Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5225,2,Mod(1,5225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("5225.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5225 = 5^{2} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5225.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: | \(41.7218350561\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 5 x^{14} - 11 x^{13} + 87 x^{12} - 4 x^{11} - 545 x^{10} + 431 x^{9} + 1480 x^{8} - 1763 x^{7} + \cdots + 15 \) |
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 | 1.10 | ||
Root | \(1.28989\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.28989 | 0.912093 | 0.456046 | − | 0.889956i | \(-0.349265\pi\) | ||||
0.456046 | + | 0.889956i | \(0.349265\pi\) | |||||||
\(3\) | 3.30063 | 1.90562 | 0.952811 | − | 0.303565i | \(-0.0981771\pi\) | ||||
0.952811 | + | 0.303565i | \(0.0981771\pi\) | |||||||
\(4\) | −0.336174 | −0.168087 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.25747 | 1.73810 | ||||||||
\(7\) | 0.563541 | 0.212998 | 0.106499 | − | 0.994313i | \(-0.466036\pi\) | ||||
0.106499 | + | 0.994313i | \(0.466036\pi\) | |||||||
\(8\) | −3.01342 | −1.06540 | ||||||||
\(9\) | 7.89418 | 2.63139 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.10959 | −0.320310 | ||||||||
\(13\) | −1.69967 | −0.471403 | −0.235702 | − | 0.971825i | \(-0.575739\pi\) | ||||
−0.235702 | + | 0.971825i | \(0.575739\pi\) | |||||||
\(14\) | 0.726907 | 0.194274 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.21464 | −0.803660 | ||||||||
\(17\) | −0.0949420 | −0.0230268 | −0.0115134 | − | 0.999934i | \(-0.503665\pi\) | ||||
−0.0115134 | + | 0.999934i | \(0.503665\pi\) | |||||||
\(18\) | 10.1826 | 2.40007 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.86004 | 0.405894 | ||||||||
\(22\) | 1.28989 | 0.275006 | ||||||||
\(23\) | 0.625186 | 0.130360 | 0.0651801 | − | 0.997874i | \(-0.479238\pi\) | ||||
0.0651801 | + | 0.997874i | \(0.479238\pi\) | |||||||
\(24\) | −9.94618 | −2.03026 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.19239 | −0.429963 | ||||||||
\(27\) | 16.1539 | 3.10882 | ||||||||
\(28\) | −0.189448 | −0.0358023 | ||||||||
\(29\) | 6.14313 | 1.14075 | 0.570376 | − | 0.821384i | \(-0.306798\pi\) | ||||
0.570376 | + | 0.821384i | \(0.306798\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.11276 | 0.559069 | 0.279534 | − | 0.960136i | \(-0.409820\pi\) | ||||
0.279534 | + | 0.960136i | \(0.409820\pi\) | |||||||
\(32\) | 1.88029 | 0.332392 | ||||||||
\(33\) | 3.30063 | 0.574566 | ||||||||
\(34\) | −0.122465 | −0.0210026 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.65382 | −0.442303 | ||||||||
\(37\) | 2.91877 | 0.479842 | 0.239921 | − | 0.970792i | \(-0.422878\pi\) | ||||
0.239921 | + | 0.970792i | \(0.422878\pi\) | |||||||
\(38\) | 1.28989 | 0.209248 | ||||||||
\(39\) | −5.60998 | −0.898316 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.562373 | 0.0878279 | 0.0439139 | − | 0.999035i | \(-0.486017\pi\) | ||||
0.0439139 | + | 0.999035i | \(0.486017\pi\) | |||||||
\(42\) | 2.39925 | 0.370213 | ||||||||
\(43\) | 10.9758 | 1.67379 | 0.836895 | − | 0.547364i | \(-0.184369\pi\) | ||||
0.836895 | + | 0.547364i | \(0.184369\pi\) | |||||||
\(44\) | −0.336174 | −0.0506802 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.806423 | 0.118901 | ||||||||
\(47\) | 8.90408 | 1.29879 | 0.649396 | − | 0.760450i | \(-0.275022\pi\) | ||||
0.649396 | + | 0.760450i | \(0.275022\pi\) | |||||||
\(48\) | −10.6103 | −1.53147 | ||||||||
\(49\) | −6.68242 | −0.954632 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.313369 | −0.0438804 | ||||||||
\(52\) | 0.571385 | 0.0792368 | ||||||||
\(53\) | −0.489328 | −0.0672144 | −0.0336072 | − | 0.999435i | \(-0.510700\pi\) | ||||
−0.0336072 | + | 0.999435i | \(0.510700\pi\) | |||||||
\(54\) | 20.8368 | 2.83553 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.69818 | −0.226929 | ||||||||
\(57\) | 3.30063 | 0.437179 | ||||||||
\(58\) | 7.92399 | 1.04047 | ||||||||
\(59\) | −11.5958 | −1.50965 | −0.754824 | − | 0.655927i | \(-0.772278\pi\) | ||||
−0.754824 | + | 0.655927i | \(0.772278\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.8576 | 1.77428 | 0.887139 | − | 0.461502i | \(-0.152689\pi\) | ||||
0.887139 | + | 0.461502i | \(0.152689\pi\) | |||||||
\(62\) | 4.01513 | 0.509922 | ||||||||
\(63\) | 4.44869 | 0.560482 | ||||||||
\(64\) | 8.85465 | 1.10683 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.25747 | 0.524058 | ||||||||
\(67\) | −2.05662 | −0.251257 | −0.125628 | − | 0.992077i | \(-0.540095\pi\) | ||||
−0.125628 | + | 0.992077i | \(0.540095\pi\) | |||||||
\(68\) | 0.0319171 | 0.00387051 | ||||||||
\(69\) | 2.06351 | 0.248417 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.06337 | 0.363556 | 0.181778 | − | 0.983340i | \(-0.441815\pi\) | ||||
0.181778 | + | 0.983340i | \(0.441815\pi\) | |||||||
\(72\) | −23.7884 | −2.80349 | ||||||||
\(73\) | −5.61322 | −0.656978 | −0.328489 | − | 0.944508i | \(-0.606539\pi\) | ||||
−0.328489 | + | 0.944508i | \(0.606539\pi\) | |||||||
\(74\) | 3.76490 | 0.437661 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.336174 | −0.0385618 | ||||||||
\(77\) | 0.563541 | 0.0642214 | ||||||||
\(78\) | −7.23628 | −0.819347 | ||||||||
\(79\) | −5.37103 | −0.604288 | −0.302144 | − | 0.953262i | \(-0.597702\pi\) | ||||
−0.302144 | + | 0.953262i | \(0.597702\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 29.6355 | 3.29283 | ||||||||
\(82\) | 0.725401 | 0.0801071 | ||||||||
\(83\) | 2.47369 | 0.271522 | 0.135761 | − | 0.990742i | \(-0.456652\pi\) | ||||
0.135761 | + | 0.990742i | \(0.456652\pi\) | |||||||
\(84\) | −0.625298 | −0.0682256 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 14.1576 | 1.52665 | ||||||||
\(87\) | 20.2762 | 2.17384 | ||||||||
\(88\) | −3.01342 | −0.321231 | ||||||||
\(89\) | −14.0050 | −1.48452 | −0.742262 | − | 0.670110i | \(-0.766247\pi\) | ||||
−0.742262 | + | 0.670110i | \(0.766247\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.957832 | −0.100408 | ||||||||
\(92\) | −0.210171 | −0.0219119 | ||||||||
\(93\) | 10.2741 | 1.06537 | ||||||||
\(94\) | 11.4853 | 1.18462 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 6.20615 | 0.633413 | ||||||||
\(97\) | 6.13801 | 0.623221 | 0.311610 | − | 0.950210i | \(-0.399132\pi\) | ||||
0.311610 | + | 0.950210i | \(0.399132\pi\) | |||||||
\(98\) | −8.61961 | −0.870712 | ||||||||
\(99\) | 7.89418 | 0.793395 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.4177 | 1.23561 | 0.617804 | − | 0.786332i | \(-0.288023\pi\) | ||||
0.617804 | + | 0.786332i | \(0.288023\pi\) | |||||||
\(102\) | −0.404212 | −0.0400230 | ||||||||
\(103\) | −10.7035 | −1.05465 | −0.527324 | − | 0.849665i | \(-0.676804\pi\) | ||||
−0.527324 | + | 0.849665i | \(0.676804\pi\) | |||||||
\(104\) | 5.12181 | 0.502234 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.631181 | −0.0613057 | ||||||||
\(107\) | 2.53215 | 0.244792 | 0.122396 | − | 0.992481i | \(-0.460942\pi\) | ||||
0.122396 | + | 0.992481i | \(0.460942\pi\) | |||||||
\(108\) | −5.43052 | −0.522552 | ||||||||
\(109\) | −10.2842 | −0.985046 | −0.492523 | − | 0.870299i | \(-0.663925\pi\) | ||||
−0.492523 | + | 0.870299i | \(0.663925\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.63378 | 0.914398 | ||||||||
\(112\) | −1.81158 | −0.171178 | ||||||||
\(113\) | −17.0132 | −1.60047 | −0.800236 | − | 0.599686i | \(-0.795292\pi\) | ||||
−0.800236 | + | 0.599686i | \(0.795292\pi\) | |||||||
\(114\) | 4.25747 | 0.398748 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.06516 | −0.191746 | ||||||||
\(117\) | −13.4175 | −1.24045 | ||||||||
\(118\) | −14.9574 | −1.37694 | ||||||||
\(119\) | −0.0535037 | −0.00490468 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 17.8748 | 1.61831 | ||||||||
\(123\) | 1.85619 | 0.167367 | ||||||||
\(124\) | −1.04643 | −0.0939723 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 5.73834 | 0.511212 | ||||||||
\(127\) | −5.76757 | −0.511789 | −0.255894 | − | 0.966705i | \(-0.582370\pi\) | ||||
−0.255894 | + | 0.966705i | \(0.582370\pi\) | |||||||
\(128\) | 7.66098 | 0.677141 | ||||||||
\(129\) | 36.2270 | 3.18961 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.29905 | −0.550351 | −0.275175 | − | 0.961394i | \(-0.588736\pi\) | ||||
−0.275175 | + | 0.961394i | \(0.588736\pi\) | |||||||
\(132\) | −1.10959 | −0.0965772 | ||||||||
\(133\) | 0.563541 | 0.0488652 | ||||||||
\(134\) | −2.65283 | −0.229169 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.286100 | 0.0245329 | ||||||||
\(137\) | 9.89969 | 0.845787 | 0.422894 | − | 0.906179i | \(-0.361014\pi\) | ||||
0.422894 | + | 0.906179i | \(0.361014\pi\) | |||||||
\(138\) | 2.66171 | 0.226579 | ||||||||
\(139\) | 21.4383 | 1.81838 | 0.909188 | − | 0.416387i | \(-0.136704\pi\) | ||||
0.909188 | + | 0.416387i | \(0.136704\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 29.3891 | 2.47501 | ||||||||
\(142\) | 3.95143 | 0.331596 | ||||||||
\(143\) | −1.69967 | −0.142133 | ||||||||
\(144\) | −25.3769 | −2.11474 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −7.24046 | −0.599225 | ||||||||
\(147\) | −22.0562 | −1.81917 | ||||||||
\(148\) | −0.981214 | −0.0806553 | ||||||||
\(149\) | −5.05856 | −0.414413 | −0.207207 | − | 0.978297i | \(-0.566437\pi\) | ||||
−0.207207 | + | 0.978297i | \(0.566437\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.4546 | −1.09492 | −0.547460 | − | 0.836832i | \(-0.684405\pi\) | ||||
−0.547460 | + | 0.836832i | \(0.684405\pi\) | |||||||
\(152\) | −3.01342 | −0.244420 | ||||||||
\(153\) | −0.749489 | −0.0605926 | ||||||||
\(154\) | 0.726907 | 0.0585759 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.88593 | 0.150995 | ||||||||
\(157\) | 2.56715 | 0.204881 | 0.102440 | − | 0.994739i | \(-0.467335\pi\) | ||||
0.102440 | + | 0.994739i | \(0.467335\pi\) | |||||||
\(158\) | −6.92806 | −0.551167 | ||||||||
\(159\) | −1.61509 | −0.128085 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.352317 | 0.0277665 | ||||||||
\(162\) | 38.2266 | 3.00337 | ||||||||
\(163\) | −14.3323 | −1.12259 | −0.561294 | − | 0.827616i | \(-0.689696\pi\) | ||||
−0.561294 | + | 0.827616i | \(0.689696\pi\) | |||||||
\(164\) | −0.189055 | −0.0147627 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.19079 | 0.247654 | ||||||||
\(167\) | −16.9732 | −1.31342 | −0.656711 | − | 0.754142i | \(-0.728053\pi\) | ||||
−0.656711 | + | 0.754142i | \(0.728053\pi\) | |||||||
\(168\) | −5.60508 | −0.432441 | ||||||||
\(169\) | −10.1111 | −0.777779 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.89418 | 0.603683 | ||||||||
\(172\) | −3.68977 | −0.281343 | ||||||||
\(173\) | −24.9706 | −1.89848 | −0.949241 | − | 0.314549i | \(-0.898147\pi\) | ||||
−0.949241 | + | 0.314549i | \(0.898147\pi\) | |||||||
\(174\) | 26.1542 | 1.98274 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.21464 | −0.242312 | ||||||||
\(177\) | −38.2736 | −2.87682 | ||||||||
\(178\) | −18.0649 | −1.35402 | ||||||||
\(179\) | 2.25582 | 0.168608 | 0.0843040 | − | 0.996440i | \(-0.473133\pi\) | ||||
0.0843040 | + | 0.996440i | \(0.473133\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.14529 | 0.382446 | 0.191223 | − | 0.981547i | \(-0.438755\pi\) | ||||
0.191223 | + | 0.981547i | \(0.438755\pi\) | |||||||
\(182\) | −1.23550 | −0.0915814 | ||||||||
\(183\) | 45.7387 | 3.38110 | ||||||||
\(184\) | −1.88394 | −0.138886 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 13.2525 | 0.971719 | ||||||||
\(187\) | −0.0949420 | −0.00694285 | ||||||||
\(188\) | −2.99332 | −0.218310 | ||||||||
\(189\) | 9.10337 | 0.662172 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.23491 | −0.0893549 | −0.0446774 | − | 0.999001i | \(-0.514226\pi\) | ||||
−0.0446774 | + | 0.999001i | \(0.514226\pi\) | |||||||
\(192\) | 29.2260 | 2.10920 | ||||||||
\(193\) | −6.39165 | −0.460081 | −0.230041 | − | 0.973181i | \(-0.573886\pi\) | ||||
−0.230041 | + | 0.973181i | \(0.573886\pi\) | |||||||
\(194\) | 7.91738 | 0.568435 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.24646 | 0.160461 | ||||||||
\(197\) | 5.23212 | 0.372773 | 0.186387 | − | 0.982476i | \(-0.440322\pi\) | ||||
0.186387 | + | 0.982476i | \(0.440322\pi\) | |||||||
\(198\) | 10.1826 | 0.723649 | ||||||||
\(199\) | −19.1059 | −1.35438 | −0.677192 | − | 0.735807i | \(-0.736803\pi\) | ||||
−0.677192 | + | 0.735807i | \(0.736803\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.78816 | −0.478800 | ||||||||
\(202\) | 16.0175 | 1.12699 | ||||||||
\(203\) | 3.46190 | 0.242978 | ||||||||
\(204\) | 0.105347 | 0.00737573 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −13.8064 | −0.961936 | ||||||||
\(207\) | 4.93532 | 0.343029 | ||||||||
\(208\) | 5.46382 | 0.378848 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.42015 | −0.235453 | −0.117726 | − | 0.993046i | \(-0.537561\pi\) | ||||
−0.117726 | + | 0.993046i | \(0.537561\pi\) | |||||||
\(212\) | 0.164499 | 0.0112979 | ||||||||
\(213\) | 10.1111 | 0.692799 | ||||||||
\(214\) | 3.26621 | 0.223273 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −48.6784 | −3.31214 | ||||||||
\(217\) | 1.75417 | 0.119081 | ||||||||
\(218\) | −13.2655 | −0.898453 | ||||||||
\(219\) | −18.5272 | −1.25195 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.161370 | 0.0108549 | ||||||||
\(222\) | 12.4265 | 0.834015 | ||||||||
\(223\) | −10.6147 | −0.710813 | −0.355406 | − | 0.934712i | \(-0.615657\pi\) | ||||
−0.355406 | + | 0.934712i | \(0.615657\pi\) | |||||||
\(224\) | 1.05962 | 0.0707989 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −21.9453 | −1.45978 | ||||||||
\(227\) | 7.18967 | 0.477195 | 0.238598 | − | 0.971119i | \(-0.423312\pi\) | ||||
0.238598 | + | 0.971119i | \(0.423312\pi\) | |||||||
\(228\) | −1.10959 | −0.0734843 | ||||||||
\(229\) | −21.1961 | −1.40067 | −0.700337 | − | 0.713812i | \(-0.746967\pi\) | ||||
−0.700337 | + | 0.713812i | \(0.746967\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.86004 | 0.122382 | ||||||||
\(232\) | −18.5118 | −1.21536 | ||||||||
\(233\) | 26.7869 | 1.75487 | 0.877433 | − | 0.479699i | \(-0.159254\pi\) | ||||
0.877433 | + | 0.479699i | \(0.159254\pi\) | |||||||
\(234\) | −17.3071 | −1.13140 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.89822 | 0.253752 | ||||||||
\(237\) | −17.7278 | −1.15154 | ||||||||
\(238\) | −0.0690141 | −0.00447352 | ||||||||
\(239\) | 5.29366 | 0.342419 | 0.171209 | − | 0.985235i | \(-0.445233\pi\) | ||||
0.171209 | + | 0.985235i | \(0.445233\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.54532 | 0.0995429 | 0.0497714 | − | 0.998761i | \(-0.484151\pi\) | ||||
0.0497714 | + | 0.998761i | \(0.484151\pi\) | |||||||
\(242\) | 1.28989 | 0.0829175 | ||||||||
\(243\) | 49.3542 | 3.16608 | ||||||||
\(244\) | −4.65856 | −0.298233 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.39428 | 0.152654 | ||||||||
\(247\) | −1.69967 | −0.108147 | ||||||||
\(248\) | −9.38005 | −0.595634 | ||||||||
\(249\) | 8.16473 | 0.517419 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.7169 | −1.49700 | −0.748500 | − | 0.663135i | \(-0.769226\pi\) | ||||
−0.748500 | + | 0.663135i | \(0.769226\pi\) | |||||||
\(252\) | −1.49553 | −0.0942098 | ||||||||
\(253\) | 0.625186 | 0.0393051 | ||||||||
\(254\) | −7.43955 | −0.466799 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.82746 | −0.489216 | ||||||||
\(257\) | −2.55273 | −0.159235 | −0.0796174 | − | 0.996825i | \(-0.525370\pi\) | ||||
−0.0796174 | + | 0.996825i | \(0.525370\pi\) | |||||||
\(258\) | 46.7290 | 2.90922 | ||||||||
\(259\) | 1.64484 | 0.102206 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 48.4950 | 3.00176 | ||||||||
\(262\) | −8.12511 | −0.501971 | ||||||||
\(263\) | −4.06910 | −0.250911 | −0.125456 | − | 0.992099i | \(-0.540039\pi\) | ||||
−0.125456 | + | 0.992099i | \(0.540039\pi\) | |||||||
\(264\) | −9.94618 | −0.612145 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.726907 | 0.0445696 | ||||||||
\(267\) | −46.2252 | −2.82894 | ||||||||
\(268\) | 0.691384 | 0.0422330 | ||||||||
\(269\) | 0.181743 | 0.0110811 | 0.00554055 | − | 0.999985i | \(-0.498236\pi\) | ||||
0.00554055 | + | 0.999985i | \(0.498236\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.15652 | −0.252491 | −0.126245 | − | 0.991999i | \(-0.540293\pi\) | ||||
−0.126245 | + | 0.991999i | \(0.540293\pi\) | |||||||
\(272\) | 0.305204 | 0.0185057 | ||||||||
\(273\) | −3.16145 | −0.191340 | ||||||||
\(274\) | 12.7695 | 0.771436 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.693698 | −0.0417557 | ||||||||
\(277\) | 31.6346 | 1.90074 | 0.950368 | − | 0.311127i | \(-0.100706\pi\) | ||||
0.950368 | + | 0.311127i | \(0.100706\pi\) | |||||||
\(278\) | 27.6532 | 1.65853 | ||||||||
\(279\) | 24.5727 | 1.47113 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.38352 | 0.0825337 | 0.0412668 | − | 0.999148i | \(-0.486861\pi\) | ||||
0.0412668 | + | 0.999148i | \(0.486861\pi\) | |||||||
\(282\) | 37.9088 | 2.25744 | ||||||||
\(283\) | 25.1918 | 1.49750 | 0.748749 | − | 0.662854i | \(-0.230655\pi\) | ||||
0.748749 | + | 0.662854i | \(0.230655\pi\) | |||||||
\(284\) | −1.02983 | −0.0611090 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.19239 | −0.129639 | ||||||||
\(287\) | 0.316920 | 0.0187072 | ||||||||
\(288\) | 14.8434 | 0.874653 | ||||||||
\(289\) | −16.9910 | −0.999470 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 20.2593 | 1.18762 | ||||||||
\(292\) | 1.88702 | 0.110430 | ||||||||
\(293\) | 11.8433 | 0.691895 | 0.345947 | − | 0.938254i | \(-0.387558\pi\) | ||||
0.345947 | + | 0.938254i | \(0.387558\pi\) | |||||||
\(294\) | −28.4502 | −1.65925 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.79546 | −0.511226 | ||||||||
\(297\) | 16.1539 | 0.937343 | ||||||||
\(298\) | −6.52500 | −0.377983 | ||||||||
\(299\) | −1.06261 | −0.0614522 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.18529 | 0.356514 | ||||||||
\(302\) | −17.3550 | −0.998668 | ||||||||
\(303\) | 40.9863 | 2.35460 | ||||||||
\(304\) | −3.21464 | −0.184372 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.966761 | −0.0552661 | ||||||||
\(307\) | −12.4995 | −0.713385 | −0.356692 | − | 0.934222i | \(-0.616096\pi\) | ||||
−0.356692 | + | 0.934222i | \(0.616096\pi\) | |||||||
\(308\) | −0.189448 | −0.0107948 | ||||||||
\(309\) | −35.3283 | −2.00976 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.01056 | −0.227418 | −0.113709 | − | 0.993514i | \(-0.536273\pi\) | ||||
−0.113709 | + | 0.993514i | \(0.536273\pi\) | |||||||
\(312\) | 16.9052 | 0.957069 | ||||||||
\(313\) | 19.8467 | 1.12180 | 0.560901 | − | 0.827883i | \(-0.310455\pi\) | ||||
0.560901 | + | 0.827883i | \(0.310455\pi\) | |||||||
\(314\) | 3.31135 | 0.186870 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.80560 | 0.101573 | ||||||||
\(317\) | −16.2627 | −0.913406 | −0.456703 | − | 0.889619i | \(-0.650970\pi\) | ||||
−0.456703 | + | 0.889619i | \(0.650970\pi\) | |||||||
\(318\) | −2.08330 | −0.116825 | ||||||||
\(319\) | 6.14313 | 0.343949 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.35770 | 0.466481 | ||||||||
\(322\) | 0.454452 | 0.0253256 | ||||||||
\(323\) | −0.0949420 | −0.00528272 | ||||||||
\(324\) | −9.96269 | −0.553483 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −18.4871 | −1.02390 | ||||||||
\(327\) | −33.9443 | −1.87712 | ||||||||
\(328\) | −1.69466 | −0.0935721 | ||||||||
\(329\) | 5.01781 | 0.276641 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.4946 | 0.961593 | 0.480796 | − | 0.876832i | \(-0.340348\pi\) | ||||
0.480796 | + | 0.876832i | \(0.340348\pi\) | |||||||
\(332\) | −0.831590 | −0.0456394 | ||||||||
\(333\) | 23.0413 | 1.26265 | ||||||||
\(334\) | −21.8936 | −1.19796 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −5.97936 | −0.326201 | ||||||||
\(337\) | −34.0435 | −1.85447 | −0.927234 | − | 0.374482i | \(-0.877821\pi\) | ||||
−0.927234 | + | 0.374482i | \(0.877821\pi\) | |||||||
\(338\) | −13.0423 | −0.709407 | ||||||||
\(339\) | −56.1545 | −3.04989 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.11276 | 0.168566 | ||||||||
\(342\) | 10.1826 | 0.550615 | ||||||||
\(343\) | −7.71060 | −0.416333 | ||||||||
\(344\) | −33.0746 | −1.78326 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −32.2095 | −1.73159 | ||||||||
\(347\) | 18.8146 | 1.01002 | 0.505011 | − | 0.863113i | \(-0.331488\pi\) | ||||
0.505011 | + | 0.863113i | \(0.331488\pi\) | |||||||
\(348\) | −6.81635 | −0.365394 | ||||||||
\(349\) | 26.8633 | 1.43796 | 0.718981 | − | 0.695030i | \(-0.244609\pi\) | ||||
0.718981 | + | 0.695030i | \(0.244609\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −27.4562 | −1.46551 | ||||||||
\(352\) | 1.88029 | 0.100220 | ||||||||
\(353\) | −8.92277 | −0.474911 | −0.237456 | − | 0.971398i | \(-0.576313\pi\) | ||||
−0.237456 | + | 0.971398i | \(0.576313\pi\) | |||||||
\(354\) | −49.3688 | −2.62392 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.70811 | 0.249529 | ||||||||
\(357\) | −0.176596 | −0.00934645 | ||||||||
\(358\) | 2.90977 | 0.153786 | ||||||||
\(359\) | 4.83871 | 0.255377 | 0.127689 | − | 0.991814i | \(-0.459244\pi\) | ||||
0.127689 | + | 0.991814i | \(0.459244\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 6.63688 | 0.348826 | ||||||||
\(363\) | 3.30063 | 0.173238 | ||||||||
\(364\) | 0.321998 | 0.0168773 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 58.9981 | 3.08388 | ||||||||
\(367\) | 17.7897 | 0.928614 | 0.464307 | − | 0.885674i | \(-0.346303\pi\) | ||||
0.464307 | + | 0.885674i | \(0.346303\pi\) | |||||||
\(368\) | −2.00975 | −0.104765 | ||||||||
\(369\) | 4.43947 | 0.231110 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.275756 | −0.0143165 | ||||||||
\(372\) | −3.45388 | −0.179076 | ||||||||
\(373\) | 6.12381 | 0.317079 | 0.158539 | − | 0.987353i | \(-0.449322\pi\) | ||||
0.158539 | + | 0.987353i | \(0.449322\pi\) | |||||||
\(374\) | −0.122465 | −0.00633252 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −26.8317 | −1.38374 | ||||||||
\(377\) | −10.4413 | −0.537753 | ||||||||
\(378\) | 11.7424 | 0.603963 | ||||||||
\(379\) | −24.5784 | −1.26251 | −0.631255 | − | 0.775575i | \(-0.717460\pi\) | ||||
−0.631255 | + | 0.775575i | \(0.717460\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.0366 | −0.975276 | ||||||||
\(382\) | −1.59290 | −0.0814999 | ||||||||
\(383\) | −29.3567 | −1.50006 | −0.750029 | − | 0.661405i | \(-0.769960\pi\) | ||||
−0.750029 | + | 0.661405i | \(0.769960\pi\) | |||||||
\(384\) | 25.2861 | 1.29037 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.24455 | −0.419637 | ||||||||
\(387\) | 86.6447 | 4.40440 | ||||||||
\(388\) | −2.06344 | −0.104755 | ||||||||
\(389\) | 23.3372 | 1.18324 | 0.591621 | − | 0.806216i | \(-0.298488\pi\) | ||||
0.591621 | + | 0.806216i | \(0.298488\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.0593564 | −0.00300178 | ||||||||
\(392\) | 20.1369 | 1.01707 | ||||||||
\(393\) | −20.7909 | −1.04876 | ||||||||
\(394\) | 6.74888 | 0.340004 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.65382 | −0.133359 | ||||||||
\(397\) | −14.4695 | −0.726202 | −0.363101 | − | 0.931750i | \(-0.618282\pi\) | ||||
−0.363101 | + | 0.931750i | \(0.618282\pi\) | |||||||
\(398\) | −24.6446 | −1.23532 | ||||||||
\(399\) | 1.86004 | 0.0931185 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.7693 | −0.637668 | −0.318834 | − | 0.947811i | \(-0.603291\pi\) | ||||
−0.318834 | + | 0.947811i | \(0.603291\pi\) | |||||||
\(402\) | −8.75600 | −0.436710 | ||||||||
\(403\) | −5.29066 | −0.263547 | ||||||||
\(404\) | −4.17451 | −0.207690 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.46549 | 0.221618 | ||||||||
\(407\) | 2.91877 | 0.144678 | ||||||||
\(408\) | 0.944311 | 0.0467504 | ||||||||
\(409\) | −23.0952 | −1.14198 | −0.570991 | − | 0.820956i | \(-0.693441\pi\) | ||||
−0.570991 | + | 0.820956i | \(0.693441\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 32.6752 | 1.61175 | ||||||||
\(412\) | 3.59824 | 0.177273 | ||||||||
\(413\) | −6.53472 | −0.321552 | ||||||||
\(414\) | 6.36604 | 0.312874 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.19587 | −0.156690 | ||||||||
\(417\) | 70.7601 | 3.46513 | ||||||||
\(418\) | 1.28989 | 0.0630908 | ||||||||
\(419\) | −2.04650 | −0.0999783 | −0.0499891 | − | 0.998750i | \(-0.515919\pi\) | ||||
−0.0499891 | + | 0.998750i | \(0.515919\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.36047 | 0.212516 | 0.106258 | − | 0.994339i | \(-0.466113\pi\) | ||||
0.106258 | + | 0.994339i | \(0.466113\pi\) | |||||||
\(422\) | −4.41163 | −0.214755 | ||||||||
\(423\) | 70.2903 | 3.41763 | ||||||||
\(424\) | 1.47455 | 0.0716104 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 13.0422 | 0.631897 | ||||||||
\(427\) | 7.80930 | 0.377918 | ||||||||
\(428\) | −0.851244 | −0.0411464 | ||||||||
\(429\) | −5.60998 | −0.270852 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.2001 | 0.732165 | 0.366083 | − | 0.930582i | \(-0.380699\pi\) | ||||
0.366083 | + | 0.930582i | \(0.380699\pi\) | |||||||
\(432\) | −51.9289 | −2.49843 | ||||||||
\(433\) | 14.5469 | 0.699081 | 0.349541 | − | 0.936921i | \(-0.386338\pi\) | ||||
0.349541 | + | 0.936921i | \(0.386338\pi\) | |||||||
\(434\) | 2.26269 | 0.108613 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.45728 | 0.165574 | ||||||||
\(437\) | 0.625186 | 0.0299067 | ||||||||
\(438\) | −23.8981 | −1.14189 | ||||||||
\(439\) | 34.3065 | 1.63736 | 0.818680 | − | 0.574250i | \(-0.194706\pi\) | ||||
0.818680 | + | 0.574250i | \(0.194706\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −52.7522 | −2.51201 | ||||||||
\(442\) | 0.208150 | 0.00990069 | ||||||||
\(443\) | 1.56134 | 0.0741813 | 0.0370907 | − | 0.999312i | \(-0.488191\pi\) | ||||
0.0370907 | + | 0.999312i | \(0.488191\pi\) | |||||||
\(444\) | −3.23863 | −0.153699 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −13.6918 | −0.648327 | ||||||||
\(447\) | −16.6964 | −0.789715 | ||||||||
\(448\) | 4.98996 | 0.235753 | ||||||||
\(449\) | −20.7918 | −0.981228 | −0.490614 | − | 0.871377i | \(-0.663227\pi\) | ||||
−0.490614 | + | 0.871377i | \(0.663227\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.562373 | 0.0264811 | ||||||||
\(452\) | 5.71942 | 0.269019 | ||||||||
\(453\) | −44.4087 | −2.08650 | ||||||||
\(454\) | 9.27391 | 0.435246 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.94618 | −0.465773 | ||||||||
\(457\) | 3.00835 | 0.140725 | 0.0703624 | − | 0.997521i | \(-0.477584\pi\) | ||||
0.0703624 | + | 0.997521i | \(0.477584\pi\) | |||||||
\(458\) | −27.3407 | −1.27755 | ||||||||
\(459\) | −1.53368 | −0.0715862 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.5782 | 0.772122 | 0.386061 | − | 0.922473i | \(-0.373835\pi\) | ||||
0.386061 | + | 0.922473i | \(0.373835\pi\) | |||||||
\(462\) | 2.39925 | 0.111623 | ||||||||
\(463\) | 28.9063 | 1.34339 | 0.671694 | − | 0.740828i | \(-0.265567\pi\) | ||||
0.671694 | + | 0.740828i | \(0.265567\pi\) | |||||||
\(464\) | −19.7479 | −0.916775 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 34.5522 | 1.60060 | ||||||||
\(467\) | 7.97738 | 0.369149 | 0.184574 | − | 0.982819i | \(-0.440909\pi\) | ||||
0.184574 | + | 0.982819i | \(0.440909\pi\) | |||||||
\(468\) | 4.51061 | 0.208503 | ||||||||
\(469\) | −1.15899 | −0.0535172 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.47321 | 0.390425 | ||||||||
\(472\) | 34.9430 | 1.60838 | ||||||||
\(473\) | 10.9758 | 0.504667 | ||||||||
\(474\) | −22.8670 | −1.05031 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.0179866 | 0.000824413 0 | ||||||||
\(477\) | −3.86284 | −0.176867 | ||||||||
\(478\) | 6.82826 | 0.312317 | ||||||||
\(479\) | −2.05076 | −0.0937014 | −0.0468507 | − | 0.998902i | \(-0.514919\pi\) | ||||
−0.0468507 | + | 0.998902i | \(0.514919\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.96093 | −0.226199 | ||||||||
\(482\) | 1.99330 | 0.0907923 | ||||||||
\(483\) | 1.16287 | 0.0529124 | ||||||||
\(484\) | −0.336174 | −0.0152807 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 63.6617 | 2.88775 | ||||||||
\(487\) | 19.7907 | 0.896804 | 0.448402 | − | 0.893832i | \(-0.351993\pi\) | ||||
0.448402 | + | 0.893832i | \(0.351993\pi\) | |||||||
\(488\) | −41.7586 | −1.89032 | ||||||||
\(489\) | −47.3055 | −2.13923 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.00033 | −0.225662 | −0.112831 | − | 0.993614i | \(-0.535992\pi\) | ||||
−0.112831 | + | 0.993614i | \(0.535992\pi\) | |||||||
\(492\) | −0.624002 | −0.0281322 | ||||||||
\(493\) | −0.583242 | −0.0262679 | ||||||||
\(494\) | −2.19239 | −0.0986403 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.0064 | −0.449301 | ||||||||
\(497\) | 1.72634 | 0.0774367 | ||||||||
\(498\) | 10.5316 | 0.471934 | ||||||||
\(499\) | 31.6046 | 1.41481 | 0.707407 | − | 0.706806i | \(-0.249865\pi\) | ||||
0.707407 | + | 0.706806i | \(0.249865\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −56.0222 | −2.50289 | ||||||||
\(502\) | −30.5923 | −1.36540 | ||||||||
\(503\) | −19.0877 | −0.851080 | −0.425540 | − | 0.904940i | \(-0.639916\pi\) | ||||
−0.425540 | + | 0.904940i | \(0.639916\pi\) | |||||||
\(504\) | −13.4058 | −0.597140 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.806423 | 0.0358499 | ||||||||
\(507\) | −33.3731 | −1.48215 | ||||||||
\(508\) | 1.93891 | 0.0860251 | ||||||||
\(509\) | 42.8558 | 1.89955 | 0.949775 | − | 0.312934i | \(-0.101312\pi\) | ||||
0.949775 | + | 0.312934i | \(0.101312\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.16328 | −0.139935 | ||||||||
\(512\) | −25.4185 | −1.12335 | ||||||||
\(513\) | 16.1539 | 0.713211 | ||||||||
\(514\) | −3.29275 | −0.145237 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −12.1786 | −0.536132 | ||||||||
\(517\) | 8.90408 | 0.391601 | ||||||||
\(518\) | 2.12167 | 0.0932210 | ||||||||
\(519\) | −82.4189 | −3.61779 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.32945 | −0.0582443 | −0.0291222 | − | 0.999576i | \(-0.509271\pi\) | ||||
−0.0291222 | + | 0.999576i | \(0.509271\pi\) | |||||||
\(522\) | 62.5534 | 2.73789 | ||||||||
\(523\) | 19.3395 | 0.845656 | 0.422828 | − | 0.906210i | \(-0.361037\pi\) | ||||
0.422828 | + | 0.906210i | \(0.361037\pi\) | |||||||
\(524\) | 2.11758 | 0.0925069 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.24871 | −0.228854 | ||||||||
\(527\) | −0.295532 | −0.0128736 | ||||||||
\(528\) | −10.6103 | −0.461756 | ||||||||
\(529\) | −22.6091 | −0.983006 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −91.5395 | −3.97248 | ||||||||
\(532\) | −0.189448 | −0.00821361 | ||||||||
\(533\) | −0.955847 | −0.0414023 | ||||||||
\(534\) | −59.6257 | −2.58025 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.19746 | 0.267690 | ||||||||
\(537\) | 7.44563 | 0.321303 | ||||||||
\(538\) | 0.234430 | 0.0101070 | ||||||||
\(539\) | −6.68242 | −0.287832 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.6158 | −0.585390 | −0.292695 | − | 0.956206i | \(-0.594552\pi\) | ||||
−0.292695 | + | 0.956206i | \(0.594552\pi\) | |||||||
\(542\) | −5.36147 | −0.230295 | ||||||||
\(543\) | 16.9827 | 0.728798 | ||||||||
\(544\) | −0.178519 | −0.00765393 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.07794 | −0.174520 | ||||||||
\(547\) | −35.4126 | −1.51413 | −0.757066 | − | 0.653339i | \(-0.773368\pi\) | ||||
−0.757066 | + | 0.653339i | \(0.773368\pi\) | |||||||
\(548\) | −3.32802 | −0.142166 | ||||||||
\(549\) | 109.394 | 4.66882 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.14313 | 0.261706 | ||||||||
\(552\) | −6.21821 | −0.264665 | ||||||||
\(553\) | −3.02679 | −0.128712 | ||||||||
\(554\) | 40.8052 | 1.73365 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.20702 | −0.305646 | ||||||||
\(557\) | −2.52845 | −0.107134 | −0.0535669 | − | 0.998564i | \(-0.517059\pi\) | ||||
−0.0535669 | + | 0.998564i | \(0.517059\pi\) | |||||||
\(558\) | 31.6962 | 1.34181 | ||||||||
\(559\) | −18.6552 | −0.789030 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.313369 | −0.0132304 | ||||||||
\(562\) | 1.78459 | 0.0752784 | ||||||||
\(563\) | −22.8087 | −0.961274 | −0.480637 | − | 0.876920i | \(-0.659594\pi\) | ||||
−0.480637 | + | 0.876920i | \(0.659594\pi\) | |||||||
\(564\) | −9.87986 | −0.416017 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 32.4948 | 1.36586 | ||||||||
\(567\) | 16.7008 | 0.701368 | ||||||||
\(568\) | −9.23122 | −0.387334 | ||||||||
\(569\) | −14.2866 | −0.598926 | −0.299463 | − | 0.954108i | \(-0.596807\pi\) | ||||
−0.299463 | + | 0.954108i | \(0.596807\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.3152 | −0.473527 | −0.236764 | − | 0.971567i | \(-0.576087\pi\) | ||||
−0.236764 | + | 0.971567i | \(0.576087\pi\) | |||||||
\(572\) | 0.571385 | 0.0238908 | ||||||||
\(573\) | −4.07598 | −0.170277 | ||||||||
\(574\) | 0.408793 | 0.0170627 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 69.9002 | 2.91251 | ||||||||
\(577\) | −43.3748 | −1.80572 | −0.902858 | − | 0.429938i | \(-0.858535\pi\) | ||||
−0.902858 | + | 0.429938i | \(0.858535\pi\) | |||||||
\(578\) | −21.9166 | −0.911609 | ||||||||
\(579\) | −21.0965 | −0.876740 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.39402 | 0.0578338 | ||||||||
\(582\) | 26.1324 | 1.08322 | ||||||||
\(583\) | −0.489328 | −0.0202659 | ||||||||
\(584\) | 16.9150 | 0.699946 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.2766 | 0.631072 | ||||||||
\(587\) | −21.8206 | −0.900633 | −0.450317 | − | 0.892869i | \(-0.648689\pi\) | ||||
−0.450317 | + | 0.892869i | \(0.648689\pi\) | |||||||
\(588\) | 7.41473 | 0.305779 | ||||||||
\(589\) | 3.11276 | 0.128259 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.2693 | 0.710365 | ||||||||
\(592\) | −9.38278 | −0.385630 | ||||||||
\(593\) | −40.6744 | −1.67030 | −0.835149 | − | 0.550025i | \(-0.814618\pi\) | ||||
−0.835149 | + | 0.550025i | \(0.814618\pi\) | |||||||
\(594\) | 20.8368 | 0.854944 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.70056 | 0.0696575 | ||||||||
\(597\) | −63.0616 | −2.58094 | ||||||||
\(598\) | −1.37065 | −0.0560501 | ||||||||
\(599\) | −33.5105 | −1.36920 | −0.684601 | − | 0.728918i | \(-0.740024\pi\) | ||||
−0.684601 | + | 0.728918i | \(0.740024\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.85454 | 0.361184 | 0.180592 | − | 0.983558i | \(-0.442199\pi\) | ||||
0.180592 | + | 0.983558i | \(0.442199\pi\) | |||||||
\(602\) | 7.97837 | 0.325174 | ||||||||
\(603\) | −16.2353 | −0.661154 | ||||||||
\(604\) | 4.52309 | 0.184042 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 52.8680 | 2.14761 | ||||||||
\(607\) | −38.7846 | −1.57422 | −0.787109 | − | 0.616814i | \(-0.788423\pi\) | ||||
−0.787109 | + | 0.616814i | \(0.788423\pi\) | |||||||
\(608\) | 1.88029 | 0.0762559 | ||||||||
\(609\) | 11.4265 | 0.463024 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.1340 | −0.612255 | ||||||||
\(612\) | 0.251959 | 0.0101848 | ||||||||
\(613\) | −11.4604 | −0.462883 | −0.231441 | − | 0.972849i | \(-0.574344\pi\) | ||||
−0.231441 | + | 0.972849i | \(0.574344\pi\) | |||||||
\(614\) | −16.1230 | −0.650673 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.69818 | −0.0684217 | ||||||||
\(617\) | 44.6630 | 1.79806 | 0.899032 | − | 0.437884i | \(-0.144272\pi\) | ||||
0.899032 | + | 0.437884i | \(0.144272\pi\) | |||||||
\(618\) | −45.5698 | −1.83309 | ||||||||
\(619\) | −10.0641 | −0.404508 | −0.202254 | − | 0.979333i | \(-0.564827\pi\) | ||||
−0.202254 | + | 0.979333i | \(0.564827\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.0992 | 0.405266 | ||||||||
\(622\) | −5.17320 | −0.207427 | ||||||||
\(623\) | −7.89237 | −0.316201 | ||||||||
\(624\) | 18.0341 | 0.721940 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 25.6001 | 1.02319 | ||||||||
\(627\) | 3.30063 | 0.131815 | ||||||||
\(628\) | −0.863009 | −0.0344378 | ||||||||
\(629\) | −0.277114 | −0.0110492 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.9805 | −1.31293 | −0.656466 | − | 0.754356i | \(-0.727949\pi\) | ||||
−0.656466 | + | 0.754356i | \(0.727949\pi\) | |||||||
\(632\) | 16.1851 | 0.643811 | ||||||||
\(633\) | −11.2887 | −0.448684 | ||||||||
\(634\) | −20.9772 | −0.833110 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.542952 | 0.0215295 | ||||||||
\(637\) | 11.3579 | 0.450016 | ||||||||
\(638\) | 7.92399 | 0.313714 | ||||||||
\(639\) | 24.1828 | 0.956658 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.4514 | −0.610292 | −0.305146 | − | 0.952306i | \(-0.598705\pi\) | ||||
−0.305146 | + | 0.952306i | \(0.598705\pi\) | |||||||
\(642\) | 10.7805 | 0.425474 | ||||||||
\(643\) | 26.4799 | 1.04427 | 0.522133 | − | 0.852864i | \(-0.325136\pi\) | ||||
0.522133 | + | 0.852864i | \(0.325136\pi\) | |||||||
\(644\) | −0.118440 | −0.00466719 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.122465 | −0.00481833 | ||||||||
\(647\) | 40.9548 | 1.61010 | 0.805050 | − | 0.593207i | \(-0.202138\pi\) | ||||
0.805050 | + | 0.593207i | \(0.202138\pi\) | |||||||
\(648\) | −89.3041 | −3.50820 | ||||||||
\(649\) | −11.5958 | −0.455176 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.78986 | 0.226923 | ||||||||
\(652\) | 4.81813 | 0.188693 | ||||||||
\(653\) | −23.3051 | −0.911997 | −0.455999 | − | 0.889980i | \(-0.650718\pi\) | ||||
−0.455999 | + | 0.889980i | \(0.650718\pi\) | |||||||
\(654\) | −43.7846 | −1.71211 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.80782 | −0.0705837 | ||||||||
\(657\) | −44.3118 | −1.72877 | ||||||||
\(658\) | 6.47244 | 0.252322 | ||||||||
\(659\) | 10.8517 | 0.422723 | 0.211361 | − | 0.977408i | \(-0.432210\pi\) | ||||
0.211361 | + | 0.977408i | \(0.432210\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.94285 | 0.347837 | 0.173918 | − | 0.984760i | \(-0.444357\pi\) | ||||
0.173918 | + | 0.984760i | \(0.444357\pi\) | |||||||
\(662\) | 22.5662 | 0.877062 | ||||||||
\(663\) | 0.532623 | 0.0206854 | ||||||||
\(664\) | −7.45425 | −0.289281 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 29.7208 | 1.15166 | ||||||||
\(667\) | 3.84060 | 0.148709 | ||||||||
\(668\) | 5.70594 | 0.220769 | ||||||||
\(669\) | −35.0352 | −1.35454 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.8576 | 0.534965 | ||||||||
\(672\) | 3.49742 | 0.134916 | ||||||||
\(673\) | −8.94979 | −0.344989 | −0.172494 | − | 0.985010i | \(-0.555183\pi\) | ||||
−0.172494 | + | 0.985010i | \(0.555183\pi\) | |||||||
\(674\) | −43.9125 | −1.69145 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.39910 | 0.130735 | ||||||||
\(677\) | 8.30060 | 0.319018 | 0.159509 | − | 0.987196i | \(-0.449009\pi\) | ||||
0.159509 | + | 0.987196i | \(0.449009\pi\) | |||||||
\(678\) | −72.4333 | −2.78178 | ||||||||
\(679\) | 3.45902 | 0.132745 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.7305 | 0.909353 | ||||||||
\(682\) | 4.01513 | 0.153747 | ||||||||
\(683\) | 37.6902 | 1.44217 | 0.721087 | − | 0.692844i | \(-0.243643\pi\) | ||||
0.721087 | + | 0.692844i | \(0.243643\pi\) | |||||||
\(684\) | −2.65382 | −0.101471 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −9.94585 | −0.379734 | ||||||||
\(687\) | −69.9604 | −2.66916 | ||||||||
\(688\) | −35.2831 | −1.34516 | ||||||||
\(689\) | 0.831695 | 0.0316851 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −49.0286 | −1.86514 | −0.932568 | − | 0.360994i | \(-0.882437\pi\) | ||||
−0.932568 | + | 0.360994i | \(0.882437\pi\) | |||||||
\(692\) | 8.39449 | 0.319111 | ||||||||
\(693\) | 4.44869 | 0.168992 | ||||||||
\(694\) | 24.2689 | 0.921234 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −61.1007 | −2.31602 | ||||||||
\(697\) | −0.0533928 | −0.00202240 | ||||||||
\(698\) | 34.6509 | 1.31155 | ||||||||
\(699\) | 88.4136 | 3.34411 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.98928 | −0.339520 | −0.169760 | − | 0.985485i | \(-0.554299\pi\) | ||||
−0.169760 | + | 0.985485i | \(0.554299\pi\) | |||||||
\(702\) | −35.4156 | −1.33668 | ||||||||
\(703\) | 2.91877 | 0.110083 | ||||||||
\(704\) | 8.85465 | 0.333722 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11.5094 | −0.433163 | ||||||||
\(707\) | 6.99788 | 0.263182 | ||||||||
\(708\) | 12.8666 | 0.483556 | ||||||||
\(709\) | 22.4894 | 0.844607 | 0.422303 | − | 0.906455i | \(-0.361222\pi\) | ||||
0.422303 | + | 0.906455i | \(0.361222\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −42.3999 | −1.59012 | ||||||||
\(712\) | 42.2028 | 1.58162 | ||||||||
\(713\) | 1.94605 | 0.0728803 | ||||||||
\(714\) | −0.227790 | −0.00852483 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.758349 | −0.0283408 | ||||||||
\(717\) | 17.4724 | 0.652520 | ||||||||
\(718\) | 6.24142 | 0.232928 | ||||||||
\(719\) | −27.3255 | −1.01907 | −0.509534 | − | 0.860450i | \(-0.670182\pi\) | ||||
−0.509534 | + | 0.860450i | \(0.670182\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.03186 | −0.224638 | ||||||||
\(722\) | 1.28989 | 0.0480049 | ||||||||
\(723\) | 5.10054 | 0.189691 | ||||||||
\(724\) | −1.72971 | −0.0642843 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.25747 | 0.158009 | ||||||||
\(727\) | 45.7801 | 1.69789 | 0.848945 | − | 0.528482i | \(-0.177238\pi\) | ||||
0.848945 | + | 0.528482i | \(0.177238\pi\) | |||||||
\(728\) | 2.88635 | 0.106975 | ||||||||
\(729\) | 73.9938 | 2.74051 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.04206 | −0.0385421 | ||||||||
\(732\) | −15.3762 | −0.568320 | ||||||||
\(733\) | 19.9594 | 0.737219 | 0.368610 | − | 0.929584i | \(-0.379834\pi\) | ||||
0.368610 | + | 0.929584i | \(0.379834\pi\) | |||||||
\(734\) | 22.9468 | 0.846982 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.17553 | 0.0433306 | ||||||||
\(737\) | −2.05662 | −0.0757567 | ||||||||
\(738\) | 5.72644 | 0.210793 | ||||||||
\(739\) | 22.5149 | 0.828226 | 0.414113 | − | 0.910226i | \(-0.364092\pi\) | ||||
0.414113 | + | 0.910226i | \(0.364092\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.60998 | −0.206088 | ||||||||
\(742\) | −0.355696 | −0.0130580 | ||||||||
\(743\) | 26.2969 | 0.964739 | 0.482370 | − | 0.875968i | \(-0.339776\pi\) | ||||
0.482370 | + | 0.875968i | \(0.339776\pi\) | |||||||
\(744\) | −30.9601 | −1.13505 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.89906 | 0.289205 | ||||||||
\(747\) | 19.5277 | 0.714482 | ||||||||
\(748\) | 0.0319171 | 0.00116700 | ||||||||
\(749\) | 1.42697 | 0.0521404 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.3472 | −0.997914 | −0.498957 | − | 0.866627i | \(-0.666283\pi\) | ||||
−0.498957 | + | 0.866627i | \(0.666283\pi\) | |||||||
\(752\) | −28.6234 | −1.04379 | ||||||||
\(753\) | −78.2809 | −2.85272 | ||||||||
\(754\) | −13.4681 | −0.490481 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.06032 | −0.111303 | ||||||||
\(757\) | 23.2243 | 0.844102 | 0.422051 | − | 0.906572i | \(-0.361310\pi\) | ||||
0.422051 | + | 0.906572i | \(0.361310\pi\) | |||||||
\(758\) | −31.7036 | −1.15153 | ||||||||
\(759\) | 2.06351 | 0.0749006 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.8028 | −1.40660 | −0.703300 | − | 0.710893i | \(-0.748291\pi\) | ||||
−0.703300 | + | 0.710893i | \(0.748291\pi\) | |||||||
\(762\) | −24.5552 | −0.889542 | ||||||||
\(763\) | −5.79555 | −0.209813 | ||||||||
\(764\) | 0.415145 | 0.0150194 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −37.8670 | −1.36819 | ||||||||
\(767\) | 19.7090 | 0.711653 | ||||||||
\(768\) | −25.8356 | −0.932261 | ||||||||
\(769\) | 2.29406 | 0.0827261 | 0.0413630 | − | 0.999144i | \(-0.486830\pi\) | ||||
0.0413630 | + | 0.999144i | \(0.486830\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.42561 | −0.303441 | ||||||||
\(772\) | 2.14871 | 0.0773337 | ||||||||
\(773\) | −52.2893 | −1.88071 | −0.940357 | − | 0.340189i | \(-0.889509\pi\) | ||||
−0.940357 | + | 0.340189i | \(0.889509\pi\) | |||||||
\(774\) | 111.762 | 4.01722 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −18.4964 | −0.663982 | ||||||||
\(777\) | 5.42902 | 0.194765 | ||||||||
\(778\) | 30.1025 | 1.07923 | ||||||||
\(779\) | 0.562373 | 0.0201491 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.06337 | 0.109616 | ||||||||
\(782\) | −0.0765634 | −0.00273790 | ||||||||
\(783\) | 99.2354 | 3.54638 | ||||||||
\(784\) | 21.4816 | 0.767199 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −26.8180 | −0.956567 | ||||||||
\(787\) | −9.08106 | −0.323705 | −0.161852 | − | 0.986815i | \(-0.551747\pi\) | ||||
−0.161852 | + | 0.986815i | \(0.551747\pi\) | |||||||
\(788\) | −1.75891 | −0.0626584 | ||||||||
\(789\) | −13.4306 | −0.478142 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.58765 | −0.340898 | ||||||||
\(792\) | −23.7884 | −0.845285 | ||||||||
\(793\) | −23.5532 | −0.836400 | ||||||||
\(794\) | −18.6641 | −0.662363 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.42292 | 0.227654 | ||||||||
\(797\) | −16.3422 | −0.578870 | −0.289435 | − | 0.957198i | \(-0.593467\pi\) | ||||
−0.289435 | + | 0.957198i | \(0.593467\pi\) | |||||||
\(798\) | 2.39925 | 0.0849327 | ||||||||
\(799\) | −0.845371 | −0.0299071 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −110.558 | −3.90636 | ||||||||
\(802\) | −16.4710 | −0.581612 | ||||||||
\(803\) | −5.61322 | −0.198086 | ||||||||
\(804\) | 2.28200 | 0.0804801 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.82439 | −0.240379 | ||||||||
\(807\) | 0.599868 | 0.0211164 | ||||||||
\(808\) | −37.4197 | −1.31642 | ||||||||
\(809\) | −3.54010 | −0.124463 | −0.0622317 | − | 0.998062i | \(-0.519822\pi\) | ||||
−0.0622317 | + | 0.998062i | \(0.519822\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.9605 | −1.15740 | −0.578699 | − | 0.815541i | \(-0.696439\pi\) | ||||
−0.578699 | + | 0.815541i | \(0.696439\pi\) | |||||||
\(812\) | −1.16380 | −0.0408415 | ||||||||
\(813\) | −13.7192 | −0.481152 | ||||||||
\(814\) | 3.76490 | 0.131960 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.00737 | 0.0352649 | ||||||||
\(817\) | 10.9758 | 0.383994 | ||||||||
\(818\) | −29.7903 | −1.04159 | ||||||||
\(819\) | −7.56129 | −0.264213 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.7416 | 0.654086 | 0.327043 | − | 0.945010i | \(-0.393948\pi\) | ||||
0.327043 | + | 0.945010i | \(0.393948\pi\) | |||||||
\(822\) | 42.1476 | 1.47007 | ||||||||
\(823\) | 22.5046 | 0.784462 | 0.392231 | − | 0.919867i | \(-0.371703\pi\) | ||||
0.392231 | + | 0.919867i | \(0.371703\pi\) | |||||||
\(824\) | 32.2541 | 1.12362 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.42909 | −0.293286 | ||||||||
\(827\) | 11.9403 | 0.415205 | 0.207603 | − | 0.978213i | \(-0.433434\pi\) | ||||
0.207603 | + | 0.978213i | \(0.433434\pi\) | |||||||
\(828\) | −1.65913 | −0.0576587 | ||||||||
\(829\) | 39.5586 | 1.37393 | 0.686964 | − | 0.726691i | \(-0.258943\pi\) | ||||
0.686964 | + | 0.726691i | \(0.258943\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 104.414 | 3.62208 | ||||||||
\(832\) | −15.0500 | −0.521764 | ||||||||
\(833\) | 0.634443 | 0.0219821 | ||||||||
\(834\) | 91.2729 | 3.16052 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.336174 | −0.0116268 | ||||||||
\(837\) | 50.2832 | 1.73804 | ||||||||
\(838\) | −2.63977 | −0.0911894 | ||||||||
\(839\) | −34.8294 | −1.20244 | −0.601222 | − | 0.799082i | \(-0.705319\pi\) | ||||
−0.601222 | + | 0.799082i | \(0.705319\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.73807 | 0.301313 | ||||||||
\(842\) | 5.62454 | 0.193835 | ||||||||
\(843\) | 4.56648 | 0.157278 | ||||||||
\(844\) | 1.14977 | 0.0395766 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 90.6671 | 3.11720 | ||||||||
\(847\) | 0.563541 | 0.0193635 | ||||||||
\(848\) | 1.57301 | 0.0540175 | ||||||||
\(849\) | 83.1489 | 2.85366 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.82477 | 0.0625523 | ||||||||
\(852\) | −3.39908 | −0.116451 | ||||||||
\(853\) | 55.1856 | 1.88952 | 0.944759 | − | 0.327765i | \(-0.106295\pi\) | ||||
0.944759 | + | 0.327765i | \(0.106295\pi\) | |||||||
\(854\) | 10.0732 | 0.344697 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.63043 | −0.260803 | ||||||||
\(857\) | 21.4134 | 0.731468 | 0.365734 | − | 0.930719i | \(-0.380818\pi\) | ||||
0.365734 | + | 0.930719i | \(0.380818\pi\) | |||||||
\(858\) | −7.23628 | −0.247042 | ||||||||
\(859\) | −36.5639 | −1.24754 | −0.623772 | − | 0.781606i | \(-0.714401\pi\) | ||||
−0.623772 | + | 0.781606i | \(0.714401\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.04604 | 0.0356488 | ||||||||
\(862\) | 19.6066 | 0.667802 | ||||||||
\(863\) | 52.7117 | 1.79433 | 0.897163 | − | 0.441699i | \(-0.145624\pi\) | ||||
0.897163 | + | 0.441699i | \(0.145624\pi\) | |||||||
\(864\) | 30.3740 | 1.03334 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 18.7640 | 0.637627 | ||||||||
\(867\) | −56.0810 | −1.90461 | ||||||||
\(868\) | −0.589706 | −0.0200159 | ||||||||
\(869\) | −5.37103 | −0.182200 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.49558 | 0.118443 | ||||||||
\(872\) | 30.9905 | 1.04947 | ||||||||
\(873\) | 48.4545 | 1.63994 | ||||||||
\(874\) | 0.806423 | 0.0272777 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.22836 | 0.210437 | ||||||||
\(877\) | 18.5720 | 0.627133 | 0.313566 | − | 0.949566i | \(-0.398476\pi\) | ||||
0.313566 | + | 0.949566i | \(0.398476\pi\) | |||||||
\(878\) | 44.2517 | 1.49342 | ||||||||
\(879\) | 39.0905 | 1.31849 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.2045 | −1.08500 | −0.542499 | − | 0.840056i | \(-0.682522\pi\) | ||||
−0.542499 | + | 0.840056i | \(0.682522\pi\) | |||||||
\(882\) | −68.0448 | −2.29119 | ||||||||
\(883\) | −41.2458 | −1.38803 | −0.694016 | − | 0.719960i | \(-0.744160\pi\) | ||||
−0.694016 | + | 0.719960i | \(0.744160\pi\) | |||||||
\(884\) | −0.0542484 | −0.00182457 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.01396 | 0.0676602 | ||||||||
\(887\) | −24.4058 | −0.819468 | −0.409734 | − | 0.912205i | \(-0.634379\pi\) | ||||
−0.409734 | + | 0.912205i | \(0.634379\pi\) | |||||||
\(888\) | −29.0306 | −0.974203 | ||||||||
\(889\) | −3.25026 | −0.109010 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 29.6355 | 0.992826 | ||||||||
\(892\) | 3.56839 | 0.119478 | ||||||||
\(893\) | 8.90408 | 0.297964 | ||||||||
\(894\) | −21.5366 | −0.720293 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.31727 | 0.144230 | ||||||||
\(897\) | −3.50728 | −0.117105 | ||||||||
\(898\) | −26.8193 | −0.894970 | ||||||||
\(899\) | 19.1221 | 0.637758 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.0464578 | 0.00154773 | ||||||||
\(902\) | 0.725401 | 0.0241532 | ||||||||
\(903\) | 20.4154 | 0.679381 | ||||||||
\(904\) | 51.2680 | 1.70515 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −57.2825 | −1.90308 | ||||||||
\(907\) | 47.4499 | 1.57555 | 0.787774 | − | 0.615965i | \(-0.211234\pi\) | ||||
0.787774 | + | 0.615965i | \(0.211234\pi\) | |||||||
\(908\) | −2.41698 | −0.0802104 | ||||||||
\(909\) | 98.0276 | 3.25137 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50.2159 | 1.66373 | 0.831863 | − | 0.554981i | \(-0.187275\pi\) | ||||
0.831863 | + | 0.554981i | \(0.187275\pi\) | |||||||
\(912\) | −10.6103 | −0.351343 | ||||||||
\(913\) | 2.47369 | 0.0818671 | ||||||||
\(914\) | 3.88046 | 0.128354 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.12557 | 0.235435 | ||||||||
\(917\) | −3.54977 | −0.117224 | ||||||||
\(918\) | −1.97829 | −0.0652932 | ||||||||
\(919\) | −0.561735 | −0.0185299 | −0.00926497 | − | 0.999957i | \(-0.502949\pi\) | ||||
−0.00926497 | + | 0.999957i | \(0.502949\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −41.2563 | −1.35944 | ||||||||
\(922\) | 21.3841 | 0.704247 | ||||||||
\(923\) | −5.20672 | −0.171381 | ||||||||
\(924\) | −0.625298 | −0.0205708 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 37.2860 | 1.22529 | ||||||||
\(927\) | −84.4953 | −2.77519 | ||||||||
\(928\) | 11.5509 | 0.379176 | ||||||||
\(929\) | 24.7806 | 0.813025 | 0.406513 | − | 0.913645i | \(-0.366745\pi\) | ||||
0.406513 | + | 0.913645i | \(0.366745\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.68242 | −0.219008 | ||||||||
\(932\) | −9.00506 | −0.294971 | ||||||||
\(933\) | −13.2374 | −0.433373 | ||||||||
\(934\) | 10.2900 | 0.336698 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 40.4324 | 1.32158 | ||||||||
\(937\) | 31.7278 | 1.03650 | 0.518251 | − | 0.855229i | \(-0.326583\pi\) | ||||
0.518251 | + | 0.855229i | \(0.326583\pi\) | |||||||
\(938\) | −1.49497 | −0.0488127 | ||||||||
\(939\) | 65.5067 | 2.13773 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.1062 | −0.785839 | −0.392920 | − | 0.919573i | \(-0.628535\pi\) | ||||
−0.392920 | + | 0.919573i | \(0.628535\pi\) | |||||||
\(942\) | 10.9295 | 0.356104 | ||||||||
\(943\) | 0.351587 | 0.0114493 | ||||||||
\(944\) | 37.2764 | 1.21324 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14.1576 | 0.460303 | ||||||||
\(947\) | −52.7844 | −1.71526 | −0.857631 | − | 0.514266i | \(-0.828064\pi\) | ||||
−0.857631 | + | 0.514266i | \(0.828064\pi\) | |||||||
\(948\) | 5.95963 | 0.193560 | ||||||||
\(949\) | 9.54061 | 0.309701 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −53.6773 | −1.74060 | ||||||||
\(952\) | 0.161229 | 0.00522546 | ||||||||
\(953\) | −43.2711 | −1.40169 | −0.700845 | − | 0.713314i | \(-0.747193\pi\) | ||||
−0.700845 | + | 0.713314i | \(0.747193\pi\) | |||||||
\(954\) | −4.98265 | −0.161319 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.77959 | −0.0575562 | ||||||||
\(957\) | 20.2762 | 0.655437 | ||||||||
\(958\) | −2.64526 | −0.0854644 | ||||||||
\(959\) | 5.57888 | 0.180151 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.3107 | −0.687442 | ||||||||
\(962\) | −6.39908 | −0.206315 | ||||||||
\(963\) | 19.9893 | 0.644145 | ||||||||
\(964\) | −0.519497 | −0.0167319 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.49998 | 0.0482610 | ||||||||
\(967\) | −28.7928 | −0.925915 | −0.462958 | − | 0.886380i | \(-0.653212\pi\) | ||||
−0.462958 | + | 0.886380i | \(0.653212\pi\) | |||||||
\(968\) | −3.01342 | −0.0968549 | ||||||||
\(969\) | −0.313369 | −0.0100669 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.3569 | 0.877923 | 0.438962 | − | 0.898506i | \(-0.355346\pi\) | ||||
0.438962 | + | 0.898506i | \(0.355346\pi\) | |||||||
\(972\) | −16.5916 | −0.532177 | ||||||||
\(973\) | 12.0814 | 0.387311 | ||||||||
\(974\) | 25.5280 | 0.817968 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −44.5470 | −1.42592 | ||||||||
\(977\) | 48.1900 | 1.54174 | 0.770868 | − | 0.636995i | \(-0.219823\pi\) | ||||
0.770868 | + | 0.636995i | \(0.219823\pi\) | |||||||
\(978\) | −61.0191 | −1.95117 | ||||||||
\(979\) | −14.0050 | −0.447601 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −81.1852 | −2.59204 | ||||||||
\(982\) | −6.44990 | −0.205824 | ||||||||
\(983\) | −38.6466 | −1.23264 | −0.616318 | − | 0.787498i | \(-0.711376\pi\) | ||||
−0.616318 | + | 0.787498i | \(0.711376\pi\) | |||||||
\(984\) | −5.59346 | −0.178313 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.752320 | −0.0239587 | ||||||||
\(987\) | 16.5619 | 0.527172 | ||||||||
\(988\) | 0.571385 | 0.0181782 | ||||||||
\(989\) | 6.86189 | 0.218196 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.47927 | 0.142289 | 0.0711444 | − | 0.997466i | \(-0.477335\pi\) | ||||
0.0711444 | + | 0.997466i | \(0.477335\pi\) | |||||||
\(992\) | 5.85290 | 0.185830 | ||||||||
\(993\) | 57.7434 | 1.83243 | ||||||||
\(994\) | 2.22679 | 0.0706295 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.74477 | −0.0869715 | ||||||||
\(997\) | 4.58855 | 0.145321 | 0.0726605 | − | 0.997357i | \(-0.476851\pi\) | ||||
0.0726605 | + | 0.997357i | \(0.476851\pi\) | |||||||
\(998\) | 40.7665 | 1.29044 | ||||||||
\(999\) | 47.1494 | 1.49174 |
(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 | 5225.2.a.y.1.10 | yes | 15 | |
5.4 | even | 2 | 5225.2.a.r.1.6 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5225.2.a.r.1.6 | ✓ | 15 | 5.4 | even | 2 | ||
5225.2.a.y.1.10 | yes | 15 | 1.1 | even | 1 | trivial |