Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1336,2,Mod(1,1336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1336, 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("1336.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1336 = 2^{3} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1336.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: | \(10.6680137100\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 13x^{7} + 8x^{6} + 56x^{5} - 15x^{4} - 81x^{3} + 2x^{2} + 13x + 1 \) |
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 | 1.1 | ||
Root | \(2.70492\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1336.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.70492 | −1.56168 | −0.780842 | − | 0.624728i | \(-0.785210\pi\) | ||||
−0.780842 | + | 0.624728i | \(0.785210\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.24392 | −1.89794 | −0.948969 | − | 0.315370i | \(-0.897871\pi\) | ||||
−0.948969 | + | 0.315370i | \(0.897871\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.27743 | 0.482824 | 0.241412 | − | 0.970423i | \(-0.422390\pi\) | ||||
0.241412 | + | 0.970423i | \(0.422390\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.31658 | 1.43886 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.403841 | −0.121763 | −0.0608813 | − | 0.998145i | \(-0.519391\pi\) | ||||
−0.0608813 | + | 0.998145i | \(0.519391\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.48621 | 0.412200 | 0.206100 | − | 0.978531i | \(-0.433923\pi\) | ||||
0.206100 | + | 0.978531i | \(0.433923\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 11.4794 | 2.96398 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.32654 | 0.806805 | 0.403403 | − | 0.915023i | \(-0.367827\pi\) | ||||
0.403403 | + | 0.915023i | \(0.367827\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.12675 | 1.40557 | 0.702786 | − | 0.711401i | \(-0.251939\pi\) | ||||
0.702786 | + | 0.711401i | \(0.251939\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.45535 | −0.754019 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.20028 | −0.875819 | −0.437910 | − | 0.899019i | \(-0.644281\pi\) | ||||
−0.437910 | + | 0.899019i | \(0.644281\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13.0108 | 2.60217 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.56123 | −0.685359 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.76774 | −1.81382 | −0.906912 | − | 0.421320i | \(-0.861567\pi\) | ||||
−0.906912 | + | 0.421320i | \(0.861567\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.32050 | 0.596379 | 0.298189 | − | 0.954507i | \(-0.403617\pi\) | ||||
0.298189 | + | 0.954507i | \(0.403617\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.09236 | 0.190155 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.42131 | −0.916369 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.09030 | −0.836839 | −0.418420 | − | 0.908254i | \(-0.637416\pi\) | ||||
−0.418420 | + | 0.908254i | \(0.637416\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.02007 | −0.643727 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.16778 | −0.650898 | −0.325449 | − | 0.945560i | \(-0.605515\pi\) | ||||
−0.325449 | + | 0.945560i | \(0.605515\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.20912 | 1.40438 | 0.702189 | − | 0.711991i | \(-0.252206\pi\) | ||||
0.702189 | + | 0.711991i | \(0.252206\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −18.3192 | −2.73086 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.54157 | 0.224860 | 0.112430 | − | 0.993660i | \(-0.464137\pi\) | ||||
0.112430 | + | 0.993660i | \(0.464137\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.36817 | −0.766881 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.99803 | −1.25998 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.932016 | −0.128022 | −0.0640111 | − | 0.997949i | \(-0.520389\pi\) | ||||
−0.0640111 | + | 0.997949i | \(0.520389\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.71387 | 0.231098 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −16.5723 | −2.19506 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.70002 | −0.221324 | −0.110662 | − | 0.993858i | \(-0.535297\pi\) | ||||
−0.110662 | + | 0.993858i | \(0.535297\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.98119 | −1.27796 | −0.638980 | − | 0.769223i | \(-0.720643\pi\) | ||||
−0.638980 | + | 0.769223i | \(0.720643\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.51413 | 0.694715 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.30735 | −0.782330 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.92232 | −0.601357 | −0.300679 | − | 0.953726i | \(-0.597213\pi\) | ||||
−0.300679 | + | 0.953726i | \(0.597213\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11.3614 | 1.36775 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.72094 | 0.797629 | 0.398814 | − | 0.917032i | \(-0.369422\pi\) | ||||
0.398814 | + | 0.917032i | \(0.369422\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.05470 | 0.825690 | 0.412845 | − | 0.910801i | \(-0.364535\pi\) | ||||
0.412845 | + | 0.910801i | \(0.364535\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −35.1932 | −4.06376 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.515879 | −0.0587899 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.843450 | −0.0948956 | −0.0474478 | − | 0.998874i | \(-0.515109\pi\) | ||||
−0.0474478 | + | 0.998874i | \(0.515109\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.31690 | −0.368545 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.04828 | 0.444357 | 0.222178 | − | 0.975006i | \(-0.428683\pi\) | ||||
0.222178 | + | 0.975006i | \(0.428683\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.1176 | −1.53127 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 26.4209 | 2.83262 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.42451 | 0.150997 | 0.0754986 | − | 0.997146i | \(-0.475945\pi\) | ||||
0.0754986 | + | 0.997146i | \(0.475945\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.89853 | 0.199020 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.98167 | −0.931356 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −26.0014 | −2.66769 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.5450 | −1.47682 | −0.738409 | − | 0.674353i | \(-0.764423\pi\) | ||||
−0.738409 | + | 0.674353i | \(0.764423\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.74321 | −0.175199 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.7304 | 1.56524 | 0.782618 | − | 0.622503i | \(-0.213884\pi\) | ||||
0.782618 | + | 0.622503i | \(0.213884\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.86506 | −0.774967 | −0.387484 | − | 0.921877i | \(-0.626656\pi\) | ||||
−0.387484 | + | 0.921877i | \(0.626656\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 14.6642 | 1.43108 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.9508 | −1.25200 | −0.625999 | − | 0.779823i | \(-0.715309\pi\) | ||||
−0.625999 | + | 0.779823i | \(0.715309\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.2339 | −1.17180 | −0.585898 | − | 0.810385i | \(-0.699258\pi\) | ||||
−0.585898 | + | 0.810385i | \(0.699258\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.7688 | 1.30688 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.89621 | −0.366525 | −0.183262 | − | 0.983064i | \(-0.558666\pi\) | ||||
−0.183262 | + | 0.983064i | \(0.558666\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 17.8256 | 1.66225 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.41533 | 0.593098 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.24943 | 0.389545 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8369 | −0.985174 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.2735 | 1.01650 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −33.9973 | −3.04081 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.72218 | −0.330290 | −0.165145 | − | 0.986269i | \(-0.552809\pi\) | ||||
−0.165145 | + | 0.986269i | \(0.552809\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −24.9099 | −2.19320 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.5303 | 1.53163 | 0.765815 | − | 0.643061i | \(-0.222336\pi\) | ||||
0.765815 | + | 0.643061i | \(0.222336\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.82650 | 0.678644 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 15.1136 | 1.30077 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.75708 | 0.833604 | 0.416802 | − | 0.908997i | \(-0.363151\pi\) | ||||
0.416802 | + | 0.908997i | \(0.363151\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.10285 | −0.432818 | −0.216409 | − | 0.976303i | \(-0.569435\pi\) | ||||
−0.216409 | + | 0.976303i | \(0.569435\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.16981 | −0.351161 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.600192 | −0.0501905 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 41.4535 | 3.44252 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 14.5204 | 1.19763 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −22.9309 | −1.87857 | −0.939287 | − | 0.343134i | \(-0.888512\pi\) | ||||
−0.939287 | + | 0.343134i | \(0.888512\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.96454 | −0.729524 | −0.364762 | − | 0.931101i | \(-0.618850\pi\) | ||||
−0.364762 | + | 0.931101i | \(0.618850\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.3593 | 1.16088 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.0919 | −1.13189 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.77912 | 0.301607 | 0.150803 | − | 0.988564i | \(-0.451814\pi\) | ||||
0.150803 | + | 0.988564i | \(0.451814\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.52103 | 0.199930 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.36557 | −0.422866 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.8808 | 1.16555 | 0.582776 | − | 0.812633i | \(-0.301966\pi\) | ||||
0.582776 | + | 0.812633i | \(0.301966\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.63587 | −0.360902 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.7912 | −0.830091 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 26.4466 | 2.02242 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.4547 | 1.78323 | 0.891615 | − | 0.452794i | \(-0.149573\pi\) | ||||
0.891615 | + | 0.452794i | \(0.149573\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 16.6204 | 1.25639 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.59841 | 0.345638 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.88961 | −0.739184 | −0.369592 | − | 0.929194i | \(-0.620503\pi\) | ||||
−0.369592 | + | 0.929194i | \(0.620503\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.80485 | −0.654460 | −0.327230 | − | 0.944945i | \(-0.606115\pi\) | ||||
−0.327230 | + | 0.944945i | \(0.606115\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 26.9983 | 1.99577 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 21.6028 | 1.58827 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.34339 | −0.0982387 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.54923 | −0.330907 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.9396 | 0.863916 | 0.431958 | − | 0.901894i | \(-0.357823\pi\) | ||||
0.431958 | + | 0.901894i | \(0.357823\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.9297 | 0.786738 | 0.393369 | − | 0.919381i | \(-0.371310\pi\) | ||||
0.393369 | + | 0.919381i | \(0.371310\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 17.0609 | 1.22175 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.63480 | −0.686451 | −0.343226 | − | 0.939253i | \(-0.611520\pi\) | ||||
−0.343226 | + | 0.939253i | \(0.611520\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.1255 | 1.28489 | 0.642443 | − | 0.766334i | \(-0.277921\pi\) | ||||
0.642443 | + | 0.766334i | \(0.277921\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.3145 | 0.939130 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.4776 | −0.875757 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.6877 | 1.23536 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −18.1308 | −1.26018 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.47423 | −0.171146 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.4655 | −1.20237 | −0.601187 | − | 0.799108i | \(-0.705305\pi\) | ||||
−0.601187 | + | 0.799108i | \(0.705305\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −18.1796 | −1.24564 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −39.0827 | −2.66542 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.24171 | 0.287946 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −19.0824 | −1.28947 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.94394 | 0.332565 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.166086 | −0.0111219 | −0.00556096 | − | 0.999985i | \(-0.501770\pi\) | ||||
−0.00556096 | + | 0.999985i | \(0.501770\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 56.1622 | 3.74415 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −26.7551 | −1.77580 | −0.887898 | − | 0.460041i | \(-0.847835\pi\) | ||||
−0.887898 | + | 0.460041i | \(0.847835\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.5428 | 1.75400 | 0.877000 | − | 0.480491i | \(-0.159542\pi\) | ||||
0.877000 | + | 0.480491i | \(0.159542\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.39541 | 0.0918112 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 27.6384 | 1.81065 | 0.905325 | − | 0.424719i | \(-0.139627\pi\) | ||||
0.905325 | + | 0.424719i | \(0.139627\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.54227 | −0.426771 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.28146 | 0.148197 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −30.3260 | −1.96163 | −0.980813 | − | 0.194951i | \(-0.937545\pi\) | ||||
−0.980813 | + | 0.194951i | \(0.937545\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.6851 | −1.59011 | −0.795054 | − | 0.606539i | \(-0.792558\pi\) | ||||
−0.795054 | + | 0.606539i | \(0.792558\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 19.6556 | 1.26091 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 22.7821 | 1.45549 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.10563 | 0.579377 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.9503 | −0.693945 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.1189 | −1.64861 | −0.824304 | − | 0.566147i | \(-0.808434\pi\) | ||||
−0.824304 | + | 0.566147i | \(0.808434\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.69624 | 0.106642 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 38.1869 | 2.39135 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.37604 | −0.210592 | −0.105296 | − | 0.994441i | \(-0.533579\pi\) | ||||
−0.105296 | + | 0.994441i | \(0.533579\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.50251 | −0.404046 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −42.1632 | −2.60984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −25.2221 | −1.55526 | −0.777631 | − | 0.628721i | \(-0.783579\pi\) | ||||
−0.777631 | + | 0.628721i | \(0.783579\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.95540 | 0.242978 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.85317 | −0.235810 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.0869 | −1.10278 | −0.551390 | − | 0.834248i | \(-0.685902\pi\) | ||||
−0.551390 | + | 0.834248i | \(0.685902\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.4229 | −1.42284 | −0.711421 | − | 0.702766i | \(-0.751948\pi\) | ||||
−0.711421 | + | 0.702766i | \(0.751948\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.13537 | −0.310807 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.25430 | −0.316846 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.90502 | 0.354798 | 0.177399 | − | 0.984139i | \(-0.443232\pi\) | ||||
0.177399 | + | 0.984139i | \(0.443232\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 14.3332 | 0.858105 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −30.9175 | −1.84439 | −0.922193 | − | 0.386730i | \(-0.873604\pi\) | ||||
−0.922193 | + | 0.386730i | \(0.873604\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.55188 | −0.211137 | −0.105569 | − | 0.994412i | \(-0.533666\pi\) | ||||
−0.105569 | + | 0.994412i | \(0.533666\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 70.3317 | 4.16609 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.32405 | −0.314269 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.93410 | −0.349065 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 39.3429 | 2.30632 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.2122 | 1.12239 | 0.561195 | − | 0.827683i | \(-0.310342\pi\) | ||||
0.561195 | + | 0.827683i | \(0.310342\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.21475 | 0.420059 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.43817 | 0.0834510 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.24250 | −0.361013 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.7640 | 0.678067 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −42.5495 | −2.44440 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 42.3593 | 2.42549 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.07774 | −0.0615096 | −0.0307548 | − | 0.999527i | \(-0.509791\pi\) | ||||
−0.0307548 | + | 0.999527i | \(0.509791\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 21.2743 | 1.21025 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.71693 | 0.324177 | 0.162089 | − | 0.986776i | \(-0.448177\pi\) | ||||
0.162089 | + | 0.986776i | \(0.448177\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.6515 | −0.658582 | −0.329291 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329291 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −23.4015 | −1.31853 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.79584 | −0.213196 | −0.106598 | − | 0.994302i | \(-0.533996\pi\) | ||||
−0.106598 | + | 0.994302i | \(0.533996\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.94461 | 0.220856 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 35.0308 | 1.95523 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.3809 | 1.13402 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.3368 | 1.07261 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 33.0917 | 1.82998 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.96924 | 0.108568 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 34.3425 | 1.88764 | 0.943818 | − | 0.330466i | \(-0.107206\pi\) | ||||
0.943818 | + | 0.330466i | \(0.107206\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −21.9726 | −1.20409 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 20.8899 | 1.14134 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.31445 | −0.289497 | −0.144748 | − | 0.989469i | \(-0.546237\pi\) | ||||
−0.144748 | + | 0.989469i | \(0.546237\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.5389 | 0.572396 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.34095 | −0.0726166 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.7995 | −0.853092 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −48.2169 | −2.59591 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.5429 | 0.780704 | 0.390352 | − | 0.920666i | \(-0.372353\pi\) | ||||
0.390352 | + | 0.920666i | \(0.372353\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.9375 | −0.638999 | −0.319499 | − | 0.947587i | \(-0.603515\pi\) | ||||
−0.319499 | + | 0.947587i | \(0.603515\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.29273 | −0.282505 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 31.5607 | 1.67980 | 0.839902 | − | 0.542738i | \(-0.182612\pi\) | ||||
0.839902 | + | 0.542738i | \(0.182612\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −28.5231 | −1.51385 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −11.4944 | −0.608346 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.8047 | 0.886916 | 0.443458 | − | 0.896295i | \(-0.353752\pi\) | ||||
0.443458 | + | 0.896295i | \(0.353752\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.5371 | 0.975634 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 29.3129 | 1.53853 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −29.9396 | −1.56711 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.86034 | −0.514705 | −0.257353 | − | 0.966318i | \(-0.582850\pi\) | ||||
−0.257353 | + | 0.966318i | \(0.582850\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −17.9905 | −0.936550 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.19059 | −0.0618122 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.70042 | −0.243379 | −0.121689 | − | 0.992568i | \(-0.538831\pi\) | ||||
−0.121689 | + | 0.992568i | \(0.538831\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 91.9599 | 4.74879 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −14.5169 | −0.747659 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.2996 | 0.734523 | 0.367261 | − | 0.930118i | \(-0.380295\pi\) | ||||
0.367261 | + | 0.930118i | \(0.380295\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.0682 | 0.515808 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.0374 | −0.666179 | −0.333089 | − | 0.942895i | \(-0.608091\pi\) | ||||
−0.333089 | + | 0.942895i | \(0.608091\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.18935 | 0.111579 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 39.7519 | 2.02070 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.2817 | 0.521305 | 0.260652 | − | 0.965433i | \(-0.416062\pi\) | ||||
0.260652 | + | 0.965433i | \(0.416062\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.9724 | −0.706616 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −47.4180 | −2.39192 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.57953 | 0.180106 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.1577 | −0.911311 | −0.455656 | − | 0.890156i | \(-0.650595\pi\) | ||||
−0.455656 | + | 0.890156i | \(0.650595\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −21.1700 | −1.05983 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.93888 | −0.446386 | −0.223193 | − | 0.974774i | \(-0.571648\pi\) | ||||
−0.223193 | + | 0.974774i | \(0.571648\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.93495 | 0.245828 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14.0767 | 0.699475 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.05567 | 0.101896 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.3707 | −0.611694 | −0.305847 | − | 0.952081i | \(-0.598940\pi\) | ||||
−0.305847 | + | 0.952081i | \(0.598940\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −26.3921 | −1.30183 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.17166 | −0.106860 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.1806 | −0.843362 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.8028 | 0.675926 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.2192 | −1.42745 | −0.713726 | − | 0.700425i | \(-0.752994\pi\) | ||||
−0.713726 | + | 0.700425i | \(0.752994\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.49591 | 0.219117 | 0.109559 | − | 0.993980i | \(-0.465056\pi\) | ||||
0.109559 | + | 0.993980i | \(0.465056\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.65428 | 0.323542 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 43.2811 | 2.09944 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.7503 | −0.617030 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.62347 | 0.0783818 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.46354 | 0.0704962 | 0.0352481 | − | 0.999379i | \(-0.488778\pi\) | ||||
0.0352481 | + | 0.999379i | \(0.488778\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.4259 | −0.837434 | −0.418717 | − | 0.908117i | \(-0.637520\pi\) | ||||
−0.418717 | + | 0.908117i | \(0.637520\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −112.128 | −5.37614 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −25.7341 | −1.23103 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.55586 | 0.169712 | 0.0848559 | − | 0.996393i | \(-0.472957\pi\) | ||||
0.0848559 | + | 0.996393i | \(0.472957\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −23.1721 | −1.10343 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.4618 | −1.35226 | −0.676131 | − | 0.736781i | \(-0.736345\pi\) | ||||
−0.676131 | + | 0.736781i | \(0.736345\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.04548 | −0.286583 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 62.0262 | 2.93374 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.59661 | −0.452892 | −0.226446 | − | 0.974024i | \(-0.572711\pi\) | ||||
−0.226446 | + | 0.974024i | \(0.572711\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.68312 | 0.0792550 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 24.2483 | 1.13929 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.05721 | −0.377728 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.7289 | −1.01644 | −0.508218 | − | 0.861228i | \(-0.669696\pi\) | ||||
−0.508218 | + | 0.861228i | \(0.669696\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11.8466 | −0.552951 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.8932 | 1.34569 | 0.672845 | − | 0.739783i | \(-0.265072\pi\) | ||||
0.672845 | + | 0.739783i | \(0.265072\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.4238 | −1.08860 | −0.544299 | − | 0.838891i | \(-0.683204\pi\) | ||||
−0.544299 | + | 0.838891i | \(0.683204\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 38.1175 | 1.76765 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 31.5852 | 1.46159 | 0.730793 | − | 0.682599i | \(-0.239150\pi\) | ||||
0.730793 | + | 0.682599i | \(0.239150\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.28793 | −0.290350 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.2222 | −0.471015 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.71902 | −0.171001 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 79.7141 | 3.65753 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.02312 | −0.184206 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.7955 | −1.54416 | −0.772078 | − | 0.635527i | \(-0.780783\pi\) | ||||
−0.772078 | + | 0.635527i | \(0.780783\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.56524 | −0.344945 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 14.5134 | 0.660384 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 61.7277 | 2.80291 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 38.2331 | 1.73251 | 0.866253 | − | 0.499605i | \(-0.166521\pi\) | ||||
0.866253 | + | 0.499605i | \(0.166521\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −40.2513 | −1.82023 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.32648 | 0.104992 | 0.0524962 | − | 0.998621i | \(-0.483282\pi\) | ||||
0.0524962 | + | 0.998621i | \(0.483282\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −32.4928 | −1.46340 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.39803 | 0.332517 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.58554 | 0.385114 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.8384 | −1.42528 | −0.712642 | − | 0.701528i | \(-0.752502\pi\) | ||||
−0.712642 | + | 0.701528i | \(0.752502\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.70492 | −0.120847 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.97511 | 0.221829 | 0.110915 | − | 0.993830i | \(-0.464622\pi\) | ||||
0.110915 | + | 0.993830i | \(0.464622\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −66.7586 | −2.97072 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 29.1893 | 1.29634 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −34.2648 | −1.51876 | −0.759381 | − | 0.650647i | \(-0.774498\pi\) | ||||
−0.759381 | + | 0.650647i | \(0.774498\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.01190 | 0.398663 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −21.8187 | −0.963321 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 33.3787 | 1.47084 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.622547 | −0.0273796 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −63.4431 | −2.78484 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.8100 | 0.473596 | 0.236798 | − | 0.971559i | \(-0.423902\pi\) | ||||
0.236798 | + | 0.971559i | \(0.423902\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.1590 | −0.662856 | −0.331428 | − | 0.943481i | \(-0.607530\pi\) | ||||
−0.331428 | + | 0.943481i | \(0.607530\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −44.9569 | −1.96208 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.0458 | 0.481162 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.35764 | −0.232941 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.33827 | −0.318454 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.19419 | −0.268300 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 54.9620 | 2.37622 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 26.7506 | 1.15437 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.16788 | 0.0933774 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.68358 | −0.330343 | −0.165171 | − | 0.986265i | \(-0.552818\pi\) | ||||
−0.165171 | + | 0.986265i | \(0.552818\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 23.8164 | 1.02206 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 51.9197 | 2.22400 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.79317 | −0.247698 | −0.123849 | − | 0.992301i | \(-0.539524\pi\) | ||||
−0.123849 | + | 0.992301i | \(0.539524\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −43.0846 | −1.83880 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −59.8445 | −2.54946 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.07745 | −0.0458178 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −58.4338 | −2.48037 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.2484 | −0.646094 | −0.323047 | − | 0.946383i | \(-0.604707\pi\) | ||||
−0.323047 | + | 0.946383i | \(0.604707\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.6867 | 0.578885 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.63377 | 0.153418 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.5679 | 0.571818 | 0.285909 | − | 0.958257i | \(-0.407704\pi\) | ||||
0.285909 | + | 0.958257i | \(0.407704\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.5352 | 0.695641 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.23712 | −0.177942 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.43479 | 0.143994 | 0.0719970 | − | 0.997405i | \(-0.477063\pi\) | ||||
0.0719970 | + | 0.997405i | \(0.477063\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 43.1389 | 1.80531 | 0.902654 | − | 0.430368i | \(-0.141616\pi\) | ||||
0.902654 | + | 0.430368i | \(0.141616\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −32.2955 | −1.34916 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −54.6491 | −2.27903 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.6883 | 0.736372 | 0.368186 | − | 0.929752i | \(-0.379979\pi\) | ||||
0.368186 | + | 0.929752i | \(0.379979\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −29.5640 | −1.22864 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.17141 | 0.214546 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.376386 | 0.0155883 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −27.2261 | −1.12566 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.5290 | 1.34261 | 0.671307 | − | 0.741180i | \(-0.265733\pi\) | ||||
0.671307 | + | 0.741180i | \(0.265733\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.3439 | 0.838254 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 26.0613 | 1.07202 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.04886 | −0.0430716 | −0.0215358 | − | 0.999768i | \(-0.506856\pi\) | ||||
−0.0215358 | + | 0.999768i | \(0.506856\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.0342 | −0.739332 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −49.0281 | −2.00659 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −42.5697 | −1.73935 | −0.869675 | − | 0.493624i | \(-0.835672\pi\) | ||||
−0.869675 | + | 0.493624i | \(0.835672\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.46471 | −0.386073 | −0.193037 | − | 0.981192i | \(-0.561834\pi\) | ||||
−0.193037 | + | 0.981192i | \(0.561834\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −21.2476 | −0.865268 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 45.9910 | 1.86980 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −34.1161 | −1.38473 | −0.692365 | − | 0.721548i | \(-0.743431\pi\) | ||||
−0.692365 | + | 0.721548i | \(0.743431\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 33.7509 | 1.36766 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.29109 | 0.0926875 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.8616 | 0.721425 | 0.360712 | − | 0.932677i | \(-0.382534\pi\) | ||||
0.360712 | + | 0.932677i | \(0.382534\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −47.8438 | −1.92925 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.4070 | −1.46569 | −0.732846 | − | 0.680395i | \(-0.761808\pi\) | ||||
−0.732846 | + | 0.680395i | \(0.761808\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.8973 | 0.638968 | 0.319484 | − | 0.947592i | \(-0.396490\pi\) | ||||
0.319484 | + | 0.947592i | \(0.396490\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14.9582 | 0.600250 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.81971 | 0.0729051 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 79.2276 | 3.16910 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.69259 | 0.267276 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16.9331 | −0.675167 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.2964 | 0.688557 | 0.344279 | − | 0.938868i | \(-0.388124\pi\) | ||||
0.344279 | + | 0.938868i | \(0.388124\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 47.2427 | 1.87773 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.7966 | 0.626869 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.97822 | −0.316109 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 29.0114 | 1.14767 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.0444 | 0.752207 | 0.376103 | − | 0.926578i | \(-0.377264\pi\) | ||||
0.376103 | + | 0.926578i | \(0.377264\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.0174 | −0.671100 | −0.335550 | − | 0.942022i | \(-0.608922\pi\) | ||||
−0.335550 | + | 0.942022i | \(0.608922\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 105.716 | 4.16255 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.0099 | 0.432844 | 0.216422 | − | 0.976300i | \(-0.430561\pi\) | ||||
0.216422 | + | 0.976300i | \(0.430561\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.686537 | 0.0269489 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.4735 | −0.449681 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.1819 | −0.750644 | −0.375322 | − | 0.926894i | \(-0.622468\pi\) | ||||
−0.375322 | + | 0.926894i | \(0.622468\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −74.3972 | −2.90694 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 30.4521 | 1.18805 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.3453 | 1.18209 | 0.591043 | − | 0.806640i | \(-0.298717\pi\) | ||||
0.591043 | + | 0.806640i | \(0.298717\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.9037 | −0.579685 | −0.289842 | − | 0.957074i | \(-0.593603\pi\) | ||||
−0.289842 | + | 0.957074i | \(0.593603\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13.3729 | −0.519362 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −33.2150 | −1.28802 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 41.0273 | 1.58858 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.449248 | 0.0173689 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.03081 | 0.155608 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.6160 | 0.486313 | 0.243156 | − | 0.969987i | \(-0.421817\pi\) | ||||
0.243156 | + | 0.969987i | \(0.421817\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −46.3345 | −1.78342 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.9550 | −0.459468 | −0.229734 | − | 0.973253i | \(-0.573786\pi\) | ||||
−0.229734 | + | 0.973253i | \(0.573786\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.5802 | −0.713043 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 72.3702 | 2.77323 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −35.8260 | −1.37084 | −0.685421 | − | 0.728147i | \(-0.740382\pi\) | ||||
−0.685421 | + | 0.728147i | \(0.740382\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −41.4082 | −1.58213 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −71.7961 | −2.73919 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.38517 | −0.0527708 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.0214 | 0.913816 | 0.456908 | − | 0.889514i | \(-0.348957\pi\) | ||||
0.456908 | + | 0.889514i | \(0.348957\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.22683 | −0.0845903 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.6561 | 0.821462 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.8643 | −0.525148 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −74.7595 | −2.82767 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.0403 | −0.945759 | −0.472879 | − | 0.881127i | \(-0.656785\pi\) | ||||
−0.472879 | + | 0.881127i | \(0.656785\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31.1870 | −1.17624 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 17.6963 | 0.666482 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20.0945 | 0.755733 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.7976 | 1.04396 | 0.521980 | − | 0.852957i | \(-0.325193\pi\) | ||||
0.521980 | + | 0.852957i | \(0.325193\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.64082 | −0.136541 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.9470 | −0.522320 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.54716 | 0.0952585 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 82.0293 | 3.06344 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.4516 | 1.35942 | 0.679708 | − | 0.733483i | \(-0.262106\pi\) | ||||
0.679708 | + | 0.733483i | \(0.262106\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.0471 | −0.374173 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 66.7712 | 2.48325 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −127.086 | −4.71987 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.0330 | −0.780070 | −0.390035 | − | 0.920800i | \(-0.627537\pi\) | ||||
−0.390035 | + | 0.920800i | \(0.627537\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.2161 | −1.60060 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.6345 | 1.13306 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.5226 | 0.425596 | 0.212798 | − | 0.977096i | \(-0.431742\pi\) | ||||
0.212798 | + | 0.977096i | \(0.431742\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −61.6236 | −2.27302 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.98783 | 0.0732228 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.4455 | −0.384245 | −0.192123 | − | 0.981371i | \(-0.561537\pi\) | ||||
−0.192123 | + | 0.981371i | \(0.561537\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −24.6300 | −0.904805 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.0541 | −1.06589 | −0.532946 | − | 0.846149i | \(-0.678915\pi\) | ||||
−0.532946 | + | 0.846149i | \(0.678915\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 97.3169 | 3.56541 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 17.4747 | 0.639367 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.5437 | −0.604495 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.3643 | −1.32695 | −0.663476 | − | 0.748198i | \(-0.730920\pi\) | ||||
−0.663476 | + | 0.748198i | \(0.730920\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 70.6494 | 2.57461 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 38.0448 | 1.38459 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.7704 | −1.33644 | −0.668221 | − | 0.743963i | \(-0.732944\pi\) | ||||
−0.668221 | + | 0.743963i | \(0.732944\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.58820 | −0.166541 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.6610 | −1.03896 | −0.519481 | − | 0.854482i | \(-0.673875\pi\) | ||||
−0.519481 | + | 0.854482i | \(0.673875\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.6280 | −0.565771 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −60.9396 | −2.20328 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.52659 | −0.0912297 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −40.6341 | −1.46530 | −0.732652 | − | 0.680604i | \(-0.761718\pi\) | ||||
−0.732652 | + | 0.680604i | \(0.761718\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.13191 | 0.328878 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.1122 | −0.435646 | −0.217823 | − | 0.975988i | \(-0.569895\pi\) | ||||
−0.217823 | + | 0.975988i | \(0.569895\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 43.2024 | 1.55188 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 17.5887 | 0.630992 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −25.5349 | −0.914884 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.71419 | −0.0971213 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 34.7852 | 1.24312 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.0383 | −0.572431 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.2132 | 1.54038 | 0.770191 | − | 0.637813i | \(-0.220161\pi\) | ||||
0.770191 | + | 0.637813i | \(0.220161\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 68.2237 | 2.42883 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.97714 | −0.176967 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.8341 | −0.526776 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.6990 | −0.379455 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32.6861 | 1.15780 | 0.578901 | − | 0.815398i | \(-0.303482\pi\) | ||||
0.578901 | + | 0.815398i | \(0.303482\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.12808 | 0.181419 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.14899 | 0.217264 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.84897 | −0.100538 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 22.7710 | 0.802574 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 48.9237 | 1.72219 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.4760 | −0.368316 | −0.184158 | − | 0.982897i | \(-0.558956\pi\) | ||||
−0.184158 | + | 0.982897i | \(0.558956\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.9589 | −0.455049 | −0.227525 | − | 0.973772i | \(-0.573063\pi\) | ||||
−0.227525 | + | 0.973772i | \(0.573063\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 63.3571 | 2.22203 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −63.1528 | −2.21215 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 56.4220 | 1.97395 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.19515 | 0.286362 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.4621 | −0.574532 | −0.287266 | − | 0.957851i | \(-0.592746\pi\) | ||||
−0.287266 | + | 0.957851i | \(0.592746\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42.7238 | 1.48926 | 0.744630 | − | 0.667478i | \(-0.232626\pi\) | ||||
0.744630 | + | 0.667478i | \(0.232626\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 14.2124 | 0.494814 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.0454 | 1.14910 | 0.574550 | − | 0.818469i | \(-0.305177\pi\) | ||||
0.574550 | + | 0.818469i | \(0.305177\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.0587 | 0.627206 | 0.313603 | − | 0.949554i | \(-0.398464\pi\) | ||||
0.313603 | + | 0.949554i | \(0.398464\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.9726 | −0.554083 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −17.8574 | −0.618724 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.24392 | −0.146867 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −11.8250 | −0.408733 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28.1830 | −0.972986 | −0.486493 | − | 0.873685i | \(-0.661724\pi\) | ||||
−0.486493 | + | 0.873685i | \(0.661724\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 66.4088 | 2.28996 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 83.6294 | 2.88035 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 45.7969 | 1.57546 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.8434 | −0.475665 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.60755 | 0.329730 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.3807 | 0.732920 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.4867 | 1.45472 | 0.727359 | − | 0.686257i | \(-0.240747\pi\) | ||||
0.727359 | + | 0.686257i | \(0.240747\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −112.237 | −3.83843 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 49.9048 | 1.70471 | 0.852357 | − | 0.522960i | \(-0.175172\pi\) | ||||
0.852357 | + | 0.522960i | \(0.175172\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.47277 | 0.289087 | 0.144544 | − | 0.989498i | \(-0.453829\pi\) | ||||
0.144544 | + | 0.989498i | \(0.453829\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.4011 | 0.490789 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.46856 | 0.0499902 | 0.0249951 | − | 0.999688i | \(-0.492043\pi\) | ||||
0.0249951 | + | 0.999688i | \(0.492043\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −99.5399 | −3.38446 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.0513 | 0.545129 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.340619 | 0.0115547 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.31560 | −0.247880 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −62.7845 | −2.12493 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −43.4292 | −1.46818 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −39.0735 | −1.31942 | −0.659709 | − | 0.751521i | \(-0.729321\pi\) | ||||
−0.659709 | + | 0.751521i | \(0.729321\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −51.9675 | −1.75282 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.4707 | −0.790747 | −0.395374 | − | 0.918520i | \(-0.629385\pi\) | ||||
−0.395374 | + | 0.918520i | \(0.629385\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.49116 | 0.285750 | 0.142875 | − | 0.989741i | \(-0.454365\pi\) | ||||
0.142875 | + | 0.989741i | \(0.454365\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −19.5153 | −0.655999 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.79252 | −0.295224 | −0.147612 | − | 0.989045i | \(-0.547159\pi\) | ||||
−0.147612 | + | 0.989045i | \(0.547159\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.75483 | −0.159472 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.33950 | 0.0448749 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.44478 | 0.316058 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 41.9707 | 1.40293 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.8854 | 0.563788 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −32.4338 | −1.08173 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.10039 | −0.103289 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −31.8207 | −1.05893 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 37.3671 | 1.24212 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.8502 | 0.659116 | 0.329558 | − | 0.944135i | \(-0.393100\pi\) | ||||
0.329558 | + | 0.944135i | \(0.393100\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 67.9016 | 2.25215 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.6417 | 0.948942 | 0.474471 | − | 0.880271i | \(-0.342639\pi\) | ||||
0.474471 | + | 0.880271i | \(0.342639\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.63486 | −0.0541060 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −114.579 | −3.78785 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 22.3938 | 0.739508 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.99821 | 0.0989018 | 0.0494509 | − | 0.998777i | \(-0.484253\pi\) | ||||
0.0494509 | + | 0.998777i | \(0.484253\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.91519 | 0.0960586 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.98872 | 0.328783 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −66.2290 | −2.17760 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −33.9501 | −1.11507 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.34190 | 0.306498 | 0.153249 | − | 0.988188i | \(-0.451026\pi\) | ||||
0.153249 | + | 0.988188i | \(0.451026\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.8894 | −1.07791 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.4638 | −0.506262 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.70125 | 0.186451 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37.3671 | −1.22073 | −0.610365 | − | 0.792121i | \(-0.708977\pi\) | ||||
−0.610365 | + | 0.792121i | \(0.708977\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 31.5164 | 1.02850 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.7055 | −0.381587 | −0.190794 | − | 0.981630i | \(-0.561106\pi\) | ||||
−0.190794 | + | 0.981630i | \(0.561106\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.5058 | 0.570069 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 19.3065 | 0.628042 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33.8526 | −1.10006 | −0.550030 | − | 0.835145i | \(-0.685384\pi\) | ||||
−0.550030 | + | 0.835145i | \(0.685384\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.4848 | 0.340350 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.2674 | 0.332944 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.3850 | 0.692728 | 0.346364 | − | 0.938100i | \(-0.387416\pi\) | ||||
0.346364 | + | 0.938100i | \(0.387416\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −50.6705 | −1.63966 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.6698 | −0.344907 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.4640 | 0.402484 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.9743 | −0.644332 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −55.9030 | −1.80145 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −46.3848 | −1.49318 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −38.4901 | −1.23776 | −0.618879 | − | 0.785486i | \(-0.712413\pi\) | ||||
−0.618879 | + | 0.785486i | \(0.712413\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −55.1286 | −1.77099 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.1981 | −0.359365 | −0.179682 | − | 0.983725i | \(-0.557507\pi\) | ||||
−0.179682 | + | 0.983725i | \(0.557507\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.51855 | −0.208975 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −52.3045 | −1.67508 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 45.5724 | 1.45799 | 0.728996 | − | 0.684518i | \(-0.239987\pi\) | ||||
0.728996 | + | 0.684518i | \(0.239987\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.575273 | −0.0183858 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −52.8086 | −1.68605 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 53.6365 | 1.71074 | 0.855370 | − | 0.518018i | \(-0.173330\pi\) | ||||
0.855370 | + | 0.518018i | \(0.173330\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 40.8893 | 1.30284 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.32664 | −0.169549 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −38.6809 | −1.22998 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.2527 | 0.865710 | 0.432855 | − | 0.901464i | \(-0.357506\pi\) | ||||
0.432855 | + | 0.901464i | \(0.357506\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −92.8937 | −2.94789 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −76.9233 | −2.43863 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.3821 | 1.05722 | 0.528610 | − | 0.848865i | \(-0.322713\pi\) | ||||
0.528610 | + | 0.848865i | \(0.322713\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 18.1277 | 0.573535 |
(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 | 1336.2.a.c.1.1 | ✓ | 9 | |
4.3 | odd | 2 | 2672.2.a.m.1.9 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1336.2.a.c.1.1 | ✓ | 9 | 1.1 | even | 1 | trivial | |
2672.2.a.m.1.9 | 9 | 4.3 | odd | 2 |