Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(2305,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.2305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.q (of order \(3\), degree \(2\), not minimal) |
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: | no |
Analytic conductor: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2305.11 | ||
Character | \(\chi\) | \(=\) | 3024.2305 |
Dual form | 3024.2.q.l.2881.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.70368 | + | 2.95086i | 0.761909 | + | 1.31967i | 0.941865 | + | 0.335991i | \(0.109071\pi\) |
−0.179956 | + | 0.983675i | \(0.557596\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.410295 | + | 2.61374i | 0.155077 | + | 0.987902i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.69819 | + | 4.67340i | −0.813535 | + | 1.40908i | 0.0968406 | + | 0.995300i | \(0.469126\pi\) |
−0.910375 | + | 0.413784i | \(0.864207\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.89598 | − | 3.28393i | 0.525850 | − | 0.910800i | −0.473696 | − | 0.880688i | \(-0.657080\pi\) |
0.999547 | − | 0.0301113i | \(-0.00958618\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.411976 | − | 0.713564i | −0.0999190 | − | 0.173065i | 0.811732 | − | 0.584030i | \(-0.198525\pi\) |
−0.911651 | + | 0.410965i | \(0.865192\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.233611 | + | 0.404626i | −0.0535940 | + | 0.0928275i | −0.891578 | − | 0.452868i | \(-0.850401\pi\) |
0.837984 | + | 0.545695i | \(0.183734\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.74950 | + | 4.76227i | 0.573309 | + | 0.993001i | 0.996223 | + | 0.0868310i | \(0.0276740\pi\) |
−0.422914 | + | 0.906170i | \(0.638993\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.30506 | + | 5.72452i | −0.661011 | + | 1.14490i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.400332 | − | 0.693396i | −0.0743399 | − | 0.128760i | 0.826459 | − | 0.562997i | \(-0.190352\pi\) |
−0.900799 | + | 0.434236i | \(0.857018\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.90732 | 1.77941 | 0.889703 | − | 0.456539i | \(-0.150911\pi\) | ||||
0.889703 | + | 0.456539i | \(0.150911\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.01378 | + | 5.66371i | −1.18555 | + | 0.957342i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.34210 | − | 7.52074i | 0.713837 | − | 1.23640i | −0.249569 | − | 0.968357i | \(-0.580289\pi\) |
0.963406 | − | 0.268045i | \(-0.0863777\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.84467 | + | 3.19507i | −0.288090 | + | 0.498986i | −0.973354 | − | 0.229309i | \(-0.926354\pi\) |
0.685264 | + | 0.728295i | \(0.259687\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.36356 | + | 7.55790i | 0.665436 | + | 1.15257i | 0.979167 | + | 0.203057i | \(0.0650878\pi\) |
−0.313731 | + | 0.949512i | \(0.601579\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.4991 | −1.53146 | −0.765728 | − | 0.643164i | \(-0.777621\pi\) | ||||
−0.765728 | + | 0.643164i | \(0.777621\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.66332 | + | 2.14481i | −0.951902 | + | 0.306402i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.71820 | + | 8.17217i | 0.648095 | + | 1.12253i | 0.983577 | + | 0.180487i | \(0.0577673\pi\) |
−0.335483 | + | 0.942046i | \(0.608899\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18.3874 | −2.47936 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.66069 | −0.216203 | −0.108102 | − | 0.994140i | \(-0.534477\pi\) | ||||
−0.108102 | + | 0.994140i | \(0.534477\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.948811 | 0.121483 | 0.0607414 | − | 0.998154i | \(-0.480654\pi\) | ||||
0.0607414 | + | 0.998154i | \(0.480654\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.9206 | 1.60260 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.539184 | −0.0658718 | −0.0329359 | − | 0.999457i | \(-0.510486\pi\) | ||||
−0.0329359 | + | 0.999457i | \(0.510486\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.86901 | −0.459167 | −0.229583 | − | 0.973289i | \(-0.573736\pi\) | ||||
−0.229583 | + | 0.973289i | \(0.573736\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.58943 | + | 4.48502i | 0.303070 | + | 0.524932i | 0.976830 | − | 0.214018i | \(-0.0686551\pi\) |
−0.673760 | + | 0.738950i | \(0.735322\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −13.3221 | − | 5.13490i | −1.51820 | − | 0.585176i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.82899 | −0.880830 | −0.440415 | − | 0.897794i | \(-0.645169\pi\) | ||||
−0.440415 | + | 0.897794i | \(0.645169\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.79623 | − | 6.57527i | −0.416691 | − | 0.721729i | 0.578914 | − | 0.815389i | \(-0.303477\pi\) |
−0.995604 | + | 0.0936595i | \(0.970143\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.40375 | − | 2.43137i | 0.152258 | − | 0.263719i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.73498 | − | 6.46917i | 0.395907 | − | 0.685730i | −0.597310 | − | 0.802011i | \(-0.703764\pi\) |
0.993216 | + | 0.116280i | \(0.0370971\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.36128 | + | 3.60823i | 0.981328 | + | 0.378245i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.59199 | −0.163335 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.22500 | − | 5.58587i | −0.327450 | − | 0.567159i | 0.654555 | − | 0.756014i | \(-0.272856\pi\) |
−0.982005 | + | 0.188855i | \(0.939522\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.09973 | + | 14.0291i | −0.805953 | + | 1.39595i | 0.109692 | + | 0.993966i | \(0.465014\pi\) |
−0.915646 | + | 0.401987i | \(0.868320\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.84930 | − | 13.5954i | −0.773414 | − | 1.33959i | −0.935681 | − | 0.352846i | \(-0.885214\pi\) |
0.162267 | − | 0.986747i | \(-0.448119\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.85024 | − | 4.93675i | 0.275543 | − | 0.477254i | −0.694729 | − | 0.719271i | \(-0.744476\pi\) |
0.970272 | + | 0.242017i | \(0.0778091\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.19196 | − | 3.79659i | −0.209952 | − | 0.363648i | 0.741747 | − | 0.670680i | \(-0.233997\pi\) |
−0.951699 | + | 0.307032i | \(0.900664\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.96607 | − | 8.60149i | 0.467169 | − | 0.809160i | −0.532128 | − | 0.846664i | \(-0.678607\pi\) |
0.999296 | + | 0.0375041i | \(0.0119407\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.36852 | + | 16.2268i | −0.873619 | + | 1.51315i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.69604 | − | 1.36957i | 0.155476 | − | 0.125549i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.06045 | − | 15.6932i | −0.823677 | − | 1.42665i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.48623 | −0.490703 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.1122 | −1.42973 | −0.714864 | − | 0.699263i | \(-0.753512\pi\) | ||||
−0.714864 | + | 0.699263i | \(0.753512\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.97039 | − | 12.0731i | −0.609006 | − | 1.05483i | −0.991405 | − | 0.130832i | \(-0.958235\pi\) |
0.382399 | − | 0.923997i | \(-0.375098\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.15344 | − | 0.444583i | −0.100016 | − | 0.0385502i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.57598 | + | 9.65787i | −0.476388 | + | 0.825128i | −0.999634 | − | 0.0270537i | \(-0.991388\pi\) |
0.523246 | + | 0.852182i | \(0.324721\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.17737 | + | 5.50337i | −0.269501 | + | 0.466790i | −0.968733 | − | 0.248105i | \(-0.920192\pi\) |
0.699232 | + | 0.714895i | \(0.253526\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.2314 | + | 17.7214i | 0.855595 | + | 1.48193i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.36408 | − | 2.36265i | 0.113280 | − | 0.196207i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.76521 | − | 9.98564i | −0.472304 | − | 0.818055i | 0.527193 | − | 0.849745i | \(-0.323244\pi\) |
−0.999498 | + | 0.0316900i | \(0.989911\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.347317 | + | 0.601571i | −0.0282643 | + | 0.0489551i | −0.879812 | − | 0.475323i | \(-0.842331\pi\) |
0.851547 | + | 0.524278i | \(0.175665\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.8789 | + | 29.2351i | 1.35575 | + | 2.34822i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.04845 | −0.323102 | −0.161551 | − | 0.986864i | \(-0.551650\pi\) | ||||
−0.161551 | + | 0.986864i | \(0.551650\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.3192 | + | 9.14041i | −0.892081 | + | 0.720365i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.05968 | − | 8.76363i | 0.396305 | − | 0.686420i | −0.596962 | − | 0.802270i | \(-0.703626\pi\) |
0.993267 | + | 0.115849i | \(0.0369590\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.76377 | − | 15.1793i | 0.678161 | − | 1.17461i | −0.297374 | − | 0.954761i | \(-0.596111\pi\) |
0.975534 | − | 0.219847i | \(-0.0705560\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.689486 | − | 1.19422i | −0.0530374 | − | 0.0918634i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.83515 | 0.595695 | 0.297848 | − | 0.954613i | \(-0.403731\pi\) | ||||
0.297848 | + | 0.954613i | \(0.403731\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.3185 | − | 6.28982i | −1.23356 | − | 0.475466i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.61920 | + | 8.00069i | 0.345255 | + | 0.597999i | 0.985400 | − | 0.170255i | \(-0.0544591\pi\) |
−0.640145 | + | 0.768254i | \(0.721126\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.45977 | 0.703139 | 0.351569 | − | 0.936162i | \(-0.385648\pi\) | ||||
0.351569 | + | 0.936162i | \(0.385648\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 29.5902 | 2.17552 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.44636 | 0.325150 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.0452967 | 0.00327756 | 0.00163878 | − | 0.999999i | \(-0.499478\pi\) | ||||
0.00163878 | + | 0.999999i | \(0.499478\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.8198 | −1.35468 | −0.677340 | − | 0.735670i | \(-0.736868\pi\) | ||||
−0.677340 | + | 0.735670i | \(0.736868\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.3886 | 1.59512 | 0.797561 | − | 0.603239i | \(-0.206123\pi\) | ||||
0.797561 | + | 0.603239i | \(0.206123\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.3709 | + | 19.6949i | 0.806060 | + | 1.39614i | 0.915573 | + | 0.402152i | \(0.131738\pi\) |
−0.109513 | + | 0.993985i | \(0.534929\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.64811 | − | 1.33086i | 0.115674 | − | 0.0934083i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.5709 | −0.877993 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.26065 | − | 2.18351i | −0.0872011 | − | 0.151037i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.95868 | − | 5.12458i | 0.203684 | − | 0.352791i | −0.746029 | − | 0.665914i | \(-0.768042\pi\) |
0.949713 | + | 0.313123i | \(0.101375\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.8682 | + | 25.7525i | −1.01400 | + | 1.75631i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.06492 | + | 25.8952i | 0.275945 | + | 1.75788i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.12440 | −0.210170 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.20124 | + | 2.08062i | 0.0804412 | + | 0.139328i | 0.903440 | − | 0.428716i | \(-0.141034\pi\) |
−0.822998 | + | 0.568044i | \(0.807700\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.48851 | − | 6.04227i | 0.231540 | − | 0.401040i | −0.726721 | − | 0.686933i | \(-0.758957\pi\) |
0.958262 | + | 0.285893i | \(0.0922901\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.60782 | + | 16.6412i | 0.634903 | + | 1.09968i | 0.986536 | + | 0.163546i | \(0.0522931\pi\) |
−0.351633 | + | 0.936138i | \(0.614374\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.9002 | + | 22.3439i | −0.845122 | + | 1.46379i | 0.0403930 | + | 0.999184i | \(0.487139\pi\) |
−0.885515 | + | 0.464611i | \(0.846194\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.8872 | − | 30.9815i | −1.16683 | − | 2.02101i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.65732 | + | 11.5308i | −0.430626 | + | 0.745866i | −0.996927 | − | 0.0783322i | \(-0.975041\pi\) |
0.566301 | + | 0.824198i | \(0.308374\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.928238 | + | 1.60776i | −0.0597931 | + | 0.103565i | −0.894372 | − | 0.447323i | \(-0.852377\pi\) |
0.834579 | + | 0.550888i | \(0.185711\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −17.6812 | − | 16.0084i | −1.12961 | − | 1.02274i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.885843 | + | 1.53432i | 0.0563648 | + | 0.0976267i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.6947 | 0.738165 | 0.369083 | − | 0.929397i | \(-0.379672\pi\) | ||||
0.369083 | + | 0.929397i | \(0.379672\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −29.6746 | −1.86563 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.46594 | + | 2.53908i | 0.0914429 | + | 0.158384i | 0.908118 | − | 0.418713i | \(-0.137519\pi\) |
−0.816676 | + | 0.577097i | \(0.804185\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.4388 | + | 8.26342i | 1.33214 | + | 0.513464i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.1420 | − | 24.4946i | 0.872032 | − | 1.51040i | 0.0121407 | − | 0.999926i | \(-0.496135\pi\) |
0.859891 | − | 0.510477i | \(-0.170531\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.0766 | + | 27.8455i | −0.987579 | + | 1.71054i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.79128 | − | 8.29874i | −0.292129 | − | 0.505983i | 0.682184 | − | 0.731181i | \(-0.261030\pi\) |
−0.974313 | + | 0.225198i | \(0.927697\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.14220 | + | 15.8348i | −0.555349 | + | 0.961893i | 0.442527 | + | 0.896755i | \(0.354082\pi\) |
−0.997876 | + | 0.0651381i | \(0.979251\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −17.8353 | − | 30.8917i | −1.07551 | − | 1.86284i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.32776 | + | 4.03180i | −0.139862 | + | 0.242248i | −0.927444 | − | 0.373962i | \(-0.877999\pi\) |
0.787582 | + | 0.616209i | \(0.211332\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.06669 | + | 15.7040i | 0.540873 | + | 0.936820i | 0.998854 | + | 0.0478580i | \(0.0152395\pi\) |
−0.457981 | + | 0.888962i | \(0.651427\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.6194 | 0.987920 | 0.493960 | − | 0.869485i | \(-0.335549\pi\) | ||||
0.493960 | + | 0.869485i | \(0.335549\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.10796 | − | 3.51059i | −0.537626 | − | 0.207223i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.16055 | − | 14.1345i | 0.480032 | − | 0.831441i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.94284 | + | 3.36510i | −0.113502 | + | 0.196591i | −0.917180 | − | 0.398473i | \(-0.869540\pi\) |
0.803678 | + | 0.595064i | \(0.202873\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.82928 | − | 4.90046i | −0.164727 | − | 0.285316i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 20.8520 | 1.20590 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.9641 | + | 14.5062i | −1.03543 | + | 0.836123i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.61647 | + | 2.79981i | 0.0925588 | + | 0.160317i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.48452 | 0.198872 | 0.0994361 | − | 0.995044i | \(-0.468296\pi\) | ||||
0.0994361 | + | 0.995044i | \(0.468296\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.9855 | −0.736338 | −0.368169 | − | 0.929759i | \(-0.620015\pi\) | ||||
−0.368169 | + | 0.929759i | \(0.620015\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.0439 | 0.850329 | 0.425164 | − | 0.905116i | \(-0.360216\pi\) | ||||
0.425164 | + | 0.905116i | \(0.360216\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.45839 | 0.475070 | 0.237535 | − | 0.971379i | \(-0.423660\pi\) | ||||
0.237535 | + | 0.971379i | \(0.423660\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.32069 | 0.241912 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.384968 | 0.0214202 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.5326 | + | 21.7072i | 0.695186 | + | 1.20410i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.30774 | − | 27.4421i | −0.237494 | − | 1.51293i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.0245 | −0.550996 | −0.275498 | − | 0.961302i | \(-0.588843\pi\) | ||||
−0.275498 | + | 0.961302i | \(0.588843\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.918597 | − | 1.59106i | −0.0501883 | − | 0.0869287i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.33242 | + | 16.1642i | −0.508369 | + | 0.880522i | 0.491584 | + | 0.870830i | \(0.336418\pi\) |
−0.999953 | + | 0.00969119i | \(0.996915\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −26.7318 | + | 46.3009i | −1.44761 | + | 2.50733i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.33992 | − | 16.5362i | −0.450313 | − | 0.892871i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.8048 | 0.848446 | 0.424223 | − | 0.905558i | \(-0.360547\pi\) | ||||
0.424223 | + | 0.905558i | \(0.360547\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.51578 | + | 7.82156i | 0.241724 | + | 0.418678i | 0.961205 | − | 0.275833i | \(-0.0889538\pi\) |
−0.719481 | + | 0.694512i | \(0.755620\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.23939 | − | 12.5390i | 0.385314 | − | 0.667383i | −0.606499 | − | 0.795084i | \(-0.707427\pi\) |
0.991813 | + | 0.127701i | \(0.0407599\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.59155 | − | 11.4169i | −0.349843 | − | 0.605947i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.85517 | − | 13.6056i | 0.414580 | − | 0.718074i | −0.580804 | − | 0.814043i | \(-0.697262\pi\) |
0.995384 | + | 0.0959695i | \(0.0305951\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.39085 | + | 16.2654i | 0.494255 | + | 0.856075i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.82312 | + | 15.2821i | −0.461823 | + | 0.799902i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.42947 | + | 16.3323i | −0.492214 | + | 0.852540i | −0.999960 | − | 0.00896710i | \(-0.997146\pi\) |
0.507746 | + | 0.861507i | \(0.330479\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.4241 | + | 15.6852i | −1.00845 | + | 0.814334i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.8568 | + | 29.1969i | 0.872814 | + | 1.51176i | 0.859073 | + | 0.511853i | \(0.171041\pi\) |
0.0137417 | + | 0.999906i | \(0.495626\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.03609 | −0.156367 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.7263 | 1.73241 | 0.866203 | − | 0.499693i | \(-0.166554\pi\) | ||||
0.866203 | + | 0.499693i | \(0.166554\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.16201 | + | 15.8691i | 0.468157 | + | 0.810871i | 0.999338 | − | 0.0363870i | \(-0.0115849\pi\) |
−0.531181 | + | 0.847258i | \(0.678252\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.54427 | − | 48.0600i | −0.384491 | − | 2.44936i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.13744 | − | 3.70216i | 0.108373 | − | 0.187707i | −0.806739 | − | 0.590909i | \(-0.798769\pi\) |
0.915111 | + | 0.403202i | \(0.132103\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.26545 | − | 3.92388i | 0.114569 | − | 0.198439i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.3381 | − | 23.1023i | −0.671112 | − | 1.16240i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.9312 | − | 31.0577i | 0.899939 | − | 1.55874i | 0.0723687 | − | 0.997378i | \(-0.476944\pi\) |
0.827570 | − | 0.561362i | \(-0.189723\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.7007 | − | 20.2663i | −0.584307 | − | 1.01205i | −0.994961 | − | 0.100259i | \(-0.968033\pi\) |
0.410654 | − | 0.911791i | \(-0.365300\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.7841 | − | 32.5350i | 0.935702 | − | 1.62068i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 23.4316 | + | 40.5848i | 1.16146 | + | 2.01171i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.8032 | 1.72091 | 0.860453 | − | 0.509530i | \(-0.170181\pi\) | ||||
0.860453 | + | 0.509530i | \(0.170181\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.681372 | − | 4.34062i | −0.0335281 | − | 0.213588i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.9351 | − | 22.4043i | 0.634961 | − | 1.09978i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.90894 | + | 5.03843i | −0.142111 | + | 0.246143i | −0.928291 | − | 0.371854i | \(-0.878722\pi\) |
0.786180 | + | 0.617997i | \(0.212056\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.7765 | − | 30.7898i | −0.866375 | − | 1.50061i | −0.865676 | − | 0.500605i | \(-0.833111\pi\) |
−0.000699237 | − | 1.00000i | \(-0.500223\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.44642 | 0.264190 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.389292 | + | 2.47995i | 0.0188392 | + | 0.120013i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.48374 | + | 4.30196i | 0.119637 | + | 0.207218i | 0.919624 | − | 0.392800i | \(-0.128493\pi\) |
−0.799987 | + | 0.600018i | \(0.795160\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.9062 | 1.10080 | 0.550401 | − | 0.834900i | \(-0.314475\pi\) | ||||
0.550401 | + | 0.834900i | \(0.314475\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.56925 | −0.122904 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.05894 | 0.384632 | 0.192316 | − | 0.981333i | \(-0.438400\pi\) | ||||
0.192316 | + | 0.981333i | \(0.438400\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.77766 | 0.179482 | 0.0897410 | − | 0.995965i | \(-0.471396\pi\) | ||||
0.0897410 | + | 0.995965i | \(0.471396\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 25.4528 | 1.20658 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.5069 | −1.58129 | −0.790644 | − | 0.612276i | \(-0.790254\pi\) | ||||
−0.790644 | + | 0.612276i | \(0.790254\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.95457 | − | 17.2418i | −0.468742 | − | 0.811885i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.30125 | + | 33.7711i | 0.248527 | + | 1.58321i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.739506 | 0.0345926 | 0.0172963 | − | 0.999850i | \(-0.494494\pi\) | ||||
0.0172963 | + | 0.999850i | \(0.494494\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.30465 | + | 5.72383i | 0.153913 | + | 0.266585i | 0.932663 | − | 0.360750i | \(-0.117479\pi\) |
−0.778750 | + | 0.627335i | \(0.784146\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.96606 | + | 10.3335i | −0.277266 | + | 0.480239i | −0.970704 | − | 0.240277i | \(-0.922762\pi\) |
0.693438 | + | 0.720516i | \(0.256095\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.11184 | − | 8.85396i | 0.236548 | − | 0.409713i | −0.723174 | − | 0.690666i | \(-0.757317\pi\) |
0.959721 | + | 0.280954i | \(0.0906507\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.221225 | − | 1.40929i | −0.0102152 | − | 0.0650749i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −47.0948 | −2.16542 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.54419 | − | 2.67462i | −0.0708524 | − | 0.122720i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.01896 | + | 1.76488i | −0.0465573 | + | 0.0806395i | −0.888365 | − | 0.459138i | \(-0.848158\pi\) |
0.841808 | + | 0.539778i | \(0.181492\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.4651 | − | 28.5184i | −0.750743 | − | 1.30033i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.9888 | − | 19.0331i | 0.498974 | − | 0.864248i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.5958 | + | 30.4767i | 0.797340 | + | 1.38103i | 0.921343 | + | 0.388751i | \(0.127093\pi\) |
−0.124003 | + | 0.992282i | \(0.539573\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.5708 | − | 30.4335i | 0.792958 | − | 1.37344i | −0.131170 | − | 0.991360i | \(-0.541873\pi\) |
0.924128 | − | 0.382083i | \(-0.124793\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.329855 | + | 0.571326i | −0.0148559 | + | 0.0257312i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.58744 | − | 10.1126i | −0.0712062 | − | 0.453612i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.32633 | − | 4.02932i | −0.104141 | − | 0.180377i | 0.809246 | − | 0.587470i | \(-0.199876\pi\) |
−0.913387 | + | 0.407093i | \(0.866543\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.0660 | −0.537997 | −0.268999 | − | 0.963141i | \(-0.586693\pi\) | ||||
−0.268999 | + | 0.963141i | \(0.586693\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −55.1974 | −2.45625 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.1739 | + | 19.3537i | 0.495273 | + | 0.857838i | 0.999985 | − | 0.00544958i | \(-0.00173466\pi\) |
−0.504712 | + | 0.863288i | \(0.668401\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.6603 | + | 8.60829i | −0.471583 | + | 0.380808i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 26.7454 | − | 46.3244i | 1.17854 | − | 2.04130i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 28.3287 | − | 49.0667i | 1.24589 | − | 2.15795i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.854260 | − | 1.47962i | −0.0374258 | − | 0.0648234i | 0.846706 | − | 0.532061i | \(-0.178582\pi\) |
−0.884132 | + | 0.467238i | \(0.845249\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.6036 | + | 18.3659i | −0.463662 | + | 0.803087i | −0.999140 | − | 0.0414627i | \(-0.986798\pi\) |
0.535478 | + | 0.844549i | \(0.320132\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.08158 | − | 7.06951i | −0.177796 | − | 0.307952i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.61945 | + | 6.26907i | −0.157367 | + | 0.272568i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.99494 | + | 12.1156i | 0.302984 | + | 0.524784i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.4236 | 0.839754 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.95532 | − | 36.9275i | 0.342660 | − | 1.59058i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.79443 | − | 8.30419i | 0.206129 | − | 0.357025i | −0.744363 | − | 0.667775i | \(-0.767247\pi\) |
0.950492 | + | 0.310750i | \(0.100580\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.46882 | − | 12.9364i | 0.319929 | − | 0.554133i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.65927 | − | 9.80214i | −0.241973 | − | 0.419109i | 0.719303 | − | 0.694696i | \(-0.244461\pi\) |
−0.961276 | + | 0.275587i | \(0.911128\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.374088 | 0.0159367 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.21220 | − | 20.4630i | −0.136596 | − | 0.870174i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.68102 | − | 2.91162i | −0.0712272 | − | 0.123369i | 0.828212 | − | 0.560415i | \(-0.189358\pi\) |
−0.899439 | + | 0.437045i | \(0.856025\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 33.0929 | 1.39968 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.0914 | 0.804606 | 0.402303 | − | 0.915506i | \(-0.368210\pi\) | ||||
0.402303 | + | 0.915506i | \(0.368210\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 33.8424 | 1.42376 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.62726 | −0.110140 | −0.0550702 | − | 0.998482i | \(-0.517538\pi\) | ||||
−0.0550702 | + | 0.998482i | \(0.517538\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.98226 | −0.417745 | −0.208872 | − | 0.977943i | \(-0.566979\pi\) | ||||
−0.208872 | + | 0.977943i | \(0.566979\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −36.3489 | −1.51586 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.05761 | + | 10.4921i | 0.252182 | + | 0.436791i | 0.964126 | − | 0.265444i | \(-0.0855187\pi\) |
−0.711945 | + | 0.702236i | \(0.752185\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.6285 | − | 12.6202i | 0.648379 | − | 0.523573i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −50.9224 | −2.10899 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.1857 | − | 26.3025i | −0.626782 | − | 1.08562i | −0.988193 | − | 0.153212i | \(-0.951038\pi\) |
0.361411 | − | 0.932407i | \(-0.382295\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.31446 | + | 4.00875i | −0.0953655 | + | 0.165178i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.5788 | − | 35.6434i | 0.845068 | − | 1.46370i | −0.0404940 | − | 0.999180i | \(-0.512893\pi\) |
0.885562 | − | 0.464521i | \(-0.153774\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.93093 | + | 2.67147i | 0.284141 | + | 0.109520i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.11041 | −0.331382 | −0.165691 | − | 0.986178i | \(-0.552986\pi\) | ||||
−0.165691 | + | 0.986178i | \(0.552986\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.8320 | + | 27.4218i | 0.645801 | + | 1.11856i | 0.984116 | + | 0.177527i | \(0.0568098\pi\) |
−0.338315 | + | 0.941033i | \(0.609857\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 30.8722 | − | 53.4723i | 1.25513 | − | 2.17396i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.5131 | + | 19.9412i | 0.467300 | + | 0.809388i | 0.999302 | − | 0.0373552i | \(-0.0118933\pi\) |
−0.532002 | + | 0.846743i | \(0.678560\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.9062 | + | 34.4785i | −0.805317 | + | 1.39485i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.4750 | + | 19.8752i | 0.463470 | + | 0.802753i | 0.999131 | − | 0.0416796i | \(-0.0132709\pi\) |
−0.535661 | + | 0.844433i | \(0.679938\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.1183 | + | 19.2574i | −0.447605 | + | 0.775274i | −0.998230 | − | 0.0594788i | \(-0.981056\pi\) |
0.550625 | + | 0.834753i | \(0.314389\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.75302 | − | 4.76836i | 0.110653 | − | 0.191657i | −0.805381 | − | 0.592758i | \(-0.798039\pi\) |
0.916034 | + | 0.401101i | \(0.131372\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.4412 | + | 7.10800i | 0.738831 | + | 0.284776i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.17850 | + | 12.4335i | 0.287140 | + | 0.497341i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.15538 | −0.285303 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.9276 | −1.31083 | −0.655413 | − | 0.755271i | \(-0.727505\pi\) | ||||
−0.655413 | + | 0.755271i | \(0.727505\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −27.4501 | − | 47.5449i | −1.08932 | − | 1.88676i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.59009 | + | 25.9484i | −0.221488 | + | 1.02811i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.945880 | + | 1.63831i | −0.0373600 | + | 0.0647095i | −0.884101 | − | 0.467296i | \(-0.845228\pi\) |
0.846741 | + | 0.532006i | \(0.178562\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.8742 | − | 39.6193i | 0.902070 | − | 1.56243i | 0.0772675 | − | 0.997010i | \(-0.475380\pi\) |
0.824803 | − | 0.565421i | \(-0.191286\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.98067 | − | 15.5550i | −0.353066 | − | 0.611529i | 0.633719 | − | 0.773564i | \(-0.281528\pi\) |
−0.986785 | + | 0.162035i | \(0.948194\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.48085 | − | 7.76106i | 0.175889 | − | 0.304648i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.0741 | − | 19.1809i | −0.433363 | − | 0.750607i | 0.563797 | − | 0.825913i | \(-0.309340\pi\) |
−0.997160 | + | 0.0753063i | \(0.976007\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.7506 | − | 41.1373i | 0.928015 | − | 1.60737i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.39543 | + | 9.34515i | 0.210176 | + | 0.364035i | 0.951769 | − | 0.306814i | \(-0.0992630\pi\) |
−0.741594 | + | 0.670850i | \(0.765930\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.13907 | −0.199887 | −0.0999434 | − | 0.994993i | \(-0.531866\pi\) | ||||
−0.0999434 | + | 0.994993i | \(0.531866\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.653187 | − | 4.16106i | −0.0253295 | − | 0.161359i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.20142 | − | 3.81298i | 0.0852395 | − | 0.147639i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.56007 | + | 4.43417i | −0.0988304 | + | 0.171179i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.9290 | + | 18.9295i | 0.421281 | + | 0.729680i | 0.996065 | − | 0.0886254i | \(-0.0282474\pi\) |
−0.574784 | + | 0.818305i | \(0.694914\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.7296 | 0.450807 | 0.225403 | − | 0.974266i | \(-0.427630\pi\) | ||||
0.225403 | + | 0.974266i | \(0.427630\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.2768 | − | 10.7212i | 0.509518 | − | 0.411442i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.260358 | + | 0.450954i | 0.00996234 | + | 0.0172553i | 0.870964 | − | 0.491348i | \(-0.163496\pi\) |
−0.861001 | + | 0.508603i | \(0.830162\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37.9987 | −1.45186 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 35.7825 | 1.36320 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 46.1912 | 1.75720 | 0.878599 | − | 0.477561i | \(-0.158479\pi\) | ||||
0.878599 | + | 0.477561i | \(0.158479\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −21.6529 | −0.821342 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.03985 | 0.115143 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.7166 | 1.23569 | 0.617844 | − | 0.786301i | \(-0.288006\pi\) | ||||
0.617844 | + | 0.786301i | \(0.288006\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.02872 | + | 3.51385i | 0.0765148 | + | 0.132527i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −39.9919 | − | 15.4145i | −1.50405 | − | 0.579723i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33.4551 | −1.25643 | −0.628216 | − | 0.778039i | \(-0.716215\pi\) | ||||
−0.628216 | + | 0.778039i | \(0.716215\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 27.2401 | + | 47.1813i | 1.02015 | + | 1.76695i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −34.8622 | + | 60.3831i | −1.30377 | + | 2.25820i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.42685 | + | 16.3278i | −0.351562 | + | 0.608924i | −0.986523 | − | 0.163621i | \(-0.947683\pi\) |
0.634961 | + | 0.772544i | \(0.281016\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 32.3143 | − | 26.0942i | 1.20345 | − | 0.971798i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.29248 | 0.196558 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.3107 | − | 33.4471i | −0.716194 | − | 1.24048i | −0.962497 | − | 0.271291i | \(-0.912549\pi\) |
0.246303 | − | 0.969193i | \(-0.420784\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.59537 | − | 6.22736i | 0.132979 | − | 0.230327i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.35591 | + | 16.2049i | 0.345569 | + | 0.598542i | 0.985457 | − | 0.169926i | \(-0.0543527\pi\) |
−0.639888 | + | 0.768468i | \(0.721019\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.45482 | − | 2.51982i | 0.0535890 | − | 0.0928189i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.15949 | + | 12.4006i | 0.263366 | + | 0.456163i | 0.967134 | − | 0.254266i | \(-0.0818340\pi\) |
−0.703768 | + | 0.710430i | \(0.748501\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.2068 | + | 24.6069i | −0.521197 | + | 0.902740i | 0.478499 | + | 0.878088i | \(0.341181\pi\) |
−0.999696 | + | 0.0246519i | \(0.992152\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.6442 | − | 34.0247i | 0.719706 | − | 1.24657i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.0729 | + | 5.42426i | 0.514211 | + | 0.198198i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.7209 | + | 27.2294i | 0.573663 | + | 0.993614i | 0.996185 | + | 0.0872612i | \(0.0278115\pi\) |
−0.422522 | + | 0.906353i | \(0.638855\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.36687 | −0.0861392 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.405916 | 0.0147533 | 0.00737663 | − | 0.999973i | \(-0.497652\pi\) | ||||
0.00737663 | + | 0.999973i | \(0.497652\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.65688 | + | 4.60184i | 0.0963117 | + | 0.166817i | 0.910155 | − | 0.414267i | \(-0.135962\pi\) |
−0.813844 | + | 0.581084i | \(0.802629\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.02397 | − | 7.28696i | 0.326690 | − | 0.263806i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.14863 | + | 5.45359i | −0.113691 | + | 0.196918i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.9430 | − | 20.6858i | 0.430674 | − | 0.745949i | −0.566258 | − | 0.824228i | \(-0.691609\pi\) |
0.996931 | + | 0.0782793i | \(0.0249426\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.8525 | − | 22.2613i | −0.462274 | − | 0.800682i | 0.536800 | − | 0.843710i | \(-0.319633\pi\) |
−0.999074 | + | 0.0430274i | \(0.986300\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −32.7442 | + | 56.7147i | −1.17621 | + | 2.03725i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.861872 | − | 1.49281i | −0.0308798 | − | 0.0534853i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.4393 | − | 18.0814i | 0.373548 | − | 0.647004i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.89727 | − | 11.9464i | −0.246174 | − | 0.426386i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.1109 | 0.574292 | 0.287146 | − | 0.957887i | \(-0.407293\pi\) | ||||
0.287146 | + | 0.957887i | \(0.407293\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.5196 | + | 9.45089i | 0.871818 | + | 0.336035i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.79893 | − | 3.11583i | 0.0638818 | − | 0.110646i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.556852 | + | 0.964495i | −0.0197247 | + | 0.0341642i | −0.875719 | − | 0.482821i | \(-0.839612\pi\) |
0.855995 | + | 0.516985i | \(0.172946\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.32540 | + | 7.49181i | 0.153022 | + | 0.265041i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −27.9471 | −0.986231 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −46.2565 | − | 17.8292i | −1.63033 | − | 0.628395i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.1461 | − | 17.5736i | −0.356718 | − | 0.617853i | 0.630693 | − | 0.776033i | \(-0.282771\pi\) |
−0.987410 | + | 0.158179i | \(0.949438\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.72686 | −0.341556 | −0.170778 | − | 0.985310i | \(-0.554628\pi\) | ||||
−0.170778 | + | 0.985310i | \(0.554628\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 34.4803 | 1.20779 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.07749 | −0.142653 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.07104 | 0.142080 | 0.0710401 | − | 0.997473i | \(-0.477368\pi\) | ||||
0.0710401 | + | 0.997473i | \(0.477368\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.61200 | 0.0910485 | 0.0455242 | − | 0.998963i | \(-0.485504\pi\) | ||||
0.0455242 | + | 0.998963i | \(0.485504\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.0054 | 1.04339 | 0.521695 | − | 0.853132i | \(-0.325300\pi\) | ||||
0.521695 | + | 0.853132i | \(0.325300\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.0676 | − | 24.3658i | −0.488588 | − | 0.846260i | 0.511325 | − | 0.859387i | \(-0.329155\pi\) |
−0.999914 | + | 0.0131272i | \(0.995821\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.27559 | + | 3.87109i | 0.148140 | + | 0.134125i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 59.7226 | 2.06679 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.61277 | + | 6.25750i | 0.124727 | + | 0.216033i | 0.921626 | − | 0.388079i | \(-0.126861\pi\) |
−0.796899 | + | 0.604112i | \(0.793528\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.1795 | − | 24.5596i | 0.488947 | − | 0.846881i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.34933 | − | 4.06915i | 0.0808193 | − | 0.139983i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 37.3005 | − | 30.1205i | 1.28166 | − | 1.03495i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 47.7544 | 1.63700 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.0767 | + | 27.8457i | 0.550457 | + | 0.953419i | 0.998242 | + | 0.0592779i | \(0.0188798\pi\) |
−0.447785 | + | 0.894141i | \(0.647787\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.48585 | + | 6.03767i | −0.119074 | + | 0.206243i | −0.919401 | − | 0.393321i | \(-0.871326\pi\) |
0.800327 | + | 0.599564i | \(0.204659\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.3523 | + | 30.0551i | 0.592054 | + | 1.02547i | 0.993955 | + | 0.109785i | \(0.0350162\pi\) |
−0.401901 | + | 0.915683i | \(0.631650\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25.9863 | + | 45.0095i | −0.884583 | + | 1.53214i | −0.0383914 | + | 0.999263i | \(0.512223\pi\) |
−0.846191 | + | 0.532879i | \(0.821110\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.3486 | + | 23.1204i | 0.453866 | + | 0.786119i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.1241 | − | 36.5880i | 0.716586 | − | 1.24116i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.02228 | + | 1.77064i | −0.0346387 | + | 0.0599960i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.25097 | − | 14.3396i | −0.0760968 | − | 0.484767i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.3822 | − | 35.3029i | −0.688257 | − | 1.19210i | −0.972401 | − | 0.233314i | \(-0.925043\pi\) |
0.284145 | − | 0.958781i | \(-0.408290\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.07339 | 0.204618 | 0.102309 | − | 0.994753i | \(-0.467377\pi\) | ||||
0.102309 | + | 0.994753i | \(0.467377\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.0958 | −0.339751 | −0.169875 | − | 0.985466i | \(-0.554336\pi\) | ||||
−0.169875 | + | 0.985466i | \(0.554336\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.55215 | + | 11.3487i | 0.220000 | + | 0.381051i | 0.954808 | − | 0.297225i | \(-0.0960610\pi\) |
−0.734808 | + | 0.678275i | \(0.762728\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.61077 | − | 42.1132i | −0.221718 | − | 1.41243i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.45271 | − | 4.24822i | 0.0820768 | − | 0.142161i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.7393 | + | 27.2612i | −0.526106 | + | 0.911242i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.96622 | − | 6.86969i | −0.132281 | − | 0.229117i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.88758 | − | 6.73348i | 0.129514 | − | 0.224325i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.1164 | + | 27.9145i | 0.535728 | + | 0.927908i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.41698 | + | 11.1145i | −0.213072 | + | 0.369052i | −0.952674 | − | 0.303992i | \(-0.901680\pi\) |
0.739602 | + | 0.673044i | \(0.235014\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.5089 | − | 30.3262i | −0.580094 | − | 1.00475i | −0.995468 | − | 0.0951015i | \(-0.969682\pi\) |
0.415373 | − | 0.909651i | \(-0.363651\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 40.9718 | 1.35597 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 28.6960 | − | 23.1723i | 0.947626 | − | 0.765218i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.12422 | + | 7.14336i | −0.136046 | + | 0.235638i | −0.925996 | − | 0.377532i | \(-0.876773\pi\) |
0.789951 | + | 0.613170i | \(0.210106\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.33557 | + | 12.7056i | −0.241453 | + | 0.418209i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28.7018 | + | 49.7129i | 0.943709 | + | 1.63455i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 56.8512 | 1.86523 | 0.932614 | − | 0.360876i | \(-0.117522\pi\) | ||||
0.932614 | + | 0.360876i | \(0.117522\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.688776 | − | 3.19720i | 0.0225737 | − | 0.104784i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.57518 | + | 13.1206i | 0.247735 | + | 0.429089i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −46.6213 | −1.52305 | −0.761526 | − | 0.648134i | \(-0.775550\pi\) | ||||
−0.761526 | + | 0.648134i | \(0.775550\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.3402 | −0.826067 | −0.413033 | − | 0.910716i | \(-0.635531\pi\) | ||||
−0.413033 | + | 0.910716i | \(0.635531\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.2877 | −0.660658 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 29.9572 | 0.973478 | 0.486739 | − | 0.873548i | \(-0.338186\pi\) | ||||
0.486739 | + | 0.873548i | \(0.338186\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.6380 | 0.637478 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.6721 | −1.25271 | −0.626356 | − | 0.779537i | \(-0.715454\pi\) | ||||
−0.626356 | + | 0.779537i | \(0.715454\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.0771711 | + | 0.133664i | 0.00249720 | + | 0.00432528i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −27.5310 | − | 10.6116i | −0.889023 | − | 0.342666i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 67.1549 | 2.16629 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −32.0630 | − | 55.5347i | −1.03214 | − | 1.78773i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.2161 | + | 28.0870i | −0.521473 | + | 0.903218i | 0.478215 | + | 0.878243i | \(0.341284\pi\) |
−0.999688 | + | 0.0249755i | \(0.992049\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.53128 | − | 14.7766i | 0.273782 | − | 0.474204i | −0.696045 | − | 0.717998i | \(-0.745059\pi\) |
0.969827 | + | 0.243794i | \(0.0783921\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.6881 | − | 6.04683i | −0.502936 | − | 0.193853i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.5513 | 0.465538 | 0.232769 | − | 0.972532i | \(-0.425221\pi\) | ||||
0.232769 | + | 0.972532i | \(0.425221\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.1553 | + | 34.9101i | 0.644168 | + | 1.11573i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.1926 | − | 28.0463i | 0.516463 | − | 0.894540i | −0.483355 | − | 0.875425i | \(-0.660582\pi\) |
0.999817 | − | 0.0191149i | \(-0.00608483\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 38.1430 | + | 66.0657i | 1.21534 | + | 2.10503i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −23.9952 | + | 41.5608i | −0.763002 | + | 1.32156i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.7165 | − | 22.0256i | −0.403952 | − | 0.699665i | 0.590247 | − | 0.807223i | \(-0.299030\pi\) |
−0.994199 | + | 0.107558i | \(0.965697\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −38.7447 | + | 67.1078i | −1.22829 | + | 2.12746i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.696665 | − | 1.20666i | 0.0220636 | − | 0.0382153i | −0.854783 | − | 0.518986i | \(-0.826310\pi\) |
0.876846 | + | 0.480771i | \(0.159643\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3024.2.q.l.2305.11 | 22 | ||
3.2 | odd | 2 | 1008.2.q.l.625.6 | 22 | |||
4.3 | odd | 2 | 1512.2.q.d.793.11 | 22 | |||
7.4 | even | 3 | 3024.2.t.k.1873.1 | 22 | |||
9.2 | odd | 6 | 1008.2.t.l.961.9 | 22 | |||
9.7 | even | 3 | 3024.2.t.k.289.1 | 22 | |||
12.11 | even | 2 | 504.2.q.c.121.6 | yes | 22 | ||
21.11 | odd | 6 | 1008.2.t.l.193.9 | 22 | |||
28.11 | odd | 6 | 1512.2.t.c.361.1 | 22 | |||
36.7 | odd | 6 | 1512.2.t.c.289.1 | 22 | |||
36.11 | even | 6 | 504.2.t.c.457.3 | yes | 22 | ||
63.11 | odd | 6 | 1008.2.q.l.529.6 | 22 | |||
63.25 | even | 3 | inner | 3024.2.q.l.2881.11 | 22 | ||
84.11 | even | 6 | 504.2.t.c.193.3 | yes | 22 | ||
252.11 | even | 6 | 504.2.q.c.25.6 | ✓ | 22 | ||
252.151 | odd | 6 | 1512.2.q.d.1369.11 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.c.25.6 | ✓ | 22 | 252.11 | even | 6 | ||
504.2.q.c.121.6 | yes | 22 | 12.11 | even | 2 | ||
504.2.t.c.193.3 | yes | 22 | 84.11 | even | 6 | ||
504.2.t.c.457.3 | yes | 22 | 36.11 | even | 6 | ||
1008.2.q.l.529.6 | 22 | 63.11 | odd | 6 | |||
1008.2.q.l.625.6 | 22 | 3.2 | odd | 2 | |||
1008.2.t.l.193.9 | 22 | 21.11 | odd | 6 | |||
1008.2.t.l.961.9 | 22 | 9.2 | odd | 6 | |||
1512.2.q.d.793.11 | 22 | 4.3 | odd | 2 | |||
1512.2.q.d.1369.11 | 22 | 252.151 | odd | 6 | |||
1512.2.t.c.289.1 | 22 | 36.7 | odd | 6 | |||
1512.2.t.c.361.1 | 22 | 28.11 | odd | 6 | |||
3024.2.q.l.2305.11 | 22 | 1.1 | even | 1 | trivial | ||
3024.2.q.l.2881.11 | 22 | 63.25 | even | 3 | inner | ||
3024.2.t.k.289.1 | 22 | 9.7 | even | 3 | |||
3024.2.t.k.1873.1 | 22 | 7.4 | even | 3 |