Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.70335 | −1.20445 | −0.602225 | − | 0.798326i | \(-0.705719\pi\) | ||||
−0.602225 | + | 0.798326i | \(0.705719\pi\) | |||||||
\(3\) | −3.34921 | −1.93367 | −0.966833 | − | 0.255411i | \(-0.917789\pi\) | ||||
−0.966833 | + | 0.255411i | \(0.917789\pi\) | |||||||
\(4\) | 0.901404 | 0.450702 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 5.70487 | 2.32900 | ||||||||
\(7\) | 4.14952 | 1.56837 | 0.784186 | − | 0.620525i | \(-0.213081\pi\) | ||||
0.784186 | + | 0.620525i | \(0.213081\pi\) | |||||||
\(8\) | 1.87129 | 0.661603 | ||||||||
\(9\) | 8.21718 | 2.73906 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.44777 | −1.03954 | −0.519771 | − | 0.854306i | \(-0.673983\pi\) | ||||
−0.519771 | + | 0.854306i | \(0.673983\pi\) | |||||||
\(12\) | −3.01899 | −0.871507 | ||||||||
\(13\) | 2.03856 | 0.565395 | 0.282697 | − | 0.959209i | \(-0.408771\pi\) | ||||
0.282697 | + | 0.959209i | \(0.408771\pi\) | |||||||
\(14\) | −7.06810 | −1.88903 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.99028 | −1.24757 | ||||||||
\(17\) | −2.85104 | −0.691479 | −0.345740 | − | 0.938330i | \(-0.612372\pi\) | ||||
−0.345740 | + | 0.938330i | \(0.612372\pi\) | |||||||
\(18\) | −13.9967 | −3.29906 | ||||||||
\(19\) | −5.67321 | −1.30152 | −0.650762 | − | 0.759282i | \(-0.725550\pi\) | ||||
−0.650762 | + | 0.759282i | \(0.725550\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −13.8976 | −3.03271 | ||||||||
\(22\) | 5.87276 | 1.25208 | ||||||||
\(23\) | 7.45830 | 1.55516 | 0.777581 | − | 0.628783i | \(-0.216446\pi\) | ||||
0.777581 | + | 0.628783i | \(0.216446\pi\) | |||||||
\(24\) | −6.26735 | −1.27932 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.47238 | −0.680991 | ||||||||
\(27\) | −17.4734 | −3.36276 | ||||||||
\(28\) | 3.74040 | 0.706869 | ||||||||
\(29\) | −9.40832 | −1.74708 | −0.873540 | − | 0.486752i | \(-0.838182\pi\) | ||||
−0.873540 | + | 0.486752i | \(0.838182\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.10525 | −0.737325 | −0.368663 | − | 0.929563i | \(-0.620184\pi\) | ||||
−0.368663 | + | 0.929563i | \(0.620184\pi\) | |||||||
\(32\) | 4.75761 | 0.841034 | ||||||||
\(33\) | 11.5473 | 2.01012 | ||||||||
\(34\) | 4.85632 | 0.832853 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 7.40700 | 1.23450 | ||||||||
\(37\) | −5.25822 | −0.864446 | −0.432223 | − | 0.901767i | \(-0.642271\pi\) | ||||
−0.432223 | + | 0.901767i | \(0.642271\pi\) | |||||||
\(38\) | 9.66347 | 1.56762 | ||||||||
\(39\) | −6.82756 | −1.09328 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.62215 | 1.03421 | 0.517103 | − | 0.855923i | \(-0.327010\pi\) | ||||
0.517103 | + | 0.855923i | \(0.327010\pi\) | |||||||
\(42\) | 23.6725 | 3.65275 | ||||||||
\(43\) | −2.58576 | −0.394324 | −0.197162 | − | 0.980371i | \(-0.563173\pi\) | ||||
−0.197162 | + | 0.980371i | \(0.563173\pi\) | |||||||
\(44\) | −3.10783 | −0.468523 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12.7041 | −1.87312 | ||||||||
\(47\) | 9.69060 | 1.41352 | 0.706760 | − | 0.707454i | \(-0.250156\pi\) | ||||
0.706760 | + | 0.707454i | \(0.250156\pi\) | |||||||
\(48\) | 16.7135 | 2.41238 | ||||||||
\(49\) | 10.2186 | 1.45979 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.54873 | 1.33709 | ||||||||
\(52\) | 1.83757 | 0.254825 | ||||||||
\(53\) | 1.63816 | 0.225018 | 0.112509 | − | 0.993651i | \(-0.464111\pi\) | ||||
0.112509 | + | 0.993651i | \(0.464111\pi\) | |||||||
\(54\) | 29.7634 | 4.05028 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 7.76498 | 1.03764 | ||||||||
\(57\) | 19.0008 | 2.51671 | ||||||||
\(58\) | 16.0257 | 2.10427 | ||||||||
\(59\) | 0.368987 | 0.0480380 | 0.0240190 | − | 0.999712i | \(-0.492354\pi\) | ||||
0.0240190 | + | 0.999712i | \(0.492354\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.74043 | 0.863024 | 0.431512 | − | 0.902107i | \(-0.357980\pi\) | ||||
0.431512 | + | 0.902107i | \(0.357980\pi\) | |||||||
\(62\) | 6.99269 | 0.888072 | ||||||||
\(63\) | 34.0974 | 4.29587 | ||||||||
\(64\) | 1.87669 | 0.234586 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −19.6691 | −2.42110 | ||||||||
\(67\) | −7.33641 | −0.896285 | −0.448142 | − | 0.893962i | \(-0.647914\pi\) | ||||
−0.448142 | + | 0.893962i | \(0.647914\pi\) | |||||||
\(68\) | −2.56994 | −0.311651 | ||||||||
\(69\) | −24.9794 | −3.00716 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.51810 | −0.892235 | −0.446117 | − | 0.894974i | \(-0.647194\pi\) | ||||
−0.446117 | + | 0.894974i | \(0.647194\pi\) | |||||||
\(72\) | 15.3768 | 1.81217 | ||||||||
\(73\) | −13.1573 | −1.53995 | −0.769973 | − | 0.638076i | \(-0.779730\pi\) | ||||
−0.769973 | + | 0.638076i | \(0.779730\pi\) | |||||||
\(74\) | 8.95659 | 1.04118 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.11386 | −0.586599 | ||||||||
\(77\) | −14.3066 | −1.63039 | ||||||||
\(78\) | 11.6297 | 1.31681 | ||||||||
\(79\) | 12.0667 | 1.35761 | 0.678803 | − | 0.734321i | \(-0.262499\pi\) | ||||
0.678803 | + | 0.734321i | \(0.262499\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 33.8706 | 3.76339 | ||||||||
\(82\) | −11.2798 | −1.24565 | ||||||||
\(83\) | 11.5430 | 1.26701 | 0.633505 | − | 0.773739i | \(-0.281616\pi\) | ||||
0.633505 | + | 0.773739i | \(0.281616\pi\) | |||||||
\(84\) | −12.5274 | −1.36685 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.40445 | 0.474944 | ||||||||
\(87\) | 31.5104 | 3.37827 | ||||||||
\(88\) | −6.45179 | −0.687763 | ||||||||
\(89\) | −18.4526 | −1.95597 | −0.977984 | − | 0.208681i | \(-0.933083\pi\) | ||||
−0.977984 | + | 0.208681i | \(0.933083\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.45906 | 0.886750 | ||||||||
\(92\) | 6.72294 | 0.700915 | ||||||||
\(93\) | 13.7493 | 1.42574 | ||||||||
\(94\) | −16.5065 | −1.70251 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −15.9342 | −1.62628 | ||||||||
\(97\) | −16.8218 | −1.70799 | −0.853996 | − | 0.520280i | \(-0.825828\pi\) | ||||
−0.853996 | + | 0.520280i | \(0.825828\pi\) | |||||||
\(98\) | −17.4058 | −1.75825 | ||||||||
\(99\) | −28.3309 | −2.84737 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.59929 | 0.656654 | 0.328327 | − | 0.944564i | \(-0.393515\pi\) | ||||
0.328327 | + | 0.944564i | \(0.393515\pi\) | |||||||
\(102\) | −16.2648 | −1.61046 | ||||||||
\(103\) | 9.15606 | 0.902174 | 0.451087 | − | 0.892480i | \(-0.351036\pi\) | ||||
0.451087 | + | 0.892480i | \(0.351036\pi\) | |||||||
\(104\) | 3.81475 | 0.374067 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.79036 | −0.271024 | ||||||||
\(107\) | −9.01519 | −0.871532 | −0.435766 | − | 0.900060i | \(-0.643522\pi\) | ||||
−0.435766 | + | 0.900060i | \(0.643522\pi\) | |||||||
\(108\) | −15.7506 | −1.51560 | ||||||||
\(109\) | −9.46531 | −0.906612 | −0.453306 | − | 0.891355i | \(-0.649756\pi\) | ||||
−0.453306 | + | 0.891355i | \(0.649756\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17.6109 | 1.67155 | ||||||||
\(112\) | −20.7073 | −1.95665 | ||||||||
\(113\) | 4.31866 | 0.406265 | 0.203133 | − | 0.979151i | \(-0.434888\pi\) | ||||
0.203133 | + | 0.979151i | \(0.434888\pi\) | |||||||
\(114\) | −32.3650 | −3.03126 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −8.48070 | −0.787413 | ||||||||
\(117\) | 16.7512 | 1.54865 | ||||||||
\(118\) | −0.628513 | −0.0578594 | ||||||||
\(119\) | −11.8305 | −1.08450 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.887101 | 0.0806456 | ||||||||
\(122\) | −11.4813 | −1.03947 | ||||||||
\(123\) | −22.1790 | −1.99981 | ||||||||
\(124\) | −3.70049 | −0.332314 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −58.0798 | −5.17416 | ||||||||
\(127\) | 6.79536 | 0.602990 | 0.301495 | − | 0.953468i | \(-0.402514\pi\) | ||||
0.301495 | + | 0.953468i | \(0.402514\pi\) | |||||||
\(128\) | −12.7119 | −1.12358 | ||||||||
\(129\) | 8.66023 | 0.762491 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.8118 | 1.03200 | 0.516000 | − | 0.856588i | \(-0.327420\pi\) | ||||
0.516000 | + | 0.856588i | \(0.327420\pi\) | |||||||
\(132\) | 10.4088 | 0.905967 | ||||||||
\(133\) | −23.5411 | −2.04128 | ||||||||
\(134\) | 12.4965 | 1.07953 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.33514 | −0.457484 | ||||||||
\(137\) | 18.5142 | 1.58178 | 0.790890 | − | 0.611959i | \(-0.209618\pi\) | ||||
0.790890 | + | 0.611959i | \(0.209618\pi\) | |||||||
\(138\) | 42.5486 | 3.62198 | ||||||||
\(139\) | 14.1839 | 1.20306 | 0.601532 | − | 0.798849i | \(-0.294557\pi\) | ||||
0.601532 | + | 0.798849i | \(0.294557\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −32.4558 | −2.73327 | ||||||||
\(142\) | 12.8060 | 1.07465 | ||||||||
\(143\) | −7.02848 | −0.587751 | ||||||||
\(144\) | −41.0060 | −3.41717 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 22.4115 | 1.85479 | ||||||||
\(147\) | −34.2241 | −2.82275 | ||||||||
\(148\) | −4.73978 | −0.389607 | ||||||||
\(149\) | 19.2334 | 1.57566 | 0.787832 | − | 0.615890i | \(-0.211204\pi\) | ||||
0.787832 | + | 0.615890i | \(0.211204\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.221080 | −0.0179912 | −0.00899561 | − | 0.999960i | \(-0.502863\pi\) | ||||
−0.00899561 | + | 0.999960i | \(0.502863\pi\) | |||||||
\(152\) | −10.6163 | −0.861092 | ||||||||
\(153\) | −23.4275 | −1.89400 | ||||||||
\(154\) | 24.3692 | 1.96372 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −6.15439 | −0.492746 | ||||||||
\(157\) | −16.5832 | −1.32348 | −0.661742 | − | 0.749732i | \(-0.730182\pi\) | ||||
−0.661742 | + | 0.749732i | \(0.730182\pi\) | |||||||
\(158\) | −20.5538 | −1.63517 | ||||||||
\(159\) | −5.48653 | −0.435110 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 30.9484 | 2.43907 | ||||||||
\(162\) | −57.6934 | −4.53282 | ||||||||
\(163\) | 9.77856 | 0.765916 | 0.382958 | − | 0.923766i | \(-0.374905\pi\) | ||||
0.382958 | + | 0.923766i | \(0.374905\pi\) | |||||||
\(164\) | 5.96923 | 0.466119 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −19.6618 | −1.52605 | ||||||||
\(167\) | 20.2250 | 1.56506 | 0.782530 | − | 0.622613i | \(-0.213929\pi\) | ||||
0.782530 | + | 0.622613i | \(0.213929\pi\) | |||||||
\(168\) | −26.0065 | −2.00645 | ||||||||
\(169\) | −8.84427 | −0.680328 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −46.6178 | −3.56495 | ||||||||
\(172\) | −2.33081 | −0.177723 | ||||||||
\(173\) | 9.77541 | 0.743211 | 0.371605 | − | 0.928391i | \(-0.378807\pi\) | ||||
0.371605 | + | 0.928391i | \(0.378807\pi\) | |||||||
\(174\) | −53.6733 | −4.06896 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 17.2053 | 1.29690 | ||||||||
\(177\) | −1.23581 | −0.0928893 | ||||||||
\(178\) | 31.4312 | 2.35587 | ||||||||
\(179\) | −10.5767 | −0.790542 | −0.395271 | − | 0.918565i | \(-0.629349\pi\) | ||||
−0.395271 | + | 0.918565i | \(0.629349\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.53036 | −0.411068 | −0.205534 | − | 0.978650i | \(-0.565893\pi\) | ||||
−0.205534 | + | 0.978650i | \(0.565893\pi\) | |||||||
\(182\) | −14.4087 | −1.06805 | ||||||||
\(183\) | −22.5751 | −1.66880 | ||||||||
\(184\) | 13.9567 | 1.02890 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −23.4200 | −1.71723 | ||||||||
\(187\) | 9.82973 | 0.718821 | ||||||||
\(188\) | 8.73515 | 0.637076 | ||||||||
\(189\) | −72.5064 | −5.27406 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.09836 | 0.441262 | 0.220631 | − | 0.975357i | \(-0.429188\pi\) | ||||
0.220631 | + | 0.975357i | \(0.429188\pi\) | |||||||
\(192\) | −6.28541 | −0.453610 | ||||||||
\(193\) | 2.25558 | 0.162360 | 0.0811801 | − | 0.996699i | \(-0.474131\pi\) | ||||
0.0811801 | + | 0.996699i | \(0.474131\pi\) | |||||||
\(194\) | 28.6534 | 2.05719 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.21105 | 0.657932 | ||||||||
\(197\) | 12.2908 | 0.875681 | 0.437840 | − | 0.899053i | \(-0.355743\pi\) | ||||
0.437840 | + | 0.899053i | \(0.355743\pi\) | |||||||
\(198\) | 48.2575 | 3.42951 | ||||||||
\(199\) | −7.85504 | −0.556829 | −0.278414 | − | 0.960461i | \(-0.589809\pi\) | ||||
−0.278414 | + | 0.960461i | \(0.589809\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 24.5711 | 1.73311 | ||||||||
\(202\) | −11.2409 | −0.790908 | ||||||||
\(203\) | −39.0400 | −2.74007 | ||||||||
\(204\) | 8.60726 | 0.602629 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −15.5960 | −1.08662 | ||||||||
\(207\) | 61.2862 | 4.25968 | ||||||||
\(208\) | −10.1730 | −0.705370 | ||||||||
\(209\) | 19.5599 | 1.35299 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.76828 | −0.121733 | −0.0608666 | − | 0.998146i | \(-0.519386\pi\) | ||||
−0.0608666 | + | 0.998146i | \(0.519386\pi\) | |||||||
\(212\) | 1.47664 | 0.101416 | ||||||||
\(213\) | 25.1797 | 1.72528 | ||||||||
\(214\) | 15.3560 | 1.04972 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −32.6979 | −2.22481 | ||||||||
\(217\) | −17.0349 | −1.15640 | ||||||||
\(218\) | 16.1227 | 1.09197 | ||||||||
\(219\) | 44.0665 | 2.97774 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.81202 | −0.390959 | ||||||||
\(222\) | −29.9975 | −2.01330 | ||||||||
\(223\) | −10.9721 | −0.734745 | −0.367373 | − | 0.930074i | \(-0.619743\pi\) | ||||
−0.367373 | + | 0.930074i | \(0.619743\pi\) | |||||||
\(224\) | 19.7418 | 1.31905 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.35619 | −0.489326 | ||||||||
\(227\) | 4.57187 | 0.303446 | 0.151723 | − | 0.988423i | \(-0.451518\pi\) | ||||
0.151723 | + | 0.988423i | \(0.451518\pi\) | |||||||
\(228\) | 17.1274 | 1.13429 | ||||||||
\(229\) | −20.3548 | −1.34509 | −0.672543 | − | 0.740058i | \(-0.734798\pi\) | ||||
−0.672543 | + | 0.740058i | \(0.734798\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 47.9157 | 3.15262 | ||||||||
\(232\) | −17.6057 | −1.15587 | ||||||||
\(233\) | 7.99344 | 0.523667 | 0.261834 | − | 0.965113i | \(-0.415673\pi\) | ||||
0.261834 | + | 0.965113i | \(0.415673\pi\) | |||||||
\(234\) | −28.5332 | −1.86527 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.332606 | 0.0216508 | ||||||||
\(237\) | −40.4137 | −2.62516 | ||||||||
\(238\) | 20.1514 | 1.30622 | ||||||||
\(239\) | −2.75869 | −0.178445 | −0.0892224 | − | 0.996012i | \(-0.528438\pi\) | ||||
−0.0892224 | + | 0.996012i | \(0.528438\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | −1.51104 | −0.0971336 | ||||||||
\(243\) | −61.0192 | −3.91438 | ||||||||
\(244\) | 6.07585 | 0.388966 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 37.7785 | 2.40867 | ||||||||
\(247\) | −11.5652 | −0.735875 | ||||||||
\(248\) | −7.68214 | −0.487816 | ||||||||
\(249\) | −38.6599 | −2.44997 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.2806 | −0.648908 | −0.324454 | − | 0.945902i | \(-0.605180\pi\) | ||||
−0.324454 | + | 0.945902i | \(0.605180\pi\) | |||||||
\(252\) | 30.7355 | 1.93616 | ||||||||
\(253\) | −25.7145 | −1.61665 | ||||||||
\(254\) | −11.5749 | −0.726272 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 17.8994 | 1.11871 | ||||||||
\(257\) | −7.25132 | −0.452325 | −0.226162 | − | 0.974090i | \(-0.572618\pi\) | ||||
−0.226162 | + | 0.974090i | \(0.572618\pi\) | |||||||
\(258\) | −14.7514 | −0.918383 | ||||||||
\(259\) | −21.8191 | −1.35577 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −77.3099 | −4.78536 | ||||||||
\(262\) | −20.1196 | −1.24299 | ||||||||
\(263\) | −7.18915 | −0.443302 | −0.221651 | − | 0.975126i | \(-0.571145\pi\) | ||||
−0.221651 | + | 0.975126i | \(0.571145\pi\) | |||||||
\(264\) | 21.6084 | 1.32990 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 40.0988 | 2.45862 | ||||||||
\(267\) | 61.8014 | 3.78219 | ||||||||
\(268\) | −6.61307 | −0.403957 | ||||||||
\(269\) | −15.4444 | −0.941662 | −0.470831 | − | 0.882223i | \(-0.656046\pi\) | ||||
−0.470831 | + | 0.882223i | \(0.656046\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.50201 | 0.0912408 | 0.0456204 | − | 0.998959i | \(-0.485474\pi\) | ||||
0.0456204 | + | 0.998959i | \(0.485474\pi\) | |||||||
\(272\) | 14.2275 | 0.862669 | ||||||||
\(273\) | −28.3311 | −1.71468 | ||||||||
\(274\) | −31.5363 | −1.90518 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −22.5165 | −1.35533 | ||||||||
\(277\) | 21.7350 | 1.30593 | 0.652964 | − | 0.757389i | \(-0.273525\pi\) | ||||
0.652964 | + | 0.757389i | \(0.273525\pi\) | |||||||
\(278\) | −24.1602 | −1.44903 | ||||||||
\(279\) | −33.7336 | −2.01958 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.2708 | 0.732014 | 0.366007 | − | 0.930612i | \(-0.380725\pi\) | ||||
0.366007 | + | 0.930612i | \(0.380725\pi\) | |||||||
\(282\) | 55.2837 | 3.29209 | ||||||||
\(283\) | 8.41799 | 0.500397 | 0.250199 | − | 0.968195i | \(-0.419504\pi\) | ||||
0.250199 | + | 0.968195i | \(0.419504\pi\) | |||||||
\(284\) | −6.77685 | −0.402132 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.9720 | 0.707918 | ||||||||
\(287\) | 27.4788 | 1.62202 | ||||||||
\(288\) | 39.0941 | 2.30364 | ||||||||
\(289\) | −8.87156 | −0.521856 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 56.3396 | 3.30268 | ||||||||
\(292\) | −11.8600 | −0.694057 | ||||||||
\(293\) | 21.5920 | 1.26142 | 0.630710 | − | 0.776018i | \(-0.282764\pi\) | ||||
0.630710 | + | 0.776018i | \(0.282764\pi\) | |||||||
\(294\) | 58.2956 | 3.39987 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −9.83967 | −0.571919 | ||||||||
\(297\) | 60.2443 | 3.49573 | ||||||||
\(298\) | −32.7613 | −1.89781 | ||||||||
\(299\) | 15.2042 | 0.879281 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.7297 | −0.618447 | ||||||||
\(302\) | 0.376576 | 0.0216695 | ||||||||
\(303\) | −22.1024 | −1.26975 | ||||||||
\(304\) | 28.3109 | 1.62374 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 39.9053 | 2.28123 | ||||||||
\(307\) | 21.2041 | 1.21018 | 0.605091 | − | 0.796156i | \(-0.293137\pi\) | ||||
0.605091 | + | 0.796156i | \(0.293137\pi\) | |||||||
\(308\) | −12.8960 | −0.734819 | ||||||||
\(309\) | −30.6655 | −1.74450 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.46816 | −0.139956 | −0.0699782 | − | 0.997549i | \(-0.522293\pi\) | ||||
−0.0699782 | + | 0.997549i | \(0.522293\pi\) | |||||||
\(312\) | −12.7764 | −0.723320 | ||||||||
\(313\) | 29.6149 | 1.67393 | 0.836966 | − | 0.547256i | \(-0.184327\pi\) | ||||
0.836966 | + | 0.547256i | \(0.184327\pi\) | |||||||
\(314\) | 28.2470 | 1.59407 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.8769 | 0.611876 | ||||||||
\(317\) | 0.493768 | 0.0277328 | 0.0138664 | − | 0.999904i | \(-0.495586\pi\) | ||||
0.0138664 | + | 0.999904i | \(0.495586\pi\) | |||||||
\(318\) | 9.34549 | 0.524069 | ||||||||
\(319\) | 32.4377 | 1.81616 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 30.1937 | 1.68525 | ||||||||
\(322\) | −52.7160 | −2.93775 | ||||||||
\(323\) | 16.1746 | 0.899977 | ||||||||
\(324\) | 30.5310 | 1.69617 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −16.6563 | −0.922508 | ||||||||
\(327\) | 31.7013 | 1.75308 | ||||||||
\(328\) | 12.3920 | 0.684234 | ||||||||
\(329\) | 40.2114 | 2.21693 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.38776 | −0.241173 | −0.120587 | − | 0.992703i | \(-0.538478\pi\) | ||||
−0.120587 | + | 0.992703i | \(0.538478\pi\) | |||||||
\(332\) | 10.4049 | 0.571044 | ||||||||
\(333\) | −43.2077 | −2.36777 | ||||||||
\(334\) | −34.4503 | −1.88504 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 69.3530 | 3.78351 | ||||||||
\(337\) | −18.0535 | −0.983438 | −0.491719 | − | 0.870754i | \(-0.663631\pi\) | ||||
−0.491719 | + | 0.870754i | \(0.663631\pi\) | |||||||
\(338\) | 15.0649 | 0.819422 | ||||||||
\(339\) | −14.4641 | −0.785581 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.1540 | 0.766480 | ||||||||
\(342\) | 79.4065 | 4.29381 | ||||||||
\(343\) | 13.3555 | 0.721128 | ||||||||
\(344\) | −4.83871 | −0.260886 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.6510 | −0.895161 | ||||||||
\(347\) | 15.8576 | 0.851278 | 0.425639 | − | 0.904893i | \(-0.360049\pi\) | ||||
0.425639 | + | 0.904893i | \(0.360049\pi\) | |||||||
\(348\) | 28.4036 | 1.52259 | ||||||||
\(349\) | 9.18886 | 0.491868 | 0.245934 | − | 0.969287i | \(-0.420905\pi\) | ||||
0.245934 | + | 0.969287i | \(0.420905\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −35.6206 | −1.90129 | ||||||||
\(352\) | −16.4031 | −0.874289 | ||||||||
\(353\) | −33.2136 | −1.76778 | −0.883890 | − | 0.467695i | \(-0.845084\pi\) | ||||
−0.883890 | + | 0.467695i | \(0.845084\pi\) | |||||||
\(354\) | 2.10502 | 0.111881 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −16.6332 | −0.881558 | ||||||||
\(357\) | 39.6227 | 2.09705 | ||||||||
\(358\) | 18.0159 | 0.952169 | ||||||||
\(359\) | 8.91354 | 0.470438 | 0.235219 | − | 0.971942i | \(-0.424419\pi\) | ||||
0.235219 | + | 0.971942i | \(0.424419\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.1853 | 0.693965 | ||||||||
\(362\) | 9.42014 | 0.495112 | ||||||||
\(363\) | −2.97109 | −0.155942 | ||||||||
\(364\) | 7.62503 | 0.399660 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 38.4533 | 2.00999 | ||||||||
\(367\) | 6.75941 | 0.352838 | 0.176419 | − | 0.984315i | \(-0.443549\pi\) | ||||
0.176419 | + | 0.984315i | \(0.443549\pi\) | |||||||
\(368\) | −37.2190 | −1.94017 | ||||||||
\(369\) | 54.4154 | 2.83276 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.79758 | 0.352913 | ||||||||
\(372\) | 12.3937 | 0.642584 | ||||||||
\(373\) | −1.71386 | −0.0887403 | −0.0443701 | − | 0.999015i | \(-0.514128\pi\) | ||||
−0.0443701 | + | 0.999015i | \(0.514128\pi\) | |||||||
\(374\) | −16.7435 | −0.865785 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 18.1340 | 0.935188 | ||||||||
\(377\) | −19.1794 | −0.987791 | ||||||||
\(378\) | 123.504 | 6.35235 | ||||||||
\(379\) | −0.756164 | −0.0388415 | −0.0194208 | − | 0.999811i | \(-0.506182\pi\) | ||||
−0.0194208 | + | 0.999811i | \(0.506182\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −22.7590 | −1.16598 | ||||||||
\(382\) | −10.3877 | −0.531479 | ||||||||
\(383\) | 14.5628 | 0.744124 | 0.372062 | − | 0.928208i | \(-0.378651\pi\) | ||||
0.372062 | + | 0.928208i | \(0.378651\pi\) | |||||||
\(384\) | 42.5747 | 2.17263 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.84204 | −0.195555 | ||||||||
\(387\) | −21.2476 | −1.08008 | ||||||||
\(388\) | −15.1632 | −0.769795 | ||||||||
\(389\) | 14.0887 | 0.714323 | 0.357162 | − | 0.934043i | \(-0.383745\pi\) | ||||
0.357162 | + | 0.934043i | \(0.383745\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.2639 | −1.07536 | ||||||||
\(392\) | 19.1219 | 0.965803 | ||||||||
\(393\) | −39.5601 | −1.99554 | ||||||||
\(394\) | −20.9355 | −1.05471 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −25.5376 | −1.28331 | ||||||||
\(397\) | −17.1658 | −0.861525 | −0.430762 | − | 0.902465i | \(-0.641755\pi\) | ||||
−0.430762 | + | 0.902465i | \(0.641755\pi\) | |||||||
\(398\) | 13.3799 | 0.670673 | ||||||||
\(399\) | 78.8441 | 3.94714 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.12010 | 0.0559354 | 0.0279677 | − | 0.999609i | \(-0.491096\pi\) | ||||
0.0279677 | + | 0.999609i | \(0.491096\pi\) | |||||||
\(402\) | −41.8533 | −2.08745 | ||||||||
\(403\) | −8.36881 | −0.416880 | ||||||||
\(404\) | 5.94863 | 0.295955 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 66.4989 | 3.30028 | ||||||||
\(407\) | 18.1291 | 0.898627 | ||||||||
\(408\) | 17.8685 | 0.884622 | ||||||||
\(409\) | −31.8966 | −1.57718 | −0.788592 | − | 0.614916i | \(-0.789190\pi\) | ||||
−0.788592 | + | 0.614916i | \(0.789190\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −62.0080 | −3.05863 | ||||||||
\(412\) | 8.25331 | 0.406611 | ||||||||
\(413\) | 1.53112 | 0.0753414 | ||||||||
\(414\) | −104.392 | −5.13058 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 9.69867 | 0.475516 | ||||||||
\(417\) | −47.5049 | −2.32632 | ||||||||
\(418\) | −33.3174 | −1.62961 | ||||||||
\(419\) | −22.4444 | −1.09648 | −0.548241 | − | 0.836320i | \(-0.684702\pi\) | ||||
−0.548241 | + | 0.836320i | \(0.684702\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.39850 | 0.214370 | 0.107185 | − | 0.994239i | \(-0.465816\pi\) | ||||
0.107185 | + | 0.994239i | \(0.465816\pi\) | |||||||
\(422\) | 3.01200 | 0.146622 | ||||||||
\(423\) | 79.6295 | 3.87172 | ||||||||
\(424\) | 3.06548 | 0.148873 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −42.8898 | −2.07802 | ||||||||
\(427\) | 27.9696 | 1.35354 | ||||||||
\(428\) | −8.12633 | −0.392801 | ||||||||
\(429\) | 23.5398 | 1.13651 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.0770 | 1.59327 | 0.796633 | − | 0.604464i | \(-0.206613\pi\) | ||||
0.796633 | + | 0.604464i | \(0.206613\pi\) | |||||||
\(432\) | 87.1973 | 4.19528 | ||||||||
\(433\) | 23.2564 | 1.11763 | 0.558815 | − | 0.829292i | \(-0.311256\pi\) | ||||
0.558815 | + | 0.829292i | \(0.311256\pi\) | |||||||
\(434\) | 29.0163 | 1.39283 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.53207 | −0.408612 | ||||||||
\(437\) | −42.3125 | −2.02408 | ||||||||
\(438\) | −75.0608 | −3.58654 | ||||||||
\(439\) | 29.1885 | 1.39309 | 0.696547 | − | 0.717511i | \(-0.254719\pi\) | ||||
0.696547 | + | 0.717511i | \(0.254719\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 83.9677 | 3.99846 | ||||||||
\(442\) | 9.89991 | 0.470891 | ||||||||
\(443\) | 33.9523 | 1.61312 | 0.806561 | − | 0.591151i | \(-0.201326\pi\) | ||||
0.806561 | + | 0.591151i | \(0.201326\pi\) | |||||||
\(444\) | 15.8745 | 0.753370 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 18.6893 | 0.884964 | ||||||||
\(447\) | −64.4167 | −3.04681 | ||||||||
\(448\) | 7.78735 | 0.367918 | ||||||||
\(449\) | −27.5194 | −1.29872 | −0.649359 | − | 0.760482i | \(-0.724963\pi\) | ||||
−0.649359 | + | 0.760482i | \(0.724963\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.8316 | −1.07510 | ||||||||
\(452\) | 3.89286 | 0.183105 | ||||||||
\(453\) | 0.740442 | 0.0347890 | ||||||||
\(454\) | −7.78751 | −0.365486 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 35.5560 | 1.66506 | ||||||||
\(457\) | −39.0884 | −1.82848 | −0.914239 | − | 0.405175i | \(-0.867211\pi\) | ||||
−0.914239 | + | 0.405175i | \(0.867211\pi\) | |||||||
\(458\) | 34.6714 | 1.62009 | ||||||||
\(459\) | 49.8175 | 2.32528 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.4048 | 1.50924 | 0.754621 | − | 0.656161i | \(-0.227821\pi\) | ||||
0.754621 | + | 0.656161i | \(0.227821\pi\) | |||||||
\(462\) | −81.6173 | −3.79718 | ||||||||
\(463\) | −4.89462 | −0.227472 | −0.113736 | − | 0.993511i | \(-0.536282\pi\) | ||||
−0.113736 | + | 0.993511i | \(0.536282\pi\) | |||||||
\(464\) | 46.9501 | 2.17961 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.6156 | −0.630732 | ||||||||
\(467\) | −28.0745 | −1.29913 | −0.649567 | − | 0.760305i | \(-0.725050\pi\) | ||||
−0.649567 | + | 0.760305i | \(0.725050\pi\) | |||||||
\(468\) | 15.0996 | 0.697980 | ||||||||
\(469\) | −30.4426 | −1.40571 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 55.5405 | 2.55917 | ||||||||
\(472\) | 0.690482 | 0.0317820 | ||||||||
\(473\) | 8.91509 | 0.409916 | ||||||||
\(474\) | 68.8388 | 3.16187 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −10.6640 | −0.488785 | ||||||||
\(477\) | 13.4610 | 0.616339 | ||||||||
\(478\) | 4.69902 | 0.214928 | ||||||||
\(479\) | −20.3401 | −0.929363 | −0.464682 | − | 0.885478i | \(-0.653831\pi\) | ||||
−0.464682 | + | 0.885478i | \(0.653831\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.7192 | −0.488753 | ||||||||
\(482\) | −1.70335 | −0.0775855 | ||||||||
\(483\) | −103.653 | −4.71635 | ||||||||
\(484\) | 0.799637 | 0.0363471 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 103.937 | 4.71468 | ||||||||
\(487\) | 9.01739 | 0.408617 | 0.204309 | − | 0.978907i | \(-0.434505\pi\) | ||||
0.204309 | + | 0.978907i | \(0.434505\pi\) | |||||||
\(488\) | 12.6133 | 0.570979 | ||||||||
\(489\) | −32.7504 | −1.48102 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.5791 | −1.10924 | −0.554620 | − | 0.832104i | \(-0.687136\pi\) | ||||
−0.554620 | + | 0.832104i | \(0.687136\pi\) | |||||||
\(492\) | −19.9922 | −0.901318 | ||||||||
\(493\) | 26.8235 | 1.20807 | ||||||||
\(494\) | 19.6996 | 0.886326 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20.4864 | 0.919865 | ||||||||
\(497\) | −31.1966 | −1.39936 | ||||||||
\(498\) | 65.8514 | 2.95087 | ||||||||
\(499\) | 2.71603 | 0.121586 | 0.0607931 | − | 0.998150i | \(-0.480637\pi\) | ||||
0.0607931 | + | 0.998150i | \(0.480637\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −67.7378 | −3.02630 | ||||||||
\(502\) | 17.5115 | 0.781577 | ||||||||
\(503\) | −7.15729 | −0.319128 | −0.159564 | − | 0.987188i | \(-0.551009\pi\) | ||||
−0.159564 | + | 0.987188i | \(0.551009\pi\) | |||||||
\(504\) | 63.8063 | 2.84216 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 43.8008 | 1.94718 | ||||||||
\(507\) | 29.6213 | 1.31553 | ||||||||
\(508\) | 6.12536 | 0.271769 | ||||||||
\(509\) | 3.93159 | 0.174265 | 0.0871324 | − | 0.996197i | \(-0.472230\pi\) | ||||
0.0871324 | + | 0.996197i | \(0.472230\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −54.5966 | −2.41521 | ||||||||
\(512\) | −5.06522 | −0.223853 | ||||||||
\(513\) | 99.1304 | 4.37672 | ||||||||
\(514\) | 12.3515 | 0.544803 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7.80637 | 0.343656 | ||||||||
\(517\) | −33.4109 | −1.46941 | ||||||||
\(518\) | 37.1656 | 1.63296 | ||||||||
\(519\) | −32.7399 | −1.43712 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.1579 | −0.576456 | −0.288228 | − | 0.957562i | \(-0.593066\pi\) | ||||
−0.288228 | + | 0.957562i | \(0.593066\pi\) | |||||||
\(522\) | 131.686 | 5.76373 | ||||||||
\(523\) | 27.2969 | 1.19361 | 0.596805 | − | 0.802386i | \(-0.296436\pi\) | ||||
0.596805 | + | 0.802386i | \(0.296436\pi\) | |||||||
\(524\) | 10.6472 | 0.465125 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.2456 | 0.533935 | ||||||||
\(527\) | 11.7043 | 0.509845 | ||||||||
\(528\) | −57.6242 | −2.50777 | ||||||||
\(529\) | 32.6262 | 1.41853 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.03203 | 0.131579 | ||||||||
\(532\) | −21.2201 | −0.920007 | ||||||||
\(533\) | 13.4997 | 0.584735 | ||||||||
\(534\) | −105.270 | −4.55546 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −13.7286 | −0.592984 | ||||||||
\(537\) | 35.4237 | 1.52864 | ||||||||
\(538\) | 26.3072 | 1.13419 | ||||||||
\(539\) | −35.2312 | −1.51752 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.1975 | 0.825366 | 0.412683 | − | 0.910875i | \(-0.364592\pi\) | ||||
0.412683 | + | 0.910875i | \(0.364592\pi\) | |||||||
\(542\) | −2.55845 | −0.109895 | ||||||||
\(543\) | 18.5223 | 0.794869 | ||||||||
\(544\) | −13.5641 | −0.581558 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 48.2579 | 2.06525 | ||||||||
\(547\) | 5.94146 | 0.254038 | 0.127019 | − | 0.991900i | \(-0.459459\pi\) | ||||
0.127019 | + | 0.991900i | \(0.459459\pi\) | |||||||
\(548\) | 16.6888 | 0.712911 | ||||||||
\(549\) | 55.3874 | 2.36387 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 53.3754 | 2.27387 | ||||||||
\(552\) | −46.7438 | −1.98955 | ||||||||
\(553\) | 50.0709 | 2.12923 | ||||||||
\(554\) | −37.0223 | −1.57293 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.7854 | 0.542223 | ||||||||
\(557\) | −4.79293 | −0.203083 | −0.101542 | − | 0.994831i | \(-0.532377\pi\) | ||||
−0.101542 | + | 0.994831i | \(0.532377\pi\) | |||||||
\(558\) | 57.4602 | 2.43248 | ||||||||
\(559\) | −5.27122 | −0.222949 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −32.9218 | −1.38996 | ||||||||
\(562\) | −20.9015 | −0.881675 | ||||||||
\(563\) | 28.7817 | 1.21300 | 0.606502 | − | 0.795082i | \(-0.292572\pi\) | ||||
0.606502 | + | 0.795082i | \(0.292572\pi\) | |||||||
\(564\) | −29.2558 | −1.23189 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −14.3388 | −0.602704 | ||||||||
\(567\) | 140.547 | 5.90241 | ||||||||
\(568\) | −14.0686 | −0.590305 | ||||||||
\(569\) | −17.0870 | −0.716325 | −0.358162 | − | 0.933659i | \(-0.616597\pi\) | ||||
−0.358162 | + | 0.933659i | \(0.616597\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.4735 | 0.940487 | 0.470244 | − | 0.882537i | \(-0.344166\pi\) | ||||
0.470244 | + | 0.882537i | \(0.344166\pi\) | |||||||
\(572\) | −6.33550 | −0.264901 | ||||||||
\(573\) | −20.4247 | −0.853253 | ||||||||
\(574\) | −46.8060 | −1.95365 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 15.4211 | 0.642544 | ||||||||
\(577\) | 13.6344 | 0.567606 | 0.283803 | − | 0.958883i | \(-0.408404\pi\) | ||||
0.283803 | + | 0.958883i | \(0.408404\pi\) | |||||||
\(578\) | 15.1114 | 0.628550 | ||||||||
\(579\) | −7.55440 | −0.313950 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 47.8980 | 1.98714 | ||||||||
\(582\) | −95.9661 | −3.97792 | ||||||||
\(583\) | −5.64799 | −0.233916 | ||||||||
\(584\) | −24.6212 | −1.01883 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −36.7788 | −1.51932 | ||||||||
\(587\) | −11.4588 | −0.472953 | −0.236477 | − | 0.971637i | \(-0.575993\pi\) | ||||
−0.236477 | + | 0.971637i | \(0.575993\pi\) | |||||||
\(588\) | −30.8497 | −1.27222 | ||||||||
\(589\) | 23.2900 | 0.959647 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −41.1643 | −1.69327 | ||||||||
\(592\) | 26.2400 | 1.07846 | ||||||||
\(593\) | −18.5153 | −0.760332 | −0.380166 | − | 0.924918i | \(-0.624133\pi\) | ||||
−0.380166 | + | 0.924918i | \(0.624133\pi\) | |||||||
\(594\) | −102.617 | −4.21043 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17.3371 | 0.710155 | ||||||||
\(597\) | 26.3081 | 1.07672 | ||||||||
\(598\) | −25.8981 | −1.05905 | ||||||||
\(599\) | −8.73124 | −0.356749 | −0.178374 | − | 0.983963i | \(-0.557084\pi\) | ||||
−0.178374 | + | 0.983963i | \(0.557084\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.8705 | 1.58556 | 0.792781 | − | 0.609507i | \(-0.208633\pi\) | ||||
0.792781 | + | 0.609507i | \(0.208633\pi\) | |||||||
\(602\) | 18.2764 | 0.744890 | ||||||||
\(603\) | −60.2846 | −2.45498 | ||||||||
\(604\) | −0.199282 | −0.00810867 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 37.6481 | 1.52935 | ||||||||
\(607\) | 0.383862 | 0.0155805 | 0.00779024 | − | 0.999970i | \(-0.497520\pi\) | ||||
0.00779024 | + | 0.999970i | \(0.497520\pi\) | |||||||
\(608\) | −26.9909 | −1.09463 | ||||||||
\(609\) | 130.753 | 5.29839 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.7549 | 0.799197 | ||||||||
\(612\) | −21.1177 | −0.853631 | ||||||||
\(613\) | 14.9460 | 0.603663 | 0.301831 | − | 0.953361i | \(-0.402402\pi\) | ||||
0.301831 | + | 0.953361i | \(0.402402\pi\) | |||||||
\(614\) | −36.1180 | −1.45761 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −26.7719 | −1.07867 | ||||||||
\(617\) | 1.94032 | 0.0781145 | 0.0390572 | − | 0.999237i | \(-0.487565\pi\) | ||||
0.0390572 | + | 0.999237i | \(0.487565\pi\) | |||||||
\(618\) | 52.2342 | 2.10117 | ||||||||
\(619\) | 33.5002 | 1.34649 | 0.673244 | − | 0.739421i | \(-0.264901\pi\) | ||||
0.673244 | + | 0.739421i | \(0.264901\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −130.322 | −5.22964 | ||||||||
\(622\) | 4.20414 | 0.168571 | ||||||||
\(623\) | −76.5694 | −3.06769 | ||||||||
\(624\) | 34.0714 | 1.36395 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −50.4445 | −2.01617 | ||||||||
\(627\) | −65.5102 | −2.61623 | ||||||||
\(628\) | −14.9482 | −0.596496 | ||||||||
\(629\) | 14.9914 | 0.597746 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.2379 | 0.447372 | 0.223686 | − | 0.974661i | \(-0.428191\pi\) | ||||
0.223686 | + | 0.974661i | \(0.428191\pi\) | |||||||
\(632\) | 22.5803 | 0.898195 | ||||||||
\(633\) | 5.92233 | 0.235391 | ||||||||
\(634\) | −0.841060 | −0.0334027 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −4.94558 | −0.196105 | ||||||||
\(637\) | 20.8311 | 0.825360 | ||||||||
\(638\) | −55.2528 | −2.18748 | ||||||||
\(639\) | −61.7776 | −2.44389 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.9440 | 0.827240 | 0.413620 | − | 0.910450i | \(-0.364264\pi\) | ||||
0.413620 | + | 0.910450i | \(0.364264\pi\) | |||||||
\(642\) | −51.4305 | −2.02980 | ||||||||
\(643\) | −35.2924 | −1.39180 | −0.695898 | − | 0.718141i | \(-0.744993\pi\) | ||||
−0.695898 | + | 0.718141i | \(0.744993\pi\) | |||||||
\(644\) | 27.8970 | 1.09930 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −27.5510 | −1.08398 | ||||||||
\(647\) | −27.2642 | −1.07186 | −0.535932 | − | 0.844261i | \(-0.680040\pi\) | ||||
−0.535932 | + | 0.844261i | \(0.680040\pi\) | |||||||
\(648\) | 63.3818 | 2.48987 | ||||||||
\(649\) | −1.27218 | −0.0499374 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 57.0532 | 2.23609 | ||||||||
\(652\) | 8.81443 | 0.345200 | ||||||||
\(653\) | −13.5779 | −0.531345 | −0.265673 | − | 0.964063i | \(-0.585594\pi\) | ||||
−0.265673 | + | 0.964063i | \(0.585594\pi\) | |||||||
\(654\) | −53.9984 | −2.11150 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −33.0464 | −1.29024 | ||||||||
\(657\) | −108.116 | −4.21801 | ||||||||
\(658\) | −68.4941 | −2.67018 | ||||||||
\(659\) | 9.26564 | 0.360938 | 0.180469 | − | 0.983581i | \(-0.442238\pi\) | ||||
0.180469 | + | 0.983581i | \(0.442238\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.59898 | −0.295566 | −0.147783 | − | 0.989020i | \(-0.547214\pi\) | ||||
−0.147783 | + | 0.989020i | \(0.547214\pi\) | |||||||
\(662\) | 7.47390 | 0.290481 | ||||||||
\(663\) | 19.4657 | 0.755984 | ||||||||
\(664\) | 21.6004 | 0.838257 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 73.5979 | 2.85186 | ||||||||
\(667\) | −70.1700 | −2.71699 | ||||||||
\(668\) | 18.2309 | 0.705376 | ||||||||
\(669\) | 36.7478 | 1.42075 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −23.2394 | −0.897149 | ||||||||
\(672\) | −66.1194 | −2.55061 | ||||||||
\(673\) | −26.4922 | −1.02120 | −0.510599 | − | 0.859819i | \(-0.670576\pi\) | ||||
−0.510599 | + | 0.859819i | \(0.670576\pi\) | |||||||
\(674\) | 30.7515 | 1.18450 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.97226 | −0.306625 | ||||||||
\(677\) | −30.7992 | −1.18371 | −0.591855 | − | 0.806044i | \(-0.701604\pi\) | ||||
−0.591855 | + | 0.806044i | \(0.701604\pi\) | |||||||
\(678\) | 24.6374 | 0.946194 | ||||||||
\(679\) | −69.8023 | −2.67877 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.3122 | −0.586763 | ||||||||
\(682\) | −24.1092 | −0.923187 | ||||||||
\(683\) | 36.6918 | 1.40397 | 0.701987 | − | 0.712190i | \(-0.252296\pi\) | ||||
0.701987 | + | 0.712190i | \(0.252296\pi\) | |||||||
\(684\) | −42.0215 | −1.60673 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −22.7491 | −0.868563 | ||||||||
\(687\) | 68.1726 | 2.60095 | ||||||||
\(688\) | 12.9036 | 0.491947 | ||||||||
\(689\) | 3.33949 | 0.127224 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.0646 | −1.29588 | −0.647939 | − | 0.761692i | \(-0.724369\pi\) | ||||
−0.647939 | + | 0.761692i | \(0.724369\pi\) | |||||||
\(692\) | 8.81159 | 0.334966 | ||||||||
\(693\) | −117.560 | −4.46573 | ||||||||
\(694\) | −27.0110 | −1.02532 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 58.9652 | 2.23507 | ||||||||
\(697\) | −18.8800 | −0.715132 | ||||||||
\(698\) | −15.6518 | −0.592431 | ||||||||
\(699\) | −26.7717 | −1.01260 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.5893 | 1.60858 | 0.804289 | − | 0.594239i | \(-0.202547\pi\) | ||||
0.804289 | + | 0.594239i | \(0.202547\pi\) | |||||||
\(702\) | 60.6744 | 2.29001 | ||||||||
\(703\) | 29.8310 | 1.12510 | ||||||||
\(704\) | −6.47037 | −0.243861 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 56.5744 | 2.12920 | ||||||||
\(707\) | 27.3839 | 1.02988 | ||||||||
\(708\) | −1.11397 | −0.0418654 | ||||||||
\(709\) | 47.5412 | 1.78545 | 0.892724 | − | 0.450605i | \(-0.148792\pi\) | ||||
0.892724 | + | 0.450605i | \(0.148792\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 99.1540 | 3.71857 | ||||||||
\(712\) | −34.5302 | −1.29407 | ||||||||
\(713\) | −30.6182 | −1.14666 | ||||||||
\(714\) | −67.4913 | −2.52580 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.53391 | −0.356299 | ||||||||
\(717\) | 9.23942 | 0.345053 | ||||||||
\(718\) | −15.1829 | −0.566620 | ||||||||
\(719\) | −27.3690 | −1.02069 | −0.510345 | − | 0.859970i | \(-0.670482\pi\) | ||||
−0.510345 | + | 0.859970i | \(0.670482\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 37.9933 | 1.41494 | ||||||||
\(722\) | −22.4593 | −0.835847 | ||||||||
\(723\) | −3.34921 | −0.124558 | ||||||||
\(724\) | −4.98509 | −0.185269 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.06080 | 0.187824 | ||||||||
\(727\) | −38.0410 | −1.41086 | −0.705431 | − | 0.708778i | \(-0.749247\pi\) | ||||
−0.705431 | + | 0.708778i | \(0.749247\pi\) | |||||||
\(728\) | 15.8294 | 0.586676 | ||||||||
\(729\) | 102.754 | 3.80571 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.37210 | 0.272667 | ||||||||
\(732\) | −20.3493 | −0.752131 | ||||||||
\(733\) | 35.5280 | 1.31226 | 0.656128 | − | 0.754649i | \(-0.272193\pi\) | ||||
0.656128 | + | 0.754649i | \(0.272193\pi\) | |||||||
\(734\) | −11.5136 | −0.424976 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 35.4836 | 1.30794 | ||||||||
\(737\) | 25.2942 | 0.931725 | ||||||||
\(738\) | −92.6886 | −3.41191 | ||||||||
\(739\) | −35.3767 | −1.30135 | −0.650676 | − | 0.759356i | \(-0.725514\pi\) | ||||
−0.650676 | + | 0.759356i | \(0.725514\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 38.7342 | 1.42294 | ||||||||
\(742\) | −11.5787 | −0.425066 | ||||||||
\(743\) | 31.3223 | 1.14910 | 0.574551 | − | 0.818469i | \(-0.305177\pi\) | ||||
0.574551 | + | 0.818469i | \(0.305177\pi\) | |||||||
\(744\) | 25.7291 | 0.943273 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.91930 | 0.106883 | ||||||||
\(747\) | 94.8510 | 3.47042 | ||||||||
\(748\) | 8.86056 | 0.323974 | ||||||||
\(749\) | −37.4088 | −1.36689 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.82636 | 0.249098 | 0.124549 | − | 0.992213i | \(-0.460252\pi\) | ||||
0.124549 | + | 0.992213i | \(0.460252\pi\) | |||||||
\(752\) | −48.3588 | −1.76346 | ||||||||
\(753\) | 34.4320 | 1.25477 | ||||||||
\(754\) | 32.6693 | 1.18975 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −65.3576 | −2.37703 | ||||||||
\(757\) | −28.2519 | −1.02683 | −0.513415 | − | 0.858140i | \(-0.671620\pi\) | ||||
−0.513415 | + | 0.858140i | \(0.671620\pi\) | |||||||
\(758\) | 1.28801 | 0.0467827 | ||||||||
\(759\) | 86.1231 | 3.12607 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.4825 | −1.21374 | −0.606870 | − | 0.794801i | \(-0.707575\pi\) | ||||
−0.606870 | + | 0.794801i | \(0.707575\pi\) | |||||||
\(762\) | 38.7666 | 1.40437 | ||||||||
\(763\) | −39.2765 | −1.42191 | ||||||||
\(764\) | 5.49709 | 0.198878 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −24.8055 | −0.896260 | ||||||||
\(767\) | 0.752201 | 0.0271604 | ||||||||
\(768\) | −59.9488 | −2.16321 | ||||||||
\(769\) | 34.2877 | 1.23645 | 0.618223 | − | 0.786003i | \(-0.287853\pi\) | ||||
0.618223 | + | 0.786003i | \(0.287853\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.2862 | 0.874645 | ||||||||
\(772\) | 2.03319 | 0.0731760 | ||||||||
\(773\) | 21.5846 | 0.776343 | 0.388171 | − | 0.921587i | \(-0.373107\pi\) | ||||
0.388171 | + | 0.921587i | \(0.373107\pi\) | |||||||
\(774\) | 36.1922 | 1.30090 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −31.4785 | −1.13001 | ||||||||
\(777\) | 73.0767 | 2.62161 | ||||||||
\(778\) | −23.9979 | −0.860367 | ||||||||
\(779\) | −37.5689 | −1.34604 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.9207 | 0.927515 | ||||||||
\(782\) | 36.2199 | 1.29522 | ||||||||
\(783\) | 164.396 | 5.87502 | ||||||||
\(784\) | −50.9934 | −1.82119 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 67.3847 | 2.40353 | ||||||||
\(787\) | 45.4179 | 1.61897 | 0.809486 | − | 0.587139i | \(-0.199746\pi\) | ||||
0.809486 | + | 0.587139i | \(0.199746\pi\) | |||||||
\(788\) | 11.0789 | 0.394671 | ||||||||
\(789\) | 24.0779 | 0.857198 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.9204 | 0.637175 | ||||||||
\(792\) | −53.0155 | −1.88382 | ||||||||
\(793\) | 13.7408 | 0.487949 | ||||||||
\(794\) | 29.2393 | 1.03766 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.08056 | −0.250964 | ||||||||
\(797\) | −27.1274 | −0.960901 | −0.480451 | − | 0.877022i | \(-0.659527\pi\) | ||||
−0.480451 | + | 0.877022i | \(0.659527\pi\) | |||||||
\(798\) | −134.299 | −4.75414 | ||||||||
\(799\) | −27.6283 | −0.977419 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −151.628 | −5.35752 | ||||||||
\(802\) | −1.90793 | −0.0673714 | ||||||||
\(803\) | 45.3633 | 1.60084 | ||||||||
\(804\) | 22.1485 | 0.781118 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 14.2550 | 0.502112 | ||||||||
\(807\) | 51.7265 | 1.82086 | ||||||||
\(808\) | 12.3492 | 0.434444 | ||||||||
\(809\) | 43.6473 | 1.53456 | 0.767278 | − | 0.641314i | \(-0.221611\pi\) | ||||
0.767278 | + | 0.641314i | \(0.221611\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.8136 | −0.449946 | −0.224973 | − | 0.974365i | \(-0.572229\pi\) | ||||
−0.224973 | + | 0.974365i | \(0.572229\pi\) | |||||||
\(812\) | −35.1909 | −1.23496 | ||||||||
\(813\) | −5.03055 | −0.176429 | ||||||||
\(814\) | −30.8802 | −1.08235 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −47.6508 | −1.66811 | ||||||||
\(817\) | 14.6695 | 0.513223 | ||||||||
\(818\) | 54.3311 | 1.89964 | ||||||||
\(819\) | 69.5096 | 2.42886 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.684233 | 0.0238799 | 0.0119399 | − | 0.999929i | \(-0.496199\pi\) | ||||
0.0119399 | + | 0.999929i | \(0.496199\pi\) | |||||||
\(822\) | 105.621 | 3.68397 | ||||||||
\(823\) | 1.37574 | 0.0479553 | 0.0239777 | − | 0.999712i | \(-0.492367\pi\) | ||||
0.0239777 | + | 0.999712i | \(0.492367\pi\) | |||||||
\(824\) | 17.1337 | 0.596880 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.60803 | −0.0907450 | ||||||||
\(827\) | −8.09126 | −0.281361 | −0.140680 | − | 0.990055i | \(-0.544929\pi\) | ||||
−0.140680 | + | 0.990055i | \(0.544929\pi\) | |||||||
\(828\) | 55.2436 | 1.91985 | ||||||||
\(829\) | −25.7872 | −0.895628 | −0.447814 | − | 0.894127i | \(-0.647797\pi\) | ||||
−0.447814 | + | 0.894127i | \(0.647797\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −72.7949 | −2.52523 | ||||||||
\(832\) | 3.82574 | 0.132634 | ||||||||
\(833\) | −29.1335 | −1.00942 | ||||||||
\(834\) | 80.9174 | 2.80194 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 17.6314 | 0.609794 | ||||||||
\(837\) | 71.7328 | 2.47945 | ||||||||
\(838\) | 38.2307 | 1.32066 | ||||||||
\(839\) | 36.3743 | 1.25578 | 0.627890 | − | 0.778302i | \(-0.283919\pi\) | ||||
0.627890 | + | 0.778302i | \(0.283919\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 59.5165 | 2.05229 | ||||||||
\(842\) | −7.49219 | −0.258198 | ||||||||
\(843\) | −41.0974 | −1.41547 | ||||||||
\(844\) | −1.59393 | −0.0548654 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −135.637 | −4.66329 | ||||||||
\(847\) | 3.68105 | 0.126482 | ||||||||
\(848\) | −8.17487 | −0.280726 | ||||||||
\(849\) | −28.1936 | −0.967601 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −39.2173 | −1.34435 | ||||||||
\(852\) | 22.6971 | 0.777589 | ||||||||
\(853\) | 51.6439 | 1.76825 | 0.884127 | − | 0.467248i | \(-0.154754\pi\) | ||||
0.884127 | + | 0.467248i | \(0.154754\pi\) | |||||||
\(854\) | −47.6420 | −1.63028 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.8701 | −0.576607 | ||||||||
\(857\) | −18.4802 | −0.631271 | −0.315636 | − | 0.948880i | \(-0.602218\pi\) | ||||
−0.315636 | + | 0.948880i | \(0.602218\pi\) | |||||||
\(858\) | −40.0966 | −1.36888 | ||||||||
\(859\) | −4.69833 | −0.160305 | −0.0801525 | − | 0.996783i | \(-0.525541\pi\) | ||||
−0.0801525 | + | 0.996783i | \(0.525541\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −92.0321 | −3.13645 | ||||||||
\(862\) | −56.3418 | −1.91901 | ||||||||
\(863\) | 32.2110 | 1.09647 | 0.548237 | − | 0.836323i | \(-0.315299\pi\) | ||||
0.548237 | + | 0.836323i | \(0.315299\pi\) | |||||||
\(864\) | −83.1317 | −2.82820 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −39.6138 | −1.34613 | ||||||||
\(867\) | 29.7127 | 1.00910 | ||||||||
\(868\) | −15.3553 | −0.521192 | ||||||||
\(869\) | −41.6031 | −1.41129 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.9557 | −0.506755 | ||||||||
\(872\) | −17.7124 | −0.599817 | ||||||||
\(873\) | −138.228 | −4.67829 | ||||||||
\(874\) | 72.0730 | 2.43791 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 39.7217 | 1.34207 | ||||||||
\(877\) | 10.4199 | 0.351855 | 0.175928 | − | 0.984403i | \(-0.443708\pi\) | ||||
0.175928 | + | 0.984403i | \(0.443708\pi\) | |||||||
\(878\) | −49.7183 | −1.67791 | ||||||||
\(879\) | −72.3162 | −2.43916 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.1951 | −0.747770 | −0.373885 | − | 0.927475i | \(-0.621975\pi\) | ||||
−0.373885 | + | 0.927475i | \(0.621975\pi\) | |||||||
\(882\) | −143.027 | −4.81595 | ||||||||
\(883\) | −4.48659 | −0.150986 | −0.0754930 | − | 0.997146i | \(-0.524053\pi\) | ||||
−0.0754930 | + | 0.997146i | \(0.524053\pi\) | |||||||
\(884\) | −5.23898 | −0.176206 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −57.8327 | −1.94293 | ||||||||
\(887\) | 28.1286 | 0.944465 | 0.472232 | − | 0.881474i | \(-0.343448\pi\) | ||||
0.472232 | + | 0.881474i | \(0.343448\pi\) | |||||||
\(888\) | 32.9551 | 1.10590 | ||||||||
\(889\) | 28.1975 | 0.945714 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −116.778 | −3.91220 | ||||||||
\(892\) | −9.89028 | −0.331151 | ||||||||
\(893\) | −54.9768 | −1.83973 | ||||||||
\(894\) | 109.724 | 3.66973 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −52.7482 | −1.76219 | ||||||||
\(897\) | −50.9220 | −1.70023 | ||||||||
\(898\) | 46.8751 | 1.56424 | ||||||||
\(899\) | 38.6235 | 1.28817 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.67046 | −0.155596 | ||||||||
\(902\) | 38.8903 | 1.29491 | ||||||||
\(903\) | 35.9359 | 1.19587 | ||||||||
\(904\) | 8.08148 | 0.268786 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.26123 | −0.0419016 | ||||||||
\(907\) | 24.5132 | 0.813948 | 0.406974 | − | 0.913440i | \(-0.366584\pi\) | ||||
0.406974 | + | 0.913440i | \(0.366584\pi\) | |||||||
\(908\) | 4.12111 | 0.136764 | ||||||||
\(909\) | 54.2276 | 1.79862 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.3648 | 1.56926 | 0.784632 | − | 0.619961i | \(-0.212852\pi\) | ||||
0.784632 | + | 0.619961i | \(0.212852\pi\) | |||||||
\(912\) | −94.8191 | −3.13977 | ||||||||
\(913\) | −39.7976 | −1.31711 | ||||||||
\(914\) | 66.5813 | 2.20231 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −18.3479 | −0.606233 | ||||||||
\(917\) | 49.0133 | 1.61856 | ||||||||
\(918\) | −84.8566 | −2.80069 | ||||||||
\(919\) | 44.5247 | 1.46873 | 0.734367 | − | 0.678753i | \(-0.237479\pi\) | ||||
0.734367 | + | 0.678753i | \(0.237479\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −71.0169 | −2.34009 | ||||||||
\(922\) | −55.1968 | −1.81781 | ||||||||
\(923\) | −15.3261 | −0.504465 | ||||||||
\(924\) | 43.1914 | 1.42089 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 8.33725 | 0.273979 | ||||||||
\(927\) | 75.2371 | 2.47111 | ||||||||
\(928\) | −44.7611 | −1.46935 | ||||||||
\(929\) | 19.3204 | 0.633882 | 0.316941 | − | 0.948445i | \(-0.397344\pi\) | ||||
0.316941 | + | 0.948445i | \(0.397344\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −57.9720 | −1.89996 | ||||||||
\(932\) | 7.20532 | 0.236018 | ||||||||
\(933\) | 8.26637 | 0.270629 | ||||||||
\(934\) | 47.8207 | 1.56474 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 31.3465 | 1.02459 | ||||||||
\(937\) | −14.0035 | −0.457474 | −0.228737 | − | 0.973488i | \(-0.573460\pi\) | ||||
−0.228737 | + | 0.973488i | \(0.573460\pi\) | |||||||
\(938\) | 51.8544 | 1.69311 | ||||||||
\(939\) | −99.1863 | −3.23682 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.4573 | 0.699487 | 0.349744 | − | 0.936845i | \(-0.386269\pi\) | ||||
0.349744 | + | 0.936845i | \(0.386269\pi\) | |||||||
\(942\) | −94.6050 | −3.08240 | ||||||||
\(943\) | 49.3900 | 1.60836 | ||||||||
\(944\) | −1.84135 | −0.0599307 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −15.1855 | −0.493724 | ||||||||
\(947\) | −19.1248 | −0.621473 | −0.310737 | − | 0.950496i | \(-0.600576\pi\) | ||||
−0.310737 | + | 0.950496i | \(0.600576\pi\) | |||||||
\(948\) | −36.4291 | −1.18316 | ||||||||
\(949\) | −26.8220 | −0.870678 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.65373 | −0.0536259 | ||||||||
\(952\) | −22.1383 | −0.717506 | ||||||||
\(953\) | −0.297849 | −0.00964829 | −0.00482414 | − | 0.999988i | \(-0.501536\pi\) | ||||
−0.00482414 | + | 0.999988i | \(0.501536\pi\) | |||||||
\(954\) | −22.9289 | −0.742350 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.48669 | −0.0804254 | ||||||||
\(957\) | −108.641 | −3.51185 | ||||||||
\(958\) | 34.6463 | 1.11937 | ||||||||
\(959\) | 76.8253 | 2.48082 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.1469 | −0.456351 | ||||||||
\(962\) | 18.2586 | 0.588679 | ||||||||
\(963\) | −74.0795 | −2.38718 | ||||||||
\(964\) | 0.901404 | 0.0290323 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 176.557 | 5.68062 | ||||||||
\(967\) | 28.6330 | 0.920775 | 0.460387 | − | 0.887718i | \(-0.347711\pi\) | ||||
0.460387 | + | 0.887718i | \(0.347711\pi\) | |||||||
\(968\) | 1.66003 | 0.0533553 | ||||||||
\(969\) | −54.1720 | −1.74025 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48.1006 | 1.54362 | 0.771811 | − | 0.635852i | \(-0.219351\pi\) | ||||
0.771811 | + | 0.635852i | \(0.219351\pi\) | |||||||
\(972\) | −55.0029 | −1.76422 | ||||||||
\(973\) | 58.8565 | 1.88685 | ||||||||
\(974\) | −15.3598 | −0.492159 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −33.6366 | −1.07668 | ||||||||
\(977\) | 50.2504 | 1.60765 | 0.803827 | − | 0.594864i | \(-0.202794\pi\) | ||||
0.803827 | + | 0.594864i | \(0.202794\pi\) | |||||||
\(978\) | 55.7854 | 1.78382 | ||||||||
\(979\) | 63.6201 | 2.03331 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −77.7782 | −2.48327 | ||||||||
\(982\) | 41.8668 | 1.33602 | ||||||||
\(983\) | 20.1224 | 0.641804 | 0.320902 | − | 0.947112i | \(-0.396014\pi\) | ||||
0.320902 | + | 0.947112i | \(0.396014\pi\) | |||||||
\(984\) | −41.5034 | −1.32308 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −45.6899 | −1.45506 | ||||||||
\(987\) | −134.676 | −4.28679 | ||||||||
\(988\) | −10.4249 | −0.331660 | ||||||||
\(989\) | −19.2853 | −0.613238 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.6831 | 0.371126 | 0.185563 | − | 0.982632i | \(-0.440589\pi\) | ||||
0.185563 | + | 0.982632i | \(0.440589\pi\) | |||||||
\(992\) | −19.5312 | −0.620116 | ||||||||
\(993\) | 14.6955 | 0.466348 | ||||||||
\(994\) | 53.1387 | 1.68546 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −34.8482 | −1.10421 | ||||||||
\(997\) | 11.1289 | 0.352457 | 0.176229 | − | 0.984349i | \(-0.443610\pi\) | ||||
0.176229 | + | 0.984349i | \(0.443610\pi\) | |||||||
\(998\) | −4.62635 | −0.146445 | ||||||||
\(999\) | 91.8791 | 2.90693 |
(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 | 6025.2.a.n.1.9 | yes | 40 | |
5.4 | even | 2 | 6025.2.a.m.1.32 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6025.2.a.m.1.32 | ✓ | 40 | 5.4 | even | 2 | ||
6025.2.a.n.1.9 | yes | 40 | 1.1 | even | 1 | trivial |