Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(289,3024)]
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, 4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.t (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 | 289.1 | ||
Character | \(\chi\) | \(=\) | 3024.289 |
Dual form | 3024.2.t.k.1873.1 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(5\) | −3.40736 | −1.52382 | −0.761909 | − | 0.647684i | \(-0.775738\pi\) | ||||
−0.761909 | + | 0.647684i | \(0.775738\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.05842 | − | 1.66220i | 0.778010 | − | 0.628252i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.39638 | 1.62707 | 0.813535 | − | 0.581516i | \(-0.197540\pi\) | ||||
0.813535 | + | 0.581516i | \(0.197540\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.89598 | + | 3.28393i | 0.525850 | + | 0.910800i | 0.999547 | + | 0.0301113i | \(0.00958618\pi\) |
−0.473696 | + | 0.880688i | \(0.657080\pi\) | |||||||
\(14\) | 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 | ||||||||
\(23\) | −5.49899 | −1.14662 | −0.573309 | − | 0.819339i | \(-0.694341\pi\) | ||||
−0.573309 | + | 0.819339i | \(0.694341\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.61011 | 1.32202 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.400332 | + | 0.693396i | −0.0743399 | + | 0.128760i | −0.900799 | − | 0.434236i | \(-0.857018\pi\) |
0.826459 | + | 0.562997i | \(0.190352\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.95366 | + | 8.57999i | −0.889703 | + | 1.54101i | −0.0494772 | + | 0.998775i | \(0.515756\pi\) |
−0.840226 | + | 0.542236i | \(0.817578\pi\) | |||||||
\(32\) | 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 | 0.685264 | − | 0.728295i | \(-0.259687\pi\) |
−0.973354 | + | 0.229309i | \(0.926354\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.36356 | − | 7.55790i | 0.665436 | − | 1.15257i | −0.313731 | − | 0.949512i | \(-0.601579\pi\) |
0.979167 | − | 0.203057i | \(-0.0650878\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.24957 | + | 9.09252i | 0.765728 | + | 1.32628i | 0.939861 | + | 0.341558i | \(0.110955\pi\) |
−0.174133 | + | 0.984722i | \(0.555712\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.47420 | − | 6.84301i | 0.210599 | − | 0.977572i | ||||
\(50\) | 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 | ||||||||
\(59\) | 0.830344 | − | 1.43820i | 0.108102 | − | 0.187238i | −0.806900 | − | 0.590689i | \(-0.798856\pi\) |
0.915001 | + | 0.403451i | \(0.132189\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.474405 | − | 0.821694i | −0.0607414 | − | 0.105207i | 0.834056 | − | 0.551680i | \(-0.186013\pi\) |
−0.894797 | + | 0.446473i | \(0.852680\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.46029 | − | 11.1896i | −0.801301 | − | 1.38789i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.269592 | − | 0.466947i | 0.0329359 | − | 0.0570467i | −0.849088 | − | 0.528252i | \(-0.822848\pi\) |
0.882024 | + | 0.471205i | \(0.156181\pi\) | |||||||
\(68\) | 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 | ||||||||
\(77\) | 11.1080 | − | 8.96985i | 1.26588 | − | 1.02221i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.91449 | + | 6.78010i | 0.440415 | + | 0.762821i | 0.997720 | − | 0.0674866i | \(-0.0214980\pi\) |
−0.557305 | + | 0.830308i | \(0.688165\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.79623 | + | 6.57527i | −0.416691 | + | 0.721729i | −0.995604 | − | 0.0936595i | \(-0.970143\pi\) |
0.578914 | + | 0.815389i | \(0.303477\pi\) | |||||||
\(84\) | 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 | ||||||||
\(95\) | 0.795996 | − | 1.37871i | 0.0816675 | − | 0.141452i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.22500 | + | 5.58587i | −0.327450 | + | 0.567159i | −0.982005 | − | 0.188855i | \(-0.939522\pi\) |
0.654555 | + | 0.756014i | \(0.272856\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.1995 | 1.61191 | 0.805953 | − | 0.591979i | \(-0.201653\pi\) | ||||
0.805953 | + | 0.591979i | \(0.201653\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.6986 | 1.54683 | 0.773414 | − | 0.633901i | \(-0.218547\pi\) | ||||
0.773414 | + | 0.633901i | \(0.218547\pi\) | |||||||
\(104\) | 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 | 0.999296 | − | 0.0375041i | \(-0.0119407\pi\) |
−0.532128 | + | 0.846664i | \(0.678607\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 18.7370 | 1.74724 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.03411 | − | 0.784029i | −0.186466 | − | 0.0718718i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.1209 | 1.64735 | ||||||||
\(122\) | 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 | ||||||||
\(131\) | 13.9408 | 1.21801 | 0.609006 | − | 0.793166i | \(-0.291569\pi\) | ||||
0.609006 | + | 0.793166i | \(0.291569\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.191699 | + | 1.22120i | 0.0166224 | + | 0.105891i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.1520 | 0.952776 | 0.476388 | − | 0.879235i | \(-0.341946\pi\) | ||||
0.476388 | + | 0.879235i | \(0.341946\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.17737 | − | 5.50337i | −0.269501 | − | 0.466790i | 0.699232 | − | 0.714895i | \(-0.253526\pi\) |
−0.968733 | + | 0.248105i | \(0.920192\pi\) | |||||||
\(140\) | 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 | ||||||||
\(149\) | 11.5304 | 0.944609 | 0.472304 | − | 0.881435i | \(-0.343422\pi\) | ||||
0.472304 | + | 0.881435i | \(0.343422\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.694634 | 0.0565285 | 0.0282643 | − | 0.999600i | \(-0.491002\pi\) | ||||
0.0282643 | + | 0.999600i | \(0.491002\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.8789 | − | 29.2351i | 1.35575 | − | 2.34822i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.02423 | − | 3.50606i | 0.161551 | − | 0.279814i | −0.773874 | − | 0.633339i | \(-0.781684\pi\) |
0.935425 | + | 0.353525i | \(0.115017\pi\) | |||||||
\(158\) | 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 | 0.975534 | + | 0.219847i | \(0.0705560\pi\) |
−0.297374 | + | 0.954761i | \(0.596111\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.689486 | + | 1.19422i | −0.0530374 | + | 0.0918634i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.91758 | − | 6.78544i | −0.297848 | − | 0.515887i | 0.677796 | − | 0.735250i | \(-0.262935\pi\) |
−0.975643 | + | 0.219363i | \(0.929602\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.6064 | − | 10.9873i | 1.02855 | − | 0.830563i | ||||
\(176\) | 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 | ||||||||
\(185\) | −14.7951 | + | 25.6259i | −1.08776 | + | 1.88405i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.22318 | − | 3.85066i | −0.162575 | − | 0.281588i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.0226484 | − | 0.0392281i | −0.00163878 | − | 0.00283845i | 0.865205 | − | 0.501419i | \(-0.167188\pi\) |
−0.866844 | + | 0.498580i | \(0.833855\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.40991 | − | 16.2984i | 0.677340 | − | 1.17319i | −0.298438 | − | 0.954429i | \(-0.596466\pi\) |
0.975779 | − | 0.218759i | \(-0.0702009\pi\) | |||||||
\(194\) | 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 | ||||||||
\(203\) | 0.328509 | + | 2.09273i | 0.0230568 | + | 0.146881i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.28547 | + | 10.8868i | 0.438997 | + | 0.760364i | ||||
\(206\) | 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 | 0.949713 | − | 0.313123i | \(-0.101375\pi\) |
−0.746029 | + | 0.665914i | \(0.768042\pi\) | |||||||
\(212\) | 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 | ||||||||
\(221\) | 1.56220 | − | 2.70581i | 0.105085 | − | 0.182012i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.20124 | − | 2.08062i | 0.0804412 | − | 0.139328i | −0.822998 | − | 0.568044i | \(-0.807700\pi\) |
0.903440 | + | 0.428716i | \(0.141034\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.97702 | −0.463081 | −0.231540 | − | 0.972825i | \(-0.574377\pi\) | ||||
−0.231540 | + | 0.972825i | \(0.574377\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.2156 | −1.26981 | −0.634903 | − | 0.772592i | \(-0.718960\pi\) | ||||
−0.634903 | + | 0.772592i | \(0.718960\pi\) | |||||||
\(230\) | 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 | 0.566301 | − | 0.824198i | \(-0.308374\pi\) |
−0.996927 | + | 0.0783322i | \(0.975041\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.85648 | 0.119586 | 0.0597931 | − | 0.998211i | \(-0.480956\pi\) | ||||
0.0597931 | + | 0.998211i | \(0.480956\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.02312 | + | 23.3166i | −0.320915 | + | 1.48964i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.77169 | −0.112730 | ||||||||
\(248\) | 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 | ||||||||
\(257\) | −2.93188 | −0.182886 | −0.0914429 | − | 0.995810i | \(-0.529148\pi\) | ||||
−0.0914429 | + | 0.995810i | \(0.529148\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.56309 | − | 22.6983i | −0.221399 | − | 1.41040i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −28.2840 | −1.74406 | −0.872032 | − | 0.489449i | \(-0.837198\pi\) | ||||
−0.872032 | + | 0.489449i | \(0.837198\pi\) | |||||||
\(264\) | 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 | ||||||||
\(275\) | 35.6707 | 2.15102 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.65553 | 0.279723 | 0.139862 | − | 0.990171i | \(-0.455334\pi\) | ||||
0.139862 | + | 0.990171i | \(0.455334\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.06669 | − | 15.7040i | 0.540873 | − | 0.936820i | −0.457981 | − | 0.888962i | \(-0.651427\pi\) |
0.998854 | − | 0.0478580i | \(-0.0152395\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.30969 | + | 14.3928i | −0.493960 | + | 0.855564i | −0.999976 | − | 0.00696045i | \(-0.997784\pi\) |
0.506016 | + | 0.862524i | \(0.331118\pi\) | |||||||
\(284\) | 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 | 0.803678 | − | 0.595064i | \(-0.202873\pi\) |
−0.917180 | + | 0.398473i | \(0.869540\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.82928 | + | 4.90046i | −0.164727 | + | 0.285316i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.4260 | − | 18.0583i | −0.602950 | − | 1.04434i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.58069 | − | 22.8104i | −0.206388 | − | 1.31477i | ||||
\(302\) | 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 | ||||||||
\(311\) | 6.49273 | − | 11.2457i | 0.368169 | − | 0.637687i | −0.621110 | − | 0.783723i | \(-0.713318\pi\) |
0.989279 | + | 0.146036i | \(0.0466515\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.52193 | − | 13.0284i | −0.425164 | − | 0.736406i | 0.571271 | − | 0.820761i | \(-0.306450\pi\) |
−0.996436 | + | 0.0843548i | \(0.973117\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.22919 | − | 7.32518i | −0.237535 | − | 0.411423i | 0.722471 | − | 0.691401i | \(-0.243006\pi\) |
−0.960006 | + | 0.279978i | \(0.909673\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.16035 | + | 3.74183i | −0.120956 | + | 0.209502i | ||||
\(320\) | 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 | ||||||||
\(329\) | 25.9194 | + | 9.99041i | 1.42898 | + | 0.550789i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.01224 | + | 8.68146i | 0.275498 | + | 0.477176i | 0.970261 | − | 0.242063i | \(-0.0778240\pi\) |
−0.694763 | + | 0.719239i | \(0.744491\pi\) | |||||||
\(332\) | 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 | −0.999953 | − | 0.00969119i | \(-0.996915\pi\) |
0.491584 | − | 0.870830i | \(-0.336418\pi\) | |||||||
\(338\) | 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 | ||||||||
\(347\) | −7.90240 | + | 13.6874i | −0.424223 | + | 0.734776i | −0.996348 | − | 0.0853910i | \(-0.972786\pi\) |
0.572125 | + | 0.820167i | \(0.306119\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.51578 | − | 7.82156i | 0.241724 | − | 0.418678i | −0.719481 | − | 0.694512i | \(-0.755620\pi\) |
0.961205 | + | 0.275833i | \(0.0889538\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.4788 | −0.770627 | −0.385314 | − | 0.922786i | \(-0.625907\pi\) | ||||
−0.385314 | + | 0.922786i | \(0.625907\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.1831 | 0.699687 | ||||||||
\(356\) | 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 | ||||||||
\(367\) | 18.8589 | 0.984428 | 0.492214 | − | 0.870474i | \(-0.336188\pi\) | ||||
0.492214 | + | 0.870474i | \(0.336188\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23.2958 | + | 8.97917i | 1.20946 | + | 0.466175i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −33.7137 | −1.74563 | −0.872814 | − | 0.488052i | \(-0.837708\pi\) | ||||
−0.872814 | + | 0.488052i | \(0.837708\pi\) | |||||||
\(374\) | 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 | ||||||||
\(383\) | −18.3240 | −0.936314 | −0.468157 | − | 0.883645i | \(-0.655082\pi\) | ||||
−0.468157 | + | 0.883645i | \(0.655082\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −37.8490 | + | 30.5635i | −1.92897 | + | 1.55766i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.27488 | −0.216745 | −0.108373 | − | 0.994110i | \(-0.534564\pi\) | ||||
−0.108373 | + | 0.994110i | \(0.534564\pi\) | |||||||
\(390\) | 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 | ||||||||
\(401\) | 23.4015 | 1.16861 | 0.584307 | − | 0.811533i | \(-0.301366\pi\) | ||||
0.584307 | + | 0.811533i | \(0.301366\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −37.5682 | −1.87140 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 23.4316 | − | 40.5848i | 1.16146 | − | 2.01171i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.4016 | + | 30.1404i | −0.860453 | + | 1.49035i | 0.0110389 | + | 0.999939i | \(0.496486\pi\) |
−0.871492 | + | 0.490410i | \(0.836847\pi\) | |||||||
\(410\) | 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 | 0.786180 | − | 0.617997i | \(-0.212056\pi\) |
−0.928291 | + | 0.371854i | \(0.878722\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.7765 | + | 30.7898i | −0.866375 | + | 1.50061i | −0.000699237 | 1.00000i | \(0.500223\pi\) | |
−0.865676 | + | 0.500605i | \(0.833111\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.72321 | − | 4.71674i | −0.132095 | − | 0.228795i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.34234 | − | 0.902837i | −0.113354 | − | 0.0436913i | ||||
\(428\) | 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 | ||||||||
\(437\) | 1.28462 | − | 2.22503i | 0.0614519 | − | 0.106438i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.02947 | − | 6.97925i | −0.192316 | − | 0.333101i | 0.753701 | − | 0.657217i | \(-0.228267\pi\) |
−0.946017 | + | 0.324116i | \(0.894933\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.88883 | − | 3.27155i | −0.0897410 | − | 0.155436i | 0.817661 | − | 0.575701i | \(-0.195271\pi\) |
−0.907402 | + | 0.420265i | \(0.861937\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.7264 | + | 22.0428i | −0.603290 | + | 1.04493i | ||||
\(446\) | 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 | ||||||||
\(455\) | −31.8973 | − | 12.2945i | −1.49537 | − | 0.576376i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.369753 | − | 0.640431i | −0.0172963 | − | 0.0299581i | 0.857248 | − | 0.514904i | \(-0.172173\pi\) |
−0.874544 | + | 0.484946i | \(0.838839\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.30465 | − | 5.72383i | 0.153913 | − | 0.266585i | −0.778750 | − | 0.627335i | \(-0.784146\pi\) |
0.932663 | + | 0.360750i | \(0.117479\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.96606 | − | 10.3335i | −0.277266 | − | 0.480239i | 0.693438 | − | 0.720516i | \(-0.256095\pi\) |
−0.970704 | + | 0.240277i | \(0.922762\pi\) | |||||||
\(464\) | 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 | ||||||||
\(473\) | 23.5474 | − | 40.7853i | 1.08271 | − | 1.87531i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.54419 | + | 2.67462i | −0.0708524 | + | 0.122720i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.03791 | 0.0931145 | 0.0465573 | − | 0.998916i | \(-0.485175\pi\) | ||||
0.0465573 | + | 0.998916i | \(0.485175\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32.9302 | 1.50149 | ||||||||
\(482\) | 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 | 0.924128 | + | 0.382083i | \(0.124793\pi\) |
−0.131170 | + | 0.991360i | \(0.541873\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.659710 | 0.0297118 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.96405 | + | 6.43106i | −0.357236 | + | 0.288472i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.65266 | 0.208282 | 0.104141 | − | 0.994563i | \(-0.466791\pi\) | ||||
0.104141 | + | 0.994563i | \(0.466791\pi\) | |||||||
\(500\) | 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 | ||||||||
\(509\) | −22.3477 | −0.990546 | −0.495273 | − | 0.868737i | \(-0.664932\pi\) | ||||
−0.495273 | + | 0.868737i | \(0.664932\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.7851 | + | 4.92792i | 0.565581 | + | 0.217998i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −53.4908 | −2.35709 | ||||||||
\(516\) | 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 | ||||||||
\(527\) | 8.16316 | 0.355593 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.23889 | 0.314735 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.99494 | − | 12.1156i | 0.302984 | − | 0.524784i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.71179 | + | 16.8213i | −0.419877 | + | 0.727248i | ||||
\(536\) | 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 | −0.961276 | − | 0.275587i | \(-0.911128\pi\) |
0.719303 | + | 0.694696i | \(0.244461\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.187044 | − | 0.323969i | −0.00796834 | − | 0.0138016i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.3275 | + | 7.44964i | 0.821891 | + | 0.316791i | ||||
\(554\) | 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 | ||||||||
\(563\) | −9.54570 | + | 16.5336i | −0.402303 | + | 0.696810i | −0.994003 | − | 0.109348i | \(-0.965124\pi\) |
0.591700 | + | 0.806158i | \(0.298457\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.9212 | − | 29.3084i | −0.711880 | − | 1.23301i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.31363 | + | 2.27527i | 0.0550702 | + | 0.0953844i | 0.892246 | − | 0.451549i | \(-0.149128\pi\) |
−0.837176 | + | 0.546933i | \(0.815795\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.99113 | − | 8.64489i | 0.208872 | − | 0.361777i | −0.742487 | − | 0.669860i | \(-0.766354\pi\) |
0.951360 | + | 0.308083i | \(0.0996874\pi\) | |||||||
\(572\) | 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 | ||||||||
\(581\) | 3.11515 | + | 19.8448i | 0.129238 | + | 0.823299i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25.4612 | + | 44.1001i | 1.05450 | + | 1.82644i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.1857 | + | 26.3025i | −0.626782 | + | 1.08562i | 0.361411 | + | 0.932407i | \(0.382295\pi\) |
−0.988193 | + | 0.153212i | \(0.951038\pi\) | |||||||
\(588\) | 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 | ||||||||
\(599\) | 4.05521 | − | 7.02382i | 0.165691 | − | 0.286986i | −0.771209 | − | 0.636582i | \(-0.780348\pi\) |
0.936901 | + | 0.349596i | \(0.113681\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.8320 | − | 27.4218i | 0.645801 | − | 1.11856i | −0.338315 | − | 0.941033i | \(-0.609857\pi\) |
0.984116 | − | 0.177527i | \(-0.0568098\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −61.7445 | −2.51027 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.0261 | −0.934601 | −0.467300 | − | 0.884099i | \(-0.654773\pi\) | ||||
−0.467300 | + | 0.884099i | \(0.654773\pi\) | |||||||
\(608\) | 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 | 0.550625 | − | 0.834753i | \(-0.314389\pi\) |
−0.998230 | + | 0.0594788i | \(0.981056\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.50603 | −0.221306 | −0.110653 | − | 0.993859i | \(-0.535294\pi\) | ||||
−0.110653 | + | 0.993859i | \(0.535294\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.06488 | − | 19.5245i | −0.122792 | − | 0.782234i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.3570 | −0.574280 | ||||||||
\(626\) | 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 | ||||||||
\(635\) | 54.9002 | 2.17865 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 25.2670 | − | 8.13305i | 1.00112 | − | 0.322243i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.89176 | 0.0747201 | 0.0373600 | − | 0.999302i | \(-0.488105\pi\) | ||||
0.0373600 | + | 0.999302i | \(0.488105\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.8742 | + | 39.6193i | 0.902070 | + | 1.56243i | 0.824803 | + | 0.565421i | \(0.191286\pi\) |
0.0772675 | + | 0.997010i | \(0.475380\pi\) | |||||||
\(644\) | 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 | ||||||||
\(653\) | 22.1482 | 0.866726 | 0.433363 | − | 0.901219i | \(-0.357327\pi\) | ||||
0.433363 | + | 0.901219i | \(0.357327\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −47.5013 | −1.85603 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.39543 | − | 9.34515i | 0.210176 | − | 0.364035i | −0.741594 | − | 0.670850i | \(-0.765930\pi\) |
0.951769 | + | 0.306814i | \(0.0992630\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.56954 | − | 4.45057i | 0.0999434 | − | 0.173107i | −0.811718 | − | 0.584050i | \(-0.801467\pi\) |
0.911661 | + | 0.410943i | \(0.134800\pi\) | |||||||
\(662\) | 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 | −0.574784 | − | 0.818305i | \(-0.694914\pi\) |
0.996065 | + | 0.0886254i | \(0.0282474\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.86482 | − | 10.1582i | −0.225403 | − | 0.390410i | 0.731037 | − | 0.682338i | \(-0.239037\pi\) |
−0.956440 | + | 0.291928i | \(0.905703\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.64641 | + | 16.8587i | 0.101560 | + | 0.646976i | ||||
\(680\) | 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 | ||||||||
\(689\) | −17.8912 | + | 30.9885i | −0.681602 | + | 1.18057i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.0956 | − | 40.0028i | −0.878599 | − | 1.52178i | −0.852879 | − | 0.522108i | \(-0.825146\pi\) |
−0.0257196 | − | 0.999669i | \(-0.508188\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.8265 | + | 18.7520i | 0.410671 | + | 0.711303i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.51993 | + | 2.63259i | −0.0575713 | + | 0.0997164i | ||||
\(698\) | 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 | ||||||||
\(707\) | 33.3453 | − | 26.9267i | 1.25408 | − | 1.01268i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.7275 | + | 28.9730i | 0.628216 | + | 1.08810i | 0.987910 | + | 0.155032i | \(0.0495480\pi\) |
−0.359693 | + | 0.933071i | \(0.617119\pi\) | |||||||
\(710\) | 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 | ||||||||
\(725\) | −2.64624 | + | 4.58342i | −0.0982789 | + | 0.170224i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.3107 | + | 33.4471i | −0.716194 | + | 1.24048i | 0.246303 | + | 0.969193i | \(0.420784\pi\) |
−0.962497 | + | 0.271291i | \(0.912549\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.19073 | −0.265959 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.7118 | −0.691137 | −0.345569 | − | 0.938394i | \(-0.612314\pi\) | ||||
−0.345569 | + | 0.938394i | \(0.612314\pi\) | |||||||
\(734\) | 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 | −0.999696 | − | 0.0246519i | \(-0.992152\pi\) |
0.478499 | − | 0.878088i | \(-0.341181\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −39.2883 | −1.43941 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.33888 | − | 14.8996i | −0.0854607 | − | 0.544419i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.4418 | −1.14733 | −0.573663 | − | 0.819091i | \(-0.694478\pi\) | ||||
−0.573663 | + | 0.819091i | \(0.694478\pi\) | |||||||
\(752\) | 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 | ||||||||
\(761\) | −5.31375 | −0.192623 | −0.0963117 | − | 0.995351i | \(-0.530705\pi\) | ||||
−0.0963117 | + | 0.995351i | \(0.530705\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.8227 | − | 4.17151i | −0.391807 | − | 0.151019i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.29727 | 0.227381 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.9430 | + | 20.6858i | 0.430674 | + | 0.745949i | 0.996931 | − | 0.0782793i | \(-0.0249426\pi\) |
−0.566258 | + | 0.824228i | \(0.691609\pi\) | |||||||
\(770\) | 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 | ||||||||
\(779\) | 1.72374 | 0.0617595 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.8786 | −0.747096 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.89727 | + | 11.9464i | −0.246174 | + | 0.426386i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.05546 | + | 13.9525i | −0.287146 | + | 0.497352i | −0.973127 | − | 0.230268i | \(-0.926040\pi\) |
0.685981 | + | 0.727619i | \(0.259373\pi\) | |||||||
\(788\) | 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 | 0.855995 | − | 0.516985i | \(-0.172946\pi\) |
−0.875719 | + | 0.482821i | \(0.839612\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.32540 | − | 7.49181i | 0.153022 | − | 0.265041i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.9735 | + | 24.2029i | 0.493116 | + | 0.854101i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 38.5687 | − | 31.1447i | 1.35937 | − | 1.09771i | ||||
\(806\) | 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 | ||||||||
\(815\) | −17.2402 | + | 29.8608i | −0.603897 | + | 1.04598i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.03875 | + | 3.53121i | 0.0713267 | + | 0.123542i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.03552 | − | 3.52562i | −0.0710401 | − | 0.123045i | 0.828317 | − | 0.560259i | \(-0.189299\pi\) |
−0.899357 | + | 0.437214i | \(0.855965\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.30600 | + | 2.26206i | −0.0455242 | + | 0.0788503i | −0.887890 | − | 0.460056i | \(-0.847829\pi\) |
0.842365 | + | 0.538907i | \(0.181162\pi\) | |||||||
\(824\) | 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 | ||||||||
\(833\) | −5.49026 | + | 1.76722i | −0.190226 | + | 0.0612307i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −29.8613 | − | 51.7213i | −1.03339 | − | 1.78989i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.61277 | − | 6.25750i | 0.124727 | − | 0.216033i | −0.796899 | − | 0.604112i | \(-0.793528\pi\) |
0.921626 | + | 0.388079i | \(0.126861\pi\) | |||||||
\(840\) | 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 | ||||||||
\(851\) | −23.8772 | + | 41.3565i | −0.818499 | + | 1.41768i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.0767 | − | 27.8457i | 0.550457 | − | 0.953419i | −0.447785 | − | 0.894141i | \(-0.647787\pi\) |
0.998242 | − | 0.0592779i | \(-0.0188798\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.97170 | 0.238149 | 0.119074 | − | 0.992885i | \(-0.462007\pi\) | ||||
0.119074 | + | 0.992885i | \(0.462007\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.7047 | −1.18411 | −0.592054 | − | 0.805898i | \(-0.701683\pi\) | ||||
−0.592054 | + | 0.805898i | \(0.701683\pi\) | |||||||
\(860\) | 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 | ||||||||
\(871\) | 2.04456 | 0.0692774 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.2930 | + | 9.11920i | −0.381772 | + | 0.308285i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40.7643 | 1.37651 | 0.688257 | − | 0.725467i | \(-0.258376\pi\) | ||||
0.688257 | + | 0.725467i | \(0.258376\pi\) | |||||||
\(878\) | 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 | ||||||||
\(887\) | −13.1043 | −0.440000 | −0.220000 | − | 0.975500i | \(-0.570606\pi\) | ||||
−0.220000 | + | 0.975500i | \(0.570606\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −33.1657 | + | 26.7817i | −1.11234 | + | 0.898230i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.90542 | −0.164154 | ||||||||
\(894\) | 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 | ||||||||
\(905\) | −32.2328 | −1.07146 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.8340 | 0.426144 | 0.213072 | − | 0.977036i | \(-0.431653\pi\) | ||||
0.213072 | + | 0.977036i | \(0.431653\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.5089 | + | 30.3262i | −0.580094 | + | 1.00475i | 0.415373 | + | 0.909651i | \(0.363651\pi\) |
−0.995468 | + | 0.0951015i | \(0.969682\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.4859 | + | 35.4826i | −0.677985 | + | 1.17430i | ||||
\(914\) | 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 | ||||||||
\(929\) | −28.4256 | − | 49.2346i | −0.932614 | − | 1.61533i | −0.778835 | − | 0.627229i | \(-0.784189\pi\) |
−0.153779 | − | 0.988105i | \(-0.549144\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.42447 | + | 2.19510i | 0.0794587 | + | 0.0719414i | ||||
\(932\) | 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 | ||||||||
\(941\) | 12.6701 | − | 21.9453i | 0.413033 | − | 0.715395i | −0.582186 | − | 0.813055i | \(-0.697803\pi\) |
0.995220 | + | 0.0976604i | \(0.0311359\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.1438 | + | 17.5697i | 0.330329 | + | 0.572147i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.9786 | − | 25.9437i | −0.486739 | − | 0.843056i | 0.513145 | − | 0.858302i | \(-0.328480\pi\) |
−0.999884 | + | 0.0152455i | \(0.995147\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.81902 | + | 17.0070i | −0.318739 | + | 0.552072i | ||||
\(950\) | 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 | ||||||||
\(959\) | 22.9554 | − | 18.5368i | 0.741269 | − | 0.598583i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −33.5775 | − | 58.1579i | −1.08314 | − | 1.87606i | ||||
\(962\) | 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 | −0.999688 | − | 0.0249755i | \(-0.992049\pi\) |
0.478215 | − | 0.878243i | \(-0.341284\pi\) | |||||||
\(968\) | 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 | ||||||||
\(977\) | −7.27566 | + | 12.6018i | −0.232769 | + | 0.403168i | −0.958622 | − | 0.284682i | \(-0.908112\pi\) |
0.725853 | + | 0.687850i | \(0.241445\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.1553 | − | 34.9101i | 0.644168 | − | 1.11573i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −32.3851 | −1.03293 | −0.516463 | − | 0.856310i | \(-0.672751\pi\) | ||||
−0.516463 | + | 0.856310i | \(0.672751\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −76.2860 | −2.43068 | ||||||||
\(986\) | 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 | ||||||||
\(997\) | −1.39333 | −0.0441272 | −0.0220636 | − | 0.999757i | \(-0.507024\pi\) | ||||
−0.0220636 | + | 0.999757i | \(0.507024\pi\) | |||||||
\(998\) | 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.t.k.289.1 | 22 | ||
3.2 | odd | 2 | 1008.2.t.l.961.9 | 22 | |||
4.3 | odd | 2 | 1512.2.t.c.289.1 | 22 | |||
7.4 | even | 3 | 3024.2.q.l.2881.11 | 22 | |||
9.4 | even | 3 | 3024.2.q.l.2305.11 | 22 | |||
9.5 | odd | 6 | 1008.2.q.l.625.6 | 22 | |||
12.11 | even | 2 | 504.2.t.c.457.3 | yes | 22 | ||
21.11 | odd | 6 | 1008.2.q.l.529.6 | 22 | |||
28.11 | odd | 6 | 1512.2.q.d.1369.11 | 22 | |||
36.23 | even | 6 | 504.2.q.c.121.6 | yes | 22 | ||
36.31 | odd | 6 | 1512.2.q.d.793.11 | 22 | |||
63.4 | even | 3 | inner | 3024.2.t.k.1873.1 | 22 | ||
63.32 | odd | 6 | 1008.2.t.l.193.9 | 22 | |||
84.11 | even | 6 | 504.2.q.c.25.6 | ✓ | 22 | ||
252.67 | odd | 6 | 1512.2.t.c.361.1 | 22 | |||
252.95 | even | 6 | 504.2.t.c.193.3 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.c.25.6 | ✓ | 22 | 84.11 | even | 6 | ||
504.2.q.c.121.6 | yes | 22 | 36.23 | even | 6 | ||
504.2.t.c.193.3 | yes | 22 | 252.95 | even | 6 | ||
504.2.t.c.457.3 | yes | 22 | 12.11 | even | 2 | ||
1008.2.q.l.529.6 | 22 | 21.11 | odd | 6 | |||
1008.2.q.l.625.6 | 22 | 9.5 | odd | 6 | |||
1008.2.t.l.193.9 | 22 | 63.32 | odd | 6 | |||
1008.2.t.l.961.9 | 22 | 3.2 | odd | 2 | |||
1512.2.q.d.793.11 | 22 | 36.31 | odd | 6 | |||
1512.2.q.d.1369.11 | 22 | 28.11 | odd | 6 | |||
1512.2.t.c.289.1 | 22 | 4.3 | odd | 2 | |||
1512.2.t.c.361.1 | 22 | 252.67 | odd | 6 | |||
3024.2.q.l.2305.11 | 22 | 9.4 | even | 3 | |||
3024.2.q.l.2881.11 | 22 | 7.4 | even | 3 | |||
3024.2.t.k.289.1 | 22 | 1.1 | even | 1 | trivial | ||
3024.2.t.k.1873.1 | 22 | 63.4 | even | 3 | inner |