Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [390,2,Mod(53,390)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(390, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("390.53");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 390.l (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: | \(3.11416567883\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 287.2 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 390.287 |
Dual form | 390.2.l.b.53.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).
\(n\) | \(131\) | \(157\) | \(301\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 1.00000 | + | 1.41421i | 0.577350 | + | 0.816497i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −0.707107 | + | 2.12132i | −0.316228 | + | 0.948683i | ||||
\(6\) | 1.70711 | + | 0.292893i | 0.696923 | + | 0.119573i | ||||
\(7\) | 0.585786 | + | 0.585786i | 0.221406 | + | 0.221406i | 0.809091 | − | 0.587684i | \(-0.199960\pi\) |
−0.587684 | + | 0.809091i | \(0.699960\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | −1.00000 | + | 2.82843i | −0.333333 | + | 0.942809i | ||||
\(10\) | 1.00000 | + | 2.00000i | 0.316228 | + | 0.632456i | ||||
\(11\) | 4.00000i | 1.20605i | 0.797724 | + | 0.603023i | \(0.206037\pi\) | ||||
−0.797724 | + | 0.603023i | \(0.793963\pi\) | |||||||
\(12\) | 1.41421 | − | 1.00000i | 0.408248 | − | 0.288675i | ||||
\(13\) | −0.707107 | + | 0.707107i | −0.196116 | + | 0.196116i | ||||
\(14\) | 0.828427 | 0.221406 | ||||||||
\(15\) | −3.70711 | + | 1.12132i | −0.957171 | + | 0.289524i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 3.00000 | − | 3.00000i | 0.727607 | − | 0.727607i | −0.242536 | − | 0.970143i | \(-0.577979\pi\) |
0.970143 | + | 0.242536i | \(0.0779791\pi\) | |||||||
\(18\) | 1.29289 | + | 2.70711i | 0.304738 | + | 0.638071i | ||||
\(19\) | − | 6.82843i | − | 1.56655i | −0.621676 | − | 0.783274i | \(-0.713548\pi\) | ||
0.621676 | − | 0.783274i | \(-0.286452\pi\) | |||||||
\(20\) | 2.12132 | + | 0.707107i | 0.474342 | + | 0.158114i | ||||
\(21\) | −0.242641 | + | 1.41421i | −0.0529485 | + | 0.308607i | ||||
\(22\) | 2.82843 | + | 2.82843i | 0.603023 | + | 0.603023i | ||||
\(23\) | 2.82843 | + | 2.82843i | 0.589768 | + | 0.589768i | 0.937568 | − | 0.347801i | \(-0.113071\pi\) |
−0.347801 | + | 0.937568i | \(0.613071\pi\) | |||||||
\(24\) | 0.292893 | − | 1.70711i | 0.0597866 | − | 0.348462i | ||||
\(25\) | −4.00000 | − | 3.00000i | −0.800000 | − | 0.600000i | ||||
\(26\) | 1.00000i | 0.196116i | ||||||||
\(27\) | −5.00000 | + | 1.41421i | −0.962250 | + | 0.272166i | ||||
\(28\) | 0.585786 | − | 0.585786i | 0.110703 | − | 0.110703i | ||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | −1.82843 | + | 3.41421i | −0.333824 | + | 0.623347i | ||||
\(31\) | 3.41421 | 0.613211 | 0.306605 | − | 0.951837i | \(-0.400807\pi\) | ||||
0.306605 | + | 0.951837i | \(0.400807\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | −5.65685 | + | 4.00000i | −0.984732 | + | 0.696311i | ||||
\(34\) | − | 4.24264i | − | 0.727607i | ||||||
\(35\) | −1.65685 | + | 0.828427i | −0.280059 | + | 0.140030i | ||||
\(36\) | 2.82843 | + | 1.00000i | 0.471405 | + | 0.166667i | ||||
\(37\) | −2.58579 | − | 2.58579i | −0.425101 | − | 0.425101i | 0.461855 | − | 0.886956i | \(-0.347184\pi\) |
−0.886956 | + | 0.461855i | \(0.847184\pi\) | |||||||
\(38\) | −4.82843 | − | 4.82843i | −0.783274 | − | 0.783274i | ||||
\(39\) | −1.70711 | − | 0.292893i | −0.273356 | − | 0.0469005i | ||||
\(40\) | 2.00000 | − | 1.00000i | 0.316228 | − | 0.158114i | ||||
\(41\) | 2.00000i | 0.312348i | 0.987730 | + | 0.156174i | \(0.0499160\pi\) | ||||
−0.987730 | + | 0.156174i | \(0.950084\pi\) | |||||||
\(42\) | 0.828427 | + | 1.17157i | 0.127829 | + | 0.180778i | ||||
\(43\) | 1.24264 | − | 1.24264i | 0.189501 | − | 0.189501i | −0.605979 | − | 0.795480i | \(-0.707219\pi\) |
0.795480 | + | 0.605979i | \(0.207219\pi\) | |||||||
\(44\) | 4.00000 | 0.603023 | ||||||||
\(45\) | −5.29289 | − | 4.12132i | −0.789018 | − | 0.614370i | ||||
\(46\) | 4.00000 | 0.589768 | ||||||||
\(47\) | 2.24264 | − | 2.24264i | 0.327123 | − | 0.327123i | −0.524369 | − | 0.851491i | \(-0.675699\pi\) |
0.851491 | + | 0.524369i | \(0.175699\pi\) | |||||||
\(48\) | −1.00000 | − | 1.41421i | −0.144338 | − | 0.204124i | ||||
\(49\) | − | 6.31371i | − | 0.901958i | ||||||
\(50\) | −4.94975 | + | 0.707107i | −0.700000 | + | 0.100000i | ||||
\(51\) | 7.24264 | + | 1.24264i | 1.01417 | + | 0.174005i | ||||
\(52\) | 0.707107 | + | 0.707107i | 0.0980581 | + | 0.0980581i | ||||
\(53\) | −0.585786 | − | 0.585786i | −0.0804640 | − | 0.0804640i | 0.665729 | − | 0.746193i | \(-0.268121\pi\) |
−0.746193 | + | 0.665729i | \(0.768121\pi\) | |||||||
\(54\) | −2.53553 | + | 4.53553i | −0.345042 | + | 0.617208i | ||||
\(55\) | −8.48528 | − | 2.82843i | −1.14416 | − | 0.381385i | ||||
\(56\) | − | 0.828427i | − | 0.110703i | ||||||
\(57\) | 9.65685 | − | 6.82843i | 1.27908 | − | 0.904447i | ||||
\(58\) | 4.24264 | − | 4.24264i | 0.557086 | − | 0.557086i | ||||
\(59\) | −4.48528 | −0.583934 | −0.291967 | − | 0.956428i | \(-0.594310\pi\) | ||||
−0.291967 | + | 0.956428i | \(0.594310\pi\) | |||||||
\(60\) | 1.12132 | + | 3.70711i | 0.144762 | + | 0.478585i | ||||
\(61\) | 4.82843 | 0.618217 | 0.309108 | − | 0.951027i | \(-0.399969\pi\) | ||||
0.309108 | + | 0.951027i | \(0.399969\pi\) | |||||||
\(62\) | 2.41421 | − | 2.41421i | 0.306605 | − | 0.306605i | ||||
\(63\) | −2.24264 | + | 1.07107i | −0.282546 | + | 0.134942i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −1.00000 | − | 2.00000i | −0.124035 | − | 0.248069i | ||||
\(66\) | −1.17157 | + | 6.82843i | −0.144211 | + | 0.840521i | ||||
\(67\) | −0.828427 | − | 0.828427i | −0.101208 | − | 0.101208i | 0.654689 | − | 0.755898i | \(-0.272799\pi\) |
−0.755898 | + | 0.654689i | \(0.772799\pi\) | |||||||
\(68\) | −3.00000 | − | 3.00000i | −0.363803 | − | 0.363803i | ||||
\(69\) | −1.17157 | + | 6.82843i | −0.141041 | + | 0.822046i | ||||
\(70\) | −0.585786 | + | 1.75736i | −0.0700149 | + | 0.210045i | ||||
\(71\) | − | 14.2426i | − | 1.69029i | −0.534537 | − | 0.845145i | \(-0.679514\pi\) | ||
0.534537 | − | 0.845145i | \(-0.320486\pi\) | |||||||
\(72\) | 2.70711 | − | 1.29289i | 0.319036 | − | 0.152369i | ||||
\(73\) | −11.0711 | + | 11.0711i | −1.29577 | + | 1.29577i | −0.364610 | + | 0.931160i | \(0.618798\pi\) |
−0.931160 | + | 0.364610i | \(0.881202\pi\) | |||||||
\(74\) | −3.65685 | −0.425101 | ||||||||
\(75\) | 0.242641 | − | 8.65685i | 0.0280177 | − | 0.999607i | ||||
\(76\) | −6.82843 | −0.783274 | ||||||||
\(77\) | −2.34315 | + | 2.34315i | −0.267026 | + | 0.267026i | ||||
\(78\) | −1.41421 | + | 1.00000i | −0.160128 | + | 0.113228i | ||||
\(79\) | − | 12.4853i | − | 1.40470i | −0.711830 | − | 0.702352i | \(-0.752133\pi\) | ||
0.711830 | − | 0.702352i | \(-0.247867\pi\) | |||||||
\(80\) | 0.707107 | − | 2.12132i | 0.0790569 | − | 0.237171i | ||||
\(81\) | −7.00000 | − | 5.65685i | −0.777778 | − | 0.628539i | ||||
\(82\) | 1.41421 | + | 1.41421i | 0.156174 | + | 0.156174i | ||||
\(83\) | 6.82843 | + | 6.82843i | 0.749517 | + | 0.749517i | 0.974388 | − | 0.224871i | \(-0.0721961\pi\) |
−0.224871 | + | 0.974388i | \(0.572196\pi\) | |||||||
\(84\) | 1.41421 | + | 0.242641i | 0.154303 | + | 0.0264743i | ||||
\(85\) | 4.24264 | + | 8.48528i | 0.460179 | + | 0.920358i | ||||
\(86\) | − | 1.75736i | − | 0.189501i | ||||||
\(87\) | 6.00000 | + | 8.48528i | 0.643268 | + | 0.909718i | ||||
\(88\) | 2.82843 | − | 2.82843i | 0.301511 | − | 0.301511i | ||||
\(89\) | −11.1716 | −1.18418 | −0.592092 | − | 0.805870i | \(-0.701698\pi\) | ||||
−0.592092 | + | 0.805870i | \(0.701698\pi\) | |||||||
\(90\) | −6.65685 | + | 0.828427i | −0.701694 | + | 0.0873239i | ||||
\(91\) | −0.828427 | −0.0868428 | ||||||||
\(92\) | 2.82843 | − | 2.82843i | 0.294884 | − | 0.294884i | ||||
\(93\) | 3.41421 | + | 4.82843i | 0.354037 | + | 0.500685i | ||||
\(94\) | − | 3.17157i | − | 0.327123i | ||||||
\(95\) | 14.4853 | + | 4.82843i | 1.48616 | + | 0.495386i | ||||
\(96\) | −1.70711 | − | 0.292893i | −0.174231 | − | 0.0298933i | ||||
\(97\) | 9.07107 | + | 9.07107i | 0.921027 | + | 0.921027i | 0.997102 | − | 0.0760747i | \(-0.0242388\pi\) |
−0.0760747 | + | 0.997102i | \(0.524239\pi\) | |||||||
\(98\) | −4.46447 | − | 4.46447i | −0.450979 | − | 0.450979i | ||||
\(99\) | −11.3137 | − | 4.00000i | −1.13707 | − | 0.402015i | ||||
\(100\) | −3.00000 | + | 4.00000i | −0.300000 | + | 0.400000i | ||||
\(101\) | 3.17157i | 0.315583i | 0.987472 | + | 0.157792i | \(0.0504374\pi\) | ||||
−0.987472 | + | 0.157792i | \(0.949563\pi\) | |||||||
\(102\) | 6.00000 | − | 4.24264i | 0.594089 | − | 0.420084i | ||||
\(103\) | 12.4853 | − | 12.4853i | 1.23021 | − | 1.23021i | 0.266329 | − | 0.963882i | \(-0.414189\pi\) |
0.963882 | − | 0.266329i | \(-0.0858108\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | −2.82843 | − | 1.51472i | −0.276026 | − | 0.147821i | ||||
\(106\) | −0.828427 | −0.0804640 | ||||||||
\(107\) | −12.0711 | + | 12.0711i | −1.16695 | + | 1.16695i | −0.184034 | + | 0.982920i | \(0.558916\pi\) |
−0.982920 | + | 0.184034i | \(0.941084\pi\) | |||||||
\(108\) | 1.41421 | + | 5.00000i | 0.136083 | + | 0.481125i | ||||
\(109\) | 4.92893i | 0.472106i | 0.971740 | + | 0.236053i | \(0.0758539\pi\) | ||||
−0.971740 | + | 0.236053i | \(0.924146\pi\) | |||||||
\(110\) | −8.00000 | + | 4.00000i | −0.762770 | + | 0.381385i | ||||
\(111\) | 1.07107 | − | 6.24264i | 0.101661 | − | 0.592525i | ||||
\(112\) | −0.585786 | − | 0.585786i | −0.0553516 | − | 0.0553516i | ||||
\(113\) | −7.00000 | − | 7.00000i | −0.658505 | − | 0.658505i | 0.296522 | − | 0.955026i | \(-0.404173\pi\) |
−0.955026 | + | 0.296522i | \(0.904173\pi\) | |||||||
\(114\) | 2.00000 | − | 11.6569i | 0.187317 | − | 1.09176i | ||||
\(115\) | −8.00000 | + | 4.00000i | −0.746004 | + | 0.373002i | ||||
\(116\) | − | 6.00000i | − | 0.557086i | ||||||
\(117\) | −1.29289 | − | 2.70711i | −0.119528 | − | 0.250272i | ||||
\(118\) | −3.17157 | + | 3.17157i | −0.291967 | + | 0.291967i | ||||
\(119\) | 3.51472 | 0.322194 | ||||||||
\(120\) | 3.41421 | + | 1.82843i | 0.311674 | + | 0.166912i | ||||
\(121\) | −5.00000 | −0.454545 | ||||||||
\(122\) | 3.41421 | − | 3.41421i | 0.309108 | − | 0.309108i | ||||
\(123\) | −2.82843 | + | 2.00000i | −0.255031 | + | 0.180334i | ||||
\(124\) | − | 3.41421i | − | 0.306605i | ||||||
\(125\) | 9.19239 | − | 6.36396i | 0.822192 | − | 0.569210i | ||||
\(126\) | −0.828427 | + | 2.34315i | −0.0738022 | + | 0.208744i | ||||
\(127\) | −3.17157 | − | 3.17157i | −0.281432 | − | 0.281432i | 0.552248 | − | 0.833680i | \(-0.313770\pi\) |
−0.833680 | + | 0.552248i | \(0.813770\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 3.00000 | + | 0.514719i | 0.264135 | + | 0.0453184i | ||||
\(130\) | −2.12132 | − | 0.707107i | −0.186052 | − | 0.0620174i | ||||
\(131\) | − | 12.9706i | − | 1.13324i | −0.823978 | − | 0.566622i | \(-0.808250\pi\) | ||
0.823978 | − | 0.566622i | \(-0.191750\pi\) | |||||||
\(132\) | 4.00000 | + | 5.65685i | 0.348155 | + | 0.492366i | ||||
\(133\) | 4.00000 | − | 4.00000i | 0.346844 | − | 0.346844i | ||||
\(134\) | −1.17157 | −0.101208 | ||||||||
\(135\) | 0.535534 | − | 11.6066i | 0.0460914 | − | 0.998937i | ||||
\(136\) | −4.24264 | −0.363803 | ||||||||
\(137\) | −15.0711 | + | 15.0711i | −1.28761 | + | 1.28761i | −0.351372 | + | 0.936236i | \(0.614285\pi\) |
−0.936236 | + | 0.351372i | \(0.885715\pi\) | |||||||
\(138\) | 4.00000 | + | 5.65685i | 0.340503 | + | 0.481543i | ||||
\(139\) | 1.65685i | 0.140533i | 0.997528 | + | 0.0702663i | \(0.0223849\pi\) | ||||
−0.997528 | + | 0.0702663i | \(0.977615\pi\) | |||||||
\(140\) | 0.828427 | + | 1.65685i | 0.0700149 | + | 0.140030i | ||||
\(141\) | 5.41421 | + | 0.928932i | 0.455959 | + | 0.0782302i | ||||
\(142\) | −10.0711 | − | 10.0711i | −0.845145 | − | 0.845145i | ||||
\(143\) | −2.82843 | − | 2.82843i | −0.236525 | − | 0.236525i | ||||
\(144\) | 1.00000 | − | 2.82843i | 0.0833333 | − | 0.235702i | ||||
\(145\) | −4.24264 | + | 12.7279i | −0.352332 | + | 1.05700i | ||||
\(146\) | 15.6569i | 1.29577i | ||||||||
\(147\) | 8.92893 | − | 6.31371i | 0.736446 | − | 0.520746i | ||||
\(148\) | −2.58579 | + | 2.58579i | −0.212550 | + | 0.212550i | ||||
\(149\) | −22.3848 | −1.83383 | −0.916916 | − | 0.399080i | \(-0.869330\pi\) | ||||
−0.916916 | + | 0.399080i | \(0.869330\pi\) | |||||||
\(150\) | −5.94975 | − | 6.29289i | −0.485795 | − | 0.513813i | ||||
\(151\) | 1.07107 | 0.0871623 | 0.0435811 | − | 0.999050i | \(-0.486123\pi\) | ||||
0.0435811 | + | 0.999050i | \(0.486123\pi\) | |||||||
\(152\) | −4.82843 | + | 4.82843i | −0.391637 | + | 0.391637i | ||||
\(153\) | 5.48528 | + | 11.4853i | 0.443459 | + | 0.928530i | ||||
\(154\) | 3.31371i | 0.267026i | ||||||||
\(155\) | −2.41421 | + | 7.24264i | −0.193914 | + | 0.581743i | ||||
\(156\) | −0.292893 | + | 1.70711i | −0.0234502 | + | 0.136678i | ||||
\(157\) | 16.2426 | + | 16.2426i | 1.29630 | + | 1.29630i | 0.930816 | + | 0.365488i | \(0.119098\pi\) |
0.365488 | + | 0.930816i | \(0.380902\pi\) | |||||||
\(158\) | −8.82843 | − | 8.82843i | −0.702352 | − | 0.702352i | ||||
\(159\) | 0.242641 | − | 1.41421i | 0.0192427 | − | 0.112154i | ||||
\(160\) | −1.00000 | − | 2.00000i | −0.0790569 | − | 0.158114i | ||||
\(161\) | 3.31371i | 0.261157i | ||||||||
\(162\) | −8.94975 | + | 0.949747i | −0.703159 | + | 0.0746192i | ||||
\(163\) | 2.34315 | − | 2.34315i | 0.183529 | − | 0.183529i | −0.609362 | − | 0.792892i | \(-0.708575\pi\) |
0.792892 | + | 0.609362i | \(0.208575\pi\) | |||||||
\(164\) | 2.00000 | 0.156174 | ||||||||
\(165\) | −4.48528 | − | 14.8284i | −0.349179 | − | 1.15439i | ||||
\(166\) | 9.65685 | 0.749517 | ||||||||
\(167\) | −3.41421 | + | 3.41421i | −0.264200 | + | 0.264200i | −0.826758 | − | 0.562558i | \(-0.809817\pi\) |
0.562558 | + | 0.826758i | \(0.309817\pi\) | |||||||
\(168\) | 1.17157 | − | 0.828427i | 0.0903888 | − | 0.0639145i | ||||
\(169\) | − | 1.00000i | − | 0.0769231i | ||||||
\(170\) | 9.00000 | + | 3.00000i | 0.690268 | + | 0.230089i | ||||
\(171\) | 19.3137 | + | 6.82843i | 1.47696 | + | 0.522183i | ||||
\(172\) | −1.24264 | − | 1.24264i | −0.0947505 | − | 0.0947505i | ||||
\(173\) | 17.0711 | + | 17.0711i | 1.29789 | + | 1.29789i | 0.929784 | + | 0.368105i | \(0.119993\pi\) |
0.368105 | + | 0.929784i | \(0.380007\pi\) | |||||||
\(174\) | 10.2426 | + | 1.75736i | 0.776493 | + | 0.133225i | ||||
\(175\) | −0.585786 | − | 4.10051i | −0.0442813 | − | 0.309969i | ||||
\(176\) | − | 4.00000i | − | 0.301511i | ||||||
\(177\) | −4.48528 | − | 6.34315i | −0.337134 | − | 0.476780i | ||||
\(178\) | −7.89949 | + | 7.89949i | −0.592092 | + | 0.592092i | ||||
\(179\) | 17.6569 | 1.31974 | 0.659868 | − | 0.751382i | \(-0.270612\pi\) | ||||
0.659868 | + | 0.751382i | \(0.270612\pi\) | |||||||
\(180\) | −4.12132 | + | 5.29289i | −0.307185 | + | 0.394509i | ||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | −0.585786 | + | 0.585786i | −0.0434214 | + | 0.0434214i | ||||
\(183\) | 4.82843 | + | 6.82843i | 0.356928 | + | 0.504772i | ||||
\(184\) | − | 4.00000i | − | 0.294884i | ||||||
\(185\) | 7.31371 | − | 3.65685i | 0.537715 | − | 0.268857i | ||||
\(186\) | 5.82843 | + | 1.00000i | 0.427361 | + | 0.0733236i | ||||
\(187\) | 12.0000 | + | 12.0000i | 0.877527 | + | 0.877527i | ||||
\(188\) | −2.24264 | − | 2.24264i | −0.163561 | − | 0.163561i | ||||
\(189\) | −3.75736 | − | 2.10051i | −0.273308 | − | 0.152789i | ||||
\(190\) | 13.6569 | − | 6.82843i | 0.990772 | − | 0.495386i | ||||
\(191\) | − | 2.82843i | − | 0.204658i | −0.994751 | − | 0.102329i | \(-0.967371\pi\) | ||
0.994751 | − | 0.102329i | \(-0.0326294\pi\) | |||||||
\(192\) | −1.41421 | + | 1.00000i | −0.102062 | + | 0.0721688i | ||||
\(193\) | 11.4142 | − | 11.4142i | 0.821613 | − | 0.821613i | −0.164726 | − | 0.986339i | \(-0.552674\pi\) |
0.986339 | + | 0.164726i | \(0.0526741\pi\) | |||||||
\(194\) | 12.8284 | 0.921027 | ||||||||
\(195\) | 1.82843 | − | 3.41421i | 0.130936 | − | 0.244497i | ||||
\(196\) | −6.31371 | −0.450979 | ||||||||
\(197\) | −3.75736 | + | 3.75736i | −0.267701 | + | 0.267701i | −0.828173 | − | 0.560472i | \(-0.810620\pi\) |
0.560472 | + | 0.828173i | \(0.310620\pi\) | |||||||
\(198\) | −10.8284 | + | 5.17157i | −0.769543 | + | 0.367528i | ||||
\(199\) | − | 22.1421i | − | 1.56961i | −0.619740 | − | 0.784807i | \(-0.712762\pi\) | ||
0.619740 | − | 0.784807i | \(-0.287238\pi\) | |||||||
\(200\) | 0.707107 | + | 4.94975i | 0.0500000 | + | 0.350000i | ||||
\(201\) | 0.343146 | − | 2.00000i | 0.0242036 | − | 0.141069i | ||||
\(202\) | 2.24264 | + | 2.24264i | 0.157792 | + | 0.157792i | ||||
\(203\) | 3.51472 | + | 3.51472i | 0.246685 | + | 0.246685i | ||||
\(204\) | 1.24264 | − | 7.24264i | 0.0870023 | − | 0.507086i | ||||
\(205\) | −4.24264 | − | 1.41421i | −0.296319 | − | 0.0987730i | ||||
\(206\) | − | 17.6569i | − | 1.23021i | ||||||
\(207\) | −10.8284 | + | 5.17157i | −0.752628 | + | 0.359449i | ||||
\(208\) | 0.707107 | − | 0.707107i | 0.0490290 | − | 0.0490290i | ||||
\(209\) | 27.3137 | 1.88933 | ||||||||
\(210\) | −3.07107 | + | 0.928932i | −0.211924 | + | 0.0641024i | ||||
\(211\) | 1.65685 | 0.114063 | 0.0570313 | − | 0.998372i | \(-0.481837\pi\) | ||||
0.0570313 | + | 0.998372i | \(0.481837\pi\) | |||||||
\(212\) | −0.585786 | + | 0.585786i | −0.0402320 | + | 0.0402320i | ||||
\(213\) | 20.1421 | − | 14.2426i | 1.38012 | − | 0.975890i | ||||
\(214\) | 17.0711i | 1.16695i | ||||||||
\(215\) | 1.75736 | + | 3.51472i | 0.119851 | + | 0.239702i | ||||
\(216\) | 4.53553 | + | 2.53553i | 0.308604 | + | 0.172521i | ||||
\(217\) | 2.00000 | + | 2.00000i | 0.135769 | + | 0.135769i | ||||
\(218\) | 3.48528 | + | 3.48528i | 0.236053 | + | 0.236053i | ||||
\(219\) | −26.7279 | − | 4.58579i | −1.80611 | − | 0.309879i | ||||
\(220\) | −2.82843 | + | 8.48528i | −0.190693 | + | 0.572078i | ||||
\(221\) | 4.24264i | 0.285391i | ||||||||
\(222\) | −3.65685 | − | 5.17157i | −0.245432 | − | 0.347093i | ||||
\(223\) | −9.65685 | + | 9.65685i | −0.646671 | + | 0.646671i | −0.952187 | − | 0.305516i | \(-0.901171\pi\) |
0.305516 | + | 0.952187i | \(0.401171\pi\) | |||||||
\(224\) | −0.828427 | −0.0553516 | ||||||||
\(225\) | 12.4853 | − | 8.31371i | 0.832352 | − | 0.554247i | ||||
\(226\) | −9.89949 | −0.658505 | ||||||||
\(227\) | −2.00000 | + | 2.00000i | −0.132745 | + | 0.132745i | −0.770357 | − | 0.637613i | \(-0.779922\pi\) |
0.637613 | + | 0.770357i | \(0.279922\pi\) | |||||||
\(228\) | −6.82843 | − | 9.65685i | −0.452224 | − | 0.639541i | ||||
\(229\) | 17.8995i | 1.18283i | 0.806367 | + | 0.591416i | \(0.201431\pi\) | ||||
−0.806367 | + | 0.591416i | \(0.798569\pi\) | |||||||
\(230\) | −2.82843 | + | 8.48528i | −0.186501 | + | 0.559503i | ||||
\(231\) | −5.65685 | − | 0.970563i | −0.372194 | − | 0.0638583i | ||||
\(232\) | −4.24264 | − | 4.24264i | −0.278543 | − | 0.278543i | ||||
\(233\) | 8.65685 | + | 8.65685i | 0.567129 | + | 0.567129i | 0.931323 | − | 0.364194i | \(-0.118655\pi\) |
−0.364194 | + | 0.931323i | \(0.618655\pi\) | |||||||
\(234\) | −2.82843 | − | 1.00000i | −0.184900 | − | 0.0653720i | ||||
\(235\) | 3.17157 | + | 6.34315i | 0.206891 | + | 0.413781i | ||||
\(236\) | 4.48528i | 0.291967i | ||||||||
\(237\) | 17.6569 | − | 12.4853i | 1.14694 | − | 0.811006i | ||||
\(238\) | 2.48528 | − | 2.48528i | 0.161097 | − | 0.161097i | ||||
\(239\) | 19.8995 | 1.28719 | 0.643596 | − | 0.765366i | \(-0.277442\pi\) | ||||
0.643596 | + | 0.765366i | \(0.277442\pi\) | |||||||
\(240\) | 3.70711 | − | 1.12132i | 0.239293 | − | 0.0723809i | ||||
\(241\) | −3.65685 | −0.235559 | −0.117779 | − | 0.993040i | \(-0.537578\pi\) | ||||
−0.117779 | + | 0.993040i | \(0.537578\pi\) | |||||||
\(242\) | −3.53553 | + | 3.53553i | −0.227273 | + | 0.227273i | ||||
\(243\) | 1.00000 | − | 15.5563i | 0.0641500 | − | 0.997940i | ||||
\(244\) | − | 4.82843i | − | 0.309108i | ||||||
\(245\) | 13.3934 | + | 4.46447i | 0.855673 | + | 0.285224i | ||||
\(246\) | −0.585786 | + | 3.41421i | −0.0373484 | + | 0.217682i | ||||
\(247\) | 4.82843 | + | 4.82843i | 0.307225 | + | 0.307225i | ||||
\(248\) | −2.41421 | − | 2.41421i | −0.153303 | − | 0.153303i | ||||
\(249\) | −2.82843 | + | 16.4853i | −0.179244 | + | 1.04471i | ||||
\(250\) | 2.00000 | − | 11.0000i | 0.126491 | − | 0.695701i | ||||
\(251\) | − | 14.3431i | − | 0.905331i | −0.891680 | − | 0.452666i | \(-0.850473\pi\) | ||
0.891680 | − | 0.452666i | \(-0.149527\pi\) | |||||||
\(252\) | 1.07107 | + | 2.24264i | 0.0674709 | + | 0.141273i | ||||
\(253\) | −11.3137 | + | 11.3137i | −0.711287 | + | 0.711287i | ||||
\(254\) | −4.48528 | −0.281432 | ||||||||
\(255\) | −7.75736 | + | 14.4853i | −0.485785 | + | 0.907104i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −7.00000 | + | 7.00000i | −0.436648 | + | 0.436648i | −0.890882 | − | 0.454234i | \(-0.849913\pi\) |
0.454234 | + | 0.890882i | \(0.349913\pi\) | |||||||
\(258\) | 2.48528 | − | 1.75736i | 0.154727 | − | 0.109408i | ||||
\(259\) | − | 3.02944i | − | 0.188240i | ||||||
\(260\) | −2.00000 | + | 1.00000i | −0.124035 | + | 0.0620174i | ||||
\(261\) | −6.00000 | + | 16.9706i | −0.371391 | + | 1.05045i | ||||
\(262\) | −9.17157 | − | 9.17157i | −0.566622 | − | 0.566622i | ||||
\(263\) | −16.0000 | − | 16.0000i | −0.986602 | − | 0.986602i | 0.0133092 | − | 0.999911i | \(-0.495763\pi\) |
−0.999911 | + | 0.0133092i | \(0.995763\pi\) | |||||||
\(264\) | 6.82843 | + | 1.17157i | 0.420261 | + | 0.0721053i | ||||
\(265\) | 1.65685 | − | 0.828427i | 0.101780 | − | 0.0508899i | ||||
\(266\) | − | 5.65685i | − | 0.346844i | ||||||
\(267\) | −11.1716 | − | 15.7990i | −0.683689 | − | 0.966882i | ||||
\(268\) | −0.828427 | + | 0.828427i | −0.0506042 | + | 0.0506042i | ||||
\(269\) | −15.1716 | −0.925027 | −0.462514 | − | 0.886612i | \(-0.653052\pi\) | ||||
−0.462514 | + | 0.886612i | \(0.653052\pi\) | |||||||
\(270\) | −7.82843 | − | 8.58579i | −0.476423 | − | 0.522514i | ||||
\(271\) | −2.24264 | −0.136231 | −0.0681154 | − | 0.997677i | \(-0.521699\pi\) | ||||
−0.0681154 | + | 0.997677i | \(0.521699\pi\) | |||||||
\(272\) | −3.00000 | + | 3.00000i | −0.181902 | + | 0.181902i | ||||
\(273\) | −0.828427 | − | 1.17157i | −0.0501387 | − | 0.0709068i | ||||
\(274\) | 21.3137i | 1.28761i | ||||||||
\(275\) | 12.0000 | − | 16.0000i | 0.723627 | − | 0.964836i | ||||
\(276\) | 6.82843 | + | 1.17157i | 0.411023 | + | 0.0705204i | ||||
\(277\) | −15.8995 | − | 15.8995i | −0.955308 | − | 0.955308i | 0.0437351 | − | 0.999043i | \(-0.486074\pi\) |
−0.999043 | + | 0.0437351i | \(0.986074\pi\) | |||||||
\(278\) | 1.17157 | + | 1.17157i | 0.0702663 | + | 0.0702663i | ||||
\(279\) | −3.41421 | + | 9.65685i | −0.204404 | + | 0.578141i | ||||
\(280\) | 1.75736 | + | 0.585786i | 0.105022 | + | 0.0350074i | ||||
\(281\) | 0.828427i | 0.0494198i | 0.999695 | + | 0.0247099i | \(0.00786621\pi\) | ||||
−0.999695 | + | 0.0247099i | \(0.992134\pi\) | |||||||
\(282\) | 4.48528 | − | 3.17157i | 0.267095 | − | 0.188864i | ||||
\(283\) | −17.2426 | + | 17.2426i | −1.02497 | + | 1.02497i | −0.0252884 | + | 0.999680i | \(0.508050\pi\) |
−0.999680 | + | 0.0252884i | \(0.991950\pi\) | |||||||
\(284\) | −14.2426 | −0.845145 | ||||||||
\(285\) | 7.65685 | + | 25.3137i | 0.453553 | + | 1.49945i | ||||
\(286\) | −4.00000 | −0.236525 | ||||||||
\(287\) | −1.17157 | + | 1.17157i | −0.0691558 | + | 0.0691558i | ||||
\(288\) | −1.29289 | − | 2.70711i | −0.0761845 | − | 0.159518i | ||||
\(289\) | − | 1.00000i | − | 0.0588235i | ||||||
\(290\) | 6.00000 | + | 12.0000i | 0.352332 | + | 0.704664i | ||||
\(291\) | −3.75736 | + | 21.8995i | −0.220260 | + | 1.28377i | ||||
\(292\) | 11.0711 | + | 11.0711i | 0.647885 | + | 0.647885i | ||||
\(293\) | 4.48528 | + | 4.48528i | 0.262033 | + | 0.262033i | 0.825880 | − | 0.563847i | \(-0.190679\pi\) |
−0.563847 | + | 0.825880i | \(0.690679\pi\) | |||||||
\(294\) | 1.84924 | − | 10.7782i | 0.107850 | − | 0.628596i | ||||
\(295\) | 3.17157 | − | 9.51472i | 0.184656 | − | 0.553968i | ||||
\(296\) | 3.65685i | 0.212550i | ||||||||
\(297\) | −5.65685 | − | 20.0000i | −0.328244 | − | 1.16052i | ||||
\(298\) | −15.8284 | + | 15.8284i | −0.916916 | + | 0.916916i | ||||
\(299\) | −4.00000 | −0.231326 | ||||||||
\(300\) | −8.65685 | − | 0.242641i | −0.499804 | − | 0.0140089i | ||||
\(301\) | 1.45584 | 0.0839135 | ||||||||
\(302\) | 0.757359 | − | 0.757359i | 0.0435811 | − | 0.0435811i | ||||
\(303\) | −4.48528 | + | 3.17157i | −0.257673 | + | 0.182202i | ||||
\(304\) | 6.82843i | 0.391637i | ||||||||
\(305\) | −3.41421 | + | 10.2426i | −0.195497 | + | 0.586492i | ||||
\(306\) | 12.0000 | + | 4.24264i | 0.685994 | + | 0.242536i | ||||
\(307\) | 7.17157 | + | 7.17157i | 0.409303 | + | 0.409303i | 0.881496 | − | 0.472192i | \(-0.156537\pi\) |
−0.472192 | + | 0.881496i | \(0.656537\pi\) | |||||||
\(308\) | 2.34315 | + | 2.34315i | 0.133513 | + | 0.133513i | ||||
\(309\) | 30.1421 | + | 5.17157i | 1.71473 | + | 0.294201i | ||||
\(310\) | 3.41421 | + | 6.82843i | 0.193914 | + | 0.387829i | ||||
\(311\) | − | 28.0000i | − | 1.58773i | −0.608091 | − | 0.793867i | \(-0.708065\pi\) | ||
0.608091 | − | 0.793867i | \(-0.291935\pi\) | |||||||
\(312\) | 1.00000 | + | 1.41421i | 0.0566139 | + | 0.0800641i | ||||
\(313\) | 1.34315 | − | 1.34315i | 0.0759191 | − | 0.0759191i | −0.668128 | − | 0.744047i | \(-0.732904\pi\) |
0.744047 | + | 0.668128i | \(0.232904\pi\) | |||||||
\(314\) | 22.9706 | 1.29630 | ||||||||
\(315\) | −0.686292 | − | 5.51472i | −0.0386681 | − | 0.310719i | ||||
\(316\) | −12.4853 | −0.702352 | ||||||||
\(317\) | 1.65685 | − | 1.65685i | 0.0930582 | − | 0.0930582i | −0.659045 | − | 0.752103i | \(-0.729039\pi\) |
0.752103 | + | 0.659045i | \(0.229039\pi\) | |||||||
\(318\) | −0.828427 | − | 1.17157i | −0.0464559 | − | 0.0656985i | ||||
\(319\) | 24.0000i | 1.34374i | ||||||||
\(320\) | −2.12132 | − | 0.707107i | −0.118585 | − | 0.0395285i | ||||
\(321\) | −29.1421 | − | 5.00000i | −1.62656 | − | 0.279073i | ||||
\(322\) | 2.34315 | + | 2.34315i | 0.130578 | + | 0.130578i | ||||
\(323\) | −20.4853 | − | 20.4853i | −1.13983 | − | 1.13983i | ||||
\(324\) | −5.65685 | + | 7.00000i | −0.314270 | + | 0.388889i | ||||
\(325\) | 4.94975 | − | 0.707107i | 0.274563 | − | 0.0392232i | ||||
\(326\) | − | 3.31371i | − | 0.183529i | ||||||
\(327\) | −6.97056 | + | 4.92893i | −0.385473 | + | 0.272571i | ||||
\(328\) | 1.41421 | − | 1.41421i | 0.0780869 | − | 0.0780869i | ||||
\(329\) | 2.62742 | 0.144854 | ||||||||
\(330\) | −13.6569 | − | 7.31371i | −0.751785 | − | 0.402606i | ||||
\(331\) | −32.2843 | −1.77450 | −0.887252 | − | 0.461285i | \(-0.847389\pi\) | ||||
−0.887252 | + | 0.461285i | \(0.847389\pi\) | |||||||
\(332\) | 6.82843 | − | 6.82843i | 0.374759 | − | 0.374759i | ||||
\(333\) | 9.89949 | − | 4.72792i | 0.542489 | − | 0.259089i | ||||
\(334\) | 4.82843i | 0.264200i | ||||||||
\(335\) | 2.34315 | − | 1.17157i | 0.128020 | − | 0.0640099i | ||||
\(336\) | 0.242641 | − | 1.41421i | 0.0132371 | − | 0.0771517i | ||||
\(337\) | −23.0000 | − | 23.0000i | −1.25289 | − | 1.25289i | −0.954419 | − | 0.298471i | \(-0.903523\pi\) |
−0.298471 | − | 0.954419i | \(-0.596477\pi\) | |||||||
\(338\) | −0.707107 | − | 0.707107i | −0.0384615 | − | 0.0384615i | ||||
\(339\) | 2.89949 | − | 16.8995i | 0.157479 | − | 0.917855i | ||||
\(340\) | 8.48528 | − | 4.24264i | 0.460179 | − | 0.230089i | ||||
\(341\) | 13.6569i | 0.739560i | ||||||||
\(342\) | 18.4853 | − | 8.82843i | 0.999570 | − | 0.477387i | ||||
\(343\) | 7.79899 | − | 7.79899i | 0.421106 | − | 0.421106i | ||||
\(344\) | −1.75736 | −0.0947505 | ||||||||
\(345\) | −13.6569 | − | 7.31371i | −0.735260 | − | 0.393757i | ||||
\(346\) | 24.1421 | 1.29789 | ||||||||
\(347\) | −10.5563 | + | 10.5563i | −0.566695 | + | 0.566695i | −0.931201 | − | 0.364506i | \(-0.881238\pi\) |
0.364506 | + | 0.931201i | \(0.381238\pi\) | |||||||
\(348\) | 8.48528 | − | 6.00000i | 0.454859 | − | 0.321634i | ||||
\(349\) | 32.7279i | 1.75189i | 0.482415 | + | 0.875943i | \(0.339760\pi\) | ||||
−0.482415 | + | 0.875943i | \(0.660240\pi\) | |||||||
\(350\) | −3.31371 | − | 2.48528i | −0.177125 | − | 0.132844i | ||||
\(351\) | 2.53553 | − | 4.53553i | 0.135337 | − | 0.242089i | ||||
\(352\) | −2.82843 | − | 2.82843i | −0.150756 | − | 0.150756i | ||||
\(353\) | −25.5563 | − | 25.5563i | −1.36023 | − | 1.36023i | −0.873622 | − | 0.486605i | \(-0.838235\pi\) |
−0.486605 | − | 0.873622i | \(-0.661765\pi\) | |||||||
\(354\) | −7.65685 | − | 1.31371i | −0.406957 | − | 0.0698228i | ||||
\(355\) | 30.2132 | + | 10.0711i | 1.60355 | + | 0.534517i | ||||
\(356\) | 11.1716i | 0.592092i | ||||||||
\(357\) | 3.51472 | + | 4.97056i | 0.186019 | + | 0.263070i | ||||
\(358\) | 12.4853 | − | 12.4853i | 0.659868 | − | 0.659868i | ||||
\(359\) | −23.4142 | −1.23575 | −0.617877 | − | 0.786274i | \(-0.712007\pi\) | ||||
−0.617877 | + | 0.786274i | \(0.712007\pi\) | |||||||
\(360\) | 0.828427 | + | 6.65685i | 0.0436619 | + | 0.350847i | ||||
\(361\) | −27.6274 | −1.45407 | ||||||||
\(362\) | 4.24264 | − | 4.24264i | 0.222988 | − | 0.222988i | ||||
\(363\) | −5.00000 | − | 7.07107i | −0.262432 | − | 0.371135i | ||||
\(364\) | 0.828427i | 0.0434214i | ||||||||
\(365\) | −15.6569 | − | 31.3137i | −0.819517 | − | 1.63903i | ||||
\(366\) | 8.24264 | + | 1.41421i | 0.430850 | + | 0.0739221i | ||||
\(367\) | 14.1421 | + | 14.1421i | 0.738213 | + | 0.738213i | 0.972232 | − | 0.234019i | \(-0.0751877\pi\) |
−0.234019 | + | 0.972232i | \(0.575188\pi\) | |||||||
\(368\) | −2.82843 | − | 2.82843i | −0.147442 | − | 0.147442i | ||||
\(369\) | −5.65685 | − | 2.00000i | −0.294484 | − | 0.104116i | ||||
\(370\) | 2.58579 | − | 7.75736i | 0.134429 | − | 0.403286i | ||||
\(371\) | − | 0.686292i | − | 0.0356305i | ||||||
\(372\) | 4.82843 | − | 3.41421i | 0.250342 | − | 0.177019i | ||||
\(373\) | 4.92893 | − | 4.92893i | 0.255210 | − | 0.255210i | −0.567892 | − | 0.823103i | \(-0.692241\pi\) |
0.823103 | + | 0.567892i | \(0.192241\pi\) | |||||||
\(374\) | 16.9706 | 0.877527 | ||||||||
\(375\) | 18.1924 | + | 6.63604i | 0.939451 | + | 0.342684i | ||||
\(376\) | −3.17157 | −0.163561 | ||||||||
\(377\) | −4.24264 | + | 4.24264i | −0.218507 | + | 0.218507i | ||||
\(378\) | −4.14214 | + | 1.17157i | −0.213048 | + | 0.0602592i | ||||
\(379\) | − | 38.1421i | − | 1.95923i | −0.200884 | − | 0.979615i | \(-0.564382\pi\) | ||
0.200884 | − | 0.979615i | \(-0.435618\pi\) | |||||||
\(380\) | 4.82843 | − | 14.4853i | 0.247693 | − | 0.743079i | ||||
\(381\) | 1.31371 | − | 7.65685i | 0.0673033 | − | 0.392273i | ||||
\(382\) | −2.00000 | − | 2.00000i | −0.102329 | − | 0.102329i | ||||
\(383\) | −1.65685 | − | 1.65685i | −0.0846613 | − | 0.0846613i | 0.663508 | − | 0.748169i | \(-0.269067\pi\) |
−0.748169 | + | 0.663508i | \(0.769067\pi\) | |||||||
\(384\) | −0.292893 | + | 1.70711i | −0.0149466 | + | 0.0871154i | ||||
\(385\) | −3.31371 | − | 6.62742i | −0.168882 | − | 0.337764i | ||||
\(386\) | − | 16.1421i | − | 0.821613i | ||||||
\(387\) | 2.27208 | + | 4.75736i | 0.115496 | + | 0.241830i | ||||
\(388\) | 9.07107 | − | 9.07107i | 0.460514 | − | 0.460514i | ||||
\(389\) | 2.00000 | 0.101404 | 0.0507020 | − | 0.998714i | \(-0.483854\pi\) | ||||
0.0507020 | + | 0.998714i | \(0.483854\pi\) | |||||||
\(390\) | −1.12132 | − | 3.70711i | −0.0567803 | − | 0.187717i | ||||
\(391\) | 16.9706 | 0.858238 | ||||||||
\(392\) | −4.46447 | + | 4.46447i | −0.225490 | + | 0.225490i | ||||
\(393\) | 18.3431 | − | 12.9706i | 0.925289 | − | 0.654278i | ||||
\(394\) | 5.31371i | 0.267701i | ||||||||
\(395\) | 26.4853 | + | 8.82843i | 1.33262 | + | 0.444206i | ||||
\(396\) | −4.00000 | + | 11.3137i | −0.201008 | + | 0.568535i | ||||
\(397\) | −9.17157 | − | 9.17157i | −0.460308 | − | 0.460308i | 0.438448 | − | 0.898756i | \(-0.355528\pi\) |
−0.898756 | + | 0.438448i | \(0.855528\pi\) | |||||||
\(398\) | −15.6569 | − | 15.6569i | −0.784807 | − | 0.784807i | ||||
\(399\) | 9.65685 | + | 1.65685i | 0.483447 | + | 0.0829465i | ||||
\(400\) | 4.00000 | + | 3.00000i | 0.200000 | + | 0.150000i | ||||
\(401\) | 1.79899i | 0.0898373i | 0.998991 | + | 0.0449186i | \(0.0143029\pi\) | ||||
−0.998991 | + | 0.0449186i | \(0.985697\pi\) | |||||||
\(402\) | −1.17157 | − | 1.65685i | −0.0584327 | − | 0.0826364i | ||||
\(403\) | −2.41421 | + | 2.41421i | −0.120261 | + | 0.120261i | ||||
\(404\) | 3.17157 | 0.157792 | ||||||||
\(405\) | 16.9497 | − | 10.8492i | 0.842240 | − | 0.539103i | ||||
\(406\) | 4.97056 | 0.246685 | ||||||||
\(407\) | 10.3431 | − | 10.3431i | 0.512691 | − | 0.512691i | ||||
\(408\) | −4.24264 | − | 6.00000i | −0.210042 | − | 0.297044i | ||||
\(409\) | − | 3.17157i | − | 0.156824i | −0.996921 | − | 0.0784121i | \(-0.975015\pi\) | ||
0.996921 | − | 0.0784121i | \(-0.0249850\pi\) | |||||||
\(410\) | −4.00000 | + | 2.00000i | −0.197546 | + | 0.0987730i | ||||
\(411\) | −36.3848 | − | 6.24264i | −1.79473 | − | 0.307927i | ||||
\(412\) | −12.4853 | − | 12.4853i | −0.615106 | − | 0.615106i | ||||
\(413\) | −2.62742 | − | 2.62742i | −0.129287 | − | 0.129287i | ||||
\(414\) | −4.00000 | + | 11.3137i | −0.196589 | + | 0.556038i | ||||
\(415\) | −19.3137 | + | 9.65685i | −0.948073 | + | 0.474036i | ||||
\(416\) | − | 1.00000i | − | 0.0490290i | ||||||
\(417\) | −2.34315 | + | 1.65685i | −0.114744 | + | 0.0811365i | ||||
\(418\) | 19.3137 | − | 19.3137i | 0.944664 | − | 0.944664i | ||||
\(419\) | 5.51472 | 0.269412 | 0.134706 | − | 0.990886i | \(-0.456991\pi\) | ||||
0.134706 | + | 0.990886i | \(0.456991\pi\) | |||||||
\(420\) | −1.51472 | + | 2.82843i | −0.0739107 | + | 0.138013i | ||||
\(421\) | 27.0711 | 1.31936 | 0.659682 | − | 0.751545i | \(-0.270691\pi\) | ||||
0.659682 | + | 0.751545i | \(0.270691\pi\) | |||||||
\(422\) | 1.17157 | − | 1.17157i | 0.0570313 | − | 0.0570313i | ||||
\(423\) | 4.10051 | + | 8.58579i | 0.199373 | + | 0.417455i | ||||
\(424\) | 0.828427i | 0.0402320i | ||||||||
\(425\) | −21.0000 | + | 3.00000i | −1.01865 | + | 0.145521i | ||||
\(426\) | 4.17157 | − | 24.3137i | 0.202113 | − | 1.17800i | ||||
\(427\) | 2.82843 | + | 2.82843i | 0.136877 | + | 0.136877i | ||||
\(428\) | 12.0711 | + | 12.0711i | 0.583477 | + | 0.583477i | ||||
\(429\) | 1.17157 | − | 6.82843i | 0.0565641 | − | 0.329680i | ||||
\(430\) | 3.72792 | + | 1.24264i | 0.179776 | + | 0.0599255i | ||||
\(431\) | 10.9289i | 0.526428i | 0.964737 | + | 0.263214i | \(0.0847826\pi\) | ||||
−0.964737 | + | 0.263214i | \(0.915217\pi\) | |||||||
\(432\) | 5.00000 | − | 1.41421i | 0.240563 | − | 0.0680414i | ||||
\(433\) | −16.3137 | + | 16.3137i | −0.783987 | + | 0.783987i | −0.980501 | − | 0.196514i | \(-0.937038\pi\) |
0.196514 | + | 0.980501i | \(0.437038\pi\) | |||||||
\(434\) | 2.82843 | 0.135769 | ||||||||
\(435\) | −22.2426 | + | 6.72792i | −1.06645 | + | 0.322579i | ||||
\(436\) | 4.92893 | 0.236053 | ||||||||
\(437\) | 19.3137 | − | 19.3137i | 0.923900 | − | 0.923900i | ||||
\(438\) | −22.1421 | + | 15.6569i | −1.05799 | + | 0.748113i | ||||
\(439\) | 18.3431i | 0.875471i | 0.899104 | + | 0.437735i | \(0.144219\pi\) | ||||
−0.899104 | + | 0.437735i | \(0.855781\pi\) | |||||||
\(440\) | 4.00000 | + | 8.00000i | 0.190693 | + | 0.381385i | ||||
\(441\) | 17.8579 | + | 6.31371i | 0.850374 | + | 0.300653i | ||||
\(442\) | 3.00000 | + | 3.00000i | 0.142695 | + | 0.142695i | ||||
\(443\) | 0.899495 | + | 0.899495i | 0.0427363 | + | 0.0427363i | 0.728152 | − | 0.685416i | \(-0.240379\pi\) |
−0.685416 | + | 0.728152i | \(0.740379\pi\) | |||||||
\(444\) | −6.24264 | − | 1.07107i | −0.296263 | − | 0.0508306i | ||||
\(445\) | 7.89949 | − | 23.6985i | 0.374472 | − | 1.12342i | ||||
\(446\) | 13.6569i | 0.646671i | ||||||||
\(447\) | −22.3848 | − | 31.6569i | −1.05876 | − | 1.49732i | ||||
\(448\) | −0.585786 | + | 0.585786i | −0.0276758 | + | 0.0276758i | ||||
\(449\) | −17.7990 | −0.839986 | −0.419993 | − | 0.907527i | \(-0.637968\pi\) | ||||
−0.419993 | + | 0.907527i | \(0.637968\pi\) | |||||||
\(450\) | 2.94975 | − | 14.7071i | 0.139052 | − | 0.693300i | ||||
\(451\) | −8.00000 | −0.376705 | ||||||||
\(452\) | −7.00000 | + | 7.00000i | −0.329252 | + | 0.329252i | ||||
\(453\) | 1.07107 | + | 1.51472i | 0.0503232 | + | 0.0711677i | ||||
\(454\) | 2.82843i | 0.132745i | ||||||||
\(455\) | 0.585786 | − | 1.75736i | 0.0274621 | − | 0.0823863i | ||||
\(456\) | −11.6569 | − | 2.00000i | −0.545882 | − | 0.0936586i | ||||
\(457\) | −21.0711 | − | 21.0711i | −0.985663 | − | 0.985663i | 0.0142357 | − | 0.999899i | \(-0.495468\pi\) |
−0.999899 | + | 0.0142357i | \(0.995468\pi\) | |||||||
\(458\) | 12.6569 | + | 12.6569i | 0.591416 | + | 0.591416i | ||||
\(459\) | −10.7574 | + | 19.2426i | −0.502111 | + | 0.898170i | ||||
\(460\) | 4.00000 | + | 8.00000i | 0.186501 | + | 0.373002i | ||||
\(461\) | − | 21.6985i | − | 1.01060i | −0.862944 | − | 0.505300i | \(-0.831382\pi\) | ||
0.862944 | − | 0.505300i | \(-0.168618\pi\) | |||||||
\(462\) | −4.68629 | + | 3.31371i | −0.218026 | + | 0.154168i | ||||
\(463\) | 5.65685 | − | 5.65685i | 0.262896 | − | 0.262896i | −0.563333 | − | 0.826230i | \(-0.690481\pi\) |
0.826230 | + | 0.563333i | \(0.190481\pi\) | |||||||
\(464\) | −6.00000 | −0.278543 | ||||||||
\(465\) | −12.6569 | + | 3.82843i | −0.586948 | + | 0.177539i | ||||
\(466\) | 12.2426 | 0.567129 | ||||||||
\(467\) | −16.8995 | + | 16.8995i | −0.782015 | + | 0.782015i | −0.980171 | − | 0.198155i | \(-0.936505\pi\) |
0.198155 | + | 0.980171i | \(0.436505\pi\) | |||||||
\(468\) | −2.70711 | + | 1.29289i | −0.125136 | + | 0.0597640i | ||||
\(469\) | − | 0.970563i | − | 0.0448164i | ||||||
\(470\) | 6.72792 | + | 2.24264i | 0.310336 | + | 0.103445i | ||||
\(471\) | −6.72792 | + | 39.2132i | −0.310006 | + | 1.80685i | ||||
\(472\) | 3.17157 | + | 3.17157i | 0.145983 | + | 0.145983i | ||||
\(473\) | 4.97056 | + | 4.97056i | 0.228547 | + | 0.228547i | ||||
\(474\) | 3.65685 | − | 21.3137i | 0.167965 | − | 0.978971i | ||||
\(475\) | −20.4853 | + | 27.3137i | −0.939929 | + | 1.25324i | ||||
\(476\) | − | 3.51472i | − | 0.161097i | ||||||
\(477\) | 2.24264 | − | 1.07107i | 0.102683 | − | 0.0490408i | ||||
\(478\) | 14.0711 | − | 14.0711i | 0.643596 | − | 0.643596i | ||||
\(479\) | 24.3848 | 1.11417 | 0.557084 | − | 0.830456i | \(-0.311920\pi\) | ||||
0.557084 | + | 0.830456i | \(0.311920\pi\) | |||||||
\(480\) | 1.82843 | − | 3.41421i | 0.0834559 | − | 0.155837i | ||||
\(481\) | 3.65685 | 0.166738 | ||||||||
\(482\) | −2.58579 | + | 2.58579i | −0.117779 | + | 0.117779i | ||||
\(483\) | −4.68629 | + | 3.31371i | −0.213234 | + | 0.150779i | ||||
\(484\) | 5.00000i | 0.227273i | ||||||||
\(485\) | −25.6569 | + | 12.8284i | −1.16502 | + | 0.582509i | ||||
\(486\) | −10.2929 | − | 11.7071i | −0.466895 | − | 0.531045i | ||||
\(487\) | 2.92893 | + | 2.92893i | 0.132723 | + | 0.132723i | 0.770347 | − | 0.637625i | \(-0.220083\pi\) |
−0.637625 | + | 0.770347i | \(0.720083\pi\) | |||||||
\(488\) | −3.41421 | − | 3.41421i | −0.154554 | − | 0.154554i | ||||
\(489\) | 5.65685 | + | 0.970563i | 0.255812 | + | 0.0438904i | ||||
\(490\) | 12.6274 | − | 6.31371i | 0.570449 | − | 0.285224i | ||||
\(491\) | 13.7990i | 0.622740i | 0.950289 | + | 0.311370i | \(0.100788\pi\) | ||||
−0.950289 | + | 0.311370i | \(0.899212\pi\) | |||||||
\(492\) | 2.00000 | + | 2.82843i | 0.0901670 | + | 0.127515i | ||||
\(493\) | 18.0000 | − | 18.0000i | 0.810679 | − | 0.810679i | ||||
\(494\) | 6.82843 | 0.307225 | ||||||||
\(495\) | 16.4853 | − | 21.1716i | 0.740958 | − | 0.951591i | ||||
\(496\) | −3.41421 | −0.153303 | ||||||||
\(497\) | 8.34315 | − | 8.34315i | 0.374241 | − | 0.374241i | ||||
\(498\) | 9.65685 | + | 13.6569i | 0.432734 | + | 0.611978i | ||||
\(499\) | − | 8.00000i | − | 0.358129i | −0.983837 | − | 0.179065i | \(-0.942693\pi\) | ||
0.983837 | − | 0.179065i | \(-0.0573071\pi\) | |||||||
\(500\) | −6.36396 | − | 9.19239i | −0.284605 | − | 0.411096i | ||||
\(501\) | −8.24264 | − | 1.41421i | −0.368254 | − | 0.0631824i | ||||
\(502\) | −10.1421 | − | 10.1421i | −0.452666 | − | 0.452666i | ||||
\(503\) | 16.1421 | + | 16.1421i | 0.719742 | + | 0.719742i | 0.968552 | − | 0.248810i | \(-0.0800395\pi\) |
−0.248810 | + | 0.968552i | \(0.580039\pi\) | |||||||
\(504\) | 2.34315 | + | 0.828427i | 0.104372 | + | 0.0369011i | ||||
\(505\) | −6.72792 | − | 2.24264i | −0.299389 | − | 0.0997962i | ||||
\(506\) | 16.0000i | 0.711287i | ||||||||
\(507\) | 1.41421 | − | 1.00000i | 0.0628074 | − | 0.0444116i | ||||
\(508\) | −3.17157 | + | 3.17157i | −0.140716 | + | 0.140716i | ||||
\(509\) | −41.2132 | −1.82674 | −0.913372 | − | 0.407127i | \(-0.866531\pi\) | ||||
−0.913372 | + | 0.407127i | \(0.866531\pi\) | |||||||
\(510\) | 4.75736 | + | 15.7279i | 0.210659 | + | 0.696444i | ||||
\(511\) | −12.9706 | −0.573784 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 9.65685 | + | 34.1421i | 0.426361 | + | 1.50741i | ||||
\(514\) | 9.89949i | 0.436648i | ||||||||
\(515\) | 17.6569 | + | 35.3137i | 0.778054 | + | 1.55611i | ||||
\(516\) | 0.514719 | − | 3.00000i | 0.0226592 | − | 0.132068i | ||||
\(517\) | 8.97056 | + | 8.97056i | 0.394525 | + | 0.394525i | ||||
\(518\) | −2.14214 | − | 2.14214i | −0.0941200 | − | 0.0941200i | ||||
\(519\) | −7.07107 | + | 41.2132i | −0.310385 | + | 1.80906i | ||||
\(520\) | −0.707107 | + | 2.12132i | −0.0310087 | + | 0.0930261i | ||||
\(521\) | 24.9706i | 1.09398i | 0.837139 | + | 0.546990i | \(0.184226\pi\) | ||||
−0.837139 | + | 0.546990i | \(0.815774\pi\) | |||||||
\(522\) | 7.75736 | + | 16.2426i | 0.339530 | + | 0.710921i | ||||
\(523\) | −6.07107 | + | 6.07107i | −0.265469 | + | 0.265469i | −0.827272 | − | 0.561802i | \(-0.810108\pi\) |
0.561802 | + | 0.827272i | \(0.310108\pi\) | |||||||
\(524\) | −12.9706 | −0.566622 | ||||||||
\(525\) | 5.21320 | − | 4.92893i | 0.227523 | − | 0.215116i | ||||
\(526\) | −22.6274 | −0.986602 | ||||||||
\(527\) | 10.2426 | − | 10.2426i | 0.446176 | − | 0.446176i | ||||
\(528\) | 5.65685 | − | 4.00000i | 0.246183 | − | 0.174078i | ||||
\(529\) | − | 7.00000i | − | 0.304348i | ||||||
\(530\) | 0.585786 | − | 1.75736i | 0.0254449 | − | 0.0763348i | ||||
\(531\) | 4.48528 | − | 12.6863i | 0.194645 | − | 0.550538i | ||||
\(532\) | −4.00000 | − | 4.00000i | −0.173422 | − | 0.173422i | ||||
\(533\) | −1.41421 | − | 1.41421i | −0.0612564 | − | 0.0612564i | ||||
\(534\) | −19.0711 | − | 3.27208i | −0.825286 | − | 0.141597i | ||||
\(535\) | −17.0711 | − | 34.1421i | −0.738047 | − | 1.47609i | ||||
\(536\) | 1.17157i | 0.0506042i | ||||||||
\(537\) | 17.6569 | + | 24.9706i | 0.761950 | + | 1.07756i | ||||
\(538\) | −10.7279 | + | 10.7279i | −0.462514 | + | 0.462514i | ||||
\(539\) | 25.2548 | 1.08780 | ||||||||
\(540\) | −11.6066 | − | 0.535534i | −0.499469 | − | 0.0230457i | ||||
\(541\) | −4.24264 | −0.182405 | −0.0912027 | − | 0.995832i | \(-0.529071\pi\) | ||||
−0.0912027 | + | 0.995832i | \(0.529071\pi\) | |||||||
\(542\) | −1.58579 | + | 1.58579i | −0.0681154 | + | 0.0681154i | ||||
\(543\) | 6.00000 | + | 8.48528i | 0.257485 | + | 0.364138i | ||||
\(544\) | 4.24264i | 0.181902i | ||||||||
\(545\) | −10.4558 | − | 3.48528i | −0.447879 | − | 0.149293i | ||||
\(546\) | −1.41421 | − | 0.242641i | −0.0605228 | − | 0.0103841i | ||||
\(547\) | −20.4142 | − | 20.4142i | −0.872849 | − | 0.872849i | 0.119933 | − | 0.992782i | \(-0.461732\pi\) |
−0.992782 | + | 0.119933i | \(0.961732\pi\) | |||||||
\(548\) | 15.0711 | + | 15.0711i | 0.643804 | + | 0.643804i | ||||
\(549\) | −4.82843 | + | 13.6569i | −0.206072 | + | 0.582860i | ||||
\(550\) | −2.82843 | − | 19.7990i | −0.120605 | − | 0.844232i | ||||
\(551\) | − | 40.9706i | − | 1.74540i | ||||||
\(552\) | 5.65685 | − | 4.00000i | 0.240772 | − | 0.170251i | ||||
\(553\) | 7.31371 | − | 7.31371i | 0.311011 | − | 0.311011i | ||||
\(554\) | −22.4853 | −0.955308 | ||||||||
\(555\) | 12.4853 | + | 6.68629i | 0.529971 | + | 0.283817i | ||||
\(556\) | 1.65685 | 0.0702663 | ||||||||
\(557\) | −0.928932 | + | 0.928932i | −0.0393601 | + | 0.0393601i | −0.726513 | − | 0.687153i | \(-0.758860\pi\) |
0.687153 | + | 0.726513i | \(0.258860\pi\) | |||||||
\(558\) | 4.41421 | + | 9.24264i | 0.186869 | + | 0.391272i | ||||
\(559\) | 1.75736i | 0.0743284i | ||||||||
\(560\) | 1.65685 | − | 0.828427i | 0.0700149 | − | 0.0350074i | ||||
\(561\) | −4.97056 | + | 28.9706i | −0.209857 | + | 1.22314i | ||||
\(562\) | 0.585786 | + | 0.585786i | 0.0247099 | + | 0.0247099i | ||||
\(563\) | 19.2426 | + | 19.2426i | 0.810981 | + | 0.810981i | 0.984781 | − | 0.173800i | \(-0.0556047\pi\) |
−0.173800 | + | 0.984781i | \(0.555605\pi\) | |||||||
\(564\) | 0.928932 | − | 5.41421i | 0.0391151 | − | 0.227980i | ||||
\(565\) | 19.7990 | − | 9.89949i | 0.832950 | − | 0.416475i | ||||
\(566\) | 24.3848i | 1.02497i | ||||||||
\(567\) | −0.786797 | − | 7.41421i | −0.0330423 | − | 0.311368i | ||||
\(568\) | −10.0711 | + | 10.0711i | −0.422573 | + | 0.422573i | ||||
\(569\) | 18.3431 | 0.768985 | 0.384492 | − | 0.923128i | \(-0.374377\pi\) | ||||
0.384492 | + | 0.923128i | \(0.374377\pi\) | |||||||
\(570\) | 23.3137 | + | 12.4853i | 0.976504 | + | 0.522951i | ||||
\(571\) | 34.4853 | 1.44316 | 0.721582 | − | 0.692329i | \(-0.243415\pi\) | ||||
0.721582 | + | 0.692329i | \(0.243415\pi\) | |||||||
\(572\) | −2.82843 | + | 2.82843i | −0.118262 | + | 0.118262i | ||||
\(573\) | 4.00000 | − | 2.82843i | 0.167102 | − | 0.118159i | ||||
\(574\) | 1.65685i | 0.0691558i | ||||||||
\(575\) | −2.82843 | − | 19.7990i | −0.117954 | − | 0.825675i | ||||
\(576\) | −2.82843 | − | 1.00000i | −0.117851 | − | 0.0416667i | ||||
\(577\) | −16.0416 | − | 16.0416i | −0.667822 | − | 0.667822i | 0.289390 | − | 0.957211i | \(-0.406548\pi\) |
−0.957211 | + | 0.289390i | \(0.906548\pi\) | |||||||
\(578\) | −0.707107 | − | 0.707107i | −0.0294118 | − | 0.0294118i | ||||
\(579\) | 27.5563 | + | 4.72792i | 1.14520 | + | 0.196486i | ||||
\(580\) | 12.7279 | + | 4.24264i | 0.528498 | + | 0.176166i | ||||
\(581\) | 8.00000i | 0.331896i | ||||||||
\(582\) | 12.8284 | + | 18.1421i | 0.531755 | + | 0.752016i | ||||
\(583\) | 2.34315 | − | 2.34315i | 0.0970432 | − | 0.0970432i | ||||
\(584\) | 15.6569 | 0.647885 | ||||||||
\(585\) | 6.65685 | − | 0.828427i | 0.275227 | − | 0.0342512i | ||||
\(586\) | 6.34315 | 0.262033 | ||||||||
\(587\) | 7.79899 | − | 7.79899i | 0.321899 | − | 0.321899i | −0.527596 | − | 0.849495i | \(-0.676907\pi\) |
0.849495 | + | 0.527596i | \(0.176907\pi\) | |||||||
\(588\) | −6.31371 | − | 8.92893i | −0.260373 | − | 0.368223i | ||||
\(589\) | − | 23.3137i | − | 0.960625i | ||||||
\(590\) | −4.48528 | − | 8.97056i | −0.184656 | − | 0.369312i | ||||
\(591\) | −9.07107 | − | 1.55635i | −0.373134 | − | 0.0640197i | ||||
\(592\) | 2.58579 | + | 2.58579i | 0.106275 | + | 0.106275i | ||||
\(593\) | −7.41421 | − | 7.41421i | −0.304465 | − | 0.304465i | 0.538293 | − | 0.842758i | \(-0.319069\pi\) |
−0.842758 | + | 0.538293i | \(0.819069\pi\) | |||||||
\(594\) | −18.1421 | − | 10.1421i | −0.744381 | − | 0.416137i | ||||
\(595\) | −2.48528 | + | 7.45584i | −0.101887 | + | 0.305660i | ||||
\(596\) | 22.3848i | 0.916916i | ||||||||
\(597\) | 31.3137 | − | 22.1421i | 1.28158 | − | 0.906217i | ||||
\(598\) | −2.82843 | + | 2.82843i | −0.115663 | + | 0.115663i | ||||
\(599\) | −16.4853 | −0.673570 | −0.336785 | − | 0.941582i | \(-0.609340\pi\) | ||||
−0.336785 | + | 0.941582i | \(0.609340\pi\) | |||||||
\(600\) | −6.29289 | + | 5.94975i | −0.256906 | + | 0.242897i | ||||
\(601\) | −17.6569 | −0.720238 | −0.360119 | − | 0.932906i | \(-0.617264\pi\) | ||||
−0.360119 | + | 0.932906i | \(0.617264\pi\) | |||||||
\(602\) | 1.02944 | − | 1.02944i | 0.0419567 | − | 0.0419567i | ||||
\(603\) | 3.17157 | − | 1.51472i | 0.129156 | − | 0.0616841i | ||||
\(604\) | − | 1.07107i | − | 0.0435811i | ||||||
\(605\) | 3.53553 | − | 10.6066i | 0.143740 | − | 0.431220i | ||||
\(606\) | −0.928932 | + | 5.41421i | −0.0377353 | + | 0.219937i | ||||
\(607\) | 14.4853 | + | 14.4853i | 0.587939 | + | 0.587939i | 0.937073 | − | 0.349134i | \(-0.113524\pi\) |
−0.349134 | + | 0.937073i | \(0.613524\pi\) | |||||||
\(608\) | 4.82843 | + | 4.82843i | 0.195819 | + | 0.195819i | ||||
\(609\) | −1.45584 | + | 8.48528i | −0.0589938 | + | 0.343841i | ||||
\(610\) | 4.82843 | + | 9.65685i | 0.195497 | + | 0.390995i | ||||
\(611\) | 3.17157i | 0.128308i | ||||||||
\(612\) | 11.4853 | − | 5.48528i | 0.464265 | − | 0.221729i | ||||
\(613\) | 10.3431 | − | 10.3431i | 0.417756 | − | 0.417756i | −0.466674 | − | 0.884430i | \(-0.654548\pi\) |
0.884430 | + | 0.466674i | \(0.154548\pi\) | |||||||
\(614\) | 10.1421 | 0.409303 | ||||||||
\(615\) | −2.24264 | − | 7.41421i | −0.0904320 | − | 0.298970i | ||||
\(616\) | 3.31371 | 0.133513 | ||||||||
\(617\) | 10.9289 | − | 10.9289i | 0.439982 | − | 0.439982i | −0.452024 | − | 0.892006i | \(-0.649298\pi\) |
0.892006 | + | 0.452024i | \(0.149298\pi\) | |||||||
\(618\) | 24.9706 | − | 17.6569i | 1.00446 | − | 0.710263i | ||||
\(619\) | 26.6274i | 1.07025i | 0.844774 | + | 0.535123i | \(0.179735\pi\) | ||||
−0.844774 | + | 0.535123i | \(0.820265\pi\) | |||||||
\(620\) | 7.24264 | + | 2.41421i | 0.290871 | + | 0.0969571i | ||||
\(621\) | −18.1421 | − | 10.1421i | −0.728019 | − | 0.406990i | ||||
\(622\) | −19.7990 | − | 19.7990i | −0.793867 | − | 0.793867i | ||||
\(623\) | −6.54416 | − | 6.54416i | −0.262186 | − | 0.262186i | ||||
\(624\) | 1.70711 | + | 0.292893i | 0.0683390 | + | 0.0117251i | ||||
\(625\) | 7.00000 | + | 24.0000i | 0.280000 | + | 0.960000i | ||||
\(626\) | − | 1.89949i | − | 0.0759191i | ||||||
\(627\) | 27.3137 | + | 38.6274i | 1.09080 | + | 1.54263i | ||||
\(628\) | 16.2426 | − | 16.2426i | 0.648152 | − | 0.648152i | ||||
\(629\) | −15.5147 | −0.618612 | ||||||||
\(630\) | −4.38478 | − | 3.41421i | −0.174694 | − | 0.136026i | ||||
\(631\) | 23.8995 | 0.951424 | 0.475712 | − | 0.879601i | \(-0.342190\pi\) | ||||
0.475712 | + | 0.879601i | \(0.342190\pi\) | |||||||
\(632\) | −8.82843 | + | 8.82843i | −0.351176 | + | 0.351176i | ||||
\(633\) | 1.65685 | + | 2.34315i | 0.0658540 | + | 0.0931317i | ||||
\(634\) | − | 2.34315i | − | 0.0930582i | ||||||
\(635\) | 8.97056 | − | 4.48528i | 0.355986 | − | 0.177993i | ||||
\(636\) | −1.41421 | − | 0.242641i | −0.0560772 | − | 0.00962133i | ||||
\(637\) | 4.46447 | + | 4.46447i | 0.176889 | + | 0.176889i | ||||
\(638\) | 16.9706 | + | 16.9706i | 0.671871 | + | 0.671871i | ||||
\(639\) | 40.2843 | + | 14.2426i | 1.59362 | + | 0.563430i | ||||
\(640\) | −2.00000 | + | 1.00000i | −0.0790569 | + | 0.0395285i | ||||
\(641\) | 10.6863i | 0.422083i | 0.977477 | + | 0.211042i | \(0.0676855\pi\) | ||||
−0.977477 | + | 0.211042i | \(0.932314\pi\) | |||||||
\(642\) | −24.1421 | + | 17.0711i | −0.952814 | + | 0.673741i | ||||
\(643\) | 22.1421 | − | 22.1421i | 0.873201 | − | 0.873201i | −0.119619 | − | 0.992820i | \(-0.538167\pi\) |
0.992820 | + | 0.119619i | \(0.0381674\pi\) | |||||||
\(644\) | 3.31371 | 0.130578 | ||||||||
\(645\) | −3.21320 | + | 6.00000i | −0.126520 | + | 0.236250i | ||||
\(646\) | −28.9706 | −1.13983 | ||||||||
\(647\) | −29.3137 | + | 29.3137i | −1.15244 | + | 1.15244i | −0.166379 | + | 0.986062i | \(0.553207\pi\) |
−0.986062 | + | 0.166379i | \(0.946793\pi\) | |||||||
\(648\) | 0.949747 | + | 8.94975i | 0.0373096 | + | 0.351579i | ||||
\(649\) | − | 17.9411i | − | 0.704251i | ||||||
\(650\) | 3.00000 | − | 4.00000i | 0.117670 | − | 0.156893i | ||||
\(651\) | −0.828427 | + | 4.82843i | −0.0324686 | + | 0.189241i | ||||
\(652\) | −2.34315 | − | 2.34315i | −0.0917647 | − | 0.0917647i | ||||
\(653\) | 4.24264 | + | 4.24264i | 0.166027 | + | 0.166027i | 0.785231 | − | 0.619203i | \(-0.212544\pi\) |
−0.619203 | + | 0.785231i | \(0.712544\pi\) | |||||||
\(654\) | −1.44365 | + | 8.41421i | −0.0564512 | + | 0.329022i | ||||
\(655\) | 27.5147 | + | 9.17157i | 1.07509 | + | 0.358363i | ||||
\(656\) | − | 2.00000i | − | 0.0780869i | ||||||
\(657\) | −20.2426 | − | 42.3848i | −0.789741 | − | 1.65359i | ||||
\(658\) | 1.85786 | − | 1.85786i | 0.0724271 | − | 0.0724271i | ||||
\(659\) | 25.5147 | 0.993912 | 0.496956 | − | 0.867776i | \(-0.334451\pi\) | ||||
0.496956 | + | 0.867776i | \(0.334451\pi\) | |||||||
\(660\) | −14.8284 | + | 4.48528i | −0.577196 | + | 0.174589i | ||||
\(661\) | 48.5269 | 1.88748 | 0.943739 | − | 0.330691i | \(-0.107282\pi\) | ||||
0.943739 | + | 0.330691i | \(0.107282\pi\) | |||||||
\(662\) | −22.8284 | + | 22.8284i | −0.887252 | + | 0.887252i | ||||
\(663\) | −6.00000 | + | 4.24264i | −0.233021 | + | 0.164771i | ||||
\(664\) | − | 9.65685i | − | 0.374759i | ||||||
\(665\) | 5.65685 | + | 11.3137i | 0.219363 | + | 0.438727i | ||||
\(666\) | 3.65685 | − | 10.3431i | 0.141700 | − | 0.400789i | ||||
\(667\) | 16.9706 | + | 16.9706i | 0.657103 | + | 0.657103i | ||||
\(668\) | 3.41421 | + | 3.41421i | 0.132100 | + | 0.132100i | ||||
\(669\) | −23.3137 | − | 4.00000i | −0.901360 | − | 0.154649i | ||||
\(670\) | 0.828427 | − | 2.48528i | 0.0320049 | − | 0.0960148i | ||||
\(671\) | 19.3137i | 0.745597i | ||||||||
\(672\) | −0.828427 | − | 1.17157i | −0.0319573 | − | 0.0451944i | ||||
\(673\) | −2.85786 | + | 2.85786i | −0.110163 | + | 0.110163i | −0.760039 | − | 0.649877i | \(-0.774820\pi\) |
0.649877 | + | 0.760039i | \(0.274820\pi\) | |||||||
\(674\) | −32.5269 | −1.25289 | ||||||||
\(675\) | 24.2426 | + | 9.34315i | 0.933100 | + | 0.359618i | ||||
\(676\) | −1.00000 | −0.0384615 | ||||||||
\(677\) | −10.3848 | + | 10.3848i | −0.399119 | + | 0.399119i | −0.877922 | − | 0.478803i | \(-0.841071\pi\) |
0.478803 | + | 0.877922i | \(0.341071\pi\) | |||||||
\(678\) | −9.89949 | − | 14.0000i | −0.380188 | − | 0.537667i | ||||
\(679\) | 10.6274i | 0.407843i | ||||||||
\(680\) | 3.00000 | − | 9.00000i | 0.115045 | − | 0.345134i | ||||
\(681\) | −4.82843 | − | 0.828427i | −0.185026 | − | 0.0317454i | ||||
\(682\) | 9.65685 | + | 9.65685i | 0.369780 | + | 0.369780i | ||||
\(683\) | −8.82843 | − | 8.82843i | −0.337810 | − | 0.337810i | 0.517732 | − | 0.855543i | \(-0.326776\pi\) |
−0.855543 | + | 0.517732i | \(0.826776\pi\) | |||||||
\(684\) | 6.82843 | − | 19.3137i | 0.261091 | − | 0.738478i | ||||
\(685\) | −21.3137 | − | 42.6274i | −0.814355 | − | 1.62871i | ||||
\(686\) | − | 11.0294i | − | 0.421106i | ||||||
\(687\) | −25.3137 | + | 17.8995i | −0.965778 | + | 0.682908i | ||||
\(688\) | −1.24264 | + | 1.24264i | −0.0473752 | + | 0.0473752i | ||||
\(689\) | 0.828427 | 0.0315606 | ||||||||
\(690\) | −14.8284 | + | 4.48528i | −0.564509 | + | 0.170752i | ||||
\(691\) | −37.6569 | −1.43253 | −0.716267 | − | 0.697826i | \(-0.754151\pi\) | ||||
−0.716267 | + | 0.697826i | \(0.754151\pi\) | |||||||
\(692\) | 17.0711 | − | 17.0711i | 0.648945 | − | 0.648945i | ||||
\(693\) | −4.28427 | − | 8.97056i | −0.162746 | − | 0.340764i | ||||
\(694\) | 14.9289i | 0.566695i | ||||||||
\(695\) | −3.51472 | − | 1.17157i | −0.133321 | − | 0.0444403i | ||||
\(696\) | 1.75736 | − | 10.2426i | 0.0666125 | − | 0.388246i | ||||
\(697\) | 6.00000 | + | 6.00000i | 0.227266 | + | 0.227266i | ||||
\(698\) | 23.1421 | + | 23.1421i | 0.875943 | + | 0.875943i | ||||
\(699\) | −3.58579 | + | 20.8995i | −0.135627 | + | 0.790491i | ||||
\(700\) | −4.10051 | + | 0.585786i | −0.154985 | + | 0.0221406i | ||||
\(701\) | − | 35.4558i | − | 1.33915i | −0.742745 | − | 0.669574i | \(-0.766477\pi\) | ||
0.742745 | − | 0.669574i | \(-0.233523\pi\) | |||||||
\(702\) | −1.41421 | − | 5.00000i | −0.0533761 | − | 0.188713i | ||||
\(703\) | −17.6569 | + | 17.6569i | −0.665941 | + | 0.665941i | ||||
\(704\) | −4.00000 | −0.150756 | ||||||||
\(705\) | −5.79899 | + | 10.8284i | −0.218403 | + | 0.407822i | ||||
\(706\) | −36.1421 | −1.36023 | ||||||||
\(707\) | −1.85786 | + | 1.85786i | −0.0698722 | + | 0.0698722i | ||||
\(708\) | −6.34315 | + | 4.48528i | −0.238390 | + | 0.168567i | ||||
\(709\) | 3.27208i | 0.122885i | 0.998111 | + | 0.0614427i | \(0.0195702\pi\) | ||||
−0.998111 | + | 0.0614427i | \(0.980430\pi\) | |||||||
\(710\) | 28.4853 | − | 14.2426i | 1.06903 | − | 0.534517i | ||||
\(711\) | 35.3137 | + | 12.4853i | 1.32437 | + | 0.468235i | ||||
\(712\) | 7.89949 | + | 7.89949i | 0.296046 | + | 0.296046i | ||||
\(713\) | 9.65685 | + | 9.65685i | 0.361652 | + | 0.361652i | ||||
\(714\) | 6.00000 | + | 1.02944i | 0.224544 | + | 0.0385257i | ||||
\(715\) | 8.00000 | − | 4.00000i | 0.299183 | − | 0.149592i | ||||
\(716\) | − | 17.6569i | − | 0.659868i | ||||||
\(717\) | 19.8995 | + | 28.1421i | 0.743160 | + | 1.05099i | ||||
\(718\) | −16.5563 | + | 16.5563i | −0.617877 | + | 0.617877i | ||||
\(719\) | −12.4853 | −0.465622 | −0.232811 | − | 0.972522i | \(-0.574792\pi\) | ||||
−0.232811 | + | 0.972522i | \(0.574792\pi\) | |||||||
\(720\) | 5.29289 | + | 4.12132i | 0.197254 | + | 0.153593i | ||||
\(721\) | 14.6274 | 0.544753 | ||||||||
\(722\) | −19.5355 | + | 19.5355i | −0.727037 | + | 0.727037i | ||||
\(723\) | −3.65685 | − | 5.17157i | −0.136000 | − | 0.192333i | ||||
\(724\) | − | 6.00000i | − | 0.222988i | ||||||
\(725\) | −24.0000 | − | 18.0000i | −0.891338 | − | 0.668503i | ||||
\(726\) | −8.53553 | − | 1.46447i | −0.316783 | − | 0.0543514i | ||||
\(727\) | −25.3137 | − | 25.3137i | −0.938833 | − | 0.938833i | 0.0594007 | − | 0.998234i | \(-0.481081\pi\) |
−0.998234 | + | 0.0594007i | \(0.981081\pi\) | |||||||
\(728\) | 0.585786 | + | 0.585786i | 0.0217107 | + | 0.0217107i | ||||
\(729\) | 23.0000 | − | 14.1421i | 0.851852 | − | 0.523783i | ||||
\(730\) | −33.2132 | − | 11.0711i | −1.22928 | − | 0.409759i | ||||
\(731\) | − | 7.45584i | − | 0.275764i | ||||||
\(732\) | 6.82843 | − | 4.82843i | 0.252386 | − | 0.178464i | ||||
\(733\) | −15.5563 | + | 15.5563i | −0.574587 | + | 0.574587i | −0.933407 | − | 0.358820i | \(-0.883179\pi\) |
0.358820 | + | 0.933407i | \(0.383179\pi\) | |||||||
\(734\) | 20.0000 | 0.738213 | ||||||||
\(735\) | 7.07969 | + | 23.4056i | 0.261138 | + | 0.863328i | ||||
\(736\) | −4.00000 | −0.147442 | ||||||||
\(737\) | 3.31371 | − | 3.31371i | 0.122062 | − | 0.122062i | ||||
\(738\) | −5.41421 | + | 2.58579i | −0.199300 | + | 0.0951841i | ||||
\(739\) | − | 10.1421i | − | 0.373084i | −0.982447 | − | 0.186542i | \(-0.940272\pi\) | ||
0.982447 | − | 0.186542i | \(-0.0597281\pi\) | |||||||
\(740\) | −3.65685 | − | 7.31371i | −0.134429 | − | 0.268857i | ||||
\(741\) | −2.00000 | + | 11.6569i | −0.0734718 | + | 0.428225i | ||||
\(742\) | −0.485281 | − | 0.485281i | −0.0178152 | − | 0.0178152i | ||||
\(743\) | −10.6274 | − | 10.6274i | −0.389882 | − | 0.389882i | 0.484763 | − | 0.874645i | \(-0.338906\pi\) |
−0.874645 | + | 0.484763i | \(0.838906\pi\) | |||||||
\(744\) | 1.00000 | − | 5.82843i | 0.0366618 | − | 0.213681i | ||||
\(745\) | 15.8284 | − | 47.4853i | 0.579909 | − | 1.73973i | ||||
\(746\) | − | 6.97056i | − | 0.255210i | ||||||
\(747\) | −26.1421 | + | 12.4853i | −0.956491 | + | 0.456813i | ||||
\(748\) | 12.0000 | − | 12.0000i | 0.438763 | − | 0.438763i | ||||
\(749\) | −14.1421 | −0.516742 | ||||||||
\(750\) | 17.5563 | − | 8.17157i | 0.641067 | − | 0.298384i | ||||
\(751\) | 36.2843 | 1.32403 | 0.662016 | − | 0.749490i | \(-0.269701\pi\) | ||||
0.662016 | + | 0.749490i | \(0.269701\pi\) | |||||||
\(752\) | −2.24264 | + | 2.24264i | −0.0817807 | + | 0.0817807i | ||||
\(753\) | 20.2843 | − | 14.3431i | 0.739200 | − | 0.522693i | ||||
\(754\) | 6.00000i | 0.218507i | ||||||||
\(755\) | −0.757359 | + | 2.27208i | −0.0275631 | + | 0.0826894i | ||||
\(756\) | −2.10051 | + | 3.75736i | −0.0763946 | + | 0.136654i | ||||
\(757\) | 3.41421 | + | 3.41421i | 0.124092 | + | 0.124092i | 0.766425 | − | 0.642334i | \(-0.222034\pi\) |
−0.642334 | + | 0.766425i | \(0.722034\pi\) | |||||||
\(758\) | −26.9706 | − | 26.9706i | −0.979615 | − | 0.979615i | ||||
\(759\) | −27.3137 | − | 4.68629i | −0.991425 | − | 0.170102i | ||||
\(760\) | −6.82843 | − | 13.6569i | −0.247693 | − | 0.495386i | ||||
\(761\) | 26.4853i | 0.960091i | 0.877244 | + | 0.480045i | \(0.159380\pi\) | ||||
−0.877244 | + | 0.480045i | \(0.840620\pi\) | |||||||
\(762\) | −4.48528 | − | 6.34315i | −0.162485 | − | 0.229788i | ||||
\(763\) | −2.88730 | + | 2.88730i | −0.104527 | + | 0.104527i | ||||
\(764\) | −2.82843 | −0.102329 | ||||||||
\(765\) | −28.2426 | + | 3.51472i | −1.02111 | + | 0.127075i | ||||
\(766\) | −2.34315 | −0.0846613 | ||||||||
\(767\) | 3.17157 | − | 3.17157i | 0.114519 | − | 0.114519i | ||||
\(768\) | 1.00000 | + | 1.41421i | 0.0360844 | + | 0.0510310i | ||||
\(769\) | 8.62742i | 0.311113i | 0.987827 | + | 0.155556i | \(0.0497170\pi\) | ||||
−0.987827 | + | 0.155556i | \(0.950283\pi\) | |||||||
\(770\) | −7.02944 | − | 2.34315i | −0.253323 | − | 0.0844411i | ||||
\(771\) | −16.8995 | − | 2.89949i | −0.608620 | − | 0.104423i | ||||
\(772\) | −11.4142 | − | 11.4142i | −0.410807 | − | 0.410807i | ||||
\(773\) | 16.2426 | + | 16.2426i | 0.584207 | + | 0.584207i | 0.936057 | − | 0.351849i | \(-0.114447\pi\) |
−0.351849 | + | 0.936057i | \(0.614447\pi\) | |||||||
\(774\) | 4.97056 | + | 1.75736i | 0.178663 | + | 0.0631670i | ||||
\(775\) | −13.6569 | − | 10.2426i | −0.490569 | − | 0.367927i | ||||
\(776\) | − | 12.8284i | − | 0.460514i | ||||||
\(777\) | 4.28427 | − | 3.02944i | 0.153697 | − | 0.108680i | ||||
\(778\) | 1.41421 | − | 1.41421i | 0.0507020 | − | 0.0507020i | ||||
\(779\) | 13.6569 | 0.489308 | ||||||||
\(780\) | −3.41421 | − | 1.82843i | −0.122248 | − | 0.0654682i | ||||
\(781\) | 56.9706 | 2.03857 | ||||||||
\(782\) | 12.0000 | − | 12.0000i | 0.429119 | − | 0.429119i | ||||
\(783\) | −30.0000 | + | 8.48528i | −1.07211 | + | 0.303239i | ||||
\(784\) | 6.31371i | 0.225490i | ||||||||
\(785\) | −45.9411 | + | 22.9706i | −1.63971 | + | 0.819855i | ||||
\(786\) | 3.79899 | − | 22.1421i | 0.135505 | − | 0.789784i | ||||
\(787\) | −5.79899 | − | 5.79899i | −0.206712 | − | 0.206712i | 0.596157 | − | 0.802868i | \(-0.296694\pi\) |
−0.802868 | + | 0.596157i | \(0.796694\pi\) | |||||||
\(788\) | 3.75736 | + | 3.75736i | 0.133850 | + | 0.133850i | ||||
\(789\) | 6.62742 | − | 38.6274i | 0.235942 | − | 1.37517i | ||||
\(790\) | 24.9706 | − | 12.4853i | 0.888413 | − | 0.444206i | ||||
\(791\) | − | 8.20101i | − | 0.291594i | ||||||
\(792\) | 5.17157 | + | 10.8284i | 0.183764 | + | 0.384771i | ||||
\(793\) | −3.41421 | + | 3.41421i | −0.121242 | + | 0.121242i | ||||
\(794\) | −12.9706 | −0.460308 | ||||||||
\(795\) | 2.82843 | + | 1.51472i | 0.100314 | + | 0.0537215i | ||||
\(796\) | −22.1421 | −0.784807 | ||||||||
\(797\) | 6.92893 | − | 6.92893i | 0.245435 | − | 0.245435i | −0.573659 | − | 0.819094i | \(-0.694476\pi\) |
0.819094 | + | 0.573659i | \(0.194476\pi\) | |||||||
\(798\) | 8.00000 | − | 5.65685i | 0.283197 | − | 0.200250i | ||||
\(799\) | − | 13.4558i | − | 0.476034i | ||||||
\(800\) | 4.94975 | − | 0.707107i | 0.175000 | − | 0.0250000i | ||||
\(801\) | 11.1716 | − | 31.5980i | 0.394728 | − | 1.11646i | ||||
\(802\) | 1.27208 | + | 1.27208i | 0.0449186 | + | 0.0449186i | ||||
\(803\) | −44.2843 | − | 44.2843i | −1.56276 | − | 1.56276i | ||||
\(804\) | −2.00000 | − | 0.343146i | −0.0705346 | − | 0.0121018i | ||||
\(805\) | −7.02944 | − | 2.34315i | −0.247755 | − | 0.0825850i | ||||
\(806\) | 3.41421i | 0.120261i | ||||||||
\(807\) | −15.1716 | − | 21.4558i | −0.534065 | − | 0.755281i | ||||
\(808\) | 2.24264 | − | 2.24264i | 0.0788958 | − | 0.0788958i | ||||
\(809\) | −22.6274 | −0.795538 | −0.397769 | − | 0.917486i | \(-0.630215\pi\) | ||||
−0.397769 | + | 0.917486i | \(0.630215\pi\) | |||||||
\(810\) | 4.31371 | − | 19.6569i | 0.151568 | − | 0.690671i | ||||
\(811\) | 22.1421 | 0.777516 | 0.388758 | − | 0.921340i | \(-0.372904\pi\) | ||||
0.388758 | + | 0.921340i | \(0.372904\pi\) | |||||||
\(812\) | 3.51472 | − | 3.51472i | 0.123342 | − | 0.123342i | ||||
\(813\) | −2.24264 | − | 3.17157i | −0.0786528 | − | 0.111232i | ||||
\(814\) | − | 14.6274i | − | 0.512691i | ||||||
\(815\) | 3.31371 | + | 6.62742i | 0.116074 | + | 0.232148i | ||||
\(816\) | −7.24264 | − | 1.24264i | −0.253543 | − | 0.0435011i | ||||
\(817\) | −8.48528 | − | 8.48528i | −0.296862 | − | 0.296862i | ||||
\(818\) | −2.24264 | − | 2.24264i | −0.0784121 | − | 0.0784121i | ||||
\(819\) | 0.828427 | − | 2.34315i | 0.0289476 | − | 0.0818761i | ||||
\(820\) | −1.41421 | + | 4.24264i | −0.0493865 | + | 0.148159i | ||||
\(821\) | 13.6985i | 0.478080i | 0.971010 | + | 0.239040i | \(0.0768328\pi\) | ||||
−0.971010 | + | 0.239040i | \(0.923167\pi\) | |||||||
\(822\) | −30.1421 | + | 21.3137i | −1.05133 | + | 0.743401i | ||||
\(823\) | −33.3137 | + | 33.3137i | −1.16124 | + | 1.16124i | −0.177039 | + | 0.984204i | \(0.556652\pi\) |
−0.984204 | + | 0.177039i | \(0.943348\pi\) | |||||||
\(824\) | −17.6569 | −0.615106 | ||||||||
\(825\) | 34.6274 | + | 0.970563i | 1.20557 | + | 0.0337907i | ||||
\(826\) | −3.71573 | −0.129287 | ||||||||
\(827\) | 32.8284 | − | 32.8284i | 1.14156 | − | 1.14156i | 0.153391 | − | 0.988166i | \(-0.450981\pi\) |
0.988166 | − | 0.153391i | \(-0.0490193\pi\) | |||||||
\(828\) | 5.17157 | + | 10.8284i | 0.179725 | + | 0.376314i | ||||
\(829\) | − | 37.5147i | − | 1.30294i | −0.758674 | − | 0.651470i | \(-0.774153\pi\) | ||
0.758674 | − | 0.651470i | \(-0.225847\pi\) | |||||||
\(830\) | −6.82843 | + | 20.4853i | −0.237018 | + | 0.711054i | ||||
\(831\) | 6.58579 | − | 38.3848i | 0.228458 | − | 1.33155i | ||||
\(832\) | −0.707107 | − | 0.707107i | −0.0245145 | − | 0.0245145i | ||||
\(833\) | −18.9411 | − | 18.9411i | −0.656271 | − | 0.656271i | ||||
\(834\) | −0.485281 | + | 2.82843i | −0.0168039 | + | 0.0979404i | ||||
\(835\) | −4.82843 | − | 9.65685i | −0.167095 | − | 0.334189i | ||||
\(836\) | − | 27.3137i | − | 0.944664i | ||||||
\(837\) | −17.0711 | + | 4.82843i | −0.590062 | + | 0.166895i | ||||
\(838\) | 3.89949 | − | 3.89949i | 0.134706 | − | 0.134706i | ||||
\(839\) | 20.1005 | 0.693946 | 0.346973 | − | 0.937875i | \(-0.387209\pi\) | ||||
0.346973 | + | 0.937875i | \(0.387209\pi\) | |||||||
\(840\) | 0.928932 | + | 3.07107i | 0.0320512 | + | 0.105962i | ||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 19.1421 | − | 19.1421i | 0.659682 | − | 0.659682i | ||||
\(843\) | −1.17157 | + | 0.828427i | −0.0403511 | + | 0.0285325i | ||||
\(844\) | − | 1.65685i | − | 0.0570313i | ||||||
\(845\) | 2.12132 | + | 0.707107i | 0.0729756 | + | 0.0243252i | ||||
\(846\) | 8.97056 | + | 3.17157i | 0.308414 | + | 0.109041i | ||||
\(847\) | −2.92893 | − | 2.92893i | −0.100639 | − | 0.100639i | ||||
\(848\) | 0.585786 | + | 0.585786i | 0.0201160 | + | 0.0201160i | ||||
\(849\) | −41.6274 | − | 7.14214i | −1.42865 | − | 0.245117i | ||||
\(850\) | −12.7279 | + | 16.9706i | −0.436564 | + | 0.582086i | ||||
\(851\) | − | 14.6274i | − | 0.501421i | ||||||
\(852\) | −14.2426 | − | 20.1421i | −0.487945 | − | 0.690058i | ||||
\(853\) | −7.02944 | + | 7.02944i | −0.240683 | + | 0.240683i | −0.817133 | − | 0.576449i | \(-0.804438\pi\) |
0.576449 | + | 0.817133i | \(0.304438\pi\) | |||||||
\(854\) | 4.00000 | 0.136877 | ||||||||
\(855\) | −28.1421 | + | 36.1421i | −0.962441 | + | 1.23603i | ||||
\(856\) | 17.0711 | 0.583477 | ||||||||
\(857\) | 20.1716 | − | 20.1716i | 0.689048 | − | 0.689048i | −0.272974 | − | 0.962021i | \(-0.588007\pi\) |
0.962021 | + | 0.272974i | \(0.0880072\pi\) | |||||||
\(858\) | −4.00000 | − | 5.65685i | −0.136558 | − | 0.193122i | ||||
\(859\) | 37.7990i | 1.28968i | 0.764316 | + | 0.644842i | \(0.223077\pi\) | ||||
−0.764316 | + | 0.644842i | \(0.776923\pi\) | |||||||
\(860\) | 3.51472 | − | 1.75736i | 0.119851 | − | 0.0599255i | ||||
\(861\) | −2.82843 | − | 0.485281i | −0.0963925 | − | 0.0165383i | ||||
\(862\) | 7.72792 | + | 7.72792i | 0.263214 | + | 0.263214i | ||||
\(863\) | −22.2426 | − | 22.2426i | −0.757148 | − | 0.757148i | 0.218654 | − | 0.975802i | \(-0.429833\pi\) |
−0.975802 | + | 0.218654i | \(0.929833\pi\) | |||||||
\(864\) | 2.53553 | − | 4.53553i | 0.0862606 | − | 0.154302i | ||||
\(865\) | −48.2843 | + | 24.1421i | −1.64171 | + | 0.820857i | ||||
\(866\) | 23.0711i | 0.783987i | ||||||||
\(867\) | 1.41421 | − | 1.00000i | 0.0480292 | − | 0.0339618i | ||||
\(868\) | 2.00000 | − | 2.00000i | 0.0678844 | − | 0.0678844i | ||||
\(869\) | 49.9411 | 1.69414 | ||||||||
\(870\) | −10.9706 | + | 20.4853i | −0.371937 | + | 0.694516i | ||||
\(871\) | 1.17157 | 0.0396972 | ||||||||
\(872\) | 3.48528 | − | 3.48528i | 0.118027 | − | 0.118027i | ||||
\(873\) | −34.7279 | + | 16.5858i | −1.17536 | + | 0.561344i | ||||
\(874\) | − | 27.3137i | − | 0.923900i | ||||||
\(875\) | 9.11270 | + | 1.65685i | 0.308065 | + | 0.0560119i | ||||
\(876\) | −4.58579 | + | 26.7279i | −0.154939 | + | 0.903053i | ||||
\(877\) | 35.3137 | + | 35.3137i | 1.19246 | + | 1.19246i | 0.976375 | + | 0.216085i | \(0.0693287\pi\) |
0.216085 | + | 0.976375i | \(0.430671\pi\) | |||||||
\(878\) | 12.9706 | + | 12.9706i | 0.437735 | + | 0.437735i | ||||
\(879\) | −1.85786 | + | 10.8284i | −0.0626642 | + | 0.365234i | ||||
\(880\) | 8.48528 | + | 2.82843i | 0.286039 | + | 0.0953463i | ||||
\(881\) | 14.0000i | 0.471672i | 0.971793 | + | 0.235836i | \(0.0757828\pi\) | ||||
−0.971793 | + | 0.235836i | \(0.924217\pi\) | |||||||
\(882\) | 17.0919 | − | 8.16295i | 0.575514 | − | 0.274861i | ||||
\(883\) | 22.2132 | − | 22.2132i | 0.747534 | − | 0.747534i | −0.226482 | − | 0.974015i | \(-0.572722\pi\) |
0.974015 | + | 0.226482i | \(0.0727223\pi\) | |||||||
\(884\) | 4.24264 | 0.142695 | ||||||||
\(885\) | 16.6274 | − | 5.02944i | 0.558925 | − | 0.169063i | ||||
\(886\) | 1.27208 | 0.0427363 | ||||||||
\(887\) | 4.00000 | − | 4.00000i | 0.134307 | − | 0.134307i | −0.636757 | − | 0.771064i | \(-0.719725\pi\) |
0.771064 | + | 0.636757i | \(0.219725\pi\) | |||||||
\(888\) | −5.17157 | + | 3.65685i | −0.173547 | + | 0.122716i | ||||
\(889\) | − | 3.71573i | − | 0.124622i | ||||||
\(890\) | −11.1716 | − | 22.3431i | −0.374472 | − | 0.748944i | ||||
\(891\) | 22.6274 | − | 28.0000i | 0.758047 | − | 0.938035i | ||||
\(892\) | 9.65685 | + | 9.65685i | 0.323335 | + | 0.323335i | ||||
\(893\) | −15.3137 | − | 15.3137i | −0.512454 | − | 0.512454i | ||||
\(894\) | −38.2132 | − | 6.55635i | −1.27804 | − | 0.219277i | ||||
\(895\) | −12.4853 | + | 37.4558i | −0.417337 | + | 1.25201i | ||||
\(896\) | 0.828427i | 0.0276758i | ||||||||
\(897\) | −4.00000 | − | 5.65685i | −0.133556 | − | 0.188877i | ||||
\(898\) | −12.5858 | + | 12.5858i | −0.419993 | + | 0.419993i | ||||
\(899\) | 20.4853 | 0.683222 | ||||||||
\(900\) | −8.31371 | − | 12.4853i | −0.277124 | − | 0.416176i | ||||
\(901\) | −3.51472 | −0.117092 | ||||||||
\(902\) | −5.65685 | + | 5.65685i | −0.188353 | + | 0.188353i | ||||
\(903\) | 1.45584 | + | 2.05887i | 0.0484475 | + | 0.0685151i | ||||
\(904\) | 9.89949i | 0.329252i | ||||||||
\(905\) | −4.24264 | + | 12.7279i | −0.141030 | + | 0.423090i | ||||
\(906\) | 1.82843 | + | 0.313708i | 0.0607454 | + | 0.0104223i | ||||
\(907\) | 5.10051 | + | 5.10051i | 0.169359 | + | 0.169359i | 0.786698 | − | 0.617338i | \(-0.211789\pi\) |
−0.617338 | + | 0.786698i | \(0.711789\pi\) | |||||||
\(908\) | 2.00000 | + | 2.00000i | 0.0663723 | + | 0.0663723i | ||||
\(909\) | −8.97056 | − | 3.17157i | −0.297535 | − | 0.105194i | ||||
\(910\) | −0.828427 | − | 1.65685i | −0.0274621 | − | 0.0549242i | ||||
\(911\) | − | 1.85786i | − | 0.0615538i | −0.999526 | − | 0.0307769i | \(-0.990202\pi\) | ||
0.999526 | − | 0.0307769i | \(-0.00979814\pi\) | |||||||
\(912\) | −9.65685 | + | 6.82843i | −0.319770 | + | 0.226112i | ||||
\(913\) | −27.3137 | + | 27.3137i | −0.903952 | + | 0.903952i | ||||
\(914\) | −29.7990 | −0.985663 | ||||||||
\(915\) | −17.8995 | + | 5.41421i | −0.591739 | + | 0.178988i | ||||
\(916\) | 17.8995 | 0.591416 | ||||||||
\(917\) | 7.59798 | − | 7.59798i | 0.250907 | − | 0.250907i | ||||
\(918\) | 6.00000 | + | 21.2132i | 0.198030 | + | 0.700140i | ||||
\(919\) | − | 9.94113i | − | 0.327927i | −0.986466 | − | 0.163964i | \(-0.947572\pi\) | ||
0.986466 | − | 0.163964i | \(-0.0524280\pi\) | |||||||
\(920\) | 8.48528 | + | 2.82843i | 0.279751 | + | 0.0932505i | ||||
\(921\) | −2.97056 | + | 17.3137i | −0.0978834 | + | 0.570506i | ||||
\(922\) | −15.3431 | − | 15.3431i | −0.505300 | − | 0.505300i | ||||
\(923\) | 10.0711 | + | 10.0711i | 0.331493 | + | 0.331493i | ||||
\(924\) | −0.970563 | + | 5.65685i | −0.0319292 | + | 0.186097i | ||||
\(925\) | 2.58579 | + | 18.1005i | 0.0850201 | + | 0.595141i | ||||
\(926\) | − | 8.00000i | − | 0.262896i | ||||||
\(927\) | 22.8284 | + | 47.7990i | 0.749784 | + | 1.56992i | ||||
\(928\) | −4.24264 | + | 4.24264i | −0.139272 | + | 0.139272i | ||||
\(929\) | 57.1127 | 1.87381 | 0.936903 | − | 0.349588i | \(-0.113679\pi\) | ||||
0.936903 | + | 0.349588i | \(0.113679\pi\) | |||||||
\(930\) | −6.24264 | + | 11.6569i | −0.204704 | + | 0.382243i | ||||
\(931\) | −43.1127 | −1.41296 | ||||||||
\(932\) | 8.65685 | − | 8.65685i | 0.283565 | − | 0.283565i | ||||
\(933\) | 39.5980 | − | 28.0000i | 1.29638 | − | 0.916679i | ||||
\(934\) | 23.8995i | 0.782015i | ||||||||
\(935\) | −33.9411 | + | 16.9706i | −1.10999 | + | 0.554997i | ||||
\(936\) | −1.00000 | + | 2.82843i | −0.0326860 | + | 0.0924500i | ||||
\(937\) | 31.9706 | + | 31.9706i | 1.04443 | + | 1.04443i | 0.998966 | + | 0.0454669i | \(0.0144776\pi\) |
0.0454669 | + | 0.998966i | \(0.485522\pi\) | |||||||
\(938\) | −0.686292 | − | 0.686292i | −0.0224082 | − | 0.0224082i | ||||
\(939\) | 3.24264 | + | 0.556349i | 0.105820 | + | 0.0181558i | ||||
\(940\) | 6.34315 | − | 3.17157i | 0.206891 | − | 0.103445i | ||||
\(941\) | − | 38.8701i | − | 1.26713i | −0.773690 | − | 0.633564i | \(-0.781591\pi\) | ||
0.773690 | − | 0.633564i | \(-0.218409\pi\) | |||||||
\(942\) | 22.9706 | + | 32.4853i | 0.748421 | + | 1.05843i | ||||
\(943\) | −5.65685 | + | 5.65685i | −0.184213 | + | 0.184213i | ||||
\(944\) | 4.48528 | 0.145983 | ||||||||
\(945\) | 7.11270 | − | 6.48528i | 0.231376 | − | 0.210966i | ||||
\(946\) | 7.02944 | 0.228547 | ||||||||
\(947\) | 12.6274 | − | 12.6274i | 0.410336 | − | 0.410336i | −0.471520 | − | 0.881856i | \(-0.656294\pi\) |
0.881856 | + | 0.471520i | \(0.156294\pi\) | |||||||
\(948\) | −12.4853 | − | 17.6569i | −0.405503 | − | 0.573468i | ||||
\(949\) | − | 15.6569i | − | 0.508243i | ||||||
\(950\) | 4.82843 | + | 33.7990i | 0.156655 | + | 1.09658i | ||||
\(951\) | 4.00000 | + | 0.686292i | 0.129709 | + | 0.0222545i | ||||
\(952\) | −2.48528 | − | 2.48528i | −0.0805484 | − | 0.0805484i | ||||
\(953\) | −4.51472 | − | 4.51472i | −0.146246 | − | 0.146246i | 0.630193 | − | 0.776439i | \(-0.282976\pi\) |
−0.776439 | + | 0.630193i | \(0.782976\pi\) | |||||||
\(954\) | 0.828427 | − | 2.34315i | 0.0268213 | − | 0.0758621i | ||||
\(955\) | 6.00000 | + | 2.00000i | 0.194155 | + | 0.0647185i | ||||
\(956\) | − | 19.8995i | − | 0.643596i | ||||||
\(957\) | −33.9411 | + | 24.0000i | −1.09716 | + | 0.775810i | ||||
\(958\) | 17.2426 | − | 17.2426i | 0.557084 | − | 0.557084i | ||||
\(959\) | −17.6569 | −0.570170 | ||||||||
\(960\) | −1.12132 | − | 3.70711i | −0.0361905 | − | 0.119646i | ||||
\(961\) | −19.3431 | −0.623972 | ||||||||
\(962\) | 2.58579 | − | 2.58579i | 0.0833691 | − | 0.0833691i | ||||
\(963\) | −22.0711 | − | 46.2132i | −0.711230 | − | 1.48920i | ||||
\(964\) | 3.65685i | 0.117779i | ||||||||
\(965\) | 16.1421 | + | 32.2843i | 0.519634 | + | 1.03927i | ||||
\(966\) | −0.970563 | + | 5.65685i | −0.0312273 | + | 0.182006i | ||||
\(967\) | 14.6274 | + | 14.6274i | 0.470386 | + | 0.470386i | 0.902040 | − | 0.431653i | \(-0.142070\pi\) |
−0.431653 | + | 0.902040i | \(0.642070\pi\) | |||||||
\(968\) | 3.53553 | + | 3.53553i | 0.113636 | + | 0.113636i | ||||
\(969\) | 8.48528 | − | 49.4558i | 0.272587 | − | 1.58875i | ||||
\(970\) | −9.07107 | + | 27.2132i | −0.291254 | + | 0.873763i | ||||
\(971\) | − | 8.14214i | − | 0.261294i | −0.991429 | − | 0.130647i | \(-0.958295\pi\) | ||
0.991429 | − | 0.130647i | \(-0.0417054\pi\) | |||||||
\(972\) | −15.5563 | − | 1.00000i | −0.498970 | − | 0.0320750i | ||||
\(973\) | −0.970563 | + | 0.970563i | −0.0311148 | + | 0.0311148i | ||||
\(974\) | 4.14214 | 0.132723 | ||||||||
\(975\) | 5.94975 | + | 6.29289i | 0.190544 | + | 0.201534i | ||||
\(976\) | −4.82843 | −0.154554 | ||||||||
\(977\) | 21.4142 | − | 21.4142i | 0.685101 | − | 0.685101i | −0.276044 | − | 0.961145i | \(-0.589023\pi\) |
0.961145 | + | 0.276044i | \(0.0890235\pi\) | |||||||
\(978\) | 4.68629 | − | 3.31371i | 0.149851 | − | 0.105961i | ||||
\(979\) | − | 44.6863i | − | 1.42818i | ||||||
\(980\) | 4.46447 | − | 13.3934i | 0.142612 | − | 0.427836i | ||||
\(981\) | −13.9411 | − | 4.92893i | −0.445106 | − | 0.157369i | ||||
\(982\) | 9.75736 | + | 9.75736i | 0.311370 | + | 0.311370i | ||||
\(983\) | −3.41421 | − | 3.41421i | −0.108897 | − | 0.108897i | 0.650559 | − | 0.759456i | \(-0.274535\pi\) |
−0.759456 | + | 0.650559i | \(0.774535\pi\) | |||||||
\(984\) | 3.41421 | + | 0.585786i | 0.108841 | + | 0.0186742i | ||||
\(985\) | −5.31371 | − | 10.6274i | −0.169309 | − | 0.338618i | ||||
\(986\) | − | 25.4558i | − | 0.810679i | ||||||
\(987\) | 2.62742 | + | 3.71573i | 0.0836316 | + | 0.118273i | ||||
\(988\) | 4.82843 | − | 4.82843i | 0.153613 | − | 0.153613i | ||||
\(989\) | 7.02944 | 0.223523 | ||||||||
\(990\) | −3.31371 | − | 26.6274i | −0.105317 | − | 0.846275i | ||||
\(991\) | −5.17157 | −0.164280 | −0.0821402 | − | 0.996621i | \(-0.526176\pi\) | ||||
−0.0821402 | + | 0.996621i | \(0.526176\pi\) | |||||||
\(992\) | −2.41421 | + | 2.41421i | −0.0766514 | + | 0.0766514i | ||||
\(993\) | −32.2843 | − | 45.6569i | −1.02451 | − | 1.44888i | ||||
\(994\) | − | 11.7990i | − | 0.374241i | ||||||
\(995\) | 46.9706 | + | 15.6569i | 1.48907 | + | 0.496356i | ||||
\(996\) | 16.4853 | + | 2.82843i | 0.522356 | + | 0.0896221i | ||||
\(997\) | 21.6985 | + | 21.6985i | 0.687198 | + | 0.687198i | 0.961612 | − | 0.274414i | \(-0.0884838\pi\) |
−0.274414 | + | 0.961612i | \(0.588484\pi\) | |||||||
\(998\) | −5.65685 | − | 5.65685i | −0.179065 | − | 0.179065i | ||||
\(999\) | 16.5858 | + | 9.27208i | 0.524751 | + | 0.293356i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 390.2.l.b.287.2 | yes | 4 | |
3.2 | odd | 2 | 390.2.l.a.287.1 | yes | 4 | ||
5.3 | odd | 4 | 390.2.l.a.53.1 | ✓ | 4 | ||
15.8 | even | 4 | inner | 390.2.l.b.53.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.l.a.53.1 | ✓ | 4 | 5.3 | odd | 4 | ||
390.2.l.a.287.1 | yes | 4 | 3.2 | odd | 2 | ||
390.2.l.b.53.2 | yes | 4 | 15.8 | even | 4 | inner | |
390.2.l.b.287.2 | yes | 4 | 1.1 | even | 1 | trivial |