Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(34,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.34");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.p (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 265.2 | ||
Root | \(1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.265 |
Dual form | 273.2.p.a.34.2 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.22474 | − | 1.22474i | 0.866025 | − | 0.866025i | −0.126004 | − | 0.992030i | \(-0.540215\pi\) |
0.992030 | + | 0.126004i | \(0.0402153\pi\) | |||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −2.00000 | − | 2.00000i | −0.894427 | − | 0.894427i | 0.100509 | − | 0.994936i | \(-0.467953\pi\) |
−0.994936 | + | 0.100509i | \(0.967953\pi\) | |||||||
\(6\) | −1.22474 | − | 1.22474i | −0.500000 | − | 0.500000i | ||||
\(7\) | 1.00000 | − | 2.44949i | 0.377964 | − | 0.925820i | ||||
\(8\) | 1.22474 | + | 1.22474i | 0.433013 | + | 0.433013i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −4.89898 | −1.54919 | ||||||||
\(11\) | −0.449490 | − | 0.449490i | −0.135526 | − | 0.135526i | 0.636089 | − | 0.771615i | \(-0.280551\pi\) |
−0.771615 | + | 0.636089i | \(0.780551\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −2.00000 | + | 3.00000i | −0.554700 | + | 0.832050i | ||||
\(14\) | −1.77526 | − | 4.22474i | −0.474457 | − | 1.12911i | ||||
\(15\) | −2.00000 | + | 2.00000i | −0.516398 | + | 0.516398i | ||||
\(16\) | 5.00000 | 1.25000 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | −1.22474 | + | 1.22474i | −0.288675 | + | 0.288675i | ||||
\(19\) | 0.550510 | + | 0.550510i | 0.126296 | + | 0.126296i | 0.767429 | − | 0.641134i | \(-0.221536\pi\) |
−0.641134 | + | 0.767429i | \(0.721536\pi\) | |||||||
\(20\) | −2.00000 | + | 2.00000i | −0.447214 | + | 0.447214i | ||||
\(21\) | −2.44949 | − | 1.00000i | −0.534522 | − | 0.218218i | ||||
\(22\) | −1.10102 | −0.234738 | ||||||||
\(23\) | − | 8.89898i | − | 1.85557i | −0.373121 | − | 0.927783i | \(-0.621712\pi\) | ||
0.373121 | − | 0.927783i | \(-0.378288\pi\) | |||||||
\(24\) | 1.22474 | − | 1.22474i | 0.250000 | − | 0.250000i | ||||
\(25\) | 3.00000i | 0.600000i | ||||||||
\(26\) | 1.22474 | + | 6.12372i | 0.240192 | + | 1.20096i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −2.44949 | − | 1.00000i | −0.462910 | − | 0.188982i | ||||
\(29\) | 2.89898 | 0.538327 | 0.269163 | − | 0.963095i | \(-0.413253\pi\) | ||||
0.269163 | + | 0.963095i | \(0.413253\pi\) | |||||||
\(30\) | 4.89898i | 0.894427i | ||||||||
\(31\) | 5.44949 | + | 5.44949i | 0.978757 | + | 0.978757i | 0.999779 | − | 0.0210218i | \(-0.00669193\pi\) |
−0.0210218 | + | 0.999779i | \(0.506692\pi\) | |||||||
\(32\) | 3.67423 | − | 3.67423i | 0.649519 | − | 0.649519i | ||||
\(33\) | −0.449490 | + | 0.449490i | −0.0782461 | + | 0.0782461i | ||||
\(34\) | 2.44949 | − | 2.44949i | 0.420084 | − | 0.420084i | ||||
\(35\) | −6.89898 | + | 2.89898i | −1.16614 | + | 0.490017i | ||||
\(36\) | 1.00000i | 0.166667i | ||||||||
\(37\) | 7.89898 | + | 7.89898i | 1.29858 | + | 1.29858i | 0.929327 | + | 0.369257i | \(0.120388\pi\) |
0.369257 | + | 0.929327i | \(0.379612\pi\) | |||||||
\(38\) | 1.34847 | 0.218751 | ||||||||
\(39\) | 3.00000 | + | 2.00000i | 0.480384 | + | 0.320256i | ||||
\(40\) | − | 4.89898i | − | 0.774597i | ||||||
\(41\) | 4.00000 | + | 4.00000i | 0.624695 | + | 0.624695i | 0.946728 | − | 0.322033i | \(-0.104366\pi\) |
−0.322033 | + | 0.946728i | \(0.604366\pi\) | |||||||
\(42\) | −4.22474 | + | 1.77526i | −0.651892 | + | 0.273928i | ||||
\(43\) | 6.89898i | 1.05208i | 0.850458 | + | 0.526042i | \(0.176325\pi\) | ||||
−0.850458 | + | 0.526042i | \(0.823675\pi\) | |||||||
\(44\) | −0.449490 | + | 0.449490i | −0.0677631 | + | 0.0677631i | ||||
\(45\) | 2.00000 | + | 2.00000i | 0.298142 | + | 0.298142i | ||||
\(46\) | −10.8990 | − | 10.8990i | −1.60697 | − | 1.60697i | ||||
\(47\) | −1.55051 | + | 1.55051i | −0.226165 | + | 0.226165i | −0.811089 | − | 0.584923i | \(-0.801125\pi\) |
0.584923 | + | 0.811089i | \(0.301125\pi\) | |||||||
\(48\) | − | 5.00000i | − | 0.721688i | ||||||
\(49\) | −5.00000 | − | 4.89898i | −0.714286 | − | 0.699854i | ||||
\(50\) | 3.67423 | + | 3.67423i | 0.519615 | + | 0.519615i | ||||
\(51\) | − | 2.00000i | − | 0.280056i | ||||||
\(52\) | 3.00000 | + | 2.00000i | 0.416025 | + | 0.277350i | ||||
\(53\) | −11.7980 | −1.62057 | −0.810287 | − | 0.586033i | \(-0.800689\pi\) | ||||
−0.810287 | + | 0.586033i | \(0.800689\pi\) | |||||||
\(54\) | 1.22474 | + | 1.22474i | 0.166667 | + | 0.166667i | ||||
\(55\) | 1.79796i | 0.242437i | ||||||||
\(56\) | 4.22474 | − | 1.77526i | 0.564555 | − | 0.237228i | ||||
\(57\) | 0.550510 | − | 0.550510i | 0.0729169 | − | 0.0729169i | ||||
\(58\) | 3.55051 | − | 3.55051i | 0.466205 | − | 0.466205i | ||||
\(59\) | 4.44949 | − | 4.44949i | 0.579274 | − | 0.579274i | −0.355429 | − | 0.934703i | \(-0.615665\pi\) |
0.934703 | + | 0.355429i | \(0.115665\pi\) | |||||||
\(60\) | 2.00000 | + | 2.00000i | 0.258199 | + | 0.258199i | ||||
\(61\) | − | 10.0000i | − | 1.28037i | −0.768221 | − | 0.640184i | \(-0.778858\pi\) | ||
0.768221 | − | 0.640184i | \(-0.221142\pi\) | |||||||
\(62\) | 13.3485 | 1.69526 | ||||||||
\(63\) | −1.00000 | + | 2.44949i | −0.125988 | + | 0.308607i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 10.0000 | − | 2.00000i | 1.24035 | − | 0.248069i | ||||
\(66\) | 1.10102i | 0.135526i | ||||||||
\(67\) | −6.34847 | + | 6.34847i | −0.775589 | + | 0.775589i | −0.979077 | − | 0.203488i | \(-0.934772\pi\) |
0.203488 | + | 0.979077i | \(0.434772\pi\) | |||||||
\(68\) | − | 2.00000i | − | 0.242536i | ||||||
\(69\) | −8.89898 | −1.07131 | ||||||||
\(70\) | −4.89898 | + | 12.0000i | −0.585540 | + | 1.43427i | ||||
\(71\) | 2.44949 | − | 2.44949i | 0.290701 | − | 0.290701i | −0.546656 | − | 0.837357i | \(-0.684100\pi\) |
0.837357 | + | 0.546656i | \(0.184100\pi\) | |||||||
\(72\) | −1.22474 | − | 1.22474i | −0.144338 | − | 0.144338i | ||||
\(73\) | −7.89898 | + | 7.89898i | −0.924506 | + | 0.924506i | −0.997344 | − | 0.0728382i | \(-0.976794\pi\) |
0.0728382 | + | 0.997344i | \(0.476794\pi\) | |||||||
\(74\) | 19.3485 | 2.24921 | ||||||||
\(75\) | 3.00000 | 0.346410 | ||||||||
\(76\) | 0.550510 | − | 0.550510i | 0.0631479 | − | 0.0631479i | ||||
\(77\) | −1.55051 | + | 0.651531i | −0.176697 | + | 0.0742488i | ||||
\(78\) | 6.12372 | − | 1.22474i | 0.693375 | − | 0.138675i | ||||
\(79\) | −2.89898 | −0.326161 | −0.163080 | − | 0.986613i | \(-0.552143\pi\) | ||||
−0.163080 | + | 0.986613i | \(0.552143\pi\) | |||||||
\(80\) | −10.0000 | − | 10.0000i | −1.11803 | − | 1.11803i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 9.79796 | 1.08200 | ||||||||
\(83\) | −0.449490 | − | 0.449490i | −0.0493379 | − | 0.0493379i | 0.682007 | − | 0.731345i | \(-0.261107\pi\) |
−0.731345 | + | 0.682007i | \(0.761107\pi\) | |||||||
\(84\) | −1.00000 | + | 2.44949i | −0.109109 | + | 0.267261i | ||||
\(85\) | −4.00000 | − | 4.00000i | −0.433861 | − | 0.433861i | ||||
\(86\) | 8.44949 | + | 8.44949i | 0.911132 | + | 0.911132i | ||||
\(87\) | − | 2.89898i | − | 0.310803i | ||||||
\(88\) | − | 1.10102i | − | 0.117369i | ||||||
\(89\) | −2.00000 | + | 2.00000i | −0.212000 | + | 0.212000i | −0.805116 | − | 0.593117i | \(-0.797897\pi\) |
0.593117 | + | 0.805116i | \(0.297897\pi\) | |||||||
\(90\) | 4.89898 | 0.516398 | ||||||||
\(91\) | 5.34847 | + | 7.89898i | 0.560672 | + | 0.828038i | ||||
\(92\) | −8.89898 | −0.927783 | ||||||||
\(93\) | 5.44949 | − | 5.44949i | 0.565086 | − | 0.565086i | ||||
\(94\) | 3.79796i | 0.391730i | ||||||||
\(95\) | − | 2.20204i | − | 0.225925i | ||||||
\(96\) | −3.67423 | − | 3.67423i | −0.375000 | − | 0.375000i | ||||
\(97\) | −7.89898 | − | 7.89898i | −0.802020 | − | 0.802020i | 0.181391 | − | 0.983411i | \(-0.441940\pi\) |
−0.983411 | + | 0.181391i | \(0.941940\pi\) | |||||||
\(98\) | −12.1237 | + | 0.123724i | −1.22468 | + | 0.0124980i | ||||
\(99\) | 0.449490 | + | 0.449490i | 0.0451754 | + | 0.0451754i | ||||
\(100\) | 3.00000 | 0.300000 | ||||||||
\(101\) | 5.10102 | 0.507571 | 0.253785 | − | 0.967261i | \(-0.418324\pi\) | ||||
0.253785 | + | 0.967261i | \(0.418324\pi\) | |||||||
\(102\) | −2.44949 | − | 2.44949i | −0.242536 | − | 0.242536i | ||||
\(103\) | 1.79796 | 0.177158 | 0.0885791 | − | 0.996069i | \(-0.471767\pi\) | ||||
0.0885791 | + | 0.996069i | \(0.471767\pi\) | |||||||
\(104\) | −6.12372 | + | 1.22474i | −0.600481 | + | 0.120096i | ||||
\(105\) | 2.89898 | + | 6.89898i | 0.282911 | + | 0.673271i | ||||
\(106\) | −14.4495 | + | 14.4495i | −1.40346 | + | 1.40346i | ||||
\(107\) | 0.898979 | 0.0869076 | 0.0434538 | − | 0.999055i | \(-0.486164\pi\) | ||||
0.0434538 | + | 0.999055i | \(0.486164\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −0.101021 | + | 0.101021i | −0.00967601 | + | 0.00967601i | −0.711928 | − | 0.702252i | \(-0.752178\pi\) |
0.702252 | + | 0.711928i | \(0.252178\pi\) | |||||||
\(110\) | 2.20204 | + | 2.20204i | 0.209956 | + | 0.209956i | ||||
\(111\) | 7.89898 | − | 7.89898i | 0.749738 | − | 0.749738i | ||||
\(112\) | 5.00000 | − | 12.2474i | 0.472456 | − | 1.15728i | ||||
\(113\) | −18.8990 | −1.77787 | −0.888933 | − | 0.458037i | \(-0.848553\pi\) | ||||
−0.888933 | + | 0.458037i | \(0.848553\pi\) | |||||||
\(114\) | − | 1.34847i | − | 0.126296i | ||||||
\(115\) | −17.7980 | + | 17.7980i | −1.65967 | + | 1.65967i | ||||
\(116\) | − | 2.89898i | − | 0.269163i | ||||||
\(117\) | 2.00000 | − | 3.00000i | 0.184900 | − | 0.277350i | ||||
\(118\) | − | 10.8990i | − | 1.00333i | ||||||
\(119\) | 2.00000 | − | 4.89898i | 0.183340 | − | 0.449089i | ||||
\(120\) | −4.89898 | −0.447214 | ||||||||
\(121\) | − | 10.5959i | − | 0.963265i | ||||||
\(122\) | −12.2474 | − | 12.2474i | −1.10883 | − | 1.10883i | ||||
\(123\) | 4.00000 | − | 4.00000i | 0.360668 | − | 0.360668i | ||||
\(124\) | 5.44949 | − | 5.44949i | 0.489379 | − | 0.489379i | ||||
\(125\) | −4.00000 | + | 4.00000i | −0.357771 | + | 0.357771i | ||||
\(126\) | 1.77526 | + | 4.22474i | 0.158152 | + | 0.376370i | ||||
\(127\) | − | 8.00000i | − | 0.709885i | −0.934888 | − | 0.354943i | \(-0.884500\pi\) | ||
0.934888 | − | 0.354943i | \(-0.115500\pi\) | |||||||
\(128\) | 8.57321 | + | 8.57321i | 0.757772 | + | 0.757772i | ||||
\(129\) | 6.89898 | 0.607421 | ||||||||
\(130\) | 9.79796 | − | 14.6969i | 0.859338 | − | 1.28901i | ||||
\(131\) | 18.6969i | 1.63356i | 0.576950 | + | 0.816780i | \(0.304243\pi\) | ||||
−0.576950 | + | 0.816780i | \(0.695757\pi\) | |||||||
\(132\) | 0.449490 | + | 0.449490i | 0.0391231 | + | 0.0391231i | ||||
\(133\) | 1.89898 | − | 0.797959i | 0.164662 | − | 0.0691918i | ||||
\(134\) | 15.5505i | 1.34336i | ||||||||
\(135\) | 2.00000 | − | 2.00000i | 0.172133 | − | 0.172133i | ||||
\(136\) | 2.44949 | + | 2.44949i | 0.210042 | + | 0.210042i | ||||
\(137\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(138\) | −10.8990 | + | 10.8990i | −0.927783 | + | 0.927783i | ||||
\(139\) | 6.89898i | 0.585164i | 0.956240 | + | 0.292582i | \(0.0945144\pi\) | ||||
−0.956240 | + | 0.292582i | \(0.905486\pi\) | |||||||
\(140\) | 2.89898 | + | 6.89898i | 0.245008 | + | 0.583070i | ||||
\(141\) | 1.55051 | + | 1.55051i | 0.130577 | + | 0.130577i | ||||
\(142\) | − | 6.00000i | − | 0.503509i | ||||||
\(143\) | 2.24745 | − | 0.449490i | 0.187941 | − | 0.0375882i | ||||
\(144\) | −5.00000 | −0.416667 | ||||||||
\(145\) | −5.79796 | − | 5.79796i | −0.481494 | − | 0.481494i | ||||
\(146\) | 19.3485i | 1.60129i | ||||||||
\(147\) | −4.89898 | + | 5.00000i | −0.404061 | + | 0.412393i | ||||
\(148\) | 7.89898 | − | 7.89898i | 0.649292 | − | 0.649292i | ||||
\(149\) | −0.898979 | + | 0.898979i | −0.0736473 | + | 0.0736473i | −0.742971 | − | 0.669324i | \(-0.766584\pi\) |
0.669324 | + | 0.742971i | \(0.266584\pi\) | |||||||
\(150\) | 3.67423 | − | 3.67423i | 0.300000 | − | 0.300000i | ||||
\(151\) | 7.44949 | + | 7.44949i | 0.606231 | + | 0.606231i | 0.941959 | − | 0.335728i | \(-0.108982\pi\) |
−0.335728 | + | 0.941959i | \(0.608982\pi\) | |||||||
\(152\) | 1.34847i | 0.109375i | ||||||||
\(153\) | −2.00000 | −0.161690 | ||||||||
\(154\) | −1.10102 | + | 2.69694i | −0.0887228 | + | 0.217325i | ||||
\(155\) | − | 21.7980i | − | 1.75085i | ||||||
\(156\) | 2.00000 | − | 3.00000i | 0.160128 | − | 0.240192i | ||||
\(157\) | − | 12.0000i | − | 0.957704i | −0.877896 | − | 0.478852i | \(-0.841053\pi\) | ||
0.877896 | − | 0.478852i | \(-0.158947\pi\) | |||||||
\(158\) | −3.55051 | + | 3.55051i | −0.282463 | + | 0.282463i | ||||
\(159\) | 11.7980i | 0.935639i | ||||||||
\(160\) | −14.6969 | −1.16190 | ||||||||
\(161\) | −21.7980 | − | 8.89898i | −1.71792 | − | 0.701338i | ||||
\(162\) | 1.22474 | − | 1.22474i | 0.0962250 | − | 0.0962250i | ||||
\(163\) | 5.44949 | + | 5.44949i | 0.426837 | + | 0.426837i | 0.887549 | − | 0.460712i | \(-0.152406\pi\) |
−0.460712 | + | 0.887549i | \(0.652406\pi\) | |||||||
\(164\) | 4.00000 | − | 4.00000i | 0.312348 | − | 0.312348i | ||||
\(165\) | 1.79796 | 0.139971 | ||||||||
\(166\) | −1.10102 | −0.0854558 | ||||||||
\(167\) | 11.3485 | − | 11.3485i | 0.878171 | − | 0.878171i | −0.115174 | − | 0.993345i | \(-0.536743\pi\) |
0.993345 | + | 0.115174i | \(0.0367427\pi\) | |||||||
\(168\) | −1.77526 | − | 4.22474i | −0.136964 | − | 0.325946i | ||||
\(169\) | −5.00000 | − | 12.0000i | −0.384615 | − | 0.923077i | ||||
\(170\) | −9.79796 | −0.751469 | ||||||||
\(171\) | −0.550510 | − | 0.550510i | −0.0420986 | − | 0.0420986i | ||||
\(172\) | 6.89898 | 0.526042 | ||||||||
\(173\) | −12.6969 | −0.965330 | −0.482665 | − | 0.875805i | \(-0.660331\pi\) | ||||
−0.482665 | + | 0.875805i | \(0.660331\pi\) | |||||||
\(174\) | −3.55051 | − | 3.55051i | −0.269163 | − | 0.269163i | ||||
\(175\) | 7.34847 | + | 3.00000i | 0.555492 | + | 0.226779i | ||||
\(176\) | −2.24745 | − | 2.24745i | −0.169408 | − | 0.169408i | ||||
\(177\) | −4.44949 | − | 4.44949i | −0.334444 | − | 0.334444i | ||||
\(178\) | 4.89898i | 0.367194i | ||||||||
\(179\) | 21.7980i | 1.62926i | 0.579984 | + | 0.814628i | \(0.303059\pi\) | ||||
−0.579984 | + | 0.814628i | \(0.696941\pi\) | |||||||
\(180\) | 2.00000 | − | 2.00000i | 0.149071 | − | 0.149071i | ||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 16.2247 | + | 3.12372i | 1.20266 | + | 0.231546i | ||||
\(183\) | −10.0000 | −0.739221 | ||||||||
\(184\) | 10.8990 | − | 10.8990i | 0.803483 | − | 0.803483i | ||||
\(185\) | − | 31.5959i | − | 2.32298i | ||||||
\(186\) | − | 13.3485i | − | 0.978757i | ||||||
\(187\) | −0.898979 | − | 0.898979i | −0.0657399 | − | 0.0657399i | ||||
\(188\) | 1.55051 | + | 1.55051i | 0.113083 | + | 0.113083i | ||||
\(189\) | 2.44949 | + | 1.00000i | 0.178174 | + | 0.0727393i | ||||
\(190\) | −2.69694 | − | 2.69694i | −0.195656 | − | 0.195656i | ||||
\(191\) | −13.7980 | −0.998385 | −0.499193 | − | 0.866491i | \(-0.666370\pi\) | ||||
−0.499193 | + | 0.866491i | \(0.666370\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 14.7980 | + | 14.7980i | 1.06518 | + | 1.06518i | 0.997722 | + | 0.0674583i | \(0.0214890\pi\) |
0.0674583 | + | 0.997722i | \(0.478511\pi\) | |||||||
\(194\) | −19.3485 | −1.38914 | ||||||||
\(195\) | −2.00000 | − | 10.0000i | −0.143223 | − | 0.716115i | ||||
\(196\) | −4.89898 | + | 5.00000i | −0.349927 | + | 0.357143i | ||||
\(197\) | −7.79796 | + | 7.79796i | −0.555582 | + | 0.555582i | −0.928046 | − | 0.372465i | \(-0.878513\pi\) |
0.372465 | + | 0.928046i | \(0.378513\pi\) | |||||||
\(198\) | 1.10102 | 0.0782461 | ||||||||
\(199\) | 22.8990 | 1.62327 | 0.811633 | − | 0.584168i | \(-0.198579\pi\) | ||||
0.811633 | + | 0.584168i | \(0.198579\pi\) | |||||||
\(200\) | −3.67423 | + | 3.67423i | −0.259808 | + | 0.259808i | ||||
\(201\) | 6.34847 | + | 6.34847i | 0.447786 | + | 0.447786i | ||||
\(202\) | 6.24745 | − | 6.24745i | 0.439569 | − | 0.439569i | ||||
\(203\) | 2.89898 | − | 7.10102i | 0.203468 | − | 0.498394i | ||||
\(204\) | −2.00000 | −0.140028 | ||||||||
\(205\) | − | 16.0000i | − | 1.11749i | ||||||
\(206\) | 2.20204 | − | 2.20204i | 0.153423 | − | 0.153423i | ||||
\(207\) | 8.89898i | 0.618522i | ||||||||
\(208\) | −10.0000 | + | 15.0000i | −0.693375 | + | 1.04006i | ||||
\(209\) | − | 0.494897i | − | 0.0342328i | ||||||
\(210\) | 12.0000 | + | 4.89898i | 0.828079 | + | 0.338062i | ||||
\(211\) | 9.10102 | 0.626540 | 0.313270 | − | 0.949664i | \(-0.398576\pi\) | ||||
0.313270 | + | 0.949664i | \(0.398576\pi\) | |||||||
\(212\) | 11.7980i | 0.810287i | ||||||||
\(213\) | −2.44949 | − | 2.44949i | −0.167836 | − | 0.167836i | ||||
\(214\) | 1.10102 | − | 1.10102i | 0.0752642 | − | 0.0752642i | ||||
\(215\) | 13.7980 | − | 13.7980i | 0.941013 | − | 0.941013i | ||||
\(216\) | −1.22474 | + | 1.22474i | −0.0833333 | + | 0.0833333i | ||||
\(217\) | 18.7980 | − | 7.89898i | 1.27609 | − | 0.536218i | ||||
\(218\) | 0.247449i | 0.0167593i | ||||||||
\(219\) | 7.89898 | + | 7.89898i | 0.533764 | + | 0.533764i | ||||
\(220\) | 1.79796 | 0.121218 | ||||||||
\(221\) | −4.00000 | + | 6.00000i | −0.269069 | + | 0.403604i | ||||
\(222\) | − | 19.3485i | − | 1.29858i | ||||||
\(223\) | −2.55051 | − | 2.55051i | −0.170795 | − | 0.170795i | 0.616534 | − | 0.787329i | \(-0.288536\pi\) |
−0.787329 | + | 0.616534i | \(0.788536\pi\) | |||||||
\(224\) | −5.32577 | − | 12.6742i | −0.355843 | − | 0.846833i | ||||
\(225\) | − | 3.00000i | − | 0.200000i | ||||||
\(226\) | −23.1464 | + | 23.1464i | −1.53968 | + | 1.53968i | ||||
\(227\) | −0.651531 | − | 0.651531i | −0.0432436 | − | 0.0432436i | 0.685154 | − | 0.728398i | \(-0.259735\pi\) |
−0.728398 | + | 0.685154i | \(0.759735\pi\) | |||||||
\(228\) | −0.550510 | − | 0.550510i | −0.0364584 | − | 0.0364584i | ||||
\(229\) | 13.0000 | − | 13.0000i | 0.859064 | − | 0.859064i | −0.132164 | − | 0.991228i | \(-0.542192\pi\) |
0.991228 | + | 0.132164i | \(0.0421925\pi\) | |||||||
\(230\) | 43.5959i | 2.87463i | ||||||||
\(231\) | 0.651531 | + | 1.55051i | 0.0428676 | + | 0.102016i | ||||
\(232\) | 3.55051 | + | 3.55051i | 0.233102 | + | 0.233102i | ||||
\(233\) | − | 11.7980i | − | 0.772910i | −0.922308 | − | 0.386455i | \(-0.873699\pi\) | ||
0.922308 | − | 0.386455i | \(-0.126301\pi\) | |||||||
\(234\) | −1.22474 | − | 6.12372i | −0.0800641 | − | 0.400320i | ||||
\(235\) | 6.20204 | 0.404577 | ||||||||
\(236\) | −4.44949 | − | 4.44949i | −0.289637 | − | 0.289637i | ||||
\(237\) | 2.89898i | 0.188309i | ||||||||
\(238\) | −3.55051 | − | 8.44949i | −0.230145 | − | 0.547699i | ||||
\(239\) | −7.34847 | + | 7.34847i | −0.475333 | + | 0.475333i | −0.903635 | − | 0.428302i | \(-0.859112\pi\) |
0.428302 | + | 0.903635i | \(0.359112\pi\) | |||||||
\(240\) | −10.0000 | + | 10.0000i | −0.645497 | + | 0.645497i | ||||
\(241\) | −13.8990 | + | 13.8990i | −0.895312 | + | 0.895312i | −0.995017 | − | 0.0997051i | \(-0.968210\pi\) |
0.0997051 | + | 0.995017i | \(0.468210\pi\) | |||||||
\(242\) | −12.9773 | − | 12.9773i | −0.834212 | − | 0.834212i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −10.0000 | −0.640184 | ||||||||
\(245\) | 0.202041 | + | 19.7980i | 0.0129079 | + | 1.26485i | ||||
\(246\) | − | 9.79796i | − | 0.624695i | ||||||
\(247\) | −2.75255 | + | 0.550510i | −0.175141 | + | 0.0350281i | ||||
\(248\) | 13.3485i | 0.847629i | ||||||||
\(249\) | −0.449490 | + | 0.449490i | −0.0284853 | + | 0.0284853i | ||||
\(250\) | 9.79796i | 0.619677i | ||||||||
\(251\) | −4.89898 | −0.309221 | −0.154610 | − | 0.987976i | \(-0.549412\pi\) | ||||
−0.154610 | + | 0.987976i | \(0.549412\pi\) | |||||||
\(252\) | 2.44949 | + | 1.00000i | 0.154303 | + | 0.0629941i | ||||
\(253\) | −4.00000 | + | 4.00000i | −0.251478 | + | 0.251478i | ||||
\(254\) | −9.79796 | − | 9.79796i | −0.614779 | − | 0.614779i | ||||
\(255\) | −4.00000 | + | 4.00000i | −0.250490 | + | 0.250490i | ||||
\(256\) | 19.0000 | 1.18750 | ||||||||
\(257\) | 20.6969 | 1.29104 | 0.645520 | − | 0.763744i | \(-0.276641\pi\) | ||||
0.645520 | + | 0.763744i | \(0.276641\pi\) | |||||||
\(258\) | 8.44949 | − | 8.44949i | 0.526042 | − | 0.526042i | ||||
\(259\) | 27.2474 | − | 11.4495i | 1.69307 | − | 0.711437i | ||||
\(260\) | −2.00000 | − | 10.0000i | −0.124035 | − | 0.620174i | ||||
\(261\) | −2.89898 | −0.179442 | ||||||||
\(262\) | 22.8990 | + | 22.8990i | 1.41470 | + | 1.41470i | ||||
\(263\) | 16.8990 | 1.04204 | 0.521018 | − | 0.853546i | \(-0.325552\pi\) | ||||
0.521018 | + | 0.853546i | \(0.325552\pi\) | |||||||
\(264\) | −1.10102 | −0.0677631 | ||||||||
\(265\) | 23.5959 | + | 23.5959i | 1.44949 | + | 1.44949i | ||||
\(266\) | 1.34847 | − | 3.30306i | 0.0826800 | − | 0.202524i | ||||
\(267\) | 2.00000 | + | 2.00000i | 0.122398 | + | 0.122398i | ||||
\(268\) | 6.34847 | + | 6.34847i | 0.387794 | + | 0.387794i | ||||
\(269\) | − | 6.00000i | − | 0.365826i | −0.983129 | − | 0.182913i | \(-0.941447\pi\) | ||
0.983129 | − | 0.182913i | \(-0.0585527\pi\) | |||||||
\(270\) | − | 4.89898i | − | 0.298142i | ||||||
\(271\) | −4.55051 | + | 4.55051i | −0.276424 | + | 0.276424i | −0.831680 | − | 0.555256i | \(-0.812620\pi\) |
0.555256 | + | 0.831680i | \(0.312620\pi\) | |||||||
\(272\) | 10.0000 | 0.606339 | ||||||||
\(273\) | 7.89898 | − | 5.34847i | 0.478068 | − | 0.323704i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.34847 | − | 1.34847i | 0.0813158 | − | 0.0813158i | ||||
\(276\) | 8.89898i | 0.535656i | ||||||||
\(277\) | 17.7980i | 1.06938i | 0.845050 | + | 0.534688i | \(0.179571\pi\) | ||||
−0.845050 | + | 0.534688i | \(0.820429\pi\) | |||||||
\(278\) | 8.44949 | + | 8.44949i | 0.506767 | + | 0.506767i | ||||
\(279\) | −5.44949 | − | 5.44949i | −0.326252 | − | 0.326252i | ||||
\(280\) | −12.0000 | − | 4.89898i | −0.717137 | − | 0.292770i | ||||
\(281\) | −4.00000 | − | 4.00000i | −0.238620 | − | 0.238620i | 0.577659 | − | 0.816279i | \(-0.303967\pi\) |
−0.816279 | + | 0.577659i | \(0.803967\pi\) | |||||||
\(282\) | 3.79796 | 0.226165 | ||||||||
\(283\) | −12.6969 | −0.754755 | −0.377377 | − | 0.926060i | \(-0.623174\pi\) | ||||
−0.377377 | + | 0.926060i | \(0.623174\pi\) | |||||||
\(284\) | −2.44949 | − | 2.44949i | −0.145350 | − | 0.145350i | ||||
\(285\) | −2.20204 | −0.130438 | ||||||||
\(286\) | 2.20204 | − | 3.30306i | 0.130209 | − | 0.195314i | ||||
\(287\) | 13.7980 | − | 5.79796i | 0.814468 | − | 0.342243i | ||||
\(288\) | −3.67423 | + | 3.67423i | −0.216506 | + | 0.216506i | ||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | −14.2020 | −0.833973 | ||||||||
\(291\) | −7.89898 | + | 7.89898i | −0.463046 | + | 0.463046i | ||||
\(292\) | 7.89898 | + | 7.89898i | 0.462253 | + | 0.462253i | ||||
\(293\) | −18.6969 | + | 18.6969i | −1.09229 | + | 1.09229i | −0.0970027 | + | 0.995284i | \(0.530926\pi\) |
−0.995284 | + | 0.0970027i | \(0.969074\pi\) | |||||||
\(294\) | 0.123724 | + | 12.1237i | 0.00721575 | + | 0.707070i | ||||
\(295\) | −17.7980 | −1.03624 | ||||||||
\(296\) | 19.3485i | 1.12461i | ||||||||
\(297\) | 0.449490 | − | 0.449490i | 0.0260820 | − | 0.0260820i | ||||
\(298\) | 2.20204i | 0.127561i | ||||||||
\(299\) | 26.6969 | + | 17.7980i | 1.54392 | + | 1.02928i | ||||
\(300\) | − | 3.00000i | − | 0.173205i | ||||||
\(301\) | 16.8990 | + | 6.89898i | 0.974041 | + | 0.397651i | ||||
\(302\) | 18.2474 | 1.05002 | ||||||||
\(303\) | − | 5.10102i | − | 0.293046i | ||||||
\(304\) | 2.75255 | + | 2.75255i | 0.157870 | + | 0.157870i | ||||
\(305\) | −20.0000 | + | 20.0000i | −1.14520 | + | 1.14520i | ||||
\(306\) | −2.44949 | + | 2.44949i | −0.140028 | + | 0.140028i | ||||
\(307\) | 13.4495 | − | 13.4495i | 0.767603 | − | 0.767603i | −0.210081 | − | 0.977684i | \(-0.567373\pi\) |
0.977684 | + | 0.210081i | \(0.0673728\pi\) | |||||||
\(308\) | 0.651531 | + | 1.55051i | 0.0371244 | + | 0.0883485i | ||||
\(309\) | − | 1.79796i | − | 0.102282i | ||||||
\(310\) | −26.6969 | − | 26.6969i | −1.51628 | − | 1.51628i | ||||
\(311\) | 15.1010 | 0.856300 | 0.428150 | − | 0.903708i | \(-0.359165\pi\) | ||||
0.428150 | + | 0.903708i | \(0.359165\pi\) | |||||||
\(312\) | 1.22474 | + | 6.12372i | 0.0693375 | + | 0.346688i | ||||
\(313\) | − | 25.5959i | − | 1.44677i | −0.690447 | − | 0.723383i | \(-0.742586\pi\) | ||
0.690447 | − | 0.723383i | \(-0.257414\pi\) | |||||||
\(314\) | −14.6969 | − | 14.6969i | −0.829396 | − | 0.829396i | ||||
\(315\) | 6.89898 | − | 2.89898i | 0.388713 | − | 0.163339i | ||||
\(316\) | 2.89898i | 0.163080i | ||||||||
\(317\) | 16.6969 | − | 16.6969i | 0.937793 | − | 0.937793i | −0.0603819 | − | 0.998175i | \(-0.519232\pi\) |
0.998175 | + | 0.0603819i | \(0.0192318\pi\) | |||||||
\(318\) | 14.4495 | + | 14.4495i | 0.810287 | + | 0.810287i | ||||
\(319\) | −1.30306 | − | 1.30306i | −0.0729574 | − | 0.0729574i | ||||
\(320\) | 2.00000 | − | 2.00000i | 0.111803 | − | 0.111803i | ||||
\(321\) | − | 0.898979i | − | 0.0501761i | ||||||
\(322\) | −37.5959 | + | 15.7980i | −2.09514 | + | 0.880386i | ||||
\(323\) | 1.10102 | + | 1.10102i | 0.0612624 | + | 0.0612624i | ||||
\(324\) | − | 1.00000i | − | 0.0555556i | ||||||
\(325\) | −9.00000 | − | 6.00000i | −0.499230 | − | 0.332820i | ||||
\(326\) | 13.3485 | 0.739303 | ||||||||
\(327\) | 0.101021 | + | 0.101021i | 0.00558645 | + | 0.00558645i | ||||
\(328\) | 9.79796i | 0.541002i | ||||||||
\(329\) | 2.24745 | + | 5.34847i | 0.123906 | + | 0.294871i | ||||
\(330\) | 2.20204 | − | 2.20204i | 0.121218 | − | 0.121218i | ||||
\(331\) | −21.2474 | + | 21.2474i | −1.16787 | + | 1.16787i | −0.185156 | + | 0.982709i | \(0.559279\pi\) |
−0.982709 | + | 0.185156i | \(0.940721\pi\) | |||||||
\(332\) | −0.449490 | + | 0.449490i | −0.0246690 | + | 0.0246690i | ||||
\(333\) | −7.89898 | − | 7.89898i | −0.432861 | − | 0.432861i | ||||
\(334\) | − | 27.7980i | − | 1.52104i | ||||||
\(335\) | 25.3939 | 1.38742 | ||||||||
\(336\) | −12.2474 | − | 5.00000i | −0.668153 | − | 0.272772i | ||||
\(337\) | − | 23.7980i | − | 1.29636i | −0.761488 | − | 0.648179i | \(-0.775531\pi\) | ||
0.761488 | − | 0.648179i | \(-0.224469\pi\) | |||||||
\(338\) | −20.8207 | − | 8.57321i | −1.13249 | − | 0.466321i | ||||
\(339\) | 18.8990i | 1.02645i | ||||||||
\(340\) | −4.00000 | + | 4.00000i | −0.216930 | + | 0.216930i | ||||
\(341\) | − | 4.89898i | − | 0.265295i | ||||||
\(342\) | −1.34847 | −0.0729169 | ||||||||
\(343\) | −17.0000 | + | 7.34847i | −0.917914 | + | 0.396780i | ||||
\(344\) | −8.44949 | + | 8.44949i | −0.455566 | + | 0.455566i | ||||
\(345\) | 17.7980 | + | 17.7980i | 0.958210 | + | 0.958210i | ||||
\(346\) | −15.5505 | + | 15.5505i | −0.836001 | + | 0.836001i | ||||
\(347\) | 2.20204 | 0.118212 | 0.0591059 | − | 0.998252i | \(-0.481175\pi\) | ||||
0.0591059 | + | 0.998252i | \(0.481175\pi\) | |||||||
\(348\) | −2.89898 | −0.155402 | ||||||||
\(349\) | 8.79796 | − | 8.79796i | 0.470944 | − | 0.470944i | −0.431276 | − | 0.902220i | \(-0.641936\pi\) |
0.902220 | + | 0.431276i | \(0.141936\pi\) | |||||||
\(350\) | 12.6742 | − | 5.32577i | 0.677466 | − | 0.284674i | ||||
\(351\) | −3.00000 | − | 2.00000i | −0.160128 | − | 0.106752i | ||||
\(352\) | −3.30306 | −0.176054 | ||||||||
\(353\) | −9.79796 | − | 9.79796i | −0.521493 | − | 0.521493i | 0.396529 | − | 0.918022i | \(-0.370215\pi\) |
−0.918022 | + | 0.396529i | \(0.870215\pi\) | |||||||
\(354\) | −10.8990 | −0.579274 | ||||||||
\(355\) | −9.79796 | −0.520022 | ||||||||
\(356\) | 2.00000 | + | 2.00000i | 0.106000 | + | 0.106000i | ||||
\(357\) | −4.89898 | − | 2.00000i | −0.259281 | − | 0.105851i | ||||
\(358\) | 26.6969 | + | 26.6969i | 1.41098 | + | 1.41098i | ||||
\(359\) | 4.44949 | + | 4.44949i | 0.234835 | + | 0.234835i | 0.814707 | − | 0.579872i | \(-0.196898\pi\) |
−0.579872 | + | 0.814707i | \(0.696898\pi\) | |||||||
\(360\) | 4.89898i | 0.258199i | ||||||||
\(361\) | − | 18.3939i | − | 0.968099i | ||||||
\(362\) | −2.44949 | + | 2.44949i | −0.128742 | + | 0.128742i | ||||
\(363\) | −10.5959 | −0.556141 | ||||||||
\(364\) | 7.89898 | − | 5.34847i | 0.414019 | − | 0.280336i | ||||
\(365\) | 31.5959 | 1.65381 | ||||||||
\(366\) | −12.2474 | + | 12.2474i | −0.640184 | + | 0.640184i | ||||
\(367\) | − | 26.4949i | − | 1.38302i | −0.722366 | − | 0.691511i | \(-0.756945\pi\) | ||
0.722366 | − | 0.691511i | \(-0.243055\pi\) | |||||||
\(368\) | − | 44.4949i | − | 2.31946i | ||||||
\(369\) | −4.00000 | − | 4.00000i | −0.208232 | − | 0.208232i | ||||
\(370\) | −38.6969 | − | 38.6969i | −2.01176 | − | 2.01176i | ||||
\(371\) | −11.7980 | + | 28.8990i | −0.612520 | + | 1.50036i | ||||
\(372\) | −5.44949 | − | 5.44949i | −0.282543 | − | 0.282543i | ||||
\(373\) | 9.79796 | 0.507319 | 0.253660 | − | 0.967294i | \(-0.418366\pi\) | ||||
0.253660 | + | 0.967294i | \(0.418366\pi\) | |||||||
\(374\) | −2.20204 | −0.113865 | ||||||||
\(375\) | 4.00000 | + | 4.00000i | 0.206559 | + | 0.206559i | ||||
\(376\) | −3.79796 | −0.195865 | ||||||||
\(377\) | −5.79796 | + | 8.69694i | −0.298610 | + | 0.447915i | ||||
\(378\) | 4.22474 | − | 1.77526i | 0.217297 | − | 0.0913093i | ||||
\(379\) | 13.4495 | − | 13.4495i | 0.690854 | − | 0.690854i | −0.271566 | − | 0.962420i | \(-0.587542\pi\) |
0.962420 | + | 0.271566i | \(0.0875415\pi\) | |||||||
\(380\) | −2.20204 | −0.112962 | ||||||||
\(381\) | −8.00000 | −0.409852 | ||||||||
\(382\) | −16.8990 | + | 16.8990i | −0.864627 | + | 0.864627i | ||||
\(383\) | −16.2474 | − | 16.2474i | −0.830206 | − | 0.830206i | 0.157339 | − | 0.987545i | \(-0.449709\pi\) |
−0.987545 | + | 0.157339i | \(0.949709\pi\) | |||||||
\(384\) | 8.57321 | − | 8.57321i | 0.437500 | − | 0.437500i | ||||
\(385\) | 4.40408 | + | 1.79796i | 0.224453 | + | 0.0916325i | ||||
\(386\) | 36.2474 | 1.84495 | ||||||||
\(387\) | − | 6.89898i | − | 0.350695i | ||||||
\(388\) | −7.89898 | + | 7.89898i | −0.401010 | + | 0.401010i | ||||
\(389\) | − | 1.10102i | − | 0.0558240i | −0.999610 | − | 0.0279120i | \(-0.991114\pi\) | ||
0.999610 | − | 0.0279120i | \(-0.00888581\pi\) | |||||||
\(390\) | −14.6969 | − | 9.79796i | −0.744208 | − | 0.496139i | ||||
\(391\) | − | 17.7980i | − | 0.900081i | ||||||
\(392\) | −0.123724 | − | 12.1237i | −0.00624902 | − | 0.612341i | ||||
\(393\) | 18.6969 | 0.943136 | ||||||||
\(394\) | 19.1010i | 0.962296i | ||||||||
\(395\) | 5.79796 | + | 5.79796i | 0.291727 | + | 0.291727i | ||||
\(396\) | 0.449490 | − | 0.449490i | 0.0225877 | − | 0.0225877i | ||||
\(397\) | −8.79796 | + | 8.79796i | −0.441557 | + | 0.441557i | −0.892535 | − | 0.450978i | \(-0.851075\pi\) |
0.450978 | + | 0.892535i | \(0.351075\pi\) | |||||||
\(398\) | 28.0454 | − | 28.0454i | 1.40579 | − | 1.40579i | ||||
\(399\) | −0.797959 | − | 1.89898i | −0.0399479 | − | 0.0950679i | ||||
\(400\) | 15.0000i | 0.750000i | ||||||||
\(401\) | −14.0000 | − | 14.0000i | −0.699127 | − | 0.699127i | 0.265096 | − | 0.964222i | \(-0.414597\pi\) |
−0.964222 | + | 0.265096i | \(0.914597\pi\) | |||||||
\(402\) | 15.5505 | 0.775589 | ||||||||
\(403\) | −27.2474 | + | 5.44949i | −1.35729 | + | 0.271458i | ||||
\(404\) | − | 5.10102i | − | 0.253785i | ||||||
\(405\) | −2.00000 | − | 2.00000i | −0.0993808 | − | 0.0993808i | ||||
\(406\) | −5.14643 | − | 12.2474i | −0.255413 | − | 0.607831i | ||||
\(407\) | − | 7.10102i | − | 0.351985i | ||||||
\(408\) | 2.44949 | − | 2.44949i | 0.121268 | − | 0.121268i | ||||
\(409\) | 5.69694 | + | 5.69694i | 0.281695 | + | 0.281695i | 0.833785 | − | 0.552089i | \(-0.186169\pi\) |
−0.552089 | + | 0.833785i | \(0.686169\pi\) | |||||||
\(410\) | −19.5959 | − | 19.5959i | −0.967773 | − | 0.967773i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 1.79796i | − | 0.0885791i | ||||||
\(413\) | −6.44949 | − | 15.3485i | −0.317359 | − | 0.755249i | ||||
\(414\) | 10.8990 | + | 10.8990i | 0.535656 | + | 0.535656i | ||||
\(415\) | 1.79796i | 0.0882583i | ||||||||
\(416\) | 3.67423 | + | 18.3712i | 0.180144 | + | 0.900721i | ||||
\(417\) | 6.89898 | 0.337844 | ||||||||
\(418\) | −0.606123 | − | 0.606123i | −0.0296464 | − | 0.0296464i | ||||
\(419\) | 34.2929i | 1.67532i | 0.546195 | + | 0.837658i | \(0.316076\pi\) | ||||
−0.546195 | + | 0.837658i | \(0.683924\pi\) | |||||||
\(420\) | 6.89898 | − | 2.89898i | 0.336636 | − | 0.141456i | ||||
\(421\) | 13.8990 | − | 13.8990i | 0.677395 | − | 0.677395i | −0.282015 | − | 0.959410i | \(-0.591003\pi\) |
0.959410 | + | 0.282015i | \(0.0910028\pi\) | |||||||
\(422\) | 11.1464 | − | 11.1464i | 0.542600 | − | 0.542600i | ||||
\(423\) | 1.55051 | − | 1.55051i | 0.0753884 | − | 0.0753884i | ||||
\(424\) | −14.4495 | − | 14.4495i | −0.701729 | − | 0.701729i | ||||
\(425\) | 6.00000i | 0.291043i | ||||||||
\(426\) | −6.00000 | −0.290701 | ||||||||
\(427\) | −24.4949 | − | 10.0000i | −1.18539 | − | 0.483934i | ||||
\(428\) | − | 0.898979i | − | 0.0434538i | ||||||
\(429\) | −0.449490 | − | 2.24745i | −0.0217016 | − | 0.108508i | ||||
\(430\) | − | 33.7980i | − | 1.62988i | ||||||
\(431\) | 24.0454 | − | 24.0454i | 1.15823 | − | 1.15823i | 0.173370 | − | 0.984857i | \(-0.444534\pi\) |
0.984857 | − | 0.173370i | \(-0.0554656\pi\) | |||||||
\(432\) | 5.00000i | 0.240563i | ||||||||
\(433\) | 10.2020 | 0.490279 | 0.245139 | − | 0.969488i | \(-0.421166\pi\) | ||||
0.245139 | + | 0.969488i | \(0.421166\pi\) | |||||||
\(434\) | 13.3485 | − | 32.6969i | 0.640747 | − | 1.56950i | ||||
\(435\) | −5.79796 | + | 5.79796i | −0.277991 | + | 0.277991i | ||||
\(436\) | 0.101021 | + | 0.101021i | 0.00483801 | + | 0.00483801i | ||||
\(437\) | 4.89898 | − | 4.89898i | 0.234350 | − | 0.234350i | ||||
\(438\) | 19.3485 | 0.924506 | ||||||||
\(439\) | −11.5959 | −0.553443 | −0.276721 | − | 0.960950i | \(-0.589248\pi\) | ||||
−0.276721 | + | 0.960950i | \(0.589248\pi\) | |||||||
\(440\) | −2.20204 | + | 2.20204i | −0.104978 | + | 0.104978i | ||||
\(441\) | 5.00000 | + | 4.89898i | 0.238095 | + | 0.233285i | ||||
\(442\) | 2.44949 | + | 12.2474i | 0.116510 | + | 0.582552i | ||||
\(443\) | −34.6969 | −1.64850 | −0.824251 | − | 0.566225i | \(-0.808403\pi\) | ||||
−0.824251 | + | 0.566225i | \(0.808403\pi\) | |||||||
\(444\) | −7.89898 | − | 7.89898i | −0.374869 | − | 0.374869i | ||||
\(445\) | 8.00000 | 0.379236 | ||||||||
\(446\) | −6.24745 | −0.295825 | ||||||||
\(447\) | 0.898979 | + | 0.898979i | 0.0425203 | + | 0.0425203i | ||||
\(448\) | 2.44949 | + | 1.00000i | 0.115728 | + | 0.0472456i | ||||
\(449\) | 5.10102 | + | 5.10102i | 0.240732 | + | 0.240732i | 0.817153 | − | 0.576421i | \(-0.195551\pi\) |
−0.576421 | + | 0.817153i | \(0.695551\pi\) | |||||||
\(450\) | −3.67423 | − | 3.67423i | −0.173205 | − | 0.173205i | ||||
\(451\) | − | 3.59592i | − | 0.169325i | ||||||
\(452\) | 18.8990i | 0.888933i | ||||||||
\(453\) | 7.44949 | − | 7.44949i | 0.350008 | − | 0.350008i | ||||
\(454\) | −1.59592 | −0.0749001 | ||||||||
\(455\) | 5.10102 | − | 26.4949i | 0.239140 | − | 1.24210i | ||||
\(456\) | 1.34847 | 0.0631479 | ||||||||
\(457\) | −12.7980 | + | 12.7980i | −0.598663 | + | 0.598663i | −0.939957 | − | 0.341294i | \(-0.889135\pi\) |
0.341294 | + | 0.939957i | \(0.389135\pi\) | |||||||
\(458\) | − | 31.8434i | − | 1.48794i | ||||||
\(459\) | 2.00000i | 0.0933520i | ||||||||
\(460\) | 17.7980 | + | 17.7980i | 0.829834 | + | 0.829834i | ||||
\(461\) | −24.6969 | − | 24.6969i | −1.15025 | − | 1.15025i | −0.986502 | − | 0.163749i | \(-0.947641\pi\) |
−0.163749 | − | 0.986502i | \(-0.552359\pi\) | |||||||
\(462\) | 2.69694 | + | 1.10102i | 0.125473 | + | 0.0512241i | ||||
\(463\) | 14.1464 | + | 14.1464i | 0.657440 | + | 0.657440i | 0.954774 | − | 0.297333i | \(-0.0960973\pi\) |
−0.297333 | + | 0.954774i | \(0.596097\pi\) | |||||||
\(464\) | 14.4949 | 0.672909 | ||||||||
\(465\) | −21.7980 | −1.01086 | ||||||||
\(466\) | −14.4495 | − | 14.4495i | −0.669360 | − | 0.669360i | ||||
\(467\) | −40.8990 | −1.89258 | −0.946290 | − | 0.323320i | \(-0.895201\pi\) | ||||
−0.946290 | + | 0.323320i | \(0.895201\pi\) | |||||||
\(468\) | −3.00000 | − | 2.00000i | −0.138675 | − | 0.0924500i | ||||
\(469\) | 9.20204 | + | 21.8990i | 0.424911 | + | 1.01120i | ||||
\(470\) | 7.59592 | − | 7.59592i | 0.350374 | − | 0.350374i | ||||
\(471\) | −12.0000 | −0.552931 | ||||||||
\(472\) | 10.8990 | 0.501666 | ||||||||
\(473\) | 3.10102 | − | 3.10102i | 0.142585 | − | 0.142585i | ||||
\(474\) | 3.55051 | + | 3.55051i | 0.163080 | + | 0.163080i | ||||
\(475\) | −1.65153 | + | 1.65153i | −0.0757774 | + | 0.0757774i | ||||
\(476\) | −4.89898 | − | 2.00000i | −0.224544 | − | 0.0916698i | ||||
\(477\) | 11.7980 | 0.540191 | ||||||||
\(478\) | 18.0000i | 0.823301i | ||||||||
\(479\) | −14.2474 | + | 14.2474i | −0.650983 | + | 0.650983i | −0.953230 | − | 0.302247i | \(-0.902263\pi\) |
0.302247 | + | 0.953230i | \(0.402263\pi\) | |||||||
\(480\) | 14.6969i | 0.670820i | ||||||||
\(481\) | −39.4949 | + | 7.89898i | −1.80081 | + | 0.360162i | ||||
\(482\) | 34.0454i | 1.55073i | ||||||||
\(483\) | −8.89898 | + | 21.7980i | −0.404918 | + | 0.991841i | ||||
\(484\) | −10.5959 | −0.481633 | ||||||||
\(485\) | 31.5959i | 1.43470i | ||||||||
\(486\) | −1.22474 | − | 1.22474i | −0.0555556 | − | 0.0555556i | ||||
\(487\) | −9.24745 | + | 9.24745i | −0.419042 | + | 0.419042i | −0.884873 | − | 0.465832i | \(-0.845755\pi\) |
0.465832 | + | 0.884873i | \(0.345755\pi\) | |||||||
\(488\) | 12.2474 | − | 12.2474i | 0.554416 | − | 0.554416i | ||||
\(489\) | 5.44949 | − | 5.44949i | 0.246434 | − | 0.246434i | ||||
\(490\) | 24.4949 | + | 24.0000i | 1.10657 | + | 1.08421i | ||||
\(491\) | − | 27.1010i | − | 1.22305i | −0.791224 | − | 0.611526i | \(-0.790556\pi\) | ||
0.791224 | − | 0.611526i | \(-0.209444\pi\) | |||||||
\(492\) | −4.00000 | − | 4.00000i | −0.180334 | − | 0.180334i | ||||
\(493\) | 5.79796 | 0.261127 | ||||||||
\(494\) | −2.69694 | + | 4.04541i | −0.121341 | + | 0.182011i | ||||
\(495\) | − | 1.79796i | − | 0.0808122i | ||||||
\(496\) | 27.2474 | + | 27.2474i | 1.22345 | + | 1.22345i | ||||
\(497\) | −3.55051 | − | 8.44949i | −0.159262 | − | 0.379011i | ||||
\(498\) | 1.10102i | 0.0493379i | ||||||||
\(499\) | 9.24745 | − | 9.24745i | 0.413973 | − | 0.413973i | −0.469147 | − | 0.883120i | \(-0.655439\pi\) |
0.883120 | + | 0.469147i | \(0.155439\pi\) | |||||||
\(500\) | 4.00000 | + | 4.00000i | 0.178885 | + | 0.178885i | ||||
\(501\) | −11.3485 | − | 11.3485i | −0.507012 | − | 0.507012i | ||||
\(502\) | −6.00000 | + | 6.00000i | −0.267793 | + | 0.267793i | ||||
\(503\) | − | 2.69694i | − | 0.120251i | −0.998191 | − | 0.0601253i | \(-0.980850\pi\) | ||
0.998191 | − | 0.0601253i | \(-0.0191500\pi\) | |||||||
\(504\) | −4.22474 | + | 1.77526i | −0.188185 | + | 0.0790761i | ||||
\(505\) | −10.2020 | − | 10.2020i | −0.453985 | − | 0.453985i | ||||
\(506\) | 9.79796i | 0.435572i | ||||||||
\(507\) | −12.0000 | + | 5.00000i | −0.532939 | + | 0.222058i | ||||
\(508\) | −8.00000 | −0.354943 | ||||||||
\(509\) | 14.8990 | + | 14.8990i | 0.660386 | + | 0.660386i | 0.955471 | − | 0.295085i | \(-0.0953481\pi\) |
−0.295085 | + | 0.955471i | \(0.595348\pi\) | |||||||
\(510\) | 9.79796i | 0.433861i | ||||||||
\(511\) | 11.4495 | + | 27.2474i | 0.506496 | + | 1.20536i | ||||
\(512\) | 6.12372 | − | 6.12372i | 0.270633 | − | 0.270633i | ||||
\(513\) | −0.550510 | + | 0.550510i | −0.0243056 | + | 0.0243056i | ||||
\(514\) | 25.3485 | − | 25.3485i | 1.11807 | − | 1.11807i | ||||
\(515\) | −3.59592 | − | 3.59592i | −0.158455 | − | 0.158455i | ||||
\(516\) | − | 6.89898i | − | 0.303711i | ||||||
\(517\) | 1.39388 | 0.0613026 | ||||||||
\(518\) | 19.3485 | − | 47.3939i | 0.850123 | − | 2.08237i | ||||
\(519\) | 12.6969i | 0.557334i | ||||||||
\(520\) | 14.6969 | + | 9.79796i | 0.644503 | + | 0.429669i | ||||
\(521\) | 27.3939i | 1.20015i | 0.799945 | + | 0.600074i | \(0.204862\pi\) | ||||
−0.799945 | + | 0.600074i | \(0.795138\pi\) | |||||||
\(522\) | −3.55051 | + | 3.55051i | −0.155402 | + | 0.155402i | ||||
\(523\) | 30.4949i | 1.33345i | 0.745304 | + | 0.666724i | \(0.232304\pi\) | ||||
−0.745304 | + | 0.666724i | \(0.767696\pi\) | |||||||
\(524\) | 18.6969 | 0.816780 | ||||||||
\(525\) | 3.00000 | − | 7.34847i | 0.130931 | − | 0.320713i | ||||
\(526\) | 20.6969 | − | 20.6969i | 0.902429 | − | 0.902429i | ||||
\(527\) | 10.8990 | + | 10.8990i | 0.474767 | + | 0.474767i | ||||
\(528\) | −2.24745 | + | 2.24745i | −0.0978077 | + | 0.0978077i | ||||
\(529\) | −56.1918 | −2.44312 | ||||||||
\(530\) | 57.7980 | 2.51058 | ||||||||
\(531\) | −4.44949 | + | 4.44949i | −0.193091 | + | 0.193091i | ||||
\(532\) | −0.797959 | − | 1.89898i | −0.0345959 | − | 0.0823312i | ||||
\(533\) | −20.0000 | + | 4.00000i | −0.866296 | + | 0.173259i | ||||
\(534\) | 4.89898 | 0.212000 | ||||||||
\(535\) | −1.79796 | − | 1.79796i | −0.0777325 | − | 0.0777325i | ||||
\(536\) | −15.5505 | −0.671680 | ||||||||
\(537\) | 21.7980 | 0.940651 | ||||||||
\(538\) | −7.34847 | − | 7.34847i | −0.316815 | − | 0.316815i | ||||
\(539\) | 0.0454077 | + | 4.44949i | 0.00195585 | + | 0.191653i | ||||
\(540\) | −2.00000 | − | 2.00000i | −0.0860663 | − | 0.0860663i | ||||
\(541\) | −11.8990 | − | 11.8990i | −0.511577 | − | 0.511577i | 0.403432 | − | 0.915009i | \(-0.367817\pi\) |
−0.915009 | + | 0.403432i | \(0.867817\pi\) | |||||||
\(542\) | 11.1464i | 0.478780i | ||||||||
\(543\) | 2.00000i | 0.0858282i | ||||||||
\(544\) | 7.34847 | − | 7.34847i | 0.315063 | − | 0.315063i | ||||
\(545\) | 0.404082 | 0.0173090 | ||||||||
\(546\) | 3.12372 | − | 16.2247i | 0.133683 | − | 0.694355i | ||||
\(547\) | 13.7980 | 0.589958 | 0.294979 | − | 0.955504i | \(-0.404687\pi\) | ||||
0.294979 | + | 0.955504i | \(0.404687\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.0000i | 0.426790i | ||||||||
\(550\) | − | 3.30306i | − | 0.140843i | ||||||
\(551\) | 1.59592 | + | 1.59592i | 0.0679884 | + | 0.0679884i | ||||
\(552\) | −10.8990 | − | 10.8990i | −0.463891 | − | 0.463891i | ||||
\(553\) | −2.89898 | + | 7.10102i | −0.123277 | + | 0.301966i | ||||
\(554\) | 21.7980 | + | 21.7980i | 0.926107 | + | 0.926107i | ||||
\(555\) | −31.5959 | −1.34117 | ||||||||
\(556\) | 6.89898 | 0.292582 | ||||||||
\(557\) | 18.6969 | + | 18.6969i | 0.792215 | + | 0.792215i | 0.981854 | − | 0.189639i | \(-0.0607318\pi\) |
−0.189639 | + | 0.981854i | \(0.560732\pi\) | |||||||
\(558\) | −13.3485 | −0.565086 | ||||||||
\(559\) | −20.6969 | − | 13.7980i | −0.875387 | − | 0.583591i | ||||
\(560\) | −34.4949 | + | 14.4949i | −1.45768 | + | 0.612521i | ||||
\(561\) | −0.898979 | + | 0.898979i | −0.0379549 | + | 0.0379549i | ||||
\(562\) | −9.79796 | −0.413302 | ||||||||
\(563\) | 21.7980 | 0.918674 | 0.459337 | − | 0.888262i | \(-0.348087\pi\) | ||||
0.459337 | + | 0.888262i | \(0.348087\pi\) | |||||||
\(564\) | 1.55051 | − | 1.55051i | 0.0652883 | − | 0.0652883i | ||||
\(565\) | 37.7980 | + | 37.7980i | 1.59017 | + | 1.59017i | ||||
\(566\) | −15.5505 | + | 15.5505i | −0.653637 | + | 0.653637i | ||||
\(567\) | 1.00000 | − | 2.44949i | 0.0419961 | − | 0.102869i | ||||
\(568\) | 6.00000 | 0.251754 | ||||||||
\(569\) | 23.3939i | 0.980722i | 0.871519 | + | 0.490361i | \(0.163135\pi\) | ||||
−0.871519 | + | 0.490361i | \(0.836865\pi\) | |||||||
\(570\) | −2.69694 | + | 2.69694i | −0.112962 | + | 0.112962i | ||||
\(571\) | − | 43.1918i | − | 1.80752i | −0.428037 | − | 0.903761i | \(-0.640795\pi\) | ||
0.428037 | − | 0.903761i | \(-0.359205\pi\) | |||||||
\(572\) | −0.449490 | − | 2.24745i | −0.0187941 | − | 0.0939706i | ||||
\(573\) | 13.7980i | 0.576418i | ||||||||
\(574\) | 9.79796 | − | 24.0000i | 0.408959 | − | 1.00174i | ||||
\(575\) | 26.6969 | 1.11334 | ||||||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | −17.8990 | − | 17.8990i | −0.745144 | − | 0.745144i | 0.228419 | − | 0.973563i | \(-0.426644\pi\) |
−0.973563 | + | 0.228419i | \(0.926644\pi\) | |||||||
\(578\) | −15.9217 | + | 15.9217i | −0.662255 | + | 0.662255i | ||||
\(579\) | 14.7980 | − | 14.7980i | 0.614982 | − | 0.614982i | ||||
\(580\) | −5.79796 | + | 5.79796i | −0.240747 | + | 0.240747i | ||||
\(581\) | −1.55051 | + | 0.651531i | −0.0643260 | + | 0.0270301i | ||||
\(582\) | 19.3485i | 0.802020i | ||||||||
\(583\) | 5.30306 | + | 5.30306i | 0.219630 | + | 0.219630i | ||||
\(584\) | −19.3485 | −0.800645 | ||||||||
\(585\) | −10.0000 | + | 2.00000i | −0.413449 | + | 0.0826898i | ||||
\(586\) | 45.7980i | 1.89190i | ||||||||
\(587\) | 3.55051 | + | 3.55051i | 0.146545 | + | 0.146545i | 0.776573 | − | 0.630028i | \(-0.216956\pi\) |
−0.630028 | + | 0.776573i | \(0.716956\pi\) | |||||||
\(588\) | 5.00000 | + | 4.89898i | 0.206197 | + | 0.202031i | ||||
\(589\) | 6.00000i | 0.247226i | ||||||||
\(590\) | −21.7980 | + | 21.7980i | −0.897408 | + | 0.897408i | ||||
\(591\) | 7.79796 | + | 7.79796i | 0.320765 | + | 0.320765i | ||||
\(592\) | 39.4949 | + | 39.4949i | 1.62323 | + | 1.62323i | ||||
\(593\) | −17.1010 | + | 17.1010i | −0.702255 | + | 0.702255i | −0.964894 | − | 0.262639i | \(-0.915407\pi\) |
0.262639 | + | 0.964894i | \(0.415407\pi\) | |||||||
\(594\) | − | 1.10102i | − | 0.0451754i | ||||||
\(595\) | −13.7980 | + | 5.79796i | −0.565661 | + | 0.237693i | ||||
\(596\) | 0.898979 | + | 0.898979i | 0.0368236 | + | 0.0368236i | ||||
\(597\) | − | 22.8990i | − | 0.937193i | ||||||
\(598\) | 54.4949 | − | 10.8990i | 2.22846 | − | 0.445692i | ||||
\(599\) | 4.49490 | 0.183657 | 0.0918283 | − | 0.995775i | \(-0.470729\pi\) | ||||
0.0918283 | + | 0.995775i | \(0.470729\pi\) | |||||||
\(600\) | 3.67423 | + | 3.67423i | 0.150000 | + | 0.150000i | ||||
\(601\) | 41.5959i | 1.69673i | 0.529409 | + | 0.848366i | \(0.322414\pi\) | ||||
−0.529409 | + | 0.848366i | \(0.677586\pi\) | |||||||
\(602\) | 29.1464 | − | 12.2474i | 1.18792 | − | 0.499169i | ||||
\(603\) | 6.34847 | − | 6.34847i | 0.258530 | − | 0.258530i | ||||
\(604\) | 7.44949 | − | 7.44949i | 0.303115 | − | 0.303115i | ||||
\(605\) | −21.1918 | + | 21.1918i | −0.861571 | + | 0.861571i | ||||
\(606\) | −6.24745 | − | 6.24745i | −0.253785 | − | 0.253785i | ||||
\(607\) | − | 14.8990i | − | 0.604731i | −0.953192 | − | 0.302365i | \(-0.902224\pi\) | ||
0.953192 | − | 0.302365i | \(-0.0977763\pi\) | |||||||
\(608\) | 4.04541 | 0.164063 | ||||||||
\(609\) | −7.10102 | − | 2.89898i | −0.287748 | − | 0.117473i | ||||
\(610\) | 48.9898i | 1.98354i | ||||||||
\(611\) | −1.55051 | − | 7.75255i | −0.0627269 | − | 0.313635i | ||||
\(612\) | 2.00000i | 0.0808452i | ||||||||
\(613\) | −7.89898 | + | 7.89898i | −0.319037 | + | 0.319037i | −0.848397 | − | 0.529360i | \(-0.822432\pi\) |
0.529360 | + | 0.848397i | \(0.322432\pi\) | |||||||
\(614\) | − | 32.9444i | − | 1.32953i | ||||||
\(615\) | −16.0000 | −0.645182 | ||||||||
\(616\) | −2.69694 | − | 1.10102i | −0.108663 | − | 0.0443614i | ||||
\(617\) | 2.20204 | − | 2.20204i | 0.0886508 | − | 0.0886508i | −0.661391 | − | 0.750042i | \(-0.730033\pi\) |
0.750042 | + | 0.661391i | \(0.230033\pi\) | |||||||
\(618\) | −2.20204 | − | 2.20204i | −0.0885791 | − | 0.0885791i | ||||
\(619\) | −10.5505 | + | 10.5505i | −0.424061 | + | 0.424061i | −0.886599 | − | 0.462538i | \(-0.846939\pi\) |
0.462538 | + | 0.886599i | \(0.346939\pi\) | |||||||
\(620\) | −21.7980 | −0.875427 | ||||||||
\(621\) | 8.89898 | 0.357104 | ||||||||
\(622\) | 18.4949 | − | 18.4949i | 0.741578 | − | 0.741578i | ||||
\(623\) | 2.89898 | + | 6.89898i | 0.116145 | + | 0.276402i | ||||
\(624\) | 15.0000 | + | 10.0000i | 0.600481 | + | 0.400320i | ||||
\(625\) | 31.0000 | 1.24000 | ||||||||
\(626\) | −31.3485 | − | 31.3485i | −1.25294 | − | 1.25294i | ||||
\(627\) | −0.494897 | −0.0197643 | ||||||||
\(628\) | −12.0000 | −0.478852 | ||||||||
\(629\) | 15.7980 | + | 15.7980i | 0.629906 | + | 0.629906i | ||||
\(630\) | 4.89898 | − | 12.0000i | 0.195180 | − | 0.478091i | ||||
\(631\) | 13.2474 | + | 13.2474i | 0.527373 | + | 0.527373i | 0.919788 | − | 0.392415i | \(-0.128360\pi\) |
−0.392415 | + | 0.919788i | \(0.628360\pi\) | |||||||
\(632\) | −3.55051 | − | 3.55051i | −0.141232 | − | 0.141232i | ||||
\(633\) | − | 9.10102i | − | 0.361733i | ||||||
\(634\) | − | 40.8990i | − | 1.62431i | ||||||
\(635\) | −16.0000 | + | 16.0000i | −0.634941 | + | 0.634941i | ||||
\(636\) | 11.7980 | 0.467820 | ||||||||
\(637\) | 24.6969 | − | 5.20204i | 0.978528 | − | 0.206112i | ||||
\(638\) | −3.19184 | −0.126366 | ||||||||
\(639\) | −2.44949 | + | 2.44949i | −0.0969003 | + | 0.0969003i | ||||
\(640\) | − | 34.2929i | − | 1.35554i | ||||||
\(641\) | − | 8.69694i | − | 0.343508i | −0.985140 | − | 0.171754i | \(-0.945057\pi\) | ||
0.985140 | − | 0.171754i | \(-0.0549435\pi\) | |||||||
\(642\) | −1.10102 | − | 1.10102i | −0.0434538 | − | 0.0434538i | ||||
\(643\) | −14.1464 | − | 14.1464i | −0.557881 | − | 0.557881i | 0.370823 | − | 0.928704i | \(-0.379076\pi\) |
−0.928704 | + | 0.370823i | \(0.879076\pi\) | |||||||
\(644\) | −8.89898 | + | 21.7980i | −0.350669 | + | 0.858960i | ||||
\(645\) | −13.7980 | − | 13.7980i | −0.543294 | − | 0.543294i | ||||
\(646\) | 2.69694 | 0.106110 | ||||||||
\(647\) | 12.0000 | 0.471769 | 0.235884 | − | 0.971781i | \(-0.424201\pi\) | ||||
0.235884 | + | 0.971781i | \(0.424201\pi\) | |||||||
\(648\) | 1.22474 | + | 1.22474i | 0.0481125 | + | 0.0481125i | ||||
\(649\) | −4.00000 | −0.157014 | ||||||||
\(650\) | −18.3712 | + | 3.67423i | −0.720577 | + | 0.144115i | ||||
\(651\) | −7.89898 | − | 18.7980i | −0.309585 | − | 0.736750i | ||||
\(652\) | 5.44949 | − | 5.44949i | 0.213418 | − | 0.213418i | ||||
\(653\) | 1.10102 | 0.0430863 | 0.0215431 | − | 0.999768i | \(-0.493142\pi\) | ||||
0.0215431 | + | 0.999768i | \(0.493142\pi\) | |||||||
\(654\) | 0.247449 | 0.00967601 | ||||||||
\(655\) | 37.3939 | − | 37.3939i | 1.46110 | − | 1.46110i | ||||
\(656\) | 20.0000 | + | 20.0000i | 0.780869 | + | 0.780869i | ||||
\(657\) | 7.89898 | − | 7.89898i | 0.308169 | − | 0.308169i | ||||
\(658\) | 9.30306 | + | 3.79796i | 0.362671 | + | 0.148060i | ||||
\(659\) | −31.5959 | −1.23080 | −0.615401 | − | 0.788214i | \(-0.711006\pi\) | ||||
−0.615401 | + | 0.788214i | \(0.711006\pi\) | |||||||
\(660\) | − | 1.79796i | − | 0.0699855i | ||||||
\(661\) | 26.3939 | − | 26.3939i | 1.02660 | − | 1.02660i | 0.0269665 | − | 0.999636i | \(-0.491415\pi\) |
0.999636 | − | 0.0269665i | \(-0.00858474\pi\) | |||||||
\(662\) | 52.0454i | 2.02280i | ||||||||
\(663\) | 6.00000 | + | 4.00000i | 0.233021 | + | 0.155347i | ||||
\(664\) | − | 1.10102i | − | 0.0427279i | ||||||
\(665\) | −5.39388 | − | 2.20204i | −0.209166 | − | 0.0853915i | ||||
\(666\) | −19.3485 | −0.749738 | ||||||||
\(667\) | − | 25.7980i | − | 0.998901i | ||||||
\(668\) | −11.3485 | − | 11.3485i | −0.439085 | − | 0.439085i | ||||
\(669\) | −2.55051 | + | 2.55051i | −0.0986084 | + | 0.0986084i | ||||
\(670\) | 31.1010 | − | 31.1010i | 1.20154 | − | 1.20154i | ||||
\(671\) | −4.49490 | + | 4.49490i | −0.173524 | + | 0.173524i | ||||
\(672\) | −12.6742 | + | 5.32577i | −0.488919 | + | 0.205446i | ||||
\(673\) | − | 13.3939i | − | 0.516296i | −0.966105 | − | 0.258148i | \(-0.916888\pi\) | ||
0.966105 | − | 0.258148i | \(-0.0831122\pi\) | |||||||
\(674\) | −29.1464 | − | 29.1464i | −1.12268 | − | 1.12268i | ||||
\(675\) | −3.00000 | −0.115470 | ||||||||
\(676\) | −12.0000 | + | 5.00000i | −0.461538 | + | 0.192308i | ||||
\(677\) | − | 34.8990i | − | 1.34128i | −0.741784 | − | 0.670638i | \(-0.766020\pi\) | ||
0.741784 | − | 0.670638i | \(-0.233980\pi\) | |||||||
\(678\) | 23.1464 | + | 23.1464i | 0.888933 | + | 0.888933i | ||||
\(679\) | −27.2474 | + | 11.4495i | −1.04566 | + | 0.439391i | ||||
\(680\) | − | 9.79796i | − | 0.375735i | ||||||
\(681\) | −0.651531 | + | 0.651531i | −0.0249667 | + | 0.0249667i | ||||
\(682\) | −6.00000 | − | 6.00000i | −0.229752 | − | 0.229752i | ||||
\(683\) | 1.75255 | + | 1.75255i | 0.0670595 | + | 0.0670595i | 0.739841 | − | 0.672782i | \(-0.234901\pi\) |
−0.672782 | + | 0.739841i | \(0.734901\pi\) | |||||||
\(684\) | −0.550510 | + | 0.550510i | −0.0210493 | + | 0.0210493i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −11.8207 | + | 29.8207i | −0.451315 | + | 1.13856i | ||||
\(687\) | −13.0000 | − | 13.0000i | −0.495981 | − | 0.495981i | ||||
\(688\) | 34.4949i | 1.31511i | ||||||||
\(689\) | 23.5959 | − | 35.3939i | 0.898933 | − | 1.34840i | ||||
\(690\) | 43.5959 | 1.65967 | ||||||||
\(691\) | −26.1464 | − | 26.1464i | −0.994657 | − | 0.994657i | 0.00532880 | − | 0.999986i | \(-0.498304\pi\) |
−0.999986 | + | 0.00532880i | \(0.998304\pi\) | |||||||
\(692\) | 12.6969i | 0.482665i | ||||||||
\(693\) | 1.55051 | − | 0.651531i | 0.0588990 | − | 0.0247496i | ||||
\(694\) | 2.69694 | − | 2.69694i | 0.102374 | − | 0.102374i | ||||
\(695\) | 13.7980 | − | 13.7980i | 0.523386 | − | 0.523386i | ||||
\(696\) | 3.55051 | − | 3.55051i | 0.134582 | − | 0.134582i | ||||
\(697\) | 8.00000 | + | 8.00000i | 0.303022 | + | 0.303022i | ||||
\(698\) | − | 21.5505i | − | 0.815699i | ||||||
\(699\) | −11.7980 | −0.446240 | ||||||||
\(700\) | 3.00000 | − | 7.34847i | 0.113389 | − | 0.277746i | ||||
\(701\) | 28.6969i | 1.08387i | 0.840421 | + | 0.541934i | \(0.182308\pi\) | ||||
−0.840421 | + | 0.541934i | \(0.817692\pi\) | |||||||
\(702\) | −6.12372 | + | 1.22474i | −0.231125 | + | 0.0462250i | ||||
\(703\) | 8.69694i | 0.328011i | ||||||||
\(704\) | 0.449490 | − | 0.449490i | 0.0169408 | − | 0.0169408i | ||||
\(705\) | − | 6.20204i | − | 0.233582i | ||||||
\(706\) | −24.0000 | −0.903252 | ||||||||
\(707\) | 5.10102 | − | 12.4949i | 0.191844 | − | 0.469919i | ||||
\(708\) | −4.44949 | + | 4.44949i | −0.167222 | + | 0.167222i | ||||
\(709\) | −19.8990 | − | 19.8990i | −0.747322 | − | 0.747322i | 0.226654 | − | 0.973975i | \(-0.427221\pi\) |
−0.973975 | + | 0.226654i | \(0.927221\pi\) | |||||||
\(710\) | −12.0000 | + | 12.0000i | −0.450352 | + | 0.450352i | ||||
\(711\) | 2.89898 | 0.108720 | ||||||||
\(712\) | −4.89898 | −0.183597 | ||||||||
\(713\) | 48.4949 | − | 48.4949i | 1.81615 | − | 1.81615i | ||||
\(714\) | −8.44949 | + | 3.55051i | −0.316214 | + | 0.132875i | ||||
\(715\) | −5.39388 | − | 3.59592i | −0.201720 | − | 0.134480i | ||||
\(716\) | 21.7980 | 0.814628 | ||||||||
\(717\) | 7.34847 | + | 7.34847i | 0.274434 | + | 0.274434i | ||||
\(718\) | 10.8990 | 0.406746 | ||||||||
\(719\) | −7.10102 | −0.264823 | −0.132412 | − | 0.991195i | \(-0.542272\pi\) | ||||
−0.132412 | + | 0.991195i | \(0.542272\pi\) | |||||||
\(720\) | 10.0000 | + | 10.0000i | 0.372678 | + | 0.372678i | ||||
\(721\) | 1.79796 | − | 4.40408i | 0.0669595 | − | 0.164017i | ||||
\(722\) | −22.5278 | − | 22.5278i | −0.838398 | − | 0.838398i | ||||
\(723\) | 13.8990 | + | 13.8990i | 0.516909 | + | 0.516909i | ||||
\(724\) | 2.00000i | 0.0743294i | ||||||||
\(725\) | 8.69694i | 0.322996i | ||||||||
\(726\) | −12.9773 | + | 12.9773i | −0.481633 | + | 0.481633i | ||||
\(727\) | 14.8990 | 0.552573 | 0.276286 | − | 0.961075i | \(-0.410896\pi\) | ||||
0.276286 | + | 0.961075i | \(0.410896\pi\) | |||||||
\(728\) | −3.12372 | + | 16.2247i | −0.115773 | + | 0.601329i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 38.6969 | − | 38.6969i | 1.43224 | − | 1.43224i | ||||
\(731\) | 13.7980i | 0.510336i | ||||||||
\(732\) | 10.0000i | 0.369611i | ||||||||
\(733\) | −9.00000 | − | 9.00000i | −0.332423 | − | 0.332423i | 0.521083 | − | 0.853506i | \(-0.325528\pi\) |
−0.853506 | + | 0.521083i | \(0.825528\pi\) | |||||||
\(734\) | −32.4495 | − | 32.4495i | −1.19773 | − | 1.19773i | ||||
\(735\) | 19.7980 | − | 0.202041i | 0.730259 | − | 0.00745240i | ||||
\(736\) | −32.6969 | − | 32.6969i | −1.20523 | − | 1.20523i | ||||
\(737\) | 5.70714 | 0.210225 | ||||||||
\(738\) | −9.79796 | −0.360668 | ||||||||
\(739\) | 22.3485 | + | 22.3485i | 0.822102 | + | 0.822102i | 0.986409 | − | 0.164307i | \(-0.0525389\pi\) |
−0.164307 | + | 0.986409i | \(0.552539\pi\) | |||||||
\(740\) | −31.5959 | −1.16149 | ||||||||
\(741\) | 0.550510 | + | 2.75255i | 0.0202235 | + | 0.101117i | ||||
\(742\) | 20.9444 | + | 49.8434i | 0.768893 | + | 1.82981i | ||||
\(743\) | 18.0454 | − | 18.0454i | 0.662022 | − | 0.662022i | −0.293835 | − | 0.955856i | \(-0.594931\pi\) |
0.955856 | + | 0.293835i | \(0.0949315\pi\) | |||||||
\(744\) | 13.3485 | 0.489379 | ||||||||
\(745\) | 3.59592 | 0.131744 | ||||||||
\(746\) | 12.0000 | − | 12.0000i | 0.439351 | − | 0.439351i | ||||
\(747\) | 0.449490 | + | 0.449490i | 0.0164460 | + | 0.0164460i | ||||
\(748\) | −0.898979 | + | 0.898979i | −0.0328699 | + | 0.0328699i | ||||
\(749\) | 0.898979 | − | 2.20204i | 0.0328480 | − | 0.0804608i | ||||
\(750\) | 9.79796 | 0.357771 | ||||||||
\(751\) | 20.2929i | 0.740497i | 0.928933 | + | 0.370248i | \(0.120727\pi\) | ||||
−0.928933 | + | 0.370248i | \(0.879273\pi\) | |||||||
\(752\) | −7.75255 | + | 7.75255i | −0.282706 | + | 0.282706i | ||||
\(753\) | 4.89898i | 0.178529i | ||||||||
\(754\) | 3.55051 | + | 17.7526i | 0.129302 | + | 0.646510i | ||||
\(755\) | − | 29.7980i | − | 1.08446i | ||||||
\(756\) | 1.00000 | − | 2.44949i | 0.0363696 | − | 0.0890871i | ||||
\(757\) | −37.7980 | −1.37379 | −0.686895 | − | 0.726757i | \(-0.741027\pi\) | ||||
−0.686895 | + | 0.726757i | \(0.741027\pi\) | |||||||
\(758\) | − | 32.9444i | − | 1.19659i | ||||||
\(759\) | 4.00000 | + | 4.00000i | 0.145191 | + | 0.145191i | ||||
\(760\) | 2.69694 | − | 2.69694i | 0.0978282 | − | 0.0978282i | ||||
\(761\) | −14.6969 | + | 14.6969i | −0.532764 | + | 0.532764i | −0.921394 | − | 0.388630i | \(-0.872948\pi\) |
0.388630 | + | 0.921394i | \(0.372948\pi\) | |||||||
\(762\) | −9.79796 | + | 9.79796i | −0.354943 | + | 0.354943i | ||||
\(763\) | 0.146428 | + | 0.348469i | 0.00530106 | + | 0.0126154i | ||||
\(764\) | 13.7980i | 0.499193i | ||||||||
\(765\) | 4.00000 | + | 4.00000i | 0.144620 | + | 0.144620i | ||||
\(766\) | −39.7980 | −1.43796 | ||||||||
\(767\) | 4.44949 | + | 22.2474i | 0.160662 | + | 0.803309i | ||||
\(768\) | − | 19.0000i | − | 0.685603i | ||||||
\(769\) | 4.10102 | + | 4.10102i | 0.147887 | + | 0.147887i | 0.777173 | − | 0.629287i | \(-0.216653\pi\) |
−0.629287 | + | 0.777173i | \(0.716653\pi\) | |||||||
\(770\) | 7.59592 | − | 3.19184i | 0.273738 | − | 0.115026i | ||||
\(771\) | − | 20.6969i | − | 0.745382i | ||||||
\(772\) | 14.7980 | − | 14.7980i | 0.532590 | − | 0.532590i | ||||
\(773\) | 36.0000 | + | 36.0000i | 1.29483 | + | 1.29483i | 0.931763 | + | 0.363067i | \(0.118270\pi\) |
0.363067 | + | 0.931763i | \(0.381730\pi\) | |||||||
\(774\) | −8.44949 | − | 8.44949i | −0.303711 | − | 0.303711i | ||||
\(775\) | −16.3485 | + | 16.3485i | −0.587254 | + | 0.587254i | ||||
\(776\) | − | 19.3485i | − | 0.694570i | ||||||
\(777\) | −11.4495 | − | 27.2474i | −0.410748 | − | 0.977497i | ||||
\(778\) | −1.34847 | − | 1.34847i | −0.0483450 | − | 0.0483450i | ||||
\(779\) | 4.40408i | 0.157793i | ||||||||
\(780\) | −10.0000 | + | 2.00000i | −0.358057 | + | 0.0716115i | ||||
\(781\) | −2.20204 | −0.0787952 | ||||||||
\(782\) | −21.7980 | − | 21.7980i | −0.779493 | − | 0.779493i | ||||
\(783\) | 2.89898i | 0.103601i | ||||||||
\(784\) | −25.0000 | − | 24.4949i | −0.892857 | − | 0.874818i | ||||
\(785\) | −24.0000 | + | 24.0000i | −0.856597 | + | 0.856597i | ||||
\(786\) | 22.8990 | − | 22.8990i | 0.816780 | − | 0.816780i | ||||
\(787\) | −15.2474 | + | 15.2474i | −0.543513 | + | 0.543513i | −0.924557 | − | 0.381044i | \(-0.875565\pi\) |
0.381044 | + | 0.924557i | \(0.375565\pi\) | |||||||
\(788\) | 7.79796 | + | 7.79796i | 0.277791 | + | 0.277791i | ||||
\(789\) | − | 16.8990i | − | 0.601620i | ||||||
\(790\) | 14.2020 | 0.505286 | ||||||||
\(791\) | −18.8990 | + | 46.2929i | −0.671970 | + | 1.64598i | ||||
\(792\) | 1.10102i | 0.0391231i | ||||||||
\(793\) | 30.0000 | + | 20.0000i | 1.06533 | + | 0.710221i | ||||
\(794\) | 21.5505i | 0.764799i | ||||||||
\(795\) | 23.5959 | − | 23.5959i | 0.836861 | − | 0.836861i | ||||
\(796\) | − | 22.8990i | − | 0.811633i | ||||||
\(797\) | −41.1918 | −1.45909 | −0.729545 | − | 0.683933i | \(-0.760268\pi\) | ||||
−0.729545 | + | 0.683933i | \(0.760268\pi\) | |||||||
\(798\) | −3.30306 | − | 1.34847i | −0.116927 | − | 0.0477353i | ||||
\(799\) | −3.10102 | + | 3.10102i | −0.109706 | + | 0.109706i | ||||
\(800\) | 11.0227 | + | 11.0227i | 0.389711 | + | 0.389711i | ||||
\(801\) | 2.00000 | − | 2.00000i | 0.0706665 | − | 0.0706665i | ||||
\(802\) | −34.2929 | −1.21092 | ||||||||
\(803\) | 7.10102 | 0.250590 | ||||||||
\(804\) | 6.34847 | − | 6.34847i | 0.223893 | − | 0.223893i | ||||
\(805\) | 25.7980 | + | 61.3939i | 0.909259 | + | 2.16385i | ||||
\(806\) | −26.6969 | + | 40.0454i | −0.940360 | + | 1.41054i | ||||
\(807\) | −6.00000 | −0.211210 | ||||||||
\(808\) | 6.24745 | + | 6.24745i | 0.219784 | + | 0.219784i | ||||
\(809\) | −22.8990 | −0.805085 | −0.402543 | − | 0.915401i | \(-0.631873\pi\) | ||||
−0.402543 | + | 0.915401i | \(0.631873\pi\) | |||||||
\(810\) | −4.89898 | −0.172133 | ||||||||
\(811\) | 7.04541 | + | 7.04541i | 0.247398 | + | 0.247398i | 0.819902 | − | 0.572504i | \(-0.194028\pi\) |
−0.572504 | + | 0.819902i | \(0.694028\pi\) | |||||||
\(812\) | −7.10102 | − | 2.89898i | −0.249197 | − | 0.101734i | ||||
\(813\) | 4.55051 | + | 4.55051i | 0.159593 | + | 0.159593i | ||||
\(814\) | −8.69694 | − | 8.69694i | −0.304828 | − | 0.304828i | ||||
\(815\) | − | 21.7980i | − | 0.763549i | ||||||
\(816\) | − | 10.0000i | − | 0.350070i | ||||||
\(817\) | −3.79796 | + | 3.79796i | −0.132874 | + | 0.132874i | ||||
\(818\) | 13.9546 | 0.487911 | ||||||||
\(819\) | −5.34847 | − | 7.89898i | −0.186891 | − | 0.276013i | ||||
\(820\) | −16.0000 | −0.558744 | ||||||||
\(821\) | −35.5959 | + | 35.5959i | −1.24231 | + | 1.24231i | −0.283264 | + | 0.959042i | \(0.591417\pi\) |
−0.959042 | + | 0.283264i | \(0.908583\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.6969i | 0.442587i | 0.975207 | + | 0.221294i | \(0.0710280\pi\) | ||||
−0.975207 | + | 0.221294i | \(0.928972\pi\) | |||||||
\(824\) | 2.20204 | + | 2.20204i | 0.0767117 | + | 0.0767117i | ||||
\(825\) | −1.34847 | − | 1.34847i | −0.0469477 | − | 0.0469477i | ||||
\(826\) | −26.6969 | − | 10.8990i | −0.928905 | − | 0.379224i | ||||
\(827\) | 9.34847 | + | 9.34847i | 0.325078 | + | 0.325078i | 0.850711 | − | 0.525633i | \(-0.176172\pi\) |
−0.525633 | + | 0.850711i | \(0.676172\pi\) | |||||||
\(828\) | 8.89898 | 0.309261 | ||||||||
\(829\) | 34.2020 | 1.18789 | 0.593943 | − | 0.804507i | \(-0.297570\pi\) | ||||
0.593943 | + | 0.804507i | \(0.297570\pi\) | |||||||
\(830\) | 2.20204 | + | 2.20204i | 0.0764340 | + | 0.0764340i | ||||
\(831\) | 17.7980 | 0.617404 | ||||||||
\(832\) | −3.00000 | − | 2.00000i | −0.104006 | − | 0.0693375i | ||||
\(833\) | −10.0000 | − | 9.79796i | −0.346479 | − | 0.339479i | ||||
\(834\) | 8.44949 | − | 8.44949i | 0.292582 | − | 0.292582i | ||||
\(835\) | −45.3939 | −1.57092 | ||||||||
\(836\) | −0.494897 | −0.0171164 | ||||||||
\(837\) | −5.44949 | + | 5.44949i | −0.188362 | + | 0.188362i | ||||
\(838\) | 42.0000 | + | 42.0000i | 1.45087 | + | 1.45087i | ||||
\(839\) | −8.44949 | + | 8.44949i | −0.291709 | + | 0.291709i | −0.837755 | − | 0.546046i | \(-0.816132\pi\) |
0.546046 | + | 0.837755i | \(0.316132\pi\) | |||||||
\(840\) | −4.89898 | + | 12.0000i | −0.169031 | + | 0.414039i | ||||
\(841\) | −20.5959 | −0.710204 | ||||||||
\(842\) | − | 34.0454i | − | 1.17328i | ||||||
\(843\) | −4.00000 | + | 4.00000i | −0.137767 | + | 0.137767i | ||||
\(844\) | − | 9.10102i | − | 0.313270i | ||||||
\(845\) | −14.0000 | + | 34.0000i | −0.481615 | + | 1.16964i | ||||
\(846\) | − | 3.79796i | − | 0.130577i | ||||||
\(847\) | −25.9546 | − | 10.5959i | −0.891810 | − | 0.364080i | ||||
\(848\) | −58.9898 | −2.02572 | ||||||||
\(849\) | 12.6969i | 0.435758i | ||||||||
\(850\) | 7.34847 | + | 7.34847i | 0.252050 | + | 0.252050i | ||||
\(851\) | 70.2929 | − | 70.2929i | 2.40961 | − | 2.40961i | ||||
\(852\) | −2.44949 | + | 2.44949i | −0.0839181 | + | 0.0839181i | ||||
\(853\) | −19.2020 | + | 19.2020i | −0.657465 | + | 0.657465i | −0.954780 | − | 0.297314i | \(-0.903909\pi\) |
0.297314 | + | 0.954780i | \(0.403909\pi\) | |||||||
\(854\) | −42.2474 | + | 17.7526i | −1.44568 | + | 0.607480i | ||||
\(855\) | 2.20204i | 0.0753082i | ||||||||
\(856\) | 1.10102 | + | 1.10102i | 0.0376321 | + | 0.0376321i | ||||
\(857\) | −22.4949 | −0.768411 | −0.384206 | − | 0.923248i | \(-0.625525\pi\) | ||||
−0.384206 | + | 0.923248i | \(0.625525\pi\) | |||||||
\(858\) | −3.30306 | − | 2.20204i | −0.112765 | − | 0.0751764i | ||||
\(859\) | − | 10.2020i | − | 0.348089i | −0.984738 | − | 0.174045i | \(-0.944316\pi\) | ||
0.984738 | − | 0.174045i | \(-0.0556837\pi\) | |||||||
\(860\) | −13.7980 | − | 13.7980i | −0.470506 | − | 0.470506i | ||||
\(861\) | −5.79796 | − | 13.7980i | −0.197594 | − | 0.470233i | ||||
\(862\) | − | 58.8990i | − | 2.00611i | ||||||
\(863\) | 15.1464 | − | 15.1464i | 0.515590 | − | 0.515590i | −0.400644 | − | 0.916234i | \(-0.631213\pi\) |
0.916234 | + | 0.400644i | \(0.131213\pi\) | |||||||
\(864\) | 3.67423 | + | 3.67423i | 0.125000 | + | 0.125000i | ||||
\(865\) | 25.3939 | + | 25.3939i | 0.863418 | + | 0.863418i | ||||
\(866\) | 12.4949 | − | 12.4949i | 0.424594 | − | 0.424594i | ||||
\(867\) | 13.0000i | 0.441503i | ||||||||
\(868\) | −7.89898 | − | 18.7980i | −0.268109 | − | 0.638044i | ||||
\(869\) | 1.30306 | + | 1.30306i | 0.0442033 | + | 0.0442033i | ||||
\(870\) | 14.2020i | 0.481494i | ||||||||
\(871\) | −6.34847 | − | 31.7423i | −0.215110 | − | 1.07555i | ||||
\(872\) | −0.247449 | −0.00837967 | ||||||||
\(873\) | 7.89898 | + | 7.89898i | 0.267340 | + | 0.267340i | ||||
\(874\) | − | 12.0000i | − | 0.405906i | ||||||
\(875\) | 5.79796 | + | 13.7980i | 0.196007 | + | 0.466456i | ||||
\(876\) | 7.89898 | − | 7.89898i | 0.266882 | − | 0.266882i | ||||
\(877\) | 11.6969 | − | 11.6969i | 0.394978 | − | 0.394978i | −0.481480 | − | 0.876457i | \(-0.659900\pi\) |
0.876457 | + | 0.481480i | \(0.159900\pi\) | |||||||
\(878\) | −14.2020 | + | 14.2020i | −0.479296 | + | 0.479296i | ||||
\(879\) | 18.6969 | + | 18.6969i | 0.630632 | + | 0.630632i | ||||
\(880\) | 8.98979i | 0.303046i | ||||||||
\(881\) | 16.6969 | 0.562534 | 0.281267 | − | 0.959630i | \(-0.409245\pi\) | ||||
0.281267 | + | 0.959630i | \(0.409245\pi\) | |||||||
\(882\) | 12.1237 | − | 0.123724i | 0.408227 | − | 0.00416602i | ||||
\(883\) | 18.2020i | 0.612547i | 0.951943 | + | 0.306274i | \(0.0990823\pi\) | ||||
−0.951943 | + | 0.306274i | \(0.900918\pi\) | |||||||
\(884\) | 6.00000 | + | 4.00000i | 0.201802 | + | 0.134535i | ||||
\(885\) | 17.7980i | 0.598272i | ||||||||
\(886\) | −42.4949 | + | 42.4949i | −1.42764 | + | 1.42764i | ||||
\(887\) | − | 12.0000i | − | 0.402921i | −0.979497 | − | 0.201460i | \(-0.935431\pi\) | ||
0.979497 | − | 0.201460i | \(-0.0645687\pi\) | |||||||
\(888\) | 19.3485 | 0.649292 | ||||||||
\(889\) | −19.5959 | − | 8.00000i | −0.657226 | − | 0.268311i | ||||
\(890\) | 9.79796 | − | 9.79796i | 0.328428 | − | 0.328428i | ||||
\(891\) | −0.449490 | − | 0.449490i | −0.0150585 | − | 0.0150585i | ||||
\(892\) | −2.55051 | + | 2.55051i | −0.0853974 | + | 0.0853974i | ||||
\(893\) | −1.70714 | −0.0571274 | ||||||||
\(894\) | 2.20204 | 0.0736473 | ||||||||
\(895\) | 43.5959 | − | 43.5959i | 1.45725 | − | 1.45725i | ||||
\(896\) | 29.5732 | − | 12.4268i | 0.987972 | − | 0.415150i | ||||
\(897\) | 17.7980 | − | 26.6969i | 0.594257 | − | 0.891385i | ||||
\(898\) | 12.4949 | 0.416960 | ||||||||
\(899\) | 15.7980 | + | 15.7980i | 0.526891 | + | 0.526891i | ||||
\(900\) | −3.00000 | −0.100000 | ||||||||
\(901\) | −23.5959 | −0.786094 | ||||||||
\(902\) | −4.40408 | − | 4.40408i | −0.146640 | − | 0.146640i | ||||
\(903\) | 6.89898 | − | 16.8990i | 0.229584 | − | 0.562363i | ||||
\(904\) | −23.1464 | − | 23.1464i | −0.769839 | − | 0.769839i | ||||
\(905\) | 4.00000 | + | 4.00000i | 0.132964 | + | 0.132964i | ||||
\(906\) | − | 18.2474i | − | 0.606231i | ||||||
\(907\) | 0.404082i | 0.0134173i | 0.999977 | + | 0.00670866i | \(0.00213545\pi\) | ||||
−0.999977 | + | 0.00670866i | \(0.997865\pi\) | |||||||
\(908\) | −0.651531 | + | 0.651531i | −0.0216218 | + | 0.0216218i | ||||
\(909\) | −5.10102 | −0.169190 | ||||||||
\(910\) | −26.2020 | − | 38.6969i | −0.868589 | − | 1.28279i | ||||
\(911\) | 12.0000 | 0.397578 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | 2.75255 | − | 2.75255i | 0.0911461 | − | 0.0911461i | ||||
\(913\) | 0.404082i | 0.0133732i | ||||||||
\(914\) | 31.3485i | 1.03692i | ||||||||
\(915\) | 20.0000 | + | 20.0000i | 0.661180 | + | 0.661180i | ||||
\(916\) | −13.0000 | − | 13.0000i | −0.429532 | − | 0.429532i | ||||
\(917\) | 45.7980 | + | 18.6969i | 1.51238 | + | 0.617427i | ||||
\(918\) | 2.44949 | + | 2.44949i | 0.0808452 | + | 0.0808452i | ||||
\(919\) | 14.4949 | 0.478143 | 0.239071 | − | 0.971002i | \(-0.423157\pi\) | ||||
0.239071 | + | 0.971002i | \(0.423157\pi\) | |||||||
\(920\) | −43.5959 | −1.43731 | ||||||||
\(921\) | −13.4495 | − | 13.4495i | −0.443176 | − | 0.443176i | ||||
\(922\) | −60.4949 | −1.99229 | ||||||||
\(923\) | 2.44949 | + | 12.2474i | 0.0806259 | + | 0.403130i | ||||
\(924\) | 1.55051 | − | 0.651531i | 0.0510080 | − | 0.0214338i | ||||
\(925\) | −23.6969 | + | 23.6969i | −0.779151 | + | 0.779151i | ||||
\(926\) | 34.6515 | 1.13872 | ||||||||
\(927\) | −1.79796 | −0.0590527 | ||||||||
\(928\) | 10.6515 | − | 10.6515i | 0.349654 | − | 0.349654i | ||||
\(929\) | 4.89898 | + | 4.89898i | 0.160730 | + | 0.160730i | 0.782890 | − | 0.622160i | \(-0.213745\pi\) |
−0.622160 | + | 0.782890i | \(0.713745\pi\) | |||||||
\(930\) | −26.6969 | + | 26.6969i | −0.875427 | + | 0.875427i | ||||
\(931\) | −0.0556128 | − | 5.44949i | −0.00182264 | − | 0.178600i | ||||
\(932\) | −11.7980 | −0.386455 | ||||||||
\(933\) | − | 15.1010i | − | 0.494385i | ||||||
\(934\) | −50.0908 | + | 50.0908i | −1.63902 | + | 1.63902i | ||||
\(935\) | 3.59592i | 0.117599i | ||||||||
\(936\) | 6.12372 | − | 1.22474i | 0.200160 | − | 0.0400320i | ||||
\(937\) | 9.59592i | 0.313485i | 0.987640 | + | 0.156742i | \(0.0500993\pi\) | ||||
−0.987640 | + | 0.156742i | \(0.949901\pi\) | |||||||
\(938\) | 38.0908 | + | 15.5505i | 1.24371 | + | 0.507742i | ||||
\(939\) | −25.5959 | −0.835291 | ||||||||
\(940\) | − | 6.20204i | − | 0.202288i | ||||||
\(941\) | 16.8990 | + | 16.8990i | 0.550891 | + | 0.550891i | 0.926698 | − | 0.375807i | \(-0.122634\pi\) |
−0.375807 | + | 0.926698i | \(0.622634\pi\) | |||||||
\(942\) | −14.6969 | + | 14.6969i | −0.478852 | + | 0.478852i | ||||
\(943\) | 35.5959 | − | 35.5959i | 1.15916 | − | 1.15916i | ||||
\(944\) | 22.2474 | − | 22.2474i | 0.724093 | − | 0.724093i | ||||
\(945\) | −2.89898 | − | 6.89898i | −0.0943038 | − | 0.224424i | ||||
\(946\) | − | 7.59592i | − | 0.246965i | ||||||
\(947\) | −13.5505 | − | 13.5505i | −0.440332 | − | 0.440332i | 0.451791 | − | 0.892124i | \(-0.350785\pi\) |
−0.892124 | + | 0.451791i | \(0.850785\pi\) | |||||||
\(948\) | 2.89898 | 0.0941545 | ||||||||
\(949\) | −7.89898 | − | 39.4949i | −0.256412 | − | 1.28206i | ||||
\(950\) | 4.04541i | 0.131250i | ||||||||
\(951\) | −16.6969 | − | 16.6969i | −0.541435 | − | 0.541435i | ||||
\(952\) | 8.44949 | − | 3.55051i | 0.273850 | − | 0.115073i | ||||
\(953\) | − | 6.00000i | − | 0.194359i | −0.995267 | − | 0.0971795i | \(-0.969018\pi\) | ||
0.995267 | − | 0.0971795i | \(-0.0309821\pi\) | |||||||
\(954\) | 14.4495 | − | 14.4495i | 0.467820 | − | 0.467820i | ||||
\(955\) | 27.5959 | + | 27.5959i | 0.892983 | + | 0.892983i | ||||
\(956\) | 7.34847 | + | 7.34847i | 0.237666 | + | 0.237666i | ||||
\(957\) | −1.30306 | + | 1.30306i | −0.0421220 | + | 0.0421220i | ||||
\(958\) | 34.8990i | 1.12753i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2.00000 | − | 2.00000i | −0.0645497 | − | 0.0645497i | ||||
\(961\) | 28.3939i | 0.915932i | ||||||||
\(962\) | −38.6969 | + | 58.0454i | −1.24764 | + | 1.87146i | ||||
\(963\) | −0.898979 | −0.0289692 | ||||||||
\(964\) | 13.8990 | + | 13.8990i | 0.447656 | + | 0.447656i | ||||
\(965\) | − | 59.1918i | − | 1.90545i | ||||||
\(966\) | 15.7980 | + | 37.5959i | 0.508291 | + | 1.20963i | ||||
\(967\) | 10.7526 | − | 10.7526i | 0.345779 | − | 0.345779i | −0.512756 | − | 0.858535i | \(-0.671375\pi\) |
0.858535 | + | 0.512756i | \(0.171375\pi\) | |||||||
\(968\) | 12.9773 | − | 12.9773i | 0.417106 | − | 0.417106i | ||||
\(969\) | 1.10102 | − | 1.10102i | 0.0353699 | − | 0.0353699i | ||||
\(970\) | 38.6969 | + | 38.6969i | 1.24248 | + | 1.24248i | ||||
\(971\) | − | 45.7980i | − | 1.46973i | −0.678215 | − | 0.734863i | \(-0.737246\pi\) | ||
0.678215 | − | 0.734863i | \(-0.262754\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 16.8990 | + | 6.89898i | 0.541756 | + | 0.221171i | ||||
\(974\) | 22.6515i | 0.725802i | ||||||||
\(975\) | −6.00000 | + | 9.00000i | −0.192154 | + | 0.288231i | ||||
\(976\) | − | 50.0000i | − | 1.60046i | ||||||
\(977\) | −33.5959 | + | 33.5959i | −1.07483 | + | 1.07483i | −0.0778647 | + | 0.996964i | \(0.524810\pi\) |
−0.996964 | + | 0.0778647i | \(0.975190\pi\) | |||||||
\(978\) | − | 13.3485i | − | 0.426837i | ||||||
\(979\) | 1.79796 | 0.0574630 | ||||||||
\(980\) | 19.7980 | − | 0.202041i | 0.632423 | − | 0.00645396i | ||||
\(981\) | 0.101021 | − | 0.101021i | 0.00322534 | − | 0.00322534i | ||||
\(982\) | −33.1918 | − | 33.1918i | −1.05919 | − | 1.05919i | ||||
\(983\) | 17.7526 | − | 17.7526i | 0.566218 | − | 0.566218i | −0.364848 | − | 0.931067i | \(-0.618879\pi\) |
0.931067 | + | 0.364848i | \(0.118879\pi\) | |||||||
\(984\) | 9.79796 | 0.312348 | ||||||||
\(985\) | 31.1918 | 0.993855 | ||||||||
\(986\) | 7.10102 | − | 7.10102i | 0.226143 | − | 0.226143i | ||||
\(987\) | 5.34847 | − | 2.24745i | 0.170244 | − | 0.0715371i | ||||
\(988\) | 0.550510 | + | 2.75255i | 0.0175141 | + | 0.0875703i | ||||
\(989\) | 61.3939 | 1.95221 | ||||||||
\(990\) | −2.20204 | − | 2.20204i | −0.0699855 | − | 0.0699855i | ||||
\(991\) | 55.1918 | 1.75323 | 0.876613 | − | 0.481196i | \(-0.159797\pi\) | ||||
0.876613 | + | 0.481196i | \(0.159797\pi\) | |||||||
\(992\) | 40.0454 | 1.27144 | ||||||||
\(993\) | 21.2474 | + | 21.2474i | 0.674267 | + | 0.674267i | ||||
\(994\) | −14.6969 | − | 6.00000i | −0.466159 | − | 0.190308i | ||||
\(995\) | −45.7980 | − | 45.7980i | −1.45189 | − | 1.45189i | ||||
\(996\) | 0.449490 | + | 0.449490i | 0.0142426 | + | 0.0142426i | ||||
\(997\) | − | 49.3939i | − | 1.56432i | −0.623078 | − | 0.782160i | \(-0.714118\pi\) | ||
0.623078 | − | 0.782160i | \(-0.285882\pi\) | |||||||
\(998\) | − | 22.6515i | − | 0.717022i | ||||||
\(999\) | −7.89898 | + | 7.89898i | −0.249913 | + | 0.249913i |
(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 | 273.2.p.a.265.2 | yes | 4 | |
3.2 | odd | 2 | 819.2.y.d.811.1 | 4 | |||
7.6 | odd | 2 | 273.2.p.d.265.2 | yes | 4 | ||
13.8 | odd | 4 | 273.2.p.d.34.2 | yes | 4 | ||
21.20 | even | 2 | 819.2.y.a.811.1 | 4 | |||
39.8 | even | 4 | 819.2.y.a.307.1 | 4 | |||
91.34 | even | 4 | inner | 273.2.p.a.34.2 | ✓ | 4 | |
273.125 | odd | 4 | 819.2.y.d.307.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.p.a.34.2 | ✓ | 4 | 91.34 | even | 4 | inner | |
273.2.p.a.265.2 | yes | 4 | 1.1 | even | 1 | trivial | |
273.2.p.d.34.2 | yes | 4 | 13.8 | odd | 4 | ||
273.2.p.d.265.2 | yes | 4 | 7.6 | odd | 2 | ||
819.2.y.a.307.1 | 4 | 39.8 | even | 4 | |||
819.2.y.a.811.1 | 4 | 21.20 | even | 2 | |||
819.2.y.d.307.1 | 4 | 273.125 | odd | 4 | |||
819.2.y.d.811.1 | 4 | 3.2 | odd | 2 |