Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(1,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, 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("1183.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.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: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 15 x^{10} + 46 x^{9} + 80 x^{8} - 246 x^{7} - 199 x^{6} + 562 x^{5} + 262 x^{4} - 542 x^{3} - 157 x^{2} + 183 x + 29 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.06743\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.06743 | −1.46189 | −0.730945 | − | 0.682436i | \(-0.760921\pi\) | ||||
−0.730945 | + | 0.682436i | \(0.760921\pi\) | |||||||
\(3\) | 2.11889 | 1.22334 | 0.611671 | − | 0.791112i | \(-0.290497\pi\) | ||||
0.611671 | + | 0.791112i | \(0.290497\pi\) | |||||||
\(4\) | 2.27425 | 1.13713 | ||||||||
\(5\) | −2.43928 | −1.09088 | −0.545439 | − | 0.838150i | \(-0.683637\pi\) | ||||
−0.545439 | + | 0.838150i | \(0.683637\pi\) | |||||||
\(6\) | −4.38065 | −1.78839 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −0.566992 | −0.200462 | ||||||||
\(9\) | 1.48970 | 0.496568 | ||||||||
\(10\) | 5.04303 | 1.59474 | ||||||||
\(11\) | 3.64779 | 1.09985 | 0.549925 | − | 0.835214i | \(-0.314656\pi\) | ||||
0.549925 | + | 0.835214i | \(0.314656\pi\) | |||||||
\(12\) | 4.81889 | 1.39109 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.06743 | 0.552543 | ||||||||
\(15\) | −5.16857 | −1.33452 | ||||||||
\(16\) | −3.37629 | −0.844072 | ||||||||
\(17\) | 7.04993 | 1.70986 | 0.854929 | − | 0.518745i | \(-0.173600\pi\) | ||||
0.854929 | + | 0.518745i | \(0.173600\pi\) | |||||||
\(18\) | −3.07985 | −0.725928 | ||||||||
\(19\) | 2.76410 | 0.634127 | 0.317063 | − | 0.948404i | \(-0.397303\pi\) | ||||
0.317063 | + | 0.948404i | \(0.397303\pi\) | |||||||
\(20\) | −5.54753 | −1.24046 | ||||||||
\(21\) | −2.11889 | −0.462380 | ||||||||
\(22\) | −7.54154 | −1.60786 | ||||||||
\(23\) | −7.75601 | −1.61724 | −0.808620 | − | 0.588332i | \(-0.799785\pi\) | ||||
−0.808620 | + | 0.588332i | \(0.799785\pi\) | |||||||
\(24\) | −1.20139 | −0.245234 | ||||||||
\(25\) | 0.950076 | 0.190015 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.20015 | −0.615870 | ||||||||
\(28\) | −2.27425 | −0.429793 | ||||||||
\(29\) | 2.31600 | 0.430071 | 0.215035 | − | 0.976606i | \(-0.431013\pi\) | ||||
0.215035 | + | 0.976606i | \(0.431013\pi\) | |||||||
\(30\) | 10.6856 | 1.95092 | ||||||||
\(31\) | −7.00738 | −1.25856 | −0.629281 | − | 0.777178i | \(-0.716651\pi\) | ||||
−0.629281 | + | 0.777178i | \(0.716651\pi\) | |||||||
\(32\) | 8.11421 | 1.43440 | ||||||||
\(33\) | 7.72927 | 1.34549 | ||||||||
\(34\) | −14.5752 | −2.49963 | ||||||||
\(35\) | 2.43928 | 0.412313 | ||||||||
\(36\) | 3.38796 | 0.564660 | ||||||||
\(37\) | 7.28412 | 1.19750 | 0.598751 | − | 0.800935i | \(-0.295664\pi\) | ||||
0.598751 | + | 0.800935i | \(0.295664\pi\) | |||||||
\(38\) | −5.71456 | −0.927024 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.38305 | 0.218679 | ||||||||
\(41\) | 3.49162 | 0.545300 | 0.272650 | − | 0.962113i | \(-0.412100\pi\) | ||||
0.272650 | + | 0.962113i | \(0.412100\pi\) | |||||||
\(42\) | 4.38065 | 0.675949 | ||||||||
\(43\) | 3.44630 | 0.525555 | 0.262778 | − | 0.964856i | \(-0.415361\pi\) | ||||
0.262778 | + | 0.964856i | \(0.415361\pi\) | |||||||
\(44\) | 8.29599 | 1.25067 | ||||||||
\(45\) | −3.63380 | −0.541695 | ||||||||
\(46\) | 16.0350 | 2.36423 | ||||||||
\(47\) | −2.66883 | −0.389289 | −0.194645 | − | 0.980874i | \(-0.562355\pi\) | ||||
−0.194645 | + | 0.980874i | \(0.562355\pi\) | |||||||
\(48\) | −7.15399 | −1.03259 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.96421 | −0.277782 | ||||||||
\(51\) | 14.9380 | 2.09174 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.3378 | 1.83208 | 0.916041 | − | 0.401086i | \(-0.131367\pi\) | ||||
0.916041 | + | 0.401086i | \(0.131367\pi\) | |||||||
\(54\) | 6.61608 | 0.900335 | ||||||||
\(55\) | −8.89797 | −1.19980 | ||||||||
\(56\) | 0.566992 | 0.0757675 | ||||||||
\(57\) | 5.85682 | 0.775755 | ||||||||
\(58\) | −4.78816 | −0.628716 | ||||||||
\(59\) | 8.24978 | 1.07403 | 0.537015 | − | 0.843573i | \(-0.319552\pi\) | ||||
0.537015 | + | 0.843573i | \(0.319552\pi\) | |||||||
\(60\) | −11.7546 | −1.51751 | ||||||||
\(61\) | 13.9465 | 1.78566 | 0.892831 | − | 0.450392i | \(-0.148716\pi\) | ||||
0.892831 | + | 0.450392i | \(0.148716\pi\) | |||||||
\(62\) | 14.4872 | 1.83988 | ||||||||
\(63\) | −1.48970 | −0.187685 | ||||||||
\(64\) | −10.0229 | −1.25287 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −15.9797 | −1.96697 | ||||||||
\(67\) | 3.20893 | 0.392033 | 0.196017 | − | 0.980601i | \(-0.437199\pi\) | ||||
0.196017 | + | 0.980601i | \(0.437199\pi\) | |||||||
\(68\) | 16.0333 | 1.94432 | ||||||||
\(69\) | −16.4341 | −1.97844 | ||||||||
\(70\) | −5.04303 | −0.602757 | ||||||||
\(71\) | 9.74080 | 1.15602 | 0.578010 | − | 0.816029i | \(-0.303829\pi\) | ||||
0.578010 | + | 0.816029i | \(0.303829\pi\) | |||||||
\(72\) | −0.844650 | −0.0995429 | ||||||||
\(73\) | 3.75697 | 0.439720 | 0.219860 | − | 0.975531i | \(-0.429440\pi\) | ||||
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(74\) | −15.0594 | −1.75062 | ||||||||
\(75\) | 2.01311 | 0.232454 | ||||||||
\(76\) | 6.28624 | 0.721082 | ||||||||
\(77\) | −3.64779 | −0.415704 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.8682 | −1.44778 | −0.723890 | − | 0.689915i | \(-0.757648\pi\) | ||||
−0.723890 | + | 0.689915i | \(0.757648\pi\) | |||||||
\(80\) | 8.23570 | 0.920779 | ||||||||
\(81\) | −11.2499 | −1.24999 | ||||||||
\(82\) | −7.21867 | −0.797168 | ||||||||
\(83\) | 5.42451 | 0.595417 | 0.297709 | − | 0.954657i | \(-0.403778\pi\) | ||||
0.297709 | + | 0.954657i | \(0.403778\pi\) | |||||||
\(84\) | −4.81889 | −0.525784 | ||||||||
\(85\) | −17.1967 | −1.86525 | ||||||||
\(86\) | −7.12496 | −0.768304 | ||||||||
\(87\) | 4.90736 | 0.526124 | ||||||||
\(88\) | −2.06827 | −0.220478 | ||||||||
\(89\) | 0.335808 | 0.0355955 | 0.0177978 | − | 0.999842i | \(-0.494334\pi\) | ||||
0.0177978 | + | 0.999842i | \(0.494334\pi\) | |||||||
\(90\) | 7.51262 | 0.791899 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −17.6391 | −1.83900 | ||||||||
\(93\) | −14.8479 | −1.53965 | ||||||||
\(94\) | 5.51762 | 0.569099 | ||||||||
\(95\) | −6.74240 | −0.691755 | ||||||||
\(96\) | 17.1931 | 1.75477 | ||||||||
\(97\) | −10.9424 | −1.11103 | −0.555517 | − | 0.831505i | \(-0.687480\pi\) | ||||
−0.555517 | + | 0.831505i | \(0.687480\pi\) | |||||||
\(98\) | −2.06743 | −0.208842 | ||||||||
\(99\) | 5.43413 | 0.546150 | ||||||||
\(100\) | 2.16071 | 0.216071 | ||||||||
\(101\) | 8.92269 | 0.887841 | 0.443920 | − | 0.896066i | \(-0.353587\pi\) | ||||
0.443920 | + | 0.896066i | \(0.353587\pi\) | |||||||
\(102\) | −30.8833 | −3.05790 | ||||||||
\(103\) | −2.66966 | −0.263049 | −0.131525 | − | 0.991313i | \(-0.541987\pi\) | ||||
−0.131525 | + | 0.991313i | \(0.541987\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.16857 | 0.504400 | ||||||||
\(106\) | −27.5748 | −2.67830 | ||||||||
\(107\) | 14.9485 | 1.44513 | 0.722563 | − | 0.691305i | \(-0.242964\pi\) | ||||
0.722563 | + | 0.691305i | \(0.242964\pi\) | |||||||
\(108\) | −7.27795 | −0.700321 | ||||||||
\(109\) | 1.45686 | 0.139542 | 0.0697710 | − | 0.997563i | \(-0.477773\pi\) | ||||
0.0697710 | + | 0.997563i | \(0.477773\pi\) | |||||||
\(110\) | 18.3959 | 1.75398 | ||||||||
\(111\) | 15.4343 | 1.46496 | ||||||||
\(112\) | 3.37629 | 0.319029 | ||||||||
\(113\) | 14.8440 | 1.39641 | 0.698204 | − | 0.715899i | \(-0.253983\pi\) | ||||
0.698204 | + | 0.715899i | \(0.253983\pi\) | |||||||
\(114\) | −12.1085 | −1.13407 | ||||||||
\(115\) | 18.9191 | 1.76421 | ||||||||
\(116\) | 5.26716 | 0.489044 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −17.0558 | −1.57011 | ||||||||
\(119\) | −7.04993 | −0.646266 | ||||||||
\(120\) | 2.93053 | 0.267520 | ||||||||
\(121\) | 2.30638 | 0.209670 | ||||||||
\(122\) | −28.8333 | −2.61044 | ||||||||
\(123\) | 7.39837 | 0.667088 | ||||||||
\(124\) | −15.9365 | −1.43114 | ||||||||
\(125\) | 9.87889 | 0.883595 | ||||||||
\(126\) | 3.07985 | 0.274375 | ||||||||
\(127\) | 5.83060 | 0.517382 | 0.258691 | − | 0.965960i | \(-0.416709\pi\) | ||||
0.258691 | + | 0.965960i | \(0.416709\pi\) | |||||||
\(128\) | 4.49329 | 0.397154 | ||||||||
\(129\) | 7.30233 | 0.642934 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.0558 | 1.31543 | 0.657714 | − | 0.753268i | \(-0.271523\pi\) | ||||
0.657714 | + | 0.753268i | \(0.271523\pi\) | |||||||
\(132\) | 17.5783 | 1.52999 | ||||||||
\(133\) | −2.76410 | −0.239677 | ||||||||
\(134\) | −6.63423 | −0.573110 | ||||||||
\(135\) | 7.80607 | 0.671839 | ||||||||
\(136\) | −3.99725 | −0.342761 | ||||||||
\(137\) | −4.23709 | −0.361999 | −0.181000 | − | 0.983483i | \(-0.557933\pi\) | ||||
−0.181000 | + | 0.983483i | \(0.557933\pi\) | |||||||
\(138\) | 33.9764 | 2.89226 | ||||||||
\(139\) | −2.70802 | −0.229691 | −0.114846 | − | 0.993383i | \(-0.536637\pi\) | ||||
−0.114846 | + | 0.993383i | \(0.536637\pi\) | |||||||
\(140\) | 5.54753 | 0.468852 | ||||||||
\(141\) | −5.65497 | −0.476235 | ||||||||
\(142\) | −20.1384 | −1.68998 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −5.02967 | −0.419139 | ||||||||
\(145\) | −5.64937 | −0.469155 | ||||||||
\(146\) | −7.76726 | −0.642823 | ||||||||
\(147\) | 2.11889 | 0.174763 | ||||||||
\(148\) | 16.5659 | 1.36171 | ||||||||
\(149\) | −0.891186 | −0.0730088 | −0.0365044 | − | 0.999333i | \(-0.511622\pi\) | ||||
−0.0365044 | + | 0.999333i | \(0.511622\pi\) | |||||||
\(150\) | −4.16195 | −0.339822 | ||||||||
\(151\) | −16.2557 | −1.32287 | −0.661436 | − | 0.750001i | \(-0.730053\pi\) | ||||
−0.661436 | + | 0.750001i | \(0.730053\pi\) | |||||||
\(152\) | −1.56722 | −0.127118 | ||||||||
\(153\) | 10.5023 | 0.849061 | ||||||||
\(154\) | 7.54154 | 0.607714 | ||||||||
\(155\) | 17.0929 | 1.37294 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.94721 | −0.315022 | −0.157511 | − | 0.987517i | \(-0.550347\pi\) | ||||
−0.157511 | + | 0.987517i | \(0.550347\pi\) | |||||||
\(158\) | 26.6040 | 2.11650 | ||||||||
\(159\) | 28.2613 | 2.24126 | ||||||||
\(160\) | −19.7928 | −1.56476 | ||||||||
\(161\) | 7.75601 | 0.611259 | ||||||||
\(162\) | 23.2583 | 1.82735 | ||||||||
\(163\) | 4.48439 | 0.351245 | 0.175622 | − | 0.984458i | \(-0.443806\pi\) | ||||
0.175622 | + | 0.984458i | \(0.443806\pi\) | |||||||
\(164\) | 7.94082 | 0.620074 | ||||||||
\(165\) | −18.8538 | −1.46777 | ||||||||
\(166\) | −11.2148 | −0.870435 | ||||||||
\(167\) | −8.06225 | −0.623875 | −0.311938 | − | 0.950103i | \(-0.600978\pi\) | ||||
−0.311938 | + | 0.950103i | \(0.600978\pi\) | |||||||
\(168\) | 1.20139 | 0.0926896 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 35.5530 | 2.72679 | ||||||||
\(171\) | 4.11768 | 0.314887 | ||||||||
\(172\) | 7.83774 | 0.597622 | ||||||||
\(173\) | −7.74395 | −0.588761 | −0.294381 | − | 0.955688i | \(-0.595113\pi\) | ||||
−0.294381 | + | 0.955688i | \(0.595113\pi\) | |||||||
\(174\) | −10.1456 | −0.769136 | ||||||||
\(175\) | −0.950076 | −0.0718190 | ||||||||
\(176\) | −12.3160 | −0.928352 | ||||||||
\(177\) | 17.4804 | 1.31391 | ||||||||
\(178\) | −0.694258 | −0.0520368 | ||||||||
\(179\) | −16.3124 | −1.21924 | −0.609621 | − | 0.792693i | \(-0.708679\pi\) | ||||
−0.609621 | + | 0.792693i | \(0.708679\pi\) | |||||||
\(180\) | −8.26417 | −0.615975 | ||||||||
\(181\) | 8.28425 | 0.615763 | 0.307882 | − | 0.951425i | \(-0.400380\pi\) | ||||
0.307882 | + | 0.951425i | \(0.400380\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 29.5510 | 2.18448 | ||||||||
\(184\) | 4.39759 | 0.324195 | ||||||||
\(185\) | −17.7680 | −1.30633 | ||||||||
\(186\) | 30.6969 | 2.25081 | ||||||||
\(187\) | 25.7167 | 1.88059 | ||||||||
\(188\) | −6.06960 | −0.442671 | ||||||||
\(189\) | 3.20015 | 0.232777 | ||||||||
\(190\) | 13.9394 | 1.01127 | ||||||||
\(191\) | 10.7356 | 0.776803 | 0.388402 | − | 0.921490i | \(-0.373027\pi\) | ||||
0.388402 | + | 0.921490i | \(0.373027\pi\) | |||||||
\(192\) | −21.2375 | −1.53269 | ||||||||
\(193\) | −0.762728 | −0.0549024 | −0.0274512 | − | 0.999623i | \(-0.508739\pi\) | ||||
−0.0274512 | + | 0.999623i | \(0.508739\pi\) | |||||||
\(194\) | 22.6226 | 1.62421 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.27425 | 0.162446 | ||||||||
\(197\) | 12.1127 | 0.862997 | 0.431498 | − | 0.902114i | \(-0.357985\pi\) | ||||
0.431498 | + | 0.902114i | \(0.357985\pi\) | |||||||
\(198\) | −11.2347 | −0.798412 | ||||||||
\(199\) | −4.27032 | −0.302715 | −0.151358 | − | 0.988479i | \(-0.548364\pi\) | ||||
−0.151358 | + | 0.988479i | \(0.548364\pi\) | |||||||
\(200\) | −0.538685 | −0.0380908 | ||||||||
\(201\) | 6.79938 | 0.479591 | ||||||||
\(202\) | −18.4470 | −1.29793 | ||||||||
\(203\) | −2.31600 | −0.162551 | ||||||||
\(204\) | 33.9728 | 2.37857 | ||||||||
\(205\) | −8.51703 | −0.594855 | ||||||||
\(206\) | 5.51932 | 0.384549 | ||||||||
\(207\) | −11.5542 | −0.803069 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.0828 | 0.697445 | ||||||||
\(210\) | −10.6856 | −0.737378 | ||||||||
\(211\) | −7.26849 | −0.500384 | −0.250192 | − | 0.968196i | \(-0.580494\pi\) | ||||
−0.250192 | + | 0.968196i | \(0.580494\pi\) | |||||||
\(212\) | 30.3334 | 2.08331 | ||||||||
\(213\) | 20.6397 | 1.41421 | ||||||||
\(214\) | −30.9049 | −2.11262 | ||||||||
\(215\) | −8.40647 | −0.573317 | ||||||||
\(216\) | 1.81446 | 0.123458 | ||||||||
\(217\) | 7.00738 | 0.475692 | ||||||||
\(218\) | −3.01195 | −0.203995 | ||||||||
\(219\) | 7.96062 | 0.537929 | ||||||||
\(220\) | −20.2362 | −1.36433 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −31.9092 | −2.14161 | ||||||||
\(223\) | 11.5634 | 0.774343 | 0.387172 | − | 0.922008i | \(-0.373452\pi\) | ||||
0.387172 | + | 0.922008i | \(0.373452\pi\) | |||||||
\(224\) | −8.11421 | −0.542153 | ||||||||
\(225\) | 1.41533 | 0.0943555 | ||||||||
\(226\) | −30.6889 | −2.04140 | ||||||||
\(227\) | 3.02967 | 0.201086 | 0.100543 | − | 0.994933i | \(-0.467942\pi\) | ||||
0.100543 | + | 0.994933i | \(0.467942\pi\) | |||||||
\(228\) | 13.3199 | 0.882130 | ||||||||
\(229\) | −3.56377 | −0.235500 | −0.117750 | − | 0.993043i | \(-0.537568\pi\) | ||||
−0.117750 | + | 0.993043i | \(0.537568\pi\) | |||||||
\(230\) | −39.1137 | −2.57908 | ||||||||
\(231\) | −7.72927 | −0.508549 | ||||||||
\(232\) | −1.31315 | −0.0862127 | ||||||||
\(233\) | −12.8151 | −0.839547 | −0.419774 | − | 0.907629i | \(-0.637891\pi\) | ||||
−0.419774 | + | 0.907629i | \(0.637891\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.51003 | 0.424667 | ||||||||
\(236\) | 18.7621 | 1.22131 | ||||||||
\(237\) | −27.2662 | −1.77113 | ||||||||
\(238\) | 14.5752 | 0.944770 | ||||||||
\(239\) | −25.3757 | −1.64142 | −0.820708 | − | 0.571347i | \(-0.806421\pi\) | ||||
−0.820708 | + | 0.571347i | \(0.806421\pi\) | |||||||
\(240\) | 17.4506 | 1.12643 | ||||||||
\(241\) | −6.80302 | −0.438221 | −0.219111 | − | 0.975700i | \(-0.570316\pi\) | ||||
−0.219111 | + | 0.975700i | \(0.570316\pi\) | |||||||
\(242\) | −4.76826 | −0.306515 | ||||||||
\(243\) | −14.2368 | −0.913294 | ||||||||
\(244\) | 31.7177 | 2.03052 | ||||||||
\(245\) | −2.43928 | −0.155840 | ||||||||
\(246\) | −15.2956 | −0.975210 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.97313 | 0.252294 | ||||||||
\(249\) | 11.4940 | 0.728400 | ||||||||
\(250\) | −20.4239 | −1.29172 | ||||||||
\(251\) | −22.8556 | −1.44263 | −0.721317 | − | 0.692605i | \(-0.756463\pi\) | ||||
−0.721317 | + | 0.692605i | \(0.756463\pi\) | |||||||
\(252\) | −3.38796 | −0.213421 | ||||||||
\(253\) | −28.2923 | −1.77872 | ||||||||
\(254\) | −12.0543 | −0.756356 | ||||||||
\(255\) | −36.4380 | −2.28184 | ||||||||
\(256\) | 10.7564 | 0.672272 | ||||||||
\(257\) | −3.85941 | −0.240743 | −0.120372 | − | 0.992729i | \(-0.538409\pi\) | ||||
−0.120372 | + | 0.992729i | \(0.538409\pi\) | |||||||
\(258\) | −15.0970 | −0.939899 | ||||||||
\(259\) | −7.28412 | −0.452613 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.45016 | 0.213559 | ||||||||
\(262\) | −31.1267 | −1.92301 | ||||||||
\(263\) | −16.2197 | −1.00015 | −0.500075 | − | 0.865982i | \(-0.666694\pi\) | ||||
−0.500075 | + | 0.865982i | \(0.666694\pi\) | |||||||
\(264\) | −4.38243 | −0.269720 | ||||||||
\(265\) | −32.5345 | −1.99858 | ||||||||
\(266\) | 5.71456 | 0.350382 | ||||||||
\(267\) | 0.711540 | 0.0435456 | ||||||||
\(268\) | 7.29791 | 0.445791 | ||||||||
\(269\) | −23.0815 | −1.40731 | −0.703653 | − | 0.710544i | \(-0.748449\pi\) | ||||
−0.703653 | + | 0.710544i | \(0.748449\pi\) | |||||||
\(270\) | −16.1385 | −0.982156 | ||||||||
\(271\) | 10.7673 | 0.654067 | 0.327034 | − | 0.945013i | \(-0.393951\pi\) | ||||
0.327034 | + | 0.945013i | \(0.393951\pi\) | |||||||
\(272\) | −23.8026 | −1.44324 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.75987 | 0.529203 | ||||||||
\(275\) | 3.46568 | 0.208988 | ||||||||
\(276\) | −37.3753 | −2.24973 | ||||||||
\(277\) | −11.7786 | −0.707708 | −0.353854 | − | 0.935301i | \(-0.615129\pi\) | ||||
−0.353854 | + | 0.935301i | \(0.615129\pi\) | |||||||
\(278\) | 5.59863 | 0.335784 | ||||||||
\(279\) | −10.4389 | −0.624962 | ||||||||
\(280\) | −1.38305 | −0.0826531 | ||||||||
\(281\) | 27.3072 | 1.62901 | 0.814507 | − | 0.580154i | \(-0.197008\pi\) | ||||
0.814507 | + | 0.580154i | \(0.197008\pi\) | |||||||
\(282\) | 11.6912 | 0.696203 | ||||||||
\(283\) | 22.8247 | 1.35679 | 0.678393 | − | 0.734699i | \(-0.262677\pi\) | ||||
0.678393 | + | 0.734699i | \(0.262677\pi\) | |||||||
\(284\) | 22.1530 | 1.31454 | ||||||||
\(285\) | −14.2864 | −0.846254 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.49162 | −0.206104 | ||||||||
\(288\) | 12.0878 | 0.712278 | ||||||||
\(289\) | 32.7015 | 1.92362 | ||||||||
\(290\) | 11.6797 | 0.685853 | ||||||||
\(291\) | −23.1858 | −1.35918 | ||||||||
\(292\) | 8.54430 | 0.500017 | ||||||||
\(293\) | 19.8388 | 1.15899 | 0.579497 | − | 0.814974i | \(-0.303249\pi\) | ||||
0.579497 | + | 0.814974i | \(0.303249\pi\) | |||||||
\(294\) | −4.38065 | −0.255485 | ||||||||
\(295\) | −20.1235 | −1.17164 | ||||||||
\(296\) | −4.13004 | −0.240054 | ||||||||
\(297\) | −11.6735 | −0.677365 | ||||||||
\(298\) | 1.84246 | 0.106731 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 4.57831 | 0.264329 | ||||||||
\(301\) | −3.44630 | −0.198641 | ||||||||
\(302\) | 33.6075 | 1.93390 | ||||||||
\(303\) | 18.9062 | 1.08613 | ||||||||
\(304\) | −9.33238 | −0.535249 | ||||||||
\(305\) | −34.0193 | −1.94794 | ||||||||
\(306\) | −21.7127 | −1.24123 | ||||||||
\(307\) | −10.3240 | −0.589219 | −0.294610 | − | 0.955618i | \(-0.595190\pi\) | ||||
−0.294610 | + | 0.955618i | \(0.595190\pi\) | |||||||
\(308\) | −8.29599 | −0.472708 | ||||||||
\(309\) | −5.65672 | −0.321800 | ||||||||
\(310\) | −35.3384 | −2.00709 | ||||||||
\(311\) | 22.2930 | 1.26412 | 0.632060 | − | 0.774919i | \(-0.282210\pi\) | ||||
0.632060 | + | 0.774919i | \(0.282210\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.4600 | −1.09995 | −0.549973 | − | 0.835182i | \(-0.685362\pi\) | ||||
−0.549973 | + | 0.835182i | \(0.685362\pi\) | |||||||
\(314\) | 8.16057 | 0.460528 | ||||||||
\(315\) | 3.63380 | 0.204742 | ||||||||
\(316\) | −29.2654 | −1.64631 | ||||||||
\(317\) | −27.4413 | −1.54126 | −0.770629 | − | 0.637284i | \(-0.780058\pi\) | ||||
−0.770629 | + | 0.637284i | \(0.780058\pi\) | |||||||
\(318\) | −58.4281 | −3.27648 | ||||||||
\(319\) | 8.44829 | 0.473013 | ||||||||
\(320\) | 24.4488 | 1.36673 | ||||||||
\(321\) | 31.6743 | 1.76789 | ||||||||
\(322\) | −16.0350 | −0.893594 | ||||||||
\(323\) | 19.4867 | 1.08427 | ||||||||
\(324\) | −25.5851 | −1.42139 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.27115 | −0.513481 | ||||||||
\(327\) | 3.08693 | 0.170708 | ||||||||
\(328\) | −1.97972 | −0.109312 | ||||||||
\(329\) | 2.66883 | 0.147138 | ||||||||
\(330\) | 38.9789 | 2.14572 | ||||||||
\(331\) | −20.3710 | −1.11969 | −0.559846 | − | 0.828596i | \(-0.689140\pi\) | ||||
−0.559846 | + | 0.828596i | \(0.689140\pi\) | |||||||
\(332\) | 12.3367 | 0.677064 | ||||||||
\(333\) | 10.8512 | 0.594641 | ||||||||
\(334\) | 16.6681 | 0.912038 | ||||||||
\(335\) | −7.82748 | −0.427661 | ||||||||
\(336\) | 7.15399 | 0.390282 | ||||||||
\(337\) | −2.67053 | −0.145473 | −0.0727366 | − | 0.997351i | \(-0.523173\pi\) | ||||
−0.0727366 | + | 0.997351i | \(0.523173\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 31.4529 | 1.70829 | ||||||||
\(340\) | −39.1097 | −2.12102 | ||||||||
\(341\) | −25.5615 | −1.38423 | ||||||||
\(342\) | −8.51301 | −0.460331 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −1.95402 | −0.105354 | ||||||||
\(345\) | 40.0874 | 2.15823 | ||||||||
\(346\) | 16.0100 | 0.860705 | ||||||||
\(347\) | −0.317819 | −0.0170614 | −0.00853071 | − | 0.999964i | \(-0.502715\pi\) | ||||
−0.00853071 | + | 0.999964i | \(0.502715\pi\) | |||||||
\(348\) | 11.1606 | 0.598268 | ||||||||
\(349\) | −0.514513 | −0.0275413 | −0.0137706 | − | 0.999905i | \(-0.504383\pi\) | ||||
−0.0137706 | + | 0.999905i | \(0.504383\pi\) | |||||||
\(350\) | 1.96421 | 0.104992 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 29.5989 | 1.57763 | ||||||||
\(353\) | −0.627678 | −0.0334080 | −0.0167040 | − | 0.999860i | \(-0.505317\pi\) | ||||
−0.0167040 | + | 0.999860i | \(0.505317\pi\) | |||||||
\(354\) | −36.1394 | −1.92079 | ||||||||
\(355\) | −23.7605 | −1.26108 | ||||||||
\(356\) | 0.763711 | 0.0404766 | ||||||||
\(357\) | −14.9380 | −0.790605 | ||||||||
\(358\) | 33.7246 | 1.78240 | ||||||||
\(359\) | −31.9224 | −1.68480 | −0.842399 | − | 0.538854i | \(-0.818857\pi\) | ||||
−0.842399 | + | 0.538854i | \(0.818857\pi\) | |||||||
\(360\) | 2.06034 | 0.108589 | ||||||||
\(361\) | −11.3598 | −0.597883 | ||||||||
\(362\) | −17.1271 | −0.900179 | ||||||||
\(363\) | 4.88696 | 0.256499 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.16430 | −0.479681 | ||||||||
\(366\) | −61.0946 | −3.19347 | ||||||||
\(367\) | 10.6064 | 0.553651 | 0.276826 | − | 0.960920i | \(-0.410718\pi\) | ||||
0.276826 | + | 0.960920i | \(0.410718\pi\) | |||||||
\(368\) | 26.1865 | 1.36507 | ||||||||
\(369\) | 5.20148 | 0.270778 | ||||||||
\(370\) | 36.7340 | 1.90971 | ||||||||
\(371\) | −13.3378 | −0.692462 | ||||||||
\(372\) | −33.7678 | −1.75078 | ||||||||
\(373\) | 10.6129 | 0.549514 | 0.274757 | − | 0.961514i | \(-0.411403\pi\) | ||||
0.274757 | + | 0.961514i | \(0.411403\pi\) | |||||||
\(374\) | −53.1673 | −2.74921 | ||||||||
\(375\) | 20.9323 | 1.08094 | ||||||||
\(376\) | 1.51321 | 0.0780377 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −6.61608 | −0.340295 | ||||||||
\(379\) | 13.5259 | 0.694779 | 0.347390 | − | 0.937721i | \(-0.387068\pi\) | ||||
0.347390 | + | 0.937721i | \(0.387068\pi\) | |||||||
\(380\) | −15.3339 | −0.786612 | ||||||||
\(381\) | 12.3544 | 0.632935 | ||||||||
\(382\) | −22.1951 | −1.13560 | ||||||||
\(383\) | 14.4264 | 0.737155 | 0.368577 | − | 0.929597i | \(-0.379845\pi\) | ||||
0.368577 | + | 0.929597i | \(0.379845\pi\) | |||||||
\(384\) | 9.52079 | 0.485856 | ||||||||
\(385\) | 8.89797 | 0.453483 | ||||||||
\(386\) | 1.57688 | 0.0802613 | ||||||||
\(387\) | 5.13396 | 0.260974 | ||||||||
\(388\) | −24.8858 | −1.26338 | ||||||||
\(389\) | 15.1018 | 0.765692 | 0.382846 | − | 0.923812i | \(-0.374944\pi\) | ||||
0.382846 | + | 0.923812i | \(0.374944\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −54.6793 | −2.76525 | ||||||||
\(392\) | −0.566992 | −0.0286374 | ||||||||
\(393\) | 31.9015 | 1.60922 | ||||||||
\(394\) | −25.0422 | −1.26161 | ||||||||
\(395\) | 31.3890 | 1.57935 | ||||||||
\(396\) | 12.3586 | 0.621041 | ||||||||
\(397\) | −15.6944 | −0.787679 | −0.393840 | − | 0.919179i | \(-0.628853\pi\) | ||||
−0.393840 | + | 0.919179i | \(0.628853\pi\) | |||||||
\(398\) | 8.82858 | 0.442536 | ||||||||
\(399\) | −5.85682 | −0.293208 | ||||||||
\(400\) | −3.20773 | −0.160386 | ||||||||
\(401\) | −18.9270 | −0.945168 | −0.472584 | − | 0.881286i | \(-0.656679\pi\) | ||||
−0.472584 | + | 0.881286i | \(0.656679\pi\) | |||||||
\(402\) | −14.0572 | −0.701110 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 20.2924 | 1.00959 | ||||||||
\(405\) | 27.4416 | 1.36358 | ||||||||
\(406\) | 4.78816 | 0.237632 | ||||||||
\(407\) | 26.5710 | 1.31707 | ||||||||
\(408\) | −8.46974 | −0.419315 | ||||||||
\(409\) | 2.37052 | 0.117215 | 0.0586074 | − | 0.998281i | \(-0.481334\pi\) | ||||
0.0586074 | + | 0.998281i | \(0.481334\pi\) | |||||||
\(410\) | 17.6083 | 0.869614 | ||||||||
\(411\) | −8.97794 | −0.442849 | ||||||||
\(412\) | −6.07147 | −0.299120 | ||||||||
\(413\) | −8.24978 | −0.405945 | ||||||||
\(414\) | 23.8874 | 1.17400 | ||||||||
\(415\) | −13.2319 | −0.649528 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.73800 | −0.280991 | ||||||||
\(418\) | −20.8455 | −1.01959 | ||||||||
\(419\) | 21.4796 | 1.04935 | 0.524673 | − | 0.851304i | \(-0.324188\pi\) | ||||
0.524673 | + | 0.851304i | \(0.324188\pi\) | |||||||
\(420\) | 11.7546 | 0.573566 | ||||||||
\(421\) | 20.1413 | 0.981626 | 0.490813 | − | 0.871265i | \(-0.336700\pi\) | ||||
0.490813 | + | 0.871265i | \(0.336700\pi\) | |||||||
\(422\) | 15.0271 | 0.731506 | ||||||||
\(423\) | −3.97577 | −0.193309 | ||||||||
\(424\) | −7.56239 | −0.367262 | ||||||||
\(425\) | 6.69797 | 0.324899 | ||||||||
\(426\) | −42.6711 | −2.06742 | ||||||||
\(427\) | −13.9465 | −0.674917 | ||||||||
\(428\) | 33.9966 | 1.64329 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 17.3798 | 0.838126 | ||||||||
\(431\) | −18.0221 | −0.868092 | −0.434046 | − | 0.900891i | \(-0.642915\pi\) | ||||
−0.434046 | + | 0.900891i | \(0.642915\pi\) | |||||||
\(432\) | 10.8046 | 0.519838 | ||||||||
\(433\) | 35.8293 | 1.72184 | 0.860922 | − | 0.508737i | \(-0.169887\pi\) | ||||
0.860922 | + | 0.508737i | \(0.169887\pi\) | |||||||
\(434\) | −14.4872 | −0.695410 | ||||||||
\(435\) | −11.9704 | −0.573937 | ||||||||
\(436\) | 3.31327 | 0.158677 | ||||||||
\(437\) | −21.4383 | −1.02553 | ||||||||
\(438\) | −16.4580 | −0.786393 | ||||||||
\(439\) | −2.24154 | −0.106983 | −0.0534914 | − | 0.998568i | \(-0.517035\pi\) | ||||
−0.0534914 | + | 0.998568i | \(0.517035\pi\) | |||||||
\(440\) | 5.04508 | 0.240515 | ||||||||
\(441\) | 1.48970 | 0.0709383 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.70925 | −0.271254 | −0.135627 | − | 0.990760i | \(-0.543305\pi\) | ||||
−0.135627 | + | 0.990760i | \(0.543305\pi\) | |||||||
\(444\) | 35.1014 | 1.66584 | ||||||||
\(445\) | −0.819128 | −0.0388304 | ||||||||
\(446\) | −23.9065 | −1.13201 | ||||||||
\(447\) | −1.88833 | −0.0893148 | ||||||||
\(448\) | 10.0229 | 0.473540 | ||||||||
\(449\) | −32.3594 | −1.52714 | −0.763568 | − | 0.645728i | \(-0.776554\pi\) | ||||
−0.763568 | + | 0.645728i | \(0.776554\pi\) | |||||||
\(450\) | −2.92609 | −0.137937 | ||||||||
\(451\) | 12.7367 | 0.599748 | ||||||||
\(452\) | 33.7590 | 1.58789 | ||||||||
\(453\) | −34.4441 | −1.61833 | ||||||||
\(454\) | −6.26362 | −0.293966 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.32077 | −0.155509 | ||||||||
\(457\) | 24.8614 | 1.16297 | 0.581483 | − | 0.813559i | \(-0.302473\pi\) | ||||
0.581483 | + | 0.813559i | \(0.302473\pi\) | |||||||
\(458\) | 7.36782 | 0.344276 | ||||||||
\(459\) | −22.5609 | −1.05305 | ||||||||
\(460\) | 43.0267 | 2.00613 | ||||||||
\(461\) | 17.5977 | 0.819607 | 0.409804 | − | 0.912174i | \(-0.365597\pi\) | ||||
0.409804 | + | 0.912174i | \(0.365597\pi\) | |||||||
\(462\) | 15.9797 | 0.743443 | ||||||||
\(463\) | 31.9863 | 1.48653 | 0.743265 | − | 0.668997i | \(-0.233276\pi\) | ||||
0.743265 | + | 0.668997i | \(0.233276\pi\) | |||||||
\(464\) | −7.81948 | −0.363010 | ||||||||
\(465\) | 36.2181 | 1.67957 | ||||||||
\(466\) | 26.4943 | 1.22733 | ||||||||
\(467\) | 2.98855 | 0.138294 | 0.0691468 | − | 0.997606i | \(-0.477972\pi\) | ||||
0.0691468 | + | 0.997606i | \(0.477972\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.20893 | −0.148175 | ||||||||
\(470\) | −13.4590 | −0.620817 | ||||||||
\(471\) | −8.36372 | −0.385380 | ||||||||
\(472\) | −4.67756 | −0.215302 | ||||||||
\(473\) | 12.5714 | 0.578032 | ||||||||
\(474\) | 56.3709 | 2.58920 | ||||||||
\(475\) | 2.62610 | 0.120494 | ||||||||
\(476\) | −16.0333 | −0.734885 | ||||||||
\(477\) | 19.8693 | 0.909753 | ||||||||
\(478\) | 52.4624 | 2.39957 | ||||||||
\(479\) | −19.2718 | −0.880553 | −0.440277 | − | 0.897862i | \(-0.645120\pi\) | ||||
−0.440277 | + | 0.897862i | \(0.645120\pi\) | |||||||
\(480\) | −41.9388 | −1.91424 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 14.0647 | 0.640632 | ||||||||
\(483\) | 16.4341 | 0.747779 | ||||||||
\(484\) | 5.24527 | 0.238422 | ||||||||
\(485\) | 26.6916 | 1.21200 | ||||||||
\(486\) | 29.4336 | 1.33514 | ||||||||
\(487\) | 18.2603 | 0.827451 | 0.413726 | − | 0.910402i | \(-0.364227\pi\) | ||||
0.413726 | + | 0.910402i | \(0.364227\pi\) | |||||||
\(488\) | −7.90753 | −0.357957 | ||||||||
\(489\) | 9.50194 | 0.429693 | ||||||||
\(490\) | 5.04303 | 0.227821 | ||||||||
\(491\) | −32.6604 | −1.47394 | −0.736971 | − | 0.675924i | \(-0.763745\pi\) | ||||
−0.736971 | + | 0.675924i | \(0.763745\pi\) | |||||||
\(492\) | 16.8257 | 0.758563 | ||||||||
\(493\) | 16.3276 | 0.735360 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13.2553 | −0.595784 | ||||||||
\(496\) | 23.6589 | 1.06232 | ||||||||
\(497\) | −9.74080 | −0.436935 | ||||||||
\(498\) | −23.7629 | −1.06484 | ||||||||
\(499\) | −5.35967 | −0.239932 | −0.119966 | − | 0.992778i | \(-0.538279\pi\) | ||||
−0.119966 | + | 0.992778i | \(0.538279\pi\) | |||||||
\(500\) | 22.4671 | 1.00476 | ||||||||
\(501\) | −17.0830 | −0.763214 | ||||||||
\(502\) | 47.2523 | 2.10897 | ||||||||
\(503\) | −20.9055 | −0.932129 | −0.466065 | − | 0.884751i | \(-0.654329\pi\) | ||||
−0.466065 | + | 0.884751i | \(0.654329\pi\) | |||||||
\(504\) | 0.844650 | 0.0376237 | ||||||||
\(505\) | −21.7649 | −0.968526 | ||||||||
\(506\) | 58.4922 | 2.60030 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.2602 | 0.588328 | ||||||||
\(509\) | −25.0852 | −1.11188 | −0.555941 | − | 0.831222i | \(-0.687642\pi\) | ||||
−0.555941 | + | 0.831222i | \(0.687642\pi\) | |||||||
\(510\) | 75.3329 | 3.33580 | ||||||||
\(511\) | −3.75697 | −0.166199 | ||||||||
\(512\) | −31.2245 | −1.37994 | ||||||||
\(513\) | −8.84553 | −0.390540 | ||||||||
\(514\) | 7.97905 | 0.351941 | ||||||||
\(515\) | 6.51204 | 0.286955 | ||||||||
\(516\) | 16.6073 | 0.731096 | ||||||||
\(517\) | −9.73535 | −0.428160 | ||||||||
\(518\) | 15.0594 | 0.661671 | ||||||||
\(519\) | −16.4086 | −0.720257 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.13575 | −0.356434 | −0.178217 | − | 0.983991i | \(-0.557033\pi\) | ||||
−0.178217 | + | 0.983991i | \(0.557033\pi\) | |||||||
\(522\) | −7.13294 | −0.312200 | ||||||||
\(523\) | 36.6634 | 1.60318 | 0.801589 | − | 0.597875i | \(-0.203988\pi\) | ||||
0.801589 | + | 0.597875i | \(0.203988\pi\) | |||||||
\(524\) | 34.2406 | 1.49581 | ||||||||
\(525\) | −2.01311 | −0.0878593 | ||||||||
\(526\) | 33.5330 | 1.46211 | ||||||||
\(527\) | −49.4015 | −2.15196 | ||||||||
\(528\) | −26.0962 | −1.13569 | ||||||||
\(529\) | 37.1556 | 1.61546 | ||||||||
\(530\) | 67.2626 | 2.92170 | ||||||||
\(531\) | 12.2897 | 0.533329 | ||||||||
\(532\) | −6.28624 | −0.272543 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −1.47106 | −0.0636589 | ||||||||
\(535\) | −36.4636 | −1.57646 | ||||||||
\(536\) | −1.81944 | −0.0785877 | ||||||||
\(537\) | −34.5641 | −1.49155 | ||||||||
\(538\) | 47.7194 | 2.05733 | ||||||||
\(539\) | 3.64779 | 0.157121 | ||||||||
\(540\) | 17.7529 | 0.763965 | ||||||||
\(541\) | −16.6320 | −0.715063 | −0.357532 | − | 0.933901i | \(-0.616382\pi\) | ||||
−0.357532 | + | 0.933901i | \(0.616382\pi\) | |||||||
\(542\) | −22.2606 | −0.956175 | ||||||||
\(543\) | 17.5534 | 0.753290 | ||||||||
\(544\) | 57.2046 | 2.45263 | ||||||||
\(545\) | −3.55369 | −0.152223 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.0139 | −1.53984 | −0.769921 | − | 0.638139i | \(-0.779704\pi\) | ||||
−0.769921 | + | 0.638139i | \(0.779704\pi\) | |||||||
\(548\) | −9.63620 | −0.411638 | ||||||||
\(549\) | 20.7761 | 0.886702 | ||||||||
\(550\) | −7.16503 | −0.305518 | ||||||||
\(551\) | 6.40165 | 0.272719 | ||||||||
\(552\) | 9.31802 | 0.396601 | ||||||||
\(553\) | 12.8682 | 0.547210 | ||||||||
\(554\) | 24.3514 | 1.03459 | ||||||||
\(555\) | −37.6485 | −1.59809 | ||||||||
\(556\) | −6.15872 | −0.261188 | ||||||||
\(557\) | 11.2328 | 0.475948 | 0.237974 | − | 0.971272i | \(-0.423517\pi\) | ||||
0.237974 | + | 0.971272i | \(0.423517\pi\) | |||||||
\(558\) | 21.5817 | 0.913626 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −8.23570 | −0.348022 | ||||||||
\(561\) | 54.4908 | 2.30060 | ||||||||
\(562\) | −56.4557 | −2.38144 | ||||||||
\(563\) | 11.1199 | 0.468649 | 0.234324 | − | 0.972158i | \(-0.424712\pi\) | ||||
0.234324 | + | 0.972158i | \(0.424712\pi\) | |||||||
\(564\) | −12.8608 | −0.541538 | ||||||||
\(565\) | −36.2087 | −1.52331 | ||||||||
\(566\) | −47.1883 | −1.98347 | ||||||||
\(567\) | 11.2499 | 0.472451 | ||||||||
\(568\) | −5.52296 | −0.231738 | ||||||||
\(569\) | −2.48545 | −0.104196 | −0.0520978 | − | 0.998642i | \(-0.516591\pi\) | ||||
−0.0520978 | + | 0.998642i | \(0.516591\pi\) | |||||||
\(570\) | 29.5361 | 1.23713 | ||||||||
\(571\) | 0.537621 | 0.0224987 | 0.0112494 | − | 0.999937i | \(-0.496419\pi\) | ||||
0.0112494 | + | 0.999937i | \(0.496419\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.7476 | 0.950297 | ||||||||
\(574\) | 7.21867 | 0.301301 | ||||||||
\(575\) | −7.36880 | −0.307300 | ||||||||
\(576\) | −14.9312 | −0.622134 | ||||||||
\(577\) | −27.0563 | −1.12637 | −0.563184 | − | 0.826331i | \(-0.690424\pi\) | ||||
−0.563184 | + | 0.826331i | \(0.690424\pi\) | |||||||
\(578\) | −67.6079 | −2.81212 | ||||||||
\(579\) | −1.61614 | −0.0671644 | ||||||||
\(580\) | −12.8481 | −0.533487 | ||||||||
\(581\) | −5.42451 | −0.225047 | ||||||||
\(582\) | 47.9349 | 1.98697 | ||||||||
\(583\) | 48.6533 | 2.01501 | ||||||||
\(584\) | −2.13017 | −0.0881472 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −41.0152 | −1.69432 | ||||||||
\(587\) | −20.7196 | −0.855189 | −0.427594 | − | 0.903971i | \(-0.640639\pi\) | ||||
−0.427594 | + | 0.903971i | \(0.640639\pi\) | |||||||
\(588\) | 4.81889 | 0.198728 | ||||||||
\(589\) | −19.3691 | −0.798089 | ||||||||
\(590\) | 41.6039 | 1.71280 | ||||||||
\(591\) | 25.6656 | 1.05574 | ||||||||
\(592\) | −24.5933 | −1.01078 | ||||||||
\(593\) | −23.2747 | −0.955776 | −0.477888 | − | 0.878421i | \(-0.658598\pi\) | ||||
−0.477888 | + | 0.878421i | \(0.658598\pi\) | |||||||
\(594\) | 24.1341 | 0.990233 | ||||||||
\(595\) | 17.1967 | 0.704997 | ||||||||
\(596\) | −2.02678 | −0.0830202 | ||||||||
\(597\) | −9.04835 | −0.370324 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.28114 | 0.379217 | 0.189609 | − | 0.981860i | \(-0.439278\pi\) | ||||
0.189609 | + | 0.981860i | \(0.439278\pi\) | |||||||
\(600\) | −1.14142 | −0.0465981 | ||||||||
\(601\) | −23.6534 | −0.964843 | −0.482421 | − | 0.875939i | \(-0.660243\pi\) | ||||
−0.482421 | + | 0.875939i | \(0.660243\pi\) | |||||||
\(602\) | 7.12496 | 0.290392 | ||||||||
\(603\) | 4.78036 | 0.194671 | ||||||||
\(604\) | −36.9696 | −1.50427 | ||||||||
\(605\) | −5.62589 | −0.228725 | ||||||||
\(606\) | −39.0872 | −1.58781 | ||||||||
\(607\) | −24.1600 | −0.980623 | −0.490312 | − | 0.871547i | \(-0.663117\pi\) | ||||
−0.490312 | + | 0.871547i | \(0.663117\pi\) | |||||||
\(608\) | 22.4284 | 0.909593 | ||||||||
\(609\) | −4.90736 | −0.198856 | ||||||||
\(610\) | 70.3324 | 2.84767 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 23.8849 | 0.965488 | ||||||||
\(613\) | 27.6780 | 1.11790 | 0.558952 | − | 0.829200i | \(-0.311204\pi\) | ||||
0.558952 | + | 0.829200i | \(0.311204\pi\) | |||||||
\(614\) | 21.3440 | 0.861374 | ||||||||
\(615\) | −18.0467 | −0.727712 | ||||||||
\(616\) | 2.06827 | 0.0833328 | ||||||||
\(617\) | 10.5982 | 0.426669 | 0.213335 | − | 0.976979i | \(-0.431568\pi\) | ||||
0.213335 | + | 0.976979i | \(0.431568\pi\) | |||||||
\(618\) | 11.6948 | 0.470436 | ||||||||
\(619\) | −42.9657 | −1.72694 | −0.863468 | − | 0.504403i | \(-0.831712\pi\) | ||||
−0.863468 | + | 0.504403i | \(0.831712\pi\) | |||||||
\(620\) | 38.8736 | 1.56120 | ||||||||
\(621\) | 24.8204 | 0.996009 | ||||||||
\(622\) | −46.0891 | −1.84801 | ||||||||
\(623\) | −0.335808 | −0.0134539 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.8477 | −1.15391 | ||||||||
\(626\) | 40.2322 | 1.60800 | ||||||||
\(627\) | 21.3645 | 0.853214 | ||||||||
\(628\) | −8.97695 | −0.358219 | ||||||||
\(629\) | 51.3525 | 2.04756 | ||||||||
\(630\) | −7.51262 | −0.299310 | ||||||||
\(631\) | −15.4963 | −0.616899 | −0.308449 | − | 0.951241i | \(-0.599810\pi\) | ||||
−0.308449 | + | 0.951241i | \(0.599810\pi\) | |||||||
\(632\) | 7.29614 | 0.290225 | ||||||||
\(633\) | −15.4012 | −0.612141 | ||||||||
\(634\) | 56.7329 | 2.25315 | ||||||||
\(635\) | −14.2224 | −0.564400 | ||||||||
\(636\) | 64.2732 | 2.54860 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −17.4662 | −0.691494 | ||||||||
\(639\) | 14.5109 | 0.574043 | ||||||||
\(640\) | −10.9604 | −0.433247 | ||||||||
\(641\) | 22.2240 | 0.877796 | 0.438898 | − | 0.898537i | \(-0.355369\pi\) | ||||
0.438898 | + | 0.898537i | \(0.355369\pi\) | |||||||
\(642\) | −65.4842 | −2.58446 | ||||||||
\(643\) | 26.6384 | 1.05052 | 0.525259 | − | 0.850943i | \(-0.323969\pi\) | ||||
0.525259 | + | 0.850943i | \(0.323969\pi\) | |||||||
\(644\) | 17.6391 | 0.695078 | ||||||||
\(645\) | −17.8124 | −0.701363 | ||||||||
\(646\) | −40.2872 | −1.58508 | ||||||||
\(647\) | 15.7389 | 0.618758 | 0.309379 | − | 0.950939i | \(-0.399879\pi\) | ||||
0.309379 | + | 0.950939i | \(0.399879\pi\) | |||||||
\(648\) | 6.37860 | 0.250575 | ||||||||
\(649\) | 30.0935 | 1.18127 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14.8479 | 0.581934 | ||||||||
\(652\) | 10.1986 | 0.399409 | ||||||||
\(653\) | −9.13364 | −0.357427 | −0.178714 | − | 0.983901i | \(-0.557194\pi\) | ||||
−0.178714 | + | 0.983901i | \(0.557194\pi\) | |||||||
\(654\) | −6.38201 | −0.249556 | ||||||||
\(655\) | −36.7252 | −1.43497 | ||||||||
\(656\) | −11.7887 | −0.460272 | ||||||||
\(657\) | 5.59678 | 0.218351 | ||||||||
\(658\) | −5.51762 | −0.215099 | ||||||||
\(659\) | 0.447782 | 0.0174431 | 0.00872156 | − | 0.999962i | \(-0.497224\pi\) | ||||
0.00872156 | + | 0.999962i | \(0.497224\pi\) | |||||||
\(660\) | −42.8784 | −1.66904 | ||||||||
\(661\) | −46.9277 | −1.82528 | −0.912638 | − | 0.408769i | \(-0.865958\pi\) | ||||
−0.912638 | + | 0.408769i | \(0.865958\pi\) | |||||||
\(662\) | 42.1156 | 1.63687 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.07565 | −0.119358 | ||||||||
\(665\) | 6.74240 | 0.261459 | ||||||||
\(666\) | −22.4340 | −0.869301 | ||||||||
\(667\) | −17.9629 | −0.695527 | ||||||||
\(668\) | −18.3356 | −0.709424 | ||||||||
\(669\) | 24.5016 | 0.947287 | ||||||||
\(670\) | 16.1827 | 0.625193 | ||||||||
\(671\) | 50.8738 | 1.96396 | ||||||||
\(672\) | −17.1931 | −0.663239 | ||||||||
\(673\) | −16.5829 | −0.639225 | −0.319612 | − | 0.947548i | \(-0.603553\pi\) | ||||
−0.319612 | + | 0.947548i | \(0.603553\pi\) | |||||||
\(674\) | 5.52113 | 0.212666 | ||||||||
\(675\) | −3.04039 | −0.117025 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.1027 | 0.618878 | 0.309439 | − | 0.950919i | \(-0.399859\pi\) | ||||
0.309439 | + | 0.950919i | \(0.399859\pi\) | |||||||
\(678\) | −65.0265 | −2.49733 | ||||||||
\(679\) | 10.9424 | 0.419931 | ||||||||
\(680\) | 9.75040 | 0.373911 | ||||||||
\(681\) | 6.41954 | 0.245997 | ||||||||
\(682\) | 52.8464 | 2.02359 | ||||||||
\(683\) | −10.7304 | −0.410589 | −0.205294 | − | 0.978700i | \(-0.565815\pi\) | ||||
−0.205294 | + | 0.978700i | \(0.565815\pi\) | |||||||
\(684\) | 9.36464 | 0.358066 | ||||||||
\(685\) | 10.3354 | 0.394897 | ||||||||
\(686\) | 2.06743 | 0.0789347 | ||||||||
\(687\) | −7.55123 | −0.288098 | ||||||||
\(688\) | −11.6357 | −0.443606 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −82.8778 | −3.15510 | ||||||||
\(691\) | 24.1742 | 0.919631 | 0.459815 | − | 0.888015i | \(-0.347916\pi\) | ||||
0.459815 | + | 0.888015i | \(0.347916\pi\) | |||||||
\(692\) | −17.6117 | −0.669495 | ||||||||
\(693\) | −5.43413 | −0.206425 | ||||||||
\(694\) | 0.657068 | 0.0249419 | ||||||||
\(695\) | 6.60562 | 0.250565 | ||||||||
\(696\) | −2.78243 | −0.105468 | ||||||||
\(697\) | 24.6157 | 0.932385 | ||||||||
\(698\) | 1.06372 | 0.0402623 | ||||||||
\(699\) | −27.1539 | −1.02705 | ||||||||
\(700\) | −2.16071 | −0.0816672 | ||||||||
\(701\) | −14.4328 | −0.545120 | −0.272560 | − | 0.962139i | \(-0.587870\pi\) | ||||
−0.272560 | + | 0.962139i | \(0.587870\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.1340 | 0.759369 | ||||||||
\(704\) | −36.5616 | −1.37797 | ||||||||
\(705\) | 13.7940 | 0.519514 | ||||||||
\(706\) | 1.29768 | 0.0488388 | ||||||||
\(707\) | −8.92269 | −0.335572 | ||||||||
\(708\) | 39.7548 | 1.49408 | ||||||||
\(709\) | 15.1940 | 0.570623 | 0.285311 | − | 0.958435i | \(-0.407903\pi\) | ||||
0.285311 | + | 0.958435i | \(0.407903\pi\) | |||||||
\(710\) | 49.1231 | 1.84356 | ||||||||
\(711\) | −19.1697 | −0.718921 | ||||||||
\(712\) | −0.190400 | −0.00713555 | ||||||||
\(713\) | 54.3493 | 2.03540 | ||||||||
\(714\) | 30.8833 | 1.15578 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −37.0984 | −1.38643 | ||||||||
\(717\) | −53.7683 | −2.00802 | ||||||||
\(718\) | 65.9971 | 2.46299 | ||||||||
\(719\) | 4.99848 | 0.186412 | 0.0932060 | − | 0.995647i | \(-0.470288\pi\) | ||||
0.0932060 | + | 0.995647i | \(0.470288\pi\) | |||||||
\(720\) | 12.2688 | 0.457230 | ||||||||
\(721\) | 2.66966 | 0.0994233 | ||||||||
\(722\) | 23.4855 | 0.874040 | ||||||||
\(723\) | −14.4149 | −0.536095 | ||||||||
\(724\) | 18.8405 | 0.700200 | ||||||||
\(725\) | 2.20038 | 0.0817199 | ||||||||
\(726\) | −10.1034 | −0.374973 | ||||||||
\(727\) | −7.22850 | −0.268090 | −0.134045 | − | 0.990975i | \(-0.542797\pi\) | ||||
−0.134045 | + | 0.990975i | \(0.542797\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.58334 | 0.132716 | ||||||||
\(730\) | 18.9465 | 0.701242 | ||||||||
\(731\) | 24.2961 | 0.898625 | ||||||||
\(732\) | 67.2065 | 2.48402 | ||||||||
\(733\) | 34.3382 | 1.26831 | 0.634154 | − | 0.773206i | \(-0.281348\pi\) | ||||
0.634154 | + | 0.773206i | \(0.281348\pi\) | |||||||
\(734\) | −21.9280 | −0.809377 | ||||||||
\(735\) | −5.16857 | −0.190645 | ||||||||
\(736\) | −62.9338 | −2.31977 | ||||||||
\(737\) | 11.7055 | 0.431178 | ||||||||
\(738\) | −10.7537 | −0.395848 | ||||||||
\(739\) | −40.3619 | −1.48474 | −0.742369 | − | 0.669992i | \(-0.766298\pi\) | ||||
−0.742369 | + | 0.669992i | \(0.766298\pi\) | |||||||
\(740\) | −40.4089 | −1.48546 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 27.5748 | 1.01230 | ||||||||
\(743\) | −15.9115 | −0.583736 | −0.291868 | − | 0.956459i | \(-0.594277\pi\) | ||||
−0.291868 | + | 0.956459i | \(0.594277\pi\) | |||||||
\(744\) | 8.41863 | 0.308642 | ||||||||
\(745\) | 2.17385 | 0.0796437 | ||||||||
\(746\) | −21.9413 | −0.803329 | ||||||||
\(747\) | 8.08091 | 0.295665 | ||||||||
\(748\) | 58.4861 | 2.13846 | ||||||||
\(749\) | −14.9485 | −0.546207 | ||||||||
\(750\) | −43.2760 | −1.58022 | ||||||||
\(751\) | 1.10100 | 0.0401760 | 0.0200880 | − | 0.999798i | \(-0.493605\pi\) | ||||
0.0200880 | + | 0.999798i | \(0.493605\pi\) | |||||||
\(752\) | 9.01075 | 0.328588 | ||||||||
\(753\) | −48.4286 | −1.76484 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 39.6522 | 1.44309 | ||||||||
\(756\) | 7.27795 | 0.264697 | ||||||||
\(757\) | −28.9466 | −1.05208 | −0.526041 | − | 0.850459i | \(-0.676324\pi\) | ||||
−0.526041 | + | 0.850459i | \(0.676324\pi\) | |||||||
\(758\) | −27.9638 | −1.01569 | ||||||||
\(759\) | −59.9483 | −2.17599 | ||||||||
\(760\) | 3.82288 | 0.138671 | ||||||||
\(761\) | −12.6820 | −0.459721 | −0.229860 | − | 0.973224i | \(-0.573827\pi\) | ||||
−0.229860 | + | 0.973224i | \(0.573827\pi\) | |||||||
\(762\) | −25.5418 | −0.925282 | ||||||||
\(763\) | −1.45686 | −0.0527419 | ||||||||
\(764\) | 24.4155 | 0.883322 | ||||||||
\(765\) | −25.6180 | −0.926222 | ||||||||
\(766\) | −29.8255 | −1.07764 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 22.7916 | 0.822419 | ||||||||
\(769\) | −40.2042 | −1.44980 | −0.724899 | − | 0.688855i | \(-0.758114\pi\) | ||||
−0.724899 | + | 0.688855i | \(0.758114\pi\) | |||||||
\(770\) | −18.3959 | −0.662942 | ||||||||
\(771\) | −8.17768 | −0.294512 | ||||||||
\(772\) | −1.73463 | −0.0624309 | ||||||||
\(773\) | 42.3905 | 1.52468 | 0.762340 | − | 0.647177i | \(-0.224051\pi\) | ||||
0.762340 | + | 0.647177i | \(0.224051\pi\) | |||||||
\(774\) | −10.6141 | −0.381515 | ||||||||
\(775\) | −6.65754 | −0.239146 | ||||||||
\(776\) | 6.20426 | 0.222720 | ||||||||
\(777\) | −15.4343 | −0.553701 | ||||||||
\(778\) | −31.2218 | −1.11936 | ||||||||
\(779\) | 9.65117 | 0.345789 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 35.5324 | 1.27145 | ||||||||
\(782\) | 113.045 | 4.04249 | ||||||||
\(783\) | −7.41156 | −0.264868 | ||||||||
\(784\) | −3.37629 | −0.120582 | ||||||||
\(785\) | 9.62835 | 0.343650 | ||||||||
\(786\) | −65.9541 | −2.35250 | ||||||||
\(787\) | 43.9833 | 1.56784 | 0.783918 | − | 0.620865i | \(-0.213218\pi\) | ||||
0.783918 | + | 0.620865i | \(0.213218\pi\) | |||||||
\(788\) | 27.5474 | 0.981335 | ||||||||
\(789\) | −34.3678 | −1.22353 | ||||||||
\(790\) | −64.8944 | −2.30884 | ||||||||
\(791\) | −14.8440 | −0.527793 | ||||||||
\(792\) | −3.08111 | −0.109482 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 32.4470 | 1.15150 | ||||||||
\(795\) | −68.9371 | −2.44495 | ||||||||
\(796\) | −9.71178 | −0.344225 | ||||||||
\(797\) | 48.0486 | 1.70197 | 0.850984 | − | 0.525192i | \(-0.176007\pi\) | ||||
0.850984 | + | 0.525192i | \(0.176007\pi\) | |||||||
\(798\) | 12.1085 | 0.428638 | ||||||||
\(799\) | −18.8151 | −0.665630 | ||||||||
\(800\) | 7.70911 | 0.272558 | ||||||||
\(801\) | 0.500254 | 0.0176756 | ||||||||
\(802\) | 39.1301 | 1.38173 | ||||||||
\(803\) | 13.7046 | 0.483627 | ||||||||
\(804\) | 15.4635 | 0.545355 | ||||||||
\(805\) | −18.9191 | −0.666809 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −48.9073 | −1.72162 | ||||||||
\(808\) | −5.05909 | −0.177978 | ||||||||
\(809\) | 0.460055 | 0.0161747 | 0.00808733 | − | 0.999967i | \(-0.497426\pi\) | ||||
0.00808733 | + | 0.999967i | \(0.497426\pi\) | |||||||
\(810\) | −56.7335 | −1.99341 | ||||||||
\(811\) | 29.7828 | 1.04582 | 0.522908 | − | 0.852389i | \(-0.324847\pi\) | ||||
0.522908 | + | 0.852389i | \(0.324847\pi\) | |||||||
\(812\) | −5.26716 | −0.184841 | ||||||||
\(813\) | 22.8148 | 0.800148 | ||||||||
\(814\) | −54.9335 | −1.92542 | ||||||||
\(815\) | −10.9387 | −0.383165 | ||||||||
\(816\) | −50.4351 | −1.76558 | ||||||||
\(817\) | 9.52589 | 0.333269 | ||||||||
\(818\) | −4.90088 | −0.171355 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −19.3699 | −0.676425 | ||||||||
\(821\) | −3.59326 | −0.125406 | −0.0627028 | − | 0.998032i | \(-0.519972\pi\) | ||||
−0.0627028 | + | 0.998032i | \(0.519972\pi\) | |||||||
\(822\) | 18.5612 | 0.647397 | ||||||||
\(823\) | 21.8141 | 0.760391 | 0.380196 | − | 0.924906i | \(-0.375857\pi\) | ||||
0.380196 | + | 0.924906i | \(0.375857\pi\) | |||||||
\(824\) | 1.51367 | 0.0527313 | ||||||||
\(825\) | 7.34340 | 0.255664 | ||||||||
\(826\) | 17.0558 | 0.593447 | ||||||||
\(827\) | −42.7217 | −1.48558 | −0.742790 | − | 0.669525i | \(-0.766498\pi\) | ||||
−0.742790 | + | 0.669525i | \(0.766498\pi\) | |||||||
\(828\) | −26.2770 | −0.913190 | ||||||||
\(829\) | −36.5078 | −1.26797 | −0.633985 | − | 0.773345i | \(-0.718582\pi\) | ||||
−0.633985 | + | 0.773345i | \(0.718582\pi\) | |||||||
\(830\) | 27.3559 | 0.949539 | ||||||||
\(831\) | −24.9576 | −0.865770 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.04993 | 0.244265 | ||||||||
\(834\) | 11.8629 | 0.410779 | ||||||||
\(835\) | 19.6661 | 0.680572 | ||||||||
\(836\) | 22.9309 | 0.793082 | ||||||||
\(837\) | 22.4247 | 0.775111 | ||||||||
\(838\) | −44.4075 | −1.53403 | ||||||||
\(839\) | 6.70588 | 0.231513 | 0.115756 | − | 0.993278i | \(-0.463071\pi\) | ||||
0.115756 | + | 0.993278i | \(0.463071\pi\) | |||||||
\(840\) | −2.93053 | −0.101113 | ||||||||
\(841\) | −23.6361 | −0.815039 | ||||||||
\(842\) | −41.6406 | −1.43503 | ||||||||
\(843\) | 57.8611 | 1.99284 | ||||||||
\(844\) | −16.5304 | −0.568999 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8.21962 | 0.282596 | ||||||||
\(847\) | −2.30638 | −0.0792480 | ||||||||
\(848\) | −45.0321 | −1.54641 | ||||||||
\(849\) | 48.3630 | 1.65981 | ||||||||
\(850\) | −13.8475 | −0.474967 | ||||||||
\(851\) | −56.4957 | −1.93665 | ||||||||
\(852\) | 46.9399 | 1.60813 | ||||||||
\(853\) | 27.2554 | 0.933207 | 0.466603 | − | 0.884467i | \(-0.345478\pi\) | ||||
0.466603 | + | 0.884467i | \(0.345478\pi\) | |||||||
\(854\) | 28.8333 | 0.986654 | ||||||||
\(855\) | −10.0442 | −0.343504 | ||||||||
\(856\) | −8.47568 | −0.289693 | ||||||||
\(857\) | 46.1474 | 1.57637 | 0.788183 | − | 0.615441i | \(-0.211022\pi\) | ||||
0.788183 | + | 0.615441i | \(0.211022\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.45682 | −0.322662 | −0.161331 | − | 0.986900i | \(-0.551579\pi\) | ||||
−0.161331 | + | 0.986900i | \(0.551579\pi\) | |||||||
\(860\) | −19.1184 | −0.651933 | ||||||||
\(861\) | −7.39837 | −0.252136 | ||||||||
\(862\) | 37.2593 | 1.26906 | ||||||||
\(863\) | 28.8550 | 0.982237 | 0.491119 | − | 0.871093i | \(-0.336588\pi\) | ||||
0.491119 | + | 0.871093i | \(0.336588\pi\) | |||||||
\(864\) | −25.9667 | −0.883406 | ||||||||
\(865\) | 18.8896 | 0.642267 | ||||||||
\(866\) | −74.0743 | −2.51715 | ||||||||
\(867\) | 69.2909 | 2.35324 | ||||||||
\(868\) | 15.9365 | 0.540921 | ||||||||
\(869\) | −46.9403 | −1.59234 | ||||||||
\(870\) | 24.7479 | 0.839033 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −0.826029 | −0.0279729 | ||||||||
\(873\) | −16.3010 | −0.551704 | ||||||||
\(874\) | 44.3222 | 1.49922 | ||||||||
\(875\) | −9.87889 | −0.333967 | ||||||||
\(876\) | 18.1044 | 0.611692 | ||||||||
\(877\) | 8.55393 | 0.288846 | 0.144423 | − | 0.989516i | \(-0.453867\pi\) | ||||
0.144423 | + | 0.989516i | \(0.453867\pi\) | |||||||
\(878\) | 4.63422 | 0.156397 | ||||||||
\(879\) | 42.0363 | 1.41785 | ||||||||
\(880\) | 30.0421 | 1.01272 | ||||||||
\(881\) | 27.9911 | 0.943046 | 0.471523 | − | 0.881854i | \(-0.343704\pi\) | ||||
0.471523 | + | 0.881854i | \(0.343704\pi\) | |||||||
\(882\) | −3.07985 | −0.103704 | ||||||||
\(883\) | −44.7564 | −1.50617 | −0.753086 | − | 0.657922i | \(-0.771436\pi\) | ||||
−0.753086 | + | 0.657922i | \(0.771436\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −42.6395 | −1.43331 | ||||||||
\(886\) | 11.8034 | 0.396544 | ||||||||
\(887\) | −9.56744 | −0.321243 | −0.160622 | − | 0.987016i | \(-0.551350\pi\) | ||||
−0.160622 | + | 0.987016i | \(0.551350\pi\) | |||||||
\(888\) | −8.75110 | −0.293668 | ||||||||
\(889\) | −5.83060 | −0.195552 | ||||||||
\(890\) | 1.69349 | 0.0567658 | ||||||||
\(891\) | −41.0373 | −1.37480 | ||||||||
\(892\) | 26.2981 | 0.880525 | ||||||||
\(893\) | −7.37691 | −0.246859 | ||||||||
\(894\) | 3.90398 | 0.130569 | ||||||||
\(895\) | 39.7904 | 1.33005 | ||||||||
\(896\) | −4.49329 | −0.150110 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 66.9007 | 2.23251 | ||||||||
\(899\) | −16.2291 | −0.541271 | ||||||||
\(900\) | 3.21882 | 0.107294 | ||||||||
\(901\) | 94.0302 | 3.13260 | ||||||||
\(902\) | −26.3322 | −0.876766 | ||||||||
\(903\) | −7.30233 | −0.243006 | ||||||||
\(904\) | −8.41644 | −0.279926 | ||||||||
\(905\) | −20.2076 | −0.671723 | ||||||||
\(906\) | 71.2107 | 2.36582 | ||||||||
\(907\) | −18.8652 | −0.626408 | −0.313204 | − | 0.949686i | \(-0.601402\pi\) | ||||
−0.313204 | + | 0.949686i | \(0.601402\pi\) | |||||||
\(908\) | 6.89023 | 0.228660 | ||||||||
\(909\) | 13.2922 | 0.440873 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.358293 | −0.0118708 | −0.00593539 | − | 0.999982i | \(-0.501889\pi\) | ||||
−0.00593539 | + | 0.999982i | \(0.501889\pi\) | |||||||
\(912\) | −19.7743 | −0.654793 | ||||||||
\(913\) | 19.7875 | 0.654870 | ||||||||
\(914\) | −51.3990 | −1.70013 | ||||||||
\(915\) | −72.0832 | −2.38300 | ||||||||
\(916\) | −8.10489 | −0.267793 | ||||||||
\(917\) | −15.0558 | −0.497185 | ||||||||
\(918\) | 46.6429 | 1.53944 | ||||||||
\(919\) | −12.0902 | −0.398818 | −0.199409 | − | 0.979916i | \(-0.563902\pi\) | ||||
−0.199409 | + | 0.979916i | \(0.563902\pi\) | |||||||
\(920\) | −10.7269 | −0.353657 | ||||||||
\(921\) | −21.8753 | −0.720817 | ||||||||
\(922\) | −36.3820 | −1.19818 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −17.5783 | −0.578284 | ||||||||
\(925\) | 6.92047 | 0.227544 | ||||||||
\(926\) | −66.1294 | −2.17315 | ||||||||
\(927\) | −3.97700 | −0.130622 | ||||||||
\(928\) | 18.7925 | 0.616894 | ||||||||
\(929\) | 4.34400 | 0.142522 | 0.0712610 | − | 0.997458i | \(-0.477298\pi\) | ||||
0.0712610 | + | 0.997458i | \(0.477298\pi\) | |||||||
\(930\) | −74.8783 | −2.45535 | ||||||||
\(931\) | 2.76410 | 0.0905896 | ||||||||
\(932\) | −29.1448 | −0.954670 | ||||||||
\(933\) | 47.2365 | 1.54645 | ||||||||
\(934\) | −6.17860 | −0.202170 | ||||||||
\(935\) | −62.7301 | −2.05149 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.7092 | 1.46059 | 0.730294 | − | 0.683133i | \(-0.239383\pi\) | ||||
0.730294 | + | 0.683133i | \(0.239383\pi\) | |||||||
\(938\) | 6.63423 | 0.216615 | ||||||||
\(939\) | −41.2337 | −1.34561 | ||||||||
\(940\) | 14.8054 | 0.482900 | ||||||||
\(941\) | 57.3375 | 1.86915 | 0.934574 | − | 0.355768i | \(-0.115781\pi\) | ||||
0.934574 | + | 0.355768i | \(0.115781\pi\) | |||||||
\(942\) | 17.2914 | 0.563383 | ||||||||
\(943\) | −27.0810 | −0.881880 | ||||||||
\(944\) | −27.8536 | −0.906558 | ||||||||
\(945\) | −7.80607 | −0.253931 | ||||||||
\(946\) | −25.9904 | −0.845020 | ||||||||
\(947\) | 46.9376 | 1.52527 | 0.762634 | − | 0.646830i | \(-0.223906\pi\) | ||||
0.762634 | + | 0.646830i | \(0.223906\pi\) | |||||||
\(948\) | −62.0102 | −2.01400 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −5.42927 | −0.176149 | ||||||||
\(951\) | −58.1452 | −1.88549 | ||||||||
\(952\) | 3.99725 | 0.129552 | ||||||||
\(953\) | −35.5773 | −1.15246 | −0.576231 | − | 0.817287i | \(-0.695477\pi\) | ||||
−0.576231 | + | 0.817287i | \(0.695477\pi\) | |||||||
\(954\) | −41.0783 | −1.32996 | ||||||||
\(955\) | −26.1872 | −0.847398 | ||||||||
\(956\) | −57.7107 | −1.86650 | ||||||||
\(957\) | 17.9010 | 0.578657 | ||||||||
\(958\) | 39.8431 | 1.28727 | ||||||||
\(959\) | 4.23709 | 0.136823 | ||||||||
\(960\) | 51.8043 | 1.67198 | ||||||||
\(961\) | 18.1034 | 0.583980 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 22.2689 | 0.717604 | ||||||||
\(964\) | −15.4718 | −0.498312 | ||||||||
\(965\) | 1.86051 | 0.0598918 | ||||||||
\(966\) | −33.9764 | −1.09317 | ||||||||
\(967\) | −18.5576 | −0.596772 | −0.298386 | − | 0.954445i | \(-0.596448\pi\) | ||||
−0.298386 | + | 0.954445i | \(0.596448\pi\) | |||||||
\(968\) | −1.30770 | −0.0420309 | ||||||||
\(969\) | 41.2902 | 1.32643 | ||||||||
\(970\) | −55.1829 | −1.77182 | ||||||||
\(971\) | 47.2286 | 1.51564 | 0.757819 | − | 0.652465i | \(-0.226265\pi\) | ||||
0.757819 | + | 0.652465i | \(0.226265\pi\) | |||||||
\(972\) | −32.3782 | −1.03853 | ||||||||
\(973\) | 2.70802 | 0.0868152 | ||||||||
\(974\) | −37.7517 | −1.20964 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −47.0873 | −1.50723 | ||||||||
\(977\) | −47.9846 | −1.53516 | −0.767582 | − | 0.640951i | \(-0.778540\pi\) | ||||
−0.767582 | + | 0.640951i | \(0.778540\pi\) | |||||||
\(978\) | −19.6446 | −0.628164 | ||||||||
\(979\) | 1.22496 | 0.0391498 | ||||||||
\(980\) | −5.54753 | −0.177209 | ||||||||
\(981\) | 2.17029 | 0.0692921 | ||||||||
\(982\) | 67.5229 | 2.15474 | ||||||||
\(983\) | 27.9789 | 0.892387 | 0.446193 | − | 0.894937i | \(-0.352779\pi\) | ||||
0.446193 | + | 0.894937i | \(0.352779\pi\) | |||||||
\(984\) | −4.19481 | −0.133726 | ||||||||
\(985\) | −29.5463 | −0.941425 | ||||||||
\(986\) | −33.7562 | −1.07502 | ||||||||
\(987\) | 5.65497 | 0.180000 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −26.7295 | −0.849948 | ||||||||
\(990\) | 27.4044 | 0.870971 | ||||||||
\(991\) | −19.4925 | −0.619199 | −0.309600 | − | 0.950867i | \(-0.600195\pi\) | ||||
−0.309600 | + | 0.950867i | \(0.600195\pi\) | |||||||
\(992\) | −56.8593 | −1.80529 | ||||||||
\(993\) | −43.1640 | −1.36977 | ||||||||
\(994\) | 20.1384 | 0.638751 | ||||||||
\(995\) | 10.4165 | 0.330225 | ||||||||
\(996\) | 26.1401 | 0.828281 | ||||||||
\(997\) | 17.2637 | 0.546748 | 0.273374 | − | 0.961908i | \(-0.411860\pi\) | ||||
0.273374 | + | 0.961908i | \(0.411860\pi\) | |||||||
\(998\) | 11.0807 | 0.350754 | ||||||||
\(999\) | −23.3103 | −0.737506 |
(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 | 1183.2.a.q.1.4 | ✓ | 12 | |
7.6 | odd | 2 | 8281.2.a.cn.1.4 | 12 | |||
13.5 | odd | 4 | 1183.2.c.j.337.19 | 24 | |||
13.8 | odd | 4 | 1183.2.c.j.337.6 | 24 | |||
13.12 | even | 2 | 1183.2.a.r.1.9 | yes | 12 | ||
91.90 | odd | 2 | 8281.2.a.cq.1.9 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1183.2.a.q.1.4 | ✓ | 12 | 1.1 | even | 1 | trivial | |
1183.2.a.r.1.9 | yes | 12 | 13.12 | even | 2 | ||
1183.2.c.j.337.6 | 24 | 13.8 | odd | 4 | |||
1183.2.c.j.337.19 | 24 | 13.5 | odd | 4 | |||
8281.2.a.cn.1.4 | 12 | 7.6 | odd | 2 | |||
8281.2.a.cq.1.9 | 12 | 91.90 | odd | 2 |