Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(559,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.559");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.bm (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: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 912) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1855.1 | ||
Root | \(1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.1855 |
Dual form | 2736.2.bm.i.559.2 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) | \(1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | − | 1.73205i | −0.447214 | − | 0.774597i | 0.550990 | − | 0.834512i | \(-0.314250\pi\) |
−0.998203 | + | 0.0599153i | \(0.980917\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.09638i | − | 0.414391i | −0.978300 | − | 0.207196i | \(-0.933566\pi\) | ||
0.978300 | − | 0.207196i | \(-0.0664337\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 5.65685i | − | 1.70561i | −0.522233 | − | 0.852803i | \(-0.674901\pi\) | ||
0.522233 | − | 0.852803i | \(-0.325099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.949490 | − | 0.548188i | −0.263341 | − | 0.152040i | 0.362517 | − | 0.931977i | \(-0.381918\pi\) |
−0.625858 | + | 0.779937i | \(0.715251\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | − | 1.73205i | −0.242536 | − | 0.420084i | 0.718900 | − | 0.695113i | \(-0.244646\pi\) |
−0.961436 | + | 0.275029i | \(0.911312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.00000 | + | 1.73205i | −0.917663 | + | 0.397360i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.89898 | + | 2.82843i | 1.02151 | + | 0.589768i | 0.914540 | − | 0.404495i | \(-0.132553\pi\) |
0.106967 | + | 0.994263i | \(0.465886\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.89898 | − | 4.56048i | −1.46680 | − | 0.846859i | −0.467493 | − | 0.883997i | \(-0.654843\pi\) |
−0.999310 | + | 0.0371370i | \(0.988176\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.89898 | 0.341067 | 0.170533 | − | 0.985352i | \(-0.445451\pi\) | ||||
0.170533 | + | 0.985352i | \(0.445451\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.89898 | + | 1.09638i | −0.320986 | + | 0.185321i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.56048i | 0.749738i | 0.927078 | + | 0.374869i | \(0.122312\pi\) | ||||
−0.927078 | + | 0.374869i | \(0.877688\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.50000 | + | 2.59808i | −0.686244 | + | 0.396203i | −0.802203 | − | 0.597051i | \(-0.796339\pi\) |
0.115960 | + | 0.993254i | \(0.463006\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.89898 | − | 1.09638i | −0.276995 | − | 0.159923i | 0.355067 | − | 0.934841i | \(-0.384458\pi\) |
−0.632062 | + | 0.774918i | \(0.717791\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.79796 | 0.828280 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.10102 | − | 0.635674i | −0.151237 | − | 0.0873166i | 0.422472 | − | 0.906376i | \(-0.361163\pi\) |
−0.573709 | + | 0.819059i | \(0.694496\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.79796 | + | 5.65685i | −1.32116 | + | 0.762770i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.89898 | + | 6.75323i | 0.507604 | + | 0.879196i | 0.999961 | + | 0.00880259i | \(0.00280199\pi\) |
−0.492357 | + | 0.870393i | \(0.663865\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.0505103 | − | 0.0874863i | 0.00646718 | − | 0.0112015i | −0.862774 | − | 0.505590i | \(-0.831275\pi\) |
0.869241 | + | 0.494389i | \(0.164608\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.19275i | 0.271977i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.39898 | + | 9.35131i | −0.659590 | + | 1.14244i | 0.321131 | + | 0.947035i | \(0.395937\pi\) |
−0.980722 | + | 0.195409i | \(0.937396\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.00000 | + | 3.46410i | 0.237356 | + | 0.411113i | 0.959955 | − | 0.280155i | \(-0.0903858\pi\) |
−0.722599 | + | 0.691268i | \(0.757052\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.39898 | − | 11.0834i | −0.748944 | − | 1.29721i | −0.948329 | − | 0.317288i | \(-0.897228\pi\) |
0.199385 | − | 0.979921i | \(-0.436105\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.20204 | −0.706788 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.94949 | + | 8.57277i | 0.556861 | + | 0.964512i | 0.997756 | + | 0.0669530i | \(0.0213278\pi\) |
−0.440895 | + | 0.897559i | \(0.645339\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 3.46410i | − | 0.380235i | −0.981761 | − | 0.190117i | \(-0.939113\pi\) | ||
0.981761 | − | 0.190117i | \(-0.0608868\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.00000 | + | 3.46410i | −0.216930 | + | 0.375735i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.89898 | − | 4.56048i | −0.837290 | − | 0.483410i | 0.0190520 | − | 0.999818i | \(-0.493935\pi\) |
−0.856342 | + | 0.516409i | \(0.827269\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.601021 | + | 1.04100i | −0.0630041 | + | 0.109126i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.00000 | + | 5.19615i | 0.718185 | + | 0.533114i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.7980 | + | 9.12096i | −1.60404 | + | 0.926093i | −0.613372 | + | 0.789794i | \(0.710187\pi\) |
−0.990668 | + | 0.136299i | \(0.956479\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | + | 10.3923i | −0.597022 | + | 1.03407i | 0.396236 | + | 0.918149i | \(0.370316\pi\) |
−0.993258 | + | 0.115924i | \(0.963017\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.8990 | 1.17244 | 0.586221 | − | 0.810151i | \(-0.300615\pi\) | ||||
0.586221 | + | 0.810151i | \(0.300615\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.00000 | −0.773389 | −0.386695 | − | 0.922208i | \(-0.626383\pi\) | ||||
−0.386695 | + | 0.922208i | \(0.626383\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.6969 | − | 8.48528i | 1.40771 | − | 0.812743i | 0.412544 | − | 0.910938i | \(-0.364640\pi\) |
0.995167 | + | 0.0981950i | \(0.0313069\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 16.0492i | − | 1.50978i | −0.655853 | − | 0.754889i | \(-0.727691\pi\) | ||
0.655853 | − | 0.754889i | \(-0.272309\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 11.3137i | − | 1.05501i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.89898 | + | 1.09638i | −0.174079 | + | 0.100505i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −21.0000 | −1.90909 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.89898 | − | 11.9494i | 0.612185 | − | 1.06034i | −0.378686 | − | 0.925525i | \(-0.623624\pi\) |
0.990871 | − | 0.134811i | \(-0.0430427\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.0000 | + | 6.92820i | −1.04844 | + | 0.605320i | −0.922214 | − | 0.386681i | \(-0.873621\pi\) |
−0.126231 | + | 0.992001i | \(0.540288\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.89898 | + | 4.38551i | 0.164662 | + | 0.380272i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.00000 | + | 10.3923i | −0.512615 | + | 0.887875i | 0.487278 | + | 0.873247i | \(0.337990\pi\) |
−0.999893 | + | 0.0146279i | \(0.995344\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.39898 | + | 3.69445i | 0.542754 | + | 0.313359i | 0.746194 | − | 0.665728i | \(-0.231879\pi\) |
−0.203440 | + | 0.979087i | \(0.565212\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.10102 | + | 5.37113i | −0.259320 | + | 0.449156i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.2419i | 1.51491i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.89898 | − | 5.02118i | −0.237494 | − | 0.411351i | 0.722501 | − | 0.691370i | \(-0.242993\pi\) |
−0.959994 | + | 0.280019i | \(0.909659\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.20204 | 0.179200 | 0.0895998 | − | 0.995978i | \(-0.471441\pi\) | ||||
0.0895998 | + | 0.995978i | \(0.471441\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.89898 | − | 3.28913i | −0.152530 | − | 0.264189i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.84847 | − | 11.8619i | −0.546567 | − | 0.946682i | −0.998506 | − | 0.0546336i | \(-0.982601\pi\) |
0.451939 | − | 0.892049i | \(-0.350732\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.10102 | − | 5.37113i | 0.244395 | − | 0.423304i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 15.5885i | − | 1.22098i | −0.792023 | − | 0.610491i | \(-0.790972\pi\) | ||
0.792023 | − | 0.610491i | \(-0.209028\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.00000 | + | 5.19615i | −0.232147 | + | 0.402090i | −0.958440 | − | 0.285295i | \(-0.907908\pi\) |
0.726293 | + | 0.687386i | \(0.241242\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.89898 | − | 10.2173i | −0.453768 | − | 0.785949i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.89898 | + | 4.56048i | −0.600548 | + | 0.346727i | −0.769257 | − | 0.638939i | \(-0.779374\pi\) |
0.168709 | + | 0.985666i | \(0.446040\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.949490 | − | 0.548188i | −0.0717747 | − | 0.0414391i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.20204 | −0.463562 | −0.231781 | − | 0.972768i | \(-0.574455\pi\) | ||||
−0.231781 | + | 0.972768i | \(0.574455\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.6969 | − | 8.48528i | −1.09241 | − | 0.630706i | −0.158196 | − | 0.987408i | \(-0.550568\pi\) |
−0.934218 | + | 0.356702i | \(0.883901\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.89898 | − | 4.56048i | 0.580745 | − | 0.335293i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.79796 | + | 5.65685i | −0.716498 | + | 0.413670i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.2487i | 1.75458i | 0.479965 | + | 0.877288i | \(0.340649\pi\) | ||||
−0.479965 | + | 0.877288i | \(0.659351\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.5000 | + | 6.06218i | −0.755807 | + | 0.436365i | −0.827788 | − | 0.561041i | \(-0.810401\pi\) |
0.0719816 | + | 0.997406i | \(0.477068\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.9495 | + | 9.20844i | 1.13063 | + | 0.652769i | 0.944093 | − | 0.329679i | \(-0.106940\pi\) |
0.186536 | + | 0.982448i | \(0.440274\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.00000 | + | 8.66025i | −0.350931 | + | 0.607831i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.79796 | + | 22.6274i | 0.677739 | + | 1.56517i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.601021 | − | 1.04100i | −0.0413760 | − | 0.0716653i | 0.844596 | − | 0.535404i | \(-0.179841\pi\) |
−0.885972 | + | 0.463739i | \(0.846507\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.00000 | + | 5.19615i | 0.613795 | + | 0.354375i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 2.08200i | − | 0.141335i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.19275i | 0.147501i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.94949 | − | 3.37662i | −0.130547 | − | 0.226115i | 0.793340 | − | 0.608778i | \(-0.208340\pi\) |
−0.923888 | + | 0.382664i | \(0.875007\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.79796 | 0.252079 | 0.126040 | − | 0.992025i | \(-0.459773\pi\) | ||||
0.126040 | + | 0.992025i | \(0.459773\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.6969 | 1.43377 | 0.716887 | − | 0.697189i | \(-0.245566\pi\) | ||||
0.716887 | + | 0.697189i | \(0.245566\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.79796 | − | 16.9706i | −0.641886 | − | 1.11178i | −0.985011 | − | 0.172489i | \(-0.944819\pi\) |
0.343126 | − | 0.939289i | \(-0.388514\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.38551i | 0.286079i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.921404i | 0.0596006i | 0.999556 | + | 0.0298003i | \(0.00948714\pi\) | ||||
−0.999556 | + | 0.0298003i | \(0.990513\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.29796 | + | 3.05878i | 0.341272 | + | 0.197033i | 0.660834 | − | 0.750532i | \(-0.270203\pi\) |
−0.319563 | + | 0.947565i | \(0.603536\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.79796 | − | 10.0424i | −0.370418 | − | 0.641583i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.74745 | + | 0.548188i | 0.302073 | + | 0.0348804i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.7980 | − | 10.8530i | −1.18652 | − | 0.685036i | −0.229004 | − | 0.973426i | \(-0.573547\pi\) |
−0.957513 | + | 0.288390i | \(0.906880\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.0000 | − | 27.7128i | 1.00591 | − | 1.74229i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.10102 | + | 0.635674i | 0.0686798 | + | 0.0396523i | 0.533947 | − | 0.845518i | \(-0.320708\pi\) |
−0.465267 | + | 0.885170i | \(0.654042\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.00000 | 0.310685 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.79796 | + | 2.19275i | −0.234192 | + | 0.135211i | −0.612505 | − | 0.790467i | \(-0.709838\pi\) |
0.378312 | + | 0.925678i | \(0.376505\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.54270i | 0.156197i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.797959 | − | 0.460702i | 0.0486524 | − | 0.0280895i | −0.475476 | − | 0.879728i | \(-0.657724\pi\) |
0.524129 | + | 0.851639i | \(0.324391\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.7980 | + | 7.38891i | −0.777421 | + | 0.448844i | −0.835515 | − | 0.549467i | \(-0.814831\pi\) |
0.0580947 | + | 0.998311i | \(0.481497\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.89898 | − | 2.82843i | −0.295420 | − | 0.170561i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.00000 | 0.120168 | 0.0600842 | − | 0.998193i | \(-0.480863\pi\) | ||||
0.0600842 | + | 0.998193i | \(0.480863\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.1010 | + | 9.29593i | 0.960506 | + | 0.554549i | 0.896329 | − | 0.443390i | \(-0.146224\pi\) |
0.0641775 | + | 0.997938i | \(0.479558\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.7980 | − | 7.38891i | 0.760760 | − | 0.439225i | −0.0688087 | − | 0.997630i | \(-0.521920\pi\) |
0.829568 | + | 0.558405i | \(0.188586\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | − | 11.2583i | 0.382353 | − | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.57826i | 0.384306i | 0.981365 | + | 0.192153i | \(0.0615470\pi\) | ||||
−0.981365 | + | 0.192153i | \(0.938453\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.79796 | − | 13.5065i | 0.454015 | − | 0.786377i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.10102 | − | 5.37113i | −0.179337 | − | 0.310620i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.84847 | + | 4.93369i | 0.164183 | + | 0.284373i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.202041 | −0.0115688 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.7980 | − | 27.3629i | −0.901637 | − | 1.56168i | −0.825369 | − | 0.564594i | \(-0.809033\pi\) |
−0.0762684 | − | 0.997087i | \(-0.524301\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 33.0197i | − | 1.87238i | −0.351499 | − | 0.936188i | \(-0.614328\pi\) | ||
0.351499 | − | 0.936188i | \(-0.385672\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.79796 | − | 15.2385i | 0.497290 | − | 0.861332i | −0.502705 | − | 0.864458i | \(-0.667662\pi\) |
0.999995 | + | 0.00312637i | \(0.000995155\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.7980 | + | 7.38891i | 0.718805 | + | 0.415002i | 0.814313 | − | 0.580426i | \(-0.197114\pi\) |
−0.0955077 | + | 0.995429i | \(0.530447\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −25.7980 | + | 44.6834i | −1.44441 | + | 2.50179i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.00000 | + | 5.19615i | 0.389490 | + | 0.289122i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.949490 | + | 0.548188i | −0.0526682 | + | 0.0304080i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.20204 | + | 2.08200i | −0.0662707 | + | 0.114784i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.20204 | 0.0660702 | 0.0330351 | − | 0.999454i | \(-0.489483\pi\) | ||||
0.0330351 | + | 0.999454i | \(0.489483\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 21.5959 | 1.17991 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.1969 | + | 12.8154i | −1.20914 | + | 0.698100i | −0.962572 | − | 0.271025i | \(-0.912637\pi\) |
−0.246572 | + | 0.969125i | \(0.579304\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 10.7423i | − | 0.581725i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 14.0314i | − | 0.757623i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.89898 | + | 1.09638i | −0.101943 | + | 0.0588566i | −0.550105 | − | 0.835096i | \(-0.685412\pi\) |
0.448162 | + | 0.893952i | \(0.352079\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.6969 | −1.16141 | −0.580705 | − | 0.814114i | \(-0.697223\pi\) | ||||
−0.580705 | + | 0.814114i | \(0.697223\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.79796 | 0.202145 | 0.101072 | − | 0.994879i | \(-0.467773\pi\) | ||||
0.101072 | + | 0.994879i | \(0.467773\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.00000 | − | 6.92820i | 0.212298 | − | 0.367711i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.79796 | + | 5.65685i | −0.517116 | + | 0.298557i | −0.735754 | − | 0.677249i | \(-0.763172\pi\) |
0.218638 | + | 0.975806i | \(0.429839\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | − | 13.8564i | 0.684211 | − | 0.729285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.7980 | + | 22.1667i | −0.669876 | + | 1.16026i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.84847 | − | 3.37662i | −0.305288 | − | 0.176258i | 0.339528 | − | 0.940596i | \(-0.389733\pi\) |
−0.644816 | + | 0.764338i | \(0.723066\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.696938 | + | 1.20713i | −0.0361832 | + | 0.0626712i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 33.3697i | 1.72782i | 0.503650 | + | 0.863908i | \(0.331990\pi\) | ||||
−0.503650 | + | 0.863908i | \(0.668010\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.00000 | + | 8.66025i | 0.257513 | + | 0.446026i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.59592 | 0.338810 | 0.169405 | − | 0.985547i | \(-0.445815\pi\) | ||||
0.169405 | + | 0.985547i | \(0.445815\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.89898 | + | 11.9494i | 0.352521 | + | 0.610585i | 0.986691 | − | 0.162609i | \(-0.0519910\pi\) |
−0.634169 | + | 0.773194i | \(0.718658\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.20204 | + | 10.7423i | 0.316085 | + | 0.547476i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.6969 | − | 32.3840i | 0.947972 | − | 1.64194i | 0.198285 | − | 0.980144i | \(-0.436463\pi\) |
0.749688 | − | 0.661792i | \(-0.230204\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 11.3137i | − | 0.572159i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.89898 | − | 17.1455i | 0.498072 | − | 0.862686i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.05051 | + | 5.28364i | 0.153101 | + | 0.265178i | 0.932366 | − | 0.361516i | \(-0.117741\pi\) |
−0.779265 | + | 0.626694i | \(0.784407\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.10102 | − | 2.36773i | 0.204795 | − | 0.118239i | −0.394095 | − | 0.919070i | \(-0.628942\pi\) |
0.598890 | + | 0.800831i | \(0.295609\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.80306 | − | 1.04100i | −0.0898169 | − | 0.0518558i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25.7980 | 1.27876 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.00000 | − | 3.46410i | −0.296681 | − | 0.171289i | 0.344270 | − | 0.938871i | \(-0.388126\pi\) |
−0.640951 | + | 0.767582i | \(0.721460\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.40408 | − | 4.27475i | 0.364331 | − | 0.210347i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.00000 | + | 3.46410i | −0.294528 | + | 0.170046i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 35.2125i | − | 1.72024i | −0.510090 | − | 0.860121i | \(-0.670388\pi\) | ||
0.510090 | − | 0.860121i | \(-0.329612\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.89898 | − | 2.82843i | 0.238762 | − | 0.137849i | −0.375846 | − | 0.926682i | \(-0.622648\pi\) |
0.614607 | + | 0.788833i | \(0.289314\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.00000 | −0.0970143 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.0959179 | − | 0.0553782i | −0.00464179 | − | 0.00267994i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.89898 | + | 13.6814i | −0.380480 | + | 0.659011i | −0.991131 | − | 0.132889i | \(-0.957575\pi\) |
0.610651 | + | 0.791900i | \(0.290908\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.1969 | + | 5.88721i | 0.490034 | + | 0.282921i | 0.724588 | − | 0.689182i | \(-0.242030\pi\) |
−0.234555 | + | 0.972103i | \(0.575363\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −24.4949 | − | 2.82843i | −1.17175 | − | 0.135302i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.8485 | + | 18.7901i | 0.517769 | + | 0.896803i | 0.999787 | + | 0.0206411i | \(0.00657073\pi\) |
−0.482018 | + | 0.876161i | \(0.660096\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.7980 | + | 10.8530i | 0.893118 | + | 0.515642i | 0.874961 | − | 0.484193i | \(-0.160887\pi\) |
0.0181569 | + | 0.999835i | \(0.494220\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.2419i | 0.864750i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 28.6342i | − | 1.35133i | −0.737208 | − | 0.675666i | \(-0.763856\pi\) | ||
0.737208 | − | 0.675666i | \(-0.236144\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.40408 | 0.112705 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.7980 | 0.972887 | 0.486444 | − | 0.873712i | \(-0.338294\pi\) | ||||
0.486444 | + | 0.873712i | \(0.338294\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.7980 | − | 18.7026i | −0.502911 | − | 0.871068i | −0.999994 | − | 0.00336470i | \(-0.998929\pi\) |
0.497083 | − | 0.867703i | \(-0.334404\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 3.28913i | − | 0.152859i | −0.997075 | − | 0.0764294i | \(-0.975648\pi\) | ||
0.997075 | − | 0.0764294i | \(-0.0243520\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 16.3991i | − | 0.758860i | −0.925220 | − | 0.379430i | \(-0.876120\pi\) | ||
0.925220 | − | 0.379430i | \(-0.123880\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.2526 | + | 5.91931i | 0.473419 | + | 0.273328i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.6969 | + | 25.4558i | 0.675766 | + | 1.17046i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.500000 | + | 4.33013i | −0.0229416 | + | 0.198680i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.7980 | − | 12.5851i | −0.995974 | − | 0.575026i | −0.0889195 | − | 0.996039i | \(-0.528341\pi\) |
−0.907055 | + | 0.421013i | \(0.861675\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.50000 | − | 4.33013i | 0.113990 | − | 0.197437i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 31.5959 | + | 18.2419i | 1.43470 | + | 0.828323i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.79796 | 0.0814733 | 0.0407366 | − | 0.999170i | \(-0.487030\pi\) | ||||
0.0407366 | + | 0.999170i | \(0.487030\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.7980 | − | 12.5851i | 0.983728 | − | 0.567956i | 0.0803345 | − | 0.996768i | \(-0.474401\pi\) |
0.903394 | + | 0.428812i | \(0.141068\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.2419i | 0.821574i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.79796 | − | 2.19275i | 0.170362 | − | 0.0983584i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.80306 | − | 1.04100i | 0.0807161 | − | 0.0466015i | −0.459099 | − | 0.888385i | \(-0.651828\pi\) |
0.539815 | + | 0.841784i | \(0.318494\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.6969 | + | 13.6814i | 1.05659 | + | 0.610025i | 0.924488 | − | 0.381211i | \(-0.124493\pi\) |
0.132106 | + | 0.991236i | \(0.457826\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.0000 | 1.06799 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 31.8990 | + | 18.4169i | 1.41390 | + | 0.816314i | 0.995753 | − | 0.0920665i | \(-0.0293472\pi\) |
0.418145 | + | 0.908381i | \(0.362681\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.1515 | + | 7.01569i | −0.537552 | + | 0.310356i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.8990 | − | 20.6096i | −0.524332 | − | 0.908169i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.20204 | + | 10.7423i | −0.272765 | + | 0.472444i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.27135i | 0.0556988i | 0.999612 | + | 0.0278494i | \(0.00886589\pi\) | ||||
−0.999612 | + | 0.0278494i | \(0.991134\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.2980 | + | 23.0327i | −0.581479 | + | 1.00715i | 0.413825 | + | 0.910356i | \(0.364192\pi\) |
−0.995304 | + | 0.0967951i | \(0.969141\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.89898 | − | 3.28913i | −0.0827208 | − | 0.143277i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.50000 | + | 7.79423i | 0.195652 | + | 0.338880i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.00000 | + | 13.8564i | 0.345870 | + | 0.599065i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 32.7982i | − | 1.41272i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.0505 | − | 19.1400i | 0.475099 | − | 0.822895i | −0.524495 | − | 0.851414i | \(-0.675746\pi\) |
0.999593 | + | 0.0285189i | \(0.00907908\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −29.3939 | − | 16.9706i | −1.25910 | − | 0.726939i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.5000 | + | 33.7750i | −0.833760 | + | 1.44411i | 0.0612764 | + | 0.998121i | \(0.480483\pi\) |
−0.895036 | + | 0.445993i | \(0.852850\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 39.4949 | + | 4.56048i | 1.68254 | + | 0.194283i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.39898 | − | 5.42650i | 0.399685 | − | 0.230758i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.0000 | + | 20.7846i | −0.508456 | + | 0.880672i | 0.491496 | + | 0.870880i | \(0.336450\pi\) |
−0.999952 | + | 0.00979220i | \(0.996883\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.69694 | 0.240955 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −43.5959 | −1.83735 | −0.918674 | − | 0.395016i | \(-0.870739\pi\) | ||||
−0.918674 | + | 0.395016i | \(0.870739\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −27.7980 | + | 16.0492i | −1.16947 | + | 0.675193i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 2.54270i | − | 0.106595i | −0.998579 | − | 0.0532977i | \(-0.983027\pi\) | ||
0.998579 | − | 0.0532977i | \(-0.0169732\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.93160i | 0.415625i | 0.978169 | + | 0.207812i | \(0.0666343\pi\) | ||||
−0.978169 | + | 0.207812i | \(0.933366\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.89898 | − | 2.82843i | 0.204302 | − | 0.117954i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.40408 | −0.100083 | −0.0500416 | − | 0.998747i | \(-0.515935\pi\) | ||||
−0.0500416 | + | 0.998747i | \(0.515935\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.79796 | −0.157566 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.59592 | + | 6.22831i | −0.148928 | + | 0.257950i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.10102 | + | 2.36773i | −0.169267 | + | 0.0977265i | −0.582240 | − | 0.813017i | \(-0.697824\pi\) |
0.412973 | + | 0.910743i | \(0.364490\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.59592 | + | 3.28913i | −0.312984 | + | 0.135526i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.89898 | − | 3.28913i | 0.0779817 | − | 0.135068i | −0.824397 | − | 0.566012i | \(-0.808486\pi\) |
0.902379 | + | 0.430943i | \(0.141819\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.79796 | + | 2.19275i | 0.155701 | + | 0.0898941i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.8990 | − | 36.1981i | 0.853909 | − | 1.47901i | −0.0237442 | − | 0.999718i | \(-0.507559\pi\) |
0.877653 | − | 0.479296i | \(-0.159108\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.2521i | 1.11164i | 0.831304 | + | 0.555818i | \(0.187595\pi\) | ||||
−0.831304 | + | 0.555818i | \(0.812405\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21.0000 | + | 36.3731i | 0.853771 | + | 1.47878i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.1010 | 0.491165 | 0.245583 | − | 0.969376i | \(-0.421021\pi\) | ||||
0.245583 | + | 0.969376i | \(0.421021\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.20204 | + | 2.08200i | 0.0486294 | + | 0.0842285i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.7980 | + | 29.0949i | 0.678463 | + | 1.17513i | 0.975444 | + | 0.220249i | \(0.0706870\pi\) |
−0.296980 | + | 0.954884i | \(0.595980\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.89898 | + | 11.9494i | −0.277742 | + | 0.481064i | −0.970823 | − | 0.239796i | \(-0.922920\pi\) |
0.693081 | + | 0.720860i | \(0.256253\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 32.5590i | − | 1.30866i | −0.756210 | − | 0.654329i | \(-0.772951\pi\) | ||
0.756210 | − | 0.654329i | \(-0.227049\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.00000 | + | 8.66025i | −0.200321 | + | 0.346966i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | + | 16.4545i | 0.380000 | + | 0.658179i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.89898 | − | 4.56048i | 0.314953 | − | 0.181838i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.6464 | − | 21.1578i | −1.45887 | − | 0.842280i | −0.459915 | − | 0.887963i | \(-0.652120\pi\) |
−0.998956 | + | 0.0456831i | \(0.985454\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −27.5959 | −1.09511 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.50510 | − | 3.17837i | −0.218120 | − | 0.125932i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.2020 | − | 6.46750i | 0.442454 | − | 0.255451i | −0.262184 | − | 0.965018i | \(-0.584443\pi\) |
0.704638 | + | 0.709567i | \(0.251109\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.0959 | − | 8.71563i | 0.595325 | − | 0.343711i | −0.171875 | − | 0.985119i | \(-0.554983\pi\) |
0.767200 | + | 0.641408i | \(0.221649\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 39.3765i | 1.54805i | 0.633156 | + | 0.774024i | \(0.281759\pi\) | ||||
−0.633156 | + | 0.774024i | \(0.718241\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 38.2020 | − | 22.0560i | 1.49956 | − | 0.865772i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 43.5959 | 1.70604 | 0.853020 | − | 0.521878i | \(-0.174768\pi\) | ||||
0.853020 | + | 0.521878i | \(0.174768\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.0000 | + | 13.8564i | 0.937758 | + | 0.541415i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.6969 | − | 32.3840i | 0.728329 | − | 1.26150i | −0.229260 | − | 0.973365i | \(-0.573630\pi\) |
0.957589 | − | 0.288138i | \(-0.0930362\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −42.4949 | − | 24.5344i | −1.65286 | − | 0.954279i | −0.975888 | − | 0.218270i | \(-0.929959\pi\) |
−0.676972 | − | 0.736009i | \(-0.736708\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.69694 | − | 7.67463i | 0.220918 | − | 0.297610i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25.7980 | − | 44.6834i | −0.998901 | − | 1.73015i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.494897 | − | 0.285729i | −0.0191053 | − | 0.0110305i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 41.3300i | − | 1.59316i | −0.604536 | − | 0.796578i | \(-0.706641\pi\) | ||
0.604536 | − | 0.796578i | \(-0.293359\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 36.8338i | − | 1.41564i | −0.706394 | − | 0.707818i | \(-0.749680\pi\) | ||
0.706394 | − | 0.707818i | \(-0.250320\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.0000 | + | 17.3205i | 0.383765 | + | 0.664700i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.7980 | 1.36977 | 0.684885 | − | 0.728651i | \(-0.259852\pi\) | ||||
0.684885 | + | 0.728651i | \(0.259852\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.0000 | 0.916993 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.696938 | + | 1.20713i | 0.0265512 | + | 0.0459881i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 24.2487i | − | 0.922464i | −0.887279 | − | 0.461232i | \(-0.847408\pi\) | ||
0.887279 | − | 0.461232i | \(-0.152592\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 14.7778i | − | 0.560554i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.0000 | + | 36.3731i | 0.793159 | + | 1.37379i | 0.924002 | + | 0.382389i | \(0.124898\pi\) |
−0.130843 | + | 0.991403i | \(0.541768\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.89898 | − | 18.2419i | −0.297916 | − | 0.688007i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.3939 | + | 6.57826i | 0.428511 | + | 0.247401i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.8485 | − | 32.6465i | 0.707869 | − | 1.22607i | −0.257777 | − | 0.966204i | \(-0.582990\pi\) |
0.965646 | − | 0.259861i | \(-0.0836767\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.30306 | + | 5.37113i | 0.348402 | + | 0.201150i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.4041 | 0.463886 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.1010 | + | 7.56388i | −0.488586 | + | 0.282085i | −0.723988 | − | 0.689813i | \(-0.757693\pi\) |
0.235402 | + | 0.971898i | \(0.424359\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 13.0458i | − | 0.485849i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.89898 | + | 4.56048i | −0.293361 | + | 0.169372i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.3434 | − | 24.4470i | 1.57043 | − | 0.906687i | 0.574313 | − | 0.818636i | \(-0.305269\pi\) |
0.996116 | − | 0.0880513i | \(-0.0280639\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.00000 | + | 5.19615i | 0.332877 | + | 0.192187i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −41.5959 | −1.53638 | −0.768190 | − | 0.640222i | \(-0.778842\pi\) | ||||
−0.768190 | + | 0.640222i | \(0.778842\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 52.8990 | + | 30.5412i | 1.94856 | + | 1.12500i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.60102 | + | 4.96580i | −0.316394 | + | 0.182670i | −0.649784 | − | 0.760119i | \(-0.725141\pi\) |
0.333390 | + | 0.942789i | \(0.391807\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.10102 | − | 1.90702i | −0.0403925 | − | 0.0699619i | 0.845122 | − | 0.534573i | \(-0.179528\pi\) |
−0.885515 | + | 0.464611i | \(0.846194\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.79796 | + | 10.0424i | −0.212421 | + | 0.367924i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.77101i | 0.320486i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.7474 | − | 35.9356i | 0.757085 | − | 1.31131i | −0.187246 | − | 0.982313i | \(-0.559956\pi\) |
0.944331 | − | 0.328997i | \(-0.106711\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.20204 | − | 3.81405i | −0.0801405 | − | 0.138807i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.7474 | − | 27.2754i | −0.572351 | − | 0.991341i | −0.996324 | − | 0.0856658i | \(-0.972698\pi\) |
0.423973 | − | 0.905675i | \(-0.360635\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.7980 | 0.572676 | 0.286338 | − | 0.958129i | \(-0.407562\pi\) | ||||
0.286338 | + | 0.958129i | \(0.407562\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.30306 | − | 16.1134i | −0.336793 | − | 0.583343i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 8.54950i | − | 0.308704i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.0959 | + | 27.8789i | −0.580434 | + | 1.00534i | 0.414994 | + | 0.909824i | \(0.363784\pi\) |
−0.995428 | + | 0.0955165i | \(0.969550\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.30306 | + | 3.63907i | 0.226705 | + | 0.130888i | 0.609051 | − | 0.793131i | \(-0.291550\pi\) |
−0.382346 | + | 0.924019i | \(0.624884\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.949490 | − | 1.64456i | 0.0341067 | − | 0.0590745i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.5959 | − | 11.3137i | 0.701197 | − | 0.404836i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13.6969 | + | 23.7238i | −0.488865 | + | 0.846738i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.5959 | 1.23321 | 0.616606 | − | 0.787272i | \(-0.288507\pi\) | ||||
0.616606 | + | 0.787272i | \(0.288507\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.5959 | −0.625639 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.0959179 | + | 0.0553782i | −0.00340615 | + | 0.00196654i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 52.1830i | − | 1.84842i | −0.381887 | − | 0.924209i | \(-0.624726\pi\) | ||
0.381887 | − | 0.924209i | \(-0.375274\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.38551i | 0.155148i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −62.6969 | + | 36.1981i | −2.21253 | + | 1.27740i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.4041 | −0.437186 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −43.3939 | −1.52565 | −0.762824 | − | 0.646606i | \(-0.776188\pi\) | ||||
−0.762824 | + | 0.646606i | \(0.776188\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.00000 | − | 6.92820i | 0.140459 | − | 0.243282i | −0.787211 | − | 0.616684i | \(-0.788476\pi\) |
0.927670 | + | 0.373402i | \(0.121809\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −27.0000 | + | 15.5885i | −0.945769 | + | 0.546040i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.5000 | − | 18.1865i | 0.472305 | − | 0.636266i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23.6969 | − | 41.0443i | 0.827029 | − | 1.43246i | −0.0733300 | − | 0.997308i | \(-0.523363\pi\) |
0.900359 | − | 0.435148i | \(-0.143304\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −38.3939 | − | 22.1667i | −1.33833 | − | 0.772683i | −0.351767 | − | 0.936088i | \(-0.614419\pi\) |
−0.986559 | + | 0.163404i | \(0.947752\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.7980 | − | 39.4872i | 0.792763 | − | 1.37311i | −0.131487 | − | 0.991318i | \(-0.541975\pi\) |
0.924250 | − | 0.381787i | \(-0.124691\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 42.3157i | − | 1.46968i | −0.678239 | − | 0.734842i | \(-0.737256\pi\) | ||
0.678239 | − | 0.734842i | \(-0.262744\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.79796 | − | 10.0424i | −0.200887 | − | 0.347947i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.0000 | 0.415277 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.00000 | + | 5.19615i | 0.103572 | + | 0.179391i | 0.913154 | − | 0.407615i | \(-0.133640\pi\) |
−0.809582 | + | 0.587007i | \(0.800306\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.0959 | + | 46.9315i | 0.934342 | + | 1.61833i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.7980 | + | 20.4347i | −0.405862 | + | 0.702974i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.0239i | 0.791111i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.8990 | + | 22.3417i | −0.442171 | + | 0.765863i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.6464 | + | 39.2248i | 0.775399 | + | 1.34303i | 0.934570 | + | 0.355779i | \(0.115785\pi\) |
−0.159171 | + | 0.987251i | \(0.550882\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −46.5959 | + | 26.9022i | −1.59169 | + | 0.918960i | −0.598668 | + | 0.800997i | \(0.704303\pi\) |
−0.993018 | + | 0.117963i | \(0.962363\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.70204 | + | 2.13737i | 0.126312 | + | 0.0729263i | 0.561825 | − | 0.827256i | \(-0.310100\pi\) |
−0.435513 | + | 0.900183i | \(0.643433\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.79796 | −0.265446 | −0.132723 | − | 0.991153i | \(-0.542372\pi\) | ||||
−0.132723 | + | 0.991153i | \(0.542372\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.7980 | + | 9.12096i | 0.537147 | + | 0.310122i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 48.4949 | − | 27.9985i | 1.64508 | − | 0.949785i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.2526 | − | 5.91931i | 0.347394 | − | 0.200568i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.1565i | 0.444771i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.5454 | − | 11.8619i | 0.693769 | − | 0.400548i | −0.111253 | − | 0.993792i | \(-0.535487\pi\) |
0.805022 | + | 0.593244i | \(0.202153\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.79796 | 0.127956 | 0.0639782 | − | 0.997951i | \(-0.479621\pi\) | ||||
0.0639782 | + | 0.997951i | \(0.479621\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.7020 | − | 10.7976i | −0.629374 | − | 0.363369i | 0.151136 | − | 0.988513i | \(-0.451707\pi\) |
−0.780510 | + | 0.625144i | \(0.785040\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.5959 | + | 21.8168i | −0.422930 | + | 0.732535i | −0.996225 | − | 0.0868136i | \(-0.972332\pi\) |
0.573295 | + | 0.819349i | \(0.305665\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.1010 | − | 7.56388i | −0.439394 | − | 0.253684i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.49490 | + | 1.09638i | 0.317735 | + | 0.0366888i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.20204 | + | 10.7423i | 0.207311 | + | 0.359074i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15.0000 | − | 8.66025i | −0.500278 | − | 0.288836i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.54270i | 0.0847096i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 33.9411i | 1.12824i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.5959 | + | 47.7975i | 0.916307 | + | 1.58709i | 0.804976 | + | 0.593308i | \(0.202178\pi\) |
0.111332 | + | 0.993783i | \(0.464488\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.5959 | −0.781768 | −0.390884 | − | 0.920440i | \(-0.627831\pi\) | ||||
−0.390884 | + | 0.920440i | \(0.627831\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19.5959 | −0.648530 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.59592 | + | 13.1565i | 0.250839 | + | 0.434466i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 36.3089i | − | 1.19772i | −0.800854 | − | 0.598859i | \(-0.795621\pi\) | ||
0.800854 | − | 0.598859i | \(-0.204379\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 4.38551i | − | 0.144351i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.94949 | + | 2.28024i | 0.129858 | + | 0.0749738i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.89898 | − | 10.2173i | −0.193539 | − | 0.335220i | 0.752881 | − | 0.658156i | \(-0.228663\pi\) |
−0.946421 | + | 0.322936i | \(0.895330\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23.1918 | + | 10.0424i | −0.760082 | + | 0.329125i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19.5959 | + | 11.3137i | 0.640855 | + | 0.369998i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.5000 | − | 25.1147i | 0.473694 | − | 0.820463i | −0.525852 | − | 0.850576i | \(-0.676253\pi\) |
0.999546 | + | 0.0301133i | \(0.00958681\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.79796 | + | 5.65685i | 0.319404 | + | 0.184408i | 0.651127 | − | 0.758969i | \(-0.274297\pi\) |
−0.331723 | + | 0.943377i | \(0.607630\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −42.0000 | + | 24.2487i | −1.36482 | + | 0.787977i | −0.990260 | − | 0.139227i | \(-0.955538\pi\) |
−0.374556 | + | 0.927204i | \(0.622205\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.0314i | 0.455478i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.8990 | − | 6.29253i | 0.353053 | − | 0.203835i | −0.312976 | − | 0.949761i | \(-0.601326\pi\) |
0.666029 | + | 0.745926i | \(0.267993\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 42.0000 | − | 24.2487i | 1.35909 | − | 0.784670i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.3939 | + | 6.57826i | 0.367927 | + | 0.212423i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.3939 | −0.883673 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.0000 | + | 12.1244i | 0.676014 | + | 0.390297i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42.3434 | + | 24.4470i | −1.36167 | + | 0.786161i | −0.989846 | − | 0.142142i | \(-0.954601\pi\) |
−0.371825 | + | 0.928303i | \(0.621268\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.5959 | − | 21.8168i | −0.404222 | − | 0.700133i | 0.590008 | − | 0.807397i | \(-0.299124\pi\) |
−0.994231 | + | 0.107264i | \(0.965791\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.05051 | − | 7.01569i | 0.129853 | − | 0.224913i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 12.2351i | − | 0.391436i | −0.980660 | − | 0.195718i | \(-0.937296\pi\) | ||
0.980660 | − | 0.195718i | \(-0.0627037\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.7980 | + | 44.6834i | −0.824506 | + | 1.42809i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.10102 | + | 15.7634i | 0.290277 | + | 0.502775i | 0.973875 | − | 0.227084i | \(-0.0729191\pi\) |
−0.683598 | + | 0.729859i | \(0.739586\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.00000 | − | 3.46410i | −0.0637253 | − | 0.110375i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −29.3939 | −0.934671 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.8485 | + | 20.5222i | 0.376379 | + | 0.651908i | 0.990532 | − | 0.137279i | \(-0.0438357\pi\) |
−0.614153 | + | 0.789187i | \(0.710502\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 36.8338i | − | 1.16771i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.9495 | + | 20.6971i | −0.378444 | + | 0.655484i | −0.990836 | − | 0.135070i | \(-0.956874\pi\) |
0.612392 | + | 0.790554i | \(0.290207\pi\) | |||||||
\(998\) | 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 | 2736.2.bm.i.1855.1 | 4 | ||
3.2 | odd | 2 | 912.2.bb.d.31.1 | yes | 4 | ||
4.3 | odd | 2 | 2736.2.bm.j.1855.2 | 4 | |||
12.11 | even | 2 | 912.2.bb.c.31.2 | ✓ | 4 | ||
19.8 | odd | 6 | 2736.2.bm.j.559.1 | 4 | |||
57.8 | even | 6 | 912.2.bb.c.559.1 | yes | 4 | ||
76.27 | even | 6 | inner | 2736.2.bm.i.559.2 | 4 | ||
228.179 | odd | 6 | 912.2.bb.d.559.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
912.2.bb.c.31.2 | ✓ | 4 | 12.11 | even | 2 | ||
912.2.bb.c.559.1 | yes | 4 | 57.8 | even | 6 | ||
912.2.bb.d.31.1 | yes | 4 | 3.2 | odd | 2 | ||
912.2.bb.d.559.2 | yes | 4 | 228.179 | odd | 6 | ||
2736.2.bm.i.559.2 | 4 | 76.27 | even | 6 | inner | ||
2736.2.bm.i.1855.1 | 4 | 1.1 | even | 1 | trivial | ||
2736.2.bm.j.559.1 | 4 | 19.8 | odd | 6 | |||
2736.2.bm.j.1855.2 | 4 | 4.3 | odd | 2 |