Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3675,2,Mod(1,3675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3675, 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("3675.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3675.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: | \(29.3450227428\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.88404.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 7x^{2} + 5x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 525) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.494173\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3675.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.494173 | −0.349433 | −0.174717 | − | 0.984619i | \(-0.555901\pi\) | ||||
−0.174717 | + | 0.984619i | \(0.555901\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.75579 | −0.877896 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.494173 | −0.201745 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.85601 | 0.656200 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.33853 | 1.60963 | 0.804814 | − | 0.593527i | \(-0.202265\pi\) | ||||
0.804814 | + | 0.593527i | \(0.202265\pi\) | |||||||
\(12\) | −1.75579 | −0.506854 | ||||||||
\(13\) | −5.09433 | −1.41291 | −0.706456 | − | 0.707757i | \(-0.749707\pi\) | ||||
−0.706456 | + | 0.707757i | \(0.749707\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.59439 | 0.648598 | ||||||||
\(17\) | −0.350186 | −0.0849326 | −0.0424663 | − | 0.999098i | \(-0.513522\pi\) | ||||
−0.0424663 | + | 0.999098i | \(0.513522\pi\) | |||||||
\(18\) | −0.494173 | −0.116478 | ||||||||
\(19\) | −2.76745 | −0.634896 | −0.317448 | − | 0.948276i | \(-0.602826\pi\) | ||||
−0.317448 | + | 0.948276i | \(0.602826\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.63816 | −0.562458 | ||||||||
\(23\) | 7.51159 | 1.56627 | 0.783137 | − | 0.621849i | \(-0.213618\pi\) | ||||
0.783137 | + | 0.621849i | \(0.213618\pi\) | |||||||
\(24\) | 1.85601 | 0.378857 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.51748 | 0.493718 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.00000 | 0.742781 | 0.371391 | − | 0.928477i | \(-0.378881\pi\) | ||||
0.371391 | + | 0.928477i | \(0.378881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.11763 | −1.09876 | −0.549380 | − | 0.835573i | \(-0.685136\pi\) | ||||
−0.549380 | + | 0.835573i | \(0.685136\pi\) | |||||||
\(32\) | −4.99411 | −0.882841 | ||||||||
\(33\) | 5.33853 | 0.929319 | ||||||||
\(34\) | 0.173053 | 0.0296783 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.75579 | −0.292632 | ||||||||
\(37\) | −3.52324 | −0.579217 | −0.289608 | − | 0.957145i | \(-0.593525\pi\) | ||||
−0.289608 | + | 0.957145i | \(0.593525\pi\) | |||||||
\(38\) | 1.36760 | 0.221854 | ||||||||
\(39\) | −5.09433 | −0.815745 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.86177 | 1.22780 | 0.613901 | − | 0.789383i | \(-0.289599\pi\) | ||||
0.613901 | + | 0.789383i | \(0.289599\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.41726 | 0.216130 | 0.108065 | − | 0.994144i | \(-0.465535\pi\) | ||||
0.108065 | + | 0.994144i | \(0.465535\pi\) | |||||||
\(44\) | −9.37336 | −1.41309 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.71203 | −0.547308 | ||||||||
\(47\) | 8.85012 | 1.29092 | 0.645461 | − | 0.763793i | \(-0.276665\pi\) | ||||
0.645461 | + | 0.763793i | \(0.276665\pi\) | |||||||
\(48\) | 2.59439 | 0.374468 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.350186 | −0.0490359 | ||||||||
\(52\) | 8.94458 | 1.24039 | ||||||||
\(53\) | −6.32688 | −0.869064 | −0.434532 | − | 0.900656i | \(-0.643086\pi\) | ||||
−0.434532 | + | 0.900656i | \(0.643086\pi\) | |||||||
\(54\) | −0.494173 | −0.0672485 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.76745 | −0.366557 | ||||||||
\(58\) | −1.97669 | −0.259553 | ||||||||
\(59\) | −12.8501 | −1.67294 | −0.836471 | − | 0.548011i | \(-0.815385\pi\) | ||||
−0.836471 | + | 0.548011i | \(0.815385\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.00000 | 0.640184 | 0.320092 | − | 0.947386i | \(-0.396286\pi\) | ||||
0.320092 | + | 0.947386i | \(0.396286\pi\) | |||||||
\(62\) | 3.02317 | 0.383943 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.72083 | −0.340104 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.63816 | −0.324735 | ||||||||
\(67\) | 3.75579 | 0.458843 | 0.229422 | − | 0.973327i | \(-0.426317\pi\) | ||||
0.229422 | + | 0.973327i | \(0.426317\pi\) | |||||||
\(68\) | 0.614854 | 0.0745620 | ||||||||
\(69\) | 7.51159 | 0.904289 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.4883 | 1.83812 | 0.919060 | − | 0.394117i | \(-0.128950\pi\) | ||||
0.919060 | + | 0.394117i | \(0.128950\pi\) | |||||||
\(72\) | 1.85601 | 0.218733 | ||||||||
\(73\) | −7.67707 | −0.898533 | −0.449266 | − | 0.893398i | \(-0.648315\pi\) | ||||
−0.449266 | + | 0.893398i | \(0.648315\pi\) | |||||||
\(74\) | 1.74109 | 0.202398 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.85906 | 0.557373 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.51748 | 0.285048 | ||||||||
\(79\) | 2.36184 | 0.265728 | 0.132864 | − | 0.991134i | \(-0.457583\pi\) | ||||
0.132864 | + | 0.991134i | \(0.457583\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.88508 | −0.429035 | ||||||||
\(83\) | 6.87342 | 0.754456 | 0.377228 | − | 0.926120i | \(-0.376877\pi\) | ||||
0.377228 | + | 0.926120i | \(0.376877\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.700372 | −0.0755231 | ||||||||
\(87\) | 4.00000 | 0.428845 | ||||||||
\(88\) | 9.90838 | 1.05624 | ||||||||
\(89\) | 4.35019 | 0.461119 | 0.230559 | − | 0.973058i | \(-0.425944\pi\) | ||||
0.230559 | + | 0.973058i | \(0.425944\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −13.1888 | −1.37503 | ||||||||
\(93\) | −6.11763 | −0.634369 | ||||||||
\(94\) | −4.37349 | −0.451091 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.99411 | −0.509709 | ||||||||
\(97\) | −5.49993 | −0.558433 | −0.279217 | − | 0.960228i | \(-0.590075\pi\) | ||||
−0.279217 | + | 0.960228i | \(0.590075\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.33853 | 0.536543 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.64981 | −0.164163 | −0.0820813 | − | 0.996626i | \(-0.526157\pi\) | ||||
−0.0820813 | + | 0.996626i | \(0.526157\pi\) | |||||||
\(102\) | 0.173053 | 0.0171348 | ||||||||
\(103\) | 10.1614 | 1.00123 | 0.500616 | − | 0.865669i | \(-0.333107\pi\) | ||||
0.500616 | + | 0.865669i | \(0.333107\pi\) | |||||||
\(104\) | −9.45513 | −0.927152 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.12658 | 0.303680 | ||||||||
\(107\) | −5.36184 | −0.518349 | −0.259174 | − | 0.965831i | \(-0.583450\pi\) | ||||
−0.259174 | + | 0.965831i | \(0.583450\pi\) | |||||||
\(108\) | −1.75579 | −0.168951 | ||||||||
\(109\) | −0.105979 | −0.0101509 | −0.00507546 | − | 0.999987i | \(-0.501616\pi\) | ||||
−0.00507546 | + | 0.999987i | \(0.501616\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.52324 | −0.334411 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.67707 | −0.439981 | −0.219991 | − | 0.975502i | \(-0.570603\pi\) | ||||
−0.219991 | + | 0.975502i | \(0.570603\pi\) | |||||||
\(114\) | 1.36760 | 0.128087 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.02317 | −0.652085 | ||||||||
\(117\) | −5.09433 | −0.470971 | ||||||||
\(118\) | 6.35019 | 0.584582 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.4999 | 1.59090 | ||||||||
\(122\) | −2.47087 | −0.223702 | ||||||||
\(123\) | 7.86177 | 0.708872 | ||||||||
\(124\) | 10.7413 | 0.964597 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.5388 | −1.55632 | −0.778160 | − | 0.628066i | \(-0.783847\pi\) | ||||
−0.778160 | + | 0.628066i | \(0.783847\pi\) | |||||||
\(128\) | 11.3328 | 1.00169 | ||||||||
\(129\) | 1.41726 | 0.124783 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.02317 | 0.788358 | 0.394179 | − | 0.919034i | \(-0.371029\pi\) | ||||
0.394179 | + | 0.919034i | \(0.371029\pi\) | |||||||
\(132\) | −9.37336 | −0.815846 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.85601 | −0.160335 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.649950 | −0.0557327 | ||||||||
\(137\) | −0.834520 | −0.0712978 | −0.0356489 | − | 0.999364i | \(-0.511350\pi\) | ||||
−0.0356489 | + | 0.999364i | \(0.511350\pi\) | |||||||
\(138\) | −3.71203 | −0.315989 | ||||||||
\(139\) | 14.3152 | 1.21420 | 0.607101 | − | 0.794625i | \(-0.292332\pi\) | ||||
0.607101 | + | 0.794625i | \(0.292332\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.85012 | 0.745314 | ||||||||
\(142\) | −7.65389 | −0.642301 | ||||||||
\(143\) | −27.1962 | −2.27426 | ||||||||
\(144\) | 2.59439 | 0.216199 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.79380 | 0.313977 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.18608 | 0.508492 | ||||||||
\(149\) | 19.3967 | 1.58904 | 0.794518 | − | 0.607240i | \(-0.207723\pi\) | ||||
0.794518 | + | 0.607240i | \(0.207723\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.5272 | 1.50772 | 0.753860 | − | 0.657035i | \(-0.228189\pi\) | ||||
0.753860 | + | 0.657035i | \(0.228189\pi\) | |||||||
\(152\) | −5.13641 | −0.416618 | ||||||||
\(153\) | −0.350186 | −0.0283109 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 8.94458 | 0.716139 | ||||||||
\(157\) | 4.79956 | 0.383047 | 0.191523 | − | 0.981488i | \(-0.438657\pi\) | ||||
0.191523 | + | 0.981488i | \(0.438657\pi\) | |||||||
\(158\) | −1.16716 | −0.0928541 | ||||||||
\(159\) | −6.32688 | −0.501754 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.494173 | −0.0388259 | ||||||||
\(163\) | 0.826947 | 0.0647715 | 0.0323858 | − | 0.999475i | \(-0.489689\pi\) | ||||
0.0323858 | + | 0.999475i | \(0.489689\pi\) | |||||||
\(164\) | −13.8036 | −1.07788 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.39666 | −0.263632 | ||||||||
\(167\) | −4.61485 | −0.357108 | −0.178554 | − | 0.983930i | \(-0.557142\pi\) | ||||
−0.178554 | + | 0.983930i | \(0.557142\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9522 | 0.996319 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.76745 | −0.211632 | ||||||||
\(172\) | −2.48841 | −0.189740 | ||||||||
\(173\) | 12.6771 | 0.963819 | 0.481910 | − | 0.876221i | \(-0.339943\pi\) | ||||
0.481910 | + | 0.876221i | \(0.339943\pi\) | |||||||
\(174\) | −1.97669 | −0.149853 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 13.8503 | 1.04400 | ||||||||
\(177\) | −12.8501 | −0.965874 | ||||||||
\(178\) | −2.14975 | −0.161130 | ||||||||
\(179\) | 13.0465 | 0.975139 | 0.487570 | − | 0.873084i | \(-0.337883\pi\) | ||||
0.487570 | + | 0.873084i | \(0.337883\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.0594 | −1.11935 | −0.559677 | − | 0.828711i | \(-0.689075\pi\) | ||||
−0.559677 | + | 0.828711i | \(0.689075\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.00000 | 0.369611 | ||||||||
\(184\) | 13.9416 | 1.02779 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.02317 | 0.221670 | ||||||||
\(187\) | −1.86948 | −0.136710 | ||||||||
\(188\) | −15.5390 | −1.13330 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.52718 | 0.689363 | 0.344681 | − | 0.938720i | \(-0.387987\pi\) | ||||
0.344681 | + | 0.938720i | \(0.387987\pi\) | |||||||
\(192\) | −2.72083 | −0.196359 | ||||||||
\(193\) | −15.1060 | −1.08735 | −0.543676 | − | 0.839295i | \(-0.682968\pi\) | ||||
−0.543676 | + | 0.839295i | \(0.682968\pi\) | |||||||
\(194\) | 2.71792 | 0.195135 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.8890 | 1.20329 | 0.601647 | − | 0.798762i | \(-0.294512\pi\) | ||||
0.601647 | + | 0.798762i | \(0.294512\pi\) | |||||||
\(198\) | −2.63816 | −0.187486 | ||||||||
\(199\) | 25.2276 | 1.78833 | 0.894167 | − | 0.447734i | \(-0.147769\pi\) | ||||
0.894167 | + | 0.447734i | \(0.147769\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.75579 | 0.264913 | ||||||||
\(202\) | 0.815294 | 0.0573639 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.614854 | 0.0430484 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.02149 | −0.349864 | ||||||||
\(207\) | 7.51159 | 0.522091 | ||||||||
\(208\) | −13.2167 | −0.916412 | ||||||||
\(209\) | −14.7741 | −1.02195 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.3967 | 1.40416 | 0.702082 | − | 0.712096i | \(-0.252254\pi\) | ||||
0.702082 | + | 0.712096i | \(0.252254\pi\) | |||||||
\(212\) | 11.1087 | 0.762948 | ||||||||
\(213\) | 15.4883 | 1.06124 | ||||||||
\(214\) | 2.64968 | 0.181128 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.85601 | 0.126286 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.0523719 | 0.00354707 | ||||||||
\(219\) | −7.67707 | −0.518768 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.78396 | 0.120002 | ||||||||
\(222\) | 1.74109 | 0.116854 | ||||||||
\(223\) | 22.5738 | 1.51165 | 0.755827 | − | 0.654772i | \(-0.227235\pi\) | ||||
0.755827 | + | 0.654772i | \(0.227235\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.31128 | 0.153744 | ||||||||
\(227\) | 14.1653 | 0.940187 | 0.470093 | − | 0.882617i | \(-0.344220\pi\) | ||||
0.470093 | + | 0.882617i | \(0.344220\pi\) | |||||||
\(228\) | 4.85906 | 0.321799 | ||||||||
\(229\) | 17.8062 | 1.17667 | 0.588334 | − | 0.808618i | \(-0.299784\pi\) | ||||
0.588334 | + | 0.808618i | \(0.299784\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.42405 | 0.487413 | ||||||||
\(233\) | 13.6498 | 0.894229 | 0.447115 | − | 0.894477i | \(-0.352452\pi\) | ||||
0.447115 | + | 0.894477i | \(0.352452\pi\) | |||||||
\(234\) | 2.51748 | 0.164573 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 22.5621 | 1.46867 | ||||||||
\(237\) | 2.36184 | 0.153418 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.53489 | −0.487392 | −0.243696 | − | 0.969852i | \(-0.578360\pi\) | ||||
−0.243696 | + | 0.969852i | \(0.578360\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.5231 | −1.83733 | −0.918667 | − | 0.395032i | \(-0.870733\pi\) | ||||
−0.918667 | + | 0.395032i | \(0.870733\pi\) | |||||||
\(242\) | −8.64800 | −0.555915 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −8.77896 | −0.562016 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.88508 | −0.247704 | ||||||||
\(247\) | 14.0983 | 0.897051 | ||||||||
\(248\) | −11.3544 | −0.721005 | ||||||||
\(249\) | 6.87342 | 0.435586 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.8501 | 1.44229 | 0.721143 | − | 0.692786i | \(-0.243617\pi\) | ||||
0.721143 | + | 0.692786i | \(0.243617\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 40.1008 | 2.52112 | ||||||||
\(254\) | 8.66723 | 0.543830 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.158689 | −0.00991808 | ||||||||
\(257\) | −25.1381 | −1.56807 | −0.784036 | − | 0.620716i | \(-0.786842\pi\) | ||||
−0.784036 | + | 0.620716i | \(0.786842\pi\) | |||||||
\(258\) | −0.700372 | −0.0436033 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.00000 | 0.247594 | ||||||||
\(262\) | −4.45901 | −0.275479 | ||||||||
\(263\) | −13.5582 | −0.836034 | −0.418017 | − | 0.908439i | \(-0.637275\pi\) | ||||
−0.418017 | + | 0.908439i | \(0.637275\pi\) | |||||||
\(264\) | 9.90838 | 0.609819 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.35019 | 0.266227 | ||||||||
\(268\) | −6.59439 | −0.402817 | ||||||||
\(269\) | 9.02725 | 0.550401 | 0.275201 | − | 0.961387i | \(-0.411256\pi\) | ||||
0.275201 | + | 0.961387i | \(0.411256\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.77639 | −0.290145 | −0.145072 | − | 0.989421i | \(-0.546342\pi\) | ||||
−0.145072 | + | 0.989421i | \(0.546342\pi\) | |||||||
\(272\) | −0.908520 | −0.0550871 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.412397 | 0.0249138 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −13.1888 | −0.793872 | ||||||||
\(277\) | 1.87071 | 0.112400 | 0.0562002 | − | 0.998420i | \(-0.482101\pi\) | ||||
0.0562002 | + | 0.998420i | \(0.482101\pi\) | |||||||
\(278\) | −7.07420 | −0.424283 | ||||||||
\(279\) | −6.11763 | −0.366253 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.972748 | 0.0580293 | 0.0290147 | − | 0.999579i | \(-0.490763\pi\) | ||||
0.0290147 | + | 0.999579i | \(0.490763\pi\) | |||||||
\(282\) | −4.37349 | −0.260438 | ||||||||
\(283\) | 24.1797 | 1.43733 | 0.718667 | − | 0.695354i | \(-0.244752\pi\) | ||||
0.718667 | + | 0.695354i | \(0.244752\pi\) | |||||||
\(284\) | −27.1942 | −1.61368 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 13.4396 | 0.794703 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4.99411 | −0.294280 | ||||||||
\(289\) | −16.8774 | −0.992786 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.49993 | −0.322412 | ||||||||
\(292\) | 13.4793 | 0.788818 | ||||||||
\(293\) | −15.5349 | −0.907558 | −0.453779 | − | 0.891114i | \(-0.649924\pi\) | ||||
−0.453779 | + | 0.891114i | \(0.649924\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.53918 | −0.380082 | ||||||||
\(297\) | 5.33853 | 0.309773 | ||||||||
\(298\) | −9.58531 | −0.555262 | ||||||||
\(299\) | −38.2665 | −2.21301 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −9.15564 | −0.526848 | ||||||||
\(303\) | −1.64981 | −0.0947793 | ||||||||
\(304\) | −7.17984 | −0.411792 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.173053 | 0.00989276 | ||||||||
\(307\) | 3.39395 | 0.193703 | 0.0968516 | − | 0.995299i | \(-0.469123\pi\) | ||||
0.0968516 | + | 0.995299i | \(0.469123\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.1614 | 0.578062 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.46511 | 0.139783 | 0.0698917 | − | 0.997555i | \(-0.477735\pi\) | ||||
0.0698917 | + | 0.997555i | \(0.477735\pi\) | |||||||
\(312\) | −9.45513 | −0.535291 | ||||||||
\(313\) | 0.475526 | 0.0268783 | 0.0134392 | − | 0.999910i | \(-0.495722\pi\) | ||||
0.0134392 | + | 0.999910i | \(0.495722\pi\) | |||||||
\(314\) | −2.37181 | −0.133849 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.14690 | −0.233281 | ||||||||
\(317\) | 14.2995 | 0.803139 | 0.401570 | − | 0.915828i | \(-0.368465\pi\) | ||||
0.401570 | + | 0.915828i | \(0.368465\pi\) | |||||||
\(318\) | 3.12658 | 0.175330 | ||||||||
\(319\) | 21.3541 | 1.19560 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.36184 | −0.299269 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.969121 | 0.0539233 | ||||||||
\(324\) | −1.75579 | −0.0975440 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.408655 | −0.0226333 | ||||||||
\(327\) | −0.105979 | −0.00586064 | ||||||||
\(328\) | 14.5915 | 0.805683 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.5855 | −1.07651 | −0.538257 | − | 0.842781i | \(-0.680917\pi\) | ||||
−0.538257 | + | 0.842781i | \(0.680917\pi\) | |||||||
\(332\) | −12.0683 | −0.662334 | ||||||||
\(333\) | −3.52324 | −0.193072 | ||||||||
\(334\) | 2.28054 | 0.124785 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.38230 | 0.238719 | 0.119360 | − | 0.992851i | \(-0.461916\pi\) | ||||
0.119360 | + | 0.992851i | \(0.461916\pi\) | |||||||
\(338\) | −6.40061 | −0.348147 | ||||||||
\(339\) | −4.67707 | −0.254023 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −32.6592 | −1.76859 | ||||||||
\(342\) | 1.36760 | 0.0739512 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.63045 | 0.141824 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.26467 | −0.336791 | ||||||||
\(347\) | −9.59710 | −0.515200 | −0.257600 | − | 0.966252i | \(-0.582932\pi\) | ||||
−0.257600 | + | 0.966252i | \(0.582932\pi\) | |||||||
\(348\) | −7.02317 | −0.376481 | ||||||||
\(349\) | 19.9007 | 1.06526 | 0.532629 | − | 0.846349i | \(-0.321204\pi\) | ||||
0.532629 | + | 0.846349i | \(0.321204\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.09433 | −0.271915 | ||||||||
\(352\) | −26.6612 | −1.42105 | ||||||||
\(353\) | −27.3967 | −1.45818 | −0.729089 | − | 0.684419i | \(-0.760056\pi\) | ||||
−0.729089 | + | 0.684419i | \(0.760056\pi\) | |||||||
\(354\) | 6.35019 | 0.337509 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.63802 | −0.404815 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.44722 | −0.340746 | ||||||||
\(359\) | 25.5505 | 1.34850 | 0.674252 | − | 0.738502i | \(-0.264466\pi\) | ||||
0.674252 | + | 0.738502i | \(0.264466\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.3412 | −0.596908 | ||||||||
\(362\) | 7.44194 | 0.391140 | ||||||||
\(363\) | 17.4999 | 0.918508 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.47087 | −0.129154 | ||||||||
\(367\) | 22.2715 | 1.16256 | 0.581280 | − | 0.813703i | \(-0.302552\pi\) | ||||
0.581280 | + | 0.813703i | \(0.302552\pi\) | |||||||
\(368\) | 19.4880 | 1.01588 | ||||||||
\(369\) | 7.86177 | 0.409267 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 10.7413 | 0.556910 | ||||||||
\(373\) | −5.29477 | −0.274153 | −0.137076 | − | 0.990560i | \(-0.543771\pi\) | ||||
−0.137076 | + | 0.990560i | \(0.543771\pi\) | |||||||
\(374\) | 0.923847 | 0.0477710 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 16.4259 | 0.847103 | ||||||||
\(377\) | −20.3773 | −1.04948 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.10203 | 0.159341 | 0.0796704 | − | 0.996821i | \(-0.474613\pi\) | ||||
0.0796704 | + | 0.996821i | \(0.474613\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.5388 | −0.898542 | ||||||||
\(382\) | −4.70808 | −0.240886 | ||||||||
\(383\) | −21.6127 | −1.10436 | −0.552179 | − | 0.833726i | \(-0.686203\pi\) | ||||
−0.552179 | + | 0.833726i | \(0.686203\pi\) | |||||||
\(384\) | 11.3328 | 0.578323 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.46497 | 0.379957 | ||||||||
\(387\) | 1.41726 | 0.0720434 | ||||||||
\(388\) | 9.65674 | 0.490247 | ||||||||
\(389\) | −12.8616 | −0.652111 | −0.326055 | − | 0.945351i | \(-0.605720\pi\) | ||||
−0.326055 | + | 0.945351i | \(0.605720\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.63045 | −0.133028 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.02317 | 0.455159 | ||||||||
\(394\) | −8.34611 | −0.420471 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −9.37336 | −0.471029 | ||||||||
\(397\) | −6.99514 | −0.351076 | −0.175538 | − | 0.984473i | \(-0.556166\pi\) | ||||
−0.175538 | + | 0.984473i | \(0.556166\pi\) | |||||||
\(398\) | −12.4668 | −0.624904 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.16140 | −0.157873 | −0.0789364 | − | 0.996880i | \(-0.525152\pi\) | ||||
−0.0789364 | + | 0.996880i | \(0.525152\pi\) | |||||||
\(402\) | −1.85601 | −0.0925695 | ||||||||
\(403\) | 31.1652 | 1.55245 | ||||||||
\(404\) | 2.89673 | 0.144118 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.8089 | −0.932324 | ||||||||
\(408\) | −0.649950 | −0.0321773 | ||||||||
\(409\) | −2.49507 | −0.123373 | −0.0616866 | − | 0.998096i | \(-0.519648\pi\) | ||||
−0.0616866 | + | 0.998096i | \(0.519648\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.834520 | −0.0411638 | ||||||||
\(412\) | −17.8413 | −0.878978 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.71203 | −0.182436 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 25.4416 | 1.24738 | ||||||||
\(417\) | 14.3152 | 0.701020 | ||||||||
\(418\) | 7.30097 | 0.357102 | ||||||||
\(419\) | 32.6748 | 1.59627 | 0.798134 | − | 0.602480i | \(-0.205821\pi\) | ||||
0.798134 | + | 0.602480i | \(0.205821\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.8774 | −1.30992 | −0.654961 | − | 0.755662i | \(-0.727315\pi\) | ||||
−0.654961 | + | 0.755662i | \(0.727315\pi\) | |||||||
\(422\) | −10.0795 | −0.490662 | ||||||||
\(423\) | 8.85012 | 0.430307 | ||||||||
\(424\) | −11.7428 | −0.570279 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −7.65389 | −0.370832 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 9.41428 | 0.455056 | ||||||||
\(429\) | −27.1962 | −1.31305 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.1887 | 0.683443 | 0.341722 | − | 0.939801i | \(-0.388990\pi\) | ||||
0.341722 | + | 0.939801i | \(0.388990\pi\) | |||||||
\(432\) | 2.59439 | 0.124823 | ||||||||
\(433\) | −29.9717 | −1.44035 | −0.720174 | − | 0.693794i | \(-0.755938\pi\) | ||||
−0.720174 | + | 0.693794i | \(0.755938\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.186077 | 0.00891146 | ||||||||
\(437\) | −20.7879 | −0.994420 | ||||||||
\(438\) | 3.79380 | 0.181275 | ||||||||
\(439\) | 2.07386 | 0.0989802 | 0.0494901 | − | 0.998775i | \(-0.484240\pi\) | ||||
0.0494901 | + | 0.998775i | \(0.484240\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.881586 | −0.0419328 | ||||||||
\(443\) | 32.0775 | 1.52405 | 0.762025 | − | 0.647548i | \(-0.224205\pi\) | ||||
0.762025 | + | 0.647548i | \(0.224205\pi\) | |||||||
\(444\) | 6.18608 | 0.293578 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11.1554 | −0.528222 | ||||||||
\(447\) | 19.3967 | 0.917431 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.46103 | −0.210529 | −0.105264 | − | 0.994444i | \(-0.533569\pi\) | ||||
−0.105264 | + | 0.994444i | \(0.533569\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 41.9703 | 1.97631 | ||||||||
\(452\) | 8.21196 | 0.386258 | ||||||||
\(453\) | 18.5272 | 0.870483 | ||||||||
\(454\) | −7.00014 | −0.328533 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.13641 | −0.240535 | ||||||||
\(457\) | −2.27022 | −0.106197 | −0.0530983 | − | 0.998589i | \(-0.516910\pi\) | ||||
−0.0530983 | + | 0.998589i | \(0.516910\pi\) | |||||||
\(458\) | −8.79936 | −0.411167 | ||||||||
\(459\) | −0.350186 | −0.0163453 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.33096 | −0.201713 | −0.100856 | − | 0.994901i | \(-0.532158\pi\) | ||||
−0.100856 | + | 0.994901i | \(0.532158\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −41.7856 | −1.94194 | −0.970971 | − | 0.239196i | \(-0.923116\pi\) | ||||
−0.970971 | + | 0.239196i | \(0.923116\pi\) | |||||||
\(464\) | 10.3776 | 0.481767 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.74537 | −0.312473 | ||||||||
\(467\) | −38.3773 | −1.77589 | −0.887945 | − | 0.459950i | \(-0.847867\pi\) | ||||
−0.887945 | + | 0.459950i | \(0.847867\pi\) | |||||||
\(468\) | 8.94458 | 0.413463 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.79956 | 0.221152 | ||||||||
\(472\) | −23.8500 | −1.09778 | ||||||||
\(473\) | 7.56609 | 0.347889 | ||||||||
\(474\) | −1.16716 | −0.0536093 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.32688 | −0.289688 | ||||||||
\(478\) | 3.72354 | 0.170311 | ||||||||
\(479\) | −38.0386 | −1.73803 | −0.869015 | − | 0.494786i | \(-0.835246\pi\) | ||||
−0.869015 | + | 0.494786i | \(0.835246\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.9485 | 0.818382 | ||||||||
\(482\) | 14.0954 | 0.642026 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −30.7263 | −1.39665 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.494173 | −0.0224162 | ||||||||
\(487\) | 22.5827 | 1.02332 | 0.511661 | − | 0.859188i | \(-0.329030\pi\) | ||||
0.511661 | + | 0.859188i | \(0.329030\pi\) | |||||||
\(488\) | 9.28006 | 0.420089 | ||||||||
\(489\) | 0.826947 | 0.0373959 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.134148 | −0.00605400 | −0.00302700 | − | 0.999995i | \(-0.500964\pi\) | ||||
−0.00302700 | + | 0.999995i | \(0.500964\pi\) | |||||||
\(492\) | −13.8036 | −0.622316 | ||||||||
\(493\) | −1.40074 | −0.0630863 | ||||||||
\(494\) | −6.96699 | −0.313460 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −15.8715 | −0.712653 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3.39666 | −0.152208 | ||||||||
\(499\) | −15.5554 | −0.696353 | −0.348177 | − | 0.937429i | \(-0.613199\pi\) | ||||
−0.348177 | + | 0.937429i | \(0.613199\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.61485 | −0.206176 | ||||||||
\(502\) | −11.2919 | −0.503983 | ||||||||
\(503\) | −4.39272 | −0.195862 | −0.0979308 | − | 0.995193i | \(-0.531222\pi\) | ||||
−0.0979308 | + | 0.995193i | \(0.531222\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −19.8168 | −0.880963 | ||||||||
\(507\) | 12.9522 | 0.575225 | ||||||||
\(508\) | 30.7946 | 1.36629 | ||||||||
\(509\) | −2.08753 | −0.0925283 | −0.0462642 | − | 0.998929i | \(-0.514732\pi\) | ||||
−0.0462642 | + | 0.998929i | \(0.514732\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.5871 | −0.998219 | ||||||||
\(513\) | −2.76745 | −0.122186 | ||||||||
\(514\) | 12.4226 | 0.547936 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.48841 | −0.109546 | ||||||||
\(517\) | 47.2466 | 2.07791 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.6771 | 0.556461 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.7001 | 1.60786 | 0.803930 | − | 0.594724i | \(-0.202738\pi\) | ||||
0.803930 | + | 0.594724i | \(0.202738\pi\) | |||||||
\(522\) | −1.97669 | −0.0865175 | ||||||||
\(523\) | −12.6291 | −0.552231 | −0.276116 | − | 0.961124i | \(-0.589047\pi\) | ||||
−0.276116 | + | 0.961124i | \(0.589047\pi\) | |||||||
\(524\) | −15.8428 | −0.692097 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.70010 | 0.292138 | ||||||||
\(527\) | 2.14231 | 0.0933205 | ||||||||
\(528\) | 13.8503 | 0.602755 | ||||||||
\(529\) | 33.4239 | 1.45321 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.8501 | −0.557648 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −40.0504 | −1.73478 | ||||||||
\(534\) | −2.14975 | −0.0930286 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.97080 | 0.301093 | ||||||||
\(537\) | 13.0465 | 0.562997 | ||||||||
\(538\) | −4.46103 | −0.192329 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.8412 | 1.66991 | 0.834956 | − | 0.550316i | \(-0.185493\pi\) | ||||
0.834956 | + | 0.550316i | \(0.185493\pi\) | |||||||
\(542\) | 2.36036 | 0.101386 | ||||||||
\(543\) | −15.0594 | −0.646259 | ||||||||
\(544\) | 1.74887 | 0.0749820 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.6010 | 0.795323 | 0.397662 | − | 0.917532i | \(-0.369822\pi\) | ||||
0.397662 | + | 0.917532i | \(0.369822\pi\) | |||||||
\(548\) | 1.46524 | 0.0625921 | ||||||||
\(549\) | 5.00000 | 0.213395 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.0698 | −0.471589 | ||||||||
\(552\) | 13.9416 | 0.593394 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −0.924457 | −0.0392764 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −25.1346 | −1.06594 | ||||||||
\(557\) | −5.16548 | −0.218868 | −0.109434 | − | 0.993994i | \(-0.534904\pi\) | ||||
−0.109434 | + | 0.993994i | \(0.534904\pi\) | |||||||
\(558\) | 3.02317 | 0.127981 | ||||||||
\(559\) | −7.21998 | −0.305373 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.86948 | −0.0789295 | ||||||||
\(562\) | −0.480706 | −0.0202774 | ||||||||
\(563\) | −12.6382 | −0.532635 | −0.266317 | − | 0.963885i | \(-0.585807\pi\) | ||||
−0.266317 | + | 0.963885i | \(0.585807\pi\) | |||||||
\(564\) | −15.5390 | −0.654309 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −11.9490 | −0.502253 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 28.7464 | 1.20617 | ||||||||
\(569\) | −8.79741 | −0.368807 | −0.184403 | − | 0.982851i | \(-0.559035\pi\) | ||||
−0.184403 | + | 0.982851i | \(0.559035\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.9033 | −1.66990 | −0.834950 | − | 0.550327i | \(-0.814503\pi\) | ||||
−0.834950 | + | 0.550327i | \(0.814503\pi\) | |||||||
\(572\) | 47.7509 | 1.99657 | ||||||||
\(573\) | 9.52718 | 0.398004 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.72083 | −0.113368 | ||||||||
\(577\) | −2.71689 | −0.113106 | −0.0565528 | − | 0.998400i | \(-0.518011\pi\) | ||||
−0.0565528 | + | 0.998400i | \(0.518011\pi\) | |||||||
\(578\) | 8.34035 | 0.346913 | ||||||||
\(579\) | −15.1060 | −0.627783 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 2.71792 | 0.112661 | ||||||||
\(583\) | −33.7763 | −1.39887 | ||||||||
\(584\) | −14.2487 | −0.589617 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.67693 | 0.317131 | ||||||||
\(587\) | −9.02317 | −0.372426 | −0.186213 | − | 0.982509i | \(-0.559621\pi\) | ||||
−0.186213 | + | 0.982509i | \(0.559621\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.9302 | 0.697597 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.8890 | 0.694722 | ||||||||
\(592\) | −9.14067 | −0.375679 | ||||||||
\(593\) | 10.4651 | 0.429750 | 0.214875 | − | 0.976642i | \(-0.431066\pi\) | ||||
0.214875 | + | 0.976642i | \(0.431066\pi\) | |||||||
\(594\) | −2.63816 | −0.108245 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −34.0565 | −1.39501 | ||||||||
\(597\) | 25.2276 | 1.03250 | ||||||||
\(598\) | 18.9103 | 0.773298 | ||||||||
\(599\) | 9.63830 | 0.393810 | 0.196905 | − | 0.980423i | \(-0.436911\pi\) | ||||
0.196905 | + | 0.980423i | \(0.436911\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.19544 | 0.293508 | 0.146754 | − | 0.989173i | \(-0.453117\pi\) | ||||
0.146754 | + | 0.989173i | \(0.453117\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.75579 | 0.152948 | ||||||||
\(604\) | −32.5299 | −1.32362 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.815294 | 0.0331191 | ||||||||
\(607\) | 39.3384 | 1.59670 | 0.798348 | − | 0.602196i | \(-0.205708\pi\) | ||||
0.798348 | + | 0.602196i | \(0.205708\pi\) | |||||||
\(608\) | 13.8209 | 0.560512 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −45.0854 | −1.82396 | ||||||||
\(612\) | 0.614854 | 0.0248540 | ||||||||
\(613\) | −19.5464 | −0.789472 | −0.394736 | − | 0.918795i | \(-0.629164\pi\) | ||||
−0.394736 | + | 0.918795i | \(0.629164\pi\) | |||||||
\(614\) | −1.67720 | −0.0676863 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.9588 | 1.44765 | 0.723824 | − | 0.689985i | \(-0.242383\pi\) | ||||
0.723824 | + | 0.689985i | \(0.242383\pi\) | |||||||
\(618\) | −5.02149 | −0.201994 | ||||||||
\(619\) | −8.55943 | −0.344033 | −0.172016 | − | 0.985094i | \(-0.555028\pi\) | ||||
−0.172016 | + | 0.985094i | \(0.555028\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.51159 | 0.301430 | ||||||||
\(622\) | −1.21819 | −0.0488450 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −13.2167 | −0.529091 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −0.234992 | −0.00939219 | ||||||||
\(627\) | −14.7741 | −0.590021 | ||||||||
\(628\) | −8.42703 | −0.336275 | ||||||||
\(629\) | 1.23379 | 0.0491944 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.5192 | −0.697427 | −0.348713 | − | 0.937229i | \(-0.613381\pi\) | ||||
−0.348713 | + | 0.937229i | \(0.613381\pi\) | |||||||
\(632\) | 4.38360 | 0.174370 | ||||||||
\(633\) | 20.3967 | 0.810695 | ||||||||
\(634\) | −7.06643 | −0.280644 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 11.1087 | 0.440488 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −10.5526 | −0.417783 | ||||||||
\(639\) | 15.4883 | 0.612707 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.2819 | 0.643095 | 0.321548 | − | 0.946893i | \(-0.395797\pi\) | ||||
0.321548 | + | 0.946893i | \(0.395797\pi\) | |||||||
\(642\) | 2.64968 | 0.104574 | ||||||||
\(643\) | 15.7544 | 0.621294 | 0.310647 | − | 0.950525i | \(-0.399454\pi\) | ||||
0.310647 | + | 0.950525i | \(0.399454\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.478914 | −0.0188426 | ||||||||
\(647\) | −45.4394 | −1.78641 | −0.893203 | − | 0.449653i | \(-0.851548\pi\) | ||||
−0.893203 | + | 0.449653i | \(0.851548\pi\) | |||||||
\(648\) | 1.85601 | 0.0729111 | ||||||||
\(649\) | −68.6008 | −2.69282 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.45195 | −0.0568627 | ||||||||
\(653\) | 19.1614 | 0.749844 | 0.374922 | − | 0.927056i | \(-0.377670\pi\) | ||||
0.374922 | + | 0.927056i | \(0.377670\pi\) | |||||||
\(654\) | 0.0523719 | 0.00204790 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 20.3965 | 0.796351 | ||||||||
\(657\) | −7.67707 | −0.299511 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.76258 | −0.341342 | −0.170671 | − | 0.985328i | \(-0.554593\pi\) | ||||
−0.170671 | + | 0.985328i | \(0.554593\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.07602 | 0.353016 | 0.176508 | − | 0.984299i | \(-0.443520\pi\) | ||||
0.176508 | + | 0.984299i | \(0.443520\pi\) | |||||||
\(662\) | 9.67861 | 0.376170 | ||||||||
\(663\) | 1.78396 | 0.0692833 | ||||||||
\(664\) | 12.7572 | 0.495074 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.74109 | 0.0674659 | ||||||||
\(667\) | 30.0463 | 1.16340 | ||||||||
\(668\) | 8.10273 | 0.313504 | ||||||||
\(669\) | 22.5738 | 0.872753 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 26.6927 | 1.03046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.3460 | −0.707185 | −0.353593 | − | 0.935400i | \(-0.615040\pi\) | ||||
−0.353593 | + | 0.935400i | \(0.615040\pi\) | |||||||
\(674\) | −2.16562 | −0.0834164 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −22.7413 | −0.874665 | ||||||||
\(677\) | 1.79593 | 0.0690233 | 0.0345116 | − | 0.999404i | \(-0.489012\pi\) | ||||
0.0345116 | + | 0.999404i | \(0.489012\pi\) | |||||||
\(678\) | 2.31128 | 0.0887642 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.1653 | 0.542817 | ||||||||
\(682\) | 16.1393 | 0.618006 | ||||||||
\(683\) | −44.3929 | −1.69865 | −0.849324 | − | 0.527873i | \(-0.822990\pi\) | ||||
−0.849324 | + | 0.527873i | \(0.822990\pi\) | |||||||
\(684\) | 4.85906 | 0.185791 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.8062 | 0.679349 | ||||||||
\(688\) | 3.67693 | 0.140182 | ||||||||
\(689\) | 32.2312 | 1.22791 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −43.1925 | −1.64312 | −0.821559 | − | 0.570123i | \(-0.806896\pi\) | ||||
−0.821559 | + | 0.570123i | \(0.806896\pi\) | |||||||
\(692\) | −22.2583 | −0.846134 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.74263 | 0.180028 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7.42405 | 0.281408 | ||||||||
\(697\) | −2.75308 | −0.104280 | ||||||||
\(698\) | −9.83438 | −0.372237 | ||||||||
\(699\) | 13.6498 | 0.516283 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.69616 | −0.366219 | −0.183109 | − | 0.983093i | \(-0.558616\pi\) | ||||
−0.183109 | + | 0.983093i | \(0.558616\pi\) | |||||||
\(702\) | 2.51748 | 0.0950162 | ||||||||
\(703\) | 9.75037 | 0.367742 | ||||||||
\(704\) | −14.5253 | −0.547441 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.5387 | 0.509536 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 22.5621 | 0.847937 | ||||||||
\(709\) | 18.1537 | 0.681776 | 0.340888 | − | 0.940104i | \(-0.389272\pi\) | ||||
0.340888 | + | 0.940104i | \(0.389272\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.36184 | 0.0885759 | ||||||||
\(712\) | 8.07400 | 0.302586 | ||||||||
\(713\) | −45.9531 | −1.72096 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −22.9069 | −0.856071 | ||||||||
\(717\) | −7.53489 | −0.281396 | ||||||||
\(718\) | −12.6264 | −0.471212 | ||||||||
\(719\) | 35.1808 | 1.31202 | 0.656011 | − | 0.754751i | \(-0.272242\pi\) | ||||
0.656011 | + | 0.754751i | \(0.272242\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 5.60454 | 0.208579 | ||||||||
\(723\) | −28.5231 | −1.06079 | ||||||||
\(724\) | 26.4411 | 0.982677 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −8.64800 | −0.320957 | ||||||||
\(727\) | 4.79075 | 0.177679 | 0.0888396 | − | 0.996046i | \(-0.471684\pi\) | ||||
0.0888396 | + | 0.996046i | \(0.471684\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.496305 | −0.0183565 | ||||||||
\(732\) | −8.77896 | −0.324480 | ||||||||
\(733\) | 12.1243 | 0.447821 | 0.223910 | − | 0.974610i | \(-0.428118\pi\) | ||||
0.223910 | + | 0.974610i | \(0.428118\pi\) | |||||||
\(734\) | −11.0060 | −0.406237 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −37.5136 | −1.38277 | ||||||||
\(737\) | 20.0504 | 0.738567 | ||||||||
\(738\) | −3.88508 | −0.143012 | ||||||||
\(739\) | −32.9163 | −1.21084 | −0.605422 | − | 0.795904i | \(-0.706996\pi\) | ||||
−0.605422 | + | 0.795904i | \(0.706996\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14.0983 | 0.517913 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −38.8112 | −1.42385 | −0.711923 | − | 0.702258i | \(-0.752175\pi\) | ||||
−0.711923 | + | 0.702258i | \(0.752175\pi\) | |||||||
\(744\) | −11.3544 | −0.416273 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.61653 | 0.0957980 | ||||||||
\(747\) | 6.87342 | 0.251485 | ||||||||
\(748\) | 3.28242 | 0.120017 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30.0682 | −1.09720 | −0.548602 | − | 0.836084i | \(-0.684840\pi\) | ||||
−0.548602 | + | 0.836084i | \(0.684840\pi\) | |||||||
\(752\) | 22.9607 | 0.837290 | ||||||||
\(753\) | 22.8501 | 0.832705 | ||||||||
\(754\) | 10.0699 | 0.366725 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.17713 | 0.260857 | 0.130429 | − | 0.991458i | \(-0.458365\pi\) | ||||
0.130429 | + | 0.991458i | \(0.458365\pi\) | |||||||
\(758\) | −1.53294 | −0.0556790 | ||||||||
\(759\) | 40.1008 | 1.45557 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.60862 | 0.275812 | 0.137906 | − | 0.990445i | \(-0.455963\pi\) | ||||
0.137906 | + | 0.990445i | \(0.455963\pi\) | |||||||
\(762\) | 8.66723 | 0.313980 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −16.7278 | −0.605189 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10.6804 | 0.385899 | ||||||||
\(767\) | 65.4627 | 2.36372 | ||||||||
\(768\) | −0.158689 | −0.00572621 | ||||||||
\(769\) | −50.2712 | −1.81283 | −0.906413 | − | 0.422393i | \(-0.861190\pi\) | ||||
−0.906413 | + | 0.422393i | \(0.861190\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.1381 | −0.905326 | ||||||||
\(772\) | 26.5230 | 0.954582 | ||||||||
\(773\) | 27.1010 | 0.974755 | 0.487377 | − | 0.873192i | \(-0.337954\pi\) | ||||
0.487377 | + | 0.873192i | \(0.337954\pi\) | |||||||
\(774\) | −0.700372 | −0.0251744 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −10.2079 | −0.366444 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.35588 | 0.227869 | ||||||||
\(779\) | −21.7570 | −0.779526 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 82.6847 | 2.95869 | ||||||||
\(782\) | 1.29990 | 0.0464843 | ||||||||
\(783\) | 4.00000 | 0.142948 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.45901 | −0.159048 | ||||||||
\(787\) | 34.3501 | 1.22445 | 0.612224 | − | 0.790685i | \(-0.290275\pi\) | ||||
0.612224 | + | 0.790685i | \(0.290275\pi\) | |||||||
\(788\) | −29.6536 | −1.05637 | ||||||||
\(789\) | −13.5582 | −0.482685 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 9.90838 | 0.352079 | ||||||||
\(793\) | −25.4716 | −0.904524 | ||||||||
\(794\) | 3.45681 | 0.122678 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −44.2944 | −1.56997 | ||||||||
\(797\) | −16.5581 | −0.586517 | −0.293258 | − | 0.956033i | \(-0.594740\pi\) | ||||
−0.293258 | + | 0.956033i | \(0.594740\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.09919 | −0.109641 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.35019 | 0.153706 | ||||||||
\(802\) | 1.56228 | 0.0551660 | ||||||||
\(803\) | −40.9843 | −1.44630 | ||||||||
\(804\) | −6.59439 | −0.232566 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −15.4010 | −0.542478 | ||||||||
\(807\) | 9.02725 | 0.317774 | ||||||||
\(808\) | −3.06208 | −0.107723 | ||||||||
\(809\) | −8.55806 | −0.300885 | −0.150443 | − | 0.988619i | \(-0.548070\pi\) | ||||
−0.150443 | + | 0.988619i | \(0.548070\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.4277 | −0.752429 | −0.376215 | − | 0.926533i | \(-0.622774\pi\) | ||||
−0.376215 | + | 0.926533i | \(0.622774\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.77639 | −0.167515 | ||||||||
\(814\) | 9.29487 | 0.325785 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.908520 | −0.0318046 | ||||||||
\(817\) | −3.92219 | −0.137220 | ||||||||
\(818\) | 1.23300 | 0.0431107 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.1202 | −0.527699 | −0.263849 | − | 0.964564i | \(-0.584992\pi\) | ||||
−0.263849 | + | 0.964564i | \(0.584992\pi\) | |||||||
\(822\) | 0.412397 | 0.0143840 | ||||||||
\(823\) | −24.7043 | −0.861138 | −0.430569 | − | 0.902558i | \(-0.641687\pi\) | ||||
−0.430569 | + | 0.902558i | \(0.641687\pi\) | |||||||
\(824\) | 18.8597 | 0.657008 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.8578 | 1.00348 | 0.501742 | − | 0.865017i | \(-0.332693\pi\) | ||||
0.501742 | + | 0.865017i | \(0.332693\pi\) | |||||||
\(828\) | −13.1888 | −0.458342 | ||||||||
\(829\) | 0.869480 | 0.0301983 | 0.0150991 | − | 0.999886i | \(-0.495194\pi\) | ||||
0.0150991 | + | 0.999886i | \(0.495194\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.87071 | 0.0648944 | ||||||||
\(832\) | 13.8608 | 0.480537 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −7.07420 | −0.244960 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 25.9403 | 0.897163 | ||||||||
\(837\) | −6.11763 | −0.211456 | ||||||||
\(838\) | −16.1470 | −0.557789 | ||||||||
\(839\) | −21.7235 | −0.749980 | −0.374990 | − | 0.927029i | \(-0.622354\pi\) | ||||
−0.374990 | + | 0.927029i | \(0.622354\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | 13.2821 | 0.457731 | ||||||||
\(843\) | 0.972748 | 0.0335032 | ||||||||
\(844\) | −35.8123 | −1.23271 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.37349 | −0.150364 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −16.4144 | −0.563673 | ||||||||
\(849\) | 24.1797 | 0.829845 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −26.4651 | −0.907212 | ||||||||
\(852\) | −27.1942 | −0.931658 | ||||||||
\(853\) | −0.670546 | −0.0229591 | −0.0114795 | − | 0.999934i | \(-0.503654\pi\) | ||||
−0.0114795 | + | 0.999934i | \(0.503654\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.95164 | −0.340140 | ||||||||
\(857\) | −24.4884 | −0.836508 | −0.418254 | − | 0.908330i | \(-0.637358\pi\) | ||||
−0.418254 | + | 0.908330i | \(0.637358\pi\) | |||||||
\(858\) | 13.4396 | 0.458822 | ||||||||
\(859\) | −9.59939 | −0.327527 | −0.163764 | − | 0.986500i | \(-0.552363\pi\) | ||||
−0.163764 | + | 0.986500i | \(0.552363\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.01165 | −0.238818 | ||||||||
\(863\) | −29.5039 | −1.00432 | −0.502162 | − | 0.864774i | \(-0.667462\pi\) | ||||
−0.502162 | + | 0.864774i | \(0.667462\pi\) | |||||||
\(864\) | −4.99411 | −0.169903 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 14.8112 | 0.503306 | ||||||||
\(867\) | −16.8774 | −0.573186 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.6088 | 0.427723 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.1332 | −0.648305 | ||||||||
\(872\) | −0.196698 | −0.00666103 | ||||||||
\(873\) | −5.49993 | −0.186144 | ||||||||
\(874\) | 10.2728 | 0.347484 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 13.4793 | 0.455425 | ||||||||
\(877\) | −5.30765 | −0.179227 | −0.0896134 | − | 0.995977i | \(-0.528563\pi\) | ||||
−0.0896134 | + | 0.995977i | \(0.528563\pi\) | |||||||
\(878\) | −1.02485 | −0.0345870 | ||||||||
\(879\) | −15.5349 | −0.523979 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −49.2817 | −1.66034 | −0.830172 | − | 0.557507i | \(-0.811758\pi\) | ||||
−0.830172 | + | 0.557507i | \(0.811758\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.02862 | −0.202879 | −0.101440 | − | 0.994842i | \(-0.532345\pi\) | ||||
−0.101440 | + | 0.994842i | \(0.532345\pi\) | |||||||
\(884\) | −3.13227 | −0.105350 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.8519 | −0.532554 | ||||||||
\(887\) | −7.98486 | −0.268105 | −0.134053 | − | 0.990974i | \(-0.542799\pi\) | ||||
−0.134053 | + | 0.990974i | \(0.542799\pi\) | |||||||
\(888\) | −6.53918 | −0.219440 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.33853 | 0.178848 | ||||||||
\(892\) | −39.6349 | −1.32707 | ||||||||
\(893\) | −24.4922 | −0.819601 | ||||||||
\(894\) | −9.58531 | −0.320581 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −38.2665 | −1.27768 | ||||||||
\(898\) | 2.20452 | 0.0735658 | ||||||||
\(899\) | −24.4705 | −0.816138 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.21558 | 0.0738118 | ||||||||
\(902\) | −20.7406 | −0.690587 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.68069 | −0.288716 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −9.15564 | −0.304176 | ||||||||
\(907\) | 2.53108 | 0.0840432 | 0.0420216 | − | 0.999117i | \(-0.486620\pi\) | ||||
0.0420216 | + | 0.999117i | \(0.486620\pi\) | |||||||
\(908\) | −24.8714 | −0.825387 | ||||||||
\(909\) | −1.64981 | −0.0547209 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.41047 | 0.0467309 | 0.0233655 | − | 0.999727i | \(-0.492562\pi\) | ||||
0.0233655 | + | 0.999727i | \(0.492562\pi\) | |||||||
\(912\) | −7.17984 | −0.237748 | ||||||||
\(913\) | 36.6940 | 1.21439 | ||||||||
\(914\) | 1.12188 | 0.0371086 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −31.2640 | −1.03299 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.173053 | 0.00571159 | ||||||||
\(919\) | 46.6836 | 1.53995 | 0.769975 | − | 0.638074i | \(-0.220269\pi\) | ||||
0.769975 | + | 0.638074i | \(0.220269\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.39395 | 0.111835 | ||||||||
\(922\) | 2.14025 | 0.0704852 | ||||||||
\(923\) | −78.9023 | −2.59710 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 20.6493 | 0.678579 | ||||||||
\(927\) | 10.1614 | 0.333744 | ||||||||
\(928\) | −19.9764 | −0.655758 | ||||||||
\(929\) | 17.8385 | 0.585261 | 0.292631 | − | 0.956226i | \(-0.405469\pi\) | ||||
0.292631 | + | 0.956226i | \(0.405469\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −23.9662 | −0.785040 | ||||||||
\(933\) | 2.46511 | 0.0807040 | ||||||||
\(934\) | 18.9650 | 0.620555 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −9.45513 | −0.309051 | ||||||||
\(937\) | 0.343849 | 0.0112330 | 0.00561652 | − | 0.999984i | \(-0.498212\pi\) | ||||
0.00561652 | + | 0.999984i | \(0.498212\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.475526 | 0.0155182 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 46.1475 | 1.50436 | 0.752182 | − | 0.658955i | \(-0.229001\pi\) | ||||
0.752182 | + | 0.658955i | \(0.229001\pi\) | |||||||
\(942\) | −2.37181 | −0.0772779 | ||||||||
\(943\) | 59.0544 | 1.92307 | ||||||||
\(944\) | −33.3383 | −1.08507 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.73896 | −0.121564 | ||||||||
\(947\) | −27.6618 | −0.898887 | −0.449444 | − | 0.893309i | \(-0.648378\pi\) | ||||
−0.449444 | + | 0.893309i | \(0.648378\pi\) | |||||||
\(948\) | −4.14690 | −0.134685 | ||||||||
\(949\) | 39.1095 | 1.26955 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.2995 | 0.463693 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.24907 | 0.137641 | 0.0688204 | − | 0.997629i | \(-0.478076\pi\) | ||||
0.0688204 | + | 0.997629i | \(0.478076\pi\) | |||||||
\(954\) | 3.12658 | 0.101227 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 13.2297 | 0.427879 | ||||||||
\(957\) | 21.3541 | 0.690281 | ||||||||
\(958\) | 18.7977 | 0.607325 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.42542 | 0.207272 | ||||||||
\(962\) | −8.86968 | −0.285970 | ||||||||
\(963\) | −5.36184 | −0.172783 | ||||||||
\(964\) | 50.0807 | 1.61299 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 59.6146 | 1.91708 | 0.958538 | − | 0.284965i | \(-0.0919820\pi\) | ||||
0.958538 | + | 0.284965i | \(0.0919820\pi\) | |||||||
\(968\) | 32.4801 | 1.04395 | ||||||||
\(969\) | 0.969121 | 0.0311327 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.951234 | 0.0305266 | 0.0152633 | − | 0.999884i | \(-0.495141\pi\) | ||||
0.0152633 | + | 0.999884i | \(0.495141\pi\) | |||||||
\(972\) | −1.75579 | −0.0563171 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −11.1598 | −0.357583 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.9720 | 0.415223 | ||||||||
\(977\) | −23.0506 | −0.737453 | −0.368726 | − | 0.929538i | \(-0.620206\pi\) | ||||
−0.368726 | + | 0.929538i | \(0.620206\pi\) | |||||||
\(978\) | −0.408655 | −0.0130674 | ||||||||
\(979\) | 23.2236 | 0.742230 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.105979 | −0.00338364 | ||||||||
\(982\) | 0.0662922 | 0.00211547 | ||||||||
\(983\) | −31.8348 | −1.01537 | −0.507687 | − | 0.861542i | \(-0.669499\pi\) | ||||
−0.507687 | + | 0.861542i | \(0.669499\pi\) | |||||||
\(984\) | 14.5915 | 0.465162 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.692210 | 0.0220445 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −24.7536 | −0.787518 | ||||||||
\(989\) | 10.6459 | 0.338519 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.10611 | −0.257499 | −0.128750 | − | 0.991677i | \(-0.541096\pi\) | ||||
−0.128750 | + | 0.991677i | \(0.541096\pi\) | |||||||
\(992\) | 30.5521 | 0.970030 | ||||||||
\(993\) | −19.5855 | −0.621525 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −12.0683 | −0.382399 | ||||||||
\(997\) | −28.2469 | −0.894589 | −0.447294 | − | 0.894387i | \(-0.647612\pi\) | ||||
−0.447294 | + | 0.894387i | \(0.647612\pi\) | |||||||
\(998\) | 7.68704 | 0.243329 | ||||||||
\(999\) | −3.52324 | −0.111470 |
(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 | 3675.2.a.bx.1.2 | 4 | ||
5.4 | even | 2 | 3675.2.a.bq.1.3 | 4 | |||
7.3 | odd | 6 | 525.2.i.i.226.3 | yes | 8 | ||
7.5 | odd | 6 | 525.2.i.i.151.3 | ✓ | 8 | ||
7.6 | odd | 2 | 3675.2.a.bw.1.2 | 4 | |||
35.3 | even | 12 | 525.2.r.h.499.4 | 16 | |||
35.12 | even | 12 | 525.2.r.h.424.4 | 16 | |||
35.17 | even | 12 | 525.2.r.h.499.5 | 16 | |||
35.19 | odd | 6 | 525.2.i.j.151.2 | yes | 8 | ||
35.24 | odd | 6 | 525.2.i.j.226.2 | yes | 8 | ||
35.33 | even | 12 | 525.2.r.h.424.5 | 16 | |||
35.34 | odd | 2 | 3675.2.a.br.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.i.i.151.3 | ✓ | 8 | 7.5 | odd | 6 | ||
525.2.i.i.226.3 | yes | 8 | 7.3 | odd | 6 | ||
525.2.i.j.151.2 | yes | 8 | 35.19 | odd | 6 | ||
525.2.i.j.226.2 | yes | 8 | 35.24 | odd | 6 | ||
525.2.r.h.424.4 | 16 | 35.12 | even | 12 | |||
525.2.r.h.424.5 | 16 | 35.33 | even | 12 | |||
525.2.r.h.499.4 | 16 | 35.3 | even | 12 | |||
525.2.r.h.499.5 | 16 | 35.17 | even | 12 | |||
3675.2.a.bq.1.3 | 4 | 5.4 | even | 2 | |||
3675.2.a.br.1.3 | 4 | 35.34 | odd | 2 | |||
3675.2.a.bw.1.2 | 4 | 7.6 | odd | 2 | |||
3675.2.a.bx.1.2 | 4 | 1.1 | even | 1 | trivial |