Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [241,2,Mod(1,241)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(241, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("241.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 241.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: | \(1.92439468871\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | 7.7.31056073.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 3x^{5} + 11x^{4} + x^{3} - 9x^{2} + 1 \) |
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 | \(-0.911223\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 241.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.91122 | −1.35144 | −0.675720 | − | 0.737159i | \(-0.736167\pi\) | ||||
−0.675720 | + | 0.737159i | \(0.736167\pi\) | |||||||
\(3\) | −0.186202 | −0.107504 | −0.0537520 | − | 0.998554i | \(-0.517118\pi\) | ||||
−0.0537520 | + | 0.998554i | \(0.517118\pi\) | |||||||
\(4\) | 1.65278 | 0.826388 | ||||||||
\(5\) | −2.25110 | −1.00672 | −0.503361 | − | 0.864076i | \(-0.667903\pi\) | ||||
−0.503361 | + | 0.864076i | \(0.667903\pi\) | |||||||
\(6\) | 0.355874 | 0.145285 | ||||||||
\(7\) | 3.52970 | 1.33410 | 0.667050 | − | 0.745013i | \(-0.267557\pi\) | ||||
0.667050 | + | 0.745013i | \(0.267557\pi\) | |||||||
\(8\) | 0.663624 | 0.234627 | ||||||||
\(9\) | −2.96533 | −0.988443 | ||||||||
\(10\) | 4.30235 | 1.36052 | ||||||||
\(11\) | 0.515564 | 0.155448 | 0.0777242 | − | 0.996975i | \(-0.475235\pi\) | ||||
0.0777242 | + | 0.996975i | \(0.475235\pi\) | |||||||
\(12\) | −0.307750 | −0.0888399 | ||||||||
\(13\) | −5.38098 | −1.49242 | −0.746208 | − | 0.665712i | \(-0.768128\pi\) | ||||
−0.746208 | + | 0.665712i | \(0.768128\pi\) | |||||||
\(14\) | −6.74604 | −1.80295 | ||||||||
\(15\) | 0.419160 | 0.108227 | ||||||||
\(16\) | −4.57388 | −1.14347 | ||||||||
\(17\) | −4.16566 | −1.01032 | −0.505161 | − | 0.863025i | \(-0.668567\pi\) | ||||
−0.505161 | + | 0.863025i | \(0.668567\pi\) | |||||||
\(18\) | 5.66741 | 1.33582 | ||||||||
\(19\) | 4.92935 | 1.13087 | 0.565436 | − | 0.824792i | \(-0.308708\pi\) | ||||
0.565436 | + | 0.824792i | \(0.308708\pi\) | |||||||
\(20\) | −3.72056 | −0.831942 | ||||||||
\(21\) | −0.657237 | −0.143421 | ||||||||
\(22\) | −0.985358 | −0.210079 | ||||||||
\(23\) | −7.69193 | −1.60388 | −0.801940 | − | 0.597405i | \(-0.796198\pi\) | ||||
−0.801940 | + | 0.597405i | \(0.796198\pi\) | |||||||
\(24\) | −0.123568 | −0.0252233 | ||||||||
\(25\) | 0.0674429 | 0.0134886 | ||||||||
\(26\) | 10.2843 | 2.01691 | ||||||||
\(27\) | 1.11076 | 0.213765 | ||||||||
\(28\) | 5.83379 | 1.10248 | ||||||||
\(29\) | −8.93755 | −1.65966 | −0.829831 | − | 0.558015i | \(-0.811563\pi\) | ||||
−0.829831 | + | 0.558015i | \(0.811563\pi\) | |||||||
\(30\) | −0.801107 | −0.146262 | ||||||||
\(31\) | −4.43182 | −0.795978 | −0.397989 | − | 0.917390i | \(-0.630292\pi\) | ||||
−0.397989 | + | 0.917390i | \(0.630292\pi\) | |||||||
\(32\) | 7.41447 | 1.31070 | ||||||||
\(33\) | −0.0959992 | −0.0167113 | ||||||||
\(34\) | 7.96151 | 1.36539 | ||||||||
\(35\) | −7.94569 | −1.34307 | ||||||||
\(36\) | −4.90102 | −0.816837 | ||||||||
\(37\) | 5.99816 | 0.986091 | 0.493046 | − | 0.870003i | \(-0.335884\pi\) | ||||
0.493046 | + | 0.870003i | \(0.335884\pi\) | |||||||
\(38\) | −9.42110 | −1.52830 | ||||||||
\(39\) | 1.00195 | 0.160441 | ||||||||
\(40\) | −1.49388 | −0.236204 | ||||||||
\(41\) | −8.99946 | −1.40548 | −0.702740 | − | 0.711447i | \(-0.748040\pi\) | ||||
−0.702740 | + | 0.711447i | \(0.748040\pi\) | |||||||
\(42\) | 1.25613 | 0.193825 | ||||||||
\(43\) | −1.66336 | −0.253660 | −0.126830 | − | 0.991924i | \(-0.540480\pi\) | ||||
−0.126830 | + | 0.991924i | \(0.540480\pi\) | |||||||
\(44\) | 0.852112 | 0.128461 | ||||||||
\(45\) | 6.67525 | 0.995087 | ||||||||
\(46\) | 14.7010 | 2.16754 | ||||||||
\(47\) | 8.55484 | 1.24785 | 0.623926 | − | 0.781483i | \(-0.285537\pi\) | ||||
0.623926 | + | 0.781483i | \(0.285537\pi\) | |||||||
\(48\) | 0.851668 | 0.122928 | ||||||||
\(49\) | 5.45876 | 0.779823 | ||||||||
\(50\) | −0.128898 | −0.0182290 | ||||||||
\(51\) | 0.775656 | 0.108614 | ||||||||
\(52\) | −8.89356 | −1.23331 | ||||||||
\(53\) | 13.1736 | 1.80954 | 0.904769 | − | 0.425903i | \(-0.140043\pi\) | ||||
0.904769 | + | 0.425903i | \(0.140043\pi\) | |||||||
\(54\) | −2.12291 | −0.288891 | ||||||||
\(55\) | −1.16059 | −0.156493 | ||||||||
\(56\) | 2.34239 | 0.313015 | ||||||||
\(57\) | −0.917857 | −0.121573 | ||||||||
\(58\) | 17.0817 | 2.24293 | ||||||||
\(59\) | 9.25521 | 1.20493 | 0.602463 | − | 0.798147i | \(-0.294186\pi\) | ||||
0.602463 | + | 0.798147i | \(0.294186\pi\) | |||||||
\(60\) | 0.692776 | 0.0894370 | ||||||||
\(61\) | −10.4203 | −1.33418 | −0.667090 | − | 0.744978i | \(-0.732460\pi\) | ||||
−0.667090 | + | 0.744978i | \(0.732460\pi\) | |||||||
\(62\) | 8.47019 | 1.07572 | ||||||||
\(63\) | −10.4667 | −1.31868 | ||||||||
\(64\) | −5.02293 | −0.627867 | ||||||||
\(65\) | 12.1131 | 1.50245 | ||||||||
\(66\) | 0.183476 | 0.0225843 | ||||||||
\(67\) | −3.91715 | −0.478555 | −0.239278 | − | 0.970951i | \(-0.576911\pi\) | ||||
−0.239278 | + | 0.970951i | \(0.576911\pi\) | |||||||
\(68\) | −6.88490 | −0.834917 | ||||||||
\(69\) | 1.43226 | 0.172423 | ||||||||
\(70\) | 15.1860 | 1.81507 | ||||||||
\(71\) | −13.6724 | −1.62262 | −0.811308 | − | 0.584619i | \(-0.801244\pi\) | ||||
−0.811308 | + | 0.584619i | \(0.801244\pi\) | |||||||
\(72\) | −1.96786 | −0.231915 | ||||||||
\(73\) | 11.5529 | 1.35217 | 0.676083 | − | 0.736825i | \(-0.263676\pi\) | ||||
0.676083 | + | 0.736825i | \(0.263676\pi\) | |||||||
\(74\) | −11.4638 | −1.33264 | ||||||||
\(75\) | −0.0125580 | −0.00145007 | ||||||||
\(76\) | 8.14711 | 0.934538 | ||||||||
\(77\) | 1.81979 | 0.207384 | ||||||||
\(78\) | −1.91495 | −0.216826 | ||||||||
\(79\) | −1.43448 | −0.161391 | −0.0806956 | − | 0.996739i | \(-0.525714\pi\) | ||||
−0.0806956 | + | 0.996739i | \(0.525714\pi\) | |||||||
\(80\) | 10.2963 | 1.15116 | ||||||||
\(81\) | 8.68916 | 0.965462 | ||||||||
\(82\) | 17.2000 | 1.89942 | ||||||||
\(83\) | 1.73047 | 0.189944 | 0.0949720 | − | 0.995480i | \(-0.469724\pi\) | ||||
0.0949720 | + | 0.995480i | \(0.469724\pi\) | |||||||
\(84\) | −1.08627 | −0.118521 | ||||||||
\(85\) | 9.37732 | 1.01711 | ||||||||
\(86\) | 3.17906 | 0.342807 | ||||||||
\(87\) | 1.66419 | 0.178420 | ||||||||
\(88\) | 0.342141 | 0.0364724 | ||||||||
\(89\) | −1.07999 | −0.114478 | −0.0572392 | − | 0.998360i | \(-0.518230\pi\) | ||||
−0.0572392 | + | 0.998360i | \(0.518230\pi\) | |||||||
\(90\) | −12.7579 | −1.34480 | ||||||||
\(91\) | −18.9932 | −1.99103 | ||||||||
\(92\) | −12.7130 | −1.32543 | ||||||||
\(93\) | 0.825214 | 0.0855707 | ||||||||
\(94\) | −16.3502 | −1.68640 | ||||||||
\(95\) | −11.0965 | −1.13847 | ||||||||
\(96\) | −1.38059 | −0.140906 | ||||||||
\(97\) | −16.0883 | −1.63352 | −0.816759 | − | 0.576979i | \(-0.804231\pi\) | ||||
−0.816759 | + | 0.576979i | \(0.804231\pi\) | |||||||
\(98\) | −10.4329 | −1.05388 | ||||||||
\(99\) | −1.52882 | −0.153652 | ||||||||
\(100\) | 0.111468 | 0.0111468 | ||||||||
\(101\) | −1.23922 | −0.123307 | −0.0616536 | − | 0.998098i | \(-0.519637\pi\) | ||||
−0.0616536 | + | 0.998098i | \(0.519637\pi\) | |||||||
\(102\) | −1.48245 | −0.146785 | ||||||||
\(103\) | 5.27633 | 0.519892 | 0.259946 | − | 0.965623i | \(-0.416295\pi\) | ||||
0.259946 | + | 0.965623i | \(0.416295\pi\) | |||||||
\(104\) | −3.57095 | −0.350161 | ||||||||
\(105\) | 1.47951 | 0.144385 | ||||||||
\(106\) | −25.1778 | −2.44548 | ||||||||
\(107\) | 10.7822 | 1.04236 | 0.521178 | − | 0.853448i | \(-0.325493\pi\) | ||||
0.521178 | + | 0.853448i | \(0.325493\pi\) | |||||||
\(108\) | 1.83583 | 0.176653 | ||||||||
\(109\) | −1.15255 | −0.110394 | −0.0551972 | − | 0.998475i | \(-0.517579\pi\) | ||||
−0.0551972 | + | 0.998475i | \(0.517579\pi\) | |||||||
\(110\) | 2.21814 | 0.211491 | ||||||||
\(111\) | −1.11687 | −0.106009 | ||||||||
\(112\) | −16.1444 | −1.52550 | ||||||||
\(113\) | −8.70999 | −0.819367 | −0.409684 | − | 0.912228i | \(-0.634361\pi\) | ||||
−0.409684 | + | 0.912228i | \(0.634361\pi\) | |||||||
\(114\) | 1.75423 | 0.164299 | ||||||||
\(115\) | 17.3153 | 1.61466 | ||||||||
\(116\) | −14.7718 | −1.37152 | ||||||||
\(117\) | 15.9564 | 1.47517 | ||||||||
\(118\) | −17.6888 | −1.62838 | ||||||||
\(119\) | −14.7035 | −1.34787 | ||||||||
\(120\) | 0.278165 | 0.0253928 | ||||||||
\(121\) | −10.7342 | −0.975836 | ||||||||
\(122\) | 19.9155 | 1.80306 | ||||||||
\(123\) | 1.67572 | 0.151095 | ||||||||
\(124\) | −7.32480 | −0.657786 | ||||||||
\(125\) | 11.1037 | 0.993142 | ||||||||
\(126\) | 20.0042 | 1.78212 | ||||||||
\(127\) | −8.22063 | −0.729463 | −0.364732 | − | 0.931113i | \(-0.618839\pi\) | ||||
−0.364732 | + | 0.931113i | \(0.618839\pi\) | |||||||
\(128\) | −5.22899 | −0.462181 | ||||||||
\(129\) | 0.309722 | 0.0272695 | ||||||||
\(130\) | −23.1509 | −2.03047 | ||||||||
\(131\) | −7.30323 | −0.638086 | −0.319043 | − | 0.947740i | \(-0.603362\pi\) | ||||
−0.319043 | + | 0.947740i | \(0.603362\pi\) | |||||||
\(132\) | −0.158665 | −0.0138100 | ||||||||
\(133\) | 17.3991 | 1.50870 | ||||||||
\(134\) | 7.48654 | 0.646739 | ||||||||
\(135\) | −2.50042 | −0.215202 | ||||||||
\(136\) | −2.76444 | −0.237048 | ||||||||
\(137\) | 5.95317 | 0.508614 | 0.254307 | − | 0.967124i | \(-0.418153\pi\) | ||||
0.254307 | + | 0.967124i | \(0.418153\pi\) | |||||||
\(138\) | −2.73736 | −0.233020 | ||||||||
\(139\) | 14.9650 | 1.26931 | 0.634656 | − | 0.772795i | \(-0.281142\pi\) | ||||
0.634656 | + | 0.772795i | \(0.281142\pi\) | |||||||
\(140\) | −13.1324 | −1.10989 | ||||||||
\(141\) | −1.59293 | −0.134149 | ||||||||
\(142\) | 26.1310 | 2.19287 | ||||||||
\(143\) | −2.77424 | −0.231994 | ||||||||
\(144\) | 13.5631 | 1.13026 | ||||||||
\(145\) | 20.1193 | 1.67082 | ||||||||
\(146\) | −22.0802 | −1.82737 | ||||||||
\(147\) | −1.01643 | −0.0838340 | ||||||||
\(148\) | 9.91361 | 0.814894 | ||||||||
\(149\) | −0.130576 | −0.0106972 | −0.00534860 | − | 0.999986i | \(-0.501703\pi\) | ||||
−0.00534860 | + | 0.999986i | \(0.501703\pi\) | |||||||
\(150\) | 0.0240012 | 0.00195969 | ||||||||
\(151\) | 0.276102 | 0.0224688 | 0.0112344 | − | 0.999937i | \(-0.496424\pi\) | ||||
0.0112344 | + | 0.999937i | \(0.496424\pi\) | |||||||
\(152\) | 3.27124 | 0.265333 | ||||||||
\(153\) | 12.3526 | 0.998645 | ||||||||
\(154\) | −3.47802 | −0.280267 | ||||||||
\(155\) | 9.97646 | 0.801328 | ||||||||
\(156\) | 1.65600 | 0.132586 | ||||||||
\(157\) | 16.1044 | 1.28527 | 0.642636 | − | 0.766172i | \(-0.277841\pi\) | ||||
0.642636 | + | 0.766172i | \(0.277841\pi\) | |||||||
\(158\) | 2.74160 | 0.218110 | ||||||||
\(159\) | −2.45296 | −0.194532 | ||||||||
\(160\) | −16.6907 | −1.31952 | ||||||||
\(161\) | −27.1502 | −2.13973 | ||||||||
\(162\) | −16.6069 | −1.30476 | ||||||||
\(163\) | −18.5215 | −1.45071 | −0.725357 | − | 0.688373i | \(-0.758325\pi\) | ||||
−0.725357 | + | 0.688373i | \(0.758325\pi\) | |||||||
\(164\) | −14.8741 | −1.16147 | ||||||||
\(165\) | 0.216104 | 0.0168236 | ||||||||
\(166\) | −3.30732 | −0.256698 | ||||||||
\(167\) | 15.5017 | 1.19956 | 0.599779 | − | 0.800166i | \(-0.295255\pi\) | ||||
0.599779 | + | 0.800166i | \(0.295255\pi\) | |||||||
\(168\) | −0.436159 | −0.0336504 | ||||||||
\(169\) | 15.9550 | 1.22731 | ||||||||
\(170\) | −17.9221 | −1.37457 | ||||||||
\(171\) | −14.6172 | −1.11780 | ||||||||
\(172\) | −2.74916 | −0.209622 | ||||||||
\(173\) | −0.366438 | −0.0278597 | −0.0139299 | − | 0.999903i | \(-0.504434\pi\) | ||||
−0.0139299 | + | 0.999903i | \(0.504434\pi\) | |||||||
\(174\) | −3.18064 | −0.241124 | ||||||||
\(175\) | 0.238053 | 0.0179951 | ||||||||
\(176\) | −2.35813 | −0.177751 | ||||||||
\(177\) | −1.72334 | −0.129534 | ||||||||
\(178\) | 2.06410 | 0.154711 | ||||||||
\(179\) | 12.8719 | 0.962090 | 0.481045 | − | 0.876696i | \(-0.340257\pi\) | ||||
0.481045 | + | 0.876696i | \(0.340257\pi\) | |||||||
\(180\) | 11.0327 | 0.822327 | ||||||||
\(181\) | −12.2125 | −0.907746 | −0.453873 | − | 0.891066i | \(-0.649958\pi\) | ||||
−0.453873 | + | 0.891066i | \(0.649958\pi\) | |||||||
\(182\) | 36.3003 | 2.69076 | ||||||||
\(183\) | 1.94028 | 0.143429 | ||||||||
\(184\) | −5.10456 | −0.376313 | ||||||||
\(185\) | −13.5024 | −0.992719 | ||||||||
\(186\) | −1.57717 | −0.115644 | ||||||||
\(187\) | −2.14767 | −0.157053 | ||||||||
\(188\) | 14.1392 | 1.03121 | ||||||||
\(189\) | 3.92064 | 0.285184 | ||||||||
\(190\) | 21.2078 | 1.53858 | ||||||||
\(191\) | −3.92400 | −0.283930 | −0.141965 | − | 0.989872i | \(-0.545342\pi\) | ||||
−0.141965 | + | 0.989872i | \(0.545342\pi\) | |||||||
\(192\) | 0.935281 | 0.0674981 | ||||||||
\(193\) | −1.69319 | −0.121879 | −0.0609393 | − | 0.998141i | \(-0.519410\pi\) | ||||
−0.0609393 | + | 0.998141i | \(0.519410\pi\) | |||||||
\(194\) | 30.7483 | 2.20760 | ||||||||
\(195\) | −2.25549 | −0.161519 | ||||||||
\(196\) | 9.02210 | 0.644436 | ||||||||
\(197\) | −2.20382 | −0.157016 | −0.0785080 | − | 0.996913i | \(-0.525016\pi\) | ||||
−0.0785080 | + | 0.996913i | \(0.525016\pi\) | |||||||
\(198\) | 2.92191 | 0.207651 | ||||||||
\(199\) | −15.5533 | −1.10255 | −0.551274 | − | 0.834324i | \(-0.685858\pi\) | ||||
−0.551274 | + | 0.834324i | \(0.685858\pi\) | |||||||
\(200\) | 0.0447567 | 0.00316478 | ||||||||
\(201\) | 0.729381 | 0.0514466 | ||||||||
\(202\) | 2.36843 | 0.166642 | ||||||||
\(203\) | −31.5468 | −2.21415 | ||||||||
\(204\) | 1.28198 | 0.0897569 | ||||||||
\(205\) | 20.2587 | 1.41493 | ||||||||
\(206\) | −10.0842 | −0.702603 | ||||||||
\(207\) | 22.8091 | 1.58534 | ||||||||
\(208\) | 24.6120 | 1.70654 | ||||||||
\(209\) | 2.54140 | 0.175792 | ||||||||
\(210\) | −2.82767 | −0.195128 | ||||||||
\(211\) | 6.55996 | 0.451606 | 0.225803 | − | 0.974173i | \(-0.427499\pi\) | ||||
0.225803 | + | 0.974173i | \(0.427499\pi\) | |||||||
\(212\) | 21.7731 | 1.49538 | ||||||||
\(213\) | 2.54583 | 0.174438 | ||||||||
\(214\) | −20.6072 | −1.40868 | ||||||||
\(215\) | 3.74439 | 0.255365 | ||||||||
\(216\) | 0.737126 | 0.0501551 | ||||||||
\(217\) | −15.6430 | −1.06191 | ||||||||
\(218\) | 2.20278 | 0.149191 | ||||||||
\(219\) | −2.15118 | −0.145363 | ||||||||
\(220\) | −1.91819 | −0.129324 | ||||||||
\(221\) | 22.4154 | 1.50782 | ||||||||
\(222\) | 2.13459 | 0.143264 | ||||||||
\(223\) | 6.53800 | 0.437817 | 0.218908 | − | 0.975745i | \(-0.429750\pi\) | ||||
0.218908 | + | 0.975745i | \(0.429750\pi\) | |||||||
\(224\) | 26.1708 | 1.74861 | ||||||||
\(225\) | −0.199990 | −0.0133327 | ||||||||
\(226\) | 16.6467 | 1.10732 | ||||||||
\(227\) | 16.1673 | 1.07306 | 0.536530 | − | 0.843881i | \(-0.319735\pi\) | ||||
0.536530 | + | 0.843881i | \(0.319735\pi\) | |||||||
\(228\) | −1.51701 | −0.100466 | ||||||||
\(229\) | 0.0208412 | 0.00137722 | 0.000688612 | − | 1.00000i | \(-0.499781\pi\) | ||||
0.000688612 | 1.00000i | \(0.499781\pi\) | ||||||||
\(230\) | −33.0934 | −2.18211 | ||||||||
\(231\) | −0.338848 | −0.0222946 | ||||||||
\(232\) | −5.93118 | −0.389401 | ||||||||
\(233\) | −0.651845 | −0.0427038 | −0.0213519 | − | 0.999772i | \(-0.506797\pi\) | ||||
−0.0213519 | + | 0.999772i | \(0.506797\pi\) | |||||||
\(234\) | −30.4962 | −1.99360 | ||||||||
\(235\) | −19.2578 | −1.25624 | ||||||||
\(236\) | 15.2968 | 0.995736 | ||||||||
\(237\) | 0.267103 | 0.0173502 | ||||||||
\(238\) | 28.1017 | 1.82156 | ||||||||
\(239\) | −8.99997 | −0.582160 | −0.291080 | − | 0.956699i | \(-0.594015\pi\) | ||||
−0.291080 | + | 0.956699i | \(0.594015\pi\) | |||||||
\(240\) | −1.91719 | −0.123754 | ||||||||
\(241\) | −1.00000 | −0.0644157 | ||||||||
\(242\) | 20.5154 | 1.31878 | ||||||||
\(243\) | −4.95021 | −0.317556 | ||||||||
\(244\) | −17.2224 | −1.10255 | ||||||||
\(245\) | −12.2882 | −0.785064 | ||||||||
\(246\) | −3.20268 | −0.204195 | ||||||||
\(247\) | −26.5248 | −1.68773 | ||||||||
\(248\) | −2.94106 | −0.186758 | ||||||||
\(249\) | −0.322218 | −0.0204197 | ||||||||
\(250\) | −21.2216 | −1.34217 | ||||||||
\(251\) | 16.4986 | 1.04138 | 0.520691 | − | 0.853745i | \(-0.325674\pi\) | ||||
0.520691 | + | 0.853745i | \(0.325674\pi\) | |||||||
\(252\) | −17.2991 | −1.08974 | ||||||||
\(253\) | −3.96569 | −0.249321 | ||||||||
\(254\) | 15.7115 | 0.985825 | ||||||||
\(255\) | −1.74608 | −0.109344 | ||||||||
\(256\) | 20.0396 | 1.25248 | ||||||||
\(257\) | 7.99029 | 0.498420 | 0.249210 | − | 0.968449i | \(-0.419829\pi\) | ||||
0.249210 | + | 0.968449i | \(0.419829\pi\) | |||||||
\(258\) | −0.591948 | −0.0368530 | ||||||||
\(259\) | 21.1717 | 1.31554 | ||||||||
\(260\) | 20.0203 | 1.24160 | ||||||||
\(261\) | 26.5028 | 1.64048 | ||||||||
\(262\) | 13.9581 | 0.862335 | ||||||||
\(263\) | −5.47488 | −0.337595 | −0.168798 | − | 0.985651i | \(-0.553988\pi\) | ||||
−0.168798 | + | 0.985651i | \(0.553988\pi\) | |||||||
\(264\) | −0.0637074 | −0.00392092 | ||||||||
\(265\) | −29.6551 | −1.82170 | ||||||||
\(266\) | −33.2536 | −2.03891 | ||||||||
\(267\) | 0.201096 | 0.0123069 | ||||||||
\(268\) | −6.47416 | −0.395472 | ||||||||
\(269\) | −2.34697 | −0.143097 | −0.0715486 | − | 0.997437i | \(-0.522794\pi\) | ||||
−0.0715486 | + | 0.997437i | \(0.522794\pi\) | |||||||
\(270\) | 4.77887 | 0.290833 | ||||||||
\(271\) | 1.60301 | 0.0973758 | 0.0486879 | − | 0.998814i | \(-0.484496\pi\) | ||||
0.0486879 | + | 0.998814i | \(0.484496\pi\) | |||||||
\(272\) | 19.0533 | 1.15527 | ||||||||
\(273\) | 3.53658 | 0.214044 | ||||||||
\(274\) | −11.3778 | −0.687360 | ||||||||
\(275\) | 0.0347711 | 0.00209678 | ||||||||
\(276\) | 2.36720 | 0.142488 | ||||||||
\(277\) | −21.6775 | −1.30247 | −0.651237 | − | 0.758875i | \(-0.725750\pi\) | ||||
−0.651237 | + | 0.758875i | \(0.725750\pi\) | |||||||
\(278\) | −28.6014 | −1.71540 | ||||||||
\(279\) | 13.1418 | 0.786779 | ||||||||
\(280\) | −5.27296 | −0.315119 | ||||||||
\(281\) | 26.9010 | 1.60478 | 0.802388 | − | 0.596802i | \(-0.203562\pi\) | ||||
0.802388 | + | 0.596802i | \(0.203562\pi\) | |||||||
\(282\) | 3.04445 | 0.181294 | ||||||||
\(283\) | 3.89230 | 0.231373 | 0.115687 | − | 0.993286i | \(-0.463093\pi\) | ||||
0.115687 | + | 0.993286i | \(0.463093\pi\) | |||||||
\(284\) | −22.5974 | −1.34091 | ||||||||
\(285\) | 2.06619 | 0.122390 | ||||||||
\(286\) | 5.30220 | 0.313526 | ||||||||
\(287\) | −31.7654 | −1.87505 | ||||||||
\(288\) | −21.9863 | −1.29556 | ||||||||
\(289\) | 0.352752 | 0.0207501 | ||||||||
\(290\) | −38.4525 | −2.25801 | ||||||||
\(291\) | 2.99567 | 0.175610 | ||||||||
\(292\) | 19.0944 | 1.11741 | ||||||||
\(293\) | −5.57389 | −0.325630 | −0.162815 | − | 0.986657i | \(-0.552057\pi\) | ||||
−0.162815 | + | 0.986657i | \(0.552057\pi\) | |||||||
\(294\) | 1.94263 | 0.113297 | ||||||||
\(295\) | −20.8344 | −1.21302 | ||||||||
\(296\) | 3.98053 | 0.231363 | ||||||||
\(297\) | 0.572667 | 0.0332295 | ||||||||
\(298\) | 0.249560 | 0.0144566 | ||||||||
\(299\) | 41.3902 | 2.39366 | ||||||||
\(300\) | −0.0207556 | −0.00119832 | ||||||||
\(301\) | −5.87116 | −0.338408 | ||||||||
\(302\) | −0.527692 | −0.0303652 | ||||||||
\(303\) | 0.230746 | 0.0132560 | ||||||||
\(304\) | −22.5463 | −1.29312 | ||||||||
\(305\) | 23.4571 | 1.34315 | ||||||||
\(306\) | −23.6085 | −1.34961 | ||||||||
\(307\) | 23.0795 | 1.31722 | 0.658608 | − | 0.752486i | \(-0.271146\pi\) | ||||
0.658608 | + | 0.752486i | \(0.271146\pi\) | |||||||
\(308\) | 3.00770 | 0.171379 | ||||||||
\(309\) | −0.982465 | −0.0558905 | ||||||||
\(310\) | −19.0672 | −1.08295 | ||||||||
\(311\) | −14.9884 | −0.849916 | −0.424958 | − | 0.905213i | \(-0.639711\pi\) | ||||
−0.424958 | + | 0.905213i | \(0.639711\pi\) | |||||||
\(312\) | 0.664919 | 0.0376437 | ||||||||
\(313\) | −2.31082 | −0.130615 | −0.0653076 | − | 0.997865i | \(-0.520803\pi\) | ||||
−0.0653076 | + | 0.997865i | \(0.520803\pi\) | |||||||
\(314\) | −30.7791 | −1.73697 | ||||||||
\(315\) | 23.5616 | 1.32755 | ||||||||
\(316\) | −2.37087 | −0.133372 | ||||||||
\(317\) | −18.3630 | −1.03137 | −0.515684 | − | 0.856779i | \(-0.672462\pi\) | ||||
−0.515684 | + | 0.856779i | \(0.672462\pi\) | |||||||
\(318\) | 4.68816 | 0.262899 | ||||||||
\(319\) | −4.60788 | −0.257992 | ||||||||
\(320\) | 11.3071 | 0.632087 | ||||||||
\(321\) | −2.00767 | −0.112057 | ||||||||
\(322\) | 51.8901 | 2.89172 | ||||||||
\(323\) | −20.5340 | −1.14254 | ||||||||
\(324\) | 14.3612 | 0.797846 | ||||||||
\(325\) | −0.362909 | −0.0201306 | ||||||||
\(326\) | 35.3987 | 1.96055 | ||||||||
\(327\) | 0.214608 | 0.0118678 | ||||||||
\(328\) | −5.97226 | −0.329763 | ||||||||
\(329\) | 30.1960 | 1.66476 | ||||||||
\(330\) | −0.413022 | −0.0227361 | ||||||||
\(331\) | −6.47933 | −0.356136 | −0.178068 | − | 0.984018i | \(-0.556985\pi\) | ||||
−0.178068 | + | 0.984018i | \(0.556985\pi\) | |||||||
\(332\) | 2.86008 | 0.156967 | ||||||||
\(333\) | −17.7865 | −0.974695 | ||||||||
\(334\) | −29.6272 | −1.62113 | ||||||||
\(335\) | 8.81788 | 0.481772 | ||||||||
\(336\) | 3.00613 | 0.163998 | ||||||||
\(337\) | −3.54257 | −0.192976 | −0.0964880 | − | 0.995334i | \(-0.530761\pi\) | ||||
−0.0964880 | + | 0.995334i | \(0.530761\pi\) | |||||||
\(338\) | −30.4936 | −1.65863 | ||||||||
\(339\) | 1.62182 | 0.0880852 | ||||||||
\(340\) | 15.4986 | 0.840529 | ||||||||
\(341\) | −2.28489 | −0.123734 | ||||||||
\(342\) | 27.9366 | 1.51064 | ||||||||
\(343\) | −5.44011 | −0.293739 | ||||||||
\(344\) | −1.10385 | −0.0595155 | ||||||||
\(345\) | −3.22415 | −0.173582 | ||||||||
\(346\) | 0.700344 | 0.0376507 | ||||||||
\(347\) | −14.4844 | −0.777566 | −0.388783 | − | 0.921329i | \(-0.627104\pi\) | ||||
−0.388783 | + | 0.921329i | \(0.627104\pi\) | |||||||
\(348\) | 2.75053 | 0.147444 | ||||||||
\(349\) | −23.6287 | −1.26482 | −0.632408 | − | 0.774636i | \(-0.717933\pi\) | ||||
−0.632408 | + | 0.774636i | \(0.717933\pi\) | |||||||
\(350\) | −0.454972 | −0.0243193 | ||||||||
\(351\) | −5.97697 | −0.319027 | ||||||||
\(352\) | 3.82263 | 0.203747 | ||||||||
\(353\) | −18.2662 | −0.972209 | −0.486105 | − | 0.873901i | \(-0.661583\pi\) | ||||
−0.486105 | + | 0.873901i | \(0.661583\pi\) | |||||||
\(354\) | 3.29369 | 0.175058 | ||||||||
\(355\) | 30.7779 | 1.63352 | ||||||||
\(356\) | −1.78498 | −0.0946036 | ||||||||
\(357\) | 2.73783 | 0.144901 | ||||||||
\(358\) | −24.6010 | −1.30021 | ||||||||
\(359\) | −20.3758 | −1.07539 | −0.537697 | − | 0.843138i | \(-0.680706\pi\) | ||||
−0.537697 | + | 0.843138i | \(0.680706\pi\) | |||||||
\(360\) | 4.42986 | 0.233474 | ||||||||
\(361\) | 5.29852 | 0.278870 | ||||||||
\(362\) | 23.3408 | 1.22676 | ||||||||
\(363\) | 1.99873 | 0.104906 | ||||||||
\(364\) | −31.3916 | −1.64536 | ||||||||
\(365\) | −26.0067 | −1.36125 | ||||||||
\(366\) | −3.70830 | −0.193836 | ||||||||
\(367\) | −1.76412 | −0.0920862 | −0.0460431 | − | 0.998939i | \(-0.514661\pi\) | ||||
−0.0460431 | + | 0.998939i | \(0.514661\pi\) | |||||||
\(368\) | 35.1820 | 1.83399 | ||||||||
\(369\) | 26.6864 | 1.38924 | ||||||||
\(370\) | 25.8062 | 1.34160 | ||||||||
\(371\) | 46.4989 | 2.41410 | ||||||||
\(372\) | 1.36389 | 0.0707146 | ||||||||
\(373\) | −32.1736 | −1.66589 | −0.832943 | − | 0.553359i | \(-0.813346\pi\) | ||||
−0.832943 | + | 0.553359i | \(0.813346\pi\) | |||||||
\(374\) | 4.10467 | 0.212247 | ||||||||
\(375\) | −2.06753 | −0.106767 | ||||||||
\(376\) | 5.67720 | 0.292779 | ||||||||
\(377\) | 48.0928 | 2.47691 | ||||||||
\(378\) | −7.49321 | −0.385409 | ||||||||
\(379\) | −31.3680 | −1.61126 | −0.805632 | − | 0.592416i | \(-0.798174\pi\) | ||||
−0.805632 | + | 0.592416i | \(0.798174\pi\) | |||||||
\(380\) | −18.3399 | −0.940820 | ||||||||
\(381\) | 1.53070 | 0.0784201 | ||||||||
\(382\) | 7.49963 | 0.383715 | ||||||||
\(383\) | 16.8623 | 0.861624 | 0.430812 | − | 0.902442i | \(-0.358227\pi\) | ||||
0.430812 | + | 0.902442i | \(0.358227\pi\) | |||||||
\(384\) | 0.973649 | 0.0496863 | ||||||||
\(385\) | −4.09651 | −0.208778 | ||||||||
\(386\) | 3.23607 | 0.164712 | ||||||||
\(387\) | 4.93242 | 0.250729 | ||||||||
\(388\) | −26.5903 | −1.34992 | ||||||||
\(389\) | −0.816001 | −0.0413729 | −0.0206864 | − | 0.999786i | \(-0.506585\pi\) | ||||
−0.0206864 | + | 0.999786i | \(0.506585\pi\) | |||||||
\(390\) | 4.31075 | 0.218283 | ||||||||
\(391\) | 32.0420 | 1.62043 | ||||||||
\(392\) | 3.62257 | 0.182967 | ||||||||
\(393\) | 1.35988 | 0.0685968 | ||||||||
\(394\) | 4.21200 | 0.212198 | ||||||||
\(395\) | 3.22915 | 0.162476 | ||||||||
\(396\) | −2.52679 | −0.126976 | ||||||||
\(397\) | −21.8279 | −1.09551 | −0.547755 | − | 0.836639i | \(-0.684517\pi\) | ||||
−0.547755 | + | 0.836639i | \(0.684517\pi\) | |||||||
\(398\) | 29.7259 | 1.49003 | ||||||||
\(399\) | −3.23976 | −0.162191 | ||||||||
\(400\) | −0.308476 | −0.0154238 | ||||||||
\(401\) | −15.4857 | −0.773321 | −0.386661 | − | 0.922222i | \(-0.626372\pi\) | ||||
−0.386661 | + | 0.922222i | \(0.626372\pi\) | |||||||
\(402\) | −1.39401 | −0.0695269 | ||||||||
\(403\) | 23.8475 | 1.18793 | ||||||||
\(404\) | −2.04816 | −0.101900 | ||||||||
\(405\) | −19.5602 | −0.971952 | ||||||||
\(406\) | 60.2931 | 2.99229 | ||||||||
\(407\) | 3.09244 | 0.153286 | ||||||||
\(408\) | 0.514744 | 0.0254836 | ||||||||
\(409\) | 26.0377 | 1.28748 | 0.643740 | − | 0.765245i | \(-0.277382\pi\) | ||||
0.643740 | + | 0.765245i | \(0.277382\pi\) | |||||||
\(410\) | −38.7189 | −1.91219 | ||||||||
\(411\) | −1.10849 | −0.0546780 | ||||||||
\(412\) | 8.72059 | 0.429633 | ||||||||
\(413\) | 32.6681 | 1.60749 | ||||||||
\(414\) | −43.5933 | −2.14249 | ||||||||
\(415\) | −3.89546 | −0.191221 | ||||||||
\(416\) | −39.8971 | −1.95612 | ||||||||
\(417\) | −2.78651 | −0.136456 | ||||||||
\(418\) | −4.85718 | −0.237572 | ||||||||
\(419\) | −33.2204 | −1.62292 | −0.811462 | − | 0.584406i | \(-0.801328\pi\) | ||||
−0.811462 | + | 0.584406i | \(0.801328\pi\) | |||||||
\(420\) | 2.44529 | 0.119318 | ||||||||
\(421\) | 2.90586 | 0.141623 | 0.0708115 | − | 0.997490i | \(-0.477441\pi\) | ||||
0.0708115 | + | 0.997490i | \(0.477441\pi\) | |||||||
\(422\) | −12.5375 | −0.610318 | ||||||||
\(423\) | −25.3679 | −1.23343 | ||||||||
\(424\) | 8.74235 | 0.424566 | ||||||||
\(425\) | −0.280944 | −0.0136278 | ||||||||
\(426\) | −4.86565 | −0.235742 | ||||||||
\(427\) | −36.7804 | −1.77993 | ||||||||
\(428\) | 17.8206 | 0.861390 | ||||||||
\(429\) | 0.516570 | 0.0249402 | ||||||||
\(430\) | −7.15637 | −0.345111 | ||||||||
\(431\) | −28.4892 | −1.37228 | −0.686139 | − | 0.727471i | \(-0.740696\pi\) | ||||
−0.686139 | + | 0.727471i | \(0.740696\pi\) | |||||||
\(432\) | −5.08048 | −0.244435 | ||||||||
\(433\) | −28.9311 | −1.39034 | −0.695169 | − | 0.718846i | \(-0.744671\pi\) | ||||
−0.695169 | + | 0.718846i | \(0.744671\pi\) | |||||||
\(434\) | 29.8972 | 1.43511 | ||||||||
\(435\) | −3.74626 | −0.179619 | ||||||||
\(436\) | −1.90491 | −0.0912286 | ||||||||
\(437\) | −37.9163 | −1.81378 | ||||||||
\(438\) | 4.11138 | 0.196449 | ||||||||
\(439\) | −8.92156 | −0.425803 | −0.212901 | − | 0.977074i | \(-0.568291\pi\) | ||||
−0.212901 | + | 0.977074i | \(0.568291\pi\) | |||||||
\(440\) | −0.770193 | −0.0367175 | ||||||||
\(441\) | −16.1870 | −0.770810 | ||||||||
\(442\) | −42.8408 | −2.03773 | ||||||||
\(443\) | 24.8216 | 1.17931 | 0.589656 | − | 0.807655i | \(-0.299264\pi\) | ||||
0.589656 | + | 0.807655i | \(0.299264\pi\) | |||||||
\(444\) | −1.84594 | −0.0876042 | ||||||||
\(445\) | 2.43116 | 0.115248 | ||||||||
\(446\) | −12.4956 | −0.591683 | ||||||||
\(447\) | 0.0243136 | 0.00114999 | ||||||||
\(448\) | −17.7294 | −0.837637 | ||||||||
\(449\) | 11.9254 | 0.562793 | 0.281397 | − | 0.959592i | \(-0.409202\pi\) | ||||
0.281397 | + | 0.959592i | \(0.409202\pi\) | |||||||
\(450\) | 0.382226 | 0.0180183 | ||||||||
\(451\) | −4.63980 | −0.218480 | ||||||||
\(452\) | −14.3957 | −0.677115 | ||||||||
\(453\) | −0.0514107 | −0.00241549 | ||||||||
\(454\) | −30.8993 | −1.45018 | ||||||||
\(455\) | 42.7557 | 2.00442 | ||||||||
\(456\) | −0.609112 | −0.0285243 | ||||||||
\(457\) | 8.44205 | 0.394902 | 0.197451 | − | 0.980313i | \(-0.436734\pi\) | ||||
0.197451 | + | 0.980313i | \(0.436734\pi\) | |||||||
\(458\) | −0.0398321 | −0.00186123 | ||||||||
\(459\) | −4.62704 | −0.215972 | ||||||||
\(460\) | 28.6183 | 1.33433 | ||||||||
\(461\) | 23.2925 | 1.08484 | 0.542419 | − | 0.840108i | \(-0.317509\pi\) | ||||
0.542419 | + | 0.840108i | \(0.317509\pi\) | |||||||
\(462\) | 0.647614 | 0.0301297 | ||||||||
\(463\) | 1.66578 | 0.0774152 | 0.0387076 | − | 0.999251i | \(-0.487676\pi\) | ||||
0.0387076 | + | 0.999251i | \(0.487676\pi\) | |||||||
\(464\) | 40.8793 | 1.89777 | ||||||||
\(465\) | −1.85764 | −0.0861459 | ||||||||
\(466\) | 1.24582 | 0.0577116 | ||||||||
\(467\) | −6.66428 | −0.308386 | −0.154193 | − | 0.988041i | \(-0.549278\pi\) | ||||
−0.154193 | + | 0.988041i | \(0.549278\pi\) | |||||||
\(468\) | 26.3723 | 1.21906 | ||||||||
\(469\) | −13.8263 | −0.638441 | ||||||||
\(470\) | 36.8059 | 1.69773 | ||||||||
\(471\) | −2.99868 | −0.138172 | ||||||||
\(472\) | 6.14198 | 0.282708 | ||||||||
\(473\) | −0.857570 | −0.0394311 | ||||||||
\(474\) | −0.510493 | −0.0234477 | ||||||||
\(475\) | 0.332450 | 0.0152538 | ||||||||
\(476\) | −24.3016 | −1.11386 | ||||||||
\(477\) | −39.0642 | −1.78863 | ||||||||
\(478\) | 17.2010 | 0.786753 | ||||||||
\(479\) | −13.6902 | −0.625523 | −0.312762 | − | 0.949832i | \(-0.601254\pi\) | ||||
−0.312762 | + | 0.949832i | \(0.601254\pi\) | |||||||
\(480\) | 3.10784 | 0.141853 | ||||||||
\(481\) | −32.2760 | −1.47166 | ||||||||
\(482\) | 1.91122 | 0.0870538 | ||||||||
\(483\) | 5.05543 | 0.230030 | ||||||||
\(484\) | −17.7412 | −0.806419 | ||||||||
\(485\) | 36.2163 | 1.64450 | ||||||||
\(486\) | 9.46096 | 0.429158 | ||||||||
\(487\) | 31.9634 | 1.44840 | 0.724200 | − | 0.689590i | \(-0.242209\pi\) | ||||
0.724200 | + | 0.689590i | \(0.242209\pi\) | |||||||
\(488\) | −6.91515 | −0.313034 | ||||||||
\(489\) | 3.44874 | 0.155957 | ||||||||
\(490\) | 23.4855 | 1.06097 | ||||||||
\(491\) | −10.0550 | −0.453777 | −0.226889 | − | 0.973921i | \(-0.572855\pi\) | ||||
−0.226889 | + | 0.973921i | \(0.572855\pi\) | |||||||
\(492\) | 2.76959 | 0.124863 | ||||||||
\(493\) | 37.2308 | 1.67679 | ||||||||
\(494\) | 50.6948 | 2.28087 | ||||||||
\(495\) | 3.44152 | 0.154685 | ||||||||
\(496\) | 20.2706 | 0.910178 | ||||||||
\(497\) | −48.2594 | −2.16473 | ||||||||
\(498\) | 0.615830 | 0.0275960 | ||||||||
\(499\) | 9.14295 | 0.409295 | 0.204647 | − | 0.978836i | \(-0.434395\pi\) | ||||
0.204647 | + | 0.978836i | \(0.434395\pi\) | |||||||
\(500\) | 18.3519 | 0.820721 | ||||||||
\(501\) | −2.88645 | −0.128957 | ||||||||
\(502\) | −31.5325 | −1.40736 | ||||||||
\(503\) | −27.2050 | −1.21301 | −0.606506 | − | 0.795079i | \(-0.707429\pi\) | ||||
−0.606506 | + | 0.795079i | \(0.707429\pi\) | |||||||
\(504\) | −6.94597 | −0.309398 | ||||||||
\(505\) | 2.78961 | 0.124136 | ||||||||
\(506\) | 7.57931 | 0.336941 | ||||||||
\(507\) | −2.97086 | −0.131940 | ||||||||
\(508\) | −13.5869 | −0.602819 | ||||||||
\(509\) | 7.79598 | 0.345551 | 0.172775 | − | 0.984961i | \(-0.444726\pi\) | ||||
0.172775 | + | 0.984961i | \(0.444726\pi\) | |||||||
\(510\) | 3.33714 | 0.147771 | ||||||||
\(511\) | 40.7783 | 1.80392 | ||||||||
\(512\) | −27.8422 | −1.23046 | ||||||||
\(513\) | 5.47532 | 0.241741 | ||||||||
\(514\) | −15.2712 | −0.673585 | ||||||||
\(515\) | −11.8775 | −0.523387 | ||||||||
\(516\) | 0.511900 | 0.0225352 | ||||||||
\(517\) | 4.41057 | 0.193977 | ||||||||
\(518\) | −40.4638 | −1.77788 | ||||||||
\(519\) | 0.0682315 | 0.00299503 | ||||||||
\(520\) | 8.03857 | 0.352514 | ||||||||
\(521\) | 32.6959 | 1.43243 | 0.716216 | − | 0.697878i | \(-0.245872\pi\) | ||||
0.716216 | + | 0.697878i | \(0.245872\pi\) | |||||||
\(522\) | −50.6527 | −2.21701 | ||||||||
\(523\) | −7.80136 | −0.341129 | −0.170565 | − | 0.985346i | \(-0.554559\pi\) | ||||
−0.170565 | + | 0.985346i | \(0.554559\pi\) | |||||||
\(524\) | −12.0706 | −0.527307 | ||||||||
\(525\) | −0.0443260 | −0.00193454 | ||||||||
\(526\) | 10.4637 | 0.456240 | ||||||||
\(527\) | 18.4615 | 0.804194 | ||||||||
\(528\) | 0.439089 | 0.0191089 | ||||||||
\(529\) | 36.1658 | 1.57243 | ||||||||
\(530\) | 56.6776 | 2.46192 | ||||||||
\(531\) | −27.4447 | −1.19100 | ||||||||
\(532\) | 28.7568 | 1.24677 | ||||||||
\(533\) | 48.4260 | 2.09756 | ||||||||
\(534\) | −0.384340 | −0.0166320 | ||||||||
\(535\) | −24.2718 | −1.04936 | ||||||||
\(536\) | −2.59951 | −0.112282 | ||||||||
\(537\) | −2.39677 | −0.103428 | ||||||||
\(538\) | 4.48558 | 0.193387 | ||||||||
\(539\) | 2.81434 | 0.121222 | ||||||||
\(540\) | −4.13264 | −0.177840 | ||||||||
\(541\) | 22.3971 | 0.962926 | 0.481463 | − | 0.876467i | \(-0.340106\pi\) | ||||
0.481463 | + | 0.876467i | \(0.340106\pi\) | |||||||
\(542\) | −3.06371 | −0.131597 | ||||||||
\(543\) | 2.27399 | 0.0975863 | ||||||||
\(544\) | −30.8862 | −1.32423 | ||||||||
\(545\) | 2.59451 | 0.111136 | ||||||||
\(546\) | −6.75920 | −0.289267 | ||||||||
\(547\) | 37.2322 | 1.59193 | 0.795966 | − | 0.605341i | \(-0.206963\pi\) | ||||
0.795966 | + | 0.605341i | \(0.206963\pi\) | |||||||
\(548\) | 9.83925 | 0.420312 | ||||||||
\(549\) | 30.8995 | 1.31876 | ||||||||
\(550\) | −0.0664554 | −0.00283367 | ||||||||
\(551\) | −44.0563 | −1.87686 | ||||||||
\(552\) | 0.950480 | 0.0404551 | ||||||||
\(553\) | −5.06326 | −0.215312 | ||||||||
\(554\) | 41.4305 | 1.76021 | ||||||||
\(555\) | 2.51419 | 0.106721 | ||||||||
\(556\) | 24.7337 | 1.04894 | ||||||||
\(557\) | −27.6457 | −1.17139 | −0.585693 | − | 0.810533i | \(-0.699177\pi\) | ||||
−0.585693 | + | 0.810533i | \(0.699177\pi\) | |||||||
\(558\) | −25.1169 | −1.06328 | ||||||||
\(559\) | 8.95053 | 0.378567 | ||||||||
\(560\) | 36.3427 | 1.53576 | ||||||||
\(561\) | 0.399900 | 0.0168838 | ||||||||
\(562\) | −51.4138 | −2.16876 | ||||||||
\(563\) | −23.3454 | −0.983891 | −0.491945 | − | 0.870626i | \(-0.663714\pi\) | ||||
−0.491945 | + | 0.870626i | \(0.663714\pi\) | |||||||
\(564\) | −2.63276 | −0.110859 | ||||||||
\(565\) | 19.6070 | 0.824875 | ||||||||
\(566\) | −7.43905 | −0.312687 | ||||||||
\(567\) | 30.6701 | 1.28802 | ||||||||
\(568\) | −9.07334 | −0.380709 | ||||||||
\(569\) | 2.61346 | 0.109562 | 0.0547811 | − | 0.998498i | \(-0.482554\pi\) | ||||
0.0547811 | + | 0.998498i | \(0.482554\pi\) | |||||||
\(570\) | −3.94894 | −0.165403 | ||||||||
\(571\) | 16.9259 | 0.708326 | 0.354163 | − | 0.935184i | \(-0.384766\pi\) | ||||
0.354163 | + | 0.935184i | \(0.384766\pi\) | |||||||
\(572\) | −4.58520 | −0.191717 | ||||||||
\(573\) | 0.730657 | 0.0305236 | ||||||||
\(574\) | 60.7107 | 2.53402 | ||||||||
\(575\) | −0.518766 | −0.0216340 | ||||||||
\(576\) | 14.8946 | 0.620610 | ||||||||
\(577\) | 4.67534 | 0.194637 | 0.0973185 | − | 0.995253i | \(-0.468973\pi\) | ||||
0.0973185 | + | 0.995253i | \(0.468973\pi\) | |||||||
\(578\) | −0.674188 | −0.0280425 | ||||||||
\(579\) | 0.315276 | 0.0131024 | ||||||||
\(580\) | 33.2527 | 1.38074 | ||||||||
\(581\) | 6.10804 | 0.253404 | ||||||||
\(582\) | −5.72540 | −0.237326 | ||||||||
\(583\) | 6.79185 | 0.281290 | ||||||||
\(584\) | 7.66680 | 0.317254 | ||||||||
\(585\) | −35.9194 | −1.48508 | ||||||||
\(586\) | 10.6530 | 0.440069 | ||||||||
\(587\) | −3.78940 | −0.156405 | −0.0782027 | − | 0.996937i | \(-0.524918\pi\) | ||||
−0.0782027 | + | 0.996937i | \(0.524918\pi\) | |||||||
\(588\) | −1.67994 | −0.0692794 | ||||||||
\(589\) | −21.8460 | −0.900148 | ||||||||
\(590\) | 39.8192 | 1.63933 | ||||||||
\(591\) | 0.410357 | 0.0168798 | ||||||||
\(592\) | −27.4349 | −1.12757 | ||||||||
\(593\) | −6.81434 | −0.279831 | −0.139916 | − | 0.990163i | \(-0.544683\pi\) | ||||
−0.139916 | + | 0.990163i | \(0.544683\pi\) | |||||||
\(594\) | −1.09449 | −0.0449076 | ||||||||
\(595\) | 33.0991 | 1.35693 | ||||||||
\(596\) | −0.215813 | −0.00884004 | ||||||||
\(597\) | 2.89607 | 0.118528 | ||||||||
\(598\) | −79.1059 | −3.23488 | ||||||||
\(599\) | −39.7739 | −1.62512 | −0.812559 | − | 0.582879i | \(-0.801926\pi\) | ||||
−0.812559 | + | 0.582879i | \(0.801926\pi\) | |||||||
\(600\) | −0.00833381 | −0.000340226 0 | ||||||||
\(601\) | 27.4256 | 1.11871 | 0.559356 | − | 0.828927i | \(-0.311048\pi\) | ||||
0.559356 | + | 0.828927i | \(0.311048\pi\) | |||||||
\(602\) | 11.2211 | 0.457338 | ||||||||
\(603\) | 11.6156 | 0.473025 | ||||||||
\(604\) | 0.456334 | 0.0185680 | ||||||||
\(605\) | 24.1637 | 0.982395 | ||||||||
\(606\) | −0.441007 | −0.0179147 | ||||||||
\(607\) | 20.6168 | 0.836811 | 0.418405 | − | 0.908260i | \(-0.362589\pi\) | ||||
0.418405 | + | 0.908260i | \(0.362589\pi\) | |||||||
\(608\) | 36.5485 | 1.48224 | ||||||||
\(609\) | 5.87409 | 0.238030 | ||||||||
\(610\) | −44.8317 | −1.81518 | ||||||||
\(611\) | −46.0335 | −1.86232 | ||||||||
\(612\) | 20.4160 | 0.825268 | ||||||||
\(613\) | −12.9127 | −0.521540 | −0.260770 | − | 0.965401i | \(-0.583976\pi\) | ||||
−0.260770 | + | 0.965401i | \(0.583976\pi\) | |||||||
\(614\) | −44.1100 | −1.78014 | ||||||||
\(615\) | −3.77221 | −0.152110 | ||||||||
\(616\) | 1.20765 | 0.0486578 | ||||||||
\(617\) | 26.3856 | 1.06225 | 0.531123 | − | 0.847295i | \(-0.321770\pi\) | ||||
0.531123 | + | 0.847295i | \(0.321770\pi\) | |||||||
\(618\) | 1.87771 | 0.0755326 | ||||||||
\(619\) | −2.30850 | −0.0927866 | −0.0463933 | − | 0.998923i | \(-0.514773\pi\) | ||||
−0.0463933 | + | 0.998923i | \(0.514773\pi\) | |||||||
\(620\) | 16.4888 | 0.662208 | ||||||||
\(621\) | −8.54387 | −0.342854 | ||||||||
\(622\) | 28.6462 | 1.14861 | ||||||||
\(623\) | −3.81203 | −0.152726 | ||||||||
\(624\) | −4.58281 | −0.183459 | ||||||||
\(625\) | −25.3327 | −1.01331 | ||||||||
\(626\) | 4.41649 | 0.176519 | ||||||||
\(627\) | −0.473214 | −0.0188983 | ||||||||
\(628\) | 26.6170 | 1.06213 | ||||||||
\(629\) | −24.9863 | −0.996270 | ||||||||
\(630\) | −45.0315 | −1.79410 | ||||||||
\(631\) | −8.60820 | −0.342687 | −0.171343 | − | 0.985211i | \(-0.554811\pi\) | ||||
−0.171343 | + | 0.985211i | \(0.554811\pi\) | |||||||
\(632\) | −0.951953 | −0.0378667 | ||||||||
\(633\) | −1.22148 | −0.0485494 | ||||||||
\(634\) | 35.0958 | 1.39383 | ||||||||
\(635\) | 18.5054 | 0.734366 | ||||||||
\(636\) | −4.05419 | −0.160759 | ||||||||
\(637\) | −29.3735 | −1.16382 | ||||||||
\(638\) | 8.80669 | 0.348660 | ||||||||
\(639\) | 40.5432 | 1.60386 | ||||||||
\(640\) | 11.7710 | 0.465288 | ||||||||
\(641\) | −11.7479 | −0.464014 | −0.232007 | − | 0.972714i | \(-0.574529\pi\) | ||||
−0.232007 | + | 0.972714i | \(0.574529\pi\) | |||||||
\(642\) | 3.83711 | 0.151439 | ||||||||
\(643\) | 15.0808 | 0.594729 | 0.297364 | − | 0.954764i | \(-0.403892\pi\) | ||||
0.297364 | + | 0.954764i | \(0.403892\pi\) | |||||||
\(644\) | −44.8732 | −1.76825 | ||||||||
\(645\) | −0.697214 | −0.0274528 | ||||||||
\(646\) | 39.2451 | 1.54408 | ||||||||
\(647\) | −5.68014 | −0.223309 | −0.111655 | − | 0.993747i | \(-0.535615\pi\) | ||||
−0.111655 | + | 0.993747i | \(0.535615\pi\) | |||||||
\(648\) | 5.76634 | 0.226523 | ||||||||
\(649\) | 4.77166 | 0.187304 | ||||||||
\(650\) | 0.693600 | 0.0272052 | ||||||||
\(651\) | 2.91276 | 0.114160 | ||||||||
\(652\) | −30.6118 | −1.19885 | ||||||||
\(653\) | −48.9941 | −1.91729 | −0.958644 | − | 0.284608i | \(-0.908137\pi\) | ||||
−0.958644 | + | 0.284608i | \(0.908137\pi\) | |||||||
\(654\) | −0.410163 | −0.0160387 | ||||||||
\(655\) | 16.4403 | 0.642375 | ||||||||
\(656\) | 41.1625 | 1.60713 | ||||||||
\(657\) | −34.2582 | −1.33654 | ||||||||
\(658\) | −57.7113 | −2.24982 | ||||||||
\(659\) | −23.5789 | −0.918505 | −0.459252 | − | 0.888306i | \(-0.651883\pi\) | ||||
−0.459252 | + | 0.888306i | \(0.651883\pi\) | |||||||
\(660\) | 0.357171 | 0.0139028 | ||||||||
\(661\) | −38.6322 | −1.50262 | −0.751310 | − | 0.659949i | \(-0.770578\pi\) | ||||
−0.751310 | + | 0.659949i | \(0.770578\pi\) | |||||||
\(662\) | 12.3835 | 0.481296 | ||||||||
\(663\) | −4.17379 | −0.162097 | ||||||||
\(664\) | 1.14838 | 0.0445659 | ||||||||
\(665\) | −39.1671 | −1.51884 | ||||||||
\(666\) | 33.9940 | 1.31724 | ||||||||
\(667\) | 68.7470 | 2.66190 | ||||||||
\(668\) | 25.6208 | 0.991300 | ||||||||
\(669\) | −1.21739 | −0.0470670 | ||||||||
\(670\) | −16.8529 | −0.651086 | ||||||||
\(671\) | −5.37232 | −0.207396 | ||||||||
\(672\) | −4.87306 | −0.187983 | ||||||||
\(673\) | −37.4530 | −1.44371 | −0.721853 | − | 0.692047i | \(-0.756709\pi\) | ||||
−0.721853 | + | 0.692047i | \(0.756709\pi\) | |||||||
\(674\) | 6.77064 | 0.260795 | ||||||||
\(675\) | 0.0749127 | 0.00288339 | ||||||||
\(676\) | 26.3700 | 1.01423 | ||||||||
\(677\) | 16.0616 | 0.617297 | 0.308649 | − | 0.951176i | \(-0.400123\pi\) | ||||
0.308649 | + | 0.951176i | \(0.400123\pi\) | |||||||
\(678\) | −3.09966 | −0.119042 | ||||||||
\(679\) | −56.7868 | −2.17928 | ||||||||
\(680\) | 6.22302 | 0.238642 | ||||||||
\(681\) | −3.01038 | −0.115358 | ||||||||
\(682\) | 4.36693 | 0.167218 | ||||||||
\(683\) | 13.5819 | 0.519696 | 0.259848 | − | 0.965649i | \(-0.416327\pi\) | ||||
0.259848 | + | 0.965649i | \(0.416327\pi\) | |||||||
\(684\) | −24.1589 | −0.923737 | ||||||||
\(685\) | −13.4012 | −0.512032 | ||||||||
\(686\) | 10.3973 | 0.396970 | ||||||||
\(687\) | −0.00388067 | −0.000148057 0 | ||||||||
\(688\) | 7.60803 | 0.290053 | ||||||||
\(689\) | −70.8871 | −2.70058 | ||||||||
\(690\) | 6.16207 | 0.234586 | ||||||||
\(691\) | −5.72328 | −0.217724 | −0.108862 | − | 0.994057i | \(-0.534721\pi\) | ||||
−0.108862 | + | 0.994057i | \(0.534721\pi\) | |||||||
\(692\) | −0.605639 | −0.0230229 | ||||||||
\(693\) | −5.39626 | −0.204987 | ||||||||
\(694\) | 27.6830 | 1.05083 | ||||||||
\(695\) | −33.6876 | −1.27784 | ||||||||
\(696\) | 1.10440 | 0.0418621 | ||||||||
\(697\) | 37.4887 | 1.41999 | ||||||||
\(698\) | 45.1597 | 1.70932 | ||||||||
\(699\) | 0.121375 | 0.00459083 | ||||||||
\(700\) | 0.393448 | 0.0148709 | ||||||||
\(701\) | −20.2921 | −0.766421 | −0.383211 | − | 0.923661i | \(-0.625182\pi\) | ||||
−0.383211 | + | 0.923661i | \(0.625182\pi\) | |||||||
\(702\) | 11.4233 | 0.431146 | ||||||||
\(703\) | 29.5670 | 1.11514 | ||||||||
\(704\) | −2.58964 | −0.0976009 | ||||||||
\(705\) | 3.58584 | 0.135051 | ||||||||
\(706\) | 34.9107 | 1.31388 | ||||||||
\(707\) | −4.37408 | −0.164504 | ||||||||
\(708\) | −2.84829 | −0.107045 | ||||||||
\(709\) | −31.5398 | −1.18450 | −0.592251 | − | 0.805754i | \(-0.701761\pi\) | ||||
−0.592251 | + | 0.805754i | \(0.701761\pi\) | |||||||
\(710\) | −58.8235 | −2.20761 | ||||||||
\(711\) | 4.25369 | 0.159526 | ||||||||
\(712\) | −0.716706 | −0.0268597 | ||||||||
\(713\) | 34.0892 | 1.27665 | ||||||||
\(714\) | −5.23260 | −0.195825 | ||||||||
\(715\) | 6.24509 | 0.233553 | ||||||||
\(716\) | 21.2743 | 0.795059 | ||||||||
\(717\) | 1.67581 | 0.0625844 | ||||||||
\(718\) | 38.9427 | 1.45333 | ||||||||
\(719\) | −11.0676 | −0.412753 | −0.206376 | − | 0.978473i | \(-0.566167\pi\) | ||||
−0.206376 | + | 0.978473i | \(0.566167\pi\) | |||||||
\(720\) | −30.5318 | −1.13785 | ||||||||
\(721\) | 18.6238 | 0.693588 | ||||||||
\(722\) | −10.1267 | −0.376875 | ||||||||
\(723\) | 0.186202 | 0.00692494 | ||||||||
\(724\) | −20.1845 | −0.750150 | ||||||||
\(725\) | −0.602774 | −0.0223865 | ||||||||
\(726\) | −3.82002 | −0.141774 | ||||||||
\(727\) | −49.5631 | −1.83819 | −0.919096 | − | 0.394033i | \(-0.871079\pi\) | ||||
−0.919096 | + | 0.394033i | \(0.871079\pi\) | |||||||
\(728\) | −12.6044 | −0.467149 | ||||||||
\(729\) | −25.1457 | −0.931324 | ||||||||
\(730\) | 49.7047 | 1.83965 | ||||||||
\(731\) | 6.92901 | 0.256279 | ||||||||
\(732\) | 3.20684 | 0.118528 | ||||||||
\(733\) | −2.44508 | −0.0903110 | −0.0451555 | − | 0.998980i | \(-0.514378\pi\) | ||||
−0.0451555 | + | 0.998980i | \(0.514378\pi\) | |||||||
\(734\) | 3.37162 | 0.124449 | ||||||||
\(735\) | 2.28809 | 0.0843975 | ||||||||
\(736\) | −57.0316 | −2.10221 | ||||||||
\(737\) | −2.01954 | −0.0743907 | ||||||||
\(738\) | −51.0036 | −1.87747 | ||||||||
\(739\) | 36.9067 | 1.35764 | 0.678818 | − | 0.734307i | \(-0.262492\pi\) | ||||
0.678818 | + | 0.734307i | \(0.262492\pi\) | |||||||
\(740\) | −22.3165 | −0.820371 | ||||||||
\(741\) | 4.93897 | 0.181438 | ||||||||
\(742\) | −88.8699 | −3.26252 | ||||||||
\(743\) | 40.6188 | 1.49016 | 0.745079 | − | 0.666976i | \(-0.232412\pi\) | ||||
0.745079 | + | 0.666976i | \(0.232412\pi\) | |||||||
\(744\) | 0.547632 | 0.0200772 | ||||||||
\(745\) | 0.293940 | 0.0107691 | ||||||||
\(746\) | 61.4909 | 2.25134 | ||||||||
\(747\) | −5.13142 | −0.187749 | ||||||||
\(748\) | −3.54961 | −0.129787 | ||||||||
\(749\) | 38.0579 | 1.39061 | ||||||||
\(750\) | 3.95151 | 0.144289 | ||||||||
\(751\) | −14.0406 | −0.512349 | −0.256174 | − | 0.966631i | \(-0.582462\pi\) | ||||
−0.256174 | + | 0.966631i | \(0.582462\pi\) | |||||||
\(752\) | −39.1289 | −1.42688 | ||||||||
\(753\) | −3.07207 | −0.111953 | ||||||||
\(754\) | −91.9161 | −3.34739 | ||||||||
\(755\) | −0.621532 | −0.0226199 | ||||||||
\(756\) | 6.47993 | 0.235673 | ||||||||
\(757\) | 24.6936 | 0.897505 | 0.448752 | − | 0.893656i | \(-0.351869\pi\) | ||||
0.448752 | + | 0.893656i | \(0.351869\pi\) | |||||||
\(758\) | 59.9512 | 2.17753 | ||||||||
\(759\) | 0.738419 | 0.0268029 | ||||||||
\(760\) | −7.36388 | −0.267116 | ||||||||
\(761\) | 12.6083 | 0.457051 | 0.228525 | − | 0.973538i | \(-0.426610\pi\) | ||||
0.228525 | + | 0.973538i | \(0.426610\pi\) | |||||||
\(762\) | −2.92551 | −0.105980 | ||||||||
\(763\) | −4.06816 | −0.147277 | ||||||||
\(764\) | −6.48548 | −0.234636 | ||||||||
\(765\) | −27.8068 | −1.00536 | ||||||||
\(766\) | −32.2276 | −1.16443 | ||||||||
\(767\) | −49.8021 | −1.79825 | ||||||||
\(768\) | −3.73142 | −0.134646 | ||||||||
\(769\) | 42.1413 | 1.51965 | 0.759827 | − | 0.650125i | \(-0.225283\pi\) | ||||
0.759827 | + | 0.650125i | \(0.225283\pi\) | |||||||
\(770\) | 7.82936 | 0.282150 | ||||||||
\(771\) | −1.48781 | −0.0535821 | ||||||||
\(772\) | −2.79847 | −0.100719 | ||||||||
\(773\) | −9.62659 | −0.346244 | −0.173122 | − | 0.984900i | \(-0.555386\pi\) | ||||
−0.173122 | + | 0.984900i | \(0.555386\pi\) | |||||||
\(774\) | −9.42695 | −0.338845 | ||||||||
\(775\) | −0.298895 | −0.0107366 | ||||||||
\(776\) | −10.6766 | −0.383267 | ||||||||
\(777\) | −3.94221 | −0.141426 | ||||||||
\(778\) | 1.55956 | 0.0559129 | ||||||||
\(779\) | −44.3615 | −1.58942 | ||||||||
\(780\) | −3.72782 | −0.133477 | ||||||||
\(781\) | −7.04900 | −0.252233 | ||||||||
\(782\) | −61.2394 | −2.18992 | ||||||||
\(783\) | −9.92745 | −0.354778 | ||||||||
\(784\) | −24.9677 | −0.891705 | ||||||||
\(785\) | −36.2526 | −1.29391 | ||||||||
\(786\) | −2.59903 | −0.0927044 | ||||||||
\(787\) | 50.4413 | 1.79804 | 0.899019 | − | 0.437909i | \(-0.144281\pi\) | ||||
0.899019 | + | 0.437909i | \(0.144281\pi\) | |||||||
\(788\) | −3.64243 | −0.129756 | ||||||||
\(789\) | 1.01943 | 0.0362928 | ||||||||
\(790\) | −6.17162 | −0.219576 | ||||||||
\(791\) | −30.7436 | −1.09312 | ||||||||
\(792\) | −1.01456 | −0.0360508 | ||||||||
\(793\) | 56.0713 | 1.99115 | ||||||||
\(794\) | 41.7179 | 1.48051 | ||||||||
\(795\) | 5.52185 | 0.195840 | ||||||||
\(796\) | −25.7062 | −0.911131 | ||||||||
\(797\) | 34.3043 | 1.21512 | 0.607561 | − | 0.794273i | \(-0.292148\pi\) | ||||
0.607561 | + | 0.794273i | \(0.292148\pi\) | |||||||
\(798\) | 6.19190 | 0.219191 | ||||||||
\(799\) | −35.6366 | −1.26073 | ||||||||
\(800\) | 0.500053 | 0.0176795 | ||||||||
\(801\) | 3.20252 | 0.113155 | ||||||||
\(802\) | 29.5967 | 1.04510 | ||||||||
\(803\) | 5.95627 | 0.210192 | ||||||||
\(804\) | 1.20550 | 0.0425148 | ||||||||
\(805\) | 61.1177 | 2.15412 | ||||||||
\(806\) | −45.5780 | −1.60542 | ||||||||
\(807\) | 0.437011 | 0.0153835 | ||||||||
\(808\) | −0.822378 | −0.0289312 | ||||||||
\(809\) | −43.9886 | −1.54656 | −0.773279 | − | 0.634066i | \(-0.781385\pi\) | ||||
−0.773279 | + | 0.634066i | \(0.781385\pi\) | |||||||
\(810\) | 37.3838 | 1.31353 | ||||||||
\(811\) | −43.0270 | −1.51088 | −0.755440 | − | 0.655217i | \(-0.772577\pi\) | ||||
−0.755440 | + | 0.655217i | \(0.772577\pi\) | |||||||
\(812\) | −52.1398 | −1.82975 | ||||||||
\(813\) | −0.298484 | −0.0104683 | ||||||||
\(814\) | −5.91034 | −0.207157 | ||||||||
\(815\) | 41.6937 | 1.46047 | ||||||||
\(816\) | −3.54776 | −0.124196 | ||||||||
\(817\) | −8.19930 | −0.286857 | ||||||||
\(818\) | −49.7638 | −1.73995 | ||||||||
\(819\) | 56.3212 | 1.96802 | ||||||||
\(820\) | 33.4830 | 1.16928 | ||||||||
\(821\) | 18.7704 | 0.655090 | 0.327545 | − | 0.944836i | \(-0.393779\pi\) | ||||
0.327545 | + | 0.944836i | \(0.393779\pi\) | |||||||
\(822\) | 2.11858 | 0.0738939 | ||||||||
\(823\) | 27.1588 | 0.946695 | 0.473348 | − | 0.880876i | \(-0.343045\pi\) | ||||
0.473348 | + | 0.880876i | \(0.343045\pi\) | |||||||
\(824\) | 3.50150 | 0.121981 | ||||||||
\(825\) | −0.00647446 | −0.000225412 0 | ||||||||
\(826\) | −62.4360 | −2.17243 | ||||||||
\(827\) | 41.5157 | 1.44364 | 0.721821 | − | 0.692079i | \(-0.243305\pi\) | ||||
0.721821 | + | 0.692079i | \(0.243305\pi\) | |||||||
\(828\) | 37.6983 | 1.31011 | ||||||||
\(829\) | −30.6349 | −1.06399 | −0.531997 | − | 0.846746i | \(-0.678558\pi\) | ||||
−0.531997 | + | 0.846746i | \(0.678558\pi\) | |||||||
\(830\) | 7.44510 | 0.258423 | ||||||||
\(831\) | 4.03640 | 0.140021 | ||||||||
\(832\) | 27.0283 | 0.937039 | ||||||||
\(833\) | −22.7394 | −0.787872 | ||||||||
\(834\) | 5.32565 | 0.184412 | ||||||||
\(835\) | −34.8959 | −1.20762 | ||||||||
\(836\) | 4.20036 | 0.145272 | ||||||||
\(837\) | −4.92267 | −0.170153 | ||||||||
\(838\) | 63.4916 | 2.19328 | ||||||||
\(839\) | 30.2456 | 1.04419 | 0.522097 | − | 0.852886i | \(-0.325150\pi\) | ||||
0.522097 | + | 0.852886i | \(0.325150\pi\) | |||||||
\(840\) | 0.981836 | 0.0338766 | ||||||||
\(841\) | 50.8798 | 1.75447 | ||||||||
\(842\) | −5.55375 | −0.191395 | ||||||||
\(843\) | −5.00902 | −0.172520 | ||||||||
\(844\) | 10.8421 | 0.373202 | ||||||||
\(845\) | −35.9163 | −1.23556 | ||||||||
\(846\) | 48.4838 | 1.66691 | ||||||||
\(847\) | −37.8884 | −1.30186 | ||||||||
\(848\) | −60.2547 | −2.06915 | ||||||||
\(849\) | −0.724755 | −0.0248735 | ||||||||
\(850\) | 0.536947 | 0.0184171 | ||||||||
\(851\) | −46.1374 | −1.58157 | ||||||||
\(852\) | 4.20769 | 0.144153 | ||||||||
\(853\) | 42.7734 | 1.46453 | 0.732267 | − | 0.681018i | \(-0.238462\pi\) | ||||
0.732267 | + | 0.681018i | \(0.238462\pi\) | |||||||
\(854\) | 70.2956 | 2.40546 | ||||||||
\(855\) | 32.9046 | 1.12532 | ||||||||
\(856\) | 7.15534 | 0.244564 | ||||||||
\(857\) | −18.8048 | −0.642361 | −0.321181 | − | 0.947018i | \(-0.604080\pi\) | ||||
−0.321181 | + | 0.947018i | \(0.604080\pi\) | |||||||
\(858\) | −0.987281 | −0.0337052 | ||||||||
\(859\) | −8.22676 | −0.280693 | −0.140347 | − | 0.990102i | \(-0.544822\pi\) | ||||
−0.140347 | + | 0.990102i | \(0.544822\pi\) | |||||||
\(860\) | 6.18864 | 0.211031 | ||||||||
\(861\) | 5.91478 | 0.201575 | ||||||||
\(862\) | 54.4493 | 1.85455 | ||||||||
\(863\) | −41.8464 | −1.42447 | −0.712235 | − | 0.701941i | \(-0.752317\pi\) | ||||
−0.712235 | + | 0.701941i | \(0.752317\pi\) | |||||||
\(864\) | 8.23567 | 0.280183 | ||||||||
\(865\) | 0.824887 | 0.0280470 | ||||||||
\(866\) | 55.2937 | 1.87896 | ||||||||
\(867\) | −0.0656832 | −0.00223072 | ||||||||
\(868\) | −25.8543 | −0.877552 | ||||||||
\(869\) | −0.739564 | −0.0250880 | ||||||||
\(870\) | 7.15994 | 0.242745 | ||||||||
\(871\) | 21.0781 | 0.714204 | ||||||||
\(872\) | −0.764862 | −0.0259015 | ||||||||
\(873\) | 47.7071 | 1.61464 | ||||||||
\(874\) | 72.4664 | 2.45121 | ||||||||
\(875\) | 39.1926 | 1.32495 | ||||||||
\(876\) | −3.55541 | −0.120126 | ||||||||
\(877\) | −6.11483 | −0.206483 | −0.103242 | − | 0.994656i | \(-0.532921\pi\) | ||||
−0.103242 | + | 0.994656i | \(0.532921\pi\) | |||||||
\(878\) | 17.0511 | 0.575446 | ||||||||
\(879\) | 1.03787 | 0.0350065 | ||||||||
\(880\) | 5.30838 | 0.178946 | ||||||||
\(881\) | −13.5157 | −0.455355 | −0.227678 | − | 0.973737i | \(-0.573113\pi\) | ||||
−0.227678 | + | 0.973737i | \(0.573113\pi\) | |||||||
\(882\) | 30.9370 | 1.04170 | ||||||||
\(883\) | 38.5489 | 1.29727 | 0.648637 | − | 0.761098i | \(-0.275339\pi\) | ||||
0.648637 | + | 0.761098i | \(0.275339\pi\) | |||||||
\(884\) | 37.0476 | 1.24604 | ||||||||
\(885\) | 3.87941 | 0.130405 | ||||||||
\(886\) | −47.4397 | −1.59377 | ||||||||
\(887\) | 40.8386 | 1.37123 | 0.685613 | − | 0.727966i | \(-0.259534\pi\) | ||||
0.685613 | + | 0.727966i | \(0.259534\pi\) | |||||||
\(888\) | −0.741183 | −0.0248725 | ||||||||
\(889\) | −29.0163 | −0.973177 | ||||||||
\(890\) | −4.64649 | −0.155751 | ||||||||
\(891\) | 4.47982 | 0.150080 | ||||||||
\(892\) | 10.8058 | 0.361806 | ||||||||
\(893\) | 42.1698 | 1.41116 | ||||||||
\(894\) | −0.0464686 | −0.00155414 | ||||||||
\(895\) | −28.9759 | −0.968557 | ||||||||
\(896\) | −18.4567 | −0.616596 | ||||||||
\(897\) | −7.70694 | −0.257327 | ||||||||
\(898\) | −22.7921 | −0.760581 | ||||||||
\(899\) | 39.6096 | 1.32105 | ||||||||
\(900\) | −0.330539 | −0.0110180 | ||||||||
\(901\) | −54.8769 | −1.82822 | ||||||||
\(902\) | 8.86770 | 0.295262 | ||||||||
\(903\) | 1.09322 | 0.0363802 | ||||||||
\(904\) | −5.78016 | −0.192245 | ||||||||
\(905\) | 27.4915 | 0.913848 | ||||||||
\(906\) | 0.0982574 | 0.00326438 | ||||||||
\(907\) | −34.3321 | −1.13998 | −0.569989 | − | 0.821652i | \(-0.693053\pi\) | ||||
−0.569989 | + | 0.821652i | \(0.693053\pi\) | |||||||
\(908\) | 26.7209 | 0.886763 | ||||||||
\(909\) | 3.67470 | 0.121882 | ||||||||
\(910\) | −81.7156 | −2.70885 | ||||||||
\(911\) | 49.0410 | 1.62480 | 0.812400 | − | 0.583100i | \(-0.198160\pi\) | ||||
0.812400 | + | 0.583100i | \(0.198160\pi\) | |||||||
\(912\) | 4.19817 | 0.139015 | ||||||||
\(913\) | 0.892169 | 0.0295265 | ||||||||
\(914\) | −16.1346 | −0.533686 | ||||||||
\(915\) | −4.36776 | −0.144394 | ||||||||
\(916\) | 0.0344458 | 0.00113812 | ||||||||
\(917\) | −25.7782 | −0.851271 | ||||||||
\(918\) | 8.84331 | 0.291873 | ||||||||
\(919\) | 48.7329 | 1.60755 | 0.803775 | − | 0.594934i | \(-0.202822\pi\) | ||||
0.803775 | + | 0.594934i | \(0.202822\pi\) | |||||||
\(920\) | 11.4909 | 0.378842 | ||||||||
\(921\) | −4.29745 | −0.141606 | ||||||||
\(922\) | −44.5171 | −1.46609 | ||||||||
\(923\) | 73.5710 | 2.42162 | ||||||||
\(924\) | −0.560040 | −0.0184240 | ||||||||
\(925\) | 0.404533 | 0.0133010 | ||||||||
\(926\) | −3.18367 | −0.104622 | ||||||||
\(927\) | −15.6461 | −0.513884 | ||||||||
\(928\) | −66.2672 | −2.17533 | ||||||||
\(929\) | 52.9031 | 1.73569 | 0.867847 | − | 0.496832i | \(-0.165504\pi\) | ||||
0.867847 | + | 0.496832i | \(0.165504\pi\) | |||||||
\(930\) | 3.55036 | 0.116421 | ||||||||
\(931\) | 26.9081 | 0.881879 | ||||||||
\(932\) | −1.07735 | −0.0352899 | ||||||||
\(933\) | 2.79088 | 0.0913693 | ||||||||
\(934\) | 12.7369 | 0.416765 | ||||||||
\(935\) | 4.83461 | 0.158109 | ||||||||
\(936\) | 10.5891 | 0.346114 | ||||||||
\(937\) | −16.1310 | −0.526976 | −0.263488 | − | 0.964663i | \(-0.584873\pi\) | ||||
−0.263488 | + | 0.964663i | \(0.584873\pi\) | |||||||
\(938\) | 26.4252 | 0.862814 | ||||||||
\(939\) | 0.430280 | 0.0140416 | ||||||||
\(940\) | −31.8288 | −1.03814 | ||||||||
\(941\) | 10.7225 | 0.349544 | 0.174772 | − | 0.984609i | \(-0.444081\pi\) | ||||
0.174772 | + | 0.984609i | \(0.444081\pi\) | |||||||
\(942\) | 5.73114 | 0.186731 | ||||||||
\(943\) | 69.2233 | 2.25422 | ||||||||
\(944\) | −42.3323 | −1.37780 | ||||||||
\(945\) | −8.82574 | −0.287101 | ||||||||
\(946\) | 1.63901 | 0.0532887 | ||||||||
\(947\) | −21.9984 | −0.714851 | −0.357426 | − | 0.933942i | \(-0.616345\pi\) | ||||
−0.357426 | + | 0.933942i | \(0.616345\pi\) | |||||||
\(948\) | 0.441460 | 0.0143380 | ||||||||
\(949\) | −62.1660 | −2.01800 | ||||||||
\(950\) | −0.635386 | −0.0206146 | ||||||||
\(951\) | 3.41923 | 0.110876 | ||||||||
\(952\) | −9.75762 | −0.316246 | ||||||||
\(953\) | −40.5214 | −1.31262 | −0.656309 | − | 0.754492i | \(-0.727883\pi\) | ||||
−0.656309 | + | 0.754492i | \(0.727883\pi\) | |||||||
\(954\) | 74.6603 | 2.41722 | ||||||||
\(955\) | 8.83330 | 0.285839 | ||||||||
\(956\) | −14.8749 | −0.481090 | ||||||||
\(957\) | 0.857998 | 0.0277351 | ||||||||
\(958\) | 26.1651 | 0.845356 | ||||||||
\(959\) | 21.0129 | 0.678542 | ||||||||
\(960\) | −2.10541 | −0.0679518 | ||||||||
\(961\) | −11.3590 | −0.366419 | ||||||||
\(962\) | 61.6867 | 1.98886 | ||||||||
\(963\) | −31.9728 | −1.03031 | ||||||||
\(964\) | −1.65278 | −0.0532323 | ||||||||
\(965\) | 3.81154 | 0.122698 | ||||||||
\(966\) | −9.66205 | −0.310871 | ||||||||
\(967\) | −46.5645 | −1.49741 | −0.748706 | − | 0.662902i | \(-0.769324\pi\) | ||||
−0.748706 | + | 0.662902i | \(0.769324\pi\) | |||||||
\(968\) | −7.12347 | −0.228957 | ||||||||
\(969\) | 3.82348 | 0.122828 | ||||||||
\(970\) | −69.2175 | −2.22244 | ||||||||
\(971\) | 2.03099 | 0.0651775 | 0.0325887 | − | 0.999469i | \(-0.489625\pi\) | ||||
0.0325887 | + | 0.999469i | \(0.489625\pi\) | |||||||
\(972\) | −8.18159 | −0.262425 | ||||||||
\(973\) | 52.8218 | 1.69339 | ||||||||
\(974\) | −61.0892 | −1.95743 | ||||||||
\(975\) | 0.0675745 | 0.00216412 | ||||||||
\(976\) | 47.6611 | 1.52560 | ||||||||
\(977\) | −45.7170 | −1.46262 | −0.731308 | − | 0.682047i | \(-0.761090\pi\) | ||||
−0.731308 | + | 0.682047i | \(0.761090\pi\) | |||||||
\(978\) | −6.59131 | −0.210767 | ||||||||
\(979\) | −0.556803 | −0.0177955 | ||||||||
\(980\) | −20.3096 | −0.648767 | ||||||||
\(981\) | 3.41770 | 0.109119 | ||||||||
\(982\) | 19.2174 | 0.613252 | ||||||||
\(983\) | −47.0190 | −1.49967 | −0.749837 | − | 0.661623i | \(-0.769868\pi\) | ||||
−0.749837 | + | 0.661623i | \(0.769868\pi\) | |||||||
\(984\) | 1.11205 | 0.0354508 | ||||||||
\(985\) | 4.96103 | 0.158071 | ||||||||
\(986\) | −71.1564 | −2.26608 | ||||||||
\(987\) | −5.62256 | −0.178968 | ||||||||
\(988\) | −43.8395 | −1.39472 | ||||||||
\(989\) | 12.7945 | 0.406841 | ||||||||
\(990\) | −6.57751 | −0.209047 | ||||||||
\(991\) | 54.4626 | 1.73006 | 0.865031 | − | 0.501718i | \(-0.167298\pi\) | ||||
0.865031 | + | 0.501718i | \(0.167298\pi\) | |||||||
\(992\) | −32.8596 | −1.04329 | ||||||||
\(993\) | 1.20647 | 0.0382860 | ||||||||
\(994\) | 92.2346 | 2.92550 | ||||||||
\(995\) | 35.0121 | 1.10996 | ||||||||
\(996\) | −0.532553 | −0.0168746 | ||||||||
\(997\) | 13.5868 | 0.430297 | 0.215149 | − | 0.976581i | \(-0.430976\pi\) | ||||
0.215149 | + | 0.976581i | \(0.430976\pi\) | |||||||
\(998\) | −17.4742 | −0.553137 | ||||||||
\(999\) | 6.66250 | 0.210792 |
(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 | 241.2.a.a.1.2 | ✓ | 7 | |
3.2 | odd | 2 | 2169.2.a.e.1.6 | 7 | |||
4.3 | odd | 2 | 3856.2.a.j.1.3 | 7 | |||
5.4 | even | 2 | 6025.2.a.f.1.6 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
241.2.a.a.1.2 | ✓ | 7 | 1.1 | even | 1 | trivial | |
2169.2.a.e.1.6 | 7 | 3.2 | odd | 2 | |||
3856.2.a.j.1.3 | 7 | 4.3 | odd | 2 | |||
6025.2.a.f.1.6 | 7 | 5.4 | even | 2 |