0960048i | ||||
\(144\) | 2.82843 | + | 2.82843i | 0.235702 | + | 0.235702i | ||||
\(145\) | −12.7279 | − | 12.7279i | −1.05700 | − | 1.05700i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.44415 | + | 8.31492i | 0.284069 | + | 0.685803i | ||||
\(148\) | 7.39104 | + | 3.06147i | 0.607539 | + | 0.251651i | ||||
\(149\) | − | 18.0000i | − | 1.47462i | −0.675556 | − | 0.737309i | \(-0.736096\pi\) | ||
0.675556 | − | 0.737309i | \(-0.263904\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.65685 | − | 5.65685i | 0.460348 | − | 0.460348i | −0.438421 | − | 0.898770i | \(-0.644462\pi\) |
0.898770 | + | 0.438421i | \(0.144462\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.24264 | + | 4.24264i | −0.340777 | + | 0.340777i | ||||
\(156\) | −0.765367 | + | 1.84776i | −0.0612784 | + | 0.147939i | ||||
\(157\) | − | 11.0000i | − | 0.877896i | −0.898513 | − | 0.438948i | \(-0.855351\pi\) | ||
0.898513 | − | 0.438948i | \(-0.144649\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.29610 | + | 5.54328i | 0.182093 | + | 0.439610i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −25.4558 | − | 25.4558i | −2.00620 | − | 2.00620i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.84776 | − | 0.765367i | 0.144728 | − | 0.0599482i | −0.309144 | − | 0.951015i | \(-0.600042\pi\) |
0.453872 | + | 0.891067i | \(0.350042\pi\) | |||||||
\(164\) | 2.29610 | + | 5.54328i | 0.179295 | + | 0.432857i | ||||
\(165\) | −8.31492 | − | 3.44415i | −0.647315 | − | 0.268127i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.03635 | − | 19.4015i | 0.621872 | − | 1.50133i | −0.227632 | − | 0.973747i | \(-0.573098\pi\) |
0.849503 | − | 0.527584i | \(-0.176902\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | −9.89949 | + | 9.89949i | −0.754829 | + | 0.754829i | ||||
\(173\) | −5.74025 | + | 13.8582i | −0.436423 | + | 1.05362i | 0.540752 | + | 0.841182i | \(0.318140\pi\) |
−0.977175 | + | 0.212437i | \(0.931860\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.7821 | + | 6.12293i | 1.11742 | + | 0.462850i | ||||
\(176\) | 4.59220 | + | 11.0866i | 0.346150 | + | 0.835680i | ||||
\(177\) | −5.54328 | + | 2.29610i | −0.416658 | + | 0.172585i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.24264 | + | 4.24264i | 0.317110 | + | 0.317110i | 0.847656 | − | 0.530546i | \(-0.178013\pi\) |
−0.530546 | + | 0.847656i | \(0.678013\pi\) | |||||||
\(180\) | −5.54328 | + | 2.29610i | −0.413171 | + | 0.171141i | ||||
\(181\) | 5.35757 | + | 12.9343i | 0.398225 | + | 0.961400i | 0.988087 | + | 0.153896i | \(0.0491821\pi\) |
−0.589862 | + | 0.807504i | \(0.700818\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.00000i | 0.591377i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.48528 | + | 8.48528i | −0.623850 | + | 0.623850i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 12.0000 | 0.875190 | ||||||||
\(189\) | 2.82843 | − | 2.82843i | 0.205738 | − | 0.205738i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 18.0000i | − | 1.30243i | −0.758891 | − | 0.651217i | \(-0.774259\pi\) | ||
0.758891 | − | 0.651217i | \(-0.225741\pi\) | |||||||
\(192\) | 7.39104 | + | 3.06147i | 0.533402 | + | 0.220942i | ||||
\(193\) | 8.41904 | + | 20.3253i | 0.606015 | + | 1.46305i | 0.867298 | + | 0.497788i | \(0.165854\pi\) |
−0.261283 | + | 0.965262i | \(0.584146\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.12132 | − | 2.12132i | −0.151911 | − | 0.151911i | ||||
\(196\) | 12.7279 | + | 12.7279i | 0.909137 | + | 0.909137i | ||||
\(197\) | 2.77164 | − | 1.14805i | 0.197471 | − | 0.0817952i | −0.281756 | − | 0.959486i | \(-0.590917\pi\) |
0.479227 | + | 0.877691i | \(0.340917\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.7821 | − | 6.12293i | −1.04787 | − | 0.434043i | −0.208741 | − | 0.977971i | \(-0.566937\pi\) |
−0.839132 | + | 0.543928i | \(0.816937\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.53073 | + | 3.69552i | −0.107970 | + | 0.260662i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 24.0000 | 1.68447 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.00000 | −0.628587 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.44415 | + | 8.31492i | −0.239385 | + | 0.577927i | ||||
\(208\) | 4.00000i | 0.277350i | ||||||||
\(209\) | −2.77164 | − | 1.14805i | −0.191718 | − | 0.0794123i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.84776 | + | 0.765367i | −0.127205 | + | 0.0526900i | −0.445378 | − | 0.895343i | \(-0.646931\pi\) |
0.318173 | + | 0.948033i | \(0.396931\pi\) | |||||||
\(212\) | 8.48528 | + | 8.48528i | 0.582772 | + | 0.582772i | ||||
\(213\) | −8.48528 | − | 8.48528i | −0.581402 | − | 0.581402i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.03635 | − | 19.4015i | −0.548075 | − | 1.32317i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 8.00000i | − | 0.543075i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.41421 | − | 1.41421i | 0.0955637 | − | 0.0955637i | ||||
\(220\) | −18.0000 | −1.21356 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.707107 | − | 0.707107i | 0.0473514 | − | 0.0473514i | −0.683035 | − | 0.730386i | \(-0.739340\pi\) |
0.730386 | + | 0.683035i | \(0.239340\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | − | 4.00000i | − | 0.266667i | ||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.14805 | − | 2.77164i | −0.0761988 | − | 0.183960i | 0.881190 | − | 0.472762i | \(-0.156743\pi\) |
−0.957389 | + | 0.288802i | \(0.906743\pi\) | |||||||
\(228\) | −1.84776 | + | 0.765367i | −0.122371 | + | 0.0506877i | ||||
\(229\) | 9.89949 | + | 9.89949i | 0.654177 | + | 0.654177i | 0.953996 | − | 0.299819i | \(-0.0969263\pi\) |
−0.299819 | + | 0.953996i | \(0.596926\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.0866 | − | 4.59220i | 0.729442 | − | 0.302145i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.4015 | + | 8.03635i | 1.27103 | + | 0.526479i | 0.913278 | − | 0.407337i | \(-0.133542\pi\) |
0.357755 | + | 0.933816i | \(0.383542\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.88830 | + | 16.6298i | −0.449343 | + | 1.08481i | ||||
\(236\) | −8.48528 | + | 8.48528i | −0.552345 | + | 0.552345i | ||||
\(237\) | 10.0000 | 0.649570 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.0000 | −0.776215 | −0.388108 | − | 0.921614i | \(-0.626871\pi\) | ||||
−0.388108 | + | 0.921614i | \(0.626871\pi\) | |||||||
\(240\) | −8.48528 | + | 8.48528i | −0.547723 | + | 0.547723i | ||||
\(241\) | −3.06147 | + | 7.39104i | −0.197206 | + | 0.476098i | −0.991288 | − | 0.131713i | \(-0.957952\pi\) |
0.794081 | + | 0.607811i | \(0.207952\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.923880 | − | 0.382683i | −0.0592669 | − | 0.0245492i | ||||
\(244\) | 6.12293 | + | 14.7821i | 0.391981 | + | 0.946325i | ||||
\(245\) | −24.9447 | + | 10.3325i | −1.59366 | + | 0.660116i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.707107 | − | 0.707107i | −0.0449921 | − | 0.0449921i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.29610 | − | 5.54328i | −0.145509 | − | 0.351291i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.0000i | 1.51487i | 0.652913 | + | 0.757433i | \(0.273547\pi\) | ||||
−0.652913 | + | 0.757433i | \(0.726453\pi\) | |||||||
\(252\) | 3.06147 | − | 7.39104i | 0.192854 | − | 0.465592i | ||||
\(253\) | −19.0919 | + | 19.0919i | −1.20030 | + | 1.20030i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | −8.48528 | + | 8.48528i | −0.529297 | + | 0.529297i | −0.920363 | − | 0.391066i | \(-0.872107\pi\) |
0.391066 | + | 0.920363i | \(0.372107\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 16.0000i | − | 0.994192i | ||||||
\(260\) | −5.54328 | − | 2.29610i | −0.343779 | − | 0.142398i | ||||
\(261\) | −2.29610 | − | 5.54328i | −0.142125 | − | 0.343120i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.48528 | + | 8.48528i | 0.523225 | + | 0.523225i | 0.918544 | − | 0.395319i | \(-0.129366\pi\) |
−0.395319 | + | 0.918544i | \(0.629366\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.6298 | + | 6.88830i | −1.02156 | + | 0.423145i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.00000i | 0.488678i | ||||||||
\(269\) | −5.74025 | + | 13.8582i | −0.349989 | + | 0.844949i | 0.646631 | + | 0.762803i | \(0.276177\pi\) |
−0.996620 | + | 0.0821460i | \(0.973823\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.0000 | −0.668202 | −0.334101 | − | 0.942537i | \(-0.608433\pi\) | ||||
−0.334101 | + | 0.942537i | \(0.608433\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.00000 | 0.242091 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.59220 | − | 11.0866i | 0.276920 | − | 0.668544i | ||||
\(276\) | 18.0000i | 1.08347i | ||||||||
\(277\) | −1.84776 | − | 0.765367i | −0.111021 | − | 0.0459864i | 0.326482 | − | 0.945204i | \(-0.394137\pi\) |
−0.437503 | + | 0.899217i | \(0.644137\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.84776 | + | 0.765367i | −0.110622 | + | 0.0458213i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.48528 | − | 8.48528i | −0.506189 | − | 0.506189i | 0.407165 | − | 0.913355i | \(-0.366517\pi\) |
−0.913355 | + | 0.407165i | \(0.866517\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.82683 | − | 9.23880i | −0.227482 | − | 0.549189i | 0.768388 | − | 0.639984i | \(-0.221059\pi\) |
−0.995870 | + | 0.0907950i | \(0.971059\pi\) | |||||||
\(284\) | −22.1731 | − | 9.18440i | −1.31573 | − | 0.544994i | ||||
\(285\) | − | 3.00000i | − | 0.177705i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.48528 | − | 8.48528i | 0.500870 | − | 0.500870i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.3137 | − | 11.3137i | 0.663221 | − | 0.663221i | ||||
\(292\) | 1.53073 | − | 3.69552i | 0.0895794 | − | 0.216264i | ||||
\(293\) | 24.0000i | 1.40209i | 0.713115 | + | 0.701047i | \(0.247284\pi\) | ||||
−0.713115 | + | 0.701047i | \(0.752716\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.88830 | − | 16.6298i | −0.401052 | − | 0.968226i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.12132 | − | 2.12132i | −0.123091 | − | 0.123091i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.31492 | + | 3.44415i | −0.480864 | + | 0.199180i | ||||
\(300\) | −3.06147 | − | 7.39104i | −0.176754 | − | 0.426722i | ||||
\(301\) | 25.8686 | + | 10.7151i | 1.49104 | + | 0.617610i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.82843 | + | 2.82843i | −0.162221 | + | 0.162221i | ||||
\(305\) | −24.0000 | −1.37424 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.0000 | 1.14146 | 0.570730 | − | 0.821138i | \(-0.306660\pi\) | ||||
0.570730 | + | 0.821138i | \(0.306660\pi\) | |||||||
\(308\) | 16.9706 | − | 16.9706i | 0.966988 | − | 0.966988i | ||||
\(309\) | −1.91342 | + | 4.61940i | −0.108850 | + | 0.262788i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.1731 | + | 9.18440i | 1.25732 | + | 0.520800i | 0.909086 | − | 0.416608i | \(-0.136781\pi\) |
0.348235 | + | 0.937407i | \(0.386781\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.7821 | − | 6.12293i | 0.835532 | − | 0.346089i | 0.0764418 | − | 0.997074i | \(-0.475644\pi\) |
0.759090 | + | 0.650985i | \(0.225644\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.48528 | + | 8.48528i | 0.478091 | + | 0.478091i | ||||
\(316\) | 18.4776 | − | 7.65367i | 1.03945 | − | 0.430552i | ||||
\(317\) | −2.29610 | − | 5.54328i | −0.128962 | − | 0.311341i | 0.846189 | − | 0.532883i | \(-0.178891\pi\) |
−0.975151 | + | 0.221541i | \(0.928891\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 18.0000i | − | 1.00781i | ||||||
\(320\) | −9.18440 | + | 22.1731i | −0.513424 | + | 1.23951i | ||||
\(321\) | 6.36396 | − | 6.36396i | 0.355202 | − | 0.355202i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −2.00000 | −0.111111 | ||||||||
\(325\) | 2.82843 | − | 2.82843i | 0.156893 | − | 0.156893i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 20.0000i | − | 1.10600i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.18440 | − | 22.1731i | −0.506352 | − | 1.22244i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.19239 | − | 9.19239i | −0.505259 | − | 0.505259i | 0.407808 | − | 0.913068i | \(-0.366293\pi\) |
−0.913068 | + | 0.407808i | \(0.866293\pi\) | |||||||
\(332\) | −8.48528 | − | 8.48528i | −0.465690 | − | 0.465690i | ||||
\(333\) | −3.69552 | + | 1.53073i | −0.202513 | + | 0.0838837i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.0866 | − | 4.59220i | −0.605723 | − | 0.250899i | ||||
\(336\) | − | 16.0000i | − | 0.872872i | ||||||
\(337\) | 5.35757 | − | 12.9343i | 0.291845 | − | 0.704577i | −0.708154 | − | 0.706058i | \(-0.750472\pi\) |
0.999999 | + | 0.00148149i | \(0.000471572\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.00000 | 0.488813 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.00000 | −0.324918 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.06147 | − | 7.39104i | 0.165304 | − | 0.399078i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −24.9447 | − | 10.3325i | −1.34298 | − | 0.556281i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.0866 | − | 4.59220i | 0.595157 | − | 0.246522i | −0.0647103 | − | 0.997904i | \(-0.520612\pi\) |
0.659868 | + | 0.751382i | \(0.270612\pi\) | |||||||
\(348\) | −8.48528 | − | 8.48528i | −0.454859 | − | 0.454859i | ||||
\(349\) | 13.4350 | + | 13.4350i | 0.719161 | + | 0.719161i | 0.968433 | − | 0.249273i | \(-0.0801916\pi\) |
−0.249273 | + | 0.968433i | \(0.580192\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.382683 | − | 0.923880i | −0.0204261 | − | 0.0493130i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.00000i | 0.319348i | 0.987170 | + | 0.159674i | \(0.0510443\pi\) | ||||
−0.987170 | + | 0.159674i | \(0.948956\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 25.4558 | − | 25.4558i | 1.35106 | − | 1.35106i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.0000i | 0.947368i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.765367 | + | 1.84776i | 0.0401713 | + | 0.0969822i | ||||
\(364\) | 7.39104 | − | 3.06147i | 0.387396 | − | 0.160464i | ||||
\(365\) | 4.24264 | + | 4.24264i | 0.222070 | + | 0.222070i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.39104 | − | 3.06147i | 0.385809 | − | 0.159807i | −0.181344 | − | 0.983420i | \(-0.558045\pi\) |
0.567153 | + | 0.823612i | \(0.308045\pi\) | |||||||
\(368\) | 13.7766 | + | 33.2597i | 0.718155 | + | 1.73378i | ||||
\(369\) | −2.77164 | − | 1.14805i | −0.144286 | − | 0.0597651i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.18440 | − | 22.1731i | 0.476830 | − | 1.15117i | ||||
\(372\) | −2.82843 | + | 2.82843i | −0.146647 | + | 0.146647i | ||||
\(373\) | 22.0000 | 1.13912 | 0.569558 | − | 0.821951i | \(-0.307114\pi\) | ||||
0.569558 | + | 0.821951i | \(0.307114\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.00000 | −0.154919 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.29610 | − | 5.54328i | 0.118255 | − | 0.285493i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.5641 | − | 12.2459i | −1.51861 | − | 0.629028i | −0.541296 | − | 0.840832i | \(-0.682066\pi\) |
−0.977312 | + | 0.211804i | \(0.932066\pi\) | |||||||
\(380\) | −2.29610 | − | 5.54328i | −0.117787 | − | 0.284364i | ||||
\(381\) | 12.0104 | − | 4.97488i | 0.615313 | − | 0.254871i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.48528 | + | 8.48528i | 0.433578 | + | 0.433578i | 0.889843 | − | 0.456266i | \(-0.150813\pi\) |
−0.456266 | + | 0.889843i | \(0.650813\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.7766 | + | 33.2597i | 0.702121 | + | 1.69507i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 7.00000i | − | 0.355830i | ||||||
\(388\) | 12.2459 | − | 29.5641i | 0.621690 | − | 1.50089i | ||||
\(389\) | 25.4558 | − | 25.4558i | 1.29066 | − | 1.29066i | 0.356285 | − | 0.934377i | \(-0.384043\pi\) |
0.934377 | − | 0.356285i | \(-0.115957\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.12132 | + | 2.12132i | −0.107006 | + | 0.107006i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 30.0000i | 1.50946i | ||||||||
\(396\) | −5.54328 | − | 2.29610i | −0.278560 | − | 0.115383i | ||||
\(397\) | −7.65367 | − | 18.4776i | −0.384127 | − | 0.927364i | −0.991158 | − | 0.132686i | \(-0.957640\pi\) |
0.607032 | − | 0.794678i | \(-0.292360\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.82843 | + | 2.82843i | 0.141598 | + | 0.141598i | ||||
\(400\) | −11.3137 | − | 11.3137i | −0.565685 | − | 0.565685i | ||||
\(401\) | −13.8582 | + | 5.74025i | −0.692045 | + | 0.286654i | −0.700852 | − | 0.713307i | \(-0.747197\pi\) |
0.00880685 | + | 0.999961i | \(0.497197\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.84776 | − | 0.765367i | −0.0920434 | − | 0.0381256i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.14805 | − | 2.77164i | 0.0570471 | − | 0.137724i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.0000 | −0.594818 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.0000 | −0.939490 | −0.469745 | − | 0.882802i | \(-0.655654\pi\) | ||||
−0.469745 | + | 0.882802i | \(0.655654\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.29610 | − | 5.54328i | 0.113258 | − | 0.273430i | ||||
\(412\) | 10.0000i | 0.492665i | ||||||||
\(413\) | 22.1731 | + | 9.18440i | 1.09107 | + | 0.451935i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.6298 | − | 6.88830i | 0.816326 | − | 0.338133i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.41421 | − | 1.41421i | −0.0692543 | − | 0.0692543i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.59220 | + | 11.0866i | 0.224344 | + | 0.541614i | 0.995471 | − | 0.0950676i | \(-0.0303067\pi\) |
−0.771127 | + | 0.636681i | \(0.780307\pi\) | |||||||
\(420\) | 22.1731 | + | 9.18440i | 1.08194 | + | 0.448153i | ||||
\(421\) | − | 25.0000i | − | 1.21843i | −0.793007 | − | 0.609213i | \(-0.791486\pi\) | ||
0.793007 | − | 0.609213i | \(-0.208514\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.24264 | + | 4.24264i | −0.206284 | + | 0.206284i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22.6274 | − | 22.6274i | 1.09502 | − | 1.09502i | ||||
\(428\) | 6.88830 | − | 16.6298i | 0.332959 | − | 0.803833i | ||||
\(429\) | − | 3.00000i | − | 0.144841i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.18440 | + | 22.1731i | 0.442397 | + | 1.06804i | 0.975105 | + | 0.221742i | \(0.0711743\pi\) |
−0.532708 | + | 0.846299i | \(0.678826\pi\) | |||||||
\(432\) | −3.69552 | + | 1.53073i | −0.177801 | + | 0.0736475i | ||||
\(433\) | −0.707107 | − | 0.707107i | −0.0339814 | − | 0.0339814i | 0.689912 | − | 0.723893i | \(-0.257649\pi\) |
−0.723893 | + | 0.689912i | \(0.757649\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.6298 | − | 6.88830i | 0.797339 | − | 0.330269i | ||||
\(436\) | −15.3073 | − | 36.9552i | −0.733089 | − | 1.76983i | ||||
\(437\) | −8.31492 | − | 3.44415i | −0.397756 | − | 0.164756i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.7151 | + | 25.8686i | −0.511406 | + | 1.23464i | 0.431660 | + | 0.902036i | \(0.357928\pi\) |
−0.943066 | + | 0.332606i | \(0.892072\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.00000 | −0.428571 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.00000 | 0.285069 | 0.142534 | − | 0.989790i | \(-0.454475\pi\) | ||||
0.142534 | + | 0.989790i | \(0.454475\pi\) | |||||||
\(444\) | −5.65685 | + | 5.65685i | −0.268462 | + | 0.268462i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.6298 | + | 6.88830i | 0.786564 | + | 0.325805i | ||||
\(448\) | −12.2459 | − | 29.5641i | −0.578563 | − | 1.39677i | ||||
\(449\) | 5.54328 | − | 2.29610i | 0.261603 | − | 0.108360i | −0.248027 | − | 0.968753i | \(-0.579782\pi\) |
0.509630 | + | 0.860393i | \(0.329782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.36396 | − | 6.36396i | −0.299667 | − | 0.299667i | ||||
\(452\) | 16.6298 | − | 6.88830i | 0.782201 | − | 0.323998i | ||||
\(453\) | 3.06147 | + | 7.39104i | 0.143840 | + | 0.347261i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.0000i | 0.562569i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.4350 | + | 13.4350i | −0.628464 | + | 0.628464i | −0.947682 | − | 0.319217i | \(-0.896580\pi\) |
0.319217 | + | 0.947682i | \(0.396580\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −54.0000 | −2.51776 | ||||||||
\(461\) | −21.2132 | + | 21.2132i | −0.987997 | + | 0.987997i | −0.999929 | − | 0.0119314i | \(-0.996202\pi\) |
0.0119314 | + | 0.999929i | \(0.496202\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 8.00000i | − | 0.371792i | −0.982569 | − | 0.185896i | \(-0.940481\pi\) | ||
0.982569 | − | 0.185896i | \(-0.0595187\pi\) | |||||||
\(464\) | −22.1731 | − | 9.18440i | −1.02936 | − | 0.426375i | ||||
\(465\) | −2.29610 | − | 5.54328i | −0.106479 | − | 0.257063i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 29.6985 | + | 29.6985i | 1.37428 | + | 1.37428i | 0.853986 | + | 0.520296i | \(0.174178\pi\) |
0.520296 | + | 0.853986i | \(0.325822\pi\) | |||||||
\(468\) | −1.41421 | − | 1.41421i | −0.0653720 | − | 0.0653720i | ||||
\(469\) | 14.7821 | − | 6.12293i | 0.682573 | − | 0.282731i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.1627 | + | 4.20952i | 0.468271 | + | 0.193964i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.03635 | − | 19.4015i | 0.369512 | − | 0.892081i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.00000 | −0.274721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.3325 | − | 24.9447i | 0.472102 | − | 1.13975i | −0.491131 | − | 0.871086i | \(-0.663416\pi\) |
0.963233 | − | 0.268669i | \(-0.0865837\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.69552 | − | 1.53073i | −0.168501 | − | 0.0697955i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 33.2597 | − | 13.7766i | 1.51337 | − | 0.626857i | ||||
\(484\) | 2.82843 | + | 2.82843i | 0.128565 | + | 0.128565i | ||||
\(485\) | 33.9411 | + | 33.9411i | 1.54119 | + | 1.54119i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.41904 | − | 20.3253i | −0.381503 | − | 0.921030i | −0.991676 | − | 0.128761i | \(-0.958900\pi\) |
0.610173 | − | 0.792268i | \(-0.291100\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.00000i | 0.0904431i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.24264 | + | 4.24264i | −0.191468 | + | 0.191468i | −0.796330 | − | 0.604862i | \(-0.793228\pi\) |
0.604862 | + | 0.796330i | \(0.293228\pi\) | |||||||
\(492\) | −6.00000 | −0.270501 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.36396 | − | 6.36396i | 0.286039 | − | 0.286039i | ||||
\(496\) | −3.06147 | + | 7.39104i | −0.137464 | + | 0.331867i | ||||
\(497\) | 48.0000i | 2.15309i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.41904 | + | 20.3253i | 0.376888 | + | 0.909888i | 0.992546 | + | 0.121874i | \(0.0388904\pi\) |
−0.615658 | + | 0.788014i | \(0.711110\pi\) | |||||||
\(500\) | −5.54328 | + | 2.29610i | −0.247903 | + | 0.102685i | ||||
\(501\) | 14.8492 | + | 14.8492i | 0.663415 | + | 0.663415i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.8582 | − | 5.74025i | 0.617906 | − | 0.255945i | −0.0516985 | − | 0.998663i | \(-0.516463\pi\) |
0.669605 | + | 0.742718i | \(0.266463\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.59220 | + | 11.0866i | −0.203947 | + | 0.492371i | ||||
\(508\) | 18.3848 | − | 18.3848i | 0.815693 | − | 0.815693i | ||||
\(509\) | −36.0000 | −1.59567 | −0.797836 | − | 0.602875i | \(-0.794022\pi\) | ||||
−0.797836 | + | 0.602875i | \(0.794022\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.00000 | −0.353899 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.382683 | − | 0.923880i | 0.0168959 | − | 0.0407903i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13.8582 | − | 5.74025i | −0.610665 | − | 0.252946i | ||||
\(516\) | −5.35757 | − | 12.9343i | −0.235854 | − | 0.569401i | ||||
\(517\) | −16.6298 | + | 6.88830i | −0.731379 | + | 0.302947i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.6066 | − | 10.6066i | −0.465578 | − | 0.465578i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.03635 | + | 19.4015i | 0.352079 | + | 0.849994i | 0.996363 | + | 0.0852077i | \(0.0271554\pi\) |
−0.644284 | + | 0.764786i | \(0.722845\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.0000i | 0.874539i | 0.899331 | + | 0.437269i | \(0.144054\pi\) | ||||
−0.899331 | + | 0.437269i | \(0.855946\pi\) | |||||||
\(524\) | −2.29610 | + | 5.54328i | −0.100306 | + | 0.242159i | ||||
\(525\) | −11.3137 | + | 11.3137i | −0.493771 | + | 0.493771i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −12.0000 | −0.522233 | ||||||||
\(529\) | −41.0122 | + | 41.0122i | −1.78314 | + | 1.78314i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 6.00000i | − | 0.260378i | ||||||
\(532\) | 7.39104 | + | 3.06147i | 0.320442 | + | 0.132731i | ||||
\(533\) | −1.14805 | − | 2.77164i | −0.0497276 | − | 0.120053i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.0919 | + | 19.0919i | 0.825414 | + | 0.825414i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.54328 | + | 2.29610i | −0.239210 | + | 0.0990841i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −24.9447 | − | 10.3325i | −1.07445 | − | 0.445050i | ||||
\(540\) | − | 6.00000i | − | 0.258199i | ||||||
\(541\) | −6.12293 | + | 14.7821i | −0.263246 | + | 0.635531i | −0.999136 | − | 0.0415701i | \(-0.986764\pi\) |
0.735890 | + | 0.677101i | \(0.236764\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14.0000 | −0.600798 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 60.0000 | 2.57012 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.06147 | + | 7.39104i | −0.130899 | + | 0.316018i | −0.975717 | − | 0.219036i | \(-0.929709\pi\) |
0.844818 | + | 0.535054i | \(0.179709\pi\) | |||||||
\(548\) | − | 12.0000i | − | 0.512615i | ||||||
\(549\) | −7.39104 | − | 3.06147i | −0.315442 | − | 0.130660i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.54328 | − | 2.29610i | 0.236152 | − | 0.0978172i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −28.2843 | − | 28.2843i | −1.20277 | − | 1.20277i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.59220 | − | 11.0866i | −0.194928 | − | 0.470598i | ||||
\(556\) | −3.69552 | − | 1.53073i | −0.156725 | − | 0.0649176i | ||||
\(557\) | − | 30.0000i | − | 1.27114i | −0.772043 | − | 0.635570i | \(-0.780765\pi\) | ||
0.772043 | − | 0.635570i | \(-0.219235\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.94975 | − | 4.94975i | 0.209352 | − | 0.209352i | ||||
\(560\) | 48.0000 | 2.02837 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.2132 | − | 21.2132i | 0.894030 | − | 0.894030i | −0.100870 | − | 0.994900i | \(-0.532163\pi\) |
0.994900 | + | 0.100870i | \(0.0321625\pi\) | |||||||
\(564\) | −4.59220 | + | 11.0866i | −0.193367 | + | 0.466828i | ||||
\(565\) | 27.0000i | 1.13590i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.53073 | + | 3.69552i | 0.0642848 | + | 0.155197i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.9706 | − | 16.9706i | −0.711443 | − | 0.711443i | 0.255394 | − | 0.966837i | \(-0.417795\pi\) |
−0.966837 | + | 0.255394i | \(0.917795\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.39104 | − | 3.06147i | 0.309305 | − | 0.128118i | −0.222631 | − | 0.974903i | \(-0.571465\pi\) |
0.531936 | + | 0.846784i | \(0.321465\pi\) | |||||||
\(572\) | −2.29610 | − | 5.54328i | −0.0960048 | − | 0.231776i | ||||
\(573\) | 16.6298 | + | 6.88830i | 0.694721 | + | 0.287763i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.7766 | − | 33.2597i | 0.574524 | − | 1.38702i | ||||
\(576\) | −5.65685 | + | 5.65685i | −0.235702 | + | 0.235702i | ||||
\(577\) | 7.00000 | 0.291414 | 0.145707 | − | 0.989328i | \(-0.453454\pi\) | ||||
0.145707 | + | 0.989328i | \(0.453454\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −22.0000 | −0.914289 | ||||||||
\(580\) | 25.4558 | − | 25.4558i | 1.05700 | − | 1.05700i | ||||
\(581\) | −9.18440 | + | 22.1731i | −0.381033 | + | 0.919896i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.6298 | − | 6.88830i | −0.688737 | − | 0.285284i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.77164 | − | 1.14805i | 0.114593 | − | 0.0474660i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.4558 | + | 25.4558i | 1.05068 | + | 1.05068i | 0.998646 | + | 0.0520296i | \(0.0165690\pi\) |
0.0520296 | + | 0.998646i | \(0.483431\pi\) | |||||||
\(588\) | −16.6298 | + | 6.88830i | −0.685803 | + | 0.284069i | ||||
\(589\) | −0.765367 | − | 1.84776i | −0.0315364 | − | 0.0761356i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.00000i | 0.123404i | ||||||||
\(592\) | −6.12293 | + | 14.7821i | −0.251651 | + | 0.607539i | ||||
\(593\) | −12.7279 | + | 12.7279i | −0.522673 | + | 0.522673i | −0.918378 | − | 0.395705i | \(-0.870500\pi\) |
0.395705 | + | 0.918378i | \(0.370500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 36.0000 | 1.47462 | ||||||||
\(597\) | 11.3137 | − | 11.3137i | 0.463039 | − | 0.463039i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.00000i | 0.245153i | 0.992459 | + | 0.122577i | \(0.0391157\pi\) | ||||
−0.992459 | + | 0.122577i | \(0.960884\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.5420 | − | 35.1074i | −0.593179 | − | 1.43206i | −0.880416 | − | 0.474202i | \(-0.842737\pi\) |
0.287237 | − | 0.957860i | \(-0.407263\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.82843 | − | 2.82843i | −0.115182 | − | 0.115182i | ||||
\(604\) | 11.3137 | + | 11.3137i | 0.460348 | + | 0.460348i | ||||
\(605\) | −5.54328 | + | 2.29610i | −0.225366 | + | 0.0933498i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.1074 | + | 14.5420i | 1.42497 | + | 0.590240i | 0.956103 | − | 0.293030i | \(-0.0946637\pi\) |
0.468863 | + | 0.883271i | \(0.344664\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.18440 | + | 22.1731i | −0.372171 | + | 0.898500i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.00000 | −0.242734 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.0000 | 0.444286 | 0.222143 | − | 0.975014i | \(-0.428695\pi\) | ||||
0.222143 | + | 0.975014i | \(0.428695\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.44415 | − | 8.31492i | 0.138882 | − | 0.335290i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.54328 | + | 2.29610i | 0.223164 | + | 0.0924375i | 0.491464 | − | 0.870898i | \(-0.336462\pi\) |
−0.268300 | + | 0.963335i | \(0.586462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.23880 | − | 3.82683i | 0.371339 | − | 0.153813i | −0.189207 | − | 0.981937i | \(-0.560592\pi\) |
0.560545 | + | 0.828124i | \(0.310592\pi\) | |||||||
\(620\) | −8.48528 | − | 8.48528i | −0.340777 | − | 0.340777i | ||||
\(621\) | −6.36396 | − | 6.36396i | −0.255377 | − | 0.255377i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.69552 | − | 1.53073i | −0.147939 | − | 0.0612784i | ||||
\(625\) | − | 29.0000i | − | 1.16000i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.12132 | − | 2.12132i | 0.0847174 | − | 0.0847174i | ||||
\(628\) | 22.0000 | 0.877896 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.1630 | − | 26.1630i | 1.04153 | − | 1.04153i | 0.0424312 | − | 0.999099i | \(-0.486490\pi\) |
0.999099 | − | 0.0424312i | \(-0.0135103\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 2.00000i | − | 0.0794929i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.9247 | + | 36.0313i | 0.592267 | + | 1.42986i | ||||
\(636\) | −11.0866 | + | 4.59220i | −0.439610 | + | 0.182093i | ||||
\(637\) | −6.36396 | − | 6.36396i | −0.252149 | − | 0.252149i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.0866 | − | 4.59220i | 0.438577 | − | 0.181665i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.4880 | − | 12.6286i | −1.20420 | − | 0.498798i | −0.311849 | − | 0.950132i | \(-0.600948\pi\) |
−0.892355 | + | 0.451334i | \(0.850948\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.2459 | − | 29.5641i | 0.482930 | − | 1.16590i | −0.475281 | − | 0.879834i | \(-0.657654\pi\) |
0.958211 | − | 0.286062i | \(-0.0923464\pi\) | |||||||
\(644\) | 50.9117 | − | 50.9117i | 2.00620 | − | 2.00620i | ||||
\(645\) | 21.0000 | 0.826874 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.0000 | 0.707653 | 0.353827 | − | 0.935311i | \(-0.384880\pi\) | ||||
0.353827 | + | 0.935311i | \(0.384880\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.88830 | − | 16.6298i | 0.270389 | − | 0.652778i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.39104 | + | 3.06147i | 0.289678 | + | 0.119988i | ||||
\(652\) | 1.53073 | + | 3.69552i | 0.0599482 | + | 0.144728i | ||||
\(653\) | −24.9447 | + | 10.3325i | −0.976163 | + | 0.404340i | −0.813003 | − | 0.582259i | \(-0.802169\pi\) |
−0.163160 | + | 0.986600i | \(0.552169\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.36396 | − | 6.36396i | −0.248661 | − | 0.248661i | ||||
\(656\) | −11.0866 | + | 4.59220i | −0.432857 | + | 0.179295i | ||||
\(657\) | 0.765367 | + | 1.84776i | 0.0298598 | + | 0.0720879i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.00000i | 0.233727i | 0.993148 | + | 0.116863i | \(0.0372840\pi\) | ||||
−0.993148 | + | 0.116863i | \(0.962716\pi\) | |||||||
\(660\) | 6.88830 | − | 16.6298i | 0.268127 | − | 0.647315i | ||||
\(661\) | −21.9203 | + | 21.9203i | −0.852601 | + | 0.852601i | −0.990453 | − | 0.137852i | \(-0.955980\pi\) |
0.137852 | + | 0.990453i | \(0.455980\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.48528 | + | 8.48528i | −0.329045 | + | 0.329045i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 54.0000i | − | 2.09089i | ||||||
\(668\) | 38.8029 | + | 16.0727i | 1.50133 | + | 0.621872i | ||||
\(669\) | 0.382683 | + | 0.923880i | 0.0147954 | + | 0.0357192i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.9706 | − | 16.9706i | −0.655141 | − | 0.655141i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.3253 | + | 8.41904i | −0.783485 | + | 0.324530i | −0.738321 | − | 0.674450i | \(-0.764381\pi\) |
−0.0451638 | + | 0.998980i | \(0.514381\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.69552 | + | 1.53073i | 0.142241 | + | 0.0589180i | ||||
\(676\) | 24.0000i | 0.923077i | ||||||||
\(677\) | −10.3325 | + | 24.9447i | −0.397108 | + | 0.958705i | 0.591240 | + | 0.806496i | \(0.298639\pi\) |
−0.988348 | + | 0.152209i | \(0.951361\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −64.0000 | −2.45609 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.00000 | 0.114960 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.14805 | + | 2.77164i | −0.0439289 | + | 0.106054i | −0.944321 | − | 0.329026i | \(-0.893280\pi\) |
0.900392 | + | 0.435079i | \(0.143280\pi\) | |||||||
\(684\) | − | 2.00000i | − | 0.0764719i | ||||||
\(685\) | 16.6298 | + | 6.88830i | 0.635393 | + | 0.263188i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.9343 | + | 5.35757i | −0.493475 | + | 0.204404i | ||||
\(688\) | −19.7990 | − | 19.7990i | −0.754829 | − | 0.754829i | ||||
\(689\) | −4.24264 | − | 4.24264i | −0.161632 | − | 0.161632i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.65367 | + | 18.4776i | 0.291159 | + | 0.702921i | 0.999997 | − | 0.00245092i | \(-0.000780153\pi\) |
−0.708838 | + | 0.705372i | \(0.750780\pi\) | |||||||
\(692\) | −27.7164 | − | 11.4805i | −1.05362 | − | 0.436423i | ||||
\(693\) | 12.0000i | 0.455842i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.24264 | − | 4.24264i | 0.160933 | − | 0.160933i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.8492 | + | 14.8492i | −0.561650 | + | 0.561650i | ||||
\(700\) | −12.2459 | + | 29.5641i | −0.462850 | + | 1.11742i | ||||
\(701\) | − | 24.0000i | − | 0.906467i | −0.891392 | − | 0.453234i | \(-0.850270\pi\) | ||
0.891392 | − | 0.453234i | \(-0.149730\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.53073 | − | 3.69552i | −0.0577327 | − | 0.139379i | ||||
\(704\) | −22.1731 | + | 9.18440i | −0.835680 | + | 0.346150i | ||||
\(705\) | −12.7279 | − | 12.7279i | −0.479361 | − | 0.479361i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4.59220 | − | 11.0866i | −0.172585 | − | 0.416658i | ||||
\(709\) | 12.9343 | + | 5.35757i | 0.485758 | + | 0.201208i | 0.612102 | − | 0.790779i | \(-0.290324\pi\) |
−0.126344 | + | 0.991987i | \(0.540324\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.82683 | + | 9.23880i | −0.143517 | + | 0.346482i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −18.0000 | −0.674105 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.00000 | 0.336581 | ||||||||
\(716\) | −8.48528 | + | 8.48528i | −0.317110 | + | 0.317110i | ||||
\(717\) | 4.59220 | − | 11.0866i | 0.171499 | − | 0.414035i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.77164 | − | 1.14805i | −0.103365 | − | 0.0428151i | 0.330402 | − | 0.943840i | \(-0.392816\pi\) |
−0.433767 | + | 0.901025i | \(0.642816\pi\) | |||||||
\(720\) | −4.59220 | − | 11.0866i | −0.171141 | − | 0.413171i | ||||
\(721\) | 18.4776 | − | 7.65367i | 0.688141 | − | 0.285038i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.65685 | − | 5.65685i | −0.210381 | − | 0.210381i | ||||
\(724\) | −25.8686 | + | 10.7151i | −0.961400 | + | 0.398225i | ||||
\(725\) | 9.18440 | + | 22.1731i | 0.341100 | + | 0.823489i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.00000i | 0.296704i | 0.988935 | + | 0.148352i | \(0.0473968\pi\) | ||||
−0.988935 | + | 0.148352i | \(0.952603\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.707107 | − | 0.707107i | 0.0261891 | − | 0.0261891i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −16.0000 | −0.591377 | ||||||||
\(733\) | −1.41421 | + | 1.41421i | −0.0522352 | + | 0.0522352i | −0.732742 | − | 0.680507i | \(-0.761760\pi\) |
0.680507 | + | 0.732742i | \(0.261760\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 27.0000i | − | 0.995910i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.59220 | − | 11.0866i | −0.169156 | − | 0.408378i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.707107 | − | 0.707107i | −0.0260113 | − | 0.0260113i | 0.693981 | − | 0.719993i | \(-0.255855\pi\) |
−0.719993 | + | 0.693981i | \(0.755855\pi\) | |||||||
\(740\) | −16.9706 | − | 16.9706i | −0.623850 | − | 0.623850i | ||||
\(741\) | 0.923880 | − | 0.382683i | 0.0339396 | − | 0.0140582i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.1731 | + | 9.18440i | 0.813452 | + | 0.336943i | 0.750331 | − | 0.661063i | \(-0.229894\pi\) |
0.0631219 | + | 0.998006i | \(0.479894\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.6649 | + | 49.8895i | −0.757104 | + | 1.82781i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.00000 | 0.219529 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −36.0000 | −1.31541 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.6034 | − | 42.4985i | 0.642359 | − | 1.55079i | −0.181131 | − | 0.983459i | \(-0.557976\pi\) |
0.823489 | − | 0.567332i | \(-0.192024\pi\) | |||||||
\(752\) | 24.0000i | 0.875190i | ||||||||
\(753\) | −22.1731 | − | 9.18440i | −0.808033 | − | 0.334698i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22.1731 | + | 9.18440i | −0.806962 | + | 0.334255i | ||||
\(756\) | 5.65685 | + | 5.65685i | 0.205738 | + | 0.205738i | ||||
\(757\) | 30.4056 | + | 30.4056i | 1.10511 | + | 1.10511i | 0.993784 | + | 0.111326i | \(0.0355098\pi\) |
0.111326 | + | 0.993784i | \(0.464490\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.3325 | − | 24.9447i | −0.375044 | − | 0.905437i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.0000i | 1.08750i | 0.839248 | + | 0.543750i | \(0.182996\pi\) | ||||
−0.839248 | + | 0.543750i | \(0.817004\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −56.5685 | + | 56.5685i | −2.04792 | + | 2.04792i | ||||
\(764\) | 36.0000 | 1.30243 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.24264 | − | 4.24264i | 0.153193 | − | 0.153193i | ||||
\(768\) | −6.12293 | + | 14.7821i | −0.220942 | + | 0.533402i | ||||
\(769\) | − | 41.0000i | − | 1.47850i | −0.673432 | − | 0.739249i | \(-0.735181\pi\) | ||
0.673432 | − | 0.739249i | \(-0.264819\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.59220 | − | 11.0866i | −0.165384 | − | 0.399273i | ||||
\(772\) | −40.6507 | + | 16.8381i | −1.46305 | + | 0.606015i | ||||
\(773\) | 16.9706 | + | 16.9706i | 0.610389 | + | 0.610389i | 0.943047 | − | 0.332659i | \(-0.107946\pi\) |
−0.332659 | + | 0.943047i | \(0.607946\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.39104 | − | 3.06147i | 0.265494 | − | 0.109971i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14.7821 | + | 6.12293i | 0.530304 | + | 0.219659i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.14805 | − | 2.77164i | 0.0411332 | − | 0.0993043i | ||||
\(780\) | 4.24264 | − | 4.24264i | 0.151911 | − | 0.151911i | ||||
\(781\) | 36.0000 | 1.28818 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.00000 | 0.214423 | ||||||||
\(784\) | −25.4558 | + | 25.4558i | −0.909137 | + | 0.909137i | ||||
\(785\) | −12.6286 | + | 30.4880i | −0.450732 | + | 1.08816i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.9552 | + | 15.3073i | 1.31731 | + | 0.545648i | 0.927009 | − | 0.375040i | \(-0.122371\pi\) |
0.390301 | + | 0.920687i | \(0.372371\pi\) | |||||||
\(788\) | 2.29610 | + | 5.54328i | 0.0817952 | + | 0.197471i | ||||
\(789\) | −11.0866 | + | 4.59220i | −0.394692 | + | 0.163487i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −25.4558 | − | 25.4558i | −0.905106 | − | 0.905106i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.06147 | − | 7.39104i | −0.108716 | − | 0.262463i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 18.0000i | − | 0.638394i | ||||||
\(796\) | 12.2459 | − | 29.5641i | 0.434043 | − | 1.04787i | ||||
\(797\) | −33.9411 | + | 33.9411i | −1.20226 | + | 1.20226i | −0.228778 | + | 0.973479i | \(0.573473\pi\) |
−0.973479 | + | 0.228778i | \(0.926527\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.00000i | 0.211735i | ||||||||
\(804\) | −7.39104 | − | 3.06147i | −0.260662 | − | 0.107970i | ||||
\(805\) | 41.3298 | + | 99.7790i | 1.45668 | + | 3.51675i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.6066 | − | 10.6066i | −0.373370 | − | 0.373370i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −47.1179 | + | 19.5169i | −1.65658 | + | 0.686176i | −0.997808 | − | 0.0661707i | \(-0.978922\pi\) |
−0.658767 | + | 0.752347i | \(0.728922\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.23880 | − | 3.82683i | −0.324418 | − | 0.134378i | 0.214530 | − | 0.976717i | \(-0.431178\pi\) |
−0.538948 | + | 0.842339i | \(0.681178\pi\) | |||||||
\(812\) | 48.0000i | 1.68447i | ||||||||
\(813\) | 4.20952 | − | 10.1627i | 0.147634 | − | 0.356421i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.00000 | −0.210171 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.00000 | 0.244899 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.53073 | + | 3.69552i | −0.0534882 | + | 0.129132i | ||||
\(820\) | − | 18.0000i | − | 0.628587i | ||||||
\(821\) | 19.4015 | + | 8.03635i | 0.677116 | + | 0.280471i | 0.694621 | − | 0.719376i | \(-0.255572\pi\) |
−0.0175047 | + | 0.999847i | \(0.505572\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.8686 | − | 10.7151i | 0.901724 | − | 0.373506i | 0.116841 | − | 0.993151i | \(-0.462723\pi\) |
0.784883 | + | 0.619644i | \(0.212723\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.48528 | + | 8.48528i | 0.295420 | + | 0.295420i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.03635 | − | 19.4015i | −0.279451 | − | 0.674655i | 0.720369 | − | 0.693591i | \(-0.243972\pi\) |
−0.999821 | + | 0.0189354i | \(0.993972\pi\) | |||||||
\(828\) | −16.6298 | − | 6.88830i | −0.577927 | − | 0.239385i | ||||
\(829\) | 14.0000i | 0.486240i | 0.969996 | + | 0.243120i | \(0.0781709\pi\) | ||||
−0.969996 | + | 0.243120i | \(0.921829\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.41421 | − | 1.41421i | 0.0490585 | − | 0.0490585i | ||||
\(832\) | −8.00000 | −0.277350 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −44.5477 | + | 44.5477i | −1.54164 | + | 1.54164i | ||||
\(836\) | 2.29610 | − | 5.54328i | 0.0794123 | − | 0.191718i | ||||
\(837\) | − | 2.00000i | − | 0.0691301i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.8130 | + | 52.6611i | 0.753067 | + | 1.81806i | 0.541500 | + | 0.840701i | \(0.317857\pi\) |
0.211567 | + | 0.977364i | \(0.432143\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.94975 | + | 4.94975i | 0.170681 | + | 0.170681i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.0866 | − | 4.59220i | 0.381841 | − | 0.158164i | ||||
\(844\) | −1.53073 | − | 3.69552i | −0.0526900 | − | 0.127205i | ||||
\(845\) | −33.2597 | − | 13.7766i | −1.14417 | − | 0.473930i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.06147 | − | 7.39104i | 0.105193 | − | 0.253959i | ||||
\(848\) | −16.9706 | + | 16.9706i | −0.582772 | + | 0.582772i | ||||
\(849\) | 10.0000 | 0.343199 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.0000 | −1.23406 | ||||||||
\(852\) | 16.9706 | − | 16.9706i | 0.581402 | − | 0.581402i | ||||
\(853\) | −9.94977 | + | 24.0209i | −0.340674 | + | 0.822459i | 0.656974 | + | 0.753913i | \(0.271836\pi\) |
−0.997648 | + | 0.0685459i | \(0.978164\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.77164 | + | 1.14805i | 0.0947880 | + | 0.0392625i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.6298 | − | 6.88830i | 0.568064 | − | 0.235300i | −0.0801177 | − | 0.996785i | \(-0.525530\pi\) |
0.648182 | + | 0.761486i | \(0.275530\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.1421 | − | 14.1421i | −0.482523 | − | 0.482523i | 0.423413 | − | 0.905937i | \(-0.360832\pi\) |
−0.905937 | + | 0.423413i | \(0.860832\pi\) | |||||||
\(860\) | 38.8029 | − | 16.0727i | 1.32317 | − | 0.548075i | ||||
\(861\) | 4.59220 | + | 11.0866i | 0.156502 | + | 0.377829i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.0000i | 0.816970i | 0.912765 | + | 0.408485i | \(0.133943\pi\) | ||||
−0.912765 | + | 0.408485i | \(0.866057\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 31.8198 | − | 31.8198i | 1.08191 | − | 1.08191i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 16.0000 | 0.543075 | ||||||||
\(869\) | −21.2132 | + | 21.2132i | −0.719609 | + | 0.719609i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 4.00000i | − | 0.135535i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.12293 | + | 14.7821i | 0.207230 | + | 0.500297i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.48528 | + | 8.48528i | 0.286855 | + | 0.286855i | ||||
\(876\) | 2.82843 | + | 2.82843i | 0.0955637 | + | 0.0955637i | ||||
\(877\) | 12.9343 | − | 5.35757i | 0.436761 | − | 0.180912i | −0.153459 | − | 0.988155i | \(-0.549041\pi\) |
0.590219 | + | 0.807243i | \(0.299041\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22.1731 | − | 9.18440i | −0.747880 | − | 0.309782i | ||||
\(880\) | − | 36.0000i | − | 1.21356i | ||||||
\(881\) | 6.88830 | − | 16.6298i | 0.232073 | − | 0.560273i | −0.764348 | − | 0.644804i | \(-0.776939\pi\) |
0.996421 | + | 0.0845306i | \(0.0269391\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.0000 | −0.370179 | −0.185090 | − | 0.982722i | \(-0.559258\pi\) | ||||
−0.185090 | + | 0.982722i | \(0.559258\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 18.0000 | 0.605063 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.9247 | + | 36.0313i | −0.501121 | + | 1.20981i | 0.447753 | + | 0.894157i | \(0.352224\pi\) |
−0.948874 | + | 0.315655i | \(0.897776\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −48.0417 | − | 19.8995i | −1.61127 | − | 0.667409i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.77164 | − | 1.14805i | 0.0928534 | − | 0.0384611i | ||||
\(892\) | 1.41421 | + | 1.41421i | 0.0473514 | + | 0.0473514i | ||||
\(893\) | −4.24264 | − | 4.24264i | −0.141975 | − | 0.141975i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.88830 | − | 16.6298i | −0.230251 | − | 0.555874i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 9.00000i | − | 0.300501i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.48528 | − | 8.48528i | 0.283000 | − | 0.283000i | ||||
\(900\) | 8.00000 | 0.266667 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −19.7990 | + | 19.7990i | −0.658869 | + | 0.658869i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 42.0000i | − | 1.39613i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.765367 | − | 1.84776i | −0.0254136 | − | 0.0613538i | 0.910663 | − | 0.413149i | \(-0.135571\pi\) |
−0.936077 | + | 0.351795i | \(0.885571\pi\) | |||||||
\(908\) | 5.54328 | − | 2.29610i | 0.183960 | − | 0.0761988i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.9447 | + | 10.3325i | −0.826456 | + | 0.342329i | −0.755499 | − | 0.655150i | \(-0.772605\pi\) |
−0.0709574 | + | 0.997479i | \(0.522605\pi\) | |||||||
\(912\) | −1.53073 | − | 3.69552i | −0.0506877 | − | 0.122371i | ||||
\(913\) | 16.6298 | + | 6.88830i | 0.550367 | + | 0.227970i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.18440 | − | 22.1731i | 0.303627 | − | 0.733020i | ||||
\(916\) | −19.7990 | + | 19.7990i | −0.654177 | + | 0.654177i | ||||
\(917\) | 12.0000 | 0.396275 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.0000 | 0.362857 | 0.181428 | − | 0.983404i | \(-0.441928\pi\) | ||||
0.181428 | + | 0.983404i | \(0.441928\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.65367 | + | 18.4776i | −0.252197 | + | 0.608857i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.0866 | + | 4.59220i | 0.364918 | + | 0.151154i | ||||
\(924\) | 9.18440 | + | 22.1731i | 0.302145 | + | 0.729442i | ||||
\(925\) | 14.7821 | − | 6.12293i | 0.486032 | − | 0.201321i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.53553 | − | 3.53553i | −0.116122 | − | 0.116122i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.74025 | + | 13.8582i | 0.188332 | + | 0.454673i | 0.989639 | − | 0.143581i | \(-0.0458617\pi\) |
−0.801307 | + | 0.598253i | \(0.795862\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 9.00000i | − | 0.294963i | ||||||
\(932\) | −16.0727 | + | 38.8029i | −0.526479 | + | 1.27103i | ||||
\(933\) | −16.9706 | + | 16.9706i | −0.555591 | + | 0.555591i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.5563 | − | 15.5563i | 0.508204 | − | 0.508204i | −0.405771 | − | 0.913975i | \(-0.632997\pi\) |
0.913975 | + | 0.405771i | \(0.132997\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.0000i | 0.522140i | ||||||||
\(940\) | −33.2597 | − | 13.7766i | −1.08481 | − | 0.449343i | ||||
\(941\) | −6.88830 | − | 16.6298i | −0.224552 | − | 0.542117i | 0.770946 | − | 0.636901i | \(-0.219784\pi\) |
−0.995498 | + | 0.0947839i | \(0.969784\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.0919 | − | 19.0919i | −0.621717 | − | 0.621717i | ||||
\(944\) | −16.9706 | − | 16.9706i | −0.552345 | − | 0.552345i | ||||
\(945\) | −11.0866 | + | 4.59220i | −0.360646 | + | 0.149384i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33.2597 | + | 13.7766i | 1.08079 | + | 0.447679i | 0.850788 | − | 0.525510i | \(-0.176125\pi\) |
0.230006 | + | 0.973189i | \(0.426125\pi\) | |||||||
\(948\) | 20.0000i | 0.649570i | ||||||||
\(949\) | −0.765367 | + | 1.84776i | −0.0248449 | + | 0.0599808i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.00000 | 0.194563 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.0000 | 1.16615 | 0.583077 | − | 0.812417i | \(-0.301849\pi\) | ||||
0.583077 | + | 0.812417i | \(0.301849\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.6649 | + | 49.8895i | −0.668701 | + | 1.61439i | ||||
\(956\) | − | 24.0000i | − | 0.776215i | ||||||
\(957\) | 16.6298 | + | 6.88830i | 0.537566 | + | 0.222667i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −22.1731 | + | 9.18440i | −0.716007 | + | 0.296580i | ||||
\(960\) | −16.9706 | − | 16.9706i | −0.547723 | − | 0.547723i | ||||
\(961\) | 19.0919 | + | 19.0919i | 0.615867 | + | 0.615867i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.44415 | + | 8.31492i | 0.110986 | + | 0.267944i | ||||
\(964\) | −14.7821 | − | 6.12293i | −0.476098 | − | 0.197206i | ||||
\(965\) | − | 66.0000i | − | 2.12462i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.9914 | − | 28.9914i | 0.932300 | − | 0.932300i | −0.0655495 | − | 0.997849i | \(-0.520880\pi\) |
0.997849 | + | 0.0655495i | \(0.0208800\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.24264 | + | 4.24264i | −0.136153 | + | 0.136153i | −0.771899 | − | 0.635746i | \(-0.780693\pi\) |
0.635746 | + | 0.771899i | \(0.280693\pi\) | |||||||
\(972\) | 0.765367 | − | 1.84776i | 0.0245492 | − | 0.0592669i | ||||
\(973\) | 8.00000i | 0.256468i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.53073 | + | 3.69552i | 0.0490227 | + | 0.118351i | ||||
\(976\) | −29.5641 | + | 12.2459i | −0.946325 | + | 0.391981i | ||||
\(977\) | −21.2132 | − | 21.2132i | −0.678671 | − | 0.678671i | 0.281029 | − | 0.959699i | \(-0.409324\pi\) |
−0.959699 | + | 0.281029i | \(0.909324\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −20.6649 | − | 49.8895i | −0.660116 | − | 1.59366i | ||||
\(981\) | 18.4776 | + | 7.65367i | 0.589944 | + | 0.244363i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.44415 | + | 8.31492i | −0.109851 | + | 0.265205i | −0.969240 | − | 0.246119i | \(-0.920845\pi\) |
0.859388 | + | 0.511324i | \(0.170845\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.00000 | −0.286764 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 24.0000 | 0.763928 | ||||||||
\(988\) | 1.41421 | − | 1.41421i | 0.0449921 | − | 0.0449921i | ||||
\(989\) | 24.1091 | − | 58.2044i | 0.766623 | − | 1.85079i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.0417 | + | 19.8995i | 1.52610 | + | 0.632130i | 0.978802 | − | 0.204811i | \(-0.0656578\pi\) |
0.547294 | + | 0.836940i | \(0.315658\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.0104 | − | 4.97488i | 0.381140 | − | 0.157873i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 33.9411 | + | 33.9411i | 1.07601 | + | 1.07601i | ||||
\(996\) | 11.0866 | − | 4.59220i | 0.351291 | − | 0.145509i | ||||
\(997\) | 23.7264 | + | 57.2805i | 0.751422 | + | 1.81409i | 0.551268 | + | 0.834328i | \(0.314144\pi\) |
0.200154 | + | 0.979765i | \(0.435856\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 4.00000i | − | 0.126554i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))