Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, 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("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.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: | \(48.1178522580\) |
Analytic rank: | \(1\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.97733 | −1.14161 | −0.570805 | − | 0.821085i | \(-0.693369\pi\) | ||||
−0.570805 | + | 0.821085i | \(0.693369\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.11644 | −1.39371 | −0.696856 | − | 0.717211i | \(-0.745419\pi\) | ||||
−0.696856 | + | 0.717211i | \(0.745419\pi\) | |||||||
\(6\) | 1.97733 | 0.807241 | ||||||||
\(7\) | −3.94255 | −1.49014 | −0.745071 | − | 0.666985i | \(-0.767585\pi\) | ||||
−0.745071 | + | 0.666985i | \(0.767585\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.909824 | 0.303275 | ||||||||
\(10\) | 3.11644 | 0.985504 | ||||||||
\(11\) | −4.52506 | −1.36436 | −0.682179 | − | 0.731185i | \(-0.738968\pi\) | ||||
−0.682179 | + | 0.731185i | \(0.738968\pi\) | |||||||
\(12\) | −1.97733 | −0.570805 | ||||||||
\(13\) | −5.66517 | −1.57123 | −0.785617 | − | 0.618713i | \(-0.787655\pi\) | ||||
−0.785617 | + | 0.618713i | \(0.787655\pi\) | |||||||
\(14\) | 3.94255 | 1.05369 | ||||||||
\(15\) | 6.16222 | 1.59108 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.59542 | 0.386945 | 0.193473 | − | 0.981106i | \(-0.438025\pi\) | ||||
0.193473 | + | 0.981106i | \(0.438025\pi\) | |||||||
\(18\) | −0.909824 | −0.214447 | ||||||||
\(19\) | −6.00815 | −1.37836 | −0.689182 | − | 0.724588i | \(-0.742030\pi\) | ||||
−0.689182 | + | 0.724588i | \(0.742030\pi\) | |||||||
\(20\) | −3.11644 | −0.696856 | ||||||||
\(21\) | 7.79571 | 1.70116 | ||||||||
\(22\) | 4.52506 | 0.964747 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 1.97733 | 0.403620 | ||||||||
\(25\) | 4.71218 | 0.942435 | ||||||||
\(26\) | 5.66517 | 1.11103 | ||||||||
\(27\) | 4.13296 | 0.795389 | ||||||||
\(28\) | −3.94255 | −0.745071 | ||||||||
\(29\) | −5.05182 | −0.938100 | −0.469050 | − | 0.883172i | \(-0.655404\pi\) | ||||
−0.469050 | + | 0.883172i | \(0.655404\pi\) | |||||||
\(30\) | −6.16222 | −1.12506 | ||||||||
\(31\) | 3.72512 | 0.669051 | 0.334525 | − | 0.942387i | \(-0.391424\pi\) | ||||
0.334525 | + | 0.942387i | \(0.391424\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 8.94753 | 1.55757 | ||||||||
\(34\) | −1.59542 | −0.273612 | ||||||||
\(35\) | 12.2867 | 2.07683 | ||||||||
\(36\) | 0.909824 | 0.151637 | ||||||||
\(37\) | 3.72100 | 0.611728 | 0.305864 | − | 0.952075i | \(-0.401055\pi\) | ||||
0.305864 | + | 0.952075i | \(0.401055\pi\) | |||||||
\(38\) | 6.00815 | 0.974651 | ||||||||
\(39\) | 11.2019 | 1.79374 | ||||||||
\(40\) | 3.11644 | 0.492752 | ||||||||
\(41\) | 2.67619 | 0.417950 | 0.208975 | − | 0.977921i | \(-0.432987\pi\) | ||||
0.208975 | + | 0.977921i | \(0.432987\pi\) | |||||||
\(42\) | −7.79571 | −1.20290 | ||||||||
\(43\) | 6.70351 | 1.02228 | 0.511138 | − | 0.859499i | \(-0.329224\pi\) | ||||
0.511138 | + | 0.859499i | \(0.329224\pi\) | |||||||
\(44\) | −4.52506 | −0.682179 | ||||||||
\(45\) | −2.83541 | −0.422678 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −2.96233 | −0.432101 | −0.216050 | − | 0.976382i | \(-0.569318\pi\) | ||||
−0.216050 | + | 0.976382i | \(0.569318\pi\) | |||||||
\(48\) | −1.97733 | −0.285403 | ||||||||
\(49\) | 8.54368 | 1.22053 | ||||||||
\(50\) | −4.71218 | −0.666402 | ||||||||
\(51\) | −3.15466 | −0.441741 | ||||||||
\(52\) | −5.66517 | −0.785617 | ||||||||
\(53\) | −2.04095 | −0.280346 | −0.140173 | − | 0.990127i | \(-0.544766\pi\) | ||||
−0.140173 | + | 0.990127i | \(0.544766\pi\) | |||||||
\(54\) | −4.13296 | −0.562425 | ||||||||
\(55\) | 14.1021 | 1.90152 | ||||||||
\(56\) | 3.94255 | 0.526845 | ||||||||
\(57\) | 11.8801 | 1.57356 | ||||||||
\(58\) | 5.05182 | 0.663337 | ||||||||
\(59\) | 1.88037 | 0.244803 | 0.122402 | − | 0.992481i | \(-0.460940\pi\) | ||||
0.122402 | + | 0.992481i | \(0.460940\pi\) | |||||||
\(60\) | 6.16222 | 0.795539 | ||||||||
\(61\) | 2.55870 | 0.327608 | 0.163804 | − | 0.986493i | \(-0.447623\pi\) | ||||
0.163804 | + | 0.986493i | \(0.447623\pi\) | |||||||
\(62\) | −3.72512 | −0.473090 | ||||||||
\(63\) | −3.58702 | −0.451922 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 17.6551 | 2.18985 | ||||||||
\(66\) | −8.94753 | −1.10136 | ||||||||
\(67\) | 4.61407 | 0.563698 | 0.281849 | − | 0.959459i | \(-0.409052\pi\) | ||||
0.281849 | + | 0.959459i | \(0.409052\pi\) | |||||||
\(68\) | 1.59542 | 0.193473 | ||||||||
\(69\) | −1.97733 | −0.238042 | ||||||||
\(70\) | −12.2867 | −1.46854 | ||||||||
\(71\) | 5.59111 | 0.663543 | 0.331772 | − | 0.943360i | \(-0.392354\pi\) | ||||
0.331772 | + | 0.943360i | \(0.392354\pi\) | |||||||
\(72\) | −0.909824 | −0.107224 | ||||||||
\(73\) | −13.5640 | −1.58755 | −0.793773 | − | 0.608215i | \(-0.791886\pi\) | ||||
−0.793773 | + | 0.608215i | \(0.791886\pi\) | |||||||
\(74\) | −3.72100 | −0.432557 | ||||||||
\(75\) | −9.31752 | −1.07589 | ||||||||
\(76\) | −6.00815 | −0.689182 | ||||||||
\(77\) | 17.8403 | 2.03309 | ||||||||
\(78\) | −11.2019 | −1.26836 | ||||||||
\(79\) | −14.9962 | −1.68720 | −0.843601 | − | 0.536971i | \(-0.819568\pi\) | ||||
−0.843601 | + | 0.536971i | \(0.819568\pi\) | |||||||
\(80\) | −3.11644 | −0.348428 | ||||||||
\(81\) | −10.9017 | −1.21130 | ||||||||
\(82\) | −2.67619 | −0.295535 | ||||||||
\(83\) | −9.80877 | −1.07665 | −0.538326 | − | 0.842737i | \(-0.680943\pi\) | ||||
−0.538326 | + | 0.842737i | \(0.680943\pi\) | |||||||
\(84\) | 7.79571 | 0.850581 | ||||||||
\(85\) | −4.97201 | −0.539290 | ||||||||
\(86\) | −6.70351 | −0.722858 | ||||||||
\(87\) | 9.98911 | 1.07095 | ||||||||
\(88\) | 4.52506 | 0.482373 | ||||||||
\(89\) | −0.355681 | −0.0377021 | −0.0188511 | − | 0.999822i | \(-0.506001\pi\) | ||||
−0.0188511 | + | 0.999822i | \(0.506001\pi\) | |||||||
\(90\) | 2.83541 | 0.298878 | ||||||||
\(91\) | 22.3352 | 2.34136 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −7.36577 | −0.763795 | ||||||||
\(94\) | 2.96233 | 0.305541 | ||||||||
\(95\) | 18.7240 | 1.92104 | ||||||||
\(96\) | 1.97733 | 0.201810 | ||||||||
\(97\) | 14.7960 | 1.50231 | 0.751154 | − | 0.660127i | \(-0.229497\pi\) | ||||
0.751154 | + | 0.660127i | \(0.229497\pi\) | |||||||
\(98\) | −8.54368 | −0.863042 | ||||||||
\(99\) | −4.11701 | −0.413775 | ||||||||
\(100\) | 4.71218 | 0.471218 | ||||||||
\(101\) | 12.7490 | 1.26858 | 0.634288 | − | 0.773097i | \(-0.281294\pi\) | ||||
0.634288 | + | 0.773097i | \(0.281294\pi\) | |||||||
\(102\) | 3.15466 | 0.312358 | ||||||||
\(103\) | 3.90007 | 0.384285 | 0.192142 | − | 0.981367i | \(-0.438456\pi\) | ||||
0.192142 | + | 0.981367i | \(0.438456\pi\) | |||||||
\(104\) | 5.66517 | 0.555515 | ||||||||
\(105\) | −24.2948 | −2.37093 | ||||||||
\(106\) | 2.04095 | 0.198234 | ||||||||
\(107\) | 5.66895 | 0.548038 | 0.274019 | − | 0.961724i | \(-0.411647\pi\) | ||||
0.274019 | + | 0.961724i | \(0.411647\pi\) | |||||||
\(108\) | 4.13296 | 0.397695 | ||||||||
\(109\) | −9.26812 | −0.887725 | −0.443862 | − | 0.896095i | \(-0.646392\pi\) | ||||
−0.443862 | + | 0.896095i | \(0.646392\pi\) | |||||||
\(110\) | −14.1021 | −1.34458 | ||||||||
\(111\) | −7.35763 | −0.698356 | ||||||||
\(112\) | −3.94255 | −0.372536 | ||||||||
\(113\) | −1.54825 | −0.145648 | −0.0728238 | − | 0.997345i | \(-0.523201\pi\) | ||||
−0.0728238 | + | 0.997345i | \(0.523201\pi\) | |||||||
\(114\) | −11.8801 | −1.11267 | ||||||||
\(115\) | −3.11644 | −0.290609 | ||||||||
\(116\) | −5.05182 | −0.469050 | ||||||||
\(117\) | −5.15430 | −0.476515 | ||||||||
\(118\) | −1.88037 | −0.173102 | ||||||||
\(119\) | −6.29000 | −0.576604 | ||||||||
\(120\) | −6.16222 | −0.562531 | ||||||||
\(121\) | 9.47620 | 0.861473 | ||||||||
\(122\) | −2.55870 | −0.231654 | ||||||||
\(123\) | −5.29170 | −0.477136 | ||||||||
\(124\) | 3.72512 | 0.334525 | ||||||||
\(125\) | 0.896982 | 0.0802285 | ||||||||
\(126\) | 3.58702 | 0.319557 | ||||||||
\(127\) | −6.92755 | −0.614721 | −0.307360 | − | 0.951593i | \(-0.599446\pi\) | ||||
−0.307360 | + | 0.951593i | \(0.599446\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −13.2550 | −1.16704 | ||||||||
\(130\) | −17.6551 | −1.54846 | ||||||||
\(131\) | 1.00000 | 0.0873704 | ||||||||
\(132\) | 8.94753 | 0.778783 | ||||||||
\(133\) | 23.6874 | 2.05396 | ||||||||
\(134\) | −4.61407 | −0.398595 | ||||||||
\(135\) | −12.8801 | −1.10854 | ||||||||
\(136\) | −1.59542 | −0.136806 | ||||||||
\(137\) | 17.0067 | 1.45298 | 0.726492 | − | 0.687175i | \(-0.241149\pi\) | ||||
0.726492 | + | 0.687175i | \(0.241149\pi\) | |||||||
\(138\) | 1.97733 | 0.168321 | ||||||||
\(139\) | −21.7796 | −1.84732 | −0.923662 | − | 0.383209i | \(-0.874819\pi\) | ||||
−0.923662 | + | 0.383209i | \(0.874819\pi\) | |||||||
\(140\) | 12.2867 | 1.03842 | ||||||||
\(141\) | 5.85750 | 0.493291 | ||||||||
\(142\) | −5.59111 | −0.469196 | ||||||||
\(143\) | 25.6352 | 2.14373 | ||||||||
\(144\) | 0.909824 | 0.0758186 | ||||||||
\(145\) | 15.7437 | 1.30744 | ||||||||
\(146\) | 13.5640 | 1.12256 | ||||||||
\(147\) | −16.8937 | −1.39337 | ||||||||
\(148\) | 3.72100 | 0.305864 | ||||||||
\(149\) | −15.8438 | −1.29798 | −0.648988 | − | 0.760799i | \(-0.724808\pi\) | ||||
−0.648988 | + | 0.760799i | \(0.724808\pi\) | |||||||
\(150\) | 9.31752 | 0.760772 | ||||||||
\(151\) | −4.72329 | −0.384376 | −0.192188 | − | 0.981358i | \(-0.561558\pi\) | ||||
−0.192188 | + | 0.981358i | \(0.561558\pi\) | |||||||
\(152\) | 6.00815 | 0.487325 | ||||||||
\(153\) | 1.45155 | 0.117351 | ||||||||
\(154\) | −17.8403 | −1.43761 | ||||||||
\(155\) | −11.6091 | −0.932464 | ||||||||
\(156\) | 11.2019 | 0.896869 | ||||||||
\(157\) | 6.34927 | 0.506727 | 0.253363 | − | 0.967371i | \(-0.418463\pi\) | ||||
0.253363 | + | 0.967371i | \(0.418463\pi\) | |||||||
\(158\) | 14.9962 | 1.19303 | ||||||||
\(159\) | 4.03562 | 0.320046 | ||||||||
\(160\) | 3.11644 | 0.246376 | ||||||||
\(161\) | −3.94255 | −0.310716 | ||||||||
\(162\) | 10.9017 | 0.856518 | ||||||||
\(163\) | −17.4955 | −1.37035 | −0.685176 | − | 0.728378i | \(-0.740275\pi\) | ||||
−0.685176 | + | 0.728378i | \(0.740275\pi\) | |||||||
\(164\) | 2.67619 | 0.208975 | ||||||||
\(165\) | −27.8844 | −2.17080 | ||||||||
\(166\) | 9.80877 | 0.761308 | ||||||||
\(167\) | 6.62277 | 0.512485 | 0.256243 | − | 0.966612i | \(-0.417515\pi\) | ||||
0.256243 | + | 0.966612i | \(0.417515\pi\) | |||||||
\(168\) | −7.79571 | −0.601452 | ||||||||
\(169\) | 19.0941 | 1.46878 | ||||||||
\(170\) | 4.97201 | 0.381336 | ||||||||
\(171\) | −5.46636 | −0.418023 | ||||||||
\(172\) | 6.70351 | 0.511138 | ||||||||
\(173\) | 16.2181 | 1.23304 | 0.616519 | − | 0.787340i | \(-0.288543\pi\) | ||||
0.616519 | + | 0.787340i | \(0.288543\pi\) | |||||||
\(174\) | −9.98911 | −0.757273 | ||||||||
\(175\) | −18.5780 | −1.40436 | ||||||||
\(176\) | −4.52506 | −0.341089 | ||||||||
\(177\) | −3.71810 | −0.279470 | ||||||||
\(178\) | 0.355681 | 0.0266594 | ||||||||
\(179\) | −10.3870 | −0.776359 | −0.388180 | − | 0.921584i | \(-0.626896\pi\) | ||||
−0.388180 | + | 0.921584i | \(0.626896\pi\) | |||||||
\(180\) | −2.83541 | −0.211339 | ||||||||
\(181\) | 6.04645 | 0.449429 | 0.224715 | − | 0.974425i | \(-0.427855\pi\) | ||||
0.224715 | + | 0.974425i | \(0.427855\pi\) | |||||||
\(182\) | −22.3352 | −1.65559 | ||||||||
\(183\) | −5.05939 | −0.374001 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −11.5963 | −0.852574 | ||||||||
\(186\) | 7.36577 | 0.540085 | ||||||||
\(187\) | −7.21936 | −0.527932 | ||||||||
\(188\) | −2.96233 | −0.216050 | ||||||||
\(189\) | −16.2944 | −1.18524 | ||||||||
\(190\) | −18.7240 | −1.35838 | ||||||||
\(191\) | −6.52512 | −0.472141 | −0.236070 | − | 0.971736i | \(-0.575860\pi\) | ||||
−0.236070 | + | 0.971736i | \(0.575860\pi\) | |||||||
\(192\) | −1.97733 | −0.142701 | ||||||||
\(193\) | −14.8862 | −1.07153 | −0.535764 | − | 0.844368i | \(-0.679976\pi\) | ||||
−0.535764 | + | 0.844368i | \(0.679976\pi\) | |||||||
\(194\) | −14.7960 | −1.06229 | ||||||||
\(195\) | −34.9100 | −2.49996 | ||||||||
\(196\) | 8.54368 | 0.610263 | ||||||||
\(197\) | 15.8551 | 1.12963 | 0.564813 | − | 0.825219i | \(-0.308948\pi\) | ||||
0.564813 | + | 0.825219i | \(0.308948\pi\) | |||||||
\(198\) | 4.11701 | 0.292583 | ||||||||
\(199\) | 24.2691 | 1.72039 | 0.860194 | − | 0.509967i | \(-0.170342\pi\) | ||||
0.860194 | + | 0.509967i | \(0.170342\pi\) | |||||||
\(200\) | −4.71218 | −0.333201 | ||||||||
\(201\) | −9.12353 | −0.643524 | ||||||||
\(202\) | −12.7490 | −0.897018 | ||||||||
\(203\) | 19.9171 | 1.39790 | ||||||||
\(204\) | −3.15466 | −0.220870 | ||||||||
\(205\) | −8.34017 | −0.582503 | ||||||||
\(206\) | −3.90007 | −0.271730 | ||||||||
\(207\) | 0.909824 | 0.0632371 | ||||||||
\(208\) | −5.66517 | −0.392809 | ||||||||
\(209\) | 27.1873 | 1.88058 | ||||||||
\(210\) | 24.2948 | 1.67650 | ||||||||
\(211\) | 10.0122 | 0.689268 | 0.344634 | − | 0.938737i | \(-0.388003\pi\) | ||||
0.344634 | + | 0.938737i | \(0.388003\pi\) | |||||||
\(212\) | −2.04095 | −0.140173 | ||||||||
\(213\) | −11.0555 | −0.757508 | ||||||||
\(214\) | −5.66895 | −0.387521 | ||||||||
\(215\) | −20.8911 | −1.42476 | ||||||||
\(216\) | −4.13296 | −0.281213 | ||||||||
\(217\) | −14.6864 | −0.996981 | ||||||||
\(218\) | 9.26812 | 0.627716 | ||||||||
\(219\) | 26.8205 | 1.81236 | ||||||||
\(220\) | 14.1021 | 0.950762 | ||||||||
\(221\) | −9.03830 | −0.607982 | ||||||||
\(222\) | 7.35763 | 0.493812 | ||||||||
\(223\) | 11.1823 | 0.748820 | 0.374410 | − | 0.927263i | \(-0.377845\pi\) | ||||
0.374410 | + | 0.927263i | \(0.377845\pi\) | |||||||
\(224\) | 3.94255 | 0.263423 | ||||||||
\(225\) | 4.28725 | 0.285817 | ||||||||
\(226\) | 1.54825 | 0.102988 | ||||||||
\(227\) | −24.6608 | −1.63680 | −0.818399 | − | 0.574651i | \(-0.805138\pi\) | ||||
−0.818399 | + | 0.574651i | \(0.805138\pi\) | |||||||
\(228\) | 11.8801 | 0.786778 | ||||||||
\(229\) | 16.5997 | 1.09694 | 0.548469 | − | 0.836171i | \(-0.315211\pi\) | ||||
0.548469 | + | 0.836171i | \(0.315211\pi\) | |||||||
\(230\) | 3.11644 | 0.205492 | ||||||||
\(231\) | −35.2761 | −2.32099 | ||||||||
\(232\) | 5.05182 | 0.331669 | ||||||||
\(233\) | −0.350756 | −0.0229788 | −0.0114894 | − | 0.999934i | \(-0.503657\pi\) | ||||
−0.0114894 | + | 0.999934i | \(0.503657\pi\) | |||||||
\(234\) | 5.15430 | 0.336947 | ||||||||
\(235\) | 9.23193 | 0.602225 | ||||||||
\(236\) | 1.88037 | 0.122402 | ||||||||
\(237\) | 29.6523 | 1.92613 | ||||||||
\(238\) | 6.29000 | 0.407720 | ||||||||
\(239\) | −11.9578 | −0.773486 | −0.386743 | − | 0.922188i | \(-0.626400\pi\) | ||||
−0.386743 | + | 0.922188i | \(0.626400\pi\) | |||||||
\(240\) | 6.16222 | 0.397769 | ||||||||
\(241\) | −5.56516 | −0.358484 | −0.179242 | − | 0.983805i | \(-0.557364\pi\) | ||||
−0.179242 | + | 0.983805i | \(0.557364\pi\) | |||||||
\(242\) | −9.47620 | −0.609153 | ||||||||
\(243\) | 9.15732 | 0.587443 | ||||||||
\(244\) | 2.55870 | 0.163804 | ||||||||
\(245\) | −26.6258 | −1.70106 | ||||||||
\(246\) | 5.29170 | 0.337386 | ||||||||
\(247\) | 34.0372 | 2.16573 | ||||||||
\(248\) | −3.72512 | −0.236545 | ||||||||
\(249\) | 19.3951 | 1.22912 | ||||||||
\(250\) | −0.896982 | −0.0567301 | ||||||||
\(251\) | −9.51128 | −0.600347 | −0.300173 | − | 0.953885i | \(-0.597045\pi\) | ||||
−0.300173 | + | 0.953885i | \(0.597045\pi\) | |||||||
\(252\) | −3.58702 | −0.225961 | ||||||||
\(253\) | −4.52506 | −0.284488 | ||||||||
\(254\) | 6.92755 | 0.434673 | ||||||||
\(255\) | 9.83130 | 0.615660 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.21716 | 0.200681 | 0.100341 | − | 0.994953i | \(-0.468007\pi\) | ||||
0.100341 | + | 0.994953i | \(0.468007\pi\) | |||||||
\(258\) | 13.2550 | 0.825223 | ||||||||
\(259\) | −14.6702 | −0.911563 | ||||||||
\(260\) | 17.6551 | 1.09493 | ||||||||
\(261\) | −4.59627 | −0.284502 | ||||||||
\(262\) | −1.00000 | −0.0617802 | ||||||||
\(263\) | 22.4649 | 1.38525 | 0.692624 | − | 0.721299i | \(-0.256455\pi\) | ||||
0.692624 | + | 0.721299i | \(0.256455\pi\) | |||||||
\(264\) | −8.94753 | −0.550682 | ||||||||
\(265\) | 6.36048 | 0.390721 | ||||||||
\(266\) | −23.6874 | −1.45237 | ||||||||
\(267\) | 0.703298 | 0.0430412 | ||||||||
\(268\) | 4.61407 | 0.281849 | ||||||||
\(269\) | 4.02909 | 0.245658 | 0.122829 | − | 0.992428i | \(-0.460803\pi\) | ||||
0.122829 | + | 0.992428i | \(0.460803\pi\) | |||||||
\(270\) | 12.8801 | 0.783859 | ||||||||
\(271\) | −14.0411 | −0.852934 | −0.426467 | − | 0.904503i | \(-0.640242\pi\) | ||||
−0.426467 | + | 0.904503i | \(0.640242\pi\) | |||||||
\(272\) | 1.59542 | 0.0967363 | ||||||||
\(273\) | −44.1640 | −2.67293 | ||||||||
\(274\) | −17.0067 | −1.02742 | ||||||||
\(275\) | −21.3229 | −1.28582 | ||||||||
\(276\) | −1.97733 | −0.119021 | ||||||||
\(277\) | −0.490680 | −0.0294821 | −0.0147410 | − | 0.999891i | \(-0.504692\pi\) | ||||
−0.0147410 | + | 0.999891i | \(0.504692\pi\) | |||||||
\(278\) | 21.7796 | 1.30625 | ||||||||
\(279\) | 3.38920 | 0.202906 | ||||||||
\(280\) | −12.2867 | −0.734271 | ||||||||
\(281\) | 23.1767 | 1.38261 | 0.691304 | − | 0.722564i | \(-0.257036\pi\) | ||||
0.691304 | + | 0.722564i | \(0.257036\pi\) | |||||||
\(282\) | −5.85750 | −0.348809 | ||||||||
\(283\) | 11.4998 | 0.683592 | 0.341796 | − | 0.939774i | \(-0.388965\pi\) | ||||
0.341796 | + | 0.939774i | \(0.388965\pi\) | |||||||
\(284\) | 5.59111 | 0.331772 | ||||||||
\(285\) | −37.0235 | −2.19308 | ||||||||
\(286\) | −25.6352 | −1.51584 | ||||||||
\(287\) | −10.5510 | −0.622806 | ||||||||
\(288\) | −0.909824 | −0.0536119 | ||||||||
\(289\) | −14.4546 | −0.850273 | ||||||||
\(290\) | −15.7437 | −0.924501 | ||||||||
\(291\) | −29.2566 | −1.71505 | ||||||||
\(292\) | −13.5640 | −0.793773 | ||||||||
\(293\) | −7.09097 | −0.414259 | −0.207129 | − | 0.978314i | \(-0.566412\pi\) | ||||
−0.207129 | + | 0.978314i | \(0.566412\pi\) | |||||||
\(294\) | 16.8937 | 0.985258 | ||||||||
\(295\) | −5.86005 | −0.341185 | ||||||||
\(296\) | −3.72100 | −0.216279 | ||||||||
\(297\) | −18.7019 | −1.08520 | ||||||||
\(298\) | 15.8438 | 0.917808 | ||||||||
\(299\) | −5.66517 | −0.327625 | ||||||||
\(300\) | −9.31752 | −0.537947 | ||||||||
\(301\) | −26.4289 | −1.52334 | ||||||||
\(302\) | 4.72329 | 0.271795 | ||||||||
\(303\) | −25.2090 | −1.44822 | ||||||||
\(304\) | −6.00815 | −0.344591 | ||||||||
\(305\) | −7.97404 | −0.456592 | ||||||||
\(306\) | −1.45155 | −0.0829794 | ||||||||
\(307\) | −13.5874 | −0.775472 | −0.387736 | − | 0.921771i | \(-0.626743\pi\) | ||||
−0.387736 | + | 0.921771i | \(0.626743\pi\) | |||||||
\(308\) | 17.8403 | 1.01654 | ||||||||
\(309\) | −7.71171 | −0.438704 | ||||||||
\(310\) | 11.6091 | 0.659352 | ||||||||
\(311\) | 24.9892 | 1.41701 | 0.708503 | − | 0.705708i | \(-0.249371\pi\) | ||||
0.708503 | + | 0.705708i | \(0.249371\pi\) | |||||||
\(312\) | −11.2019 | −0.634182 | ||||||||
\(313\) | 25.5324 | 1.44317 | 0.721587 | − | 0.692324i | \(-0.243413\pi\) | ||||
0.721587 | + | 0.692324i | \(0.243413\pi\) | |||||||
\(314\) | −6.34927 | −0.358310 | ||||||||
\(315\) | 11.1787 | 0.629850 | ||||||||
\(316\) | −14.9962 | −0.843601 | ||||||||
\(317\) | 18.1255 | 1.01803 | 0.509016 | − | 0.860757i | \(-0.330009\pi\) | ||||
0.509016 | + | 0.860757i | \(0.330009\pi\) | |||||||
\(318\) | −4.03562 | −0.226306 | ||||||||
\(319\) | 22.8598 | 1.27990 | ||||||||
\(320\) | −3.11644 | −0.174214 | ||||||||
\(321\) | −11.2094 | −0.625646 | ||||||||
\(322\) | 3.94255 | 0.219710 | ||||||||
\(323\) | −9.58550 | −0.533352 | ||||||||
\(324\) | −10.9017 | −0.605650 | ||||||||
\(325\) | −26.6953 | −1.48079 | ||||||||
\(326\) | 17.4955 | 0.968985 | ||||||||
\(327\) | 18.3261 | 1.01344 | ||||||||
\(328\) | −2.67619 | −0.147768 | ||||||||
\(329\) | 11.6791 | 0.643892 | ||||||||
\(330\) | 27.8844 | 1.53499 | ||||||||
\(331\) | −34.6744 | −1.90588 | −0.952938 | − | 0.303165i | \(-0.901957\pi\) | ||||
−0.952938 | + | 0.303165i | \(0.901957\pi\) | |||||||
\(332\) | −9.80877 | −0.538326 | ||||||||
\(333\) | 3.38545 | 0.185522 | ||||||||
\(334\) | −6.62277 | −0.362382 | ||||||||
\(335\) | −14.3795 | −0.785634 | ||||||||
\(336\) | 7.79571 | 0.425291 | ||||||||
\(337\) | 2.21349 | 0.120577 | 0.0602883 | − | 0.998181i | \(-0.480798\pi\) | ||||
0.0602883 | + | 0.998181i | \(0.480798\pi\) | |||||||
\(338\) | −19.0941 | −1.03858 | ||||||||
\(339\) | 3.06141 | 0.166273 | ||||||||
\(340\) | −4.97201 | −0.269645 | ||||||||
\(341\) | −16.8564 | −0.912825 | ||||||||
\(342\) | 5.46636 | 0.295587 | ||||||||
\(343\) | −6.08604 | −0.328615 | ||||||||
\(344\) | −6.70351 | −0.361429 | ||||||||
\(345\) | 6.16222 | 0.331763 | ||||||||
\(346\) | −16.2181 | −0.871889 | ||||||||
\(347\) | −16.0471 | −0.861451 | −0.430726 | − | 0.902483i | \(-0.641742\pi\) | ||||
−0.430726 | + | 0.902483i | \(0.641742\pi\) | |||||||
\(348\) | 9.98911 | 0.535473 | ||||||||
\(349\) | 0.832866 | 0.0445823 | 0.0222911 | − | 0.999752i | \(-0.492904\pi\) | ||||
0.0222911 | + | 0.999752i | \(0.492904\pi\) | |||||||
\(350\) | 18.5780 | 0.993035 | ||||||||
\(351\) | −23.4139 | −1.24974 | ||||||||
\(352\) | 4.52506 | 0.241187 | ||||||||
\(353\) | −1.78388 | −0.0949462 | −0.0474731 | − | 0.998873i | \(-0.515117\pi\) | ||||
−0.0474731 | + | 0.998873i | \(0.515117\pi\) | |||||||
\(354\) | 3.71810 | 0.197615 | ||||||||
\(355\) | −17.4243 | −0.924788 | ||||||||
\(356\) | −0.355681 | −0.0188511 | ||||||||
\(357\) | 12.4374 | 0.658257 | ||||||||
\(358\) | 10.3870 | 0.548969 | ||||||||
\(359\) | 23.3295 | 1.23129 | 0.615643 | − | 0.788025i | \(-0.288896\pi\) | ||||
0.615643 | + | 0.788025i | \(0.288896\pi\) | |||||||
\(360\) | 2.83541 | 0.149439 | ||||||||
\(361\) | 17.0979 | 0.899889 | ||||||||
\(362\) | −6.04645 | −0.317794 | ||||||||
\(363\) | −18.7375 | −0.983466 | ||||||||
\(364\) | 22.3352 | 1.17068 | ||||||||
\(365\) | 42.2713 | 2.21258 | ||||||||
\(366\) | 5.05939 | 0.264459 | ||||||||
\(367\) | 15.1016 | 0.788299 | 0.394149 | − | 0.919046i | \(-0.371039\pi\) | ||||
0.394149 | + | 0.919046i | \(0.371039\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 2.43486 | 0.126754 | ||||||||
\(370\) | 11.5963 | 0.602861 | ||||||||
\(371\) | 8.04653 | 0.417755 | ||||||||
\(372\) | −7.36577 | −0.381898 | ||||||||
\(373\) | 23.2013 | 1.20132 | 0.600660 | − | 0.799505i | \(-0.294905\pi\) | ||||
0.600660 | + | 0.799505i | \(0.294905\pi\) | |||||||
\(374\) | 7.21936 | 0.373304 | ||||||||
\(375\) | −1.77363 | −0.0915897 | ||||||||
\(376\) | 2.96233 | 0.152771 | ||||||||
\(377\) | 28.6194 | 1.47398 | ||||||||
\(378\) | 16.2944 | 0.838094 | ||||||||
\(379\) | −11.2140 | −0.576027 | −0.288013 | − | 0.957626i | \(-0.592995\pi\) | ||||
−0.288013 | + | 0.957626i | \(0.592995\pi\) | |||||||
\(380\) | 18.7240 | 0.960522 | ||||||||
\(381\) | 13.6980 | 0.701772 | ||||||||
\(382\) | 6.52512 | 0.333854 | ||||||||
\(383\) | 30.6759 | 1.56747 | 0.783733 | − | 0.621098i | \(-0.213313\pi\) | ||||
0.783733 | + | 0.621098i | \(0.213313\pi\) | |||||||
\(384\) | 1.97733 | 0.100905 | ||||||||
\(385\) | −55.5981 | −2.83354 | ||||||||
\(386\) | 14.8862 | 0.757685 | ||||||||
\(387\) | 6.09901 | 0.310030 | ||||||||
\(388\) | 14.7960 | 0.751154 | ||||||||
\(389\) | −23.4690 | −1.18993 | −0.594963 | − | 0.803753i | \(-0.702833\pi\) | ||||
−0.594963 | + | 0.803753i | \(0.702833\pi\) | |||||||
\(390\) | 34.9100 | 1.76774 | ||||||||
\(391\) | 1.59542 | 0.0806836 | ||||||||
\(392\) | −8.54368 | −0.431521 | ||||||||
\(393\) | −1.97733 | −0.0997430 | ||||||||
\(394\) | −15.8551 | −0.798766 | ||||||||
\(395\) | 46.7346 | 2.35147 | ||||||||
\(396\) | −4.11701 | −0.206887 | ||||||||
\(397\) | 7.94589 | 0.398793 | 0.199396 | − | 0.979919i | \(-0.436102\pi\) | ||||
0.199396 | + | 0.979919i | \(0.436102\pi\) | |||||||
\(398\) | −24.2691 | −1.21650 | ||||||||
\(399\) | −46.8378 | −2.34482 | ||||||||
\(400\) | 4.71218 | 0.235609 | ||||||||
\(401\) | 4.89362 | 0.244376 | 0.122188 | − | 0.992507i | \(-0.461009\pi\) | ||||
0.122188 | + | 0.992507i | \(0.461009\pi\) | |||||||
\(402\) | 9.12353 | 0.455040 | ||||||||
\(403\) | −21.1034 | −1.05124 | ||||||||
\(404\) | 12.7490 | 0.634288 | ||||||||
\(405\) | 33.9744 | 1.68820 | ||||||||
\(406\) | −19.9171 | −0.988467 | ||||||||
\(407\) | −16.8378 | −0.834616 | ||||||||
\(408\) | 3.15466 | 0.156179 | ||||||||
\(409\) | −0.0432583 | −0.00213899 | −0.00106949 | − | 0.999999i | \(-0.500340\pi\) | ||||
−0.00106949 | + | 0.999999i | \(0.500340\pi\) | |||||||
\(410\) | 8.34017 | 0.411892 | ||||||||
\(411\) | −33.6279 | −1.65874 | ||||||||
\(412\) | 3.90007 | 0.192142 | ||||||||
\(413\) | −7.41344 | −0.364792 | ||||||||
\(414\) | −0.909824 | −0.0447154 | ||||||||
\(415\) | 30.5684 | 1.50054 | ||||||||
\(416\) | 5.66517 | 0.277758 | ||||||||
\(417\) | 43.0654 | 2.10892 | ||||||||
\(418\) | −27.1873 | −1.32977 | ||||||||
\(419\) | −8.25349 | −0.403209 | −0.201605 | − | 0.979467i | \(-0.564616\pi\) | ||||
−0.201605 | + | 0.979467i | \(0.564616\pi\) | |||||||
\(420\) | −24.2948 | −1.18547 | ||||||||
\(421\) | −9.71405 | −0.473434 | −0.236717 | − | 0.971579i | \(-0.576071\pi\) | ||||
−0.236717 | + | 0.971579i | \(0.576071\pi\) | |||||||
\(422\) | −10.0122 | −0.487386 | ||||||||
\(423\) | −2.69520 | −0.131045 | ||||||||
\(424\) | 2.04095 | 0.0991172 | ||||||||
\(425\) | 7.51788 | 0.364671 | ||||||||
\(426\) | 11.0555 | 0.535639 | ||||||||
\(427\) | −10.0878 | −0.488183 | ||||||||
\(428\) | 5.66895 | 0.274019 | ||||||||
\(429\) | −50.6893 | −2.44730 | ||||||||
\(430\) | 20.8911 | 1.00746 | ||||||||
\(431\) | −5.93987 | −0.286114 | −0.143057 | − | 0.989714i | \(-0.545693\pi\) | ||||
−0.143057 | + | 0.989714i | \(0.545693\pi\) | |||||||
\(432\) | 4.13296 | 0.198847 | ||||||||
\(433\) | 12.8952 | 0.619704 | 0.309852 | − | 0.950785i | \(-0.399720\pi\) | ||||
0.309852 | + | 0.950785i | \(0.399720\pi\) | |||||||
\(434\) | 14.6864 | 0.704972 | ||||||||
\(435\) | −31.1304 | −1.49259 | ||||||||
\(436\) | −9.26812 | −0.443862 | ||||||||
\(437\) | −6.00815 | −0.287409 | ||||||||
\(438\) | −26.8205 | −1.28153 | ||||||||
\(439\) | −29.7579 | −1.42027 | −0.710134 | − | 0.704067i | \(-0.751365\pi\) | ||||
−0.710134 | + | 0.704067i | \(0.751365\pi\) | |||||||
\(440\) | −14.1021 | −0.672290 | ||||||||
\(441\) | 7.77324 | 0.370154 | ||||||||
\(442\) | 9.03830 | 0.429908 | ||||||||
\(443\) | −27.7112 | −1.31660 | −0.658299 | − | 0.752756i | \(-0.728724\pi\) | ||||
−0.658299 | + | 0.752756i | \(0.728724\pi\) | |||||||
\(444\) | −7.35763 | −0.349178 | ||||||||
\(445\) | 1.10846 | 0.0525460 | ||||||||
\(446\) | −11.1823 | −0.529496 | ||||||||
\(447\) | 31.3284 | 1.48178 | ||||||||
\(448\) | −3.94255 | −0.186268 | ||||||||
\(449\) | −7.22774 | −0.341098 | −0.170549 | − | 0.985349i | \(-0.554554\pi\) | ||||
−0.170549 | + | 0.985349i | \(0.554554\pi\) | |||||||
\(450\) | −4.28725 | −0.202103 | ||||||||
\(451\) | −12.1099 | −0.570234 | ||||||||
\(452\) | −1.54825 | −0.0728238 | ||||||||
\(453\) | 9.33950 | 0.438808 | ||||||||
\(454\) | 24.6608 | 1.15739 | ||||||||
\(455\) | −69.6062 | −3.26319 | ||||||||
\(456\) | −11.8801 | −0.556336 | ||||||||
\(457\) | −36.5408 | −1.70930 | −0.854652 | − | 0.519200i | \(-0.826230\pi\) | ||||
−0.854652 | + | 0.519200i | \(0.826230\pi\) | |||||||
\(458\) | −16.5997 | −0.775652 | ||||||||
\(459\) | 6.59379 | 0.307772 | ||||||||
\(460\) | −3.11644 | −0.145305 | ||||||||
\(461\) | −4.30028 | −0.200284 | −0.100142 | − | 0.994973i | \(-0.531930\pi\) | ||||
−0.100142 | + | 0.994973i | \(0.531930\pi\) | |||||||
\(462\) | 35.2761 | 1.64119 | ||||||||
\(463\) | 18.5138 | 0.860409 | 0.430204 | − | 0.902732i | \(-0.358442\pi\) | ||||
0.430204 | + | 0.902732i | \(0.358442\pi\) | |||||||
\(464\) | −5.05182 | −0.234525 | ||||||||
\(465\) | 22.9550 | 1.06451 | ||||||||
\(466\) | 0.350756 | 0.0162485 | ||||||||
\(467\) | 14.3610 | 0.664547 | 0.332273 | − | 0.943183i | \(-0.392184\pi\) | ||||
0.332273 | + | 0.943183i | \(0.392184\pi\) | |||||||
\(468\) | −5.15430 | −0.238258 | ||||||||
\(469\) | −18.1912 | −0.839991 | ||||||||
\(470\) | −9.23193 | −0.425837 | ||||||||
\(471\) | −12.5546 | −0.578485 | ||||||||
\(472\) | −1.88037 | −0.0865509 | ||||||||
\(473\) | −30.3338 | −1.39475 | ||||||||
\(474\) | −29.6523 | −1.36198 | ||||||||
\(475\) | −28.3115 | −1.29902 | ||||||||
\(476\) | −6.29000 | −0.288302 | ||||||||
\(477\) | −1.85690 | −0.0850217 | ||||||||
\(478\) | 11.9578 | 0.546937 | ||||||||
\(479\) | 19.0808 | 0.871826 | 0.435913 | − | 0.899989i | \(-0.356426\pi\) | ||||
0.435913 | + | 0.899989i | \(0.356426\pi\) | |||||||
\(480\) | −6.16222 | −0.281265 | ||||||||
\(481\) | −21.0801 | −0.961169 | ||||||||
\(482\) | 5.56516 | 0.253486 | ||||||||
\(483\) | 7.79571 | 0.354717 | ||||||||
\(484\) | 9.47620 | 0.430736 | ||||||||
\(485\) | −46.1109 | −2.09379 | ||||||||
\(486\) | −9.15732 | −0.415385 | ||||||||
\(487\) | −36.4821 | −1.65316 | −0.826580 | − | 0.562819i | \(-0.809717\pi\) | ||||
−0.826580 | + | 0.562819i | \(0.809717\pi\) | |||||||
\(488\) | −2.55870 | −0.115827 | ||||||||
\(489\) | 34.5943 | 1.56441 | ||||||||
\(490\) | 26.6258 | 1.20283 | ||||||||
\(491\) | 15.9047 | 0.717770 | 0.358885 | − | 0.933382i | \(-0.383157\pi\) | ||||
0.358885 | + | 0.933382i | \(0.383157\pi\) | |||||||
\(492\) | −5.29170 | −0.238568 | ||||||||
\(493\) | −8.05976 | −0.362993 | ||||||||
\(494\) | −34.0372 | −1.53141 | ||||||||
\(495\) | 12.8304 | 0.576684 | ||||||||
\(496\) | 3.72512 | 0.167263 | ||||||||
\(497\) | −22.0432 | −0.988774 | ||||||||
\(498\) | −19.3951 | −0.869117 | ||||||||
\(499\) | −26.2569 | −1.17542 | −0.587711 | − | 0.809071i | \(-0.699971\pi\) | ||||
−0.587711 | + | 0.809071i | \(0.699971\pi\) | |||||||
\(500\) | 0.896982 | 0.0401142 | ||||||||
\(501\) | −13.0954 | −0.585059 | ||||||||
\(502\) | 9.51128 | 0.424509 | ||||||||
\(503\) | −11.6417 | −0.519080 | −0.259540 | − | 0.965732i | \(-0.583571\pi\) | ||||
−0.259540 | + | 0.965732i | \(0.583571\pi\) | |||||||
\(504\) | 3.58702 | 0.159779 | ||||||||
\(505\) | −39.7315 | −1.76803 | ||||||||
\(506\) | 4.52506 | 0.201164 | ||||||||
\(507\) | −37.7553 | −1.67677 | ||||||||
\(508\) | −6.92755 | −0.307360 | ||||||||
\(509\) | 21.3295 | 0.945412 | 0.472706 | − | 0.881220i | \(-0.343277\pi\) | ||||
0.472706 | + | 0.881220i | \(0.343277\pi\) | |||||||
\(510\) | −9.83130 | −0.435337 | ||||||||
\(511\) | 53.4767 | 2.36567 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −24.8315 | −1.09634 | ||||||||
\(514\) | −3.21716 | −0.141903 | ||||||||
\(515\) | −12.1543 | −0.535583 | ||||||||
\(516\) | −13.2550 | −0.583521 | ||||||||
\(517\) | 13.4048 | 0.589540 | ||||||||
\(518\) | 14.6702 | 0.644572 | ||||||||
\(519\) | −32.0684 | −1.40765 | ||||||||
\(520\) | −17.6551 | −0.774229 | ||||||||
\(521\) | 14.1911 | 0.621724 | 0.310862 | − | 0.950455i | \(-0.399382\pi\) | ||||
0.310862 | + | 0.950455i | \(0.399382\pi\) | |||||||
\(522\) | 4.59627 | 0.201173 | ||||||||
\(523\) | −38.7652 | −1.69509 | −0.847543 | − | 0.530727i | \(-0.821919\pi\) | ||||
−0.847543 | + | 0.530727i | \(0.821919\pi\) | |||||||
\(524\) | 1.00000 | 0.0436852 | ||||||||
\(525\) | 36.7348 | 1.60324 | ||||||||
\(526\) | −22.4649 | −0.979518 | ||||||||
\(527\) | 5.94311 | 0.258886 | ||||||||
\(528\) | 8.94753 | 0.389391 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −6.36048 | −0.276282 | ||||||||
\(531\) | 1.71080 | 0.0742425 | ||||||||
\(532\) | 23.6874 | 1.02698 | ||||||||
\(533\) | −15.1611 | −0.656698 | ||||||||
\(534\) | −0.703298 | −0.0304347 | ||||||||
\(535\) | −17.6669 | −0.763807 | ||||||||
\(536\) | −4.61407 | −0.199297 | ||||||||
\(537\) | 20.5385 | 0.886300 | ||||||||
\(538\) | −4.02909 | −0.173706 | ||||||||
\(539\) | −38.6607 | −1.66523 | ||||||||
\(540\) | −12.8801 | −0.554272 | ||||||||
\(541\) | −39.2996 | −1.68962 | −0.844810 | − | 0.535066i | \(-0.820287\pi\) | ||||
−0.844810 | + | 0.535066i | \(0.820287\pi\) | |||||||
\(542\) | 14.0411 | 0.603116 | ||||||||
\(543\) | −11.9558 | −0.513073 | ||||||||
\(544\) | −1.59542 | −0.0684029 | ||||||||
\(545\) | 28.8835 | 1.23723 | ||||||||
\(546\) | 44.1640 | 1.89004 | ||||||||
\(547\) | 4.02526 | 0.172108 | 0.0860539 | − | 0.996290i | \(-0.472574\pi\) | ||||
0.0860539 | + | 0.996290i | \(0.472574\pi\) | |||||||
\(548\) | 17.0067 | 0.726492 | ||||||||
\(549\) | 2.32797 | 0.0993553 | ||||||||
\(550\) | 21.3229 | 0.909212 | ||||||||
\(551\) | 30.3521 | 1.29304 | ||||||||
\(552\) | 1.97733 | 0.0841606 | ||||||||
\(553\) | 59.1231 | 2.51417 | ||||||||
\(554\) | 0.490680 | 0.0208470 | ||||||||
\(555\) | 22.9296 | 0.973307 | ||||||||
\(556\) | −21.7796 | −0.923662 | ||||||||
\(557\) | 39.2374 | 1.66254 | 0.831272 | − | 0.555866i | \(-0.187613\pi\) | ||||
0.831272 | + | 0.555866i | \(0.187613\pi\) | |||||||
\(558\) | −3.38920 | −0.143476 | ||||||||
\(559\) | −37.9765 | −1.60624 | ||||||||
\(560\) | 12.2867 | 0.519208 | ||||||||
\(561\) | 14.2750 | 0.602692 | ||||||||
\(562\) | −23.1767 | −0.977652 | ||||||||
\(563\) | 5.68412 | 0.239557 | 0.119779 | − | 0.992801i | \(-0.461782\pi\) | ||||
0.119779 | + | 0.992801i | \(0.461782\pi\) | |||||||
\(564\) | 5.85750 | 0.246645 | ||||||||
\(565\) | 4.82504 | 0.202991 | ||||||||
\(566\) | −11.4998 | −0.483372 | ||||||||
\(567\) | 42.9804 | 1.80501 | ||||||||
\(568\) | −5.59111 | −0.234598 | ||||||||
\(569\) | −29.3431 | −1.23013 | −0.615063 | − | 0.788478i | \(-0.710870\pi\) | ||||
−0.615063 | + | 0.788478i | \(0.710870\pi\) | |||||||
\(570\) | 37.0235 | 1.55074 | ||||||||
\(571\) | 11.0184 | 0.461104 | 0.230552 | − | 0.973060i | \(-0.425947\pi\) | ||||
0.230552 | + | 0.973060i | \(0.425947\pi\) | |||||||
\(572\) | 25.6352 | 1.07186 | ||||||||
\(573\) | 12.9023 | 0.539001 | ||||||||
\(574\) | 10.5510 | 0.440390 | ||||||||
\(575\) | 4.71218 | 0.196511 | ||||||||
\(576\) | 0.909824 | 0.0379093 | ||||||||
\(577\) | 11.9946 | 0.499340 | 0.249670 | − | 0.968331i | \(-0.419678\pi\) | ||||
0.249670 | + | 0.968331i | \(0.419678\pi\) | |||||||
\(578\) | 14.4546 | 0.601234 | ||||||||
\(579\) | 29.4348 | 1.22327 | ||||||||
\(580\) | 15.7437 | 0.653721 | ||||||||
\(581\) | 38.6715 | 1.60437 | ||||||||
\(582\) | 29.2566 | 1.21272 | ||||||||
\(583\) | 9.23542 | 0.382492 | ||||||||
\(584\) | 13.5640 | 0.561282 | ||||||||
\(585\) | 16.0631 | 0.664126 | ||||||||
\(586\) | 7.09097 | 0.292925 | ||||||||
\(587\) | 1.99332 | 0.0822732 | 0.0411366 | − | 0.999154i | \(-0.486902\pi\) | ||||
0.0411366 | + | 0.999154i | \(0.486902\pi\) | |||||||
\(588\) | −16.8937 | −0.696683 | ||||||||
\(589\) | −22.3811 | −0.922196 | ||||||||
\(590\) | 5.86005 | 0.241254 | ||||||||
\(591\) | −31.3506 | −1.28959 | ||||||||
\(592\) | 3.72100 | 0.152932 | ||||||||
\(593\) | −28.3687 | −1.16496 | −0.582481 | − | 0.812844i | \(-0.697918\pi\) | ||||
−0.582481 | + | 0.812844i | \(0.697918\pi\) | |||||||
\(594\) | 18.7019 | 0.767349 | ||||||||
\(595\) | 19.6024 | 0.803620 | ||||||||
\(596\) | −15.8438 | −0.648988 | ||||||||
\(597\) | −47.9879 | −1.96401 | ||||||||
\(598\) | 5.66517 | 0.231666 | ||||||||
\(599\) | 34.7442 | 1.41961 | 0.709806 | − | 0.704398i | \(-0.248783\pi\) | ||||
0.709806 | + | 0.704398i | \(0.248783\pi\) | |||||||
\(600\) | 9.31752 | 0.380386 | ||||||||
\(601\) | 15.4051 | 0.628388 | 0.314194 | − | 0.949359i | \(-0.398266\pi\) | ||||
0.314194 | + | 0.949359i | \(0.398266\pi\) | |||||||
\(602\) | 26.4289 | 1.07716 | ||||||||
\(603\) | 4.19799 | 0.170955 | ||||||||
\(604\) | −4.72329 | −0.192188 | ||||||||
\(605\) | −29.5320 | −1.20065 | ||||||||
\(606\) | 25.2090 | 1.02405 | ||||||||
\(607\) | 42.5316 | 1.72631 | 0.863153 | − | 0.504942i | \(-0.168486\pi\) | ||||
0.863153 | + | 0.504942i | \(0.168486\pi\) | |||||||
\(608\) | 6.00815 | 0.243663 | ||||||||
\(609\) | −39.3825 | −1.59586 | ||||||||
\(610\) | 7.97404 | 0.322859 | ||||||||
\(611\) | 16.7821 | 0.678932 | ||||||||
\(612\) | 1.45155 | 0.0586753 | ||||||||
\(613\) | −43.7597 | −1.76744 | −0.883719 | − | 0.468018i | \(-0.844968\pi\) | ||||
−0.883719 | + | 0.468018i | \(0.844968\pi\) | |||||||
\(614\) | 13.5874 | 0.548341 | ||||||||
\(615\) | 16.4912 | 0.664991 | ||||||||
\(616\) | −17.8403 | −0.718805 | ||||||||
\(617\) | 33.3336 | 1.34196 | 0.670979 | − | 0.741476i | \(-0.265874\pi\) | ||||
0.670979 | + | 0.741476i | \(0.265874\pi\) | |||||||
\(618\) | 7.71171 | 0.310210 | ||||||||
\(619\) | 10.4754 | 0.421044 | 0.210522 | − | 0.977589i | \(-0.432484\pi\) | ||||
0.210522 | + | 0.977589i | \(0.432484\pi\) | |||||||
\(620\) | −11.6091 | −0.466232 | ||||||||
\(621\) | 4.13296 | 0.165850 | ||||||||
\(622\) | −24.9892 | −1.00197 | ||||||||
\(623\) | 1.40229 | 0.0561816 | ||||||||
\(624\) | 11.2019 | 0.448435 | ||||||||
\(625\) | −26.3563 | −1.05425 | ||||||||
\(626\) | −25.5324 | −1.02048 | ||||||||
\(627\) | −53.7581 | −2.14689 | ||||||||
\(628\) | 6.34927 | 0.253363 | ||||||||
\(629\) | 5.93654 | 0.236705 | ||||||||
\(630\) | −11.1787 | −0.445371 | ||||||||
\(631\) | −39.8346 | −1.58579 | −0.792895 | − | 0.609359i | \(-0.791427\pi\) | ||||
−0.792895 | + | 0.609359i | \(0.791427\pi\) | |||||||
\(632\) | 14.9962 | 0.596516 | ||||||||
\(633\) | −19.7974 | −0.786876 | ||||||||
\(634\) | −18.1255 | −0.719857 | ||||||||
\(635\) | 21.5893 | 0.856744 | ||||||||
\(636\) | 4.03562 | 0.160023 | ||||||||
\(637\) | −48.4014 | −1.91773 | ||||||||
\(638\) | −22.8598 | −0.905029 | ||||||||
\(639\) | 5.08693 | 0.201236 | ||||||||
\(640\) | 3.11644 | 0.123188 | ||||||||
\(641\) | 20.4704 | 0.808532 | 0.404266 | − | 0.914642i | \(-0.367527\pi\) | ||||
0.404266 | + | 0.914642i | \(0.367527\pi\) | |||||||
\(642\) | 11.2094 | 0.442398 | ||||||||
\(643\) | −28.6994 | −1.13179 | −0.565897 | − | 0.824476i | \(-0.691470\pi\) | ||||
−0.565897 | + | 0.824476i | \(0.691470\pi\) | |||||||
\(644\) | −3.94255 | −0.155358 | ||||||||
\(645\) | 41.3085 | 1.62652 | ||||||||
\(646\) | 9.58550 | 0.377136 | ||||||||
\(647\) | −28.2430 | −1.11035 | −0.555173 | − | 0.831735i | \(-0.687348\pi\) | ||||
−0.555173 | + | 0.831735i | \(0.687348\pi\) | |||||||
\(648\) | 10.9017 | 0.428259 | ||||||||
\(649\) | −8.50878 | −0.333999 | ||||||||
\(650\) | 26.6953 | 1.04707 | ||||||||
\(651\) | 29.0399 | 1.13816 | ||||||||
\(652\) | −17.4955 | −0.685176 | ||||||||
\(653\) | 17.9053 | 0.700690 | 0.350345 | − | 0.936621i | \(-0.386064\pi\) | ||||
0.350345 | + | 0.936621i | \(0.386064\pi\) | |||||||
\(654\) | −18.3261 | −0.716607 | ||||||||
\(655\) | −3.11644 | −0.121769 | ||||||||
\(656\) | 2.67619 | 0.104488 | ||||||||
\(657\) | −12.3408 | −0.481462 | ||||||||
\(658\) | −11.6791 | −0.455300 | ||||||||
\(659\) | −4.99041 | −0.194399 | −0.0971993 | − | 0.995265i | \(-0.530988\pi\) | ||||
−0.0971993 | + | 0.995265i | \(0.530988\pi\) | |||||||
\(660\) | −27.8844 | −1.08540 | ||||||||
\(661\) | 5.56723 | 0.216540 | 0.108270 | − | 0.994122i | \(-0.465469\pi\) | ||||
0.108270 | + | 0.994122i | \(0.465469\pi\) | |||||||
\(662\) | 34.6744 | 1.34766 | ||||||||
\(663\) | 17.8717 | 0.694078 | ||||||||
\(664\) | 9.80877 | 0.380654 | ||||||||
\(665\) | −73.8204 | −2.86263 | ||||||||
\(666\) | −3.38545 | −0.131184 | ||||||||
\(667\) | −5.05182 | −0.195607 | ||||||||
\(668\) | 6.62277 | 0.256243 | ||||||||
\(669\) | −22.1110 | −0.854861 | ||||||||
\(670\) | 14.3795 | 0.555527 | ||||||||
\(671\) | −11.5783 | −0.446975 | ||||||||
\(672\) | −7.79571 | −0.300726 | ||||||||
\(673\) | 35.3453 | 1.36246 | 0.681230 | − | 0.732069i | \(-0.261445\pi\) | ||||
0.681230 | + | 0.732069i | \(0.261445\pi\) | |||||||
\(674\) | −2.21349 | −0.0852606 | ||||||||
\(675\) | 19.4753 | 0.749603 | ||||||||
\(676\) | 19.0941 | 0.734389 | ||||||||
\(677\) | 32.6139 | 1.25345 | 0.626727 | − | 0.779239i | \(-0.284394\pi\) | ||||
0.626727 | + | 0.779239i | \(0.284394\pi\) | |||||||
\(678\) | −3.06141 | −0.117573 | ||||||||
\(679\) | −58.3340 | −2.23865 | ||||||||
\(680\) | 4.97201 | 0.190668 | ||||||||
\(681\) | 48.7625 | 1.86858 | ||||||||
\(682\) | 16.8564 | 0.645464 | ||||||||
\(683\) | 33.5964 | 1.28553 | 0.642766 | − | 0.766063i | \(-0.277787\pi\) | ||||
0.642766 | + | 0.766063i | \(0.277787\pi\) | |||||||
\(684\) | −5.46636 | −0.209011 | ||||||||
\(685\) | −53.0005 | −2.02504 | ||||||||
\(686\) | 6.08604 | 0.232366 | ||||||||
\(687\) | −32.8230 | −1.25228 | ||||||||
\(688\) | 6.70351 | 0.255569 | ||||||||
\(689\) | 11.5623 | 0.440489 | ||||||||
\(690\) | −6.16222 | −0.234592 | ||||||||
\(691\) | 19.3313 | 0.735396 | 0.367698 | − | 0.929945i | \(-0.380146\pi\) | ||||
0.367698 | + | 0.929945i | \(0.380146\pi\) | |||||||
\(692\) | 16.2181 | 0.616519 | ||||||||
\(693\) | 16.2315 | 0.616584 | ||||||||
\(694\) | 16.0471 | 0.609138 | ||||||||
\(695\) | 67.8748 | 2.57464 | ||||||||
\(696\) | −9.98911 | −0.378636 | ||||||||
\(697\) | 4.26963 | 0.161724 | ||||||||
\(698\) | −0.832866 | −0.0315244 | ||||||||
\(699\) | 0.693559 | 0.0262328 | ||||||||
\(700\) | −18.5780 | −0.702182 | ||||||||
\(701\) | −2.76789 | −0.104542 | −0.0522709 | − | 0.998633i | \(-0.516646\pi\) | ||||
−0.0522709 | + | 0.998633i | \(0.516646\pi\) | |||||||
\(702\) | 23.4139 | 0.883702 | ||||||||
\(703\) | −22.3563 | −0.843185 | ||||||||
\(704\) | −4.52506 | −0.170545 | ||||||||
\(705\) | −18.2545 | −0.687506 | ||||||||
\(706\) | 1.78388 | 0.0671371 | ||||||||
\(707\) | −50.2636 | −1.89036 | ||||||||
\(708\) | −3.71810 | −0.139735 | ||||||||
\(709\) | 26.9589 | 1.01246 | 0.506231 | − | 0.862398i | \(-0.331038\pi\) | ||||
0.506231 | + | 0.862398i | \(0.331038\pi\) | |||||||
\(710\) | 17.4243 | 0.653924 | ||||||||
\(711\) | −13.6439 | −0.511685 | ||||||||
\(712\) | 0.355681 | 0.0133297 | ||||||||
\(713\) | 3.72512 | 0.139507 | ||||||||
\(714\) | −12.4374 | −0.465458 | ||||||||
\(715\) | −79.8906 | −2.98774 | ||||||||
\(716\) | −10.3870 | −0.388180 | ||||||||
\(717\) | 23.6445 | 0.883019 | ||||||||
\(718\) | −23.3295 | −0.870651 | ||||||||
\(719\) | 11.9081 | 0.444096 | 0.222048 | − | 0.975036i | \(-0.428726\pi\) | ||||
0.222048 | + | 0.975036i | \(0.428726\pi\) | |||||||
\(720\) | −2.83541 | −0.105669 | ||||||||
\(721\) | −15.3762 | −0.572639 | ||||||||
\(722\) | −17.0979 | −0.636318 | ||||||||
\(723\) | 11.0041 | 0.409249 | ||||||||
\(724\) | 6.04645 | 0.224715 | ||||||||
\(725\) | −23.8051 | −0.884099 | ||||||||
\(726\) | 18.7375 | 0.695416 | ||||||||
\(727\) | 48.3390 | 1.79280 | 0.896398 | − | 0.443251i | \(-0.146175\pi\) | ||||
0.896398 | + | 0.443251i | \(0.146175\pi\) | |||||||
\(728\) | −22.3352 | −0.827797 | ||||||||
\(729\) | 14.5980 | 0.540668 | ||||||||
\(730\) | −42.2713 | −1.56453 | ||||||||
\(731\) | 10.6949 | 0.395565 | ||||||||
\(732\) | −5.05939 | −0.187001 | ||||||||
\(733\) | −20.4702 | −0.756085 | −0.378042 | − | 0.925788i | \(-0.623403\pi\) | ||||
−0.378042 | + | 0.925788i | \(0.623403\pi\) | |||||||
\(734\) | −15.1016 | −0.557412 | ||||||||
\(735\) | 52.6480 | 1.94195 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −20.8790 | −0.769086 | ||||||||
\(738\) | −2.43486 | −0.0896284 | ||||||||
\(739\) | 28.3826 | 1.04407 | 0.522035 | − | 0.852924i | \(-0.325173\pi\) | ||||
0.522035 | + | 0.852924i | \(0.325173\pi\) | |||||||
\(740\) | −11.5963 | −0.426287 | ||||||||
\(741\) | −67.3027 | −2.47243 | ||||||||
\(742\) | −8.04653 | −0.295397 | ||||||||
\(743\) | 39.3924 | 1.44517 | 0.722583 | − | 0.691284i | \(-0.242955\pi\) | ||||
0.722583 | + | 0.691284i | \(0.242955\pi\) | |||||||
\(744\) | 7.36577 | 0.270042 | ||||||||
\(745\) | 49.3763 | 1.80901 | ||||||||
\(746\) | −23.2013 | −0.849461 | ||||||||
\(747\) | −8.92425 | −0.326521 | ||||||||
\(748\) | −7.21936 | −0.263966 | ||||||||
\(749\) | −22.3501 | −0.816655 | ||||||||
\(750\) | 1.77363 | 0.0647637 | ||||||||
\(751\) | −39.3187 | −1.43476 | −0.717380 | − | 0.696682i | \(-0.754659\pi\) | ||||
−0.717380 | + | 0.696682i | \(0.754659\pi\) | |||||||
\(752\) | −2.96233 | −0.108025 | ||||||||
\(753\) | 18.8069 | 0.685362 | ||||||||
\(754\) | −28.6194 | −1.04226 | ||||||||
\(755\) | 14.7198 | 0.535710 | ||||||||
\(756\) | −16.2944 | −0.592622 | ||||||||
\(757\) | −0.804958 | −0.0292567 | −0.0146283 | − | 0.999893i | \(-0.504657\pi\) | ||||
−0.0146283 | + | 0.999893i | \(0.504657\pi\) | |||||||
\(758\) | 11.2140 | 0.407313 | ||||||||
\(759\) | 8.94753 | 0.324775 | ||||||||
\(760\) | −18.7240 | −0.679192 | ||||||||
\(761\) | 45.8676 | 1.66270 | 0.831350 | − | 0.555750i | \(-0.187569\pi\) | ||||
0.831350 | + | 0.555750i | \(0.187569\pi\) | |||||||
\(762\) | −13.6980 | −0.496227 | ||||||||
\(763\) | 36.5400 | 1.32284 | ||||||||
\(764\) | −6.52512 | −0.236070 | ||||||||
\(765\) | −4.52365 | −0.163553 | ||||||||
\(766\) | −30.6759 | −1.10837 | ||||||||
\(767\) | −10.6526 | −0.384643 | ||||||||
\(768\) | −1.97733 | −0.0713507 | ||||||||
\(769\) | −38.1167 | −1.37452 | −0.687262 | − | 0.726410i | \(-0.741187\pi\) | ||||
−0.687262 | + | 0.726410i | \(0.741187\pi\) | |||||||
\(770\) | 55.5981 | 2.00362 | ||||||||
\(771\) | −6.36138 | −0.229100 | ||||||||
\(772\) | −14.8862 | −0.535764 | ||||||||
\(773\) | −44.4507 | −1.59878 | −0.799390 | − | 0.600812i | \(-0.794844\pi\) | ||||
−0.799390 | + | 0.600812i | \(0.794844\pi\) | |||||||
\(774\) | −6.09901 | −0.219225 | ||||||||
\(775\) | 17.5534 | 0.630537 | ||||||||
\(776\) | −14.7960 | −0.531146 | ||||||||
\(777\) | 29.0078 | 1.04065 | ||||||||
\(778\) | 23.4690 | 0.841404 | ||||||||
\(779\) | −16.0789 | −0.576088 | ||||||||
\(780\) | −34.9100 | −1.24998 | ||||||||
\(781\) | −25.3001 | −0.905310 | ||||||||
\(782\) | −1.59542 | −0.0570520 | ||||||||
\(783\) | −20.8790 | −0.746155 | ||||||||
\(784\) | 8.54368 | 0.305131 | ||||||||
\(785\) | −19.7871 | −0.706232 | ||||||||
\(786\) | 1.97733 | 0.0705289 | ||||||||
\(787\) | 3.59343 | 0.128092 | 0.0640460 | − | 0.997947i | \(-0.479600\pi\) | ||||
0.0640460 | + | 0.997947i | \(0.479600\pi\) | |||||||
\(788\) | 15.8551 | 0.564813 | ||||||||
\(789\) | −44.4206 | −1.58141 | ||||||||
\(790\) | −46.7346 | −1.66274 | ||||||||
\(791\) | 6.10407 | 0.217036 | ||||||||
\(792\) | 4.11701 | 0.146292 | ||||||||
\(793\) | −14.4955 | −0.514750 | ||||||||
\(794\) | −7.94589 | −0.281989 | ||||||||
\(795\) | −12.5768 | −0.446052 | ||||||||
\(796\) | 24.2691 | 0.860194 | ||||||||
\(797\) | 20.5921 | 0.729409 | 0.364705 | − | 0.931123i | \(-0.381170\pi\) | ||||
0.364705 | + | 0.931123i | \(0.381170\pi\) | |||||||
\(798\) | 46.8378 | 1.65804 | ||||||||
\(799\) | −4.72615 | −0.167199 | ||||||||
\(800\) | −4.71218 | −0.166601 | ||||||||
\(801\) | −0.323607 | −0.0114341 | ||||||||
\(802\) | −4.89362 | −0.172800 | ||||||||
\(803\) | 61.3779 | 2.16598 | ||||||||
\(804\) | −9.12353 | −0.321762 | ||||||||
\(805\) | 12.2867 | 0.433049 | ||||||||
\(806\) | 21.1034 | 0.743336 | ||||||||
\(807\) | −7.96682 | −0.280445 | ||||||||
\(808\) | −12.7490 | −0.448509 | ||||||||
\(809\) | 33.2797 | 1.17005 | 0.585027 | − | 0.811014i | \(-0.301084\pi\) | ||||
0.585027 | + | 0.811014i | \(0.301084\pi\) | |||||||
\(810\) | −33.9744 | −1.19374 | ||||||||
\(811\) | −17.4713 | −0.613500 | −0.306750 | − | 0.951790i | \(-0.599242\pi\) | ||||
−0.306750 | + | 0.951790i | \(0.599242\pi\) | |||||||
\(812\) | 19.9171 | 0.698952 | ||||||||
\(813\) | 27.7638 | 0.973719 | ||||||||
\(814\) | 16.8378 | 0.590163 | ||||||||
\(815\) | 54.5235 | 1.90988 | ||||||||
\(816\) | −3.15466 | −0.110435 | ||||||||
\(817\) | −40.2757 | −1.40907 | ||||||||
\(818\) | 0.0432583 | 0.00151249 | ||||||||
\(819\) | 20.3211 | 0.710076 | ||||||||
\(820\) | −8.34017 | −0.291251 | ||||||||
\(821\) | 9.97398 | 0.348094 | 0.174047 | − | 0.984737i | \(-0.444315\pi\) | ||||
0.174047 | + | 0.984737i | \(0.444315\pi\) | |||||||
\(822\) | 33.6279 | 1.17291 | ||||||||
\(823\) | 36.5017 | 1.27237 | 0.636185 | − | 0.771537i | \(-0.280512\pi\) | ||||
0.636185 | + | 0.771537i | \(0.280512\pi\) | |||||||
\(824\) | −3.90007 | −0.135865 | ||||||||
\(825\) | 42.1624 | 1.46790 | ||||||||
\(826\) | 7.41344 | 0.257947 | ||||||||
\(827\) | −2.20329 | −0.0766158 | −0.0383079 | − | 0.999266i | \(-0.512197\pi\) | ||||
−0.0383079 | + | 0.999266i | \(0.512197\pi\) | |||||||
\(828\) | 0.909824 | 0.0316186 | ||||||||
\(829\) | −55.8744 | −1.94060 | −0.970299 | − | 0.241909i | \(-0.922226\pi\) | ||||
−0.970299 | + | 0.241909i | \(0.922226\pi\) | |||||||
\(830\) | −30.5684 | −1.06104 | ||||||||
\(831\) | 0.970235 | 0.0336571 | ||||||||
\(832\) | −5.66517 | −0.196404 | ||||||||
\(833\) | 13.6307 | 0.472277 | ||||||||
\(834\) | −43.0654 | −1.49123 | ||||||||
\(835\) | −20.6394 | −0.714257 | ||||||||
\(836\) | 27.1873 | 0.940291 | ||||||||
\(837\) | 15.3958 | 0.532156 | ||||||||
\(838\) | 8.25349 | 0.285112 | ||||||||
\(839\) | −24.0039 | −0.828708 | −0.414354 | − | 0.910116i | \(-0.635992\pi\) | ||||
−0.414354 | + | 0.910116i | \(0.635992\pi\) | |||||||
\(840\) | 24.2948 | 0.838251 | ||||||||
\(841\) | −3.47907 | −0.119968 | ||||||||
\(842\) | 9.71405 | 0.334768 | ||||||||
\(843\) | −45.8280 | −1.57840 | ||||||||
\(844\) | 10.0122 | 0.344634 | ||||||||
\(845\) | −59.5056 | −2.04706 | ||||||||
\(846\) | 2.69520 | 0.0926629 | ||||||||
\(847\) | −37.3604 | −1.28372 | ||||||||
\(848\) | −2.04095 | −0.0700864 | ||||||||
\(849\) | −22.7389 | −0.780395 | ||||||||
\(850\) | −7.51788 | −0.257861 | ||||||||
\(851\) | 3.72100 | 0.127554 | ||||||||
\(852\) | −11.0555 | −0.378754 | ||||||||
\(853\) | −7.28720 | −0.249509 | −0.124754 | − | 0.992188i | \(-0.539814\pi\) | ||||
−0.124754 | + | 0.992188i | \(0.539814\pi\) | |||||||
\(854\) | 10.0878 | 0.345198 | ||||||||
\(855\) | 17.0356 | 0.582604 | ||||||||
\(856\) | −5.66895 | −0.193761 | ||||||||
\(857\) | −46.5179 | −1.58902 | −0.794510 | − | 0.607250i | \(-0.792272\pi\) | ||||
−0.794510 | + | 0.607250i | \(0.792272\pi\) | |||||||
\(858\) | 50.6893 | 1.73050 | ||||||||
\(859\) | −22.0739 | −0.753150 | −0.376575 | − | 0.926386i | \(-0.622898\pi\) | ||||
−0.376575 | + | 0.926386i | \(0.622898\pi\) | |||||||
\(860\) | −20.8911 | −0.712380 | ||||||||
\(861\) | 20.8628 | 0.711001 | ||||||||
\(862\) | 5.93987 | 0.202313 | ||||||||
\(863\) | −20.9086 | −0.711738 | −0.355869 | − | 0.934536i | \(-0.615815\pi\) | ||||
−0.355869 | + | 0.934536i | \(0.615815\pi\) | |||||||
\(864\) | −4.13296 | −0.140606 | ||||||||
\(865\) | −50.5426 | −1.71850 | ||||||||
\(866\) | −12.8952 | −0.438197 | ||||||||
\(867\) | 28.5816 | 0.970681 | ||||||||
\(868\) | −14.6864 | −0.498491 | ||||||||
\(869\) | 67.8586 | 2.30195 | ||||||||
\(870\) | 31.1304 | 1.05542 | ||||||||
\(871\) | −26.1395 | −0.885703 | ||||||||
\(872\) | 9.26812 | 0.313858 | ||||||||
\(873\) | 13.4618 | 0.455612 | ||||||||
\(874\) | 6.00815 | 0.203229 | ||||||||
\(875\) | −3.53639 | −0.119552 | ||||||||
\(876\) | 26.8205 | 0.906179 | ||||||||
\(877\) | −4.40947 | −0.148897 | −0.0744485 | − | 0.997225i | \(-0.523720\pi\) | ||||
−0.0744485 | + | 0.997225i | \(0.523720\pi\) | |||||||
\(878\) | 29.7579 | 1.00428 | ||||||||
\(879\) | 14.0212 | 0.472922 | ||||||||
\(880\) | 14.1021 | 0.475381 | ||||||||
\(881\) | 24.8428 | 0.836974 | 0.418487 | − | 0.908223i | \(-0.362560\pi\) | ||||
0.418487 | + | 0.908223i | \(0.362560\pi\) | |||||||
\(882\) | −7.77324 | −0.261739 | ||||||||
\(883\) | 13.9687 | 0.470085 | 0.235043 | − | 0.971985i | \(-0.424477\pi\) | ||||
0.235043 | + | 0.971985i | \(0.424477\pi\) | |||||||
\(884\) | −9.03830 | −0.303991 | ||||||||
\(885\) | 11.5872 | 0.389501 | ||||||||
\(886\) | 27.7112 | 0.930976 | ||||||||
\(887\) | −46.7212 | −1.56874 | −0.784372 | − | 0.620291i | \(-0.787014\pi\) | ||||
−0.784372 | + | 0.620291i | \(0.787014\pi\) | |||||||
\(888\) | 7.35763 | 0.246906 | ||||||||
\(889\) | 27.3122 | 0.916022 | ||||||||
\(890\) | −1.10846 | −0.0371556 | ||||||||
\(891\) | 49.3308 | 1.65265 | ||||||||
\(892\) | 11.1823 | 0.374410 | ||||||||
\(893\) | 17.7982 | 0.595593 | ||||||||
\(894\) | −31.3284 | −1.04778 | ||||||||
\(895\) | 32.3704 | 1.08202 | ||||||||
\(896\) | 3.94255 | 0.131711 | ||||||||
\(897\) | 11.2019 | 0.374020 | ||||||||
\(898\) | 7.22774 | 0.241193 | ||||||||
\(899\) | −18.8186 | −0.627637 | ||||||||
\(900\) | 4.28725 | 0.142908 | ||||||||
\(901\) | −3.25616 | −0.108478 | ||||||||
\(902\) | 12.1099 | 0.403216 | ||||||||
\(903\) | 52.2586 | 1.73906 | ||||||||
\(904\) | 1.54825 | 0.0514942 | ||||||||
\(905\) | −18.8434 | −0.626375 | ||||||||
\(906\) | −9.33950 | −0.310284 | ||||||||
\(907\) | −9.55540 | −0.317282 | −0.158641 | − | 0.987336i | \(-0.550711\pi\) | ||||
−0.158641 | + | 0.987336i | \(0.550711\pi\) | |||||||
\(908\) | −24.6608 | −0.818399 | ||||||||
\(909\) | 11.5994 | 0.384726 | ||||||||
\(910\) | 69.6062 | 2.30742 | ||||||||
\(911\) | −16.8585 | −0.558548 | −0.279274 | − | 0.960211i | \(-0.590094\pi\) | ||||
−0.279274 | + | 0.960211i | \(0.590094\pi\) | |||||||
\(912\) | 11.8801 | 0.393389 | ||||||||
\(913\) | 44.3853 | 1.46894 | ||||||||
\(914\) | 36.5408 | 1.20866 | ||||||||
\(915\) | 15.7673 | 0.521250 | ||||||||
\(916\) | 16.5997 | 0.548469 | ||||||||
\(917\) | −3.94255 | −0.130194 | ||||||||
\(918\) | −6.59379 | −0.217628 | ||||||||
\(919\) | −39.6299 | −1.30727 | −0.653635 | − | 0.756810i | \(-0.726757\pi\) | ||||
−0.653635 | + | 0.756810i | \(0.726757\pi\) | |||||||
\(920\) | 3.11644 | 0.102746 | ||||||||
\(921\) | 26.8667 | 0.885287 | ||||||||
\(922\) | 4.30028 | 0.141622 | ||||||||
\(923\) | −31.6746 | −1.04258 | ||||||||
\(924\) | −35.2761 | −1.16050 | ||||||||
\(925\) | 17.5340 | 0.576514 | ||||||||
\(926\) | −18.5138 | −0.608401 | ||||||||
\(927\) | 3.54837 | 0.116544 | ||||||||
\(928\) | 5.05182 | 0.165834 | ||||||||
\(929\) | −10.5940 | −0.347578 | −0.173789 | − | 0.984783i | \(-0.555601\pi\) | ||||
−0.173789 | + | 0.984783i | \(0.555601\pi\) | |||||||
\(930\) | −22.9550 | −0.752723 | ||||||||
\(931\) | −51.3317 | −1.68233 | ||||||||
\(932\) | −0.350756 | −0.0114894 | ||||||||
\(933\) | −49.4118 | −1.61767 | ||||||||
\(934\) | −14.3610 | −0.469905 | ||||||||
\(935\) | 22.4987 | 0.735785 | ||||||||
\(936\) | 5.15430 | 0.168474 | ||||||||
\(937\) | 30.0662 | 0.982219 | 0.491110 | − | 0.871098i | \(-0.336591\pi\) | ||||
0.491110 | + | 0.871098i | \(0.336591\pi\) | |||||||
\(938\) | 18.1912 | 0.593963 | ||||||||
\(939\) | −50.4858 | −1.64754 | ||||||||
\(940\) | 9.23193 | 0.301112 | ||||||||
\(941\) | 32.7494 | 1.06760 | 0.533801 | − | 0.845610i | \(-0.320763\pi\) | ||||
0.533801 | + | 0.845610i | \(0.320763\pi\) | |||||||
\(942\) | 12.5546 | 0.409050 | ||||||||
\(943\) | 2.67619 | 0.0871486 | ||||||||
\(944\) | 1.88037 | 0.0612008 | ||||||||
\(945\) | 50.7805 | 1.65189 | ||||||||
\(946\) | 30.3338 | 0.986238 | ||||||||
\(947\) | −44.7569 | −1.45440 | −0.727202 | − | 0.686423i | \(-0.759180\pi\) | ||||
−0.727202 | + | 0.686423i | \(0.759180\pi\) | |||||||
\(948\) | 29.6523 | 0.963063 | ||||||||
\(949\) | 76.8423 | 2.49441 | ||||||||
\(950\) | 28.3115 | 0.918546 | ||||||||
\(951\) | −35.8401 | −1.16220 | ||||||||
\(952\) | 6.29000 | 0.203860 | ||||||||
\(953\) | 21.2296 | 0.687694 | 0.343847 | − | 0.939026i | \(-0.388270\pi\) | ||||
0.343847 | + | 0.939026i | \(0.388270\pi\) | |||||||
\(954\) | 1.85690 | 0.0601194 | ||||||||
\(955\) | 20.3351 | 0.658029 | ||||||||
\(956\) | −11.9578 | −0.386743 | ||||||||
\(957\) | −45.2014 | −1.46115 | ||||||||
\(958\) | −19.0808 | −0.616474 | ||||||||
\(959\) | −67.0499 | −2.16515 | ||||||||
\(960\) | 6.16222 | 0.198885 | ||||||||
\(961\) | −17.1235 | −0.552371 | ||||||||
\(962\) | 21.0801 | 0.679649 | ||||||||
\(963\) | 5.15774 | 0.166206 | ||||||||
\(964\) | −5.56516 | −0.179242 | ||||||||
\(965\) | 46.3917 | 1.49340 | ||||||||
\(966\) | −7.79571 | −0.250823 | ||||||||
\(967\) | −6.33670 | −0.203774 | −0.101887 | − | 0.994796i | \(-0.532488\pi\) | ||||
−0.101887 | + | 0.994796i | \(0.532488\pi\) | |||||||
\(968\) | −9.47620 | −0.304577 | ||||||||
\(969\) | 18.9537 | 0.608880 | ||||||||
\(970\) | 46.1109 | 1.48053 | ||||||||
\(971\) | 47.5951 | 1.52740 | 0.763700 | − | 0.645572i | \(-0.223381\pi\) | ||||
0.763700 | + | 0.645572i | \(0.223381\pi\) | |||||||
\(972\) | 9.15732 | 0.293721 | ||||||||
\(973\) | 85.8672 | 2.75278 | ||||||||
\(974\) | 36.4821 | 1.16896 | ||||||||
\(975\) | 52.7853 | 1.69048 | ||||||||
\(976\) | 2.55870 | 0.0819021 | ||||||||
\(977\) | 29.3380 | 0.938606 | 0.469303 | − | 0.883037i | \(-0.344505\pi\) | ||||
0.469303 | + | 0.883037i | \(0.344505\pi\) | |||||||
\(978\) | −34.5943 | −1.10620 | ||||||||
\(979\) | 1.60948 | 0.0514392 | ||||||||
\(980\) | −26.6258 | −0.850531 | ||||||||
\(981\) | −8.43235 | −0.269224 | ||||||||
\(982\) | −15.9047 | −0.507540 | ||||||||
\(983\) | −38.5444 | −1.22938 | −0.614688 | − | 0.788770i | \(-0.710718\pi\) | ||||
−0.614688 | + | 0.788770i | \(0.710718\pi\) | |||||||
\(984\) | 5.29170 | 0.168693 | ||||||||
\(985\) | −49.4113 | −1.57437 | ||||||||
\(986\) | 8.05976 | 0.256675 | ||||||||
\(987\) | −23.0935 | −0.735074 | ||||||||
\(988\) | 34.0372 | 1.08287 | ||||||||
\(989\) | 6.70351 | 0.213159 | ||||||||
\(990\) | −12.8304 | −0.407777 | ||||||||
\(991\) | −32.7952 | −1.04177 | −0.520887 | − | 0.853626i | \(-0.674399\pi\) | ||||
−0.520887 | + | 0.853626i | \(0.674399\pi\) | |||||||
\(992\) | −3.72512 | −0.118273 | ||||||||
\(993\) | 68.5626 | 2.17577 | ||||||||
\(994\) | 22.0432 | 0.699169 | ||||||||
\(995\) | −75.6330 | −2.39773 | ||||||||
\(996\) | 19.3951 | 0.614559 | ||||||||
\(997\) | −28.8581 | −0.913945 | −0.456972 | − | 0.889481i | \(-0.651066\pi\) | ||||
−0.456972 | + | 0.889481i | \(0.651066\pi\) | |||||||
\(998\) | 26.2569 | 0.831149 | ||||||||
\(999\) | 15.3787 | 0.486562 |
(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 | 6026.2.a.i.1.7 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.i.1.7 | ✓ | 25 | 1.1 | even | 1 | trivial |