Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6034,2,Mod(1,6034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6034 = 2 \cdot 7 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6034.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1817325796\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 6034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.58057 | −1.48989 | −0.744947 | − | 0.667124i | \(-0.767525\pi\) | ||||
−0.744947 | + | 0.667124i | \(0.767525\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.90281 | −1.29818 | −0.649089 | − | 0.760712i | \(-0.724850\pi\) | ||||
−0.649089 | + | 0.760712i | \(0.724850\pi\) | |||||||
\(6\) | 2.58057 | 1.05351 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 3.65935 | 1.21978 | ||||||||
\(10\) | 2.90281 | 0.917951 | ||||||||
\(11\) | 1.98237 | 0.597706 | 0.298853 | − | 0.954299i | \(-0.403396\pi\) | ||||
0.298853 | + | 0.954299i | \(0.403396\pi\) | |||||||
\(12\) | −2.58057 | −0.744947 | ||||||||
\(13\) | −1.13704 | −0.315358 | −0.157679 | − | 0.987490i | \(-0.550401\pi\) | ||||
−0.157679 | + | 0.987490i | \(0.550401\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 7.49092 | 1.93415 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.51845 | 1.58096 | 0.790479 | − | 0.612490i | \(-0.209832\pi\) | ||||
0.790479 | + | 0.612490i | \(0.209832\pi\) | |||||||
\(18\) | −3.65935 | −0.862517 | ||||||||
\(19\) | 6.40456 | 1.46931 | 0.734653 | − | 0.678443i | \(-0.237345\pi\) | ||||
0.734653 | + | 0.678443i | \(0.237345\pi\) | |||||||
\(20\) | −2.90281 | −0.649089 | ||||||||
\(21\) | 2.58057 | 0.563127 | ||||||||
\(22\) | −1.98237 | −0.422642 | ||||||||
\(23\) | 2.52978 | 0.527496 | 0.263748 | − | 0.964592i | \(-0.415041\pi\) | ||||
0.263748 | + | 0.964592i | \(0.415041\pi\) | |||||||
\(24\) | 2.58057 | 0.526757 | ||||||||
\(25\) | 3.42633 | 0.685267 | ||||||||
\(26\) | 1.13704 | 0.222992 | ||||||||
\(27\) | −1.70150 | −0.327455 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 2.57764 | 0.478656 | 0.239328 | − | 0.970939i | \(-0.423073\pi\) | ||||
0.239328 | + | 0.970939i | \(0.423073\pi\) | |||||||
\(30\) | −7.49092 | −1.36765 | ||||||||
\(31\) | 4.87090 | 0.874839 | 0.437420 | − | 0.899257i | \(-0.355892\pi\) | ||||
0.437420 | + | 0.899257i | \(0.355892\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −5.11564 | −0.890518 | ||||||||
\(34\) | −6.51845 | −1.11791 | ||||||||
\(35\) | 2.90281 | 0.490665 | ||||||||
\(36\) | 3.65935 | 0.609892 | ||||||||
\(37\) | 2.00820 | 0.330145 | 0.165073 | − | 0.986281i | \(-0.447214\pi\) | ||||
0.165073 | + | 0.986281i | \(0.447214\pi\) | |||||||
\(38\) | −6.40456 | −1.03896 | ||||||||
\(39\) | 2.93422 | 0.469851 | ||||||||
\(40\) | 2.90281 | 0.458975 | ||||||||
\(41\) | 2.58506 | 0.403718 | 0.201859 | − | 0.979415i | \(-0.435302\pi\) | ||||
0.201859 | + | 0.979415i | \(0.435302\pi\) | |||||||
\(42\) | −2.58057 | −0.398191 | ||||||||
\(43\) | −0.614210 | −0.0936661 | −0.0468330 | − | 0.998903i | \(-0.514913\pi\) | ||||
−0.0468330 | + | 0.998903i | \(0.514913\pi\) | |||||||
\(44\) | 1.98237 | 0.298853 | ||||||||
\(45\) | −10.6224 | −1.58350 | ||||||||
\(46\) | −2.52978 | −0.372996 | ||||||||
\(47\) | 6.59057 | 0.961334 | 0.480667 | − | 0.876903i | \(-0.340395\pi\) | ||||
0.480667 | + | 0.876903i | \(0.340395\pi\) | |||||||
\(48\) | −2.58057 | −0.372473 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.42633 | −0.484557 | ||||||||
\(51\) | −16.8213 | −2.35546 | ||||||||
\(52\) | −1.13704 | −0.157679 | ||||||||
\(53\) | 4.77337 | 0.655673 | 0.327837 | − | 0.944734i | \(-0.393680\pi\) | ||||
0.327837 | + | 0.944734i | \(0.393680\pi\) | |||||||
\(54\) | 1.70150 | 0.231545 | ||||||||
\(55\) | −5.75444 | −0.775928 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −16.5274 | −2.18911 | ||||||||
\(58\) | −2.57764 | −0.338461 | ||||||||
\(59\) | −4.80681 | −0.625794 | −0.312897 | − | 0.949787i | \(-0.601299\pi\) | ||||
−0.312897 | + | 0.949787i | \(0.601299\pi\) | |||||||
\(60\) | 7.49092 | 0.967074 | ||||||||
\(61\) | 5.92659 | 0.758822 | 0.379411 | − | 0.925228i | \(-0.376127\pi\) | ||||
0.379411 | + | 0.925228i | \(0.376127\pi\) | |||||||
\(62\) | −4.87090 | −0.618605 | ||||||||
\(63\) | −3.65935 | −0.461035 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.30062 | 0.409391 | ||||||||
\(66\) | 5.11564 | 0.629691 | ||||||||
\(67\) | −12.9538 | −1.58255 | −0.791277 | − | 0.611458i | \(-0.790583\pi\) | ||||
−0.791277 | + | 0.611458i | \(0.790583\pi\) | |||||||
\(68\) | 6.51845 | 0.790479 | ||||||||
\(69\) | −6.52829 | −0.785913 | ||||||||
\(70\) | −2.90281 | −0.346953 | ||||||||
\(71\) | 7.79301 | 0.924860 | 0.462430 | − | 0.886656i | \(-0.346978\pi\) | ||||
0.462430 | + | 0.886656i | \(0.346978\pi\) | |||||||
\(72\) | −3.65935 | −0.431259 | ||||||||
\(73\) | 11.5052 | 1.34658 | 0.673292 | − | 0.739377i | \(-0.264880\pi\) | ||||
0.673292 | + | 0.739377i | \(0.264880\pi\) | |||||||
\(74\) | −2.00820 | −0.233448 | ||||||||
\(75\) | −8.84190 | −1.02098 | ||||||||
\(76\) | 6.40456 | 0.734653 | ||||||||
\(77\) | −1.98237 | −0.225911 | ||||||||
\(78\) | −2.93422 | −0.332235 | ||||||||
\(79\) | −4.85103 | −0.545784 | −0.272892 | − | 0.962045i | \(-0.587980\pi\) | ||||
−0.272892 | + | 0.962045i | \(0.587980\pi\) | |||||||
\(80\) | −2.90281 | −0.324545 | ||||||||
\(81\) | −6.58720 | −0.731911 | ||||||||
\(82\) | −2.58506 | −0.285472 | ||||||||
\(83\) | −11.5978 | −1.27303 | −0.636514 | − | 0.771265i | \(-0.719624\pi\) | ||||
−0.636514 | + | 0.771265i | \(0.719624\pi\) | |||||||
\(84\) | 2.58057 | 0.281563 | ||||||||
\(85\) | −18.9219 | −2.05236 | ||||||||
\(86\) | 0.614210 | 0.0662319 | ||||||||
\(87\) | −6.65179 | −0.713147 | ||||||||
\(88\) | −1.98237 | −0.211321 | ||||||||
\(89\) | 0.899500 | 0.0953468 | 0.0476734 | − | 0.998863i | \(-0.484819\pi\) | ||||
0.0476734 | + | 0.998863i | \(0.484819\pi\) | |||||||
\(90\) | 10.6224 | 1.11970 | ||||||||
\(91\) | 1.13704 | 0.119194 | ||||||||
\(92\) | 2.52978 | 0.263748 | ||||||||
\(93\) | −12.5697 | −1.30342 | ||||||||
\(94\) | −6.59057 | −0.679766 | ||||||||
\(95\) | −18.5912 | −1.90742 | ||||||||
\(96\) | 2.58057 | 0.263379 | ||||||||
\(97\) | 7.62399 | 0.774099 | 0.387050 | − | 0.922059i | \(-0.373494\pi\) | ||||
0.387050 | + | 0.922059i | \(0.373494\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 7.25417 | 0.729072 | ||||||||
\(100\) | 3.42633 | 0.342633 | ||||||||
\(101\) | 2.33560 | 0.232401 | 0.116200 | − | 0.993226i | \(-0.462928\pi\) | ||||
0.116200 | + | 0.993226i | \(0.462928\pi\) | |||||||
\(102\) | 16.8213 | 1.66556 | ||||||||
\(103\) | 18.3712 | 1.81016 | 0.905082 | − | 0.425237i | \(-0.139809\pi\) | ||||
0.905082 | + | 0.425237i | \(0.139809\pi\) | |||||||
\(104\) | 1.13704 | 0.111496 | ||||||||
\(105\) | −7.49092 | −0.731039 | ||||||||
\(106\) | −4.77337 | −0.463631 | ||||||||
\(107\) | −2.88941 | −0.279330 | −0.139665 | − | 0.990199i | \(-0.544603\pi\) | ||||
−0.139665 | + | 0.990199i | \(0.544603\pi\) | |||||||
\(108\) | −1.70150 | −0.163727 | ||||||||
\(109\) | −2.71556 | −0.260103 | −0.130052 | − | 0.991507i | \(-0.541514\pi\) | ||||
−0.130052 | + | 0.991507i | \(0.541514\pi\) | |||||||
\(110\) | 5.75444 | 0.548664 | ||||||||
\(111\) | −5.18229 | −0.491881 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −4.37988 | −0.412024 | −0.206012 | − | 0.978549i | \(-0.566049\pi\) | ||||
−0.206012 | + | 0.978549i | \(0.566049\pi\) | |||||||
\(114\) | 16.5274 | 1.54793 | ||||||||
\(115\) | −7.34349 | −0.684784 | ||||||||
\(116\) | 2.57764 | 0.239328 | ||||||||
\(117\) | −4.16083 | −0.384669 | ||||||||
\(118\) | 4.80681 | 0.442503 | ||||||||
\(119\) | −6.51845 | −0.597546 | ||||||||
\(120\) | −7.49092 | −0.683825 | ||||||||
\(121\) | −7.07023 | −0.642748 | ||||||||
\(122\) | −5.92659 | −0.536568 | ||||||||
\(123\) | −6.67093 | −0.601497 | ||||||||
\(124\) | 4.87090 | 0.437420 | ||||||||
\(125\) | 4.56806 | 0.408580 | ||||||||
\(126\) | 3.65935 | 0.326001 | ||||||||
\(127\) | −3.46348 | −0.307334 | −0.153667 | − | 0.988123i | \(-0.549108\pi\) | ||||
−0.153667 | + | 0.988123i | \(0.549108\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 1.58501 | 0.139553 | ||||||||
\(130\) | −3.30062 | −0.289483 | ||||||||
\(131\) | 6.91733 | 0.604370 | 0.302185 | − | 0.953249i | \(-0.402284\pi\) | ||||
0.302185 | + | 0.953249i | \(0.402284\pi\) | |||||||
\(132\) | −5.11564 | −0.445259 | ||||||||
\(133\) | −6.40456 | −0.555345 | ||||||||
\(134\) | 12.9538 | 1.11903 | ||||||||
\(135\) | 4.93915 | 0.425094 | ||||||||
\(136\) | −6.51845 | −0.558953 | ||||||||
\(137\) | −9.42199 | −0.804975 | −0.402487 | − | 0.915426i | \(-0.631854\pi\) | ||||
−0.402487 | + | 0.915426i | \(0.631854\pi\) | |||||||
\(138\) | 6.52829 | 0.555725 | ||||||||
\(139\) | 13.8129 | 1.17159 | 0.585796 | − | 0.810458i | \(-0.300782\pi\) | ||||
0.585796 | + | 0.810458i | \(0.300782\pi\) | |||||||
\(140\) | 2.90281 | 0.245333 | ||||||||
\(141\) | −17.0075 | −1.43229 | ||||||||
\(142\) | −7.79301 | −0.653975 | ||||||||
\(143\) | −2.25403 | −0.188491 | ||||||||
\(144\) | 3.65935 | 0.304946 | ||||||||
\(145\) | −7.48242 | −0.621381 | ||||||||
\(146\) | −11.5052 | −0.952178 | ||||||||
\(147\) | −2.58057 | −0.212842 | ||||||||
\(148\) | 2.00820 | 0.165073 | ||||||||
\(149\) | 17.7245 | 1.45205 | 0.726024 | − | 0.687670i | \(-0.241366\pi\) | ||||
0.726024 | + | 0.687670i | \(0.241366\pi\) | |||||||
\(150\) | 8.84190 | 0.721938 | ||||||||
\(151\) | −12.8493 | −1.04566 | −0.522831 | − | 0.852436i | \(-0.675124\pi\) | ||||
−0.522831 | + | 0.852436i | \(0.675124\pi\) | |||||||
\(152\) | −6.40456 | −0.519478 | ||||||||
\(153\) | 23.8533 | 1.92843 | ||||||||
\(154\) | 1.98237 | 0.159744 | ||||||||
\(155\) | −14.1393 | −1.13570 | ||||||||
\(156\) | 2.93422 | 0.234925 | ||||||||
\(157\) | −3.64473 | −0.290881 | −0.145440 | − | 0.989367i | \(-0.546460\pi\) | ||||
−0.145440 | + | 0.989367i | \(0.546460\pi\) | |||||||
\(158\) | 4.85103 | 0.385928 | ||||||||
\(159\) | −12.3180 | −0.976883 | ||||||||
\(160\) | 2.90281 | 0.229488 | ||||||||
\(161\) | −2.52978 | −0.199375 | ||||||||
\(162\) | 6.58720 | 0.517539 | ||||||||
\(163\) | −10.5676 | −0.827719 | −0.413859 | − | 0.910341i | \(-0.635819\pi\) | ||||
−0.413859 | + | 0.910341i | \(0.635819\pi\) | |||||||
\(164\) | 2.58506 | 0.201859 | ||||||||
\(165\) | 14.8497 | 1.15605 | ||||||||
\(166\) | 11.5978 | 0.900166 | ||||||||
\(167\) | 15.6309 | 1.20956 | 0.604779 | − | 0.796393i | \(-0.293261\pi\) | ||||
0.604779 | + | 0.796393i | \(0.293261\pi\) | |||||||
\(168\) | −2.58057 | −0.199095 | ||||||||
\(169\) | −11.7071 | −0.900549 | ||||||||
\(170\) | 18.9219 | 1.45124 | ||||||||
\(171\) | 23.4365 | 1.79224 | ||||||||
\(172\) | −0.614210 | −0.0468330 | ||||||||
\(173\) | −11.8062 | −0.897605 | −0.448803 | − | 0.893631i | \(-0.648149\pi\) | ||||
−0.448803 | + | 0.893631i | \(0.648149\pi\) | |||||||
\(174\) | 6.65179 | 0.504271 | ||||||||
\(175\) | −3.42633 | −0.259007 | ||||||||
\(176\) | 1.98237 | 0.149426 | ||||||||
\(177\) | 12.4043 | 0.932366 | ||||||||
\(178\) | −0.899500 | −0.0674204 | ||||||||
\(179\) | 24.2091 | 1.80947 | 0.904736 | − | 0.425973i | \(-0.140068\pi\) | ||||
0.904736 | + | 0.425973i | \(0.140068\pi\) | |||||||
\(180\) | −10.6224 | −0.791748 | ||||||||
\(181\) | 7.57652 | 0.563158 | 0.281579 | − | 0.959538i | \(-0.409142\pi\) | ||||
0.281579 | + | 0.959538i | \(0.409142\pi\) | |||||||
\(182\) | −1.13704 | −0.0842831 | ||||||||
\(183\) | −15.2940 | −1.13056 | ||||||||
\(184\) | −2.52978 | −0.186498 | ||||||||
\(185\) | −5.82942 | −0.428587 | ||||||||
\(186\) | 12.5697 | 0.921656 | ||||||||
\(187\) | 12.9220 | 0.944947 | ||||||||
\(188\) | 6.59057 | 0.480667 | ||||||||
\(189\) | 1.70150 | 0.123766 | ||||||||
\(190\) | 18.5912 | 1.34875 | ||||||||
\(191\) | 6.92951 | 0.501401 | 0.250701 | − | 0.968065i | \(-0.419339\pi\) | ||||
0.250701 | + | 0.968065i | \(0.419339\pi\) | |||||||
\(192\) | −2.58057 | −0.186237 | ||||||||
\(193\) | −9.54025 | −0.686722 | −0.343361 | − | 0.939203i | \(-0.611565\pi\) | ||||
−0.343361 | + | 0.939203i | \(0.611565\pi\) | |||||||
\(194\) | −7.62399 | −0.547371 | ||||||||
\(195\) | −8.51749 | −0.609950 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −7.74105 | −0.551527 | −0.275764 | − | 0.961225i | \(-0.588931\pi\) | ||||
−0.275764 | + | 0.961225i | \(0.588931\pi\) | |||||||
\(198\) | −7.25417 | −0.515531 | ||||||||
\(199\) | −19.2459 | −1.36431 | −0.682155 | − | 0.731208i | \(-0.738957\pi\) | ||||
−0.682155 | + | 0.731208i | \(0.738957\pi\) | |||||||
\(200\) | −3.42633 | −0.242278 | ||||||||
\(201\) | 33.4281 | 2.35784 | ||||||||
\(202\) | −2.33560 | −0.164332 | ||||||||
\(203\) | −2.57764 | −0.180915 | ||||||||
\(204\) | −16.8213 | −1.17773 | ||||||||
\(205\) | −7.50394 | −0.524098 | ||||||||
\(206\) | −18.3712 | −1.27998 | ||||||||
\(207\) | 9.25736 | 0.643431 | ||||||||
\(208\) | −1.13704 | −0.0788396 | ||||||||
\(209\) | 12.6962 | 0.878212 | ||||||||
\(210\) | 7.49092 | 0.516923 | ||||||||
\(211\) | 8.33381 | 0.573723 | 0.286862 | − | 0.957972i | \(-0.407388\pi\) | ||||
0.286862 | + | 0.957972i | \(0.407388\pi\) | |||||||
\(212\) | 4.77337 | 0.327837 | ||||||||
\(213\) | −20.1104 | −1.37794 | ||||||||
\(214\) | 2.88941 | 0.197516 | ||||||||
\(215\) | 1.78294 | 0.121595 | ||||||||
\(216\) | 1.70150 | 0.115773 | ||||||||
\(217\) | −4.87090 | −0.330658 | ||||||||
\(218\) | 2.71556 | 0.183921 | ||||||||
\(219\) | −29.6900 | −2.00627 | ||||||||
\(220\) | −5.75444 | −0.387964 | ||||||||
\(221\) | −7.41175 | −0.498568 | ||||||||
\(222\) | 5.18229 | 0.347813 | ||||||||
\(223\) | −6.71223 | −0.449484 | −0.224742 | − | 0.974418i | \(-0.572154\pi\) | ||||
−0.224742 | + | 0.974418i | \(0.572154\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 12.5382 | 0.835878 | ||||||||
\(226\) | 4.37988 | 0.291345 | ||||||||
\(227\) | −11.3594 | −0.753948 | −0.376974 | − | 0.926224i | \(-0.623035\pi\) | ||||
−0.376974 | + | 0.926224i | \(0.623035\pi\) | |||||||
\(228\) | −16.5274 | −1.09455 | ||||||||
\(229\) | −5.31810 | −0.351430 | −0.175715 | − | 0.984441i | \(-0.556224\pi\) | ||||
−0.175715 | + | 0.984441i | \(0.556224\pi\) | |||||||
\(230\) | 7.34349 | 0.484215 | ||||||||
\(231\) | 5.11564 | 0.336584 | ||||||||
\(232\) | −2.57764 | −0.169231 | ||||||||
\(233\) | 15.7607 | 1.03252 | 0.516258 | − | 0.856433i | \(-0.327324\pi\) | ||||
0.516258 | + | 0.856433i | \(0.327324\pi\) | |||||||
\(234\) | 4.16083 | 0.272002 | ||||||||
\(235\) | −19.1312 | −1.24798 | ||||||||
\(236\) | −4.80681 | −0.312897 | ||||||||
\(237\) | 12.5184 | 0.813160 | ||||||||
\(238\) | 6.51845 | 0.422529 | ||||||||
\(239\) | 17.3945 | 1.12516 | 0.562578 | − | 0.826744i | \(-0.309810\pi\) | ||||
0.562578 | + | 0.826744i | \(0.309810\pi\) | |||||||
\(240\) | 7.49092 | 0.483537 | ||||||||
\(241\) | 19.1506 | 1.23360 | 0.616800 | − | 0.787120i | \(-0.288429\pi\) | ||||
0.616800 | + | 0.787120i | \(0.288429\pi\) | |||||||
\(242\) | 7.07023 | 0.454492 | ||||||||
\(243\) | 22.1033 | 1.41792 | ||||||||
\(244\) | 5.92659 | 0.379411 | ||||||||
\(245\) | −2.90281 | −0.185454 | ||||||||
\(246\) | 6.67093 | 0.425323 | ||||||||
\(247\) | −7.28224 | −0.463358 | ||||||||
\(248\) | −4.87090 | −0.309302 | ||||||||
\(249\) | 29.9290 | 1.89668 | ||||||||
\(250\) | −4.56806 | −0.288909 | ||||||||
\(251\) | 13.4578 | 0.849450 | 0.424725 | − | 0.905322i | \(-0.360371\pi\) | ||||
0.424725 | + | 0.905322i | \(0.360371\pi\) | |||||||
\(252\) | −3.65935 | −0.230517 | ||||||||
\(253\) | 5.01495 | 0.315287 | ||||||||
\(254\) | 3.46348 | 0.217318 | ||||||||
\(255\) | 48.8292 | 3.05780 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −12.9478 | −0.807659 | −0.403830 | − | 0.914834i | \(-0.632321\pi\) | ||||
−0.403830 | + | 0.914834i | \(0.632321\pi\) | |||||||
\(258\) | −1.58501 | −0.0986786 | ||||||||
\(259\) | −2.00820 | −0.124783 | ||||||||
\(260\) | 3.30062 | 0.204696 | ||||||||
\(261\) | 9.43250 | 0.583857 | ||||||||
\(262\) | −6.91733 | −0.427354 | ||||||||
\(263\) | −1.97613 | −0.121854 | −0.0609268 | − | 0.998142i | \(-0.519406\pi\) | ||||
−0.0609268 | + | 0.998142i | \(0.519406\pi\) | |||||||
\(264\) | 5.11564 | 0.314846 | ||||||||
\(265\) | −13.8562 | −0.851181 | ||||||||
\(266\) | 6.40456 | 0.392689 | ||||||||
\(267\) | −2.32122 | −0.142057 | ||||||||
\(268\) | −12.9538 | −0.791277 | ||||||||
\(269\) | −4.54980 | −0.277406 | −0.138703 | − | 0.990334i | \(-0.544293\pi\) | ||||
−0.138703 | + | 0.990334i | \(0.544293\pi\) | |||||||
\(270\) | −4.93915 | −0.300587 | ||||||||
\(271\) | 17.2187 | 1.04596 | 0.522979 | − | 0.852345i | \(-0.324820\pi\) | ||||
0.522979 | + | 0.852345i | \(0.324820\pi\) | |||||||
\(272\) | 6.51845 | 0.395239 | ||||||||
\(273\) | −2.93422 | −0.177587 | ||||||||
\(274\) | 9.42199 | 0.569203 | ||||||||
\(275\) | 6.79225 | 0.409588 | ||||||||
\(276\) | −6.52829 | −0.392957 | ||||||||
\(277\) | −21.9013 | −1.31592 | −0.657960 | − | 0.753053i | \(-0.728581\pi\) | ||||
−0.657960 | + | 0.753053i | \(0.728581\pi\) | |||||||
\(278\) | −13.8129 | −0.828441 | ||||||||
\(279\) | 17.8243 | 1.06712 | ||||||||
\(280\) | −2.90281 | −0.173476 | ||||||||
\(281\) | 13.3125 | 0.794156 | 0.397078 | − | 0.917785i | \(-0.370024\pi\) | ||||
0.397078 | + | 0.917785i | \(0.370024\pi\) | |||||||
\(282\) | 17.0075 | 1.01278 | ||||||||
\(283\) | −29.5155 | −1.75451 | −0.877257 | − | 0.480021i | \(-0.840629\pi\) | ||||
−0.877257 | + | 0.480021i | \(0.840629\pi\) | |||||||
\(284\) | 7.79301 | 0.462430 | ||||||||
\(285\) | 47.9760 | 2.84185 | ||||||||
\(286\) | 2.25403 | 0.133284 | ||||||||
\(287\) | −2.58506 | −0.152591 | ||||||||
\(288\) | −3.65935 | −0.215629 | ||||||||
\(289\) | 25.4902 | 1.49943 | ||||||||
\(290\) | 7.48242 | 0.439383 | ||||||||
\(291\) | −19.6743 | −1.15333 | ||||||||
\(292\) | 11.5052 | 0.673292 | ||||||||
\(293\) | −9.52720 | −0.556585 | −0.278293 | − | 0.960496i | \(-0.589768\pi\) | ||||
−0.278293 | + | 0.960496i | \(0.589768\pi\) | |||||||
\(294\) | 2.58057 | 0.150502 | ||||||||
\(295\) | 13.9533 | 0.812392 | ||||||||
\(296\) | −2.00820 | −0.116724 | ||||||||
\(297\) | −3.37300 | −0.195721 | ||||||||
\(298\) | −17.7245 | −1.02675 | ||||||||
\(299\) | −2.87647 | −0.166350 | ||||||||
\(300\) | −8.84190 | −0.510488 | ||||||||
\(301\) | 0.614210 | 0.0354025 | ||||||||
\(302\) | 12.8493 | 0.739395 | ||||||||
\(303\) | −6.02719 | −0.346253 | ||||||||
\(304\) | 6.40456 | 0.367326 | ||||||||
\(305\) | −17.2038 | −0.985086 | ||||||||
\(306\) | −23.8533 | −1.36360 | ||||||||
\(307\) | 3.69455 | 0.210859 | 0.105430 | − | 0.994427i | \(-0.466378\pi\) | ||||
0.105430 | + | 0.994427i | \(0.466378\pi\) | |||||||
\(308\) | −1.98237 | −0.112956 | ||||||||
\(309\) | −47.4081 | −2.69695 | ||||||||
\(310\) | 14.1393 | 0.803060 | ||||||||
\(311\) | 23.9231 | 1.35656 | 0.678278 | − | 0.734806i | \(-0.262727\pi\) | ||||
0.678278 | + | 0.734806i | \(0.262727\pi\) | |||||||
\(312\) | −2.93422 | −0.166117 | ||||||||
\(313\) | −33.2825 | −1.88124 | −0.940619 | − | 0.339464i | \(-0.889754\pi\) | ||||
−0.940619 | + | 0.339464i | \(0.889754\pi\) | |||||||
\(314\) | 3.64473 | 0.205684 | ||||||||
\(315\) | 10.6224 | 0.598506 | ||||||||
\(316\) | −4.85103 | −0.272892 | ||||||||
\(317\) | −19.3951 | −1.08934 | −0.544669 | − | 0.838651i | \(-0.683345\pi\) | ||||
−0.544669 | + | 0.838651i | \(0.683345\pi\) | |||||||
\(318\) | 12.3180 | 0.690761 | ||||||||
\(319\) | 5.10983 | 0.286096 | ||||||||
\(320\) | −2.90281 | −0.162272 | ||||||||
\(321\) | 7.45633 | 0.416172 | ||||||||
\(322\) | 2.52978 | 0.140979 | ||||||||
\(323\) | 41.7478 | 2.32291 | ||||||||
\(324\) | −6.58720 | −0.365956 | ||||||||
\(325\) | −3.89588 | −0.216105 | ||||||||
\(326\) | 10.5676 | 0.585285 | ||||||||
\(327\) | 7.00769 | 0.387526 | ||||||||
\(328\) | −2.58506 | −0.142736 | ||||||||
\(329\) | −6.59057 | −0.363350 | ||||||||
\(330\) | −14.8497 | −0.817451 | ||||||||
\(331\) | 27.1421 | 1.49186 | 0.745932 | − | 0.666022i | \(-0.232004\pi\) | ||||
0.745932 | + | 0.666022i | \(0.232004\pi\) | |||||||
\(332\) | −11.5978 | −0.636514 | ||||||||
\(333\) | 7.34869 | 0.402706 | ||||||||
\(334\) | −15.6309 | −0.855287 | ||||||||
\(335\) | 37.6024 | 2.05444 | ||||||||
\(336\) | 2.58057 | 0.140782 | ||||||||
\(337\) | −17.3713 | −0.946277 | −0.473139 | − | 0.880988i | \(-0.656879\pi\) | ||||
−0.473139 | + | 0.880988i | \(0.656879\pi\) | |||||||
\(338\) | 11.7071 | 0.636784 | ||||||||
\(339\) | 11.3026 | 0.613873 | ||||||||
\(340\) | −18.9219 | −1.02618 | ||||||||
\(341\) | 9.65590 | 0.522896 | ||||||||
\(342\) | −23.4365 | −1.26730 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0.614210 | 0.0331160 | ||||||||
\(345\) | 18.9504 | 1.02026 | ||||||||
\(346\) | 11.8062 | 0.634703 | ||||||||
\(347\) | −0.864319 | −0.0463991 | −0.0231995 | − | 0.999731i | \(-0.507385\pi\) | ||||
−0.0231995 | + | 0.999731i | \(0.507385\pi\) | |||||||
\(348\) | −6.65179 | −0.356574 | ||||||||
\(349\) | −25.4451 | −1.36205 | −0.681023 | − | 0.732262i | \(-0.738465\pi\) | ||||
−0.681023 | + | 0.732262i | \(0.738465\pi\) | |||||||
\(350\) | 3.42633 | 0.183145 | ||||||||
\(351\) | 1.93468 | 0.103266 | ||||||||
\(352\) | −1.98237 | −0.105660 | ||||||||
\(353\) | 15.7488 | 0.838225 | 0.419113 | − | 0.907934i | \(-0.362341\pi\) | ||||
0.419113 | + | 0.907934i | \(0.362341\pi\) | |||||||
\(354\) | −12.4043 | −0.659283 | ||||||||
\(355\) | −22.6217 | −1.20063 | ||||||||
\(356\) | 0.899500 | 0.0476734 | ||||||||
\(357\) | 16.8213 | 0.890280 | ||||||||
\(358\) | −24.2091 | −1.27949 | ||||||||
\(359\) | −0.999205 | −0.0527360 | −0.0263680 | − | 0.999652i | \(-0.508394\pi\) | ||||
−0.0263680 | + | 0.999652i | \(0.508394\pi\) | |||||||
\(360\) | 10.6224 | 0.559851 | ||||||||
\(361\) | 22.0183 | 1.15886 | ||||||||
\(362\) | −7.57652 | −0.398213 | ||||||||
\(363\) | 18.2452 | 0.957626 | ||||||||
\(364\) | 1.13704 | 0.0595971 | ||||||||
\(365\) | −33.3975 | −1.74811 | ||||||||
\(366\) | 15.2940 | 0.799429 | ||||||||
\(367\) | 4.80614 | 0.250879 | 0.125439 | − | 0.992101i | \(-0.459966\pi\) | ||||
0.125439 | + | 0.992101i | \(0.459966\pi\) | |||||||
\(368\) | 2.52978 | 0.131874 | ||||||||
\(369\) | 9.45963 | 0.492449 | ||||||||
\(370\) | 5.82942 | 0.303057 | ||||||||
\(371\) | −4.77337 | −0.247821 | ||||||||
\(372\) | −12.5697 | −0.651709 | ||||||||
\(373\) | 8.96656 | 0.464271 | 0.232135 | − | 0.972683i | \(-0.425429\pi\) | ||||
0.232135 | + | 0.972683i | \(0.425429\pi\) | |||||||
\(374\) | −12.9220 | −0.668178 | ||||||||
\(375\) | −11.7882 | −0.608740 | ||||||||
\(376\) | −6.59057 | −0.339883 | ||||||||
\(377\) | −2.93089 | −0.150948 | ||||||||
\(378\) | −1.70150 | −0.0875159 | ||||||||
\(379\) | −1.64987 | −0.0847481 | −0.0423740 | − | 0.999102i | \(-0.513492\pi\) | ||||
−0.0423740 | + | 0.999102i | \(0.513492\pi\) | |||||||
\(380\) | −18.5912 | −0.953711 | ||||||||
\(381\) | 8.93776 | 0.457896 | ||||||||
\(382\) | −6.92951 | −0.354544 | ||||||||
\(383\) | 20.0532 | 1.02467 | 0.512336 | − | 0.858785i | \(-0.328780\pi\) | ||||
0.512336 | + | 0.858785i | \(0.328780\pi\) | |||||||
\(384\) | 2.58057 | 0.131689 | ||||||||
\(385\) | 5.75444 | 0.293273 | ||||||||
\(386\) | 9.54025 | 0.485586 | ||||||||
\(387\) | −2.24761 | −0.114252 | ||||||||
\(388\) | 7.62399 | 0.387050 | ||||||||
\(389\) | −15.7411 | −0.798103 | −0.399052 | − | 0.916928i | \(-0.630661\pi\) | ||||
−0.399052 | + | 0.916928i | \(0.630661\pi\) | |||||||
\(390\) | 8.51749 | 0.431300 | ||||||||
\(391\) | 16.4903 | 0.833949 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −17.8507 | −0.900447 | ||||||||
\(394\) | 7.74105 | 0.389989 | ||||||||
\(395\) | 14.0817 | 0.708525 | ||||||||
\(396\) | 7.25417 | 0.364536 | ||||||||
\(397\) | −10.6432 | −0.534167 | −0.267084 | − | 0.963673i | \(-0.586060\pi\) | ||||
−0.267084 | + | 0.963673i | \(0.586060\pi\) | |||||||
\(398\) | 19.2459 | 0.964712 | ||||||||
\(399\) | 16.5274 | 0.827406 | ||||||||
\(400\) | 3.42633 | 0.171317 | ||||||||
\(401\) | 29.4967 | 1.47300 | 0.736498 | − | 0.676439i | \(-0.236478\pi\) | ||||
0.736498 | + | 0.676439i | \(0.236478\pi\) | |||||||
\(402\) | −33.4281 | −1.66724 | ||||||||
\(403\) | −5.53841 | −0.275888 | ||||||||
\(404\) | 2.33560 | 0.116200 | ||||||||
\(405\) | 19.1214 | 0.950151 | ||||||||
\(406\) | 2.57764 | 0.127926 | ||||||||
\(407\) | 3.98098 | 0.197330 | ||||||||
\(408\) | 16.8213 | 0.832780 | ||||||||
\(409\) | −19.1462 | −0.946721 | −0.473360 | − | 0.880869i | \(-0.656959\pi\) | ||||
−0.473360 | + | 0.880869i | \(0.656959\pi\) | |||||||
\(410\) | 7.50394 | 0.370593 | ||||||||
\(411\) | 24.3141 | 1.19933 | ||||||||
\(412\) | 18.3712 | 0.905082 | ||||||||
\(413\) | 4.80681 | 0.236528 | ||||||||
\(414\) | −9.25736 | −0.454975 | ||||||||
\(415\) | 33.6664 | 1.65262 | ||||||||
\(416\) | 1.13704 | 0.0557480 | ||||||||
\(417\) | −35.6451 | −1.74555 | ||||||||
\(418\) | −12.6962 | −0.620990 | ||||||||
\(419\) | −17.8133 | −0.870235 | −0.435117 | − | 0.900374i | \(-0.643293\pi\) | ||||
−0.435117 | + | 0.900374i | \(0.643293\pi\) | |||||||
\(420\) | −7.49092 | −0.365520 | ||||||||
\(421\) | 5.94280 | 0.289634 | 0.144817 | − | 0.989458i | \(-0.453741\pi\) | ||||
0.144817 | + | 0.989458i | \(0.453741\pi\) | |||||||
\(422\) | −8.33381 | −0.405684 | ||||||||
\(423\) | 24.1172 | 1.17262 | ||||||||
\(424\) | −4.77337 | −0.231815 | ||||||||
\(425\) | 22.3344 | 1.08338 | ||||||||
\(426\) | 20.1104 | 0.974353 | ||||||||
\(427\) | −5.92659 | −0.286808 | ||||||||
\(428\) | −2.88941 | −0.139665 | ||||||||
\(429\) | 5.81669 | 0.280832 | ||||||||
\(430\) | −1.78294 | −0.0859809 | ||||||||
\(431\) | 1.00000 | 0.0481683 | ||||||||
\(432\) | −1.70150 | −0.0818637 | ||||||||
\(433\) | 18.1765 | 0.873508 | 0.436754 | − | 0.899581i | \(-0.356128\pi\) | ||||
0.436754 | + | 0.899581i | \(0.356128\pi\) | |||||||
\(434\) | 4.87090 | 0.233811 | ||||||||
\(435\) | 19.3089 | 0.925792 | ||||||||
\(436\) | −2.71556 | −0.130052 | ||||||||
\(437\) | 16.2021 | 0.775053 | ||||||||
\(438\) | 29.6900 | 1.41864 | ||||||||
\(439\) | 17.9837 | 0.858314 | 0.429157 | − | 0.903230i | \(-0.358811\pi\) | ||||
0.429157 | + | 0.903230i | \(0.358811\pi\) | |||||||
\(440\) | 5.75444 | 0.274332 | ||||||||
\(441\) | 3.65935 | 0.174255 | ||||||||
\(442\) | 7.41175 | 0.352541 | ||||||||
\(443\) | −2.28928 | −0.108767 | −0.0543834 | − | 0.998520i | \(-0.517319\pi\) | ||||
−0.0543834 | + | 0.998520i | \(0.517319\pi\) | |||||||
\(444\) | −5.18229 | −0.245941 | ||||||||
\(445\) | −2.61108 | −0.123777 | ||||||||
\(446\) | 6.71223 | 0.317833 | ||||||||
\(447\) | −45.7393 | −2.16340 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 39.6537 | 1.87138 | 0.935688 | − | 0.352828i | \(-0.114780\pi\) | ||||
0.935688 | + | 0.352828i | \(0.114780\pi\) | |||||||
\(450\) | −12.5382 | −0.591055 | ||||||||
\(451\) | 5.12453 | 0.241305 | ||||||||
\(452\) | −4.37988 | −0.206012 | ||||||||
\(453\) | 33.1586 | 1.55793 | ||||||||
\(454\) | 11.3594 | 0.533122 | ||||||||
\(455\) | −3.30062 | −0.154735 | ||||||||
\(456\) | 16.5274 | 0.773967 | ||||||||
\(457\) | 14.7836 | 0.691547 | 0.345774 | − | 0.938318i | \(-0.387617\pi\) | ||||
0.345774 | + | 0.938318i | \(0.387617\pi\) | |||||||
\(458\) | 5.31810 | 0.248499 | ||||||||
\(459\) | −11.0912 | −0.517692 | ||||||||
\(460\) | −7.34349 | −0.342392 | ||||||||
\(461\) | 7.90304 | 0.368081 | 0.184041 | − | 0.982919i | \(-0.441082\pi\) | ||||
0.184041 | + | 0.982919i | \(0.441082\pi\) | |||||||
\(462\) | −5.11564 | −0.238001 | ||||||||
\(463\) | 3.28792 | 0.152802 | 0.0764012 | − | 0.997077i | \(-0.475657\pi\) | ||||
0.0764012 | + | 0.997077i | \(0.475657\pi\) | |||||||
\(464\) | 2.57764 | 0.119664 | ||||||||
\(465\) | 36.4875 | 1.69207 | ||||||||
\(466\) | −15.7607 | −0.730099 | ||||||||
\(467\) | 5.23293 | 0.242151 | 0.121076 | − | 0.992643i | \(-0.461366\pi\) | ||||
0.121076 | + | 0.992643i | \(0.461366\pi\) | |||||||
\(468\) | −4.16083 | −0.192335 | ||||||||
\(469\) | 12.9538 | 0.598149 | ||||||||
\(470\) | 19.1312 | 0.882457 | ||||||||
\(471\) | 9.40548 | 0.433382 | ||||||||
\(472\) | 4.80681 | 0.221252 | ||||||||
\(473\) | −1.21759 | −0.0559847 | ||||||||
\(474\) | −12.5184 | −0.574991 | ||||||||
\(475\) | 21.9442 | 1.00687 | ||||||||
\(476\) | −6.51845 | −0.298773 | ||||||||
\(477\) | 17.4674 | 0.799780 | ||||||||
\(478\) | −17.3945 | −0.795606 | ||||||||
\(479\) | 10.8596 | 0.496189 | 0.248094 | − | 0.968736i | \(-0.420196\pi\) | ||||
0.248094 | + | 0.968736i | \(0.420196\pi\) | |||||||
\(480\) | −7.49092 | −0.341912 | ||||||||
\(481\) | −2.28340 | −0.104114 | ||||||||
\(482\) | −19.1506 | −0.872287 | ||||||||
\(483\) | 6.52829 | 0.297047 | ||||||||
\(484\) | −7.07023 | −0.321374 | ||||||||
\(485\) | −22.1310 | −1.00492 | ||||||||
\(486\) | −22.1033 | −1.00262 | ||||||||
\(487\) | 2.07254 | 0.0939158 | 0.0469579 | − | 0.998897i | \(-0.485047\pi\) | ||||
0.0469579 | + | 0.998897i | \(0.485047\pi\) | |||||||
\(488\) | −5.92659 | −0.268284 | ||||||||
\(489\) | 27.2705 | 1.23321 | ||||||||
\(490\) | 2.90281 | 0.131136 | ||||||||
\(491\) | 21.7367 | 0.980962 | 0.490481 | − | 0.871452i | \(-0.336821\pi\) | ||||
0.490481 | + | 0.871452i | \(0.336821\pi\) | |||||||
\(492\) | −6.67093 | −0.300749 | ||||||||
\(493\) | 16.8022 | 0.756735 | ||||||||
\(494\) | 7.28224 | 0.327644 | ||||||||
\(495\) | −21.0575 | −0.946465 | ||||||||
\(496\) | 4.87090 | 0.218710 | ||||||||
\(497\) | −7.79301 | −0.349564 | ||||||||
\(498\) | −29.9290 | −1.34115 | ||||||||
\(499\) | 37.8548 | 1.69461 | 0.847307 | − | 0.531104i | \(-0.178223\pi\) | ||||
0.847307 | + | 0.531104i | \(0.178223\pi\) | |||||||
\(500\) | 4.56806 | 0.204290 | ||||||||
\(501\) | −40.3367 | −1.80211 | ||||||||
\(502\) | −13.4578 | −0.600652 | ||||||||
\(503\) | 34.4778 | 1.53729 | 0.768644 | − | 0.639676i | \(-0.220932\pi\) | ||||
0.768644 | + | 0.639676i | \(0.220932\pi\) | |||||||
\(504\) | 3.65935 | 0.163000 | ||||||||
\(505\) | −6.77982 | −0.301698 | ||||||||
\(506\) | −5.01495 | −0.222942 | ||||||||
\(507\) | 30.2111 | 1.34172 | ||||||||
\(508\) | −3.46348 | −0.153667 | ||||||||
\(509\) | −6.28091 | −0.278396 | −0.139198 | − | 0.990265i | \(-0.544453\pi\) | ||||
−0.139198 | + | 0.990265i | \(0.544453\pi\) | |||||||
\(510\) | −48.8292 | −2.16219 | ||||||||
\(511\) | −11.5052 | −0.508961 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −10.8974 | −0.481131 | ||||||||
\(514\) | 12.9478 | 0.571101 | ||||||||
\(515\) | −53.3281 | −2.34992 | ||||||||
\(516\) | 1.58501 | 0.0697763 | ||||||||
\(517\) | 13.0649 | 0.574595 | ||||||||
\(518\) | 2.00820 | 0.0882350 | ||||||||
\(519\) | 30.4666 | 1.33734 | ||||||||
\(520\) | −3.30062 | −0.144742 | ||||||||
\(521\) | −6.23753 | −0.273271 | −0.136636 | − | 0.990621i | \(-0.543629\pi\) | ||||
−0.136636 | + | 0.990621i | \(0.543629\pi\) | |||||||
\(522\) | −9.43250 | −0.412849 | ||||||||
\(523\) | −9.15761 | −0.400434 | −0.200217 | − | 0.979752i | \(-0.564165\pi\) | ||||
−0.200217 | + | 0.979752i | \(0.564165\pi\) | |||||||
\(524\) | 6.91733 | 0.302185 | ||||||||
\(525\) | 8.84190 | 0.385892 | ||||||||
\(526\) | 1.97613 | 0.0861635 | ||||||||
\(527\) | 31.7507 | 1.38308 | ||||||||
\(528\) | −5.11564 | −0.222629 | ||||||||
\(529\) | −16.6002 | −0.721748 | ||||||||
\(530\) | 13.8562 | 0.601876 | ||||||||
\(531\) | −17.5898 | −0.763333 | ||||||||
\(532\) | −6.40456 | −0.277673 | ||||||||
\(533\) | −2.93932 | −0.127316 | ||||||||
\(534\) | 2.32122 | 0.100449 | ||||||||
\(535\) | 8.38742 | 0.362620 | ||||||||
\(536\) | 12.9538 | 0.559517 | ||||||||
\(537\) | −62.4733 | −2.69592 | ||||||||
\(538\) | 4.54980 | 0.196156 | ||||||||
\(539\) | 1.98237 | 0.0853865 | ||||||||
\(540\) | 4.93915 | 0.212547 | ||||||||
\(541\) | −28.2732 | −1.21556 | −0.607781 | − | 0.794105i | \(-0.707940\pi\) | ||||
−0.607781 | + | 0.794105i | \(0.707940\pi\) | |||||||
\(542\) | −17.2187 | −0.739604 | ||||||||
\(543\) | −19.5518 | −0.839046 | ||||||||
\(544\) | −6.51845 | −0.279476 | ||||||||
\(545\) | 7.88276 | 0.337660 | ||||||||
\(546\) | 2.93422 | 0.125573 | ||||||||
\(547\) | 10.2786 | 0.439480 | 0.219740 | − | 0.975558i | \(-0.429479\pi\) | ||||
0.219740 | + | 0.975558i | \(0.429479\pi\) | |||||||
\(548\) | −9.42199 | −0.402487 | ||||||||
\(549\) | 21.6875 | 0.925598 | ||||||||
\(550\) | −6.79225 | −0.289622 | ||||||||
\(551\) | 16.5087 | 0.703292 | ||||||||
\(552\) | 6.52829 | 0.277862 | ||||||||
\(553\) | 4.85103 | 0.206287 | ||||||||
\(554\) | 21.9013 | 0.930496 | ||||||||
\(555\) | 15.0432 | 0.638550 | ||||||||
\(556\) | 13.8129 | 0.585796 | ||||||||
\(557\) | −24.0966 | −1.02100 | −0.510502 | − | 0.859876i | \(-0.670541\pi\) | ||||
−0.510502 | + | 0.859876i | \(0.670541\pi\) | |||||||
\(558\) | −17.8243 | −0.754564 | ||||||||
\(559\) | 0.698382 | 0.0295384 | ||||||||
\(560\) | 2.90281 | 0.122666 | ||||||||
\(561\) | −33.3460 | −1.40787 | ||||||||
\(562\) | −13.3125 | −0.561553 | ||||||||
\(563\) | 0.526606 | 0.0221938 | 0.0110969 | − | 0.999938i | \(-0.496468\pi\) | ||||
0.0110969 | + | 0.999938i | \(0.496468\pi\) | |||||||
\(564\) | −17.0075 | −0.716143 | ||||||||
\(565\) | 12.7140 | 0.534881 | ||||||||
\(566\) | 29.5155 | 1.24063 | ||||||||
\(567\) | 6.58720 | 0.276636 | ||||||||
\(568\) | −7.79301 | −0.326987 | ||||||||
\(569\) | −12.4883 | −0.523536 | −0.261768 | − | 0.965131i | \(-0.584306\pi\) | ||||
−0.261768 | + | 0.965131i | \(0.584306\pi\) | |||||||
\(570\) | −47.9760 | −2.00949 | ||||||||
\(571\) | −24.3382 | −1.01852 | −0.509261 | − | 0.860612i | \(-0.670081\pi\) | ||||
−0.509261 | + | 0.860612i | \(0.670081\pi\) | |||||||
\(572\) | −2.25403 | −0.0942457 | ||||||||
\(573\) | −17.8821 | −0.747035 | ||||||||
\(574\) | 2.58506 | 0.107898 | ||||||||
\(575\) | 8.66788 | 0.361476 | ||||||||
\(576\) | 3.65935 | 0.152473 | ||||||||
\(577\) | 5.25267 | 0.218672 | 0.109336 | − | 0.994005i | \(-0.465128\pi\) | ||||
0.109336 | + | 0.994005i | \(0.465128\pi\) | |||||||
\(578\) | −25.4902 | −1.06025 | ||||||||
\(579\) | 24.6193 | 1.02314 | ||||||||
\(580\) | −7.48242 | −0.310691 | ||||||||
\(581\) | 11.5978 | 0.481159 | ||||||||
\(582\) | 19.6743 | 0.815524 | ||||||||
\(583\) | 9.46257 | 0.391899 | ||||||||
\(584\) | −11.5052 | −0.476089 | ||||||||
\(585\) | 12.0781 | 0.499369 | ||||||||
\(586\) | 9.52720 | 0.393565 | ||||||||
\(587\) | 20.9982 | 0.866689 | 0.433344 | − | 0.901228i | \(-0.357333\pi\) | ||||
0.433344 | + | 0.901228i | \(0.357333\pi\) | |||||||
\(588\) | −2.58057 | −0.106421 | ||||||||
\(589\) | 31.1960 | 1.28541 | ||||||||
\(590\) | −13.9533 | −0.574448 | ||||||||
\(591\) | 19.9763 | 0.821717 | ||||||||
\(592\) | 2.00820 | 0.0825363 | ||||||||
\(593\) | −19.7126 | −0.809499 | −0.404749 | − | 0.914428i | \(-0.632641\pi\) | ||||
−0.404749 | + | 0.914428i | \(0.632641\pi\) | |||||||
\(594\) | 3.37300 | 0.138396 | ||||||||
\(595\) | 18.9219 | 0.775721 | ||||||||
\(596\) | 17.7245 | 0.726024 | ||||||||
\(597\) | 49.6656 | 2.03268 | ||||||||
\(598\) | 2.87647 | 0.117627 | ||||||||
\(599\) | −22.9220 | −0.936566 | −0.468283 | − | 0.883578i | \(-0.655127\pi\) | ||||
−0.468283 | + | 0.883578i | \(0.655127\pi\) | |||||||
\(600\) | 8.84190 | 0.360969 | ||||||||
\(601\) | −25.3592 | −1.03442 | −0.517212 | − | 0.855857i | \(-0.673030\pi\) | ||||
−0.517212 | + | 0.855857i | \(0.673030\pi\) | |||||||
\(602\) | −0.614210 | −0.0250333 | ||||||||
\(603\) | −47.4024 | −1.93037 | ||||||||
\(604\) | −12.8493 | −0.522831 | ||||||||
\(605\) | 20.5236 | 0.834402 | ||||||||
\(606\) | 6.02719 | 0.244838 | ||||||||
\(607\) | 29.1523 | 1.18326 | 0.591628 | − | 0.806211i | \(-0.298486\pi\) | ||||
0.591628 | + | 0.806211i | \(0.298486\pi\) | |||||||
\(608\) | −6.40456 | −0.259739 | ||||||||
\(609\) | 6.65179 | 0.269544 | ||||||||
\(610\) | 17.2038 | 0.696561 | ||||||||
\(611\) | −7.49375 | −0.303165 | ||||||||
\(612\) | 23.8533 | 0.964213 | ||||||||
\(613\) | −2.94461 | −0.118932 | −0.0594658 | − | 0.998230i | \(-0.518940\pi\) | ||||
−0.0594658 | + | 0.998230i | \(0.518940\pi\) | |||||||
\(614\) | −3.69455 | −0.149100 | ||||||||
\(615\) | 19.3645 | 0.780851 | ||||||||
\(616\) | 1.98237 | 0.0798718 | ||||||||
\(617\) | 13.7412 | 0.553202 | 0.276601 | − | 0.960985i | \(-0.410792\pi\) | ||||
0.276601 | + | 0.960985i | \(0.410792\pi\) | |||||||
\(618\) | 47.4081 | 1.90703 | ||||||||
\(619\) | −20.5462 | −0.825821 | −0.412910 | − | 0.910772i | \(-0.635488\pi\) | ||||
−0.412910 | + | 0.910772i | \(0.635488\pi\) | |||||||
\(620\) | −14.1393 | −0.567849 | ||||||||
\(621\) | −4.30444 | −0.172731 | ||||||||
\(622\) | −23.9231 | −0.959229 | ||||||||
\(623\) | −0.899500 | −0.0360377 | ||||||||
\(624\) | 2.93422 | 0.117463 | ||||||||
\(625\) | −30.3919 | −1.21568 | ||||||||
\(626\) | 33.2825 | 1.33024 | ||||||||
\(627\) | −32.7634 | −1.30844 | ||||||||
\(628\) | −3.64473 | −0.145440 | ||||||||
\(629\) | 13.0903 | 0.521946 | ||||||||
\(630\) | −10.6224 | −0.423207 | ||||||||
\(631\) | 0.981310 | 0.0390653 | 0.0195327 | − | 0.999809i | \(-0.493782\pi\) | ||||
0.0195327 | + | 0.999809i | \(0.493782\pi\) | |||||||
\(632\) | 4.85103 | 0.192964 | ||||||||
\(633\) | −21.5060 | −0.854787 | ||||||||
\(634\) | 19.3951 | 0.770278 | ||||||||
\(635\) | 10.0538 | 0.398975 | ||||||||
\(636\) | −12.3180 | −0.488442 | ||||||||
\(637\) | −1.13704 | −0.0450512 | ||||||||
\(638\) | −5.10983 | −0.202300 | ||||||||
\(639\) | 28.5174 | 1.12813 | ||||||||
\(640\) | 2.90281 | 0.114744 | ||||||||
\(641\) | −32.9942 | −1.30319 | −0.651597 | − | 0.758565i | \(-0.725901\pi\) | ||||
−0.651597 | + | 0.758565i | \(0.725901\pi\) | |||||||
\(642\) | −7.45633 | −0.294278 | ||||||||
\(643\) | −16.8176 | −0.663221 | −0.331610 | − | 0.943416i | \(-0.607592\pi\) | ||||
−0.331610 | + | 0.943416i | \(0.607592\pi\) | |||||||
\(644\) | −2.52978 | −0.0996874 | ||||||||
\(645\) | −4.60100 | −0.181164 | ||||||||
\(646\) | −41.7478 | −1.64255 | ||||||||
\(647\) | −18.2813 | −0.718710 | −0.359355 | − | 0.933201i | \(-0.617003\pi\) | ||||
−0.359355 | + | 0.933201i | \(0.617003\pi\) | |||||||
\(648\) | 6.58720 | 0.258770 | ||||||||
\(649\) | −9.52886 | −0.374040 | ||||||||
\(650\) | 3.89588 | 0.152809 | ||||||||
\(651\) | 12.5697 | 0.492646 | ||||||||
\(652\) | −10.5676 | −0.413859 | ||||||||
\(653\) | 20.3973 | 0.798208 | 0.399104 | − | 0.916906i | \(-0.369321\pi\) | ||||
0.399104 | + | 0.916906i | \(0.369321\pi\) | |||||||
\(654\) | −7.00769 | −0.274022 | ||||||||
\(655\) | −20.0797 | −0.784580 | ||||||||
\(656\) | 2.58506 | 0.100930 | ||||||||
\(657\) | 42.1016 | 1.64254 | ||||||||
\(658\) | 6.59057 | 0.256927 | ||||||||
\(659\) | 13.0636 | 0.508885 | 0.254443 | − | 0.967088i | \(-0.418108\pi\) | ||||
0.254443 | + | 0.967088i | \(0.418108\pi\) | |||||||
\(660\) | 14.8497 | 0.578025 | ||||||||
\(661\) | 33.9887 | 1.32201 | 0.661004 | − | 0.750383i | \(-0.270131\pi\) | ||||
0.661004 | + | 0.750383i | \(0.270131\pi\) | |||||||
\(662\) | −27.1421 | −1.05491 | ||||||||
\(663\) | 19.1265 | 0.742814 | ||||||||
\(664\) | 11.5978 | 0.450083 | ||||||||
\(665\) | 18.5912 | 0.720937 | ||||||||
\(666\) | −7.34869 | −0.284756 | ||||||||
\(667\) | 6.52088 | 0.252489 | ||||||||
\(668\) | 15.6309 | 0.604779 | ||||||||
\(669\) | 17.3214 | 0.669683 | ||||||||
\(670\) | −37.6024 | −1.45271 | ||||||||
\(671\) | 11.7487 | 0.453552 | ||||||||
\(672\) | −2.58057 | −0.0995477 | ||||||||
\(673\) | −26.2276 | −1.01100 | −0.505500 | − | 0.862827i | \(-0.668692\pi\) | ||||
−0.505500 | + | 0.862827i | \(0.668692\pi\) | |||||||
\(674\) | 17.3713 | 0.669119 | ||||||||
\(675\) | −5.82992 | −0.224394 | ||||||||
\(676\) | −11.7071 | −0.450275 | ||||||||
\(677\) | 20.3660 | 0.782731 | 0.391365 | − | 0.920235i | \(-0.372003\pi\) | ||||
0.391365 | + | 0.920235i | \(0.372003\pi\) | |||||||
\(678\) | −11.3026 | −0.434074 | ||||||||
\(679\) | −7.62399 | −0.292582 | ||||||||
\(680\) | 18.9219 | 0.725620 | ||||||||
\(681\) | 29.3137 | 1.12330 | ||||||||
\(682\) | −9.65590 | −0.369744 | ||||||||
\(683\) | 16.8941 | 0.646434 | 0.323217 | − | 0.946325i | \(-0.395236\pi\) | ||||
0.323217 | + | 0.946325i | \(0.395236\pi\) | |||||||
\(684\) | 23.4365 | 0.896118 | ||||||||
\(685\) | 27.3503 | 1.04500 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 13.7237 | 0.523593 | ||||||||
\(688\) | −0.614210 | −0.0234165 | ||||||||
\(689\) | −5.42752 | −0.206772 | ||||||||
\(690\) | −18.9504 | −0.721430 | ||||||||
\(691\) | −9.44415 | −0.359272 | −0.179636 | − | 0.983733i | \(-0.557492\pi\) | ||||
−0.179636 | + | 0.983733i | \(0.557492\pi\) | |||||||
\(692\) | −11.8062 | −0.448803 | ||||||||
\(693\) | −7.25417 | −0.275563 | ||||||||
\(694\) | 0.864319 | 0.0328091 | ||||||||
\(695\) | −40.0962 | −1.52094 | ||||||||
\(696\) | 6.65179 | 0.252136 | ||||||||
\(697\) | 16.8506 | 0.638261 | ||||||||
\(698\) | 25.4451 | 0.963112 | ||||||||
\(699\) | −40.6716 | −1.53834 | ||||||||
\(700\) | −3.42633 | −0.129503 | ||||||||
\(701\) | 5.24585 | 0.198133 | 0.0990665 | − | 0.995081i | \(-0.468414\pi\) | ||||
0.0990665 | + | 0.995081i | \(0.468414\pi\) | |||||||
\(702\) | −1.93468 | −0.0730198 | ||||||||
\(703\) | 12.8616 | 0.485084 | ||||||||
\(704\) | 1.98237 | 0.0747132 | ||||||||
\(705\) | 49.3695 | 1.85936 | ||||||||
\(706\) | −15.7488 | −0.592715 | ||||||||
\(707\) | −2.33560 | −0.0878393 | ||||||||
\(708\) | 12.4043 | 0.466183 | ||||||||
\(709\) | −50.6151 | −1.90089 | −0.950445 | − | 0.310893i | \(-0.899372\pi\) | ||||
−0.950445 | + | 0.310893i | \(0.899372\pi\) | |||||||
\(710\) | 22.6217 | 0.848976 | ||||||||
\(711\) | −17.7516 | −0.665739 | ||||||||
\(712\) | −0.899500 | −0.0337102 | ||||||||
\(713\) | 12.3223 | 0.461474 | ||||||||
\(714\) | −16.8213 | −0.629523 | ||||||||
\(715\) | 6.54303 | 0.244696 | ||||||||
\(716\) | 24.2091 | 0.904736 | ||||||||
\(717\) | −44.8877 | −1.67636 | ||||||||
\(718\) | 0.999205 | 0.0372900 | ||||||||
\(719\) | −42.6211 | −1.58950 | −0.794750 | − | 0.606938i | \(-0.792398\pi\) | ||||
−0.794750 | + | 0.606938i | \(0.792398\pi\) | |||||||
\(720\) | −10.6224 | −0.395874 | ||||||||
\(721\) | −18.3712 | −0.684178 | ||||||||
\(722\) | −22.0183 | −0.819438 | ||||||||
\(723\) | −49.4196 | −1.83793 | ||||||||
\(724\) | 7.57652 | 0.281579 | ||||||||
\(725\) | 8.83187 | 0.328007 | ||||||||
\(726\) | −18.2452 | −0.677144 | ||||||||
\(727\) | −8.75765 | −0.324803 | −0.162402 | − | 0.986725i | \(-0.551924\pi\) | ||||
−0.162402 | + | 0.986725i | \(0.551924\pi\) | |||||||
\(728\) | −1.13704 | −0.0421415 | ||||||||
\(729\) | −37.2774 | −1.38065 | ||||||||
\(730\) | 33.3975 | 1.23610 | ||||||||
\(731\) | −4.00370 | −0.148082 | ||||||||
\(732\) | −15.2940 | −0.565282 | ||||||||
\(733\) | 41.3253 | 1.52639 | 0.763193 | − | 0.646171i | \(-0.223631\pi\) | ||||
0.763193 | + | 0.646171i | \(0.223631\pi\) | |||||||
\(734\) | −4.80614 | −0.177398 | ||||||||
\(735\) | 7.49092 | 0.276307 | ||||||||
\(736\) | −2.52978 | −0.0932490 | ||||||||
\(737\) | −25.6791 | −0.945901 | ||||||||
\(738\) | −9.45963 | −0.348214 | ||||||||
\(739\) | −3.24551 | −0.119388 | −0.0596939 | − | 0.998217i | \(-0.519012\pi\) | ||||
−0.0596939 | + | 0.998217i | \(0.519012\pi\) | |||||||
\(740\) | −5.82942 | −0.214294 | ||||||||
\(741\) | 18.7924 | 0.690354 | ||||||||
\(742\) | 4.77337 | 0.175236 | ||||||||
\(743\) | 10.7203 | 0.393290 | 0.196645 | − | 0.980475i | \(-0.436995\pi\) | ||||
0.196645 | + | 0.980475i | \(0.436995\pi\) | |||||||
\(744\) | 12.5697 | 0.460828 | ||||||||
\(745\) | −51.4509 | −1.88502 | ||||||||
\(746\) | −8.96656 | −0.328289 | ||||||||
\(747\) | −42.4405 | −1.55282 | ||||||||
\(748\) | 12.9220 | 0.472473 | ||||||||
\(749\) | 2.88941 | 0.105577 | ||||||||
\(750\) | 11.7882 | 0.430444 | ||||||||
\(751\) | 38.3101 | 1.39795 | 0.698977 | − | 0.715144i | \(-0.253639\pi\) | ||||
0.698977 | + | 0.715144i | \(0.253639\pi\) | |||||||
\(752\) | 6.59057 | 0.240334 | ||||||||
\(753\) | −34.7289 | −1.26559 | ||||||||
\(754\) | 2.93089 | 0.106737 | ||||||||
\(755\) | 37.2992 | 1.35746 | ||||||||
\(756\) | 1.70150 | 0.0618831 | ||||||||
\(757\) | −19.3269 | −0.702448 | −0.351224 | − | 0.936291i | \(-0.614234\pi\) | ||||
−0.351224 | + | 0.936291i | \(0.614234\pi\) | |||||||
\(758\) | 1.64987 | 0.0599260 | ||||||||
\(759\) | −12.9414 | −0.469745 | ||||||||
\(760\) | 18.5912 | 0.674375 | ||||||||
\(761\) | 40.4724 | 1.46712 | 0.733562 | − | 0.679623i | \(-0.237857\pi\) | ||||
0.733562 | + | 0.679623i | \(0.237857\pi\) | |||||||
\(762\) | −8.93776 | −0.323781 | ||||||||
\(763\) | 2.71556 | 0.0983098 | ||||||||
\(764\) | 6.92951 | 0.250701 | ||||||||
\(765\) | −69.2418 | −2.50344 | ||||||||
\(766\) | −20.0532 | −0.724552 | ||||||||
\(767\) | 5.46554 | 0.197349 | ||||||||
\(768\) | −2.58057 | −0.0931184 | ||||||||
\(769\) | −39.0371 | −1.40771 | −0.703857 | − | 0.710342i | \(-0.748540\pi\) | ||||
−0.703857 | + | 0.710342i | \(0.748540\pi\) | |||||||
\(770\) | −5.75444 | −0.207376 | ||||||||
\(771\) | 33.4126 | 1.20333 | ||||||||
\(772\) | −9.54025 | −0.343361 | ||||||||
\(773\) | −1.13850 | −0.0409490 | −0.0204745 | − | 0.999790i | \(-0.506518\pi\) | ||||
−0.0204745 | + | 0.999790i | \(0.506518\pi\) | |||||||
\(774\) | 2.24761 | 0.0807886 | ||||||||
\(775\) | 16.6893 | 0.599499 | ||||||||
\(776\) | −7.62399 | −0.273685 | ||||||||
\(777\) | 5.18229 | 0.185914 | ||||||||
\(778\) | 15.7411 | 0.564344 | ||||||||
\(779\) | 16.5561 | 0.593185 | ||||||||
\(780\) | −8.51749 | −0.304975 | ||||||||
\(781\) | 15.4486 | 0.552794 | ||||||||
\(782\) | −16.4903 | −0.589691 | ||||||||
\(783\) | −4.38587 | −0.156738 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 10.5800 | 0.377615 | ||||||||
\(786\) | 17.8507 | 0.636712 | ||||||||
\(787\) | −33.4257 | −1.19150 | −0.595749 | − | 0.803171i | \(-0.703145\pi\) | ||||
−0.595749 | + | 0.803171i | \(0.703145\pi\) | |||||||
\(788\) | −7.74105 | −0.275764 | ||||||||
\(789\) | 5.09956 | 0.181549 | ||||||||
\(790\) | −14.0817 | −0.501003 | ||||||||
\(791\) | 4.37988 | 0.155731 | ||||||||
\(792\) | −7.25417 | −0.257766 | ||||||||
\(793\) | −6.73877 | −0.239301 | ||||||||
\(794\) | 10.6432 | 0.377713 | ||||||||
\(795\) | 35.7570 | 1.26817 | ||||||||
\(796\) | −19.2459 | −0.682155 | ||||||||
\(797\) | 36.2674 | 1.28466 | 0.642329 | − | 0.766429i | \(-0.277968\pi\) | ||||
0.642329 | + | 0.766429i | \(0.277968\pi\) | |||||||
\(798\) | −16.5274 | −0.585064 | ||||||||
\(799\) | 42.9604 | 1.51983 | ||||||||
\(800\) | −3.42633 | −0.121139 | ||||||||
\(801\) | 3.29159 | 0.116302 | ||||||||
\(802\) | −29.4967 | −1.04157 | ||||||||
\(803\) | 22.8075 | 0.804860 | ||||||||
\(804\) | 33.4281 | 1.17892 | ||||||||
\(805\) | 7.34349 | 0.258824 | ||||||||
\(806\) | 5.53841 | 0.195082 | ||||||||
\(807\) | 11.7411 | 0.413306 | ||||||||
\(808\) | −2.33560 | −0.0821662 | ||||||||
\(809\) | −26.1990 | −0.921109 | −0.460555 | − | 0.887631i | \(-0.652349\pi\) | ||||
−0.460555 | + | 0.887631i | \(0.652349\pi\) | |||||||
\(810\) | −19.1214 | −0.671858 | ||||||||
\(811\) | 12.7871 | 0.449017 | 0.224509 | − | 0.974472i | \(-0.427922\pi\) | ||||
0.224509 | + | 0.974472i | \(0.427922\pi\) | |||||||
\(812\) | −2.57764 | −0.0904575 | ||||||||
\(813\) | −44.4340 | −1.55837 | ||||||||
\(814\) | −3.98098 | −0.139533 | ||||||||
\(815\) | 30.6758 | 1.07453 | ||||||||
\(816\) | −16.8213 | −0.588865 | ||||||||
\(817\) | −3.93374 | −0.137624 | ||||||||
\(818\) | 19.1462 | 0.669433 | ||||||||
\(819\) | 4.16083 | 0.145391 | ||||||||
\(820\) | −7.50394 | −0.262049 | ||||||||
\(821\) | 53.2922 | 1.85991 | 0.929955 | − | 0.367673i | \(-0.119845\pi\) | ||||
0.929955 | + | 0.367673i | \(0.119845\pi\) | |||||||
\(822\) | −24.3141 | −0.848052 | ||||||||
\(823\) | 39.0942 | 1.36274 | 0.681369 | − | 0.731940i | \(-0.261385\pi\) | ||||
0.681369 | + | 0.731940i | \(0.261385\pi\) | |||||||
\(824\) | −18.3712 | −0.639990 | ||||||||
\(825\) | −17.5279 | −0.610242 | ||||||||
\(826\) | −4.80681 | −0.167250 | ||||||||
\(827\) | −0.946616 | −0.0329171 | −0.0164585 | − | 0.999865i | \(-0.505239\pi\) | ||||
−0.0164585 | + | 0.999865i | \(0.505239\pi\) | |||||||
\(828\) | 9.25736 | 0.321716 | ||||||||
\(829\) | −21.0822 | −0.732214 | −0.366107 | − | 0.930573i | \(-0.619310\pi\) | ||||
−0.366107 | + | 0.930573i | \(0.619310\pi\) | |||||||
\(830\) | −33.6664 | −1.16858 | ||||||||
\(831\) | 56.5178 | 1.96058 | ||||||||
\(832\) | −1.13704 | −0.0394198 | ||||||||
\(833\) | 6.51845 | 0.225851 | ||||||||
\(834\) | 35.6451 | 1.23429 | ||||||||
\(835\) | −45.3737 | −1.57022 | ||||||||
\(836\) | 12.6962 | 0.439106 | ||||||||
\(837\) | −8.28786 | −0.286470 | ||||||||
\(838\) | 17.8133 | 0.615349 | ||||||||
\(839\) | −9.55939 | −0.330027 | −0.165013 | − | 0.986291i | \(-0.552767\pi\) | ||||
−0.165013 | + | 0.986291i | \(0.552767\pi\) | |||||||
\(840\) | 7.49092 | 0.258461 | ||||||||
\(841\) | −22.3558 | −0.770888 | ||||||||
\(842\) | −5.94280 | −0.204802 | ||||||||
\(843\) | −34.3538 | −1.18321 | ||||||||
\(844\) | 8.33381 | 0.286862 | ||||||||
\(845\) | 33.9837 | 1.16907 | ||||||||
\(846\) | −24.1172 | −0.829167 | ||||||||
\(847\) | 7.07023 | 0.242936 | ||||||||
\(848\) | 4.77337 | 0.163918 | ||||||||
\(849\) | 76.1668 | 2.61404 | ||||||||
\(850\) | −22.3344 | −0.766064 | ||||||||
\(851\) | 5.08030 | 0.174150 | ||||||||
\(852\) | −20.1104 | −0.688972 | ||||||||
\(853\) | −7.00511 | −0.239850 | −0.119925 | − | 0.992783i | \(-0.538265\pi\) | ||||
−0.119925 | + | 0.992783i | \(0.538265\pi\) | |||||||
\(854\) | 5.92659 | 0.202804 | ||||||||
\(855\) | −68.0319 | −2.32664 | ||||||||
\(856\) | 2.88941 | 0.0987580 | ||||||||
\(857\) | 2.70650 | 0.0924524 | 0.0462262 | − | 0.998931i | \(-0.485281\pi\) | ||||
0.0462262 | + | 0.998931i | \(0.485281\pi\) | |||||||
\(858\) | −5.81669 | −0.198578 | ||||||||
\(859\) | 0.297337 | 0.0101450 | 0.00507250 | − | 0.999987i | \(-0.498385\pi\) | ||||
0.00507250 | + | 0.999987i | \(0.498385\pi\) | |||||||
\(860\) | 1.78294 | 0.0607976 | ||||||||
\(861\) | 6.67093 | 0.227345 | ||||||||
\(862\) | −1.00000 | −0.0340601 | ||||||||
\(863\) | 46.0947 | 1.56908 | 0.784541 | − | 0.620077i | \(-0.212899\pi\) | ||||
0.784541 | + | 0.620077i | \(0.212899\pi\) | |||||||
\(864\) | 1.70150 | 0.0578863 | ||||||||
\(865\) | 34.2711 | 1.16525 | ||||||||
\(866\) | −18.1765 | −0.617663 | ||||||||
\(867\) | −65.7794 | −2.23398 | ||||||||
\(868\) | −4.87090 | −0.165329 | ||||||||
\(869\) | −9.61652 | −0.326218 | ||||||||
\(870\) | −19.3089 | −0.654634 | ||||||||
\(871\) | 14.7290 | 0.499072 | ||||||||
\(872\) | 2.71556 | 0.0919604 | ||||||||
\(873\) | 27.8989 | 0.944234 | ||||||||
\(874\) | −16.2021 | −0.548045 | ||||||||
\(875\) | −4.56806 | −0.154429 | ||||||||
\(876\) | −29.6900 | −1.00313 | ||||||||
\(877\) | −44.4785 | −1.50193 | −0.750966 | − | 0.660341i | \(-0.770412\pi\) | ||||
−0.750966 | + | 0.660341i | \(0.770412\pi\) | |||||||
\(878\) | −17.9837 | −0.606920 | ||||||||
\(879\) | 24.5856 | 0.829253 | ||||||||
\(880\) | −5.75444 | −0.193982 | ||||||||
\(881\) | −29.6437 | −0.998722 | −0.499361 | − | 0.866394i | \(-0.666432\pi\) | ||||
−0.499361 | + | 0.866394i | \(0.666432\pi\) | |||||||
\(882\) | −3.65935 | −0.123217 | ||||||||
\(883\) | −25.0955 | −0.844531 | −0.422266 | − | 0.906472i | \(-0.638765\pi\) | ||||
−0.422266 | + | 0.906472i | \(0.638765\pi\) | |||||||
\(884\) | −7.41175 | −0.249284 | ||||||||
\(885\) | −36.0075 | −1.21038 | ||||||||
\(886\) | 2.28928 | 0.0769097 | ||||||||
\(887\) | −54.5257 | −1.83079 | −0.915397 | − | 0.402553i | \(-0.868123\pi\) | ||||
−0.915397 | + | 0.402553i | \(0.868123\pi\) | |||||||
\(888\) | 5.18229 | 0.173906 | ||||||||
\(889\) | 3.46348 | 0.116161 | ||||||||
\(890\) | 2.61108 | 0.0875237 | ||||||||
\(891\) | −13.0582 | −0.437467 | ||||||||
\(892\) | −6.71223 | −0.224742 | ||||||||
\(893\) | 42.2097 | 1.41249 | ||||||||
\(894\) | 45.7393 | 1.52975 | ||||||||
\(895\) | −70.2745 | −2.34902 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 7.42293 | 0.247844 | ||||||||
\(898\) | −39.6537 | −1.32326 | ||||||||
\(899\) | 12.5554 | 0.418747 | ||||||||
\(900\) | 12.5382 | 0.417939 | ||||||||
\(901\) | 31.1150 | 1.03659 | ||||||||
\(902\) | −5.12453 | −0.170628 | ||||||||
\(903\) | −1.58501 | −0.0527459 | ||||||||
\(904\) | 4.37988 | 0.145673 | ||||||||
\(905\) | −21.9932 | −0.731080 | ||||||||
\(906\) | −33.1586 | −1.10162 | ||||||||
\(907\) | 18.2279 | 0.605246 | 0.302623 | − | 0.953110i | \(-0.402138\pi\) | ||||
0.302623 | + | 0.953110i | \(0.402138\pi\) | |||||||
\(908\) | −11.3594 | −0.376974 | ||||||||
\(909\) | 8.54679 | 0.283479 | ||||||||
\(910\) | 3.30062 | 0.109414 | ||||||||
\(911\) | −22.4477 | −0.743725 | −0.371862 | − | 0.928288i | \(-0.621281\pi\) | ||||
−0.371862 | + | 0.928288i | \(0.621281\pi\) | |||||||
\(912\) | −16.5274 | −0.547277 | ||||||||
\(913\) | −22.9911 | −0.760895 | ||||||||
\(914\) | −14.7836 | −0.488998 | ||||||||
\(915\) | 44.3956 | 1.46767 | ||||||||
\(916\) | −5.31810 | −0.175715 | ||||||||
\(917\) | −6.91733 | −0.228430 | ||||||||
\(918\) | 11.0912 | 0.366063 | ||||||||
\(919\) | −4.93541 | −0.162804 | −0.0814021 | − | 0.996681i | \(-0.525940\pi\) | ||||
−0.0814021 | + | 0.996681i | \(0.525940\pi\) | |||||||
\(920\) | 7.34349 | 0.242108 | ||||||||
\(921\) | −9.53405 | −0.314158 | ||||||||
\(922\) | −7.90304 | −0.260273 | ||||||||
\(923\) | −8.86097 | −0.291662 | ||||||||
\(924\) | 5.11564 | 0.168292 | ||||||||
\(925\) | 6.88075 | 0.226238 | ||||||||
\(926\) | −3.28792 | −0.108048 | ||||||||
\(927\) | 67.2265 | 2.20801 | ||||||||
\(928\) | −2.57764 | −0.0846153 | ||||||||
\(929\) | 8.54064 | 0.280209 | 0.140105 | − | 0.990137i | \(-0.455256\pi\) | ||||
0.140105 | + | 0.990137i | \(0.455256\pi\) | |||||||
\(930\) | −36.4875 | −1.19647 | ||||||||
\(931\) | 6.40456 | 0.209901 | ||||||||
\(932\) | 15.7607 | 0.516258 | ||||||||
\(933\) | −61.7353 | −2.02112 | ||||||||
\(934\) | −5.23293 | −0.171227 | ||||||||
\(935\) | −37.5100 | −1.22671 | ||||||||
\(936\) | 4.16083 | 0.136001 | ||||||||
\(937\) | 53.8206 | 1.75824 | 0.879121 | − | 0.476598i | \(-0.158130\pi\) | ||||
0.879121 | + | 0.476598i | \(0.158130\pi\) | |||||||
\(938\) | −12.9538 | −0.422955 | ||||||||
\(939\) | 85.8879 | 2.80284 | ||||||||
\(940\) | −19.1312 | −0.623992 | ||||||||
\(941\) | −0.412475 | −0.0134463 | −0.00672315 | − | 0.999977i | \(-0.502140\pi\) | ||||
−0.00672315 | + | 0.999977i | \(0.502140\pi\) | |||||||
\(942\) | −9.40548 | −0.306447 | ||||||||
\(943\) | 6.53963 | 0.212960 | ||||||||
\(944\) | −4.80681 | −0.156448 | ||||||||
\(945\) | −4.93915 | −0.160671 | ||||||||
\(946\) | 1.21759 | 0.0395872 | ||||||||
\(947\) | 8.24183 | 0.267823 | 0.133912 | − | 0.990993i | \(-0.457246\pi\) | ||||
0.133912 | + | 0.990993i | \(0.457246\pi\) | |||||||
\(948\) | 12.5184 | 0.406580 | ||||||||
\(949\) | −13.0819 | −0.424656 | ||||||||
\(950\) | −21.9442 | −0.711962 | ||||||||
\(951\) | 50.0505 | 1.62300 | ||||||||
\(952\) | 6.51845 | 0.211264 | ||||||||
\(953\) | 18.6670 | 0.604685 | 0.302342 | − | 0.953199i | \(-0.402231\pi\) | ||||
0.302342 | + | 0.953199i | \(0.402231\pi\) | |||||||
\(954\) | −17.4674 | −0.565530 | ||||||||
\(955\) | −20.1151 | −0.650908 | ||||||||
\(956\) | 17.3945 | 0.562578 | ||||||||
\(957\) | −13.1863 | −0.426252 | ||||||||
\(958\) | −10.8596 | −0.350859 | ||||||||
\(959\) | 9.42199 | 0.304252 | ||||||||
\(960\) | 7.49092 | 0.241768 | ||||||||
\(961\) | −7.27433 | −0.234656 | ||||||||
\(962\) | 2.28340 | 0.0736198 | ||||||||
\(963\) | −10.5734 | −0.340722 | ||||||||
\(964\) | 19.1506 | 0.616800 | ||||||||
\(965\) | 27.6936 | 0.891488 | ||||||||
\(966\) | −6.52829 | −0.210044 | ||||||||
\(967\) | −8.28689 | −0.266488 | −0.133244 | − | 0.991083i | \(-0.542539\pi\) | ||||
−0.133244 | + | 0.991083i | \(0.542539\pi\) | |||||||
\(968\) | 7.07023 | 0.227246 | ||||||||
\(969\) | −107.733 | −3.46089 | ||||||||
\(970\) | 22.1310 | 0.710585 | ||||||||
\(971\) | 34.8723 | 1.11910 | 0.559552 | − | 0.828795i | \(-0.310973\pi\) | ||||
0.559552 | + | 0.828795i | \(0.310973\pi\) | |||||||
\(972\) | 22.1033 | 0.708962 | ||||||||
\(973\) | −13.8129 | −0.442820 | ||||||||
\(974\) | −2.07254 | −0.0664085 | ||||||||
\(975\) | 10.0536 | 0.321973 | ||||||||
\(976\) | 5.92659 | 0.189705 | ||||||||
\(977\) | 25.1110 | 0.803374 | 0.401687 | − | 0.915777i | \(-0.368424\pi\) | ||||
0.401687 | + | 0.915777i | \(0.368424\pi\) | |||||||
\(978\) | −27.2705 | −0.872013 | ||||||||
\(979\) | 1.78314 | 0.0569893 | ||||||||
\(980\) | −2.90281 | −0.0927270 | ||||||||
\(981\) | −9.93718 | −0.317270 | ||||||||
\(982\) | −21.7367 | −0.693645 | ||||||||
\(983\) | 2.05677 | 0.0656008 | 0.0328004 | − | 0.999462i | \(-0.489557\pi\) | ||||
0.0328004 | + | 0.999462i | \(0.489557\pi\) | |||||||
\(984\) | 6.67093 | 0.212661 | ||||||||
\(985\) | 22.4708 | 0.715981 | ||||||||
\(986\) | −16.8022 | −0.535092 | ||||||||
\(987\) | 17.0075 | 0.541353 | ||||||||
\(988\) | −7.28224 | −0.231679 | ||||||||
\(989\) | −1.55382 | −0.0494085 | ||||||||
\(990\) | 21.0575 | 0.669252 | ||||||||
\(991\) | −20.7825 | −0.660176 | −0.330088 | − | 0.943950i | \(-0.607078\pi\) | ||||
−0.330088 | + | 0.943950i | \(0.607078\pi\) | |||||||
\(992\) | −4.87090 | −0.154651 | ||||||||
\(993\) | −70.0421 | −2.22272 | ||||||||
\(994\) | 7.79301 | 0.247179 | ||||||||
\(995\) | 55.8674 | 1.77112 | ||||||||
\(996\) | 29.9290 | 0.948338 | ||||||||
\(997\) | −17.8038 | −0.563852 | −0.281926 | − | 0.959436i | \(-0.590973\pi\) | ||||
−0.281926 | + | 0.959436i | \(0.590973\pi\) | |||||||
\(998\) | −37.8548 | −1.19827 | ||||||||
\(999\) | −3.41695 | −0.108108 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6034.2.a.n.1.3 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.n.1.3 | ✓ | 24 | 1.1 | even | 1 | trivial |