Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3332,2,Mod(1,3332)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3332, 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("3332.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3332.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: | \(26.6061539535\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3332.1 |
$q$-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 | 0 | ||||||||
\(3\) | 0.381966 | 0.220528 | 0.110264 | − | 0.993902i | \(-0.464830\pi\) | ||||
0.110264 | + | 0.993902i | \(0.464830\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.38197 | 0.618034 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.85410 | −0.951367 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.23607 | −0.897524 | −0.448762 | − | 0.893651i | \(-0.648135\pi\) | ||||
−0.448762 | + | 0.893651i | \(0.648135\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.527864 | 0.136294 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.47214 | −0.567147 | −0.283573 | − | 0.958951i | \(-0.591520\pi\) | ||||
−0.283573 | + | 0.958951i | \(0.591520\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.23607 | 1.09180 | 0.545898 | − | 0.837852i | \(-0.316189\pi\) | ||||
0.545898 | + | 0.837852i | \(0.316189\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.09017 | −0.618034 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.23607 | −0.430331 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.76393 | 0.513249 | 0.256625 | − | 0.966511i | \(-0.417390\pi\) | ||||
0.256625 | + | 0.966511i | \(0.417390\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.56231 | 1.71744 | 0.858720 | − | 0.512444i | \(-0.171260\pi\) | ||||
0.858720 | + | 0.512444i | \(0.171260\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.70820 | 0.609625 | 0.304812 | − | 0.952412i | \(-0.401406\pi\) | ||||
0.304812 | + | 0.952412i | \(0.401406\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.23607 | −0.197929 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.14590 | −0.178959 | −0.0894796 | − | 0.995989i | \(-0.528520\pi\) | ||||
−0.0894796 | + | 0.995989i | \(0.528520\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.85410 | 0.740244 | 0.370122 | − | 0.928983i | \(-0.379316\pi\) | ||||
0.370122 | + | 0.928983i | \(0.379316\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.94427 | −0.587977 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.9443 | 1.59639 | 0.798193 | − | 0.602402i | \(-0.205789\pi\) | ||||
0.798193 | + | 0.602402i | \(0.205789\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.381966 | 0.0534859 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.3262 | 1.69314 | 0.846569 | − | 0.532278i | \(-0.178664\pi\) | ||||
0.846569 | + | 0.532278i | \(0.178664\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.944272 | −0.125072 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.23607 | 0.681678 | 0.340839 | − | 0.940122i | \(-0.389289\pi\) | ||||
0.340839 | + | 0.940122i | \(0.389289\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.5623 | 1.60844 | 0.804219 | − | 0.594333i | \(-0.202584\pi\) | ||||
0.804219 | + | 0.594333i | \(0.202584\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.47214 | −0.554700 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.09017 | −0.621863 | −0.310932 | − | 0.950432i | \(-0.600641\pi\) | ||||
−0.310932 | + | 0.950432i | \(0.600641\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.00000 | 0.240772 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.76393 | −0.565375 | −0.282687 | − | 0.959212i | \(-0.591226\pi\) | ||||
−0.282687 | + | 0.959212i | \(0.591226\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.85410 | −0.334047 | −0.167024 | − | 0.985953i | \(-0.553416\pi\) | ||||
−0.167024 | + | 0.985953i | \(0.553416\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.18034 | −0.136294 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.70820 | −0.192188 | −0.0960940 | − | 0.995372i | \(-0.530635\pi\) | ||||
−0.0960940 | + | 0.995372i | \(0.530635\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.70820 | 0.856467 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.52786 | −0.167705 | −0.0838524 | − | 0.996478i | \(-0.526722\pi\) | ||||
−0.0838524 | + | 0.996478i | \(0.526722\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.38197 | 0.149895 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.05573 | 0.113186 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.2361 | 1.40302 | 0.701510 | − | 0.712659i | \(-0.252509\pi\) | ||||
0.701510 | + | 0.712659i | \(0.252509\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.65248 | 0.378744 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.41641 | −0.350516 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.85410 | 0.391325 | 0.195662 | − | 0.980671i | \(-0.437314\pi\) | ||||
0.195662 | + | 0.980671i | \(0.437314\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.4721 | 1.63904 | 0.819519 | − | 0.573051i | \(-0.194240\pi\) | ||||
0.819519 | + | 0.573051i | \(0.194240\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.00000 | 0.591198 | 0.295599 | − | 0.955312i | \(-0.404481\pi\) | ||||
0.295599 | + | 0.955312i | \(0.404481\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.1803 | −0.975100 | −0.487550 | − | 0.873095i | \(-0.662109\pi\) | ||||
−0.487550 | + | 0.873095i | \(0.662109\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.41641 | 0.134439 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.94427 | −0.465118 | −0.232559 | − | 0.972582i | \(-0.574710\pi\) | ||||
−0.232559 | + | 0.972582i | \(0.574710\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.23607 | 0.674767 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.23607 | 0.853875 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.437694 | −0.0394655 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1803 | −1.00000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.3820 | −1.18746 | −0.593729 | − | 0.804665i | \(-0.702345\pi\) | ||||
−0.593729 | + | 0.804665i | \(0.702345\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.85410 | 0.163245 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.47214 | −0.215992 | −0.107996 | − | 0.994151i | \(-0.534443\pi\) | ||||
−0.107996 | + | 0.994151i | \(0.534443\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.09017 | −0.265959 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.0901699 | −0.00770374 | −0.00385187 | − | 0.999993i | \(-0.501226\pi\) | ||||
−0.00385187 | + | 0.999993i | \(0.501226\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.3820 | −0.965406 | −0.482703 | − | 0.875784i | \(-0.660345\pi\) | ||||
−0.482703 | + | 0.875784i | \(0.660345\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.18034 | 0.352048 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.81966 | 0.317206 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.61803 | −0.460247 | −0.230124 | − | 0.973161i | \(-0.573913\pi\) | ||||
−0.230124 | + | 0.973161i | \(0.573913\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.2705 | 0.998560 | 0.499280 | − | 0.866441i | \(-0.333598\pi\) | ||||
0.499280 | + | 0.866441i | \(0.333598\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.85410 | −0.230740 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.2148 | 1.06144 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.2918 | 0.821375 | 0.410687 | − | 0.911776i | \(-0.365289\pi\) | ||||
0.410687 | + | 0.911776i | \(0.365289\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.70820 | 0.373385 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.00000 | −0.469956 | −0.234978 | − | 0.972001i | \(-0.575502\pi\) | ||||
−0.234978 | + | 0.972001i | \(0.575502\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.5623 | −1.59116 | −0.795580 | − | 0.605849i | \(-0.792833\pi\) | ||||
−0.795580 | + | 0.605849i | \(0.792833\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.52786 | −0.194451 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.05573 | 0.539565 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.67376 | 0.507397 | 0.253698 | − | 0.967283i | \(-0.418353\pi\) | ||||
0.253698 | + | 0.967283i | \(0.418353\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.00000 | 0.150329 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.09017 | 0.604688 | 0.302344 | − | 0.953199i | \(-0.402231\pi\) | ||||
0.302344 | + | 0.953199i | \(0.402231\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.0000 | 1.04061 | 0.520306 | − | 0.853980i | \(-0.325818\pi\) | ||||
0.520306 | + | 0.853980i | \(0.325818\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.79837 | 0.354706 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.12461 | 0.376769 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.9098 | 0.789408 | 0.394704 | − | 0.918808i | \(-0.370847\pi\) | ||||
0.394704 | + | 0.918808i | \(0.370847\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.4721 | −1.04173 | −0.520864 | − | 0.853640i | \(-0.674390\pi\) | ||||
−0.520864 | + | 0.853640i | \(0.674390\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.70820 | −0.122327 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.29180 | −0.163284 | −0.0816419 | − | 0.996662i | \(-0.526016\pi\) | ||||
−0.0816419 | + | 0.996662i | \(0.526016\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.8541 | 1.33653 | 0.668266 | − | 0.743922i | \(-0.267037\pi\) | ||||
0.668266 | + | 0.743922i | \(0.267037\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.94427 | −0.137138 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.58359 | −0.110603 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −14.9443 | −1.03870 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.5967 | −1.76215 | −0.881076 | − | 0.472974i | \(-0.843180\pi\) | ||||
−0.881076 | + | 0.472974i | \(0.843180\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.81966 | −0.124681 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.70820 | 0.457496 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.09017 | −0.0736669 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.23607 | −0.217681 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.8885 | −1.33184 | −0.665918 | − | 0.746025i | \(-0.731960\pi\) | ||||
−0.665918 | + | 0.746025i | \(0.731960\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.81966 | 0.587977 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.8541 | −0.919529 | −0.459765 | − | 0.888041i | \(-0.652066\pi\) | ||||
−0.459765 | + | 0.888041i | \(0.652066\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.41641 | 0.622254 | 0.311127 | − | 0.950368i | \(-0.399294\pi\) | ||||
0.311127 | + | 0.950368i | \(0.399294\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.1803 | 1.32206 | 0.661029 | − | 0.750360i | \(-0.270120\pi\) | ||||
0.661029 | + | 0.750360i | \(0.270120\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.1246 | 0.986621 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.652476 | −0.0423829 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.6180 | −1.39835 | −0.699177 | − | 0.714948i | \(-0.746450\pi\) | ||||
−0.699177 | + | 0.714948i | \(0.746450\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.38197 | 0.0890203 | 0.0445101 | − | 0.999009i | \(-0.485827\pi\) | ||||
0.0445101 | + | 0.999009i | \(0.485827\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.65248 | 0.619207 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.00000 | 0.509028 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.583592 | −0.0369836 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.18034 | 0.137622 | 0.0688109 | − | 0.997630i | \(-0.478079\pi\) | ||||
0.0688109 | + | 0.997630i | \(0.478079\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.527864 | 0.0330561 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.4721 | 0.653234 | 0.326617 | − | 0.945157i | \(-0.394091\pi\) | ||||
0.326617 | + | 0.945157i | \(0.394091\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.88854 | −0.488289 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.41641 | −0.457315 | −0.228658 | − | 0.973507i | \(-0.573434\pi\) | ||||
−0.228658 | + | 0.973507i | \(0.573434\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.0344 | 1.04642 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.05573 | 0.309406 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.4164 | −0.818013 | −0.409006 | − | 0.912532i | \(-0.634125\pi\) | ||||
−0.409006 | + | 0.912532i | \(0.634125\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.5279 | −0.700268 | −0.350134 | − | 0.936700i | \(-0.613864\pi\) | ||||
−0.350134 | + | 0.936700i | \(0.613864\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.12461 | 0.548245 | 0.274122 | − | 0.961695i | \(-0.411613\pi\) | ||||
0.274122 | + | 0.961695i | \(0.411613\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −27.2918 | −1.63392 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.5066 | 0.865390 | 0.432695 | − | 0.901540i | \(-0.357563\pi\) | ||||
0.432695 | + | 0.901540i | \(0.357563\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.8541 | 1.53687 | 0.768433 | − | 0.639930i | \(-0.221037\pi\) | ||||
0.768433 | + | 0.639930i | \(0.221037\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.30495 | −0.0772987 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.47214 | 0.0862981 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.5967 | 1.26170 | 0.630848 | − | 0.775907i | \(-0.282707\pi\) | ||||
0.630848 | + | 0.775907i | \(0.282707\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.23607 | 0.421300 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.9443 | −0.979913 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.29180 | 0.361454 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 17.3607 | 0.994070 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.4164 | 0.994007 | 0.497003 | − | 0.867749i | \(-0.334434\pi\) | ||||
0.497003 | + | 0.867749i | \(0.334434\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.29180 | 0.130376 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.7426 | 0.665864 | 0.332932 | − | 0.942951i | \(-0.391962\pi\) | ||||
0.332932 | + | 0.942951i | \(0.391962\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.8541 | 1.34831 | 0.674157 | − | 0.738588i | \(-0.264507\pi\) | ||||
0.674157 | + | 0.738588i | \(0.264507\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.8885 | −0.667727 | −0.333864 | − | 0.942621i | \(-0.608352\pi\) | ||||
−0.333864 | + | 0.942621i | \(0.608352\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.47214 | −0.137553 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.0000 | 0.554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.88854 | −0.215037 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.32624 | −0.127862 | −0.0639308 | − | 0.997954i | \(-0.520364\pi\) | ||||
−0.0639308 | + | 0.997954i | \(0.520364\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10.5836 | −0.579977 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.03444 | −0.384333 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.4164 | 0.730838 | 0.365419 | − | 0.930843i | \(-0.380926\pi\) | ||||
0.365419 | + | 0.930843i | \(0.380926\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.88854 | −0.102572 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.76393 | 0.148805 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.88854 | −0.530845 | −0.265422 | − | 0.964132i | \(-0.585511\pi\) | ||||
−0.265422 | + | 0.964132i | \(0.585511\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.472136 | −0.0252729 | −0.0126364 | − | 0.999920i | \(-0.504022\pi\) | ||||
−0.0126364 | + | 0.999920i | \(0.504022\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.23607 | 0.386233 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.0689 | −1.28106 | −0.640529 | − | 0.767934i | \(-0.721285\pi\) | ||||
−0.640529 | + | 0.767934i | \(0.721285\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.58359 | −0.349421 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.14590 | 0.218812 | 0.109406 | − | 0.993997i | \(-0.465105\pi\) | ||||
0.109406 | + | 0.993997i | \(0.465105\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.8885 | −0.678344 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.20163 | −0.220528 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.94427 | −0.206453 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.6180 | −0.815255 | −0.407627 | − | 0.913148i | \(-0.633644\pi\) | ||||
−0.407627 | + | 0.913148i | \(0.633644\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.27051 | 0.170256 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.50658 | 0.388676 | 0.194338 | − | 0.980935i | \(-0.437744\pi\) | ||||
0.194338 | + | 0.980935i | \(0.437744\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.27051 | −0.220528 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.94427 | −0.460653 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.1246 | 1.59876 | 0.799382 | − | 0.600823i | \(-0.205160\pi\) | ||||
0.799382 | + | 0.600823i | \(0.205160\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.11146 | −0.261868 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.8885 | 1.32284 | 0.661421 | − | 0.750014i | \(-0.269954\pi\) | ||||
0.661421 | + | 0.750014i | \(0.269954\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.8541 | −0.704244 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.5066 | −0.532705 | −0.266352 | − | 0.963876i | \(-0.585818\pi\) | ||||
−0.266352 | + | 0.963876i | \(0.585818\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.23607 | 0.264799 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.944272 | −0.0476322 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.36068 | −0.118779 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.67376 | −0.0840037 | −0.0420019 | − | 0.999118i | \(-0.513374\pi\) | ||||
−0.0420019 | + | 0.999118i | \(0.513374\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.9443 | 1.44541 | 0.722704 | − | 0.691158i | \(-0.242899\pi\) | ||||
0.722704 | + | 0.691158i | \(0.242899\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −30.9443 | −1.54144 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.6525 | 0.529326 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.0000 | 0.791149 | 0.395575 | − | 0.918434i | \(-0.370545\pi\) | ||||
0.395575 | + | 0.918434i | \(0.370545\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.0344419 | −0.00169889 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.11146 | −0.103647 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.34752 | −0.212899 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.50658 | −0.122454 | −0.0612272 | − | 0.998124i | \(-0.519501\pi\) | ||||
−0.0612272 | + | 0.998124i | \(0.519501\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.8541 | −0.821419 | −0.410709 | − | 0.911766i | \(-0.634719\pi\) | ||||
−0.410709 | + | 0.911766i | \(0.634719\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −31.2361 | −1.51875 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.09017 | −0.149895 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.9443 | 0.719840 | 0.359920 | − | 0.932983i | \(-0.382804\pi\) | ||||
0.359920 | + | 0.932983i | \(0.382804\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.0000 | 1.44171 | 0.720854 | − | 0.693087i | \(-0.243750\pi\) | ||||
0.720854 | + | 0.693087i | \(0.243750\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.45898 | 0.0699528 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.9443 | −0.619208 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.8541 | −1.09077 | −0.545383 | − | 0.838187i | \(-0.683616\pi\) | ||||
−0.545383 | + | 0.838187i | \(0.683616\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.9443 | −1.18514 | −0.592569 | − | 0.805520i | \(-0.701886\pi\) | ||||
−0.592569 | + | 0.805520i | \(0.701886\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.2918 | 0.867114 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.14590 | −0.101497 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.9443 | −0.799650 | −0.399825 | − | 0.916592i | \(-0.630929\pi\) | ||||
−0.399825 | + | 0.916592i | \(0.630929\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.68692 | 0.220211 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.2705 | −0.994992 | −0.497496 | − | 0.867466i | \(-0.665747\pi\) | ||||
−0.497496 | + | 0.867466i | \(0.665747\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.23607 | −0.104371 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.8328 | 1.24973 | 0.624864 | − | 0.780733i | \(-0.285154\pi\) | ||||
0.624864 | + | 0.780733i | \(0.285154\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.7984 | 1.01306 | 0.506528 | − | 0.862223i | \(-0.330929\pi\) | ||||
0.506528 | + | 0.862223i | \(0.330929\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.04760 | 0.234077 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −33.2361 | −1.53798 | −0.768991 | − | 0.639260i | \(-0.779241\pi\) | ||||
−0.768991 | + | 0.639260i | \(0.779241\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.93112 | 0.181136 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.63932 | 0.350516 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −35.1803 | −1.61080 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.38197 | −0.382982 | −0.191491 | − | 0.981494i | \(-0.561332\pi\) | ||||
−0.191491 | + | 0.981494i | \(0.561332\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.0000 | −0.547153 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.32624 | 0.241852 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 36.9443 | 1.67410 | 0.837052 | − | 0.547123i | \(-0.184277\pi\) | ||||
0.837052 | + | 0.547123i | \(0.184277\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.29180 | −0.103639 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.2016 | −0.686040 | −0.343020 | − | 0.939328i | \(-0.611450\pi\) | ||||
−0.343020 | + | 0.939328i | \(0.611450\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.76393 | 0.124481 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.3050 | 1.22234 | 0.611169 | − | 0.791500i | \(-0.290700\pi\) | ||||
0.611169 | + | 0.791500i | \(0.290700\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.85410 | −0.350895 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.2705 | −0.948405 | −0.474203 | − | 0.880416i | \(-0.657264\pi\) | ||||
−0.474203 | + | 0.880416i | \(0.657264\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.7639 | 1.01298 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.965558 | −0.0428819 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.7639 | −0.831697 | −0.415848 | − | 0.909434i | \(-0.636515\pi\) | ||||
−0.415848 | + | 0.909434i | \(0.636515\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.52786 | 0.244061 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.29180 | 0.365380 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.54915 | 0.111895 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.90983 | −0.0836712 | −0.0418356 | − | 0.999125i | \(-0.513321\pi\) | ||||
−0.0418356 | + | 0.999125i | \(0.513321\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −38.6525 | −1.69015 | −0.845077 | − | 0.534644i | \(-0.820446\pi\) | ||||
−0.845077 | + | 0.534644i | \(0.820446\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.56231 | 0.416541 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.41641 | 0.192018 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.9443 | −0.648526 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.70820 | 0.160620 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.09017 | 0.133351 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.0000 | −1.28980 | −0.644900 | − | 0.764267i | \(-0.723101\pi\) | ||||
−0.644900 | + | 0.764267i | \(0.723101\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.34752 | 0.229484 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.0689 | −0.602645 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.1246 | 1.15976 | 0.579882 | − | 0.814700i | \(-0.303099\pi\) | ||||
0.579882 | + | 0.814700i | \(0.303099\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −35.8541 | −1.53022 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.83282 | −0.291088 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.95743 | 0.0830882 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.5279 | 0.657937 | 0.328968 | − | 0.944341i | \(-0.393299\pi\) | ||||
0.328968 | + | 0.944341i | \(0.393299\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.7082 | −0.664386 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.1246 | 0.974586 | 0.487293 | − | 0.873238i | \(-0.337984\pi\) | ||||
0.487293 | + | 0.873238i | \(0.337984\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.83282 | −0.287459 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.09017 | −0.171469 | −0.0857344 | − | 0.996318i | \(-0.527324\pi\) | ||||
−0.0857344 | + | 0.996318i | \(0.527324\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.65248 | −0.111003 | −0.0555013 | − | 0.998459i | \(-0.517676\pi\) | ||||
−0.0555013 | + | 0.998459i | \(0.517676\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.16718 | 0.174087 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16.1803 | −0.674767 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.5836 | 0.773645 | 0.386823 | − | 0.922154i | \(-0.373573\pi\) | ||||
0.386823 | + | 0.922154i | \(0.373573\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.52786 | −0.229730 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.7639 | 0.527724 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −30.0000 | −1.23823 | −0.619116 | − | 0.785299i | \(-0.712509\pi\) | ||||
−0.619116 | + | 0.785299i | \(0.712509\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.6393 | −0.974041 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.875388 | −0.0360087 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.5967 | −0.804742 | −0.402371 | − | 0.915477i | \(-0.631814\pi\) | ||||
−0.402371 | + | 0.915477i | \(0.631814\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.20163 | 0.294743 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.0344 | 0.696008 | 0.348004 | − | 0.937493i | \(-0.386859\pi\) | ||||
0.348004 | + | 0.937493i | \(0.386859\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.4721 | 1.32457 | 0.662283 | − | 0.749254i | \(-0.269588\pi\) | ||||
0.662283 | + | 0.749254i | \(0.269588\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.5279 | 0.591620 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.2016 | −0.618034 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.1459 | −0.736519 | −0.368260 | − | 0.929723i | \(-0.620046\pi\) | ||||
−0.368260 | + | 0.929723i | \(0.620046\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −35.4164 | −1.43279 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.85410 | 0.236445 | 0.118222 | − | 0.992987i | \(-0.462280\pi\) | ||||
0.118222 | + | 0.992987i | \(0.462280\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.604878 | −0.0243911 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.59675 | −0.144800 | −0.0723998 | − | 0.997376i | \(-0.523066\pi\) | ||||
−0.0723998 | + | 0.997376i | \(0.523066\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.83282 | −0.274634 | −0.137317 | − | 0.990527i | \(-0.543848\pi\) | ||||
−0.137317 | + | 0.990527i | \(0.543848\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.7082 | −0.469834 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.70820 | 0.147856 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.9787 | −1.23324 | −0.616622 | − | 0.787260i | \(-0.711499\pi\) | ||||
−0.616622 | + | 0.787260i | \(0.711499\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.77709 | −0.388604 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −18.4934 | −0.733889 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.5967 | 0.537879 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29.7771 | −1.17612 | −0.588062 | − | 0.808816i | \(-0.700109\pi\) | ||||
−0.588062 | + | 0.808816i | \(0.700109\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.6180 | 1.24689 | 0.623447 | − | 0.781866i | \(-0.285732\pi\) | ||||
0.623447 | + | 0.781866i | \(0.285732\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.56231 | 0.100891 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.5967 | −0.849056 | −0.424528 | − | 0.905415i | \(-0.639560\pi\) | ||||
−0.424528 | + | 0.905415i | \(0.639560\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20.7639 | −0.812555 | −0.406278 | − | 0.913750i | \(-0.633173\pi\) | ||||
−0.406278 | + | 0.913750i | \(0.633173\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.41641 | −0.133490 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.14590 | 0.317802 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.0902 | −0.821556 | −0.410778 | − | 0.911735i | \(-0.634743\pi\) | ||||
−0.410778 | + | 0.911735i | \(0.634743\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.4164 | −1.22196 | −0.610978 | − | 0.791647i | \(-0.709224\pi\) | ||||
−0.610978 | + | 0.791647i | \(0.709224\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.23607 | −0.0480049 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.4721 | 0.560363 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.59675 | −0.293707 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.9443 | −0.653154 | −0.326577 | − | 0.945171i | \(-0.605895\pi\) | ||||
−0.326577 | + | 0.945171i | \(0.605895\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.90983 | 0.265959 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.8328 | 1.26187 | 0.630934 | − | 0.775837i | \(-0.282672\pi\) | ||||
0.630934 | + | 0.775837i | \(0.282672\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.29180 | −0.202782 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.1115 | −0.386904 | −0.193452 | − | 0.981110i | \(-0.561968\pi\) | ||||
−0.193452 | + | 0.981110i | \(0.561968\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.124612 | −0.00476117 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.59675 | 0.137224 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −39.8885 | −1.51963 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.9787 | −1.36869 | −0.684347 | − | 0.729156i | \(-0.739913\pi\) | ||||
−0.684347 | + | 0.729156i | \(0.739913\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.7295 | −0.596654 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.14590 | −0.0434040 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.70820 | 0.291551 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.3050 | 1.48453 | 0.742264 | − | 0.670108i | \(-0.233752\pi\) | ||||
0.742264 | + | 0.670108i | \(0.233752\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.16718 | −0.345747 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.77709 | 0.217578 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.6525 | 1.07607 | 0.538033 | − | 0.842924i | \(-0.319168\pi\) | ||||
0.538033 | + | 0.842924i | \(0.319168\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.87539 | 0.182841 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 50.0689 | 1.87509 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.25735 | −0.308377 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.0902 | −0.823824 | −0.411912 | − | 0.911224i | \(-0.635139\pi\) | ||||
−0.411912 | + | 0.911224i | \(0.635139\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.527864 | 0.0196315 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.54102 | −0.317206 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.291796 | −0.0108221 | −0.00541106 | − | 0.999985i | \(-0.501722\pi\) | ||||
−0.00541106 | + | 0.999985i | \(0.501722\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19.4377 | −0.719915 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.85410 | 0.179535 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.2492 | −1.26502 | −0.632512 | − | 0.774551i | \(-0.717976\pi\) | ||||
−0.632512 | + | 0.774551i | \(0.717976\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.61803 | 0.353805 | 0.176903 | − | 0.984228i | \(-0.443392\pi\) | ||||
0.176903 | + | 0.984228i | \(0.443392\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.05573 | 0.112255 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.8885 | 1.31662 | 0.658311 | − | 0.752746i | \(-0.271271\pi\) | ||||
0.658311 | + | 0.752746i | \(0.271271\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.76393 | −0.284448 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.36068 | 0.159549 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.83282 | −0.103371 | −0.0516855 | − | 0.998663i | \(-0.516459\pi\) | ||||
−0.0516855 | + | 0.998663i | \(0.516459\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.832816 | 0.0303495 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.9574 | 0.617144 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.5623 | 0.529276 | 0.264638 | − | 0.964348i | \(-0.414748\pi\) | ||||
0.264638 | + | 0.964348i | \(0.414748\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 53.8885 | 1.95346 | 0.976729 | − | 0.214477i | \(-0.0688046\pi\) | ||||
0.976729 | + | 0.214477i | \(0.0688046\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.94427 | −0.142605 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −16.9443 | −0.611822 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.5967 | −0.490311 | −0.245156 | − | 0.969484i | \(-0.578839\pi\) | ||||
−0.245156 | + | 0.969484i | \(0.578839\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.00000 | 0.144056 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.4721 | −0.736332 | −0.368166 | − | 0.929760i | \(-0.620014\pi\) | ||||
−0.368166 | + | 0.929760i | \(0.620014\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −29.5492 | −1.06144 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.83282 | 0.101496 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.18034 | −0.220867 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.2229 | 0.507638 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.00000 | 0.285169 | 0.142585 | − | 0.989783i | \(-0.454459\pi\) | ||||
0.142585 | + | 0.989783i | \(0.454459\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.83282 | −0.100851 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −40.6525 | −1.44361 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.50658 | 0.230765 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.0000 | 0.425062 | 0.212531 | − | 0.977154i | \(-0.431829\pi\) | ||||
0.212531 | + | 0.977154i | \(0.431829\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.9443 | 0.387181 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −37.7771 | −1.33479 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.12461 | −0.180395 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.875388 | −0.0307770 | −0.0153885 | − | 0.999882i | \(-0.504899\pi\) | ||||
−0.0153885 | + | 0.999882i | \(0.504899\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.9787 | 1.12292 | 0.561462 | − | 0.827502i | \(-0.310239\pi\) | ||||
0.561462 | + | 0.827502i | \(0.310239\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.40325 | −0.154429 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.29180 | −0.290449 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.0000 | −0.419827 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 46.4721 | 1.62189 | 0.810944 | − | 0.585123i | \(-0.198954\pi\) | ||||
0.810944 | + | 0.585123i | \(0.198954\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.5410 | 0.855446 | 0.427723 | − | 0.903910i | \(-0.359316\pi\) | ||||
0.427723 | + | 0.903910i | \(0.359316\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −41.2361 | −1.43392 | −0.716959 | − | 0.697115i | \(-0.754467\pi\) | ||||
−0.716959 | + | 0.697115i | \(0.754467\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.5967 | 1.30579 | 0.652895 | − | 0.757449i | \(-0.273554\pi\) | ||||
0.652895 | + | 0.757449i | \(0.273554\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.48529 | 0.120903 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −28.4164 | −0.983390 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −21.3820 | −0.739069 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.0557 | −0.519781 | −0.259891 | − | 0.965638i | \(-0.583687\pi\) | ||||
−0.259891 | + | 0.965638i | \(0.583687\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.3607 | −0.736575 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.54102 | 0.190843 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.49342 | −0.120177 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.87539 | 0.338922 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.4164 | 0.665586 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45.7771 | 1.56738 | 0.783689 | − | 0.621154i | \(-0.213336\pi\) | ||||
0.783689 | + | 0.621154i | \(0.213336\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.75078 | 0.333470 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −44.7984 | −1.53028 | −0.765142 | − | 0.643862i | \(-0.777331\pi\) | ||||
−0.765142 | + | 0.643862i | \(0.777331\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.8328 | −1.25672 | −0.628360 | − | 0.777923i | \(-0.716273\pi\) | ||||
−0.628360 | + | 0.777923i | \(0.716273\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26.3262 | −0.896156 | −0.448078 | − | 0.893995i | \(-0.647891\pi\) | ||||
−0.448078 | + | 0.893995i | \(0.647891\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.22291 | 0.313588 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.381966 | 0.0129722 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.4721 | 0.558137 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11.0000 | −0.372294 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.3050 | −0.584347 | −0.292173 | − | 0.956365i | \(-0.594378\pi\) | ||||
−0.292173 | + | 0.956365i | \(0.594378\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.24922 | 0.278239 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.1591 | −0.712867 | −0.356433 | − | 0.934321i | \(-0.616007\pi\) | ||||
−0.356433 | + | 0.934321i | \(0.616007\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.6869 | −0.494254 | −0.247127 | − | 0.968983i | \(-0.579487\pi\) | ||||
−0.247127 | + | 0.968983i | \(0.579487\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.76393 | 0.0929086 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.7426 | −0.394279 | −0.197140 | − | 0.980375i | \(-0.563165\pi\) | ||||
−0.197140 | + | 0.980375i | \(0.563165\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −27.0557 | −0.905385 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.1803 | 0.373718 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.47214 | −0.216098 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 26.4296 | 0.881475 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.3262 | 0.410647 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19.3475 | 0.643133 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.1803 | −1.20135 | −0.600674 | − | 0.799494i | \(-0.705101\pi\) | ||||
−0.600674 | + | 0.799494i | \(0.705101\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −47.0132 | −1.55933 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50.7214 | 1.68047 | 0.840237 | − | 0.542220i | \(-0.182416\pi\) | ||||
0.840237 | + | 0.542220i | \(0.182416\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.63119 | 0.219220 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.6869 | −0.781359 | −0.390680 | − | 0.920527i | \(-0.627760\pi\) | ||||
−0.390680 | + | 0.920527i | \(0.627760\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.65248 | 0.219207 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15.4164 | 0.507437 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.4590 | −0.376769 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17.1246 | −0.562446 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −44.7984 | −1.46979 | −0.734893 | − | 0.678183i | \(-0.762768\pi\) | ||||
−0.734893 | + | 0.678183i | \(0.762768\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.48529 | 0.146842 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.4164 | 1.02633 | 0.513165 | − | 0.858290i | \(-0.328473\pi\) | ||||
0.513165 | + | 0.858290i | \(0.328473\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.11146 | 0.297341 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −43.7984 | −1.42779 | −0.713893 | − | 0.700255i | \(-0.753070\pi\) | ||||
−0.713893 | + | 0.700255i | \(0.753070\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.00000 | −0.195387 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 57.1935 | 1.85854 | 0.929269 | − | 0.369403i | \(-0.120438\pi\) | ||||
0.929269 | + | 0.369403i | \(0.120438\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.23607 | 0.299815 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.54102 | −0.147253 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −31.0902 | −1.00711 | −0.503555 | − | 0.863963i | \(-0.667975\pi\) | ||||
−0.503555 | + | 0.863963i | \(0.667975\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.0770 | 0.487881 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 60.4377 | 1.94960 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −20.0000 | −0.643823 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36.0902 | −1.16058 | −0.580291 | − | 0.814409i | \(-0.697061\pi\) | ||||
−0.580291 | + | 0.814409i | \(0.697061\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.944272 | −0.0303344 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.2361 | 0.874047 | 0.437024 | − | 0.899450i | \(-0.356033\pi\) | ||||
0.437024 | + | 0.899450i | \(0.356033\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.81966 | 0.122327 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.4508 | 0.622288 | 0.311144 | − | 0.950363i | \(-0.399288\pi\) | ||||
0.311144 | + | 0.950363i | \(0.399288\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 29.0557 | 0.927678 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.2705 | −1.06116 | −0.530582 | − | 0.847633i | \(-0.678027\pi\) | ||||
−0.530582 | + | 0.847633i | \(0.678027\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.16718 | −0.100915 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25.4164 | 0.808195 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −58.5410 | −1.85962 | −0.929808 | − | 0.368044i | \(-0.880028\pi\) | ||||
−0.929808 | + | 0.368044i | \(0.880028\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.888544 | −0.0281971 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 26.0557 | 0.826022 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.7426 | −0.403564 | −0.201782 | − | 0.979430i | \(-0.564673\pi\) | ||||
−0.201782 | + | 0.979430i | \(0.564673\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.29180 | −0.262341 |
(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 | 3332.2.a.o.1.1 | yes | 2 | |
7.6 | odd | 2 | 3332.2.a.g.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3332.2.a.g.1.2 | ✓ | 2 | 7.6 | odd | 2 | ||
3332.2.a.o.1.1 | yes | 2 | 1.1 | even | 1 | trivial |