Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4030,2,Mod(1,4030)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4030, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4030.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4030.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: | \(32.1797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 16x^{6} + 18x^{5} + 64x^{4} - 84x^{3} - 19x^{2} + 22x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.08271\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4030.1 |
$q$-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 | ||||||||
\(3\) | −3.08271 | −1.77980 | −0.889902 | − | 0.456151i | \(-0.849228\pi\) | ||||
−0.889902 | + | 0.456151i | \(0.849228\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −3.08271 | −1.25851 | ||||||||
\(7\) | −2.62527 | −0.992260 | −0.496130 | − | 0.868248i | \(-0.665246\pi\) | ||||
−0.496130 | + | 0.868248i | \(0.665246\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 6.50312 | 2.16771 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0.190183 | 0.0573425 | 0.0286712 | − | 0.999589i | \(-0.490872\pi\) | ||||
0.0286712 | + | 0.999589i | \(0.490872\pi\) | |||||||
\(12\) | −3.08271 | −0.889902 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −2.62527 | −0.701634 | ||||||||
\(15\) | 3.08271 | 0.795953 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.93705 | −1.68248 | −0.841241 | − | 0.540660i | \(-0.818174\pi\) | ||||
−0.841241 | + | 0.540660i | \(0.818174\pi\) | |||||||
\(18\) | 6.50312 | 1.53280 | ||||||||
\(19\) | −0.237470 | −0.0544794 | −0.0272397 | − | 0.999629i | \(-0.508672\pi\) | ||||
−0.0272397 | + | 0.999629i | \(0.508672\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 8.09297 | 1.76603 | ||||||||
\(22\) | 0.190183 | 0.0405472 | ||||||||
\(23\) | 4.00840 | 0.835810 | 0.417905 | − | 0.908491i | \(-0.362765\pi\) | ||||
0.417905 | + | 0.908491i | \(0.362765\pi\) | |||||||
\(24\) | −3.08271 | −0.629256 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −10.7991 | −2.07829 | ||||||||
\(28\) | −2.62527 | −0.496130 | ||||||||
\(29\) | 0.0461297 | 0.00856607 | 0.00428303 | − | 0.999991i | \(-0.498637\pi\) | ||||
0.00428303 | + | 0.999991i | \(0.498637\pi\) | |||||||
\(30\) | 3.08271 | 0.562824 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.586281 | −0.102058 | ||||||||
\(34\) | −6.93705 | −1.18969 | ||||||||
\(35\) | 2.62527 | 0.443752 | ||||||||
\(36\) | 6.50312 | 1.08385 | ||||||||
\(37\) | −9.02092 | −1.48303 | −0.741515 | − | 0.670936i | \(-0.765892\pi\) | ||||
−0.741515 | + | 0.670936i | \(0.765892\pi\) | |||||||
\(38\) | −0.237470 | −0.0385228 | ||||||||
\(39\) | 3.08271 | 0.493629 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −2.50696 | −0.391522 | −0.195761 | − | 0.980652i | \(-0.562718\pi\) | ||||
−0.195761 | + | 0.980652i | \(0.562718\pi\) | |||||||
\(42\) | 8.09297 | 1.24877 | ||||||||
\(43\) | −2.72309 | −0.415267 | −0.207633 | − | 0.978207i | \(-0.566576\pi\) | ||||
−0.207633 | + | 0.978207i | \(0.566576\pi\) | |||||||
\(44\) | 0.190183 | 0.0286712 | ||||||||
\(45\) | −6.50312 | −0.969427 | ||||||||
\(46\) | 4.00840 | 0.591007 | ||||||||
\(47\) | −10.0962 | −1.47268 | −0.736341 | − | 0.676611i | \(-0.763448\pi\) | ||||
−0.736341 | + | 0.676611i | \(0.763448\pi\) | |||||||
\(48\) | −3.08271 | −0.444951 | ||||||||
\(49\) | −0.107936 | −0.0154195 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 21.3849 | 2.99449 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | −1.99103 | −0.273489 | −0.136745 | − | 0.990606i | \(-0.543664\pi\) | ||||
−0.136745 | + | 0.990606i | \(0.543664\pi\) | |||||||
\(54\) | −10.7991 | −1.46957 | ||||||||
\(55\) | −0.190183 | −0.0256443 | ||||||||
\(56\) | −2.62527 | −0.350817 | ||||||||
\(57\) | 0.732053 | 0.0969628 | ||||||||
\(58\) | 0.0461297 | 0.00605712 | ||||||||
\(59\) | 10.7728 | 1.40250 | 0.701248 | − | 0.712917i | \(-0.252627\pi\) | ||||
0.701248 | + | 0.712917i | \(0.252627\pi\) | |||||||
\(60\) | 3.08271 | 0.397976 | ||||||||
\(61\) | 0.753431 | 0.0964670 | 0.0482335 | − | 0.998836i | \(-0.484641\pi\) | ||||
0.0482335 | + | 0.998836i | \(0.484641\pi\) | |||||||
\(62\) | −1.00000 | −0.127000 | ||||||||
\(63\) | −17.0725 | −2.15093 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | −0.586281 | −0.0721662 | ||||||||
\(67\) | 13.2211 | 1.61522 | 0.807608 | − | 0.589719i | \(-0.200762\pi\) | ||||
0.807608 | + | 0.589719i | \(0.200762\pi\) | |||||||
\(68\) | −6.93705 | −0.841241 | ||||||||
\(69\) | −12.3568 | −1.48758 | ||||||||
\(70\) | 2.62527 | 0.313780 | ||||||||
\(71\) | 6.14349 | 0.729098 | 0.364549 | − | 0.931184i | \(-0.381223\pi\) | ||||
0.364549 | + | 0.931184i | \(0.381223\pi\) | |||||||
\(72\) | 6.50312 | 0.766400 | ||||||||
\(73\) | −5.91955 | −0.692831 | −0.346415 | − | 0.938081i | \(-0.612601\pi\) | ||||
−0.346415 | + | 0.938081i | \(0.612601\pi\) | |||||||
\(74\) | −9.02092 | −1.04866 | ||||||||
\(75\) | −3.08271 | −0.355961 | ||||||||
\(76\) | −0.237470 | −0.0272397 | ||||||||
\(77\) | −0.499284 | −0.0568986 | ||||||||
\(78\) | 3.08271 | 0.349048 | ||||||||
\(79\) | 0.817179 | 0.0919398 | 0.0459699 | − | 0.998943i | \(-0.485362\pi\) | ||||
0.0459699 | + | 0.998943i | \(0.485362\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 13.7812 | 1.53124 | ||||||||
\(82\) | −2.50696 | −0.276848 | ||||||||
\(83\) | 0.435097 | 0.0477581 | 0.0238791 | − | 0.999715i | \(-0.492398\pi\) | ||||
0.0238791 | + | 0.999715i | \(0.492398\pi\) | |||||||
\(84\) | 8.09297 | 0.883015 | ||||||||
\(85\) | 6.93705 | 0.752429 | ||||||||
\(86\) | −2.72309 | −0.293638 | ||||||||
\(87\) | −0.142205 | −0.0152459 | ||||||||
\(88\) | 0.190183 | 0.0202736 | ||||||||
\(89\) | −1.09084 | −0.115629 | −0.0578145 | − | 0.998327i | \(-0.518413\pi\) | ||||
−0.0578145 | + | 0.998327i | \(0.518413\pi\) | |||||||
\(90\) | −6.50312 | −0.685489 | ||||||||
\(91\) | 2.62527 | 0.275203 | ||||||||
\(92\) | 4.00840 | 0.417905 | ||||||||
\(93\) | 3.08271 | 0.319662 | ||||||||
\(94\) | −10.0962 | −1.04134 | ||||||||
\(95\) | 0.237470 | 0.0243639 | ||||||||
\(96\) | −3.08271 | −0.314628 | ||||||||
\(97\) | 8.17526 | 0.830072 | 0.415036 | − | 0.909805i | \(-0.363769\pi\) | ||||
0.415036 | + | 0.909805i | \(0.363769\pi\) | |||||||
\(98\) | −0.107936 | −0.0109032 | ||||||||
\(99\) | 1.23679 | 0.124302 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −5.96499 | −0.593538 | −0.296769 | − | 0.954949i | \(-0.595909\pi\) | ||||
−0.296769 | + | 0.954949i | \(0.595909\pi\) | |||||||
\(102\) | 21.3849 | 2.11742 | ||||||||
\(103\) | 14.3243 | 1.41141 | 0.705707 | − | 0.708504i | \(-0.250629\pi\) | ||||
0.705707 | + | 0.708504i | \(0.250629\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | −8.09297 | −0.789793 | ||||||||
\(106\) | −1.99103 | −0.193386 | ||||||||
\(107\) | −1.30962 | −0.126606 | −0.0633028 | − | 0.997994i | \(-0.520163\pi\) | ||||
−0.0633028 | + | 0.997994i | \(0.520163\pi\) | |||||||
\(108\) | −10.7991 | −1.03914 | ||||||||
\(109\) | −0.402902 | −0.0385910 | −0.0192955 | − | 0.999814i | \(-0.506142\pi\) | ||||
−0.0192955 | + | 0.999814i | \(0.506142\pi\) | |||||||
\(110\) | −0.190183 | −0.0181333 | ||||||||
\(111\) | 27.8089 | 2.63950 | ||||||||
\(112\) | −2.62527 | −0.248065 | ||||||||
\(113\) | 2.66374 | 0.250584 | 0.125292 | − | 0.992120i | \(-0.460013\pi\) | ||||
0.125292 | + | 0.992120i | \(0.460013\pi\) | |||||||
\(114\) | 0.732053 | 0.0685630 | ||||||||
\(115\) | −4.00840 | −0.373786 | ||||||||
\(116\) | 0.0461297 | 0.00428303 | ||||||||
\(117\) | −6.50312 | −0.601213 | ||||||||
\(118\) | 10.7728 | 0.991714 | ||||||||
\(119\) | 18.2117 | 1.66946 | ||||||||
\(120\) | 3.08271 | 0.281412 | ||||||||
\(121\) | −10.9638 | −0.996712 | ||||||||
\(122\) | 0.753431 | 0.0682124 | ||||||||
\(123\) | 7.72824 | 0.696832 | ||||||||
\(124\) | −1.00000 | −0.0898027 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −17.0725 | −1.52094 | ||||||||
\(127\) | 10.3607 | 0.919366 | 0.459683 | − | 0.888083i | \(-0.347963\pi\) | ||||
0.459683 | + | 0.888083i | \(0.347963\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 8.39449 | 0.739094 | ||||||||
\(130\) | 1.00000 | 0.0877058 | ||||||||
\(131\) | −10.1846 | −0.889836 | −0.444918 | − | 0.895571i | \(-0.646767\pi\) | ||||
−0.444918 | + | 0.895571i | \(0.646767\pi\) | |||||||
\(132\) | −0.586281 | −0.0510292 | ||||||||
\(133\) | 0.623425 | 0.0540578 | ||||||||
\(134\) | 13.2211 | 1.14213 | ||||||||
\(135\) | 10.7991 | 0.929439 | ||||||||
\(136\) | −6.93705 | −0.594847 | ||||||||
\(137\) | 6.23374 | 0.532584 | 0.266292 | − | 0.963892i | \(-0.414201\pi\) | ||||
0.266292 | + | 0.963892i | \(0.414201\pi\) | |||||||
\(138\) | −12.3568 | −1.05188 | ||||||||
\(139\) | 3.87231 | 0.328445 | 0.164222 | − | 0.986423i | \(-0.447489\pi\) | ||||
0.164222 | + | 0.986423i | \(0.447489\pi\) | |||||||
\(140\) | 2.62527 | 0.221876 | ||||||||
\(141\) | 31.1237 | 2.62109 | ||||||||
\(142\) | 6.14349 | 0.515550 | ||||||||
\(143\) | −0.190183 | −0.0159039 | ||||||||
\(144\) | 6.50312 | 0.541926 | ||||||||
\(145\) | −0.0461297 | −0.00383086 | ||||||||
\(146\) | −5.91955 | −0.489905 | ||||||||
\(147\) | 0.332736 | 0.0274436 | ||||||||
\(148\) | −9.02092 | −0.741515 | ||||||||
\(149\) | 15.1295 | 1.23946 | 0.619729 | − | 0.784816i | \(-0.287243\pi\) | ||||
0.619729 | + | 0.784816i | \(0.287243\pi\) | |||||||
\(150\) | −3.08271 | −0.251702 | ||||||||
\(151\) | 8.12239 | 0.660991 | 0.330495 | − | 0.943808i | \(-0.392784\pi\) | ||||
0.330495 | + | 0.943808i | \(0.392784\pi\) | |||||||
\(152\) | −0.237470 | −0.0192614 | ||||||||
\(153\) | −45.1124 | −3.64713 | ||||||||
\(154\) | −0.499284 | −0.0402334 | ||||||||
\(155\) | 1.00000 | 0.0803219 | ||||||||
\(156\) | 3.08271 | 0.246815 | ||||||||
\(157\) | 19.0833 | 1.52301 | 0.761507 | − | 0.648157i | \(-0.224460\pi\) | ||||
0.761507 | + | 0.648157i | \(0.224460\pi\) | |||||||
\(158\) | 0.817179 | 0.0650113 | ||||||||
\(159\) | 6.13778 | 0.486758 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −10.5232 | −0.829341 | ||||||||
\(162\) | 13.7812 | 1.08275 | ||||||||
\(163\) | −4.24035 | −0.332130 | −0.166065 | − | 0.986115i | \(-0.553106\pi\) | ||||
−0.166065 | + | 0.986115i | \(0.553106\pi\) | |||||||
\(164\) | −2.50696 | −0.195761 | ||||||||
\(165\) | 0.586281 | 0.0456419 | ||||||||
\(166\) | 0.435097 | 0.0337701 | ||||||||
\(167\) | 13.5092 | 1.04537 | 0.522687 | − | 0.852524i | \(-0.324929\pi\) | ||||
0.522687 | + | 0.852524i | \(0.324929\pi\) | |||||||
\(168\) | 8.09297 | 0.624386 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 6.93705 | 0.532047 | ||||||||
\(171\) | −1.54430 | −0.118095 | ||||||||
\(172\) | −2.72309 | −0.207633 | ||||||||
\(173\) | 1.08997 | 0.0828688 | 0.0414344 | − | 0.999141i | \(-0.486807\pi\) | ||||
0.0414344 | + | 0.999141i | \(0.486807\pi\) | |||||||
\(174\) | −0.142205 | −0.0107805 | ||||||||
\(175\) | −2.62527 | −0.198452 | ||||||||
\(176\) | 0.190183 | 0.0143356 | ||||||||
\(177\) | −33.2094 | −2.49617 | ||||||||
\(178\) | −1.09084 | −0.0817620 | ||||||||
\(179\) | 12.1337 | 0.906915 | 0.453457 | − | 0.891278i | \(-0.350190\pi\) | ||||
0.453457 | + | 0.891278i | \(0.350190\pi\) | |||||||
\(180\) | −6.50312 | −0.484714 | ||||||||
\(181\) | 3.25448 | 0.241904 | 0.120952 | − | 0.992658i | \(-0.461405\pi\) | ||||
0.120952 | + | 0.992658i | \(0.461405\pi\) | |||||||
\(182\) | 2.62527 | 0.194598 | ||||||||
\(183\) | −2.32261 | −0.171692 | ||||||||
\(184\) | 4.00840 | 0.295503 | ||||||||
\(185\) | 9.02092 | 0.663231 | ||||||||
\(186\) | 3.08271 | 0.226035 | ||||||||
\(187\) | −1.31931 | −0.0964776 | ||||||||
\(188\) | −10.0962 | −0.736341 | ||||||||
\(189\) | 28.3506 | 2.06220 | ||||||||
\(190\) | 0.237470 | 0.0172279 | ||||||||
\(191\) | −10.6539 | −0.770892 | −0.385446 | − | 0.922730i | \(-0.625952\pi\) | ||||
−0.385446 | + | 0.922730i | \(0.625952\pi\) | |||||||
\(192\) | −3.08271 | −0.222476 | ||||||||
\(193\) | −12.5653 | −0.904472 | −0.452236 | − | 0.891898i | \(-0.649374\pi\) | ||||
−0.452236 | + | 0.891898i | \(0.649374\pi\) | |||||||
\(194\) | 8.17526 | 0.586950 | ||||||||
\(195\) | −3.08271 | −0.220758 | ||||||||
\(196\) | −0.107936 | −0.00770973 | ||||||||
\(197\) | 9.06106 | 0.645574 | 0.322787 | − | 0.946472i | \(-0.395380\pi\) | ||||
0.322787 | + | 0.946472i | \(0.395380\pi\) | |||||||
\(198\) | 1.23679 | 0.0878945 | ||||||||
\(199\) | 25.5763 | 1.81305 | 0.906527 | − | 0.422148i | \(-0.138724\pi\) | ||||
0.906527 | + | 0.422148i | \(0.138724\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −40.7569 | −2.87477 | ||||||||
\(202\) | −5.96499 | −0.419695 | ||||||||
\(203\) | −0.121103 | −0.00849977 | ||||||||
\(204\) | 21.3849 | 1.49724 | ||||||||
\(205\) | 2.50696 | 0.175094 | ||||||||
\(206\) | 14.3243 | 0.998021 | ||||||||
\(207\) | 26.0671 | 1.81179 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | −0.0451629 | −0.00312399 | ||||||||
\(210\) | −8.09297 | −0.558468 | ||||||||
\(211\) | 8.79692 | 0.605605 | 0.302802 | − | 0.953053i | \(-0.402078\pi\) | ||||
0.302802 | + | 0.953053i | \(0.402078\pi\) | |||||||
\(212\) | −1.99103 | −0.136745 | ||||||||
\(213\) | −18.9386 | −1.29765 | ||||||||
\(214\) | −1.30962 | −0.0895237 | ||||||||
\(215\) | 2.72309 | 0.185713 | ||||||||
\(216\) | −10.7991 | −0.734786 | ||||||||
\(217\) | 2.62527 | 0.178215 | ||||||||
\(218\) | −0.402902 | −0.0272880 | ||||||||
\(219\) | 18.2483 | 1.23310 | ||||||||
\(220\) | −0.190183 | −0.0128222 | ||||||||
\(221\) | 6.93705 | 0.466637 | ||||||||
\(222\) | 27.8089 | 1.86641 | ||||||||
\(223\) | −26.7938 | −1.79425 | −0.897124 | − | 0.441779i | \(-0.854347\pi\) | ||||
−0.897124 | + | 0.441779i | \(0.854347\pi\) | |||||||
\(224\) | −2.62527 | −0.175409 | ||||||||
\(225\) | 6.50312 | 0.433541 | ||||||||
\(226\) | 2.66374 | 0.177189 | ||||||||
\(227\) | 10.2446 | 0.679958 | 0.339979 | − | 0.940433i | \(-0.389580\pi\) | ||||
0.339979 | + | 0.940433i | \(0.389580\pi\) | |||||||
\(228\) | 0.732053 | 0.0484814 | ||||||||
\(229\) | −11.9399 | −0.789010 | −0.394505 | − | 0.918894i | \(-0.629084\pi\) | ||||
−0.394505 | + | 0.918894i | \(0.629084\pi\) | |||||||
\(230\) | −4.00840 | −0.264306 | ||||||||
\(231\) | 1.53915 | 0.101268 | ||||||||
\(232\) | 0.0461297 | 0.00302856 | ||||||||
\(233\) | 25.8498 | 1.69348 | 0.846739 | − | 0.532008i | \(-0.178562\pi\) | ||||
0.846739 | + | 0.532008i | \(0.178562\pi\) | |||||||
\(234\) | −6.50312 | −0.425122 | ||||||||
\(235\) | 10.0962 | 0.658603 | ||||||||
\(236\) | 10.7728 | 0.701248 | ||||||||
\(237\) | −2.51913 | −0.163635 | ||||||||
\(238\) | 18.2117 | 1.18049 | ||||||||
\(239\) | −4.74305 | −0.306802 | −0.153401 | − | 0.988164i | \(-0.549023\pi\) | ||||
−0.153401 | + | 0.988164i | \(0.549023\pi\) | |||||||
\(240\) | 3.08271 | 0.198988 | ||||||||
\(241\) | −5.76720 | −0.371498 | −0.185749 | − | 0.982597i | \(-0.559471\pi\) | ||||
−0.185749 | + | 0.982597i | \(0.559471\pi\) | |||||||
\(242\) | −10.9638 | −0.704782 | ||||||||
\(243\) | −10.0861 | −0.647024 | ||||||||
\(244\) | 0.753431 | 0.0482335 | ||||||||
\(245\) | 0.107936 | 0.00689579 | ||||||||
\(246\) | 7.72824 | 0.492735 | ||||||||
\(247\) | 0.237470 | 0.0151099 | ||||||||
\(248\) | −1.00000 | −0.0635001 | ||||||||
\(249\) | −1.34128 | −0.0850001 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 21.6019 | 1.36350 | 0.681751 | − | 0.731584i | \(-0.261219\pi\) | ||||
0.681751 | + | 0.731584i | \(0.261219\pi\) | |||||||
\(252\) | −17.0725 | −1.07546 | ||||||||
\(253\) | 0.762332 | 0.0479274 | ||||||||
\(254\) | 10.3607 | 0.650090 | ||||||||
\(255\) | −21.3849 | −1.33918 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.1584 | 0.945556 | 0.472778 | − | 0.881182i | \(-0.343251\pi\) | ||||
0.472778 | + | 0.881182i | \(0.343251\pi\) | |||||||
\(258\) | 8.39449 | 0.522618 | ||||||||
\(259\) | 23.6824 | 1.47155 | ||||||||
\(260\) | 1.00000 | 0.0620174 | ||||||||
\(261\) | 0.299987 | 0.0185687 | ||||||||
\(262\) | −10.1846 | −0.629209 | ||||||||
\(263\) | 1.44308 | 0.0889843 | 0.0444921 | − | 0.999010i | \(-0.485833\pi\) | ||||
0.0444921 | + | 0.999010i | \(0.485833\pi\) | |||||||
\(264\) | −0.586281 | −0.0360831 | ||||||||
\(265\) | 1.99103 | 0.122308 | ||||||||
\(266\) | 0.623425 | 0.0382246 | ||||||||
\(267\) | 3.36275 | 0.205797 | ||||||||
\(268\) | 13.2211 | 0.807608 | ||||||||
\(269\) | −9.94188 | −0.606167 | −0.303084 | − | 0.952964i | \(-0.598016\pi\) | ||||
−0.303084 | + | 0.952964i | \(0.598016\pi\) | |||||||
\(270\) | 10.7991 | 0.657212 | ||||||||
\(271\) | 23.9828 | 1.45685 | 0.728427 | − | 0.685124i | \(-0.240252\pi\) | ||||
0.728427 | + | 0.685124i | \(0.240252\pi\) | |||||||
\(272\) | −6.93705 | −0.420620 | ||||||||
\(273\) | −8.09297 | −0.489809 | ||||||||
\(274\) | 6.23374 | 0.376594 | ||||||||
\(275\) | 0.190183 | 0.0114685 | ||||||||
\(276\) | −12.3568 | −0.743789 | ||||||||
\(277\) | −14.2200 | −0.854394 | −0.427197 | − | 0.904158i | \(-0.640499\pi\) | ||||
−0.427197 | + | 0.904158i | \(0.640499\pi\) | |||||||
\(278\) | 3.87231 | 0.232246 | ||||||||
\(279\) | −6.50312 | −0.389331 | ||||||||
\(280\) | 2.62527 | 0.156890 | ||||||||
\(281\) | 15.7629 | 0.940339 | 0.470169 | − | 0.882576i | \(-0.344193\pi\) | ||||
0.470169 | + | 0.882576i | \(0.344193\pi\) | |||||||
\(282\) | 31.1237 | 1.85339 | ||||||||
\(283\) | −18.2060 | −1.08223 | −0.541117 | − | 0.840947i | \(-0.681999\pi\) | ||||
−0.541117 | + | 0.840947i | \(0.681999\pi\) | |||||||
\(284\) | 6.14349 | 0.364549 | ||||||||
\(285\) | −0.732053 | −0.0433631 | ||||||||
\(286\) | −0.190183 | −0.0112458 | ||||||||
\(287\) | 6.58146 | 0.388492 | ||||||||
\(288\) | 6.50312 | 0.383200 | ||||||||
\(289\) | 31.1227 | 1.83075 | ||||||||
\(290\) | −0.0461297 | −0.00270883 | ||||||||
\(291\) | −25.2020 | −1.47737 | ||||||||
\(292\) | −5.91955 | −0.346415 | ||||||||
\(293\) | 13.6870 | 0.799604 | 0.399802 | − | 0.916602i | \(-0.369079\pi\) | ||||
0.399802 | + | 0.916602i | \(0.369079\pi\) | |||||||
\(294\) | 0.332736 | 0.0194056 | ||||||||
\(295\) | −10.7728 | −0.627215 | ||||||||
\(296\) | −9.02092 | −0.524330 | ||||||||
\(297\) | −2.05381 | −0.119174 | ||||||||
\(298\) | 15.1295 | 0.876429 | ||||||||
\(299\) | −4.00840 | −0.231812 | ||||||||
\(300\) | −3.08271 | −0.177980 | ||||||||
\(301\) | 7.14884 | 0.412053 | ||||||||
\(302\) | 8.12239 | 0.467391 | ||||||||
\(303\) | 18.3883 | 1.05638 | ||||||||
\(304\) | −0.237470 | −0.0136199 | ||||||||
\(305\) | −0.753431 | −0.0431413 | ||||||||
\(306\) | −45.1124 | −2.57891 | ||||||||
\(307\) | 20.5185 | 1.17105 | 0.585527 | − | 0.810653i | \(-0.300888\pi\) | ||||
0.585527 | + | 0.810653i | \(0.300888\pi\) | |||||||
\(308\) | −0.499284 | −0.0284493 | ||||||||
\(309\) | −44.1577 | −2.51204 | ||||||||
\(310\) | 1.00000 | 0.0567962 | ||||||||
\(311\) | −18.9628 | −1.07528 | −0.537642 | − | 0.843173i | \(-0.680685\pi\) | ||||
−0.537642 | + | 0.843173i | \(0.680685\pi\) | |||||||
\(312\) | 3.08271 | 0.174524 | ||||||||
\(313\) | −15.8179 | −0.894080 | −0.447040 | − | 0.894514i | \(-0.647522\pi\) | ||||
−0.447040 | + | 0.894514i | \(0.647522\pi\) | |||||||
\(314\) | 19.0833 | 1.07693 | ||||||||
\(315\) | 17.0725 | 0.961924 | ||||||||
\(316\) | 0.817179 | 0.0459699 | ||||||||
\(317\) | 31.6064 | 1.77519 | 0.887595 | − | 0.460624i | \(-0.152374\pi\) | ||||
0.887595 | + | 0.460624i | \(0.152374\pi\) | |||||||
\(318\) | 6.13778 | 0.344190 | ||||||||
\(319\) | 0.00877310 | 0.000491199 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 4.03718 | 0.225333 | ||||||||
\(322\) | −10.5232 | −0.586433 | ||||||||
\(323\) | 1.64734 | 0.0916607 | ||||||||
\(324\) | 13.7812 | 0.765621 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | −4.24035 | −0.234851 | ||||||||
\(327\) | 1.24203 | 0.0686845 | ||||||||
\(328\) | −2.50696 | −0.138424 | ||||||||
\(329\) | 26.5053 | 1.46128 | ||||||||
\(330\) | 0.586281 | 0.0322737 | ||||||||
\(331\) | 16.2940 | 0.895600 | 0.447800 | − | 0.894134i | \(-0.352208\pi\) | ||||
0.447800 | + | 0.894134i | \(0.352208\pi\) | |||||||
\(332\) | 0.435097 | 0.0238791 | ||||||||
\(333\) | −58.6641 | −3.21477 | ||||||||
\(334\) | 13.5092 | 0.739192 | ||||||||
\(335\) | −13.2211 | −0.722347 | ||||||||
\(336\) | 8.09297 | 0.441507 | ||||||||
\(337\) | 15.4158 | 0.839753 | 0.419876 | − | 0.907581i | \(-0.362073\pi\) | ||||
0.419876 | + | 0.907581i | \(0.362073\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | −8.21155 | −0.445990 | ||||||||
\(340\) | 6.93705 | 0.376214 | ||||||||
\(341\) | −0.190183 | −0.0102990 | ||||||||
\(342\) | −1.54430 | −0.0835061 | ||||||||
\(343\) | 18.6603 | 1.00756 | ||||||||
\(344\) | −2.72309 | −0.146819 | ||||||||
\(345\) | 12.3568 | 0.665265 | ||||||||
\(346\) | 1.08997 | 0.0585971 | ||||||||
\(347\) | 7.68442 | 0.412521 | 0.206261 | − | 0.978497i | \(-0.433871\pi\) | ||||
0.206261 | + | 0.978497i | \(0.433871\pi\) | |||||||
\(348\) | −0.142205 | −0.00762296 | ||||||||
\(349\) | 16.5847 | 0.887760 | 0.443880 | − | 0.896086i | \(-0.353602\pi\) | ||||
0.443880 | + | 0.896086i | \(0.353602\pi\) | |||||||
\(350\) | −2.62527 | −0.140327 | ||||||||
\(351\) | 10.7991 | 0.576413 | ||||||||
\(352\) | 0.190183 | 0.0101368 | ||||||||
\(353\) | −33.2411 | −1.76925 | −0.884623 | − | 0.466307i | \(-0.845584\pi\) | ||||
−0.884623 | + | 0.466307i | \(0.845584\pi\) | |||||||
\(354\) | −33.2094 | −1.76506 | ||||||||
\(355\) | −6.14349 | −0.326063 | ||||||||
\(356\) | −1.09084 | −0.0578145 | ||||||||
\(357\) | −56.1413 | −2.97131 | ||||||||
\(358\) | 12.1337 | 0.641286 | ||||||||
\(359\) | 21.8698 | 1.15424 | 0.577121 | − | 0.816658i | \(-0.304176\pi\) | ||||
0.577121 | + | 0.816658i | \(0.304176\pi\) | |||||||
\(360\) | −6.50312 | −0.342744 | ||||||||
\(361\) | −18.9436 | −0.997032 | ||||||||
\(362\) | 3.25448 | 0.171052 | ||||||||
\(363\) | 33.7983 | 1.77395 | ||||||||
\(364\) | 2.62527 | 0.137602 | ||||||||
\(365\) | 5.91955 | 0.309843 | ||||||||
\(366\) | −2.32261 | −0.121405 | ||||||||
\(367\) | −33.8742 | −1.76822 | −0.884108 | − | 0.467282i | \(-0.845233\pi\) | ||||
−0.884108 | + | 0.467282i | \(0.845233\pi\) | |||||||
\(368\) | 4.00840 | 0.208952 | ||||||||
\(369\) | −16.3031 | −0.848704 | ||||||||
\(370\) | 9.02092 | 0.468975 | ||||||||
\(371\) | 5.22701 | 0.271373 | ||||||||
\(372\) | 3.08271 | 0.159831 | ||||||||
\(373\) | −15.7122 | −0.813549 | −0.406775 | − | 0.913529i | \(-0.633347\pi\) | ||||
−0.406775 | + | 0.913529i | \(0.633347\pi\) | |||||||
\(374\) | −1.31931 | −0.0682200 | ||||||||
\(375\) | 3.08271 | 0.159191 | ||||||||
\(376\) | −10.0962 | −0.520672 | ||||||||
\(377\) | −0.0461297 | −0.00237580 | ||||||||
\(378\) | 28.3506 | 1.45820 | ||||||||
\(379\) | 4.04448 | 0.207751 | 0.103875 | − | 0.994590i | \(-0.466876\pi\) | ||||
0.103875 | + | 0.994590i | \(0.466876\pi\) | |||||||
\(380\) | 0.237470 | 0.0121820 | ||||||||
\(381\) | −31.9391 | −1.63629 | ||||||||
\(382\) | −10.6539 | −0.545103 | ||||||||
\(383\) | 2.70970 | 0.138459 | 0.0692296 | − | 0.997601i | \(-0.477946\pi\) | ||||
0.0692296 | + | 0.997601i | \(0.477946\pi\) | |||||||
\(384\) | −3.08271 | −0.157314 | ||||||||
\(385\) | 0.499284 | 0.0254458 | ||||||||
\(386\) | −12.5653 | −0.639559 | ||||||||
\(387\) | −17.7085 | −0.900176 | ||||||||
\(388\) | 8.17526 | 0.415036 | ||||||||
\(389\) | 14.2920 | 0.724632 | 0.362316 | − | 0.932055i | \(-0.381986\pi\) | ||||
0.362316 | + | 0.932055i | \(0.381986\pi\) | |||||||
\(390\) | −3.08271 | −0.156099 | ||||||||
\(391\) | −27.8065 | −1.40624 | ||||||||
\(392\) | −0.107936 | −0.00545160 | ||||||||
\(393\) | 31.3963 | 1.58374 | ||||||||
\(394\) | 9.06106 | 0.456489 | ||||||||
\(395\) | −0.817179 | −0.0411167 | ||||||||
\(396\) | 1.23679 | 0.0621508 | ||||||||
\(397\) | −3.48803 | −0.175059 | −0.0875295 | − | 0.996162i | \(-0.527897\pi\) | ||||
−0.0875295 | + | 0.996162i | \(0.527897\pi\) | |||||||
\(398\) | 25.5763 | 1.28202 | ||||||||
\(399\) | −1.92184 | −0.0962123 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −20.2318 | −1.01033 | −0.505165 | − | 0.863023i | \(-0.668568\pi\) | ||||
−0.505165 | + | 0.863023i | \(0.668568\pi\) | |||||||
\(402\) | −40.7569 | −2.03277 | ||||||||
\(403\) | 1.00000 | 0.0498135 | ||||||||
\(404\) | −5.96499 | −0.296769 | ||||||||
\(405\) | −13.7812 | −0.684792 | ||||||||
\(406\) | −0.121103 | −0.00601024 | ||||||||
\(407\) | −1.71563 | −0.0850406 | ||||||||
\(408\) | 21.3849 | 1.05871 | ||||||||
\(409\) | 26.7867 | 1.32452 | 0.662259 | − | 0.749275i | \(-0.269598\pi\) | ||||
0.662259 | + | 0.749275i | \(0.269598\pi\) | |||||||
\(410\) | 2.50696 | 0.123810 | ||||||||
\(411\) | −19.2168 | −0.947896 | ||||||||
\(412\) | 14.3243 | 0.705707 | ||||||||
\(413\) | −28.2815 | −1.39164 | ||||||||
\(414\) | 26.0671 | 1.28113 | ||||||||
\(415\) | −0.435097 | −0.0213581 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −11.9372 | −0.584568 | ||||||||
\(418\) | −0.0451629 | −0.00220899 | ||||||||
\(419\) | −37.0735 | −1.81116 | −0.905579 | − | 0.424177i | \(-0.860563\pi\) | ||||
−0.905579 | + | 0.424177i | \(0.860563\pi\) | |||||||
\(420\) | −8.09297 | −0.394896 | ||||||||
\(421\) | 8.02881 | 0.391300 | 0.195650 | − | 0.980674i | \(-0.437318\pi\) | ||||
0.195650 | + | 0.980674i | \(0.437318\pi\) | |||||||
\(422\) | 8.79692 | 0.428227 | ||||||||
\(423\) | −65.6567 | −3.19234 | ||||||||
\(424\) | −1.99103 | −0.0966931 | ||||||||
\(425\) | −6.93705 | −0.336496 | ||||||||
\(426\) | −18.9386 | −0.917579 | ||||||||
\(427\) | −1.97796 | −0.0957203 | ||||||||
\(428\) | −1.30962 | −0.0633028 | ||||||||
\(429\) | 0.586281 | 0.0283059 | ||||||||
\(430\) | 2.72309 | 0.131319 | ||||||||
\(431\) | −25.3589 | −1.22149 | −0.610746 | − | 0.791826i | \(-0.709131\pi\) | ||||
−0.610746 | + | 0.791826i | \(0.709131\pi\) | |||||||
\(432\) | −10.7991 | −0.519572 | ||||||||
\(433\) | −28.3882 | −1.36425 | −0.682125 | − | 0.731236i | \(-0.738944\pi\) | ||||
−0.682125 | + | 0.731236i | \(0.738944\pi\) | |||||||
\(434\) | 2.62527 | 0.126017 | ||||||||
\(435\) | 0.142205 | 0.00681819 | ||||||||
\(436\) | −0.402902 | −0.0192955 | ||||||||
\(437\) | −0.951877 | −0.0455345 | ||||||||
\(438\) | 18.2483 | 0.871936 | ||||||||
\(439\) | −18.2165 | −0.869427 | −0.434713 | − | 0.900569i | \(-0.643150\pi\) | ||||
−0.434713 | + | 0.900569i | \(0.643150\pi\) | |||||||
\(440\) | −0.190183 | −0.00906664 | ||||||||
\(441\) | −0.701922 | −0.0334248 | ||||||||
\(442\) | 6.93705 | 0.329962 | ||||||||
\(443\) | −19.5676 | −0.929683 | −0.464842 | − | 0.885394i | \(-0.653889\pi\) | ||||
−0.464842 | + | 0.885394i | \(0.653889\pi\) | |||||||
\(444\) | 27.8089 | 1.31975 | ||||||||
\(445\) | 1.09084 | 0.0517108 | ||||||||
\(446\) | −26.7938 | −1.26872 | ||||||||
\(447\) | −46.6399 | −2.20599 | ||||||||
\(448\) | −2.62527 | −0.124033 | ||||||||
\(449\) | −8.23469 | −0.388619 | −0.194310 | − | 0.980940i | \(-0.562247\pi\) | ||||
−0.194310 | + | 0.980940i | \(0.562247\pi\) | |||||||
\(450\) | 6.50312 | 0.306560 | ||||||||
\(451\) | −0.476783 | −0.0224508 | ||||||||
\(452\) | 2.66374 | 0.125292 | ||||||||
\(453\) | −25.0390 | −1.17643 | ||||||||
\(454\) | 10.2446 | 0.480803 | ||||||||
\(455\) | −2.62527 | −0.123075 | ||||||||
\(456\) | 0.732053 | 0.0342815 | ||||||||
\(457\) | −24.4634 | −1.14435 | −0.572175 | − | 0.820131i | \(-0.693900\pi\) | ||||
−0.572175 | + | 0.820131i | \(0.693900\pi\) | |||||||
\(458\) | −11.9399 | −0.557914 | ||||||||
\(459\) | 74.9139 | 3.49668 | ||||||||
\(460\) | −4.00840 | −0.186893 | ||||||||
\(461\) | −8.11358 | −0.377887 | −0.188944 | − | 0.981988i | \(-0.560506\pi\) | ||||
−0.188944 | + | 0.981988i | \(0.560506\pi\) | |||||||
\(462\) | 1.53915 | 0.0716076 | ||||||||
\(463\) | 10.0863 | 0.468749 | 0.234375 | − | 0.972146i | \(-0.424696\pi\) | ||||
0.234375 | + | 0.972146i | \(0.424696\pi\) | |||||||
\(464\) | 0.0461297 | 0.00214152 | ||||||||
\(465\) | −3.08271 | −0.142957 | ||||||||
\(466\) | 25.8498 | 1.19747 | ||||||||
\(467\) | 25.0000 | 1.15686 | 0.578432 | − | 0.815731i | \(-0.303665\pi\) | ||||
0.578432 | + | 0.815731i | \(0.303665\pi\) | |||||||
\(468\) | −6.50312 | −0.300607 | ||||||||
\(469\) | −34.7091 | −1.60272 | ||||||||
\(470\) | 10.0962 | 0.465703 | ||||||||
\(471\) | −58.8283 | −2.71067 | ||||||||
\(472\) | 10.7728 | 0.495857 | ||||||||
\(473\) | −0.517886 | −0.0238124 | ||||||||
\(474\) | −2.51913 | −0.115707 | ||||||||
\(475\) | −0.237470 | −0.0108959 | ||||||||
\(476\) | 18.2117 | 0.834730 | ||||||||
\(477\) | −12.9479 | −0.592844 | ||||||||
\(478\) | −4.74305 | −0.216942 | ||||||||
\(479\) | −26.5870 | −1.21479 | −0.607395 | − | 0.794400i | \(-0.707785\pi\) | ||||
−0.607395 | + | 0.794400i | \(0.707785\pi\) | |||||||
\(480\) | 3.08271 | 0.140706 | ||||||||
\(481\) | 9.02092 | 0.411319 | ||||||||
\(482\) | −5.76720 | −0.262689 | ||||||||
\(483\) | 32.4399 | 1.47607 | ||||||||
\(484\) | −10.9638 | −0.498356 | ||||||||
\(485\) | −8.17526 | −0.371220 | ||||||||
\(486\) | −10.0861 | −0.457515 | ||||||||
\(487\) | −6.50732 | −0.294875 | −0.147437 | − | 0.989071i | \(-0.547103\pi\) | ||||
−0.147437 | + | 0.989071i | \(0.547103\pi\) | |||||||
\(488\) | 0.753431 | 0.0341062 | ||||||||
\(489\) | 13.0718 | 0.591126 | ||||||||
\(490\) | 0.107936 | 0.00487606 | ||||||||
\(491\) | −30.5048 | −1.37666 | −0.688331 | − | 0.725397i | \(-0.741656\pi\) | ||||
−0.688331 | + | 0.725397i | \(0.741656\pi\) | |||||||
\(492\) | 7.72824 | 0.348416 | ||||||||
\(493\) | −0.320004 | −0.0144123 | ||||||||
\(494\) | 0.237470 | 0.0106843 | ||||||||
\(495\) | −1.23679 | −0.0555894 | ||||||||
\(496\) | −1.00000 | −0.0449013 | ||||||||
\(497\) | −16.1284 | −0.723455 | ||||||||
\(498\) | −1.34128 | −0.0601042 | ||||||||
\(499\) | 12.5736 | 0.562873 | 0.281437 | − | 0.959580i | \(-0.409189\pi\) | ||||
0.281437 | + | 0.959580i | \(0.409189\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −41.6450 | −1.86056 | ||||||||
\(502\) | 21.6019 | 0.964142 | ||||||||
\(503\) | 10.9320 | 0.487436 | 0.243718 | − | 0.969846i | \(-0.421633\pi\) | ||||
0.243718 | + | 0.969846i | \(0.421633\pi\) | |||||||
\(504\) | −17.0725 | −0.760468 | ||||||||
\(505\) | 5.96499 | 0.265438 | ||||||||
\(506\) | 0.762332 | 0.0338898 | ||||||||
\(507\) | −3.08271 | −0.136908 | ||||||||
\(508\) | 10.3607 | 0.459683 | ||||||||
\(509\) | 21.9412 | 0.972525 | 0.486263 | − | 0.873813i | \(-0.338360\pi\) | ||||
0.486263 | + | 0.873813i | \(0.338360\pi\) | |||||||
\(510\) | −21.3849 | −0.946941 | ||||||||
\(511\) | 15.5404 | 0.687468 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 2.56447 | 0.113224 | ||||||||
\(514\) | 15.1584 | 0.668609 | ||||||||
\(515\) | −14.3243 | −0.631204 | ||||||||
\(516\) | 8.39449 | 0.369547 | ||||||||
\(517\) | −1.92013 | −0.0844472 | ||||||||
\(518\) | 23.6824 | 1.04054 | ||||||||
\(519\) | −3.36006 | −0.147490 | ||||||||
\(520\) | 1.00000 | 0.0438529 | ||||||||
\(521\) | 10.7473 | 0.470849 | 0.235424 | − | 0.971893i | \(-0.424352\pi\) | ||||
0.235424 | + | 0.971893i | \(0.424352\pi\) | |||||||
\(522\) | 0.299987 | 0.0131301 | ||||||||
\(523\) | 12.7032 | 0.555472 | 0.277736 | − | 0.960658i | \(-0.410416\pi\) | ||||
0.277736 | + | 0.960658i | \(0.410416\pi\) | |||||||
\(524\) | −10.1846 | −0.444918 | ||||||||
\(525\) | 8.09297 | 0.353206 | ||||||||
\(526\) | 1.44308 | 0.0629214 | ||||||||
\(527\) | 6.93705 | 0.302183 | ||||||||
\(528\) | −0.586281 | −0.0255146 | ||||||||
\(529\) | −6.93270 | −0.301422 | ||||||||
\(530\) | 1.99103 | 0.0864849 | ||||||||
\(531\) | 70.0566 | 3.04020 | ||||||||
\(532\) | 0.623425 | 0.0270289 | ||||||||
\(533\) | 2.50696 | 0.108589 | ||||||||
\(534\) | 3.36275 | 0.145520 | ||||||||
\(535\) | 1.30962 | 0.0566198 | ||||||||
\(536\) | 13.2211 | 0.571065 | ||||||||
\(537\) | −37.4047 | −1.61413 | ||||||||
\(538\) | −9.94188 | −0.428625 | ||||||||
\(539\) | −0.0205277 | −0.000884189 0 | ||||||||
\(540\) | 10.7991 | 0.464719 | ||||||||
\(541\) | 4.21317 | 0.181138 | 0.0905692 | − | 0.995890i | \(-0.471131\pi\) | ||||
0.0905692 | + | 0.995890i | \(0.471131\pi\) | |||||||
\(542\) | 23.9828 | 1.03015 | ||||||||
\(543\) | −10.0326 | −0.430541 | ||||||||
\(544\) | −6.93705 | −0.297424 | ||||||||
\(545\) | 0.402902 | 0.0172584 | ||||||||
\(546\) | −8.09297 | −0.346347 | ||||||||
\(547\) | 34.7736 | 1.48681 | 0.743406 | − | 0.668841i | \(-0.233209\pi\) | ||||
0.743406 | + | 0.668841i | \(0.233209\pi\) | |||||||
\(548\) | 6.23374 | 0.266292 | ||||||||
\(549\) | 4.89965 | 0.209112 | ||||||||
\(550\) | 0.190183 | 0.00810945 | ||||||||
\(551\) | −0.0109544 | −0.000466674 0 | ||||||||
\(552\) | −12.3568 | −0.525938 | ||||||||
\(553\) | −2.14532 | −0.0912282 | ||||||||
\(554\) | −14.2200 | −0.604148 | ||||||||
\(555\) | −27.8089 | −1.18042 | ||||||||
\(556\) | 3.87231 | 0.164222 | ||||||||
\(557\) | −28.6834 | −1.21535 | −0.607677 | − | 0.794184i | \(-0.707899\pi\) | ||||
−0.607677 | + | 0.794184i | \(0.707899\pi\) | |||||||
\(558\) | −6.50312 | −0.275299 | ||||||||
\(559\) | 2.72309 | 0.115174 | ||||||||
\(560\) | 2.62527 | 0.110938 | ||||||||
\(561\) | 4.06706 | 0.171711 | ||||||||
\(562\) | 15.7629 | 0.664920 | ||||||||
\(563\) | 38.6802 | 1.63018 | 0.815089 | − | 0.579336i | \(-0.196688\pi\) | ||||
0.815089 | + | 0.579336i | \(0.196688\pi\) | |||||||
\(564\) | 31.1237 | 1.31054 | ||||||||
\(565\) | −2.66374 | −0.112064 | ||||||||
\(566\) | −18.2060 | −0.765256 | ||||||||
\(567\) | −36.1794 | −1.51939 | ||||||||
\(568\) | 6.14349 | 0.257775 | ||||||||
\(569\) | −32.2884 | −1.35360 | −0.676801 | − | 0.736166i | \(-0.736634\pi\) | ||||
−0.676801 | + | 0.736166i | \(0.736634\pi\) | |||||||
\(570\) | −0.732053 | −0.0306623 | ||||||||
\(571\) | 23.4429 | 0.981056 | 0.490528 | − | 0.871425i | \(-0.336804\pi\) | ||||
0.490528 | + | 0.871425i | \(0.336804\pi\) | |||||||
\(572\) | −0.190183 | −0.00795197 | ||||||||
\(573\) | 32.8430 | 1.37204 | ||||||||
\(574\) | 6.58146 | 0.274705 | ||||||||
\(575\) | 4.00840 | 0.167162 | ||||||||
\(576\) | 6.50312 | 0.270963 | ||||||||
\(577\) | −41.4785 | −1.72677 | −0.863387 | − | 0.504543i | \(-0.831661\pi\) | ||||
−0.863387 | + | 0.504543i | \(0.831661\pi\) | |||||||
\(578\) | 31.1227 | 1.29453 | ||||||||
\(579\) | 38.7353 | 1.60978 | ||||||||
\(580\) | −0.0461297 | −0.00191543 | ||||||||
\(581\) | −1.14225 | −0.0473885 | ||||||||
\(582\) | −25.2020 | −1.04466 | ||||||||
\(583\) | −0.378661 | −0.0156825 | ||||||||
\(584\) | −5.91955 | −0.244953 | ||||||||
\(585\) | 6.50312 | 0.268871 | ||||||||
\(586\) | 13.6870 | 0.565405 | ||||||||
\(587\) | 11.7320 | 0.484232 | 0.242116 | − | 0.970247i | \(-0.422159\pi\) | ||||
0.242116 | + | 0.970247i | \(0.422159\pi\) | |||||||
\(588\) | 0.332736 | 0.0137218 | ||||||||
\(589\) | 0.237470 | 0.00978480 | ||||||||
\(590\) | −10.7728 | −0.443508 | ||||||||
\(591\) | −27.9326 | −1.14900 | ||||||||
\(592\) | −9.02092 | −0.370758 | ||||||||
\(593\) | 14.8281 | 0.608918 | 0.304459 | − | 0.952525i | \(-0.401524\pi\) | ||||
0.304459 | + | 0.952525i | \(0.401524\pi\) | |||||||
\(594\) | −2.05381 | −0.0842689 | ||||||||
\(595\) | −18.2117 | −0.746605 | ||||||||
\(596\) | 15.1295 | 0.619729 | ||||||||
\(597\) | −78.8443 | −3.22688 | ||||||||
\(598\) | −4.00840 | −0.163916 | ||||||||
\(599\) | −8.04349 | −0.328648 | −0.164324 | − | 0.986406i | \(-0.552544\pi\) | ||||
−0.164324 | + | 0.986406i | \(0.552544\pi\) | |||||||
\(600\) | −3.08271 | −0.125851 | ||||||||
\(601\) | −10.8367 | −0.442040 | −0.221020 | − | 0.975269i | \(-0.570939\pi\) | ||||
−0.221020 | + | 0.975269i | \(0.570939\pi\) | |||||||
\(602\) | 7.14884 | 0.291365 | ||||||||
\(603\) | 85.9785 | 3.50131 | ||||||||
\(604\) | 8.12239 | 0.330495 | ||||||||
\(605\) | 10.9638 | 0.445743 | ||||||||
\(606\) | 18.3883 | 0.746975 | ||||||||
\(607\) | 38.2829 | 1.55386 | 0.776928 | − | 0.629589i | \(-0.216777\pi\) | ||||
0.776928 | + | 0.629589i | \(0.216777\pi\) | |||||||
\(608\) | −0.237470 | −0.00963070 | ||||||||
\(609\) | 0.373326 | 0.0151279 | ||||||||
\(610\) | −0.753431 | −0.0305055 | ||||||||
\(611\) | 10.0962 | 0.408448 | ||||||||
\(612\) | −45.1124 | −1.82356 | ||||||||
\(613\) | 6.03017 | 0.243556 | 0.121778 | − | 0.992557i | \(-0.461140\pi\) | ||||
0.121778 | + | 0.992557i | \(0.461140\pi\) | |||||||
\(614\) | 20.5185 | 0.828061 | ||||||||
\(615\) | −7.72824 | −0.311633 | ||||||||
\(616\) | −0.499284 | −0.0201167 | ||||||||
\(617\) | 1.89394 | 0.0762470 | 0.0381235 | − | 0.999273i | \(-0.487862\pi\) | ||||
0.0381235 | + | 0.999273i | \(0.487862\pi\) | |||||||
\(618\) | −44.1577 | −1.77628 | ||||||||
\(619\) | −24.3574 | −0.979005 | −0.489503 | − | 0.872002i | \(-0.662822\pi\) | ||||
−0.489503 | + | 0.872002i | \(0.662822\pi\) | |||||||
\(620\) | 1.00000 | 0.0401610 | ||||||||
\(621\) | −43.2872 | −1.73705 | ||||||||
\(622\) | −18.9628 | −0.760340 | ||||||||
\(623\) | 2.86376 | 0.114734 | ||||||||
\(624\) | 3.08271 | 0.123407 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −15.8179 | −0.632210 | ||||||||
\(627\) | 0.139224 | 0.00556008 | ||||||||
\(628\) | 19.0833 | 0.761507 | ||||||||
\(629\) | 62.5786 | 2.49517 | ||||||||
\(630\) | 17.0725 | 0.680183 | ||||||||
\(631\) | −6.27936 | −0.249977 | −0.124989 | − | 0.992158i | \(-0.539889\pi\) | ||||
−0.124989 | + | 0.992158i | \(0.539889\pi\) | |||||||
\(632\) | 0.817179 | 0.0325056 | ||||||||
\(633\) | −27.1184 | −1.07786 | ||||||||
\(634\) | 31.6064 | 1.25525 | ||||||||
\(635\) | −10.3607 | −0.411153 | ||||||||
\(636\) | 6.13778 | 0.243379 | ||||||||
\(637\) | 0.107936 | 0.00427659 | ||||||||
\(638\) | 0.00877310 | 0.000347330 0 | ||||||||
\(639\) | 39.9519 | 1.58047 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −42.2402 | −1.66839 | −0.834193 | − | 0.551472i | \(-0.814066\pi\) | ||||
−0.834193 | + | 0.551472i | \(0.814066\pi\) | |||||||
\(642\) | 4.03718 | 0.159335 | ||||||||
\(643\) | 27.9359 | 1.10168 | 0.550841 | − | 0.834610i | \(-0.314307\pi\) | ||||
0.550841 | + | 0.834610i | \(0.314307\pi\) | |||||||
\(644\) | −10.5232 | −0.414671 | ||||||||
\(645\) | −8.39449 | −0.330533 | ||||||||
\(646\) | 1.64734 | 0.0648139 | ||||||||
\(647\) | 13.8574 | 0.544791 | 0.272395 | − | 0.962185i | \(-0.412184\pi\) | ||||
0.272395 | + | 0.962185i | \(0.412184\pi\) | |||||||
\(648\) | 13.7812 | 0.541376 | ||||||||
\(649\) | 2.04880 | 0.0804226 | ||||||||
\(650\) | −1.00000 | −0.0392232 | ||||||||
\(651\) | −8.09297 | −0.317188 | ||||||||
\(652\) | −4.24035 | −0.166065 | ||||||||
\(653\) | 9.24792 | 0.361899 | 0.180950 | − | 0.983492i | \(-0.442083\pi\) | ||||
0.180950 | + | 0.983492i | \(0.442083\pi\) | |||||||
\(654\) | 1.24203 | 0.0485673 | ||||||||
\(655\) | 10.1846 | 0.397947 | ||||||||
\(656\) | −2.50696 | −0.0978804 | ||||||||
\(657\) | −38.4955 | −1.50185 | ||||||||
\(658\) | 26.5053 | 1.03328 | ||||||||
\(659\) | 28.2732 | 1.10137 | 0.550685 | − | 0.834713i | \(-0.314367\pi\) | ||||
0.550685 | + | 0.834713i | \(0.314367\pi\) | |||||||
\(660\) | 0.586281 | 0.0228210 | ||||||||
\(661\) | 31.4799 | 1.22443 | 0.612213 | − | 0.790693i | \(-0.290280\pi\) | ||||
0.612213 | + | 0.790693i | \(0.290280\pi\) | |||||||
\(662\) | 16.2940 | 0.633285 | ||||||||
\(663\) | −21.3849 | −0.830522 | ||||||||
\(664\) | 0.435097 | 0.0168850 | ||||||||
\(665\) | −0.623425 | −0.0241754 | ||||||||
\(666\) | −58.6641 | −2.27319 | ||||||||
\(667\) | 0.184906 | 0.00715960 | ||||||||
\(668\) | 13.5092 | 0.522687 | ||||||||
\(669\) | 82.5977 | 3.19341 | ||||||||
\(670\) | −13.2211 | −0.510776 | ||||||||
\(671\) | 0.143290 | 0.00553165 | ||||||||
\(672\) | 8.09297 | 0.312193 | ||||||||
\(673\) | −9.55452 | −0.368300 | −0.184150 | − | 0.982898i | \(-0.558953\pi\) | ||||
−0.184150 | + | 0.982898i | \(0.558953\pi\) | |||||||
\(674\) | 15.4158 | 0.593795 | ||||||||
\(675\) | −10.7991 | −0.415658 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −32.0117 | −1.23031 | −0.615155 | − | 0.788406i | \(-0.710907\pi\) | ||||
−0.615155 | + | 0.788406i | \(0.710907\pi\) | |||||||
\(678\) | −8.21155 | −0.315363 | ||||||||
\(679\) | −21.4623 | −0.823648 | ||||||||
\(680\) | 6.93705 | 0.266024 | ||||||||
\(681\) | −31.5812 | −1.21019 | ||||||||
\(682\) | −0.190183 | −0.00728250 | ||||||||
\(683\) | −19.9713 | −0.764182 | −0.382091 | − | 0.924125i | \(-0.624796\pi\) | ||||
−0.382091 | + | 0.924125i | \(0.624796\pi\) | |||||||
\(684\) | −1.54430 | −0.0590477 | ||||||||
\(685\) | −6.23374 | −0.238179 | ||||||||
\(686\) | 18.6603 | 0.712453 | ||||||||
\(687\) | 36.8072 | 1.40428 | ||||||||
\(688\) | −2.72309 | −0.103817 | ||||||||
\(689\) | 1.99103 | 0.0758523 | ||||||||
\(690\) | 12.3568 | 0.470414 | ||||||||
\(691\) | −20.2688 | −0.771062 | −0.385531 | − | 0.922695i | \(-0.625982\pi\) | ||||
−0.385531 | + | 0.922695i | \(0.625982\pi\) | |||||||
\(692\) | 1.08997 | 0.0414344 | ||||||||
\(693\) | −3.24690 | −0.123340 | ||||||||
\(694\) | 7.68442 | 0.291696 | ||||||||
\(695\) | −3.87231 | −0.146885 | ||||||||
\(696\) | −0.142205 | −0.00539025 | ||||||||
\(697\) | 17.3909 | 0.658728 | ||||||||
\(698\) | 16.5847 | 0.627741 | ||||||||
\(699\) | −79.6876 | −3.01406 | ||||||||
\(700\) | −2.62527 | −0.0992260 | ||||||||
\(701\) | 37.6355 | 1.42147 | 0.710736 | − | 0.703458i | \(-0.248362\pi\) | ||||
0.710736 | + | 0.703458i | \(0.248362\pi\) | |||||||
\(702\) | 10.7991 | 0.407586 | ||||||||
\(703\) | 2.14220 | 0.0807947 | ||||||||
\(704\) | 0.190183 | 0.00716781 | ||||||||
\(705\) | −31.1237 | −1.17219 | ||||||||
\(706\) | −33.2411 | −1.25105 | ||||||||
\(707\) | 15.6597 | 0.588944 | ||||||||
\(708\) | −33.2094 | −1.24808 | ||||||||
\(709\) | 24.3657 | 0.915074 | 0.457537 | − | 0.889191i | \(-0.348732\pi\) | ||||
0.457537 | + | 0.889191i | \(0.348732\pi\) | |||||||
\(710\) | −6.14349 | −0.230561 | ||||||||
\(711\) | 5.31421 | 0.199298 | ||||||||
\(712\) | −1.09084 | −0.0408810 | ||||||||
\(713\) | −4.00840 | −0.150116 | ||||||||
\(714\) | −56.1413 | −2.10104 | ||||||||
\(715\) | 0.190183 | 0.00711246 | ||||||||
\(716\) | 12.1337 | 0.453457 | ||||||||
\(717\) | 14.6215 | 0.546048 | ||||||||
\(718\) | 21.8698 | 0.816173 | ||||||||
\(719\) | −18.8095 | −0.701475 | −0.350738 | − | 0.936474i | \(-0.614069\pi\) | ||||
−0.350738 | + | 0.936474i | \(0.614069\pi\) | |||||||
\(720\) | −6.50312 | −0.242357 | ||||||||
\(721\) | −37.6052 | −1.40049 | ||||||||
\(722\) | −18.9436 | −0.705008 | ||||||||
\(723\) | 17.7786 | 0.661194 | ||||||||
\(724\) | 3.25448 | 0.120952 | ||||||||
\(725\) | 0.0461297 | 0.00171321 | ||||||||
\(726\) | 33.7983 | 1.25437 | ||||||||
\(727\) | −24.4092 | −0.905286 | −0.452643 | − | 0.891692i | \(-0.649519\pi\) | ||||
−0.452643 | + | 0.891692i | \(0.649519\pi\) | |||||||
\(728\) | 2.62527 | 0.0972991 | ||||||||
\(729\) | −10.2510 | −0.379666 | ||||||||
\(730\) | 5.91955 | 0.219092 | ||||||||
\(731\) | 18.8902 | 0.698678 | ||||||||
\(732\) | −2.32261 | −0.0858462 | ||||||||
\(733\) | −1.05303 | −0.0388946 | −0.0194473 | − | 0.999811i | \(-0.506191\pi\) | ||||
−0.0194473 | + | 0.999811i | \(0.506191\pi\) | |||||||
\(734\) | −33.8742 | −1.25032 | ||||||||
\(735\) | −0.332736 | −0.0122732 | ||||||||
\(736\) | 4.00840 | 0.147752 | ||||||||
\(737\) | 2.51444 | 0.0926205 | ||||||||
\(738\) | −16.3031 | −0.600124 | ||||||||
\(739\) | −1.40499 | −0.0516834 | −0.0258417 | − | 0.999666i | \(-0.508227\pi\) | ||||
−0.0258417 | + | 0.999666i | \(0.508227\pi\) | |||||||
\(740\) | 9.02092 | 0.331616 | ||||||||
\(741\) | −0.732053 | −0.0268926 | ||||||||
\(742\) | 5.22701 | 0.191889 | ||||||||
\(743\) | −9.58396 | −0.351602 | −0.175801 | − | 0.984426i | \(-0.556251\pi\) | ||||
−0.175801 | + | 0.984426i | \(0.556251\pi\) | |||||||
\(744\) | 3.08271 | 0.113018 | ||||||||
\(745\) | −15.1295 | −0.554302 | ||||||||
\(746\) | −15.7122 | −0.575266 | ||||||||
\(747\) | 2.82949 | 0.103526 | ||||||||
\(748\) | −1.31931 | −0.0482388 | ||||||||
\(749\) | 3.43811 | 0.125626 | ||||||||
\(750\) | 3.08271 | 0.112565 | ||||||||
\(751\) | −9.05783 | −0.330525 | −0.165263 | − | 0.986250i | \(-0.552847\pi\) | ||||
−0.165263 | + | 0.986250i | \(0.552847\pi\) | |||||||
\(752\) | −10.0962 | −0.368170 | ||||||||
\(753\) | −66.5926 | −2.42677 | ||||||||
\(754\) | −0.0461297 | −0.00167994 | ||||||||
\(755\) | −8.12239 | −0.295604 | ||||||||
\(756\) | 28.3506 | 1.03110 | ||||||||
\(757\) | 38.3596 | 1.39420 | 0.697101 | − | 0.716973i | \(-0.254473\pi\) | ||||
0.697101 | + | 0.716973i | \(0.254473\pi\) | |||||||
\(758\) | 4.04448 | 0.146902 | ||||||||
\(759\) | −2.35005 | −0.0853014 | ||||||||
\(760\) | 0.237470 | 0.00861396 | ||||||||
\(761\) | 24.8063 | 0.899229 | 0.449614 | − | 0.893223i | \(-0.351561\pi\) | ||||
0.449614 | + | 0.893223i | \(0.351561\pi\) | |||||||
\(762\) | −31.9391 | −1.15703 | ||||||||
\(763\) | 1.05773 | 0.0382923 | ||||||||
\(764\) | −10.6539 | −0.385446 | ||||||||
\(765\) | 45.1124 | 1.63104 | ||||||||
\(766\) | 2.70970 | 0.0979055 | ||||||||
\(767\) | −10.7728 | −0.388982 | ||||||||
\(768\) | −3.08271 | −0.111238 | ||||||||
\(769\) | 8.41317 | 0.303387 | 0.151693 | − | 0.988428i | \(-0.451527\pi\) | ||||
0.151693 | + | 0.988428i | \(0.451527\pi\) | |||||||
\(770\) | 0.499284 | 0.0179929 | ||||||||
\(771\) | −46.7290 | −1.68290 | ||||||||
\(772\) | −12.5653 | −0.452236 | ||||||||
\(773\) | 31.5147 | 1.13350 | 0.566752 | − | 0.823888i | \(-0.308200\pi\) | ||||
0.566752 | + | 0.823888i | \(0.308200\pi\) | |||||||
\(774\) | −17.7085 | −0.636520 | ||||||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | 8.17526 | 0.293475 | ||||||||
\(777\) | −73.0060 | −2.61908 | ||||||||
\(778\) | 14.2920 | 0.512392 | ||||||||
\(779\) | 0.595329 | 0.0213299 | ||||||||
\(780\) | −3.08271 | −0.110379 | ||||||||
\(781\) | 1.16839 | 0.0418083 | ||||||||
\(782\) | −27.8065 | −0.994358 | ||||||||
\(783\) | −0.498159 | −0.0178028 | ||||||||
\(784\) | −0.107936 | −0.00385486 | ||||||||
\(785\) | −19.0833 | −0.681112 | ||||||||
\(786\) | 31.3963 | 1.11987 | ||||||||
\(787\) | −35.7119 | −1.27299 | −0.636495 | − | 0.771281i | \(-0.719616\pi\) | ||||
−0.636495 | + | 0.771281i | \(0.719616\pi\) | |||||||
\(788\) | 9.06106 | 0.322787 | ||||||||
\(789\) | −4.44861 | −0.158375 | ||||||||
\(790\) | −0.817179 | −0.0290739 | ||||||||
\(791\) | −6.99305 | −0.248644 | ||||||||
\(792\) | 1.23679 | 0.0439472 | ||||||||
\(793\) | −0.753431 | −0.0267551 | ||||||||
\(794\) | −3.48803 | −0.123785 | ||||||||
\(795\) | −6.13778 | −0.217685 | ||||||||
\(796\) | 25.5763 | 0.906527 | ||||||||
\(797\) | 20.0161 | 0.709006 | 0.354503 | − | 0.935055i | \(-0.384650\pi\) | ||||
0.354503 | + | 0.935055i | \(0.384650\pi\) | |||||||
\(798\) | −1.92184 | −0.0680324 | ||||||||
\(799\) | 70.0378 | 2.47776 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −7.09387 | −0.250650 | ||||||||
\(802\) | −20.2318 | −0.714411 | ||||||||
\(803\) | −1.12580 | −0.0397286 | ||||||||
\(804\) | −40.7569 | −1.43739 | ||||||||
\(805\) | 10.5232 | 0.370893 | ||||||||
\(806\) | 1.00000 | 0.0352235 | ||||||||
\(807\) | 30.6480 | 1.07886 | ||||||||
\(808\) | −5.96499 | −0.209847 | ||||||||
\(809\) | −14.1815 | −0.498595 | −0.249298 | − | 0.968427i | \(-0.580200\pi\) | ||||
−0.249298 | + | 0.968427i | \(0.580200\pi\) | |||||||
\(810\) | −13.7812 | −0.484221 | ||||||||
\(811\) | 12.3169 | 0.432505 | 0.216253 | − | 0.976337i | \(-0.430617\pi\) | ||||
0.216253 | + | 0.976337i | \(0.430617\pi\) | |||||||
\(812\) | −0.121103 | −0.00424988 | ||||||||
\(813\) | −73.9322 | −2.59291 | ||||||||
\(814\) | −1.71563 | −0.0601328 | ||||||||
\(815\) | 4.24035 | 0.148533 | ||||||||
\(816\) | 21.3849 | 0.748622 | ||||||||
\(817\) | 0.646652 | 0.0226235 | ||||||||
\(818\) | 26.7867 | 0.936576 | ||||||||
\(819\) | 17.0725 | 0.596560 | ||||||||
\(820\) | 2.50696 | 0.0875469 | ||||||||
\(821\) | 32.4098 | 1.13111 | 0.565554 | − | 0.824711i | \(-0.308662\pi\) | ||||
0.565554 | + | 0.824711i | \(0.308662\pi\) | |||||||
\(822\) | −19.2168 | −0.670264 | ||||||||
\(823\) | −24.0884 | −0.839670 | −0.419835 | − | 0.907600i | \(-0.637912\pi\) | ||||
−0.419835 | + | 0.907600i | \(0.637912\pi\) | |||||||
\(824\) | 14.3243 | 0.499010 | ||||||||
\(825\) | −0.586281 | −0.0204117 | ||||||||
\(826\) | −28.2815 | −0.984039 | ||||||||
\(827\) | −12.6164 | −0.438716 | −0.219358 | − | 0.975644i | \(-0.570396\pi\) | ||||
−0.219358 | + | 0.975644i | \(0.570396\pi\) | |||||||
\(828\) | 26.0671 | 0.905895 | ||||||||
\(829\) | −39.0359 | −1.35577 | −0.677887 | − | 0.735166i | \(-0.737104\pi\) | ||||
−0.677887 | + | 0.735166i | \(0.737104\pi\) | |||||||
\(830\) | −0.435097 | −0.0151024 | ||||||||
\(831\) | 43.8360 | 1.52066 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 0.748759 | 0.0259430 | ||||||||
\(834\) | −11.9372 | −0.413352 | ||||||||
\(835\) | −13.5092 | −0.467506 | ||||||||
\(836\) | −0.0451629 | −0.00156199 | ||||||||
\(837\) | 10.7991 | 0.373272 | ||||||||
\(838\) | −37.0735 | −1.28068 | ||||||||
\(839\) | 38.9273 | 1.34392 | 0.671959 | − | 0.740588i | \(-0.265453\pi\) | ||||
0.671959 | + | 0.740588i | \(0.265453\pi\) | |||||||
\(840\) | −8.09297 | −0.279234 | ||||||||
\(841\) | −28.9979 | −0.999927 | ||||||||
\(842\) | 8.02881 | 0.276691 | ||||||||
\(843\) | −48.5926 | −1.67362 | ||||||||
\(844\) | 8.79692 | 0.302802 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | −65.6567 | −2.25733 | ||||||||
\(847\) | 28.7831 | 0.988998 | ||||||||
\(848\) | −1.99103 | −0.0683723 | ||||||||
\(849\) | 56.1239 | 1.92617 | ||||||||
\(850\) | −6.93705 | −0.237939 | ||||||||
\(851\) | −36.1595 | −1.23953 | ||||||||
\(852\) | −18.9386 | −0.648827 | ||||||||
\(853\) | −15.4680 | −0.529615 | −0.264808 | − | 0.964301i | \(-0.585308\pi\) | ||||
−0.264808 | + | 0.964301i | \(0.585308\pi\) | |||||||
\(854\) | −1.97796 | −0.0676845 | ||||||||
\(855\) | 1.54430 | 0.0528139 | ||||||||
\(856\) | −1.30962 | −0.0447618 | ||||||||
\(857\) | 23.9701 | 0.818804 | 0.409402 | − | 0.912354i | \(-0.365737\pi\) | ||||
0.409402 | + | 0.912354i | \(0.365737\pi\) | |||||||
\(858\) | 0.586281 | 0.0200153 | ||||||||
\(859\) | 10.2235 | 0.348823 | 0.174411 | − | 0.984673i | \(-0.444198\pi\) | ||||
0.174411 | + | 0.984673i | \(0.444198\pi\) | |||||||
\(860\) | 2.72309 | 0.0928564 | ||||||||
\(861\) | −20.2888 | −0.691439 | ||||||||
\(862\) | −25.3589 | −0.863726 | ||||||||
\(863\) | 21.6389 | 0.736598 | 0.368299 | − | 0.929707i | \(-0.379940\pi\) | ||||
0.368299 | + | 0.929707i | \(0.379940\pi\) | |||||||
\(864\) | −10.7991 | −0.367393 | ||||||||
\(865\) | −1.08997 | −0.0370600 | ||||||||
\(866\) | −28.3882 | −0.964670 | ||||||||
\(867\) | −95.9422 | −3.25837 | ||||||||
\(868\) | 2.62527 | 0.0891076 | ||||||||
\(869\) | 0.155414 | 0.00527206 | ||||||||
\(870\) | 0.142205 | 0.00482119 | ||||||||
\(871\) | −13.2211 | −0.447980 | ||||||||
\(872\) | −0.402902 | −0.0136440 | ||||||||
\(873\) | 53.1647 | 1.79935 | ||||||||
\(874\) | −0.951877 | −0.0321977 | ||||||||
\(875\) | 2.62527 | 0.0887505 | ||||||||
\(876\) | 18.2483 | 0.616552 | ||||||||
\(877\) | 44.3224 | 1.49666 | 0.748330 | − | 0.663327i | \(-0.230856\pi\) | ||||
0.748330 | + | 0.663327i | \(0.230856\pi\) | |||||||
\(878\) | −18.2165 | −0.614778 | ||||||||
\(879\) | −42.1931 | −1.42314 | ||||||||
\(880\) | −0.190183 | −0.00641108 | ||||||||
\(881\) | 43.6937 | 1.47208 | 0.736040 | − | 0.676938i | \(-0.236694\pi\) | ||||
0.736040 | + | 0.676938i | \(0.236694\pi\) | |||||||
\(882\) | −0.701922 | −0.0236349 | ||||||||
\(883\) | 23.6293 | 0.795189 | 0.397595 | − | 0.917561i | \(-0.369845\pi\) | ||||
0.397595 | + | 0.917561i | \(0.369845\pi\) | |||||||
\(884\) | 6.93705 | 0.233318 | ||||||||
\(885\) | 33.2094 | 1.11632 | ||||||||
\(886\) | −19.5676 | −0.657385 | ||||||||
\(887\) | −26.3809 | −0.885783 | −0.442891 | − | 0.896575i | \(-0.646047\pi\) | ||||
−0.442891 | + | 0.896575i | \(0.646047\pi\) | |||||||
\(888\) | 27.8089 | 0.933206 | ||||||||
\(889\) | −27.1997 | −0.912250 | ||||||||
\(890\) | 1.09084 | 0.0365651 | ||||||||
\(891\) | 2.62095 | 0.0878052 | ||||||||
\(892\) | −26.7938 | −0.897124 | ||||||||
\(893\) | 2.39755 | 0.0802309 | ||||||||
\(894\) | −46.6399 | −1.55987 | ||||||||
\(895\) | −12.1337 | −0.405585 | ||||||||
\(896\) | −2.62527 | −0.0877043 | ||||||||
\(897\) | 12.3568 | 0.412580 | ||||||||
\(898\) | −8.23469 | −0.274795 | ||||||||
\(899\) | −0.0461297 | −0.00153851 | ||||||||
\(900\) | 6.50312 | 0.216771 | ||||||||
\(901\) | 13.8119 | 0.460141 | ||||||||
\(902\) | −0.476783 | −0.0158751 | ||||||||
\(903\) | −22.0378 | −0.733373 | ||||||||
\(904\) | 2.66374 | 0.0885947 | ||||||||
\(905\) | −3.25448 | −0.108183 | ||||||||
\(906\) | −25.0390 | −0.831865 | ||||||||
\(907\) | −15.9224 | −0.528696 | −0.264348 | − | 0.964427i | \(-0.585157\pi\) | ||||
−0.264348 | + | 0.964427i | \(0.585157\pi\) | |||||||
\(908\) | 10.2446 | 0.339979 | ||||||||
\(909\) | −38.7910 | −1.28662 | ||||||||
\(910\) | −2.62527 | −0.0870270 | ||||||||
\(911\) | −5.84421 | −0.193627 | −0.0968136 | − | 0.995303i | \(-0.530865\pi\) | ||||
−0.0968136 | + | 0.995303i | \(0.530865\pi\) | |||||||
\(912\) | 0.732053 | 0.0242407 | ||||||||
\(913\) | 0.0827483 | 0.00273857 | ||||||||
\(914\) | −24.4634 | −0.809178 | ||||||||
\(915\) | 2.32261 | 0.0767832 | ||||||||
\(916\) | −11.9399 | −0.394505 | ||||||||
\(917\) | 26.7375 | 0.882949 | ||||||||
\(918\) | 74.9139 | 2.47253 | ||||||||
\(919\) | −39.4296 | −1.30066 | −0.650331 | − | 0.759651i | \(-0.725370\pi\) | ||||
−0.650331 | + | 0.759651i | \(0.725370\pi\) | |||||||
\(920\) | −4.00840 | −0.132153 | ||||||||
\(921\) | −63.2527 | −2.08425 | ||||||||
\(922\) | −8.11358 | −0.267207 | ||||||||
\(923\) | −6.14349 | −0.202216 | ||||||||
\(924\) | 1.53915 | 0.0506342 | ||||||||
\(925\) | −9.02092 | −0.296606 | ||||||||
\(926\) | 10.0863 | 0.331456 | ||||||||
\(927\) | 93.1526 | 3.05953 | ||||||||
\(928\) | 0.0461297 | 0.00151428 | ||||||||
\(929\) | 40.9322 | 1.34294 | 0.671471 | − | 0.741031i | \(-0.265663\pi\) | ||||
0.671471 | + | 0.741031i | \(0.265663\pi\) | |||||||
\(930\) | −3.08271 | −0.101086 | ||||||||
\(931\) | 0.0256316 | 0.000840043 0 | ||||||||
\(932\) | 25.8498 | 0.846739 | ||||||||
\(933\) | 58.4570 | 1.91379 | ||||||||
\(934\) | 25.0000 | 0.818026 | ||||||||
\(935\) | 1.31931 | 0.0431461 | ||||||||
\(936\) | −6.50312 | −0.212561 | ||||||||
\(937\) | 44.8535 | 1.46530 | 0.732651 | − | 0.680605i | \(-0.238283\pi\) | ||||
0.732651 | + | 0.680605i | \(0.238283\pi\) | |||||||
\(938\) | −34.7091 | −1.13329 | ||||||||
\(939\) | 48.7620 | 1.59129 | ||||||||
\(940\) | 10.0962 | 0.329302 | ||||||||
\(941\) | 2.31410 | 0.0754376 | 0.0377188 | − | 0.999288i | \(-0.487991\pi\) | ||||
0.0377188 | + | 0.999288i | \(0.487991\pi\) | |||||||
\(942\) | −58.8283 | −1.91673 | ||||||||
\(943\) | −10.0489 | −0.327238 | ||||||||
\(944\) | 10.7728 | 0.350624 | ||||||||
\(945\) | −28.3506 | −0.922245 | ||||||||
\(946\) | −0.517886 | −0.0168379 | ||||||||
\(947\) | 9.66596 | 0.314102 | 0.157051 | − | 0.987591i | \(-0.449801\pi\) | ||||
0.157051 | + | 0.987591i | \(0.449801\pi\) | |||||||
\(948\) | −2.51913 | −0.0818175 | ||||||||
\(949\) | 5.91955 | 0.192157 | ||||||||
\(950\) | −0.237470 | −0.00770456 | ||||||||
\(951\) | −97.4334 | −3.15949 | ||||||||
\(952\) | 18.2117 | 0.590243 | ||||||||
\(953\) | −37.1792 | −1.20435 | −0.602177 | − | 0.798363i | \(-0.705700\pi\) | ||||
−0.602177 | + | 0.798363i | \(0.705700\pi\) | |||||||
\(954\) | −12.9479 | −0.419204 | ||||||||
\(955\) | 10.6539 | 0.344753 | ||||||||
\(956\) | −4.74305 | −0.153401 | ||||||||
\(957\) | −0.0270449 | −0.000874239 0 | ||||||||
\(958\) | −26.5870 | −0.858986 | ||||||||
\(959\) | −16.3653 | −0.528462 | ||||||||
\(960\) | 3.08271 | 0.0994941 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 9.02092 | 0.290846 | ||||||||
\(963\) | −8.51660 | −0.274444 | ||||||||
\(964\) | −5.76720 | −0.185749 | ||||||||
\(965\) | 12.5653 | 0.404492 | ||||||||
\(966\) | 32.4399 | 1.04374 | ||||||||
\(967\) | −21.0756 | −0.677744 | −0.338872 | − | 0.940832i | \(-0.610045\pi\) | ||||
−0.338872 | + | 0.940832i | \(0.610045\pi\) | |||||||
\(968\) | −10.9638 | −0.352391 | ||||||||
\(969\) | −5.07829 | −0.163138 | ||||||||
\(970\) | −8.17526 | −0.262492 | ||||||||
\(971\) | −23.1383 | −0.742544 | −0.371272 | − | 0.928524i | \(-0.621078\pi\) | ||||
−0.371272 | + | 0.928524i | \(0.621078\pi\) | |||||||
\(972\) | −10.0861 | −0.323512 | ||||||||
\(973\) | −10.1659 | −0.325903 | ||||||||
\(974\) | −6.50732 | −0.208508 | ||||||||
\(975\) | 3.08271 | 0.0987258 | ||||||||
\(976\) | 0.753431 | 0.0241167 | ||||||||
\(977\) | 57.3418 | 1.83453 | 0.917264 | − | 0.398280i | \(-0.130393\pi\) | ||||
0.917264 | + | 0.398280i | \(0.130393\pi\) | |||||||
\(978\) | 13.0718 | 0.417989 | ||||||||
\(979\) | −0.207460 | −0.00663045 | ||||||||
\(980\) | 0.107936 | 0.00344789 | ||||||||
\(981\) | −2.62012 | −0.0836540 | ||||||||
\(982\) | −30.5048 | −0.973447 | ||||||||
\(983\) | 30.1178 | 0.960610 | 0.480305 | − | 0.877102i | \(-0.340526\pi\) | ||||
0.480305 | + | 0.877102i | \(0.340526\pi\) | |||||||
\(984\) | 7.72824 | 0.246367 | ||||||||
\(985\) | −9.06106 | −0.288709 | ||||||||
\(986\) | −0.320004 | −0.0101910 | ||||||||
\(987\) | −81.7082 | −2.60080 | ||||||||
\(988\) | 0.237470 | 0.00755494 | ||||||||
\(989\) | −10.9152 | −0.347084 | ||||||||
\(990\) | −1.23679 | −0.0393076 | ||||||||
\(991\) | 30.2927 | 0.962280 | 0.481140 | − | 0.876644i | \(-0.340223\pi\) | ||||
0.481140 | + | 0.876644i | \(0.340223\pi\) | |||||||
\(992\) | −1.00000 | −0.0317500 | ||||||||
\(993\) | −50.2298 | −1.59399 | ||||||||
\(994\) | −16.1284 | −0.511560 | ||||||||
\(995\) | −25.5763 | −0.810822 | ||||||||
\(996\) | −1.34128 | −0.0425001 | ||||||||
\(997\) | −26.1923 | −0.829518 | −0.414759 | − | 0.909931i | \(-0.636134\pi\) | ||||
−0.414759 | + | 0.909931i | \(0.636134\pi\) | |||||||
\(998\) | 12.5736 | 0.398012 | ||||||||
\(999\) | 97.4178 | 3.08216 |
(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 | 4030.2.a.n.1.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4030.2.a.n.1.1 | ✓ | 8 | 1.1 | even | 1 | trivial |