Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, 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("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(67\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.80341 | −1.27521 | −0.637603 | − | 0.770365i | \(-0.720074\pi\) | ||||
−0.637603 | + | 0.770365i | \(0.720074\pi\) | |||||||
\(3\) | 0.567965 | 0.327915 | 0.163957 | − | 0.986467i | \(-0.447574\pi\) | ||||
0.163957 | + | 0.986467i | \(0.447574\pi\) | |||||||
\(4\) | 1.25230 | 0.626151 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.02428 | −0.418159 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.34841 | 0.476734 | ||||||||
\(9\) | −2.67742 | −0.892472 | ||||||||
\(10\) | −1.80341 | −0.570290 | ||||||||
\(11\) | 0.253853 | 0.0765395 | 0.0382697 | − | 0.999267i | \(-0.487815\pi\) | ||||
0.0382697 | + | 0.999267i | \(0.487815\pi\) | |||||||
\(12\) | 0.711264 | 0.205324 | ||||||||
\(13\) | −7.06566 | −1.95966 | −0.979831 | − | 0.199826i | \(-0.935962\pi\) | ||||
−0.979831 | + | 0.199826i | \(0.935962\pi\) | |||||||
\(14\) | 1.80341 | 0.481983 | ||||||||
\(15\) | 0.567965 | 0.146648 | ||||||||
\(16\) | −4.93634 | −1.23409 | ||||||||
\(17\) | −7.34662 | −1.78182 | −0.890908 | − | 0.454183i | \(-0.849931\pi\) | ||||
−0.890908 | + | 0.454183i | \(0.849931\pi\) | |||||||
\(18\) | 4.82849 | 1.13809 | ||||||||
\(19\) | −1.78414 | −0.409311 | −0.204655 | − | 0.978834i | \(-0.565607\pi\) | ||||
−0.204655 | + | 0.978834i | \(0.565607\pi\) | |||||||
\(20\) | 1.25230 | 0.280023 | ||||||||
\(21\) | −0.567965 | −0.123940 | ||||||||
\(22\) | −0.457801 | −0.0976036 | ||||||||
\(23\) | −5.37456 | −1.12067 | −0.560337 | − | 0.828265i | \(-0.689328\pi\) | ||||
−0.560337 | + | 0.828265i | \(0.689328\pi\) | |||||||
\(24\) | 0.765849 | 0.156328 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 12.7423 | 2.49897 | ||||||||
\(27\) | −3.22458 | −0.620570 | ||||||||
\(28\) | −1.25230 | −0.236663 | ||||||||
\(29\) | −3.96844 | −0.736921 | −0.368461 | − | 0.929643i | \(-0.620115\pi\) | ||||
−0.368461 | + | 0.929643i | \(0.620115\pi\) | |||||||
\(30\) | −1.02428 | −0.187007 | ||||||||
\(31\) | 9.37038 | 1.68297 | 0.841485 | − | 0.540281i | \(-0.181682\pi\) | ||||
0.841485 | + | 0.540281i | \(0.181682\pi\) | |||||||
\(32\) | 6.20545 | 1.09698 | ||||||||
\(33\) | 0.144180 | 0.0250984 | ||||||||
\(34\) | 13.2490 | 2.27218 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −3.35293 | −0.558822 | ||||||||
\(37\) | 6.71552 | 1.10402 | 0.552012 | − | 0.833836i | \(-0.313860\pi\) | ||||
0.552012 | + | 0.833836i | \(0.313860\pi\) | |||||||
\(38\) | 3.21755 | 0.521956 | ||||||||
\(39\) | −4.01305 | −0.642603 | ||||||||
\(40\) | 1.34841 | 0.213202 | ||||||||
\(41\) | −7.80846 | −1.21948 | −0.609739 | − | 0.792603i | \(-0.708726\pi\) | ||||
−0.609739 | + | 0.792603i | \(0.708726\pi\) | |||||||
\(42\) | 1.02428 | 0.158049 | ||||||||
\(43\) | −11.4297 | −1.74302 | −0.871510 | − | 0.490378i | \(-0.836859\pi\) | ||||
−0.871510 | + | 0.490378i | \(0.836859\pi\) | |||||||
\(44\) | 0.317900 | 0.0479253 | ||||||||
\(45\) | −2.67742 | −0.399126 | ||||||||
\(46\) | 9.69256 | 1.42909 | ||||||||
\(47\) | −2.50605 | −0.365545 | −0.182772 | − | 0.983155i | \(-0.558507\pi\) | ||||
−0.182772 | + | 0.983155i | \(0.558507\pi\) | |||||||
\(48\) | −2.80367 | −0.404675 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.80341 | −0.255041 | ||||||||
\(51\) | −4.17263 | −0.584284 | ||||||||
\(52\) | −8.84835 | −1.22705 | ||||||||
\(53\) | −5.52090 | −0.758353 | −0.379177 | − | 0.925324i | \(-0.623793\pi\) | ||||
−0.379177 | + | 0.925324i | \(0.623793\pi\) | |||||||
\(54\) | 5.81524 | 0.791355 | ||||||||
\(55\) | 0.253853 | 0.0342295 | ||||||||
\(56\) | −1.34841 | −0.180189 | ||||||||
\(57\) | −1.01333 | −0.134219 | ||||||||
\(58\) | 7.15675 | 0.939727 | ||||||||
\(59\) | −6.61859 | −0.861668 | −0.430834 | − | 0.902431i | \(-0.641780\pi\) | ||||
−0.430834 | + | 0.902431i | \(0.641780\pi\) | |||||||
\(60\) | 0.711264 | 0.0918238 | ||||||||
\(61\) | −5.87033 | −0.751618 | −0.375809 | − | 0.926697i | \(-0.622635\pi\) | ||||
−0.375809 | + | 0.926697i | \(0.622635\pi\) | |||||||
\(62\) | −16.8987 | −2.14613 | ||||||||
\(63\) | 2.67742 | 0.337323 | ||||||||
\(64\) | −1.31832 | −0.164790 | ||||||||
\(65\) | −7.06566 | −0.876388 | ||||||||
\(66\) | −0.260015 | −0.0320057 | ||||||||
\(67\) | −13.2937 | −1.62408 | −0.812039 | − | 0.583603i | \(-0.801642\pi\) | ||||
−0.812039 | + | 0.583603i | \(0.801642\pi\) | |||||||
\(68\) | −9.20019 | −1.11569 | ||||||||
\(69\) | −3.05256 | −0.367486 | ||||||||
\(70\) | 1.80341 | 0.215549 | ||||||||
\(71\) | 8.86571 | 1.05217 | 0.526083 | − | 0.850433i | \(-0.323660\pi\) | ||||
0.526083 | + | 0.850433i | \(0.323660\pi\) | |||||||
\(72\) | −3.61025 | −0.425472 | ||||||||
\(73\) | −14.8642 | −1.73973 | −0.869864 | − | 0.493291i | \(-0.835794\pi\) | ||||
−0.869864 | + | 0.493291i | \(0.835794\pi\) | |||||||
\(74\) | −12.1109 | −1.40786 | ||||||||
\(75\) | 0.567965 | 0.0655830 | ||||||||
\(76\) | −2.23429 | −0.256290 | ||||||||
\(77\) | −0.253853 | −0.0289292 | ||||||||
\(78\) | 7.23720 | 0.819451 | ||||||||
\(79\) | −1.02292 | −0.115088 | −0.0575438 | − | 0.998343i | \(-0.518327\pi\) | ||||
−0.0575438 | + | 0.998343i | \(0.518327\pi\) | |||||||
\(80\) | −4.93634 | −0.551900 | ||||||||
\(81\) | 6.20080 | 0.688978 | ||||||||
\(82\) | 14.0819 | 1.55508 | ||||||||
\(83\) | 13.5407 | 1.48628 | 0.743140 | − | 0.669136i | \(-0.233336\pi\) | ||||
0.743140 | + | 0.669136i | \(0.233336\pi\) | |||||||
\(84\) | −0.711264 | −0.0776053 | ||||||||
\(85\) | −7.34662 | −0.796853 | ||||||||
\(86\) | 20.6126 | 2.22271 | ||||||||
\(87\) | −2.25394 | −0.241648 | ||||||||
\(88\) | 0.342297 | 0.0364890 | ||||||||
\(89\) | 17.2815 | 1.83184 | 0.915920 | − | 0.401361i | \(-0.131463\pi\) | ||||
0.915920 | + | 0.401361i | \(0.131463\pi\) | |||||||
\(90\) | 4.82849 | 0.508967 | ||||||||
\(91\) | 7.06566 | 0.740683 | ||||||||
\(92\) | −6.73057 | −0.701711 | ||||||||
\(93\) | 5.32205 | 0.551871 | ||||||||
\(94\) | 4.51945 | 0.466145 | ||||||||
\(95\) | −1.78414 | −0.183049 | ||||||||
\(96\) | 3.52448 | 0.359716 | ||||||||
\(97\) | 9.22234 | 0.936387 | 0.468193 | − | 0.883626i | \(-0.344905\pi\) | ||||
0.468193 | + | 0.883626i | \(0.344905\pi\) | |||||||
\(98\) | −1.80341 | −0.182172 | ||||||||
\(99\) | −0.679669 | −0.0683093 | ||||||||
\(100\) | 1.25230 | 0.125230 | ||||||||
\(101\) | −14.5673 | −1.44950 | −0.724752 | − | 0.689010i | \(-0.758046\pi\) | ||||
−0.724752 | + | 0.689010i | \(0.758046\pi\) | |||||||
\(102\) | 7.52497 | 0.745083 | ||||||||
\(103\) | −0.709708 | −0.0699296 | −0.0349648 | − | 0.999389i | \(-0.511132\pi\) | ||||
−0.0349648 | + | 0.999389i | \(0.511132\pi\) | |||||||
\(104\) | −9.52740 | −0.934239 | ||||||||
\(105\) | −0.567965 | −0.0554277 | ||||||||
\(106\) | 9.95646 | 0.967057 | ||||||||
\(107\) | 19.5638 | 1.89130 | 0.945651 | − | 0.325182i | \(-0.105426\pi\) | ||||
0.945651 | + | 0.325182i | \(0.105426\pi\) | |||||||
\(108\) | −4.03814 | −0.388571 | ||||||||
\(109\) | 8.03820 | 0.769920 | 0.384960 | − | 0.922933i | \(-0.374215\pi\) | ||||
0.384960 | + | 0.922933i | \(0.374215\pi\) | |||||||
\(110\) | −0.457801 | −0.0436497 | ||||||||
\(111\) | 3.81418 | 0.362026 | ||||||||
\(112\) | 4.93634 | 0.466441 | ||||||||
\(113\) | 0.658377 | 0.0619349 | 0.0309674 | − | 0.999520i | \(-0.490141\pi\) | ||||
0.0309674 | + | 0.999520i | \(0.490141\pi\) | |||||||
\(114\) | 1.82746 | 0.171157 | ||||||||
\(115\) | −5.37456 | −0.501180 | ||||||||
\(116\) | −4.96969 | −0.461424 | ||||||||
\(117\) | 18.9177 | 1.74894 | ||||||||
\(118\) | 11.9361 | 1.09880 | ||||||||
\(119\) | 7.34662 | 0.673463 | ||||||||
\(120\) | 0.765849 | 0.0699122 | ||||||||
\(121\) | −10.9356 | −0.994142 | ||||||||
\(122\) | 10.5866 | 0.958468 | ||||||||
\(123\) | −4.43494 | −0.399885 | ||||||||
\(124\) | 11.7345 | 1.05379 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −4.82849 | −0.430156 | ||||||||
\(127\) | 14.3807 | 1.27608 | 0.638042 | − | 0.770001i | \(-0.279745\pi\) | ||||
0.638042 | + | 0.770001i | \(0.279745\pi\) | |||||||
\(128\) | −10.0334 | −0.886839 | ||||||||
\(129\) | −6.49170 | −0.571562 | ||||||||
\(130\) | 12.7423 | 1.11758 | ||||||||
\(131\) | 13.2094 | 1.15411 | 0.577053 | − | 0.816707i | \(-0.304203\pi\) | ||||
0.577053 | + | 0.816707i | \(0.304203\pi\) | |||||||
\(132\) | 0.180556 | 0.0157154 | ||||||||
\(133\) | 1.78414 | 0.154705 | ||||||||
\(134\) | 23.9740 | 2.07103 | ||||||||
\(135\) | −3.22458 | −0.277527 | ||||||||
\(136\) | −9.90624 | −0.849453 | ||||||||
\(137\) | 10.4819 | 0.895529 | 0.447765 | − | 0.894151i | \(-0.352220\pi\) | ||||
0.447765 | + | 0.894151i | \(0.352220\pi\) | |||||||
\(138\) | 5.50504 | 0.468620 | ||||||||
\(139\) | −2.18582 | −0.185399 | −0.0926996 | − | 0.995694i | \(-0.529550\pi\) | ||||
−0.0926996 | + | 0.995694i | \(0.529550\pi\) | |||||||
\(140\) | −1.25230 | −0.105839 | ||||||||
\(141\) | −1.42335 | −0.119868 | ||||||||
\(142\) | −15.9885 | −1.34173 | ||||||||
\(143\) | −1.79364 | −0.149992 | ||||||||
\(144\) | 13.2166 | 1.10139 | ||||||||
\(145\) | −3.96844 | −0.329561 | ||||||||
\(146\) | 26.8064 | 2.21851 | ||||||||
\(147\) | 0.567965 | 0.0468450 | ||||||||
\(148\) | 8.40986 | 0.691286 | ||||||||
\(149\) | −12.4453 | −1.01956 | −0.509778 | − | 0.860306i | \(-0.670272\pi\) | ||||
−0.509778 | + | 0.860306i | \(0.670272\pi\) | |||||||
\(150\) | −1.02428 | −0.0836319 | ||||||||
\(151\) | 10.3858 | 0.845185 | 0.422592 | − | 0.906320i | \(-0.361120\pi\) | ||||
0.422592 | + | 0.906320i | \(0.361120\pi\) | |||||||
\(152\) | −2.40575 | −0.195132 | ||||||||
\(153\) | 19.6699 | 1.59022 | ||||||||
\(154\) | 0.457801 | 0.0368907 | ||||||||
\(155\) | 9.37038 | 0.752647 | ||||||||
\(156\) | −5.02556 | −0.402367 | ||||||||
\(157\) | 0.764982 | 0.0610522 | 0.0305261 | − | 0.999534i | \(-0.490282\pi\) | ||||
0.0305261 | + | 0.999534i | \(0.490282\pi\) | |||||||
\(158\) | 1.84475 | 0.146760 | ||||||||
\(159\) | −3.13568 | −0.248675 | ||||||||
\(160\) | 6.20545 | 0.490584 | ||||||||
\(161\) | 5.37456 | 0.423575 | ||||||||
\(162\) | −11.1826 | −0.878589 | ||||||||
\(163\) | 0.501682 | 0.0392948 | 0.0196474 | − | 0.999807i | \(-0.493746\pi\) | ||||
0.0196474 | + | 0.999807i | \(0.493746\pi\) | |||||||
\(164\) | −9.77856 | −0.763577 | ||||||||
\(165\) | 0.144180 | 0.0112244 | ||||||||
\(166\) | −24.4194 | −1.89531 | ||||||||
\(167\) | 0.968483 | 0.0749435 | 0.0374717 | − | 0.999298i | \(-0.488070\pi\) | ||||
0.0374717 | + | 0.999298i | \(0.488070\pi\) | |||||||
\(168\) | −0.765849 | −0.0590866 | ||||||||
\(169\) | 36.9236 | 2.84028 | ||||||||
\(170\) | 13.2490 | 1.01615 | ||||||||
\(171\) | 4.77689 | 0.365298 | ||||||||
\(172\) | −14.3135 | −1.09139 | ||||||||
\(173\) | 2.40686 | 0.182990 | 0.0914952 | − | 0.995806i | \(-0.470835\pi\) | ||||
0.0914952 | + | 0.995806i | \(0.470835\pi\) | |||||||
\(174\) | 4.06478 | 0.308150 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | −1.25310 | −0.0944563 | ||||||||
\(177\) | −3.75913 | −0.282554 | ||||||||
\(178\) | −31.1658 | −2.33597 | ||||||||
\(179\) | 9.69352 | 0.724527 | 0.362264 | − | 0.932076i | \(-0.382004\pi\) | ||||
0.362264 | + | 0.932076i | \(0.382004\pi\) | |||||||
\(180\) | −3.35293 | −0.249913 | ||||||||
\(181\) | −5.19453 | −0.386106 | −0.193053 | − | 0.981188i | \(-0.561839\pi\) | ||||
−0.193053 | + | 0.981188i | \(0.561839\pi\) | |||||||
\(182\) | −12.7423 | −0.944524 | ||||||||
\(183\) | −3.33414 | −0.246467 | ||||||||
\(184\) | −7.24710 | −0.534263 | ||||||||
\(185\) | 6.71552 | 0.493735 | ||||||||
\(186\) | −9.59786 | −0.703749 | ||||||||
\(187\) | −1.86496 | −0.136379 | ||||||||
\(188\) | −3.13833 | −0.228886 | ||||||||
\(189\) | 3.22458 | 0.234553 | ||||||||
\(190\) | 3.21755 | 0.233426 | ||||||||
\(191\) | −14.0267 | −1.01494 | −0.507470 | − | 0.861670i | \(-0.669419\pi\) | ||||
−0.507470 | + | 0.861670i | \(0.669419\pi\) | |||||||
\(192\) | −0.748759 | −0.0540370 | ||||||||
\(193\) | −22.2322 | −1.60031 | −0.800154 | − | 0.599795i | \(-0.795249\pi\) | ||||
−0.800154 | + | 0.599795i | \(0.795249\pi\) | |||||||
\(194\) | −16.6317 | −1.19409 | ||||||||
\(195\) | −4.01305 | −0.287381 | ||||||||
\(196\) | 1.25230 | 0.0894502 | ||||||||
\(197\) | −15.4166 | −1.09839 | −0.549193 | − | 0.835696i | \(-0.685065\pi\) | ||||
−0.549193 | + | 0.835696i | \(0.685065\pi\) | |||||||
\(198\) | 1.22572 | 0.0871085 | ||||||||
\(199\) | 7.50923 | 0.532315 | 0.266157 | − | 0.963930i | \(-0.414246\pi\) | ||||
0.266157 | + | 0.963930i | \(0.414246\pi\) | |||||||
\(200\) | 1.34841 | 0.0953469 | ||||||||
\(201\) | −7.55033 | −0.532559 | ||||||||
\(202\) | 26.2709 | 1.84842 | ||||||||
\(203\) | 3.96844 | 0.278530 | ||||||||
\(204\) | −5.22539 | −0.365850 | ||||||||
\(205\) | −7.80846 | −0.545367 | ||||||||
\(206\) | 1.27990 | 0.0891747 | ||||||||
\(207\) | 14.3899 | 1.00017 | ||||||||
\(208\) | 34.8785 | 2.41839 | ||||||||
\(209\) | −0.452910 | −0.0313284 | ||||||||
\(210\) | 1.02428 | 0.0706818 | ||||||||
\(211\) | −15.0588 | −1.03669 | −0.518345 | − | 0.855172i | \(-0.673452\pi\) | ||||
−0.518345 | + | 0.855172i | \(0.673452\pi\) | |||||||
\(212\) | −6.91383 | −0.474844 | ||||||||
\(213\) | 5.03542 | 0.345021 | ||||||||
\(214\) | −35.2816 | −2.41180 | ||||||||
\(215\) | −11.4297 | −0.779502 | ||||||||
\(216\) | −4.34804 | −0.295847 | ||||||||
\(217\) | −9.37038 | −0.636103 | ||||||||
\(218\) | −14.4962 | −0.981806 | ||||||||
\(219\) | −8.44238 | −0.570483 | ||||||||
\(220\) | 0.317900 | 0.0214328 | ||||||||
\(221\) | 51.9087 | 3.49176 | ||||||||
\(222\) | −6.87855 | −0.461658 | ||||||||
\(223\) | 4.25426 | 0.284886 | 0.142443 | − | 0.989803i | \(-0.454504\pi\) | ||||
0.142443 | + | 0.989803i | \(0.454504\pi\) | |||||||
\(224\) | −6.20545 | −0.414619 | ||||||||
\(225\) | −2.67742 | −0.178494 | ||||||||
\(226\) | −1.18733 | −0.0789797 | ||||||||
\(227\) | 7.76371 | 0.515295 | 0.257648 | − | 0.966239i | \(-0.417053\pi\) | ||||
0.257648 | + | 0.966239i | \(0.417053\pi\) | |||||||
\(228\) | −1.26900 | −0.0840415 | ||||||||
\(229\) | −1.00000 | −0.0660819 | ||||||||
\(230\) | 9.69256 | 0.639108 | ||||||||
\(231\) | −0.144180 | −0.00948632 | ||||||||
\(232\) | −5.35108 | −0.351316 | ||||||||
\(233\) | −28.3137 | −1.85489 | −0.927447 | − | 0.373954i | \(-0.878002\pi\) | ||||
−0.927447 | + | 0.373954i | \(0.878002\pi\) | |||||||
\(234\) | −34.1165 | −2.23026 | ||||||||
\(235\) | −2.50605 | −0.163477 | ||||||||
\(236\) | −8.28848 | −0.539534 | ||||||||
\(237\) | −0.580983 | −0.0377389 | ||||||||
\(238\) | −13.2490 | −0.858805 | ||||||||
\(239\) | 6.04424 | 0.390969 | 0.195485 | − | 0.980707i | \(-0.437372\pi\) | ||||
0.195485 | + | 0.980707i | \(0.437372\pi\) | |||||||
\(240\) | −2.80367 | −0.180976 | ||||||||
\(241\) | −23.8746 | −1.53790 | −0.768949 | − | 0.639310i | \(-0.779220\pi\) | ||||
−0.768949 | + | 0.639310i | \(0.779220\pi\) | |||||||
\(242\) | 19.7213 | 1.26774 | ||||||||
\(243\) | 13.1956 | 0.846496 | ||||||||
\(244\) | −7.35142 | −0.470627 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 7.99803 | 0.509936 | ||||||||
\(247\) | 12.6062 | 0.802111 | ||||||||
\(248\) | 12.6351 | 0.802329 | ||||||||
\(249\) | 7.69063 | 0.487374 | ||||||||
\(250\) | −1.80341 | −0.114058 | ||||||||
\(251\) | 2.01974 | 0.127485 | 0.0637424 | − | 0.997966i | \(-0.479696\pi\) | ||||
0.0637424 | + | 0.997966i | \(0.479696\pi\) | |||||||
\(252\) | 3.35293 | 0.211215 | ||||||||
\(253\) | −1.36435 | −0.0857757 | ||||||||
\(254\) | −25.9344 | −1.62727 | ||||||||
\(255\) | −4.17263 | −0.261300 | ||||||||
\(256\) | 20.7311 | 1.29569 | ||||||||
\(257\) | 19.5485 | 1.21940 | 0.609700 | − | 0.792633i | \(-0.291290\pi\) | ||||
0.609700 | + | 0.792633i | \(0.291290\pi\) | |||||||
\(258\) | 11.7072 | 0.728860 | ||||||||
\(259\) | −6.71552 | −0.417282 | ||||||||
\(260\) | −8.84835 | −0.548751 | ||||||||
\(261\) | 10.6252 | 0.657681 | ||||||||
\(262\) | −23.8219 | −1.47172 | ||||||||
\(263\) | −5.36498 | −0.330819 | −0.165409 | − | 0.986225i | \(-0.552895\pi\) | ||||
−0.165409 | + | 0.986225i | \(0.552895\pi\) | |||||||
\(264\) | 0.194413 | 0.0119653 | ||||||||
\(265\) | −5.52090 | −0.339146 | ||||||||
\(266\) | −3.21755 | −0.197281 | ||||||||
\(267\) | 9.81532 | 0.600688 | ||||||||
\(268\) | −16.6477 | −1.01692 | ||||||||
\(269\) | −7.66329 | −0.467239 | −0.233619 | − | 0.972328i | \(-0.575057\pi\) | ||||
−0.233619 | + | 0.972328i | \(0.575057\pi\) | |||||||
\(270\) | 5.81524 | 0.353905 | ||||||||
\(271\) | 12.8071 | 0.777973 | 0.388987 | − | 0.921243i | \(-0.372825\pi\) | ||||
0.388987 | + | 0.921243i | \(0.372825\pi\) | |||||||
\(272\) | 36.2654 | 2.19891 | ||||||||
\(273\) | 4.01305 | 0.242881 | ||||||||
\(274\) | −18.9032 | −1.14198 | ||||||||
\(275\) | 0.253853 | 0.0153079 | ||||||||
\(276\) | −3.82273 | −0.230102 | ||||||||
\(277\) | 10.4276 | 0.626535 | 0.313267 | − | 0.949665i | \(-0.398576\pi\) | ||||
0.313267 | + | 0.949665i | \(0.398576\pi\) | |||||||
\(278\) | 3.94195 | 0.236422 | ||||||||
\(279\) | −25.0884 | −1.50200 | ||||||||
\(280\) | −1.34841 | −0.0805828 | ||||||||
\(281\) | −6.33500 | −0.377914 | −0.188957 | − | 0.981985i | \(-0.560511\pi\) | ||||
−0.188957 | + | 0.981985i | \(0.560511\pi\) | |||||||
\(282\) | 2.56689 | 0.152856 | ||||||||
\(283\) | −3.15301 | −0.187427 | −0.0937136 | − | 0.995599i | \(-0.529874\pi\) | ||||
−0.0937136 | + | 0.995599i | \(0.529874\pi\) | |||||||
\(284\) | 11.1025 | 0.658815 | ||||||||
\(285\) | −1.01333 | −0.0600246 | ||||||||
\(286\) | 3.23467 | 0.191270 | ||||||||
\(287\) | 7.80846 | 0.460919 | ||||||||
\(288\) | −16.6146 | −0.979023 | ||||||||
\(289\) | 36.9728 | 2.17487 | ||||||||
\(290\) | 7.15675 | 0.420259 | ||||||||
\(291\) | 5.23797 | 0.307055 | ||||||||
\(292\) | −18.6145 | −1.08933 | ||||||||
\(293\) | −11.1534 | −0.651588 | −0.325794 | − | 0.945441i | \(-0.605632\pi\) | ||||
−0.325794 | + | 0.945441i | \(0.605632\pi\) | |||||||
\(294\) | −1.02428 | −0.0597370 | ||||||||
\(295\) | −6.61859 | −0.385349 | ||||||||
\(296\) | 9.05526 | 0.526326 | ||||||||
\(297\) | −0.818567 | −0.0474981 | ||||||||
\(298\) | 22.4440 | 1.30014 | ||||||||
\(299\) | 37.9748 | 2.19614 | ||||||||
\(300\) | 0.711264 | 0.0410649 | ||||||||
\(301\) | 11.4297 | 0.658799 | ||||||||
\(302\) | −18.7299 | −1.07779 | ||||||||
\(303\) | −8.27374 | −0.475314 | ||||||||
\(304\) | 8.80715 | 0.505125 | ||||||||
\(305\) | −5.87033 | −0.336134 | ||||||||
\(306\) | −35.4731 | −2.02786 | ||||||||
\(307\) | −1.40775 | −0.0803444 | −0.0401722 | − | 0.999193i | \(-0.512791\pi\) | ||||
−0.0401722 | + | 0.999193i | \(0.512791\pi\) | |||||||
\(308\) | −0.317900 | −0.0181141 | ||||||||
\(309\) | −0.403090 | −0.0229310 | ||||||||
\(310\) | −16.8987 | −0.959780 | ||||||||
\(311\) | 23.4586 | 1.33022 | 0.665109 | − | 0.746747i | \(-0.268385\pi\) | ||||
0.665109 | + | 0.746747i | \(0.268385\pi\) | |||||||
\(312\) | −5.41123 | −0.306351 | ||||||||
\(313\) | 13.2095 | 0.746644 | 0.373322 | − | 0.927702i | \(-0.378219\pi\) | ||||
0.373322 | + | 0.927702i | \(0.378219\pi\) | |||||||
\(314\) | −1.37958 | −0.0778541 | ||||||||
\(315\) | 2.67742 | 0.150855 | ||||||||
\(316\) | −1.28101 | −0.0720622 | ||||||||
\(317\) | −12.8949 | −0.724249 | −0.362125 | − | 0.932130i | \(-0.617949\pi\) | ||||
−0.362125 | + | 0.932130i | \(0.617949\pi\) | |||||||
\(318\) | 5.65493 | 0.317112 | ||||||||
\(319\) | −1.00740 | −0.0564036 | ||||||||
\(320\) | −1.31832 | −0.0736962 | ||||||||
\(321\) | 11.1116 | 0.620187 | ||||||||
\(322\) | −9.69256 | −0.540145 | ||||||||
\(323\) | 13.1074 | 0.729317 | ||||||||
\(324\) | 7.76528 | 0.431404 | ||||||||
\(325\) | −7.06566 | −0.391933 | ||||||||
\(326\) | −0.904741 | −0.0501089 | ||||||||
\(327\) | 4.56542 | 0.252468 | ||||||||
\(328\) | −10.5290 | −0.581367 | ||||||||
\(329\) | 2.50605 | 0.138163 | ||||||||
\(330\) | −0.260015 | −0.0143134 | ||||||||
\(331\) | −6.57737 | −0.361525 | −0.180763 | − | 0.983527i | \(-0.557857\pi\) | ||||
−0.180763 | + | 0.983527i | \(0.557857\pi\) | |||||||
\(332\) | 16.9570 | 0.930636 | ||||||||
\(333\) | −17.9802 | −0.985311 | ||||||||
\(334\) | −1.74658 | −0.0955684 | ||||||||
\(335\) | −13.2937 | −0.726310 | ||||||||
\(336\) | 2.80367 | 0.152953 | ||||||||
\(337\) | −3.37880 | −0.184055 | −0.0920274 | − | 0.995756i | \(-0.529335\pi\) | ||||
−0.0920274 | + | 0.995756i | \(0.529335\pi\) | |||||||
\(338\) | −66.5886 | −3.62194 | ||||||||
\(339\) | 0.373935 | 0.0203094 | ||||||||
\(340\) | −9.20019 | −0.498950 | ||||||||
\(341\) | 2.37870 | 0.128814 | ||||||||
\(342\) | −8.61472 | −0.465831 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −15.4120 | −0.830957 | ||||||||
\(345\) | −3.05256 | −0.164345 | ||||||||
\(346\) | −4.34057 | −0.233351 | ||||||||
\(347\) | −25.4638 | −1.36697 | −0.683486 | − | 0.729964i | \(-0.739537\pi\) | ||||
−0.683486 | + | 0.729964i | \(0.739537\pi\) | |||||||
\(348\) | −2.82261 | −0.151308 | ||||||||
\(349\) | 1.60360 | 0.0858385 | 0.0429192 | − | 0.999079i | \(-0.486334\pi\) | ||||
0.0429192 | + | 0.999079i | \(0.486334\pi\) | |||||||
\(350\) | 1.80341 | 0.0963965 | ||||||||
\(351\) | 22.7838 | 1.21611 | ||||||||
\(352\) | 1.57527 | 0.0839622 | ||||||||
\(353\) | −34.4552 | −1.83386 | −0.916932 | − | 0.399043i | \(-0.869342\pi\) | ||||
−0.916932 | + | 0.399043i | \(0.869342\pi\) | |||||||
\(354\) | 6.77927 | 0.360314 | ||||||||
\(355\) | 8.86571 | 0.470543 | ||||||||
\(356\) | 21.6417 | 1.14701 | ||||||||
\(357\) | 4.17263 | 0.220839 | ||||||||
\(358\) | −17.4814 | −0.923922 | ||||||||
\(359\) | 1.57037 | 0.0828812 | 0.0414406 | − | 0.999141i | \(-0.486805\pi\) | ||||
0.0414406 | + | 0.999141i | \(0.486805\pi\) | |||||||
\(360\) | −3.61025 | −0.190277 | ||||||||
\(361\) | −15.8168 | −0.832465 | ||||||||
\(362\) | 9.36789 | 0.492365 | ||||||||
\(363\) | −6.21102 | −0.325994 | ||||||||
\(364\) | 8.84835 | 0.463779 | ||||||||
\(365\) | −14.8642 | −0.778030 | ||||||||
\(366\) | 6.01284 | 0.314296 | ||||||||
\(367\) | 25.4214 | 1.32699 | 0.663494 | − | 0.748182i | \(-0.269073\pi\) | ||||
0.663494 | + | 0.748182i | \(0.269073\pi\) | |||||||
\(368\) | 26.5307 | 1.38301 | ||||||||
\(369\) | 20.9065 | 1.08835 | ||||||||
\(370\) | −12.1109 | −0.629614 | ||||||||
\(371\) | 5.52090 | 0.286631 | ||||||||
\(372\) | 6.66482 | 0.345555 | ||||||||
\(373\) | −15.2820 | −0.791272 | −0.395636 | − | 0.918407i | \(-0.629476\pi\) | ||||
−0.395636 | + | 0.918407i | \(0.629476\pi\) | |||||||
\(374\) | 3.36329 | 0.173912 | ||||||||
\(375\) | 0.567965 | 0.0293296 | ||||||||
\(376\) | −3.37918 | −0.174268 | ||||||||
\(377\) | 28.0397 | 1.44412 | ||||||||
\(378\) | −5.81524 | −0.299104 | ||||||||
\(379\) | −23.7391 | −1.21940 | −0.609698 | − | 0.792634i | \(-0.708709\pi\) | ||||
−0.609698 | + | 0.792634i | \(0.708709\pi\) | |||||||
\(380\) | −2.23429 | −0.114617 | ||||||||
\(381\) | 8.16776 | 0.418447 | ||||||||
\(382\) | 25.2960 | 1.29426 | ||||||||
\(383\) | −19.3996 | −0.991271 | −0.495636 | − | 0.868531i | \(-0.665065\pi\) | ||||
−0.495636 | + | 0.868531i | \(0.665065\pi\) | |||||||
\(384\) | −5.69865 | −0.290808 | ||||||||
\(385\) | −0.253853 | −0.0129375 | ||||||||
\(386\) | 40.0938 | 2.04072 | ||||||||
\(387\) | 30.6022 | 1.55560 | ||||||||
\(388\) | 11.5492 | 0.586320 | ||||||||
\(389\) | 14.5046 | 0.735413 | 0.367707 | − | 0.929942i | \(-0.380143\pi\) | ||||
0.367707 | + | 0.929942i | \(0.380143\pi\) | |||||||
\(390\) | 7.23720 | 0.366470 | ||||||||
\(391\) | 39.4848 | 1.99683 | ||||||||
\(392\) | 1.34841 | 0.0681049 | ||||||||
\(393\) | 7.50245 | 0.378449 | ||||||||
\(394\) | 27.8025 | 1.40067 | ||||||||
\(395\) | −1.02292 | −0.0514687 | ||||||||
\(396\) | −0.851151 | −0.0427720 | ||||||||
\(397\) | −10.3232 | −0.518107 | −0.259054 | − | 0.965863i | \(-0.583411\pi\) | ||||
−0.259054 | + | 0.965863i | \(0.583411\pi\) | |||||||
\(398\) | −13.5422 | −0.678811 | ||||||||
\(399\) | 1.01333 | 0.0507301 | ||||||||
\(400\) | −4.93634 | −0.246817 | ||||||||
\(401\) | −12.7331 | −0.635863 | −0.317931 | − | 0.948114i | \(-0.602988\pi\) | ||||
−0.317931 | + | 0.948114i | \(0.602988\pi\) | |||||||
\(402\) | 13.6164 | 0.679123 | ||||||||
\(403\) | −66.2080 | −3.29805 | ||||||||
\(404\) | −18.2427 | −0.907609 | ||||||||
\(405\) | 6.20080 | 0.308120 | ||||||||
\(406\) | −7.15675 | −0.355183 | ||||||||
\(407\) | 1.70475 | 0.0845015 | ||||||||
\(408\) | −5.62640 | −0.278548 | ||||||||
\(409\) | 10.2733 | 0.507982 | 0.253991 | − | 0.967207i | \(-0.418257\pi\) | ||||
0.253991 | + | 0.967207i | \(0.418257\pi\) | |||||||
\(410\) | 14.0819 | 0.695455 | ||||||||
\(411\) | 5.95336 | 0.293658 | ||||||||
\(412\) | −0.888769 | −0.0437865 | ||||||||
\(413\) | 6.61859 | 0.325680 | ||||||||
\(414\) | −25.9510 | −1.27542 | ||||||||
\(415\) | 13.5407 | 0.664685 | ||||||||
\(416\) | −43.8457 | −2.14971 | ||||||||
\(417\) | −1.24147 | −0.0607952 | ||||||||
\(418\) | 0.816784 | 0.0399502 | ||||||||
\(419\) | 8.89787 | 0.434690 | 0.217345 | − | 0.976095i | \(-0.430260\pi\) | ||||
0.217345 | + | 0.976095i | \(0.430260\pi\) | |||||||
\(420\) | −0.711264 | −0.0347062 | ||||||||
\(421\) | −29.6287 | −1.44402 | −0.722008 | − | 0.691884i | \(-0.756781\pi\) | ||||
−0.722008 | + | 0.691884i | \(0.756781\pi\) | |||||||
\(422\) | 27.1572 | 1.32199 | ||||||||
\(423\) | 6.70974 | 0.326239 | ||||||||
\(424\) | −7.44442 | −0.361533 | ||||||||
\(425\) | −7.34662 | −0.356363 | ||||||||
\(426\) | −9.08094 | −0.439973 | ||||||||
\(427\) | 5.87033 | 0.284085 | ||||||||
\(428\) | 24.4998 | 1.18424 | ||||||||
\(429\) | −1.01872 | −0.0491845 | ||||||||
\(430\) | 20.6126 | 0.994026 | ||||||||
\(431\) | −17.9586 | −0.865035 | −0.432518 | − | 0.901625i | \(-0.642375\pi\) | ||||
−0.432518 | + | 0.901625i | \(0.642375\pi\) | |||||||
\(432\) | 15.9176 | 0.765836 | ||||||||
\(433\) | 37.4614 | 1.80028 | 0.900140 | − | 0.435601i | \(-0.143464\pi\) | ||||
0.900140 | + | 0.435601i | \(0.143464\pi\) | |||||||
\(434\) | 16.8987 | 0.811162 | ||||||||
\(435\) | −2.25394 | −0.108068 | ||||||||
\(436\) | 10.0663 | 0.482086 | ||||||||
\(437\) | 9.58899 | 0.458703 | ||||||||
\(438\) | 15.2251 | 0.727483 | ||||||||
\(439\) | 0.904570 | 0.0431728 | 0.0215864 | − | 0.999767i | \(-0.493128\pi\) | ||||
0.0215864 | + | 0.999767i | \(0.493128\pi\) | |||||||
\(440\) | 0.342297 | 0.0163184 | ||||||||
\(441\) | −2.67742 | −0.127496 | ||||||||
\(442\) | −93.6130 | −4.45271 | ||||||||
\(443\) | −34.6171 | −1.64471 | −0.822354 | − | 0.568976i | \(-0.807340\pi\) | ||||
−0.822354 | + | 0.568976i | \(0.807340\pi\) | |||||||
\(444\) | 4.77651 | 0.226683 | ||||||||
\(445\) | 17.2815 | 0.819224 | ||||||||
\(446\) | −7.67219 | −0.363289 | ||||||||
\(447\) | −7.06848 | −0.334327 | ||||||||
\(448\) | 1.31832 | 0.0622847 | ||||||||
\(449\) | 20.3977 | 0.962628 | 0.481314 | − | 0.876548i | \(-0.340160\pi\) | ||||
0.481314 | + | 0.876548i | \(0.340160\pi\) | |||||||
\(450\) | 4.82849 | 0.227617 | ||||||||
\(451\) | −1.98220 | −0.0933381 | ||||||||
\(452\) | 0.824487 | 0.0387806 | ||||||||
\(453\) | 5.89878 | 0.277149 | ||||||||
\(454\) | −14.0012 | −0.657108 | ||||||||
\(455\) | 7.06566 | 0.331243 | ||||||||
\(456\) | −1.36639 | −0.0639869 | ||||||||
\(457\) | 20.4069 | 0.954595 | 0.477298 | − | 0.878742i | \(-0.341616\pi\) | ||||
0.477298 | + | 0.878742i | \(0.341616\pi\) | |||||||
\(458\) | 1.80341 | 0.0842680 | ||||||||
\(459\) | 23.6897 | 1.10574 | ||||||||
\(460\) | −6.73057 | −0.313815 | ||||||||
\(461\) | 11.9880 | 0.558337 | 0.279168 | − | 0.960242i | \(-0.409941\pi\) | ||||
0.279168 | + | 0.960242i | \(0.409941\pi\) | |||||||
\(462\) | 0.260015 | 0.0120970 | ||||||||
\(463\) | 39.7677 | 1.84816 | 0.924080 | − | 0.382200i | \(-0.124833\pi\) | ||||
0.924080 | + | 0.382200i | \(0.124833\pi\) | |||||||
\(464\) | 19.5896 | 0.909424 | ||||||||
\(465\) | 5.32205 | 0.246804 | ||||||||
\(466\) | 51.0614 | 2.36537 | ||||||||
\(467\) | −32.1054 | −1.48566 | −0.742831 | − | 0.669479i | \(-0.766517\pi\) | ||||
−0.742831 | + | 0.669479i | \(0.766517\pi\) | |||||||
\(468\) | 23.6907 | 1.09510 | ||||||||
\(469\) | 13.2937 | 0.613844 | ||||||||
\(470\) | 4.51945 | 0.208466 | ||||||||
\(471\) | 0.434483 | 0.0200199 | ||||||||
\(472\) | −8.92457 | −0.410787 | ||||||||
\(473\) | −2.90147 | −0.133410 | ||||||||
\(474\) | 1.04775 | 0.0481249 | ||||||||
\(475\) | −1.78414 | −0.0818621 | ||||||||
\(476\) | 9.20019 | 0.421690 | ||||||||
\(477\) | 14.7817 | 0.676809 | ||||||||
\(478\) | −10.9003 | −0.498566 | ||||||||
\(479\) | 36.0297 | 1.64624 | 0.823120 | − | 0.567867i | \(-0.192231\pi\) | ||||
0.823120 | + | 0.567867i | \(0.192231\pi\) | |||||||
\(480\) | 3.52448 | 0.160870 | ||||||||
\(481\) | −47.4496 | −2.16352 | ||||||||
\(482\) | 43.0558 | 1.96114 | ||||||||
\(483\) | 3.05256 | 0.138896 | ||||||||
\(484\) | −13.6946 | −0.622483 | ||||||||
\(485\) | 9.22234 | 0.418765 | ||||||||
\(486\) | −23.7971 | −1.07946 | ||||||||
\(487\) | 16.9768 | 0.769292 | 0.384646 | − | 0.923064i | \(-0.374324\pi\) | ||||
0.384646 | + | 0.923064i | \(0.374324\pi\) | |||||||
\(488\) | −7.91560 | −0.358322 | ||||||||
\(489\) | 0.284938 | 0.0128853 | ||||||||
\(490\) | −1.80341 | −0.0814699 | ||||||||
\(491\) | 27.7877 | 1.25404 | 0.627021 | − | 0.779002i | \(-0.284274\pi\) | ||||
0.627021 | + | 0.779002i | \(0.284274\pi\) | |||||||
\(492\) | −5.55388 | −0.250388 | ||||||||
\(493\) | 29.1546 | 1.31306 | ||||||||
\(494\) | −22.7341 | −1.02286 | ||||||||
\(495\) | −0.679669 | −0.0305488 | ||||||||
\(496\) | −46.2554 | −2.07693 | ||||||||
\(497\) | −8.86571 | −0.397681 | ||||||||
\(498\) | −13.8694 | −0.621502 | ||||||||
\(499\) | −23.9852 | −1.07373 | −0.536863 | − | 0.843669i | \(-0.680391\pi\) | ||||
−0.536863 | + | 0.843669i | \(0.680391\pi\) | |||||||
\(500\) | 1.25230 | 0.0560047 | ||||||||
\(501\) | 0.550065 | 0.0245751 | ||||||||
\(502\) | −3.64243 | −0.162569 | ||||||||
\(503\) | 14.9662 | 0.667311 | 0.333656 | − | 0.942695i | \(-0.391718\pi\) | ||||
0.333656 | + | 0.942695i | \(0.391718\pi\) | |||||||
\(504\) | 3.61025 | 0.160813 | ||||||||
\(505\) | −14.5673 | −0.648238 | ||||||||
\(506\) | 2.46048 | 0.109382 | ||||||||
\(507\) | 20.9713 | 0.931370 | ||||||||
\(508\) | 18.0090 | 0.799022 | ||||||||
\(509\) | −29.2357 | −1.29585 | −0.647925 | − | 0.761704i | \(-0.724363\pi\) | ||||
−0.647925 | + | 0.761704i | \(0.724363\pi\) | |||||||
\(510\) | 7.52497 | 0.333211 | ||||||||
\(511\) | 14.8642 | 0.657555 | ||||||||
\(512\) | −17.3198 | −0.765436 | ||||||||
\(513\) | 5.75311 | 0.254006 | ||||||||
\(514\) | −35.2540 | −1.55499 | ||||||||
\(515\) | −0.709708 | −0.0312735 | ||||||||
\(516\) | −8.12957 | −0.357884 | ||||||||
\(517\) | −0.636167 | −0.0279786 | ||||||||
\(518\) | 12.1109 | 0.532121 | ||||||||
\(519\) | 1.36702 | 0.0600053 | ||||||||
\(520\) | −9.52740 | −0.417804 | ||||||||
\(521\) | −34.8313 | −1.52599 | −0.762993 | − | 0.646407i | \(-0.776271\pi\) | ||||
−0.762993 | + | 0.646407i | \(0.776271\pi\) | |||||||
\(522\) | −19.1616 | −0.838680 | ||||||||
\(523\) | −7.95100 | −0.347673 | −0.173836 | − | 0.984775i | \(-0.555616\pi\) | ||||
−0.173836 | + | 0.984775i | \(0.555616\pi\) | |||||||
\(524\) | 16.5421 | 0.722645 | ||||||||
\(525\) | −0.567965 | −0.0247880 | ||||||||
\(526\) | 9.67528 | 0.421862 | ||||||||
\(527\) | −68.8406 | −2.99874 | ||||||||
\(528\) | −0.711720 | −0.0309736 | ||||||||
\(529\) | 5.88589 | 0.255908 | ||||||||
\(530\) | 9.95646 | 0.432481 | ||||||||
\(531\) | 17.7207 | 0.769014 | ||||||||
\(532\) | 2.23429 | 0.0968687 | ||||||||
\(533\) | 55.1720 | 2.38976 | ||||||||
\(534\) | −17.7011 | −0.766001 | ||||||||
\(535\) | 19.5638 | 0.845816 | ||||||||
\(536\) | −17.9253 | −0.774254 | ||||||||
\(537\) | 5.50558 | 0.237583 | ||||||||
\(538\) | 13.8201 | 0.595826 | ||||||||
\(539\) | 0.253853 | 0.0109342 | ||||||||
\(540\) | −4.03814 | −0.173774 | ||||||||
\(541\) | 3.48210 | 0.149707 | 0.0748536 | − | 0.997195i | \(-0.476151\pi\) | ||||
0.0748536 | + | 0.997195i | \(0.476151\pi\) | |||||||
\(542\) | −23.0964 | −0.992077 | ||||||||
\(543\) | −2.95031 | −0.126610 | ||||||||
\(544\) | −45.5891 | −1.95462 | ||||||||
\(545\) | 8.03820 | 0.344318 | ||||||||
\(546\) | −7.23720 | −0.309723 | ||||||||
\(547\) | −11.2402 | −0.480595 | −0.240297 | − | 0.970699i | \(-0.577245\pi\) | ||||
−0.240297 | + | 0.970699i | \(0.577245\pi\) | |||||||
\(548\) | 13.1265 | 0.560737 | ||||||||
\(549\) | 15.7173 | 0.670798 | ||||||||
\(550\) | −0.457801 | −0.0195207 | ||||||||
\(551\) | 7.08027 | 0.301630 | ||||||||
\(552\) | −4.11610 | −0.175193 | ||||||||
\(553\) | 1.02292 | 0.0434990 | ||||||||
\(554\) | −18.8053 | −0.798961 | ||||||||
\(555\) | 3.81418 | 0.161903 | ||||||||
\(556\) | −2.73731 | −0.116088 | ||||||||
\(557\) | −37.4053 | −1.58491 | −0.792457 | − | 0.609928i | \(-0.791198\pi\) | ||||
−0.792457 | + | 0.609928i | \(0.791198\pi\) | |||||||
\(558\) | 45.2448 | 1.91536 | ||||||||
\(559\) | 80.7587 | 3.41573 | ||||||||
\(560\) | 4.93634 | 0.208599 | ||||||||
\(561\) | −1.05923 | −0.0447208 | ||||||||
\(562\) | 11.4246 | 0.481919 | ||||||||
\(563\) | −29.1825 | −1.22990 | −0.614948 | − | 0.788568i | \(-0.710823\pi\) | ||||
−0.614948 | + | 0.788568i | \(0.710823\pi\) | |||||||
\(564\) | −1.78246 | −0.0750553 | ||||||||
\(565\) | 0.658377 | 0.0276981 | ||||||||
\(566\) | 5.68619 | 0.239008 | ||||||||
\(567\) | −6.20080 | −0.260409 | ||||||||
\(568\) | 11.9546 | 0.501604 | ||||||||
\(569\) | −30.9907 | −1.29920 | −0.649598 | − | 0.760278i | \(-0.725063\pi\) | ||||
−0.649598 | + | 0.760278i | \(0.725063\pi\) | |||||||
\(570\) | 1.82746 | 0.0765438 | ||||||||
\(571\) | −4.33137 | −0.181262 | −0.0906312 | − | 0.995885i | \(-0.528888\pi\) | ||||
−0.0906312 | + | 0.995885i | \(0.528888\pi\) | |||||||
\(572\) | −2.24618 | −0.0939174 | ||||||||
\(573\) | −7.96671 | −0.332814 | ||||||||
\(574\) | −14.0819 | −0.587767 | ||||||||
\(575\) | −5.37456 | −0.224135 | ||||||||
\(576\) | 3.52968 | 0.147070 | ||||||||
\(577\) | 31.9870 | 1.33164 | 0.665819 | − | 0.746114i | \(-0.268082\pi\) | ||||
0.665819 | + | 0.746114i | \(0.268082\pi\) | |||||||
\(578\) | −66.6773 | −2.77341 | ||||||||
\(579\) | −12.6271 | −0.524765 | ||||||||
\(580\) | −4.96969 | −0.206355 | ||||||||
\(581\) | −13.5407 | −0.561761 | ||||||||
\(582\) | −9.44623 | −0.391559 | ||||||||
\(583\) | −1.40149 | −0.0580440 | ||||||||
\(584\) | −20.0431 | −0.829388 | ||||||||
\(585\) | 18.9177 | 0.782151 | ||||||||
\(586\) | 20.1142 | 0.830909 | ||||||||
\(587\) | 27.7099 | 1.14371 | 0.571854 | − | 0.820355i | \(-0.306224\pi\) | ||||
0.571854 | + | 0.820355i | \(0.306224\pi\) | |||||||
\(588\) | 0.711264 | 0.0293321 | ||||||||
\(589\) | −16.7181 | −0.688857 | ||||||||
\(590\) | 11.9361 | 0.491400 | ||||||||
\(591\) | −8.75608 | −0.360177 | ||||||||
\(592\) | −33.1501 | −1.36246 | ||||||||
\(593\) | 0.498493 | 0.0204706 | 0.0102353 | − | 0.999948i | \(-0.496742\pi\) | ||||
0.0102353 | + | 0.999948i | \(0.496742\pi\) | |||||||
\(594\) | 1.47622 | 0.0605699 | ||||||||
\(595\) | 7.34662 | 0.301182 | ||||||||
\(596\) | −15.5852 | −0.638396 | ||||||||
\(597\) | 4.26498 | 0.174554 | ||||||||
\(598\) | −68.4844 | −2.80053 | ||||||||
\(599\) | 34.4666 | 1.40827 | 0.704133 | − | 0.710068i | \(-0.251336\pi\) | ||||
0.704133 | + | 0.710068i | \(0.251336\pi\) | |||||||
\(600\) | 0.765849 | 0.0312657 | ||||||||
\(601\) | 6.82090 | 0.278230 | 0.139115 | − | 0.990276i | \(-0.455574\pi\) | ||||
0.139115 | + | 0.990276i | \(0.455574\pi\) | |||||||
\(602\) | −20.6126 | −0.840105 | ||||||||
\(603\) | 35.5926 | 1.44944 | ||||||||
\(604\) | 13.0062 | 0.529214 | ||||||||
\(605\) | −10.9356 | −0.444594 | ||||||||
\(606\) | 14.9210 | 0.606124 | ||||||||
\(607\) | 2.96205 | 0.120226 | 0.0601130 | − | 0.998192i | \(-0.480854\pi\) | ||||
0.0601130 | + | 0.998192i | \(0.480854\pi\) | |||||||
\(608\) | −11.0714 | −0.449006 | ||||||||
\(609\) | 2.25394 | 0.0913342 | ||||||||
\(610\) | 10.5866 | 0.428640 | ||||||||
\(611\) | 17.7069 | 0.716345 | ||||||||
\(612\) | 24.6327 | 0.995719 | ||||||||
\(613\) | −36.5458 | −1.47607 | −0.738035 | − | 0.674763i | \(-0.764246\pi\) | ||||
−0.738035 | + | 0.674763i | \(0.764246\pi\) | |||||||
\(614\) | 2.53875 | 0.102456 | ||||||||
\(615\) | −4.43494 | −0.178834 | ||||||||
\(616\) | −0.342297 | −0.0137915 | ||||||||
\(617\) | −22.4788 | −0.904963 | −0.452482 | − | 0.891774i | \(-0.649461\pi\) | ||||
−0.452482 | + | 0.891774i | \(0.649461\pi\) | |||||||
\(618\) | 0.726938 | 0.0292417 | ||||||||
\(619\) | 21.9558 | 0.882476 | 0.441238 | − | 0.897390i | \(-0.354539\pi\) | ||||
0.441238 | + | 0.897390i | \(0.354539\pi\) | |||||||
\(620\) | 11.7345 | 0.471271 | ||||||||
\(621\) | 17.3307 | 0.695456 | ||||||||
\(622\) | −42.3056 | −1.69630 | ||||||||
\(623\) | −17.2815 | −0.692370 | ||||||||
\(624\) | 19.8098 | 0.793027 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −23.8222 | −0.952125 | ||||||||
\(627\) | −0.257237 | −0.0102731 | ||||||||
\(628\) | 0.957988 | 0.0382279 | ||||||||
\(629\) | −49.3364 | −1.96717 | ||||||||
\(630\) | −4.82849 | −0.192372 | ||||||||
\(631\) | 4.94928 | 0.197028 | 0.0985139 | − | 0.995136i | \(-0.468591\pi\) | ||||
0.0985139 | + | 0.995136i | \(0.468591\pi\) | |||||||
\(632\) | −1.37931 | −0.0548662 | ||||||||
\(633\) | −8.55287 | −0.339946 | ||||||||
\(634\) | 23.2548 | 0.923568 | ||||||||
\(635\) | 14.3807 | 0.570682 | ||||||||
\(636\) | −3.92682 | −0.155708 | ||||||||
\(637\) | −7.06566 | −0.279952 | ||||||||
\(638\) | 1.81676 | 0.0719262 | ||||||||
\(639\) | −23.7372 | −0.939028 | ||||||||
\(640\) | −10.0334 | −0.396606 | ||||||||
\(641\) | −28.4431 | −1.12343 | −0.561717 | − | 0.827329i | \(-0.689859\pi\) | ||||
−0.561717 | + | 0.827329i | \(0.689859\pi\) | |||||||
\(642\) | −20.0387 | −0.790866 | ||||||||
\(643\) | −14.2150 | −0.560583 | −0.280291 | − | 0.959915i | \(-0.590431\pi\) | ||||
−0.280291 | + | 0.959915i | \(0.590431\pi\) | |||||||
\(644\) | 6.73057 | 0.265222 | ||||||||
\(645\) | −6.49170 | −0.255610 | ||||||||
\(646\) | −23.6381 | −0.930029 | ||||||||
\(647\) | 31.7896 | 1.24978 | 0.624889 | − | 0.780714i | \(-0.285144\pi\) | ||||
0.624889 | + | 0.780714i | \(0.285144\pi\) | |||||||
\(648\) | 8.36121 | 0.328459 | ||||||||
\(649\) | −1.68015 | −0.0659516 | ||||||||
\(650\) | 12.7423 | 0.499795 | ||||||||
\(651\) | −5.32205 | −0.208588 | ||||||||
\(652\) | 0.628258 | 0.0246045 | ||||||||
\(653\) | −7.21747 | −0.282441 | −0.141221 | − | 0.989978i | \(-0.545103\pi\) | ||||
−0.141221 | + | 0.989978i | \(0.545103\pi\) | |||||||
\(654\) | −8.23334 | −0.321949 | ||||||||
\(655\) | 13.2094 | 0.516132 | ||||||||
\(656\) | 38.5453 | 1.50494 | ||||||||
\(657\) | 39.7978 | 1.55266 | ||||||||
\(658\) | −4.51945 | −0.176186 | ||||||||
\(659\) | 28.9949 | 1.12948 | 0.564740 | − | 0.825269i | \(-0.308977\pi\) | ||||
0.564740 | + | 0.825269i | \(0.308977\pi\) | |||||||
\(660\) | 0.180556 | 0.00702815 | ||||||||
\(661\) | −2.87854 | −0.111962 | −0.0559811 | − | 0.998432i | \(-0.517829\pi\) | ||||
−0.0559811 | + | 0.998432i | \(0.517829\pi\) | |||||||
\(662\) | 11.8617 | 0.461019 | ||||||||
\(663\) | 29.4824 | 1.14500 | ||||||||
\(664\) | 18.2583 | 0.708561 | ||||||||
\(665\) | 1.78414 | 0.0691861 | ||||||||
\(666\) | 32.4258 | 1.25647 | ||||||||
\(667\) | 21.3286 | 0.825848 | ||||||||
\(668\) | 1.21283 | 0.0469259 | ||||||||
\(669\) | 2.41627 | 0.0934184 | ||||||||
\(670\) | 23.9740 | 0.926195 | ||||||||
\(671\) | −1.49020 | −0.0575285 | ||||||||
\(672\) | −3.52448 | −0.135960 | ||||||||
\(673\) | 10.0989 | 0.389285 | 0.194643 | − | 0.980874i | \(-0.437645\pi\) | ||||
0.194643 | + | 0.980874i | \(0.437645\pi\) | |||||||
\(674\) | 6.09337 | 0.234708 | ||||||||
\(675\) | −3.22458 | −0.124114 | ||||||||
\(676\) | 46.2395 | 1.77844 | ||||||||
\(677\) | 8.93629 | 0.343450 | 0.171725 | − | 0.985145i | \(-0.445066\pi\) | ||||
0.171725 | + | 0.985145i | \(0.445066\pi\) | |||||||
\(678\) | −0.674360 | −0.0258986 | ||||||||
\(679\) | −9.22234 | −0.353921 | ||||||||
\(680\) | −9.90624 | −0.379887 | ||||||||
\(681\) | 4.40952 | 0.168973 | ||||||||
\(682\) | −4.28977 | −0.164264 | ||||||||
\(683\) | −31.6623 | −1.21152 | −0.605761 | − | 0.795646i | \(-0.707131\pi\) | ||||
−0.605761 | + | 0.795646i | \(0.707131\pi\) | |||||||
\(684\) | 5.98212 | 0.228732 | ||||||||
\(685\) | 10.4819 | 0.400493 | ||||||||
\(686\) | 1.80341 | 0.0688547 | ||||||||
\(687\) | −0.567965 | −0.0216692 | ||||||||
\(688\) | 56.4211 | 2.15104 | ||||||||
\(689\) | 39.0088 | 1.48612 | ||||||||
\(690\) | 5.50504 | 0.209573 | ||||||||
\(691\) | 0.532114 | 0.0202426 | 0.0101213 | − | 0.999949i | \(-0.496778\pi\) | ||||
0.0101213 | + | 0.999949i | \(0.496778\pi\) | |||||||
\(692\) | 3.01412 | 0.114580 | ||||||||
\(693\) | 0.679669 | 0.0258185 | ||||||||
\(694\) | 45.9219 | 1.74317 | ||||||||
\(695\) | −2.18582 | −0.0829130 | ||||||||
\(696\) | −3.03923 | −0.115202 | ||||||||
\(697\) | 57.3658 | 2.17288 | ||||||||
\(698\) | −2.89195 | −0.109462 | ||||||||
\(699\) | −16.0812 | −0.608248 | ||||||||
\(700\) | −1.25230 | −0.0473326 | ||||||||
\(701\) | 46.0221 | 1.73823 | 0.869115 | − | 0.494609i | \(-0.164689\pi\) | ||||
0.869115 | + | 0.494609i | \(0.164689\pi\) | |||||||
\(702\) | −41.0886 | −1.55079 | ||||||||
\(703\) | −11.9815 | −0.451889 | ||||||||
\(704\) | −0.334658 | −0.0126129 | ||||||||
\(705\) | −1.42335 | −0.0536064 | ||||||||
\(706\) | 62.1370 | 2.33856 | ||||||||
\(707\) | 14.5673 | 0.547861 | ||||||||
\(708\) | −4.70757 | −0.176921 | ||||||||
\(709\) | 51.2924 | 1.92633 | 0.963163 | − | 0.268917i | \(-0.0866658\pi\) | ||||
0.963163 | + | 0.268917i | \(0.0866658\pi\) | |||||||
\(710\) | −15.9885 | −0.600039 | ||||||||
\(711\) | 2.73878 | 0.102712 | ||||||||
\(712\) | 23.3026 | 0.873301 | ||||||||
\(713\) | −50.3617 | −1.88606 | ||||||||
\(714\) | −7.52497 | −0.281615 | ||||||||
\(715\) | −1.79364 | −0.0670782 | ||||||||
\(716\) | 12.1392 | 0.453664 | ||||||||
\(717\) | 3.43292 | 0.128205 | ||||||||
\(718\) | −2.83203 | −0.105691 | ||||||||
\(719\) | −14.5026 | −0.540854 | −0.270427 | − | 0.962740i | \(-0.587165\pi\) | ||||
−0.270427 | + | 0.962740i | \(0.587165\pi\) | |||||||
\(720\) | 13.2166 | 0.492555 | ||||||||
\(721\) | 0.709708 | 0.0264309 | ||||||||
\(722\) | 28.5243 | 1.06156 | ||||||||
\(723\) | −13.5599 | −0.504300 | ||||||||
\(724\) | −6.50512 | −0.241761 | ||||||||
\(725\) | −3.96844 | −0.147384 | ||||||||
\(726\) | 11.2010 | 0.415710 | ||||||||
\(727\) | −17.9817 | −0.666904 | −0.333452 | − | 0.942767i | \(-0.608214\pi\) | ||||
−0.333452 | + | 0.942767i | \(0.608214\pi\) | |||||||
\(728\) | 9.52740 | 0.353109 | ||||||||
\(729\) | −11.1078 | −0.411399 | ||||||||
\(730\) | 26.8064 | 0.992149 | ||||||||
\(731\) | 83.9700 | 3.10574 | ||||||||
\(732\) | −4.17535 | −0.154326 | ||||||||
\(733\) | 26.5290 | 0.979870 | 0.489935 | − | 0.871759i | \(-0.337021\pi\) | ||||
0.489935 | + | 0.871759i | \(0.337021\pi\) | |||||||
\(734\) | −45.8453 | −1.69218 | ||||||||
\(735\) | 0.567965 | 0.0209497 | ||||||||
\(736\) | −33.3516 | −1.22936 | ||||||||
\(737\) | −3.37463 | −0.124306 | ||||||||
\(738\) | −37.7031 | −1.38787 | ||||||||
\(739\) | 21.5364 | 0.792228 | 0.396114 | − | 0.918201i | \(-0.370359\pi\) | ||||
0.396114 | + | 0.918201i | \(0.370359\pi\) | |||||||
\(740\) | 8.40986 | 0.309153 | ||||||||
\(741\) | 7.15986 | 0.263024 | ||||||||
\(742\) | −9.95646 | −0.365513 | ||||||||
\(743\) | 11.5664 | 0.424329 | 0.212164 | − | 0.977234i | \(-0.431949\pi\) | ||||
0.212164 | + | 0.977234i | \(0.431949\pi\) | |||||||
\(744\) | 7.17630 | 0.263096 | ||||||||
\(745\) | −12.4453 | −0.455959 | ||||||||
\(746\) | 27.5598 | 1.00903 | ||||||||
\(747\) | −36.2540 | −1.32646 | ||||||||
\(748\) | −2.33549 | −0.0853941 | ||||||||
\(749\) | −19.5638 | −0.714845 | ||||||||
\(750\) | −1.02428 | −0.0374013 | ||||||||
\(751\) | −1.72050 | −0.0627818 | −0.0313909 | − | 0.999507i | \(-0.509994\pi\) | ||||
−0.0313909 | + | 0.999507i | \(0.509994\pi\) | |||||||
\(752\) | 12.3707 | 0.451114 | ||||||||
\(753\) | 1.14714 | 0.0418042 | ||||||||
\(754\) | −50.5672 | −1.84155 | ||||||||
\(755\) | 10.3858 | 0.377978 | ||||||||
\(756\) | 4.03814 | 0.146866 | ||||||||
\(757\) | 6.14904 | 0.223491 | 0.111745 | − | 0.993737i | \(-0.464356\pi\) | ||||
0.111745 | + | 0.993737i | \(0.464356\pi\) | |||||||
\(758\) | 42.8115 | 1.55498 | ||||||||
\(759\) | −0.774901 | −0.0281271 | ||||||||
\(760\) | −2.40575 | −0.0872659 | ||||||||
\(761\) | 13.5171 | 0.489993 | 0.244997 | − | 0.969524i | \(-0.421213\pi\) | ||||
0.244997 | + | 0.969524i | \(0.421213\pi\) | |||||||
\(762\) | −14.7299 | −0.533607 | ||||||||
\(763\) | −8.03820 | −0.291002 | ||||||||
\(764\) | −17.5657 | −0.635506 | ||||||||
\(765\) | 19.6699 | 0.711169 | ||||||||
\(766\) | 34.9854 | 1.26408 | ||||||||
\(767\) | 46.7648 | 1.68858 | ||||||||
\(768\) | 11.7745 | 0.424877 | ||||||||
\(769\) | 18.0063 | 0.649324 | 0.324662 | − | 0.945830i | \(-0.394750\pi\) | ||||
0.324662 | + | 0.945830i | \(0.394750\pi\) | |||||||
\(770\) | 0.457801 | 0.0164980 | ||||||||
\(771\) | 11.1028 | 0.399859 | ||||||||
\(772\) | −27.8414 | −1.00203 | ||||||||
\(773\) | −37.2986 | −1.34154 | −0.670769 | − | 0.741667i | \(-0.734036\pi\) | ||||
−0.670769 | + | 0.741667i | \(0.734036\pi\) | |||||||
\(774\) | −55.1884 | −1.98371 | ||||||||
\(775\) | 9.37038 | 0.336594 | ||||||||
\(776\) | 12.4355 | 0.446408 | ||||||||
\(777\) | −3.81418 | −0.136833 | ||||||||
\(778\) | −26.1578 | −0.937804 | ||||||||
\(779\) | 13.9314 | 0.499145 | ||||||||
\(780\) | −5.02556 | −0.179944 | ||||||||
\(781\) | 2.25058 | 0.0805322 | ||||||||
\(782\) | −71.2075 | −2.54638 | ||||||||
\(783\) | 12.7965 | 0.457311 | ||||||||
\(784\) | −4.93634 | −0.176298 | ||||||||
\(785\) | 0.764982 | 0.0273034 | ||||||||
\(786\) | −13.5300 | −0.482600 | ||||||||
\(787\) | −20.2453 | −0.721669 | −0.360834 | − | 0.932630i | \(-0.617508\pi\) | ||||
−0.360834 | + | 0.932630i | \(0.617508\pi\) | |||||||
\(788\) | −19.3062 | −0.687756 | ||||||||
\(789\) | −3.04712 | −0.108480 | ||||||||
\(790\) | 1.84475 | 0.0656332 | ||||||||
\(791\) | −0.658377 | −0.0234092 | ||||||||
\(792\) | −0.916471 | −0.0325654 | ||||||||
\(793\) | 41.4778 | 1.47292 | ||||||||
\(794\) | 18.6170 | 0.660694 | ||||||||
\(795\) | −3.13568 | −0.111211 | ||||||||
\(796\) | 9.40382 | 0.333310 | ||||||||
\(797\) | −42.2864 | −1.49786 | −0.748931 | − | 0.662649i | \(-0.769432\pi\) | ||||
−0.748931 | + | 0.662649i | \(0.769432\pi\) | |||||||
\(798\) | −1.82746 | −0.0646913 | ||||||||
\(799\) | 18.4110 | 0.651334 | ||||||||
\(800\) | 6.20545 | 0.219396 | ||||||||
\(801\) | −46.2699 | −1.63487 | ||||||||
\(802\) | 22.9631 | 0.810856 | ||||||||
\(803\) | −3.77333 | −0.133158 | ||||||||
\(804\) | −9.45530 | −0.333463 | ||||||||
\(805\) | 5.37456 | 0.189428 | ||||||||
\(806\) | 119.400 | 4.20570 | ||||||||
\(807\) | −4.35248 | −0.153215 | ||||||||
\(808\) | −19.6427 | −0.691028 | ||||||||
\(809\) | −26.9719 | −0.948280 | −0.474140 | − | 0.880449i | \(-0.657241\pi\) | ||||
−0.474140 | + | 0.880449i | \(0.657241\pi\) | |||||||
\(810\) | −11.1826 | −0.392917 | ||||||||
\(811\) | 9.46852 | 0.332485 | 0.166242 | − | 0.986085i | \(-0.446837\pi\) | ||||
0.166242 | + | 0.986085i | \(0.446837\pi\) | |||||||
\(812\) | 4.96969 | 0.174402 | ||||||||
\(813\) | 7.27397 | 0.255109 | ||||||||
\(814\) | −3.07437 | −0.107757 | ||||||||
\(815\) | 0.501682 | 0.0175732 | ||||||||
\(816\) | 20.5975 | 0.721057 | ||||||||
\(817\) | 20.3923 | 0.713436 | ||||||||
\(818\) | −18.5270 | −0.647782 | ||||||||
\(819\) | −18.9177 | −0.661039 | ||||||||
\(820\) | −9.77856 | −0.341482 | ||||||||
\(821\) | 24.3240 | 0.848912 | 0.424456 | − | 0.905449i | \(-0.360465\pi\) | ||||
0.424456 | + | 0.905449i | \(0.360465\pi\) | |||||||
\(822\) | −10.7364 | −0.374474 | ||||||||
\(823\) | 36.7690 | 1.28169 | 0.640843 | − | 0.767672i | \(-0.278585\pi\) | ||||
0.640843 | + | 0.767672i | \(0.278585\pi\) | |||||||
\(824\) | −0.956977 | −0.0333379 | ||||||||
\(825\) | 0.144180 | 0.00501969 | ||||||||
\(826\) | −11.9361 | −0.415309 | ||||||||
\(827\) | −26.5299 | −0.922534 | −0.461267 | − | 0.887261i | \(-0.652605\pi\) | ||||
−0.461267 | + | 0.887261i | \(0.652605\pi\) | |||||||
\(828\) | 18.0205 | 0.626257 | ||||||||
\(829\) | −35.6867 | −1.23945 | −0.619725 | − | 0.784819i | \(-0.712756\pi\) | ||||
−0.619725 | + | 0.784819i | \(0.712756\pi\) | |||||||
\(830\) | −24.4194 | −0.847610 | ||||||||
\(831\) | 5.92253 | 0.205450 | ||||||||
\(832\) | 9.31479 | 0.322932 | ||||||||
\(833\) | −7.34662 | −0.254545 | ||||||||
\(834\) | 2.23889 | 0.0775264 | ||||||||
\(835\) | 0.968483 | 0.0335157 | ||||||||
\(836\) | −0.567180 | −0.0196163 | ||||||||
\(837\) | −30.2155 | −1.04440 | ||||||||
\(838\) | −16.0466 | −0.554319 | ||||||||
\(839\) | −14.6638 | −0.506250 | −0.253125 | − | 0.967434i | \(-0.581458\pi\) | ||||
−0.253125 | + | 0.967434i | \(0.581458\pi\) | |||||||
\(840\) | −0.765849 | −0.0264243 | ||||||||
\(841\) | −13.2515 | −0.456947 | ||||||||
\(842\) | 53.4329 | 1.84142 | ||||||||
\(843\) | −3.59806 | −0.123924 | ||||||||
\(844\) | −18.8581 | −0.649124 | ||||||||
\(845\) | 36.9236 | 1.27021 | ||||||||
\(846\) | −12.1004 | −0.416021 | ||||||||
\(847\) | 10.9356 | 0.375750 | ||||||||
\(848\) | 27.2530 | 0.935873 | ||||||||
\(849\) | −1.79080 | −0.0614602 | ||||||||
\(850\) | 13.2490 | 0.454437 | ||||||||
\(851\) | −36.0930 | −1.23725 | ||||||||
\(852\) | 6.30586 | 0.216035 | ||||||||
\(853\) | −18.5911 | −0.636547 | −0.318274 | − | 0.947999i | \(-0.603103\pi\) | ||||
−0.318274 | + | 0.947999i | \(0.603103\pi\) | |||||||
\(854\) | −10.5866 | −0.362267 | ||||||||
\(855\) | 4.77689 | 0.163366 | ||||||||
\(856\) | 26.3800 | 0.901649 | ||||||||
\(857\) | −49.1250 | −1.67808 | −0.839039 | − | 0.544072i | \(-0.816882\pi\) | ||||
−0.839039 | + | 0.544072i | \(0.816882\pi\) | |||||||
\(858\) | 1.83718 | 0.0627203 | ||||||||
\(859\) | −12.5111 | −0.426875 | −0.213437 | − | 0.976957i | \(-0.568466\pi\) | ||||
−0.213437 | + | 0.976957i | \(0.568466\pi\) | |||||||
\(860\) | −14.3135 | −0.488086 | ||||||||
\(861\) | 4.43494 | 0.151142 | ||||||||
\(862\) | 32.3868 | 1.10310 | ||||||||
\(863\) | −50.0062 | −1.70223 | −0.851115 | − | 0.524979i | \(-0.824073\pi\) | ||||
−0.851115 | + | 0.524979i | \(0.824073\pi\) | |||||||
\(864\) | −20.0100 | −0.680753 | ||||||||
\(865\) | 2.40686 | 0.0818358 | ||||||||
\(866\) | −67.5584 | −2.29573 | ||||||||
\(867\) | 20.9993 | 0.713173 | ||||||||
\(868\) | −11.7345 | −0.398297 | ||||||||
\(869\) | −0.259671 | −0.00880874 | ||||||||
\(870\) | 4.06478 | 0.137809 | ||||||||
\(871\) | 93.9285 | 3.18264 | ||||||||
\(872\) | 10.8388 | 0.367047 | ||||||||
\(873\) | −24.6920 | −0.835699 | ||||||||
\(874\) | −17.2929 | −0.584942 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | −10.5724 | −0.357209 | ||||||||
\(877\) | 43.4813 | 1.46826 | 0.734130 | − | 0.679009i | \(-0.237590\pi\) | ||||
0.734130 | + | 0.679009i | \(0.237590\pi\) | |||||||
\(878\) | −1.63131 | −0.0550542 | ||||||||
\(879\) | −6.33474 | −0.213665 | ||||||||
\(880\) | −1.25310 | −0.0422421 | ||||||||
\(881\) | 39.2763 | 1.32325 | 0.661627 | − | 0.749833i | \(-0.269866\pi\) | ||||
0.661627 | + | 0.749833i | \(0.269866\pi\) | |||||||
\(882\) | 4.82849 | 0.162584 | ||||||||
\(883\) | 10.2116 | 0.343649 | 0.171825 | − | 0.985128i | \(-0.445034\pi\) | ||||
0.171825 | + | 0.985128i | \(0.445034\pi\) | |||||||
\(884\) | 65.0054 | 2.18637 | ||||||||
\(885\) | −3.75913 | −0.126362 | ||||||||
\(886\) | 62.4290 | 2.09734 | ||||||||
\(887\) | −39.8900 | −1.33938 | −0.669688 | − | 0.742642i | \(-0.733572\pi\) | ||||
−0.669688 | + | 0.742642i | \(0.733572\pi\) | |||||||
\(888\) | 5.14308 | 0.172590 | ||||||||
\(889\) | −14.3807 | −0.482315 | ||||||||
\(890\) | −31.1658 | −1.04468 | ||||||||
\(891\) | 1.57409 | 0.0527340 | ||||||||
\(892\) | 5.32762 | 0.178382 | ||||||||
\(893\) | 4.47115 | 0.149621 | ||||||||
\(894\) | 12.7474 | 0.426336 | ||||||||
\(895\) | 9.69352 | 0.324019 | ||||||||
\(896\) | 10.0334 | 0.335194 | ||||||||
\(897\) | 21.5684 | 0.720148 | ||||||||
\(898\) | −36.7855 | −1.22755 | ||||||||
\(899\) | −37.1858 | −1.24022 | ||||||||
\(900\) | −3.35293 | −0.111764 | ||||||||
\(901\) | 40.5599 | 1.35125 | ||||||||
\(902\) | 3.57473 | 0.119025 | ||||||||
\(903\) | 6.49170 | 0.216030 | ||||||||
\(904\) | 0.887761 | 0.0295265 | ||||||||
\(905\) | −5.19453 | −0.172672 | ||||||||
\(906\) | −10.6379 | −0.353422 | ||||||||
\(907\) | −40.7663 | −1.35362 | −0.676811 | − | 0.736157i | \(-0.736638\pi\) | ||||
−0.676811 | + | 0.736157i | \(0.736638\pi\) | |||||||
\(908\) | 9.72251 | 0.322653 | ||||||||
\(909\) | 39.0028 | 1.29364 | ||||||||
\(910\) | −12.7423 | −0.422404 | ||||||||
\(911\) | 29.5700 | 0.979696 | 0.489848 | − | 0.871808i | \(-0.337052\pi\) | ||||
0.489848 | + | 0.871808i | \(0.337052\pi\) | |||||||
\(912\) | 5.00215 | 0.165638 | ||||||||
\(913\) | 3.43733 | 0.113759 | ||||||||
\(914\) | −36.8021 | −1.21731 | ||||||||
\(915\) | −3.33414 | −0.110223 | ||||||||
\(916\) | −1.25230 | −0.0413772 | ||||||||
\(917\) | −13.2094 | −0.436211 | ||||||||
\(918\) | −42.7224 | −1.41005 | ||||||||
\(919\) | 22.1477 | 0.730585 | 0.365292 | − | 0.930893i | \(-0.380969\pi\) | ||||
0.365292 | + | 0.930893i | \(0.380969\pi\) | |||||||
\(920\) | −7.24710 | −0.238930 | ||||||||
\(921\) | −0.799552 | −0.0263461 | ||||||||
\(922\) | −21.6193 | −0.711994 | ||||||||
\(923\) | −62.6421 | −2.06189 | ||||||||
\(924\) | −0.180556 | −0.00593987 | ||||||||
\(925\) | 6.71552 | 0.220805 | ||||||||
\(926\) | −71.7175 | −2.35678 | ||||||||
\(927\) | 1.90018 | 0.0624102 | ||||||||
\(928\) | −24.6260 | −0.808388 | ||||||||
\(929\) | −56.8486 | −1.86514 | −0.932572 | − | 0.360985i | \(-0.882441\pi\) | ||||
−0.932572 | + | 0.360985i | \(0.882441\pi\) | |||||||
\(930\) | −9.59786 | −0.314726 | ||||||||
\(931\) | −1.78414 | −0.0584730 | ||||||||
\(932\) | −35.4574 | −1.16144 | ||||||||
\(933\) | 13.3237 | 0.436198 | ||||||||
\(934\) | 57.8994 | 1.89453 | ||||||||
\(935\) | −1.86496 | −0.0609907 | ||||||||
\(936\) | 25.5088 | 0.833781 | ||||||||
\(937\) | 34.7682 | 1.13583 | 0.567913 | − | 0.823088i | \(-0.307751\pi\) | ||||
0.567913 | + | 0.823088i | \(0.307751\pi\) | |||||||
\(938\) | −23.9740 | −0.782777 | ||||||||
\(939\) | 7.50253 | 0.244836 | ||||||||
\(940\) | −3.13833 | −0.102361 | ||||||||
\(941\) | −12.3319 | −0.402008 | −0.201004 | − | 0.979590i | \(-0.564420\pi\) | ||||
−0.201004 | + | 0.979590i | \(0.564420\pi\) | |||||||
\(942\) | −0.783553 | −0.0255295 | ||||||||
\(943\) | 41.9670 | 1.36664 | ||||||||
\(944\) | 32.6717 | 1.06337 | ||||||||
\(945\) | 3.22458 | 0.104895 | ||||||||
\(946\) | 5.23255 | 0.170125 | ||||||||
\(947\) | 43.5774 | 1.41608 | 0.708038 | − | 0.706174i | \(-0.249580\pi\) | ||||
0.708038 | + | 0.706174i | \(0.249580\pi\) | |||||||
\(948\) | −0.727567 | −0.0236303 | ||||||||
\(949\) | 105.026 | 3.40928 | ||||||||
\(950\) | 3.21755 | 0.104391 | ||||||||
\(951\) | −7.32385 | −0.237492 | ||||||||
\(952\) | 9.90624 | 0.321063 | ||||||||
\(953\) | 32.5041 | 1.05291 | 0.526456 | − | 0.850203i | \(-0.323521\pi\) | ||||
0.526456 | + | 0.850203i | \(0.323521\pi\) | |||||||
\(954\) | −26.6576 | −0.863071 | ||||||||
\(955\) | −14.0267 | −0.453895 | ||||||||
\(956\) | 7.56921 | 0.244806 | ||||||||
\(957\) | −0.572168 | −0.0184956 | ||||||||
\(958\) | −64.9765 | −2.09930 | ||||||||
\(959\) | −10.4819 | −0.338478 | ||||||||
\(960\) | −0.748759 | −0.0241661 | ||||||||
\(961\) | 56.8040 | 1.83239 | ||||||||
\(962\) | 85.5713 | 2.75893 | ||||||||
\(963\) | −52.3804 | −1.68793 | ||||||||
\(964\) | −29.8982 | −0.962957 | ||||||||
\(965\) | −22.2322 | −0.715679 | ||||||||
\(966\) | −5.50504 | −0.177122 | ||||||||
\(967\) | 0.189957 | 0.00610860 | 0.00305430 | − | 0.999995i | \(-0.499028\pi\) | ||||
0.00305430 | + | 0.999995i | \(0.499028\pi\) | |||||||
\(968\) | −14.7456 | −0.473941 | ||||||||
\(969\) | 7.44456 | 0.239154 | ||||||||
\(970\) | −16.6317 | −0.534012 | ||||||||
\(971\) | 42.7552 | 1.37208 | 0.686040 | − | 0.727564i | \(-0.259348\pi\) | ||||
0.686040 | + | 0.727564i | \(0.259348\pi\) | |||||||
\(972\) | 16.5248 | 0.530034 | ||||||||
\(973\) | 2.18582 | 0.0700743 | ||||||||
\(974\) | −30.6162 | −0.981005 | ||||||||
\(975\) | −4.01305 | −0.128521 | ||||||||
\(976\) | 28.9779 | 0.927562 | ||||||||
\(977\) | −42.0326 | −1.34474 | −0.672371 | − | 0.740214i | \(-0.734724\pi\) | ||||
−0.672371 | + | 0.740214i | \(0.734724\pi\) | |||||||
\(978\) | −0.513861 | −0.0164315 | ||||||||
\(979\) | 4.38697 | 0.140208 | ||||||||
\(980\) | 1.25230 | 0.0400033 | ||||||||
\(981\) | −21.5216 | −0.687131 | ||||||||
\(982\) | −50.1128 | −1.59916 | ||||||||
\(983\) | −15.5152 | −0.494856 | −0.247428 | − | 0.968906i | \(-0.579585\pi\) | ||||
−0.247428 | + | 0.968906i | \(0.579585\pi\) | |||||||
\(984\) | −5.98011 | −0.190639 | ||||||||
\(985\) | −15.4166 | −0.491213 | ||||||||
\(986\) | −52.5779 | −1.67442 | ||||||||
\(987\) | 1.42335 | 0.0453057 | ||||||||
\(988\) | 15.7867 | 0.502243 | ||||||||
\(989\) | 61.4298 | 1.95335 | ||||||||
\(990\) | 1.22572 | 0.0389561 | ||||||||
\(991\) | 16.3529 | 0.519468 | 0.259734 | − | 0.965680i | \(-0.416365\pi\) | ||||
0.259734 | + | 0.965680i | \(0.416365\pi\) | |||||||
\(992\) | 58.1475 | 1.84618 | ||||||||
\(993\) | −3.73572 | −0.118549 | ||||||||
\(994\) | 15.9885 | 0.507126 | ||||||||
\(995\) | 7.50923 | 0.238058 | ||||||||
\(996\) | 9.63099 | 0.305170 | ||||||||
\(997\) | 11.1561 | 0.353318 | 0.176659 | − | 0.984272i | \(-0.443471\pi\) | ||||
0.176659 | + | 0.984272i | \(0.443471\pi\) | |||||||
\(998\) | 43.2553 | 1.36922 | ||||||||
\(999\) | −21.6547 | −0.685124 |
(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 | 8015.2.a.m.1.15 | ✓ | 67 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.m.1.15 | ✓ | 67 | 1.1 | even | 1 | trivial |