Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4007,2,Mod(1,4007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4007, 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("4007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4007 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4007.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: | \(31.9960560899\) |
Analytic rank: | \(1\) |
Dimension: | \(139\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 4007.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.62057 | −1.85302 | −0.926511 | − | 0.376266i | \(-0.877208\pi\) | ||||
−0.926511 | + | 0.376266i | \(0.877208\pi\) | |||||||
\(3\) | −0.101978 | −0.0588769 | −0.0294385 | − | 0.999567i | \(-0.509372\pi\) | ||||
−0.0294385 | + | 0.999567i | \(0.509372\pi\) | |||||||
\(4\) | 4.86739 | 2.43369 | ||||||||
\(5\) | 0.441388 | 0.197395 | 0.0986974 | − | 0.995117i | \(-0.468532\pi\) | ||||
0.0986974 | + | 0.995117i | \(0.468532\pi\) | |||||||
\(6\) | 0.267240 | 0.109100 | ||||||||
\(7\) | 0.132029 | 0.0499023 | 0.0249512 | − | 0.999689i | \(-0.492057\pi\) | ||||
0.0249512 | + | 0.999689i | \(0.492057\pi\) | |||||||
\(8\) | −7.51419 | −2.65667 | ||||||||
\(9\) | −2.98960 | −0.996534 | ||||||||
\(10\) | −1.15669 | −0.365777 | ||||||||
\(11\) | 3.12451 | 0.942076 | 0.471038 | − | 0.882113i | \(-0.343879\pi\) | ||||
0.471038 | + | 0.882113i | \(0.343879\pi\) | |||||||
\(12\) | −0.496366 | −0.143288 | ||||||||
\(13\) | 5.13253 | 1.42351 | 0.711754 | − | 0.702429i | \(-0.247901\pi\) | ||||
0.711754 | + | 0.702429i | \(0.247901\pi\) | |||||||
\(14\) | −0.345992 | −0.0924702 | ||||||||
\(15\) | −0.0450118 | −0.0116220 | ||||||||
\(16\) | 9.95669 | 2.48917 | ||||||||
\(17\) | 2.52799 | 0.613128 | 0.306564 | − | 0.951850i | \(-0.400821\pi\) | ||||
0.306564 | + | 0.951850i | \(0.400821\pi\) | |||||||
\(18\) | 7.83446 | 1.84660 | ||||||||
\(19\) | −2.43968 | −0.559701 | −0.279850 | − | 0.960044i | \(-0.590285\pi\) | ||||
−0.279850 | + | 0.960044i | \(0.590285\pi\) | |||||||
\(20\) | 2.14841 | 0.480398 | ||||||||
\(21\) | −0.0134641 | −0.00293810 | ||||||||
\(22\) | −8.18801 | −1.74569 | ||||||||
\(23\) | −7.28866 | −1.51979 | −0.759895 | − | 0.650045i | \(-0.774750\pi\) | ||||
−0.759895 | + | 0.650045i | \(0.774750\pi\) | |||||||
\(24\) | 0.766281 | 0.156417 | ||||||||
\(25\) | −4.80518 | −0.961035 | ||||||||
\(26\) | −13.4502 | −2.63779 | ||||||||
\(27\) | 0.610807 | 0.117550 | ||||||||
\(28\) | 0.642637 | 0.121447 | ||||||||
\(29\) | 8.24627 | 1.53129 | 0.765647 | − | 0.643261i | \(-0.222419\pi\) | ||||
0.765647 | + | 0.643261i | \(0.222419\pi\) | |||||||
\(30\) | 0.117957 | 0.0215358 | ||||||||
\(31\) | −3.97742 | −0.714366 | −0.357183 | − | 0.934034i | \(-0.616263\pi\) | ||||
−0.357183 | + | 0.934034i | \(0.616263\pi\) | |||||||
\(32\) | −11.0638 | −1.95583 | ||||||||
\(33\) | −0.318631 | −0.0554666 | ||||||||
\(34\) | −6.62478 | −1.13614 | ||||||||
\(35\) | 0.0582761 | 0.00985046 | ||||||||
\(36\) | −14.5515 | −2.42526 | ||||||||
\(37\) | −7.07808 | −1.16363 | −0.581815 | − | 0.813321i | \(-0.697657\pi\) | ||||
−0.581815 | + | 0.813321i | \(0.697657\pi\) | |||||||
\(38\) | 6.39335 | 1.03714 | ||||||||
\(39\) | −0.523404 | −0.0838118 | ||||||||
\(40\) | −3.31667 | −0.524412 | ||||||||
\(41\) | 0.835244 | 0.130443 | 0.0652216 | − | 0.997871i | \(-0.479225\pi\) | ||||
0.0652216 | + | 0.997871i | \(0.479225\pi\) | |||||||
\(42\) | 0.0352835 | 0.00544436 | ||||||||
\(43\) | −1.92142 | −0.293013 | −0.146507 | − | 0.989210i | \(-0.546803\pi\) | ||||
−0.146507 | + | 0.989210i | \(0.546803\pi\) | |||||||
\(44\) | 15.2082 | 2.29272 | ||||||||
\(45\) | −1.31957 | −0.196710 | ||||||||
\(46\) | 19.1004 | 2.81621 | ||||||||
\(47\) | 0.739888 | 0.107924 | 0.0539619 | − | 0.998543i | \(-0.482815\pi\) | ||||
0.0539619 | + | 0.998543i | \(0.482815\pi\) | |||||||
\(48\) | −1.01536 | −0.146555 | ||||||||
\(49\) | −6.98257 | −0.997510 | ||||||||
\(50\) | 12.5923 | 1.78082 | ||||||||
\(51\) | −0.257799 | −0.0360991 | ||||||||
\(52\) | 24.9820 | 3.46438 | ||||||||
\(53\) | −4.47754 | −0.615037 | −0.307519 | − | 0.951542i | \(-0.599499\pi\) | ||||
−0.307519 | + | 0.951542i | \(0.599499\pi\) | |||||||
\(54\) | −1.60066 | −0.217822 | ||||||||
\(55\) | 1.37912 | 0.185961 | ||||||||
\(56\) | −0.992093 | −0.132574 | ||||||||
\(57\) | 0.248793 | 0.0329535 | ||||||||
\(58\) | −21.6099 | −2.83752 | ||||||||
\(59\) | 6.45865 | 0.840845 | 0.420422 | − | 0.907328i | \(-0.361882\pi\) | ||||
0.420422 | + | 0.907328i | \(0.361882\pi\) | |||||||
\(60\) | −0.219090 | −0.0282844 | ||||||||
\(61\) | −5.59395 | −0.716233 | −0.358116 | − | 0.933677i | \(-0.616581\pi\) | ||||
−0.358116 | + | 0.933677i | \(0.616581\pi\) | |||||||
\(62\) | 10.4231 | 1.32374 | ||||||||
\(63\) | −0.394714 | −0.0497294 | ||||||||
\(64\) | 9.08015 | 1.13502 | ||||||||
\(65\) | 2.26544 | 0.280993 | ||||||||
\(66\) | 0.834995 | 0.102781 | ||||||||
\(67\) | −3.64941 | −0.445846 | −0.222923 | − | 0.974836i | \(-0.571560\pi\) | ||||
−0.222923 | + | 0.974836i | \(0.571560\pi\) | |||||||
\(68\) | 12.3047 | 1.49217 | ||||||||
\(69\) | 0.743282 | 0.0894806 | ||||||||
\(70\) | −0.152717 | −0.0182531 | ||||||||
\(71\) | 2.86339 | 0.339822 | 0.169911 | − | 0.985459i | \(-0.445652\pi\) | ||||
0.169911 | + | 0.985459i | \(0.445652\pi\) | |||||||
\(72\) | 22.4644 | 2.64746 | ||||||||
\(73\) | 1.69508 | 0.198394 | 0.0991970 | − | 0.995068i | \(-0.468373\pi\) | ||||
0.0991970 | + | 0.995068i | \(0.468373\pi\) | |||||||
\(74\) | 18.5486 | 2.15623 | ||||||||
\(75\) | 0.490022 | 0.0565828 | ||||||||
\(76\) | −11.8749 | −1.36214 | ||||||||
\(77\) | 0.412527 | 0.0470118 | ||||||||
\(78\) | 1.37162 | 0.155305 | ||||||||
\(79\) | 1.93943 | 0.218202 | 0.109101 | − | 0.994031i | \(-0.465203\pi\) | ||||
0.109101 | + | 0.994031i | \(0.465203\pi\) | |||||||
\(80\) | 4.39477 | 0.491350 | ||||||||
\(81\) | 8.90651 | 0.989613 | ||||||||
\(82\) | −2.18882 | −0.241714 | ||||||||
\(83\) | 5.06979 | 0.556482 | 0.278241 | − | 0.960511i | \(-0.410249\pi\) | ||||
0.278241 | + | 0.960511i | \(0.410249\pi\) | |||||||
\(84\) | −0.0655348 | −0.00715043 | ||||||||
\(85\) | 1.11582 | 0.121028 | ||||||||
\(86\) | 5.03520 | 0.542960 | ||||||||
\(87\) | −0.840937 | −0.0901579 | ||||||||
\(88\) | −23.4782 | −2.50278 | ||||||||
\(89\) | −14.4032 | −1.52674 | −0.763370 | − | 0.645961i | \(-0.776457\pi\) | ||||
−0.763370 | + | 0.645961i | \(0.776457\pi\) | |||||||
\(90\) | 3.45804 | 0.364509 | ||||||||
\(91\) | 0.677643 | 0.0710363 | ||||||||
\(92\) | −35.4767 | −3.69871 | ||||||||
\(93\) | 0.405609 | 0.0420597 | ||||||||
\(94\) | −1.93893 | −0.199985 | ||||||||
\(95\) | −1.07685 | −0.110482 | ||||||||
\(96\) | 1.12827 | 0.115153 | ||||||||
\(97\) | −12.8228 | −1.30196 | −0.650978 | − | 0.759097i | \(-0.725641\pi\) | ||||
−0.650978 | + | 0.759097i | \(0.725641\pi\) | |||||||
\(98\) | 18.2983 | 1.84841 | ||||||||
\(99\) | −9.34104 | −0.938810 | ||||||||
\(100\) | −23.3887 | −2.33887 | ||||||||
\(101\) | −6.59176 | −0.655904 | −0.327952 | − | 0.944694i | \(-0.606358\pi\) | ||||
−0.327952 | + | 0.944694i | \(0.606358\pi\) | |||||||
\(102\) | 0.675580 | 0.0668924 | ||||||||
\(103\) | −11.1920 | −1.10278 | −0.551390 | − | 0.834248i | \(-0.685902\pi\) | ||||
−0.551390 | + | 0.834248i | \(0.685902\pi\) | |||||||
\(104\) | −38.5668 | −3.78179 | ||||||||
\(105\) | −0.00594287 | −0.000579965 0 | ||||||||
\(106\) | 11.7337 | 1.13968 | ||||||||
\(107\) | 3.00077 | 0.290095 | 0.145048 | − | 0.989425i | \(-0.453666\pi\) | ||||
0.145048 | + | 0.989425i | \(0.453666\pi\) | |||||||
\(108\) | 2.97303 | 0.286080 | ||||||||
\(109\) | 0.000628692 0 | 6.02178e−5 0 | 3.01089e−5 | − | 1.00000i | \(-0.499990\pi\) | ||||
3.01089e−5 | 1.00000i | \(0.499990\pi\) | ||||||||
\(110\) | −3.61409 | −0.344590 | ||||||||
\(111\) | 0.721808 | 0.0685110 | ||||||||
\(112\) | 1.31457 | 0.124216 | ||||||||
\(113\) | 6.40332 | 0.602374 | 0.301187 | − | 0.953565i | \(-0.402617\pi\) | ||||
0.301187 | + | 0.953565i | \(0.402617\pi\) | |||||||
\(114\) | −0.651980 | −0.0610635 | ||||||||
\(115\) | −3.21713 | −0.299999 | ||||||||
\(116\) | 40.1378 | 3.72670 | ||||||||
\(117\) | −15.3442 | −1.41857 | ||||||||
\(118\) | −16.9254 | −1.55810 | ||||||||
\(119\) | 0.333768 | 0.0305965 | ||||||||
\(120\) | 0.338227 | 0.0308758 | ||||||||
\(121\) | −1.23742 | −0.112493 | ||||||||
\(122\) | 14.6594 | 1.32720 | ||||||||
\(123\) | −0.0851764 | −0.00768010 | ||||||||
\(124\) | −19.3597 | −1.73855 | ||||||||
\(125\) | −4.32789 | −0.387098 | ||||||||
\(126\) | 1.03438 | 0.0921496 | ||||||||
\(127\) | 7.04852 | 0.625455 | 0.312727 | − | 0.949843i | \(-0.398757\pi\) | ||||
0.312727 | + | 0.949843i | \(0.398757\pi\) | |||||||
\(128\) | −1.66751 | −0.147389 | ||||||||
\(129\) | 0.195942 | 0.0172517 | ||||||||
\(130\) | −5.93674 | −0.520686 | ||||||||
\(131\) | 8.21195 | 0.717481 | 0.358741 | − | 0.933437i | \(-0.383206\pi\) | ||||
0.358741 | + | 0.933437i | \(0.383206\pi\) | |||||||
\(132\) | −1.55090 | −0.134989 | ||||||||
\(133\) | −0.322109 | −0.0279304 | ||||||||
\(134\) | 9.56354 | 0.826164 | ||||||||
\(135\) | 0.269603 | 0.0232037 | ||||||||
\(136\) | −18.9958 | −1.62888 | ||||||||
\(137\) | −8.98130 | −0.767324 | −0.383662 | − | 0.923473i | \(-0.625337\pi\) | ||||
−0.383662 | + | 0.923473i | \(0.625337\pi\) | |||||||
\(138\) | −1.94782 | −0.165810 | ||||||||
\(139\) | −0.961432 | −0.0815476 | −0.0407738 | − | 0.999168i | \(-0.512982\pi\) | ||||
−0.0407738 | + | 0.999168i | \(0.512982\pi\) | |||||||
\(140\) | 0.283652 | 0.0239730 | ||||||||
\(141\) | −0.0754522 | −0.00635422 | ||||||||
\(142\) | −7.50372 | −0.629698 | ||||||||
\(143\) | 16.0367 | 1.34105 | ||||||||
\(144\) | −29.7665 | −2.48054 | ||||||||
\(145\) | 3.63981 | 0.302269 | ||||||||
\(146\) | −4.44207 | −0.367629 | ||||||||
\(147\) | 0.712067 | 0.0587303 | ||||||||
\(148\) | −34.4518 | −2.83192 | ||||||||
\(149\) | 5.83559 | 0.478070 | 0.239035 | − | 0.971011i | \(-0.423169\pi\) | ||||
0.239035 | + | 0.971011i | \(0.423169\pi\) | |||||||
\(150\) | −1.28414 | −0.104849 | ||||||||
\(151\) | −9.22654 | −0.750845 | −0.375423 | − | 0.926854i | \(-0.622502\pi\) | ||||
−0.375423 | + | 0.926854i | \(0.622502\pi\) | |||||||
\(152\) | 18.3322 | 1.48694 | ||||||||
\(153\) | −7.55768 | −0.611002 | ||||||||
\(154\) | −1.08106 | −0.0871139 | ||||||||
\(155\) | −1.75559 | −0.141012 | ||||||||
\(156\) | −2.54761 | −0.203972 | ||||||||
\(157\) | −4.41795 | −0.352591 | −0.176295 | − | 0.984337i | \(-0.556411\pi\) | ||||
−0.176295 | + | 0.984337i | \(0.556411\pi\) | |||||||
\(158\) | −5.08240 | −0.404334 | ||||||||
\(159\) | 0.456610 | 0.0362115 | ||||||||
\(160\) | −4.88344 | −0.386070 | ||||||||
\(161\) | −0.962316 | −0.0758411 | ||||||||
\(162\) | −23.3401 | −1.83377 | ||||||||
\(163\) | −15.3794 | −1.20461 | −0.602304 | − | 0.798266i | \(-0.705751\pi\) | ||||
−0.602304 | + | 0.798266i | \(0.705751\pi\) | |||||||
\(164\) | 4.06546 | 0.317459 | ||||||||
\(165\) | −0.140640 | −0.0109488 | ||||||||
\(166\) | −13.2857 | −1.03117 | ||||||||
\(167\) | 10.5422 | 0.815780 | 0.407890 | − | 0.913031i | \(-0.366265\pi\) | ||||
0.407890 | + | 0.913031i | \(0.366265\pi\) | |||||||
\(168\) | 0.101171 | 0.00780555 | ||||||||
\(169\) | 13.3428 | 1.02637 | ||||||||
\(170\) | −2.92410 | −0.224268 | ||||||||
\(171\) | 7.29367 | 0.557761 | ||||||||
\(172\) | −9.35227 | −0.713104 | ||||||||
\(173\) | −6.30537 | −0.479389 | −0.239694 | − | 0.970848i | \(-0.577047\pi\) | ||||
−0.239694 | + | 0.970848i | \(0.577047\pi\) | |||||||
\(174\) | 2.20373 | 0.167065 | ||||||||
\(175\) | −0.634423 | −0.0479579 | ||||||||
\(176\) | 31.1098 | 2.34499 | ||||||||
\(177\) | −0.658640 | −0.0495064 | ||||||||
\(178\) | 37.7447 | 2.82909 | ||||||||
\(179\) | −19.4808 | −1.45606 | −0.728032 | − | 0.685543i | \(-0.759565\pi\) | ||||
−0.728032 | + | 0.685543i | \(0.759565\pi\) | |||||||
\(180\) | −6.42288 | −0.478733 | ||||||||
\(181\) | 12.5304 | 0.931378 | 0.465689 | − | 0.884948i | \(-0.345807\pi\) | ||||
0.465689 | + | 0.884948i | \(0.345807\pi\) | |||||||
\(182\) | −1.77581 | −0.131632 | ||||||||
\(183\) | 0.570460 | 0.0421696 | ||||||||
\(184\) | 54.7684 | 4.03758 | ||||||||
\(185\) | −3.12418 | −0.229694 | ||||||||
\(186\) | −1.06293 | −0.0779376 | ||||||||
\(187\) | 7.89874 | 0.577613 | ||||||||
\(188\) | 3.60132 | 0.262653 | ||||||||
\(189\) | 0.0806443 | 0.00586601 | ||||||||
\(190\) | 2.82195 | 0.204726 | ||||||||
\(191\) | −0.363011 | −0.0262666 | −0.0131333 | − | 0.999914i | \(-0.504181\pi\) | ||||
−0.0131333 | + | 0.999914i | \(0.504181\pi\) | |||||||
\(192\) | −0.925974 | −0.0668264 | ||||||||
\(193\) | 12.6886 | 0.913343 | 0.456671 | − | 0.889635i | \(-0.349042\pi\) | ||||
0.456671 | + | 0.889635i | \(0.349042\pi\) | |||||||
\(194\) | 33.6030 | 2.41255 | ||||||||
\(195\) | −0.231024 | −0.0165440 | ||||||||
\(196\) | −33.9869 | −2.42763 | ||||||||
\(197\) | −20.1707 | −1.43710 | −0.718552 | − | 0.695473i | \(-0.755195\pi\) | ||||
−0.718552 | + | 0.695473i | \(0.755195\pi\) | |||||||
\(198\) | 24.4789 | 1.73964 | ||||||||
\(199\) | 23.8261 | 1.68899 | 0.844493 | − | 0.535566i | \(-0.179902\pi\) | ||||
0.844493 | + | 0.535566i | \(0.179902\pi\) | |||||||
\(200\) | 36.1070 | 2.55315 | ||||||||
\(201\) | 0.372159 | 0.0262501 | ||||||||
\(202\) | 17.2742 | 1.21541 | ||||||||
\(203\) | 1.08875 | 0.0764151 | ||||||||
\(204\) | −1.25481 | −0.0878541 | ||||||||
\(205\) | 0.368667 | 0.0257488 | ||||||||
\(206\) | 29.3294 | 2.04348 | ||||||||
\(207\) | 21.7902 | 1.51452 | ||||||||
\(208\) | 51.1030 | 3.54336 | ||||||||
\(209\) | −7.62281 | −0.527281 | ||||||||
\(210\) | 0.0155737 | 0.00107469 | ||||||||
\(211\) | 22.8730 | 1.57464 | 0.787321 | − | 0.616543i | \(-0.211467\pi\) | ||||
0.787321 | + | 0.616543i | \(0.211467\pi\) | |||||||
\(212\) | −21.7939 | −1.49681 | ||||||||
\(213\) | −0.292002 | −0.0200077 | ||||||||
\(214\) | −7.86373 | −0.537553 | ||||||||
\(215\) | −0.848090 | −0.0578392 | ||||||||
\(216\) | −4.58972 | −0.312291 | ||||||||
\(217\) | −0.525136 | −0.0356485 | ||||||||
\(218\) | −0.00164753 | −0.000111585 0 | ||||||||
\(219\) | −0.172861 | −0.0116808 | ||||||||
\(220\) | 6.71273 | 0.452572 | ||||||||
\(221\) | 12.9750 | 0.872792 | ||||||||
\(222\) | −1.89155 | −0.126952 | ||||||||
\(223\) | 0.647158 | 0.0433369 | 0.0216684 | − | 0.999765i | \(-0.493102\pi\) | ||||
0.0216684 | + | 0.999765i | \(0.493102\pi\) | |||||||
\(224\) | −1.46075 | −0.0976003 | ||||||||
\(225\) | 14.3656 | 0.957704 | ||||||||
\(226\) | −16.7803 | −1.11621 | ||||||||
\(227\) | −1.79489 | −0.119131 | −0.0595656 | − | 0.998224i | \(-0.518972\pi\) | ||||
−0.0595656 | + | 0.998224i | \(0.518972\pi\) | |||||||
\(228\) | 1.21097 | 0.0801987 | ||||||||
\(229\) | −4.02583 | −0.266034 | −0.133017 | − | 0.991114i | \(-0.542467\pi\) | ||||
−0.133017 | + | 0.991114i | \(0.542467\pi\) | |||||||
\(230\) | 8.43071 | 0.555905 | ||||||||
\(231\) | −0.0420686 | −0.00276791 | ||||||||
\(232\) | −61.9641 | −4.06814 | ||||||||
\(233\) | 26.6026 | 1.74280 | 0.871398 | − | 0.490577i | \(-0.163214\pi\) | ||||
0.871398 | + | 0.490577i | \(0.163214\pi\) | |||||||
\(234\) | 40.2106 | 2.62865 | ||||||||
\(235\) | 0.326578 | 0.0213036 | ||||||||
\(236\) | 31.4368 | 2.04636 | ||||||||
\(237\) | −0.197778 | −0.0128471 | ||||||||
\(238\) | −0.874664 | −0.0566960 | ||||||||
\(239\) | 5.64054 | 0.364856 | 0.182428 | − | 0.983219i | \(-0.441604\pi\) | ||||
0.182428 | + | 0.983219i | \(0.441604\pi\) | |||||||
\(240\) | −0.448169 | −0.0289292 | ||||||||
\(241\) | −1.47951 | −0.0953033 | −0.0476517 | − | 0.998864i | \(-0.515174\pi\) | ||||
−0.0476517 | + | 0.998864i | \(0.515174\pi\) | |||||||
\(242\) | 3.24275 | 0.208452 | ||||||||
\(243\) | −2.74069 | −0.175815 | ||||||||
\(244\) | −27.2279 | −1.74309 | ||||||||
\(245\) | −3.08202 | −0.196903 | ||||||||
\(246\) | 0.223211 | 0.0142314 | ||||||||
\(247\) | −12.5217 | −0.796738 | ||||||||
\(248\) | 29.8871 | 1.89783 | ||||||||
\(249\) | −0.517006 | −0.0327639 | ||||||||
\(250\) | 11.3415 | 0.717302 | ||||||||
\(251\) | 3.42852 | 0.216407 | 0.108203 | − | 0.994129i | \(-0.465490\pi\) | ||||
0.108203 | + | 0.994129i | \(0.465490\pi\) | |||||||
\(252\) | −1.92123 | −0.121026 | ||||||||
\(253\) | −22.7735 | −1.43176 | ||||||||
\(254\) | −18.4711 | −1.15898 | ||||||||
\(255\) | −0.113789 | −0.00712577 | ||||||||
\(256\) | −13.7905 | −0.861904 | ||||||||
\(257\) | −3.29679 | −0.205648 | −0.102824 | − | 0.994700i | \(-0.532788\pi\) | ||||
−0.102824 | + | 0.994700i | \(0.532788\pi\) | |||||||
\(258\) | −0.513479 | −0.0319678 | ||||||||
\(259\) | −0.934513 | −0.0580678 | ||||||||
\(260\) | 11.0268 | 0.683851 | ||||||||
\(261\) | −24.6531 | −1.52599 | ||||||||
\(262\) | −21.5200 | −1.32951 | ||||||||
\(263\) | −12.8639 | −0.793219 | −0.396610 | − | 0.917987i | \(-0.629813\pi\) | ||||
−0.396610 | + | 0.917987i | \(0.629813\pi\) | |||||||
\(264\) | 2.39426 | 0.147356 | ||||||||
\(265\) | −1.97633 | −0.121405 | ||||||||
\(266\) | 0.844109 | 0.0517556 | ||||||||
\(267\) | 1.46881 | 0.0898898 | ||||||||
\(268\) | −17.7631 | −1.08505 | ||||||||
\(269\) | 30.0794 | 1.83397 | 0.916986 | − | 0.398920i | \(-0.130615\pi\) | ||||
0.916986 | + | 0.398920i | \(0.130615\pi\) | |||||||
\(270\) | −0.706513 | −0.0429970 | ||||||||
\(271\) | 17.4311 | 1.05886 | 0.529431 | − | 0.848353i | \(-0.322406\pi\) | ||||
0.529431 | + | 0.848353i | \(0.322406\pi\) | |||||||
\(272\) | 25.1704 | 1.52618 | ||||||||
\(273\) | −0.0691046 | −0.00418240 | ||||||||
\(274\) | 23.5361 | 1.42187 | ||||||||
\(275\) | −15.0138 | −0.905368 | ||||||||
\(276\) | 3.61784 | 0.217769 | ||||||||
\(277\) | −14.6830 | −0.882214 | −0.441107 | − | 0.897454i | \(-0.645414\pi\) | ||||
−0.441107 | + | 0.897454i | \(0.645414\pi\) | |||||||
\(278\) | 2.51950 | 0.151110 | ||||||||
\(279\) | 11.8909 | 0.711890 | ||||||||
\(280\) | −0.437898 | −0.0261694 | ||||||||
\(281\) | −13.6451 | −0.813996 | −0.406998 | − | 0.913429i | \(-0.633424\pi\) | ||||
−0.406998 | + | 0.913429i | \(0.633424\pi\) | |||||||
\(282\) | 0.197728 | 0.0117745 | ||||||||
\(283\) | −13.1236 | −0.780119 | −0.390060 | − | 0.920790i | \(-0.627546\pi\) | ||||
−0.390060 | + | 0.920790i | \(0.627546\pi\) | |||||||
\(284\) | 13.9372 | 0.827023 | ||||||||
\(285\) | 0.109814 | 0.00650484 | ||||||||
\(286\) | −42.0252 | −2.48500 | ||||||||
\(287\) | 0.110277 | 0.00650942 | ||||||||
\(288\) | 33.0764 | 1.94905 | ||||||||
\(289\) | −10.6093 | −0.624075 | ||||||||
\(290\) | −9.53837 | −0.560112 | ||||||||
\(291\) | 1.30764 | 0.0766552 | ||||||||
\(292\) | 8.25061 | 0.482830 | ||||||||
\(293\) | 3.48200 | 0.203421 | 0.101710 | − | 0.994814i | \(-0.467569\pi\) | ||||
0.101710 | + | 0.994814i | \(0.467569\pi\) | |||||||
\(294\) | −1.86602 | −0.108829 | ||||||||
\(295\) | 2.85077 | 0.165978 | ||||||||
\(296\) | 53.1861 | 3.09138 | ||||||||
\(297\) | 1.90847 | 0.110741 | ||||||||
\(298\) | −15.2926 | −0.885875 | ||||||||
\(299\) | −37.4093 | −2.16343 | ||||||||
\(300\) | 2.38513 | 0.137705 | ||||||||
\(301\) | −0.253683 | −0.0146220 | ||||||||
\(302\) | 24.1788 | 1.39133 | ||||||||
\(303\) | 0.672213 | 0.0386176 | ||||||||
\(304\) | −24.2911 | −1.39319 | ||||||||
\(305\) | −2.46911 | −0.141381 | ||||||||
\(306\) | 19.8054 | 1.13220 | ||||||||
\(307\) | −24.0611 | −1.37324 | −0.686621 | − | 0.727015i | \(-0.740907\pi\) | ||||
−0.686621 | + | 0.727015i | \(0.740907\pi\) | |||||||
\(308\) | 2.00793 | 0.114412 | ||||||||
\(309\) | 1.14134 | 0.0649283 | ||||||||
\(310\) | 4.60064 | 0.261299 | ||||||||
\(311\) | −6.99993 | −0.396930 | −0.198465 | − | 0.980108i | \(-0.563596\pi\) | ||||
−0.198465 | + | 0.980108i | \(0.563596\pi\) | |||||||
\(312\) | 3.93296 | 0.222660 | ||||||||
\(313\) | 15.2908 | 0.864288 | 0.432144 | − | 0.901805i | \(-0.357757\pi\) | ||||
0.432144 | + | 0.901805i | \(0.357757\pi\) | |||||||
\(314\) | 11.5775 | 0.653358 | ||||||||
\(315\) | −0.174222 | −0.00981631 | ||||||||
\(316\) | 9.43994 | 0.531038 | ||||||||
\(317\) | −12.3778 | −0.695207 | −0.347603 | − | 0.937642i | \(-0.613004\pi\) | ||||
−0.347603 | + | 0.937642i | \(0.613004\pi\) | |||||||
\(318\) | −1.19658 | −0.0671008 | ||||||||
\(319\) | 25.7656 | 1.44260 | ||||||||
\(320\) | 4.00787 | 0.224047 | ||||||||
\(321\) | −0.306012 | −0.0170799 | ||||||||
\(322\) | 2.52182 | 0.140535 | ||||||||
\(323\) | −6.16748 | −0.343168 | ||||||||
\(324\) | 43.3515 | 2.40841 | ||||||||
\(325\) | −24.6627 | −1.36804 | ||||||||
\(326\) | 40.3028 | 2.23217 | ||||||||
\(327\) | −6.41127e−5 0 | −3.54544e−6 0 | ||||||||
\(328\) | −6.27618 | −0.346544 | ||||||||
\(329\) | 0.0976868 | 0.00538565 | ||||||||
\(330\) | 0.368557 | 0.0202884 | ||||||||
\(331\) | −8.95634 | −0.492285 | −0.246143 | − | 0.969234i | \(-0.579163\pi\) | ||||
−0.246143 | + | 0.969234i | \(0.579163\pi\) | |||||||
\(332\) | 24.6766 | 1.35431 | ||||||||
\(333\) | 21.1606 | 1.15960 | ||||||||
\(334\) | −27.6266 | −1.51166 | ||||||||
\(335\) | −1.61081 | −0.0880077 | ||||||||
\(336\) | −0.134057 | −0.00731343 | ||||||||
\(337\) | −21.0505 | −1.14669 | −0.573347 | − | 0.819312i | \(-0.694355\pi\) | ||||
−0.573347 | + | 0.819312i | \(0.694355\pi\) | |||||||
\(338\) | −34.9659 | −1.90189 | ||||||||
\(339\) | −0.652997 | −0.0354659 | ||||||||
\(340\) | 5.43115 | 0.294546 | ||||||||
\(341\) | −12.4275 | −0.672987 | ||||||||
\(342\) | −19.1136 | −1.03354 | ||||||||
\(343\) | −1.84611 | −0.0996804 | ||||||||
\(344\) | 14.4379 | 0.778439 | ||||||||
\(345\) | 0.328076 | 0.0176630 | ||||||||
\(346\) | 16.5237 | 0.888318 | ||||||||
\(347\) | −6.70775 | −0.360091 | −0.180045 | − | 0.983658i | \(-0.557624\pi\) | ||||
−0.180045 | + | 0.983658i | \(0.557624\pi\) | |||||||
\(348\) | −4.09317 | −0.219417 | ||||||||
\(349\) | −28.0734 | −1.50273 | −0.751367 | − | 0.659884i | \(-0.770605\pi\) | ||||
−0.751367 | + | 0.659884i | \(0.770605\pi\) | |||||||
\(350\) | 1.66255 | 0.0888671 | ||||||||
\(351\) | 3.13498 | 0.167333 | ||||||||
\(352\) | −34.5691 | −1.84254 | ||||||||
\(353\) | −7.65480 | −0.407424 | −0.203712 | − | 0.979031i | \(-0.565301\pi\) | ||||
−0.203712 | + | 0.979031i | \(0.565301\pi\) | |||||||
\(354\) | 1.72601 | 0.0917365 | ||||||||
\(355\) | 1.26387 | 0.0670791 | ||||||||
\(356\) | −70.1062 | −3.71562 | ||||||||
\(357\) | −0.0340370 | −0.00180143 | ||||||||
\(358\) | 51.0508 | 2.69812 | ||||||||
\(359\) | 10.6200 | 0.560500 | 0.280250 | − | 0.959927i | \(-0.409583\pi\) | ||||
0.280250 | + | 0.959927i | \(0.409583\pi\) | |||||||
\(360\) | 9.91553 | 0.522594 | ||||||||
\(361\) | −13.0480 | −0.686735 | ||||||||
\(362\) | −32.8368 | −1.72586 | ||||||||
\(363\) | 0.126189 | 0.00662323 | ||||||||
\(364\) | 3.29835 | 0.172881 | ||||||||
\(365\) | 0.748188 | 0.0391619 | ||||||||
\(366\) | −1.49493 | −0.0781412 | ||||||||
\(367\) | −25.3560 | −1.32357 | −0.661786 | − | 0.749693i | \(-0.730201\pi\) | ||||
−0.661786 | + | 0.749693i | \(0.730201\pi\) | |||||||
\(368\) | −72.5709 | −3.78302 | ||||||||
\(369\) | −2.49705 | −0.129991 | ||||||||
\(370\) | 8.18714 | 0.425629 | ||||||||
\(371\) | −0.591166 | −0.0306918 | ||||||||
\(372\) | 1.97426 | 0.102360 | ||||||||
\(373\) | −20.9890 | −1.08677 | −0.543384 | − | 0.839485i | \(-0.682857\pi\) | ||||
−0.543384 | + | 0.839485i | \(0.682857\pi\) | |||||||
\(374\) | −20.6992 | −1.07033 | ||||||||
\(375\) | 0.441349 | 0.0227912 | ||||||||
\(376\) | −5.55966 | −0.286718 | ||||||||
\(377\) | 42.3242 | 2.17981 | ||||||||
\(378\) | −0.211334 | −0.0108699 | ||||||||
\(379\) | 11.5161 | 0.591541 | 0.295771 | − | 0.955259i | \(-0.404424\pi\) | ||||
0.295771 | + | 0.955259i | \(0.404424\pi\) | |||||||
\(380\) | −5.24142 | −0.268879 | ||||||||
\(381\) | −0.718793 | −0.0368249 | ||||||||
\(382\) | 0.951297 | 0.0486726 | ||||||||
\(383\) | −31.4218 | −1.60558 | −0.802790 | − | 0.596262i | \(-0.796652\pi\) | ||||
−0.802790 | + | 0.596262i | \(0.796652\pi\) | |||||||
\(384\) | 0.170049 | 0.00867780 | ||||||||
\(385\) | 0.182084 | 0.00927988 | ||||||||
\(386\) | −33.2513 | −1.69244 | ||||||||
\(387\) | 5.74426 | 0.291997 | ||||||||
\(388\) | −62.4134 | −3.16856 | ||||||||
\(389\) | −36.4097 | −1.84605 | −0.923023 | − | 0.384744i | \(-0.874290\pi\) | ||||
−0.923023 | + | 0.384744i | \(0.874290\pi\) | |||||||
\(390\) | 0.605416 | 0.0306564 | ||||||||
\(391\) | −18.4257 | −0.931826 | ||||||||
\(392\) | 52.4684 | 2.65005 | ||||||||
\(393\) | −0.837437 | −0.0422431 | ||||||||
\(394\) | 52.8588 | 2.66299 | ||||||||
\(395\) | 0.856039 | 0.0430720 | ||||||||
\(396\) | −45.4665 | −2.28478 | ||||||||
\(397\) | 15.4754 | 0.776689 | 0.388344 | − | 0.921514i | \(-0.373047\pi\) | ||||
0.388344 | + | 0.921514i | \(0.373047\pi\) | |||||||
\(398\) | −62.4379 | −3.12973 | ||||||||
\(399\) | 0.0328480 | 0.00164446 | ||||||||
\(400\) | −47.8437 | −2.39218 | ||||||||
\(401\) | −10.0375 | −0.501251 | −0.250625 | − | 0.968084i | \(-0.580636\pi\) | ||||
−0.250625 | + | 0.968084i | \(0.580636\pi\) | |||||||
\(402\) | −0.975269 | −0.0486420 | ||||||||
\(403\) | −20.4142 | −1.01691 | ||||||||
\(404\) | −32.0846 | −1.59627 | ||||||||
\(405\) | 3.93123 | 0.195344 | ||||||||
\(406\) | −2.85314 | −0.141599 | ||||||||
\(407\) | −22.1156 | −1.09623 | ||||||||
\(408\) | 1.93715 | 0.0959033 | ||||||||
\(409\) | 9.04992 | 0.447490 | 0.223745 | − | 0.974648i | \(-0.428172\pi\) | ||||
0.223745 | + | 0.974648i | \(0.428172\pi\) | |||||||
\(410\) | −0.966117 | −0.0477131 | ||||||||
\(411\) | 0.915894 | 0.0451777 | ||||||||
\(412\) | −54.4758 | −2.68383 | ||||||||
\(413\) | 0.852731 | 0.0419601 | ||||||||
\(414\) | −57.1027 | −2.80644 | ||||||||
\(415\) | 2.23774 | 0.109847 | ||||||||
\(416\) | −56.7854 | −2.78413 | ||||||||
\(417\) | 0.0980448 | 0.00480127 | ||||||||
\(418\) | 19.9761 | 0.977063 | ||||||||
\(419\) | −1.74656 | −0.0853249 | −0.0426624 | − | 0.999090i | \(-0.513584\pi\) | ||||
−0.0426624 | + | 0.999090i | \(0.513584\pi\) | |||||||
\(420\) | −0.0289263 | −0.00141146 | ||||||||
\(421\) | 8.00195 | 0.389991 | 0.194996 | − | 0.980804i | \(-0.437531\pi\) | ||||
0.194996 | + | 0.980804i | \(0.437531\pi\) | |||||||
\(422\) | −59.9403 | −2.91785 | ||||||||
\(423\) | −2.21197 | −0.107550 | ||||||||
\(424\) | 33.6451 | 1.63395 | ||||||||
\(425\) | −12.1474 | −0.589237 | ||||||||
\(426\) | 0.765213 | 0.0370747 | ||||||||
\(427\) | −0.738565 | −0.0357417 | ||||||||
\(428\) | 14.6059 | 0.706003 | ||||||||
\(429\) | −1.63538 | −0.0789570 | ||||||||
\(430\) | 2.22248 | 0.107177 | ||||||||
\(431\) | 17.3806 | 0.837193 | 0.418597 | − | 0.908172i | \(-0.362522\pi\) | ||||
0.418597 | + | 0.908172i | \(0.362522\pi\) | |||||||
\(432\) | 6.08161 | 0.292602 | ||||||||
\(433\) | −6.35112 | −0.305216 | −0.152608 | − | 0.988287i | \(-0.548767\pi\) | ||||
−0.152608 | + | 0.988287i | \(0.548767\pi\) | |||||||
\(434\) | 1.37615 | 0.0660575 | ||||||||
\(435\) | −0.371180 | −0.0177967 | ||||||||
\(436\) | 0.00306009 | 0.000146552 0 | ||||||||
\(437\) | 17.7820 | 0.850628 | ||||||||
\(438\) | 0.452993 | 0.0216449 | ||||||||
\(439\) | −24.1826 | −1.15417 | −0.577087 | − | 0.816683i | \(-0.695811\pi\) | ||||
−0.577087 | + | 0.816683i | \(0.695811\pi\) | |||||||
\(440\) | −10.3630 | −0.494036 | ||||||||
\(441\) | 20.8751 | 0.994052 | ||||||||
\(442\) | −34.0018 | −1.61730 | ||||||||
\(443\) | −25.0523 | −1.19027 | −0.595136 | − | 0.803625i | \(-0.702902\pi\) | ||||
−0.595136 | + | 0.803625i | \(0.702902\pi\) | |||||||
\(444\) | 3.51332 | 0.166735 | ||||||||
\(445\) | −6.35742 | −0.301371 | ||||||||
\(446\) | −1.69592 | −0.0803043 | ||||||||
\(447\) | −0.595101 | −0.0281473 | ||||||||
\(448\) | 1.19884 | 0.0566401 | ||||||||
\(449\) | 26.2293 | 1.23784 | 0.618919 | − | 0.785455i | \(-0.287571\pi\) | ||||
0.618919 | + | 0.785455i | \(0.287571\pi\) | |||||||
\(450\) | −37.6460 | −1.77465 | ||||||||
\(451\) | 2.60973 | 0.122887 | ||||||||
\(452\) | 31.1674 | 1.46599 | ||||||||
\(453\) | 0.940903 | 0.0442075 | ||||||||
\(454\) | 4.70364 | 0.220753 | ||||||||
\(455\) | 0.299104 | 0.0140222 | ||||||||
\(456\) | −1.86948 | −0.0875464 | ||||||||
\(457\) | −24.4887 | −1.14554 | −0.572768 | − | 0.819718i | \(-0.694130\pi\) | ||||
−0.572768 | + | 0.819718i | \(0.694130\pi\) | |||||||
\(458\) | 10.5500 | 0.492968 | ||||||||
\(459\) | 1.54411 | 0.0720730 | ||||||||
\(460\) | −15.6590 | −0.730105 | ||||||||
\(461\) | −24.5364 | −1.14277 | −0.571386 | − | 0.820681i | \(-0.693594\pi\) | ||||
−0.571386 | + | 0.820681i | \(0.693594\pi\) | |||||||
\(462\) | 0.110244 | 0.00512900 | ||||||||
\(463\) | 14.3318 | 0.666055 | 0.333027 | − | 0.942917i | \(-0.391930\pi\) | ||||
0.333027 | + | 0.942917i | \(0.391930\pi\) | |||||||
\(464\) | 82.1056 | 3.81166 | ||||||||
\(465\) | 0.179031 | 0.00830236 | ||||||||
\(466\) | −69.7140 | −3.22944 | ||||||||
\(467\) | 2.03318 | 0.0940845 | 0.0470422 | − | 0.998893i | \(-0.485020\pi\) | ||||
0.0470422 | + | 0.998893i | \(0.485020\pi\) | |||||||
\(468\) | −74.6862 | −3.45237 | ||||||||
\(469\) | −0.481829 | −0.0222488 | ||||||||
\(470\) | −0.855820 | −0.0394760 | ||||||||
\(471\) | 0.450533 | 0.0207595 | ||||||||
\(472\) | −48.5316 | −2.23385 | ||||||||
\(473\) | −6.00349 | −0.276041 | ||||||||
\(474\) | 0.518292 | 0.0238060 | ||||||||
\(475\) | 11.7231 | 0.537892 | ||||||||
\(476\) | 1.62458 | 0.0744625 | ||||||||
\(477\) | 13.3861 | 0.612905 | ||||||||
\(478\) | −14.7814 | −0.676087 | ||||||||
\(479\) | 30.7404 | 1.40457 | 0.702283 | − | 0.711898i | \(-0.252164\pi\) | ||||
0.702283 | + | 0.711898i | \(0.252164\pi\) | |||||||
\(480\) | 0.498003 | 0.0227306 | ||||||||
\(481\) | −36.3285 | −1.65644 | ||||||||
\(482\) | 3.87715 | 0.176599 | ||||||||
\(483\) | 0.0981349 | 0.00446529 | ||||||||
\(484\) | −6.02300 | −0.273773 | ||||||||
\(485\) | −5.65982 | −0.256999 | ||||||||
\(486\) | 7.18216 | 0.325790 | ||||||||
\(487\) | 7.36486 | 0.333734 | 0.166867 | − | 0.985979i | \(-0.446635\pi\) | ||||
0.166867 | + | 0.985979i | \(0.446635\pi\) | |||||||
\(488\) | 42.0341 | 1.90279 | ||||||||
\(489\) | 1.56836 | 0.0709237 | ||||||||
\(490\) | 8.07666 | 0.364866 | ||||||||
\(491\) | 5.96760 | 0.269314 | 0.134657 | − | 0.990892i | \(-0.457007\pi\) | ||||
0.134657 | + | 0.990892i | \(0.457007\pi\) | |||||||
\(492\) | −0.414587 | −0.0186910 | ||||||||
\(493\) | 20.8465 | 0.938879 | ||||||||
\(494\) | 32.8141 | 1.47637 | ||||||||
\(495\) | −4.12303 | −0.185316 | ||||||||
\(496\) | −39.6020 | −1.77818 | ||||||||
\(497\) | 0.378051 | 0.0169579 | ||||||||
\(498\) | 1.35485 | 0.0607123 | ||||||||
\(499\) | −1.04892 | −0.0469561 | −0.0234781 | − | 0.999724i | \(-0.507474\pi\) | ||||
−0.0234781 | + | 0.999724i | \(0.507474\pi\) | |||||||
\(500\) | −21.0655 | −0.942078 | ||||||||
\(501\) | −1.07507 | −0.0480306 | ||||||||
\(502\) | −8.98469 | −0.401006 | ||||||||
\(503\) | −34.4832 | −1.53753 | −0.768764 | − | 0.639533i | \(-0.779128\pi\) | ||||
−0.768764 | + | 0.639533i | \(0.779128\pi\) | |||||||
\(504\) | 2.96596 | 0.132114 | ||||||||
\(505\) | −2.90952 | −0.129472 | ||||||||
\(506\) | 59.6796 | 2.65308 | ||||||||
\(507\) | −1.36067 | −0.0604297 | ||||||||
\(508\) | 34.3079 | 1.52217 | ||||||||
\(509\) | −0.663447 | −0.0294068 | −0.0147034 | − | 0.999892i | \(-0.504680\pi\) | ||||
−0.0147034 | + | 0.999892i | \(0.504680\pi\) | |||||||
\(510\) | 0.298193 | 0.0132042 | ||||||||
\(511\) | 0.223800 | 0.00990033 | ||||||||
\(512\) | 39.4739 | 1.74452 | ||||||||
\(513\) | −1.49017 | −0.0657927 | ||||||||
\(514\) | 8.63947 | 0.381071 | ||||||||
\(515\) | −4.94001 | −0.217683 | ||||||||
\(516\) | 0.953725 | 0.0419854 | ||||||||
\(517\) | 2.31179 | 0.101672 | ||||||||
\(518\) | 2.44896 | 0.107601 | ||||||||
\(519\) | 0.643008 | 0.0282249 | ||||||||
\(520\) | −17.0229 | −0.746505 | ||||||||
\(521\) | −1.97156 | −0.0863758 | −0.0431879 | − | 0.999067i | \(-0.513751\pi\) | ||||
−0.0431879 | + | 0.999067i | \(0.513751\pi\) | |||||||
\(522\) | 64.6051 | 2.82769 | ||||||||
\(523\) | −4.49425 | −0.196520 | −0.0982599 | − | 0.995161i | \(-0.531328\pi\) | ||||
−0.0982599 | + | 0.995161i | \(0.531328\pi\) | |||||||
\(524\) | 39.9707 | 1.74613 | ||||||||
\(525\) | 0.0646972 | 0.00282362 | ||||||||
\(526\) | 33.7106 | 1.46985 | ||||||||
\(527\) | −10.0549 | −0.437997 | ||||||||
\(528\) | −3.17251 | −0.138066 | ||||||||
\(529\) | 30.1246 | 1.30976 | ||||||||
\(530\) | 5.17912 | 0.224966 | ||||||||
\(531\) | −19.3088 | −0.837930 | ||||||||
\(532\) | −1.56783 | −0.0679740 | ||||||||
\(533\) | 4.28691 | 0.185687 | ||||||||
\(534\) | −3.84912 | −0.166568 | ||||||||
\(535\) | 1.32450 | 0.0572633 | ||||||||
\(536\) | 27.4224 | 1.18447 | ||||||||
\(537\) | 1.98661 | 0.0857286 | ||||||||
\(538\) | −78.8251 | −3.39839 | ||||||||
\(539\) | −21.8171 | −0.939730 | ||||||||
\(540\) | 1.31226 | 0.0564707 | ||||||||
\(541\) | 11.4957 | 0.494239 | 0.247120 | − | 0.968985i | \(-0.420516\pi\) | ||||
0.247120 | + | 0.968985i | \(0.420516\pi\) | |||||||
\(542\) | −45.6793 | −1.96209 | ||||||||
\(543\) | −1.27782 | −0.0548367 | ||||||||
\(544\) | −27.9692 | −1.19917 | ||||||||
\(545\) | 0.000277497 0 | 1.18867e−5 0 | ||||||||
\(546\) | 0.181094 | 0.00775009 | ||||||||
\(547\) | 32.2998 | 1.38104 | 0.690519 | − | 0.723314i | \(-0.257382\pi\) | ||||
0.690519 | + | 0.723314i | \(0.257382\pi\) | |||||||
\(548\) | −43.7155 | −1.86743 | ||||||||
\(549\) | 16.7237 | 0.713750 | ||||||||
\(550\) | 39.3448 | 1.67767 | ||||||||
\(551\) | −20.1183 | −0.857066 | ||||||||
\(552\) | −5.58516 | −0.237720 | ||||||||
\(553\) | 0.256061 | 0.0108888 | ||||||||
\(554\) | 38.4778 | 1.63476 | ||||||||
\(555\) | 0.318597 | 0.0135237 | ||||||||
\(556\) | −4.67966 | −0.198462 | ||||||||
\(557\) | −16.7448 | −0.709502 | −0.354751 | − | 0.934961i | \(-0.615434\pi\) | ||||
−0.354751 | + | 0.934961i | \(0.615434\pi\) | |||||||
\(558\) | −31.1609 | −1.31915 | ||||||||
\(559\) | −9.86172 | −0.417106 | ||||||||
\(560\) | 0.580237 | 0.0245195 | ||||||||
\(561\) | −0.805496 | −0.0340081 | ||||||||
\(562\) | 35.7578 | 1.50835 | ||||||||
\(563\) | 18.2958 | 0.771075 | 0.385537 | − | 0.922692i | \(-0.374016\pi\) | ||||
0.385537 | + | 0.922692i | \(0.374016\pi\) | |||||||
\(564\) | −0.367255 | −0.0154642 | ||||||||
\(565\) | 2.82635 | 0.118905 | ||||||||
\(566\) | 34.3914 | 1.44558 | ||||||||
\(567\) | 1.17592 | 0.0493840 | ||||||||
\(568\) | −21.5161 | −0.902794 | ||||||||
\(569\) | 9.06084 | 0.379850 | 0.189925 | − | 0.981799i | \(-0.439176\pi\) | ||||
0.189925 | + | 0.981799i | \(0.439176\pi\) | |||||||
\(570\) | −0.287776 | −0.0120536 | ||||||||
\(571\) | −3.60957 | −0.151056 | −0.0755280 | − | 0.997144i | \(-0.524064\pi\) | ||||
−0.0755280 | + | 0.997144i | \(0.524064\pi\) | |||||||
\(572\) | 78.0566 | 3.26371 | ||||||||
\(573\) | 0.0370191 | 0.00154650 | ||||||||
\(574\) | −0.288988 | −0.0120621 | ||||||||
\(575\) | 35.0233 | 1.46057 | ||||||||
\(576\) | −27.1460 | −1.13108 | ||||||||
\(577\) | −11.0761 | −0.461105 | −0.230552 | − | 0.973060i | \(-0.574053\pi\) | ||||
−0.230552 | + | 0.973060i | \(0.574053\pi\) | |||||||
\(578\) | 27.8023 | 1.15642 | ||||||||
\(579\) | −1.29395 | −0.0537748 | ||||||||
\(580\) | 17.7163 | 0.735631 | ||||||||
\(581\) | 0.669360 | 0.0277697 | ||||||||
\(582\) | −3.42676 | −0.142044 | ||||||||
\(583\) | −13.9901 | −0.579412 | ||||||||
\(584\) | −12.7372 | −0.527067 | ||||||||
\(585\) | −6.77275 | −0.280019 | ||||||||
\(586\) | −9.12482 | −0.376943 | ||||||||
\(587\) | −11.8527 | −0.489212 | −0.244606 | − | 0.969623i | \(-0.578659\pi\) | ||||
−0.244606 | + | 0.969623i | \(0.578659\pi\) | |||||||
\(588\) | 3.46591 | 0.142932 | ||||||||
\(589\) | 9.70363 | 0.399831 | ||||||||
\(590\) | −7.47065 | −0.307562 | ||||||||
\(591\) | 2.05697 | 0.0846123 | ||||||||
\(592\) | −70.4743 | −2.89648 | ||||||||
\(593\) | −7.00961 | −0.287850 | −0.143925 | − | 0.989589i | \(-0.545972\pi\) | ||||
−0.143925 | + | 0.989589i | \(0.545972\pi\) | |||||||
\(594\) | −5.00129 | −0.205205 | ||||||||
\(595\) | 0.147321 | 0.00603959 | ||||||||
\(596\) | 28.4041 | 1.16348 | ||||||||
\(597\) | −2.42973 | −0.0994424 | ||||||||
\(598\) | 98.0336 | 4.00889 | ||||||||
\(599\) | −27.7312 | −1.13307 | −0.566534 | − | 0.824038i | \(-0.691716\pi\) | ||||
−0.566534 | + | 0.824038i | \(0.691716\pi\) | |||||||
\(600\) | −3.68212 | −0.150322 | ||||||||
\(601\) | −6.34988 | −0.259017 | −0.129509 | − | 0.991578i | \(-0.541340\pi\) | ||||
−0.129509 | + | 0.991578i | \(0.541340\pi\) | |||||||
\(602\) | 0.664794 | 0.0270950 | ||||||||
\(603\) | 10.9103 | 0.444301 | ||||||||
\(604\) | −44.9092 | −1.82733 | ||||||||
\(605\) | −0.546182 | −0.0222055 | ||||||||
\(606\) | −1.76158 | −0.0715594 | ||||||||
\(607\) | −39.7937 | −1.61518 | −0.807589 | − | 0.589746i | \(-0.799228\pi\) | ||||
−0.807589 | + | 0.589746i | \(0.799228\pi\) | |||||||
\(608\) | 26.9922 | 1.09468 | ||||||||
\(609\) | −0.111028 | −0.00449909 | ||||||||
\(610\) | 6.47046 | 0.261981 | ||||||||
\(611\) | 3.79749 | 0.153630 | ||||||||
\(612\) | −36.7862 | −1.48699 | ||||||||
\(613\) | −16.3497 | −0.660358 | −0.330179 | − | 0.943918i | \(-0.607109\pi\) | ||||
−0.330179 | + | 0.943918i | \(0.607109\pi\) | |||||||
\(614\) | 63.0539 | 2.54465 | ||||||||
\(615\) | −0.0375958 | −0.00151601 | ||||||||
\(616\) | −3.09981 | −0.124895 | ||||||||
\(617\) | 5.14855 | 0.207273 | 0.103636 | − | 0.994615i | \(-0.466952\pi\) | ||||
0.103636 | + | 0.994615i | \(0.466952\pi\) | |||||||
\(618\) | −2.99095 | −0.120314 | ||||||||
\(619\) | 7.12427 | 0.286348 | 0.143174 | − | 0.989698i | \(-0.454269\pi\) | ||||
0.143174 | + | 0.989698i | \(0.454269\pi\) | |||||||
\(620\) | −8.54512 | −0.343180 | ||||||||
\(621\) | −4.45196 | −0.178651 | ||||||||
\(622\) | 18.3438 | 0.735520 | ||||||||
\(623\) | −1.90165 | −0.0761879 | ||||||||
\(624\) | −5.21137 | −0.208622 | ||||||||
\(625\) | 22.1156 | 0.884624 | ||||||||
\(626\) | −40.0706 | −1.60155 | ||||||||
\(627\) | 0.777358 | 0.0310447 | ||||||||
\(628\) | −21.5039 | −0.858098 | ||||||||
\(629\) | −17.8933 | −0.713453 | ||||||||
\(630\) | 0.456562 | 0.0181899 | ||||||||
\(631\) | −21.8705 | −0.870652 | −0.435326 | − | 0.900273i | \(-0.643367\pi\) | ||||
−0.435326 | + | 0.900273i | \(0.643367\pi\) | |||||||
\(632\) | −14.5732 | −0.579691 | ||||||||
\(633\) | −2.33254 | −0.0927101 | ||||||||
\(634\) | 32.4369 | 1.28823 | ||||||||
\(635\) | 3.11113 | 0.123462 | ||||||||
\(636\) | 2.22250 | 0.0881277 | ||||||||
\(637\) | −35.8382 | −1.41996 | ||||||||
\(638\) | −67.5205 | −2.67316 | ||||||||
\(639\) | −8.56040 | −0.338644 | ||||||||
\(640\) | −0.736020 | −0.0290938 | ||||||||
\(641\) | −10.1702 | −0.401699 | −0.200849 | − | 0.979622i | \(-0.564370\pi\) | ||||
−0.200849 | + | 0.979622i | \(0.564370\pi\) | |||||||
\(642\) | 0.801926 | 0.0316495 | ||||||||
\(643\) | −7.92988 | −0.312724 | −0.156362 | − | 0.987700i | \(-0.549977\pi\) | ||||
−0.156362 | + | 0.987700i | \(0.549977\pi\) | |||||||
\(644\) | −4.68396 | −0.184574 | ||||||||
\(645\) | 0.0864864 | 0.00340540 | ||||||||
\(646\) | 16.1623 | 0.635898 | ||||||||
\(647\) | 31.8072 | 1.25047 | 0.625234 | − | 0.780437i | \(-0.285003\pi\) | ||||
0.625234 | + | 0.780437i | \(0.285003\pi\) | |||||||
\(648\) | −66.9252 | −2.62907 | ||||||||
\(649\) | 20.1801 | 0.792140 | ||||||||
\(650\) | 64.6303 | 2.53501 | ||||||||
\(651\) | 0.0535522 | 0.00209888 | ||||||||
\(652\) | −74.8576 | −2.93165 | ||||||||
\(653\) | −19.9997 | −0.782649 | −0.391325 | − | 0.920253i | \(-0.627983\pi\) | ||||
−0.391325 | + | 0.920253i | \(0.627983\pi\) | |||||||
\(654\) | 0.000168012 0 | 6.56978e−6 0 | ||||||||
\(655\) | 3.62466 | 0.141627 | ||||||||
\(656\) | 8.31627 | 0.324696 | ||||||||
\(657\) | −5.06761 | −0.197706 | ||||||||
\(658\) | −0.255995 | −0.00997973 | ||||||||
\(659\) | 16.5548 | 0.644883 | 0.322442 | − | 0.946589i | \(-0.395496\pi\) | ||||
0.322442 | + | 0.946589i | \(0.395496\pi\) | |||||||
\(660\) | −0.684549 | −0.0266460 | ||||||||
\(661\) | 41.4304 | 1.61146 | 0.805728 | − | 0.592285i | \(-0.201774\pi\) | ||||
0.805728 | + | 0.592285i | \(0.201774\pi\) | |||||||
\(662\) | 23.4707 | 0.912216 | ||||||||
\(663\) | −1.32316 | −0.0513873 | ||||||||
\(664\) | −38.0954 | −1.47839 | ||||||||
\(665\) | −0.142175 | −0.00551331 | ||||||||
\(666\) | −55.4529 | −2.14876 | ||||||||
\(667\) | −60.1043 | −2.32725 | ||||||||
\(668\) | 51.3130 | 1.98536 | ||||||||
\(669\) | −0.0659958 | −0.00255154 | ||||||||
\(670\) | 4.22123 | 0.163080 | ||||||||
\(671\) | −17.4784 | −0.674745 | ||||||||
\(672\) | 0.148964 | 0.00574641 | ||||||||
\(673\) | 41.9546 | 1.61723 | 0.808616 | − | 0.588337i | \(-0.200217\pi\) | ||||
0.808616 | + | 0.588337i | \(0.200217\pi\) | |||||||
\(674\) | 55.1643 | 2.12485 | ||||||||
\(675\) | −2.93503 | −0.112970 | ||||||||
\(676\) | 64.9448 | 2.49788 | ||||||||
\(677\) | −30.9091 | −1.18793 | −0.593967 | − | 0.804489i | \(-0.702439\pi\) | ||||
−0.593967 | + | 0.804489i | \(0.702439\pi\) | |||||||
\(678\) | 1.71122 | 0.0657192 | ||||||||
\(679\) | −1.69298 | −0.0649706 | ||||||||
\(680\) | −8.38452 | −0.321532 | ||||||||
\(681\) | 0.183039 | 0.00701408 | ||||||||
\(682\) | 32.5671 | 1.24706 | ||||||||
\(683\) | −31.2750 | −1.19670 | −0.598352 | − | 0.801233i | \(-0.704177\pi\) | ||||
−0.598352 | + | 0.801233i | \(0.704177\pi\) | |||||||
\(684\) | 35.5011 | 1.35742 | ||||||||
\(685\) | −3.96424 | −0.151466 | ||||||||
\(686\) | 4.83785 | 0.184710 | ||||||||
\(687\) | 0.410546 | 0.0156633 | ||||||||
\(688\) | −19.1309 | −0.729360 | ||||||||
\(689\) | −22.9811 | −0.875510 | ||||||||
\(690\) | −0.859746 | −0.0327300 | ||||||||
\(691\) | −4.57116 | −0.173895 | −0.0869475 | − | 0.996213i | \(-0.527711\pi\) | ||||
−0.0869475 | + | 0.996213i | \(0.527711\pi\) | |||||||
\(692\) | −30.6907 | −1.16668 | ||||||||
\(693\) | −1.23329 | −0.0468488 | ||||||||
\(694\) | 17.5781 | 0.667256 | ||||||||
\(695\) | −0.424365 | −0.0160971 | ||||||||
\(696\) | 6.31896 | 0.239520 | ||||||||
\(697\) | 2.11149 | 0.0799783 | ||||||||
\(698\) | 73.5683 | 2.78460 | ||||||||
\(699\) | −2.71288 | −0.102610 | ||||||||
\(700\) | −3.08799 | −0.116715 | ||||||||
\(701\) | 38.9005 | 1.46925 | 0.734626 | − | 0.678472i | \(-0.237358\pi\) | ||||
0.734626 | + | 0.678472i | \(0.237358\pi\) | |||||||
\(702\) | −8.21544 | −0.310072 | ||||||||
\(703\) | 17.2682 | 0.651284 | ||||||||
\(704\) | 28.3710 | 1.06927 | ||||||||
\(705\) | −0.0333037 | −0.00125429 | ||||||||
\(706\) | 20.0599 | 0.754965 | ||||||||
\(707\) | −0.870304 | −0.0327312 | ||||||||
\(708\) | −3.20585 | −0.120483 | ||||||||
\(709\) | 6.47613 | 0.243216 | 0.121608 | − | 0.992578i | \(-0.461195\pi\) | ||||
0.121608 | + | 0.992578i | \(0.461195\pi\) | |||||||
\(710\) | −3.31205 | −0.124299 | ||||||||
\(711\) | −5.79811 | −0.217446 | ||||||||
\(712\) | 108.229 | 4.05604 | ||||||||
\(713\) | 28.9901 | 1.08569 | ||||||||
\(714\) | 0.0891963 | 0.00333809 | ||||||||
\(715\) | 7.07839 | 0.264717 | ||||||||
\(716\) | −94.8206 | −3.54361 | ||||||||
\(717\) | −0.575210 | −0.0214816 | ||||||||
\(718\) | −27.8304 | −1.03862 | ||||||||
\(719\) | −6.77978 | −0.252843 | −0.126422 | − | 0.991977i | \(-0.540349\pi\) | ||||
−0.126422 | + | 0.991977i | \(0.540349\pi\) | |||||||
\(720\) | −13.1386 | −0.489646 | ||||||||
\(721\) | −1.47767 | −0.0550313 | ||||||||
\(722\) | 34.1931 | 1.27254 | ||||||||
\(723\) | 0.150877 | 0.00561117 | ||||||||
\(724\) | 60.9904 | 2.26669 | ||||||||
\(725\) | −39.6248 | −1.47163 | ||||||||
\(726\) | −0.330688 | −0.0122730 | ||||||||
\(727\) | 1.60517 | 0.0595326 | 0.0297663 | − | 0.999557i | \(-0.490524\pi\) | ||||
0.0297663 | + | 0.999557i | \(0.490524\pi\) | |||||||
\(728\) | −5.09194 | −0.188720 | ||||||||
\(729\) | −26.4400 | −0.979261 | ||||||||
\(730\) | −1.96068 | −0.0725680 | ||||||||
\(731\) | −4.85732 | −0.179654 | ||||||||
\(732\) | 2.77665 | 0.102628 | ||||||||
\(733\) | −15.5754 | −0.575291 | −0.287646 | − | 0.957737i | \(-0.592873\pi\) | ||||
−0.287646 | + | 0.957737i | \(0.592873\pi\) | |||||||
\(734\) | 66.4472 | 2.45261 | ||||||||
\(735\) | 0.314298 | 0.0115931 | ||||||||
\(736\) | 80.6405 | 2.97245 | ||||||||
\(737\) | −11.4026 | −0.420021 | ||||||||
\(738\) | 6.54368 | 0.240876 | ||||||||
\(739\) | −45.5199 | −1.67448 | −0.837239 | − | 0.546838i | \(-0.815831\pi\) | ||||
−0.837239 | + | 0.546838i | \(0.815831\pi\) | |||||||
\(740\) | −15.2066 | −0.559006 | ||||||||
\(741\) | 1.27694 | 0.0469095 | ||||||||
\(742\) | 1.54919 | 0.0568726 | ||||||||
\(743\) | 1.55980 | 0.0572234 | 0.0286117 | − | 0.999591i | \(-0.490891\pi\) | ||||
0.0286117 | + | 0.999591i | \(0.490891\pi\) | |||||||
\(744\) | −3.04782 | −0.111739 | ||||||||
\(745\) | 2.57576 | 0.0943686 | ||||||||
\(746\) | 55.0030 | 2.01380 | ||||||||
\(747\) | −15.1566 | −0.554553 | ||||||||
\(748\) | 38.4462 | 1.40573 | ||||||||
\(749\) | 0.396189 | 0.0144764 | ||||||||
\(750\) | −1.15659 | −0.0422325 | ||||||||
\(751\) | 25.9677 | 0.947575 | 0.473788 | − | 0.880639i | \(-0.342886\pi\) | ||||
0.473788 | + | 0.880639i | \(0.342886\pi\) | |||||||
\(752\) | 7.36683 | 0.268641 | ||||||||
\(753\) | −0.349634 | −0.0127414 | ||||||||
\(754\) | −110.914 | −4.03923 | ||||||||
\(755\) | −4.07249 | −0.148213 | ||||||||
\(756\) | 0.392527 | 0.0142761 | ||||||||
\(757\) | −44.6929 | −1.62439 | −0.812195 | − | 0.583385i | \(-0.801728\pi\) | ||||
−0.812195 | + | 0.583385i | \(0.801728\pi\) | |||||||
\(758\) | −30.1787 | −1.09614 | ||||||||
\(759\) | 2.32239 | 0.0842976 | ||||||||
\(760\) | 8.09162 | 0.293514 | ||||||||
\(761\) | −10.7663 | −0.390278 | −0.195139 | − | 0.980776i | \(-0.562516\pi\) | ||||
−0.195139 | + | 0.980776i | \(0.562516\pi\) | |||||||
\(762\) | 1.88365 | 0.0682373 | ||||||||
\(763\) | 8.30057e−5 0 | 3.00501e−6 0 | ||||||||
\(764\) | −1.76692 | −0.0639248 | ||||||||
\(765\) | −3.33587 | −0.120609 | ||||||||
\(766\) | 82.3431 | 2.97518 | ||||||||
\(767\) | 33.1492 | 1.19695 | ||||||||
\(768\) | 1.40632 | 0.0507463 | ||||||||
\(769\) | 10.3293 | 0.372485 | 0.186243 | − | 0.982504i | \(-0.440369\pi\) | ||||
0.186243 | + | 0.982504i | \(0.440369\pi\) | |||||||
\(770\) | −0.477165 | −0.0171958 | ||||||||
\(771\) | 0.336200 | 0.0121079 | ||||||||
\(772\) | 61.7602 | 2.22280 | ||||||||
\(773\) | −14.7801 | −0.531605 | −0.265802 | − | 0.964028i | \(-0.585637\pi\) | ||||
−0.265802 | + | 0.964028i | \(0.585637\pi\) | |||||||
\(774\) | −15.0532 | −0.541078 | ||||||||
\(775\) | 19.1122 | 0.686531 | ||||||||
\(776\) | 96.3528 | 3.45886 | ||||||||
\(777\) | 0.0952997 | 0.00341886 | ||||||||
\(778\) | 95.4143 | 3.42077 | ||||||||
\(779\) | −2.03773 | −0.0730092 | ||||||||
\(780\) | −1.12449 | −0.0402630 | ||||||||
\(781\) | 8.94670 | 0.320138 | ||||||||
\(782\) | 48.2857 | 1.72669 | ||||||||
\(783\) | 5.03688 | 0.180003 | ||||||||
\(784\) | −69.5233 | −2.48297 | ||||||||
\(785\) | −1.95003 | −0.0695995 | ||||||||
\(786\) | 2.19456 | 0.0782774 | ||||||||
\(787\) | −46.8380 | −1.66960 | −0.834798 | − | 0.550557i | \(-0.814415\pi\) | ||||
−0.834798 | + | 0.550557i | \(0.814415\pi\) | |||||||
\(788\) | −98.1788 | −3.49747 | ||||||||
\(789\) | 1.31183 | 0.0467023 | ||||||||
\(790\) | −2.24331 | −0.0798134 | ||||||||
\(791\) | 0.845425 | 0.0300599 | ||||||||
\(792\) | 70.1904 | 2.49411 | ||||||||
\(793\) | −28.7111 | −1.01956 | ||||||||
\(794\) | −40.5544 | −1.43922 | ||||||||
\(795\) | 0.201542 | 0.00714796 | ||||||||
\(796\) | 115.971 | 4.11048 | ||||||||
\(797\) | −52.4024 | −1.85619 | −0.928094 | − | 0.372346i | \(-0.878554\pi\) | ||||
−0.928094 | + | 0.372346i | \(0.878554\pi\) | |||||||
\(798\) | −0.0860804 | −0.00304721 | ||||||||
\(799\) | 1.87043 | 0.0661710 | ||||||||
\(800\) | 53.1636 | 1.87962 | ||||||||
\(801\) | 43.0599 | 1.52145 | ||||||||
\(802\) | 26.3041 | 0.928829 | ||||||||
\(803\) | 5.29630 | 0.186902 | ||||||||
\(804\) | 1.81144 | 0.0638846 | ||||||||
\(805\) | −0.424755 | −0.0149706 | ||||||||
\(806\) | 53.4969 | 1.88435 | ||||||||
\(807\) | −3.06743 | −0.107979 | ||||||||
\(808\) | 49.5317 | 1.74252 | ||||||||
\(809\) | 3.23455 | 0.113721 | 0.0568604 | − | 0.998382i | \(-0.481891\pi\) | ||||
0.0568604 | + | 0.998382i | \(0.481891\pi\) | |||||||
\(810\) | −10.3021 | −0.361978 | ||||||||
\(811\) | −33.0582 | −1.16083 | −0.580415 | − | 0.814321i | \(-0.697110\pi\) | ||||
−0.580415 | + | 0.814321i | \(0.697110\pi\) | |||||||
\(812\) | 5.29936 | 0.185971 | ||||||||
\(813\) | −1.77758 | −0.0623425 | ||||||||
\(814\) | 57.9554 | 2.03133 | ||||||||
\(815\) | −6.78829 | −0.237783 | ||||||||
\(816\) | −2.56683 | −0.0898569 | ||||||||
\(817\) | 4.68764 | 0.164000 | ||||||||
\(818\) | −23.7159 | −0.829208 | ||||||||
\(819\) | −2.02588 | −0.0707901 | ||||||||
\(820\) | 1.79444 | 0.0626647 | ||||||||
\(821\) | 38.2559 | 1.33514 | 0.667570 | − | 0.744547i | \(-0.267335\pi\) | ||||
0.667570 | + | 0.744547i | \(0.267335\pi\) | |||||||
\(822\) | −2.40016 | −0.0837154 | ||||||||
\(823\) | −10.3868 | −0.362059 | −0.181030 | − | 0.983478i | \(-0.557943\pi\) | ||||
−0.181030 | + | 0.983478i | \(0.557943\pi\) | |||||||
\(824\) | 84.0988 | 2.92972 | ||||||||
\(825\) | 1.53108 | 0.0533053 | ||||||||
\(826\) | −2.23464 | −0.0777531 | ||||||||
\(827\) | −7.28524 | −0.253333 | −0.126666 | − | 0.991945i | \(-0.540428\pi\) | ||||
−0.126666 | + | 0.991945i | \(0.540428\pi\) | |||||||
\(828\) | 106.061 | 3.68588 | ||||||||
\(829\) | −29.6680 | −1.03041 | −0.515207 | − | 0.857066i | \(-0.672285\pi\) | ||||
−0.515207 | + | 0.857066i | \(0.672285\pi\) | |||||||
\(830\) | −5.86417 | −0.203548 | ||||||||
\(831\) | 1.49734 | 0.0519421 | ||||||||
\(832\) | 46.6041 | 1.61571 | ||||||||
\(833\) | −17.6519 | −0.611601 | ||||||||
\(834\) | −0.256933 | −0.00889687 | ||||||||
\(835\) | 4.65320 | 0.161031 | ||||||||
\(836\) | −37.1032 | −1.28324 | ||||||||
\(837\) | −2.42944 | −0.0839736 | ||||||||
\(838\) | 4.57697 | 0.158109 | ||||||||
\(839\) | −5.57662 | −0.192526 | −0.0962632 | − | 0.995356i | \(-0.530689\pi\) | ||||
−0.0962632 | + | 0.995356i | \(0.530689\pi\) | |||||||
\(840\) | 0.0446559 | 0.00154077 | ||||||||
\(841\) | 39.0010 | 1.34486 | ||||||||
\(842\) | −20.9697 | −0.722663 | ||||||||
\(843\) | 1.39149 | 0.0479256 | ||||||||
\(844\) | 111.332 | 3.83220 | ||||||||
\(845\) | 5.88937 | 0.202601 | ||||||||
\(846\) | 5.79662 | 0.199292 | ||||||||
\(847\) | −0.163376 | −0.00561365 | ||||||||
\(848\) | −44.5815 | −1.53093 | ||||||||
\(849\) | 1.33832 | 0.0459310 | ||||||||
\(850\) | 31.8332 | 1.09187 | ||||||||
\(851\) | 51.5897 | 1.76847 | ||||||||
\(852\) | −1.42129 | −0.0486926 | ||||||||
\(853\) | 6.99449 | 0.239487 | 0.119743 | − | 0.992805i | \(-0.461793\pi\) | ||||
0.119743 | + | 0.992805i | \(0.461793\pi\) | |||||||
\(854\) | 1.93546 | 0.0662301 | ||||||||
\(855\) | 3.21934 | 0.110099 | ||||||||
\(856\) | −22.5484 | −0.770687 | ||||||||
\(857\) | 42.2914 | 1.44465 | 0.722323 | − | 0.691556i | \(-0.243074\pi\) | ||||
0.722323 | + | 0.691556i | \(0.243074\pi\) | |||||||
\(858\) | 4.28564 | 0.146309 | ||||||||
\(859\) | −17.0741 | −0.582560 | −0.291280 | − | 0.956638i | \(-0.594081\pi\) | ||||
−0.291280 | + | 0.956638i | \(0.594081\pi\) | |||||||
\(860\) | −4.12798 | −0.140763 | ||||||||
\(861\) | −0.0112458 | −0.000383255 0 | ||||||||
\(862\) | −45.5470 | −1.55134 | ||||||||
\(863\) | −18.0840 | −0.615588 | −0.307794 | − | 0.951453i | \(-0.599591\pi\) | ||||
−0.307794 | + | 0.951453i | \(0.599591\pi\) | |||||||
\(864\) | −6.75786 | −0.229907 | ||||||||
\(865\) | −2.78312 | −0.0946288 | ||||||||
\(866\) | 16.6436 | 0.565571 | ||||||||
\(867\) | 1.08191 | 0.0367436 | ||||||||
\(868\) | −2.55604 | −0.0867576 | ||||||||
\(869\) | 6.05976 | 0.205563 | ||||||||
\(870\) | 0.972702 | 0.0329777 | ||||||||
\(871\) | −18.7307 | −0.634666 | ||||||||
\(872\) | −0.00472411 | −0.000159979 0 | ||||||||
\(873\) | 38.3350 | 1.29744 | ||||||||
\(874\) | −46.5990 | −1.57623 | ||||||||
\(875\) | −0.571408 | −0.0193171 | ||||||||
\(876\) | −0.841380 | −0.0284276 | ||||||||
\(877\) | −32.3366 | −1.09193 | −0.545965 | − | 0.837808i | \(-0.683837\pi\) | ||||
−0.545965 | + | 0.837808i | \(0.683837\pi\) | |||||||
\(878\) | 63.3723 | 2.13871 | ||||||||
\(879\) | −0.355087 | −0.0119768 | ||||||||
\(880\) | 13.7315 | 0.462889 | ||||||||
\(881\) | 3.89811 | 0.131331 | 0.0656653 | − | 0.997842i | \(-0.479083\pi\) | ||||
0.0656653 | + | 0.997842i | \(0.479083\pi\) | |||||||
\(882\) | −54.7046 | −1.84200 | ||||||||
\(883\) | −14.3985 | −0.484548 | −0.242274 | − | 0.970208i | \(-0.577893\pi\) | ||||
−0.242274 | + | 0.970208i | \(0.577893\pi\) | |||||||
\(884\) | 63.1543 | 2.12411 | ||||||||
\(885\) | −0.290716 | −0.00977230 | ||||||||
\(886\) | 65.6514 | 2.20560 | ||||||||
\(887\) | 17.4870 | 0.587157 | 0.293579 | − | 0.955935i | \(-0.405154\pi\) | ||||
0.293579 | + | 0.955935i | \(0.405154\pi\) | |||||||
\(888\) | −5.42380 | −0.182011 | ||||||||
\(889\) | 0.930610 | 0.0312117 | ||||||||
\(890\) | 16.6601 | 0.558447 | ||||||||
\(891\) | 27.8285 | 0.932290 | ||||||||
\(892\) | 3.14997 | 0.105469 | ||||||||
\(893\) | −1.80509 | −0.0604050 | ||||||||
\(894\) | 1.55950 | 0.0521576 | ||||||||
\(895\) | −8.59859 | −0.287419 | ||||||||
\(896\) | −0.220160 | −0.00735504 | ||||||||
\(897\) | 3.81492 | 0.127376 | ||||||||
\(898\) | −68.7357 | −2.29374 | ||||||||
\(899\) | −32.7989 | −1.09390 | ||||||||
\(900\) | 69.9227 | 2.33076 | ||||||||
\(901\) | −11.3192 | −0.377096 | ||||||||
\(902\) | −6.83898 | −0.227713 | ||||||||
\(903\) | 0.0258700 | 0.000860901 0 | ||||||||
\(904\) | −48.1158 | −1.60031 | ||||||||
\(905\) | 5.53077 | 0.183849 | ||||||||
\(906\) | −2.46570 | −0.0819175 | ||||||||
\(907\) | 46.7463 | 1.55219 | 0.776093 | − | 0.630619i | \(-0.217199\pi\) | ||||
0.776093 | + | 0.630619i | \(0.217199\pi\) | |||||||
\(908\) | −8.73644 | −0.289929 | ||||||||
\(909\) | 19.7067 | 0.653631 | ||||||||
\(910\) | −0.783822 | −0.0259835 | ||||||||
\(911\) | 26.1831 | 0.867483 | 0.433742 | − | 0.901037i | \(-0.357193\pi\) | ||||
0.433742 | + | 0.901037i | \(0.357193\pi\) | |||||||
\(912\) | 2.47716 | 0.0820269 | ||||||||
\(913\) | 15.8406 | 0.524248 | ||||||||
\(914\) | 64.1745 | 2.12270 | ||||||||
\(915\) | 0.251794 | 0.00832405 | ||||||||
\(916\) | −19.5953 | −0.647447 | ||||||||
\(917\) | 1.08422 | 0.0358040 | ||||||||
\(918\) | −4.04646 | −0.133553 | ||||||||
\(919\) | −30.0504 | −0.991273 | −0.495636 | − | 0.868530i | \(-0.665065\pi\) | ||||
−0.495636 | + | 0.868530i | \(0.665065\pi\) | |||||||
\(920\) | 24.1741 | 0.796997 | ||||||||
\(921\) | 2.45370 | 0.0808523 | ||||||||
\(922\) | 64.2993 | 2.11758 | ||||||||
\(923\) | 14.6964 | 0.483739 | ||||||||
\(924\) | −0.204764 | −0.00673625 | ||||||||
\(925\) | 34.0114 | 1.11829 | ||||||||
\(926\) | −37.5575 | −1.23421 | ||||||||
\(927\) | 33.4596 | 1.09896 | ||||||||
\(928\) | −91.2353 | −2.99495 | ||||||||
\(929\) | −5.18353 | −0.170066 | −0.0850330 | − | 0.996378i | \(-0.527100\pi\) | ||||
−0.0850330 | + | 0.996378i | \(0.527100\pi\) | |||||||
\(930\) | −0.469163 | −0.0153845 | ||||||||
\(931\) | 17.0352 | 0.558307 | ||||||||
\(932\) | 129.485 | 4.24143 | ||||||||
\(933\) | 0.713838 | 0.0233700 | ||||||||
\(934\) | −5.32810 | −0.174341 | ||||||||
\(935\) | 3.48641 | 0.114018 | ||||||||
\(936\) | 115.299 | 3.76868 | ||||||||
\(937\) | −50.0447 | −1.63489 | −0.817445 | − | 0.576007i | \(-0.804610\pi\) | ||||
−0.817445 | + | 0.576007i | \(0.804610\pi\) | |||||||
\(938\) | 1.26267 | 0.0412275 | ||||||||
\(939\) | −1.55932 | −0.0508866 | ||||||||
\(940\) | 1.58958 | 0.0518464 | ||||||||
\(941\) | −15.1265 | −0.493111 | −0.246556 | − | 0.969129i | \(-0.579299\pi\) | ||||
−0.246556 | + | 0.969129i | \(0.579299\pi\) | |||||||
\(942\) | −1.18065 | −0.0384677 | ||||||||
\(943\) | −6.08781 | −0.198246 | ||||||||
\(944\) | 64.3068 | 2.09301 | ||||||||
\(945\) | 0.0355954 | 0.00115792 | ||||||||
\(946\) | 15.7326 | 0.511510 | ||||||||
\(947\) | 57.6410 | 1.87308 | 0.936541 | − | 0.350558i | \(-0.114008\pi\) | ||||
0.936541 | + | 0.350558i | \(0.114008\pi\) | |||||||
\(948\) | −0.962665 | −0.0312659 | ||||||||
\(949\) | 8.70004 | 0.282415 | ||||||||
\(950\) | −30.7212 | −0.996727 | ||||||||
\(951\) | 1.26226 | 0.0409317 | ||||||||
\(952\) | −2.50800 | −0.0812847 | ||||||||
\(953\) | 0.813305 | 0.0263455 | 0.0131728 | − | 0.999913i | \(-0.495807\pi\) | ||||
0.0131728 | + | 0.999913i | \(0.495807\pi\) | |||||||
\(954\) | −35.0791 | −1.13573 | ||||||||
\(955\) | −0.160229 | −0.00518488 | ||||||||
\(956\) | 27.4547 | 0.887948 | ||||||||
\(957\) | −2.62752 | −0.0849356 | ||||||||
\(958\) | −80.5574 | −2.60269 | ||||||||
\(959\) | −1.18579 | −0.0382913 | ||||||||
\(960\) | −0.408714 | −0.0131912 | ||||||||
\(961\) | −15.1801 | −0.489681 | ||||||||
\(962\) | 95.2013 | 3.06941 | ||||||||
\(963\) | −8.97110 | −0.289090 | ||||||||
\(964\) | −7.20133 | −0.231939 | ||||||||
\(965\) | 5.60058 | 0.180289 | ||||||||
\(966\) | −0.257169 | −0.00827429 | ||||||||
\(967\) | 8.27797 | 0.266202 | 0.133101 | − | 0.991103i | \(-0.457507\pi\) | ||||
0.133101 | + | 0.991103i | \(0.457507\pi\) | |||||||
\(968\) | 9.29821 | 0.298856 | ||||||||
\(969\) | 0.628947 | 0.0202047 | ||||||||
\(970\) | 14.8320 | 0.476225 | ||||||||
\(971\) | −31.8997 | −1.02371 | −0.511855 | − | 0.859072i | \(-0.671042\pi\) | ||||
−0.511855 | + | 0.859072i | \(0.671042\pi\) | |||||||
\(972\) | −13.3400 | −0.427880 | ||||||||
\(973\) | −0.126937 | −0.00406942 | ||||||||
\(974\) | −19.3001 | −0.618416 | ||||||||
\(975\) | 2.51505 | 0.0805461 | ||||||||
\(976\) | −55.6973 | −1.78283 | ||||||||
\(977\) | −31.0871 | −0.994563 | −0.497282 | − | 0.867589i | \(-0.665668\pi\) | ||||
−0.497282 | + | 0.867589i | \(0.665668\pi\) | |||||||
\(978\) | −4.11000 | −0.131423 | ||||||||
\(979\) | −45.0031 | −1.43831 | ||||||||
\(980\) | −15.0014 | −0.479202 | ||||||||
\(981\) | −0.00187954 | −6.00090e−5 0 | ||||||||
\(982\) | −15.6385 | −0.499045 | ||||||||
\(983\) | −16.1716 | −0.515793 | −0.257896 | − | 0.966173i | \(-0.583029\pi\) | ||||
−0.257896 | + | 0.966173i | \(0.583029\pi\) | |||||||
\(984\) | 0.640032 | 0.0204035 | ||||||||
\(985\) | −8.90312 | −0.283677 | ||||||||
\(986\) | −54.6297 | −1.73976 | ||||||||
\(987\) | −0.00996189 | −0.000317090 0 | ||||||||
\(988\) | −60.9481 | −1.93902 | ||||||||
\(989\) | 14.0045 | 0.445319 | ||||||||
\(990\) | 10.8047 | 0.343395 | ||||||||
\(991\) | −1.12799 | −0.0358317 | −0.0179159 | − | 0.999839i | \(-0.505703\pi\) | ||||
−0.0179159 | + | 0.999839i | \(0.505703\pi\) | |||||||
\(992\) | 44.0055 | 1.39718 | ||||||||
\(993\) | 0.913349 | 0.0289842 | ||||||||
\(994\) | −0.990710 | −0.0314234 | ||||||||
\(995\) | 10.5166 | 0.333397 | ||||||||
\(996\) | −2.51647 | −0.0797374 | ||||||||
\(997\) | −26.0257 | −0.824242 | −0.412121 | − | 0.911129i | \(-0.635212\pi\) | ||||
−0.412121 | + | 0.911129i | \(0.635212\pi\) | |||||||
\(998\) | 2.74877 | 0.0870108 | ||||||||
\(999\) | −4.32334 | −0.136784 |
(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 | 4007.2.a.a.1.6 | ✓ | 139 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4007.2.a.a.1.6 | ✓ | 139 | 1.1 | even | 1 | trivial |