Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(529,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.q (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: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 625.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.625 |
Dual form | 1008.2.q.f.529.1 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.50000 | + | 0.866025i | 0.866025 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | − | 1.73205i | −0.447214 | − | 0.774597i | 0.550990 | − | 0.834512i | \(-0.314250\pi\) |
−0.998203 | + | 0.0599153i | \(0.980917\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.50000 | − | 0.866025i | 0.944911 | − | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | + | 2.59808i | 0.500000 | + | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | − | 3.46410i | 0.603023 | − | 1.04447i | −0.389338 | − | 0.921095i | \(-0.627296\pi\) |
0.992361 | − | 0.123371i | \(-0.0393705\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.50000 | + | 2.59808i | −0.416025 | + | 0.720577i | −0.995535 | − | 0.0943882i | \(-0.969911\pi\) |
0.579510 | + | 0.814965i | \(0.303244\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 3.46410i | − | 0.894427i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.50000 | − | 6.06218i | −0.848875 | − | 1.47029i | −0.882213 | − | 0.470850i | \(-0.843947\pi\) |
0.0333386 | − | 0.999444i | \(-0.489386\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.50000 | − | 4.33013i | 0.573539 | − | 0.993399i | −0.422659 | − | 0.906289i | \(-0.638903\pi\) |
0.996199 | − | 0.0871106i | \(-0.0277634\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.50000 | + | 0.866025i | 0.981981 | + | 0.188982i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.00000 | + | 3.46410i | 0.417029 | + | 0.722315i | 0.995639 | − | 0.0932891i | \(-0.0297381\pi\) |
−0.578610 | + | 0.815604i | \(0.696405\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.500000 | + | 0.866025i | 0.0928477 | + | 0.160817i | 0.908708 | − | 0.417432i | \(-0.137070\pi\) |
−0.815861 | + | 0.578249i | \(0.803736\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00000 | 0.538816 | 0.269408 | − | 0.963026i | \(-0.413172\pi\) | ||||
0.269408 | + | 0.963026i | \(0.413172\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.00000 | − | 3.46410i | 1.04447 | − | 0.603023i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.00000 | − | 3.46410i | −0.676123 | − | 0.585540i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.50000 | + | 9.52628i | −0.904194 | + | 1.56611i | −0.0821995 | + | 0.996616i | \(0.526194\pi\) |
−0.821995 | + | 0.569495i | \(0.807139\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.50000 | + | 2.59808i | −0.720577 | + | 0.416025i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.50000 | − | 7.79423i | 0.702782 | − | 1.21725i | −0.264704 | − | 0.964330i | \(-0.585274\pi\) |
0.967486 | − | 0.252924i | \(-0.0813924\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.50000 | + | 4.33013i | 0.381246 | + | 0.660338i | 0.991241 | − | 0.132068i | \(-0.0421616\pi\) |
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.00000 | − | 5.19615i | 0.447214 | − | 0.774597i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00000 | −0.437595 | −0.218797 | − | 0.975770i | \(-0.570213\pi\) | ||||
−0.218797 | + | 0.975770i | \(0.570213\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 12.1244i | − | 1.69775i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.50000 | − | 2.59808i | −0.206041 | − | 0.356873i | 0.744423 | − | 0.667708i | \(-0.232725\pi\) |
−0.950464 | + | 0.310835i | \(0.899391\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.00000 | −1.07872 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.50000 | − | 4.33013i | 0.993399 | − | 0.573539i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.00000 | 0.911322 | 0.455661 | − | 0.890153i | \(-0.349403\pi\) | ||||
0.455661 | + | 0.890153i | \(0.349403\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.00000 | 0.384111 | 0.192055 | − | 0.981384i | \(-0.438485\pi\) | ||||
0.192055 | + | 0.981384i | \(0.438485\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.00000 | + | 5.19615i | 0.755929 | + | 0.654654i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.00000 | 0.744208 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.0000 | −1.58820 | −0.794101 | − | 0.607785i | \(-0.792058\pi\) | ||||
−0.794101 | + | 0.607785i | \(0.792058\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.92820i | 0.834058i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.50000 | − | 6.06218i | −0.409644 | − | 0.709524i | 0.585206 | − | 0.810885i | \(-0.301014\pi\) |
−0.994850 | + | 0.101361i | \(0.967680\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.50000 | − | 0.866025i | 0.173205 | − | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.00000 | − | 10.3923i | 0.227921 | − | 1.18431i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.00000 | 1.01258 | 0.506290 | − | 0.862364i | \(-0.331017\pi\) | ||||
0.506290 | + | 0.862364i | \(0.331017\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.500000 | + | 0.866025i | 0.0548821 | + | 0.0950586i | 0.892161 | − | 0.451717i | \(-0.149188\pi\) |
−0.837279 | + | 0.546776i | \(0.815855\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.00000 | + | 12.1244i | −0.759257 | + | 1.31507i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.73205i | 0.185695i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.50000 | + | 12.9904i | −0.794998 | + | 1.37698i | 0.127842 | + | 0.991795i | \(0.459195\pi\) |
−0.922840 | + | 0.385183i | \(0.874138\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.50000 | + | 7.79423i | −0.157243 | + | 0.817057i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.50000 | + | 2.59808i | 0.466628 | + | 0.269408i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.0000 | −1.02598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.50000 | + | 14.7224i | 0.863044 | + | 1.49484i | 0.868976 | + | 0.494854i | \(0.164778\pi\) |
−0.00593185 | + | 0.999982i | \(0.501888\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.0000 | 1.20605 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.00000 | + | 1.73205i | −0.0995037 | + | 0.172345i | −0.911479 | − | 0.411346i | \(-0.865059\pi\) |
0.811976 | + | 0.583691i | \(0.198392\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.00000 | + | 6.92820i | 0.394132 | + | 0.682656i | 0.992990 | − | 0.118199i | \(-0.0377120\pi\) |
−0.598858 | + | 0.800855i | \(0.704379\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.00000 | − | 8.66025i | −0.292770 | − | 0.845154i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.50000 | + | 2.59808i | −0.145010 | + | 0.251166i | −0.929377 | − | 0.369132i | \(-0.879655\pi\) |
0.784366 | + | 0.620298i | \(0.212988\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.50000 | − | 6.06218i | −0.335239 | − | 0.580651i | 0.648292 | − | 0.761392i | \(-0.275484\pi\) |
−0.983531 | + | 0.180741i | \(0.942150\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −16.5000 | + | 9.52628i | −1.56611 | + | 0.904194i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.500000 | − | 0.866025i | 0.0470360 | − | 0.0814688i | −0.841549 | − | 0.540181i | \(-0.818356\pi\) |
0.888585 | + | 0.458712i | \(0.151689\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.00000 | − | 6.92820i | 0.373002 | − | 0.646058i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.00000 | −0.832050 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.0000 | − | 12.1244i | −1.28338 | − | 1.11144i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.50000 | − | 4.33013i | −0.227273 | − | 0.393648i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.5000 | − | 7.79423i | 1.21725 | − | 0.702782i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.66025i | 0.762493i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.00000 | − | 3.46410i | −0.174741 | − | 0.302660i | 0.765331 | − | 0.643637i | \(-0.222575\pi\) |
−0.940072 | + | 0.340977i | \(0.889242\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.50000 | − | 12.9904i | 0.216777 | − | 1.12641i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.00000 | − | 5.19615i | 0.774597 | − | 0.447214i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.00000 | + | 12.1244i | −0.598050 | + | 1.03585i | 0.395058 | + | 0.918656i | \(0.370724\pi\) |
−0.993109 | + | 0.117198i | \(0.962609\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.50000 | + | 4.33013i | −0.212047 | + | 0.367277i | −0.952355 | − | 0.304991i | \(-0.901346\pi\) |
0.740308 | + | 0.672268i | \(0.234680\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.50000 | − | 2.59808i | −0.378968 | − | 0.218797i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.00000 | + | 10.3923i | 0.501745 | + | 0.869048i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.00000 | − | 1.73205i | 0.0830455 | − | 0.143839i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.0000 | − | 1.73205i | 0.989743 | − | 0.142857i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.00000 | + | 5.19615i | 0.245770 | + | 0.425685i | 0.962348 | − | 0.271821i | \(-0.0876260\pi\) |
−0.716578 | + | 0.697507i | \(0.754293\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00000 | + | 6.92820i | −0.325515 | + | 0.563809i | −0.981617 | − | 0.190864i | \(-0.938871\pi\) |
0.656101 | + | 0.754673i | \(0.272204\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.5000 | − | 18.1865i | 0.848875 | − | 1.47029i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.00000 | − | 5.19615i | −0.240966 | − | 0.417365i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.0000 | −1.03751 | −0.518756 | − | 0.854922i | \(-0.673605\pi\) | ||||
−0.518756 | + | 0.854922i | \(0.673605\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 5.19615i | − | 0.412082i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.00000 | + | 6.92820i | 0.630488 | + | 0.546019i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.50000 | + | 16.4545i | −0.744097 | + | 1.28881i | 0.206518 | + | 0.978443i | \(0.433787\pi\) |
−0.950615 | + | 0.310372i | \(0.899546\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −12.0000 | − | 6.92820i | −0.934199 | − | 0.539360i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.5000 | − | 19.9186i | 0.889897 | − | 1.54135i | 0.0499004 | − | 0.998754i | \(-0.484110\pi\) |
0.839996 | − | 0.542592i | \(-0.182557\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.00000 | + | 3.46410i | 0.153846 | + | 0.266469i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 15.0000 | 1.14708 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.00000 | −0.0760286 | −0.0380143 | − | 0.999277i | \(-0.512103\pi\) | ||||
−0.0380143 | + | 0.999277i | \(0.512103\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.500000 | − | 2.59808i | 0.0377964 | − | 0.196396i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.5000 | + | 6.06218i | 0.789228 | + | 0.455661i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.5000 | − | 18.1865i | −0.784807 | − | 1.35933i | −0.929114 | − | 0.369792i | \(-0.879429\pi\) |
0.144308 | − | 0.989533i | \(-0.453905\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.00000 | −0.445976 | −0.222988 | − | 0.974821i | \(-0.571581\pi\) | ||||
−0.222988 | + | 0.974821i | \(0.571581\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.50000 | + | 2.59808i | 0.332650 | + | 0.192055i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 22.0000 | 1.61747 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −28.0000 | −2.04756 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.50000 | + | 12.9904i | 0.327327 | + | 0.944911i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.0000 | −1.08536 | −0.542681 | − | 0.839939i | \(-0.682591\pi\) | ||||
−0.542681 | + | 0.839939i | \(0.682591\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.00000 | −0.0719816 | −0.0359908 | − | 0.999352i | \(-0.511459\pi\) | ||||
−0.0359908 | + | 0.999352i | \(0.511459\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 9.00000 | + | 5.19615i | 0.644503 | + | 0.372104i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −26.0000 | −1.85242 | −0.926212 | − | 0.377004i | \(-0.876954\pi\) | ||||
−0.926212 | + | 0.377004i | \(0.876954\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.50000 | − | 11.2583i | −0.460773 | − | 0.798082i | 0.538227 | − | 0.842800i | \(-0.319094\pi\) |
−0.999000 | + | 0.0447181i | \(0.985761\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.5000 | − | 11.2583i | −1.37542 | − | 0.794101i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.00000 | + | 1.73205i | 0.140372 | + | 0.121566i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.0000 | −1.25717 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.00000 | + | 10.3923i | −0.417029 | + | 0.722315i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.0000 | − | 17.3205i | −0.691714 | − | 1.19808i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.50000 | + | 11.2583i | −0.447478 | + | 0.775055i | −0.998221 | − | 0.0596196i | \(-0.981011\pi\) |
0.550743 | + | 0.834675i | \(0.314345\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.0000 | + | 6.92820i | 0.822226 | + | 0.474713i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.00000 | − | 8.66025i | 0.340997 | − | 0.590624i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.50000 | − | 2.59808i | 0.509133 | − | 0.176369i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 12.1244i | − | 0.819288i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.0000 | 1.41261 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.50000 | − | 6.06218i | −0.234377 | − | 0.405953i | 0.724714 | − | 0.689050i | \(-0.241972\pi\) |
−0.959092 | + | 0.283096i | \(0.908638\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | 0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.00000 | + | 10.3923i | −0.398234 | + | 0.689761i | −0.993508 | − | 0.113761i | \(-0.963710\pi\) |
0.595274 | + | 0.803523i | \(0.297043\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.00000 | + | 12.1244i | 0.462573 | + | 0.801200i | 0.999088 | − | 0.0426906i | \(-0.0135930\pi\) |
−0.536515 | + | 0.843891i | \(0.680260\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.0000 | − | 13.8564i | 0.789542 | − | 0.911685i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.5000 | − | 25.1147i | 0.949927 | − | 1.64532i | 0.204354 | − | 0.978897i | \(-0.434491\pi\) |
0.745573 | − | 0.666424i | \(-0.232176\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.00000 | + | 5.19615i | 0.195698 | + | 0.338960i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.5000 | + | 7.79423i | 0.876919 | + | 0.506290i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.5000 | + | 18.1865i | −0.679189 | + | 1.17639i | 0.296037 | + | 0.955176i | \(0.404335\pi\) |
−0.975226 | + | 0.221213i | \(0.928999\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.00000 | − | 8.66025i | 0.322078 | − | 0.557856i | −0.658838 | − | 0.752285i | \(-0.728952\pi\) |
0.980917 | + | 0.194429i | \(0.0622852\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.5000 | + | 7.79423i | −0.866025 | + | 0.500000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.0000 | − | 5.19615i | −0.830540 | − | 0.331970i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.50000 | + | 12.9904i | 0.477214 | + | 0.826558i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.73205i | 0.109764i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.0000 | 1.00591 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −21.0000 | + | 12.1244i | −1.31507 | + | 0.759257i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.00000 | − | 15.5885i | −0.561405 | − | 0.972381i | −0.997374 | − | 0.0724199i | \(-0.976928\pi\) |
0.435970 | − | 0.899961i | \(-0.356405\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.50000 | + | 28.5788i | −0.341753 | + | 1.77580i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.50000 | + | 2.59808i | −0.0928477 | + | 0.160817i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.00000 | + | 5.19615i | −0.184289 | + | 0.319197i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −22.5000 | + | 12.9904i | −1.37698 | + | 0.794998i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.500000 | + | 0.866025i | 0.0304855 | + | 0.0528025i | 0.880866 | − | 0.473366i | \(-0.156961\pi\) |
−0.850380 | + | 0.526169i | \(0.823628\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.50000 | + | 2.59808i | −0.0911185 | + | 0.157822i | −0.907982 | − | 0.419009i | \(-0.862378\pi\) |
0.816864 | + | 0.576831i | \(0.195711\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.00000 | + | 10.3923i | −0.544705 | + | 0.628971i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.00000 | − | 3.46410i | −0.120605 | − | 0.208893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.00000 | + | 1.73205i | −0.0600842 | + | 0.104069i | −0.894503 | − | 0.447062i | \(-0.852470\pi\) |
0.834419 | + | 0.551131i | \(0.185804\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.50000 | + | 7.79423i | 0.269408 | + | 0.466628i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.50000 | + | 14.7224i | 0.507067 | + | 0.878267i | 0.999967 | + | 0.00818015i | \(0.00260385\pi\) |
−0.492899 | + | 0.870087i | \(0.664063\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.00000 | −0.0594438 | −0.0297219 | − | 0.999558i | \(-0.509462\pi\) | ||||
−0.0297219 | + | 0.999558i | \(0.509462\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −15.0000 | − | 8.66025i | −0.888523 | − | 0.512989i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.50000 | − | 23.3827i | 0.265627 | − | 1.38024i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0000 | + | 27.7128i | −0.941176 | + | 1.63017i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 29.4449i | 1.72609i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.5000 | + | 23.3827i | −0.788678 | + | 1.36603i | 0.138098 | + | 0.990419i | \(0.455901\pi\) |
−0.926777 | + | 0.375613i | \(0.877432\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.00000 | − | 12.1244i | −0.407556 | − | 0.705907i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.0000 | + | 10.3923i | 1.04447 | + | 0.603023i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.0000 | −0.693978 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.0000 | + | 8.66025i | 0.576390 | + | 0.499169i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.00000 | + | 1.73205i | −0.172345 | + | 0.0995037i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.00000 | − | 5.19615i | −0.171780 | − | 0.297531i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.00000 | 0.456584 | 0.228292 | − | 0.973593i | \(-0.426686\pi\) | ||||
0.228292 | + | 0.973593i | \(0.426686\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.8564i | 0.788263i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 31.0000 | 1.75785 | 0.878924 | − | 0.476961i | \(-0.158262\pi\) | ||||
0.878924 | + | 0.476961i | \(0.158262\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.0000 | −0.960897 | −0.480448 | − | 0.877023i | \(-0.659526\pi\) | ||||
−0.480448 | + | 0.877023i | \(0.659526\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.00000 | − | 15.5885i | 0.169031 | − | 0.878310i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.00000 | −0.505490 | −0.252745 | − | 0.967533i | \(-0.581333\pi\) | ||||
−0.252745 | + | 0.967533i | \(0.581333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.00000 | 0.223957 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.50000 | + | 2.59808i | −0.251166 | + | 0.145010i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −35.0000 | −1.94745 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.50000 | + | 2.59808i | 0.0832050 | + | 0.144115i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 12.1244i | − | 0.670478i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.50000 | + | 2.59808i | −0.413488 | + | 0.143237i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.0000 | 1.37412 | 0.687062 | − | 0.726599i | \(-0.258900\pi\) | ||||
0.687062 | + | 0.726599i | \(0.258900\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −33.0000 | −1.80839 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13.0000 | + | 22.5167i | 0.710266 | + | 1.23022i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.50000 | + | 2.59808i | −0.0817102 | + | 0.141526i | −0.903985 | − | 0.427565i | \(-0.859372\pi\) |
0.822274 | + | 0.569091i | \(0.192705\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.50000 | − | 0.866025i | 0.0814688 | − | 0.0470360i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.00000 | − | 10.3923i | 0.324918 | − | 0.562775i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.0000 | − | 6.92820i | 0.646058 | − | 0.373002i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.0000 | 0.805242 | 0.402621 | − | 0.915367i | \(-0.368099\pi\) | ||||
0.402621 | + | 0.915367i | \(0.368099\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.50000 | + | 4.33013i | 0.133822 | + | 0.231786i | 0.925147 | − | 0.379610i | \(-0.123942\pi\) |
−0.791325 | + | 0.611396i | \(0.790608\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.5000 | − | 7.79423i | −0.720577 | − | 0.416025i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.00000 | + | 5.19615i | −0.159674 | + | 0.276563i | −0.934751 | − | 0.355303i | \(-0.884378\pi\) |
0.775077 | + | 0.631867i | \(0.217711\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.00000 | − | 13.8564i | −0.424596 | − | 0.735422i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.5000 | − | 30.3109i | −0.555719 | − | 1.60422i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.5000 | + | 26.8468i | −0.818059 | + | 1.41692i | 0.0890519 | + | 0.996027i | \(0.471616\pi\) |
−0.907111 | + | 0.420892i | \(0.861717\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | − | 5.19615i | −0.157895 | − | 0.273482i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 8.66025i | − | 0.454545i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.00000 | + | 12.1244i | −0.366397 | + | 0.634618i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.0000 | − | 27.7128i | 0.835193 | − | 1.44660i | −0.0586798 | − | 0.998277i | \(-0.518689\pi\) |
0.893873 | − | 0.448320i | \(-0.147978\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 27.0000 | 1.40556 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.00000 | − | 5.19615i | −0.311504 | − | 0.269771i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.0000 | − | 19.0526i | −0.569558 | − | 0.986504i | −0.996610 | − | 0.0822766i | \(-0.973781\pi\) |
0.427051 | − | 0.904227i | \(-0.359552\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −18.0000 | − | 10.3923i | −0.929516 | − | 0.536656i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.00000 | −0.154508 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.0000 | 1.02733 | 0.513665 | − | 0.857991i | \(-0.328287\pi\) | ||||
0.513665 | + | 0.857991i | \(0.328287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.00000 | + | 13.8564i | 0.408781 | + | 0.708029i | 0.994753 | − | 0.102302i | \(-0.0326207\pi\) |
−0.585973 | + | 0.810331i | \(0.699287\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −20.0000 | + | 6.92820i | −1.01929 | + | 0.353094i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.50000 | + | 12.9904i | −0.381246 | + | 0.660338i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.0000 | + | 22.5167i | −0.659126 | + | 1.14164i | 0.321716 | + | 0.946836i | \(0.395740\pi\) |
−0.980842 | + | 0.194804i | \(0.937593\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.0000 | − | 24.2487i | 0.708010 | − | 1.22631i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 6.92820i | − | 0.349482i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.00000 | − | 15.5885i | −0.452839 | − | 0.784340i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.5000 | − | 18.1865i | 0.526980 | − | 0.912756i | −0.472526 | − | 0.881317i | \(-0.656658\pi\) |
0.999506 | − | 0.0314391i | \(-0.0100090\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 15.0000 | − | 17.3205i | 0.750939 | − | 0.867110i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.0000 | − | 25.9808i | −0.749064 | − | 1.29742i | −0.948272 | − | 0.317460i | \(-0.897170\pi\) |
0.199207 | − | 0.979957i | \(-0.436163\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.50000 | + | 7.79423i | −0.224161 | + | 0.388258i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.0000 | 0.894427 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 22.0000 | + | 38.1051i | 1.09050 | + | 1.88880i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.0000 | 1.13728 | 0.568638 | − | 0.822588i | \(-0.307470\pi\) | ||||
0.568638 | + | 0.822588i | \(0.307470\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −21.0000 | + | 12.1244i | −1.03585 | + | 0.598050i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17.5000 | − | 6.06218i | 0.861119 | − | 0.298300i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.00000 | − | 1.73205i | 0.0490881 | − | 0.0850230i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.50000 | + | 4.33013i | −0.367277 | + | 0.212047i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.50000 | − | 12.9904i | 0.366399 | − | 0.634622i | −0.622601 | − | 0.782540i | \(-0.713924\pi\) |
0.989000 | + | 0.147918i | \(0.0472572\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.50000 | + | 7.79423i | 0.219317 | + | 0.379867i | 0.954599 | − | 0.297893i | \(-0.0962839\pi\) |
−0.735283 | + | 0.677761i | \(0.762951\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.50000 | − | 7.79423i | −0.218797 | − | 0.378968i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.00000 | −0.339550 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.50000 | − | 2.59808i | 0.362950 | − | 0.125730i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 20.7846i | 1.00349i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.5000 | + | 33.7750i | 0.939282 | + | 1.62688i | 0.766814 | + | 0.641869i | \(0.221841\pi\) |
0.172468 | + | 0.985015i | \(0.444826\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.00000 | 0.0961139 | 0.0480569 | − | 0.998845i | \(-0.484697\pi\) | ||||
0.0480569 | + | 0.998845i | \(0.484697\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.00000 | − | 1.73205i | 0.143839 | − | 0.0830455i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.0000 | 0.956730 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.0000 | 1.00228 | 0.501138 | − | 0.865368i | \(-0.332915\pi\) | ||||
0.501138 | + | 0.865368i | \(0.332915\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.5000 | + | 7.79423i | 0.928571 | + | 0.371154i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.0000 | 1.37783 | 0.688916 | − | 0.724841i | \(-0.258087\pi\) | ||||
0.688916 | + | 0.724841i | \(0.258087\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 30.0000 | 1.42214 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.3923i | 0.491539i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.00000 | 0.0943858 | 0.0471929 | − | 0.998886i | \(-0.484972\pi\) | ||||
0.0471929 | + | 0.998886i | \(0.484972\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.0000 | − | 31.1769i | −0.847587 | − | 1.46806i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.0000 | + | 6.92820i | −0.563809 | + | 0.325515i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15.0000 | − | 5.19615i | 0.703211 | − | 0.243599i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.0000 | 1.45012 | 0.725059 | − | 0.688686i | \(-0.241812\pi\) | ||||
0.725059 | + | 0.688686i | \(0.241812\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 31.5000 | − | 18.1865i | 1.47029 | − | 0.848875i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.5000 | − | 19.9186i | −0.535608 | − | 0.927701i | −0.999134 | − | 0.0416172i | \(-0.986749\pi\) |
0.463525 | − | 0.886084i | \(-0.346584\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.50000 | + | 4.33013i | −0.116185 | + | 0.201238i | −0.918253 | − | 0.395995i | \(-0.870400\pi\) |
0.802068 | + | 0.597233i | \(0.203733\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 10.3923i | − | 0.481932i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.50000 | − | 14.7224i | 0.393333 | − | 0.681273i | −0.599554 | − | 0.800334i | \(-0.704655\pi\) |
0.992887 | + | 0.119062i | \(0.0379886\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −32.5000 | + | 11.2583i | −1.50071 | + | 0.519861i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.5000 | − | 11.2583i | −0.898513 | − | 0.518756i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.0000 | 0.919601 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.50000 | − | 4.33013i | −0.114708 | − | 0.198680i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.50000 | − | 7.79423i | 0.206041 | − | 0.356873i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.00000 | + | 6.92820i | −0.182765 | + | 0.316558i | −0.942821 | − | 0.333300i | \(-0.891838\pi\) |
0.760056 | + | 0.649857i | \(0.225171\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.5000 | − | 28.5788i | −0.752335 | − | 1.30308i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.00000 | + | 17.3205i | 0.273009 | + | 0.788110i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.0000 | − | 29.4449i | 0.771930 | − | 1.33702i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.500000 | − | 0.866025i | −0.0226572 | − | 0.0392434i | 0.854475 | − | 0.519493i | \(-0.173879\pi\) |
−0.877132 | + | 0.480250i | \(0.840546\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −28.5000 | + | 16.4545i | −1.28881 | + | 0.744097i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.50000 | + | 7.79423i | −0.203082 | + | 0.351749i | −0.949520 | − | 0.313707i | \(-0.898429\pi\) |
0.746438 | + | 0.665455i | \(0.231763\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.50000 | − | 6.06218i | 0.157632 | − | 0.273027i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −12.0000 | − | 20.7846i | −0.539360 | − | 0.934199i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 20.0000 | − | 6.92820i | 0.897123 | − | 0.310772i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.00000 | + | 3.46410i | 0.0895323 | + | 0.155074i | 0.907314 | − | 0.420455i | \(-0.138129\pi\) |
−0.817781 | + | 0.575529i | \(0.804796\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 34.5000 | − | 19.9186i | 1.54135 | − | 0.889897i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.0000 | −1.07011 | −0.535054 | − | 0.844818i | \(-0.679709\pi\) | ||||
−0.535054 | + | 0.844818i | \(0.679709\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.00000 | 0.177998 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.92820i | 0.307692i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.00000 | + | 15.5885i | 0.398918 | + | 0.690946i | 0.993593 | − | 0.113020i | \(-0.0360525\pi\) |
−0.594675 | + | 0.803966i | \(0.702719\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.0000 | − | 12.1244i | −0.619324 | − | 0.536350i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 22.5000 | + | 12.9904i | 0.993399 | + | 0.573539i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.00000 | − | 13.8564i | 0.352522 | − | 0.610586i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.00000 | + | 10.3923i | −0.263880 | + | 0.457053i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.50000 | − | 0.866025i | −0.0658427 | − | 0.0380143i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.50000 | − | 2.59808i | −0.0657162 | − | 0.113824i | 0.831295 | − | 0.555831i | \(-0.187600\pi\) |
−0.897011 | + | 0.442007i | \(0.854267\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.5000 | − | 25.1147i | 0.634041 | − | 1.09819i | −0.352677 | − | 0.935745i | \(-0.614728\pi\) |
0.986718 | − | 0.162446i | \(-0.0519382\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.00000 | − | 3.46410i | 0.130931 | − | 0.151186i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.5000 | − | 18.1865i | −0.457387 | − | 0.792218i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.5000 | + | 18.1865i | 0.455661 | + | 0.789228i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.5000 | + | 23.3827i | 0.584750 | + | 1.01282i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.00000 | 0.259403 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 36.3731i | − | 1.56961i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.00000 | − | 27.7128i | −0.172292 | − | 1.19368i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.5000 | − | 28.5788i | 0.709390 | − | 1.22870i | −0.255693 | − | 0.966758i | \(-0.582304\pi\) |
0.965084 | − | 0.261942i | \(-0.0843630\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.00000 | − | 5.19615i | −0.386227 | − | 0.222988i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.00000 | + | 12.1244i | −0.299847 | + | 0.519350i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.5000 | + | 28.5788i | 0.705489 | + | 1.22194i | 0.966515 | + | 0.256611i | \(0.0826059\pi\) |
−0.261026 | + | 0.965332i | \(0.584061\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.50000 | + | 7.79423i | 0.192055 | + | 0.332650i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.00000 | 0.213007 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.5000 | − | 7.79423i | 0.956797 | − | 0.331444i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 33.0000 | + | 19.0526i | 1.40077 | + | 0.808736i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.50000 | − | 9.52628i | −0.233042 | − | 0.403641i | 0.725660 | − | 0.688054i | \(-0.241535\pi\) |
−0.958702 | + | 0.284413i | \(0.908201\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.0000 | −0.634432 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −42.0000 | − | 24.2487i | −1.77324 | − | 1.02378i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.0000 | −0.547885 | −0.273942 | − | 0.961746i | \(-0.588328\pi\) | ||||
−0.273942 | + | 0.961746i | \(0.588328\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.00000 | −0.0841406 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.50000 | + | 23.3827i | −0.188982 | + | 0.981981i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.0000 | 1.13190 | 0.565949 | − | 0.824440i | \(-0.308510\pi\) | ||||
0.565949 | + | 0.824440i | \(0.308510\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.00000 | 0.125546 | 0.0627730 | − | 0.998028i | \(-0.480006\pi\) | ||||
0.0627730 | + | 0.998028i | \(0.480006\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −22.5000 | − | 12.9904i | −0.939951 | − | 0.542681i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.00000 | 0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.50000 | − | 6.06218i | −0.145707 | − | 0.252372i | 0.783930 | − | 0.620850i | \(-0.213212\pi\) |
−0.929636 | + | 0.368478i | \(0.879879\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.50000 | − | 0.866025i | −0.0623379 | − | 0.0359908i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.00000 | + | 1.73205i | 0.0829740 | + | 0.0718576i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.0000 | −0.496989 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.00000 | + | 15.5885i | 0.372104 | + | 0.644503i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.5000 | + | 32.0429i | 0.763577 | + | 1.32255i | 0.940996 | + | 0.338418i | \(0.109892\pi\) |
−0.177419 | + | 0.984135i | \(0.556775\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.50000 | − | 12.9904i | 0.309032 | − | 0.535259i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −39.0000 | − | 22.5167i | −1.60425 | − | 0.926212i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.5000 | + | 23.3827i | −0.554379 | + | 0.960212i | 0.443573 | + | 0.896238i | \(0.353711\pi\) |
−0.997952 | + | 0.0639736i | \(0.979623\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.00000 | + | 36.3731i | −0.286972 | + | 1.49115i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 22.5167i | − | 0.921546i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.00000 | 0.122577 | 0.0612883 | − | 0.998120i | \(-0.480479\pi\) | ||||
0.0612883 | + | 0.998120i | \(0.480479\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.5000 | − | 30.3109i | −0.713840 | − | 1.23641i | −0.963405 | − | 0.268049i | \(-0.913621\pi\) |
0.249565 | − | 0.968358i | \(-0.419712\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −19.5000 | − | 33.7750i | −0.794101 | − | 1.37542i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.00000 | + | 8.66025i | −0.203279 | + | 0.352089i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.0000 | − | 41.5692i | −0.974130 | − | 1.68724i | −0.682777 | − | 0.730627i | \(-0.739228\pi\) |
−0.291353 | − | 0.956616i | \(-0.594105\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.50000 | + | 4.33013i | 0.0607831 | + | 0.175466i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.50000 | − | 7.79423i | 0.182051 | − | 0.315321i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.50000 | + | 7.79423i | 0.181753 | + | 0.314806i | 0.942478 | − | 0.334269i | \(-0.108489\pi\) |
−0.760724 | + | 0.649075i | \(0.775156\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −27.0000 | − | 15.5885i | −1.08875 | − | 0.628587i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.5000 | + | 37.2391i | −0.865557 | + | 1.49919i | 0.000935233 | 1.00000i | \(0.499702\pi\) | |
−0.866493 | + | 0.499190i | \(0.833631\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.0000 | + | 17.3205i | −0.401934 | + | 0.696170i | −0.993959 | − | 0.109749i | \(-0.964995\pi\) |
0.592025 | + | 0.805919i | \(0.298329\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.0000 | + | 10.3923i | −0.722315 | + | 0.417029i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.50000 | + | 38.9711i | −0.300481 | + | 1.56135i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | + | 16.4545i | 0.380000 | + | 0.658179i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 34.6410i | − | 1.38343i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 77.0000 | 3.07019 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.0000 | 0.636950 | 0.318475 | − | 0.947931i | \(-0.396829\pi\) | ||||
0.318475 | + | 0.947931i | \(0.396829\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −19.5000 | + | 11.2583i | −0.775055 | + | 0.447478i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.00000 | + | 20.7846i | 0.118864 | + | 0.823516i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.0000 | + | 20.7846i | 0.474713 | + | 0.822226i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.00000 | − | 1.73205i | 0.0394976 | − | 0.0684119i | −0.845601 | − | 0.533816i | \(-0.820758\pi\) |
0.885098 | + | 0.465404i | \(0.154091\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.50000 | + | 11.2583i | −0.256335 | + | 0.443985i | −0.965257 | − | 0.261301i | \(-0.915848\pi\) |
0.708922 | + | 0.705287i | \(0.249182\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15.0000 | − | 8.66025i | 0.590624 | − | 0.340997i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.50000 | + | 2.59808i | 0.0589711 | + | 0.102141i | 0.894004 | − | 0.448059i | \(-0.147885\pi\) |
−0.835033 | + | 0.550200i | \(0.814551\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.0000 | − | 24.2487i | 0.549548 | − | 0.951845i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13.5000 | + | 2.59808i | 0.529107 | + | 0.101827i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.00000 | + | 15.5885i | 0.352197 | + | 0.610023i | 0.986634 | − | 0.162951i | \(-0.0521013\pi\) |
−0.634437 | + | 0.772975i | \(0.718768\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.00000 | + | 6.92820i | −0.156293 | + | 0.270707i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.5000 | − | 18.1865i | 0.409644 | − | 0.709524i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.5000 | + | 21.6506i | 0.486931 | + | 0.843389i | 0.999887 | − | 0.0150258i | \(-0.00478303\pi\) |
−0.512956 | + | 0.858415i | \(0.671450\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.0000 | −0.661223 | −0.330612 | − | 0.943767i | \(-0.607255\pi\) | ||||
−0.330612 | + | 0.943767i | \(0.607255\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 31.5000 | + | 18.1865i | 1.22336 | + | 0.706306i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −25.0000 | + | 8.66025i | −0.969458 | + | 0.335830i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.00000 | + | 3.46410i | −0.0774403 | + | 0.134131i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 12.1244i | − | 0.468755i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.00000 | − | 10.3923i | 0.231627 | − | 0.401190i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.5000 | + | 21.6506i | 0.481840 | + | 0.834571i | 0.999783 | − | 0.0208444i | \(-0.00663546\pi\) |
−0.517943 | + | 0.855415i | \(0.673302\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.50000 | + | 2.59808i | 0.173205 | + | 0.100000i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.0000 | 1.03769 | 0.518847 | − | 0.854867i | \(-0.326361\pi\) | ||||
0.518847 | + | 0.854867i | \(0.326361\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 34.0000 | + | 29.4449i | 1.30480 | + | 1.12999i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.0000 | + | 10.3923i | −0.689761 | + | 0.398234i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.5000 | − | 18.1865i | −0.401771 | − | 0.695888i | 0.592168 | − | 0.805814i | \(-0.298272\pi\) |
−0.993940 | + | 0.109926i | \(0.964939\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.0000 | 1.06983 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.2487i | 0.925146i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.00000 | 0.342873 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.0000 | −0.418460 | −0.209230 | − | 0.977866i | \(-0.567096\pi\) | ||||
−0.209230 | + | 0.977866i | \(0.567096\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 30.0000 | − | 10.3923i | 1.13961 | − | 0.394771i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.0000 | 0.379322 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −63.0000 | −2.38630 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 43.5000 | − | 25.1147i | 1.64532 | − | 0.949927i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.0000 | −0.830929 | −0.415464 | − | 0.909610i | \(-0.636381\pi\) | ||||
−0.415464 | + | 0.909610i | \(0.636381\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27.5000 | + | 47.6314i | 1.03718 | + | 1.79645i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.3923i | 0.391397i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.00000 | + | 5.19615i | −0.0376089 | + | 0.195421i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.0000 | −0.938895 | −0.469447 | − | 0.882960i | \(-0.655547\pi\) | ||||
−0.469447 | + | 0.882960i | \(0.655547\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.5000 | + | 23.3827i | 0.506290 | + | 0.876919i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.00000 | + | 10.3923i | 0.224702 | + | 0.389195i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.0000 | − | 20.7846i | 0.448775 | − | 0.777300i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −31.5000 | + | 18.1865i | −1.17639 | + | 0.679189i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.50000 | + | 12.9904i | −0.279703 | + | 0.484459i | −0.971311 | − | 0.237814i | \(-0.923569\pi\) |
0.691608 | + | 0.722273i | \(0.256903\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.0000 | + | 13.8564i | 0.595871 | + | 0.516040i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.0000 | − | 8.66025i | 0.557856 | − | 0.322078i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.00000 | 0.0371391 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.5000 | − | 40.7032i | −0.871567 | − | 1.50960i | −0.860376 | − | 0.509661i | \(-0.829771\pi\) |
−0.0111912 | − | 0.999937i | \(-0.503562\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.5000 | − | 30.3109i | 0.647261 | − | 1.12109i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.0000 | − | 25.9808i | −0.554038 | − | 0.959621i | −0.997978 | − | 0.0635649i | \(-0.979753\pi\) |
0.443940 | − | 0.896056i | \(-0.353580\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −15.0000 | − | 19.0526i | −0.553283 | − | 0.702764i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −26.0000 | + | 45.0333i | −0.957722 | + | 1.65882i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.5000 | − | 18.1865i | −0.386249 | − | 0.669002i | 0.605693 | − | 0.795699i | \(-0.292896\pi\) |
−0.991942 | + | 0.126696i | \(0.959563\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 25.9808i | 0.954427i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.50000 | + | 7.79423i | −0.165089 | + | 0.285943i | −0.936687 | − | 0.350168i | \(-0.886124\pi\) |
0.771598 | + | 0.636111i | \(0.219458\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.00000 | − | 10.3923i | 0.219823 | − | 0.380745i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.50000 | + | 2.59808i | −0.0548821 | + | 0.0950586i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.50000 | + | 7.79423i | −0.0548088 | + | 0.284795i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.0000 | − | 20.7846i | −0.437886 | − | 0.758441i | 0.559640 | − | 0.828736i | \(-0.310939\pi\) |
−0.997526 | + | 0.0702946i | \(0.977606\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.0000 | 0.582300 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.0000 | 1.52652 | 0.763258 | − | 0.646094i | \(-0.223599\pi\) | ||||
0.763258 | + | 0.646094i | \(0.223599\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 24.0000 | + | 13.8564i | 0.871145 | + | 0.502956i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.00000 | + | 1.73205i | 0.0362500 | + | 0.0627868i | 0.883581 | − | 0.468278i | \(-0.155125\pi\) |
−0.847331 | + | 0.531065i | \(0.821792\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.0000 | − | 12.1244i | −0.506834 | − | 0.438931i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −42.0000 | −1.51851 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.5000 | + | 18.1865i | −0.379133 | + | 0.656678i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.50000 | − | 4.33013i | 0.0901523 | − | 0.156148i | −0.817423 | − | 0.576038i | \(-0.804598\pi\) |
0.907575 | + | 0.419890i | \(0.137931\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 31.1769i | − | 1.12281i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.5000 | − | 19.9186i | −0.413626 | − | 0.716422i | 0.581657 | − | 0.813434i | \(-0.302405\pi\) |
−0.995283 | + | 0.0970125i | \(0.969071\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.50000 | − | 2.59808i | 0.0538816 | − | 0.0933257i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −33.0000 | + | 38.1051i | −1.18387 | + | 1.36701i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22.5000 | − | 38.9711i | −0.806146 | − | 1.39629i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.0000 | − | 27.7128i | 0.572525 | − | 0.991642i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.50000 | + | 2.59808i | −0.160817 | + | 0.0928477i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.0000 | + | 22.5167i | 0.463990 | + | 0.803654i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.0000 | −0.748569 | −0.374285 | − | 0.927314i | \(-0.622112\pi\) | ||||
−0.374285 | + | 0.927314i | \(0.622112\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.500000 | − | 2.59808i | 0.0177780 | − | 0.0923770i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.50000 | + | 7.79423i | −0.159800 | + | 0.276781i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.00000 | + | 5.19615i | −0.319197 | + | 0.184289i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.50000 | + | 12.9904i | −0.265664 | + | 0.460143i | −0.967737 | − | 0.251961i | \(-0.918924\pi\) |
0.702074 | + | 0.712104i | \(0.252258\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.5000 | + | 18.1865i | 0.371463 | + | 0.643393i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −45.0000 | −1.59000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −28.0000 | −0.988099 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.00000 | − | 20.7846i | 0.140981 | − | 0.732561i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.73205i | 0.0609711i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.500000 | + | 0.866025i | 0.0175791 | + | 0.0304478i | 0.874681 | − | 0.484699i | \(-0.161071\pi\) |
−0.857102 | + | 0.515147i | \(0.827737\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.0000 | 0.702295 | 0.351147 | − | 0.936320i | \(-0.385792\pi\) | ||||
0.351147 | + | 0.936320i | \(0.385792\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.50000 | + | 2.59808i | −0.157822 | + | 0.0911185i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 38.0000 | 1.33108 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25.0000 | 0.874639 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −22.5000 | + | 7.79423i | −0.786214 | + | 0.272352i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −53.0000 | −1.84971 | −0.924856 | − | 0.380317i | \(-0.875815\pi\) | ||||
−0.924856 | + | 0.380317i | \(0.875815\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.0000 | 0.801730 | 0.400865 | − | 0.916137i | \(-0.368710\pi\) | ||||
0.400865 | + | 0.916137i | \(0.368710\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 6.92820i | − | 0.241209i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.0000 | −0.417281 | −0.208640 | − | 0.977992i | \(-0.566904\pi\) | ||||
−0.208640 | + | 0.977992i | \(0.566904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.50000 | − | 16.4545i | −0.329949 | − | 0.571488i | 0.652553 | − | 0.757743i | \(-0.273698\pi\) |
−0.982501 | + | 0.186256i | \(0.940365\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.00000 | + | 1.73205i | −0.104069 | + | 0.0600842i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −45.5000 | − | 18.1865i | −1.57648 | − | 0.630126i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −46.0000 | −1.59190 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15.5885i | 0.538816i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11.5000 | − | 19.9186i | −0.397024 | − | 0.687666i | 0.596333 | − | 0.802737i | \(-0.296624\pi\) |
−0.993357 | + | 0.115071i | \(0.963290\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.0000 | − | 24.2487i | 0.482759 | − | 0.836162i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 29.4449i | 1.01413i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.00000 | − | 6.92820i | 0.137604 | − | 0.238337i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.0000 | − | 8.66025i | −0.343604 | − | 0.297570i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.50000 | − | 0.866025i | −0.0514799 | − | 0.0297219i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −44.0000 | −1.50830 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.5000 | − | 30.3109i | −0.599189 | − | 1.03783i | −0.992941 | − | 0.118609i | \(-0.962157\pi\) |
0.393753 | − | 0.919216i | \(-0.371177\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −15.0000 | − | 25.9808i | −0.512989 | − | 0.888523i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.00000 | − | 15.5885i | 0.307434 | − | 0.532492i | −0.670366 | − | 0.742030i | \(-0.733863\pi\) |
0.977800 | + | 0.209539i | \(0.0671963\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.0000 | + | 38.1051i | 0.750630 | + | 1.30013i | 0.947518 | + | 0.319704i | \(0.103583\pi\) |
−0.196887 | + | 0.980426i | \(0.563083\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 27.0000 | − | 31.1769i | 0.920158 | − | 1.06251i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.5000 | − | 35.5070i | 0.697828 | − | 1.20867i | −0.271390 | − | 0.962470i | \(-0.587483\pi\) |
0.969218 | − | 0.246204i | \(-0.0791834\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.00000 | + | 1.73205i | 0.0340010 | + | 0.0588915i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −48.0000 | + | 27.7128i | −1.63017 | + | 0.941176i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.0000 | − | 31.1769i | 0.610608 | − | 1.05760i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.5000 | − | 33.7750i | 0.660732 | − | 1.14442i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −25.5000 | + | 44.1673i | −0.863044 | + | 1.49484i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −30.0000 | + | 10.3923i | −1.01419 | + | 0.351324i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.0000 | + | 32.9090i | 0.641584 | + | 1.11126i | 0.985079 | + | 0.172102i | \(0.0550559\pi\) |
−0.343495 | + | 0.939155i | \(0.611611\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −40.5000 | + | 23.3827i | −1.36603 | + | 0.788678i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.0000 | 1.01073 | 0.505363 | − | 0.862907i | \(-0.331359\pi\) | ||||
0.505363 | + | 0.862907i | \(0.331359\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.0000 | 0.942275 | 0.471138 | − | 0.882060i | \(-0.343844\pi\) | ||||
0.471138 | + | 0.882060i | \(0.343844\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 24.2487i | − | 0.815112i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.00000 | + | 10.3923i | 0.201460 | + | 0.348939i | 0.948999 | − | 0.315279i | \(-0.102098\pi\) |
−0.747539 | + | 0.664218i | \(0.768765\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 18.0000 | + | 31.1769i | 0.603023 | + | 1.04447i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.50000 | + | 12.9904i | −0.250978 | + | 0.434707i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.0000 | + | 36.3731i | −0.701953 | + | 1.21582i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18.0000 | − | 10.3923i | −0.601003 | − | 0.346989i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.50000 | + | 2.59808i | 0.0500278 | + | 0.0866507i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.5000 | + | 18.1865i | −0.349806 | + | 0.605881i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.50000 | + | 21.6506i | 0.249584 | + | 0.720488i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.00000 | + | 10.3923i | 0.199447 | + | 0.345452i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.0000 | − | 31.1769i | 0.597680 | − | 1.03521i | −0.395482 | − | 0.918474i | \(-0.629423\pi\) |
0.993163 | − | 0.116739i | \(-0.0372441\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.00000 | −0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.5000 | − | 33.7750i | −0.646064 | − | 1.11902i | −0.984055 | − | 0.177866i | \(-0.943081\pi\) |
0.337991 | − | 0.941149i | \(-0.390253\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.00000 | 0.132381 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 10.3923i | − | 0.343559i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.00000 | − | 6.92820i | −0.264183 | − | 0.228789i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.5000 | + | 30.3109i | −0.577272 | + | 0.999864i | 0.418519 | + | 0.908208i | \(0.362549\pi\) |
−0.995791 | + | 0.0916559i | \(0.970784\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.0000 | + | 6.92820i | 0.395413 | + | 0.228292i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.0000 | + | 20.7846i | −0.394985 | + | 0.684134i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.50000 | + | 9.52628i | 0.180839 | + | 0.313222i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.0000 | + | 20.7846i | −0.394132 | + | 0.682656i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.00000 | 0.0984268 | 0.0492134 | − | 0.998788i | \(-0.484329\pi\) | ||||
0.0492134 | + | 0.998788i | \(0.484329\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.00000 | − | 34.6410i | −0.163868 | − | 1.13531i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 46.5000 | + | 26.8468i | 1.52234 | + | 0.878924i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 28.0000 | + | 48.4974i | 0.915698 | + | 1.58604i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.0000 | −1.11073 | −0.555366 | − | 0.831606i | \(-0.687422\pi\) | ||||
−0.555366 | + | 0.831606i | \(0.687422\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.5000 | − | 14.7224i | −0.832161 | − | 0.480448i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 59.0000 | 1.92335 | 0.961673 | − | 0.274201i | \(-0.0884132\pi\) | ||||
0.961673 | + | 0.274201i | \(0.0884132\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36.0000 | 1.17232 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 18.0000 | − | 20.7846i | 0.585540 | − | 0.676123i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.0000 | 0.812391 | 0.406195 | − | 0.913786i | \(-0.366855\pi\) | ||||
0.406195 | + | 0.913786i | \(0.366855\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.0000 | 0.681689 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13.5000 | − | 7.79423i | −0.437767 | − | 0.252745i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.0000 | −0.842223 | −0.421111 | − | 0.907009i | \(-0.638360\pi\) | ||||
−0.421111 | + | 0.907009i | \(0.638360\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.0000 | + | 25.9808i | 0.485389 | + | 0.840718i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.00000 | + | 3.46410i | 0.193952 | + | 0.111979i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.00000 | + | 36.3731i | −0.226042 | + | 1.17455i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.00000 | −0.290021 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.00000 | + | 1.73205i | 0.0321911 | + | 0.0557567i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.5000 | − | 40.7032i | 0.755709 | − | 1.30893i | −0.189312 | − | 0.981917i | \(-0.560626\pi\) |
0.945021 | − | 0.327009i | \(-0.106041\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −52.5000 | − | 30.3109i | −1.68654 | − | 0.973726i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.50000 | + | 12.9904i | −0.240686 | + | 0.416881i | −0.960910 | − | 0.276861i | \(-0.910706\pi\) |
0.720224 | + | 0.693742i | \(0.244039\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.50000 | + | 12.9904i | −0.0801463 | + | 0.416452i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.19615i | 0.166410i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.00000 | 0.0959785 | 0.0479893 | − | 0.998848i | \(-0.484719\pi\) | ||||
0.0479893 | + | 0.998848i | \(0.484719\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30.0000 | + | 51.9615i | 0.958804 | + | 1.66070i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.5000 | − | 18.1865i | 0.335239 | − | 0.580651i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.0000 | + | 31.1769i | −0.574111 | + | 0.994389i | 0.422027 | + | 0.906583i | \(0.361319\pi\) |
−0.996138 | + | 0.0878058i | \(0.972015\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26.0000 | + | 45.0333i | 0.828429 | + | 1.43488i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −13.5000 | − | 2.59808i | −0.429710 | − | 0.0826977i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10.0000 | + | 17.3205i | −0.317982 | + | 0.550760i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.5000 | − | 32.0429i | −0.587672 | − | 1.01788i | −0.994537 | − | 0.104389i | \(-0.966711\pi\) |
0.406865 | − | 0.913488i | \(-0.366622\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 37.5000 | + | 21.6506i | 1.19003 | + | 0.687062i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.0000 | + | 22.5167i | −0.412128 | + | 0.713826i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.0000 | − | 19.0526i | 0.348373 | − | 0.603401i | −0.637587 | − | 0.770378i | \(-0.720067\pi\) |
0.985961 | + | 0.166978i | \(0.0534008\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −49.5000 | − | 28.5788i | −1.56611 | − | 0.904194i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))