Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [133,2,Mod(1,133)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(133, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("133.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 133 = 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 133.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: | \(1.06201034688\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.86081\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 133.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.46260 | 1.03421 | 0.517107 | − | 0.855921i | \(-0.327009\pi\) | ||||
0.517107 | + | 0.855921i | \(0.327009\pi\) | |||||||
\(3\) | 2.86081 | 1.65169 | 0.825844 | − | 0.563899i | \(-0.190699\pi\) | ||||
0.825844 | + | 0.563899i | \(0.190699\pi\) | |||||||
\(4\) | 0.139194 | 0.0695971 | ||||||||
\(5\) | −3.32340 | −1.48627 | −0.743136 | − | 0.669141i | \(-0.766662\pi\) | ||||
−0.743136 | + | 0.669141i | \(0.766662\pi\) | |||||||
\(6\) | 4.18421 | 1.70820 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.72161 | −0.962235 | ||||||||
\(9\) | 5.18421 | 1.72807 | ||||||||
\(10\) | −4.86081 | −1.53712 | ||||||||
\(11\) | 1.53740 | 0.463544 | 0.231772 | − | 0.972770i | \(-0.425548\pi\) | ||||
0.231772 | + | 0.972770i | \(0.425548\pi\) | |||||||
\(12\) | 0.398207 | 0.114953 | ||||||||
\(13\) | −3.32340 | −0.921747 | −0.460873 | − | 0.887466i | \(-0.652464\pi\) | ||||
−0.460873 | + | 0.887466i | \(0.652464\pi\) | |||||||
\(14\) | −1.46260 | −0.390896 | ||||||||
\(15\) | −9.50761 | −2.45486 | ||||||||
\(16\) | −4.25901 | −1.06475 | ||||||||
\(17\) | 5.25901 | 1.27550 | 0.637749 | − | 0.770244i | \(-0.279866\pi\) | ||||
0.637749 | + | 0.770244i | \(0.279866\pi\) | |||||||
\(18\) | 7.58242 | 1.78719 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −0.462598 | −0.103440 | ||||||||
\(21\) | −2.86081 | −0.624279 | ||||||||
\(22\) | 2.24860 | 0.479403 | ||||||||
\(23\) | 3.60179 | 0.751026 | 0.375513 | − | 0.926817i | \(-0.377467\pi\) | ||||
0.375513 | + | 0.926817i | \(0.377467\pi\) | |||||||
\(24\) | −7.78600 | −1.58931 | ||||||||
\(25\) | 6.04502 | 1.20900 | ||||||||
\(26\) | −4.86081 | −0.953282 | ||||||||
\(27\) | 6.24860 | 1.20254 | ||||||||
\(28\) | −0.139194 | −0.0263052 | ||||||||
\(29\) | 8.83102 | 1.63988 | 0.819940 | − | 0.572450i | \(-0.194007\pi\) | ||||
0.819940 | + | 0.572450i | \(0.194007\pi\) | |||||||
\(30\) | −13.9058 | −2.53884 | ||||||||
\(31\) | −8.18421 | −1.46993 | −0.734964 | − | 0.678106i | \(-0.762801\pi\) | ||||
−0.734964 | + | 0.678106i | \(0.762801\pi\) | |||||||
\(32\) | −0.786003 | −0.138947 | ||||||||
\(33\) | 4.39821 | 0.765630 | ||||||||
\(34\) | 7.69182 | 1.31914 | ||||||||
\(35\) | 3.32340 | 0.561758 | ||||||||
\(36\) | 0.721612 | 0.120269 | ||||||||
\(37\) | 4.24860 | 0.698466 | 0.349233 | − | 0.937036i | \(-0.386442\pi\) | ||||
0.349233 | + | 0.937036i | \(0.386442\pi\) | |||||||
\(38\) | 1.46260 | 0.237265 | ||||||||
\(39\) | −9.50761 | −1.52244 | ||||||||
\(40\) | 9.04502 | 1.43014 | ||||||||
\(41\) | −12.7022 | −1.98376 | −0.991878 | − | 0.127193i | \(-0.959403\pi\) | ||||
−0.991878 | + | 0.127193i | \(0.959403\pi\) | |||||||
\(42\) | −4.18421 | −0.645638 | ||||||||
\(43\) | −6.64681 | −1.01363 | −0.506814 | − | 0.862055i | \(-0.669177\pi\) | ||||
−0.506814 | + | 0.862055i | \(0.669177\pi\) | |||||||
\(44\) | 0.213997 | 0.0322613 | ||||||||
\(45\) | −17.2292 | −2.56838 | ||||||||
\(46\) | 5.26798 | 0.776721 | ||||||||
\(47\) | −2.11982 | −0.309207 | −0.154604 | − | 0.987977i | \(-0.549410\pi\) | ||||
−0.154604 | + | 0.987977i | \(0.549410\pi\) | |||||||
\(48\) | −12.1842 | −1.75864 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 8.84143 | 1.25037 | ||||||||
\(51\) | 15.0450 | 2.10672 | ||||||||
\(52\) | −0.462598 | −0.0641509 | ||||||||
\(53\) | −0.0643910 | −0.00884478 | −0.00442239 | − | 0.999990i | \(-0.501408\pi\) | ||||
−0.00442239 | + | 0.999990i | \(0.501408\pi\) | |||||||
\(54\) | 9.13919 | 1.24369 | ||||||||
\(55\) | −5.10941 | −0.688952 | ||||||||
\(56\) | 2.72161 | 0.363691 | ||||||||
\(57\) | 2.86081 | 0.378923 | ||||||||
\(58\) | 12.9162 | 1.69598 | ||||||||
\(59\) | 3.04502 | 0.396427 | 0.198214 | − | 0.980159i | \(-0.436486\pi\) | ||||
0.198214 | + | 0.980159i | \(0.436486\pi\) | |||||||
\(60\) | −1.32340 | −0.170851 | ||||||||
\(61\) | −1.47301 | −0.188600 | −0.0942998 | − | 0.995544i | \(-0.530061\pi\) | ||||
−0.0942998 | + | 0.995544i | \(0.530061\pi\) | |||||||
\(62\) | −11.9702 | −1.52022 | ||||||||
\(63\) | −5.18421 | −0.653149 | ||||||||
\(64\) | 7.36842 | 0.921053 | ||||||||
\(65\) | 11.0450 | 1.36997 | ||||||||
\(66\) | 6.43281 | 0.791824 | ||||||||
\(67\) | −2.33382 | −0.285121 | −0.142561 | − | 0.989786i | \(-0.545534\pi\) | ||||
−0.142561 | + | 0.989786i | \(0.545534\pi\) | |||||||
\(68\) | 0.732024 | 0.0887709 | ||||||||
\(69\) | 10.3040 | 1.24046 | ||||||||
\(70\) | 4.86081 | 0.580977 | ||||||||
\(71\) | −0.526989 | −0.0625421 | −0.0312711 | − | 0.999511i | \(-0.509956\pi\) | ||||
−0.0312711 | + | 0.999511i | \(0.509956\pi\) | |||||||
\(72\) | −14.1094 | −1.66281 | ||||||||
\(73\) | −0.989588 | −0.115822 | −0.0579112 | − | 0.998322i | \(-0.518444\pi\) | ||||
−0.0579112 | + | 0.998322i | \(0.518444\pi\) | |||||||
\(74\) | 6.21400 | 0.722363 | ||||||||
\(75\) | 17.2936 | 1.99689 | ||||||||
\(76\) | 0.139194 | 0.0159667 | ||||||||
\(77\) | −1.53740 | −0.175203 | ||||||||
\(78\) | −13.9058 | −1.57452 | ||||||||
\(79\) | 0.796415 | 0.0896037 | 0.0448018 | − | 0.998996i | \(-0.485734\pi\) | ||||
0.0448018 | + | 0.998996i | \(0.485734\pi\) | |||||||
\(80\) | 14.1544 | 1.58251 | ||||||||
\(81\) | 2.32340 | 0.258156 | ||||||||
\(82\) | −18.5783 | −2.05163 | ||||||||
\(83\) | 10.0644 | 1.10471 | 0.552355 | − | 0.833609i | \(-0.313729\pi\) | ||||
0.552355 | + | 0.833609i | \(0.313729\pi\) | |||||||
\(84\) | −0.398207 | −0.0434480 | ||||||||
\(85\) | −17.4778 | −1.89574 | ||||||||
\(86\) | −9.72161 | −1.04831 | ||||||||
\(87\) | 25.2638 | 2.70857 | ||||||||
\(88\) | −4.18421 | −0.446038 | ||||||||
\(89\) | 5.01523 | 0.531613 | 0.265807 | − | 0.964026i | \(-0.414362\pi\) | ||||
0.265807 | + | 0.964026i | \(0.414362\pi\) | |||||||
\(90\) | −25.1994 | −2.65625 | ||||||||
\(91\) | 3.32340 | 0.348387 | ||||||||
\(92\) | 0.501348 | 0.0522692 | ||||||||
\(93\) | −23.4134 | −2.42786 | ||||||||
\(94\) | −3.10044 | −0.319786 | ||||||||
\(95\) | −3.32340 | −0.340974 | ||||||||
\(96\) | −2.24860 | −0.229497 | ||||||||
\(97\) | −17.9702 | −1.82460 | −0.912299 | − | 0.409524i | \(-0.865695\pi\) | ||||
−0.912299 | + | 0.409524i | \(0.865695\pi\) | |||||||
\(98\) | 1.46260 | 0.147745 | ||||||||
\(99\) | 7.97021 | 0.801037 | ||||||||
\(100\) | 0.841431 | 0.0841431 | ||||||||
\(101\) | 6.89541 | 0.686119 | 0.343059 | − | 0.939314i | \(-0.388537\pi\) | ||||
0.343059 | + | 0.939314i | \(0.388537\pi\) | |||||||
\(102\) | 22.0048 | 2.17880 | ||||||||
\(103\) | 13.1350 | 1.29423 | 0.647117 | − | 0.762390i | \(-0.275974\pi\) | ||||
0.647117 | + | 0.762390i | \(0.275974\pi\) | |||||||
\(104\) | 9.04502 | 0.886937 | ||||||||
\(105\) | 9.50761 | 0.927848 | ||||||||
\(106\) | −0.0941782 | −0.00914739 | ||||||||
\(107\) | 10.6766 | 1.03215 | 0.516073 | − | 0.856545i | \(-0.327393\pi\) | ||||
0.516073 | + | 0.856545i | \(0.327393\pi\) | |||||||
\(108\) | 0.869769 | 0.0836935 | ||||||||
\(109\) | 9.97021 | 0.954973 | 0.477487 | − | 0.878639i | \(-0.341548\pi\) | ||||
0.477487 | + | 0.878639i | \(0.341548\pi\) | |||||||
\(110\) | −7.47301 | −0.712524 | ||||||||
\(111\) | 12.1544 | 1.15365 | ||||||||
\(112\) | 4.25901 | 0.402439 | ||||||||
\(113\) | −18.5228 | −1.74248 | −0.871241 | − | 0.490855i | \(-0.836684\pi\) | ||||
−0.871241 | + | 0.490855i | \(0.836684\pi\) | |||||||
\(114\) | 4.18421 | 0.391887 | ||||||||
\(115\) | −11.9702 | −1.11623 | ||||||||
\(116\) | 1.22923 | 0.114131 | ||||||||
\(117\) | −17.2292 | −1.59284 | ||||||||
\(118\) | 4.45364 | 0.409990 | ||||||||
\(119\) | −5.25901 | −0.482093 | ||||||||
\(120\) | 25.8760 | 2.36215 | ||||||||
\(121\) | −8.63640 | −0.785127 | ||||||||
\(122\) | −2.15442 | −0.195052 | ||||||||
\(123\) | −36.3386 | −3.27654 | ||||||||
\(124\) | −1.13919 | −0.102303 | ||||||||
\(125\) | −3.47301 | −0.310636 | ||||||||
\(126\) | −7.58242 | −0.675495 | ||||||||
\(127\) | −6.77559 | −0.601236 | −0.300618 | − | 0.953745i | \(-0.597193\pi\) | ||||
−0.300618 | + | 0.953745i | \(0.597193\pi\) | |||||||
\(128\) | 12.3490 | 1.09151 | ||||||||
\(129\) | −19.0152 | −1.67420 | ||||||||
\(130\) | 16.1544 | 1.41684 | ||||||||
\(131\) | 7.25901 | 0.634223 | 0.317111 | − | 0.948388i | \(-0.397287\pi\) | ||||
0.317111 | + | 0.948388i | \(0.397287\pi\) | |||||||
\(132\) | 0.612205 | 0.0532856 | ||||||||
\(133\) | −1.00000 | −0.0867110 | ||||||||
\(134\) | −3.41344 | −0.294876 | ||||||||
\(135\) | −20.7666 | −1.78731 | ||||||||
\(136\) | −14.3130 | −1.22733 | ||||||||
\(137\) | 15.2936 | 1.30662 | 0.653311 | − | 0.757090i | \(-0.273379\pi\) | ||||
0.653311 | + | 0.757090i | \(0.273379\pi\) | |||||||
\(138\) | 15.0707 | 1.28290 | ||||||||
\(139\) | −9.82061 | −0.832973 | −0.416486 | − | 0.909142i | \(-0.636739\pi\) | ||||
−0.416486 | + | 0.909142i | \(0.636739\pi\) | |||||||
\(140\) | 0.462598 | 0.0390967 | ||||||||
\(141\) | −6.06439 | −0.510714 | ||||||||
\(142\) | −0.770774 | −0.0646819 | ||||||||
\(143\) | −5.10941 | −0.427270 | ||||||||
\(144\) | −22.0796 | −1.83997 | ||||||||
\(145\) | −29.3490 | −2.43731 | ||||||||
\(146\) | −1.44737 | −0.119785 | ||||||||
\(147\) | 2.86081 | 0.235955 | ||||||||
\(148\) | 0.591380 | 0.0486112 | ||||||||
\(149\) | −13.5422 | −1.10942 | −0.554711 | − | 0.832043i | \(-0.687171\pi\) | ||||
−0.554711 | + | 0.832043i | \(0.687171\pi\) | |||||||
\(150\) | 25.2936 | 2.06522 | ||||||||
\(151\) | 8.18421 | 0.666022 | 0.333011 | − | 0.942923i | \(-0.391935\pi\) | ||||
0.333011 | + | 0.942923i | \(0.391935\pi\) | |||||||
\(152\) | −2.72161 | −0.220752 | ||||||||
\(153\) | 27.2638 | 2.20415 | ||||||||
\(154\) | −2.24860 | −0.181197 | ||||||||
\(155\) | 27.1994 | 2.18471 | ||||||||
\(156\) | −1.32340 | −0.105957 | ||||||||
\(157\) | 5.13023 | 0.409437 | 0.204719 | − | 0.978821i | \(-0.434372\pi\) | ||||
0.204719 | + | 0.978821i | \(0.434372\pi\) | |||||||
\(158\) | 1.16484 | 0.0926693 | ||||||||
\(159\) | −0.184210 | −0.0146088 | ||||||||
\(160\) | 2.61220 | 0.206513 | ||||||||
\(161\) | −3.60179 | −0.283861 | ||||||||
\(162\) | 3.39821 | 0.266988 | ||||||||
\(163\) | −1.37883 | −0.107998 | −0.0539992 | − | 0.998541i | \(-0.517197\pi\) | ||||
−0.0539992 | + | 0.998541i | \(0.517197\pi\) | |||||||
\(164\) | −1.76808 | −0.138064 | ||||||||
\(165\) | −14.6170 | −1.13793 | ||||||||
\(166\) | 14.7202 | 1.14251 | ||||||||
\(167\) | 21.5630 | 1.66860 | 0.834299 | − | 0.551312i | \(-0.185873\pi\) | ||||
0.834299 | + | 0.551312i | \(0.185873\pi\) | |||||||
\(168\) | 7.78600 | 0.600703 | ||||||||
\(169\) | −1.95498 | −0.150383 | ||||||||
\(170\) | −25.5630 | −1.96060 | ||||||||
\(171\) | 5.18421 | 0.396446 | ||||||||
\(172\) | −0.925197 | −0.0705456 | ||||||||
\(173\) | −19.1648 | −1.45708 | −0.728538 | − | 0.685006i | \(-0.759800\pi\) | ||||
−0.728538 | + | 0.685006i | \(0.759800\pi\) | |||||||
\(174\) | 36.9508 | 2.80124 | ||||||||
\(175\) | −6.04502 | −0.456960 | ||||||||
\(176\) | −6.54781 | −0.493560 | ||||||||
\(177\) | 8.71120 | 0.654774 | ||||||||
\(178\) | 7.33527 | 0.549801 | ||||||||
\(179\) | −15.1994 | −1.13606 | −0.568030 | − | 0.823008i | \(-0.692294\pi\) | ||||
−0.568030 | + | 0.823008i | \(0.692294\pi\) | |||||||
\(180\) | −2.39821 | −0.178752 | ||||||||
\(181\) | 2.31299 | 0.171923 | 0.0859617 | − | 0.996298i | \(-0.472604\pi\) | ||||
0.0859617 | + | 0.996298i | \(0.472604\pi\) | |||||||
\(182\) | 4.86081 | 0.360307 | ||||||||
\(183\) | −4.21400 | −0.311508 | ||||||||
\(184\) | −9.80268 | −0.722663 | ||||||||
\(185\) | −14.1198 | −1.03811 | ||||||||
\(186\) | −34.2445 | −2.51093 | ||||||||
\(187\) | 8.08522 | 0.591250 | ||||||||
\(188\) | −0.295066 | −0.0215199 | ||||||||
\(189\) | −6.24860 | −0.454519 | ||||||||
\(190\) | −4.86081 | −0.352640 | ||||||||
\(191\) | −0.0852153 | −0.00616596 | −0.00308298 | − | 0.999995i | \(-0.500981\pi\) | ||||
−0.00308298 | + | 0.999995i | \(0.500981\pi\) | |||||||
\(192\) | 21.0796 | 1.52129 | ||||||||
\(193\) | 1.75622 | 0.126415 | 0.0632076 | − | 0.998000i | \(-0.479867\pi\) | ||||
0.0632076 | + | 0.998000i | \(0.479867\pi\) | |||||||
\(194\) | −26.2832 | −1.88702 | ||||||||
\(195\) | 31.5976 | 2.26275 | ||||||||
\(196\) | 0.139194 | 0.00994244 | ||||||||
\(197\) | 10.8400 | 0.772317 | 0.386158 | − | 0.922433i | \(-0.373802\pi\) | ||||
0.386158 | + | 0.922433i | \(0.373802\pi\) | |||||||
\(198\) | 11.6572 | 0.828443 | ||||||||
\(199\) | −4.82620 | −0.342120 | −0.171060 | − | 0.985261i | \(-0.554719\pi\) | ||||
−0.171060 | + | 0.985261i | \(0.554719\pi\) | |||||||
\(200\) | −16.4522 | −1.16335 | ||||||||
\(201\) | −6.67660 | −0.470931 | ||||||||
\(202\) | 10.0852 | 0.709593 | ||||||||
\(203\) | −8.83102 | −0.619816 | ||||||||
\(204\) | 2.09418 | 0.146622 | ||||||||
\(205\) | 42.2147 | 2.94840 | ||||||||
\(206\) | 19.2113 | 1.33851 | ||||||||
\(207\) | 18.6724 | 1.29782 | ||||||||
\(208\) | 14.1544 | 0.981433 | ||||||||
\(209\) | 1.53740 | 0.106344 | ||||||||
\(210\) | 13.9058 | 0.959593 | ||||||||
\(211\) | −3.91478 | −0.269505 | −0.134752 | − | 0.990879i | \(-0.543024\pi\) | ||||
−0.134752 | + | 0.990879i | \(0.543024\pi\) | |||||||
\(212\) | −0.00896285 | −0.000615571 0 | ||||||||
\(213\) | −1.50761 | −0.103300 | ||||||||
\(214\) | 15.6156 | 1.06746 | ||||||||
\(215\) | 22.0900 | 1.50653 | ||||||||
\(216\) | −17.0063 | −1.15713 | ||||||||
\(217\) | 8.18421 | 0.555580 | ||||||||
\(218\) | 14.5824 | 0.987646 | ||||||||
\(219\) | −2.83102 | −0.191303 | ||||||||
\(220\) | −0.711200 | −0.0479491 | ||||||||
\(221\) | −17.4778 | −1.17569 | ||||||||
\(222\) | 17.7770 | 1.19312 | ||||||||
\(223\) | −2.11982 | −0.141954 | −0.0709768 | − | 0.997478i | \(-0.522612\pi\) | ||||
−0.0709768 | + | 0.997478i | \(0.522612\pi\) | |||||||
\(224\) | 0.786003 | 0.0525170 | ||||||||
\(225\) | 31.3386 | 2.08924 | ||||||||
\(226\) | −27.0915 | −1.80210 | ||||||||
\(227\) | 10.9598 | 0.727428 | 0.363714 | − | 0.931511i | \(-0.381509\pi\) | ||||
0.363714 | + | 0.931511i | \(0.381509\pi\) | |||||||
\(228\) | 0.398207 | 0.0263719 | ||||||||
\(229\) | 9.70079 | 0.641046 | 0.320523 | − | 0.947241i | \(-0.396141\pi\) | ||||
0.320523 | + | 0.947241i | \(0.396141\pi\) | |||||||
\(230\) | −17.5076 | −1.15442 | ||||||||
\(231\) | −4.39821 | −0.289381 | ||||||||
\(232\) | −24.0346 | −1.57795 | ||||||||
\(233\) | −9.62743 | −0.630714 | −0.315357 | − | 0.948973i | \(-0.602124\pi\) | ||||
−0.315357 | + | 0.948973i | \(0.602124\pi\) | |||||||
\(234\) | −25.1994 | −1.64734 | ||||||||
\(235\) | 7.04502 | 0.459566 | ||||||||
\(236\) | 0.423848 | 0.0275902 | ||||||||
\(237\) | 2.27839 | 0.147997 | ||||||||
\(238\) | −7.69182 | −0.498587 | ||||||||
\(239\) | 4.39821 | 0.284496 | 0.142248 | − | 0.989831i | \(-0.454567\pi\) | ||||
0.142248 | + | 0.989831i | \(0.454567\pi\) | |||||||
\(240\) | 40.4931 | 2.61382 | ||||||||
\(241\) | 26.3684 | 1.69854 | 0.849270 | − | 0.527959i | \(-0.177043\pi\) | ||||
0.849270 | + | 0.527959i | \(0.177043\pi\) | |||||||
\(242\) | −12.6316 | −0.811989 | ||||||||
\(243\) | −12.0990 | −0.776151 | ||||||||
\(244\) | −0.205034 | −0.0131260 | ||||||||
\(245\) | −3.32340 | −0.212325 | ||||||||
\(246\) | −53.1488 | −3.38865 | ||||||||
\(247\) | −3.32340 | −0.211463 | ||||||||
\(248\) | 22.2742 | 1.41442 | ||||||||
\(249\) | 28.7923 | 1.82464 | ||||||||
\(250\) | −5.07962 | −0.321263 | ||||||||
\(251\) | −5.34905 | −0.337629 | −0.168814 | − | 0.985648i | \(-0.553994\pi\) | ||||
−0.168814 | + | 0.985648i | \(0.553994\pi\) | |||||||
\(252\) | −0.721612 | −0.0454573 | ||||||||
\(253\) | 5.53740 | 0.348133 | ||||||||
\(254\) | −9.90997 | −0.621807 | ||||||||
\(255\) | −50.0007 | −3.13116 | ||||||||
\(256\) | 3.32485 | 0.207803 | ||||||||
\(257\) | −24.9300 | −1.55509 | −0.777546 | − | 0.628826i | \(-0.783536\pi\) | ||||
−0.777546 | + | 0.628826i | \(0.783536\pi\) | |||||||
\(258\) | −27.8116 | −1.73148 | ||||||||
\(259\) | −4.24860 | −0.263995 | ||||||||
\(260\) | 1.53740 | 0.0953456 | ||||||||
\(261\) | 45.7819 | 2.83383 | ||||||||
\(262\) | 10.6170 | 0.655922 | ||||||||
\(263\) | −4.21400 | −0.259846 | −0.129923 | − | 0.991524i | \(-0.541473\pi\) | ||||
−0.129923 | + | 0.991524i | \(0.541473\pi\) | |||||||
\(264\) | −11.9702 | −0.736716 | ||||||||
\(265\) | 0.213997 | 0.0131457 | ||||||||
\(266\) | −1.46260 | −0.0896777 | ||||||||
\(267\) | 14.3476 | 0.878059 | ||||||||
\(268\) | −0.324854 | −0.0198436 | ||||||||
\(269\) | −4.98959 | −0.304221 | −0.152110 | − | 0.988364i | \(-0.548607\pi\) | ||||
−0.152110 | + | 0.988364i | \(0.548607\pi\) | |||||||
\(270\) | −30.3732 | −1.84846 | ||||||||
\(271\) | −31.0707 | −1.88741 | −0.943704 | − | 0.330791i | \(-0.892684\pi\) | ||||
−0.943704 | + | 0.330791i | \(0.892684\pi\) | |||||||
\(272\) | −22.3982 | −1.35809 | ||||||||
\(273\) | 9.50761 | 0.575427 | ||||||||
\(274\) | 22.3684 | 1.35133 | ||||||||
\(275\) | 9.29362 | 0.560426 | ||||||||
\(276\) | 1.43426 | 0.0863323 | ||||||||
\(277\) | −17.2549 | −1.03674 | −0.518372 | − | 0.855155i | \(-0.673462\pi\) | ||||
−0.518372 | + | 0.855155i | \(0.673462\pi\) | |||||||
\(278\) | −14.3636 | −0.861472 | ||||||||
\(279\) | −42.4287 | −2.54014 | ||||||||
\(280\) | −9.04502 | −0.540543 | ||||||||
\(281\) | −4.61702 | −0.275428 | −0.137714 | − | 0.990472i | \(-0.543976\pi\) | ||||
−0.137714 | + | 0.990472i | \(0.543976\pi\) | |||||||
\(282\) | −8.86977 | −0.528187 | ||||||||
\(283\) | 24.7804 | 1.47304 | 0.736521 | − | 0.676415i | \(-0.236467\pi\) | ||||
0.736521 | + | 0.676415i | \(0.236467\pi\) | |||||||
\(284\) | −0.0733538 | −0.00435275 | ||||||||
\(285\) | −9.50761 | −0.563182 | ||||||||
\(286\) | −7.47301 | −0.441888 | ||||||||
\(287\) | 12.7022 | 0.749789 | ||||||||
\(288\) | −4.07480 | −0.240110 | ||||||||
\(289\) | 10.6572 | 0.626895 | ||||||||
\(290\) | −42.9259 | −2.52069 | ||||||||
\(291\) | −51.4093 | −3.01367 | ||||||||
\(292\) | −0.137745 | −0.00806091 | ||||||||
\(293\) | 9.28465 | 0.542415 | 0.271208 | − | 0.962521i | \(-0.412577\pi\) | ||||
0.271208 | + | 0.962521i | \(0.412577\pi\) | |||||||
\(294\) | 4.18421 | 0.244028 | ||||||||
\(295\) | −10.1198 | −0.589199 | ||||||||
\(296\) | −11.5630 | −0.672088 | ||||||||
\(297\) | 9.60661 | 0.557432 | ||||||||
\(298\) | −19.8068 | −1.14738 | ||||||||
\(299\) | −11.9702 | −0.692255 | ||||||||
\(300\) | 2.40717 | 0.138978 | ||||||||
\(301\) | 6.64681 | 0.383116 | ||||||||
\(302\) | 11.9702 | 0.688808 | ||||||||
\(303\) | 19.7264 | 1.13325 | ||||||||
\(304\) | −4.25901 | −0.244271 | ||||||||
\(305\) | 4.89541 | 0.280310 | ||||||||
\(306\) | 39.8760 | 2.27956 | ||||||||
\(307\) | −3.81579 | −0.217779 | −0.108889 | − | 0.994054i | \(-0.534729\pi\) | ||||
−0.108889 | + | 0.994054i | \(0.534729\pi\) | |||||||
\(308\) | −0.213997 | −0.0121936 | ||||||||
\(309\) | 37.5768 | 2.13767 | ||||||||
\(310\) | 39.7819 | 2.25946 | ||||||||
\(311\) | 0.354641 | 0.0201098 | 0.0100549 | − | 0.999949i | \(-0.496799\pi\) | ||||
0.0100549 | + | 0.999949i | \(0.496799\pi\) | |||||||
\(312\) | 25.8760 | 1.46494 | ||||||||
\(313\) | 9.63158 | 0.544409 | 0.272205 | − | 0.962239i | \(-0.412247\pi\) | ||||
0.272205 | + | 0.962239i | \(0.412247\pi\) | |||||||
\(314\) | 7.50347 | 0.423445 | ||||||||
\(315\) | 17.2292 | 0.970757 | ||||||||
\(316\) | 0.110856 | 0.00623615 | ||||||||
\(317\) | −13.4432 | −0.755047 | −0.377523 | − | 0.926000i | \(-0.623224\pi\) | ||||
−0.377523 | + | 0.926000i | \(0.623224\pi\) | |||||||
\(318\) | −0.269425 | −0.0151086 | ||||||||
\(319\) | 13.5768 | 0.760156 | ||||||||
\(320\) | −24.4882 | −1.36893 | ||||||||
\(321\) | 30.5437 | 1.70478 | ||||||||
\(322\) | −5.26798 | −0.293573 | ||||||||
\(323\) | 5.25901 | 0.292619 | ||||||||
\(324\) | 0.323404 | 0.0179669 | ||||||||
\(325\) | −20.0900 | −1.11439 | ||||||||
\(326\) | −2.01668 | −0.111693 | ||||||||
\(327\) | 28.5228 | 1.57732 | ||||||||
\(328\) | 34.5706 | 1.90884 | ||||||||
\(329\) | 2.11982 | 0.116869 | ||||||||
\(330\) | −21.3788 | −1.17687 | ||||||||
\(331\) | 11.6572 | 0.640739 | 0.320369 | − | 0.947293i | \(-0.396193\pi\) | ||||
0.320369 | + | 0.947293i | \(0.396193\pi\) | |||||||
\(332\) | 1.40090 | 0.0768846 | ||||||||
\(333\) | 22.0256 | 1.20700 | ||||||||
\(334\) | 31.5381 | 1.72569 | ||||||||
\(335\) | 7.75622 | 0.423767 | ||||||||
\(336\) | 12.1842 | 0.664703 | ||||||||
\(337\) | 19.6662 | 1.07129 | 0.535643 | − | 0.844445i | \(-0.320069\pi\) | ||||
0.535643 | + | 0.844445i | \(0.320069\pi\) | |||||||
\(338\) | −2.85936 | −0.155528 | ||||||||
\(339\) | −52.9903 | −2.87804 | ||||||||
\(340\) | −2.43281 | −0.131938 | ||||||||
\(341\) | −12.5824 | −0.681376 | ||||||||
\(342\) | 7.58242 | 0.410010 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 18.0900 | 0.975349 | ||||||||
\(345\) | −34.2445 | −1.84366 | ||||||||
\(346\) | −28.0305 | −1.50693 | ||||||||
\(347\) | 34.4328 | 1.84845 | 0.924225 | − | 0.381848i | \(-0.124712\pi\) | ||||
0.924225 | + | 0.381848i | \(0.124712\pi\) | |||||||
\(348\) | 3.51658 | 0.188508 | ||||||||
\(349\) | −9.48679 | −0.507816 | −0.253908 | − | 0.967228i | \(-0.581716\pi\) | ||||
−0.253908 | + | 0.967228i | \(0.581716\pi\) | |||||||
\(350\) | −8.84143 | −0.472594 | ||||||||
\(351\) | −20.7666 | −1.10844 | ||||||||
\(352\) | −1.20840 | −0.0644080 | ||||||||
\(353\) | 22.3130 | 1.18760 | 0.593800 | − | 0.804612i | \(-0.297627\pi\) | ||||
0.593800 | + | 0.804612i | \(0.297627\pi\) | |||||||
\(354\) | 12.7410 | 0.677176 | ||||||||
\(355\) | 1.75140 | 0.0929546 | ||||||||
\(356\) | 0.698090 | 0.0369987 | ||||||||
\(357\) | −15.0450 | −0.796267 | ||||||||
\(358\) | −22.2307 | −1.17493 | ||||||||
\(359\) | −8.61220 | −0.454535 | −0.227267 | − | 0.973832i | \(-0.572979\pi\) | ||||
−0.227267 | + | 0.973832i | \(0.572979\pi\) | |||||||
\(360\) | 46.8913 | 2.47139 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 3.38298 | 0.177805 | ||||||||
\(363\) | −24.7071 | −1.29678 | ||||||||
\(364\) | 0.462598 | 0.0242467 | ||||||||
\(365\) | 3.28880 | 0.172144 | ||||||||
\(366\) | −6.16339 | −0.322165 | ||||||||
\(367\) | 13.3926 | 0.699089 | 0.349544 | − | 0.936920i | \(-0.386336\pi\) | ||||
0.349544 | + | 0.936920i | \(0.386336\pi\) | |||||||
\(368\) | −15.3401 | −0.799657 | ||||||||
\(369\) | −65.8511 | −3.42807 | ||||||||
\(370\) | −20.6516 | −1.07363 | ||||||||
\(371\) | 0.0643910 | 0.00334301 | ||||||||
\(372\) | −3.25901 | −0.168972 | ||||||||
\(373\) | −12.1932 | −0.631339 | −0.315669 | − | 0.948869i | \(-0.602229\pi\) | ||||
−0.315669 | + | 0.948869i | \(0.602229\pi\) | |||||||
\(374\) | 11.8254 | 0.611478 | ||||||||
\(375\) | −9.93561 | −0.513073 | ||||||||
\(376\) | 5.76932 | 0.297530 | ||||||||
\(377\) | −29.3490 | −1.51155 | ||||||||
\(378\) | −9.13919 | −0.470069 | ||||||||
\(379\) | 15.2847 | 0.785120 | 0.392560 | − | 0.919726i | \(-0.371590\pi\) | ||||
0.392560 | + | 0.919726i | \(0.371590\pi\) | |||||||
\(380\) | −0.462598 | −0.0237308 | ||||||||
\(381\) | −19.3836 | −0.993054 | ||||||||
\(382\) | −0.124636 | −0.00637692 | ||||||||
\(383\) | 7.04502 | 0.359984 | 0.179992 | − | 0.983668i | \(-0.442393\pi\) | ||||
0.179992 | + | 0.983668i | \(0.442393\pi\) | |||||||
\(384\) | 35.3282 | 1.80284 | ||||||||
\(385\) | 5.10941 | 0.260399 | ||||||||
\(386\) | 2.56864 | 0.130740 | ||||||||
\(387\) | −34.4585 | −1.75162 | ||||||||
\(388\) | −2.50135 | −0.126987 | ||||||||
\(389\) | 17.0014 | 0.862008 | 0.431004 | − | 0.902350i | \(-0.358160\pi\) | ||||
0.431004 | + | 0.902350i | \(0.358160\pi\) | |||||||
\(390\) | 46.2147 | 2.34017 | ||||||||
\(391\) | 18.9419 | 0.957932 | ||||||||
\(392\) | −2.72161 | −0.137462 | ||||||||
\(393\) | 20.7666 | 1.04754 | ||||||||
\(394\) | 15.8545 | 0.798740 | ||||||||
\(395\) | −2.64681 | −0.133175 | ||||||||
\(396\) | 1.10941 | 0.0557498 | ||||||||
\(397\) | 29.1953 | 1.46527 | 0.732635 | − | 0.680622i | \(-0.238290\pi\) | ||||
0.732635 | + | 0.680622i | \(0.238290\pi\) | |||||||
\(398\) | −7.05880 | −0.353825 | ||||||||
\(399\) | −2.86081 | −0.143219 | ||||||||
\(400\) | −25.7458 | −1.28729 | ||||||||
\(401\) | −13.3878 | −0.668555 | −0.334277 | − | 0.942475i | \(-0.608492\pi\) | ||||
−0.334277 | + | 0.942475i | \(0.608492\pi\) | |||||||
\(402\) | −9.76518 | −0.487043 | ||||||||
\(403\) | 27.1994 | 1.35490 | ||||||||
\(404\) | 0.959801 | 0.0477519 | ||||||||
\(405\) | −7.72161 | −0.383690 | ||||||||
\(406\) | −12.9162 | −0.641022 | ||||||||
\(407\) | 6.53181 | 0.323770 | ||||||||
\(408\) | −40.9467 | −2.02716 | ||||||||
\(409\) | 20.9300 | 1.03492 | 0.517461 | − | 0.855707i | \(-0.326877\pi\) | ||||
0.517461 | + | 0.855707i | \(0.326877\pi\) | |||||||
\(410\) | 61.7431 | 3.04927 | ||||||||
\(411\) | 43.7521 | 2.15813 | ||||||||
\(412\) | 1.82832 | 0.0900749 | ||||||||
\(413\) | −3.04502 | −0.149835 | ||||||||
\(414\) | 27.3103 | 1.34223 | ||||||||
\(415\) | −33.4480 | −1.64190 | ||||||||
\(416\) | 2.61220 | 0.128074 | ||||||||
\(417\) | −28.0948 | −1.37581 | ||||||||
\(418\) | 2.24860 | 0.109983 | ||||||||
\(419\) | −16.7666 | −0.819103 | −0.409552 | − | 0.912287i | \(-0.634315\pi\) | ||||
−0.409552 | + | 0.912287i | \(0.634315\pi\) | |||||||
\(420\) | 1.32340 | 0.0645755 | ||||||||
\(421\) | −17.7819 | −0.866635 | −0.433317 | − | 0.901241i | \(-0.642657\pi\) | ||||
−0.433317 | + | 0.901241i | \(0.642657\pi\) | |||||||
\(422\) | −5.72576 | −0.278726 | ||||||||
\(423\) | −10.9896 | −0.534332 | ||||||||
\(424\) | 0.175247 | 0.00851076 | ||||||||
\(425\) | 31.7908 | 1.54208 | ||||||||
\(426\) | −2.20503 | −0.106834 | ||||||||
\(427\) | 1.47301 | 0.0712840 | ||||||||
\(428\) | 1.48612 | 0.0718343 | ||||||||
\(429\) | −14.6170 | −0.705716 | ||||||||
\(430\) | 32.3088 | 1.55807 | ||||||||
\(431\) | 29.8325 | 1.43698 | 0.718490 | − | 0.695538i | \(-0.244834\pi\) | ||||
0.718490 | + | 0.695538i | \(0.244834\pi\) | |||||||
\(432\) | −26.6129 | −1.28041 | ||||||||
\(433\) | −11.1350 | −0.535116 | −0.267558 | − | 0.963542i | \(-0.586217\pi\) | ||||
−0.267558 | + | 0.963542i | \(0.586217\pi\) | |||||||
\(434\) | 11.9702 | 0.574589 | ||||||||
\(435\) | −83.9619 | −4.02567 | ||||||||
\(436\) | 1.38780 | 0.0664633 | ||||||||
\(437\) | 3.60179 | 0.172297 | ||||||||
\(438\) | −4.14064 | −0.197848 | ||||||||
\(439\) | 14.8864 | 0.710491 | 0.355246 | − | 0.934773i | \(-0.384397\pi\) | ||||
0.355246 | + | 0.934773i | \(0.384397\pi\) | |||||||
\(440\) | 13.9058 | 0.662934 | ||||||||
\(441\) | 5.18421 | 0.246867 | ||||||||
\(442\) | −25.5630 | −1.21591 | ||||||||
\(443\) | 30.4149 | 1.44505 | 0.722527 | − | 0.691342i | \(-0.242980\pi\) | ||||
0.722527 | + | 0.691342i | \(0.242980\pi\) | |||||||
\(444\) | 1.69182 | 0.0802904 | ||||||||
\(445\) | −16.6676 | −0.790122 | ||||||||
\(446\) | −3.10044 | −0.146810 | ||||||||
\(447\) | −38.7417 | −1.83242 | ||||||||
\(448\) | −7.36842 | −0.348125 | ||||||||
\(449\) | −9.35801 | −0.441632 | −0.220816 | − | 0.975316i | \(-0.570872\pi\) | ||||
−0.220816 | + | 0.975316i | \(0.570872\pi\) | |||||||
\(450\) | 45.8358 | 2.16072 | ||||||||
\(451\) | −19.5284 | −0.919558 | ||||||||
\(452\) | −2.57827 | −0.121272 | ||||||||
\(453\) | 23.4134 | 1.10006 | ||||||||
\(454\) | 16.0298 | 0.752315 | ||||||||
\(455\) | −11.0450 | −0.517798 | ||||||||
\(456\) | −7.78600 | −0.364613 | ||||||||
\(457\) | −29.8552 | −1.39657 | −0.698284 | − | 0.715821i | \(-0.746053\pi\) | ||||
−0.698284 | + | 0.715821i | \(0.746053\pi\) | |||||||
\(458\) | 14.1884 | 0.662978 | ||||||||
\(459\) | 32.8615 | 1.53384 | ||||||||
\(460\) | −1.66618 | −0.0776862 | ||||||||
\(461\) | −16.8608 | −0.785286 | −0.392643 | − | 0.919691i | \(-0.628439\pi\) | ||||
−0.392643 | + | 0.919691i | \(0.628439\pi\) | |||||||
\(462\) | −6.43281 | −0.299281 | ||||||||
\(463\) | −9.86226 | −0.458338 | −0.229169 | − | 0.973387i | \(-0.573601\pi\) | ||||
−0.229169 | + | 0.973387i | \(0.573601\pi\) | |||||||
\(464\) | −37.6114 | −1.74607 | ||||||||
\(465\) | 77.8123 | 3.60846 | ||||||||
\(466\) | −14.0811 | −0.652293 | ||||||||
\(467\) | 18.4924 | 0.855726 | 0.427863 | − | 0.903844i | \(-0.359267\pi\) | ||||
0.427863 | + | 0.903844i | \(0.359267\pi\) | |||||||
\(468\) | −2.39821 | −0.110857 | ||||||||
\(469\) | 2.33382 | 0.107766 | ||||||||
\(470\) | 10.3040 | 0.475289 | ||||||||
\(471\) | 14.6766 | 0.676262 | ||||||||
\(472\) | −8.28735 | −0.381456 | ||||||||
\(473\) | −10.2188 | −0.469862 | ||||||||
\(474\) | 3.33237 | 0.153061 | ||||||||
\(475\) | 6.04502 | 0.277364 | ||||||||
\(476\) | −0.732024 | −0.0335523 | ||||||||
\(477\) | −0.333816 | −0.0152844 | ||||||||
\(478\) | 6.43281 | 0.294230 | ||||||||
\(479\) | −32.2951 | −1.47560 | −0.737800 | − | 0.675020i | \(-0.764135\pi\) | ||||
−0.737800 | + | 0.675020i | \(0.764135\pi\) | |||||||
\(480\) | 7.47301 | 0.341095 | ||||||||
\(481\) | −14.1198 | −0.643808 | ||||||||
\(482\) | 38.5664 | 1.75665 | ||||||||
\(483\) | −10.3040 | −0.468850 | ||||||||
\(484\) | −1.20214 | −0.0546425 | ||||||||
\(485\) | 59.7223 | 2.71185 | ||||||||
\(486\) | −17.6960 | −0.802706 | ||||||||
\(487\) | −27.1142 | −1.22866 | −0.614331 | − | 0.789048i | \(-0.710574\pi\) | ||||
−0.614331 | + | 0.789048i | \(0.710574\pi\) | |||||||
\(488\) | 4.00896 | 0.181477 | ||||||||
\(489\) | −3.94457 | −0.178380 | ||||||||
\(490\) | −4.86081 | −0.219589 | ||||||||
\(491\) | 6.58723 | 0.297278 | 0.148639 | − | 0.988892i | \(-0.452511\pi\) | ||||
0.148639 | + | 0.988892i | \(0.452511\pi\) | |||||||
\(492\) | −5.05813 | −0.228038 | ||||||||
\(493\) | 46.4424 | 2.09166 | ||||||||
\(494\) | −4.86081 | −0.218698 | ||||||||
\(495\) | −26.4882 | −1.19056 | ||||||||
\(496\) | 34.8567 | 1.56511 | ||||||||
\(497\) | 0.526989 | 0.0236387 | ||||||||
\(498\) | 42.1115 | 1.88706 | ||||||||
\(499\) | 23.4689 | 1.05061 | 0.525305 | − | 0.850914i | \(-0.323951\pi\) | ||||
0.525305 | + | 0.850914i | \(0.323951\pi\) | |||||||
\(500\) | −0.483423 | −0.0216193 | ||||||||
\(501\) | 61.6877 | 2.75600 | ||||||||
\(502\) | −7.82351 | −0.349180 | ||||||||
\(503\) | 20.1801 | 0.899785 | 0.449892 | − | 0.893083i | \(-0.351462\pi\) | ||||
0.449892 | + | 0.893083i | \(0.351462\pi\) | |||||||
\(504\) | 14.1094 | 0.628483 | ||||||||
\(505\) | −22.9162 | −1.01976 | ||||||||
\(506\) | 8.09899 | 0.360044 | ||||||||
\(507\) | −5.59283 | −0.248386 | ||||||||
\(508\) | −0.943123 | −0.0418443 | ||||||||
\(509\) | −28.8448 | −1.27852 | −0.639262 | − | 0.768989i | \(-0.720760\pi\) | ||||
−0.639262 | + | 0.768989i | \(0.720760\pi\) | |||||||
\(510\) | −73.1309 | −3.23829 | ||||||||
\(511\) | 0.989588 | 0.0437768 | ||||||||
\(512\) | −19.8352 | −0.876599 | ||||||||
\(513\) | 6.24860 | 0.275882 | ||||||||
\(514\) | −36.4626 | −1.60830 | ||||||||
\(515\) | −43.6531 | −1.92358 | ||||||||
\(516\) | −2.64681 | −0.116519 | ||||||||
\(517\) | −3.25901 | −0.143331 | ||||||||
\(518\) | −6.21400 | −0.273027 | ||||||||
\(519\) | −54.8269 | −2.40663 | ||||||||
\(520\) | −30.0602 | −1.31823 | ||||||||
\(521\) | −5.36215 | −0.234920 | −0.117460 | − | 0.993078i | \(-0.537475\pi\) | ||||
−0.117460 | + | 0.993078i | \(0.537475\pi\) | |||||||
\(522\) | 66.9605 | 2.93078 | ||||||||
\(523\) | −1.56304 | −0.0683471 | −0.0341735 | − | 0.999416i | \(-0.510880\pi\) | ||||
−0.0341735 | + | 0.999416i | \(0.510880\pi\) | |||||||
\(524\) | 1.01041 | 0.0441401 | ||||||||
\(525\) | −17.2936 | −0.754755 | ||||||||
\(526\) | −6.16339 | −0.268736 | ||||||||
\(527\) | −43.0409 | −1.87489 | ||||||||
\(528\) | −18.7320 | −0.815207 | ||||||||
\(529\) | −10.0271 | −0.435960 | ||||||||
\(530\) | 0.312992 | 0.0135955 | ||||||||
\(531\) | 15.7860 | 0.685054 | ||||||||
\(532\) | −0.139194 | −0.00603483 | ||||||||
\(533\) | 42.2147 | 1.82852 | ||||||||
\(534\) | 20.9848 | 0.908100 | ||||||||
\(535\) | −35.4826 | −1.53405 | ||||||||
\(536\) | 6.35174 | 0.274353 | ||||||||
\(537\) | −43.4826 | −1.87641 | ||||||||
\(538\) | −7.29776 | −0.314629 | ||||||||
\(539\) | 1.53740 | 0.0662206 | ||||||||
\(540\) | −2.89059 | −0.124391 | ||||||||
\(541\) | 20.8864 | 0.897978 | 0.448989 | − | 0.893537i | \(-0.351784\pi\) | ||||
0.448989 | + | 0.893537i | \(0.351784\pi\) | |||||||
\(542\) | −45.4439 | −1.95198 | ||||||||
\(543\) | 6.61702 | 0.283964 | ||||||||
\(544\) | −4.13360 | −0.177227 | ||||||||
\(545\) | −33.1350 | −1.41935 | ||||||||
\(546\) | 13.9058 | 0.595114 | ||||||||
\(547\) | 21.8165 | 0.932804 | 0.466402 | − | 0.884573i | \(-0.345550\pi\) | ||||
0.466402 | + | 0.884573i | \(0.345550\pi\) | |||||||
\(548\) | 2.12878 | 0.0909371 | ||||||||
\(549\) | −7.63640 | −0.325913 | ||||||||
\(550\) | 13.5928 | 0.579600 | ||||||||
\(551\) | 8.83102 | 0.376214 | ||||||||
\(552\) | −28.0436 | −1.19361 | ||||||||
\(553\) | −0.796415 | −0.0338670 | ||||||||
\(554\) | −25.2369 | −1.07221 | ||||||||
\(555\) | −40.3941 | −1.71463 | ||||||||
\(556\) | −1.36697 | −0.0579725 | ||||||||
\(557\) | 11.7950 | 0.499769 | 0.249884 | − | 0.968276i | \(-0.419607\pi\) | ||||
0.249884 | + | 0.968276i | \(0.419607\pi\) | |||||||
\(558\) | −62.0561 | −2.62704 | ||||||||
\(559\) | 22.0900 | 0.934309 | ||||||||
\(560\) | −14.1544 | −0.598134 | ||||||||
\(561\) | 23.1302 | 0.976559 | ||||||||
\(562\) | −6.75285 | −0.284852 | ||||||||
\(563\) | 35.8414 | 1.51054 | 0.755268 | − | 0.655416i | \(-0.227507\pi\) | ||||
0.755268 | + | 0.655416i | \(0.227507\pi\) | |||||||
\(564\) | −0.844128 | −0.0355442 | ||||||||
\(565\) | 61.5589 | 2.58980 | ||||||||
\(566\) | 36.2438 | 1.52344 | ||||||||
\(567\) | −2.32340 | −0.0975738 | ||||||||
\(568\) | 1.43426 | 0.0601802 | ||||||||
\(569\) | −8.29025 | −0.347545 | −0.173773 | − | 0.984786i | \(-0.555596\pi\) | ||||
−0.173773 | + | 0.984786i | \(0.555596\pi\) | |||||||
\(570\) | −13.9058 | −0.582451 | ||||||||
\(571\) | 8.50906 | 0.356093 | 0.178047 | − | 0.984022i | \(-0.443022\pi\) | ||||
0.178047 | + | 0.984022i | \(0.443022\pi\) | |||||||
\(572\) | −0.711200 | −0.0297367 | ||||||||
\(573\) | −0.243784 | −0.0101842 | ||||||||
\(574\) | 18.5783 | 0.775442 | ||||||||
\(575\) | 21.7729 | 0.907992 | ||||||||
\(576\) | 38.1994 | 1.59164 | ||||||||
\(577\) | −12.3732 | −0.515105 | −0.257552 | − | 0.966264i | \(-0.582916\pi\) | ||||
−0.257552 | + | 0.966264i | \(0.582916\pi\) | |||||||
\(578\) | 15.5872 | 0.648343 | ||||||||
\(579\) | 5.02419 | 0.208798 | ||||||||
\(580\) | −4.08522 | −0.169629 | ||||||||
\(581\) | −10.0644 | −0.417541 | ||||||||
\(582\) | −75.1911 | −3.11677 | ||||||||
\(583\) | −0.0989948 | −0.00409995 | ||||||||
\(584\) | 2.69327 | 0.111448 | ||||||||
\(585\) | 57.2597 | 2.36740 | ||||||||
\(586\) | 13.5797 | 0.560973 | ||||||||
\(587\) | −44.6773 | −1.84403 | −0.922014 | − | 0.387156i | \(-0.873457\pi\) | ||||
−0.922014 | + | 0.387156i | \(0.873457\pi\) | |||||||
\(588\) | 0.398207 | 0.0164218 | ||||||||
\(589\) | −8.18421 | −0.337225 | ||||||||
\(590\) | −14.8012 | −0.609357 | ||||||||
\(591\) | 31.0111 | 1.27563 | ||||||||
\(592\) | −18.0948 | −0.743694 | ||||||||
\(593\) | 1.84143 | 0.0756185 | 0.0378093 | − | 0.999285i | \(-0.487962\pi\) | ||||
0.0378093 | + | 0.999285i | \(0.487962\pi\) | |||||||
\(594\) | 14.0506 | 0.576504 | ||||||||
\(595\) | 17.4778 | 0.716521 | ||||||||
\(596\) | −1.88500 | −0.0772125 | ||||||||
\(597\) | −13.8068 | −0.565076 | ||||||||
\(598\) | −17.5076 | −0.715940 | ||||||||
\(599\) | −30.5437 | −1.24798 | −0.623990 | − | 0.781432i | \(-0.714489\pi\) | ||||
−0.623990 | + | 0.781432i | \(0.714489\pi\) | |||||||
\(600\) | −47.0665 | −1.92148 | ||||||||
\(601\) | −34.8913 | −1.42324 | −0.711622 | − | 0.702562i | \(-0.752039\pi\) | ||||
−0.711622 | + | 0.702562i | \(0.752039\pi\) | |||||||
\(602\) | 9.72161 | 0.396223 | ||||||||
\(603\) | −12.0990 | −0.492709 | ||||||||
\(604\) | 1.13919 | 0.0463532 | ||||||||
\(605\) | 28.7022 | 1.16691 | ||||||||
\(606\) | 28.8518 | 1.17203 | ||||||||
\(607\) | −29.3926 | −1.19301 | −0.596505 | − | 0.802610i | \(-0.703444\pi\) | ||||
−0.596505 | + | 0.802610i | \(0.703444\pi\) | |||||||
\(608\) | −0.786003 | −0.0318766 | ||||||||
\(609\) | −25.2638 | −1.02374 | ||||||||
\(610\) | 7.16002 | 0.289901 | ||||||||
\(611\) | 7.04502 | 0.285011 | ||||||||
\(612\) | 3.79497 | 0.153402 | ||||||||
\(613\) | −40.0561 | −1.61785 | −0.808925 | − | 0.587911i | \(-0.799950\pi\) | ||||
−0.808925 | + | 0.587911i | \(0.799950\pi\) | |||||||
\(614\) | −5.58097 | −0.225230 | ||||||||
\(615\) | 120.768 | 4.86983 | ||||||||
\(616\) | 4.18421 | 0.168587 | ||||||||
\(617\) | 24.9002 | 1.00245 | 0.501223 | − | 0.865318i | \(-0.332884\pi\) | ||||
0.501223 | + | 0.865318i | \(0.332884\pi\) | |||||||
\(618\) | 54.9598 | 2.21081 | ||||||||
\(619\) | −15.7264 | −0.632099 | −0.316049 | − | 0.948743i | \(-0.602356\pi\) | ||||
−0.316049 | + | 0.948743i | \(0.602356\pi\) | |||||||
\(620\) | 3.78600 | 0.152050 | ||||||||
\(621\) | 22.5062 | 0.903141 | ||||||||
\(622\) | 0.518697 | 0.0207979 | ||||||||
\(623\) | −5.01523 | −0.200931 | ||||||||
\(624\) | 40.4931 | 1.62102 | ||||||||
\(625\) | −18.6829 | −0.747314 | ||||||||
\(626\) | 14.0871 | 0.563035 | ||||||||
\(627\) | 4.39821 | 0.175647 | ||||||||
\(628\) | 0.714098 | 0.0284956 | ||||||||
\(629\) | 22.3434 | 0.890892 | ||||||||
\(630\) | 25.1994 | 1.00397 | ||||||||
\(631\) | −38.2999 | −1.52469 | −0.762347 | − | 0.647168i | \(-0.775953\pi\) | ||||
−0.762347 | + | 0.647168i | \(0.775953\pi\) | |||||||
\(632\) | −2.16753 | −0.0862198 | ||||||||
\(633\) | −11.1994 | −0.445138 | ||||||||
\(634\) | −19.6620 | −0.780879 | ||||||||
\(635\) | 22.5180 | 0.893601 | ||||||||
\(636\) | −0.0256410 | −0.00101673 | ||||||||
\(637\) | −3.32340 | −0.131678 | ||||||||
\(638\) | 19.8574 | 0.786164 | ||||||||
\(639\) | −2.73202 | −0.108077 | ||||||||
\(640\) | −41.0409 | −1.62228 | ||||||||
\(641\) | −41.9363 | −1.65638 | −0.828192 | − | 0.560445i | \(-0.810630\pi\) | ||||
−0.828192 | + | 0.560445i | \(0.810630\pi\) | |||||||
\(642\) | 44.6731 | 1.76311 | ||||||||
\(643\) | −16.9371 | −0.667932 | −0.333966 | − | 0.942585i | \(-0.608387\pi\) | ||||
−0.333966 | + | 0.942585i | \(0.608387\pi\) | |||||||
\(644\) | −0.501348 | −0.0197559 | ||||||||
\(645\) | 63.1953 | 2.48831 | ||||||||
\(646\) | 7.69182 | 0.302631 | ||||||||
\(647\) | 4.50906 | 0.177270 | 0.0886348 | − | 0.996064i | \(-0.471750\pi\) | ||||
0.0886348 | + | 0.996064i | \(0.471750\pi\) | |||||||
\(648\) | −6.32340 | −0.248407 | ||||||||
\(649\) | 4.68141 | 0.183762 | ||||||||
\(650\) | −29.3836 | −1.15252 | ||||||||
\(651\) | 23.4134 | 0.917645 | ||||||||
\(652\) | −0.191925 | −0.00751638 | ||||||||
\(653\) | −15.0242 | −0.587942 | −0.293971 | − | 0.955814i | \(-0.594977\pi\) | ||||
−0.293971 | + | 0.955814i | \(0.594977\pi\) | |||||||
\(654\) | 41.7175 | 1.63128 | ||||||||
\(655\) | −24.1246 | −0.942628 | ||||||||
\(656\) | 54.0990 | 2.11221 | ||||||||
\(657\) | −5.13023 | −0.200149 | ||||||||
\(658\) | 3.10044 | 0.120868 | ||||||||
\(659\) | 24.7410 | 0.963772 | 0.481886 | − | 0.876234i | \(-0.339952\pi\) | ||||
0.481886 | + | 0.876234i | \(0.339952\pi\) | |||||||
\(660\) | −2.03460 | −0.0791968 | ||||||||
\(661\) | −9.62329 | −0.374302 | −0.187151 | − | 0.982331i | \(-0.559925\pi\) | ||||
−0.187151 | + | 0.982331i | \(0.559925\pi\) | |||||||
\(662\) | 17.0498 | 0.662661 | ||||||||
\(663\) | −50.0007 | −1.94187 | ||||||||
\(664\) | −27.3914 | −1.06299 | ||||||||
\(665\) | 3.32340 | 0.128876 | ||||||||
\(666\) | 32.2147 | 1.24829 | ||||||||
\(667\) | 31.8075 | 1.23159 | ||||||||
\(668\) | 3.00145 | 0.116130 | ||||||||
\(669\) | −6.06439 | −0.234463 | ||||||||
\(670\) | 11.3442 | 0.438266 | ||||||||
\(671\) | −2.26461 | −0.0874243 | ||||||||
\(672\) | 2.24860 | 0.0867417 | ||||||||
\(673\) | −11.1213 | −0.428693 | −0.214347 | − | 0.976758i | \(-0.568762\pi\) | ||||
−0.214347 | + | 0.976758i | \(0.568762\pi\) | |||||||
\(674\) | 28.7637 | 1.10794 | ||||||||
\(675\) | 37.7729 | 1.45388 | ||||||||
\(676\) | −0.272122 | −0.0104662 | ||||||||
\(677\) | 16.5616 | 0.636514 | 0.318257 | − | 0.948005i | \(-0.396903\pi\) | ||||
0.318257 | + | 0.948005i | \(0.396903\pi\) | |||||||
\(678\) | −77.5035 | −2.97650 | ||||||||
\(679\) | 17.9702 | 0.689633 | ||||||||
\(680\) | 47.5679 | 1.82414 | ||||||||
\(681\) | 31.3539 | 1.20148 | ||||||||
\(682\) | −18.4030 | −0.704688 | ||||||||
\(683\) | 9.62262 | 0.368199 | 0.184100 | − | 0.982908i | \(-0.441063\pi\) | ||||
0.184100 | + | 0.982908i | \(0.441063\pi\) | |||||||
\(684\) | 0.721612 | 0.0275915 | ||||||||
\(685\) | −50.8269 | −1.94199 | ||||||||
\(686\) | −1.46260 | −0.0558423 | ||||||||
\(687\) | 27.7521 | 1.05881 | ||||||||
\(688\) | 28.3088 | 1.07926 | ||||||||
\(689\) | 0.213997 | 0.00815265 | ||||||||
\(690\) | −50.0859 | −1.90674 | ||||||||
\(691\) | 11.5720 | 0.440220 | 0.220110 | − | 0.975475i | \(-0.429358\pi\) | ||||
0.220110 | + | 0.975475i | \(0.429358\pi\) | |||||||
\(692\) | −2.66763 | −0.101408 | ||||||||
\(693\) | −7.97021 | −0.302763 | ||||||||
\(694\) | 50.3614 | 1.91169 | ||||||||
\(695\) | 32.6378 | 1.23802 | ||||||||
\(696\) | −68.7583 | −2.60628 | ||||||||
\(697\) | −66.8012 | −2.53028 | ||||||||
\(698\) | −13.8754 | −0.525190 | ||||||||
\(699\) | −27.5422 | −1.04174 | ||||||||
\(700\) | −0.841431 | −0.0318031 | ||||||||
\(701\) | −46.3781 | −1.75167 | −0.875837 | − | 0.482606i | \(-0.839690\pi\) | ||||
−0.875837 | + | 0.482606i | \(0.839690\pi\) | |||||||
\(702\) | −30.3732 | −1.14636 | ||||||||
\(703\) | 4.24860 | 0.160239 | ||||||||
\(704\) | 11.3282 | 0.426948 | ||||||||
\(705\) | 20.1544 | 0.759059 | ||||||||
\(706\) | 32.6349 | 1.22823 | ||||||||
\(707\) | −6.89541 | −0.259329 | ||||||||
\(708\) | 1.21255 | 0.0455703 | ||||||||
\(709\) | −26.2099 | −0.984332 | −0.492166 | − | 0.870501i | \(-0.663795\pi\) | ||||
−0.492166 | + | 0.870501i | \(0.663795\pi\) | |||||||
\(710\) | 2.56159 | 0.0961349 | ||||||||
\(711\) | 4.12878 | 0.154841 | ||||||||
\(712\) | −13.6495 | −0.511537 | ||||||||
\(713\) | −29.4778 | −1.10395 | ||||||||
\(714\) | −22.0048 | −0.823510 | ||||||||
\(715\) | 16.9806 | 0.635039 | ||||||||
\(716\) | −2.11567 | −0.0790664 | ||||||||
\(717\) | 12.5824 | 0.469899 | ||||||||
\(718\) | −12.5962 | −0.470086 | ||||||||
\(719\) | −11.4432 | −0.426760 | −0.213380 | − | 0.976969i | \(-0.568447\pi\) | ||||
−0.213380 | + | 0.976969i | \(0.568447\pi\) | |||||||
\(720\) | 73.3795 | 2.73469 | ||||||||
\(721\) | −13.1350 | −0.489175 | ||||||||
\(722\) | 1.46260 | 0.0544323 | ||||||||
\(723\) | 75.4349 | 2.80546 | ||||||||
\(724\) | 0.321955 | 0.0119654 | ||||||||
\(725\) | 53.3836 | 1.98262 | ||||||||
\(726\) | −36.1365 | −1.34115 | ||||||||
\(727\) | 26.8054 | 0.994156 | 0.497078 | − | 0.867706i | \(-0.334406\pi\) | ||||
0.497078 | + | 0.867706i | \(0.334406\pi\) | |||||||
\(728\) | −9.04502 | −0.335231 | ||||||||
\(729\) | −41.5831 | −1.54011 | ||||||||
\(730\) | 4.81019 | 0.178033 | ||||||||
\(731\) | −34.9557 | −1.29288 | ||||||||
\(732\) | −0.586564 | −0.0216800 | ||||||||
\(733\) | 42.7189 | 1.57786 | 0.788930 | − | 0.614484i | \(-0.210636\pi\) | ||||
0.788930 | + | 0.614484i | \(0.210636\pi\) | |||||||
\(734\) | 19.5880 | 0.723007 | ||||||||
\(735\) | −9.50761 | −0.350694 | ||||||||
\(736\) | −2.83102 | −0.104353 | ||||||||
\(737\) | −3.58801 | −0.132166 | ||||||||
\(738\) | −96.3137 | −3.54535 | ||||||||
\(739\) | 4.35656 | 0.160259 | 0.0801293 | − | 0.996784i | \(-0.474467\pi\) | ||||
0.0801293 | + | 0.996784i | \(0.474467\pi\) | |||||||
\(740\) | −1.96540 | −0.0722494 | ||||||||
\(741\) | −9.50761 | −0.349271 | ||||||||
\(742\) | 0.0941782 | 0.00345739 | ||||||||
\(743\) | −2.11982 | −0.0777686 | −0.0388843 | − | 0.999244i | \(-0.512380\pi\) | ||||
−0.0388843 | + | 0.999244i | \(0.512380\pi\) | |||||||
\(744\) | 63.7223 | 2.33617 | ||||||||
\(745\) | 45.0063 | 1.64890 | ||||||||
\(746\) | −17.8337 | −0.652939 | ||||||||
\(747\) | 52.1759 | 1.90902 | ||||||||
\(748\) | 1.12541 | 0.0411492 | ||||||||
\(749\) | −10.6766 | −0.390114 | ||||||||
\(750\) | −14.5318 | −0.530627 | ||||||||
\(751\) | −27.1004 | −0.988909 | −0.494455 | − | 0.869203i | \(-0.664632\pi\) | ||||
−0.494455 | + | 0.869203i | \(0.664632\pi\) | |||||||
\(752\) | 9.02834 | 0.329230 | ||||||||
\(753\) | −15.3026 | −0.557657 | ||||||||
\(754\) | −42.9259 | −1.56327 | ||||||||
\(755\) | −27.1994 | −0.989889 | ||||||||
\(756\) | −0.869769 | −0.0316332 | ||||||||
\(757\) | 40.3297 | 1.46581 | 0.732903 | − | 0.680333i | \(-0.238165\pi\) | ||||
0.732903 | + | 0.680333i | \(0.238165\pi\) | |||||||
\(758\) | 22.3553 | 0.811981 | ||||||||
\(759\) | 15.8414 | 0.575008 | ||||||||
\(760\) | 9.04502 | 0.328097 | ||||||||
\(761\) | 15.8206 | 0.573497 | 0.286748 | − | 0.958006i | \(-0.407426\pi\) | ||||
0.286748 | + | 0.958006i | \(0.407426\pi\) | |||||||
\(762\) | −28.3505 | −1.02703 | ||||||||
\(763\) | −9.97021 | −0.360946 | ||||||||
\(764\) | −0.0118615 | −0.000429133 0 | ||||||||
\(765\) | −90.6087 | −3.27597 | ||||||||
\(766\) | 10.3040 | 0.372300 | ||||||||
\(767\) | −10.1198 | −0.365405 | ||||||||
\(768\) | 9.51176 | 0.343226 | ||||||||
\(769\) | 33.6829 | 1.21464 | 0.607318 | − | 0.794459i | \(-0.292246\pi\) | ||||
0.607318 | + | 0.794459i | \(0.292246\pi\) | |||||||
\(770\) | 7.47301 | 0.269309 | ||||||||
\(771\) | −71.3199 | −2.56852 | ||||||||
\(772\) | 0.244455 | 0.00879813 | ||||||||
\(773\) | −22.9252 | −0.824562 | −0.412281 | − | 0.911057i | \(-0.635268\pi\) | ||||
−0.412281 | + | 0.911057i | \(0.635268\pi\) | |||||||
\(774\) | −50.3989 | −1.81155 | ||||||||
\(775\) | −49.4737 | −1.77715 | ||||||||
\(776\) | 48.9079 | 1.75569 | ||||||||
\(777\) | −12.1544 | −0.436037 | ||||||||
\(778\) | 24.8663 | 0.891500 | ||||||||
\(779\) | −12.7022 | −0.455105 | ||||||||
\(780\) | 4.39821 | 0.157481 | ||||||||
\(781\) | −0.810194 | −0.0289910 | ||||||||
\(782\) | 27.7044 | 0.990706 | ||||||||
\(783\) | 55.1815 | 1.97203 | ||||||||
\(784\) | −4.25901 | −0.152108 | ||||||||
\(785\) | −17.0498 | −0.608535 | ||||||||
\(786\) | 30.3732 | 1.08338 | ||||||||
\(787\) | 7.70079 | 0.274503 | 0.137252 | − | 0.990536i | \(-0.456173\pi\) | ||||
0.137252 | + | 0.990536i | \(0.456173\pi\) | |||||||
\(788\) | 1.50886 | 0.0537510 | ||||||||
\(789\) | −12.0554 | −0.429185 | ||||||||
\(790\) | −3.87122 | −0.137732 | ||||||||
\(791\) | 18.5228 | 0.658596 | ||||||||
\(792\) | −21.6918 | −0.770785 | ||||||||
\(793\) | 4.89541 | 0.173841 | ||||||||
\(794\) | 42.7010 | 1.51540 | ||||||||
\(795\) | 0.612205 | 0.0217127 | ||||||||
\(796\) | −0.671779 | −0.0238106 | ||||||||
\(797\) | −16.5914 | −0.587697 | −0.293848 | − | 0.955852i | \(-0.594936\pi\) | ||||
−0.293848 | + | 0.955852i | \(0.594936\pi\) | |||||||
\(798\) | −4.18421 | −0.148119 | ||||||||
\(799\) | −11.1482 | −0.394393 | ||||||||
\(800\) | −4.75140 | −0.167987 | ||||||||
\(801\) | 26.0000 | 0.918665 | ||||||||
\(802\) | −19.5810 | −0.691428 | ||||||||
\(803\) | −1.52139 | −0.0536888 | ||||||||
\(804\) | −0.929343 | −0.0327754 | ||||||||
\(805\) | 11.9702 | 0.421895 | ||||||||
\(806\) | 39.7819 | 1.40126 | ||||||||
\(807\) | −14.2742 | −0.502477 | ||||||||
\(808\) | −18.7666 | −0.660208 | ||||||||
\(809\) | 1.41344 | 0.0496938 | 0.0248469 | − | 0.999691i | \(-0.492090\pi\) | ||||
0.0248469 | + | 0.999691i | \(0.492090\pi\) | |||||||
\(810\) | −11.2936 | −0.396817 | ||||||||
\(811\) | 28.1980 | 0.990165 | 0.495083 | − | 0.868846i | \(-0.335138\pi\) | ||||
0.495083 | + | 0.868846i | \(0.335138\pi\) | |||||||
\(812\) | −1.22923 | −0.0431374 | ||||||||
\(813\) | −88.8871 | −3.11741 | ||||||||
\(814\) | 9.55341 | 0.334847 | ||||||||
\(815\) | 4.58242 | 0.160515 | ||||||||
\(816\) | −64.0769 | −2.24314 | ||||||||
\(817\) | −6.64681 | −0.232542 | ||||||||
\(818\) | 30.6122 | 1.07033 | ||||||||
\(819\) | 17.2292 | 0.602038 | ||||||||
\(820\) | 5.87603 | 0.205200 | ||||||||
\(821\) | 26.9765 | 0.941486 | 0.470743 | − | 0.882270i | \(-0.343986\pi\) | ||||
0.470743 | + | 0.882270i | \(0.343986\pi\) | |||||||
\(822\) | 63.9917 | 2.23197 | ||||||||
\(823\) | 25.6441 | 0.893898 | 0.446949 | − | 0.894560i | \(-0.352511\pi\) | ||||
0.446949 | + | 0.894560i | \(0.352511\pi\) | |||||||
\(824\) | −35.7485 | −1.24536 | ||||||||
\(825\) | 26.5872 | 0.925649 | ||||||||
\(826\) | −4.45364 | −0.154962 | ||||||||
\(827\) | 29.5451 | 1.02738 | 0.513692 | − | 0.857975i | \(-0.328277\pi\) | ||||
0.513692 | + | 0.857975i | \(0.328277\pi\) | |||||||
\(828\) | 2.59910 | 0.0903248 | ||||||||
\(829\) | 4.82687 | 0.167644 | 0.0838221 | − | 0.996481i | \(-0.473287\pi\) | ||||
0.0838221 | + | 0.996481i | \(0.473287\pi\) | |||||||
\(830\) | −48.9211 | −1.69807 | ||||||||
\(831\) | −49.3628 | −1.71238 | ||||||||
\(832\) | −24.4882 | −0.848977 | ||||||||
\(833\) | 5.25901 | 0.182214 | ||||||||
\(834\) | −41.0915 | −1.42288 | ||||||||
\(835\) | −71.6627 | −2.47999 | ||||||||
\(836\) | 0.213997 | 0.00740125 | ||||||||
\(837\) | −51.1399 | −1.76765 | ||||||||
\(838\) | −24.5228 | −0.847128 | ||||||||
\(839\) | −35.3241 | −1.21952 | −0.609761 | − | 0.792585i | \(-0.708735\pi\) | ||||
−0.609761 | + | 0.792585i | \(0.708735\pi\) | |||||||
\(840\) | −25.8760 | −0.892808 | ||||||||
\(841\) | 48.9869 | 1.68920 | ||||||||
\(842\) | −26.0077 | −0.896285 | ||||||||
\(843\) | −13.2084 | −0.454922 | ||||||||
\(844\) | −0.544915 | −0.0187568 | ||||||||
\(845\) | 6.49720 | 0.223511 | ||||||||
\(846\) | −16.0734 | −0.552613 | ||||||||
\(847\) | 8.63640 | 0.296750 | ||||||||
\(848\) | 0.274242 | 0.00941751 | ||||||||
\(849\) | 70.8919 | 2.43300 | ||||||||
\(850\) | 46.4972 | 1.59484 | ||||||||
\(851\) | 15.3026 | 0.524566 | ||||||||
\(852\) | −0.209851 | −0.00718938 | ||||||||
\(853\) | 40.6129 | 1.39056 | 0.695279 | − | 0.718740i | \(-0.255281\pi\) | ||||
0.695279 | + | 0.718740i | \(0.255281\pi\) | |||||||
\(854\) | 2.15442 | 0.0737228 | ||||||||
\(855\) | −17.2292 | −0.589227 | ||||||||
\(856\) | −29.0575 | −0.993167 | ||||||||
\(857\) | 21.4570 | 0.732957 | 0.366479 | − | 0.930426i | \(-0.380563\pi\) | ||||
0.366479 | + | 0.930426i | \(0.380563\pi\) | |||||||
\(858\) | −21.3788 | −0.729861 | ||||||||
\(859\) | 21.9237 | 0.748029 | 0.374014 | − | 0.927423i | \(-0.377981\pi\) | ||||
0.374014 | + | 0.927423i | \(0.377981\pi\) | |||||||
\(860\) | 3.07480 | 0.104850 | ||||||||
\(861\) | 36.3386 | 1.23842 | ||||||||
\(862\) | 43.6329 | 1.48614 | ||||||||
\(863\) | −27.1004 | −0.922510 | −0.461255 | − | 0.887268i | \(-0.652601\pi\) | ||||
−0.461255 | + | 0.887268i | \(0.652601\pi\) | |||||||
\(864\) | −4.91142 | −0.167090 | ||||||||
\(865\) | 63.6925 | 2.16561 | ||||||||
\(866\) | −16.2861 | −0.553424 | ||||||||
\(867\) | 30.4882 | 1.03543 | ||||||||
\(868\) | 1.13919 | 0.0386668 | ||||||||
\(869\) | 1.22441 | 0.0415352 | ||||||||
\(870\) | −122.803 | −4.16340 | ||||||||
\(871\) | 7.75622 | 0.262809 | ||||||||
\(872\) | −27.1350 | −0.918909 | ||||||||
\(873\) | −93.1614 | −3.15303 | ||||||||
\(874\) | 5.26798 | 0.178192 | ||||||||
\(875\) | 3.47301 | 0.117409 | ||||||||
\(876\) | −0.394061 | −0.0133141 | ||||||||
\(877\) | −40.7160 | −1.37488 | −0.687441 | − | 0.726240i | \(-0.741266\pi\) | ||||
−0.687441 | + | 0.726240i | \(0.741266\pi\) | |||||||
\(878\) | 21.7729 | 0.734800 | ||||||||
\(879\) | 26.5616 | 0.895900 | ||||||||
\(880\) | 21.7610 | 0.733564 | ||||||||
\(881\) | −10.2653 | −0.345846 | −0.172923 | − | 0.984935i | \(-0.555321\pi\) | ||||
−0.172923 | + | 0.984935i | \(0.555321\pi\) | |||||||
\(882\) | 7.58242 | 0.255313 | ||||||||
\(883\) | −13.7514 | −0.462771 | −0.231386 | − | 0.972862i | \(-0.574326\pi\) | ||||
−0.231386 | + | 0.972862i | \(0.574326\pi\) | |||||||
\(884\) | −2.43281 | −0.0818243 | ||||||||
\(885\) | −28.9508 | −0.973172 | ||||||||
\(886\) | 44.4848 | 1.49449 | ||||||||
\(887\) | 55.6710 | 1.86925 | 0.934625 | − | 0.355636i | \(-0.115736\pi\) | ||||
0.934625 | + | 0.355636i | \(0.115736\pi\) | |||||||
\(888\) | −33.0796 | −1.11008 | ||||||||
\(889\) | 6.77559 | 0.227246 | ||||||||
\(890\) | −24.3781 | −0.817154 | ||||||||
\(891\) | 3.57201 | 0.119667 | ||||||||
\(892\) | −0.295066 | −0.00987955 | ||||||||
\(893\) | −2.11982 | −0.0709370 | ||||||||
\(894\) | −56.6635 | −1.89511 | ||||||||
\(895\) | 50.5139 | 1.68849 | ||||||||
\(896\) | −12.3490 | −0.412553 | ||||||||
\(897\) | −34.2445 | −1.14339 | ||||||||
\(898\) | −13.6870 | −0.456741 | ||||||||
\(899\) | −72.2749 | −2.41050 | ||||||||
\(900\) | 4.36215 | 0.145405 | ||||||||
\(901\) | −0.338633 | −0.0112815 | ||||||||
\(902\) | −28.5623 | −0.951019 | ||||||||
\(903\) | 19.0152 | 0.632787 | ||||||||
\(904\) | 50.4120 | 1.67668 | ||||||||
\(905\) | −7.68701 | −0.255525 | ||||||||
\(906\) | 34.2445 | 1.13770 | ||||||||
\(907\) | 5.21255 | 0.173080 | 0.0865399 | − | 0.996248i | \(-0.472419\pi\) | ||||
0.0865399 | + | 0.996248i | \(0.472419\pi\) | |||||||
\(908\) | 1.52554 | 0.0506268 | ||||||||
\(909\) | 35.7473 | 1.18566 | ||||||||
\(910\) | −16.1544 | −0.535514 | ||||||||
\(911\) | −38.0900 | −1.26198 | −0.630990 | − | 0.775791i | \(-0.717351\pi\) | ||||
−0.630990 | + | 0.775791i | \(0.717351\pi\) | |||||||
\(912\) | −12.1842 | −0.403460 | ||||||||
\(913\) | 15.4730 | 0.512082 | ||||||||
\(914\) | −43.6662 | −1.44435 | ||||||||
\(915\) | 14.0048 | 0.462985 | ||||||||
\(916\) | 1.35029 | 0.0446149 | ||||||||
\(917\) | −7.25901 | −0.239714 | ||||||||
\(918\) | 48.0631 | 1.58632 | ||||||||
\(919\) | 43.3955 | 1.43149 | 0.715743 | − | 0.698364i | \(-0.246088\pi\) | ||||
0.715743 | + | 0.698364i | \(0.246088\pi\) | |||||||
\(920\) | 32.5783 | 1.07407 | ||||||||
\(921\) | −10.9162 | −0.359702 | ||||||||
\(922\) | −24.6606 | −0.812153 | ||||||||
\(923\) | 1.75140 | 0.0576480 | ||||||||
\(924\) | −0.612205 | −0.0201401 | ||||||||
\(925\) | 25.6829 | 0.844447 | ||||||||
\(926\) | −14.4245 | −0.474019 | ||||||||
\(927\) | 68.0948 | 2.23653 | ||||||||
\(928\) | −6.94120 | −0.227856 | ||||||||
\(929\) | −6.34278 | −0.208100 | −0.104050 | − | 0.994572i | \(-0.533180\pi\) | ||||
−0.104050 | + | 0.994572i | \(0.533180\pi\) | |||||||
\(930\) | 113.808 | 3.73192 | ||||||||
\(931\) | 1.00000 | 0.0327737 | ||||||||
\(932\) | −1.34008 | −0.0438959 | ||||||||
\(933\) | 1.01456 | 0.0332151 | ||||||||
\(934\) | 27.0469 | 0.885003 | ||||||||
\(935\) | −26.8704 | −0.878757 | ||||||||
\(936\) | 46.8913 | 1.53269 | ||||||||
\(937\) | 0.444673 | 0.0145268 | 0.00726341 | − | 0.999974i | \(-0.497688\pi\) | ||||
0.00726341 | + | 0.999974i | \(0.497688\pi\) | |||||||
\(938\) | 3.41344 | 0.111453 | ||||||||
\(939\) | 27.5541 | 0.899193 | ||||||||
\(940\) | 0.980625 | 0.0319845 | ||||||||
\(941\) | −15.2936 | −0.498558 | −0.249279 | − | 0.968432i | \(-0.580194\pi\) | ||||
−0.249279 | + | 0.968432i | \(0.580194\pi\) | |||||||
\(942\) | 21.4660 | 0.699399 | ||||||||
\(943\) | −45.7508 | −1.48985 | ||||||||
\(944\) | −12.9688 | −0.422097 | ||||||||
\(945\) | 20.7666 | 0.675538 | ||||||||
\(946\) | −14.9460 | −0.485937 | ||||||||
\(947\) | 44.7112 | 1.45292 | 0.726459 | − | 0.687209i | \(-0.241165\pi\) | ||||
0.726459 | + | 0.687209i | \(0.241165\pi\) | |||||||
\(948\) | 0.317138 | 0.0103002 | ||||||||
\(949\) | 3.28880 | 0.106759 | ||||||||
\(950\) | 8.84143 | 0.286854 | ||||||||
\(951\) | −38.4585 | −1.24710 | ||||||||
\(952\) | 14.3130 | 0.463887 | ||||||||
\(953\) | −48.3434 | −1.56600 | −0.782999 | − | 0.622023i | \(-0.786311\pi\) | ||||
−0.782999 | + | 0.622023i | \(0.786311\pi\) | |||||||
\(954\) | −0.488239 | −0.0158073 | ||||||||
\(955\) | 0.283205 | 0.00916430 | ||||||||
\(956\) | 0.612205 | 0.0198001 | ||||||||
\(957\) | 38.8407 | 1.25554 | ||||||||
\(958\) | −47.2347 | −1.52608 | ||||||||
\(959\) | −15.2936 | −0.493857 | ||||||||
\(960\) | −70.0561 | −2.26105 | ||||||||
\(961\) | 35.9813 | 1.16069 | ||||||||
\(962\) | −20.6516 | −0.665835 | ||||||||
\(963\) | 55.3497 | 1.78362 | ||||||||
\(964\) | 3.67033 | 0.118213 | ||||||||
\(965\) | −5.83661 | −0.187887 | ||||||||
\(966\) | −15.0707 | −0.484890 | ||||||||
\(967\) | 56.1759 | 1.80650 | 0.903248 | − | 0.429119i | \(-0.141176\pi\) | ||||
0.903248 | + | 0.429119i | \(0.141176\pi\) | |||||||
\(968\) | 23.5049 | 0.755477 | ||||||||
\(969\) | 15.0450 | 0.483316 | ||||||||
\(970\) | 87.3497 | 2.80463 | ||||||||
\(971\) | −48.5603 | −1.55838 | −0.779188 | − | 0.626791i | \(-0.784368\pi\) | ||||
−0.779188 | + | 0.626791i | \(0.784368\pi\) | |||||||
\(972\) | −1.68411 | −0.0540178 | ||||||||
\(973\) | 9.82061 | 0.314834 | ||||||||
\(974\) | −39.6572 | −1.27070 | ||||||||
\(975\) | −57.4737 | −1.84063 | ||||||||
\(976\) | 6.27357 | 0.200812 | ||||||||
\(977\) | 29.6925 | 0.949947 | 0.474974 | − | 0.880000i | \(-0.342458\pi\) | ||||
0.474974 | + | 0.880000i | \(0.342458\pi\) | |||||||
\(978\) | −5.76932 | −0.184483 | ||||||||
\(979\) | 7.71042 | 0.246426 | ||||||||
\(980\) | −0.462598 | −0.0147772 | ||||||||
\(981\) | 51.6877 | 1.65026 | ||||||||
\(982\) | 9.63448 | 0.307449 | ||||||||
\(983\) | 16.8358 | 0.536980 | 0.268490 | − | 0.963283i | \(-0.413475\pi\) | ||||
0.268490 | + | 0.963283i | \(0.413475\pi\) | |||||||
\(984\) | 98.8996 | 3.15281 | ||||||||
\(985\) | −36.0256 | −1.14787 | ||||||||
\(986\) | 67.9266 | 2.16323 | ||||||||
\(987\) | 6.06439 | 0.193032 | ||||||||
\(988\) | −0.462598 | −0.0147172 | ||||||||
\(989\) | −23.9404 | −0.761261 | ||||||||
\(990\) | −38.7417 | −1.23129 | ||||||||
\(991\) | −2.53595 | −0.0805572 | −0.0402786 | − | 0.999188i | \(-0.512825\pi\) | ||||
−0.0402786 | + | 0.999188i | \(0.512825\pi\) | |||||||
\(992\) | 6.43281 | 0.204242 | ||||||||
\(993\) | 33.3490 | 1.05830 | ||||||||
\(994\) | 0.770774 | 0.0244475 | ||||||||
\(995\) | 16.0394 | 0.508484 | ||||||||
\(996\) | 4.00772 | 0.126989 | ||||||||
\(997\) | −36.9217 | −1.16932 | −0.584661 | − | 0.811277i | \(-0.698773\pi\) | ||||
−0.584661 | + | 0.811277i | \(0.698773\pi\) | |||||||
\(998\) | 34.3255 | 1.08656 | ||||||||
\(999\) | 26.5478 | 0.839936 |
(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 | 133.2.a.d.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 1197.2.a.k.1.2 | 3 | |||
4.3 | odd | 2 | 2128.2.a.p.1.1 | 3 | |||
5.4 | even | 2 | 3325.2.a.r.1.2 | 3 | |||
7.2 | even | 3 | 931.2.f.l.704.2 | 6 | |||
7.3 | odd | 6 | 931.2.f.m.324.2 | 6 | |||
7.4 | even | 3 | 931.2.f.l.324.2 | 6 | |||
7.5 | odd | 6 | 931.2.f.m.704.2 | 6 | |||
7.6 | odd | 2 | 931.2.a.k.1.2 | 3 | |||
8.3 | odd | 2 | 8512.2.a.bp.1.3 | 3 | |||
8.5 | even | 2 | 8512.2.a.bi.1.1 | 3 | |||
19.18 | odd | 2 | 2527.2.a.f.1.2 | 3 | |||
21.20 | even | 2 | 8379.2.a.bo.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
133.2.a.d.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
931.2.a.k.1.2 | 3 | 7.6 | odd | 2 | |||
931.2.f.l.324.2 | 6 | 7.4 | even | 3 | |||
931.2.f.l.704.2 | 6 | 7.2 | even | 3 | |||
931.2.f.m.324.2 | 6 | 7.3 | odd | 6 | |||
931.2.f.m.704.2 | 6 | 7.5 | odd | 6 | |||
1197.2.a.k.1.2 | 3 | 3.2 | odd | 2 | |||
2128.2.a.p.1.1 | 3 | 4.3 | odd | 2 | |||
2527.2.a.f.1.2 | 3 | 19.18 | odd | 2 | |||
3325.2.a.r.1.2 | 3 | 5.4 | even | 2 | |||
8379.2.a.bo.1.2 | 3 | 21.20 | even | 2 | |||
8512.2.a.bi.1.1 | 3 | 8.5 | even | 2 | |||
8512.2.a.bp.1.3 | 3 | 8.3 | odd | 2 |