Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(28.3389076774\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.17428.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - x^{3} - 6x^{2} + 4x + 6 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 273) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.52616\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.670843 | 0.474358 | 0.237179 | − | 0.971466i | \(-0.423777\pi\) | ||||
0.237179 | + | 0.971466i | \(0.423777\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.54997 | −0.774985 | ||||||||
\(5\) | −2.54997 | −1.14038 | −0.570191 | − | 0.821512i | \(-0.693131\pi\) | ||||
−0.570191 | + | 0.821512i | \(0.693131\pi\) | |||||||
\(6\) | 0.670843 | 0.273870 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.38147 | −0.841978 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.71063 | −0.540948 | ||||||||
\(11\) | 3.05232 | 0.920308 | 0.460154 | − | 0.887839i | \(-0.347794\pi\) | ||||
0.460154 | + | 0.887839i | \(0.347794\pi\) | |||||||
\(12\) | −1.54997 | −0.447438 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.670843 | −0.179290 | ||||||||
\(15\) | −2.54997 | −0.658399 | ||||||||
\(16\) | 1.50235 | 0.375586 | ||||||||
\(17\) | 1.34169 | 0.325407 | 0.162703 | − | 0.986675i | \(-0.447979\pi\) | ||||
0.162703 | + | 0.986675i | \(0.447979\pi\) | |||||||
\(18\) | 0.670843 | 0.158119 | ||||||||
\(19\) | −7.60228 | −1.74408 | −0.872042 | − | 0.489431i | \(-0.837204\pi\) | ||||
−0.872042 | + | 0.489431i | \(0.837204\pi\) | |||||||
\(20\) | 3.95238 | 0.883778 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 2.04762 | 0.436555 | ||||||||
\(23\) | 1.84403 | 0.384507 | 0.192254 | − | 0.981345i | \(-0.438420\pi\) | ||||
0.192254 | + | 0.981345i | \(0.438420\pi\) | |||||||
\(24\) | −2.38147 | −0.486116 | ||||||||
\(25\) | 1.50235 | 0.300469 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.54997 | 0.292917 | ||||||||
\(29\) | −5.60228 | −1.04032 | −0.520159 | − | 0.854069i | \(-0.674127\pi\) | ||||
−0.520159 | + | 0.854069i | \(0.674127\pi\) | |||||||
\(30\) | −1.71063 | −0.312317 | ||||||||
\(31\) | −10.2857 | −1.84736 | −0.923679 | − | 0.383167i | \(-0.874834\pi\) | ||||
−0.923679 | + | 0.383167i | \(0.874834\pi\) | |||||||
\(32\) | 5.77078 | 1.02014 | ||||||||
\(33\) | 3.05232 | 0.531340 | ||||||||
\(34\) | 0.900061 | 0.154359 | ||||||||
\(35\) | 2.54997 | 0.431024 | ||||||||
\(36\) | −1.54997 | −0.258328 | ||||||||
\(37\) | 9.20457 | 1.51322 | 0.756611 | − | 0.653865i | \(-0.226854\pi\) | ||||
0.756611 | + | 0.653865i | \(0.226854\pi\) | |||||||
\(38\) | −5.09994 | −0.827319 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.07268 | 0.960175 | ||||||||
\(41\) | 8.04762 | 1.25683 | 0.628414 | − | 0.777879i | \(-0.283704\pi\) | ||||
0.628414 | + | 0.777879i | \(0.283704\pi\) | |||||||
\(42\) | −0.670843 | −0.103513 | ||||||||
\(43\) | 1.49765 | 0.228390 | 0.114195 | − | 0.993458i | \(-0.463571\pi\) | ||||
0.114195 | + | 0.993458i | \(0.463571\pi\) | |||||||
\(44\) | −4.73100 | −0.713224 | ||||||||
\(45\) | −2.54997 | −0.380127 | ||||||||
\(46\) | 1.23706 | 0.182394 | ||||||||
\(47\) | 3.89166 | 0.567656 | 0.283828 | − | 0.958875i | \(-0.408395\pi\) | ||||
0.283828 | + | 0.958875i | \(0.408395\pi\) | |||||||
\(48\) | 1.50235 | 0.216845 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00784 | 0.142530 | ||||||||
\(51\) | 1.34169 | 0.187874 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.502345 | 0.0690025 | 0.0345012 | − | 0.999405i | \(-0.489016\pi\) | ||||
0.0345012 | + | 0.999405i | \(0.489016\pi\) | |||||||
\(54\) | 0.670843 | 0.0912902 | ||||||||
\(55\) | −7.78331 | −1.04950 | ||||||||
\(56\) | 2.38147 | 0.318238 | ||||||||
\(57\) | −7.60228 | −1.00695 | ||||||||
\(58\) | −3.75825 | −0.493483 | ||||||||
\(59\) | 4.28937 | 0.558429 | 0.279214 | − | 0.960229i | \(-0.409926\pi\) | ||||
0.279214 | + | 0.960229i | \(0.409926\pi\) | |||||||
\(60\) | 3.95238 | 0.510250 | ||||||||
\(61\) | −0.683372 | −0.0874968 | −0.0437484 | − | 0.999043i | \(-0.513930\pi\) | ||||
−0.0437484 | + | 0.999043i | \(0.513930\pi\) | |||||||
\(62\) | −6.90006 | −0.876309 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0.866598 | 0.108325 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.04762 | 0.252045 | ||||||||
\(67\) | 7.68806 | 0.939246 | 0.469623 | − | 0.882867i | \(-0.344390\pi\) | ||||
0.469623 | + | 0.882867i | \(0.344390\pi\) | |||||||
\(68\) | −2.07957 | −0.252185 | ||||||||
\(69\) | 1.84403 | 0.221995 | ||||||||
\(70\) | 1.71063 | 0.204459 | ||||||||
\(71\) | 14.2569 | 1.69198 | 0.845990 | − | 0.533198i | \(-0.179010\pi\) | ||||
0.845990 | + | 0.533198i | \(0.179010\pi\) | |||||||
\(72\) | −2.38147 | −0.280659 | ||||||||
\(73\) | 12.0189 | 1.40670 | 0.703350 | − | 0.710844i | \(-0.251687\pi\) | ||||
0.703350 | + | 0.710844i | \(0.251687\pi\) | |||||||
\(74\) | 6.17482 | 0.717808 | ||||||||
\(75\) | 1.50235 | 0.173476 | ||||||||
\(76\) | 11.7833 | 1.35164 | ||||||||
\(77\) | −3.05232 | −0.347844 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.91891 | 0.553421 | 0.276710 | − | 0.960953i | \(-0.410756\pi\) | ||||
0.276710 | + | 0.960953i | \(0.410756\pi\) | |||||||
\(80\) | −3.83094 | −0.428312 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.39869 | 0.596186 | ||||||||
\(83\) | 1.20828 | 0.132626 | 0.0663132 | − | 0.997799i | \(-0.478876\pi\) | ||||
0.0663132 | + | 0.997799i | \(0.478876\pi\) | |||||||
\(84\) | 1.54997 | 0.169116 | ||||||||
\(85\) | −3.42126 | −0.371088 | ||||||||
\(86\) | 1.00469 | 0.108339 | ||||||||
\(87\) | −5.60228 | −0.600628 | ||||||||
\(88\) | −7.26900 | −0.774878 | ||||||||
\(89\) | −13.7545 | −1.45798 | −0.728989 | − | 0.684525i | \(-0.760010\pi\) | ||||
−0.728989 | + | 0.684525i | \(0.760010\pi\) | |||||||
\(90\) | −1.71063 | −0.180316 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.85819 | −0.297987 | ||||||||
\(93\) | −10.2857 | −1.06657 | ||||||||
\(94\) | 2.61069 | 0.269272 | ||||||||
\(95\) | 19.3856 | 1.98892 | ||||||||
\(96\) | 5.77078 | 0.588978 | ||||||||
\(97\) | 7.18572 | 0.729599 | 0.364800 | − | 0.931086i | \(-0.381138\pi\) | ||||
0.364800 | + | 0.931086i | \(0.381138\pi\) | |||||||
\(98\) | 0.670843 | 0.0677654 | ||||||||
\(99\) | 3.05232 | 0.306769 | ||||||||
\(100\) | −2.32859 | −0.232859 | ||||||||
\(101\) | −18.4416 | −1.83501 | −0.917505 | − | 0.397724i | \(-0.869800\pi\) | ||||
−0.917505 | + | 0.397724i | \(0.869800\pi\) | |||||||
\(102\) | 0.900061 | 0.0891193 | ||||||||
\(103\) | 1.89537 | 0.186756 | 0.0933782 | − | 0.995631i | \(-0.470233\pi\) | ||||
0.0933782 | + | 0.995631i | \(0.470233\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.54997 | 0.248852 | ||||||||
\(106\) | 0.336995 | 0.0327318 | ||||||||
\(107\) | 18.5463 | 1.79293 | 0.896467 | − | 0.443110i | \(-0.146125\pi\) | ||||
0.896467 | + | 0.443110i | \(0.146125\pi\) | |||||||
\(108\) | −1.54997 | −0.149146 | ||||||||
\(109\) | 1.42126 | 0.136132 | 0.0680659 | − | 0.997681i | \(-0.478317\pi\) | ||||
0.0680659 | + | 0.997681i | \(0.478317\pi\) | |||||||
\(110\) | −5.22138 | −0.497839 | ||||||||
\(111\) | 9.20457 | 0.873659 | ||||||||
\(112\) | −1.50235 | −0.141958 | ||||||||
\(113\) | 5.60228 | 0.527019 | 0.263509 | − | 0.964657i | \(-0.415120\pi\) | ||||
0.263509 | + | 0.964657i | \(0.415120\pi\) | |||||||
\(114\) | −5.09994 | −0.477653 | ||||||||
\(115\) | −4.70222 | −0.438485 | ||||||||
\(116\) | 8.68337 | 0.806231 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.87749 | 0.264895 | ||||||||
\(119\) | −1.34169 | −0.122992 | ||||||||
\(120\) | 6.07268 | 0.554357 | ||||||||
\(121\) | −1.68337 | −0.153034 | ||||||||
\(122\) | −0.458435 | −0.0415048 | ||||||||
\(123\) | 8.04762 | 0.725630 | ||||||||
\(124\) | 15.9425 | 1.43167 | ||||||||
\(125\) | 8.91891 | 0.797732 | ||||||||
\(126\) | −0.670843 | −0.0597634 | ||||||||
\(127\) | 14.1046 | 1.25158 | 0.625792 | − | 0.779990i | \(-0.284776\pi\) | ||||
0.625792 | + | 0.779990i | \(0.284776\pi\) | |||||||
\(128\) | −10.9602 | −0.968755 | ||||||||
\(129\) | 1.49765 | 0.131861 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.78800 | −0.767811 | −0.383906 | − | 0.923372i | \(-0.625421\pi\) | ||||
−0.383906 | + | 0.923372i | \(0.625421\pi\) | |||||||
\(132\) | −4.73100 | −0.411780 | ||||||||
\(133\) | 7.60228 | 0.659202 | ||||||||
\(134\) | 5.15748 | 0.445539 | ||||||||
\(135\) | −2.54997 | −0.219466 | ||||||||
\(136\) | −3.19519 | −0.273985 | ||||||||
\(137\) | 1.97743 | 0.168944 | 0.0844718 | − | 0.996426i | \(-0.473080\pi\) | ||||
0.0844718 | + | 0.996426i | \(0.473080\pi\) | |||||||
\(138\) | 1.23706 | 0.105305 | ||||||||
\(139\) | 13.0999 | 1.11112 | 0.555561 | − | 0.831476i | \(-0.312503\pi\) | ||||
0.555561 | + | 0.831476i | \(0.312503\pi\) | |||||||
\(140\) | −3.95238 | −0.334037 | ||||||||
\(141\) | 3.89166 | 0.327737 | ||||||||
\(142\) | 9.56413 | 0.802604 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.50235 | 0.125195 | ||||||||
\(145\) | 14.2857 | 1.18636 | ||||||||
\(146\) | 8.06276 | 0.667279 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −14.2668 | −1.17272 | ||||||||
\(149\) | −14.5939 | −1.19558 | −0.597789 | − | 0.801654i | \(-0.703954\pi\) | ||||
−0.597789 | + | 0.801654i | \(0.703954\pi\) | |||||||
\(150\) | 1.00784 | 0.0822896 | ||||||||
\(151\) | 5.41188 | 0.440412 | 0.220206 | − | 0.975453i | \(-0.429327\pi\) | ||||
0.220206 | + | 0.975453i | \(0.429327\pi\) | |||||||
\(152\) | 18.1046 | 1.46848 | ||||||||
\(153\) | 1.34169 | 0.108469 | ||||||||
\(154\) | −2.04762 | −0.165002 | ||||||||
\(155\) | 26.2281 | 2.10669 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 23.4044 | 1.86788 | 0.933939 | − | 0.357432i | \(-0.116348\pi\) | ||||
0.933939 | + | 0.357432i | \(0.116348\pi\) | |||||||
\(158\) | 3.29982 | 0.262519 | ||||||||
\(159\) | 0.502345 | 0.0398386 | ||||||||
\(160\) | −14.7153 | −1.16335 | ||||||||
\(161\) | −1.84403 | −0.145330 | ||||||||
\(162\) | 0.670843 | 0.0527064 | ||||||||
\(163\) | 10.1046 | 0.791456 | 0.395728 | − | 0.918368i | \(-0.370492\pi\) | ||||
0.395728 | + | 0.918368i | \(0.370492\pi\) | |||||||
\(164\) | −12.4736 | −0.974022 | ||||||||
\(165\) | −7.78331 | −0.605930 | ||||||||
\(166\) | 0.810569 | 0.0629123 | ||||||||
\(167\) | 3.09623 | 0.239593 | 0.119797 | − | 0.992798i | \(-0.461776\pi\) | ||||
0.119797 | + | 0.992798i | \(0.461776\pi\) | |||||||
\(168\) | 2.38147 | 0.183735 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −2.29513 | −0.176028 | ||||||||
\(171\) | −7.60228 | −0.581361 | ||||||||
\(172\) | −2.32132 | −0.176999 | ||||||||
\(173\) | 2.75356 | 0.209349 | 0.104675 | − | 0.994507i | \(-0.466620\pi\) | ||||
0.104675 | + | 0.994507i | \(0.466620\pi\) | |||||||
\(174\) | −3.75825 | −0.284912 | ||||||||
\(175\) | −1.50235 | −0.113567 | ||||||||
\(176\) | 4.58563 | 0.345655 | ||||||||
\(177\) | 4.28937 | 0.322409 | ||||||||
\(178\) | −9.22714 | −0.691603 | ||||||||
\(179\) | −1.57723 | −0.117887 | −0.0589437 | − | 0.998261i | \(-0.518773\pi\) | ||||
−0.0589437 | + | 0.998261i | \(0.518773\pi\) | |||||||
\(180\) | 3.95238 | 0.294593 | ||||||||
\(181\) | 9.51651 | 0.707356 | 0.353678 | − | 0.935367i | \(-0.384931\pi\) | ||||
0.353678 | + | 0.935367i | \(0.384931\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.683372 | −0.0505163 | ||||||||
\(184\) | −4.39151 | −0.323746 | ||||||||
\(185\) | −23.4714 | −1.72565 | ||||||||
\(186\) | −6.90006 | −0.505937 | ||||||||
\(187\) | 4.09525 | 0.299474 | ||||||||
\(188\) | −6.03195 | −0.439925 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 13.0047 | 0.943459 | ||||||||
\(191\) | −22.8508 | −1.65342 | −0.826712 | − | 0.562626i | \(-0.809791\pi\) | ||||
−0.826712 | + | 0.562626i | \(0.809791\pi\) | |||||||
\(192\) | 0.866598 | 0.0625413 | ||||||||
\(193\) | −19.5760 | −1.40911 | −0.704556 | − | 0.709649i | \(-0.748854\pi\) | ||||
−0.704556 | + | 0.709649i | \(0.748854\pi\) | |||||||
\(194\) | 4.82049 | 0.346091 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.54997 | −0.110712 | ||||||||
\(197\) | 21.2271 | 1.51237 | 0.756185 | − | 0.654357i | \(-0.227061\pi\) | ||||
0.756185 | + | 0.654357i | \(0.227061\pi\) | |||||||
\(198\) | 2.04762 | 0.145518 | ||||||||
\(199\) | −6.68337 | −0.473772 | −0.236886 | − | 0.971537i | \(-0.576127\pi\) | ||||
−0.236886 | + | 0.971537i | \(0.576127\pi\) | |||||||
\(200\) | −3.57779 | −0.252988 | ||||||||
\(201\) | 7.68806 | 0.542274 | ||||||||
\(202\) | −12.3714 | −0.870451 | ||||||||
\(203\) | 5.60228 | 0.393203 | ||||||||
\(204\) | −2.07957 | −0.145599 | ||||||||
\(205\) | −20.5212 | −1.43326 | ||||||||
\(206\) | 1.27150 | 0.0885893 | ||||||||
\(207\) | 1.84403 | 0.128169 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −23.2046 | −1.60509 | ||||||||
\(210\) | 1.71063 | 0.118045 | ||||||||
\(211\) | −4.60698 | −0.317157 | −0.158579 | − | 0.987346i | \(-0.550691\pi\) | ||||
−0.158579 | + | 0.987346i | \(0.550691\pi\) | |||||||
\(212\) | −0.778620 | −0.0534759 | ||||||||
\(213\) | 14.2569 | 0.976866 | ||||||||
\(214\) | 12.4416 | 0.850492 | ||||||||
\(215\) | −3.81897 | −0.260452 | ||||||||
\(216\) | −2.38147 | −0.162039 | ||||||||
\(217\) | 10.2857 | 0.698236 | ||||||||
\(218\) | 0.953441 | 0.0645752 | ||||||||
\(219\) | 12.0189 | 0.812159 | ||||||||
\(220\) | 12.0639 | 0.813348 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 6.17482 | 0.414427 | ||||||||
\(223\) | −8.60698 | −0.576366 | −0.288183 | − | 0.957575i | \(-0.593051\pi\) | ||||
−0.288183 | + | 0.957575i | \(0.593051\pi\) | |||||||
\(224\) | −5.77078 | −0.385577 | ||||||||
\(225\) | 1.50235 | 0.100156 | ||||||||
\(226\) | 3.75825 | 0.249995 | ||||||||
\(227\) | 14.4892 | 0.961685 | 0.480843 | − | 0.876807i | \(-0.340331\pi\) | ||||
0.480843 | + | 0.876807i | \(0.340331\pi\) | |||||||
\(228\) | 11.7833 | 0.780369 | ||||||||
\(229\) | 20.1999 | 1.33485 | 0.667423 | − | 0.744679i | \(-0.267397\pi\) | ||||
0.667423 | + | 0.744679i | \(0.267397\pi\) | |||||||
\(230\) | −3.15445 | −0.207999 | ||||||||
\(231\) | −3.05232 | −0.200828 | ||||||||
\(232\) | 13.3417 | 0.875925 | ||||||||
\(233\) | 7.28097 | 0.476992 | 0.238496 | − | 0.971143i | \(-0.423346\pi\) | ||||
0.238496 | + | 0.971143i | \(0.423346\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.92360 | −0.647345 | ||||||||
\(236\) | −6.64839 | −0.432774 | ||||||||
\(237\) | 4.91891 | 0.319518 | ||||||||
\(238\) | −0.900061 | −0.0583423 | ||||||||
\(239\) | −27.6688 | −1.78974 | −0.894872 | − | 0.446323i | \(-0.852733\pi\) | ||||
−0.894872 | + | 0.446323i | \(0.852733\pi\) | |||||||
\(240\) | −3.83094 | −0.247286 | ||||||||
\(241\) | 22.2187 | 1.43123 | 0.715617 | − | 0.698493i | \(-0.246146\pi\) | ||||
0.715617 | + | 0.698493i | \(0.246146\pi\) | |||||||
\(242\) | −1.12928 | −0.0725928 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 1.05921 | 0.0678087 | ||||||||
\(245\) | −2.54997 | −0.162912 | ||||||||
\(246\) | 5.39869 | 0.344208 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 24.4950 | 1.55543 | ||||||||
\(249\) | 1.20828 | 0.0765719 | ||||||||
\(250\) | 5.98319 | 0.378410 | ||||||||
\(251\) | 17.3092 | 1.09255 | 0.546274 | − | 0.837607i | \(-0.316046\pi\) | ||||
0.546274 | + | 0.837607i | \(0.316046\pi\) | |||||||
\(252\) | 1.54997 | 0.0976389 | ||||||||
\(253\) | 5.62857 | 0.353865 | ||||||||
\(254\) | 9.46199 | 0.593698 | ||||||||
\(255\) | −3.42126 | −0.214248 | ||||||||
\(256\) | −9.08578 | −0.567861 | ||||||||
\(257\) | −5.55837 | −0.346722 | −0.173361 | − | 0.984858i | \(-0.555463\pi\) | ||||
−0.173361 | + | 0.984858i | \(0.555463\pi\) | |||||||
\(258\) | 1.00469 | 0.0625493 | ||||||||
\(259\) | −9.20457 | −0.571944 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.60228 | −0.346773 | ||||||||
\(262\) | −5.89537 | −0.364217 | ||||||||
\(263\) | 25.0486 | 1.54456 | 0.772281 | − | 0.635281i | \(-0.219116\pi\) | ||||
0.772281 | + | 0.635281i | \(0.219116\pi\) | |||||||
\(264\) | −7.26900 | −0.447376 | ||||||||
\(265\) | −1.28097 | −0.0786891 | ||||||||
\(266\) | 5.09994 | 0.312697 | ||||||||
\(267\) | −13.7545 | −0.841764 | ||||||||
\(268\) | −11.9163 | −0.727902 | ||||||||
\(269\) | −4.55368 | −0.277643 | −0.138821 | − | 0.990317i | \(-0.544331\pi\) | ||||
−0.138821 | + | 0.990317i | \(0.544331\pi\) | |||||||
\(270\) | −1.71063 | −0.104106 | ||||||||
\(271\) | −8.88325 | −0.539619 | −0.269810 | − | 0.962914i | \(-0.586961\pi\) | ||||
−0.269810 | + | 0.962914i | \(0.586961\pi\) | |||||||
\(272\) | 2.01568 | 0.122218 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.32655 | 0.0801397 | ||||||||
\(275\) | 4.58563 | 0.276524 | ||||||||
\(276\) | −2.85819 | −0.172043 | ||||||||
\(277\) | −5.38560 | −0.323589 | −0.161795 | − | 0.986824i | \(-0.551728\pi\) | ||||
−0.161795 | + | 0.986824i | \(0.551728\pi\) | |||||||
\(278\) | 8.78800 | 0.527069 | ||||||||
\(279\) | −10.2857 | −0.615786 | ||||||||
\(280\) | −6.07268 | −0.362912 | ||||||||
\(281\) | 12.9727 | 0.773889 | 0.386944 | − | 0.922103i | \(-0.373531\pi\) | ||||
0.386944 | + | 0.922103i | \(0.373531\pi\) | |||||||
\(282\) | 2.61069 | 0.155464 | ||||||||
\(283\) | −1.52589 | −0.0907047 | −0.0453523 | − | 0.998971i | \(-0.514441\pi\) | ||||
−0.0453523 | + | 0.998971i | \(0.514441\pi\) | |||||||
\(284\) | −22.0977 | −1.31126 | ||||||||
\(285\) | 19.3856 | 1.14830 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.04762 | −0.475036 | ||||||||
\(288\) | 5.77078 | 0.340047 | ||||||||
\(289\) | −15.1999 | −0.894111 | ||||||||
\(290\) | 9.58343 | 0.562759 | ||||||||
\(291\) | 7.18572 | 0.421234 | ||||||||
\(292\) | −18.6289 | −1.09017 | ||||||||
\(293\) | −18.8545 | −1.10149 | −0.550745 | − | 0.834673i | \(-0.685656\pi\) | ||||
−0.550745 | + | 0.834673i | \(0.685656\pi\) | |||||||
\(294\) | 0.670843 | 0.0391244 | ||||||||
\(295\) | −10.9378 | −0.636821 | ||||||||
\(296\) | −21.9204 | −1.27410 | ||||||||
\(297\) | 3.05232 | 0.177113 | ||||||||
\(298\) | −9.79020 | −0.567131 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −2.32859 | −0.134441 | ||||||||
\(301\) | −1.49765 | −0.0863234 | ||||||||
\(302\) | 3.63052 | 0.208913 | ||||||||
\(303\) | −18.4416 | −1.05944 | ||||||||
\(304\) | −11.4213 | −0.655054 | ||||||||
\(305\) | 1.74258 | 0.0997797 | ||||||||
\(306\) | 0.900061 | 0.0514530 | ||||||||
\(307\) | −15.3856 | −0.878102 | −0.439051 | − | 0.898462i | \(-0.644685\pi\) | ||||
−0.439051 | + | 0.898462i | \(0.644685\pi\) | |||||||
\(308\) | 4.73100 | 0.269574 | ||||||||
\(309\) | 1.89537 | 0.107824 | ||||||||
\(310\) | 17.5949 | 0.999326 | ||||||||
\(311\) | −17.0999 | −0.969649 | −0.484824 | − | 0.874612i | \(-0.661116\pi\) | ||||
−0.484824 | + | 0.874612i | \(0.661116\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.89263 | 0.276548 | 0.138274 | − | 0.990394i | \(-0.455845\pi\) | ||||
0.138274 | + | 0.990394i | \(0.455845\pi\) | |||||||
\(314\) | 15.7007 | 0.886042 | ||||||||
\(315\) | 2.54997 | 0.143675 | ||||||||
\(316\) | −7.62417 | −0.428893 | ||||||||
\(317\) | −1.44382 | −0.0810933 | −0.0405466 | − | 0.999178i | \(-0.512910\pi\) | ||||
−0.0405466 | + | 0.999178i | \(0.512910\pi\) | |||||||
\(318\) | 0.336995 | 0.0188977 | ||||||||
\(319\) | −17.0999 | −0.957413 | ||||||||
\(320\) | −2.20980 | −0.123531 | ||||||||
\(321\) | 18.5463 | 1.03515 | ||||||||
\(322\) | −1.23706 | −0.0689384 | ||||||||
\(323\) | −10.1999 | −0.567536 | ||||||||
\(324\) | −1.54997 | −0.0861094 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.77862 | 0.375433 | ||||||||
\(327\) | 1.42126 | 0.0785958 | ||||||||
\(328\) | −19.1652 | −1.05822 | ||||||||
\(329\) | −3.89166 | −0.214554 | ||||||||
\(330\) | −5.22138 | −0.287427 | ||||||||
\(331\) | 14.9953 | 0.824217 | 0.412108 | − | 0.911135i | \(-0.364793\pi\) | ||||
0.412108 | + | 0.911135i | \(0.364793\pi\) | |||||||
\(332\) | −1.87280 | −0.102783 | ||||||||
\(333\) | 9.20457 | 0.504407 | ||||||||
\(334\) | 2.07708 | 0.113653 | ||||||||
\(335\) | −19.6043 | −1.07110 | ||||||||
\(336\) | −1.50235 | −0.0819597 | ||||||||
\(337\) | −14.9115 | −0.812280 | −0.406140 | − | 0.913811i | \(-0.633126\pi\) | ||||
−0.406140 | + | 0.913811i | \(0.633126\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.60228 | 0.304274 | ||||||||
\(340\) | 5.30285 | 0.287587 | ||||||||
\(341\) | −31.3951 | −1.70014 | ||||||||
\(342\) | −5.09994 | −0.275773 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −3.56662 | −0.192299 | ||||||||
\(345\) | −4.70222 | −0.253159 | ||||||||
\(346\) | 1.84721 | 0.0993065 | ||||||||
\(347\) | 7.07488 | 0.379800 | 0.189900 | − | 0.981803i | \(-0.439184\pi\) | ||||
0.189900 | + | 0.981803i | \(0.439184\pi\) | |||||||
\(348\) | 8.68337 | 0.465478 | ||||||||
\(349\) | −21.1188 | −1.13046 | −0.565232 | − | 0.824932i | \(-0.691213\pi\) | ||||
−0.565232 | + | 0.824932i | \(0.691213\pi\) | |||||||
\(350\) | −1.00784 | −0.0538712 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 17.6142 | 0.938843 | ||||||||
\(353\) | 17.3643 | 0.924206 | 0.462103 | − | 0.886826i | \(-0.347095\pi\) | ||||
0.462103 | + | 0.886826i | \(0.347095\pi\) | |||||||
\(354\) | 2.87749 | 0.152937 | ||||||||
\(355\) | −36.3546 | −1.92950 | ||||||||
\(356\) | 21.3191 | 1.12991 | ||||||||
\(357\) | −1.34169 | −0.0710096 | ||||||||
\(358\) | −1.05807 | −0.0559208 | ||||||||
\(359\) | −18.3521 | −0.968589 | −0.484294 | − | 0.874905i | \(-0.660924\pi\) | ||||
−0.484294 | + | 0.874905i | \(0.660924\pi\) | |||||||
\(360\) | 6.07268 | 0.320058 | ||||||||
\(361\) | 38.7947 | 2.04183 | ||||||||
\(362\) | 6.38408 | 0.335540 | ||||||||
\(363\) | −1.68337 | −0.0883541 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −30.6477 | −1.60417 | ||||||||
\(366\) | −0.458435 | −0.0239628 | ||||||||
\(367\) | 8.40719 | 0.438852 | 0.219426 | − | 0.975629i | \(-0.429582\pi\) | ||||
0.219426 | + | 0.975629i | \(0.429582\pi\) | |||||||
\(368\) | 2.77037 | 0.144416 | ||||||||
\(369\) | 8.04762 | 0.418943 | ||||||||
\(370\) | −15.7456 | −0.818575 | ||||||||
\(371\) | −0.502345 | −0.0260805 | ||||||||
\(372\) | 15.9425 | 0.826578 | ||||||||
\(373\) | 27.0925 | 1.40280 | 0.701399 | − | 0.712769i | \(-0.252559\pi\) | ||||
0.701399 | + | 0.712769i | \(0.252559\pi\) | |||||||
\(374\) | 2.74727 | 0.142058 | ||||||||
\(375\) | 8.91891 | 0.460571 | ||||||||
\(376\) | −9.26787 | −0.477954 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.670843 | −0.0345044 | ||||||||
\(379\) | 6.41657 | 0.329597 | 0.164798 | − | 0.986327i | \(-0.447303\pi\) | ||||
0.164798 | + | 0.986327i | \(0.447303\pi\) | |||||||
\(380\) | −30.0471 | −1.54138 | ||||||||
\(381\) | 14.1046 | 0.722602 | ||||||||
\(382\) | −15.3293 | −0.784314 | ||||||||
\(383\) | −32.5939 | −1.66547 | −0.832735 | − | 0.553672i | \(-0.813226\pi\) | ||||
−0.832735 | + | 0.553672i | \(0.813226\pi\) | |||||||
\(384\) | −10.9602 | −0.559311 | ||||||||
\(385\) | 7.78331 | 0.396674 | ||||||||
\(386\) | −13.1324 | −0.668423 | ||||||||
\(387\) | 1.49765 | 0.0761301 | ||||||||
\(388\) | −11.1376 | −0.565428 | ||||||||
\(389\) | 6.00000 | 0.304212 | 0.152106 | − | 0.988364i | \(-0.451394\pi\) | ||||
0.152106 | + | 0.988364i | \(0.451394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.47411 | 0.125121 | ||||||||
\(392\) | −2.38147 | −0.120283 | ||||||||
\(393\) | −8.78800 | −0.443296 | ||||||||
\(394\) | 14.2401 | 0.717405 | ||||||||
\(395\) | −12.5431 | −0.631111 | ||||||||
\(396\) | −4.73100 | −0.237741 | ||||||||
\(397\) | −15.7520 | −0.790573 | −0.395286 | − | 0.918558i | \(-0.629355\pi\) | ||||
−0.395286 | + | 0.918558i | \(0.629355\pi\) | |||||||
\(398\) | −4.48349 | −0.224737 | ||||||||
\(399\) | 7.60228 | 0.380590 | ||||||||
\(400\) | 2.25704 | 0.112852 | ||||||||
\(401\) | −26.1867 | −1.30770 | −0.653851 | − | 0.756624i | \(-0.726848\pi\) | ||||
−0.653851 | + | 0.756624i | \(0.726848\pi\) | |||||||
\(402\) | 5.15748 | 0.257232 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 28.5840 | 1.42211 | ||||||||
\(405\) | −2.54997 | −0.126709 | ||||||||
\(406\) | 3.75825 | 0.186519 | ||||||||
\(407\) | 28.0952 | 1.39263 | ||||||||
\(408\) | −3.19519 | −0.158185 | ||||||||
\(409\) | 17.3856 | 0.859662 | 0.429831 | − | 0.902909i | \(-0.358573\pi\) | ||||
0.429831 | + | 0.902909i | \(0.358573\pi\) | |||||||
\(410\) | −13.7665 | −0.679879 | ||||||||
\(411\) | 1.97743 | 0.0975396 | ||||||||
\(412\) | −2.93777 | −0.144733 | ||||||||
\(413\) | −4.28937 | −0.211066 | ||||||||
\(414\) | 1.23706 | 0.0607980 | ||||||||
\(415\) | −3.08109 | −0.151245 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.0999 | 0.641507 | ||||||||
\(418\) | −15.5666 | −0.761388 | ||||||||
\(419\) | −12.4761 | −0.609496 | −0.304748 | − | 0.952433i | \(-0.598572\pi\) | ||||
−0.304748 | + | 0.952433i | \(0.598572\pi\) | |||||||
\(420\) | −3.95238 | −0.192856 | ||||||||
\(421\) | −9.57405 | −0.466611 | −0.233305 | − | 0.972404i | \(-0.574954\pi\) | ||||
−0.233305 | + | 0.972404i | \(0.574954\pi\) | |||||||
\(422\) | −3.09056 | −0.150446 | ||||||||
\(423\) | 3.89166 | 0.189219 | ||||||||
\(424\) | −1.19632 | −0.0580985 | ||||||||
\(425\) | 2.01568 | 0.0977746 | ||||||||
\(426\) | 9.56413 | 0.463384 | ||||||||
\(427\) | 0.683372 | 0.0330707 | ||||||||
\(428\) | −28.7461 | −1.38950 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.56193 | −0.123547 | ||||||||
\(431\) | −5.20208 | −0.250575 | −0.125288 | − | 0.992120i | \(-0.539985\pi\) | ||||
−0.125288 | + | 0.992120i | \(0.539985\pi\) | |||||||
\(432\) | 1.50235 | 0.0722816 | ||||||||
\(433\) | −17.2547 | −0.829207 | −0.414604 | − | 0.910002i | \(-0.636080\pi\) | ||||
−0.414604 | + | 0.910002i | \(0.636080\pi\) | |||||||
\(434\) | 6.90006 | 0.331214 | ||||||||
\(435\) | 14.2857 | 0.684945 | ||||||||
\(436\) | −2.20291 | −0.105500 | ||||||||
\(437\) | −14.0189 | −0.670613 | ||||||||
\(438\) | 8.06276 | 0.385254 | ||||||||
\(439\) | −22.1925 | −1.05919 | −0.529594 | − | 0.848251i | \(-0.677656\pi\) | ||||
−0.529594 | + | 0.848251i | \(0.677656\pi\) | |||||||
\(440\) | 18.5357 | 0.883657 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −37.9319 | −1.80220 | −0.901098 | − | 0.433615i | \(-0.857238\pi\) | ||||
−0.901098 | + | 0.433615i | \(0.857238\pi\) | |||||||
\(444\) | −14.2668 | −0.677073 | ||||||||
\(445\) | 35.0737 | 1.66265 | ||||||||
\(446\) | −5.77393 | −0.273403 | ||||||||
\(447\) | −14.5939 | −0.690267 | ||||||||
\(448\) | −0.866598 | −0.0409429 | ||||||||
\(449\) | 33.3150 | 1.57223 | 0.786115 | − | 0.618080i | \(-0.212089\pi\) | ||||
0.786115 | + | 0.618080i | \(0.212089\pi\) | |||||||
\(450\) | 1.00784 | 0.0475099 | ||||||||
\(451\) | 24.5639 | 1.15667 | ||||||||
\(452\) | −8.68337 | −0.408431 | ||||||||
\(453\) | 5.41188 | 0.254272 | ||||||||
\(454\) | 9.72001 | 0.456183 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 18.1046 | 0.847827 | ||||||||
\(457\) | 7.79269 | 0.364527 | 0.182263 | − | 0.983250i | \(-0.441658\pi\) | ||||
0.182263 | + | 0.983250i | \(0.441658\pi\) | |||||||
\(458\) | 13.5509 | 0.633194 | ||||||||
\(459\) | 1.34169 | 0.0626245 | ||||||||
\(460\) | 7.28831 | 0.339819 | ||||||||
\(461\) | −30.4568 | −1.41851 | −0.709256 | − | 0.704951i | \(-0.750969\pi\) | ||||
−0.709256 | + | 0.704951i | \(0.750969\pi\) | |||||||
\(462\) | −2.04762 | −0.0952641 | ||||||||
\(463\) | −39.4639 | −1.83405 | −0.917023 | − | 0.398835i | \(-0.869415\pi\) | ||||
−0.917023 | + | 0.398835i | \(0.869415\pi\) | |||||||
\(464\) | −8.41657 | −0.390729 | ||||||||
\(465\) | 26.2281 | 1.21630 | ||||||||
\(466\) | 4.88438 | 0.226265 | ||||||||
\(467\) | −9.93307 | −0.459648 | −0.229824 | − | 0.973232i | \(-0.573815\pi\) | ||||
−0.229824 | + | 0.973232i | \(0.573815\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.68806 | −0.355002 | ||||||||
\(470\) | −6.65718 | −0.307073 | ||||||||
\(471\) | 23.4044 | 1.07842 | ||||||||
\(472\) | −10.2150 | −0.470184 | ||||||||
\(473\) | 4.57131 | 0.210189 | ||||||||
\(474\) | 3.29982 | 0.151566 | ||||||||
\(475\) | −11.4213 | −0.524043 | ||||||||
\(476\) | 2.07957 | 0.0953171 | ||||||||
\(477\) | 0.502345 | 0.0230008 | ||||||||
\(478\) | −18.5614 | −0.848978 | ||||||||
\(479\) | 0.941479 | 0.0430173 | 0.0215086 | − | 0.999769i | \(-0.493153\pi\) | ||||
0.0215086 | + | 0.999769i | \(0.493153\pi\) | |||||||
\(480\) | −14.7153 | −0.671659 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 14.9053 | 0.678917 | ||||||||
\(483\) | −1.84403 | −0.0839063 | ||||||||
\(484\) | 2.60918 | 0.118599 | ||||||||
\(485\) | −18.3234 | −0.832021 | ||||||||
\(486\) | 0.670843 | 0.0304301 | ||||||||
\(487\) | 39.3499 | 1.78312 | 0.891558 | − | 0.452907i | \(-0.149613\pi\) | ||||
0.891558 | + | 0.452907i | \(0.149613\pi\) | |||||||
\(488\) | 1.62743 | 0.0736703 | ||||||||
\(489\) | 10.1046 | 0.456947 | ||||||||
\(490\) | −1.71063 | −0.0772784 | ||||||||
\(491\) | 5.45374 | 0.246124 | 0.123062 | − | 0.992399i | \(-0.460729\pi\) | ||||
0.123062 | + | 0.992399i | \(0.460729\pi\) | |||||||
\(492\) | −12.4736 | −0.562352 | ||||||||
\(493\) | −7.51651 | −0.338526 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.78331 | −0.349834 | ||||||||
\(496\) | −15.4526 | −0.693843 | ||||||||
\(497\) | −14.2569 | −0.639509 | ||||||||
\(498\) | 0.810569 | 0.0363225 | ||||||||
\(499\) | 31.3574 | 1.40375 | 0.701874 | − | 0.712301i | \(-0.252347\pi\) | ||||
0.701874 | + | 0.712301i | \(0.252347\pi\) | |||||||
\(500\) | −13.8240 | −0.618230 | ||||||||
\(501\) | 3.09623 | 0.138329 | ||||||||
\(502\) | 11.6118 | 0.518258 | ||||||||
\(503\) | 43.9926 | 1.96153 | 0.980766 | − | 0.195188i | \(-0.0625316\pi\) | ||||
0.980766 | + | 0.195188i | \(0.0625316\pi\) | |||||||
\(504\) | 2.38147 | 0.106079 | ||||||||
\(505\) | 47.0256 | 2.09261 | ||||||||
\(506\) | 3.77588 | 0.167858 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −21.8617 | −0.969958 | ||||||||
\(509\) | 41.8498 | 1.85496 | 0.927480 | − | 0.373874i | \(-0.121971\pi\) | ||||
0.927480 | + | 0.373874i | \(0.121971\pi\) | |||||||
\(510\) | −2.29513 | −0.101630 | ||||||||
\(511\) | −12.0189 | −0.531683 | ||||||||
\(512\) | 15.8253 | 0.699386 | ||||||||
\(513\) | −7.60228 | −0.335649 | ||||||||
\(514\) | −3.72880 | −0.164470 | ||||||||
\(515\) | −4.83314 | −0.212973 | ||||||||
\(516\) | −2.32132 | −0.102190 | ||||||||
\(517\) | 11.8786 | 0.522418 | ||||||||
\(518\) | −6.17482 | −0.271306 | ||||||||
\(519\) | 2.75356 | 0.120868 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.32957 | 0.364925 | 0.182462 | − | 0.983213i | \(-0.441593\pi\) | ||||
0.182462 | + | 0.983213i | \(0.441593\pi\) | |||||||
\(522\) | −3.75825 | −0.164494 | ||||||||
\(523\) | 25.3092 | 1.10669 | 0.553347 | − | 0.832951i | \(-0.313350\pi\) | ||||
0.553347 | + | 0.832951i | \(0.313350\pi\) | |||||||
\(524\) | 13.6211 | 0.595042 | ||||||||
\(525\) | −1.50235 | −0.0655677 | ||||||||
\(526\) | 16.8037 | 0.732675 | ||||||||
\(527\) | −13.8001 | −0.601143 | ||||||||
\(528\) | 4.58563 | 0.199564 | ||||||||
\(529\) | −19.5995 | −0.852154 | ||||||||
\(530\) | −0.859327 | −0.0373268 | ||||||||
\(531\) | 4.28937 | 0.186143 | ||||||||
\(532\) | −11.7833 | −0.510871 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −9.22714 | −0.399297 | ||||||||
\(535\) | −47.2924 | −2.04463 | ||||||||
\(536\) | −18.3089 | −0.790824 | ||||||||
\(537\) | −1.57723 | −0.0680624 | ||||||||
\(538\) | −3.05481 | −0.131702 | ||||||||
\(539\) | 3.05232 | 0.131473 | ||||||||
\(540\) | 3.95238 | 0.170083 | ||||||||
\(541\) | −27.1501 | −1.16727 | −0.583636 | − | 0.812015i | \(-0.698370\pi\) | ||||
−0.583636 | + | 0.812015i | \(0.698370\pi\) | |||||||
\(542\) | −5.95927 | −0.255972 | ||||||||
\(543\) | 9.51651 | 0.408392 | ||||||||
\(544\) | 7.74258 | 0.331960 | ||||||||
\(545\) | −3.62417 | −0.155242 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.5949 | 1.17987 | 0.589935 | − | 0.807450i | \(-0.299153\pi\) | ||||
0.589935 | + | 0.807450i | \(0.299153\pi\) | |||||||
\(548\) | −3.06496 | −0.130929 | ||||||||
\(549\) | −0.683372 | −0.0291656 | ||||||||
\(550\) | 3.07624 | 0.131171 | ||||||||
\(551\) | 42.5902 | 1.81440 | ||||||||
\(552\) | −4.39151 | −0.186915 | ||||||||
\(553\) | −4.91891 | −0.209173 | ||||||||
\(554\) | −3.61289 | −0.153497 | ||||||||
\(555\) | −23.4714 | −0.996304 | ||||||||
\(556\) | −20.3045 | −0.861103 | ||||||||
\(557\) | −7.19881 | −0.305024 | −0.152512 | − | 0.988302i | \(-0.548736\pi\) | ||||
−0.152512 | + | 0.988302i | \(0.548736\pi\) | |||||||
\(558\) | −6.90006 | −0.292103 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 3.83094 | 0.161887 | ||||||||
\(561\) | 4.09525 | 0.172902 | ||||||||
\(562\) | 8.70267 | 0.367100 | ||||||||
\(563\) | −20.2594 | −0.853831 | −0.426915 | − | 0.904292i | \(-0.640400\pi\) | ||||
−0.426915 | + | 0.904292i | \(0.640400\pi\) | |||||||
\(564\) | −6.03195 | −0.253991 | ||||||||
\(565\) | −14.2857 | −0.601002 | ||||||||
\(566\) | −1.02363 | −0.0430265 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −33.9524 | −1.42461 | ||||||||
\(569\) | 7.28097 | 0.305234 | 0.152617 | − | 0.988285i | \(-0.451230\pi\) | ||||
0.152617 | + | 0.988285i | \(0.451230\pi\) | |||||||
\(570\) | 13.0047 | 0.544707 | ||||||||
\(571\) | −22.1141 | −0.925446 | −0.462723 | − | 0.886503i | \(-0.653128\pi\) | ||||
−0.462723 | + | 0.886503i | \(0.653128\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −22.8508 | −0.954604 | ||||||||
\(574\) | −5.39869 | −0.225337 | ||||||||
\(575\) | 2.77037 | 0.115533 | ||||||||
\(576\) | 0.866598 | 0.0361082 | ||||||||
\(577\) | −20.3139 | −0.845678 | −0.422839 | − | 0.906205i | \(-0.638966\pi\) | ||||
−0.422839 | + | 0.906205i | \(0.638966\pi\) | |||||||
\(578\) | −10.1967 | −0.424128 | ||||||||
\(579\) | −19.5760 | −0.813551 | ||||||||
\(580\) | −22.1423 | −0.919410 | ||||||||
\(581\) | −1.20828 | −0.0501281 | ||||||||
\(582\) | 4.82049 | 0.199816 | ||||||||
\(583\) | 1.53332 | 0.0635035 | ||||||||
\(584\) | −28.6226 | −1.18441 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.6484 | −0.522500 | ||||||||
\(587\) | −35.8842 | −1.48110 | −0.740550 | − | 0.672001i | \(-0.765435\pi\) | ||||
−0.740550 | + | 0.672001i | \(0.765435\pi\) | |||||||
\(588\) | −1.54997 | −0.0639197 | ||||||||
\(589\) | 78.1945 | 3.22195 | ||||||||
\(590\) | −7.33752 | −0.302081 | ||||||||
\(591\) | 21.2271 | 0.873168 | ||||||||
\(592\) | 13.8284 | 0.568346 | ||||||||
\(593\) | −20.2664 | −0.832239 | −0.416120 | − | 0.909310i | \(-0.636610\pi\) | ||||
−0.416120 | + | 0.909310i | \(0.636610\pi\) | |||||||
\(594\) | 2.04762 | 0.0840150 | ||||||||
\(595\) | 3.42126 | 0.140258 | ||||||||
\(596\) | 22.6201 | 0.926554 | ||||||||
\(597\) | −6.68337 | −0.273532 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.9365 | 0.610291 | 0.305145 | − | 0.952306i | \(-0.401295\pi\) | ||||
0.305145 | + | 0.952306i | \(0.401295\pi\) | |||||||
\(600\) | −3.57779 | −0.146063 | ||||||||
\(601\) | 4.89263 | 0.199575 | 0.0997873 | − | 0.995009i | \(-0.468184\pi\) | ||||
0.0997873 | + | 0.995009i | \(0.468184\pi\) | |||||||
\(602\) | −1.00469 | −0.0409481 | ||||||||
\(603\) | 7.68806 | 0.313082 | ||||||||
\(604\) | −8.38824 | −0.341313 | ||||||||
\(605\) | 4.29255 | 0.174517 | ||||||||
\(606\) | −12.3714 | −0.502555 | ||||||||
\(607\) | 20.6164 | 0.836796 | 0.418398 | − | 0.908264i | \(-0.362592\pi\) | ||||
0.418398 | + | 0.908264i | \(0.362592\pi\) | |||||||
\(608\) | −43.8711 | −1.77921 | ||||||||
\(609\) | 5.60228 | 0.227016 | ||||||||
\(610\) | 1.16900 | 0.0473313 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2.07957 | −0.0840617 | ||||||||
\(613\) | 9.73818 | 0.393321 | 0.196661 | − | 0.980472i | \(-0.436990\pi\) | ||||
0.196661 | + | 0.980472i | \(0.436990\pi\) | |||||||
\(614\) | −10.3213 | −0.416535 | ||||||||
\(615\) | −20.5212 | −0.827495 | ||||||||
\(616\) | 7.26900 | 0.292877 | ||||||||
\(617\) | 0.763482 | 0.0307366 | 0.0153683 | − | 0.999882i | \(-0.495108\pi\) | ||||
0.0153683 | + | 0.999882i | \(0.495108\pi\) | |||||||
\(618\) | 1.27150 | 0.0511470 | ||||||||
\(619\) | 41.0925 | 1.65165 | 0.825824 | − | 0.563928i | \(-0.190711\pi\) | ||||
0.825824 | + | 0.563928i | \(0.190711\pi\) | |||||||
\(620\) | −40.6528 | −1.63265 | ||||||||
\(621\) | 1.84403 | 0.0739984 | ||||||||
\(622\) | −11.4714 | −0.459960 | ||||||||
\(623\) | 13.7545 | 0.551064 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.2547 | −1.21019 | ||||||||
\(626\) | 3.28219 | 0.131183 | ||||||||
\(627\) | −23.2046 | −0.926701 | ||||||||
\(628\) | −36.2762 | −1.44758 | ||||||||
\(629\) | 12.3496 | 0.492412 | ||||||||
\(630\) | 1.71063 | 0.0681531 | ||||||||
\(631\) | 14.4667 | 0.575910 | 0.287955 | − | 0.957644i | \(-0.407025\pi\) | ||||
0.287955 | + | 0.957644i | \(0.407025\pi\) | |||||||
\(632\) | −11.7143 | −0.465968 | ||||||||
\(633\) | −4.60698 | −0.183111 | ||||||||
\(634\) | −0.968580 | −0.0384672 | ||||||||
\(635\) | −35.9664 | −1.42728 | ||||||||
\(636\) | −0.778620 | −0.0308743 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −11.4714 | −0.454156 | ||||||||
\(639\) | 14.2569 | 0.563994 | ||||||||
\(640\) | 27.9482 | 1.10475 | ||||||||
\(641\) | 35.7069 | 1.41034 | 0.705169 | − | 0.709039i | \(-0.250871\pi\) | ||||
0.705169 | + | 0.709039i | \(0.250871\pi\) | |||||||
\(642\) | 12.4416 | 0.491032 | ||||||||
\(643\) | 26.4091 | 1.04147 | 0.520737 | − | 0.853717i | \(-0.325657\pi\) | ||||
0.520737 | + | 0.853717i | \(0.325657\pi\) | |||||||
\(644\) | 2.85819 | 0.112629 | ||||||||
\(645\) | −3.81897 | −0.150372 | ||||||||
\(646\) | −6.84252 | −0.269215 | ||||||||
\(647\) | 37.3543 | 1.46855 | 0.734275 | − | 0.678852i | \(-0.237522\pi\) | ||||
0.734275 | + | 0.678852i | \(0.237522\pi\) | |||||||
\(648\) | −2.38147 | −0.0935531 | ||||||||
\(649\) | 13.0925 | 0.513926 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.2857 | 0.403127 | ||||||||
\(652\) | −15.6619 | −0.613366 | ||||||||
\(653\) | −0.987881 | −0.0386588 | −0.0193294 | − | 0.999813i | \(-0.506153\pi\) | ||||
−0.0193294 | + | 0.999813i | \(0.506153\pi\) | |||||||
\(654\) | 0.953441 | 0.0372825 | ||||||||
\(655\) | 22.4091 | 0.875598 | ||||||||
\(656\) | 12.0903 | 0.472047 | ||||||||
\(657\) | 12.0189 | 0.468900 | ||||||||
\(658\) | −2.61069 | −0.101775 | ||||||||
\(659\) | −1.24653 | −0.0485578 | −0.0242789 | − | 0.999705i | \(-0.507729\pi\) | ||||
−0.0242789 | + | 0.999705i | \(0.507729\pi\) | |||||||
\(660\) | 12.0639 | 0.469587 | ||||||||
\(661\) | 33.8994 | 1.31853 | 0.659266 | − | 0.751910i | \(-0.270867\pi\) | ||||
0.659266 | + | 0.751910i | \(0.270867\pi\) | |||||||
\(662\) | 10.0595 | 0.390973 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.87749 | −0.111668 | ||||||||
\(665\) | −19.3856 | −0.751741 | ||||||||
\(666\) | 6.17482 | 0.239269 | ||||||||
\(667\) | −10.3308 | −0.400010 | ||||||||
\(668\) | −4.79906 | −0.185681 | ||||||||
\(669\) | −8.60698 | −0.332765 | ||||||||
\(670\) | −13.1514 | −0.508084 | ||||||||
\(671\) | −2.08587 | −0.0805240 | ||||||||
\(672\) | −5.77078 | −0.222613 | ||||||||
\(673\) | 42.5808 | 1.64137 | 0.820684 | − | 0.571382i | \(-0.193592\pi\) | ||||
0.820684 | + | 0.571382i | \(0.193592\pi\) | |||||||
\(674\) | −10.0033 | −0.385311 | ||||||||
\(675\) | 1.50235 | 0.0578253 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.8629 | −1.30146 | −0.650728 | − | 0.759311i | \(-0.725536\pi\) | ||||
−0.650728 | + | 0.759311i | \(0.725536\pi\) | |||||||
\(678\) | 3.75825 | 0.144335 | ||||||||
\(679\) | −7.18572 | −0.275763 | ||||||||
\(680\) | 8.14763 | 0.312447 | ||||||||
\(681\) | 14.4892 | 0.555229 | ||||||||
\(682\) | −21.0612 | −0.806473 | ||||||||
\(683\) | 34.5163 | 1.32073 | 0.660364 | − | 0.750946i | \(-0.270402\pi\) | ||||
0.660364 | + | 0.750946i | \(0.270402\pi\) | |||||||
\(684\) | 11.7833 | 0.450546 | ||||||||
\(685\) | −5.04240 | −0.192660 | ||||||||
\(686\) | −0.670843 | −0.0256129 | ||||||||
\(687\) | 20.1999 | 0.770673 | ||||||||
\(688\) | 2.24999 | 0.0857802 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −3.15445 | −0.120088 | ||||||||
\(691\) | 7.90679 | 0.300789 | 0.150394 | − | 0.988626i | \(-0.451946\pi\) | ||||
0.150394 | + | 0.988626i | \(0.451946\pi\) | |||||||
\(692\) | −4.26794 | −0.162243 | ||||||||
\(693\) | −3.05232 | −0.115948 | ||||||||
\(694\) | 4.74613 | 0.180161 | ||||||||
\(695\) | −33.4044 | −1.26710 | ||||||||
\(696\) | 13.3417 | 0.505715 | ||||||||
\(697\) | 10.7974 | 0.408980 | ||||||||
\(698\) | −14.1674 | −0.536244 | ||||||||
\(699\) | 7.28097 | 0.275391 | ||||||||
\(700\) | 2.32859 | 0.0880124 | ||||||||
\(701\) | −5.19510 | −0.196216 | −0.0981081 | − | 0.995176i | \(-0.531279\pi\) | ||||
−0.0981081 | + | 0.995176i | \(0.531279\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −69.9758 | −2.63919 | ||||||||
\(704\) | 2.64513 | 0.0996921 | ||||||||
\(705\) | −9.92360 | −0.373745 | ||||||||
\(706\) | 11.6487 | 0.438404 | ||||||||
\(707\) | 18.4416 | 0.693569 | ||||||||
\(708\) | −6.64839 | −0.249862 | ||||||||
\(709\) | −33.1971 | −1.24674 | −0.623372 | − | 0.781925i | \(-0.714238\pi\) | ||||
−0.623372 | + | 0.781925i | \(0.714238\pi\) | |||||||
\(710\) | −24.3882 | −0.915275 | ||||||||
\(711\) | 4.91891 | 0.184474 | ||||||||
\(712\) | 32.7561 | 1.22759 | ||||||||
\(713\) | −18.9671 | −0.710323 | ||||||||
\(714\) | −0.900061 | −0.0336839 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.44465 | 0.0913610 | ||||||||
\(717\) | −27.6688 | −1.03331 | ||||||||
\(718\) | −12.3114 | −0.459457 | ||||||||
\(719\) | 30.7261 | 1.14589 | 0.572944 | − | 0.819594i | \(-0.305801\pi\) | ||||
0.572944 | + | 0.819594i | \(0.305801\pi\) | |||||||
\(720\) | −3.83094 | −0.142771 | ||||||||
\(721\) | −1.89537 | −0.0705873 | ||||||||
\(722\) | 26.0252 | 0.968557 | ||||||||
\(723\) | 22.2187 | 0.826324 | ||||||||
\(724\) | −14.7503 | −0.548190 | ||||||||
\(725\) | −8.41657 | −0.312583 | ||||||||
\(726\) | −1.12928 | −0.0419114 | ||||||||
\(727\) | 1.83783 | 0.0681612 | 0.0340806 | − | 0.999419i | \(-0.489150\pi\) | ||||
0.0340806 | + | 0.999419i | \(0.489150\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −20.5598 | −0.760952 | ||||||||
\(731\) | 2.00938 | 0.0743197 | ||||||||
\(732\) | 1.05921 | 0.0391494 | ||||||||
\(733\) | 19.1857 | 0.708641 | 0.354320 | − | 0.935124i | \(-0.384712\pi\) | ||||
0.354320 | + | 0.935124i | \(0.384712\pi\) | |||||||
\(734\) | 5.63990 | 0.208173 | ||||||||
\(735\) | −2.54997 | −0.0940570 | ||||||||
\(736\) | 10.6415 | 0.392251 | ||||||||
\(737\) | 23.4664 | 0.864396 | ||||||||
\(738\) | 5.39869 | 0.198729 | ||||||||
\(739\) | 21.4882 | 0.790456 | 0.395228 | − | 0.918583i | \(-0.370666\pi\) | ||||
0.395228 | + | 0.918583i | \(0.370666\pi\) | |||||||
\(740\) | 36.3799 | 1.33735 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.336995 | −0.0123715 | ||||||||
\(743\) | −19.9430 | −0.731637 | −0.365819 | − | 0.930686i | \(-0.619211\pi\) | ||||
−0.365819 | + | 0.930686i | \(0.619211\pi\) | |||||||
\(744\) | 24.4950 | 0.898030 | ||||||||
\(745\) | 37.2140 | 1.36341 | ||||||||
\(746\) | 18.1748 | 0.665427 | ||||||||
\(747\) | 1.20828 | 0.0442088 | ||||||||
\(748\) | −6.34751 | −0.232088 | ||||||||
\(749\) | −18.5463 | −0.677665 | ||||||||
\(750\) | 5.98319 | 0.218475 | ||||||||
\(751\) | 38.4498 | 1.40305 | 0.701526 | − | 0.712644i | \(-0.252502\pi\) | ||||
0.701526 | + | 0.712644i | \(0.252502\pi\) | |||||||
\(752\) | 5.84661 | 0.213204 | ||||||||
\(753\) | 17.3092 | 0.630782 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13.8001 | −0.502238 | ||||||||
\(756\) | 1.54997 | 0.0563719 | ||||||||
\(757\) | −16.2931 | −0.592182 | −0.296091 | − | 0.955160i | \(-0.595683\pi\) | ||||
−0.296091 | + | 0.955160i | \(0.595683\pi\) | |||||||
\(758\) | 4.30451 | 0.156347 | ||||||||
\(759\) | 5.62857 | 0.204304 | ||||||||
\(760\) | −46.1663 | −1.67463 | ||||||||
\(761\) | −35.3380 | −1.28100 | −0.640500 | − | 0.767958i | \(-0.721273\pi\) | ||||
−0.640500 | + | 0.767958i | \(0.721273\pi\) | |||||||
\(762\) | 9.46199 | 0.342772 | ||||||||
\(763\) | −1.42126 | −0.0514530 | ||||||||
\(764\) | 35.4180 | 1.28138 | ||||||||
\(765\) | −3.42126 | −0.123696 | ||||||||
\(766\) | −21.8654 | −0.790028 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −9.08578 | −0.327855 | ||||||||
\(769\) | 11.5428 | 0.416244 | 0.208122 | − | 0.978103i | \(-0.433265\pi\) | ||||
0.208122 | + | 0.978103i | \(0.433265\pi\) | |||||||
\(770\) | 5.22138 | 0.188165 | ||||||||
\(771\) | −5.55837 | −0.200180 | ||||||||
\(772\) | 30.3422 | 1.09204 | ||||||||
\(773\) | 5.89786 | 0.212131 | 0.106066 | − | 0.994359i | \(-0.466175\pi\) | ||||
0.106066 | + | 0.994359i | \(0.466175\pi\) | |||||||
\(774\) | 1.00469 | 0.0361129 | ||||||||
\(775\) | −15.4526 | −0.555074 | ||||||||
\(776\) | −17.1126 | −0.614306 | ||||||||
\(777\) | −9.20457 | −0.330212 | ||||||||
\(778\) | 4.02506 | 0.144305 | ||||||||
\(779\) | −61.1803 | −2.19201 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 43.5165 | 1.55714 | ||||||||
\(782\) | 1.65974 | 0.0593522 | ||||||||
\(783\) | −5.60228 | −0.200209 | ||||||||
\(784\) | 1.50235 | 0.0536552 | ||||||||
\(785\) | −59.6806 | −2.13009 | ||||||||
\(786\) | −5.89537 | −0.210281 | ||||||||
\(787\) | −6.33079 | −0.225668 | −0.112834 | − | 0.993614i | \(-0.535993\pi\) | ||||
−0.112834 | + | 0.993614i | \(0.535993\pi\) | |||||||
\(788\) | −32.9014 | −1.17206 | ||||||||
\(789\) | 25.0486 | 0.891754 | ||||||||
\(790\) | −8.41444 | −0.299372 | ||||||||
\(791\) | −5.60228 | −0.199194 | ||||||||
\(792\) | −7.26900 | −0.258293 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −10.5672 | −0.375014 | ||||||||
\(795\) | −1.28097 | −0.0454312 | ||||||||
\(796\) | 10.3590 | 0.367166 | ||||||||
\(797\) | −22.0721 | −0.781835 | −0.390918 | − | 0.920426i | \(-0.627842\pi\) | ||||
−0.390918 | + | 0.920426i | \(0.627842\pi\) | |||||||
\(798\) | 5.09994 | 0.180536 | ||||||||
\(799\) | 5.22138 | 0.184719 | ||||||||
\(800\) | 8.66971 | 0.306520 | ||||||||
\(801\) | −13.7545 | −0.485993 | ||||||||
\(802\) | −17.5672 | −0.620318 | ||||||||
\(803\) | 36.6853 | 1.29460 | ||||||||
\(804\) | −11.9163 | −0.420254 | ||||||||
\(805\) | 4.70222 | 0.165732 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.55368 | −0.160297 | ||||||||
\(808\) | 43.9182 | 1.54504 | ||||||||
\(809\) | 36.2019 | 1.27279 | 0.636396 | − | 0.771363i | \(-0.280424\pi\) | ||||
0.636396 | + | 0.771363i | \(0.280424\pi\) | |||||||
\(810\) | −1.71063 | −0.0601054 | ||||||||
\(811\) | 52.4950 | 1.84335 | 0.921674 | − | 0.387964i | \(-0.126822\pi\) | ||||
0.921674 | + | 0.387964i | \(0.126822\pi\) | |||||||
\(812\) | −8.68337 | −0.304727 | ||||||||
\(813\) | −8.88325 | −0.311549 | ||||||||
\(814\) | 18.8475 | 0.660605 | ||||||||
\(815\) | −25.7665 | −0.902561 | ||||||||
\(816\) | 2.01568 | 0.0705628 | ||||||||
\(817\) | −11.3856 | −0.398332 | ||||||||
\(818\) | 11.6630 | 0.407787 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 31.8072 | 1.11076 | ||||||||
\(821\) | 0.972743 | 0.0339490 | 0.0169745 | − | 0.999856i | \(-0.494597\pi\) | ||||
0.0169745 | + | 0.999856i | \(0.494597\pi\) | |||||||
\(822\) | 1.32655 | 0.0462687 | ||||||||
\(823\) | −29.5572 | −1.03030 | −0.515150 | − | 0.857100i | \(-0.672264\pi\) | ||||
−0.515150 | + | 0.857100i | \(0.672264\pi\) | |||||||
\(824\) | −4.51377 | −0.157245 | ||||||||
\(825\) | 4.58563 | 0.159651 | ||||||||
\(826\) | −2.87749 | −0.100121 | ||||||||
\(827\) | −15.3191 | −0.532698 | −0.266349 | − | 0.963877i | \(-0.585817\pi\) | ||||
−0.266349 | + | 0.963877i | \(0.585817\pi\) | |||||||
\(828\) | −2.85819 | −0.0993291 | ||||||||
\(829\) | 27.0236 | 0.938570 | 0.469285 | − | 0.883047i | \(-0.344512\pi\) | ||||
0.469285 | + | 0.883047i | \(0.344512\pi\) | |||||||
\(830\) | −2.06693 | −0.0717440 | ||||||||
\(831\) | −5.38560 | −0.186824 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.34169 | 0.0464867 | ||||||||
\(834\) | 8.78800 | 0.304304 | ||||||||
\(835\) | −7.89528 | −0.273227 | ||||||||
\(836\) | 35.9664 | 1.24392 | ||||||||
\(837\) | −10.2857 | −0.355524 | ||||||||
\(838\) | −8.36948 | −0.289119 | ||||||||
\(839\) | −46.2200 | −1.59569 | −0.797846 | − | 0.602862i | \(-0.794027\pi\) | ||||
−0.797846 | + | 0.602862i | \(0.794027\pi\) | |||||||
\(840\) | −6.07268 | −0.209527 | ||||||||
\(841\) | 2.38560 | 0.0822619 | ||||||||
\(842\) | −6.42268 | −0.221340 | ||||||||
\(843\) | 12.9727 | 0.446805 | ||||||||
\(844\) | 7.14067 | 0.245792 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.61069 | 0.0897574 | ||||||||
\(847\) | 1.68337 | 0.0578413 | ||||||||
\(848\) | 0.754696 | 0.0259164 | ||||||||
\(849\) | −1.52589 | −0.0523684 | ||||||||
\(850\) | 1.35220 | 0.0463801 | ||||||||
\(851\) | 16.9735 | 0.581845 | ||||||||
\(852\) | −22.0977 | −0.757056 | ||||||||
\(853\) | 15.1094 | 0.517336 | 0.258668 | − | 0.965966i | \(-0.416716\pi\) | ||||
0.258668 | + | 0.965966i | \(0.416716\pi\) | |||||||
\(854\) | 0.458435 | 0.0156873 | ||||||||
\(855\) | 19.3856 | 0.662973 | ||||||||
\(856\) | −44.1674 | −1.50961 | ||||||||
\(857\) | −0.191631 | −0.00654599 | −0.00327299 | − | 0.999995i | \(-0.501042\pi\) | ||||
−0.00327299 | + | 0.999995i | \(0.501042\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.06419 | 0.241027 | 0.120514 | − | 0.992712i | \(-0.461546\pi\) | ||||
0.120514 | + | 0.992712i | \(0.461546\pi\) | |||||||
\(860\) | 5.91929 | 0.201846 | ||||||||
\(861\) | −8.04762 | −0.274262 | ||||||||
\(862\) | −3.48978 | −0.118862 | ||||||||
\(863\) | −41.6142 | −1.41657 | −0.708283 | − | 0.705929i | \(-0.750530\pi\) | ||||
−0.708283 | + | 0.705929i | \(0.750530\pi\) | |||||||
\(864\) | 5.77078 | 0.196326 | ||||||||
\(865\) | −7.02150 | −0.238738 | ||||||||
\(866\) | −11.5752 | −0.393341 | ||||||||
\(867\) | −15.1999 | −0.516215 | ||||||||
\(868\) | −15.9425 | −0.541122 | ||||||||
\(869\) | 15.0141 | 0.509318 | ||||||||
\(870\) | 9.58343 | 0.324909 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −3.38469 | −0.114620 | ||||||||
\(873\) | 7.18572 | 0.243200 | ||||||||
\(874\) | −9.40445 | −0.318110 | ||||||||
\(875\) | −8.91891 | −0.301514 | ||||||||
\(876\) | −18.6289 | −0.629411 | ||||||||
\(877\) | 52.5471 | 1.77439 | 0.887194 | − | 0.461396i | \(-0.152651\pi\) | ||||
0.887194 | + | 0.461396i | \(0.152651\pi\) | |||||||
\(878\) | −14.8876 | −0.502434 | ||||||||
\(879\) | −18.8545 | −0.635946 | ||||||||
\(880\) | −11.6932 | −0.394178 | ||||||||
\(881\) | 0.934500 | 0.0314841 | 0.0157421 | − | 0.999876i | \(-0.494989\pi\) | ||||
0.0157421 | + | 0.999876i | \(0.494989\pi\) | |||||||
\(882\) | 0.670843 | 0.0225885 | ||||||||
\(883\) | −42.6448 | −1.43511 | −0.717555 | − | 0.696501i | \(-0.754739\pi\) | ||||
−0.717555 | + | 0.696501i | \(0.754739\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.9378 | −0.367669 | ||||||||
\(886\) | −25.4463 | −0.854886 | ||||||||
\(887\) | 24.8833 | 0.835498 | 0.417749 | − | 0.908563i | \(-0.362819\pi\) | ||||
0.417749 | + | 0.908563i | \(0.362819\pi\) | |||||||
\(888\) | −21.9204 | −0.735601 | ||||||||
\(889\) | −14.1046 | −0.473054 | ||||||||
\(890\) | 23.5289 | 0.788691 | ||||||||
\(891\) | 3.05232 | 0.102256 | ||||||||
\(892\) | 13.3406 | 0.446675 | ||||||||
\(893\) | −29.5855 | −0.990040 | ||||||||
\(894\) | −9.79020 | −0.327433 | ||||||||
\(895\) | 4.02188 | 0.134437 | ||||||||
\(896\) | 10.9602 | 0.366155 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 22.3491 | 0.745799 | ||||||||
\(899\) | 57.6232 | 1.92184 | ||||||||
\(900\) | −2.32859 | −0.0776197 | ||||||||
\(901\) | 0.673990 | 0.0224539 | ||||||||
\(902\) | 16.4785 | 0.548674 | ||||||||
\(903\) | −1.49765 | −0.0498388 | ||||||||
\(904\) | −13.3417 | −0.443738 | ||||||||
\(905\) | −24.2668 | −0.806656 | ||||||||
\(906\) | 3.63052 | 0.120616 | ||||||||
\(907\) | 42.2207 | 1.40191 | 0.700957 | − | 0.713203i | \(-0.252756\pi\) | ||||
0.700957 | + | 0.713203i | \(0.252756\pi\) | |||||||
\(908\) | −22.4579 | −0.745292 | ||||||||
\(909\) | −18.4416 | −0.611670 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.1108 | 0.467513 | 0.233756 | − | 0.972295i | \(-0.424898\pi\) | ||||
0.233756 | + | 0.972295i | \(0.424898\pi\) | |||||||
\(912\) | −11.4213 | −0.378196 | ||||||||
\(913\) | 3.68806 | 0.122057 | ||||||||
\(914\) | 5.22767 | 0.172916 | ||||||||
\(915\) | 1.74258 | 0.0576078 | ||||||||
\(916\) | −31.3092 | −1.03449 | ||||||||
\(917\) | 8.78800 | 0.290205 | ||||||||
\(918\) | 0.900061 | 0.0297064 | ||||||||
\(919\) | −18.1547 | −0.598870 | −0.299435 | − | 0.954117i | \(-0.596798\pi\) | ||||
−0.299435 | + | 0.954117i | \(0.596798\pi\) | |||||||
\(920\) | 11.1982 | 0.369194 | ||||||||
\(921\) | −15.3856 | −0.506973 | ||||||||
\(922\) | −20.4317 | −0.672882 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 4.73100 | 0.155638 | ||||||||
\(925\) | 13.8284 | 0.454676 | ||||||||
\(926\) | −26.4741 | −0.869993 | ||||||||
\(927\) | 1.89537 | 0.0622521 | ||||||||
\(928\) | −32.3296 | −1.06127 | ||||||||
\(929\) | 8.24741 | 0.270589 | 0.135294 | − | 0.990805i | \(-0.456802\pi\) | ||||
0.135294 | + | 0.990805i | \(0.456802\pi\) | |||||||
\(930\) | 17.5949 | 0.576961 | ||||||||
\(931\) | −7.60228 | −0.249155 | ||||||||
\(932\) | −11.2853 | −0.369662 | ||||||||
\(933\) | −17.0999 | −0.559827 | ||||||||
\(934\) | −6.66353 | −0.218037 | ||||||||
\(935\) | −10.4428 | −0.341515 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.6693 | −0.707905 | −0.353953 | − | 0.935263i | \(-0.615163\pi\) | ||||
−0.353953 | + | 0.935263i | \(0.615163\pi\) | |||||||
\(938\) | −5.15748 | −0.168398 | ||||||||
\(939\) | 4.89263 | 0.159665 | ||||||||
\(940\) | 15.3813 | 0.501682 | ||||||||
\(941\) | −42.5238 | −1.38624 | −0.693118 | − | 0.720824i | \(-0.743763\pi\) | ||||
−0.693118 | + | 0.720824i | \(0.743763\pi\) | |||||||
\(942\) | 15.7007 | 0.511557 | ||||||||
\(943\) | 14.8401 | 0.483259 | ||||||||
\(944\) | 6.44412 | 0.209738 | ||||||||
\(945\) | 2.54997 | 0.0829505 | ||||||||
\(946\) | 3.06663 | 0.0997049 | ||||||||
\(947\) | 6.79792 | 0.220903 | 0.110451 | − | 0.993882i | \(-0.464770\pi\) | ||||
0.110451 | + | 0.993882i | \(0.464770\pi\) | |||||||
\(948\) | −7.62417 | −0.247621 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −7.66187 | −0.248584 | ||||||||
\(951\) | −1.44382 | −0.0468192 | ||||||||
\(952\) | 3.19519 | 0.103557 | ||||||||
\(953\) | 57.3782 | 1.85866 | 0.929331 | − | 0.369249i | \(-0.120385\pi\) | ||||
0.929331 | + | 0.369249i | \(0.120385\pi\) | |||||||
\(954\) | 0.336995 | 0.0109106 | ||||||||
\(955\) | 58.2688 | 1.88553 | ||||||||
\(956\) | 42.8857 | 1.38702 | ||||||||
\(957\) | −17.0999 | −0.552763 | ||||||||
\(958\) | 0.631585 | 0.0204056 | ||||||||
\(959\) | −1.97743 | −0.0638547 | ||||||||
\(960\) | −2.20980 | −0.0713209 | ||||||||
\(961\) | 74.7947 | 2.41273 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.5463 | 0.597645 | ||||||||
\(964\) | −34.4384 | −1.10918 | ||||||||
\(965\) | 49.9182 | 1.60692 | ||||||||
\(966\) | −1.23706 | −0.0398016 | ||||||||
\(967\) | −7.52393 | −0.241953 | −0.120977 | − | 0.992655i | \(-0.538603\pi\) | ||||
−0.120977 | + | 0.992655i | \(0.538603\pi\) | |||||||
\(968\) | 4.00890 | 0.128851 | ||||||||
\(969\) | −10.1999 | −0.327667 | ||||||||
\(970\) | −12.2921 | −0.394675 | ||||||||
\(971\) | −18.5807 | −0.596283 | −0.298141 | − | 0.954522i | \(-0.596367\pi\) | ||||
−0.298141 | + | 0.954522i | \(0.596367\pi\) | |||||||
\(972\) | −1.54997 | −0.0497153 | ||||||||
\(973\) | −13.0999 | −0.419965 | ||||||||
\(974\) | 26.3976 | 0.845835 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.02666 | −0.0328626 | ||||||||
\(977\) | 38.5939 | 1.23473 | 0.617364 | − | 0.786678i | \(-0.288201\pi\) | ||||
0.617364 | + | 0.786678i | \(0.288201\pi\) | |||||||
\(978\) | 6.77862 | 0.216756 | ||||||||
\(979\) | −41.9832 | −1.34179 | ||||||||
\(980\) | 3.95238 | 0.126254 | ||||||||
\(981\) | 1.42126 | 0.0453773 | ||||||||
\(982\) | 3.65861 | 0.116751 | ||||||||
\(983\) | 0.591837 | 0.0188767 | 0.00943834 | − | 0.999955i | \(-0.496996\pi\) | ||||
0.00943834 | + | 0.999955i | \(0.496996\pi\) | |||||||
\(984\) | −19.1652 | −0.610964 | ||||||||
\(985\) | −54.1286 | −1.72468 | ||||||||
\(986\) | −5.04240 | −0.160583 | ||||||||
\(987\) | −3.89166 | −0.123873 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.76172 | 0.0878177 | ||||||||
\(990\) | −5.22138 | −0.165946 | ||||||||
\(991\) | 9.41686 | 0.299136 | 0.149568 | − | 0.988751i | \(-0.452212\pi\) | ||||
0.149568 | + | 0.988751i | \(0.452212\pi\) | |||||||
\(992\) | −59.3563 | −1.88456 | ||||||||
\(993\) | 14.9953 | 0.475862 | ||||||||
\(994\) | −9.56413 | −0.303356 | ||||||||
\(995\) | 17.0424 | 0.540280 | ||||||||
\(996\) | −1.87280 | −0.0593420 | ||||||||
\(997\) | 22.1716 | 0.702180 | 0.351090 | − | 0.936342i | \(-0.385811\pi\) | ||||
0.351090 | + | 0.936342i | \(0.385811\pi\) | |||||||
\(998\) | 21.0359 | 0.665879 | ||||||||
\(999\) | 9.20457 | 0.291220 |
(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 | 3549.2.a.w.1.3 | 4 | ||
13.12 | even | 2 | 273.2.a.e.1.2 | ✓ | 4 | ||
39.38 | odd | 2 | 819.2.a.k.1.3 | 4 | |||
52.51 | odd | 2 | 4368.2.a.br.1.4 | 4 | |||
65.64 | even | 2 | 6825.2.a.bg.1.3 | 4 | |||
91.90 | odd | 2 | 1911.2.a.s.1.2 | 4 | |||
273.272 | even | 2 | 5733.2.a.bf.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.a.e.1.2 | ✓ | 4 | 13.12 | even | 2 | ||
819.2.a.k.1.3 | 4 | 39.38 | odd | 2 | |||
1911.2.a.s.1.2 | 4 | 91.90 | odd | 2 | |||
3549.2.a.w.1.3 | 4 | 1.1 | even | 1 | trivial | ||
4368.2.a.br.1.4 | 4 | 52.51 | odd | 2 | |||
5733.2.a.bf.1.3 | 4 | 273.272 | even | 2 | |||
6825.2.a.bg.1.3 | 4 | 65.64 | even | 2 |