Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, 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("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.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: | \(32.1717269744\) |
Analytic rank: | \(1\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} - 10 x^{16} + 120 x^{15} - 56 x^{14} - 921 x^{13} + 1181 x^{12} + 3316 x^{11} - 6280 x^{10} - 5249 x^{9} + 15005 x^{8} + 1809 x^{7} - 16711 x^{6} + 2434 x^{5} + \cdots + 138 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-0.239152\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.239152 | 0.169106 | 0.0845530 | − | 0.996419i | \(-0.473054\pi\) | ||||
0.0845530 | + | 0.996419i | \(0.473054\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.94281 | −0.971403 | ||||||||
\(5\) | −0.863011 | −0.385950 | −0.192975 | − | 0.981204i | \(-0.561814\pi\) | ||||
−0.192975 | + | 0.981204i | \(0.561814\pi\) | |||||||
\(6\) | 0.239152 | 0.0976333 | ||||||||
\(7\) | −3.18045 | −1.20210 | −0.601048 | − | 0.799213i | \(-0.705250\pi\) | ||||
−0.601048 | + | 0.799213i | \(0.705250\pi\) | |||||||
\(8\) | −0.942930 | −0.333376 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.206391 | −0.0652665 | ||||||||
\(11\) | 2.43892 | 0.735362 | 0.367681 | − | 0.929952i | \(-0.380152\pi\) | ||||
0.367681 | + | 0.929952i | \(0.380152\pi\) | |||||||
\(12\) | −1.94281 | −0.560840 | ||||||||
\(13\) | 2.64738 | 0.734252 | 0.367126 | − | 0.930171i | \(-0.380342\pi\) | ||||
0.367126 | + | 0.930171i | \(0.380342\pi\) | |||||||
\(14\) | −0.760610 | −0.203282 | ||||||||
\(15\) | −0.863011 | −0.222828 | ||||||||
\(16\) | 3.66011 | 0.915027 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0.239152 | 0.0563686 | ||||||||
\(19\) | −5.74248 | −1.31742 | −0.658708 | − | 0.752399i | \(-0.728897\pi\) | ||||
−0.658708 | + | 0.752399i | \(0.728897\pi\) | |||||||
\(20\) | 1.67666 | 0.374913 | ||||||||
\(21\) | −3.18045 | −0.694031 | ||||||||
\(22\) | 0.583272 | 0.124354 | ||||||||
\(23\) | 5.49541 | 1.14587 | 0.572936 | − | 0.819600i | \(-0.305805\pi\) | ||||
0.572936 | + | 0.819600i | \(0.305805\pi\) | |||||||
\(24\) | −0.942930 | −0.192475 | ||||||||
\(25\) | −4.25521 | −0.851042 | ||||||||
\(26\) | 0.633127 | 0.124166 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 6.17900 | 1.16772 | ||||||||
\(29\) | 1.07170 | 0.199010 | 0.0995052 | − | 0.995037i | \(-0.468274\pi\) | ||||
0.0995052 | + | 0.995037i | \(0.468274\pi\) | |||||||
\(30\) | −0.206391 | −0.0376816 | ||||||||
\(31\) | 1.96792 | 0.353449 | 0.176724 | − | 0.984260i | \(-0.443450\pi\) | ||||
0.176724 | + | 0.984260i | \(0.443450\pi\) | |||||||
\(32\) | 2.76118 | 0.488112 | ||||||||
\(33\) | 2.43892 | 0.424561 | ||||||||
\(34\) | 0.239152 | 0.0410142 | ||||||||
\(35\) | 2.74476 | 0.463950 | ||||||||
\(36\) | −1.94281 | −0.323801 | ||||||||
\(37\) | 2.75352 | 0.452675 | 0.226338 | − | 0.974049i | \(-0.427325\pi\) | ||||
0.226338 | + | 0.974049i | \(0.427325\pi\) | |||||||
\(38\) | −1.37333 | −0.222783 | ||||||||
\(39\) | 2.64738 | 0.423921 | ||||||||
\(40\) | 0.813758 | 0.128667 | ||||||||
\(41\) | 7.09994 | 1.10882 | 0.554412 | − | 0.832242i | \(-0.312943\pi\) | ||||
0.554412 | + | 0.832242i | \(0.312943\pi\) | |||||||
\(42\) | −0.760610 | −0.117365 | ||||||||
\(43\) | −10.2572 | −1.56421 | −0.782105 | − | 0.623146i | \(-0.785854\pi\) | ||||
−0.782105 | + | 0.623146i | \(0.785854\pi\) | |||||||
\(44\) | −4.73835 | −0.714333 | ||||||||
\(45\) | −0.863011 | −0.128650 | ||||||||
\(46\) | 1.31424 | 0.193774 | ||||||||
\(47\) | −3.04303 | −0.443872 | −0.221936 | − | 0.975061i | \(-0.571238\pi\) | ||||
−0.221936 | + | 0.975061i | \(0.571238\pi\) | |||||||
\(48\) | 3.66011 | 0.528291 | ||||||||
\(49\) | 3.11526 | 0.445037 | ||||||||
\(50\) | −1.01764 | −0.143916 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −5.14335 | −0.713255 | ||||||||
\(53\) | 0.934787 | 0.128403 | 0.0642015 | − | 0.997937i | \(-0.479550\pi\) | ||||
0.0642015 | + | 0.997937i | \(0.479550\pi\) | |||||||
\(54\) | 0.239152 | 0.0325444 | ||||||||
\(55\) | −2.10481 | −0.283813 | ||||||||
\(56\) | 2.99894 | 0.400750 | ||||||||
\(57\) | −5.74248 | −0.760611 | ||||||||
\(58\) | 0.256300 | 0.0336538 | ||||||||
\(59\) | −2.02087 | −0.263095 | −0.131547 | − | 0.991310i | \(-0.541995\pi\) | ||||
−0.131547 | + | 0.991310i | \(0.541995\pi\) | |||||||
\(60\) | 1.67666 | 0.216456 | ||||||||
\(61\) | −6.53682 | −0.836955 | −0.418477 | − | 0.908227i | \(-0.637436\pi\) | ||||
−0.418477 | + | 0.908227i | \(0.637436\pi\) | |||||||
\(62\) | 0.470632 | 0.0597703 | ||||||||
\(63\) | −3.18045 | −0.400699 | ||||||||
\(64\) | −6.65988 | −0.832485 | ||||||||
\(65\) | −2.28472 | −0.283385 | ||||||||
\(66\) | 0.583272 | 0.0717959 | ||||||||
\(67\) | −7.65642 | −0.935380 | −0.467690 | − | 0.883892i | \(-0.654914\pi\) | ||||
−0.467690 | + | 0.883892i | \(0.654914\pi\) | |||||||
\(68\) | −1.94281 | −0.235600 | ||||||||
\(69\) | 5.49541 | 0.661569 | ||||||||
\(70\) | 0.656415 | 0.0784566 | ||||||||
\(71\) | −13.3580 | −1.58530 | −0.792652 | − | 0.609675i | \(-0.791300\pi\) | ||||
−0.792652 | + | 0.609675i | \(0.791300\pi\) | |||||||
\(72\) | −0.942930 | −0.111125 | ||||||||
\(73\) | 9.05559 | 1.05988 | 0.529938 | − | 0.848036i | \(-0.322215\pi\) | ||||
0.529938 | + | 0.848036i | \(0.322215\pi\) | |||||||
\(74\) | 0.658509 | 0.0765501 | ||||||||
\(75\) | −4.25521 | −0.491350 | ||||||||
\(76\) | 11.1565 | 1.27974 | ||||||||
\(77\) | −7.75686 | −0.883976 | ||||||||
\(78\) | 0.633127 | 0.0716875 | ||||||||
\(79\) | −1.00000 | −0.112509 | ||||||||
\(80\) | −3.15871 | −0.353155 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.69796 | 0.187509 | ||||||||
\(83\) | −3.01545 | −0.330988 | −0.165494 | − | 0.986211i | \(-0.552922\pi\) | ||||
−0.165494 | + | 0.986211i | \(0.552922\pi\) | |||||||
\(84\) | 6.17900 | 0.674184 | ||||||||
\(85\) | −0.863011 | −0.0936067 | ||||||||
\(86\) | −2.45303 | −0.264517 | ||||||||
\(87\) | 1.07170 | 0.114899 | ||||||||
\(88\) | −2.29973 | −0.245152 | ||||||||
\(89\) | 1.39929 | 0.148325 | 0.0741623 | − | 0.997246i | \(-0.476372\pi\) | ||||
0.0741623 | + | 0.997246i | \(0.476372\pi\) | |||||||
\(90\) | −0.206391 | −0.0217555 | ||||||||
\(91\) | −8.41987 | −0.882642 | ||||||||
\(92\) | −10.6765 | −1.11310 | ||||||||
\(93\) | 1.96792 | 0.204064 | ||||||||
\(94\) | −0.727747 | −0.0750614 | ||||||||
\(95\) | 4.95583 | 0.508457 | ||||||||
\(96\) | 2.76118 | 0.281812 | ||||||||
\(97\) | 11.3288 | 1.15027 | 0.575134 | − | 0.818059i | \(-0.304950\pi\) | ||||
0.575134 | + | 0.818059i | \(0.304950\pi\) | |||||||
\(98\) | 0.745020 | 0.0752584 | ||||||||
\(99\) | 2.43892 | 0.245121 | ||||||||
\(100\) | 8.26705 | 0.826705 | ||||||||
\(101\) | −10.4012 | −1.03496 | −0.517480 | − | 0.855695i | \(-0.673130\pi\) | ||||
−0.517480 | + | 0.855695i | \(0.673130\pi\) | |||||||
\(102\) | 0.239152 | 0.0236796 | ||||||||
\(103\) | −10.8386 | −1.06796 | −0.533979 | − | 0.845498i | \(-0.679304\pi\) | ||||
−0.533979 | + | 0.845498i | \(0.679304\pi\) | |||||||
\(104\) | −2.49630 | −0.244782 | ||||||||
\(105\) | 2.74476 | 0.267861 | ||||||||
\(106\) | 0.223556 | 0.0217137 | ||||||||
\(107\) | 2.62365 | 0.253638 | 0.126819 | − | 0.991926i | \(-0.459523\pi\) | ||||
0.126819 | + | 0.991926i | \(0.459523\pi\) | |||||||
\(108\) | −1.94281 | −0.186947 | ||||||||
\(109\) | −3.82176 | −0.366058 | −0.183029 | − | 0.983108i | \(-0.558590\pi\) | ||||
−0.183029 | + | 0.983108i | \(0.558590\pi\) | |||||||
\(110\) | −0.503370 | −0.0479945 | ||||||||
\(111\) | 2.75352 | 0.261352 | ||||||||
\(112\) | −11.6408 | −1.09995 | ||||||||
\(113\) | 6.14277 | 0.577864 | 0.288932 | − | 0.957350i | \(-0.406700\pi\) | ||||
0.288932 | + | 0.957350i | \(0.406700\pi\) | |||||||
\(114\) | −1.37333 | −0.128624 | ||||||||
\(115\) | −4.74259 | −0.442249 | ||||||||
\(116\) | −2.08211 | −0.193319 | ||||||||
\(117\) | 2.64738 | 0.244751 | ||||||||
\(118\) | −0.483295 | −0.0444909 | ||||||||
\(119\) | −3.18045 | −0.291551 | ||||||||
\(120\) | 0.813758 | 0.0742856 | ||||||||
\(121\) | −5.05167 | −0.459243 | ||||||||
\(122\) | −1.56329 | −0.141534 | ||||||||
\(123\) | 7.09994 | 0.640180 | ||||||||
\(124\) | −3.82329 | −0.343341 | ||||||||
\(125\) | 7.98735 | 0.714410 | ||||||||
\(126\) | −0.760610 | −0.0677606 | ||||||||
\(127\) | −16.8085 | −1.49151 | −0.745754 | − | 0.666221i | \(-0.767911\pi\) | ||||
−0.745754 | + | 0.666221i | \(0.767911\pi\) | |||||||
\(128\) | −7.11508 | −0.628891 | ||||||||
\(129\) | −10.2572 | −0.903097 | ||||||||
\(130\) | −0.546395 | −0.0479220 | ||||||||
\(131\) | 18.0054 | 1.57314 | 0.786570 | − | 0.617502i | \(-0.211855\pi\) | ||||
0.786570 | + | 0.617502i | \(0.211855\pi\) | |||||||
\(132\) | −4.73835 | −0.412420 | ||||||||
\(133\) | 18.2637 | 1.58366 | ||||||||
\(134\) | −1.83105 | −0.158178 | ||||||||
\(135\) | −0.863011 | −0.0742762 | ||||||||
\(136\) | −0.942930 | −0.0808555 | ||||||||
\(137\) | −12.8425 | −1.09721 | −0.548603 | − | 0.836083i | \(-0.684840\pi\) | ||||
−0.548603 | + | 0.836083i | \(0.684840\pi\) | |||||||
\(138\) | 1.31424 | 0.111875 | ||||||||
\(139\) | −13.7287 | −1.16445 | −0.582226 | − | 0.813027i | \(-0.697818\pi\) | ||||
−0.582226 | + | 0.813027i | \(0.697818\pi\) | |||||||
\(140\) | −5.33254 | −0.450682 | ||||||||
\(141\) | −3.04303 | −0.256270 | ||||||||
\(142\) | −3.19459 | −0.268084 | ||||||||
\(143\) | 6.45676 | 0.539941 | ||||||||
\(144\) | 3.66011 | 0.305009 | ||||||||
\(145\) | −0.924892 | −0.0768081 | ||||||||
\(146\) | 2.16566 | 0.179231 | ||||||||
\(147\) | 3.11526 | 0.256942 | ||||||||
\(148\) | −5.34955 | −0.439730 | ||||||||
\(149\) | −14.2939 | −1.17100 | −0.585499 | − | 0.810673i | \(-0.699102\pi\) | ||||
−0.585499 | + | 0.810673i | \(0.699102\pi\) | |||||||
\(150\) | −1.01764 | −0.0830901 | ||||||||
\(151\) | 2.98397 | 0.242832 | 0.121416 | − | 0.992602i | \(-0.461257\pi\) | ||||
0.121416 | + | 0.992602i | \(0.461257\pi\) | |||||||
\(152\) | 5.41476 | 0.439195 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −1.85507 | −0.149486 | ||||||||
\(155\) | −1.69834 | −0.136414 | ||||||||
\(156\) | −5.14335 | −0.411798 | ||||||||
\(157\) | −20.5319 | −1.63862 | −0.819310 | − | 0.573350i | \(-0.805643\pi\) | ||||
−0.819310 | + | 0.573350i | \(0.805643\pi\) | |||||||
\(158\) | −0.239152 | −0.0190259 | ||||||||
\(159\) | 0.934787 | 0.0741335 | ||||||||
\(160\) | −2.38293 | −0.188387 | ||||||||
\(161\) | −17.4779 | −1.37745 | ||||||||
\(162\) | 0.239152 | 0.0187895 | ||||||||
\(163\) | −19.9448 | −1.56220 | −0.781099 | − | 0.624407i | \(-0.785341\pi\) | ||||
−0.781099 | + | 0.624407i | \(0.785341\pi\) | |||||||
\(164\) | −13.7938 | −1.07712 | ||||||||
\(165\) | −2.10481 | −0.163860 | ||||||||
\(166\) | −0.721149 | −0.0559721 | ||||||||
\(167\) | 3.27693 | 0.253576 | 0.126788 | − | 0.991930i | \(-0.459533\pi\) | ||||
0.126788 | + | 0.991930i | \(0.459533\pi\) | |||||||
\(168\) | 2.99894 | 0.231373 | ||||||||
\(169\) | −5.99136 | −0.460874 | ||||||||
\(170\) | −0.206391 | −0.0158294 | ||||||||
\(171\) | −5.74248 | −0.439139 | ||||||||
\(172\) | 19.9278 | 1.51948 | ||||||||
\(173\) | −12.0891 | −0.919116 | −0.459558 | − | 0.888148i | \(-0.651992\pi\) | ||||
−0.459558 | + | 0.888148i | \(0.651992\pi\) | |||||||
\(174\) | 0.256300 | 0.0194300 | ||||||||
\(175\) | 13.5335 | 1.02304 | ||||||||
\(176\) | 8.92671 | 0.672876 | ||||||||
\(177\) | −2.02087 | −0.151898 | ||||||||
\(178\) | 0.334643 | 0.0250826 | ||||||||
\(179\) | 6.13052 | 0.458217 | 0.229108 | − | 0.973401i | \(-0.426419\pi\) | ||||
0.229108 | + | 0.973401i | \(0.426419\pi\) | |||||||
\(180\) | 1.67666 | 0.124971 | ||||||||
\(181\) | 0.327510 | 0.0243437 | 0.0121718 | − | 0.999926i | \(-0.496125\pi\) | ||||
0.0121718 | + | 0.999926i | \(0.496125\pi\) | |||||||
\(182\) | −2.01363 | −0.149260 | ||||||||
\(183\) | −6.53682 | −0.483216 | ||||||||
\(184\) | −5.18178 | −0.382006 | ||||||||
\(185\) | −2.37632 | −0.174710 | ||||||||
\(186\) | 0.470632 | 0.0345084 | ||||||||
\(187\) | 2.43892 | 0.178351 | ||||||||
\(188\) | 5.91202 | 0.431179 | ||||||||
\(189\) | −3.18045 | −0.231344 | ||||||||
\(190\) | 1.18520 | 0.0859831 | ||||||||
\(191\) | −1.51939 | −0.109939 | −0.0549695 | − | 0.998488i | \(-0.517506\pi\) | ||||
−0.0549695 | + | 0.998488i | \(0.517506\pi\) | |||||||
\(192\) | −6.65988 | −0.480635 | ||||||||
\(193\) | −3.54344 | −0.255062 | −0.127531 | − | 0.991835i | \(-0.540705\pi\) | ||||
−0.127531 | + | 0.991835i | \(0.540705\pi\) | |||||||
\(194\) | 2.70931 | 0.194517 | ||||||||
\(195\) | −2.28472 | −0.163612 | ||||||||
\(196\) | −6.05234 | −0.432310 | ||||||||
\(197\) | −22.7150 | −1.61838 | −0.809188 | − | 0.587549i | \(-0.800093\pi\) | ||||
−0.809188 | + | 0.587549i | \(0.800093\pi\) | |||||||
\(198\) | 0.583272 | 0.0414514 | ||||||||
\(199\) | 8.31730 | 0.589597 | 0.294799 | − | 0.955559i | \(-0.404747\pi\) | ||||
0.294799 | + | 0.955559i | \(0.404747\pi\) | |||||||
\(200\) | 4.01237 | 0.283717 | ||||||||
\(201\) | −7.65642 | −0.540042 | ||||||||
\(202\) | −2.48747 | −0.175018 | ||||||||
\(203\) | −3.40850 | −0.239230 | ||||||||
\(204\) | −1.94281 | −0.136024 | ||||||||
\(205\) | −6.12733 | −0.427951 | ||||||||
\(206\) | −2.59207 | −0.180598 | ||||||||
\(207\) | 5.49541 | 0.381957 | ||||||||
\(208\) | 9.68971 | 0.671861 | ||||||||
\(209\) | −14.0055 | −0.968778 | ||||||||
\(210\) | 0.656415 | 0.0452969 | ||||||||
\(211\) | −8.09013 | −0.556948 | −0.278474 | − | 0.960444i | \(-0.589829\pi\) | ||||
−0.278474 | + | 0.960444i | \(0.589829\pi\) | |||||||
\(212\) | −1.81611 | −0.124731 | ||||||||
\(213\) | −13.3580 | −0.915275 | ||||||||
\(214\) | 0.627451 | 0.0428917 | ||||||||
\(215\) | 8.85209 | 0.603707 | ||||||||
\(216\) | −0.942930 | −0.0641582 | ||||||||
\(217\) | −6.25887 | −0.424880 | ||||||||
\(218\) | −0.913980 | −0.0619026 | ||||||||
\(219\) | 9.05559 | 0.611920 | ||||||||
\(220\) | 4.08925 | 0.275697 | ||||||||
\(221\) | 2.64738 | 0.178082 | ||||||||
\(222\) | 0.658509 | 0.0441962 | ||||||||
\(223\) | 13.9274 | 0.932646 | 0.466323 | − | 0.884614i | \(-0.345578\pi\) | ||||
0.466323 | + | 0.884614i | \(0.345578\pi\) | |||||||
\(224\) | −8.78180 | −0.586758 | ||||||||
\(225\) | −4.25521 | −0.283681 | ||||||||
\(226\) | 1.46906 | 0.0977201 | ||||||||
\(227\) | −16.9103 | −1.12238 | −0.561189 | − | 0.827688i | \(-0.689656\pi\) | ||||
−0.561189 | + | 0.827688i | \(0.689656\pi\) | |||||||
\(228\) | 11.1565 | 0.738860 | ||||||||
\(229\) | 9.20668 | 0.608395 | 0.304197 | − | 0.952609i | \(-0.401612\pi\) | ||||
0.304197 | + | 0.952609i | \(0.401612\pi\) | |||||||
\(230\) | −1.13420 | −0.0747870 | ||||||||
\(231\) | −7.75686 | −0.510364 | ||||||||
\(232\) | −1.01054 | −0.0663452 | ||||||||
\(233\) | 5.70441 | 0.373709 | 0.186854 | − | 0.982388i | \(-0.440171\pi\) | ||||
0.186854 | + | 0.982388i | \(0.440171\pi\) | |||||||
\(234\) | 0.633127 | 0.0413888 | ||||||||
\(235\) | 2.62617 | 0.171312 | ||||||||
\(236\) | 3.92616 | 0.255571 | ||||||||
\(237\) | −1.00000 | −0.0649570 | ||||||||
\(238\) | −0.760610 | −0.0493030 | ||||||||
\(239\) | 8.86534 | 0.573451 | 0.286725 | − | 0.958013i | \(-0.407433\pi\) | ||||
0.286725 | + | 0.958013i | \(0.407433\pi\) | |||||||
\(240\) | −3.15871 | −0.203894 | ||||||||
\(241\) | −22.9479 | −1.47821 | −0.739104 | − | 0.673592i | \(-0.764751\pi\) | ||||
−0.739104 | + | 0.673592i | \(0.764751\pi\) | |||||||
\(242\) | −1.20812 | −0.0776606 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 12.6998 | 0.813020 | ||||||||
\(245\) | −2.68850 | −0.171762 | ||||||||
\(246\) | 1.69796 | 0.108258 | ||||||||
\(247\) | −15.2026 | −0.967316 | ||||||||
\(248\) | −1.85561 | −0.117831 | ||||||||
\(249\) | −3.01545 | −0.191096 | ||||||||
\(250\) | 1.91019 | 0.120811 | ||||||||
\(251\) | −19.6612 | −1.24100 | −0.620501 | − | 0.784206i | \(-0.713071\pi\) | ||||
−0.620501 | + | 0.784206i | \(0.713071\pi\) | |||||||
\(252\) | 6.17900 | 0.389240 | ||||||||
\(253\) | 13.4029 | 0.842630 | ||||||||
\(254\) | −4.01977 | −0.252223 | ||||||||
\(255\) | −0.863011 | −0.0540438 | ||||||||
\(256\) | 11.6182 | 0.726136 | ||||||||
\(257\) | 6.41479 | 0.400144 | 0.200072 | − | 0.979781i | \(-0.435882\pi\) | ||||
0.200072 | + | 0.979781i | \(0.435882\pi\) | |||||||
\(258\) | −2.45303 | −0.152719 | ||||||||
\(259\) | −8.75742 | −0.544160 | ||||||||
\(260\) | 4.43877 | 0.275281 | ||||||||
\(261\) | 1.07170 | 0.0663368 | ||||||||
\(262\) | 4.30603 | 0.266027 | ||||||||
\(263\) | −0.0287981 | −0.00177577 | −0.000887883 | − | 1.00000i | \(-0.500283\pi\) | ||||
−0.000887883 | 1.00000i | \(0.500283\pi\) | ||||||||
\(264\) | −2.29973 | −0.141539 | ||||||||
\(265\) | −0.806732 | −0.0495571 | ||||||||
\(266\) | 4.36779 | 0.267807 | ||||||||
\(267\) | 1.39929 | 0.0856352 | ||||||||
\(268\) | 14.8749 | 0.908632 | ||||||||
\(269\) | 21.0821 | 1.28540 | 0.642699 | − | 0.766119i | \(-0.277815\pi\) | ||||
0.642699 | + | 0.766119i | \(0.277815\pi\) | |||||||
\(270\) | −0.206391 | −0.0125605 | ||||||||
\(271\) | 29.6658 | 1.80207 | 0.901034 | − | 0.433749i | \(-0.142809\pi\) | ||||
0.901034 | + | 0.433749i | \(0.142809\pi\) | |||||||
\(272\) | 3.66011 | 0.221927 | ||||||||
\(273\) | −8.41987 | −0.509594 | ||||||||
\(274\) | −3.07130 | −0.185544 | ||||||||
\(275\) | −10.3781 | −0.625824 | ||||||||
\(276\) | −10.6765 | −0.642650 | ||||||||
\(277\) | 13.6618 | 0.820856 | 0.410428 | − | 0.911893i | \(-0.365379\pi\) | ||||
0.410428 | + | 0.911893i | \(0.365379\pi\) | |||||||
\(278\) | −3.28324 | −0.196916 | ||||||||
\(279\) | 1.96792 | 0.117816 | ||||||||
\(280\) | −2.58812 | −0.154670 | ||||||||
\(281\) | 14.8601 | 0.886480 | 0.443240 | − | 0.896403i | \(-0.353829\pi\) | ||||
0.443240 | + | 0.896403i | \(0.353829\pi\) | |||||||
\(282\) | −0.727747 | −0.0433367 | ||||||||
\(283\) | 1.34731 | 0.0800895 | 0.0400448 | − | 0.999198i | \(-0.487250\pi\) | ||||
0.0400448 | + | 0.999198i | \(0.487250\pi\) | |||||||
\(284\) | 25.9520 | 1.53997 | ||||||||
\(285\) | 4.95583 | 0.293558 | ||||||||
\(286\) | 1.54415 | 0.0913072 | ||||||||
\(287\) | −22.5810 | −1.33291 | ||||||||
\(288\) | 2.76118 | 0.162704 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −0.221190 | −0.0129887 | ||||||||
\(291\) | 11.3288 | 0.664108 | ||||||||
\(292\) | −17.5933 | −1.02957 | ||||||||
\(293\) | 22.8657 | 1.33583 | 0.667915 | − | 0.744237i | \(-0.267187\pi\) | ||||
0.667915 | + | 0.744237i | \(0.267187\pi\) | |||||||
\(294\) | 0.745020 | 0.0434504 | ||||||||
\(295\) | 1.74403 | 0.101542 | ||||||||
\(296\) | −2.59637 | −0.150911 | ||||||||
\(297\) | 2.43892 | 0.141520 | ||||||||
\(298\) | −3.41840 | −0.198023 | ||||||||
\(299\) | 14.5484 | 0.841358 | ||||||||
\(300\) | 8.26705 | 0.477299 | ||||||||
\(301\) | 32.6225 | 1.88033 | ||||||||
\(302\) | 0.713621 | 0.0410643 | ||||||||
\(303\) | −10.4012 | −0.597534 | ||||||||
\(304\) | −21.0181 | −1.20547 | ||||||||
\(305\) | 5.64135 | 0.323023 | ||||||||
\(306\) | 0.239152 | 0.0136714 | ||||||||
\(307\) | −31.9557 | −1.82381 | −0.911905 | − | 0.410402i | \(-0.865388\pi\) | ||||
−0.911905 | + | 0.410402i | \(0.865388\pi\) | |||||||
\(308\) | 15.0701 | 0.858697 | ||||||||
\(309\) | −10.8386 | −0.616586 | ||||||||
\(310\) | −0.406160 | −0.0230684 | ||||||||
\(311\) | 0.969169 | 0.0549565 | 0.0274783 | − | 0.999622i | \(-0.491252\pi\) | ||||
0.0274783 | + | 0.999622i | \(0.491252\pi\) | |||||||
\(312\) | −2.49630 | −0.141325 | ||||||||
\(313\) | −11.2022 | −0.633183 | −0.316592 | − | 0.948562i | \(-0.602538\pi\) | ||||
−0.316592 | + | 0.948562i | \(0.602538\pi\) | |||||||
\(314\) | −4.91023 | −0.277100 | ||||||||
\(315\) | 2.74476 | 0.154650 | ||||||||
\(316\) | 1.94281 | 0.109291 | ||||||||
\(317\) | 4.44816 | 0.249833 | 0.124917 | − | 0.992167i | \(-0.460134\pi\) | ||||
0.124917 | + | 0.992167i | \(0.460134\pi\) | |||||||
\(318\) | 0.223556 | 0.0125364 | ||||||||
\(319\) | 2.61380 | 0.146345 | ||||||||
\(320\) | 5.74755 | 0.321298 | ||||||||
\(321\) | 2.62365 | 0.146438 | ||||||||
\(322\) | −4.17986 | −0.232935 | ||||||||
\(323\) | −5.74248 | −0.319520 | ||||||||
\(324\) | −1.94281 | −0.107934 | ||||||||
\(325\) | −11.2652 | −0.624880 | ||||||||
\(326\) | −4.76984 | −0.264177 | ||||||||
\(327\) | −3.82176 | −0.211344 | ||||||||
\(328\) | −6.69475 | −0.369655 | ||||||||
\(329\) | 9.67821 | 0.533577 | ||||||||
\(330\) | −0.503370 | −0.0277096 | ||||||||
\(331\) | 26.2905 | 1.44506 | 0.722530 | − | 0.691340i | \(-0.242979\pi\) | ||||
0.722530 | + | 0.691340i | \(0.242979\pi\) | |||||||
\(332\) | 5.85843 | 0.321523 | ||||||||
\(333\) | 2.75352 | 0.150892 | ||||||||
\(334\) | 0.783683 | 0.0428812 | ||||||||
\(335\) | 6.60757 | 0.361010 | ||||||||
\(336\) | −11.6408 | −0.635057 | ||||||||
\(337\) | 8.13050 | 0.442896 | 0.221448 | − | 0.975172i | \(-0.428922\pi\) | ||||
0.221448 | + | 0.975172i | \(0.428922\pi\) | |||||||
\(338\) | −1.43285 | −0.0779365 | ||||||||
\(339\) | 6.14277 | 0.333630 | ||||||||
\(340\) | 1.67666 | 0.0909298 | ||||||||
\(341\) | 4.79960 | 0.259913 | ||||||||
\(342\) | −1.37333 | −0.0742610 | ||||||||
\(343\) | 12.3552 | 0.667119 | ||||||||
\(344\) | 9.67183 | 0.521470 | ||||||||
\(345\) | −4.74259 | −0.255333 | ||||||||
\(346\) | −2.89113 | −0.155428 | ||||||||
\(347\) | −35.3063 | −1.89534 | −0.947672 | − | 0.319247i | \(-0.896570\pi\) | ||||
−0.947672 | + | 0.319247i | \(0.896570\pi\) | |||||||
\(348\) | −2.08211 | −0.111613 | ||||||||
\(349\) | 32.4168 | 1.73523 | 0.867615 | − | 0.497237i | \(-0.165652\pi\) | ||||
0.867615 | + | 0.497237i | \(0.165652\pi\) | |||||||
\(350\) | 3.23656 | 0.173001 | ||||||||
\(351\) | 2.64738 | 0.141307 | ||||||||
\(352\) | 6.73430 | 0.358939 | ||||||||
\(353\) | 14.7374 | 0.784395 | 0.392198 | − | 0.919881i | \(-0.371715\pi\) | ||||
0.392198 | + | 0.919881i | \(0.371715\pi\) | |||||||
\(354\) | −0.483295 | −0.0256868 | ||||||||
\(355\) | 11.5281 | 0.611848 | ||||||||
\(356\) | −2.71855 | −0.144083 | ||||||||
\(357\) | −3.18045 | −0.168327 | ||||||||
\(358\) | 1.46613 | 0.0774872 | ||||||||
\(359\) | −28.0424 | −1.48002 | −0.740011 | − | 0.672595i | \(-0.765180\pi\) | ||||
−0.740011 | + | 0.672595i | \(0.765180\pi\) | |||||||
\(360\) | 0.813758 | 0.0428888 | ||||||||
\(361\) | 13.9761 | 0.735586 | ||||||||
\(362\) | 0.0783247 | 0.00411666 | ||||||||
\(363\) | −5.05167 | −0.265144 | ||||||||
\(364\) | 16.3582 | 0.857401 | ||||||||
\(365\) | −7.81507 | −0.409060 | ||||||||
\(366\) | −1.56329 | −0.0817147 | ||||||||
\(367\) | 7.99865 | 0.417526 | 0.208763 | − | 0.977966i | \(-0.433056\pi\) | ||||
0.208763 | + | 0.977966i | \(0.433056\pi\) | |||||||
\(368\) | 20.1138 | 1.04850 | ||||||||
\(369\) | 7.09994 | 0.369608 | ||||||||
\(370\) | −0.568300 | −0.0295445 | ||||||||
\(371\) | −2.97304 | −0.154353 | ||||||||
\(372\) | −3.82329 | −0.198228 | ||||||||
\(373\) | 16.4571 | 0.852116 | 0.426058 | − | 0.904696i | \(-0.359902\pi\) | ||||
0.426058 | + | 0.904696i | \(0.359902\pi\) | |||||||
\(374\) | 0.583272 | 0.0301603 | ||||||||
\(375\) | 7.98735 | 0.412465 | ||||||||
\(376\) | 2.86937 | 0.147976 | ||||||||
\(377\) | 2.83721 | 0.146124 | ||||||||
\(378\) | −0.760610 | −0.0391216 | ||||||||
\(379\) | −30.8578 | −1.58506 | −0.792529 | − | 0.609834i | \(-0.791236\pi\) | ||||
−0.792529 | + | 0.609834i | \(0.791236\pi\) | |||||||
\(380\) | −9.62821 | −0.493917 | ||||||||
\(381\) | −16.8085 | −0.861123 | ||||||||
\(382\) | −0.363364 | −0.0185913 | ||||||||
\(383\) | −32.9059 | −1.68141 | −0.840705 | − | 0.541493i | \(-0.817859\pi\) | ||||
−0.840705 | + | 0.541493i | \(0.817859\pi\) | |||||||
\(384\) | −7.11508 | −0.363090 | ||||||||
\(385\) | 6.69426 | 0.341171 | ||||||||
\(386\) | −0.847420 | −0.0431325 | ||||||||
\(387\) | −10.2572 | −0.521403 | ||||||||
\(388\) | −22.0097 | −1.11737 | ||||||||
\(389\) | −8.82733 | −0.447563 | −0.223782 | − | 0.974639i | \(-0.571840\pi\) | ||||
−0.223782 | + | 0.974639i | \(0.571840\pi\) | |||||||
\(390\) | −0.546395 | −0.0276678 | ||||||||
\(391\) | 5.49541 | 0.277915 | ||||||||
\(392\) | −2.93747 | −0.148365 | ||||||||
\(393\) | 18.0054 | 0.908252 | ||||||||
\(394\) | −5.43233 | −0.273677 | ||||||||
\(395\) | 0.863011 | 0.0434228 | ||||||||
\(396\) | −4.73835 | −0.238111 | ||||||||
\(397\) | −23.1481 | −1.16177 | −0.580885 | − | 0.813985i | \(-0.697294\pi\) | ||||
−0.580885 | + | 0.813985i | \(0.697294\pi\) | |||||||
\(398\) | 1.98910 | 0.0997044 | ||||||||
\(399\) | 18.2637 | 0.914328 | ||||||||
\(400\) | −15.5745 | −0.778727 | ||||||||
\(401\) | −3.34254 | −0.166919 | −0.0834593 | − | 0.996511i | \(-0.526597\pi\) | ||||
−0.0834593 | + | 0.996511i | \(0.526597\pi\) | |||||||
\(402\) | −1.83105 | −0.0913243 | ||||||||
\(403\) | 5.20984 | 0.259521 | ||||||||
\(404\) | 20.2075 | 1.00536 | ||||||||
\(405\) | −0.863011 | −0.0428834 | ||||||||
\(406\) | −0.815149 | −0.0404551 | ||||||||
\(407\) | 6.71561 | 0.332880 | ||||||||
\(408\) | −0.942930 | −0.0466820 | ||||||||
\(409\) | 10.8048 | 0.534261 | 0.267130 | − | 0.963660i | \(-0.413925\pi\) | ||||
0.267130 | + | 0.963660i | \(0.413925\pi\) | |||||||
\(410\) | −1.46536 | −0.0723691 | ||||||||
\(411\) | −12.8425 | −0.633472 | ||||||||
\(412\) | 21.0573 | 1.03742 | ||||||||
\(413\) | 6.42727 | 0.316266 | ||||||||
\(414\) | 1.31424 | 0.0645912 | ||||||||
\(415\) | 2.60236 | 0.127745 | ||||||||
\(416\) | 7.30990 | 0.358398 | ||||||||
\(417\) | −13.7287 | −0.672297 | ||||||||
\(418\) | −3.34943 | −0.163826 | ||||||||
\(419\) | −22.9673 | −1.12203 | −0.561014 | − | 0.827806i | \(-0.689589\pi\) | ||||
−0.561014 | + | 0.827806i | \(0.689589\pi\) | |||||||
\(420\) | −5.33254 | −0.260201 | ||||||||
\(421\) | −28.1847 | −1.37364 | −0.686818 | − | 0.726829i | \(-0.740993\pi\) | ||||
−0.686818 | + | 0.726829i | \(0.740993\pi\) | |||||||
\(422\) | −1.93477 | −0.0941831 | ||||||||
\(423\) | −3.04303 | −0.147957 | ||||||||
\(424\) | −0.881439 | −0.0428064 | ||||||||
\(425\) | −4.25521 | −0.206408 | ||||||||
\(426\) | −3.19459 | −0.154778 | ||||||||
\(427\) | 20.7900 | 1.00610 | ||||||||
\(428\) | −5.09725 | −0.246385 | ||||||||
\(429\) | 6.45676 | 0.311735 | ||||||||
\(430\) | 2.11699 | 0.102090 | ||||||||
\(431\) | 0.0906693 | 0.00436739 | 0.00218369 | − | 0.999998i | \(-0.499305\pi\) | ||||
0.00218369 | + | 0.999998i | \(0.499305\pi\) | |||||||
\(432\) | 3.66011 | 0.176097 | ||||||||
\(433\) | 32.5020 | 1.56195 | 0.780973 | − | 0.624564i | \(-0.214723\pi\) | ||||
0.780973 | + | 0.624564i | \(0.214723\pi\) | |||||||
\(434\) | −1.49682 | −0.0718497 | ||||||||
\(435\) | −0.924892 | −0.0443452 | ||||||||
\(436\) | 7.42494 | 0.355590 | ||||||||
\(437\) | −31.5573 | −1.50959 | ||||||||
\(438\) | 2.16566 | 0.103479 | ||||||||
\(439\) | 11.3014 | 0.539386 | 0.269693 | − | 0.962946i | \(-0.413078\pi\) | ||||
0.269693 | + | 0.962946i | \(0.413078\pi\) | |||||||
\(440\) | 1.98469 | 0.0946165 | ||||||||
\(441\) | 3.11526 | 0.148346 | ||||||||
\(442\) | 0.633127 | 0.0301148 | ||||||||
\(443\) | 40.8366 | 1.94021 | 0.970103 | − | 0.242695i | \(-0.0780314\pi\) | ||||
0.970103 | + | 0.242695i | \(0.0780314\pi\) | |||||||
\(444\) | −5.34955 | −0.253878 | ||||||||
\(445\) | −1.20760 | −0.0572459 | ||||||||
\(446\) | 3.33076 | 0.157716 | ||||||||
\(447\) | −14.2939 | −0.676077 | ||||||||
\(448\) | 21.1814 | 1.00073 | ||||||||
\(449\) | 5.87709 | 0.277357 | 0.138678 | − | 0.990337i | \(-0.455715\pi\) | ||||
0.138678 | + | 0.990337i | \(0.455715\pi\) | |||||||
\(450\) | −1.01764 | −0.0479721 | ||||||||
\(451\) | 17.3162 | 0.815388 | ||||||||
\(452\) | −11.9342 | −0.561338 | ||||||||
\(453\) | 2.98397 | 0.140199 | ||||||||
\(454\) | −4.04413 | −0.189801 | ||||||||
\(455\) | 7.26644 | 0.340656 | ||||||||
\(456\) | 5.41476 | 0.253569 | ||||||||
\(457\) | 35.7045 | 1.67019 | 0.835093 | − | 0.550108i | \(-0.185414\pi\) | ||||
0.835093 | + | 0.550108i | \(0.185414\pi\) | |||||||
\(458\) | 2.20180 | 0.102883 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 9.21394 | 0.429602 | ||||||||
\(461\) | −35.7072 | −1.66305 | −0.831524 | − | 0.555488i | \(-0.812531\pi\) | ||||
−0.831524 | + | 0.555488i | \(0.812531\pi\) | |||||||
\(462\) | −1.85507 | −0.0863056 | ||||||||
\(463\) | 14.5370 | 0.675593 | 0.337796 | − | 0.941219i | \(-0.390319\pi\) | ||||
0.337796 | + | 0.941219i | \(0.390319\pi\) | |||||||
\(464\) | 3.92255 | 0.182100 | ||||||||
\(465\) | −1.69834 | −0.0787585 | ||||||||
\(466\) | 1.36422 | 0.0631963 | ||||||||
\(467\) | −10.0292 | −0.464094 | −0.232047 | − | 0.972705i | \(-0.574542\pi\) | ||||
−0.232047 | + | 0.972705i | \(0.574542\pi\) | |||||||
\(468\) | −5.14335 | −0.237752 | ||||||||
\(469\) | 24.3509 | 1.12442 | ||||||||
\(470\) | 0.628054 | 0.0289700 | ||||||||
\(471\) | −20.5319 | −0.946058 | ||||||||
\(472\) | 1.90554 | 0.0877095 | ||||||||
\(473\) | −25.0165 | −1.15026 | ||||||||
\(474\) | −0.239152 | −0.0109846 | ||||||||
\(475\) | 24.4355 | 1.12118 | ||||||||
\(476\) | 6.17900 | 0.283214 | ||||||||
\(477\) | 0.934787 | 0.0428010 | ||||||||
\(478\) | 2.12016 | 0.0969739 | ||||||||
\(479\) | 5.86372 | 0.267920 | 0.133960 | − | 0.990987i | \(-0.457231\pi\) | ||||
0.133960 | + | 0.990987i | \(0.457231\pi\) | |||||||
\(480\) | −2.38293 | −0.108765 | ||||||||
\(481\) | 7.28962 | 0.332378 | ||||||||
\(482\) | −5.48804 | −0.249974 | ||||||||
\(483\) | −17.4779 | −0.795270 | ||||||||
\(484\) | 9.81442 | 0.446110 | ||||||||
\(485\) | −9.77690 | −0.443946 | ||||||||
\(486\) | 0.239152 | 0.0108481 | ||||||||
\(487\) | 7.90286 | 0.358113 | 0.179056 | − | 0.983839i | \(-0.442696\pi\) | ||||
0.179056 | + | 0.983839i | \(0.442696\pi\) | |||||||
\(488\) | 6.16376 | 0.279020 | ||||||||
\(489\) | −19.9448 | −0.901936 | ||||||||
\(490\) | −0.642960 | −0.0290460 | ||||||||
\(491\) | 35.6953 | 1.61091 | 0.805454 | − | 0.592659i | \(-0.201922\pi\) | ||||
0.805454 | + | 0.592659i | \(0.201922\pi\) | |||||||
\(492\) | −13.7938 | −0.621873 | ||||||||
\(493\) | 1.07170 | 0.0482671 | ||||||||
\(494\) | −3.63572 | −0.163579 | ||||||||
\(495\) | −2.10481 | −0.0946044 | ||||||||
\(496\) | 7.20280 | 0.323415 | ||||||||
\(497\) | 42.4844 | 1.90569 | ||||||||
\(498\) | −0.721149 | −0.0323155 | ||||||||
\(499\) | −22.8901 | −1.02470 | −0.512352 | − | 0.858776i | \(-0.671226\pi\) | ||||
−0.512352 | + | 0.858776i | \(0.671226\pi\) | |||||||
\(500\) | −15.5179 | −0.693980 | ||||||||
\(501\) | 3.27693 | 0.146402 | ||||||||
\(502\) | −4.70200 | −0.209861 | ||||||||
\(503\) | −15.5920 | −0.695211 | −0.347606 | − | 0.937641i | \(-0.613005\pi\) | ||||
−0.347606 | + | 0.937641i | \(0.613005\pi\) | |||||||
\(504\) | 2.99894 | 0.133583 | ||||||||
\(505\) | 8.97636 | 0.399443 | ||||||||
\(506\) | 3.20532 | 0.142494 | ||||||||
\(507\) | −5.99136 | −0.266086 | ||||||||
\(508\) | 32.6556 | 1.44886 | ||||||||
\(509\) | −42.0078 | −1.86196 | −0.930982 | − | 0.365064i | \(-0.881047\pi\) | ||||
−0.930982 | + | 0.365064i | \(0.881047\pi\) | |||||||
\(510\) | −0.206391 | −0.00913913 | ||||||||
\(511\) | −28.8008 | −1.27407 | ||||||||
\(512\) | 17.0087 | 0.751684 | ||||||||
\(513\) | −5.74248 | −0.253537 | ||||||||
\(514\) | 1.53411 | 0.0676666 | ||||||||
\(515\) | 9.35383 | 0.412179 | ||||||||
\(516\) | 19.9278 | 0.877272 | ||||||||
\(517\) | −7.42171 | −0.326407 | ||||||||
\(518\) | −2.09435 | −0.0920206 | ||||||||
\(519\) | −12.0891 | −0.530652 | ||||||||
\(520\) | 2.15433 | 0.0944736 | ||||||||
\(521\) | −24.8991 | −1.09085 | −0.545424 | − | 0.838160i | \(-0.683631\pi\) | ||||
−0.545424 | + | 0.838160i | \(0.683631\pi\) | |||||||
\(522\) | 0.256300 | 0.0112179 | ||||||||
\(523\) | 13.3217 | 0.582518 | 0.291259 | − | 0.956644i | \(-0.405926\pi\) | ||||
0.291259 | + | 0.956644i | \(0.405926\pi\) | |||||||
\(524\) | −34.9810 | −1.52815 | ||||||||
\(525\) | 13.5335 | 0.590650 | ||||||||
\(526\) | −0.00688711 | −0.000300292 0 | ||||||||
\(527\) | 1.96792 | 0.0857240 | ||||||||
\(528\) | 8.92671 | 0.388485 | ||||||||
\(529\) | 7.19948 | 0.313021 | ||||||||
\(530\) | −0.192931 | −0.00838040 | ||||||||
\(531\) | −2.02087 | −0.0876983 | ||||||||
\(532\) | −35.4828 | −1.53837 | ||||||||
\(533\) | 18.7963 | 0.814157 | ||||||||
\(534\) | 0.334643 | 0.0144814 | ||||||||
\(535\) | −2.26424 | −0.0978917 | ||||||||
\(536\) | 7.21946 | 0.311833 | ||||||||
\(537\) | 6.13052 | 0.264552 | ||||||||
\(538\) | 5.04182 | 0.217368 | ||||||||
\(539\) | 7.59786 | 0.327263 | ||||||||
\(540\) | 1.67666 | 0.0721521 | ||||||||
\(541\) | 18.7724 | 0.807088 | 0.403544 | − | 0.914960i | \(-0.367778\pi\) | ||||
0.403544 | + | 0.914960i | \(0.367778\pi\) | |||||||
\(542\) | 7.09463 | 0.304740 | ||||||||
\(543\) | 0.327510 | 0.0140548 | ||||||||
\(544\) | 2.76118 | 0.118385 | ||||||||
\(545\) | 3.29822 | 0.141280 | ||||||||
\(546\) | −2.01363 | −0.0861753 | ||||||||
\(547\) | −12.8576 | −0.549751 | −0.274875 | − | 0.961480i | \(-0.588637\pi\) | ||||
−0.274875 | + | 0.961480i | \(0.588637\pi\) | |||||||
\(548\) | 24.9504 | 1.06583 | ||||||||
\(549\) | −6.53682 | −0.278985 | ||||||||
\(550\) | −2.48195 | −0.105831 | ||||||||
\(551\) | −6.15424 | −0.262179 | ||||||||
\(552\) | −5.18178 | −0.220551 | ||||||||
\(553\) | 3.18045 | 0.135246 | ||||||||
\(554\) | 3.26724 | 0.138812 | ||||||||
\(555\) | −2.37632 | −0.100869 | ||||||||
\(556\) | 26.6722 | 1.13115 | ||||||||
\(557\) | −3.20201 | −0.135673 | −0.0678367 | − | 0.997696i | \(-0.521610\pi\) | ||||
−0.0678367 | + | 0.997696i | \(0.521610\pi\) | |||||||
\(558\) | 0.470632 | 0.0199234 | ||||||||
\(559\) | −27.1548 | −1.14852 | ||||||||
\(560\) | 10.0461 | 0.424527 | ||||||||
\(561\) | 2.43892 | 0.102971 | ||||||||
\(562\) | 3.55382 | 0.149909 | ||||||||
\(563\) | 3.76069 | 0.158494 | 0.0792472 | − | 0.996855i | \(-0.474748\pi\) | ||||
0.0792472 | + | 0.996855i | \(0.474748\pi\) | |||||||
\(564\) | 5.91202 | 0.248941 | ||||||||
\(565\) | −5.30128 | −0.223027 | ||||||||
\(566\) | 0.322213 | 0.0135436 | ||||||||
\(567\) | −3.18045 | −0.133566 | ||||||||
\(568\) | 12.5957 | 0.528502 | ||||||||
\(569\) | −12.8179 | −0.537356 | −0.268678 | − | 0.963230i | \(-0.586587\pi\) | ||||
−0.268678 | + | 0.963230i | \(0.586587\pi\) | |||||||
\(570\) | 1.18520 | 0.0496424 | ||||||||
\(571\) | −7.95308 | −0.332826 | −0.166413 | − | 0.986056i | \(-0.553219\pi\) | ||||
−0.166413 | + | 0.986056i | \(0.553219\pi\) | |||||||
\(572\) | −12.5442 | −0.524500 | ||||||||
\(573\) | −1.51939 | −0.0634733 | ||||||||
\(574\) | −5.40029 | −0.225404 | ||||||||
\(575\) | −23.3841 | −0.975185 | ||||||||
\(576\) | −6.65988 | −0.277495 | ||||||||
\(577\) | 24.2094 | 1.00785 | 0.503925 | − | 0.863747i | \(-0.331889\pi\) | ||||
0.503925 | + | 0.863747i | \(0.331889\pi\) | |||||||
\(578\) | 0.239152 | 0.00994741 | ||||||||
\(579\) | −3.54344 | −0.147260 | ||||||||
\(580\) | 1.79689 | 0.0746116 | ||||||||
\(581\) | 9.59047 | 0.397880 | ||||||||
\(582\) | 2.70931 | 0.112305 | ||||||||
\(583\) | 2.27987 | 0.0944226 | ||||||||
\(584\) | −8.53878 | −0.353337 | ||||||||
\(585\) | −2.28472 | −0.0944616 | ||||||||
\(586\) | 5.46838 | 0.225897 | ||||||||
\(587\) | −5.53028 | −0.228259 | −0.114130 | − | 0.993466i | \(-0.536408\pi\) | ||||
−0.114130 | + | 0.993466i | \(0.536408\pi\) | |||||||
\(588\) | −6.05234 | −0.249594 | ||||||||
\(589\) | −11.3008 | −0.465639 | ||||||||
\(590\) | 0.417089 | 0.0171713 | ||||||||
\(591\) | −22.7150 | −0.934370 | ||||||||
\(592\) | 10.0782 | 0.414210 | ||||||||
\(593\) | −44.8582 | −1.84211 | −0.921053 | − | 0.389438i | \(-0.872669\pi\) | ||||
−0.921053 | + | 0.389438i | \(0.872669\pi\) | |||||||
\(594\) | 0.583272 | 0.0239320 | ||||||||
\(595\) | 2.74476 | 0.112524 | ||||||||
\(596\) | 27.7702 | 1.13751 | ||||||||
\(597\) | 8.31730 | 0.340404 | ||||||||
\(598\) | 3.47929 | 0.142279 | ||||||||
\(599\) | 42.7788 | 1.74790 | 0.873948 | − | 0.486019i | \(-0.161551\pi\) | ||||
0.873948 | + | 0.486019i | \(0.161551\pi\) | |||||||
\(600\) | 4.01237 | 0.163804 | ||||||||
\(601\) | 23.2667 | 0.949069 | 0.474535 | − | 0.880237i | \(-0.342616\pi\) | ||||
0.474535 | + | 0.880237i | \(0.342616\pi\) | |||||||
\(602\) | 7.80174 | 0.317975 | ||||||||
\(603\) | −7.65642 | −0.311793 | ||||||||
\(604\) | −5.79727 | −0.235888 | ||||||||
\(605\) | 4.35965 | 0.177245 | ||||||||
\(606\) | −2.48747 | −0.101047 | ||||||||
\(607\) | −25.7282 | −1.04428 | −0.522138 | − | 0.852861i | \(-0.674865\pi\) | ||||
−0.522138 | + | 0.852861i | \(0.674865\pi\) | |||||||
\(608\) | −15.8560 | −0.643047 | ||||||||
\(609\) | −3.40850 | −0.138119 | ||||||||
\(610\) | 1.34914 | 0.0546251 | ||||||||
\(611\) | −8.05608 | −0.325914 | ||||||||
\(612\) | −1.94281 | −0.0785333 | ||||||||
\(613\) | 2.00650 | 0.0810416 | 0.0405208 | − | 0.999179i | \(-0.487098\pi\) | ||||
0.0405208 | + | 0.999179i | \(0.487098\pi\) | |||||||
\(614\) | −7.64227 | −0.308417 | ||||||||
\(615\) | −6.12733 | −0.247078 | ||||||||
\(616\) | 7.31417 | 0.294696 | ||||||||
\(617\) | −34.1639 | −1.37539 | −0.687694 | − | 0.726000i | \(-0.741377\pi\) | ||||
−0.687694 | + | 0.726000i | \(0.741377\pi\) | |||||||
\(618\) | −2.59207 | −0.104268 | ||||||||
\(619\) | −2.06276 | −0.0829093 | −0.0414547 | − | 0.999140i | \(-0.513199\pi\) | ||||
−0.0414547 | + | 0.999140i | \(0.513199\pi\) | |||||||
\(620\) | 3.29954 | 0.132513 | ||||||||
\(621\) | 5.49541 | 0.220523 | ||||||||
\(622\) | 0.231779 | 0.00929348 | ||||||||
\(623\) | −4.45038 | −0.178301 | ||||||||
\(624\) | 9.68971 | 0.387899 | ||||||||
\(625\) | 14.3829 | 0.575316 | ||||||||
\(626\) | −2.67902 | −0.107075 | ||||||||
\(627\) | −14.0055 | −0.559324 | ||||||||
\(628\) | 39.8894 | 1.59176 | ||||||||
\(629\) | 2.75352 | 0.109790 | ||||||||
\(630\) | 0.656415 | 0.0261522 | ||||||||
\(631\) | 15.8528 | 0.631089 | 0.315545 | − | 0.948911i | \(-0.397813\pi\) | ||||
0.315545 | + | 0.948911i | \(0.397813\pi\) | |||||||
\(632\) | 0.942930 | 0.0375077 | ||||||||
\(633\) | −8.09013 | −0.321554 | ||||||||
\(634\) | 1.06378 | 0.0422483 | ||||||||
\(635\) | 14.5059 | 0.575648 | ||||||||
\(636\) | −1.81611 | −0.0720135 | ||||||||
\(637\) | 8.24728 | 0.326769 | ||||||||
\(638\) | 0.625095 | 0.0247477 | ||||||||
\(639\) | −13.3580 | −0.528434 | ||||||||
\(640\) | 6.14040 | 0.242720 | ||||||||
\(641\) | −37.8179 | −1.49372 | −0.746859 | − | 0.664982i | \(-0.768439\pi\) | ||||
−0.746859 | + | 0.664982i | \(0.768439\pi\) | |||||||
\(642\) | 0.627451 | 0.0247635 | ||||||||
\(643\) | 3.96886 | 0.156517 | 0.0782583 | − | 0.996933i | \(-0.475064\pi\) | ||||
0.0782583 | + | 0.996933i | \(0.475064\pi\) | |||||||
\(644\) | 33.9561 | 1.33806 | ||||||||
\(645\) | 8.85209 | 0.348551 | ||||||||
\(646\) | −1.37333 | −0.0540328 | ||||||||
\(647\) | −8.04118 | −0.316131 | −0.158066 | − | 0.987429i | \(-0.550526\pi\) | ||||
−0.158066 | + | 0.987429i | \(0.550526\pi\) | |||||||
\(648\) | −0.942930 | −0.0370418 | ||||||||
\(649\) | −4.92874 | −0.193470 | ||||||||
\(650\) | −2.69409 | −0.105671 | ||||||||
\(651\) | −6.25887 | −0.245304 | ||||||||
\(652\) | 38.7489 | 1.51752 | ||||||||
\(653\) | 30.2921 | 1.18542 | 0.592710 | − | 0.805416i | \(-0.298058\pi\) | ||||
0.592710 | + | 0.805416i | \(0.298058\pi\) | |||||||
\(654\) | −0.913980 | −0.0357395 | ||||||||
\(655\) | −15.5389 | −0.607153 | ||||||||
\(656\) | 25.9866 | 1.01461 | ||||||||
\(657\) | 9.05559 | 0.353292 | ||||||||
\(658\) | 2.31456 | 0.0902310 | ||||||||
\(659\) | 33.5567 | 1.30718 | 0.653591 | − | 0.756848i | \(-0.273262\pi\) | ||||
0.653591 | + | 0.756848i | \(0.273262\pi\) | |||||||
\(660\) | 4.08925 | 0.159174 | ||||||||
\(661\) | −5.23536 | −0.203632 | −0.101816 | − | 0.994803i | \(-0.532465\pi\) | ||||
−0.101816 | + | 0.994803i | \(0.532465\pi\) | |||||||
\(662\) | 6.28743 | 0.244368 | ||||||||
\(663\) | 2.64738 | 0.102816 | ||||||||
\(664\) | 2.84335 | 0.110343 | ||||||||
\(665\) | −15.7618 | −0.611215 | ||||||||
\(666\) | 0.658509 | 0.0255167 | ||||||||
\(667\) | 5.88944 | 0.228040 | ||||||||
\(668\) | −6.36643 | −0.246325 | ||||||||
\(669\) | 13.9274 | 0.538464 | ||||||||
\(670\) | 1.58021 | 0.0610490 | ||||||||
\(671\) | −15.9428 | −0.615465 | ||||||||
\(672\) | −8.78180 | −0.338765 | ||||||||
\(673\) | −20.5506 | −0.792169 | −0.396084 | − | 0.918214i | \(-0.629631\pi\) | ||||
−0.396084 | + | 0.918214i | \(0.629631\pi\) | |||||||
\(674\) | 1.94442 | 0.0748964 | ||||||||
\(675\) | −4.25521 | −0.163783 | ||||||||
\(676\) | 11.6401 | 0.447694 | ||||||||
\(677\) | 19.0877 | 0.733601 | 0.366801 | − | 0.930300i | \(-0.380453\pi\) | ||||
0.366801 | + | 0.930300i | \(0.380453\pi\) | |||||||
\(678\) | 1.46906 | 0.0564187 | ||||||||
\(679\) | −36.0308 | −1.38273 | ||||||||
\(680\) | 0.813758 | 0.0312062 | ||||||||
\(681\) | −16.9103 | −0.648005 | ||||||||
\(682\) | 1.14783 | 0.0439528 | ||||||||
\(683\) | 25.1210 | 0.961229 | 0.480615 | − | 0.876932i | \(-0.340414\pi\) | ||||
0.480615 | + | 0.876932i | \(0.340414\pi\) | |||||||
\(684\) | 11.1565 | 0.426581 | ||||||||
\(685\) | 11.0832 | 0.423467 | ||||||||
\(686\) | 2.95478 | 0.112814 | ||||||||
\(687\) | 9.20668 | 0.351257 | ||||||||
\(688\) | −37.5425 | −1.43130 | ||||||||
\(689\) | 2.47474 | 0.0942801 | ||||||||
\(690\) | −1.13420 | −0.0431783 | ||||||||
\(691\) | 24.7036 | 0.939771 | 0.469885 | − | 0.882728i | \(-0.344295\pi\) | ||||
0.469885 | + | 0.882728i | \(0.344295\pi\) | |||||||
\(692\) | 23.4868 | 0.892832 | ||||||||
\(693\) | −7.75686 | −0.294659 | ||||||||
\(694\) | −8.44357 | −0.320514 | ||||||||
\(695\) | 11.8480 | 0.449420 | ||||||||
\(696\) | −1.01054 | −0.0383044 | ||||||||
\(697\) | 7.09994 | 0.268930 | ||||||||
\(698\) | 7.75253 | 0.293438 | ||||||||
\(699\) | 5.70441 | 0.215761 | ||||||||
\(700\) | −26.2929 | −0.993780 | ||||||||
\(701\) | −39.8419 | −1.50481 | −0.752403 | − | 0.658703i | \(-0.771105\pi\) | ||||
−0.752403 | + | 0.658703i | \(0.771105\pi\) | |||||||
\(702\) | 0.633127 | 0.0238958 | ||||||||
\(703\) | −15.8120 | −0.596362 | ||||||||
\(704\) | −16.2429 | −0.612178 | ||||||||
\(705\) | 2.62617 | 0.0989073 | ||||||||
\(706\) | 3.52449 | 0.132646 | ||||||||
\(707\) | 33.0805 | 1.24412 | ||||||||
\(708\) | 3.92616 | 0.147554 | ||||||||
\(709\) | 38.5043 | 1.44606 | 0.723030 | − | 0.690817i | \(-0.242749\pi\) | ||||
0.723030 | + | 0.690817i | \(0.242749\pi\) | |||||||
\(710\) | 2.75697 | 0.103467 | ||||||||
\(711\) | −1.00000 | −0.0375029 | ||||||||
\(712\) | −1.31943 | −0.0494478 | ||||||||
\(713\) | 10.8145 | 0.405007 | ||||||||
\(714\) | −0.760610 | −0.0284651 | ||||||||
\(715\) | −5.57225 | −0.208390 | ||||||||
\(716\) | −11.9104 | −0.445113 | ||||||||
\(717\) | 8.86534 | 0.331082 | ||||||||
\(718\) | −6.70640 | −0.250280 | ||||||||
\(719\) | −33.8862 | −1.26374 | −0.631872 | − | 0.775073i | \(-0.717713\pi\) | ||||
−0.631872 | + | 0.775073i | \(0.717713\pi\) | |||||||
\(720\) | −3.15871 | −0.117718 | ||||||||
\(721\) | 34.4716 | 1.28379 | ||||||||
\(722\) | 3.34242 | 0.124392 | ||||||||
\(723\) | −22.9479 | −0.853443 | ||||||||
\(724\) | −0.636289 | −0.0236475 | ||||||||
\(725\) | −4.56032 | −0.169366 | ||||||||
\(726\) | −1.20812 | −0.0448374 | ||||||||
\(727\) | 1.02338 | 0.0379549 | 0.0189775 | − | 0.999820i | \(-0.493959\pi\) | ||||
0.0189775 | + | 0.999820i | \(0.493959\pi\) | |||||||
\(728\) | 7.93934 | 0.294252 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.86899 | −0.0691744 | ||||||||
\(731\) | −10.2572 | −0.379377 | ||||||||
\(732\) | 12.6998 | 0.469397 | ||||||||
\(733\) | −14.6930 | −0.542697 | −0.271349 | − | 0.962481i | \(-0.587470\pi\) | ||||
−0.271349 | + | 0.962481i | \(0.587470\pi\) | |||||||
\(734\) | 1.91289 | 0.0706061 | ||||||||
\(735\) | −2.68850 | −0.0991669 | ||||||||
\(736\) | 15.1738 | 0.559314 | ||||||||
\(737\) | −18.6734 | −0.687843 | ||||||||
\(738\) | 1.69796 | 0.0625029 | ||||||||
\(739\) | −52.7776 | −1.94145 | −0.970727 | − | 0.240185i | \(-0.922792\pi\) | ||||
−0.970727 | + | 0.240185i | \(0.922792\pi\) | |||||||
\(740\) | 4.61672 | 0.169714 | ||||||||
\(741\) | −15.2026 | −0.558480 | ||||||||
\(742\) | −0.711009 | −0.0261020 | ||||||||
\(743\) | −10.7061 | −0.392769 | −0.196384 | − | 0.980527i | \(-0.562920\pi\) | ||||
−0.196384 | + | 0.980527i | \(0.562920\pi\) | |||||||
\(744\) | −1.85561 | −0.0680300 | ||||||||
\(745\) | 12.3358 | 0.451947 | ||||||||
\(746\) | 3.93575 | 0.144098 | ||||||||
\(747\) | −3.01545 | −0.110329 | ||||||||
\(748\) | −4.73835 | −0.173251 | ||||||||
\(749\) | −8.34439 | −0.304898 | ||||||||
\(750\) | 1.91019 | 0.0697503 | ||||||||
\(751\) | 47.8336 | 1.74547 | 0.872736 | − | 0.488193i | \(-0.162344\pi\) | ||||
0.872736 | + | 0.488193i | \(0.162344\pi\) | |||||||
\(752\) | −11.1378 | −0.406155 | ||||||||
\(753\) | −19.6612 | −0.716492 | ||||||||
\(754\) | 0.678524 | 0.0247104 | ||||||||
\(755\) | −2.57520 | −0.0937210 | ||||||||
\(756\) | 6.17900 | 0.224728 | ||||||||
\(757\) | 10.5151 | 0.382176 | 0.191088 | − | 0.981573i | \(-0.438798\pi\) | ||||
0.191088 | + | 0.981573i | \(0.438798\pi\) | |||||||
\(758\) | −7.37970 | −0.268043 | ||||||||
\(759\) | 13.4029 | 0.486493 | ||||||||
\(760\) | −4.67300 | −0.169507 | ||||||||
\(761\) | 16.1834 | 0.586647 | 0.293323 | − | 0.956013i | \(-0.405239\pi\) | ||||
0.293323 | + | 0.956013i | \(0.405239\pi\) | |||||||
\(762\) | −4.01977 | −0.145621 | ||||||||
\(763\) | 12.1549 | 0.440037 | ||||||||
\(764\) | 2.95187 | 0.106795 | ||||||||
\(765\) | −0.863011 | −0.0312022 | ||||||||
\(766\) | −7.86950 | −0.284337 | ||||||||
\(767\) | −5.35002 | −0.193178 | ||||||||
\(768\) | 11.6182 | 0.419235 | ||||||||
\(769\) | −4.82718 | −0.174073 | −0.0870363 | − | 0.996205i | \(-0.527740\pi\) | ||||
−0.0870363 | + | 0.996205i | \(0.527740\pi\) | |||||||
\(770\) | 1.60094 | 0.0576940 | ||||||||
\(771\) | 6.41479 | 0.231023 | ||||||||
\(772\) | 6.88421 | 0.247768 | ||||||||
\(773\) | −31.7089 | −1.14049 | −0.570245 | − | 0.821475i | \(-0.693152\pi\) | ||||
−0.570245 | + | 0.821475i | \(0.693152\pi\) | |||||||
\(774\) | −2.45303 | −0.0881724 | ||||||||
\(775\) | −8.37392 | −0.300800 | ||||||||
\(776\) | −10.6823 | −0.383472 | ||||||||
\(777\) | −8.75742 | −0.314171 | ||||||||
\(778\) | −2.11107 | −0.0756856 | ||||||||
\(779\) | −40.7713 | −1.46078 | ||||||||
\(780\) | 4.43877 | 0.158933 | ||||||||
\(781\) | −32.5791 | −1.16577 | ||||||||
\(782\) | 1.31424 | 0.0469970 | ||||||||
\(783\) | 1.07170 | 0.0382996 | ||||||||
\(784\) | 11.4022 | 0.407221 | ||||||||
\(785\) | 17.7192 | 0.632426 | ||||||||
\(786\) | 4.30603 | 0.153591 | ||||||||
\(787\) | −2.74964 | −0.0980140 | −0.0490070 | − | 0.998798i | \(-0.515606\pi\) | ||||
−0.0490070 | + | 0.998798i | \(0.515606\pi\) | |||||||
\(788\) | 44.1308 | 1.57210 | ||||||||
\(789\) | −0.0287981 | −0.00102524 | ||||||||
\(790\) | 0.206391 | 0.00734305 | ||||||||
\(791\) | −19.5368 | −0.694648 | ||||||||
\(792\) | −2.29973 | −0.0817173 | ||||||||
\(793\) | −17.3055 | −0.614536 | ||||||||
\(794\) | −5.53591 | −0.196462 | ||||||||
\(795\) | −0.806732 | −0.0286118 | ||||||||
\(796\) | −16.1589 | −0.572737 | ||||||||
\(797\) | 44.0207 | 1.55929 | 0.779647 | − | 0.626220i | \(-0.215399\pi\) | ||||
0.779647 | + | 0.626220i | \(0.215399\pi\) | |||||||
\(798\) | 4.36779 | 0.154618 | ||||||||
\(799\) | −3.04303 | −0.107655 | ||||||||
\(800\) | −11.7494 | −0.415404 | ||||||||
\(801\) | 1.39929 | 0.0494415 | ||||||||
\(802\) | −0.799375 | −0.0282269 | ||||||||
\(803\) | 22.0859 | 0.779393 | ||||||||
\(804\) | 14.8749 | 0.524599 | ||||||||
\(805\) | 15.0836 | 0.531626 | ||||||||
\(806\) | 1.24594 | 0.0438865 | ||||||||
\(807\) | 21.0821 | 0.742125 | ||||||||
\(808\) | 9.80761 | 0.345031 | ||||||||
\(809\) | −3.47782 | −0.122274 | −0.0611369 | − | 0.998129i | \(-0.519473\pi\) | ||||
−0.0611369 | + | 0.998129i | \(0.519473\pi\) | |||||||
\(810\) | −0.206391 | −0.00725183 | ||||||||
\(811\) | −4.82488 | −0.169424 | −0.0847122 | − | 0.996405i | \(-0.526997\pi\) | ||||
−0.0847122 | + | 0.996405i | \(0.526997\pi\) | |||||||
\(812\) | 6.62205 | 0.232388 | ||||||||
\(813\) | 29.6658 | 1.04042 | ||||||||
\(814\) | 1.60605 | 0.0562920 | ||||||||
\(815\) | 17.2126 | 0.602931 | ||||||||
\(816\) | 3.66011 | 0.128129 | ||||||||
\(817\) | 58.9019 | 2.06072 | ||||||||
\(818\) | 2.58398 | 0.0903467 | ||||||||
\(819\) | −8.41987 | −0.294214 | ||||||||
\(820\) | 11.9042 | 0.415713 | ||||||||
\(821\) | −16.2032 | −0.565497 | −0.282748 | − | 0.959194i | \(-0.591246\pi\) | ||||
−0.282748 | + | 0.959194i | \(0.591246\pi\) | |||||||
\(822\) | −3.07130 | −0.107124 | ||||||||
\(823\) | −1.17277 | −0.0408803 | −0.0204401 | − | 0.999791i | \(-0.506507\pi\) | ||||
−0.0204401 | + | 0.999791i | \(0.506507\pi\) | |||||||
\(824\) | 10.2200 | 0.356032 | ||||||||
\(825\) | −10.3781 | −0.361320 | ||||||||
\(826\) | 1.53709 | 0.0534824 | ||||||||
\(827\) | −20.0839 | −0.698386 | −0.349193 | − | 0.937051i | \(-0.613544\pi\) | ||||
−0.349193 | + | 0.937051i | \(0.613544\pi\) | |||||||
\(828\) | −10.6765 | −0.371034 | ||||||||
\(829\) | −40.0111 | −1.38964 | −0.694821 | − | 0.719182i | \(-0.744517\pi\) | ||||
−0.694821 | + | 0.719182i | \(0.744517\pi\) | |||||||
\(830\) | 0.622360 | 0.0216024 | ||||||||
\(831\) | 13.6618 | 0.473921 | ||||||||
\(832\) | −17.6312 | −0.611254 | ||||||||
\(833\) | 3.11526 | 0.107937 | ||||||||
\(834\) | −3.28324 | −0.113689 | ||||||||
\(835\) | −2.82802 | −0.0978678 | ||||||||
\(836\) | 27.2099 | 0.941074 | ||||||||
\(837\) | 1.96792 | 0.0680213 | ||||||||
\(838\) | −5.49268 | −0.189742 | ||||||||
\(839\) | −4.32613 | −0.149355 | −0.0746773 | − | 0.997208i | \(-0.523793\pi\) | ||||
−0.0746773 | + | 0.997208i | \(0.523793\pi\) | |||||||
\(840\) | −2.58812 | −0.0892985 | ||||||||
\(841\) | −27.8515 | −0.960395 | ||||||||
\(842\) | −6.74041 | −0.232290 | ||||||||
\(843\) | 14.8601 | 0.511809 | ||||||||
\(844\) | 15.7176 | 0.541021 | ||||||||
\(845\) | 5.17061 | 0.177874 | ||||||||
\(846\) | −0.727747 | −0.0250205 | ||||||||
\(847\) | 16.0666 | 0.552054 | ||||||||
\(848\) | 3.42142 | 0.117492 | ||||||||
\(849\) | 1.34731 | 0.0462397 | ||||||||
\(850\) | −1.01764 | −0.0349048 | ||||||||
\(851\) | 15.1317 | 0.518708 | ||||||||
\(852\) | 25.9520 | 0.889101 | ||||||||
\(853\) | 10.1701 | 0.348217 | 0.174109 | − | 0.984726i | \(-0.444296\pi\) | ||||
0.174109 | + | 0.984726i | \(0.444296\pi\) | |||||||
\(854\) | 4.97198 | 0.170138 | ||||||||
\(855\) | 4.95583 | 0.169486 | ||||||||
\(856\) | −2.47392 | −0.0845568 | ||||||||
\(857\) | −50.1986 | −1.71475 | −0.857375 | − | 0.514692i | \(-0.827906\pi\) | ||||
−0.857375 | + | 0.514692i | \(0.827906\pi\) | |||||||
\(858\) | 1.54415 | 0.0527163 | ||||||||
\(859\) | −51.8503 | −1.76911 | −0.884555 | − | 0.466437i | \(-0.845538\pi\) | ||||
−0.884555 | + | 0.466437i | \(0.845538\pi\) | |||||||
\(860\) | −17.1979 | −0.586443 | ||||||||
\(861\) | −22.5810 | −0.769559 | ||||||||
\(862\) | 0.0216837 | 0.000738551 0 | ||||||||
\(863\) | 41.6870 | 1.41904 | 0.709521 | − | 0.704684i | \(-0.248911\pi\) | ||||
0.709521 | + | 0.704684i | \(0.248911\pi\) | |||||||
\(864\) | 2.76118 | 0.0939373 | ||||||||
\(865\) | 10.4330 | 0.354733 | ||||||||
\(866\) | 7.77292 | 0.264134 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 12.1598 | 0.412730 | ||||||||
\(869\) | −2.43892 | −0.0827347 | ||||||||
\(870\) | −0.221190 | −0.00749903 | ||||||||
\(871\) | −20.2695 | −0.686805 | ||||||||
\(872\) | 3.60365 | 0.122035 | ||||||||
\(873\) | 11.3288 | 0.383423 | ||||||||
\(874\) | −7.54698 | −0.255280 | ||||||||
\(875\) | −25.4034 | −0.858790 | ||||||||
\(876\) | −17.5933 | −0.594421 | ||||||||
\(877\) | 39.6264 | 1.33809 | 0.669045 | − | 0.743222i | \(-0.266703\pi\) | ||||
0.669045 | + | 0.743222i | \(0.266703\pi\) | |||||||
\(878\) | 2.70275 | 0.0912134 | ||||||||
\(879\) | 22.8657 | 0.771242 | ||||||||
\(880\) | −7.70385 | −0.259697 | ||||||||
\(881\) | 12.5505 | 0.422838 | 0.211419 | − | 0.977396i | \(-0.432192\pi\) | ||||
0.211419 | + | 0.977396i | \(0.432192\pi\) | |||||||
\(882\) | 0.745020 | 0.0250861 | ||||||||
\(883\) | −29.9924 | −1.00933 | −0.504663 | − | 0.863317i | \(-0.668383\pi\) | ||||
−0.504663 | + | 0.863317i | \(0.668383\pi\) | |||||||
\(884\) | −5.14335 | −0.172990 | ||||||||
\(885\) | 1.74403 | 0.0586250 | ||||||||
\(886\) | 9.76615 | 0.328100 | ||||||||
\(887\) | −6.05781 | −0.203401 | −0.101701 | − | 0.994815i | \(-0.532428\pi\) | ||||
−0.101701 | + | 0.994815i | \(0.532428\pi\) | |||||||
\(888\) | −2.59637 | −0.0871286 | ||||||||
\(889\) | 53.4584 | 1.79294 | ||||||||
\(890\) | −0.288801 | −0.00968062 | ||||||||
\(891\) | 2.43892 | 0.0817069 | ||||||||
\(892\) | −27.0582 | −0.905975 | ||||||||
\(893\) | 17.4746 | 0.584764 | ||||||||
\(894\) | −3.41840 | −0.114329 | ||||||||
\(895\) | −5.29071 | −0.176849 | ||||||||
\(896\) | 22.6292 | 0.755987 | ||||||||
\(897\) | 14.5484 | 0.485758 | ||||||||
\(898\) | 1.40552 | 0.0469027 | ||||||||
\(899\) | 2.10903 | 0.0703400 | ||||||||
\(900\) | 8.26705 | 0.275568 | ||||||||
\(901\) | 0.934787 | 0.0311423 | ||||||||
\(902\) | 4.14120 | 0.137887 | ||||||||
\(903\) | 32.6225 | 1.08561 | ||||||||
\(904\) | −5.79220 | −0.192646 | ||||||||
\(905\) | −0.282645 | −0.00939544 | ||||||||
\(906\) | 0.713621 | 0.0237085 | ||||||||
\(907\) | −15.0098 | −0.498391 | −0.249196 | − | 0.968453i | \(-0.580166\pi\) | ||||
−0.249196 | + | 0.968453i | \(0.580166\pi\) | |||||||
\(908\) | 32.8535 | 1.09028 | ||||||||
\(909\) | −10.4012 | −0.344987 | ||||||||
\(910\) | 1.73778 | 0.0576069 | ||||||||
\(911\) | 2.98742 | 0.0989777 | 0.0494888 | − | 0.998775i | \(-0.484241\pi\) | ||||
0.0494888 | + | 0.998775i | \(0.484241\pi\) | |||||||
\(912\) | −21.0181 | −0.695980 | ||||||||
\(913\) | −7.35443 | −0.243396 | ||||||||
\(914\) | 8.53880 | 0.282438 | ||||||||
\(915\) | 5.64135 | 0.186497 | ||||||||
\(916\) | −17.8868 | −0.590997 | ||||||||
\(917\) | −57.2653 | −1.89107 | ||||||||
\(918\) | 0.239152 | 0.00789319 | ||||||||
\(919\) | 39.7421 | 1.31097 | 0.655486 | − | 0.755207i | \(-0.272464\pi\) | ||||
0.655486 | + | 0.755207i | \(0.272464\pi\) | |||||||
\(920\) | 4.47193 | 0.147435 | ||||||||
\(921\) | −31.9557 | −1.05298 | ||||||||
\(922\) | −8.53944 | −0.281231 | ||||||||
\(923\) | −35.3638 | −1.16401 | ||||||||
\(924\) | 15.0701 | 0.495769 | ||||||||
\(925\) | −11.7168 | −0.385246 | ||||||||
\(926\) | 3.47655 | 0.114247 | ||||||||
\(927\) | −10.8386 | −0.355986 | ||||||||
\(928\) | 2.95917 | 0.0971394 | ||||||||
\(929\) | 5.97867 | 0.196154 | 0.0980769 | − | 0.995179i | \(-0.468731\pi\) | ||||
0.0980769 | + | 0.995179i | \(0.468731\pi\) | |||||||
\(930\) | −0.406160 | −0.0133185 | ||||||||
\(931\) | −17.8893 | −0.586299 | ||||||||
\(932\) | −11.0826 | −0.363022 | ||||||||
\(933\) | 0.969169 | 0.0317292 | ||||||||
\(934\) | −2.39849 | −0.0784810 | ||||||||
\(935\) | −2.10481 | −0.0688348 | ||||||||
\(936\) | −2.49630 | −0.0815940 | ||||||||
\(937\) | −32.5487 | −1.06332 | −0.531659 | − | 0.846958i | \(-0.678431\pi\) | ||||
−0.531659 | + | 0.846958i | \(0.678431\pi\) | |||||||
\(938\) | 5.82355 | 0.190146 | ||||||||
\(939\) | −11.2022 | −0.365568 | ||||||||
\(940\) | −5.10214 | −0.166414 | ||||||||
\(941\) | 11.0582 | 0.360488 | 0.180244 | − | 0.983622i | \(-0.442311\pi\) | ||||
0.180244 | + | 0.983622i | \(0.442311\pi\) | |||||||
\(942\) | −4.91023 | −0.159984 | ||||||||
\(943\) | 39.0171 | 1.27057 | ||||||||
\(944\) | −7.39661 | −0.240739 | ||||||||
\(945\) | 2.74476 | 0.0892871 | ||||||||
\(946\) | −5.98275 | −0.194516 | ||||||||
\(947\) | 6.89840 | 0.224168 | 0.112084 | − | 0.993699i | \(-0.464247\pi\) | ||||
0.112084 | + | 0.993699i | \(0.464247\pi\) | |||||||
\(948\) | 1.94281 | 0.0630994 | ||||||||
\(949\) | 23.9736 | 0.778216 | ||||||||
\(950\) | 5.84379 | 0.189598 | ||||||||
\(951\) | 4.44816 | 0.144241 | ||||||||
\(952\) | 2.99894 | 0.0971962 | ||||||||
\(953\) | 49.5728 | 1.60582 | 0.802911 | − | 0.596099i | \(-0.203284\pi\) | ||||
0.802911 | + | 0.596099i | \(0.203284\pi\) | |||||||
\(954\) | 0.223556 | 0.00723790 | ||||||||
\(955\) | 1.31125 | 0.0424309 | ||||||||
\(956\) | −17.2236 | −0.557052 | ||||||||
\(957\) | 2.61380 | 0.0844921 | ||||||||
\(958\) | 1.40232 | 0.0453069 | ||||||||
\(959\) | 40.8448 | 1.31895 | ||||||||
\(960\) | 5.74755 | 0.185501 | ||||||||
\(961\) | −27.1273 | −0.875074 | ||||||||
\(962\) | 1.74333 | 0.0562071 | ||||||||
\(963\) | 2.62365 | 0.0845460 | ||||||||
\(964\) | 44.5834 | 1.43594 | ||||||||
\(965\) | 3.05802 | 0.0984413 | ||||||||
\(966\) | −4.17986 | −0.134485 | ||||||||
\(967\) | 2.22239 | 0.0714671 | 0.0357336 | − | 0.999361i | \(-0.488623\pi\) | ||||
0.0357336 | + | 0.999361i | \(0.488623\pi\) | |||||||
\(968\) | 4.76337 | 0.153100 | ||||||||
\(969\) | −5.74248 | −0.184475 | ||||||||
\(970\) | −2.33816 | −0.0750739 | ||||||||
\(971\) | −3.76483 | −0.120819 | −0.0604096 | − | 0.998174i | \(-0.519241\pi\) | ||||
−0.0604096 | + | 0.998174i | \(0.519241\pi\) | |||||||
\(972\) | −1.94281 | −0.0623155 | ||||||||
\(973\) | 43.6634 | 1.39978 | ||||||||
\(974\) | 1.88998 | 0.0605590 | ||||||||
\(975\) | −11.2652 | −0.360774 | ||||||||
\(976\) | −23.9255 | −0.765836 | ||||||||
\(977\) | 32.9125 | 1.05296 | 0.526482 | − | 0.850186i | \(-0.323511\pi\) | ||||
0.526482 | + | 0.850186i | \(0.323511\pi\) | |||||||
\(978\) | −4.76984 | −0.152523 | ||||||||
\(979\) | 3.41276 | 0.109072 | ||||||||
\(980\) | 5.22324 | 0.166850 | ||||||||
\(981\) | −3.82176 | −0.122019 | ||||||||
\(982\) | 8.53660 | 0.272414 | ||||||||
\(983\) | 59.7889 | 1.90697 | 0.953484 | − | 0.301442i | \(-0.0974680\pi\) | ||||
0.953484 | + | 0.301442i | \(0.0974680\pi\) | |||||||
\(984\) | −6.69475 | −0.213421 | ||||||||
\(985\) | 19.6033 | 0.624613 | ||||||||
\(986\) | 0.256300 | 0.00816225 | ||||||||
\(987\) | 9.67821 | 0.308061 | ||||||||
\(988\) | 29.5356 | 0.939654 | ||||||||
\(989\) | −56.3675 | −1.79238 | ||||||||
\(990\) | −0.503370 | −0.0159982 | ||||||||
\(991\) | −8.30891 | −0.263941 | −0.131971 | − | 0.991254i | \(-0.542130\pi\) | ||||
−0.131971 | + | 0.991254i | \(0.542130\pi\) | |||||||
\(992\) | 5.43378 | 0.172523 | ||||||||
\(993\) | 26.2905 | 0.834305 | ||||||||
\(994\) | 10.1602 | 0.322263 | ||||||||
\(995\) | −7.17792 | −0.227555 | ||||||||
\(996\) | 5.85843 | 0.185631 | ||||||||
\(997\) | 5.07254 | 0.160649 | 0.0803245 | − | 0.996769i | \(-0.474404\pi\) | ||||
0.0803245 | + | 0.996769i | \(0.474404\pi\) | |||||||
\(998\) | −5.47422 | −0.173283 | ||||||||
\(999\) | 2.75352 | 0.0871174 |
(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 | 4029.2.a.e.1.11 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.e.1.11 | ✓ | 18 | 1.1 | even | 1 | trivial |