Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [129,2,Mod(1,129)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(129, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("129.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 129 = 3 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 129.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(1.03007018607\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.12489\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 129.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.12489 | 1.50252 | 0.751260 | − | 0.660006i | \(-0.229446\pi\) | ||||
0.751260 | + | 0.660006i | \(0.229446\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.51514 | 1.25757 | ||||||||
\(5\) | −4.12489 | −1.84470 | −0.922352 | − | 0.386350i | \(-0.873736\pi\) | ||||
−0.922352 | + | 0.386350i | \(0.873736\pi\) | |||||||
\(6\) | 2.12489 | 0.867481 | ||||||||
\(7\) | 1.48486 | 0.561225 | 0.280613 | − | 0.959821i | \(-0.409462\pi\) | ||||
0.280613 | + | 0.959821i | \(0.409462\pi\) | |||||||
\(8\) | 1.09461 | 0.387003 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −8.76491 | −2.77171 | ||||||||
\(11\) | −2.60975 | −0.786868 | −0.393434 | − | 0.919353i | \(-0.628713\pi\) | ||||
−0.393434 | + | 0.919353i | \(0.628713\pi\) | |||||||
\(12\) | 2.51514 | 0.726058 | ||||||||
\(13\) | 3.00000 | 0.832050 | 0.416025 | − | 0.909353i | \(-0.363423\pi\) | ||||
0.416025 | + | 0.909353i | \(0.363423\pi\) | |||||||
\(14\) | 3.15516 | 0.843252 | ||||||||
\(15\) | −4.12489 | −1.06504 | ||||||||
\(16\) | −2.70436 | −0.676089 | ||||||||
\(17\) | 0.484862 | 0.117596 | 0.0587981 | − | 0.998270i | \(-0.481273\pi\) | ||||
0.0587981 | + | 0.998270i | \(0.481273\pi\) | |||||||
\(18\) | 2.12489 | 0.500840 | ||||||||
\(19\) | −6.76491 | −1.55198 | −0.775988 | − | 0.630747i | \(-0.782748\pi\) | ||||
−0.775988 | + | 0.630747i | \(0.782748\pi\) | |||||||
\(20\) | −10.3747 | −2.31984 | ||||||||
\(21\) | 1.48486 | 0.324023 | ||||||||
\(22\) | −5.54541 | −1.18229 | ||||||||
\(23\) | 8.79518 | 1.83392 | 0.916961 | − | 0.398976i | \(-0.130634\pi\) | ||||
0.916961 | + | 0.398976i | \(0.130634\pi\) | |||||||
\(24\) | 1.09461 | 0.223436 | ||||||||
\(25\) | 12.0147 | 2.40294 | ||||||||
\(26\) | 6.37466 | 1.25017 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 3.73463 | 0.705779 | ||||||||
\(29\) | −2.12489 | −0.394581 | −0.197291 | − | 0.980345i | \(-0.563214\pi\) | ||||
−0.197291 | + | 0.980345i | \(0.563214\pi\) | |||||||
\(30\) | −8.76491 | −1.60025 | ||||||||
\(31\) | 3.76491 | 0.676198 | 0.338099 | − | 0.941111i | \(-0.390216\pi\) | ||||
0.338099 | + | 0.941111i | \(0.390216\pi\) | |||||||
\(32\) | −7.93567 | −1.40284 | ||||||||
\(33\) | −2.60975 | −0.454299 | ||||||||
\(34\) | 1.03028 | 0.176691 | ||||||||
\(35\) | −6.12489 | −1.03529 | ||||||||
\(36\) | 2.51514 | 0.419190 | ||||||||
\(37\) | 5.28005 | 0.868034 | 0.434017 | − | 0.900905i | \(-0.357096\pi\) | ||||
0.434017 | + | 0.900905i | \(0.357096\pi\) | |||||||
\(38\) | −14.3747 | −2.33188 | ||||||||
\(39\) | 3.00000 | 0.480384 | ||||||||
\(40\) | −4.51514 | −0.713906 | ||||||||
\(41\) | 0.734633 | 0.114730 | 0.0573652 | − | 0.998353i | \(-0.481730\pi\) | ||||
0.0573652 | + | 0.998353i | \(0.481730\pi\) | |||||||
\(42\) | 3.15516 | 0.486852 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | −6.56387 | −0.989541 | ||||||||
\(45\) | −4.12489 | −0.614902 | ||||||||
\(46\) | 18.6888 | 2.75551 | ||||||||
\(47\) | −8.43521 | −1.23040 | −0.615201 | − | 0.788370i | \(-0.710925\pi\) | ||||
−0.615201 | + | 0.788370i | \(0.710925\pi\) | |||||||
\(48\) | −2.70436 | −0.390340 | ||||||||
\(49\) | −4.79518 | −0.685026 | ||||||||
\(50\) | 25.5298 | 3.61046 | ||||||||
\(51\) | 0.484862 | 0.0678943 | ||||||||
\(52\) | 7.54541 | 1.04636 | ||||||||
\(53\) | 3.76491 | 0.517150 | 0.258575 | − | 0.965991i | \(-0.416747\pi\) | ||||
0.258575 | + | 0.965991i | \(0.416747\pi\) | |||||||
\(54\) | 2.12489 | 0.289160 | ||||||||
\(55\) | 10.7649 | 1.45154 | ||||||||
\(56\) | 1.62534 | 0.217196 | ||||||||
\(57\) | −6.76491 | −0.896034 | ||||||||
\(58\) | −4.51514 | −0.592867 | ||||||||
\(59\) | 2.96972 | 0.386625 | 0.193313 | − | 0.981137i | \(-0.438077\pi\) | ||||
0.193313 | + | 0.981137i | \(0.438077\pi\) | |||||||
\(60\) | −10.3747 | −1.33936 | ||||||||
\(61\) | −11.2195 | −1.43651 | −0.718255 | − | 0.695780i | \(-0.755059\pi\) | ||||
−0.718255 | + | 0.695780i | \(0.755059\pi\) | |||||||
\(62\) | 8.00000 | 1.01600 | ||||||||
\(63\) | 1.48486 | 0.187075 | ||||||||
\(64\) | −11.4537 | −1.43171 | ||||||||
\(65\) | −12.3747 | −1.53489 | ||||||||
\(66\) | −5.54541 | −0.682593 | ||||||||
\(67\) | 7.04496 | 0.860678 | 0.430339 | − | 0.902667i | \(-0.358394\pi\) | ||||
0.430339 | + | 0.902667i | \(0.358394\pi\) | |||||||
\(68\) | 1.21949 | 0.147885 | ||||||||
\(69\) | 8.79518 | 1.05882 | ||||||||
\(70\) | −13.0147 | −1.55555 | ||||||||
\(71\) | 13.2195 | 1.56887 | 0.784433 | − | 0.620214i | \(-0.212954\pi\) | ||||
0.784433 | + | 0.620214i | \(0.212954\pi\) | |||||||
\(72\) | 1.09461 | 0.129001 | ||||||||
\(73\) | −5.03028 | −0.588749 | −0.294375 | − | 0.955690i | \(-0.595111\pi\) | ||||
−0.294375 | + | 0.955690i | \(0.595111\pi\) | |||||||
\(74\) | 11.2195 | 1.30424 | ||||||||
\(75\) | 12.0147 | 1.38734 | ||||||||
\(76\) | −17.0147 | −1.95172 | ||||||||
\(77\) | −3.87511 | −0.441610 | ||||||||
\(78\) | 6.37466 | 0.721788 | ||||||||
\(79\) | 2.71995 | 0.306019 | 0.153009 | − | 0.988225i | \(-0.451104\pi\) | ||||
0.153009 | + | 0.988225i | \(0.451104\pi\) | |||||||
\(80\) | 11.1552 | 1.24718 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.56101 | 0.172385 | ||||||||
\(83\) | −5.57947 | −0.612427 | −0.306213 | − | 0.951963i | \(-0.599062\pi\) | ||||
−0.306213 | + | 0.951963i | \(0.599062\pi\) | |||||||
\(84\) | 3.73463 | 0.407482 | ||||||||
\(85\) | −2.00000 | −0.216930 | ||||||||
\(86\) | −2.12489 | −0.229132 | ||||||||
\(87\) | −2.12489 | −0.227812 | ||||||||
\(88\) | −2.85665 | −0.304520 | ||||||||
\(89\) | −18.2498 | −1.93447 | −0.967236 | − | 0.253879i | \(-0.918293\pi\) | ||||
−0.967236 | + | 0.253879i | \(0.918293\pi\) | |||||||
\(90\) | −8.76491 | −0.923903 | ||||||||
\(91\) | 4.45459 | 0.466967 | ||||||||
\(92\) | 22.1211 | 2.30628 | ||||||||
\(93\) | 3.76491 | 0.390403 | ||||||||
\(94\) | −17.9239 | −1.84870 | ||||||||
\(95\) | 27.9045 | 2.86294 | ||||||||
\(96\) | −7.93567 | −0.809931 | ||||||||
\(97\) | 6.21949 | 0.631494 | 0.315747 | − | 0.948843i | \(-0.397745\pi\) | ||||
0.315747 | + | 0.948843i | \(0.397745\pi\) | |||||||
\(98\) | −10.1892 | −1.02927 | ||||||||
\(99\) | −2.60975 | −0.262289 | ||||||||
\(100\) | 30.2186 | 3.02186 | ||||||||
\(101\) | 7.76491 | 0.772637 | 0.386319 | − | 0.922365i | \(-0.373747\pi\) | ||||
0.386319 | + | 0.922365i | \(0.373747\pi\) | |||||||
\(102\) | 1.03028 | 0.102013 | ||||||||
\(103\) | 2.54541 | 0.250807 | 0.125404 | − | 0.992106i | \(-0.459977\pi\) | ||||
0.125404 | + | 0.992106i | \(0.459977\pi\) | |||||||
\(104\) | 3.28383 | 0.322006 | ||||||||
\(105\) | −6.12489 | −0.597728 | ||||||||
\(106\) | 8.00000 | 0.777029 | ||||||||
\(107\) | −3.15516 | −0.305021 | −0.152510 | − | 0.988302i | \(-0.548736\pi\) | ||||
−0.152510 | + | 0.988302i | \(0.548736\pi\) | |||||||
\(108\) | 2.51514 | 0.242019 | ||||||||
\(109\) | −9.24977 | −0.885967 | −0.442984 | − | 0.896530i | \(-0.646080\pi\) | ||||
−0.442984 | + | 0.896530i | \(0.646080\pi\) | |||||||
\(110\) | 22.8742 | 2.18097 | ||||||||
\(111\) | 5.28005 | 0.501160 | ||||||||
\(112\) | −4.01560 | −0.379438 | ||||||||
\(113\) | 3.40493 | 0.320309 | 0.160155 | − | 0.987092i | \(-0.448801\pi\) | ||||
0.160155 | + | 0.987092i | \(0.448801\pi\) | |||||||
\(114\) | −14.3747 | −1.34631 | ||||||||
\(115\) | −36.2791 | −3.38305 | ||||||||
\(116\) | −5.34438 | −0.496213 | ||||||||
\(117\) | 3.00000 | 0.277350 | ||||||||
\(118\) | 6.31032 | 0.580912 | ||||||||
\(119\) | 0.719953 | 0.0659980 | ||||||||
\(120\) | −4.51514 | −0.412174 | ||||||||
\(121\) | −4.18922 | −0.380838 | ||||||||
\(122\) | −23.8401 | −2.15838 | ||||||||
\(123\) | 0.734633 | 0.0662396 | ||||||||
\(124\) | 9.46927 | 0.850365 | ||||||||
\(125\) | −28.9348 | −2.58800 | ||||||||
\(126\) | 3.15516 | 0.281084 | ||||||||
\(127\) | −9.04496 | −0.802610 | −0.401305 | − | 0.915944i | \(-0.631443\pi\) | ||||
−0.401305 | + | 0.915944i | \(0.631443\pi\) | |||||||
\(128\) | −8.46640 | −0.748331 | ||||||||
\(129\) | −1.00000 | −0.0880451 | ||||||||
\(130\) | −26.2947 | −2.30620 | ||||||||
\(131\) | 19.0596 | 1.66525 | 0.832624 | − | 0.553839i | \(-0.186838\pi\) | ||||
0.832624 | + | 0.553839i | \(0.186838\pi\) | |||||||
\(132\) | −6.56387 | −0.571312 | ||||||||
\(133\) | −10.0450 | −0.871008 | ||||||||
\(134\) | 14.9697 | 1.29319 | ||||||||
\(135\) | −4.12489 | −0.355014 | ||||||||
\(136\) | 0.530734 | 0.0455101 | ||||||||
\(137\) | −20.8742 | −1.78340 | −0.891702 | − | 0.452624i | \(-0.850488\pi\) | ||||
−0.891702 | + | 0.452624i | \(0.850488\pi\) | |||||||
\(138\) | 18.6888 | 1.59089 | ||||||||
\(139\) | −13.2342 | −1.12251 | −0.561254 | − | 0.827644i | \(-0.689681\pi\) | ||||
−0.561254 | + | 0.827644i | \(0.689681\pi\) | |||||||
\(140\) | −15.4049 | −1.30195 | ||||||||
\(141\) | −8.43521 | −0.710373 | ||||||||
\(142\) | 28.0899 | 2.35725 | ||||||||
\(143\) | −7.82924 | −0.654714 | ||||||||
\(144\) | −2.70436 | −0.225363 | ||||||||
\(145\) | 8.76491 | 0.727886 | ||||||||
\(146\) | −10.6888 | −0.884608 | ||||||||
\(147\) | −4.79518 | −0.395500 | ||||||||
\(148\) | 13.2800 | 1.09161 | ||||||||
\(149\) | −11.2195 | −0.919137 | −0.459568 | − | 0.888142i | \(-0.651996\pi\) | ||||
−0.459568 | + | 0.888142i | \(0.651996\pi\) | |||||||
\(150\) | 25.5298 | 2.08450 | ||||||||
\(151\) | 7.52982 | 0.612768 | 0.306384 | − | 0.951908i | \(-0.400881\pi\) | ||||
0.306384 | + | 0.951908i | \(0.400881\pi\) | |||||||
\(152\) | −7.40493 | −0.600619 | ||||||||
\(153\) | 0.484862 | 0.0391988 | ||||||||
\(154\) | −8.23417 | −0.663529 | ||||||||
\(155\) | −15.5298 | −1.24738 | ||||||||
\(156\) | 7.54541 | 0.604117 | ||||||||
\(157\) | 24.8099 | 1.98004 | 0.990021 | − | 0.140917i | \(-0.0450051\pi\) | ||||
0.990021 | + | 0.140917i | \(0.0450051\pi\) | |||||||
\(158\) | 5.77959 | 0.459799 | ||||||||
\(159\) | 3.76491 | 0.298577 | ||||||||
\(160\) | 32.7337 | 2.58783 | ||||||||
\(161\) | 13.0596 | 1.02924 | ||||||||
\(162\) | 2.12489 | 0.166947 | ||||||||
\(163\) | −1.42431 | −0.111561 | −0.0557803 | − | 0.998443i | \(-0.517765\pi\) | ||||
−0.0557803 | + | 0.998443i | \(0.517765\pi\) | |||||||
\(164\) | 1.84770 | 0.144281 | ||||||||
\(165\) | 10.7649 | 0.838047 | ||||||||
\(166\) | −11.8557 | −0.920184 | ||||||||
\(167\) | 8.35998 | 0.646914 | 0.323457 | − | 0.946243i | \(-0.395155\pi\) | ||||
0.323457 | + | 0.946243i | \(0.395155\pi\) | |||||||
\(168\) | 1.62534 | 0.125398 | ||||||||
\(169\) | −4.00000 | −0.307692 | ||||||||
\(170\) | −4.24977 | −0.325943 | ||||||||
\(171\) | −6.76491 | −0.517326 | ||||||||
\(172\) | −2.51514 | −0.191777 | ||||||||
\(173\) | 12.4390 | 0.945719 | 0.472859 | − | 0.881138i | \(-0.343222\pi\) | ||||
0.472859 | + | 0.881138i | \(0.343222\pi\) | |||||||
\(174\) | −4.51514 | −0.342292 | ||||||||
\(175\) | 17.8401 | 1.34859 | ||||||||
\(176\) | 7.05769 | 0.531993 | ||||||||
\(177\) | 2.96972 | 0.223218 | ||||||||
\(178\) | −38.7787 | −2.90658 | ||||||||
\(179\) | 2.24977 | 0.168156 | 0.0840779 | − | 0.996459i | \(-0.473206\pi\) | ||||
0.0840779 | + | 0.996459i | \(0.473206\pi\) | |||||||
\(180\) | −10.3747 | −0.773281 | ||||||||
\(181\) | −6.88601 | −0.511833 | −0.255917 | − | 0.966699i | \(-0.582377\pi\) | ||||
−0.255917 | + | 0.966699i | \(0.582377\pi\) | |||||||
\(182\) | 9.46548 | 0.701628 | ||||||||
\(183\) | −11.2195 | −0.829369 | ||||||||
\(184\) | 9.62729 | 0.709733 | ||||||||
\(185\) | −21.7796 | −1.60127 | ||||||||
\(186\) | 8.00000 | 0.586588 | ||||||||
\(187\) | −1.26537 | −0.0925328 | ||||||||
\(188\) | −21.2157 | −1.54731 | ||||||||
\(189\) | 1.48486 | 0.108008 | ||||||||
\(190\) | 59.2938 | 4.30163 | ||||||||
\(191\) | 6.47018 | 0.468166 | 0.234083 | − | 0.972217i | \(-0.424791\pi\) | ||||
0.234083 | + | 0.972217i | \(0.424791\pi\) | |||||||
\(192\) | −11.4537 | −0.826597 | ||||||||
\(193\) | 2.23509 | 0.160885 | 0.0804427 | − | 0.996759i | \(-0.474367\pi\) | ||||
0.0804427 | + | 0.996759i | \(0.474367\pi\) | |||||||
\(194\) | 13.2157 | 0.948833 | ||||||||
\(195\) | −12.3747 | −0.886168 | ||||||||
\(196\) | −12.0606 | −0.861468 | ||||||||
\(197\) | 7.77959 | 0.554273 | 0.277136 | − | 0.960831i | \(-0.410615\pi\) | ||||
0.277136 | + | 0.960831i | \(0.410615\pi\) | |||||||
\(198\) | −5.54541 | −0.394095 | ||||||||
\(199\) | 6.90917 | 0.489778 | 0.244889 | − | 0.969551i | \(-0.421248\pi\) | ||||
0.244889 | + | 0.969551i | \(0.421248\pi\) | |||||||
\(200\) | 13.1514 | 0.929943 | ||||||||
\(201\) | 7.04496 | 0.496913 | ||||||||
\(202\) | 16.4995 | 1.16090 | ||||||||
\(203\) | −3.15516 | −0.221449 | ||||||||
\(204\) | 1.21949 | 0.0853817 | ||||||||
\(205\) | −3.03028 | −0.211644 | ||||||||
\(206\) | 5.40871 | 0.376843 | ||||||||
\(207\) | 8.79518 | 0.611308 | ||||||||
\(208\) | −8.11307 | −0.562540 | ||||||||
\(209\) | 17.6547 | 1.22120 | ||||||||
\(210\) | −13.0147 | −0.898098 | ||||||||
\(211\) | 3.42431 | 0.235739 | 0.117870 | − | 0.993029i | \(-0.462394\pi\) | ||||
0.117870 | + | 0.993029i | \(0.462394\pi\) | |||||||
\(212\) | 9.46927 | 0.650352 | ||||||||
\(213\) | 13.2195 | 0.905785 | ||||||||
\(214\) | −6.70436 | −0.458300 | ||||||||
\(215\) | 4.12489 | 0.281315 | ||||||||
\(216\) | 1.09461 | 0.0744787 | ||||||||
\(217\) | 5.59037 | 0.379499 | ||||||||
\(218\) | −19.6547 | −1.33118 | ||||||||
\(219\) | −5.03028 | −0.339915 | ||||||||
\(220\) | 27.0752 | 1.82541 | ||||||||
\(221\) | 1.45459 | 0.0978460 | ||||||||
\(222\) | 11.2195 | 0.753003 | ||||||||
\(223\) | −9.73463 | −0.651879 | −0.325940 | − | 0.945391i | \(-0.605681\pi\) | ||||
−0.325940 | + | 0.945391i | \(0.605681\pi\) | |||||||
\(224\) | −11.7834 | −0.787310 | ||||||||
\(225\) | 12.0147 | 0.800979 | ||||||||
\(226\) | 7.23509 | 0.481271 | ||||||||
\(227\) | 3.09083 | 0.205145 | 0.102573 | − | 0.994726i | \(-0.467293\pi\) | ||||
0.102573 | + | 0.994726i | \(0.467293\pi\) | |||||||
\(228\) | −17.0147 | −1.12682 | ||||||||
\(229\) | 3.20482 | 0.211780 | 0.105890 | − | 0.994378i | \(-0.466231\pi\) | ||||
0.105890 | + | 0.994378i | \(0.466231\pi\) | |||||||
\(230\) | −77.0890 | −5.08310 | ||||||||
\(231\) | −3.87511 | −0.254964 | ||||||||
\(232\) | −2.32592 | −0.152704 | ||||||||
\(233\) | 11.0946 | 0.726832 | 0.363416 | − | 0.931627i | \(-0.381610\pi\) | ||||
0.363416 | + | 0.931627i | \(0.381610\pi\) | |||||||
\(234\) | 6.37466 | 0.416724 | ||||||||
\(235\) | 34.7943 | 2.26973 | ||||||||
\(236\) | 7.46927 | 0.486208 | ||||||||
\(237\) | 2.71995 | 0.176680 | ||||||||
\(238\) | 1.52982 | 0.0991634 | ||||||||
\(239\) | 17.0946 | 1.10576 | 0.552879 | − | 0.833261i | \(-0.313529\pi\) | ||||
0.552879 | + | 0.833261i | \(0.313529\pi\) | |||||||
\(240\) | 11.1552 | 0.720063 | ||||||||
\(241\) | 22.5601 | 1.45322 | 0.726612 | − | 0.687048i | \(-0.241094\pi\) | ||||
0.726612 | + | 0.687048i | \(0.241094\pi\) | |||||||
\(242\) | −8.90161 | −0.572217 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −28.2186 | −1.80651 | ||||||||
\(245\) | 19.7796 | 1.26367 | ||||||||
\(246\) | 1.56101 | 0.0995264 | ||||||||
\(247\) | −20.2947 | −1.29132 | ||||||||
\(248\) | 4.12110 | 0.261690 | ||||||||
\(249\) | −5.57947 | −0.353585 | ||||||||
\(250\) | −61.4830 | −3.88853 | ||||||||
\(251\) | 15.6400 | 0.987190 | 0.493595 | − | 0.869692i | \(-0.335683\pi\) | ||||
0.493595 | + | 0.869692i | \(0.335683\pi\) | |||||||
\(252\) | 3.73463 | 0.235260 | ||||||||
\(253\) | −22.9532 | −1.44306 | ||||||||
\(254\) | −19.2195 | −1.20594 | ||||||||
\(255\) | −2.00000 | −0.125245 | ||||||||
\(256\) | 4.91721 | 0.307325 | ||||||||
\(257\) | −17.5336 | −1.09372 | −0.546858 | − | 0.837225i | \(-0.684176\pi\) | ||||
−0.546858 | + | 0.837225i | \(0.684176\pi\) | |||||||
\(258\) | −2.12489 | −0.132290 | ||||||||
\(259\) | 7.84014 | 0.487163 | ||||||||
\(260\) | −31.1240 | −1.93023 | ||||||||
\(261\) | −2.12489 | −0.131527 | ||||||||
\(262\) | 40.4995 | 2.50207 | ||||||||
\(263\) | −6.37088 | −0.392845 | −0.196422 | − | 0.980519i | \(-0.562932\pi\) | ||||
−0.196422 | + | 0.980519i | \(0.562932\pi\) | |||||||
\(264\) | −2.85665 | −0.175815 | ||||||||
\(265\) | −15.5298 | −0.953989 | ||||||||
\(266\) | −21.3444 | −1.30871 | ||||||||
\(267\) | −18.2498 | −1.11687 | ||||||||
\(268\) | 17.7190 | 1.08236 | ||||||||
\(269\) | 29.5445 | 1.80136 | 0.900680 | − | 0.434483i | \(-0.143069\pi\) | ||||
0.900680 | + | 0.434483i | \(0.143069\pi\) | |||||||
\(270\) | −8.76491 | −0.533415 | ||||||||
\(271\) | −11.8255 | −0.718346 | −0.359173 | − | 0.933271i | \(-0.616941\pi\) | ||||
−0.359173 | + | 0.933271i | \(0.616941\pi\) | |||||||
\(272\) | −1.31124 | −0.0795056 | ||||||||
\(273\) | 4.45459 | 0.269604 | ||||||||
\(274\) | −44.3553 | −2.67960 | ||||||||
\(275\) | −31.3553 | −1.89079 | ||||||||
\(276\) | 22.1211 | 1.33153 | ||||||||
\(277\) | −15.7796 | −0.948104 | −0.474052 | − | 0.880497i | \(-0.657209\pi\) | ||||
−0.474052 | + | 0.880497i | \(0.657209\pi\) | |||||||
\(278\) | −28.1211 | −1.68659 | ||||||||
\(279\) | 3.76491 | 0.225399 | ||||||||
\(280\) | −6.70436 | −0.400662 | ||||||||
\(281\) | −18.0147 | −1.07467 | −0.537333 | − | 0.843370i | \(-0.680568\pi\) | ||||
−0.537333 | + | 0.843370i | \(0.680568\pi\) | |||||||
\(282\) | −17.9239 | −1.06735 | ||||||||
\(283\) | 5.64380 | 0.335489 | 0.167745 | − | 0.985830i | \(-0.446352\pi\) | ||||
0.167745 | + | 0.985830i | \(0.446352\pi\) | |||||||
\(284\) | 33.2489 | 1.97296 | ||||||||
\(285\) | 27.9045 | 1.65292 | ||||||||
\(286\) | −16.6362 | −0.983722 | ||||||||
\(287\) | 1.09083 | 0.0643896 | ||||||||
\(288\) | −7.93567 | −0.467614 | ||||||||
\(289\) | −16.7649 | −0.986171 | ||||||||
\(290\) | 18.6244 | 1.09366 | ||||||||
\(291\) | 6.21949 | 0.364593 | ||||||||
\(292\) | −12.6518 | −0.740393 | ||||||||
\(293\) | 1.34060 | 0.0783186 | 0.0391593 | − | 0.999233i | \(-0.487532\pi\) | ||||
0.0391593 | + | 0.999233i | \(0.487532\pi\) | |||||||
\(294\) | −10.1892 | −0.594247 | ||||||||
\(295\) | −12.2498 | −0.713209 | ||||||||
\(296\) | 5.77959 | 0.335932 | ||||||||
\(297\) | −2.60975 | −0.151433 | ||||||||
\(298\) | −23.8401 | −1.38102 | ||||||||
\(299\) | 26.3856 | 1.52592 | ||||||||
\(300\) | 30.2186 | 1.74467 | ||||||||
\(301\) | −1.48486 | −0.0855860 | ||||||||
\(302\) | 16.0000 | 0.920697 | ||||||||
\(303\) | 7.76491 | 0.446082 | ||||||||
\(304\) | 18.2947 | 1.04927 | ||||||||
\(305\) | 46.2791 | 2.64994 | ||||||||
\(306\) | 1.03028 | 0.0588970 | ||||||||
\(307\) | −0.424310 | −0.0242166 | −0.0121083 | − | 0.999927i | \(-0.503854\pi\) | ||||
−0.0121083 | + | 0.999927i | \(0.503854\pi\) | |||||||
\(308\) | −9.74645 | −0.555355 | ||||||||
\(309\) | 2.54541 | 0.144804 | ||||||||
\(310\) | −32.9991 | −1.87422 | ||||||||
\(311\) | 0.110206 | 0.00624919 | 0.00312460 | − | 0.999995i | \(-0.499005\pi\) | ||||
0.00312460 | + | 0.999995i | \(0.499005\pi\) | |||||||
\(312\) | 3.28383 | 0.185910 | ||||||||
\(313\) | −2.96972 | −0.167859 | −0.0839294 | − | 0.996472i | \(-0.526747\pi\) | ||||
−0.0839294 | + | 0.996472i | \(0.526747\pi\) | |||||||
\(314\) | 52.7181 | 2.97506 | ||||||||
\(315\) | −6.12489 | −0.345098 | ||||||||
\(316\) | 6.84106 | 0.384840 | ||||||||
\(317\) | −12.4243 | −0.697819 | −0.348909 | − | 0.937156i | \(-0.613448\pi\) | ||||
−0.348909 | + | 0.937156i | \(0.613448\pi\) | |||||||
\(318\) | 8.00000 | 0.448618 | ||||||||
\(319\) | 5.54541 | 0.310484 | ||||||||
\(320\) | 47.2451 | 2.64108 | ||||||||
\(321\) | −3.15516 | −0.176104 | ||||||||
\(322\) | 27.7502 | 1.54646 | ||||||||
\(323\) | −3.28005 | −0.182507 | ||||||||
\(324\) | 2.51514 | 0.139730 | ||||||||
\(325\) | 36.0440 | 1.99936 | ||||||||
\(326\) | −3.02650 | −0.167622 | ||||||||
\(327\) | −9.24977 | −0.511513 | ||||||||
\(328\) | 0.804136 | 0.0444010 | ||||||||
\(329\) | −12.5251 | −0.690532 | ||||||||
\(330\) | 22.8742 | 1.25918 | ||||||||
\(331\) | 31.2938 | 1.72006 | 0.860032 | − | 0.510241i | \(-0.170444\pi\) | ||||
0.860032 | + | 0.510241i | \(0.170444\pi\) | |||||||
\(332\) | −14.0331 | −0.770169 | ||||||||
\(333\) | 5.28005 | 0.289345 | ||||||||
\(334\) | 17.7640 | 0.972002 | ||||||||
\(335\) | −29.0596 | −1.58770 | ||||||||
\(336\) | −4.01560 | −0.219069 | ||||||||
\(337\) | −14.8401 | −0.808394 | −0.404197 | − | 0.914672i | \(-0.632449\pi\) | ||||
−0.404197 | + | 0.914672i | \(0.632449\pi\) | |||||||
\(338\) | −8.49954 | −0.462314 | ||||||||
\(339\) | 3.40493 | 0.184931 | ||||||||
\(340\) | −5.03028 | −0.272805 | ||||||||
\(341\) | −9.82546 | −0.532079 | ||||||||
\(342\) | −14.3747 | −0.777292 | ||||||||
\(343\) | −17.5142 | −0.945679 | ||||||||
\(344\) | −1.09461 | −0.0590174 | ||||||||
\(345\) | −36.2791 | −1.95320 | ||||||||
\(346\) | 26.4314 | 1.42096 | ||||||||
\(347\) | 17.0984 | 0.917890 | 0.458945 | − | 0.888465i | \(-0.348228\pi\) | ||||
0.458945 | + | 0.888465i | \(0.348228\pi\) | |||||||
\(348\) | −5.34438 | −0.286489 | ||||||||
\(349\) | −12.3784 | −0.662603 | −0.331301 | − | 0.943525i | \(-0.607488\pi\) | ||||
−0.331301 | + | 0.943525i | \(0.607488\pi\) | |||||||
\(350\) | 37.9083 | 2.02628 | ||||||||
\(351\) | 3.00000 | 0.160128 | ||||||||
\(352\) | 20.7101 | 1.10385 | ||||||||
\(353\) | 15.4546 | 0.822565 | 0.411282 | − | 0.911508i | \(-0.365081\pi\) | ||||
0.411282 | + | 0.911508i | \(0.365081\pi\) | |||||||
\(354\) | 6.31032 | 0.335390 | ||||||||
\(355\) | −54.5289 | −2.89409 | ||||||||
\(356\) | −45.9007 | −2.43273 | ||||||||
\(357\) | 0.719953 | 0.0381040 | ||||||||
\(358\) | 4.78051 | 0.252658 | ||||||||
\(359\) | 15.3553 | 0.810421 | 0.405210 | − | 0.914223i | \(-0.367198\pi\) | ||||
0.405210 | + | 0.914223i | \(0.367198\pi\) | |||||||
\(360\) | −4.51514 | −0.237969 | ||||||||
\(361\) | 26.7640 | 1.40863 | ||||||||
\(362\) | −14.6320 | −0.769040 | ||||||||
\(363\) | −4.18922 | −0.219877 | ||||||||
\(364\) | 11.2039 | 0.587244 | ||||||||
\(365\) | 20.7493 | 1.08607 | ||||||||
\(366\) | −23.8401 | −1.24614 | ||||||||
\(367\) | −0.530734 | −0.0277041 | −0.0138521 | − | 0.999904i | \(-0.504409\pi\) | ||||
−0.0138521 | + | 0.999904i | \(0.504409\pi\) | |||||||
\(368\) | −23.7853 | −1.23990 | ||||||||
\(369\) | 0.734633 | 0.0382435 | ||||||||
\(370\) | −46.2791 | −2.40594 | ||||||||
\(371\) | 5.59037 | 0.290238 | ||||||||
\(372\) | 9.46927 | 0.490959 | ||||||||
\(373\) | −6.02936 | −0.312188 | −0.156094 | − | 0.987742i | \(-0.549890\pi\) | ||||
−0.156094 | + | 0.987742i | \(0.549890\pi\) | |||||||
\(374\) | −2.68876 | −0.139032 | ||||||||
\(375\) | −28.9348 | −1.49418 | ||||||||
\(376\) | −9.23326 | −0.476169 | ||||||||
\(377\) | −6.37466 | −0.328312 | ||||||||
\(378\) | 3.15516 | 0.162284 | ||||||||
\(379\) | 11.8936 | 0.610932 | 0.305466 | − | 0.952203i | \(-0.401188\pi\) | ||||
0.305466 | + | 0.952203i | \(0.401188\pi\) | |||||||
\(380\) | 70.1836 | 3.60034 | ||||||||
\(381\) | −9.04496 | −0.463387 | ||||||||
\(382\) | 13.7484 | 0.703429 | ||||||||
\(383\) | 17.7796 | 0.908495 | 0.454247 | − | 0.890876i | \(-0.349908\pi\) | ||||
0.454247 | + | 0.890876i | \(0.349908\pi\) | |||||||
\(384\) | −8.46640 | −0.432049 | ||||||||
\(385\) | 15.9844 | 0.814641 | ||||||||
\(386\) | 4.74931 | 0.241734 | ||||||||
\(387\) | −1.00000 | −0.0508329 | ||||||||
\(388\) | 15.6429 | 0.794147 | ||||||||
\(389\) | −24.4646 | −1.24040 | −0.620201 | − | 0.784443i | \(-0.712949\pi\) | ||||
−0.620201 | + | 0.784443i | \(0.712949\pi\) | |||||||
\(390\) | −26.2947 | −1.33149 | ||||||||
\(391\) | 4.26445 | 0.215663 | ||||||||
\(392\) | −5.24885 | −0.265107 | ||||||||
\(393\) | 19.0596 | 0.961431 | ||||||||
\(394\) | 16.5307 | 0.832806 | ||||||||
\(395\) | −11.2195 | −0.564514 | ||||||||
\(396\) | −6.56387 | −0.329847 | ||||||||
\(397\) | −38.5739 | −1.93597 | −0.967983 | − | 0.251015i | \(-0.919236\pi\) | ||||
−0.967983 | + | 0.251015i | \(0.919236\pi\) | |||||||
\(398\) | 14.6812 | 0.735902 | ||||||||
\(399\) | −10.0450 | −0.502877 | ||||||||
\(400\) | −32.4920 | −1.62460 | ||||||||
\(401\) | −4.51422 | −0.225429 | −0.112715 | − | 0.993627i | \(-0.535955\pi\) | ||||
−0.112715 | + | 0.993627i | \(0.535955\pi\) | |||||||
\(402\) | 14.9697 | 0.746622 | ||||||||
\(403\) | 11.2947 | 0.562630 | ||||||||
\(404\) | 19.5298 | 0.971645 | ||||||||
\(405\) | −4.12489 | −0.204967 | ||||||||
\(406\) | −6.70436 | −0.332732 | ||||||||
\(407\) | −13.7796 | −0.683029 | ||||||||
\(408\) | 0.530734 | 0.0262753 | ||||||||
\(409\) | 17.7190 | 0.876150 | 0.438075 | − | 0.898938i | \(-0.355660\pi\) | ||||
0.438075 | + | 0.898938i | \(0.355660\pi\) | |||||||
\(410\) | −6.43899 | −0.317999 | ||||||||
\(411\) | −20.8742 | −1.02965 | ||||||||
\(412\) | 6.40207 | 0.315407 | ||||||||
\(413\) | 4.40963 | 0.216984 | ||||||||
\(414\) | 18.6888 | 0.918502 | ||||||||
\(415\) | 23.0147 | 1.12975 | ||||||||
\(416\) | −23.8070 | −1.16723 | ||||||||
\(417\) | −13.2342 | −0.648080 | ||||||||
\(418\) | 37.5142 | 1.83488 | ||||||||
\(419\) | 16.4390 | 0.803097 | 0.401549 | − | 0.915838i | \(-0.368472\pi\) | ||||
0.401549 | + | 0.915838i | \(0.368472\pi\) | |||||||
\(420\) | −15.4049 | −0.751684 | ||||||||
\(421\) | 23.9083 | 1.16522 | 0.582609 | − | 0.812753i | \(-0.302032\pi\) | ||||
0.582609 | + | 0.812753i | \(0.302032\pi\) | |||||||
\(422\) | 7.27627 | 0.354203 | ||||||||
\(423\) | −8.43521 | −0.410134 | ||||||||
\(424\) | 4.12110 | 0.200139 | ||||||||
\(425\) | 5.82546 | 0.282576 | ||||||||
\(426\) | 28.0899 | 1.36096 | ||||||||
\(427\) | −16.6594 | −0.806205 | ||||||||
\(428\) | −7.93567 | −0.383585 | ||||||||
\(429\) | −7.82924 | −0.377999 | ||||||||
\(430\) | 8.76491 | 0.422681 | ||||||||
\(431\) | −15.6088 | −0.751851 | −0.375925 | − | 0.926650i | \(-0.622675\pi\) | ||||
−0.375925 | + | 0.926650i | \(0.622675\pi\) | |||||||
\(432\) | −2.70436 | −0.130113 | ||||||||
\(433\) | −10.9092 | −0.524261 | −0.262131 | − | 0.965032i | \(-0.584425\pi\) | ||||
−0.262131 | + | 0.965032i | \(0.584425\pi\) | |||||||
\(434\) | 11.8789 | 0.570205 | ||||||||
\(435\) | 8.76491 | 0.420245 | ||||||||
\(436\) | −23.2645 | −1.11417 | ||||||||
\(437\) | −59.4986 | −2.84621 | ||||||||
\(438\) | −10.6888 | −0.510729 | ||||||||
\(439\) | 19.8255 | 0.946218 | 0.473109 | − | 0.881004i | \(-0.343132\pi\) | ||||
0.473109 | + | 0.881004i | \(0.343132\pi\) | |||||||
\(440\) | 11.7834 | 0.561750 | ||||||||
\(441\) | −4.79518 | −0.228342 | ||||||||
\(442\) | 3.09083 | 0.147016 | ||||||||
\(443\) | −0.314104 | −0.0149235 | −0.00746177 | − | 0.999972i | \(-0.502375\pi\) | ||||
−0.00746177 | + | 0.999972i | \(0.502375\pi\) | |||||||
\(444\) | 13.2800 | 0.630243 | ||||||||
\(445\) | 75.2782 | 3.56853 | ||||||||
\(446\) | −20.6850 | −0.979462 | ||||||||
\(447\) | −11.2195 | −0.530664 | ||||||||
\(448\) | −17.0071 | −0.803511 | ||||||||
\(449\) | 10.2536 | 0.483895 | 0.241948 | − | 0.970289i | \(-0.422214\pi\) | ||||
0.241948 | + | 0.970289i | \(0.422214\pi\) | |||||||
\(450\) | 25.5298 | 1.20349 | ||||||||
\(451\) | −1.91721 | −0.0902777 | ||||||||
\(452\) | 8.56387 | 0.402811 | ||||||||
\(453\) | 7.52982 | 0.353782 | ||||||||
\(454\) | 6.56766 | 0.308235 | ||||||||
\(455\) | −18.3747 | −0.861417 | ||||||||
\(456\) | −7.40493 | −0.346768 | ||||||||
\(457\) | 3.21949 | 0.150602 | 0.0753008 | − | 0.997161i | \(-0.476008\pi\) | ||||
0.0753008 | + | 0.997161i | \(0.476008\pi\) | |||||||
\(458\) | 6.80986 | 0.318204 | ||||||||
\(459\) | 0.484862 | 0.0226314 | ||||||||
\(460\) | −91.2470 | −4.25441 | ||||||||
\(461\) | −16.1892 | −0.754007 | −0.377004 | − | 0.926212i | \(-0.623046\pi\) | ||||
−0.377004 | + | 0.926212i | \(0.623046\pi\) | |||||||
\(462\) | −8.23417 | −0.383088 | ||||||||
\(463\) | 14.8860 | 0.691812 | 0.345906 | − | 0.938269i | \(-0.387572\pi\) | ||||
0.345906 | + | 0.938269i | \(0.387572\pi\) | |||||||
\(464\) | 5.74645 | 0.266772 | ||||||||
\(465\) | −15.5298 | −0.720178 | ||||||||
\(466\) | 23.5748 | 1.09208 | ||||||||
\(467\) | −8.22041 | −0.380395 | −0.190198 | − | 0.981746i | \(-0.560913\pi\) | ||||
−0.190198 | + | 0.981746i | \(0.560913\pi\) | |||||||
\(468\) | 7.54541 | 0.348787 | ||||||||
\(469\) | 10.4608 | 0.483034 | ||||||||
\(470\) | 73.9338 | 3.41031 | ||||||||
\(471\) | 24.8099 | 1.14318 | ||||||||
\(472\) | 3.25069 | 0.149625 | ||||||||
\(473\) | 2.60975 | 0.119996 | ||||||||
\(474\) | 5.77959 | 0.265465 | ||||||||
\(475\) | −81.2782 | −3.72930 | ||||||||
\(476\) | 1.81078 | 0.0829970 | ||||||||
\(477\) | 3.76491 | 0.172383 | ||||||||
\(478\) | 36.3241 | 1.66143 | ||||||||
\(479\) | 9.41961 | 0.430393 | 0.215197 | − | 0.976571i | \(-0.430961\pi\) | ||||
0.215197 | + | 0.976571i | \(0.430961\pi\) | |||||||
\(480\) | 32.7337 | 1.49408 | ||||||||
\(481\) | 15.8401 | 0.722248 | ||||||||
\(482\) | 47.9376 | 2.18350 | ||||||||
\(483\) | 13.0596 | 0.594234 | ||||||||
\(484\) | −10.5365 | −0.478930 | ||||||||
\(485\) | −25.6547 | −1.16492 | ||||||||
\(486\) | 2.12489 | 0.0963868 | ||||||||
\(487\) | −6.71995 | −0.304510 | −0.152255 | − | 0.988341i | \(-0.548654\pi\) | ||||
−0.152255 | + | 0.988341i | \(0.548654\pi\) | |||||||
\(488\) | −12.2810 | −0.555933 | ||||||||
\(489\) | −1.42431 | −0.0644095 | ||||||||
\(490\) | 42.0294 | 1.89869 | ||||||||
\(491\) | −36.2186 | −1.63452 | −0.817261 | − | 0.576268i | \(-0.804508\pi\) | ||||
−0.817261 | + | 0.576268i | \(0.804508\pi\) | |||||||
\(492\) | 1.84770 | 0.0833009 | ||||||||
\(493\) | −1.03028 | −0.0464013 | ||||||||
\(494\) | −43.1240 | −1.94024 | ||||||||
\(495\) | 10.7649 | 0.483847 | ||||||||
\(496\) | −10.1817 | −0.457170 | ||||||||
\(497\) | 19.6291 | 0.880487 | ||||||||
\(498\) | −11.8557 | −0.531268 | ||||||||
\(499\) | −29.8245 | −1.33513 | −0.667565 | − | 0.744552i | \(-0.732663\pi\) | ||||
−0.667565 | + | 0.744552i | \(0.732663\pi\) | |||||||
\(500\) | −72.7749 | −3.25459 | ||||||||
\(501\) | 8.35998 | 0.373496 | ||||||||
\(502\) | 33.2333 | 1.48327 | ||||||||
\(503\) | −22.2498 | −0.992068 | −0.496034 | − | 0.868303i | \(-0.665211\pi\) | ||||
−0.496034 | + | 0.868303i | \(0.665211\pi\) | |||||||
\(504\) | 1.62534 | 0.0723986 | ||||||||
\(505\) | −32.0294 | −1.42529 | ||||||||
\(506\) | −48.7729 | −2.16822 | ||||||||
\(507\) | −4.00000 | −0.177646 | ||||||||
\(508\) | −22.7493 | −1.00934 | ||||||||
\(509\) | 1.26537 | 0.0560864 | 0.0280432 | − | 0.999607i | \(-0.491072\pi\) | ||||
0.0280432 | + | 0.999607i | \(0.491072\pi\) | |||||||
\(510\) | −4.24977 | −0.188183 | ||||||||
\(511\) | −7.46927 | −0.330421 | ||||||||
\(512\) | 27.3813 | 1.21009 | ||||||||
\(513\) | −6.76491 | −0.298678 | ||||||||
\(514\) | −37.2569 | −1.64333 | ||||||||
\(515\) | −10.4995 | −0.462665 | ||||||||
\(516\) | −2.51514 | −0.110723 | ||||||||
\(517\) | 22.0138 | 0.968164 | ||||||||
\(518\) | 16.6594 | 0.731972 | ||||||||
\(519\) | 12.4390 | 0.546011 | ||||||||
\(520\) | −13.5454 | −0.594006 | ||||||||
\(521\) | 21.4343 | 0.939053 | 0.469527 | − | 0.882918i | \(-0.344425\pi\) | ||||
0.469527 | + | 0.882918i | \(0.344425\pi\) | |||||||
\(522\) | −4.51514 | −0.197622 | ||||||||
\(523\) | 5.11399 | 0.223619 | 0.111810 | − | 0.993730i | \(-0.464335\pi\) | ||||
0.111810 | + | 0.993730i | \(0.464335\pi\) | |||||||
\(524\) | 47.9376 | 2.09416 | ||||||||
\(525\) | 17.8401 | 0.778608 | ||||||||
\(526\) | −13.5374 | −0.590258 | ||||||||
\(527\) | 1.82546 | 0.0795183 | ||||||||
\(528\) | 7.05769 | 0.307146 | ||||||||
\(529\) | 54.3553 | 2.36327 | ||||||||
\(530\) | −32.9991 | −1.43339 | ||||||||
\(531\) | 2.96972 | 0.128875 | ||||||||
\(532\) | −25.2645 | −1.09535 | ||||||||
\(533\) | 2.20390 | 0.0954614 | ||||||||
\(534\) | −38.7787 | −1.67812 | ||||||||
\(535\) | 13.0147 | 0.562674 | ||||||||
\(536\) | 7.71147 | 0.333085 | ||||||||
\(537\) | 2.24977 | 0.0970848 | ||||||||
\(538\) | 62.7787 | 2.70658 | ||||||||
\(539\) | 12.5142 | 0.539026 | ||||||||
\(540\) | −10.3747 | −0.446454 | ||||||||
\(541\) | −44.2333 | −1.90174 | −0.950868 | − | 0.309596i | \(-0.899806\pi\) | ||||
−0.950868 | + | 0.309596i | \(0.899806\pi\) | |||||||
\(542\) | −25.1277 | −1.07933 | ||||||||
\(543\) | −6.88601 | −0.295507 | ||||||||
\(544\) | −3.84770 | −0.164969 | ||||||||
\(545\) | 38.1542 | 1.63435 | ||||||||
\(546\) | 9.46548 | 0.405085 | ||||||||
\(547\) | 31.0743 | 1.32864 | 0.664321 | − | 0.747447i | \(-0.268721\pi\) | ||||
0.664321 | + | 0.747447i | \(0.268721\pi\) | |||||||
\(548\) | −52.5015 | −2.24275 | ||||||||
\(549\) | −11.2195 | −0.478836 | ||||||||
\(550\) | −66.6264 | −2.84096 | ||||||||
\(551\) | 14.3747 | 0.612381 | ||||||||
\(552\) | 9.62729 | 0.409765 | ||||||||
\(553\) | 4.03875 | 0.171745 | ||||||||
\(554\) | −33.5298 | −1.42455 | ||||||||
\(555\) | −21.7796 | −0.924492 | ||||||||
\(556\) | −33.2858 | −1.41163 | ||||||||
\(557\) | −20.7952 | −0.881120 | −0.440560 | − | 0.897723i | \(-0.645220\pi\) | ||||
−0.440560 | + | 0.897723i | \(0.645220\pi\) | |||||||
\(558\) | 8.00000 | 0.338667 | ||||||||
\(559\) | −3.00000 | −0.126886 | ||||||||
\(560\) | 16.5639 | 0.699951 | ||||||||
\(561\) | −1.26537 | −0.0534238 | ||||||||
\(562\) | −38.2791 | −1.61471 | ||||||||
\(563\) | 4.82454 | 0.203330 | 0.101665 | − | 0.994819i | \(-0.467583\pi\) | ||||
0.101665 | + | 0.994819i | \(0.467583\pi\) | |||||||
\(564\) | −21.2157 | −0.893343 | ||||||||
\(565\) | −14.0450 | −0.590876 | ||||||||
\(566\) | 11.9924 | 0.504080 | ||||||||
\(567\) | 1.48486 | 0.0623583 | ||||||||
\(568\) | 14.4702 | 0.607155 | ||||||||
\(569\) | 25.0450 | 1.04994 | 0.524970 | − | 0.851121i | \(-0.324077\pi\) | ||||
0.524970 | + | 0.851121i | \(0.324077\pi\) | |||||||
\(570\) | 59.2938 | 2.48354 | ||||||||
\(571\) | 15.4849 | 0.648021 | 0.324011 | − | 0.946053i | \(-0.394969\pi\) | ||||
0.324011 | + | 0.946053i | \(0.394969\pi\) | |||||||
\(572\) | −19.6916 | −0.823348 | ||||||||
\(573\) | 6.47018 | 0.270296 | ||||||||
\(574\) | 2.31789 | 0.0967467 | ||||||||
\(575\) | 105.671 | 4.40680 | ||||||||
\(576\) | −11.4537 | −0.477236 | ||||||||
\(577\) | −18.8704 | −0.785586 | −0.392793 | − | 0.919627i | \(-0.628491\pi\) | ||||
−0.392793 | + | 0.919627i | \(0.628491\pi\) | |||||||
\(578\) | −35.6235 | −1.48174 | ||||||||
\(579\) | 2.23509 | 0.0928872 | ||||||||
\(580\) | 22.0450 | 0.915367 | ||||||||
\(581\) | −8.28474 | −0.343709 | ||||||||
\(582\) | 13.2157 | 0.547809 | ||||||||
\(583\) | −9.82546 | −0.406929 | ||||||||
\(584\) | −5.50619 | −0.227848 | ||||||||
\(585\) | −12.3747 | −0.511629 | ||||||||
\(586\) | 2.84862 | 0.117675 | ||||||||
\(587\) | −37.1883 | −1.53493 | −0.767463 | − | 0.641094i | \(-0.778481\pi\) | ||||
−0.767463 | + | 0.641094i | \(0.778481\pi\) | |||||||
\(588\) | −12.0606 | −0.497369 | ||||||||
\(589\) | −25.4693 | −1.04944 | ||||||||
\(590\) | −26.0294 | −1.07161 | ||||||||
\(591\) | 7.77959 | 0.320010 | ||||||||
\(592\) | −14.2791 | −0.586869 | ||||||||
\(593\) | 9.87133 | 0.405367 | 0.202684 | − | 0.979244i | \(-0.435034\pi\) | ||||
0.202684 | + | 0.979244i | \(0.435034\pi\) | |||||||
\(594\) | −5.54541 | −0.227531 | ||||||||
\(595\) | −2.96972 | −0.121747 | ||||||||
\(596\) | −28.2186 | −1.15588 | ||||||||
\(597\) | 6.90917 | 0.282774 | ||||||||
\(598\) | 56.0663 | 2.29272 | ||||||||
\(599\) | −41.2598 | −1.68583 | −0.842914 | − | 0.538048i | \(-0.819162\pi\) | ||||
−0.842914 | + | 0.538048i | \(0.819162\pi\) | |||||||
\(600\) | 13.1514 | 0.536903 | ||||||||
\(601\) | −44.3397 | −1.80865 | −0.904327 | − | 0.426841i | \(-0.859626\pi\) | ||||
−0.904327 | + | 0.426841i | \(0.859626\pi\) | |||||||
\(602\) | −3.15516 | −0.128595 | ||||||||
\(603\) | 7.04496 | 0.286893 | ||||||||
\(604\) | 18.9385 | 0.770598 | ||||||||
\(605\) | 17.2800 | 0.702534 | ||||||||
\(606\) | 16.4995 | 0.670248 | ||||||||
\(607\) | −5.76399 | −0.233953 | −0.116977 | − | 0.993135i | \(-0.537320\pi\) | ||||
−0.116977 | + | 0.993135i | \(0.537320\pi\) | |||||||
\(608\) | 53.6841 | 2.17718 | ||||||||
\(609\) | −3.15516 | −0.127854 | ||||||||
\(610\) | 98.3378 | 3.98158 | ||||||||
\(611\) | −25.3056 | −1.02376 | ||||||||
\(612\) | 1.21949 | 0.0492952 | ||||||||
\(613\) | 26.8780 | 1.08559 | 0.542796 | − | 0.839865i | \(-0.317366\pi\) | ||||
0.542796 | + | 0.839865i | \(0.317366\pi\) | |||||||
\(614\) | −0.901610 | −0.0363860 | ||||||||
\(615\) | −3.03028 | −0.122193 | ||||||||
\(616\) | −4.24174 | −0.170904 | ||||||||
\(617\) | 18.3250 | 0.737737 | 0.368868 | − | 0.929482i | \(-0.379745\pi\) | ||||
0.368868 | + | 0.929482i | \(0.379745\pi\) | |||||||
\(618\) | 5.40871 | 0.217570 | ||||||||
\(619\) | −26.9697 | −1.08400 | −0.542002 | − | 0.840377i | \(-0.682334\pi\) | ||||
−0.542002 | + | 0.840377i | \(0.682334\pi\) | |||||||
\(620\) | −39.0596 | −1.56867 | ||||||||
\(621\) | 8.79518 | 0.352939 | ||||||||
\(622\) | 0.234174 | 0.00938954 | ||||||||
\(623\) | −27.0984 | −1.08567 | ||||||||
\(624\) | −8.11307 | −0.324783 | ||||||||
\(625\) | 59.2791 | 2.37117 | ||||||||
\(626\) | −6.31032 | −0.252211 | ||||||||
\(627\) | 17.6547 | 0.705061 | ||||||||
\(628\) | 62.4002 | 2.49004 | ||||||||
\(629\) | 2.56009 | 0.102078 | ||||||||
\(630\) | −13.0147 | −0.518517 | ||||||||
\(631\) | 15.1514 | 0.603167 | 0.301583 | − | 0.953440i | \(-0.402485\pi\) | ||||
0.301583 | + | 0.953440i | \(0.402485\pi\) | |||||||
\(632\) | 2.97729 | 0.118430 | ||||||||
\(633\) | 3.42431 | 0.136104 | ||||||||
\(634\) | −26.4002 | −1.04849 | ||||||||
\(635\) | 37.3094 | 1.48058 | ||||||||
\(636\) | 9.46927 | 0.375481 | ||||||||
\(637\) | −14.3856 | −0.569976 | ||||||||
\(638\) | 11.7834 | 0.466508 | ||||||||
\(639\) | 13.2195 | 0.522955 | ||||||||
\(640\) | 34.9229 | 1.38045 | ||||||||
\(641\) | −4.06811 | −0.160681 | −0.0803404 | − | 0.996767i | \(-0.525601\pi\) | ||||
−0.0803404 | + | 0.996767i | \(0.525601\pi\) | |||||||
\(642\) | −6.70436 | −0.264600 | ||||||||
\(643\) | 12.6594 | 0.499238 | 0.249619 | − | 0.968344i | \(-0.419695\pi\) | ||||
0.249619 | + | 0.968344i | \(0.419695\pi\) | |||||||
\(644\) | 32.8468 | 1.29434 | ||||||||
\(645\) | 4.12489 | 0.162417 | ||||||||
\(646\) | −6.96972 | −0.274220 | ||||||||
\(647\) | 0.128666 | 0.00505840 | 0.00252920 | − | 0.999997i | \(-0.499195\pi\) | ||||
0.00252920 | + | 0.999997i | \(0.499195\pi\) | |||||||
\(648\) | 1.09461 | 0.0430003 | ||||||||
\(649\) | −7.75023 | −0.304223 | ||||||||
\(650\) | 76.5895 | 3.00409 | ||||||||
\(651\) | 5.59037 | 0.219104 | ||||||||
\(652\) | −3.58234 | −0.140295 | ||||||||
\(653\) | −37.7834 | −1.47858 | −0.739289 | − | 0.673389i | \(-0.764838\pi\) | ||||
−0.739289 | + | 0.673389i | \(0.764838\pi\) | |||||||
\(654\) | −19.6547 | −0.768560 | ||||||||
\(655\) | −78.6188 | −3.07189 | ||||||||
\(656\) | −1.98671 | −0.0775680 | ||||||||
\(657\) | −5.03028 | −0.196250 | ||||||||
\(658\) | −26.6144 | −1.03754 | ||||||||
\(659\) | −29.9154 | −1.16534 | −0.582669 | − | 0.812710i | \(-0.697991\pi\) | ||||
−0.582669 | + | 0.812710i | \(0.697991\pi\) | |||||||
\(660\) | 27.0752 | 1.05390 | ||||||||
\(661\) | 20.7796 | 0.808232 | 0.404116 | − | 0.914708i | \(-0.367579\pi\) | ||||
0.404116 | + | 0.914708i | \(0.367579\pi\) | |||||||
\(662\) | 66.4958 | 2.58443 | ||||||||
\(663\) | 1.45459 | 0.0564914 | ||||||||
\(664\) | −6.10734 | −0.237011 | ||||||||
\(665\) | 41.4343 | 1.60675 | ||||||||
\(666\) | 11.2195 | 0.434747 | ||||||||
\(667\) | −18.6888 | −0.723632 | ||||||||
\(668\) | 21.0265 | 0.813540 | ||||||||
\(669\) | −9.73463 | −0.376363 | ||||||||
\(670\) | −61.7484 | −2.38555 | ||||||||
\(671\) | 29.2800 | 1.13034 | ||||||||
\(672\) | −11.7834 | −0.454553 | ||||||||
\(673\) | −48.7181 | −1.87795 | −0.938973 | − | 0.343992i | \(-0.888221\pi\) | ||||
−0.938973 | + | 0.343992i | \(0.888221\pi\) | |||||||
\(674\) | −31.5336 | −1.21463 | ||||||||
\(675\) | 12.0147 | 0.462445 | ||||||||
\(676\) | −10.0606 | −0.386944 | ||||||||
\(677\) | −46.2498 | −1.77752 | −0.888762 | − | 0.458370i | \(-0.848434\pi\) | ||||
−0.888762 | + | 0.458370i | \(0.848434\pi\) | |||||||
\(678\) | 7.23509 | 0.277862 | ||||||||
\(679\) | 9.23509 | 0.354410 | ||||||||
\(680\) | −2.18922 | −0.0839527 | ||||||||
\(681\) | 3.09083 | 0.118441 | ||||||||
\(682\) | −20.8780 | −0.799459 | ||||||||
\(683\) | 4.17454 | 0.159734 | 0.0798671 | − | 0.996806i | \(-0.474550\pi\) | ||||
0.0798671 | + | 0.996806i | \(0.474550\pi\) | |||||||
\(684\) | −17.0147 | −0.650573 | ||||||||
\(685\) | 86.1037 | 3.28985 | ||||||||
\(686\) | −37.2157 | −1.42090 | ||||||||
\(687\) | 3.20482 | 0.122271 | ||||||||
\(688\) | 2.70436 | 0.103103 | ||||||||
\(689\) | 11.2947 | 0.430295 | ||||||||
\(690\) | −77.0890 | −2.93473 | ||||||||
\(691\) | −25.5904 | −0.973504 | −0.486752 | − | 0.873540i | \(-0.661818\pi\) | ||||
−0.486752 | + | 0.873540i | \(0.661818\pi\) | |||||||
\(692\) | 31.2858 | 1.18931 | ||||||||
\(693\) | −3.87511 | −0.147203 | ||||||||
\(694\) | 36.3321 | 1.37915 | ||||||||
\(695\) | 54.5895 | 2.07070 | ||||||||
\(696\) | −2.32592 | −0.0881637 | ||||||||
\(697\) | 0.356195 | 0.0134919 | ||||||||
\(698\) | −26.3028 | −0.995574 | ||||||||
\(699\) | 11.0946 | 0.419637 | ||||||||
\(700\) | 44.8704 | 1.69594 | ||||||||
\(701\) | −15.0303 | −0.567686 | −0.283843 | − | 0.958871i | \(-0.591609\pi\) | ||||
−0.283843 | + | 0.958871i | \(0.591609\pi\) | |||||||
\(702\) | 6.37466 | 0.240596 | ||||||||
\(703\) | −35.7190 | −1.34717 | ||||||||
\(704\) | 29.8912 | 1.12657 | ||||||||
\(705\) | 34.7943 | 1.31043 | ||||||||
\(706\) | 32.8392 | 1.23592 | ||||||||
\(707\) | 11.5298 | 0.433623 | ||||||||
\(708\) | 7.46927 | 0.280712 | ||||||||
\(709\) | 3.12110 | 0.117216 | 0.0586078 | − | 0.998281i | \(-0.481334\pi\) | ||||
0.0586078 | + | 0.998281i | \(0.481334\pi\) | |||||||
\(710\) | −115.868 | −4.34844 | ||||||||
\(711\) | 2.71995 | 0.102006 | ||||||||
\(712\) | −19.9764 | −0.748646 | ||||||||
\(713\) | 33.1131 | 1.24009 | ||||||||
\(714\) | 1.52982 | 0.0572520 | ||||||||
\(715\) | 32.2947 | 1.20775 | ||||||||
\(716\) | 5.65848 | 0.211467 | ||||||||
\(717\) | 17.0946 | 0.638410 | ||||||||
\(718\) | 32.6282 | 1.21767 | ||||||||
\(719\) | −12.5895 | −0.469507 | −0.234754 | − | 0.972055i | \(-0.575428\pi\) | ||||
−0.234754 | + | 0.972055i | \(0.575428\pi\) | |||||||
\(720\) | 11.1552 | 0.415728 | ||||||||
\(721\) | 3.77959 | 0.140759 | ||||||||
\(722\) | 56.8704 | 2.11650 | ||||||||
\(723\) | 22.5601 | 0.839019 | ||||||||
\(724\) | −17.3193 | −0.643666 | ||||||||
\(725\) | −25.5298 | −0.948154 | ||||||||
\(726\) | −8.90161 | −0.330370 | ||||||||
\(727\) | 19.4537 | 0.721497 | 0.360748 | − | 0.932663i | \(-0.382521\pi\) | ||||
0.360748 | + | 0.932663i | \(0.382521\pi\) | |||||||
\(728\) | 4.87603 | 0.180718 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 44.0899 | 1.63184 | ||||||||
\(731\) | −0.484862 | −0.0179333 | ||||||||
\(732\) | −28.2186 | −1.04299 | ||||||||
\(733\) | 25.9394 | 0.958095 | 0.479048 | − | 0.877789i | \(-0.340982\pi\) | ||||
0.479048 | + | 0.877789i | \(0.340982\pi\) | |||||||
\(734\) | −1.12775 | −0.0416260 | ||||||||
\(735\) | 19.7796 | 0.729581 | ||||||||
\(736\) | −69.7957 | −2.57270 | ||||||||
\(737\) | −18.3856 | −0.677241 | ||||||||
\(738\) | 1.56101 | 0.0574616 | ||||||||
\(739\) | −49.4225 | −1.81804 | −0.909018 | − | 0.416758i | \(-0.863166\pi\) | ||||
−0.909018 | + | 0.416758i | \(0.863166\pi\) | |||||||
\(740\) | −54.7787 | −2.01370 | ||||||||
\(741\) | −20.2947 | −0.745545 | ||||||||
\(742\) | 11.8789 | 0.436088 | ||||||||
\(743\) | −30.5677 | −1.12142 | −0.560709 | − | 0.828013i | \(-0.689471\pi\) | ||||
−0.560709 | + | 0.828013i | \(0.689471\pi\) | |||||||
\(744\) | 4.12110 | 0.151087 | ||||||||
\(745\) | 46.2791 | 1.69554 | ||||||||
\(746\) | −12.8117 | −0.469070 | ||||||||
\(747\) | −5.57947 | −0.204142 | ||||||||
\(748\) | −3.18257 | −0.116366 | ||||||||
\(749\) | −4.68498 | −0.171185 | ||||||||
\(750\) | −61.4830 | −2.24504 | ||||||||
\(751\) | 2.73555 | 0.0998216 | 0.0499108 | − | 0.998754i | \(-0.484106\pi\) | ||||
0.0499108 | + | 0.998754i | \(0.484106\pi\) | |||||||
\(752\) | 22.8118 | 0.831861 | ||||||||
\(753\) | 15.6400 | 0.569954 | ||||||||
\(754\) | −13.5454 | −0.493295 | ||||||||
\(755\) | −31.0596 | −1.13038 | ||||||||
\(756\) | 3.73463 | 0.135827 | ||||||||
\(757\) | −2.68876 | −0.0977247 | −0.0488623 | − | 0.998806i | \(-0.515560\pi\) | ||||
−0.0488623 | + | 0.998806i | \(0.515560\pi\) | |||||||
\(758\) | 25.2725 | 0.917938 | ||||||||
\(759\) | −22.9532 | −0.833149 | ||||||||
\(760\) | 30.5445 | 1.10797 | ||||||||
\(761\) | −42.4002 | −1.53701 | −0.768504 | − | 0.639845i | \(-0.778998\pi\) | ||||
−0.768504 | + | 0.639845i | \(0.778998\pi\) | |||||||
\(762\) | −19.2195 | −0.696249 | ||||||||
\(763\) | −13.7346 | −0.497227 | ||||||||
\(764\) | 16.2734 | 0.588751 | ||||||||
\(765\) | −2.00000 | −0.0723102 | ||||||||
\(766\) | 37.7796 | 1.36503 | ||||||||
\(767\) | 8.90917 | 0.321692 | ||||||||
\(768\) | 4.91721 | 0.177434 | ||||||||
\(769\) | −35.1046 | −1.26590 | −0.632952 | − | 0.774191i | \(-0.718157\pi\) | ||||
−0.632952 | + | 0.774191i | \(0.718157\pi\) | |||||||
\(770\) | 33.9650 | 1.22401 | ||||||||
\(771\) | −17.5336 | −0.631457 | ||||||||
\(772\) | 5.62156 | 0.202324 | ||||||||
\(773\) | −15.0946 | −0.542915 | −0.271458 | − | 0.962450i | \(-0.587506\pi\) | ||||
−0.271458 | + | 0.962450i | \(0.587506\pi\) | |||||||
\(774\) | −2.12489 | −0.0763774 | ||||||||
\(775\) | 45.2342 | 1.62486 | ||||||||
\(776\) | 6.80792 | 0.244390 | ||||||||
\(777\) | 7.84014 | 0.281263 | ||||||||
\(778\) | −51.9844 | −1.86373 | ||||||||
\(779\) | −4.96972 | −0.178059 | ||||||||
\(780\) | −31.1240 | −1.11442 | ||||||||
\(781\) | −34.4995 | −1.23449 | ||||||||
\(782\) | 9.06147 | 0.324037 | ||||||||
\(783\) | −2.12489 | −0.0759372 | ||||||||
\(784\) | 12.9679 | 0.463139 | ||||||||
\(785\) | −102.338 | −3.65259 | ||||||||
\(786\) | 40.4995 | 1.44457 | ||||||||
\(787\) | 41.1202 | 1.46578 | 0.732888 | − | 0.680349i | \(-0.238172\pi\) | ||||
0.732888 | + | 0.680349i | \(0.238172\pi\) | |||||||
\(788\) | 19.5667 | 0.697036 | ||||||||
\(789\) | −6.37088 | −0.226809 | ||||||||
\(790\) | −23.8401 | −0.848194 | ||||||||
\(791\) | 5.05585 | 0.179765 | ||||||||
\(792\) | −2.85665 | −0.101507 | ||||||||
\(793\) | −33.6585 | −1.19525 | ||||||||
\(794\) | −81.9650 | −2.90883 | ||||||||
\(795\) | −15.5298 | −0.550786 | ||||||||
\(796\) | 17.3775 | 0.615930 | ||||||||
\(797\) | 2.78807 | 0.0987584 | 0.0493792 | − | 0.998780i | \(-0.484276\pi\) | ||||
0.0493792 | + | 0.998780i | \(0.484276\pi\) | |||||||
\(798\) | −21.3444 | −0.755583 | ||||||||
\(799\) | −4.08991 | −0.144691 | ||||||||
\(800\) | −95.3445 | −3.37094 | ||||||||
\(801\) | −18.2498 | −0.644824 | ||||||||
\(802\) | −9.59220 | −0.338712 | ||||||||
\(803\) | 13.1277 | 0.463268 | ||||||||
\(804\) | 17.7190 | 0.624902 | ||||||||
\(805\) | −53.8695 | −1.89865 | ||||||||
\(806\) | 24.0000 | 0.845364 | ||||||||
\(807\) | 29.5445 | 1.04002 | ||||||||
\(808\) | 8.49954 | 0.299013 | ||||||||
\(809\) | −8.27913 | −0.291079 | −0.145539 | − | 0.989352i | \(-0.546492\pi\) | ||||
−0.145539 | + | 0.989352i | \(0.546492\pi\) | |||||||
\(810\) | −8.76491 | −0.307968 | ||||||||
\(811\) | 47.1807 | 1.65674 | 0.828370 | − | 0.560181i | \(-0.189269\pi\) | ||||
0.828370 | + | 0.560181i | \(0.189269\pi\) | |||||||
\(812\) | −7.93567 | −0.278487 | ||||||||
\(813\) | −11.8255 | −0.414737 | ||||||||
\(814\) | −29.2800 | −1.02627 | ||||||||
\(815\) | 5.87511 | 0.205796 | ||||||||
\(816\) | −1.31124 | −0.0459026 | ||||||||
\(817\) | 6.76491 | 0.236674 | ||||||||
\(818\) | 37.6509 | 1.31643 | ||||||||
\(819\) | 4.45459 | 0.155656 | ||||||||
\(820\) | −7.62156 | −0.266157 | ||||||||
\(821\) | 38.7640 | 1.35287 | 0.676436 | − | 0.736501i | \(-0.263523\pi\) | ||||
0.676436 | + | 0.736501i | \(0.263523\pi\) | |||||||
\(822\) | −44.3553 | −1.54707 | ||||||||
\(823\) | 36.1433 | 1.25988 | 0.629939 | − | 0.776645i | \(-0.283080\pi\) | ||||
0.629939 | + | 0.776645i | \(0.283080\pi\) | |||||||
\(824\) | 2.78623 | 0.0970631 | ||||||||
\(825\) | −31.3553 | −1.09165 | ||||||||
\(826\) | 9.36996 | 0.326023 | ||||||||
\(827\) | 30.4958 | 1.06044 | 0.530221 | − | 0.847860i | \(-0.322109\pi\) | ||||
0.530221 | + | 0.847860i | \(0.322109\pi\) | |||||||
\(828\) | 22.1211 | 0.768762 | ||||||||
\(829\) | 38.5601 | 1.33925 | 0.669624 | − | 0.742701i | \(-0.266455\pi\) | ||||
0.669624 | + | 0.742701i | \(0.266455\pi\) | |||||||
\(830\) | 48.9036 | 1.69747 | ||||||||
\(831\) | −15.7796 | −0.547388 | ||||||||
\(832\) | −34.3610 | −1.19125 | ||||||||
\(833\) | −2.32500 | −0.0805566 | ||||||||
\(834\) | −28.1211 | −0.973754 | ||||||||
\(835\) | −34.4839 | −1.19337 | ||||||||
\(836\) | 44.4040 | 1.53574 | ||||||||
\(837\) | 3.76491 | 0.130134 | ||||||||
\(838\) | 34.9310 | 1.20667 | ||||||||
\(839\) | −44.2791 | −1.52869 | −0.764343 | − | 0.644810i | \(-0.776936\pi\) | ||||
−0.764343 | + | 0.644810i | \(0.776936\pi\) | |||||||
\(840\) | −6.70436 | −0.231322 | ||||||||
\(841\) | −24.4849 | −0.844306 | ||||||||
\(842\) | 50.8023 | 1.75076 | ||||||||
\(843\) | −18.0147 | −0.620459 | ||||||||
\(844\) | 8.61261 | 0.296458 | ||||||||
\(845\) | 16.4995 | 0.567601 | ||||||||
\(846\) | −17.9239 | −0.616235 | ||||||||
\(847\) | −6.22041 | −0.213736 | ||||||||
\(848\) | −10.1817 | −0.349640 | ||||||||
\(849\) | 5.64380 | 0.193695 | ||||||||
\(850\) | 12.3784 | 0.424577 | ||||||||
\(851\) | 46.4390 | 1.59191 | ||||||||
\(852\) | 33.2489 | 1.13909 | ||||||||
\(853\) | 29.2716 | 1.00224 | 0.501120 | − | 0.865378i | \(-0.332922\pi\) | ||||
0.501120 | + | 0.865378i | \(0.332922\pi\) | |||||||
\(854\) | −35.3993 | −1.21134 | ||||||||
\(855\) | 27.9045 | 0.954313 | ||||||||
\(856\) | −3.45367 | −0.118044 | ||||||||
\(857\) | 6.37088 | 0.217625 | 0.108812 | − | 0.994062i | \(-0.465295\pi\) | ||||
0.108812 | + | 0.994062i | \(0.465295\pi\) | |||||||
\(858\) | −16.6362 | −0.567952 | ||||||||
\(859\) | 32.4839 | 1.10834 | 0.554169 | − | 0.832404i | \(-0.313036\pi\) | ||||
0.554169 | + | 0.832404i | \(0.313036\pi\) | |||||||
\(860\) | 10.3747 | 0.353773 | ||||||||
\(861\) | 1.09083 | 0.0371753 | ||||||||
\(862\) | −33.1670 | −1.12967 | ||||||||
\(863\) | 32.2791 | 1.09879 | 0.549397 | − | 0.835561i | \(-0.314857\pi\) | ||||
0.549397 | + | 0.835561i | \(0.314857\pi\) | |||||||
\(864\) | −7.93567 | −0.269977 | ||||||||
\(865\) | −51.3094 | −1.74457 | ||||||||
\(866\) | −23.1807 | −0.787714 | ||||||||
\(867\) | −16.7649 | −0.569366 | ||||||||
\(868\) | 14.0606 | 0.477246 | ||||||||
\(869\) | −7.09839 | −0.240796 | ||||||||
\(870\) | 18.6244 | 0.631427 | ||||||||
\(871\) | 21.1349 | 0.716128 | ||||||||
\(872\) | −10.1249 | −0.342872 | ||||||||
\(873\) | 6.21949 | 0.210498 | ||||||||
\(874\) | −126.428 | −4.27648 | ||||||||
\(875\) | −42.9641 | −1.45245 | ||||||||
\(876\) | −12.6518 | −0.427466 | ||||||||
\(877\) | −0.674081 | −0.0227621 | −0.0113810 | − | 0.999935i | \(-0.503623\pi\) | ||||
−0.0113810 | + | 0.999935i | \(0.503623\pi\) | |||||||
\(878\) | 42.1268 | 1.42171 | ||||||||
\(879\) | 1.34060 | 0.0452173 | ||||||||
\(880\) | −29.1122 | −0.981370 | ||||||||
\(881\) | 1.01560 | 0.0342163 | 0.0171082 | − | 0.999854i | \(-0.494554\pi\) | ||||
0.0171082 | + | 0.999854i | \(0.494554\pi\) | |||||||
\(882\) | −10.1892 | −0.343089 | ||||||||
\(883\) | −31.6732 | −1.06589 | −0.532943 | − | 0.846151i | \(-0.678914\pi\) | ||||
−0.532943 | + | 0.846151i | \(0.678914\pi\) | |||||||
\(884\) | 3.65848 | 0.123048 | ||||||||
\(885\) | −12.2498 | −0.411772 | ||||||||
\(886\) | −0.667435 | −0.0224229 | ||||||||
\(887\) | 40.8686 | 1.37223 | 0.686116 | − | 0.727492i | \(-0.259314\pi\) | ||||
0.686116 | + | 0.727492i | \(0.259314\pi\) | |||||||
\(888\) | 5.77959 | 0.193950 | ||||||||
\(889\) | −13.4305 | −0.450445 | ||||||||
\(890\) | 159.958 | 5.36179 | ||||||||
\(891\) | −2.60975 | −0.0874298 | ||||||||
\(892\) | −24.4839 | −0.819783 | ||||||||
\(893\) | 57.0634 | 1.90955 | ||||||||
\(894\) | −23.8401 | −0.797334 | ||||||||
\(895\) | −9.28005 | −0.310198 | ||||||||
\(896\) | −12.5714 | −0.419982 | ||||||||
\(897\) | 26.3856 | 0.880988 | ||||||||
\(898\) | 21.7876 | 0.727062 | ||||||||
\(899\) | −8.00000 | −0.266815 | ||||||||
\(900\) | 30.2186 | 1.00729 | ||||||||
\(901\) | 1.82546 | 0.0608149 | ||||||||
\(902\) | −4.07384 | −0.135644 | ||||||||
\(903\) | −1.48486 | −0.0494131 | ||||||||
\(904\) | 3.72707 | 0.123961 | ||||||||
\(905\) | 28.4040 | 0.944181 | ||||||||
\(906\) | 16.0000 | 0.531564 | ||||||||
\(907\) | −16.0828 | −0.534020 | −0.267010 | − | 0.963694i | \(-0.586036\pi\) | ||||
−0.267010 | + | 0.963694i | \(0.586036\pi\) | |||||||
\(908\) | 7.77386 | 0.257985 | ||||||||
\(909\) | 7.76491 | 0.257546 | ||||||||
\(910\) | −39.0440 | −1.29430 | ||||||||
\(911\) | 37.1277 | 1.23010 | 0.615049 | − | 0.788489i | \(-0.289136\pi\) | ||||
0.615049 | + | 0.788489i | \(0.289136\pi\) | |||||||
\(912\) | 18.2947 | 0.605799 | ||||||||
\(913\) | 14.5610 | 0.481899 | ||||||||
\(914\) | 6.84106 | 0.226282 | ||||||||
\(915\) | 46.2791 | 1.52994 | ||||||||
\(916\) | 8.06055 | 0.266328 | ||||||||
\(917\) | 28.3009 | 0.934579 | ||||||||
\(918\) | 1.03028 | 0.0340042 | ||||||||
\(919\) | 27.3940 | 0.903646 | 0.451823 | − | 0.892108i | \(-0.350774\pi\) | ||||
0.451823 | + | 0.892108i | \(0.350774\pi\) | |||||||
\(920\) | −39.7115 | −1.30925 | ||||||||
\(921\) | −0.424310 | −0.0139815 | ||||||||
\(922\) | −34.4002 | −1.13291 | ||||||||
\(923\) | 39.6585 | 1.30537 | ||||||||
\(924\) | −9.74645 | −0.320635 | ||||||||
\(925\) | 63.4381 | 2.08583 | ||||||||
\(926\) | 31.6311 | 1.03946 | ||||||||
\(927\) | 2.54541 | 0.0836024 | ||||||||
\(928\) | 16.8624 | 0.553535 | ||||||||
\(929\) | 30.5639 | 1.00277 | 0.501384 | − | 0.865225i | \(-0.332824\pi\) | ||||
0.501384 | + | 0.865225i | \(0.332824\pi\) | |||||||
\(930\) | −32.9991 | −1.08208 | ||||||||
\(931\) | 32.4390 | 1.06314 | ||||||||
\(932\) | 27.9045 | 0.914041 | ||||||||
\(933\) | 0.110206 | 0.00360797 | ||||||||
\(934\) | −17.4674 | −0.571552 | ||||||||
\(935\) | 5.21949 | 0.170696 | ||||||||
\(936\) | 3.28383 | 0.107335 | ||||||||
\(937\) | −20.4702 | −0.668732 | −0.334366 | − | 0.942443i | \(-0.608522\pi\) | ||||
−0.334366 | + | 0.942443i | \(0.608522\pi\) | |||||||
\(938\) | 22.2280 | 0.725769 | ||||||||
\(939\) | −2.96972 | −0.0969133 | ||||||||
\(940\) | 87.5124 | 2.85434 | ||||||||
\(941\) | 1.89358 | 0.0617288 | 0.0308644 | − | 0.999524i | \(-0.490174\pi\) | ||||
0.0308644 | + | 0.999524i | \(0.490174\pi\) | |||||||
\(942\) | 52.7181 | 1.71765 | ||||||||
\(943\) | 6.46123 | 0.210407 | ||||||||
\(944\) | −8.03119 | −0.261393 | ||||||||
\(945\) | −6.12489 | −0.199243 | ||||||||
\(946\) | 5.54541 | 0.180297 | ||||||||
\(947\) | −33.1311 | −1.07662 | −0.538308 | − | 0.842748i | \(-0.680936\pi\) | ||||
−0.538308 | + | 0.842748i | \(0.680936\pi\) | |||||||
\(948\) | 6.84106 | 0.222187 | ||||||||
\(949\) | −15.0908 | −0.489869 | ||||||||
\(950\) | −172.707 | −5.60335 | ||||||||
\(951\) | −12.4243 | −0.402886 | ||||||||
\(952\) | 0.788067 | 0.0255414 | ||||||||
\(953\) | −29.5942 | −0.958649 | −0.479324 | − | 0.877638i | \(-0.659118\pi\) | ||||
−0.479324 | + | 0.877638i | \(0.659118\pi\) | |||||||
\(954\) | 8.00000 | 0.259010 | ||||||||
\(955\) | −26.6888 | −0.863628 | ||||||||
\(956\) | 42.9953 | 1.39057 | ||||||||
\(957\) | 5.54541 | 0.179258 | ||||||||
\(958\) | 20.0156 | 0.646675 | ||||||||
\(959\) | −30.9953 | −1.00089 | ||||||||
\(960\) | 47.2451 | 1.52483 | ||||||||
\(961\) | −16.8255 | −0.542757 | ||||||||
\(962\) | 33.6585 | 1.08519 | ||||||||
\(963\) | −3.15516 | −0.101674 | ||||||||
\(964\) | 56.7418 | 1.82753 | ||||||||
\(965\) | −9.21949 | −0.296786 | ||||||||
\(966\) | 27.7502 | 0.892849 | ||||||||
\(967\) | 15.4234 | 0.495983 | 0.247991 | − | 0.968762i | \(-0.420230\pi\) | ||||
0.247991 | + | 0.968762i | \(0.420230\pi\) | |||||||
\(968\) | −4.58556 | −0.147385 | ||||||||
\(969\) | −3.28005 | −0.105370 | ||||||||
\(970\) | −54.5133 | −1.75032 | ||||||||
\(971\) | −25.6438 | −0.822949 | −0.411474 | − | 0.911421i | \(-0.634986\pi\) | ||||
−0.411474 | + | 0.911421i | \(0.634986\pi\) | |||||||
\(972\) | 2.51514 | 0.0806731 | ||||||||
\(973\) | −19.6509 | −0.629980 | ||||||||
\(974\) | −14.2791 | −0.457533 | ||||||||
\(975\) | 36.0440 | 1.15433 | ||||||||
\(976\) | 30.3415 | 0.971208 | ||||||||
\(977\) | 11.1202 | 0.355766 | 0.177883 | − | 0.984052i | \(-0.443075\pi\) | ||||
0.177883 | + | 0.984052i | \(0.443075\pi\) | |||||||
\(978\) | −3.02650 | −0.0967766 | ||||||||
\(979\) | 47.6273 | 1.52217 | ||||||||
\(980\) | 49.7484 | 1.58915 | ||||||||
\(981\) | −9.24977 | −0.295322 | ||||||||
\(982\) | −76.9603 | −2.45590 | ||||||||
\(983\) | −36.9697 | −1.17915 | −0.589576 | − | 0.807713i | \(-0.700705\pi\) | ||||
−0.589576 | + | 0.807713i | \(0.700705\pi\) | |||||||
\(984\) | 0.804136 | 0.0256349 | ||||||||
\(985\) | −32.0899 | −1.02247 | ||||||||
\(986\) | −2.18922 | −0.0697189 | ||||||||
\(987\) | −12.5251 | −0.398679 | ||||||||
\(988\) | −51.0440 | −1.62393 | ||||||||
\(989\) | −8.79518 | −0.279671 | ||||||||
\(990\) | 22.8742 | 0.726990 | ||||||||
\(991\) | 9.70527 | 0.308298 | 0.154149 | − | 0.988048i | \(-0.450736\pi\) | ||||
0.154149 | + | 0.988048i | \(0.450736\pi\) | |||||||
\(992\) | −29.8771 | −0.948598 | ||||||||
\(993\) | 31.2938 | 0.993079 | ||||||||
\(994\) | 41.7096 | 1.32295 | ||||||||
\(995\) | −28.4995 | −0.903496 | ||||||||
\(996\) | −14.0331 | −0.444657 | ||||||||
\(997\) | −23.2413 | −0.736059 | −0.368030 | − | 0.929814i | \(-0.619967\pi\) | ||||
−0.368030 | + | 0.929814i | \(0.619967\pi\) | |||||||
\(998\) | −63.3737 | −2.00606 | ||||||||
\(999\) | 5.28005 | 0.167053 |
(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 | 129.2.a.d.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 387.2.a.i.1.1 | 3 | |||
4.3 | odd | 2 | 2064.2.a.x.1.1 | 3 | |||
5.4 | even | 2 | 3225.2.a.t.1.1 | 3 | |||
7.6 | odd | 2 | 6321.2.a.p.1.3 | 3 | |||
8.3 | odd | 2 | 8256.2.a.cu.1.3 | 3 | |||
8.5 | even | 2 | 8256.2.a.cr.1.3 | 3 | |||
12.11 | even | 2 | 6192.2.a.bw.1.3 | 3 | |||
15.14 | odd | 2 | 9675.2.a.bq.1.3 | 3 | |||
43.42 | odd | 2 | 5547.2.a.p.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
129.2.a.d.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
387.2.a.i.1.1 | 3 | 3.2 | odd | 2 | |||
2064.2.a.x.1.1 | 3 | 4.3 | odd | 2 | |||
3225.2.a.t.1.1 | 3 | 5.4 | even | 2 | |||
5547.2.a.p.1.1 | 3 | 43.42 | odd | 2 | |||
6192.2.a.bw.1.3 | 3 | 12.11 | even | 2 | |||
6321.2.a.p.1.3 | 3 | 7.6 | odd | 2 | |||
8256.2.a.cr.1.3 | 3 | 8.5 | even | 2 | |||
8256.2.a.cu.1.3 | 3 | 8.3 | odd | 2 | |||
9675.2.a.bq.1.3 | 3 | 15.14 | odd | 2 |