Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6034,2,Mod(1,6034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6034 = 2 \cdot 7 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6034.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: | \(48.1817325796\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 6034.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.44122 | −0.832087 | −0.416043 | − | 0.909345i | \(-0.636584\pi\) | ||||
−0.416043 | + | 0.909345i | \(0.636584\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.06061 | −0.921534 | −0.460767 | − | 0.887521i | \(-0.652426\pi\) | ||||
−0.460767 | + | 0.887521i | \(0.652426\pi\) | |||||||
\(6\) | 1.44122 | 0.588374 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.922894 | −0.307631 | ||||||||
\(10\) | 2.06061 | 0.651623 | ||||||||
\(11\) | 5.36187 | 1.61666 | 0.808332 | − | 0.588727i | \(-0.200371\pi\) | ||||
0.808332 | + | 0.588727i | \(0.200371\pi\) | |||||||
\(12\) | −1.44122 | −0.416043 | ||||||||
\(13\) | −1.30949 | −0.363186 | −0.181593 | − | 0.983374i | \(-0.558125\pi\) | ||||
−0.181593 | + | 0.983374i | \(0.558125\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 2.96979 | 0.766796 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.952708 | 0.231066 | 0.115533 | − | 0.993304i | \(-0.463142\pi\) | ||||
0.115533 | + | 0.993304i | \(0.463142\pi\) | |||||||
\(18\) | 0.922894 | 0.217528 | ||||||||
\(19\) | 0.858033 | 0.196846 | 0.0984231 | − | 0.995145i | \(-0.468620\pi\) | ||||
0.0984231 | + | 0.995145i | \(0.468620\pi\) | |||||||
\(20\) | −2.06061 | −0.460767 | ||||||||
\(21\) | 1.44122 | 0.314499 | ||||||||
\(22\) | −5.36187 | −1.14315 | ||||||||
\(23\) | −3.31160 | −0.690517 | −0.345258 | − | 0.938508i | \(-0.612209\pi\) | ||||
−0.345258 | + | 0.938508i | \(0.612209\pi\) | |||||||
\(24\) | 1.44122 | 0.294187 | ||||||||
\(25\) | −0.753879 | −0.150776 | ||||||||
\(26\) | 1.30949 | 0.256811 | ||||||||
\(27\) | 5.65374 | 1.08806 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −6.46534 | −1.20058 | −0.600292 | − | 0.799781i | \(-0.704949\pi\) | ||||
−0.600292 | + | 0.799781i | \(0.704949\pi\) | |||||||
\(30\) | −2.96979 | −0.542207 | ||||||||
\(31\) | −1.34002 | −0.240674 | −0.120337 | − | 0.992733i | \(-0.538398\pi\) | ||||
−0.120337 | + | 0.992733i | \(0.538398\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −7.72761 | −1.34520 | ||||||||
\(34\) | −0.952708 | −0.163388 | ||||||||
\(35\) | 2.06061 | 0.348307 | ||||||||
\(36\) | −0.922894 | −0.153816 | ||||||||
\(37\) | 10.6717 | 1.75441 | 0.877205 | − | 0.480115i | \(-0.159405\pi\) | ||||
0.877205 | + | 0.480115i | \(0.159405\pi\) | |||||||
\(38\) | −0.858033 | −0.139191 | ||||||||
\(39\) | 1.88725 | 0.302202 | ||||||||
\(40\) | 2.06061 | 0.325811 | ||||||||
\(41\) | 10.3312 | 1.61346 | 0.806729 | − | 0.590921i | \(-0.201236\pi\) | ||||
0.806729 | + | 0.590921i | \(0.201236\pi\) | |||||||
\(42\) | −1.44122 | −0.222385 | ||||||||
\(43\) | −12.4429 | −1.89753 | −0.948765 | − | 0.315984i | \(-0.897665\pi\) | ||||
−0.948765 | + | 0.315984i | \(0.897665\pi\) | |||||||
\(44\) | 5.36187 | 0.808332 | ||||||||
\(45\) | 1.90173 | 0.283493 | ||||||||
\(46\) | 3.31160 | 0.488269 | ||||||||
\(47\) | −0.731597 | −0.106714 | −0.0533572 | − | 0.998575i | \(-0.516992\pi\) | ||||
−0.0533572 | + | 0.998575i | \(0.516992\pi\) | |||||||
\(48\) | −1.44122 | −0.208022 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.753879 | 0.106615 | ||||||||
\(51\) | −1.37306 | −0.192267 | ||||||||
\(52\) | −1.30949 | −0.181593 | ||||||||
\(53\) | −5.33616 | −0.732978 | −0.366489 | − | 0.930422i | \(-0.619440\pi\) | ||||
−0.366489 | + | 0.930422i | \(0.619440\pi\) | |||||||
\(54\) | −5.65374 | −0.769377 | ||||||||
\(55\) | −11.0487 | −1.48981 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −1.23661 | −0.163793 | ||||||||
\(58\) | 6.46534 | 0.848941 | ||||||||
\(59\) | 3.54084 | 0.460978 | 0.230489 | − | 0.973075i | \(-0.425967\pi\) | ||||
0.230489 | + | 0.973075i | \(0.425967\pi\) | |||||||
\(60\) | 2.96979 | 0.383398 | ||||||||
\(61\) | 10.5771 | 1.35426 | 0.677132 | − | 0.735862i | \(-0.263223\pi\) | ||||
0.677132 | + | 0.735862i | \(0.263223\pi\) | |||||||
\(62\) | 1.34002 | 0.170182 | ||||||||
\(63\) | 0.922894 | 0.116274 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.69834 | 0.334688 | ||||||||
\(66\) | 7.72761 | 0.951204 | ||||||||
\(67\) | 5.59410 | 0.683429 | 0.341714 | − | 0.939804i | \(-0.388992\pi\) | ||||
0.341714 | + | 0.939804i | \(0.388992\pi\) | |||||||
\(68\) | 0.952708 | 0.115533 | ||||||||
\(69\) | 4.77274 | 0.574570 | ||||||||
\(70\) | −2.06061 | −0.246290 | ||||||||
\(71\) | −6.54641 | −0.776916 | −0.388458 | − | 0.921467i | \(-0.626992\pi\) | ||||
−0.388458 | + | 0.921467i | \(0.626992\pi\) | |||||||
\(72\) | 0.922894 | 0.108764 | ||||||||
\(73\) | −14.5970 | −1.70845 | −0.854224 | − | 0.519905i | \(-0.825967\pi\) | ||||
−0.854224 | + | 0.519905i | \(0.825967\pi\) | |||||||
\(74\) | −10.6717 | −1.24056 | ||||||||
\(75\) | 1.08650 | 0.125459 | ||||||||
\(76\) | 0.858033 | 0.0984231 | ||||||||
\(77\) | −5.36187 | −0.611042 | ||||||||
\(78\) | −1.88725 | −0.213689 | ||||||||
\(79\) | 7.82490 | 0.880370 | 0.440185 | − | 0.897907i | \(-0.354913\pi\) | ||||
0.440185 | + | 0.897907i | \(0.354913\pi\) | |||||||
\(80\) | −2.06061 | −0.230383 | ||||||||
\(81\) | −5.37959 | −0.597732 | ||||||||
\(82\) | −10.3312 | −1.14089 | ||||||||
\(83\) | −8.16771 | −0.896522 | −0.448261 | − | 0.893903i | \(-0.647957\pi\) | ||||
−0.448261 | + | 0.893903i | \(0.647957\pi\) | |||||||
\(84\) | 1.44122 | 0.157250 | ||||||||
\(85\) | −1.96316 | −0.212935 | ||||||||
\(86\) | 12.4429 | 1.34176 | ||||||||
\(87\) | 9.31796 | 0.998990 | ||||||||
\(88\) | −5.36187 | −0.571577 | ||||||||
\(89\) | −9.24161 | −0.979609 | −0.489804 | − | 0.871832i | \(-0.662932\pi\) | ||||
−0.489804 | + | 0.871832i | \(0.662932\pi\) | |||||||
\(90\) | −1.90173 | −0.200460 | ||||||||
\(91\) | 1.30949 | 0.137271 | ||||||||
\(92\) | −3.31160 | −0.345258 | ||||||||
\(93\) | 1.93126 | 0.200262 | ||||||||
\(94\) | 0.731597 | 0.0754585 | ||||||||
\(95\) | −1.76807 | −0.181400 | ||||||||
\(96\) | 1.44122 | 0.147094 | ||||||||
\(97\) | −7.78207 | −0.790150 | −0.395075 | − | 0.918649i | \(-0.629281\pi\) | ||||
−0.395075 | + | 0.918649i | \(0.629281\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −4.94844 | −0.497336 | ||||||||
\(100\) | −0.753879 | −0.0753879 | ||||||||
\(101\) | 2.58345 | 0.257063 | 0.128532 | − | 0.991705i | \(-0.458974\pi\) | ||||
0.128532 | + | 0.991705i | \(0.458974\pi\) | |||||||
\(102\) | 1.37306 | 0.135953 | ||||||||
\(103\) | −7.45659 | −0.734720 | −0.367360 | − | 0.930079i | \(-0.619738\pi\) | ||||
−0.367360 | + | 0.930079i | \(0.619738\pi\) | |||||||
\(104\) | 1.30949 | 0.128406 | ||||||||
\(105\) | −2.96979 | −0.289822 | ||||||||
\(106\) | 5.33616 | 0.518294 | ||||||||
\(107\) | −15.1193 | −1.46164 | −0.730819 | − | 0.682571i | \(-0.760862\pi\) | ||||
−0.730819 | + | 0.682571i | \(0.760862\pi\) | |||||||
\(108\) | 5.65374 | 0.544031 | ||||||||
\(109\) | −11.0227 | −1.05578 | −0.527892 | − | 0.849311i | \(-0.677017\pi\) | ||||
−0.527892 | + | 0.849311i | \(0.677017\pi\) | |||||||
\(110\) | 11.0487 | 1.05345 | ||||||||
\(111\) | −15.3802 | −1.45982 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 7.36105 | 0.692469 | 0.346235 | − | 0.938148i | \(-0.387460\pi\) | ||||
0.346235 | + | 0.938148i | \(0.387460\pi\) | |||||||
\(114\) | 1.23661 | 0.115819 | ||||||||
\(115\) | 6.82393 | 0.636334 | ||||||||
\(116\) | −6.46534 | −0.600292 | ||||||||
\(117\) | 1.20852 | 0.111727 | ||||||||
\(118\) | −3.54084 | −0.325961 | ||||||||
\(119\) | −0.952708 | −0.0873346 | ||||||||
\(120\) | −2.96979 | −0.271103 | ||||||||
\(121\) | 17.7496 | 1.61360 | ||||||||
\(122\) | −10.5771 | −0.957609 | ||||||||
\(123\) | −14.8895 | −1.34254 | ||||||||
\(124\) | −1.34002 | −0.120337 | ||||||||
\(125\) | 11.8565 | 1.06048 | ||||||||
\(126\) | −0.922894 | −0.0822179 | ||||||||
\(127\) | 1.48055 | 0.131378 | 0.0656888 | − | 0.997840i | \(-0.479076\pi\) | ||||
0.0656888 | + | 0.997840i | \(0.479076\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 17.9330 | 1.57891 | ||||||||
\(130\) | −2.69834 | −0.236660 | ||||||||
\(131\) | 10.7800 | 0.941849 | 0.470924 | − | 0.882174i | \(-0.343920\pi\) | ||||
0.470924 | + | 0.882174i | \(0.343920\pi\) | |||||||
\(132\) | −7.72761 | −0.672602 | ||||||||
\(133\) | −0.858033 | −0.0744009 | ||||||||
\(134\) | −5.59410 | −0.483257 | ||||||||
\(135\) | −11.6502 | −1.00269 | ||||||||
\(136\) | −0.952708 | −0.0816940 | ||||||||
\(137\) | −1.96379 | −0.167778 | −0.0838891 | − | 0.996475i | \(-0.526734\pi\) | ||||
−0.0838891 | + | 0.996475i | \(0.526734\pi\) | |||||||
\(138\) | −4.77274 | −0.406282 | ||||||||
\(139\) | −19.5278 | −1.65632 | −0.828162 | − | 0.560489i | \(-0.810613\pi\) | ||||
−0.828162 | + | 0.560489i | \(0.810613\pi\) | |||||||
\(140\) | 2.06061 | 0.174153 | ||||||||
\(141\) | 1.05439 | 0.0887957 | ||||||||
\(142\) | 6.54641 | 0.549362 | ||||||||
\(143\) | −7.02129 | −0.587149 | ||||||||
\(144\) | −0.922894 | −0.0769078 | ||||||||
\(145\) | 13.3226 | 1.10638 | ||||||||
\(146\) | 14.5970 | 1.20806 | ||||||||
\(147\) | −1.44122 | −0.118870 | ||||||||
\(148\) | 10.6717 | 0.877205 | ||||||||
\(149\) | −12.5231 | −1.02593 | −0.512967 | − | 0.858408i | \(-0.671454\pi\) | ||||
−0.512967 | + | 0.858408i | \(0.671454\pi\) | |||||||
\(150\) | −1.08650 | −0.0887126 | ||||||||
\(151\) | 7.93284 | 0.645565 | 0.322783 | − | 0.946473i | \(-0.395382\pi\) | ||||
0.322783 | + | 0.946473i | \(0.395382\pi\) | |||||||
\(152\) | −0.858033 | −0.0695956 | ||||||||
\(153\) | −0.879248 | −0.0710830 | ||||||||
\(154\) | 5.36187 | 0.432072 | ||||||||
\(155\) | 2.76126 | 0.221789 | ||||||||
\(156\) | 1.88725 | 0.151101 | ||||||||
\(157\) | −20.4111 | −1.62898 | −0.814491 | − | 0.580176i | \(-0.802984\pi\) | ||||
−0.814491 | + | 0.580176i | \(0.802984\pi\) | |||||||
\(158\) | −7.82490 | −0.622516 | ||||||||
\(159\) | 7.69057 | 0.609902 | ||||||||
\(160\) | 2.06061 | 0.162906 | ||||||||
\(161\) | 3.31160 | 0.260991 | ||||||||
\(162\) | 5.37959 | 0.422660 | ||||||||
\(163\) | 11.7522 | 0.920505 | 0.460252 | − | 0.887788i | \(-0.347759\pi\) | ||||
0.460252 | + | 0.887788i | \(0.347759\pi\) | |||||||
\(164\) | 10.3312 | 0.806729 | ||||||||
\(165\) | 15.9236 | 1.23965 | ||||||||
\(166\) | 8.16771 | 0.633937 | ||||||||
\(167\) | 4.08743 | 0.316295 | 0.158148 | − | 0.987415i | \(-0.449448\pi\) | ||||
0.158148 | + | 0.987415i | \(0.449448\pi\) | |||||||
\(168\) | −1.44122 | −0.111192 | ||||||||
\(169\) | −11.2852 | −0.868096 | ||||||||
\(170\) | 1.96316 | 0.150568 | ||||||||
\(171\) | −0.791873 | −0.0605561 | ||||||||
\(172\) | −12.4429 | −0.948765 | ||||||||
\(173\) | 12.9144 | 0.981862 | 0.490931 | − | 0.871198i | \(-0.336657\pi\) | ||||
0.490931 | + | 0.871198i | \(0.336657\pi\) | |||||||
\(174\) | −9.31796 | −0.706393 | ||||||||
\(175\) | 0.753879 | 0.0569879 | ||||||||
\(176\) | 5.36187 | 0.404166 | ||||||||
\(177\) | −5.10312 | −0.383574 | ||||||||
\(178\) | 9.24161 | 0.692688 | ||||||||
\(179\) | −14.0782 | −1.05225 | −0.526127 | − | 0.850406i | \(-0.676356\pi\) | ||||
−0.526127 | + | 0.850406i | \(0.676356\pi\) | |||||||
\(180\) | 1.90173 | 0.141746 | ||||||||
\(181\) | 14.5243 | 1.07958 | 0.539790 | − | 0.841800i | \(-0.318504\pi\) | ||||
0.539790 | + | 0.841800i | \(0.318504\pi\) | |||||||
\(182\) | −1.30949 | −0.0970655 | ||||||||
\(183\) | −15.2440 | −1.12687 | ||||||||
\(184\) | 3.31160 | 0.244135 | ||||||||
\(185\) | −21.9902 | −1.61675 | ||||||||
\(186\) | −1.93126 | −0.141607 | ||||||||
\(187\) | 5.10829 | 0.373555 | ||||||||
\(188\) | −0.731597 | −0.0533572 | ||||||||
\(189\) | −5.65374 | −0.411249 | ||||||||
\(190\) | 1.76807 | 0.128269 | ||||||||
\(191\) | 16.4301 | 1.18884 | 0.594421 | − | 0.804154i | \(-0.297381\pi\) | ||||
0.594421 | + | 0.804154i | \(0.297381\pi\) | |||||||
\(192\) | −1.44122 | −0.104011 | ||||||||
\(193\) | 1.84467 | 0.132782 | 0.0663912 | − | 0.997794i | \(-0.478851\pi\) | ||||
0.0663912 | + | 0.997794i | \(0.478851\pi\) | |||||||
\(194\) | 7.78207 | 0.558720 | ||||||||
\(195\) | −3.88889 | −0.278489 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 21.6830 | 1.54485 | 0.772424 | − | 0.635107i | \(-0.219044\pi\) | ||||
0.772424 | + | 0.635107i | \(0.219044\pi\) | |||||||
\(198\) | 4.94844 | 0.351670 | ||||||||
\(199\) | 2.47717 | 0.175602 | 0.0878008 | − | 0.996138i | \(-0.472016\pi\) | ||||
0.0878008 | + | 0.996138i | \(0.472016\pi\) | |||||||
\(200\) | 0.753879 | 0.0533073 | ||||||||
\(201\) | −8.06232 | −0.568672 | ||||||||
\(202\) | −2.58345 | −0.181771 | ||||||||
\(203\) | 6.46534 | 0.453778 | ||||||||
\(204\) | −1.37306 | −0.0961333 | ||||||||
\(205\) | −21.2885 | −1.48686 | ||||||||
\(206\) | 7.45659 | 0.519526 | ||||||||
\(207\) | 3.05626 | 0.212425 | ||||||||
\(208\) | −1.30949 | −0.0907965 | ||||||||
\(209\) | 4.60066 | 0.318234 | ||||||||
\(210\) | 2.96979 | 0.204935 | ||||||||
\(211\) | −0.834672 | −0.0574612 | −0.0287306 | − | 0.999587i | \(-0.509146\pi\) | ||||
−0.0287306 | + | 0.999587i | \(0.509146\pi\) | |||||||
\(212\) | −5.33616 | −0.366489 | ||||||||
\(213\) | 9.43479 | 0.646461 | ||||||||
\(214\) | 15.1193 | 1.03353 | ||||||||
\(215\) | 25.6400 | 1.74864 | ||||||||
\(216\) | −5.65374 | −0.384688 | ||||||||
\(217\) | 1.34002 | 0.0909663 | ||||||||
\(218\) | 11.0227 | 0.746552 | ||||||||
\(219\) | 21.0374 | 1.42158 | ||||||||
\(220\) | −11.0487 | −0.744905 | ||||||||
\(221\) | −1.24756 | −0.0839197 | ||||||||
\(222\) | 15.3802 | 1.03225 | ||||||||
\(223\) | −10.1578 | −0.680219 | −0.340110 | − | 0.940386i | \(-0.610464\pi\) | ||||
−0.340110 | + | 0.940386i | \(0.610464\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0.695750 | 0.0463833 | ||||||||
\(226\) | −7.36105 | −0.489650 | ||||||||
\(227\) | 6.81561 | 0.452368 | 0.226184 | − | 0.974085i | \(-0.427375\pi\) | ||||
0.226184 | + | 0.974085i | \(0.427375\pi\) | |||||||
\(228\) | −1.23661 | −0.0818966 | ||||||||
\(229\) | 13.1381 | 0.868188 | 0.434094 | − | 0.900868i | \(-0.357069\pi\) | ||||
0.434094 | + | 0.900868i | \(0.357069\pi\) | |||||||
\(230\) | −6.82393 | −0.449956 | ||||||||
\(231\) | 7.72761 | 0.508440 | ||||||||
\(232\) | 6.46534 | 0.424471 | ||||||||
\(233\) | 15.4705 | 1.01351 | 0.506753 | − | 0.862092i | \(-0.330846\pi\) | ||||
0.506753 | + | 0.862092i | \(0.330846\pi\) | |||||||
\(234\) | −1.20852 | −0.0790032 | ||||||||
\(235\) | 1.50754 | 0.0983409 | ||||||||
\(236\) | 3.54084 | 0.230489 | ||||||||
\(237\) | −11.2774 | −0.732545 | ||||||||
\(238\) | 0.952708 | 0.0617549 | ||||||||
\(239\) | −26.3858 | −1.70675 | −0.853376 | − | 0.521295i | \(-0.825449\pi\) | ||||
−0.853376 | + | 0.521295i | \(0.825449\pi\) | |||||||
\(240\) | 2.96979 | 0.191699 | ||||||||
\(241\) | −3.18617 | −0.205240 | −0.102620 | − | 0.994721i | \(-0.532722\pi\) | ||||
−0.102620 | + | 0.994721i | \(0.532722\pi\) | |||||||
\(242\) | −17.7496 | −1.14099 | ||||||||
\(243\) | −9.20807 | −0.590698 | ||||||||
\(244\) | 10.5771 | 0.677132 | ||||||||
\(245\) | −2.06061 | −0.131648 | ||||||||
\(246\) | 14.8895 | 0.949318 | ||||||||
\(247\) | −1.12358 | −0.0714918 | ||||||||
\(248\) | 1.34002 | 0.0850912 | ||||||||
\(249\) | 11.7714 | 0.745985 | ||||||||
\(250\) | −11.8565 | −0.749872 | ||||||||
\(251\) | 26.4734 | 1.67099 | 0.835493 | − | 0.549501i | \(-0.185182\pi\) | ||||
0.835493 | + | 0.549501i | \(0.185182\pi\) | |||||||
\(252\) | 0.922894 | 0.0581369 | ||||||||
\(253\) | −17.7564 | −1.11633 | ||||||||
\(254\) | −1.48055 | −0.0928980 | ||||||||
\(255\) | 2.82934 | 0.177180 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 23.9020 | 1.49097 | 0.745484 | − | 0.666524i | \(-0.232219\pi\) | ||||
0.745484 | + | 0.666524i | \(0.232219\pi\) | |||||||
\(258\) | −17.9330 | −1.11646 | ||||||||
\(259\) | −10.6717 | −0.663105 | ||||||||
\(260\) | 2.69834 | 0.167344 | ||||||||
\(261\) | 5.96683 | 0.369337 | ||||||||
\(262\) | −10.7800 | −0.665988 | ||||||||
\(263\) | −11.0210 | −0.679582 | −0.339791 | − | 0.940501i | \(-0.610356\pi\) | ||||
−0.339791 | + | 0.940501i | \(0.610356\pi\) | |||||||
\(264\) | 7.72761 | 0.475602 | ||||||||
\(265\) | 10.9958 | 0.675464 | ||||||||
\(266\) | 0.858033 | 0.0526094 | ||||||||
\(267\) | 13.3192 | 0.815120 | ||||||||
\(268\) | 5.59410 | 0.341714 | ||||||||
\(269\) | 14.5455 | 0.886852 | 0.443426 | − | 0.896311i | \(-0.353763\pi\) | ||||
0.443426 | + | 0.896311i | \(0.353763\pi\) | |||||||
\(270\) | 11.6502 | 0.709007 | ||||||||
\(271\) | 8.59631 | 0.522189 | 0.261094 | − | 0.965313i | \(-0.415917\pi\) | ||||
0.261094 | + | 0.965313i | \(0.415917\pi\) | |||||||
\(272\) | 0.952708 | 0.0577664 | ||||||||
\(273\) | −1.88725 | −0.114222 | ||||||||
\(274\) | 1.96379 | 0.118637 | ||||||||
\(275\) | −4.04220 | −0.243754 | ||||||||
\(276\) | 4.77274 | 0.287285 | ||||||||
\(277\) | 15.0235 | 0.902674 | 0.451337 | − | 0.892354i | \(-0.350947\pi\) | ||||
0.451337 | + | 0.892354i | \(0.350947\pi\) | |||||||
\(278\) | 19.5278 | 1.17120 | ||||||||
\(279\) | 1.23669 | 0.0740390 | ||||||||
\(280\) | −2.06061 | −0.123145 | ||||||||
\(281\) | −1.41898 | −0.0846493 | −0.0423247 | − | 0.999104i | \(-0.513476\pi\) | ||||
−0.0423247 | + | 0.999104i | \(0.513476\pi\) | |||||||
\(282\) | −1.05439 | −0.0627880 | ||||||||
\(283\) | 27.0107 | 1.60562 | 0.802810 | − | 0.596235i | \(-0.203337\pi\) | ||||
0.802810 | + | 0.596235i | \(0.203337\pi\) | |||||||
\(284\) | −6.54641 | −0.388458 | ||||||||
\(285\) | 2.54818 | 0.150941 | ||||||||
\(286\) | 7.02129 | 0.415177 | ||||||||
\(287\) | −10.3312 | −0.609830 | ||||||||
\(288\) | 0.922894 | 0.0543820 | ||||||||
\(289\) | −16.0923 | −0.946609 | ||||||||
\(290\) | −13.3226 | −0.782328 | ||||||||
\(291\) | 11.2157 | 0.657473 | ||||||||
\(292\) | −14.5970 | −0.854224 | ||||||||
\(293\) | 17.7650 | 1.03785 | 0.518923 | − | 0.854821i | \(-0.326333\pi\) | ||||
0.518923 | + | 0.854821i | \(0.326333\pi\) | |||||||
\(294\) | 1.44122 | 0.0840535 | ||||||||
\(295\) | −7.29630 | −0.424807 | ||||||||
\(296\) | −10.6717 | −0.620278 | ||||||||
\(297\) | 30.3146 | 1.75903 | ||||||||
\(298\) | 12.5231 | 0.725445 | ||||||||
\(299\) | 4.33649 | 0.250786 | ||||||||
\(300\) | 1.08650 | 0.0627293 | ||||||||
\(301\) | 12.4429 | 0.717199 | ||||||||
\(302\) | −7.93284 | −0.456484 | ||||||||
\(303\) | −3.72332 | −0.213899 | ||||||||
\(304\) | 0.858033 | 0.0492116 | ||||||||
\(305\) | −21.7954 | −1.24800 | ||||||||
\(306\) | 0.879248 | 0.0502633 | ||||||||
\(307\) | −10.8429 | −0.618836 | −0.309418 | − | 0.950926i | \(-0.600134\pi\) | ||||
−0.309418 | + | 0.950926i | \(0.600134\pi\) | |||||||
\(308\) | −5.36187 | −0.305521 | ||||||||
\(309\) | 10.7466 | 0.611351 | ||||||||
\(310\) | −2.76126 | −0.156829 | ||||||||
\(311\) | 19.1207 | 1.08423 | 0.542117 | − | 0.840303i | \(-0.317623\pi\) | ||||
0.542117 | + | 0.840303i | \(0.317623\pi\) | |||||||
\(312\) | −1.88725 | −0.106845 | ||||||||
\(313\) | 3.54610 | 0.200438 | 0.100219 | − | 0.994965i | \(-0.468046\pi\) | ||||
0.100219 | + | 0.994965i | \(0.468046\pi\) | |||||||
\(314\) | 20.4111 | 1.15186 | ||||||||
\(315\) | −1.90173 | −0.107150 | ||||||||
\(316\) | 7.82490 | 0.440185 | ||||||||
\(317\) | 14.8345 | 0.833187 | 0.416594 | − | 0.909093i | \(-0.363224\pi\) | ||||
0.416594 | + | 0.909093i | \(0.363224\pi\) | |||||||
\(318\) | −7.69057 | −0.431265 | ||||||||
\(319\) | −34.6663 | −1.94094 | ||||||||
\(320\) | −2.06061 | −0.115192 | ||||||||
\(321\) | 21.7902 | 1.21621 | ||||||||
\(322\) | −3.31160 | −0.184548 | ||||||||
\(323\) | 0.817454 | 0.0454844 | ||||||||
\(324\) | −5.37959 | −0.298866 | ||||||||
\(325\) | 0.987193 | 0.0547596 | ||||||||
\(326\) | −11.7522 | −0.650895 | ||||||||
\(327\) | 15.8861 | 0.878504 | ||||||||
\(328\) | −10.3312 | −0.570444 | ||||||||
\(329\) | 0.731597 | 0.0403343 | ||||||||
\(330\) | −15.9236 | −0.876566 | ||||||||
\(331\) | −5.85968 | −0.322077 | −0.161039 | − | 0.986948i | \(-0.551484\pi\) | ||||
−0.161039 | + | 0.986948i | \(0.551484\pi\) | |||||||
\(332\) | −8.16771 | −0.448261 | ||||||||
\(333\) | −9.84881 | −0.539712 | ||||||||
\(334\) | −4.08743 | −0.223654 | ||||||||
\(335\) | −11.5273 | −0.629802 | ||||||||
\(336\) | 1.44122 | 0.0786248 | ||||||||
\(337\) | −35.6583 | −1.94243 | −0.971216 | − | 0.238201i | \(-0.923442\pi\) | ||||
−0.971216 | + | 0.238201i | \(0.923442\pi\) | |||||||
\(338\) | 11.2852 | 0.613837 | ||||||||
\(339\) | −10.6089 | −0.576195 | ||||||||
\(340\) | −1.96316 | −0.106467 | ||||||||
\(341\) | −7.18500 | −0.389090 | ||||||||
\(342\) | 0.791873 | 0.0428196 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 12.4429 | 0.670878 | ||||||||
\(345\) | −9.83476 | −0.529486 | ||||||||
\(346\) | −12.9144 | −0.694281 | ||||||||
\(347\) | −30.3916 | −1.63151 | −0.815753 | − | 0.578401i | \(-0.803677\pi\) | ||||
−0.815753 | + | 0.578401i | \(0.803677\pi\) | |||||||
\(348\) | 9.31796 | 0.499495 | ||||||||
\(349\) | 20.1347 | 1.07779 | 0.538894 | − | 0.842373i | \(-0.318842\pi\) | ||||
0.538894 | + | 0.842373i | \(0.318842\pi\) | |||||||
\(350\) | −0.753879 | −0.0402965 | ||||||||
\(351\) | −7.40349 | −0.395169 | ||||||||
\(352\) | −5.36187 | −0.285789 | ||||||||
\(353\) | 2.93478 | 0.156202 | 0.0781012 | − | 0.996945i | \(-0.475114\pi\) | ||||
0.0781012 | + | 0.996945i | \(0.475114\pi\) | |||||||
\(354\) | 5.10312 | 0.271228 | ||||||||
\(355\) | 13.4896 | 0.715954 | ||||||||
\(356\) | −9.24161 | −0.489804 | ||||||||
\(357\) | 1.37306 | 0.0726700 | ||||||||
\(358\) | 14.0782 | 0.744056 | ||||||||
\(359\) | 7.85580 | 0.414613 | 0.207307 | − | 0.978276i | \(-0.433530\pi\) | ||||
0.207307 | + | 0.978276i | \(0.433530\pi\) | |||||||
\(360\) | −1.90173 | −0.100230 | ||||||||
\(361\) | −18.2638 | −0.961252 | ||||||||
\(362\) | −14.5243 | −0.763379 | ||||||||
\(363\) | −25.5811 | −1.34266 | ||||||||
\(364\) | 1.30949 | 0.0686357 | ||||||||
\(365\) | 30.0787 | 1.57439 | ||||||||
\(366\) | 15.2440 | 0.796814 | ||||||||
\(367\) | 33.3337 | 1.74001 | 0.870004 | − | 0.493045i | \(-0.164116\pi\) | ||||
0.870004 | + | 0.493045i | \(0.164116\pi\) | |||||||
\(368\) | −3.31160 | −0.172629 | ||||||||
\(369\) | −9.53458 | −0.496350 | ||||||||
\(370\) | 21.9902 | 1.14321 | ||||||||
\(371\) | 5.33616 | 0.277040 | ||||||||
\(372\) | 1.93126 | 0.100131 | ||||||||
\(373\) | 3.92427 | 0.203191 | 0.101596 | − | 0.994826i | \(-0.467605\pi\) | ||||
0.101596 | + | 0.994826i | \(0.467605\pi\) | |||||||
\(374\) | −5.10829 | −0.264144 | ||||||||
\(375\) | −17.0878 | −0.882410 | ||||||||
\(376\) | 0.731597 | 0.0377292 | ||||||||
\(377\) | 8.46627 | 0.436035 | ||||||||
\(378\) | 5.65374 | 0.290797 | ||||||||
\(379\) | 10.4331 | 0.535913 | 0.267956 | − | 0.963431i | \(-0.413652\pi\) | ||||
0.267956 | + | 0.963431i | \(0.413652\pi\) | |||||||
\(380\) | −1.76807 | −0.0907002 | ||||||||
\(381\) | −2.13379 | −0.109318 | ||||||||
\(382\) | −16.4301 | −0.840639 | ||||||||
\(383\) | −20.5998 | −1.05260 | −0.526301 | − | 0.850298i | \(-0.676421\pi\) | ||||
−0.526301 | + | 0.850298i | \(0.676421\pi\) | |||||||
\(384\) | 1.44122 | 0.0735468 | ||||||||
\(385\) | 11.0487 | 0.563095 | ||||||||
\(386\) | −1.84467 | −0.0938913 | ||||||||
\(387\) | 11.4835 | 0.583739 | ||||||||
\(388\) | −7.78207 | −0.395075 | ||||||||
\(389\) | 33.3523 | 1.69103 | 0.845515 | − | 0.533952i | \(-0.179294\pi\) | ||||
0.845515 | + | 0.533952i | \(0.179294\pi\) | |||||||
\(390\) | 3.88889 | 0.196922 | ||||||||
\(391\) | −3.15499 | −0.159555 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −15.5363 | −0.783700 | ||||||||
\(394\) | −21.6830 | −1.09237 | ||||||||
\(395\) | −16.1241 | −0.811291 | ||||||||
\(396\) | −4.94844 | −0.248668 | ||||||||
\(397\) | −13.6159 | −0.683363 | −0.341681 | − | 0.939816i | \(-0.610996\pi\) | ||||
−0.341681 | + | 0.939816i | \(0.610996\pi\) | |||||||
\(398\) | −2.47717 | −0.124169 | ||||||||
\(399\) | 1.23661 | 0.0619080 | ||||||||
\(400\) | −0.753879 | −0.0376939 | ||||||||
\(401\) | −2.99379 | −0.149503 | −0.0747513 | − | 0.997202i | \(-0.523816\pi\) | ||||
−0.0747513 | + | 0.997202i | \(0.523816\pi\) | |||||||
\(402\) | 8.06232 | 0.402112 | ||||||||
\(403\) | 1.75473 | 0.0874095 | ||||||||
\(404\) | 2.58345 | 0.128532 | ||||||||
\(405\) | 11.0852 | 0.550830 | ||||||||
\(406\) | −6.46534 | −0.320870 | ||||||||
\(407\) | 57.2201 | 2.83629 | ||||||||
\(408\) | 1.37306 | 0.0679765 | ||||||||
\(409\) | 3.45863 | 0.171018 | 0.0855091 | − | 0.996337i | \(-0.472748\pi\) | ||||
0.0855091 | + | 0.996337i | \(0.472748\pi\) | |||||||
\(410\) | 21.2885 | 1.05137 | ||||||||
\(411\) | 2.83025 | 0.139606 | ||||||||
\(412\) | −7.45659 | −0.367360 | ||||||||
\(413\) | −3.54084 | −0.174233 | ||||||||
\(414\) | −3.05626 | −0.150207 | ||||||||
\(415\) | 16.8305 | 0.826176 | ||||||||
\(416\) | 1.30949 | 0.0642028 | ||||||||
\(417\) | 28.1438 | 1.37821 | ||||||||
\(418\) | −4.60066 | −0.225026 | ||||||||
\(419\) | −0.276812 | −0.0135231 | −0.00676156 | − | 0.999977i | \(-0.502152\pi\) | ||||
−0.00676156 | + | 0.999977i | \(0.502152\pi\) | |||||||
\(420\) | −2.96979 | −0.144911 | ||||||||
\(421\) | −22.1698 | −1.08049 | −0.540245 | − | 0.841508i | \(-0.681668\pi\) | ||||
−0.540245 | + | 0.841508i | \(0.681668\pi\) | |||||||
\(422\) | 0.834672 | 0.0406312 | ||||||||
\(423\) | 0.675187 | 0.0328287 | ||||||||
\(424\) | 5.33616 | 0.259147 | ||||||||
\(425\) | −0.718226 | −0.0348391 | ||||||||
\(426\) | −9.43479 | −0.457117 | ||||||||
\(427\) | −10.5771 | −0.511864 | ||||||||
\(428\) | −15.1193 | −0.730819 | ||||||||
\(429\) | 10.1192 | 0.488559 | ||||||||
\(430\) | −25.6400 | −1.23647 | ||||||||
\(431\) | 1.00000 | 0.0481683 | ||||||||
\(432\) | 5.65374 | 0.272016 | ||||||||
\(433\) | 3.21212 | 0.154365 | 0.0771823 | − | 0.997017i | \(-0.475408\pi\) | ||||
0.0771823 | + | 0.997017i | \(0.475408\pi\) | |||||||
\(434\) | −1.34002 | −0.0643229 | ||||||||
\(435\) | −19.2007 | −0.920603 | ||||||||
\(436\) | −11.0227 | −0.527892 | ||||||||
\(437\) | −2.84146 | −0.135926 | ||||||||
\(438\) | −21.0374 | −1.00521 | ||||||||
\(439\) | 24.6687 | 1.17737 | 0.588686 | − | 0.808362i | \(-0.299645\pi\) | ||||
0.588686 | + | 0.808362i | \(0.299645\pi\) | |||||||
\(440\) | 11.0487 | 0.526727 | ||||||||
\(441\) | −0.922894 | −0.0439473 | ||||||||
\(442\) | 1.24756 | 0.0593402 | ||||||||
\(443\) | 11.4123 | 0.542215 | 0.271108 | − | 0.962549i | \(-0.412610\pi\) | ||||
0.271108 | + | 0.962549i | \(0.412610\pi\) | |||||||
\(444\) | −15.3802 | −0.729911 | ||||||||
\(445\) | 19.0434 | 0.902742 | ||||||||
\(446\) | 10.1578 | 0.480988 | ||||||||
\(447\) | 18.0485 | 0.853666 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 12.3645 | 0.583518 | 0.291759 | − | 0.956492i | \(-0.405760\pi\) | ||||
0.291759 | + | 0.956492i | \(0.405760\pi\) | |||||||
\(450\) | −0.695750 | −0.0327980 | ||||||||
\(451\) | 55.3944 | 2.60842 | ||||||||
\(452\) | 7.36105 | 0.346235 | ||||||||
\(453\) | −11.4329 | −0.537166 | ||||||||
\(454\) | −6.81561 | −0.319872 | ||||||||
\(455\) | −2.69834 | −0.126500 | ||||||||
\(456\) | 1.23661 | 0.0579096 | ||||||||
\(457\) | 11.0586 | 0.517298 | 0.258649 | − | 0.965971i | \(-0.416723\pi\) | ||||
0.258649 | + | 0.965971i | \(0.416723\pi\) | |||||||
\(458\) | −13.1381 | −0.613902 | ||||||||
\(459\) | 5.38636 | 0.251414 | ||||||||
\(460\) | 6.82393 | 0.318167 | ||||||||
\(461\) | 7.74473 | 0.360708 | 0.180354 | − | 0.983602i | \(-0.442276\pi\) | ||||
0.180354 | + | 0.983602i | \(0.442276\pi\) | |||||||
\(462\) | −7.72761 | −0.359521 | ||||||||
\(463\) | 26.8388 | 1.24730 | 0.623652 | − | 0.781702i | \(-0.285648\pi\) | ||||
0.623652 | + | 0.781702i | \(0.285648\pi\) | |||||||
\(464\) | −6.46534 | −0.300146 | ||||||||
\(465\) | −3.97957 | −0.184548 | ||||||||
\(466\) | −15.4705 | −0.716656 | ||||||||
\(467\) | 14.2019 | 0.657184 | 0.328592 | − | 0.944472i | \(-0.393426\pi\) | ||||
0.328592 | + | 0.944472i | \(0.393426\pi\) | |||||||
\(468\) | 1.20852 | 0.0558637 | ||||||||
\(469\) | −5.59410 | −0.258312 | ||||||||
\(470\) | −1.50754 | −0.0695375 | ||||||||
\(471\) | 29.4168 | 1.35545 | ||||||||
\(472\) | −3.54084 | −0.162980 | ||||||||
\(473\) | −66.7173 | −3.06767 | ||||||||
\(474\) | 11.2774 | 0.517987 | ||||||||
\(475\) | −0.646853 | −0.0296796 | ||||||||
\(476\) | −0.952708 | −0.0436673 | ||||||||
\(477\) | 4.92471 | 0.225487 | ||||||||
\(478\) | 26.3858 | 1.20686 | ||||||||
\(479\) | 25.3041 | 1.15617 | 0.578086 | − | 0.815976i | \(-0.303800\pi\) | ||||
0.578086 | + | 0.815976i | \(0.303800\pi\) | |||||||
\(480\) | −2.96979 | −0.135552 | ||||||||
\(481\) | −13.9744 | −0.637177 | ||||||||
\(482\) | 3.18617 | 0.145126 | ||||||||
\(483\) | −4.77274 | −0.217167 | ||||||||
\(484\) | 17.7496 | 0.806801 | ||||||||
\(485\) | 16.0358 | 0.728150 | ||||||||
\(486\) | 9.20807 | 0.417687 | ||||||||
\(487\) | 6.27381 | 0.284293 | 0.142147 | − | 0.989846i | \(-0.454600\pi\) | ||||
0.142147 | + | 0.989846i | \(0.454600\pi\) | |||||||
\(488\) | −10.5771 | −0.478805 | ||||||||
\(489\) | −16.9375 | −0.765940 | ||||||||
\(490\) | 2.06061 | 0.0930890 | ||||||||
\(491\) | 38.7200 | 1.74741 | 0.873705 | − | 0.486456i | \(-0.161711\pi\) | ||||
0.873705 | + | 0.486456i | \(0.161711\pi\) | |||||||
\(492\) | −14.8895 | −0.671269 | ||||||||
\(493\) | −6.15958 | −0.277414 | ||||||||
\(494\) | 1.12358 | 0.0505523 | ||||||||
\(495\) | 10.1968 | 0.458312 | ||||||||
\(496\) | −1.34002 | −0.0601686 | ||||||||
\(497\) | 6.54641 | 0.293647 | ||||||||
\(498\) | −11.7714 | −0.527491 | ||||||||
\(499\) | −23.5779 | −1.05549 | −0.527745 | − | 0.849403i | \(-0.676962\pi\) | ||||
−0.527745 | + | 0.849403i | \(0.676962\pi\) | |||||||
\(500\) | 11.8565 | 0.530239 | ||||||||
\(501\) | −5.89088 | −0.263185 | ||||||||
\(502\) | −26.4734 | −1.18157 | ||||||||
\(503\) | 41.8306 | 1.86513 | 0.932566 | − | 0.360999i | \(-0.117564\pi\) | ||||
0.932566 | + | 0.360999i | \(0.117564\pi\) | |||||||
\(504\) | −0.922894 | −0.0411090 | ||||||||
\(505\) | −5.32349 | −0.236892 | ||||||||
\(506\) | 17.7564 | 0.789367 | ||||||||
\(507\) | 16.2645 | 0.722331 | ||||||||
\(508\) | 1.48055 | 0.0656888 | ||||||||
\(509\) | 28.4218 | 1.25978 | 0.629888 | − | 0.776686i | \(-0.283101\pi\) | ||||
0.629888 | + | 0.776686i | \(0.283101\pi\) | |||||||
\(510\) | −2.82934 | −0.125285 | ||||||||
\(511\) | 14.5970 | 0.645733 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 4.85109 | 0.214181 | ||||||||
\(514\) | −23.9020 | −1.05427 | ||||||||
\(515\) | 15.3651 | 0.677069 | ||||||||
\(516\) | 17.9330 | 0.789455 | ||||||||
\(517\) | −3.92273 | −0.172521 | ||||||||
\(518\) | 10.6717 | 0.468886 | ||||||||
\(519\) | −18.6124 | −0.816995 | ||||||||
\(520\) | −2.69834 | −0.118330 | ||||||||
\(521\) | 31.0440 | 1.36006 | 0.680030 | − | 0.733184i | \(-0.261967\pi\) | ||||
0.680030 | + | 0.733184i | \(0.261967\pi\) | |||||||
\(522\) | −5.96683 | −0.261161 | ||||||||
\(523\) | 3.22234 | 0.140903 | 0.0704516 | − | 0.997515i | \(-0.477556\pi\) | ||||
0.0704516 | + | 0.997515i | \(0.477556\pi\) | |||||||
\(524\) | 10.7800 | 0.470924 | ||||||||
\(525\) | −1.08650 | −0.0474189 | ||||||||
\(526\) | 11.0210 | 0.480537 | ||||||||
\(527\) | −1.27665 | −0.0556116 | ||||||||
\(528\) | −7.72761 | −0.336301 | ||||||||
\(529\) | −12.0333 | −0.523187 | ||||||||
\(530\) | −10.9958 | −0.477625 | ||||||||
\(531\) | −3.26782 | −0.141811 | ||||||||
\(532\) | −0.858033 | −0.0372004 | ||||||||
\(533\) | −13.5285 | −0.585985 | ||||||||
\(534\) | −13.3192 | −0.576377 | ||||||||
\(535\) | 31.1550 | 1.34695 | ||||||||
\(536\) | −5.59410 | −0.241629 | ||||||||
\(537\) | 20.2897 | 0.875567 | ||||||||
\(538\) | −14.5455 | −0.627099 | ||||||||
\(539\) | 5.36187 | 0.230952 | ||||||||
\(540\) | −11.6502 | −0.501343 | ||||||||
\(541\) | −6.35637 | −0.273282 | −0.136641 | − | 0.990621i | \(-0.543631\pi\) | ||||
−0.136641 | + | 0.990621i | \(0.543631\pi\) | |||||||
\(542\) | −8.59631 | −0.369243 | ||||||||
\(543\) | −20.9326 | −0.898305 | ||||||||
\(544\) | −0.952708 | −0.0408470 | ||||||||
\(545\) | 22.7135 | 0.972941 | ||||||||
\(546\) | 1.88725 | 0.0807669 | ||||||||
\(547\) | −15.1207 | −0.646513 | −0.323257 | − | 0.946311i | \(-0.604778\pi\) | ||||
−0.323257 | + | 0.946311i | \(0.604778\pi\) | |||||||
\(548\) | −1.96379 | −0.0838891 | ||||||||
\(549\) | −9.76158 | −0.416614 | ||||||||
\(550\) | 4.04220 | 0.172360 | ||||||||
\(551\) | −5.54748 | −0.236330 | ||||||||
\(552\) | −4.77274 | −0.203141 | ||||||||
\(553\) | −7.82490 | −0.332749 | ||||||||
\(554\) | −15.0235 | −0.638287 | ||||||||
\(555\) | 31.6926 | 1.34528 | ||||||||
\(556\) | −19.5278 | −0.828162 | ||||||||
\(557\) | −14.8428 | −0.628909 | −0.314454 | − | 0.949273i | \(-0.601822\pi\) | ||||
−0.314454 | + | 0.949273i | \(0.601822\pi\) | |||||||
\(558\) | −1.23669 | −0.0523535 | ||||||||
\(559\) | 16.2938 | 0.689156 | ||||||||
\(560\) | 2.06061 | 0.0870767 | ||||||||
\(561\) | −7.36216 | −0.310831 | ||||||||
\(562\) | 1.41898 | 0.0598561 | ||||||||
\(563\) | −24.0489 | −1.01354 | −0.506770 | − | 0.862081i | \(-0.669161\pi\) | ||||
−0.506770 | + | 0.862081i | \(0.669161\pi\) | |||||||
\(564\) | 1.05439 | 0.0443978 | ||||||||
\(565\) | −15.1683 | −0.638134 | ||||||||
\(566\) | −27.0107 | −1.13534 | ||||||||
\(567\) | 5.37959 | 0.225921 | ||||||||
\(568\) | 6.54641 | 0.274681 | ||||||||
\(569\) | −34.0739 | −1.42845 | −0.714226 | − | 0.699915i | \(-0.753221\pi\) | ||||
−0.714226 | + | 0.699915i | \(0.753221\pi\) | |||||||
\(570\) | −2.54818 | −0.106731 | ||||||||
\(571\) | −11.9891 | −0.501729 | −0.250865 | − | 0.968022i | \(-0.580715\pi\) | ||||
−0.250865 | + | 0.968022i | \(0.580715\pi\) | |||||||
\(572\) | −7.02129 | −0.293575 | ||||||||
\(573\) | −23.6794 | −0.989221 | ||||||||
\(574\) | 10.3312 | 0.431215 | ||||||||
\(575\) | 2.49655 | 0.104113 | ||||||||
\(576\) | −0.922894 | −0.0384539 | ||||||||
\(577\) | −31.6775 | −1.31875 | −0.659376 | − | 0.751814i | \(-0.729179\pi\) | ||||
−0.659376 | + | 0.751814i | \(0.729179\pi\) | |||||||
\(578\) | 16.0923 | 0.669353 | ||||||||
\(579\) | −2.65857 | −0.110486 | ||||||||
\(580\) | 13.3226 | 0.553189 | ||||||||
\(581\) | 8.16771 | 0.338854 | ||||||||
\(582\) | −11.2157 | −0.464904 | ||||||||
\(583\) | −28.6118 | −1.18498 | ||||||||
\(584\) | 14.5970 | 0.604028 | ||||||||
\(585\) | −2.49028 | −0.102960 | ||||||||
\(586\) | −17.7650 | −0.733867 | ||||||||
\(587\) | 11.8890 | 0.490710 | 0.245355 | − | 0.969433i | \(-0.421095\pi\) | ||||
0.245355 | + | 0.969433i | \(0.421095\pi\) | |||||||
\(588\) | −1.44122 | −0.0594348 | ||||||||
\(589\) | −1.14978 | −0.0473758 | ||||||||
\(590\) | 7.29630 | 0.300384 | ||||||||
\(591\) | −31.2499 | −1.28545 | ||||||||
\(592\) | 10.6717 | 0.438603 | ||||||||
\(593\) | 5.09907 | 0.209394 | 0.104697 | − | 0.994504i | \(-0.466613\pi\) | ||||
0.104697 | + | 0.994504i | \(0.466613\pi\) | |||||||
\(594\) | −30.3146 | −1.24382 | ||||||||
\(595\) | 1.96316 | 0.0804818 | ||||||||
\(596\) | −12.5231 | −0.512967 | ||||||||
\(597\) | −3.57013 | −0.146116 | ||||||||
\(598\) | −4.33649 | −0.177332 | ||||||||
\(599\) | 23.2671 | 0.950668 | 0.475334 | − | 0.879805i | \(-0.342327\pi\) | ||||
0.475334 | + | 0.879805i | \(0.342327\pi\) | |||||||
\(600\) | −1.08650 | −0.0443563 | ||||||||
\(601\) | −13.7735 | −0.561834 | −0.280917 | − | 0.959732i | \(-0.590639\pi\) | ||||
−0.280917 | + | 0.959732i | \(0.590639\pi\) | |||||||
\(602\) | −12.4429 | −0.507136 | ||||||||
\(603\) | −5.16276 | −0.210244 | ||||||||
\(604\) | 7.93284 | 0.322783 | ||||||||
\(605\) | −36.5751 | −1.48699 | ||||||||
\(606\) | 3.72332 | 0.151249 | ||||||||
\(607\) | 29.9745 | 1.21663 | 0.608314 | − | 0.793697i | \(-0.291846\pi\) | ||||
0.608314 | + | 0.793697i | \(0.291846\pi\) | |||||||
\(608\) | −0.858033 | −0.0347978 | ||||||||
\(609\) | −9.31796 | −0.377583 | ||||||||
\(610\) | 21.7954 | 0.882469 | ||||||||
\(611\) | 0.958016 | 0.0387572 | ||||||||
\(612\) | −0.879248 | −0.0355415 | ||||||||
\(613\) | 4.61196 | 0.186275 | 0.0931377 | − | 0.995653i | \(-0.470310\pi\) | ||||
0.0931377 | + | 0.995653i | \(0.470310\pi\) | |||||||
\(614\) | 10.8429 | 0.437583 | ||||||||
\(615\) | 30.6814 | 1.23719 | ||||||||
\(616\) | 5.36187 | 0.216036 | ||||||||
\(617\) | −0.189931 | −0.00764632 | −0.00382316 | − | 0.999993i | \(-0.501217\pi\) | ||||
−0.00382316 | + | 0.999993i | \(0.501217\pi\) | |||||||
\(618\) | −10.7466 | −0.432290 | ||||||||
\(619\) | 26.2899 | 1.05668 | 0.528340 | − | 0.849033i | \(-0.322815\pi\) | ||||
0.528340 | + | 0.849033i | \(0.322815\pi\) | |||||||
\(620\) | 2.76126 | 0.110895 | ||||||||
\(621\) | −18.7229 | −0.751326 | ||||||||
\(622\) | −19.1207 | −0.766670 | ||||||||
\(623\) | 9.24161 | 0.370257 | ||||||||
\(624\) | 1.88725 | 0.0755505 | ||||||||
\(625\) | −20.6623 | −0.826491 | ||||||||
\(626\) | −3.54610 | −0.141731 | ||||||||
\(627\) | −6.63055 | −0.264798 | ||||||||
\(628\) | −20.4111 | −0.814491 | ||||||||
\(629\) | 10.1670 | 0.405384 | ||||||||
\(630\) | 1.90173 | 0.0757666 | ||||||||
\(631\) | 26.7760 | 1.06594 | 0.532968 | − | 0.846136i | \(-0.321077\pi\) | ||||
0.532968 | + | 0.846136i | \(0.321077\pi\) | |||||||
\(632\) | −7.82490 | −0.311258 | ||||||||
\(633\) | 1.20294 | 0.0478127 | ||||||||
\(634\) | −14.8345 | −0.589152 | ||||||||
\(635\) | −3.05084 | −0.121069 | ||||||||
\(636\) | 7.69057 | 0.304951 | ||||||||
\(637\) | −1.30949 | −0.0518837 | ||||||||
\(638\) | 34.6663 | 1.37245 | ||||||||
\(639\) | 6.04164 | 0.239004 | ||||||||
\(640\) | 2.06061 | 0.0814528 | ||||||||
\(641\) | 1.83176 | 0.0723502 | 0.0361751 | − | 0.999345i | \(-0.488483\pi\) | ||||
0.0361751 | + | 0.999345i | \(0.488483\pi\) | |||||||
\(642\) | −21.7902 | −0.859991 | ||||||||
\(643\) | 42.4874 | 1.67554 | 0.837770 | − | 0.546024i | \(-0.183859\pi\) | ||||
0.837770 | + | 0.546024i | \(0.183859\pi\) | |||||||
\(644\) | 3.31160 | 0.130495 | ||||||||
\(645\) | −36.9529 | −1.45502 | ||||||||
\(646\) | −0.817454 | −0.0321623 | ||||||||
\(647\) | −10.3764 | −0.407940 | −0.203970 | − | 0.978977i | \(-0.565385\pi\) | ||||
−0.203970 | + | 0.978977i | \(0.565385\pi\) | |||||||
\(648\) | 5.37959 | 0.211330 | ||||||||
\(649\) | 18.9855 | 0.745247 | ||||||||
\(650\) | −0.987193 | −0.0387209 | ||||||||
\(651\) | −1.93126 | −0.0756919 | ||||||||
\(652\) | 11.7522 | 0.460252 | ||||||||
\(653\) | 13.8983 | 0.543881 | 0.271940 | − | 0.962314i | \(-0.412335\pi\) | ||||
0.271940 | + | 0.962314i | \(0.412335\pi\) | |||||||
\(654\) | −15.8861 | −0.621196 | ||||||||
\(655\) | −22.2133 | −0.867946 | ||||||||
\(656\) | 10.3312 | 0.403365 | ||||||||
\(657\) | 13.4715 | 0.525572 | ||||||||
\(658\) | −0.731597 | −0.0285206 | ||||||||
\(659\) | 39.5933 | 1.54234 | 0.771168 | − | 0.636632i | \(-0.219673\pi\) | ||||
0.771168 | + | 0.636632i | \(0.219673\pi\) | |||||||
\(660\) | 15.9236 | 0.619826 | ||||||||
\(661\) | −45.8999 | −1.78530 | −0.892649 | − | 0.450752i | \(-0.851156\pi\) | ||||
−0.892649 | + | 0.450752i | \(0.851156\pi\) | |||||||
\(662\) | 5.85968 | 0.227743 | ||||||||
\(663\) | 1.79800 | 0.0698285 | ||||||||
\(664\) | 8.16771 | 0.316969 | ||||||||
\(665\) | 1.76807 | 0.0685629 | ||||||||
\(666\) | 9.84881 | 0.381634 | ||||||||
\(667\) | 21.4106 | 0.829023 | ||||||||
\(668\) | 4.08743 | 0.158148 | ||||||||
\(669\) | 14.6397 | 0.566002 | ||||||||
\(670\) | 11.5273 | 0.445338 | ||||||||
\(671\) | 56.7132 | 2.18939 | ||||||||
\(672\) | −1.44122 | −0.0555961 | ||||||||
\(673\) | −34.4120 | −1.32648 | −0.663242 | − | 0.748405i | \(-0.730820\pi\) | ||||
−0.663242 | + | 0.748405i | \(0.730820\pi\) | |||||||
\(674\) | 35.6583 | 1.37351 | ||||||||
\(675\) | −4.26223 | −0.164053 | ||||||||
\(676\) | −11.2852 | −0.434048 | ||||||||
\(677\) | −1.23111 | −0.0473152 | −0.0236576 | − | 0.999720i | \(-0.507531\pi\) | ||||
−0.0236576 | + | 0.999720i | \(0.507531\pi\) | |||||||
\(678\) | 10.6089 | 0.407431 | ||||||||
\(679\) | 7.78207 | 0.298649 | ||||||||
\(680\) | 1.96316 | 0.0752838 | ||||||||
\(681\) | −9.82277 | −0.376409 | ||||||||
\(682\) | 7.18500 | 0.275128 | ||||||||
\(683\) | −1.44557 | −0.0553133 | −0.0276566 | − | 0.999617i | \(-0.508805\pi\) | ||||
−0.0276566 | + | 0.999617i | \(0.508805\pi\) | |||||||
\(684\) | −0.791873 | −0.0302780 | ||||||||
\(685\) | 4.04662 | 0.154613 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −18.9348 | −0.722408 | ||||||||
\(688\) | −12.4429 | −0.474382 | ||||||||
\(689\) | 6.98762 | 0.266207 | ||||||||
\(690\) | 9.83476 | 0.374403 | ||||||||
\(691\) | −12.0649 | −0.458970 | −0.229485 | − | 0.973312i | \(-0.573704\pi\) | ||||
−0.229485 | + | 0.973312i | \(0.573704\pi\) | |||||||
\(692\) | 12.9144 | 0.490931 | ||||||||
\(693\) | 4.94844 | 0.187976 | ||||||||
\(694\) | 30.3916 | 1.15365 | ||||||||
\(695\) | 40.2392 | 1.52636 | ||||||||
\(696\) | −9.31796 | −0.353196 | ||||||||
\(697\) | 9.84259 | 0.372815 | ||||||||
\(698\) | −20.1347 | −0.762111 | ||||||||
\(699\) | −22.2963 | −0.843324 | ||||||||
\(700\) | 0.753879 | 0.0284939 | ||||||||
\(701\) | −9.83329 | −0.371398 | −0.185699 | − | 0.982607i | \(-0.559455\pi\) | ||||
−0.185699 | + | 0.982607i | \(0.559455\pi\) | |||||||
\(702\) | 7.40349 | 0.279427 | ||||||||
\(703\) | 9.15664 | 0.345349 | ||||||||
\(704\) | 5.36187 | 0.202083 | ||||||||
\(705\) | −2.17269 | −0.0818282 | ||||||||
\(706\) | −2.93478 | −0.110452 | ||||||||
\(707\) | −2.58345 | −0.0971607 | ||||||||
\(708\) | −5.10312 | −0.191787 | ||||||||
\(709\) | 45.2023 | 1.69761 | 0.848804 | − | 0.528708i | \(-0.177323\pi\) | ||||
0.848804 | + | 0.528708i | \(0.177323\pi\) | |||||||
\(710\) | −13.4896 | −0.506256 | ||||||||
\(711\) | −7.22156 | −0.270829 | ||||||||
\(712\) | 9.24161 | 0.346344 | ||||||||
\(713\) | 4.43761 | 0.166190 | ||||||||
\(714\) | −1.37306 | −0.0513854 | ||||||||
\(715\) | 14.4681 | 0.541078 | ||||||||
\(716\) | −14.0782 | −0.526127 | ||||||||
\(717\) | 38.0276 | 1.42017 | ||||||||
\(718\) | −7.85580 | −0.293176 | ||||||||
\(719\) | 10.7166 | 0.399662 | 0.199831 | − | 0.979830i | \(-0.435961\pi\) | ||||
0.199831 | + | 0.979830i | \(0.435961\pi\) | |||||||
\(720\) | 1.90173 | 0.0708731 | ||||||||
\(721\) | 7.45659 | 0.277698 | ||||||||
\(722\) | 18.2638 | 0.679708 | ||||||||
\(723\) | 4.59197 | 0.170777 | ||||||||
\(724\) | 14.5243 | 0.539790 | ||||||||
\(725\) | 4.87408 | 0.181019 | ||||||||
\(726\) | 25.5811 | 0.949402 | ||||||||
\(727\) | 23.6351 | 0.876577 | 0.438288 | − | 0.898834i | \(-0.355585\pi\) | ||||
0.438288 | + | 0.898834i | \(0.355585\pi\) | |||||||
\(728\) | −1.30949 | −0.0485327 | ||||||||
\(729\) | 29.4096 | 1.08924 | ||||||||
\(730\) | −30.0787 | −1.11326 | ||||||||
\(731\) | −11.8545 | −0.438454 | ||||||||
\(732\) | −15.2440 | −0.563433 | ||||||||
\(733\) | 20.9517 | 0.773868 | 0.386934 | − | 0.922107i | \(-0.373534\pi\) | ||||
0.386934 | + | 0.922107i | \(0.373534\pi\) | |||||||
\(734\) | −33.3337 | −1.23037 | ||||||||
\(735\) | 2.96979 | 0.109542 | ||||||||
\(736\) | 3.31160 | 0.122067 | ||||||||
\(737\) | 29.9948 | 1.10487 | ||||||||
\(738\) | 9.53458 | 0.350973 | ||||||||
\(739\) | −21.8405 | −0.803417 | −0.401708 | − | 0.915768i | \(-0.631583\pi\) | ||||
−0.401708 | + | 0.915768i | \(0.631583\pi\) | |||||||
\(740\) | −21.9902 | −0.808374 | ||||||||
\(741\) | 1.61932 | 0.0594874 | ||||||||
\(742\) | −5.33616 | −0.195897 | ||||||||
\(743\) | −13.4089 | −0.491924 | −0.245962 | − | 0.969279i | \(-0.579104\pi\) | ||||
−0.245962 | + | 0.969279i | \(0.579104\pi\) | |||||||
\(744\) | −1.93126 | −0.0708033 | ||||||||
\(745\) | 25.8053 | 0.945433 | ||||||||
\(746\) | −3.92427 | −0.143678 | ||||||||
\(747\) | 7.53793 | 0.275798 | ||||||||
\(748\) | 5.10829 | 0.186778 | ||||||||
\(749\) | 15.1193 | 0.552447 | ||||||||
\(750\) | 17.0878 | 0.623958 | ||||||||
\(751\) | 45.4168 | 1.65728 | 0.828642 | − | 0.559779i | \(-0.189114\pi\) | ||||
0.828642 | + | 0.559779i | \(0.189114\pi\) | |||||||
\(752\) | −0.731597 | −0.0266786 | ||||||||
\(753\) | −38.1539 | −1.39041 | ||||||||
\(754\) | −8.46627 | −0.308323 | ||||||||
\(755\) | −16.3465 | −0.594910 | ||||||||
\(756\) | −5.65374 | −0.205625 | ||||||||
\(757\) | −16.7771 | −0.609775 | −0.304887 | − | 0.952388i | \(-0.598619\pi\) | ||||
−0.304887 | + | 0.952388i | \(0.598619\pi\) | |||||||
\(758\) | −10.4331 | −0.378947 | ||||||||
\(759\) | 25.5908 | 0.928886 | ||||||||
\(760\) | 1.76807 | 0.0641347 | ||||||||
\(761\) | 9.96107 | 0.361089 | 0.180544 | − | 0.983567i | \(-0.442214\pi\) | ||||
0.180544 | + | 0.983567i | \(0.442214\pi\) | |||||||
\(762\) | 2.13379 | 0.0772992 | ||||||||
\(763\) | 11.0227 | 0.399049 | ||||||||
\(764\) | 16.4301 | 0.594421 | ||||||||
\(765\) | 1.81179 | 0.0655054 | ||||||||
\(766\) | 20.5998 | 0.744302 | ||||||||
\(767\) | −4.63668 | −0.167421 | ||||||||
\(768\) | −1.44122 | −0.0520054 | ||||||||
\(769\) | 26.1494 | 0.942971 | 0.471485 | − | 0.881874i | \(-0.343718\pi\) | ||||
0.471485 | + | 0.881874i | \(0.343718\pi\) | |||||||
\(770\) | −11.0487 | −0.398169 | ||||||||
\(771\) | −34.4480 | −1.24061 | ||||||||
\(772\) | 1.84467 | 0.0663912 | ||||||||
\(773\) | −10.2663 | −0.369253 | −0.184626 | − | 0.982809i | \(-0.559108\pi\) | ||||
−0.184626 | + | 0.982809i | \(0.559108\pi\) | |||||||
\(774\) | −11.4835 | −0.412766 | ||||||||
\(775\) | 1.01021 | 0.0362878 | ||||||||
\(776\) | 7.78207 | 0.279360 | ||||||||
\(777\) | 15.3802 | 0.551761 | ||||||||
\(778\) | −33.3523 | −1.19574 | ||||||||
\(779\) | 8.86449 | 0.317603 | ||||||||
\(780\) | −3.88889 | −0.139245 | ||||||||
\(781\) | −35.1010 | −1.25601 | ||||||||
\(782\) | 3.15499 | 0.112822 | ||||||||
\(783\) | −36.5534 | −1.30631 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 42.0593 | 1.50116 | ||||||||
\(786\) | 15.5363 | 0.554160 | ||||||||
\(787\) | −29.9952 | −1.06922 | −0.534608 | − | 0.845100i | \(-0.679541\pi\) | ||||
−0.534608 | + | 0.845100i | \(0.679541\pi\) | |||||||
\(788\) | 21.6830 | 0.772424 | ||||||||
\(789\) | 15.8836 | 0.565471 | ||||||||
\(790\) | 16.1241 | 0.573669 | ||||||||
\(791\) | −7.36105 | −0.261729 | ||||||||
\(792\) | 4.94844 | 0.175835 | ||||||||
\(793\) | −13.8506 | −0.491849 | ||||||||
\(794\) | 13.6159 | 0.483210 | ||||||||
\(795\) | −15.8473 | −0.562045 | ||||||||
\(796\) | 2.47717 | 0.0878008 | ||||||||
\(797\) | −35.2420 | −1.24833 | −0.624167 | − | 0.781291i | \(-0.714562\pi\) | ||||
−0.624167 | + | 0.781291i | \(0.714562\pi\) | |||||||
\(798\) | −1.23661 | −0.0437756 | ||||||||
\(799\) | −0.696998 | −0.0246580 | ||||||||
\(800\) | 0.753879 | 0.0266536 | ||||||||
\(801\) | 8.52903 | 0.301358 | ||||||||
\(802\) | 2.99379 | 0.105714 | ||||||||
\(803\) | −78.2671 | −2.76199 | ||||||||
\(804\) | −8.06232 | −0.284336 | ||||||||
\(805\) | −6.82393 | −0.240512 | ||||||||
\(806\) | −1.75473 | −0.0618079 | ||||||||
\(807\) | −20.9632 | −0.737938 | ||||||||
\(808\) | −2.58345 | −0.0908855 | ||||||||
\(809\) | 49.1607 | 1.72840 | 0.864198 | − | 0.503151i | \(-0.167826\pi\) | ||||
0.864198 | + | 0.503151i | \(0.167826\pi\) | |||||||
\(810\) | −11.0852 | −0.389496 | ||||||||
\(811\) | 14.9889 | 0.526333 | 0.263166 | − | 0.964750i | \(-0.415233\pi\) | ||||
0.263166 | + | 0.964750i | \(0.415233\pi\) | |||||||
\(812\) | 6.46534 | 0.226889 | ||||||||
\(813\) | −12.3891 | −0.434506 | ||||||||
\(814\) | −57.2201 | −2.00556 | ||||||||
\(815\) | −24.2168 | −0.848276 | ||||||||
\(816\) | −1.37306 | −0.0480667 | ||||||||
\(817\) | −10.6764 | −0.373521 | ||||||||
\(818\) | −3.45863 | −0.120928 | ||||||||
\(819\) | −1.20852 | −0.0422290 | ||||||||
\(820\) | −21.2885 | −0.743428 | ||||||||
\(821\) | −19.6250 | −0.684919 | −0.342459 | − | 0.939533i | \(-0.611260\pi\) | ||||
−0.342459 | + | 0.939533i | \(0.611260\pi\) | |||||||
\(822\) | −2.83025 | −0.0987164 | ||||||||
\(823\) | −2.90579 | −0.101289 | −0.0506447 | − | 0.998717i | \(-0.516128\pi\) | ||||
−0.0506447 | + | 0.998717i | \(0.516128\pi\) | |||||||
\(824\) | 7.45659 | 0.259763 | ||||||||
\(825\) | 5.82568 | 0.202824 | ||||||||
\(826\) | 3.54084 | 0.123202 | ||||||||
\(827\) | 35.6584 | 1.23996 | 0.619981 | − | 0.784617i | \(-0.287140\pi\) | ||||
0.619981 | + | 0.784617i | \(0.287140\pi\) | |||||||
\(828\) | 3.05626 | 0.106212 | ||||||||
\(829\) | −28.9160 | −1.00429 | −0.502147 | − | 0.864782i | \(-0.667456\pi\) | ||||
−0.502147 | + | 0.864782i | \(0.667456\pi\) | |||||||
\(830\) | −16.8305 | −0.584194 | ||||||||
\(831\) | −21.6521 | −0.751103 | ||||||||
\(832\) | −1.30949 | −0.0453982 | ||||||||
\(833\) | 0.952708 | 0.0330094 | ||||||||
\(834\) | −28.1438 | −0.974539 | ||||||||
\(835\) | −8.42262 | −0.291477 | ||||||||
\(836\) | 4.60066 | 0.159117 | ||||||||
\(837\) | −7.57611 | −0.261869 | ||||||||
\(838\) | 0.276812 | 0.00956230 | ||||||||
\(839\) | 23.1069 | 0.797740 | 0.398870 | − | 0.917007i | \(-0.369402\pi\) | ||||
0.398870 | + | 0.917007i | \(0.369402\pi\) | |||||||
\(840\) | 2.96979 | 0.102467 | ||||||||
\(841\) | 12.8007 | 0.441402 | ||||||||
\(842\) | 22.1698 | 0.764022 | ||||||||
\(843\) | 2.04506 | 0.0704356 | ||||||||
\(844\) | −0.834672 | −0.0287306 | ||||||||
\(845\) | 23.2545 | 0.799980 | ||||||||
\(846\) | −0.675187 | −0.0232134 | ||||||||
\(847\) | −17.7496 | −0.609884 | ||||||||
\(848\) | −5.33616 | −0.183245 | ||||||||
\(849\) | −38.9283 | −1.33602 | ||||||||
\(850\) | 0.718226 | 0.0246350 | ||||||||
\(851\) | −35.3403 | −1.21145 | ||||||||
\(852\) | 9.43479 | 0.323231 | ||||||||
\(853\) | −42.3833 | −1.45118 | −0.725588 | − | 0.688130i | \(-0.758432\pi\) | ||||
−0.725588 | + | 0.688130i | \(0.758432\pi\) | |||||||
\(854\) | 10.5771 | 0.361942 | ||||||||
\(855\) | 1.63174 | 0.0558044 | ||||||||
\(856\) | 15.1193 | 0.516767 | ||||||||
\(857\) | −26.8447 | −0.916999 | −0.458499 | − | 0.888695i | \(-0.651613\pi\) | ||||
−0.458499 | + | 0.888695i | \(0.651613\pi\) | |||||||
\(858\) | −10.1192 | −0.345464 | ||||||||
\(859\) | −23.2718 | −0.794025 | −0.397013 | − | 0.917813i | \(-0.629953\pi\) | ||||
−0.397013 | + | 0.917813i | \(0.629953\pi\) | |||||||
\(860\) | 25.6400 | 0.874318 | ||||||||
\(861\) | 14.8895 | 0.507432 | ||||||||
\(862\) | −1.00000 | −0.0340601 | ||||||||
\(863\) | 11.2400 | 0.382615 | 0.191307 | − | 0.981530i | \(-0.438727\pi\) | ||||
0.191307 | + | 0.981530i | \(0.438727\pi\) | |||||||
\(864\) | −5.65374 | −0.192344 | ||||||||
\(865\) | −26.6115 | −0.904819 | ||||||||
\(866\) | −3.21212 | −0.109152 | ||||||||
\(867\) | 23.1926 | 0.787661 | ||||||||
\(868\) | 1.34002 | 0.0454832 | ||||||||
\(869\) | 41.9561 | 1.42326 | ||||||||
\(870\) | 19.2007 | 0.650965 | ||||||||
\(871\) | −7.32540 | −0.248212 | ||||||||
\(872\) | 11.0227 | 0.373276 | ||||||||
\(873\) | 7.18203 | 0.243075 | ||||||||
\(874\) | 2.84146 | 0.0961139 | ||||||||
\(875\) | −11.8565 | −0.400823 | ||||||||
\(876\) | 21.0374 | 0.710789 | ||||||||
\(877\) | 33.0853 | 1.11721 | 0.558605 | − | 0.829434i | \(-0.311337\pi\) | ||||
0.558605 | + | 0.829434i | \(0.311337\pi\) | |||||||
\(878\) | −24.6687 | −0.832528 | ||||||||
\(879\) | −25.6033 | −0.863577 | ||||||||
\(880\) | −11.0487 | −0.372453 | ||||||||
\(881\) | 2.80931 | 0.0946480 | 0.0473240 | − | 0.998880i | \(-0.484931\pi\) | ||||
0.0473240 | + | 0.998880i | \(0.484931\pi\) | |||||||
\(882\) | 0.922894 | 0.0310755 | ||||||||
\(883\) | 47.4740 | 1.59763 | 0.798814 | − | 0.601578i | \(-0.205461\pi\) | ||||
0.798814 | + | 0.601578i | \(0.205461\pi\) | |||||||
\(884\) | −1.24756 | −0.0419599 | ||||||||
\(885\) | 10.5156 | 0.353476 | ||||||||
\(886\) | −11.4123 | −0.383404 | ||||||||
\(887\) | 19.3974 | 0.651301 | 0.325651 | − | 0.945490i | \(-0.394417\pi\) | ||||
0.325651 | + | 0.945490i | \(0.394417\pi\) | |||||||
\(888\) | 15.3802 | 0.516125 | ||||||||
\(889\) | −1.48055 | −0.0496561 | ||||||||
\(890\) | −19.0434 | −0.638335 | ||||||||
\(891\) | −28.8446 | −0.966331 | ||||||||
\(892\) | −10.1578 | −0.340110 | ||||||||
\(893\) | −0.627734 | −0.0210063 | ||||||||
\(894\) | −18.0485 | −0.603633 | ||||||||
\(895\) | 29.0097 | 0.969687 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −6.24983 | −0.208676 | ||||||||
\(898\) | −12.3645 | −0.412609 | ||||||||
\(899\) | 8.66368 | 0.288950 | ||||||||
\(900\) | 0.695750 | 0.0231917 | ||||||||
\(901\) | −5.08380 | −0.169366 | ||||||||
\(902\) | −55.3944 | −1.84443 | ||||||||
\(903\) | −17.9330 | −0.596772 | ||||||||
\(904\) | −7.36105 | −0.244825 | ||||||||
\(905\) | −29.9289 | −0.994870 | ||||||||
\(906\) | 11.4329 | 0.379834 | ||||||||
\(907\) | −7.54944 | −0.250675 | −0.125338 | − | 0.992114i | \(-0.540001\pi\) | ||||
−0.125338 | + | 0.992114i | \(0.540001\pi\) | |||||||
\(908\) | 6.81561 | 0.226184 | ||||||||
\(909\) | −2.38425 | −0.0790807 | ||||||||
\(910\) | 2.69834 | 0.0894491 | ||||||||
\(911\) | 33.8218 | 1.12057 | 0.560283 | − | 0.828302i | \(-0.310693\pi\) | ||||
0.560283 | + | 0.828302i | \(0.310693\pi\) | |||||||
\(912\) | −1.23661 | −0.0409483 | ||||||||
\(913\) | −43.7942 | −1.44938 | ||||||||
\(914\) | −11.0586 | −0.365785 | ||||||||
\(915\) | 31.4119 | 1.03844 | ||||||||
\(916\) | 13.1381 | 0.434094 | ||||||||
\(917\) | −10.7800 | −0.355985 | ||||||||
\(918\) | −5.38636 | −0.177776 | ||||||||
\(919\) | −27.9602 | −0.922320 | −0.461160 | − | 0.887317i | \(-0.652567\pi\) | ||||
−0.461160 | + | 0.887317i | \(0.652567\pi\) | |||||||
\(920\) | −6.82393 | −0.224978 | ||||||||
\(921\) | 15.6269 | 0.514925 | ||||||||
\(922\) | −7.74473 | −0.255059 | ||||||||
\(923\) | 8.57242 | 0.282165 | ||||||||
\(924\) | 7.72761 | 0.254220 | ||||||||
\(925\) | −8.04514 | −0.264523 | ||||||||
\(926\) | −26.8388 | −0.881976 | ||||||||
\(927\) | 6.88165 | 0.226023 | ||||||||
\(928\) | 6.46534 | 0.212235 | ||||||||
\(929\) | −14.7532 | −0.484038 | −0.242019 | − | 0.970271i | \(-0.577810\pi\) | ||||
−0.242019 | + | 0.970271i | \(0.577810\pi\) | |||||||
\(930\) | 3.97957 | 0.130495 | ||||||||
\(931\) | 0.858033 | 0.0281209 | ||||||||
\(932\) | 15.4705 | 0.506753 | ||||||||
\(933\) | −27.5571 | −0.902178 | ||||||||
\(934\) | −14.2019 | −0.464700 | ||||||||
\(935\) | −10.5262 | −0.344244 | ||||||||
\(936\) | −1.20852 | −0.0395016 | ||||||||
\(937\) | −29.6050 | −0.967154 | −0.483577 | − | 0.875302i | \(-0.660663\pi\) | ||||
−0.483577 | + | 0.875302i | \(0.660663\pi\) | |||||||
\(938\) | 5.59410 | 0.182654 | ||||||||
\(939\) | −5.11070 | −0.166782 | ||||||||
\(940\) | 1.50754 | 0.0491705 | ||||||||
\(941\) | 17.2183 | 0.561301 | 0.280651 | − | 0.959810i | \(-0.409450\pi\) | ||||
0.280651 | + | 0.959810i | \(0.409450\pi\) | |||||||
\(942\) | −29.4168 | −0.958451 | ||||||||
\(943\) | −34.2127 | −1.11412 | ||||||||
\(944\) | 3.54084 | 0.115245 | ||||||||
\(945\) | 11.6502 | 0.378980 | ||||||||
\(946\) | 66.7173 | 2.16917 | ||||||||
\(947\) | −6.41790 | −0.208554 | −0.104277 | − | 0.994548i | \(-0.533253\pi\) | ||||
−0.104277 | + | 0.994548i | \(0.533253\pi\) | |||||||
\(948\) | −11.2774 | −0.366272 | ||||||||
\(949\) | 19.1145 | 0.620484 | ||||||||
\(950\) | 0.646853 | 0.0209867 | ||||||||
\(951\) | −21.3797 | −0.693284 | ||||||||
\(952\) | 0.952708 | 0.0308774 | ||||||||
\(953\) | 5.91434 | 0.191584 | 0.0957922 | − | 0.995401i | \(-0.469462\pi\) | ||||
0.0957922 | + | 0.995401i | \(0.469462\pi\) | |||||||
\(954\) | −4.92471 | −0.159443 | ||||||||
\(955\) | −33.8561 | −1.09556 | ||||||||
\(956\) | −26.3858 | −0.853376 | ||||||||
\(957\) | 49.9617 | 1.61503 | ||||||||
\(958\) | −25.3041 | −0.817537 | ||||||||
\(959\) | 1.96379 | 0.0634142 | ||||||||
\(960\) | 2.96979 | 0.0958495 | ||||||||
\(961\) | −29.2044 | −0.942076 | ||||||||
\(962\) | 13.9744 | 0.450552 | ||||||||
\(963\) | 13.9535 | 0.449646 | ||||||||
\(964\) | −3.18617 | −0.102620 | ||||||||
\(965\) | −3.80115 | −0.122363 | ||||||||
\(966\) | 4.77274 | 0.153560 | ||||||||
\(967\) | 3.59789 | 0.115700 | 0.0578501 | − | 0.998325i | \(-0.481575\pi\) | ||||
0.0578501 | + | 0.998325i | \(0.481575\pi\) | |||||||
\(968\) | −17.7496 | −0.570495 | ||||||||
\(969\) | −1.17813 | −0.0378470 | ||||||||
\(970\) | −16.0358 | −0.514879 | ||||||||
\(971\) | 6.16633 | 0.197887 | 0.0989434 | − | 0.995093i | \(-0.468454\pi\) | ||||
0.0989434 | + | 0.995093i | \(0.468454\pi\) | |||||||
\(972\) | −9.20807 | −0.295349 | ||||||||
\(973\) | 19.5278 | 0.626032 | ||||||||
\(974\) | −6.27381 | −0.201026 | ||||||||
\(975\) | −1.42276 | −0.0455648 | ||||||||
\(976\) | 10.5771 | 0.338566 | ||||||||
\(977\) | 19.0140 | 0.608312 | 0.304156 | − | 0.952622i | \(-0.401626\pi\) | ||||
0.304156 | + | 0.952622i | \(0.401626\pi\) | |||||||
\(978\) | 16.9375 | 0.541601 | ||||||||
\(979\) | −49.5523 | −1.58370 | ||||||||
\(980\) | −2.06061 | −0.0658238 | ||||||||
\(981\) | 10.1728 | 0.324792 | ||||||||
\(982\) | −38.7200 | −1.23561 | ||||||||
\(983\) | 42.9016 | 1.36835 | 0.684175 | − | 0.729318i | \(-0.260163\pi\) | ||||
0.684175 | + | 0.729318i | \(0.260163\pi\) | |||||||
\(984\) | 14.8895 | 0.474659 | ||||||||
\(985\) | −44.6802 | −1.42363 | ||||||||
\(986\) | 6.15958 | 0.196161 | ||||||||
\(987\) | −1.05439 | −0.0335616 | ||||||||
\(988\) | −1.12358 | −0.0357459 | ||||||||
\(989\) | 41.2060 | 1.31028 | ||||||||
\(990\) | −10.1968 | −0.324076 | ||||||||
\(991\) | 46.1663 | 1.46652 | 0.733260 | − | 0.679949i | \(-0.237998\pi\) | ||||
0.733260 | + | 0.679949i | \(0.237998\pi\) | |||||||
\(992\) | 1.34002 | 0.0425456 | ||||||||
\(993\) | 8.44507 | 0.267996 | ||||||||
\(994\) | −6.54641 | −0.207639 | ||||||||
\(995\) | −5.10448 | −0.161823 | ||||||||
\(996\) | 11.7714 | 0.372992 | ||||||||
\(997\) | 9.25911 | 0.293239 | 0.146619 | − | 0.989193i | \(-0.453161\pi\) | ||||
0.146619 | + | 0.989193i | \(0.453161\pi\) | |||||||
\(998\) | 23.5779 | 0.746345 | ||||||||
\(999\) | 60.3348 | 1.90891 |
(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 | 6034.2.a.n.1.7 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.n.1.7 | ✓ | 24 | 1.1 | even | 1 | trivial |