Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(1549,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2646.1549");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.e (of order \(3\), degree \(2\), 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: | \(21.1284163748\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1549.2 | ||
Root | \(1.68614 + 0.396143i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.1549 |
Dual form | 2646.2.e.n.2125.2 |
$q$-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 \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.18614 | + | 3.78651i | 0.977672 | + | 1.69338i | 0.670820 | + | 0.741620i | \(0.265942\pi\) |
0.306851 | + | 0.951757i | \(0.400725\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.18614 | + | 3.78651i | 0.691318 | + | 1.19740i | ||||
\(11\) | −0.686141 | + | 1.18843i | −0.206879 | + | 0.358325i | −0.950730 | − | 0.310021i | \(-0.899664\pi\) |
0.743851 | + | 0.668346i | \(0.232997\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | + | 1.73205i | −0.277350 | + | 0.480384i | −0.970725 | − | 0.240192i | \(-0.922790\pi\) |
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.686141 | + | 1.18843i | 0.166414 | + | 0.288237i | 0.937156 | − | 0.348910i | \(-0.113448\pi\) |
−0.770743 | + | 0.637146i | \(0.780115\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.50000 | + | 4.33013i | −0.573539 | + | 0.993399i | 0.422659 | + | 0.906289i | \(0.361097\pi\) |
−0.996199 | + | 0.0871106i | \(0.972237\pi\) | |||||||
\(20\) | 2.18614 | + | 3.78651i | 0.488836 | + | 0.846689i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.686141 | + | 1.18843i | −0.146286 | + | 0.253374i | ||||
\(23\) | −0.813859 | − | 1.40965i | −0.169701 | − | 0.293931i | 0.768613 | − | 0.639713i | \(-0.220947\pi\) |
−0.938315 | + | 0.345782i | \(0.887614\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.05842 | + | 12.2255i | −1.41168 | + | 2.44511i | ||||
\(26\) | −1.00000 | + | 1.73205i | −0.196116 | + | 0.339683i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.37228 | − | 7.57301i | −0.811912 | − | 1.40627i | −0.911524 | − | 0.411247i | \(-0.865093\pi\) |
0.0996117 | − | 0.995026i | \(-0.468240\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.686141 | + | 1.18843i | 0.117672 | + | 0.203814i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | + | 1.73205i | −0.164399 | + | 0.284747i | −0.936442 | − | 0.350823i | \(-0.885902\pi\) |
0.772043 | + | 0.635571i | \(0.219235\pi\) | |||||||
\(38\) | −2.50000 | + | 4.33013i | −0.405554 | + | 0.702439i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.18614 | + | 3.78651i | 0.345659 | + | 0.598699i | ||||
\(41\) | 2.31386 | − | 4.00772i | 0.361364 | − | 0.625901i | −0.626821 | − | 0.779163i | \(-0.715644\pi\) |
0.988186 | + | 0.153262i | \(0.0489778\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.05842 | + | 7.02939i | 0.618904 | + | 1.07197i | 0.989686 | + | 0.143253i | \(0.0457562\pi\) |
−0.370783 | + | 0.928720i | \(0.620910\pi\) | |||||||
\(44\) | −0.686141 | + | 1.18843i | −0.103440 | + | 0.179163i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.813859 | − | 1.40965i | −0.119997 | − | 0.207841i | ||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −7.05842 | + | 12.2255i | −0.998212 | + | 1.72895i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.00000 | + | 1.73205i | −0.138675 | + | 0.240192i | ||||
\(53\) | −4.37228 | − | 7.57301i | −0.600579 | − | 1.04023i | −0.992733 | − | 0.120334i | \(-0.961603\pi\) |
0.392154 | − | 0.919899i | \(-0.371730\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.00000 | −0.809040 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.37228 | − | 7.57301i | −0.574109 | − | 0.994385i | ||||
\(59\) | 10.1168 | 1.31710 | 0.658550 | − | 0.752537i | \(-0.271170\pi\) | ||||
0.658550 | + | 0.752537i | \(0.271170\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.11684 | 0.399071 | 0.199535 | − | 0.979891i | \(-0.436057\pi\) | ||||
0.199535 | + | 0.979891i | \(0.436057\pi\) | |||||||
\(62\) | 2.00000 | 0.254000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −8.74456 | −1.08463 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.11684 | −0.258614 | −0.129307 | − | 0.991605i | \(-0.541275\pi\) | ||||
−0.129307 | + | 0.991605i | \(0.541275\pi\) | |||||||
\(68\) | 0.686141 | + | 1.18843i | 0.0832068 | + | 0.144118i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.11684 | 0.844614 | 0.422307 | − | 0.906453i | \(-0.361220\pi\) | ||||
0.422307 | + | 0.906453i | \(0.361220\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.05842 | − | 10.4935i | −0.709085 | − | 1.22817i | −0.965197 | − | 0.261524i | \(-0.915775\pi\) |
0.256112 | − | 0.966647i | \(-0.417558\pi\) | |||||||
\(74\) | −1.00000 | + | 1.73205i | −0.116248 | + | 0.201347i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.50000 | + | 4.33013i | −0.286770 | + | 0.496700i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.11684 | −0.575690 | −0.287845 | − | 0.957677i | \(-0.592939\pi\) | ||||
−0.287845 | + | 0.957677i | \(0.592939\pi\) | |||||||
\(80\) | 2.18614 | + | 3.78651i | 0.244418 | + | 0.423344i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.31386 | − | 4.00772i | 0.255523 | − | 0.442579i | ||||
\(83\) | 8.74456 | + | 15.1460i | 0.959840 | + | 1.66249i | 0.722881 | + | 0.690973i | \(0.242818\pi\) |
0.236960 | + | 0.971519i | \(0.423849\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.00000 | + | 5.19615i | −0.325396 | + | 0.563602i | ||||
\(86\) | 4.05842 | + | 7.02939i | 0.437631 | + | 0.757999i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.686141 | + | 1.18843i | −0.0731428 | + | 0.126687i | ||||
\(89\) | 7.37228 | − | 12.7692i | 0.781460 | − | 1.35353i | −0.149631 | − | 0.988742i | \(-0.547808\pi\) |
0.931091 | − | 0.364787i | \(-0.118858\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.813859 | − | 1.40965i | −0.0848507 | − | 0.146966i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −21.8614 | −2.24293 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.05842 | + | 7.02939i | 0.412070 | + | 0.713727i | 0.995116 | − | 0.0987127i | \(-0.0314725\pi\) |
−0.583046 | + | 0.812439i | \(0.698139\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.05842 | + | 12.2255i | −0.705842 | + | 1.22255i | ||||
\(101\) | 0.813859 | − | 1.40965i | 0.0809820 | − | 0.140265i | −0.822690 | − | 0.568490i | \(-0.807528\pi\) |
0.903672 | + | 0.428225i | \(0.140861\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.00000 | + | 8.66025i | 0.492665 | + | 0.853320i | 0.999964 | − | 0.00844953i | \(-0.00268960\pi\) |
−0.507300 | + | 0.861770i | \(0.669356\pi\) | |||||||
\(104\) | −1.00000 | + | 1.73205i | −0.0980581 | + | 0.169842i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.37228 | − | 7.57301i | −0.424674 | − | 0.735556i | ||||
\(107\) | −3.68614 | + | 6.38458i | −0.356353 | + | 0.617221i | −0.987348 | − | 0.158565i | \(-0.949313\pi\) |
0.630996 | + | 0.775786i | \(0.282646\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.00000 | − | 12.1244i | −0.670478 | − | 1.16130i | −0.977769 | − | 0.209687i | \(-0.932756\pi\) |
0.307290 | − | 0.951616i | \(-0.400578\pi\) | |||||||
\(110\) | −6.00000 | −0.572078 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.18614 | + | 3.78651i | −0.205655 | + | 0.356205i | −0.950341 | − | 0.311210i | \(-0.899266\pi\) |
0.744686 | + | 0.667415i | \(0.232599\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.55842 | − | 6.16337i | 0.331825 | − | 0.574737i | ||||
\(116\) | −4.37228 | − | 7.57301i | −0.405956 | − | 0.703137i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.1168 | 0.931331 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.55842 | + | 7.89542i | 0.414402 | + | 0.717765i | ||||
\(122\) | 3.11684 | 0.282186 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.00000 | 0.179605 | ||||||||
\(125\) | −39.8614 | −3.56531 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.11684 | 0.276575 | 0.138288 | − | 0.990392i | \(-0.455840\pi\) | ||||
0.138288 | + | 0.990392i | \(0.455840\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.74456 | −0.766949 | ||||||||
\(131\) | −0.813859 | − | 1.40965i | −0.0711072 | − | 0.123161i | 0.828280 | − | 0.560315i | \(-0.189320\pi\) |
−0.899387 | + | 0.437154i | \(0.855987\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.11684 | −0.182867 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.686141 | + | 1.18843i | 0.0588361 | + | 0.101907i | ||||
\(137\) | 5.31386 | − | 9.20387i | 0.453994 | − | 0.786340i | −0.544636 | − | 0.838672i | \(-0.683332\pi\) |
0.998630 | + | 0.0523324i | \(0.0166655\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.61684 | + | 11.4607i | −0.561233 | + | 0.972085i | 0.436156 | + | 0.899871i | \(0.356340\pi\) |
−0.997389 | + | 0.0722136i | \(0.976994\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.11684 | 0.597232 | ||||||||
\(143\) | −1.37228 | − | 2.37686i | −0.114756 | − | 0.198763i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19.1168 | − | 33.1113i | 1.58757 | − | 2.74975i | ||||
\(146\) | −6.05842 | − | 10.4935i | −0.501399 | − | 0.868448i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.00000 | + | 1.73205i | −0.0821995 | + | 0.142374i | ||||
\(149\) | 1.62772 | + | 2.81929i | 0.133348 | + | 0.230965i | 0.924965 | − | 0.380052i | \(-0.124094\pi\) |
−0.791617 | + | 0.611017i | \(0.790761\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.55842 | + | 7.89542i | −0.370959 | + | 0.642520i | −0.989713 | − | 0.143065i | \(-0.954304\pi\) |
0.618754 | + | 0.785585i | \(0.287638\pi\) | |||||||
\(152\) | −2.50000 | + | 4.33013i | −0.202777 | + | 0.351220i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.37228 | + | 7.57301i | 0.351190 | + | 0.608279i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.11684 | 0.727603 | 0.363802 | − | 0.931476i | \(-0.381479\pi\) | ||||
0.363802 | + | 0.931476i | \(0.381479\pi\) | |||||||
\(158\) | −5.11684 | −0.407074 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.18614 | + | 3.78651i | 0.172830 | + | 0.299350i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.11684 | − | 15.7908i | 0.714086 | − | 1.23683i | −0.249225 | − | 0.968446i | \(-0.580176\pi\) |
0.963311 | − | 0.268388i | \(-0.0864909\pi\) | |||||||
\(164\) | 2.31386 | − | 4.00772i | 0.180682 | − | 0.312951i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.74456 | + | 15.1460i | 0.678710 | + | 1.17556i | ||||
\(167\) | −2.74456 | + | 4.75372i | −0.212381 | + | 0.367854i | −0.952459 | − | 0.304666i | \(-0.901455\pi\) |
0.740078 | + | 0.672521i | \(0.234788\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.50000 | + | 7.79423i | 0.346154 | + | 0.599556i | ||||
\(170\) | −3.00000 | + | 5.19615i | −0.230089 | + | 0.398527i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.05842 | + | 7.02939i | 0.309452 | + | 0.535986i | ||||
\(173\) | 6.00000 | 0.456172 | 0.228086 | − | 0.973641i | \(-0.426753\pi\) | ||||
0.228086 | + | 0.973641i | \(0.426753\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.686141 | + | 1.18843i | −0.0517198 | + | 0.0895813i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.37228 | − | 12.7692i | 0.552576 | − | 0.957089i | ||||
\(179\) | 1.62772 | + | 2.81929i | 0.121661 | + | 0.210724i | 0.920423 | − | 0.390924i | \(-0.127844\pi\) |
−0.798762 | + | 0.601648i | \(0.794511\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.883156 | 0.0656445 | 0.0328222 | − | 0.999461i | \(-0.489550\pi\) | ||||
0.0328222 | + | 0.999461i | \(0.489550\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.813859 | − | 1.40965i | −0.0599985 | − | 0.103920i | ||||
\(185\) | −8.74456 | −0.642913 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.88316 | −0.137710 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −21.8614 | −1.58599 | ||||||||
\(191\) | 19.1168 | 1.38325 | 0.691623 | − | 0.722259i | \(-0.256896\pi\) | ||||
0.691623 | + | 0.722259i | \(0.256896\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.00000 | −0.503871 | −0.251936 | − | 0.967744i | \(-0.581067\pi\) | ||||
−0.251936 | + | 0.967744i | \(0.581067\pi\) | |||||||
\(194\) | 4.05842 | + | 7.02939i | 0.291378 | + | 0.504681i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.00000 | + | 8.66025i | 0.354441 | + | 0.613909i | 0.987022 | − | 0.160585i | \(-0.0513380\pi\) |
−0.632581 | + | 0.774494i | \(0.718005\pi\) | |||||||
\(200\) | −7.05842 | + | 12.2255i | −0.499106 | + | 0.864477i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.813859 | − | 1.40965i | 0.0572629 | − | 0.0991823i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.2337 | 1.41318 | ||||||||
\(206\) | 5.00000 | + | 8.66025i | 0.348367 | + | 0.603388i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.00000 | + | 1.73205i | −0.0693375 | + | 0.120096i | ||||
\(209\) | −3.43070 | − | 5.94215i | −0.237307 | − | 0.411027i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.00000 | − | 13.8564i | 0.550743 | − | 0.953914i | −0.447478 | − | 0.894295i | \(-0.647678\pi\) |
0.998221 | − | 0.0596196i | \(-0.0189888\pi\) | |||||||
\(212\) | −4.37228 | − | 7.57301i | −0.300290 | − | 0.520117i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.68614 | + | 6.38458i | −0.251979 | + | 0.436441i | ||||
\(215\) | −17.7446 | + | 30.7345i | −1.21017 | + | 2.09607i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.00000 | − | 12.1244i | −0.474100 | − | 0.821165i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.00000 | −0.404520 | ||||||||
\(221\) | −2.74456 | −0.184619 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.00000 | + | 3.46410i | 0.133930 | + | 0.231973i | 0.925188 | − | 0.379509i | \(-0.123907\pi\) |
−0.791258 | + | 0.611482i | \(0.790574\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.18614 | + | 3.78651i | −0.145420 | + | 0.251875i | ||||
\(227\) | −6.12772 | + | 10.6135i | −0.406711 | + | 0.704444i | −0.994519 | − | 0.104556i | \(-0.966658\pi\) |
0.587808 | + | 0.809000i | \(0.299991\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.44158 | + | 2.49689i | 0.0952622 | + | 0.164999i | 0.909718 | − | 0.415227i | \(-0.136298\pi\) |
−0.814456 | + | 0.580226i | \(0.802964\pi\) | |||||||
\(230\) | 3.55842 | − | 6.16337i | 0.234635 | − | 0.406400i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.37228 | − | 7.57301i | −0.287054 | − | 0.497193i | ||||
\(233\) | −0.127719 | + | 0.221215i | −0.00836713 | + | 0.0144923i | −0.870179 | − | 0.492736i | \(-0.835997\pi\) |
0.861812 | + | 0.507229i | \(0.169330\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 10.1168 | 0.658550 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.93070 | − | 8.54023i | 0.318941 | − | 0.552421i | −0.661327 | − | 0.750098i | \(-0.730006\pi\) |
0.980267 | + | 0.197677i | \(0.0633396\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.05842 | + | 15.6896i | −0.583504 | + | 1.01066i | 0.411556 | + | 0.911385i | \(0.364986\pi\) |
−0.995060 | + | 0.0992745i | \(0.968348\pi\) | |||||||
\(242\) | 4.55842 | + | 7.89542i | 0.293026 | + | 0.507537i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.11684 | 0.199535 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.00000 | − | 8.66025i | −0.318142 | − | 0.551039i | ||||
\(248\) | 2.00000 | 0.127000 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −39.8614 | −2.52106 | ||||||||
\(251\) | 9.00000 | 0.568075 | 0.284037 | − | 0.958813i | \(-0.408326\pi\) | ||||
0.284037 | + | 0.958813i | \(0.408326\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.23369 | 0.140431 | ||||||||
\(254\) | 3.11684 | 0.195568 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.43070 | − | 5.94215i | −0.214001 | − | 0.370661i | 0.738962 | − | 0.673747i | \(-0.235316\pi\) |
−0.952963 | + | 0.303086i | \(0.901983\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −8.74456 | −0.542315 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.813859 | − | 1.40965i | −0.0502804 | − | 0.0870882i | ||||
\(263\) | 3.81386 | − | 6.60580i | 0.235173 | − | 0.407331i | −0.724150 | − | 0.689642i | \(-0.757768\pi\) |
0.959323 | + | 0.282311i | \(0.0911011\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.1168 | − | 33.1113i | 1.17434 | − | 2.03401i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.11684 | −0.129307 | ||||||||
\(269\) | −0.813859 | − | 1.40965i | −0.0496219 | − | 0.0859476i | 0.840148 | − | 0.542358i | \(-0.182468\pi\) |
−0.889769 | + | 0.456410i | \(0.849135\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.11684 | + | 14.0588i | −0.493063 | + | 0.854010i | −0.999968 | − | 0.00799154i | \(-0.997456\pi\) |
0.506905 | + | 0.862002i | \(0.330790\pi\) | |||||||
\(272\) | 0.686141 | + | 1.18843i | 0.0416034 | + | 0.0720592i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.31386 | − | 9.20387i | 0.321022 | − | 0.556026i | ||||
\(275\) | −9.68614 | − | 16.7769i | −0.584096 | − | 1.01168i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.11684 | − | 10.5947i | 0.367526 | − | 0.636573i | −0.621652 | − | 0.783293i | \(-0.713538\pi\) |
0.989178 | + | 0.146720i | \(0.0468717\pi\) | |||||||
\(278\) | −6.61684 | + | 11.4607i | −0.396852 | + | 0.687368i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.18614 | + | 14.1788i | 0.488344 | + | 0.845837i | 0.999910 | − | 0.0134071i | \(-0.00426773\pi\) |
−0.511566 | + | 0.859244i | \(0.670934\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.1168 | 1.61193 | 0.805965 | − | 0.591964i | \(-0.201647\pi\) | ||||
0.805965 | + | 0.591964i | \(0.201647\pi\) | |||||||
\(284\) | 7.11684 | 0.422307 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.37228 | − | 2.37686i | −0.0811447 | − | 0.140547i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.55842 | − | 13.0916i | 0.444613 | − | 0.770092i | ||||
\(290\) | 19.1168 | − | 33.1113i | 1.12258 | − | 1.94437i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.05842 | − | 10.4935i | −0.354542 | − | 0.614085i | ||||
\(293\) | −5.18614 | + | 8.98266i | −0.302978 | + | 0.524773i | −0.976809 | − | 0.214113i | \(-0.931314\pi\) |
0.673831 | + | 0.738885i | \(0.264647\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 22.1168 | + | 38.3075i | 1.28769 | + | 2.23035i | ||||
\(296\) | −1.00000 | + | 1.73205i | −0.0581238 | + | 0.100673i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.62772 | + | 2.81929i | 0.0942912 | + | 0.163317i | ||||
\(299\) | 3.25544 | 0.188267 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −4.55842 | + | 7.89542i | −0.262308 | + | 0.454330i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.50000 | + | 4.33013i | −0.143385 | + | 0.248350i | ||||
\(305\) | 6.81386 | + | 11.8020i | 0.390160 | + | 0.675778i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.0000 | −0.741949 | −0.370975 | − | 0.928643i | \(-0.620976\pi\) | ||||
−0.370975 | + | 0.928643i | \(0.620976\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.37228 | + | 7.57301i | 0.248329 | + | 0.430118i | ||||
\(311\) | −8.23369 | −0.466890 | −0.233445 | − | 0.972370i | \(-0.575000\pi\) | ||||
−0.233445 | + | 0.972370i | \(0.575000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.1168 | −1.13707 | −0.568536 | − | 0.822659i | \(-0.692490\pi\) | ||||
−0.568536 | + | 0.822659i | \(0.692490\pi\) | |||||||
\(314\) | 9.11684 | 0.514493 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.11684 | −0.287845 | ||||||||
\(317\) | 6.00000 | 0.336994 | 0.168497 | − | 0.985702i | \(-0.446109\pi\) | ||||
0.168497 | + | 0.985702i | \(0.446109\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.0000 | 0.671871 | ||||||||
\(320\) | 2.18614 | + | 3.78651i | 0.122209 | + | 0.211672i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.86141 | −0.381779 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.1168 | − | 24.4511i | −0.783062 | − | 1.35630i | ||||
\(326\) | 9.11684 | − | 15.7908i | 0.504935 | − | 0.874574i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.31386 | − | 4.00772i | 0.127762 | − | 0.221289i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.2337 | 1.22207 | 0.611037 | − | 0.791602i | \(-0.290753\pi\) | ||||
0.611037 | + | 0.791602i | \(0.290753\pi\) | |||||||
\(332\) | 8.74456 | + | 15.1460i | 0.479920 | + | 0.831246i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.74456 | + | 4.75372i | −0.150176 | + | 0.260112i | ||||
\(335\) | −4.62772 | − | 8.01544i | −0.252839 | − | 0.437930i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.05842 | − | 7.02939i | 0.221076 | − | 0.382915i | −0.734059 | − | 0.679086i | \(-0.762376\pi\) |
0.955135 | + | 0.296171i | \(0.0957097\pi\) | |||||||
\(338\) | 4.50000 | + | 7.79423i | 0.244768 | + | 0.423950i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.00000 | + | 5.19615i | −0.162698 | + | 0.281801i | ||||
\(341\) | −1.37228 | + | 2.37686i | −0.0743132 | + | 0.128714i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.05842 | + | 7.02939i | 0.218815 | + | 0.378999i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.00000 | 0.322562 | ||||||||
\(347\) | 10.1168 | 0.543101 | 0.271550 | − | 0.962424i | \(-0.412464\pi\) | ||||
0.271550 | + | 0.962424i | \(0.412464\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.0000 | + | 19.0526i | 0.588817 | + | 1.01986i | 0.994388 | + | 0.105797i | \(0.0337393\pi\) |
−0.405571 | + | 0.914063i | \(0.632927\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.686141 | + | 1.18843i | −0.0365714 | + | 0.0633436i | ||||
\(353\) | −6.68614 | + | 11.5807i | −0.355867 | + | 0.616380i | −0.987266 | − | 0.159078i | \(-0.949148\pi\) |
0.631399 | + | 0.775458i | \(0.282481\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.5584 | + | 26.9480i | 0.825755 | + | 1.43025i | ||||
\(356\) | 7.37228 | − | 12.7692i | 0.390730 | − | 0.676764i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.62772 | + | 2.81929i | 0.0860276 | + | 0.149004i | ||||
\(359\) | 10.9307 | − | 18.9325i | 0.576900 | − | 0.999221i | −0.418932 | − | 0.908018i | \(-0.637595\pi\) |
0.995832 | − | 0.0912032i | \(-0.0290713\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | − | 5.19615i | −0.157895 | − | 0.273482i | ||||
\(362\) | 0.883156 | 0.0464177 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 26.4891 | − | 45.8805i | 1.38650 | − | 2.40150i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.11684 | − | 10.5947i | 0.319297 | − | 0.553038i | −0.661045 | − | 0.750346i | \(-0.729887\pi\) |
0.980341 | + | 0.197308i | \(0.0632200\pi\) | |||||||
\(368\) | −0.813859 | − | 1.40965i | −0.0424254 | − | 0.0734829i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.74456 | −0.454608 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.00000 | + | 8.66025i | 0.258890 | + | 0.448411i | 0.965945 | − | 0.258748i | \(-0.0833099\pi\) |
−0.707055 | + | 0.707159i | \(0.749977\pi\) | |||||||
\(374\) | −1.88316 | −0.0973757 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 17.4891 | 0.900736 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.11684 | −0.416934 | −0.208467 | − | 0.978029i | \(-0.566847\pi\) | ||||
−0.208467 | + | 0.978029i | \(0.566847\pi\) | |||||||
\(380\) | −21.8614 | −1.12147 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 19.1168 | 0.978103 | ||||||||
\(383\) | −16.3723 | − | 28.3576i | −0.836584 | − | 1.44901i | −0.892734 | − | 0.450584i | \(-0.851216\pi\) |
0.0561493 | − | 0.998422i | \(-0.482118\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.00000 | −0.356291 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.05842 | + | 7.02939i | 0.206035 | + | 0.356863i | ||||
\(389\) | 5.48913 | − | 9.50744i | 0.278310 | − | 0.482047i | −0.692655 | − | 0.721269i | \(-0.743559\pi\) |
0.970965 | + | 0.239222i | \(0.0768925\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.11684 | − | 1.93443i | 0.0564812 | − | 0.0978284i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.00000 | 0.302276 | ||||||||
\(395\) | −11.1861 | − | 19.3750i | −0.562836 | − | 0.974860i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.0000 | − | 19.0526i | 0.552074 | − | 0.956221i | −0.446051 | − | 0.895008i | \(-0.647170\pi\) |
0.998125 | − | 0.0612128i | \(-0.0194968\pi\) | |||||||
\(398\) | 5.00000 | + | 8.66025i | 0.250627 | + | 0.434099i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.05842 | + | 12.2255i | −0.352921 | + | 0.611277i | ||||
\(401\) | −5.87228 | − | 10.1711i | −0.293248 | − | 0.507920i | 0.681328 | − | 0.731978i | \(-0.261403\pi\) |
−0.974576 | + | 0.224058i | \(0.928069\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.00000 | + | 3.46410i | −0.0996271 | + | 0.172559i | ||||
\(404\) | 0.813859 | − | 1.40965i | 0.0404910 | − | 0.0701325i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.37228 | − | 2.37686i | −0.0680215 | − | 0.117817i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.3505 | −1.10516 | −0.552581 | − | 0.833459i | \(-0.686357\pi\) | ||||
−0.552581 | + | 0.833459i | \(0.686357\pi\) | |||||||
\(410\) | 20.2337 | 0.999271 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.00000 | + | 8.66025i | 0.246332 | + | 0.426660i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −38.2337 | + | 66.2227i | −1.87682 | + | 3.25074i | ||||
\(416\) | −1.00000 | + | 1.73205i | −0.0490290 | + | 0.0849208i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.43070 | − | 5.94215i | −0.167801 | − | 0.290640i | ||||
\(419\) | −6.30298 | + | 10.9171i | −0.307921 | + | 0.533335i | −0.977907 | − | 0.209039i | \(-0.932967\pi\) |
0.669986 | + | 0.742373i | \(0.266300\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.1168 | − | 29.6472i | −0.834224 | − | 1.44492i | −0.894661 | − | 0.446746i | \(-0.852583\pi\) |
0.0604368 | − | 0.998172i | \(-0.480751\pi\) | |||||||
\(422\) | 8.00000 | − | 13.8564i | 0.389434 | − | 0.674519i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.37228 | − | 7.57301i | −0.212337 | − | 0.367778i | ||||
\(425\) | −19.3723 | −0.939694 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.68614 | + | 6.38458i | −0.178176 | + | 0.308610i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −17.7446 | + | 30.7345i | −0.855719 | + | 1.48215i | ||||
\(431\) | −3.25544 | − | 5.63858i | −0.156809 | − | 0.271601i | 0.776907 | − | 0.629615i | \(-0.216787\pi\) |
−0.933716 | + | 0.358014i | \(0.883454\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.1168 | −0.966754 | −0.483377 | − | 0.875412i | \(-0.660590\pi\) | ||||
−0.483377 | + | 0.875412i | \(0.660590\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.00000 | − | 12.1244i | −0.335239 | − | 0.580651i | ||||
\(437\) | 8.13859 | 0.389322 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.00000 | 0.381819 | 0.190910 | − | 0.981608i | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(440\) | −6.00000 | −0.286039 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.74456 | −0.130546 | ||||||||
\(443\) | 40.1168 | 1.90601 | 0.953004 | − | 0.302956i | \(-0.0979737\pi\) | ||||
0.953004 | + | 0.302956i | \(0.0979737\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 64.4674 | 3.05605 | ||||||||
\(446\) | 2.00000 | + | 3.46410i | 0.0947027 | + | 0.164030i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.0000 | −1.55737 | −0.778683 | − | 0.627417i | \(-0.784112\pi\) | ||||
−0.778683 | + | 0.627417i | \(0.784112\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.17527 | + | 5.49972i | 0.149517 | + | 0.258972i | ||||
\(452\) | −2.18614 | + | 3.78651i | −0.102827 | + | 0.178102i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.12772 | + | 10.6135i | −0.287588 | + | 0.498117i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35.4674 | −1.65909 | −0.829547 | − | 0.558437i | \(-0.811401\pi\) | ||||
−0.829547 | + | 0.558437i | \(0.811401\pi\) | |||||||
\(458\) | 1.44158 | + | 2.49689i | 0.0673605 | + | 0.116672i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.55842 | − | 6.16337i | 0.165912 | − | 0.287368i | ||||
\(461\) | 1.06930 | + | 1.85208i | 0.0498021 | + | 0.0862598i | 0.889852 | − | 0.456250i | \(-0.150808\pi\) |
−0.840050 | + | 0.542509i | \(0.817474\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.5584 | − | 20.0198i | 0.537165 | − | 0.930398i | −0.461890 | − | 0.886937i | \(-0.652828\pi\) |
0.999055 | − | 0.0434604i | \(-0.0138382\pi\) | |||||||
\(464\) | −4.37228 | − | 7.57301i | −0.202978 | − | 0.351568i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.127719 | + | 0.221215i | −0.00591645 | + | 0.0102476i | ||||
\(467\) | 16.5475 | − | 28.6612i | 0.765729 | − | 1.32628i | −0.174131 | − | 0.984722i | \(-0.555712\pi\) |
0.939860 | − | 0.341559i | \(-0.110955\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10.1168 | 0.465665 | ||||||||
\(473\) | −11.1386 | −0.512153 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −35.2921 | − | 61.1277i | −1.61931 | − | 2.80473i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.93070 | − | 8.54023i | 0.225525 | − | 0.390621i | ||||
\(479\) | 16.3723 | − | 28.3576i | 0.748069 | − | 1.29569i | −0.200679 | − | 0.979657i | \(-0.564315\pi\) |
0.948747 | − | 0.316036i | \(-0.102352\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.00000 | − | 3.46410i | −0.0911922 | − | 0.157949i | ||||
\(482\) | −9.05842 | + | 15.6896i | −0.412600 | + | 0.714644i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.55842 | + | 7.89542i | 0.207201 | + | 0.358883i | ||||
\(485\) | −17.7446 | + | 30.7345i | −0.805739 | + | 1.39558i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.6753 | − | 30.6145i | −0.800943 | − | 1.38727i | −0.918996 | − | 0.394266i | \(-0.870999\pi\) |
0.118053 | − | 0.993007i | \(-0.462335\pi\) | |||||||
\(488\) | 3.11684 | 0.141093 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.6861 | + | 21.9730i | −0.572518 | + | 0.991629i | 0.423789 | + | 0.905761i | \(0.360700\pi\) |
−0.996306 | + | 0.0858685i | \(0.972634\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.00000 | − | 10.3923i | 0.270226 | − | 0.468046i | ||||
\(494\) | −5.00000 | − | 8.66025i | −0.224961 | − | 0.389643i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.05842 | − | 15.6896i | −0.405511 | − | 0.702365i | 0.588870 | − | 0.808228i | \(-0.299573\pi\) |
−0.994381 | + | 0.105863i | \(0.966240\pi\) | |||||||
\(500\) | −39.8614 | −1.78266 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.00000 | 0.401690 | ||||||||
\(503\) | 32.2337 | 1.43723 | 0.718615 | − | 0.695409i | \(-0.244777\pi\) | ||||
0.718615 | + | 0.695409i | \(0.244777\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.11684 | 0.316695 | ||||||||
\(506\) | 2.23369 | 0.0992995 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.11684 | 0.138288 | ||||||||
\(509\) | −14.4891 | − | 25.0959i | −0.642219 | − | 1.11236i | −0.984936 | − | 0.172918i | \(-0.944681\pi\) |
0.342717 | − | 0.939439i | \(-0.388653\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.43070 | − | 5.94215i | −0.151322 | − | 0.262097i | ||||
\(515\) | −21.8614 | + | 37.8651i | −0.963329 | + | 1.66853i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.74456 | −0.383474 | ||||||||
\(521\) | −12.4307 | − | 21.5306i | −0.544599 | − | 0.943273i | −0.998632 | − | 0.0522883i | \(-0.983349\pi\) |
0.454033 | − | 0.890985i | \(-0.349985\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.5584 | − | 30.4121i | 0.767776 | − | 1.32983i | −0.170990 | − | 0.985273i | \(-0.554697\pi\) |
0.938766 | − | 0.344555i | \(-0.111970\pi\) | |||||||
\(524\) | −0.813859 | − | 1.40965i | −0.0355536 | − | 0.0615807i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.81386 | − | 6.60580i | 0.166292 | − | 0.288026i | ||||
\(527\) | 1.37228 | + | 2.37686i | 0.0597775 | + | 0.103538i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.1753 | − | 17.6241i | 0.442403 | − | 0.766264i | ||||
\(530\) | 19.1168 | − | 33.1113i | 0.830383 | − | 1.43826i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.62772 | + | 8.01544i | 0.200449 | + | 0.347187i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −32.2337 | −1.39358 | ||||||||
\(536\) | −2.11684 | −0.0914337 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.813859 | − | 1.40965i | −0.0350880 | − | 0.0607741i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.11684 | − | 5.39853i | 0.134004 | − | 0.232101i | −0.791213 | − | 0.611541i | \(-0.790550\pi\) |
0.925216 | + | 0.379440i | \(0.123883\pi\) | |||||||
\(542\) | −8.11684 | + | 14.0588i | −0.348648 | + | 0.603877i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.686141 | + | 1.18843i | 0.0294180 | + | 0.0509535i | ||||
\(545\) | 30.6060 | − | 53.0111i | 1.31102 | − | 2.27075i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.05842 | − | 15.6896i | −0.387310 | − | 0.670841i | 0.604777 | − | 0.796395i | \(-0.293262\pi\) |
−0.992087 | + | 0.125554i | \(0.959929\pi\) | |||||||
\(548\) | 5.31386 | − | 9.20387i | 0.226997 | − | 0.393170i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −9.68614 | − | 16.7769i | −0.413018 | − | 0.715369i | ||||
\(551\) | 43.7228 | 1.86265 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 6.11684 | − | 10.5947i | 0.259880 | − | 0.450125i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.61684 | + | 11.4607i | −0.280617 | + | 0.486042i | ||||
\(557\) | 14.7446 | + | 25.5383i | 0.624747 | + | 1.08209i | 0.988590 | + | 0.150633i | \(0.0481313\pi\) |
−0.363843 | + | 0.931460i | \(0.618535\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.2337 | −0.686612 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.18614 | + | 14.1788i | 0.345312 | + | 0.598097i | ||||
\(563\) | −3.00000 | −0.126435 | −0.0632175 | − | 0.998000i | \(-0.520136\pi\) | ||||
−0.0632175 | + | 0.998000i | \(0.520136\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.1168 | −0.804252 | ||||||||
\(566\) | 27.1168 | 1.13981 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.11684 | 0.298616 | ||||||||
\(569\) | −16.1168 | −0.675653 | −0.337827 | − | 0.941208i | \(-0.609692\pi\) | ||||
−0.337827 | + | 0.941208i | \(0.609692\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.3505 | −0.935341 | −0.467670 | − | 0.883903i | \(-0.654907\pi\) | ||||
−0.467670 | + | 0.883903i | \(0.654907\pi\) | |||||||
\(572\) | −1.37228 | − | 2.37686i | −0.0573780 | − | 0.0993815i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22.9783 | 0.958259 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.94158 | − | 8.55906i | −0.205721 | − | 0.356319i | 0.744641 | − | 0.667465i | \(-0.232620\pi\) |
−0.950362 | + | 0.311146i | \(0.899287\pi\) | |||||||
\(578\) | 7.55842 | − | 13.0916i | 0.314389 | − | 0.544538i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 19.1168 | − | 33.1113i | 0.793784 | − | 1.37487i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.0000 | 0.496989 | ||||||||
\(584\) | −6.05842 | − | 10.4935i | −0.250699 | − | 0.434224i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.18614 | + | 8.98266i | −0.214237 | + | 0.371070i | ||||
\(587\) | 7.24456 | + | 12.5480i | 0.299015 | + | 0.517909i | 0.975911 | − | 0.218170i | \(-0.0700086\pi\) |
−0.676896 | + | 0.736079i | \(0.736675\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.00000 | + | 8.66025i | −0.206021 | + | 0.356840i | ||||
\(590\) | 22.1168 | + | 38.3075i | 0.910536 | + | 1.57709i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.00000 | + | 1.73205i | −0.0410997 | + | 0.0711868i | ||||
\(593\) | 7.37228 | − | 12.7692i | 0.302743 | − | 0.524367i | −0.674013 | − | 0.738719i | \(-0.735431\pi\) |
0.976756 | + | 0.214353i | \(0.0687642\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.62772 | + | 2.81929i | 0.0666740 | + | 0.115483i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.25544 | 0.133125 | ||||||||
\(599\) | −24.0000 | −0.980613 | −0.490307 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490307 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.0584 | − | 20.8858i | −0.491873 | − | 0.851950i | 0.508083 | − | 0.861308i | \(-0.330354\pi\) |
−0.999956 | + | 0.00935863i | \(0.997021\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.55842 | + | 7.89542i | −0.185480 | + | 0.321260i | ||||
\(605\) | −19.9307 | + | 34.5210i | −0.810298 | + | 1.40348i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.1168 | − | 19.2549i | −0.451219 | − | 0.781534i | 0.547243 | − | 0.836974i | \(-0.315677\pi\) |
−0.998462 | + | 0.0554398i | \(0.982344\pi\) | |||||||
\(608\) | −2.50000 | + | 4.33013i | −0.101388 | + | 0.175610i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.81386 | + | 11.8020i | 0.275885 | + | 0.477847i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.1168 | + | 31.3793i | 0.731732 | + | 1.26740i | 0.956142 | + | 0.292903i | \(0.0946213\pi\) |
−0.224410 | + | 0.974495i | \(0.572045\pi\) | |||||||
\(614\) | −13.0000 | −0.524637 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.43070 | − | 16.3345i | 0.379666 | − | 0.657600i | −0.611348 | − | 0.791362i | \(-0.709372\pi\) |
0.991014 | + | 0.133762i | \(0.0427056\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.7337 | + | 39.3759i | −0.913744 | + | 1.58265i | −0.105014 | + | 0.994471i | \(0.533489\pi\) |
−0.808730 | + | 0.588180i | \(0.799844\pi\) | |||||||
\(620\) | 4.37228 | + | 7.57301i | 0.175595 | + | 0.304140i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −8.23369 | −0.330141 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −51.8505 | − | 89.8078i | −2.07402 | − | 3.59231i | ||||
\(626\) | −20.1168 | −0.804031 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.11684 | 0.363802 | ||||||||
\(629\) | −2.74456 | −0.109433 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.3505 | −1.48690 | −0.743451 | − | 0.668791i | \(-0.766812\pi\) | ||||
−0.743451 | + | 0.668791i | \(0.766812\pi\) | |||||||
\(632\) | −5.11684 | −0.203537 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.00000 | 0.238290 | ||||||||
\(635\) | 6.81386 | + | 11.8020i | 0.270400 | + | 0.468346i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 12.0000 | 0.475085 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.18614 | + | 3.78651i | 0.0864148 | + | 0.149675i | ||||
\(641\) | 17.1060 | − | 29.6284i | 0.675645 | − | 1.17025i | −0.300635 | − | 0.953739i | \(-0.597198\pi\) |
0.976280 | − | 0.216512i | \(-0.0694682\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.1753 | + | 22.8202i | −0.519582 | + | 0.899942i | 0.480159 | + | 0.877181i | \(0.340579\pi\) |
−0.999741 | + | 0.0227606i | \(0.992754\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.86141 | −0.269958 | ||||||||
\(647\) | 2.74456 | + | 4.75372i | 0.107900 | + | 0.186888i | 0.914919 | − | 0.403637i | \(-0.132254\pi\) |
−0.807019 | + | 0.590525i | \(0.798921\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.94158 | + | 12.0232i | −0.272481 | + | 0.471951i | ||||
\(650\) | −14.1168 | − | 24.4511i | −0.553708 | − | 0.959051i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.11684 | − | 15.7908i | 0.357043 | − | 0.618417i | ||||
\(653\) | −13.3723 | − | 23.1615i | −0.523298 | − | 0.906378i | −0.999632 | − | 0.0271143i | \(-0.991368\pi\) |
0.476335 | − | 0.879264i | \(-0.341965\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.55842 | − | 6.16337i | 0.139039 | − | 0.240823i | ||||
\(656\) | 2.31386 | − | 4.00772i | 0.0903410 | − | 0.156475i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.3723 | − | 17.9653i | −0.404047 | − | 0.699829i | 0.590163 | − | 0.807284i | \(-0.299063\pi\) |
−0.994210 | + | 0.107454i | \(0.965730\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.1168 | 1.05472 | 0.527361 | − | 0.849641i | \(-0.323181\pi\) | ||||
0.527361 | + | 0.849641i | \(0.323181\pi\) | |||||||
\(662\) | 22.2337 | 0.864137 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.74456 | + | 15.1460i | 0.339355 | + | 0.587780i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.11684 | + | 12.3267i | −0.275565 | + | 0.477293i | ||||
\(668\) | −2.74456 | + | 4.75372i | −0.106190 | + | 0.183927i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.62772 | − | 8.01544i | −0.178784 | − | 0.309664i | ||||
\(671\) | −2.13859 | + | 3.70415i | −0.0825595 | + | 0.142997i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.44158 | + | 2.49689i | 0.0555687 | + | 0.0962479i | 0.892472 | − | 0.451103i | \(-0.148969\pi\) |
−0.836903 | + | 0.547351i | \(0.815636\pi\) | |||||||
\(674\) | 4.05842 | − | 7.02939i | 0.156325 | − | 0.270762i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.50000 | + | 7.79423i | 0.173077 | + | 0.299778i | ||||
\(677\) | −34.4674 | −1.32469 | −0.662344 | − | 0.749199i | \(-0.730438\pi\) | ||||
−0.662344 | + | 0.749199i | \(0.730438\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.00000 | + | 5.19615i | −0.115045 | + | 0.199263i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.37228 | + | 2.37686i | −0.0525474 | + | 0.0910147i | ||||
\(683\) | 14.9198 | + | 25.8419i | 0.570891 | + | 0.988813i | 0.996475 | + | 0.0838936i | \(0.0267356\pi\) |
−0.425583 | + | 0.904919i | \(0.639931\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 46.4674 | 1.77543 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.05842 | + | 7.02939i | 0.154726 | + | 0.267993i | ||||
\(689\) | 17.4891 | 0.666283 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.1168 | −0.879406 | −0.439703 | − | 0.898143i | \(-0.644916\pi\) | ||||
−0.439703 | + | 0.898143i | \(0.644916\pi\) | |||||||
\(692\) | 6.00000 | 0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.1168 | 0.384030 | ||||||||
\(695\) | −57.8614 | −2.19481 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.35053 | 0.240544 | ||||||||
\(698\) | 11.0000 | + | 19.0526i | 0.416356 | + | 0.721150i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.2337 | 1.44407 | 0.722033 | − | 0.691858i | \(-0.243208\pi\) | ||||
0.722033 | + | 0.691858i | \(0.243208\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.00000 | − | 8.66025i | −0.188579 | − | 0.326628i | ||||
\(704\) | −0.686141 | + | 1.18843i | −0.0258599 | + | 0.0447907i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.68614 | + | 11.5807i | −0.251636 | + | 0.435847i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 44.0000 | 1.65245 | 0.826227 | − | 0.563337i | \(-0.190483\pi\) | ||||
0.826227 | + | 0.563337i | \(0.190483\pi\) | |||||||
\(710\) | 15.5584 | + | 26.9480i | 0.583897 | + | 1.01134i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.37228 | − | 12.7692i | 0.276288 | − | 0.478545i | ||||
\(713\) | −1.62772 | − | 2.81929i | −0.0609585 | − | 0.105583i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.00000 | − | 10.3923i | 0.224387 | − | 0.388650i | ||||
\(716\) | 1.62772 | + | 2.81929i | 0.0608307 | + | 0.105362i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.9307 | − | 18.9325i | 0.407930 | − | 0.706556i | ||||
\(719\) | 1.37228 | − | 2.37686i | 0.0511775 | − | 0.0886420i | −0.839302 | − | 0.543666i | \(-0.817036\pi\) |
0.890479 | + | 0.455024i | \(0.150369\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −3.00000 | − | 5.19615i | −0.111648 | − | 0.193381i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.883156 | 0.0328222 | ||||||||
\(725\) | 123.446 | 4.58466 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.1168 | + | 31.3793i | 0.671917 | + | 1.16379i | 0.977360 | + | 0.211583i | \(0.0678620\pi\) |
−0.305443 | + | 0.952210i | \(0.598805\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 26.4891 | − | 45.8805i | 0.980407 | − | 1.69811i | ||||
\(731\) | −5.56930 | + | 9.64630i | −0.205988 | + | 0.356781i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.5584 | + | 35.6082i | 0.759343 | + | 1.31522i | 0.943186 | + | 0.332265i | \(0.107813\pi\) |
−0.183844 | + | 0.982956i | \(0.558854\pi\) | |||||||
\(734\) | 6.11684 | − | 10.5947i | 0.225777 | − | 0.391057i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.813859 | − | 1.40965i | −0.0299993 | − | 0.0519602i | ||||
\(737\) | 1.45245 | − | 2.51572i | 0.0535018 | − | 0.0926678i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.05842 | + | 7.02939i | 0.149291 | + | 0.258580i | 0.930966 | − | 0.365106i | \(-0.118967\pi\) |
−0.781674 | + | 0.623687i | \(0.785634\pi\) | |||||||
\(740\) | −8.74456 | −0.321457 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.86141 | + | 11.8843i | −0.251721 | + | 0.435993i | −0.964000 | − | 0.265904i | \(-0.914330\pi\) |
0.712279 | + | 0.701896i | \(0.247663\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.11684 | + | 12.3267i | −0.260741 | + | 0.451617i | ||||
\(746\) | 5.00000 | + | 8.66025i | 0.183063 | + | 0.317074i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.88316 | −0.0688550 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.55842 | + | 14.8236i | 0.312301 | + | 0.540922i | 0.978860 | − | 0.204531i | \(-0.0655668\pi\) |
−0.666559 | + | 0.745452i | \(0.732234\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 17.4891 | 0.636916 | ||||||||
\(755\) | −39.8614 | −1.45071 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 46.2337 | 1.68039 | 0.840196 | − | 0.542283i | \(-0.182440\pi\) | ||||
0.840196 | + | 0.542283i | \(0.182440\pi\) | |||||||
\(758\) | −8.11684 | −0.294817 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −21.8614 | −0.792997 | ||||||||
\(761\) | 17.7446 | + | 30.7345i | 0.643240 | + | 1.11412i | 0.984705 | + | 0.174230i | \(0.0557435\pi\) |
−0.341465 | + | 0.939894i | \(0.610923\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 19.1168 | 0.691623 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.3723 | − | 28.3576i | −0.591555 | − | 1.02460i | ||||
\(767\) | −10.1168 | + | 17.5229i | −0.365298 | + | 0.632715i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.00000 | − | 8.66025i | 0.180305 | − | 0.312297i | −0.761680 | − | 0.647954i | \(-0.775625\pi\) |
0.941984 | + | 0.335657i | \(0.108958\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.00000 | −0.251936 | ||||||||
\(773\) | −19.9307 | − | 34.5210i | −0.716858 | − | 1.24163i | −0.962239 | − | 0.272207i | \(-0.912246\pi\) |
0.245381 | − | 0.969427i | \(-0.421087\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14.1168 | + | 24.4511i | −0.507092 | + | 0.878309i | ||||
\(776\) | 4.05842 | + | 7.02939i | 0.145689 | + | 0.252341i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.48913 | − | 9.50744i | 0.196795 | − | 0.340858i | ||||
\(779\) | 11.5693 | + | 20.0386i | 0.414513 | + | 0.717958i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.88316 | + | 8.45787i | −0.174733 | + | 0.302647i | ||||
\(782\) | 1.11684 | − | 1.93443i | 0.0399383 | − | 0.0691751i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19.9307 | + | 34.5210i | 0.711357 | + | 1.23211i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.00000 | −0.142585 | −0.0712923 | − | 0.997455i | \(-0.522712\pi\) | ||||
−0.0712923 | + | 0.997455i | \(0.522712\pi\) | |||||||
\(788\) | 6.00000 | 0.213741 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −11.1861 | − | 19.3750i | −0.397985 | − | 0.689330i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.11684 | + | 5.39853i | −0.110682 | + | 0.191707i | ||||
\(794\) | 11.0000 | − | 19.0526i | 0.390375 | − | 0.676150i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.00000 | + | 8.66025i | 0.177220 | + | 0.306955i | ||||
\(797\) | −4.06930 | + | 7.04823i | −0.144142 | + | 0.249661i | −0.929052 | − | 0.369948i | \(-0.879376\pi\) |
0.784911 | + | 0.619609i | \(0.212709\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −7.05842 | + | 12.2255i | −0.249553 | + | 0.432238i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5.87228 | − | 10.1711i | −0.207357 | − | 0.359154i | ||||
\(803\) | 16.6277 | 0.586779 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.00000 | + | 3.46410i | −0.0704470 | + | 0.122018i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.813859 | − | 1.40965i | 0.0286315 | − | 0.0495912i | ||||
\(809\) | −3.43070 | − | 5.94215i | −0.120617 | − | 0.208915i | 0.799394 | − | 0.600807i | \(-0.205154\pi\) |
−0.920011 | + | 0.391892i | \(0.871821\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.1168 | 1.47892 | 0.739461 | − | 0.673199i | \(-0.235080\pi\) | ||||
0.739461 | + | 0.673199i | \(0.235080\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.37228 | − | 2.37686i | −0.0480984 | − | 0.0833089i | ||||
\(815\) | 79.7228 | 2.79257 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −40.5842 | −1.41986 | ||||||||
\(818\) | −22.3505 | −0.781468 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 20.2337 | 0.706591 | ||||||||
\(821\) | 3.76631 | 0.131445 | 0.0657226 | − | 0.997838i | \(-0.479065\pi\) | ||||
0.0657226 | + | 0.997838i | \(0.479065\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.2337 | −0.426440 | −0.213220 | − | 0.977004i | \(-0.568395\pi\) | ||||
−0.213220 | + | 0.977004i | \(0.568395\pi\) | |||||||
\(824\) | 5.00000 | + | 8.66025i | 0.174183 | + | 0.301694i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.0000 | −0.417281 | −0.208640 | − | 0.977992i | \(-0.566904\pi\) | ||||
−0.208640 | + | 0.977992i | \(0.566904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.88316 | + | 11.9220i | 0.239062 | + | 0.414067i | 0.960445 | − | 0.278468i | \(-0.0898268\pi\) |
−0.721383 | + | 0.692536i | \(0.756493\pi\) | |||||||
\(830\) | −38.2337 | + | 66.2227i | −1.32711 | + | 2.29862i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.00000 | + | 1.73205i | −0.0346688 | + | 0.0600481i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.0000 | −0.830554 | ||||||||
\(836\) | −3.43070 | − | 5.94215i | −0.118653 | − | 0.205514i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.30298 | + | 10.9171i | −0.217733 | + | 0.377125i | ||||
\(839\) | 2.74456 | + | 4.75372i | 0.0947528 | + | 0.164117i | 0.909505 | − | 0.415692i | \(-0.136461\pi\) |
−0.814753 | + | 0.579809i | \(0.803127\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.7337 | + | 41.1080i | −0.818403 | + | 1.41752i | ||||
\(842\) | −17.1168 | − | 29.6472i | −0.589885 | − | 1.02171i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.00000 | − | 13.8564i | 0.275371 | − | 0.476957i | ||||
\(845\) | −19.6753 | + | 34.0786i | −0.676850 | + | 1.17234i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.37228 | − | 7.57301i | −0.150145 | − | 0.260058i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −19.3723 | −0.664464 | ||||||||
\(851\) | 3.25544 | 0.111595 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.5584 | + | 30.4121i | 0.601189 | + | 1.04129i | 0.992641 | + | 0.121091i | \(0.0386394\pi\) |
−0.391452 | + | 0.920198i | \(0.628027\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.68614 | + | 6.38458i | −0.125990 | + | 0.218221i | ||||
\(857\) | −19.9783 | + | 34.6033i | −0.682444 | + | 1.18203i | 0.291789 | + | 0.956483i | \(0.405750\pi\) |
−0.974233 | + | 0.225545i | \(0.927584\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.9416 | − | 29.3437i | −0.578039 | − | 1.00119i | −0.995704 | − | 0.0925921i | \(-0.970485\pi\) |
0.417665 | − | 0.908601i | \(-0.362849\pi\) | |||||||
\(860\) | −17.7446 | + | 30.7345i | −0.605085 | + | 1.04804i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.25544 | − | 5.63858i | −0.110881 | − | 0.192051i | ||||
\(863\) | 4.93070 | − | 8.54023i | 0.167843 | − | 0.290713i | −0.769818 | − | 0.638263i | \(-0.779653\pi\) |
0.937661 | + | 0.347550i | \(0.112986\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.1168 | + | 22.7190i | 0.445986 | + | 0.772471i | ||||
\(866\) | −20.1168 | −0.683598 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.51087 | − | 6.08101i | 0.119098 | − | 0.206284i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.11684 | − | 3.66648i | 0.0717265 | − | 0.124234i | ||||
\(872\) | −7.00000 | − | 12.1244i | −0.237050 | − | 0.410582i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.13859 | 0.275292 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.3505 | + | 50.8366i | 0.991097 | + | 1.71663i | 0.610852 | + | 0.791744i | \(0.290827\pi\) |
0.380245 | + | 0.924886i | \(0.375840\pi\) | |||||||
\(878\) | 8.00000 | 0.269987 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.00000 | −0.202260 | ||||||||
\(881\) | 20.2337 | 0.681690 | 0.340845 | − | 0.940119i | \(-0.389287\pi\) | ||||
0.340845 | + | 0.940119i | \(0.389287\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.3505 | −1.35790 | −0.678952 | − | 0.734183i | \(-0.737565\pi\) | ||||
−0.678952 | + | 0.734183i | \(0.737565\pi\) | |||||||
\(884\) | −2.74456 | −0.0923096 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 40.1168 | 1.34775 | ||||||||
\(887\) | 12.8614 | + | 22.2766i | 0.431844 | + | 0.747975i | 0.997032 | − | 0.0769865i | \(-0.0245298\pi\) |
−0.565188 | + | 0.824962i | \(0.691197\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 64.4674 | 2.16095 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.00000 | + | 3.46410i | 0.0669650 | + | 0.115987i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.11684 | + | 12.3267i | −0.237890 | + | 0.412037i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −33.0000 | −1.10122 | ||||||||
\(899\) | −8.74456 | − | 15.1460i | −0.291647 | − | 0.505148i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.00000 | − | 10.3923i | 0.199889 | − | 0.346218i | ||||
\(902\) | 3.17527 | + | 5.49972i | 0.105725 | + | 0.183121i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.18614 | + | 3.78651i | −0.0727100 | + | 0.125937i | ||||
\(905\) | 1.93070 | + | 3.34408i | 0.0641787 | + | 0.111161i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.0584 | − | 22.6179i | 0.433598 | − | 0.751013i | −0.563582 | − | 0.826060i | \(-0.690577\pi\) |
0.997180 | + | 0.0750466i | \(0.0239105\pi\) | |||||||
\(908\) | −6.12772 | + | 10.6135i | −0.203355 | + | 0.352222i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.8139 | − | 32.5866i | −0.623331 | − | 1.07964i | −0.988861 | − | 0.148841i | \(-0.952446\pi\) |
0.365530 | − | 0.930800i | \(-0.380888\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.0000 | −0.794284 | ||||||||
\(914\) | −35.4674 | −1.17316 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.44158 | + | 2.49689i | 0.0476311 | + | 0.0824994i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.5584 | − | 40.8044i | 0.777121 | − | 1.34601i | −0.156474 | − | 0.987682i | \(-0.550013\pi\) |
0.933595 | − | 0.358330i | \(-0.116654\pi\) | |||||||
\(920\) | 3.55842 | − | 6.16337i | 0.117318 | − | 0.203200i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.06930 | + | 1.85208i | 0.0352154 | + | 0.0609949i | ||||
\(923\) | −7.11684 | + | 12.3267i | −0.234254 | + | 0.405739i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.1168 | − | 24.4511i | −0.464159 | − | 0.803947i | ||||
\(926\) | 11.5584 | − | 20.0198i | 0.379833 | − | 0.657891i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.37228 | − | 7.57301i | −0.143527 | − | 0.248596i | ||||
\(929\) | −44.2337 | −1.45126 | −0.725630 | − | 0.688085i | \(-0.758452\pi\) | ||||
−0.725630 | + | 0.688085i | \(0.758452\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.127719 | + | 0.221215i | −0.00418356 | + | 0.00724615i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 16.5475 | − | 28.6612i | 0.541452 | − | 0.937823i | ||||
\(935\) | −4.11684 | − | 7.13058i | −0.134635 | − | 0.233195i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.4674 | 0.995326 | 0.497663 | − | 0.867371i | \(-0.334192\pi\) | ||||
0.497663 | + | 0.867371i | \(0.334192\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.1168 | −0.623191 | −0.311596 | − | 0.950215i | \(-0.600863\pi\) | ||||
−0.311596 | + | 0.950215i | \(0.600863\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.53262 | −0.245296 | ||||||||
\(944\) | 10.1168 | 0.329275 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.1386 | −0.362147 | ||||||||
\(947\) | −34.1168 | −1.10865 | −0.554324 | − | 0.832301i | \(-0.687023\pi\) | ||||
−0.554324 | + | 0.832301i | \(0.687023\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.2337 | 0.786659 | ||||||||
\(950\) | −35.2921 | − | 61.1277i | −1.14503 | − | 1.98325i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28.1168 | −0.910794 | −0.455397 | − | 0.890288i | \(-0.650503\pi\) | ||||
−0.455397 | + | 0.890288i | \(0.650503\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 41.7921 | + | 72.3861i | 1.35236 | + | 2.34236i | ||||
\(956\) | 4.93070 | − | 8.54023i | 0.159470 | − | 0.276211i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 16.3723 | − | 28.3576i | 0.528964 | − | 0.916193i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | −2.00000 | − | 3.46410i | −0.0644826 | − | 0.111687i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9.05842 | + | 15.6896i | −0.291752 | + | 0.505330i | ||||
\(965\) | −15.3030 | − | 26.5055i | −0.492621 | − | 0.853244i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.4416 | + | 26.7456i | −0.496568 | + | 0.860080i | −0.999992 | − | 0.00395879i | \(-0.998740\pi\) |
0.503424 | + | 0.864039i | \(0.332073\pi\) | |||||||
\(968\) | 4.55842 | + | 7.89542i | 0.146513 | + | 0.253768i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −17.7446 | + | 30.7345i | −0.569744 | + | 0.986825i | ||||
\(971\) | 0.813859 | − | 1.40965i | 0.0261180 | − | 0.0452377i | −0.852671 | − | 0.522448i | \(-0.825019\pi\) |
0.878789 | + | 0.477211i | \(0.158352\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −17.6753 | − | 30.6145i | −0.566352 | − | 0.980951i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.11684 | 0.0997677 | ||||||||
\(977\) | −40.1168 | −1.28345 | −0.641726 | − | 0.766934i | \(-0.721781\pi\) | ||||
−0.641726 | + | 0.766934i | \(0.721781\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.1168 | + | 17.5229i | 0.323336 | + | 0.560034i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −12.6861 | + | 21.9730i | −0.404831 | + | 0.701188i | ||||
\(983\) | −19.6277 | + | 33.9962i | −0.626027 | + | 1.08431i | 0.362314 | + | 0.932056i | \(0.381987\pi\) |
−0.988341 | + | 0.152255i | \(0.951347\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.1168 | + | 22.7190i | 0.417937 | + | 0.723889i | ||||
\(986\) | 6.00000 | − | 10.3923i | 0.191079 | − | 0.330958i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.00000 | − | 8.66025i | −0.159071 | − | 0.275519i | ||||
\(989\) | 6.60597 | − | 11.4419i | 0.210058 | − | 0.363830i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.2337 | − | 41.9740i | −0.769808 | − | 1.33335i | −0.937667 | − | 0.347536i | \(-0.887018\pi\) |
0.167858 | − | 0.985811i | \(-0.446315\pi\) | |||||||
\(992\) | 2.00000 | 0.0635001 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.8614 | + | 37.8651i | −0.693053 | + | 1.20040i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.55842 | − | 4.43132i | 0.0810260 | − | 0.140341i | −0.822665 | − | 0.568527i | \(-0.807514\pi\) |
0.903691 | + | 0.428185i | \(0.140847\pi\) | |||||||
\(998\) | −9.05842 | − | 15.6896i | −0.286739 | − | 0.496647i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))