Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, 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("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.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: | \(48.2216577807\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.23548 | −1.58073 | −0.790363 | − | 0.612639i | \(-0.790108\pi\) | ||||
−0.790363 | + | 0.612639i | \(0.790108\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.99739 | 1.49869 | ||||||||
\(5\) | −2.10645 | −0.942033 | −0.471016 | − | 0.882125i | \(-0.656113\pi\) | ||||
−0.471016 | + | 0.882125i | \(0.656113\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.54970 | −0.585733 | −0.292867 | − | 0.956153i | \(-0.594609\pi\) | ||||
−0.292867 | + | 0.956153i | \(0.594609\pi\) | |||||||
\(8\) | −2.22964 | −0.788296 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.70893 | 1.48909 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.11724 | −1.97397 | −0.986983 | − | 0.160824i | \(-0.948585\pi\) | ||||
−0.986983 | + | 0.160824i | \(0.948585\pi\) | |||||||
\(14\) | 3.46434 | 0.925884 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.01045 | −0.252613 | ||||||||
\(17\) | −3.21614 | −0.780029 | −0.390015 | − | 0.920809i | \(-0.627530\pi\) | ||||
−0.390015 | + | 0.920809i | \(0.627530\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.37299 | −0.773818 | −0.386909 | − | 0.922118i | \(-0.626457\pi\) | ||||
−0.386909 | + | 0.922118i | \(0.626457\pi\) | |||||||
\(20\) | −6.31384 | −1.41182 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.23548 | −0.476607 | ||||||||
\(23\) | 5.08722 | 1.06076 | 0.530379 | − | 0.847760i | \(-0.322049\pi\) | ||||
0.530379 | + | 0.847760i | \(0.322049\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.562873 | −0.112575 | ||||||||
\(26\) | 15.9105 | 3.12030 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.64506 | −0.877834 | ||||||||
\(29\) | 2.29976 | 0.427055 | 0.213527 | − | 0.976937i | \(-0.431505\pi\) | ||||
0.213527 | + | 0.976937i | \(0.431505\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.78435 | −0.500083 | −0.250042 | − | 0.968235i | \(-0.580444\pi\) | ||||
−0.250042 | + | 0.968235i | \(0.580444\pi\) | |||||||
\(32\) | 6.71812 | 1.18761 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.18963 | 1.23301 | ||||||||
\(35\) | 3.26437 | 0.551780 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.34514 | −1.53633 | −0.768166 | − | 0.640251i | \(-0.778830\pi\) | ||||
−0.768166 | + | 0.640251i | \(0.778830\pi\) | |||||||
\(38\) | 7.54027 | 1.22319 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.69662 | 0.742601 | ||||||||
\(41\) | −0.774810 | −0.121005 | −0.0605025 | − | 0.998168i | \(-0.519270\pi\) | ||||
−0.0605025 | + | 0.998168i | \(0.519270\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.87964 | −0.591640 | −0.295820 | − | 0.955244i | \(-0.595593\pi\) | ||||
−0.295820 | + | 0.955244i | \(0.595593\pi\) | |||||||
\(44\) | 2.99739 | 0.451873 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −11.3724 | −1.67677 | ||||||||
\(47\) | −9.43926 | −1.37686 | −0.688429 | − | 0.725304i | \(-0.741699\pi\) | ||||
−0.688429 | + | 0.725304i | \(0.741699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.59842 | −0.656916 | ||||||||
\(50\) | 1.25829 | 0.177949 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −21.3331 | −2.95837 | ||||||||
\(53\) | −5.79127 | −0.795492 | −0.397746 | − | 0.917496i | \(-0.630207\pi\) | ||||
−0.397746 | + | 0.917496i | \(0.630207\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.10645 | −0.284034 | ||||||||
\(56\) | 3.45528 | 0.461731 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.14108 | −0.675057 | ||||||||
\(59\) | −8.69383 | −1.13184 | −0.565920 | − | 0.824460i | \(-0.691479\pi\) | ||||
−0.565920 | + | 0.824460i | \(0.691479\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | 6.22436 | 0.790494 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.9974 | −1.62467 | ||||||||
\(65\) | 14.9921 | 1.85954 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.877000 | 0.107143 | 0.0535713 | − | 0.998564i | \(-0.482940\pi\) | ||||
0.0535713 | + | 0.998564i | \(0.482940\pi\) | |||||||
\(68\) | −9.64002 | −1.16902 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.29745 | −0.872212 | ||||||||
\(71\) | −8.01889 | −0.951668 | −0.475834 | − | 0.879535i | \(-0.657854\pi\) | ||||
−0.475834 | + | 0.879535i | \(0.657854\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.3797 | 1.33190 | 0.665948 | − | 0.745998i | \(-0.268027\pi\) | ||||
0.665948 | + | 0.745998i | \(0.268027\pi\) | |||||||
\(74\) | 20.8909 | 2.42852 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.1102 | −1.15971 | ||||||||
\(77\) | −1.54970 | −0.176605 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.88549 | 0.437151 | 0.218576 | − | 0.975820i | \(-0.429859\pi\) | ||||
0.218576 | + | 0.975820i | \(0.429859\pi\) | |||||||
\(80\) | 2.12846 | 0.237970 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.73207 | 0.191276 | ||||||||
\(83\) | 10.6148 | 1.16513 | 0.582563 | − | 0.812785i | \(-0.302050\pi\) | ||||
0.582563 | + | 0.812785i | \(0.302050\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.77464 | 0.734813 | ||||||||
\(86\) | 8.67288 | 0.935221 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.22964 | −0.237680 | ||||||||
\(89\) | 7.33188 | 0.777177 | 0.388589 | − | 0.921411i | \(-0.372963\pi\) | ||||
0.388589 | + | 0.921411i | \(0.372963\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.0296 | 1.15622 | ||||||||
\(92\) | 15.2484 | 1.58975 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 21.1013 | 2.17643 | ||||||||
\(95\) | 7.10504 | 0.728961 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.1464 | −1.74096 | −0.870478 | − | 0.492207i | \(-0.836190\pi\) | ||||
−0.870478 | + | 0.492207i | \(0.836190\pi\) | |||||||
\(98\) | 10.2797 | 1.03840 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.68715 | −0.168715 | ||||||||
\(101\) | −14.9192 | −1.48452 | −0.742258 | − | 0.670115i | \(-0.766245\pi\) | ||||
−0.742258 | + | 0.670115i | \(0.766245\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.1942 | −1.20153 | −0.600763 | − | 0.799427i | \(-0.705137\pi\) | ||||
−0.600763 | + | 0.799427i | \(0.705137\pi\) | |||||||
\(104\) | 15.8689 | 1.55607 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.9463 | 1.25745 | ||||||||
\(107\) | −10.5505 | −1.01995 | −0.509977 | − | 0.860188i | \(-0.670346\pi\) | ||||
−0.509977 | + | 0.860188i | \(0.670346\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.68537 | 0.544559 | 0.272280 | − | 0.962218i | \(-0.412222\pi\) | ||||
0.272280 | + | 0.962218i | \(0.412222\pi\) | |||||||
\(110\) | 4.70893 | 0.448979 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.56590 | 0.147964 | ||||||||
\(113\) | −8.06689 | −0.758869 | −0.379435 | − | 0.925219i | \(-0.623882\pi\) | ||||
−0.379435 | + | 0.925219i | \(0.623882\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.7160 | −0.999269 | ||||||||
\(116\) | 6.89327 | 0.640024 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 19.4349 | 1.78913 | ||||||||
\(119\) | 4.98407 | 0.456889 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 2.23548 | 0.202391 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.34576 | −0.749471 | ||||||||
\(125\) | 11.7179 | 1.04808 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.7131 | 1.83799 | 0.918995 | − | 0.394268i | \(-0.129002\pi\) | ||||
0.918995 | + | 0.394268i | \(0.129002\pi\) | |||||||
\(128\) | 15.6191 | 1.38055 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −33.5146 | −2.93942 | ||||||||
\(131\) | −0.647790 | −0.0565977 | −0.0282989 | − | 0.999600i | \(-0.509009\pi\) | ||||
−0.0282989 | + | 0.999600i | \(0.509009\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.22714 | 0.453251 | ||||||||
\(134\) | −1.96052 | −0.169363 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.17084 | 0.614894 | ||||||||
\(137\) | −12.2116 | −1.04331 | −0.521656 | − | 0.853156i | \(-0.674685\pi\) | ||||
−0.521656 | + | 0.853156i | \(0.674685\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.9723 | −1.60921 | −0.804603 | − | 0.593813i | \(-0.797622\pi\) | ||||
−0.804603 | + | 0.593813i | \(0.797622\pi\) | |||||||
\(140\) | 9.78459 | 0.826949 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 17.9261 | 1.50432 | ||||||||
\(143\) | −7.11724 | −0.595173 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.84433 | −0.402300 | ||||||||
\(146\) | −25.4392 | −2.10536 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −28.0110 | −2.30249 | ||||||||
\(149\) | 3.23280 | 0.264841 | 0.132421 | − | 0.991194i | \(-0.457725\pi\) | ||||
0.132421 | + | 0.991194i | \(0.457725\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.86619 | 0.721521 | 0.360760 | − | 0.932659i | \(-0.382517\pi\) | ||||
0.360760 | + | 0.932659i | \(0.382517\pi\) | |||||||
\(152\) | 7.52055 | 0.609998 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.46434 | 0.279164 | ||||||||
\(155\) | 5.86508 | 0.471095 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.3956 | −1.38832 | −0.694159 | − | 0.719822i | \(-0.744224\pi\) | ||||
−0.694159 | + | 0.719822i | \(0.744224\pi\) | |||||||
\(158\) | −8.68594 | −0.691016 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −14.1514 | −1.11877 | ||||||||
\(161\) | −7.88369 | −0.621322 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.29493 | 0.493057 | 0.246528 | − | 0.969136i | \(-0.420710\pi\) | ||||
0.246528 | + | 0.969136i | \(0.420710\pi\) | |||||||
\(164\) | −2.32240 | −0.181349 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −23.7292 | −1.84174 | ||||||||
\(167\) | 6.53551 | 0.505733 | 0.252867 | − | 0.967501i | \(-0.418627\pi\) | ||||
0.252867 | + | 0.967501i | \(0.418627\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 37.6550 | 2.89654 | ||||||||
\(170\) | −15.1446 | −1.16154 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −11.6288 | −0.886687 | ||||||||
\(173\) | −22.9563 | −1.74534 | −0.872668 | − | 0.488315i | \(-0.837612\pi\) | ||||
−0.872668 | + | 0.488315i | \(0.837612\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.872287 | 0.0659387 | ||||||||
\(176\) | −1.01045 | −0.0761656 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −16.3903 | −1.22850 | ||||||||
\(179\) | 13.2157 | 0.987791 | 0.493895 | − | 0.869521i | \(-0.335573\pi\) | ||||
0.493895 | + | 0.869521i | \(0.335573\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.9759 | −0.964493 | −0.482247 | − | 0.876035i | \(-0.660179\pi\) | ||||
−0.482247 | + | 0.876035i | \(0.660179\pi\) | |||||||
\(182\) | −24.6565 | −1.82766 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −11.3427 | −0.836192 | ||||||||
\(185\) | 19.6851 | 1.44727 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.21614 | −0.235188 | ||||||||
\(188\) | −28.2931 | −2.06349 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −15.8832 | −1.15229 | ||||||||
\(191\) | 14.7375 | 1.06637 | 0.533185 | − | 0.845999i | \(-0.320995\pi\) | ||||
0.533185 | + | 0.845999i | \(0.320995\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.9417 | −1.36345 | −0.681726 | − | 0.731608i | \(-0.738770\pi\) | ||||
−0.681726 | + | 0.731608i | \(0.738770\pi\) | |||||||
\(194\) | 38.3306 | 2.75197 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −13.7832 | −0.984516 | ||||||||
\(197\) | −14.6396 | −1.04303 | −0.521516 | − | 0.853242i | \(-0.674633\pi\) | ||||
−0.521516 | + | 0.853242i | \(0.674633\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.2753 | −1.64994 | −0.824972 | − | 0.565174i | \(-0.808809\pi\) | ||||
−0.824972 | + | 0.565174i | \(0.808809\pi\) | |||||||
\(200\) | 1.25500 | 0.0887421 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 33.3516 | 2.34661 | ||||||||
\(203\) | −3.56395 | −0.250140 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.63210 | 0.113991 | ||||||||
\(206\) | 27.2599 | 1.89928 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.19162 | 0.498649 | ||||||||
\(209\) | −3.37299 | −0.233315 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.3597 | 1.60815 | 0.804073 | − | 0.594531i | \(-0.202662\pi\) | ||||
0.804073 | + | 0.594531i | \(0.202662\pi\) | |||||||
\(212\) | −17.3587 | −1.19220 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 23.5854 | 1.61227 | ||||||||
\(215\) | 8.17227 | 0.557344 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.31491 | 0.292915 | ||||||||
\(218\) | −12.7095 | −0.860799 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.31384 | −0.425679 | ||||||||
\(221\) | 22.8900 | 1.53975 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.09514 | −0.274231 | −0.137115 | − | 0.990555i | \(-0.543783\pi\) | ||||
−0.137115 | + | 0.990555i | \(0.543783\pi\) | |||||||
\(224\) | −10.4111 | −0.695621 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 18.0334 | 1.19956 | ||||||||
\(227\) | −5.37273 | −0.356600 | −0.178300 | − | 0.983976i | \(-0.557060\pi\) | ||||
−0.178300 | + | 0.983976i | \(0.557060\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.6663 | −0.837011 | −0.418505 | − | 0.908214i | \(-0.637446\pi\) | ||||
−0.418505 | + | 0.908214i | \(0.637446\pi\) | |||||||
\(230\) | 23.9554 | 1.57957 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.12764 | −0.336646 | ||||||||
\(233\) | 19.1609 | 1.25527 | 0.627636 | − | 0.778507i | \(-0.284022\pi\) | ||||
0.627636 | + | 0.778507i | \(0.284022\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 19.8833 | 1.29705 | ||||||||
\(236\) | −26.0588 | −1.69628 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −11.1418 | −0.722216 | ||||||||
\(239\) | 13.0438 | 0.843731 | 0.421865 | − | 0.906658i | \(-0.361375\pi\) | ||||
0.421865 | + | 0.906658i | \(0.361375\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.51420 | 0.161954 | 0.0809769 | − | 0.996716i | \(-0.474196\pi\) | ||||
0.0809769 | + | 0.996716i | \(0.474196\pi\) | |||||||
\(242\) | −2.23548 | −0.143702 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.99739 | −0.191888 | ||||||||
\(245\) | 9.68633 | 0.618837 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.0064 | 1.52749 | ||||||||
\(248\) | 6.20808 | 0.394214 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −26.1952 | −1.65673 | ||||||||
\(251\) | 3.87919 | 0.244852 | 0.122426 | − | 0.992478i | \(-0.460933\pi\) | ||||
0.122426 | + | 0.992478i | \(0.460933\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.08722 | 0.319831 | ||||||||
\(254\) | −46.3038 | −2.90536 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.92156 | −0.557598 | ||||||||
\(257\) | −20.1362 | −1.25606 | −0.628030 | − | 0.778189i | \(-0.716139\pi\) | ||||
−0.628030 | + | 0.778189i | \(0.716139\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.4822 | 0.899880 | ||||||||
\(260\) | 44.9371 | 2.78688 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.44812 | 0.0894654 | ||||||||
\(263\) | 9.01852 | 0.556106 | 0.278053 | − | 0.960566i | \(-0.410311\pi\) | ||||
0.278053 | + | 0.960566i | \(0.410311\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.1990 | 0.749379 | ||||||||
\(266\) | −11.6852 | −0.716465 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.62871 | 0.160574 | ||||||||
\(269\) | 4.39179 | 0.267772 | 0.133886 | − | 0.990997i | \(-0.457254\pi\) | ||||
0.133886 | + | 0.990997i | \(0.457254\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.66984 | −0.283673 | −0.141836 | − | 0.989890i | \(-0.545301\pi\) | ||||
−0.141836 | + | 0.989890i | \(0.545301\pi\) | |||||||
\(272\) | 3.24976 | 0.197045 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 27.2989 | 1.64919 | ||||||||
\(275\) | −0.562873 | −0.0339425 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.4584 | −1.40948 | −0.704740 | − | 0.709466i | \(-0.748936\pi\) | ||||
−0.704740 | + | 0.709466i | \(0.748936\pi\) | |||||||
\(278\) | 42.4122 | 2.54371 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.27837 | −0.434966 | ||||||||
\(281\) | 22.8244 | 1.36159 | 0.680793 | − | 0.732475i | \(-0.261635\pi\) | ||||
0.680793 | + | 0.732475i | \(0.261635\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.43936 | −0.204449 | −0.102224 | − | 0.994761i | \(-0.532596\pi\) | ||||
−0.102224 | + | 0.994761i | \(0.532596\pi\) | |||||||
\(284\) | −24.0357 | −1.42626 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.9105 | 0.940805 | ||||||||
\(287\) | 1.20073 | 0.0708766 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.65642 | −0.391554 | ||||||||
\(290\) | 10.8294 | 0.635925 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 34.1094 | 1.99610 | ||||||||
\(293\) | −8.66879 | −0.506436 | −0.253218 | − | 0.967409i | \(-0.581489\pi\) | ||||
−0.253218 | + | 0.967409i | \(0.581489\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.3131 | 1.06623 | ||||||||
\(296\) | 20.8363 | 1.21108 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.22687 | −0.418641 | ||||||||
\(299\) | −36.2069 | −2.09390 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.01230 | 0.346543 | ||||||||
\(302\) | −19.8202 | −1.14053 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.40824 | 0.195476 | ||||||||
\(305\) | 2.10645 | 0.120615 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.2928 | 1.61475 | 0.807376 | − | 0.590037i | \(-0.200887\pi\) | ||||
0.807376 | + | 0.590037i | \(0.200887\pi\) | |||||||
\(308\) | −4.64506 | −0.264677 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −13.1113 | −0.744671 | ||||||||
\(311\) | −31.8058 | −1.80354 | −0.901771 | − | 0.432214i | \(-0.857733\pi\) | ||||
−0.901771 | + | 0.432214i | \(0.857733\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.6585 | −1.16768 | −0.583842 | − | 0.811867i | \(-0.698451\pi\) | ||||
−0.583842 | + | 0.811867i | \(0.698451\pi\) | |||||||
\(314\) | 38.8875 | 2.19455 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.6463 | 0.655156 | ||||||||
\(317\) | −8.16217 | −0.458433 | −0.229217 | − | 0.973375i | \(-0.573616\pi\) | ||||
−0.229217 | + | 0.973375i | \(0.573616\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.29976 | 0.128762 | ||||||||
\(320\) | 27.3783 | 1.53049 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 17.6239 | 0.982139 | ||||||||
\(323\) | 10.8480 | 0.603600 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.00610 | 0.222218 | ||||||||
\(326\) | −14.0722 | −0.779388 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.72755 | 0.0953877 | ||||||||
\(329\) | 14.6281 | 0.806472 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.73896 | −0.535301 | −0.267651 | − | 0.963516i | \(-0.586247\pi\) | ||||
−0.267651 | + | 0.963516i | \(0.586247\pi\) | |||||||
\(332\) | 31.8167 | 1.74617 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −14.6100 | −0.799425 | ||||||||
\(335\) | −1.84736 | −0.100932 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.8005 | −0.969656 | −0.484828 | − | 0.874609i | \(-0.661118\pi\) | ||||
−0.484828 | + | 0.874609i | \(0.661118\pi\) | |||||||
\(338\) | −84.1772 | −4.57864 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 20.3062 | 1.10126 | ||||||||
\(341\) | −2.78435 | −0.150781 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.9741 | 0.970511 | ||||||||
\(344\) | 8.65021 | 0.466388 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 51.3184 | 2.75890 | ||||||||
\(347\) | −14.5629 | −0.781780 | −0.390890 | − | 0.920437i | \(-0.627833\pi\) | ||||
−0.390890 | + | 0.920437i | \(0.627833\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.54031 | −0.135980 | −0.0679900 | − | 0.997686i | \(-0.521659\pi\) | ||||
−0.0679900 | + | 0.997686i | \(0.521659\pi\) | |||||||
\(350\) | −1.94998 | −0.104231 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.71812 | 0.358077 | ||||||||
\(353\) | −5.44682 | −0.289905 | −0.144953 | − | 0.989439i | \(-0.546303\pi\) | ||||
−0.144953 | + | 0.989439i | \(0.546303\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.8914 | 0.896502 | ||||||||
\(356\) | 21.9765 | 1.16475 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −29.5436 | −1.56143 | ||||||||
\(359\) | −28.6322 | −1.51115 | −0.755574 | − | 0.655063i | \(-0.772642\pi\) | ||||
−0.755574 | + | 0.655063i | \(0.772642\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.62292 | −0.401206 | ||||||||
\(362\) | 29.0075 | 1.52460 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 33.0600 | 1.73282 | ||||||||
\(365\) | −23.9708 | −1.25469 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.2752 | 1.42375 | 0.711876 | − | 0.702305i | \(-0.247846\pi\) | ||||
0.711876 | + | 0.702305i | \(0.247846\pi\) | |||||||
\(368\) | −5.14039 | −0.267961 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −44.0056 | −2.28774 | ||||||||
\(371\) | 8.97475 | 0.465946 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −31.8258 | −1.64788 | −0.823938 | − | 0.566681i | \(-0.808227\pi\) | ||||
−0.823938 | + | 0.566681i | \(0.808227\pi\) | |||||||
\(374\) | 7.18963 | 0.371767 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 21.0461 | 1.08537 | ||||||||
\(377\) | −16.3679 | −0.842992 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.68480 | 0.292009 | 0.146004 | − | 0.989284i | \(-0.453359\pi\) | ||||
0.146004 | + | 0.989284i | \(0.453359\pi\) | |||||||
\(380\) | 21.2965 | 1.09249 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −32.9455 | −1.68564 | ||||||||
\(383\) | 30.6669 | 1.56701 | 0.783503 | − | 0.621388i | \(-0.213431\pi\) | ||||
0.783503 | + | 0.621388i | \(0.213431\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.26437 | 0.166368 | ||||||||
\(386\) | 42.3438 | 2.15524 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −51.3945 | −2.60916 | ||||||||
\(389\) | 18.9933 | 0.963001 | 0.481500 | − | 0.876446i | \(-0.340092\pi\) | ||||
0.481500 | + | 0.876446i | \(0.340092\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.3612 | −0.827423 | ||||||||
\(392\) | 10.2528 | 0.517845 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 32.7267 | 1.64875 | ||||||||
\(395\) | −8.18458 | −0.411811 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.7287 | 0.939966 | 0.469983 | − | 0.882676i | \(-0.344260\pi\) | ||||
0.469983 | + | 0.882676i | \(0.344260\pi\) | |||||||
\(398\) | 52.0316 | 2.60811 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.568755 | 0.0284378 | ||||||||
\(401\) | −5.05574 | −0.252472 | −0.126236 | − | 0.992000i | \(-0.540290\pi\) | ||||
−0.126236 | + | 0.992000i | \(0.540290\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.8168 | 0.987147 | ||||||||
\(404\) | −44.7186 | −2.22483 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.96715 | 0.395403 | ||||||||
\(407\) | −9.34514 | −0.463221 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.7592 | −1.37260 | −0.686301 | − | 0.727318i | \(-0.740767\pi\) | ||||
−0.686301 | + | 0.727318i | \(0.740767\pi\) | |||||||
\(410\) | −3.64853 | −0.180188 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −36.5506 | −1.80072 | ||||||||
\(413\) | 13.4729 | 0.662957 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.3595 | −1.09759 | ||||||||
\(416\) | −47.8145 | −2.34430 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.54027 | 0.368807 | ||||||||
\(419\) | 5.10399 | 0.249346 | 0.124673 | − | 0.992198i | \(-0.460212\pi\) | ||||
0.124673 | + | 0.992198i | \(0.460212\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.1769 | 0.885890 | 0.442945 | − | 0.896549i | \(-0.353934\pi\) | ||||
0.442945 | + | 0.896549i | \(0.353934\pi\) | |||||||
\(422\) | −52.2201 | −2.54204 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.9124 | 0.627083 | ||||||||
\(425\) | 1.81028 | 0.0878114 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.54970 | 0.0749955 | ||||||||
\(428\) | −31.6239 | −1.52860 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −18.2690 | −0.881009 | ||||||||
\(431\) | 40.6305 | 1.95710 | 0.978552 | − | 0.205998i | \(-0.0660441\pi\) | ||||
0.978552 | + | 0.205998i | \(0.0660441\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.4178 | −0.500650 | −0.250325 | − | 0.968162i | \(-0.580537\pi\) | ||||
−0.250325 | + | 0.968162i | \(0.580537\pi\) | |||||||
\(434\) | −9.64592 | −0.463019 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 17.0412 | 0.816127 | ||||||||
\(437\) | −17.1592 | −0.820834 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.9407 | 1.04717 | 0.523585 | − | 0.851973i | \(-0.324594\pi\) | ||||
0.523585 | + | 0.851973i | \(0.324594\pi\) | |||||||
\(440\) | 4.69662 | 0.223903 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −51.1703 | −2.43392 | ||||||||
\(443\) | 32.4428 | 1.54140 | 0.770702 | − | 0.637196i | \(-0.219906\pi\) | ||||
0.770702 | + | 0.637196i | \(0.219906\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.4442 | −0.732126 | ||||||||
\(446\) | 9.15462 | 0.433484 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 20.1421 | 0.951623 | ||||||||
\(449\) | 35.5000 | 1.67535 | 0.837675 | − | 0.546169i | \(-0.183914\pi\) | ||||
0.837675 | + | 0.546169i | \(0.183914\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.774810 | −0.0364844 | ||||||||
\(452\) | −24.1796 | −1.13731 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12.0106 | 0.563687 | ||||||||
\(455\) | −23.2333 | −1.08919 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.69562 | 0.453542 | 0.226771 | − | 0.973948i | \(-0.427183\pi\) | ||||
0.226771 | + | 0.973948i | \(0.427183\pi\) | |||||||
\(458\) | 28.3152 | 1.32308 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −32.1199 | −1.49760 | ||||||||
\(461\) | −14.5967 | −0.679836 | −0.339918 | − | 0.940455i | \(-0.610399\pi\) | ||||
−0.339918 | + | 0.940455i | \(0.610399\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.8989 | −0.831832 | −0.415916 | − | 0.909403i | \(-0.636539\pi\) | ||||
−0.415916 | + | 0.909403i | \(0.636539\pi\) | |||||||
\(464\) | −2.32380 | −0.107880 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −42.8339 | −1.98424 | ||||||||
\(467\) | 23.4186 | 1.08368 | 0.541841 | − | 0.840481i | \(-0.317727\pi\) | ||||
0.541841 | + | 0.840481i | \(0.317727\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.35909 | −0.0627570 | ||||||||
\(470\) | −44.4488 | −2.05027 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 19.3841 | 0.892226 | ||||||||
\(473\) | −3.87964 | −0.178386 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.89857 | 0.0871122 | ||||||||
\(476\) | 14.9392 | 0.684736 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −29.1591 | −1.33371 | ||||||||
\(479\) | 31.0334 | 1.41795 | 0.708976 | − | 0.705232i | \(-0.249157\pi\) | ||||
0.708976 | + | 0.705232i | \(0.249157\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 66.5116 | 3.03267 | ||||||||
\(482\) | −5.62045 | −0.256004 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.99739 | 0.136245 | ||||||||
\(485\) | 36.1181 | 1.64004 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.3844 | −0.787764 | −0.393882 | − | 0.919161i | \(-0.628868\pi\) | ||||
−0.393882 | + | 0.919161i | \(0.628868\pi\) | |||||||
\(488\) | 2.22964 | 0.100931 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −21.6536 | −0.978211 | ||||||||
\(491\) | 15.9176 | 0.718350 | 0.359175 | − | 0.933270i | \(-0.383058\pi\) | ||||
0.359175 | + | 0.933270i | \(0.383058\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.39636 | −0.333115 | ||||||||
\(494\) | −53.6659 | −2.41454 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.81345 | 0.126327 | ||||||||
\(497\) | 12.4269 | 0.557423 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.7123 | 0.703380 | 0.351690 | − | 0.936116i | \(-0.385607\pi\) | ||||
0.351690 | + | 0.936116i | \(0.385607\pi\) | |||||||
\(500\) | 35.1231 | 1.57075 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8.67186 | −0.387044 | ||||||||
\(503\) | −9.04696 | −0.403384 | −0.201692 | − | 0.979449i | \(-0.564644\pi\) | ||||
−0.201692 | + | 0.979449i | \(0.564644\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 31.4265 | 1.39846 | ||||||||
\(506\) | −11.3724 | −0.505565 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 62.0852 | 2.75458 | ||||||||
\(509\) | 35.8487 | 1.58896 | 0.794482 | − | 0.607287i | \(-0.207742\pi\) | ||||
0.794482 | + | 0.607287i | \(0.207742\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.6352 | −0.780136 | ||||||||
\(512\) | −11.2942 | −0.499139 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 45.0141 | 1.98549 | ||||||||
\(515\) | 25.6864 | 1.13188 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.43926 | −0.415138 | ||||||||
\(518\) | −32.3747 | −1.42246 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −33.4270 | −1.46587 | ||||||||
\(521\) | 33.9162 | 1.48589 | 0.742947 | − | 0.669350i | \(-0.233427\pi\) | ||||
0.742947 | + | 0.669350i | \(0.233427\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.886999 | 0.0387858 | 0.0193929 | − | 0.999812i | \(-0.493827\pi\) | ||||
0.0193929 | + | 0.999812i | \(0.493827\pi\) | |||||||
\(524\) | −1.94168 | −0.0848226 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20.1608 | −0.879051 | ||||||||
\(527\) | 8.95485 | 0.390080 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.87981 | 0.125209 | ||||||||
\(530\) | −27.2707 | −1.18456 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 15.6678 | 0.679284 | ||||||||
\(533\) | 5.51450 | 0.238860 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.2241 | 0.960830 | ||||||||
\(536\) | −1.95539 | −0.0844601 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −9.81778 | −0.423275 | ||||||||
\(539\) | −4.59842 | −0.198068 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.433662 | 0.0186446 | 0.00932230 | − | 0.999957i | \(-0.497033\pi\) | ||||
0.00932230 | + | 0.999957i | \(0.497033\pi\) | |||||||
\(542\) | 10.4393 | 0.448408 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −21.6064 | −0.926369 | ||||||||
\(545\) | −11.9759 | −0.512993 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.5202 | 1.04841 | 0.524203 | − | 0.851593i | \(-0.324363\pi\) | ||||
0.524203 | + | 0.851593i | \(0.324363\pi\) | |||||||
\(548\) | −36.6030 | −1.56360 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.25829 | 0.0536538 | ||||||||
\(551\) | −7.75708 | −0.330463 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.02136 | −0.256054 | ||||||||
\(554\) | 52.4409 | 2.22800 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −56.8672 | −2.41171 | ||||||||
\(557\) | −28.2399 | −1.19656 | −0.598281 | − | 0.801286i | \(-0.704149\pi\) | ||||
−0.598281 | + | 0.801286i | \(0.704149\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 27.6123 | 1.16788 | ||||||||
\(560\) | −3.29849 | −0.139387 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −51.0235 | −2.15229 | ||||||||
\(563\) | −25.1017 | −1.05791 | −0.528956 | − | 0.848649i | \(-0.677416\pi\) | ||||
−0.528956 | + | 0.848649i | \(0.677416\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.9925 | 0.714880 | ||||||||
\(566\) | 7.68863 | 0.323177 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 17.8792 | 0.750196 | ||||||||
\(569\) | 14.3208 | 0.600357 | 0.300179 | − | 0.953883i | \(-0.402954\pi\) | ||||
0.300179 | + | 0.953883i | \(0.402954\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.2540 | −0.722056 | −0.361028 | − | 0.932555i | \(-0.617574\pi\) | ||||
−0.361028 | + | 0.932555i | \(0.617574\pi\) | |||||||
\(572\) | −21.3331 | −0.891982 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.68420 | −0.112036 | ||||||||
\(575\) | −2.86346 | −0.119414 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −35.4179 | −1.47447 | −0.737234 | − | 0.675638i | \(-0.763868\pi\) | ||||
−0.737234 | + | 0.675638i | \(0.763868\pi\) | |||||||
\(578\) | 14.8803 | 0.618940 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −14.5203 | −0.602924 | ||||||||
\(581\) | −16.4498 | −0.682453 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.79127 | −0.239850 | ||||||||
\(584\) | −25.3727 | −1.04993 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 19.3789 | 0.800536 | ||||||||
\(587\) | −29.9672 | −1.23688 | −0.618439 | − | 0.785833i | \(-0.712235\pi\) | ||||
−0.618439 | + | 0.785833i | \(0.712235\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.39158 | 0.386973 | ||||||||
\(590\) | −40.9387 | −1.68542 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.44281 | 0.388097 | ||||||||
\(593\) | 20.2261 | 0.830585 | 0.415292 | − | 0.909688i | \(-0.363679\pi\) | ||||
0.415292 | + | 0.909688i | \(0.363679\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.4987 | −0.430404 | ||||||||
\(596\) | 9.68995 | 0.396916 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 80.9400 | 3.30988 | ||||||||
\(599\) | −32.1119 | −1.31206 | −0.656029 | − | 0.754735i | \(-0.727765\pi\) | ||||
−0.656029 | + | 0.754735i | \(0.727765\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.92875 | 0.405002 | 0.202501 | − | 0.979282i | \(-0.435093\pi\) | ||||
0.202501 | + | 0.979282i | \(0.435093\pi\) | |||||||
\(602\) | −13.4404 | −0.547790 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 26.5754 | 1.08134 | ||||||||
\(605\) | −2.10645 | −0.0856393 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.2430 | −0.740460 | −0.370230 | − | 0.928940i | \(-0.620721\pi\) | ||||
−0.370230 | + | 0.928940i | \(0.620721\pi\) | |||||||
\(608\) | −22.6602 | −0.918992 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.70893 | −0.190659 | ||||||||
\(611\) | 67.1815 | 2.71787 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.4164 | 0.501493 | 0.250746 | − | 0.968053i | \(-0.419324\pi\) | ||||
0.250746 | + | 0.968053i | \(0.419324\pi\) | |||||||
\(614\) | −63.2480 | −2.55248 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.45528 | 0.139217 | ||||||||
\(617\) | 15.0465 | 0.605748 | 0.302874 | − | 0.953031i | \(-0.402054\pi\) | ||||
0.302874 | + | 0.953031i | \(0.402054\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.2051 | −0.731724 | −0.365862 | − | 0.930669i | \(-0.619226\pi\) | ||||
−0.365862 | + | 0.930669i | \(0.619226\pi\) | |||||||
\(620\) | 17.5799 | 0.706026 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 71.1014 | 2.85091 | ||||||||
\(623\) | −11.3622 | −0.455219 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.8688 | −0.874752 | ||||||||
\(626\) | 46.1816 | 1.84579 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −52.1412 | −2.08066 | ||||||||
\(629\) | 30.0553 | 1.19838 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.4681 | 0.974058 | 0.487029 | − | 0.873386i | \(-0.338081\pi\) | ||||
0.487029 | + | 0.873386i | \(0.338081\pi\) | |||||||
\(632\) | −8.66323 | −0.344605 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 18.2464 | 0.724657 | ||||||||
\(635\) | −43.6311 | −1.73145 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 32.7280 | 1.29673 | ||||||||
\(638\) | −5.14108 | −0.203537 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −32.9009 | −1.30052 | ||||||||
\(641\) | 21.5755 | 0.852182 | 0.426091 | − | 0.904680i | \(-0.359890\pi\) | ||||
0.426091 | + | 0.904680i | \(0.359890\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.6728 | 1.01244 | 0.506218 | − | 0.862406i | \(-0.331043\pi\) | ||||
0.506218 | + | 0.862406i | \(0.331043\pi\) | |||||||
\(644\) | −23.6305 | −0.931170 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −24.2506 | −0.954126 | ||||||||
\(647\) | 13.9609 | 0.548861 | 0.274430 | − | 0.961607i | \(-0.411511\pi\) | ||||
0.274430 | + | 0.961607i | \(0.411511\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.69383 | −0.341263 | ||||||||
\(650\) | −8.95557 | −0.351266 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 18.8683 | 0.738941 | ||||||||
\(653\) | −24.3856 | −0.954281 | −0.477141 | − | 0.878827i | \(-0.658327\pi\) | ||||
−0.477141 | + | 0.878827i | \(0.658327\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.36454 | 0.0533169 | ||||||||
\(656\) | 0.782907 | 0.0305674 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −32.7008 | −1.27481 | ||||||||
\(659\) | −7.00856 | −0.273015 | −0.136507 | − | 0.990639i | \(-0.543588\pi\) | ||||
−0.136507 | + | 0.990639i | \(0.543588\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.46887 | −0.0571324 | −0.0285662 | − | 0.999592i | \(-0.509094\pi\) | ||||
−0.0285662 | + | 0.999592i | \(0.509094\pi\) | |||||||
\(662\) | 21.7713 | 0.846165 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −23.6672 | −0.918465 | ||||||||
\(665\) | −11.0107 | −0.426977 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.6994 | 0.453002 | ||||||||
\(668\) | 19.5895 | 0.757939 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.12973 | 0.159545 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.0943 | 1.19860 | 0.599298 | − | 0.800526i | \(-0.295446\pi\) | ||||
0.599298 | + | 0.800526i | \(0.295446\pi\) | |||||||
\(674\) | 39.7928 | 1.53276 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 112.867 | 4.34103 | ||||||||
\(677\) | 26.3752 | 1.01368 | 0.506840 | − | 0.862040i | \(-0.330813\pi\) | ||||
0.506840 | + | 0.862040i | \(0.330813\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.5719 | 1.01974 | ||||||||
\(680\) | −15.1050 | −0.579250 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.22436 | 0.238343 | ||||||||
\(683\) | 39.5612 | 1.51377 | 0.756883 | − | 0.653550i | \(-0.226721\pi\) | ||||
0.756883 | + | 0.653550i | \(0.226721\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 25.7232 | 0.982833 | ||||||||
\(686\) | −40.1808 | −1.53411 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.92019 | 0.149456 | ||||||||
\(689\) | 41.2178 | 1.57027 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.6958 | 1.43401 | 0.717007 | − | 0.697066i | \(-0.245511\pi\) | ||||
0.717007 | + | 0.697066i | \(0.245511\pi\) | |||||||
\(692\) | −68.8089 | −2.61572 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 32.5552 | 1.23578 | ||||||||
\(695\) | 39.9641 | 1.51593 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.49190 | 0.0943874 | ||||||||
\(698\) | 5.67883 | 0.214947 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.61458 | 0.0988218 | ||||||||
\(701\) | −24.0001 | −0.906473 | −0.453236 | − | 0.891390i | \(-0.649731\pi\) | ||||
−0.453236 | + | 0.891390i | \(0.649731\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.5211 | 1.18884 | ||||||||
\(704\) | −12.9974 | −0.489856 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.1763 | 0.458260 | ||||||||
\(707\) | 23.1203 | 0.869530 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.9608 | −0.899865 | −0.449933 | − | 0.893062i | \(-0.648552\pi\) | ||||
−0.449933 | + | 0.893062i | \(0.648552\pi\) | |||||||
\(710\) | −37.7604 | −1.41712 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −16.3474 | −0.612646 | ||||||||
\(713\) | −14.1646 | −0.530468 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.9921 | 0.560673 | ||||||||
\(716\) | 39.6127 | 1.48039 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 64.0067 | 2.38871 | ||||||||
\(719\) | −43.2374 | −1.61248 | −0.806241 | − | 0.591587i | \(-0.798501\pi\) | ||||
−0.806241 | + | 0.591587i | \(0.798501\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.8974 | 0.703774 | ||||||||
\(722\) | 17.0409 | 0.634197 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −38.8939 | −1.44548 | ||||||||
\(725\) | −1.29447 | −0.0480755 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 49.7051 | 1.84346 | 0.921730 | − | 0.387832i | \(-0.126776\pi\) | ||||
0.921730 | + | 0.387832i | \(0.126776\pi\) | |||||||
\(728\) | −24.5921 | −0.911442 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 53.5863 | 1.98332 | ||||||||
\(731\) | 12.4775 | 0.461497 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.6594 | 1.31711 | 0.658555 | − | 0.752533i | \(-0.271168\pi\) | ||||
0.658555 | + | 0.752533i | \(0.271168\pi\) | |||||||
\(734\) | −60.9732 | −2.25056 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 34.1766 | 1.25977 | ||||||||
\(737\) | 0.877000 | 0.0323047 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.9753 | −1.10266 | −0.551330 | − | 0.834288i | \(-0.685879\pi\) | ||||
−0.551330 | + | 0.834288i | \(0.685879\pi\) | |||||||
\(740\) | 59.0037 | 2.16902 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −20.0629 | −0.736533 | ||||||||
\(743\) | −22.1438 | −0.812378 | −0.406189 | − | 0.913789i | \(-0.633143\pi\) | ||||
−0.406189 | + | 0.913789i | \(0.633143\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.80973 | −0.249489 | ||||||||
\(746\) | 71.1459 | 2.60484 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −9.64002 | −0.352474 | ||||||||
\(749\) | 16.3501 | 0.597421 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.9030 | −0.872232 | −0.436116 | − | 0.899890i | \(-0.643646\pi\) | ||||
−0.436116 | + | 0.899890i | \(0.643646\pi\) | |||||||
\(752\) | 9.53791 | 0.347812 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 36.5903 | 1.33254 | ||||||||
\(755\) | −18.6762 | −0.679696 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.04527 | −0.0743367 | −0.0371683 | − | 0.999309i | \(-0.511834\pi\) | ||||
−0.0371683 | + | 0.999309i | \(0.511834\pi\) | |||||||
\(758\) | −12.7083 | −0.461585 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −15.8417 | −0.574638 | ||||||||
\(761\) | −4.94826 | −0.179374 | −0.0896872 | − | 0.995970i | \(-0.528587\pi\) | ||||
−0.0896872 | + | 0.995970i | \(0.528587\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.81064 | −0.318966 | ||||||||
\(764\) | 44.1740 | 1.59816 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −68.5553 | −2.47701 | ||||||||
\(767\) | 61.8760 | 2.23421 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.1395 | 1.01474 | 0.507368 | − | 0.861729i | \(-0.330618\pi\) | ||||
0.507368 | + | 0.861729i | \(0.330618\pi\) | |||||||
\(770\) | −7.29745 | −0.262982 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −56.7755 | −2.04340 | ||||||||
\(773\) | 43.9205 | 1.57971 | 0.789856 | − | 0.613293i | \(-0.210155\pi\) | ||||
0.789856 | + | 0.613293i | \(0.210155\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.56723 | 0.0562967 | ||||||||
\(776\) | 38.2304 | 1.37239 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −42.4593 | −1.52224 | ||||||||
\(779\) | 2.61343 | 0.0936357 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.01889 | −0.286939 | ||||||||
\(782\) | 36.5753 | 1.30793 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.64647 | 0.165946 | ||||||||
\(785\) | 36.6429 | 1.30784 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.1447 | −0.718080 | −0.359040 | − | 0.933322i | \(-0.616896\pi\) | ||||
−0.359040 | + | 0.933322i | \(0.616896\pi\) | |||||||
\(788\) | −43.8806 | −1.56318 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 18.2965 | 0.650960 | ||||||||
\(791\) | 12.5013 | 0.444495 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.11724 | 0.252740 | ||||||||
\(794\) | −41.8677 | −1.48583 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −69.7651 | −2.47276 | ||||||||
\(797\) | −29.0609 | −1.02939 | −0.514695 | − | 0.857373i | \(-0.672095\pi\) | ||||
−0.514695 | + | 0.857373i | \(0.672095\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.3580 | 1.07399 | ||||||||
\(800\) | −3.78145 | −0.133694 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 11.3020 | 0.399088 | ||||||||
\(803\) | 11.3797 | 0.401582 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.6066 | 0.585305 | ||||||||
\(806\) | −44.3002 | −1.56041 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 33.2644 | 1.17024 | ||||||||
\(809\) | 32.8239 | 1.15403 | 0.577014 | − | 0.816734i | \(-0.304218\pi\) | ||||
0.577014 | + | 0.816734i | \(0.304218\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.3460 | 0.573984 | 0.286992 | − | 0.957933i | \(-0.407345\pi\) | ||||
0.286992 | + | 0.957933i | \(0.407345\pi\) | |||||||
\(812\) | −10.6825 | −0.374884 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 20.8909 | 0.732226 | ||||||||
\(815\) | −13.2599 | −0.464476 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.0860 | 0.457822 | ||||||||
\(818\) | 62.0551 | 2.16971 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.89202 | 0.170837 | ||||||||
\(821\) | −33.3538 | −1.16406 | −0.582029 | − | 0.813168i | \(-0.697741\pi\) | ||||
−0.582029 | + | 0.813168i | \(0.697741\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.2115 | −0.495382 | −0.247691 | − | 0.968839i | \(-0.579672\pi\) | ||||
−0.247691 | + | 0.968839i | \(0.579672\pi\) | |||||||
\(824\) | 27.1886 | 0.947159 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −30.1184 | −1.04795 | ||||||||
\(827\) | −11.7177 | −0.407464 | −0.203732 | − | 0.979027i | \(-0.565307\pi\) | ||||
−0.203732 | + | 0.979027i | \(0.565307\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39.9499 | 1.38752 | 0.693759 | − | 0.720207i | \(-0.255953\pi\) | ||||
0.693759 | + | 0.720207i | \(0.255953\pi\) | |||||||
\(830\) | 49.9844 | 1.73498 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 92.5052 | 3.20704 | ||||||||
\(833\) | 14.7892 | 0.512414 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.7667 | −0.476417 | ||||||||
\(836\) | −10.1102 | −0.349667 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −11.4099 | −0.394148 | ||||||||
\(839\) | 11.9102 | 0.411185 | 0.205593 | − | 0.978638i | \(-0.434088\pi\) | ||||
0.205593 | + | 0.978638i | \(0.434088\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.7111 | −0.817624 | ||||||||
\(842\) | −40.6343 | −1.40035 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 70.0179 | 2.41012 | ||||||||
\(845\) | −79.3184 | −2.72864 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.54970 | −0.0532485 | ||||||||
\(848\) | 5.85179 | 0.200951 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4.04685 | −0.138806 | ||||||||
\(851\) | −47.5408 | −1.62968 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.3527 | −0.868059 | −0.434029 | − | 0.900899i | \(-0.642909\pi\) | ||||
−0.434029 | + | 0.900899i | \(0.642909\pi\) | |||||||
\(854\) | −3.46434 | −0.118547 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 23.5238 | 0.804026 | ||||||||
\(857\) | 38.1116 | 1.30187 | 0.650933 | − | 0.759135i | \(-0.274378\pi\) | ||||
0.650933 | + | 0.759135i | \(0.274378\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.8693 | −0.985006 | −0.492503 | − | 0.870311i | \(-0.663918\pi\) | ||||
−0.492503 | + | 0.870311i | \(0.663918\pi\) | |||||||
\(860\) | 24.4955 | 0.835288 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −90.8289 | −3.09365 | ||||||||
\(863\) | −26.1740 | −0.890972 | −0.445486 | − | 0.895289i | \(-0.646969\pi\) | ||||
−0.445486 | + | 0.895289i | \(0.646969\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 48.3563 | 1.64416 | ||||||||
\(866\) | 23.2889 | 0.791390 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 12.9335 | 0.438990 | ||||||||
\(869\) | 3.88549 | 0.131806 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.24181 | −0.211496 | ||||||||
\(872\) | −12.6763 | −0.429274 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 38.3590 | 1.29751 | ||||||||
\(875\) | −18.1593 | −0.613896 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.0105 | −0.574405 | −0.287202 | − | 0.957870i | \(-0.592725\pi\) | ||||
−0.287202 | + | 0.957870i | \(0.592725\pi\) | |||||||
\(878\) | −49.0480 | −1.65529 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.12846 | 0.0717505 | ||||||||
\(881\) | −9.70384 | −0.326931 | −0.163465 | − | 0.986549i | \(-0.552267\pi\) | ||||
−0.163465 | + | 0.986549i | \(0.552267\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.1772 | 0.813627 | 0.406814 | − | 0.913511i | \(-0.366640\pi\) | ||||
0.406814 | + | 0.913511i | \(0.366640\pi\) | |||||||
\(884\) | 68.6103 | 2.30761 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −72.5253 | −2.43653 | ||||||||
\(887\) | −13.7330 | −0.461109 | −0.230555 | − | 0.973059i | \(-0.574054\pi\) | ||||
−0.230555 | + | 0.973059i | \(0.574054\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32.0992 | −1.07657 | ||||||||
\(890\) | 34.5253 | 1.15729 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.2747 | −0.410988 | ||||||||
\(893\) | 31.8386 | 1.06544 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −27.8383 | −0.930531 | ||||||||
\(896\) | −24.2050 | −0.808633 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −79.3597 | −2.64827 | ||||||||
\(899\) | −6.40333 | −0.213563 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.6255 | 0.620507 | ||||||||
\(902\) | 1.73207 | 0.0576718 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 17.9863 | 0.598214 | ||||||||
\(905\) | 27.3331 | 0.908584 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38.3704 | −1.27407 | −0.637034 | − | 0.770836i | \(-0.719839\pi\) | ||||
−0.637034 | + | 0.770836i | \(0.719839\pi\) | |||||||
\(908\) | −16.1041 | −0.534434 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 51.9377 | 1.72172 | ||||||||
\(911\) | −0.616414 | −0.0204227 | −0.0102113 | − | 0.999948i | \(-0.503250\pi\) | ||||
−0.0102113 | + | 0.999948i | \(0.503250\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.6148 | 0.351299 | ||||||||
\(914\) | −21.6744 | −0.716926 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −37.9657 | −1.25442 | ||||||||
\(917\) | 1.00388 | 0.0331512 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.8597 | −0.919005 | −0.459503 | − | 0.888176i | \(-0.651972\pi\) | ||||
−0.459503 | + | 0.888176i | \(0.651972\pi\) | |||||||
\(920\) | 23.8927 | 0.787720 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 32.6307 | 1.07463 | ||||||||
\(923\) | 57.0724 | 1.87856 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.26012 | 0.172952 | ||||||||
\(926\) | 40.0127 | 1.31490 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 15.4501 | 0.507174 | ||||||||
\(929\) | 12.1882 | 0.399882 | 0.199941 | − | 0.979808i | \(-0.435925\pi\) | ||||
0.199941 | + | 0.979808i | \(0.435925\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.5104 | 0.508334 | ||||||||
\(932\) | 57.4326 | 1.88127 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −52.3518 | −1.71300 | ||||||||
\(935\) | 6.77464 | 0.221554 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.2225 | 0.399291 | 0.199645 | − | 0.979868i | \(-0.436021\pi\) | ||||
0.199645 | + | 0.979868i | \(0.436021\pi\) | |||||||
\(938\) | 3.03822 | 0.0992015 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 59.5980 | 1.94387 | ||||||||
\(941\) | −10.9884 | −0.358210 | −0.179105 | − | 0.983830i | \(-0.557320\pi\) | ||||
−0.179105 | + | 0.983830i | \(0.557320\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.94163 | −0.128357 | ||||||||
\(944\) | 8.78469 | 0.285917 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.67288 | 0.281980 | ||||||||
\(947\) | 1.56638 | 0.0509006 | 0.0254503 | − | 0.999676i | \(-0.491898\pi\) | ||||
0.0254503 | + | 0.999676i | \(0.491898\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −80.9922 | −2.62912 | ||||||||
\(950\) | −4.24421 | −0.137700 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −11.1127 | −0.360164 | ||||||||
\(953\) | 23.8850 | 0.773709 | 0.386855 | − | 0.922141i | \(-0.373561\pi\) | ||||
0.386855 | + | 0.922141i | \(0.373561\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −31.0438 | −1.00455 | ||||||||
\(956\) | 39.0972 | 1.26449 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −69.3747 | −2.24139 | ||||||||
\(959\) | 18.9244 | 0.611102 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.2474 | −0.749917 | ||||||||
\(962\) | −148.685 | −4.79381 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 7.53602 | 0.242719 | ||||||||
\(965\) | 39.8997 | 1.28442 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.73197 | −0.280801 | −0.140401 | − | 0.990095i | \(-0.544839\pi\) | ||||
−0.140401 | + | 0.990095i | \(0.544839\pi\) | |||||||
\(968\) | −2.22964 | −0.0716633 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −80.7414 | −2.59245 | ||||||||
\(971\) | −32.3589 | −1.03845 | −0.519223 | − | 0.854639i | \(-0.673779\pi\) | ||||
−0.519223 | + | 0.854639i | \(0.673779\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.4014 | 0.942566 | ||||||||
\(974\) | 38.8626 | 1.24524 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.01045 | 0.0323438 | ||||||||
\(977\) | −24.1370 | −0.772210 | −0.386105 | − | 0.922455i | \(-0.626180\pi\) | ||||
−0.386105 | + | 0.922455i | \(0.626180\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.33188 | 0.234328 | ||||||||
\(980\) | 29.0337 | 0.927446 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −35.5835 | −1.13551 | ||||||||
\(983\) | −14.7630 | −0.470866 | −0.235433 | − | 0.971891i | \(-0.575651\pi\) | ||||
−0.235433 | + | 0.971891i | \(0.575651\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 30.8377 | 0.982569 | ||||||||
\(986\) | 16.5344 | 0.526564 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 71.9564 | 2.28924 | ||||||||
\(989\) | −19.7366 | −0.627588 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.70493 | −0.181223 | −0.0906116 | − | 0.995886i | \(-0.528882\pi\) | ||||
−0.0906116 | + | 0.995886i | \(0.528882\pi\) | |||||||
\(992\) | −18.7056 | −0.593903 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −27.7802 | −0.881133 | ||||||||
\(995\) | 49.0283 | 1.55430 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 55.3076 | 1.75161 | 0.875805 | − | 0.482664i | \(-0.160331\pi\) | ||||
0.875805 | + | 0.482664i | \(0.160331\pi\) | |||||||
\(998\) | −35.1246 | −1.11185 | ||||||||
\(999\) | 0 | 0 |
(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 | 6039.2.a.o.1.3 | yes | 25 | |
3.2 | odd | 2 | 6039.2.a.n.1.23 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6039.2.a.n.1.23 | ✓ | 25 | 3.2 | odd | 2 | ||
6039.2.a.o.1.3 | yes | 25 | 1.1 | even | 1 | trivial |