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: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.536820 | 0.379589 | 0.189795 | − | 0.981824i | \(-0.439218\pi\) | ||||
0.189795 | + | 0.981824i | \(0.439218\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.71182 | −0.855912 | ||||||||
\(5\) | 1.82707 | 0.817089 | 0.408544 | − | 0.912738i | \(-0.366037\pi\) | ||||
0.408544 | + | 0.912738i | \(0.366037\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.96010 | 1.11881 | 0.559407 | − | 0.828893i | \(-0.311029\pi\) | ||||
0.559407 | + | 0.828893i | \(0.311029\pi\) | |||||||
\(8\) | −1.99258 | −0.704484 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.980806 | 0.310158 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.10754 | 1.13923 | 0.569613 | − | 0.821913i | \(-0.307093\pi\) | ||||
0.569613 | + | 0.821913i | \(0.307093\pi\) | |||||||
\(14\) | 1.58904 | 0.424690 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.35399 | 0.588497 | ||||||||
\(17\) | −0.658907 | −0.159808 | −0.0799042 | − | 0.996803i | \(-0.525461\pi\) | ||||
−0.0799042 | + | 0.996803i | \(0.525461\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.67764 | −1.07312 | −0.536562 | − | 0.843861i | \(-0.680277\pi\) | ||||
−0.536562 | + | 0.843861i | \(0.680277\pi\) | |||||||
\(20\) | −3.12762 | −0.699356 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.536820 | −0.114450 | ||||||||
\(23\) | 1.60420 | 0.334499 | 0.167250 | − | 0.985915i | \(-0.446511\pi\) | ||||
0.167250 | + | 0.985915i | \(0.446511\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.66183 | −0.332366 | ||||||||
\(26\) | 2.20501 | 0.432438 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.06718 | −0.957606 | ||||||||
\(29\) | 6.71713 | 1.24734 | 0.623670 | − | 0.781688i | \(-0.285641\pi\) | ||||
0.623670 | + | 0.781688i | \(0.285641\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.25036 | −0.583781 | −0.291891 | − | 0.956452i | \(-0.594284\pi\) | ||||
−0.291891 | + | 0.956452i | \(0.594284\pi\) | |||||||
\(32\) | 5.24883 | 0.927872 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.353714 | −0.0606615 | ||||||||
\(35\) | 5.40831 | 0.914170 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.16378 | 0.520123 | 0.260062 | − | 0.965592i | \(-0.416257\pi\) | ||||
0.260062 | + | 0.965592i | \(0.416257\pi\) | |||||||
\(38\) | −2.51105 | −0.407346 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.64058 | −0.575626 | ||||||||
\(41\) | 9.51933 | 1.48667 | 0.743335 | − | 0.668920i | \(-0.233243\pi\) | ||||
0.743335 | + | 0.668920i | \(0.233243\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.90466 | 1.20545 | 0.602725 | − | 0.797949i | \(-0.294082\pi\) | ||||
0.602725 | + | 0.797949i | \(0.294082\pi\) | |||||||
\(44\) | 1.71182 | 0.258067 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.861168 | 0.126972 | ||||||||
\(47\) | 3.05519 | 0.445645 | 0.222823 | − | 0.974859i | \(-0.428473\pi\) | ||||
0.222823 | + | 0.974859i | \(0.428473\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.76221 | 0.251745 | ||||||||
\(50\) | −0.892104 | −0.126163 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.03138 | −0.975077 | ||||||||
\(53\) | −6.17173 | −0.847752 | −0.423876 | − | 0.905720i | \(-0.639331\pi\) | ||||
−0.423876 | + | 0.905720i | \(0.639331\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.82707 | −0.246362 | ||||||||
\(56\) | −5.89825 | −0.788187 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.60589 | 0.473477 | ||||||||
\(59\) | −4.74234 | −0.617400 | −0.308700 | − | 0.951159i | \(-0.599894\pi\) | ||||
−0.308700 | + | 0.951159i | \(0.599894\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | −1.74486 | −0.221597 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.89030 | −0.236287 | ||||||||
\(65\) | 7.50474 | 0.930848 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.1663 | −1.24201 | −0.621006 | − | 0.783805i | \(-0.713276\pi\) | ||||
−0.621006 | + | 0.783805i | \(0.713276\pi\) | |||||||
\(68\) | 1.12793 | 0.136782 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.90329 | 0.347009 | ||||||||
\(71\) | −3.32298 | −0.394365 | −0.197183 | − | 0.980367i | \(-0.563179\pi\) | ||||
−0.197183 | + | 0.980367i | \(0.563179\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.59025 | 0.537248 | 0.268624 | − | 0.963245i | \(-0.413431\pi\) | ||||
0.268624 | + | 0.963245i | \(0.413431\pi\) | |||||||
\(74\) | 1.69838 | 0.197433 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.00729 | 0.918499 | ||||||||
\(77\) | −2.96010 | −0.337335 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.97046 | 0.896747 | 0.448373 | − | 0.893846i | \(-0.352003\pi\) | ||||
0.448373 | + | 0.893846i | \(0.352003\pi\) | |||||||
\(80\) | 4.30089 | 0.480855 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.11017 | 0.564324 | ||||||||
\(83\) | 10.7338 | 1.17819 | 0.589093 | − | 0.808065i | \(-0.299485\pi\) | ||||
0.589093 | + | 0.808065i | \(0.299485\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.20387 | −0.130578 | ||||||||
\(86\) | 4.24338 | 0.457576 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.99258 | 0.212410 | ||||||||
\(89\) | −6.38437 | −0.676742 | −0.338371 | − | 0.941013i | \(-0.609876\pi\) | ||||
−0.338371 | + | 0.941013i | \(0.609876\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.1587 | 1.27458 | ||||||||
\(92\) | −2.74611 | −0.286302 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.64009 | 0.169162 | ||||||||
\(95\) | −8.54635 | −0.876837 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.3258 | 1.65763 | 0.828816 | − | 0.559522i | \(-0.189015\pi\) | ||||
0.828816 | + | 0.559522i | \(0.189015\pi\) | |||||||
\(98\) | 0.945992 | 0.0955596 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.84476 | 0.284476 | ||||||||
\(101\) | 9.93237 | 0.988308 | 0.494154 | − | 0.869374i | \(-0.335478\pi\) | ||||
0.494154 | + | 0.869374i | \(0.335478\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.27839 | −0.618628 | −0.309314 | − | 0.950960i | \(-0.600099\pi\) | ||||
−0.309314 | + | 0.950960i | \(0.600099\pi\) | |||||||
\(104\) | −8.18460 | −0.802566 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.31311 | −0.321797 | ||||||||
\(107\) | −0.939378 | −0.0908131 | −0.0454066 | − | 0.998969i | \(-0.514458\pi\) | ||||
−0.0454066 | + | 0.998969i | \(0.514458\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.15498 | 0.493757 | 0.246879 | − | 0.969046i | \(-0.420595\pi\) | ||||
0.246879 | + | 0.969046i | \(0.420595\pi\) | |||||||
\(110\) | −0.980806 | −0.0935162 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 6.96805 | 0.658419 | ||||||||
\(113\) | 6.15127 | 0.578662 | 0.289331 | − | 0.957229i | \(-0.406567\pi\) | ||||
0.289331 | + | 0.957229i | \(0.406567\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.93098 | 0.273316 | ||||||||
\(116\) | −11.4985 | −1.06761 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.54578 | −0.234358 | ||||||||
\(119\) | −1.95043 | −0.178796 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0.536820 | 0.0486014 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.56404 | 0.499665 | ||||||||
\(125\) | −12.1716 | −1.08866 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.9037 | 0.967547 | 0.483774 | − | 0.875193i | \(-0.339266\pi\) | ||||
0.483774 | + | 0.875193i | \(0.339266\pi\) | |||||||
\(128\) | −11.5124 | −1.01756 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.02870 | 0.353340 | ||||||||
\(131\) | −6.64522 | −0.580596 | −0.290298 | − | 0.956936i | \(-0.593754\pi\) | ||||
−0.290298 | + | 0.956936i | \(0.593754\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.8463 | −1.20063 | ||||||||
\(134\) | −5.45748 | −0.471455 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.31293 | 0.112582 | ||||||||
\(137\) | 16.2075 | 1.38470 | 0.692350 | − | 0.721562i | \(-0.256576\pi\) | ||||
0.692350 | + | 0.721562i | \(0.256576\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.4228 | −1.73224 | −0.866120 | − | 0.499836i | \(-0.833394\pi\) | ||||
−0.866120 | + | 0.499836i | \(0.833394\pi\) | |||||||
\(140\) | −9.25807 | −0.782449 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.78384 | −0.149697 | ||||||||
\(143\) | −4.10754 | −0.343489 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.2726 | 1.01919 | ||||||||
\(146\) | 2.46414 | 0.203934 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.41584 | −0.445180 | ||||||||
\(149\) | 13.6619 | 1.11923 | 0.559613 | − | 0.828754i | \(-0.310950\pi\) | ||||
0.559613 | + | 0.828754i | \(0.310950\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.844381 | 0.0687147 | 0.0343574 | − | 0.999410i | \(-0.489062\pi\) | ||||
0.0343574 | + | 0.999410i | \(0.489062\pi\) | |||||||
\(152\) | 9.32057 | 0.755998 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.58904 | −0.128049 | ||||||||
\(155\) | −5.93861 | −0.477001 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −24.1223 | −1.92517 | −0.962585 | − | 0.270979i | \(-0.912653\pi\) | ||||
−0.962585 | + | 0.270979i | \(0.912653\pi\) | |||||||
\(158\) | 4.27870 | 0.340395 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 9.58997 | 0.758153 | ||||||||
\(161\) | 4.74861 | 0.374243 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.32068 | −0.573400 | −0.286700 | − | 0.958020i | \(-0.592558\pi\) | ||||
−0.286700 | + | 0.958020i | \(0.592558\pi\) | |||||||
\(164\) | −16.2954 | −1.27246 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.76211 | 0.447227 | ||||||||
\(167\) | 7.32205 | 0.566597 | 0.283299 | − | 0.959032i | \(-0.408571\pi\) | ||||
0.283299 | + | 0.959032i | \(0.408571\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.87184 | 0.297834 | ||||||||
\(170\) | −0.646260 | −0.0495659 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −13.5314 | −1.03176 | ||||||||
\(173\) | −13.2768 | −1.00942 | −0.504709 | − | 0.863289i | \(-0.668400\pi\) | ||||
−0.504709 | + | 0.863289i | \(0.668400\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.91919 | −0.371856 | ||||||||
\(176\) | −2.35399 | −0.177439 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.42726 | −0.256884 | ||||||||
\(179\) | −4.61966 | −0.345290 | −0.172645 | − | 0.984984i | \(-0.555231\pi\) | ||||
−0.172645 | + | 0.984984i | \(0.555231\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.1579 | −0.903693 | −0.451847 | − | 0.892096i | \(-0.649235\pi\) | ||||
−0.451847 | + | 0.892096i | \(0.649235\pi\) | |||||||
\(182\) | 6.52705 | 0.483817 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.19651 | −0.235650 | ||||||||
\(185\) | 5.78044 | 0.424987 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.658907 | 0.0481840 | ||||||||
\(188\) | −5.22995 | −0.381433 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.58785 | −0.332838 | ||||||||
\(191\) | 24.0576 | 1.74075 | 0.870374 | − | 0.492392i | \(-0.163877\pi\) | ||||
0.870374 | + | 0.492392i | \(0.163877\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.60630 | −0.115624 | −0.0578121 | − | 0.998327i | \(-0.518412\pi\) | ||||
−0.0578121 | + | 0.998327i | \(0.518412\pi\) | |||||||
\(194\) | 8.76401 | 0.629219 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.01660 | −0.215471 | ||||||||
\(197\) | 17.1109 | 1.21910 | 0.609551 | − | 0.792746i | \(-0.291350\pi\) | ||||
0.609551 | + | 0.792746i | \(0.291350\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.9889 | 0.991645 | 0.495822 | − | 0.868424i | \(-0.334867\pi\) | ||||
0.495822 | + | 0.868424i | \(0.334867\pi\) | |||||||
\(200\) | 3.31133 | 0.234147 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.33190 | 0.375151 | ||||||||
\(203\) | 19.8834 | 1.39554 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.3924 | 1.21474 | ||||||||
\(206\) | −3.37036 | −0.234824 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 9.66909 | 0.670431 | ||||||||
\(209\) | 4.67764 | 0.323559 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.66352 | 0.183364 | 0.0916821 | − | 0.995788i | \(-0.470776\pi\) | ||||
0.0916821 | + | 0.995788i | \(0.470776\pi\) | |||||||
\(212\) | 10.5649 | 0.725601 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.504277 | −0.0344717 | ||||||||
\(215\) | 14.4423 | 0.984959 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.62139 | −0.653142 | ||||||||
\(218\) | 2.76730 | 0.187425 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.12762 | 0.210864 | ||||||||
\(221\) | −2.70648 | −0.182058 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.81616 | −0.121619 | −0.0608096 | − | 0.998149i | \(-0.519368\pi\) | ||||
−0.0608096 | + | 0.998149i | \(0.519368\pi\) | |||||||
\(224\) | 15.5371 | 1.03812 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.30212 | 0.219654 | ||||||||
\(227\) | −2.64065 | −0.175266 | −0.0876331 | − | 0.996153i | \(-0.527930\pi\) | ||||
−0.0876331 | + | 0.996153i | \(0.527930\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.0352 | 1.19180 | 0.595899 | − | 0.803059i | \(-0.296796\pi\) | ||||
0.595899 | + | 0.803059i | \(0.296796\pi\) | |||||||
\(230\) | 1.57341 | 0.103748 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −13.3844 | −0.878731 | ||||||||
\(233\) | 14.7825 | 0.968433 | 0.484217 | − | 0.874948i | \(-0.339105\pi\) | ||||
0.484217 | + | 0.874948i | \(0.339105\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.58204 | 0.364132 | ||||||||
\(236\) | 8.11805 | 0.528440 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.04703 | −0.0678690 | ||||||||
\(239\) | −4.75396 | −0.307508 | −0.153754 | − | 0.988109i | \(-0.549136\pi\) | ||||
−0.153754 | + | 0.988109i | \(0.549136\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.2189 | 0.851505 | 0.425753 | − | 0.904840i | \(-0.360009\pi\) | ||||
0.425753 | + | 0.904840i | \(0.360009\pi\) | |||||||
\(242\) | 0.536820 | 0.0345081 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.71182 | −0.109588 | ||||||||
\(245\) | 3.21968 | 0.205698 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −19.2136 | −1.22253 | ||||||||
\(248\) | 6.47660 | 0.411265 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.53396 | −0.413244 | ||||||||
\(251\) | −4.35690 | −0.275005 | −0.137503 | − | 0.990501i | \(-0.543908\pi\) | ||||
−0.137503 | + | 0.990501i | \(0.543908\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.60420 | −0.100855 | ||||||||
\(254\) | 5.85333 | 0.367270 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.39950 | −0.149969 | ||||||||
\(257\) | 24.7380 | 1.54311 | 0.771557 | − | 0.636160i | \(-0.219478\pi\) | ||||
0.771557 | + | 0.636160i | \(0.219478\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.36513 | 0.581921 | ||||||||
\(260\) | −12.8468 | −0.796724 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.56729 | −0.220388 | ||||||||
\(263\) | 10.8043 | 0.666223 | 0.333112 | − | 0.942887i | \(-0.391901\pi\) | ||||
0.333112 | + | 0.942887i | \(0.391901\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.2762 | −0.692688 | ||||||||
\(266\) | −7.43297 | −0.455744 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 17.4029 | 1.06305 | ||||||||
\(269\) | 16.9256 | 1.03197 | 0.515986 | − | 0.856597i | \(-0.327426\pi\) | ||||
0.515986 | + | 0.856597i | \(0.327426\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.7489 | −0.713695 | −0.356847 | − | 0.934163i | \(-0.616148\pi\) | ||||
−0.356847 | + | 0.934163i | \(0.616148\pi\) | |||||||
\(272\) | −1.55106 | −0.0940468 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.70051 | 0.525617 | ||||||||
\(275\) | 1.66183 | 0.100212 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.40038 | 0.0841406 | 0.0420703 | − | 0.999115i | \(-0.486605\pi\) | ||||
0.0420703 | + | 0.999115i | \(0.486605\pi\) | |||||||
\(278\) | −10.9634 | −0.657540 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −10.7765 | −0.644019 | ||||||||
\(281\) | −32.3460 | −1.92960 | −0.964802 | − | 0.262979i | \(-0.915295\pi\) | ||||
−0.964802 | + | 0.262979i | \(0.915295\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31.2262 | 1.85620 | 0.928102 | − | 0.372327i | \(-0.121440\pi\) | ||||
0.928102 | + | 0.372327i | \(0.121440\pi\) | |||||||
\(284\) | 5.68835 | 0.337542 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.20501 | −0.130385 | ||||||||
\(287\) | 28.1782 | 1.66331 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5658 | −0.974461 | ||||||||
\(290\) | 6.58820 | 0.386872 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.85770 | −0.459837 | ||||||||
\(293\) | 2.69227 | 0.157284 | 0.0786422 | − | 0.996903i | \(-0.474942\pi\) | ||||
0.0786422 | + | 0.996903i | \(0.474942\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.66457 | −0.504471 | ||||||||
\(296\) | −6.30410 | −0.366418 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.33398 | 0.424846 | ||||||||
\(299\) | 6.58932 | 0.381070 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.3986 | 1.34867 | ||||||||
\(302\) | 0.453281 | 0.0260834 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −11.0111 | −0.631530 | ||||||||
\(305\) | 1.82707 | 0.104618 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.697397 | 0.0398025 | 0.0199013 | − | 0.999802i | \(-0.493665\pi\) | ||||
0.0199013 | + | 0.999802i | \(0.493665\pi\) | |||||||
\(308\) | 5.06718 | 0.288729 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.18797 | −0.181064 | ||||||||
\(311\) | 16.7415 | 0.949324 | 0.474662 | − | 0.880168i | \(-0.342570\pi\) | ||||
0.474662 | + | 0.880168i | \(0.342570\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.8295 | 0.668643 | 0.334321 | − | 0.942459i | \(-0.391493\pi\) | ||||
0.334321 | + | 0.942459i | \(0.391493\pi\) | |||||||
\(314\) | −12.9493 | −0.730774 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.6440 | −0.767536 | ||||||||
\(317\) | 32.2617 | 1.81200 | 0.905999 | − | 0.423279i | \(-0.139121\pi\) | ||||
0.905999 | + | 0.423279i | \(0.139121\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.71713 | −0.376087 | ||||||||
\(320\) | −3.45370 | −0.193068 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.54915 | 0.142058 | ||||||||
\(323\) | 3.08213 | 0.171494 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.82602 | −0.378640 | ||||||||
\(326\) | −3.92989 | −0.217656 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −18.9680 | −1.04733 | ||||||||
\(329\) | 9.04368 | 0.498594 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.54175 | 0.414532 | 0.207266 | − | 0.978285i | \(-0.433543\pi\) | ||||
0.207266 | + | 0.978285i | \(0.433543\pi\) | |||||||
\(332\) | −18.3744 | −1.00842 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.93062 | 0.215074 | ||||||||
\(335\) | −18.5745 | −1.01483 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.21029 | −0.0659287 | −0.0329644 | − | 0.999457i | \(-0.510495\pi\) | ||||
−0.0329644 | + | 0.999457i | \(0.510495\pi\) | |||||||
\(338\) | 2.07848 | 0.113055 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.06081 | 0.111763 | ||||||||
\(341\) | 3.25036 | 0.176017 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.5044 | −0.837158 | ||||||||
\(344\) | −15.7507 | −0.849220 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.12727 | −0.383164 | ||||||||
\(347\) | 8.00583 | 0.429775 | 0.214888 | − | 0.976639i | \(-0.431061\pi\) | ||||
0.214888 | + | 0.976639i | \(0.431061\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.03771 | −0.430249 | −0.215124 | − | 0.976587i | \(-0.569016\pi\) | ||||
−0.215124 | + | 0.976587i | \(0.569016\pi\) | |||||||
\(350\) | −2.64072 | −0.141152 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.24883 | −0.279764 | ||||||||
\(353\) | 12.1828 | 0.648423 | 0.324211 | − | 0.945985i | \(-0.394901\pi\) | ||||
0.324211 | + | 0.945985i | \(0.394901\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.07130 | −0.322231 | ||||||||
\(356\) | 10.9289 | 0.579231 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.47993 | −0.131068 | ||||||||
\(359\) | 34.8027 | 1.83681 | 0.918407 | − | 0.395636i | \(-0.129476\pi\) | ||||
0.918407 | + | 0.395636i | \(0.129476\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.88028 | 0.151593 | ||||||||
\(362\) | −6.52663 | −0.343032 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −20.8136 | −1.09093 | ||||||||
\(365\) | 8.38669 | 0.438980 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.7187 | −1.02931 | −0.514653 | − | 0.857399i | \(-0.672079\pi\) | ||||
−0.514653 | + | 0.857399i | \(0.672079\pi\) | |||||||
\(368\) | 3.77628 | 0.196852 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.10306 | 0.161320 | ||||||||
\(371\) | −18.2689 | −0.948477 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 32.1156 | 1.66289 | 0.831443 | − | 0.555611i | \(-0.187515\pi\) | ||||
0.831443 | + | 0.555611i | \(0.187515\pi\) | |||||||
\(374\) | 0.353714 | 0.0182901 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.08772 | −0.313950 | ||||||||
\(377\) | 27.5908 | 1.42100 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.494227 | 0.0253868 | 0.0126934 | − | 0.999919i | \(-0.495959\pi\) | ||||
0.0126934 | + | 0.999919i | \(0.495959\pi\) | |||||||
\(380\) | 14.6298 | 0.750495 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 12.9146 | 0.660769 | ||||||||
\(383\) | −12.0656 | −0.616525 | −0.308262 | − | 0.951301i | \(-0.599747\pi\) | ||||
−0.308262 | + | 0.951301i | \(0.599747\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.40831 | −0.275633 | ||||||||
\(386\) | −0.862296 | −0.0438897 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −27.9469 | −1.41879 | ||||||||
\(389\) | 9.69134 | 0.491370 | 0.245685 | − | 0.969350i | \(-0.420987\pi\) | ||||
0.245685 | + | 0.969350i | \(0.420987\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.05702 | −0.0534558 | ||||||||
\(392\) | −3.51136 | −0.177350 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.18549 | 0.462758 | ||||||||
\(395\) | 14.5626 | 0.732722 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.1784 | −1.11310 | −0.556550 | − | 0.830814i | \(-0.687875\pi\) | ||||
−0.556550 | + | 0.830814i | \(0.687875\pi\) | |||||||
\(398\) | 7.50951 | 0.376418 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.91193 | −0.195596 | ||||||||
\(401\) | 18.4895 | 0.923320 | 0.461660 | − | 0.887057i | \(-0.347254\pi\) | ||||
0.461660 | + | 0.887057i | \(0.347254\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.3509 | −0.665058 | ||||||||
\(404\) | −17.0025 | −0.845905 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.6738 | 0.529732 | ||||||||
\(407\) | −3.16378 | −0.156823 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.87986 | 0.0929531 | 0.0464765 | − | 0.998919i | \(-0.485201\pi\) | ||||
0.0464765 | + | 0.998919i | \(0.485201\pi\) | |||||||
\(410\) | 9.33661 | 0.461103 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10.7475 | 0.529491 | ||||||||
\(413\) | −14.0378 | −0.690756 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19.6113 | 0.962683 | ||||||||
\(416\) | 21.5598 | 1.05705 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.51105 | 0.122819 | ||||||||
\(419\) | −9.60282 | −0.469128 | −0.234564 | − | 0.972101i | \(-0.575366\pi\) | ||||
−0.234564 | + | 0.972101i | \(0.575366\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.3356 | 0.844884 | 0.422442 | − | 0.906390i | \(-0.361173\pi\) | ||||
0.422442 | + | 0.906390i | \(0.361173\pi\) | |||||||
\(422\) | 1.42983 | 0.0696031 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.2977 | 0.597228 | ||||||||
\(425\) | 1.09499 | 0.0531148 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.96010 | 0.143249 | ||||||||
\(428\) | 1.60805 | 0.0777280 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.75294 | 0.373880 | ||||||||
\(431\) | 21.8464 | 1.05231 | 0.526153 | − | 0.850390i | \(-0.323634\pi\) | ||||
0.526153 | + | 0.850390i | \(0.323634\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.7062 | 1.23536 | 0.617680 | − | 0.786429i | \(-0.288073\pi\) | ||||
0.617680 | + | 0.786429i | \(0.288073\pi\) | |||||||
\(434\) | −5.16496 | −0.247926 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.82442 | −0.422613 | ||||||||
\(437\) | −7.50388 | −0.358959 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.504684 | 0.0240872 | 0.0120436 | − | 0.999927i | \(-0.496166\pi\) | ||||
0.0120436 | + | 0.999927i | \(0.496166\pi\) | |||||||
\(440\) | 3.64058 | 0.173558 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.45289 | −0.0691072 | ||||||||
\(443\) | −5.62560 | −0.267280 | −0.133640 | − | 0.991030i | \(-0.542667\pi\) | ||||
−0.133640 | + | 0.991030i | \(0.542667\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.6647 | −0.552958 | ||||||||
\(446\) | −0.974953 | −0.0461654 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.59548 | −0.264362 | ||||||||
\(449\) | −29.3841 | −1.38672 | −0.693361 | − | 0.720591i | \(-0.743871\pi\) | ||||
−0.693361 | + | 0.720591i | \(0.743871\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.51933 | −0.448248 | ||||||||
\(452\) | −10.5299 | −0.495284 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.41756 | −0.0665292 | ||||||||
\(455\) | 22.2148 | 1.04145 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.5675 | −1.00889 | −0.504443 | − | 0.863445i | \(-0.668302\pi\) | ||||
−0.504443 | + | 0.863445i | \(0.668302\pi\) | |||||||
\(458\) | 9.68165 | 0.452394 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5.01733 | −0.233934 | ||||||||
\(461\) | −13.0759 | −0.609007 | −0.304503 | − | 0.952511i | \(-0.598491\pi\) | ||||
−0.304503 | + | 0.952511i | \(0.598491\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.4764 | −0.812199 | −0.406100 | − | 0.913829i | \(-0.633111\pi\) | ||||
−0.406100 | + | 0.913829i | \(0.633111\pi\) | |||||||
\(464\) | 15.8120 | 0.734056 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.93554 | 0.367607 | ||||||||
\(467\) | −1.67808 | −0.0776524 | −0.0388262 | − | 0.999246i | \(-0.512362\pi\) | ||||
−0.0388262 | + | 0.999246i | \(0.512362\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −30.0933 | −1.38958 | ||||||||
\(470\) | 2.99655 | 0.138221 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9.44950 | 0.434949 | ||||||||
\(473\) | −7.90466 | −0.363457 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.77343 | 0.356670 | ||||||||
\(476\) | 3.33880 | 0.153034 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.55202 | −0.116727 | ||||||||
\(479\) | −30.7304 | −1.40411 | −0.702054 | − | 0.712124i | \(-0.747733\pi\) | ||||
−0.702054 | + | 0.712124i | \(0.747733\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.9954 | 0.592537 | ||||||||
\(482\) | 7.09618 | 0.323222 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.71182 | −0.0778102 | ||||||||
\(485\) | 29.8283 | 1.35443 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −38.0671 | −1.72498 | −0.862492 | − | 0.506071i | \(-0.831097\pi\) | ||||
−0.862492 | + | 0.506071i | \(0.831097\pi\) | |||||||
\(488\) | −1.99258 | −0.0902000 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.72839 | 0.0780807 | ||||||||
\(491\) | 29.7719 | 1.34359 | 0.671793 | − | 0.740739i | \(-0.265524\pi\) | ||||
0.671793 | + | 0.740739i | \(0.265524\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.42596 | −0.199335 | ||||||||
\(494\) | −10.3142 | −0.464059 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.65130 | −0.343554 | ||||||||
\(497\) | −9.83636 | −0.441221 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.7321 | −1.24146 | −0.620729 | − | 0.784025i | \(-0.713163\pi\) | ||||
−0.620729 | + | 0.784025i | \(0.713163\pi\) | |||||||
\(500\) | 20.8356 | 0.931798 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.33887 | −0.104389 | ||||||||
\(503\) | −6.89167 | −0.307284 | −0.153642 | − | 0.988127i | \(-0.549100\pi\) | ||||
−0.153642 | + | 0.988127i | \(0.549100\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.1471 | 0.807535 | ||||||||
\(506\) | −0.861168 | −0.0382836 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −18.6652 | −0.828135 | ||||||||
\(509\) | −25.8868 | −1.14741 | −0.573706 | − | 0.819061i | \(-0.694495\pi\) | ||||
−0.573706 | + | 0.819061i | \(0.694495\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.5876 | 0.601081 | ||||||||
\(512\) | 21.7367 | 0.960637 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13.2799 | 0.585749 | ||||||||
\(515\) | −11.4710 | −0.505474 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.05519 | −0.134367 | ||||||||
\(518\) | 5.02739 | 0.220891 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −14.9538 | −0.655768 | ||||||||
\(521\) | −15.7926 | −0.691886 | −0.345943 | − | 0.938255i | \(-0.612441\pi\) | ||||
−0.345943 | + | 0.938255i | \(0.612441\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.7661 | −0.733131 | −0.366565 | − | 0.930392i | \(-0.619466\pi\) | ||||
−0.366565 | + | 0.930392i | \(0.619466\pi\) | |||||||
\(524\) | 11.3755 | 0.496939 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.79998 | 0.252891 | ||||||||
\(527\) | 2.14168 | 0.0932931 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.4265 | −0.888110 | ||||||||
\(530\) | −6.05327 | −0.262937 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 23.7024 | 1.02763 | ||||||||
\(533\) | 39.1010 | 1.69365 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.71631 | −0.0742024 | ||||||||
\(536\) | 20.2572 | 0.874979 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9.08600 | 0.391725 | ||||||||
\(539\) | −1.76221 | −0.0759039 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.8101 | 1.02367 | 0.511837 | − | 0.859083i | \(-0.328965\pi\) | ||||
0.511837 | + | 0.859083i | \(0.328965\pi\) | |||||||
\(542\) | −6.30705 | −0.270911 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.45849 | −0.148282 | ||||||||
\(545\) | 9.41849 | 0.403444 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.1878 | 1.67555 | 0.837774 | − | 0.546018i | \(-0.183857\pi\) | ||||
0.837774 | + | 0.546018i | \(0.183857\pi\) | |||||||
\(548\) | −27.7444 | −1.18518 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.892104 | 0.0380394 | ||||||||
\(551\) | −31.4203 | −1.33855 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23.5934 | 1.00329 | ||||||||
\(554\) | 0.751751 | 0.0319389 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 34.9603 | 1.48265 | ||||||||
\(557\) | 14.1224 | 0.598387 | 0.299193 | − | 0.954193i | \(-0.403282\pi\) | ||||
0.299193 | + | 0.954193i | \(0.403282\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.4687 | 1.37328 | ||||||||
\(560\) | 12.7311 | 0.537987 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −17.3640 | −0.732457 | ||||||||
\(563\) | −3.46110 | −0.145868 | −0.0729341 | − | 0.997337i | \(-0.523236\pi\) | ||||
−0.0729341 | + | 0.997337i | \(0.523236\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.2388 | 0.472819 | ||||||||
\(566\) | 16.7628 | 0.704595 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.62131 | 0.277824 | ||||||||
\(569\) | −41.8059 | −1.75259 | −0.876297 | − | 0.481771i | \(-0.839994\pi\) | ||||
−0.876297 | + | 0.481771i | \(0.839994\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.5434 | −1.48745 | −0.743723 | − | 0.668488i | \(-0.766942\pi\) | ||||
−0.743723 | + | 0.668488i | \(0.766942\pi\) | |||||||
\(572\) | 7.03138 | 0.293997 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 15.1266 | 0.631373 | ||||||||
\(575\) | −2.66591 | −0.111176 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −35.5075 | −1.47820 | −0.739098 | − | 0.673597i | \(-0.764748\pi\) | ||||
−0.739098 | + | 0.673597i | \(0.764748\pi\) | |||||||
\(578\) | −8.89288 | −0.369895 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −21.0086 | −0.872334 | ||||||||
\(581\) | 31.7731 | 1.31817 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.17173 | 0.255607 | ||||||||
\(584\) | −9.14645 | −0.378483 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.44527 | 0.0597035 | ||||||||
\(587\) | 3.20023 | 0.132087 | 0.0660437 | − | 0.997817i | \(-0.478962\pi\) | ||||
0.0660437 | + | 0.997817i | \(0.478962\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.2040 | 0.626469 | ||||||||
\(590\) | −4.65132 | −0.191492 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.44752 | 0.306091 | ||||||||
\(593\) | 5.07358 | 0.208347 | 0.104174 | − | 0.994559i | \(-0.466780\pi\) | ||||
0.104174 | + | 0.994559i | \(0.466780\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.56357 | −0.146092 | ||||||||
\(596\) | −23.3868 | −0.957959 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.53728 | 0.144650 | ||||||||
\(599\) | −37.0798 | −1.51504 | −0.757519 | − | 0.652813i | \(-0.773589\pi\) | ||||
−0.757519 | + | 0.652813i | \(0.773589\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.4700 | −0.671825 | −0.335912 | − | 0.941893i | \(-0.609045\pi\) | ||||
−0.335912 | + | 0.941893i | \(0.609045\pi\) | |||||||
\(602\) | 12.5608 | 0.511942 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.44543 | −0.0588138 | ||||||||
\(605\) | 1.82707 | 0.0742808 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.2240 | 1.59205 | 0.796027 | − | 0.605261i | \(-0.206931\pi\) | ||||
0.796027 | + | 0.605261i | \(0.206931\pi\) | |||||||
\(608\) | −24.5521 | −0.995720 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.980806 | 0.0397117 | ||||||||
\(611\) | 12.5493 | 0.507690 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.9678 | −0.442987 | −0.221494 | − | 0.975162i | \(-0.571093\pi\) | ||||
−0.221494 | + | 0.975162i | \(0.571093\pi\) | |||||||
\(614\) | 0.374377 | 0.0151086 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.89825 | 0.237647 | ||||||||
\(617\) | −31.2353 | −1.25748 | −0.628742 | − | 0.777614i | \(-0.716430\pi\) | ||||
−0.628742 | + | 0.777614i | \(0.716430\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.3446 | −0.817718 | −0.408859 | − | 0.912597i | \(-0.634073\pi\) | ||||
−0.408859 | + | 0.912597i | \(0.634073\pi\) | |||||||
\(620\) | 10.1659 | 0.408271 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.98718 | 0.360353 | ||||||||
\(623\) | −18.8984 | −0.757148 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.9292 | −0.557167 | ||||||||
\(626\) | 6.35031 | 0.253810 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 41.2932 | 1.64778 | ||||||||
\(629\) | −2.08464 | −0.0831200 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.7537 | 0.786381 | 0.393190 | − | 0.919457i | \(-0.371371\pi\) | ||||
0.393190 | + | 0.919457i | \(0.371371\pi\) | |||||||
\(632\) | −15.8818 | −0.631744 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 17.3187 | 0.687815 | ||||||||
\(635\) | 19.9218 | 0.790572 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.23835 | 0.286794 | ||||||||
\(638\) | −3.60589 | −0.142759 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −21.0339 | −0.831440 | ||||||||
\(641\) | 23.4802 | 0.927412 | 0.463706 | − | 0.885989i | \(-0.346519\pi\) | ||||
0.463706 | + | 0.885989i | \(0.346519\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.39790 | 0.0551278 | 0.0275639 | − | 0.999620i | \(-0.491225\pi\) | ||||
0.0275639 | + | 0.999620i | \(0.491225\pi\) | |||||||
\(644\) | −8.12878 | −0.320319 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.65455 | 0.0650973 | ||||||||
\(647\) | 22.2494 | 0.874715 | 0.437358 | − | 0.899288i | \(-0.355914\pi\) | ||||
0.437358 | + | 0.899288i | \(0.355914\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.74234 | 0.186153 | ||||||||
\(650\) | −3.66435 | −0.143728 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.5317 | 0.490780 | ||||||||
\(653\) | 45.9766 | 1.79920 | 0.899602 | − | 0.436711i | \(-0.143857\pi\) | ||||
0.899602 | + | 0.436711i | \(0.143857\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.1413 | −0.474398 | ||||||||
\(656\) | 22.4084 | 0.874901 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.85483 | 0.189261 | ||||||||
\(659\) | −19.9901 | −0.778705 | −0.389353 | − | 0.921089i | \(-0.627301\pi\) | ||||
−0.389353 | + | 0.921089i | \(0.627301\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.35196 | 0.0914808 | 0.0457404 | − | 0.998953i | \(-0.485435\pi\) | ||||
0.0457404 | + | 0.998953i | \(0.485435\pi\) | |||||||
\(662\) | 4.04856 | 0.157352 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −21.3880 | −0.830014 | ||||||||
\(665\) | −25.2981 | −0.981018 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.7756 | 0.417234 | ||||||||
\(668\) | −12.5341 | −0.484957 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −9.97118 | −0.385220 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.24577 | −0.0480210 | −0.0240105 | − | 0.999712i | \(-0.507644\pi\) | ||||
−0.0240105 | + | 0.999712i | \(0.507644\pi\) | |||||||
\(674\) | −0.649708 | −0.0250258 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.62792 | −0.254920 | ||||||||
\(677\) | −4.04512 | −0.155467 | −0.0777333 | − | 0.996974i | \(-0.524768\pi\) | ||||
−0.0777333 | + | 0.996974i | \(0.524768\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 48.3260 | 1.85458 | ||||||||
\(680\) | 2.39880 | 0.0919899 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.74486 | 0.0668140 | ||||||||
\(683\) | 37.1501 | 1.42151 | 0.710755 | − | 0.703440i | \(-0.248354\pi\) | ||||
0.710755 | + | 0.703440i | \(0.248354\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 29.6122 | 1.13142 | ||||||||
\(686\) | −8.32307 | −0.317776 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 18.6075 | 0.709404 | ||||||||
\(689\) | −25.3506 | −0.965780 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.675687 | −0.0257044 | −0.0128522 | − | 0.999917i | \(-0.504091\pi\) | ||||
−0.0128522 | + | 0.999917i | \(0.504091\pi\) | |||||||
\(692\) | 22.7276 | 0.863973 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.29769 | 0.163138 | ||||||||
\(695\) | −37.3138 | −1.41539 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.27235 | −0.237582 | ||||||||
\(698\) | −4.31481 | −0.163318 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8.42078 | 0.318276 | ||||||||
\(701\) | −39.7941 | −1.50300 | −0.751502 | − | 0.659731i | \(-0.770670\pi\) | ||||
−0.751502 | + | 0.659731i | \(0.770670\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.7990 | −0.558156 | ||||||||
\(704\) | 1.89030 | 0.0712433 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.53995 | 0.246134 | ||||||||
\(707\) | 29.4009 | 1.10573 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.3479 | −1.40263 | −0.701315 | − | 0.712851i | \(-0.747404\pi\) | ||||
−0.701315 | + | 0.712851i | \(0.747404\pi\) | |||||||
\(710\) | −3.25920 | −0.122316 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.7214 | 0.476754 | ||||||||
\(713\) | −5.21423 | −0.195274 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.50474 | −0.280661 | ||||||||
\(716\) | 7.90805 | 0.295538 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 18.6828 | 0.697235 | ||||||||
\(719\) | −4.88561 | −0.182202 | −0.0911012 | − | 0.995842i | \(-0.529039\pi\) | ||||
−0.0911012 | + | 0.995842i | \(0.529039\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.5847 | −0.692129 | ||||||||
\(722\) | 1.54619 | 0.0575433 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 20.8123 | 0.773482 | ||||||||
\(725\) | −11.1627 | −0.414573 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.91715 | −0.0711033 | −0.0355516 | − | 0.999368i | \(-0.511319\pi\) | ||||
−0.0355516 | + | 0.999368i | \(0.511319\pi\) | |||||||
\(728\) | −24.2273 | −0.897922 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.50215 | 0.166632 | ||||||||
\(731\) | −5.20843 | −0.192641 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.0332 | 0.666071 | 0.333036 | − | 0.942914i | \(-0.391927\pi\) | ||||
0.333036 | + | 0.942914i | \(0.391927\pi\) | |||||||
\(734\) | −10.5854 | −0.390713 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.42019 | 0.310372 | ||||||||
\(737\) | 10.1663 | 0.374481 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.76304 | 0.175211 | 0.0876057 | − | 0.996155i | \(-0.472078\pi\) | ||||
0.0876057 | + | 0.996155i | \(0.472078\pi\) | |||||||
\(740\) | −9.89510 | −0.363751 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.80714 | −0.360031 | ||||||||
\(743\) | 36.9064 | 1.35396 | 0.676982 | − | 0.736000i | \(-0.263287\pi\) | ||||
0.676982 | + | 0.736000i | \(0.263287\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.9612 | 0.914507 | ||||||||
\(746\) | 17.2403 | 0.631213 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.12793 | −0.0412413 | ||||||||
\(749\) | −2.78066 | −0.101603 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.2591 | −1.03119 | −0.515594 | − | 0.856833i | \(-0.672429\pi\) | ||||
−0.515594 | + | 0.856833i | \(0.672429\pi\) | |||||||
\(752\) | 7.19189 | 0.262261 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 14.8113 | 0.539396 | ||||||||
\(755\) | 1.54274 | 0.0561460 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.90282 | −0.105505 | −0.0527523 | − | 0.998608i | \(-0.516799\pi\) | ||||
−0.0527523 | + | 0.998608i | \(0.516799\pi\) | |||||||
\(758\) | 0.265311 | 0.00963654 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 17.0293 | 0.617718 | ||||||||
\(761\) | 24.0628 | 0.872276 | 0.436138 | − | 0.899880i | \(-0.356346\pi\) | ||||
0.436138 | + | 0.899880i | \(0.356346\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.2593 | 0.552423 | ||||||||
\(764\) | −41.1824 | −1.48993 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.47707 | −0.234026 | ||||||||
\(767\) | −19.4793 | −0.703358 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.6169 | −1.14013 | −0.570067 | − | 0.821598i | \(-0.693083\pi\) | ||||
−0.570067 | + | 0.821598i | \(0.693083\pi\) | |||||||
\(770\) | −2.90329 | −0.104627 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.74971 | 0.0989642 | ||||||||
\(773\) | 13.9588 | 0.502064 | 0.251032 | − | 0.967979i | \(-0.419230\pi\) | ||||
0.251032 | + | 0.967979i | \(0.419230\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.40154 | 0.194029 | ||||||||
\(776\) | −32.5305 | −1.16778 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.20251 | 0.186519 | ||||||||
\(779\) | −44.5279 | −1.59538 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.32298 | 0.118906 | ||||||||
\(782\) | −0.567430 | −0.0202912 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.14823 | 0.148151 | ||||||||
\(785\) | −44.0731 | −1.57304 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40.5357 | −1.44494 | −0.722470 | − | 0.691402i | \(-0.756993\pi\) | ||||
−0.722470 | + | 0.691402i | \(0.756993\pi\) | |||||||
\(788\) | −29.2909 | −1.04344 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.81748 | 0.278133 | ||||||||
\(791\) | 18.2084 | 0.647416 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.10754 | 0.145863 | ||||||||
\(794\) | −11.9058 | −0.422521 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −23.9465 | −0.848761 | ||||||||
\(797\) | 21.5848 | 0.764571 | 0.382286 | − | 0.924044i | \(-0.375137\pi\) | ||||
0.382286 | + | 0.924044i | \(0.375137\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.01309 | −0.0712179 | ||||||||
\(800\) | −8.72267 | −0.308393 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.92553 | 0.350483 | ||||||||
\(803\) | −4.59025 | −0.161986 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.67602 | 0.305789 | ||||||||
\(806\) | −7.16706 | −0.252449 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −19.7911 | −0.696247 | ||||||||
\(809\) | −2.71633 | −0.0955010 | −0.0477505 | − | 0.998859i | \(-0.515205\pi\) | ||||
−0.0477505 | + | 0.998859i | \(0.515205\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.3769 | −1.41782 | −0.708912 | − | 0.705297i | \(-0.750814\pi\) | ||||
−0.708912 | + | 0.705297i | \(0.750814\pi\) | |||||||
\(812\) | −34.0369 | −1.19446 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.69838 | −0.0595283 | ||||||||
\(815\) | −13.3754 | −0.468519 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36.9751 | −1.29360 | ||||||||
\(818\) | 1.00915 | 0.0352840 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −29.7728 | −1.03971 | ||||||||
\(821\) | 23.0630 | 0.804904 | 0.402452 | − | 0.915441i | \(-0.368158\pi\) | ||||
0.402452 | + | 0.915441i | \(0.368158\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.4394 | −0.398754 | −0.199377 | − | 0.979923i | \(-0.563892\pi\) | ||||
−0.199377 | + | 0.979923i | \(0.563892\pi\) | |||||||
\(824\) | 12.5102 | 0.435814 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.53579 | −0.262203 | ||||||||
\(827\) | 25.5440 | 0.888251 | 0.444125 | − | 0.895965i | \(-0.353514\pi\) | ||||
0.444125 | + | 0.895965i | \(0.353514\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.83211 | 0.133095 | 0.0665474 | − | 0.997783i | \(-0.478802\pi\) | ||||
0.0665474 | + | 0.997783i | \(0.478802\pi\) | |||||||
\(830\) | 10.5278 | 0.365424 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −7.76447 | −0.269184 | ||||||||
\(833\) | −1.16113 | −0.0402309 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.3779 | 0.462960 | ||||||||
\(836\) | −8.00729 | −0.276938 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.15499 | −0.178076 | ||||||||
\(839\) | 35.8072 | 1.23620 | 0.618101 | − | 0.786098i | \(-0.287902\pi\) | ||||
0.618101 | + | 0.786098i | \(0.287902\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.1198 | 0.555855 | ||||||||
\(842\) | 9.30609 | 0.320709 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.55947 | −0.156944 | ||||||||
\(845\) | 7.07412 | 0.243357 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.96010 | 0.101710 | ||||||||
\(848\) | −14.5282 | −0.498900 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.587813 | 0.0201618 | ||||||||
\(851\) | 5.07535 | 0.173981 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.2174 | −0.760708 | −0.380354 | − | 0.924841i | \(-0.624198\pi\) | ||||
−0.380354 | + | 0.924841i | \(0.624198\pi\) | |||||||
\(854\) | 1.58904 | 0.0543760 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.87179 | 0.0639764 | ||||||||
\(857\) | −10.9067 | −0.372564 | −0.186282 | − | 0.982496i | \(-0.559644\pi\) | ||||
−0.186282 | + | 0.982496i | \(0.559644\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.5394 | −0.564317 | −0.282158 | − | 0.959368i | \(-0.591050\pi\) | ||||
−0.282158 | + | 0.959368i | \(0.591050\pi\) | |||||||
\(860\) | −24.7227 | −0.843038 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 11.7276 | 0.399444 | ||||||||
\(863\) | −43.9687 | −1.49671 | −0.748356 | − | 0.663297i | \(-0.769157\pi\) | ||||
−0.748356 | + | 0.663297i | \(0.769157\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.2576 | −0.824785 | ||||||||
\(866\) | 13.7996 | 0.468930 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 16.4701 | 0.559032 | ||||||||
\(869\) | −7.97046 | −0.270379 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −41.7585 | −1.41493 | ||||||||
\(872\) | −10.2717 | −0.347844 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.02823 | −0.136257 | ||||||||
\(875\) | −36.0292 | −1.21801 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.9662 | 1.51840 | 0.759200 | − | 0.650857i | \(-0.225590\pi\) | ||||
0.759200 | + | 0.650857i | \(0.225590\pi\) | |||||||
\(878\) | 0.270924 | 0.00914326 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.30089 | −0.144983 | ||||||||
\(881\) | −25.7353 | −0.867044 | −0.433522 | − | 0.901143i | \(-0.642729\pi\) | ||||
−0.433522 | + | 0.901143i | \(0.642729\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.61567 | −0.289940 | −0.144970 | − | 0.989436i | \(-0.546309\pi\) | ||||
−0.144970 | + | 0.989436i | \(0.546309\pi\) | |||||||
\(884\) | 4.63302 | 0.155825 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.01994 | −0.101457 | ||||||||
\(887\) | 33.1107 | 1.11175 | 0.555874 | − | 0.831266i | \(-0.312384\pi\) | ||||
0.555874 | + | 0.831266i | \(0.312384\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 32.2761 | 1.08251 | ||||||||
\(890\) | −6.26183 | −0.209897 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.10895 | 0.104095 | ||||||||
\(893\) | −14.2911 | −0.478232 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.44043 | −0.282132 | ||||||||
\(896\) | −34.0780 | −1.13846 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15.7740 | −0.526384 | ||||||||
\(899\) | −21.8331 | −0.728173 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.06659 | 0.135478 | ||||||||
\(902\) | −5.11017 | −0.170150 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.2569 | −0.407659 | ||||||||
\(905\) | −22.2134 | −0.738397 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.90022 | 0.0630959 | 0.0315480 | − | 0.999502i | \(-0.489956\pi\) | ||||
0.0315480 | + | 0.999502i | \(0.489956\pi\) | |||||||
\(908\) | 4.52033 | 0.150013 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 11.9254 | 0.395322 | ||||||||
\(911\) | −19.9002 | −0.659323 | −0.329661 | − | 0.944099i | \(-0.606935\pi\) | ||||
−0.329661 | + | 0.944099i | \(0.606935\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.7338 | −0.355236 | ||||||||
\(914\) | −11.5779 | −0.382963 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −30.8731 | −1.02007 | ||||||||
\(917\) | −19.6706 | −0.649579 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.5758 | −1.33847 | −0.669236 | − | 0.743049i | \(-0.733379\pi\) | ||||
−0.669236 | + | 0.743049i | \(0.733379\pi\) | |||||||
\(920\) | −5.84023 | −0.192547 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −7.01942 | −0.231172 | ||||||||
\(923\) | −13.6493 | −0.449271 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.25767 | −0.172871 | ||||||||
\(926\) | −9.38171 | −0.308302 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 35.2571 | 1.15737 | ||||||||
\(929\) | −11.4805 | −0.376662 | −0.188331 | − | 0.982106i | \(-0.560308\pi\) | ||||
−0.188331 | + | 0.982106i | \(0.560308\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.24299 | −0.270153 | ||||||||
\(932\) | −25.3050 | −0.828894 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.900828 | −0.0294760 | ||||||||
\(935\) | 1.20387 | 0.0393706 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.18099 | 0.0385811 | 0.0192906 | − | 0.999814i | \(-0.493859\pi\) | ||||
0.0192906 | + | 0.999814i | \(0.493859\pi\) | |||||||
\(938\) | −16.1547 | −0.527470 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9.55546 | −0.311665 | ||||||||
\(941\) | 30.1737 | 0.983634 | 0.491817 | − | 0.870699i | \(-0.336333\pi\) | ||||
0.491817 | + | 0.870699i | \(0.336333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.2709 | 0.497290 | ||||||||
\(944\) | −11.1634 | −0.363338 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.24338 | −0.137964 | ||||||||
\(947\) | 7.72440 | 0.251009 | 0.125505 | − | 0.992093i | \(-0.459945\pi\) | ||||
0.125505 | + | 0.992093i | \(0.459945\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.8546 | 0.612047 | ||||||||
\(950\) | 4.17294 | 0.135388 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.88640 | 0.125959 | ||||||||
\(953\) | −20.4499 | −0.662439 | −0.331219 | − | 0.943554i | \(-0.607460\pi\) | ||||
−0.331219 | + | 0.943554i | \(0.607460\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 43.9548 | 1.42235 | ||||||||
\(956\) | 8.13794 | 0.263200 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16.4967 | −0.532984 | ||||||||
\(959\) | 47.9758 | 1.54922 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.4352 | −0.659200 | ||||||||
\(962\) | 6.97617 | 0.224921 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −22.6285 | −0.728813 | ||||||||
\(965\) | −2.93482 | −0.0944753 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.76713 | 0.217616 | 0.108808 | − | 0.994063i | \(-0.465297\pi\) | ||||
0.108808 | + | 0.994063i | \(0.465297\pi\) | |||||||
\(968\) | −1.99258 | −0.0640440 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 16.0124 | 0.514128 | ||||||||
\(971\) | −52.4375 | −1.68280 | −0.841400 | − | 0.540413i | \(-0.818268\pi\) | ||||
−0.841400 | + | 0.540413i | \(0.818268\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −60.4536 | −1.93805 | ||||||||
\(974\) | −20.4352 | −0.654785 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.35399 | 0.0753494 | ||||||||
\(977\) | −26.4722 | −0.846921 | −0.423461 | − | 0.905915i | \(-0.639185\pi\) | ||||
−0.423461 | + | 0.905915i | \(0.639185\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.38437 | 0.204045 | ||||||||
\(980\) | −5.51153 | −0.176059 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 15.9822 | 0.510011 | ||||||||
\(983\) | −38.6605 | −1.23308 | −0.616538 | − | 0.787325i | \(-0.711466\pi\) | ||||
−0.616538 | + | 0.787325i | \(0.711466\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 31.2628 | 0.996115 | ||||||||
\(986\) | −2.37595 | −0.0756655 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 32.8902 | 1.04638 | ||||||||
\(989\) | 12.6807 | 0.403222 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.47031 | −0.0784719 | −0.0392360 | − | 0.999230i | \(-0.512492\pi\) | ||||
−0.0392360 | + | 0.999230i | \(0.512492\pi\) | |||||||
\(992\) | −17.0606 | −0.541674 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5.28036 | −0.167483 | ||||||||
\(995\) | 25.5586 | 0.810262 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −52.1001 | −1.65003 | −0.825014 | − | 0.565113i | \(-0.808833\pi\) | ||||
−0.825014 | + | 0.565113i | \(0.808833\pi\) | |||||||
\(998\) | −14.8871 | −0.471244 | ||||||||
\(999\) | 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.p.1.13 | yes | 25 | |
3.2 | odd | 2 | 6039.2.a.m.1.13 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6039.2.a.m.1.13 | ✓ | 25 | 3.2 | odd | 2 | ||
6039.2.a.p.1.13 | yes | 25 | 1.1 | even | 1 | trivial |