Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.21 | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.48810 | 1.75935 | 0.879675 | − | 0.475576i | \(-0.157760\pi\) | ||||
0.879675 | + | 0.475576i | \(0.157760\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.19062 | 2.09531 | ||||||||
\(5\) | −2.36641 | −1.05829 | −0.529145 | − | 0.848531i | \(-0.677487\pi\) | ||||
−0.529145 | + | 0.848531i | \(0.677487\pi\) | |||||||
\(6\) | −2.48810 | −1.01576 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 5.45047 | 1.92703 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −5.88785 | −1.86190 | ||||||||
\(11\) | 4.46600 | 1.34655 | 0.673275 | − | 0.739392i | \(-0.264887\pi\) | ||||
0.673275 | + | 0.739392i | \(0.264887\pi\) | |||||||
\(12\) | −4.19062 | −1.20973 | ||||||||
\(13\) | 5.01637 | 1.39129 | 0.695645 | − | 0.718385i | \(-0.255118\pi\) | ||||
0.695645 | + | 0.718385i | \(0.255118\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.36641 | 0.611004 | ||||||||
\(16\) | 5.18004 | 1.29501 | ||||||||
\(17\) | −4.88608 | −1.18505 | −0.592524 | − | 0.805552i | \(-0.701869\pi\) | ||||
−0.592524 | + | 0.805552i | \(0.701869\pi\) | |||||||
\(18\) | 2.48810 | 0.586450 | ||||||||
\(19\) | 3.64438 | 0.836078 | 0.418039 | − | 0.908429i | \(-0.362718\pi\) | ||||
0.418039 | + | 0.908429i | \(0.362718\pi\) | |||||||
\(20\) | −9.91672 | −2.21745 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 11.1118 | 2.36905 | ||||||||
\(23\) | −2.22001 | −0.462904 | −0.231452 | − | 0.972846i | \(-0.574348\pi\) | ||||
−0.231452 | + | 0.972846i | \(0.574348\pi\) | |||||||
\(24\) | −5.45047 | −1.11257 | ||||||||
\(25\) | 0.599893 | 0.119979 | ||||||||
\(26\) | 12.4812 | 2.44777 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.88239 | 0.535246 | 0.267623 | − | 0.963524i | \(-0.413762\pi\) | ||||
0.267623 | + | 0.963524i | \(0.413762\pi\) | |||||||
\(30\) | 5.88785 | 1.07497 | ||||||||
\(31\) | −1.18084 | −0.212085 | −0.106043 | − | 0.994362i | \(-0.533818\pi\) | ||||
−0.106043 | + | 0.994362i | \(0.533818\pi\) | |||||||
\(32\) | 1.98751 | 0.351345 | ||||||||
\(33\) | −4.46600 | −0.777431 | ||||||||
\(34\) | −12.1570 | −2.08491 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.19062 | 0.698436 | ||||||||
\(37\) | −0.748295 | −0.123019 | −0.0615095 | − | 0.998107i | \(-0.519591\pi\) | ||||
−0.0615095 | + | 0.998107i | \(0.519591\pi\) | |||||||
\(38\) | 9.06756 | 1.47095 | ||||||||
\(39\) | −5.01637 | −0.803262 | ||||||||
\(40\) | −12.8980 | −2.03936 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.98238 | 1.06480 | 0.532402 | − | 0.846492i | \(-0.321290\pi\) | ||||
0.532402 | + | 0.846492i | \(0.321290\pi\) | |||||||
\(44\) | 18.7153 | 2.82144 | ||||||||
\(45\) | −2.36641 | −0.352763 | ||||||||
\(46\) | −5.52359 | −0.814409 | ||||||||
\(47\) | 7.64313 | 1.11486 | 0.557432 | − | 0.830222i | \(-0.311787\pi\) | ||||
0.557432 | + | 0.830222i | \(0.311787\pi\) | |||||||
\(48\) | −5.18004 | −0.747675 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.49259 | 0.211084 | ||||||||
\(51\) | 4.88608 | 0.684188 | ||||||||
\(52\) | 21.0217 | 2.91518 | ||||||||
\(53\) | 10.3267 | 1.41848 | 0.709238 | − | 0.704969i | \(-0.249039\pi\) | ||||
0.709238 | + | 0.704969i | \(0.249039\pi\) | |||||||
\(54\) | −2.48810 | −0.338587 | ||||||||
\(55\) | −10.5684 | −1.42504 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.64438 | −0.482710 | ||||||||
\(58\) | 7.17166 | 0.941685 | ||||||||
\(59\) | −8.70177 | −1.13287 | −0.566437 | − | 0.824105i | \(-0.691679\pi\) | ||||
−0.566437 | + | 0.824105i | \(0.691679\pi\) | |||||||
\(60\) | 9.91672 | 1.28024 | ||||||||
\(61\) | −8.35367 | −1.06958 | −0.534789 | − | 0.844986i | \(-0.679609\pi\) | ||||
−0.534789 | + | 0.844986i | \(0.679609\pi\) | |||||||
\(62\) | −2.93804 | −0.373132 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.41498 | −0.676872 | ||||||||
\(65\) | −11.8708 | −1.47239 | ||||||||
\(66\) | −11.1118 | −1.36777 | ||||||||
\(67\) | −0.0922892 | −0.0112749 | −0.00563746 | − | 0.999984i | \(-0.501794\pi\) | ||||
−0.00563746 | + | 0.999984i | \(0.501794\pi\) | |||||||
\(68\) | −20.4757 | −2.48304 | ||||||||
\(69\) | 2.22001 | 0.267258 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.08552 | 0.366184 | 0.183092 | − | 0.983096i | \(-0.441389\pi\) | ||||
0.183092 | + | 0.983096i | \(0.441389\pi\) | |||||||
\(72\) | 5.45047 | 0.642344 | ||||||||
\(73\) | 9.88365 | 1.15679 | 0.578397 | − | 0.815755i | \(-0.303678\pi\) | ||||
0.578397 | + | 0.815755i | \(0.303678\pi\) | |||||||
\(74\) | −1.86183 | −0.216433 | ||||||||
\(75\) | −0.599893 | −0.0692696 | ||||||||
\(76\) | 15.2722 | 1.75184 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −12.4812 | −1.41322 | ||||||||
\(79\) | 7.87830 | 0.886378 | 0.443189 | − | 0.896428i | \(-0.353847\pi\) | ||||
0.443189 | + | 0.896428i | \(0.353847\pi\) | |||||||
\(80\) | −12.2581 | −1.37050 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.48810 | 0.274764 | ||||||||
\(83\) | 6.26355 | 0.687514 | 0.343757 | − | 0.939059i | \(-0.388300\pi\) | ||||
0.343757 | + | 0.939059i | \(0.388300\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.5625 | 1.25413 | ||||||||
\(86\) | 17.3728 | 1.87336 | ||||||||
\(87\) | −2.88239 | −0.309024 | ||||||||
\(88\) | 24.3418 | 2.59484 | ||||||||
\(89\) | 10.3142 | 1.09330 | 0.546652 | − | 0.837360i | \(-0.315902\pi\) | ||||
0.546652 | + | 0.837360i | \(0.315902\pi\) | |||||||
\(90\) | −5.88785 | −0.620634 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −9.30321 | −0.969926 | ||||||||
\(93\) | 1.18084 | 0.122447 | ||||||||
\(94\) | 19.0168 | 1.96144 | ||||||||
\(95\) | −8.62409 | −0.884813 | ||||||||
\(96\) | −1.98751 | −0.202849 | ||||||||
\(97\) | 4.64324 | 0.471449 | 0.235725 | − | 0.971820i | \(-0.424254\pi\) | ||||
0.235725 | + | 0.971820i | \(0.424254\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.46600 | 0.448850 | ||||||||
\(100\) | 2.51392 | 0.251392 | ||||||||
\(101\) | 13.8197 | 1.37511 | 0.687555 | − | 0.726133i | \(-0.258684\pi\) | ||||
0.687555 | + | 0.726133i | \(0.258684\pi\) | |||||||
\(102\) | 12.1570 | 1.20373 | ||||||||
\(103\) | 13.0191 | 1.28281 | 0.641403 | − | 0.767204i | \(-0.278353\pi\) | ||||
0.641403 | + | 0.767204i | \(0.278353\pi\) | |||||||
\(104\) | 27.3416 | 2.68106 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 25.6937 | 2.49560 | ||||||||
\(107\) | −19.9762 | −1.93117 | −0.965586 | − | 0.260083i | \(-0.916250\pi\) | ||||
−0.965586 | + | 0.260083i | \(0.916250\pi\) | |||||||
\(108\) | −4.19062 | −0.403242 | ||||||||
\(109\) | 4.41695 | 0.423067 | 0.211533 | − | 0.977371i | \(-0.432154\pi\) | ||||
0.211533 | + | 0.977371i | \(0.432154\pi\) | |||||||
\(110\) | −26.2952 | −2.50714 | ||||||||
\(111\) | 0.748295 | 0.0710250 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.4815 | −1.36230 | −0.681151 | − | 0.732143i | \(-0.738520\pi\) | ||||
−0.681151 | + | 0.732143i | \(0.738520\pi\) | |||||||
\(114\) | −9.06756 | −0.849255 | ||||||||
\(115\) | 5.25345 | 0.489887 | ||||||||
\(116\) | 12.0790 | 1.12151 | ||||||||
\(117\) | 5.01637 | 0.463764 | ||||||||
\(118\) | −21.6508 | −1.99312 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 12.8980 | 1.17742 | ||||||||
\(121\) | 8.94517 | 0.813197 | ||||||||
\(122\) | −20.7847 | −1.88176 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | −4.94845 | −0.444384 | ||||||||
\(125\) | 10.4125 | 0.931318 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.9357 | 1.59154 | 0.795769 | − | 0.605600i | \(-0.207067\pi\) | ||||
0.795769 | + | 0.605600i | \(0.207067\pi\) | |||||||
\(128\) | −17.4480 | −1.54220 | ||||||||
\(129\) | −6.98238 | −0.614765 | ||||||||
\(130\) | −29.5356 | −2.59045 | ||||||||
\(131\) | −1.81416 | −0.158504 | −0.0792518 | − | 0.996855i | \(-0.525253\pi\) | ||||
−0.0792518 | + | 0.996855i | \(0.525253\pi\) | |||||||
\(132\) | −18.7153 | −1.62896 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.229624 | −0.0198365 | ||||||||
\(135\) | 2.36641 | 0.203668 | ||||||||
\(136\) | −26.6314 | −2.28363 | ||||||||
\(137\) | 10.3191 | 0.881623 | 0.440811 | − | 0.897600i | \(-0.354691\pi\) | ||||
0.440811 | + | 0.897600i | \(0.354691\pi\) | |||||||
\(138\) | 5.52359 | 0.470199 | ||||||||
\(139\) | 12.1318 | 1.02901 | 0.514504 | − | 0.857488i | \(-0.327976\pi\) | ||||
0.514504 | + | 0.857488i | \(0.327976\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.64313 | −0.643667 | ||||||||
\(142\) | 7.67708 | 0.644246 | ||||||||
\(143\) | 22.4031 | 1.87344 | ||||||||
\(144\) | 5.18004 | 0.431670 | ||||||||
\(145\) | −6.82091 | −0.566446 | ||||||||
\(146\) | 24.5915 | 2.03520 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.13582 | −0.257763 | ||||||||
\(149\) | −16.8170 | −1.37771 | −0.688853 | − | 0.724901i | \(-0.741886\pi\) | ||||
−0.688853 | + | 0.724901i | \(0.741886\pi\) | |||||||
\(150\) | −1.49259 | −0.121869 | ||||||||
\(151\) | −16.1017 | −1.31034 | −0.655168 | − | 0.755483i | \(-0.727402\pi\) | ||||
−0.655168 | + | 0.755483i | \(0.727402\pi\) | |||||||
\(152\) | 19.8636 | 1.61115 | ||||||||
\(153\) | −4.88608 | −0.395016 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.79435 | 0.224448 | ||||||||
\(156\) | −21.0217 | −1.68308 | ||||||||
\(157\) | −7.43656 | −0.593502 | −0.296751 | − | 0.954955i | \(-0.595903\pi\) | ||||
−0.296751 | + | 0.954955i | \(0.595903\pi\) | |||||||
\(158\) | 19.6020 | 1.55945 | ||||||||
\(159\) | −10.3267 | −0.818958 | ||||||||
\(160\) | −4.70326 | −0.371825 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.48810 | 0.195483 | ||||||||
\(163\) | 19.1144 | 1.49715 | 0.748576 | − | 0.663049i | \(-0.230738\pi\) | ||||
0.748576 | + | 0.663049i | \(0.230738\pi\) | |||||||
\(164\) | 4.19062 | 0.327232 | ||||||||
\(165\) | 10.5684 | 0.822748 | ||||||||
\(166\) | 15.5843 | 1.20958 | ||||||||
\(167\) | 3.05717 | 0.236571 | 0.118285 | − | 0.992980i | \(-0.462260\pi\) | ||||
0.118285 | + | 0.992980i | \(0.462260\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.1640 | 0.935690 | ||||||||
\(170\) | 28.7685 | 2.20645 | ||||||||
\(171\) | 3.64438 | 0.278693 | ||||||||
\(172\) | 29.2605 | 2.23109 | ||||||||
\(173\) | −12.6063 | −0.958439 | −0.479219 | − | 0.877695i | \(-0.659080\pi\) | ||||
−0.479219 | + | 0.877695i | \(0.659080\pi\) | |||||||
\(174\) | −7.17166 | −0.543682 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 23.1341 | 1.74380 | ||||||||
\(177\) | 8.70177 | 0.654065 | ||||||||
\(178\) | 25.6627 | 1.92350 | ||||||||
\(179\) | −6.53673 | −0.488578 | −0.244289 | − | 0.969702i | \(-0.578555\pi\) | ||||
−0.244289 | + | 0.969702i | \(0.578555\pi\) | |||||||
\(180\) | −9.91672 | −0.739148 | ||||||||
\(181\) | −1.75566 | −0.130497 | −0.0652487 | − | 0.997869i | \(-0.520784\pi\) | ||||
−0.0652487 | + | 0.997869i | \(0.520784\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.35367 | 0.617521 | ||||||||
\(184\) | −12.1001 | −0.892030 | ||||||||
\(185\) | 1.77077 | 0.130190 | ||||||||
\(186\) | 2.93804 | 0.215428 | ||||||||
\(187\) | −21.8212 | −1.59573 | ||||||||
\(188\) | 32.0294 | 2.33599 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −21.4576 | −1.55669 | ||||||||
\(191\) | 3.79254 | 0.274418 | 0.137209 | − | 0.990542i | \(-0.456187\pi\) | ||||
0.137209 | + | 0.990542i | \(0.456187\pi\) | |||||||
\(192\) | 5.41498 | 0.390792 | ||||||||
\(193\) | −0.179574 | −0.0129260 | −0.00646302 | − | 0.999979i | \(-0.502057\pi\) | ||||
−0.00646302 | + | 0.999979i | \(0.502057\pi\) | |||||||
\(194\) | 11.5528 | 0.829444 | ||||||||
\(195\) | 11.8708 | 0.850085 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.2115 | −0.941280 | −0.470640 | − | 0.882325i | \(-0.655977\pi\) | ||||
−0.470640 | + | 0.882325i | \(0.655977\pi\) | |||||||
\(198\) | 11.1118 | 0.789684 | ||||||||
\(199\) | −5.46727 | −0.387564 | −0.193782 | − | 0.981045i | \(-0.562075\pi\) | ||||
−0.193782 | + | 0.981045i | \(0.562075\pi\) | |||||||
\(200\) | 3.26969 | 0.231202 | ||||||||
\(201\) | 0.0922892 | 0.00650958 | ||||||||
\(202\) | 34.3847 | 2.41930 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 20.4757 | 1.43359 | ||||||||
\(205\) | −2.36641 | −0.165277 | ||||||||
\(206\) | 32.3926 | 2.25690 | ||||||||
\(207\) | −2.22001 | −0.154301 | ||||||||
\(208\) | 25.9850 | 1.80174 | ||||||||
\(209\) | 16.2758 | 1.12582 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.8035 | 0.881430 | 0.440715 | − | 0.897647i | \(-0.354725\pi\) | ||||
0.440715 | + | 0.897647i | \(0.354725\pi\) | |||||||
\(212\) | 43.2751 | 2.97215 | ||||||||
\(213\) | −3.08552 | −0.211417 | ||||||||
\(214\) | −49.7027 | −3.39761 | ||||||||
\(215\) | −16.5232 | −1.12687 | ||||||||
\(216\) | −5.45047 | −0.370857 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 10.9898 | 0.744322 | ||||||||
\(219\) | −9.88365 | −0.667875 | ||||||||
\(220\) | −44.2881 | −2.98590 | ||||||||
\(221\) | −24.5104 | −1.64875 | ||||||||
\(222\) | 1.86183 | 0.124958 | ||||||||
\(223\) | 1.61990 | 0.108477 | 0.0542383 | − | 0.998528i | \(-0.482727\pi\) | ||||
0.0542383 | + | 0.998528i | \(0.482727\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.599893 | 0.0399928 | ||||||||
\(226\) | −36.0313 | −2.39676 | ||||||||
\(227\) | 7.09352 | 0.470813 | 0.235407 | − | 0.971897i | \(-0.424358\pi\) | ||||
0.235407 | + | 0.971897i | \(0.424358\pi\) | |||||||
\(228\) | −15.2722 | −1.01143 | ||||||||
\(229\) | −10.2801 | −0.679326 | −0.339663 | − | 0.940547i | \(-0.610313\pi\) | ||||
−0.339663 | + | 0.940547i | \(0.610313\pi\) | |||||||
\(230\) | 13.0711 | 0.861882 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 15.7104 | 1.03144 | ||||||||
\(233\) | 26.2441 | 1.71931 | 0.859656 | − | 0.510874i | \(-0.170678\pi\) | ||||
0.859656 | + | 0.510874i | \(0.170678\pi\) | |||||||
\(234\) | 12.4812 | 0.815922 | ||||||||
\(235\) | −18.0868 | −1.17985 | ||||||||
\(236\) | −36.4658 | −2.37372 | ||||||||
\(237\) | −7.87830 | −0.511750 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.99590 | 0.646581 | 0.323290 | − | 0.946300i | \(-0.395211\pi\) | ||||
0.323290 | + | 0.946300i | \(0.395211\pi\) | |||||||
\(240\) | 12.2581 | 0.791257 | ||||||||
\(241\) | 2.67886 | 0.172560 | 0.0862801 | − | 0.996271i | \(-0.472502\pi\) | ||||
0.0862801 | + | 0.996271i | \(0.472502\pi\) | |||||||
\(242\) | 22.2564 | 1.43070 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −35.0071 | −2.24110 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.48810 | −0.158635 | ||||||||
\(247\) | 18.2815 | 1.16323 | ||||||||
\(248\) | −6.43613 | −0.408695 | ||||||||
\(249\) | −6.26355 | −0.396936 | ||||||||
\(250\) | 25.9072 | 1.63851 | ||||||||
\(251\) | 23.4644 | 1.48106 | 0.740529 | − | 0.672024i | \(-0.234575\pi\) | ||||
0.740529 | + | 0.672024i | \(0.234575\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.91456 | −0.623323 | ||||||||
\(254\) | 44.6258 | 2.80007 | ||||||||
\(255\) | −11.5625 | −0.724070 | ||||||||
\(256\) | −32.5823 | −2.03639 | ||||||||
\(257\) | −20.6351 | −1.28718 | −0.643590 | − | 0.765370i | \(-0.722556\pi\) | ||||
−0.643590 | + | 0.765370i | \(0.722556\pi\) | |||||||
\(258\) | −17.3728 | −1.08159 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −49.7459 | −3.08511 | ||||||||
\(261\) | 2.88239 | 0.178415 | ||||||||
\(262\) | −4.51380 | −0.278863 | ||||||||
\(263\) | 10.4139 | 0.642152 | 0.321076 | − | 0.947054i | \(-0.395956\pi\) | ||||
0.321076 | + | 0.947054i | \(0.395956\pi\) | |||||||
\(264\) | −24.3418 | −1.49813 | ||||||||
\(265\) | −24.4371 | −1.50116 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.3142 | −0.631219 | ||||||||
\(268\) | −0.386749 | −0.0236244 | ||||||||
\(269\) | −18.0405 | −1.09995 | −0.549973 | − | 0.835182i | \(-0.685362\pi\) | ||||
−0.549973 | + | 0.835182i | \(0.685362\pi\) | |||||||
\(270\) | 5.88785 | 0.358323 | ||||||||
\(271\) | 30.1360 | 1.83063 | 0.915315 | − | 0.402739i | \(-0.131942\pi\) | ||||
0.915315 | + | 0.402739i | \(0.131942\pi\) | |||||||
\(272\) | −25.3101 | −1.53465 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 25.6750 | 1.55108 | ||||||||
\(275\) | 2.67912 | 0.161557 | ||||||||
\(276\) | 9.30321 | 0.559987 | ||||||||
\(277\) | −15.2878 | −0.918558 | −0.459279 | − | 0.888292i | \(-0.651892\pi\) | ||||
−0.459279 | + | 0.888292i | \(0.651892\pi\) | |||||||
\(278\) | 30.1851 | 1.81038 | ||||||||
\(279\) | −1.18084 | −0.0706950 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.02679 | 0.240218 | 0.120109 | − | 0.992761i | \(-0.461676\pi\) | ||||
0.120109 | + | 0.992761i | \(0.461676\pi\) | |||||||
\(282\) | −19.0168 | −1.13244 | ||||||||
\(283\) | −18.0462 | −1.07274 | −0.536368 | − | 0.843984i | \(-0.680204\pi\) | ||||
−0.536368 | + | 0.843984i | \(0.680204\pi\) | |||||||
\(284\) | 12.9303 | 0.767269 | ||||||||
\(285\) | 8.62409 | 0.510847 | ||||||||
\(286\) | 55.7411 | 3.29604 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.98751 | 0.117115 | ||||||||
\(289\) | 6.87380 | 0.404341 | ||||||||
\(290\) | −16.9711 | −0.996576 | ||||||||
\(291\) | −4.64324 | −0.272191 | ||||||||
\(292\) | 41.4186 | 2.42384 | ||||||||
\(293\) | −5.56871 | −0.325327 | −0.162664 | − | 0.986682i | \(-0.552009\pi\) | ||||
−0.162664 | + | 0.986682i | \(0.552009\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.5920 | 1.19891 | ||||||||
\(296\) | −4.07856 | −0.237061 | ||||||||
\(297\) | −4.46600 | −0.259144 | ||||||||
\(298\) | −41.8424 | −2.42387 | ||||||||
\(299\) | −11.1364 | −0.644034 | ||||||||
\(300\) | −2.51392 | −0.145141 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −40.0625 | −2.30534 | ||||||||
\(303\) | −13.8197 | −0.793920 | ||||||||
\(304\) | 18.8780 | 1.08273 | ||||||||
\(305\) | 19.7682 | 1.13192 | ||||||||
\(306\) | −12.1570 | −0.694972 | ||||||||
\(307\) | 20.3285 | 1.16021 | 0.580106 | − | 0.814541i | \(-0.303011\pi\) | ||||
0.580106 | + | 0.814541i | \(0.303011\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.0191 | −0.740628 | ||||||||
\(310\) | 6.95261 | 0.394882 | ||||||||
\(311\) | 24.9893 | 1.41701 | 0.708505 | − | 0.705705i | \(-0.249370\pi\) | ||||
0.708505 | + | 0.705705i | \(0.249370\pi\) | |||||||
\(312\) | −27.3416 | −1.54791 | ||||||||
\(313\) | 19.0197 | 1.07506 | 0.537529 | − | 0.843245i | \(-0.319358\pi\) | ||||
0.537529 | + | 0.843245i | \(0.319358\pi\) | |||||||
\(314\) | −18.5029 | −1.04418 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 33.0149 | 1.85724 | ||||||||
\(317\) | −26.7130 | −1.50035 | −0.750177 | − | 0.661237i | \(-0.770032\pi\) | ||||
−0.750177 | + | 0.661237i | \(0.770032\pi\) | |||||||
\(318\) | −25.6937 | −1.44083 | ||||||||
\(319\) | 12.8728 | 0.720736 | ||||||||
\(320\) | 12.8140 | 0.716327 | ||||||||
\(321\) | 19.9762 | 1.11496 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.8067 | −0.990793 | ||||||||
\(324\) | 4.19062 | 0.232812 | ||||||||
\(325\) | 3.00928 | 0.166925 | ||||||||
\(326\) | 47.5583 | 2.63401 | ||||||||
\(327\) | −4.41695 | −0.244258 | ||||||||
\(328\) | 5.45047 | 0.300952 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 26.2952 | 1.44750 | ||||||||
\(331\) | −28.7281 | −1.57904 | −0.789519 | − | 0.613726i | \(-0.789670\pi\) | ||||
−0.789519 | + | 0.613726i | \(0.789670\pi\) | |||||||
\(332\) | 26.2481 | 1.44055 | ||||||||
\(333\) | −0.748295 | −0.0410063 | ||||||||
\(334\) | 7.60652 | 0.416210 | ||||||||
\(335\) | 0.218394 | 0.0119321 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.39749 | 0.294020 | 0.147010 | − | 0.989135i | \(-0.453035\pi\) | ||||
0.147010 | + | 0.989135i | \(0.453035\pi\) | |||||||
\(338\) | 30.2651 | 1.64621 | ||||||||
\(339\) | 14.4815 | 0.786525 | ||||||||
\(340\) | 48.4539 | 2.62778 | ||||||||
\(341\) | −5.27363 | −0.285583 | ||||||||
\(342\) | 9.06756 | 0.490317 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 38.0573 | 2.05191 | ||||||||
\(345\) | −5.25345 | −0.282836 | ||||||||
\(346\) | −31.3657 | −1.68623 | ||||||||
\(347\) | −11.2384 | −0.603308 | −0.301654 | − | 0.953418i | \(-0.597539\pi\) | ||||
−0.301654 | + | 0.953418i | \(0.597539\pi\) | |||||||
\(348\) | −12.0790 | −0.647502 | ||||||||
\(349\) | 32.7910 | 1.75526 | 0.877631 | − | 0.479337i | \(-0.159123\pi\) | ||||
0.877631 | + | 0.479337i | \(0.159123\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.01637 | −0.267754 | ||||||||
\(352\) | 8.87622 | 0.473104 | ||||||||
\(353\) | −37.0316 | −1.97099 | −0.985496 | − | 0.169699i | \(-0.945720\pi\) | ||||
−0.985496 | + | 0.169699i | \(0.945720\pi\) | |||||||
\(354\) | 21.6508 | 1.15073 | ||||||||
\(355\) | −7.30161 | −0.387529 | ||||||||
\(356\) | 43.2229 | 2.29081 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −16.2640 | −0.859579 | ||||||||
\(359\) | −28.8297 | −1.52157 | −0.760786 | − | 0.649003i | \(-0.775186\pi\) | ||||
−0.760786 | + | 0.649003i | \(0.775186\pi\) | |||||||
\(360\) | −12.8980 | −0.679786 | ||||||||
\(361\) | −5.71851 | −0.300974 | ||||||||
\(362\) | −4.36826 | −0.229590 | ||||||||
\(363\) | −8.94517 | −0.469499 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −23.3888 | −1.22422 | ||||||||
\(366\) | 20.7847 | 1.08644 | ||||||||
\(367\) | −30.4855 | −1.59133 | −0.795664 | − | 0.605738i | \(-0.792878\pi\) | ||||
−0.795664 | + | 0.605738i | \(0.792878\pi\) | |||||||
\(368\) | −11.4997 | −0.599465 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | 4.40585 | 0.229049 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.94845 | 0.256565 | ||||||||
\(373\) | 11.0618 | 0.572758 | 0.286379 | − | 0.958116i | \(-0.407548\pi\) | ||||
0.286379 | + | 0.958116i | \(0.407548\pi\) | |||||||
\(374\) | −54.2933 | −2.80744 | ||||||||
\(375\) | −10.4125 | −0.537697 | ||||||||
\(376\) | 41.6586 | 2.14838 | ||||||||
\(377\) | 14.4591 | 0.744683 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.5413 | 0.952404 | 0.476202 | − | 0.879336i | \(-0.342013\pi\) | ||||
0.476202 | + | 0.879336i | \(0.342013\pi\) | |||||||
\(380\) | −36.1403 | −1.85396 | ||||||||
\(381\) | −17.9357 | −0.918875 | ||||||||
\(382\) | 9.43620 | 0.482798 | ||||||||
\(383\) | −25.7669 | −1.31663 | −0.658313 | − | 0.752745i | \(-0.728729\pi\) | ||||
−0.658313 | + | 0.752745i | \(0.728729\pi\) | |||||||
\(384\) | 17.4480 | 0.890389 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.446798 | −0.0227414 | ||||||||
\(387\) | 6.98238 | 0.354935 | ||||||||
\(388\) | 19.4580 | 0.987832 | ||||||||
\(389\) | 8.98025 | 0.455317 | 0.227658 | − | 0.973741i | \(-0.426893\pi\) | ||||
0.227658 | + | 0.973741i | \(0.426893\pi\) | |||||||
\(390\) | 29.5356 | 1.49560 | ||||||||
\(391\) | 10.8471 | 0.548564 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.81416 | 0.0915121 | ||||||||
\(394\) | −32.8715 | −1.65604 | ||||||||
\(395\) | −18.6433 | −0.938045 | ||||||||
\(396\) | 18.7153 | 0.940479 | ||||||||
\(397\) | −29.8142 | −1.49633 | −0.748165 | − | 0.663513i | \(-0.769065\pi\) | ||||
−0.748165 | + | 0.663513i | \(0.769065\pi\) | |||||||
\(398\) | −13.6031 | −0.681861 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.10747 | 0.155373 | ||||||||
\(401\) | 30.6347 | 1.52983 | 0.764913 | − | 0.644134i | \(-0.222782\pi\) | ||||
0.764913 | + | 0.644134i | \(0.222782\pi\) | |||||||
\(402\) | 0.229624 | 0.0114526 | ||||||||
\(403\) | −5.92353 | −0.295072 | ||||||||
\(404\) | 57.9130 | 2.88128 | ||||||||
\(405\) | −2.36641 | −0.117588 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.34189 | −0.165651 | ||||||||
\(408\) | 26.6314 | 1.31845 | ||||||||
\(409\) | −9.88842 | −0.488951 | −0.244475 | − | 0.969656i | \(-0.578616\pi\) | ||||
−0.244475 | + | 0.969656i | \(0.578616\pi\) | |||||||
\(410\) | −5.88785 | −0.290780 | ||||||||
\(411\) | −10.3191 | −0.509005 | ||||||||
\(412\) | 54.5579 | 2.68787 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −5.52359 | −0.271470 | ||||||||
\(415\) | −14.8221 | −0.727589 | ||||||||
\(416\) | 9.97008 | 0.488823 | ||||||||
\(417\) | −12.1318 | −0.594098 | ||||||||
\(418\) | 40.4957 | 1.98071 | ||||||||
\(419\) | 7.68415 | 0.375395 | 0.187698 | − | 0.982227i | \(-0.439897\pi\) | ||||
0.187698 | + | 0.982227i | \(0.439897\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.53541 | −0.269780 | −0.134890 | − | 0.990861i | \(-0.543068\pi\) | ||||
−0.134890 | + | 0.990861i | \(0.543068\pi\) | |||||||
\(422\) | 31.8563 | 1.55074 | ||||||||
\(423\) | 7.64313 | 0.371622 | ||||||||
\(424\) | 56.2851 | 2.73345 | ||||||||
\(425\) | −2.93112 | −0.142180 | ||||||||
\(426\) | −7.67708 | −0.371956 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −83.7126 | −4.04640 | ||||||||
\(429\) | −22.4031 | −1.08163 | ||||||||
\(430\) | −41.1112 | −1.98256 | ||||||||
\(431\) | −34.5461 | −1.66403 | −0.832014 | − | 0.554755i | \(-0.812812\pi\) | ||||
−0.832014 | + | 0.554755i | \(0.812812\pi\) | |||||||
\(432\) | −5.18004 | −0.249225 | ||||||||
\(433\) | 1.93996 | 0.0932284 | 0.0466142 | − | 0.998913i | \(-0.485157\pi\) | ||||
0.0466142 | + | 0.998913i | \(0.485157\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.82091 | 0.327038 | ||||||||
\(436\) | 18.5097 | 0.886455 | ||||||||
\(437\) | −8.09055 | −0.387023 | ||||||||
\(438\) | −24.5915 | −1.17503 | ||||||||
\(439\) | −36.9625 | −1.76412 | −0.882062 | − | 0.471134i | \(-0.843845\pi\) | ||||
−0.882062 | + | 0.471134i | \(0.843845\pi\) | |||||||
\(440\) | −57.6026 | −2.74610 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −60.9842 | −2.90072 | ||||||||
\(443\) | −28.9153 | −1.37381 | −0.686903 | − | 0.726749i | \(-0.741030\pi\) | ||||
−0.686903 | + | 0.726749i | \(0.741030\pi\) | |||||||
\(444\) | 3.13582 | 0.148819 | ||||||||
\(445\) | −24.4076 | −1.15703 | ||||||||
\(446\) | 4.03047 | 0.190848 | ||||||||
\(447\) | 16.8170 | 0.795419 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.04865 | −0.379839 | −0.189920 | − | 0.981800i | \(-0.560823\pi\) | ||||
−0.189920 | + | 0.981800i | \(0.560823\pi\) | |||||||
\(450\) | 1.49259 | 0.0703614 | ||||||||
\(451\) | 4.46600 | 0.210296 | ||||||||
\(452\) | −60.6863 | −2.85444 | ||||||||
\(453\) | 16.1017 | 0.756523 | ||||||||
\(454\) | 17.6493 | 0.828325 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −19.8636 | −0.930196 | ||||||||
\(457\) | 4.73364 | 0.221430 | 0.110715 | − | 0.993852i | \(-0.464686\pi\) | ||||
0.110715 | + | 0.993852i | \(0.464686\pi\) | |||||||
\(458\) | −25.5778 | −1.19517 | ||||||||
\(459\) | 4.88608 | 0.228063 | ||||||||
\(460\) | 22.0152 | 1.02646 | ||||||||
\(461\) | −36.8719 | −1.71730 | −0.858648 | − | 0.512567i | \(-0.828695\pi\) | ||||
−0.858648 | + | 0.512567i | \(0.828695\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.4447 | 0.531880 | 0.265940 | − | 0.963990i | \(-0.414318\pi\) | ||||
0.265940 | + | 0.963990i | \(0.414318\pi\) | |||||||
\(464\) | 14.9309 | 0.693150 | ||||||||
\(465\) | −2.79435 | −0.129585 | ||||||||
\(466\) | 65.2979 | 3.02487 | ||||||||
\(467\) | −9.31809 | −0.431190 | −0.215595 | − | 0.976483i | \(-0.569169\pi\) | ||||
−0.215595 | + | 0.976483i | \(0.569169\pi\) | |||||||
\(468\) | 21.0217 | 0.971728 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −45.0016 | −2.07577 | ||||||||
\(471\) | 7.43656 | 0.342658 | ||||||||
\(472\) | −47.4287 | −2.18308 | ||||||||
\(473\) | 31.1833 | 1.43381 | ||||||||
\(474\) | −19.6020 | −0.900348 | ||||||||
\(475\) | 2.18624 | 0.100311 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.3267 | 0.472826 | ||||||||
\(478\) | 24.8707 | 1.13756 | ||||||||
\(479\) | −39.5784 | −1.80838 | −0.904191 | − | 0.427128i | \(-0.859525\pi\) | ||||
−0.904191 | + | 0.427128i | \(0.859525\pi\) | |||||||
\(480\) | 4.70326 | 0.214673 | ||||||||
\(481\) | −3.75372 | −0.171155 | ||||||||
\(482\) | 6.66525 | 0.303594 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 37.4858 | 1.70390 | ||||||||
\(485\) | −10.9878 | −0.498930 | ||||||||
\(486\) | −2.48810 | −0.112862 | ||||||||
\(487\) | 25.9347 | 1.17521 | 0.587607 | − | 0.809147i | \(-0.300070\pi\) | ||||
0.587607 | + | 0.809147i | \(0.300070\pi\) | |||||||
\(488\) | −45.5314 | −2.06111 | ||||||||
\(489\) | −19.1144 | −0.864381 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.5856 | −0.522851 | −0.261426 | − | 0.965224i | \(-0.584193\pi\) | ||||
−0.261426 | + | 0.965224i | \(0.584193\pi\) | |||||||
\(492\) | −4.19062 | −0.188928 | ||||||||
\(493\) | −14.0836 | −0.634293 | ||||||||
\(494\) | 45.4862 | 2.04652 | ||||||||
\(495\) | −10.5684 | −0.475014 | ||||||||
\(496\) | −6.11680 | −0.274653 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −15.5843 | −0.698349 | ||||||||
\(499\) | 22.5754 | 1.01061 | 0.505306 | − | 0.862940i | \(-0.331380\pi\) | ||||
0.505306 | + | 0.862940i | \(0.331380\pi\) | |||||||
\(500\) | 43.6346 | 1.95140 | ||||||||
\(501\) | −3.05717 | −0.136584 | ||||||||
\(502\) | 58.3816 | 2.60570 | ||||||||
\(503\) | −23.5474 | −1.04993 | −0.524963 | − | 0.851125i | \(-0.675921\pi\) | ||||
−0.524963 | + | 0.851125i | \(0.675921\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −32.7030 | −1.45527 | ||||||||
\(506\) | −24.6684 | −1.09664 | ||||||||
\(507\) | −12.1640 | −0.540221 | ||||||||
\(508\) | 75.1618 | 3.33476 | ||||||||
\(509\) | −27.1606 | −1.20387 | −0.601937 | − | 0.798543i | \(-0.705604\pi\) | ||||
−0.601937 | + | 0.798543i | \(0.705604\pi\) | |||||||
\(510\) | −28.7685 | −1.27389 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −46.1719 | −2.04053 | ||||||||
\(513\) | −3.64438 | −0.160903 | ||||||||
\(514\) | −51.3420 | −2.26460 | ||||||||
\(515\) | −30.8084 | −1.35758 | ||||||||
\(516\) | −29.2605 | −1.28812 | ||||||||
\(517\) | 34.1342 | 1.50122 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.6063 | 0.553355 | ||||||||
\(520\) | −64.7013 | −2.83734 | ||||||||
\(521\) | 19.8395 | 0.869183 | 0.434592 | − | 0.900628i | \(-0.356893\pi\) | ||||
0.434592 | + | 0.900628i | \(0.356893\pi\) | |||||||
\(522\) | 7.17166 | 0.313895 | ||||||||
\(523\) | 3.17412 | 0.138795 | 0.0693974 | − | 0.997589i | \(-0.477892\pi\) | ||||
0.0693974 | + | 0.997589i | \(0.477892\pi\) | |||||||
\(524\) | −7.60244 | −0.332114 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 25.9109 | 1.12977 | ||||||||
\(527\) | 5.76968 | 0.251331 | ||||||||
\(528\) | −23.1341 | −1.00678 | ||||||||
\(529\) | −18.0716 | −0.785720 | ||||||||
\(530\) | −60.8019 | −2.64106 | ||||||||
\(531\) | −8.70177 | −0.377625 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.01637 | 0.217283 | ||||||||
\(534\) | −25.6627 | −1.11054 | ||||||||
\(535\) | 47.2719 | 2.04374 | ||||||||
\(536\) | −0.503019 | −0.0217271 | ||||||||
\(537\) | 6.53673 | 0.282081 | ||||||||
\(538\) | −44.8864 | −1.93519 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 9.91672 | 0.426748 | ||||||||
\(541\) | −25.4484 | −1.09411 | −0.547057 | − | 0.837096i | \(-0.684252\pi\) | ||||
−0.547057 | + | 0.837096i | \(0.684252\pi\) | |||||||
\(542\) | 74.9812 | 3.22072 | ||||||||
\(543\) | 1.75566 | 0.0753427 | ||||||||
\(544\) | −9.71113 | −0.416361 | ||||||||
\(545\) | −10.4523 | −0.447727 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −41.5789 | −1.77779 | −0.888893 | − | 0.458116i | \(-0.848525\pi\) | ||||
−0.888893 | + | 0.458116i | \(0.848525\pi\) | |||||||
\(548\) | 43.2435 | 1.84727 | ||||||||
\(549\) | −8.35367 | −0.356526 | ||||||||
\(550\) | 6.66591 | 0.284235 | ||||||||
\(551\) | 10.5045 | 0.447507 | ||||||||
\(552\) | 12.1001 | 0.515014 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −38.0376 | −1.61606 | ||||||||
\(555\) | −1.77077 | −0.0751651 | ||||||||
\(556\) | 50.8398 | 2.15609 | ||||||||
\(557\) | 40.8397 | 1.73043 | 0.865217 | − | 0.501398i | \(-0.167181\pi\) | ||||
0.865217 | + | 0.501398i | \(0.167181\pi\) | |||||||
\(558\) | −2.93804 | −0.124377 | ||||||||
\(559\) | 35.0262 | 1.48145 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.8212 | 0.921294 | ||||||||
\(562\) | 10.0190 | 0.422627 | ||||||||
\(563\) | −7.56052 | −0.318638 | −0.159319 | − | 0.987227i | \(-0.550930\pi\) | ||||
−0.159319 | + | 0.987227i | \(0.550930\pi\) | |||||||
\(564\) | −32.0294 | −1.34868 | ||||||||
\(565\) | 34.2691 | 1.44171 | ||||||||
\(566\) | −44.9007 | −1.88732 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 16.8175 | 0.705649 | ||||||||
\(569\) | −20.8842 | −0.875513 | −0.437756 | − | 0.899094i | \(-0.644227\pi\) | ||||
−0.437756 | + | 0.899094i | \(0.644227\pi\) | |||||||
\(570\) | 21.4576 | 0.898758 | ||||||||
\(571\) | −29.6774 | −1.24196 | −0.620980 | − | 0.783827i | \(-0.713265\pi\) | ||||
−0.620980 | + | 0.783827i | \(0.713265\pi\) | |||||||
\(572\) | 93.8829 | 3.92544 | ||||||||
\(573\) | −3.79254 | −0.158436 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.33177 | −0.0555385 | ||||||||
\(576\) | −5.41498 | −0.225624 | ||||||||
\(577\) | 0.394080 | 0.0164057 | 0.00820287 | − | 0.999966i | \(-0.497389\pi\) | ||||
0.00820287 | + | 0.999966i | \(0.497389\pi\) | |||||||
\(578\) | 17.1027 | 0.711377 | ||||||||
\(579\) | 0.179574 | 0.00746285 | ||||||||
\(580\) | −28.5838 | −1.18688 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −11.5528 | −0.478879 | ||||||||
\(583\) | 46.1189 | 1.91005 | ||||||||
\(584\) | 53.8705 | 2.22918 | ||||||||
\(585\) | −11.8708 | −0.490797 | ||||||||
\(586\) | −13.8555 | −0.572364 | ||||||||
\(587\) | 12.0519 | 0.497435 | 0.248717 | − | 0.968576i | \(-0.419991\pi\) | ||||
0.248717 | + | 0.968576i | \(0.419991\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.30343 | −0.177320 | ||||||||
\(590\) | 51.2348 | 2.10930 | ||||||||
\(591\) | 13.2115 | 0.543448 | ||||||||
\(592\) | −3.87620 | −0.159311 | ||||||||
\(593\) | 34.1529 | 1.40249 | 0.701246 | − | 0.712919i | \(-0.252627\pi\) | ||||
0.701246 | + | 0.712919i | \(0.252627\pi\) | |||||||
\(594\) | −11.1118 | −0.455924 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −70.4738 | −2.88672 | ||||||||
\(597\) | 5.46727 | 0.223760 | ||||||||
\(598\) | −27.7084 | −1.13308 | ||||||||
\(599\) | −2.14962 | −0.0878312 | −0.0439156 | − | 0.999035i | \(-0.513983\pi\) | ||||
−0.0439156 | + | 0.999035i | \(0.513983\pi\) | |||||||
\(600\) | −3.26969 | −0.133485 | ||||||||
\(601\) | 15.3782 | 0.627291 | 0.313646 | − | 0.949540i | \(-0.398450\pi\) | ||||
0.313646 | + | 0.949540i | \(0.398450\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.0922892 | −0.00375831 | ||||||||
\(604\) | −67.4760 | −2.74556 | ||||||||
\(605\) | −21.1679 | −0.860598 | ||||||||
\(606\) | −34.3847 | −1.39678 | ||||||||
\(607\) | −31.2239 | −1.26734 | −0.633669 | − | 0.773604i | \(-0.718452\pi\) | ||||
−0.633669 | + | 0.773604i | \(0.718452\pi\) | |||||||
\(608\) | 7.24323 | 0.293752 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 49.1852 | 1.99145 | ||||||||
\(611\) | 38.3408 | 1.55110 | ||||||||
\(612\) | −20.4757 | −0.827681 | ||||||||
\(613\) | 32.6293 | 1.31789 | 0.658943 | − | 0.752193i | \(-0.271004\pi\) | ||||
0.658943 | + | 0.752193i | \(0.271004\pi\) | |||||||
\(614\) | 50.5794 | 2.04122 | ||||||||
\(615\) | 2.36641 | 0.0954228 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −33.6100 | −1.35309 | −0.676544 | − | 0.736402i | \(-0.736523\pi\) | ||||
−0.676544 | + | 0.736402i | \(0.736523\pi\) | |||||||
\(618\) | −32.3926 | −1.30302 | ||||||||
\(619\) | 24.9576 | 1.00313 | 0.501566 | − | 0.865119i | \(-0.332757\pi\) | ||||
0.501566 | + | 0.865119i | \(0.332757\pi\) | |||||||
\(620\) | 11.7101 | 0.470287 | ||||||||
\(621\) | 2.22001 | 0.0890859 | ||||||||
\(622\) | 62.1757 | 2.49302 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −25.9850 | −1.04023 | ||||||||
\(625\) | −27.6396 | −1.10558 | ||||||||
\(626\) | 47.3229 | 1.89140 | ||||||||
\(627\) | −16.2758 | −0.649993 | ||||||||
\(628\) | −31.1638 | −1.24357 | ||||||||
\(629\) | 3.65623 | 0.145783 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.2251 | −1.00420 | −0.502099 | − | 0.864810i | \(-0.667439\pi\) | ||||
−0.502099 | + | 0.864810i | \(0.667439\pi\) | |||||||
\(632\) | 42.9404 | 1.70808 | ||||||||
\(633\) | −12.8035 | −0.508894 | ||||||||
\(634\) | −66.4646 | −2.63965 | ||||||||
\(635\) | −42.4433 | −1.68431 | ||||||||
\(636\) | −43.2751 | −1.71597 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 32.0286 | 1.26803 | ||||||||
\(639\) | 3.08552 | 0.122061 | ||||||||
\(640\) | 41.2891 | 1.63209 | ||||||||
\(641\) | 0.428767 | 0.0169353 | 0.00846764 | − | 0.999964i | \(-0.497305\pi\) | ||||
0.00846764 | + | 0.999964i | \(0.497305\pi\) | |||||||
\(642\) | 49.7027 | 1.96161 | ||||||||
\(643\) | −35.6986 | −1.40781 | −0.703907 | − | 0.710292i | \(-0.748563\pi\) | ||||
−0.703907 | + | 0.710292i | \(0.748563\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16.5232 | 0.650600 | ||||||||
\(646\) | −44.3048 | −1.74315 | ||||||||
\(647\) | 1.15325 | 0.0453389 | 0.0226695 | − | 0.999743i | \(-0.492783\pi\) | ||||
0.0226695 | + | 0.999743i | \(0.492783\pi\) | |||||||
\(648\) | 5.45047 | 0.214115 | ||||||||
\(649\) | −38.8621 | −1.52547 | ||||||||
\(650\) | 7.48738 | 0.293679 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 80.1010 | 3.13700 | ||||||||
\(653\) | −10.8046 | −0.422815 | −0.211408 | − | 0.977398i | \(-0.567805\pi\) | ||||
−0.211408 | + | 0.977398i | \(0.567805\pi\) | |||||||
\(654\) | −10.9898 | −0.429734 | ||||||||
\(655\) | 4.29304 | 0.167743 | ||||||||
\(656\) | 5.18004 | 0.202247 | ||||||||
\(657\) | 9.88365 | 0.385598 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.9857 | −0.856441 | −0.428220 | − | 0.903674i | \(-0.640859\pi\) | ||||
−0.428220 | + | 0.903674i | \(0.640859\pi\) | |||||||
\(660\) | 44.2881 | 1.72391 | ||||||||
\(661\) | 12.5178 | 0.486885 | 0.243443 | − | 0.969915i | \(-0.421723\pi\) | ||||
0.243443 | + | 0.969915i | \(0.421723\pi\) | |||||||
\(662\) | −71.4782 | −2.77808 | ||||||||
\(663\) | 24.5104 | 0.951905 | ||||||||
\(664\) | 34.1393 | 1.32486 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.86183 | −0.0721444 | ||||||||
\(667\) | −6.39893 | −0.247767 | ||||||||
\(668\) | 12.8114 | 0.495689 | ||||||||
\(669\) | −1.61990 | −0.0626290 | ||||||||
\(670\) | 0.543385 | 0.0209928 | ||||||||
\(671\) | −37.3075 | −1.44024 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.4333 | −1.21166 | −0.605832 | − | 0.795593i | \(-0.707160\pi\) | ||||
−0.605832 | + | 0.795593i | \(0.707160\pi\) | |||||||
\(674\) | 13.4295 | 0.517284 | ||||||||
\(675\) | −0.599893 | −0.0230899 | ||||||||
\(676\) | 50.9746 | 1.96056 | ||||||||
\(677\) | 35.2655 | 1.35536 | 0.677682 | − | 0.735355i | \(-0.262985\pi\) | ||||
0.677682 | + | 0.735355i | \(0.262985\pi\) | |||||||
\(678\) | 36.0313 | 1.38377 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 63.0208 | 2.41674 | ||||||||
\(681\) | −7.09352 | −0.271824 | ||||||||
\(682\) | −13.1213 | −0.502441 | ||||||||
\(683\) | 9.57717 | 0.366460 | 0.183230 | − | 0.983070i | \(-0.441345\pi\) | ||||
0.183230 | + | 0.983070i | \(0.441345\pi\) | |||||||
\(684\) | 15.2722 | 0.583947 | ||||||||
\(685\) | −24.4193 | −0.933013 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.2801 | 0.392209 | ||||||||
\(688\) | 36.1691 | 1.37893 | ||||||||
\(689\) | 51.8024 | 1.97351 | ||||||||
\(690\) | −13.0711 | −0.497608 | ||||||||
\(691\) | −37.0205 | −1.40832 | −0.704162 | − | 0.710039i | \(-0.748677\pi\) | ||||
−0.704162 | + | 0.710039i | \(0.748677\pi\) | |||||||
\(692\) | −52.8282 | −2.00823 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −27.9622 | −1.06143 | ||||||||
\(695\) | −28.7089 | −1.08899 | ||||||||
\(696\) | −15.7104 | −0.595500 | ||||||||
\(697\) | −4.88608 | −0.185074 | ||||||||
\(698\) | 81.5871 | 3.08812 | ||||||||
\(699\) | −26.2441 | −0.992645 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.3692 | −0.882641 | −0.441320 | − | 0.897350i | \(-0.645490\pi\) | ||||
−0.441320 | + | 0.897350i | \(0.645490\pi\) | |||||||
\(702\) | −12.4812 | −0.471073 | ||||||||
\(703\) | −2.72707 | −0.102853 | ||||||||
\(704\) | −24.1833 | −0.911442 | ||||||||
\(705\) | 18.0868 | 0.681187 | ||||||||
\(706\) | −92.1381 | −3.46766 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 36.4658 | 1.37047 | ||||||||
\(709\) | −14.6548 | −0.550371 | −0.275185 | − | 0.961391i | \(-0.588739\pi\) | ||||
−0.275185 | + | 0.961391i | \(0.588739\pi\) | |||||||
\(710\) | −18.1671 | −0.681799 | ||||||||
\(711\) | 7.87830 | 0.295459 | ||||||||
\(712\) | 56.2173 | 2.10683 | ||||||||
\(713\) | 2.62148 | 0.0981750 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −53.0149 | −1.98265 | ||||||||
\(716\) | −27.3929 | −1.02372 | ||||||||
\(717\) | −9.99590 | −0.373304 | ||||||||
\(718\) | −71.7309 | −2.67697 | ||||||||
\(719\) | −30.4680 | −1.13626 | −0.568132 | − | 0.822937i | \(-0.692334\pi\) | ||||
−0.568132 | + | 0.822937i | \(0.692334\pi\) | |||||||
\(720\) | −12.2581 | −0.456833 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −14.2282 | −0.529519 | ||||||||
\(723\) | −2.67886 | −0.0996277 | ||||||||
\(724\) | −7.35731 | −0.273432 | ||||||||
\(725\) | 1.72912 | 0.0642180 | ||||||||
\(726\) | −22.2564 | −0.826013 | ||||||||
\(727\) | 15.9546 | 0.591723 | 0.295861 | − | 0.955231i | \(-0.404393\pi\) | ||||
0.295861 | + | 0.955231i | \(0.404393\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −58.1935 | −2.15384 | ||||||||
\(731\) | −34.1165 | −1.26184 | ||||||||
\(732\) | 35.0071 | 1.29390 | ||||||||
\(733\) | −0.380394 | −0.0140502 | −0.00702509 | − | 0.999975i | \(-0.502236\pi\) | ||||
−0.00702509 | + | 0.999975i | \(0.502236\pi\) | |||||||
\(734\) | −75.8507 | −2.79970 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.41229 | −0.162639 | ||||||||
\(737\) | −0.412163 | −0.0151822 | ||||||||
\(738\) | 2.48810 | 0.0915881 | ||||||||
\(739\) | 2.04392 | 0.0751868 | 0.0375934 | − | 0.999293i | \(-0.488031\pi\) | ||||
0.0375934 | + | 0.999293i | \(0.488031\pi\) | |||||||
\(740\) | 7.42063 | 0.272788 | ||||||||
\(741\) | −18.2815 | −0.671589 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.1113 | 0.370948 | 0.185474 | − | 0.982649i | \(-0.440618\pi\) | ||||
0.185474 | + | 0.982649i | \(0.440618\pi\) | |||||||
\(744\) | 6.43613 | 0.235960 | ||||||||
\(745\) | 39.7960 | 1.45801 | ||||||||
\(746\) | 27.5228 | 1.00768 | ||||||||
\(747\) | 6.26355 | 0.229171 | ||||||||
\(748\) | −91.4445 | −3.34354 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −25.9072 | −0.945996 | ||||||||
\(751\) | 35.9620 | 1.31227 | 0.656136 | − | 0.754643i | \(-0.272190\pi\) | ||||
0.656136 | + | 0.754643i | \(0.272190\pi\) | |||||||
\(752\) | 39.5917 | 1.44376 | ||||||||
\(753\) | −23.4644 | −0.855090 | ||||||||
\(754\) | 35.9757 | 1.31016 | ||||||||
\(755\) | 38.1032 | 1.38672 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.05727 | 0.220155 | 0.110078 | − | 0.993923i | \(-0.464890\pi\) | ||||
0.110078 | + | 0.993923i | \(0.464890\pi\) | |||||||
\(758\) | 46.1326 | 1.67561 | ||||||||
\(759\) | 9.91456 | 0.359876 | ||||||||
\(760\) | −47.0053 | −1.70506 | ||||||||
\(761\) | −51.1971 | −1.85589 | −0.927947 | − | 0.372712i | \(-0.878428\pi\) | ||||
−0.927947 | + | 0.372712i | \(0.878428\pi\) | |||||||
\(762\) | −44.6258 | −1.61662 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 15.8931 | 0.574991 | ||||||||
\(765\) | 11.5625 | 0.418042 | ||||||||
\(766\) | −64.1104 | −2.31640 | ||||||||
\(767\) | −43.6513 | −1.57616 | ||||||||
\(768\) | 32.5823 | 1.17571 | ||||||||
\(769\) | −24.5528 | −0.885396 | −0.442698 | − | 0.896671i | \(-0.645979\pi\) | ||||
−0.442698 | + | 0.896671i | \(0.645979\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.6351 | 0.743154 | ||||||||
\(772\) | −0.752527 | −0.0270840 | ||||||||
\(773\) | 51.3061 | 1.84535 | 0.922676 | − | 0.385577i | \(-0.125998\pi\) | ||||
0.922676 | + | 0.385577i | \(0.125998\pi\) | |||||||
\(774\) | 17.3728 | 0.624454 | ||||||||
\(775\) | −0.708377 | −0.0254457 | ||||||||
\(776\) | 25.3078 | 0.908497 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 22.3437 | 0.801061 | ||||||||
\(779\) | 3.64438 | 0.130573 | ||||||||
\(780\) | 49.7459 | 1.78119 | ||||||||
\(781\) | 13.7800 | 0.493086 | ||||||||
\(782\) | 26.9887 | 0.965115 | ||||||||
\(783\) | −2.88239 | −0.103008 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.5979 | 0.628097 | ||||||||
\(786\) | 4.51380 | 0.161002 | ||||||||
\(787\) | −8.42945 | −0.300478 | −0.150239 | − | 0.988650i | \(-0.548004\pi\) | ||||
−0.150239 | + | 0.988650i | \(0.548004\pi\) | |||||||
\(788\) | −55.3643 | −1.97227 | ||||||||
\(789\) | −10.4139 | −0.370746 | ||||||||
\(790\) | −46.3862 | −1.65035 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 24.3418 | 0.864948 | ||||||||
\(793\) | −41.9051 | −1.48809 | ||||||||
\(794\) | −74.1805 | −2.63257 | ||||||||
\(795\) | 24.4371 | 0.866695 | ||||||||
\(796\) | −22.9112 | −0.812067 | ||||||||
\(797\) | 43.9602 | 1.55715 | 0.778575 | − | 0.627551i | \(-0.215943\pi\) | ||||
0.778575 | + | 0.627551i | \(0.215943\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −37.3449 | −1.32117 | ||||||||
\(800\) | 1.19229 | 0.0421539 | ||||||||
\(801\) | 10.3142 | 0.364435 | ||||||||
\(802\) | 76.2222 | 2.69150 | ||||||||
\(803\) | 44.1404 | 1.55768 | ||||||||
\(804\) | 0.386749 | 0.0136396 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −14.7383 | −0.519135 | ||||||||
\(807\) | 18.0405 | 0.635054 | ||||||||
\(808\) | 75.3237 | 2.64988 | ||||||||
\(809\) | 41.9373 | 1.47444 | 0.737218 | − | 0.675655i | \(-0.236139\pi\) | ||||
0.737218 | + | 0.675655i | \(0.236139\pi\) | |||||||
\(810\) | −5.88785 | −0.206878 | ||||||||
\(811\) | 1.50049 | 0.0526892 | 0.0263446 | − | 0.999653i | \(-0.491613\pi\) | ||||
0.0263446 | + | 0.999653i | \(0.491613\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −30.1360 | −1.05691 | ||||||||
\(814\) | −8.31493 | −0.291438 | ||||||||
\(815\) | −45.2324 | −1.58442 | ||||||||
\(816\) | 25.3101 | 0.886031 | ||||||||
\(817\) | 25.4464 | 0.890259 | ||||||||
\(818\) | −24.6033 | −0.860235 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.91672 | −0.346307 | ||||||||
\(821\) | 46.6313 | 1.62744 | 0.813722 | − | 0.581255i | \(-0.197438\pi\) | ||||
0.813722 | + | 0.581255i | \(0.197438\pi\) | |||||||
\(822\) | −25.6750 | −0.895518 | ||||||||
\(823\) | 12.4390 | 0.433595 | 0.216797 | − | 0.976217i | \(-0.430439\pi\) | ||||
0.216797 | + | 0.976217i | \(0.430439\pi\) | |||||||
\(824\) | 70.9599 | 2.47201 | ||||||||
\(825\) | −2.67912 | −0.0932750 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.6272 | 0.891147 | 0.445573 | − | 0.895245i | \(-0.353000\pi\) | ||||
0.445573 | + | 0.895245i | \(0.353000\pi\) | |||||||
\(828\) | −9.30321 | −0.323309 | ||||||||
\(829\) | 8.98335 | 0.312005 | 0.156002 | − | 0.987757i | \(-0.450139\pi\) | ||||
0.156002 | + | 0.987757i | \(0.450139\pi\) | |||||||
\(830\) | −36.8788 | −1.28008 | ||||||||
\(831\) | 15.2878 | 0.530329 | ||||||||
\(832\) | −27.1635 | −0.941726 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −30.1851 | −1.04523 | ||||||||
\(835\) | −7.23451 | −0.250360 | ||||||||
\(836\) | 68.2056 | 2.35894 | ||||||||
\(837\) | 1.18084 | 0.0408158 | ||||||||
\(838\) | 19.1189 | 0.660451 | ||||||||
\(839\) | −14.9267 | −0.515326 | −0.257663 | − | 0.966235i | \(-0.582952\pi\) | ||||
−0.257663 | + | 0.966235i | \(0.582952\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.6918 | −0.713512 | ||||||||
\(842\) | −13.7726 | −0.474636 | ||||||||
\(843\) | −4.02679 | −0.138690 | ||||||||
\(844\) | 53.6546 | 1.84687 | ||||||||
\(845\) | −28.7849 | −0.990232 | ||||||||
\(846\) | 19.0168 | 0.653812 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 53.4926 | 1.83694 | ||||||||
\(849\) | 18.0462 | 0.619345 | ||||||||
\(850\) | −7.29292 | −0.250145 | ||||||||
\(851\) | 1.66122 | 0.0569459 | ||||||||
\(852\) | −12.9303 | −0.442983 | ||||||||
\(853\) | −29.3002 | −1.00322 | −0.501610 | − | 0.865094i | \(-0.667259\pi\) | ||||
−0.501610 | + | 0.865094i | \(0.667259\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.62409 | −0.294938 | ||||||||
\(856\) | −108.880 | −3.72143 | ||||||||
\(857\) | −0.206054 | −0.00703868 | −0.00351934 | − | 0.999994i | \(-0.501120\pi\) | ||||
−0.00351934 | + | 0.999994i | \(0.501120\pi\) | |||||||
\(858\) | −55.7411 | −1.90297 | ||||||||
\(859\) | 10.3195 | 0.352096 | 0.176048 | − | 0.984382i | \(-0.443669\pi\) | ||||
0.176048 | + | 0.984382i | \(0.443669\pi\) | |||||||
\(860\) | −69.2423 | −2.36114 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −85.9540 | −2.92761 | ||||||||
\(863\) | 2.67563 | 0.0910796 | 0.0455398 | − | 0.998963i | \(-0.485499\pi\) | ||||
0.0455398 | + | 0.998963i | \(0.485499\pi\) | |||||||
\(864\) | −1.98751 | −0.0676164 | ||||||||
\(865\) | 29.8317 | 1.01431 | ||||||||
\(866\) | 4.82680 | 0.164021 | ||||||||
\(867\) | −6.87380 | −0.233446 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 35.1845 | 1.19355 | ||||||||
\(870\) | 16.9711 | 0.575373 | ||||||||
\(871\) | −0.462957 | −0.0156867 | ||||||||
\(872\) | 24.0744 | 0.815263 | ||||||||
\(873\) | 4.64324 | 0.157150 | ||||||||
\(874\) | −20.1301 | −0.680909 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −41.4186 | −1.39941 | ||||||||
\(877\) | 28.0493 | 0.947158 | 0.473579 | − | 0.880751i | \(-0.342962\pi\) | ||||
0.473579 | + | 0.880751i | \(0.342962\pi\) | |||||||
\(878\) | −91.9662 | −3.10371 | ||||||||
\(879\) | 5.56871 | 0.187828 | ||||||||
\(880\) | −54.7447 | −1.84544 | ||||||||
\(881\) | −2.95290 | −0.0994856 | −0.0497428 | − | 0.998762i | \(-0.515840\pi\) | ||||
−0.0497428 | + | 0.998762i | \(0.515840\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.2203 | 0.411246 | 0.205623 | − | 0.978631i | \(-0.434078\pi\) | ||||
0.205623 | + | 0.978631i | \(0.434078\pi\) | |||||||
\(884\) | −102.714 | −3.45464 | ||||||||
\(885\) | −20.5920 | −0.692191 | ||||||||
\(886\) | −71.9440 | −2.41700 | ||||||||
\(887\) | −10.3073 | −0.346084 | −0.173042 | − | 0.984914i | \(-0.555360\pi\) | ||||
−0.173042 | + | 0.984914i | \(0.555360\pi\) | |||||||
\(888\) | 4.07856 | 0.136867 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −60.7285 | −2.03563 | ||||||||
\(891\) | 4.46600 | 0.149617 | ||||||||
\(892\) | 6.78838 | 0.227292 | ||||||||
\(893\) | 27.8544 | 0.932113 | ||||||||
\(894\) | 41.8424 | 1.39942 | ||||||||
\(895\) | 15.4686 | 0.517057 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.1364 | 0.371833 | ||||||||
\(898\) | −20.0258 | −0.668270 | ||||||||
\(899\) | −3.40364 | −0.113518 | ||||||||
\(900\) | 2.51392 | 0.0837974 | ||||||||
\(901\) | −50.4569 | −1.68096 | ||||||||
\(902\) | 11.1118 | 0.369984 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −78.9308 | −2.62520 | ||||||||
\(905\) | 4.15462 | 0.138104 | ||||||||
\(906\) | 40.0625 | 1.33099 | ||||||||
\(907\) | 29.2512 | 0.971269 | 0.485635 | − | 0.874162i | \(-0.338589\pi\) | ||||
0.485635 | + | 0.874162i | \(0.338589\pi\) | |||||||
\(908\) | 29.7262 | 0.986499 | ||||||||
\(909\) | 13.8197 | 0.458370 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.2520 | 0.472190 | 0.236095 | − | 0.971730i | \(-0.424132\pi\) | ||||
0.236095 | + | 0.971730i | \(0.424132\pi\) | |||||||
\(912\) | −18.8780 | −0.625114 | ||||||||
\(913\) | 27.9730 | 0.925772 | ||||||||
\(914\) | 11.7777 | 0.389573 | ||||||||
\(915\) | −19.7682 | −0.653517 | ||||||||
\(916\) | −43.0799 | −1.42340 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 12.1570 | 0.401242 | ||||||||
\(919\) | 21.2445 | 0.700791 | 0.350395 | − | 0.936602i | \(-0.386047\pi\) | ||||
0.350395 | + | 0.936602i | \(0.386047\pi\) | |||||||
\(920\) | 28.6337 | 0.944027 | ||||||||
\(921\) | −20.3285 | −0.669848 | ||||||||
\(922\) | −91.7408 | −3.02132 | ||||||||
\(923\) | 15.4781 | 0.509469 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.448897 | −0.0147596 | ||||||||
\(926\) | 28.4755 | 0.935763 | ||||||||
\(927\) | 13.0191 | 0.427602 | ||||||||
\(928\) | 5.72877 | 0.188056 | ||||||||
\(929\) | −32.1903 | −1.05613 | −0.528064 | − | 0.849204i | \(-0.677082\pi\) | ||||
−0.528064 | + | 0.849204i | \(0.677082\pi\) | |||||||
\(930\) | −6.95261 | −0.227985 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 109.979 | 3.60249 | ||||||||
\(933\) | −24.9893 | −0.818112 | ||||||||
\(934\) | −23.1843 | −0.758613 | ||||||||
\(935\) | 51.6380 | 1.68874 | ||||||||
\(936\) | 27.3416 | 0.893687 | ||||||||
\(937\) | 30.2630 | 0.988649 | 0.494324 | − | 0.869278i | \(-0.335415\pi\) | ||||
0.494324 | + | 0.869278i | \(0.335415\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.0197 | −0.620685 | ||||||||
\(940\) | −75.7947 | −2.47215 | ||||||||
\(941\) | 21.1631 | 0.689897 | 0.344948 | − | 0.938622i | \(-0.387896\pi\) | ||||
0.344948 | + | 0.938622i | \(0.387896\pi\) | |||||||
\(942\) | 18.5029 | 0.602856 | ||||||||
\(943\) | −2.22001 | −0.0722934 | ||||||||
\(944\) | −45.0756 | −1.46708 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 77.5871 | 2.52257 | ||||||||
\(947\) | 49.3799 | 1.60463 | 0.802316 | − | 0.596900i | \(-0.203601\pi\) | ||||
0.802316 | + | 0.596900i | \(0.203601\pi\) | |||||||
\(948\) | −33.0149 | −1.07228 | ||||||||
\(949\) | 49.5801 | 1.60944 | ||||||||
\(950\) | 5.43956 | 0.176483 | ||||||||
\(951\) | 26.7130 | 0.866230 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.6273 | 1.38083 | 0.690417 | − | 0.723412i | \(-0.257427\pi\) | ||||
0.690417 | + | 0.723412i | \(0.257427\pi\) | |||||||
\(954\) | 25.6937 | 0.831865 | ||||||||
\(955\) | −8.97470 | −0.290414 | ||||||||
\(956\) | 41.8890 | 1.35479 | ||||||||
\(957\) | −12.8728 | −0.416117 | ||||||||
\(958\) | −98.4748 | −3.18158 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −12.8140 | −0.413572 | ||||||||
\(961\) | −29.6056 | −0.955020 | ||||||||
\(962\) | −9.33962 | −0.301122 | ||||||||
\(963\) | −19.9762 | −0.643724 | ||||||||
\(964\) | 11.2261 | 0.361567 | ||||||||
\(965\) | 0.424946 | 0.0136795 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.3526 | 1.29765 | 0.648826 | − | 0.760937i | \(-0.275260\pi\) | ||||
0.648826 | + | 0.760937i | \(0.275260\pi\) | |||||||
\(968\) | 48.7553 | 1.56706 | ||||||||
\(969\) | 17.8067 | 0.572035 | ||||||||
\(970\) | −27.3387 | −0.877792 | ||||||||
\(971\) | 58.4250 | 1.87495 | 0.937474 | − | 0.348057i | \(-0.113158\pi\) | ||||
0.937474 | + | 0.348057i | \(0.113158\pi\) | |||||||
\(972\) | −4.19062 | −0.134414 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 64.5280 | 2.06761 | ||||||||
\(975\) | −3.00928 | −0.0963742 | ||||||||
\(976\) | −43.2724 | −1.38512 | ||||||||
\(977\) | −0.829520 | −0.0265387 | −0.0132694 | − | 0.999912i | \(-0.504224\pi\) | ||||
−0.0132694 | + | 0.999912i | \(0.504224\pi\) | |||||||
\(978\) | −47.5583 | −1.52075 | ||||||||
\(979\) | 46.0633 | 1.47219 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.41695 | 0.141022 | ||||||||
\(982\) | −28.8261 | −0.919877 | ||||||||
\(983\) | 2.32545 | 0.0741703 | 0.0370852 | − | 0.999312i | \(-0.488193\pi\) | ||||
0.0370852 | + | 0.999312i | \(0.488193\pi\) | |||||||
\(984\) | −5.45047 | −0.173755 | ||||||||
\(985\) | 31.2638 | 0.996148 | ||||||||
\(986\) | −35.0413 | −1.11594 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 76.6110 | 2.43732 | ||||||||
\(989\) | −15.5010 | −0.492902 | ||||||||
\(990\) | −26.2952 | −0.835715 | ||||||||
\(991\) | −16.1129 | −0.511843 | −0.255921 | − | 0.966698i | \(-0.582379\pi\) | ||||
−0.255921 | + | 0.966698i | \(0.582379\pi\) | |||||||
\(992\) | −2.34693 | −0.0745151 | ||||||||
\(993\) | 28.7281 | 0.911659 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.9378 | 0.410156 | ||||||||
\(996\) | −26.2481 | −0.831704 | ||||||||
\(997\) | 0.484528 | 0.0153452 | 0.00767258 | − | 0.999971i | \(-0.497558\pi\) | ||||
0.00767258 | + | 0.999971i | \(0.497558\pi\) | |||||||
\(998\) | 56.1697 | 1.77802 | ||||||||
\(999\) | 0.748295 | 0.0236750 |
(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 | 6027.2.a.bn.1.21 | ✓ | 24 | |
7.6 | odd | 2 | 6027.2.a.bo.1.21 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.bn.1.21 | ✓ | 24 | 1.1 | even | 1 | trivial | |
6027.2.a.bo.1.21 | yes | 24 | 7.6 | odd | 2 |