Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2216577807\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 2 x^{12} - 19 x^{11} + 35 x^{10} + 136 x^{9} - 220 x^{8} - 469 x^{7} + 610 x^{6} + 841 x^{5} - 760 x^{4} - 742 x^{3} + 366 x^{2} + 236 x - 47 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2013) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.61181\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.61181 | −1.13972 | −0.569860 | − | 0.821742i | \(-0.693003\pi\) | ||||
−0.569860 | + | 0.821742i | \(0.693003\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.597924 | 0.298962 | ||||||||
\(5\) | −4.27930 | −1.91376 | −0.956881 | − | 0.290481i | \(-0.906185\pi\) | ||||
−0.956881 | + | 0.290481i | \(0.906185\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.98799 | 0.751390 | 0.375695 | − | 0.926743i | \(-0.377404\pi\) | ||||
0.375695 | + | 0.926743i | \(0.377404\pi\) | |||||||
\(8\) | 2.25988 | 0.798987 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.89741 | 2.18115 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.250746 | 0.0695444 | 0.0347722 | − | 0.999395i | \(-0.488929\pi\) | ||||
0.0347722 | + | 0.999395i | \(0.488929\pi\) | |||||||
\(14\) | −3.20426 | −0.856374 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.83834 | −1.20958 | ||||||||
\(17\) | −3.17083 | −0.769040 | −0.384520 | − | 0.923117i | \(-0.625633\pi\) | ||||
−0.384520 | + | 0.923117i | \(0.625633\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.76446 | −0.863627 | −0.431814 | − | 0.901963i | \(-0.642126\pi\) | ||||
−0.431814 | + | 0.901963i | \(0.642126\pi\) | |||||||
\(20\) | −2.55870 | −0.572142 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.61181 | 0.343639 | ||||||||
\(23\) | −8.19125 | −1.70799 | −0.853997 | − | 0.520278i | \(-0.825828\pi\) | ||||
−0.853997 | + | 0.520278i | \(0.825828\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13.3124 | 2.66248 | ||||||||
\(26\) | −0.404154 | −0.0792611 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.18867 | 0.224637 | ||||||||
\(29\) | 4.02069 | 0.746623 | 0.373312 | − | 0.927706i | \(-0.378222\pi\) | ||||
0.373312 | + | 0.927706i | \(0.378222\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.98063 | 0.535337 | 0.267669 | − | 0.963511i | \(-0.413747\pi\) | ||||
0.267669 | + | 0.963511i | \(0.413747\pi\) | |||||||
\(32\) | 3.27871 | 0.579600 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.11077 | 0.876490 | ||||||||
\(35\) | −8.50721 | −1.43798 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.39318 | −1.37983 | −0.689916 | − | 0.723890i | \(-0.742352\pi\) | ||||
−0.689916 | + | 0.723890i | \(0.742352\pi\) | |||||||
\(38\) | 6.06759 | 0.984293 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −9.67069 | −1.52907 | ||||||||
\(41\) | 2.30573 | 0.360094 | 0.180047 | − | 0.983658i | \(-0.442375\pi\) | ||||
0.180047 | + | 0.983658i | \(0.442375\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.83567 | 1.19493 | 0.597464 | − | 0.801896i | \(-0.296175\pi\) | ||||
0.597464 | + | 0.801896i | \(0.296175\pi\) | |||||||
\(44\) | −0.597924 | −0.0901405 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 13.2027 | 1.94663 | ||||||||
\(47\) | −0.852827 | −0.124398 | −0.0621988 | − | 0.998064i | \(-0.519811\pi\) | ||||
−0.0621988 | + | 0.998064i | \(0.519811\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.04789 | −0.435413 | ||||||||
\(50\) | −21.4571 | −3.03449 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.149927 | 0.0207911 | ||||||||
\(53\) | 7.07558 | 0.971906 | 0.485953 | − | 0.873985i | \(-0.338473\pi\) | ||||
0.485953 | + | 0.873985i | \(0.338473\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.27930 | 0.577021 | ||||||||
\(56\) | 4.49261 | 0.600351 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.48058 | −0.850942 | ||||||||
\(59\) | −9.77116 | −1.27210 | −0.636048 | − | 0.771649i | \(-0.719432\pi\) | ||||
−0.636048 | + | 0.771649i | \(0.719432\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | −4.80420 | −0.610135 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.39201 | 0.549002 | ||||||||
\(65\) | −1.07302 | −0.133091 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.1758 | −1.60968 | −0.804841 | − | 0.593490i | \(-0.797750\pi\) | ||||
−0.804841 | + | 0.593490i | \(0.797750\pi\) | |||||||
\(68\) | −1.89592 | −0.229914 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 13.7120 | 1.63890 | ||||||||
\(71\) | −2.07157 | −0.245850 | −0.122925 | − | 0.992416i | \(-0.539227\pi\) | ||||
−0.122925 | + | 0.992416i | \(0.539227\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.20929 | −0.141537 | −0.0707686 | − | 0.997493i | \(-0.522545\pi\) | ||||
−0.0707686 | + | 0.997493i | \(0.522545\pi\) | |||||||
\(74\) | 13.5282 | 1.57262 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.25086 | −0.258192 | ||||||||
\(77\) | −1.98799 | −0.226553 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.92819 | 0.329447 | 0.164723 | − | 0.986340i | \(-0.447327\pi\) | ||||
0.164723 | + | 0.986340i | \(0.447327\pi\) | |||||||
\(80\) | 20.7047 | 2.31486 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.71639 | −0.410407 | ||||||||
\(83\) | −12.1817 | −1.33712 | −0.668558 | − | 0.743660i | \(-0.733088\pi\) | ||||
−0.668558 | + | 0.743660i | \(0.733088\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.5689 | 1.47176 | ||||||||
\(86\) | −12.6296 | −1.36188 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.25988 | −0.240904 | ||||||||
\(89\) | 9.78144 | 1.03683 | 0.518415 | − | 0.855129i | \(-0.326522\pi\) | ||||
0.518415 | + | 0.855129i | \(0.326522\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.498480 | 0.0522549 | ||||||||
\(92\) | −4.89775 | −0.510626 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.37459 | 0.141778 | ||||||||
\(95\) | 16.1093 | 1.65278 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.01824 | 0.306456 | 0.153228 | − | 0.988191i | \(-0.451033\pi\) | ||||
0.153228 | + | 0.988191i | \(0.451033\pi\) | |||||||
\(98\) | 4.91261 | 0.496249 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.95982 | 0.795982 | ||||||||
\(101\) | −5.62832 | −0.560039 | −0.280020 | − | 0.959994i | \(-0.590341\pi\) | ||||
−0.280020 | + | 0.959994i | \(0.590341\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.3398 | −1.61001 | −0.805003 | − | 0.593270i | \(-0.797837\pi\) | ||||
−0.805003 | + | 0.593270i | \(0.797837\pi\) | |||||||
\(104\) | 0.566654 | 0.0555650 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.4045 | −1.10770 | ||||||||
\(107\) | −13.4737 | −1.30255 | −0.651276 | − | 0.758841i | \(-0.725766\pi\) | ||||
−0.651276 | + | 0.758841i | \(0.725766\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.5673 | 1.29951 | 0.649757 | − | 0.760142i | \(-0.274871\pi\) | ||||
0.649757 | + | 0.760142i | \(0.274871\pi\) | |||||||
\(110\) | −6.89741 | −0.657642 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −9.61857 | −0.908869 | ||||||||
\(113\) | 0.0631308 | 0.00593884 | 0.00296942 | − | 0.999996i | \(-0.499055\pi\) | ||||
0.00296942 | + | 0.999996i | \(0.499055\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 35.0528 | 3.26869 | ||||||||
\(116\) | 2.40407 | 0.223212 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 15.7492 | 1.44983 | ||||||||
\(119\) | −6.30359 | −0.577849 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.61181 | 0.145926 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.78219 | 0.160046 | ||||||||
\(125\) | −35.5713 | −3.18160 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.04839 | 0.447972 | 0.223986 | − | 0.974592i | \(-0.428093\pi\) | ||||
0.223986 | + | 0.974592i | \(0.428093\pi\) | |||||||
\(128\) | −13.6365 | −1.20531 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.72950 | 0.151687 | ||||||||
\(131\) | −19.1064 | −1.66933 | −0.834665 | − | 0.550757i | \(-0.814339\pi\) | ||||
−0.834665 | + | 0.550757i | \(0.814339\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.48372 | −0.648921 | ||||||||
\(134\) | 21.2369 | 1.83459 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.16569 | −0.614453 | ||||||||
\(137\) | 8.39986 | 0.717649 | 0.358824 | − | 0.933405i | \(-0.383178\pi\) | ||||
0.358824 | + | 0.933405i | \(0.383178\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.05747 | 0.598607 | 0.299303 | − | 0.954158i | \(-0.403246\pi\) | ||||
0.299303 | + | 0.954158i | \(0.403246\pi\) | |||||||
\(140\) | −5.08667 | −0.429902 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.33897 | 0.280200 | ||||||||
\(143\) | −0.250746 | −0.0209684 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −17.2057 | −1.42886 | ||||||||
\(146\) | 1.94915 | 0.161313 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.01849 | −0.412517 | ||||||||
\(149\) | 19.9863 | 1.63734 | 0.818672 | − | 0.574262i | \(-0.194711\pi\) | ||||
0.818672 | + | 0.574262i | \(0.194711\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.0434 | −1.22421 | −0.612107 | − | 0.790775i | \(-0.709678\pi\) | ||||
−0.612107 | + | 0.790775i | \(0.709678\pi\) | |||||||
\(152\) | −8.50722 | −0.690027 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.20426 | 0.258207 | ||||||||
\(155\) | −12.7550 | −1.02451 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.2863 | −1.14017 | −0.570086 | − | 0.821585i | \(-0.693090\pi\) | ||||
−0.570086 | + | 0.821585i | \(0.693090\pi\) | |||||||
\(158\) | −4.71967 | −0.375477 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −14.0306 | −1.10922 | ||||||||
\(161\) | −16.2841 | −1.28337 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.0009 | −0.939983 | −0.469991 | − | 0.882671i | \(-0.655743\pi\) | ||||
−0.469991 | + | 0.882671i | \(0.655743\pi\) | |||||||
\(164\) | 1.37865 | 0.107655 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 19.6346 | 1.52394 | ||||||||
\(167\) | 17.9733 | 1.39082 | 0.695408 | − | 0.718615i | \(-0.255224\pi\) | ||||
0.695408 | + | 0.718615i | \(0.255224\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9371 | −0.995164 | ||||||||
\(170\) | −21.8705 | −1.67739 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.68514 | 0.357238 | ||||||||
\(173\) | 5.97151 | 0.454006 | 0.227003 | − | 0.973894i | \(-0.427107\pi\) | ||||
0.227003 | + | 0.973894i | \(0.427107\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 26.4650 | 2.00056 | ||||||||
\(176\) | 4.83834 | 0.364703 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −15.7658 | −1.18170 | ||||||||
\(179\) | −22.5218 | −1.68336 | −0.841678 | − | 0.539980i | \(-0.818432\pi\) | ||||
−0.841678 | + | 0.539980i | \(0.818432\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.7687 | −1.24641 | −0.623205 | − | 0.782058i | \(-0.714170\pi\) | ||||
−0.623205 | + | 0.782058i | \(0.714170\pi\) | |||||||
\(182\) | −0.803455 | −0.0595560 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −18.5112 | −1.36466 | ||||||||
\(185\) | 35.9170 | 2.64067 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.17083 | 0.231874 | ||||||||
\(188\) | −0.509926 | −0.0371902 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −25.9651 | −1.88370 | ||||||||
\(191\) | −23.1333 | −1.67386 | −0.836932 | − | 0.547307i | \(-0.815653\pi\) | ||||
−0.836932 | + | 0.547307i | \(0.815653\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.54885 | 0.111489 | 0.0557443 | − | 0.998445i | \(-0.482247\pi\) | ||||
0.0557443 | + | 0.998445i | \(0.482247\pi\) | |||||||
\(194\) | −4.86482 | −0.349274 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.82241 | −0.130172 | ||||||||
\(197\) | 3.90674 | 0.278344 | 0.139172 | − | 0.990268i | \(-0.455556\pi\) | ||||
0.139172 | + | 0.990268i | \(0.455556\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.2931 | −0.800544 | −0.400272 | − | 0.916396i | \(-0.631084\pi\) | ||||
−0.400272 | + | 0.916396i | \(0.631084\pi\) | |||||||
\(200\) | 30.0844 | 2.12729 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.07178 | 0.638288 | ||||||||
\(203\) | 7.99309 | 0.561005 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.86690 | −0.689134 | ||||||||
\(206\) | 26.3366 | 1.83496 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.21319 | −0.0841197 | ||||||||
\(209\) | 3.76446 | 0.260393 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.2658 | 1.18863 | 0.594314 | − | 0.804233i | \(-0.297424\pi\) | ||||
0.594314 | + | 0.804233i | \(0.297424\pi\) | |||||||
\(212\) | 4.23066 | 0.290563 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 21.7170 | 1.48454 | ||||||||
\(215\) | −33.5312 | −2.28681 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.92547 | 0.402247 | ||||||||
\(218\) | −21.8679 | −1.48108 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.55870 | 0.172507 | ||||||||
\(221\) | −0.795073 | −0.0534824 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −28.3241 | −1.89672 | −0.948362 | − | 0.317191i | \(-0.897260\pi\) | ||||
−0.948362 | + | 0.317191i | \(0.897260\pi\) | |||||||
\(224\) | 6.51805 | 0.435506 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.101755 | −0.00676862 | ||||||||
\(227\) | 14.3403 | 0.951800 | 0.475900 | − | 0.879500i | \(-0.342123\pi\) | ||||
0.475900 | + | 0.879500i | \(0.342123\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.21589 | −0.609003 | −0.304502 | − | 0.952512i | \(-0.598490\pi\) | ||||
−0.304502 | + | 0.952512i | \(0.598490\pi\) | |||||||
\(230\) | −56.4984 | −3.72540 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.08626 | 0.596542 | ||||||||
\(233\) | 25.2945 | 1.65710 | 0.828550 | − | 0.559915i | \(-0.189166\pi\) | ||||
0.828550 | + | 0.559915i | \(0.189166\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.64950 | 0.238067 | ||||||||
\(236\) | −5.84241 | −0.380309 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 10.1602 | 0.658586 | ||||||||
\(239\) | 19.2893 | 1.24772 | 0.623860 | − | 0.781536i | \(-0.285563\pi\) | ||||
0.623860 | + | 0.781536i | \(0.285563\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.4108 | 0.799448 | 0.399724 | − | 0.916636i | \(-0.369106\pi\) | ||||
0.399724 | + | 0.916636i | \(0.369106\pi\) | |||||||
\(242\) | −1.61181 | −0.103611 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.597924 | −0.0382782 | ||||||||
\(245\) | 13.0428 | 0.833277 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.943924 | −0.0600604 | ||||||||
\(248\) | 6.73586 | 0.427727 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 57.3342 | 3.62613 | ||||||||
\(251\) | 13.9303 | 0.879270 | 0.439635 | − | 0.898176i | \(-0.355108\pi\) | ||||
0.439635 | + | 0.898176i | \(0.355108\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.19125 | 0.514979 | ||||||||
\(254\) | −8.13703 | −0.510562 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.1954 | 0.824713 | ||||||||
\(257\) | 8.15779 | 0.508869 | 0.254434 | − | 0.967090i | \(-0.418111\pi\) | ||||
0.254434 | + | 0.967090i | \(0.418111\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.6856 | −1.03679 | ||||||||
\(260\) | −0.641583 | −0.0397893 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 30.7958 | 1.90257 | ||||||||
\(263\) | 16.6378 | 1.02593 | 0.512966 | − | 0.858409i | \(-0.328547\pi\) | ||||
0.512966 | + | 0.858409i | \(0.328547\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −30.2785 | −1.86000 | ||||||||
\(266\) | 12.0623 | 0.739588 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.87815 | −0.481234 | ||||||||
\(269\) | −1.23389 | −0.0752315 | −0.0376158 | − | 0.999292i | \(-0.511976\pi\) | ||||
−0.0376158 | + | 0.999292i | \(0.511976\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.48114 | 0.272210 | 0.136105 | − | 0.990694i | \(-0.456542\pi\) | ||||
0.136105 | + | 0.990694i | \(0.456542\pi\) | |||||||
\(272\) | 15.3415 | 0.930218 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.5390 | −0.817919 | ||||||||
\(275\) | −13.3124 | −0.802769 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.3235 | 1.34129 | 0.670644 | − | 0.741779i | \(-0.266018\pi\) | ||||
0.670644 | + | 0.741779i | \(0.266018\pi\) | |||||||
\(278\) | −11.3753 | −0.682244 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −19.2252 | −1.14893 | ||||||||
\(281\) | −1.20667 | −0.0719840 | −0.0359920 | − | 0.999352i | \(-0.511459\pi\) | ||||
−0.0359920 | + | 0.999352i | \(0.511459\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.8779 | −0.765509 | −0.382755 | − | 0.923850i | \(-0.625025\pi\) | ||||
−0.382755 | + | 0.923850i | \(0.625025\pi\) | |||||||
\(284\) | −1.23864 | −0.0734997 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.404154 | 0.0238981 | ||||||||
\(287\) | 4.58377 | 0.270571 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.94583 | −0.408578 | ||||||||
\(290\) | 27.7323 | 1.62850 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.723066 | −0.0423142 | ||||||||
\(293\) | −3.55779 | −0.207848 | −0.103924 | − | 0.994585i | \(-0.533140\pi\) | ||||
−0.103924 | + | 0.994585i | \(0.533140\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 41.8137 | 2.43449 | ||||||||
\(296\) | −18.9676 | −1.10247 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −32.2141 | −1.86611 | ||||||||
\(299\) | −2.05392 | −0.118781 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.5772 | 0.897857 | ||||||||
\(302\) | 24.2471 | 1.39526 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 18.2137 | 1.04463 | ||||||||
\(305\) | 4.27930 | 0.245032 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.7013 | 0.896118 | 0.448059 | − | 0.894004i | \(-0.352115\pi\) | ||||
0.448059 | + | 0.894004i | \(0.352115\pi\) | |||||||
\(308\) | −1.18867 | −0.0677307 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 20.5586 | 1.16765 | ||||||||
\(311\) | 20.3629 | 1.15467 | 0.577336 | − | 0.816507i | \(-0.304092\pi\) | ||||
0.577336 | + | 0.816507i | \(0.304092\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.37471 | 0.303797 | 0.151898 | − | 0.988396i | \(-0.451461\pi\) | ||||
0.151898 | + | 0.988396i | \(0.451461\pi\) | |||||||
\(314\) | 23.0268 | 1.29948 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.75083 | 0.0984921 | ||||||||
\(317\) | 3.60000 | 0.202196 | 0.101098 | − | 0.994876i | \(-0.467764\pi\) | ||||
0.101098 | + | 0.994876i | \(0.467764\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.02069 | −0.225115 | ||||||||
\(320\) | −18.7948 | −1.05066 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 26.2469 | 1.46268 | ||||||||
\(323\) | 11.9365 | 0.664164 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.33803 | 0.185161 | ||||||||
\(326\) | 19.3431 | 1.07132 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.21066 | 0.287710 | ||||||||
\(329\) | −1.69541 | −0.0934711 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 35.9801 | 1.97765 | 0.988823 | − | 0.149092i | \(-0.0476351\pi\) | ||||
0.988823 | + | 0.149092i | \(0.0476351\pi\) | |||||||
\(332\) | −7.28374 | −0.399747 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −28.9695 | −1.58514 | ||||||||
\(335\) | 56.3833 | 3.08055 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.79883 | 0.261409 | 0.130704 | − | 0.991421i | \(-0.458276\pi\) | ||||
0.130704 | + | 0.991421i | \(0.458276\pi\) | |||||||
\(338\) | 20.8522 | 1.13421 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8.11320 | 0.440000 | ||||||||
\(341\) | −2.98063 | −0.161410 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.9751 | −1.07856 | ||||||||
\(344\) | 17.7076 | 0.954732 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.62493 | −0.517439 | ||||||||
\(347\) | −3.83919 | −0.206099 | −0.103049 | − | 0.994676i | \(-0.532860\pi\) | ||||
−0.103049 | + | 0.994676i | \(0.532860\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.105346 | 0.00563902 | 0.00281951 | − | 0.999996i | \(-0.499103\pi\) | ||||
0.00281951 | + | 0.999996i | \(0.499103\pi\) | |||||||
\(350\) | −42.6564 | −2.28008 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.27871 | −0.174756 | ||||||||
\(353\) | 34.3508 | 1.82831 | 0.914155 | − | 0.405364i | \(-0.132855\pi\) | ||||
0.914155 | + | 0.405364i | \(0.132855\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.86485 | 0.470497 | ||||||||
\(356\) | 5.84856 | 0.309973 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 36.3007 | 1.91855 | ||||||||
\(359\) | 13.8877 | 0.732965 | 0.366483 | − | 0.930425i | \(-0.380562\pi\) | ||||
0.366483 | + | 0.930425i | \(0.380562\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.82881 | −0.254148 | ||||||||
\(362\) | 27.0280 | 1.42056 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.298054 | 0.0156223 | ||||||||
\(365\) | 5.17493 | 0.270868 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.2286 | −0.638330 | −0.319165 | − | 0.947699i | \(-0.603402\pi\) | ||||
−0.319165 | + | 0.947699i | \(0.603402\pi\) | |||||||
\(368\) | 39.6320 | 2.06596 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −57.8912 | −3.00962 | ||||||||
\(371\) | 14.0662 | 0.730280 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.3245 | 1.25948 | 0.629738 | − | 0.776808i | \(-0.283162\pi\) | ||||
0.629738 | + | 0.776808i | \(0.283162\pi\) | |||||||
\(374\) | −5.11077 | −0.264272 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.92728 | −0.0993921 | ||||||||
\(377\) | 1.00817 | 0.0519234 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.33650 | 0.120018 | 0.0600090 | − | 0.998198i | \(-0.480887\pi\) | ||||
0.0600090 | + | 0.998198i | \(0.480887\pi\) | |||||||
\(380\) | 9.63213 | 0.494118 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 37.2864 | 1.90774 | ||||||||
\(383\) | 29.8315 | 1.52432 | 0.762160 | − | 0.647389i | \(-0.224139\pi\) | ||||
0.762160 | + | 0.647389i | \(0.224139\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.50721 | 0.433568 | ||||||||
\(386\) | −2.49645 | −0.127066 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.80468 | 0.0916187 | ||||||||
\(389\) | −4.92145 | −0.249528 | −0.124764 | − | 0.992186i | \(-0.539817\pi\) | ||||
−0.124764 | + | 0.992186i | \(0.539817\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.9731 | 1.31351 | ||||||||
\(392\) | −6.88786 | −0.347889 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.29692 | −0.317234 | ||||||||
\(395\) | −12.5306 | −0.630482 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.06135 | −0.254022 | −0.127011 | − | 0.991901i | \(-0.540538\pi\) | ||||
−0.127011 | + | 0.991901i | \(0.540538\pi\) | |||||||
\(398\) | 18.2023 | 0.912396 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −64.4099 | −3.22050 | ||||||||
\(401\) | −1.55341 | −0.0775736 | −0.0387868 | − | 0.999248i | \(-0.512349\pi\) | ||||
−0.0387868 | + | 0.999248i | \(0.512349\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.747381 | 0.0372297 | ||||||||
\(404\) | −3.36531 | −0.167431 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.8833 | −0.639389 | ||||||||
\(407\) | 8.39318 | 0.416035 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.42819 | −0.416747 | −0.208373 | − | 0.978049i | \(-0.566817\pi\) | ||||
−0.208373 | + | 0.978049i | \(0.566817\pi\) | |||||||
\(410\) | 15.9035 | 0.785420 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.76995 | −0.481331 | ||||||||
\(413\) | −19.4250 | −0.955841 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 52.1292 | 2.55892 | ||||||||
\(416\) | 0.822124 | 0.0403079 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.06759 | −0.296776 | ||||||||
\(419\) | 32.6335 | 1.59425 | 0.797125 | − | 0.603814i | \(-0.206353\pi\) | ||||
0.797125 | + | 0.603814i | \(0.206353\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.65215 | −0.275469 | −0.137735 | − | 0.990469i | \(-0.543982\pi\) | ||||
−0.137735 | + | 0.990469i | \(0.543982\pi\) | |||||||
\(422\) | −27.8292 | −1.35470 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 15.9899 | 0.776540 | ||||||||
\(425\) | −42.2114 | −2.04756 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.98799 | −0.0962056 | ||||||||
\(428\) | −8.05625 | −0.389414 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 54.0458 | 2.60632 | ||||||||
\(431\) | 23.6079 | 1.13715 | 0.568576 | − | 0.822631i | \(-0.307495\pi\) | ||||
0.568576 | + | 0.822631i | \(0.307495\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.9983 | 0.576600 | 0.288300 | − | 0.957540i | \(-0.406910\pi\) | ||||
0.288300 | + | 0.957540i | \(0.406910\pi\) | |||||||
\(434\) | −9.55072 | −0.458449 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.11223 | 0.388505 | ||||||||
\(437\) | 30.8357 | 1.47507 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.34054 | −0.445799 | −0.222900 | − | 0.974841i | \(-0.571552\pi\) | ||||
−0.222900 | + | 0.974841i | \(0.571552\pi\) | |||||||
\(440\) | 9.67069 | 0.461032 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.28150 | 0.0609550 | ||||||||
\(443\) | −26.2123 | −1.24538 | −0.622692 | − | 0.782467i | \(-0.713961\pi\) | ||||
−0.622692 | + | 0.782467i | \(0.713961\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −41.8577 | −1.98425 | ||||||||
\(446\) | 45.6530 | 2.16173 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.73129 | 0.412514 | ||||||||
\(449\) | 11.4987 | 0.542658 | 0.271329 | − | 0.962487i | \(-0.412537\pi\) | ||||
0.271329 | + | 0.962487i | \(0.412537\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.30573 | −0.108572 | ||||||||
\(452\) | 0.0377474 | 0.00177549 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −23.1138 | −1.08479 | ||||||||
\(455\) | −2.13315 | −0.100004 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.8251 | 1.62905 | 0.814525 | − | 0.580128i | \(-0.196997\pi\) | ||||
0.814525 | + | 0.580128i | \(0.196997\pi\) | |||||||
\(458\) | 14.8543 | 0.694094 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 20.9589 | 0.977216 | ||||||||
\(461\) | −30.9884 | −1.44327 | −0.721637 | − | 0.692272i | \(-0.756610\pi\) | ||||
−0.721637 | + | 0.692272i | \(0.756610\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.65194 | −0.169720 | −0.0848599 | − | 0.996393i | \(-0.527044\pi\) | ||||
−0.0848599 | + | 0.996393i | \(0.527044\pi\) | |||||||
\(464\) | −19.4534 | −0.903103 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −40.7699 | −1.88863 | ||||||||
\(467\) | −33.6723 | −1.55817 | −0.779084 | − | 0.626920i | \(-0.784315\pi\) | ||||
−0.779084 | + | 0.626920i | \(0.784315\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −26.1934 | −1.20950 | ||||||||
\(470\) | −5.88230 | −0.271330 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −22.0816 | −1.01639 | ||||||||
\(473\) | −7.83567 | −0.360284 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −50.1141 | −2.29939 | ||||||||
\(476\) | −3.76907 | −0.172755 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −31.0906 | −1.42205 | ||||||||
\(479\) | 0.0546621 | 0.00249757 | 0.00124879 | − | 0.999999i | \(-0.499602\pi\) | ||||
0.00124879 | + | 0.999999i | \(0.499602\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.10456 | −0.0959595 | ||||||||
\(482\) | −20.0038 | −0.911147 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.597924 | 0.0271784 | ||||||||
\(485\) | −12.9160 | −0.586484 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.1791 | 0.733145 | 0.366573 | − | 0.930389i | \(-0.380531\pi\) | ||||
0.366573 | + | 0.930389i | \(0.380531\pi\) | |||||||
\(488\) | −2.25988 | −0.102300 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −21.0226 | −0.949702 | ||||||||
\(491\) | 0.996030 | 0.0449502 | 0.0224751 | − | 0.999747i | \(-0.492845\pi\) | ||||
0.0224751 | + | 0.999747i | \(0.492845\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.7489 | −0.574183 | ||||||||
\(494\) | 1.52142 | 0.0684521 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.4213 | −0.647535 | ||||||||
\(497\) | −4.11825 | −0.184729 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.3156 | −1.31235 | −0.656173 | − | 0.754610i | \(-0.727826\pi\) | ||||
−0.656173 | + | 0.754610i | \(0.727826\pi\) | |||||||
\(500\) | −21.2690 | −0.951177 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −22.4529 | −1.00212 | ||||||||
\(503\) | −19.9254 | −0.888431 | −0.444216 | − | 0.895920i | \(-0.646518\pi\) | ||||
−0.444216 | + | 0.895920i | \(0.646518\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.0853 | 1.07178 | ||||||||
\(506\) | −13.2027 | −0.586933 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.01855 | 0.133927 | ||||||||
\(509\) | 32.0673 | 1.42136 | 0.710679 | − | 0.703516i | \(-0.248388\pi\) | ||||
0.710679 | + | 0.703516i | \(0.248388\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.40407 | −0.106350 | ||||||||
\(512\) | 6.00456 | 0.265367 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −13.1488 | −0.579968 | ||||||||
\(515\) | 69.9228 | 3.08117 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.852827 | 0.0375073 | ||||||||
\(518\) | 26.8939 | 1.18165 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.42489 | −0.106338 | ||||||||
\(521\) | −11.7487 | −0.514719 | −0.257360 | − | 0.966316i | \(-0.582852\pi\) | ||||
−0.257360 | + | 0.966316i | \(0.582852\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.66102 | 0.334993 | 0.167497 | − | 0.985873i | \(-0.446432\pi\) | ||||
0.167497 | + | 0.985873i | \(0.446432\pi\) | |||||||
\(524\) | −11.4242 | −0.499067 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −26.8170 | −1.16928 | ||||||||
\(527\) | −9.45108 | −0.411696 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 44.0966 | 1.91724 | ||||||||
\(530\) | 48.8032 | 2.11988 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.47470 | −0.194003 | ||||||||
\(533\) | 0.578151 | 0.0250425 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 57.6580 | 2.49277 | ||||||||
\(536\) | −29.7757 | −1.28612 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.98879 | 0.0857429 | ||||||||
\(539\) | 3.04789 | 0.131282 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.4982 | −0.881286 | −0.440643 | − | 0.897682i | \(-0.645250\pi\) | ||||
−0.440643 | + | 0.897682i | \(0.645250\pi\) | |||||||
\(542\) | −7.22274 | −0.310243 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −10.3962 | −0.445736 | ||||||||
\(545\) | −58.0586 | −2.48696 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.0674 | −0.644234 | −0.322117 | − | 0.946700i | \(-0.604394\pi\) | ||||
−0.322117 | + | 0.946700i | \(0.604394\pi\) | |||||||
\(548\) | 5.02248 | 0.214550 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 21.4571 | 0.914932 | ||||||||
\(551\) | −15.1357 | −0.644804 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.82121 | 0.247543 | ||||||||
\(554\) | −35.9812 | −1.52869 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.21983 | 0.178961 | ||||||||
\(557\) | −22.0552 | −0.934508 | −0.467254 | − | 0.884123i | \(-0.654757\pi\) | ||||
−0.467254 | + | 0.884123i | \(0.654757\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.96476 | 0.0831005 | ||||||||
\(560\) | 41.1607 | 1.73936 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.94492 | 0.0820417 | ||||||||
\(563\) | 16.2194 | 0.683566 | 0.341783 | − | 0.939779i | \(-0.388969\pi\) | ||||
0.341783 | + | 0.939779i | \(0.388969\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.270156 | −0.0113655 | ||||||||
\(566\) | 20.7566 | 0.872466 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.68148 | −0.196431 | ||||||||
\(569\) | 35.7962 | 1.50065 | 0.750326 | − | 0.661068i | \(-0.229896\pi\) | ||||
0.750326 | + | 0.661068i | \(0.229896\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.2967 | −0.556450 | −0.278225 | − | 0.960516i | \(-0.589746\pi\) | ||||
−0.278225 | + | 0.960516i | \(0.589746\pi\) | |||||||
\(572\) | −0.149927 | −0.00626876 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7.38815 | −0.308375 | ||||||||
\(575\) | −109.045 | −4.54751 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.2277 | −0.800462 | −0.400231 | − | 0.916414i | \(-0.631070\pi\) | ||||
−0.400231 | + | 0.916414i | \(0.631070\pi\) | |||||||
\(578\) | 11.1953 | 0.465665 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −10.2877 | −0.427175 | ||||||||
\(581\) | −24.2171 | −1.00470 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.07558 | −0.293041 | ||||||||
\(584\) | −2.73285 | −0.113086 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.73447 | 0.236889 | ||||||||
\(587\) | −5.61715 | −0.231845 | −0.115922 | − | 0.993258i | \(-0.536982\pi\) | ||||
−0.115922 | + | 0.993258i | \(0.536982\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.2205 | −0.462332 | ||||||||
\(590\) | −67.3957 | −2.77464 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 40.6090 | 1.66902 | ||||||||
\(593\) | −18.0517 | −0.741295 | −0.370648 | − | 0.928774i | \(-0.620864\pi\) | ||||
−0.370648 | + | 0.928774i | \(0.620864\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 26.9749 | 1.10586 | ||||||||
\(596\) | 11.9503 | 0.489504 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.31053 | 0.135378 | ||||||||
\(599\) | −0.631254 | −0.0257923 | −0.0128962 | − | 0.999917i | \(-0.504105\pi\) | ||||
−0.0128962 | + | 0.999917i | \(0.504105\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.3195 | 0.869641 | 0.434820 | − | 0.900517i | \(-0.356812\pi\) | ||||
0.434820 | + | 0.900517i | \(0.356812\pi\) | |||||||
\(602\) | −25.1075 | −1.02331 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.99481 | −0.365994 | ||||||||
\(605\) | −4.27930 | −0.173978 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.8171 | 1.61613 | 0.808063 | − | 0.589096i | \(-0.200516\pi\) | ||||
0.808063 | + | 0.589096i | \(0.200516\pi\) | |||||||
\(608\) | −12.3426 | −0.500559 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.89741 | −0.279268 | ||||||||
\(611\) | −0.213843 | −0.00865115 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 43.2039 | 1.74499 | 0.872494 | − | 0.488624i | \(-0.162501\pi\) | ||||
0.872494 | + | 0.488624i | \(0.162501\pi\) | |||||||
\(614\) | −25.3074 | −1.02132 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.49261 | −0.181013 | ||||||||
\(617\) | −3.91242 | −0.157508 | −0.0787540 | − | 0.996894i | \(-0.525094\pi\) | ||||
−0.0787540 | + | 0.996894i | \(0.525094\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.0600 | 0.967051 | 0.483526 | − | 0.875330i | \(-0.339356\pi\) | ||||
0.483526 | + | 0.875330i | \(0.339356\pi\) | |||||||
\(620\) | −7.62654 | −0.306289 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −32.8210 | −1.31600 | ||||||||
\(623\) | 19.4454 | 0.779064 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 85.6584 | 3.42633 | ||||||||
\(626\) | −8.66301 | −0.346243 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.54213 | −0.340868 | ||||||||
\(629\) | 26.6134 | 1.06114 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.3657 | −1.40789 | −0.703943 | − | 0.710256i | \(-0.748579\pi\) | ||||
−0.703943 | + | 0.710256i | \(0.748579\pi\) | |||||||
\(632\) | 6.61734 | 0.263224 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.80251 | −0.230447 | ||||||||
\(635\) | −21.6036 | −0.857311 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.764246 | −0.0302805 | ||||||||
\(638\) | 6.48058 | 0.256569 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 58.3547 | 2.30667 | ||||||||
\(641\) | 10.9245 | 0.431493 | 0.215747 | − | 0.976449i | \(-0.430781\pi\) | ||||
0.215747 | + | 0.976449i | \(0.430781\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 46.6869 | 1.84115 | 0.920576 | − | 0.390564i | \(-0.127720\pi\) | ||||
0.920576 | + | 0.390564i | \(0.127720\pi\) | |||||||
\(644\) | −9.73668 | −0.383679 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −19.2393 | −0.756961 | ||||||||
\(647\) | −22.9120 | −0.900764 | −0.450382 | − | 0.892836i | \(-0.648712\pi\) | ||||
−0.450382 | + | 0.892836i | \(0.648712\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.77116 | 0.383551 | ||||||||
\(650\) | −5.38027 | −0.211031 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.17563 | −0.281019 | ||||||||
\(653\) | 6.74465 | 0.263938 | 0.131969 | − | 0.991254i | \(-0.457870\pi\) | ||||
0.131969 | + | 0.991254i | \(0.457870\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 81.7619 | 3.19470 | ||||||||
\(656\) | −11.1559 | −0.435564 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.73268 | 0.106531 | ||||||||
\(659\) | 37.7263 | 1.46961 | 0.734805 | − | 0.678279i | \(-0.237274\pi\) | ||||
0.734805 | + | 0.678279i | \(0.237274\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.7549 | 1.58518 | 0.792591 | − | 0.609754i | \(-0.208732\pi\) | ||||
0.792591 | + | 0.609754i | \(0.208732\pi\) | |||||||
\(662\) | −57.9930 | −2.25396 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −27.5291 | −1.06834 | ||||||||
\(665\) | 32.0251 | 1.24188 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −32.9345 | −1.27523 | ||||||||
\(668\) | 10.7467 | 0.415801 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −90.8791 | −3.51096 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.5148 | −0.867882 | −0.433941 | − | 0.900941i | \(-0.642877\pi\) | ||||
−0.433941 | + | 0.900941i | \(0.642877\pi\) | |||||||
\(674\) | −7.73479 | −0.297933 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.73542 | −0.297516 | ||||||||
\(677\) | 0.489159 | 0.0187999 | 0.00939995 | − | 0.999956i | \(-0.497008\pi\) | ||||
0.00939995 | + | 0.999956i | \(0.497008\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.00024 | 0.230268 | ||||||||
\(680\) | 30.6641 | 1.17592 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.80420 | 0.183963 | ||||||||
\(683\) | 6.05286 | 0.231606 | 0.115803 | − | 0.993272i | \(-0.463056\pi\) | ||||
0.115803 | + | 0.993272i | \(0.463056\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −35.9455 | −1.37341 | ||||||||
\(686\) | 32.1961 | 1.22925 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −37.9116 | −1.44537 | ||||||||
\(689\) | 1.77417 | 0.0675906 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.2515 | 1.68341 | 0.841704 | − | 0.539939i | \(-0.181553\pi\) | ||||
0.841704 | + | 0.539939i | \(0.181553\pi\) | |||||||
\(692\) | 3.57051 | 0.135730 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.18804 | 0.234895 | ||||||||
\(695\) | −30.2010 | −1.14559 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.31107 | −0.276927 | ||||||||
\(698\) | −0.169797 | −0.00642691 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 15.8240 | 0.598093 | ||||||||
\(701\) | 46.3230 | 1.74960 | 0.874798 | − | 0.484488i | \(-0.160994\pi\) | ||||
0.874798 | + | 0.484488i | \(0.160994\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.5958 | 1.19166 | ||||||||
\(704\) | −4.39201 | −0.165530 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −55.3670 | −2.08376 | ||||||||
\(707\) | −11.1891 | −0.420808 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.4425 | −0.542401 | −0.271201 | − | 0.962523i | \(-0.587421\pi\) | ||||
−0.271201 | + | 0.962523i | \(0.587421\pi\) | |||||||
\(710\) | −14.2884 | −0.536235 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 22.1049 | 0.828414 | ||||||||
\(713\) | −24.4151 | −0.914353 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.07302 | 0.0401286 | ||||||||
\(716\) | −13.4663 | −0.503260 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −22.3843 | −0.835375 | ||||||||
\(719\) | 24.6340 | 0.918693 | 0.459346 | − | 0.888257i | \(-0.348084\pi\) | ||||
0.459346 | + | 0.888257i | \(0.348084\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.4833 | −1.20974 | ||||||||
\(722\) | 7.78311 | 0.289658 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10.0264 | −0.372630 | ||||||||
\(725\) | 53.5251 | 1.98787 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.6426 | 1.32191 | 0.660956 | − | 0.750425i | \(-0.270151\pi\) | ||||
0.660956 | + | 0.750425i | \(0.270151\pi\) | |||||||
\(728\) | 1.12650 | 0.0417510 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.34100 | −0.308714 | ||||||||
\(731\) | −24.8456 | −0.918947 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.8831 | 0.549720 | 0.274860 | − | 0.961484i | \(-0.411369\pi\) | ||||
0.274860 | + | 0.961484i | \(0.411369\pi\) | |||||||
\(734\) | 19.7102 | 0.727518 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −26.8568 | −0.989953 | ||||||||
\(737\) | 13.1758 | 0.485338 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.9543 | −0.550104 | −0.275052 | − | 0.961429i | \(-0.588695\pi\) | ||||
−0.275052 | + | 0.961429i | \(0.588695\pi\) | |||||||
\(740\) | 21.4756 | 0.789460 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −22.6720 | −0.832315 | ||||||||
\(743\) | 17.4486 | 0.640126 | 0.320063 | − | 0.947396i | \(-0.396296\pi\) | ||||
0.320063 | + | 0.947396i | \(0.396296\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −85.5275 | −3.13348 | ||||||||
\(746\) | −39.2064 | −1.43545 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.89592 | 0.0693216 | ||||||||
\(749\) | −26.7856 | −0.978724 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.2302 | 0.774700 | 0.387350 | − | 0.921933i | \(-0.373390\pi\) | ||||
0.387350 | + | 0.921933i | \(0.373390\pi\) | |||||||
\(752\) | 4.12626 | 0.150469 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.62498 | −0.0591782 | ||||||||
\(755\) | 64.3752 | 2.34285 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.8953 | 1.45002 | 0.725010 | − | 0.688739i | \(-0.241835\pi\) | ||||
0.725010 | + | 0.688739i | \(0.241835\pi\) | |||||||
\(758\) | −3.76599 | −0.136787 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 36.4050 | 1.32055 | ||||||||
\(761\) | −24.3669 | −0.883301 | −0.441651 | − | 0.897187i | \(-0.645607\pi\) | ||||
−0.441651 | + | 0.897187i | \(0.645607\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 26.9717 | 0.976441 | ||||||||
\(764\) | −13.8319 | −0.500422 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −48.0827 | −1.73730 | ||||||||
\(767\) | −2.45008 | −0.0884671 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.9871 | 0.612572 | 0.306286 | − | 0.951940i | \(-0.400914\pi\) | ||||
0.306286 | + | 0.951940i | \(0.400914\pi\) | |||||||
\(770\) | −13.7120 | −0.494146 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.926094 | 0.0333309 | ||||||||
\(773\) | −50.0956 | −1.80181 | −0.900907 | − | 0.434012i | \(-0.857097\pi\) | ||||
−0.900907 | + | 0.434012i | \(0.857097\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 39.6794 | 1.42533 | ||||||||
\(776\) | 6.82085 | 0.244854 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.93244 | 0.284392 | ||||||||
\(779\) | −8.67983 | −0.310987 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.07157 | 0.0741264 | ||||||||
\(782\) | −41.8636 | −1.49704 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 14.7467 | 0.526669 | ||||||||
\(785\) | 61.1354 | 2.18202 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.7557 | −1.38149 | −0.690746 | − | 0.723098i | \(-0.742718\pi\) | ||||
−0.690746 | + | 0.723098i | \(0.742718\pi\) | |||||||
\(788\) | 2.33594 | 0.0832143 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 20.1969 | 0.718573 | ||||||||
\(791\) | 0.125503 | 0.00446239 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.250746 | −0.00890424 | ||||||||
\(794\) | 8.15792 | 0.289514 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.75240 | −0.239332 | ||||||||
\(797\) | −44.4888 | −1.57588 | −0.787938 | − | 0.615755i | \(-0.788851\pi\) | ||||
−0.787938 | + | 0.615755i | \(0.788851\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.70417 | 0.0956667 | ||||||||
\(800\) | 43.6476 | 1.54318 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.50380 | 0.0884122 | ||||||||
\(803\) | 1.20929 | 0.0426750 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 69.6847 | 2.45606 | ||||||||
\(806\) | −1.20463 | −0.0424314 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −12.7193 | −0.447464 | ||||||||
\(809\) | 38.6506 | 1.35888 | 0.679442 | − | 0.733729i | \(-0.262222\pi\) | ||||
0.679442 | + | 0.733729i | \(0.262222\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.9320 | 0.699906 | 0.349953 | − | 0.936767i | \(-0.386198\pi\) | ||||
0.349953 | + | 0.936767i | \(0.386198\pi\) | |||||||
\(812\) | 4.77927 | 0.167719 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −13.5282 | −0.474163 | ||||||||
\(815\) | 51.3554 | 1.79890 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −29.4971 | −1.03197 | ||||||||
\(818\) | 13.5846 | 0.474975 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.89966 | −0.206025 | ||||||||
\(821\) | −17.0881 | −0.596379 | −0.298189 | − | 0.954507i | \(-0.596383\pi\) | ||||
−0.298189 | + | 0.954507i | \(0.596383\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.4950 | −0.574980 | −0.287490 | − | 0.957784i | \(-0.592821\pi\) | ||||
−0.287490 | + | 0.957784i | \(0.592821\pi\) | |||||||
\(824\) | −36.9259 | −1.28637 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 31.3093 | 1.08939 | ||||||||
\(827\) | −3.49254 | −0.121447 | −0.0607237 | − | 0.998155i | \(-0.519341\pi\) | ||||
−0.0607237 | + | 0.998155i | \(0.519341\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.26456 | 0.182846 | 0.0914228 | − | 0.995812i | \(-0.470859\pi\) | ||||
0.0914228 | + | 0.995812i | \(0.470859\pi\) | |||||||
\(830\) | −84.0222 | −2.91645 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.10128 | 0.0381800 | ||||||||
\(833\) | 9.66435 | 0.334850 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −76.9132 | −2.66169 | ||||||||
\(836\) | 2.25086 | 0.0778478 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −52.5989 | −1.81700 | ||||||||
\(839\) | −22.8286 | −0.788130 | −0.394065 | − | 0.919083i | \(-0.628932\pi\) | ||||
−0.394065 | + | 0.919083i | \(0.628932\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.8341 | −0.442554 | ||||||||
\(842\) | 9.11018 | 0.313958 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10.3237 | 0.355355 | ||||||||
\(845\) | 55.3619 | 1.90451 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.98799 | 0.0683082 | ||||||||
\(848\) | −34.2340 | −1.17560 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 68.0367 | 2.33364 | ||||||||
\(851\) | 68.7507 | 2.35674 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.5640 | 0.978014 | 0.489007 | − | 0.872280i | \(-0.337359\pi\) | ||||
0.489007 | + | 0.872280i | \(0.337359\pi\) | |||||||
\(854\) | 3.20426 | 0.109648 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −30.4489 | −1.04072 | ||||||||
\(857\) | −15.5911 | −0.532582 | −0.266291 | − | 0.963893i | \(-0.585798\pi\) | ||||
−0.266291 | + | 0.963893i | \(0.585798\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.92436 | −0.168017 | −0.0840085 | − | 0.996465i | \(-0.526772\pi\) | ||||
−0.0840085 | + | 0.996465i | \(0.526772\pi\) | |||||||
\(860\) | −20.0491 | −0.683669 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −38.0514 | −1.29603 | ||||||||
\(863\) | −29.5907 | −1.00728 | −0.503640 | − | 0.863914i | \(-0.668006\pi\) | ||||
−0.503640 | + | 0.863914i | \(0.668006\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −25.5539 | −0.868858 | ||||||||
\(866\) | −19.3389 | −0.657163 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.54298 | 0.120257 | ||||||||
\(869\) | −2.92819 | −0.0993319 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.30378 | −0.111944 | ||||||||
\(872\) | 30.6605 | 1.03829 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −49.7012 | −1.68117 | ||||||||
\(875\) | −70.7155 | −2.39062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −57.3331 | −1.93600 | −0.968001 | − | 0.250947i | \(-0.919258\pi\) | ||||
−0.968001 | + | 0.250947i | \(0.919258\pi\) | |||||||
\(878\) | 15.0551 | 0.508087 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −20.7047 | −0.697955 | ||||||||
\(881\) | 8.30122 | 0.279675 | 0.139838 | − | 0.990174i | \(-0.455342\pi\) | ||||
0.139838 | + | 0.990174i | \(0.455342\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.59069 | −0.289100 | −0.144550 | − | 0.989498i | \(-0.546173\pi\) | ||||
−0.144550 | + | 0.989498i | \(0.546173\pi\) | |||||||
\(884\) | −0.475393 | −0.0159892 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 42.2492 | 1.41939 | ||||||||
\(887\) | −26.4726 | −0.888864 | −0.444432 | − | 0.895813i | \(-0.646595\pi\) | ||||
−0.444432 | + | 0.895813i | \(0.646595\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.0361 | 0.336602 | ||||||||
\(890\) | 67.4666 | 2.26149 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −16.9357 | −0.567048 | ||||||||
\(893\) | 3.21044 | 0.107433 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 96.3774 | 3.22154 | ||||||||
\(896\) | −27.1093 | −0.905657 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.5337 | −0.618478 | ||||||||
\(899\) | 11.9842 | 0.399695 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.4355 | −0.747434 | ||||||||
\(902\) | 3.71639 | 0.123742 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.142668 | 0.00474506 | ||||||||
\(905\) | 71.7585 | 2.38533 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 54.7146 | 1.81677 | 0.908384 | − | 0.418136i | \(-0.137316\pi\) | ||||
0.908384 | + | 0.418136i | \(0.137316\pi\) | |||||||
\(908\) | 8.57442 | 0.284552 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.43822 | 0.113976 | ||||||||
\(911\) | 14.0636 | 0.465947 | 0.232974 | − | 0.972483i | \(-0.425154\pi\) | ||||
0.232974 | + | 0.972483i | \(0.425154\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.1817 | 0.403156 | ||||||||
\(914\) | −56.1314 | −1.85666 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.51041 | −0.182069 | ||||||||
\(917\) | −37.9833 | −1.25432 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.8036 | −0.620274 | −0.310137 | − | 0.950692i | \(-0.600375\pi\) | ||||
−0.310137 | + | 0.950692i | \(0.600375\pi\) | |||||||
\(920\) | 79.2151 | 2.61164 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 49.9474 | 1.64493 | ||||||||
\(923\) | −0.519436 | −0.0170975 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −111.734 | −3.67378 | ||||||||
\(926\) | 5.88622 | 0.193433 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 13.1827 | 0.432743 | ||||||||
\(929\) | −13.3631 | −0.438429 | −0.219214 | − | 0.975677i | \(-0.570349\pi\) | ||||
−0.219214 | + | 0.975677i | \(0.570349\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.4737 | 0.376035 | ||||||||
\(932\) | 15.1242 | 0.495410 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 54.2732 | 1.77587 | ||||||||
\(935\) | −13.5689 | −0.443752 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.26525 | 0.237345 | 0.118673 | − | 0.992933i | \(-0.462136\pi\) | ||||
0.118673 | + | 0.992933i | \(0.462136\pi\) | |||||||
\(938\) | 42.2188 | 1.37849 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.18213 | 0.0711731 | ||||||||
\(941\) | −25.5547 | −0.833061 | −0.416530 | − | 0.909122i | \(-0.636754\pi\) | ||||
−0.416530 | + | 0.909122i | \(0.636754\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.8868 | −0.615038 | ||||||||
\(944\) | 47.2761 | 1.53871 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.6296 | 0.410623 | ||||||||
\(947\) | 29.0368 | 0.943570 | 0.471785 | − | 0.881714i | \(-0.343610\pi\) | ||||
0.471785 | + | 0.881714i | \(0.343610\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.303225 | −0.00984311 | ||||||||
\(950\) | 80.7743 | 2.62067 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −14.2453 | −0.461694 | ||||||||
\(953\) | −41.2250 | −1.33541 | −0.667705 | − | 0.744426i | \(-0.732723\pi\) | ||||
−0.667705 | + | 0.744426i | \(0.732723\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 98.9942 | 3.20338 | ||||||||
\(956\) | 11.5335 | 0.373021 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −0.0881048 | −0.00284654 | ||||||||
\(959\) | 16.6989 | 0.539234 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.1158 | −0.713414 | ||||||||
\(962\) | 3.39214 | 0.109367 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 7.42070 | 0.239005 | ||||||||
\(965\) | −6.62799 | −0.213362 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.8906 | 0.446690 | 0.223345 | − | 0.974739i | \(-0.428302\pi\) | ||||
0.223345 | + | 0.974739i | \(0.428302\pi\) | |||||||
\(968\) | 2.25988 | 0.0726352 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 20.8180 | 0.668427 | ||||||||
\(971\) | 32.4127 | 1.04017 | 0.520086 | − | 0.854114i | \(-0.325900\pi\) | ||||
0.520086 | + | 0.854114i | \(0.325900\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.0302 | 0.449787 | ||||||||
\(974\) | −26.0776 | −0.835580 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.83834 | 0.154871 | ||||||||
\(977\) | −32.1328 | −1.02802 | −0.514010 | − | 0.857784i | \(-0.671841\pi\) | ||||
−0.514010 | + | 0.857784i | \(0.671841\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.78144 | −0.312616 | ||||||||
\(980\) | 7.79863 | 0.249118 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.60541 | −0.0512307 | ||||||||
\(983\) | −3.66030 | −0.116745 | −0.0583727 | − | 0.998295i | \(-0.518591\pi\) | ||||
−0.0583727 | + | 0.998295i | \(0.518591\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.7181 | −0.532684 | ||||||||
\(986\) | 20.5488 | 0.654408 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.564395 | −0.0179558 | ||||||||
\(989\) | −64.1839 | −2.04093 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.8517 | −0.757674 | −0.378837 | − | 0.925463i | \(-0.623676\pi\) | ||||
−0.378837 | + | 0.925463i | \(0.623676\pi\) | |||||||
\(992\) | 9.77264 | 0.310282 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.63783 | 0.210539 | ||||||||
\(995\) | 48.3264 | 1.53205 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −54.6646 | −1.73124 | −0.865622 | − | 0.500698i | \(-0.833077\pi\) | ||||
−0.865622 | + | 0.500698i | \(0.833077\pi\) | |||||||
\(998\) | 47.2511 | 1.49571 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6039.2.a.i.1.4 | 13 | ||
3.2 | odd | 2 | 2013.2.a.e.1.10 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.e.1.10 | ✓ | 13 | 3.2 | odd | 2 | ||
6039.2.a.i.1.4 | 13 | 1.1 | even | 1 | trivial |