Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, 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("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.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: | \(64.2077082653\) |
Analytic rank: | \(0\) |
Dimension: | \(78\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.68205 | −1.89650 | −0.948249 | − | 0.317528i | \(-0.897147\pi\) | ||||
−0.948249 | + | 0.317528i | \(0.897147\pi\) | |||||||
\(3\) | 1.14586 | 0.661564 | 0.330782 | − | 0.943707i | \(-0.392688\pi\) | ||||
0.330782 | + | 0.943707i | \(0.392688\pi\) | |||||||
\(4\) | 5.19341 | 2.59670 | ||||||||
\(5\) | 0.981432 | 0.438910 | 0.219455 | − | 0.975623i | \(-0.429572\pi\) | ||||
0.219455 | + | 0.975623i | \(0.429572\pi\) | |||||||
\(6\) | −3.07326 | −1.25465 | ||||||||
\(7\) | −5.03314 | −1.90235 | −0.951173 | − | 0.308657i | \(-0.900120\pi\) | ||||
−0.951173 | + | 0.308657i | \(0.900120\pi\) | |||||||
\(8\) | −8.56488 | −3.02814 | ||||||||
\(9\) | −1.68700 | −0.562334 | ||||||||
\(10\) | −2.63225 | −0.832391 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 5.95092 | 1.71788 | ||||||||
\(13\) | −2.90244 | −0.804993 | −0.402497 | − | 0.915422i | \(-0.631857\pi\) | ||||
−0.402497 | + | 0.915422i | \(0.631857\pi\) | |||||||
\(14\) | 13.4991 | 3.60780 | ||||||||
\(15\) | 1.12458 | 0.290367 | ||||||||
\(16\) | 12.5847 | 3.14616 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 4.52463 | 1.06646 | ||||||||
\(19\) | −0.273183 | −0.0626725 | −0.0313363 | − | 0.999509i | \(-0.509976\pi\) | ||||
−0.0313363 | + | 0.999509i | \(0.509976\pi\) | |||||||
\(20\) | 5.09697 | 1.13972 | ||||||||
\(21\) | −5.76728 | −1.25852 | ||||||||
\(22\) | −2.68205 | −0.571816 | ||||||||
\(23\) | −0.344383 | −0.0718089 | −0.0359044 | − | 0.999355i | \(-0.511431\pi\) | ||||
−0.0359044 | + | 0.999355i | \(0.511431\pi\) | |||||||
\(24\) | −9.81417 | −2.00331 | ||||||||
\(25\) | −4.03679 | −0.807358 | ||||||||
\(26\) | 7.78451 | 1.52667 | ||||||||
\(27\) | −5.37065 | −1.03358 | ||||||||
\(28\) | −26.1391 | −4.93983 | ||||||||
\(29\) | −5.98996 | −1.11231 | −0.556153 | − | 0.831080i | \(-0.687723\pi\) | ||||
−0.556153 | + | 0.831080i | \(0.687723\pi\) | |||||||
\(30\) | −3.01620 | −0.550679 | ||||||||
\(31\) | 0.228383 | 0.0410188 | 0.0205094 | − | 0.999790i | \(-0.493471\pi\) | ||||
0.0205094 | + | 0.999790i | \(0.493471\pi\) | |||||||
\(32\) | −16.6229 | −2.93855 | ||||||||
\(33\) | 1.14586 | 0.199469 | ||||||||
\(34\) | 2.68205 | 0.459968 | ||||||||
\(35\) | −4.93968 | −0.834958 | ||||||||
\(36\) | −8.76128 | −1.46021 | ||||||||
\(37\) | 0.957214 | 0.157365 | 0.0786825 | − | 0.996900i | \(-0.474929\pi\) | ||||
0.0786825 | + | 0.996900i | \(0.474929\pi\) | |||||||
\(38\) | 0.732692 | 0.118858 | ||||||||
\(39\) | −3.32580 | −0.532554 | ||||||||
\(40\) | −8.40585 | −1.32908 | ||||||||
\(41\) | −8.93139 | −1.39485 | −0.697425 | − | 0.716658i | \(-0.745671\pi\) | ||||
−0.697425 | + | 0.716658i | \(0.745671\pi\) | |||||||
\(42\) | 15.4681 | 2.38679 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | 5.19341 | 0.782935 | ||||||||
\(45\) | −1.65568 | −0.246814 | ||||||||
\(46\) | 0.923654 | 0.136185 | ||||||||
\(47\) | −5.63631 | −0.822140 | −0.411070 | − | 0.911604i | \(-0.634845\pi\) | ||||
−0.411070 | + | 0.911604i | \(0.634845\pi\) | |||||||
\(48\) | 14.4203 | 2.08139 | ||||||||
\(49\) | 18.3325 | 2.61892 | ||||||||
\(50\) | 10.8269 | 1.53115 | ||||||||
\(51\) | −1.14586 | −0.160453 | ||||||||
\(52\) | −15.0736 | −2.09033 | ||||||||
\(53\) | 0.243489 | 0.0334458 | 0.0167229 | − | 0.999860i | \(-0.494677\pi\) | ||||
0.0167229 | + | 0.999860i | \(0.494677\pi\) | |||||||
\(54\) | 14.4044 | 1.96019 | ||||||||
\(55\) | 0.981432 | 0.132336 | ||||||||
\(56\) | 43.1082 | 5.76058 | ||||||||
\(57\) | −0.313030 | −0.0414619 | ||||||||
\(58\) | 16.0654 | 2.10949 | ||||||||
\(59\) | 6.15588 | 0.801427 | 0.400713 | − | 0.916203i | \(-0.368762\pi\) | ||||
0.400713 | + | 0.916203i | \(0.368762\pi\) | |||||||
\(60\) | 5.84043 | 0.753996 | ||||||||
\(61\) | 3.10856 | 0.398010 | 0.199005 | − | 0.979998i | \(-0.436229\pi\) | ||||
0.199005 | + | 0.979998i | \(0.436229\pi\) | |||||||
\(62\) | −0.612535 | −0.0777920 | ||||||||
\(63\) | 8.49091 | 1.06975 | ||||||||
\(64\) | 19.4143 | 2.42679 | ||||||||
\(65\) | −2.84855 | −0.353319 | ||||||||
\(66\) | −3.07326 | −0.378292 | ||||||||
\(67\) | −9.16623 | −1.11983 | −0.559917 | − | 0.828549i | \(-0.689167\pi\) | ||||
−0.559917 | + | 0.828549i | \(0.689167\pi\) | |||||||
\(68\) | −5.19341 | −0.629793 | ||||||||
\(69\) | −0.394615 | −0.0475061 | ||||||||
\(70\) | 13.2485 | 1.58350 | ||||||||
\(71\) | −0.195261 | −0.0231732 | −0.0115866 | − | 0.999933i | \(-0.503688\pi\) | ||||
−0.0115866 | + | 0.999933i | \(0.503688\pi\) | |||||||
\(72\) | 14.4490 | 1.70283 | ||||||||
\(73\) | 0.0243280 | 0.00284738 | 0.00142369 | − | 0.999999i | \(-0.499547\pi\) | ||||
0.00142369 | + | 0.999999i | \(0.499547\pi\) | |||||||
\(74\) | −2.56730 | −0.298442 | ||||||||
\(75\) | −4.62560 | −0.534119 | ||||||||
\(76\) | −1.41875 | −0.162742 | ||||||||
\(77\) | −5.03314 | −0.573579 | ||||||||
\(78\) | 8.91997 | 1.00999 | ||||||||
\(79\) | 0.00321078 | 0.000361241 0 | 0.000180621 | − | 1.00000i | \(-0.499943\pi\) | ||||
0.000180621 | 1.00000i | \(0.499943\pi\) | ||||||||
\(80\) | 12.3510 | 1.38088 | ||||||||
\(81\) | −1.09302 | −0.121447 | ||||||||
\(82\) | 23.9545 | 2.64533 | ||||||||
\(83\) | −10.2623 | −1.12643 | −0.563217 | − | 0.826309i | \(-0.690437\pi\) | ||||
−0.563217 | + | 0.826309i | \(0.690437\pi\) | |||||||
\(84\) | −29.9518 | −3.26801 | ||||||||
\(85\) | −0.981432 | −0.106451 | ||||||||
\(86\) | 2.68205 | 0.289213 | ||||||||
\(87\) | −6.86366 | −0.735862 | ||||||||
\(88\) | −8.56488 | −0.913020 | ||||||||
\(89\) | −1.74790 | −0.185278 | −0.0926388 | − | 0.995700i | \(-0.529530\pi\) | ||||
−0.0926388 | + | 0.995700i | \(0.529530\pi\) | |||||||
\(90\) | 4.44061 | 0.468081 | ||||||||
\(91\) | 14.6084 | 1.53138 | ||||||||
\(92\) | −1.78852 | −0.186466 | ||||||||
\(93\) | 0.261695 | 0.0271365 | ||||||||
\(94\) | 15.1169 | 1.55919 | ||||||||
\(95\) | −0.268111 | −0.0275076 | ||||||||
\(96\) | −19.0476 | −1.94404 | ||||||||
\(97\) | 16.2141 | 1.64629 | 0.823145 | − | 0.567832i | \(-0.192218\pi\) | ||||
0.823145 | + | 0.567832i | \(0.192218\pi\) | |||||||
\(98\) | −49.1686 | −4.96678 | ||||||||
\(99\) | −1.68700 | −0.169550 | ||||||||
\(100\) | −20.9647 | −2.09647 | ||||||||
\(101\) | 1.13915 | 0.113350 | 0.0566748 | − | 0.998393i | \(-0.481950\pi\) | ||||
0.0566748 | + | 0.998393i | \(0.481950\pi\) | |||||||
\(102\) | 3.07326 | 0.304298 | ||||||||
\(103\) | −0.788327 | −0.0776762 | −0.0388381 | − | 0.999246i | \(-0.512366\pi\) | ||||
−0.0388381 | + | 0.999246i | \(0.512366\pi\) | |||||||
\(104\) | 24.8591 | 2.43763 | ||||||||
\(105\) | −5.66019 | −0.552378 | ||||||||
\(106\) | −0.653051 | −0.0634299 | ||||||||
\(107\) | 2.16497 | 0.209295 | 0.104648 | − | 0.994509i | \(-0.466629\pi\) | ||||
0.104648 | + | 0.994509i | \(0.466629\pi\) | |||||||
\(108\) | −27.8920 | −2.68391 | ||||||||
\(109\) | 0.912693 | 0.0874201 | 0.0437101 | − | 0.999044i | \(-0.486082\pi\) | ||||
0.0437101 | + | 0.999044i | \(0.486082\pi\) | |||||||
\(110\) | −2.63225 | −0.250975 | ||||||||
\(111\) | 1.09683 | 0.104107 | ||||||||
\(112\) | −63.3403 | −5.98509 | ||||||||
\(113\) | −17.3980 | −1.63667 | −0.818334 | − | 0.574743i | \(-0.805102\pi\) | ||||
−0.818334 | + | 0.574743i | \(0.805102\pi\) | |||||||
\(114\) | 0.839564 | 0.0786323 | ||||||||
\(115\) | −0.337989 | −0.0315176 | ||||||||
\(116\) | −31.1083 | −2.88833 | ||||||||
\(117\) | 4.89643 | 0.452675 | ||||||||
\(118\) | −16.5104 | −1.51990 | ||||||||
\(119\) | 5.03314 | 0.461387 | ||||||||
\(120\) | −9.63194 | −0.879272 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −8.33731 | −0.754825 | ||||||||
\(123\) | −10.2341 | −0.922781 | ||||||||
\(124\) | 1.18609 | 0.106514 | ||||||||
\(125\) | −8.86899 | −0.793267 | ||||||||
\(126\) | −22.7731 | −2.02879 | ||||||||
\(127\) | −16.4896 | −1.46321 | −0.731606 | − | 0.681728i | \(-0.761229\pi\) | ||||
−0.731606 | + | 0.681728i | \(0.761229\pi\) | |||||||
\(128\) | −18.8243 | −1.66385 | ||||||||
\(129\) | −1.14586 | −0.100887 | ||||||||
\(130\) | 7.63996 | 0.670069 | ||||||||
\(131\) | 7.12350 | 0.622383 | 0.311191 | − | 0.950347i | \(-0.399272\pi\) | ||||
0.311191 | + | 0.950347i | \(0.399272\pi\) | |||||||
\(132\) | 5.95092 | 0.517962 | ||||||||
\(133\) | 1.37497 | 0.119225 | ||||||||
\(134\) | 24.5843 | 2.12376 | ||||||||
\(135\) | −5.27093 | −0.453649 | ||||||||
\(136\) | 8.56488 | 0.734433 | ||||||||
\(137\) | −12.6086 | −1.07723 | −0.538614 | − | 0.842553i | \(-0.681052\pi\) | ||||
−0.538614 | + | 0.842553i | \(0.681052\pi\) | |||||||
\(138\) | 1.05838 | 0.0900952 | ||||||||
\(139\) | −19.9661 | −1.69350 | −0.846752 | − | 0.531987i | \(-0.821445\pi\) | ||||
−0.846752 | + | 0.531987i | \(0.821445\pi\) | |||||||
\(140\) | −25.6538 | −2.16814 | ||||||||
\(141\) | −6.45843 | −0.543898 | ||||||||
\(142\) | 0.523699 | 0.0439479 | ||||||||
\(143\) | −2.90244 | −0.242715 | ||||||||
\(144\) | −21.2303 | −1.76919 | ||||||||
\(145\) | −5.87873 | −0.488202 | ||||||||
\(146\) | −0.0652490 | −0.00540005 | ||||||||
\(147\) | 21.0065 | 1.73258 | ||||||||
\(148\) | 4.97120 | 0.408630 | ||||||||
\(149\) | 23.1013 | 1.89254 | 0.946268 | − | 0.323384i | \(-0.104821\pi\) | ||||
0.946268 | + | 0.323384i | \(0.104821\pi\) | |||||||
\(150\) | 12.4061 | 1.01296 | ||||||||
\(151\) | 23.6025 | 1.92074 | 0.960370 | − | 0.278728i | \(-0.0899126\pi\) | ||||
0.960370 | + | 0.278728i | \(0.0899126\pi\) | |||||||
\(152\) | 2.33978 | 0.189781 | ||||||||
\(153\) | 1.68700 | 0.136386 | ||||||||
\(154\) | 13.4991 | 1.08779 | ||||||||
\(155\) | 0.224142 | 0.0180035 | ||||||||
\(156\) | −17.2722 | −1.38288 | ||||||||
\(157\) | −8.05506 | −0.642864 | −0.321432 | − | 0.946933i | \(-0.604164\pi\) | ||||
−0.321432 | + | 0.946933i | \(0.604164\pi\) | |||||||
\(158\) | −0.00861148 | −0.000685093 0 | ||||||||
\(159\) | 0.279005 | 0.0221265 | ||||||||
\(160\) | −16.3143 | −1.28976 | ||||||||
\(161\) | 1.73333 | 0.136605 | ||||||||
\(162\) | 2.93155 | 0.230324 | ||||||||
\(163\) | 5.59141 | 0.437953 | 0.218976 | − | 0.975730i | \(-0.429728\pi\) | ||||
0.218976 | + | 0.975730i | \(0.429728\pi\) | |||||||
\(164\) | −46.3844 | −3.62201 | ||||||||
\(165\) | 1.12458 | 0.0875488 | ||||||||
\(166\) | 27.5241 | 2.13628 | ||||||||
\(167\) | 14.9658 | 1.15809 | 0.579044 | − | 0.815296i | \(-0.303426\pi\) | ||||
0.579044 | + | 0.815296i | \(0.303426\pi\) | |||||||
\(168\) | 49.3961 | 3.81099 | ||||||||
\(169\) | −4.57582 | −0.351986 | ||||||||
\(170\) | 2.63225 | 0.201884 | ||||||||
\(171\) | 0.460861 | 0.0352429 | ||||||||
\(172\) | −5.19341 | −0.395994 | ||||||||
\(173\) | −8.18974 | −0.622655 | −0.311327 | − | 0.950303i | \(-0.600774\pi\) | ||||
−0.311327 | + | 0.950303i | \(0.600774\pi\) | |||||||
\(174\) | 18.4087 | 1.39556 | ||||||||
\(175\) | 20.3177 | 1.53588 | ||||||||
\(176\) | 12.5847 | 0.948604 | ||||||||
\(177\) | 7.05378 | 0.530195 | ||||||||
\(178\) | 4.68797 | 0.351378 | ||||||||
\(179\) | 3.99655 | 0.298716 | 0.149358 | − | 0.988783i | \(-0.452279\pi\) | ||||
0.149358 | + | 0.988783i | \(0.452279\pi\) | |||||||
\(180\) | −8.59860 | −0.640902 | ||||||||
\(181\) | −16.1486 | −1.20032 | −0.600158 | − | 0.799881i | \(-0.704896\pi\) | ||||
−0.600158 | + | 0.799881i | \(0.704896\pi\) | |||||||
\(182\) | −39.1805 | −2.90425 | ||||||||
\(183\) | 3.56198 | 0.263309 | ||||||||
\(184\) | 2.94960 | 0.217448 | ||||||||
\(185\) | 0.939440 | 0.0690690 | ||||||||
\(186\) | −0.701880 | −0.0514644 | ||||||||
\(187\) | −1.00000 | −0.0731272 | ||||||||
\(188\) | −29.2716 | −2.13485 | ||||||||
\(189\) | 27.0312 | 1.96623 | ||||||||
\(190\) | 0.719087 | 0.0521681 | ||||||||
\(191\) | 15.2302 | 1.10202 | 0.551009 | − | 0.834500i | \(-0.314243\pi\) | ||||
0.551009 | + | 0.834500i | \(0.314243\pi\) | |||||||
\(192\) | 22.2461 | 1.60547 | ||||||||
\(193\) | 9.01455 | 0.648882 | 0.324441 | − | 0.945906i | \(-0.394824\pi\) | ||||
0.324441 | + | 0.945906i | \(0.394824\pi\) | |||||||
\(194\) | −43.4870 | −3.12218 | ||||||||
\(195\) | −3.26404 | −0.233743 | ||||||||
\(196\) | 95.2079 | 6.80056 | ||||||||
\(197\) | 6.50400 | 0.463391 | 0.231695 | − | 0.972788i | \(-0.425573\pi\) | ||||
0.231695 | + | 0.972788i | \(0.425573\pi\) | |||||||
\(198\) | 4.52463 | 0.321551 | ||||||||
\(199\) | −4.19871 | −0.297639 | −0.148819 | − | 0.988864i | \(-0.547547\pi\) | ||||
−0.148819 | + | 0.988864i | \(0.547547\pi\) | |||||||
\(200\) | 34.5747 | 2.44480 | ||||||||
\(201\) | −10.5032 | −0.740841 | ||||||||
\(202\) | −3.05526 | −0.214967 | ||||||||
\(203\) | 30.1483 | 2.11599 | ||||||||
\(204\) | −5.95092 | −0.416648 | ||||||||
\(205\) | −8.76555 | −0.612213 | ||||||||
\(206\) | 2.11434 | 0.147313 | ||||||||
\(207\) | 0.580975 | 0.0403805 | ||||||||
\(208\) | −36.5263 | −2.53264 | ||||||||
\(209\) | −0.273183 | −0.0188965 | ||||||||
\(210\) | 15.1809 | 1.04758 | ||||||||
\(211\) | −22.6661 | −1.56040 | −0.780198 | − | 0.625532i | \(-0.784882\pi\) | ||||
−0.780198 | + | 0.625532i | \(0.784882\pi\) | |||||||
\(212\) | 1.26454 | 0.0868489 | ||||||||
\(213\) | −0.223742 | −0.0153305 | ||||||||
\(214\) | −5.80656 | −0.396928 | ||||||||
\(215\) | −0.981432 | −0.0669331 | ||||||||
\(216\) | 45.9990 | 3.12984 | ||||||||
\(217\) | −1.14948 | −0.0780319 | ||||||||
\(218\) | −2.44789 | −0.165792 | ||||||||
\(219\) | 0.0278765 | 0.00188372 | ||||||||
\(220\) | 5.09697 | 0.343638 | ||||||||
\(221\) | 2.90244 | 0.195240 | ||||||||
\(222\) | −2.94177 | −0.197439 | ||||||||
\(223\) | −22.3465 | −1.49644 | −0.748218 | − | 0.663453i | \(-0.769090\pi\) | ||||
−0.748218 | + | 0.663453i | \(0.769090\pi\) | |||||||
\(224\) | 83.6655 | 5.59014 | ||||||||
\(225\) | 6.81007 | 0.454005 | ||||||||
\(226\) | 46.6624 | 3.10394 | ||||||||
\(227\) | 19.2243 | 1.27596 | 0.637981 | − | 0.770052i | \(-0.279770\pi\) | ||||
0.637981 | + | 0.770052i | \(0.279770\pi\) | |||||||
\(228\) | −1.62569 | −0.107664 | ||||||||
\(229\) | 18.0906 | 1.19546 | 0.597729 | − | 0.801698i | \(-0.296070\pi\) | ||||
0.597729 | + | 0.801698i | \(0.296070\pi\) | |||||||
\(230\) | 0.906503 | 0.0597730 | ||||||||
\(231\) | −5.76728 | −0.379459 | ||||||||
\(232\) | 51.3033 | 3.36822 | ||||||||
\(233\) | 22.0896 | 1.44714 | 0.723569 | − | 0.690252i | \(-0.242500\pi\) | ||||
0.723569 | + | 0.690252i | \(0.242500\pi\) | |||||||
\(234\) | −13.1325 | −0.858497 | ||||||||
\(235\) | −5.53165 | −0.360845 | ||||||||
\(236\) | 31.9700 | 2.08107 | ||||||||
\(237\) | 0.00367911 | 0.000238984 0 | ||||||||
\(238\) | −13.4991 | −0.875019 | ||||||||
\(239\) | −14.5934 | −0.943968 | −0.471984 | − | 0.881607i | \(-0.656462\pi\) | ||||
−0.471984 | + | 0.881607i | \(0.656462\pi\) | |||||||
\(240\) | 14.1525 | 0.913541 | ||||||||
\(241\) | −5.77517 | −0.372012 | −0.186006 | − | 0.982549i | \(-0.559554\pi\) | ||||
−0.186006 | + | 0.982549i | \(0.559554\pi\) | |||||||
\(242\) | −2.68205 | −0.172409 | ||||||||
\(243\) | 14.8595 | 0.953238 | ||||||||
\(244\) | 16.1440 | 1.03351 | ||||||||
\(245\) | 17.9921 | 1.14947 | ||||||||
\(246\) | 27.4485 | 1.75005 | ||||||||
\(247\) | 0.792899 | 0.0504510 | ||||||||
\(248\) | −1.95607 | −0.124211 | ||||||||
\(249\) | −11.7592 | −0.745208 | ||||||||
\(250\) | 23.7871 | 1.50443 | ||||||||
\(251\) | 11.9139 | 0.751999 | 0.375999 | − | 0.926620i | \(-0.377299\pi\) | ||||
0.375999 | + | 0.926620i | \(0.377299\pi\) | |||||||
\(252\) | 44.0967 | 2.77783 | ||||||||
\(253\) | −0.344383 | −0.0216512 | ||||||||
\(254\) | 44.2259 | 2.77498 | ||||||||
\(255\) | −1.12458 | −0.0704242 | ||||||||
\(256\) | 11.6591 | 0.728693 | ||||||||
\(257\) | 23.4005 | 1.45968 | 0.729841 | − | 0.683617i | \(-0.239594\pi\) | ||||
0.729841 | + | 0.683617i | \(0.239594\pi\) | |||||||
\(258\) | 3.07326 | 0.191333 | ||||||||
\(259\) | −4.81779 | −0.299363 | ||||||||
\(260\) | −14.7937 | −0.917465 | ||||||||
\(261\) | 10.1051 | 0.625488 | ||||||||
\(262\) | −19.1056 | −1.18035 | ||||||||
\(263\) | 18.0538 | 1.11325 | 0.556623 | − | 0.830765i | \(-0.312097\pi\) | ||||
0.556623 | + | 0.830765i | \(0.312097\pi\) | |||||||
\(264\) | −9.81417 | −0.604020 | ||||||||
\(265\) | 0.238968 | 0.0146797 | ||||||||
\(266\) | −3.68774 | −0.226110 | ||||||||
\(267\) | −2.00286 | −0.122573 | ||||||||
\(268\) | −47.6040 | −2.90788 | ||||||||
\(269\) | −12.6976 | −0.774188 | −0.387094 | − | 0.922040i | \(-0.626521\pi\) | ||||
−0.387094 | + | 0.922040i | \(0.626521\pi\) | |||||||
\(270\) | 14.1369 | 0.860345 | ||||||||
\(271\) | −13.5090 | −0.820615 | −0.410308 | − | 0.911947i | \(-0.634579\pi\) | ||||
−0.410308 | + | 0.911947i | \(0.634579\pi\) | |||||||
\(272\) | −12.5847 | −0.763057 | ||||||||
\(273\) | 16.7392 | 1.01310 | ||||||||
\(274\) | 33.8170 | 2.04296 | ||||||||
\(275\) | −4.03679 | −0.243428 | ||||||||
\(276\) | −2.04940 | −0.123359 | ||||||||
\(277\) | 2.26865 | 0.136310 | 0.0681550 | − | 0.997675i | \(-0.478289\pi\) | ||||
0.0681550 | + | 0.997675i | \(0.478289\pi\) | |||||||
\(278\) | 53.5502 | 3.21173 | ||||||||
\(279\) | −0.385282 | −0.0230662 | ||||||||
\(280\) | 42.3078 | 2.52837 | ||||||||
\(281\) | 18.5367 | 1.10581 | 0.552903 | − | 0.833245i | \(-0.313520\pi\) | ||||
0.552903 | + | 0.833245i | \(0.313520\pi\) | |||||||
\(282\) | 17.3218 | 1.03150 | ||||||||
\(283\) | 1.92296 | 0.114308 | 0.0571541 | − | 0.998365i | \(-0.481797\pi\) | ||||
0.0571541 | + | 0.998365i | \(0.481797\pi\) | |||||||
\(284\) | −1.01407 | −0.0601739 | ||||||||
\(285\) | −0.307218 | −0.0181980 | ||||||||
\(286\) | 7.78451 | 0.460308 | ||||||||
\(287\) | 44.9529 | 2.65349 | ||||||||
\(288\) | 28.0429 | 1.65244 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 15.7671 | 0.925874 | ||||||||
\(291\) | 18.5791 | 1.08912 | ||||||||
\(292\) | 0.126345 | 0.00739380 | ||||||||
\(293\) | 4.95214 | 0.289307 | 0.144653 | − | 0.989482i | \(-0.453793\pi\) | ||||
0.144653 | + | 0.989482i | \(0.453793\pi\) | |||||||
\(294\) | −56.3404 | −3.28584 | ||||||||
\(295\) | 6.04157 | 0.351754 | ||||||||
\(296\) | −8.19842 | −0.476524 | ||||||||
\(297\) | −5.37065 | −0.311637 | ||||||||
\(298\) | −61.9590 | −3.58919 | ||||||||
\(299\) | 0.999553 | 0.0578056 | ||||||||
\(300\) | −24.0226 | −1.38695 | ||||||||
\(301\) | 5.03314 | 0.290105 | ||||||||
\(302\) | −63.3030 | −3.64268 | ||||||||
\(303\) | 1.30531 | 0.0749879 | ||||||||
\(304\) | −3.43792 | −0.197178 | ||||||||
\(305\) | 3.05084 | 0.174690 | ||||||||
\(306\) | −4.52463 | −0.258656 | ||||||||
\(307\) | −22.0202 | −1.25676 | −0.628379 | − | 0.777907i | \(-0.716281\pi\) | ||||
−0.628379 | + | 0.777907i | \(0.716281\pi\) | |||||||
\(308\) | −26.1391 | −1.48941 | ||||||||
\(309\) | −0.903314 | −0.0513878 | ||||||||
\(310\) | −0.601161 | −0.0341437 | ||||||||
\(311\) | 18.4222 | 1.04463 | 0.522314 | − | 0.852753i | \(-0.325069\pi\) | ||||
0.522314 | + | 0.852753i | \(0.325069\pi\) | |||||||
\(312\) | 28.4851 | 1.61265 | ||||||||
\(313\) | −7.01710 | −0.396630 | −0.198315 | − | 0.980138i | \(-0.563547\pi\) | ||||
−0.198315 | + | 0.980138i | \(0.563547\pi\) | |||||||
\(314\) | 21.6041 | 1.21919 | ||||||||
\(315\) | 8.33324 | 0.469525 | ||||||||
\(316\) | 0.0166749 | 0.000938036 0 | ||||||||
\(317\) | 4.68555 | 0.263167 | 0.131583 | − | 0.991305i | \(-0.457994\pi\) | ||||
0.131583 | + | 0.991305i | \(0.457994\pi\) | |||||||
\(318\) | −0.748306 | −0.0419629 | ||||||||
\(319\) | −5.98996 | −0.335373 | ||||||||
\(320\) | 19.0538 | 1.06514 | ||||||||
\(321\) | 2.48075 | 0.138462 | ||||||||
\(322\) | −4.64887 | −0.259072 | ||||||||
\(323\) | 0.273183 | 0.0152003 | ||||||||
\(324\) | −5.67652 | −0.315362 | ||||||||
\(325\) | 11.7166 | 0.649918 | ||||||||
\(326\) | −14.9964 | −0.830576 | ||||||||
\(327\) | 1.04582 | 0.0578340 | ||||||||
\(328\) | 76.4963 | 4.22380 | ||||||||
\(329\) | 28.3683 | 1.56399 | ||||||||
\(330\) | −3.01620 | −0.166036 | ||||||||
\(331\) | −14.7801 | −0.812389 | −0.406195 | − | 0.913787i | \(-0.633145\pi\) | ||||
−0.406195 | + | 0.913787i | \(0.633145\pi\) | |||||||
\(332\) | −53.2963 | −2.92502 | ||||||||
\(333\) | −1.61482 | −0.0884916 | ||||||||
\(334\) | −40.1391 | −2.19631 | ||||||||
\(335\) | −8.99603 | −0.491506 | ||||||||
\(336\) | −72.5792 | −3.95952 | ||||||||
\(337\) | −3.99398 | −0.217566 | −0.108783 | − | 0.994066i | \(-0.534695\pi\) | ||||
−0.108783 | + | 0.994066i | \(0.534695\pi\) | |||||||
\(338\) | 12.2726 | 0.667541 | ||||||||
\(339\) | −19.9357 | −1.08276 | ||||||||
\(340\) | −5.09697 | −0.276422 | ||||||||
\(341\) | 0.228383 | 0.0123676 | ||||||||
\(342\) | −1.23605 | −0.0668380 | ||||||||
\(343\) | −57.0378 | −3.07975 | ||||||||
\(344\) | 8.56488 | 0.461788 | ||||||||
\(345\) | −0.387288 | −0.0208509 | ||||||||
\(346\) | 21.9653 | 1.18086 | ||||||||
\(347\) | 28.7142 | 1.54146 | 0.770729 | − | 0.637163i | \(-0.219892\pi\) | ||||
0.770729 | + | 0.637163i | \(0.219892\pi\) | |||||||
\(348\) | −35.6458 | −1.91081 | ||||||||
\(349\) | −28.5594 | −1.52875 | −0.764375 | − | 0.644772i | \(-0.776952\pi\) | ||||
−0.764375 | + | 0.644772i | \(0.776952\pi\) | |||||||
\(350\) | −54.4932 | −2.91278 | ||||||||
\(351\) | 15.5880 | 0.832027 | ||||||||
\(352\) | −16.6229 | −0.886006 | ||||||||
\(353\) | −6.44851 | −0.343220 | −0.171610 | − | 0.985165i | \(-0.554897\pi\) | ||||
−0.171610 | + | 0.985165i | \(0.554897\pi\) | |||||||
\(354\) | −18.9186 | −1.00551 | ||||||||
\(355\) | −0.191635 | −0.0101709 | ||||||||
\(356\) | −9.07758 | −0.481111 | ||||||||
\(357\) | 5.76728 | 0.305237 | ||||||||
\(358\) | −10.7189 | −0.566514 | ||||||||
\(359\) | −1.78918 | −0.0944293 | −0.0472147 | − | 0.998885i | \(-0.515034\pi\) | ||||
−0.0472147 | + | 0.998885i | \(0.515034\pi\) | |||||||
\(360\) | 14.1807 | 0.747387 | ||||||||
\(361\) | −18.9254 | −0.996072 | ||||||||
\(362\) | 43.3114 | 2.27640 | ||||||||
\(363\) | 1.14586 | 0.0601421 | ||||||||
\(364\) | 75.8673 | 3.97653 | ||||||||
\(365\) | 0.0238763 | 0.00124974 | ||||||||
\(366\) | −9.55341 | −0.499365 | ||||||||
\(367\) | −12.9632 | −0.676675 | −0.338338 | − | 0.941025i | \(-0.609865\pi\) | ||||
−0.338338 | + | 0.941025i | \(0.609865\pi\) | |||||||
\(368\) | −4.33394 | −0.225922 | ||||||||
\(369\) | 15.0673 | 0.784371 | ||||||||
\(370\) | −2.51963 | −0.130989 | ||||||||
\(371\) | −1.22551 | −0.0636255 | ||||||||
\(372\) | 1.35909 | 0.0704655 | ||||||||
\(373\) | 4.98892 | 0.258317 | 0.129158 | − | 0.991624i | \(-0.458772\pi\) | ||||
0.129158 | + | 0.991624i | \(0.458772\pi\) | |||||||
\(374\) | 2.68205 | 0.138686 | ||||||||
\(375\) | −10.1626 | −0.524796 | ||||||||
\(376\) | 48.2743 | 2.48956 | ||||||||
\(377\) | 17.3855 | 0.895399 | ||||||||
\(378\) | −72.4992 | −3.72896 | ||||||||
\(379\) | 30.6359 | 1.57366 | 0.786830 | − | 0.617170i | \(-0.211721\pi\) | ||||
0.786830 | + | 0.617170i | \(0.211721\pi\) | |||||||
\(380\) | −1.39241 | −0.0714290 | ||||||||
\(381\) | −18.8947 | −0.968007 | ||||||||
\(382\) | −40.8481 | −2.08997 | ||||||||
\(383\) | 22.8370 | 1.16692 | 0.583458 | − | 0.812144i | \(-0.301699\pi\) | ||||
0.583458 | + | 0.812144i | \(0.301699\pi\) | |||||||
\(384\) | −21.5700 | −1.10074 | ||||||||
\(385\) | −4.93968 | −0.251749 | ||||||||
\(386\) | −24.1775 | −1.23060 | ||||||||
\(387\) | 1.68700 | 0.0857551 | ||||||||
\(388\) | 84.2062 | 4.27492 | ||||||||
\(389\) | 7.90735 | 0.400918 | 0.200459 | − | 0.979702i | \(-0.435757\pi\) | ||||
0.200459 | + | 0.979702i | \(0.435757\pi\) | |||||||
\(390\) | 8.75434 | 0.443293 | ||||||||
\(391\) | 0.344383 | 0.0174162 | ||||||||
\(392\) | −157.015 | −7.93047 | ||||||||
\(393\) | 8.16254 | 0.411746 | ||||||||
\(394\) | −17.4441 | −0.878819 | ||||||||
\(395\) | 0.00315116 | 0.000158552 0 | ||||||||
\(396\) | −8.76128 | −0.440271 | ||||||||
\(397\) | −23.4770 | −1.17828 | −0.589139 | − | 0.808031i | \(-0.700533\pi\) | ||||
−0.589139 | + | 0.808031i | \(0.700533\pi\) | |||||||
\(398\) | 11.2612 | 0.564471 | ||||||||
\(399\) | 1.57552 | 0.0788748 | ||||||||
\(400\) | −50.8016 | −2.54008 | ||||||||
\(401\) | −3.80819 | −0.190172 | −0.0950859 | − | 0.995469i | \(-0.530313\pi\) | ||||
−0.0950859 | + | 0.995469i | \(0.530313\pi\) | |||||||
\(402\) | 28.1702 | 1.40500 | ||||||||
\(403\) | −0.662868 | −0.0330198 | ||||||||
\(404\) | 5.91606 | 0.294335 | ||||||||
\(405\) | −1.07273 | −0.0533043 | ||||||||
\(406\) | −80.8592 | −4.01298 | ||||||||
\(407\) | 0.957214 | 0.0474473 | ||||||||
\(408\) | 9.81417 | 0.485874 | ||||||||
\(409\) | 38.4371 | 1.90059 | 0.950296 | − | 0.311347i | \(-0.100780\pi\) | ||||
0.950296 | + | 0.311347i | \(0.100780\pi\) | |||||||
\(410\) | 23.5097 | 1.16106 | ||||||||
\(411\) | −14.4477 | −0.712654 | ||||||||
\(412\) | −4.09410 | −0.201702 | ||||||||
\(413\) | −30.9834 | −1.52459 | ||||||||
\(414\) | −1.55820 | −0.0765816 | ||||||||
\(415\) | −10.0718 | −0.494403 | ||||||||
\(416\) | 48.2472 | 2.36551 | ||||||||
\(417\) | −22.8784 | −1.12036 | ||||||||
\(418\) | 0.732692 | 0.0358371 | ||||||||
\(419\) | −12.2719 | −0.599524 | −0.299762 | − | 0.954014i | \(-0.596907\pi\) | ||||
−0.299762 | + | 0.954014i | \(0.596907\pi\) | |||||||
\(420\) | −29.3957 | −1.43436 | ||||||||
\(421\) | 7.64573 | 0.372630 | 0.186315 | − | 0.982490i | \(-0.440345\pi\) | ||||
0.186315 | + | 0.982490i | \(0.440345\pi\) | |||||||
\(422\) | 60.7916 | 2.95929 | ||||||||
\(423\) | 9.50846 | 0.462317 | ||||||||
\(424\) | −2.08546 | −0.101279 | ||||||||
\(425\) | 4.03679 | 0.195813 | ||||||||
\(426\) | 0.600087 | 0.0290743 | ||||||||
\(427\) | −15.6458 | −0.757153 | ||||||||
\(428\) | 11.2436 | 0.543478 | ||||||||
\(429\) | −3.32580 | −0.160571 | ||||||||
\(430\) | 2.63225 | 0.126938 | ||||||||
\(431\) | −4.49698 | −0.216612 | −0.108306 | − | 0.994118i | \(-0.534543\pi\) | ||||
−0.108306 | + | 0.994118i | \(0.534543\pi\) | |||||||
\(432\) | −67.5878 | −3.25182 | ||||||||
\(433\) | 31.0069 | 1.49010 | 0.745048 | − | 0.667011i | \(-0.232427\pi\) | ||||
0.745048 | + | 0.667011i | \(0.232427\pi\) | |||||||
\(434\) | 3.08297 | 0.147987 | ||||||||
\(435\) | −6.73621 | −0.322977 | ||||||||
\(436\) | 4.73999 | 0.227004 | ||||||||
\(437\) | 0.0940797 | 0.00450044 | ||||||||
\(438\) | −0.0747663 | −0.00357247 | ||||||||
\(439\) | 38.9290 | 1.85798 | 0.928989 | − | 0.370106i | \(-0.120679\pi\) | ||||
0.928989 | + | 0.370106i | \(0.120679\pi\) | |||||||
\(440\) | −8.40585 | −0.400733 | ||||||||
\(441\) | −30.9269 | −1.47271 | ||||||||
\(442\) | −7.78451 | −0.370271 | ||||||||
\(443\) | −36.9343 | −1.75480 | −0.877401 | − | 0.479758i | \(-0.840725\pi\) | ||||
−0.877401 | + | 0.479758i | \(0.840725\pi\) | |||||||
\(444\) | 5.69631 | 0.270335 | ||||||||
\(445\) | −1.71545 | −0.0813201 | ||||||||
\(446\) | 59.9346 | 2.83799 | ||||||||
\(447\) | 26.4709 | 1.25203 | ||||||||
\(448\) | −97.7148 | −4.61659 | ||||||||
\(449\) | 4.58261 | 0.216267 | 0.108133 | − | 0.994136i | \(-0.465513\pi\) | ||||
0.108133 | + | 0.994136i | \(0.465513\pi\) | |||||||
\(450\) | −18.2650 | −0.861019 | ||||||||
\(451\) | −8.93139 | −0.420563 | ||||||||
\(452\) | −90.3550 | −4.24994 | ||||||||
\(453\) | 27.0451 | 1.27069 | ||||||||
\(454\) | −51.5606 | −2.41986 | ||||||||
\(455\) | 14.3371 | 0.672136 | ||||||||
\(456\) | 2.68107 | 0.125552 | ||||||||
\(457\) | 15.0410 | 0.703590 | 0.351795 | − | 0.936077i | \(-0.385571\pi\) | ||||
0.351795 | + | 0.936077i | \(0.385571\pi\) | |||||||
\(458\) | −48.5198 | −2.26718 | ||||||||
\(459\) | 5.37065 | 0.250681 | ||||||||
\(460\) | −1.75531 | −0.0818418 | ||||||||
\(461\) | 18.7453 | 0.873057 | 0.436529 | − | 0.899690i | \(-0.356208\pi\) | ||||
0.436529 | + | 0.899690i | \(0.356208\pi\) | |||||||
\(462\) | 15.4681 | 0.719643 | ||||||||
\(463\) | −21.0570 | −0.978602 | −0.489301 | − | 0.872115i | \(-0.662748\pi\) | ||||
−0.489301 | + | 0.872115i | \(0.662748\pi\) | |||||||
\(464\) | −75.3815 | −3.49950 | ||||||||
\(465\) | 0.256836 | 0.0119105 | ||||||||
\(466\) | −59.2455 | −2.74449 | ||||||||
\(467\) | 21.1238 | 0.977495 | 0.488747 | − | 0.872425i | \(-0.337454\pi\) | ||||
0.488747 | + | 0.872425i | \(0.337454\pi\) | |||||||
\(468\) | 25.4291 | 1.17546 | ||||||||
\(469\) | 46.1349 | 2.13031 | ||||||||
\(470\) | 14.8362 | 0.684342 | ||||||||
\(471\) | −9.22998 | −0.425295 | ||||||||
\(472\) | −52.7244 | −2.42684 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | −0.00986757 | −0.000453232 0 | ||||||||
\(475\) | 1.10278 | 0.0505992 | ||||||||
\(476\) | 26.1391 | 1.19808 | ||||||||
\(477\) | −0.410767 | −0.0188077 | ||||||||
\(478\) | 39.1403 | 1.79023 | ||||||||
\(479\) | 29.4813 | 1.34703 | 0.673517 | − | 0.739172i | \(-0.264783\pi\) | ||||
0.673517 | + | 0.739172i | \(0.264783\pi\) | |||||||
\(480\) | −18.6939 | −0.853256 | ||||||||
\(481\) | −2.77826 | −0.126678 | ||||||||
\(482\) | 15.4893 | 0.705519 | ||||||||
\(483\) | 1.98615 | 0.0903731 | ||||||||
\(484\) | 5.19341 | 0.236064 | ||||||||
\(485\) | 15.9130 | 0.722572 | ||||||||
\(486\) | −39.8540 | −1.80781 | ||||||||
\(487\) | 21.0030 | 0.951738 | 0.475869 | − | 0.879516i | \(-0.342134\pi\) | ||||
0.475869 | + | 0.879516i | \(0.342134\pi\) | |||||||
\(488\) | −26.6244 | −1.20523 | ||||||||
\(489\) | 6.40698 | 0.289734 | ||||||||
\(490\) | −48.2556 | −2.17997 | ||||||||
\(491\) | −26.1681 | −1.18095 | −0.590476 | − | 0.807055i | \(-0.701060\pi\) | ||||
−0.590476 | + | 0.807055i | \(0.701060\pi\) | |||||||
\(492\) | −53.1501 | −2.39619 | ||||||||
\(493\) | 5.98996 | 0.269774 | ||||||||
\(494\) | −2.12660 | −0.0956801 | ||||||||
\(495\) | −1.65568 | −0.0744171 | ||||||||
\(496\) | 2.87412 | 0.129052 | ||||||||
\(497\) | 0.982774 | 0.0440834 | ||||||||
\(498\) | 31.5388 | 1.41329 | ||||||||
\(499\) | 25.2566 | 1.13064 | 0.565321 | − | 0.824871i | \(-0.308752\pi\) | ||||
0.565321 | + | 0.824871i | \(0.308752\pi\) | |||||||
\(500\) | −46.0603 | −2.05988 | ||||||||
\(501\) | 17.1487 | 0.766149 | ||||||||
\(502\) | −31.9537 | −1.42616 | ||||||||
\(503\) | −28.2099 | −1.25782 | −0.628909 | − | 0.777479i | \(-0.716498\pi\) | ||||
−0.628909 | + | 0.777479i | \(0.716498\pi\) | |||||||
\(504\) | −72.7236 | −3.23937 | ||||||||
\(505\) | 1.11800 | 0.0497502 | ||||||||
\(506\) | 0.923654 | 0.0410614 | ||||||||
\(507\) | −5.24326 | −0.232861 | ||||||||
\(508\) | −85.6370 | −3.79953 | ||||||||
\(509\) | 5.62121 | 0.249156 | 0.124578 | − | 0.992210i | \(-0.460242\pi\) | ||||
0.124578 | + | 0.992210i | \(0.460242\pi\) | |||||||
\(510\) | 3.01620 | 0.133559 | ||||||||
\(511\) | −0.122446 | −0.00541670 | ||||||||
\(512\) | 6.37823 | 0.281881 | ||||||||
\(513\) | 1.46717 | 0.0647773 | ||||||||
\(514\) | −62.7613 | −2.76828 | ||||||||
\(515\) | −0.773690 | −0.0340928 | ||||||||
\(516\) | −5.95092 | −0.261975 | ||||||||
\(517\) | −5.63631 | −0.247884 | ||||||||
\(518\) | 12.9216 | 0.567741 | ||||||||
\(519\) | −9.38431 | −0.411926 | ||||||||
\(520\) | 24.3975 | 1.06990 | ||||||||
\(521\) | 0.0571298 | 0.00250290 | 0.00125145 | − | 0.999999i | \(-0.499602\pi\) | ||||
0.00125145 | + | 0.999999i | \(0.499602\pi\) | |||||||
\(522\) | −27.1023 | −1.18624 | ||||||||
\(523\) | −27.4976 | −1.20238 | −0.601192 | − | 0.799104i | \(-0.705307\pi\) | ||||
−0.601192 | + | 0.799104i | \(0.705307\pi\) | |||||||
\(524\) | 36.9952 | 1.61614 | ||||||||
\(525\) | 23.2813 | 1.01608 | ||||||||
\(526\) | −48.4213 | −2.11127 | ||||||||
\(527\) | −0.228383 | −0.00994851 | ||||||||
\(528\) | 14.4203 | 0.627562 | ||||||||
\(529\) | −22.8814 | −0.994843 | ||||||||
\(530\) | −0.640925 | −0.0278400 | ||||||||
\(531\) | −10.3850 | −0.450669 | ||||||||
\(532\) | 7.14077 | 0.309592 | ||||||||
\(533\) | 25.9229 | 1.12284 | ||||||||
\(534\) | 5.37177 | 0.232459 | ||||||||
\(535\) | 2.12477 | 0.0918617 | ||||||||
\(536\) | 78.5077 | 3.39102 | ||||||||
\(537\) | 4.57949 | 0.197620 | ||||||||
\(538\) | 34.0557 | 1.46825 | ||||||||
\(539\) | 18.3325 | 0.789635 | ||||||||
\(540\) | −27.3741 | −1.17799 | ||||||||
\(541\) | 1.81798 | 0.0781610 | 0.0390805 | − | 0.999236i | \(-0.487557\pi\) | ||||
0.0390805 | + | 0.999236i | \(0.487557\pi\) | |||||||
\(542\) | 36.2319 | 1.55629 | ||||||||
\(543\) | −18.5041 | −0.794085 | ||||||||
\(544\) | 16.6229 | 0.712703 | ||||||||
\(545\) | 0.895746 | 0.0383695 | ||||||||
\(546\) | −44.8954 | −1.92135 | ||||||||
\(547\) | −11.3395 | −0.484842 | −0.242421 | − | 0.970171i | \(-0.577941\pi\) | ||||
−0.242421 | + | 0.970171i | \(0.577941\pi\) | |||||||
\(548\) | −65.4817 | −2.79724 | ||||||||
\(549\) | −5.24414 | −0.223814 | ||||||||
\(550\) | 10.8269 | 0.461660 | ||||||||
\(551\) | 1.63636 | 0.0697111 | ||||||||
\(552\) | 3.37984 | 0.143855 | ||||||||
\(553\) | −0.0161603 | −0.000687206 0 | ||||||||
\(554\) | −6.08464 | −0.258512 | ||||||||
\(555\) | 1.07647 | 0.0456935 | ||||||||
\(556\) | −103.692 | −4.39753 | ||||||||
\(557\) | −2.94061 | −0.124598 | −0.0622988 | − | 0.998058i | \(-0.519843\pi\) | ||||
−0.0622988 | + | 0.998058i | \(0.519843\pi\) | |||||||
\(558\) | 1.03335 | 0.0437451 | ||||||||
\(559\) | 2.90244 | 0.122760 | ||||||||
\(560\) | −62.1642 | −2.62692 | ||||||||
\(561\) | −1.14586 | −0.0483783 | ||||||||
\(562\) | −49.7164 | −2.09716 | ||||||||
\(563\) | −37.1914 | −1.56743 | −0.783715 | − | 0.621121i | \(-0.786678\pi\) | ||||
−0.783715 | + | 0.621121i | \(0.786678\pi\) | |||||||
\(564\) | −33.5412 | −1.41234 | ||||||||
\(565\) | −17.0750 | −0.718349 | ||||||||
\(566\) | −5.15749 | −0.216785 | ||||||||
\(567\) | 5.50134 | 0.231034 | ||||||||
\(568\) | 1.67239 | 0.0701717 | ||||||||
\(569\) | 0.857071 | 0.0359303 | 0.0179652 | − | 0.999839i | \(-0.494281\pi\) | ||||
0.0179652 | + | 0.999839i | \(0.494281\pi\) | |||||||
\(570\) | 0.823974 | 0.0345125 | ||||||||
\(571\) | 11.4881 | 0.480762 | 0.240381 | − | 0.970679i | \(-0.422728\pi\) | ||||
0.240381 | + | 0.970679i | \(0.422728\pi\) | |||||||
\(572\) | −15.0736 | −0.630258 | ||||||||
\(573\) | 17.4517 | 0.729054 | ||||||||
\(574\) | −120.566 | −5.03233 | ||||||||
\(575\) | 1.39020 | 0.0579755 | ||||||||
\(576\) | −32.7519 | −1.36466 | ||||||||
\(577\) | 28.7769 | 1.19800 | 0.598998 | − | 0.800751i | \(-0.295566\pi\) | ||||
0.598998 | + | 0.800751i | \(0.295566\pi\) | |||||||
\(578\) | −2.68205 | −0.111559 | ||||||||
\(579\) | 10.3294 | 0.429277 | ||||||||
\(580\) | −30.5306 | −1.26772 | ||||||||
\(581\) | 51.6516 | 2.14287 | ||||||||
\(582\) | −49.8301 | −2.06552 | ||||||||
\(583\) | 0.243489 | 0.0100843 | ||||||||
\(584\) | −0.208367 | −0.00862227 | ||||||||
\(585\) | 4.80551 | 0.198683 | ||||||||
\(586\) | −13.2819 | −0.548670 | ||||||||
\(587\) | 1.69810 | 0.0700880 | 0.0350440 | − | 0.999386i | \(-0.488843\pi\) | ||||
0.0350440 | + | 0.999386i | \(0.488843\pi\) | |||||||
\(588\) | 109.095 | 4.49900 | ||||||||
\(589\) | −0.0623904 | −0.00257075 | ||||||||
\(590\) | −16.2038 | −0.667100 | ||||||||
\(591\) | 7.45268 | 0.306562 | ||||||||
\(592\) | 12.0462 | 0.495096 | ||||||||
\(593\) | −38.6960 | −1.58905 | −0.794527 | − | 0.607228i | \(-0.792281\pi\) | ||||
−0.794527 | + | 0.607228i | \(0.792281\pi\) | |||||||
\(594\) | 14.4044 | 0.591019 | ||||||||
\(595\) | 4.93968 | 0.202507 | ||||||||
\(596\) | 119.975 | 4.91435 | ||||||||
\(597\) | −4.81114 | −0.196907 | ||||||||
\(598\) | −2.68085 | −0.109628 | ||||||||
\(599\) | 32.5578 | 1.33028 | 0.665139 | − | 0.746720i | \(-0.268372\pi\) | ||||
0.665139 | + | 0.746720i | \(0.268372\pi\) | |||||||
\(600\) | 39.6178 | 1.61739 | ||||||||
\(601\) | −12.4198 | −0.506615 | −0.253307 | − | 0.967386i | \(-0.581518\pi\) | ||||
−0.253307 | + | 0.967386i | \(0.581518\pi\) | |||||||
\(602\) | −13.4991 | −0.550184 | ||||||||
\(603\) | 15.4634 | 0.629720 | ||||||||
\(604\) | 122.577 | 4.98759 | ||||||||
\(605\) | 0.981432 | 0.0399009 | ||||||||
\(606\) | −3.50090 | −0.142214 | ||||||||
\(607\) | 8.29832 | 0.336818 | 0.168409 | − | 0.985717i | \(-0.446137\pi\) | ||||
0.168409 | + | 0.985717i | \(0.446137\pi\) | |||||||
\(608\) | 4.54111 | 0.184166 | ||||||||
\(609\) | 34.5457 | 1.39986 | ||||||||
\(610\) | −8.18250 | −0.331300 | ||||||||
\(611\) | 16.3591 | 0.661817 | ||||||||
\(612\) | 8.76128 | 0.354154 | ||||||||
\(613\) | −19.1583 | −0.773795 | −0.386898 | − | 0.922123i | \(-0.626453\pi\) | ||||
−0.386898 | + | 0.922123i | \(0.626453\pi\) | |||||||
\(614\) | 59.0593 | 2.38344 | ||||||||
\(615\) | −10.0441 | −0.405018 | ||||||||
\(616\) | 43.1082 | 1.73688 | ||||||||
\(617\) | 8.08259 | 0.325393 | 0.162696 | − | 0.986676i | \(-0.447981\pi\) | ||||
0.162696 | + | 0.986676i | \(0.447981\pi\) | |||||||
\(618\) | 2.42274 | 0.0974567 | ||||||||
\(619\) | 27.3218 | 1.09815 | 0.549077 | − | 0.835771i | \(-0.314979\pi\) | ||||
0.549077 | + | 0.835771i | \(0.314979\pi\) | |||||||
\(620\) | 1.16406 | 0.0467498 | ||||||||
\(621\) | 1.84956 | 0.0742204 | ||||||||
\(622\) | −49.4094 | −1.98113 | ||||||||
\(623\) | 8.79744 | 0.352462 | ||||||||
\(624\) | −41.8540 | −1.67550 | ||||||||
\(625\) | 11.4796 | 0.459186 | ||||||||
\(626\) | 18.8202 | 0.752207 | ||||||||
\(627\) | −0.313030 | −0.0125012 | ||||||||
\(628\) | −41.8332 | −1.66933 | ||||||||
\(629\) | −0.957214 | −0.0381666 | ||||||||
\(630\) | −22.3502 | −0.890453 | ||||||||
\(631\) | −22.7858 | −0.907089 | −0.453544 | − | 0.891234i | \(-0.649841\pi\) | ||||
−0.453544 | + | 0.891234i | \(0.649841\pi\) | |||||||
\(632\) | −0.0275000 | −0.00109389 | ||||||||
\(633\) | −25.9722 | −1.03230 | ||||||||
\(634\) | −12.5669 | −0.499095 | ||||||||
\(635\) | −16.1834 | −0.642217 | ||||||||
\(636\) | 1.44899 | 0.0574560 | ||||||||
\(637\) | −53.2089 | −2.10821 | ||||||||
\(638\) | 16.0654 | 0.636034 | ||||||||
\(639\) | 0.329405 | 0.0130311 | ||||||||
\(640\) | −18.4747 | −0.730278 | ||||||||
\(641\) | −29.9983 | −1.18486 | −0.592431 | − | 0.805622i | \(-0.701832\pi\) | ||||
−0.592431 | + | 0.805622i | \(0.701832\pi\) | |||||||
\(642\) | −6.65351 | −0.262593 | ||||||||
\(643\) | −10.9536 | −0.431967 | −0.215983 | − | 0.976397i | \(-0.569296\pi\) | ||||
−0.215983 | + | 0.976397i | \(0.569296\pi\) | |||||||
\(644\) | 9.00187 | 0.354723 | ||||||||
\(645\) | −1.12458 | −0.0442805 | ||||||||
\(646\) | −0.732692 | −0.0288274 | ||||||||
\(647\) | 10.3836 | 0.408223 | 0.204111 | − | 0.978948i | \(-0.434570\pi\) | ||||
0.204111 | + | 0.978948i | \(0.434570\pi\) | |||||||
\(648\) | 9.36162 | 0.367759 | ||||||||
\(649\) | 6.15588 | 0.241639 | ||||||||
\(650\) | −31.4244 | −1.23257 | ||||||||
\(651\) | −1.31715 | −0.0516231 | ||||||||
\(652\) | 29.0384 | 1.13723 | ||||||||
\(653\) | −12.8307 | −0.502106 | −0.251053 | − | 0.967973i | \(-0.580777\pi\) | ||||
−0.251053 | + | 0.967973i | \(0.580777\pi\) | |||||||
\(654\) | −2.80494 | −0.109682 | ||||||||
\(655\) | 6.99123 | 0.273170 | ||||||||
\(656\) | −112.399 | −4.38842 | ||||||||
\(657\) | −0.0410414 | −0.00160118 | ||||||||
\(658\) | −76.0853 | −2.96611 | ||||||||
\(659\) | 45.1519 | 1.75887 | 0.879434 | − | 0.476020i | \(-0.157921\pi\) | ||||
0.879434 | + | 0.476020i | \(0.157921\pi\) | |||||||
\(660\) | 5.84043 | 0.227338 | ||||||||
\(661\) | 20.0011 | 0.777953 | 0.388976 | − | 0.921248i | \(-0.372829\pi\) | ||||
0.388976 | + | 0.921248i | \(0.372829\pi\) | |||||||
\(662\) | 39.6411 | 1.54069 | ||||||||
\(663\) | 3.32580 | 0.129163 | ||||||||
\(664\) | 87.8955 | 3.41101 | ||||||||
\(665\) | 1.34944 | 0.0523290 | ||||||||
\(666\) | 4.33103 | 0.167824 | ||||||||
\(667\) | 2.06284 | 0.0798735 | ||||||||
\(668\) | 77.7235 | 3.00721 | ||||||||
\(669\) | −25.6061 | −0.989987 | ||||||||
\(670\) | 24.1278 | 0.932139 | ||||||||
\(671\) | 3.10856 | 0.120005 | ||||||||
\(672\) | 95.8691 | 3.69823 | ||||||||
\(673\) | −14.1438 | −0.545205 | −0.272602 | − | 0.962127i | \(-0.587884\pi\) | ||||
−0.272602 | + | 0.962127i | \(0.587884\pi\) | |||||||
\(674\) | 10.7121 | 0.412613 | ||||||||
\(675\) | 21.6802 | 0.834472 | ||||||||
\(676\) | −23.7641 | −0.914003 | ||||||||
\(677\) | −47.0578 | −1.80858 | −0.904289 | − | 0.426920i | \(-0.859599\pi\) | ||||
−0.904289 | + | 0.426920i | \(0.859599\pi\) | |||||||
\(678\) | 53.4687 | 2.05345 | ||||||||
\(679\) | −81.6076 | −3.13181 | ||||||||
\(680\) | 8.40585 | 0.322350 | ||||||||
\(681\) | 22.0284 | 0.844130 | ||||||||
\(682\) | −0.612535 | −0.0234552 | ||||||||
\(683\) | −46.1301 | −1.76512 | −0.882560 | − | 0.470201i | \(-0.844182\pi\) | ||||
−0.882560 | + | 0.470201i | \(0.844182\pi\) | |||||||
\(684\) | 2.39344 | 0.0915153 | ||||||||
\(685\) | −12.3745 | −0.472805 | ||||||||
\(686\) | 152.978 | 5.84074 | ||||||||
\(687\) | 20.7293 | 0.790871 | ||||||||
\(688\) | −12.5847 | −0.479785 | ||||||||
\(689\) | −0.706714 | −0.0269237 | ||||||||
\(690\) | 1.03873 | 0.0395437 | ||||||||
\(691\) | 11.5960 | 0.441131 | 0.220566 | − | 0.975372i | \(-0.429210\pi\) | ||||
0.220566 | + | 0.975372i | \(0.429210\pi\) | |||||||
\(692\) | −42.5327 | −1.61685 | ||||||||
\(693\) | 8.49091 | 0.322543 | ||||||||
\(694\) | −77.0129 | −2.92337 | ||||||||
\(695\) | −19.5954 | −0.743295 | ||||||||
\(696\) | 58.7865 | 2.22829 | ||||||||
\(697\) | 8.93139 | 0.338301 | ||||||||
\(698\) | 76.5978 | 2.89927 | ||||||||
\(699\) | 25.3116 | 0.957374 | ||||||||
\(700\) | 105.518 | 3.98821 | ||||||||
\(701\) | 16.5468 | 0.624963 | 0.312481 | − | 0.949924i | \(-0.398840\pi\) | ||||
0.312481 | + | 0.949924i | \(0.398840\pi\) | |||||||
\(702\) | −41.8079 | −1.57794 | ||||||||
\(703\) | −0.261495 | −0.00986246 | ||||||||
\(704\) | 19.4143 | 0.731704 | ||||||||
\(705\) | −6.33851 | −0.238722 | ||||||||
\(706\) | 17.2953 | 0.650916 | ||||||||
\(707\) | −5.73349 | −0.215630 | ||||||||
\(708\) | 36.6332 | 1.37676 | ||||||||
\(709\) | −34.2212 | −1.28520 | −0.642602 | − | 0.766200i | \(-0.722145\pi\) | ||||
−0.642602 | + | 0.766200i | \(0.722145\pi\) | |||||||
\(710\) | 0.513975 | 0.0192891 | ||||||||
\(711\) | −0.00541659 | −0.000203138 0 | ||||||||
\(712\) | 14.9706 | 0.561047 | ||||||||
\(713\) | −0.0786512 | −0.00294551 | ||||||||
\(714\) | −15.4681 | −0.578881 | ||||||||
\(715\) | −2.84855 | −0.106530 | ||||||||
\(716\) | 20.7557 | 0.775676 | ||||||||
\(717\) | −16.7220 | −0.624495 | ||||||||
\(718\) | 4.79868 | 0.179085 | ||||||||
\(719\) | 23.2293 | 0.866306 | 0.433153 | − | 0.901320i | \(-0.357401\pi\) | ||||
0.433153 | + | 0.901320i | \(0.357401\pi\) | |||||||
\(720\) | −20.8361 | −0.776516 | ||||||||
\(721\) | 3.96776 | 0.147767 | ||||||||
\(722\) | 50.7588 | 1.88905 | ||||||||
\(723\) | −6.61755 | −0.246109 | ||||||||
\(724\) | −83.8662 | −3.11686 | ||||||||
\(725\) | 24.1802 | 0.898030 | ||||||||
\(726\) | −3.07326 | −0.114059 | ||||||||
\(727\) | 31.2635 | 1.15950 | 0.579749 | − | 0.814795i | \(-0.303151\pi\) | ||||
0.579749 | + | 0.814795i | \(0.303151\pi\) | |||||||
\(728\) | −125.119 | −4.63723 | ||||||||
\(729\) | 20.3060 | 0.752075 | ||||||||
\(730\) | −0.0640374 | −0.00237013 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | 18.4988 | 0.683735 | ||||||||
\(733\) | 14.6776 | 0.542130 | 0.271065 | − | 0.962561i | \(-0.412624\pi\) | ||||
0.271065 | + | 0.962561i | \(0.412624\pi\) | |||||||
\(734\) | 34.7681 | 1.28331 | ||||||||
\(735\) | 20.6164 | 0.760447 | ||||||||
\(736\) | 5.72466 | 0.211014 | ||||||||
\(737\) | −9.16623 | −0.337643 | ||||||||
\(738\) | −40.4112 | −1.48756 | ||||||||
\(739\) | −19.4465 | −0.715352 | −0.357676 | − | 0.933846i | \(-0.616431\pi\) | ||||
−0.357676 | + | 0.933846i | \(0.616431\pi\) | |||||||
\(740\) | 4.87889 | 0.179352 | ||||||||
\(741\) | 0.908553 | 0.0333765 | ||||||||
\(742\) | 3.28689 | 0.120666 | ||||||||
\(743\) | 27.8622 | 1.02217 | 0.511083 | − | 0.859531i | \(-0.329245\pi\) | ||||
0.511083 | + | 0.859531i | \(0.329245\pi\) | |||||||
\(744\) | −2.24139 | −0.0821733 | ||||||||
\(745\) | 22.6724 | 0.830652 | ||||||||
\(746\) | −13.3806 | −0.489897 | ||||||||
\(747\) | 17.3125 | 0.633432 | ||||||||
\(748\) | −5.19341 | −0.189890 | ||||||||
\(749\) | −10.8966 | −0.398152 | ||||||||
\(750\) | 27.2567 | 0.995275 | ||||||||
\(751\) | 37.2067 | 1.35769 | 0.678845 | − | 0.734282i | \(-0.262481\pi\) | ||||
0.678845 | + | 0.734282i | \(0.262481\pi\) | |||||||
\(752\) | −70.9310 | −2.58659 | ||||||||
\(753\) | 13.6517 | 0.497495 | ||||||||
\(754\) | −46.6289 | −1.69812 | ||||||||
\(755\) | 23.1642 | 0.843031 | ||||||||
\(756\) | 140.384 | 5.10572 | ||||||||
\(757\) | 44.1438 | 1.60443 | 0.802216 | − | 0.597033i | \(-0.203654\pi\) | ||||
0.802216 | + | 0.597033i | \(0.203654\pi\) | |||||||
\(758\) | −82.1671 | −2.98444 | ||||||||
\(759\) | −0.394615 | −0.0143236 | ||||||||
\(760\) | 2.29634 | 0.0832969 | ||||||||
\(761\) | 11.7585 | 0.426247 | 0.213123 | − | 0.977025i | \(-0.431636\pi\) | ||||
0.213123 | + | 0.977025i | \(0.431636\pi\) | |||||||
\(762\) | 50.6767 | 1.83582 | ||||||||
\(763\) | −4.59371 | −0.166303 | ||||||||
\(764\) | 79.0965 | 2.86161 | ||||||||
\(765\) | 1.65568 | 0.0598611 | ||||||||
\(766\) | −61.2500 | −2.21305 | ||||||||
\(767\) | −17.8671 | −0.645143 | ||||||||
\(768\) | 13.3597 | 0.482077 | ||||||||
\(769\) | −3.97356 | −0.143290 | −0.0716451 | − | 0.997430i | \(-0.522825\pi\) | ||||
−0.0716451 | + | 0.997430i | \(0.522825\pi\) | |||||||
\(770\) | 13.2485 | 0.477442 | ||||||||
\(771\) | 26.8137 | 0.965672 | ||||||||
\(772\) | 46.8162 | 1.68495 | ||||||||
\(773\) | −24.4234 | −0.878447 | −0.439223 | − | 0.898378i | \(-0.644746\pi\) | ||||
−0.439223 | + | 0.898378i | \(0.644746\pi\) | |||||||
\(774\) | −4.52463 | −0.162634 | ||||||||
\(775\) | −0.921934 | −0.0331169 | ||||||||
\(776\) | −138.872 | −4.98520 | ||||||||
\(777\) | −5.52052 | −0.198047 | ||||||||
\(778\) | −21.2079 | −0.760341 | ||||||||
\(779\) | 2.43991 | 0.0874188 | ||||||||
\(780\) | −16.9515 | −0.606961 | ||||||||
\(781\) | −0.195261 | −0.00698698 | ||||||||
\(782\) | −0.923654 | −0.0330298 | ||||||||
\(783\) | 32.1700 | 1.14966 | ||||||||
\(784\) | 230.708 | 8.23956 | ||||||||
\(785\) | −7.90549 | −0.282159 | ||||||||
\(786\) | −21.8924 | −0.780875 | ||||||||
\(787\) | 33.5515 | 1.19598 | 0.597991 | − | 0.801503i | \(-0.295966\pi\) | ||||
0.597991 | + | 0.801503i | \(0.295966\pi\) | |||||||
\(788\) | 33.7779 | 1.20329 | ||||||||
\(789\) | 20.6872 | 0.736483 | ||||||||
\(790\) | −0.00845158 | −0.000300694 0 | ||||||||
\(791\) | 87.5666 | 3.11351 | ||||||||
\(792\) | 14.4490 | 0.513422 | ||||||||
\(793\) | −9.02241 | −0.320395 | ||||||||
\(794\) | 62.9667 | 2.23460 | ||||||||
\(795\) | 0.273824 | 0.00971155 | ||||||||
\(796\) | −21.8056 | −0.772879 | ||||||||
\(797\) | −12.0487 | −0.426786 | −0.213393 | − | 0.976966i | \(-0.568451\pi\) | ||||
−0.213393 | + | 0.976966i | \(0.568451\pi\) | |||||||
\(798\) | −4.22564 | −0.149586 | ||||||||
\(799\) | 5.63631 | 0.199398 | ||||||||
\(800\) | 67.1034 | 2.37246 | ||||||||
\(801\) | 2.94872 | 0.104188 | ||||||||
\(802\) | 10.2138 | 0.360660 | ||||||||
\(803\) | 0.0243280 | 0.000858517 0 | ||||||||
\(804\) | −54.5476 | −1.92374 | ||||||||
\(805\) | 1.70114 | 0.0599574 | ||||||||
\(806\) | 1.77785 | 0.0626220 | ||||||||
\(807\) | −14.5497 | −0.512174 | ||||||||
\(808\) | −9.75668 | −0.343239 | ||||||||
\(809\) | −3.70740 | −0.130345 | −0.0651726 | − | 0.997874i | \(-0.520760\pi\) | ||||
−0.0651726 | + | 0.997874i | \(0.520760\pi\) | |||||||
\(810\) | 2.87711 | 0.101091 | ||||||||
\(811\) | −20.2513 | −0.711121 | −0.355560 | − | 0.934653i | \(-0.615710\pi\) | ||||
−0.355560 | + | 0.934653i | \(0.615710\pi\) | |||||||
\(812\) | 156.572 | 5.49461 | ||||||||
\(813\) | −15.4795 | −0.542889 | ||||||||
\(814\) | −2.56730 | −0.0899837 | ||||||||
\(815\) | 5.48758 | 0.192222 | ||||||||
\(816\) | −14.4203 | −0.504811 | ||||||||
\(817\) | 0.273183 | 0.00955747 | ||||||||
\(818\) | −103.090 | −3.60447 | ||||||||
\(819\) | −24.6444 | −0.861144 | ||||||||
\(820\) | −45.5231 | −1.58973 | ||||||||
\(821\) | −2.72666 | −0.0951612 | −0.0475806 | − | 0.998867i | \(-0.515151\pi\) | ||||
−0.0475806 | + | 0.998867i | \(0.515151\pi\) | |||||||
\(822\) | 38.7496 | 1.35155 | ||||||||
\(823\) | −1.30669 | −0.0455485 | −0.0227742 | − | 0.999741i | \(-0.507250\pi\) | ||||
−0.0227742 | + | 0.999741i | \(0.507250\pi\) | |||||||
\(824\) | 6.75193 | 0.235215 | ||||||||
\(825\) | −4.62560 | −0.161043 | ||||||||
\(826\) | 83.0990 | 2.89138 | ||||||||
\(827\) | 8.93328 | 0.310641 | 0.155320 | − | 0.987864i | \(-0.450359\pi\) | ||||
0.155320 | + | 0.987864i | \(0.450359\pi\) | |||||||
\(828\) | 3.01724 | 0.104856 | ||||||||
\(829\) | 10.0858 | 0.350293 | 0.175147 | − | 0.984542i | \(-0.443960\pi\) | ||||
0.175147 | + | 0.984542i | \(0.443960\pi\) | |||||||
\(830\) | 27.0130 | 0.937634 | ||||||||
\(831\) | 2.59956 | 0.0901777 | ||||||||
\(832\) | −56.3489 | −1.95355 | ||||||||
\(833\) | −18.3325 | −0.635182 | ||||||||
\(834\) | 61.3611 | 2.12476 | ||||||||
\(835\) | 14.6879 | 0.508296 | ||||||||
\(836\) | −1.41875 | −0.0490686 | ||||||||
\(837\) | −1.22657 | −0.0423963 | ||||||||
\(838\) | 32.9140 | 1.13700 | ||||||||
\(839\) | −6.52371 | −0.225223 | −0.112612 | − | 0.993639i | \(-0.535922\pi\) | ||||
−0.112612 | + | 0.993639i | \(0.535922\pi\) | |||||||
\(840\) | 48.4789 | 1.67268 | ||||||||
\(841\) | 6.87957 | 0.237227 | ||||||||
\(842\) | −20.5062 | −0.706692 | ||||||||
\(843\) | 21.2405 | 0.731561 | ||||||||
\(844\) | −117.714 | −4.05189 | ||||||||
\(845\) | −4.49085 | −0.154490 | ||||||||
\(846\) | −25.5022 | −0.876783 | ||||||||
\(847\) | −5.03314 | −0.172941 | ||||||||
\(848\) | 3.06423 | 0.105226 | ||||||||
\(849\) | 2.20345 | 0.0756222 | ||||||||
\(850\) | −10.8269 | −0.371359 | ||||||||
\(851\) | −0.329648 | −0.0113002 | ||||||||
\(852\) | −1.16198 | −0.0398088 | ||||||||
\(853\) | 5.04085 | 0.172595 | 0.0862977 | − | 0.996269i | \(-0.472496\pi\) | ||||
0.0862977 | + | 0.996269i | \(0.472496\pi\) | |||||||
\(854\) | 41.9628 | 1.43594 | ||||||||
\(855\) | 0.452303 | 0.0154684 | ||||||||
\(856\) | −18.5427 | −0.633776 | ||||||||
\(857\) | −13.1579 | −0.449465 | −0.224732 | − | 0.974421i | \(-0.572151\pi\) | ||||
−0.224732 | + | 0.974421i | \(0.572151\pi\) | |||||||
\(858\) | 8.91997 | 0.304523 | ||||||||
\(859\) | −46.3631 | −1.58189 | −0.790945 | − | 0.611888i | \(-0.790411\pi\) | ||||
−0.790945 | + | 0.611888i | \(0.790411\pi\) | |||||||
\(860\) | −5.09697 | −0.173805 | ||||||||
\(861\) | 51.5098 | 1.75545 | ||||||||
\(862\) | 12.0611 | 0.410804 | ||||||||
\(863\) | 39.6295 | 1.34900 | 0.674501 | − | 0.738274i | \(-0.264359\pi\) | ||||
0.674501 | + | 0.738274i | \(0.264359\pi\) | |||||||
\(864\) | 89.2761 | 3.03723 | ||||||||
\(865\) | −8.03767 | −0.273289 | ||||||||
\(866\) | −83.1621 | −2.82596 | ||||||||
\(867\) | 1.14586 | 0.0389155 | ||||||||
\(868\) | −5.96973 | −0.202626 | ||||||||
\(869\) | 0.00321078 | 0.000108918 0 | ||||||||
\(870\) | 18.0669 | 0.612525 | ||||||||
\(871\) | 26.6045 | 0.901458 | ||||||||
\(872\) | −7.81711 | −0.264721 | ||||||||
\(873\) | −27.3531 | −0.925764 | ||||||||
\(874\) | −0.252327 | −0.00853508 | ||||||||
\(875\) | 44.6389 | 1.50907 | ||||||||
\(876\) | 0.144774 | 0.00489147 | ||||||||
\(877\) | 9.70909 | 0.327853 | 0.163926 | − | 0.986473i | \(-0.447584\pi\) | ||||
0.163926 | + | 0.986473i | \(0.447584\pi\) | |||||||
\(878\) | −104.410 | −3.52365 | ||||||||
\(879\) | 5.67447 | 0.191395 | ||||||||
\(880\) | 12.3510 | 0.416351 | ||||||||
\(881\) | 9.22782 | 0.310893 | 0.155447 | − | 0.987844i | \(-0.450318\pi\) | ||||
0.155447 | + | 0.987844i | \(0.450318\pi\) | |||||||
\(882\) | 82.9475 | 2.79299 | ||||||||
\(883\) | −18.2323 | −0.613565 | −0.306783 | − | 0.951780i | \(-0.599252\pi\) | ||||
−0.306783 | + | 0.951780i | \(0.599252\pi\) | |||||||
\(884\) | 15.0736 | 0.506979 | ||||||||
\(885\) | 6.92281 | 0.232708 | ||||||||
\(886\) | 99.0598 | 3.32798 | ||||||||
\(887\) | 21.9751 | 0.737852 | 0.368926 | − | 0.929459i | \(-0.379726\pi\) | ||||
0.368926 | + | 0.929459i | \(0.379726\pi\) | |||||||
\(888\) | −9.39426 | −0.315251 | ||||||||
\(889\) | 82.9942 | 2.78353 | ||||||||
\(890\) | 4.60092 | 0.154223 | ||||||||
\(891\) | −1.09302 | −0.0366177 | ||||||||
\(892\) | −116.055 | −3.88580 | ||||||||
\(893\) | 1.53974 | 0.0515256 | ||||||||
\(894\) | −70.9964 | −2.37448 | ||||||||
\(895\) | 3.92234 | 0.131109 | ||||||||
\(896\) | 94.7451 | 3.16521 | ||||||||
\(897\) | 1.14535 | 0.0382421 | ||||||||
\(898\) | −12.2908 | −0.410149 | ||||||||
\(899\) | −1.36800 | −0.0456255 | ||||||||
\(900\) | 35.3675 | 1.17892 | ||||||||
\(901\) | −0.243489 | −0.00811180 | ||||||||
\(902\) | 23.9545 | 0.797597 | ||||||||
\(903\) | 5.76728 | 0.191923 | ||||||||
\(904\) | 149.012 | 4.95607 | ||||||||
\(905\) | −15.8487 | −0.526830 | ||||||||
\(906\) | −72.5365 | −2.40986 | ||||||||
\(907\) | 14.0340 | 0.465990 | 0.232995 | − | 0.972478i | \(-0.425147\pi\) | ||||
0.232995 | + | 0.972478i | \(0.425147\pi\) | |||||||
\(908\) | 99.8397 | 3.31330 | ||||||||
\(909\) | −1.92175 | −0.0637403 | ||||||||
\(910\) | −38.4530 | −1.27470 | ||||||||
\(911\) | 9.68789 | 0.320974 | 0.160487 | − | 0.987038i | \(-0.448694\pi\) | ||||
0.160487 | + | 0.987038i | \(0.448694\pi\) | |||||||
\(912\) | −3.93938 | −0.130446 | ||||||||
\(913\) | −10.2623 | −0.339633 | ||||||||
\(914\) | −40.3408 | −1.33436 | ||||||||
\(915\) | 3.49584 | 0.115569 | ||||||||
\(916\) | 93.9516 | 3.10425 | ||||||||
\(917\) | −35.8535 | −1.18399 | ||||||||
\(918\) | −14.4044 | −0.475415 | ||||||||
\(919\) | −0.446725 | −0.0147361 | −0.00736804 | − | 0.999973i | \(-0.502345\pi\) | ||||
−0.00736804 | + | 0.999973i | \(0.502345\pi\) | |||||||
\(920\) | 2.89483 | 0.0954398 | ||||||||
\(921\) | −25.2321 | −0.831425 | ||||||||
\(922\) | −50.2760 | −1.65575 | ||||||||
\(923\) | 0.566733 | 0.0186543 | ||||||||
\(924\) | −29.9518 | −0.985342 | ||||||||
\(925\) | −3.86407 | −0.127050 | ||||||||
\(926\) | 56.4760 | 1.85592 | ||||||||
\(927\) | 1.32991 | 0.0436800 | ||||||||
\(928\) | 99.5707 | 3.26857 | ||||||||
\(929\) | 23.3522 | 0.766160 | 0.383080 | − | 0.923715i | \(-0.374863\pi\) | ||||
0.383080 | + | 0.923715i | \(0.374863\pi\) | |||||||
\(930\) | −0.688847 | −0.0225882 | ||||||||
\(931\) | −5.00812 | −0.164135 | ||||||||
\(932\) | 114.720 | 3.75779 | ||||||||
\(933\) | 21.1093 | 0.691088 | ||||||||
\(934\) | −56.6552 | −1.85382 | ||||||||
\(935\) | −0.981432 | −0.0320962 | ||||||||
\(936\) | −41.9373 | −1.37076 | ||||||||
\(937\) | 10.9116 | 0.356468 | 0.178234 | − | 0.983988i | \(-0.442962\pi\) | ||||
0.178234 | + | 0.983988i | \(0.442962\pi\) | |||||||
\(938\) | −123.736 | −4.04013 | ||||||||
\(939\) | −8.04062 | −0.262396 | ||||||||
\(940\) | −28.7281 | −0.937007 | ||||||||
\(941\) | 15.2914 | 0.498484 | 0.249242 | − | 0.968441i | \(-0.419819\pi\) | ||||
0.249242 | + | 0.968441i | \(0.419819\pi\) | |||||||
\(942\) | 24.7553 | 0.806571 | ||||||||
\(943\) | 3.07582 | 0.100163 | ||||||||
\(944\) | 77.4696 | 2.52142 | ||||||||
\(945\) | 26.5293 | 0.862999 | ||||||||
\(946\) | 2.68205 | 0.0872011 | ||||||||
\(947\) | −10.5487 | −0.342787 | −0.171393 | − | 0.985203i | \(-0.554827\pi\) | ||||
−0.171393 | + | 0.985203i | \(0.554827\pi\) | |||||||
\(948\) | 0.0191071 | 0.000620570 0 | ||||||||
\(949\) | −0.0706107 | −0.00229212 | ||||||||
\(950\) | −2.95773 | −0.0959613 | ||||||||
\(951\) | 5.36899 | 0.174101 | ||||||||
\(952\) | −43.1082 | −1.39715 | ||||||||
\(953\) | 6.98516 | 0.226271 | 0.113136 | − | 0.993580i | \(-0.463911\pi\) | ||||
0.113136 | + | 0.993580i | \(0.463911\pi\) | |||||||
\(954\) | 1.10170 | 0.0356688 | ||||||||
\(955\) | 14.9474 | 0.483686 | ||||||||
\(956\) | −75.7894 | −2.45121 | ||||||||
\(957\) | −6.86366 | −0.221871 | ||||||||
\(958\) | −79.0704 | −2.55465 | ||||||||
\(959\) | 63.4609 | 2.04926 | ||||||||
\(960\) | 21.8330 | 0.704658 | ||||||||
\(961\) | −30.9478 | −0.998317 | ||||||||
\(962\) | 7.45144 | 0.240244 | ||||||||
\(963\) | −3.65230 | −0.117694 | ||||||||
\(964\) | −29.9928 | −0.966004 | ||||||||
\(965\) | 8.84717 | 0.284800 | ||||||||
\(966\) | −5.32697 | −0.171392 | ||||||||
\(967\) | 6.54757 | 0.210556 | 0.105278 | − | 0.994443i | \(-0.466427\pi\) | ||||
0.105278 | + | 0.994443i | \(0.466427\pi\) | |||||||
\(968\) | −8.56488 | −0.275286 | ||||||||
\(969\) | 0.313030 | 0.0100560 | ||||||||
\(970\) | −42.6795 | −1.37036 | ||||||||
\(971\) | −51.9599 | −1.66747 | −0.833737 | − | 0.552162i | \(-0.813803\pi\) | ||||
−0.833737 | + | 0.552162i | \(0.813803\pi\) | |||||||
\(972\) | 77.1715 | 2.47528 | ||||||||
\(973\) | 100.492 | 3.22163 | ||||||||
\(974\) | −56.3312 | −1.80497 | ||||||||
\(975\) | 13.4256 | 0.429962 | ||||||||
\(976\) | 39.1201 | 1.25220 | ||||||||
\(977\) | −21.7013 | −0.694287 | −0.347143 | − | 0.937812i | \(-0.612848\pi\) | ||||
−0.347143 | + | 0.937812i | \(0.612848\pi\) | |||||||
\(978\) | −17.1839 | −0.549479 | ||||||||
\(979\) | −1.74790 | −0.0558633 | ||||||||
\(980\) | 93.4400 | 2.98483 | ||||||||
\(981\) | −1.53971 | −0.0491593 | ||||||||
\(982\) | 70.1844 | 2.23967 | ||||||||
\(983\) | 52.3229 | 1.66884 | 0.834421 | − | 0.551128i | \(-0.185802\pi\) | ||||
0.834421 | + | 0.551128i | \(0.185802\pi\) | |||||||
\(984\) | 87.6542 | 2.79431 | ||||||||
\(985\) | 6.38323 | 0.203387 | ||||||||
\(986\) | −16.0654 | −0.511626 | ||||||||
\(987\) | 32.5061 | 1.03468 | ||||||||
\(988\) | 4.11785 | 0.131006 | ||||||||
\(989\) | 0.344383 | 0.0109507 | ||||||||
\(990\) | 4.44061 | 0.141132 | ||||||||
\(991\) | 5.07432 | 0.161191 | 0.0805956 | − | 0.996747i | \(-0.474318\pi\) | ||||
0.0805956 | + | 0.996747i | \(0.474318\pi\) | |||||||
\(992\) | −3.79640 | −0.120536 | ||||||||
\(993\) | −16.9360 | −0.537447 | ||||||||
\(994\) | −2.63585 | −0.0836041 | ||||||||
\(995\) | −4.12075 | −0.130636 | ||||||||
\(996\) | −61.0702 | −1.93508 | ||||||||
\(997\) | 32.1989 | 1.01975 | 0.509874 | − | 0.860249i | \(-0.329692\pi\) | ||||
0.509874 | + | 0.860249i | \(0.329692\pi\) | |||||||
\(998\) | −67.7397 | −2.14426 | ||||||||
\(999\) | −5.14086 | −0.162650 |
(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 | 8041.2.a.i.1.2 | ✓ | 78 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.i.1.2 | ✓ | 78 | 1.1 | even | 1 | trivial |