Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(101,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.101");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.p (of order \(6\), degree \(2\), 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: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 401.7 | ||
Character | \(\chi\) | \(=\) | 900.401 |
Dual form | 900.3.p.f.101.7 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0.0930019 | + | 2.99856i | 0.0310006 | + | 0.999519i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.67363 | − | 6.36292i | −0.524804 | − | 0.908988i | −0.999583 | − | 0.0288825i | \(-0.990805\pi\) |
0.474778 | − | 0.880105i | \(-0.342528\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.98270 | + | 0.557743i | −0.998078 | + | 0.0619715i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.35448 | + | 4.82346i | −0.759498 | + | 0.438496i | −0.829115 | − | 0.559077i | \(-0.811155\pi\) |
0.0696175 | + | 0.997574i | \(0.477822\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8.34294 | + | 14.4504i | −0.641765 | + | 1.11157i | 0.343274 | + | 0.939235i | \(0.388464\pi\) |
−0.985039 | + | 0.172334i | \(0.944869\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 15.4743i | − | 0.910251i | −0.890427 | − | 0.455125i | \(-0.849594\pi\) | ||
0.890427 | − | 0.455125i | \(-0.150406\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 17.4865 | 0.920344 | 0.460172 | − | 0.887830i | \(-0.347788\pi\) | ||||
0.460172 | + | 0.887830i | \(0.347788\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 18.7379 | − | 11.6074i | 0.892282 | − | 0.552731i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.16415 | + | 5.29093i | 0.398441 | + | 0.230040i | 0.685811 | − | 0.727779i | \(-0.259448\pi\) |
−0.287370 | + | 0.957820i | \(0.592781\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.50783 | − | 26.8833i | −0.0928827 | − | 0.995677i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 36.2049 | − | 20.9029i | 1.24844 | − | 0.720789i | 0.277644 | − | 0.960684i | \(-0.410446\pi\) |
0.970799 | + | 0.239895i | \(0.0771130\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 24.3641 | − | 42.1998i | 0.785937 | − | 1.36128i | −0.142500 | − | 0.989795i | \(-0.545514\pi\) |
0.928438 | − | 0.371489i | \(-0.121153\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −15.2404 | − | 24.6028i | −0.461831 | − | 0.745539i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −20.4792 | −0.553492 | −0.276746 | − | 0.960943i | \(-0.589256\pi\) | ||||
−0.276746 | + | 0.960943i | \(0.589256\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −44.1063 | − | 23.6729i | −1.13093 | − | 0.606997i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 24.1640 | + | 13.9511i | 0.589365 | + | 0.340270i | 0.764846 | − | 0.644213i | \(-0.222815\pi\) |
−0.175482 | + | 0.984483i | \(0.556148\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −15.1046 | − | 26.1619i | −0.351269 | − | 0.608416i | 0.635203 | − | 0.772345i | \(-0.280916\pi\) |
−0.986472 | + | 0.163930i | \(0.947583\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −36.4814 | + | 21.0626i | −0.776200 | + | 0.448139i | −0.835082 | − | 0.550126i | \(-0.814580\pi\) |
0.0588817 | + | 0.998265i | \(0.481247\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.49113 | + | 4.31476i | −0.0508393 | + | 0.0880562i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 46.4005 | − | 1.43914i | 0.909813 | − | 0.0282183i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 90.4314i | − | 1.70625i | −0.521704 | − | 0.853127i | \(-0.674703\pi\) | ||
0.521704 | − | 0.853127i | \(-0.325297\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.62628 | + | 52.4344i | 0.0285312 | + | 0.919901i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 48.0096 | + | 27.7184i | 0.813722 | + | 0.469803i | 0.848247 | − | 0.529601i | \(-0.177658\pi\) |
−0.0345248 | + | 0.999404i | \(0.510992\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −58.3790 | − | 101.115i | −0.957034 | − | 1.65763i | −0.729644 | − | 0.683827i | \(-0.760314\pi\) |
−0.227389 | − | 0.973804i | \(-0.573019\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 36.5480 | + | 55.1072i | 0.580127 | + | 0.874718i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.64187 | − | 14.9682i | 0.128983 | − | 0.223405i | −0.794300 | − | 0.607526i | \(-0.792162\pi\) |
0.923283 | + | 0.384121i | \(0.125495\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −15.0129 | + | 27.9713i | −0.217578 | + | 0.405381i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 38.4861i | − | 0.542058i | −0.962571 | − | 0.271029i | \(-0.912636\pi\) | ||
0.962571 | − | 0.271029i | \(-0.0873640\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.38815 | 0.101208 | 0.0506038 | − | 0.998719i | \(-0.483885\pi\) | ||||
0.0506038 | + | 0.998719i | \(0.483885\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 61.3825 | + | 35.4392i | 0.797176 | + | 0.460250i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.8497 | + | 20.5242i | 0.149996 | + | 0.259800i | 0.931226 | − | 0.364443i | \(-0.118741\pi\) |
−0.781230 | + | 0.624244i | \(0.785407\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 80.3778 | − | 10.0201i | 0.992319 | − | 0.123705i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.69783 | + | 2.13494i | −0.0445522 | + | 0.0257222i | −0.522111 | − | 0.852878i | \(-0.674855\pi\) |
0.477558 | + | 0.878600i | \(0.341522\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 66.0456 | + | 106.618i | 0.759145 | + | 1.22550i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 145.034i | − | 1.62959i | −0.579746 | − | 0.814797i | \(-0.696848\pi\) | ||
0.579746 | − | 0.814797i | \(-0.303152\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 122.596 | 1.34720 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 128.804 | + | 69.1324i | 1.38499 | + | 0.743359i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 51.3498 | + | 88.9405i | 0.529379 | + | 0.916912i | 0.999413 | + | 0.0342635i | \(0.0109085\pi\) |
−0.470033 | + | 0.882649i | \(0.655758\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 72.3555 | − | 47.9874i | 0.730864 | − | 0.484721i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 96.0083 | − | 55.4304i | 0.950577 | − | 0.548816i | 0.0573168 | − | 0.998356i | \(-0.481745\pi\) |
0.893260 | + | 0.449540i | \(0.148412\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −93.9245 | + | 162.682i | −0.911888 | + | 1.57944i | −0.100494 | + | 0.994938i | \(0.532042\pi\) |
−0.811394 | + | 0.584499i | \(0.801291\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 121.767i | − | 1.13801i | −0.822334 | − | 0.569005i | \(-0.807328\pi\) | ||
0.822334 | − | 0.569005i | \(-0.192672\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 45.3350 | 0.415918 | 0.207959 | − | 0.978138i | \(-0.433318\pi\) | ||||
0.207959 | + | 0.978138i | \(0.433318\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.90461 | − | 61.4081i | −0.0171586 | − | 0.553226i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.6356 | + | 9.60459i | 0.147218 | + | 0.0849963i | 0.571800 | − | 0.820393i | \(-0.306245\pi\) |
−0.424582 | + | 0.905390i | \(0.639579\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 66.8826 | − | 134.457i | 0.571646 | − | 1.14920i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −98.4614 | + | 56.8467i | −0.827407 | + | 0.477704i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.9685 | + | 24.1941i | −0.115442 | + | 0.199951i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −39.5858 | + | 73.7545i | −0.321836 | + | 0.599630i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −179.244 | −1.41137 | −0.705684 | − | 0.708527i | \(-0.749360\pi\) | ||||
−0.705684 | + | 0.708527i | \(0.749360\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 77.0431 | − | 47.7250i | 0.597234 | − | 0.369961i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −73.6059 | − | 42.4964i | −0.561877 | − | 0.324400i | 0.192021 | − | 0.981391i | \(-0.438496\pi\) |
−0.753899 | + | 0.656991i | \(0.771829\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −64.2390 | − | 111.265i | −0.483000 | − | 0.836581i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 57.2217 | − | 33.0370i | 0.417677 | − | 0.241146i | −0.276406 | − | 0.961041i | \(-0.589144\pi\) |
0.694083 | + | 0.719895i | \(0.255810\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.71021 | + | 8.15832i | −0.0338864 | + | 0.0586929i | −0.882471 | − | 0.470366i | \(-0.844122\pi\) |
0.848585 | + | 0.529059i | \(0.177455\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −66.5501 | − | 107.433i | −0.471987 | − | 0.761935i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 160.967i | − | 1.12565i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.1697 | − | 7.06850i | −0.0895900 | − | 0.0480851i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −108.044 | − | 62.3792i | −0.725128 | − | 0.418653i | 0.0915094 | − | 0.995804i | \(-0.470831\pi\) |
−0.816637 | + | 0.577152i | \(0.804164\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 145.981 | + | 252.847i | 0.966763 | + | 1.67448i | 0.704802 | + | 0.709404i | \(0.251036\pi\) |
0.261961 | + | 0.965078i | \(0.415631\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.63066 | + | 139.001i | 0.0564096 | + | 0.908501i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 71.6347 | − | 124.075i | 0.456272 | − | 0.790286i | −0.542489 | − | 0.840063i | \(-0.682518\pi\) |
0.998760 | + | 0.0497773i | \(0.0158512\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 271.164 | − | 8.41029i | 1.70543 | − | 0.0528949i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 77.7476i | − | 0.482904i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −228.204 | −1.40002 | −0.700011 | − | 0.714132i | \(-0.746822\pi\) | ||||
−0.700011 | + | 0.714132i | \(0.746822\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −52.6156 | − | 30.3776i | −0.315063 | − | 0.181902i | 0.334127 | − | 0.942528i | \(-0.391559\pi\) |
−0.649190 | + | 0.760626i | \(0.724892\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −54.7094 | − | 94.7595i | −0.323725 | − | 0.560707i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −157.076 | + | 9.75299i | −0.918575 | + | 0.0570350i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 240.435 | − | 138.815i | 1.38980 | − | 0.802400i | 0.396506 | − | 0.918032i | \(-0.370223\pi\) |
0.993292 | + | 0.115632i | \(0.0368892\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −78.6501 | + | 146.537i | −0.444351 | + | 0.827895i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 272.749i | 1.52374i | 0.647731 | + | 0.761869i | \(0.275718\pi\) | ||||
−0.647731 | + | 0.761869i | \(0.724282\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −110.378 | −0.609824 | −0.304912 | − | 0.952380i | \(-0.598627\pi\) | ||||
−0.304912 | + | 0.952380i | \(0.598627\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 297.771 | − | 184.457i | 1.62717 | − | 1.00796i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 74.6395 | + | 129.279i | 0.399142 | + | 0.691334i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −161.843 | + | 114.716i | −0.856313 | + | 0.606965i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 29.1046 | − | 16.8036i | 0.152380 | − | 0.0879768i | −0.421871 | − | 0.906656i | \(-0.638627\pi\) |
0.574251 | + | 0.818679i | \(0.305293\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −135.342 | + | 234.419i | −0.701255 | + | 1.21461i | 0.266772 | + | 0.963760i | \(0.414043\pi\) |
−0.968026 | + | 0.250849i | \(0.919290\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 63.0978i | − | 0.320293i | −0.987093 | − | 0.160147i | \(-0.948803\pi\) | ||
0.987093 | − | 0.160147i | \(-0.0511967\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −283.032 | −1.42227 | −0.711135 | − | 0.703056i | \(-0.751818\pi\) | ||||
−0.711135 | + | 0.703056i | \(0.751818\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 45.6866 | + | 24.5211i | 0.227297 | + | 0.121995i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −266.007 | − | 153.579i | −1.31038 | − | 0.756547i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −85.2698 | − | 42.4156i | −0.411931 | − | 0.204906i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −146.091 | + | 84.3456i | −0.698999 | + | 0.403567i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −56.9312 | + | 98.6078i | −0.269816 | + | 0.467336i | −0.968814 | − | 0.247788i | \(-0.920296\pi\) |
0.698998 | + | 0.715124i | \(0.253630\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 115.403 | − | 3.57928i | 0.541798 | − | 0.0168042i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −358.018 | −1.64985 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.687112 | + | 22.1538i | 0.00313750 | + | 0.101159i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 223.609 | + | 129.101i | 1.01181 | + | 0.584167i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −108.929 | − | 188.670i | −0.488471 | − | 0.846056i | 0.511441 | − | 0.859318i | \(-0.329112\pi\) |
−0.999912 | + | 0.0132622i | \(0.995778\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 45.8299 | − | 26.4599i | 0.201894 | − | 0.116563i | −0.395645 | − | 0.918404i | \(-0.629479\pi\) |
0.597539 | + | 0.801840i | \(0.296145\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 195.660 | − | 338.894i | 0.854413 | − | 1.47989i | −0.0227762 | − | 0.999741i | \(-0.507251\pi\) |
0.877189 | − | 0.480146i | \(-0.159416\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −100.558 | + | 187.355i | −0.435315 | + | 0.811061i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 178.384i | − | 0.765596i | −0.923832 | − | 0.382798i | \(-0.874961\pi\) | ||
0.923832 | − | 0.382798i | \(-0.125039\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −60.4411 | + | 37.4407i | −0.255026 | + | 0.157978i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 314.501 | + | 181.577i | 1.31591 | + | 0.759738i | 0.983067 | − | 0.183246i | \(-0.0586604\pi\) |
0.332838 | + | 0.942984i | \(0.391994\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −90.3219 | − | 156.442i | −0.374780 | − | 0.649137i | 0.615514 | − | 0.788126i | \(-0.288948\pi\) |
−0.990294 | + | 0.138988i | \(0.955615\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 37.5211 | + | 240.086i | 0.154408 | + | 0.988007i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −145.889 | + | 252.687i | −0.590644 | + | 1.02303i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.74566 | − | 10.8896i | −0.0270910 | − | 0.0437334i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 73.5509i | − | 0.293032i | −0.989208 | − | 0.146516i | \(-0.953194\pi\) | ||
0.989208 | − | 0.146516i | \(-0.0468059\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −102.082 | −0.403487 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −125.532 | − | 72.4759i | −0.488451 | − | 0.282007i | 0.235481 | − | 0.971879i | \(-0.424334\pi\) |
−0.723932 | + | 0.689872i | \(0.757667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 75.2331 | + | 130.308i | 0.290475 | + | 0.503118i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −313.559 | + | 207.957i | −1.20138 | + | 0.796772i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 284.803 | − | 164.431i | 1.08290 | − | 0.625213i | 0.151223 | − | 0.988500i | \(-0.451679\pi\) |
0.931677 | + | 0.363287i | \(0.118346\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 434.892 | − | 13.4884i | 1.62881 | − | 0.0505184i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 355.832i | − | 1.32280i | −0.750035 | − | 0.661398i | \(-0.769963\pi\) | ||
0.750035 | − | 0.661398i | \(-0.230037\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −128.345 | −0.473599 | −0.236799 | − | 0.971559i | \(-0.576098\pi\) | ||||
−0.236799 | + | 0.971559i | \(0.576098\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.4016 | + | 367.610i | 0.0417642 | + | 1.34656i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −135.277 | − | 234.307i | −0.488365 | − | 0.845872i | 0.511546 | − | 0.859256i | \(-0.329073\pi\) |
−0.999910 | + | 0.0133837i | \(0.995740\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −195.318 | + | 392.657i | −0.700066 | + | 1.40737i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −454.766 | + | 262.559i | −1.61838 | + | 0.934374i | −0.631044 | + | 0.775747i | \(0.717373\pi\) |
−0.987339 | + | 0.158627i | \(0.949293\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −104.798 | + | 181.516i | −0.370311 | + | 0.641398i | −0.989613 | − | 0.143755i | \(-0.954082\pi\) |
0.619302 | + | 0.785153i | \(0.287416\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 205.004i | − | 0.714300i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 49.5472 | 0.171444 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −261.918 | + | 162.247i | −0.900060 | + | 0.557550i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −103.694 | − | 59.8679i | −0.353905 | − | 0.204327i | 0.312499 | − | 0.949918i | \(-0.398834\pi\) |
−0.666404 | + | 0.745591i | \(0.732167\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 150.622 | + | 212.499i | 0.507145 | + | 0.715486i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −152.912 | + | 88.2838i | −0.511411 | + | 0.295264i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −110.977 | + | 192.218i | −0.368695 | + | 0.638598i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 175.140 | + | 282.731i | 0.578021 | + | 0.933106i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 435.735 | 1.41933 | 0.709666 | − | 0.704538i | \(-0.248846\pi\) | ||||
0.709666 | + | 0.704538i | \(0.248846\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −496.547 | − | 266.508i | −1.60695 | − | 0.862487i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 59.2451 | + | 34.2052i | 0.190499 | + | 0.109985i | 0.592216 | − | 0.805779i | \(-0.298253\pi\) |
−0.401717 | + | 0.915764i | \(0.631587\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.9685 | − | 38.0506i | −0.0701870 | − | 0.121567i | 0.828796 | − | 0.559551i | \(-0.189026\pi\) |
−0.898983 | + | 0.437983i | \(0.855693\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 231.691 | − | 133.767i | 0.730885 | − | 0.421977i | −0.0878609 | − | 0.996133i | \(-0.528003\pi\) |
0.818746 | + | 0.574156i | \(0.194670\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −201.648 | + | 349.265i | −0.632127 | + | 1.09488i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 365.126 | − | 11.3246i | 1.13746 | − | 0.0352791i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 270.591i | − | 0.837743i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.21625 | + | 135.940i | 0.0128937 | + | 0.415718i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 268.038 | + | 154.752i | 0.814707 | + | 0.470371i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −36.0615 | − | 62.4604i | −0.108947 | − | 0.188702i | 0.806397 | − | 0.591375i | \(-0.201415\pi\) |
−0.915344 | + | 0.402673i | \(0.868081\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 183.959 | − | 11.4221i | 0.552429 | − | 0.0343007i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 97.8962 | − | 169.561i | 0.290493 | − | 0.503149i | −0.683433 | − | 0.730013i | \(-0.739514\pi\) |
0.973926 | + | 0.226864i | \(0.0728473\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −27.2528 | + | 50.7762i | −0.0803916 | + | 0.149782i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 470.076i | 1.37852i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −323.410 | −0.942886 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −109.827 | − | 63.4084i | −0.316503 | − | 0.182733i | 0.333330 | − | 0.942810i | \(-0.391828\pi\) |
−0.649833 | + | 0.760077i | \(0.725161\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 65.2764 | + | 113.062i | 0.187038 | + | 0.323960i | 0.944261 | − | 0.329196i | \(-0.106778\pi\) |
−0.757223 | + | 0.653156i | \(0.773444\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 409.397 | + | 188.047i | 1.16637 | + | 0.535745i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −226.254 | + | 130.628i | −0.640947 | + | 0.370051i | −0.784979 | − | 0.619522i | \(-0.787326\pi\) |
0.144032 | + | 0.989573i | \(0.453993\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −179.615 | − | 289.955i | −0.503124 | − | 0.812200i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 390.386i | − | 1.08743i | −0.839271 | − | 0.543713i | \(-0.817018\pi\) | ||
0.839271 | − | 0.543713i | \(-0.182982\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −55.2213 | −0.152968 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −73.8465 | − | 39.6352i | −0.203434 | − | 0.109188i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −42.1665 | − | 73.0345i | −0.114895 | − | 0.199004i | 0.802843 | − | 0.596191i | \(-0.203320\pi\) |
−0.917738 | + | 0.397187i | \(0.869987\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −224.839 | − | 111.841i | −0.609319 | − | 0.303092i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −575.407 | + | 332.212i | −1.55096 | + | 0.895449i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −88.5806 | + | 153.426i | −0.237482 | + | 0.411330i | −0.959991 | − | 0.280031i | \(-0.909655\pi\) |
0.722509 | + | 0.691361i | \(0.242989\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 697.566i | 1.85031i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 291.976 | 0.770386 | 0.385193 | − | 0.922836i | \(-0.374135\pi\) | ||||
0.385193 | + | 0.922836i | \(0.374135\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.6700 | − | 537.473i | −0.0437533 | − | 1.41069i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 236.884 | + | 136.765i | 0.618497 | + | 0.357090i | 0.776284 | − | 0.630384i | \(-0.217102\pi\) |
−0.157786 | + | 0.987473i | \(0.550436\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 150.271 | + | 226.580i | 0.388298 | + | 0.585478i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −206.095 | + | 118.989i | −0.529808 | + | 0.305885i | −0.740938 | − | 0.671573i | \(-0.765619\pi\) |
0.211130 | + | 0.977458i | \(0.432286\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 81.8732 | − | 141.808i | 0.209394 | − | 0.362682i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 120.582 | − | 224.664i | 0.306826 | − | 0.571664i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −76.9037 | −0.193712 | −0.0968560 | − | 0.995298i | \(-0.530879\pi\) | ||||
−0.0968560 | + | 0.995298i | \(0.530879\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 327.661 | − | 202.972i | 0.821206 | − | 0.508703i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −473.107 | − | 273.149i | −1.17982 | − | 0.681169i | −0.223846 | − | 0.974625i | \(-0.571861\pi\) |
−0.955973 | + | 0.293456i | \(0.905195\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 406.536 | + | 704.141i | 1.00877 | + | 1.74725i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 171.093 | − | 98.7807i | 0.420376 | − | 0.242704i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −281.051 | + | 486.795i | −0.687166 | + | 1.19021i | 0.285585 | + | 0.958353i | \(0.407812\pi\) |
−0.972751 | + | 0.231853i | \(0.925521\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 104.385 | + | 168.510i | 0.253978 | + | 0.410000i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 407.308i | − | 0.986218i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −24.9012 | − | 13.3651i | −0.0597152 | − | 0.0320506i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 209.645 | + | 121.038i | 0.500345 | + | 0.288874i | 0.728856 | − | 0.684667i | \(-0.240052\pi\) |
−0.228511 | + | 0.973541i | \(0.573386\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.10023 | − | 14.0300i | −0.0192405 | − | 0.0333255i | 0.856245 | − | 0.516570i | \(-0.172791\pi\) |
−0.875485 | + | 0.483245i | \(0.839458\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 315.954 | − | 209.546i | 0.746937 | − | 0.495380i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −428.926 | + | 742.922i | −1.00451 | + | 1.73986i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 482.670 | − | 14.9703i | 1.12511 | − | 0.0348957i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 50.0624i | 0.116154i | 0.998312 | + | 0.0580770i | \(0.0184969\pi\) | ||||
−0.998312 | + | 0.0580770i | \(0.981503\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −452.725 | −1.04556 | −0.522778 | − | 0.852469i | \(-0.675104\pi\) | ||||
−0.522778 | + | 0.852469i | \(0.675104\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 160.249 | + | 92.5199i | 0.366703 | + | 0.211716i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 115.139 | + | 199.426i | 0.262275 | + | 0.454274i | 0.966846 | − | 0.255360i | \(-0.0821938\pi\) |
−0.704571 | + | 0.709634i | \(0.748860\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.9705 | − | 40.1476i | 0.0452846 | − | 0.0910376i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 517.751 | − | 298.924i | 1.16874 | − | 0.674772i | 0.215356 | − | 0.976536i | \(-0.430909\pi\) |
0.953383 | + | 0.301764i | \(0.0975754\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 176.999 | − | 329.778i | 0.395972 | − | 0.737758i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 642.091i | − | 1.43005i | −0.699101 | − | 0.715023i | \(-0.746416\pi\) | ||
0.699101 | − | 0.715023i | \(-0.253584\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −269.170 | −0.596828 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −744.600 | + | 461.248i | −1.64371 | + | 1.01821i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 44.2091 | + | 76.5724i | 0.0967376 | + | 0.167554i | 0.910332 | − | 0.413878i | \(-0.135826\pi\) |
−0.813595 | + | 0.581432i | \(0.802493\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −415.999 | + | 38.8069i | −0.906316 | + | 0.0845466i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 421.874 | − | 243.569i | 0.915127 | − | 0.528349i | 0.0330498 | − | 0.999454i | \(-0.489478\pi\) |
0.882077 | + | 0.471105i | \(0.156145\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 313.941 | − | 543.761i | 0.678058 | − | 1.17443i | −0.297507 | − | 0.954720i | \(-0.596155\pi\) |
0.975565 | − | 0.219711i | \(-0.0705115\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 323.410i | − | 0.692527i | −0.938137 | − | 0.346263i | \(-0.887450\pi\) | ||
0.938137 | − | 0.346263i | \(-0.112550\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −126.988 | −0.270764 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 378.708 | + | 203.261i | 0.804051 | + | 0.431553i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 252.381 | + | 145.713i | 0.533576 | + | 0.308060i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 50.4375 | + | 812.318i | 0.105739 | + | 1.70297i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −137.174 | + | 79.1972i | −0.286375 | + | 0.165339i | −0.636306 | − | 0.771437i | \(-0.719538\pi\) |
0.349931 | + | 0.936776i | \(0.386205\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 170.857 | − | 295.933i | 0.355212 | − | 0.615245i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 233.131 | − | 7.23068i | 0.482672 | − | 0.0149703i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −108.301 | −0.222385 | −0.111192 | − | 0.993799i | \(-0.535467\pi\) | ||||
−0.111192 | + | 0.993799i | \(0.535467\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −21.2234 | − | 684.282i | −0.0434016 | − | 1.39935i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 588.153 | + | 339.570i | 1.19787 | + | 0.691589i | 0.960079 | − | 0.279728i | \(-0.0902444\pi\) |
0.237788 | + | 0.971317i | \(0.423578\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −323.457 | − | 560.243i | −0.656099 | − | 1.13640i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −244.884 | + | 141.384i | −0.492725 | + | 0.284475i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −37.1564 | + | 64.3568i | −0.0744618 | + | 0.128972i | −0.900852 | − | 0.434126i | \(-0.857057\pi\) |
0.826390 | + | 0.563098i | \(0.190391\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 86.1957 | − | 160.596i | 0.172047 | − | 0.320551i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 278.694i | 0.554063i | 0.960861 | + | 0.277031i | \(0.0893506\pi\) | ||||
−0.960861 | + | 0.277031i | \(0.910649\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 279.054 | − | 172.862i | 0.550402 | − | 0.340951i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −239.428 | − | 138.234i | −0.470390 | − | 0.271580i | 0.246013 | − | 0.969267i | \(-0.420879\pi\) |
−0.716403 | + | 0.697687i | \(0.754213\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.1413 | − | 47.0102i | −0.0531141 | − | 0.0919964i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −43.8533 | − | 470.095i | −0.0854840 | − | 0.916365i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 203.189 | − | 351.933i | 0.393015 | − | 0.680722i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 438.607 | + | 708.049i | 0.845099 | + | 1.36426i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 929.478i | − | 1.78403i | −0.452008 | − | 0.892014i | \(-0.649292\pi\) | ||
0.452008 | − | 0.892014i | \(-0.350708\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −217.275 | −0.415439 | −0.207719 | − | 0.978188i | \(-0.566604\pi\) | ||||
−0.207719 | + | 0.978188i | \(0.566604\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −653.011 | − | 377.016i | −1.23911 | − | 0.715400i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −208.512 | − | 361.154i | −0.394163 | − | 0.682710i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −446.716 | − | 222.209i | −0.841272 | − | 0.418472i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −403.197 | + | 232.786i | −0.756467 | + | 0.436747i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −817.854 | + | 25.3662i | −1.52301 | + | 0.0472368i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 48.0634i | − | 0.0891714i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 393.139 | 0.726690 | 0.363345 | − | 0.931655i | \(-0.381635\pi\) | ||||
0.363345 | + | 0.931655i | \(0.381635\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.2654 | − | 330.975i | −0.0189049 | − | 0.609531i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −438.342 | − | 759.230i | −0.801356 | − | 1.38799i | −0.918724 | − | 0.394900i | \(-0.870779\pi\) |
0.117368 | − | 0.993088i | \(-0.462554\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 580.798 | + | 875.730i | 1.05792 | + | 1.59514i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 633.097 | − | 365.519i | 1.14900 | − | 0.663374i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 87.0626 | − | 150.797i | 0.157437 | − | 0.272689i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 546.180i | − | 0.980575i | −0.871561 | − | 0.490287i | \(-0.836892\pi\) | ||
0.871561 | − | 0.490287i | \(-0.163108\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 504.066 | 0.901728 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −380.710 | + | 235.834i | −0.678628 | + | 0.420382i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −821.569 | − | 474.333i | −1.45927 | − | 0.842510i | −0.460294 | − | 0.887766i | \(-0.652256\pi\) |
−0.998975 | + | 0.0452567i | \(0.985589\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −359.035 | − | 474.627i | −0.633219 | − | 0.837085i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −101.288 | + | 58.4785i | −0.178010 | + | 0.102774i | −0.586357 | − | 0.810052i | \(-0.699439\pi\) |
0.408347 | + | 0.912827i | \(0.366105\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 71.9220 | − | 124.573i | 0.125958 | − | 0.218166i | −0.796149 | − | 0.605101i | \(-0.793133\pi\) |
0.922107 | + | 0.386935i | \(0.126466\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 53.0933 | + | 85.7092i | 0.0926584 | + | 0.149580i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 665.087 | 1.15266 | 0.576332 | − | 0.817216i | \(-0.304484\pi\) | ||||
0.576332 | + | 0.817216i | \(0.304484\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −715.507 | − | 384.030i | −1.23576 | − | 0.663264i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 27.1689 | + | 15.6860i | 0.0467624 | + | 0.0269983i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 436.192 | + | 755.507i | 0.748186 | + | 1.29590i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −193.390 | + | 111.654i | −0.329454 | + | 0.190210i | −0.655599 | − | 0.755109i | \(-0.727584\pi\) |
0.326145 | + | 0.945320i | \(0.394250\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 426.043 | − | 737.928i | 0.723332 | − | 1.25285i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 189.202 | − | 5.86822i | 0.320140 | − | 0.00992930i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 320.932i | 0.541200i | 0.962692 | + | 0.270600i | \(0.0872221\pi\) | ||||
−0.962692 | + | 0.270600i | \(0.912778\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −26.3225 | − | 848.687i | −0.0440913 | − | 1.42159i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 536.544 | + | 309.774i | 0.895732 | + | 0.517151i | 0.875813 | − | 0.482650i | \(-0.160326\pi\) |
0.0199193 | + | 0.999802i | \(0.493659\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 291.655 | + | 505.162i | 0.485283 | + | 0.840535i | 0.999857 | − | 0.0169108i | \(-0.00538313\pi\) |
−0.514574 | + | 0.857446i | \(0.672050\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −69.2790 | + | 139.274i | −0.114890 | + | 0.230969i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −74.8229 | + | 129.597i | −0.123267 | + | 0.213504i | −0.921054 | − | 0.389435i | \(-0.872670\pi\) |
0.797787 | + | 0.602939i | \(0.206004\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 435.776 | − | 811.919i | 0.715560 | − | 1.33320i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 702.895i | − | 1.15040i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 775.281 | 1.26473 | 0.632367 | − | 0.774669i | \(-0.282084\pi\) | ||||
0.632367 | + | 0.774669i | \(0.282084\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1035.34 | + | 597.754i | 1.67802 | + | 0.968807i | 0.962920 | + | 0.269787i | \(0.0869534\pi\) |
0.715103 | + | 0.699019i | \(0.246380\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −417.536 | − | 723.194i | −0.674533 | − | 1.16833i | −0.976605 | − | 0.215041i | \(-0.931011\pi\) |
0.302072 | − | 0.953285i | \(-0.402322\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 119.255 | − | 259.631i | 0.192037 | − | 0.418086i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −922.838 | + | 532.801i | −1.48128 | + | 0.855218i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −266.502 | − | 430.217i | −0.425043 | − | 0.686152i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 316.901i | 0.503817i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 378.090 | 0.599191 | 0.299596 | − | 0.954066i | \(-0.403148\pi\) | ||||
0.299596 | + | 0.954066i | \(0.403148\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −300.976 | − | 161.541i | −0.475475 | − | 0.255199i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −41.5666 | − | 71.9955i | −0.0652538 | − | 0.113023i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 21.4654 | + | 345.710i | 0.0335922 | + | 0.541017i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 70.5646 | − | 40.7405i | 0.110085 | − | 0.0635577i | −0.443947 | − | 0.896053i | \(-0.646422\pi\) |
0.554032 | + | 0.832496i | \(0.313089\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 424.883 | − | 735.919i | 0.660783 | − | 1.14451i | −0.319628 | − | 0.947543i | \(-0.603558\pi\) |
0.980410 | − | 0.196966i | \(-0.0631088\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 569.387i | 0.880042i | 0.897988 | + | 0.440021i | \(0.145029\pi\) | ||||
−0.897988 | + | 0.440021i | \(0.854971\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −534.793 | −0.824027 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −33.2964 | − | 1073.54i | −0.0511465 | − | 1.64906i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 814.403 | + | 470.196i | 1.24717 | + | 0.720055i | 0.970544 | − | 0.240922i | \(-0.0774499\pi\) |
0.276627 | + | 0.960977i | \(0.410783\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −66.3655 | + | 4.12069i | −0.101013 | + | 0.00627198i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1094.20 | + | 631.738i | −1.66040 | + | 0.958631i | −0.687873 | + | 0.725831i | \(0.741456\pi\) |
−0.972525 | + | 0.232800i | \(0.925211\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −65.8107 | + | 113.987i | −0.0995623 | + | 0.172447i | −0.911504 | − | 0.411292i | \(-0.865078\pi\) |
0.811941 | + | 0.583739i | \(0.198411\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −366.320 | + | 682.512i | −0.552520 | + | 1.02943i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 442.382 | 0.663242 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 555.609 | − | 344.176i | 0.830506 | − | 0.514464i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 975.453 | + | 563.178i | 1.45373 | + | 0.839311i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 119.398 | + | 206.803i | 0.177411 | + | 0.307285i | 0.940993 | − | 0.338426i | \(-0.109894\pi\) |
−0.763582 | + | 0.645711i | \(0.776561\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 304.426 | − | 175.760i | 0.449669 | − | 0.259617i | −0.258021 | − | 0.966139i | \(-0.583070\pi\) |
0.707691 | + | 0.706523i | \(0.249737\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 377.280 | − | 653.469i | 0.555641 | − | 0.962399i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 83.6039 | + | 134.963i | 0.122766 | + | 0.198183i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1067.52i | 1.56299i | 0.623911 | + | 0.781495i | \(0.285543\pi\) | ||||
−0.623911 | + | 0.781495i | \(0.714457\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1034.39 | + | 555.182i | 1.50566 | + | 0.808125i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1306.77 | + | 754.464i | 1.89662 | + | 1.09501i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −231.293 | − | 400.611i | −0.334722 | − | 0.579755i | 0.648709 | − | 0.761036i | \(-0.275309\pi\) |
−0.983431 | + | 0.181281i | \(0.941976\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −571.147 | − | 284.104i | −0.824166 | − | 0.409963i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 215.882 | − | 373.919i | 0.309731 | − | 0.536470i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 534.894 | − | 16.5900i | 0.765228 | − | 0.0237340i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 519.309i | − | 0.740812i | −0.928870 | − | 0.370406i | \(-0.879219\pi\) | ||
0.928870 | − | 0.370406i | \(-0.120781\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −358.110 | −0.509403 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −705.398 | − | 407.262i | −0.997734 | − | 0.576042i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −312.572 | − | 541.391i | −0.440863 | − | 0.763598i | 0.556890 | − | 0.830586i | \(-0.311994\pi\) |
−0.997754 | + | 0.0669881i | \(0.978661\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −117.889 | − | 177.754i | −0.165808 | − | 0.250006i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 446.552 | − | 257.817i | 0.626300 | − | 0.361594i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −515.221 | + | 959.938i | −0.718579 | + | 1.33883i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1385.24i | − | 1.92662i | −0.268400 | − | 0.963308i | \(-0.586495\pi\) | ||
0.268400 | − | 0.963308i | \(-0.413505\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1380.18 | 1.91425 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 460.701 | − | 285.385i | 0.637207 | − | 0.394723i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 679.246 | + | 1176.49i | 0.934314 | + | 1.61828i | 0.775853 | + | 0.630914i | \(0.217320\pi\) |
0.158461 | + | 0.987365i | \(0.449347\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −716.422 | + | 134.838i | −0.982746 | + | 0.184962i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −404.836 | + | 233.732i | −0.553811 | + | 0.319743i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 463.215 | − | 802.313i | 0.631945 | − | 1.09456i | −0.355209 | − | 0.934787i | \(-0.615590\pi\) |
0.987154 | − | 0.159773i | \(-0.0510764\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 166.735i | 0.226235i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 693.908 | 0.938983 | 0.469491 | − | 0.882937i | \(-0.344437\pi\) | ||||
0.469491 | + | 0.882937i | \(0.344437\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −771.266 | − | 413.957i | −1.04084 | − | 0.558646i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −86.9306 | − | 50.1894i | −0.116999 | − | 0.0675497i | 0.440358 | − | 0.897822i | \(-0.354851\pi\) |
−0.557358 | + | 0.830272i | \(0.688185\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 32.0258 | − | 21.2400i | 0.0428725 | − | 0.0284337i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −774.794 | + | 447.328i | −1.03444 | + | 0.597233i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.35903 | + | 4.08596i | −0.00314118 | + | 0.00544069i | −0.867592 | − | 0.497277i | \(-0.834333\pi\) |
0.864451 | + | 0.502718i | \(0.167667\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 220.547 | − | 6.84038i | 0.292891 | − | 0.00908417i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 133.356 | 0.176163 | 0.0880816 | − | 0.996113i | \(-0.471926\pi\) | ||||
0.0880816 | + | 0.996113i | \(0.471926\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.49384 | − | 306.100i | −0.0125084 | − | 0.403293i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −190.293 | − | 109.866i | −0.250057 | − | 0.144371i | 0.369733 | − | 0.929138i | \(-0.379449\pi\) |
−0.619790 | + | 0.784767i | \(0.712782\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −166.544 | − | 288.463i | −0.218276 | − | 0.378064i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −801.083 | + | 462.505i | −1.04444 | + | 0.603006i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −319.416 | + | 553.246i | −0.415366 | + | 0.719435i | −0.995467 | − | 0.0951097i | \(-0.969680\pi\) |
0.580101 | + | 0.814545i | \(0.303013\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 205.648 | − | 383.155i | 0.266729 | − | 0.496958i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1244.36i | 1.60978i | 0.593426 | + | 0.804888i | \(0.297775\pi\) | ||||
−0.593426 | + | 0.804888i | \(0.702225\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −383.738 | + | 237.710i | −0.493871 | + | 0.305933i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 422.544 | + | 243.956i | 0.542418 | + | 0.313165i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 185.636 | + | 321.532i | 0.237691 | + | 0.411692i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −652.734 | − | 920.884i | −0.833632 | − | 1.17610i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −569.367 | + | 986.173i | −0.723466 | + | 1.25308i | 0.236137 | + | 0.971720i | \(0.424119\pi\) |
−0.959602 | + | 0.281359i | \(0.909215\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 519.543 | + | 838.705i | 0.658483 | + | 1.06300i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 141.135i | − | 0.178426i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1948.21 | 2.45676 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1182.74 | + | 682.858i | 1.48400 | + | 0.856785i | 0.999834 | − | 0.0181932i | \(-0.00579141\pi\) |
0.484161 | + | 0.874979i | \(0.339125\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 325.927 | + | 564.523i | 0.407919 | + | 0.706537i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 80.8916 | + | 1302.80i | 0.100988 | + | 1.62646i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −61.7241 | + | 35.6364i | −0.0768669 | + | 0.0443791i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1066.98 | − | 33.0931i | 1.32216 | − | 0.0410075i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 504.881i | 0.624080i | 0.950069 | + | 0.312040i | \(0.101012\pi\) | ||||
−0.950069 | + | 0.312040i | \(0.898988\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1484.09 | −1.82995 | −0.914974 | − | 0.403514i | \(-0.867789\pi\) | ||||
−0.914974 | + | 0.403514i | \(0.867789\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.9363 | − | 384.851i | −0.0146819 | − | 0.473371i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −264.126 | − | 457.480i | −0.323288 | − | 0.559951i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1101.24 | + | 68.3769i | −1.34461 | + | 0.0834882i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 343.313 | − | 198.212i | 0.418165 | − | 0.241428i | −0.276127 | − | 0.961121i | \(-0.589051\pi\) |
0.694292 | + | 0.719694i | \(0.255718\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −355.569 | + | 615.863i | −0.432040 | + | 0.748315i | −0.997049 | − | 0.0767697i | \(-0.975539\pi\) |
0.565009 | + | 0.825085i | \(0.308873\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 296.720i | 0.358791i | 0.983777 | + | 0.179396i | \(0.0574142\pi\) | ||||
−0.983777 | + | 0.179396i | \(0.942586\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −252.785 | −0.304928 | −0.152464 | − | 0.988309i | \(-0.548721\pi\) | ||||
−0.152464 | + | 0.988309i | \(0.548721\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 690.001 | − | 427.427i | 0.830326 | − | 0.514352i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 66.7677 | + | 38.5483i | 0.0801533 | + | 0.0462765i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1195.57 | − | 549.156i | −1.42840 | − | 0.656100i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 252.022 | − | 145.505i | 0.300384 | − | 0.173427i | −0.342231 | − | 0.939616i | \(-0.611183\pi\) |
0.642615 | + | 0.766189i | \(0.277849\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 453.361 | − | 785.244i | 0.539074 | − | 0.933703i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −829.592 | − | 1339.22i | −0.984095 | − | 1.58864i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 205.260 | 0.242338 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −554.032 | − | 297.362i | −0.652570 | − | 0.350250i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −187.675 | − | 108.354i | −0.220534 | − | 0.127326i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.8099 | − | 37.7759i | −0.0255685 | − | 0.0442859i | 0.852958 | − | 0.521980i | \(-0.174806\pi\) |
−0.878527 | + | 0.477694i | \(0.841473\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −297.359 | + | 171.680i | −0.346977 | + | 0.200327i | −0.663353 | − | 0.748307i | \(-0.730867\pi\) |
0.316376 | + | 0.948634i | \(0.397534\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.74411 | − | 13.4132i | 0.00901526 | − | 0.0156149i | −0.861483 | − | 0.507787i | \(-0.830464\pi\) |
0.870498 | + | 0.492172i | \(0.163797\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 614.717 | − | 19.0658i | 0.713957 | − | 0.0221438i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 880.604i | − | 1.02040i | −0.860056 | − | 0.510199i | \(-0.829572\pi\) | ||
0.860056 | − | 0.510199i | \(-0.170428\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.60798 | + | 148.570i | 0.00531486 | + | 0.171361i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −197.996 | − | 114.313i | −0.227843 | − | 0.131545i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 144.197 | + | 249.757i | 0.165554 | + | 0.286748i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −510.866 | − | 770.286i | −0.585184 | − | 0.882343i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 621.717 | − | 1076.84i | 0.708913 | − | 1.22787i | −0.256348 | − | 0.966585i | \(-0.582519\pi\) |
0.965261 | − | 0.261289i | \(-0.0841475\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 169.874 | − | 316.501i | 0.193258 | − | 0.360069i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1006.63i | 1.14260i | 0.820742 | + | 0.571299i | \(0.193560\pi\) | ||||
−0.820742 | + | 0.571299i | \(0.806440\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 765.263 | 0.866662 | 0.433331 | − | 0.901235i | \(-0.357338\pi\) | ||||
0.433331 | + | 0.901235i | \(0.357338\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 586.263 | + | 338.479i | 0.660951 | + | 0.381600i | 0.792639 | − | 0.609691i | \(-0.208706\pi\) |
−0.131688 | + | 0.991291i | \(0.542040\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 658.475 | + | 1140.51i | 0.740692 | + | 1.28292i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −623.183 | + | 471.412i | −0.699420 | + | 0.529082i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −637.933 | + | 368.311i | −0.714371 | + | 0.412442i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −278.945 | − | 450.305i | −0.310976 | − | 0.502012i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 2037.12i | − | 2.26598i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1399.36 | −1.55312 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −586.698 | − | 314.895i | −0.649721 | − | 0.348721i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.7176 | − | 20.2956i | −0.0129191 | − | 0.0223766i | 0.859494 | − | 0.511147i | \(-0.170779\pi\) |
−0.872413 | + | 0.488770i | \(0.837446\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −831.498 | + | 551.463i | −0.914739 | + | 0.606670i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1085.84 | + | 626.910i | −1.19192 | + | 0.688156i | −0.958742 | − | 0.284278i | \(-0.908246\pi\) |
−0.233179 | + | 0.972434i | \(0.574913\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.5956 | − | 35.6727i | 0.0225582 | − | 0.0390719i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 624.464i | 0.680986i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1113.99 | −1.21217 | −0.606087 | − | 0.795398i | \(-0.707262\pi\) | ||||
−0.606087 | + | 0.795398i | \(0.707262\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 40.5242 | + | 1306.58i | 0.0440002 | + | 1.41865i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 556.140 | + | 321.088i | 0.602536 | + | 0.347874i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 752.961 | − | 1513.71i | 0.812256 | − | 1.63291i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 550.765 | − | 317.984i | 0.592858 | − | 0.342286i | −0.173369 | − | 0.984857i | \(-0.555465\pi\) |
0.766227 | + | 0.642570i | \(0.222132\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −43.5611 | + | 75.4501i | −0.0467896 | + | 0.0810420i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −97.0563 | + | 180.831i | −0.104026 | + | 0.193817i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 81.1236 | 0.0865780 | 0.0432890 | − | 0.999063i | \(-0.486216\pi\) | ||||
0.0432890 | + | 0.999063i | \(0.486216\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 112.054 | − | 69.4127i | 0.119333 | − | 0.0739219i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −292.823 | − | 169.061i | −0.311183 | − | 0.179661i | 0.336273 | − | 0.941765i | \(-0.390834\pi\) |
−0.647456 | + | 0.762103i | \(0.724167\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 147.628 | + | 255.699i | 0.156552 | + | 0.271155i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 337.557 | − | 194.889i | 0.356449 | − | 0.205796i | −0.311073 | − | 0.950386i | \(-0.600688\pi\) |
0.667522 | + | 0.744590i | \(0.267355\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −61.6389 | + | 106.762i | −0.0649514 | + | 0.112499i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 422.655 | + | 682.297i | 0.444432 | + | 0.717452i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1439.63i | 1.51063i | 0.655363 | + | 0.755314i | \(0.272516\pi\) | ||||
−0.655363 | + | 0.755314i | \(0.727484\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1066.05 | − | 572.172i | −1.11395 | − | 0.597881i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −420.423 | − | 242.731i | −0.438397 | − | 0.253109i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −706.715 | − | 1224.07i | −0.735395 | − | 1.27374i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 67.9148 | + | 1093.80i | 0.0705242 | + | 1.13582i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 332.808 | − | 576.441i | 0.344166 | − | 0.596113i | −0.641036 | − | 0.767511i | \(-0.721495\pi\) |
0.985202 | + | 0.171398i | \(0.0548284\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 811.383 | − | 25.1655i | 0.837341 | − | 0.0259706i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 437.415i | 0.450479i | 0.974303 | + | 0.225239i | \(0.0723164\pi\) | ||||
−0.974303 | + | 0.225239i | \(0.927684\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 69.2142 | 0.0711349 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1070.94 | − | 618.306i | −1.09615 | − | 0.632862i | −0.160942 | − | 0.986964i | \(-0.551453\pi\) |
−0.935207 | + | 0.354102i | \(0.884786\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 699.565 | + | 1211.68i | 0.714571 | + | 1.23767i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −407.231 | + | 25.2853i | −0.415118 | + | 0.0257750i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1102.74 | + | 636.669i | −1.12181 | + | 0.647680i | −0.941864 | − | 0.335996i | \(-0.890927\pi\) |
−0.179951 | + | 0.983676i | \(0.557594\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −439.105 | + | 818.121i | −0.444889 | + | 0.828897i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 319.668i | − | 0.323224i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 443.540 | 0.447568 | 0.223784 | − | 0.974639i | \(-0.428159\pi\) | ||||
0.223784 | + | 0.974639i | \(0.428159\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 183.937 | − | 113.942i | 0.185234 | − | 0.114745i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −278.990 | − | 483.225i | −0.279830 | − | 0.484679i | 0.691513 | − | 0.722364i | \(-0.256945\pi\) |
−0.971342 | + | 0.237685i | \(0.923611\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 51.3585 | + | 550.549i | 0.0514099 | + | 0.551100i |
(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 | 900.3.p.f.401.7 | 24 | ||
3.2 | odd | 2 | 2700.3.p.f.2501.3 | 24 | |||
5.2 | odd | 4 | 180.3.t.a.149.12 | yes | 24 | ||
5.3 | odd | 4 | 180.3.t.a.149.1 | yes | 24 | ||
5.4 | even | 2 | inner | 900.3.p.f.401.6 | 24 | ||
9.2 | odd | 6 | inner | 900.3.p.f.101.7 | 24 | ||
9.7 | even | 3 | 2700.3.p.f.1601.3 | 24 | |||
15.2 | even | 4 | 540.3.t.a.449.7 | 24 | |||
15.8 | even | 4 | 540.3.t.a.449.3 | 24 | |||
15.14 | odd | 2 | 2700.3.p.f.2501.10 | 24 | |||
45.2 | even | 12 | 180.3.t.a.29.1 | ✓ | 24 | ||
45.7 | odd | 12 | 540.3.t.a.89.3 | 24 | |||
45.13 | odd | 12 | 1620.3.b.b.809.1 | 24 | |||
45.22 | odd | 12 | 1620.3.b.b.809.23 | 24 | |||
45.23 | even | 12 | 1620.3.b.b.809.24 | 24 | |||
45.29 | odd | 6 | inner | 900.3.p.f.101.6 | 24 | ||
45.32 | even | 12 | 1620.3.b.b.809.2 | 24 | |||
45.34 | even | 6 | 2700.3.p.f.1601.10 | 24 | |||
45.38 | even | 12 | 180.3.t.a.29.12 | yes | 24 | ||
45.43 | odd | 12 | 540.3.t.a.89.7 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.3.t.a.29.1 | ✓ | 24 | 45.2 | even | 12 | ||
180.3.t.a.29.12 | yes | 24 | 45.38 | even | 12 | ||
180.3.t.a.149.1 | yes | 24 | 5.3 | odd | 4 | ||
180.3.t.a.149.12 | yes | 24 | 5.2 | odd | 4 | ||
540.3.t.a.89.3 | 24 | 45.7 | odd | 12 | |||
540.3.t.a.89.7 | 24 | 45.43 | odd | 12 | |||
540.3.t.a.449.3 | 24 | 15.8 | even | 4 | |||
540.3.t.a.449.7 | 24 | 15.2 | even | 4 | |||
900.3.p.f.101.6 | 24 | 45.29 | odd | 6 | inner | ||
900.3.p.f.101.7 | 24 | 9.2 | odd | 6 | inner | ||
900.3.p.f.401.6 | 24 | 5.4 | even | 2 | inner | ||
900.3.p.f.401.7 | 24 | 1.1 | even | 1 | trivial | ||
1620.3.b.b.809.1 | 24 | 45.13 | odd | 12 | |||
1620.3.b.b.809.2 | 24 | 45.32 | even | 12 | |||
1620.3.b.b.809.23 | 24 | 45.22 | odd | 12 | |||
1620.3.b.b.809.24 | 24 | 45.23 | even | 12 | |||
2700.3.p.f.1601.3 | 24 | 9.7 | even | 3 | |||
2700.3.p.f.1601.10 | 24 | 45.34 | even | 6 | |||
2700.3.p.f.2501.3 | 24 | 3.2 | odd | 2 | |||
2700.3.p.f.2501.10 | 24 | 15.14 | odd | 2 |