Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,2,Mod(25,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("252.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.01223013094\) |
Analytic rank: | \(1\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 25.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.25 |
Dual form | 252.2.i.a.121.1 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.50000 | + | 0.866025i | −0.866025 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | + | 1.73205i | −0.447214 | + | 0.774597i | −0.998203 | − | 0.0599153i | \(-0.980917\pi\) |
0.550990 | + | 0.834512i | \(0.314250\pi\) | |||||||
\(6\) | 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 | −0.992361 | − | 0.123371i | \(-0.960630\pi\) |
0.389338 | − | 0.921095i | \(-0.372704\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.50000 | − | 2.59808i | −0.416025 | − | 0.720577i | 0.579510 | − | 0.814965i | \(-0.303244\pi\) |
−0.995535 | + | 0.0943882i | \(0.969911\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 3.46410i | − | 0.894427i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.50000 | + | 6.06218i | −0.848875 | + | 1.47029i | 0.0333386 | + | 0.999444i | \(0.489386\pi\) |
−0.882213 | + | 0.470850i | \(0.843947\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.50000 | − | 4.33013i | −0.573539 | − | 0.993399i | −0.996199 | − | 0.0871106i | \(-0.972237\pi\) |
0.422659 | − | 0.906289i | \(-0.361097\pi\) | |||||||
\(20\) | 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 | \(-0.970262\pi\) |
0.578610 | + | 0.815604i | \(0.303595\pi\) | |||||||
\(24\) | 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 | −0.815861 | − | 0.578249i | \(-0.803736\pi\) |
0.908708 | + | 0.417432i | \(0.137070\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | −0.538816 | −0.269408 | − | 0.963026i | \(-0.586828\pi\) | ||||
−0.269408 | + | 0.963026i | \(0.586828\pi\) | |||||||
\(32\) | 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 | −0.821995 | − | 0.569495i | \(-0.807139\pi\) |
−0.0821995 | − | 0.996616i | \(-0.526194\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.50000 | + | 2.59808i | 0.720577 | + | 0.416025i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.50000 | + | 7.79423i | 0.702782 | + | 1.21725i | 0.967486 | + | 0.252924i | \(0.0813924\pi\) |
−0.264704 | + | 0.964330i | \(0.585274\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.50000 | + | 4.33013i | −0.381246 | + | 0.660338i | −0.991241 | − | 0.132068i | \(-0.957838\pi\) |
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.00000 | + | 5.19615i | 0.447214 | + | 0.774597i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.00000 | 0.437595 | 0.218797 | − | 0.975770i | \(-0.429787\pi\) | ||||
0.218797 | + | 0.975770i | \(0.429787\pi\) | |||||||
\(48\) | 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 | −0.950464 | − | 0.310835i | \(-0.899391\pi\) |
0.744423 | + | 0.667708i | \(0.232725\pi\) | |||||||
\(54\) | 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 | \(-0.650597\pi\) | ||||
−0.455661 | + | 0.890153i | \(0.650597\pi\) | |||||||
\(60\) | 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 | \(-0.207942\pi\) | ||||
0.794101 | + | 0.607785i | \(0.207942\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 6.92820i | − | 0.834058i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.50000 | + | 6.06218i | −0.409644 | + | 0.709524i | −0.994850 | − | 0.101361i | \(-0.967680\pi\) |
0.585206 | + | 0.810885i | \(0.301014\pi\) | |||||||
\(74\) | 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 | \(-0.668983\pi\) | ||||
−0.506290 | + | 0.862364i | \(0.668983\pi\) | |||||||
\(80\) | 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 | \(-0.850812\pi\) |
0.837279 | + | 0.546776i | \(0.184145\pi\) | |||||||
\(84\) | 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 | −0.922840 | − | 0.385183i | \(-0.874138\pi\) |
0.127842 | − | 0.991795i | \(-0.459195\pi\) | |||||||
\(90\) | 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 | −0.00593185 | − | 0.999982i | \(-0.501888\pi\) |
0.868976 | − | 0.494854i | \(-0.164778\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.0000 | −1.20605 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.00000 | − | 1.73205i | −0.0995037 | − | 0.172345i | 0.811976 | − | 0.583691i | \(-0.198392\pi\) |
−0.911479 | + | 0.411346i | \(0.865059\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | + | 6.92820i | −0.394132 | + | 0.682656i | −0.992990 | − | 0.118199i | \(-0.962288\pi\) |
0.598858 | + | 0.800855i | \(0.295621\pi\) | |||||||
\(104\) | 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 | \(-0.120345\pi\) |
−0.784366 | + | 0.620298i | \(0.787012\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.50000 | + | 6.06218i | −0.335239 | + | 0.580651i | −0.983531 | − | 0.180741i | \(-0.942150\pi\) |
0.648292 | + | 0.761392i | \(0.275484\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 16.5000 | + | 9.52628i | 1.56611 | + | 0.904194i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.500000 | + | 0.866025i | 0.0470360 | + | 0.0814688i | 0.888585 | − | 0.458712i | \(-0.151689\pi\) |
−0.841549 | + | 0.540181i | \(0.818356\pi\) | |||||||
\(114\) | 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 | \(-0.777425\pi\) |
0.940072 | + | 0.340977i | \(0.110758\pi\) | |||||||
\(132\) | 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 | −0.993109 | − | 0.117198i | \(-0.962609\pi\) |
0.395058 | − | 0.918656i | \(-0.370724\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.50000 | + | 4.33013i | 0.212047 | + | 0.367277i | 0.952355 | − | 0.304991i | \(-0.0986536\pi\) |
−0.740308 | + | 0.672268i | \(0.765320\pi\) | |||||||
\(140\) | 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 | −0.716578 | − | 0.697507i | \(-0.754293\pi\) |
0.962348 | + | 0.271821i | \(0.0876260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | + | 6.92820i | 0.325515 | + | 0.563809i | 0.981617 | − | 0.190864i | \(-0.0611289\pi\) |
−0.656101 | + | 0.754673i | \(0.727796\pi\) | |||||||
\(152\) | 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 | 0.950615 | + | 0.310372i | \(0.100454\pi\) |
−0.206518 | + | 0.978443i | \(0.566213\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −12.0000 | + | 6.92820i | −0.934199 | + | 0.539360i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.5000 | − | 19.9186i | −0.889897 | − | 1.54135i | −0.839996 | − | 0.542592i | \(-0.817443\pi\) |
−0.0499004 | − | 0.998754i | \(-0.515890\pi\) | |||||||
\(168\) | 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 | −0.144308 | − | 0.989533i | \(-0.546095\pi\) |
0.929114 | − | 0.369792i | \(-0.120571\pi\) | |||||||
\(180\) | 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 | \(-0.317409\pi\) | ||||
0.542681 | + | 0.839939i | \(0.317409\pi\) | |||||||
\(192\) | 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 | \(-0.680906\pi\) |
0.999000 | + | 0.0447181i | \(0.0142390\pi\) | |||||||
\(200\) | 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 | \(-0.0189888\pi\) |
−0.550743 | + | 0.834675i | \(0.685655\pi\) | |||||||
\(212\) | 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 | \(-0.758028\pi\) |
0.959092 | + | 0.283096i | \(0.0913615\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | 0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.00000 | + | 10.3923i | 0.398234 | + | 0.689761i | 0.993508 | − | 0.113761i | \(-0.0362899\pi\) |
−0.595274 | + | 0.803523i | \(0.702957\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.00000 | − | 12.1244i | 0.462573 | − | 0.801200i | −0.536515 | − | 0.843891i | \(-0.680260\pi\) |
0.999088 | + | 0.0426906i | \(0.0135930\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.0000 | − | 13.8564i | −0.789542 | − | 0.911685i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.5000 | + | 25.1147i | 0.949927 | + | 1.64532i | 0.745573 | + | 0.666424i | \(0.232176\pi\) |
0.204354 | + | 0.978897i | \(0.434491\pi\) | |||||||
\(234\) | 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 | 0.975226 | + | 0.221213i | \(0.0710015\pi\) |
−0.296037 | + | 0.955176i | \(0.595665\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.00000 | + | 8.66025i | 0.322078 | + | 0.557856i | 0.980917 | − | 0.194429i | \(-0.0622852\pi\) |
−0.658838 | + | 0.752285i | \(0.728952\pi\) | |||||||
\(242\) | 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 | 0.435970 | + | 0.899961i | \(0.356405\pi\) |
−0.997374 | + | 0.0724199i | \(0.976928\pi\) | |||||||
\(258\) | 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 | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(264\) | 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 | −0.850380 | − | 0.526169i | \(-0.823628\pi\) |
0.880866 | + | 0.473366i | \(0.156961\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.50000 | + | 2.59808i | 0.0911185 | + | 0.157822i | 0.907982 | − | 0.419009i | \(-0.137622\pi\) |
−0.816864 | + | 0.576831i | \(0.804289\pi\) | |||||||
\(272\) | 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 | 0.834419 | − | 0.551131i | \(-0.185804\pi\) |
−0.894503 | + | 0.447062i | \(0.852470\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.50000 | + | 7.79423i | −0.269408 | + | 0.466628i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.50000 | − | 14.7224i | 0.507067 | − | 0.878267i | −0.492899 | − | 0.870087i | \(-0.664063\pi\) |
0.999967 | − | 0.00818015i | \(-0.00260385\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.00000 | 0.0594438 | 0.0297219 | − | 0.999558i | \(-0.490538\pi\) | ||||
0.0297219 | + | 0.999558i | \(0.490538\pi\) | |||||||
\(284\) | 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 | −0.926777 | − | 0.375613i | \(-0.877432\pi\) |
0.138098 | − | 0.990419i | \(-0.455901\pi\) | |||||||
\(294\) | 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 | \(-0.573314\pi\) | ||||
−0.228292 | + | 0.973593i | \(0.573314\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 13.8564i | − | 0.788263i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.0000 | −1.75785 | −0.878924 | − | 0.476961i | \(-0.841738\pi\) | ||||
−0.878924 | + | 0.476961i | \(0.841738\pi\) | |||||||
\(312\) | 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 | \(-0.741100\pi\) | ||||
−0.687062 | + | 0.726599i | \(0.741100\pi\) | |||||||
\(332\) | 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 | 0.822274 | − | 0.569091i | \(-0.192705\pi\) |
−0.903985 | + | 0.427565i | \(0.859372\pi\) | |||||||
\(338\) | 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 | \(-0.631901\pi\) | ||||
−0.402621 | + | 0.915367i | \(0.631901\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.50000 | − | 4.33013i | 0.133822 | − | 0.231786i | −0.791325 | − | 0.611396i | \(-0.790608\pi\) |
0.925147 | + | 0.379610i | \(0.123942\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.5000 | − | 7.79423i | 0.720577 | − | 0.416025i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.00000 | − | 5.19615i | −0.159674 | − | 0.276563i | 0.775077 | − | 0.631867i | \(-0.217711\pi\) |
−0.934751 | + | 0.355303i | \(0.884378\pi\) | |||||||
\(354\) | 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 | 0.907111 | + | 0.420892i | \(0.138283\pi\) |
−0.0890519 | + | 0.996027i | \(0.528384\pi\) | |||||||
\(360\) | 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 | −0.893873 | − | 0.448320i | \(-0.852022\pi\) |
0.0586798 | − | 0.998277i | \(-0.481311\pi\) | |||||||
\(368\) | 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 | 0.427051 | + | 0.904227i | \(0.359552\pi\) |
−0.996610 | + | 0.0822766i | \(0.973781\pi\) | |||||||
\(374\) | 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 | \(-0.671713\pi\) | ||||
−0.513665 | + | 0.857991i | \(0.671713\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.00000 | + | 13.8564i | −0.408781 | + | 0.708029i | −0.994753 | − | 0.102302i | \(-0.967379\pi\) |
0.585973 | + | 0.810331i | \(0.300713\pi\) | |||||||
\(384\) | 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 | −0.980842 | − | 0.194804i | \(-0.937593\pi\) |
0.321716 | − | 0.946836i | \(-0.395740\pi\) | |||||||
\(390\) | 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 | 0.999506 | + | 0.0314391i | \(0.0100090\pi\) |
−0.472526 | + | 0.881317i | \(0.656658\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −15.0000 | − | 17.3205i | −0.750939 | − | 0.867110i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.0000 | + | 25.9808i | −0.749064 | + | 1.29742i | 0.199207 | + | 0.979957i | \(0.436163\pi\) |
−0.948272 | + | 0.317460i | \(0.897170\pi\) | |||||||
\(402\) | 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 | \(-0.286076\pi\) |
−0.989000 | + | 0.147918i | \(0.952743\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.50000 | − | 7.79423i | 0.219317 | − | 0.379867i | −0.735283 | − | 0.677761i | \(-0.762951\pi\) |
0.954599 | + | 0.297893i | \(0.0962839\pi\) | |||||||
\(422\) | 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 | −0.172468 | + | 0.985015i | \(0.555174\pi\) |
−0.766814 | + | 0.641869i | \(0.778159\pi\) | |||||||
\(432\) | 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 | \(-0.667085\pi\) | ||||
−0.501138 | + | 0.865368i | \(0.667085\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.5000 | − | 7.79423i | 0.928571 | − | 0.371154i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −29.0000 | −1.37783 | −0.688916 | − | 0.724841i | \(-0.741913\pi\) | ||||
−0.688916 | + | 0.724841i | \(0.741913\pi\) | |||||||
\(444\) | 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 | 0.463525 | + | 0.886084i | \(0.346584\pi\) |
−0.999134 | + | 0.0416172i | \(0.986749\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.50000 | + | 4.33013i | 0.116185 | + | 0.201238i | 0.918253 | − | 0.395995i | \(-0.129600\pi\) |
−0.802068 | + | 0.597233i | \(0.796267\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10.3923i | 0.481932i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.50000 | − | 14.7224i | −0.393333 | − | 0.681273i | 0.599554 | − | 0.800334i | \(-0.295345\pi\) |
−0.992887 | + | 0.119062i | \(0.962011\pi\) | |||||||
\(468\) | 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 | \(-0.108162\pi\) |
−0.760056 | + | 0.649857i | \(0.774829\pi\) | |||||||
\(480\) | 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 | \(-0.826121\pi\) |
0.877132 | + | 0.480250i | \(0.159454\pi\) | |||||||
\(488\) | 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 | \(-0.101571\pi\) |
−0.746438 | + | 0.665455i | \(0.768237\pi\) | |||||||
\(492\) | 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 | \(-0.861871\pi\) |
0.817781 | + | 0.575529i | \(0.195204\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 34.5000 | + | 19.9186i | 1.54135 | + | 0.889897i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.0000 | 1.07011 | 0.535054 | − | 0.844818i | \(-0.320291\pi\) | ||||
0.535054 | + | 0.844818i | \(0.320291\pi\) | |||||||
\(504\) | 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 | −0.594675 | − | 0.803966i | \(-0.702719\pi\) |
0.993593 | + | 0.113020i | \(0.0360525\pi\) | |||||||
\(510\) | 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 | −0.897011 | − | 0.442007i | \(-0.854267\pi\) |
0.831295 | + | 0.555831i | \(0.187600\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.5000 | − | 25.1147i | −0.634041 | − | 1.09819i | −0.986718 | − | 0.162446i | \(-0.948062\pi\) |
0.352677 | − | 0.935745i | \(-0.385272\pi\) | |||||||
\(524\) | 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 | 0.965084 | + | 0.261942i | \(0.0843630\pi\) |
−0.255693 | + | 0.966758i | \(0.582304\pi\) | |||||||
\(542\) | 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 | 0.261026 | + | 0.965332i | \(0.415939\pi\) |
−0.966515 | + | 0.256611i | \(0.917394\pi\) | |||||||
\(548\) | 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 | −0.958702 | − | 0.284413i | \(-0.908201\pi\) |
0.725660 | + | 0.688054i | \(0.241535\pi\) | |||||||
\(558\) | 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 | \(-0.411672\pi\) | ||||
0.273942 | + | 0.961746i | \(0.411672\pi\) | |||||||
\(564\) | 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 | \(-0.519994\pi\) | ||||
−0.0627730 | + | 0.998028i | \(0.519994\pi\) | |||||||
\(572\) | 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 | −0.929636 | − | 0.368478i | \(-0.879879\pi\) |
0.783930 | + | 0.620850i | \(0.213212\pi\) | |||||||
\(578\) | 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 | 0.177419 | + | 0.984135i | \(0.443225\pi\) |
−0.940996 | + | 0.338418i | \(0.890108\pi\) | |||||||
\(588\) | 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 | −0.997952 | − | 0.0639736i | \(-0.979623\pi\) |
0.443573 | − | 0.896238i | \(-0.353711\pi\) | |||||||
\(594\) | 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 | \(-0.519521\pi\) | ||||
−0.0612883 | + | 0.998120i | \(0.519521\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.5000 | + | 30.3109i | −0.713840 | + | 1.23641i | 0.249565 | + | 0.968358i | \(0.419712\pi\) |
−0.963405 | + | 0.268049i | \(0.913621\pi\) | |||||||
\(602\) | 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 | 0.291353 | − | 0.956616i | \(-0.405895\pi\) |
0.682777 | − | 0.730627i | \(-0.260772\pi\) | |||||||
\(608\) | 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 | −0.760724 | − | 0.649075i | \(-0.775156\pi\) |
0.942478 | + | 0.334269i | \(0.108489\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 27.0000 | − | 15.5885i | 1.08875 | − | 0.628587i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.5000 | − | 37.2391i | −0.865557 | − | 1.49919i | −0.866493 | − | 0.499190i | \(-0.833631\pi\) |
0.000935233 | − | 1.00000i | \(-0.499702\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.0000 | + | 17.3205i | 0.401934 | + | 0.696170i | 0.993959 | − | 0.109749i | \(-0.0350048\pi\) |
−0.592025 | + | 0.805919i | \(0.701671\pi\) | |||||||
\(620\) | 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 | \(-0.603171\pi\) | ||||
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(632\) | 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 | 0.885098 | − | 0.465404i | \(-0.154091\pi\) |
−0.845601 | + | 0.533816i | \(0.820758\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.50000 | + | 11.2583i | 0.256335 | + | 0.443985i | 0.965257 | − | 0.261301i | \(-0.0841516\pi\) |
−0.708922 | + | 0.705287i | \(0.750818\pi\) | |||||||
\(644\) | 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 | \(-0.852115\pi\) |
0.835033 | + | 0.550200i | \(0.185449\pi\) | |||||||
\(648\) | 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 | −0.634437 | − | 0.772975i | \(-0.718768\pi\) |
0.986634 | + | 0.162951i | \(0.0521013\pi\) | |||||||
\(654\) | 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 | \(-0.995217\pi\) |
0.512956 | + | 0.858415i | \(0.328550\pi\) | |||||||
\(660\) | 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 | −0.517943 | − | 0.855415i | \(-0.673302\pi\) |
0.999783 | + | 0.0208444i | \(0.00663546\pi\) | |||||||
\(674\) | 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 | \(-0.701728\pi\) |
0.993940 | + | 0.109926i | \(0.0350613\pi\) | |||||||
\(684\) | 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 | \(-0.432904\pi\) | ||||
0.209230 | + | 0.977866i | \(0.432904\pi\) | |||||||
\(692\) | 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 | \(-0.0764307\pi\) |
−0.691608 | + | 0.722273i | \(0.743097\pi\) | |||||||
\(720\) | 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 | 0.0111912 | − | 0.999937i | \(-0.496438\pi\) |
0.860376 | − | 0.509661i | \(-0.170229\pi\) | |||||||
\(728\) | 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 | 0.443940 | + | 0.896056i | \(0.353580\pi\) |
−0.997978 | + | 0.0635649i | \(0.979753\pi\) | |||||||
\(734\) | 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 | \(-0.707104\pi\) |
0.991942 | + | 0.126696i | \(0.0404373\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 25.9808i | − | 0.954427i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.50000 | + | 7.79423i | 0.165089 | + | 0.285943i | 0.936687 | − | 0.350168i | \(-0.113876\pi\) |
−0.771598 | + | 0.636111i | \(0.780542\pi\) | |||||||
\(744\) | 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 | \(-0.689061\pi\) |
0.997526 | + | 0.0702946i | \(0.0223939\pi\) | |||||||
\(752\) | 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 | −0.847331 | − | 0.531065i | \(-0.821792\pi\) |
0.883581 | + | 0.468278i | \(0.155125\pi\) | |||||||
\(762\) | 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 | 0.907575 | − | 0.419890i | \(-0.137931\pi\) |
−0.817423 | + | 0.576038i | \(0.804598\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 31.1769i | − | 1.12281i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.5000 | + | 19.9186i | −0.413626 | + | 0.716422i | −0.995283 | − | 0.0970125i | \(-0.969071\pi\) |
0.581657 | + | 0.813434i | \(0.302405\pi\) | |||||||
\(774\) | 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 | \(-0.377888\pi\) | ||||
0.374285 | + | 0.927314i | \(0.377888\pi\) | |||||||
\(788\) | 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 | 0.702074 | − | 0.712104i | \(-0.252258\pi\) |
−0.967737 | + | 0.251961i | \(0.918924\pi\) | |||||||
\(798\) | 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 | −0.857102 | − | 0.515147i | \(-0.827737\pi\) |
0.874681 | + | 0.484699i | \(0.161071\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.0000 | −0.702295 | −0.351147 | − | 0.936320i | \(-0.614208\pi\) | ||||
−0.351147 | + | 0.936320i | \(0.614208\pi\) | |||||||
\(812\) | 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 | \(-0.631290\pi\) | ||||
−0.400865 | + | 0.916137i | \(0.631290\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.92820i | 0.241209i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.0000 | 0.417281 | 0.208640 | − | 0.977992i | \(-0.433096\pi\) | ||||
0.208640 | + | 0.977992i | \(0.433096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.50000 | + | 16.4545i | −0.329949 | + | 0.571488i | −0.982501 | − | 0.186256i | \(-0.940365\pi\) |
0.652553 | + | 0.757743i | \(0.273698\pi\) | |||||||
\(830\) | 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 | \(-0.703376\pi\) |
0.993357 | + | 0.115071i | \(0.0367096\pi\) | |||||||
\(840\) | 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 | 0.393753 | + | 0.919216i | \(0.371177\pi\) |
−0.992941 | + | 0.118609i | \(0.962157\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15.0000 | − | 25.9808i | 0.512989 | − | 0.888523i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.00000 | + | 15.5885i | 0.307434 | + | 0.532492i | 0.977800 | − | 0.209539i | \(-0.0671963\pi\) |
−0.670366 | + | 0.742030i | \(0.733863\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.0000 | + | 38.1051i | −0.750630 | + | 1.30013i | 0.196887 | + | 0.980426i | \(0.436917\pi\) |
−0.947518 | + | 0.319704i | \(0.896417\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 27.0000 | + | 31.1769i | 0.920158 | + | 1.06251i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20.5000 | − | 35.5070i | −0.697828 | − | 1.20867i | −0.969218 | − | 0.246204i | \(-0.920817\pi\) |
0.271390 | − | 0.962470i | \(-0.412517\pi\) | |||||||
\(864\) | 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 | −0.343495 | − | 0.939155i | \(-0.611611\pi\) |
0.985079 | − | 0.172102i | \(-0.0550559\pi\) | |||||||
\(878\) | 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 | \(-0.656156\pi\) | ||||
−0.471138 | + | 0.882060i | \(0.656156\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 24.2487i | 0.815112i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.00000 | + | 10.3923i | −0.201460 | + | 0.348939i | −0.948999 | − | 0.315279i | \(-0.897902\pi\) |
0.747539 | + | 0.664218i | \(0.231235\pi\) | |||||||
\(888\) | 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 | −0.993163 | − | 0.116739i | \(-0.962756\pi\) |
0.395482 | − | 0.918474i | \(-0.370577\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.00000 | −0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.5000 | − | 33.7750i | 0.646064 | − | 1.11902i | −0.337991 | − | 0.941149i | \(-0.609747\pi\) |
0.984055 | − | 0.177866i | \(-0.0569194\pi\) | |||||||
\(912\) | 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 | 0.995791 | + | 0.0916559i | \(0.0292160\pi\) |
−0.418519 | + | 0.908208i | \(0.637451\pi\) | |||||||
\(920\) | 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 | \(-0.633145\pi\) | ||||
−0.406195 | + | 0.913786i | \(0.633145\pi\) | |||||||
\(948\) | 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 | −0.945021 | − | 0.327009i | \(-0.893959\pi\) |
0.189312 | − | 0.981917i | \(-0.439374\pi\) | |||||||
\(968\) | 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 | \(-0.0892941\pi\) |
−0.720224 | + | 0.693742i | \(0.755961\pi\) | |||||||
\(972\) | 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 | 0.996138 | + | 0.0878058i | \(0.0279855\pi\) |
−0.422027 | + | 0.906583i | \(0.638681\pi\) | |||||||
\(984\) | 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 | −0.406865 | − | 0.913488i | \(-0.633378\pi\) |
0.994537 | − | 0.104389i | \(-0.0332887\pi\) | |||||||
\(992\) | 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 | 0.985961 | − | 0.166978i | \(-0.0534008\pi\) |
−0.637587 | + | 0.770378i | \(0.720067\pi\) | |||||||
\(998\) | 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 \(a_p\))