Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [927,2,Mod(1,927)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(927, 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("927.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 927 = 3^{2} \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 927.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: | \(7.40213226737\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 24x^{12} + 221x^{10} - 980x^{8} + 2160x^{6} - 2203x^{4} + 808x^{2} - 75 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(1.46308\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 927.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.46308 | 1.03455 | 0.517277 | − | 0.855818i | \(-0.326946\pi\) | ||||
0.517277 | + | 0.855818i | \(0.326946\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.140605 | 0.0703025 | ||||||||
\(5\) | 0.979247 | 0.437932 | 0.218966 | − | 0.975732i | \(-0.429732\pi\) | ||||
0.218966 | + | 0.975732i | \(0.429732\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.33523 | 1.63856 | 0.819281 | − | 0.573392i | \(-0.194373\pi\) | ||||
0.819281 | + | 0.573392i | \(0.194373\pi\) | |||||||
\(8\) | −2.72044 | −0.961822 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.43272 | 0.453065 | ||||||||
\(11\) | 3.10803 | 0.937106 | 0.468553 | − | 0.883435i | \(-0.344776\pi\) | ||||
0.468553 | + | 0.883435i | \(0.344776\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.57505 | −0.436839 | −0.218420 | − | 0.975855i | \(-0.570090\pi\) | ||||
−0.218420 | + | 0.975855i | \(0.570090\pi\) | |||||||
\(14\) | 6.34279 | 1.69518 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.26144 | −1.06536 | ||||||||
\(17\) | −3.47437 | −0.842658 | −0.421329 | − | 0.906908i | \(-0.638436\pi\) | ||||
−0.421329 | + | 0.906908i | \(0.638436\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.01333 | 1.83838 | 0.919191 | − | 0.393811i | \(-0.128844\pi\) | ||||
0.919191 | + | 0.393811i | \(0.128844\pi\) | |||||||
\(20\) | 0.137687 | 0.0307877 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.54730 | 0.969487 | ||||||||
\(23\) | −0.212350 | −0.0442781 | −0.0221391 | − | 0.999755i | \(-0.507048\pi\) | ||||
−0.0221391 | + | 0.999755i | \(0.507048\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.04108 | −0.808215 | ||||||||
\(26\) | −2.30442 | −0.451934 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.609555 | 0.115195 | ||||||||
\(29\) | 8.02086 | 1.48944 | 0.744718 | − | 0.667379i | \(-0.232584\pi\) | ||||
0.744718 | + | 0.667379i | \(0.232584\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.88887 | 0.878067 | 0.439034 | − | 0.898471i | \(-0.355321\pi\) | ||||
0.439034 | + | 0.898471i | \(0.355321\pi\) | |||||||
\(32\) | −0.793941 | −0.140350 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.08328 | −0.871775 | ||||||||
\(35\) | 4.24526 | 0.717580 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.21775 | −1.18659 | −0.593296 | − | 0.804985i | \(-0.702174\pi\) | ||||
−0.593296 | + | 0.804985i | \(0.702174\pi\) | |||||||
\(38\) | 11.7241 | 1.90191 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.66399 | −0.421213 | ||||||||
\(41\) | −9.99565 | −1.56106 | −0.780529 | − | 0.625119i | \(-0.785050\pi\) | ||||
−0.780529 | + | 0.625119i | \(0.785050\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.71738 | 1.17689 | 0.588444 | − | 0.808538i | \(-0.299741\pi\) | ||||
0.588444 | + | 0.808538i | \(0.299741\pi\) | |||||||
\(44\) | 0.437004 | 0.0658809 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.310686 | −0.0458081 | ||||||||
\(47\) | 9.94129 | 1.45009 | 0.725043 | − | 0.688704i | \(-0.241820\pi\) | ||||
0.725043 | + | 0.688704i | \(0.241820\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.7942 | 1.68489 | ||||||||
\(50\) | −5.91242 | −0.836142 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.221459 | −0.0307109 | ||||||||
\(53\) | −4.48025 | −0.615410 | −0.307705 | − | 0.951482i | \(-0.599561\pi\) | ||||
−0.307705 | + | 0.951482i | \(0.599561\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.04353 | 0.410389 | ||||||||
\(56\) | −11.7938 | −1.57601 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 11.7352 | 1.54090 | ||||||||
\(59\) | −10.5542 | −1.37404 | −0.687020 | − | 0.726639i | \(-0.741081\pi\) | ||||
−0.687020 | + | 0.726639i | \(0.741081\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.834851 | 0.106892 | 0.0534459 | − | 0.998571i | \(-0.482980\pi\) | ||||
0.0534459 | + | 0.998571i | \(0.482980\pi\) | |||||||
\(62\) | 7.15281 | 0.908408 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.36128 | 0.920160 | ||||||||
\(65\) | −1.54236 | −0.191306 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.10798 | 0.257531 | 0.128765 | − | 0.991675i | \(-0.458899\pi\) | ||||
0.128765 | + | 0.991675i | \(0.458899\pi\) | |||||||
\(68\) | −0.488513 | −0.0592409 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.21116 | 0.742375 | ||||||||
\(71\) | −15.3566 | −1.82249 | −0.911247 | − | 0.411861i | \(-0.864879\pi\) | ||||
−0.911247 | + | 0.411861i | \(0.864879\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.99789 | 0.819041 | 0.409520 | − | 0.912301i | \(-0.365696\pi\) | ||||
0.409520 | + | 0.912301i | \(0.365696\pi\) | |||||||
\(74\) | −10.5602 | −1.22759 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.12671 | 0.129243 | ||||||||
\(77\) | 13.4740 | 1.53551 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.80934 | 0.316075 | 0.158038 | − | 0.987433i | \(-0.449483\pi\) | ||||
0.158038 | + | 0.987433i | \(0.449483\pi\) | |||||||
\(80\) | −4.17300 | −0.466556 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −14.6244 | −1.61500 | ||||||||
\(83\) | −5.64397 | −0.619506 | −0.309753 | − | 0.950817i | \(-0.600246\pi\) | ||||
−0.309753 | + | 0.950817i | \(0.600246\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.40226 | −0.369027 | ||||||||
\(86\) | 11.2911 | 1.21756 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.45522 | −0.901329 | ||||||||
\(89\) | −15.1339 | −1.60419 | −0.802096 | − | 0.597195i | \(-0.796282\pi\) | ||||
−0.802096 | + | 0.597195i | \(0.796282\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.82819 | −0.715789 | ||||||||
\(92\) | −0.0298575 | −0.00311286 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 14.5449 | 1.50019 | ||||||||
\(95\) | 7.84702 | 0.805087 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.98706 | 0.303290 | 0.151645 | − | 0.988435i | \(-0.451543\pi\) | ||||
0.151645 | + | 0.988435i | \(0.451543\pi\) | |||||||
\(98\) | 17.2559 | 1.74311 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.568196 | −0.0568196 | ||||||||
\(101\) | −4.39525 | −0.437344 | −0.218672 | − | 0.975798i | \(-0.570172\pi\) | ||||
−0.218672 | + | 0.975798i | \(0.570172\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | 4.28483 | 0.420162 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.55497 | −0.636675 | ||||||||
\(107\) | −8.27003 | −0.799494 | −0.399747 | − | 0.916625i | \(-0.630902\pi\) | ||||
−0.399747 | + | 0.916625i | \(0.630902\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.6360 | −1.49766 | −0.748831 | − | 0.662761i | \(-0.769384\pi\) | ||||
−0.748831 | + | 0.662761i | \(0.769384\pi\) | |||||||
\(110\) | 4.45292 | 0.424570 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −18.4743 | −1.74566 | ||||||||
\(113\) | 11.6331 | 1.09435 | 0.547173 | − | 0.837019i | \(-0.315704\pi\) | ||||
0.547173 | + | 0.837019i | \(0.315704\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.207943 | −0.0193908 | ||||||||
\(116\) | 1.12777 | 0.104711 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −15.4416 | −1.42152 | ||||||||
\(119\) | −15.0622 | −1.38075 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.34016 | −0.121833 | ||||||||
\(122\) | 1.22145 | 0.110585 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.687400 | 0.0617303 | ||||||||
\(125\) | −8.85344 | −0.791876 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.71393 | 0.152086 | 0.0760432 | − | 0.997105i | \(-0.475771\pi\) | ||||
0.0760432 | + | 0.997105i | \(0.475771\pi\) | |||||||
\(128\) | 12.3580 | 1.09231 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.25660 | −0.197917 | ||||||||
\(131\) | 2.06767 | 0.180653 | 0.0903267 | − | 0.995912i | \(-0.471209\pi\) | ||||
0.0903267 | + | 0.995912i | \(0.471209\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 34.7396 | 3.01231 | ||||||||
\(134\) | 3.08415 | 0.266430 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.45182 | 0.810487 | ||||||||
\(137\) | −21.9363 | −1.87414 | −0.937070 | − | 0.349141i | \(-0.886474\pi\) | ||||
−0.937070 | + | 0.349141i | \(0.886474\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.2602 | −1.20954 | −0.604769 | − | 0.796401i | \(-0.706735\pi\) | ||||
−0.604769 | + | 0.796401i | \(0.706735\pi\) | |||||||
\(140\) | 0.596905 | 0.0504477 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −22.4680 | −1.88547 | ||||||||
\(143\) | −4.89529 | −0.409365 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.85440 | 0.652272 | ||||||||
\(146\) | 10.2385 | 0.847342 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.01485 | −0.0834204 | ||||||||
\(149\) | 3.03336 | 0.248503 | 0.124251 | − | 0.992251i | \(-0.460347\pi\) | ||||
0.124251 | + | 0.992251i | \(0.460347\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.9542 | −1.62385 | −0.811924 | − | 0.583763i | \(-0.801580\pi\) | ||||
−0.811924 | + | 0.583763i | \(0.801580\pi\) | |||||||
\(152\) | −21.7998 | −1.76820 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 19.7136 | 1.58856 | ||||||||
\(155\) | 4.78741 | 0.384534 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.6062 | 0.846471 | 0.423235 | − | 0.906020i | \(-0.360894\pi\) | ||||
0.423235 | + | 0.906020i | \(0.360894\pi\) | |||||||
\(158\) | 4.11029 | 0.326997 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.777464 | −0.0614639 | ||||||||
\(161\) | −0.920587 | −0.0725525 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.48743 | 0.508135 | 0.254068 | − | 0.967186i | \(-0.418231\pi\) | ||||
0.254068 | + | 0.967186i | \(0.418231\pi\) | |||||||
\(164\) | −1.40544 | −0.109746 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.25758 | −0.640913 | ||||||||
\(167\) | −23.5567 | −1.82287 | −0.911437 | − | 0.411439i | \(-0.865026\pi\) | ||||
−0.911437 | + | 0.411439i | \(0.865026\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.5192 | −0.809171 | ||||||||
\(170\) | −4.97778 | −0.381779 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.08510 | 0.0827382 | ||||||||
\(173\) | −0.491094 | −0.0373372 | −0.0186686 | − | 0.999826i | \(-0.505943\pi\) | ||||
−0.0186686 | + | 0.999826i | \(0.505943\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −17.5190 | −1.32431 | ||||||||
\(176\) | −13.2447 | −0.998355 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −22.1421 | −1.65962 | ||||||||
\(179\) | 22.7912 | 1.70349 | 0.851747 | − | 0.523953i | \(-0.175543\pi\) | ||||
0.851747 | + | 0.523953i | \(0.175543\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.97860 | −0.593045 | −0.296522 | − | 0.955026i | \(-0.595827\pi\) | ||||
−0.296522 | + | 0.955026i | \(0.595827\pi\) | |||||||
\(182\) | −9.99019 | −0.740522 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.577687 | 0.0425877 | ||||||||
\(185\) | −7.06796 | −0.519647 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.7984 | −0.789659 | ||||||||
\(188\) | 1.39779 | 0.101945 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 11.4808 | 0.832907 | ||||||||
\(191\) | 3.70508 | 0.268091 | 0.134045 | − | 0.990975i | \(-0.457203\pi\) | ||||
0.134045 | + | 0.990975i | \(0.457203\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.6246 | −1.34063 | −0.670316 | − | 0.742076i | \(-0.733841\pi\) | ||||
−0.670316 | + | 0.742076i | \(0.733841\pi\) | |||||||
\(194\) | 4.37030 | 0.313770 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.65833 | 0.118452 | ||||||||
\(197\) | 7.14218 | 0.508859 | 0.254430 | − | 0.967091i | \(-0.418112\pi\) | ||||
0.254430 | + | 0.967091i | \(0.418112\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.36675 | 0.0968861 | 0.0484431 | − | 0.998826i | \(-0.484574\pi\) | ||||
0.0484431 | + | 0.998826i | \(0.484574\pi\) | |||||||
\(200\) | 10.9935 | 0.777360 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.43060 | −0.452456 | ||||||||
\(203\) | 34.7723 | 2.44053 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.78821 | −0.683638 | ||||||||
\(206\) | 1.46308 | 0.101938 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.71197 | 0.465391 | ||||||||
\(209\) | 24.9056 | 1.72276 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.0681 | 1.10617 | 0.553086 | − | 0.833124i | \(-0.313450\pi\) | ||||
0.553086 | + | 0.833124i | \(0.313450\pi\) | |||||||
\(212\) | −0.629946 | −0.0432649 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −12.0997 | −0.827120 | ||||||||
\(215\) | 7.55722 | 0.515398 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 21.1944 | 1.43877 | ||||||||
\(218\) | −22.8768 | −1.54941 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.427935 | 0.0288514 | ||||||||
\(221\) | 5.47229 | 0.368106 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.0765 | 1.67925 | 0.839623 | − | 0.543170i | \(-0.182776\pi\) | ||||
0.839623 | + | 0.543170i | \(0.182776\pi\) | |||||||
\(224\) | −3.44192 | −0.229973 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 17.0201 | 1.13216 | ||||||||
\(227\) | −12.6856 | −0.841972 | −0.420986 | − | 0.907067i | \(-0.638316\pi\) | ||||
−0.420986 | + | 0.907067i | \(0.638316\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.83561 | 0.517792 | 0.258896 | − | 0.965905i | \(-0.416641\pi\) | ||||
0.258896 | + | 0.965905i | \(0.416641\pi\) | |||||||
\(230\) | −0.304238 | −0.0200609 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −21.8203 | −1.43257 | ||||||||
\(233\) | 24.3548 | 1.59554 | 0.797769 | − | 0.602963i | \(-0.206013\pi\) | ||||
0.797769 | + | 0.602963i | \(0.206013\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.73497 | 0.635040 | ||||||||
\(236\) | −1.48397 | −0.0965984 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −22.0372 | −1.42846 | ||||||||
\(239\) | 7.16618 | 0.463542 | 0.231771 | − | 0.972770i | \(-0.425548\pi\) | ||||
0.231771 | + | 0.972770i | \(0.425548\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.54070 | 0.228076 | 0.114038 | − | 0.993476i | \(-0.463621\pi\) | ||||
0.114038 | + | 0.993476i | \(0.463621\pi\) | |||||||
\(242\) | −1.96076 | −0.126043 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.117384 | 0.00751476 | ||||||||
\(245\) | 11.5494 | 0.737867 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.6214 | −0.803078 | ||||||||
\(248\) | −13.2999 | −0.844545 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −12.9533 | −0.819239 | ||||||||
\(251\) | 2.20675 | 0.139289 | 0.0696445 | − | 0.997572i | \(-0.477814\pi\) | ||||
0.0696445 | + | 0.997572i | \(0.477814\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.659991 | −0.0414933 | ||||||||
\(254\) | 2.50761 | 0.157342 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.35823 | 0.209890 | ||||||||
\(257\) | 9.79114 | 0.610755 | 0.305377 | − | 0.952231i | \(-0.401217\pi\) | ||||
0.305377 | + | 0.952231i | \(0.401217\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −31.2906 | −1.94430 | ||||||||
\(260\) | −0.216863 | −0.0134493 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.02517 | 0.186896 | ||||||||
\(263\) | 16.8549 | 1.03932 | 0.519660 | − | 0.854373i | \(-0.326059\pi\) | ||||
0.519660 | + | 0.854373i | \(0.326059\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.38727 | −0.269508 | ||||||||
\(266\) | 50.8268 | 3.11639 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.296393 | 0.0181051 | ||||||||
\(269\) | 10.9935 | 0.670286 | 0.335143 | − | 0.942167i | \(-0.391215\pi\) | ||||
0.335143 | + | 0.942167i | \(0.391215\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.5156 | 1.24624 | 0.623118 | − | 0.782128i | \(-0.285866\pi\) | ||||
0.623118 | + | 0.782128i | \(0.285866\pi\) | |||||||
\(272\) | 14.8058 | 0.897734 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −32.0945 | −1.93890 | ||||||||
\(275\) | −12.5598 | −0.757383 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.05999 | 0.484278 | 0.242139 | − | 0.970242i | \(-0.422151\pi\) | ||||
0.242139 | + | 0.970242i | \(0.422151\pi\) | |||||||
\(278\) | −20.8639 | −1.25133 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −11.5490 | −0.690184 | ||||||||
\(281\) | −22.1078 | −1.31884 | −0.659420 | − | 0.751775i | \(-0.729198\pi\) | ||||
−0.659420 | + | 0.751775i | \(0.729198\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.9634 | −1.48392 | −0.741960 | − | 0.670444i | \(-0.766103\pi\) | ||||
−0.741960 | + | 0.670444i | \(0.766103\pi\) | |||||||
\(284\) | −2.15922 | −0.128126 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.16220 | −0.423510 | ||||||||
\(287\) | −43.3334 | −2.55789 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.92878 | −0.289928 | ||||||||
\(290\) | 11.4916 | 0.674811 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.983938 | 0.0575806 | ||||||||
\(293\) | −9.34592 | −0.545994 | −0.272997 | − | 0.962015i | \(-0.588015\pi\) | ||||
−0.272997 | + | 0.962015i | \(0.588015\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.3352 | −0.601736 | ||||||||
\(296\) | 19.6355 | 1.14129 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.43806 | 0.257090 | ||||||||
\(299\) | 0.334462 | 0.0193424 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 33.4566 | 1.92841 | ||||||||
\(302\) | −29.1946 | −1.67996 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −34.1483 | −1.95854 | ||||||||
\(305\) | 0.817525 | 0.0468114 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.3889 | −0.592924 | −0.296462 | − | 0.955045i | \(-0.595807\pi\) | ||||
−0.296462 | + | 0.955045i | \(0.595807\pi\) | |||||||
\(308\) | 1.89451 | 0.107950 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 7.00437 | 0.397821 | ||||||||
\(311\) | −10.9179 | −0.619099 | −0.309549 | − | 0.950883i | \(-0.600178\pi\) | ||||
−0.309549 | + | 0.950883i | \(0.600178\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.9374 | 0.674742 | 0.337371 | − | 0.941372i | \(-0.390462\pi\) | ||||
0.337371 | + | 0.941372i | \(0.390462\pi\) | |||||||
\(314\) | 15.5178 | 0.875720 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.395007 | 0.0222209 | ||||||||
\(317\) | 30.9368 | 1.73758 | 0.868792 | − | 0.495177i | \(-0.164897\pi\) | ||||
0.868792 | + | 0.495177i | \(0.164897\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.9291 | 1.39576 | ||||||||
\(320\) | 7.20851 | 0.402968 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.34689 | −0.0750595 | ||||||||
\(323\) | −27.8412 | −1.54913 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.36488 | 0.353060 | ||||||||
\(326\) | 9.49164 | 0.525693 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 27.1926 | 1.50146 | ||||||||
\(329\) | 43.0978 | 2.37606 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.1740 | −0.834038 | −0.417019 | − | 0.908898i | \(-0.636925\pi\) | ||||
−0.417019 | + | 0.908898i | \(0.636925\pi\) | |||||||
\(332\) | −0.793570 | −0.0435528 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −34.4654 | −1.88586 | ||||||||
\(335\) | 2.06423 | 0.112781 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.0575 | 1.20155 | 0.600776 | − | 0.799418i | \(-0.294859\pi\) | ||||
0.600776 | + | 0.799418i | \(0.294859\pi\) | |||||||
\(338\) | −15.3905 | −0.837132 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.478375 | −0.0259435 | ||||||||
\(341\) | 15.1947 | 0.822842 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.7840 | 1.12223 | ||||||||
\(344\) | −20.9947 | −1.13196 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.718510 | −0.0386273 | ||||||||
\(347\) | 8.28373 | 0.444694 | 0.222347 | − | 0.974968i | \(-0.428628\pi\) | ||||
0.222347 | + | 0.974968i | \(0.428628\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.479634 | −0.0256742 | −0.0128371 | − | 0.999918i | \(-0.504086\pi\) | ||||
−0.0128371 | + | 0.999918i | \(0.504086\pi\) | |||||||
\(350\) | −25.6317 | −1.37007 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.46759 | −0.131523 | ||||||||
\(353\) | −10.0710 | −0.536024 | −0.268012 | − | 0.963416i | \(-0.586367\pi\) | ||||
−0.268012 | + | 0.963416i | \(0.586367\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.0379 | −0.798129 | ||||||||
\(356\) | −2.12790 | −0.112779 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 33.3454 | 1.76236 | ||||||||
\(359\) | 11.4814 | 0.605964 | 0.302982 | − | 0.952996i | \(-0.402018\pi\) | ||||
0.302982 | + | 0.952996i | \(0.402018\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 45.2134 | 2.37965 | ||||||||
\(362\) | −11.6733 | −0.613537 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.960078 | −0.0503217 | ||||||||
\(365\) | 6.85266 | 0.358685 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.34573 | 0.279045 | 0.139523 | − | 0.990219i | \(-0.455443\pi\) | ||||
0.139523 | + | 0.990219i | \(0.455443\pi\) | |||||||
\(368\) | 0.904918 | 0.0471721 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −10.3410 | −0.537603 | ||||||||
\(371\) | −19.4229 | −1.00839 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.54266 | −0.286988 | −0.143494 | − | 0.989651i | \(-0.545834\pi\) | ||||
−0.143494 | + | 0.989651i | \(0.545834\pi\) | |||||||
\(374\) | −15.7990 | −0.816945 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −27.0447 | −1.39473 | ||||||||
\(377\) | −12.6332 | −0.650644 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.6803 | 1.11364 | 0.556820 | − | 0.830633i | \(-0.312021\pi\) | ||||
0.556820 | + | 0.830633i | \(0.312021\pi\) | |||||||
\(380\) | 1.10333 | 0.0565997 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.42084 | 0.277354 | ||||||||
\(383\) | 20.5723 | 1.05120 | 0.525598 | − | 0.850733i | \(-0.323842\pi\) | ||||
0.525598 | + | 0.850733i | \(0.323842\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.1944 | 0.672448 | ||||||||
\(386\) | −27.2494 | −1.38696 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.419995 | 0.0213220 | ||||||||
\(389\) | −31.0468 | −1.57413 | −0.787067 | − | 0.616868i | \(-0.788401\pi\) | ||||
−0.787067 | + | 0.616868i | \(0.788401\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.737783 | 0.0373113 | ||||||||
\(392\) | −32.0855 | −1.62056 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.4496 | 0.526442 | ||||||||
\(395\) | 2.75104 | 0.138420 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.94041 | −0.498895 | −0.249448 | − | 0.968388i | \(-0.580249\pi\) | ||||
−0.249448 | + | 0.968388i | \(0.580249\pi\) | |||||||
\(398\) | 1.99966 | 0.100234 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 17.2208 | 0.861040 | ||||||||
\(401\) | −3.11063 | −0.155338 | −0.0776688 | − | 0.996979i | \(-0.524748\pi\) | ||||
−0.0776688 | + | 0.996979i | \(0.524748\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.70020 | −0.383574 | ||||||||
\(404\) | −0.617994 | −0.0307464 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 50.8746 | 2.52487 | ||||||||
\(407\) | −22.4330 | −1.11196 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.7133 | −0.974758 | −0.487379 | − | 0.873190i | \(-0.662047\pi\) | ||||
−0.487379 | + | 0.873190i | \(0.662047\pi\) | |||||||
\(410\) | −14.3209 | −0.707261 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.140605 | 0.00692711 | ||||||||
\(413\) | −45.7549 | −2.25145 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.52684 | −0.271302 | ||||||||
\(416\) | 1.25049 | 0.0613105 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 36.4390 | 1.78229 | ||||||||
\(419\) | 10.3921 | 0.507686 | 0.253843 | − | 0.967245i | \(-0.418305\pi\) | ||||
0.253843 | + | 0.967245i | \(0.418305\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.6436 | −0.664946 | −0.332473 | − | 0.943113i | \(-0.607883\pi\) | ||||
−0.332473 | + | 0.943113i | \(0.607883\pi\) | |||||||
\(422\) | 23.5089 | 1.14439 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.1883 | 0.591915 | ||||||||
\(425\) | 14.0402 | 0.681049 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.61927 | 0.175149 | ||||||||
\(428\) | −1.16281 | −0.0562065 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 11.0568 | 0.533207 | ||||||||
\(431\) | 17.8981 | 0.862122 | 0.431061 | − | 0.902323i | \(-0.358139\pi\) | ||||
0.431061 | + | 0.902323i | \(0.358139\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.4912 | 1.17697 | 0.588485 | − | 0.808508i | \(-0.299725\pi\) | ||||
0.588485 | + | 0.808508i | \(0.299725\pi\) | |||||||
\(434\) | 31.0091 | 1.48848 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.19851 | −0.105289 | ||||||||
\(437\) | −1.70163 | −0.0814001 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −28.5922 | −1.36463 | −0.682314 | − | 0.731059i | \(-0.739026\pi\) | ||||
−0.682314 | + | 0.731059i | \(0.739026\pi\) | |||||||
\(440\) | −8.27975 | −0.394721 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.00640 | 0.380826 | ||||||||
\(443\) | 11.1639 | 0.530415 | 0.265207 | − | 0.964191i | \(-0.414560\pi\) | ||||
0.265207 | + | 0.964191i | \(0.414560\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.8198 | −0.702528 | ||||||||
\(446\) | 36.6889 | 1.73727 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 31.9128 | 1.50774 | ||||||||
\(449\) | −2.83705 | −0.133889 | −0.0669444 | − | 0.997757i | \(-0.521325\pi\) | ||||
−0.0669444 | + | 0.997757i | \(0.521325\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −31.0668 | −1.46288 | ||||||||
\(452\) | 1.63567 | 0.0769353 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −18.5600 | −0.871065 | ||||||||
\(455\) | −6.68648 | −0.313467 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.2362 | 1.64828 | 0.824139 | − | 0.566388i | \(-0.191660\pi\) | ||||
0.824139 | + | 0.566388i | \(0.191660\pi\) | |||||||
\(458\) | 11.4641 | 0.535683 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.0292379 | −0.00136322 | ||||||||
\(461\) | −35.0373 | −1.63185 | −0.815925 | − | 0.578158i | \(-0.803772\pi\) | ||||
−0.815925 | + | 0.578158i | \(0.803772\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.5134 | −1.32513 | −0.662565 | − | 0.749005i | \(-0.730532\pi\) | ||||
−0.662565 | + | 0.749005i | \(0.730532\pi\) | |||||||
\(464\) | −34.1804 | −1.58679 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 35.6331 | 1.65067 | ||||||||
\(467\) | 18.7973 | 0.869835 | 0.434918 | − | 0.900470i | \(-0.356778\pi\) | ||||
0.434918 | + | 0.900470i | \(0.356778\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.13858 | 0.421980 | ||||||||
\(470\) | 14.2430 | 0.656983 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 28.7121 | 1.32158 | ||||||||
\(473\) | 23.9858 | 1.10287 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −32.3825 | −1.48581 | ||||||||
\(476\) | −2.11782 | −0.0970700 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10.4847 | 0.479559 | ||||||||
\(479\) | 21.1909 | 0.968236 | 0.484118 | − | 0.875003i | \(-0.339141\pi\) | ||||
0.484118 | + | 0.875003i | \(0.339141\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.3683 | 0.518350 | ||||||||
\(482\) | 5.18033 | 0.235957 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.188433 | −0.00856515 | ||||||||
\(485\) | 2.92507 | 0.132820 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.3700 | −0.696479 | −0.348240 | − | 0.937406i | \(-0.613220\pi\) | ||||
−0.348240 | + | 0.937406i | \(0.613220\pi\) | |||||||
\(488\) | −2.27117 | −0.102811 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 16.8978 | 0.763363 | ||||||||
\(491\) | 17.7551 | 0.801278 | 0.400639 | − | 0.916236i | \(-0.368788\pi\) | ||||
0.400639 | + | 0.916236i | \(0.368788\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27.8674 | −1.25508 | ||||||||
\(494\) | −18.4661 | −0.830828 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −20.8336 | −0.935458 | ||||||||
\(497\) | −66.5744 | −2.98627 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.61856 | 0.385820 | 0.192910 | − | 0.981216i | \(-0.438207\pi\) | ||||
0.192910 | + | 0.981216i | \(0.438207\pi\) | |||||||
\(500\) | −1.24484 | −0.0556709 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.22866 | 0.144102 | ||||||||
\(503\) | 9.97468 | 0.444749 | 0.222374 | − | 0.974961i | \(-0.428619\pi\) | ||||
0.222374 | + | 0.974961i | \(0.428619\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.30403 | −0.191527 | ||||||||
\(506\) | −0.965620 | −0.0429270 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.240987 | 0.0106921 | ||||||||
\(509\) | 20.3784 | 0.903258 | 0.451629 | − | 0.892206i | \(-0.350843\pi\) | ||||
0.451629 | + | 0.892206i | \(0.350843\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.3375 | 1.34205 | ||||||||
\(512\) | −19.8027 | −0.875164 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14.3252 | 0.631859 | ||||||||
\(515\) | 0.979247 | 0.0431508 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 30.8978 | 1.35888 | ||||||||
\(518\) | −45.7807 | −2.01149 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.19590 | 0.184003 | ||||||||
\(521\) | −27.7767 | −1.21692 | −0.608460 | − | 0.793585i | \(-0.708212\pi\) | ||||
−0.608460 | + | 0.793585i | \(0.708212\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.5219 | −1.50954 | −0.754768 | − | 0.655992i | \(-0.772251\pi\) | ||||
−0.754768 | + | 0.655992i | \(0.772251\pi\) | |||||||
\(524\) | 0.290725 | 0.0127004 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.6601 | 1.07523 | ||||||||
\(527\) | −16.9857 | −0.739910 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9549 | −0.998039 | ||||||||
\(530\) | −6.41893 | −0.278821 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.88456 | 0.211773 | ||||||||
\(533\) | 15.7436 | 0.681932 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.09840 | −0.350125 | ||||||||
\(536\) | −5.73465 | −0.247699 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 16.0844 | 0.693447 | ||||||||
\(539\) | 36.6568 | 1.57892 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.65994 | −0.114360 | −0.0571800 | − | 0.998364i | \(-0.518211\pi\) | ||||
−0.0571800 | + | 0.998364i | \(0.518211\pi\) | |||||||
\(542\) | 30.0160 | 1.28930 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.75844 | 0.118267 | ||||||||
\(545\) | −15.3115 | −0.655875 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.7884 | −0.846091 | −0.423046 | − | 0.906108i | \(-0.639039\pi\) | ||||
−0.423046 | + | 0.906108i | \(0.639039\pi\) | |||||||
\(548\) | −3.08435 | −0.131757 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −18.3760 | −0.783554 | ||||||||
\(551\) | 64.2737 | 2.73815 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.1791 | 0.517909 | ||||||||
\(554\) | 11.7924 | 0.501012 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.00506 | −0.0850336 | ||||||||
\(557\) | −0.506629 | −0.0214666 | −0.0107333 | − | 0.999942i | \(-0.503417\pi\) | ||||
−0.0107333 | + | 0.999942i | \(0.503417\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.1552 | −0.514111 | ||||||||
\(560\) | −18.0909 | −0.764481 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −32.3455 | −1.36441 | ||||||||
\(563\) | 34.8259 | 1.46774 | 0.733868 | − | 0.679292i | \(-0.237713\pi\) | ||||
0.733868 | + | 0.679292i | \(0.237713\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.3916 | 0.479250 | ||||||||
\(566\) | −36.5235 | −1.53520 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 41.7768 | 1.75292 | ||||||||
\(569\) | 26.0444 | 1.09184 | 0.545919 | − | 0.837838i | \(-0.316181\pi\) | ||||
0.545919 | + | 0.837838i | \(0.316181\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.04232 | −0.336560 | −0.168280 | − | 0.985739i | \(-0.553821\pi\) | ||||
−0.168280 | + | 0.985739i | \(0.553821\pi\) | |||||||
\(572\) | −0.688302 | −0.0287794 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −63.4003 | −2.64628 | ||||||||
\(575\) | 0.858124 | 0.0357862 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.8734 | 0.910602 | 0.455301 | − | 0.890338i | \(-0.349532\pi\) | ||||
0.455301 | + | 0.890338i | \(0.349532\pi\) | |||||||
\(578\) | −7.21120 | −0.299947 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.10437 | 0.0458564 | ||||||||
\(581\) | −24.4679 | −1.01510 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.9247 | −0.576704 | ||||||||
\(584\) | −19.0374 | −0.787772 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13.6738 | −0.564861 | ||||||||
\(587\) | −42.2010 | −1.74182 | −0.870911 | − | 0.491441i | \(-0.836470\pi\) | ||||
−0.870911 | + | 0.491441i | \(0.836470\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 39.1761 | 1.61422 | ||||||||
\(590\) | −15.1212 | −0.622529 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 30.7580 | 1.26415 | ||||||||
\(593\) | −13.4590 | −0.552695 | −0.276347 | − | 0.961058i | \(-0.589124\pi\) | ||||
−0.276347 | + | 0.961058i | \(0.589124\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.7496 | −0.604674 | ||||||||
\(596\) | 0.426506 | 0.0174704 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.489344 | 0.0200108 | ||||||||
\(599\) | 16.7357 | 0.683802 | 0.341901 | − | 0.939736i | \(-0.388929\pi\) | ||||
0.341901 | + | 0.939736i | \(0.388929\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.09244 | −0.0853523 | −0.0426762 | − | 0.999089i | \(-0.513588\pi\) | ||||
−0.0426762 | + | 0.999089i | \(0.513588\pi\) | |||||||
\(602\) | 48.9497 | 1.99504 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.80566 | −0.114161 | ||||||||
\(605\) | −1.31235 | −0.0533546 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 40.1523 | 1.62973 | 0.814866 | − | 0.579649i | \(-0.196810\pi\) | ||||
0.814866 | + | 0.579649i | \(0.196810\pi\) | |||||||
\(608\) | −6.36211 | −0.258018 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.19611 | 0.0484289 | ||||||||
\(611\) | −15.6580 | −0.633454 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.75493 | −0.192050 | −0.0960250 | − | 0.995379i | \(-0.530613\pi\) | ||||
−0.0960250 | + | 0.995379i | \(0.530613\pi\) | |||||||
\(614\) | −15.1998 | −0.613412 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −36.6553 | −1.47688 | ||||||||
\(617\) | 24.9336 | 1.00379 | 0.501895 | − | 0.864929i | \(-0.332636\pi\) | ||||
0.501895 | + | 0.864929i | \(0.332636\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.85141 | 0.395962 | 0.197981 | − | 0.980206i | \(-0.436562\pi\) | ||||
0.197981 | + | 0.980206i | \(0.436562\pi\) | |||||||
\(620\) | 0.673134 | 0.0270337 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −15.9738 | −0.640491 | ||||||||
\(623\) | −65.6090 | −2.62857 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.5357 | 0.461427 | ||||||||
\(626\) | 17.4654 | 0.698057 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.49129 | 0.0595090 | ||||||||
\(629\) | 25.0771 | 0.999890 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.7231 | 0.944403 | 0.472201 | − | 0.881491i | \(-0.343460\pi\) | ||||
0.472201 | + | 0.881491i | \(0.343460\pi\) | |||||||
\(632\) | −7.64265 | −0.304008 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 45.2630 | 1.79763 | ||||||||
\(635\) | 1.67836 | 0.0666036 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.5764 | −0.736025 | ||||||||
\(638\) | 36.4732 | 1.44399 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 12.1016 | 0.478356 | ||||||||
\(641\) | 27.7679 | 1.09677 | 0.548384 | − | 0.836227i | \(-0.315243\pi\) | ||||
0.548384 | + | 0.836227i | \(0.315243\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.6986 | 1.01345 | 0.506727 | − | 0.862107i | \(-0.330855\pi\) | ||||
0.506727 | + | 0.862107i | \(0.330855\pi\) | |||||||
\(644\) | −0.129439 | −0.00510062 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −40.7340 | −1.60266 | ||||||||
\(647\) | 10.6804 | 0.419890 | 0.209945 | − | 0.977713i | \(-0.432671\pi\) | ||||
0.209945 | + | 0.977713i | \(0.432671\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −32.8027 | −1.28762 | ||||||||
\(650\) | 9.31234 | 0.365260 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.912166 | 0.0357232 | ||||||||
\(653\) | 29.3551 | 1.14875 | 0.574377 | − | 0.818591i | \(-0.305244\pi\) | ||||
0.574377 | + | 0.818591i | \(0.305244\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.02476 | 0.0791140 | ||||||||
\(656\) | 42.5959 | 1.66309 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 63.0555 | 2.45816 | ||||||||
\(659\) | −8.85132 | −0.344799 | −0.172399 | − | 0.985027i | \(-0.555152\pi\) | ||||
−0.172399 | + | 0.985027i | \(0.555152\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.4372 | −0.522645 | −0.261323 | − | 0.965252i | \(-0.584159\pi\) | ||||
−0.261323 | + | 0.965252i | \(0.584159\pi\) | |||||||
\(662\) | −22.2008 | −0.862857 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15.3541 | 0.595855 | ||||||||
\(665\) | 34.0186 | 1.31919 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.70323 | −0.0659494 | ||||||||
\(668\) | −3.31219 | −0.128153 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.02014 | 0.116678 | ||||||||
\(671\) | 2.59474 | 0.100169 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.9587 | 1.34756 | 0.673780 | − | 0.738932i | \(-0.264670\pi\) | ||||
0.673780 | + | 0.738932i | \(0.264670\pi\) | |||||||
\(674\) | 32.2720 | 1.24307 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.47906 | −0.0568868 | ||||||||
\(677\) | 13.6610 | 0.525035 | 0.262518 | − | 0.964927i | \(-0.415447\pi\) | ||||
0.262518 | + | 0.964927i | \(0.415447\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.9496 | 0.496959 | ||||||||
\(680\) | 9.25566 | 0.354939 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 22.2311 | 0.851274 | ||||||||
\(683\) | 14.8886 | 0.569696 | 0.284848 | − | 0.958573i | \(-0.408057\pi\) | ||||
0.284848 | + | 0.958573i | \(0.408057\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.4810 | −0.820747 | ||||||||
\(686\) | 30.4087 | 1.16101 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −32.8871 | −1.25381 | ||||||||
\(689\) | 7.05661 | 0.268835 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.5534 | −1.20035 | −0.600175 | − | 0.799869i | \(-0.704902\pi\) | ||||
−0.600175 | + | 0.799869i | \(0.704902\pi\) | |||||||
\(692\) | −0.0690503 | −0.00262490 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.1198 | 0.460060 | ||||||||
\(695\) | −13.9643 | −0.529696 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34.7286 | 1.31544 | ||||||||
\(698\) | −0.701744 | −0.0265614 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.46326 | −0.0931024 | ||||||||
\(701\) | −13.0497 | −0.492880 | −0.246440 | − | 0.969158i | \(-0.579261\pi\) | ||||
−0.246440 | + | 0.969158i | \(0.579261\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −57.8382 | −2.18141 | ||||||||
\(704\) | 22.8791 | 0.862287 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.7347 | −0.554546 | ||||||||
\(707\) | −19.0544 | −0.716615 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.7328 | 1.22931 | 0.614654 | − | 0.788797i | \(-0.289296\pi\) | ||||
0.614654 | + | 0.788797i | \(0.289296\pi\) | |||||||
\(710\) | −22.0017 | −0.825708 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 41.1710 | 1.54295 | ||||||||
\(713\) | −1.03815 | −0.0388791 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.79370 | −0.179274 | ||||||||
\(716\) | 3.20456 | 0.119760 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 16.7982 | 0.626903 | ||||||||
\(719\) | 24.6578 | 0.919579 | 0.459790 | − | 0.888028i | \(-0.347925\pi\) | ||||
0.459790 | + | 0.888028i | \(0.347925\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.33523 | 0.161452 | ||||||||
\(722\) | 66.1508 | 2.46188 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.12183 | −0.0416925 | ||||||||
\(725\) | −32.4129 | −1.20378 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.6030 | 0.615773 | 0.307886 | − | 0.951423i | \(-0.400378\pi\) | ||||
0.307886 | + | 0.951423i | \(0.400378\pi\) | |||||||
\(728\) | 18.5757 | 0.688462 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10.0260 | 0.371079 | ||||||||
\(731\) | −26.8130 | −0.991714 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.4874 | −0.904464 | −0.452232 | − | 0.891900i | \(-0.649372\pi\) | ||||
−0.452232 | + | 0.891900i | \(0.649372\pi\) | |||||||
\(734\) | 7.82124 | 0.288687 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.168594 | 0.00621445 | ||||||||
\(737\) | 6.55166 | 0.241334 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.79794 | −0.250066 | −0.125033 | − | 0.992153i | \(-0.539904\pi\) | ||||
−0.125033 | + | 0.992153i | \(0.539904\pi\) | |||||||
\(740\) | −0.993791 | −0.0365325 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −28.4173 | −1.04323 | ||||||||
\(743\) | 3.60079 | 0.132100 | 0.0660501 | − | 0.997816i | \(-0.478960\pi\) | ||||
0.0660501 | + | 0.997816i | \(0.478960\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.97041 | 0.108827 | ||||||||
\(746\) | −8.10937 | −0.296905 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.51831 | −0.0555150 | ||||||||
\(749\) | −35.8525 | −1.31002 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.43327 | −0.344225 | −0.172112 | − | 0.985077i | \(-0.555059\pi\) | ||||
−0.172112 | + | 0.985077i | \(0.555059\pi\) | |||||||
\(752\) | −42.3642 | −1.54486 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −18.4834 | −0.673127 | ||||||||
\(755\) | −19.5401 | −0.711136 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.03704 | 0.110383 | 0.0551916 | − | 0.998476i | \(-0.482423\pi\) | ||||
0.0551916 | + | 0.998476i | \(0.482423\pi\) | |||||||
\(758\) | 31.7200 | 1.15212 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −21.3474 | −0.774351 | ||||||||
\(761\) | −42.5238 | −1.54149 | −0.770743 | − | 0.637146i | \(-0.780115\pi\) | ||||
−0.770743 | + | 0.637146i | \(0.780115\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −67.7858 | −2.45401 | ||||||||
\(764\) | 0.520954 | 0.0188474 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 30.0989 | 1.08752 | ||||||||
\(767\) | 16.6234 | 0.600234 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.2938 | −0.876056 | −0.438028 | − | 0.898961i | \(-0.644323\pi\) | ||||
−0.438028 | + | 0.898961i | \(0.644323\pi\) | |||||||
\(770\) | 19.3044 | 0.695684 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.61872 | −0.0942497 | ||||||||
\(773\) | −22.0091 | −0.791614 | −0.395807 | − | 0.918334i | \(-0.629535\pi\) | ||||
−0.395807 | + | 0.918334i | \(0.629535\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19.7563 | −0.709667 | ||||||||
\(776\) | −8.12612 | −0.291711 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −45.4239 | −1.62853 | ||||||||
\(779\) | −80.0984 | −2.86982 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −47.7288 | −1.70787 | ||||||||
\(782\) | 1.07944 | 0.0386005 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −50.2603 | −1.79501 | ||||||||
\(785\) | 10.3861 | 0.370697 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.72444 | 0.0614697 | 0.0307349 | − | 0.999528i | \(-0.490215\pi\) | ||||
0.0307349 | + | 0.999528i | \(0.490215\pi\) | |||||||
\(788\) | 1.00423 | 0.0357741 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.02499 | 0.143203 | ||||||||
\(791\) | 50.4320 | 1.79316 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.31493 | −0.0466945 | ||||||||
\(794\) | −14.5436 | −0.516134 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.192171 | 0.00681134 | ||||||||
\(797\) | −11.6138 | −0.411383 | −0.205692 | − | 0.978617i | \(-0.565944\pi\) | ||||
−0.205692 | + | 0.978617i | \(0.565944\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −34.5397 | −1.22193 | ||||||||
\(800\) | 3.20838 | 0.113433 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4.55111 | −0.160705 | ||||||||
\(803\) | 21.7496 | 0.767528 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.901482 | −0.0317731 | ||||||||
\(806\) | −11.2660 | −0.396828 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 11.9570 | 0.420647 | ||||||||
\(809\) | 29.9527 | 1.05308 | 0.526541 | − | 0.850150i | \(-0.323489\pi\) | ||||
0.526541 | + | 0.850150i | \(0.323489\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.3973 | −1.20785 | −0.603926 | − | 0.797041i | \(-0.706398\pi\) | ||||
−0.603926 | + | 0.797041i | \(0.706398\pi\) | |||||||
\(812\) | 4.88915 | 0.171576 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −32.8213 | −1.15038 | ||||||||
\(815\) | 6.35280 | 0.222529 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 61.8418 | 2.16357 | ||||||||
\(818\) | −28.8421 | −1.00844 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.37627 | −0.0480615 | ||||||||
\(821\) | −5.39340 | −0.188231 | −0.0941155 | − | 0.995561i | \(-0.530002\pi\) | ||||
−0.0941155 | + | 0.995561i | \(0.530002\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.7578 | 0.828145 | 0.414072 | − | 0.910244i | \(-0.364106\pi\) | ||||
0.414072 | + | 0.910244i | \(0.364106\pi\) | |||||||
\(824\) | −2.72044 | −0.0947712 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −66.9430 | −2.32925 | ||||||||
\(827\) | 33.7726 | 1.17439 | 0.587194 | − | 0.809446i | \(-0.300233\pi\) | ||||
0.587194 | + | 0.809446i | \(0.300233\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −46.4676 | −1.61389 | −0.806944 | − | 0.590628i | \(-0.798880\pi\) | ||||
−0.806944 | + | 0.590628i | \(0.798880\pi\) | |||||||
\(830\) | −8.08621 | −0.280676 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −11.5944 | −0.401962 | ||||||||
\(833\) | −40.9774 | −1.41978 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −23.0678 | −0.798296 | ||||||||
\(836\) | 3.50186 | 0.121114 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 15.2044 | 0.525229 | ||||||||
\(839\) | −7.72365 | −0.266650 | −0.133325 | − | 0.991072i | \(-0.542565\pi\) | ||||
−0.133325 | + | 0.991072i | \(0.542565\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.3342 | 1.21842 | ||||||||
\(842\) | −19.9616 | −0.687923 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.25925 | 0.0777666 | ||||||||
\(845\) | −10.3009 | −0.354362 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.80991 | −0.199631 | ||||||||
\(848\) | 19.0923 | 0.655633 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 20.5419 | 0.704582 | ||||||||
\(851\) | 1.53269 | 0.0525400 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.0384 | 0.446425 | 0.223213 | − | 0.974770i | \(-0.428346\pi\) | ||||
0.223213 | + | 0.974770i | \(0.428346\pi\) | |||||||
\(854\) | 5.29529 | 0.181201 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 22.4982 | 0.768972 | ||||||||
\(857\) | −17.4262 | −0.595267 | −0.297634 | − | 0.954680i | \(-0.596197\pi\) | ||||
−0.297634 | + | 0.954680i | \(0.596197\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −50.1030 | −1.70949 | −0.854747 | − | 0.519045i | \(-0.826288\pi\) | ||||
−0.854747 | + | 0.519045i | \(0.826288\pi\) | |||||||
\(860\) | 1.06258 | 0.0362338 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 26.1864 | 0.891911 | ||||||||
\(863\) | −20.3805 | −0.693762 | −0.346881 | − | 0.937909i | \(-0.612759\pi\) | ||||
−0.346881 | + | 0.937909i | \(0.612759\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.480902 | −0.0163512 | ||||||||
\(866\) | 35.8325 | 1.21764 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.98004 | 0.101149 | ||||||||
\(869\) | 8.73151 | 0.296196 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.32017 | −0.112500 | ||||||||
\(872\) | 42.5370 | 1.44048 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.48963 | −0.0842128 | ||||||||
\(875\) | −38.3817 | −1.29754 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.0756 | −0.981814 | −0.490907 | − | 0.871212i | \(-0.663335\pi\) | ||||
−0.490907 | + | 0.871212i | \(0.663335\pi\) | |||||||
\(878\) | −41.8326 | −1.41178 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −12.9698 | −0.437212 | ||||||||
\(881\) | −5.99800 | −0.202078 | −0.101039 | − | 0.994882i | \(-0.532217\pi\) | ||||
−0.101039 | + | 0.994882i | \(0.532217\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.5048 | 0.555431 | 0.277715 | − | 0.960663i | \(-0.410423\pi\) | ||||
0.277715 | + | 0.960663i | \(0.410423\pi\) | |||||||
\(884\) | 0.769431 | 0.0258788 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.3337 | 0.548743 | ||||||||
\(887\) | −1.75149 | −0.0588093 | −0.0294047 | − | 0.999568i | \(-0.509361\pi\) | ||||
−0.0294047 | + | 0.999568i | \(0.509361\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.43027 | 0.249203 | ||||||||
\(890\) | −21.6826 | −0.726803 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.52588 | 0.118055 | ||||||||
\(893\) | 79.6628 | 2.66581 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.3182 | 0.746015 | ||||||||
\(896\) | 53.5749 | 1.78981 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.15083 | −0.138515 | ||||||||
\(899\) | 39.2129 | 1.30782 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.5660 | 0.518580 | ||||||||
\(902\) | −45.4532 | −1.51343 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −31.6471 | −1.05257 | ||||||||
\(905\) | −7.81302 | −0.259713 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.1269 | −0.701508 | −0.350754 | − | 0.936468i | \(-0.614075\pi\) | ||||
−0.350754 | + | 0.936468i | \(0.614075\pi\) | |||||||
\(908\) | −1.78366 | −0.0591927 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −9.78286 | −0.324299 | ||||||||
\(911\) | −4.02983 | −0.133514 | −0.0667571 | − | 0.997769i | \(-0.521265\pi\) | ||||
−0.0667571 | + | 0.997769i | \(0.521265\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.5416 | −0.580543 | ||||||||
\(914\) | 51.5533 | 1.70523 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.10173 | 0.0364020 | ||||||||
\(917\) | 8.96384 | 0.296012 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.1329 | −1.19191 | −0.595956 | − | 0.803017i | \(-0.703227\pi\) | ||||
−0.595956 | + | 0.803017i | \(0.703227\pi\) | |||||||
\(920\) | 0.565698 | 0.0186505 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −51.2624 | −1.68824 | ||||||||
\(923\) | 24.1874 | 0.796137 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 29.1675 | 0.959021 | ||||||||
\(926\) | −41.7174 | −1.37092 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.36809 | −0.209043 | ||||||||
\(929\) | 3.54245 | 0.116224 | 0.0581121 | − | 0.998310i | \(-0.481492\pi\) | ||||
0.0581121 | + | 0.998310i | \(0.481492\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 94.5109 | 3.09747 | ||||||||
\(932\) | 3.42441 | 0.112170 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 27.5020 | 0.899892 | ||||||||
\(935\) | −10.5743 | −0.345817 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.6110 | −0.673333 | −0.336666 | − | 0.941624i | \(-0.609299\pi\) | ||||
−0.336666 | + | 0.941624i | \(0.609299\pi\) | |||||||
\(938\) | 13.3705 | 0.436562 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.36879 | 0.0446449 | ||||||||
\(941\) | 34.8331 | 1.13553 | 0.567764 | − | 0.823191i | \(-0.307809\pi\) | ||||
0.567764 | + | 0.823191i | \(0.307809\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.12258 | 0.0691207 | ||||||||
\(944\) | 44.9761 | 1.46385 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 35.0932 | 1.14098 | ||||||||
\(947\) | −24.7436 | −0.804060 | −0.402030 | − | 0.915627i | \(-0.631695\pi\) | ||||
−0.402030 | + | 0.915627i | \(0.631695\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.0220 | −0.357789 | ||||||||
\(950\) | −47.3781 | −1.53715 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 40.9758 | 1.32803 | ||||||||
\(953\) | −43.2497 | −1.40099 | −0.700497 | − | 0.713655i | \(-0.747038\pi\) | ||||
−0.700497 | + | 0.713655i | \(0.747038\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.62819 | 0.117406 | ||||||||
\(956\) | 1.00760 | 0.0325882 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 31.0040 | 1.00169 | ||||||||
\(959\) | −95.0987 | −3.07090 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.09894 | −0.228998 | ||||||||
\(962\) | 16.6327 | 0.536261 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.497840 | 0.0160343 | ||||||||
\(965\) | −18.2381 | −0.587106 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.0346 | 0.837216 | 0.418608 | − | 0.908167i | \(-0.362518\pi\) | ||||
0.418608 | + | 0.908167i | \(0.362518\pi\) | |||||||
\(968\) | 3.64583 | 0.117182 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.27961 | 0.137410 | ||||||||
\(971\) | −42.3145 | −1.35794 | −0.678968 | − | 0.734168i | \(-0.737572\pi\) | ||||
−0.678968 | + | 0.734168i | \(0.737572\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −61.8214 | −1.98190 | ||||||||
\(974\) | −22.4875 | −0.720546 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.55767 | −0.113878 | ||||||||
\(977\) | 9.09981 | 0.291129 | 0.145564 | − | 0.989349i | \(-0.453500\pi\) | ||||
0.145564 | + | 0.989349i | \(0.453500\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −47.0366 | −1.50330 | ||||||||
\(980\) | 1.62391 | 0.0518739 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 25.9772 | 0.828966 | ||||||||
\(983\) | 5.72010 | 0.182443 | 0.0912214 | − | 0.995831i | \(-0.470923\pi\) | ||||
0.0912214 | + | 0.995831i | \(0.470923\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.99395 | 0.222846 | ||||||||
\(986\) | −40.7723 | −1.29845 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.77463 | −0.0564584 | ||||||||
\(989\) | −1.63879 | −0.0521104 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.92547 | −0.315293 | −0.157646 | − | 0.987496i | \(-0.550391\pi\) | ||||
−0.157646 | + | 0.987496i | \(0.550391\pi\) | |||||||
\(992\) | −3.88148 | −0.123237 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −97.4037 | −3.08946 | ||||||||
\(995\) | 1.33838 | 0.0424296 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.90856 | 0.0604446 | 0.0302223 | − | 0.999543i | \(-0.490378\pi\) | ||||
0.0302223 | + | 0.999543i | \(0.490378\pi\) | |||||||
\(998\) | 12.6096 | 0.399151 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 927.2.a.h.1.10 | yes | 14 | |
3.2 | odd | 2 | inner | 927.2.a.h.1.5 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
927.2.a.h.1.5 | ✓ | 14 | 3.2 | odd | 2 | inner | |
927.2.a.h.1.10 | yes | 14 | 1.1 | even | 1 | trivial |