Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6013,2,Mod(1,6013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6013, 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("6013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6013 = 7 \cdot 859 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6013.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: | \(48.0140467354\) |
Analytic rank: | \(0\) |
Dimension: | \(110\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 6013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.55830 | −1.80899 | −0.904496 | − | 0.426482i | \(-0.859753\pi\) | ||||
−0.904496 | + | 0.426482i | \(0.859753\pi\) | |||||||
\(3\) | −1.85077 | −1.06854 | −0.534270 | − | 0.845314i | \(-0.679413\pi\) | ||||
−0.534270 | + | 0.845314i | \(0.679413\pi\) | |||||||
\(4\) | 4.54491 | 2.27245 | ||||||||
\(5\) | 3.83295 | 1.71415 | 0.857074 | − | 0.515192i | \(-0.172280\pi\) | ||||
0.857074 | + | 0.515192i | \(0.172280\pi\) | |||||||
\(6\) | 4.73481 | 1.93298 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −6.51064 | −2.30186 | ||||||||
\(9\) | 0.425331 | 0.141777 | ||||||||
\(10\) | −9.80585 | −3.10088 | ||||||||
\(11\) | 3.01326 | 0.908532 | 0.454266 | − | 0.890866i | \(-0.349902\pi\) | ||||
0.454266 | + | 0.890866i | \(0.349902\pi\) | |||||||
\(12\) | −8.41155 | −2.42821 | ||||||||
\(13\) | 2.53009 | 0.701721 | 0.350861 | − | 0.936428i | \(-0.385889\pi\) | ||||
0.350861 | + | 0.936428i | \(0.385889\pi\) | |||||||
\(14\) | 2.55830 | 0.683735 | ||||||||
\(15\) | −7.09390 | −1.83164 | ||||||||
\(16\) | 7.56636 | 1.89159 | ||||||||
\(17\) | 0.588414 | 0.142711 | 0.0713557 | − | 0.997451i | \(-0.477267\pi\) | ||||
0.0713557 | + | 0.997451i | \(0.477267\pi\) | |||||||
\(18\) | −1.08813 | −0.256474 | ||||||||
\(19\) | 0.607741 | 0.139425 | 0.0697127 | − | 0.997567i | \(-0.477792\pi\) | ||||
0.0697127 | + | 0.997567i | \(0.477792\pi\) | |||||||
\(20\) | 17.4204 | 3.89532 | ||||||||
\(21\) | 1.85077 | 0.403870 | ||||||||
\(22\) | −7.70883 | −1.64353 | ||||||||
\(23\) | 6.48122 | 1.35143 | 0.675714 | − | 0.737164i | \(-0.263835\pi\) | ||||
0.675714 | + | 0.737164i | \(0.263835\pi\) | |||||||
\(24\) | 12.0497 | 2.45963 | ||||||||
\(25\) | 9.69153 | 1.93831 | ||||||||
\(26\) | −6.47274 | −1.26941 | ||||||||
\(27\) | 4.76511 | 0.917045 | ||||||||
\(28\) | −4.54491 | −0.858907 | ||||||||
\(29\) | 2.43029 | 0.451294 | 0.225647 | − | 0.974209i | \(-0.427550\pi\) | ||||
0.225647 | + | 0.974209i | \(0.427550\pi\) | |||||||
\(30\) | 18.1483 | 3.31342 | ||||||||
\(31\) | 1.55962 | 0.280117 | 0.140058 | − | 0.990143i | \(-0.455271\pi\) | ||||
0.140058 | + | 0.990143i | \(0.455271\pi\) | |||||||
\(32\) | −6.33575 | −1.12001 | ||||||||
\(33\) | −5.57683 | −0.970802 | ||||||||
\(34\) | −1.50534 | −0.258164 | ||||||||
\(35\) | −3.83295 | −0.647887 | ||||||||
\(36\) | 1.93309 | 0.322182 | ||||||||
\(37\) | 7.58953 | 1.24771 | 0.623855 | − | 0.781540i | \(-0.285565\pi\) | ||||
0.623855 | + | 0.781540i | \(0.285565\pi\) | |||||||
\(38\) | −1.55478 | −0.252219 | ||||||||
\(39\) | −4.68261 | −0.749817 | ||||||||
\(40\) | −24.9550 | −3.94573 | ||||||||
\(41\) | −7.23818 | −1.13041 | −0.565207 | − | 0.824949i | \(-0.691204\pi\) | ||||
−0.565207 | + | 0.824949i | \(0.691204\pi\) | |||||||
\(42\) | −4.73481 | −0.730598 | ||||||||
\(43\) | 7.92709 | 1.20887 | 0.604435 | − | 0.796655i | \(-0.293399\pi\) | ||||
0.604435 | + | 0.796655i | \(0.293399\pi\) | |||||||
\(44\) | 13.6950 | 2.06460 | ||||||||
\(45\) | 1.63027 | 0.243027 | ||||||||
\(46\) | −16.5809 | −2.44472 | ||||||||
\(47\) | −4.57924 | −0.667950 | −0.333975 | − | 0.942582i | \(-0.608390\pi\) | ||||
−0.333975 | + | 0.942582i | \(0.608390\pi\) | |||||||
\(48\) | −14.0036 | −2.02124 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −24.7939 | −3.50638 | ||||||||
\(51\) | −1.08902 | −0.152493 | ||||||||
\(52\) | 11.4990 | 1.59463 | ||||||||
\(53\) | 4.74654 | 0.651988 | 0.325994 | − | 0.945372i | \(-0.394301\pi\) | ||||
0.325994 | + | 0.945372i | \(0.394301\pi\) | |||||||
\(54\) | −12.1906 | −1.65893 | ||||||||
\(55\) | 11.5497 | 1.55736 | ||||||||
\(56\) | 6.51064 | 0.870020 | ||||||||
\(57\) | −1.12479 | −0.148982 | ||||||||
\(58\) | −6.21742 | −0.816387 | ||||||||
\(59\) | −2.37049 | −0.308611 | −0.154306 | − | 0.988023i | \(-0.549314\pi\) | ||||
−0.154306 | + | 0.988023i | \(0.549314\pi\) | |||||||
\(60\) | −32.2411 | −4.16231 | ||||||||
\(61\) | −8.64949 | −1.10745 | −0.553727 | − | 0.832698i | \(-0.686795\pi\) | ||||
−0.553727 | + | 0.832698i | \(0.686795\pi\) | |||||||
\(62\) | −3.98999 | −0.506729 | ||||||||
\(63\) | −0.425331 | −0.0535867 | ||||||||
\(64\) | 1.07605 | 0.134506 | ||||||||
\(65\) | 9.69773 | 1.20286 | ||||||||
\(66\) | 14.2672 | 1.75617 | ||||||||
\(67\) | 7.62289 | 0.931284 | 0.465642 | − | 0.884973i | \(-0.345823\pi\) | ||||
0.465642 | + | 0.884973i | \(0.345823\pi\) | |||||||
\(68\) | 2.67429 | 0.324305 | ||||||||
\(69\) | −11.9952 | −1.44405 | ||||||||
\(70\) | 9.80585 | 1.17202 | ||||||||
\(71\) | 8.52939 | 1.01225 | 0.506126 | − | 0.862460i | \(-0.331077\pi\) | ||||
0.506126 | + | 0.862460i | \(0.331077\pi\) | |||||||
\(72\) | −2.76918 | −0.326351 | ||||||||
\(73\) | −9.65113 | −1.12958 | −0.564789 | − | 0.825235i | \(-0.691043\pi\) | ||||
−0.564789 | + | 0.825235i | \(0.691043\pi\) | |||||||
\(74\) | −19.4163 | −2.25710 | ||||||||
\(75\) | −17.9368 | −2.07116 | ||||||||
\(76\) | 2.76213 | 0.316838 | ||||||||
\(77\) | −3.01326 | −0.343393 | ||||||||
\(78\) | 11.9795 | 1.35641 | ||||||||
\(79\) | 13.0359 | 1.46665 | 0.733327 | − | 0.679876i | \(-0.237966\pi\) | ||||
0.733327 | + | 0.679876i | \(0.237966\pi\) | |||||||
\(80\) | 29.0015 | 3.24247 | ||||||||
\(81\) | −10.0951 | −1.12168 | ||||||||
\(82\) | 18.5174 | 2.04491 | ||||||||
\(83\) | −5.55090 | −0.609290 | −0.304645 | − | 0.952466i | \(-0.598538\pi\) | ||||
−0.304645 | + | 0.952466i | \(0.598538\pi\) | |||||||
\(84\) | 8.41155 | 0.917776 | ||||||||
\(85\) | 2.25536 | 0.244628 | ||||||||
\(86\) | −20.2799 | −2.18684 | ||||||||
\(87\) | −4.49790 | −0.482225 | ||||||||
\(88\) | −19.6182 | −2.09131 | ||||||||
\(89\) | −4.67862 | −0.495933 | −0.247966 | − | 0.968769i | \(-0.579762\pi\) | ||||
−0.247966 | + | 0.968769i | \(0.579762\pi\) | |||||||
\(90\) | −4.17073 | −0.439634 | ||||||||
\(91\) | −2.53009 | −0.265226 | ||||||||
\(92\) | 29.4565 | 3.07106 | ||||||||
\(93\) | −2.88650 | −0.299316 | ||||||||
\(94\) | 11.7151 | 1.20832 | ||||||||
\(95\) | 2.32944 | 0.238996 | ||||||||
\(96\) | 11.7260 | 1.19678 | ||||||||
\(97\) | 11.3067 | 1.14802 | 0.574012 | − | 0.818847i | \(-0.305386\pi\) | ||||
0.574012 | + | 0.818847i | \(0.305386\pi\) | |||||||
\(98\) | −2.55830 | −0.258427 | ||||||||
\(99\) | 1.28163 | 0.128809 | ||||||||
\(100\) | 44.0471 | 4.40471 | ||||||||
\(101\) | 6.39357 | 0.636184 | 0.318092 | − | 0.948060i | \(-0.396958\pi\) | ||||
0.318092 | + | 0.948060i | \(0.396958\pi\) | |||||||
\(102\) | 2.78603 | 0.275858 | ||||||||
\(103\) | −0.822863 | −0.0810791 | −0.0405395 | − | 0.999178i | \(-0.512908\pi\) | ||||
−0.0405395 | + | 0.999178i | \(0.512908\pi\) | |||||||
\(104\) | −16.4725 | −1.61526 | ||||||||
\(105\) | 7.09390 | 0.692293 | ||||||||
\(106\) | −12.1431 | −1.17944 | ||||||||
\(107\) | 10.7560 | 1.03982 | 0.519911 | − | 0.854221i | \(-0.325965\pi\) | ||||
0.519911 | + | 0.854221i | \(0.325965\pi\) | |||||||
\(108\) | 21.6570 | 2.08394 | ||||||||
\(109\) | −1.02527 | −0.0982027 | −0.0491014 | − | 0.998794i | \(-0.515636\pi\) | ||||
−0.0491014 | + | 0.998794i | \(0.515636\pi\) | |||||||
\(110\) | −29.5476 | −2.81725 | ||||||||
\(111\) | −14.0464 | −1.33323 | ||||||||
\(112\) | −7.56636 | −0.714954 | ||||||||
\(113\) | −1.23970 | −0.116621 | −0.0583106 | − | 0.998298i | \(-0.518571\pi\) | ||||
−0.0583106 | + | 0.998298i | \(0.518571\pi\) | |||||||
\(114\) | 2.87754 | 0.269506 | ||||||||
\(115\) | 24.8422 | 2.31655 | ||||||||
\(116\) | 11.0454 | 1.02554 | ||||||||
\(117\) | 1.07613 | 0.0994880 | ||||||||
\(118\) | 6.06442 | 0.558275 | ||||||||
\(119\) | −0.588414 | −0.0539398 | ||||||||
\(120\) | 46.1858 | 4.21617 | ||||||||
\(121\) | −1.92027 | −0.174570 | ||||||||
\(122\) | 22.1280 | 2.00338 | ||||||||
\(123\) | 13.3962 | 1.20789 | ||||||||
\(124\) | 7.08835 | 0.636553 | ||||||||
\(125\) | 17.9824 | 1.60840 | ||||||||
\(126\) | 1.08813 | 0.0969379 | ||||||||
\(127\) | 6.62139 | 0.587554 | 0.293777 | − | 0.955874i | \(-0.405088\pi\) | ||||
0.293777 | + | 0.955874i | \(0.405088\pi\) | |||||||
\(128\) | 9.91865 | 0.876693 | ||||||||
\(129\) | −14.6712 | −1.29172 | ||||||||
\(130\) | −24.8097 | −2.17596 | ||||||||
\(131\) | 11.6986 | 1.02211 | 0.511056 | − | 0.859547i | \(-0.329254\pi\) | ||||
0.511056 | + | 0.859547i | \(0.329254\pi\) | |||||||
\(132\) | −25.3462 | −2.20610 | ||||||||
\(133\) | −0.607741 | −0.0526978 | ||||||||
\(134\) | −19.5017 | −1.68469 | ||||||||
\(135\) | 18.2644 | 1.57195 | ||||||||
\(136\) | −3.83095 | −0.328501 | ||||||||
\(137\) | 3.43535 | 0.293502 | 0.146751 | − | 0.989173i | \(-0.453118\pi\) | ||||
0.146751 | + | 0.989173i | \(0.453118\pi\) | |||||||
\(138\) | 30.6874 | 2.61228 | ||||||||
\(139\) | −9.60680 | −0.814838 | −0.407419 | − | 0.913241i | \(-0.633571\pi\) | ||||
−0.407419 | + | 0.913241i | \(0.633571\pi\) | |||||||
\(140\) | −17.4204 | −1.47229 | ||||||||
\(141\) | 8.47509 | 0.713731 | ||||||||
\(142\) | −21.8207 | −1.83116 | ||||||||
\(143\) | 7.62383 | 0.637536 | ||||||||
\(144\) | 3.21821 | 0.268184 | ||||||||
\(145\) | 9.31519 | 0.773585 | ||||||||
\(146\) | 24.6905 | 2.04340 | ||||||||
\(147\) | −1.85077 | −0.152649 | ||||||||
\(148\) | 34.4937 | 2.83536 | ||||||||
\(149\) | −1.23243 | −0.100964 | −0.0504822 | − | 0.998725i | \(-0.516076\pi\) | ||||
−0.0504822 | + | 0.998725i | \(0.516076\pi\) | |||||||
\(150\) | 45.8876 | 3.74671 | ||||||||
\(151\) | 1.90347 | 0.154903 | 0.0774513 | − | 0.996996i | \(-0.475322\pi\) | ||||
0.0774513 | + | 0.996996i | \(0.475322\pi\) | |||||||
\(152\) | −3.95678 | −0.320937 | ||||||||
\(153\) | 0.250271 | 0.0202332 | ||||||||
\(154\) | 7.70883 | 0.621195 | ||||||||
\(155\) | 5.97797 | 0.480162 | ||||||||
\(156\) | −21.2820 | −1.70392 | ||||||||
\(157\) | 4.96227 | 0.396032 | 0.198016 | − | 0.980199i | \(-0.436550\pi\) | ||||
0.198016 | + | 0.980199i | \(0.436550\pi\) | |||||||
\(158\) | −33.3498 | −2.65317 | ||||||||
\(159\) | −8.78474 | −0.696675 | ||||||||
\(160\) | −24.2846 | −1.91987 | ||||||||
\(161\) | −6.48122 | −0.510792 | ||||||||
\(162\) | 25.8263 | 2.02910 | ||||||||
\(163\) | 3.40621 | 0.266795 | 0.133397 | − | 0.991063i | \(-0.457411\pi\) | ||||
0.133397 | + | 0.991063i | \(0.457411\pi\) | |||||||
\(164\) | −32.8968 | −2.56881 | ||||||||
\(165\) | −21.3757 | −1.66410 | ||||||||
\(166\) | 14.2009 | 1.10220 | ||||||||
\(167\) | −17.0296 | −1.31779 | −0.658897 | − | 0.752233i | \(-0.728977\pi\) | ||||
−0.658897 | + | 0.752233i | \(0.728977\pi\) | |||||||
\(168\) | −12.0497 | −0.929651 | ||||||||
\(169\) | −6.59863 | −0.507587 | ||||||||
\(170\) | −5.76990 | −0.442531 | ||||||||
\(171\) | 0.258491 | 0.0197673 | ||||||||
\(172\) | 36.0279 | 2.74710 | ||||||||
\(173\) | −1.80965 | −0.137585 | −0.0687925 | − | 0.997631i | \(-0.521915\pi\) | ||||
−0.0687925 | + | 0.997631i | \(0.521915\pi\) | |||||||
\(174\) | 11.5070 | 0.872342 | ||||||||
\(175\) | −9.69153 | −0.732611 | ||||||||
\(176\) | 22.7994 | 1.71857 | ||||||||
\(177\) | 4.38722 | 0.329763 | ||||||||
\(178\) | 11.9693 | 0.897139 | ||||||||
\(179\) | 12.5438 | 0.937570 | 0.468785 | − | 0.883312i | \(-0.344692\pi\) | ||||
0.468785 | + | 0.883312i | \(0.344692\pi\) | |||||||
\(180\) | 7.40945 | 0.552268 | ||||||||
\(181\) | −17.2011 | −1.27855 | −0.639273 | − | 0.768980i | \(-0.720764\pi\) | ||||
−0.639273 | + | 0.768980i | \(0.720764\pi\) | |||||||
\(182\) | 6.47274 | 0.479791 | ||||||||
\(183\) | 16.0082 | 1.18336 | ||||||||
\(184\) | −42.1969 | −3.11080 | ||||||||
\(185\) | 29.0903 | 2.13876 | ||||||||
\(186\) | 7.38454 | 0.541460 | ||||||||
\(187\) | 1.77304 | 0.129658 | ||||||||
\(188\) | −20.8122 | −1.51789 | ||||||||
\(189\) | −4.76511 | −0.346611 | ||||||||
\(190\) | −5.95942 | −0.432342 | ||||||||
\(191\) | 1.44289 | 0.104404 | 0.0522020 | − | 0.998637i | \(-0.483376\pi\) | ||||
0.0522020 | + | 0.998637i | \(0.483376\pi\) | |||||||
\(192\) | −1.99151 | −0.143725 | ||||||||
\(193\) | −8.66495 | −0.623717 | −0.311858 | − | 0.950129i | \(-0.600951\pi\) | ||||
−0.311858 | + | 0.950129i | \(0.600951\pi\) | |||||||
\(194\) | −28.9260 | −2.07676 | ||||||||
\(195\) | −17.9482 | −1.28530 | ||||||||
\(196\) | 4.54491 | 0.324636 | ||||||||
\(197\) | 1.41847 | 0.101062 | 0.0505309 | − | 0.998722i | \(-0.483909\pi\) | ||||
0.0505309 | + | 0.998722i | \(0.483909\pi\) | |||||||
\(198\) | −3.27880 | −0.233014 | ||||||||
\(199\) | −6.43989 | −0.456511 | −0.228256 | − | 0.973601i | \(-0.573302\pi\) | ||||
−0.228256 | + | 0.973601i | \(0.573302\pi\) | |||||||
\(200\) | −63.0981 | −4.46171 | ||||||||
\(201\) | −14.1082 | −0.995114 | ||||||||
\(202\) | −16.3567 | −1.15085 | ||||||||
\(203\) | −2.43029 | −0.170573 | ||||||||
\(204\) | −4.94947 | −0.346533 | ||||||||
\(205\) | −27.7436 | −1.93770 | ||||||||
\(206\) | 2.10513 | 0.146671 | ||||||||
\(207\) | 2.75667 | 0.191602 | ||||||||
\(208\) | 19.1436 | 1.32737 | ||||||||
\(209\) | 1.83128 | 0.126672 | ||||||||
\(210\) | −18.1483 | −1.25235 | ||||||||
\(211\) | −25.6402 | −1.76514 | −0.882571 | − | 0.470180i | \(-0.844189\pi\) | ||||
−0.882571 | + | 0.470180i | \(0.844189\pi\) | |||||||
\(212\) | 21.5726 | 1.48161 | ||||||||
\(213\) | −15.7859 | −1.08163 | ||||||||
\(214\) | −27.5171 | −1.88103 | ||||||||
\(215\) | 30.3842 | 2.07218 | ||||||||
\(216\) | −31.0239 | −2.11091 | ||||||||
\(217\) | −1.55962 | −0.105874 | ||||||||
\(218\) | 2.62294 | 0.177648 | ||||||||
\(219\) | 17.8620 | 1.20700 | ||||||||
\(220\) | 52.4922 | 3.53902 | ||||||||
\(221\) | 1.48874 | 0.100144 | ||||||||
\(222\) | 35.9350 | 2.41180 | ||||||||
\(223\) | 28.9900 | 1.94131 | 0.970657 | − | 0.240469i | \(-0.0773013\pi\) | ||||
0.970657 | + | 0.240469i | \(0.0773013\pi\) | |||||||
\(224\) | 6.33575 | 0.423325 | ||||||||
\(225\) | 4.12211 | 0.274807 | ||||||||
\(226\) | 3.17153 | 0.210967 | ||||||||
\(227\) | −2.58993 | −0.171900 | −0.0859500 | − | 0.996299i | \(-0.527393\pi\) | ||||
−0.0859500 | + | 0.996299i | \(0.527393\pi\) | |||||||
\(228\) | −5.11205 | −0.338554 | ||||||||
\(229\) | −15.1296 | −0.999789 | −0.499895 | − | 0.866086i | \(-0.666628\pi\) | ||||
−0.499895 | + | 0.866086i | \(0.666628\pi\) | |||||||
\(230\) | −63.5539 | −4.19062 | ||||||||
\(231\) | 5.57683 | 0.366929 | ||||||||
\(232\) | −15.8227 | −1.03881 | ||||||||
\(233\) | −9.67737 | −0.633986 | −0.316993 | − | 0.948428i | \(-0.602673\pi\) | ||||
−0.316993 | + | 0.948428i | \(0.602673\pi\) | |||||||
\(234\) | −2.75306 | −0.179973 | ||||||||
\(235\) | −17.5520 | −1.14497 | ||||||||
\(236\) | −10.7736 | −0.701305 | ||||||||
\(237\) | −24.1264 | −1.56718 | ||||||||
\(238\) | 1.50534 | 0.0975767 | ||||||||
\(239\) | −18.9515 | −1.22587 | −0.612936 | − | 0.790133i | \(-0.710012\pi\) | ||||
−0.612936 | + | 0.790133i | \(0.710012\pi\) | |||||||
\(240\) | −53.6750 | −3.46470 | ||||||||
\(241\) | 12.2145 | 0.786802 | 0.393401 | − | 0.919367i | \(-0.371298\pi\) | ||||
0.393401 | + | 0.919367i | \(0.371298\pi\) | |||||||
\(242\) | 4.91263 | 0.315796 | ||||||||
\(243\) | 4.38831 | 0.281510 | ||||||||
\(244\) | −39.3111 | −2.51664 | ||||||||
\(245\) | 3.83295 | 0.244878 | ||||||||
\(246\) | −34.2714 | −2.18507 | ||||||||
\(247\) | 1.53764 | 0.0978378 | ||||||||
\(248\) | −10.1542 | −0.644789 | ||||||||
\(249\) | 10.2734 | 0.651051 | ||||||||
\(250\) | −46.0045 | −2.90958 | ||||||||
\(251\) | −5.06686 | −0.319817 | −0.159909 | − | 0.987132i | \(-0.551120\pi\) | ||||
−0.159909 | + | 0.987132i | \(0.551120\pi\) | |||||||
\(252\) | −1.93309 | −0.121773 | ||||||||
\(253\) | 19.5296 | 1.22782 | ||||||||
\(254\) | −16.9395 | −1.06288 | ||||||||
\(255\) | −4.17415 | −0.261395 | ||||||||
\(256\) | −27.5270 | −1.72044 | ||||||||
\(257\) | −16.4911 | −1.02869 | −0.514344 | − | 0.857584i | \(-0.671964\pi\) | ||||
−0.514344 | + | 0.857584i | \(0.671964\pi\) | |||||||
\(258\) | 37.5333 | 2.33672 | ||||||||
\(259\) | −7.58953 | −0.471590 | ||||||||
\(260\) | 44.0753 | 2.73343 | ||||||||
\(261\) | 1.03368 | 0.0639831 | ||||||||
\(262\) | −29.9286 | −1.84899 | ||||||||
\(263\) | 17.2961 | 1.06652 | 0.533262 | − | 0.845950i | \(-0.320966\pi\) | ||||
0.533262 | + | 0.845950i | \(0.320966\pi\) | |||||||
\(264\) | 36.3087 | 2.23465 | ||||||||
\(265\) | 18.1933 | 1.11760 | ||||||||
\(266\) | 1.55478 | 0.0953300 | ||||||||
\(267\) | 8.65903 | 0.529924 | ||||||||
\(268\) | 34.6453 | 2.11630 | ||||||||
\(269\) | 11.9981 | 0.731539 | 0.365770 | − | 0.930705i | \(-0.380806\pi\) | ||||
0.365770 | + | 0.930705i | \(0.380806\pi\) | |||||||
\(270\) | −46.7259 | −2.84365 | ||||||||
\(271\) | 25.1684 | 1.52887 | 0.764437 | − | 0.644699i | \(-0.223017\pi\) | ||||
0.764437 | + | 0.644699i | \(0.223017\pi\) | |||||||
\(272\) | 4.45215 | 0.269951 | ||||||||
\(273\) | 4.68261 | 0.283404 | ||||||||
\(274\) | −8.78867 | −0.530943 | ||||||||
\(275\) | 29.2031 | 1.76101 | ||||||||
\(276\) | −54.5171 | −3.28155 | ||||||||
\(277\) | −26.2855 | −1.57934 | −0.789670 | − | 0.613532i | \(-0.789748\pi\) | ||||
−0.789670 | + | 0.613532i | \(0.789748\pi\) | |||||||
\(278\) | 24.5771 | 1.47404 | ||||||||
\(279\) | 0.663357 | 0.0397142 | ||||||||
\(280\) | 24.9550 | 1.49134 | ||||||||
\(281\) | −10.6651 | −0.636226 | −0.318113 | − | 0.948053i | \(-0.603049\pi\) | ||||
−0.318113 | + | 0.948053i | \(0.603049\pi\) | |||||||
\(282\) | −21.6818 | −1.29113 | ||||||||
\(283\) | −26.0535 | −1.54872 | −0.774359 | − | 0.632746i | \(-0.781928\pi\) | ||||
−0.774359 | + | 0.632746i | \(0.781928\pi\) | |||||||
\(284\) | 38.7653 | 2.30030 | ||||||||
\(285\) | −4.31125 | −0.255377 | ||||||||
\(286\) | −19.5040 | −1.15330 | ||||||||
\(287\) | 7.23818 | 0.427256 | ||||||||
\(288\) | −2.69479 | −0.158792 | ||||||||
\(289\) | −16.6538 | −0.979633 | ||||||||
\(290\) | −23.8311 | −1.39941 | ||||||||
\(291\) | −20.9261 | −1.22671 | ||||||||
\(292\) | −43.8635 | −2.56692 | ||||||||
\(293\) | 29.5087 | 1.72392 | 0.861959 | − | 0.506979i | \(-0.169238\pi\) | ||||
0.861959 | + | 0.506979i | \(0.169238\pi\) | |||||||
\(294\) | 4.73481 | 0.276140 | ||||||||
\(295\) | −9.08597 | −0.529006 | ||||||||
\(296\) | −49.4127 | −2.87205 | ||||||||
\(297\) | 14.3585 | 0.833165 | ||||||||
\(298\) | 3.15292 | 0.182644 | ||||||||
\(299\) | 16.3981 | 0.948326 | ||||||||
\(300\) | −81.5209 | −4.70661 | ||||||||
\(301\) | −7.92709 | −0.456910 | ||||||||
\(302\) | −4.86966 | −0.280218 | ||||||||
\(303\) | −11.8330 | −0.679788 | ||||||||
\(304\) | 4.59839 | 0.263736 | ||||||||
\(305\) | −33.1531 | −1.89834 | ||||||||
\(306\) | −0.640268 | −0.0366017 | ||||||||
\(307\) | −3.39435 | −0.193726 | −0.0968629 | − | 0.995298i | \(-0.530881\pi\) | ||||
−0.0968629 | + | 0.995298i | \(0.530881\pi\) | |||||||
\(308\) | −13.6950 | −0.780344 | ||||||||
\(309\) | 1.52293 | 0.0866362 | ||||||||
\(310\) | −15.2934 | −0.868610 | ||||||||
\(311\) | 10.5514 | 0.598313 | 0.299156 | − | 0.954204i | \(-0.403295\pi\) | ||||
0.299156 | + | 0.954204i | \(0.403295\pi\) | |||||||
\(312\) | 30.4868 | 1.72597 | ||||||||
\(313\) | 2.56305 | 0.144872 | 0.0724362 | − | 0.997373i | \(-0.476923\pi\) | ||||
0.0724362 | + | 0.997373i | \(0.476923\pi\) | |||||||
\(314\) | −12.6950 | −0.716420 | ||||||||
\(315\) | −1.63027 | −0.0918556 | ||||||||
\(316\) | 59.2470 | 3.33290 | ||||||||
\(317\) | −3.57584 | −0.200839 | −0.100420 | − | 0.994945i | \(-0.532019\pi\) | ||||
−0.100420 | + | 0.994945i | \(0.532019\pi\) | |||||||
\(318\) | 22.4740 | 1.26028 | ||||||||
\(319\) | 7.32310 | 0.410015 | ||||||||
\(320\) | 4.12444 | 0.230563 | ||||||||
\(321\) | −19.9068 | −1.11109 | ||||||||
\(322\) | 16.5809 | 0.924019 | ||||||||
\(323\) | 0.357603 | 0.0198976 | ||||||||
\(324\) | −45.8812 | −2.54896 | ||||||||
\(325\) | 24.5205 | 1.36015 | ||||||||
\(326\) | −8.71411 | −0.482630 | ||||||||
\(327\) | 1.89753 | 0.104934 | ||||||||
\(328\) | 47.1252 | 2.60205 | ||||||||
\(329\) | 4.57924 | 0.252461 | ||||||||
\(330\) | 54.6856 | 3.01034 | ||||||||
\(331\) | −5.84170 | −0.321089 | −0.160544 | − | 0.987029i | \(-0.551325\pi\) | ||||
−0.160544 | + | 0.987029i | \(0.551325\pi\) | |||||||
\(332\) | −25.2283 | −1.38458 | ||||||||
\(333\) | 3.22806 | 0.176897 | ||||||||
\(334\) | 43.5670 | 2.38388 | ||||||||
\(335\) | 29.2182 | 1.59636 | ||||||||
\(336\) | 14.0036 | 0.763956 | ||||||||
\(337\) | −16.8025 | −0.915292 | −0.457646 | − | 0.889134i | \(-0.651307\pi\) | ||||
−0.457646 | + | 0.889134i | \(0.651307\pi\) | |||||||
\(338\) | 16.8813 | 0.918221 | ||||||||
\(339\) | 2.29439 | 0.124614 | ||||||||
\(340\) | 10.2504 | 0.555907 | ||||||||
\(341\) | 4.69955 | 0.254495 | ||||||||
\(342\) | −0.661299 | −0.0357589 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −51.6104 | −2.78264 | ||||||||
\(345\) | −45.9771 | −2.47533 | ||||||||
\(346\) | 4.62963 | 0.248890 | ||||||||
\(347\) | 23.1847 | 1.24462 | 0.622309 | − | 0.782772i | \(-0.286195\pi\) | ||||
0.622309 | + | 0.782772i | \(0.286195\pi\) | |||||||
\(348\) | −20.4425 | −1.09583 | ||||||||
\(349\) | −24.0418 | −1.28693 | −0.643465 | − | 0.765475i | \(-0.722504\pi\) | ||||
−0.643465 | + | 0.765475i | \(0.722504\pi\) | |||||||
\(350\) | 24.7939 | 1.32529 | ||||||||
\(351\) | 12.0562 | 0.643510 | ||||||||
\(352\) | −19.0913 | −1.01757 | ||||||||
\(353\) | 5.48505 | 0.291940 | 0.145970 | − | 0.989289i | \(-0.453370\pi\) | ||||
0.145970 | + | 0.989289i | \(0.453370\pi\) | |||||||
\(354\) | −11.2238 | −0.596539 | ||||||||
\(355\) | 32.6927 | 1.73515 | ||||||||
\(356\) | −21.2639 | −1.12698 | ||||||||
\(357\) | 1.08902 | 0.0576368 | ||||||||
\(358\) | −32.0909 | −1.69606 | ||||||||
\(359\) | −17.7830 | −0.938550 | −0.469275 | − | 0.883052i | \(-0.655485\pi\) | ||||
−0.469275 | + | 0.883052i | \(0.655485\pi\) | |||||||
\(360\) | −10.6141 | −0.559414 | ||||||||
\(361\) | −18.6307 | −0.980561 | ||||||||
\(362\) | 44.0055 | 2.31288 | ||||||||
\(363\) | 3.55397 | 0.186535 | ||||||||
\(364\) | −11.4990 | −0.602713 | ||||||||
\(365\) | −36.9923 | −1.93627 | ||||||||
\(366\) | −40.9537 | −2.14069 | ||||||||
\(367\) | 13.3238 | 0.695499 | 0.347750 | − | 0.937587i | \(-0.386946\pi\) | ||||
0.347750 | + | 0.937587i | \(0.386946\pi\) | |||||||
\(368\) | 49.0393 | 2.55635 | ||||||||
\(369\) | −3.07862 | −0.160267 | ||||||||
\(370\) | −74.4218 | −3.86900 | ||||||||
\(371\) | −4.74654 | −0.246428 | ||||||||
\(372\) | −13.1189 | −0.680182 | ||||||||
\(373\) | 4.06440 | 0.210447 | 0.105223 | − | 0.994449i | \(-0.466444\pi\) | ||||
0.105223 | + | 0.994449i | \(0.466444\pi\) | |||||||
\(374\) | −4.53598 | −0.234550 | ||||||||
\(375\) | −33.2813 | −1.71864 | ||||||||
\(376\) | 29.8137 | 1.53753 | ||||||||
\(377\) | 6.14886 | 0.316682 | ||||||||
\(378\) | 12.1906 | 0.627016 | ||||||||
\(379\) | −3.64075 | −0.187013 | −0.0935064 | − | 0.995619i | \(-0.529808\pi\) | ||||
−0.0935064 | + | 0.995619i | \(0.529808\pi\) | |||||||
\(380\) | 10.5871 | 0.543107 | ||||||||
\(381\) | −12.2546 | −0.627824 | ||||||||
\(382\) | −3.69136 | −0.188866 | ||||||||
\(383\) | −29.2045 | −1.49228 | −0.746140 | − | 0.665789i | \(-0.768095\pi\) | ||||
−0.746140 | + | 0.665789i | \(0.768095\pi\) | |||||||
\(384\) | −18.3571 | −0.936782 | ||||||||
\(385\) | −11.5497 | −0.588626 | ||||||||
\(386\) | 22.1676 | 1.12830 | ||||||||
\(387\) | 3.37164 | 0.171390 | ||||||||
\(388\) | 51.3880 | 2.60883 | ||||||||
\(389\) | 22.0212 | 1.11652 | 0.558259 | − | 0.829667i | \(-0.311470\pi\) | ||||
0.558259 | + | 0.829667i | \(0.311470\pi\) | |||||||
\(390\) | 45.9169 | 2.32509 | ||||||||
\(391\) | 3.81364 | 0.192864 | ||||||||
\(392\) | −6.51064 | −0.328837 | ||||||||
\(393\) | −21.6514 | −1.09217 | ||||||||
\(394\) | −3.62888 | −0.182820 | ||||||||
\(395\) | 49.9661 | 2.51406 | ||||||||
\(396\) | 5.82490 | 0.292712 | ||||||||
\(397\) | −0.118644 | −0.00595457 | −0.00297728 | − | 0.999996i | \(-0.500948\pi\) | ||||
−0.00297728 | + | 0.999996i | \(0.500948\pi\) | |||||||
\(398\) | 16.4752 | 0.825826 | ||||||||
\(399\) | 1.12479 | 0.0563097 | ||||||||
\(400\) | 73.3296 | 3.66648 | ||||||||
\(401\) | 26.4976 | 1.32323 | 0.661613 | − | 0.749845i | \(-0.269872\pi\) | ||||
0.661613 | + | 0.749845i | \(0.269872\pi\) | |||||||
\(402\) | 36.0930 | 1.80015 | ||||||||
\(403\) | 3.94600 | 0.196564 | ||||||||
\(404\) | 29.0582 | 1.44570 | ||||||||
\(405\) | −38.6940 | −1.92272 | ||||||||
\(406\) | 6.21742 | 0.308565 | ||||||||
\(407\) | 22.8692 | 1.13358 | ||||||||
\(408\) | 7.09019 | 0.351017 | ||||||||
\(409\) | −6.69220 | −0.330908 | −0.165454 | − | 0.986218i | \(-0.552909\pi\) | ||||
−0.165454 | + | 0.986218i | \(0.552909\pi\) | |||||||
\(410\) | 70.9765 | 3.50528 | ||||||||
\(411\) | −6.35803 | −0.313619 | ||||||||
\(412\) | −3.73983 | −0.184248 | ||||||||
\(413\) | 2.37049 | 0.116644 | ||||||||
\(414\) | −7.05238 | −0.346606 | ||||||||
\(415\) | −21.2763 | −1.04441 | ||||||||
\(416\) | −16.0300 | −0.785937 | ||||||||
\(417\) | 17.7799 | 0.870687 | ||||||||
\(418\) | −4.68497 | −0.229149 | ||||||||
\(419\) | −25.8202 | −1.26140 | −0.630700 | − | 0.776027i | \(-0.717232\pi\) | ||||
−0.630700 | + | 0.776027i | \(0.717232\pi\) | |||||||
\(420\) | 32.2411 | 1.57320 | ||||||||
\(421\) | −26.6015 | −1.29648 | −0.648239 | − | 0.761437i | \(-0.724494\pi\) | ||||
−0.648239 | + | 0.761437i | \(0.724494\pi\) | |||||||
\(422\) | 65.5952 | 3.19313 | ||||||||
\(423\) | −1.94769 | −0.0947000 | ||||||||
\(424\) | −30.9030 | −1.50078 | ||||||||
\(425\) | 5.70263 | 0.276618 | ||||||||
\(426\) | 40.3851 | 1.95666 | ||||||||
\(427\) | 8.64949 | 0.418578 | ||||||||
\(428\) | 48.8850 | 2.36294 | ||||||||
\(429\) | −14.1099 | −0.681233 | ||||||||
\(430\) | −77.7318 | −3.74856 | ||||||||
\(431\) | 22.7380 | 1.09525 | 0.547625 | − | 0.836724i | \(-0.315532\pi\) | ||||
0.547625 | + | 0.836724i | \(0.315532\pi\) | |||||||
\(432\) | 36.0545 | 1.73467 | ||||||||
\(433\) | 18.9072 | 0.908623 | 0.454312 | − | 0.890843i | \(-0.349885\pi\) | ||||
0.454312 | + | 0.890843i | \(0.349885\pi\) | |||||||
\(434\) | 3.98999 | 0.191526 | ||||||||
\(435\) | −17.2402 | −0.826606 | ||||||||
\(436\) | −4.65974 | −0.223161 | ||||||||
\(437\) | 3.93890 | 0.188423 | ||||||||
\(438\) | −45.6963 | −2.18345 | ||||||||
\(439\) | −41.4772 | −1.97960 | −0.989799 | − | 0.142473i | \(-0.954495\pi\) | ||||
−0.989799 | + | 0.142473i | \(0.954495\pi\) | |||||||
\(440\) | −75.1958 | −3.58482 | ||||||||
\(441\) | 0.425331 | 0.0202539 | ||||||||
\(442\) | −3.80865 | −0.181159 | ||||||||
\(443\) | −22.2612 | −1.05766 | −0.528831 | − | 0.848727i | \(-0.677370\pi\) | ||||
−0.528831 | + | 0.848727i | \(0.677370\pi\) | |||||||
\(444\) | −63.8397 | −3.02970 | ||||||||
\(445\) | −17.9329 | −0.850103 | ||||||||
\(446\) | −74.1651 | −3.51182 | ||||||||
\(447\) | 2.28093 | 0.107884 | ||||||||
\(448\) | −1.07605 | −0.0508385 | ||||||||
\(449\) | 26.6003 | 1.25534 | 0.627672 | − | 0.778478i | \(-0.284008\pi\) | ||||
0.627672 | + | 0.778478i | \(0.284008\pi\) | |||||||
\(450\) | −10.5456 | −0.497125 | ||||||||
\(451\) | −21.8105 | −1.02702 | ||||||||
\(452\) | −5.63432 | −0.265016 | ||||||||
\(453\) | −3.52288 | −0.165520 | ||||||||
\(454\) | 6.62583 | 0.310966 | ||||||||
\(455\) | −9.69773 | −0.454637 | ||||||||
\(456\) | 7.32307 | 0.342934 | ||||||||
\(457\) | −19.8068 | −0.926521 | −0.463261 | − | 0.886222i | \(-0.653321\pi\) | ||||
−0.463261 | + | 0.886222i | \(0.653321\pi\) | |||||||
\(458\) | 38.7060 | 1.80861 | ||||||||
\(459\) | 2.80386 | 0.130873 | ||||||||
\(460\) | 112.906 | 5.26425 | ||||||||
\(461\) | −3.50274 | −0.163139 | −0.0815695 | − | 0.996668i | \(-0.525993\pi\) | ||||
−0.0815695 | + | 0.996668i | \(0.525993\pi\) | |||||||
\(462\) | −14.2672 | −0.663771 | ||||||||
\(463\) | 27.0011 | 1.25485 | 0.627423 | − | 0.778679i | \(-0.284110\pi\) | ||||
0.627423 | + | 0.778679i | \(0.284110\pi\) | |||||||
\(464\) | 18.3885 | 0.853662 | ||||||||
\(465\) | −11.0638 | −0.513072 | ||||||||
\(466\) | 24.7576 | 1.14687 | ||||||||
\(467\) | −26.8543 | −1.24267 | −0.621334 | − | 0.783546i | \(-0.713409\pi\) | ||||
−0.621334 | + | 0.783546i | \(0.713409\pi\) | |||||||
\(468\) | 4.89090 | 0.226082 | ||||||||
\(469\) | −7.62289 | −0.351992 | ||||||||
\(470\) | 44.9033 | 2.07123 | ||||||||
\(471\) | −9.18400 | −0.423176 | ||||||||
\(472\) | 15.4334 | 0.710379 | ||||||||
\(473\) | 23.8864 | 1.09830 | ||||||||
\(474\) | 61.7226 | 2.83501 | ||||||||
\(475\) | 5.88994 | 0.270249 | ||||||||
\(476\) | −2.67429 | −0.122576 | ||||||||
\(477\) | 2.01885 | 0.0924369 | ||||||||
\(478\) | 48.4837 | 2.21759 | ||||||||
\(479\) | 28.8894 | 1.31999 | 0.659995 | − | 0.751270i | \(-0.270558\pi\) | ||||
0.659995 | + | 0.751270i | \(0.270558\pi\) | |||||||
\(480\) | 44.9452 | 2.05146 | ||||||||
\(481\) | 19.2022 | 0.875545 | ||||||||
\(482\) | −31.2483 | −1.42332 | ||||||||
\(483\) | 11.9952 | 0.545801 | ||||||||
\(484\) | −8.72744 | −0.396702 | ||||||||
\(485\) | 43.3381 | 1.96788 | ||||||||
\(486\) | −11.2266 | −0.509250 | ||||||||
\(487\) | 12.7904 | 0.579589 | 0.289794 | − | 0.957089i | \(-0.406413\pi\) | ||||
0.289794 | + | 0.957089i | \(0.406413\pi\) | |||||||
\(488\) | 56.3137 | 2.54920 | ||||||||
\(489\) | −6.30409 | −0.285081 | ||||||||
\(490\) | −9.80585 | −0.442983 | ||||||||
\(491\) | −0.546492 | −0.0246628 | −0.0123314 | − | 0.999924i | \(-0.503925\pi\) | ||||
−0.0123314 | + | 0.999924i | \(0.503925\pi\) | |||||||
\(492\) | 60.8843 | 2.74488 | ||||||||
\(493\) | 1.43002 | 0.0644047 | ||||||||
\(494\) | −3.93375 | −0.176988 | ||||||||
\(495\) | 4.91244 | 0.220798 | ||||||||
\(496\) | 11.8007 | 0.529866 | ||||||||
\(497\) | −8.52939 | −0.382595 | ||||||||
\(498\) | −26.2825 | −1.17775 | ||||||||
\(499\) | 25.2296 | 1.12943 | 0.564716 | − | 0.825285i | \(-0.308986\pi\) | ||||
0.564716 | + | 0.825285i | \(0.308986\pi\) | |||||||
\(500\) | 81.7285 | 3.65501 | ||||||||
\(501\) | 31.5179 | 1.40811 | ||||||||
\(502\) | 12.9625 | 0.578547 | ||||||||
\(503\) | 13.8465 | 0.617386 | 0.308693 | − | 0.951162i | \(-0.400108\pi\) | ||||
0.308693 | + | 0.951162i | \(0.400108\pi\) | |||||||
\(504\) | 2.76918 | 0.123349 | ||||||||
\(505\) | 24.5062 | 1.09051 | ||||||||
\(506\) | −49.9626 | −2.22111 | ||||||||
\(507\) | 12.2125 | 0.542377 | ||||||||
\(508\) | 30.0936 | 1.33519 | ||||||||
\(509\) | −23.3875 | −1.03663 | −0.518316 | − | 0.855189i | \(-0.673441\pi\) | ||||
−0.518316 | + | 0.855189i | \(0.673441\pi\) | |||||||
\(510\) | 10.6787 | 0.472862 | ||||||||
\(511\) | 9.65113 | 0.426941 | ||||||||
\(512\) | 50.5850 | 2.23556 | ||||||||
\(513\) | 2.89595 | 0.127859 | ||||||||
\(514\) | 42.1893 | 1.86089 | ||||||||
\(515\) | −3.15399 | −0.138982 | ||||||||
\(516\) | −66.6791 | −2.93538 | ||||||||
\(517\) | −13.7984 | −0.606854 | ||||||||
\(518\) | 19.4163 | 0.853103 | ||||||||
\(519\) | 3.34924 | 0.147015 | ||||||||
\(520\) | −63.1384 | −2.76880 | ||||||||
\(521\) | −23.3759 | −1.02412 | −0.512059 | − | 0.858950i | \(-0.671117\pi\) | ||||
−0.512059 | + | 0.858950i | \(0.671117\pi\) | |||||||
\(522\) | −2.64446 | −0.115745 | ||||||||
\(523\) | −3.25169 | −0.142186 | −0.0710932 | − | 0.997470i | \(-0.522649\pi\) | ||||
−0.0710932 | + | 0.997470i | \(0.522649\pi\) | |||||||
\(524\) | 53.1691 | 2.32270 | ||||||||
\(525\) | 17.9368 | 0.782824 | ||||||||
\(526\) | −44.2487 | −1.92933 | ||||||||
\(527\) | 0.917705 | 0.0399759 | ||||||||
\(528\) | −42.1963 | −1.83636 | ||||||||
\(529\) | 19.0062 | 0.826359 | ||||||||
\(530\) | −46.5439 | −2.02174 | ||||||||
\(531\) | −1.00824 | −0.0437540 | ||||||||
\(532\) | −2.76213 | −0.119753 | ||||||||
\(533\) | −18.3133 | −0.793236 | ||||||||
\(534\) | −22.1524 | −0.958629 | ||||||||
\(535\) | 41.2272 | 1.78241 | ||||||||
\(536\) | −49.6299 | −2.14368 | ||||||||
\(537\) | −23.2157 | −1.00183 | ||||||||
\(538\) | −30.6948 | −1.32335 | ||||||||
\(539\) | 3.01326 | 0.129790 | ||||||||
\(540\) | 83.0101 | 3.57219 | ||||||||
\(541\) | 19.9560 | 0.857976 | 0.428988 | − | 0.903310i | \(-0.358870\pi\) | ||||
0.428988 | + | 0.903310i | \(0.358870\pi\) | |||||||
\(542\) | −64.3884 | −2.76572 | ||||||||
\(543\) | 31.8351 | 1.36618 | ||||||||
\(544\) | −3.72804 | −0.159839 | ||||||||
\(545\) | −3.92980 | −0.168334 | ||||||||
\(546\) | −11.9795 | −0.512676 | ||||||||
\(547\) | −40.5135 | −1.73223 | −0.866116 | − | 0.499842i | \(-0.833391\pi\) | ||||
−0.866116 | + | 0.499842i | \(0.833391\pi\) | |||||||
\(548\) | 15.6134 | 0.666970 | ||||||||
\(549\) | −3.67890 | −0.157012 | ||||||||
\(550\) | −74.7103 | −3.18566 | ||||||||
\(551\) | 1.47699 | 0.0629218 | ||||||||
\(552\) | 78.0965 | 3.32401 | ||||||||
\(553\) | −13.0359 | −0.554343 | ||||||||
\(554\) | 67.2461 | 2.85701 | ||||||||
\(555\) | −53.8393 | −2.28535 | ||||||||
\(556\) | −43.6620 | −1.85168 | ||||||||
\(557\) | 8.75113 | 0.370797 | 0.185399 | − | 0.982663i | \(-0.440642\pi\) | ||||
0.185399 | + | 0.982663i | \(0.440642\pi\) | |||||||
\(558\) | −1.69707 | −0.0718426 | ||||||||
\(559\) | 20.0563 | 0.848289 | ||||||||
\(560\) | −29.0015 | −1.22554 | ||||||||
\(561\) | −3.28149 | −0.138544 | ||||||||
\(562\) | 27.2845 | 1.15093 | ||||||||
\(563\) | 9.42636 | 0.397274 | 0.198637 | − | 0.980073i | \(-0.436349\pi\) | ||||
0.198637 | + | 0.980073i | \(0.436349\pi\) | |||||||
\(564\) | 38.5185 | 1.62192 | ||||||||
\(565\) | −4.75171 | −0.199906 | ||||||||
\(566\) | 66.6526 | 2.80162 | ||||||||
\(567\) | 10.0951 | 0.423954 | ||||||||
\(568\) | −55.5317 | −2.33006 | ||||||||
\(569\) | 34.0319 | 1.42669 | 0.713345 | − | 0.700813i | \(-0.247179\pi\) | ||||
0.713345 | + | 0.700813i | \(0.247179\pi\) | |||||||
\(570\) | 11.0295 | 0.461974 | ||||||||
\(571\) | 11.4667 | 0.479867 | 0.239933 | − | 0.970789i | \(-0.422874\pi\) | ||||
0.239933 | + | 0.970789i | \(0.422874\pi\) | |||||||
\(572\) | 34.6496 | 1.44877 | ||||||||
\(573\) | −2.67046 | −0.111560 | ||||||||
\(574\) | −18.5174 | −0.772903 | ||||||||
\(575\) | 62.8130 | 2.61948 | ||||||||
\(576\) | 0.457677 | 0.0190699 | ||||||||
\(577\) | −23.3162 | −0.970667 | −0.485334 | − | 0.874329i | \(-0.661302\pi\) | ||||
−0.485334 | + | 0.874329i | \(0.661302\pi\) | |||||||
\(578\) | 42.6054 | 1.77215 | ||||||||
\(579\) | 16.0368 | 0.666466 | ||||||||
\(580\) | 42.3367 | 1.75793 | ||||||||
\(581\) | 5.55090 | 0.230290 | ||||||||
\(582\) | 53.5352 | 2.21911 | ||||||||
\(583\) | 14.3026 | 0.592352 | ||||||||
\(584\) | 62.8350 | 2.60013 | ||||||||
\(585\) | 4.12475 | 0.170537 | ||||||||
\(586\) | −75.4922 | −3.11855 | ||||||||
\(587\) | 30.3804 | 1.25393 | 0.626967 | − | 0.779046i | \(-0.284296\pi\) | ||||
0.626967 | + | 0.779046i | \(0.284296\pi\) | |||||||
\(588\) | −8.41155 | −0.346887 | ||||||||
\(589\) | 0.947848 | 0.0390554 | ||||||||
\(590\) | 23.2447 | 0.956967 | ||||||||
\(591\) | −2.62526 | −0.107989 | ||||||||
\(592\) | 57.4251 | 2.36016 | ||||||||
\(593\) | −11.7729 | −0.483453 | −0.241727 | − | 0.970344i | \(-0.577714\pi\) | ||||
−0.241727 | + | 0.970344i | \(0.577714\pi\) | |||||||
\(594\) | −36.7334 | −1.50719 | ||||||||
\(595\) | −2.25536 | −0.0924609 | ||||||||
\(596\) | −5.60127 | −0.229437 | ||||||||
\(597\) | 11.9187 | 0.487801 | ||||||||
\(598\) | −41.9513 | −1.71551 | ||||||||
\(599\) | 20.2918 | 0.829102 | 0.414551 | − | 0.910026i | \(-0.363939\pi\) | ||||
0.414551 | + | 0.910026i | \(0.363939\pi\) | |||||||
\(600\) | 116.780 | 4.76751 | ||||||||
\(601\) | −32.5012 | −1.32575 | −0.662876 | − | 0.748729i | \(-0.730664\pi\) | ||||
−0.662876 | + | 0.748729i | \(0.730664\pi\) | |||||||
\(602\) | 20.2799 | 0.826546 | ||||||||
\(603\) | 3.24225 | 0.132035 | ||||||||
\(604\) | 8.65111 | 0.352009 | ||||||||
\(605\) | −7.36030 | −0.299239 | ||||||||
\(606\) | 30.2724 | 1.22973 | ||||||||
\(607\) | 15.6391 | 0.634771 | 0.317385 | − | 0.948297i | \(-0.397195\pi\) | ||||
0.317385 | + | 0.948297i | \(0.397195\pi\) | |||||||
\(608\) | −3.85050 | −0.156158 | ||||||||
\(609\) | 4.49790 | 0.182264 | ||||||||
\(610\) | 84.8156 | 3.43408 | ||||||||
\(611\) | −11.5859 | −0.468715 | ||||||||
\(612\) | 1.13746 | 0.0459790 | ||||||||
\(613\) | 1.48390 | 0.0599341 | 0.0299670 | − | 0.999551i | \(-0.490460\pi\) | ||||
0.0299670 | + | 0.999551i | \(0.490460\pi\) | |||||||
\(614\) | 8.68377 | 0.350448 | ||||||||
\(615\) | 51.3469 | 2.07051 | ||||||||
\(616\) | 19.6182 | 0.790441 | ||||||||
\(617\) | 13.5220 | 0.544375 | 0.272188 | − | 0.962244i | \(-0.412253\pi\) | ||||
0.272188 | + | 0.962244i | \(0.412253\pi\) | |||||||
\(618\) | −3.89610 | −0.156724 | ||||||||
\(619\) | 26.9685 | 1.08396 | 0.541979 | − | 0.840392i | \(-0.317675\pi\) | ||||
0.541979 | + | 0.840392i | \(0.317675\pi\) | |||||||
\(620\) | 27.1693 | 1.09115 | ||||||||
\(621\) | 30.8837 | 1.23932 | ||||||||
\(622\) | −26.9936 | −1.08234 | ||||||||
\(623\) | 4.67862 | 0.187445 | ||||||||
\(624\) | −35.4303 | −1.41835 | ||||||||
\(625\) | 20.4682 | 0.818726 | ||||||||
\(626\) | −6.55706 | −0.262073 | ||||||||
\(627\) | −3.38927 | −0.135354 | ||||||||
\(628\) | 22.5531 | 0.899965 | ||||||||
\(629\) | 4.46578 | 0.178062 | ||||||||
\(630\) | 4.17073 | 0.166166 | ||||||||
\(631\) | −22.6779 | −0.902795 | −0.451397 | − | 0.892323i | \(-0.649074\pi\) | ||||
−0.451397 | + | 0.892323i | \(0.649074\pi\) | |||||||
\(632\) | −84.8721 | −3.37603 | ||||||||
\(633\) | 47.4539 | 1.88612 | ||||||||
\(634\) | 9.14809 | 0.363317 | ||||||||
\(635\) | 25.3795 | 1.00715 | ||||||||
\(636\) | −39.9258 | −1.58316 | ||||||||
\(637\) | 2.53009 | 0.100246 | ||||||||
\(638\) | −18.7347 | −0.741713 | ||||||||
\(639\) | 3.62781 | 0.143514 | ||||||||
\(640\) | 38.0177 | 1.50278 | ||||||||
\(641\) | 6.13553 | 0.242339 | 0.121169 | − | 0.992632i | \(-0.461336\pi\) | ||||
0.121169 | + | 0.992632i | \(0.461336\pi\) | |||||||
\(642\) | 50.9276 | 2.00995 | ||||||||
\(643\) | 40.7041 | 1.60521 | 0.802606 | − | 0.596509i | \(-0.203446\pi\) | ||||
0.802606 | + | 0.596509i | \(0.203446\pi\) | |||||||
\(644\) | −29.4565 | −1.16075 | ||||||||
\(645\) | −56.2339 | −2.21421 | ||||||||
\(646\) | −0.914857 | −0.0359946 | ||||||||
\(647\) | −3.90482 | −0.153514 | −0.0767571 | − | 0.997050i | \(-0.524457\pi\) | ||||
−0.0767571 | + | 0.997050i | \(0.524457\pi\) | |||||||
\(648\) | 65.7254 | 2.58194 | ||||||||
\(649\) | −7.14289 | −0.280383 | ||||||||
\(650\) | −62.7308 | −2.46050 | ||||||||
\(651\) | 2.88650 | 0.113131 | ||||||||
\(652\) | 15.4809 | 0.606279 | ||||||||
\(653\) | 17.8347 | 0.697926 | 0.348963 | − | 0.937136i | \(-0.386534\pi\) | ||||
0.348963 | + | 0.937136i | \(0.386534\pi\) | |||||||
\(654\) | −4.85445 | −0.189824 | ||||||||
\(655\) | 44.8402 | 1.75205 | ||||||||
\(656\) | −54.7667 | −2.13828 | ||||||||
\(657\) | −4.10493 | −0.160148 | ||||||||
\(658\) | −11.7151 | −0.456701 | ||||||||
\(659\) | 11.5763 | 0.450950 | 0.225475 | − | 0.974249i | \(-0.427607\pi\) | ||||
0.225475 | + | 0.974249i | \(0.427607\pi\) | |||||||
\(660\) | −97.1508 | −3.78159 | ||||||||
\(661\) | 46.9192 | 1.82495 | 0.912473 | − | 0.409138i | \(-0.134170\pi\) | ||||
0.912473 | + | 0.409138i | \(0.134170\pi\) | |||||||
\(662\) | 14.9448 | 0.580847 | ||||||||
\(663\) | −2.75531 | −0.107007 | ||||||||
\(664\) | 36.1399 | 1.40250 | ||||||||
\(665\) | −2.32944 | −0.0903319 | ||||||||
\(666\) | −8.25836 | −0.320005 | ||||||||
\(667\) | 15.7513 | 0.609891 | ||||||||
\(668\) | −77.3981 | −2.99462 | ||||||||
\(669\) | −53.6537 | −2.07437 | ||||||||
\(670\) | −74.7489 | −2.88780 | ||||||||
\(671\) | −26.0632 | −1.00616 | ||||||||
\(672\) | −11.7260 | −0.452340 | ||||||||
\(673\) | 20.7132 | 0.798436 | 0.399218 | − | 0.916856i | \(-0.369282\pi\) | ||||
0.399218 | + | 0.916856i | \(0.369282\pi\) | |||||||
\(674\) | 42.9859 | 1.65576 | ||||||||
\(675\) | 46.1812 | 1.77752 | ||||||||
\(676\) | −29.9902 | −1.15347 | ||||||||
\(677\) | −9.43630 | −0.362666 | −0.181333 | − | 0.983422i | \(-0.558041\pi\) | ||||
−0.181333 | + | 0.983422i | \(0.558041\pi\) | |||||||
\(678\) | −5.86975 | −0.225426 | ||||||||
\(679\) | −11.3067 | −0.433912 | ||||||||
\(680\) | −14.6839 | −0.563100 | ||||||||
\(681\) | 4.79336 | 0.183682 | ||||||||
\(682\) | −12.0229 | −0.460380 | ||||||||
\(683\) | 18.5390 | 0.709376 | 0.354688 | − | 0.934985i | \(-0.384587\pi\) | ||||
0.354688 | + | 0.934985i | \(0.384587\pi\) | |||||||
\(684\) | 1.17482 | 0.0449203 | ||||||||
\(685\) | 13.1676 | 0.503106 | ||||||||
\(686\) | 2.55830 | 0.0976764 | ||||||||
\(687\) | 28.0013 | 1.06831 | ||||||||
\(688\) | 59.9792 | 2.28668 | ||||||||
\(689\) | 12.0092 | 0.457514 | ||||||||
\(690\) | 117.623 | 4.47784 | ||||||||
\(691\) | −35.7212 | −1.35890 | −0.679449 | − | 0.733723i | \(-0.737781\pi\) | ||||
−0.679449 | + | 0.733723i | \(0.737781\pi\) | |||||||
\(692\) | −8.22468 | −0.312656 | ||||||||
\(693\) | −1.28163 | −0.0486852 | ||||||||
\(694\) | −59.3134 | −2.25150 | ||||||||
\(695\) | −36.8224 | −1.39675 | ||||||||
\(696\) | 29.2842 | 1.11001 | ||||||||
\(697\) | −4.25905 | −0.161323 | ||||||||
\(698\) | 61.5063 | 2.32805 | ||||||||
\(699\) | 17.9105 | 0.677439 | ||||||||
\(700\) | −44.0471 | −1.66482 | ||||||||
\(701\) | 2.00593 | 0.0757628 | 0.0378814 | − | 0.999282i | \(-0.487939\pi\) | ||||
0.0378814 | + | 0.999282i | \(0.487939\pi\) | |||||||
\(702\) | −30.8433 | −1.16411 | ||||||||
\(703\) | 4.61247 | 0.173963 | ||||||||
\(704\) | 3.24241 | 0.122203 | ||||||||
\(705\) | 32.4846 | 1.22344 | ||||||||
\(706\) | −14.0324 | −0.528117 | ||||||||
\(707\) | −6.39357 | −0.240455 | ||||||||
\(708\) | 19.9395 | 0.749372 | ||||||||
\(709\) | −50.5425 | −1.89816 | −0.949081 | − | 0.315032i | \(-0.897985\pi\) | ||||
−0.949081 | + | 0.315032i | \(0.897985\pi\) | |||||||
\(710\) | −83.6379 | −3.13887 | ||||||||
\(711\) | 5.54458 | 0.207938 | ||||||||
\(712\) | 30.4608 | 1.14157 | ||||||||
\(713\) | 10.1083 | 0.378558 | ||||||||
\(714\) | −2.78603 | −0.104265 | ||||||||
\(715\) | 29.2218 | 1.09283 | ||||||||
\(716\) | 57.0106 | 2.13058 | ||||||||
\(717\) | 35.0748 | 1.30989 | ||||||||
\(718\) | 45.4943 | 1.69783 | ||||||||
\(719\) | 28.5287 | 1.06394 | 0.531970 | − | 0.846763i | \(-0.321452\pi\) | ||||
0.531970 | + | 0.846763i | \(0.321452\pi\) | |||||||
\(720\) | 12.3352 | 0.459707 | ||||||||
\(721\) | 0.822863 | 0.0306450 | ||||||||
\(722\) | 47.6628 | 1.77383 | ||||||||
\(723\) | −22.6061 | −0.840729 | ||||||||
\(724\) | −78.1772 | −2.90543 | ||||||||
\(725\) | 23.5532 | 0.874746 | ||||||||
\(726\) | −9.09212 | −0.337440 | ||||||||
\(727\) | −25.4645 | −0.944427 | −0.472213 | − | 0.881484i | \(-0.656545\pi\) | ||||
−0.472213 | + | 0.881484i | \(0.656545\pi\) | |||||||
\(728\) | 16.4725 | 0.610512 | ||||||||
\(729\) | 22.1635 | 0.820871 | ||||||||
\(730\) | 94.6375 | 3.50269 | ||||||||
\(731\) | 4.66441 | 0.172519 | ||||||||
\(732\) | 72.7557 | 2.68913 | ||||||||
\(733\) | 34.0604 | 1.25805 | 0.629025 | − | 0.777385i | \(-0.283454\pi\) | ||||
0.629025 | + | 0.777385i | \(0.283454\pi\) | |||||||
\(734\) | −34.0864 | −1.25815 | ||||||||
\(735\) | −7.09390 | −0.261662 | ||||||||
\(736\) | −41.0634 | −1.51362 | ||||||||
\(737\) | 22.9697 | 0.846102 | ||||||||
\(738\) | 7.87605 | 0.289921 | ||||||||
\(739\) | −24.7602 | −0.910819 | −0.455409 | − | 0.890282i | \(-0.650507\pi\) | ||||
−0.455409 | + | 0.890282i | \(0.650507\pi\) | |||||||
\(740\) | 132.213 | 4.86024 | ||||||||
\(741\) | −2.84581 | −0.104544 | ||||||||
\(742\) | 12.1431 | 0.445787 | ||||||||
\(743\) | −41.4839 | −1.52190 | −0.760948 | − | 0.648813i | \(-0.775266\pi\) | ||||
−0.760948 | + | 0.648813i | \(0.775266\pi\) | |||||||
\(744\) | 18.7929 | 0.688983 | ||||||||
\(745\) | −4.72384 | −0.173068 | ||||||||
\(746\) | −10.3980 | −0.380697 | ||||||||
\(747\) | −2.36097 | −0.0863834 | ||||||||
\(748\) | 8.05832 | 0.294641 | ||||||||
\(749\) | −10.7560 | −0.393015 | ||||||||
\(750\) | 85.1435 | 3.10900 | ||||||||
\(751\) | −3.35334 | −0.122365 | −0.0611826 | − | 0.998127i | \(-0.519487\pi\) | ||||
−0.0611826 | + | 0.998127i | \(0.519487\pi\) | |||||||
\(752\) | −34.6481 | −1.26349 | ||||||||
\(753\) | 9.37756 | 0.341737 | ||||||||
\(754\) | −15.7306 | −0.572876 | ||||||||
\(755\) | 7.29593 | 0.265526 | ||||||||
\(756\) | −21.6570 | −0.787656 | ||||||||
\(757\) | −26.9951 | −0.981154 | −0.490577 | − | 0.871398i | \(-0.663214\pi\) | ||||
−0.490577 | + | 0.871398i | \(0.663214\pi\) | |||||||
\(758\) | 9.31413 | 0.338305 | ||||||||
\(759\) | −36.1447 | −1.31197 | ||||||||
\(760\) | −15.1662 | −0.550134 | ||||||||
\(761\) | −2.45226 | −0.0888943 | −0.0444472 | − | 0.999012i | \(-0.514153\pi\) | ||||
−0.0444472 | + | 0.999012i | \(0.514153\pi\) | |||||||
\(762\) | 31.3511 | 1.13573 | ||||||||
\(763\) | 1.02527 | 0.0371171 | ||||||||
\(764\) | 6.55781 | 0.237253 | ||||||||
\(765\) | 0.959276 | 0.0346827 | ||||||||
\(766\) | 74.7139 | 2.69952 | ||||||||
\(767\) | −5.99755 | −0.216559 | ||||||||
\(768\) | 50.9460 | 1.83836 | ||||||||
\(769\) | −44.3677 | −1.59994 | −0.799971 | − | 0.600039i | \(-0.795152\pi\) | ||||
−0.799971 | + | 0.600039i | \(0.795152\pi\) | |||||||
\(770\) | 29.5476 | 1.06482 | ||||||||
\(771\) | 30.5212 | 1.09919 | ||||||||
\(772\) | −39.3814 | −1.41737 | ||||||||
\(773\) | 31.4987 | 1.13293 | 0.566465 | − | 0.824086i | \(-0.308311\pi\) | ||||
0.566465 | + | 0.824086i | \(0.308311\pi\) | |||||||
\(774\) | −8.62566 | −0.310043 | ||||||||
\(775\) | 15.1152 | 0.542953 | ||||||||
\(776\) | −73.6139 | −2.64259 | ||||||||
\(777\) | 14.0464 | 0.503913 | ||||||||
\(778\) | −56.3368 | −2.01977 | ||||||||
\(779\) | −4.39894 | −0.157608 | ||||||||
\(780\) | −81.5730 | −2.92078 | ||||||||
\(781\) | 25.7013 | 0.919663 | ||||||||
\(782\) | −9.75644 | −0.348890 | ||||||||
\(783\) | 11.5806 | 0.413857 | ||||||||
\(784\) | 7.56636 | 0.270227 | ||||||||
\(785\) | 19.0202 | 0.678859 | ||||||||
\(786\) | 55.3907 | 1.97572 | ||||||||
\(787\) | 0.621994 | 0.0221717 | 0.0110859 | − | 0.999939i | \(-0.496471\pi\) | ||||
0.0110859 | + | 0.999939i | \(0.496471\pi\) | |||||||
\(788\) | 6.44682 | 0.229658 | ||||||||
\(789\) | −32.0110 | −1.13962 | ||||||||
\(790\) | −127.828 | −4.54792 | ||||||||
\(791\) | 1.23970 | 0.0440787 | ||||||||
\(792\) | −8.34425 | −0.296500 | ||||||||
\(793\) | −21.8840 | −0.777124 | ||||||||
\(794\) | 0.303527 | 0.0107718 | ||||||||
\(795\) | −33.6715 | −1.19420 | ||||||||
\(796\) | −29.2687 | −1.03740 | ||||||||
\(797\) | −6.58566 | −0.233276 | −0.116638 | − | 0.993174i | \(-0.537212\pi\) | ||||
−0.116638 | + | 0.993174i | \(0.537212\pi\) | |||||||
\(798\) | −2.87754 | −0.101864 | ||||||||
\(799\) | −2.69449 | −0.0953241 | ||||||||
\(800\) | −61.4032 | −2.17093 | ||||||||
\(801\) | −1.98996 | −0.0703119 | ||||||||
\(802\) | −67.7888 | −2.39371 | ||||||||
\(803\) | −29.0813 | −1.02626 | ||||||||
\(804\) | −64.1204 | −2.26135 | ||||||||
\(805\) | −24.8422 | −0.875573 | ||||||||
\(806\) | −10.0950 | −0.355583 | ||||||||
\(807\) | −22.2057 | −0.781679 | ||||||||
\(808\) | −41.6262 | −1.46440 | ||||||||
\(809\) | 33.7002 | 1.18483 | 0.592417 | − | 0.805631i | \(-0.298174\pi\) | ||||
0.592417 | + | 0.805631i | \(0.298174\pi\) | |||||||
\(810\) | 98.9909 | 3.47819 | ||||||||
\(811\) | 12.4840 | 0.438374 | 0.219187 | − | 0.975683i | \(-0.429659\pi\) | ||||
0.219187 | + | 0.975683i | \(0.429659\pi\) | |||||||
\(812\) | −11.0454 | −0.387619 | ||||||||
\(813\) | −46.5808 | −1.63366 | ||||||||
\(814\) | −58.5063 | −2.05065 | ||||||||
\(815\) | 13.0558 | 0.457326 | ||||||||
\(816\) | −8.23988 | −0.288454 | ||||||||
\(817\) | 4.81761 | 0.168547 | ||||||||
\(818\) | 17.1207 | 0.598610 | ||||||||
\(819\) | −1.07613 | −0.0376029 | ||||||||
\(820\) | −126.092 | −4.40333 | ||||||||
\(821\) | 15.8237 | 0.552251 | 0.276125 | − | 0.961122i | \(-0.410949\pi\) | ||||
0.276125 | + | 0.961122i | \(0.410949\pi\) | |||||||
\(822\) | 16.2658 | 0.567334 | ||||||||
\(823\) | 40.2189 | 1.40194 | 0.700971 | − | 0.713189i | \(-0.252750\pi\) | ||||
0.700971 | + | 0.713189i | \(0.252750\pi\) | |||||||
\(824\) | 5.35736 | 0.186632 | ||||||||
\(825\) | −54.0481 | −1.88171 | ||||||||
\(826\) | −6.06442 | −0.211008 | ||||||||
\(827\) | −6.76248 | −0.235154 | −0.117577 | − | 0.993064i | \(-0.537513\pi\) | ||||
−0.117577 | + | 0.993064i | \(0.537513\pi\) | |||||||
\(828\) | 12.5288 | 0.435406 | ||||||||
\(829\) | 39.9123 | 1.38621 | 0.693105 | − | 0.720837i | \(-0.256242\pi\) | ||||
0.693105 | + | 0.720837i | \(0.256242\pi\) | |||||||
\(830\) | 54.4313 | 1.88934 | ||||||||
\(831\) | 48.6482 | 1.68759 | ||||||||
\(832\) | 2.72250 | 0.0943857 | ||||||||
\(833\) | 0.588414 | 0.0203873 | ||||||||
\(834\) | −45.4864 | −1.57507 | ||||||||
\(835\) | −65.2738 | −2.25889 | ||||||||
\(836\) | 8.32300 | 0.287857 | ||||||||
\(837\) | 7.43178 | 0.256880 | ||||||||
\(838\) | 66.0559 | 2.28186 | ||||||||
\(839\) | −10.9686 | −0.378678 | −0.189339 | − | 0.981912i | \(-0.560635\pi\) | ||||
−0.189339 | + | 0.981912i | \(0.560635\pi\) | |||||||
\(840\) | −46.1858 | −1.59356 | ||||||||
\(841\) | −23.0937 | −0.796334 | ||||||||
\(842\) | 68.0547 | 2.34532 | ||||||||
\(843\) | 19.7386 | 0.679833 | ||||||||
\(844\) | −116.532 | −4.01120 | ||||||||
\(845\) | −25.2922 | −0.870080 | ||||||||
\(846\) | 4.98278 | 0.171312 | ||||||||
\(847\) | 1.92027 | 0.0659812 | ||||||||
\(848\) | 35.9140 | 1.23329 | ||||||||
\(849\) | 48.2189 | 1.65487 | ||||||||
\(850\) | −14.5891 | −0.500400 | ||||||||
\(851\) | 49.1894 | 1.68619 | ||||||||
\(852\) | −71.7454 | −2.45796 | ||||||||
\(853\) | 45.7276 | 1.56568 | 0.782841 | − | 0.622222i | \(-0.213770\pi\) | ||||
0.782841 | + | 0.622222i | \(0.213770\pi\) | |||||||
\(854\) | −22.1280 | −0.757205 | ||||||||
\(855\) | 0.990785 | 0.0338841 | ||||||||
\(856\) | −70.0284 | −2.39352 | ||||||||
\(857\) | 30.5859 | 1.04479 | 0.522397 | − | 0.852702i | \(-0.325038\pi\) | ||||
0.522397 | + | 0.852702i | \(0.325038\pi\) | |||||||
\(858\) | 36.0974 | 1.23234 | ||||||||
\(859\) | 1.00000 | 0.0341196 | ||||||||
\(860\) | 138.093 | 4.70894 | ||||||||
\(861\) | −13.3962 | −0.456540 | ||||||||
\(862\) | −58.1706 | −1.98130 | ||||||||
\(863\) | −33.5198 | −1.14103 | −0.570514 | − | 0.821288i | \(-0.693256\pi\) | ||||
−0.570514 | + | 0.821288i | \(0.693256\pi\) | |||||||
\(864\) | −30.1905 | −1.02710 | ||||||||
\(865\) | −6.93630 | −0.235841 | ||||||||
\(866\) | −48.3704 | −1.64369 | ||||||||
\(867\) | 30.8222 | 1.04678 | ||||||||
\(868\) | −7.08835 | −0.240594 | ||||||||
\(869\) | 39.2806 | 1.33250 | ||||||||
\(870\) | 44.1057 | 1.49532 | ||||||||
\(871\) | 19.2866 | 0.653502 | ||||||||
\(872\) | 6.67514 | 0.226049 | ||||||||
\(873\) | 4.80910 | 0.162763 | ||||||||
\(874\) | −10.0769 | −0.340856 | ||||||||
\(875\) | −17.9824 | −0.607917 | ||||||||
\(876\) | 81.1810 | 2.74285 | ||||||||
\(877\) | −20.9869 | −0.708676 | −0.354338 | − | 0.935117i | \(-0.615294\pi\) | ||||
−0.354338 | + | 0.935117i | \(0.615294\pi\) | |||||||
\(878\) | 106.111 | 3.58108 | ||||||||
\(879\) | −54.6137 | −1.84207 | ||||||||
\(880\) | 87.3890 | 2.94588 | ||||||||
\(881\) | −42.9643 | −1.44750 | −0.723752 | − | 0.690060i | \(-0.757584\pi\) | ||||
−0.723752 | + | 0.690060i | \(0.757584\pi\) | |||||||
\(882\) | −1.08813 | −0.0366391 | ||||||||
\(883\) | −28.0293 | −0.943262 | −0.471631 | − | 0.881796i | \(-0.656335\pi\) | ||||
−0.471631 | + | 0.881796i | \(0.656335\pi\) | |||||||
\(884\) | 6.76619 | 0.227572 | ||||||||
\(885\) | 16.8160 | 0.565264 | ||||||||
\(886\) | 56.9509 | 1.91330 | ||||||||
\(887\) | −27.0923 | −0.909670 | −0.454835 | − | 0.890576i | \(-0.650302\pi\) | ||||
−0.454835 | + | 0.890576i | \(0.650302\pi\) | |||||||
\(888\) | 91.4512 | 3.06890 | ||||||||
\(889\) | −6.62139 | −0.222074 | ||||||||
\(890\) | 45.8779 | 1.53783 | ||||||||
\(891\) | −30.4191 | −1.01908 | ||||||||
\(892\) | 131.757 | 4.41154 | ||||||||
\(893\) | −2.78299 | −0.0931292 | ||||||||
\(894\) | −5.83531 | −0.195162 | ||||||||
\(895\) | 48.0799 | 1.60714 | ||||||||
\(896\) | −9.91865 | −0.331359 | ||||||||
\(897\) | −30.3490 | −1.01332 | ||||||||
\(898\) | −68.0515 | −2.27091 | ||||||||
\(899\) | 3.79034 | 0.126415 | ||||||||
\(900\) | 18.7346 | 0.624487 | ||||||||
\(901\) | 2.79293 | 0.0930461 | ||||||||
\(902\) | 55.7979 | 1.85787 | ||||||||
\(903\) | 14.6712 | 0.488226 | ||||||||
\(904\) | 8.07124 | 0.268445 | ||||||||
\(905\) | −65.9309 | −2.19162 | ||||||||
\(906\) | 9.01260 | 0.299424 | ||||||||
\(907\) | −7.90802 | −0.262582 | −0.131291 | − | 0.991344i | \(-0.541912\pi\) | ||||
−0.131291 | + | 0.991344i | \(0.541912\pi\) | |||||||
\(908\) | −11.7710 | −0.390635 | ||||||||
\(909\) | 2.71938 | 0.0901963 | ||||||||
\(910\) | 24.8097 | 0.822434 | ||||||||
\(911\) | 49.3470 | 1.63494 | 0.817470 | − | 0.575971i | \(-0.195376\pi\) | ||||
0.817470 | + | 0.575971i | \(0.195376\pi\) | |||||||
\(912\) | −8.51053 | −0.281812 | ||||||||
\(913\) | −16.7263 | −0.553559 | ||||||||
\(914\) | 50.6717 | 1.67607 | ||||||||
\(915\) | 61.3586 | 2.02845 | ||||||||
\(916\) | −68.7624 | −2.27197 | ||||||||
\(917\) | −11.6986 | −0.386322 | ||||||||
\(918\) | −7.17311 | −0.236748 | ||||||||
\(919\) | −0.871430 | −0.0287458 | −0.0143729 | − | 0.999897i | \(-0.504575\pi\) | ||||
−0.0143729 | + | 0.999897i | \(0.504575\pi\) | |||||||
\(920\) | −161.739 | −5.33237 | ||||||||
\(921\) | 6.28214 | 0.207004 | ||||||||
\(922\) | 8.96108 | 0.295117 | ||||||||
\(923\) | 21.5801 | 0.710319 | ||||||||
\(924\) | 25.3462 | 0.833828 | ||||||||
\(925\) | 73.5542 | 2.41845 | ||||||||
\(926\) | −69.0769 | −2.27001 | ||||||||
\(927\) | −0.349989 | −0.0114952 | ||||||||
\(928\) | −15.3977 | −0.505455 | ||||||||
\(929\) | 28.0615 | 0.920667 | 0.460333 | − | 0.887746i | \(-0.347730\pi\) | ||||
0.460333 | + | 0.887746i | \(0.347730\pi\) | |||||||
\(930\) | 28.3046 | 0.928144 | ||||||||
\(931\) | 0.607741 | 0.0199179 | ||||||||
\(932\) | −43.9827 | −1.44070 | ||||||||
\(933\) | −19.5281 | −0.639321 | ||||||||
\(934\) | 68.7013 | 2.24798 | ||||||||
\(935\) | 6.79599 | 0.222253 | ||||||||
\(936\) | −7.00628 | −0.229007 | ||||||||
\(937\) | 30.8453 | 1.00767 | 0.503835 | − | 0.863800i | \(-0.331922\pi\) | ||||
0.503835 | + | 0.863800i | \(0.331922\pi\) | |||||||
\(938\) | 19.5017 | 0.636752 | ||||||||
\(939\) | −4.74361 | −0.154802 | ||||||||
\(940\) | −79.7722 | −2.60188 | ||||||||
\(941\) | 9.87376 | 0.321875 | 0.160938 | − | 0.986965i | \(-0.448548\pi\) | ||||
0.160938 | + | 0.986965i | \(0.448548\pi\) | |||||||
\(942\) | 23.4954 | 0.765523 | ||||||||
\(943\) | −46.9123 | −1.52767 | ||||||||
\(944\) | −17.9360 | −0.583766 | ||||||||
\(945\) | −18.2644 | −0.594142 | ||||||||
\(946\) | −61.1085 | −1.98681 | ||||||||
\(947\) | −9.10722 | −0.295945 | −0.147972 | − | 0.988991i | \(-0.547275\pi\) | ||||
−0.147972 | + | 0.988991i | \(0.547275\pi\) | |||||||
\(948\) | −109.652 | −3.56134 | ||||||||
\(949\) | −24.4182 | −0.792650 | ||||||||
\(950\) | −15.0682 | −0.488879 | ||||||||
\(951\) | 6.61805 | 0.214605 | ||||||||
\(952\) | 3.83095 | 0.124162 | ||||||||
\(953\) | 4.15647 | 0.134641 | 0.0673207 | − | 0.997731i | \(-0.478555\pi\) | ||||
0.0673207 | + | 0.997731i | \(0.478555\pi\) | |||||||
\(954\) | −5.16483 | −0.167218 | ||||||||
\(955\) | 5.53054 | 0.178964 | ||||||||
\(956\) | −86.1329 | −2.78574 | ||||||||
\(957\) | −13.5533 | −0.438117 | ||||||||
\(958\) | −73.9078 | −2.38785 | ||||||||
\(959\) | −3.43535 | −0.110933 | ||||||||
\(960\) | −7.63337 | −0.246366 | ||||||||
\(961\) | −28.5676 | −0.921535 | ||||||||
\(962\) | −49.1250 | −1.58385 | ||||||||
\(963\) | 4.57486 | 0.147423 | ||||||||
\(964\) | 55.5135 | 1.78797 | ||||||||
\(965\) | −33.2124 | −1.06914 | ||||||||
\(966\) | −30.6874 | −0.987351 | ||||||||
\(967\) | −34.7051 | −1.11604 | −0.558020 | − | 0.829827i | \(-0.688439\pi\) | ||||
−0.558020 | + | 0.829827i | \(0.688439\pi\) | |||||||
\(968\) | 12.5022 | 0.401835 | ||||||||
\(969\) | −0.661840 | −0.0212614 | ||||||||
\(970\) | −110.872 | −3.55988 | ||||||||
\(971\) | 17.3111 | 0.555539 | 0.277769 | − | 0.960648i | \(-0.410405\pi\) | ||||
0.277769 | + | 0.960648i | \(0.410405\pi\) | |||||||
\(972\) | 19.9445 | 0.639719 | ||||||||
\(973\) | 9.60680 | 0.307980 | ||||||||
\(974\) | −32.7217 | −1.04847 | ||||||||
\(975\) | −45.3816 | −1.45338 | ||||||||
\(976\) | −65.4452 | −2.09485 | ||||||||
\(977\) | 9.67847 | 0.309642 | 0.154821 | − | 0.987943i | \(-0.450520\pi\) | ||||
0.154821 | + | 0.987943i | \(0.450520\pi\) | |||||||
\(978\) | 16.1278 | 0.515709 | ||||||||
\(979\) | −14.0979 | −0.450571 | ||||||||
\(980\) | 17.4204 | 0.556475 | ||||||||
\(981\) | −0.436078 | −0.0139229 | ||||||||
\(982\) | 1.39809 | 0.0446149 | ||||||||
\(983\) | 20.3636 | 0.649497 | 0.324749 | − | 0.945800i | \(-0.394720\pi\) | ||||
0.324749 | + | 0.945800i | \(0.394720\pi\) | |||||||
\(984\) | −87.2176 | −2.78040 | ||||||||
\(985\) | 5.43693 | 0.173235 | ||||||||
\(986\) | −3.65841 | −0.116508 | ||||||||
\(987\) | −8.47509 | −0.269765 | ||||||||
\(988\) | 6.98843 | 0.222332 | ||||||||
\(989\) | 51.3772 | 1.63370 | ||||||||
\(990\) | −12.5675 | −0.399422 | ||||||||
\(991\) | 61.7469 | 1.96145 | 0.980727 | − | 0.195382i | \(-0.0625947\pi\) | ||||
0.980727 | + | 0.195382i | \(0.0625947\pi\) | |||||||
\(992\) | −9.88140 | −0.313735 | ||||||||
\(993\) | 10.8116 | 0.343096 | ||||||||
\(994\) | 21.8207 | 0.692112 | ||||||||
\(995\) | −24.6838 | −0.782529 | ||||||||
\(996\) | 46.6917 | 1.47948 | ||||||||
\(997\) | −51.8110 | −1.64087 | −0.820436 | − | 0.571739i | \(-0.806269\pi\) | ||||
−0.820436 | + | 0.571739i | \(0.806269\pi\) | |||||||
\(998\) | −64.5449 | −2.04313 | ||||||||
\(999\) | 36.1649 | 1.14421 |
(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 | 6013.2.a.f.1.7 | ✓ | 110 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6013.2.a.f.1.7 | ✓ | 110 | 1.1 | even | 1 | trivial |