Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4026,2,Mod(1,4026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4026, 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("4026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4026.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1477718538\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1129.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 7x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.440808\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4026.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.44081 | −0.644349 | −0.322174 | − | 0.946680i | \(-0.604414\pi\) | ||||
−0.322174 | + | 0.946680i | \(0.604414\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 3.36488 | 1.27181 | 0.635903 | − | 0.771769i | \(-0.280628\pi\) | ||||
0.635903 | + | 0.771769i | \(0.280628\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.44081 | −0.455623 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −5.92407 | −1.64304 | −0.821521 | − | 0.570178i | \(-0.806874\pi\) | ||||
−0.821521 | + | 0.570178i | \(0.806874\pi\) | |||||||
\(14\) | 3.36488 | 0.899302 | ||||||||
\(15\) | 1.44081 | 0.372015 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | 0.242536 | 0.121268 | − | 0.992620i | \(-0.461304\pi\) | ||||
0.121268 | + | 0.992620i | \(0.461304\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −2.92407 | −0.670828 | −0.335414 | − | 0.942071i | \(-0.608876\pi\) | ||||
−0.335414 | + | 0.942071i | \(0.608876\pi\) | |||||||
\(20\) | −1.44081 | −0.322174 | ||||||||
\(21\) | −3.36488 | −0.734277 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −4.92407 | −1.02674 | −0.513370 | − | 0.858167i | \(-0.671603\pi\) | ||||
−0.513370 | + | 0.858167i | \(0.671603\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −2.92407 | −0.584815 | ||||||||
\(26\) | −5.92407 | −1.16181 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.36488 | 0.635903 | ||||||||
\(29\) | 2.24650 | 0.417164 | 0.208582 | − | 0.978005i | \(-0.433115\pi\) | ||||
0.208582 | + | 0.978005i | \(0.433115\pi\) | |||||||
\(30\) | 1.44081 | 0.263054 | ||||||||
\(31\) | −1.63512 | −0.293676 | −0.146838 | − | 0.989161i | \(-0.546910\pi\) | ||||
−0.146838 | + | 0.989161i | \(0.546910\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | −4.84815 | −0.819486 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −0.194311 | −0.0319446 | −0.0159723 | − | 0.999872i | \(-0.505084\pi\) | ||||
−0.0159723 | + | 0.999872i | \(0.505084\pi\) | |||||||
\(38\) | −2.92407 | −0.474347 | ||||||||
\(39\) | 5.92407 | 0.948611 | ||||||||
\(40\) | −1.44081 | −0.227812 | ||||||||
\(41\) | −10.6114 | −1.65722 | −0.828609 | − | 0.559827i | \(-0.810867\pi\) | ||||
−0.828609 | + | 0.559827i | \(0.810867\pi\) | |||||||
\(42\) | −3.36488 | −0.519212 | ||||||||
\(43\) | −0.440808 | −0.0672225 | −0.0336113 | − | 0.999435i | \(-0.510701\pi\) | ||||
−0.0336113 | + | 0.999435i | \(0.510701\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | −1.44081 | −0.214783 | ||||||||
\(46\) | −4.92407 | −0.726015 | ||||||||
\(47\) | −11.0522 | −1.61213 | −0.806063 | − | 0.591829i | \(-0.798406\pi\) | ||||
−0.806063 | + | 0.591829i | \(0.798406\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 4.32242 | 0.617489 | ||||||||
\(50\) | −2.92407 | −0.413526 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −5.92407 | −0.821521 | ||||||||
\(53\) | 10.2890 | 1.41330 | 0.706648 | − | 0.707565i | \(-0.250206\pi\) | ||||
0.706648 | + | 0.707565i | \(0.250206\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −1.44081 | −0.194278 | ||||||||
\(56\) | 3.36488 | 0.449651 | ||||||||
\(57\) | 2.92407 | 0.387303 | ||||||||
\(58\) | 2.24650 | 0.294979 | ||||||||
\(59\) | 10.1281 | 1.31857 | 0.659284 | − | 0.751894i | \(-0.270860\pi\) | ||||
0.659284 | + | 0.751894i | \(0.270860\pi\) | |||||||
\(60\) | 1.44081 | 0.186007 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | −1.63512 | −0.207660 | ||||||||
\(63\) | 3.36488 | 0.423935 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 8.53545 | 1.05869 | ||||||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | 1.63512 | 0.199762 | 0.0998808 | − | 0.994999i | \(-0.468154\pi\) | ||||
0.0998808 | + | 0.994999i | \(0.468154\pi\) | |||||||
\(68\) | 1.00000 | 0.121268 | ||||||||
\(69\) | 4.92407 | 0.592789 | ||||||||
\(70\) | −4.84815 | −0.579464 | ||||||||
\(71\) | −1.63512 | −0.194053 | −0.0970265 | − | 0.995282i | \(-0.530933\pi\) | ||||
−0.0970265 | + | 0.995282i | \(0.530933\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 8.24650 | 0.965179 | 0.482590 | − | 0.875847i | \(-0.339696\pi\) | ||||
0.482590 | + | 0.875847i | \(0.339696\pi\) | |||||||
\(74\) | −0.194311 | −0.0225882 | ||||||||
\(75\) | 2.92407 | 0.337643 | ||||||||
\(76\) | −2.92407 | −0.335414 | ||||||||
\(77\) | 3.36488 | 0.383464 | ||||||||
\(78\) | 5.92407 | 0.670769 | ||||||||
\(79\) | −5.92407 | −0.666510 | −0.333255 | − | 0.942837i | \(-0.608147\pi\) | ||||
−0.333255 | + | 0.942837i | \(0.608147\pi\) | |||||||
\(80\) | −1.44081 | −0.161087 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −10.6114 | −1.17183 | ||||||||
\(83\) | −2.39835 | −0.263253 | −0.131627 | − | 0.991299i | \(-0.542020\pi\) | ||||
−0.131627 | + | 0.991299i | \(0.542020\pi\) | |||||||
\(84\) | −3.36488 | −0.367139 | ||||||||
\(85\) | −1.44081 | −0.156278 | ||||||||
\(86\) | −0.440808 | −0.0475335 | ||||||||
\(87\) | −2.24650 | −0.240850 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −17.9338 | −1.90098 | −0.950490 | − | 0.310757i | \(-0.899418\pi\) | ||||
−0.950490 | + | 0.310757i | \(0.899418\pi\) | |||||||
\(90\) | −1.44081 | −0.151874 | ||||||||
\(91\) | −19.9338 | −2.08963 | ||||||||
\(92\) | −4.92407 | −0.513370 | ||||||||
\(93\) | 1.63512 | 0.169554 | ||||||||
\(94\) | −11.0522 | −1.13995 | ||||||||
\(95\) | 4.21303 | 0.432247 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −4.60165 | −0.467227 | −0.233613 | − | 0.972330i | \(-0.575055\pi\) | ||||
−0.233613 | + | 0.972330i | \(0.575055\pi\) | |||||||
\(98\) | 4.32242 | 0.436631 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −2.92407 | −0.292407 | ||||||||
\(101\) | −1.20404 | −0.119806 | −0.0599032 | − | 0.998204i | \(-0.519079\pi\) | ||||
−0.0599032 | + | 0.998204i | \(0.519079\pi\) | |||||||
\(102\) | −1.00000 | −0.0990148 | ||||||||
\(103\) | −6.32242 | −0.622967 | −0.311483 | − | 0.950252i | \(-0.600826\pi\) | ||||
−0.311483 | + | 0.950252i | \(0.600826\pi\) | |||||||
\(104\) | −5.92407 | −0.580903 | ||||||||
\(105\) | 4.84815 | 0.473131 | ||||||||
\(106\) | 10.2890 | 0.999352 | ||||||||
\(107\) | −15.5355 | −1.50187 | −0.750934 | − | 0.660377i | \(-0.770397\pi\) | ||||
−0.750934 | + | 0.660377i | \(0.770397\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 13.1468 | 1.25924 | 0.629619 | − | 0.776904i | \(-0.283211\pi\) | ||||
0.629619 | + | 0.776904i | \(0.283211\pi\) | |||||||
\(110\) | −1.44081 | −0.137376 | ||||||||
\(111\) | 0.194311 | 0.0184432 | ||||||||
\(112\) | 3.36488 | 0.317951 | ||||||||
\(113\) | 1.32242 | 0.124403 | 0.0622016 | − | 0.998064i | \(-0.480188\pi\) | ||||
0.0622016 | + | 0.998064i | \(0.480188\pi\) | |||||||
\(114\) | 2.92407 | 0.273865 | ||||||||
\(115\) | 7.09464 | 0.661579 | ||||||||
\(116\) | 2.24650 | 0.208582 | ||||||||
\(117\) | −5.92407 | −0.547681 | ||||||||
\(118\) | 10.1281 | 0.932368 | ||||||||
\(119\) | 3.36488 | 0.308458 | ||||||||
\(120\) | 1.44081 | 0.131527 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.00000 | −0.0905357 | ||||||||
\(123\) | 10.6114 | 0.956796 | ||||||||
\(124\) | −1.63512 | −0.146838 | ||||||||
\(125\) | 11.4171 | 1.02117 | ||||||||
\(126\) | 3.36488 | 0.299767 | ||||||||
\(127\) | 1.88162 | 0.166966 | 0.0834832 | − | 0.996509i | \(-0.473396\pi\) | ||||
0.0834832 | + | 0.996509i | \(0.473396\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0.440808 | 0.0388110 | ||||||||
\(130\) | 8.53545 | 0.748609 | ||||||||
\(131\) | −18.0522 | −1.57723 | −0.788613 | − | 0.614889i | \(-0.789201\pi\) | ||||
−0.788613 | + | 0.614889i | \(0.789201\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | −9.83916 | −0.853163 | ||||||||
\(134\) | 1.63512 | 0.141253 | ||||||||
\(135\) | 1.44081 | 0.124005 | ||||||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | −9.88162 | −0.844243 | −0.422122 | − | 0.906539i | \(-0.638715\pi\) | ||||
−0.422122 | + | 0.906539i | \(0.638715\pi\) | |||||||
\(138\) | 4.92407 | 0.419165 | ||||||||
\(139\) | 7.77222 | 0.659231 | 0.329616 | − | 0.944115i | \(-0.393081\pi\) | ||||
0.329616 | + | 0.944115i | \(0.393081\pi\) | |||||||
\(140\) | −4.84815 | −0.409743 | ||||||||
\(141\) | 11.0522 | 0.930762 | ||||||||
\(142\) | −1.63512 | −0.137216 | ||||||||
\(143\) | −5.92407 | −0.495396 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −3.23677 | −0.268799 | ||||||||
\(146\) | 8.24650 | 0.682485 | ||||||||
\(147\) | −4.32242 | −0.356507 | ||||||||
\(148\) | −0.194311 | −0.0159723 | ||||||||
\(149\) | −9.64485 | −0.790137 | −0.395068 | − | 0.918652i | \(-0.629279\pi\) | ||||
−0.395068 | + | 0.918652i | \(0.629279\pi\) | |||||||
\(150\) | 2.92407 | 0.238750 | ||||||||
\(151\) | 7.76323 | 0.631763 | 0.315881 | − | 0.948799i | \(-0.397700\pi\) | ||||
0.315881 | + | 0.948799i | \(0.397700\pi\) | |||||||
\(152\) | −2.92407 | −0.237174 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 3.36488 | 0.271150 | ||||||||
\(155\) | 2.35589 | 0.189230 | ||||||||
\(156\) | 5.92407 | 0.474305 | ||||||||
\(157\) | 3.12811 | 0.249650 | 0.124825 | − | 0.992179i | \(-0.460163\pi\) | ||||
0.124825 | + | 0.992179i | \(0.460163\pi\) | |||||||
\(158\) | −5.92407 | −0.471294 | ||||||||
\(159\) | −10.2890 | −0.815967 | ||||||||
\(160\) | −1.44081 | −0.113906 | ||||||||
\(161\) | −16.5689 | −1.30581 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 4.63512 | 0.363051 | 0.181525 | − | 0.983386i | \(-0.441897\pi\) | ||||
0.181525 | + | 0.983386i | \(0.441897\pi\) | |||||||
\(164\) | −10.6114 | −0.828609 | ||||||||
\(165\) | 1.44081 | 0.112167 | ||||||||
\(166\) | −2.39835 | −0.186148 | ||||||||
\(167\) | −15.1706 | −1.17393 | −0.586967 | − | 0.809611i | \(-0.699678\pi\) | ||||
−0.586967 | + | 0.809611i | \(0.699678\pi\) | |||||||
\(168\) | −3.36488 | −0.259606 | ||||||||
\(169\) | 22.0946 | 1.69959 | ||||||||
\(170\) | −1.44081 | −0.110505 | ||||||||
\(171\) | −2.92407 | −0.223609 | ||||||||
\(172\) | −0.440808 | −0.0336113 | ||||||||
\(173\) | 0.246496 | 0.0187408 | 0.00937038 | − | 0.999956i | \(-0.497017\pi\) | ||||
0.00937038 | + | 0.999956i | \(0.497017\pi\) | |||||||
\(174\) | −2.24650 | −0.170306 | ||||||||
\(175\) | −9.83916 | −0.743770 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −10.1281 | −0.761275 | ||||||||
\(178\) | −17.9338 | −1.34420 | ||||||||
\(179\) | −18.5117 | −1.38363 | −0.691815 | − | 0.722075i | \(-0.743189\pi\) | ||||
−0.691815 | + | 0.722075i | \(0.743189\pi\) | |||||||
\(180\) | −1.44081 | −0.107391 | ||||||||
\(181\) | −18.3746 | −1.36577 | −0.682887 | − | 0.730524i | \(-0.739276\pi\) | ||||
−0.682887 | + | 0.730524i | \(0.739276\pi\) | |||||||
\(182\) | −19.9338 | −1.47759 | ||||||||
\(183\) | 1.00000 | 0.0739221 | ||||||||
\(184\) | −4.92407 | −0.363007 | ||||||||
\(185\) | 0.279965 | 0.0205835 | ||||||||
\(186\) | 1.63512 | 0.119893 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | −11.0522 | −0.806063 | ||||||||
\(189\) | −3.36488 | −0.244759 | ||||||||
\(190\) | 4.21303 | 0.305645 | ||||||||
\(191\) | −8.41707 | −0.609037 | −0.304519 | − | 0.952506i | \(-0.598496\pi\) | ||||
−0.304519 | + | 0.952506i | \(0.598496\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 0.905357 | 0.0651691 | 0.0325845 | − | 0.999469i | \(-0.489626\pi\) | ||||
0.0325845 | + | 0.999469i | \(0.489626\pi\) | |||||||
\(194\) | −4.60165 | −0.330379 | ||||||||
\(195\) | −8.53545 | −0.611236 | ||||||||
\(196\) | 4.32242 | 0.308745 | ||||||||
\(197\) | 8.97626 | 0.639532 | 0.319766 | − | 0.947497i | \(-0.396396\pi\) | ||||
0.319766 | + | 0.947497i | \(0.396396\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | 0.492993 | 0.0349473 | 0.0174737 | − | 0.999847i | \(-0.494438\pi\) | ||||
0.0174737 | + | 0.999847i | \(0.494438\pi\) | |||||||
\(200\) | −2.92407 | −0.206763 | ||||||||
\(201\) | −1.63512 | −0.115332 | ||||||||
\(202\) | −1.20404 | −0.0847159 | ||||||||
\(203\) | 7.55919 | 0.530551 | ||||||||
\(204\) | −1.00000 | −0.0700140 | ||||||||
\(205\) | 15.2890 | 1.06783 | ||||||||
\(206\) | −6.32242 | −0.440504 | ||||||||
\(207\) | −4.92407 | −0.342247 | ||||||||
\(208\) | −5.92407 | −0.410761 | ||||||||
\(209\) | −2.92407 | −0.202262 | ||||||||
\(210\) | 4.84815 | 0.334554 | ||||||||
\(211\) | 28.1893 | 1.94063 | 0.970315 | − | 0.241844i | \(-0.0777521\pi\) | ||||
0.970315 | + | 0.241844i | \(0.0777521\pi\) | |||||||
\(212\) | 10.2890 | 0.706648 | ||||||||
\(213\) | 1.63512 | 0.112037 | ||||||||
\(214\) | −15.5355 | −1.06198 | ||||||||
\(215\) | 0.635119 | 0.0433148 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −5.50198 | −0.373499 | ||||||||
\(218\) | 13.1468 | 0.890416 | ||||||||
\(219\) | −8.24650 | −0.557247 | ||||||||
\(220\) | −1.44081 | −0.0971392 | ||||||||
\(221\) | −5.92407 | −0.398496 | ||||||||
\(222\) | 0.194311 | 0.0130413 | ||||||||
\(223\) | 18.4408 | 1.23489 | 0.617444 | − | 0.786615i | \(-0.288168\pi\) | ||||
0.617444 | + | 0.786615i | \(0.288168\pi\) | |||||||
\(224\) | 3.36488 | 0.224826 | ||||||||
\(225\) | −2.92407 | −0.194938 | ||||||||
\(226\) | 1.32242 | 0.0879663 | ||||||||
\(227\) | −27.2130 | −1.80619 | −0.903096 | − | 0.429439i | \(-0.858711\pi\) | ||||
−0.903096 | + | 0.429439i | \(0.858711\pi\) | |||||||
\(228\) | 2.92407 | 0.193651 | ||||||||
\(229\) | −26.5355 | −1.75351 | −0.876756 | − | 0.480936i | \(-0.840297\pi\) | ||||
−0.876756 | + | 0.480936i | \(0.840297\pi\) | |||||||
\(230\) | 7.09464 | 0.467807 | ||||||||
\(231\) | −3.36488 | −0.221393 | ||||||||
\(232\) | 2.24650 | 0.147490 | ||||||||
\(233\) | 4.34114 | 0.284397 | 0.142199 | − | 0.989838i | \(-0.454583\pi\) | ||||
0.142199 | + | 0.989838i | \(0.454583\pi\) | |||||||
\(234\) | −5.92407 | −0.387269 | ||||||||
\(235\) | 15.9241 | 1.03877 | ||||||||
\(236\) | 10.1281 | 0.659284 | ||||||||
\(237\) | 5.92407 | 0.384810 | ||||||||
\(238\) | 3.36488 | 0.218113 | ||||||||
\(239\) | −10.9003 | −0.705084 | −0.352542 | − | 0.935796i | \(-0.614683\pi\) | ||||
−0.352542 | + | 0.935796i | \(0.614683\pi\) | |||||||
\(240\) | 1.44081 | 0.0930037 | ||||||||
\(241\) | 10.0425 | 0.646892 | 0.323446 | − | 0.946247i | \(-0.395159\pi\) | ||||
0.323446 | + | 0.946247i | \(0.395159\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.00000 | −0.0640184 | ||||||||
\(245\) | −6.22778 | −0.397878 | ||||||||
\(246\) | 10.6114 | 0.676557 | ||||||||
\(247\) | 17.3224 | 1.10220 | ||||||||
\(248\) | −1.63512 | −0.103830 | ||||||||
\(249\) | 2.39835 | 0.151989 | ||||||||
\(250\) | 11.4171 | 0.722079 | ||||||||
\(251\) | 15.0612 | 0.950653 | 0.475326 | − | 0.879810i | \(-0.342330\pi\) | ||||
0.475326 | + | 0.879810i | \(0.342330\pi\) | |||||||
\(252\) | 3.36488 | 0.211968 | ||||||||
\(253\) | −4.92407 | −0.309574 | ||||||||
\(254\) | 1.88162 | 0.118063 | ||||||||
\(255\) | 1.44081 | 0.0902269 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.0097 | 0.686768 | 0.343384 | − | 0.939195i | \(-0.388427\pi\) | ||||
0.343384 | + | 0.939195i | \(0.388427\pi\) | |||||||
\(258\) | 0.440808 | 0.0274435 | ||||||||
\(259\) | −0.653835 | −0.0406273 | ||||||||
\(260\) | 8.53545 | 0.529346 | ||||||||
\(261\) | 2.24650 | 0.139055 | ||||||||
\(262\) | −18.0522 | −1.11527 | ||||||||
\(263\) | −30.7395 | −1.89548 | −0.947739 | − | 0.319047i | \(-0.896637\pi\) | ||||
−0.947739 | + | 0.319047i | \(0.896637\pi\) | |||||||
\(264\) | −1.00000 | −0.0615457 | ||||||||
\(265\) | −14.8244 | −0.910656 | ||||||||
\(266\) | −9.83916 | −0.603277 | ||||||||
\(267\) | 17.9338 | 1.09753 | ||||||||
\(268\) | 1.63512 | 0.0998808 | ||||||||
\(269\) | −21.0000 | −1.28039 | −0.640196 | − | 0.768211i | \(-0.721147\pi\) | ||||
−0.640196 | + | 0.768211i | \(0.721147\pi\) | |||||||
\(270\) | 1.44081 | 0.0876848 | ||||||||
\(271\) | −9.07593 | −0.551323 | −0.275662 | − | 0.961255i | \(-0.588897\pi\) | ||||
−0.275662 | + | 0.961255i | \(0.588897\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | 19.9338 | 1.20645 | ||||||||
\(274\) | −9.88162 | −0.596970 | ||||||||
\(275\) | −2.92407 | −0.176328 | ||||||||
\(276\) | 4.92407 | 0.296394 | ||||||||
\(277\) | −19.2987 | −1.15955 | −0.579773 | − | 0.814778i | \(-0.696859\pi\) | ||||
−0.579773 | + | 0.814778i | \(0.696859\pi\) | |||||||
\(278\) | 7.77222 | 0.466147 | ||||||||
\(279\) | −1.63512 | −0.0978920 | ||||||||
\(280\) | −4.84815 | −0.289732 | ||||||||
\(281\) | −0.398350 | −0.0237636 | −0.0118818 | − | 0.999929i | \(-0.503782\pi\) | ||||
−0.0118818 | + | 0.999929i | \(0.503782\pi\) | |||||||
\(282\) | 11.0522 | 0.658148 | ||||||||
\(283\) | 15.5592 | 0.924898 | 0.462449 | − | 0.886646i | \(-0.346971\pi\) | ||||
0.462449 | + | 0.886646i | \(0.346971\pi\) | |||||||
\(284\) | −1.63512 | −0.0970265 | ||||||||
\(285\) | −4.21303 | −0.249558 | ||||||||
\(286\) | −5.92407 | −0.350298 | ||||||||
\(287\) | −35.7060 | −2.10766 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −16.0000 | −0.941176 | ||||||||
\(290\) | −3.23677 | −0.190070 | ||||||||
\(291\) | 4.60165 | 0.269754 | ||||||||
\(292\) | 8.24650 | 0.482590 | ||||||||
\(293\) | 10.6776 | 0.623791 | 0.311895 | − | 0.950116i | \(-0.399036\pi\) | ||||
0.311895 | + | 0.950116i | \(0.399036\pi\) | |||||||
\(294\) | −4.32242 | −0.252089 | ||||||||
\(295\) | −14.5927 | −0.849618 | ||||||||
\(296\) | −0.194311 | −0.0112941 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −9.64485 | −0.558711 | ||||||||
\(299\) | 29.1706 | 1.68698 | ||||||||
\(300\) | 2.92407 | 0.168821 | ||||||||
\(301\) | −1.48327 | −0.0854940 | ||||||||
\(302\) | 7.76323 | 0.446724 | ||||||||
\(303\) | 1.20404 | 0.0691702 | ||||||||
\(304\) | −2.92407 | −0.167707 | ||||||||
\(305\) | 1.44081 | 0.0825004 | ||||||||
\(306\) | 1.00000 | 0.0571662 | ||||||||
\(307\) | 5.07593 | 0.289698 | 0.144849 | − | 0.989454i | \(-0.453730\pi\) | ||||
0.144849 | + | 0.989454i | \(0.453730\pi\) | |||||||
\(308\) | 3.36488 | 0.191732 | ||||||||
\(309\) | 6.32242 | 0.359670 | ||||||||
\(310\) | 2.35589 | 0.133806 | ||||||||
\(311\) | 11.9101 | 0.675357 | 0.337679 | − | 0.941261i | \(-0.390358\pi\) | ||||
0.337679 | + | 0.941261i | \(0.390358\pi\) | |||||||
\(312\) | 5.92407 | 0.335385 | ||||||||
\(313\) | 29.7582 | 1.68203 | 0.841017 | − | 0.541009i | \(-0.181958\pi\) | ||||
0.841017 | + | 0.541009i | \(0.181958\pi\) | |||||||
\(314\) | 3.12811 | 0.176530 | ||||||||
\(315\) | −4.84815 | −0.273162 | ||||||||
\(316\) | −5.92407 | −0.333255 | ||||||||
\(317\) | 8.84888 | 0.497003 | 0.248501 | − | 0.968632i | \(-0.420062\pi\) | ||||
0.248501 | + | 0.968632i | \(0.420062\pi\) | |||||||
\(318\) | −10.2890 | −0.576976 | ||||||||
\(319\) | 2.24650 | 0.125780 | ||||||||
\(320\) | −1.44081 | −0.0805436 | ||||||||
\(321\) | 15.5355 | 0.867104 | ||||||||
\(322\) | −16.5689 | −0.923350 | ||||||||
\(323\) | −2.92407 | −0.162700 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 17.3224 | 0.960875 | ||||||||
\(326\) | 4.63512 | 0.256716 | ||||||||
\(327\) | −13.1468 | −0.727021 | ||||||||
\(328\) | −10.6114 | −0.585915 | ||||||||
\(329\) | −37.1893 | −2.05031 | ||||||||
\(330\) | 1.44081 | 0.0793139 | ||||||||
\(331\) | 3.00973 | 0.165430 | 0.0827148 | − | 0.996573i | \(-0.473641\pi\) | ||||
0.0827148 | + | 0.996573i | \(0.473641\pi\) | |||||||
\(332\) | −2.39835 | −0.131627 | ||||||||
\(333\) | −0.194311 | −0.0106482 | ||||||||
\(334\) | −15.1706 | −0.830097 | ||||||||
\(335\) | −2.35589 | −0.128716 | ||||||||
\(336\) | −3.36488 | −0.183569 | ||||||||
\(337\) | −22.6823 | −1.23558 | −0.617791 | − | 0.786342i | \(-0.711972\pi\) | ||||
−0.617791 | + | 0.786342i | \(0.711972\pi\) | |||||||
\(338\) | 22.0946 | 1.20179 | ||||||||
\(339\) | −1.32242 | −0.0718242 | ||||||||
\(340\) | −1.44081 | −0.0781388 | ||||||||
\(341\) | −1.63512 | −0.0885467 | ||||||||
\(342\) | −2.92407 | −0.158116 | ||||||||
\(343\) | −9.00973 | −0.486480 | ||||||||
\(344\) | −0.440808 | −0.0237668 | ||||||||
\(345\) | −7.09464 | −0.381963 | ||||||||
\(346\) | 0.246496 | 0.0132517 | ||||||||
\(347\) | 18.4073 | 0.988158 | 0.494079 | − | 0.869417i | \(-0.335505\pi\) | ||||
0.494079 | + | 0.869417i | \(0.335505\pi\) | |||||||
\(348\) | −2.24650 | −0.120425 | ||||||||
\(349\) | 18.2562 | 0.977233 | 0.488617 | − | 0.872499i | \(-0.337502\pi\) | ||||
0.488617 | + | 0.872499i | \(0.337502\pi\) | |||||||
\(350\) | −9.83916 | −0.525925 | ||||||||
\(351\) | 5.92407 | 0.316204 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −13.8392 | −0.736584 | −0.368292 | − | 0.929710i | \(-0.620057\pi\) | ||||
−0.368292 | + | 0.929710i | \(0.620057\pi\) | |||||||
\(354\) | −10.1281 | −0.538303 | ||||||||
\(355\) | 2.35589 | 0.125038 | ||||||||
\(356\) | −17.9338 | −0.950490 | ||||||||
\(357\) | −3.36488 | −0.178088 | ||||||||
\(358\) | −18.5117 | −0.978374 | ||||||||
\(359\) | −22.6963 | −1.19786 | −0.598932 | − | 0.800800i | \(-0.704408\pi\) | ||||
−0.598932 | + | 0.800800i | \(0.704408\pi\) | |||||||
\(360\) | −1.44081 | −0.0759372 | ||||||||
\(361\) | −10.4498 | −0.549989 | ||||||||
\(362\) | −18.3746 | −0.965748 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | −19.9338 | −1.04482 | ||||||||
\(365\) | −11.8816 | −0.621912 | ||||||||
\(366\) | 1.00000 | 0.0522708 | ||||||||
\(367\) | 22.3077 | 1.16445 | 0.582225 | − | 0.813027i | \(-0.302182\pi\) | ||||
0.582225 | + | 0.813027i | \(0.302182\pi\) | |||||||
\(368\) | −4.92407 | −0.256685 | ||||||||
\(369\) | −10.6114 | −0.552406 | ||||||||
\(370\) | 0.279965 | 0.0145547 | ||||||||
\(371\) | 34.6211 | 1.79744 | ||||||||
\(372\) | 1.63512 | 0.0847770 | ||||||||
\(373\) | 21.0946 | 1.09224 | 0.546120 | − | 0.837707i | \(-0.316104\pi\) | ||||
0.546120 | + | 0.837707i | \(0.316104\pi\) | |||||||
\(374\) | 1.00000 | 0.0517088 | ||||||||
\(375\) | −11.4171 | −0.589575 | ||||||||
\(376\) | −11.0522 | −0.569973 | ||||||||
\(377\) | −13.3084 | −0.685418 | ||||||||
\(378\) | −3.36488 | −0.173071 | ||||||||
\(379\) | −25.1044 | −1.28952 | −0.644762 | − | 0.764383i | \(-0.723044\pi\) | ||||
−0.644762 | + | 0.764383i | \(0.723044\pi\) | |||||||
\(380\) | 4.21303 | 0.216124 | ||||||||
\(381\) | −1.88162 | −0.0963981 | ||||||||
\(382\) | −8.41707 | −0.430655 | ||||||||
\(383\) | 16.7632 | 0.856561 | 0.428281 | − | 0.903646i | \(-0.359120\pi\) | ||||
0.428281 | + | 0.903646i | \(0.359120\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −4.84815 | −0.247084 | ||||||||
\(386\) | 0.905357 | 0.0460815 | ||||||||
\(387\) | −0.440808 | −0.0224075 | ||||||||
\(388\) | −4.60165 | −0.233613 | ||||||||
\(389\) | 20.6351 | 1.04624 | 0.523121 | − | 0.852258i | \(-0.324768\pi\) | ||||
0.523121 | + | 0.852258i | \(0.324768\pi\) | |||||||
\(390\) | −8.53545 | −0.432209 | ||||||||
\(391\) | −4.92407 | −0.249021 | ||||||||
\(392\) | 4.32242 | 0.218315 | ||||||||
\(393\) | 18.0522 | 0.910612 | ||||||||
\(394\) | 8.97626 | 0.452217 | ||||||||
\(395\) | 8.53545 | 0.429465 | ||||||||
\(396\) | 1.00000 | 0.0502519 | ||||||||
\(397\) | −4.10866 | −0.206208 | −0.103104 | − | 0.994671i | \(-0.532877\pi\) | ||||
−0.103104 | + | 0.994671i | \(0.532877\pi\) | |||||||
\(398\) | 0.492993 | 0.0247115 | ||||||||
\(399\) | 9.83916 | 0.492574 | ||||||||
\(400\) | −2.92407 | −0.146204 | ||||||||
\(401\) | 10.7298 | 0.535819 | 0.267909 | − | 0.963444i | \(-0.413667\pi\) | ||||
0.267909 | + | 0.963444i | \(0.413667\pi\) | |||||||
\(402\) | −1.63512 | −0.0815523 | ||||||||
\(403\) | 9.68657 | 0.482522 | ||||||||
\(404\) | −1.20404 | −0.0599032 | ||||||||
\(405\) | −1.44081 | −0.0715943 | ||||||||
\(406\) | 7.55919 | 0.375156 | ||||||||
\(407\) | −0.194311 | −0.00963166 | ||||||||
\(408\) | −1.00000 | −0.0495074 | ||||||||
\(409\) | 27.4358 | 1.35661 | 0.678306 | − | 0.734780i | \(-0.262714\pi\) | ||||
0.678306 | + | 0.734780i | \(0.262714\pi\) | |||||||
\(410\) | 15.2890 | 0.755068 | ||||||||
\(411\) | 9.88162 | 0.487424 | ||||||||
\(412\) | −6.32242 | −0.311483 | ||||||||
\(413\) | 34.0799 | 1.67696 | ||||||||
\(414\) | −4.92407 | −0.242005 | ||||||||
\(415\) | 3.45556 | 0.169627 | ||||||||
\(416\) | −5.92407 | −0.290452 | ||||||||
\(417\) | −7.77222 | −0.380607 | ||||||||
\(418\) | −2.92407 | −0.143021 | ||||||||
\(419\) | −18.6538 | −0.911299 | −0.455650 | − | 0.890159i | \(-0.650593\pi\) | ||||
−0.455650 | + | 0.890159i | \(0.650593\pi\) | |||||||
\(420\) | 4.84815 | 0.236565 | ||||||||
\(421\) | −10.1468 | −0.494526 | −0.247263 | − | 0.968948i | \(-0.579531\pi\) | ||||
−0.247263 | + | 0.968948i | \(0.579531\pi\) | |||||||
\(422\) | 28.1893 | 1.37223 | ||||||||
\(423\) | −11.0522 | −0.537376 | ||||||||
\(424\) | 10.2890 | 0.499676 | ||||||||
\(425\) | −2.92407 | −0.141838 | ||||||||
\(426\) | 1.63512 | 0.0792218 | ||||||||
\(427\) | −3.36488 | −0.162838 | ||||||||
\(428\) | −15.5355 | −0.750934 | ||||||||
\(429\) | 5.92407 | 0.286017 | ||||||||
\(430\) | 0.635119 | 0.0306282 | ||||||||
\(431\) | −3.38862 | −0.163224 | −0.0816121 | − | 0.996664i | \(-0.526007\pi\) | ||||
−0.0816121 | + | 0.996664i | \(0.526007\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −25.2562 | −1.21374 | −0.606868 | − | 0.794802i | \(-0.707574\pi\) | ||||
−0.606868 | + | 0.794802i | \(0.707574\pi\) | |||||||
\(434\) | −5.50198 | −0.264104 | ||||||||
\(435\) | 3.23677 | 0.155191 | ||||||||
\(436\) | 13.1468 | 0.629619 | ||||||||
\(437\) | 14.3983 | 0.688766 | ||||||||
\(438\) | −8.24650 | −0.394033 | ||||||||
\(439\) | −7.19431 | −0.343366 | −0.171683 | − | 0.985152i | \(-0.554920\pi\) | ||||
−0.171683 | + | 0.985152i | \(0.554920\pi\) | |||||||
\(440\) | −1.44081 | −0.0686878 | ||||||||
\(441\) | 4.32242 | 0.205830 | ||||||||
\(442\) | −5.92407 | −0.281779 | ||||||||
\(443\) | 32.1461 | 1.52731 | 0.763653 | − | 0.645626i | \(-0.223404\pi\) | ||||
0.763653 | + | 0.645626i | \(0.223404\pi\) | |||||||
\(444\) | 0.194311 | 0.00922161 | ||||||||
\(445\) | 25.8392 | 1.22489 | ||||||||
\(446\) | 18.4408 | 0.873198 | ||||||||
\(447\) | 9.64485 | 0.456186 | ||||||||
\(448\) | 3.36488 | 0.158976 | ||||||||
\(449\) | −27.2562 | −1.28630 | −0.643150 | − | 0.765740i | \(-0.722373\pi\) | ||||
−0.643150 | + | 0.765740i | \(0.722373\pi\) | |||||||
\(450\) | −2.92407 | −0.137842 | ||||||||
\(451\) | −10.6114 | −0.499670 | ||||||||
\(452\) | 1.32242 | 0.0622016 | ||||||||
\(453\) | −7.76323 | −0.364748 | ||||||||
\(454\) | −27.2130 | −1.27717 | ||||||||
\(455\) | 28.7208 | 1.34645 | ||||||||
\(456\) | 2.92407 | 0.136932 | ||||||||
\(457\) | 7.97626 | 0.373114 | 0.186557 | − | 0.982444i | \(-0.440267\pi\) | ||||
0.186557 | + | 0.982444i | \(0.440267\pi\) | |||||||
\(458\) | −26.5355 | −1.23992 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 7.09464 | 0.330789 | ||||||||
\(461\) | 28.3411 | 1.31998 | 0.659989 | − | 0.751275i | \(-0.270561\pi\) | ||||
0.659989 | + | 0.751275i | \(0.270561\pi\) | |||||||
\(462\) | −3.36488 | −0.156548 | ||||||||
\(463\) | 24.6538 | 1.14576 | 0.572880 | − | 0.819639i | \(-0.305826\pi\) | ||||
0.572880 | + | 0.819639i | \(0.305826\pi\) | |||||||
\(464\) | 2.24650 | 0.104291 | ||||||||
\(465\) | −2.35589 | −0.109252 | ||||||||
\(466\) | 4.34114 | 0.201099 | ||||||||
\(467\) | 25.1803 | 1.16521 | 0.582603 | − | 0.812757i | \(-0.302034\pi\) | ||||
0.582603 | + | 0.812757i | \(0.302034\pi\) | |||||||
\(468\) | −5.92407 | −0.273840 | ||||||||
\(469\) | 5.50198 | 0.254058 | ||||||||
\(470\) | 15.9241 | 0.734523 | ||||||||
\(471\) | −3.12811 | −0.144136 | ||||||||
\(472\) | 10.1281 | 0.466184 | ||||||||
\(473\) | −0.440808 | −0.0202684 | ||||||||
\(474\) | 5.92407 | 0.272102 | ||||||||
\(475\) | 8.55020 | 0.392310 | ||||||||
\(476\) | 3.36488 | 0.154229 | ||||||||
\(477\) | 10.2890 | 0.471099 | ||||||||
\(478\) | −10.9003 | −0.498570 | ||||||||
\(479\) | 9.40734 | 0.429832 | 0.214916 | − | 0.976633i | \(-0.431052\pi\) | ||||
0.214916 | + | 0.976633i | \(0.431052\pi\) | |||||||
\(480\) | 1.44081 | 0.0657636 | ||||||||
\(481\) | 1.15112 | 0.0524863 | ||||||||
\(482\) | 10.0425 | 0.457421 | ||||||||
\(483\) | 16.5689 | 0.753912 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 6.63009 | 0.301057 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 32.2465 | 1.46123 | 0.730614 | − | 0.682791i | \(-0.239234\pi\) | ||||
0.730614 | + | 0.682791i | \(0.239234\pi\) | |||||||
\(488\) | −1.00000 | −0.0452679 | ||||||||
\(489\) | −4.63512 | −0.209607 | ||||||||
\(490\) | −6.22778 | −0.281342 | ||||||||
\(491\) | −1.79596 | −0.0810506 | −0.0405253 | − | 0.999179i | \(-0.512903\pi\) | ||||
−0.0405253 | + | 0.999179i | \(0.512903\pi\) | |||||||
\(492\) | 10.6114 | 0.478398 | ||||||||
\(493\) | 2.24650 | 0.101177 | ||||||||
\(494\) | 17.3224 | 0.779373 | ||||||||
\(495\) | −1.44081 | −0.0647595 | ||||||||
\(496\) | −1.63512 | −0.0734190 | ||||||||
\(497\) | −5.50198 | −0.246798 | ||||||||
\(498\) | 2.39835 | 0.107473 | ||||||||
\(499\) | 22.0759 | 0.988254 | 0.494127 | − | 0.869390i | \(-0.335488\pi\) | ||||
0.494127 | + | 0.869390i | \(0.335488\pi\) | |||||||
\(500\) | 11.4171 | 0.510587 | ||||||||
\(501\) | 15.1706 | 0.677771 | ||||||||
\(502\) | 15.0612 | 0.672213 | ||||||||
\(503\) | 17.4358 | 0.777423 | 0.388712 | − | 0.921360i | \(-0.372920\pi\) | ||||
0.388712 | + | 0.921360i | \(0.372920\pi\) | |||||||
\(504\) | 3.36488 | 0.149884 | ||||||||
\(505\) | 1.73479 | 0.0771971 | ||||||||
\(506\) | −4.92407 | −0.218902 | ||||||||
\(507\) | −22.0946 | −0.981258 | ||||||||
\(508\) | 1.88162 | 0.0834832 | ||||||||
\(509\) | −41.3501 | −1.83281 | −0.916406 | − | 0.400250i | \(-0.868923\pi\) | ||||
−0.916406 | + | 0.400250i | \(0.868923\pi\) | |||||||
\(510\) | 1.44081 | 0.0638000 | ||||||||
\(511\) | 27.7485 | 1.22752 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 2.92407 | 0.129101 | ||||||||
\(514\) | 11.0097 | 0.485618 | ||||||||
\(515\) | 9.10940 | 0.401408 | ||||||||
\(516\) | 0.440808 | 0.0194055 | ||||||||
\(517\) | −11.0522 | −0.486075 | ||||||||
\(518\) | −0.653835 | −0.0287279 | ||||||||
\(519\) | −0.246496 | −0.0108200 | ||||||||
\(520\) | 8.53545 | 0.374304 | ||||||||
\(521\) | −5.90536 | −0.258718 | −0.129359 | − | 0.991598i | \(-0.541292\pi\) | ||||
−0.129359 | + | 0.991598i | \(0.541292\pi\) | |||||||
\(522\) | 2.24650 | 0.0983265 | ||||||||
\(523\) | −40.3458 | −1.76420 | −0.882100 | − | 0.471062i | \(-0.843871\pi\) | ||||
−0.882100 | + | 0.471062i | \(0.843871\pi\) | |||||||
\(524\) | −18.0522 | −0.788613 | ||||||||
\(525\) | 9.83916 | 0.429416 | ||||||||
\(526\) | −30.7395 | −1.34031 | ||||||||
\(527\) | −1.63512 | −0.0712269 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | 1.24650 | 0.0541955 | ||||||||
\(530\) | −14.8244 | −0.643931 | ||||||||
\(531\) | 10.1281 | 0.439523 | ||||||||
\(532\) | −9.83916 | −0.426582 | ||||||||
\(533\) | 62.8626 | 2.72288 | ||||||||
\(534\) | 17.9338 | 0.776071 | ||||||||
\(535\) | 22.3836 | 0.967727 | ||||||||
\(536\) | 1.63512 | 0.0706264 | ||||||||
\(537\) | 18.5117 | 0.798839 | ||||||||
\(538\) | −21.0000 | −0.905374 | ||||||||
\(539\) | 4.32242 | 0.186180 | ||||||||
\(540\) | 1.44081 | 0.0620025 | ||||||||
\(541\) | −8.39332 | −0.360857 | −0.180429 | − | 0.983588i | \(-0.557748\pi\) | ||||
−0.180429 | + | 0.983588i | \(0.557748\pi\) | |||||||
\(542\) | −9.07593 | −0.389844 | ||||||||
\(543\) | 18.3746 | 0.788530 | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | −18.9421 | −0.811388 | ||||||||
\(546\) | 19.9338 | 0.853088 | ||||||||
\(547\) | 15.7722 | 0.674371 | 0.337186 | − | 0.941438i | \(-0.390525\pi\) | ||||
0.337186 | + | 0.941438i | \(0.390525\pi\) | |||||||
\(548\) | −9.88162 | −0.422122 | ||||||||
\(549\) | −1.00000 | −0.0426790 | ||||||||
\(550\) | −2.92407 | −0.124683 | ||||||||
\(551\) | −6.56892 | −0.279845 | ||||||||
\(552\) | 4.92407 | 0.209582 | ||||||||
\(553\) | −19.9338 | −0.847671 | ||||||||
\(554\) | −19.2987 | −0.819922 | ||||||||
\(555\) | −0.279965 | −0.0118839 | ||||||||
\(556\) | 7.77222 | 0.329616 | ||||||||
\(557\) | −20.1281 | −0.852855 | −0.426428 | − | 0.904522i | \(-0.640228\pi\) | ||||
−0.426428 | + | 0.904522i | \(0.640228\pi\) | |||||||
\(558\) | −1.63512 | −0.0692201 | ||||||||
\(559\) | 2.61138 | 0.110449 | ||||||||
\(560\) | −4.84815 | −0.204872 | ||||||||
\(561\) | −1.00000 | −0.0422200 | ||||||||
\(562\) | −0.398350 | −0.0168034 | ||||||||
\(563\) | 44.8856 | 1.89170 | 0.945851 | − | 0.324602i | \(-0.105230\pi\) | ||||
0.945851 | + | 0.324602i | \(0.105230\pi\) | |||||||
\(564\) | 11.0522 | 0.465381 | ||||||||
\(565\) | −1.90536 | −0.0801590 | ||||||||
\(566\) | 15.5592 | 0.654002 | ||||||||
\(567\) | 3.36488 | 0.141312 | ||||||||
\(568\) | −1.63512 | −0.0686081 | ||||||||
\(569\) | 31.1796 | 1.30712 | 0.653558 | − | 0.756877i | \(-0.273276\pi\) | ||||
0.653558 | + | 0.756877i | \(0.273276\pi\) | |||||||
\(570\) | −4.21303 | −0.176464 | ||||||||
\(571\) | 21.5257 | 0.900823 | 0.450412 | − | 0.892821i | \(-0.351277\pi\) | ||||
0.450412 | + | 0.892821i | \(0.351277\pi\) | |||||||
\(572\) | −5.92407 | −0.247698 | ||||||||
\(573\) | 8.41707 | 0.351628 | ||||||||
\(574\) | −35.7060 | −1.49034 | ||||||||
\(575\) | 14.3983 | 0.600453 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 4.36414 | 0.181682 | 0.0908408 | − | 0.995865i | \(-0.471045\pi\) | ||||
0.0908408 | + | 0.995865i | \(0.471045\pi\) | |||||||
\(578\) | −16.0000 | −0.665512 | ||||||||
\(579\) | −0.905357 | −0.0376254 | ||||||||
\(580\) | −3.23677 | −0.134400 | ||||||||
\(581\) | −8.07016 | −0.334807 | ||||||||
\(582\) | 4.60165 | 0.190745 | ||||||||
\(583\) | 10.2890 | 0.426125 | ||||||||
\(584\) | 8.24650 | 0.341242 | ||||||||
\(585\) | 8.53545 | 0.352897 | ||||||||
\(586\) | 10.6776 | 0.441087 | ||||||||
\(587\) | 31.4163 | 1.29669 | 0.648345 | − | 0.761346i | \(-0.275461\pi\) | ||||
0.648345 | + | 0.761346i | \(0.275461\pi\) | |||||||
\(588\) | −4.32242 | −0.178254 | ||||||||
\(589\) | 4.78121 | 0.197006 | ||||||||
\(590\) | −14.5927 | −0.600770 | ||||||||
\(591\) | −8.97626 | −0.369234 | ||||||||
\(592\) | −0.194311 | −0.00798615 | ||||||||
\(593\) | −39.5117 | −1.62255 | −0.811276 | − | 0.584664i | \(-0.801226\pi\) | ||||
−0.811276 | + | 0.584664i | \(0.801226\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | −4.84815 | −0.198755 | ||||||||
\(596\) | −9.64485 | −0.395068 | ||||||||
\(597\) | −0.492993 | −0.0201768 | ||||||||
\(598\) | 29.1706 | 1.19287 | ||||||||
\(599\) | 24.4171 | 0.997654 | 0.498827 | − | 0.866702i | \(-0.333764\pi\) | ||||
0.498827 | + | 0.866702i | \(0.333764\pi\) | |||||||
\(600\) | 2.92407 | 0.119375 | ||||||||
\(601\) | 10.2228 | 0.416995 | 0.208497 | − | 0.978023i | \(-0.433143\pi\) | ||||
0.208497 | + | 0.978023i | \(0.433143\pi\) | |||||||
\(602\) | −1.48327 | −0.0604534 | ||||||||
\(603\) | 1.63512 | 0.0665872 | ||||||||
\(604\) | 7.76323 | 0.315881 | ||||||||
\(605\) | −1.44081 | −0.0585772 | ||||||||
\(606\) | 1.20404 | 0.0489107 | ||||||||
\(607\) | −47.6495 | −1.93404 | −0.967018 | − | 0.254709i | \(-0.918020\pi\) | ||||
−0.967018 | + | 0.254709i | \(0.918020\pi\) | |||||||
\(608\) | −2.92407 | −0.118587 | ||||||||
\(609\) | −7.55919 | −0.306314 | ||||||||
\(610\) | 1.44081 | 0.0583366 | ||||||||
\(611\) | 65.4740 | 2.64879 | ||||||||
\(612\) | 1.00000 | 0.0404226 | ||||||||
\(613\) | −31.9950 | −1.29226 | −0.646132 | − | 0.763225i | \(-0.723615\pi\) | ||||
−0.646132 | + | 0.763225i | \(0.723615\pi\) | |||||||
\(614\) | 5.07593 | 0.204848 | ||||||||
\(615\) | −15.2890 | −0.616510 | ||||||||
\(616\) | 3.36488 | 0.135575 | ||||||||
\(617\) | 12.4163 | 0.499863 | 0.249931 | − | 0.968264i | \(-0.419592\pi\) | ||||
0.249931 | + | 0.968264i | \(0.419592\pi\) | |||||||
\(618\) | 6.32242 | 0.254325 | ||||||||
\(619\) | 27.8863 | 1.12085 | 0.560423 | − | 0.828207i | \(-0.310639\pi\) | ||||
0.560423 | + | 0.828207i | \(0.310639\pi\) | |||||||
\(620\) | 2.35589 | 0.0946149 | ||||||||
\(621\) | 4.92407 | 0.197596 | ||||||||
\(622\) | 11.9101 | 0.477550 | ||||||||
\(623\) | −60.3451 | −2.41768 | ||||||||
\(624\) | 5.92407 | 0.237153 | ||||||||
\(625\) | −1.82943 | −0.0731772 | ||||||||
\(626\) | 29.7582 | 1.18938 | ||||||||
\(627\) | 2.92407 | 0.116776 | ||||||||
\(628\) | 3.12811 | 0.124825 | ||||||||
\(629\) | −0.194311 | −0.00774770 | ||||||||
\(630\) | −4.84815 | −0.193155 | ||||||||
\(631\) | −12.4693 | −0.496393 | −0.248197 | − | 0.968710i | \(-0.579838\pi\) | ||||
−0.248197 | + | 0.968710i | \(0.579838\pi\) | |||||||
\(632\) | −5.92407 | −0.235647 | ||||||||
\(633\) | −28.1893 | −1.12042 | ||||||||
\(634\) | 8.84888 | 0.351434 | ||||||||
\(635\) | −2.71105 | −0.107585 | ||||||||
\(636\) | −10.2890 | −0.407984 | ||||||||
\(637\) | −25.6064 | −1.01456 | ||||||||
\(638\) | 2.24650 | 0.0889396 | ||||||||
\(639\) | −1.63512 | −0.0646843 | ||||||||
\(640\) | −1.44081 | −0.0569529 | ||||||||
\(641\) | 49.0904 | 1.93895 | 0.969476 | − | 0.245185i | \(-0.0788488\pi\) | ||||
0.969476 | + | 0.245185i | \(0.0788488\pi\) | |||||||
\(642\) | 15.5355 | 0.613135 | ||||||||
\(643\) | 6.55919 | 0.258669 | 0.129335 | − | 0.991601i | \(-0.458716\pi\) | ||||
0.129335 | + | 0.991601i | \(0.458716\pi\) | |||||||
\(644\) | −16.5689 | −0.652907 | ||||||||
\(645\) | −0.635119 | −0.0250078 | ||||||||
\(646\) | −2.92407 | −0.115046 | ||||||||
\(647\) | −19.8154 | −0.779024 | −0.389512 | − | 0.921021i | \(-0.627356\pi\) | ||||
−0.389512 | + | 0.921021i | \(0.627356\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 10.1281 | 0.397563 | ||||||||
\(650\) | 17.3224 | 0.679441 | ||||||||
\(651\) | 5.50198 | 0.215640 | ||||||||
\(652\) | 4.63512 | 0.181525 | ||||||||
\(653\) | 15.7298 | 0.615553 | 0.307777 | − | 0.951459i | \(-0.400415\pi\) | ||||
0.307777 | + | 0.951459i | \(0.400415\pi\) | |||||||
\(654\) | −13.1468 | −0.514082 | ||||||||
\(655\) | 26.0097 | 1.01628 | ||||||||
\(656\) | −10.6114 | −0.414305 | ||||||||
\(657\) | 8.24650 | 0.321726 | ||||||||
\(658\) | −37.1893 | −1.44979 | ||||||||
\(659\) | 10.7967 | 0.420580 | 0.210290 | − | 0.977639i | \(-0.432559\pi\) | ||||
0.210290 | + | 0.977639i | \(0.432559\pi\) | |||||||
\(660\) | 1.44081 | 0.0560834 | ||||||||
\(661\) | −7.24576 | −0.281827 | −0.140914 | − | 0.990022i | \(-0.545004\pi\) | ||||
−0.140914 | + | 0.990022i | \(0.545004\pi\) | |||||||
\(662\) | 3.00973 | 0.116976 | ||||||||
\(663\) | 5.92407 | 0.230072 | ||||||||
\(664\) | −2.39835 | −0.0930740 | ||||||||
\(665\) | 14.1763 | 0.549735 | ||||||||
\(666\) | −0.194311 | −0.00752942 | ||||||||
\(667\) | −11.0619 | −0.428319 | ||||||||
\(668\) | −15.1706 | −0.586967 | ||||||||
\(669\) | −18.4408 | −0.712963 | ||||||||
\(670\) | −2.35589 | −0.0910161 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | −3.36488 | −0.129803 | ||||||||
\(673\) | −14.6636 | −0.565239 | −0.282619 | − | 0.959232i | \(-0.591203\pi\) | ||||
−0.282619 | + | 0.959232i | \(0.591203\pi\) | |||||||
\(674\) | −22.6823 | −0.873689 | ||||||||
\(675\) | 2.92407 | 0.112548 | ||||||||
\(676\) | 22.0946 | 0.849794 | ||||||||
\(677\) | −7.67758 | −0.295073 | −0.147537 | − | 0.989057i | \(-0.547134\pi\) | ||||
−0.147537 | + | 0.989057i | \(0.547134\pi\) | |||||||
\(678\) | −1.32242 | −0.0507874 | ||||||||
\(679\) | −15.4840 | −0.594222 | ||||||||
\(680\) | −1.44081 | −0.0552525 | ||||||||
\(681\) | 27.2130 | 1.04281 | ||||||||
\(682\) | −1.63512 | −0.0626119 | ||||||||
\(683\) | 8.32168 | 0.318420 | 0.159210 | − | 0.987245i | \(-0.449105\pi\) | ||||
0.159210 | + | 0.987245i | \(0.449105\pi\) | |||||||
\(684\) | −2.92407 | −0.111805 | ||||||||
\(685\) | 14.2375 | 0.543987 | ||||||||
\(686\) | −9.00973 | −0.343993 | ||||||||
\(687\) | 26.5355 | 1.01239 | ||||||||
\(688\) | −0.440808 | −0.0168056 | ||||||||
\(689\) | −60.9525 | −2.32211 | ||||||||
\(690\) | −7.09464 | −0.270088 | ||||||||
\(691\) | 9.35087 | 0.355724 | 0.177862 | − | 0.984055i | \(-0.443082\pi\) | ||||
0.177862 | + | 0.984055i | \(0.443082\pi\) | |||||||
\(692\) | 0.246496 | 0.00937038 | ||||||||
\(693\) | 3.36488 | 0.127821 | ||||||||
\(694\) | 18.4073 | 0.698733 | ||||||||
\(695\) | −11.1983 | −0.424775 | ||||||||
\(696\) | −2.24650 | −0.0851532 | ||||||||
\(697\) | −10.6114 | −0.401935 | ||||||||
\(698\) | 18.2562 | 0.691008 | ||||||||
\(699\) | −4.34114 | −0.164197 | ||||||||
\(700\) | −9.83916 | −0.371885 | ||||||||
\(701\) | 6.38360 | 0.241105 | 0.120553 | − | 0.992707i | \(-0.461533\pi\) | ||||
0.120553 | + | 0.992707i | \(0.461533\pi\) | |||||||
\(702\) | 5.92407 | 0.223590 | ||||||||
\(703\) | 0.568181 | 0.0214293 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | −15.9241 | −0.599735 | ||||||||
\(706\) | −13.8392 | −0.520844 | ||||||||
\(707\) | −4.05145 | −0.152370 | ||||||||
\(708\) | −10.1281 | −0.380638 | ||||||||
\(709\) | 30.0849 | 1.12986 | 0.564931 | − | 0.825138i | \(-0.308903\pi\) | ||||
0.564931 | + | 0.825138i | \(0.308903\pi\) | |||||||
\(710\) | 2.35589 | 0.0884151 | ||||||||
\(711\) | −5.92407 | −0.222170 | ||||||||
\(712\) | −17.9338 | −0.672098 | ||||||||
\(713\) | 8.05145 | 0.301529 | ||||||||
\(714\) | −3.36488 | −0.125928 | ||||||||
\(715\) | 8.53545 | 0.319208 | ||||||||
\(716\) | −18.5117 | −0.691815 | ||||||||
\(717\) | 10.9003 | 0.407080 | ||||||||
\(718\) | −22.6963 | −0.847018 | ||||||||
\(719\) | 20.5020 | 0.764595 | 0.382297 | − | 0.924039i | \(-0.375133\pi\) | ||||
0.382297 | + | 0.924039i | \(0.375133\pi\) | |||||||
\(720\) | −1.44081 | −0.0536957 | ||||||||
\(721\) | −21.2742 | −0.792293 | ||||||||
\(722\) | −10.4498 | −0.388901 | ||||||||
\(723\) | −10.0425 | −0.373483 | ||||||||
\(724\) | −18.3746 | −0.682887 | ||||||||
\(725\) | −6.56892 | −0.243964 | ||||||||
\(726\) | −1.00000 | −0.0371135 | ||||||||
\(727\) | 11.1990 | 0.415348 | 0.207674 | − | 0.978198i | \(-0.433411\pi\) | ||||
0.207674 | + | 0.978198i | \(0.433411\pi\) | |||||||
\(728\) | −19.9338 | −0.738796 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −11.8816 | −0.439758 | ||||||||
\(731\) | −0.440808 | −0.0163039 | ||||||||
\(732\) | 1.00000 | 0.0369611 | ||||||||
\(733\) | 18.7730 | 0.693395 | 0.346698 | − | 0.937977i | \(-0.387303\pi\) | ||||
0.346698 | + | 0.937977i | \(0.387303\pi\) | |||||||
\(734\) | 22.3077 | 0.823391 | ||||||||
\(735\) | 6.22778 | 0.229715 | ||||||||
\(736\) | −4.92407 | −0.181504 | ||||||||
\(737\) | 1.63512 | 0.0602304 | ||||||||
\(738\) | −10.6114 | −0.390610 | ||||||||
\(739\) | −8.11336 | −0.298455 | −0.149227 | − | 0.988803i | \(-0.547679\pi\) | ||||
−0.149227 | + | 0.988803i | \(0.547679\pi\) | |||||||
\(740\) | 0.279965 | 0.0102917 | ||||||||
\(741\) | −17.3224 | −0.636355 | ||||||||
\(742\) | 34.6211 | 1.27098 | ||||||||
\(743\) | −7.37461 | −0.270548 | −0.135274 | − | 0.990808i | \(-0.543191\pi\) | ||||
−0.135274 | + | 0.990808i | \(0.543191\pi\) | |||||||
\(744\) | 1.63512 | 0.0599464 | ||||||||
\(745\) | 13.8964 | 0.509124 | ||||||||
\(746\) | 21.0946 | 0.772330 | ||||||||
\(747\) | −2.39835 | −0.0877510 | ||||||||
\(748\) | 1.00000 | 0.0365636 | ||||||||
\(749\) | −52.2749 | −1.91008 | ||||||||
\(750\) | −11.4171 | −0.416892 | ||||||||
\(751\) | −21.2235 | −0.774456 | −0.387228 | − | 0.921984i | \(-0.626567\pi\) | ||||
−0.387228 | + | 0.921984i | \(0.626567\pi\) | |||||||
\(752\) | −11.0522 | −0.403032 | ||||||||
\(753\) | −15.0612 | −0.548860 | ||||||||
\(754\) | −13.3084 | −0.484664 | ||||||||
\(755\) | −11.1853 | −0.407076 | ||||||||
\(756\) | −3.36488 | −0.122380 | ||||||||
\(757\) | 28.6920 | 1.04283 | 0.521414 | − | 0.853304i | \(-0.325405\pi\) | ||||
0.521414 | + | 0.853304i | \(0.325405\pi\) | |||||||
\(758\) | −25.1044 | −0.911832 | ||||||||
\(759\) | 4.92407 | 0.178733 | ||||||||
\(760\) | 4.21303 | 0.152823 | ||||||||
\(761\) | −37.4700 | −1.35829 | −0.679143 | − | 0.734006i | \(-0.737648\pi\) | ||||
−0.679143 | + | 0.734006i | \(0.737648\pi\) | |||||||
\(762\) | −1.88162 | −0.0681637 | ||||||||
\(763\) | 44.2375 | 1.60151 | ||||||||
\(764\) | −8.41707 | −0.304519 | ||||||||
\(765\) | −1.44081 | −0.0520925 | ||||||||
\(766\) | 16.7632 | 0.605680 | ||||||||
\(767\) | −59.9997 | −2.16646 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −23.9770 | −0.864633 | −0.432316 | − | 0.901722i | \(-0.642304\pi\) | ||||
−0.432316 | + | 0.901722i | \(0.642304\pi\) | |||||||
\(770\) | −4.84815 | −0.174715 | ||||||||
\(771\) | −11.0097 | −0.396506 | ||||||||
\(772\) | 0.905357 | 0.0325845 | ||||||||
\(773\) | −9.53545 | −0.342966 | −0.171483 | − | 0.985187i | \(-0.554856\pi\) | ||||
−0.171483 | + | 0.985187i | \(0.554856\pi\) | |||||||
\(774\) | −0.440808 | −0.0158445 | ||||||||
\(775\) | 4.78121 | 0.171746 | ||||||||
\(776\) | −4.60165 | −0.165190 | ||||||||
\(777\) | 0.653835 | 0.0234562 | ||||||||
\(778\) | 20.6351 | 0.739805 | ||||||||
\(779\) | 31.0284 | 1.11171 | ||||||||
\(780\) | −8.53545 | −0.305618 | ||||||||
\(781\) | −1.63512 | −0.0585092 | ||||||||
\(782\) | −4.92407 | −0.176084 | ||||||||
\(783\) | −2.24650 | −0.0802832 | ||||||||
\(784\) | 4.32242 | 0.154372 | ||||||||
\(785\) | −4.50701 | −0.160862 | ||||||||
\(786\) | 18.0522 | 0.643900 | ||||||||
\(787\) | 9.74452 | 0.347354 | 0.173677 | − | 0.984803i | \(-0.444435\pi\) | ||||
0.173677 | + | 0.984803i | \(0.444435\pi\) | |||||||
\(788\) | 8.97626 | 0.319766 | ||||||||
\(789\) | 30.7395 | 1.09435 | ||||||||
\(790\) | 8.53545 | 0.303678 | ||||||||
\(791\) | 4.44980 | 0.158217 | ||||||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | 5.92407 | 0.210370 | ||||||||
\(794\) | −4.10866 | −0.145811 | ||||||||
\(795\) | 14.8244 | 0.525767 | ||||||||
\(796\) | 0.492993 | 0.0174737 | ||||||||
\(797\) | −53.6398 | −1.90002 | −0.950010 | − | 0.312220i | \(-0.898928\pi\) | ||||
−0.950010 | + | 0.312220i | \(0.898928\pi\) | |||||||
\(798\) | 9.83916 | 0.348302 | ||||||||
\(799\) | −11.0522 | −0.390998 | ||||||||
\(800\) | −2.92407 | −0.103382 | ||||||||
\(801\) | −17.9338 | −0.633660 | ||||||||
\(802\) | 10.7298 | 0.378881 | ||||||||
\(803\) | 8.24650 | 0.291013 | ||||||||
\(804\) | −1.63512 | −0.0576662 | ||||||||
\(805\) | 23.8726 | 0.841400 | ||||||||
\(806\) | 9.68657 | 0.341195 | ||||||||
\(807\) | 21.0000 | 0.739235 | ||||||||
\(808\) | −1.20404 | −0.0423579 | ||||||||
\(809\) | −40.8816 | −1.43732 | −0.718661 | − | 0.695361i | \(-0.755244\pi\) | ||||
−0.718661 | + | 0.695361i | \(0.755244\pi\) | |||||||
\(810\) | −1.44081 | −0.0506248 | ||||||||
\(811\) | 24.5876 | 0.863389 | 0.431694 | − | 0.902020i | \(-0.357916\pi\) | ||||
0.431694 | + | 0.902020i | \(0.357916\pi\) | |||||||
\(812\) | 7.55919 | 0.265276 | ||||||||
\(813\) | 9.07593 | 0.318307 | ||||||||
\(814\) | −0.194311 | −0.00681061 | ||||||||
\(815\) | −6.67832 | −0.233931 | ||||||||
\(816\) | −1.00000 | −0.0350070 | ||||||||
\(817\) | 1.28895 | 0.0450948 | ||||||||
\(818\) | 27.4358 | 0.959270 | ||||||||
\(819\) | −19.9338 | −0.696543 | ||||||||
\(820\) | 15.2890 | 0.533913 | ||||||||
\(821\) | −36.6308 | −1.27842 | −0.639212 | − | 0.769030i | \(-0.720740\pi\) | ||||
−0.639212 | + | 0.769030i | \(0.720740\pi\) | |||||||
\(822\) | 9.88162 | 0.344661 | ||||||||
\(823\) | 47.3084 | 1.64907 | 0.824534 | − | 0.565813i | \(-0.191438\pi\) | ||||
0.824534 | + | 0.565813i | \(0.191438\pi\) | |||||||
\(824\) | −6.32242 | −0.220252 | ||||||||
\(825\) | 2.92407 | 0.101803 | ||||||||
\(826\) | 34.0799 | 1.18579 | ||||||||
\(827\) | 37.7917 | 1.31415 | 0.657073 | − | 0.753827i | \(-0.271794\pi\) | ||||
0.657073 | + | 0.753827i | \(0.271794\pi\) | |||||||
\(828\) | −4.92407 | −0.171123 | ||||||||
\(829\) | 38.0806 | 1.32259 | 0.661297 | − | 0.750124i | \(-0.270006\pi\) | ||||
0.661297 | + | 0.750124i | \(0.270006\pi\) | |||||||
\(830\) | 3.45556 | 0.119944 | ||||||||
\(831\) | 19.2987 | 0.669464 | ||||||||
\(832\) | −5.92407 | −0.205380 | ||||||||
\(833\) | 4.32242 | 0.149763 | ||||||||
\(834\) | −7.77222 | −0.269130 | ||||||||
\(835\) | 21.8579 | 0.756423 | ||||||||
\(836\) | −2.92407 | −0.101131 | ||||||||
\(837\) | 1.63512 | 0.0565180 | ||||||||
\(838\) | −18.6538 | −0.644386 | ||||||||
\(839\) | 23.0709 | 0.796496 | 0.398248 | − | 0.917278i | \(-0.369618\pi\) | ||||
0.398248 | + | 0.917278i | \(0.369618\pi\) | |||||||
\(840\) | 4.84815 | 0.167277 | ||||||||
\(841\) | −23.9533 | −0.825974 | ||||||||
\(842\) | −10.1468 | −0.349683 | ||||||||
\(843\) | 0.398350 | 0.0137199 | ||||||||
\(844\) | 28.1893 | 0.970315 | ||||||||
\(845\) | −31.8341 | −1.09513 | ||||||||
\(846\) | −11.0522 | −0.379982 | ||||||||
\(847\) | 3.36488 | 0.115619 | ||||||||
\(848\) | 10.2890 | 0.353324 | ||||||||
\(849\) | −15.5592 | −0.533990 | ||||||||
\(850\) | −2.92407 | −0.100295 | ||||||||
\(851\) | 0.956804 | 0.0327988 | ||||||||
\(852\) | 1.63512 | 0.0560183 | ||||||||
\(853\) | 5.89060 | 0.201690 | 0.100845 | − | 0.994902i | \(-0.467845\pi\) | ||||
0.100845 | + | 0.994902i | \(0.467845\pi\) | |||||||
\(854\) | −3.36488 | −0.115144 | ||||||||
\(855\) | 4.21303 | 0.144082 | ||||||||
\(856\) | −15.5355 | −0.530991 | ||||||||
\(857\) | −20.1706 | −0.689014 | −0.344507 | − | 0.938784i | \(-0.611954\pi\) | ||||
−0.344507 | + | 0.938784i | \(0.611954\pi\) | |||||||
\(858\) | 5.92407 | 0.202245 | ||||||||
\(859\) | 8.11336 | 0.276824 | 0.138412 | − | 0.990375i | \(-0.455800\pi\) | ||||
0.138412 | + | 0.990375i | \(0.455800\pi\) | |||||||
\(860\) | 0.635119 | 0.0216574 | ||||||||
\(861\) | 35.7060 | 1.21686 | ||||||||
\(862\) | −3.38862 | −0.115417 | ||||||||
\(863\) | −22.8528 | −0.777920 | −0.388960 | − | 0.921255i | \(-0.627166\pi\) | ||||
−0.388960 | + | 0.921255i | \(0.627166\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −0.355154 | −0.0120756 | ||||||||
\(866\) | −25.2562 | −0.858241 | ||||||||
\(867\) | 16.0000 | 0.543388 | ||||||||
\(868\) | −5.50198 | −0.186749 | ||||||||
\(869\) | −5.92407 | −0.200960 | ||||||||
\(870\) | 3.23677 | 0.109737 | ||||||||
\(871\) | −9.68657 | −0.328217 | ||||||||
\(872\) | 13.1468 | 0.445208 | ||||||||
\(873\) | −4.60165 | −0.155742 | ||||||||
\(874\) | 14.3983 | 0.487031 | ||||||||
\(875\) | 38.4171 | 1.29873 | ||||||||
\(876\) | −8.24650 | −0.278623 | ||||||||
\(877\) | 3.67758 | 0.124183 | 0.0620915 | − | 0.998070i | \(-0.480223\pi\) | ||||
0.0620915 | + | 0.998070i | \(0.480223\pi\) | |||||||
\(878\) | −7.19431 | −0.242796 | ||||||||
\(879\) | −10.6776 | −0.360146 | ||||||||
\(880\) | −1.44081 | −0.0485696 | ||||||||
\(881\) | −39.3933 | −1.32719 | −0.663597 | − | 0.748090i | \(-0.730971\pi\) | ||||
−0.663597 | + | 0.748090i | \(0.730971\pi\) | |||||||
\(882\) | 4.32242 | 0.145544 | ||||||||
\(883\) | −26.3181 | −0.885676 | −0.442838 | − | 0.896602i | \(-0.646028\pi\) | ||||
−0.442838 | + | 0.896602i | \(0.646028\pi\) | |||||||
\(884\) | −5.92407 | −0.199248 | ||||||||
\(885\) | 14.5927 | 0.490527 | ||||||||
\(886\) | 32.1461 | 1.07997 | ||||||||
\(887\) | −22.9950 | −0.772096 | −0.386048 | − | 0.922479i | \(-0.626160\pi\) | ||||
−0.386048 | + | 0.922479i | \(0.626160\pi\) | |||||||
\(888\) | 0.194311 | 0.00652066 | ||||||||
\(889\) | 6.33141 | 0.212349 | ||||||||
\(890\) | 25.8392 | 0.866131 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 18.4408 | 0.617444 | ||||||||
\(893\) | 32.3174 | 1.08146 | ||||||||
\(894\) | 9.64485 | 0.322572 | ||||||||
\(895\) | 26.6718 | 0.891540 | ||||||||
\(896\) | 3.36488 | 0.112413 | ||||||||
\(897\) | −29.1706 | −0.973977 | ||||||||
\(898\) | −27.2562 | −0.909552 | ||||||||
\(899\) | −3.67329 | −0.122511 | ||||||||
\(900\) | −2.92407 | −0.0974691 | ||||||||
\(901\) | 10.2890 | 0.342775 | ||||||||
\(902\) | −10.6114 | −0.353320 | ||||||||
\(903\) | 1.48327 | 0.0493600 | ||||||||
\(904\) | 1.32242 | 0.0439831 | ||||||||
\(905\) | 26.4743 | 0.880035 | ||||||||
\(906\) | −7.76323 | −0.257916 | ||||||||
\(907\) | 29.4700 | 0.978535 | 0.489267 | − | 0.872134i | \(-0.337264\pi\) | ||||
0.489267 | + | 0.872134i | \(0.337264\pi\) | |||||||
\(908\) | −27.2130 | −0.903096 | ||||||||
\(909\) | −1.20404 | −0.0399354 | ||||||||
\(910\) | 28.7208 | 0.952084 | ||||||||
\(911\) | 3.34188 | 0.110721 | 0.0553607 | − | 0.998466i | \(-0.482369\pi\) | ||||
0.0553607 | + | 0.998466i | \(0.482369\pi\) | |||||||
\(912\) | 2.92407 | 0.0968257 | ||||||||
\(913\) | −2.39835 | −0.0793738 | ||||||||
\(914\) | 7.97626 | 0.263831 | ||||||||
\(915\) | −1.44081 | −0.0476316 | ||||||||
\(916\) | −26.5355 | −0.876756 | ||||||||
\(917\) | −60.7435 | −2.00593 | ||||||||
\(918\) | −1.00000 | −0.0330049 | ||||||||
\(919\) | −37.7255 | −1.24445 | −0.622224 | − | 0.782839i | \(-0.713771\pi\) | ||||
−0.622224 | + | 0.782839i | \(0.713771\pi\) | |||||||
\(920\) | 7.09464 | 0.233903 | ||||||||
\(921\) | −5.07593 | −0.167257 | ||||||||
\(922\) | 28.3411 | 0.933366 | ||||||||
\(923\) | 9.68657 | 0.318837 | ||||||||
\(924\) | −3.36488 | −0.110696 | ||||||||
\(925\) | 0.568181 | 0.0186817 | ||||||||
\(926\) | 24.6538 | 0.810175 | ||||||||
\(927\) | −6.32242 | −0.207656 | ||||||||
\(928\) | 2.24650 | 0.0737449 | ||||||||
\(929\) | 30.7632 | 1.00931 | 0.504654 | − | 0.863321i | \(-0.331620\pi\) | ||||
0.504654 | + | 0.863321i | \(0.331620\pi\) | |||||||
\(930\) | −2.35589 | −0.0772528 | ||||||||
\(931\) | −12.6391 | −0.414229 | ||||||||
\(932\) | 4.34114 | 0.142199 | ||||||||
\(933\) | −11.9101 | −0.389918 | ||||||||
\(934\) | 25.1803 | 0.823924 | ||||||||
\(935\) | −1.44081 | −0.0471195 | ||||||||
\(936\) | −5.92407 | −0.193634 | ||||||||
\(937\) | 41.6873 | 1.36186 | 0.680932 | − | 0.732346i | \(-0.261575\pi\) | ||||
0.680932 | + | 0.732346i | \(0.261575\pi\) | |||||||
\(938\) | 5.50198 | 0.179646 | ||||||||
\(939\) | −29.7582 | −0.971122 | ||||||||
\(940\) | 15.9241 | 0.519386 | ||||||||
\(941\) | 7.54048 | 0.245813 | 0.122906 | − | 0.992418i | \(-0.460779\pi\) | ||||
0.122906 | + | 0.992418i | \(0.460779\pi\) | |||||||
\(942\) | −3.12811 | −0.101919 | ||||||||
\(943\) | 52.2512 | 1.70153 | ||||||||
\(944\) | 10.1281 | 0.329642 | ||||||||
\(945\) | 4.84815 | 0.157710 | ||||||||
\(946\) | −0.440808 | −0.0143319 | ||||||||
\(947\) | −20.3976 | −0.662833 | −0.331417 | − | 0.943484i | \(-0.607527\pi\) | ||||
−0.331417 | + | 0.943484i | \(0.607527\pi\) | |||||||
\(948\) | 5.92407 | 0.192405 | ||||||||
\(949\) | −48.8528 | −1.58583 | ||||||||
\(950\) | 8.55020 | 0.277405 | ||||||||
\(951\) | −8.84888 | −0.286945 | ||||||||
\(952\) | 3.36488 | 0.109056 | ||||||||
\(953\) | −5.05721 | −0.163819 | −0.0819096 | − | 0.996640i | \(-0.526102\pi\) | ||||
−0.0819096 | + | 0.996640i | \(0.526102\pi\) | |||||||
\(954\) | 10.2890 | 0.333117 | ||||||||
\(955\) | 12.1274 | 0.392433 | ||||||||
\(956\) | −10.9003 | −0.352542 | ||||||||
\(957\) | −2.24650 | −0.0726189 | ||||||||
\(958\) | 9.40734 | 0.303937 | ||||||||
\(959\) | −33.2505 | −1.07371 | ||||||||
\(960\) | 1.44081 | 0.0465019 | ||||||||
\(961\) | −28.3264 | −0.913754 | ||||||||
\(962\) | 1.15112 | 0.0371134 | ||||||||
\(963\) | −15.5355 | −0.500623 | ||||||||
\(964\) | 10.0425 | 0.323446 | ||||||||
\(965\) | −1.30445 | −0.0419916 | ||||||||
\(966\) | 16.5689 | 0.533096 | ||||||||
\(967\) | 22.1796 | 0.713247 | 0.356623 | − | 0.934248i | \(-0.383928\pi\) | ||||
0.356623 | + | 0.934248i | \(0.383928\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 2.92407 | 0.0939348 | ||||||||
\(970\) | 6.63009 | 0.212879 | ||||||||
\(971\) | 14.4693 | 0.464340 | 0.232170 | − | 0.972675i | \(-0.425417\pi\) | ||||
0.232170 | + | 0.972675i | \(0.425417\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 26.1526 | 0.838414 | ||||||||
\(974\) | 32.2465 | 1.03324 | ||||||||
\(975\) | −17.3224 | −0.554762 | ||||||||
\(976\) | −1.00000 | −0.0320092 | ||||||||
\(977\) | −54.1885 | −1.73365 | −0.866823 | − | 0.498617i | \(-0.833842\pi\) | ||||
−0.866823 | + | 0.498617i | \(0.833842\pi\) | |||||||
\(978\) | −4.63512 | −0.148215 | ||||||||
\(979\) | −17.9338 | −0.573167 | ||||||||
\(980\) | −6.22778 | −0.198939 | ||||||||
\(981\) | 13.1468 | 0.419746 | ||||||||
\(982\) | −1.79596 | −0.0573114 | ||||||||
\(983\) | 55.0619 | 1.75620 | 0.878101 | − | 0.478475i | \(-0.158810\pi\) | ||||
0.878101 | + | 0.478475i | \(0.158810\pi\) | |||||||
\(984\) | 10.6114 | 0.338278 | ||||||||
\(985\) | −12.9331 | −0.412082 | ||||||||
\(986\) | 2.24650 | 0.0715430 | ||||||||
\(987\) | 37.1893 | 1.18375 | ||||||||
\(988\) | 17.3224 | 0.551100 | ||||||||
\(989\) | 2.17057 | 0.0690201 | ||||||||
\(990\) | −1.44081 | −0.0457919 | ||||||||
\(991\) | −47.0799 | −1.49554 | −0.747771 | − | 0.663957i | \(-0.768876\pi\) | ||||
−0.747771 | + | 0.663957i | \(0.768876\pi\) | |||||||
\(992\) | −1.63512 | −0.0519151 | ||||||||
\(993\) | −3.00973 | −0.0955108 | ||||||||
\(994\) | −5.50198 | −0.174512 | ||||||||
\(995\) | −0.710307 | −0.0225183 | ||||||||
\(996\) | 2.39835 | 0.0759946 | ||||||||
\(997\) | −49.6251 | −1.57164 | −0.785821 | − | 0.618454i | \(-0.787759\pi\) | ||||
−0.785821 | + | 0.618454i | \(0.787759\pi\) | |||||||
\(998\) | 22.0759 | 0.698801 | ||||||||
\(999\) | 0.194311 | 0.00614774 |
(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 | 4026.2.a.o.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4026.2.a.o.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial |