Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,2,Mod(193,252)]
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, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.l (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: | \(0\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 205.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.205 |
Dual form | 252.2.l.a.193.1 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | − | 1.73205i | − | 1.00000i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | 0.894427 | 0.447214 | − | 0.894427i | \(-0.352416\pi\) | ||||
0.447214 | + | 0.894427i | \(0.352416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | + | 1.73205i | 0.755929 | + | 0.654654i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.00000 | 1.20605 | 0.603023 | − | 0.797724i | \(-0.293963\pi\) | ||||
0.603023 | + | 0.797724i | \(0.293963\pi\) | |||||||
\(12\) | 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 | −0.882213 | − | 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 | \(0.361097\pi\) |
−0.996199 | + | 0.0871106i | \(0.972237\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.00000 | − | 3.46410i | 0.654654 | − | 0.755929i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 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 | ||||||||
\(31\) | 1.50000 | − | 2.59808i | 0.269408 | − | 0.466628i | −0.699301 | − | 0.714827i | \(-0.746505\pi\) |
0.968709 | + | 0.248199i | \(0.0798387\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 6.92820i | − | 1.20605i | ||||||
\(34\) | 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 | 0.967486 | + | 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 | ||||||||
\(45\) | −6.00000 | −0.894427 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.50000 | − | 2.59808i | −0.218797 | − | 0.378968i | 0.735643 | − | 0.677369i | \(-0.236880\pi\) |
−0.954441 | + | 0.298401i | \(0.903547\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.5000 | + | 6.06218i | −1.47029 | + | 0.848875i | ||||
\(52\) | 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 | ||||||||
\(59\) | 3.50000 | − | 6.06218i | 0.455661 | − | 0.789228i | −0.543065 | − | 0.839691i | \(-0.682736\pi\) |
0.998726 | + | 0.0504625i | \(0.0160695\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.50000 | − | 2.59808i | −0.192055 | − | 0.332650i | 0.753876 | − | 0.657017i | \(-0.228182\pi\) |
−0.945931 | + | 0.324367i | \(0.894849\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.00000 | − | 5.19615i | −0.755929 | − | 0.654654i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.00000 | − | 5.19615i | −0.372104 | − | 0.644503i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.50000 | + | 11.2583i | −0.794101 | + | 1.37542i | 0.129307 | + | 0.991605i | \(0.458725\pi\) |
−0.923408 | + | 0.383819i | \(0.874609\pi\) | |||||||
\(68\) | 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 | 0.585206 | − | 0.810885i | \(-0.301014\pi\) |
−0.994850 | + | 0.101361i | \(0.967680\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.73205i | 0.200000i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.00000 | + | 6.92820i | 0.911685 | + | 0.789542i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.50000 | + | 7.79423i | 0.506290 | + | 0.876919i | 0.999974 | + | 0.00727784i | \(0.00231663\pi\) |
−0.493684 | + | 0.869641i | \(0.664350\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 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 | ||||||||
\(87\) | −1.50000 | − | 0.866025i | −0.160817 | − | 0.0928477i | ||||
\(88\) | 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 | ||||||||
\(95\) | −5.00000 | + | 8.66025i | −0.512989 | + | 0.888523i | ||||
\(96\) | 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 | ||||||||
\(101\) | 2.00000 | 0.199007 | 0.0995037 | − | 0.995037i | \(-0.468274\pi\) | ||||
0.0995037 | + | 0.995037i | \(0.468274\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000 | 0.788263 | 0.394132 | − | 0.919054i | \(-0.371045\pi\) | ||||
0.394132 | + | 0.919054i | \(0.371045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.00000 | − | 6.92820i | 0.585540 | − | 0.676123i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.50000 | − | 2.59808i | 0.145010 | − | 0.251166i | −0.784366 | − | 0.620298i | \(-0.787012\pi\) |
0.929377 | + | 0.369132i | \(0.120345\pi\) | |||||||
\(108\) | 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 | 0.888585 | − | 0.458712i | \(-0.151689\pi\) |
−0.841549 | + | 0.540181i | \(0.818356\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.00000 | 0.746004 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.50000 | + | 7.79423i | 0.416025 | + | 0.720577i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.50000 | − | 18.1865i | 0.320844 | − | 1.66716i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 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 | ||||||||
\(129\) | 7.50000 | + | 4.33013i | 0.660338 | + | 0.381246i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.00000 | −0.349482 | −0.174741 | − | 0.984614i | \(-0.555909\pi\) | ||||
−0.174741 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.5000 | + | 4.33013i | −1.08389 | + | 0.375470i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10.3923i | 0.894427i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.0000 | 1.19610 | 0.598050 | − | 0.801459i | \(-0.295942\pi\) | ||||
0.598050 | + | 0.801459i | \(0.295942\pi\) | |||||||
\(138\) | 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 | ||||||||
\(149\) | −6.00000 | −0.491539 | −0.245770 | − | 0.969328i | \(-0.579041\pi\) | ||||
−0.245770 | + | 0.969328i | \(0.579041\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | 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 | ||||||||
\(157\) | 6.50000 | − | 11.2583i | 0.518756 | − | 0.898513i | −0.481006 | − | 0.876717i | \(-0.659728\pi\) |
0.999762 | − | 0.0217953i | \(-0.00693820\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.50000 | + | 2.59808i | −0.356873 | + | 0.206041i | ||||
\(160\) | 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 | \(-0.566213\pi\) |
0.950615 | − | 0.310372i | \(-0.100454\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 13.8564i | − | 1.07872i | ||||||
\(166\) | 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 | ||||||||
\(171\) | 7.50000 | − | 12.9904i | 0.573539 | − | 0.993399i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.500000 | + | 0.866025i | 0.0380143 | + | 0.0658427i | 0.884407 | − | 0.466717i | \(-0.154563\pi\) |
−0.846392 | + | 0.532560i | \(0.821230\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.00000 | − | 1.73205i | −0.151186 | − | 0.130931i | ||||
\(176\) | 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 | \(0.120571\pi\) |
−0.144308 | + | 0.989533i | \(0.546095\pi\) | |||||||
\(180\) | 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 | ||||||||
\(185\) | −11.0000 | + | 19.0526i | −0.808736 | + | 1.40077i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.0000 | − | 24.2487i | −1.02378 | − | 1.77324i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.00000 | + | 10.3923i | −0.654654 | + | 0.755929i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.50000 | − | 12.9904i | −0.542681 | − | 0.939951i | −0.998749 | − | 0.0500060i | \(-0.984076\pi\) |
0.456068 | − | 0.889945i | \(-0.349257\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.500000 | − | 0.866025i | 0.0359908 | − | 0.0623379i | −0.847469 | − | 0.530845i | \(-0.821875\pi\) |
0.883460 | + | 0.468507i | \(0.155208\pi\) | |||||||
\(194\) | 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 | 0.999000 | − | 0.0447181i | \(-0.0142390\pi\) |
−0.538227 | + | 0.842800i | \(0.680906\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 19.5000 | + | 11.2583i | 1.37542 | + | 0.794101i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.50000 | − | 0.866025i | 0.175466 | − | 0.0607831i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.00000 | + | 15.5885i | 0.628587 | + | 1.08875i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −12.0000 | −0.834058 | ||||||||
\(208\) | 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 | ||||||||
\(213\) | 13.8564i | 0.949425i | ||||||||
\(214\) | 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 | ||||||||
\(219\) | −10.5000 | + | 6.06218i | −0.709524 | + | 0.409644i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.5000 | + | 18.1865i | −0.706306 | + | 1.22336i | ||||
\(222\) | 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 | ||||||||
\(227\) | −12.0000 | −0.796468 | −0.398234 | − | 0.917284i | \(-0.630377\pi\) | ||||
−0.398234 | + | 0.917284i | \(0.630377\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.0000 | −0.925146 | −0.462573 | − | 0.886581i | \(-0.653074\pi\) | ||||
−0.462573 | + | 0.886581i | \(0.653074\pi\) | |||||||
\(230\) | 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 | 0.975226 | + | 0.221213i | \(0.0710015\pi\) |
−0.296037 | + | 0.955176i | \(0.595665\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0000 | −0.644157 | −0.322078 | − | 0.946713i | \(-0.604381\pi\) | ||||
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 15.5885i | − | 1.00000i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.00000 | + | 13.8564i | 0.127775 | + | 0.885253i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.0000 | 0.954427 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.50000 | + | 0.866025i | 0.0950586 | + | 0.0548821i | ||||
\(250\) | 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 | ||||||||
\(257\) | 18.0000 | 1.12281 | 0.561405 | − | 0.827541i | \(-0.310261\pi\) | ||||
0.561405 | + | 0.827541i | \(0.310261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −27.5000 | + | 9.52628i | −1.70877 | + | 0.591934i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.50000 | + | 2.59808i | −0.0928477 | + | 0.160817i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 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 | −0.816864 | − | 0.576831i | \(-0.804289\pi\) |
0.907982 | + | 0.419009i | \(0.137622\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13.5000 | − | 2.59808i | −0.817057 | − | 0.157243i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.00000 | −0.241209 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.00000 | 0.120168 | 0.0600842 | − | 0.998193i | \(-0.480863\pi\) | ||||
0.0600842 | + | 0.998193i | \(0.480863\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | −0.500000 | + | 0.866025i | −0.0297219 | + | 0.0514799i | −0.880504 | − | 0.474039i | \(-0.842796\pi\) |
0.850782 | + | 0.525519i | \(0.176129\pi\) | |||||||
\(284\) | 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 | ||||||||
\(291\) | −25.5000 | − | 14.7224i | −1.49484 | − | 0.863044i | ||||
\(292\) | 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 | ||||||||
\(297\) | 20.7846i | 1.20605i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.00000 | − | 10.3923i | −0.346989 | − | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.5000 | + | 4.33013i | −0.720488 | + | 0.249584i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 3.46410i | − | 0.199007i | ||||||
\(304\) | 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 | ||||||||
\(311\) | 15.5000 | − | 26.8468i | 0.878924 | − | 1.52234i | 0.0264017 | − | 0.999651i | \(-0.491595\pi\) |
0.852523 | − | 0.522690i | \(-0.175072\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.50000 | + | 14.7224i | 0.480448 | + | 0.832161i | 0.999748 | − | 0.0224310i | \(-0.00714060\pi\) |
−0.519300 | + | 0.854592i | \(0.673807\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −12.0000 | − | 10.3923i | −0.676123 | − | 0.585540i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.50000 | + | 7.79423i | 0.252745 | + | 0.437767i | 0.964281 | − | 0.264883i | \(-0.0853332\pi\) |
−0.711535 | + | 0.702650i | \(0.752000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.00000 | − | 3.46410i | 0.111979 | − | 0.193952i | ||||
\(320\) | 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 | ||||||||
\(327\) | −10.5000 | + | 6.06218i | −0.580651 | + | 0.335239i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.50000 | − | 7.79423i | 0.0826977 | − | 0.429710i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.5000 | + | 21.6506i | 0.687062 | + | 1.19003i | 0.972784 | + | 0.231714i | \(0.0744333\pi\) |
−0.285722 | + | 0.958313i | \(0.592233\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 16.5000 | − | 28.5788i | 0.904194 | − | 1.56611i | ||||
\(334\) | 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 | ||||||||
\(345\) | − | 13.8564i | − | 0.746004i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.50000 | − | 12.9904i | 0.402621 | − | 0.697360i | −0.591420 | − | 0.806363i | \(-0.701433\pi\) |
0.994041 | + | 0.109003i | \(0.0347659\pi\) | |||||||
\(348\) | 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 | ||||||||
\(353\) | 6.00000 | 0.319348 | 0.159674 | − | 0.987170i | \(-0.448956\pi\) | ||||
0.159674 | + | 0.987170i | \(0.448956\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.0000 | −0.849192 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −31.5000 | − | 6.06218i | −1.66716 | − | 0.320844i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.5000 | − | 26.8468i | 0.818059 | − | 1.41692i | −0.0890519 | − | 0.996027i | \(-0.528384\pi\) |
0.907111 | − | 0.420892i | \(-0.138283\pi\) | |||||||
\(360\) | 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 | ||||||||
\(367\) | 32.0000 | 1.67039 | 0.835193 | − | 0.549957i | \(-0.185356\pi\) | ||||
0.835193 | + | 0.549957i | \(0.185356\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −13.5000 | − | 23.3827i | −0.702782 | − | 1.21725i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.50000 | − | 7.79423i | 0.0778761 | − | 0.404656i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.0000 | 1.13912 | 0.569558 | − | 0.821951i | \(-0.307114\pi\) | ||||
0.569558 | + | 0.821951i | \(0.307114\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 20.7846i | 1.07331i | ||||||||
\(376\) | 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 | ||||||||
\(383\) | 16.0000 | 0.817562 | 0.408781 | − | 0.912633i | \(-0.365954\pi\) | ||||
0.408781 | + | 0.912633i | \(0.365954\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.0000 | + | 13.8564i | 0.815436 | + | 0.706188i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.50000 | − | 12.9904i | 0.381246 | − | 0.660338i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.0000 | 1.31825 | 0.659126 | − | 0.752032i | \(-0.270926\pi\) | ||||
0.659126 | + | 0.752032i | \(0.270926\pi\) | |||||||
\(390\) | 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 | ||||||||
\(399\) | 7.50000 | + | 21.6506i | 0.375470 | + | 1.08389i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.0000 | 1.49813 | 0.749064 | − | 0.662497i | \(-0.230503\pi\) | ||||
0.749064 | + | 0.662497i | \(0.230503\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.00000 | −0.448322 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.0000 | 0.894427 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −22.0000 | + | 38.1051i | −1.09050 | + | 1.88880i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.5000 | + | 19.9186i | −0.568638 | + | 0.984911i | 0.428063 | + | 0.903749i | \(0.359196\pi\) |
−0.996701 | + | 0.0811615i | \(0.974137\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 24.2487i | − | 1.19610i | ||||||
\(412\) | 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 | ||||||||
\(425\) | 3.50000 | + | 6.06218i | 0.169775 | + | 0.294059i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.50000 | − | 7.79423i | 0.0725901 | − | 0.377189i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −18.0000 | + | 10.3923i | −0.869048 | + | 0.501745i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.5000 | − | 33.7750i | −0.939282 | − | 1.62688i | −0.766814 | − | 0.641869i | \(-0.778159\pi\) |
−0.172468 | − | 0.985015i | \(-0.555174\pi\) | |||||||
\(432\) | 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 | ||||||||
\(437\) | −10.0000 | + | 17.3205i | −0.478365 | + | 0.828552i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.5000 | + | 18.1865i | 0.501138 | + | 0.867996i | 0.999999 | + | 0.00131415i | \(0.000418308\pi\) |
−0.498861 | + | 0.866682i | \(0.666248\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | − | 20.7846i | −0.142857 | − | 0.989743i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.5000 | + | 25.1147i | 0.688916 | + | 1.19324i | 0.972189 | + | 0.234198i | \(0.0752464\pi\) |
−0.283273 | + | 0.959039i | \(0.591420\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.0000 | + | 25.9808i | −0.711068 | + | 1.23161i | ||||
\(446\) | 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 | ||||||||
\(453\) | 13.8564i | 0.651031i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.00000 | − | 15.5885i | 0.140642 | − | 0.730798i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.5000 | − | 26.8468i | −0.725059 | − | 1.25584i | −0.958950 | − | 0.283577i | \(-0.908479\pi\) |
0.233890 | − | 0.972263i | \(-0.424854\pi\) | |||||||
\(458\) | 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 | ||||||||
\(465\) | −9.00000 | − | 5.19615i | −0.417365 | − | 0.240966i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.50000 | + | 14.7224i | −0.393333 | + | 0.681273i | −0.992887 | − | 0.119062i | \(-0.962011\pi\) |
0.599554 | + | 0.800334i | \(0.295345\pi\) | |||||||
\(468\) | 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 | ||||||||
\(473\) | −10.0000 | + | 17.3205i | −0.459800 | + | 0.796398i | ||||
\(474\) | 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 | ||||||||
\(479\) | −8.00000 | −0.365529 | −0.182765 | − | 0.983157i | \(-0.558505\pi\) | ||||
−0.182765 | + | 0.983157i | \(0.558505\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 33.0000 | 1.50467 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.0000 | − | 13.8564i | 0.546019 | − | 0.630488i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.0000 | − | 29.4449i | 0.771930 | − | 1.33702i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.500000 | + | 0.866025i | 0.0226572 | + | 0.0392434i | 0.877132 | − | 0.480250i | \(-0.159454\pi\) |
−0.854475 | + | 0.519493i | \(0.826121\pi\) | |||||||
\(488\) | 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 | ||||||||
\(493\) | −7.00000 | −0.315264 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −24.0000 | −1.07872 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.0000 | − | 13.8564i | −0.717698 | − | 0.621545i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.00000 | 0.179065 | 0.0895323 | − | 0.995984i | \(-0.471463\pi\) | ||||
0.0895323 | + | 0.995984i | \(0.471463\pi\) | |||||||
\(500\) | 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 | ||||||||
\(507\) | −6.00000 | − | 3.46410i | −0.266469 | − | 0.153846i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.0000 | −0.797836 | −0.398918 | − | 0.916987i | \(-0.630614\pi\) | ||||
−0.398918 | + | 0.916987i | \(0.630614\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.50000 | − | 18.1865i | 0.154831 | − | 0.804525i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −22.5000 | − | 12.9904i | −0.993399 | − | 0.573539i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.0000 | 0.705044 | ||||||||
\(516\) | 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 | \(0.385272\pi\) |
−0.986718 | + | 0.162446i | \(0.948062\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.00000 | + | 3.46410i | −0.130931 | + | 0.151186i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.0000 | −0.914774 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 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 | ||||||||
\(535\) | 3.00000 | − | 5.19615i | 0.129701 | − | 0.224649i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 31.5000 | − | 18.1865i | 1.35933 | − | 0.784807i | ||||
\(538\) | 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 | ||||||||
\(543\) | 10.3923i | 0.445976i | ||||||||
\(544\) | 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 | ||||||||
\(551\) | 2.50000 | + | 4.33013i | 0.106504 | + | 0.184470i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.50000 | + | 23.3827i | −0.191359 | + | 0.994333i | ||||
\(554\) | 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 | ||||||||
\(563\) | −6.50000 | + | 11.2583i | −0.273942 | + | 0.474482i | −0.969868 | − | 0.243632i | \(-0.921661\pi\) |
0.695925 | + | 0.718114i | \(0.254994\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.00000 | + | 1.73205i | 0.0420703 | + | 0.0728679i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18.0000 | + | 15.5885i | 0.755929 | + | 0.654654i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.5000 | − | 23.3827i | −0.565949 | − | 0.980253i | −0.996961 | − | 0.0779066i | \(-0.975176\pi\) |
0.431011 | − | 0.902347i | \(-0.358157\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.50000 | − | 2.59808i | 0.0627730 | − | 0.108726i | −0.832931 | − | 0.553377i | \(-0.813339\pi\) |
0.895704 | + | 0.444651i | \(0.146672\pi\) | |||||||
\(572\) | 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 | ||||||||
\(581\) | −2.50000 | + | 0.866025i | −0.103717 | + | 0.0359288i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.00000 | − | 10.3923i | −0.248495 | − | 0.430405i | ||||
\(584\) | 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 | ||||||||
\(591\) | 45.0333i | 1.85242i | ||||||||
\(592\) | 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 | ||||||||
\(597\) | 19.5000 | − | 11.2583i | 0.798082 | − | 0.460773i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.50000 | − | 2.59808i | 0.0612883 | − | 0.106155i | −0.833753 | − | 0.552137i | \(-0.813812\pi\) |
0.895042 | + | 0.445983i | \(0.147146\pi\) | |||||||
\(600\) | 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 | ||||||||
\(605\) | 10.0000 | 0.406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −48.0000 | −1.94826 | −0.974130 | − | 0.225989i | \(-0.927439\pi\) | ||||
−0.974130 | + | 0.225989i | \(0.927439\pi\) | |||||||
\(608\) | 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 | −0.866493 | − | 0.499190i | \(-0.833631\pi\) |
0.000935233 | − | 1.00000i | \(-0.499702\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.0000 | −0.803868 | −0.401934 | − | 0.915669i | \(-0.631662\pi\) | ||||
−0.401934 | + | 0.915669i | \(0.631662\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 20.7846i | 0.834058i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −37.5000 | + | 12.9904i | −1.50241 | + | 0.520449i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 30.0000 | + | 17.3205i | 1.19808 | + | 0.691714i | ||||
\(628\) | 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 | ||||||||
\(637\) | 16.5000 | − | 12.9904i | 0.653754 | − | 0.514698i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 24.0000 | 0.949425 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.00000 | −0.0789953 | −0.0394976 | − | 0.999220i | \(-0.512576\pi\) | ||||
−0.0394976 | + | 0.999220i | \(0.512576\pi\) | |||||||
\(642\) | 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 | 0.835033 | − | 0.550200i | \(-0.185449\pi\) |
−0.894004 | + | 0.448059i | \(0.852115\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.0000 | − | 24.2487i | 0.549548 | − | 0.951845i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.50000 | − | 12.9904i | −0.176369 | − | 0.509133i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.0000 | −0.704394 | −0.352197 | − | 0.935926i | \(-0.614565\pi\) | ||||
−0.352197 | + | 0.935926i | \(0.614565\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.00000 | −0.312586 | ||||||||
\(656\) | 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 | ||||||||
\(661\) | 8.50000 | − | 14.7224i | 0.330612 | − | 0.572636i | −0.652020 | − | 0.758202i | \(-0.726078\pi\) |
0.982632 | + | 0.185565i | \(0.0594116\pi\) | |||||||
\(662\) | 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 | ||||||||
\(669\) | −10.5000 | − | 6.06218i | −0.405953 | − | 0.234377i | ||||
\(670\) | 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 | ||||||||
\(675\) | − | 5.19615i | − | 0.200000i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.5000 | − | 23.3827i | −0.518847 | − | 0.898670i | −0.999760 | − | 0.0219013i | \(-0.993028\pi\) |
0.480913 | − | 0.876768i | \(-0.340305\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 42.5000 | − | 14.7224i | 1.63100 | − | 0.564995i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20.7846i | 0.796468i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.5000 | + | 18.1865i | 0.401771 | + | 0.695888i | 0.993940 | − | 0.109926i | \(-0.0350613\pi\) |
−0.592168 | + | 0.805814i | \(0.701728\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.0000 | 1.06983 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.2487i | 0.925146i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.50000 | + | 7.79423i | −0.171436 | + | 0.296936i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.50000 | − | 9.52628i | −0.209230 | − | 0.362397i | 0.742242 | − | 0.670132i | \(-0.233762\pi\) |
−0.951472 | + | 0.307735i | \(0.900429\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −24.0000 | − | 20.7846i | −0.911685 | − | 0.789542i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.00000 | + | 8.66025i | 0.189661 | + | 0.328502i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31.5000 | − | 54.5596i | 1.19315 | − | 2.06659i | ||||
\(698\) | 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 | ||||||||
\(705\) | −9.00000 | + | 5.19615i | −0.338960 | + | 0.195698i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.00000 | + | 3.46410i | 0.150435 | + | 0.130281i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.5000 | + | 21.6506i | 0.469447 | + | 0.813107i | 0.999390 | − | 0.0349269i | \(-0.0111198\pi\) |
−0.529943 | + | 0.848034i | \(0.677787\pi\) | |||||||
\(710\) | 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 | −0.691608 | − | 0.722273i | \(-0.743097\pi\) |
0.971311 | + | 0.237814i | \(0.0764307\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.0000 | + | 13.8564i | 0.595871 | + | 0.516040i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.3205i | 0.644157i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.500000 | + | 0.866025i | −0.0185695 | + | 0.0321634i | ||||
\(726\) | 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 | ||||||||
\(731\) | 35.0000 | 1.29452 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.0000 | 1.10808 | 0.554038 | − | 0.832492i | \(-0.313086\pi\) | ||||
0.554038 | + | 0.832492i | \(0.313086\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 24.0000 | − | 3.46410i | 0.885253 | − | 0.127775i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −26.0000 | + | 45.0333i | −0.957722 | + | 1.65882i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.5000 | + | 18.1865i | 0.386249 | + | 0.669002i | 0.991942 | − | 0.126696i | \(-0.0404373\pi\) |
−0.605693 | + | 0.795699i | \(0.707104\pi\) | |||||||
\(740\) | 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 | ||||||||
\(745\) | −12.0000 | −0.439646 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.50000 | − | 2.59808i | 0.0548821 | − | 0.0950586i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.50000 | − | 2.59808i | 0.274044 | − | 0.0949316i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.0000 | −0.875772 | −0.437886 | − | 0.899030i | \(-0.644273\pi\) | ||||
−0.437886 | + | 0.899030i | \(0.644273\pi\) | |||||||
\(752\) | 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 | ||||||||
\(759\) | − | 27.7128i | − | 1.00591i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.00000 | −0.0724999 | −0.0362500 | − | 0.999343i | \(-0.511541\pi\) | ||||
−0.0362500 | + | 0.999343i | \(0.511541\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.50000 | − | 18.1865i | 0.126709 | − | 0.658397i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 21.0000 | + | 36.3731i | 0.759257 | + | 1.31507i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21.0000 | −0.758266 | ||||||||
\(768\) | 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 | 0.581657 | − | 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 | ||||||||
\(777\) | 16.5000 | + | 47.6314i | 0.591934 | + | 1.70877i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −45.0000 | −1.61229 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.0000 | −1.14505 | ||||||||
\(782\) | 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 | ||||||||
\(787\) | −10.5000 | + | 18.1865i | −0.374285 | + | 0.648280i | −0.990220 | − | 0.139517i | \(-0.955445\pi\) |
0.615935 | + | 0.787797i | \(0.288778\pi\) | |||||||
\(788\) | 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 | ||||||||
\(801\) | 22.5000 | − | 38.9711i | 0.794998 | − | 1.37698i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.0000 | − | 24.2487i | −0.494049 | − | 0.855718i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.0000 | + | 13.8564i | 0.563926 | + | 0.488374i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.50000 | − | 0.866025i | 0.0528025 | − | 0.0304855i | ||||
\(808\) | 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 | \(-0.614208\pi\) | ||||
−0.351147 | + | 0.936320i | \(0.614208\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.50000 | − | 2.59808i | −0.157822 | − | 0.0911185i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.0000 | − | 32.9090i | 0.665541 | − | 1.15275i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.5000 | − | 21.6506i | −0.437320 | − | 0.757460i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.50000 | + | 23.3827i | −0.157243 | + | 0.817057i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.5000 | + | 45.8993i | 0.924856 | + | 1.60190i | 0.791792 | + | 0.610791i | \(0.209148\pi\) |
0.133064 | + | 0.991107i | \(0.457518\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.5000 | − | 19.9186i | 0.400865 | − | 0.694318i | −0.592966 | − | 0.805228i | \(-0.702043\pi\) |
0.993831 | + | 0.110910i | \(0.0353764\pi\) | |||||||
\(824\) | 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 | 0.652553 | − | 0.757743i | \(-0.273698\pi\) |
−0.982501 | + | 0.186256i | \(0.940365\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 3.46410i | − | 0.120168i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 38.5000 | − | 30.3109i | 1.33395 | − | 1.05021i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −23.0000 | − | 39.8372i | −0.795948 | − | 1.37862i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13.5000 | + | 7.79423i | 0.466628 | + | 0.269408i | ||||
\(838\) | 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 | ||||||||
\(843\) | −25.5000 | − | 14.7224i | −0.878267 | − | 0.507067i | ||||
\(844\) | 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 | ||||||||
\(851\) | −22.0000 | + | 38.1051i | −0.754150 | + | 1.30623i | ||||
\(852\) | 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 | ||||||||
\(857\) | −18.0000 | −0.614868 | −0.307434 | − | 0.951569i | \(-0.599470\pi\) | ||||
−0.307434 | + | 0.951569i | \(0.599470\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.0000 | 1.50126 | 0.750630 | − | 0.660722i | \(-0.229750\pi\) | ||||
0.750630 | + | 0.660722i | \(0.229750\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 40.5000 | + | 7.79423i | 1.38024 | + | 0.265627i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20.5000 | + | 35.5070i | −0.697828 | + | 1.20867i | 0.271390 | + | 0.962470i | \(0.412517\pi\) |
−0.969218 | + | 0.246204i | \(0.920817\pi\) | |||||||
\(864\) | 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 | ||||||||
\(871\) | 39.0000 | 1.32146 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −25.5000 | + | 44.1673i | −0.863044 | + | 1.49484i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −24.0000 | − | 20.7846i | −0.811348 | − | 0.702648i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38.0000 | −1.28317 | −0.641584 | − | 0.767052i | \(-0.721723\pi\) | ||||
−0.641584 | + | 0.767052i | \(0.721723\pi\) | |||||||
\(878\) | 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 | ||||||||
\(885\) | −21.0000 | − | 12.1244i | −0.705907 | − | 0.407556i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.0000 | 0.402921 | 0.201460 | − | 0.979497i | \(-0.435431\pi\) | ||||
0.201460 | + | 0.979497i | \(0.435431\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 36.0000 | 1.20605 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.0000 | 0.501956 | ||||||||
\(894\) | 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 | ||||||||
\(905\) | −12.0000 | −0.398893 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.0000 | 1.19536 | 0.597680 | − | 0.801735i | \(-0.296089\pi\) | ||||
0.597680 | + | 0.801735i | \(0.296089\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | −2.00000 | + | 3.46410i | −0.0661903 | + | 0.114645i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.00000 | + | 5.19615i | −0.297531 | + | 0.171780i | ||||
\(916\) | 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 | \(-0.637451\pi\) |
0.995791 | − | 0.0916559i | \(-0.0292160\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.8564i | 0.456584i | ||||||||
\(922\) | 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 | ||||||||
\(927\) | −24.0000 | −0.788263 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.50000 | − | 2.59808i | −0.0492134 | − | 0.0852401i | 0.840369 | − | 0.542014i | \(-0.182338\pi\) |
−0.889583 | + | 0.456774i | \(0.849005\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.5000 | − | 12.9904i | −1.06514 | − | 0.425743i | ||||
\(932\) | 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 | ||||||||
\(941\) | −29.5000 | + | 51.0955i | −0.961673 | + | 1.66567i | −0.243372 | + | 0.969933i | \(0.578253\pi\) |
−0.718301 | + | 0.695733i | \(0.755080\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.0000 | + | 31.1769i | 0.586161 | + | 1.01526i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −18.0000 | + | 20.7846i | −0.585540 | + | 0.676123i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.5000 | + | 21.6506i | 0.406195 | + | 0.703551i | 0.994460 | − | 0.105118i | \(-0.0335219\pi\) |
−0.588264 | + | 0.808669i | \(0.700189\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.5000 | + | 18.1865i | −0.340844 | + | 0.590360i | ||||
\(950\) | 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 | ||||||||
\(959\) | 28.0000 | + | 24.2487i | 0.904167 | + | 0.783032i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.0000 | + | 19.0526i | 0.354839 | + | 0.614599i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.50000 | + | 7.79423i | −0.145010 | + | 0.251166i | ||||
\(964\) | 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 | ||||||||
\(969\) | − | 60.6218i | − | 1.94745i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.50000 | − | 12.9904i | 0.240686 | − | 0.416881i | −0.720224 | − | 0.693742i | \(-0.755961\pi\) |
0.960910 | + | 0.276861i | \(0.0892941\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.50000 | + | 12.9904i | −0.0801463 | + | 0.416452i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.50000 | − | 2.59808i | 0.144115 | − | 0.0832050i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.50000 | + | 2.59808i | −0.0479893 | + | 0.0831198i | −0.889022 | − | 0.457864i | \(-0.848615\pi\) |
0.841033 | + | 0.540984i | \(0.181948\pi\) | |||||||
\(978\) | 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 | ||||||||
\(983\) | −36.0000 | −1.14822 | −0.574111 | − | 0.818778i | \(-0.694652\pi\) | ||||
−0.574111 | + | 0.818778i | \(0.694652\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −52.0000 | −1.65686 | ||||||||
\(986\) | 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 | \(0.0332887\pi\) |
−0.406865 | + | 0.913488i | \(0.633378\pi\) | |||||||
\(992\) | 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 | ||||||||
\(997\) | −22.0000 | −0.696747 | −0.348373 | − | 0.937356i | \(-0.613266\pi\) | ||||
−0.348373 | + | 0.937356i | \(0.613266\pi\) | |||||||
\(998\) | 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 \(a_p\))