Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8006,2,Mod(1,8006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8006, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8006 = 2 \cdot 4003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8006.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: | \(63.9282318582\) |
Analytic rank: | \(0\) |
Dimension: | \(98\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 8006.1 |
$q$-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 | ||||||||
\(3\) | −2.29904 | −1.32735 | −0.663676 | − | 0.748020i | \(-0.731005\pi\) | ||||
−0.663676 | + | 0.748020i | \(0.731005\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.379667 | −0.169792 | −0.0848961 | − | 0.996390i | \(-0.527056\pi\) | ||||
−0.0848961 | + | 0.996390i | \(0.527056\pi\) | |||||||
\(6\) | −2.29904 | −0.938579 | ||||||||
\(7\) | −2.21994 | −0.839058 | −0.419529 | − | 0.907742i | \(-0.637805\pi\) | ||||
−0.419529 | + | 0.907742i | \(0.637805\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.28559 | 0.761862 | ||||||||
\(10\) | −0.379667 | −0.120061 | ||||||||
\(11\) | −3.25470 | −0.981329 | −0.490665 | − | 0.871348i | \(-0.663246\pi\) | ||||
−0.490665 | + | 0.871348i | \(0.663246\pi\) | |||||||
\(12\) | −2.29904 | −0.663676 | ||||||||
\(13\) | −0.129405 | −0.0358904 | −0.0179452 | − | 0.999839i | \(-0.505712\pi\) | ||||
−0.0179452 | + | 0.999839i | \(0.505712\pi\) | |||||||
\(14\) | −2.21994 | −0.593303 | ||||||||
\(15\) | 0.872870 | 0.225374 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.78903 | −0.918974 | −0.459487 | − | 0.888184i | \(-0.651967\pi\) | ||||
−0.459487 | + | 0.888184i | \(0.651967\pi\) | |||||||
\(18\) | 2.28559 | 0.538718 | ||||||||
\(19\) | 7.10879 | 1.63087 | 0.815434 | − | 0.578850i | \(-0.196498\pi\) | ||||
0.815434 | + | 0.578850i | \(0.196498\pi\) | |||||||
\(20\) | −0.379667 | −0.0848961 | ||||||||
\(21\) | 5.10373 | 1.11372 | ||||||||
\(22\) | −3.25470 | −0.693905 | ||||||||
\(23\) | −8.35620 | −1.74239 | −0.871194 | − | 0.490938i | \(-0.836654\pi\) | ||||
−0.871194 | + | 0.490938i | \(0.836654\pi\) | |||||||
\(24\) | −2.29904 | −0.469290 | ||||||||
\(25\) | −4.85585 | −0.971171 | ||||||||
\(26\) | −0.129405 | −0.0253783 | ||||||||
\(27\) | 1.64246 | 0.316092 | ||||||||
\(28\) | −2.21994 | −0.419529 | ||||||||
\(29\) | −0.188981 | −0.0350929 | −0.0175464 | − | 0.999846i | \(-0.505585\pi\) | ||||
−0.0175464 | + | 0.999846i | \(0.505585\pi\) | |||||||
\(30\) | 0.872870 | 0.159363 | ||||||||
\(31\) | −3.93199 | −0.706206 | −0.353103 | − | 0.935585i | \(-0.614873\pi\) | ||||
−0.353103 | + | 0.935585i | \(0.614873\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 7.48269 | 1.30257 | ||||||||
\(34\) | −3.78903 | −0.649813 | ||||||||
\(35\) | 0.842837 | 0.142465 | ||||||||
\(36\) | 2.28559 | 0.380931 | ||||||||
\(37\) | 2.45468 | 0.403546 | 0.201773 | − | 0.979432i | \(-0.435330\pi\) | ||||
0.201773 | + | 0.979432i | \(0.435330\pi\) | |||||||
\(38\) | 7.10879 | 1.15320 | ||||||||
\(39\) | 0.297507 | 0.0476392 | ||||||||
\(40\) | −0.379667 | −0.0600306 | ||||||||
\(41\) | −2.16972 | −0.338853 | −0.169426 | − | 0.985543i | \(-0.554191\pi\) | ||||
−0.169426 | + | 0.985543i | \(0.554191\pi\) | |||||||
\(42\) | 5.10373 | 0.787522 | ||||||||
\(43\) | −1.66164 | −0.253398 | −0.126699 | − | 0.991941i | \(-0.540438\pi\) | ||||
−0.126699 | + | 0.991941i | \(0.540438\pi\) | |||||||
\(44\) | −3.25470 | −0.490665 | ||||||||
\(45\) | −0.867762 | −0.129358 | ||||||||
\(46\) | −8.35620 | −1.23205 | ||||||||
\(47\) | −9.30575 | −1.35738 | −0.678692 | − | 0.734423i | \(-0.737453\pi\) | ||||
−0.678692 | + | 0.734423i | \(0.737453\pi\) | |||||||
\(48\) | −2.29904 | −0.331838 | ||||||||
\(49\) | −2.07188 | −0.295982 | ||||||||
\(50\) | −4.85585 | −0.686721 | ||||||||
\(51\) | 8.71113 | 1.21980 | ||||||||
\(52\) | −0.129405 | −0.0179452 | ||||||||
\(53\) | 6.81916 | 0.936684 | 0.468342 | − | 0.883547i | \(-0.344852\pi\) | ||||
0.468342 | + | 0.883547i | \(0.344852\pi\) | |||||||
\(54\) | 1.64246 | 0.223511 | ||||||||
\(55\) | 1.23570 | 0.166622 | ||||||||
\(56\) | −2.21994 | −0.296652 | ||||||||
\(57\) | −16.3434 | −2.16474 | ||||||||
\(58\) | −0.188981 | −0.0248144 | ||||||||
\(59\) | 5.28745 | 0.688367 | 0.344183 | − | 0.938902i | \(-0.388156\pi\) | ||||
0.344183 | + | 0.938902i | \(0.388156\pi\) | |||||||
\(60\) | 0.872870 | 0.112687 | ||||||||
\(61\) | −0.787063 | −0.100773 | −0.0503865 | − | 0.998730i | \(-0.516045\pi\) | ||||
−0.0503865 | + | 0.998730i | \(0.516045\pi\) | |||||||
\(62\) | −3.93199 | −0.499363 | ||||||||
\(63\) | −5.07386 | −0.639246 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.0491307 | 0.00609391 | ||||||||
\(66\) | 7.48269 | 0.921055 | ||||||||
\(67\) | −2.62637 | −0.320863 | −0.160431 | − | 0.987047i | \(-0.551289\pi\) | ||||
−0.160431 | + | 0.987047i | \(0.551289\pi\) | |||||||
\(68\) | −3.78903 | −0.459487 | ||||||||
\(69\) | 19.2112 | 2.31276 | ||||||||
\(70\) | 0.842837 | 0.100738 | ||||||||
\(71\) | 11.3258 | 1.34412 | 0.672060 | − | 0.740497i | \(-0.265410\pi\) | ||||
0.672060 | + | 0.740497i | \(0.265410\pi\) | |||||||
\(72\) | 2.28559 | 0.269359 | ||||||||
\(73\) | −15.0058 | −1.75630 | −0.878148 | − | 0.478390i | \(-0.841221\pi\) | ||||
−0.878148 | + | 0.478390i | \(0.841221\pi\) | |||||||
\(74\) | 2.45468 | 0.285350 | ||||||||
\(75\) | 11.1638 | 1.28908 | ||||||||
\(76\) | 7.10879 | 0.815434 | ||||||||
\(77\) | 7.22523 | 0.823392 | ||||||||
\(78\) | 0.297507 | 0.0336860 | ||||||||
\(79\) | 4.38020 | 0.492812 | 0.246406 | − | 0.969167i | \(-0.420750\pi\) | ||||
0.246406 | + | 0.969167i | \(0.420750\pi\) | |||||||
\(80\) | −0.379667 | −0.0424481 | ||||||||
\(81\) | −10.6329 | −1.18143 | ||||||||
\(82\) | −2.16972 | −0.239605 | ||||||||
\(83\) | 9.50181 | 1.04296 | 0.521480 | − | 0.853264i | \(-0.325380\pi\) | ||||
0.521480 | + | 0.853264i | \(0.325380\pi\) | |||||||
\(84\) | 5.10373 | 0.556862 | ||||||||
\(85\) | 1.43857 | 0.156035 | ||||||||
\(86\) | −1.66164 | −0.179180 | ||||||||
\(87\) | 0.434475 | 0.0465806 | ||||||||
\(88\) | −3.25470 | −0.346952 | ||||||||
\(89\) | −13.8358 | −1.46659 | −0.733293 | − | 0.679912i | \(-0.762018\pi\) | ||||
−0.733293 | + | 0.679912i | \(0.762018\pi\) | |||||||
\(90\) | −0.867762 | −0.0914701 | ||||||||
\(91\) | 0.287270 | 0.0301141 | ||||||||
\(92\) | −8.35620 | −0.871194 | ||||||||
\(93\) | 9.03979 | 0.937383 | ||||||||
\(94\) | −9.30575 | −0.959815 | ||||||||
\(95\) | −2.69897 | −0.276909 | ||||||||
\(96\) | −2.29904 | −0.234645 | ||||||||
\(97\) | −2.61324 | −0.265335 | −0.132667 | − | 0.991161i | \(-0.542354\pi\) | ||||
−0.132667 | + | 0.991161i | \(0.542354\pi\) | |||||||
\(98\) | −2.07188 | −0.209291 | ||||||||
\(99\) | −7.43890 | −0.747638 | ||||||||
\(100\) | −4.85585 | −0.485585 | ||||||||
\(101\) | 0.258204 | 0.0256922 | 0.0128461 | − | 0.999917i | \(-0.495911\pi\) | ||||
0.0128461 | + | 0.999917i | \(0.495911\pi\) | |||||||
\(102\) | 8.71113 | 0.862530 | ||||||||
\(103\) | 12.6133 | 1.24283 | 0.621414 | − | 0.783483i | \(-0.286559\pi\) | ||||
0.621414 | + | 0.783483i | \(0.286559\pi\) | |||||||
\(104\) | −0.129405 | −0.0126892 | ||||||||
\(105\) | −1.93772 | −0.189102 | ||||||||
\(106\) | 6.81916 | 0.662335 | ||||||||
\(107\) | 0.595991 | 0.0576166 | 0.0288083 | − | 0.999585i | \(-0.490829\pi\) | ||||
0.0288083 | + | 0.999585i | \(0.490829\pi\) | |||||||
\(108\) | 1.64246 | 0.158046 | ||||||||
\(109\) | −6.41836 | −0.614768 | −0.307384 | − | 0.951586i | \(-0.599454\pi\) | ||||
−0.307384 | + | 0.951586i | \(0.599454\pi\) | |||||||
\(110\) | 1.23570 | 0.117820 | ||||||||
\(111\) | −5.64340 | −0.535648 | ||||||||
\(112\) | −2.21994 | −0.209764 | ||||||||
\(113\) | −13.6994 | −1.28873 | −0.644364 | − | 0.764719i | \(-0.722878\pi\) | ||||
−0.644364 | + | 0.764719i | \(0.722878\pi\) | |||||||
\(114\) | −16.3434 | −1.53070 | ||||||||
\(115\) | 3.17257 | 0.295844 | ||||||||
\(116\) | −0.188981 | −0.0175464 | ||||||||
\(117\) | −0.295766 | −0.0273435 | ||||||||
\(118\) | 5.28745 | 0.486749 | ||||||||
\(119\) | 8.41141 | 0.771072 | ||||||||
\(120\) | 0.872870 | 0.0796817 | ||||||||
\(121\) | −0.406920 | −0.0369927 | ||||||||
\(122\) | −0.787063 | −0.0712573 | ||||||||
\(123\) | 4.98827 | 0.449777 | ||||||||
\(124\) | −3.93199 | −0.353103 | ||||||||
\(125\) | 3.74194 | 0.334689 | ||||||||
\(126\) | −5.07386 | −0.452015 | ||||||||
\(127\) | 2.57216 | 0.228243 | 0.114121 | − | 0.993467i | \(-0.463595\pi\) | ||||
0.114121 | + | 0.993467i | \(0.463595\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 3.82019 | 0.336349 | ||||||||
\(130\) | 0.0491307 | 0.00430905 | ||||||||
\(131\) | −7.36658 | −0.643621 | −0.321811 | − | 0.946804i | \(-0.604291\pi\) | ||||
−0.321811 | + | 0.946804i | \(0.604291\pi\) | |||||||
\(132\) | 7.48269 | 0.651285 | ||||||||
\(133\) | −15.7811 | −1.36839 | ||||||||
\(134\) | −2.62637 | −0.226884 | ||||||||
\(135\) | −0.623589 | −0.0536700 | ||||||||
\(136\) | −3.78903 | −0.324906 | ||||||||
\(137\) | 3.12853 | 0.267288 | 0.133644 | − | 0.991029i | \(-0.457332\pi\) | ||||
0.133644 | + | 0.991029i | \(0.457332\pi\) | |||||||
\(138\) | 19.2112 | 1.63537 | ||||||||
\(139\) | 10.9914 | 0.932278 | 0.466139 | − | 0.884711i | \(-0.345645\pi\) | ||||
0.466139 | + | 0.884711i | \(0.345645\pi\) | |||||||
\(140\) | 0.842837 | 0.0712327 | ||||||||
\(141\) | 21.3943 | 1.80173 | ||||||||
\(142\) | 11.3258 | 0.950436 | ||||||||
\(143\) | 0.421174 | 0.0352203 | ||||||||
\(144\) | 2.28559 | 0.190466 | ||||||||
\(145\) | 0.0717498 | 0.00595849 | ||||||||
\(146\) | −15.0058 | −1.24189 | ||||||||
\(147\) | 4.76333 | 0.392872 | ||||||||
\(148\) | 2.45468 | 0.201773 | ||||||||
\(149\) | −2.96340 | −0.242771 | −0.121385 | − | 0.992605i | \(-0.538734\pi\) | ||||
−0.121385 | + | 0.992605i | \(0.538734\pi\) | |||||||
\(150\) | 11.1638 | 0.911521 | ||||||||
\(151\) | 5.97398 | 0.486156 | 0.243078 | − | 0.970007i | \(-0.421843\pi\) | ||||
0.243078 | + | 0.970007i | \(0.421843\pi\) | |||||||
\(152\) | 7.10879 | 0.576599 | ||||||||
\(153\) | −8.66015 | −0.700132 | ||||||||
\(154\) | 7.22523 | 0.582226 | ||||||||
\(155\) | 1.49284 | 0.119908 | ||||||||
\(156\) | 0.297507 | 0.0238196 | ||||||||
\(157\) | 17.5520 | 1.40080 | 0.700401 | − | 0.713750i | \(-0.253005\pi\) | ||||
0.700401 | + | 0.713750i | \(0.253005\pi\) | |||||||
\(158\) | 4.38020 | 0.348470 | ||||||||
\(159\) | −15.6775 | −1.24331 | ||||||||
\(160\) | −0.379667 | −0.0300153 | ||||||||
\(161\) | 18.5502 | 1.46196 | ||||||||
\(162\) | −10.6329 | −0.835396 | ||||||||
\(163\) | 11.9347 | 0.934794 | 0.467397 | − | 0.884048i | \(-0.345192\pi\) | ||||
0.467397 | + | 0.884048i | \(0.345192\pi\) | |||||||
\(164\) | −2.16972 | −0.169426 | ||||||||
\(165\) | −2.84093 | −0.221166 | ||||||||
\(166\) | 9.50181 | 0.737484 | ||||||||
\(167\) | 10.6172 | 0.821581 | 0.410790 | − | 0.911730i | \(-0.365253\pi\) | ||||
0.410790 | + | 0.911730i | \(0.365253\pi\) | |||||||
\(168\) | 5.10373 | 0.393761 | ||||||||
\(169\) | −12.9833 | −0.998712 | ||||||||
\(170\) | 1.43857 | 0.110333 | ||||||||
\(171\) | 16.2478 | 1.24250 | ||||||||
\(172\) | −1.66164 | −0.126699 | ||||||||
\(173\) | 12.1446 | 0.923338 | 0.461669 | − | 0.887052i | \(-0.347251\pi\) | ||||
0.461669 | + | 0.887052i | \(0.347251\pi\) | |||||||
\(174\) | 0.434475 | 0.0329374 | ||||||||
\(175\) | 10.7797 | 0.814868 | ||||||||
\(176\) | −3.25470 | −0.245332 | ||||||||
\(177\) | −12.1561 | −0.913705 | ||||||||
\(178\) | −13.8358 | −1.03703 | ||||||||
\(179\) | −5.31074 | −0.396944 | −0.198472 | − | 0.980107i | \(-0.563598\pi\) | ||||
−0.198472 | + | 0.980107i | \(0.563598\pi\) | |||||||
\(180\) | −0.867762 | −0.0646791 | ||||||||
\(181\) | 18.4867 | 1.37410 | 0.687052 | − | 0.726608i | \(-0.258905\pi\) | ||||
0.687052 | + | 0.726608i | \(0.258905\pi\) | |||||||
\(182\) | 0.287270 | 0.0212939 | ||||||||
\(183\) | 1.80949 | 0.133761 | ||||||||
\(184\) | −8.35620 | −0.616027 | ||||||||
\(185\) | −0.931959 | −0.0685190 | ||||||||
\(186\) | 9.03979 | 0.662830 | ||||||||
\(187\) | 12.3322 | 0.901816 | ||||||||
\(188\) | −9.30575 | −0.678692 | ||||||||
\(189\) | −3.64617 | −0.265220 | ||||||||
\(190\) | −2.69897 | −0.195804 | ||||||||
\(191\) | −3.66049 | −0.264864 | −0.132432 | − | 0.991192i | \(-0.542279\pi\) | ||||
−0.132432 | + | 0.991192i | \(0.542279\pi\) | |||||||
\(192\) | −2.29904 | −0.165919 | ||||||||
\(193\) | −6.83330 | −0.491872 | −0.245936 | − | 0.969286i | \(-0.579095\pi\) | ||||
−0.245936 | + | 0.969286i | \(0.579095\pi\) | |||||||
\(194\) | −2.61324 | −0.187620 | ||||||||
\(195\) | −0.112953 | −0.00808876 | ||||||||
\(196\) | −2.07188 | −0.147991 | ||||||||
\(197\) | −0.268417 | −0.0191239 | −0.00956196 | − | 0.999954i | \(-0.503044\pi\) | ||||
−0.00956196 | + | 0.999954i | \(0.503044\pi\) | |||||||
\(198\) | −7.43890 | −0.528660 | ||||||||
\(199\) | 16.9192 | 1.19937 | 0.599687 | − | 0.800235i | \(-0.295292\pi\) | ||||
0.599687 | + | 0.800235i | \(0.295292\pi\) | |||||||
\(200\) | −4.85585 | −0.343361 | ||||||||
\(201\) | 6.03814 | 0.425898 | ||||||||
\(202\) | 0.258204 | 0.0181672 | ||||||||
\(203\) | 0.419526 | 0.0294449 | ||||||||
\(204\) | 8.71113 | 0.609901 | ||||||||
\(205\) | 0.823770 | 0.0575346 | ||||||||
\(206\) | 12.6133 | 0.878812 | ||||||||
\(207\) | −19.0988 | −1.32746 | ||||||||
\(208\) | −0.129405 | −0.00897260 | ||||||||
\(209\) | −23.1370 | −1.60042 | ||||||||
\(210\) | −1.93772 | −0.133715 | ||||||||
\(211\) | 5.39436 | 0.371363 | 0.185682 | − | 0.982610i | \(-0.440551\pi\) | ||||
0.185682 | + | 0.982610i | \(0.440551\pi\) | |||||||
\(212\) | 6.81916 | 0.468342 | ||||||||
\(213\) | −26.0384 | −1.78412 | ||||||||
\(214\) | 0.595991 | 0.0407411 | ||||||||
\(215\) | 0.630871 | 0.0430251 | ||||||||
\(216\) | 1.64246 | 0.111756 | ||||||||
\(217\) | 8.72876 | 0.592547 | ||||||||
\(218\) | −6.41836 | −0.434706 | ||||||||
\(219\) | 34.4989 | 2.33122 | ||||||||
\(220\) | 1.23570 | 0.0833110 | ||||||||
\(221\) | 0.490318 | 0.0329824 | ||||||||
\(222\) | −5.64340 | −0.378760 | ||||||||
\(223\) | 13.4992 | 0.903977 | 0.451988 | − | 0.892024i | \(-0.350715\pi\) | ||||
0.451988 | + | 0.892024i | \(0.350715\pi\) | |||||||
\(224\) | −2.21994 | −0.148326 | ||||||||
\(225\) | −11.0985 | −0.739898 | ||||||||
\(226\) | −13.6994 | −0.911268 | ||||||||
\(227\) | −21.3499 | −1.41704 | −0.708520 | − | 0.705690i | \(-0.750637\pi\) | ||||
−0.708520 | + | 0.705690i | \(0.750637\pi\) | |||||||
\(228\) | −16.3434 | −1.08237 | ||||||||
\(229\) | 6.46004 | 0.426891 | 0.213446 | − | 0.976955i | \(-0.431531\pi\) | ||||
0.213446 | + | 0.976955i | \(0.431531\pi\) | |||||||
\(230\) | 3.17257 | 0.209193 | ||||||||
\(231\) | −16.6111 | −1.09293 | ||||||||
\(232\) | −0.188981 | −0.0124072 | ||||||||
\(233\) | 3.80737 | 0.249429 | 0.124715 | − | 0.992193i | \(-0.460198\pi\) | ||||
0.124715 | + | 0.992193i | \(0.460198\pi\) | |||||||
\(234\) | −0.295766 | −0.0193348 | ||||||||
\(235\) | 3.53309 | 0.230473 | ||||||||
\(236\) | 5.28745 | 0.344183 | ||||||||
\(237\) | −10.0703 | −0.654134 | ||||||||
\(238\) | 8.41141 | 0.545231 | ||||||||
\(239\) | 24.4880 | 1.58400 | 0.791999 | − | 0.610523i | \(-0.209041\pi\) | ||||
0.791999 | + | 0.610523i | \(0.209041\pi\) | |||||||
\(240\) | 0.872870 | 0.0563435 | ||||||||
\(241\) | 17.3310 | 1.11639 | 0.558195 | − | 0.829710i | \(-0.311494\pi\) | ||||
0.558195 | + | 0.829710i | \(0.311494\pi\) | |||||||
\(242\) | −0.406920 | −0.0261578 | ||||||||
\(243\) | 19.5180 | 1.25208 | ||||||||
\(244\) | −0.787063 | −0.0503865 | ||||||||
\(245\) | 0.786623 | 0.0502555 | ||||||||
\(246\) | 4.98827 | 0.318040 | ||||||||
\(247\) | −0.919911 | −0.0585325 | ||||||||
\(248\) | −3.93199 | −0.249681 | ||||||||
\(249\) | −21.8451 | −1.38437 | ||||||||
\(250\) | 3.74194 | 0.236661 | ||||||||
\(251\) | −7.93796 | −0.501040 | −0.250520 | − | 0.968111i | \(-0.580602\pi\) | ||||
−0.250520 | + | 0.968111i | \(0.580602\pi\) | |||||||
\(252\) | −5.07386 | −0.319623 | ||||||||
\(253\) | 27.1969 | 1.70986 | ||||||||
\(254\) | 2.57216 | 0.161392 | ||||||||
\(255\) | −3.30733 | −0.207113 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −20.2607 | −1.26383 | −0.631913 | − | 0.775039i | \(-0.717730\pi\) | ||||
−0.631913 | + | 0.775039i | \(0.717730\pi\) | |||||||
\(258\) | 3.82019 | 0.237834 | ||||||||
\(259\) | −5.44923 | −0.338599 | ||||||||
\(260\) | 0.0491307 | 0.00304696 | ||||||||
\(261\) | −0.431932 | −0.0267359 | ||||||||
\(262\) | −7.36658 | −0.455109 | ||||||||
\(263\) | −20.8160 | −1.28357 | −0.641783 | − | 0.766886i | \(-0.721805\pi\) | ||||
−0.641783 | + | 0.766886i | \(0.721805\pi\) | |||||||
\(264\) | 7.48269 | 0.460528 | ||||||||
\(265\) | −2.58901 | −0.159042 | ||||||||
\(266\) | −15.7811 | −0.967599 | ||||||||
\(267\) | 31.8090 | 1.94668 | ||||||||
\(268\) | −2.62637 | −0.160431 | ||||||||
\(269\) | 12.9346 | 0.788635 | 0.394317 | − | 0.918974i | \(-0.370981\pi\) | ||||
0.394317 | + | 0.918974i | \(0.370981\pi\) | |||||||
\(270\) | −0.623589 | −0.0379504 | ||||||||
\(271\) | 17.2294 | 1.04661 | 0.523306 | − | 0.852145i | \(-0.324699\pi\) | ||||
0.523306 | + | 0.852145i | \(0.324699\pi\) | |||||||
\(272\) | −3.78903 | −0.229744 | ||||||||
\(273\) | −0.660446 | −0.0399720 | ||||||||
\(274\) | 3.12853 | 0.189001 | ||||||||
\(275\) | 15.8044 | 0.953038 | ||||||||
\(276\) | 19.2112 | 1.15638 | ||||||||
\(277\) | −2.29192 | −0.137708 | −0.0688541 | − | 0.997627i | \(-0.521934\pi\) | ||||
−0.0688541 | + | 0.997627i | \(0.521934\pi\) | |||||||
\(278\) | 10.9914 | 0.659220 | ||||||||
\(279\) | −8.98690 | −0.538031 | ||||||||
\(280\) | 0.842837 | 0.0503691 | ||||||||
\(281\) | 21.7249 | 1.29600 | 0.647998 | − | 0.761642i | \(-0.275606\pi\) | ||||
0.647998 | + | 0.761642i | \(0.275606\pi\) | |||||||
\(282\) | 21.3943 | 1.27401 | ||||||||
\(283\) | −4.54744 | −0.270317 | −0.135159 | − | 0.990824i | \(-0.543154\pi\) | ||||
−0.135159 | + | 0.990824i | \(0.543154\pi\) | |||||||
\(284\) | 11.3258 | 0.672060 | ||||||||
\(285\) | 6.20505 | 0.367555 | ||||||||
\(286\) | 0.421174 | 0.0249045 | ||||||||
\(287\) | 4.81664 | 0.284317 | ||||||||
\(288\) | 2.28559 | 0.134679 | ||||||||
\(289\) | −2.64327 | −0.155486 | ||||||||
\(290\) | 0.0717498 | 0.00421329 | ||||||||
\(291\) | 6.00795 | 0.352192 | ||||||||
\(292\) | −15.0058 | −0.878148 | ||||||||
\(293\) | −14.7163 | −0.859737 | −0.429869 | − | 0.902891i | \(-0.641440\pi\) | ||||
−0.429869 | + | 0.902891i | \(0.641440\pi\) | |||||||
\(294\) | 4.76333 | 0.277803 | ||||||||
\(295\) | −2.00747 | −0.116879 | ||||||||
\(296\) | 2.45468 | 0.142675 | ||||||||
\(297\) | −5.34573 | −0.310191 | ||||||||
\(298\) | −2.96340 | −0.171665 | ||||||||
\(299\) | 1.08133 | 0.0625350 | ||||||||
\(300\) | 11.1638 | 0.644542 | ||||||||
\(301\) | 3.68875 | 0.212616 | ||||||||
\(302\) | 5.97398 | 0.343764 | ||||||||
\(303\) | −0.593621 | −0.0341026 | ||||||||
\(304\) | 7.10879 | 0.407717 | ||||||||
\(305\) | 0.298822 | 0.0171105 | ||||||||
\(306\) | −8.66015 | −0.495068 | ||||||||
\(307\) | 8.51726 | 0.486106 | 0.243053 | − | 0.970013i | \(-0.421851\pi\) | ||||
0.243053 | + | 0.970013i | \(0.421851\pi\) | |||||||
\(308\) | 7.22523 | 0.411696 | ||||||||
\(309\) | −28.9985 | −1.64967 | ||||||||
\(310\) | 1.49284 | 0.0847879 | ||||||||
\(311\) | 6.96597 | 0.395004 | 0.197502 | − | 0.980302i | \(-0.436717\pi\) | ||||
0.197502 | + | 0.980302i | \(0.436717\pi\) | |||||||
\(312\) | 0.297507 | 0.0168430 | ||||||||
\(313\) | −12.1299 | −0.685623 | −0.342811 | − | 0.939404i | \(-0.611379\pi\) | ||||
−0.342811 | + | 0.939404i | \(0.611379\pi\) | |||||||
\(314\) | 17.5520 | 0.990516 | ||||||||
\(315\) | 1.92638 | 0.108539 | ||||||||
\(316\) | 4.38020 | 0.246406 | ||||||||
\(317\) | 24.8250 | 1.39431 | 0.697154 | − | 0.716921i | \(-0.254449\pi\) | ||||
0.697154 | + | 0.716921i | \(0.254449\pi\) | |||||||
\(318\) | −15.6775 | −0.879152 | ||||||||
\(319\) | 0.615076 | 0.0344376 | ||||||||
\(320\) | −0.379667 | −0.0212240 | ||||||||
\(321\) | −1.37021 | −0.0764775 | ||||||||
\(322\) | 18.5502 | 1.03377 | ||||||||
\(323\) | −26.9354 | −1.49873 | ||||||||
\(324\) | −10.6329 | −0.590714 | ||||||||
\(325\) | 0.628370 | 0.0348557 | ||||||||
\(326\) | 11.9347 | 0.660999 | ||||||||
\(327\) | 14.7561 | 0.816013 | ||||||||
\(328\) | −2.16972 | −0.119803 | ||||||||
\(329\) | 20.6582 | 1.13892 | ||||||||
\(330\) | −2.84093 | −0.156388 | ||||||||
\(331\) | 21.9163 | 1.20463 | 0.602314 | − | 0.798259i | \(-0.294246\pi\) | ||||
0.602314 | + | 0.798259i | \(0.294246\pi\) | |||||||
\(332\) | 9.50181 | 0.521480 | ||||||||
\(333\) | 5.61038 | 0.307447 | ||||||||
\(334\) | 10.6172 | 0.580945 | ||||||||
\(335\) | 0.997148 | 0.0544800 | ||||||||
\(336\) | 5.10373 | 0.278431 | ||||||||
\(337\) | 32.4362 | 1.76691 | 0.883456 | − | 0.468515i | \(-0.155211\pi\) | ||||
0.883456 | + | 0.468515i | \(0.155211\pi\) | |||||||
\(338\) | −12.9833 | −0.706196 | ||||||||
\(339\) | 31.4954 | 1.71059 | ||||||||
\(340\) | 1.43857 | 0.0780173 | ||||||||
\(341\) | 12.7974 | 0.693020 | ||||||||
\(342\) | 16.2478 | 0.878578 | ||||||||
\(343\) | 20.1390 | 1.08740 | ||||||||
\(344\) | −1.66164 | −0.0895898 | ||||||||
\(345\) | −7.29387 | −0.392689 | ||||||||
\(346\) | 12.1446 | 0.652899 | ||||||||
\(347\) | −18.7842 | −1.00839 | −0.504193 | − | 0.863591i | \(-0.668210\pi\) | ||||
−0.504193 | + | 0.863591i | \(0.668210\pi\) | |||||||
\(348\) | 0.434475 | 0.0232903 | ||||||||
\(349\) | −5.81954 | −0.311513 | −0.155756 | − | 0.987795i | \(-0.549782\pi\) | ||||
−0.155756 | + | 0.987795i | \(0.549782\pi\) | |||||||
\(350\) | 10.7797 | 0.576199 | ||||||||
\(351\) | −0.212543 | −0.0113447 | ||||||||
\(352\) | −3.25470 | −0.173476 | ||||||||
\(353\) | 13.3356 | 0.709781 | 0.354891 | − | 0.934908i | \(-0.384518\pi\) | ||||
0.354891 | + | 0.934908i | \(0.384518\pi\) | |||||||
\(354\) | −12.1561 | −0.646087 | ||||||||
\(355\) | −4.30001 | −0.228221 | ||||||||
\(356\) | −13.8358 | −0.733293 | ||||||||
\(357\) | −19.3382 | −1.02348 | ||||||||
\(358\) | −5.31074 | −0.280682 | ||||||||
\(359\) | −22.4544 | −1.18510 | −0.592549 | − | 0.805534i | \(-0.701878\pi\) | ||||
−0.592549 | + | 0.805534i | \(0.701878\pi\) | |||||||
\(360\) | −0.867762 | −0.0457351 | ||||||||
\(361\) | 31.5349 | 1.65973 | ||||||||
\(362\) | 18.4867 | 0.971638 | ||||||||
\(363\) | 0.935525 | 0.0491023 | ||||||||
\(364\) | 0.287270 | 0.0150571 | ||||||||
\(365\) | 5.69720 | 0.298205 | ||||||||
\(366\) | 1.80949 | 0.0945835 | ||||||||
\(367\) | −14.2920 | −0.746038 | −0.373019 | − | 0.927824i | \(-0.621677\pi\) | ||||
−0.373019 | + | 0.927824i | \(0.621677\pi\) | |||||||
\(368\) | −8.35620 | −0.435597 | ||||||||
\(369\) | −4.95908 | −0.258159 | ||||||||
\(370\) | −0.931959 | −0.0484503 | ||||||||
\(371\) | −15.1381 | −0.785932 | ||||||||
\(372\) | 9.03979 | 0.468692 | ||||||||
\(373\) | −0.0528215 | −0.00273499 | −0.00136750 | − | 0.999999i | \(-0.500435\pi\) | ||||
−0.00136750 | + | 0.999999i | \(0.500435\pi\) | |||||||
\(374\) | 12.3322 | 0.637680 | ||||||||
\(375\) | −8.60287 | −0.444251 | ||||||||
\(376\) | −9.30575 | −0.479908 | ||||||||
\(377\) | 0.0244550 | 0.00125950 | ||||||||
\(378\) | −3.64617 | −0.187539 | ||||||||
\(379\) | 11.7126 | 0.601636 | 0.300818 | − | 0.953682i | \(-0.402740\pi\) | ||||
0.300818 | + | 0.953682i | \(0.402740\pi\) | |||||||
\(380\) | −2.69897 | −0.138454 | ||||||||
\(381\) | −5.91351 | −0.302958 | ||||||||
\(382\) | −3.66049 | −0.187287 | ||||||||
\(383\) | −28.1142 | −1.43657 | −0.718284 | − | 0.695750i | \(-0.755072\pi\) | ||||
−0.718284 | + | 0.695750i | \(0.755072\pi\) | |||||||
\(384\) | −2.29904 | −0.117322 | ||||||||
\(385\) | −2.74318 | −0.139806 | ||||||||
\(386\) | −6.83330 | −0.347806 | ||||||||
\(387\) | −3.79783 | −0.193055 | ||||||||
\(388\) | −2.61324 | −0.132667 | ||||||||
\(389\) | 8.14156 | 0.412794 | 0.206397 | − | 0.978468i | \(-0.433826\pi\) | ||||
0.206397 | + | 0.978468i | \(0.433826\pi\) | |||||||
\(390\) | −0.112953 | −0.00571962 | ||||||||
\(391\) | 31.6619 | 1.60121 | ||||||||
\(392\) | −2.07188 | −0.104646 | ||||||||
\(393\) | 16.9361 | 0.854311 | ||||||||
\(394\) | −0.268417 | −0.0135226 | ||||||||
\(395\) | −1.66302 | −0.0836756 | ||||||||
\(396\) | −7.43890 | −0.373819 | ||||||||
\(397\) | −35.2797 | −1.77064 | −0.885319 | − | 0.464984i | \(-0.846060\pi\) | ||||
−0.885319 | + | 0.464984i | \(0.846060\pi\) | |||||||
\(398\) | 16.9192 | 0.848085 | ||||||||
\(399\) | 36.2813 | 1.81634 | ||||||||
\(400\) | −4.85585 | −0.242793 | ||||||||
\(401\) | −4.54194 | −0.226813 | −0.113407 | − | 0.993549i | \(-0.536176\pi\) | ||||
−0.113407 | + | 0.993549i | \(0.536176\pi\) | |||||||
\(402\) | 6.03814 | 0.301155 | ||||||||
\(403\) | 0.508817 | 0.0253460 | ||||||||
\(404\) | 0.258204 | 0.0128461 | ||||||||
\(405\) | 4.03694 | 0.200597 | ||||||||
\(406\) | 0.419526 | 0.0208207 | ||||||||
\(407\) | −7.98924 | −0.396012 | ||||||||
\(408\) | 8.71113 | 0.431265 | ||||||||
\(409\) | 26.4967 | 1.31018 | 0.655088 | − | 0.755553i | \(-0.272632\pi\) | ||||
0.655088 | + | 0.755553i | \(0.272632\pi\) | |||||||
\(410\) | 0.823770 | 0.0406831 | ||||||||
\(411\) | −7.19262 | −0.354786 | ||||||||
\(412\) | 12.6133 | 0.621414 | ||||||||
\(413\) | −11.7378 | −0.577580 | ||||||||
\(414\) | −19.0988 | −0.938656 | ||||||||
\(415\) | −3.60752 | −0.177086 | ||||||||
\(416\) | −0.129405 | −0.00634459 | ||||||||
\(417\) | −25.2697 | −1.23746 | ||||||||
\(418\) | −23.1370 | −1.13167 | ||||||||
\(419\) | 18.0410 | 0.881362 | 0.440681 | − | 0.897664i | \(-0.354737\pi\) | ||||
0.440681 | + | 0.897664i | \(0.354737\pi\) | |||||||
\(420\) | −1.93772 | −0.0945509 | ||||||||
\(421\) | 23.7255 | 1.15631 | 0.578154 | − | 0.815927i | \(-0.303773\pi\) | ||||
0.578154 | + | 0.815927i | \(0.303773\pi\) | |||||||
\(422\) | 5.39436 | 0.262593 | ||||||||
\(423\) | −21.2691 | −1.03414 | ||||||||
\(424\) | 6.81916 | 0.331168 | ||||||||
\(425\) | 18.3990 | 0.892481 | ||||||||
\(426\) | −26.0384 | −1.26156 | ||||||||
\(427\) | 1.74723 | 0.0845544 | ||||||||
\(428\) | 0.595991 | 0.0288083 | ||||||||
\(429\) | −0.968295 | −0.0467497 | ||||||||
\(430\) | 0.630871 | 0.0304233 | ||||||||
\(431\) | 8.25690 | 0.397721 | 0.198860 | − | 0.980028i | \(-0.436276\pi\) | ||||
0.198860 | + | 0.980028i | \(0.436276\pi\) | |||||||
\(432\) | 1.64246 | 0.0790231 | ||||||||
\(433\) | −16.6226 | −0.798833 | −0.399416 | − | 0.916770i | \(-0.630787\pi\) | ||||
−0.399416 | + | 0.916770i | \(0.630787\pi\) | |||||||
\(434\) | 8.72876 | 0.418994 | ||||||||
\(435\) | −0.164956 | −0.00790902 | ||||||||
\(436\) | −6.41836 | −0.307384 | ||||||||
\(437\) | −59.4025 | −2.84161 | ||||||||
\(438\) | 34.4989 | 1.64842 | ||||||||
\(439\) | −39.1742 | −1.86968 | −0.934842 | − | 0.355064i | \(-0.884459\pi\) | ||||
−0.934842 | + | 0.355064i | \(0.884459\pi\) | |||||||
\(440\) | 1.23570 | 0.0589098 | ||||||||
\(441\) | −4.73545 | −0.225498 | ||||||||
\(442\) | 0.490318 | 0.0233220 | ||||||||
\(443\) | 39.7801 | 1.89001 | 0.945005 | − | 0.327056i | \(-0.106056\pi\) | ||||
0.945005 | + | 0.327056i | \(0.106056\pi\) | |||||||
\(444\) | −5.64340 | −0.267824 | ||||||||
\(445\) | 5.25298 | 0.249015 | ||||||||
\(446\) | 13.4992 | 0.639208 | ||||||||
\(447\) | 6.81297 | 0.322242 | ||||||||
\(448\) | −2.21994 | −0.104882 | ||||||||
\(449\) | −21.3558 | −1.00784 | −0.503920 | − | 0.863750i | \(-0.668109\pi\) | ||||
−0.503920 | + | 0.863750i | \(0.668109\pi\) | |||||||
\(450\) | −11.0985 | −0.523187 | ||||||||
\(451\) | 7.06178 | 0.332526 | ||||||||
\(452\) | −13.6994 | −0.644364 | ||||||||
\(453\) | −13.7344 | −0.645300 | ||||||||
\(454\) | −21.3499 | −1.00200 | ||||||||
\(455\) | −0.109067 | −0.00511314 | ||||||||
\(456\) | −16.3434 | −0.765349 | ||||||||
\(457\) | −2.29166 | −0.107199 | −0.0535997 | − | 0.998563i | \(-0.517069\pi\) | ||||
−0.0535997 | + | 0.998563i | \(0.517069\pi\) | |||||||
\(458\) | 6.46004 | 0.301858 | ||||||||
\(459\) | −6.22334 | −0.290481 | ||||||||
\(460\) | 3.17257 | 0.147922 | ||||||||
\(461\) | 4.84273 | 0.225548 | 0.112774 | − | 0.993621i | \(-0.464026\pi\) | ||||
0.112774 | + | 0.993621i | \(0.464026\pi\) | |||||||
\(462\) | −16.6111 | −0.772819 | ||||||||
\(463\) | 19.7826 | 0.919376 | 0.459688 | − | 0.888081i | \(-0.347961\pi\) | ||||
0.459688 | + | 0.888081i | \(0.347961\pi\) | |||||||
\(464\) | −0.188981 | −0.00877321 | ||||||||
\(465\) | −3.43211 | −0.159160 | ||||||||
\(466\) | 3.80737 | 0.176373 | ||||||||
\(467\) | 10.9655 | 0.507421 | 0.253710 | − | 0.967280i | \(-0.418349\pi\) | ||||
0.253710 | + | 0.967280i | \(0.418349\pi\) | |||||||
\(468\) | −0.295766 | −0.0136718 | ||||||||
\(469\) | 5.83039 | 0.269222 | ||||||||
\(470\) | 3.53309 | 0.162969 | ||||||||
\(471\) | −40.3527 | −1.85936 | ||||||||
\(472\) | 5.28745 | 0.243374 | ||||||||
\(473\) | 5.40815 | 0.248667 | ||||||||
\(474\) | −10.0703 | −0.462543 | ||||||||
\(475\) | −34.5192 | −1.58385 | ||||||||
\(476\) | 8.41141 | 0.385536 | ||||||||
\(477\) | 15.5858 | 0.713624 | ||||||||
\(478\) | 24.4880 | 1.12006 | ||||||||
\(479\) | −17.7629 | −0.811608 | −0.405804 | − | 0.913960i | \(-0.633009\pi\) | ||||
−0.405804 | + | 0.913960i | \(0.633009\pi\) | |||||||
\(480\) | 0.872870 | 0.0398409 | ||||||||
\(481\) | −0.317647 | −0.0144834 | ||||||||
\(482\) | 17.3310 | 0.789407 | ||||||||
\(483\) | −42.6478 | −1.94054 | ||||||||
\(484\) | −0.406920 | −0.0184963 | ||||||||
\(485\) | 0.992162 | 0.0450518 | ||||||||
\(486\) | 19.5180 | 0.885353 | ||||||||
\(487\) | −11.2771 | −0.511015 | −0.255508 | − | 0.966807i | \(-0.582243\pi\) | ||||
−0.255508 | + | 0.966807i | \(0.582243\pi\) | |||||||
\(488\) | −0.787063 | −0.0356287 | ||||||||
\(489\) | −27.4382 | −1.24080 | ||||||||
\(490\) | 0.786623 | 0.0355360 | ||||||||
\(491\) | 26.9438 | 1.21596 | 0.607978 | − | 0.793954i | \(-0.291981\pi\) | ||||
0.607978 | + | 0.793954i | \(0.291981\pi\) | |||||||
\(492\) | 4.98827 | 0.224888 | ||||||||
\(493\) | 0.716054 | 0.0322494 | ||||||||
\(494\) | −0.919911 | −0.0413887 | ||||||||
\(495\) | 2.82431 | 0.126943 | ||||||||
\(496\) | −3.93199 | −0.176551 | ||||||||
\(497\) | −25.1425 | −1.12779 | ||||||||
\(498\) | −21.8451 | −0.978900 | ||||||||
\(499\) | −4.45445 | −0.199409 | −0.0997043 | − | 0.995017i | \(-0.531790\pi\) | ||||
−0.0997043 | + | 0.995017i | \(0.531790\pi\) | |||||||
\(500\) | 3.74194 | 0.167345 | ||||||||
\(501\) | −24.4093 | −1.09053 | ||||||||
\(502\) | −7.93796 | −0.354288 | ||||||||
\(503\) | −6.89740 | −0.307540 | −0.153770 | − | 0.988107i | \(-0.549141\pi\) | ||||
−0.153770 | + | 0.988107i | \(0.549141\pi\) | |||||||
\(504\) | −5.07386 | −0.226008 | ||||||||
\(505\) | −0.0980315 | −0.00436234 | ||||||||
\(506\) | 27.1969 | 1.20905 | ||||||||
\(507\) | 29.8490 | 1.32564 | ||||||||
\(508\) | 2.57216 | 0.114121 | ||||||||
\(509\) | 41.1512 | 1.82399 | 0.911997 | − | 0.410196i | \(-0.134540\pi\) | ||||
0.911997 | + | 0.410196i | \(0.134540\pi\) | |||||||
\(510\) | −3.30733 | −0.146451 | ||||||||
\(511\) | 33.3119 | 1.47363 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 11.6759 | 0.515505 | ||||||||
\(514\) | −20.2607 | −0.893660 | ||||||||
\(515\) | −4.78886 | −0.211022 | ||||||||
\(516\) | 3.82019 | 0.168174 | ||||||||
\(517\) | 30.2874 | 1.33204 | ||||||||
\(518\) | −5.44923 | −0.239425 | ||||||||
\(519\) | −27.9210 | −1.22559 | ||||||||
\(520\) | 0.0491307 | 0.00215452 | ||||||||
\(521\) | 25.4981 | 1.11709 | 0.558546 | − | 0.829473i | \(-0.311359\pi\) | ||||
0.558546 | + | 0.829473i | \(0.311359\pi\) | |||||||
\(522\) | −0.431932 | −0.0189052 | ||||||||
\(523\) | −7.20845 | −0.315204 | −0.157602 | − | 0.987503i | \(-0.550376\pi\) | ||||
−0.157602 | + | 0.987503i | \(0.550376\pi\) | |||||||
\(524\) | −7.36658 | −0.321811 | ||||||||
\(525\) | −24.7829 | −1.08162 | ||||||||
\(526\) | −20.8160 | −0.907619 | ||||||||
\(527\) | 14.8984 | 0.648985 | ||||||||
\(528\) | 7.48269 | 0.325642 | ||||||||
\(529\) | 46.8261 | 2.03592 | ||||||||
\(530\) | −2.58901 | −0.112459 | ||||||||
\(531\) | 12.0849 | 0.524441 | ||||||||
\(532\) | −15.7811 | −0.684196 | ||||||||
\(533\) | 0.280771 | 0.0121616 | ||||||||
\(534\) | 31.8090 | 1.37651 | ||||||||
\(535\) | −0.226278 | −0.00978285 | ||||||||
\(536\) | −2.62637 | −0.113442 | ||||||||
\(537\) | 12.2096 | 0.526884 | ||||||||
\(538\) | 12.9346 | 0.557649 | ||||||||
\(539\) | 6.74334 | 0.290456 | ||||||||
\(540\) | −0.623589 | −0.0268350 | ||||||||
\(541\) | 27.7047 | 1.19112 | 0.595558 | − | 0.803312i | \(-0.296931\pi\) | ||||
0.595558 | + | 0.803312i | \(0.296931\pi\) | |||||||
\(542\) | 17.2294 | 0.740066 | ||||||||
\(543\) | −42.5016 | −1.82392 | ||||||||
\(544\) | −3.78903 | −0.162453 | ||||||||
\(545\) | 2.43684 | 0.104383 | ||||||||
\(546\) | −0.660446 | −0.0282645 | ||||||||
\(547\) | 29.1504 | 1.24638 | 0.623190 | − | 0.782071i | \(-0.285837\pi\) | ||||
0.623190 | + | 0.782071i | \(0.285837\pi\) | |||||||
\(548\) | 3.12853 | 0.133644 | ||||||||
\(549\) | −1.79890 | −0.0767752 | ||||||||
\(550\) | 15.8044 | 0.673900 | ||||||||
\(551\) | −1.34342 | −0.0572318 | ||||||||
\(552\) | 19.2112 | 0.817685 | ||||||||
\(553\) | −9.72378 | −0.413497 | ||||||||
\(554\) | −2.29192 | −0.0973744 | ||||||||
\(555\) | 2.14261 | 0.0909488 | ||||||||
\(556\) | 10.9914 | 0.466139 | ||||||||
\(557\) | −42.3723 | −1.79537 | −0.897687 | − | 0.440634i | \(-0.854754\pi\) | ||||
−0.897687 | + | 0.440634i | \(0.854754\pi\) | |||||||
\(558\) | −8.98690 | −0.380446 | ||||||||
\(559\) | 0.215025 | 0.00909457 | ||||||||
\(560\) | 0.842837 | 0.0356164 | ||||||||
\(561\) | −28.3521 | −1.19703 | ||||||||
\(562\) | 21.7249 | 0.916408 | ||||||||
\(563\) | −13.7209 | −0.578268 | −0.289134 | − | 0.957289i | \(-0.593367\pi\) | ||||
−0.289134 | + | 0.957289i | \(0.593367\pi\) | |||||||
\(564\) | 21.3943 | 0.900863 | ||||||||
\(565\) | 5.20119 | 0.218816 | ||||||||
\(566\) | −4.54744 | −0.191143 | ||||||||
\(567\) | 23.6043 | 0.991286 | ||||||||
\(568\) | 11.3258 | 0.475218 | ||||||||
\(569\) | −13.9442 | −0.584570 | −0.292285 | − | 0.956331i | \(-0.594416\pi\) | ||||
−0.292285 | + | 0.956331i | \(0.594416\pi\) | |||||||
\(570\) | 6.20505 | 0.259901 | ||||||||
\(571\) | 22.0617 | 0.923251 | 0.461626 | − | 0.887075i | \(-0.347266\pi\) | ||||
0.461626 | + | 0.887075i | \(0.347266\pi\) | |||||||
\(572\) | 0.421174 | 0.0176102 | ||||||||
\(573\) | 8.41562 | 0.351568 | ||||||||
\(574\) | 4.81664 | 0.201042 | ||||||||
\(575\) | 40.5765 | 1.69216 | ||||||||
\(576\) | 2.28559 | 0.0952328 | ||||||||
\(577\) | −36.9418 | −1.53791 | −0.768953 | − | 0.639306i | \(-0.779222\pi\) | ||||
−0.768953 | + | 0.639306i | \(0.779222\pi\) | |||||||
\(578\) | −2.64327 | −0.109945 | ||||||||
\(579\) | 15.7100 | 0.652887 | ||||||||
\(580\) | 0.0717498 | 0.00297925 | ||||||||
\(581\) | −21.0934 | −0.875103 | ||||||||
\(582\) | 6.00795 | 0.249038 | ||||||||
\(583\) | −22.1943 | −0.919195 | ||||||||
\(584\) | −15.0058 | −0.620944 | ||||||||
\(585\) | 0.112292 | 0.00464272 | ||||||||
\(586\) | −14.7163 | −0.607926 | ||||||||
\(587\) | −11.7370 | −0.484436 | −0.242218 | − | 0.970222i | \(-0.577875\pi\) | ||||
−0.242218 | + | 0.970222i | \(0.577875\pi\) | |||||||
\(588\) | 4.76333 | 0.196436 | ||||||||
\(589\) | −27.9517 | −1.15173 | ||||||||
\(590\) | −2.00747 | −0.0826462 | ||||||||
\(591\) | 0.617101 | 0.0253842 | ||||||||
\(592\) | 2.45468 | 0.100887 | ||||||||
\(593\) | 31.9252 | 1.31101 | 0.655505 | − | 0.755191i | \(-0.272456\pi\) | ||||
0.655505 | + | 0.755191i | \(0.272456\pi\) | |||||||
\(594\) | −5.34573 | −0.219338 | ||||||||
\(595\) | −3.19353 | −0.130922 | ||||||||
\(596\) | −2.96340 | −0.121385 | ||||||||
\(597\) | −38.8980 | −1.59199 | ||||||||
\(598\) | 1.08133 | 0.0442189 | ||||||||
\(599\) | 46.3703 | 1.89464 | 0.947320 | − | 0.320289i | \(-0.103780\pi\) | ||||
0.947320 | + | 0.320289i | \(0.103780\pi\) | |||||||
\(600\) | 11.1638 | 0.455760 | ||||||||
\(601\) | 6.53899 | 0.266731 | 0.133366 | − | 0.991067i | \(-0.457422\pi\) | ||||
0.133366 | + | 0.991067i | \(0.457422\pi\) | |||||||
\(602\) | 3.68875 | 0.150342 | ||||||||
\(603\) | −6.00281 | −0.244453 | ||||||||
\(604\) | 5.97398 | 0.243078 | ||||||||
\(605\) | 0.154494 | 0.00628107 | ||||||||
\(606\) | −0.593621 | −0.0241142 | ||||||||
\(607\) | 21.3440 | 0.866327 | 0.433164 | − | 0.901315i | \(-0.357397\pi\) | ||||
0.433164 | + | 0.901315i | \(0.357397\pi\) | |||||||
\(608\) | 7.10879 | 0.288299 | ||||||||
\(609\) | −0.964506 | −0.0390838 | ||||||||
\(610\) | 0.298822 | 0.0120989 | ||||||||
\(611\) | 1.20421 | 0.0487170 | ||||||||
\(612\) | −8.66015 | −0.350066 | ||||||||
\(613\) | 24.8282 | 1.00280 | 0.501401 | − | 0.865215i | \(-0.332818\pi\) | ||||
0.501401 | + | 0.865215i | \(0.332818\pi\) | |||||||
\(614\) | 8.51726 | 0.343729 | ||||||||
\(615\) | −1.89388 | −0.0763686 | ||||||||
\(616\) | 7.22523 | 0.291113 | ||||||||
\(617\) | 8.51019 | 0.342607 | 0.171304 | − | 0.985218i | \(-0.445202\pi\) | ||||
0.171304 | + | 0.985218i | \(0.445202\pi\) | |||||||
\(618\) | −28.9985 | −1.16649 | ||||||||
\(619\) | 30.7570 | 1.23623 | 0.618114 | − | 0.786088i | \(-0.287897\pi\) | ||||
0.618114 | + | 0.786088i | \(0.287897\pi\) | |||||||
\(620\) | 1.49284 | 0.0599541 | ||||||||
\(621\) | −13.7248 | −0.550756 | ||||||||
\(622\) | 6.96597 | 0.279310 | ||||||||
\(623\) | 30.7145 | 1.23055 | ||||||||
\(624\) | 0.297507 | 0.0119098 | ||||||||
\(625\) | 22.8586 | 0.914343 | ||||||||
\(626\) | −12.1299 | −0.484808 | ||||||||
\(627\) | 53.1929 | 2.12432 | ||||||||
\(628\) | 17.5520 | 0.700401 | ||||||||
\(629\) | −9.30084 | −0.370849 | ||||||||
\(630\) | 1.92638 | 0.0767487 | ||||||||
\(631\) | −15.7094 | −0.625380 | −0.312690 | − | 0.949855i | \(-0.601230\pi\) | ||||
−0.312690 | + | 0.949855i | \(0.601230\pi\) | |||||||
\(632\) | 4.38020 | 0.174235 | ||||||||
\(633\) | −12.4019 | −0.492929 | ||||||||
\(634\) | 24.8250 | 0.985925 | ||||||||
\(635\) | −0.976565 | −0.0387538 | ||||||||
\(636\) | −15.6775 | −0.621654 | ||||||||
\(637\) | 0.268110 | 0.0106229 | ||||||||
\(638\) | 0.615076 | 0.0243511 | ||||||||
\(639\) | 25.8860 | 1.02403 | ||||||||
\(640\) | −0.379667 | −0.0150077 | ||||||||
\(641\) | −9.75381 | −0.385252 | −0.192626 | − | 0.981272i | \(-0.561700\pi\) | ||||
−0.192626 | + | 0.981272i | \(0.561700\pi\) | |||||||
\(642\) | −1.37021 | −0.0540777 | ||||||||
\(643\) | −18.7144 | −0.738022 | −0.369011 | − | 0.929425i | \(-0.620304\pi\) | ||||
−0.369011 | + | 0.929425i | \(0.620304\pi\) | |||||||
\(644\) | 18.5502 | 0.730982 | ||||||||
\(645\) | −1.45040 | −0.0571094 | ||||||||
\(646\) | −26.9354 | −1.05976 | ||||||||
\(647\) | −1.48690 | −0.0584560 | −0.0292280 | − | 0.999573i | \(-0.509305\pi\) | ||||
−0.0292280 | + | 0.999573i | \(0.509305\pi\) | |||||||
\(648\) | −10.6329 | −0.417698 | ||||||||
\(649\) | −17.2091 | −0.675515 | ||||||||
\(650\) | 0.628370 | 0.0246467 | ||||||||
\(651\) | −20.0678 | −0.786518 | ||||||||
\(652\) | 11.9347 | 0.467397 | ||||||||
\(653\) | −9.77388 | −0.382481 | −0.191241 | − | 0.981543i | \(-0.561251\pi\) | ||||
−0.191241 | + | 0.981543i | \(0.561251\pi\) | |||||||
\(654\) | 14.7561 | 0.577008 | ||||||||
\(655\) | 2.79685 | 0.109282 | ||||||||
\(656\) | −2.16972 | −0.0847132 | ||||||||
\(657\) | −34.2970 | −1.33806 | ||||||||
\(658\) | 20.6582 | 0.805340 | ||||||||
\(659\) | 26.0386 | 1.01432 | 0.507160 | − | 0.861852i | \(-0.330695\pi\) | ||||
0.507160 | + | 0.861852i | \(0.330695\pi\) | |||||||
\(660\) | −2.84093 | −0.110583 | ||||||||
\(661\) | −32.5010 | −1.26414 | −0.632071 | − | 0.774910i | \(-0.717795\pi\) | ||||
−0.632071 | + | 0.774910i | \(0.717795\pi\) | |||||||
\(662\) | 21.9163 | 0.851801 | ||||||||
\(663\) | −1.12726 | −0.0437792 | ||||||||
\(664\) | 9.50181 | 0.368742 | ||||||||
\(665\) | 5.99155 | 0.232342 | ||||||||
\(666\) | 5.61038 | 0.217398 | ||||||||
\(667\) | 1.57916 | 0.0611454 | ||||||||
\(668\) | 10.6172 | 0.410790 | ||||||||
\(669\) | −31.0353 | −1.19989 | ||||||||
\(670\) | 0.997148 | 0.0385232 | ||||||||
\(671\) | 2.56165 | 0.0988916 | ||||||||
\(672\) | 5.10373 | 0.196881 | ||||||||
\(673\) | −23.0520 | −0.888590 | −0.444295 | − | 0.895881i | \(-0.646546\pi\) | ||||
−0.444295 | + | 0.895881i | \(0.646546\pi\) | |||||||
\(674\) | 32.4362 | 1.24940 | ||||||||
\(675\) | −7.97557 | −0.306980 | ||||||||
\(676\) | −12.9833 | −0.499356 | ||||||||
\(677\) | −7.79858 | −0.299724 | −0.149862 | − | 0.988707i | \(-0.547883\pi\) | ||||
−0.149862 | + | 0.988707i | \(0.547883\pi\) | |||||||
\(678\) | 31.4954 | 1.20957 | ||||||||
\(679\) | 5.80124 | 0.222631 | ||||||||
\(680\) | 1.43857 | 0.0551666 | ||||||||
\(681\) | 49.0842 | 1.88091 | ||||||||
\(682\) | 12.7974 | 0.490039 | ||||||||
\(683\) | 1.74670 | 0.0668357 | 0.0334178 | − | 0.999441i | \(-0.489361\pi\) | ||||
0.0334178 | + | 0.999441i | \(0.489361\pi\) | |||||||
\(684\) | 16.2478 | 0.621248 | ||||||||
\(685\) | −1.18780 | −0.0453835 | ||||||||
\(686\) | 20.1390 | 0.768911 | ||||||||
\(687\) | −14.8519 | −0.566635 | ||||||||
\(688\) | −1.66164 | −0.0633496 | ||||||||
\(689\) | −0.882431 | −0.0336180 | ||||||||
\(690\) | −7.29387 | −0.277673 | ||||||||
\(691\) | 6.87317 | 0.261468 | 0.130734 | − | 0.991417i | \(-0.458267\pi\) | ||||
0.130734 | + | 0.991417i | \(0.458267\pi\) | |||||||
\(692\) | 12.1446 | 0.461669 | ||||||||
\(693\) | 16.5139 | 0.627311 | ||||||||
\(694\) | −18.7842 | −0.713037 | ||||||||
\(695\) | −4.17307 | −0.158294 | ||||||||
\(696\) | 0.434475 | 0.0164687 | ||||||||
\(697\) | 8.22112 | 0.311397 | ||||||||
\(698\) | −5.81954 | −0.220273 | ||||||||
\(699\) | −8.75330 | −0.331080 | ||||||||
\(700\) | 10.7797 | 0.407434 | ||||||||
\(701\) | 5.00366 | 0.188986 | 0.0944928 | − | 0.995526i | \(-0.469877\pi\) | ||||
0.0944928 | + | 0.995526i | \(0.469877\pi\) | |||||||
\(702\) | −0.212543 | −0.00802190 | ||||||||
\(703\) | 17.4498 | 0.658131 | ||||||||
\(704\) | −3.25470 | −0.122666 | ||||||||
\(705\) | −8.12271 | −0.305919 | ||||||||
\(706\) | 13.3356 | 0.501891 | ||||||||
\(707\) | −0.573197 | −0.0215573 | ||||||||
\(708\) | −12.1561 | −0.456852 | ||||||||
\(709\) | −36.7030 | −1.37841 | −0.689204 | − | 0.724567i | \(-0.742040\pi\) | ||||
−0.689204 | + | 0.724567i | \(0.742040\pi\) | |||||||
\(710\) | −4.30001 | −0.161377 | ||||||||
\(711\) | 10.0113 | 0.375455 | ||||||||
\(712\) | −13.8358 | −0.518517 | ||||||||
\(713\) | 32.8565 | 1.23048 | ||||||||
\(714\) | −19.3382 | −0.723713 | ||||||||
\(715\) | −0.159906 | −0.00598013 | ||||||||
\(716\) | −5.31074 | −0.198472 | ||||||||
\(717\) | −56.2989 | −2.10252 | ||||||||
\(718\) | −22.4544 | −0.837991 | ||||||||
\(719\) | −23.4988 | −0.876359 | −0.438180 | − | 0.898887i | \(-0.644377\pi\) | ||||
−0.438180 | + | 0.898887i | \(0.644377\pi\) | |||||||
\(720\) | −0.867762 | −0.0323396 | ||||||||
\(721\) | −28.0008 | −1.04280 | ||||||||
\(722\) | 31.5349 | 1.17361 | ||||||||
\(723\) | −39.8448 | −1.48184 | ||||||||
\(724\) | 18.4867 | 0.687052 | ||||||||
\(725\) | 0.917663 | 0.0340811 | ||||||||
\(726\) | 0.935525 | 0.0347206 | ||||||||
\(727\) | −43.8647 | −1.62685 | −0.813426 | − | 0.581668i | \(-0.802400\pi\) | ||||
−0.813426 | + | 0.581668i | \(0.802400\pi\) | |||||||
\(728\) | 0.287270 | 0.0106469 | ||||||||
\(729\) | −12.9740 | −0.480520 | ||||||||
\(730\) | 5.69720 | 0.210863 | ||||||||
\(731\) | 6.29602 | 0.232867 | ||||||||
\(732\) | 1.80949 | 0.0668807 | ||||||||
\(733\) | 37.8623 | 1.39847 | 0.699237 | − | 0.714890i | \(-0.253523\pi\) | ||||
0.699237 | + | 0.714890i | \(0.253523\pi\) | |||||||
\(734\) | −14.2920 | −0.527529 | ||||||||
\(735\) | −1.80848 | −0.0667067 | ||||||||
\(736\) | −8.35620 | −0.308014 | ||||||||
\(737\) | 8.54807 | 0.314872 | ||||||||
\(738\) | −4.95908 | −0.182546 | ||||||||
\(739\) | −10.4108 | −0.382969 | −0.191484 | − | 0.981496i | \(-0.561330\pi\) | ||||
−0.191484 | + | 0.981496i | \(0.561330\pi\) | |||||||
\(740\) | −0.931959 | −0.0342595 | ||||||||
\(741\) | 2.11491 | 0.0776932 | ||||||||
\(742\) | −15.1381 | −0.555738 | ||||||||
\(743\) | 49.9992 | 1.83429 | 0.917147 | − | 0.398549i | \(-0.130486\pi\) | ||||
0.917147 | + | 0.398549i | \(0.130486\pi\) | |||||||
\(744\) | 9.03979 | 0.331415 | ||||||||
\(745\) | 1.12510 | 0.0412206 | ||||||||
\(746\) | −0.0528215 | −0.00193393 | ||||||||
\(747\) | 21.7172 | 0.794592 | ||||||||
\(748\) | 12.3322 | 0.450908 | ||||||||
\(749\) | −1.32306 | −0.0483436 | ||||||||
\(750\) | −8.60287 | −0.314133 | ||||||||
\(751\) | 46.8122 | 1.70820 | 0.854101 | − | 0.520107i | \(-0.174108\pi\) | ||||
0.854101 | + | 0.520107i | \(0.174108\pi\) | |||||||
\(752\) | −9.30575 | −0.339346 | ||||||||
\(753\) | 18.2497 | 0.665056 | ||||||||
\(754\) | 0.0244550 | 0.000890599 0 | ||||||||
\(755\) | −2.26812 | −0.0825455 | ||||||||
\(756\) | −3.64617 | −0.132610 | ||||||||
\(757\) | 27.8507 | 1.01225 | 0.506126 | − | 0.862460i | \(-0.331077\pi\) | ||||
0.506126 | + | 0.862460i | \(0.331077\pi\) | |||||||
\(758\) | 11.7126 | 0.425421 | ||||||||
\(759\) | −62.5269 | −2.26958 | ||||||||
\(760\) | −2.69897 | −0.0979020 | ||||||||
\(761\) | 3.95804 | 0.143479 | 0.0717395 | − | 0.997423i | \(-0.477145\pi\) | ||||
0.0717395 | + | 0.997423i | \(0.477145\pi\) | |||||||
\(762\) | −5.91351 | −0.214224 | ||||||||
\(763\) | 14.2484 | 0.515826 | ||||||||
\(764\) | −3.66049 | −0.132432 | ||||||||
\(765\) | 3.28797 | 0.118877 | ||||||||
\(766\) | −28.1142 | −1.01581 | ||||||||
\(767\) | −0.684220 | −0.0247058 | ||||||||
\(768\) | −2.29904 | −0.0829595 | ||||||||
\(769\) | 48.9333 | 1.76458 | 0.882289 | − | 0.470708i | \(-0.156001\pi\) | ||||
0.882289 | + | 0.470708i | \(0.156001\pi\) | |||||||
\(770\) | −2.74318 | −0.0988574 | ||||||||
\(771\) | 46.5801 | 1.67754 | ||||||||
\(772\) | −6.83330 | −0.245936 | ||||||||
\(773\) | 2.17902 | 0.0783740 | 0.0391870 | − | 0.999232i | \(-0.487523\pi\) | ||||
0.0391870 | + | 0.999232i | \(0.487523\pi\) | |||||||
\(774\) | −3.79783 | −0.136510 | ||||||||
\(775\) | 19.0931 | 0.685846 | ||||||||
\(776\) | −2.61324 | −0.0938100 | ||||||||
\(777\) | 12.5280 | 0.449439 | ||||||||
\(778\) | 8.14156 | 0.291889 | ||||||||
\(779\) | −15.4241 | −0.552624 | ||||||||
\(780\) | −0.112953 | −0.00404438 | ||||||||
\(781\) | −36.8619 | −1.31902 | ||||||||
\(782\) | 31.6619 | 1.13223 | ||||||||
\(783\) | −0.310394 | −0.0110926 | ||||||||
\(784\) | −2.07188 | −0.0739956 | ||||||||
\(785\) | −6.66391 | −0.237845 | ||||||||
\(786\) | 16.9361 | 0.604089 | ||||||||
\(787\) | −22.6975 | −0.809077 | −0.404539 | − | 0.914521i | \(-0.632568\pi\) | ||||
−0.404539 | + | 0.914521i | \(0.632568\pi\) | |||||||
\(788\) | −0.268417 | −0.00956196 | ||||||||
\(789\) | 47.8567 | 1.70374 | ||||||||
\(790\) | −1.66302 | −0.0591675 | ||||||||
\(791\) | 30.4117 | 1.08132 | ||||||||
\(792\) | −7.43890 | −0.264330 | ||||||||
\(793\) | 0.101850 | 0.00361679 | ||||||||
\(794\) | −35.2797 | −1.25203 | ||||||||
\(795\) | 5.95224 | 0.211104 | ||||||||
\(796\) | 16.9192 | 0.599687 | ||||||||
\(797\) | 42.6147 | 1.50949 | 0.754745 | − | 0.656019i | \(-0.227761\pi\) | ||||
0.754745 | + | 0.656019i | \(0.227761\pi\) | |||||||
\(798\) | 36.2813 | 1.28434 | ||||||||
\(799\) | 35.2598 | 1.24740 | ||||||||
\(800\) | −4.85585 | −0.171680 | ||||||||
\(801\) | −31.6228 | −1.11734 | ||||||||
\(802\) | −4.54194 | −0.160381 | ||||||||
\(803\) | 48.8394 | 1.72350 | ||||||||
\(804\) | 6.03814 | 0.212949 | ||||||||
\(805\) | −7.04292 | −0.248230 | ||||||||
\(806\) | 0.508817 | 0.0179223 | ||||||||
\(807\) | −29.7371 | −1.04680 | ||||||||
\(808\) | 0.258204 | 0.00908358 | ||||||||
\(809\) | −24.6488 | −0.866606 | −0.433303 | − | 0.901248i | \(-0.642652\pi\) | ||||
−0.433303 | + | 0.901248i | \(0.642652\pi\) | |||||||
\(810\) | 4.03694 | 0.141844 | ||||||||
\(811\) | −26.2859 | −0.923021 | −0.461511 | − | 0.887135i | \(-0.652692\pi\) | ||||
−0.461511 | + | 0.887135i | \(0.652692\pi\) | |||||||
\(812\) | 0.419526 | 0.0147225 | ||||||||
\(813\) | −39.6111 | −1.38922 | ||||||||
\(814\) | −7.98924 | −0.280023 | ||||||||
\(815\) | −4.53119 | −0.158721 | ||||||||
\(816\) | 8.71113 | 0.304950 | ||||||||
\(817\) | −11.8123 | −0.413259 | ||||||||
\(818\) | 26.4967 | 0.926434 | ||||||||
\(819\) | 0.656581 | 0.0229428 | ||||||||
\(820\) | 0.823770 | 0.0287673 | ||||||||
\(821\) | −10.1238 | −0.353322 | −0.176661 | − | 0.984272i | \(-0.556530\pi\) | ||||
−0.176661 | + | 0.984272i | \(0.556530\pi\) | |||||||
\(822\) | −7.19262 | −0.250871 | ||||||||
\(823\) | −43.7943 | −1.52657 | −0.763286 | − | 0.646061i | \(-0.776415\pi\) | ||||
−0.763286 | + | 0.646061i | \(0.776415\pi\) | |||||||
\(824\) | 12.6133 | 0.439406 | ||||||||
\(825\) | −36.3348 | −1.26502 | ||||||||
\(826\) | −11.7378 | −0.408410 | ||||||||
\(827\) | 6.47610 | 0.225196 | 0.112598 | − | 0.993641i | \(-0.464083\pi\) | ||||
0.112598 | + | 0.993641i | \(0.464083\pi\) | |||||||
\(828\) | −19.0988 | −0.663730 | ||||||||
\(829\) | −52.2306 | −1.81404 | −0.907022 | − | 0.421083i | \(-0.861650\pi\) | ||||
−0.907022 | + | 0.421083i | \(0.861650\pi\) | |||||||
\(830\) | −3.60752 | −0.125219 | ||||||||
\(831\) | 5.26922 | 0.182787 | ||||||||
\(832\) | −0.129405 | −0.00448630 | ||||||||
\(833\) | 7.85039 | 0.272000 | ||||||||
\(834\) | −25.2697 | −0.875017 | ||||||||
\(835\) | −4.03099 | −0.139498 | ||||||||
\(836\) | −23.1370 | −0.800209 | ||||||||
\(837\) | −6.45815 | −0.223226 | ||||||||
\(838\) | 18.0410 | 0.623217 | ||||||||
\(839\) | −49.4850 | −1.70841 | −0.854206 | − | 0.519935i | \(-0.825956\pi\) | ||||
−0.854206 | + | 0.519935i | \(0.825956\pi\) | |||||||
\(840\) | −1.93772 | −0.0668576 | ||||||||
\(841\) | −28.9643 | −0.998768 | ||||||||
\(842\) | 23.7255 | 0.817634 | ||||||||
\(843\) | −49.9463 | −1.72024 | ||||||||
\(844\) | 5.39436 | 0.185682 | ||||||||
\(845\) | 4.92931 | 0.169573 | ||||||||
\(846\) | −21.2691 | −0.731247 | ||||||||
\(847\) | 0.903336 | 0.0310390 | ||||||||
\(848\) | 6.81916 | 0.234171 | ||||||||
\(849\) | 10.4547 | 0.358806 | ||||||||
\(850\) | 18.3990 | 0.631079 | ||||||||
\(851\) | −20.5118 | −0.703134 | ||||||||
\(852\) | −26.0384 | −0.892060 | ||||||||
\(853\) | −24.8949 | −0.852386 | −0.426193 | − | 0.904632i | \(-0.640146\pi\) | ||||
−0.426193 | + | 0.904632i | \(0.640146\pi\) | |||||||
\(854\) | 1.74723 | 0.0597890 | ||||||||
\(855\) | −6.16873 | −0.210966 | ||||||||
\(856\) | 0.595991 | 0.0203705 | ||||||||
\(857\) | −6.78744 | −0.231854 | −0.115927 | − | 0.993258i | \(-0.536984\pi\) | ||||
−0.115927 | + | 0.993258i | \(0.536984\pi\) | |||||||
\(858\) | −0.968295 | −0.0330570 | ||||||||
\(859\) | 9.04897 | 0.308747 | 0.154373 | − | 0.988013i | \(-0.450664\pi\) | ||||
0.154373 | + | 0.988013i | \(0.450664\pi\) | |||||||
\(860\) | 0.630871 | 0.0215125 | ||||||||
\(861\) | −11.0736 | −0.377389 | ||||||||
\(862\) | 8.25690 | 0.281231 | ||||||||
\(863\) | −8.11789 | −0.276336 | −0.138168 | − | 0.990409i | \(-0.544121\pi\) | ||||
−0.138168 | + | 0.990409i | \(0.544121\pi\) | |||||||
\(864\) | 1.64246 | 0.0558778 | ||||||||
\(865\) | −4.61091 | −0.156776 | ||||||||
\(866\) | −16.6226 | −0.564860 | ||||||||
\(867\) | 6.07698 | 0.206385 | ||||||||
\(868\) | 8.72876 | 0.296274 | ||||||||
\(869\) | −14.2563 | −0.483610 | ||||||||
\(870\) | −0.164956 | −0.00559252 | ||||||||
\(871\) | 0.339865 | 0.0115159 | ||||||||
\(872\) | −6.41836 | −0.217353 | ||||||||
\(873\) | −5.97280 | −0.202148 | ||||||||
\(874\) | −59.4025 | −2.00932 | ||||||||
\(875\) | −8.30688 | −0.280824 | ||||||||
\(876\) | 34.4989 | 1.16561 | ||||||||
\(877\) | −17.7430 | −0.599137 | −0.299569 | − | 0.954075i | \(-0.596843\pi\) | ||||
−0.299569 | + | 0.954075i | \(0.596843\pi\) | |||||||
\(878\) | −39.1742 | −1.32207 | ||||||||
\(879\) | 33.8334 | 1.14117 | ||||||||
\(880\) | 1.23570 | 0.0416555 | ||||||||
\(881\) | −0.380184 | −0.0128087 | −0.00640436 | − | 0.999979i | \(-0.502039\pi\) | ||||
−0.00640436 | + | 0.999979i | \(0.502039\pi\) | |||||||
\(882\) | −4.73545 | −0.159451 | ||||||||
\(883\) | 27.7162 | 0.932726 | 0.466363 | − | 0.884593i | \(-0.345564\pi\) | ||||
0.466363 | + | 0.884593i | \(0.345564\pi\) | |||||||
\(884\) | 0.490318 | 0.0164912 | ||||||||
\(885\) | 4.61525 | 0.155140 | ||||||||
\(886\) | 39.7801 | 1.33644 | ||||||||
\(887\) | 35.2256 | 1.18276 | 0.591381 | − | 0.806393i | \(-0.298583\pi\) | ||||
0.591381 | + | 0.806393i | \(0.298583\pi\) | |||||||
\(888\) | −5.64340 | −0.189380 | ||||||||
\(889\) | −5.71004 | −0.191509 | ||||||||
\(890\) | 5.25298 | 0.176080 | ||||||||
\(891\) | 34.6068 | 1.15937 | ||||||||
\(892\) | 13.4992 | 0.451988 | ||||||||
\(893\) | −66.1526 | −2.21371 | ||||||||
\(894\) | 6.81297 | 0.227860 | ||||||||
\(895\) | 2.01631 | 0.0673979 | ||||||||
\(896\) | −2.21994 | −0.0741629 | ||||||||
\(897\) | −2.48603 | −0.0830060 | ||||||||
\(898\) | −21.3558 | −0.712651 | ||||||||
\(899\) | 0.743070 | 0.0247828 | ||||||||
\(900\) | −11.0985 | −0.369949 | ||||||||
\(901\) | −25.8380 | −0.860788 | ||||||||
\(902\) | 7.06178 | 0.235132 | ||||||||
\(903\) | −8.48058 | −0.282216 | ||||||||
\(904\) | −13.6994 | −0.455634 | ||||||||
\(905\) | −7.01878 | −0.233312 | ||||||||
\(906\) | −13.7344 | −0.456296 | ||||||||
\(907\) | 18.1720 | 0.603390 | 0.301695 | − | 0.953404i | \(-0.402448\pi\) | ||||
0.301695 | + | 0.953404i | \(0.402448\pi\) | |||||||
\(908\) | −21.3499 | −0.708520 | ||||||||
\(909\) | 0.590147 | 0.0195740 | ||||||||
\(910\) | −0.109067 | −0.00361554 | ||||||||
\(911\) | −34.6244 | −1.14716 | −0.573579 | − | 0.819151i | \(-0.694445\pi\) | ||||
−0.573579 | + | 0.819151i | \(0.694445\pi\) | |||||||
\(912\) | −16.3434 | −0.541184 | ||||||||
\(913\) | −30.9256 | −1.02349 | ||||||||
\(914\) | −2.29166 | −0.0758014 | ||||||||
\(915\) | −0.687003 | −0.0227116 | ||||||||
\(916\) | 6.46004 | 0.213446 | ||||||||
\(917\) | 16.3533 | 0.540035 | ||||||||
\(918\) | −6.22334 | −0.205401 | ||||||||
\(919\) | −12.1005 | −0.399159 | −0.199579 | − | 0.979882i | \(-0.563958\pi\) | ||||
−0.199579 | + | 0.979882i | \(0.563958\pi\) | |||||||
\(920\) | 3.17257 | 0.104597 | ||||||||
\(921\) | −19.5815 | −0.645233 | ||||||||
\(922\) | 4.84273 | 0.159487 | ||||||||
\(923\) | −1.46561 | −0.0482410 | ||||||||
\(924\) | −16.6111 | −0.546465 | ||||||||
\(925\) | −11.9195 | −0.391912 | ||||||||
\(926\) | 19.7826 | 0.650097 | ||||||||
\(927\) | 28.8288 | 0.946863 | ||||||||
\(928\) | −0.188981 | −0.00620360 | ||||||||
\(929\) | −20.5697 | −0.674869 | −0.337434 | − | 0.941349i | \(-0.609559\pi\) | ||||
−0.337434 | + | 0.941349i | \(0.609559\pi\) | |||||||
\(930\) | −3.43211 | −0.112543 | ||||||||
\(931\) | −14.7285 | −0.482708 | ||||||||
\(932\) | 3.80737 | 0.124715 | ||||||||
\(933\) | −16.0150 | −0.524309 | ||||||||
\(934\) | 10.9655 | 0.358801 | ||||||||
\(935\) | −4.68211 | −0.153121 | ||||||||
\(936\) | −0.295766 | −0.00966740 | ||||||||
\(937\) | −28.8771 | −0.943374 | −0.471687 | − | 0.881766i | \(-0.656355\pi\) | ||||
−0.471687 | + | 0.881766i | \(0.656355\pi\) | |||||||
\(938\) | 5.83039 | 0.190369 | ||||||||
\(939\) | 27.8871 | 0.910062 | ||||||||
\(940\) | 3.53309 | 0.115237 | ||||||||
\(941\) | −46.9007 | −1.52892 | −0.764460 | − | 0.644671i | \(-0.776994\pi\) | ||||
−0.764460 | + | 0.644671i | \(0.776994\pi\) | |||||||
\(942\) | −40.3527 | −1.31476 | ||||||||
\(943\) | 18.1306 | 0.590413 | ||||||||
\(944\) | 5.28745 | 0.172092 | ||||||||
\(945\) | 1.38433 | 0.0450323 | ||||||||
\(946\) | 5.40815 | 0.175834 | ||||||||
\(947\) | −45.5153 | −1.47905 | −0.739523 | − | 0.673131i | \(-0.764949\pi\) | ||||
−0.739523 | + | 0.673131i | \(0.764949\pi\) | |||||||
\(948\) | −10.0703 | −0.327067 | ||||||||
\(949\) | 1.94182 | 0.0630341 | ||||||||
\(950\) | −34.5192 | −1.11995 | ||||||||
\(951\) | −57.0736 | −1.85074 | ||||||||
\(952\) | 8.41141 | 0.272615 | ||||||||
\(953\) | 15.1338 | 0.490233 | 0.245116 | − | 0.969494i | \(-0.421174\pi\) | ||||
0.245116 | + | 0.969494i | \(0.421174\pi\) | |||||||
\(954\) | 15.5858 | 0.504608 | ||||||||
\(955\) | 1.38977 | 0.0449718 | ||||||||
\(956\) | 24.4880 | 0.791999 | ||||||||
\(957\) | −1.41408 | −0.0457109 | ||||||||
\(958\) | −17.7629 | −0.573894 | ||||||||
\(959\) | −6.94514 | −0.224270 | ||||||||
\(960\) | 0.872870 | 0.0281717 | ||||||||
\(961\) | −15.5395 | −0.501274 | ||||||||
\(962\) | −0.317647 | −0.0102413 | ||||||||
\(963\) | 1.36219 | 0.0438959 | ||||||||
\(964\) | 17.3310 | 0.558195 | ||||||||
\(965\) | 2.59438 | 0.0835160 | ||||||||
\(966\) | −42.6478 | −1.37217 | ||||||||
\(967\) | 14.4144 | 0.463536 | 0.231768 | − | 0.972771i | \(-0.425549\pi\) | ||||
0.231768 | + | 0.972771i | \(0.425549\pi\) | |||||||
\(968\) | −0.406920 | −0.0130789 | ||||||||
\(969\) | 61.9256 | 1.98934 | ||||||||
\(970\) | 0.992162 | 0.0318564 | ||||||||
\(971\) | −31.1751 | −1.00046 | −0.500228 | − | 0.865894i | \(-0.666751\pi\) | ||||
−0.500228 | + | 0.865894i | \(0.666751\pi\) | |||||||
\(972\) | 19.5180 | 0.626039 | ||||||||
\(973\) | −24.4002 | −0.782235 | ||||||||
\(974\) | −11.2771 | −0.361342 | ||||||||
\(975\) | −1.44465 | −0.0462658 | ||||||||
\(976\) | −0.787063 | −0.0251933 | ||||||||
\(977\) | 39.5180 | 1.26429 | 0.632146 | − | 0.774849i | \(-0.282174\pi\) | ||||
0.632146 | + | 0.774849i | \(0.282174\pi\) | |||||||
\(978\) | −27.4382 | −0.877378 | ||||||||
\(979\) | 45.0312 | 1.43920 | ||||||||
\(980\) | 0.786623 | 0.0251277 | ||||||||
\(981\) | −14.6697 | −0.468368 | ||||||||
\(982\) | 26.9438 | 0.859811 | ||||||||
\(983\) | −52.2456 | −1.66637 | −0.833187 | − | 0.552991i | \(-0.813486\pi\) | ||||
−0.833187 | + | 0.552991i | \(0.813486\pi\) | |||||||
\(984\) | 4.98827 | 0.159020 | ||||||||
\(985\) | 0.101909 | 0.00324709 | ||||||||
\(986\) | 0.716054 | 0.0228038 | ||||||||
\(987\) | −47.4940 | −1.51175 | ||||||||
\(988\) | −0.919911 | −0.0292663 | ||||||||
\(989\) | 13.8850 | 0.441518 | ||||||||
\(990\) | 2.82431 | 0.0897623 | ||||||||
\(991\) | 12.2889 | 0.390371 | 0.195185 | − | 0.980766i | \(-0.437469\pi\) | ||||
0.195185 | + | 0.980766i | \(0.437469\pi\) | |||||||
\(992\) | −3.93199 | −0.124841 | ||||||||
\(993\) | −50.3864 | −1.59896 | ||||||||
\(994\) | −25.1425 | −0.797471 | ||||||||
\(995\) | −6.42368 | −0.203644 | ||||||||
\(996\) | −21.8451 | −0.692187 | ||||||||
\(997\) | −38.7950 | −1.22865 | −0.614324 | − | 0.789054i | \(-0.710571\pi\) | ||||
−0.614324 | + | 0.789054i | \(0.710571\pi\) | |||||||
\(998\) | −4.45445 | −0.141003 | ||||||||
\(999\) | 4.03172 | 0.127558 |
(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 | 8006.2.a.d.1.16 | ✓ | 98 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8006.2.a.d.1.16 | ✓ | 98 | 1.1 | even | 1 | trivial |