Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7942,2,Mod(1,7942)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7942, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7942.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7942 = 2 \cdot 11 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7942.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.4171892853\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7942.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.381966 | −0.220528 | −0.110264 | − | 0.993902i | \(-0.535170\pi\) | ||||
−0.110264 | + | 0.993902i | \(0.535170\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.381966 | −0.170820 | −0.0854102 | − | 0.996346i | \(-0.527220\pi\) | ||||
−0.0854102 | + | 0.996346i | \(0.527220\pi\) | |||||||
\(6\) | 0.381966 | 0.155937 | ||||||||
\(7\) | −1.85410 | −0.700785 | −0.350392 | − | 0.936603i | \(-0.613952\pi\) | ||||
−0.350392 | + | 0.936603i | \(0.613952\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.85410 | −0.951367 | ||||||||
\(10\) | 0.381966 | 0.120788 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −0.381966 | −0.110264 | ||||||||
\(13\) | −5.85410 | −1.62364 | −0.811818 | − | 0.583911i | \(-0.801522\pi\) | ||||
−0.811818 | + | 0.583911i | \(0.801522\pi\) | |||||||
\(14\) | 1.85410 | 0.495530 | ||||||||
\(15\) | 0.145898 | 0.0376707 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.47214 | 1.56972 | 0.784862 | − | 0.619671i | \(-0.212734\pi\) | ||||
0.784862 | + | 0.619671i | \(0.212734\pi\) | |||||||
\(18\) | 2.85410 | 0.672718 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −0.381966 | −0.0854102 | ||||||||
\(21\) | 0.708204 | 0.154543 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 4.76393 | 0.993348 | 0.496674 | − | 0.867937i | \(-0.334554\pi\) | ||||
0.496674 | + | 0.867937i | \(0.334554\pi\) | |||||||
\(24\) | 0.381966 | 0.0779685 | ||||||||
\(25\) | −4.85410 | −0.970820 | ||||||||
\(26\) | 5.85410 | 1.14808 | ||||||||
\(27\) | 2.23607 | 0.430331 | ||||||||
\(28\) | −1.85410 | −0.350392 | ||||||||
\(29\) | 8.09017 | 1.50231 | 0.751153 | − | 0.660128i | \(-0.229498\pi\) | ||||
0.751153 | + | 0.660128i | \(0.229498\pi\) | |||||||
\(30\) | −0.145898 | −0.0266372 | ||||||||
\(31\) | −0.145898 | −0.0262041 | −0.0131020 | − | 0.999914i | \(-0.504171\pi\) | ||||
−0.0131020 | + | 0.999914i | \(0.504171\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.381966 | 0.0664917 | ||||||||
\(34\) | −6.47214 | −1.10996 | ||||||||
\(35\) | 0.708204 | 0.119708 | ||||||||
\(36\) | −2.85410 | −0.475684 | ||||||||
\(37\) | −1.23607 | −0.203208 | −0.101604 | − | 0.994825i | \(-0.532398\pi\) | ||||
−0.101604 | + | 0.994825i | \(0.532398\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.23607 | 0.358057 | ||||||||
\(40\) | 0.381966 | 0.0603941 | ||||||||
\(41\) | −1.09017 | −0.170256 | −0.0851280 | − | 0.996370i | \(-0.527130\pi\) | ||||
−0.0851280 | + | 0.996370i | \(0.527130\pi\) | |||||||
\(42\) | −0.708204 | −0.109278 | ||||||||
\(43\) | −2.38197 | −0.363246 | −0.181623 | − | 0.983368i | \(-0.558135\pi\) | ||||
−0.181623 | + | 0.983368i | \(0.558135\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 1.09017 | 0.162513 | ||||||||
\(46\) | −4.76393 | −0.702403 | ||||||||
\(47\) | 9.23607 | 1.34722 | 0.673609 | − | 0.739087i | \(-0.264743\pi\) | ||||
0.673609 | + | 0.739087i | \(0.264743\pi\) | |||||||
\(48\) | −0.381966 | −0.0551320 | ||||||||
\(49\) | −3.56231 | −0.508901 | ||||||||
\(50\) | 4.85410 | 0.686474 | ||||||||
\(51\) | −2.47214 | −0.346168 | ||||||||
\(52\) | −5.85410 | −0.811818 | ||||||||
\(53\) | −6.76393 | −0.929098 | −0.464549 | − | 0.885548i | \(-0.653783\pi\) | ||||
−0.464549 | + | 0.885548i | \(0.653783\pi\) | |||||||
\(54\) | −2.23607 | −0.304290 | ||||||||
\(55\) | 0.381966 | 0.0515043 | ||||||||
\(56\) | 1.85410 | 0.247765 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.09017 | −1.06229 | ||||||||
\(59\) | 4.94427 | 0.643689 | 0.321845 | − | 0.946792i | \(-0.395697\pi\) | ||||
0.321845 | + | 0.946792i | \(0.395697\pi\) | |||||||
\(60\) | 0.145898 | 0.0188354 | ||||||||
\(61\) | 7.70820 | 0.986934 | 0.493467 | − | 0.869764i | \(-0.335729\pi\) | ||||
0.493467 | + | 0.869764i | \(0.335729\pi\) | |||||||
\(62\) | 0.145898 | 0.0185291 | ||||||||
\(63\) | 5.29180 | 0.666704 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.23607 | 0.277350 | ||||||||
\(66\) | −0.381966 | −0.0470168 | ||||||||
\(67\) | 11.0902 | 1.35488 | 0.677440 | − | 0.735578i | \(-0.263089\pi\) | ||||
0.677440 | + | 0.735578i | \(0.263089\pi\) | |||||||
\(68\) | 6.47214 | 0.784862 | ||||||||
\(69\) | −1.81966 | −0.219061 | ||||||||
\(70\) | −0.708204 | −0.0846466 | ||||||||
\(71\) | −7.14590 | −0.848062 | −0.424031 | − | 0.905648i | \(-0.639385\pi\) | ||||
−0.424031 | + | 0.905648i | \(0.639385\pi\) | |||||||
\(72\) | 2.85410 | 0.336359 | ||||||||
\(73\) | 9.23607 | 1.08100 | 0.540500 | − | 0.841344i | \(-0.318235\pi\) | ||||
0.540500 | + | 0.841344i | \(0.318235\pi\) | |||||||
\(74\) | 1.23607 | 0.143690 | ||||||||
\(75\) | 1.85410 | 0.214093 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.85410 | 0.211295 | ||||||||
\(78\) | −2.23607 | −0.253185 | ||||||||
\(79\) | −3.23607 | −0.364086 | −0.182043 | − | 0.983291i | \(-0.558271\pi\) | ||||
−0.182043 | + | 0.983291i | \(0.558271\pi\) | |||||||
\(80\) | −0.381966 | −0.0427051 | ||||||||
\(81\) | 7.70820 | 0.856467 | ||||||||
\(82\) | 1.09017 | 0.120389 | ||||||||
\(83\) | 0.0901699 | 0.00989744 | 0.00494872 | − | 0.999988i | \(-0.498425\pi\) | ||||
0.00494872 | + | 0.999988i | \(0.498425\pi\) | |||||||
\(84\) | 0.708204 | 0.0772714 | ||||||||
\(85\) | −2.47214 | −0.268141 | ||||||||
\(86\) | 2.38197 | 0.256854 | ||||||||
\(87\) | −3.09017 | −0.331301 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 16.6525 | 1.76516 | 0.882579 | − | 0.470163i | \(-0.155805\pi\) | ||||
0.882579 | + | 0.470163i | \(0.155805\pi\) | |||||||
\(90\) | −1.09017 | −0.114914 | ||||||||
\(91\) | 10.8541 | 1.13782 | ||||||||
\(92\) | 4.76393 | 0.496674 | ||||||||
\(93\) | 0.0557281 | 0.00577873 | ||||||||
\(94\) | −9.23607 | −0.952628 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.381966 | 0.0389842 | ||||||||
\(97\) | 8.00000 | 0.812277 | 0.406138 | − | 0.913812i | \(-0.366875\pi\) | ||||
0.406138 | + | 0.913812i | \(0.366875\pi\) | |||||||
\(98\) | 3.56231 | 0.359847 | ||||||||
\(99\) | 2.85410 | 0.286848 | ||||||||
\(100\) | −4.85410 | −0.485410 | ||||||||
\(101\) | 13.4164 | 1.33498 | 0.667491 | − | 0.744618i | \(-0.267368\pi\) | ||||
0.667491 | + | 0.744618i | \(0.267368\pi\) | |||||||
\(102\) | 2.47214 | 0.244778 | ||||||||
\(103\) | −18.5623 | −1.82900 | −0.914499 | − | 0.404588i | \(-0.867415\pi\) | ||||
−0.914499 | + | 0.404588i | \(0.867415\pi\) | |||||||
\(104\) | 5.85410 | 0.574042 | ||||||||
\(105\) | −0.270510 | −0.0263991 | ||||||||
\(106\) | 6.76393 | 0.656971 | ||||||||
\(107\) | −7.23607 | −0.699537 | −0.349769 | − | 0.936836i | \(-0.613740\pi\) | ||||
−0.349769 | + | 0.936836i | \(0.613740\pi\) | |||||||
\(108\) | 2.23607 | 0.215166 | ||||||||
\(109\) | −13.4164 | −1.28506 | −0.642529 | − | 0.766261i | \(-0.722115\pi\) | ||||
−0.642529 | + | 0.766261i | \(0.722115\pi\) | |||||||
\(110\) | −0.381966 | −0.0364190 | ||||||||
\(111\) | 0.472136 | 0.0448132 | ||||||||
\(112\) | −1.85410 | −0.175196 | ||||||||
\(113\) | 2.29180 | 0.215594 | 0.107797 | − | 0.994173i | \(-0.465620\pi\) | ||||
0.107797 | + | 0.994173i | \(0.465620\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.81966 | −0.169684 | ||||||||
\(116\) | 8.09017 | 0.751153 | ||||||||
\(117\) | 16.7082 | 1.54467 | ||||||||
\(118\) | −4.94427 | −0.455157 | ||||||||
\(119\) | −12.0000 | −1.10004 | ||||||||
\(120\) | −0.145898 | −0.0133186 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −7.70820 | −0.697868 | ||||||||
\(123\) | 0.416408 | 0.0375462 | ||||||||
\(124\) | −0.145898 | −0.0131020 | ||||||||
\(125\) | 3.76393 | 0.336656 | ||||||||
\(126\) | −5.29180 | −0.471431 | ||||||||
\(127\) | −21.7082 | −1.92629 | −0.963146 | − | 0.268980i | \(-0.913313\pi\) | ||||
−0.963146 | + | 0.268980i | \(0.913313\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0.909830 | 0.0801061 | ||||||||
\(130\) | −2.23607 | −0.196116 | ||||||||
\(131\) | −15.2705 | −1.33419 | −0.667095 | − | 0.744972i | \(-0.732463\pi\) | ||||
−0.667095 | + | 0.744972i | \(0.732463\pi\) | |||||||
\(132\) | 0.381966 | 0.0332459 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −11.0902 | −0.958045 | ||||||||
\(135\) | −0.854102 | −0.0735094 | ||||||||
\(136\) | −6.47214 | −0.554981 | ||||||||
\(137\) | −0.326238 | −0.0278724 | −0.0139362 | − | 0.999903i | \(-0.504436\pi\) | ||||
−0.0139362 | + | 0.999903i | \(0.504436\pi\) | |||||||
\(138\) | 1.81966 | 0.154900 | ||||||||
\(139\) | 23.3262 | 1.97851 | 0.989253 | − | 0.146215i | \(-0.0467091\pi\) | ||||
0.989253 | + | 0.146215i | \(0.0467091\pi\) | |||||||
\(140\) | 0.708204 | 0.0598542 | ||||||||
\(141\) | −3.52786 | −0.297100 | ||||||||
\(142\) | 7.14590 | 0.599670 | ||||||||
\(143\) | 5.85410 | 0.489545 | ||||||||
\(144\) | −2.85410 | −0.237842 | ||||||||
\(145\) | −3.09017 | −0.256625 | ||||||||
\(146\) | −9.23607 | −0.764382 | ||||||||
\(147\) | 1.36068 | 0.112227 | ||||||||
\(148\) | −1.23607 | −0.101604 | ||||||||
\(149\) | −12.9443 | −1.06044 | −0.530218 | − | 0.847861i | \(-0.677890\pi\) | ||||
−0.530218 | + | 0.847861i | \(0.677890\pi\) | |||||||
\(150\) | −1.85410 | −0.151387 | ||||||||
\(151\) | −16.9443 | −1.37891 | −0.689453 | − | 0.724331i | \(-0.742149\pi\) | ||||
−0.689453 | + | 0.724331i | \(0.742149\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −18.4721 | −1.49338 | ||||||||
\(154\) | −1.85410 | −0.149408 | ||||||||
\(155\) | 0.0557281 | 0.00447619 | ||||||||
\(156\) | 2.23607 | 0.179029 | ||||||||
\(157\) | −7.61803 | −0.607985 | −0.303993 | − | 0.952674i | \(-0.598320\pi\) | ||||
−0.303993 | + | 0.952674i | \(0.598320\pi\) | |||||||
\(158\) | 3.23607 | 0.257448 | ||||||||
\(159\) | 2.58359 | 0.204892 | ||||||||
\(160\) | 0.381966 | 0.0301971 | ||||||||
\(161\) | −8.83282 | −0.696123 | ||||||||
\(162\) | −7.70820 | −0.605614 | ||||||||
\(163\) | −13.2361 | −1.03673 | −0.518364 | − | 0.855160i | \(-0.673459\pi\) | ||||
−0.518364 | + | 0.855160i | \(0.673459\pi\) | |||||||
\(164\) | −1.09017 | −0.0851280 | ||||||||
\(165\) | −0.145898 | −0.0113581 | ||||||||
\(166\) | −0.0901699 | −0.00699854 | ||||||||
\(167\) | 4.47214 | 0.346064 | 0.173032 | − | 0.984916i | \(-0.444644\pi\) | ||||
0.173032 | + | 0.984916i | \(0.444644\pi\) | |||||||
\(168\) | −0.708204 | −0.0546391 | ||||||||
\(169\) | 21.2705 | 1.63619 | ||||||||
\(170\) | 2.47214 | 0.189604 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.38197 | −0.181623 | ||||||||
\(173\) | −1.61803 | −0.123017 | −0.0615084 | − | 0.998107i | \(-0.519591\pi\) | ||||
−0.0615084 | + | 0.998107i | \(0.519591\pi\) | |||||||
\(174\) | 3.09017 | 0.234265 | ||||||||
\(175\) | 9.00000 | 0.680336 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | −1.88854 | −0.141952 | ||||||||
\(178\) | −16.6525 | −1.24816 | ||||||||
\(179\) | −20.0344 | −1.49744 | −0.748722 | − | 0.662884i | \(-0.769332\pi\) | ||||
−0.748722 | + | 0.662884i | \(0.769332\pi\) | |||||||
\(180\) | 1.09017 | 0.0812565 | ||||||||
\(181\) | −8.65248 | −0.643133 | −0.321567 | − | 0.946887i | \(-0.604209\pi\) | ||||
−0.321567 | + | 0.946887i | \(0.604209\pi\) | |||||||
\(182\) | −10.8541 | −0.804560 | ||||||||
\(183\) | −2.94427 | −0.217647 | ||||||||
\(184\) | −4.76393 | −0.351202 | ||||||||
\(185\) | 0.472136 | 0.0347121 | ||||||||
\(186\) | −0.0557281 | −0.00408618 | ||||||||
\(187\) | −6.47214 | −0.473289 | ||||||||
\(188\) | 9.23607 | 0.673609 | ||||||||
\(189\) | −4.14590 | −0.301570 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.4164 | 1.40492 | 0.702461 | − | 0.711722i | \(-0.252085\pi\) | ||||
0.702461 | + | 0.711722i | \(0.252085\pi\) | |||||||
\(192\) | −0.381966 | −0.0275660 | ||||||||
\(193\) | −8.56231 | −0.616328 | −0.308164 | − | 0.951333i | \(-0.599715\pi\) | ||||
−0.308164 | + | 0.951333i | \(0.599715\pi\) | |||||||
\(194\) | −8.00000 | −0.574367 | ||||||||
\(195\) | −0.854102 | −0.0611635 | ||||||||
\(196\) | −3.56231 | −0.254450 | ||||||||
\(197\) | 16.4721 | 1.17359 | 0.586796 | − | 0.809735i | \(-0.300389\pi\) | ||||
0.586796 | + | 0.809735i | \(0.300389\pi\) | |||||||
\(198\) | −2.85410 | −0.202832 | ||||||||
\(199\) | −2.47214 | −0.175245 | −0.0876225 | − | 0.996154i | \(-0.527927\pi\) | ||||
−0.0876225 | + | 0.996154i | \(0.527927\pi\) | |||||||
\(200\) | 4.85410 | 0.343237 | ||||||||
\(201\) | −4.23607 | −0.298789 | ||||||||
\(202\) | −13.4164 | −0.943975 | ||||||||
\(203\) | −15.0000 | −1.05279 | ||||||||
\(204\) | −2.47214 | −0.173084 | ||||||||
\(205\) | 0.416408 | 0.0290832 | ||||||||
\(206\) | 18.5623 | 1.29330 | ||||||||
\(207\) | −13.5967 | −0.945039 | ||||||||
\(208\) | −5.85410 | −0.405909 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.270510 | 0.0186670 | ||||||||
\(211\) | −3.41641 | −0.235195 | −0.117598 | − | 0.993061i | \(-0.537519\pi\) | ||||
−0.117598 | + | 0.993061i | \(0.537519\pi\) | |||||||
\(212\) | −6.76393 | −0.464549 | ||||||||
\(213\) | 2.72949 | 0.187022 | ||||||||
\(214\) | 7.23607 | 0.494647 | ||||||||
\(215\) | 0.909830 | 0.0620499 | ||||||||
\(216\) | −2.23607 | −0.152145 | ||||||||
\(217\) | 0.270510 | 0.0183634 | ||||||||
\(218\) | 13.4164 | 0.908674 | ||||||||
\(219\) | −3.52786 | −0.238391 | ||||||||
\(220\) | 0.381966 | 0.0257521 | ||||||||
\(221\) | −37.8885 | −2.54866 | ||||||||
\(222\) | −0.472136 | −0.0316877 | ||||||||
\(223\) | −8.00000 | −0.535720 | −0.267860 | − | 0.963458i | \(-0.586316\pi\) | ||||
−0.267860 | + | 0.963458i | \(0.586316\pi\) | |||||||
\(224\) | 1.85410 | 0.123882 | ||||||||
\(225\) | 13.8541 | 0.923607 | ||||||||
\(226\) | −2.29180 | −0.152448 | ||||||||
\(227\) | 29.5967 | 1.96441 | 0.982203 | − | 0.187825i | \(-0.0601437\pi\) | ||||
0.982203 | + | 0.187825i | \(0.0601437\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.3820 | −1.14863 | −0.574316 | − | 0.818633i | \(-0.694732\pi\) | ||||
−0.574316 | + | 0.818633i | \(0.694732\pi\) | |||||||
\(230\) | 1.81966 | 0.119985 | ||||||||
\(231\) | −0.708204 | −0.0465964 | ||||||||
\(232\) | −8.09017 | −0.531146 | ||||||||
\(233\) | −3.05573 | −0.200187 | −0.100094 | − | 0.994978i | \(-0.531914\pi\) | ||||
−0.100094 | + | 0.994978i | \(0.531914\pi\) | |||||||
\(234\) | −16.7082 | −1.09225 | ||||||||
\(235\) | −3.52786 | −0.230132 | ||||||||
\(236\) | 4.94427 | 0.321845 | ||||||||
\(237\) | 1.23607 | 0.0802912 | ||||||||
\(238\) | 12.0000 | 0.777844 | ||||||||
\(239\) | 8.56231 | 0.553850 | 0.276925 | − | 0.960892i | \(-0.410685\pi\) | ||||
0.276925 | + | 0.960892i | \(0.410685\pi\) | |||||||
\(240\) | 0.145898 | 0.00941768 | ||||||||
\(241\) | −10.8541 | −0.699174 | −0.349587 | − | 0.936904i | \(-0.613678\pi\) | ||||
−0.349587 | + | 0.936904i | \(0.613678\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −9.65248 | −0.619207 | ||||||||
\(244\) | 7.70820 | 0.493467 | ||||||||
\(245\) | 1.36068 | 0.0869306 | ||||||||
\(246\) | −0.416408 | −0.0265492 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.145898 | 0.00926453 | ||||||||
\(249\) | −0.0344419 | −0.00218266 | ||||||||
\(250\) | −3.76393 | −0.238052 | ||||||||
\(251\) | 7.52786 | 0.475155 | 0.237577 | − | 0.971369i | \(-0.423647\pi\) | ||||
0.237577 | + | 0.971369i | \(0.423647\pi\) | |||||||
\(252\) | 5.29180 | 0.333352 | ||||||||
\(253\) | −4.76393 | −0.299506 | ||||||||
\(254\) | 21.7082 | 1.36209 | ||||||||
\(255\) | 0.944272 | 0.0591326 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −21.7082 | −1.35412 | −0.677060 | − | 0.735928i | \(-0.736746\pi\) | ||||
−0.677060 | + | 0.735928i | \(0.736746\pi\) | |||||||
\(258\) | −0.909830 | −0.0566435 | ||||||||
\(259\) | 2.29180 | 0.142405 | ||||||||
\(260\) | 2.23607 | 0.138675 | ||||||||
\(261\) | −23.0902 | −1.42925 | ||||||||
\(262\) | 15.2705 | 0.943415 | ||||||||
\(263\) | −10.8541 | −0.669293 | −0.334646 | − | 0.942344i | \(-0.608617\pi\) | ||||
−0.334646 | + | 0.942344i | \(0.608617\pi\) | |||||||
\(264\) | −0.381966 | −0.0235084 | ||||||||
\(265\) | 2.58359 | 0.158709 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.36068 | −0.389267 | ||||||||
\(268\) | 11.0902 | 0.677440 | ||||||||
\(269\) | 17.5967 | 1.07289 | 0.536446 | − | 0.843934i | \(-0.319766\pi\) | ||||
0.536446 | + | 0.843934i | \(0.319766\pi\) | |||||||
\(270\) | 0.854102 | 0.0519790 | ||||||||
\(271\) | 2.43769 | 0.148079 | 0.0740397 | − | 0.997255i | \(-0.476411\pi\) | ||||
0.0740397 | + | 0.997255i | \(0.476411\pi\) | |||||||
\(272\) | 6.47214 | 0.392431 | ||||||||
\(273\) | −4.14590 | −0.250921 | ||||||||
\(274\) | 0.326238 | 0.0197088 | ||||||||
\(275\) | 4.85410 | 0.292713 | ||||||||
\(276\) | −1.81966 | −0.109531 | ||||||||
\(277\) | −0.944272 | −0.0567358 | −0.0283679 | − | 0.999598i | \(-0.509031\pi\) | ||||
−0.0283679 | + | 0.999598i | \(0.509031\pi\) | |||||||
\(278\) | −23.3262 | −1.39901 | ||||||||
\(279\) | 0.416408 | 0.0249297 | ||||||||
\(280\) | −0.708204 | −0.0423233 | ||||||||
\(281\) | −30.2705 | −1.80579 | −0.902894 | − | 0.429864i | \(-0.858561\pi\) | ||||
−0.902894 | + | 0.429864i | \(0.858561\pi\) | |||||||
\(282\) | 3.52786 | 0.210081 | ||||||||
\(283\) | 18.0344 | 1.07204 | 0.536018 | − | 0.844206i | \(-0.319928\pi\) | ||||
0.536018 | + | 0.844206i | \(0.319928\pi\) | |||||||
\(284\) | −7.14590 | −0.424031 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.85410 | −0.346160 | ||||||||
\(287\) | 2.02129 | 0.119313 | ||||||||
\(288\) | 2.85410 | 0.168180 | ||||||||
\(289\) | 24.8885 | 1.46403 | ||||||||
\(290\) | 3.09017 | 0.181461 | ||||||||
\(291\) | −3.05573 | −0.179130 | ||||||||
\(292\) | 9.23607 | 0.540500 | ||||||||
\(293\) | −8.03444 | −0.469377 | −0.234689 | − | 0.972071i | \(-0.575407\pi\) | ||||
−0.234689 | + | 0.972071i | \(0.575407\pi\) | |||||||
\(294\) | −1.36068 | −0.0793565 | ||||||||
\(295\) | −1.88854 | −0.109955 | ||||||||
\(296\) | 1.23607 | 0.0718450 | ||||||||
\(297\) | −2.23607 | −0.129750 | ||||||||
\(298\) | 12.9443 | 0.749842 | ||||||||
\(299\) | −27.8885 | −1.61284 | ||||||||
\(300\) | 1.85410 | 0.107047 | ||||||||
\(301\) | 4.41641 | 0.254558 | ||||||||
\(302\) | 16.9443 | 0.975033 | ||||||||
\(303\) | −5.12461 | −0.294401 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.94427 | −0.168589 | ||||||||
\(306\) | 18.4721 | 1.05598 | ||||||||
\(307\) | 25.2361 | 1.44030 | 0.720149 | − | 0.693819i | \(-0.244073\pi\) | ||||
0.720149 | + | 0.693819i | \(0.244073\pi\) | |||||||
\(308\) | 1.85410 | 0.105647 | ||||||||
\(309\) | 7.09017 | 0.403346 | ||||||||
\(310\) | −0.0557281 | −0.00316514 | ||||||||
\(311\) | 14.4721 | 0.820640 | 0.410320 | − | 0.911942i | \(-0.365417\pi\) | ||||
0.410320 | + | 0.911942i | \(0.365417\pi\) | |||||||
\(312\) | −2.23607 | −0.126592 | ||||||||
\(313\) | −18.5623 | −1.04920 | −0.524602 | − | 0.851348i | \(-0.675786\pi\) | ||||
−0.524602 | + | 0.851348i | \(0.675786\pi\) | |||||||
\(314\) | 7.61803 | 0.429911 | ||||||||
\(315\) | −2.02129 | −0.113887 | ||||||||
\(316\) | −3.23607 | −0.182043 | ||||||||
\(317\) | −24.1803 | −1.35810 | −0.679052 | − | 0.734091i | \(-0.737609\pi\) | ||||
−0.679052 | + | 0.734091i | \(0.737609\pi\) | |||||||
\(318\) | −2.58359 | −0.144881 | ||||||||
\(319\) | −8.09017 | −0.452963 | ||||||||
\(320\) | −0.381966 | −0.0213525 | ||||||||
\(321\) | 2.76393 | 0.154268 | ||||||||
\(322\) | 8.83282 | 0.492234 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 7.70820 | 0.428234 | ||||||||
\(325\) | 28.4164 | 1.57626 | ||||||||
\(326\) | 13.2361 | 0.733078 | ||||||||
\(327\) | 5.12461 | 0.283392 | ||||||||
\(328\) | 1.09017 | 0.0601946 | ||||||||
\(329\) | −17.1246 | −0.944110 | ||||||||
\(330\) | 0.145898 | 0.00803142 | ||||||||
\(331\) | −12.7426 | −0.700399 | −0.350200 | − | 0.936675i | \(-0.613886\pi\) | ||||
−0.350200 | + | 0.936675i | \(0.613886\pi\) | |||||||
\(332\) | 0.0901699 | 0.00494872 | ||||||||
\(333\) | 3.52786 | 0.193326 | ||||||||
\(334\) | −4.47214 | −0.244704 | ||||||||
\(335\) | −4.23607 | −0.231441 | ||||||||
\(336\) | 0.708204 | 0.0386357 | ||||||||
\(337\) | 7.85410 | 0.427840 | 0.213920 | − | 0.976851i | \(-0.431377\pi\) | ||||
0.213920 | + | 0.976851i | \(0.431377\pi\) | |||||||
\(338\) | −21.2705 | −1.15696 | ||||||||
\(339\) | −0.875388 | −0.0475446 | ||||||||
\(340\) | −2.47214 | −0.134070 | ||||||||
\(341\) | 0.145898 | 0.00790082 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.5836 | 1.05741 | ||||||||
\(344\) | 2.38197 | 0.128427 | ||||||||
\(345\) | 0.695048 | 0.0374201 | ||||||||
\(346\) | 1.61803 | 0.0869860 | ||||||||
\(347\) | −13.5279 | −0.726214 | −0.363107 | − | 0.931747i | \(-0.618284\pi\) | ||||
−0.363107 | + | 0.931747i | \(0.618284\pi\) | |||||||
\(348\) | −3.09017 | −0.165650 | ||||||||
\(349\) | −16.7639 | −0.897353 | −0.448676 | − | 0.893694i | \(-0.648104\pi\) | ||||
−0.448676 | + | 0.893694i | \(0.648104\pi\) | |||||||
\(350\) | −9.00000 | −0.481070 | ||||||||
\(351\) | −13.0902 | −0.698702 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −20.4721 | −1.08962 | −0.544811 | − | 0.838559i | \(-0.683399\pi\) | ||||
−0.544811 | + | 0.838559i | \(0.683399\pi\) | |||||||
\(354\) | 1.88854 | 0.100375 | ||||||||
\(355\) | 2.72949 | 0.144866 | ||||||||
\(356\) | 16.6525 | 0.882579 | ||||||||
\(357\) | 4.58359 | 0.242589 | ||||||||
\(358\) | 20.0344 | 1.05885 | ||||||||
\(359\) | 16.0344 | 0.846265 | 0.423133 | − | 0.906068i | \(-0.360930\pi\) | ||||
0.423133 | + | 0.906068i | \(0.360930\pi\) | |||||||
\(360\) | −1.09017 | −0.0574570 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 8.65248 | 0.454764 | ||||||||
\(363\) | −0.381966 | −0.0200480 | ||||||||
\(364\) | 10.8541 | 0.568910 | ||||||||
\(365\) | −3.52786 | −0.184657 | ||||||||
\(366\) | 2.94427 | 0.153900 | ||||||||
\(367\) | 29.1246 | 1.52029 | 0.760146 | − | 0.649752i | \(-0.225127\pi\) | ||||
0.760146 | + | 0.649752i | \(0.225127\pi\) | |||||||
\(368\) | 4.76393 | 0.248337 | ||||||||
\(369\) | 3.11146 | 0.161976 | ||||||||
\(370\) | −0.472136 | −0.0245452 | ||||||||
\(371\) | 12.5410 | 0.651097 | ||||||||
\(372\) | 0.0557281 | 0.00288937 | ||||||||
\(373\) | 5.79837 | 0.300228 | 0.150114 | − | 0.988669i | \(-0.452036\pi\) | ||||
0.150114 | + | 0.988669i | \(0.452036\pi\) | |||||||
\(374\) | 6.47214 | 0.334666 | ||||||||
\(375\) | −1.43769 | −0.0742422 | ||||||||
\(376\) | −9.23607 | −0.476314 | ||||||||
\(377\) | −47.3607 | −2.43920 | ||||||||
\(378\) | 4.14590 | 0.213242 | ||||||||
\(379\) | −34.5066 | −1.77248 | −0.886242 | − | 0.463223i | \(-0.846693\pi\) | ||||
−0.886242 | + | 0.463223i | \(0.846693\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.29180 | 0.424802 | ||||||||
\(382\) | −19.4164 | −0.993430 | ||||||||
\(383\) | 0.798374 | 0.0407950 | 0.0203975 | − | 0.999792i | \(-0.493507\pi\) | ||||
0.0203975 | + | 0.999792i | \(0.493507\pi\) | |||||||
\(384\) | 0.381966 | 0.0194921 | ||||||||
\(385\) | −0.708204 | −0.0360934 | ||||||||
\(386\) | 8.56231 | 0.435810 | ||||||||
\(387\) | 6.79837 | 0.345581 | ||||||||
\(388\) | 8.00000 | 0.406138 | ||||||||
\(389\) | −16.3820 | −0.830599 | −0.415299 | − | 0.909685i | \(-0.636323\pi\) | ||||
−0.415299 | + | 0.909685i | \(0.636323\pi\) | |||||||
\(390\) | 0.854102 | 0.0432491 | ||||||||
\(391\) | 30.8328 | 1.55928 | ||||||||
\(392\) | 3.56231 | 0.179924 | ||||||||
\(393\) | 5.83282 | 0.294227 | ||||||||
\(394\) | −16.4721 | −0.829854 | ||||||||
\(395\) | 1.23607 | 0.0621933 | ||||||||
\(396\) | 2.85410 | 0.143424 | ||||||||
\(397\) | −26.9787 | −1.35402 | −0.677011 | − | 0.735973i | \(-0.736725\pi\) | ||||
−0.677011 | + | 0.735973i | \(0.736725\pi\) | |||||||
\(398\) | 2.47214 | 0.123917 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.85410 | −0.242705 | ||||||||
\(401\) | 18.4721 | 0.922454 | 0.461227 | − | 0.887282i | \(-0.347409\pi\) | ||||
0.461227 | + | 0.887282i | \(0.347409\pi\) | |||||||
\(402\) | 4.23607 | 0.211276 | ||||||||
\(403\) | 0.854102 | 0.0425458 | ||||||||
\(404\) | 13.4164 | 0.667491 | ||||||||
\(405\) | −2.94427 | −0.146302 | ||||||||
\(406\) | 15.0000 | 0.744438 | ||||||||
\(407\) | 1.23607 | 0.0612696 | ||||||||
\(408\) | 2.47214 | 0.122389 | ||||||||
\(409\) | 22.4508 | 1.11012 | 0.555062 | − | 0.831809i | \(-0.312695\pi\) | ||||
0.555062 | + | 0.831809i | \(0.312695\pi\) | |||||||
\(410\) | −0.416408 | −0.0205649 | ||||||||
\(411\) | 0.124612 | 0.00614665 | ||||||||
\(412\) | −18.5623 | −0.914499 | ||||||||
\(413\) | −9.16718 | −0.451088 | ||||||||
\(414\) | 13.5967 | 0.668244 | ||||||||
\(415\) | −0.0344419 | −0.00169068 | ||||||||
\(416\) | 5.85410 | 0.287021 | ||||||||
\(417\) | −8.90983 | −0.436316 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.23607 | −0.158092 | −0.0790461 | − | 0.996871i | \(-0.525187\pi\) | ||||
−0.0790461 | + | 0.996871i | \(0.525187\pi\) | |||||||
\(420\) | −0.270510 | −0.0131995 | ||||||||
\(421\) | 37.4164 | 1.82356 | 0.911782 | − | 0.410674i | \(-0.134707\pi\) | ||||
0.911782 | + | 0.410674i | \(0.134707\pi\) | |||||||
\(422\) | 3.41641 | 0.166308 | ||||||||
\(423\) | −26.3607 | −1.28170 | ||||||||
\(424\) | 6.76393 | 0.328486 | ||||||||
\(425\) | −31.4164 | −1.52392 | ||||||||
\(426\) | −2.72949 | −0.132244 | ||||||||
\(427\) | −14.2918 | −0.691628 | ||||||||
\(428\) | −7.23607 | −0.349769 | ||||||||
\(429\) | −2.23607 | −0.107958 | ||||||||
\(430\) | −0.909830 | −0.0438759 | ||||||||
\(431\) | 13.4164 | 0.646246 | 0.323123 | − | 0.946357i | \(-0.395267\pi\) | ||||
0.323123 | + | 0.946357i | \(0.395267\pi\) | |||||||
\(432\) | 2.23607 | 0.107583 | ||||||||
\(433\) | 14.3607 | 0.690130 | 0.345065 | − | 0.938579i | \(-0.387857\pi\) | ||||
0.345065 | + | 0.938579i | \(0.387857\pi\) | |||||||
\(434\) | −0.270510 | −0.0129849 | ||||||||
\(435\) | 1.18034 | 0.0565930 | ||||||||
\(436\) | −13.4164 | −0.642529 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 3.52786 | 0.168568 | ||||||||
\(439\) | 11.4164 | 0.544875 | 0.272438 | − | 0.962173i | \(-0.412170\pi\) | ||||
0.272438 | + | 0.962173i | \(0.412170\pi\) | |||||||
\(440\) | −0.381966 | −0.0182095 | ||||||||
\(441\) | 10.1672 | 0.484152 | ||||||||
\(442\) | 37.8885 | 1.80217 | ||||||||
\(443\) | −16.7639 | −0.796478 | −0.398239 | − | 0.917282i | \(-0.630379\pi\) | ||||
−0.398239 | + | 0.917282i | \(0.630379\pi\) | |||||||
\(444\) | 0.472136 | 0.0224066 | ||||||||
\(445\) | −6.36068 | −0.301525 | ||||||||
\(446\) | 8.00000 | 0.378811 | ||||||||
\(447\) | 4.94427 | 0.233856 | ||||||||
\(448\) | −1.85410 | −0.0875981 | ||||||||
\(449\) | −4.47214 | −0.211053 | −0.105527 | − | 0.994416i | \(-0.533653\pi\) | ||||
−0.105527 | + | 0.994416i | \(0.533653\pi\) | |||||||
\(450\) | −13.8541 | −0.653089 | ||||||||
\(451\) | 1.09017 | 0.0513341 | ||||||||
\(452\) | 2.29180 | 0.107797 | ||||||||
\(453\) | 6.47214 | 0.304087 | ||||||||
\(454\) | −29.5967 | −1.38904 | ||||||||
\(455\) | −4.14590 | −0.194363 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.52786 | −0.165027 | −0.0825133 | − | 0.996590i | \(-0.526295\pi\) | ||||
−0.0825133 | + | 0.996590i | \(0.526295\pi\) | |||||||
\(458\) | 17.3820 | 0.812206 | ||||||||
\(459\) | 14.4721 | 0.675501 | ||||||||
\(460\) | −1.81966 | −0.0848421 | ||||||||
\(461\) | −18.0000 | −0.838344 | −0.419172 | − | 0.907907i | \(-0.637680\pi\) | ||||
−0.419172 | + | 0.907907i | \(0.637680\pi\) | |||||||
\(462\) | 0.708204 | 0.0329486 | ||||||||
\(463\) | −7.12461 | −0.331109 | −0.165554 | − | 0.986201i | \(-0.552941\pi\) | ||||
−0.165554 | + | 0.986201i | \(0.552941\pi\) | |||||||
\(464\) | 8.09017 | 0.375577 | ||||||||
\(465\) | −0.0212862 | −0.000987126 0 | ||||||||
\(466\) | 3.05573 | 0.141554 | ||||||||
\(467\) | −14.1803 | −0.656188 | −0.328094 | − | 0.944645i | \(-0.606406\pi\) | ||||
−0.328094 | + | 0.944645i | \(0.606406\pi\) | |||||||
\(468\) | 16.7082 | 0.772337 | ||||||||
\(469\) | −20.5623 | −0.949479 | ||||||||
\(470\) | 3.52786 | 0.162728 | ||||||||
\(471\) | 2.90983 | 0.134078 | ||||||||
\(472\) | −4.94427 | −0.227579 | ||||||||
\(473\) | 2.38197 | 0.109523 | ||||||||
\(474\) | −1.23607 | −0.0567745 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −12.0000 | −0.550019 | ||||||||
\(477\) | 19.3050 | 0.883913 | ||||||||
\(478\) | −8.56231 | −0.391631 | ||||||||
\(479\) | −27.3820 | −1.25111 | −0.625557 | − | 0.780178i | \(-0.715128\pi\) | ||||
−0.625557 | + | 0.780178i | \(0.715128\pi\) | |||||||
\(480\) | −0.145898 | −0.00665930 | ||||||||
\(481\) | 7.23607 | 0.329936 | ||||||||
\(482\) | 10.8541 | 0.494391 | ||||||||
\(483\) | 3.37384 | 0.153515 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −3.05573 | −0.138753 | ||||||||
\(486\) | 9.65248 | 0.437845 | ||||||||
\(487\) | −10.5623 | −0.478624 | −0.239312 | − | 0.970943i | \(-0.576922\pi\) | ||||
−0.239312 | + | 0.970943i | \(0.576922\pi\) | |||||||
\(488\) | −7.70820 | −0.348934 | ||||||||
\(489\) | 5.05573 | 0.228628 | ||||||||
\(490\) | −1.36068 | −0.0614692 | ||||||||
\(491\) | 23.5623 | 1.06335 | 0.531676 | − | 0.846948i | \(-0.321562\pi\) | ||||
0.531676 | + | 0.846948i | \(0.321562\pi\) | |||||||
\(492\) | 0.416408 | 0.0187731 | ||||||||
\(493\) | 52.3607 | 2.35821 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.09017 | −0.0489995 | ||||||||
\(496\) | −0.145898 | −0.00655102 | ||||||||
\(497\) | 13.2492 | 0.594309 | ||||||||
\(498\) | 0.0344419 | 0.00154338 | ||||||||
\(499\) | −23.7082 | −1.06132 | −0.530662 | − | 0.847583i | \(-0.678057\pi\) | ||||
−0.530662 | + | 0.847583i | \(0.678057\pi\) | |||||||
\(500\) | 3.76393 | 0.168328 | ||||||||
\(501\) | −1.70820 | −0.0763169 | ||||||||
\(502\) | −7.52786 | −0.335985 | ||||||||
\(503\) | 24.9230 | 1.11126 | 0.555631 | − | 0.831429i | \(-0.312477\pi\) | ||||
0.555631 | + | 0.831429i | \(0.312477\pi\) | |||||||
\(504\) | −5.29180 | −0.235715 | ||||||||
\(505\) | −5.12461 | −0.228042 | ||||||||
\(506\) | 4.76393 | 0.211783 | ||||||||
\(507\) | −8.12461 | −0.360827 | ||||||||
\(508\) | −21.7082 | −0.963146 | ||||||||
\(509\) | 0.180340 | 0.00799342 | 0.00399671 | − | 0.999992i | \(-0.498728\pi\) | ||||
0.00399671 | + | 0.999992i | \(0.498728\pi\) | |||||||
\(510\) | −0.944272 | −0.0418131 | ||||||||
\(511\) | −17.1246 | −0.757548 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 21.7082 | 0.957508 | ||||||||
\(515\) | 7.09017 | 0.312430 | ||||||||
\(516\) | 0.909830 | 0.0400530 | ||||||||
\(517\) | −9.23607 | −0.406202 | ||||||||
\(518\) | −2.29180 | −0.100696 | ||||||||
\(519\) | 0.618034 | 0.0271287 | ||||||||
\(520\) | −2.23607 | −0.0980581 | ||||||||
\(521\) | −38.0689 | −1.66783 | −0.833914 | − | 0.551894i | \(-0.813905\pi\) | ||||
−0.833914 | + | 0.551894i | \(0.813905\pi\) | |||||||
\(522\) | 23.0902 | 1.01063 | ||||||||
\(523\) | 9.34752 | 0.408739 | 0.204369 | − | 0.978894i | \(-0.434486\pi\) | ||||
0.204369 | + | 0.978894i | \(0.434486\pi\) | |||||||
\(524\) | −15.2705 | −0.667095 | ||||||||
\(525\) | −3.43769 | −0.150033 | ||||||||
\(526\) | 10.8541 | 0.473261 | ||||||||
\(527\) | −0.944272 | −0.0411331 | ||||||||
\(528\) | 0.381966 | 0.0166229 | ||||||||
\(529\) | −0.304952 | −0.0132588 | ||||||||
\(530\) | −2.58359 | −0.112224 | ||||||||
\(531\) | −14.1115 | −0.612385 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.38197 | 0.276434 | ||||||||
\(534\) | 6.36068 | 0.275254 | ||||||||
\(535\) | 2.76393 | 0.119495 | ||||||||
\(536\) | −11.0902 | −0.479022 | ||||||||
\(537\) | 7.65248 | 0.330229 | ||||||||
\(538\) | −17.5967 | −0.758650 | ||||||||
\(539\) | 3.56231 | 0.153439 | ||||||||
\(540\) | −0.854102 | −0.0367547 | ||||||||
\(541\) | −8.00000 | −0.343947 | −0.171973 | − | 0.985102i | \(-0.555014\pi\) | ||||
−0.171973 | + | 0.985102i | \(0.555014\pi\) | |||||||
\(542\) | −2.43769 | −0.104708 | ||||||||
\(543\) | 3.30495 | 0.141829 | ||||||||
\(544\) | −6.47214 | −0.277491 | ||||||||
\(545\) | 5.12461 | 0.219514 | ||||||||
\(546\) | 4.14590 | 0.177428 | ||||||||
\(547\) | −4.18034 | −0.178738 | −0.0893692 | − | 0.995999i | \(-0.528485\pi\) | ||||
−0.0893692 | + | 0.995999i | \(0.528485\pi\) | |||||||
\(548\) | −0.326238 | −0.0139362 | ||||||||
\(549\) | −22.0000 | −0.938937 | ||||||||
\(550\) | −4.85410 | −0.206980 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 1.81966 | 0.0774499 | ||||||||
\(553\) | 6.00000 | 0.255146 | ||||||||
\(554\) | 0.944272 | 0.0401183 | ||||||||
\(555\) | −0.180340 | −0.00765500 | ||||||||
\(556\) | 23.3262 | 0.989253 | ||||||||
\(557\) | 14.9443 | 0.633209 | 0.316605 | − | 0.948558i | \(-0.397457\pi\) | ||||
0.316605 | + | 0.948558i | \(0.397457\pi\) | |||||||
\(558\) | −0.416408 | −0.0176280 | ||||||||
\(559\) | 13.9443 | 0.589780 | ||||||||
\(560\) | 0.708204 | 0.0299271 | ||||||||
\(561\) | 2.47214 | 0.104374 | ||||||||
\(562\) | 30.2705 | 1.27688 | ||||||||
\(563\) | −33.2361 | −1.40073 | −0.700367 | − | 0.713783i | \(-0.746980\pi\) | ||||
−0.700367 | + | 0.713783i | \(0.746980\pi\) | |||||||
\(564\) | −3.52786 | −0.148550 | ||||||||
\(565\) | −0.875388 | −0.0368279 | ||||||||
\(566\) | −18.0344 | −0.758044 | ||||||||
\(567\) | −14.2918 | −0.600199 | ||||||||
\(568\) | 7.14590 | 0.299835 | ||||||||
\(569\) | −30.9787 | −1.29870 | −0.649348 | − | 0.760492i | \(-0.724958\pi\) | ||||
−0.649348 | + | 0.760492i | \(0.724958\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.38197 | −0.225228 | −0.112614 | − | 0.993639i | \(-0.535922\pi\) | ||||
−0.112614 | + | 0.993639i | \(0.535922\pi\) | |||||||
\(572\) | 5.85410 | 0.244772 | ||||||||
\(573\) | −7.41641 | −0.309825 | ||||||||
\(574\) | −2.02129 | −0.0843669 | ||||||||
\(575\) | −23.1246 | −0.964363 | ||||||||
\(576\) | −2.85410 | −0.118921 | ||||||||
\(577\) | −10.7295 | −0.446675 | −0.223337 | − | 0.974741i | \(-0.571695\pi\) | ||||
−0.223337 | + | 0.974741i | \(0.571695\pi\) | |||||||
\(578\) | −24.8885 | −1.03523 | ||||||||
\(579\) | 3.27051 | 0.135918 | ||||||||
\(580\) | −3.09017 | −0.128312 | ||||||||
\(581\) | −0.167184 | −0.00693597 | ||||||||
\(582\) | 3.05573 | 0.126664 | ||||||||
\(583\) | 6.76393 | 0.280133 | ||||||||
\(584\) | −9.23607 | −0.382191 | ||||||||
\(585\) | −6.38197 | −0.263862 | ||||||||
\(586\) | 8.03444 | 0.331900 | ||||||||
\(587\) | −42.6525 | −1.76046 | −0.880228 | − | 0.474551i | \(-0.842610\pi\) | ||||
−0.880228 | + | 0.474551i | \(0.842610\pi\) | |||||||
\(588\) | 1.36068 | 0.0561135 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 1.88854 | 0.0777501 | ||||||||
\(591\) | −6.29180 | −0.258810 | ||||||||
\(592\) | −1.23607 | −0.0508021 | ||||||||
\(593\) | 14.2918 | 0.586894 | 0.293447 | − | 0.955975i | \(-0.405198\pi\) | ||||
0.293447 | + | 0.955975i | \(0.405198\pi\) | |||||||
\(594\) | 2.23607 | 0.0917470 | ||||||||
\(595\) | 4.58359 | 0.187909 | ||||||||
\(596\) | −12.9443 | −0.530218 | ||||||||
\(597\) | 0.944272 | 0.0386465 | ||||||||
\(598\) | 27.8885 | 1.14045 | ||||||||
\(599\) | 41.6180 | 1.70047 | 0.850233 | − | 0.526406i | \(-0.176461\pi\) | ||||
0.850233 | + | 0.526406i | \(0.176461\pi\) | |||||||
\(600\) | −1.85410 | −0.0756934 | ||||||||
\(601\) | 6.03444 | 0.246150 | 0.123075 | − | 0.992397i | \(-0.460724\pi\) | ||||
0.123075 | + | 0.992397i | \(0.460724\pi\) | |||||||
\(602\) | −4.41641 | −0.179999 | ||||||||
\(603\) | −31.6525 | −1.28899 | ||||||||
\(604\) | −16.9443 | −0.689453 | ||||||||
\(605\) | −0.381966 | −0.0155291 | ||||||||
\(606\) | 5.12461 | 0.208173 | ||||||||
\(607\) | 35.3050 | 1.43298 | 0.716492 | − | 0.697595i | \(-0.245747\pi\) | ||||
0.716492 | + | 0.697595i | \(0.245747\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.72949 | 0.232171 | ||||||||
\(610\) | 2.94427 | 0.119210 | ||||||||
\(611\) | −54.0689 | −2.18739 | ||||||||
\(612\) | −18.4721 | −0.746692 | ||||||||
\(613\) | −36.0000 | −1.45403 | −0.727013 | − | 0.686624i | \(-0.759092\pi\) | ||||
−0.727013 | + | 0.686624i | \(0.759092\pi\) | |||||||
\(614\) | −25.2361 | −1.01844 | ||||||||
\(615\) | −0.159054 | −0.00641366 | ||||||||
\(616\) | −1.85410 | −0.0747039 | ||||||||
\(617\) | −13.8541 | −0.557745 | −0.278873 | − | 0.960328i | \(-0.589961\pi\) | ||||
−0.278873 | + | 0.960328i | \(0.589961\pi\) | |||||||
\(618\) | −7.09017 | −0.285208 | ||||||||
\(619\) | 25.7082 | 1.03330 | 0.516650 | − | 0.856197i | \(-0.327179\pi\) | ||||
0.516650 | + | 0.856197i | \(0.327179\pi\) | |||||||
\(620\) | 0.0557281 | 0.00223809 | ||||||||
\(621\) | 10.6525 | 0.427469 | ||||||||
\(622\) | −14.4721 | −0.580280 | ||||||||
\(623\) | −30.8754 | −1.23700 | ||||||||
\(624\) | 2.23607 | 0.0895144 | ||||||||
\(625\) | 22.8328 | 0.913313 | ||||||||
\(626\) | 18.5623 | 0.741899 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.61803 | −0.303993 | ||||||||
\(629\) | −8.00000 | −0.318981 | ||||||||
\(630\) | 2.02129 | 0.0805300 | ||||||||
\(631\) | −42.3607 | −1.68635 | −0.843176 | − | 0.537638i | \(-0.819317\pi\) | ||||
−0.843176 | + | 0.537638i | \(0.819317\pi\) | |||||||
\(632\) | 3.23607 | 0.128724 | ||||||||
\(633\) | 1.30495 | 0.0518672 | ||||||||
\(634\) | 24.1803 | 0.960324 | ||||||||
\(635\) | 8.29180 | 0.329050 | ||||||||
\(636\) | 2.58359 | 0.102446 | ||||||||
\(637\) | 20.8541 | 0.826270 | ||||||||
\(638\) | 8.09017 | 0.320293 | ||||||||
\(639\) | 20.3951 | 0.806819 | ||||||||
\(640\) | 0.381966 | 0.0150985 | ||||||||
\(641\) | 29.2361 | 1.15476 | 0.577378 | − | 0.816477i | \(-0.304076\pi\) | ||||
0.577378 | + | 0.816477i | \(0.304076\pi\) | |||||||
\(642\) | −2.76393 | −0.109084 | ||||||||
\(643\) | −21.4164 | −0.844581 | −0.422290 | − | 0.906461i | \(-0.638774\pi\) | ||||
−0.422290 | + | 0.906461i | \(0.638774\pi\) | |||||||
\(644\) | −8.83282 | −0.348062 | ||||||||
\(645\) | −0.347524 | −0.0136838 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.29180 | −0.0900998 | −0.0450499 | − | 0.998985i | \(-0.514345\pi\) | ||||
−0.0450499 | + | 0.998985i | \(0.514345\pi\) | |||||||
\(648\) | −7.70820 | −0.302807 | ||||||||
\(649\) | −4.94427 | −0.194080 | ||||||||
\(650\) | −28.4164 | −1.11458 | ||||||||
\(651\) | −0.103326 | −0.00404965 | ||||||||
\(652\) | −13.2361 | −0.518364 | ||||||||
\(653\) | −37.1591 | −1.45415 | −0.727073 | − | 0.686560i | \(-0.759120\pi\) | ||||
−0.727073 | + | 0.686560i | \(0.759120\pi\) | |||||||
\(654\) | −5.12461 | −0.200388 | ||||||||
\(655\) | 5.83282 | 0.227907 | ||||||||
\(656\) | −1.09017 | −0.0425640 | ||||||||
\(657\) | −26.3607 | −1.02843 | ||||||||
\(658\) | 17.1246 | 0.667587 | ||||||||
\(659\) | 2.18034 | 0.0849340 | 0.0424670 | − | 0.999098i | \(-0.486478\pi\) | ||||
0.0424670 | + | 0.999098i | \(0.486478\pi\) | |||||||
\(660\) | −0.145898 | −0.00567907 | ||||||||
\(661\) | 1.23607 | 0.0480775 | 0.0240387 | − | 0.999711i | \(-0.492347\pi\) | ||||
0.0240387 | + | 0.999711i | \(0.492347\pi\) | |||||||
\(662\) | 12.7426 | 0.495257 | ||||||||
\(663\) | 14.4721 | 0.562051 | ||||||||
\(664\) | −0.0901699 | −0.00349927 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.52786 | −0.136702 | ||||||||
\(667\) | 38.5410 | 1.49231 | ||||||||
\(668\) | 4.47214 | 0.173032 | ||||||||
\(669\) | 3.05573 | 0.118141 | ||||||||
\(670\) | 4.23607 | 0.163654 | ||||||||
\(671\) | −7.70820 | −0.297572 | ||||||||
\(672\) | −0.708204 | −0.0273196 | ||||||||
\(673\) | 26.9787 | 1.03995 | 0.519976 | − | 0.854181i | \(-0.325941\pi\) | ||||
0.519976 | + | 0.854181i | \(0.325941\pi\) | |||||||
\(674\) | −7.85410 | −0.302529 | ||||||||
\(675\) | −10.8541 | −0.417775 | ||||||||
\(676\) | 21.2705 | 0.818097 | ||||||||
\(677\) | −26.3820 | −1.01394 | −0.506971 | − | 0.861963i | \(-0.669235\pi\) | ||||
−0.506971 | + | 0.861963i | \(0.669235\pi\) | |||||||
\(678\) | 0.875388 | 0.0336191 | ||||||||
\(679\) | −14.8328 | −0.569231 | ||||||||
\(680\) | 2.47214 | 0.0948021 | ||||||||
\(681\) | −11.3050 | −0.433207 | ||||||||
\(682\) | −0.145898 | −0.00558672 | ||||||||
\(683\) | −21.8885 | −0.837542 | −0.418771 | − | 0.908092i | \(-0.637539\pi\) | ||||
−0.418771 | + | 0.908092i | \(0.637539\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.124612 | 0.00476117 | ||||||||
\(686\) | −19.5836 | −0.747705 | ||||||||
\(687\) | 6.63932 | 0.253306 | ||||||||
\(688\) | −2.38197 | −0.0908116 | ||||||||
\(689\) | 39.5967 | 1.50852 | ||||||||
\(690\) | −0.695048 | −0.0264600 | ||||||||
\(691\) | 8.29180 | 0.315435 | 0.157717 | − | 0.987484i | \(-0.449586\pi\) | ||||
0.157717 | + | 0.987484i | \(0.449586\pi\) | |||||||
\(692\) | −1.61803 | −0.0615084 | ||||||||
\(693\) | −5.29180 | −0.201019 | ||||||||
\(694\) | 13.5279 | 0.513511 | ||||||||
\(695\) | −8.90983 | −0.337969 | ||||||||
\(696\) | 3.09017 | 0.117133 | ||||||||
\(697\) | −7.05573 | −0.267255 | ||||||||
\(698\) | 16.7639 | 0.634524 | ||||||||
\(699\) | 1.16718 | 0.0441470 | ||||||||
\(700\) | 9.00000 | 0.340168 | ||||||||
\(701\) | −32.6525 | −1.23327 | −0.616633 | − | 0.787250i | \(-0.711504\pi\) | ||||
−0.616633 | + | 0.787250i | \(0.711504\pi\) | |||||||
\(702\) | 13.0902 | 0.494057 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 1.34752 | 0.0507507 | ||||||||
\(706\) | 20.4721 | 0.770479 | ||||||||
\(707\) | −24.8754 | −0.935535 | ||||||||
\(708\) | −1.88854 | −0.0709758 | ||||||||
\(709\) | 24.1459 | 0.906818 | 0.453409 | − | 0.891303i | \(-0.350208\pi\) | ||||
0.453409 | + | 0.891303i | \(0.350208\pi\) | |||||||
\(710\) | −2.72949 | −0.102436 | ||||||||
\(711\) | 9.23607 | 0.346380 | ||||||||
\(712\) | −16.6525 | −0.624078 | ||||||||
\(713\) | −0.695048 | −0.0260298 | ||||||||
\(714\) | −4.58359 | −0.171537 | ||||||||
\(715\) | −2.23607 | −0.0836242 | ||||||||
\(716\) | −20.0344 | −0.748722 | ||||||||
\(717\) | −3.27051 | −0.122139 | ||||||||
\(718\) | −16.0344 | −0.598400 | ||||||||
\(719\) | 8.47214 | 0.315957 | 0.157979 | − | 0.987443i | \(-0.449502\pi\) | ||||
0.157979 | + | 0.987443i | \(0.449502\pi\) | |||||||
\(720\) | 1.09017 | 0.0406282 | ||||||||
\(721\) | 34.4164 | 1.28173 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.14590 | 0.154188 | ||||||||
\(724\) | −8.65248 | −0.321567 | ||||||||
\(725\) | −39.2705 | −1.45847 | ||||||||
\(726\) | 0.381966 | 0.0141761 | ||||||||
\(727\) | −3.63932 | −0.134975 | −0.0674875 | − | 0.997720i | \(-0.521498\pi\) | ||||
−0.0674875 | + | 0.997720i | \(0.521498\pi\) | |||||||
\(728\) | −10.8541 | −0.402280 | ||||||||
\(729\) | −19.4377 | −0.719915 | ||||||||
\(730\) | 3.52786 | 0.130572 | ||||||||
\(731\) | −15.4164 | −0.570196 | ||||||||
\(732\) | −2.94427 | −0.108823 | ||||||||
\(733\) | −0.472136 | −0.0174387 | −0.00871937 | − | 0.999962i | \(-0.502775\pi\) | ||||
−0.00871937 | + | 0.999962i | \(0.502775\pi\) | |||||||
\(734\) | −29.1246 | −1.07501 | ||||||||
\(735\) | −0.519733 | −0.0191707 | ||||||||
\(736\) | −4.76393 | −0.175601 | ||||||||
\(737\) | −11.0902 | −0.408512 | ||||||||
\(738\) | −3.11146 | −0.114534 | ||||||||
\(739\) | 32.6312 | 1.20036 | 0.600179 | − | 0.799866i | \(-0.295096\pi\) | ||||
0.600179 | + | 0.799866i | \(0.295096\pi\) | |||||||
\(740\) | 0.472136 | 0.0173561 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −12.5410 | −0.460395 | ||||||||
\(743\) | 18.1115 | 0.664445 | 0.332222 | − | 0.943201i | \(-0.392202\pi\) | ||||
0.332222 | + | 0.943201i | \(0.392202\pi\) | |||||||
\(744\) | −0.0557281 | −0.00204309 | ||||||||
\(745\) | 4.94427 | 0.181144 | ||||||||
\(746\) | −5.79837 | −0.212294 | ||||||||
\(747\) | −0.257354 | −0.00941610 | ||||||||
\(748\) | −6.47214 | −0.236645 | ||||||||
\(749\) | 13.4164 | 0.490225 | ||||||||
\(750\) | 1.43769 | 0.0524972 | ||||||||
\(751\) | −38.2492 | −1.39573 | −0.697867 | − | 0.716227i | \(-0.745867\pi\) | ||||
−0.697867 | + | 0.716227i | \(0.745867\pi\) | |||||||
\(752\) | 9.23607 | 0.336805 | ||||||||
\(753\) | −2.87539 | −0.104785 | ||||||||
\(754\) | 47.3607 | 1.72477 | ||||||||
\(755\) | 6.47214 | 0.235545 | ||||||||
\(756\) | −4.14590 | −0.150785 | ||||||||
\(757\) | 24.5623 | 0.892732 | 0.446366 | − | 0.894850i | \(-0.352718\pi\) | ||||
0.446366 | + | 0.894850i | \(0.352718\pi\) | |||||||
\(758\) | 34.5066 | 1.25334 | ||||||||
\(759\) | 1.81966 | 0.0660495 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.7639 | 1.18769 | 0.593846 | − | 0.804579i | \(-0.297609\pi\) | ||||
0.593846 | + | 0.804579i | \(0.297609\pi\) | |||||||
\(762\) | −8.29180 | −0.300380 | ||||||||
\(763\) | 24.8754 | 0.900550 | ||||||||
\(764\) | 19.4164 | 0.702461 | ||||||||
\(765\) | 7.05573 | 0.255100 | ||||||||
\(766\) | −0.798374 | −0.0288464 | ||||||||
\(767\) | −28.9443 | −1.04512 | ||||||||
\(768\) | −0.381966 | −0.0137830 | ||||||||
\(769\) | −20.2918 | −0.731741 | −0.365870 | − | 0.930666i | \(-0.619229\pi\) | ||||
−0.365870 | + | 0.930666i | \(0.619229\pi\) | |||||||
\(770\) | 0.708204 | 0.0255219 | ||||||||
\(771\) | 8.29180 | 0.298622 | ||||||||
\(772\) | −8.56231 | −0.308164 | ||||||||
\(773\) | −18.6525 | −0.670883 | −0.335441 | − | 0.942061i | \(-0.608885\pi\) | ||||
−0.335441 | + | 0.942061i | \(0.608885\pi\) | |||||||
\(774\) | −6.79837 | −0.244363 | ||||||||
\(775\) | 0.708204 | 0.0254394 | ||||||||
\(776\) | −8.00000 | −0.287183 | ||||||||
\(777\) | −0.875388 | −0.0314044 | ||||||||
\(778\) | 16.3820 | 0.587322 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −0.854102 | −0.0305818 | ||||||||
\(781\) | 7.14590 | 0.255700 | ||||||||
\(782\) | −30.8328 | −1.10258 | ||||||||
\(783\) | 18.0902 | 0.646490 | ||||||||
\(784\) | −3.56231 | −0.127225 | ||||||||
\(785\) | 2.90983 | 0.103856 | ||||||||
\(786\) | −5.83282 | −0.208050 | ||||||||
\(787\) | −16.1115 | −0.574311 | −0.287156 | − | 0.957884i | \(-0.592710\pi\) | ||||
−0.287156 | + | 0.957884i | \(0.592710\pi\) | |||||||
\(788\) | 16.4721 | 0.586796 | ||||||||
\(789\) | 4.14590 | 0.147598 | ||||||||
\(790\) | −1.23607 | −0.0439773 | ||||||||
\(791\) | −4.24922 | −0.151085 | ||||||||
\(792\) | −2.85410 | −0.101416 | ||||||||
\(793\) | −45.1246 | −1.60242 | ||||||||
\(794\) | 26.9787 | 0.957439 | ||||||||
\(795\) | −0.986844 | −0.0349998 | ||||||||
\(796\) | −2.47214 | −0.0876225 | ||||||||
\(797\) | −15.0557 | −0.533301 | −0.266651 | − | 0.963793i | \(-0.585917\pi\) | ||||
−0.266651 | + | 0.963793i | \(0.585917\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 59.7771 | 2.11476 | ||||||||
\(800\) | 4.85410 | 0.171618 | ||||||||
\(801\) | −47.5279 | −1.67931 | ||||||||
\(802\) | −18.4721 | −0.652274 | ||||||||
\(803\) | −9.23607 | −0.325934 | ||||||||
\(804\) | −4.23607 | −0.149395 | ||||||||
\(805\) | 3.37384 | 0.118912 | ||||||||
\(806\) | −0.854102 | −0.0300845 | ||||||||
\(807\) | −6.72136 | −0.236603 | ||||||||
\(808\) | −13.4164 | −0.471988 | ||||||||
\(809\) | −8.06888 | −0.283687 | −0.141843 | − | 0.989889i | \(-0.545303\pi\) | ||||
−0.141843 | + | 0.989889i | \(0.545303\pi\) | |||||||
\(810\) | 2.94427 | 0.103451 | ||||||||
\(811\) | 25.7771 | 0.905156 | 0.452578 | − | 0.891725i | \(-0.350504\pi\) | ||||
0.452578 | + | 0.891725i | \(0.350504\pi\) | |||||||
\(812\) | −15.0000 | −0.526397 | ||||||||
\(813\) | −0.931116 | −0.0326557 | ||||||||
\(814\) | −1.23607 | −0.0433242 | ||||||||
\(815\) | 5.05573 | 0.177094 | ||||||||
\(816\) | −2.47214 | −0.0865421 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −22.4508 | −0.784976 | ||||||||
\(819\) | −30.9787 | −1.08248 | ||||||||
\(820\) | 0.416408 | 0.0145416 | ||||||||
\(821\) | 38.0689 | 1.32861 | 0.664307 | − | 0.747460i | \(-0.268727\pi\) | ||||
0.664307 | + | 0.747460i | \(0.268727\pi\) | |||||||
\(822\) | −0.124612 | −0.00434634 | ||||||||
\(823\) | −25.5967 | −0.892247 | −0.446123 | − | 0.894972i | \(-0.647196\pi\) | ||||
−0.446123 | + | 0.894972i | \(0.647196\pi\) | |||||||
\(824\) | 18.5623 | 0.646649 | ||||||||
\(825\) | −1.85410 | −0.0645515 | ||||||||
\(826\) | 9.16718 | 0.318967 | ||||||||
\(827\) | −36.5410 | −1.27066 | −0.635328 | − | 0.772243i | \(-0.719135\pi\) | ||||
−0.635328 | + | 0.772243i | \(0.719135\pi\) | |||||||
\(828\) | −13.5967 | −0.472520 | ||||||||
\(829\) | −21.4164 | −0.743823 | −0.371911 | − | 0.928268i | \(-0.621297\pi\) | ||||
−0.371911 | + | 0.928268i | \(0.621297\pi\) | |||||||
\(830\) | 0.0344419 | 0.00119549 | ||||||||
\(831\) | 0.360680 | 0.0125118 | ||||||||
\(832\) | −5.85410 | −0.202954 | ||||||||
\(833\) | −23.0557 | −0.798834 | ||||||||
\(834\) | 8.90983 | 0.308522 | ||||||||
\(835\) | −1.70820 | −0.0591148 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.326238 | −0.0112764 | ||||||||
\(838\) | 3.23607 | 0.111788 | ||||||||
\(839\) | 34.3820 | 1.18700 | 0.593499 | − | 0.804835i | \(-0.297746\pi\) | ||||
0.593499 | + | 0.804835i | \(0.297746\pi\) | |||||||
\(840\) | 0.270510 | 0.00933348 | ||||||||
\(841\) | 36.4508 | 1.25693 | ||||||||
\(842\) | −37.4164 | −1.28945 | ||||||||
\(843\) | 11.5623 | 0.398227 | ||||||||
\(844\) | −3.41641 | −0.117598 | ||||||||
\(845\) | −8.12461 | −0.279495 | ||||||||
\(846\) | 26.3607 | 0.906299 | ||||||||
\(847\) | −1.85410 | −0.0637077 | ||||||||
\(848\) | −6.76393 | −0.232274 | ||||||||
\(849\) | −6.88854 | −0.236414 | ||||||||
\(850\) | 31.4164 | 1.07757 | ||||||||
\(851\) | −5.88854 | −0.201857 | ||||||||
\(852\) | 2.72949 | 0.0935108 | ||||||||
\(853\) | −35.7082 | −1.22263 | −0.611313 | − | 0.791389i | \(-0.709358\pi\) | ||||
−0.611313 | + | 0.791389i | \(0.709358\pi\) | |||||||
\(854\) | 14.2918 | 0.489055 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.23607 | 0.247324 | ||||||||
\(857\) | −53.3820 | −1.82349 | −0.911747 | − | 0.410753i | \(-0.865266\pi\) | ||||
−0.911747 | + | 0.410753i | \(0.865266\pi\) | |||||||
\(858\) | 2.23607 | 0.0763381 | ||||||||
\(859\) | 37.0132 | 1.26287 | 0.631436 | − | 0.775428i | \(-0.282466\pi\) | ||||
0.631436 | + | 0.775428i | \(0.282466\pi\) | |||||||
\(860\) | 0.909830 | 0.0310249 | ||||||||
\(861\) | −0.772063 | −0.0263118 | ||||||||
\(862\) | −13.4164 | −0.456965 | ||||||||
\(863\) | −27.2016 | −0.925954 | −0.462977 | − | 0.886370i | \(-0.653219\pi\) | ||||
−0.462977 | + | 0.886370i | \(0.653219\pi\) | |||||||
\(864\) | −2.23607 | −0.0760726 | ||||||||
\(865\) | 0.618034 | 0.0210138 | ||||||||
\(866\) | −14.3607 | −0.487996 | ||||||||
\(867\) | −9.50658 | −0.322860 | ||||||||
\(868\) | 0.270510 | 0.00918170 | ||||||||
\(869\) | 3.23607 | 0.109776 | ||||||||
\(870\) | −1.18034 | −0.0400173 | ||||||||
\(871\) | −64.9230 | −2.19983 | ||||||||
\(872\) | 13.4164 | 0.454337 | ||||||||
\(873\) | −22.8328 | −0.772774 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.97871 | −0.235924 | ||||||||
\(876\) | −3.52786 | −0.119195 | ||||||||
\(877\) | 23.3262 | 0.787671 | 0.393836 | − | 0.919181i | \(-0.371148\pi\) | ||||
0.393836 | + | 0.919181i | \(0.371148\pi\) | |||||||
\(878\) | −11.4164 | −0.385285 | ||||||||
\(879\) | 3.06888 | 0.103511 | ||||||||
\(880\) | 0.381966 | 0.0128761 | ||||||||
\(881\) | 3.67376 | 0.123772 | 0.0618861 | − | 0.998083i | \(-0.480288\pi\) | ||||
0.0618861 | + | 0.998083i | \(0.480288\pi\) | |||||||
\(882\) | −10.1672 | −0.342347 | ||||||||
\(883\) | −49.1246 | −1.65317 | −0.826587 | − | 0.562808i | \(-0.809721\pi\) | ||||
−0.826587 | + | 0.562808i | \(0.809721\pi\) | |||||||
\(884\) | −37.8885 | −1.27433 | ||||||||
\(885\) | 0.721360 | 0.0242482 | ||||||||
\(886\) | 16.7639 | 0.563195 | ||||||||
\(887\) | −20.0689 | −0.673847 | −0.336924 | − | 0.941532i | \(-0.609386\pi\) | ||||
−0.336924 | + | 0.941532i | \(0.609386\pi\) | |||||||
\(888\) | −0.472136 | −0.0158438 | ||||||||
\(889\) | 40.2492 | 1.34992 | ||||||||
\(890\) | 6.36068 | 0.213210 | ||||||||
\(891\) | −7.70820 | −0.258235 | ||||||||
\(892\) | −8.00000 | −0.267860 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −4.94427 | −0.165361 | ||||||||
\(895\) | 7.65248 | 0.255794 | ||||||||
\(896\) | 1.85410 | 0.0619412 | ||||||||
\(897\) | 10.6525 | 0.355676 | ||||||||
\(898\) | 4.47214 | 0.149237 | ||||||||
\(899\) | −1.18034 | −0.0393665 | ||||||||
\(900\) | 13.8541 | 0.461803 | ||||||||
\(901\) | −43.7771 | −1.45843 | ||||||||
\(902\) | −1.09017 | −0.0362987 | ||||||||
\(903\) | −1.68692 | −0.0561371 | ||||||||
\(904\) | −2.29180 | −0.0762240 | ||||||||
\(905\) | 3.30495 | 0.109860 | ||||||||
\(906\) | −6.47214 | −0.215022 | ||||||||
\(907\) | 47.4164 | 1.57444 | 0.787218 | − | 0.616675i | \(-0.211521\pi\) | ||||
0.787218 | + | 0.616675i | \(0.211521\pi\) | |||||||
\(908\) | 29.5967 | 0.982203 | ||||||||
\(909\) | −38.2918 | −1.27006 | ||||||||
\(910\) | 4.14590 | 0.137435 | ||||||||
\(911\) | 31.4164 | 1.04087 | 0.520436 | − | 0.853901i | \(-0.325769\pi\) | ||||
0.520436 | + | 0.853901i | \(0.325769\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.0901699 | −0.00298419 | ||||||||
\(914\) | 3.52786 | 0.116691 | ||||||||
\(915\) | 1.12461 | 0.0371785 | ||||||||
\(916\) | −17.3820 | −0.574316 | ||||||||
\(917\) | 28.3131 | 0.934980 | ||||||||
\(918\) | −14.4721 | −0.477652 | ||||||||
\(919\) | −17.3262 | −0.571540 | −0.285770 | − | 0.958298i | \(-0.592249\pi\) | ||||
−0.285770 | + | 0.958298i | \(0.592249\pi\) | |||||||
\(920\) | 1.81966 | 0.0599924 | ||||||||
\(921\) | −9.63932 | −0.317626 | ||||||||
\(922\) | 18.0000 | 0.592798 | ||||||||
\(923\) | 41.8328 | 1.37694 | ||||||||
\(924\) | −0.708204 | −0.0232982 | ||||||||
\(925\) | 6.00000 | 0.197279 | ||||||||
\(926\) | 7.12461 | 0.234129 | ||||||||
\(927\) | 52.9787 | 1.74005 | ||||||||
\(928\) | −8.09017 | −0.265573 | ||||||||
\(929\) | −20.6180 | −0.676456 | −0.338228 | − | 0.941064i | \(-0.609827\pi\) | ||||
−0.338228 | + | 0.941064i | \(0.609827\pi\) | |||||||
\(930\) | 0.0212862 | 0.000698003 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.05573 | −0.100094 | ||||||||
\(933\) | −5.52786 | −0.180974 | ||||||||
\(934\) | 14.1803 | 0.463995 | ||||||||
\(935\) | 2.47214 | 0.0808475 | ||||||||
\(936\) | −16.7082 | −0.546125 | ||||||||
\(937\) | −10.7639 | −0.351642 | −0.175821 | − | 0.984422i | \(-0.556258\pi\) | ||||
−0.175821 | + | 0.984422i | \(0.556258\pi\) | |||||||
\(938\) | 20.5623 | 0.671383 | ||||||||
\(939\) | 7.09017 | 0.231379 | ||||||||
\(940\) | −3.52786 | −0.115066 | ||||||||
\(941\) | 21.0557 | 0.686397 | 0.343199 | − | 0.939263i | \(-0.388490\pi\) | ||||
0.343199 | + | 0.939263i | \(0.388490\pi\) | |||||||
\(942\) | −2.90983 | −0.0948074 | ||||||||
\(943\) | −5.19350 | −0.169123 | ||||||||
\(944\) | 4.94427 | 0.160922 | ||||||||
\(945\) | 1.58359 | 0.0515143 | ||||||||
\(946\) | −2.38197 | −0.0774444 | ||||||||
\(947\) | −13.3050 | −0.432353 | −0.216176 | − | 0.976354i | \(-0.569359\pi\) | ||||
−0.216176 | + | 0.976354i | \(0.569359\pi\) | |||||||
\(948\) | 1.23607 | 0.0401456 | ||||||||
\(949\) | −54.0689 | −1.75515 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.23607 | 0.299500 | ||||||||
\(952\) | 12.0000 | 0.388922 | ||||||||
\(953\) | −29.0557 | −0.941207 | −0.470604 | − | 0.882345i | \(-0.655964\pi\) | ||||
−0.470604 | + | 0.882345i | \(0.655964\pi\) | |||||||
\(954\) | −19.3050 | −0.625021 | ||||||||
\(955\) | −7.41641 | −0.239989 | ||||||||
\(956\) | 8.56231 | 0.276925 | ||||||||
\(957\) | 3.09017 | 0.0998910 | ||||||||
\(958\) | 27.3820 | 0.884671 | ||||||||
\(959\) | 0.604878 | 0.0195325 | ||||||||
\(960\) | 0.145898 | 0.00470884 | ||||||||
\(961\) | −30.9787 | −0.999313 | ||||||||
\(962\) | −7.23607 | −0.233300 | ||||||||
\(963\) | 20.6525 | 0.665517 | ||||||||
\(964\) | −10.8541 | −0.349587 | ||||||||
\(965\) | 3.27051 | 0.105281 | ||||||||
\(966\) | −3.37384 | −0.108551 | ||||||||
\(967\) | 58.8328 | 1.89194 | 0.945968 | − | 0.324260i | \(-0.105115\pi\) | ||||
0.945968 | + | 0.324260i | \(0.105115\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.05573 | 0.0981135 | ||||||||
\(971\) | −14.6738 | −0.470903 | −0.235452 | − | 0.971886i | \(-0.575657\pi\) | ||||
−0.235452 | + | 0.971886i | \(0.575657\pi\) | |||||||
\(972\) | −9.65248 | −0.309603 | ||||||||
\(973\) | −43.2492 | −1.38651 | ||||||||
\(974\) | 10.5623 | 0.338438 | ||||||||
\(975\) | −10.8541 | −0.347609 | ||||||||
\(976\) | 7.70820 | 0.246734 | ||||||||
\(977\) | 8.83282 | 0.282587 | 0.141293 | − | 0.989968i | \(-0.454874\pi\) | ||||
0.141293 | + | 0.989968i | \(0.454874\pi\) | |||||||
\(978\) | −5.05573 | −0.161664 | ||||||||
\(979\) | −16.6525 | −0.532215 | ||||||||
\(980\) | 1.36068 | 0.0434653 | ||||||||
\(981\) | 38.2918 | 1.22256 | ||||||||
\(982\) | −23.5623 | −0.751903 | ||||||||
\(983\) | 26.0344 | 0.830370 | 0.415185 | − | 0.909737i | \(-0.363717\pi\) | ||||
0.415185 | + | 0.909737i | \(0.363717\pi\) | |||||||
\(984\) | −0.416408 | −0.0132746 | ||||||||
\(985\) | −6.29180 | −0.200473 | ||||||||
\(986\) | −52.3607 | −1.66750 | ||||||||
\(987\) | 6.54102 | 0.208203 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.3475 | −0.360830 | ||||||||
\(990\) | 1.09017 | 0.0346479 | ||||||||
\(991\) | −10.3262 | −0.328024 | −0.164012 | − | 0.986458i | \(-0.552444\pi\) | ||||
−0.164012 | + | 0.986458i | \(0.552444\pi\) | |||||||
\(992\) | 0.145898 | 0.00463227 | ||||||||
\(993\) | 4.86726 | 0.154458 | ||||||||
\(994\) | −13.2492 | −0.420240 | ||||||||
\(995\) | 0.944272 | 0.0299354 | ||||||||
\(996\) | −0.0344419 | −0.00109133 | ||||||||
\(997\) | 41.4853 | 1.31385 | 0.656926 | − | 0.753955i | \(-0.271856\pi\) | ||||
0.656926 | + | 0.753955i | \(0.271856\pi\) | |||||||
\(998\) | 23.7082 | 0.750470 | ||||||||
\(999\) | −2.76393 | −0.0874469 |
(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 | 7942.2.a.t.1.2 | ✓ | 2 | |
19.18 | odd | 2 | 7942.2.a.ba.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7942.2.a.t.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
7942.2.a.ba.1.1 | yes | 2 | 19.18 | odd | 2 |