Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1441,2,Mod(1,1441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1441, 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("1441.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1441 = 11 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1441.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: | \(11.5064429313\) |
Analytic rank: | \(1\) |
Dimension: | \(23\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 1441.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.169669 | −0.119974 | −0.0599869 | − | 0.998199i | \(-0.519106\pi\) | ||||
−0.0599869 | + | 0.998199i | \(0.519106\pi\) | |||||||
\(3\) | −1.85024 | −1.06823 | −0.534117 | − | 0.845411i | \(-0.679356\pi\) | ||||
−0.534117 | + | 0.845411i | \(0.679356\pi\) | |||||||
\(4\) | −1.97121 | −0.985606 | ||||||||
\(5\) | −3.73136 | −1.66872 | −0.834358 | − | 0.551223i | \(-0.814161\pi\) | ||||
−0.834358 | + | 0.551223i | \(0.814161\pi\) | |||||||
\(6\) | 0.313927 | 0.128160 | ||||||||
\(7\) | 1.69497 | 0.640640 | 0.320320 | − | 0.947309i | \(-0.396210\pi\) | ||||
0.320320 | + | 0.947309i | \(0.396210\pi\) | |||||||
\(8\) | 0.673790 | 0.238221 | ||||||||
\(9\) | 0.423370 | 0.141123 | ||||||||
\(10\) | 0.633095 | 0.200202 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 3.64721 | 1.05286 | ||||||||
\(13\) | 0.706466 | 0.195938 | 0.0979691 | − | 0.995189i | \(-0.468765\pi\) | ||||
0.0979691 | + | 0.995189i | \(0.468765\pi\) | |||||||
\(14\) | −0.287584 | −0.0768600 | ||||||||
\(15\) | 6.90390 | 1.78258 | ||||||||
\(16\) | 3.82810 | 0.957026 | ||||||||
\(17\) | −0.521224 | −0.126415 | −0.0632077 | − | 0.998000i | \(-0.520133\pi\) | ||||
−0.0632077 | + | 0.998000i | \(0.520133\pi\) | |||||||
\(18\) | −0.0718326 | −0.0169311 | ||||||||
\(19\) | 5.59979 | 1.28468 | 0.642340 | − | 0.766420i | \(-0.277964\pi\) | ||||
0.642340 | + | 0.766420i | \(0.277964\pi\) | |||||||
\(20\) | 7.35531 | 1.64470 | ||||||||
\(21\) | −3.13610 | −0.684353 | ||||||||
\(22\) | −0.169669 | −0.0361735 | ||||||||
\(23\) | 3.04720 | 0.635386 | 0.317693 | − | 0.948194i | \(-0.397092\pi\) | ||||
0.317693 | + | 0.948194i | \(0.397092\pi\) | |||||||
\(24\) | −1.24667 | −0.254476 | ||||||||
\(25\) | 8.92307 | 1.78461 | ||||||||
\(26\) | −0.119865 | −0.0235075 | ||||||||
\(27\) | 4.76737 | 0.917481 | ||||||||
\(28\) | −3.34115 | −0.631418 | ||||||||
\(29\) | −8.02530 | −1.49026 | −0.745130 | − | 0.666919i | \(-0.767613\pi\) | ||||
−0.745130 | + | 0.666919i | \(0.767613\pi\) | |||||||
\(30\) | −1.17137 | −0.213863 | ||||||||
\(31\) | 1.55904 | 0.280012 | 0.140006 | − | 0.990151i | \(-0.455288\pi\) | ||||
0.140006 | + | 0.990151i | \(0.455288\pi\) | |||||||
\(32\) | −1.99709 | −0.353039 | ||||||||
\(33\) | −1.85024 | −0.322085 | ||||||||
\(34\) | 0.0884353 | 0.0151665 | ||||||||
\(35\) | −6.32456 | −1.06905 | ||||||||
\(36\) | −0.834552 | −0.139092 | ||||||||
\(37\) | −7.66615 | −1.26031 | −0.630154 | − | 0.776471i | \(-0.717008\pi\) | ||||
−0.630154 | + | 0.776471i | \(0.717008\pi\) | |||||||
\(38\) | −0.950109 | −0.154128 | ||||||||
\(39\) | −1.30713 | −0.209308 | ||||||||
\(40\) | −2.51416 | −0.397523 | ||||||||
\(41\) | −5.80718 | −0.906929 | −0.453465 | − | 0.891274i | \(-0.649812\pi\) | ||||
−0.453465 | + | 0.891274i | \(0.649812\pi\) | |||||||
\(42\) | 0.532098 | 0.0821044 | ||||||||
\(43\) | 5.42776 | 0.827725 | 0.413863 | − | 0.910339i | \(-0.364179\pi\) | ||||
0.413863 | + | 0.910339i | \(0.364179\pi\) | |||||||
\(44\) | −1.97121 | −0.297171 | ||||||||
\(45\) | −1.57975 | −0.235495 | ||||||||
\(46\) | −0.517015 | −0.0762297 | ||||||||
\(47\) | −9.01069 | −1.31434 | −0.657172 | − | 0.753740i | \(-0.728248\pi\) | ||||
−0.657172 | + | 0.753740i | \(0.728248\pi\) | |||||||
\(48\) | −7.08289 | −1.02233 | ||||||||
\(49\) | −4.12707 | −0.589581 | ||||||||
\(50\) | −1.51396 | −0.214107 | ||||||||
\(51\) | 0.964386 | 0.135041 | ||||||||
\(52\) | −1.39259 | −0.193118 | ||||||||
\(53\) | 7.15431 | 0.982720 | 0.491360 | − | 0.870957i | \(-0.336500\pi\) | ||||
0.491360 | + | 0.870957i | \(0.336500\pi\) | |||||||
\(54\) | −0.808873 | −0.110074 | ||||||||
\(55\) | −3.73136 | −0.503137 | ||||||||
\(56\) | 1.14206 | 0.152614 | ||||||||
\(57\) | −10.3609 | −1.37234 | ||||||||
\(58\) | 1.36164 | 0.178792 | ||||||||
\(59\) | 15.1410 | 1.97119 | 0.985597 | − | 0.169111i | \(-0.0540897\pi\) | ||||
0.985597 | + | 0.169111i | \(0.0540897\pi\) | |||||||
\(60\) | −13.6090 | −1.75692 | ||||||||
\(61\) | 9.76953 | 1.25086 | 0.625430 | − | 0.780280i | \(-0.284924\pi\) | ||||
0.625430 | + | 0.780280i | \(0.284924\pi\) | |||||||
\(62\) | −0.264520 | −0.0335941 | ||||||||
\(63\) | 0.717601 | 0.0904092 | ||||||||
\(64\) | −7.31736 | −0.914671 | ||||||||
\(65\) | −2.63608 | −0.326965 | ||||||||
\(66\) | 0.313927 | 0.0386417 | ||||||||
\(67\) | 3.25036 | 0.397095 | 0.198547 | − | 0.980091i | \(-0.436378\pi\) | ||||
0.198547 | + | 0.980091i | \(0.436378\pi\) | |||||||
\(68\) | 1.02744 | 0.124596 | ||||||||
\(69\) | −5.63805 | −0.678741 | ||||||||
\(70\) | 1.07308 | 0.128257 | ||||||||
\(71\) | −10.0834 | −1.19668 | −0.598341 | − | 0.801241i | \(-0.704173\pi\) | ||||
−0.598341 | + | 0.801241i | \(0.704173\pi\) | |||||||
\(72\) | 0.285262 | 0.0336185 | ||||||||
\(73\) | −9.77990 | −1.14465 | −0.572325 | − | 0.820027i | \(-0.693959\pi\) | ||||
−0.572325 | + | 0.820027i | \(0.693959\pi\) | |||||||
\(74\) | 1.30071 | 0.151204 | ||||||||
\(75\) | −16.5098 | −1.90638 | ||||||||
\(76\) | −11.0384 | −1.26619 | ||||||||
\(77\) | 1.69497 | 0.193160 | ||||||||
\(78\) | 0.221779 | 0.0251115 | ||||||||
\(79\) | 10.7868 | 1.21361 | 0.606807 | − | 0.794849i | \(-0.292450\pi\) | ||||
0.606807 | + | 0.794849i | \(0.292450\pi\) | |||||||
\(80\) | −14.2840 | −1.59700 | ||||||||
\(81\) | −10.0909 | −1.12121 | ||||||||
\(82\) | 0.985297 | 0.108808 | ||||||||
\(83\) | −6.21910 | −0.682635 | −0.341317 | − | 0.939948i | \(-0.610873\pi\) | ||||
−0.341317 | + | 0.939948i | \(0.610873\pi\) | |||||||
\(84\) | 6.18192 | 0.674502 | ||||||||
\(85\) | 1.94487 | 0.210951 | ||||||||
\(86\) | −0.920920 | −0.0993054 | ||||||||
\(87\) | 14.8487 | 1.59195 | ||||||||
\(88\) | 0.673790 | 0.0718263 | ||||||||
\(89\) | −2.41089 | −0.255553 | −0.127777 | − | 0.991803i | \(-0.540784\pi\) | ||||
−0.127777 | + | 0.991803i | \(0.540784\pi\) | |||||||
\(90\) | 0.268033 | 0.0282532 | ||||||||
\(91\) | 1.19744 | 0.125526 | ||||||||
\(92\) | −6.00669 | −0.626241 | ||||||||
\(93\) | −2.88459 | −0.299118 | ||||||||
\(94\) | 1.52883 | 0.157687 | ||||||||
\(95\) | −20.8948 | −2.14377 | ||||||||
\(96\) | 3.69509 | 0.377128 | ||||||||
\(97\) | 15.0150 | 1.52454 | 0.762272 | − | 0.647257i | \(-0.224084\pi\) | ||||
0.762272 | + | 0.647257i | \(0.224084\pi\) | |||||||
\(98\) | 0.700234 | 0.0707343 | ||||||||
\(99\) | 0.423370 | 0.0425503 | ||||||||
\(100\) | −17.5893 | −1.75893 | ||||||||
\(101\) | 1.26835 | 0.126205 | 0.0631026 | − | 0.998007i | \(-0.479900\pi\) | ||||
0.0631026 | + | 0.998007i | \(0.479900\pi\) | |||||||
\(102\) | −0.163626 | −0.0162014 | ||||||||
\(103\) | −17.8358 | −1.75741 | −0.878707 | − | 0.477362i | \(-0.841593\pi\) | ||||
−0.878707 | + | 0.477362i | \(0.841593\pi\) | |||||||
\(104\) | 0.476010 | 0.0466766 | ||||||||
\(105\) | 11.7019 | 1.14199 | ||||||||
\(106\) | −1.21386 | −0.117901 | ||||||||
\(107\) | 14.2338 | 1.37604 | 0.688018 | − | 0.725694i | \(-0.258481\pi\) | ||||
0.688018 | + | 0.725694i | \(0.258481\pi\) | |||||||
\(108\) | −9.39750 | −0.904275 | ||||||||
\(109\) | −19.1489 | −1.83413 | −0.917065 | − | 0.398738i | \(-0.869448\pi\) | ||||
−0.917065 | + | 0.398738i | \(0.869448\pi\) | |||||||
\(110\) | 0.633095 | 0.0603633 | ||||||||
\(111\) | 14.1842 | 1.34630 | ||||||||
\(112\) | 6.48853 | 0.613109 | ||||||||
\(113\) | −13.0974 | −1.23210 | −0.616048 | − | 0.787709i | \(-0.711267\pi\) | ||||
−0.616048 | + | 0.787709i | \(0.711267\pi\) | |||||||
\(114\) | 1.75792 | 0.164645 | ||||||||
\(115\) | −11.3702 | −1.06028 | ||||||||
\(116\) | 15.8196 | 1.46881 | ||||||||
\(117\) | 0.299096 | 0.0276515 | ||||||||
\(118\) | −2.56896 | −0.236492 | ||||||||
\(119\) | −0.883460 | −0.0809867 | ||||||||
\(120\) | 4.65178 | 0.424647 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.65758 | −0.150070 | ||||||||
\(123\) | 10.7447 | 0.968813 | ||||||||
\(124\) | −3.07320 | −0.275981 | ||||||||
\(125\) | −14.6384 | −1.30930 | ||||||||
\(126\) | −0.121754 | −0.0108467 | ||||||||
\(127\) | −0.202132 | −0.0179363 | −0.00896816 | − | 0.999960i | \(-0.502855\pi\) | ||||
−0.00896816 | + | 0.999960i | \(0.502855\pi\) | |||||||
\(128\) | 5.23571 | 0.462775 | ||||||||
\(129\) | −10.0426 | −0.884204 | ||||||||
\(130\) | 0.447260 | 0.0392273 | ||||||||
\(131\) | 1.00000 | 0.0873704 | ||||||||
\(132\) | 3.64721 | 0.317449 | ||||||||
\(133\) | 9.49149 | 0.823017 | ||||||||
\(134\) | −0.551484 | −0.0476410 | ||||||||
\(135\) | −17.7888 | −1.53102 | ||||||||
\(136\) | −0.351195 | −0.0301148 | ||||||||
\(137\) | −8.05468 | −0.688158 | −0.344079 | − | 0.938941i | \(-0.611809\pi\) | ||||
−0.344079 | + | 0.938941i | \(0.611809\pi\) | |||||||
\(138\) | 0.956599 | 0.0814311 | ||||||||
\(139\) | −6.95248 | −0.589702 | −0.294851 | − | 0.955543i | \(-0.595270\pi\) | ||||
−0.294851 | + | 0.955543i | \(0.595270\pi\) | |||||||
\(140\) | 12.4670 | 1.05366 | ||||||||
\(141\) | 16.6719 | 1.40403 | ||||||||
\(142\) | 1.71084 | 0.143571 | ||||||||
\(143\) | 0.706466 | 0.0590776 | ||||||||
\(144\) | 1.62070 | 0.135059 | ||||||||
\(145\) | 29.9453 | 2.48682 | ||||||||
\(146\) | 1.65934 | 0.137328 | ||||||||
\(147\) | 7.63604 | 0.629810 | ||||||||
\(148\) | 15.1116 | 1.24217 | ||||||||
\(149\) | −10.8467 | −0.888599 | −0.444299 | − | 0.895878i | \(-0.646547\pi\) | ||||
−0.444299 | + | 0.895878i | \(0.646547\pi\) | |||||||
\(150\) | 2.80119 | 0.228716 | ||||||||
\(151\) | 16.9912 | 1.38273 | 0.691364 | − | 0.722507i | \(-0.257010\pi\) | ||||
0.691364 | + | 0.722507i | \(0.257010\pi\) | |||||||
\(152\) | 3.77308 | 0.306038 | ||||||||
\(153\) | −0.220670 | −0.0178401 | ||||||||
\(154\) | −0.287584 | −0.0231742 | ||||||||
\(155\) | −5.81734 | −0.467260 | ||||||||
\(156\) | 2.57663 | 0.206295 | ||||||||
\(157\) | −12.2112 | −0.974563 | −0.487282 | − | 0.873245i | \(-0.662012\pi\) | ||||
−0.487282 | + | 0.873245i | \(0.662012\pi\) | |||||||
\(158\) | −1.83019 | −0.145602 | ||||||||
\(159\) | −13.2371 | −1.04977 | ||||||||
\(160\) | 7.45187 | 0.589122 | ||||||||
\(161\) | 5.16493 | 0.407053 | ||||||||
\(162\) | 1.71210 | 0.134516 | ||||||||
\(163\) | −7.17497 | −0.561987 | −0.280993 | − | 0.959710i | \(-0.590664\pi\) | ||||
−0.280993 | + | 0.959710i | \(0.590664\pi\) | |||||||
\(164\) | 11.4472 | 0.893875 | ||||||||
\(165\) | 6.90390 | 0.537468 | ||||||||
\(166\) | 1.05519 | 0.0818983 | ||||||||
\(167\) | −3.96016 | −0.306446 | −0.153223 | − | 0.988192i | \(-0.548965\pi\) | ||||
−0.153223 | + | 0.988192i | \(0.548965\pi\) | |||||||
\(168\) | −2.11307 | −0.163027 | ||||||||
\(169\) | −12.5009 | −0.961608 | ||||||||
\(170\) | −0.329984 | −0.0253086 | ||||||||
\(171\) | 2.37078 | 0.181298 | ||||||||
\(172\) | −10.6993 | −0.815811 | ||||||||
\(173\) | 10.5669 | 0.803386 | 0.401693 | − | 0.915774i | \(-0.368422\pi\) | ||||
0.401693 | + | 0.915774i | \(0.368422\pi\) | |||||||
\(174\) | −2.51936 | −0.190992 | ||||||||
\(175\) | 15.1244 | 1.14329 | ||||||||
\(176\) | 3.82810 | 0.288554 | ||||||||
\(177\) | −28.0145 | −2.10570 | ||||||||
\(178\) | 0.409052 | 0.0306597 | ||||||||
\(179\) | −15.2272 | −1.13813 | −0.569066 | − | 0.822292i | \(-0.692695\pi\) | ||||
−0.569066 | + | 0.822292i | \(0.692695\pi\) | |||||||
\(180\) | 3.11402 | 0.232105 | ||||||||
\(181\) | 1.23727 | 0.0919657 | 0.0459829 | − | 0.998942i | \(-0.485358\pi\) | ||||
0.0459829 | + | 0.998942i | \(0.485358\pi\) | |||||||
\(182\) | −0.203168 | −0.0150598 | ||||||||
\(183\) | −18.0759 | −1.33621 | ||||||||
\(184\) | 2.05318 | 0.151362 | ||||||||
\(185\) | 28.6052 | 2.10309 | ||||||||
\(186\) | 0.489424 | 0.0358863 | ||||||||
\(187\) | −0.521224 | −0.0381157 | ||||||||
\(188\) | 17.7620 | 1.29543 | ||||||||
\(189\) | 8.08057 | 0.587775 | ||||||||
\(190\) | 3.54520 | 0.257196 | ||||||||
\(191\) | 6.30901 | 0.456504 | 0.228252 | − | 0.973602i | \(-0.426699\pi\) | ||||
0.228252 | + | 0.973602i | \(0.426699\pi\) | |||||||
\(192\) | 13.5388 | 0.977082 | ||||||||
\(193\) | 9.66439 | 0.695658 | 0.347829 | − | 0.937558i | \(-0.386919\pi\) | ||||
0.347829 | + | 0.937558i | \(0.386919\pi\) | |||||||
\(194\) | −2.54758 | −0.182905 | ||||||||
\(195\) | 4.87737 | 0.349275 | ||||||||
\(196\) | 8.13533 | 0.581095 | ||||||||
\(197\) | 2.80309 | 0.199712 | 0.0998560 | − | 0.995002i | \(-0.468162\pi\) | ||||
0.0998560 | + | 0.995002i | \(0.468162\pi\) | |||||||
\(198\) | −0.0718326 | −0.00510492 | ||||||||
\(199\) | 14.2375 | 1.00927 | 0.504634 | − | 0.863333i | \(-0.331627\pi\) | ||||
0.504634 | + | 0.863333i | \(0.331627\pi\) | |||||||
\(200\) | 6.01227 | 0.425132 | ||||||||
\(201\) | −6.01393 | −0.424190 | ||||||||
\(202\) | −0.215199 | −0.0151413 | ||||||||
\(203\) | −13.6027 | −0.954720 | ||||||||
\(204\) | −1.90101 | −0.133097 | ||||||||
\(205\) | 21.6687 | 1.51341 | ||||||||
\(206\) | 3.02618 | 0.210844 | ||||||||
\(207\) | 1.29009 | 0.0896678 | ||||||||
\(208\) | 2.70442 | 0.187518 | ||||||||
\(209\) | 5.59979 | 0.387346 | ||||||||
\(210\) | −1.98545 | −0.137009 | ||||||||
\(211\) | 19.1971 | 1.32158 | 0.660790 | − | 0.750571i | \(-0.270221\pi\) | ||||
0.660790 | + | 0.750571i | \(0.270221\pi\) | |||||||
\(212\) | −14.1027 | −0.968575 | ||||||||
\(213\) | 18.6567 | 1.27834 | ||||||||
\(214\) | −2.41503 | −0.165088 | ||||||||
\(215\) | −20.2529 | −1.38124 | ||||||||
\(216\) | 3.21221 | 0.218563 | ||||||||
\(217\) | 2.64253 | 0.179387 | ||||||||
\(218\) | 3.24896 | 0.220048 | ||||||||
\(219\) | 18.0951 | 1.22275 | ||||||||
\(220\) | 7.35531 | 0.495895 | ||||||||
\(221\) | −0.368227 | −0.0247696 | ||||||||
\(222\) | −2.40661 | −0.161521 | ||||||||
\(223\) | −17.8071 | −1.19245 | −0.596225 | − | 0.802817i | \(-0.703333\pi\) | ||||
−0.596225 | + | 0.802817i | \(0.703333\pi\) | |||||||
\(224\) | −3.38501 | −0.226171 | ||||||||
\(225\) | 3.77776 | 0.251850 | ||||||||
\(226\) | 2.22221 | 0.147819 | ||||||||
\(227\) | 8.57424 | 0.569092 | 0.284546 | − | 0.958662i | \(-0.408157\pi\) | ||||
0.284546 | + | 0.958662i | \(0.408157\pi\) | |||||||
\(228\) | 20.4236 | 1.35259 | ||||||||
\(229\) | −23.5161 | −1.55399 | −0.776995 | − | 0.629506i | \(-0.783257\pi\) | ||||
−0.776995 | + | 0.629506i | \(0.783257\pi\) | |||||||
\(230\) | 1.92917 | 0.127206 | ||||||||
\(231\) | −3.13610 | −0.206340 | ||||||||
\(232\) | −5.40737 | −0.355011 | ||||||||
\(233\) | −4.28472 | −0.280701 | −0.140351 | − | 0.990102i | \(-0.544823\pi\) | ||||
−0.140351 | + | 0.990102i | \(0.544823\pi\) | |||||||
\(234\) | −0.0507473 | −0.00331745 | ||||||||
\(235\) | 33.6222 | 2.19327 | ||||||||
\(236\) | −29.8462 | −1.94282 | ||||||||
\(237\) | −19.9582 | −1.29642 | ||||||||
\(238\) | 0.149895 | 0.00971628 | ||||||||
\(239\) | −29.0657 | −1.88011 | −0.940054 | − | 0.341027i | \(-0.889225\pi\) | ||||
−0.940054 | + | 0.341027i | \(0.889225\pi\) | |||||||
\(240\) | 26.4288 | 1.70597 | ||||||||
\(241\) | 21.2610 | 1.36954 | 0.684771 | − | 0.728758i | \(-0.259902\pi\) | ||||
0.684771 | + | 0.728758i | \(0.259902\pi\) | |||||||
\(242\) | −0.169669 | −0.0109067 | ||||||||
\(243\) | 4.36836 | 0.280231 | ||||||||
\(244\) | −19.2578 | −1.23286 | ||||||||
\(245\) | 15.3996 | 0.983843 | ||||||||
\(246\) | −1.82303 | −0.116232 | ||||||||
\(247\) | 3.95606 | 0.251718 | ||||||||
\(248\) | 1.05046 | 0.0667046 | ||||||||
\(249\) | 11.5068 | 0.729213 | ||||||||
\(250\) | 2.48367 | 0.157081 | ||||||||
\(251\) | 10.6137 | 0.669934 | 0.334967 | − | 0.942230i | \(-0.391275\pi\) | ||||
0.334967 | + | 0.942230i | \(0.391275\pi\) | |||||||
\(252\) | −1.41454 | −0.0891078 | ||||||||
\(253\) | 3.04720 | 0.191576 | ||||||||
\(254\) | 0.0342955 | 0.00215189 | ||||||||
\(255\) | −3.59848 | −0.225345 | ||||||||
\(256\) | 13.7464 | 0.859150 | ||||||||
\(257\) | 10.6188 | 0.662383 | 0.331191 | − | 0.943564i | \(-0.392549\pi\) | ||||
0.331191 | + | 0.943564i | \(0.392549\pi\) | |||||||
\(258\) | 1.70392 | 0.106081 | ||||||||
\(259\) | −12.9939 | −0.807403 | ||||||||
\(260\) | 5.19627 | 0.322259 | ||||||||
\(261\) | −3.39767 | −0.210310 | ||||||||
\(262\) | −0.169669 | −0.0104822 | ||||||||
\(263\) | −17.4277 | −1.07464 | −0.537318 | − | 0.843380i | \(-0.680562\pi\) | ||||
−0.537318 | + | 0.843380i | \(0.680562\pi\) | |||||||
\(264\) | −1.24667 | −0.0767273 | ||||||||
\(265\) | −26.6953 | −1.63988 | ||||||||
\(266\) | −1.61041 | −0.0987405 | ||||||||
\(267\) | 4.46071 | 0.272991 | ||||||||
\(268\) | −6.40715 | −0.391379 | ||||||||
\(269\) | −19.9432 | −1.21596 | −0.607979 | − | 0.793953i | \(-0.708019\pi\) | ||||
−0.607979 | + | 0.793953i | \(0.708019\pi\) | |||||||
\(270\) | 3.01820 | 0.183682 | ||||||||
\(271\) | −5.94312 | −0.361019 | −0.180510 | − | 0.983573i | \(-0.557775\pi\) | ||||
−0.180510 | + | 0.983573i | \(0.557775\pi\) | |||||||
\(272\) | −1.99530 | −0.120983 | ||||||||
\(273\) | −2.21555 | −0.134091 | ||||||||
\(274\) | 1.36663 | 0.0825609 | ||||||||
\(275\) | 8.92307 | 0.538081 | ||||||||
\(276\) | 11.1138 | 0.668971 | ||||||||
\(277\) | 8.29721 | 0.498531 | 0.249266 | − | 0.968435i | \(-0.419811\pi\) | ||||
0.249266 | + | 0.968435i | \(0.419811\pi\) | |||||||
\(278\) | 1.17962 | 0.0707488 | ||||||||
\(279\) | 0.660050 | 0.0395162 | ||||||||
\(280\) | −4.26143 | −0.254669 | ||||||||
\(281\) | −25.1363 | −1.49951 | −0.749754 | − | 0.661717i | \(-0.769828\pi\) | ||||
−0.749754 | + | 0.661717i | \(0.769828\pi\) | |||||||
\(282\) | −2.82870 | −0.168447 | ||||||||
\(283\) | 32.6083 | 1.93836 | 0.969180 | − | 0.246353i | \(-0.0792323\pi\) | ||||
0.969180 | + | 0.246353i | \(0.0792323\pi\) | |||||||
\(284\) | 19.8766 | 1.17946 | ||||||||
\(285\) | 38.6604 | 2.29004 | ||||||||
\(286\) | −0.119865 | −0.00708777 | ||||||||
\(287\) | −9.84302 | −0.581015 | ||||||||
\(288\) | −0.845508 | −0.0498220 | ||||||||
\(289\) | −16.7283 | −0.984019 | ||||||||
\(290\) | −5.08078 | −0.298353 | ||||||||
\(291\) | −27.7813 | −1.62857 | ||||||||
\(292\) | 19.2783 | 1.12817 | ||||||||
\(293\) | −13.0820 | −0.764258 | −0.382129 | − | 0.924109i | \(-0.624809\pi\) | ||||
−0.382129 | + | 0.924109i | \(0.624809\pi\) | |||||||
\(294\) | −1.29560 | −0.0755608 | ||||||||
\(295\) | −56.4967 | −3.28936 | ||||||||
\(296\) | −5.16538 | −0.300231 | ||||||||
\(297\) | 4.76737 | 0.276631 | ||||||||
\(298\) | 1.84035 | 0.106609 | ||||||||
\(299\) | 2.15275 | 0.124496 | ||||||||
\(300\) | 32.5443 | 1.87894 | ||||||||
\(301\) | 9.19990 | 0.530274 | ||||||||
\(302\) | −2.88288 | −0.165891 | ||||||||
\(303\) | −2.34674 | −0.134817 | ||||||||
\(304\) | 21.4366 | 1.22947 | ||||||||
\(305\) | −36.4537 | −2.08733 | ||||||||
\(306\) | 0.0374409 | 0.00214035 | ||||||||
\(307\) | −27.6124 | −1.57592 | −0.787962 | − | 0.615724i | \(-0.788864\pi\) | ||||
−0.787962 | + | 0.615724i | \(0.788864\pi\) | |||||||
\(308\) | −3.34115 | −0.190380 | ||||||||
\(309\) | 33.0004 | 1.87733 | ||||||||
\(310\) | 0.987020 | 0.0560590 | ||||||||
\(311\) | −0.798921 | −0.0453027 | −0.0226513 | − | 0.999743i | \(-0.507211\pi\) | ||||
−0.0226513 | + | 0.999743i | \(0.507211\pi\) | |||||||
\(312\) | −0.880730 | −0.0498615 | ||||||||
\(313\) | 14.7962 | 0.836332 | 0.418166 | − | 0.908371i | \(-0.362673\pi\) | ||||
0.418166 | + | 0.908371i | \(0.362673\pi\) | |||||||
\(314\) | 2.07187 | 0.116922 | ||||||||
\(315\) | −2.67763 | −0.150867 | ||||||||
\(316\) | −21.2632 | −1.19615 | ||||||||
\(317\) | 21.2000 | 1.19071 | 0.595356 | − | 0.803462i | \(-0.297011\pi\) | ||||
0.595356 | + | 0.803462i | \(0.297011\pi\) | |||||||
\(318\) | 2.24593 | 0.125945 | ||||||||
\(319\) | −8.02530 | −0.449330 | ||||||||
\(320\) | 27.3037 | 1.52633 | ||||||||
\(321\) | −26.3359 | −1.46993 | ||||||||
\(322\) | −0.876327 | −0.0488358 | ||||||||
\(323\) | −2.91874 | −0.162403 | ||||||||
\(324\) | 19.8912 | 1.10507 | ||||||||
\(325\) | 6.30384 | 0.349674 | ||||||||
\(326\) | 1.21737 | 0.0674237 | ||||||||
\(327\) | 35.4299 | 1.95928 | ||||||||
\(328\) | −3.91282 | −0.216049 | ||||||||
\(329\) | −15.2729 | −0.842021 | ||||||||
\(330\) | −1.17137 | −0.0644821 | ||||||||
\(331\) | −23.1324 | −1.27147 | −0.635735 | − | 0.771907i | \(-0.719303\pi\) | ||||
−0.635735 | + | 0.771907i | \(0.719303\pi\) | |||||||
\(332\) | 12.2592 | 0.672809 | ||||||||
\(333\) | −3.24562 | −0.177859 | ||||||||
\(334\) | 0.671915 | 0.0367655 | ||||||||
\(335\) | −12.1283 | −0.662639 | ||||||||
\(336\) | −12.0053 | −0.654943 | ||||||||
\(337\) | −15.3775 | −0.837666 | −0.418833 | − | 0.908063i | \(-0.637561\pi\) | ||||
−0.418833 | + | 0.908063i | \(0.637561\pi\) | |||||||
\(338\) | 2.12101 | 0.115368 | ||||||||
\(339\) | 24.2332 | 1.31617 | ||||||||
\(340\) | −3.83376 | −0.207915 | ||||||||
\(341\) | 1.55904 | 0.0844267 | ||||||||
\(342\) | −0.402247 | −0.0217511 | ||||||||
\(343\) | −18.8601 | −1.01835 | ||||||||
\(344\) | 3.65717 | 0.197181 | ||||||||
\(345\) | 21.0376 | 1.13263 | ||||||||
\(346\) | −1.79287 | −0.0963853 | ||||||||
\(347\) | 23.5512 | 1.26430 | 0.632148 | − | 0.774848i | \(-0.282174\pi\) | ||||
0.632148 | + | 0.774848i | \(0.282174\pi\) | |||||||
\(348\) | −29.2699 | −1.56903 | ||||||||
\(349\) | −18.8954 | −1.01145 | −0.505723 | − | 0.862696i | \(-0.668774\pi\) | ||||
−0.505723 | + | 0.862696i | \(0.668774\pi\) | |||||||
\(350\) | −2.56613 | −0.137165 | ||||||||
\(351\) | 3.36798 | 0.179770 | ||||||||
\(352\) | −1.99709 | −0.106445 | ||||||||
\(353\) | 4.74491 | 0.252546 | 0.126273 | − | 0.991996i | \(-0.459698\pi\) | ||||
0.126273 | + | 0.991996i | \(0.459698\pi\) | |||||||
\(354\) | 4.75318 | 0.252628 | ||||||||
\(355\) | 37.6249 | 1.99692 | ||||||||
\(356\) | 4.75237 | 0.251875 | ||||||||
\(357\) | 1.63461 | 0.0865127 | ||||||||
\(358\) | 2.58357 | 0.136546 | ||||||||
\(359\) | −22.4361 | −1.18413 | −0.592067 | − | 0.805889i | \(-0.701688\pi\) | ||||
−0.592067 | + | 0.805889i | \(0.701688\pi\) | |||||||
\(360\) | −1.06442 | −0.0560997 | ||||||||
\(361\) | 12.3577 | 0.650403 | ||||||||
\(362\) | −0.209926 | −0.0110335 | ||||||||
\(363\) | −1.85024 | −0.0971122 | ||||||||
\(364\) | −2.36041 | −0.123719 | ||||||||
\(365\) | 36.4923 | 1.91010 | ||||||||
\(366\) | 3.06692 | 0.160310 | ||||||||
\(367\) | −22.9276 | −1.19681 | −0.598407 | − | 0.801193i | \(-0.704199\pi\) | ||||
−0.598407 | + | 0.801193i | \(0.704199\pi\) | |||||||
\(368\) | 11.6650 | 0.608081 | ||||||||
\(369\) | −2.45859 | −0.127989 | ||||||||
\(370\) | −4.85340 | −0.252316 | ||||||||
\(371\) | 12.1264 | 0.629569 | ||||||||
\(372\) | 5.68614 | 0.294812 | ||||||||
\(373\) | −25.0533 | −1.29721 | −0.648605 | − | 0.761125i | \(-0.724647\pi\) | ||||
−0.648605 | + | 0.761125i | \(0.724647\pi\) | |||||||
\(374\) | 0.0884353 | 0.00457288 | ||||||||
\(375\) | 27.0844 | 1.39863 | ||||||||
\(376\) | −6.07132 | −0.313104 | ||||||||
\(377\) | −5.66960 | −0.291999 | ||||||||
\(378\) | −1.37102 | −0.0705176 | ||||||||
\(379\) | −23.8218 | −1.22364 | −0.611822 | − | 0.790995i | \(-0.709563\pi\) | ||||
−0.611822 | + | 0.790995i | \(0.709563\pi\) | |||||||
\(380\) | 41.1882 | 2.11291 | ||||||||
\(381\) | 0.373992 | 0.0191602 | ||||||||
\(382\) | −1.07044 | −0.0547686 | ||||||||
\(383\) | −21.9958 | −1.12393 | −0.561966 | − | 0.827160i | \(-0.689955\pi\) | ||||
−0.561966 | + | 0.827160i | \(0.689955\pi\) | |||||||
\(384\) | −9.68729 | −0.494352 | ||||||||
\(385\) | −6.32456 | −0.322329 | ||||||||
\(386\) | −1.63974 | −0.0834608 | ||||||||
\(387\) | 2.29795 | 0.116811 | ||||||||
\(388\) | −29.5978 | −1.50260 | ||||||||
\(389\) | 8.51697 | 0.431827 | 0.215914 | − | 0.976412i | \(-0.430727\pi\) | ||||
0.215914 | + | 0.976412i | \(0.430727\pi\) | |||||||
\(390\) | −0.827536 | −0.0419039 | ||||||||
\(391\) | −1.58828 | −0.0803225 | ||||||||
\(392\) | −2.78078 | −0.140450 | ||||||||
\(393\) | −1.85024 | −0.0933320 | ||||||||
\(394\) | −0.475597 | −0.0239602 | ||||||||
\(395\) | −40.2496 | −2.02518 | ||||||||
\(396\) | −0.834552 | −0.0419378 | ||||||||
\(397\) | 15.0440 | 0.755036 | 0.377518 | − | 0.926002i | \(-0.376778\pi\) | ||||
0.377518 | + | 0.926002i | \(0.376778\pi\) | |||||||
\(398\) | −2.41565 | −0.121086 | ||||||||
\(399\) | −17.5615 | −0.879174 | ||||||||
\(400\) | 34.1584 | 1.70792 | ||||||||
\(401\) | −9.69600 | −0.484195 | −0.242098 | − | 0.970252i | \(-0.577835\pi\) | ||||
−0.242098 | + | 0.970252i | \(0.577835\pi\) | |||||||
\(402\) | 1.02038 | 0.0508917 | ||||||||
\(403\) | 1.10141 | 0.0548650 | ||||||||
\(404\) | −2.50018 | −0.124389 | ||||||||
\(405\) | 37.6527 | 1.87098 | ||||||||
\(406\) | 2.30794 | 0.114541 | ||||||||
\(407\) | −7.66615 | −0.379997 | ||||||||
\(408\) | 0.649794 | 0.0321696 | ||||||||
\(409\) | 18.2291 | 0.901372 | 0.450686 | − | 0.892683i | \(-0.351179\pi\) | ||||
0.450686 | + | 0.892683i | \(0.351179\pi\) | |||||||
\(410\) | −3.67650 | −0.181569 | ||||||||
\(411\) | 14.9031 | 0.735113 | ||||||||
\(412\) | 35.1582 | 1.73212 | ||||||||
\(413\) | 25.6636 | 1.26282 | ||||||||
\(414\) | −0.218889 | −0.0107578 | ||||||||
\(415\) | 23.2057 | 1.13912 | ||||||||
\(416\) | −1.41088 | −0.0691738 | ||||||||
\(417\) | 12.8637 | 0.629939 | ||||||||
\(418\) | −0.950109 | −0.0464713 | ||||||||
\(419\) | 22.1174 | 1.08050 | 0.540252 | − | 0.841503i | \(-0.318329\pi\) | ||||
0.540252 | + | 0.841503i | \(0.318329\pi\) | |||||||
\(420\) | −23.0670 | −1.12555 | ||||||||
\(421\) | 9.04911 | 0.441026 | 0.220513 | − | 0.975384i | \(-0.429227\pi\) | ||||
0.220513 | + | 0.975384i | \(0.429227\pi\) | |||||||
\(422\) | −3.25714 | −0.158555 | ||||||||
\(423\) | −3.81486 | −0.185485 | ||||||||
\(424\) | 4.82050 | 0.234104 | ||||||||
\(425\) | −4.65091 | −0.225602 | ||||||||
\(426\) | −3.16546 | −0.153367 | ||||||||
\(427\) | 16.5591 | 0.801351 | ||||||||
\(428\) | −28.0579 | −1.35623 | ||||||||
\(429\) | −1.30713 | −0.0631087 | ||||||||
\(430\) | 3.43629 | 0.165712 | ||||||||
\(431\) | −17.3177 | −0.834163 | −0.417082 | − | 0.908869i | \(-0.636947\pi\) | ||||
−0.417082 | + | 0.908869i | \(0.636947\pi\) | |||||||
\(432\) | 18.2500 | 0.878053 | ||||||||
\(433\) | 11.8615 | 0.570029 | 0.285014 | − | 0.958523i | \(-0.408002\pi\) | ||||
0.285014 | + | 0.958523i | \(0.408002\pi\) | |||||||
\(434\) | −0.448354 | −0.0215217 | ||||||||
\(435\) | −55.4058 | −2.65651 | ||||||||
\(436\) | 37.7465 | 1.80773 | ||||||||
\(437\) | 17.0637 | 0.816268 | ||||||||
\(438\) | −3.07017 | −0.146699 | ||||||||
\(439\) | −5.35065 | −0.255373 | −0.127686 | − | 0.991815i | \(-0.540755\pi\) | ||||
−0.127686 | + | 0.991815i | \(0.540755\pi\) | |||||||
\(440\) | −2.51416 | −0.119858 | ||||||||
\(441\) | −1.74728 | −0.0832036 | ||||||||
\(442\) | 0.0624765 | 0.00297170 | ||||||||
\(443\) | −19.0560 | −0.905380 | −0.452690 | − | 0.891668i | \(-0.649536\pi\) | ||||
−0.452690 | + | 0.891668i | \(0.649536\pi\) | |||||||
\(444\) | −27.9600 | −1.32692 | ||||||||
\(445\) | 8.99589 | 0.426446 | ||||||||
\(446\) | 3.02130 | 0.143063 | ||||||||
\(447\) | 20.0690 | 0.949231 | ||||||||
\(448\) | −12.4027 | −0.585974 | ||||||||
\(449\) | −31.5950 | −1.49106 | −0.745530 | − | 0.666472i | \(-0.767804\pi\) | ||||
−0.745530 | + | 0.666472i | \(0.767804\pi\) | |||||||
\(450\) | −0.640967 | −0.0302155 | ||||||||
\(451\) | −5.80718 | −0.273450 | ||||||||
\(452\) | 25.8177 | 1.21436 | ||||||||
\(453\) | −31.4378 | −1.47708 | ||||||||
\(454\) | −1.45478 | −0.0682761 | ||||||||
\(455\) | −4.46808 | −0.209467 | ||||||||
\(456\) | −6.98109 | −0.326920 | ||||||||
\(457\) | −4.73166 | −0.221338 | −0.110669 | − | 0.993857i | \(-0.535299\pi\) | ||||
−0.110669 | + | 0.993857i | \(0.535299\pi\) | |||||||
\(458\) | 3.98995 | 0.186438 | ||||||||
\(459\) | −2.48487 | −0.115984 | ||||||||
\(460\) | 22.4131 | 1.04502 | ||||||||
\(461\) | 18.2439 | 0.849704 | 0.424852 | − | 0.905263i | \(-0.360326\pi\) | ||||
0.424852 | + | 0.905263i | \(0.360326\pi\) | |||||||
\(462\) | 0.532098 | 0.0247554 | ||||||||
\(463\) | −7.03634 | −0.327006 | −0.163503 | − | 0.986543i | \(-0.552279\pi\) | ||||
−0.163503 | + | 0.986543i | \(0.552279\pi\) | |||||||
\(464\) | −30.7217 | −1.42622 | ||||||||
\(465\) | 10.7634 | 0.499143 | ||||||||
\(466\) | 0.726982 | 0.0336768 | ||||||||
\(467\) | −13.1043 | −0.606397 | −0.303198 | − | 0.952927i | \(-0.598054\pi\) | ||||
−0.303198 | + | 0.952927i | \(0.598054\pi\) | |||||||
\(468\) | −0.589582 | −0.0272535 | ||||||||
\(469\) | 5.50928 | 0.254395 | ||||||||
\(470\) | −5.70463 | −0.263135 | ||||||||
\(471\) | 22.5937 | 1.04106 | ||||||||
\(472\) | 10.2019 | 0.469579 | ||||||||
\(473\) | 5.42776 | 0.249569 | ||||||||
\(474\) | 3.38628 | 0.155537 | ||||||||
\(475\) | 49.9673 | 2.29266 | ||||||||
\(476\) | 1.74149 | 0.0798210 | ||||||||
\(477\) | 3.02892 | 0.138685 | ||||||||
\(478\) | 4.93155 | 0.225564 | ||||||||
\(479\) | 10.2936 | 0.470326 | 0.235163 | − | 0.971956i | \(-0.424438\pi\) | ||||
0.235163 | + | 0.971956i | \(0.424438\pi\) | |||||||
\(480\) | −13.7877 | −0.629320 | ||||||||
\(481\) | −5.41587 | −0.246942 | ||||||||
\(482\) | −3.60733 | −0.164309 | ||||||||
\(483\) | −9.55633 | −0.434828 | ||||||||
\(484\) | −1.97121 | −0.0896006 | ||||||||
\(485\) | −56.0265 | −2.54403 | ||||||||
\(486\) | −0.741174 | −0.0336203 | ||||||||
\(487\) | 25.3382 | 1.14818 | 0.574092 | − | 0.818791i | \(-0.305355\pi\) | ||||
0.574092 | + | 0.818791i | \(0.305355\pi\) | |||||||
\(488\) | 6.58261 | 0.297981 | ||||||||
\(489\) | 13.2754 | 0.600333 | ||||||||
\(490\) | −2.61283 | −0.118035 | ||||||||
\(491\) | 5.67127 | 0.255941 | 0.127970 | − | 0.991778i | \(-0.459154\pi\) | ||||
0.127970 | + | 0.991778i | \(0.459154\pi\) | |||||||
\(492\) | −21.1800 | −0.954868 | ||||||||
\(493\) | 4.18298 | 0.188392 | ||||||||
\(494\) | −0.671219 | −0.0301996 | ||||||||
\(495\) | −1.57975 | −0.0710043 | ||||||||
\(496\) | 5.96816 | 0.267978 | ||||||||
\(497\) | −17.0911 | −0.766642 | ||||||||
\(498\) | −1.95234 | −0.0874865 | ||||||||
\(499\) | −4.67814 | −0.209422 | −0.104711 | − | 0.994503i | \(-0.533392\pi\) | ||||
−0.104711 | + | 0.994503i | \(0.533392\pi\) | |||||||
\(500\) | 28.8554 | 1.29045 | ||||||||
\(501\) | 7.32722 | 0.327356 | ||||||||
\(502\) | −1.80082 | −0.0803745 | ||||||||
\(503\) | 2.94166 | 0.131162 | 0.0655810 | − | 0.997847i | \(-0.479110\pi\) | ||||
0.0655810 | + | 0.997847i | \(0.479110\pi\) | |||||||
\(504\) | 0.483512 | 0.0215373 | ||||||||
\(505\) | −4.73266 | −0.210601 | ||||||||
\(506\) | −0.517015 | −0.0229841 | ||||||||
\(507\) | 23.1296 | 1.02722 | ||||||||
\(508\) | 0.398445 | 0.0176781 | ||||||||
\(509\) | −3.58093 | −0.158722 | −0.0793611 | − | 0.996846i | \(-0.525288\pi\) | ||||
−0.0793611 | + | 0.996846i | \(0.525288\pi\) | |||||||
\(510\) | 0.610548 | 0.0270355 | ||||||||
\(511\) | −16.5767 | −0.733308 | ||||||||
\(512\) | −12.8037 | −0.565851 | ||||||||
\(513\) | 26.6963 | 1.17867 | ||||||||
\(514\) | −1.80168 | −0.0794686 | ||||||||
\(515\) | 66.5518 | 2.93262 | ||||||||
\(516\) | 19.7962 | 0.871477 | ||||||||
\(517\) | −9.01069 | −0.396290 | ||||||||
\(518\) | 2.20466 | 0.0968672 | ||||||||
\(519\) | −19.5512 | −0.858204 | ||||||||
\(520\) | −1.77616 | −0.0778900 | ||||||||
\(521\) | −16.0319 | −0.702372 | −0.351186 | − | 0.936306i | \(-0.614222\pi\) | ||||
−0.351186 | + | 0.936306i | \(0.614222\pi\) | |||||||
\(522\) | 0.576478 | 0.0252317 | ||||||||
\(523\) | −4.51329 | −0.197353 | −0.0986763 | − | 0.995120i | \(-0.531461\pi\) | ||||
−0.0986763 | + | 0.995120i | \(0.531461\pi\) | |||||||
\(524\) | −1.97121 | −0.0861128 | ||||||||
\(525\) | −27.9836 | −1.22130 | ||||||||
\(526\) | 2.95693 | 0.128928 | ||||||||
\(527\) | −0.812608 | −0.0353978 | ||||||||
\(528\) | −7.08289 | −0.308243 | ||||||||
\(529\) | −13.7145 | −0.596284 | ||||||||
\(530\) | 4.52936 | 0.196743 | ||||||||
\(531\) | 6.41026 | 0.278181 | ||||||||
\(532\) | −18.7098 | −0.811171 | ||||||||
\(533\) | −4.10257 | −0.177702 | ||||||||
\(534\) | −0.756842 | −0.0327517 | ||||||||
\(535\) | −53.1115 | −2.29621 | ||||||||
\(536\) | 2.19006 | 0.0945963 | ||||||||
\(537\) | 28.1739 | 1.21579 | ||||||||
\(538\) | 3.38373 | 0.145883 | ||||||||
\(539\) | −4.12707 | −0.177765 | ||||||||
\(540\) | 35.0655 | 1.50898 | ||||||||
\(541\) | 16.6375 | 0.715304 | 0.357652 | − | 0.933855i | \(-0.383577\pi\) | ||||
0.357652 | + | 0.933855i | \(0.383577\pi\) | |||||||
\(542\) | 1.00836 | 0.0433128 | ||||||||
\(543\) | −2.28924 | −0.0982409 | ||||||||
\(544\) | 1.04093 | 0.0446295 | ||||||||
\(545\) | 71.4514 | 3.06064 | ||||||||
\(546\) | 0.375909 | 0.0160874 | ||||||||
\(547\) | −19.7965 | −0.846436 | −0.423218 | − | 0.906028i | \(-0.639100\pi\) | ||||
−0.423218 | + | 0.906028i | \(0.639100\pi\) | |||||||
\(548\) | 15.8775 | 0.678253 | ||||||||
\(549\) | 4.13612 | 0.176526 | ||||||||
\(550\) | −1.51396 | −0.0645557 | ||||||||
\(551\) | −44.9400 | −1.91451 | ||||||||
\(552\) | −3.79886 | −0.161690 | ||||||||
\(553\) | 18.2834 | 0.777489 | ||||||||
\(554\) | −1.40778 | −0.0598107 | ||||||||
\(555\) | −52.9263 | −2.24660 | ||||||||
\(556\) | 13.7048 | 0.581214 | ||||||||
\(557\) | 16.9738 | 0.719201 | 0.359601 | − | 0.933106i | \(-0.382913\pi\) | ||||
0.359601 | + | 0.933106i | \(0.382913\pi\) | |||||||
\(558\) | −0.111990 | −0.00474091 | ||||||||
\(559\) | 3.83452 | 0.162183 | ||||||||
\(560\) | −24.2111 | −1.02310 | ||||||||
\(561\) | 0.964386 | 0.0407164 | ||||||||
\(562\) | 4.26485 | 0.179902 | ||||||||
\(563\) | 30.8525 | 1.30028 | 0.650138 | − | 0.759816i | \(-0.274711\pi\) | ||||
0.650138 | + | 0.759816i | \(0.274711\pi\) | |||||||
\(564\) | −32.8639 | −1.38382 | ||||||||
\(565\) | 48.8710 | 2.05602 | ||||||||
\(566\) | −5.53260 | −0.232553 | ||||||||
\(567\) | −17.1037 | −0.718290 | ||||||||
\(568\) | −6.79411 | −0.285075 | ||||||||
\(569\) | −40.8503 | −1.71253 | −0.856266 | − | 0.516535i | \(-0.827222\pi\) | ||||
−0.856266 | + | 0.516535i | \(0.827222\pi\) | |||||||
\(570\) | −6.55945 | −0.274745 | ||||||||
\(571\) | 21.3968 | 0.895429 | 0.447714 | − | 0.894177i | \(-0.352238\pi\) | ||||
0.447714 | + | 0.894177i | \(0.352238\pi\) | |||||||
\(572\) | −1.39259 | −0.0582273 | ||||||||
\(573\) | −11.6732 | −0.487653 | ||||||||
\(574\) | 1.67005 | 0.0697066 | ||||||||
\(575\) | 27.1904 | 1.13392 | ||||||||
\(576\) | −3.09795 | −0.129081 | ||||||||
\(577\) | −39.5247 | −1.64544 | −0.822718 | − | 0.568449i | \(-0.807543\pi\) | ||||
−0.822718 | + | 0.568449i | \(0.807543\pi\) | |||||||
\(578\) | 2.83827 | 0.118057 | ||||||||
\(579\) | −17.8814 | −0.743125 | ||||||||
\(580\) | −59.0285 | −2.45103 | ||||||||
\(581\) | −10.5412 | −0.437323 | ||||||||
\(582\) | 4.71362 | 0.195386 | ||||||||
\(583\) | 7.15431 | 0.296301 | ||||||||
\(584\) | −6.58960 | −0.272680 | ||||||||
\(585\) | −1.11604 | −0.0461424 | ||||||||
\(586\) | 2.21960 | 0.0916910 | ||||||||
\(587\) | −43.1312 | −1.78021 | −0.890107 | − | 0.455751i | \(-0.849371\pi\) | ||||
−0.890107 | + | 0.455751i | \(0.849371\pi\) | |||||||
\(588\) | −15.0523 | −0.620745 | ||||||||
\(589\) | 8.73029 | 0.359725 | ||||||||
\(590\) | 9.58571 | 0.394638 | ||||||||
\(591\) | −5.18638 | −0.213339 | ||||||||
\(592\) | −29.3468 | −1.20615 | ||||||||
\(593\) | 31.6926 | 1.30146 | 0.650729 | − | 0.759310i | \(-0.274463\pi\) | ||||
0.650729 | + | 0.759310i | \(0.274463\pi\) | |||||||
\(594\) | −0.808873 | −0.0331885 | ||||||||
\(595\) | 3.29651 | 0.135144 | ||||||||
\(596\) | 21.3812 | 0.875809 | ||||||||
\(597\) | −26.3427 | −1.07813 | ||||||||
\(598\) | −0.365253 | −0.0149363 | ||||||||
\(599\) | −7.66688 | −0.313260 | −0.156630 | − | 0.987657i | \(-0.550063\pi\) | ||||
−0.156630 | + | 0.987657i | \(0.550063\pi\) | |||||||
\(600\) | −11.1241 | −0.454140 | ||||||||
\(601\) | −44.1467 | −1.80078 | −0.900390 | − | 0.435084i | \(-0.856719\pi\) | ||||
−0.900390 | + | 0.435084i | \(0.856719\pi\) | |||||||
\(602\) | −1.56093 | −0.0636190 | ||||||||
\(603\) | 1.37611 | 0.0560393 | ||||||||
\(604\) | −33.4933 | −1.36283 | ||||||||
\(605\) | −3.73136 | −0.151701 | ||||||||
\(606\) | 0.398168 | 0.0161745 | ||||||||
\(607\) | 45.0640 | 1.82909 | 0.914546 | − | 0.404481i | \(-0.132548\pi\) | ||||
0.914546 | + | 0.404481i | \(0.132548\pi\) | |||||||
\(608\) | −11.1833 | −0.453542 | ||||||||
\(609\) | 25.1681 | 1.01986 | ||||||||
\(610\) | 6.18504 | 0.250425 | ||||||||
\(611\) | −6.36574 | −0.257530 | ||||||||
\(612\) | 0.434988 | 0.0175834 | ||||||||
\(613\) | −18.1499 | −0.733068 | −0.366534 | − | 0.930405i | \(-0.619456\pi\) | ||||
−0.366534 | + | 0.930405i | \(0.619456\pi\) | |||||||
\(614\) | 4.68496 | 0.189070 | ||||||||
\(615\) | −40.0922 | −1.61667 | ||||||||
\(616\) | 1.14206 | 0.0460148 | ||||||||
\(617\) | −18.6177 | −0.749522 | −0.374761 | − | 0.927121i | \(-0.622275\pi\) | ||||
−0.374761 | + | 0.927121i | \(0.622275\pi\) | |||||||
\(618\) | −5.59914 | −0.225230 | ||||||||
\(619\) | 7.95905 | 0.319901 | 0.159951 | − | 0.987125i | \(-0.448866\pi\) | ||||
0.159951 | + | 0.987125i | \(0.448866\pi\) | |||||||
\(620\) | 11.4672 | 0.460534 | ||||||||
\(621\) | 14.5272 | 0.582955 | ||||||||
\(622\) | 0.135552 | 0.00543513 | ||||||||
\(623\) | −4.08639 | −0.163718 | ||||||||
\(624\) | −5.00382 | −0.200313 | ||||||||
\(625\) | 10.0058 | 0.400231 | ||||||||
\(626\) | −2.51046 | −0.100338 | ||||||||
\(627\) | −10.3609 | −0.413776 | ||||||||
\(628\) | 24.0710 | 0.960536 | ||||||||
\(629\) | 3.99578 | 0.159322 | ||||||||
\(630\) | 0.454309 | 0.0181001 | ||||||||
\(631\) | 6.83700 | 0.272177 | 0.136088 | − | 0.990697i | \(-0.456547\pi\) | ||||
0.136088 | + | 0.990697i | \(0.456547\pi\) | |||||||
\(632\) | 7.26807 | 0.289108 | ||||||||
\(633\) | −35.5191 | −1.41176 | ||||||||
\(634\) | −3.59698 | −0.142854 | ||||||||
\(635\) | 0.754228 | 0.0299306 | ||||||||
\(636\) | 26.0932 | 1.03466 | ||||||||
\(637\) | −2.91563 | −0.115521 | ||||||||
\(638\) | 1.36164 | 0.0539079 | ||||||||
\(639\) | −4.26902 | −0.168880 | ||||||||
\(640\) | −19.5363 | −0.772241 | ||||||||
\(641\) | 3.02283 | 0.119394 | 0.0596972 | − | 0.998217i | \(-0.480986\pi\) | ||||
0.0596972 | + | 0.998217i | \(0.480986\pi\) | |||||||
\(642\) | 4.46838 | 0.176353 | ||||||||
\(643\) | −9.62454 | −0.379555 | −0.189777 | − | 0.981827i | \(-0.560777\pi\) | ||||
−0.189777 | + | 0.981827i | \(0.560777\pi\) | |||||||
\(644\) | −10.1812 | −0.401194 | ||||||||
\(645\) | 37.4727 | 1.47549 | ||||||||
\(646\) | 0.495219 | 0.0194841 | ||||||||
\(647\) | −21.1105 | −0.829939 | −0.414970 | − | 0.909835i | \(-0.636208\pi\) | ||||
−0.414970 | + | 0.909835i | \(0.636208\pi\) | |||||||
\(648\) | −6.79913 | −0.267095 | ||||||||
\(649\) | 15.1410 | 0.594337 | ||||||||
\(650\) | −1.06956 | −0.0419517 | ||||||||
\(651\) | −4.88930 | −0.191627 | ||||||||
\(652\) | 14.1434 | 0.553898 | ||||||||
\(653\) | −9.03588 | −0.353601 | −0.176801 | − | 0.984247i | \(-0.556575\pi\) | ||||
−0.176801 | + | 0.984247i | \(0.556575\pi\) | |||||||
\(654\) | −6.01135 | −0.235062 | ||||||||
\(655\) | −3.73136 | −0.145796 | ||||||||
\(656\) | −22.2305 | −0.867955 | ||||||||
\(657\) | −4.14051 | −0.161537 | ||||||||
\(658\) | 2.59133 | 0.101021 | ||||||||
\(659\) | −46.2534 | −1.80178 | −0.900888 | − | 0.434052i | \(-0.857083\pi\) | ||||
−0.900888 | + | 0.434052i | \(0.857083\pi\) | |||||||
\(660\) | −13.6090 | −0.529732 | ||||||||
\(661\) | −10.3055 | −0.400838 | −0.200419 | − | 0.979710i | \(-0.564230\pi\) | ||||
−0.200419 | + | 0.979710i | \(0.564230\pi\) | |||||||
\(662\) | 3.92484 | 0.152543 | ||||||||
\(663\) | 0.681306 | 0.0264597 | ||||||||
\(664\) | −4.19037 | −0.162618 | ||||||||
\(665\) | −35.4162 | −1.37338 | ||||||||
\(666\) | 0.550679 | 0.0213384 | ||||||||
\(667\) | −24.4547 | −0.946891 | ||||||||
\(668\) | 7.80631 | 0.302035 | ||||||||
\(669\) | 32.9473 | 1.27382 | ||||||||
\(670\) | 2.05779 | 0.0794993 | ||||||||
\(671\) | 9.76953 | 0.377149 | ||||||||
\(672\) | 6.26307 | 0.241603 | ||||||||
\(673\) | 3.83786 | 0.147939 | 0.0739693 | − | 0.997261i | \(-0.476433\pi\) | ||||
0.0739693 | + | 0.997261i | \(0.476433\pi\) | |||||||
\(674\) | 2.60908 | 0.100498 | ||||||||
\(675\) | 42.5396 | 1.63735 | ||||||||
\(676\) | 24.6419 | 0.947767 | ||||||||
\(677\) | 20.9587 | 0.805507 | 0.402753 | − | 0.915309i | \(-0.368053\pi\) | ||||
0.402753 | + | 0.915309i | \(0.368053\pi\) | |||||||
\(678\) | −4.11161 | −0.157906 | ||||||||
\(679\) | 25.4501 | 0.976683 | ||||||||
\(680\) | 1.31044 | 0.0502530 | ||||||||
\(681\) | −15.8644 | −0.607923 | ||||||||
\(682\) | −0.264520 | −0.0101290 | ||||||||
\(683\) | −6.73646 | −0.257763 | −0.128882 | − | 0.991660i | \(-0.541139\pi\) | ||||
−0.128882 | + | 0.991660i | \(0.541139\pi\) | |||||||
\(684\) | −4.67332 | −0.178689 | ||||||||
\(685\) | 30.0549 | 1.14834 | ||||||||
\(686\) | 3.19996 | 0.122175 | ||||||||
\(687\) | 43.5104 | 1.66003 | ||||||||
\(688\) | 20.7780 | 0.792155 | ||||||||
\(689\) | 5.05427 | 0.192552 | ||||||||
\(690\) | −3.56942 | −0.135885 | ||||||||
\(691\) | 5.38833 | 0.204982 | 0.102491 | − | 0.994734i | \(-0.467319\pi\) | ||||
0.102491 | + | 0.994734i | \(0.467319\pi\) | |||||||
\(692\) | −20.8296 | −0.791822 | ||||||||
\(693\) | 0.717601 | 0.0272594 | ||||||||
\(694\) | −3.99590 | −0.151682 | ||||||||
\(695\) | 25.9422 | 0.984045 | ||||||||
\(696\) | 10.0049 | 0.379235 | ||||||||
\(697\) | 3.02684 | 0.114650 | ||||||||
\(698\) | 3.20595 | 0.121347 | ||||||||
\(699\) | 7.92774 | 0.299855 | ||||||||
\(700\) | −29.8133 | −1.12684 | ||||||||
\(701\) | −7.23905 | −0.273415 | −0.136708 | − | 0.990611i | \(-0.543652\pi\) | ||||
−0.136708 | + | 0.990611i | \(0.543652\pi\) | |||||||
\(702\) | −0.571441 | −0.0215677 | ||||||||
\(703\) | −42.9288 | −1.61909 | ||||||||
\(704\) | −7.31736 | −0.275784 | ||||||||
\(705\) | −62.2089 | −2.34292 | ||||||||
\(706\) | −0.805062 | −0.0302989 | ||||||||
\(707\) | 2.14981 | 0.0808521 | ||||||||
\(708\) | 55.2225 | 2.07539 | ||||||||
\(709\) | −19.5149 | −0.732898 | −0.366449 | − | 0.930438i | \(-0.619427\pi\) | ||||
−0.366449 | + | 0.930438i | \(0.619427\pi\) | |||||||
\(710\) | −6.38377 | −0.239579 | ||||||||
\(711\) | 4.56682 | 0.171269 | ||||||||
\(712\) | −1.62443 | −0.0608781 | ||||||||
\(713\) | 4.75071 | 0.177915 | ||||||||
\(714\) | −0.277342 | −0.0103793 | ||||||||
\(715\) | −2.63608 | −0.0985838 | ||||||||
\(716\) | 30.0160 | 1.12175 | ||||||||
\(717\) | 53.7785 | 2.00839 | ||||||||
\(718\) | 3.80671 | 0.142065 | ||||||||
\(719\) | −17.1330 | −0.638952 | −0.319476 | − | 0.947594i | \(-0.603507\pi\) | ||||
−0.319476 | + | 0.947594i | \(0.603507\pi\) | |||||||
\(720\) | −6.04743 | −0.225375 | ||||||||
\(721\) | −30.2312 | −1.12587 | ||||||||
\(722\) | −2.09671 | −0.0780313 | ||||||||
\(723\) | −39.3379 | −1.46299 | ||||||||
\(724\) | −2.43893 | −0.0906420 | ||||||||
\(725\) | −71.6102 | −2.65954 | ||||||||
\(726\) | 0.313927 | 0.0116509 | ||||||||
\(727\) | 21.8597 | 0.810732 | 0.405366 | − | 0.914155i | \(-0.367144\pi\) | ||||
0.405366 | + | 0.914155i | \(0.367144\pi\) | |||||||
\(728\) | 0.806823 | 0.0299029 | ||||||||
\(729\) | 22.1901 | 0.821856 | ||||||||
\(730\) | −6.19161 | −0.229162 | ||||||||
\(731\) | −2.82908 | −0.104637 | ||||||||
\(732\) | 35.6315 | 1.31698 | ||||||||
\(733\) | 23.2014 | 0.856965 | 0.428482 | − | 0.903550i | \(-0.359048\pi\) | ||||
0.428482 | + | 0.903550i | \(0.359048\pi\) | |||||||
\(734\) | 3.89010 | 0.143586 | ||||||||
\(735\) | −28.4928 | −1.05097 | ||||||||
\(736\) | −6.08554 | −0.224316 | ||||||||
\(737\) | 3.25036 | 0.119729 | ||||||||
\(738\) | 0.417145 | 0.0153553 | ||||||||
\(739\) | 5.25297 | 0.193234 | 0.0966168 | − | 0.995322i | \(-0.469198\pi\) | ||||
0.0966168 | + | 0.995322i | \(0.469198\pi\) | |||||||
\(740\) | −56.3869 | −2.07282 | ||||||||
\(741\) | −7.31964 | −0.268894 | ||||||||
\(742\) | −2.05746 | −0.0755318 | ||||||||
\(743\) | −18.3377 | −0.672744 | −0.336372 | − | 0.941729i | \(-0.609200\pi\) | ||||
−0.336372 | + | 0.941729i | \(0.609200\pi\) | |||||||
\(744\) | −1.94361 | −0.0712561 | ||||||||
\(745\) | 40.4731 | 1.48282 | ||||||||
\(746\) | 4.25076 | 0.155631 | ||||||||
\(747\) | −2.63298 | −0.0963357 | ||||||||
\(748\) | 1.02744 | 0.0375670 | ||||||||
\(749\) | 24.1259 | 0.881543 | ||||||||
\(750\) | −4.59538 | −0.167800 | ||||||||
\(751\) | 33.0227 | 1.20502 | 0.602508 | − | 0.798113i | \(-0.294168\pi\) | ||||
0.602508 | + | 0.798113i | \(0.294168\pi\) | |||||||
\(752\) | −34.4939 | −1.25786 | ||||||||
\(753\) | −19.6379 | −0.715646 | ||||||||
\(754\) | 0.961953 | 0.0350322 | ||||||||
\(755\) | −63.4005 | −2.30738 | ||||||||
\(756\) | −15.9285 | −0.579314 | ||||||||
\(757\) | −30.7380 | −1.11719 | −0.558597 | − | 0.829439i | \(-0.688660\pi\) | ||||
−0.558597 | + | 0.829439i | \(0.688660\pi\) | |||||||
\(758\) | 4.04182 | 0.146805 | ||||||||
\(759\) | −5.63805 | −0.204648 | ||||||||
\(760\) | −14.0787 | −0.510690 | ||||||||
\(761\) | 41.6276 | 1.50900 | 0.754499 | − | 0.656301i | \(-0.227880\pi\) | ||||
0.754499 | + | 0.656301i | \(0.227880\pi\) | |||||||
\(762\) | −0.0634547 | −0.00229872 | ||||||||
\(763\) | −32.4568 | −1.17502 | ||||||||
\(764\) | −12.4364 | −0.449933 | ||||||||
\(765\) | 0.823401 | 0.0297701 | ||||||||
\(766\) | 3.73200 | 0.134842 | ||||||||
\(767\) | 10.6966 | 0.386232 | ||||||||
\(768\) | −25.4341 | −0.917773 | ||||||||
\(769\) | 22.3836 | 0.807173 | 0.403587 | − | 0.914941i | \(-0.367763\pi\) | ||||
0.403587 | + | 0.914941i | \(0.367763\pi\) | |||||||
\(770\) | 1.07308 | 0.0386711 | ||||||||
\(771\) | −19.6473 | −0.707580 | ||||||||
\(772\) | −19.0506 | −0.685645 | ||||||||
\(773\) | 43.0000 | 1.54660 | 0.773302 | − | 0.634038i | \(-0.218604\pi\) | ||||
0.773302 | + | 0.634038i | \(0.218604\pi\) | |||||||
\(774\) | −0.389890 | −0.0140143 | ||||||||
\(775\) | 13.9114 | 0.499712 | ||||||||
\(776\) | 10.1170 | 0.363178 | ||||||||
\(777\) | 24.0418 | 0.862495 | ||||||||
\(778\) | −1.44506 | −0.0518080 | ||||||||
\(779\) | −32.5190 | −1.16511 | ||||||||
\(780\) | −9.61433 | −0.344248 | ||||||||
\(781\) | −10.0834 | −0.360813 | ||||||||
\(782\) | 0.269481 | 0.00963660 | ||||||||
\(783\) | −38.2596 | −1.36729 | ||||||||
\(784\) | −15.7988 | −0.564244 | ||||||||
\(785\) | 45.5646 | 1.62627 | ||||||||
\(786\) | 0.313927 | 0.0111974 | ||||||||
\(787\) | −46.4223 | −1.65478 | −0.827388 | − | 0.561631i | \(-0.810174\pi\) | ||||
−0.827388 | + | 0.561631i | \(0.810174\pi\) | |||||||
\(788\) | −5.52549 | −0.196837 | ||||||||
\(789\) | 32.2453 | 1.14796 | ||||||||
\(790\) | 6.82910 | 0.242968 | ||||||||
\(791\) | −22.1997 | −0.789329 | ||||||||
\(792\) | 0.285262 | 0.0101364 | ||||||||
\(793\) | 6.90184 | 0.245091 | ||||||||
\(794\) | −2.55249 | −0.0905846 | ||||||||
\(795\) | 49.3926 | 1.75178 | ||||||||
\(796\) | −28.0651 | −0.994742 | ||||||||
\(797\) | 19.6731 | 0.696857 | 0.348428 | − | 0.937335i | \(-0.386715\pi\) | ||||
0.348428 | + | 0.937335i | \(0.386715\pi\) | |||||||
\(798\) | 2.97963 | 0.105478 | ||||||||
\(799\) | 4.69659 | 0.166153 | ||||||||
\(800\) | −17.8202 | −0.630038 | ||||||||
\(801\) | −1.02070 | −0.0360645 | ||||||||
\(802\) | 1.64511 | 0.0580908 | ||||||||
\(803\) | −9.77990 | −0.345125 | ||||||||
\(804\) | 11.8547 | 0.418084 | ||||||||
\(805\) | −19.2722 | −0.679257 | ||||||||
\(806\) | −0.186874 | −0.00658236 | ||||||||
\(807\) | 36.8996 | 1.29893 | ||||||||
\(808\) | 0.854600 | 0.0300647 | ||||||||
\(809\) | −15.6349 | −0.549694 | −0.274847 | − | 0.961488i | \(-0.588627\pi\) | ||||
−0.274847 | + | 0.961488i | \(0.588627\pi\) | |||||||
\(810\) | −6.38848 | −0.224468 | ||||||||
\(811\) | 23.4806 | 0.824516 | 0.412258 | − | 0.911067i | \(-0.364740\pi\) | ||||
0.412258 | + | 0.911067i | \(0.364740\pi\) | |||||||
\(812\) | 26.8137 | 0.940978 | ||||||||
\(813\) | 10.9962 | 0.385653 | ||||||||
\(814\) | 1.30071 | 0.0455897 | ||||||||
\(815\) | 26.7724 | 0.937796 | ||||||||
\(816\) | 3.69177 | 0.129238 | ||||||||
\(817\) | 30.3943 | 1.06336 | ||||||||
\(818\) | −3.09291 | −0.108141 | ||||||||
\(819\) | 0.506960 | 0.0177146 | ||||||||
\(820\) | −42.7136 | −1.49162 | ||||||||
\(821\) | −19.3735 | −0.676139 | −0.338070 | − | 0.941121i | \(-0.609774\pi\) | ||||
−0.338070 | + | 0.941121i | \(0.609774\pi\) | |||||||
\(822\) | −2.52858 | −0.0881944 | ||||||||
\(823\) | 41.2602 | 1.43824 | 0.719120 | − | 0.694886i | \(-0.244545\pi\) | ||||
0.719120 | + | 0.694886i | \(0.244545\pi\) | |||||||
\(824\) | −12.0176 | −0.418653 | ||||||||
\(825\) | −16.5098 | −0.574796 | ||||||||
\(826\) | −4.35431 | −0.151506 | ||||||||
\(827\) | −31.5500 | −1.09710 | −0.548551 | − | 0.836117i | \(-0.684820\pi\) | ||||
−0.548551 | + | 0.836117i | \(0.684820\pi\) | |||||||
\(828\) | −2.54305 | −0.0883771 | ||||||||
\(829\) | 42.0294 | 1.45974 | 0.729870 | − | 0.683586i | \(-0.239581\pi\) | ||||
0.729870 | + | 0.683586i | \(0.239581\pi\) | |||||||
\(830\) | −3.93728 | −0.136665 | ||||||||
\(831\) | −15.3518 | −0.532548 | ||||||||
\(832\) | −5.16947 | −0.179219 | ||||||||
\(833\) | 2.15113 | 0.0745321 | ||||||||
\(834\) | −2.18257 | −0.0755762 | ||||||||
\(835\) | 14.7768 | 0.511372 | ||||||||
\(836\) | −11.0384 | −0.381770 | ||||||||
\(837\) | 7.43252 | 0.256905 | ||||||||
\(838\) | −3.75262 | −0.129632 | ||||||||
\(839\) | −1.20123 | −0.0414711 | −0.0207355 | − | 0.999785i | \(-0.506601\pi\) | ||||
−0.0207355 | + | 0.999785i | \(0.506601\pi\) | |||||||
\(840\) | 7.88464 | 0.272046 | ||||||||
\(841\) | 35.4054 | 1.22088 | ||||||||
\(842\) | −1.53535 | −0.0529116 | ||||||||
\(843\) | 46.5081 | 1.60182 | ||||||||
\(844\) | −37.8415 | −1.30256 | ||||||||
\(845\) | 46.6454 | 1.60465 | ||||||||
\(846\) | 0.647261 | 0.0222533 | ||||||||
\(847\) | 1.69497 | 0.0582400 | ||||||||
\(848\) | 27.3874 | 0.940488 | ||||||||
\(849\) | −60.3330 | −2.07062 | ||||||||
\(850\) | 0.789114 | 0.0270664 | ||||||||
\(851\) | −23.3603 | −0.800782 | ||||||||
\(852\) | −36.7763 | −1.25994 | ||||||||
\(853\) | 9.60648 | 0.328920 | 0.164460 | − | 0.986384i | \(-0.447412\pi\) | ||||
0.164460 | + | 0.986384i | \(0.447412\pi\) | |||||||
\(854\) | −2.80956 | −0.0961411 | ||||||||
\(855\) | −8.84625 | −0.302535 | ||||||||
\(856\) | 9.59061 | 0.327800 | ||||||||
\(857\) | 45.1086 | 1.54088 | 0.770441 | − | 0.637511i | \(-0.220036\pi\) | ||||
0.770441 | + | 0.637511i | \(0.220036\pi\) | |||||||
\(858\) | 0.221779 | 0.00757139 | ||||||||
\(859\) | 54.0072 | 1.84270 | 0.921350 | − | 0.388733i | \(-0.127087\pi\) | ||||
0.921350 | + | 0.388733i | \(0.127087\pi\) | |||||||
\(860\) | 39.9228 | 1.36136 | ||||||||
\(861\) | 18.2119 | 0.620660 | ||||||||
\(862\) | 2.93827 | 0.100078 | ||||||||
\(863\) | 33.0125 | 1.12376 | 0.561879 | − | 0.827220i | \(-0.310079\pi\) | ||||
0.561879 | + | 0.827220i | \(0.310079\pi\) | |||||||
\(864\) | −9.52087 | −0.323907 | ||||||||
\(865\) | −39.4289 | −1.34062 | ||||||||
\(866\) | −2.01253 | −0.0683886 | ||||||||
\(867\) | 30.9513 | 1.05116 | ||||||||
\(868\) | −5.20899 | −0.176804 | ||||||||
\(869\) | 10.7868 | 0.365919 | ||||||||
\(870\) | 9.40063 | 0.318711 | ||||||||
\(871\) | 2.29627 | 0.0778061 | ||||||||
\(872\) | −12.9023 | −0.436928 | ||||||||
\(873\) | 6.35691 | 0.215149 | ||||||||
\(874\) | −2.89518 | −0.0979308 | ||||||||
\(875\) | −24.8117 | −0.838787 | ||||||||
\(876\) | −35.6693 | −1.20515 | ||||||||
\(877\) | −33.3170 | −1.12504 | −0.562518 | − | 0.826785i | \(-0.690167\pi\) | ||||
−0.562518 | + | 0.826785i | \(0.690167\pi\) | |||||||
\(878\) | 0.907838 | 0.0306380 | ||||||||
\(879\) | 24.2048 | 0.816406 | ||||||||
\(880\) | −14.2840 | −0.481515 | ||||||||
\(881\) | −50.5974 | −1.70467 | −0.852334 | − | 0.522998i | \(-0.824814\pi\) | ||||
−0.852334 | + | 0.522998i | \(0.824814\pi\) | |||||||
\(882\) | 0.296458 | 0.00998226 | ||||||||
\(883\) | −0.190888 | −0.00642388 | −0.00321194 | − | 0.999995i | \(-0.501022\pi\) | ||||
−0.00321194 | + | 0.999995i | \(0.501022\pi\) | |||||||
\(884\) | 0.725853 | 0.0244131 | ||||||||
\(885\) | 104.532 | 3.51381 | ||||||||
\(886\) | 3.23321 | 0.108622 | ||||||||
\(887\) | 24.0851 | 0.808697 | 0.404349 | − | 0.914605i | \(-0.367498\pi\) | ||||
0.404349 | + | 0.914605i | \(0.367498\pi\) | |||||||
\(888\) | 9.55716 | 0.320717 | ||||||||
\(889\) | −0.342608 | −0.0114907 | ||||||||
\(890\) | −1.52632 | −0.0511624 | ||||||||
\(891\) | −10.0909 | −0.338057 | ||||||||
\(892\) | 35.1015 | 1.17529 | ||||||||
\(893\) | −50.4580 | −1.68851 | ||||||||
\(894\) | −3.40508 | −0.113883 | ||||||||
\(895\) | 56.8181 | 1.89922 | ||||||||
\(896\) | 8.87438 | 0.296472 | ||||||||
\(897\) | −3.98308 | −0.132991 | ||||||||
\(898\) | 5.36068 | 0.178888 | ||||||||
\(899\) | −12.5117 | −0.417290 | ||||||||
\(900\) | −7.44676 | −0.248225 | ||||||||
\(901\) | −3.72899 | −0.124231 | ||||||||
\(902\) | 0.985297 | 0.0328068 | ||||||||
\(903\) | −17.0220 | −0.566456 | ||||||||
\(904\) | −8.82487 | −0.293511 | ||||||||
\(905\) | −4.61671 | −0.153465 | ||||||||
\(906\) | 5.33401 | 0.177211 | ||||||||
\(907\) | −0.0488386 | −0.00162166 | −0.000810830 | − | 1.00000i | \(-0.500258\pi\) | ||||
−0.000810830 | 1.00000i | \(0.500258\pi\) | ||||||||
\(908\) | −16.9016 | −0.560901 | ||||||||
\(909\) | 0.536980 | 0.0178105 | ||||||||
\(910\) | 0.758094 | 0.0251306 | ||||||||
\(911\) | −39.1384 | −1.29671 | −0.648356 | − | 0.761337i | \(-0.724543\pi\) | ||||
−0.648356 | + | 0.761337i | \(0.724543\pi\) | |||||||
\(912\) | −39.6627 | −1.31336 | ||||||||
\(913\) | −6.21910 | −0.205822 | ||||||||
\(914\) | 0.802814 | 0.0265547 | ||||||||
\(915\) | 67.4478 | 2.22976 | ||||||||
\(916\) | 46.3553 | 1.53162 | ||||||||
\(917\) | 1.69497 | 0.0559729 | ||||||||
\(918\) | 0.421604 | 0.0139150 | ||||||||
\(919\) | −29.7830 | −0.982451 | −0.491225 | − | 0.871033i | \(-0.663451\pi\) | ||||
−0.491225 | + | 0.871033i | \(0.663451\pi\) | |||||||
\(920\) | −7.66115 | −0.252581 | ||||||||
\(921\) | 51.0895 | 1.68345 | ||||||||
\(922\) | −3.09542 | −0.101942 | ||||||||
\(923\) | −7.12359 | −0.234476 | ||||||||
\(924\) | 6.18192 | 0.203370 | ||||||||
\(925\) | −68.4056 | −2.24916 | ||||||||
\(926\) | 1.19385 | 0.0392322 | ||||||||
\(927\) | −7.55114 | −0.248012 | ||||||||
\(928\) | 16.0272 | 0.526120 | ||||||||
\(929\) | 7.57004 | 0.248365 | 0.124183 | − | 0.992259i | \(-0.460369\pi\) | ||||
0.124183 | + | 0.992259i | \(0.460369\pi\) | |||||||
\(930\) | −1.82622 | −0.0598841 | ||||||||
\(931\) | −23.1107 | −0.757423 | ||||||||
\(932\) | 8.44609 | 0.276661 | ||||||||
\(933\) | 1.47819 | 0.0483938 | ||||||||
\(934\) | 2.22340 | 0.0727517 | ||||||||
\(935\) | 1.94487 | 0.0636042 | ||||||||
\(936\) | 0.201528 | 0.00658715 | ||||||||
\(937\) | 54.2383 | 1.77189 | 0.885944 | − | 0.463793i | \(-0.153512\pi\) | ||||
0.885944 | + | 0.463793i | \(0.153512\pi\) | |||||||
\(938\) | −0.934751 | −0.0305207 | ||||||||
\(939\) | −27.3765 | −0.893399 | ||||||||
\(940\) | −66.2764 | −2.16170 | ||||||||
\(941\) | −18.7474 | −0.611146 | −0.305573 | − | 0.952169i | \(-0.598848\pi\) | ||||
−0.305573 | + | 0.952169i | \(0.598848\pi\) | |||||||
\(942\) | −3.83344 | −0.124900 | ||||||||
\(943\) | −17.6957 | −0.576250 | ||||||||
\(944\) | 57.9614 | 1.88648 | ||||||||
\(945\) | −30.1515 | −0.980829 | ||||||||
\(946\) | −0.920920 | −0.0299417 | ||||||||
\(947\) | −5.67738 | −0.184490 | −0.0922451 | − | 0.995736i | \(-0.529404\pi\) | ||||
−0.0922451 | + | 0.995736i | \(0.529404\pi\) | |||||||
\(948\) | 39.3418 | 1.27776 | ||||||||
\(949\) | −6.90916 | −0.224281 | ||||||||
\(950\) | −8.47788 | −0.275059 | ||||||||
\(951\) | −39.2251 | −1.27196 | ||||||||
\(952\) | −0.595267 | −0.0192927 | ||||||||
\(953\) | −4.83583 | −0.156648 | −0.0783240 | − | 0.996928i | \(-0.524957\pi\) | ||||
−0.0783240 | + | 0.996928i | \(0.524957\pi\) | |||||||
\(954\) | −0.513912 | −0.0166385 | ||||||||
\(955\) | −23.5412 | −0.761776 | ||||||||
\(956\) | 57.2948 | 1.85305 | ||||||||
\(957\) | 14.8487 | 0.479990 | ||||||||
\(958\) | −1.74650 | −0.0564268 | ||||||||
\(959\) | −13.6525 | −0.440861 | ||||||||
\(960\) | −50.5183 | −1.63047 | ||||||||
\(961\) | −28.5694 | −0.921594 | ||||||||
\(962\) | 0.918903 | 0.0296266 | ||||||||
\(963\) | 6.02617 | 0.194191 | ||||||||
\(964\) | −41.9100 | −1.34983 | ||||||||
\(965\) | −36.0613 | −1.16086 | ||||||||
\(966\) | 1.62141 | 0.0521680 | ||||||||
\(967\) | 58.0129 | 1.86557 | 0.932784 | − | 0.360436i | \(-0.117372\pi\) | ||||
0.932784 | + | 0.360436i | \(0.117372\pi\) | |||||||
\(968\) | 0.673790 | 0.0216564 | ||||||||
\(969\) | 5.40036 | 0.173485 | ||||||||
\(970\) | 9.50594 | 0.305217 | ||||||||
\(971\) | −24.1014 | −0.773452 | −0.386726 | − | 0.922195i | \(-0.626394\pi\) | ||||
−0.386726 | + | 0.922195i | \(0.626394\pi\) | |||||||
\(972\) | −8.61097 | −0.276197 | ||||||||
\(973\) | −11.7843 | −0.377786 | ||||||||
\(974\) | −4.29910 | −0.137752 | ||||||||
\(975\) | −11.6636 | −0.373534 | ||||||||
\(976\) | 37.3988 | 1.19711 | ||||||||
\(977\) | 20.9187 | 0.669249 | 0.334625 | − | 0.942352i | \(-0.391391\pi\) | ||||
0.334625 | + | 0.942352i | \(0.391391\pi\) | |||||||
\(978\) | −2.25241 | −0.0720243 | ||||||||
\(979\) | −2.41089 | −0.0770522 | ||||||||
\(980\) | −30.3558 | −0.969682 | ||||||||
\(981\) | −8.10706 | −0.258838 | ||||||||
\(982\) | −0.962237 | −0.0307062 | ||||||||
\(983\) | −6.65887 | −0.212385 | −0.106193 | − | 0.994346i | \(-0.533866\pi\) | ||||
−0.106193 | + | 0.994346i | \(0.533866\pi\) | |||||||
\(984\) | 7.23964 | 0.230791 | ||||||||
\(985\) | −10.4594 | −0.333263 | ||||||||
\(986\) | −0.709720 | −0.0226021 | ||||||||
\(987\) | 28.2584 | 0.899476 | ||||||||
\(988\) | −7.79823 | −0.248095 | ||||||||
\(989\) | 16.5395 | 0.525925 | ||||||||
\(990\) | 0.268033 | 0.00851866 | ||||||||
\(991\) | −19.3853 | −0.615794 | −0.307897 | − | 0.951420i | \(-0.599625\pi\) | ||||
−0.307897 | + | 0.951420i | \(0.599625\pi\) | |||||||
\(992\) | −3.11354 | −0.0988550 | ||||||||
\(993\) | 42.8003 | 1.35823 | ||||||||
\(994\) | 2.89983 | 0.0919770 | ||||||||
\(995\) | −53.1252 | −1.68418 | ||||||||
\(996\) | −22.6823 | −0.718717 | ||||||||
\(997\) | 1.44161 | 0.0456562 | 0.0228281 | − | 0.999739i | \(-0.492733\pi\) | ||||
0.0228281 | + | 0.999739i | \(0.492733\pi\) | |||||||
\(998\) | 0.793734 | 0.0251252 | ||||||||
\(999\) | −36.5474 | −1.15631 |
(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 | 1441.2.a.c.1.13 | ✓ | 23 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1441.2.a.c.1.13 | ✓ | 23 | 1.1 | even | 1 | trivial |