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: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
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 | ||||||||
\(3\) | −0.394534 | −0.227784 | −0.113892 | − | 0.993493i | \(-0.536332\pi\) | ||||
−0.113892 | + | 0.993493i | \(0.536332\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.36123 | 1.95040 | 0.975201 | − | 0.221322i | \(-0.0710373\pi\) | ||||
0.975201 | + | 0.221322i | \(0.0710373\pi\) | |||||||
\(6\) | 0.394534 | 0.161068 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.84434 | −0.948114 | ||||||||
\(10\) | −4.36123 | −1.37914 | ||||||||
\(11\) | −1.35764 | −0.409344 | −0.204672 | − | 0.978831i | \(-0.565613\pi\) | ||||
−0.204672 | + | 0.978831i | \(0.565613\pi\) | |||||||
\(12\) | −0.394534 | −0.113892 | ||||||||
\(13\) | −3.09098 | −0.857284 | −0.428642 | − | 0.903474i | \(-0.641008\pi\) | ||||
−0.428642 | + | 0.903474i | \(0.641008\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −1.72065 | −0.444271 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.52186 | −0.854176 | −0.427088 | − | 0.904210i | \(-0.640460\pi\) | ||||
−0.427088 | + | 0.904210i | \(0.640460\pi\) | |||||||
\(18\) | 2.84434 | 0.670418 | ||||||||
\(19\) | 3.98583 | 0.914413 | 0.457206 | − | 0.889361i | \(-0.348850\pi\) | ||||
0.457206 | + | 0.889361i | \(0.348850\pi\) | |||||||
\(20\) | 4.36123 | 0.975201 | ||||||||
\(21\) | −0.394534 | −0.0860944 | ||||||||
\(22\) | 1.35764 | 0.289450 | ||||||||
\(23\) | −0.903008 | −0.188290 | −0.0941451 | − | 0.995558i | \(-0.530012\pi\) | ||||
−0.0941451 | + | 0.995558i | \(0.530012\pi\) | |||||||
\(24\) | 0.394534 | 0.0805339 | ||||||||
\(25\) | 14.0203 | 2.80407 | ||||||||
\(26\) | 3.09098 | 0.606191 | ||||||||
\(27\) | 2.30579 | 0.443750 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 2.54612 | 0.472803 | 0.236402 | − | 0.971655i | \(-0.424032\pi\) | ||||
0.236402 | + | 0.971655i | \(0.424032\pi\) | |||||||
\(30\) | 1.72065 | 0.314147 | ||||||||
\(31\) | −5.16014 | −0.926789 | −0.463395 | − | 0.886152i | \(-0.653369\pi\) | ||||
−0.463395 | + | 0.886152i | \(0.653369\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.535636 | 0.0932423 | ||||||||
\(34\) | 3.52186 | 0.603993 | ||||||||
\(35\) | 4.36123 | 0.737182 | ||||||||
\(36\) | −2.84434 | −0.474057 | ||||||||
\(37\) | −9.36407 | −1.53944 | −0.769722 | − | 0.638380i | \(-0.779605\pi\) | ||||
−0.769722 | + | 0.638380i | \(0.779605\pi\) | |||||||
\(38\) | −3.98583 | −0.646587 | ||||||||
\(39\) | 1.21950 | 0.195276 | ||||||||
\(40\) | −4.36123 | −0.689571 | ||||||||
\(41\) | −0.259660 | −0.0405521 | −0.0202760 | − | 0.999794i | \(-0.506455\pi\) | ||||
−0.0202760 | + | 0.999794i | \(0.506455\pi\) | |||||||
\(42\) | 0.394534 | 0.0608779 | ||||||||
\(43\) | 7.42347 | 1.13207 | 0.566034 | − | 0.824382i | \(-0.308477\pi\) | ||||
0.566034 | + | 0.824382i | \(0.308477\pi\) | |||||||
\(44\) | −1.35764 | −0.204672 | ||||||||
\(45\) | −12.4048 | −1.84920 | ||||||||
\(46\) | 0.903008 | 0.133141 | ||||||||
\(47\) | −8.45701 | −1.23358 | −0.616791 | − | 0.787127i | \(-0.711568\pi\) | ||||
−0.616791 | + | 0.787127i | \(0.711568\pi\) | |||||||
\(48\) | −0.394534 | −0.0569461 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −14.0203 | −1.98277 | ||||||||
\(51\) | 1.38949 | 0.194568 | ||||||||
\(52\) | −3.09098 | −0.428642 | ||||||||
\(53\) | 14.4498 | 1.98484 | 0.992418 | − | 0.122906i | \(-0.0392213\pi\) | ||||
0.992418 | + | 0.122906i | \(0.0392213\pi\) | |||||||
\(54\) | −2.30579 | −0.313779 | ||||||||
\(55\) | −5.92099 | −0.798386 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −1.57255 | −0.208289 | ||||||||
\(58\) | −2.54612 | −0.334322 | ||||||||
\(59\) | 7.10247 | 0.924663 | 0.462332 | − | 0.886707i | \(-0.347013\pi\) | ||||
0.462332 | + | 0.886707i | \(0.347013\pi\) | |||||||
\(60\) | −1.72065 | −0.222136 | ||||||||
\(61\) | 8.93330 | 1.14379 | 0.571896 | − | 0.820326i | \(-0.306208\pi\) | ||||
0.571896 | + | 0.820326i | \(0.306208\pi\) | |||||||
\(62\) | 5.16014 | 0.655339 | ||||||||
\(63\) | −2.84434 | −0.358354 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −13.4805 | −1.67205 | ||||||||
\(66\) | −0.535636 | −0.0659323 | ||||||||
\(67\) | −8.46286 | −1.03390 | −0.516952 | − | 0.856015i | \(-0.672933\pi\) | ||||
−0.516952 | + | 0.856015i | \(0.672933\pi\) | |||||||
\(68\) | −3.52186 | −0.427088 | ||||||||
\(69\) | 0.356268 | 0.0428896 | ||||||||
\(70\) | −4.36123 | −0.521267 | ||||||||
\(71\) | 3.07426 | 0.364847 | 0.182424 | − | 0.983220i | \(-0.441606\pi\) | ||||
0.182424 | + | 0.983220i | \(0.441606\pi\) | |||||||
\(72\) | 2.84434 | 0.335209 | ||||||||
\(73\) | 7.04932 | 0.825061 | 0.412530 | − | 0.910944i | \(-0.364645\pi\) | ||||
0.412530 | + | 0.910944i | \(0.364645\pi\) | |||||||
\(74\) | 9.36407 | 1.08855 | ||||||||
\(75\) | −5.53150 | −0.638722 | ||||||||
\(76\) | 3.98583 | 0.457206 | ||||||||
\(77\) | −1.35764 | −0.154718 | ||||||||
\(78\) | −1.21950 | −0.138081 | ||||||||
\(79\) | 10.4298 | 1.17344 | 0.586722 | − | 0.809788i | \(-0.300418\pi\) | ||||
0.586722 | + | 0.809788i | \(0.300418\pi\) | |||||||
\(80\) | 4.36123 | 0.487600 | ||||||||
\(81\) | 7.62331 | 0.847035 | ||||||||
\(82\) | 0.259660 | 0.0286747 | ||||||||
\(83\) | 5.97823 | 0.656196 | 0.328098 | − | 0.944644i | \(-0.393592\pi\) | ||||
0.328098 | + | 0.944644i | \(0.393592\pi\) | |||||||
\(84\) | −0.394534 | −0.0430472 | ||||||||
\(85\) | −15.3596 | −1.66599 | ||||||||
\(86\) | −7.42347 | −0.800493 | ||||||||
\(87\) | −1.00453 | −0.107697 | ||||||||
\(88\) | 1.35764 | 0.144725 | ||||||||
\(89\) | 16.5792 | 1.75739 | 0.878697 | − | 0.477380i | \(-0.158413\pi\) | ||||
0.878697 | + | 0.477380i | \(0.158413\pi\) | |||||||
\(90\) | 12.4048 | 1.30758 | ||||||||
\(91\) | −3.09098 | −0.324023 | ||||||||
\(92\) | −0.903008 | −0.0941451 | ||||||||
\(93\) | 2.03585 | 0.211108 | ||||||||
\(94\) | 8.45701 | 0.872274 | ||||||||
\(95\) | 17.3831 | 1.78347 | ||||||||
\(96\) | 0.394534 | 0.0402670 | ||||||||
\(97\) | −7.70375 | −0.782198 | −0.391099 | − | 0.920349i | \(-0.627905\pi\) | ||||
−0.391099 | + | 0.920349i | \(0.627905\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 3.86160 | 0.388105 | ||||||||
\(100\) | 14.0203 | 1.40203 | ||||||||
\(101\) | −16.4046 | −1.63232 | −0.816161 | − | 0.577824i | \(-0.803902\pi\) | ||||
−0.816161 | + | 0.577824i | \(0.803902\pi\) | |||||||
\(102\) | −1.38949 | −0.137580 | ||||||||
\(103\) | 10.8336 | 1.06746 | 0.533731 | − | 0.845654i | \(-0.320789\pi\) | ||||
0.533731 | + | 0.845654i | \(0.320789\pi\) | |||||||
\(104\) | 3.09098 | 0.303096 | ||||||||
\(105\) | −1.72065 | −0.167919 | ||||||||
\(106\) | −14.4498 | −1.40349 | ||||||||
\(107\) | 17.4950 | 1.69130 | 0.845651 | − | 0.533736i | \(-0.179212\pi\) | ||||
0.845651 | + | 0.533736i | \(0.179212\pi\) | |||||||
\(108\) | 2.30579 | 0.221875 | ||||||||
\(109\) | 8.89206 | 0.851705 | 0.425853 | − | 0.904793i | \(-0.359974\pi\) | ||||
0.425853 | + | 0.904793i | \(0.359974\pi\) | |||||||
\(110\) | 5.92099 | 0.564544 | ||||||||
\(111\) | 3.69445 | 0.350661 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 7.02869 | 0.661203 | 0.330602 | − | 0.943770i | \(-0.392748\pi\) | ||||
0.330602 | + | 0.943770i | \(0.392748\pi\) | |||||||
\(114\) | 1.57255 | 0.147283 | ||||||||
\(115\) | −3.93823 | −0.367241 | ||||||||
\(116\) | 2.54612 | 0.236402 | ||||||||
\(117\) | 8.79181 | 0.812803 | ||||||||
\(118\) | −7.10247 | −0.653836 | ||||||||
\(119\) | −3.52186 | −0.322848 | ||||||||
\(120\) | 1.72065 | 0.157074 | ||||||||
\(121\) | −9.15681 | −0.832437 | ||||||||
\(122\) | −8.93330 | −0.808783 | ||||||||
\(123\) | 0.102445 | 0.00923713 | ||||||||
\(124\) | −5.16014 | −0.463395 | ||||||||
\(125\) | 39.3397 | 3.51865 | ||||||||
\(126\) | 2.84434 | 0.253394 | ||||||||
\(127\) | 20.9612 | 1.86001 | 0.930003 | − | 0.367552i | \(-0.119804\pi\) | ||||
0.930003 | + | 0.367552i | \(0.119804\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −2.92881 | −0.257867 | ||||||||
\(130\) | 13.4805 | 1.18232 | ||||||||
\(131\) | 16.5111 | 1.44258 | 0.721290 | − | 0.692633i | \(-0.243549\pi\) | ||||
0.721290 | + | 0.692633i | \(0.243549\pi\) | |||||||
\(132\) | 0.535636 | 0.0466211 | ||||||||
\(133\) | 3.98583 | 0.345615 | ||||||||
\(134\) | 8.46286 | 0.731080 | ||||||||
\(135\) | 10.0561 | 0.865491 | ||||||||
\(136\) | 3.52186 | 0.301997 | ||||||||
\(137\) | −1.63908 | −0.140036 | −0.0700179 | − | 0.997546i | \(-0.522306\pi\) | ||||
−0.0700179 | + | 0.997546i | \(0.522306\pi\) | |||||||
\(138\) | −0.356268 | −0.0303275 | ||||||||
\(139\) | −14.4616 | −1.22662 | −0.613310 | − | 0.789843i | \(-0.710162\pi\) | ||||
−0.613310 | + | 0.789843i | \(0.710162\pi\) | |||||||
\(140\) | 4.36123 | 0.368591 | ||||||||
\(141\) | 3.33658 | 0.280991 | ||||||||
\(142\) | −3.07426 | −0.257986 | ||||||||
\(143\) | 4.19645 | 0.350924 | ||||||||
\(144\) | −2.84434 | −0.237029 | ||||||||
\(145\) | 11.1042 | 0.922156 | ||||||||
\(146\) | −7.04932 | −0.583406 | ||||||||
\(147\) | −0.394534 | −0.0325406 | ||||||||
\(148\) | −9.36407 | −0.769722 | ||||||||
\(149\) | 23.3780 | 1.91520 | 0.957601 | − | 0.288097i | \(-0.0930225\pi\) | ||||
0.957601 | + | 0.288097i | \(0.0930225\pi\) | |||||||
\(150\) | 5.53150 | 0.451645 | ||||||||
\(151\) | 5.96165 | 0.485152 | 0.242576 | − | 0.970132i | \(-0.422008\pi\) | ||||
0.242576 | + | 0.970132i | \(0.422008\pi\) | |||||||
\(152\) | −3.98583 | −0.323294 | ||||||||
\(153\) | 10.0174 | 0.809856 | ||||||||
\(154\) | 1.35764 | 0.109402 | ||||||||
\(155\) | −22.5046 | −1.80761 | ||||||||
\(156\) | 1.21950 | 0.0976380 | ||||||||
\(157\) | 19.5839 | 1.56297 | 0.781483 | − | 0.623926i | \(-0.214463\pi\) | ||||
0.781483 | + | 0.623926i | \(0.214463\pi\) | |||||||
\(158\) | −10.4298 | −0.829750 | ||||||||
\(159\) | −5.70095 | −0.452115 | ||||||||
\(160\) | −4.36123 | −0.344786 | ||||||||
\(161\) | −0.903008 | −0.0711670 | ||||||||
\(162\) | −7.62331 | −0.598944 | ||||||||
\(163\) | 3.94704 | 0.309156 | 0.154578 | − | 0.987981i | \(-0.450598\pi\) | ||||
0.154578 | + | 0.987981i | \(0.450598\pi\) | |||||||
\(164\) | −0.259660 | −0.0202760 | ||||||||
\(165\) | 2.33603 | 0.181860 | ||||||||
\(166\) | −5.97823 | −0.464001 | ||||||||
\(167\) | −17.9985 | −1.39277 | −0.696384 | − | 0.717670i | \(-0.745209\pi\) | ||||
−0.696384 | + | 0.717670i | \(0.745209\pi\) | |||||||
\(168\) | 0.394534 | 0.0304390 | ||||||||
\(169\) | −3.44584 | −0.265064 | ||||||||
\(170\) | 15.3596 | 1.17803 | ||||||||
\(171\) | −11.3371 | −0.866968 | ||||||||
\(172\) | 7.42347 | 0.566034 | ||||||||
\(173\) | −15.2602 | −1.16021 | −0.580105 | − | 0.814542i | \(-0.696988\pi\) | ||||
−0.580105 | + | 0.814542i | \(0.696988\pi\) | |||||||
\(174\) | 1.00453 | 0.0761534 | ||||||||
\(175\) | 14.0203 | 1.05984 | ||||||||
\(176\) | −1.35764 | −0.102336 | ||||||||
\(177\) | −2.80217 | −0.210624 | ||||||||
\(178\) | −16.5792 | −1.24267 | ||||||||
\(179\) | 23.3598 | 1.74599 | 0.872997 | − | 0.487726i | \(-0.162173\pi\) | ||||
0.872997 | + | 0.487726i | \(0.162173\pi\) | |||||||
\(180\) | −12.4048 | −0.924602 | ||||||||
\(181\) | −3.89088 | −0.289207 | −0.144603 | − | 0.989490i | \(-0.546191\pi\) | ||||
−0.144603 | + | 0.989490i | \(0.546191\pi\) | |||||||
\(182\) | 3.09098 | 0.229119 | ||||||||
\(183\) | −3.52449 | −0.260538 | ||||||||
\(184\) | 0.903008 | 0.0665706 | ||||||||
\(185\) | −40.8389 | −3.00253 | ||||||||
\(186\) | −2.03585 | −0.149276 | ||||||||
\(187\) | 4.78142 | 0.349652 | ||||||||
\(188\) | −8.45701 | −0.616791 | ||||||||
\(189\) | 2.30579 | 0.167722 | ||||||||
\(190\) | −17.3831 | −1.26110 | ||||||||
\(191\) | −6.48366 | −0.469141 | −0.234571 | − | 0.972099i | \(-0.575368\pi\) | ||||
−0.234571 | + | 0.972099i | \(0.575368\pi\) | |||||||
\(192\) | −0.394534 | −0.0284731 | ||||||||
\(193\) | −24.9775 | −1.79792 | −0.898962 | − | 0.438028i | \(-0.855677\pi\) | ||||
−0.898962 | + | 0.438028i | \(0.855677\pi\) | |||||||
\(194\) | 7.70375 | 0.553097 | ||||||||
\(195\) | 5.31851 | 0.380866 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −6.06704 | −0.432259 | −0.216129 | − | 0.976365i | \(-0.569343\pi\) | ||||
−0.216129 | + | 0.976365i | \(0.569343\pi\) | |||||||
\(198\) | −3.86160 | −0.274432 | ||||||||
\(199\) | 16.3363 | 1.15805 | 0.579025 | − | 0.815310i | \(-0.303434\pi\) | ||||
0.579025 | + | 0.815310i | \(0.303434\pi\) | |||||||
\(200\) | −14.0203 | −0.991387 | ||||||||
\(201\) | 3.33889 | 0.235507 | ||||||||
\(202\) | 16.4046 | 1.15423 | ||||||||
\(203\) | 2.54612 | 0.178703 | ||||||||
\(204\) | 1.38949 | 0.0972839 | ||||||||
\(205\) | −1.13244 | −0.0790929 | ||||||||
\(206\) | −10.8336 | −0.754810 | ||||||||
\(207\) | 2.56846 | 0.178521 | ||||||||
\(208\) | −3.09098 | −0.214321 | ||||||||
\(209\) | −5.41133 | −0.374310 | ||||||||
\(210\) | 1.72065 | 0.118736 | ||||||||
\(211\) | 11.3837 | 0.783683 | 0.391842 | − | 0.920033i | \(-0.371838\pi\) | ||||
0.391842 | + | 0.920033i | \(0.371838\pi\) | |||||||
\(212\) | 14.4498 | 0.992418 | ||||||||
\(213\) | −1.21290 | −0.0831065 | ||||||||
\(214\) | −17.4950 | −1.19593 | ||||||||
\(215\) | 32.3754 | 2.20799 | ||||||||
\(216\) | −2.30579 | −0.156889 | ||||||||
\(217\) | −5.16014 | −0.350293 | ||||||||
\(218\) | −8.89206 | −0.602246 | ||||||||
\(219\) | −2.78120 | −0.187936 | ||||||||
\(220\) | −5.92099 | −0.399193 | ||||||||
\(221\) | 10.8860 | 0.732271 | ||||||||
\(222\) | −3.69445 | −0.247955 | ||||||||
\(223\) | −5.11012 | −0.342199 | −0.171100 | − | 0.985254i | \(-0.554732\pi\) | ||||
−0.171100 | + | 0.985254i | \(0.554732\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −39.8786 | −2.65857 | ||||||||
\(226\) | −7.02869 | −0.467541 | ||||||||
\(227\) | 2.63322 | 0.174773 | 0.0873864 | − | 0.996174i | \(-0.472149\pi\) | ||||
0.0873864 | + | 0.996174i | \(0.472149\pi\) | |||||||
\(228\) | −1.57255 | −0.104144 | ||||||||
\(229\) | 18.2735 | 1.20755 | 0.603773 | − | 0.797156i | \(-0.293663\pi\) | ||||
0.603773 | + | 0.797156i | \(0.293663\pi\) | |||||||
\(230\) | 3.93823 | 0.259679 | ||||||||
\(231\) | 0.535636 | 0.0352423 | ||||||||
\(232\) | −2.54612 | −0.167161 | ||||||||
\(233\) | −18.5926 | −1.21804 | −0.609022 | − | 0.793154i | \(-0.708438\pi\) | ||||
−0.609022 | + | 0.793154i | \(0.708438\pi\) | |||||||
\(234\) | −8.79181 | −0.574739 | ||||||||
\(235\) | −36.8830 | −2.40598 | ||||||||
\(236\) | 7.10247 | 0.462332 | ||||||||
\(237\) | −4.11491 | −0.267292 | ||||||||
\(238\) | 3.52186 | 0.228288 | ||||||||
\(239\) | −17.6002 | −1.13846 | −0.569232 | − | 0.822177i | \(-0.692759\pi\) | ||||
−0.569232 | + | 0.822177i | \(0.692759\pi\) | |||||||
\(240\) | −1.72065 | −0.111068 | ||||||||
\(241\) | 14.6839 | 0.945874 | 0.472937 | − | 0.881096i | \(-0.343194\pi\) | ||||
0.472937 | + | 0.881096i | \(0.343194\pi\) | |||||||
\(242\) | 9.15681 | 0.588622 | ||||||||
\(243\) | −9.92504 | −0.636691 | ||||||||
\(244\) | 8.93330 | 0.571896 | ||||||||
\(245\) | 4.36123 | 0.278629 | ||||||||
\(246\) | −0.102445 | −0.00653164 | ||||||||
\(247\) | −12.3201 | −0.783911 | ||||||||
\(248\) | 5.16014 | 0.327669 | ||||||||
\(249\) | −2.35862 | −0.149471 | ||||||||
\(250\) | −39.3397 | −2.48806 | ||||||||
\(251\) | −20.5652 | −1.29807 | −0.649033 | − | 0.760761i | \(-0.724826\pi\) | ||||
−0.649033 | + | 0.760761i | \(0.724826\pi\) | |||||||
\(252\) | −2.84434 | −0.179177 | ||||||||
\(253\) | 1.22596 | 0.0770755 | ||||||||
\(254\) | −20.9612 | −1.31522 | ||||||||
\(255\) | 6.05990 | 0.379485 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.0028 | −0.686334 | −0.343167 | − | 0.939274i | \(-0.611500\pi\) | ||||
−0.343167 | + | 0.939274i | \(0.611500\pi\) | |||||||
\(258\) | 2.92881 | 0.182340 | ||||||||
\(259\) | −9.36407 | −0.581855 | ||||||||
\(260\) | −13.4805 | −0.836024 | ||||||||
\(261\) | −7.24205 | −0.448271 | ||||||||
\(262\) | −16.5111 | −1.02006 | ||||||||
\(263\) | 0.890541 | 0.0549131 | 0.0274566 | − | 0.999623i | \(-0.491259\pi\) | ||||
0.0274566 | + | 0.999623i | \(0.491259\pi\) | |||||||
\(264\) | −0.535636 | −0.0329661 | ||||||||
\(265\) | 63.0190 | 3.87123 | ||||||||
\(266\) | −3.98583 | −0.244387 | ||||||||
\(267\) | −6.54107 | −0.400307 | ||||||||
\(268\) | −8.46286 | −0.516952 | ||||||||
\(269\) | −8.01173 | −0.488484 | −0.244242 | − | 0.969714i | \(-0.578539\pi\) | ||||
−0.244242 | + | 0.969714i | \(0.578539\pi\) | |||||||
\(270\) | −10.0561 | −0.611994 | ||||||||
\(271\) | −4.76535 | −0.289475 | −0.144737 | − | 0.989470i | \(-0.546234\pi\) | ||||
−0.144737 | + | 0.989470i | \(0.546234\pi\) | |||||||
\(272\) | −3.52186 | −0.213544 | ||||||||
\(273\) | 1.21950 | 0.0738074 | ||||||||
\(274\) | 1.63908 | 0.0990203 | ||||||||
\(275\) | −19.0346 | −1.14783 | ||||||||
\(276\) | 0.356268 | 0.0214448 | ||||||||
\(277\) | −20.6479 | −1.24061 | −0.620305 | − | 0.784360i | \(-0.712991\pi\) | ||||
−0.620305 | + | 0.784360i | \(0.712991\pi\) | |||||||
\(278\) | 14.4616 | 0.867351 | ||||||||
\(279\) | 14.6772 | 0.878702 | ||||||||
\(280\) | −4.36123 | −0.260633 | ||||||||
\(281\) | −27.4714 | −1.63880 | −0.819402 | − | 0.573219i | \(-0.805694\pi\) | ||||
−0.819402 | + | 0.573219i | \(0.805694\pi\) | |||||||
\(282\) | −3.33658 | −0.198690 | ||||||||
\(283\) | 26.4442 | 1.57195 | 0.785973 | − | 0.618261i | \(-0.212162\pi\) | ||||
0.785973 | + | 0.618261i | \(0.212162\pi\) | |||||||
\(284\) | 3.07426 | 0.182424 | ||||||||
\(285\) | −6.85824 | −0.406247 | ||||||||
\(286\) | −4.19645 | −0.248141 | ||||||||
\(287\) | −0.259660 | −0.0153273 | ||||||||
\(288\) | 2.84434 | 0.167605 | ||||||||
\(289\) | −4.59653 | −0.270384 | ||||||||
\(290\) | −11.1042 | −0.652063 | ||||||||
\(291\) | 3.03939 | 0.178172 | ||||||||
\(292\) | 7.04932 | 0.412530 | ||||||||
\(293\) | −6.05329 | −0.353637 | −0.176818 | − | 0.984243i | \(-0.556581\pi\) | ||||
−0.176818 | + | 0.984243i | \(0.556581\pi\) | |||||||
\(294\) | 0.394534 | 0.0230097 | ||||||||
\(295\) | 30.9755 | 1.80346 | ||||||||
\(296\) | 9.36407 | 0.544275 | ||||||||
\(297\) | −3.13044 | −0.181647 | ||||||||
\(298\) | −23.3780 | −1.35425 | ||||||||
\(299\) | 2.79118 | 0.161418 | ||||||||
\(300\) | −5.53150 | −0.319361 | ||||||||
\(301\) | 7.42347 | 0.427882 | ||||||||
\(302\) | −5.96165 | −0.343054 | ||||||||
\(303\) | 6.47219 | 0.371818 | ||||||||
\(304\) | 3.98583 | 0.228603 | ||||||||
\(305\) | 38.9602 | 2.23085 | ||||||||
\(306\) | −10.0174 | −0.572655 | ||||||||
\(307\) | 14.3662 | 0.819924 | 0.409962 | − | 0.912103i | \(-0.365542\pi\) | ||||
0.409962 | + | 0.912103i | \(0.365542\pi\) | |||||||
\(308\) | −1.35764 | −0.0773588 | ||||||||
\(309\) | −4.27421 | −0.243151 | ||||||||
\(310\) | 22.5046 | 1.27817 | ||||||||
\(311\) | 5.12859 | 0.290816 | 0.145408 | − | 0.989372i | \(-0.453551\pi\) | ||||
0.145408 | + | 0.989372i | \(0.453551\pi\) | |||||||
\(312\) | −1.21950 | −0.0690405 | ||||||||
\(313\) | −1.99777 | −0.112920 | −0.0564602 | − | 0.998405i | \(-0.517981\pi\) | ||||
−0.0564602 | + | 0.998405i | \(0.517981\pi\) | |||||||
\(314\) | −19.5839 | −1.10518 | ||||||||
\(315\) | −12.4048 | −0.698933 | ||||||||
\(316\) | 10.4298 | 0.586722 | ||||||||
\(317\) | 31.6073 | 1.77524 | 0.887622 | − | 0.460573i | \(-0.152356\pi\) | ||||
0.887622 | + | 0.460573i | \(0.152356\pi\) | |||||||
\(318\) | 5.70095 | 0.319693 | ||||||||
\(319\) | −3.45672 | −0.193539 | ||||||||
\(320\) | 4.36123 | 0.243800 | ||||||||
\(321\) | −6.90236 | −0.385252 | ||||||||
\(322\) | 0.903008 | 0.0503227 | ||||||||
\(323\) | −14.0375 | −0.781069 | ||||||||
\(324\) | 7.62331 | 0.423517 | ||||||||
\(325\) | −43.3366 | −2.40388 | ||||||||
\(326\) | −3.94704 | −0.218606 | ||||||||
\(327\) | −3.50822 | −0.194005 | ||||||||
\(328\) | 0.259660 | 0.0143373 | ||||||||
\(329\) | −8.45701 | −0.466250 | ||||||||
\(330\) | −2.33603 | −0.128594 | ||||||||
\(331\) | −3.66999 | −0.201721 | −0.100861 | − | 0.994901i | \(-0.532160\pi\) | ||||
−0.100861 | + | 0.994901i | \(0.532160\pi\) | |||||||
\(332\) | 5.97823 | 0.328098 | ||||||||
\(333\) | 26.6346 | 1.45957 | ||||||||
\(334\) | 17.9985 | 0.984835 | ||||||||
\(335\) | −36.9085 | −2.01653 | ||||||||
\(336\) | −0.394534 | −0.0215236 | ||||||||
\(337\) | 3.64064 | 0.198318 | 0.0991592 | − | 0.995072i | \(-0.468385\pi\) | ||||
0.0991592 | + | 0.995072i | \(0.468385\pi\) | |||||||
\(338\) | 3.44584 | 0.187429 | ||||||||
\(339\) | −2.77306 | −0.150612 | ||||||||
\(340\) | −15.3596 | −0.832993 | ||||||||
\(341\) | 7.00563 | 0.379376 | ||||||||
\(342\) | 11.3371 | 0.613039 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −7.42347 | −0.400247 | ||||||||
\(345\) | 1.55376 | 0.0836519 | ||||||||
\(346\) | 15.2602 | 0.820392 | ||||||||
\(347\) | −20.9412 | −1.12418 | −0.562091 | − | 0.827075i | \(-0.690003\pi\) | ||||
−0.562091 | + | 0.827075i | \(0.690003\pi\) | |||||||
\(348\) | −1.00453 | −0.0538486 | ||||||||
\(349\) | 17.5132 | 0.937460 | 0.468730 | − | 0.883341i | \(-0.344712\pi\) | ||||
0.468730 | + | 0.883341i | \(0.344712\pi\) | |||||||
\(350\) | −14.0203 | −0.749418 | ||||||||
\(351\) | −7.12716 | −0.380420 | ||||||||
\(352\) | 1.35764 | 0.0723626 | ||||||||
\(353\) | 18.2425 | 0.970951 | 0.485475 | − | 0.874250i | \(-0.338647\pi\) | ||||
0.485475 | + | 0.874250i | \(0.338647\pi\) | |||||||
\(354\) | 2.80217 | 0.148934 | ||||||||
\(355\) | 13.4075 | 0.711599 | ||||||||
\(356\) | 16.5792 | 0.878697 | ||||||||
\(357\) | 1.38949 | 0.0735397 | ||||||||
\(358\) | −23.3598 | −1.23460 | ||||||||
\(359\) | 25.9880 | 1.37159 | 0.685796 | − | 0.727793i | \(-0.259454\pi\) | ||||
0.685796 | + | 0.727793i | \(0.259454\pi\) | |||||||
\(360\) | 12.4048 | 0.653792 | ||||||||
\(361\) | −3.11314 | −0.163850 | ||||||||
\(362\) | 3.89088 | 0.204500 | ||||||||
\(363\) | 3.61267 | 0.189616 | ||||||||
\(364\) | −3.09098 | −0.162011 | ||||||||
\(365\) | 30.7437 | 1.60920 | ||||||||
\(366\) | 3.52449 | 0.184228 | ||||||||
\(367\) | 16.2164 | 0.846491 | 0.423246 | − | 0.906015i | \(-0.360891\pi\) | ||||
0.423246 | + | 0.906015i | \(0.360891\pi\) | |||||||
\(368\) | −0.903008 | −0.0470725 | ||||||||
\(369\) | 0.738562 | 0.0384480 | ||||||||
\(370\) | 40.8389 | 2.12311 | ||||||||
\(371\) | 14.4498 | 0.750198 | ||||||||
\(372\) | 2.03585 | 0.105554 | ||||||||
\(373\) | −26.3843 | −1.36613 | −0.683063 | − | 0.730359i | \(-0.739353\pi\) | ||||
−0.683063 | + | 0.730359i | \(0.739353\pi\) | |||||||
\(374\) | −4.78142 | −0.247241 | ||||||||
\(375\) | −15.5209 | −0.801494 | ||||||||
\(376\) | 8.45701 | 0.436137 | ||||||||
\(377\) | −7.87002 | −0.405327 | ||||||||
\(378\) | −2.30579 | −0.118597 | ||||||||
\(379\) | −12.7881 | −0.656880 | −0.328440 | − | 0.944525i | \(-0.606523\pi\) | ||||
−0.328440 | + | 0.944525i | \(0.606523\pi\) | |||||||
\(380\) | 17.3831 | 0.891736 | ||||||||
\(381\) | −8.26991 | −0.423680 | ||||||||
\(382\) | 6.48366 | 0.331733 | ||||||||
\(383\) | −8.81531 | −0.450441 | −0.225221 | − | 0.974308i | \(-0.572310\pi\) | ||||
−0.225221 | + | 0.974308i | \(0.572310\pi\) | |||||||
\(384\) | 0.394534 | 0.0201335 | ||||||||
\(385\) | −5.92099 | −0.301762 | ||||||||
\(386\) | 24.9775 | 1.27132 | ||||||||
\(387\) | −21.1149 | −1.07333 | ||||||||
\(388\) | −7.70375 | −0.391099 | ||||||||
\(389\) | −15.9743 | −0.809928 | −0.404964 | − | 0.914333i | \(-0.632716\pi\) | ||||
−0.404964 | + | 0.914333i | \(0.632716\pi\) | |||||||
\(390\) | −5.31851 | −0.269313 | ||||||||
\(391\) | 3.18026 | 0.160833 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −6.51419 | −0.328597 | ||||||||
\(394\) | 6.06704 | 0.305653 | ||||||||
\(395\) | 45.4868 | 2.28869 | ||||||||
\(396\) | 3.86160 | 0.194053 | ||||||||
\(397\) | −30.9786 | −1.55477 | −0.777386 | − | 0.629024i | \(-0.783455\pi\) | ||||
−0.777386 | + | 0.629024i | \(0.783455\pi\) | |||||||
\(398\) | −16.3363 | −0.818864 | ||||||||
\(399\) | −1.57255 | −0.0787258 | ||||||||
\(400\) | 14.0203 | 0.701016 | ||||||||
\(401\) | −4.67504 | −0.233460 | −0.116730 | − | 0.993164i | \(-0.537241\pi\) | ||||
−0.116730 | + | 0.993164i | \(0.537241\pi\) | |||||||
\(402\) | −3.33889 | −0.166529 | ||||||||
\(403\) | 15.9499 | 0.794521 | ||||||||
\(404\) | −16.4046 | −0.816161 | ||||||||
\(405\) | 33.2470 | 1.65206 | ||||||||
\(406\) | −2.54612 | −0.126362 | ||||||||
\(407\) | 12.7131 | 0.630163 | ||||||||
\(408\) | −1.38949 | −0.0687901 | ||||||||
\(409\) | −15.6899 | −0.775813 | −0.387907 | − | 0.921699i | \(-0.626802\pi\) | ||||
−0.387907 | + | 0.921699i | \(0.626802\pi\) | |||||||
\(410\) | 1.13244 | 0.0559271 | ||||||||
\(411\) | 0.646672 | 0.0318980 | ||||||||
\(412\) | 10.8336 | 0.533731 | ||||||||
\(413\) | 7.10247 | 0.349490 | ||||||||
\(414\) | −2.56846 | −0.126233 | ||||||||
\(415\) | 26.0724 | 1.27985 | ||||||||
\(416\) | 3.09098 | 0.151548 | ||||||||
\(417\) | 5.70561 | 0.279405 | ||||||||
\(418\) | 5.41133 | 0.264677 | ||||||||
\(419\) | −17.6854 | −0.863987 | −0.431993 | − | 0.901877i | \(-0.642190\pi\) | ||||
−0.431993 | + | 0.901877i | \(0.642190\pi\) | |||||||
\(420\) | −1.72065 | −0.0839593 | ||||||||
\(421\) | 24.2089 | 1.17987 | 0.589935 | − | 0.807451i | \(-0.299153\pi\) | ||||
0.589935 | + | 0.807451i | \(0.299153\pi\) | |||||||
\(422\) | −11.3837 | −0.554148 | ||||||||
\(423\) | 24.0546 | 1.16958 | ||||||||
\(424\) | −14.4498 | −0.701746 | ||||||||
\(425\) | −49.3776 | −2.39516 | ||||||||
\(426\) | 1.21290 | 0.0587652 | ||||||||
\(427\) | 8.93330 | 0.432313 | ||||||||
\(428\) | 17.4950 | 0.845651 | ||||||||
\(429\) | −1.65564 | −0.0799351 | ||||||||
\(430\) | −32.3754 | −1.56128 | ||||||||
\(431\) | −1.00000 | −0.0481683 | ||||||||
\(432\) | 2.30579 | 0.110938 | ||||||||
\(433\) | −15.1216 | −0.726698 | −0.363349 | − | 0.931653i | \(-0.618367\pi\) | ||||
−0.363349 | + | 0.931653i | \(0.618367\pi\) | |||||||
\(434\) | 5.16014 | 0.247695 | ||||||||
\(435\) | −4.38100 | −0.210053 | ||||||||
\(436\) | 8.89206 | 0.425853 | ||||||||
\(437\) | −3.59924 | −0.172175 | ||||||||
\(438\) | 2.78120 | 0.132891 | ||||||||
\(439\) | −9.71123 | −0.463492 | −0.231746 | − | 0.972776i | \(-0.574444\pi\) | ||||
−0.231746 | + | 0.972776i | \(0.574444\pi\) | |||||||
\(440\) | 5.92099 | 0.282272 | ||||||||
\(441\) | −2.84434 | −0.135445 | ||||||||
\(442\) | −10.8860 | −0.517794 | ||||||||
\(443\) | 18.4989 | 0.878908 | 0.439454 | − | 0.898265i | \(-0.355172\pi\) | ||||
0.439454 | + | 0.898265i | \(0.355172\pi\) | |||||||
\(444\) | 3.69445 | 0.175331 | ||||||||
\(445\) | 72.3058 | 3.42762 | ||||||||
\(446\) | 5.11012 | 0.241971 | ||||||||
\(447\) | −9.22343 | −0.436253 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −4.48720 | −0.211764 | −0.105882 | − | 0.994379i | \(-0.533767\pi\) | ||||
−0.105882 | + | 0.994379i | \(0.533767\pi\) | |||||||
\(450\) | 39.8786 | 1.87990 | ||||||||
\(451\) | 0.352525 | 0.0165998 | ||||||||
\(452\) | 7.02869 | 0.330602 | ||||||||
\(453\) | −2.35207 | −0.110510 | ||||||||
\(454\) | −2.63322 | −0.123583 | ||||||||
\(455\) | −13.4805 | −0.631975 | ||||||||
\(456\) | 1.57255 | 0.0736413 | ||||||||
\(457\) | −20.0945 | −0.939980 | −0.469990 | − | 0.882672i | \(-0.655742\pi\) | ||||
−0.469990 | + | 0.882672i | \(0.655742\pi\) | |||||||
\(458\) | −18.2735 | −0.853864 | ||||||||
\(459\) | −8.12067 | −0.379040 | ||||||||
\(460\) | −3.93823 | −0.183621 | ||||||||
\(461\) | 10.5920 | 0.493319 | 0.246660 | − | 0.969102i | \(-0.420667\pi\) | ||||
0.246660 | + | 0.969102i | \(0.420667\pi\) | |||||||
\(462\) | −0.535636 | −0.0249200 | ||||||||
\(463\) | −27.8033 | −1.29213 | −0.646064 | − | 0.763284i | \(-0.723586\pi\) | ||||
−0.646064 | + | 0.763284i | \(0.723586\pi\) | |||||||
\(464\) | 2.54612 | 0.118201 | ||||||||
\(465\) | 8.87882 | 0.411746 | ||||||||
\(466\) | 18.5926 | 0.861287 | ||||||||
\(467\) | 30.3975 | 1.40663 | 0.703314 | − | 0.710879i | \(-0.251703\pi\) | ||||
0.703314 | + | 0.710879i | \(0.251703\pi\) | |||||||
\(468\) | 8.79181 | 0.406402 | ||||||||
\(469\) | −8.46286 | −0.390779 | ||||||||
\(470\) | 36.8830 | 1.70128 | ||||||||
\(471\) | −7.72652 | −0.356019 | ||||||||
\(472\) | −7.10247 | −0.326918 | ||||||||
\(473\) | −10.0784 | −0.463406 | ||||||||
\(474\) | 4.11491 | 0.189004 | ||||||||
\(475\) | 55.8827 | 2.56407 | ||||||||
\(476\) | −3.52186 | −0.161424 | ||||||||
\(477\) | −41.1003 | −1.88185 | ||||||||
\(478\) | 17.6002 | 0.805015 | ||||||||
\(479\) | 25.6190 | 1.17056 | 0.585280 | − | 0.810831i | \(-0.300985\pi\) | ||||
0.585280 | + | 0.810831i | \(0.300985\pi\) | |||||||
\(480\) | 1.72065 | 0.0785368 | ||||||||
\(481\) | 28.9442 | 1.31974 | ||||||||
\(482\) | −14.6839 | −0.668834 | ||||||||
\(483\) | 0.356268 | 0.0162107 | ||||||||
\(484\) | −9.15681 | −0.416219 | ||||||||
\(485\) | −33.5978 | −1.52560 | ||||||||
\(486\) | 9.92504 | 0.450209 | ||||||||
\(487\) | 9.16834 | 0.415457 | 0.207728 | − | 0.978187i | \(-0.433393\pi\) | ||||
0.207728 | + | 0.978187i | \(0.433393\pi\) | |||||||
\(488\) | −8.93330 | −0.404392 | ||||||||
\(489\) | −1.55724 | −0.0704209 | ||||||||
\(490\) | −4.36123 | −0.197020 | ||||||||
\(491\) | 20.2230 | 0.912650 | 0.456325 | − | 0.889813i | \(-0.349165\pi\) | ||||
0.456325 | + | 0.889813i | \(0.349165\pi\) | |||||||
\(492\) | 0.102445 | 0.00461857 | ||||||||
\(493\) | −8.96708 | −0.403857 | ||||||||
\(494\) | 12.3201 | 0.554309 | ||||||||
\(495\) | 16.8413 | 0.756961 | ||||||||
\(496\) | −5.16014 | −0.231697 | ||||||||
\(497\) | 3.07426 | 0.137899 | ||||||||
\(498\) | 2.35862 | 0.105692 | ||||||||
\(499\) | −30.2185 | −1.35277 | −0.676384 | − | 0.736549i | \(-0.736454\pi\) | ||||
−0.676384 | + | 0.736549i | \(0.736454\pi\) | |||||||
\(500\) | 39.3397 | 1.75933 | ||||||||
\(501\) | 7.10103 | 0.317251 | ||||||||
\(502\) | 20.5652 | 0.917871 | ||||||||
\(503\) | 2.33522 | 0.104122 | 0.0520611 | − | 0.998644i | \(-0.483421\pi\) | ||||
0.0520611 | + | 0.998644i | \(0.483421\pi\) | |||||||
\(504\) | 2.84434 | 0.126697 | ||||||||
\(505\) | −71.5444 | −3.18368 | ||||||||
\(506\) | −1.22596 | −0.0545006 | ||||||||
\(507\) | 1.35950 | 0.0603775 | ||||||||
\(508\) | 20.9612 | 0.930003 | ||||||||
\(509\) | 5.10020 | 0.226063 | 0.113031 | − | 0.993591i | \(-0.463944\pi\) | ||||
0.113031 | + | 0.993591i | \(0.463944\pi\) | |||||||
\(510\) | −6.05990 | −0.268337 | ||||||||
\(511\) | 7.04932 | 0.311844 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 9.19050 | 0.405771 | ||||||||
\(514\) | 11.0028 | 0.485312 | ||||||||
\(515\) | 47.2477 | 2.08198 | ||||||||
\(516\) | −2.92881 | −0.128934 | ||||||||
\(517\) | 11.4816 | 0.504960 | ||||||||
\(518\) | 9.36407 | 0.411434 | ||||||||
\(519\) | 6.02066 | 0.264278 | ||||||||
\(520\) | 13.4805 | 0.591158 | ||||||||
\(521\) | 11.8819 | 0.520558 | 0.260279 | − | 0.965533i | \(-0.416186\pi\) | ||||
0.260279 | + | 0.965533i | \(0.416186\pi\) | |||||||
\(522\) | 7.24205 | 0.316976 | ||||||||
\(523\) | −13.4111 | −0.586428 | −0.293214 | − | 0.956047i | \(-0.594725\pi\) | ||||
−0.293214 | + | 0.956047i | \(0.594725\pi\) | |||||||
\(524\) | 16.5111 | 0.721290 | ||||||||
\(525\) | −5.53150 | −0.241414 | ||||||||
\(526\) | −0.890541 | −0.0388294 | ||||||||
\(527\) | 18.1733 | 0.791641 | ||||||||
\(528\) | 0.535636 | 0.0233106 | ||||||||
\(529\) | −22.1846 | −0.964547 | ||||||||
\(530\) | −63.0190 | −2.73737 | ||||||||
\(531\) | −20.2019 | −0.876687 | ||||||||
\(532\) | 3.98583 | 0.172808 | ||||||||
\(533\) | 0.802604 | 0.0347647 | ||||||||
\(534\) | 6.54107 | 0.283060 | ||||||||
\(535\) | 76.2996 | 3.29872 | ||||||||
\(536\) | 8.46286 | 0.365540 | ||||||||
\(537\) | −9.21624 | −0.397710 | ||||||||
\(538\) | 8.01173 | 0.345410 | ||||||||
\(539\) | −1.35764 | −0.0584778 | ||||||||
\(540\) | 10.0561 | 0.432745 | ||||||||
\(541\) | −11.2452 | −0.483471 | −0.241735 | − | 0.970342i | \(-0.577717\pi\) | ||||
−0.241735 | + | 0.970342i | \(0.577717\pi\) | |||||||
\(542\) | 4.76535 | 0.204689 | ||||||||
\(543\) | 1.53508 | 0.0658768 | ||||||||
\(544\) | 3.52186 | 0.150998 | ||||||||
\(545\) | 38.7803 | 1.66117 | ||||||||
\(546\) | −1.21950 | −0.0521897 | ||||||||
\(547\) | −28.5990 | −1.22280 | −0.611402 | − | 0.791320i | \(-0.709394\pi\) | ||||
−0.611402 | + | 0.791320i | \(0.709394\pi\) | |||||||
\(548\) | −1.63908 | −0.0700179 | ||||||||
\(549\) | −25.4094 | −1.08445 | ||||||||
\(550\) | 19.0346 | 0.811637 | ||||||||
\(551\) | 10.1484 | 0.432337 | ||||||||
\(552\) | −0.356268 | −0.0151638 | ||||||||
\(553\) | 10.4298 | 0.443520 | ||||||||
\(554\) | 20.6479 | 0.877244 | ||||||||
\(555\) | 16.1123 | 0.683930 | ||||||||
\(556\) | −14.4616 | −0.613310 | ||||||||
\(557\) | −14.1575 | −0.599874 | −0.299937 | − | 0.953959i | \(-0.596966\pi\) | ||||
−0.299937 | + | 0.953959i | \(0.596966\pi\) | |||||||
\(558\) | −14.6772 | −0.621336 | ||||||||
\(559\) | −22.9458 | −0.970504 | ||||||||
\(560\) | 4.36123 | 0.184296 | ||||||||
\(561\) | −1.88643 | −0.0796453 | ||||||||
\(562\) | 27.4714 | 1.15881 | ||||||||
\(563\) | 4.75532 | 0.200413 | 0.100206 | − | 0.994967i | \(-0.468050\pi\) | ||||
0.100206 | + | 0.994967i | \(0.468050\pi\) | |||||||
\(564\) | 3.33658 | 0.140495 | ||||||||
\(565\) | 30.6537 | 1.28961 | ||||||||
\(566\) | −26.4442 | −1.11153 | ||||||||
\(567\) | 7.62331 | 0.320149 | ||||||||
\(568\) | −3.07426 | −0.128993 | ||||||||
\(569\) | −1.94720 | −0.0816309 | −0.0408155 | − | 0.999167i | \(-0.512996\pi\) | ||||
−0.0408155 | + | 0.999167i | \(0.512996\pi\) | |||||||
\(570\) | 6.85824 | 0.287260 | ||||||||
\(571\) | 6.19322 | 0.259178 | 0.129589 | − | 0.991568i | \(-0.458634\pi\) | ||||
0.129589 | + | 0.991568i | \(0.458634\pi\) | |||||||
\(572\) | 4.19645 | 0.175462 | ||||||||
\(573\) | 2.55803 | 0.106863 | ||||||||
\(574\) | 0.259660 | 0.0108380 | ||||||||
\(575\) | −12.6605 | −0.527978 | ||||||||
\(576\) | −2.84434 | −0.118514 | ||||||||
\(577\) | −5.67958 | −0.236444 | −0.118222 | − | 0.992987i | \(-0.537719\pi\) | ||||
−0.118222 | + | 0.992987i | \(0.537719\pi\) | |||||||
\(578\) | 4.59653 | 0.191190 | ||||||||
\(579\) | 9.85449 | 0.409539 | ||||||||
\(580\) | 11.1042 | 0.461078 | ||||||||
\(581\) | 5.97823 | 0.248019 | ||||||||
\(582\) | −3.03939 | −0.125987 | ||||||||
\(583\) | −19.6177 | −0.812482 | ||||||||
\(584\) | −7.04932 | −0.291703 | ||||||||
\(585\) | 38.3431 | 1.58529 | ||||||||
\(586\) | 6.05329 | 0.250059 | ||||||||
\(587\) | 43.8327 | 1.80917 | 0.904584 | − | 0.426295i | \(-0.140181\pi\) | ||||
0.904584 | + | 0.426295i | \(0.140181\pi\) | |||||||
\(588\) | −0.394534 | −0.0162703 | ||||||||
\(589\) | −20.5675 | −0.847468 | ||||||||
\(590\) | −30.9755 | −1.27524 | ||||||||
\(591\) | 2.39365 | 0.0984618 | ||||||||
\(592\) | −9.36407 | −0.384861 | ||||||||
\(593\) | −11.1452 | −0.457678 | −0.228839 | − | 0.973464i | \(-0.573493\pi\) | ||||
−0.228839 | + | 0.973464i | \(0.573493\pi\) | |||||||
\(594\) | 3.13044 | 0.128444 | ||||||||
\(595\) | −15.3596 | −0.629683 | ||||||||
\(596\) | 23.3780 | 0.957601 | ||||||||
\(597\) | −6.44523 | −0.263786 | ||||||||
\(598\) | −2.79118 | −0.114140 | ||||||||
\(599\) | −14.4273 | −0.589484 | −0.294742 | − | 0.955577i | \(-0.595234\pi\) | ||||
−0.294742 | + | 0.955577i | \(0.595234\pi\) | |||||||
\(600\) | 5.53150 | 0.225822 | ||||||||
\(601\) | −18.8864 | −0.770394 | −0.385197 | − | 0.922834i | \(-0.625866\pi\) | ||||
−0.385197 | + | 0.922834i | \(0.625866\pi\) | |||||||
\(602\) | −7.42347 | −0.302558 | ||||||||
\(603\) | 24.0713 | 0.980258 | ||||||||
\(604\) | 5.96165 | 0.242576 | ||||||||
\(605\) | −39.9349 | −1.62359 | ||||||||
\(606\) | −6.47219 | −0.262915 | ||||||||
\(607\) | −9.84799 | −0.399718 | −0.199859 | − | 0.979825i | \(-0.564048\pi\) | ||||
−0.199859 | + | 0.979825i | \(0.564048\pi\) | |||||||
\(608\) | −3.98583 | −0.161647 | ||||||||
\(609\) | −1.00453 | −0.0407057 | ||||||||
\(610\) | −38.9602 | −1.57745 | ||||||||
\(611\) | 26.1405 | 1.05753 | ||||||||
\(612\) | 10.0174 | 0.404928 | ||||||||
\(613\) | 32.0775 | 1.29560 | 0.647798 | − | 0.761812i | \(-0.275690\pi\) | ||||
0.647798 | + | 0.761812i | \(0.275690\pi\) | |||||||
\(614\) | −14.3662 | −0.579774 | ||||||||
\(615\) | 0.446785 | 0.0180161 | ||||||||
\(616\) | 1.35764 | 0.0547010 | ||||||||
\(617\) | 29.0669 | 1.17019 | 0.585096 | − | 0.810964i | \(-0.301057\pi\) | ||||
0.585096 | + | 0.810964i | \(0.301057\pi\) | |||||||
\(618\) | 4.27421 | 0.171934 | ||||||||
\(619\) | 3.16253 | 0.127113 | 0.0635565 | − | 0.997978i | \(-0.479756\pi\) | ||||
0.0635565 | + | 0.997978i | \(0.479756\pi\) | |||||||
\(620\) | −22.5046 | −0.903805 | ||||||||
\(621\) | −2.08215 | −0.0835538 | ||||||||
\(622\) | −5.12859 | −0.205638 | ||||||||
\(623\) | 16.5792 | 0.664233 | ||||||||
\(624\) | 1.21950 | 0.0488190 | ||||||||
\(625\) | 101.468 | 4.05872 | ||||||||
\(626\) | 1.99777 | 0.0798468 | ||||||||
\(627\) | 2.13496 | 0.0852619 | ||||||||
\(628\) | 19.5839 | 0.781483 | ||||||||
\(629\) | 32.9789 | 1.31495 | ||||||||
\(630\) | 12.4048 | 0.494220 | ||||||||
\(631\) | −38.8808 | −1.54782 | −0.773909 | − | 0.633296i | \(-0.781701\pi\) | ||||
−0.773909 | + | 0.633296i | \(0.781701\pi\) | |||||||
\(632\) | −10.4298 | −0.414875 | ||||||||
\(633\) | −4.49124 | −0.178511 | ||||||||
\(634\) | −31.6073 | −1.25529 | ||||||||
\(635\) | 91.4166 | 3.62776 | ||||||||
\(636\) | −5.70095 | −0.226057 | ||||||||
\(637\) | −3.09098 | −0.122469 | ||||||||
\(638\) | 3.45672 | 0.136853 | ||||||||
\(639\) | −8.74424 | −0.345917 | ||||||||
\(640\) | −4.36123 | −0.172393 | ||||||||
\(641\) | 31.6863 | 1.25153 | 0.625767 | − | 0.780010i | \(-0.284786\pi\) | ||||
0.625767 | + | 0.780010i | \(0.284786\pi\) | |||||||
\(642\) | 6.90236 | 0.272415 | ||||||||
\(643\) | −19.9290 | −0.785923 | −0.392961 | − | 0.919555i | \(-0.628549\pi\) | ||||
−0.392961 | + | 0.919555i | \(0.628549\pi\) | |||||||
\(644\) | −0.903008 | −0.0355835 | ||||||||
\(645\) | −12.7732 | −0.502945 | ||||||||
\(646\) | 14.0375 | 0.552299 | ||||||||
\(647\) | −37.0848 | −1.45795 | −0.728977 | − | 0.684538i | \(-0.760004\pi\) | ||||
−0.728977 | + | 0.684538i | \(0.760004\pi\) | |||||||
\(648\) | −7.62331 | −0.299472 | ||||||||
\(649\) | −9.64262 | −0.378506 | ||||||||
\(650\) | 43.3366 | 1.69980 | ||||||||
\(651\) | 2.03585 | 0.0797914 | ||||||||
\(652\) | 3.94704 | 0.154578 | ||||||||
\(653\) | −21.6565 | −0.847485 | −0.423743 | − | 0.905783i | \(-0.639284\pi\) | ||||
−0.423743 | + | 0.905783i | \(0.639284\pi\) | |||||||
\(654\) | 3.50822 | 0.137182 | ||||||||
\(655\) | 72.0086 | 2.81361 | ||||||||
\(656\) | −0.259660 | −0.0101380 | ||||||||
\(657\) | −20.0507 | −0.782252 | ||||||||
\(658\) | 8.45701 | 0.329689 | ||||||||
\(659\) | −1.11710 | −0.0435160 | −0.0217580 | − | 0.999763i | \(-0.506926\pi\) | ||||
−0.0217580 | + | 0.999763i | \(0.506926\pi\) | |||||||
\(660\) | 2.33603 | 0.0909299 | ||||||||
\(661\) | −10.2585 | −0.399009 | −0.199505 | − | 0.979897i | \(-0.563933\pi\) | ||||
−0.199505 | + | 0.979897i | \(0.563933\pi\) | |||||||
\(662\) | 3.66999 | 0.142638 | ||||||||
\(663\) | −4.29490 | −0.166800 | ||||||||
\(664\) | −5.97823 | −0.232000 | ||||||||
\(665\) | 17.3831 | 0.674089 | ||||||||
\(666\) | −26.6346 | −1.03207 | ||||||||
\(667\) | −2.29917 | −0.0890242 | ||||||||
\(668\) | −17.9985 | −0.696384 | ||||||||
\(669\) | 2.01612 | 0.0779476 | ||||||||
\(670\) | 36.9085 | 1.42590 | ||||||||
\(671\) | −12.1282 | −0.468205 | ||||||||
\(672\) | 0.394534 | 0.0152195 | ||||||||
\(673\) | 28.6171 | 1.10311 | 0.551555 | − | 0.834139i | \(-0.314035\pi\) | ||||
0.551555 | + | 0.834139i | \(0.314035\pi\) | |||||||
\(674\) | −3.64064 | −0.140232 | ||||||||
\(675\) | 32.3280 | 1.24430 | ||||||||
\(676\) | −3.44584 | −0.132532 | ||||||||
\(677\) | −9.77999 | −0.375875 | −0.187938 | − | 0.982181i | \(-0.560180\pi\) | ||||
−0.187938 | + | 0.982181i | \(0.560180\pi\) | |||||||
\(678\) | 2.77306 | 0.106499 | ||||||||
\(679\) | −7.70375 | −0.295643 | ||||||||
\(680\) | 15.3596 | 0.589015 | ||||||||
\(681\) | −1.03889 | −0.0398105 | ||||||||
\(682\) | −7.00563 | −0.268259 | ||||||||
\(683\) | 22.4568 | 0.859286 | 0.429643 | − | 0.902999i | \(-0.358639\pi\) | ||||
0.429643 | + | 0.902999i | \(0.358639\pi\) | |||||||
\(684\) | −11.3371 | −0.433484 | ||||||||
\(685\) | −7.14839 | −0.273126 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −7.20951 | −0.275060 | ||||||||
\(688\) | 7.42347 | 0.283017 | ||||||||
\(689\) | −44.6641 | −1.70157 | ||||||||
\(690\) | −1.55376 | −0.0591508 | ||||||||
\(691\) | 48.9818 | 1.86335 | 0.931677 | − | 0.363287i | \(-0.118346\pi\) | ||||
0.931677 | + | 0.363287i | \(0.118346\pi\) | |||||||
\(692\) | −15.2602 | −0.580105 | ||||||||
\(693\) | 3.86160 | 0.146690 | ||||||||
\(694\) | 20.9412 | 0.794917 | ||||||||
\(695\) | −63.0705 | −2.39240 | ||||||||
\(696\) | 1.00453 | 0.0380767 | ||||||||
\(697\) | 0.914485 | 0.0346386 | ||||||||
\(698\) | −17.5132 | −0.662885 | ||||||||
\(699\) | 7.33542 | 0.277451 | ||||||||
\(700\) | 14.0203 | 0.529919 | ||||||||
\(701\) | 1.43535 | 0.0542124 | 0.0271062 | − | 0.999633i | \(-0.491371\pi\) | ||||
0.0271062 | + | 0.999633i | \(0.491371\pi\) | |||||||
\(702\) | 7.12716 | 0.268997 | ||||||||
\(703\) | −37.3236 | −1.40769 | ||||||||
\(704\) | −1.35764 | −0.0511681 | ||||||||
\(705\) | 14.5516 | 0.548045 | ||||||||
\(706\) | −18.2425 | −0.686566 | ||||||||
\(707\) | −16.4046 | −0.616960 | ||||||||
\(708\) | −2.80217 | −0.105312 | ||||||||
\(709\) | 8.47048 | 0.318116 | 0.159058 | − | 0.987269i | \(-0.449154\pi\) | ||||
0.159058 | + | 0.987269i | \(0.449154\pi\) | |||||||
\(710\) | −13.4075 | −0.503176 | ||||||||
\(711\) | −29.6659 | −1.11256 | ||||||||
\(712\) | −16.5792 | −0.621333 | ||||||||
\(713\) | 4.65965 | 0.174505 | ||||||||
\(714\) | −1.38949 | −0.0520004 | ||||||||
\(715\) | 18.3017 | 0.684444 | ||||||||
\(716\) | 23.3598 | 0.872997 | ||||||||
\(717\) | 6.94389 | 0.259324 | ||||||||
\(718\) | −25.9880 | −0.969863 | ||||||||
\(719\) | −17.9697 | −0.670158 | −0.335079 | − | 0.942190i | \(-0.608763\pi\) | ||||
−0.335079 | + | 0.942190i | \(0.608763\pi\) | |||||||
\(720\) | −12.4048 | −0.462301 | ||||||||
\(721\) | 10.8336 | 0.403463 | ||||||||
\(722\) | 3.11314 | 0.115859 | ||||||||
\(723\) | −5.79331 | −0.215455 | ||||||||
\(724\) | −3.89088 | −0.144603 | ||||||||
\(725\) | 35.6975 | 1.32577 | ||||||||
\(726\) | −3.61267 | −0.134079 | ||||||||
\(727\) | 43.2500 | 1.60405 | 0.802027 | − | 0.597287i | \(-0.203755\pi\) | ||||
0.802027 | + | 0.597287i | \(0.203755\pi\) | |||||||
\(728\) | 3.09098 | 0.114559 | ||||||||
\(729\) | −18.9542 | −0.702007 | ||||||||
\(730\) | −30.7437 | −1.13788 | ||||||||
\(731\) | −26.1444 | −0.966985 | ||||||||
\(732\) | −3.52449 | −0.130269 | ||||||||
\(733\) | −28.3661 | −1.04772 | −0.523862 | − | 0.851803i | \(-0.675509\pi\) | ||||
−0.523862 | + | 0.851803i | \(0.675509\pi\) | |||||||
\(734\) | −16.2164 | −0.598560 | ||||||||
\(735\) | −1.72065 | −0.0634673 | ||||||||
\(736\) | 0.903008 | 0.0332853 | ||||||||
\(737\) | 11.4895 | 0.423223 | ||||||||
\(738\) | −0.738562 | −0.0271869 | ||||||||
\(739\) | 34.1770 | 1.25722 | 0.628610 | − | 0.777721i | \(-0.283624\pi\) | ||||
0.628610 | + | 0.777721i | \(0.283624\pi\) | |||||||
\(740\) | −40.8389 | −1.50127 | ||||||||
\(741\) | 4.86071 | 0.178563 | ||||||||
\(742\) | −14.4498 | −0.530470 | ||||||||
\(743\) | −39.2682 | −1.44061 | −0.720305 | − | 0.693657i | \(-0.755998\pi\) | ||||
−0.720305 | + | 0.693657i | \(0.755998\pi\) | |||||||
\(744\) | −2.03585 | −0.0746380 | ||||||||
\(745\) | 101.957 | 3.73541 | ||||||||
\(746\) | 26.3843 | 0.965998 | ||||||||
\(747\) | −17.0041 | −0.622149 | ||||||||
\(748\) | 4.78142 | 0.174826 | ||||||||
\(749\) | 17.4950 | 0.639252 | ||||||||
\(750\) | 15.5209 | 0.566742 | ||||||||
\(751\) | 13.7769 | 0.502727 | 0.251363 | − | 0.967893i | \(-0.419121\pi\) | ||||
0.251363 | + | 0.967893i | \(0.419121\pi\) | |||||||
\(752\) | −8.45701 | −0.308395 | ||||||||
\(753\) | 8.11368 | 0.295679 | ||||||||
\(754\) | 7.87002 | 0.286609 | ||||||||
\(755\) | 26.0001 | 0.946241 | ||||||||
\(756\) | 2.30579 | 0.0838609 | ||||||||
\(757\) | 34.6043 | 1.25771 | 0.628857 | − | 0.777521i | \(-0.283523\pi\) | ||||
0.628857 | + | 0.777521i | \(0.283523\pi\) | |||||||
\(758\) | 12.7881 | 0.464485 | ||||||||
\(759\) | −0.483684 | −0.0175566 | ||||||||
\(760\) | −17.3831 | −0.630552 | ||||||||
\(761\) | −28.1535 | −1.02056 | −0.510282 | − | 0.860007i | \(-0.670459\pi\) | ||||
−0.510282 | + | 0.860007i | \(0.670459\pi\) | |||||||
\(762\) | 8.26991 | 0.299587 | ||||||||
\(763\) | 8.89206 | 0.321914 | ||||||||
\(764\) | −6.48366 | −0.234571 | ||||||||
\(765\) | 43.6880 | 1.57954 | ||||||||
\(766\) | 8.81531 | 0.318510 | ||||||||
\(767\) | −21.9536 | −0.792699 | ||||||||
\(768\) | −0.394534 | −0.0142365 | ||||||||
\(769\) | −47.7602 | −1.72228 | −0.861138 | − | 0.508372i | \(-0.830248\pi\) | ||||
−0.861138 | + | 0.508372i | \(0.830248\pi\) | |||||||
\(770\) | 5.92099 | 0.213378 | ||||||||
\(771\) | 4.34097 | 0.156336 | ||||||||
\(772\) | −24.9775 | −0.898962 | ||||||||
\(773\) | 38.5450 | 1.38637 | 0.693183 | − | 0.720762i | \(-0.256208\pi\) | ||||
0.693183 | + | 0.720762i | \(0.256208\pi\) | |||||||
\(774\) | 21.1149 | 0.758959 | ||||||||
\(775\) | −72.3469 | −2.59878 | ||||||||
\(776\) | 7.70375 | 0.276549 | ||||||||
\(777\) | 3.69445 | 0.132537 | ||||||||
\(778\) | 15.9743 | 0.572705 | ||||||||
\(779\) | −1.03496 | −0.0370813 | ||||||||
\(780\) | 5.31851 | 0.190433 | ||||||||
\(781\) | −4.17374 | −0.149348 | ||||||||
\(782\) | −3.18026 | −0.113726 | ||||||||
\(783\) | 5.87083 | 0.209806 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 85.4100 | 3.04841 | ||||||||
\(786\) | 6.51419 | 0.232353 | ||||||||
\(787\) | 45.8605 | 1.63475 | 0.817375 | − | 0.576107i | \(-0.195429\pi\) | ||||
0.817375 | + | 0.576107i | \(0.195429\pi\) | |||||||
\(788\) | −6.06704 | −0.216129 | ||||||||
\(789\) | −0.351349 | −0.0125083 | ||||||||
\(790\) | −45.4868 | −1.61835 | ||||||||
\(791\) | 7.02869 | 0.249911 | ||||||||
\(792\) | −3.86160 | −0.137216 | ||||||||
\(793\) | −27.6127 | −0.980554 | ||||||||
\(794\) | 30.9786 | 1.09939 | ||||||||
\(795\) | −24.8632 | −0.881805 | ||||||||
\(796\) | 16.3363 | 0.579025 | ||||||||
\(797\) | 25.9398 | 0.918833 | 0.459417 | − | 0.888221i | \(-0.348058\pi\) | ||||
0.459417 | + | 0.888221i | \(0.348058\pi\) | |||||||
\(798\) | 1.57255 | 0.0556676 | ||||||||
\(799\) | 29.7844 | 1.05370 | ||||||||
\(800\) | −14.0203 | −0.495693 | ||||||||
\(801\) | −47.1570 | −1.66621 | ||||||||
\(802\) | 4.67504 | 0.165081 | ||||||||
\(803\) | −9.57045 | −0.337734 | ||||||||
\(804\) | 3.33889 | 0.117754 | ||||||||
\(805\) | −3.93823 | −0.138804 | ||||||||
\(806\) | −15.9499 | −0.561811 | ||||||||
\(807\) | 3.16090 | 0.111269 | ||||||||
\(808\) | 16.4046 | 0.577113 | ||||||||
\(809\) | −9.18215 | −0.322827 | −0.161414 | − | 0.986887i | \(-0.551605\pi\) | ||||
−0.161414 | + | 0.986887i | \(0.551605\pi\) | |||||||
\(810\) | −33.2470 | −1.16818 | ||||||||
\(811\) | 0.639239 | 0.0224467 | 0.0112234 | − | 0.999937i | \(-0.496427\pi\) | ||||
0.0112234 | + | 0.999937i | \(0.496427\pi\) | |||||||
\(812\) | 2.54612 | 0.0893514 | ||||||||
\(813\) | 1.88009 | 0.0659378 | ||||||||
\(814\) | −12.7131 | −0.445592 | ||||||||
\(815\) | 17.2139 | 0.602978 | ||||||||
\(816\) | 1.38949 | 0.0486420 | ||||||||
\(817\) | 29.5887 | 1.03518 | ||||||||
\(818\) | 15.6899 | 0.548583 | ||||||||
\(819\) | 8.79181 | 0.307211 | ||||||||
\(820\) | −1.13244 | −0.0395464 | ||||||||
\(821\) | −48.8106 | −1.70350 | −0.851751 | − | 0.523947i | \(-0.824459\pi\) | ||||
−0.851751 | + | 0.523947i | \(0.824459\pi\) | |||||||
\(822\) | −0.646672 | −0.0225553 | ||||||||
\(823\) | 27.7749 | 0.968172 | 0.484086 | − | 0.875020i | \(-0.339152\pi\) | ||||
0.484086 | + | 0.875020i | \(0.339152\pi\) | |||||||
\(824\) | −10.8336 | −0.377405 | ||||||||
\(825\) | 7.50979 | 0.261457 | ||||||||
\(826\) | −7.10247 | −0.247127 | ||||||||
\(827\) | 39.4657 | 1.37236 | 0.686178 | − | 0.727434i | \(-0.259287\pi\) | ||||
0.686178 | + | 0.727434i | \(0.259287\pi\) | |||||||
\(828\) | 2.56846 | 0.0892603 | ||||||||
\(829\) | −14.3461 | −0.498262 | −0.249131 | − | 0.968470i | \(-0.580145\pi\) | ||||
−0.249131 | + | 0.968470i | \(0.580145\pi\) | |||||||
\(830\) | −26.0724 | −0.904988 | ||||||||
\(831\) | 8.14629 | 0.282592 | ||||||||
\(832\) | −3.09098 | −0.107160 | ||||||||
\(833\) | −3.52186 | −0.122025 | ||||||||
\(834\) | −5.70561 | −0.197569 | ||||||||
\(835\) | −78.4957 | −2.71646 | ||||||||
\(836\) | −5.41133 | −0.187155 | ||||||||
\(837\) | −11.8982 | −0.411263 | ||||||||
\(838\) | 17.6854 | 0.610931 | ||||||||
\(839\) | 42.7812 | 1.47697 | 0.738486 | − | 0.674269i | \(-0.235541\pi\) | ||||
0.738486 | + | 0.674269i | \(0.235541\pi\) | |||||||
\(840\) | 1.72065 | 0.0593682 | ||||||||
\(841\) | −22.5173 | −0.776457 | ||||||||
\(842\) | −24.2089 | −0.834294 | ||||||||
\(843\) | 10.8384 | 0.373294 | ||||||||
\(844\) | 11.3837 | 0.391842 | ||||||||
\(845\) | −15.0281 | −0.516982 | ||||||||
\(846\) | −24.0546 | −0.827016 | ||||||||
\(847\) | −9.15681 | −0.314632 | ||||||||
\(848\) | 14.4498 | 0.496209 | ||||||||
\(849\) | −10.4332 | −0.358065 | ||||||||
\(850\) | 49.3776 | 1.69364 | ||||||||
\(851\) | 8.45583 | 0.289862 | ||||||||
\(852\) | −1.21290 | −0.0415533 | ||||||||
\(853\) | 16.2227 | 0.555455 | 0.277727 | − | 0.960660i | \(-0.410419\pi\) | ||||
0.277727 | + | 0.960660i | \(0.410419\pi\) | |||||||
\(854\) | −8.93330 | −0.305691 | ||||||||
\(855\) | −49.4436 | −1.69093 | ||||||||
\(856\) | −17.4950 | −0.597966 | ||||||||
\(857\) | −26.5321 | −0.906318 | −0.453159 | − | 0.891430i | \(-0.649703\pi\) | ||||
−0.453159 | + | 0.891430i | \(0.649703\pi\) | |||||||
\(858\) | 1.65564 | 0.0565227 | ||||||||
\(859\) | −27.0108 | −0.921598 | −0.460799 | − | 0.887505i | \(-0.652437\pi\) | ||||
−0.460799 | + | 0.887505i | \(0.652437\pi\) | |||||||
\(860\) | 32.3754 | 1.10399 | ||||||||
\(861\) | 0.102445 | 0.00349131 | ||||||||
\(862\) | 1.00000 | 0.0340601 | ||||||||
\(863\) | 23.6051 | 0.803528 | 0.401764 | − | 0.915743i | \(-0.368397\pi\) | ||||
0.401764 | + | 0.915743i | \(0.368397\pi\) | |||||||
\(864\) | −2.30579 | −0.0784447 | ||||||||
\(865\) | −66.5531 | −2.26287 | ||||||||
\(866\) | 15.1216 | 0.513853 | ||||||||
\(867\) | 1.81349 | 0.0615893 | ||||||||
\(868\) | −5.16014 | −0.175147 | ||||||||
\(869\) | −14.1599 | −0.480343 | ||||||||
\(870\) | 4.38100 | 0.148530 | ||||||||
\(871\) | 26.1585 | 0.886349 | ||||||||
\(872\) | −8.89206 | −0.301123 | ||||||||
\(873\) | 21.9121 | 0.741613 | ||||||||
\(874\) | 3.59924 | 0.121746 | ||||||||
\(875\) | 39.3397 | 1.32993 | ||||||||
\(876\) | −2.78120 | −0.0939680 | ||||||||
\(877\) | −37.5779 | −1.26891 | −0.634457 | − | 0.772958i | \(-0.718776\pi\) | ||||
−0.634457 | + | 0.772958i | \(0.718776\pi\) | |||||||
\(878\) | 9.71123 | 0.327738 | ||||||||
\(879\) | 2.38823 | 0.0805529 | ||||||||
\(880\) | −5.92099 | −0.199597 | ||||||||
\(881\) | −26.0606 | −0.878003 | −0.439001 | − | 0.898486i | \(-0.644668\pi\) | ||||
−0.439001 | + | 0.898486i | \(0.644668\pi\) | |||||||
\(882\) | 2.84434 | 0.0957740 | ||||||||
\(883\) | −45.9346 | −1.54582 | −0.772911 | − | 0.634515i | \(-0.781200\pi\) | ||||
−0.772911 | + | 0.634515i | \(0.781200\pi\) | |||||||
\(884\) | 10.8860 | 0.366135 | ||||||||
\(885\) | −12.2209 | −0.410801 | ||||||||
\(886\) | −18.4989 | −0.621482 | ||||||||
\(887\) | 27.1187 | 0.910556 | 0.455278 | − | 0.890349i | \(-0.349540\pi\) | ||||
0.455278 | + | 0.890349i | \(0.349540\pi\) | |||||||
\(888\) | −3.69445 | −0.123977 | ||||||||
\(889\) | 20.9612 | 0.703016 | ||||||||
\(890\) | −72.3058 | −2.42370 | ||||||||
\(891\) | −10.3497 | −0.346729 | ||||||||
\(892\) | −5.11012 | −0.171100 | ||||||||
\(893\) | −33.7082 | −1.12800 | ||||||||
\(894\) | 9.22343 | 0.308478 | ||||||||
\(895\) | 101.877 | 3.40539 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −1.10122 | −0.0367685 | ||||||||
\(898\) | 4.48720 | 0.149740 | ||||||||
\(899\) | −13.1384 | −0.438189 | ||||||||
\(900\) | −39.8786 | −1.32929 | ||||||||
\(901\) | −50.8902 | −1.69540 | ||||||||
\(902\) | −0.352525 | −0.0117378 | ||||||||
\(903\) | −2.92881 | −0.0974647 | ||||||||
\(904\) | −7.02869 | −0.233771 | ||||||||
\(905\) | −16.9690 | −0.564069 | ||||||||
\(906\) | 2.35207 | 0.0781424 | ||||||||
\(907\) | −38.5684 | −1.28064 | −0.640321 | − | 0.768107i | \(-0.721199\pi\) | ||||
−0.640321 | + | 0.768107i | \(0.721199\pi\) | |||||||
\(908\) | 2.63322 | 0.0873864 | ||||||||
\(909\) | 46.6604 | 1.54763 | ||||||||
\(910\) | 13.4805 | 0.446874 | ||||||||
\(911\) | 19.9873 | 0.662209 | 0.331105 | − | 0.943594i | \(-0.392579\pi\) | ||||
0.331105 | + | 0.943594i | \(0.392579\pi\) | |||||||
\(912\) | −1.57255 | −0.0520722 | ||||||||
\(913\) | −8.11630 | −0.268610 | ||||||||
\(914\) | 20.0945 | 0.664666 | ||||||||
\(915\) | −15.3711 | −0.508154 | ||||||||
\(916\) | 18.2735 | 0.603773 | ||||||||
\(917\) | 16.5111 | 0.545244 | ||||||||
\(918\) | 8.12067 | 0.268022 | ||||||||
\(919\) | 17.3188 | 0.571294 | 0.285647 | − | 0.958335i | \(-0.407792\pi\) | ||||
0.285647 | + | 0.958335i | \(0.407792\pi\) | |||||||
\(920\) | 3.93823 | 0.129839 | ||||||||
\(921\) | −5.66797 | −0.186766 | ||||||||
\(922\) | −10.5920 | −0.348829 | ||||||||
\(923\) | −9.50247 | −0.312778 | ||||||||
\(924\) | 0.535636 | 0.0176211 | ||||||||
\(925\) | −131.287 | −4.31670 | ||||||||
\(926\) | 27.8033 | 0.913672 | ||||||||
\(927\) | −30.8144 | −1.01208 | ||||||||
\(928\) | −2.54612 | −0.0835806 | ||||||||
\(929\) | −54.0384 | −1.77294 | −0.886471 | − | 0.462784i | \(-0.846850\pi\) | ||||
−0.886471 | + | 0.462784i | \(0.846850\pi\) | |||||||
\(930\) | −8.87882 | −0.291148 | ||||||||
\(931\) | 3.98583 | 0.130630 | ||||||||
\(932\) | −18.5926 | −0.609022 | ||||||||
\(933\) | −2.02340 | −0.0662433 | ||||||||
\(934\) | −30.3975 | −0.994636 | ||||||||
\(935\) | 20.8529 | 0.681962 | ||||||||
\(936\) | −8.79181 | −0.287369 | ||||||||
\(937\) | −18.9391 | −0.618712 | −0.309356 | − | 0.950946i | \(-0.600114\pi\) | ||||
−0.309356 | + | 0.950946i | \(0.600114\pi\) | |||||||
\(938\) | 8.46286 | 0.276322 | ||||||||
\(939\) | 0.788187 | 0.0257215 | ||||||||
\(940\) | −36.8830 | −1.20299 | ||||||||
\(941\) | 17.2105 | 0.561048 | 0.280524 | − | 0.959847i | \(-0.409492\pi\) | ||||
0.280524 | + | 0.959847i | \(0.409492\pi\) | |||||||
\(942\) | 7.72652 | 0.251744 | ||||||||
\(943\) | 0.234475 | 0.00763556 | ||||||||
\(944\) | 7.10247 | 0.231166 | ||||||||
\(945\) | 10.0561 | 0.327125 | ||||||||
\(946\) | 10.0784 | 0.327677 | ||||||||
\(947\) | 33.9255 | 1.10243 | 0.551215 | − | 0.834363i | \(-0.314165\pi\) | ||||
0.551215 | + | 0.834363i | \(0.314165\pi\) | |||||||
\(948\) | −4.11491 | −0.133646 | ||||||||
\(949\) | −21.7893 | −0.707311 | ||||||||
\(950\) | −55.8827 | −1.81307 | ||||||||
\(951\) | −12.4702 | −0.404373 | ||||||||
\(952\) | 3.52186 | 0.114144 | ||||||||
\(953\) | −0.934417 | −0.0302688 | −0.0151344 | − | 0.999885i | \(-0.504818\pi\) | ||||
−0.0151344 | + | 0.999885i | \(0.504818\pi\) | |||||||
\(954\) | 41.1003 | 1.33067 | ||||||||
\(955\) | −28.2767 | −0.915013 | ||||||||
\(956\) | −17.6002 | −0.569232 | ||||||||
\(957\) | 1.36380 | 0.0440853 | ||||||||
\(958\) | −25.6190 | −0.827711 | ||||||||
\(959\) | −1.63908 | −0.0529286 | ||||||||
\(960\) | −1.72065 | −0.0555339 | ||||||||
\(961\) | −4.37292 | −0.141062 | ||||||||
\(962\) | −28.9442 | −0.933197 | ||||||||
\(963\) | −49.7617 | −1.60355 | ||||||||
\(964\) | 14.6839 | 0.472937 | ||||||||
\(965\) | −108.933 | −3.50667 | ||||||||
\(966\) | −0.356268 | −0.0114627 | ||||||||
\(967\) | 11.1288 | 0.357878 | 0.178939 | − | 0.983860i | \(-0.442734\pi\) | ||||
0.178939 | + | 0.983860i | \(0.442734\pi\) | |||||||
\(968\) | 9.15681 | 0.294311 | ||||||||
\(969\) | 5.53828 | 0.177915 | ||||||||
\(970\) | 33.5978 | 1.07876 | ||||||||
\(971\) | 19.2648 | 0.618238 | 0.309119 | − | 0.951023i | \(-0.399966\pi\) | ||||
0.309119 | + | 0.951023i | \(0.399966\pi\) | |||||||
\(972\) | −9.92504 | −0.318346 | ||||||||
\(973\) | −14.4616 | −0.463619 | ||||||||
\(974\) | −9.16834 | −0.293772 | ||||||||
\(975\) | 17.0978 | 0.547566 | ||||||||
\(976\) | 8.93330 | 0.285948 | ||||||||
\(977\) | 29.5133 | 0.944216 | 0.472108 | − | 0.881541i | \(-0.343493\pi\) | ||||
0.472108 | + | 0.881541i | \(0.343493\pi\) | |||||||
\(978\) | 1.55724 | 0.0497951 | ||||||||
\(979\) | −22.5087 | −0.719380 | ||||||||
\(980\) | 4.36123 | 0.139314 | ||||||||
\(981\) | −25.2921 | −0.807514 | ||||||||
\(982\) | −20.2230 | −0.645341 | ||||||||
\(983\) | −1.11612 | −0.0355986 | −0.0177993 | − | 0.999842i | \(-0.505666\pi\) | ||||
−0.0177993 | + | 0.999842i | \(0.505666\pi\) | |||||||
\(984\) | −0.102445 | −0.00326582 | ||||||||
\(985\) | −26.4598 | −0.843078 | ||||||||
\(986\) | 8.96708 | 0.285570 | ||||||||
\(987\) | 3.33658 | 0.106205 | ||||||||
\(988\) | −12.3201 | −0.391956 | ||||||||
\(989\) | −6.70345 | −0.213157 | ||||||||
\(990\) | −16.8413 | −0.535252 | ||||||||
\(991\) | 55.4777 | 1.76231 | 0.881153 | − | 0.472831i | \(-0.156768\pi\) | ||||
0.881153 | + | 0.472831i | \(0.156768\pi\) | |||||||
\(992\) | 5.16014 | 0.163835 | ||||||||
\(993\) | 1.44794 | 0.0459489 | ||||||||
\(994\) | −3.07426 | −0.0975095 | ||||||||
\(995\) | 71.2463 | 2.25866 | ||||||||
\(996\) | −2.35862 | −0.0747356 | ||||||||
\(997\) | 6.33246 | 0.200551 | 0.100276 | − | 0.994960i | \(-0.468028\pi\) | ||||
0.100276 | + | 0.994960i | \(0.468028\pi\) | |||||||
\(998\) | 30.2185 | 0.956551 | ||||||||
\(999\) | −21.5916 | −0.683128 |
(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.p.1.11 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.p.1.11 | ✓ | 27 | 1.1 | even | 1 | trivial |