Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7942,2,Mod(1,7942)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7942, 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("7942.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7942 = 2 \cdot 11 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7942.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: | \(63.4171892853\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1940.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 8x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 418) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.94600\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7942.1 |
$q$-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 | ||||||||
\(3\) | −2.94600 | −1.70087 | −0.850436 | − | 0.526079i | \(-0.823662\pi\) | ||||
−0.850436 | + | 0.526079i | \(0.823662\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.00000 | 0.894427 | 0.447214 | − | 0.894427i | \(-0.352416\pi\) | ||||
0.447214 | + | 0.894427i | \(0.352416\pi\) | |||||||
\(6\) | 2.94600 | 1.20270 | ||||||||
\(7\) | 4.94600 | 1.86941 | 0.934705 | − | 0.355424i | \(-0.115663\pi\) | ||||
0.934705 | + | 0.355424i | \(0.115663\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 5.67889 | 1.89296 | ||||||||
\(10\) | −2.00000 | −0.632456 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −2.94600 | −0.850436 | ||||||||
\(13\) | 5.67889 | 1.57504 | 0.787520 | − | 0.616289i | \(-0.211365\pi\) | ||||
0.787520 | + | 0.616289i | \(0.211365\pi\) | |||||||
\(14\) | −4.94600 | −1.32187 | ||||||||
\(15\) | −5.89199 | −1.52131 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.73289 | 0.905359 | 0.452680 | − | 0.891673i | \(-0.350468\pi\) | ||||
0.452680 | + | 0.891673i | \(0.350468\pi\) | |||||||
\(18\) | −5.67889 | −1.33853 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 2.00000 | 0.447214 | ||||||||
\(21\) | −14.5709 | −3.17963 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −1.89199 | −0.394507 | −0.197254 | − | 0.980352i | \(-0.563202\pi\) | ||||
−0.197254 | + | 0.980352i | \(0.563202\pi\) | |||||||
\(24\) | 2.94600 | 0.601349 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −5.67889 | −1.11372 | ||||||||
\(27\) | −7.89199 | −1.51881 | ||||||||
\(28\) | 4.94600 | 0.934705 | ||||||||
\(29\) | −1.00000 | −0.185695 | −0.0928477 | − | 0.995680i | \(-0.529597\pi\) | ||||
−0.0928477 | + | 0.995680i | \(0.529597\pi\) | |||||||
\(30\) | 5.89199 | 1.07573 | ||||||||
\(31\) | 3.21310 | 0.577090 | 0.288545 | − | 0.957466i | \(-0.406828\pi\) | ||||
0.288545 | + | 0.957466i | \(0.406828\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.94600 | −0.512832 | ||||||||
\(34\) | −3.73289 | −0.640186 | ||||||||
\(35\) | 9.89199 | 1.67205 | ||||||||
\(36\) | 5.67889 | 0.946481 | ||||||||
\(37\) | −4.15910 | −0.683751 | −0.341876 | − | 0.939745i | \(-0.611062\pi\) | ||||
−0.341876 | + | 0.939745i | \(0.611062\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −16.7300 | −2.67894 | ||||||||
\(40\) | −2.00000 | −0.316228 | ||||||||
\(41\) | 9.62488 | 1.50315 | 0.751577 | − | 0.659645i | \(-0.229293\pi\) | ||||
0.751577 | + | 0.659645i | \(0.229293\pi\) | |||||||
\(42\) | 14.5709 | 2.24834 | ||||||||
\(43\) | −4.62488 | −0.705288 | −0.352644 | − | 0.935758i | \(-0.614717\pi\) | ||||
−0.352644 | + | 0.935758i | \(0.614717\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 11.3578 | 1.69312 | ||||||||
\(46\) | 1.89199 | 0.278959 | ||||||||
\(47\) | −7.41178 | −1.08112 | −0.540560 | − | 0.841306i | \(-0.681787\pi\) | ||||
−0.540560 | + | 0.841306i | \(0.681787\pi\) | |||||||
\(48\) | −2.94600 | −0.425218 | ||||||||
\(49\) | 17.4629 | 2.49470 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −10.9971 | −1.53990 | ||||||||
\(52\) | 5.67889 | 0.787520 | ||||||||
\(53\) | 11.7840 | 1.61865 | 0.809327 | − | 0.587358i | \(-0.199832\pi\) | ||||
0.809327 | + | 0.587358i | \(0.199832\pi\) | |||||||
\(54\) | 7.89199 | 1.07396 | ||||||||
\(55\) | 2.00000 | 0.269680 | ||||||||
\(56\) | −4.94600 | −0.660936 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.00000 | 0.131306 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | −5.89199 | −0.760653 | ||||||||
\(61\) | −5.57088 | −0.713278 | −0.356639 | − | 0.934242i | \(-0.616077\pi\) | ||||
−0.356639 | + | 0.934242i | \(0.616077\pi\) | |||||||
\(62\) | −3.21310 | −0.408064 | ||||||||
\(63\) | 28.0878 | 3.53872 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 11.3578 | 1.40876 | ||||||||
\(66\) | 2.94600 | 0.362627 | ||||||||
\(67\) | 8.83799 | 1.07973 | 0.539866 | − | 0.841751i | \(-0.318475\pi\) | ||||
0.539866 | + | 0.841751i | \(0.318475\pi\) | |||||||
\(68\) | 3.73289 | 0.452680 | ||||||||
\(69\) | 5.57379 | 0.671006 | ||||||||
\(70\) | −9.89199 | −1.18232 | ||||||||
\(71\) | 4.62488 | 0.548873 | 0.274436 | − | 0.961605i | \(-0.411509\pi\) | ||||
0.274436 | + | 0.961605i | \(0.411509\pi\) | |||||||
\(72\) | −5.67889 | −0.669263 | ||||||||
\(73\) | −3.62488 | −0.424260 | −0.212130 | − | 0.977241i | \(-0.568040\pi\) | ||||
−0.212130 | + | 0.977241i | \(0.568040\pi\) | |||||||
\(74\) | 4.15910 | 0.483485 | ||||||||
\(75\) | 2.94600 | 0.340174 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.94600 | 0.563648 | ||||||||
\(78\) | 16.7300 | 1.89430 | ||||||||
\(79\) | −6.83799 | −0.769333 | −0.384667 | − | 0.923056i | \(-0.625684\pi\) | ||||
−0.384667 | + | 0.923056i | \(0.625684\pi\) | |||||||
\(80\) | 2.00000 | 0.223607 | ||||||||
\(81\) | 6.21310 | 0.690345 | ||||||||
\(82\) | −9.62488 | −1.06289 | ||||||||
\(83\) | 14.5169 | 1.59343 | 0.796717 | − | 0.604353i | \(-0.206568\pi\) | ||||
0.796717 | + | 0.604353i | \(0.206568\pi\) | |||||||
\(84\) | −14.5709 | −1.58981 | ||||||||
\(85\) | 7.46579 | 0.809778 | ||||||||
\(86\) | 4.62488 | 0.498714 | ||||||||
\(87\) | 2.94600 | 0.315844 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −0.465785 | −0.0493731 | −0.0246866 | − | 0.999695i | \(-0.507859\pi\) | ||||
−0.0246866 | + | 0.999695i | \(0.507859\pi\) | |||||||
\(90\) | −11.3578 | −1.19721 | ||||||||
\(91\) | 28.0878 | 2.94440 | ||||||||
\(92\) | −1.89199 | −0.197254 | ||||||||
\(93\) | −9.46579 | −0.981556 | ||||||||
\(94\) | 7.41178 | 0.764467 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.94600 | 0.300674 | ||||||||
\(97\) | −1.53421 | −0.155776 | −0.0778880 | − | 0.996962i | \(-0.524818\pi\) | ||||
−0.0778880 | + | 0.996962i | \(0.524818\pi\) | |||||||
\(98\) | −17.4629 | −1.76402 | ||||||||
\(99\) | 5.67889 | 0.570750 | ||||||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | −1.67889 | −0.167056 | −0.0835278 | − | 0.996505i | \(-0.526619\pi\) | ||||
−0.0835278 | + | 0.996505i | \(0.526619\pi\) | |||||||
\(102\) | 10.9971 | 1.08887 | ||||||||
\(103\) | −7.41178 | −0.730304 | −0.365152 | − | 0.930948i | \(-0.618983\pi\) | ||||
−0.365152 | + | 0.930948i | \(0.618983\pi\) | |||||||
\(104\) | −5.67889 | −0.556861 | ||||||||
\(105\) | −29.1418 | −2.84394 | ||||||||
\(106\) | −11.7840 | −1.14456 | ||||||||
\(107\) | 16.3722 | 1.58276 | 0.791380 | − | 0.611324i | \(-0.209363\pi\) | ||||
0.791380 | + | 0.611324i | \(0.209363\pi\) | |||||||
\(108\) | −7.89199 | −0.759407 | ||||||||
\(109\) | 17.4629 | 1.67264 | 0.836320 | − | 0.548242i | \(-0.184703\pi\) | ||||
0.836320 | + | 0.548242i | \(0.184703\pi\) | |||||||
\(110\) | −2.00000 | −0.190693 | ||||||||
\(111\) | 12.2527 | 1.16297 | ||||||||
\(112\) | 4.94600 | 0.467353 | ||||||||
\(113\) | −3.53421 | −0.332471 | −0.166235 | − | 0.986086i | \(-0.553161\pi\) | ||||
−0.166235 | + | 0.986086i | \(0.553161\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.78398 | −0.352858 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | 32.2498 | 2.98149 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.4629 | 1.69249 | ||||||||
\(120\) | 5.89199 | 0.537863 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 5.57088 | 0.504364 | ||||||||
\(123\) | −28.3549 | −2.55667 | ||||||||
\(124\) | 3.21310 | 0.288545 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | −28.0878 | −2.50226 | ||||||||
\(127\) | −5.35778 | −0.475426 | −0.237713 | − | 0.971335i | \(-0.576398\pi\) | ||||
−0.237713 | + | 0.971335i | \(0.576398\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 13.6249 | 1.19960 | ||||||||
\(130\) | −11.3578 | −0.996143 | ||||||||
\(131\) | 10.3722 | 0.906223 | 0.453112 | − | 0.891454i | \(-0.350314\pi\) | ||||
0.453112 | + | 0.891454i | \(0.350314\pi\) | |||||||
\(132\) | −2.94600 | −0.256416 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −8.83799 | −0.763486 | ||||||||
\(135\) | −15.7840 | −1.35847 | ||||||||
\(136\) | −3.73289 | −0.320093 | ||||||||
\(137\) | 14.1051 | 1.20508 | 0.602540 | − | 0.798089i | \(-0.294156\pi\) | ||||
0.602540 | + | 0.798089i | \(0.294156\pi\) | |||||||
\(138\) | −5.57379 | −0.474473 | ||||||||
\(139\) | −13.6760 | −1.15998 | −0.579990 | − | 0.814623i | \(-0.696944\pi\) | ||||
−0.579990 | + | 0.814623i | \(0.696944\pi\) | |||||||
\(140\) | 9.89199 | 0.836026 | ||||||||
\(141\) | 21.8351 | 1.83884 | ||||||||
\(142\) | −4.62488 | −0.388112 | ||||||||
\(143\) | 5.67889 | 0.474892 | ||||||||
\(144\) | 5.67889 | 0.473241 | ||||||||
\(145\) | −2.00000 | −0.166091 | ||||||||
\(146\) | 3.62488 | 0.299997 | ||||||||
\(147\) | −51.4455 | −4.24316 | ||||||||
\(148\) | −4.15910 | −0.341876 | ||||||||
\(149\) | 18.9971 | 1.55630 | 0.778151 | − | 0.628077i | \(-0.216158\pi\) | ||||
0.778151 | + | 0.628077i | \(0.216158\pi\) | |||||||
\(150\) | −2.94600 | −0.240540 | ||||||||
\(151\) | −23.6615 | −1.92555 | −0.962775 | − | 0.270305i | \(-0.912875\pi\) | ||||
−0.962775 | + | 0.270305i | \(0.912875\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 21.1987 | 1.71381 | ||||||||
\(154\) | −4.94600 | −0.398560 | ||||||||
\(155\) | 6.42621 | 0.516165 | ||||||||
\(156\) | −16.7300 | −1.33947 | ||||||||
\(157\) | −11.7840 | −0.940464 | −0.470232 | − | 0.882543i | \(-0.655830\pi\) | ||||
−0.470232 | + | 0.882543i | \(0.655830\pi\) | |||||||
\(158\) | 6.83799 | 0.544001 | ||||||||
\(159\) | −34.7156 | −2.75312 | ||||||||
\(160\) | −2.00000 | −0.158114 | ||||||||
\(161\) | −9.35778 | −0.737496 | ||||||||
\(162\) | −6.21310 | −0.488147 | ||||||||
\(163\) | −10.8236 | −0.847767 | −0.423883 | − | 0.905717i | \(-0.639333\pi\) | ||||
−0.423883 | + | 0.905717i | \(0.639333\pi\) | |||||||
\(164\) | 9.62488 | 0.751577 | ||||||||
\(165\) | −5.89199 | −0.458691 | ||||||||
\(166\) | −14.5169 | −1.12673 | ||||||||
\(167\) | 4.01443 | 0.310646 | 0.155323 | − | 0.987864i | \(-0.450358\pi\) | ||||
0.155323 | + | 0.987864i | \(0.450358\pi\) | |||||||
\(168\) | 14.5709 | 1.12417 | ||||||||
\(169\) | 19.2498 | 1.48075 | ||||||||
\(170\) | −7.46579 | −0.572600 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.62488 | −0.352644 | ||||||||
\(173\) | −7.21310 | −0.548402 | −0.274201 | − | 0.961672i | \(-0.588413\pi\) | ||||
−0.274201 | + | 0.961672i | \(0.588413\pi\) | |||||||
\(174\) | −2.94600 | −0.223335 | ||||||||
\(175\) | −4.94600 | −0.373882 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.465785 | 0.0349121 | ||||||||
\(179\) | 4.10801 | 0.307047 | 0.153524 | − | 0.988145i | \(-0.450938\pi\) | ||||
0.153524 | + | 0.988145i | \(0.450938\pi\) | |||||||
\(180\) | 11.3578 | 0.846559 | ||||||||
\(181\) | 15.4089 | 1.14533 | 0.572666 | − | 0.819789i | \(-0.305909\pi\) | ||||
0.572666 | + | 0.819789i | \(0.305909\pi\) | |||||||
\(182\) | −28.0878 | −2.08200 | ||||||||
\(183\) | 16.4118 | 1.21319 | ||||||||
\(184\) | 1.89199 | 0.139479 | ||||||||
\(185\) | −8.31820 | −0.611566 | ||||||||
\(186\) | 9.46579 | 0.694065 | ||||||||
\(187\) | 3.73289 | 0.272976 | ||||||||
\(188\) | −7.41178 | −0.540560 | ||||||||
\(189\) | −39.0337 | −2.83929 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.5882 | 0.766137 | 0.383068 | − | 0.923720i | \(-0.374867\pi\) | ||||
0.383068 | + | 0.923720i | \(0.374867\pi\) | |||||||
\(192\) | −2.94600 | −0.212609 | ||||||||
\(193\) | −5.51687 | −0.397113 | −0.198557 | − | 0.980089i | \(-0.563625\pi\) | ||||
−0.198557 | + | 0.980089i | \(0.563625\pi\) | |||||||
\(194\) | 1.53421 | 0.110150 | ||||||||
\(195\) | −33.4600 | −2.39612 | ||||||||
\(196\) | 17.4629 | 1.24735 | ||||||||
\(197\) | −9.53421 | −0.679285 | −0.339642 | − | 0.940555i | \(-0.610306\pi\) | ||||
−0.339642 | + | 0.940555i | \(0.610306\pi\) | |||||||
\(198\) | −5.67889 | −0.403581 | ||||||||
\(199\) | 20.6249 | 1.46206 | 0.731030 | − | 0.682346i | \(-0.239040\pi\) | ||||
0.731030 | + | 0.682346i | \(0.239040\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −26.0367 | −1.83648 | ||||||||
\(202\) | 1.67889 | 0.118126 | ||||||||
\(203\) | −4.94600 | −0.347141 | ||||||||
\(204\) | −10.9971 | −0.769950 | ||||||||
\(205\) | 19.2498 | 1.34446 | ||||||||
\(206\) | 7.41178 | 0.516403 | ||||||||
\(207\) | −10.7444 | −0.746787 | ||||||||
\(208\) | 5.67889 | 0.393760 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 29.1418 | 2.01097 | ||||||||
\(211\) | −25.6760 | −1.76761 | −0.883803 | − | 0.467859i | \(-0.845026\pi\) | ||||
−0.883803 | + | 0.467859i | \(0.845026\pi\) | |||||||
\(212\) | 11.7840 | 0.809327 | ||||||||
\(213\) | −13.6249 | −0.933562 | ||||||||
\(214\) | −16.3722 | −1.11918 | ||||||||
\(215\) | −9.24977 | −0.630829 | ||||||||
\(216\) | 7.89199 | 0.536982 | ||||||||
\(217\) | 15.8920 | 1.07882 | ||||||||
\(218\) | −17.4629 | −1.18273 | ||||||||
\(219\) | 10.6789 | 0.721612 | ||||||||
\(220\) | 2.00000 | 0.134840 | ||||||||
\(221\) | 21.1987 | 1.42598 | ||||||||
\(222\) | −12.2527 | −0.822346 | ||||||||
\(223\) | −7.37512 | −0.493874 | −0.246937 | − | 0.969031i | \(-0.579424\pi\) | ||||
−0.246937 | + | 0.969031i | \(0.579424\pi\) | |||||||
\(224\) | −4.94600 | −0.330468 | ||||||||
\(225\) | −5.67889 | −0.378593 | ||||||||
\(226\) | 3.53421 | 0.235092 | ||||||||
\(227\) | −28.3549 | −1.88198 | −0.940989 | − | 0.338437i | \(-0.890102\pi\) | ||||
−0.940989 | + | 0.338437i | \(0.890102\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.98266 | −0.329263 | −0.164632 | − | 0.986355i | \(-0.552644\pi\) | ||||
−0.164632 | + | 0.986355i | \(0.552644\pi\) | |||||||
\(230\) | 3.78398 | 0.249508 | ||||||||
\(231\) | −14.5709 | −0.958693 | ||||||||
\(232\) | 1.00000 | 0.0656532 | ||||||||
\(233\) | 22.4484 | 1.47065 | 0.735323 | − | 0.677717i | \(-0.237030\pi\) | ||||
0.735323 | + | 0.677717i | \(0.237030\pi\) | |||||||
\(234\) | −32.2498 | −2.10823 | ||||||||
\(235\) | −14.8236 | −0.966982 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 20.1447 | 1.30854 | ||||||||
\(238\) | −18.4629 | −1.19677 | ||||||||
\(239\) | −23.7840 | −1.53846 | −0.769229 | − | 0.638973i | \(-0.779359\pi\) | ||||
−0.769229 | + | 0.638973i | \(0.779359\pi\) | |||||||
\(240\) | −5.89199 | −0.380326 | ||||||||
\(241\) | −21.1418 | −1.36186 | −0.680930 | − | 0.732348i | \(-0.738424\pi\) | ||||
−0.680930 | + | 0.732348i | \(0.738424\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 5.37220 | 0.344627 | ||||||||
\(244\) | −5.57088 | −0.356639 | ||||||||
\(245\) | 34.9257 | 2.23132 | ||||||||
\(246\) | 28.3549 | 1.80784 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −3.21310 | −0.204032 | ||||||||
\(249\) | −42.7666 | −2.71023 | ||||||||
\(250\) | 12.0000 | 0.758947 | ||||||||
\(251\) | 0.519790 | 0.0328088 | 0.0164044 | − | 0.999865i | \(-0.494778\pi\) | ||||
0.0164044 | + | 0.999865i | \(0.494778\pi\) | |||||||
\(252\) | 28.0878 | 1.76936 | ||||||||
\(253\) | −1.89199 | −0.118948 | ||||||||
\(254\) | 5.35778 | 0.336177 | ||||||||
\(255\) | −21.9942 | −1.37733 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −10.8236 | −0.675155 | −0.337578 | − | 0.941298i | \(-0.609608\pi\) | ||||
−0.337578 | + | 0.941298i | \(0.609608\pi\) | |||||||
\(258\) | −13.6249 | −0.848248 | ||||||||
\(259\) | −20.5709 | −1.27821 | ||||||||
\(260\) | 11.3578 | 0.704379 | ||||||||
\(261\) | −5.67889 | −0.351514 | ||||||||
\(262\) | −10.3722 | −0.640797 | ||||||||
\(263\) | −13.0337 | −0.803695 | −0.401848 | − | 0.915707i | \(-0.631632\pi\) | ||||
−0.401848 | + | 0.915707i | \(0.631632\pi\) | |||||||
\(264\) | 2.94600 | 0.181313 | ||||||||
\(265\) | 23.5680 | 1.44777 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.37220 | 0.0839773 | ||||||||
\(268\) | 8.83799 | 0.539866 | ||||||||
\(269\) | −5.73289 | −0.349541 | −0.174770 | − | 0.984609i | \(-0.555918\pi\) | ||||
−0.174770 | + | 0.984609i | \(0.555918\pi\) | |||||||
\(270\) | 15.7840 | 0.960582 | ||||||||
\(271\) | −12.0000 | −0.728948 | −0.364474 | − | 0.931214i | \(-0.618751\pi\) | ||||
−0.364474 | + | 0.931214i | \(0.618751\pi\) | |||||||
\(272\) | 3.73289 | 0.226340 | ||||||||
\(273\) | −82.7464 | −5.00804 | ||||||||
\(274\) | −14.1051 | −0.852120 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 5.57379 | 0.335503 | ||||||||
\(277\) | 13.5709 | 0.815395 | 0.407698 | − | 0.913117i | \(-0.366332\pi\) | ||||
0.407698 | + | 0.913117i | \(0.366332\pi\) | |||||||
\(278\) | 13.6760 | 0.820230 | ||||||||
\(279\) | 18.2468 | 1.09241 | ||||||||
\(280\) | −9.89199 | −0.591159 | ||||||||
\(281\) | 1.19868 | 0.0715071 | 0.0357536 | − | 0.999361i | \(-0.488617\pi\) | ||||
0.0357536 | + | 0.999361i | \(0.488617\pi\) | |||||||
\(282\) | −21.8351 | −1.30026 | ||||||||
\(283\) | −4.82356 | −0.286731 | −0.143365 | − | 0.989670i | \(-0.545792\pi\) | ||||
−0.143365 | + | 0.989670i | \(0.545792\pi\) | |||||||
\(284\) | 4.62488 | 0.274436 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.67889 | −0.335800 | ||||||||
\(287\) | 47.6046 | 2.81001 | ||||||||
\(288\) | −5.67889 | −0.334632 | ||||||||
\(289\) | −3.06551 | −0.180324 | ||||||||
\(290\) | 2.00000 | 0.117444 | ||||||||
\(291\) | 4.51979 | 0.264955 | ||||||||
\(292\) | −3.62488 | −0.212130 | ||||||||
\(293\) | 1.21602 | 0.0710406 | 0.0355203 | − | 0.999369i | \(-0.488691\pi\) | ||||
0.0355203 | + | 0.999369i | \(0.488691\pi\) | |||||||
\(294\) | 51.4455 | 3.00036 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.15910 | 0.241743 | ||||||||
\(297\) | −7.89199 | −0.457940 | ||||||||
\(298\) | −18.9971 | −1.10047 | ||||||||
\(299\) | −10.7444 | −0.621365 | ||||||||
\(300\) | 2.94600 | 0.170087 | ||||||||
\(301\) | −22.8746 | −1.31847 | ||||||||
\(302\) | 23.6615 | 1.36157 | ||||||||
\(303\) | 4.94600 | 0.284140 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.1418 | −0.637975 | ||||||||
\(306\) | −21.1987 | −1.21185 | ||||||||
\(307\) | 32.0482 | 1.82909 | 0.914543 | − | 0.404489i | \(-0.132551\pi\) | ||||
0.914543 | + | 0.404489i | \(0.132551\pi\) | |||||||
\(308\) | 4.94600 | 0.281824 | ||||||||
\(309\) | 21.8351 | 1.24215 | ||||||||
\(310\) | −6.42621 | −0.364984 | ||||||||
\(311\) | −18.3722 | −1.04179 | −0.520896 | − | 0.853620i | \(-0.674402\pi\) | ||||
−0.520896 | + | 0.853620i | \(0.674402\pi\) | |||||||
\(312\) | 16.7300 | 0.947148 | ||||||||
\(313\) | 1.14467 | 0.0647007 | 0.0323504 | − | 0.999477i | \(-0.489701\pi\) | ||||
0.0323504 | + | 0.999477i | \(0.489701\pi\) | |||||||
\(314\) | 11.7840 | 0.665009 | ||||||||
\(315\) | 56.1755 | 3.16513 | ||||||||
\(316\) | −6.83799 | −0.384667 | ||||||||
\(317\) | 24.4484 | 1.37316 | 0.686581 | − | 0.727054i | \(-0.259111\pi\) | ||||
0.686581 | + | 0.727054i | \(0.259111\pi\) | |||||||
\(318\) | 34.7156 | 1.94675 | ||||||||
\(319\) | −1.00000 | −0.0559893 | ||||||||
\(320\) | 2.00000 | 0.111803 | ||||||||
\(321\) | −48.2324 | −2.69207 | ||||||||
\(322\) | 9.35778 | 0.521488 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 6.21310 | 0.345172 | ||||||||
\(325\) | −5.67889 | −0.315008 | ||||||||
\(326\) | 10.8236 | 0.599462 | ||||||||
\(327\) | −51.4455 | −2.84494 | ||||||||
\(328\) | −9.62488 | −0.531445 | ||||||||
\(329\) | −36.6586 | −2.02106 | ||||||||
\(330\) | 5.89199 | 0.324343 | ||||||||
\(331\) | −6.30377 | −0.346487 | −0.173243 | − | 0.984879i | \(-0.555425\pi\) | ||||
−0.173243 | + | 0.984879i | \(0.555425\pi\) | |||||||
\(332\) | 14.5169 | 0.796717 | ||||||||
\(333\) | −23.6190 | −1.29432 | ||||||||
\(334\) | −4.01443 | −0.219660 | ||||||||
\(335\) | 17.6760 | 0.965741 | ||||||||
\(336\) | −14.5709 | −0.794907 | ||||||||
\(337\) | −10.2893 | −0.560496 | −0.280248 | − | 0.959928i | \(-0.590417\pi\) | ||||
−0.280248 | + | 0.959928i | \(0.590417\pi\) | |||||||
\(338\) | −19.2498 | −1.04705 | ||||||||
\(339\) | 10.4118 | 0.565490 | ||||||||
\(340\) | 7.46579 | 0.404889 | ||||||||
\(341\) | 3.21310 | 0.173999 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 51.7493 | 2.79420 | ||||||||
\(344\) | 4.62488 | 0.249357 | ||||||||
\(345\) | 11.1476 | 0.600166 | ||||||||
\(346\) | 7.21310 | 0.387779 | ||||||||
\(347\) | −19.1958 | −1.03048 | −0.515241 | − | 0.857045i | \(-0.672298\pi\) | ||||
−0.515241 | + | 0.857045i | \(0.672298\pi\) | |||||||
\(348\) | 2.94600 | 0.157922 | ||||||||
\(349\) | 32.9653 | 1.76459 | 0.882296 | − | 0.470694i | \(-0.155996\pi\) | ||||
0.882296 | + | 0.470694i | \(0.155996\pi\) | |||||||
\(350\) | 4.94600 | 0.264375 | ||||||||
\(351\) | −44.8177 | −2.39219 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 33.2835 | 1.77150 | 0.885751 | − | 0.464160i | \(-0.153644\pi\) | ||||
0.885751 | + | 0.464160i | \(0.153644\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.24977 | 0.490927 | ||||||||
\(356\) | −0.465785 | −0.0246866 | ||||||||
\(357\) | −54.3915 | −2.87870 | ||||||||
\(358\) | −4.10801 | −0.217115 | ||||||||
\(359\) | 5.68180 | 0.299874 | 0.149937 | − | 0.988696i | \(-0.452093\pi\) | ||||
0.149937 | + | 0.988696i | \(0.452093\pi\) | |||||||
\(360\) | −11.3578 | −0.598607 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −15.4089 | −0.809872 | ||||||||
\(363\) | −2.94600 | −0.154625 | ||||||||
\(364\) | 28.0878 | 1.47220 | ||||||||
\(365\) | −7.24977 | −0.379470 | ||||||||
\(366\) | −16.4118 | −0.857857 | ||||||||
\(367\) | 17.6933 | 0.923583 | 0.461792 | − | 0.886988i | \(-0.347207\pi\) | ||||
0.461792 | + | 0.886988i | \(0.347207\pi\) | |||||||
\(368\) | −1.89199 | −0.0986268 | ||||||||
\(369\) | 54.6586 | 2.84541 | ||||||||
\(370\) | 8.31820 | 0.432442 | ||||||||
\(371\) | 58.2835 | 3.02593 | ||||||||
\(372\) | −9.46579 | −0.490778 | ||||||||
\(373\) | −37.1051 | −1.92123 | −0.960614 | − | 0.277885i | \(-0.910367\pi\) | ||||
−0.960614 | + | 0.277885i | \(0.910367\pi\) | |||||||
\(374\) | −3.73289 | −0.193023 | ||||||||
\(375\) | 35.3519 | 1.82557 | ||||||||
\(376\) | 7.41178 | 0.382233 | ||||||||
\(377\) | −5.67889 | −0.292478 | ||||||||
\(378\) | 39.0337 | 2.00768 | ||||||||
\(379\) | 13.5535 | 0.696198 | 0.348099 | − | 0.937458i | \(-0.386827\pi\) | ||||
0.348099 | + | 0.937458i | \(0.386827\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.7840 | 0.808638 | ||||||||
\(382\) | −10.5882 | −0.541740 | ||||||||
\(383\) | 9.67597 | 0.494419 | 0.247210 | − | 0.968962i | \(-0.420486\pi\) | ||||
0.247210 | + | 0.968962i | \(0.420486\pi\) | |||||||
\(384\) | 2.94600 | 0.150337 | ||||||||
\(385\) | 9.89199 | 0.504143 | ||||||||
\(386\) | 5.51687 | 0.280801 | ||||||||
\(387\) | −26.2642 | −1.33508 | ||||||||
\(388\) | −1.53421 | −0.0778880 | ||||||||
\(389\) | 12.8013 | 0.649053 | 0.324526 | − | 0.945877i | \(-0.394795\pi\) | ||||
0.324526 | + | 0.945877i | \(0.394795\pi\) | |||||||
\(390\) | 33.4600 | 1.69431 | ||||||||
\(391\) | −7.06260 | −0.357171 | ||||||||
\(392\) | −17.4629 | −0.882008 | ||||||||
\(393\) | −30.5565 | −1.54137 | ||||||||
\(394\) | 9.53421 | 0.480327 | ||||||||
\(395\) | −13.6760 | −0.688113 | ||||||||
\(396\) | 5.67889 | 0.285375 | ||||||||
\(397\) | −18.1591 | −0.911379 | −0.455689 | − | 0.890139i | \(-0.650607\pi\) | ||||
−0.455689 | + | 0.890139i | \(0.650607\pi\) | |||||||
\(398\) | −20.6249 | −1.03383 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | −7.82064 | −0.390544 | −0.195272 | − | 0.980749i | \(-0.562559\pi\) | ||||
−0.195272 | + | 0.980749i | \(0.562559\pi\) | |||||||
\(402\) | 26.0367 | 1.29859 | ||||||||
\(403\) | 18.2468 | 0.908940 | ||||||||
\(404\) | −1.67889 | −0.0835278 | ||||||||
\(405\) | 12.4262 | 0.617463 | ||||||||
\(406\) | 4.94600 | 0.245466 | ||||||||
\(407\) | −4.15910 | −0.206159 | ||||||||
\(408\) | 10.9971 | 0.544437 | ||||||||
\(409\) | −21.0115 | −1.03895 | −0.519476 | − | 0.854485i | \(-0.673873\pi\) | ||||
−0.519476 | + | 0.854485i | \(0.673873\pi\) | |||||||
\(410\) | −19.2498 | −0.950678 | ||||||||
\(411\) | −41.5535 | −2.04968 | ||||||||
\(412\) | −7.41178 | −0.365152 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 10.7444 | 0.528059 | ||||||||
\(415\) | 29.0337 | 1.42521 | ||||||||
\(416\) | −5.67889 | −0.278430 | ||||||||
\(417\) | 40.2893 | 1.97298 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.0540 | −0.540023 | −0.270012 | − | 0.962857i | \(-0.587028\pi\) | ||||
−0.270012 | + | 0.962857i | \(0.587028\pi\) | |||||||
\(420\) | −29.1418 | −1.42197 | ||||||||
\(421\) | 4.48313 | 0.218494 | 0.109247 | − | 0.994015i | \(-0.465156\pi\) | ||||
0.109247 | + | 0.994015i | \(0.465156\pi\) | |||||||
\(422\) | 25.6760 | 1.24989 | ||||||||
\(423\) | −42.0907 | −2.04652 | ||||||||
\(424\) | −11.7840 | −0.572281 | ||||||||
\(425\) | −3.73289 | −0.181072 | ||||||||
\(426\) | 13.6249 | 0.660128 | ||||||||
\(427\) | −27.5535 | −1.33341 | ||||||||
\(428\) | 16.3722 | 0.791380 | ||||||||
\(429\) | −16.7300 | −0.807731 | ||||||||
\(430\) | 9.24977 | 0.446063 | ||||||||
\(431\) | 2.19576 | 0.105766 | 0.0528830 | − | 0.998601i | \(-0.483159\pi\) | ||||
0.0528830 | + | 0.998601i | \(0.483159\pi\) | |||||||
\(432\) | −7.89199 | −0.379704 | ||||||||
\(433\) | −31.8602 | −1.53110 | −0.765552 | − | 0.643374i | \(-0.777534\pi\) | ||||
−0.765552 | + | 0.643374i | \(0.777534\pi\) | |||||||
\(434\) | −15.8920 | −0.762840 | ||||||||
\(435\) | 5.89199 | 0.282499 | ||||||||
\(436\) | 17.4629 | 0.836320 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −10.6789 | −0.510257 | ||||||||
\(439\) | −10.6422 | −0.507926 | −0.253963 | − | 0.967214i | \(-0.581734\pi\) | ||||
−0.253963 | + | 0.967214i | \(0.581734\pi\) | |||||||
\(440\) | −2.00000 | −0.0953463 | ||||||||
\(441\) | 99.1697 | 4.72237 | ||||||||
\(442\) | −21.1987 | −1.00832 | ||||||||
\(443\) | 31.4455 | 1.49402 | 0.747011 | − | 0.664812i | \(-0.231488\pi\) | ||||
0.747011 | + | 0.664812i | \(0.231488\pi\) | |||||||
\(444\) | 12.2527 | 0.581487 | ||||||||
\(445\) | −0.931570 | −0.0441607 | ||||||||
\(446\) | 7.37512 | 0.349222 | ||||||||
\(447\) | −55.9653 | −2.64707 | ||||||||
\(448\) | 4.94600 | 0.233676 | ||||||||
\(449\) | 13.8553 | 0.653873 | 0.326937 | − | 0.945046i | \(-0.393984\pi\) | ||||
0.326937 | + | 0.945046i | \(0.393984\pi\) | |||||||
\(450\) | 5.67889 | 0.267705 | ||||||||
\(451\) | 9.62488 | 0.453218 | ||||||||
\(452\) | −3.53421 | −0.166235 | ||||||||
\(453\) | 69.7068 | 3.27511 | ||||||||
\(454\) | 28.3549 | 1.33076 | ||||||||
\(455\) | 56.1755 | 2.63355 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.7329 | −0.735954 | −0.367977 | − | 0.929835i | \(-0.619949\pi\) | ||||
−0.367977 | + | 0.929835i | \(0.619949\pi\) | |||||||
\(458\) | 4.98266 | 0.232824 | ||||||||
\(459\) | −29.4600 | −1.37507 | ||||||||
\(460\) | −3.78398 | −0.176429 | ||||||||
\(461\) | −20.7126 | −0.964684 | −0.482342 | − | 0.875983i | \(-0.660214\pi\) | ||||
−0.482342 | + | 0.875983i | \(0.660214\pi\) | |||||||
\(462\) | 14.5709 | 0.677899 | ||||||||
\(463\) | −14.3722 | −0.667933 | −0.333966 | − | 0.942585i | \(-0.608387\pi\) | ||||
−0.333966 | + | 0.942585i | \(0.608387\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | −18.9316 | −0.877931 | ||||||||
\(466\) | −22.4484 | −1.03990 | ||||||||
\(467\) | −10.3038 | −0.476802 | −0.238401 | − | 0.971167i | \(-0.576623\pi\) | ||||
−0.238401 | + | 0.971167i | \(0.576623\pi\) | |||||||
\(468\) | 32.2498 | 1.49075 | ||||||||
\(469\) | 43.7126 | 2.01846 | ||||||||
\(470\) | 14.8236 | 0.683760 | ||||||||
\(471\) | 34.7156 | 1.59961 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.62488 | −0.212652 | ||||||||
\(474\) | −20.1447 | −0.925275 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 18.4629 | 0.846244 | ||||||||
\(477\) | 66.9199 | 3.06405 | ||||||||
\(478\) | 23.7840 | 1.08785 | ||||||||
\(479\) | 7.58822 | 0.346715 | 0.173357 | − | 0.984859i | \(-0.444538\pi\) | ||||
0.173357 | + | 0.984859i | \(0.444538\pi\) | |||||||
\(480\) | 5.89199 | 0.268931 | ||||||||
\(481\) | −23.6190 | −1.07694 | ||||||||
\(482\) | 21.1418 | 0.962981 | ||||||||
\(483\) | 27.5680 | 1.25439 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −3.06843 | −0.139330 | ||||||||
\(486\) | −5.37220 | −0.243688 | ||||||||
\(487\) | −0.414697 | −0.0187917 | −0.00939585 | − | 0.999956i | \(-0.502991\pi\) | ||||
−0.00939585 | + | 0.999956i | \(0.502991\pi\) | |||||||
\(488\) | 5.57088 | 0.252182 | ||||||||
\(489\) | 31.8862 | 1.44194 | ||||||||
\(490\) | −34.9257 | −1.57778 | ||||||||
\(491\) | −0.823561 | −0.0371668 | −0.0185834 | − | 0.999827i | \(-0.505916\pi\) | ||||
−0.0185834 | + | 0.999827i | \(0.505916\pi\) | |||||||
\(492\) | −28.3549 | −1.27834 | ||||||||
\(493\) | −3.73289 | −0.168121 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.3578 | 0.510494 | ||||||||
\(496\) | 3.21310 | 0.144273 | ||||||||
\(497\) | 22.8746 | 1.02607 | ||||||||
\(498\) | 42.7666 | 1.91642 | ||||||||
\(499\) | 5.35778 | 0.239847 | 0.119923 | − | 0.992783i | \(-0.461735\pi\) | ||||
0.119923 | + | 0.992783i | \(0.461735\pi\) | |||||||
\(500\) | −12.0000 | −0.536656 | ||||||||
\(501\) | −11.8265 | −0.528368 | ||||||||
\(502\) | −0.519790 | −0.0231994 | ||||||||
\(503\) | 5.57379 | 0.248523 | 0.124262 | − | 0.992249i | \(-0.460344\pi\) | ||||
0.124262 | + | 0.992249i | \(0.460344\pi\) | |||||||
\(504\) | −28.0878 | −1.25113 | ||||||||
\(505\) | −3.35778 | −0.149419 | ||||||||
\(506\) | 1.89199 | 0.0841092 | ||||||||
\(507\) | −56.7097 | −2.51857 | ||||||||
\(508\) | −5.35778 | −0.237713 | ||||||||
\(509\) | −18.4262 | −0.816727 | −0.408364 | − | 0.912819i | \(-0.633900\pi\) | ||||
−0.408364 | + | 0.912819i | \(0.633900\pi\) | |||||||
\(510\) | 21.9942 | 0.973918 | ||||||||
\(511\) | −17.9287 | −0.793117 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10.8236 | 0.477407 | ||||||||
\(515\) | −14.8236 | −0.653204 | ||||||||
\(516\) | 13.6249 | 0.599802 | ||||||||
\(517\) | −7.41178 | −0.325970 | ||||||||
\(518\) | 20.5709 | 0.903832 | ||||||||
\(519\) | 21.2498 | 0.932761 | ||||||||
\(520\) | −11.3578 | −0.498071 | ||||||||
\(521\) | −9.24685 | −0.405112 | −0.202556 | − | 0.979271i | \(-0.564925\pi\) | ||||
−0.202556 | + | 0.979271i | \(0.564925\pi\) | |||||||
\(522\) | 5.67889 | 0.248558 | ||||||||
\(523\) | −19.4118 | −0.848818 | −0.424409 | − | 0.905471i | \(-0.639518\pi\) | ||||
−0.424409 | + | 0.905471i | \(0.639518\pi\) | |||||||
\(524\) | 10.3722 | 0.453112 | ||||||||
\(525\) | 14.5709 | 0.635925 | ||||||||
\(526\) | 13.0337 | 0.568298 | ||||||||
\(527\) | 11.9942 | 0.522474 | ||||||||
\(528\) | −2.94600 | −0.128208 | ||||||||
\(529\) | −19.4204 | −0.844364 | ||||||||
\(530\) | −23.5680 | −1.02373 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 54.6586 | 2.36753 | ||||||||
\(534\) | −1.37220 | −0.0593809 | ||||||||
\(535\) | 32.7444 | 1.41566 | ||||||||
\(536\) | −8.83799 | −0.381743 | ||||||||
\(537\) | −12.1022 | −0.522247 | ||||||||
\(538\) | 5.73289 | 0.247163 | ||||||||
\(539\) | 17.4629 | 0.752179 | ||||||||
\(540\) | −15.7840 | −0.679234 | ||||||||
\(541\) | 19.6046 | 0.842869 | 0.421434 | − | 0.906859i | \(-0.361527\pi\) | ||||
0.421434 | + | 0.906859i | \(0.361527\pi\) | |||||||
\(542\) | 12.0000 | 0.515444 | ||||||||
\(543\) | −45.3944 | −1.94806 | ||||||||
\(544\) | −3.73289 | −0.160046 | ||||||||
\(545\) | 34.9257 | 1.49605 | ||||||||
\(546\) | 82.7464 | 3.54122 | ||||||||
\(547\) | −4.62488 | −0.197746 | −0.0988729 | − | 0.995100i | \(-0.531524\pi\) | ||||
−0.0988729 | + | 0.995100i | \(0.531524\pi\) | |||||||
\(548\) | 14.1051 | 0.602540 | ||||||||
\(549\) | −31.6364 | −1.35021 | ||||||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −5.57379 | −0.237236 | ||||||||
\(553\) | −33.8206 | −1.43820 | ||||||||
\(554\) | −13.5709 | −0.576571 | ||||||||
\(555\) | 24.5054 | 1.04019 | ||||||||
\(556\) | −13.6760 | −0.579990 | ||||||||
\(557\) | 22.3211 | 0.945776 | 0.472888 | − | 0.881123i | \(-0.343212\pi\) | ||||
0.472888 | + | 0.881123i | \(0.343212\pi\) | |||||||
\(558\) | −18.2468 | −0.772451 | ||||||||
\(559\) | −26.2642 | −1.11086 | ||||||||
\(560\) | 9.89199 | 0.418013 | ||||||||
\(561\) | −10.9971 | −0.464297 | ||||||||
\(562\) | −1.19868 | −0.0505632 | ||||||||
\(563\) | 29.6760 | 1.25069 | 0.625347 | − | 0.780347i | \(-0.284958\pi\) | ||||
0.625347 | + | 0.780347i | \(0.284958\pi\) | |||||||
\(564\) | 21.8351 | 0.919422 | ||||||||
\(565\) | −7.06843 | −0.297371 | ||||||||
\(566\) | 4.82356 | 0.202749 | ||||||||
\(567\) | 30.7300 | 1.29054 | ||||||||
\(568\) | −4.62488 | −0.194056 | ||||||||
\(569\) | −34.0733 | −1.42843 | −0.714214 | − | 0.699927i | \(-0.753216\pi\) | ||||
−0.714214 | + | 0.699927i | \(0.753216\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.3722 | 0.685155 | 0.342578 | − | 0.939490i | \(-0.388700\pi\) | ||||
0.342578 | + | 0.939490i | \(0.388700\pi\) | |||||||
\(572\) | 5.67889 | 0.237446 | ||||||||
\(573\) | −31.1928 | −1.30310 | ||||||||
\(574\) | −47.6046 | −1.98698 | ||||||||
\(575\) | 1.89199 | 0.0789015 | ||||||||
\(576\) | 5.67889 | 0.236620 | ||||||||
\(577\) | 23.2864 | 0.969427 | 0.484713 | − | 0.874673i | \(-0.338924\pi\) | ||||
0.484713 | + | 0.874673i | \(0.338924\pi\) | |||||||
\(578\) | 3.06551 | 0.127509 | ||||||||
\(579\) | 16.2527 | 0.675438 | ||||||||
\(580\) | −2.00000 | −0.0830455 | ||||||||
\(581\) | 71.8004 | 2.97878 | ||||||||
\(582\) | −4.51979 | −0.187351 | ||||||||
\(583\) | 11.7840 | 0.488043 | ||||||||
\(584\) | 3.62488 | 0.149999 | ||||||||
\(585\) | 64.4995 | 2.66673 | ||||||||
\(586\) | −1.21602 | −0.0502333 | ||||||||
\(587\) | 19.0540 | 0.786443 | 0.393221 | − | 0.919444i | \(-0.371361\pi\) | ||||
0.393221 | + | 0.919444i | \(0.371361\pi\) | |||||||
\(588\) | −51.4455 | −2.12158 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 28.0878 | 1.15538 | ||||||||
\(592\) | −4.15910 | −0.170938 | ||||||||
\(593\) | 1.57379 | 0.0646280 | 0.0323140 | − | 0.999478i | \(-0.489712\pi\) | ||||
0.0323140 | + | 0.999478i | \(0.489712\pi\) | |||||||
\(594\) | 7.89199 | 0.323812 | ||||||||
\(595\) | 36.9257 | 1.51381 | ||||||||
\(596\) | 18.9971 | 0.778151 | ||||||||
\(597\) | −60.7608 | −2.48677 | ||||||||
\(598\) | 10.7444 | 0.439371 | ||||||||
\(599\) | −22.7329 | −0.928841 | −0.464420 | − | 0.885615i | \(-0.653737\pi\) | ||||
−0.464420 | + | 0.885615i | \(0.653737\pi\) | |||||||
\(600\) | −2.94600 | −0.120270 | ||||||||
\(601\) | 10.8524 | 0.442679 | 0.221340 | − | 0.975197i | \(-0.428957\pi\) | ||||
0.221340 | + | 0.975197i | \(0.428957\pi\) | |||||||
\(602\) | 22.8746 | 0.932301 | ||||||||
\(603\) | 50.1899 | 2.04389 | ||||||||
\(604\) | −23.6615 | −0.962775 | ||||||||
\(605\) | 2.00000 | 0.0813116 | ||||||||
\(606\) | −4.94600 | −0.200917 | ||||||||
\(607\) | −12.3038 | −0.499395 | −0.249697 | − | 0.968324i | \(-0.580331\pi\) | ||||
−0.249697 | + | 0.968324i | \(0.580331\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 14.5709 | 0.590442 | ||||||||
\(610\) | 11.1418 | 0.451117 | ||||||||
\(611\) | −42.0907 | −1.70281 | ||||||||
\(612\) | 21.1987 | 0.856906 | ||||||||
\(613\) | 45.0308 | 1.81878 | 0.909389 | − | 0.415947i | \(-0.136550\pi\) | ||||
0.909389 | + | 0.415947i | \(0.136550\pi\) | |||||||
\(614\) | −32.0482 | −1.29336 | ||||||||
\(615\) | −56.7097 | −2.28676 | ||||||||
\(616\) | −4.94600 | −0.199280 | ||||||||
\(617\) | 21.4629 | 0.864063 | 0.432031 | − | 0.901859i | \(-0.357797\pi\) | ||||
0.432031 | + | 0.901859i | \(0.357797\pi\) | |||||||
\(618\) | −21.8351 | −0.878335 | ||||||||
\(619\) | 6.96625 | 0.279997 | 0.139999 | − | 0.990152i | \(-0.455290\pi\) | ||||
0.139999 | + | 0.990152i | \(0.455290\pi\) | |||||||
\(620\) | 6.42621 | 0.258083 | ||||||||
\(621\) | 14.9316 | 0.599183 | ||||||||
\(622\) | 18.3722 | 0.736658 | ||||||||
\(623\) | −2.30377 | −0.0922986 | ||||||||
\(624\) | −16.7300 | −0.669735 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | −1.14467 | −0.0457503 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.7840 | −0.470232 | ||||||||
\(629\) | −15.5255 | −0.619041 | ||||||||
\(630\) | −56.1755 | −2.23809 | ||||||||
\(631\) | −40.4089 | −1.60865 | −0.804326 | − | 0.594189i | \(-0.797473\pi\) | ||||
−0.804326 | + | 0.594189i | \(0.797473\pi\) | |||||||
\(632\) | 6.83799 | 0.272000 | ||||||||
\(633\) | 75.6413 | 3.00647 | ||||||||
\(634\) | −24.4484 | −0.970972 | ||||||||
\(635\) | −10.7156 | −0.425234 | ||||||||
\(636\) | −34.7156 | −1.37656 | ||||||||
\(637\) | 99.1697 | 3.92925 | ||||||||
\(638\) | 1.00000 | 0.0395904 | ||||||||
\(639\) | 26.2642 | 1.03900 | ||||||||
\(640\) | −2.00000 | −0.0790569 | ||||||||
\(641\) | −26.7840 | −1.05790 | −0.528952 | − | 0.848652i | \(-0.677415\pi\) | ||||
−0.528952 | + | 0.848652i | \(0.677415\pi\) | |||||||
\(642\) | 48.2324 | 1.90358 | ||||||||
\(643\) | −3.26419 | −0.128727 | −0.0643636 | − | 0.997927i | \(-0.520502\pi\) | ||||
−0.0643636 | + | 0.997927i | \(0.520502\pi\) | |||||||
\(644\) | −9.35778 | −0.368748 | ||||||||
\(645\) | 27.2498 | 1.07296 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.3355 | −0.406332 | −0.203166 | − | 0.979144i | \(-0.565123\pi\) | ||||
−0.203166 | + | 0.979144i | \(0.565123\pi\) | |||||||
\(648\) | −6.21310 | −0.244074 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 5.67889 | 0.222744 | ||||||||
\(651\) | −46.8177 | −1.83493 | ||||||||
\(652\) | −10.8236 | −0.423883 | ||||||||
\(653\) | 16.5853 | 0.649033 | 0.324517 | − | 0.945880i | \(-0.394798\pi\) | ||||
0.324517 | + | 0.945880i | \(0.394798\pi\) | |||||||
\(654\) | 51.4455 | 2.01168 | ||||||||
\(655\) | 20.7444 | 0.810551 | ||||||||
\(656\) | 9.62488 | 0.375789 | ||||||||
\(657\) | −20.5853 | −0.803109 | ||||||||
\(658\) | 36.6586 | 1.42910 | ||||||||
\(659\) | −33.4118 | −1.30154 | −0.650769 | − | 0.759276i | \(-0.725553\pi\) | ||||
−0.650769 | + | 0.759276i | \(0.725553\pi\) | |||||||
\(660\) | −5.89199 | −0.229345 | ||||||||
\(661\) | −10.2671 | −0.399344 | −0.199672 | − | 0.979863i | \(-0.563988\pi\) | ||||
−0.199672 | + | 0.979863i | \(0.563988\pi\) | |||||||
\(662\) | 6.30377 | 0.245003 | ||||||||
\(663\) | −62.4512 | −2.42540 | ||||||||
\(664\) | −14.5169 | −0.563364 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 23.6190 | 0.915220 | ||||||||
\(667\) | 1.89199 | 0.0732582 | ||||||||
\(668\) | 4.01443 | 0.155323 | ||||||||
\(669\) | 21.7271 | 0.840017 | ||||||||
\(670\) | −17.6760 | −0.682882 | ||||||||
\(671\) | −5.57088 | −0.215061 | ||||||||
\(672\) | 14.5709 | 0.562084 | ||||||||
\(673\) | 47.6190 | 1.83558 | 0.917790 | − | 0.397067i | \(-0.129972\pi\) | ||||
0.917790 | + | 0.397067i | \(0.129972\pi\) | |||||||
\(674\) | 10.2893 | 0.396331 | ||||||||
\(675\) | 7.89199 | 0.303763 | ||||||||
\(676\) | 19.2498 | 0.740376 | ||||||||
\(677\) | 6.64514 | 0.255394 | 0.127697 | − | 0.991813i | \(-0.459242\pi\) | ||||
0.127697 | + | 0.991813i | \(0.459242\pi\) | |||||||
\(678\) | −10.4118 | −0.399862 | ||||||||
\(679\) | −7.58822 | −0.291209 | ||||||||
\(680\) | −7.46579 | −0.286300 | ||||||||
\(681\) | 83.5333 | 3.20100 | ||||||||
\(682\) | −3.21310 | −0.123036 | ||||||||
\(683\) | 21.7984 | 0.834093 | 0.417046 | − | 0.908885i | \(-0.363065\pi\) | ||||
0.417046 | + | 0.908885i | \(0.363065\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.2102 | 1.07786 | ||||||||
\(686\) | −51.7493 | −1.97580 | ||||||||
\(687\) | 14.6789 | 0.560034 | ||||||||
\(688\) | −4.62488 | −0.176322 | ||||||||
\(689\) | 66.9199 | 2.54945 | ||||||||
\(690\) | −11.1476 | −0.424381 | ||||||||
\(691\) | −13.2700 | −0.504816 | −0.252408 | − | 0.967621i | \(-0.581222\pi\) | ||||
−0.252408 | + | 0.967621i | \(0.581222\pi\) | |||||||
\(692\) | −7.21310 | −0.274201 | ||||||||
\(693\) | 28.0878 | 1.06697 | ||||||||
\(694\) | 19.1958 | 0.728661 | ||||||||
\(695\) | −27.3519 | −1.03752 | ||||||||
\(696\) | −2.94600 | −0.111668 | ||||||||
\(697\) | 35.9287 | 1.36089 | ||||||||
\(698\) | −32.9653 | −1.24776 | ||||||||
\(699\) | −66.1330 | −2.50138 | ||||||||
\(700\) | −4.94600 | −0.186941 | ||||||||
\(701\) | 12.6818 | 0.478985 | 0.239493 | − | 0.970898i | \(-0.423019\pi\) | ||||
0.239493 | + | 0.970898i | \(0.423019\pi\) | |||||||
\(702\) | 44.8177 | 1.69154 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 43.6701 | 1.64471 | ||||||||
\(706\) | −33.2835 | −1.25264 | ||||||||
\(707\) | −8.30377 | −0.312295 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.5680 | 1.41089 | 0.705447 | − | 0.708762i | \(-0.250746\pi\) | ||||
0.705447 | + | 0.708762i | \(0.250746\pi\) | |||||||
\(710\) | −9.24977 | −0.347138 | ||||||||
\(711\) | −38.8322 | −1.45632 | ||||||||
\(712\) | 0.465785 | 0.0174560 | ||||||||
\(713\) | −6.07916 | −0.227666 | ||||||||
\(714\) | 54.3915 | 2.03555 | ||||||||
\(715\) | 11.3578 | 0.424757 | ||||||||
\(716\) | 4.10801 | 0.153524 | ||||||||
\(717\) | 70.0675 | 2.61672 | ||||||||
\(718\) | −5.68180 | −0.212043 | ||||||||
\(719\) | −2.94308 | −0.109758 | −0.0548792 | − | 0.998493i | \(-0.517477\pi\) | ||||
−0.0548792 | + | 0.998493i | \(0.517477\pi\) | |||||||
\(720\) | 11.3578 | 0.423279 | ||||||||
\(721\) | −36.6586 | −1.36524 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 62.2835 | 2.31635 | ||||||||
\(724\) | 15.4089 | 0.572666 | ||||||||
\(725\) | 1.00000 | 0.0371391 | ||||||||
\(726\) | 2.94600 | 0.109336 | ||||||||
\(727\) | 27.5506 | 1.02180 | 0.510898 | − | 0.859641i | \(-0.329313\pi\) | ||||
0.510898 | + | 0.859641i | \(0.329313\pi\) | |||||||
\(728\) | −28.0878 | −1.04100 | ||||||||
\(729\) | −34.4658 | −1.27651 | ||||||||
\(730\) | 7.24977 | 0.268326 | ||||||||
\(731\) | −17.2642 | −0.638539 | ||||||||
\(732\) | 16.4118 | 0.606597 | ||||||||
\(733\) | 37.6393 | 1.39024 | 0.695120 | − | 0.718894i | \(-0.255351\pi\) | ||||
0.695120 | + | 0.718894i | \(0.255351\pi\) | |||||||
\(734\) | −17.6933 | −0.653072 | ||||||||
\(735\) | −102.891 | −3.79519 | ||||||||
\(736\) | 1.89199 | 0.0697397 | ||||||||
\(737\) | 8.83799 | 0.325551 | ||||||||
\(738\) | −54.6586 | −2.01201 | ||||||||
\(739\) | 5.19576 | 0.191129 | 0.0955646 | − | 0.995423i | \(-0.469534\pi\) | ||||
0.0955646 | + | 0.995423i | \(0.469534\pi\) | |||||||
\(740\) | −8.31820 | −0.305783 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −58.2835 | −2.13966 | ||||||||
\(743\) | −1.97974 | −0.0726297 | −0.0363148 | − | 0.999340i | \(-0.511562\pi\) | ||||
−0.0363148 | + | 0.999340i | \(0.511562\pi\) | |||||||
\(744\) | 9.46579 | 0.347033 | ||||||||
\(745\) | 37.9942 | 1.39200 | ||||||||
\(746\) | 37.1051 | 1.35851 | ||||||||
\(747\) | 82.4397 | 3.01631 | ||||||||
\(748\) | 3.73289 | 0.136488 | ||||||||
\(749\) | 80.9768 | 2.95883 | ||||||||
\(750\) | −35.3519 | −1.29087 | ||||||||
\(751\) | −3.34043 | −0.121894 | −0.0609471 | − | 0.998141i | \(-0.519412\pi\) | ||||
−0.0609471 | + | 0.998141i | \(0.519412\pi\) | |||||||
\(752\) | −7.41178 | −0.270280 | ||||||||
\(753\) | −1.53130 | −0.0558036 | ||||||||
\(754\) | 5.67889 | 0.206813 | ||||||||
\(755\) | −47.3231 | −1.72226 | ||||||||
\(756\) | −39.0337 | −1.41964 | ||||||||
\(757\) | −42.7097 | −1.55231 | −0.776156 | − | 0.630541i | \(-0.782833\pi\) | ||||
−0.776156 | + | 0.630541i | \(0.782833\pi\) | |||||||
\(758\) | −13.5535 | −0.492287 | ||||||||
\(759\) | 5.57379 | 0.202316 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.5054 | −0.380819 | −0.190410 | − | 0.981705i | \(-0.560982\pi\) | ||||
−0.190410 | + | 0.981705i | \(0.560982\pi\) | |||||||
\(762\) | −15.7840 | −0.571793 | ||||||||
\(763\) | 86.3713 | 3.12685 | ||||||||
\(764\) | 10.5882 | 0.383068 | ||||||||
\(765\) | 42.3974 | 1.53288 | ||||||||
\(766\) | −9.67597 | −0.349607 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −2.94600 | −0.106304 | ||||||||
\(769\) | −3.07426 | −0.110861 | −0.0554304 | − | 0.998463i | \(-0.517653\pi\) | ||||
−0.0554304 | + | 0.998463i | \(0.517653\pi\) | |||||||
\(770\) | −9.89199 | −0.356483 | ||||||||
\(771\) | 31.8862 | 1.14835 | ||||||||
\(772\) | −5.51687 | −0.198557 | ||||||||
\(773\) | 5.44355 | 0.195791 | 0.0978954 | − | 0.995197i | \(-0.468789\pi\) | ||||
0.0978954 | + | 0.995197i | \(0.468789\pi\) | |||||||
\(774\) | 26.2642 | 0.944047 | ||||||||
\(775\) | −3.21310 | −0.115418 | ||||||||
\(776\) | 1.53421 | 0.0550751 | ||||||||
\(777\) | 60.6017 | 2.17407 | ||||||||
\(778\) | −12.8013 | −0.458950 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −33.4600 | −1.19806 | ||||||||
\(781\) | 4.62488 | 0.165491 | ||||||||
\(782\) | 7.06260 | 0.252558 | ||||||||
\(783\) | 7.89199 | 0.282037 | ||||||||
\(784\) | 17.4629 | 0.623674 | ||||||||
\(785\) | −23.5680 | −0.841177 | ||||||||
\(786\) | 30.5565 | 1.08991 | ||||||||
\(787\) | −4.22753 | −0.150695 | −0.0753475 | − | 0.997157i | \(-0.524007\pi\) | ||||
−0.0753475 | + | 0.997157i | \(0.524007\pi\) | |||||||
\(788\) | −9.53421 | −0.339642 | ||||||||
\(789\) | 38.3974 | 1.36698 | ||||||||
\(790\) | 13.6760 | 0.486569 | ||||||||
\(791\) | −17.4802 | −0.621525 | ||||||||
\(792\) | −5.67889 | −0.201790 | ||||||||
\(793\) | −31.6364 | −1.12344 | ||||||||
\(794\) | 18.1591 | 0.644442 | ||||||||
\(795\) | −69.4311 | −2.46247 | ||||||||
\(796\) | 20.6249 | 0.731030 | ||||||||
\(797\) | −1.44355 | −0.0511331 | −0.0255665 | − | 0.999673i | \(-0.508139\pi\) | ||||
−0.0255665 | + | 0.999673i | \(0.508139\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27.6674 | −0.978802 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −2.64514 | −0.0934615 | ||||||||
\(802\) | 7.82064 | 0.276157 | ||||||||
\(803\) | −3.62488 | −0.127919 | ||||||||
\(804\) | −26.0367 | −0.918242 | ||||||||
\(805\) | −18.7156 | −0.659636 | ||||||||
\(806\) | −18.2468 | −0.642718 | ||||||||
\(807\) | 16.8891 | 0.594524 | ||||||||
\(808\) | 1.67889 | 0.0590631 | ||||||||
\(809\) | −28.7378 | −1.01037 | −0.505183 | − | 0.863012i | \(-0.668575\pi\) | ||||
−0.505183 | + | 0.863012i | \(0.668575\pi\) | |||||||
\(810\) | −12.4262 | −0.436612 | ||||||||
\(811\) | −25.4484 | −0.893616 | −0.446808 | − | 0.894630i | \(-0.647439\pi\) | ||||
−0.446808 | + | 0.894630i | \(0.647439\pi\) | |||||||
\(812\) | −4.94600 | −0.173570 | ||||||||
\(813\) | 35.3519 | 1.23985 | ||||||||
\(814\) | 4.15910 | 0.145776 | ||||||||
\(815\) | −21.6471 | −0.758266 | ||||||||
\(816\) | −10.9971 | −0.384975 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 21.0115 | 0.734650 | ||||||||
\(819\) | 159.507 | 5.57363 | ||||||||
\(820\) | 19.2498 | 0.672231 | ||||||||
\(821\) | −27.5024 | −0.959842 | −0.479921 | − | 0.877312i | \(-0.659335\pi\) | ||||
−0.479921 | + | 0.877312i | \(0.659335\pi\) | |||||||
\(822\) | 41.5535 | 1.44935 | ||||||||
\(823\) | 17.5486 | 0.611707 | 0.305854 | − | 0.952079i | \(-0.401058\pi\) | ||||
0.305854 | + | 0.952079i | \(0.401058\pi\) | |||||||
\(824\) | 7.41178 | 0.258202 | ||||||||
\(825\) | 2.94600 | 0.102566 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.2324 | −1.15560 | −0.577802 | − | 0.816177i | \(-0.696090\pi\) | ||||
−0.577802 | + | 0.816177i | \(0.696090\pi\) | |||||||
\(828\) | −10.7444 | −0.373394 | ||||||||
\(829\) | 31.8062 | 1.10468 | 0.552338 | − | 0.833620i | \(-0.313736\pi\) | ||||
0.552338 | + | 0.833620i | \(0.313736\pi\) | |||||||
\(830\) | −29.0337 | −1.00778 | ||||||||
\(831\) | −39.9797 | −1.38688 | ||||||||
\(832\) | 5.67889 | 0.196880 | ||||||||
\(833\) | 65.1870 | 2.25860 | ||||||||
\(834\) | −40.2893 | −1.39511 | ||||||||
\(835\) | 8.02885 | 0.277850 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −25.3578 | −0.876493 | ||||||||
\(838\) | 11.0540 | 0.381854 | ||||||||
\(839\) | −2.33554 | −0.0806317 | −0.0403159 | − | 0.999187i | \(-0.512836\pi\) | ||||
−0.0403159 | + | 0.999187i | \(0.512836\pi\) | |||||||
\(840\) | 29.1418 | 1.00549 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | −4.48313 | −0.154499 | ||||||||
\(843\) | −3.53130 | −0.121624 | ||||||||
\(844\) | −25.6760 | −0.883803 | ||||||||
\(845\) | 38.4995 | 1.32442 | ||||||||
\(846\) | 42.0907 | 1.44711 | ||||||||
\(847\) | 4.94600 | 0.169946 | ||||||||
\(848\) | 11.7840 | 0.404664 | ||||||||
\(849\) | 14.2102 | 0.487692 | ||||||||
\(850\) | 3.73289 | 0.128037 | ||||||||
\(851\) | 7.86897 | 0.269745 | ||||||||
\(852\) | −13.6249 | −0.466781 | ||||||||
\(853\) | −5.03177 | −0.172284 | −0.0861422 | − | 0.996283i | \(-0.527454\pi\) | ||||
−0.0861422 | + | 0.996283i | \(0.527454\pi\) | |||||||
\(854\) | 27.5535 | 0.942863 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.3722 | −0.559590 | ||||||||
\(857\) | 9.30085 | 0.317711 | 0.158856 | − | 0.987302i | \(-0.449220\pi\) | ||||
0.158856 | + | 0.987302i | \(0.449220\pi\) | |||||||
\(858\) | 16.7300 | 0.571152 | ||||||||
\(859\) | −33.5391 | −1.14434 | −0.572170 | − | 0.820135i | \(-0.693898\pi\) | ||||
−0.572170 | + | 0.820135i | \(0.693898\pi\) | |||||||
\(860\) | −9.24977 | −0.315414 | ||||||||
\(861\) | −140.243 | −4.77947 | ||||||||
\(862\) | −2.19576 | −0.0747879 | ||||||||
\(863\) | 52.6557 | 1.79242 | 0.896211 | − | 0.443629i | \(-0.146309\pi\) | ||||
0.896211 | + | 0.443629i | \(0.146309\pi\) | |||||||
\(864\) | 7.89199 | 0.268491 | ||||||||
\(865\) | −14.4262 | −0.490506 | ||||||||
\(866\) | 31.8602 | 1.08265 | ||||||||
\(867\) | 9.03099 | 0.306708 | ||||||||
\(868\) | 15.8920 | 0.539409 | ||||||||
\(869\) | −6.83799 | −0.231963 | ||||||||
\(870\) | −5.89199 | −0.199757 | ||||||||
\(871\) | 50.1899 | 1.70062 | ||||||||
\(872\) | −17.4629 | −0.591367 | ||||||||
\(873\) | −8.71263 | −0.294878 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −59.3519 | −2.00646 | ||||||||
\(876\) | 10.6789 | 0.360806 | ||||||||
\(877\) | 11.2844 | 0.381049 | 0.190524 | − | 0.981682i | \(-0.438981\pi\) | ||||
0.190524 | + | 0.981682i | \(0.438981\pi\) | |||||||
\(878\) | 10.6422 | 0.359158 | ||||||||
\(879\) | −3.58239 | −0.120831 | ||||||||
\(880\) | 2.00000 | 0.0674200 | ||||||||
\(881\) | −21.6105 | −0.728075 | −0.364037 | − | 0.931384i | \(-0.618602\pi\) | ||||
−0.364037 | + | 0.931384i | \(0.618602\pi\) | |||||||
\(882\) | −99.1697 | −3.33922 | ||||||||
\(883\) | 16.9402 | 0.570082 | 0.285041 | − | 0.958515i | \(-0.407993\pi\) | ||||
0.285041 | + | 0.958515i | \(0.407993\pi\) | |||||||
\(884\) | 21.1987 | 0.712989 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −31.4455 | −1.05643 | ||||||||
\(887\) | −44.5873 | −1.49709 | −0.748547 | − | 0.663081i | \(-0.769248\pi\) | ||||
−0.748547 | + | 0.663081i | \(0.769248\pi\) | |||||||
\(888\) | −12.2527 | −0.411173 | ||||||||
\(889\) | −26.4995 | −0.888766 | ||||||||
\(890\) | 0.931570 | 0.0312263 | ||||||||
\(891\) | 6.21310 | 0.208147 | ||||||||
\(892\) | −7.37512 | −0.246937 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 55.9653 | 1.87176 | ||||||||
\(895\) | 8.21602 | 0.274631 | ||||||||
\(896\) | −4.94600 | −0.165234 | ||||||||
\(897\) | 31.6530 | 1.05686 | ||||||||
\(898\) | −13.8553 | −0.462358 | ||||||||
\(899\) | −3.21310 | −0.107163 | ||||||||
\(900\) | −5.67889 | −0.189296 | ||||||||
\(901\) | 43.9883 | 1.46546 | ||||||||
\(902\) | −9.62488 | −0.320474 | ||||||||
\(903\) | 67.3886 | 2.24255 | ||||||||
\(904\) | 3.53421 | 0.117546 | ||||||||
\(905\) | 30.8177 | 1.02442 | ||||||||
\(906\) | −69.7068 | −2.31585 | ||||||||
\(907\) | 34.8969 | 1.15873 | 0.579366 | − | 0.815067i | \(-0.303300\pi\) | ||||
0.579366 | + | 0.815067i | \(0.303300\pi\) | |||||||
\(908\) | −28.3549 | −0.940989 | ||||||||
\(909\) | −9.53421 | −0.316230 | ||||||||
\(910\) | −56.1755 | −1.86220 | ||||||||
\(911\) | 21.8631 | 0.724358 | 0.362179 | − | 0.932109i | \(-0.382033\pi\) | ||||
0.362179 | + | 0.932109i | \(0.382033\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.5169 | 0.480438 | ||||||||
\(914\) | 15.7329 | 0.520398 | ||||||||
\(915\) | 32.8236 | 1.08511 | ||||||||
\(916\) | −4.98266 | −0.164632 | ||||||||
\(917\) | 51.3009 | 1.69410 | ||||||||
\(918\) | 29.4600 | 0.972323 | ||||||||
\(919\) | 31.9509 | 1.05396 | 0.526981 | − | 0.849877i | \(-0.323324\pi\) | ||||
0.526981 | + | 0.849877i | \(0.323324\pi\) | |||||||
\(920\) | 3.78398 | 0.124754 | ||||||||
\(921\) | −94.4138 | −3.11104 | ||||||||
\(922\) | 20.7126 | 0.682134 | ||||||||
\(923\) | 26.2642 | 0.864496 | ||||||||
\(924\) | −14.5709 | −0.479347 | ||||||||
\(925\) | 4.15910 | 0.136750 | ||||||||
\(926\) | 14.3722 | 0.472300 | ||||||||
\(927\) | −42.0907 | −1.38244 | ||||||||
\(928\) | 1.00000 | 0.0328266 | ||||||||
\(929\) | 20.0684 | 0.658424 | 0.329212 | − | 0.944256i | \(-0.393217\pi\) | ||||
0.329212 | + | 0.944256i | \(0.393217\pi\) | |||||||
\(930\) | 18.9316 | 0.620791 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 22.4484 | 0.735323 | ||||||||
\(933\) | 54.1244 | 1.77195 | ||||||||
\(934\) | 10.3038 | 0.337150 | ||||||||
\(935\) | 7.46579 | 0.244157 | ||||||||
\(936\) | −32.2498 | −1.05412 | ||||||||
\(937\) | −45.1359 | −1.47453 | −0.737263 | − | 0.675606i | \(-0.763882\pi\) | ||||
−0.737263 | + | 0.675606i | \(0.763882\pi\) | |||||||
\(938\) | −43.7126 | −1.42727 | ||||||||
\(939\) | −3.37220 | −0.110048 | ||||||||
\(940\) | −14.8236 | −0.483491 | ||||||||
\(941\) | 34.0020 | 1.10843 | 0.554216 | − | 0.832373i | \(-0.313018\pi\) | ||||
0.554216 | + | 0.832373i | \(0.313018\pi\) | |||||||
\(942\) | −34.7156 | −1.13109 | ||||||||
\(943\) | −18.2102 | −0.593005 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −78.0675 | −2.53954 | ||||||||
\(946\) | 4.62488 | 0.150368 | ||||||||
\(947\) | −52.8177 | −1.71635 | −0.858173 | − | 0.513361i | \(-0.828400\pi\) | ||||
−0.858173 | + | 0.513361i | \(0.828400\pi\) | |||||||
\(948\) | 20.1447 | 0.654269 | ||||||||
\(949\) | −20.5853 | −0.668227 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −72.0250 | −2.33557 | ||||||||
\(952\) | −18.4629 | −0.598385 | ||||||||
\(953\) | −12.7156 | −0.411897 | −0.205949 | − | 0.978563i | \(-0.566028\pi\) | ||||
−0.205949 | + | 0.978563i | \(0.566028\pi\) | |||||||
\(954\) | −66.9199 | −2.16661 | ||||||||
\(955\) | 21.1764 | 0.685253 | ||||||||
\(956\) | −23.7840 | −0.769229 | ||||||||
\(957\) | 2.94600 | 0.0952305 | ||||||||
\(958\) | −7.58822 | −0.245164 | ||||||||
\(959\) | 69.7637 | 2.25279 | ||||||||
\(960\) | −5.89199 | −0.190163 | ||||||||
\(961\) | −20.6760 | −0.666967 | ||||||||
\(962\) | 23.6190 | 0.761509 | ||||||||
\(963\) | 92.9759 | 2.99611 | ||||||||
\(964\) | −21.1418 | −0.680930 | ||||||||
\(965\) | −11.0337 | −0.355189 | ||||||||
\(966\) | −27.5680 | −0.886985 | ||||||||
\(967\) | −9.46579 | −0.304399 | −0.152200 | − | 0.988350i | \(-0.548636\pi\) | ||||
−0.152200 | + | 0.988350i | \(0.548636\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.06843 | 0.0985213 | ||||||||
\(971\) | −29.1215 | −0.934553 | −0.467277 | − | 0.884111i | \(-0.654765\pi\) | ||||
−0.467277 | + | 0.884111i | \(0.654765\pi\) | |||||||
\(972\) | 5.37220 | 0.172313 | ||||||||
\(973\) | −67.6413 | −2.16848 | ||||||||
\(974\) | 0.414697 | 0.0132877 | ||||||||
\(975\) | 16.7300 | 0.535788 | ||||||||
\(976\) | −5.57088 | −0.178319 | ||||||||
\(977\) | −1.75023 | −0.0559950 | −0.0279975 | − | 0.999608i | \(-0.508913\pi\) | ||||
−0.0279975 | + | 0.999608i | \(0.508913\pi\) | |||||||
\(978\) | −31.8862 | −1.01961 | ||||||||
\(979\) | −0.465785 | −0.0148866 | ||||||||
\(980\) | 34.9257 | 1.11566 | ||||||||
\(981\) | 99.1697 | 3.16624 | ||||||||
\(982\) | 0.823561 | 0.0262809 | ||||||||
\(983\) | −24.0115 | −0.765848 | −0.382924 | − | 0.923780i | \(-0.625083\pi\) | ||||
−0.382924 | + | 0.923780i | \(0.625083\pi\) | |||||||
\(984\) | 28.3549 | 0.903920 | ||||||||
\(985\) | −19.0684 | −0.607571 | ||||||||
\(986\) | 3.73289 | 0.118880 | ||||||||
\(987\) | 107.996 | 3.43756 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.75023 | 0.278241 | ||||||||
\(990\) | −11.3578 | −0.360974 | ||||||||
\(991\) | 45.8033 | 1.45499 | 0.727495 | − | 0.686113i | \(-0.240684\pi\) | ||||
0.727495 | + | 0.686113i | \(0.240684\pi\) | |||||||
\(992\) | −3.21310 | −0.102016 | ||||||||
\(993\) | 18.5709 | 0.589329 | ||||||||
\(994\) | −22.8746 | −0.725540 | ||||||||
\(995\) | 41.2498 | 1.30771 | ||||||||
\(996\) | −42.7666 | −1.35511 | ||||||||
\(997\) | 5.14759 | 0.163026 | 0.0815129 | − | 0.996672i | \(-0.474025\pi\) | ||||
0.0815129 | + | 0.996672i | \(0.474025\pi\) | |||||||
\(998\) | −5.35778 | −0.169597 | ||||||||
\(999\) | 32.8236 | 1.03849 |
(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 | 7942.2.a.bd.1.1 | 3 | ||
19.7 | even | 3 | 418.2.e.i.353.3 | yes | 6 | ||
19.11 | even | 3 | 418.2.e.i.45.3 | ✓ | 6 | ||
19.18 | odd | 2 | 7942.2.a.bj.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.e.i.45.3 | ✓ | 6 | 19.11 | even | 3 | ||
418.2.e.i.353.3 | yes | 6 | 19.7 | even | 3 | ||
7942.2.a.bd.1.1 | 3 | 1.1 | even | 1 | trivial | ||
7942.2.a.bj.1.3 | 3 | 19.18 | odd | 2 |