Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(1,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.a (trivial) |
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: | yes |
Analytic conductor: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.81361\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.81361 | −1.28241 | −0.641207 | − | 0.767368i | \(-0.721566\pi\) | ||||
−0.641207 | + | 0.767368i | \(0.721566\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.28917 | 0.644584 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.81361 | 0.740402 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.28917 | 0.455790 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.81361 | −0.573513 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −1.28917 | −0.372151 | ||||||||
\(13\) | 5.10278 | 1.41526 | 0.707628 | − | 0.706586i | \(-0.249765\pi\) | ||||
0.707628 | + | 0.706586i | \(0.249765\pi\) | |||||||
\(14\) | 1.81361 | 0.484707 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −4.91638 | −1.22910 | ||||||||
\(17\) | 4.28917 | 1.04028 | 0.520138 | − | 0.854082i | \(-0.325880\pi\) | ||||
0.520138 | + | 0.854082i | \(0.325880\pi\) | |||||||
\(18\) | −1.81361 | −0.427471 | ||||||||
\(19\) | −3.33804 | −0.765800 | −0.382900 | − | 0.923790i | \(-0.625075\pi\) | ||||
−0.382900 | + | 0.923790i | \(0.625075\pi\) | |||||||
\(20\) | 1.28917 | 0.288267 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 1.81361 | 0.386662 | ||||||||
\(23\) | −3.91638 | −0.816622 | −0.408311 | − | 0.912843i | \(-0.633882\pi\) | ||||
−0.408311 | + | 0.912843i | \(0.633882\pi\) | |||||||
\(24\) | −1.28917 | −0.263150 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −9.25443 | −1.81494 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.28917 | −0.243630 | ||||||||
\(29\) | 9.01916 | 1.67482 | 0.837408 | − | 0.546579i | \(-0.184070\pi\) | ||||
0.837408 | + | 0.546579i | \(0.184070\pi\) | |||||||
\(30\) | 1.81361 | 0.331118 | ||||||||
\(31\) | −3.68111 | −0.661147 | −0.330574 | − | 0.943780i | \(-0.607242\pi\) | ||||
−0.330574 | + | 0.943780i | \(0.607242\pi\) | |||||||
\(32\) | 6.33804 | 1.12042 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | −7.77886 | −1.33406 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 1.28917 | 0.214861 | ||||||||
\(37\) | −1.10278 | −0.181295 | −0.0906476 | − | 0.995883i | \(-0.528894\pi\) | ||||
−0.0906476 | + | 0.995883i | \(0.528894\pi\) | |||||||
\(38\) | 6.05390 | 0.982072 | ||||||||
\(39\) | −5.10278 | −0.817098 | ||||||||
\(40\) | 1.28917 | 0.203835 | ||||||||
\(41\) | −6.72999 | −1.05105 | −0.525524 | − | 0.850779i | \(-0.676131\pi\) | ||||
−0.525524 | + | 0.850779i | \(0.676131\pi\) | |||||||
\(42\) | −1.81361 | −0.279846 | ||||||||
\(43\) | −5.39194 | −0.822264 | −0.411132 | − | 0.911576i | \(-0.634866\pi\) | ||||
−0.411132 | + | 0.911576i | \(0.634866\pi\) | |||||||
\(44\) | −1.28917 | −0.194349 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 7.10278 | 1.04725 | ||||||||
\(47\) | 8.72999 | 1.27340 | 0.636700 | − | 0.771112i | \(-0.280299\pi\) | ||||
0.636700 | + | 0.771112i | \(0.280299\pi\) | |||||||
\(48\) | 4.91638 | 0.709619 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.81361 | −0.256483 | ||||||||
\(51\) | −4.28917 | −0.600604 | ||||||||
\(52\) | 6.57834 | 0.912251 | ||||||||
\(53\) | 8.75971 | 1.20324 | 0.601619 | − | 0.798783i | \(-0.294522\pi\) | ||||
0.601619 | + | 0.798783i | \(0.294522\pi\) | |||||||
\(54\) | 1.81361 | 0.246801 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | −1.28917 | −0.172272 | ||||||||
\(57\) | 3.33804 | 0.442135 | ||||||||
\(58\) | −16.3572 | −2.14781 | ||||||||
\(59\) | −5.39194 | −0.701971 | −0.350986 | − | 0.936381i | \(-0.614153\pi\) | ||||
−0.350986 | + | 0.936381i | \(0.614153\pi\) | |||||||
\(60\) | −1.28917 | −0.166431 | ||||||||
\(61\) | −13.7491 | −1.76040 | −0.880199 | − | 0.474605i | \(-0.842591\pi\) | ||||
−0.880199 | + | 0.474605i | \(0.842591\pi\) | |||||||
\(62\) | 6.67609 | 0.847864 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −1.66196 | −0.207744 | ||||||||
\(65\) | 5.10278 | 0.632921 | ||||||||
\(66\) | −1.81361 | −0.223240 | ||||||||
\(67\) | 10.6761 | 1.30429 | 0.652146 | − | 0.758093i | \(-0.273869\pi\) | ||||
0.652146 | + | 0.758093i | \(0.273869\pi\) | |||||||
\(68\) | 5.52946 | 0.670546 | ||||||||
\(69\) | 3.91638 | 0.471477 | ||||||||
\(70\) | 1.81361 | 0.216767 | ||||||||
\(71\) | 10.3572 | 1.22917 | 0.614587 | − | 0.788849i | \(-0.289323\pi\) | ||||
0.614587 | + | 0.788849i | \(0.289323\pi\) | |||||||
\(72\) | 1.28917 | 0.151930 | ||||||||
\(73\) | 3.62721 | 0.424533 | 0.212267 | − | 0.977212i | \(-0.431915\pi\) | ||||
0.212267 | + | 0.977212i | \(0.431915\pi\) | |||||||
\(74\) | 2.00000 | 0.232495 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −4.30330 | −0.493623 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 9.25443 | 1.04786 | ||||||||
\(79\) | −12.1517 | −1.36717 | −0.683584 | − | 0.729872i | \(-0.739580\pi\) | ||||
−0.683584 | + | 0.729872i | \(0.739580\pi\) | |||||||
\(80\) | −4.91638 | −0.549668 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 12.2056 | 1.34788 | ||||||||
\(83\) | −4.96526 | −0.545008 | −0.272504 | − | 0.962155i | \(-0.587852\pi\) | ||||
−0.272504 | + | 0.962155i | \(0.587852\pi\) | |||||||
\(84\) | 1.28917 | 0.140660 | ||||||||
\(85\) | 4.28917 | 0.465226 | ||||||||
\(86\) | 9.77886 | 1.05448 | ||||||||
\(87\) | −9.01916 | −0.966955 | ||||||||
\(88\) | −1.28917 | −0.137426 | ||||||||
\(89\) | 15.1169 | 1.60239 | 0.801195 | − | 0.598404i | \(-0.204198\pi\) | ||||
0.801195 | + | 0.598404i | \(0.204198\pi\) | |||||||
\(90\) | −1.81361 | −0.191171 | ||||||||
\(91\) | −5.10278 | −0.534916 | ||||||||
\(92\) | −5.04888 | −0.526382 | ||||||||
\(93\) | 3.68111 | 0.381714 | ||||||||
\(94\) | −15.8328 | −1.63302 | ||||||||
\(95\) | −3.33804 | −0.342476 | ||||||||
\(96\) | −6.33804 | −0.646874 | ||||||||
\(97\) | 11.8625 | 1.20445 | 0.602226 | − | 0.798325i | \(-0.294280\pi\) | ||||
0.602226 | + | 0.798325i | \(0.294280\pi\) | |||||||
\(98\) | −1.81361 | −0.183202 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 1.28917 | 0.128917 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 7.77886 | 0.770222 | ||||||||
\(103\) | 15.5975 | 1.53687 | 0.768433 | − | 0.639930i | \(-0.221037\pi\) | ||||
0.768433 | + | 0.639930i | \(0.221037\pi\) | |||||||
\(104\) | 6.57834 | 0.645059 | ||||||||
\(105\) | 1.00000 | 0.0975900 | ||||||||
\(106\) | −15.8867 | −1.54305 | ||||||||
\(107\) | 17.7789 | 1.71875 | 0.859374 | − | 0.511348i | \(-0.170854\pi\) | ||||
0.859374 | + | 0.511348i | \(0.170854\pi\) | |||||||
\(108\) | −1.28917 | −0.124050 | ||||||||
\(109\) | 8.35720 | 0.800475 | 0.400237 | − | 0.916412i | \(-0.368928\pi\) | ||||
0.400237 | + | 0.916412i | \(0.368928\pi\) | |||||||
\(110\) | 1.81361 | 0.172921 | ||||||||
\(111\) | 1.10278 | 0.104671 | ||||||||
\(112\) | 4.91638 | 0.464554 | ||||||||
\(113\) | 16.7003 | 1.57103 | 0.785515 | − | 0.618843i | \(-0.212398\pi\) | ||||
0.785515 | + | 0.618843i | \(0.212398\pi\) | |||||||
\(114\) | −6.05390 | −0.567000 | ||||||||
\(115\) | −3.91638 | −0.365204 | ||||||||
\(116\) | 11.6272 | 1.07956 | ||||||||
\(117\) | 5.10278 | 0.471752 | ||||||||
\(118\) | 9.77886 | 0.900217 | ||||||||
\(119\) | −4.28917 | −0.393187 | ||||||||
\(120\) | −1.28917 | −0.117684 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 24.9355 | 2.25756 | ||||||||
\(123\) | 6.72999 | 0.606823 | ||||||||
\(124\) | −4.74557 | −0.426165 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 1.81361 | 0.161569 | ||||||||
\(127\) | −12.8136 | −1.13702 | −0.568512 | − | 0.822675i | \(-0.692481\pi\) | ||||
−0.568512 | + | 0.822675i | \(0.692481\pi\) | |||||||
\(128\) | −9.66196 | −0.854004 | ||||||||
\(129\) | 5.39194 | 0.474734 | ||||||||
\(130\) | −9.25443 | −0.811667 | ||||||||
\(131\) | 18.9355 | 1.65441 | 0.827203 | − | 0.561903i | \(-0.189931\pi\) | ||||
0.827203 | + | 0.561903i | \(0.189931\pi\) | |||||||
\(132\) | 1.28917 | 0.112208 | ||||||||
\(133\) | 3.33804 | 0.289445 | ||||||||
\(134\) | −19.3622 | −1.67264 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 5.52946 | 0.474147 | ||||||||
\(137\) | −4.03831 | −0.345016 | −0.172508 | − | 0.985008i | \(-0.555187\pi\) | ||||
−0.172508 | + | 0.985008i | \(0.555187\pi\) | |||||||
\(138\) | −7.10278 | −0.604628 | ||||||||
\(139\) | 20.1361 | 1.70792 | 0.853959 | − | 0.520340i | \(-0.174195\pi\) | ||||
0.853959 | + | 0.520340i | \(0.174195\pi\) | |||||||
\(140\) | −1.28917 | −0.108955 | ||||||||
\(141\) | −8.72999 | −0.735198 | ||||||||
\(142\) | −18.7839 | −1.57631 | ||||||||
\(143\) | −5.10278 | −0.426715 | ||||||||
\(144\) | −4.91638 | −0.409698 | ||||||||
\(145\) | 9.01916 | 0.749000 | ||||||||
\(146\) | −6.57834 | −0.544427 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −1.42166 | −0.116860 | ||||||||
\(149\) | −20.6167 | −1.68898 | −0.844491 | − | 0.535570i | \(-0.820097\pi\) | ||||
−0.844491 | + | 0.535570i | \(0.820097\pi\) | |||||||
\(150\) | 1.81361 | 0.148080 | ||||||||
\(151\) | 5.73501 | 0.466709 | 0.233354 | − | 0.972392i | \(-0.425030\pi\) | ||||
0.233354 | + | 0.972392i | \(0.425030\pi\) | |||||||
\(152\) | −4.30330 | −0.349044 | ||||||||
\(153\) | 4.28917 | 0.346759 | ||||||||
\(154\) | −1.81361 | −0.146145 | ||||||||
\(155\) | −3.68111 | −0.295674 | ||||||||
\(156\) | −6.57834 | −0.526688 | ||||||||
\(157\) | −10.0680 | −0.803516 | −0.401758 | − | 0.915746i | \(-0.631601\pi\) | ||||
−0.401758 | + | 0.915746i | \(0.631601\pi\) | |||||||
\(158\) | 22.0383 | 1.75327 | ||||||||
\(159\) | −8.75971 | −0.694690 | ||||||||
\(160\) | 6.33804 | 0.501066 | ||||||||
\(161\) | 3.91638 | 0.308654 | ||||||||
\(162\) | −1.81361 | −0.142490 | ||||||||
\(163\) | 0.837786 | 0.0656205 | 0.0328102 | − | 0.999462i | \(-0.489554\pi\) | ||||
0.0328102 | + | 0.999462i | \(0.489554\pi\) | |||||||
\(164\) | −8.67609 | −0.677489 | ||||||||
\(165\) | 1.00000 | 0.0778499 | ||||||||
\(166\) | 9.00502 | 0.698925 | ||||||||
\(167\) | 24.1361 | 1.86770 | 0.933852 | − | 0.357659i | \(-0.116425\pi\) | ||||
0.933852 | + | 0.357659i | \(0.116425\pi\) | |||||||
\(168\) | 1.28917 | 0.0994615 | ||||||||
\(169\) | 13.0383 | 1.00295 | ||||||||
\(170\) | −7.77886 | −0.596612 | ||||||||
\(171\) | −3.33804 | −0.255267 | ||||||||
\(172\) | −6.95112 | −0.530018 | ||||||||
\(173\) | −19.2927 | −1.46680 | −0.733400 | − | 0.679797i | \(-0.762068\pi\) | ||||
−0.733400 | + | 0.679797i | \(0.762068\pi\) | |||||||
\(174\) | 16.3572 | 1.24004 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 4.91638 | 0.370586 | ||||||||
\(177\) | 5.39194 | 0.405283 | ||||||||
\(178\) | −27.4161 | −2.05493 | ||||||||
\(179\) | 6.35720 | 0.475160 | 0.237580 | − | 0.971368i | \(-0.423646\pi\) | ||||
0.237580 | + | 0.971368i | \(0.423646\pi\) | |||||||
\(180\) | 1.28917 | 0.0960890 | ||||||||
\(181\) | −3.15667 | −0.234634 | −0.117317 | − | 0.993095i | \(-0.537429\pi\) | ||||
−0.117317 | + | 0.993095i | \(0.537429\pi\) | |||||||
\(182\) | 9.25443 | 0.685984 | ||||||||
\(183\) | 13.7491 | 1.01637 | ||||||||
\(184\) | −5.04888 | −0.372208 | ||||||||
\(185\) | −1.10278 | −0.0810776 | ||||||||
\(186\) | −6.67609 | −0.489515 | ||||||||
\(187\) | −4.28917 | −0.313655 | ||||||||
\(188\) | 11.2544 | 0.820813 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 6.05390 | 0.439196 | ||||||||
\(191\) | −11.2544 | −0.814342 | −0.407171 | − | 0.913352i | \(-0.633485\pi\) | ||||
−0.407171 | + | 0.913352i | \(0.633485\pi\) | |||||||
\(192\) | 1.66196 | 0.119941 | ||||||||
\(193\) | −23.4600 | −1.68869 | −0.844343 | − | 0.535803i | \(-0.820009\pi\) | ||||
−0.844343 | + | 0.535803i | \(0.820009\pi\) | |||||||
\(194\) | −21.5139 | −1.54461 | ||||||||
\(195\) | −5.10278 | −0.365417 | ||||||||
\(196\) | 1.28917 | 0.0920835 | ||||||||
\(197\) | 8.78389 | 0.625826 | 0.312913 | − | 0.949782i | \(-0.398695\pi\) | ||||
0.312913 | + | 0.949782i | \(0.398695\pi\) | |||||||
\(198\) | 1.81361 | 0.128887 | ||||||||
\(199\) | 15.6655 | 1.11050 | 0.555250 | − | 0.831684i | \(-0.312623\pi\) | ||||
0.555250 | + | 0.831684i | \(0.312623\pi\) | |||||||
\(200\) | 1.28917 | 0.0911580 | ||||||||
\(201\) | −10.6761 | −0.753033 | ||||||||
\(202\) | −10.8816 | −0.765629 | ||||||||
\(203\) | −9.01916 | −0.633021 | ||||||||
\(204\) | −5.52946 | −0.387140 | ||||||||
\(205\) | −6.72999 | −0.470043 | ||||||||
\(206\) | −28.2877 | −1.97090 | ||||||||
\(207\) | −3.91638 | −0.272207 | ||||||||
\(208\) | −25.0872 | −1.73948 | ||||||||
\(209\) | 3.33804 | 0.230897 | ||||||||
\(210\) | −1.81361 | −0.125151 | ||||||||
\(211\) | 0.881639 | 0.0606945 | 0.0303473 | − | 0.999539i | \(-0.490339\pi\) | ||||
0.0303473 | + | 0.999539i | \(0.490339\pi\) | |||||||
\(212\) | 11.2927 | 0.775589 | ||||||||
\(213\) | −10.3572 | −0.709664 | ||||||||
\(214\) | −32.2439 | −2.20415 | ||||||||
\(215\) | −5.39194 | −0.367728 | ||||||||
\(216\) | −1.28917 | −0.0877168 | ||||||||
\(217\) | 3.68111 | 0.249890 | ||||||||
\(218\) | −15.1567 | −1.02654 | ||||||||
\(219\) | −3.62721 | −0.245104 | ||||||||
\(220\) | −1.28917 | −0.0869157 | ||||||||
\(221\) | 21.8867 | 1.47226 | ||||||||
\(222\) | −2.00000 | −0.134231 | ||||||||
\(223\) | −0.235269 | −0.0157548 | −0.00787740 | − | 0.999969i | \(-0.502507\pi\) | ||||
−0.00787740 | + | 0.999969i | \(0.502507\pi\) | |||||||
\(224\) | −6.33804 | −0.423478 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −30.2877 | −2.01471 | ||||||||
\(227\) | 9.71083 | 0.644531 | 0.322265 | − | 0.946649i | \(-0.395556\pi\) | ||||
0.322265 | + | 0.946649i | \(0.395556\pi\) | |||||||
\(228\) | 4.30330 | 0.284993 | ||||||||
\(229\) | 18.6705 | 1.23378 | 0.616892 | − | 0.787048i | \(-0.288391\pi\) | ||||
0.616892 | + | 0.787048i | \(0.288391\pi\) | |||||||
\(230\) | 7.10278 | 0.468343 | ||||||||
\(231\) | −1.00000 | −0.0657952 | ||||||||
\(232\) | 11.6272 | 0.763364 | ||||||||
\(233\) | −20.9355 | −1.37153 | −0.685766 | − | 0.727822i | \(-0.740533\pi\) | ||||
−0.685766 | + | 0.727822i | \(0.740533\pi\) | |||||||
\(234\) | −9.25443 | −0.604981 | ||||||||
\(235\) | 8.72999 | 0.569482 | ||||||||
\(236\) | −6.95112 | −0.452480 | ||||||||
\(237\) | 12.1517 | 0.789335 | ||||||||
\(238\) | 7.77886 | 0.504229 | ||||||||
\(239\) | 28.3119 | 1.83134 | 0.915672 | − | 0.401926i | \(-0.131659\pi\) | ||||
0.915672 | + | 0.401926i | \(0.131659\pi\) | |||||||
\(240\) | 4.91638 | 0.317351 | ||||||||
\(241\) | 4.26499 | 0.274732 | 0.137366 | − | 0.990520i | \(-0.456136\pi\) | ||||
0.137366 | + | 0.990520i | \(0.456136\pi\) | |||||||
\(242\) | −1.81361 | −0.116583 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −17.7250 | −1.13472 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −12.2056 | −0.778197 | ||||||||
\(247\) | −17.0333 | −1.08380 | ||||||||
\(248\) | −4.74557 | −0.301344 | ||||||||
\(249\) | 4.96526 | 0.314660 | ||||||||
\(250\) | −1.81361 | −0.114703 | ||||||||
\(251\) | −18.7244 | −1.18188 | −0.590938 | − | 0.806717i | \(-0.701242\pi\) | ||||
−0.590938 | + | 0.806717i | \(0.701242\pi\) | |||||||
\(252\) | −1.28917 | −0.0812100 | ||||||||
\(253\) | 3.91638 | 0.246221 | ||||||||
\(254\) | 23.2388 | 1.45813 | ||||||||
\(255\) | −4.28917 | −0.268598 | ||||||||
\(256\) | 20.8469 | 1.30293 | ||||||||
\(257\) | −4.63224 | −0.288951 | −0.144475 | − | 0.989508i | \(-0.546149\pi\) | ||||
−0.144475 | + | 0.989508i | \(0.546149\pi\) | |||||||
\(258\) | −9.77886 | −0.608805 | ||||||||
\(259\) | 1.10278 | 0.0685231 | ||||||||
\(260\) | 6.57834 | 0.407971 | ||||||||
\(261\) | 9.01916 | 0.558272 | ||||||||
\(262\) | −34.3416 | −2.12163 | ||||||||
\(263\) | −12.7144 | −0.784004 | −0.392002 | − | 0.919964i | \(-0.628217\pi\) | ||||
−0.392002 | + | 0.919964i | \(0.628217\pi\) | |||||||
\(264\) | 1.28917 | 0.0793428 | ||||||||
\(265\) | 8.75971 | 0.538105 | ||||||||
\(266\) | −6.05390 | −0.371188 | ||||||||
\(267\) | −15.1169 | −0.925140 | ||||||||
\(268\) | 13.7633 | 0.840726 | ||||||||
\(269\) | −21.3225 | −1.30005 | −0.650027 | − | 0.759911i | \(-0.725242\pi\) | ||||
−0.650027 | + | 0.759911i | \(0.725242\pi\) | |||||||
\(270\) | 1.81361 | 0.110373 | ||||||||
\(271\) | 4.21968 | 0.256328 | 0.128164 | − | 0.991753i | \(-0.459092\pi\) | ||||
0.128164 | + | 0.991753i | \(0.459092\pi\) | |||||||
\(272\) | −21.0872 | −1.27860 | ||||||||
\(273\) | 5.10278 | 0.308834 | ||||||||
\(274\) | 7.32391 | 0.442454 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 5.04888 | 0.303907 | ||||||||
\(277\) | 9.08719 | 0.545996 | 0.272998 | − | 0.962015i | \(-0.411985\pi\) | ||||
0.272998 | + | 0.962015i | \(0.411985\pi\) | |||||||
\(278\) | −36.5189 | −2.19026 | ||||||||
\(279\) | −3.68111 | −0.220382 | ||||||||
\(280\) | −1.28917 | −0.0770426 | ||||||||
\(281\) | −20.6761 | −1.23343 | −0.616716 | − | 0.787186i | \(-0.711537\pi\) | ||||
−0.616716 | + | 0.787186i | \(0.711537\pi\) | |||||||
\(282\) | 15.8328 | 0.942827 | ||||||||
\(283\) | −7.04334 | −0.418683 | −0.209341 | − | 0.977843i | \(-0.567132\pi\) | ||||
−0.209341 | + | 0.977843i | \(0.567132\pi\) | |||||||
\(284\) | 13.3522 | 0.792306 | ||||||||
\(285\) | 3.33804 | 0.197729 | ||||||||
\(286\) | 9.25443 | 0.547226 | ||||||||
\(287\) | 6.72999 | 0.397259 | ||||||||
\(288\) | 6.33804 | 0.373473 | ||||||||
\(289\) | 1.39697 | 0.0821745 | ||||||||
\(290\) | −16.3572 | −0.960528 | ||||||||
\(291\) | −11.8625 | −0.695391 | ||||||||
\(292\) | 4.67609 | 0.273647 | ||||||||
\(293\) | −4.59247 | −0.268295 | −0.134147 | − | 0.990961i | \(-0.542830\pi\) | ||||
−0.134147 | + | 0.990961i | \(0.542830\pi\) | |||||||
\(294\) | 1.81361 | 0.105772 | ||||||||
\(295\) | −5.39194 | −0.313931 | ||||||||
\(296\) | −1.42166 | −0.0826325 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 37.3905 | 2.16597 | ||||||||
\(299\) | −19.9844 | −1.15573 | ||||||||
\(300\) | −1.28917 | −0.0744302 | ||||||||
\(301\) | 5.39194 | 0.310786 | ||||||||
\(302\) | −10.4011 | −0.598513 | ||||||||
\(303\) | −6.00000 | −0.344691 | ||||||||
\(304\) | 16.4111 | 0.941241 | ||||||||
\(305\) | −13.7491 | −0.787274 | ||||||||
\(306\) | −7.77886 | −0.444688 | ||||||||
\(307\) | 26.0383 | 1.48609 | 0.743043 | − | 0.669244i | \(-0.233382\pi\) | ||||
0.743043 | + | 0.669244i | \(0.233382\pi\) | |||||||
\(308\) | 1.28917 | 0.0734572 | ||||||||
\(309\) | −15.5975 | −0.887310 | ||||||||
\(310\) | 6.67609 | 0.379176 | ||||||||
\(311\) | −16.3033 | −0.924475 | −0.462238 | − | 0.886756i | \(-0.652953\pi\) | ||||
−0.462238 | + | 0.886756i | \(0.652953\pi\) | |||||||
\(312\) | −6.57834 | −0.372425 | ||||||||
\(313\) | 26.3713 | 1.49060 | 0.745298 | − | 0.666732i | \(-0.232307\pi\) | ||||
0.745298 | + | 0.666732i | \(0.232307\pi\) | |||||||
\(314\) | 18.2594 | 1.03044 | ||||||||
\(315\) | −1.00000 | −0.0563436 | ||||||||
\(316\) | −15.6655 | −0.881255 | ||||||||
\(317\) | 17.4217 | 0.978498 | 0.489249 | − | 0.872144i | \(-0.337271\pi\) | ||||
0.489249 | + | 0.872144i | \(0.337271\pi\) | |||||||
\(318\) | 15.8867 | 0.890880 | ||||||||
\(319\) | −9.01916 | −0.504976 | ||||||||
\(320\) | −1.66196 | −0.0929061 | ||||||||
\(321\) | −17.7789 | −0.992319 | ||||||||
\(322\) | −7.10278 | −0.395822 | ||||||||
\(323\) | −14.3174 | −0.796643 | ||||||||
\(324\) | 1.28917 | 0.0716205 | ||||||||
\(325\) | 5.10278 | 0.283051 | ||||||||
\(326\) | −1.51941 | −0.0841526 | ||||||||
\(327\) | −8.35720 | −0.462154 | ||||||||
\(328\) | −8.67609 | −0.479057 | ||||||||
\(329\) | −8.72999 | −0.481300 | ||||||||
\(330\) | −1.81361 | −0.0998358 | ||||||||
\(331\) | −16.2197 | −0.891514 | −0.445757 | − | 0.895154i | \(-0.647066\pi\) | ||||
−0.445757 | + | 0.895154i | \(0.647066\pi\) | |||||||
\(332\) | −6.40105 | −0.351303 | ||||||||
\(333\) | −1.10278 | −0.0604317 | ||||||||
\(334\) | −43.7733 | −2.39517 | ||||||||
\(335\) | 10.6761 | 0.583297 | ||||||||
\(336\) | −4.91638 | −0.268211 | ||||||||
\(337\) | −6.92140 | −0.377033 | −0.188516 | − | 0.982070i | \(-0.560368\pi\) | ||||
−0.188516 | + | 0.982070i | \(0.560368\pi\) | |||||||
\(338\) | −23.6464 | −1.28619 | ||||||||
\(339\) | −16.7003 | −0.907034 | ||||||||
\(340\) | 5.52946 | 0.299877 | ||||||||
\(341\) | 3.68111 | 0.199343 | ||||||||
\(342\) | 6.05390 | 0.327357 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −6.95112 | −0.374779 | ||||||||
\(345\) | 3.91638 | 0.210851 | ||||||||
\(346\) | 34.9894 | 1.88104 | ||||||||
\(347\) | −17.8711 | −0.959370 | −0.479685 | − | 0.877441i | \(-0.659249\pi\) | ||||
−0.479685 | + | 0.877441i | \(0.659249\pi\) | |||||||
\(348\) | −11.6272 | −0.623284 | ||||||||
\(349\) | 2.72139 | 0.145673 | 0.0728364 | − | 0.997344i | \(-0.476795\pi\) | ||||
0.0728364 | + | 0.997344i | \(0.476795\pi\) | |||||||
\(350\) | 1.81361 | 0.0969413 | ||||||||
\(351\) | −5.10278 | −0.272366 | ||||||||
\(352\) | −6.33804 | −0.337819 | ||||||||
\(353\) | −18.7144 | −0.996067 | −0.498034 | − | 0.867158i | \(-0.665944\pi\) | ||||
−0.498034 | + | 0.867158i | \(0.665944\pi\) | |||||||
\(354\) | −9.77886 | −0.519741 | ||||||||
\(355\) | 10.3572 | 0.549703 | ||||||||
\(356\) | 19.4882 | 1.03287 | ||||||||
\(357\) | 4.28917 | 0.227007 | ||||||||
\(358\) | −11.5295 | −0.609351 | ||||||||
\(359\) | 6.30475 | 0.332752 | 0.166376 | − | 0.986062i | \(-0.446793\pi\) | ||||
0.166376 | + | 0.986062i | \(0.446793\pi\) | |||||||
\(360\) | 1.28917 | 0.0679451 | ||||||||
\(361\) | −7.85746 | −0.413550 | ||||||||
\(362\) | 5.72496 | 0.300897 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | −6.57834 | −0.344799 | ||||||||
\(365\) | 3.62721 | 0.189857 | ||||||||
\(366\) | −24.9355 | −1.30340 | ||||||||
\(367\) | 19.0192 | 0.992792 | 0.496396 | − | 0.868096i | \(-0.334656\pi\) | ||||
0.496396 | + | 0.868096i | \(0.334656\pi\) | |||||||
\(368\) | 19.2544 | 1.00371 | ||||||||
\(369\) | −6.72999 | −0.350349 | ||||||||
\(370\) | 2.00000 | 0.103975 | ||||||||
\(371\) | −8.75971 | −0.454781 | ||||||||
\(372\) | 4.74557 | 0.246047 | ||||||||
\(373\) | −14.0086 | −0.725337 | −0.362669 | − | 0.931918i | \(-0.618134\pi\) | ||||
−0.362669 | + | 0.931918i | \(0.618134\pi\) | |||||||
\(374\) | 7.77886 | 0.402235 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 11.2544 | 0.580403 | ||||||||
\(377\) | 46.0227 | 2.37029 | ||||||||
\(378\) | −1.81361 | −0.0932819 | ||||||||
\(379\) | 13.2686 | 0.681560 | 0.340780 | − | 0.940143i | \(-0.389309\pi\) | ||||
0.340780 | + | 0.940143i | \(0.389309\pi\) | |||||||
\(380\) | −4.30330 | −0.220755 | ||||||||
\(381\) | 12.8136 | 0.656461 | ||||||||
\(382\) | 20.4111 | 1.04432 | ||||||||
\(383\) | 18.6917 | 0.955100 | 0.477550 | − | 0.878605i | \(-0.341525\pi\) | ||||
0.477550 | + | 0.878605i | \(0.341525\pi\) | |||||||
\(384\) | 9.66196 | 0.493060 | ||||||||
\(385\) | 1.00000 | 0.0509647 | ||||||||
\(386\) | 42.5472 | 2.16559 | ||||||||
\(387\) | −5.39194 | −0.274088 | ||||||||
\(388\) | 15.2927 | 0.776371 | ||||||||
\(389\) | −4.35720 | −0.220919 | −0.110459 | − | 0.993881i | \(-0.535232\pi\) | ||||
−0.110459 | + | 0.993881i | \(0.535232\pi\) | |||||||
\(390\) | 9.25443 | 0.468616 | ||||||||
\(391\) | −16.7980 | −0.849512 | ||||||||
\(392\) | 1.28917 | 0.0651128 | ||||||||
\(393\) | −18.9355 | −0.955172 | ||||||||
\(394\) | −15.9305 | −0.802568 | ||||||||
\(395\) | −12.1517 | −0.611416 | ||||||||
\(396\) | −1.28917 | −0.0647832 | ||||||||
\(397\) | −14.5783 | −0.731666 | −0.365833 | − | 0.930681i | \(-0.619216\pi\) | ||||
−0.365833 | + | 0.930681i | \(0.619216\pi\) | |||||||
\(398\) | −28.4111 | −1.42412 | ||||||||
\(399\) | −3.33804 | −0.167111 | ||||||||
\(400\) | −4.91638 | −0.245819 | ||||||||
\(401\) | 10.0922 | 0.503981 | 0.251991 | − | 0.967730i | \(-0.418915\pi\) | ||||
0.251991 | + | 0.967730i | \(0.418915\pi\) | |||||||
\(402\) | 19.3622 | 0.965700 | ||||||||
\(403\) | −18.7839 | −0.935692 | ||||||||
\(404\) | 7.73501 | 0.384831 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 16.3572 | 0.811794 | ||||||||
\(407\) | 1.10278 | 0.0546625 | ||||||||
\(408\) | −5.52946 | −0.273749 | ||||||||
\(409\) | 32.5572 | 1.60985 | 0.804925 | − | 0.593376i | \(-0.202205\pi\) | ||||
0.804925 | + | 0.593376i | \(0.202205\pi\) | |||||||
\(410\) | 12.2056 | 0.602789 | ||||||||
\(411\) | 4.03831 | 0.199195 | ||||||||
\(412\) | 20.1078 | 0.990640 | ||||||||
\(413\) | 5.39194 | 0.265320 | ||||||||
\(414\) | 7.10278 | 0.349082 | ||||||||
\(415\) | −4.96526 | −0.243735 | ||||||||
\(416\) | 32.3416 | 1.58568 | ||||||||
\(417\) | −20.1361 | −0.986067 | ||||||||
\(418\) | −6.05390 | −0.296106 | ||||||||
\(419\) | 1.66698 | 0.0814372 | 0.0407186 | − | 0.999171i | \(-0.487035\pi\) | ||||
0.0407186 | + | 0.999171i | \(0.487035\pi\) | |||||||
\(420\) | 1.28917 | 0.0629050 | ||||||||
\(421\) | −24.0625 | −1.17273 | −0.586367 | − | 0.810045i | \(-0.699442\pi\) | ||||
−0.586367 | + | 0.810045i | \(0.699442\pi\) | |||||||
\(422\) | −1.59895 | −0.0778355 | ||||||||
\(423\) | 8.72999 | 0.424467 | ||||||||
\(424\) | 11.2927 | 0.548424 | ||||||||
\(425\) | 4.28917 | 0.208055 | ||||||||
\(426\) | 18.7839 | 0.910082 | ||||||||
\(427\) | 13.7491 | 0.665368 | ||||||||
\(428\) | 22.9200 | 1.10788 | ||||||||
\(429\) | 5.10278 | 0.246364 | ||||||||
\(430\) | 9.77886 | 0.471579 | ||||||||
\(431\) | −0.637776 | −0.0307206 | −0.0153603 | − | 0.999882i | \(-0.504890\pi\) | ||||
−0.0153603 | + | 0.999882i | \(0.504890\pi\) | |||||||
\(432\) | 4.91638 | 0.236540 | ||||||||
\(433\) | 1.69670 | 0.0815381 | 0.0407691 | − | 0.999169i | \(-0.487019\pi\) | ||||
0.0407691 | + | 0.999169i | \(0.487019\pi\) | |||||||
\(434\) | −6.67609 | −0.320463 | ||||||||
\(435\) | −9.01916 | −0.432435 | ||||||||
\(436\) | 10.7738 | 0.515973 | ||||||||
\(437\) | 13.0731 | 0.625369 | ||||||||
\(438\) | 6.57834 | 0.314325 | ||||||||
\(439\) | −15.8569 | −0.756811 | −0.378405 | − | 0.925640i | \(-0.623527\pi\) | ||||
−0.378405 | + | 0.925640i | \(0.623527\pi\) | |||||||
\(440\) | −1.28917 | −0.0614587 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −39.6938 | −1.88804 | ||||||||
\(443\) | 40.7628 | 1.93670 | 0.968349 | − | 0.249602i | \(-0.0802996\pi\) | ||||
0.968349 | + | 0.249602i | \(0.0802996\pi\) | |||||||
\(444\) | 1.42166 | 0.0674691 | ||||||||
\(445\) | 15.1169 | 0.716610 | ||||||||
\(446\) | 0.426686 | 0.0202042 | ||||||||
\(447\) | 20.6167 | 0.975134 | ||||||||
\(448\) | 1.66196 | 0.0785200 | ||||||||
\(449\) | 1.78891 | 0.0844239 | 0.0422120 | − | 0.999109i | \(-0.486560\pi\) | ||||
0.0422120 | + | 0.999109i | \(0.486560\pi\) | |||||||
\(450\) | −1.81361 | −0.0854942 | ||||||||
\(451\) | 6.72999 | 0.316903 | ||||||||
\(452\) | 21.5295 | 1.01266 | ||||||||
\(453\) | −5.73501 | −0.269454 | ||||||||
\(454\) | −17.6116 | −0.826555 | ||||||||
\(455\) | −5.10278 | −0.239222 | ||||||||
\(456\) | 4.30330 | 0.201521 | ||||||||
\(457\) | 3.39194 | 0.158668 | 0.0793342 | − | 0.996848i | \(-0.474721\pi\) | ||||
0.0793342 | + | 0.996848i | \(0.474721\pi\) | |||||||
\(458\) | −33.8610 | −1.58222 | ||||||||
\(459\) | −4.28917 | −0.200201 | ||||||||
\(460\) | −5.04888 | −0.235405 | ||||||||
\(461\) | 33.7733 | 1.57298 | 0.786490 | − | 0.617603i | \(-0.211896\pi\) | ||||
0.786490 | + | 0.617603i | \(0.211896\pi\) | |||||||
\(462\) | 1.81361 | 0.0843766 | ||||||||
\(463\) | 11.7250 | 0.544905 | 0.272453 | − | 0.962169i | \(-0.412165\pi\) | ||||
0.272453 | + | 0.962169i | \(0.412165\pi\) | |||||||
\(464\) | −44.3416 | −2.05851 | ||||||||
\(465\) | 3.68111 | 0.170707 | ||||||||
\(466\) | 37.9688 | 1.75887 | ||||||||
\(467\) | 29.4600 | 1.36325 | 0.681623 | − | 0.731704i | \(-0.261275\pi\) | ||||
0.681623 | + | 0.731704i | \(0.261275\pi\) | |||||||
\(468\) | 6.57834 | 0.304084 | ||||||||
\(469\) | −10.6761 | −0.492976 | ||||||||
\(470\) | −15.8328 | −0.730311 | ||||||||
\(471\) | 10.0680 | 0.463910 | ||||||||
\(472\) | −6.95112 | −0.319951 | ||||||||
\(473\) | 5.39194 | 0.247922 | ||||||||
\(474\) | −22.0383 | −1.01225 | ||||||||
\(475\) | −3.33804 | −0.153160 | ||||||||
\(476\) | −5.52946 | −0.253442 | ||||||||
\(477\) | 8.75971 | 0.401079 | ||||||||
\(478\) | −51.3466 | −2.34854 | ||||||||
\(479\) | −17.6711 | −0.807412 | −0.403706 | − | 0.914889i | \(-0.632278\pi\) | ||||
−0.403706 | + | 0.914889i | \(0.632278\pi\) | |||||||
\(480\) | −6.33804 | −0.289291 | ||||||||
\(481\) | −5.62721 | −0.256579 | ||||||||
\(482\) | −7.73501 | −0.352320 | ||||||||
\(483\) | −3.91638 | −0.178202 | ||||||||
\(484\) | 1.28917 | 0.0585986 | ||||||||
\(485\) | 11.8625 | 0.538648 | ||||||||
\(486\) | 1.81361 | 0.0822669 | ||||||||
\(487\) | −18.7839 | −0.851179 | −0.425590 | − | 0.904916i | \(-0.639933\pi\) | ||||
−0.425590 | + | 0.904916i | \(0.639933\pi\) | |||||||
\(488\) | −17.7250 | −0.802371 | ||||||||
\(489\) | −0.837786 | −0.0378860 | ||||||||
\(490\) | −1.81361 | −0.0819304 | ||||||||
\(491\) | −5.08864 | −0.229647 | −0.114824 | − | 0.993386i | \(-0.536630\pi\) | ||||
−0.114824 | + | 0.993386i | \(0.536630\pi\) | |||||||
\(492\) | 8.67609 | 0.391148 | ||||||||
\(493\) | 38.6847 | 1.74227 | ||||||||
\(494\) | 30.8917 | 1.38988 | ||||||||
\(495\) | −1.00000 | −0.0449467 | ||||||||
\(496\) | 18.0978 | 0.812613 | ||||||||
\(497\) | −10.3572 | −0.464584 | ||||||||
\(498\) | −9.00502 | −0.403525 | ||||||||
\(499\) | 8.72139 | 0.390423 | 0.195212 | − | 0.980761i | \(-0.437461\pi\) | ||||
0.195212 | + | 0.980761i | \(0.437461\pi\) | |||||||
\(500\) | 1.28917 | 0.0576534 | ||||||||
\(501\) | −24.1361 | −1.07832 | ||||||||
\(502\) | 33.9588 | 1.51565 | ||||||||
\(503\) | −17.4842 | −0.779580 | −0.389790 | − | 0.920904i | \(-0.627452\pi\) | ||||
−0.389790 | + | 0.920904i | \(0.627452\pi\) | |||||||
\(504\) | −1.28917 | −0.0574241 | ||||||||
\(505\) | 6.00000 | 0.266996 | ||||||||
\(506\) | −7.10278 | −0.315757 | ||||||||
\(507\) | −13.0383 | −0.579052 | ||||||||
\(508\) | −16.5189 | −0.732908 | ||||||||
\(509\) | −1.46143 | −0.0647767 | −0.0323883 | − | 0.999475i | \(-0.510311\pi\) | ||||
−0.0323883 | + | 0.999475i | \(0.510311\pi\) | |||||||
\(510\) | 7.77886 | 0.344454 | ||||||||
\(511\) | −3.62721 | −0.160458 | ||||||||
\(512\) | −18.4842 | −0.816892 | ||||||||
\(513\) | 3.33804 | 0.147378 | ||||||||
\(514\) | 8.40105 | 0.370555 | ||||||||
\(515\) | 15.5975 | 0.687308 | ||||||||
\(516\) | 6.95112 | 0.306006 | ||||||||
\(517\) | −8.72999 | −0.383944 | ||||||||
\(518\) | −2.00000 | −0.0878750 | ||||||||
\(519\) | 19.2927 | 0.846857 | ||||||||
\(520\) | 6.57834 | 0.288479 | ||||||||
\(521\) | 12.8036 | 0.560934 | 0.280467 | − | 0.959864i | \(-0.409511\pi\) | ||||
0.280467 | + | 0.959864i | \(0.409511\pi\) | |||||||
\(522\) | −16.3572 | −0.715935 | ||||||||
\(523\) | 5.67557 | 0.248175 | 0.124088 | − | 0.992271i | \(-0.460400\pi\) | ||||
0.124088 | + | 0.992271i | \(0.460400\pi\) | |||||||
\(524\) | 24.4111 | 1.06640 | ||||||||
\(525\) | 1.00000 | 0.0436436 | ||||||||
\(526\) | 23.0589 | 1.00542 | ||||||||
\(527\) | −15.7889 | −0.687776 | ||||||||
\(528\) | −4.91638 | −0.213958 | ||||||||
\(529\) | −7.66196 | −0.333129 | ||||||||
\(530\) | −15.8867 | −0.690073 | ||||||||
\(531\) | −5.39194 | −0.233990 | ||||||||
\(532\) | 4.30330 | 0.186572 | ||||||||
\(533\) | −34.3416 | −1.48750 | ||||||||
\(534\) | 27.4161 | 1.18641 | ||||||||
\(535\) | 17.7789 | 0.768647 | ||||||||
\(536\) | 13.7633 | 0.594483 | ||||||||
\(537\) | −6.35720 | −0.274333 | ||||||||
\(538\) | 38.6705 | 1.66721 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | −1.28917 | −0.0554770 | ||||||||
\(541\) | 27.2772 | 1.17274 | 0.586368 | − | 0.810045i | \(-0.300557\pi\) | ||||
0.586368 | + | 0.810045i | \(0.300557\pi\) | |||||||
\(542\) | −7.65285 | −0.328718 | ||||||||
\(543\) | 3.15667 | 0.135466 | ||||||||
\(544\) | 27.1849 | 1.16554 | ||||||||
\(545\) | 8.35720 | 0.357983 | ||||||||
\(546\) | −9.25443 | −0.396053 | ||||||||
\(547\) | −30.3330 | −1.29695 | −0.648473 | − | 0.761238i | \(-0.724592\pi\) | ||||
−0.648473 | + | 0.761238i | \(0.724592\pi\) | |||||||
\(548\) | −5.20607 | −0.222392 | ||||||||
\(549\) | −13.7491 | −0.586799 | ||||||||
\(550\) | 1.81361 | 0.0773324 | ||||||||
\(551\) | −30.1063 | −1.28257 | ||||||||
\(552\) | 5.04888 | 0.214894 | ||||||||
\(553\) | 12.1517 | 0.516741 | ||||||||
\(554\) | −16.4806 | −0.700193 | ||||||||
\(555\) | 1.10278 | 0.0468102 | ||||||||
\(556\) | 25.9588 | 1.10090 | ||||||||
\(557\) | −3.45998 | −0.146604 | −0.0733019 | − | 0.997310i | \(-0.523354\pi\) | ||||
−0.0733019 | + | 0.997310i | \(0.523354\pi\) | |||||||
\(558\) | 6.67609 | 0.282621 | ||||||||
\(559\) | −27.5139 | −1.16371 | ||||||||
\(560\) | 4.91638 | 0.207755 | ||||||||
\(561\) | 4.28917 | 0.181089 | ||||||||
\(562\) | 37.4983 | 1.58177 | ||||||||
\(563\) | 20.9894 | 0.884599 | 0.442300 | − | 0.896867i | \(-0.354163\pi\) | ||||
0.442300 | + | 0.896867i | \(0.354163\pi\) | |||||||
\(564\) | −11.2544 | −0.473897 | ||||||||
\(565\) | 16.7003 | 0.702586 | ||||||||
\(566\) | 12.7738 | 0.536925 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 13.3522 | 0.560245 | ||||||||
\(569\) | 19.1763 | 0.803914 | 0.401957 | − | 0.915658i | \(-0.368330\pi\) | ||||
0.401957 | + | 0.915658i | \(0.368330\pi\) | |||||||
\(570\) | −6.05390 | −0.253570 | ||||||||
\(571\) | −8.45495 | −0.353829 | −0.176914 | − | 0.984226i | \(-0.556612\pi\) | ||||
−0.176914 | + | 0.984226i | \(0.556612\pi\) | |||||||
\(572\) | −6.57834 | −0.275054 | ||||||||
\(573\) | 11.2544 | 0.470160 | ||||||||
\(574\) | −12.2056 | −0.509450 | ||||||||
\(575\) | −3.91638 | −0.163324 | ||||||||
\(576\) | −1.66196 | −0.0692481 | ||||||||
\(577\) | −12.1744 | −0.506826 | −0.253413 | − | 0.967358i | \(-0.581553\pi\) | ||||
−0.253413 | + | 0.967358i | \(0.581553\pi\) | |||||||
\(578\) | −2.53355 | −0.105382 | ||||||||
\(579\) | 23.4600 | 0.974963 | ||||||||
\(580\) | 11.6272 | 0.482794 | ||||||||
\(581\) | 4.96526 | 0.205994 | ||||||||
\(582\) | 21.5139 | 0.891779 | ||||||||
\(583\) | −8.75971 | −0.362790 | ||||||||
\(584\) | 4.67609 | 0.193498 | ||||||||
\(585\) | 5.10278 | 0.210974 | ||||||||
\(586\) | 8.32893 | 0.344065 | ||||||||
\(587\) | −23.2983 | −0.961623 | −0.480811 | − | 0.876824i | \(-0.659658\pi\) | ||||
−0.480811 | + | 0.876824i | \(0.659658\pi\) | |||||||
\(588\) | −1.28917 | −0.0531644 | ||||||||
\(589\) | 12.2877 | 0.506307 | ||||||||
\(590\) | 9.77886 | 0.402589 | ||||||||
\(591\) | −8.78389 | −0.361321 | ||||||||
\(592\) | 5.42166 | 0.222829 | ||||||||
\(593\) | −3.73501 | −0.153379 | −0.0766893 | − | 0.997055i | \(-0.524435\pi\) | ||||
−0.0766893 | + | 0.997055i | \(0.524435\pi\) | |||||||
\(594\) | −1.81361 | −0.0744132 | ||||||||
\(595\) | −4.28917 | −0.175839 | ||||||||
\(596\) | −26.5783 | −1.08869 | ||||||||
\(597\) | −15.6655 | −0.641147 | ||||||||
\(598\) | 36.2439 | 1.48212 | ||||||||
\(599\) | 9.62721 | 0.393357 | 0.196679 | − | 0.980468i | \(-0.436984\pi\) | ||||
0.196679 | + | 0.980468i | \(0.436984\pi\) | |||||||
\(600\) | −1.28917 | −0.0526301 | ||||||||
\(601\) | −17.2786 | −0.704809 | −0.352405 | − | 0.935848i | \(-0.614636\pi\) | ||||
−0.352405 | + | 0.935848i | \(0.614636\pi\) | |||||||
\(602\) | −9.77886 | −0.398557 | ||||||||
\(603\) | 10.6761 | 0.434764 | ||||||||
\(604\) | 7.39340 | 0.300833 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 10.8816 | 0.442036 | ||||||||
\(607\) | −47.1950 | −1.91559 | −0.957793 | − | 0.287460i | \(-0.907189\pi\) | ||||
−0.957793 | + | 0.287460i | \(0.907189\pi\) | |||||||
\(608\) | −21.1567 | −0.858016 | ||||||||
\(609\) | 9.01916 | 0.365475 | ||||||||
\(610\) | 24.9355 | 1.00961 | ||||||||
\(611\) | 44.5472 | 1.80219 | ||||||||
\(612\) | 5.52946 | 0.223515 | ||||||||
\(613\) | 27.0177 | 1.09123 | 0.545617 | − | 0.838034i | \(-0.316295\pi\) | ||||
0.545617 | + | 0.838034i | \(0.316295\pi\) | |||||||
\(614\) | −47.2233 | −1.90578 | ||||||||
\(615\) | 6.72999 | 0.271379 | ||||||||
\(616\) | 1.28917 | 0.0519421 | ||||||||
\(617\) | −30.6550 | −1.23412 | −0.617061 | − | 0.786915i | \(-0.711677\pi\) | ||||
−0.617061 | + | 0.786915i | \(0.711677\pi\) | |||||||
\(618\) | 28.2877 | 1.13790 | ||||||||
\(619\) | 5.93051 | 0.238368 | 0.119184 | − | 0.992872i | \(-0.461972\pi\) | ||||
0.119184 | + | 0.992872i | \(0.461972\pi\) | |||||||
\(620\) | −4.74557 | −0.190587 | ||||||||
\(621\) | 3.91638 | 0.157159 | ||||||||
\(622\) | 29.5678 | 1.18556 | ||||||||
\(623\) | −15.1169 | −0.605646 | ||||||||
\(624\) | 25.0872 | 1.00429 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −47.8272 | −1.91156 | ||||||||
\(627\) | −3.33804 | −0.133309 | ||||||||
\(628\) | −12.9794 | −0.517934 | ||||||||
\(629\) | −4.72999 | −0.188597 | ||||||||
\(630\) | 1.81361 | 0.0722558 | ||||||||
\(631\) | −32.1602 | −1.28028 | −0.640140 | − | 0.768259i | \(-0.721123\pi\) | ||||
−0.640140 | + | 0.768259i | \(0.721123\pi\) | |||||||
\(632\) | −15.6655 | −0.623141 | ||||||||
\(633\) | −0.881639 | −0.0350420 | ||||||||
\(634\) | −31.5960 | −1.25484 | ||||||||
\(635\) | −12.8136 | −0.508492 | ||||||||
\(636\) | −11.2927 | −0.447786 | ||||||||
\(637\) | 5.10278 | 0.202179 | ||||||||
\(638\) | 16.3572 | 0.647588 | ||||||||
\(639\) | 10.3572 | 0.409725 | ||||||||
\(640\) | −9.66196 | −0.381922 | ||||||||
\(641\) | −19.5678 | −0.772881 | −0.386440 | − | 0.922314i | \(-0.626295\pi\) | ||||
−0.386440 | + | 0.922314i | \(0.626295\pi\) | |||||||
\(642\) | 32.2439 | 1.27256 | ||||||||
\(643\) | −16.0086 | −0.631317 | −0.315659 | − | 0.948873i | \(-0.602225\pi\) | ||||
−0.315659 | + | 0.948873i | \(0.602225\pi\) | |||||||
\(644\) | 5.04888 | 0.198954 | ||||||||
\(645\) | 5.39194 | 0.212308 | ||||||||
\(646\) | 25.9662 | 1.02163 | ||||||||
\(647\) | 1.45998 | 0.0573976 | 0.0286988 | − | 0.999588i | \(-0.490864\pi\) | ||||
0.0286988 | + | 0.999588i | \(0.490864\pi\) | |||||||
\(648\) | 1.28917 | 0.0506433 | ||||||||
\(649\) | 5.39194 | 0.211652 | ||||||||
\(650\) | −9.25443 | −0.362988 | ||||||||
\(651\) | −3.68111 | −0.144274 | ||||||||
\(652\) | 1.08005 | 0.0422979 | ||||||||
\(653\) | 23.6514 | 0.925551 | 0.462775 | − | 0.886476i | \(-0.346854\pi\) | ||||
0.462775 | + | 0.886476i | \(0.346854\pi\) | |||||||
\(654\) | 15.1567 | 0.592673 | ||||||||
\(655\) | 18.9355 | 0.739873 | ||||||||
\(656\) | 33.0872 | 1.29184 | ||||||||
\(657\) | 3.62721 | 0.141511 | ||||||||
\(658\) | 15.8328 | 0.617225 | ||||||||
\(659\) | 27.2147 | 1.06013 | 0.530066 | − | 0.847956i | \(-0.322167\pi\) | ||||
0.530066 | + | 0.847956i | \(0.322167\pi\) | |||||||
\(660\) | 1.28917 | 0.0501808 | ||||||||
\(661\) | 34.6705 | 1.34853 | 0.674264 | − | 0.738490i | \(-0.264461\pi\) | ||||
0.674264 | + | 0.738490i | \(0.264461\pi\) | |||||||
\(662\) | 29.4161 | 1.14329 | ||||||||
\(663\) | −21.8867 | −0.850008 | ||||||||
\(664\) | −6.40105 | −0.248409 | ||||||||
\(665\) | 3.33804 | 0.129444 | ||||||||
\(666\) | 2.00000 | 0.0774984 | ||||||||
\(667\) | −35.3225 | −1.36769 | ||||||||
\(668\) | 31.1155 | 1.20389 | ||||||||
\(669\) | 0.235269 | 0.00909604 | ||||||||
\(670\) | −19.3622 | −0.748028 | ||||||||
\(671\) | 13.7491 | 0.530780 | ||||||||
\(672\) | 6.33804 | 0.244495 | ||||||||
\(673\) | −27.1169 | −1.04528 | −0.522640 | − | 0.852553i | \(-0.675053\pi\) | ||||
−0.522640 | + | 0.852553i | \(0.675053\pi\) | |||||||
\(674\) | 12.5527 | 0.483512 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 16.8086 | 0.646484 | ||||||||
\(677\) | 34.0524 | 1.30874 | 0.654371 | − | 0.756174i | \(-0.272934\pi\) | ||||
0.654371 | + | 0.756174i | \(0.272934\pi\) | |||||||
\(678\) | 30.2877 | 1.16319 | ||||||||
\(679\) | −11.8625 | −0.455240 | ||||||||
\(680\) | 5.52946 | 0.212045 | ||||||||
\(681\) | −9.71083 | −0.372120 | ||||||||
\(682\) | −6.67609 | −0.255641 | ||||||||
\(683\) | 24.1955 | 0.925815 | 0.462908 | − | 0.886407i | \(-0.346806\pi\) | ||||
0.462908 | + | 0.886407i | \(0.346806\pi\) | |||||||
\(684\) | −4.30330 | −0.164541 | ||||||||
\(685\) | −4.03831 | −0.154296 | ||||||||
\(686\) | 1.81361 | 0.0692438 | ||||||||
\(687\) | −18.6705 | −0.712326 | ||||||||
\(688\) | 26.5089 | 1.01064 | ||||||||
\(689\) | 44.6988 | 1.70289 | ||||||||
\(690\) | −7.10278 | −0.270398 | ||||||||
\(691\) | 30.8716 | 1.17441 | 0.587205 | − | 0.809438i | \(-0.300228\pi\) | ||||
0.587205 | + | 0.809438i | \(0.300228\pi\) | |||||||
\(692\) | −24.8716 | −0.945476 | ||||||||
\(693\) | 1.00000 | 0.0379869 | ||||||||
\(694\) | 32.4111 | 1.23031 | ||||||||
\(695\) | 20.1361 | 0.763804 | ||||||||
\(696\) | −11.6272 | −0.440728 | ||||||||
\(697\) | −28.8661 | −1.09338 | ||||||||
\(698\) | −4.93554 | −0.186813 | ||||||||
\(699\) | 20.9355 | 0.791855 | ||||||||
\(700\) | −1.28917 | −0.0487260 | ||||||||
\(701\) | −26.7058 | −1.00866 | −0.504332 | − | 0.863510i | \(-0.668261\pi\) | ||||
−0.504332 | + | 0.863510i | \(0.668261\pi\) | |||||||
\(702\) | 9.25443 | 0.349286 | ||||||||
\(703\) | 3.68111 | 0.138836 | ||||||||
\(704\) | 1.66196 | 0.0626373 | ||||||||
\(705\) | −8.72999 | −0.328790 | ||||||||
\(706\) | 33.9406 | 1.27737 | ||||||||
\(707\) | −6.00000 | −0.225653 | ||||||||
\(708\) | 6.95112 | 0.261239 | ||||||||
\(709\) | 4.21254 | 0.158205 | 0.0791027 | − | 0.996866i | \(-0.474795\pi\) | ||||
0.0791027 | + | 0.996866i | \(0.474795\pi\) | |||||||
\(710\) | −18.7839 | −0.704947 | ||||||||
\(711\) | −12.1517 | −0.455723 | ||||||||
\(712\) | 19.4882 | 0.730353 | ||||||||
\(713\) | 14.4166 | 0.539907 | ||||||||
\(714\) | −7.77886 | −0.291117 | ||||||||
\(715\) | −5.10278 | −0.190833 | ||||||||
\(716\) | 8.19550 | 0.306280 | ||||||||
\(717\) | −28.3119 | −1.05733 | ||||||||
\(718\) | −11.4343 | −0.426726 | ||||||||
\(719\) | 11.3536 | 0.423419 | 0.211709 | − | 0.977333i | \(-0.432097\pi\) | ||||
0.211709 | + | 0.977333i | \(0.432097\pi\) | |||||||
\(720\) | −4.91638 | −0.183223 | ||||||||
\(721\) | −15.5975 | −0.580881 | ||||||||
\(722\) | 14.2503 | 0.530343 | ||||||||
\(723\) | −4.26499 | −0.158617 | ||||||||
\(724\) | −4.06949 | −0.151241 | ||||||||
\(725\) | 9.01916 | 0.334963 | ||||||||
\(726\) | 1.81361 | 0.0673093 | ||||||||
\(727\) | 42.2141 | 1.56564 | 0.782818 | − | 0.622251i | \(-0.213782\pi\) | ||||
0.782818 | + | 0.622251i | \(0.213782\pi\) | |||||||
\(728\) | −6.57834 | −0.243809 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −6.57834 | −0.243475 | ||||||||
\(731\) | −23.1270 | −0.855381 | ||||||||
\(732\) | 17.7250 | 0.655134 | ||||||||
\(733\) | 26.9300 | 0.994682 | 0.497341 | − | 0.867555i | \(-0.334310\pi\) | ||||
0.497341 | + | 0.867555i | \(0.334310\pi\) | |||||||
\(734\) | −34.4933 | −1.27317 | ||||||||
\(735\) | −1.00000 | −0.0368856 | ||||||||
\(736\) | −24.8222 | −0.914958 | ||||||||
\(737\) | −10.6761 | −0.393259 | ||||||||
\(738\) | 12.2056 | 0.449293 | ||||||||
\(739\) | −37.6272 | −1.38414 | −0.692070 | − | 0.721831i | \(-0.743301\pi\) | ||||
−0.692070 | + | 0.721831i | \(0.743301\pi\) | |||||||
\(740\) | −1.42166 | −0.0522614 | ||||||||
\(741\) | 17.0333 | 0.625734 | ||||||||
\(742\) | 15.8867 | 0.583218 | ||||||||
\(743\) | −14.0383 | −0.515016 | −0.257508 | − | 0.966276i | \(-0.582901\pi\) | ||||
−0.257508 | + | 0.966276i | \(0.582901\pi\) | |||||||
\(744\) | 4.74557 | 0.173981 | ||||||||
\(745\) | −20.6167 | −0.755336 | ||||||||
\(746\) | 25.4061 | 0.930183 | ||||||||
\(747\) | −4.96526 | −0.181669 | ||||||||
\(748\) | −5.52946 | −0.202177 | ||||||||
\(749\) | −17.7789 | −0.649626 | ||||||||
\(750\) | 1.81361 | 0.0662235 | ||||||||
\(751\) | −27.2786 | −0.995410 | −0.497705 | − | 0.867346i | \(-0.665824\pi\) | ||||
−0.497705 | + | 0.867346i | \(0.665824\pi\) | |||||||
\(752\) | −42.9200 | −1.56513 | ||||||||
\(753\) | 18.7244 | 0.682357 | ||||||||
\(754\) | −83.4671 | −3.03969 | ||||||||
\(755\) | 5.73501 | 0.208718 | ||||||||
\(756\) | 1.28917 | 0.0468866 | ||||||||
\(757\) | −15.9900 | −0.581165 | −0.290582 | − | 0.956850i | \(-0.593849\pi\) | ||||
−0.290582 | + | 0.956850i | \(0.593849\pi\) | |||||||
\(758\) | −24.0639 | −0.874042 | ||||||||
\(759\) | −3.91638 | −0.142156 | ||||||||
\(760\) | −4.30330 | −0.156097 | ||||||||
\(761\) | −0.432226 | −0.0156682 | −0.00783408 | − | 0.999969i | \(-0.502494\pi\) | ||||
−0.00783408 | + | 0.999969i | \(0.502494\pi\) | |||||||
\(762\) | −23.2388 | −0.841854 | ||||||||
\(763\) | −8.35720 | −0.302551 | ||||||||
\(764\) | −14.5089 | −0.524912 | ||||||||
\(765\) | 4.28917 | 0.155075 | ||||||||
\(766\) | −33.8993 | −1.22483 | ||||||||
\(767\) | −27.5139 | −0.993468 | ||||||||
\(768\) | −20.8469 | −0.752248 | ||||||||
\(769\) | 3.46697 | 0.125022 | 0.0625110 | − | 0.998044i | \(-0.480089\pi\) | ||||
0.0625110 | + | 0.998044i | \(0.480089\pi\) | |||||||
\(770\) | −1.81361 | −0.0653578 | ||||||||
\(771\) | 4.63224 | 0.166826 | ||||||||
\(772\) | −30.2439 | −1.08850 | ||||||||
\(773\) | −12.7355 | −0.458065 | −0.229033 | − | 0.973419i | \(-0.573556\pi\) | ||||
−0.229033 | + | 0.973419i | \(0.573556\pi\) | |||||||
\(774\) | 9.77886 | 0.351494 | ||||||||
\(775\) | −3.68111 | −0.132229 | ||||||||
\(776\) | 15.2927 | 0.548977 | ||||||||
\(777\) | −1.10278 | −0.0395618 | ||||||||
\(778\) | 7.90225 | 0.283309 | ||||||||
\(779\) | 22.4650 | 0.804892 | ||||||||
\(780\) | −6.57834 | −0.235542 | ||||||||
\(781\) | −10.3572 | −0.370610 | ||||||||
\(782\) | 30.4650 | 1.08943 | ||||||||
\(783\) | −9.01916 | −0.322318 | ||||||||
\(784\) | −4.91638 | −0.175585 | ||||||||
\(785\) | −10.0680 | −0.359343 | ||||||||
\(786\) | 34.3416 | 1.22492 | ||||||||
\(787\) | −10.6277 | −0.378838 | −0.189419 | − | 0.981896i | \(-0.560660\pi\) | ||||
−0.189419 | + | 0.981896i | \(0.560660\pi\) | |||||||
\(788\) | 11.3239 | 0.403398 | ||||||||
\(789\) | 12.7144 | 0.452645 | ||||||||
\(790\) | 22.0383 | 0.784088 | ||||||||
\(791\) | −16.7003 | −0.593793 | ||||||||
\(792\) | −1.28917 | −0.0458086 | ||||||||
\(793\) | −70.1588 | −2.49141 | ||||||||
\(794\) | 26.4394 | 0.938298 | ||||||||
\(795\) | −8.75971 | −0.310675 | ||||||||
\(796\) | 20.1955 | 0.715811 | ||||||||
\(797\) | −2.85337 | −0.101072 | −0.0505358 | − | 0.998722i | \(-0.516093\pi\) | ||||
−0.0505358 | + | 0.998722i | \(0.516093\pi\) | |||||||
\(798\) | 6.05390 | 0.214306 | ||||||||
\(799\) | 37.4444 | 1.32469 | ||||||||
\(800\) | 6.33804 | 0.224084 | ||||||||
\(801\) | 15.1169 | 0.534130 | ||||||||
\(802\) | −18.3033 | −0.646312 | ||||||||
\(803\) | −3.62721 | −0.128002 | ||||||||
\(804\) | −13.7633 | −0.485393 | ||||||||
\(805\) | 3.91638 | 0.138034 | ||||||||
\(806\) | 34.0666 | 1.19994 | ||||||||
\(807\) | 21.3225 | 0.750586 | ||||||||
\(808\) | 7.73501 | 0.272117 | ||||||||
\(809\) | −36.8122 | −1.29425 | −0.647123 | − | 0.762385i | \(-0.724028\pi\) | ||||
−0.647123 | + | 0.762385i | \(0.724028\pi\) | |||||||
\(810\) | −1.81361 | −0.0637236 | ||||||||
\(811\) | −14.3133 | −0.502610 | −0.251305 | − | 0.967908i | \(-0.580860\pi\) | ||||
−0.251305 | + | 0.967908i | \(0.580860\pi\) | |||||||
\(812\) | −11.6272 | −0.408035 | ||||||||
\(813\) | −4.21968 | −0.147991 | ||||||||
\(814\) | −2.00000 | −0.0701000 | ||||||||
\(815\) | 0.837786 | 0.0293464 | ||||||||
\(816\) | 21.0872 | 0.738199 | ||||||||
\(817\) | 17.9985 | 0.629689 | ||||||||
\(818\) | −59.0460 | −2.06449 | ||||||||
\(819\) | −5.10278 | −0.178305 | ||||||||
\(820\) | −8.67609 | −0.302982 | ||||||||
\(821\) | −46.9185 | −1.63747 | −0.818733 | − | 0.574174i | \(-0.805323\pi\) | ||||
−0.818733 | + | 0.574174i | \(0.805323\pi\) | |||||||
\(822\) | −7.32391 | −0.255451 | ||||||||
\(823\) | 4.31889 | 0.150547 | 0.0752735 | − | 0.997163i | \(-0.476017\pi\) | ||||
0.0752735 | + | 0.997163i | \(0.476017\pi\) | |||||||
\(824\) | 20.1078 | 0.700488 | ||||||||
\(825\) | 1.00000 | 0.0348155 | ||||||||
\(826\) | −9.77886 | −0.340250 | ||||||||
\(827\) | −54.0666 | −1.88008 | −0.940040 | − | 0.341065i | \(-0.889212\pi\) | ||||
−0.940040 | + | 0.341065i | \(0.889212\pi\) | |||||||
\(828\) | −5.04888 | −0.175461 | ||||||||
\(829\) | 9.89220 | 0.343570 | 0.171785 | − | 0.985134i | \(-0.445047\pi\) | ||||
0.171785 | + | 0.985134i | \(0.445047\pi\) | |||||||
\(830\) | 9.00502 | 0.312569 | ||||||||
\(831\) | −9.08719 | −0.315231 | ||||||||
\(832\) | −8.48059 | −0.294011 | ||||||||
\(833\) | 4.28917 | 0.148611 | ||||||||
\(834\) | 36.5189 | 1.26455 | ||||||||
\(835\) | 24.1361 | 0.835263 | ||||||||
\(836\) | 4.30330 | 0.148833 | ||||||||
\(837\) | 3.68111 | 0.127238 | ||||||||
\(838\) | −3.02324 | −0.104436 | ||||||||
\(839\) | −37.3325 | −1.28886 | −0.644431 | − | 0.764663i | \(-0.722906\pi\) | ||||
−0.644431 | + | 0.764663i | \(0.722906\pi\) | |||||||
\(840\) | 1.28917 | 0.0444805 | ||||||||
\(841\) | 52.3452 | 1.80501 | ||||||||
\(842\) | 43.6399 | 1.50393 | ||||||||
\(843\) | 20.6761 | 0.712122 | ||||||||
\(844\) | 1.13658 | 0.0391227 | ||||||||
\(845\) | 13.0383 | 0.448532 | ||||||||
\(846\) | −15.8328 | −0.544342 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | −43.0661 | −1.47889 | ||||||||
\(849\) | 7.04334 | 0.241727 | ||||||||
\(850\) | −7.77886 | −0.266813 | ||||||||
\(851\) | 4.31889 | 0.148050 | ||||||||
\(852\) | −13.3522 | −0.457438 | ||||||||
\(853\) | −21.7688 | −0.745350 | −0.372675 | − | 0.927962i | \(-0.621559\pi\) | ||||
−0.372675 | + | 0.927962i | \(0.621559\pi\) | |||||||
\(854\) | −24.9355 | −0.853277 | ||||||||
\(855\) | −3.33804 | −0.114159 | ||||||||
\(856\) | 22.9200 | 0.783388 | ||||||||
\(857\) | 46.6832 | 1.59467 | 0.797334 | − | 0.603538i | \(-0.206243\pi\) | ||||
0.797334 | + | 0.603538i | \(0.206243\pi\) | |||||||
\(858\) | −9.25443 | −0.315941 | ||||||||
\(859\) | −22.8277 | −0.778872 | −0.389436 | − | 0.921053i | \(-0.627330\pi\) | ||||
−0.389436 | + | 0.921053i | \(0.627330\pi\) | |||||||
\(860\) | −6.95112 | −0.237031 | ||||||||
\(861\) | −6.72999 | −0.229357 | ||||||||
\(862\) | 1.15667 | 0.0393965 | ||||||||
\(863\) | −4.08362 | −0.139008 | −0.0695040 | − | 0.997582i | \(-0.522142\pi\) | ||||
−0.0695040 | + | 0.997582i | \(0.522142\pi\) | |||||||
\(864\) | −6.33804 | −0.215625 | ||||||||
\(865\) | −19.2927 | −0.655973 | ||||||||
\(866\) | −3.07714 | −0.104566 | ||||||||
\(867\) | −1.39697 | −0.0474435 | ||||||||
\(868\) | 4.74557 | 0.161075 | ||||||||
\(869\) | 12.1517 | 0.412217 | ||||||||
\(870\) | 16.3572 | 0.554561 | ||||||||
\(871\) | 54.4777 | 1.84591 | ||||||||
\(872\) | 10.7738 | 0.364848 | ||||||||
\(873\) | 11.8625 | 0.401484 | ||||||||
\(874\) | −23.7094 | −0.801982 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | −4.67609 | −0.157990 | ||||||||
\(877\) | −34.8419 | −1.17653 | −0.588263 | − | 0.808670i | \(-0.700188\pi\) | ||||
−0.588263 | + | 0.808670i | \(0.700188\pi\) | |||||||
\(878\) | 28.7583 | 0.970544 | ||||||||
\(879\) | 4.59247 | 0.154900 | ||||||||
\(880\) | 4.91638 | 0.165731 | ||||||||
\(881\) | −49.1864 | −1.65713 | −0.828566 | − | 0.559892i | \(-0.810843\pi\) | ||||
−0.828566 | + | 0.559892i | \(0.810843\pi\) | |||||||
\(882\) | −1.81361 | −0.0610673 | ||||||||
\(883\) | 29.4600 | 0.991407 | 0.495704 | − | 0.868492i | \(-0.334910\pi\) | ||||
0.495704 | + | 0.868492i | \(0.334910\pi\) | |||||||
\(884\) | 28.2156 | 0.948993 | ||||||||
\(885\) | 5.39194 | 0.181248 | ||||||||
\(886\) | −73.9276 | −2.48365 | ||||||||
\(887\) | 7.47411 | 0.250956 | 0.125478 | − | 0.992096i | \(-0.459954\pi\) | ||||
0.125478 | + | 0.992096i | \(0.459954\pi\) | |||||||
\(888\) | 1.42166 | 0.0477079 | ||||||||
\(889\) | 12.8136 | 0.429755 | ||||||||
\(890\) | −27.4161 | −0.918991 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −0.303302 | −0.0101553 | ||||||||
\(893\) | −29.1411 | −0.975169 | ||||||||
\(894\) | −37.3905 | −1.25053 | ||||||||
\(895\) | 6.35720 | 0.212498 | ||||||||
\(896\) | 9.66196 | 0.322783 | ||||||||
\(897\) | 19.9844 | 0.667260 | ||||||||
\(898\) | −3.24438 | −0.108266 | ||||||||
\(899\) | −33.2005 | −1.10730 | ||||||||
\(900\) | 1.28917 | 0.0429723 | ||||||||
\(901\) | 37.5719 | 1.25170 | ||||||||
\(902\) | −12.2056 | −0.406400 | ||||||||
\(903\) | −5.39194 | −0.179433 | ||||||||
\(904\) | 21.5295 | 0.716059 | ||||||||
\(905\) | −3.15667 | −0.104931 | ||||||||
\(906\) | 10.4011 | 0.345552 | ||||||||
\(907\) | −43.1200 | −1.43177 | −0.715887 | − | 0.698216i | \(-0.753978\pi\) | ||||
−0.715887 | + | 0.698216i | \(0.753978\pi\) | |||||||
\(908\) | 12.5189 | 0.415454 | ||||||||
\(909\) | 6.00000 | 0.199007 | ||||||||
\(910\) | 9.25443 | 0.306781 | ||||||||
\(911\) | 31.0278 | 1.02800 | 0.513998 | − | 0.857792i | \(-0.328164\pi\) | ||||
0.513998 | + | 0.857792i | \(0.328164\pi\) | |||||||
\(912\) | −16.4111 | −0.543426 | ||||||||
\(913\) | 4.96526 | 0.164326 | ||||||||
\(914\) | −6.15165 | −0.203479 | ||||||||
\(915\) | 13.7491 | 0.454533 | ||||||||
\(916\) | 24.0695 | 0.795278 | ||||||||
\(917\) | −18.9355 | −0.625307 | ||||||||
\(918\) | 7.77886 | 0.256741 | ||||||||
\(919\) | −43.3028 | −1.42843 | −0.714214 | − | 0.699928i | \(-0.753215\pi\) | ||||
−0.714214 | + | 0.699928i | \(0.753215\pi\) | |||||||
\(920\) | −5.04888 | −0.166457 | ||||||||
\(921\) | −26.0383 | −0.857992 | ||||||||
\(922\) | −61.2515 | −2.01721 | ||||||||
\(923\) | 52.8505 | 1.73959 | ||||||||
\(924\) | −1.28917 | −0.0424105 | ||||||||
\(925\) | −1.10278 | −0.0362590 | ||||||||
\(926\) | −21.2645 | −0.698794 | ||||||||
\(927\) | 15.5975 | 0.512289 | ||||||||
\(928\) | 57.1638 | 1.87649 | ||||||||
\(929\) | 14.4595 | 0.474399 | 0.237200 | − | 0.971461i | \(-0.423770\pi\) | ||||
0.237200 | + | 0.971461i | \(0.423770\pi\) | |||||||
\(930\) | −6.67609 | −0.218918 | ||||||||
\(931\) | −3.33804 | −0.109400 | ||||||||
\(932\) | −26.9894 | −0.884068 | ||||||||
\(933\) | 16.3033 | 0.533746 | ||||||||
\(934\) | −53.4288 | −1.74824 | ||||||||
\(935\) | −4.28917 | −0.140271 | ||||||||
\(936\) | 6.57834 | 0.215020 | ||||||||
\(937\) | −16.3088 | −0.532787 | −0.266393 | − | 0.963864i | \(-0.585832\pi\) | ||||
−0.266393 | + | 0.963864i | \(0.585832\pi\) | |||||||
\(938\) | 19.3622 | 0.632199 | ||||||||
\(939\) | −26.3713 | −0.860596 | ||||||||
\(940\) | 11.2544 | 0.367079 | ||||||||
\(941\) | 21.1028 | 0.687931 | 0.343965 | − | 0.938982i | \(-0.388230\pi\) | ||||
0.343965 | + | 0.938982i | \(0.388230\pi\) | |||||||
\(942\) | −18.2594 | −0.594925 | ||||||||
\(943\) | 26.3572 | 0.858309 | ||||||||
\(944\) | 26.5089 | 0.862790 | ||||||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | −9.77886 | −0.317938 | ||||||||
\(947\) | 25.5436 | 0.830055 | 0.415028 | − | 0.909809i | \(-0.363772\pi\) | ||||
0.415028 | + | 0.909809i | \(0.363772\pi\) | |||||||
\(948\) | 15.6655 | 0.508793 | ||||||||
\(949\) | 18.5089 | 0.600823 | ||||||||
\(950\) | 6.05390 | 0.196414 | ||||||||
\(951\) | −17.4217 | −0.564936 | ||||||||
\(952\) | −5.52946 | −0.179211 | ||||||||
\(953\) | 22.0766 | 0.715132 | 0.357566 | − | 0.933888i | \(-0.383607\pi\) | ||||
0.357566 | + | 0.933888i | \(0.383607\pi\) | |||||||
\(954\) | −15.8867 | −0.514350 | ||||||||
\(955\) | −11.2544 | −0.364185 | ||||||||
\(956\) | 36.4988 | 1.18046 | ||||||||
\(957\) | 9.01916 | 0.291548 | ||||||||
\(958\) | 32.0484 | 1.03544 | ||||||||
\(959\) | 4.03831 | 0.130404 | ||||||||
\(960\) | 1.66196 | 0.0536394 | ||||||||
\(961\) | −17.4494 | −0.562884 | ||||||||
\(962\) | 10.2056 | 0.329040 | ||||||||
\(963\) | 17.7789 | 0.572916 | ||||||||
\(964\) | 5.49829 | 0.177088 | ||||||||
\(965\) | −23.4600 | −0.755203 | ||||||||
\(966\) | 7.10278 | 0.228528 | ||||||||
\(967\) | −57.9985 | −1.86511 | −0.932554 | − | 0.361031i | \(-0.882425\pi\) | ||||
−0.932554 | + | 0.361031i | \(0.882425\pi\) | |||||||
\(968\) | 1.28917 | 0.0414354 | ||||||||
\(969\) | 14.3174 | 0.459942 | ||||||||
\(970\) | −21.5139 | −0.690769 | ||||||||
\(971\) | −10.9114 | −0.350162 | −0.175081 | − | 0.984554i | \(-0.556019\pi\) | ||||
−0.175081 | + | 0.984554i | \(0.556019\pi\) | |||||||
\(972\) | −1.28917 | −0.0413501 | ||||||||
\(973\) | −20.1361 | −0.645533 | ||||||||
\(974\) | 34.0666 | 1.09156 | ||||||||
\(975\) | −5.10278 | −0.163420 | ||||||||
\(976\) | 67.5960 | 2.16370 | ||||||||
\(977\) | −20.0625 | −0.641856 | −0.320928 | − | 0.947104i | \(-0.603995\pi\) | ||||
−0.320928 | + | 0.947104i | \(0.603995\pi\) | |||||||
\(978\) | 1.51941 | 0.0485855 | ||||||||
\(979\) | −15.1169 | −0.483138 | ||||||||
\(980\) | 1.28917 | 0.0411810 | ||||||||
\(981\) | 8.35720 | 0.266825 | ||||||||
\(982\) | 9.22879 | 0.294503 | ||||||||
\(983\) | −8.95827 | −0.285724 | −0.142862 | − | 0.989743i | \(-0.545631\pi\) | ||||
−0.142862 | + | 0.989743i | \(0.545631\pi\) | |||||||
\(984\) | 8.67609 | 0.276584 | ||||||||
\(985\) | 8.78389 | 0.279878 | ||||||||
\(986\) | −70.1588 | −2.23431 | ||||||||
\(987\) | 8.72999 | 0.277879 | ||||||||
\(988\) | −21.9588 | −0.698602 | ||||||||
\(989\) | 21.1169 | 0.671479 | ||||||||
\(990\) | 1.81361 | 0.0576402 | ||||||||
\(991\) | 22.2297 | 0.706151 | 0.353075 | − | 0.935595i | \(-0.385136\pi\) | ||||
0.353075 | + | 0.935595i | \(0.385136\pi\) | |||||||
\(992\) | −23.3311 | −0.740762 | ||||||||
\(993\) | 16.2197 | 0.514716 | ||||||||
\(994\) | 18.7839 | 0.595789 | ||||||||
\(995\) | 15.6655 | 0.496631 | ||||||||
\(996\) | 6.40105 | 0.202825 | ||||||||
\(997\) | 1.37330 | 0.0434930 | 0.0217465 | − | 0.999764i | \(-0.493077\pi\) | ||||
0.0217465 | + | 0.999764i | \(0.493077\pi\) | |||||||
\(998\) | −15.8172 | −0.500684 | ||||||||
\(999\) | 1.10278 | 0.0348903 |
(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 | 1155.2.a.s.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 3465.2.a.bc.1.3 | 3 | |||
5.4 | even | 2 | 5775.2.a.br.1.3 | 3 | |||
7.6 | odd | 2 | 8085.2.a.bm.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.a.s.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
3465.2.a.bc.1.3 | 3 | 3.2 | odd | 2 | |||
5775.2.a.br.1.3 | 3 | 5.4 | even | 2 | |||
8085.2.a.bm.1.1 | 3 | 7.6 | odd | 2 |