Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4011,2,Mod(1,4011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4011, 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("4011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4011 = 3 \cdot 7 \cdot 191 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4011.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: | \(32.0279962507\) |
Analytic rank: | \(0\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 4011.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.74433 | 1.23343 | 0.616713 | − | 0.787188i | \(-0.288464\pi\) | ||||
0.616713 | + | 0.787188i | \(0.288464\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.04268 | 0.521338 | ||||||||
\(5\) | −1.87140 | −0.836917 | −0.418459 | − | 0.908236i | \(-0.637429\pi\) | ||||
−0.418459 | + | 0.908236i | \(0.637429\pi\) | |||||||
\(6\) | 1.74433 | 0.712118 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.66989 | −0.590394 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.26434 | −1.03227 | ||||||||
\(11\) | −1.19331 | −0.359796 | −0.179898 | − | 0.983685i | \(-0.557577\pi\) | ||||
−0.179898 | + | 0.983685i | \(0.557577\pi\) | |||||||
\(12\) | 1.04268 | 0.300995 | ||||||||
\(13\) | −2.11385 | −0.586276 | −0.293138 | − | 0.956070i | \(-0.594699\pi\) | ||||
−0.293138 | + | 0.956070i | \(0.594699\pi\) | |||||||
\(14\) | 1.74433 | 0.466191 | ||||||||
\(15\) | −1.87140 | −0.483194 | ||||||||
\(16\) | −4.99818 | −1.24954 | ||||||||
\(17\) | 2.89464 | 0.702054 | 0.351027 | − | 0.936365i | \(-0.385832\pi\) | ||||
0.351027 | + | 0.936365i | \(0.385832\pi\) | |||||||
\(18\) | 1.74433 | 0.411142 | ||||||||
\(19\) | 4.97899 | 1.14226 | 0.571130 | − | 0.820860i | \(-0.306505\pi\) | ||||
0.571130 | + | 0.820860i | \(0.306505\pi\) | |||||||
\(20\) | −1.95127 | −0.436317 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −2.08152 | −0.443781 | ||||||||
\(23\) | 9.10126 | 1.89774 | 0.948872 | − | 0.315662i | \(-0.102227\pi\) | ||||
0.948872 | + | 0.315662i | \(0.102227\pi\) | |||||||
\(24\) | −1.66989 | −0.340864 | ||||||||
\(25\) | −1.49785 | −0.299570 | ||||||||
\(26\) | −3.68724 | −0.723127 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.04268 | 0.197047 | ||||||||
\(29\) | −0.663516 | −0.123212 | −0.0616059 | − | 0.998101i | \(-0.519622\pi\) | ||||
−0.0616059 | + | 0.998101i | \(0.519622\pi\) | |||||||
\(30\) | −3.26434 | −0.595984 | ||||||||
\(31\) | −2.67099 | −0.479725 | −0.239862 | − | 0.970807i | \(-0.577102\pi\) | ||||
−0.239862 | + | 0.970807i | \(0.577102\pi\) | |||||||
\(32\) | −5.37868 | −0.950826 | ||||||||
\(33\) | −1.19331 | −0.207728 | ||||||||
\(34\) | 5.04921 | 0.865932 | ||||||||
\(35\) | −1.87140 | −0.316325 | ||||||||
\(36\) | 1.04268 | 0.173779 | ||||||||
\(37\) | 10.3910 | 1.70827 | 0.854133 | − | 0.520055i | \(-0.174089\pi\) | ||||
0.854133 | + | 0.520055i | \(0.174089\pi\) | |||||||
\(38\) | 8.68499 | 1.40889 | ||||||||
\(39\) | −2.11385 | −0.338486 | ||||||||
\(40\) | 3.12503 | 0.494111 | ||||||||
\(41\) | 8.03278 | 1.25451 | 0.627255 | − | 0.778814i | \(-0.284178\pi\) | ||||
0.627255 | + | 0.778814i | \(0.284178\pi\) | |||||||
\(42\) | 1.74433 | 0.269155 | ||||||||
\(43\) | 8.48602 | 1.29411 | 0.647053 | − | 0.762445i | \(-0.276001\pi\) | ||||
0.647053 | + | 0.762445i | \(0.276001\pi\) | |||||||
\(44\) | −1.24423 | −0.187575 | ||||||||
\(45\) | −1.87140 | −0.278972 | ||||||||
\(46\) | 15.8756 | 2.34072 | ||||||||
\(47\) | 10.9554 | 1.59800 | 0.799002 | − | 0.601328i | \(-0.205362\pi\) | ||||
0.799002 | + | 0.601328i | \(0.205362\pi\) | |||||||
\(48\) | −4.99818 | −0.721425 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.61274 | −0.369497 | ||||||||
\(51\) | 2.89464 | 0.405331 | ||||||||
\(52\) | −2.20406 | −0.305648 | ||||||||
\(53\) | −5.09321 | −0.699606 | −0.349803 | − | 0.936823i | \(-0.613751\pi\) | ||||
−0.349803 | + | 0.936823i | \(0.613751\pi\) | |||||||
\(54\) | 1.74433 | 0.237373 | ||||||||
\(55\) | 2.23316 | 0.301119 | ||||||||
\(56\) | −1.66989 | −0.223148 | ||||||||
\(57\) | 4.97899 | 0.659484 | ||||||||
\(58\) | −1.15739 | −0.151973 | ||||||||
\(59\) | −2.67136 | −0.347781 | −0.173891 | − | 0.984765i | \(-0.555634\pi\) | ||||
−0.173891 | + | 0.984765i | \(0.555634\pi\) | |||||||
\(60\) | −1.95127 | −0.251908 | ||||||||
\(61\) | 1.17563 | 0.150525 | 0.0752623 | − | 0.997164i | \(-0.476021\pi\) | ||||
0.0752623 | + | 0.997164i | \(0.476021\pi\) | |||||||
\(62\) | −4.65909 | −0.591705 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0.614175 | 0.0767719 | ||||||||
\(65\) | 3.95586 | 0.490664 | ||||||||
\(66\) | −2.08152 | −0.256217 | ||||||||
\(67\) | −1.69768 | −0.207404 | −0.103702 | − | 0.994608i | \(-0.533069\pi\) | ||||
−0.103702 | + | 0.994608i | \(0.533069\pi\) | |||||||
\(68\) | 3.01818 | 0.366007 | ||||||||
\(69\) | 9.10126 | 1.09566 | ||||||||
\(70\) | −3.26434 | −0.390163 | ||||||||
\(71\) | 2.80656 | 0.333077 | 0.166538 | − | 0.986035i | \(-0.446741\pi\) | ||||
0.166538 | + | 0.986035i | \(0.446741\pi\) | |||||||
\(72\) | −1.66989 | −0.196798 | ||||||||
\(73\) | 5.86075 | 0.685949 | 0.342974 | − | 0.939345i | \(-0.388566\pi\) | ||||
0.342974 | + | 0.939345i | \(0.388566\pi\) | |||||||
\(74\) | 18.1253 | 2.10702 | ||||||||
\(75\) | −1.49785 | −0.172957 | ||||||||
\(76\) | 5.19147 | 0.595503 | ||||||||
\(77\) | −1.19331 | −0.135990 | ||||||||
\(78\) | −3.68724 | −0.417498 | ||||||||
\(79\) | −3.80396 | −0.427979 | −0.213989 | − | 0.976836i | \(-0.568646\pi\) | ||||
−0.213989 | + | 0.976836i | \(0.568646\pi\) | |||||||
\(80\) | 9.35361 | 1.04577 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 14.0118 | 1.54734 | ||||||||
\(83\) | −0.958929 | −0.105256 | −0.0526281 | − | 0.998614i | \(-0.516760\pi\) | ||||
−0.0526281 | + | 0.998614i | \(0.516760\pi\) | |||||||
\(84\) | 1.04268 | 0.113765 | ||||||||
\(85\) | −5.41705 | −0.587561 | ||||||||
\(86\) | 14.8024 | 1.59618 | ||||||||
\(87\) | −0.663516 | −0.0711364 | ||||||||
\(88\) | 1.99269 | 0.212421 | ||||||||
\(89\) | −15.9305 | −1.68863 | −0.844317 | − | 0.535843i | \(-0.819994\pi\) | ||||
−0.844317 | + | 0.535843i | \(0.819994\pi\) | |||||||
\(90\) | −3.26434 | −0.344092 | ||||||||
\(91\) | −2.11385 | −0.221591 | ||||||||
\(92\) | 9.48966 | 0.989365 | ||||||||
\(93\) | −2.67099 | −0.276969 | ||||||||
\(94\) | 19.1097 | 1.97102 | ||||||||
\(95\) | −9.31770 | −0.955976 | ||||||||
\(96\) | −5.37868 | −0.548960 | ||||||||
\(97\) | −2.11325 | −0.214568 | −0.107284 | − | 0.994228i | \(-0.534215\pi\) | ||||
−0.107284 | + | 0.994228i | \(0.534215\pi\) | |||||||
\(98\) | 1.74433 | 0.176204 | ||||||||
\(99\) | −1.19331 | −0.119932 | ||||||||
\(100\) | −1.56177 | −0.156177 | ||||||||
\(101\) | −4.15733 | −0.413670 | −0.206835 | − | 0.978376i | \(-0.566316\pi\) | ||||
−0.206835 | + | 0.978376i | \(0.566316\pi\) | |||||||
\(102\) | 5.04921 | 0.499946 | ||||||||
\(103\) | 1.26695 | 0.124837 | 0.0624184 | − | 0.998050i | \(-0.480119\pi\) | ||||
0.0624184 | + | 0.998050i | \(0.480119\pi\) | |||||||
\(104\) | 3.52988 | 0.346134 | ||||||||
\(105\) | −1.87140 | −0.182630 | ||||||||
\(106\) | −8.88422 | −0.862912 | ||||||||
\(107\) | 12.9122 | 1.24827 | 0.624134 | − | 0.781317i | \(-0.285452\pi\) | ||||
0.624134 | + | 0.781317i | \(0.285452\pi\) | |||||||
\(108\) | 1.04268 | 0.100332 | ||||||||
\(109\) | −3.62522 | −0.347234 | −0.173617 | − | 0.984813i | \(-0.555545\pi\) | ||||
−0.173617 | + | 0.984813i | \(0.555545\pi\) | |||||||
\(110\) | 3.89536 | 0.371408 | ||||||||
\(111\) | 10.3910 | 0.986268 | ||||||||
\(112\) | −4.99818 | −0.472284 | ||||||||
\(113\) | −10.2145 | −0.960900 | −0.480450 | − | 0.877022i | \(-0.659527\pi\) | ||||
−0.480450 | + | 0.877022i | \(0.659527\pi\) | |||||||
\(114\) | 8.68499 | 0.813424 | ||||||||
\(115\) | −17.0321 | −1.58825 | ||||||||
\(116\) | −0.691832 | −0.0642350 | ||||||||
\(117\) | −2.11385 | −0.195425 | ||||||||
\(118\) | −4.65972 | −0.428962 | ||||||||
\(119\) | 2.89464 | 0.265352 | ||||||||
\(120\) | 3.12503 | 0.285275 | ||||||||
\(121\) | −9.57602 | −0.870547 | ||||||||
\(122\) | 2.05069 | 0.185661 | ||||||||
\(123\) | 8.03278 | 0.724291 | ||||||||
\(124\) | −2.78498 | −0.250099 | ||||||||
\(125\) | 12.1601 | 1.08763 | ||||||||
\(126\) | 1.74433 | 0.155397 | ||||||||
\(127\) | 1.42098 | 0.126092 | 0.0630458 | − | 0.998011i | \(-0.479919\pi\) | ||||
0.0630458 | + | 0.998011i | \(0.479919\pi\) | |||||||
\(128\) | 11.8287 | 1.04552 | ||||||||
\(129\) | 8.48602 | 0.747152 | ||||||||
\(130\) | 6.90031 | 0.605197 | ||||||||
\(131\) | 13.5004 | 1.17953 | 0.589766 | − | 0.807574i | \(-0.299220\pi\) | ||||
0.589766 | + | 0.807574i | \(0.299220\pi\) | |||||||
\(132\) | −1.24423 | −0.108297 | ||||||||
\(133\) | 4.97899 | 0.431733 | ||||||||
\(134\) | −2.96130 | −0.255817 | ||||||||
\(135\) | −1.87140 | −0.161065 | ||||||||
\(136\) | −4.83373 | −0.414489 | ||||||||
\(137\) | 8.34007 | 0.712540 | 0.356270 | − | 0.934383i | \(-0.384048\pi\) | ||||
0.356270 | + | 0.934383i | \(0.384048\pi\) | |||||||
\(138\) | 15.8756 | 1.35142 | ||||||||
\(139\) | 9.97805 | 0.846327 | 0.423164 | − | 0.906053i | \(-0.360920\pi\) | ||||
0.423164 | + | 0.906053i | \(0.360920\pi\) | |||||||
\(140\) | −1.95127 | −0.164912 | ||||||||
\(141\) | 10.9554 | 0.922608 | ||||||||
\(142\) | 4.89555 | 0.410825 | ||||||||
\(143\) | 2.52247 | 0.210939 | ||||||||
\(144\) | −4.99818 | −0.416515 | ||||||||
\(145\) | 1.24171 | 0.103118 | ||||||||
\(146\) | 10.2231 | 0.846066 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 10.8344 | 0.890584 | ||||||||
\(149\) | 6.09003 | 0.498915 | 0.249457 | − | 0.968386i | \(-0.419748\pi\) | ||||
0.249457 | + | 0.968386i | \(0.419748\pi\) | |||||||
\(150\) | −2.61274 | −0.213329 | ||||||||
\(151\) | −8.01799 | −0.652495 | −0.326247 | − | 0.945284i | \(-0.605784\pi\) | ||||
−0.326247 | + | 0.945284i | \(0.605784\pi\) | |||||||
\(152\) | −8.31435 | −0.674383 | ||||||||
\(153\) | 2.89464 | 0.234018 | ||||||||
\(154\) | −2.08152 | −0.167733 | ||||||||
\(155\) | 4.99851 | 0.401490 | ||||||||
\(156\) | −2.20406 | −0.176466 | ||||||||
\(157\) | 4.97201 | 0.396810 | 0.198405 | − | 0.980120i | \(-0.436424\pi\) | ||||
0.198405 | + | 0.980120i | \(0.436424\pi\) | |||||||
\(158\) | −6.63535 | −0.527880 | ||||||||
\(159\) | −5.09321 | −0.403918 | ||||||||
\(160\) | 10.0657 | 0.795763 | ||||||||
\(161\) | 9.10126 | 0.717280 | ||||||||
\(162\) | 1.74433 | 0.137047 | ||||||||
\(163\) | −8.88541 | −0.695959 | −0.347980 | − | 0.937502i | \(-0.613132\pi\) | ||||
−0.347980 | + | 0.937502i | \(0.613132\pi\) | |||||||
\(164\) | 8.37558 | 0.654023 | ||||||||
\(165\) | 2.23316 | 0.173851 | ||||||||
\(166\) | −1.67269 | −0.129826 | ||||||||
\(167\) | 12.1209 | 0.937944 | 0.468972 | − | 0.883213i | \(-0.344624\pi\) | ||||
0.468972 | + | 0.883213i | \(0.344624\pi\) | |||||||
\(168\) | −1.66989 | −0.128835 | ||||||||
\(169\) | −8.53165 | −0.656281 | ||||||||
\(170\) | −9.44910 | −0.724713 | ||||||||
\(171\) | 4.97899 | 0.380753 | ||||||||
\(172\) | 8.84816 | 0.674666 | ||||||||
\(173\) | −3.49909 | −0.266031 | −0.133016 | − | 0.991114i | \(-0.542466\pi\) | ||||
−0.133016 | + | 0.991114i | \(0.542466\pi\) | |||||||
\(174\) | −1.15739 | −0.0877414 | ||||||||
\(175\) | −1.49785 | −0.113227 | ||||||||
\(176\) | 5.96436 | 0.449581 | ||||||||
\(177\) | −2.67136 | −0.200792 | ||||||||
\(178\) | −27.7881 | −2.08280 | ||||||||
\(179\) | −22.3558 | −1.67095 | −0.835476 | − | 0.549527i | \(-0.814808\pi\) | ||||
−0.835476 | + | 0.549527i | \(0.814808\pi\) | |||||||
\(180\) | −1.95127 | −0.145439 | ||||||||
\(181\) | −3.53843 | −0.263010 | −0.131505 | − | 0.991316i | \(-0.541981\pi\) | ||||
−0.131505 | + | 0.991316i | \(0.541981\pi\) | |||||||
\(182\) | −3.68724 | −0.273316 | ||||||||
\(183\) | 1.17563 | 0.0869054 | ||||||||
\(184\) | −15.1981 | −1.12042 | ||||||||
\(185\) | −19.4457 | −1.42968 | ||||||||
\(186\) | −4.65909 | −0.341621 | ||||||||
\(187\) | −3.45420 | −0.252596 | ||||||||
\(188\) | 11.4229 | 0.833100 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −16.2531 | −1.17913 | ||||||||
\(191\) | 1.00000 | 0.0723575 | ||||||||
\(192\) | 0.614175 | 0.0443243 | ||||||||
\(193\) | −11.4616 | −0.825021 | −0.412511 | − | 0.910953i | \(-0.635348\pi\) | ||||
−0.412511 | + | 0.910953i | \(0.635348\pi\) | |||||||
\(194\) | −3.68620 | −0.264654 | ||||||||
\(195\) | 3.95586 | 0.283285 | ||||||||
\(196\) | 1.04268 | 0.0744768 | ||||||||
\(197\) | 1.31757 | 0.0938732 | 0.0469366 | − | 0.998898i | \(-0.485054\pi\) | ||||
0.0469366 | + | 0.998898i | \(0.485054\pi\) | |||||||
\(198\) | −2.08152 | −0.147927 | ||||||||
\(199\) | −0.890668 | −0.0631378 | −0.0315689 | − | 0.999502i | \(-0.510050\pi\) | ||||
−0.0315689 | + | 0.999502i | \(0.510050\pi\) | |||||||
\(200\) | 2.50124 | 0.176864 | ||||||||
\(201\) | −1.69768 | −0.119745 | ||||||||
\(202\) | −7.25175 | −0.510231 | ||||||||
\(203\) | −0.663516 | −0.0465697 | ||||||||
\(204\) | 3.01818 | 0.211315 | ||||||||
\(205\) | −15.0326 | −1.04992 | ||||||||
\(206\) | 2.20998 | 0.153977 | ||||||||
\(207\) | 9.10126 | 0.632581 | ||||||||
\(208\) | 10.5654 | 0.732577 | ||||||||
\(209\) | −5.94147 | −0.410980 | ||||||||
\(210\) | −3.26434 | −0.225261 | ||||||||
\(211\) | −5.16839 | −0.355807 | −0.177903 | − | 0.984048i | \(-0.556931\pi\) | ||||
−0.177903 | + | 0.984048i | \(0.556931\pi\) | |||||||
\(212\) | −5.31056 | −0.364731 | ||||||||
\(213\) | 2.80656 | 0.192302 | ||||||||
\(214\) | 22.5231 | 1.53964 | ||||||||
\(215\) | −15.8808 | −1.08306 | ||||||||
\(216\) | −1.66989 | −0.113621 | ||||||||
\(217\) | −2.67099 | −0.181319 | ||||||||
\(218\) | −6.32358 | −0.428287 | ||||||||
\(219\) | 5.86075 | 0.396033 | ||||||||
\(220\) | 2.32846 | 0.156985 | ||||||||
\(221\) | −6.11883 | −0.411597 | ||||||||
\(222\) | 18.1253 | 1.21649 | ||||||||
\(223\) | −2.49900 | −0.167346 | −0.0836728 | − | 0.996493i | \(-0.526665\pi\) | ||||
−0.0836728 | + | 0.996493i | \(0.526665\pi\) | |||||||
\(224\) | −5.37868 | −0.359378 | ||||||||
\(225\) | −1.49785 | −0.0998565 | ||||||||
\(226\) | −17.8174 | −1.18520 | ||||||||
\(227\) | 25.9976 | 1.72552 | 0.862762 | − | 0.505611i | \(-0.168733\pi\) | ||||
0.862762 | + | 0.505611i | \(0.168733\pi\) | |||||||
\(228\) | 5.19147 | 0.343814 | ||||||||
\(229\) | −27.7577 | −1.83428 | −0.917141 | − | 0.398563i | \(-0.869509\pi\) | ||||
−0.917141 | + | 0.398563i | \(0.869509\pi\) | |||||||
\(230\) | −29.7096 | −1.95899 | ||||||||
\(231\) | −1.19331 | −0.0785138 | ||||||||
\(232\) | 1.10800 | 0.0727435 | ||||||||
\(233\) | 16.5811 | 1.08626 | 0.543131 | − | 0.839648i | \(-0.317239\pi\) | ||||
0.543131 | + | 0.839648i | \(0.317239\pi\) | |||||||
\(234\) | −3.68724 | −0.241042 | ||||||||
\(235\) | −20.5019 | −1.33740 | ||||||||
\(236\) | −2.78536 | −0.181312 | ||||||||
\(237\) | −3.80396 | −0.247094 | ||||||||
\(238\) | 5.04921 | 0.327291 | ||||||||
\(239\) | −6.39071 | −0.413381 | −0.206690 | − | 0.978406i | \(-0.566269\pi\) | ||||
−0.206690 | + | 0.978406i | \(0.566269\pi\) | |||||||
\(240\) | 9.35361 | 0.603773 | ||||||||
\(241\) | 4.04283 | 0.260422 | 0.130211 | − | 0.991486i | \(-0.458435\pi\) | ||||
0.130211 | + | 0.991486i | \(0.458435\pi\) | |||||||
\(242\) | −16.7037 | −1.07375 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 1.22581 | 0.0784742 | ||||||||
\(245\) | −1.87140 | −0.119560 | ||||||||
\(246\) | 14.0118 | 0.893359 | ||||||||
\(247\) | −10.5248 | −0.669679 | ||||||||
\(248\) | 4.46026 | 0.283227 | ||||||||
\(249\) | −0.958929 | −0.0607696 | ||||||||
\(250\) | 21.2112 | 1.34151 | ||||||||
\(251\) | 4.27687 | 0.269953 | 0.134977 | − | 0.990849i | \(-0.456904\pi\) | ||||
0.134977 | + | 0.990849i | \(0.456904\pi\) | |||||||
\(252\) | 1.04268 | 0.0656824 | ||||||||
\(253\) | −10.8606 | −0.682800 | ||||||||
\(254\) | 2.47865 | 0.155525 | ||||||||
\(255\) | −5.41705 | −0.339229 | ||||||||
\(256\) | 19.4048 | 1.21280 | ||||||||
\(257\) | −13.2499 | −0.826509 | −0.413254 | − | 0.910616i | \(-0.635608\pi\) | ||||
−0.413254 | + | 0.910616i | \(0.635608\pi\) | |||||||
\(258\) | 14.8024 | 0.921556 | ||||||||
\(259\) | 10.3910 | 0.645664 | ||||||||
\(260\) | 4.12468 | 0.255802 | ||||||||
\(261\) | −0.663516 | −0.0410706 | ||||||||
\(262\) | 23.5490 | 1.45486 | ||||||||
\(263\) | 10.8844 | 0.671158 | 0.335579 | − | 0.942012i | \(-0.391068\pi\) | ||||
0.335579 | + | 0.942012i | \(0.391068\pi\) | |||||||
\(264\) | 1.99269 | 0.122641 | ||||||||
\(265\) | 9.53145 | 0.585512 | ||||||||
\(266\) | 8.68499 | 0.532511 | ||||||||
\(267\) | −15.9305 | −0.974934 | ||||||||
\(268\) | −1.77013 | −0.108128 | ||||||||
\(269\) | 30.0174 | 1.83019 | 0.915096 | − | 0.403236i | \(-0.132114\pi\) | ||||
0.915096 | + | 0.403236i | \(0.132114\pi\) | |||||||
\(270\) | −3.26434 | −0.198661 | ||||||||
\(271\) | 15.5158 | 0.942519 | 0.471260 | − | 0.881995i | \(-0.343800\pi\) | ||||
0.471260 | + | 0.881995i | \(0.343800\pi\) | |||||||
\(272\) | −14.4679 | −0.877248 | ||||||||
\(273\) | −2.11385 | −0.127936 | ||||||||
\(274\) | 14.5478 | 0.878865 | ||||||||
\(275\) | 1.78739 | 0.107784 | ||||||||
\(276\) | 9.48966 | 0.571210 | ||||||||
\(277\) | 7.69366 | 0.462267 | 0.231134 | − | 0.972922i | \(-0.425757\pi\) | ||||
0.231134 | + | 0.972922i | \(0.425757\pi\) | |||||||
\(278\) | 17.4050 | 1.04388 | ||||||||
\(279\) | −2.67099 | −0.159908 | ||||||||
\(280\) | 3.12503 | 0.186756 | ||||||||
\(281\) | −19.9318 | −1.18903 | −0.594516 | − | 0.804084i | \(-0.702656\pi\) | ||||
−0.594516 | + | 0.804084i | \(0.702656\pi\) | |||||||
\(282\) | 19.1097 | 1.13797 | ||||||||
\(283\) | 19.7645 | 1.17488 | 0.587438 | − | 0.809269i | \(-0.300136\pi\) | ||||
0.587438 | + | 0.809269i | \(0.300136\pi\) | |||||||
\(284\) | 2.92633 | 0.173646 | ||||||||
\(285\) | −9.31770 | −0.551933 | ||||||||
\(286\) | 4.40001 | 0.260178 | ||||||||
\(287\) | 8.03278 | 0.474160 | ||||||||
\(288\) | −5.37868 | −0.316942 | ||||||||
\(289\) | −8.62104 | −0.507120 | ||||||||
\(290\) | 2.16594 | 0.127188 | ||||||||
\(291\) | −2.11325 | −0.123881 | ||||||||
\(292\) | 6.11086 | 0.357611 | ||||||||
\(293\) | 2.77679 | 0.162222 | 0.0811110 | − | 0.996705i | \(-0.474153\pi\) | ||||
0.0811110 | + | 0.996705i | \(0.474153\pi\) | |||||||
\(294\) | 1.74433 | 0.101731 | ||||||||
\(295\) | 4.99919 | 0.291064 | ||||||||
\(296\) | −17.3517 | −1.00855 | ||||||||
\(297\) | −1.19331 | −0.0692427 | ||||||||
\(298\) | 10.6230 | 0.615374 | ||||||||
\(299\) | −19.2387 | −1.11260 | ||||||||
\(300\) | −1.56177 | −0.0901688 | ||||||||
\(301\) | 8.48602 | 0.489126 | ||||||||
\(302\) | −13.9860 | −0.804804 | ||||||||
\(303\) | −4.15733 | −0.238833 | ||||||||
\(304\) | −24.8859 | −1.42730 | ||||||||
\(305\) | −2.20009 | −0.125977 | ||||||||
\(306\) | 5.04921 | 0.288644 | ||||||||
\(307\) | 4.37277 | 0.249567 | 0.124784 | − | 0.992184i | \(-0.460176\pi\) | ||||
0.124784 | + | 0.992184i | \(0.460176\pi\) | |||||||
\(308\) | −1.24423 | −0.0708967 | ||||||||
\(309\) | 1.26695 | 0.0720745 | ||||||||
\(310\) | 8.71903 | 0.495208 | ||||||||
\(311\) | −15.7813 | −0.894874 | −0.447437 | − | 0.894315i | \(-0.647663\pi\) | ||||
−0.447437 | + | 0.894315i | \(0.647663\pi\) | |||||||
\(312\) | 3.52988 | 0.199840 | ||||||||
\(313\) | −1.93348 | −0.109287 | −0.0546433 | − | 0.998506i | \(-0.517402\pi\) | ||||
−0.0546433 | + | 0.998506i | \(0.517402\pi\) | |||||||
\(314\) | 8.67282 | 0.489435 | ||||||||
\(315\) | −1.87140 | −0.105442 | ||||||||
\(316\) | −3.96630 | −0.223122 | ||||||||
\(317\) | 13.1928 | 0.740983 | 0.370492 | − | 0.928836i | \(-0.379189\pi\) | ||||
0.370492 | + | 0.928836i | \(0.379189\pi\) | |||||||
\(318\) | −8.88422 | −0.498202 | ||||||||
\(319\) | 0.791778 | 0.0443311 | ||||||||
\(320\) | −1.14937 | −0.0642517 | ||||||||
\(321\) | 12.9122 | 0.720688 | ||||||||
\(322\) | 15.8756 | 0.884711 | ||||||||
\(323\) | 14.4124 | 0.801928 | ||||||||
\(324\) | 1.04268 | 0.0579264 | ||||||||
\(325\) | 3.16622 | 0.175630 | ||||||||
\(326\) | −15.4991 | −0.858414 | ||||||||
\(327\) | −3.62522 | −0.200475 | ||||||||
\(328\) | −13.4138 | −0.740655 | ||||||||
\(329\) | 10.9554 | 0.603989 | ||||||||
\(330\) | 3.89536 | 0.214432 | ||||||||
\(331\) | −1.05675 | −0.0580844 | −0.0290422 | − | 0.999578i | \(-0.509246\pi\) | ||||
−0.0290422 | + | 0.999578i | \(0.509246\pi\) | |||||||
\(332\) | −0.999852 | −0.0548740 | ||||||||
\(333\) | 10.3910 | 0.569422 | ||||||||
\(334\) | 21.1428 | 1.15688 | ||||||||
\(335\) | 3.17704 | 0.173580 | ||||||||
\(336\) | −4.99818 | −0.272673 | ||||||||
\(337\) | −11.6724 | −0.635833 | −0.317917 | − | 0.948119i | \(-0.602983\pi\) | ||||
−0.317917 | + | 0.948119i | \(0.602983\pi\) | |||||||
\(338\) | −14.8820 | −0.809474 | ||||||||
\(339\) | −10.2145 | −0.554776 | ||||||||
\(340\) | −5.64822 | −0.306318 | ||||||||
\(341\) | 3.18732 | 0.172603 | ||||||||
\(342\) | 8.68499 | 0.469630 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −14.1707 | −0.764032 | ||||||||
\(345\) | −17.0321 | −0.916979 | ||||||||
\(346\) | −6.10356 | −0.328130 | ||||||||
\(347\) | 33.7606 | 1.81236 | 0.906182 | − | 0.422887i | \(-0.138983\pi\) | ||||
0.906182 | + | 0.422887i | \(0.138983\pi\) | |||||||
\(348\) | −0.691832 | −0.0370861 | ||||||||
\(349\) | 25.0202 | 1.33930 | 0.669650 | − | 0.742677i | \(-0.266444\pi\) | ||||
0.669650 | + | 0.742677i | \(0.266444\pi\) | |||||||
\(350\) | −2.61274 | −0.139657 | ||||||||
\(351\) | −2.11385 | −0.112829 | ||||||||
\(352\) | 6.41842 | 0.342103 | ||||||||
\(353\) | 1.44275 | 0.0767899 | 0.0383950 | − | 0.999263i | \(-0.487775\pi\) | ||||
0.0383950 | + | 0.999263i | \(0.487775\pi\) | |||||||
\(354\) | −4.65972 | −0.247661 | ||||||||
\(355\) | −5.25220 | −0.278758 | ||||||||
\(356\) | −16.6104 | −0.880349 | ||||||||
\(357\) | 2.89464 | 0.153201 | ||||||||
\(358\) | −38.9958 | −2.06099 | ||||||||
\(359\) | −10.0965 | −0.532875 | −0.266437 | − | 0.963852i | \(-0.585847\pi\) | ||||
−0.266437 | + | 0.963852i | \(0.585847\pi\) | |||||||
\(360\) | 3.12503 | 0.164704 | ||||||||
\(361\) | 5.79036 | 0.304756 | ||||||||
\(362\) | −6.17219 | −0.324403 | ||||||||
\(363\) | −9.57602 | −0.502611 | ||||||||
\(364\) | −2.20406 | −0.115524 | ||||||||
\(365\) | −10.9678 | −0.574082 | ||||||||
\(366\) | 2.05069 | 0.107191 | ||||||||
\(367\) | −13.3640 | −0.697594 | −0.348797 | − | 0.937198i | \(-0.613410\pi\) | ||||
−0.348797 | + | 0.937198i | \(0.613410\pi\) | |||||||
\(368\) | −45.4897 | −2.37132 | ||||||||
\(369\) | 8.03278 | 0.418170 | ||||||||
\(370\) | −33.9197 | −1.76340 | ||||||||
\(371\) | −5.09321 | −0.264426 | ||||||||
\(372\) | −2.78498 | −0.144395 | ||||||||
\(373\) | −15.2020 | −0.787128 | −0.393564 | − | 0.919297i | \(-0.628758\pi\) | ||||
−0.393564 | + | 0.919297i | \(0.628758\pi\) | |||||||
\(374\) | −6.02525 | −0.311558 | ||||||||
\(375\) | 12.1601 | 0.627945 | ||||||||
\(376\) | −18.2942 | −0.943452 | ||||||||
\(377\) | 1.40257 | 0.0722361 | ||||||||
\(378\) | 1.74433 | 0.0897185 | ||||||||
\(379\) | −22.3389 | −1.14747 | −0.573736 | − | 0.819041i | \(-0.694506\pi\) | ||||
−0.573736 | + | 0.819041i | \(0.694506\pi\) | |||||||
\(380\) | −9.71534 | −0.498387 | ||||||||
\(381\) | 1.42098 | 0.0727991 | ||||||||
\(382\) | 1.74433 | 0.0892475 | ||||||||
\(383\) | 20.9179 | 1.06885 | 0.534427 | − | 0.845215i | \(-0.320527\pi\) | ||||
0.534427 | + | 0.845215i | \(0.320527\pi\) | |||||||
\(384\) | 11.8287 | 0.603630 | ||||||||
\(385\) | 2.23316 | 0.113812 | ||||||||
\(386\) | −19.9927 | −1.01760 | ||||||||
\(387\) | 8.48602 | 0.431368 | ||||||||
\(388\) | −2.20343 | −0.111862 | ||||||||
\(389\) | −11.8457 | −0.600599 | −0.300300 | − | 0.953845i | \(-0.597087\pi\) | ||||
−0.300300 | + | 0.953845i | \(0.597087\pi\) | |||||||
\(390\) | 6.90031 | 0.349411 | ||||||||
\(391\) | 26.3449 | 1.33232 | ||||||||
\(392\) | −1.66989 | −0.0843420 | ||||||||
\(393\) | 13.5004 | 0.681003 | ||||||||
\(394\) | 2.29828 | 0.115786 | ||||||||
\(395\) | 7.11875 | 0.358183 | ||||||||
\(396\) | −1.24423 | −0.0625250 | ||||||||
\(397\) | −4.73582 | −0.237684 | −0.118842 | − | 0.992913i | \(-0.537918\pi\) | ||||
−0.118842 | + | 0.992913i | \(0.537918\pi\) | |||||||
\(398\) | −1.55362 | −0.0778757 | ||||||||
\(399\) | 4.97899 | 0.249261 | ||||||||
\(400\) | 7.48651 | 0.374326 | ||||||||
\(401\) | 0.0642921 | 0.00321059 | 0.00160530 | − | 0.999999i | \(-0.499489\pi\) | ||||
0.00160530 | + | 0.999999i | \(0.499489\pi\) | |||||||
\(402\) | −2.96130 | −0.147696 | ||||||||
\(403\) | 5.64607 | 0.281251 | ||||||||
\(404\) | −4.33475 | −0.215662 | ||||||||
\(405\) | −1.87140 | −0.0929908 | ||||||||
\(406\) | −1.15739 | −0.0574402 | ||||||||
\(407\) | −12.3996 | −0.614626 | ||||||||
\(408\) | −4.83373 | −0.239305 | ||||||||
\(409\) | −28.4542 | −1.40697 | −0.703484 | − | 0.710711i | \(-0.748373\pi\) | ||||
−0.703484 | + | 0.710711i | \(0.748373\pi\) | |||||||
\(410\) | −26.2217 | −1.29500 | ||||||||
\(411\) | 8.34007 | 0.411385 | ||||||||
\(412\) | 1.32102 | 0.0650821 | ||||||||
\(413\) | −2.67136 | −0.131449 | ||||||||
\(414\) | 15.8756 | 0.780242 | ||||||||
\(415\) | 1.79454 | 0.0880906 | ||||||||
\(416\) | 11.3697 | 0.557446 | ||||||||
\(417\) | 9.97805 | 0.488627 | ||||||||
\(418\) | −10.3639 | −0.506913 | ||||||||
\(419\) | 23.2025 | 1.13352 | 0.566759 | − | 0.823884i | \(-0.308197\pi\) | ||||
0.566759 | + | 0.823884i | \(0.308197\pi\) | |||||||
\(420\) | −1.95127 | −0.0952121 | ||||||||
\(421\) | −29.0806 | −1.41730 | −0.708650 | − | 0.705560i | \(-0.750696\pi\) | ||||
−0.708650 | + | 0.705560i | \(0.750696\pi\) | |||||||
\(422\) | −9.01536 | −0.438861 | ||||||||
\(423\) | 10.9554 | 0.532668 | ||||||||
\(424\) | 8.50508 | 0.413043 | ||||||||
\(425\) | −4.33574 | −0.210314 | ||||||||
\(426\) | 4.89555 | 0.237190 | ||||||||
\(427\) | 1.17563 | 0.0568929 | ||||||||
\(428\) | 13.4632 | 0.650769 | ||||||||
\(429\) | 2.52247 | 0.121786 | ||||||||
\(430\) | −27.7012 | −1.33587 | ||||||||
\(431\) | 3.01578 | 0.145265 | 0.0726325 | − | 0.997359i | \(-0.476860\pi\) | ||||
0.0726325 | + | 0.997359i | \(0.476860\pi\) | |||||||
\(432\) | −4.99818 | −0.240475 | ||||||||
\(433\) | −12.1615 | −0.584443 | −0.292222 | − | 0.956351i | \(-0.594394\pi\) | ||||
−0.292222 | + | 0.956351i | \(0.594394\pi\) | |||||||
\(434\) | −4.65909 | −0.223643 | ||||||||
\(435\) | 1.24171 | 0.0595352 | ||||||||
\(436\) | −3.77993 | −0.181026 | ||||||||
\(437\) | 45.3151 | 2.16771 | ||||||||
\(438\) | 10.2231 | 0.488477 | ||||||||
\(439\) | −3.12241 | −0.149024 | −0.0745122 | − | 0.997220i | \(-0.523740\pi\) | ||||
−0.0745122 | + | 0.997220i | \(0.523740\pi\) | |||||||
\(440\) | −3.72912 | −0.177779 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −10.6732 | −0.507674 | ||||||||
\(443\) | −29.8597 | −1.41868 | −0.709340 | − | 0.704867i | \(-0.751007\pi\) | ||||
−0.709340 | + | 0.704867i | \(0.751007\pi\) | |||||||
\(444\) | 10.8344 | 0.514179 | ||||||||
\(445\) | 29.8125 | 1.41325 | ||||||||
\(446\) | −4.35908 | −0.206408 | ||||||||
\(447\) | 6.09003 | 0.288049 | ||||||||
\(448\) | 0.614175 | 0.0290171 | ||||||||
\(449\) | −36.1871 | −1.70778 | −0.853888 | − | 0.520457i | \(-0.825762\pi\) | ||||
−0.853888 | + | 0.520457i | \(0.825762\pi\) | |||||||
\(450\) | −2.61274 | −0.123166 | ||||||||
\(451\) | −9.58557 | −0.451367 | ||||||||
\(452\) | −10.6504 | −0.500954 | ||||||||
\(453\) | −8.01799 | −0.376718 | ||||||||
\(454\) | 45.3484 | 2.12830 | ||||||||
\(455\) | 3.95586 | 0.185454 | ||||||||
\(456\) | −8.31435 | −0.389355 | ||||||||
\(457\) | −9.14910 | −0.427977 | −0.213988 | − | 0.976836i | \(-0.568646\pi\) | ||||
−0.213988 | + | 0.976836i | \(0.568646\pi\) | |||||||
\(458\) | −48.4185 | −2.26245 | ||||||||
\(459\) | 2.89464 | 0.135110 | ||||||||
\(460\) | −17.7590 | −0.828017 | ||||||||
\(461\) | 10.3470 | 0.481907 | 0.240954 | − | 0.970537i | \(-0.422540\pi\) | ||||
0.240954 | + | 0.970537i | \(0.422540\pi\) | |||||||
\(462\) | −2.08152 | −0.0968409 | ||||||||
\(463\) | 1.51973 | 0.0706280 | 0.0353140 | − | 0.999376i | \(-0.488757\pi\) | ||||
0.0353140 | + | 0.999376i | \(0.488757\pi\) | |||||||
\(464\) | 3.31637 | 0.153959 | ||||||||
\(465\) | 4.99851 | 0.231800 | ||||||||
\(466\) | 28.9228 | 1.33982 | ||||||||
\(467\) | 25.1510 | 1.16385 | 0.581925 | − | 0.813243i | \(-0.302300\pi\) | ||||
0.581925 | + | 0.813243i | \(0.302300\pi\) | |||||||
\(468\) | −2.20406 | −0.101883 | ||||||||
\(469\) | −1.69768 | −0.0783914 | ||||||||
\(470\) | −35.7620 | −1.64958 | ||||||||
\(471\) | 4.97201 | 0.229098 | ||||||||
\(472\) | 4.46087 | 0.205328 | ||||||||
\(473\) | −10.1264 | −0.465613 | ||||||||
\(474\) | −6.63535 | −0.304772 | ||||||||
\(475\) | −7.45777 | −0.342186 | ||||||||
\(476\) | 3.01818 | 0.138338 | ||||||||
\(477\) | −5.09321 | −0.233202 | ||||||||
\(478\) | −11.1475 | −0.509874 | ||||||||
\(479\) | −18.3268 | −0.837374 | −0.418687 | − | 0.908131i | \(-0.637510\pi\) | ||||
−0.418687 | + | 0.908131i | \(0.637510\pi\) | |||||||
\(480\) | 10.0657 | 0.459434 | ||||||||
\(481\) | −21.9649 | −1.00151 | ||||||||
\(482\) | 7.05202 | 0.321211 | ||||||||
\(483\) | 9.10126 | 0.414122 | ||||||||
\(484\) | −9.98468 | −0.453849 | ||||||||
\(485\) | 3.95474 | 0.179576 | ||||||||
\(486\) | 1.74433 | 0.0791243 | ||||||||
\(487\) | 11.6153 | 0.526338 | 0.263169 | − | 0.964750i | \(-0.415232\pi\) | ||||
0.263169 | + | 0.964750i | \(0.415232\pi\) | |||||||
\(488\) | −1.96318 | −0.0888688 | ||||||||
\(489\) | −8.88541 | −0.401812 | ||||||||
\(490\) | −3.26434 | −0.147468 | ||||||||
\(491\) | −16.3636 | −0.738481 | −0.369241 | − | 0.929334i | \(-0.620382\pi\) | ||||
−0.369241 | + | 0.929334i | \(0.620382\pi\) | |||||||
\(492\) | 8.37558 | 0.377601 | ||||||||
\(493\) | −1.92064 | −0.0865014 | ||||||||
\(494\) | −18.3587 | −0.825998 | ||||||||
\(495\) | 2.23316 | 0.100373 | ||||||||
\(496\) | 13.3501 | 0.599438 | ||||||||
\(497\) | 2.80656 | 0.125891 | ||||||||
\(498\) | −1.67269 | −0.0749548 | ||||||||
\(499\) | 10.4577 | 0.468150 | 0.234075 | − | 0.972219i | \(-0.424794\pi\) | ||||
0.234075 | + | 0.972219i | \(0.424794\pi\) | |||||||
\(500\) | 12.6790 | 0.567024 | ||||||||
\(501\) | 12.1209 | 0.541522 | ||||||||
\(502\) | 7.46025 | 0.332967 | ||||||||
\(503\) | −32.9249 | −1.46805 | −0.734025 | − | 0.679123i | \(-0.762360\pi\) | ||||
−0.734025 | + | 0.679123i | \(0.762360\pi\) | |||||||
\(504\) | −1.66989 | −0.0743827 | ||||||||
\(505\) | 7.78005 | 0.346208 | ||||||||
\(506\) | −18.9444 | −0.842182 | ||||||||
\(507\) | −8.53165 | −0.378904 | ||||||||
\(508\) | 1.48162 | 0.0657364 | ||||||||
\(509\) | −8.83675 | −0.391682 | −0.195841 | − | 0.980636i | \(-0.562744\pi\) | ||||
−0.195841 | + | 0.980636i | \(0.562744\pi\) | |||||||
\(510\) | −9.44910 | −0.418413 | ||||||||
\(511\) | 5.86075 | 0.259264 | ||||||||
\(512\) | 10.1908 | 0.450376 | ||||||||
\(513\) | 4.97899 | 0.219828 | ||||||||
\(514\) | −23.1122 | −1.01944 | ||||||||
\(515\) | −2.37098 | −0.104478 | ||||||||
\(516\) | 8.84816 | 0.389519 | ||||||||
\(517\) | −13.0731 | −0.574955 | ||||||||
\(518\) | 18.1253 | 0.796378 | ||||||||
\(519\) | −3.49909 | −0.153593 | ||||||||
\(520\) | −6.60584 | −0.289685 | ||||||||
\(521\) | 5.14641 | 0.225468 | 0.112734 | − | 0.993625i | \(-0.464039\pi\) | ||||
0.112734 | + | 0.993625i | \(0.464039\pi\) | |||||||
\(522\) | −1.15739 | −0.0506575 | ||||||||
\(523\) | 28.0016 | 1.22443 | 0.612213 | − | 0.790693i | \(-0.290280\pi\) | ||||
0.612213 | + | 0.790693i | \(0.290280\pi\) | |||||||
\(524\) | 14.0765 | 0.614935 | ||||||||
\(525\) | −1.49785 | −0.0653715 | ||||||||
\(526\) | 18.9859 | 0.827823 | ||||||||
\(527\) | −7.73158 | −0.336793 | ||||||||
\(528\) | 5.96436 | 0.259566 | ||||||||
\(529\) | 59.8329 | 2.60143 | ||||||||
\(530\) | 16.6260 | 0.722186 | ||||||||
\(531\) | −2.67136 | −0.115927 | ||||||||
\(532\) | 5.19147 | 0.225079 | ||||||||
\(533\) | −16.9801 | −0.735488 | ||||||||
\(534\) | −27.7881 | −1.20251 | ||||||||
\(535\) | −24.1639 | −1.04470 | ||||||||
\(536\) | 2.83493 | 0.122450 | ||||||||
\(537\) | −22.3558 | −0.964725 | ||||||||
\(538\) | 52.3601 | 2.25741 | ||||||||
\(539\) | −1.19331 | −0.0513994 | ||||||||
\(540\) | −1.95127 | −0.0839692 | ||||||||
\(541\) | −0.570971 | −0.0245479 | −0.0122740 | − | 0.999925i | \(-0.503907\pi\) | ||||
−0.0122740 | + | 0.999925i | \(0.503907\pi\) | |||||||
\(542\) | 27.0647 | 1.16253 | ||||||||
\(543\) | −3.53843 | −0.151849 | ||||||||
\(544\) | −15.5694 | −0.667531 | ||||||||
\(545\) | 6.78426 | 0.290606 | ||||||||
\(546\) | −3.68724 | −0.157799 | ||||||||
\(547\) | 21.0063 | 0.898165 | 0.449083 | − | 0.893490i | \(-0.351751\pi\) | ||||
0.449083 | + | 0.893490i | \(0.351751\pi\) | |||||||
\(548\) | 8.69599 | 0.371474 | ||||||||
\(549\) | 1.17563 | 0.0501749 | ||||||||
\(550\) | 3.11780 | 0.132943 | ||||||||
\(551\) | −3.30364 | −0.140740 | ||||||||
\(552\) | −15.1981 | −0.646873 | ||||||||
\(553\) | −3.80396 | −0.161761 | ||||||||
\(554\) | 13.4203 | 0.570172 | ||||||||
\(555\) | −19.4457 | −0.825424 | ||||||||
\(556\) | 10.4039 | 0.441222 | ||||||||
\(557\) | 36.5376 | 1.54815 | 0.774074 | − | 0.633095i | \(-0.218216\pi\) | ||||
0.774074 | + | 0.633095i | \(0.218216\pi\) | |||||||
\(558\) | −4.65909 | −0.197235 | ||||||||
\(559\) | −17.9381 | −0.758702 | ||||||||
\(560\) | 9.35361 | 0.395262 | ||||||||
\(561\) | −3.45420 | −0.145836 | ||||||||
\(562\) | −34.7676 | −1.46658 | ||||||||
\(563\) | −41.6454 | −1.75514 | −0.877572 | − | 0.479445i | \(-0.840838\pi\) | ||||
−0.877572 | + | 0.479445i | \(0.840838\pi\) | |||||||
\(564\) | 11.4229 | 0.480991 | ||||||||
\(565\) | 19.1155 | 0.804194 | ||||||||
\(566\) | 34.4757 | 1.44912 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −4.68663 | −0.196647 | ||||||||
\(569\) | −9.06089 | −0.379852 | −0.189926 | − | 0.981798i | \(-0.560825\pi\) | ||||
−0.189926 | + | 0.981798i | \(0.560825\pi\) | |||||||
\(570\) | −16.2531 | −0.680768 | ||||||||
\(571\) | −37.9576 | −1.58848 | −0.794238 | − | 0.607607i | \(-0.792130\pi\) | ||||
−0.794238 | + | 0.607607i | \(0.792130\pi\) | |||||||
\(572\) | 2.63012 | 0.109971 | ||||||||
\(573\) | 1.00000 | 0.0417756 | ||||||||
\(574\) | 14.0118 | 0.584841 | ||||||||
\(575\) | −13.6323 | −0.568506 | ||||||||
\(576\) | 0.614175 | 0.0255906 | ||||||||
\(577\) | −3.14027 | −0.130731 | −0.0653656 | − | 0.997861i | \(-0.520821\pi\) | ||||
−0.0653656 | + | 0.997861i | \(0.520821\pi\) | |||||||
\(578\) | −15.0379 | −0.625494 | ||||||||
\(579\) | −11.4616 | −0.476326 | ||||||||
\(580\) | 1.29470 | 0.0537593 | ||||||||
\(581\) | −0.958929 | −0.0397831 | ||||||||
\(582\) | −3.68620 | −0.152798 | ||||||||
\(583\) | 6.07776 | 0.251715 | ||||||||
\(584\) | −9.78678 | −0.404980 | ||||||||
\(585\) | 3.95586 | 0.163555 | ||||||||
\(586\) | 4.84363 | 0.200089 | ||||||||
\(587\) | −3.44905 | −0.142357 | −0.0711787 | − | 0.997464i | \(-0.522676\pi\) | ||||
−0.0711787 | + | 0.997464i | \(0.522676\pi\) | |||||||
\(588\) | 1.04268 | 0.0429992 | ||||||||
\(589\) | −13.2989 | −0.547970 | ||||||||
\(590\) | 8.72022 | 0.359006 | ||||||||
\(591\) | 1.31757 | 0.0541977 | ||||||||
\(592\) | −51.9359 | −2.13455 | ||||||||
\(593\) | 24.8186 | 1.01918 | 0.509590 | − | 0.860417i | \(-0.329797\pi\) | ||||
0.509590 | + | 0.860417i | \(0.329797\pi\) | |||||||
\(594\) | −2.08152 | −0.0854057 | ||||||||
\(595\) | −5.41705 | −0.222077 | ||||||||
\(596\) | 6.34993 | 0.260103 | ||||||||
\(597\) | −0.890668 | −0.0364526 | ||||||||
\(598\) | −33.5585 | −1.37231 | ||||||||
\(599\) | 21.6010 | 0.882594 | 0.441297 | − | 0.897361i | \(-0.354519\pi\) | ||||
0.441297 | + | 0.897361i | \(0.354519\pi\) | |||||||
\(600\) | 2.50124 | 0.102113 | ||||||||
\(601\) | 11.9822 | 0.488763 | 0.244381 | − | 0.969679i | \(-0.421415\pi\) | ||||
0.244381 | + | 0.969679i | \(0.421415\pi\) | |||||||
\(602\) | 14.8024 | 0.603300 | ||||||||
\(603\) | −1.69768 | −0.0691347 | ||||||||
\(604\) | −8.36016 | −0.340170 | ||||||||
\(605\) | 17.9206 | 0.728576 | ||||||||
\(606\) | −7.25175 | −0.294582 | ||||||||
\(607\) | 10.0436 | 0.407659 | 0.203829 | − | 0.979006i | \(-0.434661\pi\) | ||||
0.203829 | + | 0.979006i | \(0.434661\pi\) | |||||||
\(608\) | −26.7804 | −1.08609 | ||||||||
\(609\) | −0.663516 | −0.0268870 | ||||||||
\(610\) | −3.83767 | −0.155383 | ||||||||
\(611\) | −23.1580 | −0.936871 | ||||||||
\(612\) | 3.01818 | 0.122002 | ||||||||
\(613\) | −28.3627 | −1.14556 | −0.572780 | − | 0.819709i | \(-0.694135\pi\) | ||||
−0.572780 | + | 0.819709i | \(0.694135\pi\) | |||||||
\(614\) | 7.62755 | 0.307823 | ||||||||
\(615\) | −15.0326 | −0.606172 | ||||||||
\(616\) | 1.99269 | 0.0802876 | ||||||||
\(617\) | −22.7217 | −0.914742 | −0.457371 | − | 0.889276i | \(-0.651209\pi\) | ||||
−0.457371 | + | 0.889276i | \(0.651209\pi\) | |||||||
\(618\) | 2.20998 | 0.0888985 | ||||||||
\(619\) | 12.3376 | 0.495888 | 0.247944 | − | 0.968774i | \(-0.420245\pi\) | ||||
0.247944 | + | 0.968774i | \(0.420245\pi\) | |||||||
\(620\) | 5.21182 | 0.209312 | ||||||||
\(621\) | 9.10126 | 0.365221 | ||||||||
\(622\) | −27.5277 | −1.10376 | ||||||||
\(623\) | −15.9305 | −0.638244 | ||||||||
\(624\) | 10.5654 | 0.422954 | ||||||||
\(625\) | −15.2672 | −0.610688 | ||||||||
\(626\) | −3.37262 | −0.134797 | ||||||||
\(627\) | −5.94147 | −0.237279 | ||||||||
\(628\) | 5.18420 | 0.206872 | ||||||||
\(629\) | 30.0782 | 1.19930 | ||||||||
\(630\) | −3.26434 | −0.130054 | ||||||||
\(631\) | −12.6695 | −0.504366 | −0.252183 | − | 0.967680i | \(-0.581149\pi\) | ||||
−0.252183 | + | 0.967680i | \(0.581149\pi\) | |||||||
\(632\) | 6.35218 | 0.252676 | ||||||||
\(633\) | −5.16839 | −0.205425 | ||||||||
\(634\) | 23.0126 | 0.913947 | ||||||||
\(635\) | −2.65923 | −0.105528 | ||||||||
\(636\) | −5.31056 | −0.210578 | ||||||||
\(637\) | −2.11385 | −0.0837536 | ||||||||
\(638\) | 1.38112 | 0.0546790 | ||||||||
\(639\) | 2.80656 | 0.111026 | ||||||||
\(640\) | −22.1363 | −0.875012 | ||||||||
\(641\) | −41.5428 | −1.64084 | −0.820421 | − | 0.571760i | \(-0.806261\pi\) | ||||
−0.820421 | + | 0.571760i | \(0.806261\pi\) | |||||||
\(642\) | 22.5231 | 0.888914 | ||||||||
\(643\) | 3.70465 | 0.146097 | 0.0730485 | − | 0.997328i | \(-0.476727\pi\) | ||||
0.0730485 | + | 0.997328i | \(0.476727\pi\) | |||||||
\(644\) | 9.48966 | 0.373945 | ||||||||
\(645\) | −15.8808 | −0.625304 | ||||||||
\(646\) | 25.1400 | 0.989118 | ||||||||
\(647\) | 32.5100 | 1.27810 | 0.639049 | − | 0.769166i | \(-0.279328\pi\) | ||||
0.639049 | + | 0.769166i | \(0.279328\pi\) | |||||||
\(648\) | −1.66989 | −0.0655993 | ||||||||
\(649\) | 3.18775 | 0.125130 | ||||||||
\(650\) | 5.52292 | 0.216627 | ||||||||
\(651\) | −2.67099 | −0.104685 | ||||||||
\(652\) | −9.26460 | −0.362830 | ||||||||
\(653\) | 44.6626 | 1.74778 | 0.873891 | − | 0.486123i | \(-0.161589\pi\) | ||||
0.873891 | + | 0.486123i | \(0.161589\pi\) | |||||||
\(654\) | −6.32358 | −0.247271 | ||||||||
\(655\) | −25.2646 | −0.987170 | ||||||||
\(656\) | −40.1493 | −1.56757 | ||||||||
\(657\) | 5.86075 | 0.228650 | ||||||||
\(658\) | 19.1097 | 0.744975 | ||||||||
\(659\) | 14.1852 | 0.552578 | 0.276289 | − | 0.961075i | \(-0.410895\pi\) | ||||
0.276289 | + | 0.961075i | \(0.410895\pi\) | |||||||
\(660\) | 2.32846 | 0.0906352 | ||||||||
\(661\) | 8.42642 | 0.327750 | 0.163875 | − | 0.986481i | \(-0.447601\pi\) | ||||
0.163875 | + | 0.986481i | \(0.447601\pi\) | |||||||
\(662\) | −1.84332 | −0.0716428 | ||||||||
\(663\) | −6.11883 | −0.237636 | ||||||||
\(664\) | 1.60130 | 0.0621426 | ||||||||
\(665\) | −9.31770 | −0.361325 | ||||||||
\(666\) | 18.1253 | 0.702339 | ||||||||
\(667\) | −6.03883 | −0.233824 | ||||||||
\(668\) | 12.6382 | 0.488986 | ||||||||
\(669\) | −2.49900 | −0.0966170 | ||||||||
\(670\) | 5.54179 | 0.214098 | ||||||||
\(671\) | −1.40289 | −0.0541581 | ||||||||
\(672\) | −5.37868 | −0.207487 | ||||||||
\(673\) | −26.5093 | −1.02186 | −0.510929 | − | 0.859623i | \(-0.670699\pi\) | ||||
−0.510929 | + | 0.859623i | \(0.670699\pi\) | |||||||
\(674\) | −20.3604 | −0.784253 | ||||||||
\(675\) | −1.49785 | −0.0576522 | ||||||||
\(676\) | −8.89575 | −0.342144 | ||||||||
\(677\) | 12.5731 | 0.483225 | 0.241612 | − | 0.970373i | \(-0.422324\pi\) | ||||
0.241612 | + | 0.970373i | \(0.422324\pi\) | |||||||
\(678\) | −17.8174 | −0.684275 | ||||||||
\(679\) | −2.11325 | −0.0810991 | ||||||||
\(680\) | 9.04585 | 0.346893 | ||||||||
\(681\) | 25.9976 | 0.996231 | ||||||||
\(682\) | 5.55972 | 0.212893 | ||||||||
\(683\) | 11.4779 | 0.439191 | 0.219596 | − | 0.975591i | \(-0.429526\pi\) | ||||
0.219596 | + | 0.975591i | \(0.429526\pi\) | |||||||
\(684\) | 5.19147 | 0.198501 | ||||||||
\(685\) | −15.6076 | −0.596337 | ||||||||
\(686\) | 1.74433 | 0.0665987 | ||||||||
\(687\) | −27.7577 | −1.05902 | ||||||||
\(688\) | −42.4146 | −1.61704 | ||||||||
\(689\) | 10.7663 | 0.410162 | ||||||||
\(690\) | −29.7096 | −1.13102 | ||||||||
\(691\) | −11.8473 | −0.450693 | −0.225347 | − | 0.974279i | \(-0.572351\pi\) | ||||
−0.225347 | + | 0.974279i | \(0.572351\pi\) | |||||||
\(692\) | −3.64842 | −0.138692 | ||||||||
\(693\) | −1.19331 | −0.0453300 | ||||||||
\(694\) | 58.8895 | 2.23542 | ||||||||
\(695\) | −18.6730 | −0.708306 | ||||||||
\(696\) | 1.10800 | 0.0419985 | ||||||||
\(697\) | 23.2520 | 0.880734 | ||||||||
\(698\) | 43.6434 | 1.65193 | ||||||||
\(699\) | 16.5811 | 0.627153 | ||||||||
\(700\) | −1.56177 | −0.0590294 | ||||||||
\(701\) | 8.20019 | 0.309717 | 0.154858 | − | 0.987937i | \(-0.450508\pi\) | ||||
0.154858 | + | 0.987937i | \(0.450508\pi\) | |||||||
\(702\) | −3.68724 | −0.139166 | ||||||||
\(703\) | 51.7366 | 1.95128 | ||||||||
\(704\) | −0.732900 | −0.0276222 | ||||||||
\(705\) | −20.5019 | −0.772147 | ||||||||
\(706\) | 2.51663 | 0.0947147 | ||||||||
\(707\) | −4.15733 | −0.156353 | ||||||||
\(708\) | −2.78536 | −0.104680 | ||||||||
\(709\) | 14.3879 | 0.540347 | 0.270174 | − | 0.962812i | \(-0.412919\pi\) | ||||
0.270174 | + | 0.962812i | \(0.412919\pi\) | |||||||
\(710\) | −9.16155 | −0.343827 | ||||||||
\(711\) | −3.80396 | −0.142660 | ||||||||
\(712\) | 26.6022 | 0.996960 | ||||||||
\(713\) | −24.3094 | −0.910395 | ||||||||
\(714\) | 5.04921 | 0.188962 | ||||||||
\(715\) | −4.72056 | −0.176539 | ||||||||
\(716\) | −23.3099 | −0.871130 | ||||||||
\(717\) | −6.39071 | −0.238666 | ||||||||
\(718\) | −17.6117 | −0.657261 | ||||||||
\(719\) | 31.5914 | 1.17816 | 0.589080 | − | 0.808075i | \(-0.299490\pi\) | ||||
0.589080 | + | 0.808075i | \(0.299490\pi\) | |||||||
\(720\) | 9.35361 | 0.348588 | ||||||||
\(721\) | 1.26695 | 0.0471838 | ||||||||
\(722\) | 10.1003 | 0.375894 | ||||||||
\(723\) | 4.04283 | 0.150355 | ||||||||
\(724\) | −3.68944 | −0.137117 | ||||||||
\(725\) | 0.993846 | 0.0369105 | ||||||||
\(726\) | −16.7037 | −0.619933 | ||||||||
\(727\) | −19.8546 | −0.736367 | −0.368183 | − | 0.929753i | \(-0.620020\pi\) | ||||
−0.368183 | + | 0.929753i | \(0.620020\pi\) | |||||||
\(728\) | 3.52988 | 0.130826 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −19.1315 | −0.708088 | ||||||||
\(731\) | 24.5640 | 0.908532 | ||||||||
\(732\) | 1.22581 | 0.0453071 | ||||||||
\(733\) | −8.62949 | −0.318737 | −0.159369 | − | 0.987219i | \(-0.550946\pi\) | ||||
−0.159369 | + | 0.987219i | \(0.550946\pi\) | |||||||
\(734\) | −23.3111 | −0.860430 | ||||||||
\(735\) | −1.87140 | −0.0690278 | ||||||||
\(736\) | −48.9528 | −1.80442 | ||||||||
\(737\) | 2.02585 | 0.0746231 | ||||||||
\(738\) | 14.0118 | 0.515781 | ||||||||
\(739\) | −14.0396 | −0.516455 | −0.258227 | − | 0.966084i | \(-0.583138\pi\) | ||||
−0.258227 | + | 0.966084i | \(0.583138\pi\) | |||||||
\(740\) | −20.2756 | −0.745345 | ||||||||
\(741\) | −10.5248 | −0.386639 | ||||||||
\(742\) | −8.88422 | −0.326150 | ||||||||
\(743\) | 25.8650 | 0.948894 | 0.474447 | − | 0.880284i | \(-0.342648\pi\) | ||||
0.474447 | + | 0.880284i | \(0.342648\pi\) | |||||||
\(744\) | 4.46026 | 0.163521 | ||||||||
\(745\) | −11.3969 | −0.417550 | ||||||||
\(746\) | −26.5172 | −0.970864 | ||||||||
\(747\) | −0.958929 | −0.0350854 | ||||||||
\(748\) | −3.60161 | −0.131688 | ||||||||
\(749\) | 12.9122 | 0.471801 | ||||||||
\(750\) | 21.2112 | 0.774523 | ||||||||
\(751\) | 27.8804 | 1.01737 | 0.508686 | − | 0.860952i | \(-0.330131\pi\) | ||||
0.508686 | + | 0.860952i | \(0.330131\pi\) | |||||||
\(752\) | −54.7569 | −1.99678 | ||||||||
\(753\) | 4.27687 | 0.155858 | ||||||||
\(754\) | 2.44654 | 0.0890978 | ||||||||
\(755\) | 15.0049 | 0.546084 | ||||||||
\(756\) | 1.04268 | 0.0379217 | ||||||||
\(757\) | 10.2067 | 0.370970 | 0.185485 | − | 0.982647i | \(-0.440614\pi\) | ||||
0.185485 | + | 0.982647i | \(0.440614\pi\) | |||||||
\(758\) | −38.9663 | −1.41532 | ||||||||
\(759\) | −10.8606 | −0.394215 | ||||||||
\(760\) | 15.5595 | 0.564403 | ||||||||
\(761\) | 21.5048 | 0.779548 | 0.389774 | − | 0.920911i | \(-0.372553\pi\) | ||||
0.389774 | + | 0.920911i | \(0.372553\pi\) | |||||||
\(762\) | 2.47865 | 0.0897922 | ||||||||
\(763\) | −3.62522 | −0.131242 | ||||||||
\(764\) | 1.04268 | 0.0377227 | ||||||||
\(765\) | −5.41705 | −0.195854 | ||||||||
\(766\) | 36.4876 | 1.31835 | ||||||||
\(767\) | 5.64684 | 0.203896 | ||||||||
\(768\) | 19.4048 | 0.700209 | ||||||||
\(769\) | 28.7488 | 1.03671 | 0.518353 | − | 0.855167i | \(-0.326545\pi\) | ||||
0.518353 | + | 0.855167i | \(0.326545\pi\) | |||||||
\(770\) | 3.89536 | 0.140379 | ||||||||
\(771\) | −13.2499 | −0.477185 | ||||||||
\(772\) | −11.9507 | −0.430115 | ||||||||
\(773\) | −45.9669 | −1.65332 | −0.826658 | − | 0.562705i | \(-0.809761\pi\) | ||||
−0.826658 | + | 0.562705i | \(0.809761\pi\) | |||||||
\(774\) | 14.8024 | 0.532061 | ||||||||
\(775\) | 4.00075 | 0.143711 | ||||||||
\(776\) | 3.52889 | 0.126680 | ||||||||
\(777\) | 10.3910 | 0.372774 | ||||||||
\(778\) | −20.6627 | −0.740795 | ||||||||
\(779\) | 39.9952 | 1.43297 | ||||||||
\(780\) | 4.12468 | 0.147687 | ||||||||
\(781\) | −3.34908 | −0.119840 | ||||||||
\(782\) | 45.9541 | 1.64332 | ||||||||
\(783\) | −0.663516 | −0.0237121 | ||||||||
\(784\) | −4.99818 | −0.178506 | ||||||||
\(785\) | −9.30465 | −0.332097 | ||||||||
\(786\) | 23.5490 | 0.839966 | ||||||||
\(787\) | −29.1275 | −1.03828 | −0.519142 | − | 0.854688i | \(-0.673749\pi\) | ||||
−0.519142 | + | 0.854688i | \(0.673749\pi\) | |||||||
\(788\) | 1.37380 | 0.0489396 | ||||||||
\(789\) | 10.8844 | 0.387493 | ||||||||
\(790\) | 12.4174 | 0.441792 | ||||||||
\(791\) | −10.2145 | −0.363186 | ||||||||
\(792\) | 1.99269 | 0.0708071 | ||||||||
\(793\) | −2.48511 | −0.0882489 | ||||||||
\(794\) | −8.26081 | −0.293165 | ||||||||
\(795\) | 9.53145 | 0.338046 | ||||||||
\(796\) | −0.928678 | −0.0329161 | ||||||||
\(797\) | −16.2211 | −0.574582 | −0.287291 | − | 0.957843i | \(-0.592755\pi\) | ||||
−0.287291 | + | 0.957843i | \(0.592755\pi\) | |||||||
\(798\) | 8.68499 | 0.307445 | ||||||||
\(799\) | 31.7119 | 1.12189 | ||||||||
\(800\) | 8.05645 | 0.284839 | ||||||||
\(801\) | −15.9305 | −0.562878 | ||||||||
\(802\) | 0.112146 | 0.00396003 | ||||||||
\(803\) | −6.99367 | −0.246801 | ||||||||
\(804\) | −1.77013 | −0.0624275 | ||||||||
\(805\) | −17.0321 | −0.600304 | ||||||||
\(806\) | 9.84860 | 0.346902 | ||||||||
\(807\) | 30.0174 | 1.05666 | ||||||||
\(808\) | 6.94227 | 0.244228 | ||||||||
\(809\) | −25.6243 | −0.900901 | −0.450451 | − | 0.892801i | \(-0.648737\pi\) | ||||
−0.450451 | + | 0.892801i | \(0.648737\pi\) | |||||||
\(810\) | −3.26434 | −0.114697 | ||||||||
\(811\) | −10.8034 | −0.379357 | −0.189679 | − | 0.981846i | \(-0.560745\pi\) | ||||
−0.189679 | + | 0.981846i | \(0.560745\pi\) | |||||||
\(812\) | −0.691832 | −0.0242785 | ||||||||
\(813\) | 15.5158 | 0.544164 | ||||||||
\(814\) | −21.6290 | −0.758096 | ||||||||
\(815\) | 16.6282 | 0.582460 | ||||||||
\(816\) | −14.4679 | −0.506480 | ||||||||
\(817\) | 42.2518 | 1.47820 | ||||||||
\(818\) | −49.6334 | −1.73539 | ||||||||
\(819\) | −2.11385 | −0.0738638 | ||||||||
\(820\) | −15.6741 | −0.547363 | ||||||||
\(821\) | 17.4363 | 0.608531 | 0.304265 | − | 0.952587i | \(-0.401589\pi\) | ||||
0.304265 | + | 0.952587i | \(0.401589\pi\) | |||||||
\(822\) | 14.5478 | 0.507413 | ||||||||
\(823\) | −52.2204 | −1.82029 | −0.910144 | − | 0.414293i | \(-0.864029\pi\) | ||||
−0.910144 | + | 0.414293i | \(0.864029\pi\) | |||||||
\(824\) | −2.11567 | −0.0737028 | ||||||||
\(825\) | 1.78739 | 0.0622290 | ||||||||
\(826\) | −4.65972 | −0.162133 | ||||||||
\(827\) | 2.95955 | 0.102914 | 0.0514568 | − | 0.998675i | \(-0.483614\pi\) | ||||
0.0514568 | + | 0.998675i | \(0.483614\pi\) | |||||||
\(828\) | 9.48966 | 0.329788 | ||||||||
\(829\) | 19.2721 | 0.669349 | 0.334675 | − | 0.942334i | \(-0.391374\pi\) | ||||
0.334675 | + | 0.942334i | \(0.391374\pi\) | |||||||
\(830\) | 3.13027 | 0.108653 | ||||||||
\(831\) | 7.69366 | 0.266890 | ||||||||
\(832\) | −1.29827 | −0.0450095 | ||||||||
\(833\) | 2.89464 | 0.100293 | ||||||||
\(834\) | 17.4050 | 0.602685 | ||||||||
\(835\) | −22.6831 | −0.784982 | ||||||||
\(836\) | −6.19502 | −0.214259 | ||||||||
\(837\) | −2.67099 | −0.0923231 | ||||||||
\(838\) | 40.4728 | 1.39811 | ||||||||
\(839\) | 7.51821 | 0.259557 | 0.129779 | − | 0.991543i | \(-0.458573\pi\) | ||||
0.129779 | + | 0.991543i | \(0.458573\pi\) | |||||||
\(840\) | 3.12503 | 0.107824 | ||||||||
\(841\) | −28.5597 | −0.984819 | ||||||||
\(842\) | −50.7260 | −1.74813 | ||||||||
\(843\) | −19.9318 | −0.686488 | ||||||||
\(844\) | −5.38895 | −0.185495 | ||||||||
\(845\) | 15.9662 | 0.549253 | ||||||||
\(846\) | 19.1097 | 0.657006 | ||||||||
\(847\) | −9.57602 | −0.329036 | ||||||||
\(848\) | 25.4568 | 0.874189 | ||||||||
\(849\) | 19.7645 | 0.678315 | ||||||||
\(850\) | −7.56294 | −0.259407 | ||||||||
\(851\) | 94.5709 | 3.24185 | ||||||||
\(852\) | 2.92633 | 0.100254 | ||||||||
\(853\) | −5.08900 | −0.174244 | −0.0871220 | − | 0.996198i | \(-0.527767\pi\) | ||||
−0.0871220 | + | 0.996198i | \(0.527767\pi\) | |||||||
\(854\) | 2.05069 | 0.0701732 | ||||||||
\(855\) | −9.31770 | −0.318659 | ||||||||
\(856\) | −21.5619 | −0.736970 | ||||||||
\(857\) | 13.7352 | 0.469186 | 0.234593 | − | 0.972094i | \(-0.424624\pi\) | ||||
0.234593 | + | 0.972094i | \(0.424624\pi\) | |||||||
\(858\) | 4.40001 | 0.150214 | ||||||||
\(859\) | −22.6856 | −0.774024 | −0.387012 | − | 0.922075i | \(-0.626493\pi\) | ||||
−0.387012 | + | 0.922075i | \(0.626493\pi\) | |||||||
\(860\) | −16.5585 | −0.564640 | ||||||||
\(861\) | 8.03278 | 0.273756 | ||||||||
\(862\) | 5.26050 | 0.179174 | ||||||||
\(863\) | 14.3486 | 0.488433 | 0.244217 | − | 0.969721i | \(-0.421469\pi\) | ||||
0.244217 | + | 0.969721i | \(0.421469\pi\) | |||||||
\(864\) | −5.37868 | −0.182987 | ||||||||
\(865\) | 6.54822 | 0.222646 | ||||||||
\(866\) | −21.2136 | −0.720867 | ||||||||
\(867\) | −8.62104 | −0.292786 | ||||||||
\(868\) | −2.78498 | −0.0945284 | ||||||||
\(869\) | 4.53929 | 0.153985 | ||||||||
\(870\) | 2.16594 | 0.0734323 | ||||||||
\(871\) | 3.58863 | 0.121596 | ||||||||
\(872\) | 6.05371 | 0.205005 | ||||||||
\(873\) | −2.11325 | −0.0715227 | ||||||||
\(874\) | 79.0443 | 2.67371 | ||||||||
\(875\) | 12.1601 | 0.411086 | ||||||||
\(876\) | 6.11086 | 0.206467 | ||||||||
\(877\) | −33.1203 | −1.11839 | −0.559197 | − | 0.829035i | \(-0.688891\pi\) | ||||
−0.559197 | + | 0.829035i | \(0.688891\pi\) | |||||||
\(878\) | −5.44650 | −0.183810 | ||||||||
\(879\) | 2.77679 | 0.0936589 | ||||||||
\(880\) | −11.1617 | −0.376262 | ||||||||
\(881\) | −51.1113 | −1.72198 | −0.860992 | − | 0.508618i | \(-0.830156\pi\) | ||||
−0.860992 | + | 0.508618i | \(0.830156\pi\) | |||||||
\(882\) | 1.74433 | 0.0587345 | ||||||||
\(883\) | 36.6046 | 1.23184 | 0.615922 | − | 0.787807i | \(-0.288784\pi\) | ||||
0.615922 | + | 0.787807i | \(0.288784\pi\) | |||||||
\(884\) | −6.37996 | −0.214581 | ||||||||
\(885\) | 4.99919 | 0.168046 | ||||||||
\(886\) | −52.0852 | −1.74984 | ||||||||
\(887\) | −33.5638 | −1.12696 | −0.563482 | − | 0.826129i | \(-0.690538\pi\) | ||||
−0.563482 | + | 0.826129i | \(0.690538\pi\) | |||||||
\(888\) | −17.3517 | −0.582287 | ||||||||
\(889\) | 1.42098 | 0.0476582 | ||||||||
\(890\) | 52.0027 | 1.74314 | ||||||||
\(891\) | −1.19331 | −0.0399773 | ||||||||
\(892\) | −2.60565 | −0.0872436 | ||||||||
\(893\) | 54.5467 | 1.82533 | ||||||||
\(894\) | 10.6230 | 0.355286 | ||||||||
\(895\) | 41.8367 | 1.39845 | ||||||||
\(896\) | 11.8287 | 0.395169 | ||||||||
\(897\) | −19.2387 | −0.642360 | ||||||||
\(898\) | −63.1222 | −2.10641 | ||||||||
\(899\) | 1.77225 | 0.0591078 | ||||||||
\(900\) | −1.56177 | −0.0520590 | ||||||||
\(901\) | −14.7430 | −0.491161 | ||||||||
\(902\) | −16.7204 | −0.556727 | ||||||||
\(903\) | 8.48602 | 0.282397 | ||||||||
\(904\) | 17.0571 | 0.567310 | ||||||||
\(905\) | 6.62184 | 0.220117 | ||||||||
\(906\) | −13.9860 | −0.464654 | ||||||||
\(907\) | −8.96103 | −0.297546 | −0.148773 | − | 0.988871i | \(-0.547532\pi\) | ||||
−0.148773 | + | 0.988871i | \(0.547532\pi\) | |||||||
\(908\) | 27.1071 | 0.899580 | ||||||||
\(909\) | −4.15733 | −0.137890 | ||||||||
\(910\) | 6.90031 | 0.228743 | ||||||||
\(911\) | −48.9566 | −1.62200 | −0.811002 | − | 0.585044i | \(-0.801077\pi\) | ||||
−0.811002 | + | 0.585044i | \(0.801077\pi\) | |||||||
\(912\) | −24.8859 | −0.824054 | ||||||||
\(913\) | 1.14430 | 0.0378707 | ||||||||
\(914\) | −15.9590 | −0.527878 | ||||||||
\(915\) | −2.20009 | −0.0727326 | ||||||||
\(916\) | −28.9423 | −0.956280 | ||||||||
\(917\) | 13.5004 | 0.445821 | ||||||||
\(918\) | 5.04921 | 0.166649 | ||||||||
\(919\) | −24.1408 | −0.796332 | −0.398166 | − | 0.917313i | \(-0.630353\pi\) | ||||
−0.398166 | + | 0.917313i | \(0.630353\pi\) | |||||||
\(920\) | 28.4417 | 0.937696 | ||||||||
\(921\) | 4.37277 | 0.144088 | ||||||||
\(922\) | 18.0485 | 0.594397 | ||||||||
\(923\) | −5.93263 | −0.195275 | ||||||||
\(924\) | −1.24423 | −0.0409322 | ||||||||
\(925\) | −15.5641 | −0.511745 | ||||||||
\(926\) | 2.65091 | 0.0871143 | ||||||||
\(927\) | 1.26695 | 0.0416122 | ||||||||
\(928\) | 3.56884 | 0.117153 | ||||||||
\(929\) | 50.7288 | 1.66436 | 0.832179 | − | 0.554507i | \(-0.187093\pi\) | ||||
0.832179 | + | 0.554507i | \(0.187093\pi\) | |||||||
\(930\) | 8.71903 | 0.285908 | ||||||||
\(931\) | 4.97899 | 0.163180 | ||||||||
\(932\) | 17.2887 | 0.566309 | ||||||||
\(933\) | −15.7813 | −0.516656 | ||||||||
\(934\) | 43.8716 | 1.43552 | ||||||||
\(935\) | 6.46420 | 0.211402 | ||||||||
\(936\) | 3.52988 | 0.115378 | ||||||||
\(937\) | −14.4717 | −0.472768 | −0.236384 | − | 0.971660i | \(-0.575962\pi\) | ||||
−0.236384 | + | 0.971660i | \(0.575962\pi\) | |||||||
\(938\) | −2.96130 | −0.0966899 | ||||||||
\(939\) | −1.93348 | −0.0630967 | ||||||||
\(940\) | −21.3768 | −0.697236 | ||||||||
\(941\) | −48.1384 | −1.56927 | −0.784633 | − | 0.619961i | \(-0.787149\pi\) | ||||
−0.784633 | + | 0.619961i | \(0.787149\pi\) | |||||||
\(942\) | 8.67282 | 0.282576 | ||||||||
\(943\) | 73.1084 | 2.38074 | ||||||||
\(944\) | 13.3519 | 0.434568 | ||||||||
\(945\) | −1.87140 | −0.0608768 | ||||||||
\(946\) | −17.6638 | −0.574299 | ||||||||
\(947\) | −7.02153 | −0.228169 | −0.114084 | − | 0.993471i | \(-0.536393\pi\) | ||||
−0.114084 | + | 0.993471i | \(0.536393\pi\) | |||||||
\(948\) | −3.96630 | −0.128819 | ||||||||
\(949\) | −12.3887 | −0.402155 | ||||||||
\(950\) | −13.0088 | −0.422061 | ||||||||
\(951\) | 13.1928 | 0.427807 | ||||||||
\(952\) | −4.83373 | −0.156662 | ||||||||
\(953\) | 40.9881 | 1.32774 | 0.663868 | − | 0.747850i | \(-0.268914\pi\) | ||||
0.663868 | + | 0.747850i | \(0.268914\pi\) | |||||||
\(954\) | −8.88422 | −0.287637 | ||||||||
\(955\) | −1.87140 | −0.0605572 | ||||||||
\(956\) | −6.66344 | −0.215511 | ||||||||
\(957\) | 0.791778 | 0.0255945 | ||||||||
\(958\) | −31.9680 | −1.03284 | ||||||||
\(959\) | 8.34007 | 0.269315 | ||||||||
\(960\) | −1.14937 | −0.0370958 | ||||||||
\(961\) | −23.8658 | −0.769864 | ||||||||
\(962\) | −38.3140 | −1.23529 | ||||||||
\(963\) | 12.9122 | 0.416089 | ||||||||
\(964\) | 4.21536 | 0.135768 | ||||||||
\(965\) | 21.4492 | 0.690474 | ||||||||
\(966\) | 15.8756 | 0.510788 | ||||||||
\(967\) | −4.78789 | −0.153968 | −0.0769840 | − | 0.997032i | \(-0.524529\pi\) | ||||
−0.0769840 | + | 0.997032i | \(0.524529\pi\) | |||||||
\(968\) | 15.9909 | 0.513966 | ||||||||
\(969\) | 14.4124 | 0.462993 | ||||||||
\(970\) | 6.89836 | 0.221493 | ||||||||
\(971\) | 31.5156 | 1.01138 | 0.505692 | − | 0.862714i | \(-0.331237\pi\) | ||||
0.505692 | + | 0.862714i | \(0.331237\pi\) | |||||||
\(972\) | 1.04268 | 0.0334438 | ||||||||
\(973\) | 9.97805 | 0.319882 | ||||||||
\(974\) | 20.2608 | 0.649199 | ||||||||
\(975\) | 3.16622 | 0.101400 | ||||||||
\(976\) | −5.87603 | −0.188087 | ||||||||
\(977\) | −57.6499 | −1.84438 | −0.922192 | − | 0.386733i | \(-0.873604\pi\) | ||||
−0.922192 | + | 0.386733i | \(0.873604\pi\) | |||||||
\(978\) | −15.4991 | −0.495605 | ||||||||
\(979\) | 19.0100 | 0.607563 | ||||||||
\(980\) | −1.95127 | −0.0623309 | ||||||||
\(981\) | −3.62522 | −0.115745 | ||||||||
\(982\) | −28.5435 | −0.910861 | ||||||||
\(983\) | 23.0117 | 0.733958 | 0.366979 | − | 0.930229i | \(-0.380392\pi\) | ||||
0.366979 | + | 0.930229i | \(0.380392\pi\) | |||||||
\(984\) | −13.4138 | −0.427617 | ||||||||
\(985\) | −2.46571 | −0.0785641 | ||||||||
\(986\) | −3.35023 | −0.106693 | ||||||||
\(987\) | 10.9554 | 0.348713 | ||||||||
\(988\) | −10.9740 | −0.349129 | ||||||||
\(989\) | 77.2334 | 2.45588 | ||||||||
\(990\) | 3.89536 | 0.123803 | ||||||||
\(991\) | −1.75027 | −0.0555991 | −0.0277995 | − | 0.999614i | \(-0.508850\pi\) | ||||
−0.0277995 | + | 0.999614i | \(0.508850\pi\) | |||||||
\(992\) | 14.3664 | 0.456135 | ||||||||
\(993\) | −1.05675 | −0.0335351 | ||||||||
\(994\) | 4.89555 | 0.155277 | ||||||||
\(995\) | 1.66680 | 0.0528411 | ||||||||
\(996\) | −0.999852 | −0.0316815 | ||||||||
\(997\) | −25.8661 | −0.819189 | −0.409594 | − | 0.912268i | \(-0.634330\pi\) | ||||
−0.409594 | + | 0.912268i | \(0.634330\pi\) | |||||||
\(998\) | 18.2416 | 0.577428 | ||||||||
\(999\) | 10.3910 | 0.328756 |
(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 | 4011.2.a.k.1.20 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4011.2.a.k.1.20 | ✓ | 27 | 1.1 | even | 1 | trivial |