Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.44064 | −1.01869 | −0.509345 | − | 0.860563i | \(-0.670112\pi\) | ||||
−0.509345 | + | 0.860563i | \(0.670112\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.0754557 | 0.0377279 | ||||||||
\(5\) | −3.22452 | −1.44205 | −0.721024 | − | 0.692911i | \(-0.756328\pi\) | ||||
−0.721024 | + | 0.692911i | \(0.756328\pi\) | |||||||
\(6\) | 1.44064 | 0.588141 | ||||||||
\(7\) | 1.08354 | 0.409538 | 0.204769 | − | 0.978810i | \(-0.434356\pi\) | ||||
0.204769 | + | 0.978810i | \(0.434356\pi\) | |||||||
\(8\) | 2.77258 | 0.980256 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 4.64538 | 1.46900 | ||||||||
\(11\) | 4.97469 | 1.49993 | 0.749963 | − | 0.661480i | \(-0.230071\pi\) | ||||
0.749963 | + | 0.661480i | \(0.230071\pi\) | |||||||
\(12\) | −0.0754557 | −0.0217822 | ||||||||
\(13\) | 1.59786 | 0.443166 | 0.221583 | − | 0.975141i | \(-0.428878\pi\) | ||||
0.221583 | + | 0.975141i | \(0.428878\pi\) | |||||||
\(14\) | −1.56099 | −0.417192 | ||||||||
\(15\) | 3.22452 | 0.832566 | ||||||||
\(16\) | −4.14522 | −1.03630 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −1.44064 | −0.339563 | ||||||||
\(19\) | 5.94298 | 1.36341 | 0.681707 | − | 0.731626i | \(-0.261238\pi\) | ||||
0.681707 | + | 0.731626i | \(0.261238\pi\) | |||||||
\(20\) | −0.243308 | −0.0544053 | ||||||||
\(21\) | −1.08354 | −0.236447 | ||||||||
\(22\) | −7.16676 | −1.52796 | ||||||||
\(23\) | 2.41663 | 0.503902 | 0.251951 | − | 0.967740i | \(-0.418928\pi\) | ||||
0.251951 | + | 0.967740i | \(0.418928\pi\) | |||||||
\(24\) | −2.77258 | −0.565951 | ||||||||
\(25\) | 5.39750 | 1.07950 | ||||||||
\(26\) | −2.30195 | −0.451449 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.0817590 | 0.0154510 | ||||||||
\(29\) | 1.75504 | 0.325904 | 0.162952 | − | 0.986634i | \(-0.447898\pi\) | ||||
0.162952 | + | 0.986634i | \(0.447898\pi\) | |||||||
\(30\) | −4.64538 | −0.848126 | ||||||||
\(31\) | −2.72016 | −0.488555 | −0.244277 | − | 0.969705i | \(-0.578551\pi\) | ||||
−0.244277 | + | 0.969705i | \(0.578551\pi\) | |||||||
\(32\) | 0.426617 | 0.0754159 | ||||||||
\(33\) | −4.97469 | −0.865983 | ||||||||
\(34\) | 1.44064 | 0.247068 | ||||||||
\(35\) | −3.49388 | −0.590574 | ||||||||
\(36\) | 0.0754557 | 0.0125760 | ||||||||
\(37\) | −6.48548 | −1.06621 | −0.533103 | − | 0.846050i | \(-0.678974\pi\) | ||||
−0.533103 | + | 0.846050i | \(0.678974\pi\) | |||||||
\(38\) | −8.56172 | −1.38889 | ||||||||
\(39\) | −1.59786 | −0.255862 | ||||||||
\(40\) | −8.94024 | −1.41358 | ||||||||
\(41\) | −1.55199 | −0.242380 | −0.121190 | − | 0.992629i | \(-0.538671\pi\) | ||||
−0.121190 | + | 0.992629i | \(0.538671\pi\) | |||||||
\(42\) | 1.56099 | 0.240866 | ||||||||
\(43\) | −9.84359 | −1.50113 | −0.750566 | − | 0.660795i | \(-0.770219\pi\) | ||||
−0.750566 | + | 0.660795i | \(0.770219\pi\) | |||||||
\(44\) | 0.375369 | 0.0565890 | ||||||||
\(45\) | −3.22452 | −0.480682 | ||||||||
\(46\) | −3.48150 | −0.513319 | ||||||||
\(47\) | −11.2096 | −1.63509 | −0.817545 | − | 0.575865i | \(-0.804665\pi\) | ||||
−0.817545 | + | 0.575865i | \(0.804665\pi\) | |||||||
\(48\) | 4.14522 | 0.598311 | ||||||||
\(49\) | −5.82595 | −0.832278 | ||||||||
\(50\) | −7.77588 | −1.09967 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 0.120568 | 0.0167197 | ||||||||
\(53\) | −2.06350 | −0.283443 | −0.141722 | − | 0.989907i | \(-0.545264\pi\) | ||||
−0.141722 | + | 0.989907i | \(0.545264\pi\) | |||||||
\(54\) | 1.44064 | 0.196047 | ||||||||
\(55\) | −16.0410 | −2.16296 | ||||||||
\(56\) | 3.00420 | 0.401453 | ||||||||
\(57\) | −5.94298 | −0.787167 | ||||||||
\(58\) | −2.52839 | −0.331994 | ||||||||
\(59\) | 7.21706 | 0.939582 | 0.469791 | − | 0.882778i | \(-0.344329\pi\) | ||||
0.469791 | + | 0.882778i | \(0.344329\pi\) | |||||||
\(60\) | 0.243308 | 0.0314109 | ||||||||
\(61\) | 8.92460 | 1.14268 | 0.571339 | − | 0.820714i | \(-0.306424\pi\) | ||||
0.571339 | + | 0.820714i | \(0.306424\pi\) | |||||||
\(62\) | 3.91878 | 0.497686 | ||||||||
\(63\) | 1.08354 | 0.136513 | ||||||||
\(64\) | 7.67583 | 0.959479 | ||||||||
\(65\) | −5.15232 | −0.639067 | ||||||||
\(66\) | 7.16676 | 0.882167 | ||||||||
\(67\) | −12.8646 | −1.57166 | −0.785830 | − | 0.618443i | \(-0.787764\pi\) | ||||
−0.785830 | + | 0.618443i | \(0.787764\pi\) | |||||||
\(68\) | −0.0754557 | −0.00915035 | ||||||||
\(69\) | −2.41663 | −0.290928 | ||||||||
\(70\) | 5.03344 | 0.601611 | ||||||||
\(71\) | 9.11371 | 1.08160 | 0.540799 | − | 0.841152i | \(-0.318122\pi\) | ||||
0.540799 | + | 0.841152i | \(0.318122\pi\) | |||||||
\(72\) | 2.77258 | 0.326752 | ||||||||
\(73\) | −10.7119 | −1.25373 | −0.626866 | − | 0.779127i | \(-0.715662\pi\) | ||||
−0.626866 | + | 0.779127i | \(0.715662\pi\) | |||||||
\(74\) | 9.34326 | 1.08613 | ||||||||
\(75\) | −5.39750 | −0.623249 | ||||||||
\(76\) | 0.448432 | 0.0514387 | ||||||||
\(77\) | 5.39026 | 0.614277 | ||||||||
\(78\) | 2.30195 | 0.260644 | ||||||||
\(79\) | 11.7872 | 1.32616 | 0.663082 | − | 0.748547i | \(-0.269248\pi\) | ||||
0.663082 | + | 0.748547i | \(0.269248\pi\) | |||||||
\(80\) | 13.3663 | 1.49440 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.23587 | 0.246910 | ||||||||
\(83\) | 10.6849 | 1.17282 | 0.586412 | − | 0.810013i | \(-0.300540\pi\) | ||||
0.586412 | + | 0.810013i | \(0.300540\pi\) | |||||||
\(84\) | −0.0817590 | −0.00892064 | ||||||||
\(85\) | 3.22452 | 0.349748 | ||||||||
\(86\) | 14.1811 | 1.52919 | ||||||||
\(87\) | −1.75504 | −0.188161 | ||||||||
\(88\) | 13.7928 | 1.47031 | ||||||||
\(89\) | 6.95174 | 0.736883 | 0.368441 | − | 0.929651i | \(-0.379891\pi\) | ||||
0.368441 | + | 0.929651i | \(0.379891\pi\) | |||||||
\(90\) | 4.64538 | 0.489666 | ||||||||
\(91\) | 1.73134 | 0.181494 | ||||||||
\(92\) | 0.182348 | 0.0190111 | ||||||||
\(93\) | 2.72016 | 0.282067 | ||||||||
\(94\) | 16.1491 | 1.66565 | ||||||||
\(95\) | −19.1632 | −1.96611 | ||||||||
\(96\) | −0.426617 | −0.0435414 | ||||||||
\(97\) | −2.86124 | −0.290515 | −0.145258 | − | 0.989394i | \(-0.546401\pi\) | ||||
−0.145258 | + | 0.989394i | \(0.546401\pi\) | |||||||
\(98\) | 8.39312 | 0.847833 | ||||||||
\(99\) | 4.97469 | 0.499975 | ||||||||
\(100\) | 0.407272 | 0.0407272 | ||||||||
\(101\) | 0.822654 | 0.0818572 | 0.0409286 | − | 0.999162i | \(-0.486968\pi\) | ||||
0.0409286 | + | 0.999162i | \(0.486968\pi\) | |||||||
\(102\) | −1.44064 | −0.142645 | ||||||||
\(103\) | −3.10872 | −0.306311 | −0.153156 | − | 0.988202i | \(-0.548944\pi\) | ||||
−0.153156 | + | 0.988202i | \(0.548944\pi\) | |||||||
\(104\) | 4.43020 | 0.434417 | ||||||||
\(105\) | 3.49388 | 0.340968 | ||||||||
\(106\) | 2.97277 | 0.288741 | ||||||||
\(107\) | −10.7151 | −1.03586 | −0.517932 | − | 0.855422i | \(-0.673298\pi\) | ||||
−0.517932 | + | 0.855422i | \(0.673298\pi\) | |||||||
\(108\) | −0.0754557 | −0.00726073 | ||||||||
\(109\) | −6.33348 | −0.606637 | −0.303319 | − | 0.952889i | \(-0.598095\pi\) | ||||
−0.303319 | + | 0.952889i | \(0.598095\pi\) | |||||||
\(110\) | 23.1093 | 2.20339 | ||||||||
\(111\) | 6.48548 | 0.615574 | ||||||||
\(112\) | −4.49150 | −0.424407 | ||||||||
\(113\) | −9.64053 | −0.906905 | −0.453453 | − | 0.891280i | \(-0.649808\pi\) | ||||
−0.453453 | + | 0.891280i | \(0.649808\pi\) | |||||||
\(114\) | 8.56172 | 0.801879 | ||||||||
\(115\) | −7.79245 | −0.726650 | ||||||||
\(116\) | 0.132428 | 0.0122956 | ||||||||
\(117\) | 1.59786 | 0.147722 | ||||||||
\(118\) | −10.3972 | −0.957142 | ||||||||
\(119\) | −1.08354 | −0.0993277 | ||||||||
\(120\) | 8.94024 | 0.816128 | ||||||||
\(121\) | 13.7476 | 1.24978 | ||||||||
\(122\) | −12.8572 | −1.16403 | ||||||||
\(123\) | 1.55199 | 0.139938 | ||||||||
\(124\) | −0.205251 | −0.0184321 | ||||||||
\(125\) | −1.28174 | −0.114642 | ||||||||
\(126\) | −1.56099 | −0.139064 | ||||||||
\(127\) | 12.5431 | 1.11302 | 0.556509 | − | 0.830842i | \(-0.312140\pi\) | ||||
0.556509 | + | 0.830842i | \(0.312140\pi\) | |||||||
\(128\) | −11.9114 | −1.05283 | ||||||||
\(129\) | 9.84359 | 0.866679 | ||||||||
\(130\) | 7.42266 | 0.651010 | ||||||||
\(131\) | 14.3554 | 1.25424 | 0.627119 | − | 0.778924i | \(-0.284234\pi\) | ||||
0.627119 | + | 0.778924i | \(0.284234\pi\) | |||||||
\(132\) | −0.375369 | −0.0326717 | ||||||||
\(133\) | 6.43944 | 0.558370 | ||||||||
\(134\) | 18.5333 | 1.60103 | ||||||||
\(135\) | 3.22452 | 0.277522 | ||||||||
\(136\) | −2.77258 | −0.237747 | ||||||||
\(137\) | 5.93871 | 0.507378 | 0.253689 | − | 0.967286i | \(-0.418356\pi\) | ||||
0.253689 | + | 0.967286i | \(0.418356\pi\) | |||||||
\(138\) | 3.48150 | 0.296365 | ||||||||
\(139\) | −21.7332 | −1.84339 | −0.921694 | − | 0.387917i | \(-0.873195\pi\) | ||||
−0.921694 | + | 0.387917i | \(0.873195\pi\) | |||||||
\(140\) | −0.263633 | −0.0222811 | ||||||||
\(141\) | 11.2096 | 0.944019 | ||||||||
\(142\) | −13.1296 | −1.10181 | ||||||||
\(143\) | 7.94886 | 0.664717 | ||||||||
\(144\) | −4.14522 | −0.345435 | ||||||||
\(145\) | −5.65917 | −0.469968 | ||||||||
\(146\) | 15.4320 | 1.27716 | ||||||||
\(147\) | 5.82595 | 0.480516 | ||||||||
\(148\) | −0.489366 | −0.0402257 | ||||||||
\(149\) | −0.666766 | −0.0546236 | −0.0273118 | − | 0.999627i | \(-0.508695\pi\) | ||||
−0.0273118 | + | 0.999627i | \(0.508695\pi\) | |||||||
\(150\) | 7.77588 | 0.634898 | ||||||||
\(151\) | 0.698424 | 0.0568370 | 0.0284185 | − | 0.999596i | \(-0.490953\pi\) | ||||
0.0284185 | + | 0.999596i | \(0.490953\pi\) | |||||||
\(152\) | 16.4774 | 1.33649 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −7.76545 | −0.625758 | ||||||||
\(155\) | 8.77119 | 0.704519 | ||||||||
\(156\) | −0.120568 | −0.00965313 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | −16.9812 | −1.35095 | ||||||||
\(159\) | 2.06350 | 0.163646 | ||||||||
\(160\) | −1.37563 | −0.108753 | ||||||||
\(161\) | 2.61851 | 0.206367 | ||||||||
\(162\) | −1.44064 | −0.113188 | ||||||||
\(163\) | −11.8082 | −0.924893 | −0.462447 | − | 0.886647i | \(-0.653028\pi\) | ||||
−0.462447 | + | 0.886647i | \(0.653028\pi\) | |||||||
\(164\) | −0.117107 | −0.00914449 | ||||||||
\(165\) | 16.0410 | 1.24879 | ||||||||
\(166\) | −15.3932 | −1.19474 | ||||||||
\(167\) | −10.5976 | −0.820068 | −0.410034 | − | 0.912070i | \(-0.634483\pi\) | ||||
−0.410034 | + | 0.912070i | \(0.634483\pi\) | |||||||
\(168\) | −3.00420 | −0.231779 | ||||||||
\(169\) | −10.4468 | −0.803604 | ||||||||
\(170\) | −4.64538 | −0.356284 | ||||||||
\(171\) | 5.94298 | 0.454471 | ||||||||
\(172\) | −0.742755 | −0.0566345 | ||||||||
\(173\) | −15.2338 | −1.15821 | −0.579104 | − | 0.815254i | \(-0.696597\pi\) | ||||
−0.579104 | + | 0.815254i | \(0.696597\pi\) | |||||||
\(174\) | 2.52839 | 0.191677 | ||||||||
\(175\) | 5.84839 | 0.442097 | ||||||||
\(176\) | −20.6212 | −1.55438 | ||||||||
\(177\) | −7.21706 | −0.542468 | ||||||||
\(178\) | −10.0150 | −0.750655 | ||||||||
\(179\) | −13.0103 | −0.972435 | −0.486217 | − | 0.873838i | \(-0.661624\pi\) | ||||
−0.486217 | + | 0.873838i | \(0.661624\pi\) | |||||||
\(180\) | −0.243308 | −0.0181351 | ||||||||
\(181\) | −23.2066 | −1.72493 | −0.862466 | − | 0.506115i | \(-0.831081\pi\) | ||||
−0.862466 | + | 0.506115i | \(0.831081\pi\) | |||||||
\(182\) | −2.49424 | −0.184886 | ||||||||
\(183\) | −8.92460 | −0.659726 | ||||||||
\(184\) | 6.70030 | 0.493953 | ||||||||
\(185\) | 20.9125 | 1.53752 | ||||||||
\(186\) | −3.91878 | −0.287339 | ||||||||
\(187\) | −4.97469 | −0.363786 | ||||||||
\(188\) | −0.845829 | −0.0616884 | ||||||||
\(189\) | −1.08354 | −0.0788157 | ||||||||
\(190\) | 27.6074 | 2.00285 | ||||||||
\(191\) | −14.9928 | −1.08484 | −0.542420 | − | 0.840107i | \(-0.682492\pi\) | ||||
−0.542420 | + | 0.840107i | \(0.682492\pi\) | |||||||
\(192\) | −7.67583 | −0.553955 | ||||||||
\(193\) | 13.0199 | 0.937196 | 0.468598 | − | 0.883412i | \(-0.344759\pi\) | ||||
0.468598 | + | 0.883412i | \(0.344759\pi\) | |||||||
\(194\) | 4.12203 | 0.295945 | ||||||||
\(195\) | 5.15232 | 0.368965 | ||||||||
\(196\) | −0.439601 | −0.0314001 | ||||||||
\(197\) | 11.4527 | 0.815971 | 0.407985 | − | 0.912988i | \(-0.366231\pi\) | ||||
0.407985 | + | 0.912988i | \(0.366231\pi\) | |||||||
\(198\) | −7.16676 | −0.509320 | ||||||||
\(199\) | 7.91095 | 0.560793 | 0.280396 | − | 0.959884i | \(-0.409534\pi\) | ||||
0.280396 | + | 0.959884i | \(0.409534\pi\) | |||||||
\(200\) | 14.9650 | 1.05819 | ||||||||
\(201\) | 12.8646 | 0.907398 | ||||||||
\(202\) | −1.18515 | −0.0833870 | ||||||||
\(203\) | 1.90166 | 0.133470 | ||||||||
\(204\) | 0.0754557 | 0.00528296 | ||||||||
\(205\) | 5.00442 | 0.349524 | ||||||||
\(206\) | 4.47856 | 0.312036 | ||||||||
\(207\) | 2.41663 | 0.167967 | ||||||||
\(208\) | −6.62347 | −0.459255 | ||||||||
\(209\) | 29.5645 | 2.04502 | ||||||||
\(210\) | −5.03344 | −0.347340 | ||||||||
\(211\) | −3.28941 | −0.226452 | −0.113226 | − | 0.993569i | \(-0.536118\pi\) | ||||
−0.113226 | + | 0.993569i | \(0.536118\pi\) | |||||||
\(212\) | −0.155703 | −0.0106937 | ||||||||
\(213\) | −9.11371 | −0.624461 | ||||||||
\(214\) | 15.4366 | 1.05522 | ||||||||
\(215\) | 31.7408 | 2.16470 | ||||||||
\(216\) | −2.77258 | −0.188650 | ||||||||
\(217\) | −2.94739 | −0.200082 | ||||||||
\(218\) | 9.12429 | 0.617975 | ||||||||
\(219\) | 10.7119 | 0.723842 | ||||||||
\(220\) | −1.21038 | −0.0816040 | ||||||||
\(221\) | −1.59786 | −0.107484 | ||||||||
\(222\) | −9.34326 | −0.627079 | ||||||||
\(223\) | 15.2355 | 1.02024 | 0.510122 | − | 0.860102i | \(-0.329600\pi\) | ||||
0.510122 | + | 0.860102i | \(0.329600\pi\) | |||||||
\(224\) | 0.462255 | 0.0308857 | ||||||||
\(225\) | 5.39750 | 0.359833 | ||||||||
\(226\) | 13.8886 | 0.923855 | ||||||||
\(227\) | −2.95734 | −0.196286 | −0.0981429 | − | 0.995172i | \(-0.531290\pi\) | ||||
−0.0981429 | + | 0.995172i | \(0.531290\pi\) | |||||||
\(228\) | −0.448432 | −0.0296981 | ||||||||
\(229\) | −1.99894 | −0.132093 | −0.0660467 | − | 0.997817i | \(-0.521039\pi\) | ||||
−0.0660467 | + | 0.997817i | \(0.521039\pi\) | |||||||
\(230\) | 11.2262 | 0.740231 | ||||||||
\(231\) | −5.39026 | −0.354653 | ||||||||
\(232\) | 4.86601 | 0.319469 | ||||||||
\(233\) | 5.10521 | 0.334453 | 0.167227 | − | 0.985918i | \(-0.446519\pi\) | ||||
0.167227 | + | 0.985918i | \(0.446519\pi\) | |||||||
\(234\) | −2.30195 | −0.150483 | ||||||||
\(235\) | 36.1456 | 2.35788 | ||||||||
\(236\) | 0.544569 | 0.0354484 | ||||||||
\(237\) | −11.7872 | −0.765661 | ||||||||
\(238\) | 1.56099 | 0.101184 | ||||||||
\(239\) | −23.7050 | −1.53335 | −0.766674 | − | 0.642036i | \(-0.778090\pi\) | ||||
−0.766674 | + | 0.642036i | \(0.778090\pi\) | |||||||
\(240\) | −13.3663 | −0.862792 | ||||||||
\(241\) | 29.6586 | 1.91048 | 0.955239 | − | 0.295834i | \(-0.0955976\pi\) | ||||
0.955239 | + | 0.295834i | \(0.0955976\pi\) | |||||||
\(242\) | −19.8054 | −1.27314 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0.673412 | 0.0431108 | ||||||||
\(245\) | 18.7859 | 1.20018 | ||||||||
\(246\) | −2.23587 | −0.142554 | ||||||||
\(247\) | 9.49605 | 0.604219 | ||||||||
\(248\) | −7.54187 | −0.478909 | ||||||||
\(249\) | −10.6849 | −0.677130 | ||||||||
\(250\) | 1.84653 | 0.116785 | ||||||||
\(251\) | 6.58481 | 0.415629 | 0.207815 | − | 0.978168i | \(-0.433365\pi\) | ||||
0.207815 | + | 0.978168i | \(0.433365\pi\) | |||||||
\(252\) | 0.0817590 | 0.00515034 | ||||||||
\(253\) | 12.0220 | 0.755816 | ||||||||
\(254\) | −18.0701 | −1.13382 | ||||||||
\(255\) | −3.22452 | −0.201927 | ||||||||
\(256\) | 1.80839 | 0.113024 | ||||||||
\(257\) | −6.17406 | −0.385127 | −0.192564 | − | 0.981285i | \(-0.561680\pi\) | ||||
−0.192564 | + | 0.981285i | \(0.561680\pi\) | |||||||
\(258\) | −14.1811 | −0.882877 | ||||||||
\(259\) | −7.02725 | −0.436652 | ||||||||
\(260\) | −0.388772 | −0.0241106 | ||||||||
\(261\) | 1.75504 | 0.108635 | ||||||||
\(262\) | −20.6810 | −1.27768 | ||||||||
\(263\) | 18.8480 | 1.16222 | 0.581110 | − | 0.813825i | \(-0.302619\pi\) | ||||
0.581110 | + | 0.813825i | \(0.302619\pi\) | |||||||
\(264\) | −13.7928 | −0.848885 | ||||||||
\(265\) | 6.65379 | 0.408739 | ||||||||
\(266\) | −9.27694 | −0.568806 | ||||||||
\(267\) | −6.95174 | −0.425440 | ||||||||
\(268\) | −0.970706 | −0.0592953 | ||||||||
\(269\) | 7.85901 | 0.479172 | 0.239586 | − | 0.970875i | \(-0.422988\pi\) | ||||
0.239586 | + | 0.970875i | \(0.422988\pi\) | |||||||
\(270\) | −4.64538 | −0.282709 | ||||||||
\(271\) | −19.5449 | −1.18727 | −0.593633 | − | 0.804736i | \(-0.702307\pi\) | ||||
−0.593633 | + | 0.804736i | \(0.702307\pi\) | |||||||
\(272\) | 4.14522 | 0.251341 | ||||||||
\(273\) | −1.73134 | −0.104785 | ||||||||
\(274\) | −8.55557 | −0.516861 | ||||||||
\(275\) | 26.8509 | 1.61917 | ||||||||
\(276\) | −0.182348 | −0.0109761 | ||||||||
\(277\) | −15.9152 | −0.956249 | −0.478125 | − | 0.878292i | \(-0.658683\pi\) | ||||
−0.478125 | + | 0.878292i | \(0.658683\pi\) | |||||||
\(278\) | 31.3099 | 1.87784 | ||||||||
\(279\) | −2.72016 | −0.162852 | ||||||||
\(280\) | −9.68708 | −0.578914 | ||||||||
\(281\) | −7.55302 | −0.450576 | −0.225288 | − | 0.974292i | \(-0.572332\pi\) | ||||
−0.225288 | + | 0.974292i | \(0.572332\pi\) | |||||||
\(282\) | −16.1491 | −0.961662 | ||||||||
\(283\) | −2.35210 | −0.139818 | −0.0699090 | − | 0.997553i | \(-0.522271\pi\) | ||||
−0.0699090 | + | 0.997553i | \(0.522271\pi\) | |||||||
\(284\) | 0.687682 | 0.0408064 | ||||||||
\(285\) | 19.1632 | 1.13513 | ||||||||
\(286\) | −11.4515 | −0.677140 | ||||||||
\(287\) | −1.68164 | −0.0992641 | ||||||||
\(288\) | 0.426617 | 0.0251386 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 8.15285 | 0.478752 | ||||||||
\(291\) | 2.86124 | 0.167729 | ||||||||
\(292\) | −0.808273 | −0.0473006 | ||||||||
\(293\) | 21.2244 | 1.23994 | 0.619972 | − | 0.784624i | \(-0.287144\pi\) | ||||
0.619972 | + | 0.784624i | \(0.287144\pi\) | |||||||
\(294\) | −8.39312 | −0.489497 | ||||||||
\(295\) | −23.2715 | −1.35492 | ||||||||
\(296\) | −17.9815 | −1.04515 | ||||||||
\(297\) | −4.97469 | −0.288661 | ||||||||
\(298\) | 0.960572 | 0.0556445 | ||||||||
\(299\) | 3.86143 | 0.223312 | ||||||||
\(300\) | −0.407272 | −0.0235139 | ||||||||
\(301\) | −10.6659 | −0.614772 | ||||||||
\(302\) | −1.00618 | −0.0578992 | ||||||||
\(303\) | −0.822654 | −0.0472603 | ||||||||
\(304\) | −24.6349 | −1.41291 | ||||||||
\(305\) | −28.7775 | −1.64780 | ||||||||
\(306\) | 1.44064 | 0.0823561 | ||||||||
\(307\) | −26.0338 | −1.48583 | −0.742914 | − | 0.669387i | \(-0.766557\pi\) | ||||
−0.742914 | + | 0.669387i | \(0.766557\pi\) | |||||||
\(308\) | 0.406726 | 0.0231754 | ||||||||
\(309\) | 3.10872 | 0.176849 | ||||||||
\(310\) | −12.6362 | −0.717686 | ||||||||
\(311\) | 2.02959 | 0.115087 | 0.0575437 | − | 0.998343i | \(-0.481673\pi\) | ||||
0.0575437 | + | 0.998343i | \(0.481673\pi\) | |||||||
\(312\) | −4.43020 | −0.250811 | ||||||||
\(313\) | −1.69194 | −0.0956340 | −0.0478170 | − | 0.998856i | \(-0.515226\pi\) | ||||
−0.0478170 | + | 0.998856i | \(0.515226\pi\) | |||||||
\(314\) | 1.44064 | 0.0813003 | ||||||||
\(315\) | −3.49388 | −0.196858 | ||||||||
\(316\) | 0.889412 | 0.0500333 | ||||||||
\(317\) | 17.8299 | 1.00142 | 0.500712 | − | 0.865614i | \(-0.333072\pi\) | ||||
0.500712 | + | 0.865614i | \(0.333072\pi\) | |||||||
\(318\) | −2.97277 | −0.166705 | ||||||||
\(319\) | 8.73081 | 0.488831 | ||||||||
\(320\) | −24.7508 | −1.38361 | ||||||||
\(321\) | 10.7151 | 0.598056 | ||||||||
\(322\) | −3.77234 | −0.210224 | ||||||||
\(323\) | −5.94298 | −0.330676 | ||||||||
\(324\) | 0.0754557 | 0.00419198 | ||||||||
\(325\) | 8.62444 | 0.478398 | ||||||||
\(326\) | 17.0115 | 0.942179 | ||||||||
\(327\) | 6.33348 | 0.350242 | ||||||||
\(328\) | −4.30303 | −0.237595 | ||||||||
\(329\) | −12.1460 | −0.669632 | ||||||||
\(330\) | −23.1093 | −1.27213 | ||||||||
\(331\) | −32.7132 | −1.79808 | −0.899039 | − | 0.437868i | \(-0.855734\pi\) | ||||
−0.899039 | + | 0.437868i | \(0.855734\pi\) | |||||||
\(332\) | 0.806239 | 0.0442481 | ||||||||
\(333\) | −6.48548 | −0.355402 | ||||||||
\(334\) | 15.2674 | 0.835395 | ||||||||
\(335\) | 41.4820 | 2.26641 | ||||||||
\(336\) | 4.49150 | 0.245031 | ||||||||
\(337\) | 4.69479 | 0.255742 | 0.127871 | − | 0.991791i | \(-0.459186\pi\) | ||||
0.127871 | + | 0.991791i | \(0.459186\pi\) | |||||||
\(338\) | 15.0502 | 0.818622 | ||||||||
\(339\) | 9.64053 | 0.523602 | ||||||||
\(340\) | 0.243308 | 0.0131952 | ||||||||
\(341\) | −13.5320 | −0.732796 | ||||||||
\(342\) | −8.56172 | −0.462965 | ||||||||
\(343\) | −13.8974 | −0.750388 | ||||||||
\(344\) | −27.2922 | −1.47149 | ||||||||
\(345\) | 7.79245 | 0.419532 | ||||||||
\(346\) | 21.9465 | 1.17985 | ||||||||
\(347\) | 22.5102 | 1.20841 | 0.604205 | − | 0.796829i | \(-0.293491\pi\) | ||||
0.604205 | + | 0.796829i | \(0.293491\pi\) | |||||||
\(348\) | −0.132428 | −0.00709889 | ||||||||
\(349\) | 11.0522 | 0.591613 | 0.295806 | − | 0.955248i | \(-0.404412\pi\) | ||||
0.295806 | + | 0.955248i | \(0.404412\pi\) | |||||||
\(350\) | −8.42545 | −0.450359 | ||||||||
\(351\) | −1.59786 | −0.0852874 | ||||||||
\(352\) | 2.12229 | 0.113118 | ||||||||
\(353\) | 3.52561 | 0.187649 | 0.0938246 | − | 0.995589i | \(-0.470091\pi\) | ||||
0.0938246 | + | 0.995589i | \(0.470091\pi\) | |||||||
\(354\) | 10.3972 | 0.552606 | ||||||||
\(355\) | −29.3873 | −1.55972 | ||||||||
\(356\) | 0.524549 | 0.0278010 | ||||||||
\(357\) | 1.08354 | 0.0573469 | ||||||||
\(358\) | 18.7432 | 0.990609 | ||||||||
\(359\) | 2.47303 | 0.130522 | 0.0652608 | − | 0.997868i | \(-0.479212\pi\) | ||||
0.0652608 | + | 0.997868i | \(0.479212\pi\) | |||||||
\(360\) | −8.94024 | −0.471192 | ||||||||
\(361\) | 16.3190 | 0.858896 | ||||||||
\(362\) | 33.4324 | 1.75717 | ||||||||
\(363\) | −13.7476 | −0.721560 | ||||||||
\(364\) | 0.130639 | 0.00684737 | ||||||||
\(365\) | 34.5406 | 1.80794 | ||||||||
\(366\) | 12.8572 | 0.672055 | ||||||||
\(367\) | −21.7186 | −1.13370 | −0.566850 | − | 0.823821i | \(-0.691838\pi\) | ||||
−0.566850 | + | 0.823821i | \(0.691838\pi\) | |||||||
\(368\) | −10.0175 | −0.522196 | ||||||||
\(369\) | −1.55199 | −0.0807935 | ||||||||
\(370\) | −30.1275 | −1.56625 | ||||||||
\(371\) | −2.23588 | −0.116081 | ||||||||
\(372\) | 0.205251 | 0.0106418 | ||||||||
\(373\) | −0.199314 | −0.0103201 | −0.00516005 | − | 0.999987i | \(-0.501643\pi\) | ||||
−0.00516005 | + | 0.999987i | \(0.501643\pi\) | |||||||
\(374\) | 7.16676 | 0.370584 | ||||||||
\(375\) | 1.28174 | 0.0661888 | ||||||||
\(376\) | −31.0796 | −1.60281 | ||||||||
\(377\) | 2.80431 | 0.144430 | ||||||||
\(378\) | 1.56099 | 0.0802887 | ||||||||
\(379\) | −10.2598 | −0.527009 | −0.263505 | − | 0.964658i | \(-0.584878\pi\) | ||||
−0.263505 | + | 0.964658i | \(0.584878\pi\) | |||||||
\(380\) | −1.44598 | −0.0741770 | ||||||||
\(381\) | −12.5431 | −0.642601 | ||||||||
\(382\) | 21.5993 | 1.10511 | ||||||||
\(383\) | −2.71079 | −0.138515 | −0.0692574 | − | 0.997599i | \(-0.522063\pi\) | ||||
−0.0692574 | + | 0.997599i | \(0.522063\pi\) | |||||||
\(384\) | 11.9114 | 0.607850 | ||||||||
\(385\) | −17.3810 | −0.885817 | ||||||||
\(386\) | −18.7571 | −0.954711 | ||||||||
\(387\) | −9.84359 | −0.500378 | ||||||||
\(388\) | −0.215897 | −0.0109605 | ||||||||
\(389\) | −13.7991 | −0.699643 | −0.349821 | − | 0.936816i | \(-0.613758\pi\) | ||||
−0.349821 | + | 0.936816i | \(0.613758\pi\) | |||||||
\(390\) | −7.42266 | −0.375861 | ||||||||
\(391\) | −2.41663 | −0.122214 | ||||||||
\(392\) | −16.1529 | −0.815846 | ||||||||
\(393\) | −14.3554 | −0.724134 | ||||||||
\(394\) | −16.4993 | −0.831221 | ||||||||
\(395\) | −38.0080 | −1.91239 | ||||||||
\(396\) | 0.375369 | 0.0188630 | ||||||||
\(397\) | −21.9553 | −1.10190 | −0.550952 | − | 0.834537i | \(-0.685735\pi\) | ||||
−0.550952 | + | 0.834537i | \(0.685735\pi\) | |||||||
\(398\) | −11.3969 | −0.571273 | ||||||||
\(399\) | −6.43944 | −0.322375 | ||||||||
\(400\) | −22.3738 | −1.11869 | ||||||||
\(401\) | −18.9824 | −0.947938 | −0.473969 | − | 0.880542i | \(-0.657179\pi\) | ||||
−0.473969 | + | 0.880542i | \(0.657179\pi\) | |||||||
\(402\) | −18.5333 | −0.924356 | ||||||||
\(403\) | −4.34643 | −0.216511 | ||||||||
\(404\) | 0.0620740 | 0.00308830 | ||||||||
\(405\) | −3.22452 | −0.160227 | ||||||||
\(406\) | −2.73961 | −0.135964 | ||||||||
\(407\) | −32.2633 | −1.59923 | ||||||||
\(408\) | 2.77258 | 0.137263 | ||||||||
\(409\) | 18.1615 | 0.898028 | 0.449014 | − | 0.893525i | \(-0.351775\pi\) | ||||
0.449014 | + | 0.893525i | \(0.351775\pi\) | |||||||
\(410\) | −7.20959 | −0.356056 | ||||||||
\(411\) | −5.93871 | −0.292935 | ||||||||
\(412\) | −0.234571 | −0.0115565 | ||||||||
\(413\) | 7.81995 | 0.384795 | ||||||||
\(414\) | −3.48150 | −0.171106 | ||||||||
\(415\) | −34.4537 | −1.69127 | ||||||||
\(416\) | 0.681674 | 0.0334218 | ||||||||
\(417\) | 21.7332 | 1.06428 | ||||||||
\(418\) | −42.5919 | −2.08324 | ||||||||
\(419\) | −6.78463 | −0.331451 | −0.165725 | − | 0.986172i | \(-0.552997\pi\) | ||||
−0.165725 | + | 0.986172i | \(0.552997\pi\) | |||||||
\(420\) | 0.263633 | 0.0128640 | ||||||||
\(421\) | 15.5643 | 0.758560 | 0.379280 | − | 0.925282i | \(-0.376172\pi\) | ||||
0.379280 | + | 0.925282i | \(0.376172\pi\) | |||||||
\(422\) | 4.73886 | 0.230684 | ||||||||
\(423\) | −11.2096 | −0.545030 | ||||||||
\(424\) | −5.72123 | −0.277847 | ||||||||
\(425\) | −5.39750 | −0.261817 | ||||||||
\(426\) | 13.1296 | 0.636132 | ||||||||
\(427\) | 9.67013 | 0.467971 | ||||||||
\(428\) | −0.808512 | −0.0390809 | ||||||||
\(429\) | −7.94886 | −0.383775 | ||||||||
\(430\) | −45.7272 | −2.20516 | ||||||||
\(431\) | 18.2215 | 0.877699 | 0.438849 | − | 0.898561i | \(-0.355386\pi\) | ||||
0.438849 | + | 0.898561i | \(0.355386\pi\) | |||||||
\(432\) | 4.14522 | 0.199437 | ||||||||
\(433\) | 23.7452 | 1.14112 | 0.570562 | − | 0.821255i | \(-0.306726\pi\) | ||||
0.570562 | + | 0.821255i | \(0.306726\pi\) | |||||||
\(434\) | 4.24614 | 0.203821 | ||||||||
\(435\) | 5.65917 | 0.271336 | ||||||||
\(436\) | −0.477897 | −0.0228871 | ||||||||
\(437\) | 14.3620 | 0.687026 | ||||||||
\(438\) | −15.4320 | −0.737370 | ||||||||
\(439\) | 0.570618 | 0.0272341 | 0.0136171 | − | 0.999907i | \(-0.495665\pi\) | ||||
0.0136171 | + | 0.999907i | \(0.495665\pi\) | |||||||
\(440\) | −44.4749 | −2.12026 | ||||||||
\(441\) | −5.82595 | −0.277426 | ||||||||
\(442\) | 2.30195 | 0.109492 | ||||||||
\(443\) | 33.3830 | 1.58607 | 0.793037 | − | 0.609173i | \(-0.208498\pi\) | ||||
0.793037 | + | 0.609173i | \(0.208498\pi\) | |||||||
\(444\) | 0.489366 | 0.0232243 | ||||||||
\(445\) | −22.4160 | −1.06262 | ||||||||
\(446\) | −21.9489 | −1.03931 | ||||||||
\(447\) | 0.666766 | 0.0315369 | ||||||||
\(448\) | 8.31705 | 0.392944 | ||||||||
\(449\) | 9.73144 | 0.459255 | 0.229627 | − | 0.973279i | \(-0.426249\pi\) | ||||
0.229627 | + | 0.973279i | \(0.426249\pi\) | |||||||
\(450\) | −7.77588 | −0.366558 | ||||||||
\(451\) | −7.72068 | −0.363553 | ||||||||
\(452\) | −0.727433 | −0.0342156 | ||||||||
\(453\) | −0.698424 | −0.0328148 | ||||||||
\(454\) | 4.26048 | 0.199954 | ||||||||
\(455\) | −5.58273 | −0.261722 | ||||||||
\(456\) | −16.4774 | −0.771625 | ||||||||
\(457\) | −2.66595 | −0.124708 | −0.0623541 | − | 0.998054i | \(-0.519861\pi\) | ||||
−0.0623541 | + | 0.998054i | \(0.519861\pi\) | |||||||
\(458\) | 2.87976 | 0.134562 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −0.587985 | −0.0274150 | ||||||||
\(461\) | 23.6917 | 1.10343 | 0.551717 | − | 0.834032i | \(-0.313973\pi\) | ||||
0.551717 | + | 0.834032i | \(0.313973\pi\) | |||||||
\(462\) | 7.76545 | 0.361281 | ||||||||
\(463\) | −6.56637 | −0.305165 | −0.152583 | − | 0.988291i | \(-0.548759\pi\) | ||||
−0.152583 | + | 0.988291i | \(0.548759\pi\) | |||||||
\(464\) | −7.27504 | −0.337735 | ||||||||
\(465\) | −8.77119 | −0.406754 | ||||||||
\(466\) | −7.35478 | −0.340704 | ||||||||
\(467\) | −10.2933 | −0.476319 | −0.238160 | − | 0.971226i | \(-0.576544\pi\) | ||||
−0.238160 | + | 0.971226i | \(0.576544\pi\) | |||||||
\(468\) | 0.120568 | 0.00557324 | ||||||||
\(469\) | −13.9392 | −0.643655 | ||||||||
\(470\) | −52.0729 | −2.40194 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | 20.0099 | 0.921031 | ||||||||
\(473\) | −48.9688 | −2.25159 | ||||||||
\(474\) | 16.9812 | 0.779971 | ||||||||
\(475\) | 32.0772 | 1.47180 | ||||||||
\(476\) | −0.0817590 | −0.00374742 | ||||||||
\(477\) | −2.06350 | −0.0944812 | ||||||||
\(478\) | 34.1505 | 1.56201 | ||||||||
\(479\) | 36.0257 | 1.64605 | 0.823027 | − | 0.568002i | \(-0.192283\pi\) | ||||
0.823027 | + | 0.568002i | \(0.192283\pi\) | |||||||
\(480\) | 1.37563 | 0.0627888 | ||||||||
\(481\) | −10.3629 | −0.472507 | ||||||||
\(482\) | −42.7275 | −1.94618 | ||||||||
\(483\) | −2.61851 | −0.119146 | ||||||||
\(484\) | 1.03733 | 0.0471515 | ||||||||
\(485\) | 9.22612 | 0.418936 | ||||||||
\(486\) | 1.44064 | 0.0653489 | ||||||||
\(487\) | −29.1194 | −1.31953 | −0.659763 | − | 0.751474i | \(-0.729343\pi\) | ||||
−0.659763 | + | 0.751474i | \(0.729343\pi\) | |||||||
\(488\) | 24.7442 | 1.12012 | ||||||||
\(489\) | 11.8082 | 0.533987 | ||||||||
\(490\) | −27.0637 | −1.22262 | ||||||||
\(491\) | 18.2037 | 0.821522 | 0.410761 | − | 0.911743i | \(-0.365263\pi\) | ||||
0.410761 | + | 0.911743i | \(0.365263\pi\) | |||||||
\(492\) | 0.117107 | 0.00527958 | ||||||||
\(493\) | −1.75504 | −0.0790432 | ||||||||
\(494\) | −13.6804 | −0.615511 | ||||||||
\(495\) | −16.0410 | −0.720988 | ||||||||
\(496\) | 11.2756 | 0.506292 | ||||||||
\(497\) | 9.87504 | 0.442956 | ||||||||
\(498\) | 15.3932 | 0.689785 | ||||||||
\(499\) | −16.2743 | −0.728539 | −0.364270 | − | 0.931294i | \(-0.618681\pi\) | ||||
−0.364270 | + | 0.931294i | \(0.618681\pi\) | |||||||
\(500\) | −0.0967147 | −0.00432521 | ||||||||
\(501\) | 10.5976 | 0.473467 | ||||||||
\(502\) | −9.48637 | −0.423397 | ||||||||
\(503\) | −24.0561 | −1.07261 | −0.536305 | − | 0.844024i | \(-0.680180\pi\) | ||||
−0.536305 | + | 0.844024i | \(0.680180\pi\) | |||||||
\(504\) | 3.00420 | 0.133818 | ||||||||
\(505\) | −2.65266 | −0.118042 | ||||||||
\(506\) | −17.3194 | −0.769941 | ||||||||
\(507\) | 10.4468 | 0.463961 | ||||||||
\(508\) | 0.946447 | 0.0419918 | ||||||||
\(509\) | −24.7201 | −1.09570 | −0.547850 | − | 0.836576i | \(-0.684554\pi\) | ||||
−0.547850 | + | 0.836576i | \(0.684554\pi\) | |||||||
\(510\) | 4.64538 | 0.205701 | ||||||||
\(511\) | −11.6067 | −0.513451 | ||||||||
\(512\) | 21.2175 | 0.937690 | ||||||||
\(513\) | −5.94298 | −0.262389 | ||||||||
\(514\) | 8.89462 | 0.392325 | ||||||||
\(515\) | 10.0241 | 0.441715 | ||||||||
\(516\) | 0.742755 | 0.0326980 | ||||||||
\(517\) | −55.7644 | −2.45251 | ||||||||
\(518\) | 10.1238 | 0.444813 | ||||||||
\(519\) | 15.2338 | 0.668691 | ||||||||
\(520\) | −14.2852 | −0.626449 | ||||||||
\(521\) | −15.3498 | −0.672489 | −0.336244 | − | 0.941775i | \(-0.609157\pi\) | ||||
−0.336244 | + | 0.941775i | \(0.609157\pi\) | |||||||
\(522\) | −2.52839 | −0.110665 | ||||||||
\(523\) | −1.62146 | −0.0709016 | −0.0354508 | − | 0.999371i | \(-0.511287\pi\) | ||||
−0.0354508 | + | 0.999371i | \(0.511287\pi\) | |||||||
\(524\) | 1.08320 | 0.0473197 | ||||||||
\(525\) | −5.84839 | −0.255245 | ||||||||
\(526\) | −27.1533 | −1.18394 | ||||||||
\(527\) | 2.72016 | 0.118492 | ||||||||
\(528\) | 20.6212 | 0.897422 | ||||||||
\(529\) | −17.1599 | −0.746083 | ||||||||
\(530\) | −9.58574 | −0.416378 | ||||||||
\(531\) | 7.21706 | 0.313194 | ||||||||
\(532\) | 0.485892 | 0.0210661 | ||||||||
\(533\) | −2.47986 | −0.107415 | ||||||||
\(534\) | 10.0150 | 0.433391 | ||||||||
\(535\) | 34.5509 | 1.49376 | ||||||||
\(536\) | −35.6681 | −1.54063 | ||||||||
\(537\) | 13.0103 | 0.561436 | ||||||||
\(538\) | −11.3220 | −0.488128 | ||||||||
\(539\) | −28.9823 | −1.24836 | ||||||||
\(540\) | 0.243308 | 0.0104703 | ||||||||
\(541\) | −37.5059 | −1.61251 | −0.806253 | − | 0.591572i | \(-0.798508\pi\) | ||||
−0.806253 | + | 0.591572i | \(0.798508\pi\) | |||||||
\(542\) | 28.1572 | 1.20946 | ||||||||
\(543\) | 23.2066 | 0.995890 | ||||||||
\(544\) | −0.426617 | −0.0182911 | ||||||||
\(545\) | 20.4224 | 0.874799 | ||||||||
\(546\) | 2.49424 | 0.106744 | ||||||||
\(547\) | 11.7635 | 0.502970 | 0.251485 | − | 0.967861i | \(-0.419081\pi\) | ||||
0.251485 | + | 0.967861i | \(0.419081\pi\) | |||||||
\(548\) | 0.448110 | 0.0191423 | ||||||||
\(549\) | 8.92460 | 0.380893 | ||||||||
\(550\) | −38.6826 | −1.64943 | ||||||||
\(551\) | 10.4302 | 0.444341 | ||||||||
\(552\) | −6.70030 | −0.285184 | ||||||||
\(553\) | 12.7719 | 0.543115 | ||||||||
\(554\) | 22.9281 | 0.974121 | ||||||||
\(555\) | −20.9125 | −0.887687 | ||||||||
\(556\) | −1.63990 | −0.0695471 | ||||||||
\(557\) | 8.83557 | 0.374375 | 0.187188 | − | 0.982324i | \(-0.440063\pi\) | ||||
0.187188 | + | 0.982324i | \(0.440063\pi\) | |||||||
\(558\) | 3.91878 | 0.165895 | ||||||||
\(559\) | −15.7287 | −0.665252 | ||||||||
\(560\) | 14.4829 | 0.612014 | ||||||||
\(561\) | 4.97469 | 0.210032 | ||||||||
\(562\) | 10.8812 | 0.458997 | ||||||||
\(563\) | 8.07419 | 0.340287 | 0.170143 | − | 0.985419i | \(-0.445577\pi\) | ||||
0.170143 | + | 0.985419i | \(0.445577\pi\) | |||||||
\(564\) | 0.845829 | 0.0356158 | ||||||||
\(565\) | 31.0861 | 1.30780 | ||||||||
\(566\) | 3.38854 | 0.142431 | ||||||||
\(567\) | 1.08354 | 0.0455043 | ||||||||
\(568\) | 25.2685 | 1.06024 | ||||||||
\(569\) | −8.32544 | −0.349021 | −0.174510 | − | 0.984655i | \(-0.555834\pi\) | ||||
−0.174510 | + | 0.984655i | \(0.555834\pi\) | |||||||
\(570\) | −27.6074 | −1.15635 | ||||||||
\(571\) | −4.51807 | −0.189075 | −0.0945376 | − | 0.995521i | \(-0.530137\pi\) | ||||
−0.0945376 | + | 0.995521i | \(0.530137\pi\) | |||||||
\(572\) | 0.599787 | 0.0250783 | ||||||||
\(573\) | 14.9928 | 0.626333 | ||||||||
\(574\) | 2.42265 | 0.101119 | ||||||||
\(575\) | 13.0437 | 0.543962 | ||||||||
\(576\) | 7.67583 | 0.319826 | ||||||||
\(577\) | 36.5029 | 1.51963 | 0.759817 | − | 0.650137i | \(-0.225288\pi\) | ||||
0.759817 | + | 0.650137i | \(0.225288\pi\) | |||||||
\(578\) | −1.44064 | −0.0599229 | ||||||||
\(579\) | −13.0199 | −0.541090 | ||||||||
\(580\) | −0.427017 | −0.0177309 | ||||||||
\(581\) | 11.5775 | 0.480316 | ||||||||
\(582\) | −4.12203 | −0.170864 | ||||||||
\(583\) | −10.2653 | −0.425144 | ||||||||
\(584\) | −29.6996 | −1.22898 | ||||||||
\(585\) | −5.15232 | −0.213022 | ||||||||
\(586\) | −30.5769 | −1.26312 | ||||||||
\(587\) | −3.91386 | −0.161542 | −0.0807710 | − | 0.996733i | \(-0.525738\pi\) | ||||
−0.0807710 | + | 0.996733i | \(0.525738\pi\) | |||||||
\(588\) | 0.439601 | 0.0181288 | ||||||||
\(589\) | −16.1658 | −0.666102 | ||||||||
\(590\) | 33.5260 | 1.38024 | ||||||||
\(591\) | −11.4527 | −0.471101 | ||||||||
\(592\) | 26.8837 | 1.10491 | ||||||||
\(593\) | 5.82169 | 0.239068 | 0.119534 | − | 0.992830i | \(-0.461860\pi\) | ||||
0.119534 | + | 0.992830i | \(0.461860\pi\) | |||||||
\(594\) | 7.16676 | 0.294056 | ||||||||
\(595\) | 3.49388 | 0.143235 | ||||||||
\(596\) | −0.0503113 | −0.00206083 | ||||||||
\(597\) | −7.91095 | −0.323774 | ||||||||
\(598\) | −5.56295 | −0.227486 | ||||||||
\(599\) | −27.4925 | −1.12331 | −0.561656 | − | 0.827371i | \(-0.689836\pi\) | ||||
−0.561656 | + | 0.827371i | \(0.689836\pi\) | |||||||
\(600\) | −14.9650 | −0.610944 | ||||||||
\(601\) | 47.4556 | 1.93575 | 0.967876 | − | 0.251427i | \(-0.0808999\pi\) | ||||
0.967876 | + | 0.251427i | \(0.0808999\pi\) | |||||||
\(602\) | 15.3657 | 0.626261 | ||||||||
\(603\) | −12.8646 | −0.523886 | ||||||||
\(604\) | 0.0527001 | 0.00214434 | ||||||||
\(605\) | −44.3292 | −1.80224 | ||||||||
\(606\) | 1.18515 | 0.0481435 | ||||||||
\(607\) | −38.0691 | −1.54518 | −0.772588 | − | 0.634907i | \(-0.781038\pi\) | ||||
−0.772588 | + | 0.634907i | \(0.781038\pi\) | |||||||
\(608\) | 2.53538 | 0.102823 | ||||||||
\(609\) | −1.90166 | −0.0770590 | ||||||||
\(610\) | 41.4582 | 1.67859 | ||||||||
\(611\) | −17.9114 | −0.724617 | ||||||||
\(612\) | −0.0754557 | −0.00305012 | ||||||||
\(613\) | −0.539040 | −0.0217716 | −0.0108858 | − | 0.999941i | \(-0.503465\pi\) | ||||
−0.0108858 | + | 0.999941i | \(0.503465\pi\) | |||||||
\(614\) | 37.5055 | 1.51360 | ||||||||
\(615\) | −5.00442 | −0.201798 | ||||||||
\(616\) | 14.9450 | 0.602149 | ||||||||
\(617\) | −7.54171 | −0.303618 | −0.151809 | − | 0.988410i | \(-0.548510\pi\) | ||||
−0.151809 | + | 0.988410i | \(0.548510\pi\) | |||||||
\(618\) | −4.47856 | −0.180154 | ||||||||
\(619\) | −8.96790 | −0.360450 | −0.180225 | − | 0.983625i | \(-0.557683\pi\) | ||||
−0.180225 | + | 0.983625i | \(0.557683\pi\) | |||||||
\(620\) | 0.661837 | 0.0265800 | ||||||||
\(621\) | −2.41663 | −0.0969759 | ||||||||
\(622\) | −2.92391 | −0.117238 | ||||||||
\(623\) | 7.53247 | 0.301782 | ||||||||
\(624\) | 6.62347 | 0.265151 | ||||||||
\(625\) | −22.8545 | −0.914180 | ||||||||
\(626\) | 2.43748 | 0.0974213 | ||||||||
\(627\) | −29.5645 | −1.18069 | ||||||||
\(628\) | −0.0754557 | −0.00301101 | ||||||||
\(629\) | 6.48548 | 0.258593 | ||||||||
\(630\) | 5.03344 | 0.200537 | ||||||||
\(631\) | 2.30162 | 0.0916261 | 0.0458130 | − | 0.998950i | \(-0.485412\pi\) | ||||
0.0458130 | + | 0.998950i | \(0.485412\pi\) | |||||||
\(632\) | 32.6810 | 1.29998 | ||||||||
\(633\) | 3.28941 | 0.130742 | ||||||||
\(634\) | −25.6865 | −1.02014 | ||||||||
\(635\) | −40.4453 | −1.60502 | ||||||||
\(636\) | 0.155703 | 0.00617402 | ||||||||
\(637\) | −9.30904 | −0.368838 | ||||||||
\(638\) | −12.5780 | −0.497967 | ||||||||
\(639\) | 9.11371 | 0.360533 | ||||||||
\(640\) | 38.4084 | 1.51823 | ||||||||
\(641\) | 32.8329 | 1.29682 | 0.648412 | − | 0.761290i | \(-0.275434\pi\) | ||||
0.648412 | + | 0.761290i | \(0.275434\pi\) | |||||||
\(642\) | −15.4366 | −0.609233 | ||||||||
\(643\) | 22.0372 | 0.869063 | 0.434531 | − | 0.900657i | \(-0.356914\pi\) | ||||
0.434531 | + | 0.900657i | \(0.356914\pi\) | |||||||
\(644\) | 0.197581 | 0.00778579 | ||||||||
\(645\) | −31.7408 | −1.24979 | ||||||||
\(646\) | 8.56172 | 0.336856 | ||||||||
\(647\) | 6.27790 | 0.246810 | 0.123405 | − | 0.992356i | \(-0.460619\pi\) | ||||
0.123405 | + | 0.992356i | \(0.460619\pi\) | |||||||
\(648\) | 2.77258 | 0.108917 | ||||||||
\(649\) | 35.9027 | 1.40930 | ||||||||
\(650\) | −12.4248 | −0.487339 | ||||||||
\(651\) | 2.94739 | 0.115517 | ||||||||
\(652\) | −0.891000 | −0.0348942 | ||||||||
\(653\) | 11.5242 | 0.450978 | 0.225489 | − | 0.974246i | \(-0.427602\pi\) | ||||
0.225489 | + | 0.974246i | \(0.427602\pi\) | |||||||
\(654\) | −9.12429 | −0.356788 | ||||||||
\(655\) | −46.2892 | −1.80867 | ||||||||
\(656\) | 6.43334 | 0.251180 | ||||||||
\(657\) | −10.7119 | −0.417910 | ||||||||
\(658\) | 17.4981 | 0.682147 | ||||||||
\(659\) | −8.75496 | −0.341045 | −0.170522 | − | 0.985354i | \(-0.554546\pi\) | ||||
−0.170522 | + | 0.985354i | \(0.554546\pi\) | |||||||
\(660\) | 1.21038 | 0.0471141 | ||||||||
\(661\) | −1.74453 | −0.0678543 | −0.0339271 | − | 0.999424i | \(-0.510801\pi\) | ||||
−0.0339271 | + | 0.999424i | \(0.510801\pi\) | |||||||
\(662\) | 47.1280 | 1.83168 | ||||||||
\(663\) | 1.59786 | 0.0620557 | ||||||||
\(664\) | 29.6249 | 1.14967 | ||||||||
\(665\) | −20.7641 | −0.805196 | ||||||||
\(666\) | 9.34326 | 0.362044 | ||||||||
\(667\) | 4.24129 | 0.164223 | ||||||||
\(668\) | −0.799651 | −0.0309394 | ||||||||
\(669\) | −15.2355 | −0.589038 | ||||||||
\(670\) | −59.7609 | −2.30876 | ||||||||
\(671\) | 44.3972 | 1.71393 | ||||||||
\(672\) | −0.462255 | −0.0178319 | ||||||||
\(673\) | −15.4975 | −0.597387 | −0.298693 | − | 0.954349i | \(-0.596551\pi\) | ||||
−0.298693 | + | 0.954349i | \(0.596551\pi\) | |||||||
\(674\) | −6.76352 | −0.260521 | ||||||||
\(675\) | −5.39750 | −0.207750 | ||||||||
\(676\) | −0.788274 | −0.0303182 | ||||||||
\(677\) | −14.2413 | −0.547339 | −0.273669 | − | 0.961824i | \(-0.588237\pi\) | ||||
−0.273669 | + | 0.961824i | \(0.588237\pi\) | |||||||
\(678\) | −13.8886 | −0.533388 | ||||||||
\(679\) | −3.10026 | −0.118977 | ||||||||
\(680\) | 8.94024 | 0.342842 | ||||||||
\(681\) | 2.95734 | 0.113326 | ||||||||
\(682\) | 19.4947 | 0.746492 | ||||||||
\(683\) | −11.0917 | −0.424412 | −0.212206 | − | 0.977225i | \(-0.568065\pi\) | ||||
−0.212206 | + | 0.977225i | \(0.568065\pi\) | |||||||
\(684\) | 0.448432 | 0.0171462 | ||||||||
\(685\) | −19.1495 | −0.731663 | ||||||||
\(686\) | 20.0212 | 0.764413 | ||||||||
\(687\) | 1.99894 | 0.0762642 | ||||||||
\(688\) | 40.8038 | 1.55563 | ||||||||
\(689\) | −3.29718 | −0.125613 | ||||||||
\(690\) | −11.2262 | −0.427372 | ||||||||
\(691\) | −28.9163 | −1.10003 | −0.550014 | − | 0.835155i | \(-0.685378\pi\) | ||||
−0.550014 | + | 0.835155i | \(0.685378\pi\) | |||||||
\(692\) | −1.14948 | −0.0436967 | ||||||||
\(693\) | 5.39026 | 0.204759 | ||||||||
\(694\) | −32.4292 | −1.23099 | ||||||||
\(695\) | 70.0791 | 2.65825 | ||||||||
\(696\) | −4.86601 | −0.184446 | ||||||||
\(697\) | 1.55199 | 0.0587859 | ||||||||
\(698\) | −15.9223 | −0.602669 | ||||||||
\(699\) | −5.10521 | −0.193097 | ||||||||
\(700\) | 0.441294 | 0.0166794 | ||||||||
\(701\) | 25.4593 | 0.961583 | 0.480791 | − | 0.876835i | \(-0.340349\pi\) | ||||
0.480791 | + | 0.876835i | \(0.340349\pi\) | |||||||
\(702\) | 2.30195 | 0.0868814 | ||||||||
\(703\) | −38.5431 | −1.45368 | ||||||||
\(704\) | 38.1849 | 1.43915 | ||||||||
\(705\) | −36.1456 | −1.36132 | ||||||||
\(706\) | −5.07915 | −0.191156 | ||||||||
\(707\) | 0.891376 | 0.0335237 | ||||||||
\(708\) | −0.544569 | −0.0204661 | ||||||||
\(709\) | 14.6781 | 0.551246 | 0.275623 | − | 0.961266i | \(-0.411116\pi\) | ||||
0.275623 | + | 0.961266i | \(0.411116\pi\) | |||||||
\(710\) | 42.3367 | 1.58887 | ||||||||
\(711\) | 11.7872 | 0.442055 | ||||||||
\(712\) | 19.2743 | 0.722334 | ||||||||
\(713\) | −6.57361 | −0.246184 | ||||||||
\(714\) | −1.56099 | −0.0584186 | ||||||||
\(715\) | −25.6312 | −0.958553 | ||||||||
\(716\) | −0.981701 | −0.0366879 | ||||||||
\(717\) | 23.7050 | 0.885279 | ||||||||
\(718\) | −3.56276 | −0.132961 | ||||||||
\(719\) | 2.04707 | 0.0763429 | 0.0381715 | − | 0.999271i | \(-0.487847\pi\) | ||||
0.0381715 | + | 0.999271i | \(0.487847\pi\) | |||||||
\(720\) | 13.3663 | 0.498133 | ||||||||
\(721\) | −3.36841 | −0.125446 | ||||||||
\(722\) | −23.5099 | −0.874948 | ||||||||
\(723\) | −29.6586 | −1.10302 | ||||||||
\(724\) | −1.75107 | −0.0650780 | ||||||||
\(725\) | 9.47285 | 0.351813 | ||||||||
\(726\) | 19.8054 | 0.735046 | ||||||||
\(727\) | 17.3293 | 0.642709 | 0.321354 | − | 0.946959i | \(-0.395862\pi\) | ||||
0.321354 | + | 0.946959i | \(0.395862\pi\) | |||||||
\(728\) | 4.80028 | 0.177910 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −49.7608 | −1.84173 | ||||||||
\(731\) | 9.84359 | 0.364078 | ||||||||
\(732\) | −0.673412 | −0.0248900 | ||||||||
\(733\) | −17.7168 | −0.654386 | −0.327193 | − | 0.944957i | \(-0.606103\pi\) | ||||
−0.327193 | + | 0.944957i | \(0.606103\pi\) | |||||||
\(734\) | 31.2887 | 1.15489 | ||||||||
\(735\) | −18.7859 | −0.692927 | ||||||||
\(736\) | 1.03097 | 0.0380022 | ||||||||
\(737\) | −63.9974 | −2.35737 | ||||||||
\(738\) | 2.23587 | 0.0823034 | ||||||||
\(739\) | −33.0929 | −1.21734 | −0.608671 | − | 0.793423i | \(-0.708297\pi\) | ||||
−0.608671 | + | 0.793423i | \(0.708297\pi\) | |||||||
\(740\) | 1.57797 | 0.0580073 | ||||||||
\(741\) | −9.49605 | −0.348846 | ||||||||
\(742\) | 3.22110 | 0.118250 | ||||||||
\(743\) | −30.0436 | −1.10219 | −0.551096 | − | 0.834442i | \(-0.685790\pi\) | ||||
−0.551096 | + | 0.834442i | \(0.685790\pi\) | |||||||
\(744\) | 7.54187 | 0.276498 | ||||||||
\(745\) | 2.15000 | 0.0787698 | ||||||||
\(746\) | 0.287141 | 0.0105130 | ||||||||
\(747\) | 10.6849 | 0.390941 | ||||||||
\(748\) | −0.375369 | −0.0137249 | ||||||||
\(749\) | −11.6102 | −0.424226 | ||||||||
\(750\) | −1.84653 | −0.0674259 | ||||||||
\(751\) | −8.16981 | −0.298121 | −0.149060 | − | 0.988828i | \(-0.547625\pi\) | ||||
−0.149060 | + | 0.988828i | \(0.547625\pi\) | |||||||
\(752\) | 46.4663 | 1.69445 | ||||||||
\(753\) | −6.58481 | −0.239964 | ||||||||
\(754\) | −4.04002 | −0.147129 | ||||||||
\(755\) | −2.25208 | −0.0819616 | ||||||||
\(756\) | −0.0817590 | −0.00297355 | ||||||||
\(757\) | 39.9107 | 1.45058 | 0.725289 | − | 0.688444i | \(-0.241706\pi\) | ||||
0.725289 | + | 0.688444i | \(0.241706\pi\) | |||||||
\(758\) | 14.7807 | 0.536859 | ||||||||
\(759\) | −12.0220 | −0.436370 | ||||||||
\(760\) | −53.1317 | −1.92729 | ||||||||
\(761\) | −21.7192 | −0.787320 | −0.393660 | − | 0.919256i | \(-0.628791\pi\) | ||||
−0.393660 | + | 0.919256i | \(0.628791\pi\) | |||||||
\(762\) | 18.0701 | 0.654611 | ||||||||
\(763\) | −6.86256 | −0.248441 | ||||||||
\(764\) | −1.13129 | −0.0409287 | ||||||||
\(765\) | 3.22452 | 0.116583 | ||||||||
\(766\) | 3.90528 | 0.141103 | ||||||||
\(767\) | 11.5319 | 0.416391 | ||||||||
\(768\) | −1.80839 | −0.0652547 | ||||||||
\(769\) | 51.1796 | 1.84558 | 0.922792 | − | 0.385298i | \(-0.125901\pi\) | ||||
0.922792 | + | 0.385298i | \(0.125901\pi\) | |||||||
\(770\) | 25.0398 | 0.902372 | ||||||||
\(771\) | 6.17406 | 0.222353 | ||||||||
\(772\) | 0.982429 | 0.0353584 | ||||||||
\(773\) | −34.8182 | −1.25232 | −0.626162 | − | 0.779693i | \(-0.715375\pi\) | ||||
−0.626162 | + | 0.779693i | \(0.715375\pi\) | |||||||
\(774\) | 14.1811 | 0.509729 | ||||||||
\(775\) | −14.6820 | −0.527395 | ||||||||
\(776\) | −7.93303 | −0.284779 | ||||||||
\(777\) | 7.02725 | 0.252101 | ||||||||
\(778\) | 19.8796 | 0.712719 | ||||||||
\(779\) | −9.22346 | −0.330465 | ||||||||
\(780\) | 0.388772 | 0.0139203 | ||||||||
\(781\) | 45.3379 | 1.62232 | ||||||||
\(782\) | 3.48150 | 0.124498 | ||||||||
\(783\) | −1.75504 | −0.0627202 | ||||||||
\(784\) | 24.1498 | 0.862494 | ||||||||
\(785\) | 3.22452 | 0.115088 | ||||||||
\(786\) | 20.6810 | 0.737668 | ||||||||
\(787\) | −43.4460 | −1.54868 | −0.774341 | − | 0.632768i | \(-0.781919\pi\) | ||||
−0.774341 | + | 0.632768i | \(0.781919\pi\) | |||||||
\(788\) | 0.864171 | 0.0307848 | ||||||||
\(789\) | −18.8480 | −0.671008 | ||||||||
\(790\) | 54.7560 | 1.94813 | ||||||||
\(791\) | −10.4459 | −0.371413 | ||||||||
\(792\) | 13.7928 | 0.490104 | ||||||||
\(793\) | 14.2603 | 0.506397 | ||||||||
\(794\) | 31.6297 | 1.12250 | ||||||||
\(795\) | −6.65379 | −0.235985 | ||||||||
\(796\) | 0.596927 | 0.0211575 | ||||||||
\(797\) | 34.5791 | 1.22485 | 0.612427 | − | 0.790527i | \(-0.290193\pi\) | ||||
0.612427 | + | 0.790527i | \(0.290193\pi\) | |||||||
\(798\) | 9.27694 | 0.328400 | ||||||||
\(799\) | 11.2096 | 0.396567 | ||||||||
\(800\) | 2.30266 | 0.0814115 | ||||||||
\(801\) | 6.95174 | 0.245628 | ||||||||
\(802\) | 27.3469 | 0.965654 | ||||||||
\(803\) | −53.2883 | −1.88050 | ||||||||
\(804\) | 0.970706 | 0.0342342 | ||||||||
\(805\) | −8.44341 | −0.297591 | ||||||||
\(806\) | 6.26166 | 0.220557 | ||||||||
\(807\) | −7.85901 | −0.276650 | ||||||||
\(808\) | 2.28088 | 0.0802410 | ||||||||
\(809\) | −18.4701 | −0.649376 | −0.324688 | − | 0.945821i | \(-0.605259\pi\) | ||||
−0.324688 | + | 0.945821i | \(0.605259\pi\) | |||||||
\(810\) | 4.64538 | 0.163222 | ||||||||
\(811\) | 12.6510 | 0.444235 | 0.222118 | − | 0.975020i | \(-0.428703\pi\) | ||||
0.222118 | + | 0.975020i | \(0.428703\pi\) | |||||||
\(812\) | 0.143491 | 0.00503554 | ||||||||
\(813\) | 19.5449 | 0.685469 | ||||||||
\(814\) | 46.4799 | 1.62912 | ||||||||
\(815\) | 38.0759 | 1.33374 | ||||||||
\(816\) | −4.14522 | −0.145112 | ||||||||
\(817\) | −58.5002 | −2.04666 | ||||||||
\(818\) | −26.1643 | −0.914812 | ||||||||
\(819\) | 1.73134 | 0.0604979 | ||||||||
\(820\) | 0.377612 | 0.0131868 | ||||||||
\(821\) | 8.18318 | 0.285595 | 0.142797 | − | 0.989752i | \(-0.454390\pi\) | ||||
0.142797 | + | 0.989752i | \(0.454390\pi\) | |||||||
\(822\) | 8.55557 | 0.298410 | ||||||||
\(823\) | 15.6202 | 0.544487 | 0.272243 | − | 0.962228i | \(-0.412234\pi\) | ||||
0.272243 | + | 0.962228i | \(0.412234\pi\) | |||||||
\(824\) | −8.61918 | −0.300264 | ||||||||
\(825\) | −26.8509 | −0.934828 | ||||||||
\(826\) | −11.2658 | −0.391986 | ||||||||
\(827\) | −34.5939 | −1.20295 | −0.601474 | − | 0.798892i | \(-0.705420\pi\) | ||||
−0.601474 | + | 0.798892i | \(0.705420\pi\) | |||||||
\(828\) | 0.182348 | 0.00633705 | ||||||||
\(829\) | 24.2848 | 0.843446 | 0.421723 | − | 0.906725i | \(-0.361425\pi\) | ||||
0.421723 | + | 0.906725i | \(0.361425\pi\) | |||||||
\(830\) | 49.6356 | 1.72288 | ||||||||
\(831\) | 15.9152 | 0.552091 | ||||||||
\(832\) | 12.2649 | 0.425209 | ||||||||
\(833\) | 5.82595 | 0.201857 | ||||||||
\(834\) | −31.3099 | −1.08417 | ||||||||
\(835\) | 34.1722 | 1.18258 | ||||||||
\(836\) | 2.23081 | 0.0771542 | ||||||||
\(837\) | 2.72016 | 0.0940224 | ||||||||
\(838\) | 9.77424 | 0.337645 | ||||||||
\(839\) | 34.9491 | 1.20658 | 0.603288 | − | 0.797523i | \(-0.293857\pi\) | ||||
0.603288 | + | 0.797523i | \(0.293857\pi\) | |||||||
\(840\) | 9.68708 | 0.334236 | ||||||||
\(841\) | −25.9198 | −0.893787 | ||||||||
\(842\) | −22.4227 | −0.772737 | ||||||||
\(843\) | 7.55302 | 0.260140 | ||||||||
\(844\) | −0.248205 | −0.00854355 | ||||||||
\(845\) | 33.6860 | 1.15883 | ||||||||
\(846\) | 16.1491 | 0.555216 | ||||||||
\(847\) | 14.8960 | 0.511833 | ||||||||
\(848\) | 8.55366 | 0.293734 | ||||||||
\(849\) | 2.35210 | 0.0807240 | ||||||||
\(850\) | 7.77588 | 0.266710 | ||||||||
\(851\) | −15.6730 | −0.537263 | ||||||||
\(852\) | −0.687682 | −0.0235596 | ||||||||
\(853\) | −39.0378 | −1.33663 | −0.668315 | − | 0.743879i | \(-0.732984\pi\) | ||||
−0.668315 | + | 0.743879i | \(0.732984\pi\) | |||||||
\(854\) | −13.9312 | −0.476717 | ||||||||
\(855\) | −19.1632 | −0.655369 | ||||||||
\(856\) | −29.7084 | −1.01541 | ||||||||
\(857\) | 20.9236 | 0.714738 | 0.357369 | − | 0.933963i | \(-0.383674\pi\) | ||||
0.357369 | + | 0.933963i | \(0.383674\pi\) | |||||||
\(858\) | 11.4515 | 0.390947 | ||||||||
\(859\) | −2.54949 | −0.0869875 | −0.0434938 | − | 0.999054i | \(-0.513849\pi\) | ||||
−0.0434938 | + | 0.999054i | \(0.513849\pi\) | |||||||
\(860\) | 2.39502 | 0.0816696 | ||||||||
\(861\) | 1.68164 | 0.0573102 | ||||||||
\(862\) | −26.2507 | −0.894102 | ||||||||
\(863\) | −30.0634 | −1.02337 | −0.511686 | − | 0.859173i | \(-0.670979\pi\) | ||||
−0.511686 | + | 0.859173i | \(0.670979\pi\) | |||||||
\(864\) | −0.426617 | −0.0145138 | ||||||||
\(865\) | 49.1217 | 1.67019 | ||||||||
\(866\) | −34.2084 | −1.16245 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −0.222398 | −0.00754866 | ||||||||
\(869\) | 58.6377 | 1.98915 | ||||||||
\(870\) | −8.15285 | −0.276407 | ||||||||
\(871\) | −20.5558 | −0.696506 | ||||||||
\(872\) | −17.5601 | −0.594660 | ||||||||
\(873\) | −2.86124 | −0.0968383 | ||||||||
\(874\) | −20.6905 | −0.699866 | ||||||||
\(875\) | −1.38881 | −0.0469505 | ||||||||
\(876\) | 0.808273 | 0.0273090 | ||||||||
\(877\) | 19.7246 | 0.666051 | 0.333026 | − | 0.942918i | \(-0.391930\pi\) | ||||
0.333026 | + | 0.942918i | \(0.391930\pi\) | |||||||
\(878\) | −0.822058 | −0.0277431 | ||||||||
\(879\) | −21.2244 | −0.715882 | ||||||||
\(880\) | 66.4933 | 2.24149 | ||||||||
\(881\) | −55.8107 | −1.88031 | −0.940154 | − | 0.340749i | \(-0.889319\pi\) | ||||
−0.940154 | + | 0.340749i | \(0.889319\pi\) | |||||||
\(882\) | 8.39312 | 0.282611 | ||||||||
\(883\) | 40.2068 | 1.35307 | 0.676534 | − | 0.736411i | \(-0.263481\pi\) | ||||
0.676534 | + | 0.736411i | \(0.263481\pi\) | |||||||
\(884\) | −0.120568 | −0.00405513 | ||||||||
\(885\) | 23.2715 | 0.782264 | ||||||||
\(886\) | −48.0930 | −1.61572 | ||||||||
\(887\) | −51.0012 | −1.71245 | −0.856226 | − | 0.516602i | \(-0.827197\pi\) | ||||
−0.856226 | + | 0.516602i | \(0.827197\pi\) | |||||||
\(888\) | 17.9815 | 0.603420 | ||||||||
\(889\) | 13.5909 | 0.455824 | ||||||||
\(890\) | 32.2935 | 1.08248 | ||||||||
\(891\) | 4.97469 | 0.166658 | ||||||||
\(892\) | 1.14960 | 0.0384916 | ||||||||
\(893\) | −66.6185 | −2.22930 | ||||||||
\(894\) | −0.960572 | −0.0321263 | ||||||||
\(895\) | 41.9519 | 1.40230 | ||||||||
\(896\) | −12.9064 | −0.431173 | ||||||||
\(897\) | −3.86143 | −0.128929 | ||||||||
\(898\) | −14.0195 | −0.467838 | ||||||||
\(899\) | −4.77400 | −0.159222 | ||||||||
\(900\) | 0.407272 | 0.0135757 | ||||||||
\(901\) | 2.06350 | 0.0687451 | ||||||||
\(902\) | 11.1228 | 0.370347 | ||||||||
\(903\) | 10.6659 | 0.354938 | ||||||||
\(904\) | −26.7292 | −0.889000 | ||||||||
\(905\) | 74.8300 | 2.48743 | ||||||||
\(906\) | 1.00618 | 0.0334281 | ||||||||
\(907\) | 3.88582 | 0.129026 | 0.0645132 | − | 0.997917i | \(-0.479451\pi\) | ||||
0.0645132 | + | 0.997917i | \(0.479451\pi\) | |||||||
\(908\) | −0.223149 | −0.00740544 | ||||||||
\(909\) | 0.822654 | 0.0272857 | ||||||||
\(910\) | 8.04273 | 0.266614 | ||||||||
\(911\) | −42.0118 | −1.39191 | −0.695956 | − | 0.718084i | \(-0.745019\pi\) | ||||
−0.695956 | + | 0.718084i | \(0.745019\pi\) | |||||||
\(912\) | 24.6349 | 0.815745 | ||||||||
\(913\) | 53.1543 | 1.75915 | ||||||||
\(914\) | 3.84069 | 0.127039 | ||||||||
\(915\) | 28.7775 | 0.951355 | ||||||||
\(916\) | −0.150831 | −0.00498360 | ||||||||
\(917\) | 15.5546 | 0.513658 | ||||||||
\(918\) | −1.44064 | −0.0475483 | ||||||||
\(919\) | −41.3234 | −1.36313 | −0.681567 | − | 0.731755i | \(-0.738701\pi\) | ||||
−0.681567 | + | 0.731755i | \(0.738701\pi\) | |||||||
\(920\) | −21.6052 | −0.712303 | ||||||||
\(921\) | 26.0338 | 0.857844 | ||||||||
\(922\) | −34.1313 | −1.12406 | ||||||||
\(923\) | 14.5624 | 0.479328 | ||||||||
\(924\) | −0.406726 | −0.0133803 | ||||||||
\(925\) | −35.0053 | −1.15097 | ||||||||
\(926\) | 9.45981 | 0.310869 | ||||||||
\(927\) | −3.10872 | −0.102104 | ||||||||
\(928\) | 0.748732 | 0.0245783 | ||||||||
\(929\) | −36.3212 | −1.19166 | −0.595830 | − | 0.803110i | \(-0.703177\pi\) | ||||
−0.595830 | + | 0.803110i | \(0.703177\pi\) | |||||||
\(930\) | 12.6362 | 0.414356 | ||||||||
\(931\) | −34.6235 | −1.13474 | ||||||||
\(932\) | 0.385217 | 0.0126182 | ||||||||
\(933\) | −2.02959 | −0.0664457 | ||||||||
\(934\) | 14.8291 | 0.485221 | ||||||||
\(935\) | 16.0410 | 0.524596 | ||||||||
\(936\) | 4.43020 | 0.144806 | ||||||||
\(937\) | −36.5702 | −1.19470 | −0.597348 | − | 0.801982i | \(-0.703779\pi\) | ||||
−0.597348 | + | 0.801982i | \(0.703779\pi\) | |||||||
\(938\) | 20.0815 | 0.655684 | ||||||||
\(939\) | 1.69194 | 0.0552143 | ||||||||
\(940\) | 2.72739 | 0.0889576 | ||||||||
\(941\) | −29.7322 | −0.969244 | −0.484622 | − | 0.874724i | \(-0.661043\pi\) | ||||
−0.484622 | + | 0.874724i | \(0.661043\pi\) | |||||||
\(942\) | −1.44064 | −0.0469387 | ||||||||
\(943\) | −3.75059 | −0.122136 | ||||||||
\(944\) | −29.9163 | −0.973693 | ||||||||
\(945\) | 3.49388 | 0.113656 | ||||||||
\(946\) | 70.5466 | 2.29367 | ||||||||
\(947\) | −4.74210 | −0.154098 | −0.0770488 | − | 0.997027i | \(-0.524550\pi\) | ||||
−0.0770488 | + | 0.997027i | \(0.524550\pi\) | |||||||
\(948\) | −0.889412 | −0.0288868 | ||||||||
\(949\) | −17.1161 | −0.555612 | ||||||||
\(950\) | −46.2119 | −1.49931 | ||||||||
\(951\) | −17.8299 | −0.578173 | ||||||||
\(952\) | −3.00420 | −0.0973666 | ||||||||
\(953\) | −23.1658 | −0.750413 | −0.375207 | − | 0.926941i | \(-0.622428\pi\) | ||||
−0.375207 | + | 0.926941i | \(0.622428\pi\) | |||||||
\(954\) | 2.97277 | 0.0962469 | ||||||||
\(955\) | 48.3445 | 1.56439 | ||||||||
\(956\) | −1.78868 | −0.0578500 | ||||||||
\(957\) | −8.73081 | −0.282227 | ||||||||
\(958\) | −51.9002 | −1.67682 | ||||||||
\(959\) | 6.43481 | 0.207791 | ||||||||
\(960\) | 24.7508 | 0.798830 | ||||||||
\(961\) | −23.6007 | −0.761314 | ||||||||
\(962\) | 14.9292 | 0.481337 | ||||||||
\(963\) | −10.7151 | −0.345288 | ||||||||
\(964\) | 2.23791 | 0.0720783 | ||||||||
\(965\) | −41.9830 | −1.35148 | ||||||||
\(966\) | 3.77234 | 0.121373 | ||||||||
\(967\) | 2.56051 | 0.0823406 | 0.0411703 | − | 0.999152i | \(-0.486891\pi\) | ||||
0.0411703 | + | 0.999152i | \(0.486891\pi\) | |||||||
\(968\) | 38.1163 | 1.22510 | ||||||||
\(969\) | 5.94298 | 0.190916 | ||||||||
\(970\) | −13.2916 | −0.426766 | ||||||||
\(971\) | 17.7103 | 0.568350 | 0.284175 | − | 0.958773i | \(-0.408280\pi\) | ||||
0.284175 | + | 0.958773i | \(0.408280\pi\) | |||||||
\(972\) | −0.0754557 | −0.00242024 | ||||||||
\(973\) | −23.5488 | −0.754938 | ||||||||
\(974\) | 41.9507 | 1.34419 | ||||||||
\(975\) | −8.62444 | −0.276203 | ||||||||
\(976\) | −36.9944 | −1.18416 | ||||||||
\(977\) | −7.90255 | −0.252825 | −0.126413 | − | 0.991978i | \(-0.540346\pi\) | ||||
−0.126413 | + | 0.991978i | \(0.540346\pi\) | |||||||
\(978\) | −17.0115 | −0.543967 | ||||||||
\(979\) | 34.5828 | 1.10527 | ||||||||
\(980\) | 1.41750 | 0.0452804 | ||||||||
\(981\) | −6.33348 | −0.202212 | ||||||||
\(982\) | −26.2251 | −0.836876 | ||||||||
\(983\) | −24.8779 | −0.793483 | −0.396741 | − | 0.917930i | \(-0.629859\pi\) | ||||
−0.396741 | + | 0.917930i | \(0.629859\pi\) | |||||||
\(984\) | 4.30303 | 0.137176 | ||||||||
\(985\) | −36.9294 | −1.17667 | ||||||||
\(986\) | 2.52839 | 0.0805205 | ||||||||
\(987\) | 12.1460 | 0.386612 | ||||||||
\(988\) | 0.716531 | 0.0227959 | ||||||||
\(989\) | −23.7883 | −0.756423 | ||||||||
\(990\) | 23.1093 | 0.734463 | ||||||||
\(991\) | −1.10168 | −0.0349959 | −0.0174979 | − | 0.999847i | \(-0.505570\pi\) | ||||
−0.0174979 | + | 0.999847i | \(0.505570\pi\) | |||||||
\(992\) | −1.16047 | −0.0368448 | ||||||||
\(993\) | 32.7132 | 1.03812 | ||||||||
\(994\) | −14.2264 | −0.451235 | ||||||||
\(995\) | −25.5090 | −0.808689 | ||||||||
\(996\) | −0.806239 | −0.0255467 | ||||||||
\(997\) | 3.04994 | 0.0965926 | 0.0482963 | − | 0.998833i | \(-0.484621\pi\) | ||||
0.0482963 | + | 0.998833i | \(0.484621\pi\) | |||||||
\(998\) | 23.4455 | 0.742155 | ||||||||
\(999\) | 6.48548 | 0.205191 |
(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 | 8007.2.a.f.1.14 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.f.1.14 | ✓ | 48 | 1.1 | even | 1 | trivial |