Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.938469 | −0.663598 | −0.331799 | − | 0.943350i | \(-0.607656\pi\) | ||||
−0.331799 | + | 0.943350i | \(0.607656\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.11928 | −0.559638 | ||||||||
\(5\) | −3.16176 | −1.41398 | −0.706991 | − | 0.707223i | \(-0.749948\pi\) | ||||
−0.706991 | + | 0.707223i | \(0.749948\pi\) | |||||||
\(6\) | −0.938469 | −0.383128 | ||||||||
\(7\) | 3.19339 | 1.20699 | 0.603494 | − | 0.797367i | \(-0.293775\pi\) | ||||
0.603494 | + | 0.797367i | \(0.293775\pi\) | |||||||
\(8\) | 2.92734 | 1.03497 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.96721 | 0.938315 | ||||||||
\(11\) | −3.89690 | −1.17496 | −0.587480 | − | 0.809239i | \(-0.699880\pi\) | ||||
−0.587480 | + | 0.809239i | \(0.699880\pi\) | |||||||
\(12\) | −1.11928 | −0.323107 | ||||||||
\(13\) | 3.99640 | 1.10840 | 0.554201 | − | 0.832383i | \(-0.313024\pi\) | ||||
0.554201 | + | 0.832383i | \(0.313024\pi\) | |||||||
\(14\) | −2.99690 | −0.800955 | ||||||||
\(15\) | −3.16176 | −0.816363 | ||||||||
\(16\) | −0.508669 | −0.127167 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −0.938469 | −0.221199 | ||||||||
\(19\) | −2.61070 | −0.598936 | −0.299468 | − | 0.954106i | \(-0.596809\pi\) | ||||
−0.299468 | + | 0.954106i | \(0.596809\pi\) | |||||||
\(20\) | 3.53888 | 0.791318 | ||||||||
\(21\) | 3.19339 | 0.696855 | ||||||||
\(22\) | 3.65712 | 0.779701 | ||||||||
\(23\) | −2.63739 | −0.549934 | −0.274967 | − | 0.961454i | \(-0.588667\pi\) | ||||
−0.274967 | + | 0.961454i | \(0.588667\pi\) | |||||||
\(24\) | 2.92734 | 0.597542 | ||||||||
\(25\) | 4.99672 | 0.999344 | ||||||||
\(26\) | −3.75050 | −0.735533 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −3.57429 | −0.675477 | ||||||||
\(29\) | −8.17474 | −1.51801 | −0.759005 | − | 0.651084i | \(-0.774314\pi\) | ||||
−0.759005 | + | 0.651084i | \(0.774314\pi\) | |||||||
\(30\) | 2.96721 | 0.541736 | ||||||||
\(31\) | 9.36114 | 1.68131 | 0.840656 | − | 0.541570i | \(-0.182170\pi\) | ||||
0.840656 | + | 0.541570i | \(0.182170\pi\) | |||||||
\(32\) | −5.37732 | −0.950584 | ||||||||
\(33\) | −3.89690 | −0.678364 | ||||||||
\(34\) | 0.938469 | 0.160946 | ||||||||
\(35\) | −10.0967 | −1.70666 | ||||||||
\(36\) | −1.11928 | −0.186546 | ||||||||
\(37\) | 6.64774 | 1.09288 | 0.546441 | − | 0.837498i | \(-0.315982\pi\) | ||||
0.546441 | + | 0.837498i | \(0.315982\pi\) | |||||||
\(38\) | 2.45006 | 0.397453 | ||||||||
\(39\) | 3.99640 | 0.639936 | ||||||||
\(40\) | −9.25556 | −1.46343 | ||||||||
\(41\) | 0.367288 | 0.0573607 | 0.0286804 | − | 0.999589i | \(-0.490870\pi\) | ||||
0.0286804 | + | 0.999589i | \(0.490870\pi\) | |||||||
\(42\) | −2.99690 | −0.462432 | ||||||||
\(43\) | 5.19918 | 0.792868 | 0.396434 | − | 0.918063i | \(-0.370248\pi\) | ||||
0.396434 | + | 0.918063i | \(0.370248\pi\) | |||||||
\(44\) | 4.36171 | 0.657552 | ||||||||
\(45\) | −3.16176 | −0.471327 | ||||||||
\(46\) | 2.47511 | 0.364935 | ||||||||
\(47\) | −8.99268 | −1.31172 | −0.655859 | − | 0.754884i | \(-0.727693\pi\) | ||||
−0.655859 | + | 0.754884i | \(0.727693\pi\) | |||||||
\(48\) | −0.508669 | −0.0734200 | ||||||||
\(49\) | 3.19775 | 0.456821 | ||||||||
\(50\) | −4.68927 | −0.663162 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −4.47307 | −0.620304 | ||||||||
\(53\) | 10.5866 | 1.45418 | 0.727090 | − | 0.686543i | \(-0.240872\pi\) | ||||
0.727090 | + | 0.686543i | \(0.240872\pi\) | |||||||
\(54\) | −0.938469 | −0.127709 | ||||||||
\(55\) | 12.3211 | 1.66137 | ||||||||
\(56\) | 9.34815 | 1.24920 | ||||||||
\(57\) | −2.61070 | −0.345796 | ||||||||
\(58\) | 7.67174 | 1.00735 | ||||||||
\(59\) | 5.79433 | 0.754358 | 0.377179 | − | 0.926140i | \(-0.376894\pi\) | ||||
0.377179 | + | 0.926140i | \(0.376894\pi\) | |||||||
\(60\) | 3.53888 | 0.456868 | ||||||||
\(61\) | −8.59133 | −1.10001 | −0.550004 | − | 0.835162i | \(-0.685374\pi\) | ||||
−0.550004 | + | 0.835162i | \(0.685374\pi\) | |||||||
\(62\) | −8.78514 | −1.11571 | ||||||||
\(63\) | 3.19339 | 0.402330 | ||||||||
\(64\) | 6.06378 | 0.757973 | ||||||||
\(65\) | −12.6357 | −1.56726 | ||||||||
\(66\) | 3.65712 | 0.450161 | ||||||||
\(67\) | −13.3867 | −1.63545 | −0.817723 | − | 0.575612i | \(-0.804764\pi\) | ||||
−0.817723 | + | 0.575612i | \(0.804764\pi\) | |||||||
\(68\) | 1.11928 | 0.135732 | ||||||||
\(69\) | −2.63739 | −0.317504 | ||||||||
\(70\) | 9.47547 | 1.13254 | ||||||||
\(71\) | −11.1243 | −1.32021 | −0.660103 | − | 0.751175i | \(-0.729487\pi\) | ||||
−0.660103 | + | 0.751175i | \(0.729487\pi\) | |||||||
\(72\) | 2.92734 | 0.344991 | ||||||||
\(73\) | −8.17971 | −0.957362 | −0.478681 | − | 0.877989i | \(-0.658885\pi\) | ||||
−0.478681 | + | 0.877989i | \(0.658885\pi\) | |||||||
\(74\) | −6.23870 | −0.725234 | ||||||||
\(75\) | 4.99672 | 0.576972 | ||||||||
\(76\) | 2.92210 | 0.335187 | ||||||||
\(77\) | −12.4443 | −1.41816 | ||||||||
\(78\) | −3.75050 | −0.424660 | ||||||||
\(79\) | 6.91010 | 0.777447 | 0.388724 | − | 0.921354i | \(-0.372916\pi\) | ||||
0.388724 | + | 0.921354i | \(0.372916\pi\) | |||||||
\(80\) | 1.60829 | 0.179812 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.344688 | −0.0380645 | ||||||||
\(83\) | 4.30590 | 0.472634 | 0.236317 | − | 0.971676i | \(-0.424060\pi\) | ||||
0.236317 | + | 0.971676i | \(0.424060\pi\) | |||||||
\(84\) | −3.57429 | −0.389987 | ||||||||
\(85\) | 3.16176 | 0.342941 | ||||||||
\(86\) | −4.87927 | −0.526145 | ||||||||
\(87\) | −8.17474 | −0.876424 | ||||||||
\(88\) | −11.4076 | −1.21605 | ||||||||
\(89\) | −0.653746 | −0.0692970 | −0.0346485 | − | 0.999400i | \(-0.511031\pi\) | ||||
−0.0346485 | + | 0.999400i | \(0.511031\pi\) | |||||||
\(90\) | 2.96721 | 0.312772 | ||||||||
\(91\) | 12.7621 | 1.33783 | ||||||||
\(92\) | 2.95197 | 0.307764 | ||||||||
\(93\) | 9.36114 | 0.970706 | ||||||||
\(94\) | 8.43935 | 0.870453 | ||||||||
\(95\) | 8.25441 | 0.846885 | ||||||||
\(96\) | −5.37732 | −0.548820 | ||||||||
\(97\) | 17.7265 | 1.79985 | 0.899926 | − | 0.436043i | \(-0.143620\pi\) | ||||
0.899926 | + | 0.436043i | \(0.143620\pi\) | |||||||
\(98\) | −3.00099 | −0.303146 | ||||||||
\(99\) | −3.89690 | −0.391653 | ||||||||
\(100\) | −5.59271 | −0.559271 | ||||||||
\(101\) | 4.42409 | 0.440214 | 0.220107 | − | 0.975476i | \(-0.429359\pi\) | ||||
0.220107 | + | 0.975476i | \(0.429359\pi\) | |||||||
\(102\) | 0.938469 | 0.0929223 | ||||||||
\(103\) | −4.43823 | −0.437312 | −0.218656 | − | 0.975802i | \(-0.570167\pi\) | ||||
−0.218656 | + | 0.975802i | \(0.570167\pi\) | |||||||
\(104\) | 11.6988 | 1.14717 | ||||||||
\(105\) | −10.0967 | −0.985340 | ||||||||
\(106\) | −9.93518 | −0.964990 | ||||||||
\(107\) | −7.01299 | −0.677971 | −0.338986 | − | 0.940792i | \(-0.610084\pi\) | ||||
−0.338986 | + | 0.940792i | \(0.610084\pi\) | |||||||
\(108\) | −1.11928 | −0.107702 | ||||||||
\(109\) | −2.69617 | −0.258246 | −0.129123 | − | 0.991629i | \(-0.541216\pi\) | ||||
−0.129123 | + | 0.991629i | \(0.541216\pi\) | |||||||
\(110\) | −11.5629 | −1.10248 | ||||||||
\(111\) | 6.64774 | 0.630976 | ||||||||
\(112\) | −1.62438 | −0.153489 | ||||||||
\(113\) | 3.47775 | 0.327159 | 0.163579 | − | 0.986530i | \(-0.447696\pi\) | ||||
0.163579 | + | 0.986530i | \(0.447696\pi\) | |||||||
\(114\) | 2.45006 | 0.229469 | ||||||||
\(115\) | 8.33879 | 0.777596 | ||||||||
\(116\) | 9.14979 | 0.849537 | ||||||||
\(117\) | 3.99640 | 0.369467 | ||||||||
\(118\) | −5.43780 | −0.500590 | ||||||||
\(119\) | −3.19339 | −0.292738 | ||||||||
\(120\) | −9.25556 | −0.844913 | ||||||||
\(121\) | 4.18585 | 0.380532 | ||||||||
\(122\) | 8.06270 | 0.729962 | ||||||||
\(123\) | 0.367288 | 0.0331172 | ||||||||
\(124\) | −10.4777 | −0.940926 | ||||||||
\(125\) | 0.0103688 | 0.000927417 0 | ||||||||
\(126\) | −2.99690 | −0.266985 | ||||||||
\(127\) | −15.2780 | −1.35571 | −0.677853 | − | 0.735197i | \(-0.737090\pi\) | ||||
−0.677853 | + | 0.735197i | \(0.737090\pi\) | |||||||
\(128\) | 5.06396 | 0.447595 | ||||||||
\(129\) | 5.19918 | 0.457762 | ||||||||
\(130\) | 11.8582 | 1.04003 | ||||||||
\(131\) | 13.0166 | 1.13727 | 0.568633 | − | 0.822591i | \(-0.307472\pi\) | ||||
0.568633 | + | 0.822591i | \(0.307472\pi\) | |||||||
\(132\) | 4.36171 | 0.379638 | ||||||||
\(133\) | −8.33699 | −0.722909 | ||||||||
\(134\) | 12.5630 | 1.08528 | ||||||||
\(135\) | −3.16176 | −0.272121 | ||||||||
\(136\) | −2.92734 | −0.251018 | ||||||||
\(137\) | −8.48559 | −0.724973 | −0.362486 | − | 0.931989i | \(-0.618072\pi\) | ||||
−0.362486 | + | 0.931989i | \(0.618072\pi\) | |||||||
\(138\) | 2.47511 | 0.210695 | ||||||||
\(139\) | −16.1044 | −1.36596 | −0.682980 | − | 0.730437i | \(-0.739316\pi\) | ||||
−0.682980 | + | 0.730437i | \(0.739316\pi\) | |||||||
\(140\) | 11.3010 | 0.955112 | ||||||||
\(141\) | −8.99268 | −0.757320 | ||||||||
\(142\) | 10.4398 | 0.876086 | ||||||||
\(143\) | −15.5736 | −1.30233 | ||||||||
\(144\) | −0.508669 | −0.0423891 | ||||||||
\(145\) | 25.8466 | 2.14644 | ||||||||
\(146\) | 7.67640 | 0.635303 | ||||||||
\(147\) | 3.19775 | 0.263746 | ||||||||
\(148\) | −7.44066 | −0.611618 | ||||||||
\(149\) | −7.77400 | −0.636871 | −0.318436 | − | 0.947945i | \(-0.603157\pi\) | ||||
−0.318436 | + | 0.947945i | \(0.603157\pi\) | |||||||
\(150\) | −4.68927 | −0.382877 | ||||||||
\(151\) | −6.12281 | −0.498267 | −0.249134 | − | 0.968469i | \(-0.580146\pi\) | ||||
−0.249134 | + | 0.968469i | \(0.580146\pi\) | |||||||
\(152\) | −7.64242 | −0.619882 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 11.6786 | 0.941090 | ||||||||
\(155\) | −29.5977 | −2.37734 | ||||||||
\(156\) | −4.47307 | −0.358133 | ||||||||
\(157\) | 1.00000 | 0.0798087 | ||||||||
\(158\) | −6.48492 | −0.515912 | ||||||||
\(159\) | 10.5866 | 0.839571 | ||||||||
\(160\) | 17.0018 | 1.34411 | ||||||||
\(161\) | −8.42222 | −0.663764 | ||||||||
\(162\) | −0.938469 | −0.0737331 | ||||||||
\(163\) | 18.3261 | 1.43541 | 0.717705 | − | 0.696347i | \(-0.245192\pi\) | ||||
0.717705 | + | 0.696347i | \(0.245192\pi\) | |||||||
\(164\) | −0.411097 | −0.0321013 | ||||||||
\(165\) | 12.3211 | 0.959194 | ||||||||
\(166\) | −4.04095 | −0.313639 | ||||||||
\(167\) | 7.02150 | 0.543340 | 0.271670 | − | 0.962390i | \(-0.412424\pi\) | ||||
0.271670 | + | 0.962390i | \(0.412424\pi\) | |||||||
\(168\) | 9.34815 | 0.721226 | ||||||||
\(169\) | 2.97121 | 0.228555 | ||||||||
\(170\) | −2.96721 | −0.227575 | ||||||||
\(171\) | −2.61070 | −0.199645 | ||||||||
\(172\) | −5.81932 | −0.443719 | ||||||||
\(173\) | 7.26500 | 0.552348 | 0.276174 | − | 0.961108i | \(-0.410933\pi\) | ||||
0.276174 | + | 0.961108i | \(0.410933\pi\) | |||||||
\(174\) | 7.67174 | 0.581593 | ||||||||
\(175\) | 15.9565 | 1.20620 | ||||||||
\(176\) | 1.98223 | 0.149416 | ||||||||
\(177\) | 5.79433 | 0.435529 | ||||||||
\(178\) | 0.613521 | 0.0459853 | ||||||||
\(179\) | 23.1191 | 1.72800 | 0.864001 | − | 0.503490i | \(-0.167951\pi\) | ||||
0.864001 | + | 0.503490i | \(0.167951\pi\) | |||||||
\(180\) | 3.53888 | 0.263773 | ||||||||
\(181\) | −9.53173 | −0.708488 | −0.354244 | − | 0.935153i | \(-0.615262\pi\) | ||||
−0.354244 | + | 0.935153i | \(0.615262\pi\) | |||||||
\(182\) | −11.9768 | −0.887780 | ||||||||
\(183\) | −8.59133 | −0.635089 | ||||||||
\(184\) | −7.72054 | −0.569166 | ||||||||
\(185\) | −21.0186 | −1.54531 | ||||||||
\(186\) | −8.78514 | −0.644158 | ||||||||
\(187\) | 3.89690 | 0.284970 | ||||||||
\(188\) | 10.0653 | 0.734087 | ||||||||
\(189\) | 3.19339 | 0.232285 | ||||||||
\(190\) | −7.74651 | −0.561991 | ||||||||
\(191\) | 21.7974 | 1.57720 | 0.788601 | − | 0.614906i | \(-0.210806\pi\) | ||||
0.788601 | + | 0.614906i | \(0.210806\pi\) | |||||||
\(192\) | 6.06378 | 0.437616 | ||||||||
\(193\) | 3.66453 | 0.263779 | 0.131889 | − | 0.991264i | \(-0.457896\pi\) | ||||
0.131889 | + | 0.991264i | \(0.457896\pi\) | |||||||
\(194\) | −16.6358 | −1.19438 | ||||||||
\(195\) | −12.6357 | −0.904858 | ||||||||
\(196\) | −3.57916 | −0.255655 | ||||||||
\(197\) | 11.3572 | 0.809168 | 0.404584 | − | 0.914501i | \(-0.367416\pi\) | ||||
0.404584 | + | 0.914501i | \(0.367416\pi\) | |||||||
\(198\) | 3.65712 | 0.259900 | ||||||||
\(199\) | −6.77838 | −0.480506 | −0.240253 | − | 0.970710i | \(-0.577230\pi\) | ||||
−0.240253 | + | 0.970710i | \(0.577230\pi\) | |||||||
\(200\) | 14.6271 | 1.03429 | ||||||||
\(201\) | −13.3867 | −0.944225 | ||||||||
\(202\) | −4.15187 | −0.292125 | ||||||||
\(203\) | −26.1051 | −1.83222 | ||||||||
\(204\) | 1.11928 | 0.0783650 | ||||||||
\(205\) | −1.16128 | −0.0811070 | ||||||||
\(206\) | 4.16514 | 0.290199 | ||||||||
\(207\) | −2.63739 | −0.183311 | ||||||||
\(208\) | −2.03284 | −0.140952 | ||||||||
\(209\) | 10.1736 | 0.703726 | ||||||||
\(210\) | 9.47547 | 0.653870 | ||||||||
\(211\) | −0.321094 | −0.0221050 | −0.0110525 | − | 0.999939i | \(-0.503518\pi\) | ||||
−0.0110525 | + | 0.999939i | \(0.503518\pi\) | |||||||
\(212\) | −11.8493 | −0.813814 | ||||||||
\(213\) | −11.1243 | −0.762221 | ||||||||
\(214\) | 6.58147 | 0.449900 | ||||||||
\(215\) | −16.4386 | −1.12110 | ||||||||
\(216\) | 2.92734 | 0.199181 | ||||||||
\(217\) | 29.8938 | 2.02932 | ||||||||
\(218\) | 2.53027 | 0.171371 | ||||||||
\(219\) | −8.17971 | −0.552733 | ||||||||
\(220\) | −13.7907 | −0.929767 | ||||||||
\(221\) | −3.99640 | −0.268827 | ||||||||
\(222\) | −6.23870 | −0.418714 | ||||||||
\(223\) | 5.06897 | 0.339444 | 0.169722 | − | 0.985492i | \(-0.445713\pi\) | ||||
0.169722 | + | 0.985492i | \(0.445713\pi\) | |||||||
\(224\) | −17.1719 | −1.14734 | ||||||||
\(225\) | 4.99672 | 0.333115 | ||||||||
\(226\) | −3.26376 | −0.217102 | ||||||||
\(227\) | −12.3705 | −0.821061 | −0.410530 | − | 0.911847i | \(-0.634656\pi\) | ||||
−0.410530 | + | 0.911847i | \(0.634656\pi\) | |||||||
\(228\) | 2.92210 | 0.193521 | ||||||||
\(229\) | 4.56787 | 0.301853 | 0.150927 | − | 0.988545i | \(-0.451774\pi\) | ||||
0.150927 | + | 0.988545i | \(0.451774\pi\) | |||||||
\(230\) | −7.82569 | −0.516011 | ||||||||
\(231\) | −12.4443 | −0.818777 | ||||||||
\(232\) | −23.9303 | −1.57110 | ||||||||
\(233\) | −26.2130 | −1.71727 | −0.858636 | − | 0.512585i | \(-0.828688\pi\) | ||||
−0.858636 | + | 0.512585i | \(0.828688\pi\) | |||||||
\(234\) | −3.75050 | −0.245178 | ||||||||
\(235\) | 28.4327 | 1.85474 | ||||||||
\(236\) | −6.48546 | −0.422167 | ||||||||
\(237\) | 6.91010 | 0.448859 | ||||||||
\(238\) | 2.99690 | 0.194260 | ||||||||
\(239\) | 14.5206 | 0.939262 | 0.469631 | − | 0.882863i | \(-0.344387\pi\) | ||||
0.469631 | + | 0.882863i | \(0.344387\pi\) | |||||||
\(240\) | 1.60829 | 0.103815 | ||||||||
\(241\) | −17.0645 | −1.09922 | −0.549611 | − | 0.835421i | \(-0.685224\pi\) | ||||
−0.549611 | + | 0.835421i | \(0.685224\pi\) | |||||||
\(242\) | −3.92829 | −0.252520 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 9.61607 | 0.615606 | ||||||||
\(245\) | −10.1105 | −0.645937 | ||||||||
\(246\) | −0.344688 | −0.0219765 | ||||||||
\(247\) | −10.4334 | −0.663862 | ||||||||
\(248\) | 27.4033 | 1.74011 | ||||||||
\(249\) | 4.30590 | 0.272875 | ||||||||
\(250\) | −0.00973083 | −0.000615432 0 | ||||||||
\(251\) | 12.1258 | 0.765375 | 0.382687 | − | 0.923878i | \(-0.374999\pi\) | ||||
0.382687 | + | 0.923878i | \(0.374999\pi\) | |||||||
\(252\) | −3.57429 | −0.225159 | ||||||||
\(253\) | 10.2776 | 0.646150 | ||||||||
\(254\) | 14.3380 | 0.899644 | ||||||||
\(255\) | 3.16176 | 0.197997 | ||||||||
\(256\) | −16.8799 | −1.05500 | ||||||||
\(257\) | −4.73637 | −0.295446 | −0.147723 | − | 0.989029i | \(-0.547194\pi\) | ||||
−0.147723 | + | 0.989029i | \(0.547194\pi\) | |||||||
\(258\) | −4.87927 | −0.303770 | ||||||||
\(259\) | 21.2288 | 1.31910 | ||||||||
\(260\) | 14.1428 | 0.877098 | ||||||||
\(261\) | −8.17474 | −0.506004 | ||||||||
\(262\) | −12.2157 | −0.754687 | ||||||||
\(263\) | 0.820477 | 0.0505928 | 0.0252964 | − | 0.999680i | \(-0.491947\pi\) | ||||
0.0252964 | + | 0.999680i | \(0.491947\pi\) | |||||||
\(264\) | −11.4076 | −0.702088 | ||||||||
\(265\) | −33.4722 | −2.05618 | ||||||||
\(266\) | 7.82401 | 0.479721 | ||||||||
\(267\) | −0.653746 | −0.0400086 | ||||||||
\(268\) | 14.9834 | 0.915258 | ||||||||
\(269\) | −21.8863 | −1.33443 | −0.667214 | − | 0.744866i | \(-0.732514\pi\) | ||||
−0.667214 | + | 0.744866i | \(0.732514\pi\) | |||||||
\(270\) | 2.96721 | 0.180579 | ||||||||
\(271\) | −30.4449 | −1.84940 | −0.924698 | − | 0.380703i | \(-0.875682\pi\) | ||||
−0.924698 | + | 0.380703i | \(0.875682\pi\) | |||||||
\(272\) | 0.508669 | 0.0308426 | ||||||||
\(273\) | 12.7621 | 0.772396 | ||||||||
\(274\) | 7.96346 | 0.481090 | ||||||||
\(275\) | −19.4717 | −1.17419 | ||||||||
\(276\) | 2.95197 | 0.177687 | ||||||||
\(277\) | −14.7706 | −0.887481 | −0.443741 | − | 0.896155i | \(-0.646349\pi\) | ||||
−0.443741 | + | 0.896155i | \(0.646349\pi\) | |||||||
\(278\) | 15.1135 | 0.906448 | ||||||||
\(279\) | 9.36114 | 0.560437 | ||||||||
\(280\) | −29.5566 | −1.76635 | ||||||||
\(281\) | 4.52998 | 0.270236 | 0.135118 | − | 0.990830i | \(-0.456859\pi\) | ||||
0.135118 | + | 0.990830i | \(0.456859\pi\) | |||||||
\(282\) | 8.43935 | 0.502556 | ||||||||
\(283\) | 23.1198 | 1.37433 | 0.687164 | − | 0.726503i | \(-0.258856\pi\) | ||||
0.687164 | + | 0.726503i | \(0.258856\pi\) | |||||||
\(284\) | 12.4511 | 0.738838 | ||||||||
\(285\) | 8.25441 | 0.488949 | ||||||||
\(286\) | 14.6153 | 0.864222 | ||||||||
\(287\) | 1.17289 | 0.0692338 | ||||||||
\(288\) | −5.37732 | −0.316861 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −24.2562 | −1.42437 | ||||||||
\(291\) | 17.7265 | 1.03914 | ||||||||
\(292\) | 9.15535 | 0.535776 | ||||||||
\(293\) | 10.0891 | 0.589413 | 0.294706 | − | 0.955588i | \(-0.404778\pi\) | ||||
0.294706 | + | 0.955588i | \(0.404778\pi\) | |||||||
\(294\) | −3.00099 | −0.175021 | ||||||||
\(295\) | −18.3203 | −1.06665 | ||||||||
\(296\) | 19.4602 | 1.13110 | ||||||||
\(297\) | −3.89690 | −0.226121 | ||||||||
\(298\) | 7.29566 | 0.422626 | ||||||||
\(299\) | −10.5401 | −0.609547 | ||||||||
\(300\) | −5.59271 | −0.322895 | ||||||||
\(301\) | 16.6030 | 0.956982 | ||||||||
\(302\) | 5.74607 | 0.330649 | ||||||||
\(303\) | 4.42409 | 0.254157 | ||||||||
\(304\) | 1.32798 | 0.0761650 | ||||||||
\(305\) | 27.1637 | 1.55539 | ||||||||
\(306\) | 0.938469 | 0.0536487 | ||||||||
\(307\) | −1.13614 | −0.0648432 | −0.0324216 | − | 0.999474i | \(-0.510322\pi\) | ||||
−0.0324216 | + | 0.999474i | \(0.510322\pi\) | |||||||
\(308\) | 13.9286 | 0.793658 | ||||||||
\(309\) | −4.43823 | −0.252482 | ||||||||
\(310\) | 27.7765 | 1.57760 | ||||||||
\(311\) | −16.6346 | −0.943262 | −0.471631 | − | 0.881796i | \(-0.656335\pi\) | ||||
−0.471631 | + | 0.881796i | \(0.656335\pi\) | |||||||
\(312\) | 11.6988 | 0.662316 | ||||||||
\(313\) | −21.6848 | −1.22570 | −0.612849 | − | 0.790200i | \(-0.709977\pi\) | ||||
−0.612849 | + | 0.790200i | \(0.709977\pi\) | |||||||
\(314\) | −0.938469 | −0.0529609 | ||||||||
\(315\) | −10.0967 | −0.568887 | ||||||||
\(316\) | −7.73431 | −0.435089 | ||||||||
\(317\) | 23.3728 | 1.31275 | 0.656373 | − | 0.754436i | \(-0.272090\pi\) | ||||
0.656373 | + | 0.754436i | \(0.272090\pi\) | |||||||
\(318\) | −9.93518 | −0.557137 | ||||||||
\(319\) | 31.8562 | 1.78360 | ||||||||
\(320\) | −19.1722 | −1.07176 | ||||||||
\(321\) | −7.01299 | −0.391427 | ||||||||
\(322\) | 7.90399 | 0.440472 | ||||||||
\(323\) | 2.61070 | 0.145263 | ||||||||
\(324\) | −1.11928 | −0.0621820 | ||||||||
\(325\) | 19.9689 | 1.10767 | ||||||||
\(326\) | −17.1985 | −0.952535 | ||||||||
\(327\) | −2.69617 | −0.149098 | ||||||||
\(328\) | 1.07518 | 0.0593668 | ||||||||
\(329\) | −28.7172 | −1.58323 | ||||||||
\(330\) | −11.5629 | −0.636519 | ||||||||
\(331\) | −31.4738 | −1.72996 | −0.864978 | − | 0.501809i | \(-0.832668\pi\) | ||||
−0.864978 | + | 0.501809i | \(0.832668\pi\) | |||||||
\(332\) | −4.81949 | −0.264504 | ||||||||
\(333\) | 6.64774 | 0.364294 | ||||||||
\(334\) | −6.58946 | −0.360559 | ||||||||
\(335\) | 42.3255 | 2.31249 | ||||||||
\(336\) | −1.62438 | −0.0886171 | ||||||||
\(337\) | 28.1301 | 1.53234 | 0.766172 | − | 0.642636i | \(-0.222159\pi\) | ||||
0.766172 | + | 0.642636i | \(0.222159\pi\) | |||||||
\(338\) | −2.78839 | −0.151668 | ||||||||
\(339\) | 3.47775 | 0.188885 | ||||||||
\(340\) | −3.53888 | −0.191923 | ||||||||
\(341\) | −36.4795 | −1.97547 | ||||||||
\(342\) | 2.45006 | 0.132484 | ||||||||
\(343\) | −12.1421 | −0.655610 | ||||||||
\(344\) | 15.2198 | 0.820596 | ||||||||
\(345\) | 8.33879 | 0.448945 | ||||||||
\(346\) | −6.81798 | −0.366537 | ||||||||
\(347\) | 3.22192 | 0.172962 | 0.0864810 | − | 0.996254i | \(-0.472438\pi\) | ||||
0.0864810 | + | 0.996254i | \(0.472438\pi\) | |||||||
\(348\) | 9.14979 | 0.490480 | ||||||||
\(349\) | −14.1179 | −0.755714 | −0.377857 | − | 0.925864i | \(-0.623339\pi\) | ||||
−0.377857 | + | 0.925864i | \(0.623339\pi\) | |||||||
\(350\) | −14.9747 | −0.800430 | ||||||||
\(351\) | 3.99640 | 0.213312 | ||||||||
\(352\) | 20.9549 | 1.11690 | ||||||||
\(353\) | −2.75038 | −0.146388 | −0.0731941 | − | 0.997318i | \(-0.523319\pi\) | ||||
−0.0731941 | + | 0.997318i | \(0.523319\pi\) | |||||||
\(354\) | −5.43780 | −0.289016 | ||||||||
\(355\) | 35.1722 | 1.86675 | ||||||||
\(356\) | 0.731723 | 0.0387812 | ||||||||
\(357\) | −3.19339 | −0.169012 | ||||||||
\(358\) | −21.6966 | −1.14670 | ||||||||
\(359\) | −20.4598 | −1.07983 | −0.539913 | − | 0.841721i | \(-0.681543\pi\) | ||||
−0.539913 | + | 0.841721i | \(0.681543\pi\) | |||||||
\(360\) | −9.25556 | −0.487811 | ||||||||
\(361\) | −12.1842 | −0.641276 | ||||||||
\(362\) | 8.94523 | 0.470151 | ||||||||
\(363\) | 4.18585 | 0.219700 | ||||||||
\(364\) | −14.2843 | −0.748700 | ||||||||
\(365\) | 25.8623 | 1.35369 | ||||||||
\(366\) | 8.06270 | 0.421444 | ||||||||
\(367\) | −5.34969 | −0.279252 | −0.139626 | − | 0.990204i | \(-0.544590\pi\) | ||||
−0.139626 | + | 0.990204i | \(0.544590\pi\) | |||||||
\(368\) | 1.34156 | 0.0699335 | ||||||||
\(369\) | 0.367288 | 0.0191202 | ||||||||
\(370\) | 19.7253 | 1.02547 | ||||||||
\(371\) | 33.8071 | 1.75518 | ||||||||
\(372\) | −10.4777 | −0.543244 | ||||||||
\(373\) | 11.3104 | 0.585632 | 0.292816 | − | 0.956169i | \(-0.405408\pi\) | ||||
0.292816 | + | 0.956169i | \(0.405408\pi\) | |||||||
\(374\) | −3.65712 | −0.189105 | ||||||||
\(375\) | 0.0103688 | 0.000535444 0 | ||||||||
\(376\) | −26.3247 | −1.35759 | ||||||||
\(377\) | −32.6695 | −1.68257 | ||||||||
\(378\) | −2.99690 | −0.154144 | ||||||||
\(379\) | 21.2526 | 1.09167 | 0.545836 | − | 0.837892i | \(-0.316212\pi\) | ||||
0.545836 | + | 0.837892i | \(0.316212\pi\) | |||||||
\(380\) | −9.23896 | −0.473949 | ||||||||
\(381\) | −15.2780 | −0.782718 | ||||||||
\(382\) | −20.4561 | −1.04663 | ||||||||
\(383\) | −7.00071 | −0.357720 | −0.178860 | − | 0.983875i | \(-0.557241\pi\) | ||||
−0.178860 | + | 0.983875i | \(0.557241\pi\) | |||||||
\(384\) | 5.06396 | 0.258419 | ||||||||
\(385\) | 39.3460 | 2.00526 | ||||||||
\(386\) | −3.43905 | −0.175043 | ||||||||
\(387\) | 5.19918 | 0.264289 | ||||||||
\(388\) | −19.8408 | −1.00727 | ||||||||
\(389\) | −32.5726 | −1.65150 | −0.825748 | − | 0.564039i | \(-0.809247\pi\) | ||||
−0.825748 | + | 0.564039i | \(0.809247\pi\) | |||||||
\(390\) | 11.8582 | 0.600462 | ||||||||
\(391\) | 2.63739 | 0.133378 | ||||||||
\(392\) | 9.36091 | 0.472797 | ||||||||
\(393\) | 13.0166 | 0.656601 | ||||||||
\(394\) | −10.6584 | −0.536962 | ||||||||
\(395\) | −21.8481 | −1.09930 | ||||||||
\(396\) | 4.36171 | 0.219184 | ||||||||
\(397\) | −32.0993 | −1.61102 | −0.805508 | − | 0.592585i | \(-0.798108\pi\) | ||||
−0.805508 | + | 0.592585i | \(0.798108\pi\) | |||||||
\(398\) | 6.36130 | 0.318863 | ||||||||
\(399\) | −8.33699 | −0.417372 | ||||||||
\(400\) | −2.54168 | −0.127084 | ||||||||
\(401\) | −33.7957 | −1.68768 | −0.843839 | − | 0.536596i | \(-0.819710\pi\) | ||||
−0.843839 | + | 0.536596i | \(0.819710\pi\) | |||||||
\(402\) | 12.5630 | 0.626586 | ||||||||
\(403\) | 37.4109 | 1.86357 | ||||||||
\(404\) | −4.95178 | −0.246360 | ||||||||
\(405\) | −3.16176 | −0.157109 | ||||||||
\(406\) | 24.4989 | 1.21586 | ||||||||
\(407\) | −25.9056 | −1.28409 | ||||||||
\(408\) | −2.92734 | −0.144925 | ||||||||
\(409\) | −21.7914 | −1.07751 | −0.538757 | − | 0.842461i | \(-0.681106\pi\) | ||||
−0.538757 | + | 0.842461i | \(0.681106\pi\) | |||||||
\(410\) | 1.08982 | 0.0538224 | ||||||||
\(411\) | −8.48559 | −0.418563 | ||||||||
\(412\) | 4.96760 | 0.244736 | ||||||||
\(413\) | 18.5036 | 0.910501 | ||||||||
\(414\) | 2.47511 | 0.121645 | ||||||||
\(415\) | −13.6142 | −0.668295 | ||||||||
\(416\) | −21.4899 | −1.05363 | ||||||||
\(417\) | −16.1044 | −0.788637 | ||||||||
\(418\) | −9.54765 | −0.466991 | ||||||||
\(419\) | −35.1932 | −1.71930 | −0.859650 | − | 0.510883i | \(-0.829319\pi\) | ||||
−0.859650 | + | 0.510883i | \(0.829319\pi\) | |||||||
\(420\) | 11.3010 | 0.551434 | ||||||||
\(421\) | −26.1770 | −1.27579 | −0.637895 | − | 0.770124i | \(-0.720194\pi\) | ||||
−0.637895 | + | 0.770124i | \(0.720194\pi\) | |||||||
\(422\) | 0.301337 | 0.0146689 | ||||||||
\(423\) | −8.99268 | −0.437239 | ||||||||
\(424\) | 30.9906 | 1.50504 | ||||||||
\(425\) | −4.99672 | −0.242377 | ||||||||
\(426\) | 10.4398 | 0.505808 | ||||||||
\(427\) | −27.4355 | −1.32770 | ||||||||
\(428\) | 7.84947 | 0.379418 | ||||||||
\(429\) | −15.5736 | −0.751900 | ||||||||
\(430\) | 15.4271 | 0.743960 | ||||||||
\(431\) | 7.91517 | 0.381260 | 0.190630 | − | 0.981662i | \(-0.438947\pi\) | ||||
0.190630 | + | 0.981662i | \(0.438947\pi\) | |||||||
\(432\) | −0.508669 | −0.0244733 | ||||||||
\(433\) | −19.3800 | −0.931345 | −0.465673 | − | 0.884957i | \(-0.654188\pi\) | ||||
−0.465673 | + | 0.884957i | \(0.654188\pi\) | |||||||
\(434\) | −28.0544 | −1.34665 | ||||||||
\(435\) | 25.8466 | 1.23925 | ||||||||
\(436\) | 3.01775 | 0.144524 | ||||||||
\(437\) | 6.88544 | 0.329375 | ||||||||
\(438\) | 7.67640 | 0.366793 | ||||||||
\(439\) | −16.6192 | −0.793190 | −0.396595 | − | 0.917994i | \(-0.629808\pi\) | ||||
−0.396595 | + | 0.917994i | \(0.629808\pi\) | |||||||
\(440\) | 36.0680 | 1.71947 | ||||||||
\(441\) | 3.19775 | 0.152274 | ||||||||
\(442\) | 3.75050 | 0.178393 | ||||||||
\(443\) | −26.8218 | −1.27434 | −0.637171 | − | 0.770723i | \(-0.719895\pi\) | ||||
−0.637171 | + | 0.770723i | \(0.719895\pi\) | |||||||
\(444\) | −7.44066 | −0.353118 | ||||||||
\(445\) | 2.06699 | 0.0979846 | ||||||||
\(446\) | −4.75707 | −0.225254 | ||||||||
\(447\) | −7.77400 | −0.367698 | ||||||||
\(448\) | 19.3640 | 0.914865 | ||||||||
\(449\) | −28.1842 | −1.33010 | −0.665048 | − | 0.746800i | \(-0.731589\pi\) | ||||
−0.665048 | + | 0.746800i | \(0.731589\pi\) | |||||||
\(450\) | −4.68927 | −0.221054 | ||||||||
\(451\) | −1.43129 | −0.0673966 | ||||||||
\(452\) | −3.89256 | −0.183091 | ||||||||
\(453\) | −6.12281 | −0.287675 | ||||||||
\(454\) | 11.6094 | 0.544854 | ||||||||
\(455\) | −40.3506 | −1.89166 | ||||||||
\(456\) | −7.64242 | −0.357889 | ||||||||
\(457\) | −31.2171 | −1.46027 | −0.730136 | − | 0.683302i | \(-0.760543\pi\) | ||||
−0.730136 | + | 0.683302i | \(0.760543\pi\) | |||||||
\(458\) | −4.28680 | −0.200309 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −9.33341 | −0.435172 | ||||||||
\(461\) | −11.1046 | −0.517194 | −0.258597 | − | 0.965985i | \(-0.583260\pi\) | ||||
−0.258597 | + | 0.965985i | \(0.583260\pi\) | |||||||
\(462\) | 11.6786 | 0.543339 | ||||||||
\(463\) | −31.2253 | −1.45116 | −0.725581 | − | 0.688137i | \(-0.758429\pi\) | ||||
−0.725581 | + | 0.688137i | \(0.758429\pi\) | |||||||
\(464\) | 4.15823 | 0.193041 | ||||||||
\(465\) | −29.5977 | −1.37256 | ||||||||
\(466\) | 24.6001 | 1.13958 | ||||||||
\(467\) | −5.84983 | −0.270698 | −0.135349 | − | 0.990798i | \(-0.543216\pi\) | ||||
−0.135349 | + | 0.990798i | \(0.543216\pi\) | |||||||
\(468\) | −4.47307 | −0.206768 | ||||||||
\(469\) | −42.7490 | −1.97396 | ||||||||
\(470\) | −26.6832 | −1.23080 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | 16.9620 | 0.780740 | ||||||||
\(473\) | −20.2607 | −0.931588 | ||||||||
\(474\) | −6.48492 | −0.297862 | ||||||||
\(475\) | −13.0449 | −0.598543 | ||||||||
\(476\) | 3.57429 | 0.163827 | ||||||||
\(477\) | 10.5866 | 0.484726 | ||||||||
\(478\) | −13.6272 | −0.623292 | ||||||||
\(479\) | −11.6305 | −0.531412 | −0.265706 | − | 0.964054i | \(-0.585605\pi\) | ||||
−0.265706 | + | 0.964054i | \(0.585605\pi\) | |||||||
\(480\) | 17.0018 | 0.776022 | ||||||||
\(481\) | 26.5670 | 1.21135 | ||||||||
\(482\) | 16.0145 | 0.729441 | ||||||||
\(483\) | −8.42222 | −0.383224 | ||||||||
\(484\) | −4.68512 | −0.212960 | ||||||||
\(485\) | −56.0469 | −2.54496 | ||||||||
\(486\) | −0.938469 | −0.0425698 | ||||||||
\(487\) | −13.6357 | −0.617894 | −0.308947 | − | 0.951079i | \(-0.599976\pi\) | ||||
−0.308947 | + | 0.951079i | \(0.599976\pi\) | |||||||
\(488\) | −25.1498 | −1.13848 | ||||||||
\(489\) | 18.3261 | 0.828735 | ||||||||
\(490\) | 9.48840 | 0.428642 | ||||||||
\(491\) | 17.2416 | 0.778101 | 0.389050 | − | 0.921216i | \(-0.372803\pi\) | ||||
0.389050 | + | 0.921216i | \(0.372803\pi\) | |||||||
\(492\) | −0.411097 | −0.0185337 | ||||||||
\(493\) | 8.17474 | 0.368172 | ||||||||
\(494\) | 9.79143 | 0.440537 | ||||||||
\(495\) | 12.3211 | 0.553791 | ||||||||
\(496\) | −4.76172 | −0.213808 | ||||||||
\(497\) | −35.5241 | −1.59347 | ||||||||
\(498\) | −4.04095 | −0.181079 | ||||||||
\(499\) | 9.47865 | 0.424323 | 0.212161 | − | 0.977235i | \(-0.431950\pi\) | ||||
0.212161 | + | 0.977235i | \(0.431950\pi\) | |||||||
\(500\) | −0.0116056 | −0.000519018 0 | ||||||||
\(501\) | 7.02150 | 0.313697 | ||||||||
\(502\) | −11.3797 | −0.507901 | ||||||||
\(503\) | 20.6318 | 0.919928 | 0.459964 | − | 0.887938i | \(-0.347862\pi\) | ||||
0.459964 | + | 0.887938i | \(0.347862\pi\) | |||||||
\(504\) | 9.34815 | 0.416400 | ||||||||
\(505\) | −13.9879 | −0.622454 | ||||||||
\(506\) | −9.64525 | −0.428784 | ||||||||
\(507\) | 2.97121 | 0.131956 | ||||||||
\(508\) | 17.1003 | 0.758705 | ||||||||
\(509\) | −19.1511 | −0.848858 | −0.424429 | − | 0.905461i | \(-0.639525\pi\) | ||||
−0.424429 | + | 0.905461i | \(0.639525\pi\) | |||||||
\(510\) | −2.96721 | −0.131390 | ||||||||
\(511\) | −26.1210 | −1.15553 | ||||||||
\(512\) | 5.71337 | 0.252498 | ||||||||
\(513\) | −2.61070 | −0.115265 | ||||||||
\(514\) | 4.44493 | 0.196058 | ||||||||
\(515\) | 14.0326 | 0.618351 | ||||||||
\(516\) | −5.81932 | −0.256181 | ||||||||
\(517\) | 35.0436 | 1.54122 | ||||||||
\(518\) | −19.9226 | −0.875349 | ||||||||
\(519\) | 7.26500 | 0.318898 | ||||||||
\(520\) | −36.9889 | −1.62207 | ||||||||
\(521\) | 1.14721 | 0.0502601 | 0.0251301 | − | 0.999684i | \(-0.492000\pi\) | ||||
0.0251301 | + | 0.999684i | \(0.492000\pi\) | |||||||
\(522\) | 7.67174 | 0.335783 | ||||||||
\(523\) | −3.21216 | −0.140458 | −0.0702289 | − | 0.997531i | \(-0.522373\pi\) | ||||
−0.0702289 | + | 0.997531i | \(0.522373\pi\) | |||||||
\(524\) | −14.5692 | −0.636457 | ||||||||
\(525\) | 15.9565 | 0.696398 | ||||||||
\(526\) | −0.769992 | −0.0335732 | ||||||||
\(527\) | −9.36114 | −0.407778 | ||||||||
\(528\) | 1.98223 | 0.0862656 | ||||||||
\(529\) | −16.0442 | −0.697573 | ||||||||
\(530\) | 31.4126 | 1.36448 | ||||||||
\(531\) | 5.79433 | 0.251453 | ||||||||
\(532\) | 9.33140 | 0.404567 | ||||||||
\(533\) | 1.46783 | 0.0635788 | ||||||||
\(534\) | 0.613521 | 0.0265496 | ||||||||
\(535\) | 22.1734 | 0.958639 | ||||||||
\(536\) | −39.1875 | −1.69264 | ||||||||
\(537\) | 23.1191 | 0.997663 | ||||||||
\(538\) | 20.5396 | 0.885524 | ||||||||
\(539\) | −12.4613 | −0.536747 | ||||||||
\(540\) | 3.53888 | 0.152289 | ||||||||
\(541\) | −22.0075 | −0.946176 | −0.473088 | − | 0.881015i | \(-0.656861\pi\) | ||||
−0.473088 | + | 0.881015i | \(0.656861\pi\) | |||||||
\(542\) | 28.5716 | 1.22725 | ||||||||
\(543\) | −9.53173 | −0.409046 | ||||||||
\(544\) | 5.37732 | 0.230551 | ||||||||
\(545\) | 8.52463 | 0.365155 | ||||||||
\(546\) | −11.9768 | −0.512560 | ||||||||
\(547\) | −13.7768 | −0.589053 | −0.294526 | − | 0.955643i | \(-0.595162\pi\) | ||||
−0.294526 | + | 0.955643i | \(0.595162\pi\) | |||||||
\(548\) | 9.49771 | 0.405722 | ||||||||
\(549\) | −8.59133 | −0.366669 | ||||||||
\(550\) | 18.2736 | 0.779190 | ||||||||
\(551\) | 21.3418 | 0.909191 | ||||||||
\(552\) | −7.72054 | −0.328608 | ||||||||
\(553\) | 22.0667 | 0.938370 | ||||||||
\(554\) | 13.8618 | 0.588930 | ||||||||
\(555\) | −21.0186 | −0.892188 | ||||||||
\(556\) | 18.0253 | 0.764443 | ||||||||
\(557\) | −2.29854 | −0.0973923 | −0.0486961 | − | 0.998814i | \(-0.515507\pi\) | ||||
−0.0486961 | + | 0.998814i | \(0.515507\pi\) | |||||||
\(558\) | −8.78514 | −0.371905 | ||||||||
\(559\) | 20.7780 | 0.878816 | ||||||||
\(560\) | 5.13589 | 0.217031 | ||||||||
\(561\) | 3.89690 | 0.164527 | ||||||||
\(562\) | −4.25125 | −0.179328 | ||||||||
\(563\) | −5.41074 | −0.228035 | −0.114018 | − | 0.993479i | \(-0.536372\pi\) | ||||
−0.114018 | + | 0.993479i | \(0.536372\pi\) | |||||||
\(564\) | 10.0653 | 0.423825 | ||||||||
\(565\) | −10.9958 | −0.462597 | ||||||||
\(566\) | −21.6972 | −0.912000 | ||||||||
\(567\) | 3.19339 | 0.134110 | ||||||||
\(568\) | −32.5645 | −1.36638 | ||||||||
\(569\) | 41.5767 | 1.74299 | 0.871493 | − | 0.490408i | \(-0.163152\pi\) | ||||
0.871493 | + | 0.490408i | \(0.163152\pi\) | |||||||
\(570\) | −7.74651 | −0.324465 | ||||||||
\(571\) | −26.5040 | −1.10916 | −0.554579 | − | 0.832131i | \(-0.687121\pi\) | ||||
−0.554579 | + | 0.832131i | \(0.687121\pi\) | |||||||
\(572\) | 17.4311 | 0.728832 | ||||||||
\(573\) | 21.7974 | 0.910598 | ||||||||
\(574\) | −1.10072 | −0.0459434 | ||||||||
\(575\) | −13.1783 | −0.549573 | ||||||||
\(576\) | 6.06378 | 0.252658 | ||||||||
\(577\) | 40.9331 | 1.70407 | 0.852033 | − | 0.523488i | \(-0.175370\pi\) | ||||
0.852033 | + | 0.523488i | \(0.175370\pi\) | |||||||
\(578\) | −0.938469 | −0.0390352 | ||||||||
\(579\) | 3.66453 | 0.152293 | ||||||||
\(580\) | −28.9294 | −1.20123 | ||||||||
\(581\) | 13.7504 | 0.570464 | ||||||||
\(582\) | −16.6358 | −0.689574 | ||||||||
\(583\) | −41.2549 | −1.70860 | ||||||||
\(584\) | −23.9448 | −0.990843 | ||||||||
\(585\) | −12.6357 | −0.522420 | ||||||||
\(586\) | −9.46832 | −0.391133 | ||||||||
\(587\) | −2.78441 | −0.114925 | −0.0574625 | − | 0.998348i | \(-0.518301\pi\) | ||||
−0.0574625 | + | 0.998348i | \(0.518301\pi\) | |||||||
\(588\) | −3.57916 | −0.147602 | ||||||||
\(589\) | −24.4392 | −1.00700 | ||||||||
\(590\) | 17.1930 | 0.707825 | ||||||||
\(591\) | 11.3572 | 0.467173 | ||||||||
\(592\) | −3.38150 | −0.138979 | ||||||||
\(593\) | 13.5205 | 0.555222 | 0.277611 | − | 0.960694i | \(-0.410457\pi\) | ||||
0.277611 | + | 0.960694i | \(0.410457\pi\) | |||||||
\(594\) | 3.65712 | 0.150054 | ||||||||
\(595\) | 10.0967 | 0.413926 | ||||||||
\(596\) | 8.70125 | 0.356417 | ||||||||
\(597\) | −6.77838 | −0.277421 | ||||||||
\(598\) | 9.89152 | 0.404494 | ||||||||
\(599\) | 13.9623 | 0.570483 | 0.285241 | − | 0.958456i | \(-0.407926\pi\) | ||||
0.285241 | + | 0.958456i | \(0.407926\pi\) | |||||||
\(600\) | 14.6271 | 0.597150 | ||||||||
\(601\) | −35.0318 | −1.42898 | −0.714488 | − | 0.699647i | \(-0.753341\pi\) | ||||
−0.714488 | + | 0.699647i | \(0.753341\pi\) | |||||||
\(602\) | −15.5814 | −0.635051 | ||||||||
\(603\) | −13.3867 | −0.545149 | ||||||||
\(604\) | 6.85311 | 0.278849 | ||||||||
\(605\) | −13.2346 | −0.538065 | ||||||||
\(606\) | −4.15187 | −0.168658 | ||||||||
\(607\) | −7.49108 | −0.304054 | −0.152027 | − | 0.988376i | \(-0.548580\pi\) | ||||
−0.152027 | + | 0.988376i | \(0.548580\pi\) | |||||||
\(608\) | 14.0386 | 0.569339 | ||||||||
\(609\) | −26.1051 | −1.05783 | ||||||||
\(610\) | −25.4923 | −1.03215 | ||||||||
\(611\) | −35.9384 | −1.45391 | ||||||||
\(612\) | 1.11928 | 0.0452441 | ||||||||
\(613\) | 45.0264 | 1.81860 | 0.909301 | − | 0.416140i | \(-0.136617\pi\) | ||||
0.909301 | + | 0.416140i | \(0.136617\pi\) | |||||||
\(614\) | 1.06624 | 0.0430298 | ||||||||
\(615\) | −1.16128 | −0.0468272 | ||||||||
\(616\) | −36.4288 | −1.46776 | ||||||||
\(617\) | −27.3417 | −1.10074 | −0.550368 | − | 0.834922i | \(-0.685513\pi\) | ||||
−0.550368 | + | 0.834922i | \(0.685513\pi\) | |||||||
\(618\) | 4.16514 | 0.167546 | ||||||||
\(619\) | −0.00114521 | −4.60299e−5 0 | −2.30149e−5 | − | 1.00000i | \(-0.500007\pi\) | ||||
−2.30149e−5 | 1.00000i | \(0.500007\pi\) | ||||||||
\(620\) | 33.1280 | 1.33045 | ||||||||
\(621\) | −2.63739 | −0.105835 | ||||||||
\(622\) | 15.6111 | 0.625946 | ||||||||
\(623\) | −2.08767 | −0.0836406 | ||||||||
\(624\) | −2.03284 | −0.0813789 | ||||||||
\(625\) | −25.0164 | −1.00066 | ||||||||
\(626\) | 20.3505 | 0.813371 | ||||||||
\(627\) | 10.1736 | 0.406296 | ||||||||
\(628\) | −1.11928 | −0.0446640 | ||||||||
\(629\) | −6.64774 | −0.265063 | ||||||||
\(630\) | 9.47547 | 0.377512 | ||||||||
\(631\) | −19.2656 | −0.766949 | −0.383475 | − | 0.923551i | \(-0.625273\pi\) | ||||
−0.383475 | + | 0.923551i | \(0.625273\pi\) | |||||||
\(632\) | 20.2282 | 0.804636 | ||||||||
\(633\) | −0.321094 | −0.0127623 | ||||||||
\(634\) | −21.9346 | −0.871136 | ||||||||
\(635\) | 48.3055 | 1.91694 | ||||||||
\(636\) | −11.8493 | −0.469856 | ||||||||
\(637\) | 12.7795 | 0.506342 | ||||||||
\(638\) | −29.8960 | −1.18359 | ||||||||
\(639\) | −11.1243 | −0.440069 | ||||||||
\(640\) | −16.0110 | −0.632892 | ||||||||
\(641\) | 30.9125 | 1.22097 | 0.610486 | − | 0.792027i | \(-0.290974\pi\) | ||||
0.610486 | + | 0.792027i | \(0.290974\pi\) | |||||||
\(642\) | 6.58147 | 0.259750 | ||||||||
\(643\) | −8.79402 | −0.346802 | −0.173401 | − | 0.984851i | \(-0.555476\pi\) | ||||
−0.173401 | + | 0.984851i | \(0.555476\pi\) | |||||||
\(644\) | 9.42678 | 0.371467 | ||||||||
\(645\) | −16.4386 | −0.647268 | ||||||||
\(646\) | −2.45006 | −0.0963964 | ||||||||
\(647\) | 7.62021 | 0.299581 | 0.149791 | − | 0.988718i | \(-0.452140\pi\) | ||||
0.149791 | + | 0.988718i | \(0.452140\pi\) | |||||||
\(648\) | 2.92734 | 0.114997 | ||||||||
\(649\) | −22.5800 | −0.886341 | ||||||||
\(650\) | −18.7402 | −0.735051 | ||||||||
\(651\) | 29.8938 | 1.17163 | ||||||||
\(652\) | −20.5120 | −0.803311 | ||||||||
\(653\) | −25.8874 | −1.01305 | −0.506526 | − | 0.862225i | \(-0.669070\pi\) | ||||
−0.506526 | + | 0.862225i | \(0.669070\pi\) | |||||||
\(654\) | 2.53027 | 0.0989413 | ||||||||
\(655\) | −41.1554 | −1.60807 | ||||||||
\(656\) | −0.186828 | −0.00729441 | ||||||||
\(657\) | −8.17971 | −0.319121 | ||||||||
\(658\) | 26.9502 | 1.05063 | ||||||||
\(659\) | −31.3890 | −1.22274 | −0.611371 | − | 0.791344i | \(-0.709382\pi\) | ||||
−0.611371 | + | 0.791344i | \(0.709382\pi\) | |||||||
\(660\) | −13.7907 | −0.536801 | ||||||||
\(661\) | 23.3594 | 0.908576 | 0.454288 | − | 0.890855i | \(-0.349894\pi\) | ||||
0.454288 | + | 0.890855i | \(0.349894\pi\) | |||||||
\(662\) | 29.5372 | 1.14800 | ||||||||
\(663\) | −3.99640 | −0.155207 | ||||||||
\(664\) | 12.6048 | 0.489163 | ||||||||
\(665\) | 26.3596 | 1.02218 | ||||||||
\(666\) | −6.23870 | −0.241745 | ||||||||
\(667\) | 21.5600 | 0.834805 | ||||||||
\(668\) | −7.85899 | −0.304074 | ||||||||
\(669\) | 5.06897 | 0.195978 | ||||||||
\(670\) | −39.7212 | −1.53456 | ||||||||
\(671\) | 33.4796 | 1.29246 | ||||||||
\(672\) | −17.1719 | −0.662420 | ||||||||
\(673\) | −34.9821 | −1.34846 | −0.674231 | − | 0.738520i | \(-0.735525\pi\) | ||||
−0.674231 | + | 0.738520i | \(0.735525\pi\) | |||||||
\(674\) | −26.3992 | −1.01686 | ||||||||
\(675\) | 4.99672 | 0.192324 | ||||||||
\(676\) | −3.32561 | −0.127908 | ||||||||
\(677\) | −6.96778 | −0.267794 | −0.133897 | − | 0.990995i | \(-0.542749\pi\) | ||||
−0.133897 | + | 0.990995i | \(0.542749\pi\) | |||||||
\(678\) | −3.26376 | −0.125344 | ||||||||
\(679\) | 56.6076 | 2.17240 | ||||||||
\(680\) | 9.25556 | 0.354934 | ||||||||
\(681\) | −12.3705 | −0.474040 | ||||||||
\(682\) | 34.2348 | 1.31092 | ||||||||
\(683\) | 24.1975 | 0.925890 | 0.462945 | − | 0.886387i | \(-0.346793\pi\) | ||||
0.462945 | + | 0.886387i | \(0.346793\pi\) | |||||||
\(684\) | 2.92210 | 0.111729 | ||||||||
\(685\) | 26.8294 | 1.02510 | ||||||||
\(686\) | 11.3950 | 0.435062 | ||||||||
\(687\) | 4.56787 | 0.174275 | ||||||||
\(688\) | −2.64466 | −0.100827 | ||||||||
\(689\) | 42.3082 | 1.61182 | ||||||||
\(690\) | −7.82569 | −0.297919 | ||||||||
\(691\) | −32.2655 | −1.22744 | −0.613719 | − | 0.789525i | \(-0.710327\pi\) | ||||
−0.613719 | + | 0.789525i | \(0.710327\pi\) | |||||||
\(692\) | −8.13154 | −0.309115 | ||||||||
\(693\) | −12.4443 | −0.472721 | ||||||||
\(694\) | −3.02368 | −0.114777 | ||||||||
\(695\) | 50.9183 | 1.93144 | ||||||||
\(696\) | −23.9303 | −0.907074 | ||||||||
\(697\) | −0.367288 | −0.0139120 | ||||||||
\(698\) | 13.2492 | 0.501490 | ||||||||
\(699\) | −26.2130 | −0.991468 | ||||||||
\(700\) | −17.8597 | −0.675034 | ||||||||
\(701\) | −7.90448 | −0.298548 | −0.149274 | − | 0.988796i | \(-0.547694\pi\) | ||||
−0.149274 | + | 0.988796i | \(0.547694\pi\) | |||||||
\(702\) | −3.75050 | −0.141553 | ||||||||
\(703\) | −17.3553 | −0.654566 | ||||||||
\(704\) | −23.6300 | −0.890588 | ||||||||
\(705\) | 28.4327 | 1.07084 | ||||||||
\(706\) | 2.58115 | 0.0971428 | ||||||||
\(707\) | 14.1279 | 0.531333 | ||||||||
\(708\) | −6.48546 | −0.243738 | ||||||||
\(709\) | −19.3028 | −0.724931 | −0.362466 | − | 0.931997i | \(-0.618065\pi\) | ||||
−0.362466 | + | 0.931997i | \(0.618065\pi\) | |||||||
\(710\) | −33.0080 | −1.23877 | ||||||||
\(711\) | 6.91010 | 0.259149 | ||||||||
\(712\) | −1.91374 | −0.0717204 | ||||||||
\(713\) | −24.6890 | −0.924610 | ||||||||
\(714\) | 2.99690 | 0.112156 | ||||||||
\(715\) | 49.2399 | 1.84147 | ||||||||
\(716\) | −25.8767 | −0.967056 | ||||||||
\(717\) | 14.5206 | 0.542283 | ||||||||
\(718\) | 19.2009 | 0.716570 | ||||||||
\(719\) | −43.6511 | −1.62791 | −0.813957 | − | 0.580926i | \(-0.802691\pi\) | ||||
−0.813957 | + | 0.580926i | \(0.802691\pi\) | |||||||
\(720\) | 1.60829 | 0.0599374 | ||||||||
\(721\) | −14.1730 | −0.527830 | ||||||||
\(722\) | 11.4345 | 0.425549 | ||||||||
\(723\) | −17.0645 | −0.634636 | ||||||||
\(724\) | 10.6686 | 0.396497 | ||||||||
\(725\) | −40.8469 | −1.51702 | ||||||||
\(726\) | −3.92829 | −0.145792 | ||||||||
\(727\) | 10.6095 | 0.393484 | 0.196742 | − | 0.980455i | \(-0.436964\pi\) | ||||
0.196742 | + | 0.980455i | \(0.436964\pi\) | |||||||
\(728\) | 37.3590 | 1.38462 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −24.2709 | −0.898307 | ||||||||
\(731\) | −5.19918 | −0.192299 | ||||||||
\(732\) | 9.61607 | 0.355420 | ||||||||
\(733\) | −14.4560 | −0.533943 | −0.266972 | − | 0.963704i | \(-0.586023\pi\) | ||||
−0.266972 | + | 0.963704i | \(0.586023\pi\) | |||||||
\(734\) | 5.02052 | 0.185311 | ||||||||
\(735\) | −10.1105 | −0.372932 | ||||||||
\(736\) | 14.1821 | 0.522758 | ||||||||
\(737\) | 52.1667 | 1.92158 | ||||||||
\(738\) | −0.344688 | −0.0126882 | ||||||||
\(739\) | 25.0656 | 0.922051 | 0.461026 | − | 0.887387i | \(-0.347482\pi\) | ||||
0.461026 | + | 0.887387i | \(0.347482\pi\) | |||||||
\(740\) | 23.5256 | 0.864817 | ||||||||
\(741\) | −10.4334 | −0.383281 | ||||||||
\(742\) | −31.7269 | −1.16473 | ||||||||
\(743\) | 39.2069 | 1.43836 | 0.719180 | − | 0.694824i | \(-0.244518\pi\) | ||||
0.719180 | + | 0.694824i | \(0.244518\pi\) | |||||||
\(744\) | 27.4033 | 1.00465 | ||||||||
\(745\) | 24.5795 | 0.900524 | ||||||||
\(746\) | −10.6145 | −0.388624 | ||||||||
\(747\) | 4.30590 | 0.157545 | ||||||||
\(748\) | −4.36171 | −0.159480 | ||||||||
\(749\) | −22.3952 | −0.818303 | ||||||||
\(750\) | −0.00973083 | −0.000355320 0 | ||||||||
\(751\) | 3.99017 | 0.145603 | 0.0728016 | − | 0.997346i | \(-0.476806\pi\) | ||||
0.0728016 | + | 0.997346i | \(0.476806\pi\) | |||||||
\(752\) | 4.57430 | 0.166807 | ||||||||
\(753\) | 12.1258 | 0.441889 | ||||||||
\(754\) | 30.6593 | 1.11655 | ||||||||
\(755\) | 19.3589 | 0.704541 | ||||||||
\(756\) | −3.57429 | −0.129996 | ||||||||
\(757\) | 11.8841 | 0.431936 | 0.215968 | − | 0.976400i | \(-0.430709\pi\) | ||||
0.215968 | + | 0.976400i | \(0.430709\pi\) | |||||||
\(758\) | −19.9449 | −0.724431 | ||||||||
\(759\) | 10.2776 | 0.373055 | ||||||||
\(760\) | 24.1635 | 0.876502 | ||||||||
\(761\) | 14.8864 | 0.539633 | 0.269816 | − | 0.962912i | \(-0.413037\pi\) | ||||
0.269816 | + | 0.962912i | \(0.413037\pi\) | |||||||
\(762\) | 14.3380 | 0.519410 | ||||||||
\(763\) | −8.60991 | −0.311700 | ||||||||
\(764\) | −24.3973 | −0.882662 | ||||||||
\(765\) | 3.16176 | 0.114314 | ||||||||
\(766\) | 6.56995 | 0.237382 | ||||||||
\(767\) | 23.1565 | 0.836132 | ||||||||
\(768\) | −16.8799 | −0.609102 | ||||||||
\(769\) | 49.8262 | 1.79678 | 0.898389 | − | 0.439201i | \(-0.144738\pi\) | ||||
0.898389 | + | 0.439201i | \(0.144738\pi\) | |||||||
\(770\) | −36.9250 | −1.33068 | ||||||||
\(771\) | −4.73637 | −0.170576 | ||||||||
\(772\) | −4.10162 | −0.147621 | ||||||||
\(773\) | 21.2647 | 0.764838 | 0.382419 | − | 0.923989i | \(-0.375091\pi\) | ||||
0.382419 | + | 0.923989i | \(0.375091\pi\) | |||||||
\(774\) | −4.87927 | −0.175382 | ||||||||
\(775\) | 46.7750 | 1.68021 | ||||||||
\(776\) | 51.8915 | 1.86280 | ||||||||
\(777\) | 21.2288 | 0.761580 | ||||||||
\(778\) | 30.5684 | 1.09593 | ||||||||
\(779\) | −0.958879 | −0.0343554 | ||||||||
\(780\) | 14.1428 | 0.506393 | ||||||||
\(781\) | 43.3501 | 1.55119 | ||||||||
\(782\) | −2.47511 | −0.0885097 | ||||||||
\(783\) | −8.17474 | −0.292141 | ||||||||
\(784\) | −1.62660 | −0.0580927 | ||||||||
\(785\) | −3.16176 | −0.112848 | ||||||||
\(786\) | −12.2157 | −0.435719 | ||||||||
\(787\) | 16.9550 | 0.604380 | 0.302190 | − | 0.953248i | \(-0.402282\pi\) | ||||
0.302190 | + | 0.953248i | \(0.402282\pi\) | |||||||
\(788\) | −12.7119 | −0.452841 | ||||||||
\(789\) | 0.820477 | 0.0292097 | ||||||||
\(790\) | 20.5037 | 0.729490 | ||||||||
\(791\) | 11.1058 | 0.394877 | ||||||||
\(792\) | −11.4076 | −0.405350 | ||||||||
\(793\) | −34.3344 | −1.21925 | ||||||||
\(794\) | 30.1242 | 1.06907 | ||||||||
\(795\) | −33.4722 | −1.18714 | ||||||||
\(796\) | 7.58688 | 0.268910 | ||||||||
\(797\) | 47.3156 | 1.67600 | 0.838001 | − | 0.545668i | \(-0.183724\pi\) | ||||
0.838001 | + | 0.545668i | \(0.183724\pi\) | |||||||
\(798\) | 7.82401 | 0.276967 | ||||||||
\(799\) | 8.99268 | 0.318138 | ||||||||
\(800\) | −26.8690 | −0.949961 | ||||||||
\(801\) | −0.653746 | −0.0230990 | ||||||||
\(802\) | 31.7162 | 1.11994 | ||||||||
\(803\) | 31.8755 | 1.12486 | ||||||||
\(804\) | 14.9834 | 0.528424 | ||||||||
\(805\) | 26.6290 | 0.938549 | ||||||||
\(806\) | −35.1089 | −1.23666 | ||||||||
\(807\) | −21.8863 | −0.770433 | ||||||||
\(808\) | 12.9508 | 0.455609 | ||||||||
\(809\) | −3.49688 | −0.122944 | −0.0614718 | − | 0.998109i | \(-0.519579\pi\) | ||||
−0.0614718 | + | 0.998109i | \(0.519579\pi\) | |||||||
\(810\) | 2.96721 | 0.104257 | ||||||||
\(811\) | 36.6303 | 1.28626 | 0.643132 | − | 0.765755i | \(-0.277635\pi\) | ||||
0.643132 | + | 0.765755i | \(0.277635\pi\) | |||||||
\(812\) | 29.2189 | 1.02538 | ||||||||
\(813\) | −30.4449 | −1.06775 | ||||||||
\(814\) | 24.3116 | 0.852121 | ||||||||
\(815\) | −57.9427 | −2.02964 | ||||||||
\(816\) | 0.508669 | 0.0178070 | ||||||||
\(817\) | −13.5735 | −0.474877 | ||||||||
\(818\) | 20.4505 | 0.715036 | ||||||||
\(819\) | 12.7621 | 0.445943 | ||||||||
\(820\) | 1.29979 | 0.0453906 | ||||||||
\(821\) | −31.6148 | −1.10337 | −0.551683 | − | 0.834054i | \(-0.686014\pi\) | ||||
−0.551683 | + | 0.834054i | \(0.686014\pi\) | |||||||
\(822\) | 7.96346 | 0.277758 | ||||||||
\(823\) | −26.5119 | −0.924146 | −0.462073 | − | 0.886842i | \(-0.652894\pi\) | ||||
−0.462073 | + | 0.886842i | \(0.652894\pi\) | |||||||
\(824\) | −12.9922 | −0.452605 | ||||||||
\(825\) | −19.4717 | −0.677919 | ||||||||
\(826\) | −17.3650 | −0.604207 | ||||||||
\(827\) | 39.6677 | 1.37938 | 0.689690 | − | 0.724105i | \(-0.257747\pi\) | ||||
0.689690 | + | 0.724105i | \(0.257747\pi\) | |||||||
\(828\) | 2.95197 | 0.102588 | ||||||||
\(829\) | 36.5725 | 1.27022 | 0.635108 | − | 0.772423i | \(-0.280955\pi\) | ||||
0.635108 | + | 0.772423i | \(0.280955\pi\) | |||||||
\(830\) | 12.7765 | 0.443479 | ||||||||
\(831\) | −14.7706 | −0.512387 | ||||||||
\(832\) | 24.2333 | 0.840139 | ||||||||
\(833\) | −3.19775 | −0.110795 | ||||||||
\(834\) | 15.1135 | 0.523338 | ||||||||
\(835\) | −22.2003 | −0.768272 | ||||||||
\(836\) | −11.3871 | −0.393832 | ||||||||
\(837\) | 9.36114 | 0.323569 | ||||||||
\(838\) | 33.0277 | 1.14092 | ||||||||
\(839\) | −46.3732 | −1.60098 | −0.800490 | − | 0.599346i | \(-0.795427\pi\) | ||||
−0.800490 | + | 0.599346i | \(0.795427\pi\) | |||||||
\(840\) | −29.5566 | −1.01980 | ||||||||
\(841\) | 37.8263 | 1.30436 | ||||||||
\(842\) | 24.5663 | 0.846611 | ||||||||
\(843\) | 4.52998 | 0.156021 | ||||||||
\(844\) | 0.359393 | 0.0123708 | ||||||||
\(845\) | −9.39426 | −0.323172 | ||||||||
\(846\) | 8.43935 | 0.290151 | ||||||||
\(847\) | 13.3671 | 0.459297 | ||||||||
\(848\) | −5.38507 | −0.184924 | ||||||||
\(849\) | 23.1198 | 0.793468 | ||||||||
\(850\) | 4.68927 | 0.160841 | ||||||||
\(851\) | −17.5327 | −0.601012 | ||||||||
\(852\) | 12.4511 | 0.426568 | ||||||||
\(853\) | 42.1101 | 1.44182 | 0.720911 | − | 0.693027i | \(-0.243723\pi\) | ||||
0.720911 | + | 0.693027i | \(0.243723\pi\) | |||||||
\(854\) | 25.7473 | 0.881056 | ||||||||
\(855\) | 8.25441 | 0.282295 | ||||||||
\(856\) | −20.5294 | −0.701681 | ||||||||
\(857\) | 13.0924 | 0.447229 | 0.223615 | − | 0.974678i | \(-0.428214\pi\) | ||||
0.223615 | + | 0.974678i | \(0.428214\pi\) | |||||||
\(858\) | 14.6153 | 0.498959 | ||||||||
\(859\) | −44.8238 | −1.52937 | −0.764684 | − | 0.644406i | \(-0.777105\pi\) | ||||
−0.764684 | + | 0.644406i | \(0.777105\pi\) | |||||||
\(860\) | 18.3993 | 0.627410 | ||||||||
\(861\) | 1.17289 | 0.0399721 | ||||||||
\(862\) | −7.42814 | −0.253004 | ||||||||
\(863\) | 5.07199 | 0.172653 | 0.0863263 | − | 0.996267i | \(-0.472487\pi\) | ||||
0.0863263 | + | 0.996267i | \(0.472487\pi\) | |||||||
\(864\) | −5.37732 | −0.182940 | ||||||||
\(865\) | −22.9702 | −0.781010 | ||||||||
\(866\) | 18.1876 | 0.618039 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −33.4594 | −1.13569 | ||||||||
\(869\) | −26.9280 | −0.913470 | ||||||||
\(870\) | −24.2562 | −0.822362 | ||||||||
\(871\) | −53.4986 | −1.81273 | ||||||||
\(872\) | −7.89261 | −0.267277 | ||||||||
\(873\) | 17.7265 | 0.599951 | ||||||||
\(874\) | −6.46177 | −0.218573 | ||||||||
\(875\) | 0.0331118 | 0.00111938 | ||||||||
\(876\) | 9.15535 | 0.309331 | ||||||||
\(877\) | 39.2280 | 1.32463 | 0.662317 | − | 0.749223i | \(-0.269573\pi\) | ||||
0.662317 | + | 0.749223i | \(0.269573\pi\) | |||||||
\(878\) | 15.5966 | 0.526359 | ||||||||
\(879\) | 10.0891 | 0.340298 | ||||||||
\(880\) | −6.26734 | −0.211272 | ||||||||
\(881\) | 27.9967 | 0.943232 | 0.471616 | − | 0.881804i | \(-0.343671\pi\) | ||||
0.471616 | + | 0.881804i | \(0.343671\pi\) | |||||||
\(882\) | −3.00099 | −0.101049 | ||||||||
\(883\) | 50.0321 | 1.68371 | 0.841857 | − | 0.539701i | \(-0.181463\pi\) | ||||
0.841857 | + | 0.539701i | \(0.181463\pi\) | |||||||
\(884\) | 4.47307 | 0.150446 | ||||||||
\(885\) | −18.3203 | −0.615830 | ||||||||
\(886\) | 25.1714 | 0.845650 | ||||||||
\(887\) | −52.7111 | −1.76986 | −0.884932 | − | 0.465720i | \(-0.845796\pi\) | ||||
−0.884932 | + | 0.465720i | \(0.845796\pi\) | |||||||
\(888\) | 19.4602 | 0.653042 | ||||||||
\(889\) | −48.7888 | −1.63632 | ||||||||
\(890\) | −1.93980 | −0.0650224 | ||||||||
\(891\) | −3.89690 | −0.130551 | ||||||||
\(892\) | −5.67358 | −0.189966 | ||||||||
\(893\) | 23.4772 | 0.785635 | ||||||||
\(894\) | 7.29566 | 0.244003 | ||||||||
\(895\) | −73.0970 | −2.44336 | ||||||||
\(896\) | 16.1712 | 0.540242 | ||||||||
\(897\) | −10.5401 | −0.351922 | ||||||||
\(898\) | 26.4500 | 0.882649 | ||||||||
\(899\) | −76.5249 | −2.55225 | ||||||||
\(900\) | −5.59271 | −0.186424 | ||||||||
\(901\) | −10.5866 | −0.352690 | ||||||||
\(902\) | 1.34322 | 0.0447242 | ||||||||
\(903\) | 16.6030 | 0.552514 | ||||||||
\(904\) | 10.1806 | 0.338600 | ||||||||
\(905\) | 30.1370 | 1.00179 | ||||||||
\(906\) | 5.74607 | 0.190900 | ||||||||
\(907\) | −31.8539 | −1.05769 | −0.528846 | − | 0.848718i | \(-0.677375\pi\) | ||||
−0.528846 | + | 0.848718i | \(0.677375\pi\) | |||||||
\(908\) | 13.8460 | 0.459497 | ||||||||
\(909\) | 4.42409 | 0.146738 | ||||||||
\(910\) | 37.8678 | 1.25530 | ||||||||
\(911\) | −7.88328 | −0.261185 | −0.130592 | − | 0.991436i | \(-0.541688\pi\) | ||||
−0.130592 | + | 0.991436i | \(0.541688\pi\) | |||||||
\(912\) | 1.32798 | 0.0439739 | ||||||||
\(913\) | −16.7797 | −0.555326 | ||||||||
\(914\) | 29.2962 | 0.969034 | ||||||||
\(915\) | 27.1637 | 0.898005 | ||||||||
\(916\) | −5.11271 | −0.168929 | ||||||||
\(917\) | 41.5671 | 1.37267 | ||||||||
\(918\) | 0.938469 | 0.0309741 | ||||||||
\(919\) | 8.67506 | 0.286164 | 0.143082 | − | 0.989711i | \(-0.454299\pi\) | ||||
0.143082 | + | 0.989711i | \(0.454299\pi\) | |||||||
\(920\) | 24.4105 | 0.804790 | ||||||||
\(921\) | −1.13614 | −0.0374372 | ||||||||
\(922\) | 10.4214 | 0.343209 | ||||||||
\(923\) | −44.4570 | −1.46332 | ||||||||
\(924\) | 13.9286 | 0.458219 | ||||||||
\(925\) | 33.2169 | 1.09216 | ||||||||
\(926\) | 29.3040 | 0.962988 | ||||||||
\(927\) | −4.43823 | −0.145771 | ||||||||
\(928\) | 43.9582 | 1.44300 | ||||||||
\(929\) | 0.0643093 | 0.00210992 | 0.00105496 | − | 0.999999i | \(-0.499664\pi\) | ||||
0.00105496 | + | 0.999999i | \(0.499664\pi\) | |||||||
\(930\) | 27.7765 | 0.910828 | ||||||||
\(931\) | −8.34837 | −0.273607 | ||||||||
\(932\) | 29.3396 | 0.961051 | ||||||||
\(933\) | −16.6346 | −0.544592 | ||||||||
\(934\) | 5.48989 | 0.179635 | ||||||||
\(935\) | −12.3211 | −0.402942 | ||||||||
\(936\) | 11.6988 | 0.382388 | ||||||||
\(937\) | 19.3821 | 0.633185 | 0.316593 | − | 0.948562i | \(-0.397461\pi\) | ||||
0.316593 | + | 0.948562i | \(0.397461\pi\) | |||||||
\(938\) | 40.1186 | 1.30992 | ||||||||
\(939\) | −21.6848 | −0.707657 | ||||||||
\(940\) | −31.8240 | −1.03799 | ||||||||
\(941\) | 25.3346 | 0.825885 | 0.412942 | − | 0.910757i | \(-0.364501\pi\) | ||||
0.412942 | + | 0.910757i | \(0.364501\pi\) | |||||||
\(942\) | −0.938469 | −0.0305770 | ||||||||
\(943\) | −0.968681 | −0.0315446 | ||||||||
\(944\) | −2.94740 | −0.0959296 | ||||||||
\(945\) | −10.0967 | −0.328447 | ||||||||
\(946\) | 19.0140 | 0.618200 | ||||||||
\(947\) | 54.7938 | 1.78056 | 0.890280 | − | 0.455413i | \(-0.150508\pi\) | ||||
0.890280 | + | 0.455413i | \(0.150508\pi\) | |||||||
\(948\) | −7.73431 | −0.251199 | ||||||||
\(949\) | −32.6894 | −1.06114 | ||||||||
\(950\) | 12.2423 | 0.397192 | ||||||||
\(951\) | 23.3728 | 0.757915 | ||||||||
\(952\) | −9.34815 | −0.302975 | ||||||||
\(953\) | 46.8870 | 1.51882 | 0.759410 | − | 0.650612i | \(-0.225488\pi\) | ||||
0.759410 | + | 0.650612i | \(0.225488\pi\) | |||||||
\(954\) | −9.93518 | −0.321663 | ||||||||
\(955\) | −68.9180 | −2.23013 | ||||||||
\(956\) | −16.2526 | −0.525647 | ||||||||
\(957\) | 31.8562 | 1.02976 | ||||||||
\(958\) | 10.9149 | 0.352644 | ||||||||
\(959\) | −27.0978 | −0.875034 | ||||||||
\(960\) | −19.1722 | −0.618781 | ||||||||
\(961\) | 56.6310 | 1.82681 | ||||||||
\(962\) | −24.9323 | −0.803851 | ||||||||
\(963\) | −7.01299 | −0.225990 | ||||||||
\(964\) | 19.0999 | 0.615167 | ||||||||
\(965\) | −11.5864 | −0.372978 | ||||||||
\(966\) | 7.90399 | 0.254307 | ||||||||
\(967\) | 19.3935 | 0.623652 | 0.311826 | − | 0.950139i | \(-0.399059\pi\) | ||||
0.311826 | + | 0.950139i | \(0.399059\pi\) | |||||||
\(968\) | 12.2534 | 0.393840 | ||||||||
\(969\) | 2.61070 | 0.0838678 | ||||||||
\(970\) | 52.5983 | 1.68883 | ||||||||
\(971\) | −11.5844 | −0.371761 | −0.185881 | − | 0.982572i | \(-0.559514\pi\) | ||||
−0.185881 | + | 0.982572i | \(0.559514\pi\) | |||||||
\(972\) | −1.11928 | −0.0359008 | ||||||||
\(973\) | −51.4277 | −1.64870 | ||||||||
\(974\) | 12.7967 | 0.410033 | ||||||||
\(975\) | 19.9689 | 0.639516 | ||||||||
\(976\) | 4.37014 | 0.139885 | ||||||||
\(977\) | 28.4649 | 0.910674 | 0.455337 | − | 0.890319i | \(-0.349519\pi\) | ||||
0.455337 | + | 0.890319i | \(0.349519\pi\) | |||||||
\(978\) | −17.1985 | −0.549947 | ||||||||
\(979\) | 2.54759 | 0.0814212 | ||||||||
\(980\) | 11.3165 | 0.361491 | ||||||||
\(981\) | −2.69617 | −0.0860820 | ||||||||
\(982\) | −16.1807 | −0.516346 | ||||||||
\(983\) | −35.7667 | −1.14078 | −0.570390 | − | 0.821374i | \(-0.693208\pi\) | ||||
−0.570390 | + | 0.821374i | \(0.693208\pi\) | |||||||
\(984\) | 1.07518 | 0.0342754 | ||||||||
\(985\) | −35.9088 | −1.14415 | ||||||||
\(986\) | −7.67174 | −0.244318 | ||||||||
\(987\) | −28.7172 | −0.914077 | ||||||||
\(988\) | 11.6779 | 0.371522 | ||||||||
\(989\) | −13.7123 | −0.436025 | ||||||||
\(990\) | −11.5629 | −0.367494 | ||||||||
\(991\) | 1.18549 | 0.0376582 | 0.0188291 | − | 0.999823i | \(-0.494006\pi\) | ||||
0.0188291 | + | 0.999823i | \(0.494006\pi\) | |||||||
\(992\) | −50.3378 | −1.59823 | ||||||||
\(993\) | −31.4738 | −0.998791 | ||||||||
\(994\) | 33.3383 | 1.05743 | ||||||||
\(995\) | 21.4316 | 0.679427 | ||||||||
\(996\) | −4.81949 | −0.152711 | ||||||||
\(997\) | −9.92711 | −0.314395 | −0.157197 | − | 0.987567i | \(-0.550246\pi\) | ||||
−0.157197 | + | 0.987567i | \(0.550246\pi\) | |||||||
\(998\) | −8.89542 | −0.281580 | ||||||||
\(999\) | 6.64774 | 0.210325 |
(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 | 8007.2.a.e.1.18 | ✓ | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.e.1.18 | ✓ | 46 | 1.1 | even | 1 | trivial |