Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [390,2,Mod(121,390)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(390, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("390.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 390.bb (of order \(6\), 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: | \(3.11416567883\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.17284886784.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 2x^{6} + 30x^{5} + 185x^{4} + 36x^{3} + 8x^{2} + 208x + 2704 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 121.2 | ||
Root | \(-1.80668 - 1.80668i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 390.121 |
Dual form | 390.2.bb.c.361.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).
\(n\) | \(131\) | \(157\) | \(301\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0.866025 | − | 0.500000i | 0.353553 | − | 0.204124i | ||||
\(7\) | 1.14539 | − | 0.661290i | 0.432916 | − | 0.249944i | −0.267672 | − | 0.963510i | \(-0.586254\pi\) |
0.700588 | + | 0.713566i | \(0.252921\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −0.500000 | + | 0.866025i | −0.158114 | + | 0.273861i | ||||
\(11\) | −3.99528 | − | 2.30668i | −1.20462 | − | 0.695489i | −0.243043 | − | 0.970015i | \(-0.578146\pi\) |
−0.961580 | + | 0.274526i | \(0.911479\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 3.20002 | − | 1.66129i | 0.887525 | − | 0.460759i | ||||
\(14\) | −1.32258 | −0.353474 | ||||||||
\(15\) | 0.866025 | + | 0.500000i | 0.223607 | + | 0.129099i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 2.00000 | + | 3.46410i | 0.485071 | + | 0.840168i | 0.999853 | − | 0.0171533i | \(-0.00546033\pi\) |
−0.514782 | + | 0.857321i | \(0.672127\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 1.98387 | − | 1.14539i | 0.455131 | − | 0.262770i | −0.254864 | − | 0.966977i | \(-0.582031\pi\) |
0.709995 | + | 0.704207i | \(0.248697\pi\) | |||||||
\(20\) | 0.866025 | − | 0.500000i | 0.193649 | − | 0.111803i | ||||
\(21\) | 1.32258i | 0.288611i | ||||||||
\(22\) | 2.30668 | + | 3.99528i | 0.491785 | + | 0.851797i | ||||
\(23\) | 4.33399 | − | 7.50670i | 0.903700 | − | 1.56525i | 0.0810471 | − | 0.996710i | \(-0.474174\pi\) |
0.822653 | − | 0.568544i | \(-0.192493\pi\) | |||||||
\(24\) | 0.866025 | + | 0.500000i | 0.176777 | + | 0.102062i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −3.60194 | − | 0.161290i | −0.706399 | − | 0.0316315i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.14539 | + | 0.661290i | 0.216458 | + | 0.124972i | ||||
\(29\) | 1.01141 | − | 1.75182i | 0.187815 | − | 0.325305i | −0.756707 | − | 0.653755i | \(-0.773193\pi\) |
0.944521 | + | 0.328450i | \(0.106526\pi\) | |||||||
\(30\) | −0.500000 | − | 0.866025i | −0.0912871 | − | 0.158114i | ||||
\(31\) | − | 10.1321i | − | 1.81978i | −0.414853 | − | 0.909888i | \(-0.636167\pi\) | ||
0.414853 | − | 0.909888i | \(-0.363833\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 3.99528 | − | 2.30668i | 0.695489 | − | 0.401541i | ||||
\(34\) | − | 4.00000i | − | 0.685994i | ||||||
\(35\) | −0.661290 | − | 1.14539i | −0.111778 | − | 0.193606i | ||||
\(36\) | 0.500000 | − | 0.866025i | 0.0833333 | − | 0.144338i | ||||
\(37\) | 5.89721 | + | 3.40475i | 0.969495 | + | 0.559738i | 0.899082 | − | 0.437780i | \(-0.144235\pi\) |
0.0704126 | + | 0.997518i | \(0.477568\pi\) | |||||||
\(38\) | −2.29078 | −0.371613 | ||||||||
\(39\) | −0.161290 | + | 3.60194i | −0.0258270 | + | 0.576772i | ||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −4.02283 | − | 2.32258i | −0.628260 | − | 0.362726i | 0.151818 | − | 0.988408i | \(-0.451487\pi\) |
−0.780078 | + | 0.625682i | \(0.784821\pi\) | |||||||
\(42\) | 0.661290 | − | 1.14539i | 0.102039 | − | 0.176737i | ||||
\(43\) | 4.30281 | + | 7.45269i | 0.656173 | + | 1.13652i | 0.981598 | + | 0.190957i | \(0.0611590\pi\) |
−0.325426 | + | 0.945568i | \(0.605508\pi\) | |||||||
\(44\) | − | 4.61335i | − | 0.695489i | ||||||
\(45\) | −0.866025 | + | 0.500000i | −0.129099 | + | 0.0745356i | ||||
\(46\) | −7.50670 | + | 4.33399i | −1.10680 | + | 0.639012i | ||||
\(47\) | − | 9.10926i | − | 1.32872i | −0.747412 | − | 0.664361i | \(-0.768704\pi\) | ||
0.747412 | − | 0.664361i | \(-0.231296\pi\) | |||||||
\(48\) | −0.500000 | − | 0.866025i | −0.0721688 | − | 0.125000i | ||||
\(49\) | −2.62539 | + | 4.54731i | −0.375056 | + | 0.649616i | ||||
\(50\) | 0.866025 | + | 0.500000i | 0.122474 | + | 0.0707107i | ||||
\(51\) | −4.00000 | −0.560112 | ||||||||
\(52\) | 3.03873 | + | 1.94065i | 0.421396 | + | 0.269120i | ||||
\(53\) | 0.826674 | 0.113552 | 0.0567762 | − | 0.998387i | \(-0.481918\pi\) | ||||
0.0567762 | + | 0.998387i | \(0.481918\pi\) | |||||||
\(54\) | −0.866025 | − | 0.500000i | −0.117851 | − | 0.0680414i | ||||
\(55\) | −2.30668 | + | 3.99528i | −0.311032 | + | 0.538724i | ||||
\(56\) | −0.661290 | − | 1.14539i | −0.0883686 | − | 0.153059i | ||||
\(57\) | 2.29078i | 0.303421i | ||||||||
\(58\) | −1.75182 | + | 1.01141i | −0.230025 | + | 0.132805i | ||||
\(59\) | 2.72064 | − | 1.57076i | 0.354197 | − | 0.204496i | −0.312335 | − | 0.949972i | \(-0.601111\pi\) |
0.666532 | + | 0.745476i | \(0.267778\pi\) | |||||||
\(60\) | 1.00000i | 0.129099i | ||||||||
\(61\) | −0.267949 | − | 0.464102i | −0.0343074 | − | 0.0594221i | 0.848362 | − | 0.529417i | \(-0.177589\pi\) |
−0.882669 | + | 0.469995i | \(0.844256\pi\) | |||||||
\(62\) | −5.06604 | + | 8.77464i | −0.643388 | + | 1.11438i | ||||
\(63\) | −1.14539 | − | 0.661290i | −0.144305 | − | 0.0833147i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −1.66129 | − | 3.20002i | −0.206058 | − | 0.396913i | ||||
\(66\) | −4.61335 | −0.567865 | ||||||||
\(67\) | −2.75488 | − | 1.59053i | −0.336562 | − | 0.194314i | 0.322189 | − | 0.946675i | \(-0.395581\pi\) |
−0.658751 | + | 0.752361i | \(0.728915\pi\) | |||||||
\(68\) | −2.00000 | + | 3.46410i | −0.242536 | + | 0.420084i | ||||
\(69\) | 4.33399 | + | 7.50670i | 0.521751 | + | 0.903700i | ||||
\(70\) | 1.32258i | 0.158079i | ||||||||
\(71\) | −9.81724 | + | 5.66799i | −1.16509 | + | 0.672666i | −0.952519 | − | 0.304479i | \(-0.901518\pi\) |
−0.212573 | + | 0.977145i | \(0.568184\pi\) | |||||||
\(72\) | −0.866025 | + | 0.500000i | −0.102062 | + | 0.0589256i | ||||
\(73\) | − | 6.28304i | − | 0.735375i | −0.929949 | − | 0.367687i | \(-0.880150\pi\) | ||
0.929949 | − | 0.367687i | \(-0.119850\pi\) | |||||||
\(74\) | −3.40475 | − | 5.89721i | −0.395795 | − | 0.685536i | ||||
\(75\) | 0.500000 | − | 0.866025i | 0.0577350 | − | 0.100000i | ||||
\(76\) | 1.98387 | + | 1.14539i | 0.227565 | + | 0.131385i | ||||
\(77\) | −6.10153 | −0.695334 | ||||||||
\(78\) | 1.94065 | − | 3.03873i | 0.219736 | − | 0.344068i | ||||
\(79\) | 2.96774 | 0.333897 | 0.166948 | − | 0.985966i | \(-0.446609\pi\) | ||||
0.166948 | + | 0.985966i | \(0.446609\pi\) | |||||||
\(80\) | 0.866025 | + | 0.500000i | 0.0968246 | + | 0.0559017i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 2.32258 | + | 4.02283i | 0.256486 | + | 0.444247i | ||||
\(83\) | 15.8719i | 1.74216i | 0.491138 | + | 0.871082i | \(0.336581\pi\) | ||||
−0.491138 | + | 0.871082i | \(0.663419\pi\) | |||||||
\(84\) | −1.14539 | + | 0.661290i | −0.124972 | + | 0.0721526i | ||||
\(85\) | 3.46410 | − | 2.00000i | 0.375735 | − | 0.216930i | ||||
\(86\) | − | 8.60562i | − | 0.927968i | ||||||
\(87\) | 1.01141 | + | 1.75182i | 0.108435 | + | 0.187815i | ||||
\(88\) | −2.30668 | + | 3.99528i | −0.245893 | + | 0.425899i | ||||
\(89\) | 10.2746 | + | 5.93207i | 1.08911 | + | 0.628798i | 0.933339 | − | 0.358995i | \(-0.116881\pi\) |
0.155771 | + | 0.987793i | \(0.450214\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 2.56667 | − | 4.01896i | 0.269060 | − | 0.421302i | ||||
\(92\) | 8.66799 | 0.903700 | ||||||||
\(93\) | 8.77464 | + | 5.06604i | 0.909888 | + | 0.525324i | ||||
\(94\) | −4.55463 | + | 7.88885i | −0.469774 | + | 0.813673i | ||||
\(95\) | −1.14539 | − | 1.98387i | −0.117514 | − | 0.203541i | ||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | −7.63743 | + | 4.40947i | −0.775463 | + | 0.447714i | −0.834820 | − | 0.550523i | \(-0.814428\pi\) |
0.0593568 | + | 0.998237i | \(0.481095\pi\) | |||||||
\(98\) | 4.54731 | − | 2.62539i | 0.459348 | − | 0.265205i | ||||
\(99\) | 4.61335i | 0.463660i | ||||||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | −3.61335 | + | 6.25851i | −0.359542 | + | 0.622745i | −0.987884 | − | 0.155192i | \(-0.950400\pi\) |
0.628342 | + | 0.777937i | \(0.283734\pi\) | |||||||
\(102\) | 3.46410 | + | 2.00000i | 0.342997 | + | 0.198030i | ||||
\(103\) | −18.4000 | −1.81301 | −0.906505 | − | 0.422196i | \(-0.861260\pi\) | ||||
−0.906505 | + | 0.422196i | \(0.861260\pi\) | |||||||
\(104\) | −1.66129 | − | 3.20002i | −0.162903 | − | 0.313788i | ||||
\(105\) | 1.32258 | 0.129071 | ||||||||
\(106\) | −0.715920 | − | 0.413337i | −0.0695363 | − | 0.0401468i | ||||
\(107\) | −1.53590 | + | 2.66025i | −0.148481 | + | 0.257176i | −0.930666 | − | 0.365869i | \(-0.880772\pi\) |
0.782185 | + | 0.623046i | \(0.214105\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | 13.2267i | 1.26689i | 0.773788 | + | 0.633445i | \(0.218360\pi\) | ||||
−0.773788 | + | 0.633445i | \(0.781640\pi\) | |||||||
\(110\) | 3.99528 | − | 2.30668i | 0.380935 | − | 0.219933i | ||||
\(111\) | −5.89721 | + | 3.40475i | −0.559738 | + | 0.323165i | ||||
\(112\) | 1.32258i | 0.124972i | ||||||||
\(113\) | 4.04322 | + | 7.00306i | 0.380354 | + | 0.658792i | 0.991113 | − | 0.133024i | \(-0.0424689\pi\) |
−0.610759 | + | 0.791817i | \(0.709136\pi\) | |||||||
\(114\) | 1.14539 | − | 1.98387i | 0.107275 | − | 0.185806i | ||||
\(115\) | −7.50670 | − | 4.33399i | −0.700003 | − | 0.404147i | ||||
\(116\) | 2.02283 | 0.187815 | ||||||||
\(117\) | −3.03873 | − | 1.94065i | −0.280931 | − | 0.179413i | ||||
\(118\) | −3.14152 | −0.289201 | ||||||||
\(119\) | 4.58155 | + | 2.64516i | 0.419990 | + | 0.242481i | ||||
\(120\) | 0.500000 | − | 0.866025i | 0.0456435 | − | 0.0790569i | ||||
\(121\) | 5.14152 | + | 8.90538i | 0.467411 | + | 0.809580i | ||||
\(122\) | 0.535898i | 0.0485180i | ||||||||
\(123\) | 4.02283 | − | 2.32258i | 0.362726 | − | 0.209420i | ||||
\(124\) | 8.77464 | − | 5.06604i | 0.787986 | − | 0.454944i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0.661290 | + | 1.14539i | 0.0589124 | + | 0.102039i | ||||
\(127\) | 5.73592 | − | 9.93490i | 0.508980 | − | 0.881580i | −0.490966 | − | 0.871179i | \(-0.663356\pi\) |
0.999946 | − | 0.0104008i | \(-0.00331073\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | −8.60562 | −0.757683 | ||||||||
\(130\) | −0.161290 | + | 3.60194i | −0.0141461 | + | 0.315911i | ||||
\(131\) | −15.9906 | −1.39710 | −0.698551 | − | 0.715560i | \(-0.746172\pi\) | ||||
−0.698551 | + | 0.715560i | \(0.746172\pi\) | |||||||
\(132\) | 3.99528 | + | 2.30668i | 0.347745 | + | 0.200771i | ||||
\(133\) | 1.51487 | − | 2.62383i | 0.131356 | − | 0.227515i | ||||
\(134\) | 1.59053 | + | 2.75488i | 0.137401 | + | 0.237985i | ||||
\(135\) | − | 1.00000i | − | 0.0860663i | ||||||
\(136\) | 3.46410 | − | 2.00000i | 0.297044 | − | 0.171499i | ||||
\(137\) | 13.9168 | − | 8.03486i | 1.18899 | − | 0.686465i | 0.230914 | − | 0.972974i | \(-0.425828\pi\) |
0.958077 | + | 0.286509i | \(0.0924950\pi\) | |||||||
\(138\) | − | 8.66799i | − | 0.737868i | ||||||
\(139\) | −4.66129 | − | 8.07359i | −0.395365 | − | 0.684793i | 0.597782 | − | 0.801658i | \(-0.296049\pi\) |
−0.993148 | + | 0.116865i | \(0.962715\pi\) | |||||||
\(140\) | 0.661290 | − | 1.14539i | 0.0558892 | − | 0.0968029i | ||||
\(141\) | 7.88885 | + | 4.55463i | 0.664361 | + | 0.383569i | ||||
\(142\) | 11.3360 | 0.951294 | ||||||||
\(143\) | −16.6170 | − | 0.744087i | −1.38959 | − | 0.0622237i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −1.75182 | − | 1.01141i | −0.145481 | − | 0.0839933i | ||||
\(146\) | −3.14152 | + | 5.44128i | −0.259994 | + | 0.450323i | ||||
\(147\) | −2.62539 | − | 4.54731i | −0.216539 | − | 0.375056i | ||||
\(148\) | 6.80951i | 0.559738i | ||||||||
\(149\) | 3.53788 | − | 2.04259i | 0.289834 | − | 0.167336i | −0.348033 | − | 0.937482i | \(-0.613150\pi\) |
0.637867 | + | 0.770146i | \(0.279817\pi\) | |||||||
\(150\) | −0.866025 | + | 0.500000i | −0.0707107 | + | 0.0408248i | ||||
\(151\) | − | 19.9811i | − | 1.62604i | −0.582235 | − | 0.813021i | \(-0.697822\pi\) | ||
0.582235 | − | 0.813021i | \(-0.302178\pi\) | |||||||
\(152\) | −1.14539 | − | 1.98387i | −0.0929032 | − | 0.160913i | ||||
\(153\) | 2.00000 | − | 3.46410i | 0.161690 | − | 0.280056i | ||||
\(154\) | 5.28408 | + | 3.05076i | 0.425803 | + | 0.245838i | ||||
\(155\) | −10.1321 | −0.813829 | ||||||||
\(156\) | −3.20002 | + | 1.66129i | −0.256206 | + | 0.133010i | ||||
\(157\) | 7.13379 | 0.569338 | 0.284669 | − | 0.958626i | \(-0.408116\pi\) | ||||
0.284669 | + | 0.958626i | \(0.408116\pi\) | |||||||
\(158\) | −2.57014 | − | 1.48387i | −0.204469 | − | 0.118050i | ||||
\(159\) | −0.413337 | + | 0.715920i | −0.0327797 | + | 0.0567762i | ||||
\(160\) | −0.500000 | − | 0.866025i | −0.0395285 | − | 0.0684653i | ||||
\(161\) | − | 11.4641i | − | 0.903498i | ||||||
\(162\) | 0.866025 | − | 0.500000i | 0.0680414 | − | 0.0392837i | ||||
\(163\) | −8.56906 | + | 4.94735i | −0.671180 | + | 0.387506i | −0.796524 | − | 0.604607i | \(-0.793330\pi\) |
0.125343 | + | 0.992113i | \(0.459997\pi\) | |||||||
\(164\) | − | 4.64516i | − | 0.362726i | ||||||
\(165\) | −2.30668 | − | 3.99528i | −0.179575 | − | 0.311032i | ||||
\(166\) | 7.93593 | − | 13.7454i | 0.615948 | − | 1.06685i | ||||
\(167\) | 20.8171 | + | 12.0187i | 1.61087 | + | 0.930037i | 0.989168 | + | 0.146785i | \(0.0468925\pi\) |
0.621704 | + | 0.783253i | \(0.286441\pi\) | |||||||
\(168\) | 1.32258 | 0.102039 | ||||||||
\(169\) | 7.48023 | − | 10.6323i | 0.575402 | − | 0.817870i | ||||
\(170\) | −4.00000 | −0.306786 | ||||||||
\(171\) | −1.98387 | − | 1.14539i | −0.151710 | − | 0.0875900i | ||||
\(172\) | −4.30281 | + | 7.45269i | −0.328086 | + | 0.568262i | ||||
\(173\) | 1.26408 | + | 2.18946i | 0.0961065 | + | 0.166461i | 0.910070 | − | 0.414455i | \(-0.136028\pi\) |
−0.813963 | + | 0.580916i | \(0.802694\pi\) | |||||||
\(174\) | − | 2.02283i | − | 0.153350i | ||||||
\(175\) | −1.14539 | + | 0.661290i | −0.0865832 | + | 0.0499888i | ||||
\(176\) | 3.99528 | − | 2.30668i | 0.301156 | − | 0.173872i | ||||
\(177\) | 3.14152i | 0.236131i | ||||||||
\(178\) | −5.93207 | − | 10.2746i | −0.444627 | − | 0.770117i | ||||
\(179\) | −3.13784 | + | 5.43490i | −0.234533 | + | 0.406223i | −0.959137 | − | 0.282942i | \(-0.908689\pi\) |
0.724604 | + | 0.689166i | \(0.242023\pi\) | |||||||
\(180\) | −0.866025 | − | 0.500000i | −0.0645497 | − | 0.0372678i | ||||
\(181\) | −12.2830 | −0.912991 | −0.456496 | − | 0.889726i | \(-0.650896\pi\) | ||||
−0.456496 | + | 0.889726i | \(0.650896\pi\) | |||||||
\(182\) | −4.23228 | + | 2.19719i | −0.313717 | + | 0.162866i | ||||
\(183\) | 0.535898 | 0.0396147 | ||||||||
\(184\) | −7.50670 | − | 4.33399i | −0.553401 | − | 0.319506i | ||||
\(185\) | 3.40475 | − | 5.89721i | 0.250322 | − | 0.433571i | ||||
\(186\) | −5.06604 | − | 8.77464i | −0.371460 | − | 0.643388i | ||||
\(187\) | − | 18.4534i | − | 1.34945i | ||||||
\(188\) | 7.88885 | − | 4.55463i | 0.575354 | − | 0.332181i | ||||
\(189\) | 1.14539 | − | 0.661290i | 0.0833147 | − | 0.0481018i | ||||
\(190\) | 2.29078i | 0.166190i | ||||||||
\(191\) | 4.87357 | + | 8.44128i | 0.352639 | + | 0.610789i | 0.986711 | − | 0.162485i | \(-0.0519509\pi\) |
−0.634072 | + | 0.773274i | \(0.718618\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | −11.9188 | − | 6.88130i | −0.857932 | − | 0.495327i | 0.00538741 | − | 0.999985i | \(-0.498285\pi\) |
−0.863319 | + | 0.504658i | \(0.831618\pi\) | |||||||
\(194\) | 8.81894 | 0.633163 | ||||||||
\(195\) | 3.60194 | + | 0.161290i | 0.257940 | + | 0.0115502i | ||||
\(196\) | −5.25078 | −0.375056 | ||||||||
\(197\) | −8.78282 | − | 5.07076i | −0.625750 | − | 0.361277i | 0.153354 | − | 0.988171i | \(-0.450992\pi\) |
−0.779104 | + | 0.626894i | \(0.784326\pi\) | |||||||
\(198\) | 2.30668 | − | 3.99528i | 0.163928 | − | 0.283932i | ||||
\(199\) | 4.78668 | + | 8.29078i | 0.339319 | + | 0.587717i | 0.984305 | − | 0.176477i | \(-0.0564701\pi\) |
−0.644986 | + | 0.764194i | \(0.723137\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 2.75488 | − | 1.59053i | 0.194314 | − | 0.112187i | ||||
\(202\) | 6.25851 | − | 3.61335i | 0.440348 | − | 0.254235i | ||||
\(203\) | − | 2.67535i | − | 0.187773i | ||||||
\(204\) | −2.00000 | − | 3.46410i | −0.140028 | − | 0.242536i | ||||
\(205\) | −2.32258 | + | 4.02283i | −0.162216 | + | 0.280966i | ||||
\(206\) | 15.9349 | + | 9.20002i | 1.11024 | + | 0.640996i | ||||
\(207\) | −8.66799 | −0.602467 | ||||||||
\(208\) | −0.161290 | + | 3.60194i | −0.0111834 | + | 0.249750i | ||||
\(209\) | −10.5682 | −0.731015 | ||||||||
\(210\) | −1.14539 | − | 0.661290i | −0.0790393 | − | 0.0456333i | ||||
\(211\) | 0.542594 | − | 0.939800i | 0.0373537 | − | 0.0646985i | −0.846744 | − | 0.532000i | \(-0.821441\pi\) |
0.884098 | + | 0.467302i | \(0.154774\pi\) | |||||||
\(212\) | 0.413337 | + | 0.715920i | 0.0283881 | + | 0.0491696i | ||||
\(213\) | − | 11.3360i | − | 0.776728i | ||||||
\(214\) | 2.66025 | − | 1.53590i | 0.181851 | − | 0.104992i | ||||
\(215\) | 7.45269 | − | 4.30281i | 0.508269 | − | 0.293449i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −6.70025 | − | 11.6052i | −0.454842 | − | 0.787810i | ||||
\(218\) | 6.61335 | − | 11.4547i | 0.447913 | − | 0.775808i | ||||
\(219\) | 5.44128 | + | 3.14152i | 0.367687 | + | 0.212284i | ||||
\(220\) | −4.61335 | −0.311032 | ||||||||
\(221\) | 12.1549 | + | 7.76261i | 0.817628 | + | 0.522170i | ||||
\(222\) | 6.80951 | 0.457024 | ||||||||
\(223\) | 21.6001 | + | 12.4708i | 1.44645 | + | 0.835106i | 0.998268 | − | 0.0588375i | \(-0.0187394\pi\) |
0.448179 | + | 0.893944i | \(0.352073\pi\) | |||||||
\(224\) | 0.661290 | − | 1.14539i | 0.0441843 | − | 0.0765294i | ||||
\(225\) | 0.500000 | + | 0.866025i | 0.0333333 | + | 0.0577350i | ||||
\(226\) | − | 8.08643i | − | 0.537902i | ||||||
\(227\) | −16.7321 | + | 9.66025i | −1.11055 | + | 0.641174i | −0.938971 | − | 0.343998i | \(-0.888219\pi\) |
−0.171575 | + | 0.985171i | \(0.554885\pi\) | |||||||
\(228\) | −1.98387 | + | 1.14539i | −0.131385 | + | 0.0758551i | ||||
\(229\) | 4.15491i | 0.274564i | 0.990532 | + | 0.137282i | \(0.0438367\pi\) | ||||
−0.990532 | + | 0.137282i | \(0.956163\pi\) | |||||||
\(230\) | 4.33399 | + | 7.50670i | 0.285775 | + | 0.494977i | ||||
\(231\) | 3.05076 | − | 5.28408i | 0.200726 | − | 0.347667i | ||||
\(232\) | −1.75182 | − | 1.01141i | −0.115013 | − | 0.0664025i | ||||
\(233\) | 16.9665 | 1.11151 | 0.555756 | − | 0.831346i | \(-0.312429\pi\) | ||||
0.555756 | + | 0.831346i | \(0.312429\pi\) | |||||||
\(234\) | 1.66129 | + | 3.20002i | 0.108602 | + | 0.209192i | ||||
\(235\) | −9.10926 | −0.594223 | ||||||||
\(236\) | 2.72064 | + | 1.57076i | 0.177098 | + | 0.102248i | ||||
\(237\) | −1.48387 | + | 2.57014i | −0.0963877 | + | 0.166948i | ||||
\(238\) | −2.64516 | − | 4.58155i | −0.171460 | − | 0.296978i | ||||
\(239\) | − | 6.34416i | − | 0.410370i | −0.978723 | − | 0.205185i | \(-0.934220\pi\) | ||
0.978723 | − | 0.205185i | \(-0.0657795\pi\) | |||||||
\(240\) | −0.866025 | + | 0.500000i | −0.0559017 | + | 0.0322749i | ||||
\(241\) | 20.9452 | − | 12.0927i | 1.34920 | − | 0.778962i | 0.361065 | − | 0.932541i | \(-0.382413\pi\) |
0.988136 | + | 0.153579i | \(0.0490800\pi\) | |||||||
\(242\) | − | 10.2830i | − | 0.661019i | ||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 0.267949 | − | 0.464102i | 0.0171537 | − | 0.0297111i | ||||
\(245\) | 4.54731 | + | 2.62539i | 0.290517 | + | 0.167730i | ||||
\(246\) | −4.64516 | −0.296165 | ||||||||
\(247\) | 4.44560 | − | 6.96104i | 0.282867 | − | 0.442921i | ||||
\(248\) | −10.1321 | −0.643388 | ||||||||
\(249\) | −13.7454 | − | 7.93593i | −0.871082 | − | 0.502919i | ||||
\(250\) | 0.500000 | − | 0.866025i | 0.0316228 | − | 0.0547723i | ||||
\(251\) | 4.41249 | + | 7.64265i | 0.278514 | + | 0.482400i | 0.971016 | − | 0.239016i | \(-0.0768249\pi\) |
−0.692502 | + | 0.721416i | \(0.743492\pi\) | |||||||
\(252\) | − | 1.32258i | − | 0.0833147i | ||||||
\(253\) | −34.6311 | + | 19.9942i | −2.17724 | + | 1.25703i | ||||
\(254\) | −9.93490 | + | 5.73592i | −0.623371 | + | 0.359903i | ||||
\(255\) | 4.00000i | 0.250490i | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 4.19247 | − | 7.26157i | 0.261519 | − | 0.452964i | −0.705127 | − | 0.709081i | \(-0.749110\pi\) |
0.966646 | + | 0.256117i | \(0.0824432\pi\) | |||||||
\(258\) | 7.45269 | + | 4.30281i | 0.463984 | + | 0.267881i | ||||
\(259\) | 9.00612 | 0.559613 | ||||||||
\(260\) | 1.94065 | − | 3.03873i | 0.120354 | − | 0.188454i | ||||
\(261\) | −2.02283 | −0.125210 | ||||||||
\(262\) | 13.8482 | + | 7.99528i | 0.855547 | + | 0.493950i | ||||
\(263\) | −0.960648 | + | 1.66389i | −0.0592361 | + | 0.102600i | −0.894123 | − | 0.447822i | \(-0.852200\pi\) |
0.834887 | + | 0.550422i | \(0.185533\pi\) | |||||||
\(264\) | −2.30668 | − | 3.99528i | −0.141966 | − | 0.245893i | ||||
\(265\) | − | 0.826674i | − | 0.0507822i | ||||||
\(266\) | −2.62383 | + | 1.51487i | −0.160877 | + | 0.0928824i | ||||
\(267\) | −10.2746 | + | 5.93207i | −0.628798 | + | 0.363037i | ||||
\(268\) | − | 3.18106i | − | 0.194314i | ||||||
\(269\) | 16.1549 | + | 27.9811i | 0.984982 | + | 1.70604i | 0.642014 | + | 0.766693i | \(0.278099\pi\) |
0.342968 | + | 0.939347i | \(0.388568\pi\) | |||||||
\(270\) | −0.500000 | + | 0.866025i | −0.0304290 | + | 0.0527046i | ||||
\(271\) | 20.3105 | + | 11.7263i | 1.23378 | + | 0.712322i | 0.967815 | − | 0.251662i | \(-0.0809770\pi\) |
0.265962 | + | 0.963983i | \(0.414310\pi\) | |||||||
\(272\) | −4.00000 | −0.242536 | ||||||||
\(273\) | 2.19719 | + | 4.23228i | 0.132980 | + | 0.256149i | ||||
\(274\) | −16.0697 | −0.970808 | ||||||||
\(275\) | 3.99528 | + | 2.30668i | 0.240925 | + | 0.139098i | ||||
\(276\) | −4.33399 | + | 7.50670i | −0.260876 | + | 0.451850i | ||||
\(277\) | −4.50283 | − | 7.79913i | −0.270549 | − | 0.468604i | 0.698454 | − | 0.715655i | \(-0.253872\pi\) |
−0.969002 | + | 0.247051i | \(0.920538\pi\) | |||||||
\(278\) | 9.32258i | 0.559131i | ||||||||
\(279\) | −8.77464 | + | 5.06604i | −0.525324 | + | 0.303296i | ||||
\(280\) | −1.14539 | + | 0.661290i | −0.0684500 | + | 0.0395196i | ||||
\(281\) | 1.71696i | 0.102425i | 0.998688 | + | 0.0512125i | \(0.0163086\pi\) | ||||
−0.998688 | + | 0.0512125i | \(0.983691\pi\) | |||||||
\(282\) | −4.55463 | − | 7.88885i | −0.271224 | − | 0.469774i | ||||
\(283\) | −0.774645 | + | 1.34172i | −0.0460479 | + | 0.0797572i | −0.888131 | − | 0.459591i | \(-0.847996\pi\) |
0.842083 | + | 0.539348i | \(0.181329\pi\) | |||||||
\(284\) | −9.81724 | − | 5.66799i | −0.582546 | − | 0.336333i | ||||
\(285\) | 2.29078 | 0.135694 | ||||||||
\(286\) | 14.0187 | + | 8.95292i | 0.828945 | + | 0.529397i | ||||
\(287\) | −6.14359 | −0.362645 | ||||||||
\(288\) | −0.866025 | − | 0.500000i | −0.0510310 | − | 0.0294628i | ||||
\(289\) | 0.500000 | − | 0.866025i | 0.0294118 | − | 0.0509427i | ||||
\(290\) | 1.01141 | + | 1.75182i | 0.0593922 | + | 0.102870i | ||||
\(291\) | − | 8.81894i | − | 0.516976i | ||||||
\(292\) | 5.44128 | − | 3.14152i | 0.318427 | − | 0.183844i | ||||
\(293\) | 26.3321 | − | 15.2028i | 1.53834 | − | 0.888160i | 0.539402 | − | 0.842049i | \(-0.318650\pi\) |
0.998936 | − | 0.0461113i | \(-0.0146829\pi\) | |||||||
\(294\) | 5.25078i | 0.306232i | ||||||||
\(295\) | −1.57076 | − | 2.72064i | −0.0914532 | − | 0.158402i | ||||
\(296\) | 3.40475 | − | 5.89721i | 0.197897 | − | 0.342768i | ||||
\(297\) | −3.99528 | − | 2.30668i | −0.231830 | − | 0.133847i | ||||
\(298\) | −4.08519 | −0.236649 | ||||||||
\(299\) | 1.39806 | − | 31.2216i | 0.0808518 | − | 1.80559i | ||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 9.85677 | + | 5.69081i | 0.568135 | + | 0.328013i | ||||
\(302\) | −9.99057 | + | 17.3042i | −0.574892 | + | 0.995743i | ||||
\(303\) | −3.61335 | − | 6.25851i | −0.207582 | − | 0.359542i | ||||
\(304\) | 2.29078i | 0.131385i | ||||||||
\(305\) | −0.464102 | + | 0.267949i | −0.0265744 | + | 0.0153427i | ||||
\(306\) | −3.46410 | + | 2.00000i | −0.198030 | + | 0.114332i | ||||
\(307\) | 9.82622i | 0.560812i | 0.959882 | + | 0.280406i | \(0.0904691\pi\) | ||||
−0.959882 | + | 0.280406i | \(0.909531\pi\) | |||||||
\(308\) | −3.05076 | − | 5.28408i | −0.173833 | − | 0.301088i | ||||
\(309\) | 9.20002 | − | 15.9349i | 0.523371 | − | 0.906505i | ||||
\(310\) | 8.77464 | + | 5.06604i | 0.498366 | + | 0.287732i | ||||
\(311\) | −3.40049 | −0.192824 | −0.0964121 | − | 0.995342i | \(-0.530737\pi\) | ||||
−0.0964121 | + | 0.995342i | \(0.530737\pi\) | |||||||
\(312\) | 3.60194 | + | 0.161290i | 0.203920 | + | 0.00913124i | ||||
\(313\) | −16.2340 | −0.917599 | −0.458800 | − | 0.888540i | \(-0.651720\pi\) | ||||
−0.458800 | + | 0.888540i | \(0.651720\pi\) | |||||||
\(314\) | −6.17804 | − | 3.56690i | −0.348647 | − | 0.201292i | ||||
\(315\) | −0.661290 | + | 1.14539i | −0.0372595 | + | 0.0645353i | ||||
\(316\) | 1.48387 | + | 2.57014i | 0.0834742 | + | 0.144582i | ||||
\(317\) | 23.5231i | 1.32119i | 0.750742 | + | 0.660596i | \(0.229696\pi\) | ||||
−0.750742 | + | 0.660596i | \(0.770304\pi\) | |||||||
\(318\) | 0.715920 | − | 0.413337i | 0.0401468 | − | 0.0231788i | ||||
\(319\) | −8.08176 | + | 4.66601i | −0.452492 | + | 0.261246i | ||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | −1.53590 | − | 2.66025i | −0.0857255 | − | 0.148481i | ||||
\(322\) | −5.73205 | + | 9.92820i | −0.319435 | + | 0.553277i | ||||
\(323\) | 7.93548 | + | 4.58155i | 0.441542 | + | 0.254924i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −3.20002 | + | 1.66129i | −0.177505 | + | 0.0921518i | ||||
\(326\) | 9.89470 | 0.548016 | ||||||||
\(327\) | −11.4547 | − | 6.61335i | −0.633445 | − | 0.365719i | ||||
\(328\) | −2.32258 | + | 4.02283i | −0.128243 | + | 0.222123i | ||||
\(329\) | −6.02386 | − | 10.4336i | −0.332106 | − | 0.575225i | ||||
\(330\) | 4.61335i | 0.253957i | ||||||||
\(331\) | 15.6667 | − | 9.04520i | 0.861122 | − | 0.497169i | −0.00326597 | − | 0.999995i | \(-0.501040\pi\) |
0.864388 | + | 0.502826i | \(0.167706\pi\) | |||||||
\(332\) | −13.7454 | + | 7.93593i | −0.754379 | + | 0.435541i | ||||
\(333\) | − | 6.80951i | − | 0.373159i | ||||||
\(334\) | −12.0187 | − | 20.8171i | −0.657636 | − | 1.13906i | ||||
\(335\) | −1.59053 | + | 2.75488i | −0.0868999 | + | 0.150515i | ||||
\(336\) | −1.14539 | − | 0.661290i | −0.0624860 | − | 0.0360763i | ||||
\(337\) | −5.69900 | −0.310444 | −0.155222 | − | 0.987880i | \(-0.549609\pi\) | ||||
−0.155222 | + | 0.987880i | \(0.549609\pi\) | |||||||
\(338\) | −11.7942 | + | 5.46774i | −0.641521 | + | 0.297406i | ||||
\(339\) | −8.08643 | −0.439195 | ||||||||
\(340\) | 3.46410 | + | 2.00000i | 0.187867 | + | 0.108465i | ||||
\(341\) | −23.3715 | + | 40.4806i | −1.26564 | + | 2.19214i | ||||
\(342\) | 1.14539 | + | 1.98387i | 0.0619355 | + | 0.107275i | ||||
\(343\) | 16.2026i | 0.874860i | ||||||||
\(344\) | 7.45269 | − | 4.30281i | 0.401822 | − | 0.231992i | ||||
\(345\) | 7.50670 | − | 4.33399i | 0.404147 | − | 0.233334i | ||||
\(346\) | − | 2.52817i | − | 0.135915i | ||||||
\(347\) | 7.87357 | + | 13.6374i | 0.422676 | + | 0.732095i | 0.996200 | − | 0.0870928i | \(-0.0277577\pi\) |
−0.573525 | + | 0.819188i | \(0.694424\pi\) | |||||||
\(348\) | −1.01141 | + | 1.75182i | −0.0542174 | + | 0.0939073i | ||||
\(349\) | 13.2679 | + | 7.66025i | 0.710217 | + | 0.410044i | 0.811141 | − | 0.584850i | \(-0.198847\pi\) |
−0.100924 | + | 0.994894i | \(0.532180\pi\) | |||||||
\(350\) | 1.32258 | 0.0706949 | ||||||||
\(351\) | 3.20002 | − | 1.66129i | 0.170804 | − | 0.0886731i | ||||
\(352\) | −4.61335 | −0.245893 | ||||||||
\(353\) | 1.03917 | + | 0.599964i | 0.0553093 | + | 0.0319328i | 0.527400 | − | 0.849617i | \(-0.323167\pi\) |
−0.472090 | + | 0.881550i | \(0.656500\pi\) | |||||||
\(354\) | 1.57076 | − | 2.72064i | 0.0834850 | − | 0.144600i | ||||
\(355\) | 5.66799 | + | 9.81724i | 0.300825 | + | 0.521045i | ||||
\(356\) | 11.8641i | 0.628798i | ||||||||
\(357\) | −4.58155 | + | 2.64516i | −0.242481 | + | 0.139997i | ||||
\(358\) | 5.43490 | − | 3.13784i | 0.287243 | − | 0.165840i | ||||
\(359\) | 16.2830i | 0.859386i | 0.902975 | + | 0.429693i | \(0.141378\pi\) | ||||
−0.902975 | + | 0.429693i | \(0.858622\pi\) | |||||||
\(360\) | 0.500000 | + | 0.866025i | 0.0263523 | + | 0.0456435i | ||||
\(361\) | −6.87617 | + | 11.9099i | −0.361904 | + | 0.626836i | ||||
\(362\) | 10.6374 | + | 6.14152i | 0.559091 | + | 0.322791i | ||||
\(363\) | −10.2830 | −0.539720 | ||||||||
\(364\) | 4.76386 | + | 0.213319i | 0.249694 | + | 0.0111809i | ||||
\(365\) | −6.28304 | −0.328870 | ||||||||
\(366\) | −0.464102 | − | 0.267949i | −0.0242590 | − | 0.0140059i | ||||
\(367\) | 9.81724 | − | 17.0040i | 0.512456 | − | 0.887599i | −0.487440 | − | 0.873156i | \(-0.662069\pi\) |
0.999896 | − | 0.0144428i | \(-0.00459745\pi\) | |||||||
\(368\) | 4.33399 | + | 7.50670i | 0.225925 | + | 0.391314i | ||||
\(369\) | 4.64516i | 0.241817i | ||||||||
\(370\) | −5.89721 | + | 3.40475i | −0.306581 | + | 0.177005i | ||||
\(371\) | 0.946862 | − | 0.546671i | 0.0491586 | − | 0.0283817i | ||||
\(372\) | 10.1321i | 0.525324i | ||||||||
\(373\) | 1.27874 | + | 2.21484i | 0.0662106 | + | 0.114680i | 0.897230 | − | 0.441563i | \(-0.145576\pi\) |
−0.831020 | + | 0.556243i | \(0.812242\pi\) | |||||||
\(374\) | −9.22671 | + | 15.9811i | −0.477102 | + | 0.826365i | ||||
\(375\) | −0.866025 | − | 0.500000i | −0.0447214 | − | 0.0258199i | ||||
\(376\) | −9.10926 | −0.469774 | ||||||||
\(377\) | 0.326261 | − | 7.28610i | 0.0168033 | − | 0.375253i | ||||
\(378\) | −1.32258 | −0.0680262 | ||||||||
\(379\) | −13.0846 | − | 7.55440i | −0.672111 | − | 0.388044i | 0.124765 | − | 0.992186i | \(-0.460182\pi\) |
−0.796876 | + | 0.604143i | \(0.793516\pi\) | |||||||
\(380\) | 1.14539 | − | 1.98387i | 0.0587571 | − | 0.101770i | ||||
\(381\) | 5.73592 | + | 9.93490i | 0.293860 | + | 0.508980i | ||||
\(382\) | − | 9.74715i | − | 0.498707i | ||||||
\(383\) | −16.2210 | + | 9.36517i | −0.828852 | + | 0.478538i | −0.853459 | − | 0.521159i | \(-0.825500\pi\) |
0.0246073 | + | 0.999697i | \(0.492166\pi\) | |||||||
\(384\) | −0.866025 | + | 0.500000i | −0.0441942 | + | 0.0255155i | ||||
\(385\) | 6.10153i | 0.310963i | ||||||||
\(386\) | 6.88130 | + | 11.9188i | 0.350249 | + | 0.606649i | ||||
\(387\) | 4.30281 | − | 7.45269i | 0.218724 | − | 0.378841i | ||||
\(388\) | −7.63743 | − | 4.40947i | −0.387732 | − | 0.223857i | ||||
\(389\) | 6.96899 | 0.353342 | 0.176671 | − | 0.984270i | \(-0.443467\pi\) | ||||
0.176671 | + | 0.984270i | \(0.443467\pi\) | |||||||
\(390\) | −3.03873 | − | 1.94065i | −0.153872 | − | 0.0982687i | ||||
\(391\) | 34.6719 | 1.75344 | ||||||||
\(392\) | 4.54731 | + | 2.62539i | 0.229674 | + | 0.132602i | ||||
\(393\) | 7.99528 | − | 13.8482i | 0.403309 | − | 0.698551i | ||||
\(394\) | 5.07076 | + | 8.78282i | 0.255461 | + | 0.442472i | ||||
\(395\) | − | 2.96774i | − | 0.149323i | ||||||
\(396\) | −3.99528 | + | 2.30668i | −0.200771 | + | 0.115915i | ||||
\(397\) | −16.0839 | + | 9.28606i | −0.807229 | + | 0.466054i | −0.845993 | − | 0.533195i | \(-0.820991\pi\) |
0.0387637 | + | 0.999248i | \(0.487658\pi\) | |||||||
\(398\) | − | 9.57336i | − | 0.479869i | ||||||
\(399\) | 1.51487 | + | 2.62383i | 0.0758382 | + | 0.131356i | ||||
\(400\) | 0.500000 | − | 0.866025i | 0.0250000 | − | 0.0433013i | ||||
\(401\) | −25.7126 | − | 14.8452i | −1.28403 | − | 0.741333i | −0.306444 | − | 0.951889i | \(-0.599139\pi\) |
−0.977582 | + | 0.210556i | \(0.932473\pi\) | |||||||
\(402\) | −3.18106 | −0.158657 | ||||||||
\(403\) | −16.8323 | − | 32.4229i | −0.838478 | − | 1.61510i | ||||
\(404\) | −7.22671 | −0.359542 | ||||||||
\(405\) | 0.866025 | + | 0.500000i | 0.0430331 | + | 0.0248452i | ||||
\(406\) | −1.33767 | + | 2.31692i | −0.0663877 | + | 0.114987i | ||||
\(407\) | −15.7073 | − | 27.2059i | −0.778584 | − | 1.34855i | ||||
\(408\) | 4.00000i | 0.198030i | ||||||||
\(409\) | −21.0752 | + | 12.1678i | −1.04210 | + | 0.601657i | −0.920427 | − | 0.390913i | \(-0.872159\pi\) |
−0.121673 | + | 0.992570i | \(0.538826\pi\) | |||||||
\(410\) | 4.02283 | − | 2.32258i | 0.198673 | − | 0.114704i | ||||
\(411\) | 16.0697i | 0.792661i | ||||||||
\(412\) | −9.20002 | − | 15.9349i | −0.453252 | − | 0.785056i | ||||
\(413\) | 2.07746 | − | 3.59826i | 0.102225 | − | 0.177059i | ||||
\(414\) | 7.50670 | + | 4.33399i | 0.368934 | + | 0.213004i | ||||
\(415\) | 15.8719 | 0.779119 | ||||||||
\(416\) | 1.94065 | − | 3.03873i | 0.0951483 | − | 0.148986i | ||||
\(417\) | 9.32258 | 0.456529 | ||||||||
\(418\) | 9.15229 | + | 5.28408i | 0.447653 | + | 0.258453i | ||||
\(419\) | 1.44128 | − | 2.49636i | 0.0704109 | − | 0.121955i | −0.828671 | − | 0.559737i | \(-0.810902\pi\) |
0.899081 | + | 0.437781i | \(0.144236\pi\) | |||||||
\(420\) | 0.661290 | + | 1.14539i | 0.0322676 | + | 0.0558892i | ||||
\(421\) | − | 4.94707i | − | 0.241106i | −0.992707 | − | 0.120553i | \(-0.961533\pi\) | ||
0.992707 | − | 0.120553i | \(-0.0384667\pi\) | |||||||
\(422\) | −0.939800 | + | 0.542594i | −0.0457488 | + | 0.0264131i | ||||
\(423\) | −7.88885 | + | 4.55463i | −0.383569 | + | 0.221454i | ||||
\(424\) | − | 0.826674i | − | 0.0401468i | ||||||
\(425\) | −2.00000 | − | 3.46410i | −0.0970143 | − | 0.168034i | ||||
\(426\) | −5.66799 | + | 9.81724i | −0.274615 | + | 0.475647i | ||||
\(427\) | −0.613811 | − | 0.354384i | −0.0297044 | − | 0.0171499i | ||||
\(428\) | −3.07180 | −0.148481 | ||||||||
\(429\) | 8.95292 | − | 14.0187i | 0.432251 | − | 0.676831i | ||||
\(430\) | −8.60562 | −0.415000 | ||||||||
\(431\) | −15.3829 | − | 8.88130i | −0.740967 | − | 0.427797i | 0.0814539 | − | 0.996677i | \(-0.474044\pi\) |
−0.822421 | + | 0.568880i | \(0.807377\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | 17.9188 | + | 31.0362i | 0.861121 | + | 1.49151i | 0.870848 | + | 0.491553i | \(0.163570\pi\) |
−0.00972676 | + | 0.999953i | \(0.503096\pi\) | |||||||
\(434\) | 13.4005i | 0.643244i | ||||||||
\(435\) | 1.75182 | − | 1.01141i | 0.0839933 | − | 0.0484935i | ||||
\(436\) | −11.4547 | + | 6.61335i | −0.548579 | + | 0.316722i | ||||
\(437\) | − | 19.8564i | − | 0.949861i | ||||||
\(438\) | −3.14152 | − | 5.44128i | −0.150108 | − | 0.259994i | ||||
\(439\) | 5.04520 | − | 8.73854i | 0.240794 | − | 0.417068i | −0.720147 | − | 0.693822i | \(-0.755925\pi\) |
0.960941 | + | 0.276754i | \(0.0892588\pi\) | |||||||
\(440\) | 3.99528 | + | 2.30668i | 0.190468 | + | 0.109967i | ||||
\(441\) | 5.25078 | 0.250037 | ||||||||
\(442\) | −6.64516 | − | 12.8001i | −0.316078 | − | 0.608837i | ||||
\(443\) | 13.6981 | 0.650816 | 0.325408 | − | 0.945574i | \(-0.394498\pi\) | ||||
0.325408 | + | 0.945574i | \(0.394498\pi\) | |||||||
\(444\) | −5.89721 | − | 3.40475i | −0.279869 | − | 0.161582i | ||||
\(445\) | 5.93207 | − | 10.2746i | 0.281207 | − | 0.487065i | ||||
\(446\) | −12.4708 | − | 21.6001i | −0.590509 | − | 1.02279i | ||||
\(447\) | 4.08519i | 0.193223i | ||||||||
\(448\) | −1.14539 | + | 0.661290i | −0.0541145 | + | 0.0312430i | ||||
\(449\) | 13.2613 | − | 7.65639i | 0.625837 | − | 0.361327i | −0.153301 | − | 0.988180i | \(-0.548990\pi\) |
0.779138 | + | 0.626852i | \(0.215657\pi\) | |||||||
\(450\) | − | 1.00000i | − | 0.0471405i | ||||||
\(451\) | 10.7149 | + | 18.5587i | 0.504544 | + | 0.873896i | ||||
\(452\) | −4.04322 | + | 7.00306i | −0.190177 | + | 0.329396i | ||||
\(453\) | 17.3042 | + | 9.99057i | 0.813021 | + | 0.469398i | ||||
\(454\) | 19.3205 | 0.906756 | ||||||||
\(455\) | −4.01896 | − | 2.56667i | −0.188412 | − | 0.120327i | ||||
\(456\) | 2.29078 | 0.107275 | ||||||||
\(457\) | −13.4714 | − | 7.77770i | −0.630164 | − | 0.363826i | 0.150651 | − | 0.988587i | \(-0.451863\pi\) |
−0.780816 | + | 0.624761i | \(0.785196\pi\) | |||||||
\(458\) | 2.07746 | − | 3.59826i | 0.0970732 | − | 0.168136i | ||||
\(459\) | 2.00000 | + | 3.46410i | 0.0933520 | + | 0.161690i | ||||
\(460\) | − | 8.66799i | − | 0.404147i | ||||||
\(461\) | 13.5473 | − | 7.82154i | 0.630961 | − | 0.364286i | −0.150163 | − | 0.988661i | \(-0.547980\pi\) |
0.781124 | + | 0.624376i | \(0.214647\pi\) | |||||||
\(462\) | −5.28408 | + | 3.05076i | −0.245838 | + | 0.141934i | ||||
\(463\) | 13.7170i | 0.637481i | 0.947842 | + | 0.318741i | \(0.103260\pi\) | ||||
−0.947842 | + | 0.318741i | \(0.896740\pi\) | |||||||
\(464\) | 1.01141 | + | 1.75182i | 0.0469537 | + | 0.0813261i | ||||
\(465\) | 5.06604 | − | 8.77464i | 0.234932 | − | 0.406914i | ||||
\(466\) | −14.6934 | − | 8.48325i | −0.680659 | − | 0.392979i | ||||
\(467\) | −0.943666 | −0.0436677 | −0.0218338 | − | 0.999762i | \(-0.506950\pi\) | ||||
−0.0218338 | + | 0.999762i | \(0.506950\pi\) | |||||||
\(468\) | 0.161290 | − | 3.60194i | 0.00745563 | − | 0.166500i | ||||
\(469\) | −4.20720 | −0.194271 | ||||||||
\(470\) | 7.88885 | + | 4.55463i | 0.363886 | + | 0.210089i | ||||
\(471\) | −3.56690 | + | 6.17804i | −0.164354 | + | 0.284669i | ||||
\(472\) | −1.57076 | − | 2.72064i | −0.0723001 | − | 0.125228i | ||||
\(473\) | − | 39.7008i | − | 1.82544i | ||||||
\(474\) | 2.57014 | − | 1.48387i | 0.118050 | − | 0.0681564i | ||||
\(475\) | −1.98387 | + | 1.14539i | −0.0910262 | + | 0.0525540i | ||||
\(476\) | 5.29032i | 0.242481i | ||||||||
\(477\) | −0.413337 | − | 0.715920i | −0.0189254 | − | 0.0327797i | ||||
\(478\) | −3.17208 | + | 5.49420i | −0.145088 | + | 0.251299i | ||||
\(479\) | −9.61460 | − | 5.55099i | −0.439302 | − | 0.253631i | 0.263999 | − | 0.964523i | \(-0.414958\pi\) |
−0.703302 | + | 0.710892i | \(0.748292\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 24.5275 | + | 1.09830i | 1.11836 | + | 0.0500784i | ||||
\(482\) | −24.1855 | −1.10162 | ||||||||
\(483\) | 9.92820 | + | 5.73205i | 0.451749 | + | 0.260817i | ||||
\(484\) | −5.14152 | + | 8.90538i | −0.233706 | + | 0.404790i | ||||
\(485\) | 4.40947 | + | 7.63743i | 0.200224 | + | 0.346798i | ||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | −28.5283 | + | 16.4708i | −1.29274 | + | 0.746363i | −0.979139 | − | 0.203192i | \(-0.934868\pi\) |
−0.313600 | + | 0.949555i | \(0.601535\pi\) | |||||||
\(488\) | −0.464102 | + | 0.267949i | −0.0210089 | + | 0.0121295i | ||||
\(489\) | − | 9.89470i | − | 0.447454i | ||||||
\(490\) | −2.62539 | − | 4.54731i | −0.118603 | − | 0.205427i | ||||
\(491\) | 14.2257 | − | 24.6396i | 0.641996 | − | 1.11197i | −0.342991 | − | 0.939339i | \(-0.611440\pi\) |
0.984987 | − | 0.172630i | \(-0.0552266\pi\) | |||||||
\(492\) | 4.02283 | + | 2.32258i | 0.181363 | + | 0.104710i | ||||
\(493\) | 8.09130 | 0.364414 | ||||||||
\(494\) | −7.33052 | + | 3.80564i | −0.329816 | + | 0.171224i | ||||
\(495\) | 4.61335 | 0.207355 | ||||||||
\(496\) | 8.77464 | + | 5.06604i | 0.393993 | + | 0.227472i | ||||
\(497\) | −7.49636 | + | 12.9841i | −0.336258 | + | 0.582416i | ||||
\(498\) | 7.93593 | + | 13.7454i | 0.355618 | + | 0.615948i | ||||
\(499\) | − | 4.10926i | − | 0.183956i | −0.995761 | − | 0.0919779i | \(-0.970681\pi\) | ||
0.995761 | − | 0.0919779i | \(-0.0293189\pi\) | |||||||
\(500\) | −0.866025 | + | 0.500000i | −0.0387298 | + | 0.0223607i | ||||
\(501\) | −20.8171 | + | 12.0187i | −0.930037 | + | 0.536957i | ||||
\(502\) | − | 8.82497i | − | 0.393878i | ||||||
\(503\) | −2.86800 | − | 4.96753i | −0.127878 | − | 0.221491i | 0.794976 | − | 0.606641i | \(-0.207483\pi\) |
−0.922854 | + | 0.385149i | \(0.874150\pi\) | |||||||
\(504\) | −0.661290 | + | 1.14539i | −0.0294562 | + | 0.0510196i | ||||
\(505\) | 6.25851 | + | 3.61335i | 0.278500 | + | 0.160792i | ||||
\(506\) | 39.9885 | 1.77771 | ||||||||
\(507\) | 5.46774 | + | 11.7942i | 0.242831 | + | 0.523800i | ||||
\(508\) | 11.4718 | 0.508980 | ||||||||
\(509\) | −13.1129 | − | 7.57076i | −0.581221 | − | 0.335568i | 0.180397 | − | 0.983594i | \(-0.442262\pi\) |
−0.761618 | + | 0.648026i | \(0.775595\pi\) | |||||||
\(510\) | 2.00000 | − | 3.46410i | 0.0885615 | − | 0.153393i | ||||
\(511\) | −4.15491 | − | 7.19652i | −0.183803 | − | 0.318355i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 1.98387 | − | 1.14539i | 0.0875900 | − | 0.0505701i | ||||
\(514\) | −7.26157 | + | 4.19247i | −0.320294 | + | 0.184922i | ||||
\(515\) | 18.4000i | 0.810802i | ||||||||
\(516\) | −4.30281 | − | 7.45269i | −0.189421 | − | 0.328086i | ||||
\(517\) | −21.0121 | + | 36.3941i | −0.924112 | + | 1.60061i | ||||
\(518\) | −7.79953 | − | 4.50306i | −0.342691 | − | 0.197853i | ||||
\(519\) | −2.52817 | −0.110974 | ||||||||
\(520\) | −3.20002 | + | 1.66129i | −0.140330 | + | 0.0728524i | ||||
\(521\) | 8.93027 | 0.391242 | 0.195621 | − | 0.980680i | \(-0.437328\pi\) | ||||
0.195621 | + | 0.980680i | \(0.437328\pi\) | |||||||
\(522\) | 1.75182 | + | 1.01141i | 0.0766750 | + | 0.0442683i | ||||
\(523\) | 4.90844 | − | 8.50166i | 0.214631 | − | 0.371752i | −0.738527 | − | 0.674223i | \(-0.764478\pi\) |
0.953158 | + | 0.302472i | \(0.0978118\pi\) | |||||||
\(524\) | −7.99528 | − | 13.8482i | −0.349276 | − | 0.604963i | ||||
\(525\) | − | 1.32258i | − | 0.0577221i | ||||||
\(526\) | 1.66389 | − | 0.960648i | 0.0725491 | − | 0.0418863i | ||||
\(527\) | 35.0986 | − | 20.2642i | 1.52892 | − | 0.882721i | ||||
\(528\) | 4.61335i | 0.200771i | ||||||||
\(529\) | −26.0670 | − | 45.1493i | −1.13335 | − | 1.96301i | ||||
\(530\) | −0.413337 | + | 0.715920i | −0.0179542 | + | 0.0310976i | ||||
\(531\) | −2.72064 | − | 1.57076i | −0.118066 | − | 0.0681652i | ||||
\(532\) | 3.02973 | 0.131356 | ||||||||
\(533\) | −16.7316 | − | 0.749217i | −0.724726 | − | 0.0324522i | ||||
\(534\) | 11.8641 | 0.513411 | ||||||||
\(535\) | 2.66025 | + | 1.53590i | 0.115013 | + | 0.0664027i | ||||
\(536\) | −1.59053 | + | 2.75488i | −0.0687004 | + | 0.118993i | ||||
\(537\) | −3.13784 | − | 5.43490i | −0.135408 | − | 0.234533i | ||||
\(538\) | − | 32.3098i | − | 1.39298i | ||||||
\(539\) | 20.9784 | − | 12.1119i | 0.903602 | − | 0.521695i | ||||
\(540\) | 0.866025 | − | 0.500000i | 0.0372678 | − | 0.0215166i | ||||
\(541\) | 3.80826i | 0.163730i | 0.996643 | + | 0.0818650i | \(0.0260876\pi\) | ||||
−0.996643 | + | 0.0818650i | \(0.973912\pi\) | |||||||
\(542\) | −11.7263 | − | 20.3105i | −0.503688 | − | 0.872413i | ||||
\(543\) | 6.14152 | − | 10.6374i | 0.263558 | − | 0.456496i | ||||
\(544\) | 3.46410 | + | 2.00000i | 0.148522 | + | 0.0857493i | ||||
\(545\) | 13.2267 | 0.566570 | ||||||||
\(546\) | 0.213319 | − | 4.76386i | 0.00912920 | − | 0.203874i | ||||
\(547\) | 45.5847 | 1.94906 | 0.974530 | − | 0.224257i | \(-0.0719954\pi\) | ||||
0.974530 | + | 0.224257i | \(0.0719954\pi\) | |||||||
\(548\) | 13.9168 | + | 8.03486i | 0.594496 | + | 0.343232i | ||||
\(549\) | −0.267949 | + | 0.464102i | −0.0114358 | + | 0.0198074i | ||||
\(550\) | −2.30668 | − | 3.99528i | −0.0983571 | − | 0.170359i | ||||
\(551\) | − | 4.63384i | − | 0.197408i | ||||||
\(552\) | 7.50670 | − | 4.33399i | 0.319506 | − | 0.184467i | ||||
\(553\) | 3.39921 | − | 1.96254i | 0.144549 | − | 0.0834555i | ||||
\(554\) | 9.00566i | 0.382614i | ||||||||
\(555\) | 3.40475 | + | 5.89721i | 0.144524 | + | 0.250322i | ||||
\(556\) | 4.66129 | − | 8.07359i | 0.197683 | − | 0.342397i | ||||
\(557\) | −31.9209 | − | 18.4296i | −1.35253 | − | 0.780885i | −0.363929 | − | 0.931427i | \(-0.618565\pi\) |
−0.988604 | + | 0.150541i | \(0.951898\pi\) | |||||||
\(558\) | 10.1321 | 0.428925 | ||||||||
\(559\) | 26.1502 | + | 16.7005i | 1.10603 | + | 0.706357i | ||||
\(560\) | 1.32258 | 0.0558892 | ||||||||
\(561\) | 15.9811 | + | 9.22671i | 0.674724 | + | 0.389552i | ||||
\(562\) | 0.858478 | − | 1.48693i | 0.0362127 | − | 0.0627223i | ||||
\(563\) | 16.8870 | + | 29.2491i | 0.711701 | + | 1.23270i | 0.964218 | + | 0.265109i | \(0.0854081\pi\) |
−0.252518 | + | 0.967592i | \(0.581259\pi\) | |||||||
\(564\) | 9.10926i | 0.383569i | ||||||||
\(565\) | 7.00306 | − | 4.04322i | 0.294621 | − | 0.170099i | ||||
\(566\) | 1.34172 | − | 0.774645i | 0.0563969 | − | 0.0325607i | ||||
\(567\) | 1.32258i | 0.0555431i | ||||||||
\(568\) | 5.66799 | + | 9.81724i | 0.237823 | + | 0.411922i | ||||
\(569\) | −12.7159 | + | 22.0246i | −0.533079 | + | 0.923320i | 0.466175 | + | 0.884693i | \(0.345632\pi\) |
−0.999254 | + | 0.0386274i | \(0.987701\pi\) | |||||||
\(570\) | −1.98387 | − | 1.14539i | −0.0830952 | − | 0.0479750i | ||||
\(571\) | 13.3682 | 0.559443 | 0.279722 | − | 0.960081i | \(-0.409758\pi\) | ||||
0.279722 | + | 0.960081i | \(0.409758\pi\) | |||||||
\(572\) | −7.66412 | − | 14.7628i | −0.320453 | − | 0.617264i | ||||
\(573\) | −9.74715 | −0.407193 | ||||||||
\(574\) | 5.32051 | + | 3.07180i | 0.222074 | + | 0.128214i | ||||
\(575\) | −4.33399 | + | 7.50670i | −0.180740 | + | 0.313051i | ||||
\(576\) | 0.500000 | + | 0.866025i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | − | 9.57428i | − | 0.398582i | −0.979940 | − | 0.199291i | \(-0.936136\pi\) | ||
0.979940 | − | 0.199291i | \(-0.0638639\pi\) | |||||||
\(578\) | −0.866025 | + | 0.500000i | −0.0360219 | + | 0.0207973i | ||||
\(579\) | 11.9188 | − | 6.88130i | 0.495327 | − | 0.285977i | ||||
\(580\) | − | 2.02283i | − | 0.0839933i | ||||||
\(581\) | 10.4959 | + | 18.1794i | 0.435444 | + | 0.754210i | ||||
\(582\) | −4.40947 | + | 7.63743i | −0.182778 | + | 0.316582i | ||||
\(583\) | −3.30279 | − | 1.90687i | −0.136788 | − | 0.0789745i | ||||
\(584\) | −6.28304 | −0.259994 | ||||||||
\(585\) | −1.94065 | + | 3.03873i | −0.0802361 | + | 0.125636i | ||||
\(586\) | −30.4057 | −1.25605 | ||||||||
\(587\) | 1.21286 | + | 0.700246i | 0.0500602 | + | 0.0289023i | 0.524821 | − | 0.851212i | \(-0.324132\pi\) |
−0.474761 | + | 0.880115i | \(0.657466\pi\) | |||||||
\(588\) | 2.62539 | − | 4.54731i | 0.108269 | − | 0.187528i | ||||
\(589\) | −11.6052 | − | 20.1007i | −0.478183 | − | 0.828237i | ||||
\(590\) | 3.14152i | 0.129334i | ||||||||
\(591\) | 8.78282 | − | 5.07076i | 0.361277 | − | 0.208583i | ||||
\(592\) | −5.89721 | + | 3.40475i | −0.242374 | + | 0.139935i | ||||
\(593\) | − | 10.7303i | − | 0.440643i | −0.975427 | − | 0.220321i | \(-0.929289\pi\) | ||
0.975427 | − | 0.220321i | \(-0.0707106\pi\) | |||||||
\(594\) | 2.30668 | + | 3.99528i | 0.0946441 | + | 0.163928i | ||||
\(595\) | 2.64516 | − | 4.58155i | 0.108441 | − | 0.187825i | ||||
\(596\) | 3.53788 | + | 2.04259i | 0.144917 | + | 0.0836679i | ||||
\(597\) | −9.57336 | −0.391812 | ||||||||
\(598\) | −16.8215 | + | 26.3397i | −0.687884 | + | 1.07711i | ||||
\(599\) | −40.7967 | −1.66691 | −0.833453 | − | 0.552590i | \(-0.813640\pi\) | ||||
−0.833453 | + | 0.552590i | \(0.813640\pi\) | |||||||
\(600\) | −0.866025 | − | 0.500000i | −0.0353553 | − | 0.0204124i | ||||
\(601\) | −21.4416 | + | 37.1379i | −0.874621 | + | 1.51489i | −0.0174548 | + | 0.999848i | \(0.505556\pi\) |
−0.857166 | + | 0.515040i | \(0.827777\pi\) | |||||||
\(602\) | −5.69081 | − | 9.85677i | −0.231940 | − | 0.401732i | ||||
\(603\) | 3.18106i | 0.129543i | ||||||||
\(604\) | 17.3042 | − | 9.99057i | 0.704097 | − | 0.406510i | ||||
\(605\) | 8.90538 | − | 5.14152i | 0.362055 | − | 0.209033i | ||||
\(606\) | 7.22671i | 0.293565i | ||||||||
\(607\) | 3.43616 | + | 5.95161i | 0.139470 | + | 0.241568i | 0.927296 | − | 0.374329i | \(-0.122127\pi\) |
−0.787826 | + | 0.615897i | \(0.788794\pi\) | |||||||
\(608\) | 1.14539 | − | 1.98387i | 0.0464516 | − | 0.0804565i | ||||
\(609\) | 2.31692 | + | 1.33767i | 0.0938863 | + | 0.0542053i | ||||
\(610\) | 0.535898 | 0.0216979 | ||||||||
\(611\) | −15.1331 | − | 29.1498i | −0.612221 | − | 1.17927i | ||||
\(612\) | 4.00000 | 0.161690 | ||||||||
\(613\) | −0.659358 | − | 0.380681i | −0.0266312 | − | 0.0153755i | 0.486625 | − | 0.873611i | \(-0.338228\pi\) |
−0.513257 | + | 0.858235i | \(0.671561\pi\) | |||||||
\(614\) | 4.91311 | − | 8.50975i | 0.198277 | − | 0.343426i | ||||
\(615\) | −2.32258 | − | 4.02283i | −0.0936555 | − | 0.162216i | ||||
\(616\) | 6.10153i | 0.245838i | ||||||||
\(617\) | 21.3061 | − | 12.3011i | 0.857753 | − | 0.495224i | −0.00550613 | − | 0.999985i | \(-0.501753\pi\) |
0.863259 | + | 0.504761i | \(0.168419\pi\) | |||||||
\(618\) | −15.9349 | + | 9.20002i | −0.640996 | + | 0.370079i | ||||
\(619\) | 17.2035i | 0.691468i | 0.938333 | + | 0.345734i | \(0.112370\pi\) | ||||
−0.938333 | + | 0.345734i | \(0.887630\pi\) | |||||||
\(620\) | −5.06604 | − | 8.77464i | −0.203457 | − | 0.352398i | ||||
\(621\) | 4.33399 | − | 7.50670i | 0.173917 | − | 0.301233i | ||||
\(622\) | 2.94491 | + | 1.70025i | 0.118080 | + | 0.0681737i | ||||
\(623\) | 15.6913 | 0.628657 | ||||||||
\(624\) | −3.03873 | − | 1.94065i | −0.121646 | − | 0.0776883i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 14.0590 | + | 8.11699i | 0.561912 | + | 0.324420i | ||||
\(627\) | 5.28408 | − | 9.15229i | 0.211026 | − | 0.365507i | ||||
\(628\) | 3.56690 | + | 6.17804i | 0.142335 | + | 0.246531i | ||||
\(629\) | 27.2380i | 1.08605i | ||||||||
\(630\) | 1.14539 | − | 0.661290i | 0.0456333 | − | 0.0263464i | ||||
\(631\) | 2.08519 | − | 1.20388i | 0.0830100 | − | 0.0479259i | −0.457920 | − | 0.888993i | \(-0.651406\pi\) |
0.540930 | + | 0.841067i | \(0.318072\pi\) | |||||||
\(632\) | − | 2.96774i | − | 0.118050i | ||||||
\(633\) | 0.542594 | + | 0.939800i | 0.0215662 | + | 0.0373537i | ||||
\(634\) | 11.7616 | − | 20.3716i | 0.467112 | − | 0.809061i | ||||
\(635\) | −9.93490 | − | 5.73592i | −0.394254 | − | 0.227623i | ||||
\(636\) | −0.826674 | −0.0327797 | ||||||||
\(637\) | −0.846898 | + | 18.9130i | −0.0335553 | + | 0.749361i | ||||
\(638\) | 9.33201 | 0.369458 | ||||||||
\(639\) | 9.81724 | + | 5.66799i | 0.388364 | + | 0.224222i | ||||
\(640\) | 0.500000 | − | 0.866025i | 0.0197642 | − | 0.0342327i | ||||
\(641\) | −9.73875 | − | 16.8680i | −0.384657 | − | 0.666246i | 0.607064 | − | 0.794653i | \(-0.292347\pi\) |
−0.991722 | + | 0.128407i | \(0.959014\pi\) | |||||||
\(642\) | 3.07180i | 0.121234i | ||||||||
\(643\) | −20.7451 | + | 11.9772i | −0.818106 | + | 0.472334i | −0.849763 | − | 0.527165i | \(-0.823255\pi\) |
0.0316570 | + | 0.999499i | \(0.489922\pi\) | |||||||
\(644\) | 9.92820 | − | 5.73205i | 0.391226 | − | 0.225874i | ||||
\(645\) | 8.60562i | 0.338846i | ||||||||
\(646\) | −4.58155 | − | 7.93548i | −0.180259 | − | 0.312217i | ||||
\(647\) | 9.10540 | − | 15.7710i | 0.357970 | − | 0.620022i | −0.629652 | − | 0.776878i | \(-0.716802\pi\) |
0.987622 | + | 0.156855i | \(0.0501357\pi\) | |||||||
\(648\) | 0.866025 | + | 0.500000i | 0.0340207 | + | 0.0196419i | ||||
\(649\) | −14.4930 | −0.568898 | ||||||||
\(650\) | 3.60194 | + | 0.161290i | 0.141280 | + | 0.00632631i | ||||
\(651\) | 13.4005 | 0.525207 | ||||||||
\(652\) | −8.56906 | − | 4.94735i | −0.335590 | − | 0.193753i | ||||
\(653\) | 24.0793 | − | 41.7065i | 0.942294 | − | 1.63210i | 0.181213 | − | 0.983444i | \(-0.441998\pi\) |
0.761081 | − | 0.648657i | \(-0.224669\pi\) | |||||||
\(654\) | 6.61335 | + | 11.4547i | 0.258603 | + | 0.447913i | ||||
\(655\) | 15.9906i | 0.624803i | ||||||||
\(656\) | 4.02283 | − | 2.32258i | 0.157065 | − | 0.0906815i | ||||
\(657\) | −5.44128 | + | 3.14152i | −0.212284 | + | 0.122562i | ||||
\(658\) | 12.0477i | 0.469669i | ||||||||
\(659\) | 18.4127 | + | 31.8917i | 0.717257 | + | 1.24233i | 0.962083 | + | 0.272758i | \(0.0879359\pi\) |
−0.244826 | + | 0.969567i | \(0.578731\pi\) | |||||||
\(660\) | 2.30668 | − | 3.99528i | 0.0897873 | − | 0.155516i | ||||
\(661\) | −19.5131 | − | 11.2659i | −0.758971 | − | 0.438192i | 0.0699555 | − | 0.997550i | \(-0.477714\pi\) |
−0.828926 | + | 0.559358i | \(0.811048\pi\) | |||||||
\(662\) | −18.0904 | −0.703103 | ||||||||
\(663\) | −12.8001 | + | 6.64516i | −0.497114 | + | 0.258077i | ||||
\(664\) | 15.8719 | 0.615948 | ||||||||
\(665\) | −2.62383 | − | 1.51487i | −0.101748 | − | 0.0587440i | ||||
\(666\) | −3.40475 | + | 5.89721i | −0.131932 | + | 0.228512i | ||||
\(667\) | −8.76691 | − | 15.1847i | −0.339456 | − | 0.587955i | ||||
\(668\) | 24.0375i | 0.930037i | ||||||||
\(669\) | −21.6001 | + | 12.4708i | −0.835106 | + | 0.482149i | ||||
\(670\) | 2.75488 | − | 1.59053i | 0.106430 | − | 0.0614475i | ||||
\(671\) | 2.47229i | 0.0954417i | ||||||||
\(672\) | 0.661290 | + | 1.14539i | 0.0255098 | + | 0.0441843i | ||||
\(673\) | 11.8719 | − | 20.5627i | 0.457627 | − | 0.792633i | −0.541208 | − | 0.840889i | \(-0.682033\pi\) |
0.998835 | + | 0.0482556i | \(0.0153662\pi\) | |||||||
\(674\) | 4.93548 | + | 2.84950i | 0.190108 | + | 0.109759i | ||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 12.9480 | + | 1.16191i | 0.497999 | + | 0.0446890i | ||||
\(677\) | 1.16559 | 0.0447975 | 0.0223987 | − | 0.999749i | \(-0.492870\pi\) | ||||
0.0223987 | + | 0.999749i | \(0.492870\pi\) | |||||||
\(678\) | 7.00306 | + | 4.04322i | 0.268951 | + | 0.155279i | ||||
\(679\) | −5.83188 | + | 10.1011i | −0.223807 | + | 0.387645i | ||||
\(680\) | −2.00000 | − | 3.46410i | −0.0766965 | − | 0.132842i | ||||
\(681\) | − | 19.3205i | − | 0.740363i | ||||||
\(682\) | 40.4806 | − | 23.3715i | 1.55008 | − | 0.894939i | ||||
\(683\) | 12.0134 | − | 6.93593i | 0.459680 | − | 0.265396i | −0.252230 | − | 0.967667i | \(-0.581164\pi\) |
0.711910 | + | 0.702271i | \(0.247831\pi\) | |||||||
\(684\) | − | 2.29078i | − | 0.0875900i | ||||||
\(685\) | −8.03486 | − | 13.9168i | −0.306996 | − | 0.531733i | ||||
\(686\) | 8.10132 | − | 14.0319i | 0.309310 | − | 0.535740i | ||||
\(687\) | −3.59826 | − | 2.07746i | −0.137282 | − | 0.0792599i | ||||
\(688\) | −8.60562 | −0.328086 | ||||||||
\(689\) | 2.64537 | − | 1.37334i | 0.100781 | − | 0.0523203i | ||||
\(690\) | −8.66799 | −0.329985 | ||||||||
\(691\) | −35.6967 | − | 20.6095i | −1.35797 | − | 0.784022i | −0.368616 | − | 0.929582i | \(-0.620168\pi\) |
−0.989349 | + | 0.145560i | \(0.953502\pi\) | |||||||
\(692\) | −1.26408 | + | 2.18946i | −0.0480532 | + | 0.0832307i | ||||
\(693\) | 3.05076 | + | 5.28408i | 0.115889 | + | 0.200726i | ||||
\(694\) | − | 15.7471i | − | 0.597753i | ||||||
\(695\) | −8.07359 | + | 4.66129i | −0.306249 | + | 0.176813i | ||||
\(696\) | 1.75182 | − | 1.01141i | 0.0664025 | − | 0.0383375i | ||||
\(697\) | − | 18.5806i | − | 0.703792i | ||||||
\(698\) | −7.66025 | − | 13.2679i | −0.289945 | − | 0.502199i | ||||
\(699\) | −8.48325 | + | 14.6934i | −0.320866 | + | 0.555756i | ||||
\(700\) | −1.14539 | − | 0.661290i | −0.0432916 | − | 0.0249944i | ||||
\(701\) | −23.0112 | −0.869122 | −0.434561 | − | 0.900642i | \(-0.643096\pi\) | ||||
−0.434561 | + | 0.900642i | \(0.643096\pi\) | |||||||
\(702\) | −3.60194 | − | 0.161290i | −0.135947 | − | 0.00608749i | ||||
\(703\) | 15.5991 | 0.588329 | ||||||||
\(704\) | 3.99528 | + | 2.30668i | 0.150578 | + | 0.0869362i | ||||
\(705\) | 4.55463 | − | 7.88885i | 0.171537 | − | 0.297111i | ||||
\(706\) | −0.599964 | − | 1.03917i | −0.0225799 | − | 0.0391096i | ||||
\(707\) | 9.55790i | 0.359462i | ||||||||
\(708\) | −2.72064 | + | 1.57076i | −0.102248 | + | 0.0590328i | ||||
\(709\) | −14.7944 | + | 8.54156i | −0.555616 | + | 0.320785i | −0.751384 | − | 0.659865i | \(-0.770613\pi\) |
0.195768 | + | 0.980650i | \(0.437280\pi\) | |||||||
\(710\) | − | 11.3360i | − | 0.425431i | ||||||
\(711\) | −1.48387 | − | 2.57014i | −0.0556495 | − | 0.0963877i | ||||
\(712\) | 5.93207 | − | 10.2746i | 0.222314 | − | 0.385059i | ||||
\(713\) | −76.0585 | − | 43.9124i | −2.84841 | − | 1.64453i | ||||
\(714\) | 5.29032 | 0.197985 | ||||||||
\(715\) | −0.744087 | + | 16.6170i | −0.0278273 | + | 0.621442i | ||||
\(716\) | −6.27568 | −0.234533 | ||||||||
\(717\) | 5.49420 | + | 3.17208i | 0.205185 | + | 0.118463i | ||||
\(718\) | 8.14152 | − | 14.1015i | 0.303839 | − | 0.526264i | ||||
\(719\) | −21.8564 | − | 37.8564i | −0.815106 | − | 1.41181i | −0.909251 | − | 0.416247i | \(-0.863345\pi\) |
0.0941451 | − | 0.995558i | \(-0.469988\pi\) | |||||||
\(720\) | − | 1.00000i | − | 0.0372678i | ||||||
\(721\) | −21.0752 | + | 12.1678i | −0.784880 | + | 0.453151i | ||||
\(722\) | 11.9099 | − | 6.87617i | 0.443240 | − | 0.255905i | ||||
\(723\) | 24.1855i | 0.899467i | ||||||||
\(724\) | −6.14152 | − | 10.6374i | −0.228248 | − | 0.395337i | ||||
\(725\) | −1.01141 | + | 1.75182i | −0.0375629 | + | 0.0650609i | ||||
\(726\) | 8.90538 | + | 5.14152i | 0.330510 | + | 0.190820i | ||||
\(727\) | 31.8453 | 1.18108 | 0.590538 | − | 0.807010i | \(-0.298916\pi\) | ||||
0.590538 | + | 0.807010i | \(0.298916\pi\) | |||||||
\(728\) | −4.01896 | − | 2.56667i | −0.148953 | − | 0.0951270i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 5.44128 | + | 3.14152i | 0.201391 | + | 0.116273i | ||||
\(731\) | −17.2112 | + | 29.8108i | −0.636581 | + | 1.10259i | ||||
\(732\) | 0.267949 | + | 0.464102i | 0.00990369 | + | 0.0171537i | ||||
\(733\) | − | 5.96774i | − | 0.220423i | −0.993908 | − | 0.110212i | \(-0.964847\pi\) | ||
0.993908 | − | 0.110212i | \(-0.0351529\pi\) | |||||||
\(734\) | −17.0040 | + | 9.81724i | −0.627627 | + | 0.362361i | ||||
\(735\) | −4.54731 | + | 2.62539i | −0.167730 | + | 0.0968390i | ||||
\(736\) | − | 8.66799i | − | 0.319506i | ||||||
\(737\) | 7.33767 | + | 12.7092i | 0.270287 | + | 0.468150i | ||||
\(738\) | 2.32258 | − | 4.02283i | 0.0854953 | − | 0.148082i | ||||
\(739\) | 9.37833 | + | 5.41458i | 0.344988 | + | 0.199179i | 0.662475 | − | 0.749084i | \(-0.269506\pi\) |
−0.317488 | + | 0.948262i | \(0.602839\pi\) | |||||||
\(740\) | 6.80951 | 0.250322 | ||||||||
\(741\) | 3.80564 | + | 7.33052i | 0.139804 | + | 0.269293i | ||||
\(742\) | −1.09334 | −0.0401378 | ||||||||
\(743\) | 17.1909 | + | 9.92515i | 0.630671 | + | 0.364118i | 0.781012 | − | 0.624516i | \(-0.214704\pi\) |
−0.150341 | + | 0.988634i | \(0.548037\pi\) | |||||||
\(744\) | 5.06604 | − | 8.77464i | 0.185730 | − | 0.321694i | ||||
\(745\) | −2.04259 | − | 3.53788i | −0.0748349 | − | 0.129618i | ||||
\(746\) | − | 2.55748i | − | 0.0936359i | ||||||
\(747\) | 13.7454 | − | 7.93593i | 0.502919 | − | 0.290361i | ||||
\(748\) | 15.9811 | − | 9.22671i | 0.584328 | − | 0.337362i | ||||
\(749\) | 4.06270i | 0.148448i | ||||||||
\(750\) | 0.500000 | + | 0.866025i | 0.0182574 | + | 0.0316228i | ||||
\(751\) | −7.66538 | + | 13.2768i | −0.279714 | + | 0.484479i | −0.971314 | − | 0.237802i | \(-0.923573\pi\) |
0.691600 | + | 0.722281i | \(0.256906\pi\) | |||||||
\(752\) | 7.88885 | + | 4.55463i | 0.287677 | + | 0.166090i | ||||
\(753\) | −8.82497 | −0.321600 | ||||||||
\(754\) | −3.92560 | + | 6.14682i | −0.142962 | + | 0.223854i | ||||
\(755\) | −19.9811 | −0.727188 | ||||||||
\(756\) | 1.14539 | + | 0.661290i | 0.0416573 | + | 0.0240509i | ||||
\(757\) | −22.5816 | + | 39.1125i | −0.820744 | + | 1.42157i | 0.0843855 | + | 0.996433i | \(0.473107\pi\) |
−0.905129 | + | 0.425137i | \(0.860226\pi\) | |||||||
\(758\) | 7.55440 | + | 13.0846i | 0.274388 | + | 0.475254i | ||||
\(759\) | − | 39.9885i | − | 1.45149i | ||||||
\(760\) | −1.98387 | + | 1.14539i | −0.0719625 | + | 0.0415476i | ||||
\(761\) | −18.7978 | + | 10.8529i | −0.681419 | + | 0.393418i | −0.800390 | − | 0.599480i | \(-0.795374\pi\) |
0.118970 | + | 0.992898i | \(0.462041\pi\) | |||||||
\(762\) | − | 11.4718i | − | 0.415581i | ||||||
\(763\) | 8.74669 | + | 15.1497i | 0.316651 | + | 0.548456i | ||||
\(764\) | −4.87357 | + | 8.44128i | −0.176320 | + | 0.305395i | ||||
\(765\) | −3.46410 | − | 2.00000i | −0.125245 | − | 0.0723102i | ||||
\(766\) | 18.7303 | 0.676755 | ||||||||
\(767\) | 6.09660 | − | 9.54623i | 0.220136 | − | 0.344694i | ||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 36.4711 | + | 21.0566i | 1.31518 | + | 0.759321i | 0.982949 | − | 0.183877i | \(-0.0588647\pi\) |
0.332233 | + | 0.943197i | \(0.392198\pi\) | |||||||
\(770\) | 3.05076 | − | 5.28408i | 0.109942 | − | 0.190425i | ||||
\(771\) | 4.19247 | + | 7.26157i | 0.150988 | + | 0.261519i | ||||
\(772\) | − | 13.7626i | − | 0.495327i | ||||||
\(773\) | 25.7734 | − | 14.8803i | 0.927004 | − | 0.535206i | 0.0411413 | − | 0.999153i | \(-0.486901\pi\) |
0.885863 | + | 0.463947i | \(0.153567\pi\) | |||||||
\(774\) | −7.45269 | + | 4.30281i | −0.267881 | + | 0.154661i | ||||
\(775\) | 10.1321i | 0.363955i | ||||||||
\(776\) | 4.40947 | + | 7.63743i | 0.158291 | + | 0.274168i | ||||
\(777\) | −4.50306 | + | 7.79953i | −0.161546 | + | 0.279806i | ||||
\(778\) | −6.03532 | − | 3.48449i | −0.216377 | − | 0.124925i | ||||
\(779\) | −10.6410 | −0.381254 | ||||||||
\(780\) | 1.66129 | + | 3.20002i | 0.0594837 | + | 0.114579i | ||||
\(781\) | 52.2969 | 1.87133 | ||||||||
\(782\) | −30.0268 | − | 17.3360i | −1.07376 | − | 0.619933i | ||||
\(783\) | 1.01141 | − | 1.75182i | 0.0361450 | − | 0.0626049i | ||||
\(784\) | −2.62539 | − | 4.54731i | −0.0937640 | − | 0.162404i | ||||
\(785\) | − | 7.13379i | − | 0.254616i | ||||||
\(786\) | −13.8482 | + | 7.99528i | −0.493950 | + | 0.285182i | ||||
\(787\) | −35.5459 | + | 20.5224i | −1.26707 | + | 0.731545i | −0.974433 | − | 0.224678i | \(-0.927867\pi\) |
−0.292640 | + | 0.956223i | \(0.594534\pi\) | |||||||
\(788\) | − | 10.1415i | − | 0.361277i | ||||||
\(789\) | −0.960648 | − | 1.66389i | −0.0342000 | − | 0.0592361i | ||||
\(790\) | −1.48387 | + | 2.57014i | −0.0527937 | + | 0.0914414i | ||||
\(791\) | 9.26210 | + | 5.34748i | 0.329322 | + | 0.190134i | ||||
\(792\) | 4.61335 | 0.163928 | ||||||||
\(793\) | −1.62845 | − | 1.03999i | −0.0578279 | − | 0.0369312i | ||||
\(794\) | 18.5721 | 0.659100 | ||||||||
\(795\) | 0.715920 | + | 0.413337i | 0.0253911 | + | 0.0146595i | ||||
\(796\) | −4.78668 | + | 8.29078i | −0.169659 | + | 0.293859i | ||||
\(797\) | 22.6263 | + | 39.1899i | 0.801464 | + | 1.38818i | 0.918652 | + | 0.395067i | \(0.129279\pi\) |
−0.117188 | + | 0.993110i | \(0.537388\pi\) | |||||||
\(798\) | − | 3.02973i | − | 0.107251i | ||||||
\(799\) | 31.5554 | − | 18.2185i | 1.11635 | − | 0.644525i | ||||
\(800\) | −0.866025 | + | 0.500000i | −0.0306186 | + | 0.0176777i | ||||
\(801\) | − | 11.8641i | − | 0.419199i | ||||||
\(802\) | 14.8452 | + | 25.7126i | 0.524201 | + | 0.907944i | ||||
\(803\) | −14.4930 | + | 25.1025i | −0.511445 | + | 0.885849i | ||||
\(804\) | 2.75488 | + | 1.59053i | 0.0971570 | + | 0.0560936i | ||||
\(805\) | −11.4641 | −0.404056 | ||||||||
\(806\) | −1.63420 | + | 36.4952i | −0.0575623 | + | 1.28549i | ||||
\(807\) | −32.3098 | −1.13736 | ||||||||
\(808\) | 6.25851 | + | 3.61335i | 0.220174 | + | 0.127117i | ||||
\(809\) | 14.2267 | − | 24.6414i | 0.500184 | − | 0.866345i | −0.499815 | − | 0.866132i | \(-0.666599\pi\) |
1.00000 | 0.000213036i | \(-6.78113e-5\pi\) | ||||||||
\(810\) | −0.500000 | − | 0.866025i | −0.0175682 | − | 0.0304290i | ||||
\(811\) | − | 44.4114i | − | 1.55949i | −0.626095 | − | 0.779747i | \(-0.715348\pi\) | ||
0.626095 | − | 0.779747i | \(-0.284652\pi\) | |||||||
\(812\) | 2.31692 | − | 1.33767i | 0.0813079 | − | 0.0469432i | ||||
\(813\) | −20.3105 | + | 11.7263i | −0.712322 | + | 0.411259i | ||||
\(814\) | 31.4147i | 1.10108i | ||||||||
\(815\) | 4.94735 | + | 8.56906i | 0.173298 | + | 0.300161i | ||||
\(816\) | 2.00000 | − | 3.46410i | 0.0700140 | − | 0.121268i | ||||
\(817\) | 17.0724 | + | 9.85677i | 0.597289 | + | 0.344845i | ||||
\(818\) | 24.3355 | 0.850871 | ||||||||
\(819\) | −4.76386 | − | 0.213319i | −0.166463 | − | 0.00745396i | ||||
\(820\) | −4.64516 | −0.162216 | ||||||||
\(821\) | −39.1169 | − | 22.5842i | −1.36519 | − | 0.788192i | −0.374880 | − | 0.927073i | \(-0.622316\pi\) |
−0.990309 | + | 0.138881i | \(0.955649\pi\) | |||||||
\(822\) | 8.03486 | − | 13.9168i | 0.280248 | − | 0.485404i | ||||
\(823\) | 1.20900 | + | 2.09404i | 0.0421430 | + | 0.0729938i | 0.886328 | − | 0.463059i | \(-0.153248\pi\) |
−0.844185 | + | 0.536053i | \(0.819915\pi\) | |||||||
\(824\) | 18.4000i | 0.640996i | ||||||||
\(825\) | −3.99528 | + | 2.30668i | −0.139098 | + | 0.0803082i | ||||
\(826\) | −3.59826 | + | 2.07746i | −0.125199 | + | 0.0722840i | ||||
\(827\) | 4.26832i | 0.148424i | 0.997242 | + | 0.0742120i | \(0.0236441\pi\) | ||||
−0.997242 | + | 0.0742120i | \(0.976356\pi\) | |||||||
\(828\) | −4.33399 | − | 7.50670i | −0.150617 | − | 0.260876i | ||||
\(829\) | −21.4926 | + | 37.2263i | −0.746468 | + | 1.29292i | 0.203037 | + | 0.979171i | \(0.434919\pi\) |
−0.949506 | + | 0.313750i | \(0.898415\pi\) | |||||||
\(830\) | −13.7454 | − | 7.93593i | −0.477111 | − | 0.275460i | ||||
\(831\) | 9.00566 | 0.312403 | ||||||||
\(832\) | −3.20002 | + | 1.66129i | −0.110941 | + | 0.0575949i | ||||
\(833\) | −21.0031 | −0.727715 | ||||||||
\(834\) | −8.07359 | − | 4.66129i | −0.279566 | − | 0.161407i | ||||
\(835\) | 12.0187 | − | 20.8171i | 0.415925 | − | 0.720404i | ||||
\(836\) | −5.28408 | − | 9.15229i | −0.182754 | − | 0.316539i | ||||
\(837\) | − | 10.1321i | − | 0.350216i | ||||||
\(838\) | −2.49636 | + | 1.44128i | −0.0862354 | + | 0.0497880i | ||||
\(839\) | −20.1798 | + | 11.6508i | −0.696684 | + | 0.402231i | −0.806111 | − | 0.591764i | \(-0.798432\pi\) |
0.109427 | + | 0.993995i | \(0.465098\pi\) | |||||||
\(840\) | − | 1.32258i | − | 0.0456333i | ||||||
\(841\) | 12.4541 | + | 21.5711i | 0.429451 | + | 0.743831i | ||||
\(842\) | −2.47354 | + | 4.28429i | −0.0852437 | + | 0.147646i | ||||
\(843\) | −1.48693 | − | 0.858478i | −0.0512125 | − | 0.0295676i | ||||
\(844\) | 1.08519 | 0.0373537 | ||||||||
\(845\) | −10.6323 | − | 7.48023i | −0.365763 | − | 0.257328i | ||||
\(846\) | 9.10926 | 0.313183 | ||||||||
\(847\) | 11.7781 | + | 6.80007i | 0.404699 | + | 0.233653i | ||||
\(848\) | −0.413337 | + | 0.715920i | −0.0141940 | + | 0.0245848i | ||||
\(849\) | −0.774645 | − | 1.34172i | −0.0265857 | − | 0.0460479i | ||||
\(850\) | 4.00000i | 0.137199i | ||||||||
\(851\) | 51.1169 | − | 29.5124i | 1.75226 | − | 1.01167i | ||||
\(852\) | 9.81724 | − | 5.66799i | 0.336333 | − | 0.194182i | ||||
\(853\) | 20.8418i | 0.713609i | 0.934179 | + | 0.356804i | \(0.116134\pi\) | ||||
−0.934179 | + | 0.356804i | \(0.883866\pi\) | |||||||
\(854\) | 0.354384 | + | 0.613811i | 0.0121268 | + | 0.0210042i | ||||
\(855\) | −1.14539 | + | 1.98387i | −0.0391714 | + | 0.0678469i | ||||
\(856\) | 2.66025 | + | 1.53590i | 0.0909256 | + | 0.0524959i | ||||
\(857\) | 36.7250 | 1.25450 | 0.627250 | − | 0.778818i | \(-0.284180\pi\) | ||||
0.627250 | + | 0.778818i | \(0.284180\pi\) | |||||||
\(858\) | −14.7628 | + | 7.66412i | −0.503994 | + | 0.261649i | ||||
\(859\) | 0.914812 | 0.0312130 | 0.0156065 | − | 0.999878i | \(-0.495032\pi\) | ||||
0.0156065 | + | 0.999878i | \(0.495032\pi\) | |||||||
\(860\) | 7.45269 | + | 4.30281i | 0.254135 | + | 0.146725i | ||||
\(861\) | 3.07180 | − | 5.32051i | 0.104687 | − | 0.181322i | ||||
\(862\) | 8.88130 | + | 15.3829i | 0.302498 | + | 0.523943i | ||||
\(863\) | 33.6104i | 1.14411i | 0.820215 | + | 0.572056i | \(0.193854\pi\) | ||||
−0.820215 | + | 0.572056i | \(0.806146\pi\) | |||||||
\(864\) | 0.866025 | − | 0.500000i | 0.0294628 | − | 0.0170103i | ||||
\(865\) | 2.18946 | − | 1.26408i | 0.0744438 | − | 0.0429801i | ||||
\(866\) | − | 35.8375i | − | 1.21781i | ||||||
\(867\) | 0.500000 | + | 0.866025i | 0.0169809 | + | 0.0294118i | ||||
\(868\) | 6.70025 | − | 11.6052i | 0.227421 | − | 0.393905i | ||||
\(869\) | −11.8570 | − | 6.84562i | −0.402220 | − | 0.232222i | ||||
\(870\) | −2.02283 | −0.0685802 | ||||||||
\(871\) | −11.4580 | − | 0.513072i | −0.388239 | − | 0.0173848i | ||||
\(872\) | 13.2267 | 0.447913 | ||||||||
\(873\) | 7.63743 | + | 4.40947i | 0.258488 | + | 0.149238i | ||||
\(874\) | −9.92820 | + | 17.1962i | −0.335826 | + | 0.581669i | ||||
\(875\) | 0.661290 | + | 1.14539i | 0.0223557 | + | 0.0387212i | ||||
\(876\) | 6.28304i | 0.212284i | ||||||||
\(877\) | −21.0629 | + | 12.1607i | −0.711243 | + | 0.410637i | −0.811521 | − | 0.584323i | \(-0.801360\pi\) |
0.100278 | + | 0.994959i | \(0.468027\pi\) | |||||||
\(878\) | −8.73854 | + | 5.04520i | −0.294911 | + | 0.170267i | ||||
\(879\) | 30.4057i | 1.02556i | ||||||||
\(880\) | −2.30668 | − | 3.99528i | −0.0777581 | − | 0.134681i | ||||
\(881\) | −4.95207 | + | 8.57723i | −0.166839 | + | 0.288974i | −0.937307 | − | 0.348505i | \(-0.886689\pi\) |
0.770468 | + | 0.637479i | \(0.220023\pi\) | |||||||
\(882\) | −4.54731 | − | 2.62539i | −0.153116 | − | 0.0884015i | ||||
\(883\) | −43.9718 | −1.47977 | −0.739884 | − | 0.672734i | \(-0.765120\pi\) | ||||
−0.739884 | + | 0.672734i | \(0.765120\pi\) | |||||||
\(884\) | −0.645159 | + | 14.4078i | −0.0216991 | + | 0.484586i | ||||
\(885\) | 3.14152 | 0.105601 | ||||||||
\(886\) | −11.8629 | − | 6.84904i | −0.398542 | − | 0.230098i | ||||
\(887\) | −25.2807 | + | 43.7875i | −0.848843 | + | 1.47024i | 0.0333988 | + | 0.999442i | \(0.489367\pi\) |
−0.882242 | + | 0.470797i | \(0.843966\pi\) | |||||||
\(888\) | 3.40475 | + | 5.89721i | 0.114256 | + | 0.197897i | ||||
\(889\) | − | 15.1724i | − | 0.508866i | ||||||
\(890\) | −10.2746 | + | 5.93207i | −0.344407 | + | 0.198843i | ||||
\(891\) | 3.99528 | − | 2.30668i | 0.133847 | − | 0.0772766i | ||||
\(892\) | 24.9416i | 0.835106i | ||||||||
\(893\) | −10.4336 | − | 18.0716i | −0.349148 | − | 0.604743i | ||||
\(894\) | 2.04259 | − | 3.53788i | 0.0683146 | − | 0.118324i | ||||
\(895\) | 5.43490 | + | 3.13784i | 0.181669 | + | 0.104886i | ||||
\(896\) | 1.32258 | 0.0441843 | ||||||||
\(897\) | 26.3397 | + | 16.8215i | 0.879455 | + | 0.561655i | ||||
\(898\) | −15.3128 | −0.510994 | ||||||||
\(899\) | −17.7496 | − | 10.2477i | −0.591982 | − | 0.341781i | ||||
\(900\) | −0.500000 | + | 0.866025i | −0.0166667 | + | 0.0288675i | ||||
\(901\) | 1.65335 | + | 2.86368i | 0.0550810 | + | 0.0954031i | ||||
\(902\) | − | 21.4298i | − | 0.713533i | ||||||
\(903\) | −9.85677 | + | 5.69081i | −0.328013 | + | 0.189378i | ||||
\(904\) | 7.00306 | − | 4.04322i | 0.232918 | − | 0.134475i | ||||
\(905\) | 12.2830i | 0.408302i | ||||||||
\(906\) | −9.99057 | − | 17.3042i | −0.331914 | − | 0.574892i | ||||
\(907\) | 7.12175 | − | 12.3352i | 0.236474 | − | 0.409585i | −0.723226 | − | 0.690611i | \(-0.757342\pi\) |
0.959700 | + | 0.281026i | \(0.0906749\pi\) | |||||||
\(908\) | −16.7321 | − | 9.66025i | −0.555273 | − | 0.320587i | ||||
\(909\) | 7.22671 | 0.239695 | ||||||||
\(910\) | 2.19719 | + | 4.23228i | 0.0728361 | + | 0.140299i | ||||
\(911\) | 21.8108 | 0.722623 | 0.361311 | − | 0.932445i | \(-0.382329\pi\) | ||||
0.361311 | + | 0.932445i | \(0.382329\pi\) | |||||||
\(912\) | −1.98387 | − | 1.14539i | −0.0656925 | − | 0.0379276i | ||||
\(913\) | 36.6113 | − | 63.4126i | 1.21166 | − | 2.09865i | ||||
\(914\) | 7.77770 | + | 13.4714i | 0.257264 | + | 0.445594i | ||||
\(915\) | − | 0.535898i | − | 0.0177163i | ||||||
\(916\) | −3.59826 | + | 2.07746i | −0.118890 | + | 0.0686411i | ||||
\(917\) | −18.3154 | + | 10.5744i | −0.604828 | + | 0.349197i | ||||
\(918\) | − | 4.00000i | − | 0.132020i | ||||||
\(919\) | 2.65289 | + | 4.59494i | 0.0875108 | + | 0.151573i | 0.906458 | − | 0.422295i | \(-0.138775\pi\) |
−0.818948 | + | 0.573868i | \(0.805442\pi\) | |||||||
\(920\) | −4.33399 | + | 7.50670i | −0.142888 | + | 0.247488i | ||||
\(921\) | −8.50975 | − | 4.91311i | −0.280406 | − | 0.161892i | ||||
\(922\) | −15.6431 | −0.515178 | ||||||||
\(923\) | −21.9992 | + | 34.4469i | −0.724112 | + | 1.13383i | ||||
\(924\) | 6.10153 | 0.200726 | ||||||||
\(925\) | −5.89721 | − | 3.40475i | −0.193899 | − | 0.111948i | ||||
\(926\) | 6.85848 | − | 11.8792i | 0.225384 | − | 0.390376i | ||||
\(927\) | 9.20002 | + | 15.9349i | 0.302168 | + | 0.523371i | ||||
\(928\) | − | 2.02283i | − | 0.0664025i | ||||||
\(929\) | −38.4002 | + | 22.1704i | −1.25987 | + | 0.727386i | −0.973049 | − | 0.230598i | \(-0.925932\pi\) |
−0.286821 | + | 0.957984i | \(0.592599\pi\) | |||||||
\(930\) | −8.77464 | + | 5.06604i | −0.287732 | + | 0.166122i | ||||
\(931\) | 12.0284i | 0.394214i | ||||||||
\(932\) | 8.48325 | + | 14.6934i | 0.277878 | + | 0.481299i | ||||
\(933\) | 1.70025 | − | 2.94491i | 0.0556636 | − | 0.0964121i | ||||
\(934\) | 0.817239 | + | 0.471833i | 0.0267409 | + | 0.0154388i | ||||
\(935\) | −18.4534 | −0.603491 | ||||||||
\(936\) | −1.94065 | + | 3.03873i | −0.0634322 | + | 0.0993239i | ||||
\(937\) | 38.5283 | 1.25867 | 0.629333 | − | 0.777136i | \(-0.283328\pi\) | ||||
0.629333 | + | 0.777136i | \(0.283328\pi\) | |||||||
\(938\) | 3.64354 | + | 2.10360i | 0.118966 | + | 0.0686850i | ||||
\(939\) | 8.11699 | − | 14.0590i | 0.264888 | − | 0.458800i | ||||
\(940\) | −4.55463 | − | 7.88885i | −0.148556 | − | 0.257306i | ||||
\(941\) | 28.8637i | 0.940929i | 0.882419 | + | 0.470465i | \(0.155914\pi\) | ||||
−0.882419 | + | 0.470465i | \(0.844086\pi\) | |||||||
\(942\) | 6.17804 | − | 3.56690i | 0.201292 | − | 0.116216i | ||||
\(943\) | −34.8698 | + | 20.1321i | −1.13552 | + | 0.655591i | ||||
\(944\) | 3.14152i | 0.102248i | ||||||||
\(945\) | −0.661290 | − | 1.14539i | −0.0215118 | − | 0.0372595i | ||||
\(946\) | −19.8504 | + | 34.3819i | −0.645392 | + | 1.11785i | ||||
\(947\) | 42.6384 | + | 24.6173i | 1.38556 | + | 0.799955i | 0.992811 | − | 0.119689i | \(-0.0381899\pi\) |
0.392752 | + | 0.919645i | \(0.371523\pi\) | |||||||
\(948\) | −2.96774 | −0.0963877 | ||||||||
\(949\) | −10.4380 | − | 20.1059i | −0.338830 | − | 0.652664i | ||||
\(950\) | 2.29078 | 0.0743226 | ||||||||
\(951\) | −20.3716 | − | 11.7616i | −0.660596 | − | 0.381395i | ||||
\(952\) | 2.64516 | − | 4.58155i | 0.0857301 | − | 0.148489i | ||||
\(953\) | −13.2548 | − | 22.9580i | −0.429366 | − | 0.743684i | 0.567451 | − | 0.823407i | \(-0.307930\pi\) |
−0.996817 | + | 0.0797233i | \(0.974596\pi\) | |||||||
\(954\) | 0.826674i | 0.0267645i | ||||||||
\(955\) | 8.44128 | − | 4.87357i | 0.273153 | − | 0.157705i | ||||
\(956\) | 5.49420 | − | 3.17208i | 0.177695 | − | 0.102592i | ||||
\(957\) | − | 9.33201i | − | 0.301661i | ||||||
\(958\) | 5.55099 | + | 9.61460i | 0.179344 | + | 0.310634i | ||||
\(959\) | 10.6267 | − | 18.4061i | 0.343156 | − | 0.594363i | ||||
\(960\) | −0.866025 | − | 0.500000i | −0.0279508 | − | 0.0161374i | ||||
\(961\) | −71.6592 | −2.31159 | ||||||||
\(962\) | −20.6922 | − | 13.2149i | −0.667145 | − | 0.426065i | ||||
\(963\) | 3.07180 | 0.0989873 | ||||||||
\(964\) | 20.9452 | + | 12.0927i | 0.674600 | + | 0.389481i | ||||
\(965\) | −6.88130 | + | 11.9188i | −0.221517 | + | 0.383679i | ||||
\(966\) | −5.73205 | − | 9.92820i | −0.184426 | − | 0.319435i | ||||
\(967\) | 52.3877i | 1.68468i | 0.538950 | + | 0.842338i | \(0.318821\pi\) | ||||
−0.538950 | + | 0.842338i | \(0.681179\pi\) | |||||||
\(968\) | 8.90538 | − | 5.14152i | 0.286230 | − | 0.165255i | ||||
\(969\) | −7.93548 | + | 4.58155i | −0.254924 | + | 0.147181i | ||||
\(970\) | − | 8.81894i | − | 0.283159i | ||||||
\(971\) | 14.3215 | + | 24.8056i | 0.459600 | + | 0.796051i | 0.998940 | − | 0.0460375i | \(-0.0146594\pi\) |
−0.539339 | + | 0.842088i | \(0.681326\pi\) | |||||||
\(972\) | 0.500000 | − | 0.866025i | 0.0160375 | − | 0.0277778i | ||||
\(973\) | −10.6780 | − | 6.16493i | −0.342320 | − | 0.197638i | ||||
\(974\) | 32.9416 | 1.05552 | ||||||||
\(975\) | 0.161290 | − | 3.60194i | 0.00516541 | − | 0.115354i | ||||
\(976\) | 0.535898 | 0.0171537 | ||||||||
\(977\) | 35.1173 | + | 20.2750i | 1.12350 | + | 0.648654i | 0.942292 | − | 0.334791i | \(-0.108666\pi\) |
0.181209 | + | 0.983445i | \(0.441999\pi\) | |||||||
\(978\) | −4.94735 | + | 8.56906i | −0.158199 | + | 0.274008i | ||||
\(979\) | −27.3667 | − | 47.4006i | −0.874645 | − | 1.51493i | ||||
\(980\) | 5.25078i | 0.167730i | ||||||||
\(981\) | 11.4547 | − | 6.61335i | 0.365719 | − | 0.211148i | ||||
\(982\) | −24.6396 | + | 14.2257i | −0.786281 | + | 0.453960i | ||||
\(983\) | 22.4160i | 0.714958i | 0.933921 | + | 0.357479i | \(0.116364\pi\) | ||||
−0.933921 | + | 0.357479i | \(0.883636\pi\) | |||||||
\(984\) | −2.32258 | − | 4.02283i | −0.0740411 | − | 0.128243i | ||||
\(985\) | −5.07076 | + | 8.78282i | −0.161568 | + | 0.279844i | ||||
\(986\) | −7.00727 | − | 4.04565i | −0.223157 | − | 0.128840i | ||||
\(987\) | 12.0477 | 0.383483 | ||||||||
\(988\) | 8.25124 | + | 0.369479i | 0.262507 | + | 0.0117547i | ||||
\(989\) | 74.5934 | 2.37193 | ||||||||
\(990\) | −3.99528 | − | 2.30668i | −0.126978 | − | 0.0733110i | ||||
\(991\) | 14.2844 | − | 24.7413i | 0.453759 | − | 0.785933i | −0.544857 | − | 0.838529i | \(-0.683416\pi\) |
0.998616 | + | 0.0525955i | \(0.0167494\pi\) | |||||||
\(992\) | −5.06604 | − | 8.77464i | −0.160847 | − | 0.278595i | ||||
\(993\) | 18.0904i | 0.574081i | ||||||||
\(994\) | 12.9841 | − | 7.49636i | 0.411830 | − | 0.237770i | ||||
\(995\) | 8.29078 | − | 4.78668i | 0.262835 | − | 0.151748i | ||||
\(996\) | − | 15.8719i | − | 0.502919i | ||||||
\(997\) | 17.2000 | + | 29.7913i | 0.544730 | + | 0.943500i | 0.998624 | + | 0.0524443i | \(0.0167012\pi\) |
−0.453894 | + | 0.891056i | \(0.649965\pi\) | |||||||
\(998\) | −2.05463 | + | 3.55872i | −0.0650382 | + | 0.112649i | ||||
\(999\) | 5.89721 | + | 3.40475i | 0.186579 | + | 0.107722i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 390.2.bb.c.121.2 | ✓ | 8 | |
3.2 | odd | 2 | 1170.2.bs.f.901.4 | 8 | |||
5.2 | odd | 4 | 1950.2.y.k.199.4 | 8 | |||
5.3 | odd | 4 | 1950.2.y.j.199.1 | 8 | |||
5.4 | even | 2 | 1950.2.bc.g.901.3 | 8 | |||
13.4 | even | 6 | 5070.2.b.ba.1351.2 | 8 | |||
13.6 | odd | 12 | 5070.2.a.ca.1.2 | 4 | |||
13.7 | odd | 12 | 5070.2.a.bz.1.3 | 4 | |||
13.9 | even | 3 | 5070.2.b.ba.1351.7 | 8 | |||
13.10 | even | 6 | inner | 390.2.bb.c.361.2 | yes | 8 | |
39.23 | odd | 6 | 1170.2.bs.f.361.4 | 8 | |||
65.23 | odd | 12 | 1950.2.y.k.49.4 | 8 | |||
65.49 | even | 6 | 1950.2.bc.g.751.3 | 8 | |||
65.62 | odd | 12 | 1950.2.y.j.49.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.bb.c.121.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
390.2.bb.c.361.2 | yes | 8 | 13.10 | even | 6 | inner | |
1170.2.bs.f.361.4 | 8 | 39.23 | odd | 6 | |||
1170.2.bs.f.901.4 | 8 | 3.2 | odd | 2 | |||
1950.2.y.j.49.1 | 8 | 65.62 | odd | 12 | |||
1950.2.y.j.199.1 | 8 | 5.3 | odd | 4 | |||
1950.2.y.k.49.4 | 8 | 65.23 | odd | 12 | |||
1950.2.y.k.199.4 | 8 | 5.2 | odd | 4 | |||
1950.2.bc.g.751.3 | 8 | 65.49 | even | 6 | |||
1950.2.bc.g.901.3 | 8 | 5.4 | even | 2 | |||
5070.2.a.bz.1.3 | 4 | 13.7 | odd | 12 | |||
5070.2.a.ca.1.2 | 4 | 13.6 | odd | 12 | |||
5070.2.b.ba.1351.2 | 8 | 13.4 | even | 6 | |||
5070.2.b.ba.1351.7 | 8 | 13.9 | even | 3 |