Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4021,2,Mod(1,4021)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4021, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4021.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4021 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4021.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1078466528\) |
Analytic rank: | \(1\) |
Dimension: | \(151\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 4021.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.49227 | −1.76230 | −0.881151 | − | 0.472835i | \(-0.843231\pi\) | ||||
−0.881151 | + | 0.472835i | \(0.843231\pi\) | |||||||
\(3\) | −2.01078 | −1.16092 | −0.580461 | − | 0.814288i | \(-0.697128\pi\) | ||||
−0.580461 | + | 0.814288i | \(0.697128\pi\) | |||||||
\(4\) | 4.21142 | 2.10571 | ||||||||
\(5\) | 3.04731 | 1.36280 | 0.681399 | − | 0.731912i | \(-0.261372\pi\) | ||||
0.681399 | + | 0.731912i | \(0.261372\pi\) | |||||||
\(6\) | 5.01140 | 2.04590 | ||||||||
\(7\) | −1.48654 | −0.561860 | −0.280930 | − | 0.959728i | \(-0.590643\pi\) | ||||
−0.280930 | + | 0.959728i | \(0.590643\pi\) | |||||||
\(8\) | −5.51145 | −1.94859 | ||||||||
\(9\) | 1.04322 | 0.347740 | ||||||||
\(10\) | −7.59472 | −2.40166 | ||||||||
\(11\) | 1.81295 | 0.546626 | 0.273313 | − | 0.961925i | \(-0.411881\pi\) | ||||
0.273313 | + | 0.961925i | \(0.411881\pi\) | |||||||
\(12\) | −8.46822 | −2.44456 | ||||||||
\(13\) | −0.734695 | −0.203768 | −0.101884 | − | 0.994796i | \(-0.532487\pi\) | ||||
−0.101884 | + | 0.994796i | \(0.532487\pi\) | |||||||
\(14\) | 3.70486 | 0.990167 | ||||||||
\(15\) | −6.12746 | −1.58210 | ||||||||
\(16\) | 5.31320 | 1.32830 | ||||||||
\(17\) | 7.10259 | 1.72263 | 0.861316 | − | 0.508070i | \(-0.169641\pi\) | ||||
0.861316 | + | 0.508070i | \(0.169641\pi\) | |||||||
\(18\) | −2.59999 | −0.612823 | ||||||||
\(19\) | −7.26677 | −1.66711 | −0.833556 | − | 0.552435i | \(-0.813699\pi\) | ||||
−0.833556 | + | 0.552435i | \(0.813699\pi\) | |||||||
\(20\) | 12.8335 | 2.86966 | ||||||||
\(21\) | 2.98910 | 0.652275 | ||||||||
\(22\) | −4.51837 | −0.963320 | ||||||||
\(23\) | −7.33280 | −1.52899 | −0.764497 | − | 0.644627i | \(-0.777013\pi\) | ||||
−0.764497 | + | 0.644627i | \(0.777013\pi\) | |||||||
\(24\) | 11.0823 | 2.26216 | ||||||||
\(25\) | 4.28610 | 0.857220 | ||||||||
\(26\) | 1.83106 | 0.359100 | ||||||||
\(27\) | 3.93465 | 0.757223 | ||||||||
\(28\) | −6.26044 | −1.18311 | ||||||||
\(29\) | 0.894451 | 0.166095 | 0.0830477 | − | 0.996546i | \(-0.473535\pi\) | ||||
0.0830477 | + | 0.996546i | \(0.473535\pi\) | |||||||
\(30\) | 15.2713 | 2.78814 | ||||||||
\(31\) | 3.59164 | 0.645077 | 0.322539 | − | 0.946556i | \(-0.395464\pi\) | ||||
0.322539 | + | 0.946556i | \(0.395464\pi\) | |||||||
\(32\) | −2.21904 | −0.392274 | ||||||||
\(33\) | −3.64544 | −0.634590 | ||||||||
\(34\) | −17.7016 | −3.03580 | ||||||||
\(35\) | −4.52995 | −0.765702 | ||||||||
\(36\) | 4.39343 | 0.732239 | ||||||||
\(37\) | 5.71887 | 0.940176 | 0.470088 | − | 0.882620i | \(-0.344222\pi\) | ||||
0.470088 | + | 0.882620i | \(0.344222\pi\) | |||||||
\(38\) | 18.1108 | 2.93796 | ||||||||
\(39\) | 1.47731 | 0.236558 | ||||||||
\(40\) | −16.7951 | −2.65554 | ||||||||
\(41\) | 0.487859 | 0.0761907 | 0.0380954 | − | 0.999274i | \(-0.487871\pi\) | ||||
0.0380954 | + | 0.999274i | \(0.487871\pi\) | |||||||
\(42\) | −7.44965 | −1.14951 | ||||||||
\(43\) | −5.93769 | −0.905489 | −0.452744 | − | 0.891640i | \(-0.649555\pi\) | ||||
−0.452744 | + | 0.891640i | \(0.649555\pi\) | |||||||
\(44\) | 7.63510 | 1.15104 | ||||||||
\(45\) | 3.17901 | 0.473900 | ||||||||
\(46\) | 18.2753 | 2.69455 | ||||||||
\(47\) | 8.29421 | 1.20984 | 0.604918 | − | 0.796288i | \(-0.293206\pi\) | ||||
0.604918 | + | 0.796288i | \(0.293206\pi\) | |||||||
\(48\) | −10.6837 | −1.54205 | ||||||||
\(49\) | −4.79020 | −0.684314 | ||||||||
\(50\) | −10.6821 | −1.51068 | ||||||||
\(51\) | −14.2817 | −1.99984 | ||||||||
\(52\) | −3.09411 | −0.429075 | ||||||||
\(53\) | 6.24641 | 0.858011 | 0.429005 | − | 0.903302i | \(-0.358864\pi\) | ||||
0.429005 | + | 0.903302i | \(0.358864\pi\) | |||||||
\(54\) | −9.80621 | −1.33446 | ||||||||
\(55\) | 5.52463 | 0.744941 | ||||||||
\(56\) | 8.19300 | 1.09484 | ||||||||
\(57\) | 14.6119 | 1.93539 | ||||||||
\(58\) | −2.22922 | −0.292710 | ||||||||
\(59\) | −6.10515 | −0.794823 | −0.397411 | − | 0.917641i | \(-0.630091\pi\) | ||||
−0.397411 | + | 0.917641i | \(0.630091\pi\) | |||||||
\(60\) | −25.8053 | −3.33145 | ||||||||
\(61\) | −10.4333 | −1.33584 | −0.667921 | − | 0.744232i | \(-0.732816\pi\) | ||||
−0.667921 | + | 0.744232i | \(0.732816\pi\) | |||||||
\(62\) | −8.95134 | −1.13682 | ||||||||
\(63\) | −1.55079 | −0.195381 | ||||||||
\(64\) | −5.09596 | −0.636995 | ||||||||
\(65\) | −2.23884 | −0.277694 | ||||||||
\(66\) | 9.08543 | 1.11834 | ||||||||
\(67\) | 1.55032 | 0.189402 | 0.0947010 | − | 0.995506i | \(-0.469810\pi\) | ||||
0.0947010 | + | 0.995506i | \(0.469810\pi\) | |||||||
\(68\) | 29.9120 | 3.62736 | ||||||||
\(69\) | 14.7446 | 1.77504 | ||||||||
\(70\) | 11.2899 | 1.34940 | ||||||||
\(71\) | −15.8532 | −1.88143 | −0.940716 | − | 0.339197i | \(-0.889845\pi\) | ||||
−0.940716 | + | 0.339197i | \(0.889845\pi\) | |||||||
\(72\) | −5.74966 | −0.677604 | ||||||||
\(73\) | 2.48293 | 0.290605 | 0.145302 | − | 0.989387i | \(-0.453585\pi\) | ||||
0.145302 | + | 0.989387i | \(0.453585\pi\) | |||||||
\(74\) | −14.2530 | −1.65687 | ||||||||
\(75\) | −8.61839 | −0.995166 | ||||||||
\(76\) | −30.6034 | −3.51045 | ||||||||
\(77\) | −2.69503 | −0.307127 | ||||||||
\(78\) | −3.68185 | −0.416887 | ||||||||
\(79\) | −2.62028 | −0.294805 | −0.147403 | − | 0.989077i | \(-0.547091\pi\) | ||||
−0.147403 | + | 0.989077i | \(0.547091\pi\) | |||||||
\(80\) | 16.1910 | 1.81021 | ||||||||
\(81\) | −11.0414 | −1.22682 | ||||||||
\(82\) | −1.21588 | −0.134271 | ||||||||
\(83\) | −3.52124 | −0.386507 | −0.193253 | − | 0.981149i | \(-0.561904\pi\) | ||||
−0.193253 | + | 0.981149i | \(0.561904\pi\) | |||||||
\(84\) | 12.5884 | 1.37350 | ||||||||
\(85\) | 21.6438 | 2.34760 | ||||||||
\(86\) | 14.7983 | 1.59575 | ||||||||
\(87\) | −1.79854 | −0.192824 | ||||||||
\(88\) | −9.99201 | −1.06515 | ||||||||
\(89\) | −13.4056 | −1.42099 | −0.710495 | − | 0.703702i | \(-0.751529\pi\) | ||||
−0.710495 | + | 0.703702i | \(0.751529\pi\) | |||||||
\(90\) | −7.92297 | −0.835154 | ||||||||
\(91\) | 1.09215 | 0.114489 | ||||||||
\(92\) | −30.8815 | −3.21962 | ||||||||
\(93\) | −7.22198 | −0.748885 | ||||||||
\(94\) | −20.6714 | −2.13210 | ||||||||
\(95\) | −22.1441 | −2.27194 | ||||||||
\(96\) | 4.46199 | 0.455400 | ||||||||
\(97\) | 4.09184 | 0.415464 | 0.207732 | − | 0.978186i | \(-0.433392\pi\) | ||||
0.207732 | + | 0.978186i | \(0.433392\pi\) | |||||||
\(98\) | 11.9385 | 1.20597 | ||||||||
\(99\) | 1.89131 | 0.190084 | ||||||||
\(100\) | 18.0506 | 1.80506 | ||||||||
\(101\) | 8.05217 | 0.801221 | 0.400610 | − | 0.916248i | \(-0.368798\pi\) | ||||
0.400610 | + | 0.916248i | \(0.368798\pi\) | |||||||
\(102\) | 35.5939 | 3.52432 | ||||||||
\(103\) | −13.9340 | −1.37295 | −0.686477 | − | 0.727152i | \(-0.740844\pi\) | ||||
−0.686477 | + | 0.727152i | \(0.740844\pi\) | |||||||
\(104\) | 4.04923 | 0.397060 | ||||||||
\(105\) | 9.10872 | 0.888920 | ||||||||
\(106\) | −15.5678 | −1.51207 | ||||||||
\(107\) | 9.16976 | 0.886474 | 0.443237 | − | 0.896404i | \(-0.353830\pi\) | ||||
0.443237 | + | 0.896404i | \(0.353830\pi\) | |||||||
\(108\) | 16.5704 | 1.59449 | ||||||||
\(109\) | 9.83060 | 0.941600 | 0.470800 | − | 0.882240i | \(-0.343965\pi\) | ||||
0.470800 | + | 0.882240i | \(0.343965\pi\) | |||||||
\(110\) | −13.7689 | −1.31281 | ||||||||
\(111\) | −11.4994 | −1.09147 | ||||||||
\(112\) | −7.89829 | −0.746319 | ||||||||
\(113\) | −0.698955 | −0.0657521 | −0.0328761 | − | 0.999459i | \(-0.510467\pi\) | ||||
−0.0328761 | + | 0.999459i | \(0.510467\pi\) | |||||||
\(114\) | −36.4167 | −3.41074 | ||||||||
\(115\) | −22.3453 | −2.08371 | ||||||||
\(116\) | 3.76691 | 0.349749 | ||||||||
\(117\) | −0.766448 | −0.0708581 | ||||||||
\(118\) | 15.2157 | 1.40072 | ||||||||
\(119\) | −10.5583 | −0.967877 | ||||||||
\(120\) | 33.7712 | 3.08287 | ||||||||
\(121\) | −7.71320 | −0.701200 | ||||||||
\(122\) | 26.0025 | 2.35416 | ||||||||
\(123\) | −0.980975 | −0.0884515 | ||||||||
\(124\) | 15.1259 | 1.35835 | ||||||||
\(125\) | −2.17547 | −0.194580 | ||||||||
\(126\) | 3.86499 | 0.344321 | ||||||||
\(127\) | 12.5016 | 1.10934 | 0.554670 | − | 0.832071i | \(-0.312845\pi\) | ||||
0.554670 | + | 0.832071i | \(0.312845\pi\) | |||||||
\(128\) | 17.1386 | 1.51485 | ||||||||
\(129\) | 11.9394 | 1.05120 | ||||||||
\(130\) | 5.57980 | 0.489381 | ||||||||
\(131\) | −2.29618 | −0.200618 | −0.100309 | − | 0.994956i | \(-0.531983\pi\) | ||||
−0.100309 | + | 0.994956i | \(0.531983\pi\) | |||||||
\(132\) | −15.3525 | −1.33626 | ||||||||
\(133\) | 10.8024 | 0.936683 | ||||||||
\(134\) | −3.86382 | −0.333784 | ||||||||
\(135\) | 11.9901 | 1.03194 | ||||||||
\(136\) | −39.1456 | −3.35671 | ||||||||
\(137\) | 19.3488 | 1.65308 | 0.826540 | − | 0.562878i | \(-0.190306\pi\) | ||||
0.826540 | + | 0.562878i | \(0.190306\pi\) | |||||||
\(138\) | −36.7476 | −3.12816 | ||||||||
\(139\) | 15.8109 | 1.34106 | 0.670532 | − | 0.741881i | \(-0.266066\pi\) | ||||
0.670532 | + | 0.741881i | \(0.266066\pi\) | |||||||
\(140\) | −19.0775 | −1.61234 | ||||||||
\(141\) | −16.6778 | −1.40452 | ||||||||
\(142\) | 39.5105 | 3.31565 | ||||||||
\(143\) | −1.33197 | −0.111385 | ||||||||
\(144\) | 5.54284 | 0.461903 | ||||||||
\(145\) | 2.72567 | 0.226355 | ||||||||
\(146\) | −6.18813 | −0.512133 | ||||||||
\(147\) | 9.63201 | 0.794435 | ||||||||
\(148\) | 24.0845 | 1.97974 | ||||||||
\(149\) | −20.3051 | −1.66346 | −0.831728 | − | 0.555183i | \(-0.812648\pi\) | ||||
−0.831728 | + | 0.555183i | \(0.812648\pi\) | |||||||
\(150\) | 21.4794 | 1.75378 | ||||||||
\(151\) | 7.43802 | 0.605298 | 0.302649 | − | 0.953102i | \(-0.402129\pi\) | ||||
0.302649 | + | 0.953102i | \(0.402129\pi\) | |||||||
\(152\) | 40.0505 | 3.24852 | ||||||||
\(153\) | 7.40957 | 0.599028 | ||||||||
\(154\) | 6.71675 | 0.541251 | ||||||||
\(155\) | 10.9448 | 0.879111 | ||||||||
\(156\) | 6.22155 | 0.498123 | ||||||||
\(157\) | 0.278065 | 0.0221920 | 0.0110960 | − | 0.999938i | \(-0.496468\pi\) | ||||
0.0110960 | + | 0.999938i | \(0.496468\pi\) | |||||||
\(158\) | 6.53046 | 0.519536 | ||||||||
\(159\) | −12.5601 | −0.996084 | ||||||||
\(160\) | −6.76210 | −0.534591 | ||||||||
\(161\) | 10.9005 | 0.859081 | ||||||||
\(162\) | 27.5180 | 2.16202 | ||||||||
\(163\) | −12.6709 | −0.992463 | −0.496231 | − | 0.868190i | \(-0.665283\pi\) | ||||
−0.496231 | + | 0.868190i | \(0.665283\pi\) | |||||||
\(164\) | 2.05458 | 0.160436 | ||||||||
\(165\) | −11.1088 | −0.864819 | ||||||||
\(166\) | 8.77590 | 0.681142 | ||||||||
\(167\) | −0.515837 | −0.0399167 | −0.0199583 | − | 0.999801i | \(-0.506353\pi\) | ||||
−0.0199583 | + | 0.999801i | \(0.506353\pi\) | |||||||
\(168\) | −16.4743 | −1.27102 | ||||||||
\(169\) | −12.4602 | −0.958479 | ||||||||
\(170\) | −53.9422 | −4.13718 | ||||||||
\(171\) | −7.58084 | −0.579722 | ||||||||
\(172\) | −25.0061 | −1.90670 | ||||||||
\(173\) | −14.5396 | −1.10543 | −0.552713 | − | 0.833372i | \(-0.686407\pi\) | ||||
−0.552713 | + | 0.833372i | \(0.686407\pi\) | |||||||
\(174\) | 4.48245 | 0.339814 | ||||||||
\(175\) | −6.37146 | −0.481637 | ||||||||
\(176\) | 9.63259 | 0.726084 | ||||||||
\(177\) | 12.2761 | 0.922727 | ||||||||
\(178\) | 33.4104 | 2.50421 | ||||||||
\(179\) | −14.0619 | −1.05103 | −0.525517 | − | 0.850783i | \(-0.676128\pi\) | ||||
−0.525517 | + | 0.850783i | \(0.676128\pi\) | |||||||
\(180\) | 13.3882 | 0.997894 | ||||||||
\(181\) | 15.7429 | 1.17016 | 0.585079 | − | 0.810976i | \(-0.301063\pi\) | ||||
0.585079 | + | 0.810976i | \(0.301063\pi\) | |||||||
\(182\) | −2.72194 | −0.201764 | ||||||||
\(183\) | 20.9789 | 1.55081 | ||||||||
\(184\) | 40.4144 | 2.97939 | ||||||||
\(185\) | 17.4272 | 1.28127 | ||||||||
\(186\) | 17.9991 | 1.31976 | ||||||||
\(187\) | 12.8767 | 0.941635 | ||||||||
\(188\) | 34.9304 | 2.54756 | ||||||||
\(189\) | −5.84901 | −0.425453 | ||||||||
\(190\) | 55.1891 | 4.00384 | ||||||||
\(191\) | 9.92586 | 0.718210 | 0.359105 | − | 0.933297i | \(-0.383082\pi\) | ||||
0.359105 | + | 0.933297i | \(0.383082\pi\) | |||||||
\(192\) | 10.2468 | 0.739502 | ||||||||
\(193\) | −3.93472 | −0.283227 | −0.141614 | − | 0.989922i | \(-0.545229\pi\) | ||||
−0.141614 | + | 0.989922i | \(0.545229\pi\) | |||||||
\(194\) | −10.1980 | −0.732173 | ||||||||
\(195\) | 4.50181 | 0.322381 | ||||||||
\(196\) | −20.1735 | −1.44097 | ||||||||
\(197\) | 1.85955 | 0.132487 | 0.0662437 | − | 0.997803i | \(-0.478899\pi\) | ||||
0.0662437 | + | 0.997803i | \(0.478899\pi\) | |||||||
\(198\) | −4.71366 | −0.334985 | ||||||||
\(199\) | 18.9615 | 1.34415 | 0.672073 | − | 0.740485i | \(-0.265404\pi\) | ||||
0.672073 | + | 0.740485i | \(0.265404\pi\) | |||||||
\(200\) | −23.6226 | −1.67037 | ||||||||
\(201\) | −3.11735 | −0.219881 | ||||||||
\(202\) | −20.0682 | −1.41199 | ||||||||
\(203\) | −1.32964 | −0.0933223 | ||||||||
\(204\) | −60.1463 | −4.21108 | ||||||||
\(205\) | 1.48666 | 0.103833 | ||||||||
\(206\) | 34.7272 | 2.41956 | ||||||||
\(207\) | −7.64972 | −0.531693 | ||||||||
\(208\) | −3.90358 | −0.270665 | ||||||||
\(209\) | −13.1743 | −0.911287 | ||||||||
\(210\) | −22.7014 | −1.56655 | ||||||||
\(211\) | 12.8299 | 0.883243 | 0.441622 | − | 0.897201i | \(-0.354403\pi\) | ||||
0.441622 | + | 0.897201i | \(0.354403\pi\) | |||||||
\(212\) | 26.3063 | 1.80672 | ||||||||
\(213\) | 31.8773 | 2.18419 | ||||||||
\(214\) | −22.8535 | −1.56223 | ||||||||
\(215\) | −18.0940 | −1.23400 | ||||||||
\(216\) | −21.6856 | −1.47552 | ||||||||
\(217\) | −5.33912 | −0.362443 | ||||||||
\(218\) | −24.5005 | −1.65938 | ||||||||
\(219\) | −4.99261 | −0.337369 | ||||||||
\(220\) | 23.2665 | 1.56863 | ||||||||
\(221\) | −5.21824 | −0.351016 | ||||||||
\(222\) | 28.6595 | 1.92350 | ||||||||
\(223\) | −12.1613 | −0.814384 | −0.407192 | − | 0.913343i | \(-0.633492\pi\) | ||||
−0.407192 | + | 0.913343i | \(0.633492\pi\) | |||||||
\(224\) | 3.29869 | 0.220403 | ||||||||
\(225\) | 4.47135 | 0.298090 | ||||||||
\(226\) | 1.74198 | 0.115875 | ||||||||
\(227\) | 3.60780 | 0.239458 | 0.119729 | − | 0.992807i | \(-0.461797\pi\) | ||||
0.119729 | + | 0.992807i | \(0.461797\pi\) | |||||||
\(228\) | 61.5366 | 4.07536 | ||||||||
\(229\) | −0.397109 | −0.0262417 | −0.0131209 | − | 0.999914i | \(-0.504177\pi\) | ||||
−0.0131209 | + | 0.999914i | \(0.504177\pi\) | |||||||
\(230\) | 55.6906 | 3.67213 | ||||||||
\(231\) | 5.41910 | 0.356551 | ||||||||
\(232\) | −4.92973 | −0.323652 | ||||||||
\(233\) | 2.37248 | 0.155426 | 0.0777132 | − | 0.996976i | \(-0.475238\pi\) | ||||
0.0777132 | + | 0.996976i | \(0.475238\pi\) | |||||||
\(234\) | 1.91020 | 0.124873 | ||||||||
\(235\) | 25.2750 | 1.64876 | ||||||||
\(236\) | −25.7113 | −1.67367 | ||||||||
\(237\) | 5.26881 | 0.342246 | ||||||||
\(238\) | 26.3141 | 1.70569 | ||||||||
\(239\) | −6.20313 | −0.401247 | −0.200624 | − | 0.979668i | \(-0.564297\pi\) | ||||
−0.200624 | + | 0.979668i | \(0.564297\pi\) | |||||||
\(240\) | −32.5564 | −2.10151 | ||||||||
\(241\) | 27.9970 | 1.80345 | 0.901724 | − | 0.432313i | \(-0.142302\pi\) | ||||
0.901724 | + | 0.432313i | \(0.142302\pi\) | |||||||
\(242\) | 19.2234 | 1.23573 | ||||||||
\(243\) | 10.3977 | 0.667016 | ||||||||
\(244\) | −43.9388 | −2.81289 | ||||||||
\(245\) | −14.5972 | −0.932582 | ||||||||
\(246\) | 2.44486 | 0.155878 | ||||||||
\(247\) | 5.33886 | 0.339703 | ||||||||
\(248\) | −19.7952 | −1.25699 | ||||||||
\(249\) | 7.08043 | 0.448704 | ||||||||
\(250\) | 5.42187 | 0.342909 | ||||||||
\(251\) | −12.7734 | −0.806252 | −0.403126 | − | 0.915145i | \(-0.632076\pi\) | ||||
−0.403126 | + | 0.915145i | \(0.632076\pi\) | |||||||
\(252\) | −6.53102 | −0.411416 | ||||||||
\(253\) | −13.2940 | −0.835788 | ||||||||
\(254\) | −31.1574 | −1.95499 | ||||||||
\(255\) | −43.5208 | −2.72538 | ||||||||
\(256\) | −32.5221 | −2.03263 | ||||||||
\(257\) | 14.7897 | 0.922553 | 0.461277 | − | 0.887256i | \(-0.347392\pi\) | ||||
0.461277 | + | 0.887256i | \(0.347392\pi\) | |||||||
\(258\) | −29.7561 | −1.85254 | ||||||||
\(259\) | −8.50133 | −0.528247 | ||||||||
\(260\) | −9.42870 | −0.584743 | ||||||||
\(261\) | 0.933110 | 0.0577580 | ||||||||
\(262\) | 5.72269 | 0.353549 | ||||||||
\(263\) | 9.62545 | 0.593530 | 0.296765 | − | 0.954950i | \(-0.404092\pi\) | ||||
0.296765 | + | 0.954950i | \(0.404092\pi\) | |||||||
\(264\) | 20.0917 | 1.23656 | ||||||||
\(265\) | 19.0348 | 1.16930 | ||||||||
\(266\) | −26.9224 | −1.65072 | ||||||||
\(267\) | 26.9556 | 1.64966 | ||||||||
\(268\) | 6.52906 | 0.398826 | ||||||||
\(269\) | −2.87302 | −0.175171 | −0.0875855 | − | 0.996157i | \(-0.527915\pi\) | ||||
−0.0875855 | + | 0.996157i | \(0.527915\pi\) | |||||||
\(270\) | −29.8826 | −1.81859 | ||||||||
\(271\) | −13.2464 | −0.804664 | −0.402332 | − | 0.915494i | \(-0.631800\pi\) | ||||
−0.402332 | + | 0.915494i | \(0.631800\pi\) | |||||||
\(272\) | 37.7375 | 2.28817 | ||||||||
\(273\) | −2.19608 | −0.132913 | ||||||||
\(274\) | −48.2225 | −2.91323 | ||||||||
\(275\) | 7.77050 | 0.468579 | ||||||||
\(276\) | 62.0958 | 3.73773 | ||||||||
\(277\) | −18.5693 | −1.11572 | −0.557862 | − | 0.829934i | \(-0.688378\pi\) | ||||
−0.557862 | + | 0.829934i | \(0.688378\pi\) | |||||||
\(278\) | −39.4051 | −2.36336 | ||||||||
\(279\) | 3.74687 | 0.224319 | ||||||||
\(280\) | 24.9666 | 1.49204 | ||||||||
\(281\) | −7.62473 | −0.454853 | −0.227427 | − | 0.973795i | \(-0.573031\pi\) | ||||
−0.227427 | + | 0.973795i | \(0.573031\pi\) | |||||||
\(282\) | 41.5656 | 2.47520 | ||||||||
\(283\) | −20.7301 | −1.23227 | −0.616137 | − | 0.787639i | \(-0.711303\pi\) | ||||
−0.616137 | + | 0.787639i | \(0.711303\pi\) | |||||||
\(284\) | −66.7645 | −3.96175 | ||||||||
\(285\) | 44.5268 | 2.63754 | ||||||||
\(286\) | 3.31962 | 0.196293 | ||||||||
\(287\) | −0.725222 | −0.0428085 | ||||||||
\(288\) | −2.31494 | −0.136409 | ||||||||
\(289\) | 33.4468 | 1.96746 | ||||||||
\(290\) | −6.79311 | −0.398905 | ||||||||
\(291\) | −8.22778 | −0.482321 | ||||||||
\(292\) | 10.4566 | 0.611929 | ||||||||
\(293\) | −7.54055 | −0.440524 | −0.220262 | − | 0.975441i | \(-0.570691\pi\) | ||||
−0.220262 | + | 0.975441i | \(0.570691\pi\) | |||||||
\(294\) | −24.0056 | −1.40003 | ||||||||
\(295\) | −18.6043 | −1.08318 | ||||||||
\(296\) | −31.5193 | −1.83202 | ||||||||
\(297\) | 7.13333 | 0.413918 | ||||||||
\(298\) | 50.6057 | 2.93151 | ||||||||
\(299\) | 5.38737 | 0.311560 | ||||||||
\(300\) | −36.2956 | −2.09553 | ||||||||
\(301\) | 8.82662 | 0.508758 | ||||||||
\(302\) | −18.5376 | −1.06672 | ||||||||
\(303\) | −16.1911 | −0.930155 | ||||||||
\(304\) | −38.6098 | −2.21443 | ||||||||
\(305\) | −31.7934 | −1.82048 | ||||||||
\(306\) | −18.4666 | −1.05567 | ||||||||
\(307\) | −11.6224 | −0.663324 | −0.331662 | − | 0.943398i | \(-0.607609\pi\) | ||||
−0.331662 | + | 0.943398i | \(0.607609\pi\) | |||||||
\(308\) | −11.3499 | −0.646720 | ||||||||
\(309\) | 28.0181 | 1.59389 | ||||||||
\(310\) | −27.2775 | −1.54926 | ||||||||
\(311\) | −17.5002 | −0.992347 | −0.496174 | − | 0.868223i | \(-0.665262\pi\) | ||||
−0.496174 | + | 0.868223i | \(0.665262\pi\) | |||||||
\(312\) | −8.14210 | −0.460956 | ||||||||
\(313\) | −19.3837 | −1.09563 | −0.547816 | − | 0.836599i | \(-0.684541\pi\) | ||||
−0.547816 | + | 0.836599i | \(0.684541\pi\) | |||||||
\(314\) | −0.693013 | −0.0391090 | ||||||||
\(315\) | −4.72574 | −0.266265 | ||||||||
\(316\) | −11.0351 | −0.620774 | ||||||||
\(317\) | −31.1785 | −1.75116 | −0.875579 | − | 0.483075i | \(-0.839520\pi\) | ||||
−0.875579 | + | 0.483075i | \(0.839520\pi\) | |||||||
\(318\) | 31.3033 | 1.75540 | ||||||||
\(319\) | 1.62160 | 0.0907921 | ||||||||
\(320\) | −15.5290 | −0.868096 | ||||||||
\(321\) | −18.4383 | −1.02913 | ||||||||
\(322\) | −27.1670 | −1.51396 | ||||||||
\(323\) | −51.6129 | −2.87182 | ||||||||
\(324\) | −46.4997 | −2.58332 | ||||||||
\(325\) | −3.14897 | −0.174674 | ||||||||
\(326\) | 31.5794 | 1.74902 | ||||||||
\(327\) | −19.7671 | −1.09312 | ||||||||
\(328\) | −2.68881 | −0.148465 | ||||||||
\(329\) | −12.3297 | −0.679758 | ||||||||
\(330\) | 27.6861 | 1.52407 | ||||||||
\(331\) | −7.32259 | −0.402486 | −0.201243 | − | 0.979541i | \(-0.564498\pi\) | ||||
−0.201243 | + | 0.979541i | \(0.564498\pi\) | |||||||
\(332\) | −14.8294 | −0.813871 | ||||||||
\(333\) | 5.96604 | 0.326937 | ||||||||
\(334\) | 1.28561 | 0.0703452 | ||||||||
\(335\) | 4.72431 | 0.258117 | ||||||||
\(336\) | 15.8817 | 0.866418 | ||||||||
\(337\) | 2.10284 | 0.114549 | 0.0572744 | − | 0.998358i | \(-0.481759\pi\) | ||||
0.0572744 | + | 0.998358i | \(0.481759\pi\) | |||||||
\(338\) | 31.0543 | 1.68913 | ||||||||
\(339\) | 1.40544 | 0.0763331 | ||||||||
\(340\) | 91.1511 | 4.94336 | ||||||||
\(341\) | 6.51147 | 0.352616 | ||||||||
\(342\) | 18.8935 | 1.02164 | ||||||||
\(343\) | 17.5266 | 0.946348 | ||||||||
\(344\) | 32.7253 | 1.76443 | ||||||||
\(345\) | 44.9314 | 2.41903 | ||||||||
\(346\) | 36.2366 | 1.94809 | ||||||||
\(347\) | 8.14453 | 0.437221 | 0.218611 | − | 0.975812i | \(-0.429848\pi\) | ||||
0.218611 | + | 0.975812i | \(0.429848\pi\) | |||||||
\(348\) | −7.57441 | −0.406031 | ||||||||
\(349\) | 26.2246 | 1.40377 | 0.701886 | − | 0.712289i | \(-0.252341\pi\) | ||||
0.701886 | + | 0.712289i | \(0.252341\pi\) | |||||||
\(350\) | 15.8794 | 0.848791 | ||||||||
\(351\) | −2.89076 | −0.154298 | ||||||||
\(352\) | −4.02301 | −0.214427 | ||||||||
\(353\) | 1.76259 | 0.0938135 | 0.0469067 | − | 0.998899i | \(-0.485064\pi\) | ||||
0.0469067 | + | 0.998899i | \(0.485064\pi\) | |||||||
\(354\) | −30.5953 | −1.62612 | ||||||||
\(355\) | −48.3097 | −2.56401 | ||||||||
\(356\) | −56.4565 | −2.99219 | ||||||||
\(357\) | 21.2304 | 1.12363 | ||||||||
\(358\) | 35.0460 | 1.85224 | ||||||||
\(359\) | −14.8849 | −0.785595 | −0.392797 | − | 0.919625i | \(-0.628493\pi\) | ||||
−0.392797 | + | 0.919625i | \(0.628493\pi\) | |||||||
\(360\) | −17.5210 | −0.923437 | ||||||||
\(361\) | 33.8060 | 1.77926 | ||||||||
\(362\) | −39.2355 | −2.06217 | ||||||||
\(363\) | 15.5095 | 0.814039 | ||||||||
\(364\) | 4.59951 | 0.241080 | ||||||||
\(365\) | 7.56625 | 0.396036 | ||||||||
\(366\) | −52.2852 | −2.73299 | ||||||||
\(367\) | −13.5553 | −0.707579 | −0.353789 | − | 0.935325i | \(-0.615107\pi\) | ||||
−0.353789 | + | 0.935325i | \(0.615107\pi\) | |||||||
\(368\) | −38.9607 | −2.03096 | ||||||||
\(369\) | 0.508944 | 0.0264946 | ||||||||
\(370\) | −43.4332 | −2.25799 | ||||||||
\(371\) | −9.28555 | −0.482082 | ||||||||
\(372\) | −30.4148 | −1.57693 | ||||||||
\(373\) | −1.10446 | −0.0571869 | −0.0285934 | − | 0.999591i | \(-0.509103\pi\) | ||||
−0.0285934 | + | 0.999591i | \(0.509103\pi\) | |||||||
\(374\) | −32.0921 | −1.65945 | ||||||||
\(375\) | 4.37439 | 0.225893 | ||||||||
\(376\) | −45.7132 | −2.35748 | ||||||||
\(377\) | −0.657149 | −0.0338449 | ||||||||
\(378\) | 14.5773 | 0.749777 | ||||||||
\(379\) | 12.7896 | 0.656959 | 0.328479 | − | 0.944511i | \(-0.393464\pi\) | ||||
0.328479 | + | 0.944511i | \(0.393464\pi\) | |||||||
\(380\) | −93.2581 | −4.78404 | ||||||||
\(381\) | −25.1380 | −1.28786 | ||||||||
\(382\) | −24.7379 | −1.26570 | ||||||||
\(383\) | 15.8206 | 0.808397 | 0.404198 | − | 0.914671i | \(-0.367551\pi\) | ||||
0.404198 | + | 0.914671i | \(0.367551\pi\) | |||||||
\(384\) | −34.4619 | −1.75862 | ||||||||
\(385\) | −8.21259 | −0.418552 | ||||||||
\(386\) | 9.80640 | 0.499132 | ||||||||
\(387\) | −6.19431 | −0.314875 | ||||||||
\(388\) | 17.2325 | 0.874846 | ||||||||
\(389\) | −19.8797 | −1.00794 | −0.503971 | − | 0.863721i | \(-0.668128\pi\) | ||||
−0.503971 | + | 0.863721i | \(0.668128\pi\) | |||||||
\(390\) | −11.2197 | −0.568133 | ||||||||
\(391\) | −52.0819 | −2.63389 | ||||||||
\(392\) | 26.4009 | 1.33345 | ||||||||
\(393\) | 4.61710 | 0.232902 | ||||||||
\(394\) | −4.63450 | −0.233483 | ||||||||
\(395\) | −7.98482 | −0.401760 | ||||||||
\(396\) | 7.96509 | 0.400261 | ||||||||
\(397\) | −35.5478 | −1.78409 | −0.892046 | − | 0.451945i | \(-0.850730\pi\) | ||||
−0.892046 | + | 0.451945i | \(0.850730\pi\) | |||||||
\(398\) | −47.2572 | −2.36879 | ||||||||
\(399\) | −21.7211 | −1.08742 | ||||||||
\(400\) | 22.7729 | 1.13865 | ||||||||
\(401\) | −9.54487 | −0.476648 | −0.238324 | − | 0.971186i | \(-0.576598\pi\) | ||||
−0.238324 | + | 0.971186i | \(0.576598\pi\) | |||||||
\(402\) | 7.76929 | 0.387497 | ||||||||
\(403\) | −2.63876 | −0.131446 | ||||||||
\(404\) | 33.9111 | 1.68714 | ||||||||
\(405\) | −33.6464 | −1.67190 | ||||||||
\(406\) | 3.31382 | 0.164462 | ||||||||
\(407\) | 10.3680 | 0.513925 | ||||||||
\(408\) | 78.7130 | 3.89688 | ||||||||
\(409\) | 3.91223 | 0.193447 | 0.0967236 | − | 0.995311i | \(-0.469164\pi\) | ||||
0.0967236 | + | 0.995311i | \(0.469164\pi\) | |||||||
\(410\) | −3.70515 | −0.182984 | ||||||||
\(411\) | −38.9061 | −1.91910 | ||||||||
\(412\) | −58.6817 | −2.89104 | ||||||||
\(413\) | 9.07556 | 0.446579 | ||||||||
\(414\) | 19.0652 | 0.937003 | ||||||||
\(415\) | −10.7303 | −0.526731 | ||||||||
\(416\) | 1.63032 | 0.0799328 | ||||||||
\(417\) | −31.7922 | −1.55687 | ||||||||
\(418\) | 32.8340 | 1.60596 | ||||||||
\(419\) | 19.7545 | 0.965071 | 0.482536 | − | 0.875876i | \(-0.339716\pi\) | ||||
0.482536 | + | 0.875876i | \(0.339716\pi\) | |||||||
\(420\) | 38.3606 | 1.87181 | ||||||||
\(421\) | 26.6962 | 1.30109 | 0.650547 | − | 0.759466i | \(-0.274540\pi\) | ||||
0.650547 | + | 0.759466i | \(0.274540\pi\) | |||||||
\(422\) | −31.9755 | −1.55654 | ||||||||
\(423\) | 8.65269 | 0.420708 | ||||||||
\(424\) | −34.4268 | −1.67191 | ||||||||
\(425\) | 30.4424 | 1.47667 | ||||||||
\(426\) | −79.4468 | −3.84921 | ||||||||
\(427\) | 15.5095 | 0.750556 | ||||||||
\(428\) | 38.6177 | 1.86666 | ||||||||
\(429\) | 2.67829 | 0.129309 | ||||||||
\(430\) | 45.0951 | 2.17468 | ||||||||
\(431\) | −5.57555 | −0.268565 | −0.134282 | − | 0.990943i | \(-0.542873\pi\) | ||||
−0.134282 | + | 0.990943i | \(0.542873\pi\) | |||||||
\(432\) | 20.9056 | 1.00582 | ||||||||
\(433\) | −36.9350 | −1.77498 | −0.887490 | − | 0.460826i | \(-0.847553\pi\) | ||||
−0.887490 | + | 0.460826i | \(0.847553\pi\) | |||||||
\(434\) | 13.3065 | 0.638734 | ||||||||
\(435\) | −5.48071 | −0.262780 | ||||||||
\(436\) | 41.4007 | 1.98274 | ||||||||
\(437\) | 53.2858 | 2.54901 | ||||||||
\(438\) | 12.4429 | 0.594547 | ||||||||
\(439\) | −16.8592 | −0.804645 | −0.402322 | − | 0.915498i | \(-0.631797\pi\) | ||||
−0.402322 | + | 0.915498i | \(0.631797\pi\) | |||||||
\(440\) | −30.4487 | −1.45159 | ||||||||
\(441\) | −4.99723 | −0.237963 | ||||||||
\(442\) | 13.0053 | 0.618597 | ||||||||
\(443\) | −32.8414 | −1.56034 | −0.780171 | − | 0.625566i | \(-0.784868\pi\) | ||||
−0.780171 | + | 0.625566i | \(0.784868\pi\) | |||||||
\(444\) | −48.4286 | −2.29832 | ||||||||
\(445\) | −40.8510 | −1.93652 | ||||||||
\(446\) | 30.3094 | 1.43519 | ||||||||
\(447\) | 40.8289 | 1.93114 | ||||||||
\(448\) | 7.57535 | 0.357902 | ||||||||
\(449\) | −33.4724 | −1.57966 | −0.789830 | − | 0.613326i | \(-0.789831\pi\) | ||||
−0.789830 | + | 0.613326i | \(0.789831\pi\) | |||||||
\(450\) | −11.1438 | −0.525324 | ||||||||
\(451\) | 0.884465 | 0.0416478 | ||||||||
\(452\) | −2.94359 | −0.138455 | ||||||||
\(453\) | −14.9562 | −0.702703 | ||||||||
\(454\) | −8.99162 | −0.421997 | ||||||||
\(455\) | 3.32813 | 0.156025 | ||||||||
\(456\) | −80.5325 | −3.77128 | ||||||||
\(457\) | −1.45656 | −0.0681349 | −0.0340674 | − | 0.999420i | \(-0.510846\pi\) | ||||
−0.0340674 | + | 0.999420i | \(0.510846\pi\) | |||||||
\(458\) | 0.989704 | 0.0462458 | ||||||||
\(459\) | 27.9462 | 1.30442 | ||||||||
\(460\) | −94.1055 | −4.38769 | ||||||||
\(461\) | −28.8383 | −1.34313 | −0.671566 | − | 0.740945i | \(-0.734378\pi\) | ||||
−0.671566 | + | 0.740945i | \(0.734378\pi\) | |||||||
\(462\) | −13.5059 | −0.628350 | ||||||||
\(463\) | 1.65131 | 0.0767427 | 0.0383713 | − | 0.999264i | \(-0.487783\pi\) | ||||
0.0383713 | + | 0.999264i | \(0.487783\pi\) | |||||||
\(464\) | 4.75240 | 0.220625 | ||||||||
\(465\) | −22.0076 | −1.02058 | ||||||||
\(466\) | −5.91287 | −0.273908 | ||||||||
\(467\) | −11.1947 | −0.518028 | −0.259014 | − | 0.965874i | \(-0.583398\pi\) | ||||
−0.259014 | + | 0.965874i | \(0.583398\pi\) | |||||||
\(468\) | −3.22783 | −0.149207 | ||||||||
\(469\) | −2.30462 | −0.106417 | ||||||||
\(470\) | −62.9923 | −2.90562 | ||||||||
\(471\) | −0.559126 | −0.0257632 | ||||||||
\(472\) | 33.6482 | 1.54879 | ||||||||
\(473\) | −10.7648 | −0.494964 | ||||||||
\(474\) | −13.1313 | −0.603140 | ||||||||
\(475\) | −31.1461 | −1.42908 | ||||||||
\(476\) | −44.4654 | −2.03807 | ||||||||
\(477\) | 6.51638 | 0.298365 | ||||||||
\(478\) | 15.4599 | 0.707119 | ||||||||
\(479\) | −19.9607 | −0.912027 | −0.456013 | − | 0.889973i | \(-0.650723\pi\) | ||||
−0.456013 | + | 0.889973i | \(0.650723\pi\) | |||||||
\(480\) | 13.5971 | 0.620618 | ||||||||
\(481\) | −4.20162 | −0.191577 | ||||||||
\(482\) | −69.7762 | −3.17822 | ||||||||
\(483\) | −21.9185 | −0.997326 | ||||||||
\(484\) | −32.4835 | −1.47652 | ||||||||
\(485\) | 12.4691 | 0.566193 | ||||||||
\(486\) | −25.9140 | −1.17548 | ||||||||
\(487\) | −23.2666 | −1.05431 | −0.527155 | − | 0.849769i | \(-0.676741\pi\) | ||||
−0.527155 | + | 0.849769i | \(0.676741\pi\) | |||||||
\(488\) | 57.5024 | 2.60301 | ||||||||
\(489\) | 25.4784 | 1.15217 | ||||||||
\(490\) | 36.3802 | 1.64349 | ||||||||
\(491\) | 11.4382 | 0.516197 | 0.258099 | − | 0.966119i | \(-0.416904\pi\) | ||||
0.258099 | + | 0.966119i | \(0.416904\pi\) | |||||||
\(492\) | −4.13129 | −0.186253 | ||||||||
\(493\) | 6.35292 | 0.286121 | ||||||||
\(494\) | −13.3059 | −0.598660 | ||||||||
\(495\) | 5.76341 | 0.259046 | ||||||||
\(496\) | 19.0831 | 0.856857 | ||||||||
\(497\) | 23.5665 | 1.05710 | ||||||||
\(498\) | −17.6464 | −0.790752 | ||||||||
\(499\) | 36.0134 | 1.61218 | 0.806090 | − | 0.591793i | \(-0.201580\pi\) | ||||
0.806090 | + | 0.591793i | \(0.201580\pi\) | |||||||
\(500\) | −9.16183 | −0.409730 | ||||||||
\(501\) | 1.03723 | 0.0463401 | ||||||||
\(502\) | 31.8349 | 1.42086 | ||||||||
\(503\) | −22.1046 | −0.985597 | −0.492798 | − | 0.870144i | \(-0.664026\pi\) | ||||
−0.492798 | + | 0.870144i | \(0.664026\pi\) | |||||||
\(504\) | 8.54710 | 0.380718 | ||||||||
\(505\) | 24.5375 | 1.09190 | ||||||||
\(506\) | 33.1323 | 1.47291 | ||||||||
\(507\) | 25.0547 | 1.11272 | ||||||||
\(508\) | 52.6496 | 2.33595 | ||||||||
\(509\) | −10.1137 | −0.448282 | −0.224141 | − | 0.974557i | \(-0.571958\pi\) | ||||
−0.224141 | + | 0.974557i | \(0.571958\pi\) | |||||||
\(510\) | 108.466 | 4.80294 | ||||||||
\(511\) | −3.69097 | −0.163279 | ||||||||
\(512\) | 46.7767 | 2.06726 | ||||||||
\(513\) | −28.5922 | −1.26238 | ||||||||
\(514\) | −36.8598 | −1.62582 | ||||||||
\(515\) | −42.4611 | −1.87106 | ||||||||
\(516\) | 50.2816 | 2.21353 | ||||||||
\(517\) | 15.0370 | 0.661328 | ||||||||
\(518\) | 21.1876 | 0.930931 | ||||||||
\(519\) | 29.2359 | 1.28331 | ||||||||
\(520\) | 12.3393 | 0.541113 | ||||||||
\(521\) | −8.77705 | −0.384530 | −0.192265 | − | 0.981343i | \(-0.561583\pi\) | ||||
−0.192265 | + | 0.981343i | \(0.561583\pi\) | |||||||
\(522\) | −2.32556 | −0.101787 | ||||||||
\(523\) | 0.378503 | 0.0165508 | 0.00827540 | − | 0.999966i | \(-0.497366\pi\) | ||||
0.00827540 | + | 0.999966i | \(0.497366\pi\) | |||||||
\(524\) | −9.67016 | −0.422443 | ||||||||
\(525\) | 12.8116 | 0.559143 | ||||||||
\(526\) | −23.9892 | −1.04598 | ||||||||
\(527\) | 25.5099 | 1.11123 | ||||||||
\(528\) | −19.3690 | −0.842927 | ||||||||
\(529\) | 30.7700 | 1.33783 | ||||||||
\(530\) | −47.4398 | −2.06065 | ||||||||
\(531\) | −6.36901 | −0.276392 | ||||||||
\(532\) | 45.4932 | 1.97238 | ||||||||
\(533\) | −0.358427 | −0.0155252 | ||||||||
\(534\) | −67.1808 | −2.90720 | ||||||||
\(535\) | 27.9431 | 1.20809 | ||||||||
\(536\) | −8.54453 | −0.369067 | ||||||||
\(537\) | 28.2753 | 1.22017 | ||||||||
\(538\) | 7.16034 | 0.308704 | ||||||||
\(539\) | −8.68440 | −0.374064 | ||||||||
\(540\) | 50.4953 | 2.17297 | ||||||||
\(541\) | 24.0453 | 1.03379 | 0.516894 | − | 0.856049i | \(-0.327088\pi\) | ||||
0.516894 | + | 0.856049i | \(0.327088\pi\) | |||||||
\(542\) | 33.0137 | 1.41806 | ||||||||
\(543\) | −31.6554 | −1.35846 | ||||||||
\(544\) | −15.7609 | −0.675744 | ||||||||
\(545\) | 29.9569 | 1.28321 | ||||||||
\(546\) | 5.47322 | 0.234232 | ||||||||
\(547\) | 15.3017 | 0.654254 | 0.327127 | − | 0.944980i | \(-0.393920\pi\) | ||||
0.327127 | + | 0.944980i | \(0.393920\pi\) | |||||||
\(548\) | 81.4859 | 3.48091 | ||||||||
\(549\) | −10.8842 | −0.464526 | ||||||||
\(550\) | −19.3662 | −0.825777 | ||||||||
\(551\) | −6.49978 | −0.276900 | ||||||||
\(552\) | −81.2643 | −3.45884 | ||||||||
\(553\) | 3.89516 | 0.165639 | ||||||||
\(554\) | 46.2798 | 1.96624 | ||||||||
\(555\) | −35.0421 | −1.48746 | ||||||||
\(556\) | 66.5863 | 2.82389 | ||||||||
\(557\) | −44.3719 | −1.88010 | −0.940048 | − | 0.341043i | \(-0.889220\pi\) | ||||
−0.940048 | + | 0.341043i | \(0.889220\pi\) | |||||||
\(558\) | −9.33822 | −0.395318 | ||||||||
\(559\) | 4.36239 | 0.184509 | ||||||||
\(560\) | −24.0686 | −1.01708 | ||||||||
\(561\) | −25.8921 | −1.09316 | ||||||||
\(562\) | 19.0029 | 0.801589 | ||||||||
\(563\) | 45.9532 | 1.93669 | 0.968347 | − | 0.249606i | \(-0.0803013\pi\) | ||||
0.968347 | + | 0.249606i | \(0.0803013\pi\) | |||||||
\(564\) | −70.2372 | −2.95752 | ||||||||
\(565\) | −2.12993 | −0.0896069 | ||||||||
\(566\) | 51.6649 | 2.17164 | ||||||||
\(567\) | 16.4134 | 0.689299 | ||||||||
\(568\) | 87.3743 | 3.66614 | ||||||||
\(569\) | 15.6044 | 0.654171 | 0.327086 | − | 0.944995i | \(-0.393933\pi\) | ||||
0.327086 | + | 0.944995i | \(0.393933\pi\) | |||||||
\(570\) | −110.973 | −4.64815 | ||||||||
\(571\) | −23.1792 | −0.970020 | −0.485010 | − | 0.874509i | \(-0.661184\pi\) | ||||
−0.485010 | + | 0.874509i | \(0.661184\pi\) | |||||||
\(572\) | −5.60947 | −0.234544 | ||||||||
\(573\) | −19.9587 | −0.833786 | ||||||||
\(574\) | 1.80745 | 0.0754415 | ||||||||
\(575\) | −31.4291 | −1.31068 | ||||||||
\(576\) | −5.31621 | −0.221509 | ||||||||
\(577\) | 5.25001 | 0.218561 | 0.109280 | − | 0.994011i | \(-0.465145\pi\) | ||||
0.109280 | + | 0.994011i | \(0.465145\pi\) | |||||||
\(578\) | −83.3585 | −3.46726 | ||||||||
\(579\) | 7.91184 | 0.328805 | ||||||||
\(580\) | 11.4789 | 0.476637 | ||||||||
\(581\) | 5.23447 | 0.217163 | ||||||||
\(582\) | 20.5059 | 0.849995 | ||||||||
\(583\) | 11.3245 | 0.469011 | ||||||||
\(584\) | −13.6845 | −0.566270 | ||||||||
\(585\) | −2.33561 | −0.0965654 | ||||||||
\(586\) | 18.7931 | 0.776336 | ||||||||
\(587\) | −19.2267 | −0.793572 | −0.396786 | − | 0.917911i | \(-0.629874\pi\) | ||||
−0.396786 | + | 0.917911i | \(0.629874\pi\) | |||||||
\(588\) | 40.5644 | 1.67285 | ||||||||
\(589\) | −26.0996 | −1.07542 | ||||||||
\(590\) | 46.3669 | 1.90890 | ||||||||
\(591\) | −3.73914 | −0.153807 | ||||||||
\(592\) | 30.3855 | 1.24884 | ||||||||
\(593\) | 20.7962 | 0.853997 | 0.426999 | − | 0.904252i | \(-0.359571\pi\) | ||||
0.426999 | + | 0.904252i | \(0.359571\pi\) | |||||||
\(594\) | −17.7782 | −0.729448 | ||||||||
\(595\) | −32.1744 | −1.31902 | ||||||||
\(596\) | −85.5131 | −3.50275 | ||||||||
\(597\) | −38.1273 | −1.56045 | ||||||||
\(598\) | −13.4268 | −0.549062 | ||||||||
\(599\) | 6.37206 | 0.260355 | 0.130178 | − | 0.991491i | \(-0.458445\pi\) | ||||
0.130178 | + | 0.991491i | \(0.458445\pi\) | |||||||
\(600\) | 47.4998 | 1.93917 | ||||||||
\(601\) | −21.3356 | −0.870298 | −0.435149 | − | 0.900358i | \(-0.643304\pi\) | ||||
−0.435149 | + | 0.900358i | \(0.643304\pi\) | |||||||
\(602\) | −21.9983 | −0.896585 | ||||||||
\(603\) | 1.61733 | 0.0658627 | ||||||||
\(604\) | 31.3246 | 1.27458 | ||||||||
\(605\) | −23.5045 | −0.955594 | ||||||||
\(606\) | 40.3526 | 1.63921 | ||||||||
\(607\) | −8.37527 | −0.339942 | −0.169971 | − | 0.985449i | \(-0.554367\pi\) | ||||
−0.169971 | + | 0.985449i | \(0.554367\pi\) | |||||||
\(608\) | 16.1252 | 0.653965 | ||||||||
\(609\) | 2.67361 | 0.108340 | ||||||||
\(610\) | 79.2377 | 3.20824 | ||||||||
\(611\) | −6.09371 | −0.246525 | ||||||||
\(612\) | 31.2048 | 1.26138 | ||||||||
\(613\) | −25.7291 | −1.03919 | −0.519594 | − | 0.854414i | \(-0.673917\pi\) | ||||
−0.519594 | + | 0.854414i | \(0.673917\pi\) | |||||||
\(614\) | 28.9661 | 1.16898 | ||||||||
\(615\) | −2.98933 | −0.120542 | ||||||||
\(616\) | 14.8535 | 0.598466 | ||||||||
\(617\) | −24.0046 | −0.966387 | −0.483194 | − | 0.875513i | \(-0.660523\pi\) | ||||
−0.483194 | + | 0.875513i | \(0.660523\pi\) | |||||||
\(618\) | −69.8286 | −2.80892 | ||||||||
\(619\) | −20.7203 | −0.832821 | −0.416411 | − | 0.909177i | \(-0.636712\pi\) | ||||
−0.416411 | + | 0.909177i | \(0.636712\pi\) | |||||||
\(620\) | 46.0933 | 1.85115 | ||||||||
\(621\) | −28.8520 | −1.15779 | ||||||||
\(622\) | 43.6153 | 1.74882 | ||||||||
\(623\) | 19.9280 | 0.798397 | ||||||||
\(624\) | 7.84923 | 0.314221 | ||||||||
\(625\) | −28.0598 | −1.12239 | ||||||||
\(626\) | 48.3095 | 1.93084 | ||||||||
\(627\) | 26.4906 | 1.05793 | ||||||||
\(628\) | 1.17105 | 0.0467299 | ||||||||
\(629\) | 40.6188 | 1.61958 | ||||||||
\(630\) | 11.7778 | 0.469239 | ||||||||
\(631\) | 30.7767 | 1.22520 | 0.612601 | − | 0.790392i | \(-0.290123\pi\) | ||||
0.612601 | + | 0.790392i | \(0.290123\pi\) | |||||||
\(632\) | 14.4416 | 0.574455 | ||||||||
\(633\) | −25.7980 | −1.02538 | ||||||||
\(634\) | 77.7053 | 3.08607 | ||||||||
\(635\) | 38.0963 | 1.51181 | ||||||||
\(636\) | −52.8960 | −2.09746 | ||||||||
\(637\) | 3.51933 | 0.139441 | ||||||||
\(638\) | −4.04146 | −0.160003 | ||||||||
\(639\) | −16.5384 | −0.654249 | ||||||||
\(640\) | 52.2266 | 2.06444 | ||||||||
\(641\) | −34.9482 | −1.38037 | −0.690186 | − | 0.723632i | \(-0.742471\pi\) | ||||
−0.690186 | + | 0.723632i | \(0.742471\pi\) | |||||||
\(642\) | 45.9533 | 1.81363 | ||||||||
\(643\) | −24.1299 | −0.951589 | −0.475795 | − | 0.879556i | \(-0.657839\pi\) | ||||
−0.475795 | + | 0.879556i | \(0.657839\pi\) | |||||||
\(644\) | 45.9066 | 1.80897 | ||||||||
\(645\) | 36.3829 | 1.43258 | ||||||||
\(646\) | 128.633 | 5.06101 | ||||||||
\(647\) | −38.9842 | −1.53263 | −0.766314 | − | 0.642467i | \(-0.777911\pi\) | ||||
−0.766314 | + | 0.642467i | \(0.777911\pi\) | |||||||
\(648\) | 60.8539 | 2.39057 | ||||||||
\(649\) | −11.0684 | −0.434471 | ||||||||
\(650\) | 7.84810 | 0.307828 | ||||||||
\(651\) | 10.7358 | 0.420768 | ||||||||
\(652\) | −53.3625 | −2.08984 | ||||||||
\(653\) | 27.0495 | 1.05853 | 0.529264 | − | 0.848457i | \(-0.322468\pi\) | ||||
0.529264 | + | 0.848457i | \(0.322468\pi\) | |||||||
\(654\) | 49.2651 | 1.92642 | ||||||||
\(655\) | −6.99716 | −0.273402 | ||||||||
\(656\) | 2.59209 | 0.101204 | ||||||||
\(657\) | 2.59024 | 0.101055 | ||||||||
\(658\) | 30.7289 | 1.19794 | ||||||||
\(659\) | 46.4477 | 1.80935 | 0.904674 | − | 0.426105i | \(-0.140115\pi\) | ||||
0.904674 | + | 0.426105i | \(0.140115\pi\) | |||||||
\(660\) | −46.7838 | −1.82106 | ||||||||
\(661\) | 15.3565 | 0.597298 | 0.298649 | − | 0.954363i | \(-0.403464\pi\) | ||||
0.298649 | + | 0.954363i | \(0.403464\pi\) | |||||||
\(662\) | 18.2499 | 0.709302 | ||||||||
\(663\) | 10.4927 | 0.407503 | ||||||||
\(664\) | 19.4072 | 0.753144 | ||||||||
\(665\) | 32.9181 | 1.27651 | ||||||||
\(666\) | −14.8690 | −0.576161 | ||||||||
\(667\) | −6.55883 | −0.253959 | ||||||||
\(668\) | −2.17241 | −0.0840529 | ||||||||
\(669\) | 24.4537 | 0.945436 | ||||||||
\(670\) | −11.7743 | −0.454880 | ||||||||
\(671\) | −18.9150 | −0.730206 | ||||||||
\(672\) | −6.63293 | −0.255871 | ||||||||
\(673\) | 22.1275 | 0.852952 | 0.426476 | − | 0.904499i | \(-0.359755\pi\) | ||||
0.426476 | + | 0.904499i | \(0.359755\pi\) | |||||||
\(674\) | −5.24084 | −0.201870 | ||||||||
\(675\) | 16.8643 | 0.649107 | ||||||||
\(676\) | −52.4752 | −2.01828 | ||||||||
\(677\) | 45.0914 | 1.73300 | 0.866501 | − | 0.499175i | \(-0.166363\pi\) | ||||
0.866501 | + | 0.499175i | \(0.166363\pi\) | |||||||
\(678\) | −3.50274 | −0.134522 | ||||||||
\(679\) | −6.08269 | −0.233432 | ||||||||
\(680\) | −119.289 | −4.57452 | ||||||||
\(681\) | −7.25448 | −0.277992 | ||||||||
\(682\) | −16.2284 | −0.621416 | ||||||||
\(683\) | 6.70640 | 0.256613 | 0.128307 | − | 0.991735i | \(-0.459046\pi\) | ||||
0.128307 | + | 0.991735i | \(0.459046\pi\) | |||||||
\(684\) | −31.9261 | −1.22072 | ||||||||
\(685\) | 58.9618 | 2.25282 | ||||||||
\(686\) | −43.6811 | −1.66775 | ||||||||
\(687\) | 0.798497 | 0.0304646 | ||||||||
\(688\) | −31.5481 | −1.20276 | ||||||||
\(689\) | −4.58921 | −0.174835 | ||||||||
\(690\) | −111.981 | −4.26306 | ||||||||
\(691\) | −14.2057 | −0.540409 | −0.270205 | − | 0.962803i | \(-0.587091\pi\) | ||||
−0.270205 | + | 0.962803i | \(0.587091\pi\) | |||||||
\(692\) | −61.2323 | −2.32770 | ||||||||
\(693\) | −2.81151 | −0.106800 | ||||||||
\(694\) | −20.2984 | −0.770516 | ||||||||
\(695\) | 48.1807 | 1.82760 | ||||||||
\(696\) | 9.91258 | 0.375735 | ||||||||
\(697\) | 3.46506 | 0.131249 | ||||||||
\(698\) | −65.3589 | −2.47387 | ||||||||
\(699\) | −4.77053 | −0.180438 | ||||||||
\(700\) | −26.8329 | −1.01419 | ||||||||
\(701\) | −15.2076 | −0.574382 | −0.287191 | − | 0.957873i | \(-0.592722\pi\) | ||||
−0.287191 | + | 0.957873i | \(0.592722\pi\) | |||||||
\(702\) | 7.20457 | 0.271919 | ||||||||
\(703\) | −41.5577 | −1.56738 | ||||||||
\(704\) | −9.23874 | −0.348198 | ||||||||
\(705\) | −50.8225 | −1.91408 | ||||||||
\(706\) | −4.39286 | −0.165328 | ||||||||
\(707\) | −11.9699 | −0.450174 | ||||||||
\(708\) | 51.6997 | 1.94300 | ||||||||
\(709\) | −40.2206 | −1.51052 | −0.755258 | − | 0.655428i | \(-0.772488\pi\) | ||||
−0.755258 | + | 0.655428i | \(0.772488\pi\) | |||||||
\(710\) | 120.401 | 4.51856 | ||||||||
\(711\) | −2.73353 | −0.102516 | ||||||||
\(712\) | 73.8843 | 2.76893 | ||||||||
\(713\) | −26.3368 | −0.986320 | ||||||||
\(714\) | −52.9118 | −1.98018 | ||||||||
\(715\) | −4.05892 | −0.151795 | ||||||||
\(716\) | −59.2204 | −2.21317 | ||||||||
\(717\) | 12.4731 | 0.465817 | ||||||||
\(718\) | 37.0972 | 1.38446 | ||||||||
\(719\) | −13.0822 | −0.487885 | −0.243943 | − | 0.969790i | \(-0.578441\pi\) | ||||
−0.243943 | + | 0.969790i | \(0.578441\pi\) | |||||||
\(720\) | 16.8908 | 0.629481 | ||||||||
\(721\) | 20.7134 | 0.771407 | ||||||||
\(722\) | −84.2537 | −3.13560 | ||||||||
\(723\) | −56.2958 | −2.09366 | ||||||||
\(724\) | 66.2998 | 2.46401 | ||||||||
\(725\) | 3.83371 | 0.142380 | ||||||||
\(726\) | −38.6539 | −1.43458 | ||||||||
\(727\) | 52.3050 | 1.93988 | 0.969942 | − | 0.243337i | \(-0.0782422\pi\) | ||||
0.969942 | + | 0.243337i | \(0.0782422\pi\) | |||||||
\(728\) | −6.01935 | −0.223092 | ||||||||
\(729\) | 12.2165 | 0.452464 | ||||||||
\(730\) | −18.8571 | −0.697934 | ||||||||
\(731\) | −42.1730 | −1.55982 | ||||||||
\(732\) | 88.3511 | 3.26555 | ||||||||
\(733\) | 36.8407 | 1.36074 | 0.680371 | − | 0.732867i | \(-0.261818\pi\) | ||||
0.680371 | + | 0.732867i | \(0.261818\pi\) | |||||||
\(734\) | 33.7834 | 1.24697 | ||||||||
\(735\) | 29.3517 | 1.08265 | ||||||||
\(736\) | 16.2718 | 0.599785 | ||||||||
\(737\) | 2.81066 | 0.103532 | ||||||||
\(738\) | −1.26843 | −0.0466914 | ||||||||
\(739\) | −19.2840 | −0.709374 | −0.354687 | − | 0.934985i | \(-0.615413\pi\) | ||||
−0.354687 | + | 0.934985i | \(0.615413\pi\) | |||||||
\(740\) | 73.3931 | 2.69798 | ||||||||
\(741\) | −10.7352 | −0.394369 | ||||||||
\(742\) | 23.1421 | 0.849574 | ||||||||
\(743\) | 44.5137 | 1.63305 | 0.816525 | − | 0.577311i | \(-0.195898\pi\) | ||||
0.816525 | + | 0.577311i | \(0.195898\pi\) | |||||||
\(744\) | 39.8036 | 1.45927 | ||||||||
\(745\) | −61.8758 | −2.26696 | ||||||||
\(746\) | 2.75262 | 0.100781 | ||||||||
\(747\) | −3.67343 | −0.134404 | ||||||||
\(748\) | 54.2290 | 1.98281 | ||||||||
\(749\) | −13.6312 | −0.498074 | ||||||||
\(750\) | −10.9022 | −0.398091 | ||||||||
\(751\) | 52.6786 | 1.92227 | 0.961134 | − | 0.276082i | \(-0.0890363\pi\) | ||||
0.961134 | + | 0.276082i | \(0.0890363\pi\) | |||||||
\(752\) | 44.0688 | 1.60703 | ||||||||
\(753\) | 25.6845 | 0.935995 | ||||||||
\(754\) | 1.63779 | 0.0596449 | ||||||||
\(755\) | 22.6660 | 0.824899 | ||||||||
\(756\) | −24.6326 | −0.895880 | ||||||||
\(757\) | −5.41857 | −0.196941 | −0.0984706 | − | 0.995140i | \(-0.531395\pi\) | ||||
−0.0984706 | + | 0.995140i | \(0.531395\pi\) | |||||||
\(758\) | −31.8752 | −1.15776 | ||||||||
\(759\) | 26.7313 | 0.970285 | ||||||||
\(760\) | 122.046 | 4.42708 | ||||||||
\(761\) | −28.3297 | −1.02695 | −0.513476 | − | 0.858104i | \(-0.671643\pi\) | ||||
−0.513476 | + | 0.858104i | \(0.671643\pi\) | |||||||
\(762\) | 62.6506 | 2.26959 | ||||||||
\(763\) | −14.6136 | −0.529047 | ||||||||
\(764\) | 41.8019 | 1.51234 | ||||||||
\(765\) | 22.5792 | 0.816354 | ||||||||
\(766\) | −39.4293 | −1.42464 | ||||||||
\(767\) | 4.48542 | 0.161959 | ||||||||
\(768\) | 65.3947 | 2.35973 | ||||||||
\(769\) | −26.6659 | −0.961598 | −0.480799 | − | 0.876831i | \(-0.659653\pi\) | ||||
−0.480799 | + | 0.876831i | \(0.659653\pi\) | |||||||
\(770\) | 20.4680 | 0.737616 | ||||||||
\(771\) | −29.7387 | −1.07101 | ||||||||
\(772\) | −16.5708 | −0.596395 | ||||||||
\(773\) | −11.3726 | −0.409045 | −0.204523 | − | 0.978862i | \(-0.565564\pi\) | ||||
−0.204523 | + | 0.978862i | \(0.565564\pi\) | |||||||
\(774\) | 15.4379 | 0.554904 | ||||||||
\(775\) | 15.3941 | 0.552973 | ||||||||
\(776\) | −22.5520 | −0.809570 | ||||||||
\(777\) | 17.0943 | 0.613254 | ||||||||
\(778\) | 49.5456 | 1.77630 | ||||||||
\(779\) | −3.54516 | −0.127018 | ||||||||
\(780\) | 18.9590 | 0.678841 | ||||||||
\(781\) | −28.7411 | −1.02844 | ||||||||
\(782\) | 129.802 | 4.64172 | ||||||||
\(783\) | 3.51935 | 0.125771 | ||||||||
\(784\) | −25.4513 | −0.908974 | ||||||||
\(785\) | 0.847350 | 0.0302432 | ||||||||
\(786\) | −11.5071 | −0.410443 | ||||||||
\(787\) | −42.0610 | −1.49931 | −0.749656 | − | 0.661828i | \(-0.769781\pi\) | ||||
−0.749656 | + | 0.661828i | \(0.769781\pi\) | |||||||
\(788\) | 7.83133 | 0.278980 | ||||||||
\(789\) | −19.3546 | −0.689043 | ||||||||
\(790\) | 19.9003 | 0.708022 | ||||||||
\(791\) | 1.03902 | 0.0369435 | ||||||||
\(792\) | −10.4239 | −0.370396 | ||||||||
\(793\) | 7.66526 | 0.272201 | ||||||||
\(794\) | 88.5947 | 3.14411 | ||||||||
\(795\) | −38.2746 | −1.35746 | ||||||||
\(796\) | 79.8548 | 2.83038 | ||||||||
\(797\) | −36.8507 | −1.30532 | −0.652659 | − | 0.757652i | \(-0.726347\pi\) | ||||
−0.652659 | + | 0.757652i | \(0.726347\pi\) | |||||||
\(798\) | 54.1349 | 1.91636 | ||||||||
\(799\) | 58.9104 | 2.08410 | ||||||||
\(800\) | −9.51102 | −0.336265 | ||||||||
\(801\) | −13.9850 | −0.494135 | ||||||||
\(802\) | 23.7884 | 0.839997 | ||||||||
\(803\) | 4.50143 | 0.158852 | ||||||||
\(804\) | −13.1285 | −0.463005 | ||||||||
\(805\) | 33.2172 | 1.17075 | ||||||||
\(806\) | 6.57650 | 0.231647 | ||||||||
\(807\) | 5.77700 | 0.203360 | ||||||||
\(808\) | −44.3792 | −1.56125 | ||||||||
\(809\) | −31.1210 | −1.09416 | −0.547078 | − | 0.837081i | \(-0.684260\pi\) | ||||
−0.547078 | + | 0.837081i | \(0.684260\pi\) | |||||||
\(810\) | 83.8560 | 2.94640 | ||||||||
\(811\) | −12.3799 | −0.434717 | −0.217359 | − | 0.976092i | \(-0.569744\pi\) | ||||
−0.217359 | + | 0.976092i | \(0.569744\pi\) | |||||||
\(812\) | −5.59966 | −0.196510 | ||||||||
\(813\) | 26.6356 | 0.934153 | ||||||||
\(814\) | −25.8400 | −0.905690 | ||||||||
\(815\) | −38.6122 | −1.35253 | ||||||||
\(816\) | −75.8817 | −2.65639 | ||||||||
\(817\) | 43.1478 | 1.50955 | ||||||||
\(818\) | −9.75033 | −0.340912 | ||||||||
\(819\) | 1.13936 | 0.0398123 | ||||||||
\(820\) | 6.26093 | 0.218641 | ||||||||
\(821\) | −38.7074 | −1.35090 | −0.675449 | − | 0.737407i | \(-0.736050\pi\) | ||||
−0.675449 | + | 0.737407i | \(0.736050\pi\) | |||||||
\(822\) | 96.9646 | 3.38203 | ||||||||
\(823\) | 3.21963 | 0.112229 | 0.0561146 | − | 0.998424i | \(-0.482129\pi\) | ||||
0.0561146 | + | 0.998424i | \(0.482129\pi\) | |||||||
\(824\) | 76.7964 | 2.67533 | ||||||||
\(825\) | −15.6247 | −0.543983 | ||||||||
\(826\) | −22.6187 | −0.787007 | ||||||||
\(827\) | −40.6278 | −1.41277 | −0.706383 | − | 0.707829i | \(-0.749675\pi\) | ||||
−0.706383 | + | 0.707829i | \(0.749675\pi\) | |||||||
\(828\) | −32.2162 | −1.11959 | ||||||||
\(829\) | −49.0885 | −1.70491 | −0.852457 | − | 0.522797i | \(-0.824889\pi\) | ||||
−0.852457 | + | 0.522797i | \(0.824889\pi\) | |||||||
\(830\) | 26.7429 | 0.928259 | ||||||||
\(831\) | 37.3388 | 1.29527 | ||||||||
\(832\) | 3.74397 | 0.129799 | ||||||||
\(833\) | −34.0228 | −1.17882 | ||||||||
\(834\) | 79.2348 | 2.74368 | ||||||||
\(835\) | −1.57192 | −0.0543984 | ||||||||
\(836\) | −55.4826 | −1.91890 | ||||||||
\(837\) | 14.1318 | 0.488468 | ||||||||
\(838\) | −49.2336 | −1.70075 | ||||||||
\(839\) | −33.8274 | −1.16785 | −0.583925 | − | 0.811807i | \(-0.698484\pi\) | ||||
−0.583925 | + | 0.811807i | \(0.698484\pi\) | |||||||
\(840\) | −50.2023 | −1.73214 | ||||||||
\(841\) | −28.2000 | −0.972412 | ||||||||
\(842\) | −66.5342 | −2.29292 | ||||||||
\(843\) | 15.3316 | 0.528049 | ||||||||
\(844\) | 54.0319 | 1.85985 | ||||||||
\(845\) | −37.9702 | −1.30621 | ||||||||
\(846\) | −21.5649 | −0.741415 | ||||||||
\(847\) | 11.4660 | 0.393976 | ||||||||
\(848\) | 33.1885 | 1.13970 | ||||||||
\(849\) | 41.6835 | 1.43057 | ||||||||
\(850\) | −75.8708 | −2.60235 | ||||||||
\(851\) | −41.9353 | −1.43752 | ||||||||
\(852\) | 134.249 | 4.59928 | ||||||||
\(853\) | 18.6848 | 0.639754 | 0.319877 | − | 0.947459i | \(-0.396358\pi\) | ||||
0.319877 | + | 0.947459i | \(0.396358\pi\) | |||||||
\(854\) | −38.6538 | −1.32271 | ||||||||
\(855\) | −23.1012 | −0.790044 | ||||||||
\(856\) | −50.5387 | −1.72738 | ||||||||
\(857\) | 41.1963 | 1.40724 | 0.703620 | − | 0.710577i | \(-0.251566\pi\) | ||||
0.703620 | + | 0.710577i | \(0.251566\pi\) | |||||||
\(858\) | −6.67502 | −0.227881 | ||||||||
\(859\) | 25.7853 | 0.879783 | 0.439892 | − | 0.898051i | \(-0.355017\pi\) | ||||
0.439892 | + | 0.898051i | \(0.355017\pi\) | |||||||
\(860\) | −76.2013 | −2.59844 | ||||||||
\(861\) | 1.45826 | 0.0496973 | ||||||||
\(862\) | 13.8958 | 0.473292 | ||||||||
\(863\) | 26.3058 | 0.895461 | 0.447731 | − | 0.894169i | \(-0.352232\pi\) | ||||
0.447731 | + | 0.894169i | \(0.352232\pi\) | |||||||
\(864\) | −8.73113 | −0.297039 | ||||||||
\(865\) | −44.3067 | −1.50647 | ||||||||
\(866\) | 92.0519 | 3.12805 | ||||||||
\(867\) | −67.2540 | −2.28407 | ||||||||
\(868\) | −22.4853 | −0.763199 | ||||||||
\(869\) | −4.75045 | −0.161148 | ||||||||
\(870\) | 13.6594 | 0.463098 | ||||||||
\(871\) | −1.13901 | −0.0385940 | ||||||||
\(872\) | −54.1809 | −1.83480 | ||||||||
\(873\) | 4.26869 | 0.144473 | ||||||||
\(874\) | −132.803 | −4.49212 | ||||||||
\(875\) | 3.23393 | 0.109327 | ||||||||
\(876\) | −21.0260 | −0.710401 | ||||||||
\(877\) | 34.1517 | 1.15322 | 0.576610 | − | 0.817020i | \(-0.304375\pi\) | ||||
0.576610 | + | 0.817020i | \(0.304375\pi\) | |||||||
\(878\) | 42.0177 | 1.41803 | ||||||||
\(879\) | 15.1624 | 0.511414 | ||||||||
\(880\) | 29.3535 | 0.989506 | ||||||||
\(881\) | −29.6422 | −0.998670 | −0.499335 | − | 0.866409i | \(-0.666422\pi\) | ||||
−0.499335 | + | 0.866409i | \(0.666422\pi\) | |||||||
\(882\) | 12.4544 | 0.419363 | ||||||||
\(883\) | 5.95819 | 0.200509 | 0.100255 | − | 0.994962i | \(-0.468034\pi\) | ||||
0.100255 | + | 0.994962i | \(0.468034\pi\) | |||||||
\(884\) | −21.9762 | −0.739139 | ||||||||
\(885\) | 37.4091 | 1.25749 | ||||||||
\(886\) | 81.8497 | 2.74979 | ||||||||
\(887\) | −39.9739 | −1.34219 | −0.671096 | − | 0.741371i | \(-0.734176\pi\) | ||||
−0.671096 | + | 0.741371i | \(0.734176\pi\) | |||||||
\(888\) | 63.3782 | 2.12683 | ||||||||
\(889\) | −18.5842 | −0.623293 | ||||||||
\(890\) | 101.812 | 3.41274 | ||||||||
\(891\) | −20.0175 | −0.670610 | ||||||||
\(892\) | −51.2165 | −1.71486 | ||||||||
\(893\) | −60.2722 | −2.01693 | ||||||||
\(894\) | −101.757 | −3.40326 | ||||||||
\(895\) | −42.8509 | −1.43235 | ||||||||
\(896\) | −25.4772 | −0.851134 | ||||||||
\(897\) | −10.8328 | −0.361696 | ||||||||
\(898\) | 83.4223 | 2.78384 | ||||||||
\(899\) | 3.21255 | 0.107144 | ||||||||
\(900\) | 18.8307 | 0.627690 | ||||||||
\(901\) | 44.3657 | 1.47804 | ||||||||
\(902\) | −2.20433 | −0.0733961 | ||||||||
\(903\) | −17.7483 | −0.590628 | ||||||||
\(904\) | 3.85226 | 0.128124 | ||||||||
\(905\) | 47.9734 | 1.59469 | ||||||||
\(906\) | 37.2749 | 1.23838 | ||||||||
\(907\) | −17.9986 | −0.597635 | −0.298818 | − | 0.954310i | \(-0.596592\pi\) | ||||
−0.298818 | + | 0.954310i | \(0.596592\pi\) | |||||||
\(908\) | 15.1939 | 0.504229 | ||||||||
\(909\) | 8.40019 | 0.278617 | ||||||||
\(910\) | −8.29461 | −0.274964 | ||||||||
\(911\) | −42.8797 | −1.42067 | −0.710335 | − | 0.703864i | \(-0.751456\pi\) | ||||
−0.710335 | + | 0.703864i | \(0.751456\pi\) | |||||||
\(912\) | 77.6357 | 2.57078 | ||||||||
\(913\) | −6.38385 | −0.211275 | ||||||||
\(914\) | 3.63014 | 0.120074 | ||||||||
\(915\) | 63.9294 | 2.11344 | ||||||||
\(916\) | −1.67239 | −0.0552574 | ||||||||
\(917\) | 3.41336 | 0.112719 | ||||||||
\(918\) | −69.6495 | −2.29878 | ||||||||
\(919\) | −30.7738 | −1.01513 | −0.507566 | − | 0.861613i | \(-0.669455\pi\) | ||||
−0.507566 | + | 0.861613i | \(0.669455\pi\) | |||||||
\(920\) | 123.155 | 4.06031 | ||||||||
\(921\) | 23.3700 | 0.770068 | ||||||||
\(922\) | 71.8728 | 2.36700 | ||||||||
\(923\) | 11.6473 | 0.383375 | ||||||||
\(924\) | 22.8221 | 0.750792 | ||||||||
\(925\) | 24.5116 | 0.805938 | ||||||||
\(926\) | −4.11550 | −0.135244 | ||||||||
\(927\) | −14.5362 | −0.477431 | ||||||||
\(928\) | −1.98482 | −0.0651550 | ||||||||
\(929\) | 42.3287 | 1.38876 | 0.694380 | − | 0.719609i | \(-0.255679\pi\) | ||||
0.694380 | + | 0.719609i | \(0.255679\pi\) | |||||||
\(930\) | 54.8490 | 1.79857 | ||||||||
\(931\) | 34.8093 | 1.14083 | ||||||||
\(932\) | 9.99151 | 0.327283 | ||||||||
\(933\) | 35.1891 | 1.15204 | ||||||||
\(934\) | 27.9002 | 0.912922 | ||||||||
\(935\) | 39.2392 | 1.28326 | ||||||||
\(936\) | 4.22424 | 0.138074 | ||||||||
\(937\) | −35.4622 | −1.15850 | −0.579250 | − | 0.815150i | \(-0.696655\pi\) | ||||
−0.579250 | + | 0.815150i | \(0.696655\pi\) | |||||||
\(938\) | 5.74373 | 0.187540 | ||||||||
\(939\) | 38.9763 | 1.27194 | ||||||||
\(940\) | 106.444 | 3.47181 | ||||||||
\(941\) | 29.9952 | 0.977816 | 0.488908 | − | 0.872335i | \(-0.337395\pi\) | ||||
0.488908 | + | 0.872335i | \(0.337395\pi\) | |||||||
\(942\) | 1.39349 | 0.0454025 | ||||||||
\(943\) | −3.57737 | −0.116495 | ||||||||
\(944\) | −32.4379 | −1.05576 | ||||||||
\(945\) | −17.8238 | −0.579807 | ||||||||
\(946\) | 26.8287 | 0.872276 | ||||||||
\(947\) | −47.5511 | −1.54520 | −0.772601 | − | 0.634892i | \(-0.781045\pi\) | ||||
−0.772601 | + | 0.634892i | \(0.781045\pi\) | |||||||
\(948\) | 22.1891 | 0.720670 | ||||||||
\(949\) | −1.82419 | −0.0592158 | ||||||||
\(950\) | 77.6246 | 2.51847 | ||||||||
\(951\) | 62.6930 | 2.03296 | ||||||||
\(952\) | 58.1915 | 1.88600 | ||||||||
\(953\) | −10.7101 | −0.346935 | −0.173468 | − | 0.984840i | \(-0.555497\pi\) | ||||
−0.173468 | + | 0.984840i | \(0.555497\pi\) | |||||||
\(954\) | −16.2406 | −0.525809 | ||||||||
\(955\) | 30.2472 | 0.978776 | ||||||||
\(956\) | −26.1240 | −0.844910 | ||||||||
\(957\) | −3.26067 | −0.105403 | ||||||||
\(958\) | 49.7474 | 1.60727 | ||||||||
\(959\) | −28.7628 | −0.928799 | ||||||||
\(960\) | 31.2253 | 1.00779 | ||||||||
\(961\) | −18.1001 | −0.583875 | ||||||||
\(962\) | 10.4716 | 0.337617 | ||||||||
\(963\) | 9.56607 | 0.308262 | ||||||||
\(964\) | 117.907 | 3.79753 | ||||||||
\(965\) | −11.9903 | −0.385982 | ||||||||
\(966\) | 54.6268 | 1.75759 | ||||||||
\(967\) | −6.24475 | −0.200818 | −0.100409 | − | 0.994946i | \(-0.532015\pi\) | ||||
−0.100409 | + | 0.994946i | \(0.532015\pi\) | |||||||
\(968\) | 42.5109 | 1.36635 | ||||||||
\(969\) | 103.782 | 3.33396 | ||||||||
\(970\) | −31.0764 | −0.997804 | ||||||||
\(971\) | −49.1036 | −1.57581 | −0.787905 | − | 0.615797i | \(-0.788834\pi\) | ||||
−0.787905 | + | 0.615797i | \(0.788834\pi\) | |||||||
\(972\) | 43.7893 | 1.40454 | ||||||||
\(973\) | −23.5036 | −0.753489 | ||||||||
\(974\) | 57.9867 | 1.85801 | ||||||||
\(975\) | 6.33188 | 0.202783 | ||||||||
\(976\) | −55.4340 | −1.77440 | ||||||||
\(977\) | 56.4243 | 1.80517 | 0.902587 | − | 0.430508i | \(-0.141665\pi\) | ||||
0.902587 | + | 0.430508i | \(0.141665\pi\) | |||||||
\(978\) | −63.4990 | −2.03047 | ||||||||
\(979\) | −24.3037 | −0.776750 | ||||||||
\(980\) | −61.4750 | −1.96375 | ||||||||
\(981\) | 10.2555 | 0.327432 | ||||||||
\(982\) | −28.5070 | −0.909696 | ||||||||
\(983\) | −25.4853 | −0.812856 | −0.406428 | − | 0.913683i | \(-0.633226\pi\) | ||||
−0.406428 | + | 0.913683i | \(0.633226\pi\) | |||||||
\(984\) | 5.40660 | 0.172356 | ||||||||
\(985\) | 5.66662 | 0.180554 | ||||||||
\(986\) | −15.8332 | −0.504232 | ||||||||
\(987\) | 24.7922 | 0.789146 | ||||||||
\(988\) | 22.4842 | 0.715316 | ||||||||
\(989\) | 43.5399 | 1.38449 | ||||||||
\(990\) | −14.3640 | −0.456517 | ||||||||
\(991\) | −23.9611 | −0.761149 | −0.380574 | − | 0.924750i | \(-0.624274\pi\) | ||||
−0.380574 | + | 0.924750i | \(0.624274\pi\) | |||||||
\(992\) | −7.96998 | −0.253047 | ||||||||
\(993\) | 14.7241 | 0.467255 | ||||||||
\(994\) | −58.7340 | −1.86293 | ||||||||
\(995\) | 57.7816 | 1.83180 | ||||||||
\(996\) | 29.8187 | 0.944840 | ||||||||
\(997\) | −58.4761 | −1.85196 | −0.925978 | − | 0.377578i | \(-0.876757\pi\) | ||||
−0.925978 | + | 0.377578i | \(0.876757\pi\) | |||||||
\(998\) | −89.7551 | −2.84115 | ||||||||
\(999\) | 22.5017 | 0.711923 |
(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 | 4021.2.a.b.1.12 | ✓ | 151 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4021.2.a.b.1.12 | ✓ | 151 | 1.1 | even | 1 | trivial |