Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.65285 | −1.16874 | −0.584372 | − | 0.811486i | \(-0.698659\pi\) | ||||
−0.584372 | + | 0.811486i | \(0.698659\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.731922 | 0.365961 | ||||||||
\(5\) | 2.84674 | 1.27310 | 0.636551 | − | 0.771235i | \(-0.280361\pi\) | ||||
0.636551 | + | 0.771235i | \(0.280361\pi\) | |||||||
\(6\) | 1.65285 | 0.674774 | ||||||||
\(7\) | −0.210210 | −0.0794519 | −0.0397260 | − | 0.999211i | \(-0.512648\pi\) | ||||
−0.0397260 | + | 0.999211i | \(0.512648\pi\) | |||||||
\(8\) | 2.09595 | 0.741029 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −4.70524 | −1.48793 | ||||||||
\(11\) | 5.85789 | 1.76622 | 0.883110 | − | 0.469167i | \(-0.155446\pi\) | ||||
0.883110 | + | 0.469167i | \(0.155446\pi\) | |||||||
\(12\) | −0.731922 | −0.211288 | ||||||||
\(13\) | 5.94416 | 1.64861 | 0.824307 | − | 0.566143i | \(-0.191565\pi\) | ||||
0.824307 | + | 0.566143i | \(0.191565\pi\) | |||||||
\(14\) | 0.347446 | 0.0928589 | ||||||||
\(15\) | −2.84674 | −0.735026 | ||||||||
\(16\) | −4.92813 | −1.23203 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −1.65285 | −0.389581 | ||||||||
\(19\) | −6.00132 | −1.37680 | −0.688399 | − | 0.725333i | \(-0.741686\pi\) | ||||
−0.688399 | + | 0.725333i | \(0.741686\pi\) | |||||||
\(20\) | 2.08359 | 0.465905 | ||||||||
\(21\) | 0.210210 | 0.0458716 | ||||||||
\(22\) | −9.68222 | −2.06426 | ||||||||
\(23\) | −1.53863 | −0.320826 | −0.160413 | − | 0.987050i | \(-0.551283\pi\) | ||||
−0.160413 | + | 0.987050i | \(0.551283\pi\) | |||||||
\(24\) | −2.09595 | −0.427833 | ||||||||
\(25\) | 3.10394 | 0.620788 | ||||||||
\(26\) | −9.82483 | −1.92681 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.153857 | −0.0290763 | ||||||||
\(29\) | 4.06149 | 0.754201 | 0.377100 | − | 0.926172i | \(-0.376921\pi\) | ||||
0.377100 | + | 0.926172i | \(0.376921\pi\) | |||||||
\(30\) | 4.70524 | 0.859056 | ||||||||
\(31\) | 1.55353 | 0.279022 | 0.139511 | − | 0.990221i | \(-0.455447\pi\) | ||||
0.139511 | + | 0.990221i | \(0.455447\pi\) | |||||||
\(32\) | 3.95359 | 0.698902 | ||||||||
\(33\) | −5.85789 | −1.01973 | ||||||||
\(34\) | −1.65285 | −0.283462 | ||||||||
\(35\) | −0.598414 | −0.101150 | ||||||||
\(36\) | 0.731922 | 0.121987 | ||||||||
\(37\) | 0.569477 | 0.0936214 | 0.0468107 | − | 0.998904i | \(-0.485094\pi\) | ||||
0.0468107 | + | 0.998904i | \(0.485094\pi\) | |||||||
\(38\) | 9.91930 | 1.60912 | ||||||||
\(39\) | −5.94416 | −0.951828 | ||||||||
\(40\) | 5.96662 | 0.943405 | ||||||||
\(41\) | −0.500994 | −0.0782422 | −0.0391211 | − | 0.999234i | \(-0.512456\pi\) | ||||
−0.0391211 | + | 0.999234i | \(0.512456\pi\) | |||||||
\(42\) | −0.347446 | −0.0536121 | ||||||||
\(43\) | −11.8990 | −1.81458 | −0.907290 | − | 0.420506i | \(-0.861852\pi\) | ||||
−0.907290 | + | 0.420506i | \(0.861852\pi\) | |||||||
\(44\) | 4.28751 | 0.646367 | ||||||||
\(45\) | 2.84674 | 0.424367 | ||||||||
\(46\) | 2.54313 | 0.374964 | ||||||||
\(47\) | 6.53043 | 0.952561 | 0.476281 | − | 0.879293i | \(-0.341985\pi\) | ||||
0.476281 | + | 0.879293i | \(0.341985\pi\) | |||||||
\(48\) | 4.92813 | 0.711315 | ||||||||
\(49\) | −6.95581 | −0.993687 | ||||||||
\(50\) | −5.13035 | −0.725541 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 4.35066 | 0.603328 | ||||||||
\(53\) | 7.14559 | 0.981522 | 0.490761 | − | 0.871294i | \(-0.336719\pi\) | ||||
0.490761 | + | 0.871294i | \(0.336719\pi\) | |||||||
\(54\) | 1.65285 | 0.224925 | ||||||||
\(55\) | 16.6759 | 2.24858 | ||||||||
\(56\) | −0.440589 | −0.0588762 | ||||||||
\(57\) | 6.00132 | 0.794894 | ||||||||
\(58\) | −6.71305 | −0.881467 | ||||||||
\(59\) | 7.13227 | 0.928542 | 0.464271 | − | 0.885693i | \(-0.346316\pi\) | ||||
0.464271 | + | 0.885693i | \(0.346316\pi\) | |||||||
\(60\) | −2.08359 | −0.268991 | ||||||||
\(61\) | −1.20114 | −0.153791 | −0.0768954 | − | 0.997039i | \(-0.524501\pi\) | ||||
−0.0768954 | + | 0.997039i | \(0.524501\pi\) | |||||||
\(62\) | −2.56776 | −0.326105 | ||||||||
\(63\) | −0.210210 | −0.0264840 | ||||||||
\(64\) | 3.32157 | 0.415197 | ||||||||
\(65\) | 16.9215 | 2.09885 | ||||||||
\(66\) | 9.68222 | 1.19180 | ||||||||
\(67\) | 7.38532 | 0.902260 | 0.451130 | − | 0.892458i | \(-0.351021\pi\) | ||||
0.451130 | + | 0.892458i | \(0.351021\pi\) | |||||||
\(68\) | 0.731922 | 0.0887585 | ||||||||
\(69\) | 1.53863 | 0.185229 | ||||||||
\(70\) | 0.989090 | 0.118219 | ||||||||
\(71\) | 13.3151 | 1.58022 | 0.790109 | − | 0.612967i | \(-0.210024\pi\) | ||||
0.790109 | + | 0.612967i | \(0.210024\pi\) | |||||||
\(72\) | 2.09595 | 0.247010 | ||||||||
\(73\) | −10.9391 | −1.28033 | −0.640163 | − | 0.768239i | \(-0.721133\pi\) | ||||
−0.640163 | + | 0.768239i | \(0.721133\pi\) | |||||||
\(74\) | −0.941261 | −0.109419 | ||||||||
\(75\) | −3.10394 | −0.358412 | ||||||||
\(76\) | −4.39250 | −0.503854 | ||||||||
\(77\) | −1.23139 | −0.140330 | ||||||||
\(78\) | 9.82483 | 1.11244 | ||||||||
\(79\) | 11.8246 | 1.33037 | 0.665184 | − | 0.746679i | \(-0.268353\pi\) | ||||
0.665184 | + | 0.746679i | \(0.268353\pi\) | |||||||
\(80\) | −14.0291 | −1.56850 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.828070 | 0.0914450 | ||||||||
\(83\) | −14.1343 | −1.55144 | −0.775721 | − | 0.631076i | \(-0.782614\pi\) | ||||
−0.775721 | + | 0.631076i | \(0.782614\pi\) | |||||||
\(84\) | 0.153857 | 0.0167872 | ||||||||
\(85\) | 2.84674 | 0.308772 | ||||||||
\(86\) | 19.6673 | 2.12078 | ||||||||
\(87\) | −4.06149 | −0.435438 | ||||||||
\(88\) | 12.2778 | 1.30882 | ||||||||
\(89\) | 13.5101 | 1.43207 | 0.716034 | − | 0.698066i | \(-0.245956\pi\) | ||||
0.716034 | + | 0.698066i | \(0.245956\pi\) | |||||||
\(90\) | −4.70524 | −0.495976 | ||||||||
\(91\) | −1.24952 | −0.130986 | ||||||||
\(92\) | −1.12616 | −0.117410 | ||||||||
\(93\) | −1.55353 | −0.161094 | ||||||||
\(94\) | −10.7938 | −1.11330 | ||||||||
\(95\) | −17.0842 | −1.75280 | ||||||||
\(96\) | −3.95359 | −0.403511 | ||||||||
\(97\) | 17.2545 | 1.75193 | 0.875963 | − | 0.482378i | \(-0.160227\pi\) | ||||
0.875963 | + | 0.482378i | \(0.160227\pi\) | |||||||
\(98\) | 11.4969 | 1.16137 | ||||||||
\(99\) | 5.85789 | 0.588740 | ||||||||
\(100\) | 2.27184 | 0.227184 | ||||||||
\(101\) | −5.72965 | −0.570121 | −0.285061 | − | 0.958509i | \(-0.592014\pi\) | ||||
−0.285061 | + | 0.958509i | \(0.592014\pi\) | |||||||
\(102\) | 1.65285 | 0.163657 | ||||||||
\(103\) | 2.69854 | 0.265895 | 0.132948 | − | 0.991123i | \(-0.457556\pi\) | ||||
0.132948 | + | 0.991123i | \(0.457556\pi\) | |||||||
\(104\) | 12.4587 | 1.22167 | ||||||||
\(105\) | 0.598414 | 0.0583992 | ||||||||
\(106\) | −11.8106 | −1.14715 | ||||||||
\(107\) | −0.371109 | −0.0358765 | −0.0179382 | − | 0.999839i | \(-0.505710\pi\) | ||||
−0.0179382 | + | 0.999839i | \(0.505710\pi\) | |||||||
\(108\) | −0.731922 | −0.0704292 | ||||||||
\(109\) | −15.6145 | −1.49560 | −0.747800 | − | 0.663925i | \(-0.768890\pi\) | ||||
−0.747800 | + | 0.663925i | \(0.768890\pi\) | |||||||
\(110\) | −27.5628 | −2.62801 | ||||||||
\(111\) | −0.569477 | −0.0540523 | ||||||||
\(112\) | 1.03594 | 0.0978875 | ||||||||
\(113\) | 21.0031 | 1.97580 | 0.987902 | − | 0.155081i | \(-0.0495639\pi\) | ||||
0.987902 | + | 0.155081i | \(0.0495639\pi\) | |||||||
\(114\) | −9.91930 | −0.929027 | ||||||||
\(115\) | −4.38008 | −0.408445 | ||||||||
\(116\) | 2.97270 | 0.276008 | ||||||||
\(117\) | 5.94416 | 0.549538 | ||||||||
\(118\) | −11.7886 | −1.08523 | ||||||||
\(119\) | −0.210210 | −0.0192699 | ||||||||
\(120\) | −5.96662 | −0.544675 | ||||||||
\(121\) | 23.3148 | 2.11953 | ||||||||
\(122\) | 1.98531 | 0.179742 | ||||||||
\(123\) | 0.500994 | 0.0451731 | ||||||||
\(124\) | 1.13706 | 0.102111 | ||||||||
\(125\) | −5.39760 | −0.482776 | ||||||||
\(126\) | 0.347446 | 0.0309530 | ||||||||
\(127\) | −1.47857 | −0.131202 | −0.0656010 | − | 0.997846i | \(-0.520896\pi\) | ||||
−0.0656010 | + | 0.997846i | \(0.520896\pi\) | |||||||
\(128\) | −13.3972 | −1.18416 | ||||||||
\(129\) | 11.8990 | 1.04765 | ||||||||
\(130\) | −27.9687 | −2.45302 | ||||||||
\(131\) | 4.20037 | 0.366988 | 0.183494 | − | 0.983021i | \(-0.441259\pi\) | ||||
0.183494 | + | 0.983021i | \(0.441259\pi\) | |||||||
\(132\) | −4.28751 | −0.373180 | ||||||||
\(133\) | 1.26154 | 0.109389 | ||||||||
\(134\) | −12.2068 | −1.05451 | ||||||||
\(135\) | −2.84674 | −0.245009 | ||||||||
\(136\) | 2.09595 | 0.179726 | ||||||||
\(137\) | −1.25383 | −0.107122 | −0.0535611 | − | 0.998565i | \(-0.517057\pi\) | ||||
−0.0535611 | + | 0.998565i | \(0.517057\pi\) | |||||||
\(138\) | −2.54313 | −0.216485 | ||||||||
\(139\) | −9.42391 | −0.799326 | −0.399663 | − | 0.916662i | \(-0.630873\pi\) | ||||
−0.399663 | + | 0.916662i | \(0.630873\pi\) | |||||||
\(140\) | −0.437992 | −0.0370171 | ||||||||
\(141\) | −6.53043 | −0.549961 | ||||||||
\(142\) | −22.0080 | −1.84687 | ||||||||
\(143\) | 34.8202 | 2.91181 | ||||||||
\(144\) | −4.92813 | −0.410678 | ||||||||
\(145\) | 11.5620 | 0.960174 | ||||||||
\(146\) | 18.0807 | 1.49637 | ||||||||
\(147\) | 6.95581 | 0.573706 | ||||||||
\(148\) | 0.416812 | 0.0342617 | ||||||||
\(149\) | −12.6997 | −1.04040 | −0.520200 | − | 0.854044i | \(-0.674143\pi\) | ||||
−0.520200 | + | 0.854044i | \(0.674143\pi\) | |||||||
\(150\) | 5.13035 | 0.418891 | ||||||||
\(151\) | −6.93626 | −0.564465 | −0.282233 | − | 0.959346i | \(-0.591075\pi\) | ||||
−0.282233 | + | 0.959346i | \(0.591075\pi\) | |||||||
\(152\) | −12.5784 | −1.02025 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 2.03530 | 0.164009 | ||||||||
\(155\) | 4.42250 | 0.355224 | ||||||||
\(156\) | −4.35066 | −0.348332 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | −19.5443 | −1.55486 | ||||||||
\(159\) | −7.14559 | −0.566682 | ||||||||
\(160\) | 11.2548 | 0.889773 | ||||||||
\(161\) | 0.323435 | 0.0254903 | ||||||||
\(162\) | −1.65285 | −0.129860 | ||||||||
\(163\) | 7.01983 | 0.549835 | 0.274918 | − | 0.961468i | \(-0.411349\pi\) | ||||
0.274918 | + | 0.961468i | \(0.411349\pi\) | |||||||
\(164\) | −0.366689 | −0.0286336 | ||||||||
\(165\) | −16.6759 | −1.29822 | ||||||||
\(166\) | 23.3619 | 1.81324 | ||||||||
\(167\) | −0.568370 | −0.0439818 | −0.0219909 | − | 0.999758i | \(-0.507000\pi\) | ||||
−0.0219909 | + | 0.999758i | \(0.507000\pi\) | |||||||
\(168\) | 0.440589 | 0.0339922 | ||||||||
\(169\) | 22.3331 | 1.71793 | ||||||||
\(170\) | −4.70524 | −0.360876 | ||||||||
\(171\) | −6.00132 | −0.458932 | ||||||||
\(172\) | −8.70913 | −0.664065 | ||||||||
\(173\) | 15.5216 | 1.18008 | 0.590042 | − | 0.807373i | \(-0.299111\pi\) | ||||
0.590042 | + | 0.807373i | \(0.299111\pi\) | |||||||
\(174\) | 6.71305 | 0.508915 | ||||||||
\(175\) | −0.652479 | −0.0493228 | ||||||||
\(176\) | −28.8684 | −2.17604 | ||||||||
\(177\) | −7.13227 | −0.536094 | ||||||||
\(178\) | −22.3302 | −1.67372 | ||||||||
\(179\) | −16.3427 | −1.22151 | −0.610754 | − | 0.791820i | \(-0.709134\pi\) | ||||
−0.610754 | + | 0.791820i | \(0.709134\pi\) | |||||||
\(180\) | 2.08359 | 0.155302 | ||||||||
\(181\) | −18.7319 | −1.39233 | −0.696165 | − | 0.717882i | \(-0.745112\pi\) | ||||
−0.696165 | + | 0.717882i | \(0.745112\pi\) | |||||||
\(182\) | 2.06528 | 0.153089 | ||||||||
\(183\) | 1.20114 | 0.0887911 | ||||||||
\(184\) | −3.22489 | −0.237742 | ||||||||
\(185\) | 1.62115 | 0.119190 | ||||||||
\(186\) | 2.56776 | 0.188277 | ||||||||
\(187\) | 5.85789 | 0.428371 | ||||||||
\(188\) | 4.77976 | 0.348600 | ||||||||
\(189\) | 0.210210 | 0.0152905 | ||||||||
\(190\) | 28.2377 | 2.04858 | ||||||||
\(191\) | 8.17914 | 0.591822 | 0.295911 | − | 0.955216i | \(-0.404377\pi\) | ||||
0.295911 | + | 0.955216i | \(0.404377\pi\) | |||||||
\(192\) | −3.32157 | −0.239714 | ||||||||
\(193\) | 3.76066 | 0.270699 | 0.135349 | − | 0.990798i | \(-0.456784\pi\) | ||||
0.135349 | + | 0.990798i | \(0.456784\pi\) | |||||||
\(194\) | −28.5191 | −2.04755 | ||||||||
\(195\) | −16.9215 | −1.21177 | ||||||||
\(196\) | −5.09111 | −0.363651 | ||||||||
\(197\) | 3.74230 | 0.266628 | 0.133314 | − | 0.991074i | \(-0.457438\pi\) | ||||
0.133314 | + | 0.991074i | \(0.457438\pi\) | |||||||
\(198\) | −9.68222 | −0.688086 | ||||||||
\(199\) | 5.15903 | 0.365714 | 0.182857 | − | 0.983140i | \(-0.441465\pi\) | ||||
0.182857 | + | 0.983140i | \(0.441465\pi\) | |||||||
\(200\) | 6.50569 | 0.460022 | ||||||||
\(201\) | −7.38532 | −0.520920 | ||||||||
\(202\) | 9.47026 | 0.666325 | ||||||||
\(203\) | −0.853767 | −0.0599227 | ||||||||
\(204\) | −0.731922 | −0.0512448 | ||||||||
\(205\) | −1.42620 | −0.0996102 | ||||||||
\(206\) | −4.46030 | −0.310764 | ||||||||
\(207\) | −1.53863 | −0.106942 | ||||||||
\(208\) | −29.2936 | −2.03115 | ||||||||
\(209\) | −35.1550 | −2.43173 | ||||||||
\(210\) | −0.989090 | −0.0682537 | ||||||||
\(211\) | 9.06044 | 0.623747 | 0.311873 | − | 0.950124i | \(-0.399044\pi\) | ||||
0.311873 | + | 0.950124i | \(0.399044\pi\) | |||||||
\(212\) | 5.23001 | 0.359199 | ||||||||
\(213\) | −13.3151 | −0.912339 | ||||||||
\(214\) | 0.613388 | 0.0419304 | ||||||||
\(215\) | −33.8734 | −2.31014 | ||||||||
\(216\) | −2.09595 | −0.142611 | ||||||||
\(217\) | −0.326568 | −0.0221689 | ||||||||
\(218\) | 25.8085 | 1.74797 | ||||||||
\(219\) | 10.9391 | 0.739197 | ||||||||
\(220\) | 12.2054 | 0.822891 | ||||||||
\(221\) | 5.94416 | 0.399848 | ||||||||
\(222\) | 0.941261 | 0.0631733 | ||||||||
\(223\) | −20.7564 | −1.38995 | −0.694974 | − | 0.719035i | \(-0.744584\pi\) | ||||
−0.694974 | + | 0.719035i | \(0.744584\pi\) | |||||||
\(224\) | −0.831084 | −0.0555291 | ||||||||
\(225\) | 3.10394 | 0.206929 | ||||||||
\(226\) | −34.7150 | −2.30921 | ||||||||
\(227\) | 2.50847 | 0.166493 | 0.0832466 | − | 0.996529i | \(-0.473471\pi\) | ||||
0.0832466 | + | 0.996529i | \(0.473471\pi\) | |||||||
\(228\) | 4.39250 | 0.290900 | ||||||||
\(229\) | 26.5594 | 1.75509 | 0.877546 | − | 0.479493i | \(-0.159179\pi\) | ||||
0.877546 | + | 0.479493i | \(0.159179\pi\) | |||||||
\(230\) | 7.23963 | 0.477367 | ||||||||
\(231\) | 1.23139 | 0.0810193 | ||||||||
\(232\) | 8.51268 | 0.558885 | ||||||||
\(233\) | 22.3359 | 1.46327 | 0.731636 | − | 0.681695i | \(-0.238757\pi\) | ||||
0.731636 | + | 0.681695i | \(0.238757\pi\) | |||||||
\(234\) | −9.82483 | −0.642269 | ||||||||
\(235\) | 18.5904 | 1.21271 | ||||||||
\(236\) | 5.22026 | 0.339810 | ||||||||
\(237\) | −11.8246 | −0.768088 | ||||||||
\(238\) | 0.347446 | 0.0225216 | ||||||||
\(239\) | 7.22761 | 0.467515 | 0.233758 | − | 0.972295i | \(-0.424898\pi\) | ||||
0.233758 | + | 0.972295i | \(0.424898\pi\) | |||||||
\(240\) | 14.0291 | 0.905576 | ||||||||
\(241\) | 7.00840 | 0.451451 | 0.225725 | − | 0.974191i | \(-0.427525\pi\) | ||||
0.225725 | + | 0.974191i | \(0.427525\pi\) | |||||||
\(242\) | −38.5360 | −2.47719 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −0.879143 | −0.0562814 | ||||||||
\(245\) | −19.8014 | −1.26506 | ||||||||
\(246\) | −0.828070 | −0.0527958 | ||||||||
\(247\) | −35.6728 | −2.26981 | ||||||||
\(248\) | 3.25612 | 0.206764 | ||||||||
\(249\) | 14.1343 | 0.895726 | ||||||||
\(250\) | 8.92144 | 0.564241 | ||||||||
\(251\) | −6.24384 | −0.394107 | −0.197054 | − | 0.980393i | \(-0.563137\pi\) | ||||
−0.197054 | + | 0.980393i | \(0.563137\pi\) | |||||||
\(252\) | −0.153857 | −0.00969210 | ||||||||
\(253\) | −9.01312 | −0.566650 | ||||||||
\(254\) | 2.44386 | 0.153341 | ||||||||
\(255\) | −2.84674 | −0.178270 | ||||||||
\(256\) | 15.5005 | 0.968782 | ||||||||
\(257\) | 20.5485 | 1.28178 | 0.640890 | − | 0.767633i | \(-0.278565\pi\) | ||||
0.640890 | + | 0.767633i | \(0.278565\pi\) | |||||||
\(258\) | −19.6673 | −1.22443 | ||||||||
\(259\) | −0.119710 | −0.00743840 | ||||||||
\(260\) | 12.3852 | 0.768098 | ||||||||
\(261\) | 4.06149 | 0.251400 | ||||||||
\(262\) | −6.94259 | −0.428915 | ||||||||
\(263\) | −11.0544 | −0.681643 | −0.340821 | − | 0.940128i | \(-0.610705\pi\) | ||||
−0.340821 | + | 0.940128i | \(0.610705\pi\) | |||||||
\(264\) | −12.2778 | −0.755647 | ||||||||
\(265\) | 20.3416 | 1.24958 | ||||||||
\(266\) | −2.08514 | −0.127848 | ||||||||
\(267\) | −13.5101 | −0.826804 | ||||||||
\(268\) | 5.40548 | 0.330192 | ||||||||
\(269\) | −6.38068 | −0.389037 | −0.194518 | − | 0.980899i | \(-0.562314\pi\) | ||||
−0.194518 | + | 0.980899i | \(0.562314\pi\) | |||||||
\(270\) | 4.70524 | 0.286352 | ||||||||
\(271\) | −7.66461 | −0.465592 | −0.232796 | − | 0.972526i | \(-0.574787\pi\) | ||||
−0.232796 | + | 0.972526i | \(0.574787\pi\) | |||||||
\(272\) | −4.92813 | −0.298812 | ||||||||
\(273\) | 1.24952 | 0.0756246 | ||||||||
\(274\) | 2.07240 | 0.125198 | ||||||||
\(275\) | 18.1825 | 1.09645 | ||||||||
\(276\) | 1.12616 | 0.0677866 | ||||||||
\(277\) | 5.75758 | 0.345940 | 0.172970 | − | 0.984927i | \(-0.444664\pi\) | ||||
0.172970 | + | 0.984927i | \(0.444664\pi\) | |||||||
\(278\) | 15.5763 | 0.934206 | ||||||||
\(279\) | 1.55353 | 0.0930074 | ||||||||
\(280\) | −1.25424 | −0.0749554 | ||||||||
\(281\) | 17.7636 | 1.05969 | 0.529845 | − | 0.848095i | \(-0.322250\pi\) | ||||
0.529845 | + | 0.848095i | \(0.322250\pi\) | |||||||
\(282\) | 10.7938 | 0.642764 | ||||||||
\(283\) | −30.0100 | −1.78391 | −0.891955 | − | 0.452124i | \(-0.850666\pi\) | ||||
−0.891955 | + | 0.452124i | \(0.850666\pi\) | |||||||
\(284\) | 9.74564 | 0.578298 | ||||||||
\(285\) | 17.0842 | 1.01198 | ||||||||
\(286\) | −57.5527 | −3.40316 | ||||||||
\(287\) | 0.105314 | 0.00621649 | ||||||||
\(288\) | 3.95359 | 0.232967 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −19.1103 | −1.12220 | ||||||||
\(291\) | −17.2545 | −1.01147 | ||||||||
\(292\) | −8.00658 | −0.468549 | ||||||||
\(293\) | −2.13300 | −0.124611 | −0.0623055 | − | 0.998057i | \(-0.519845\pi\) | ||||
−0.0623055 | + | 0.998057i | \(0.519845\pi\) | |||||||
\(294\) | −11.4969 | −0.670515 | ||||||||
\(295\) | 20.3037 | 1.18213 | ||||||||
\(296\) | 1.19359 | 0.0693761 | ||||||||
\(297\) | −5.85789 | −0.339909 | ||||||||
\(298\) | 20.9907 | 1.21596 | ||||||||
\(299\) | −9.14587 | −0.528919 | ||||||||
\(300\) | −2.27184 | −0.131165 | ||||||||
\(301\) | 2.50129 | 0.144172 | ||||||||
\(302\) | 11.4646 | 0.659715 | ||||||||
\(303\) | 5.72965 | 0.329160 | ||||||||
\(304\) | 29.5753 | 1.69626 | ||||||||
\(305\) | −3.41935 | −0.195791 | ||||||||
\(306\) | −1.65285 | −0.0944873 | ||||||||
\(307\) | −29.6255 | −1.69082 | −0.845409 | − | 0.534119i | \(-0.820643\pi\) | ||||
−0.845409 | + | 0.534119i | \(0.820643\pi\) | |||||||
\(308\) | −0.901279 | −0.0513551 | ||||||||
\(309\) | −2.69854 | −0.153515 | ||||||||
\(310\) | −7.30974 | −0.415165 | ||||||||
\(311\) | −10.9032 | −0.618262 | −0.309131 | − | 0.951019i | \(-0.600038\pi\) | ||||
−0.309131 | + | 0.951019i | \(0.600038\pi\) | |||||||
\(312\) | −12.4587 | −0.705332 | ||||||||
\(313\) | −6.91690 | −0.390967 | −0.195483 | − | 0.980707i | \(-0.562628\pi\) | ||||
−0.195483 | + | 0.980707i | \(0.562628\pi\) | |||||||
\(314\) | 1.65285 | 0.0932759 | ||||||||
\(315\) | −0.598414 | −0.0337168 | ||||||||
\(316\) | 8.65466 | 0.486863 | ||||||||
\(317\) | −11.9804 | −0.672886 | −0.336443 | − | 0.941704i | \(-0.609224\pi\) | ||||
−0.336443 | + | 0.941704i | \(0.609224\pi\) | |||||||
\(318\) | 11.8106 | 0.662306 | ||||||||
\(319\) | 23.7918 | 1.33208 | ||||||||
\(320\) | 9.45566 | 0.528588 | ||||||||
\(321\) | 0.371109 | 0.0207133 | ||||||||
\(322\) | −0.534591 | −0.0297916 | ||||||||
\(323\) | −6.00132 | −0.333922 | ||||||||
\(324\) | 0.731922 | 0.0406623 | ||||||||
\(325\) | 18.4503 | 1.02344 | ||||||||
\(326\) | −11.6027 | −0.642616 | ||||||||
\(327\) | 15.6145 | 0.863485 | ||||||||
\(328\) | −1.05006 | −0.0579797 | ||||||||
\(329\) | −1.37276 | −0.0756828 | ||||||||
\(330\) | 27.5628 | 1.51728 | ||||||||
\(331\) | 24.3174 | 1.33660 | 0.668302 | − | 0.743890i | \(-0.267021\pi\) | ||||
0.668302 | + | 0.743890i | \(0.267021\pi\) | |||||||
\(332\) | −10.3452 | −0.567767 | ||||||||
\(333\) | 0.569477 | 0.0312071 | ||||||||
\(334\) | 0.939432 | 0.0514034 | ||||||||
\(335\) | 21.0241 | 1.14867 | ||||||||
\(336\) | −1.03594 | −0.0565154 | ||||||||
\(337\) | 5.25268 | 0.286132 | 0.143066 | − | 0.989713i | \(-0.454304\pi\) | ||||
0.143066 | + | 0.989713i | \(0.454304\pi\) | |||||||
\(338\) | −36.9133 | −2.00782 | ||||||||
\(339\) | −21.0031 | −1.14073 | ||||||||
\(340\) | 2.08359 | 0.112999 | ||||||||
\(341\) | 9.10040 | 0.492814 | ||||||||
\(342\) | 9.91930 | 0.536374 | ||||||||
\(343\) | 2.93365 | 0.158402 | ||||||||
\(344\) | −24.9397 | −1.34466 | ||||||||
\(345\) | 4.38008 | 0.235816 | ||||||||
\(346\) | −25.6549 | −1.37921 | ||||||||
\(347\) | 9.58455 | 0.514526 | 0.257263 | − | 0.966341i | \(-0.417179\pi\) | ||||
0.257263 | + | 0.966341i | \(0.417179\pi\) | |||||||
\(348\) | −2.97270 | −0.159353 | ||||||||
\(349\) | 21.1760 | 1.13352 | 0.566762 | − | 0.823882i | \(-0.308196\pi\) | ||||
0.566762 | + | 0.823882i | \(0.308196\pi\) | |||||||
\(350\) | 1.07845 | 0.0576457 | ||||||||
\(351\) | −5.94416 | −0.317276 | ||||||||
\(352\) | 23.1597 | 1.23441 | ||||||||
\(353\) | −6.29101 | −0.334836 | −0.167418 | − | 0.985886i | \(-0.553543\pi\) | ||||
−0.167418 | + | 0.985886i | \(0.553543\pi\) | |||||||
\(354\) | 11.7886 | 0.626556 | ||||||||
\(355\) | 37.9048 | 2.01178 | ||||||||
\(356\) | 9.88833 | 0.524080 | ||||||||
\(357\) | 0.210210 | 0.0111255 | ||||||||
\(358\) | 27.0120 | 1.42763 | ||||||||
\(359\) | −26.9110 | −1.42031 | −0.710153 | − | 0.704047i | \(-0.751374\pi\) | ||||
−0.710153 | + | 0.704047i | \(0.751374\pi\) | |||||||
\(360\) | 5.96662 | 0.314468 | ||||||||
\(361\) | 17.0158 | 0.895570 | ||||||||
\(362\) | 30.9610 | 1.62728 | ||||||||
\(363\) | −23.3148 | −1.22371 | ||||||||
\(364\) | −0.914553 | −0.0479356 | ||||||||
\(365\) | −31.1408 | −1.62999 | ||||||||
\(366\) | −1.98531 | −0.103774 | ||||||||
\(367\) | 37.1513 | 1.93928 | 0.969641 | − | 0.244532i | \(-0.0786342\pi\) | ||||
0.969641 | + | 0.244532i | \(0.0786342\pi\) | |||||||
\(368\) | 7.58257 | 0.395269 | ||||||||
\(369\) | −0.500994 | −0.0260807 | ||||||||
\(370\) | −2.67953 | −0.139302 | ||||||||
\(371\) | −1.50208 | −0.0779839 | ||||||||
\(372\) | −1.13706 | −0.0589539 | ||||||||
\(373\) | 25.9318 | 1.34270 | 0.671349 | − | 0.741142i | \(-0.265715\pi\) | ||||
0.671349 | + | 0.741142i | \(0.265715\pi\) | |||||||
\(374\) | −9.68222 | −0.500656 | ||||||||
\(375\) | 5.39760 | 0.278731 | ||||||||
\(376\) | 13.6874 | 0.705875 | ||||||||
\(377\) | 24.1422 | 1.24339 | ||||||||
\(378\) | −0.347446 | −0.0178707 | ||||||||
\(379\) | −10.2382 | −0.525901 | −0.262951 | − | 0.964809i | \(-0.584696\pi\) | ||||
−0.262951 | + | 0.964809i | \(0.584696\pi\) | |||||||
\(380\) | −12.5043 | −0.641457 | ||||||||
\(381\) | 1.47857 | 0.0757495 | ||||||||
\(382\) | −13.5189 | −0.691688 | ||||||||
\(383\) | −15.2298 | −0.778205 | −0.389103 | − | 0.921194i | \(-0.627215\pi\) | ||||
−0.389103 | + | 0.921194i | \(0.627215\pi\) | |||||||
\(384\) | 13.3972 | 0.683675 | ||||||||
\(385\) | −3.50544 | −0.178654 | ||||||||
\(386\) | −6.21582 | −0.316377 | ||||||||
\(387\) | −11.8990 | −0.604860 | ||||||||
\(388\) | 12.6289 | 0.641136 | ||||||||
\(389\) | 9.97651 | 0.505829 | 0.252915 | − | 0.967489i | \(-0.418611\pi\) | ||||
0.252915 | + | 0.967489i | \(0.418611\pi\) | |||||||
\(390\) | 27.9687 | 1.41625 | ||||||||
\(391\) | −1.53863 | −0.0778118 | ||||||||
\(392\) | −14.5790 | −0.736351 | ||||||||
\(393\) | −4.20037 | −0.211881 | ||||||||
\(394\) | −6.18546 | −0.311619 | ||||||||
\(395\) | 33.6615 | 1.69369 | ||||||||
\(396\) | 4.28751 | 0.215456 | ||||||||
\(397\) | 22.1562 | 1.11199 | 0.555993 | − | 0.831187i | \(-0.312338\pi\) | ||||
0.555993 | + | 0.831187i | \(0.312338\pi\) | |||||||
\(398\) | −8.52711 | −0.427426 | ||||||||
\(399\) | −1.26154 | −0.0631559 | ||||||||
\(400\) | −15.2966 | −0.764831 | ||||||||
\(401\) | −25.2019 | −1.25852 | −0.629261 | − | 0.777194i | \(-0.716643\pi\) | ||||
−0.629261 | + | 0.777194i | \(0.716643\pi\) | |||||||
\(402\) | 12.2068 | 0.608822 | ||||||||
\(403\) | 9.23444 | 0.460000 | ||||||||
\(404\) | −4.19365 | −0.208642 | ||||||||
\(405\) | 2.84674 | 0.141456 | ||||||||
\(406\) | 1.41115 | 0.0700343 | ||||||||
\(407\) | 3.33593 | 0.165356 | ||||||||
\(408\) | −2.09595 | −0.103765 | ||||||||
\(409\) | −25.0276 | −1.23753 | −0.618767 | − | 0.785574i | \(-0.712368\pi\) | ||||
−0.618767 | + | 0.785574i | \(0.712368\pi\) | |||||||
\(410\) | 2.35730 | 0.116419 | ||||||||
\(411\) | 1.25383 | 0.0618470 | ||||||||
\(412\) | 1.97512 | 0.0973073 | ||||||||
\(413\) | −1.49927 | −0.0737745 | ||||||||
\(414\) | 2.54313 | 0.124988 | ||||||||
\(415\) | −40.2367 | −1.97514 | ||||||||
\(416\) | 23.5008 | 1.15222 | ||||||||
\(417\) | 9.42391 | 0.461491 | ||||||||
\(418\) | 58.1061 | 2.84206 | ||||||||
\(419\) | 3.94598 | 0.192774 | 0.0963869 | − | 0.995344i | \(-0.469271\pi\) | ||||
0.0963869 | + | 0.995344i | \(0.469271\pi\) | |||||||
\(420\) | 0.437992 | 0.0213718 | ||||||||
\(421\) | 5.67669 | 0.276665 | 0.138332 | − | 0.990386i | \(-0.455826\pi\) | ||||
0.138332 | + | 0.990386i | \(0.455826\pi\) | |||||||
\(422\) | −14.9756 | −0.729000 | ||||||||
\(423\) | 6.53043 | 0.317520 | ||||||||
\(424\) | 14.9768 | 0.727336 | ||||||||
\(425\) | 3.10394 | 0.150563 | ||||||||
\(426\) | 22.0080 | 1.06629 | ||||||||
\(427\) | 0.252493 | 0.0122190 | ||||||||
\(428\) | −0.271623 | −0.0131294 | ||||||||
\(429\) | −34.8202 | −1.68114 | ||||||||
\(430\) | 55.9877 | 2.69996 | ||||||||
\(431\) | 18.8191 | 0.906483 | 0.453242 | − | 0.891388i | \(-0.350268\pi\) | ||||
0.453242 | + | 0.891388i | \(0.350268\pi\) | |||||||
\(432\) | 4.92813 | 0.237105 | ||||||||
\(433\) | −20.4465 | −0.982596 | −0.491298 | − | 0.870991i | \(-0.663477\pi\) | ||||
−0.491298 | + | 0.870991i | \(0.663477\pi\) | |||||||
\(434\) | 0.539768 | 0.0259097 | ||||||||
\(435\) | −11.5620 | −0.554357 | ||||||||
\(436\) | −11.4286 | −0.547331 | ||||||||
\(437\) | 9.23381 | 0.441713 | ||||||||
\(438\) | −18.0807 | −0.863932 | ||||||||
\(439\) | 11.7561 | 0.561089 | 0.280545 | − | 0.959841i | \(-0.409485\pi\) | ||||
0.280545 | + | 0.959841i | \(0.409485\pi\) | |||||||
\(440\) | 34.9518 | 1.66626 | ||||||||
\(441\) | −6.95581 | −0.331229 | ||||||||
\(442\) | −9.82483 | −0.467319 | ||||||||
\(443\) | −36.7025 | −1.74379 | −0.871894 | − | 0.489695i | \(-0.837108\pi\) | ||||
−0.871894 | + | 0.489695i | \(0.837108\pi\) | |||||||
\(444\) | −0.416812 | −0.0197810 | ||||||||
\(445\) | 38.4597 | 1.82317 | ||||||||
\(446\) | 34.3072 | 1.62449 | ||||||||
\(447\) | 12.6997 | 0.600675 | ||||||||
\(448\) | −0.698228 | −0.0329882 | ||||||||
\(449\) | −3.82195 | −0.180369 | −0.0901845 | − | 0.995925i | \(-0.528746\pi\) | ||||
−0.0901845 | + | 0.995925i | \(0.528746\pi\) | |||||||
\(450\) | −5.13035 | −0.241847 | ||||||||
\(451\) | −2.93477 | −0.138193 | ||||||||
\(452\) | 15.3726 | 0.723067 | ||||||||
\(453\) | 6.93626 | 0.325894 | ||||||||
\(454\) | −4.14614 | −0.194588 | ||||||||
\(455\) | −3.55707 | −0.166758 | ||||||||
\(456\) | 12.5784 | 0.589040 | ||||||||
\(457\) | 0.447567 | 0.0209363 | 0.0104682 | − | 0.999945i | \(-0.496668\pi\) | ||||
0.0104682 | + | 0.999945i | \(0.496668\pi\) | |||||||
\(458\) | −43.8987 | −2.05125 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −3.20588 | −0.149475 | ||||||||
\(461\) | −12.4428 | −0.579518 | −0.289759 | − | 0.957100i | \(-0.593575\pi\) | ||||
−0.289759 | + | 0.957100i | \(0.593575\pi\) | |||||||
\(462\) | −2.03530 | −0.0946908 | ||||||||
\(463\) | 21.0256 | 0.977141 | 0.488570 | − | 0.872524i | \(-0.337519\pi\) | ||||
0.488570 | + | 0.872524i | \(0.337519\pi\) | |||||||
\(464\) | −20.0156 | −0.929200 | ||||||||
\(465\) | −4.42250 | −0.205088 | ||||||||
\(466\) | −36.9179 | −1.71019 | ||||||||
\(467\) | −26.3427 | −1.21899 | −0.609497 | − | 0.792788i | \(-0.708629\pi\) | ||||
−0.609497 | + | 0.792788i | \(0.708629\pi\) | |||||||
\(468\) | 4.35066 | 0.201109 | ||||||||
\(469\) | −1.55247 | −0.0716863 | ||||||||
\(470\) | −30.7273 | −1.41734 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | 14.9488 | 0.688077 | ||||||||
\(473\) | −69.7029 | −3.20494 | ||||||||
\(474\) | 19.5443 | 0.897698 | ||||||||
\(475\) | −18.6277 | −0.854698 | ||||||||
\(476\) | −0.153857 | −0.00705204 | ||||||||
\(477\) | 7.14559 | 0.327174 | ||||||||
\(478\) | −11.9462 | −0.546405 | ||||||||
\(479\) | 0.464318 | 0.0212152 | 0.0106076 | − | 0.999944i | \(-0.496623\pi\) | ||||
0.0106076 | + | 0.999944i | \(0.496623\pi\) | |||||||
\(480\) | −11.2548 | −0.513711 | ||||||||
\(481\) | 3.38506 | 0.154346 | ||||||||
\(482\) | −11.5838 | −0.527630 | ||||||||
\(483\) | −0.323435 | −0.0147168 | ||||||||
\(484\) | 17.0646 | 0.775665 | ||||||||
\(485\) | 49.1190 | 2.23038 | ||||||||
\(486\) | 1.65285 | 0.0749749 | ||||||||
\(487\) | 41.5963 | 1.88491 | 0.942454 | − | 0.334335i | \(-0.108512\pi\) | ||||
0.942454 | + | 0.334335i | \(0.108512\pi\) | |||||||
\(488\) | −2.51753 | −0.113963 | ||||||||
\(489\) | −7.01983 | −0.317448 | ||||||||
\(490\) | 32.7288 | 1.47854 | ||||||||
\(491\) | −35.5969 | −1.60647 | −0.803233 | − | 0.595666i | \(-0.796888\pi\) | ||||
−0.803233 | + | 0.595666i | \(0.796888\pi\) | |||||||
\(492\) | 0.366689 | 0.0165316 | ||||||||
\(493\) | 4.06149 | 0.182920 | ||||||||
\(494\) | 58.9619 | 2.65282 | ||||||||
\(495\) | 16.6759 | 0.749525 | ||||||||
\(496\) | −7.65600 | −0.343765 | ||||||||
\(497\) | −2.79898 | −0.125551 | ||||||||
\(498\) | −23.3619 | −1.04687 | ||||||||
\(499\) | −14.2150 | −0.636351 | −0.318176 | − | 0.948032i | \(-0.603070\pi\) | ||||
−0.318176 | + | 0.948032i | \(0.603070\pi\) | |||||||
\(500\) | −3.95062 | −0.176677 | ||||||||
\(501\) | 0.568370 | 0.0253929 | ||||||||
\(502\) | 10.3201 | 0.460610 | ||||||||
\(503\) | −27.1384 | −1.21004 | −0.605021 | − | 0.796210i | \(-0.706835\pi\) | ||||
−0.605021 | + | 0.796210i | \(0.706835\pi\) | |||||||
\(504\) | −0.440589 | −0.0196254 | ||||||||
\(505\) | −16.3108 | −0.725822 | ||||||||
\(506\) | 14.8974 | 0.662268 | ||||||||
\(507\) | −22.3331 | −0.991847 | ||||||||
\(508\) | −1.08220 | −0.0480148 | ||||||||
\(509\) | 27.5884 | 1.22284 | 0.611418 | − | 0.791308i | \(-0.290600\pi\) | ||||
0.611418 | + | 0.791308i | \(0.290600\pi\) | |||||||
\(510\) | 4.70524 | 0.208352 | ||||||||
\(511\) | 2.29951 | 0.101724 | ||||||||
\(512\) | 1.17441 | 0.0519022 | ||||||||
\(513\) | 6.00132 | 0.264965 | ||||||||
\(514\) | −33.9636 | −1.49807 | ||||||||
\(515\) | 7.68206 | 0.338512 | ||||||||
\(516\) | 8.70913 | 0.383398 | ||||||||
\(517\) | 38.2545 | 1.68243 | ||||||||
\(518\) | 0.197863 | 0.00869358 | ||||||||
\(519\) | −15.5216 | −0.681322 | ||||||||
\(520\) | 35.4666 | 1.55531 | ||||||||
\(521\) | −11.7955 | −0.516768 | −0.258384 | − | 0.966042i | \(-0.583190\pi\) | ||||
−0.258384 | + | 0.966042i | \(0.583190\pi\) | |||||||
\(522\) | −6.71305 | −0.293822 | ||||||||
\(523\) | −24.7555 | −1.08248 | −0.541241 | − | 0.840868i | \(-0.682045\pi\) | ||||
−0.541241 | + | 0.840868i | \(0.682045\pi\) | |||||||
\(524\) | 3.07434 | 0.134303 | ||||||||
\(525\) | 0.652479 | 0.0284765 | ||||||||
\(526\) | 18.2713 | 0.796666 | ||||||||
\(527\) | 1.55353 | 0.0676728 | ||||||||
\(528\) | 28.8684 | 1.25634 | ||||||||
\(529\) | −20.6326 | −0.897070 | ||||||||
\(530\) | −33.6217 | −1.46044 | ||||||||
\(531\) | 7.13227 | 0.309514 | ||||||||
\(532\) | 0.923347 | 0.0400322 | ||||||||
\(533\) | −2.97799 | −0.128991 | ||||||||
\(534\) | 22.3302 | 0.966322 | ||||||||
\(535\) | −1.05645 | −0.0456744 | ||||||||
\(536\) | 15.4792 | 0.668601 | ||||||||
\(537\) | 16.3427 | 0.705238 | ||||||||
\(538\) | 10.5463 | 0.454684 | ||||||||
\(539\) | −40.7464 | −1.75507 | ||||||||
\(540\) | −2.08359 | −0.0896635 | ||||||||
\(541\) | −2.81676 | −0.121102 | −0.0605510 | − | 0.998165i | \(-0.519286\pi\) | ||||
−0.0605510 | + | 0.998165i | \(0.519286\pi\) | |||||||
\(542\) | 12.6685 | 0.544157 | ||||||||
\(543\) | 18.7319 | 0.803862 | ||||||||
\(544\) | 3.95359 | 0.169509 | ||||||||
\(545\) | −44.4505 | −1.90405 | ||||||||
\(546\) | −2.06528 | −0.0883857 | ||||||||
\(547\) | −19.1349 | −0.818147 | −0.409074 | − | 0.912501i | \(-0.634148\pi\) | ||||
−0.409074 | + | 0.912501i | \(0.634148\pi\) | |||||||
\(548\) | −0.917708 | −0.0392025 | ||||||||
\(549\) | −1.20114 | −0.0512636 | ||||||||
\(550\) | −30.0530 | −1.28146 | ||||||||
\(551\) | −24.3743 | −1.03838 | ||||||||
\(552\) | 3.22489 | 0.137260 | ||||||||
\(553\) | −2.48564 | −0.105700 | ||||||||
\(554\) | −9.51644 | −0.404315 | ||||||||
\(555\) | −1.62115 | −0.0688141 | ||||||||
\(556\) | −6.89756 | −0.292522 | ||||||||
\(557\) | −37.1017 | −1.57205 | −0.786025 | − | 0.618195i | \(-0.787864\pi\) | ||||
−0.786025 | + | 0.618195i | \(0.787864\pi\) | |||||||
\(558\) | −2.56776 | −0.108702 | ||||||||
\(559\) | −70.7296 | −2.99154 | ||||||||
\(560\) | 2.94906 | 0.124621 | ||||||||
\(561\) | −5.85789 | −0.247320 | ||||||||
\(562\) | −29.3607 | −1.23850 | ||||||||
\(563\) | −23.4607 | −0.988750 | −0.494375 | − | 0.869249i | \(-0.664603\pi\) | ||||
−0.494375 | + | 0.869249i | \(0.664603\pi\) | |||||||
\(564\) | −4.77976 | −0.201264 | ||||||||
\(565\) | 59.7903 | 2.51540 | ||||||||
\(566\) | 49.6021 | 2.08493 | ||||||||
\(567\) | −0.210210 | −0.00882799 | ||||||||
\(568\) | 27.9078 | 1.17099 | ||||||||
\(569\) | 32.6525 | 1.36886 | 0.684432 | − | 0.729077i | \(-0.260050\pi\) | ||||
0.684432 | + | 0.729077i | \(0.260050\pi\) | |||||||
\(570\) | −28.2377 | −1.18275 | ||||||||
\(571\) | 21.2570 | 0.889579 | 0.444790 | − | 0.895635i | \(-0.353278\pi\) | ||||
0.444790 | + | 0.895635i | \(0.353278\pi\) | |||||||
\(572\) | 25.4857 | 1.06561 | ||||||||
\(573\) | −8.17914 | −0.341688 | ||||||||
\(574\) | −0.174069 | −0.00726549 | ||||||||
\(575\) | −4.77581 | −0.199165 | ||||||||
\(576\) | 3.32157 | 0.138399 | ||||||||
\(577\) | 4.16749 | 0.173495 | 0.0867473 | − | 0.996230i | \(-0.472353\pi\) | ||||
0.0867473 | + | 0.996230i | \(0.472353\pi\) | |||||||
\(578\) | −1.65285 | −0.0687496 | ||||||||
\(579\) | −3.76066 | −0.156288 | ||||||||
\(580\) | 8.46250 | 0.351386 | ||||||||
\(581\) | 2.97118 | 0.123265 | ||||||||
\(582\) | 28.5191 | 1.18215 | ||||||||
\(583\) | 41.8581 | 1.73358 | ||||||||
\(584\) | −22.9278 | −0.948759 | ||||||||
\(585\) | 16.9215 | 0.699618 | ||||||||
\(586\) | 3.52553 | 0.145638 | ||||||||
\(587\) | 18.1590 | 0.749503 | 0.374752 | − | 0.927125i | \(-0.377728\pi\) | ||||
0.374752 | + | 0.927125i | \(0.377728\pi\) | |||||||
\(588\) | 5.09111 | 0.209954 | ||||||||
\(589\) | −9.32323 | −0.384157 | ||||||||
\(590\) | −33.5591 | −1.38160 | ||||||||
\(591\) | −3.74230 | −0.153937 | ||||||||
\(592\) | −2.80646 | −0.115345 | ||||||||
\(593\) | −17.0261 | −0.699176 | −0.349588 | − | 0.936903i | \(-0.613679\pi\) | ||||
−0.349588 | + | 0.936903i | \(0.613679\pi\) | |||||||
\(594\) | 9.68222 | 0.397266 | ||||||||
\(595\) | −0.598414 | −0.0245326 | ||||||||
\(596\) | −9.29518 | −0.380746 | ||||||||
\(597\) | −5.15903 | −0.211145 | ||||||||
\(598\) | 15.1168 | 0.618171 | ||||||||
\(599\) | −36.1876 | −1.47859 | −0.739293 | − | 0.673384i | \(-0.764840\pi\) | ||||
−0.739293 | + | 0.673384i | \(0.764840\pi\) | |||||||
\(600\) | −6.50569 | −0.265594 | ||||||||
\(601\) | −9.97149 | −0.406745 | −0.203373 | − | 0.979101i | \(-0.565190\pi\) | ||||
−0.203373 | + | 0.979101i | \(0.565190\pi\) | |||||||
\(602\) | −4.13426 | −0.168500 | ||||||||
\(603\) | 7.38532 | 0.300753 | ||||||||
\(604\) | −5.07680 | −0.206572 | ||||||||
\(605\) | 66.3713 | 2.69838 | ||||||||
\(606\) | −9.47026 | −0.384703 | ||||||||
\(607\) | −9.22939 | −0.374609 | −0.187305 | − | 0.982302i | \(-0.559975\pi\) | ||||
−0.187305 | + | 0.982302i | \(0.559975\pi\) | |||||||
\(608\) | −23.7267 | −0.962246 | ||||||||
\(609\) | 0.853767 | 0.0345964 | ||||||||
\(610\) | 5.65168 | 0.228830 | ||||||||
\(611\) | 38.8179 | 1.57041 | ||||||||
\(612\) | 0.731922 | 0.0295862 | ||||||||
\(613\) | 0.424459 | 0.0171437 | 0.00857187 | − | 0.999963i | \(-0.497271\pi\) | ||||
0.00857187 | + | 0.999963i | \(0.497271\pi\) | |||||||
\(614\) | 48.9666 | 1.97613 | ||||||||
\(615\) | 1.42620 | 0.0575100 | ||||||||
\(616\) | −2.58092 | −0.103988 | ||||||||
\(617\) | −12.0404 | −0.484727 | −0.242363 | − | 0.970186i | \(-0.577923\pi\) | ||||
−0.242363 | + | 0.970186i | \(0.577923\pi\) | |||||||
\(618\) | 4.46030 | 0.179419 | ||||||||
\(619\) | 10.3292 | 0.415166 | 0.207583 | − | 0.978217i | \(-0.433440\pi\) | ||||
0.207583 | + | 0.978217i | \(0.433440\pi\) | |||||||
\(620\) | 3.23692 | 0.129998 | ||||||||
\(621\) | 1.53863 | 0.0617431 | ||||||||
\(622\) | 18.0213 | 0.722590 | ||||||||
\(623\) | −2.83996 | −0.113781 | ||||||||
\(624\) | 29.2936 | 1.17268 | ||||||||
\(625\) | −30.8853 | −1.23541 | ||||||||
\(626\) | 11.4326 | 0.456940 | ||||||||
\(627\) | 35.1550 | 1.40396 | ||||||||
\(628\) | −0.731922 | −0.0292069 | ||||||||
\(629\) | 0.569477 | 0.0227065 | ||||||||
\(630\) | 0.989090 | 0.0394063 | ||||||||
\(631\) | −3.47025 | −0.138149 | −0.0690743 | − | 0.997612i | \(-0.522005\pi\) | ||||
−0.0690743 | + | 0.997612i | \(0.522005\pi\) | |||||||
\(632\) | 24.7837 | 0.985841 | ||||||||
\(633\) | −9.06044 | −0.360120 | ||||||||
\(634\) | 19.8018 | 0.786431 | ||||||||
\(635\) | −4.20911 | −0.167033 | ||||||||
\(636\) | −5.23001 | −0.207383 | ||||||||
\(637\) | −41.3465 | −1.63821 | ||||||||
\(638\) | −39.3243 | −1.55686 | ||||||||
\(639\) | 13.3151 | 0.526739 | ||||||||
\(640\) | −38.1385 | −1.50756 | ||||||||
\(641\) | 35.4357 | 1.39963 | 0.699813 | − | 0.714326i | \(-0.253266\pi\) | ||||
0.699813 | + | 0.714326i | \(0.253266\pi\) | |||||||
\(642\) | −0.613388 | −0.0242085 | ||||||||
\(643\) | 27.4759 | 1.08355 | 0.541773 | − | 0.840525i | \(-0.317753\pi\) | ||||
0.541773 | + | 0.840525i | \(0.317753\pi\) | |||||||
\(644\) | 0.236729 | 0.00932845 | ||||||||
\(645\) | 33.8734 | 1.33376 | ||||||||
\(646\) | 9.91930 | 0.390269 | ||||||||
\(647\) | −6.36602 | −0.250274 | −0.125137 | − | 0.992139i | \(-0.539937\pi\) | ||||
−0.125137 | + | 0.992139i | \(0.539937\pi\) | |||||||
\(648\) | 2.09595 | 0.0823366 | ||||||||
\(649\) | 41.7800 | 1.64001 | ||||||||
\(650\) | −30.4957 | −1.19614 | ||||||||
\(651\) | 0.326568 | 0.0127992 | ||||||||
\(652\) | 5.13796 | 0.201218 | ||||||||
\(653\) | 12.1322 | 0.474769 | 0.237384 | − | 0.971416i | \(-0.423710\pi\) | ||||
0.237384 | + | 0.971416i | \(0.423710\pi\) | |||||||
\(654\) | −25.8085 | −1.00919 | ||||||||
\(655\) | 11.9574 | 0.467213 | ||||||||
\(656\) | 2.46897 | 0.0963970 | ||||||||
\(657\) | −10.9391 | −0.426776 | ||||||||
\(658\) | 2.26897 | 0.0884538 | ||||||||
\(659\) | −33.7255 | −1.31376 | −0.656880 | − | 0.753996i | \(-0.728124\pi\) | ||||
−0.656880 | + | 0.753996i | \(0.728124\pi\) | |||||||
\(660\) | −12.2054 | −0.475096 | ||||||||
\(661\) | 47.2399 | 1.83742 | 0.918709 | − | 0.394935i | \(-0.129233\pi\) | ||||
0.918709 | + | 0.394935i | \(0.129233\pi\) | |||||||
\(662\) | −40.1931 | −1.56215 | ||||||||
\(663\) | −5.94416 | −0.230852 | ||||||||
\(664\) | −29.6248 | −1.14966 | ||||||||
\(665\) | 3.59127 | 0.139264 | ||||||||
\(666\) | −0.941261 | −0.0364731 | ||||||||
\(667\) | −6.24914 | −0.241967 | ||||||||
\(668\) | −0.416002 | −0.0160956 | ||||||||
\(669\) | 20.7564 | 0.802487 | ||||||||
\(670\) | −34.7497 | −1.34250 | ||||||||
\(671\) | −7.03617 | −0.271628 | ||||||||
\(672\) | 0.831084 | 0.0320597 | ||||||||
\(673\) | 25.1249 | 0.968493 | 0.484246 | − | 0.874932i | \(-0.339094\pi\) | ||||
0.484246 | + | 0.874932i | \(0.339094\pi\) | |||||||
\(674\) | −8.68191 | −0.334415 | ||||||||
\(675\) | −3.10394 | −0.119471 | ||||||||
\(676\) | 16.3461 | 0.628695 | ||||||||
\(677\) | 47.4437 | 1.82341 | 0.911705 | − | 0.410847i | \(-0.134767\pi\) | ||||
0.911705 | + | 0.410847i | \(0.134767\pi\) | |||||||
\(678\) | 34.7150 | 1.33322 | ||||||||
\(679\) | −3.62706 | −0.139194 | ||||||||
\(680\) | 5.96662 | 0.228809 | ||||||||
\(681\) | −2.50847 | −0.0961249 | ||||||||
\(682\) | −15.0416 | −0.575973 | ||||||||
\(683\) | 28.0943 | 1.07500 | 0.537500 | − | 0.843264i | \(-0.319369\pi\) | ||||
0.537500 | + | 0.843264i | \(0.319369\pi\) | |||||||
\(684\) | −4.39250 | −0.167951 | ||||||||
\(685\) | −3.56934 | −0.136377 | ||||||||
\(686\) | −4.84890 | −0.185132 | ||||||||
\(687\) | −26.5594 | −1.01330 | ||||||||
\(688\) | 58.6398 | 2.23562 | ||||||||
\(689\) | 42.4746 | 1.61815 | ||||||||
\(690\) | −7.23963 | −0.275608 | ||||||||
\(691\) | 8.06370 | 0.306758 | 0.153379 | − | 0.988167i | \(-0.450985\pi\) | ||||
0.153379 | + | 0.988167i | \(0.450985\pi\) | |||||||
\(692\) | 11.3606 | 0.431864 | ||||||||
\(693\) | −1.23139 | −0.0467765 | ||||||||
\(694\) | −15.8419 | −0.601349 | ||||||||
\(695\) | −26.8274 | −1.01762 | ||||||||
\(696\) | −8.51268 | −0.322672 | ||||||||
\(697\) | −0.500994 | −0.0189765 | ||||||||
\(698\) | −35.0008 | −1.32480 | ||||||||
\(699\) | −22.3359 | −0.844821 | ||||||||
\(700\) | −0.477564 | −0.0180502 | ||||||||
\(701\) | 19.9738 | 0.754398 | 0.377199 | − | 0.926132i | \(-0.376887\pi\) | ||||
0.377199 | + | 0.926132i | \(0.376887\pi\) | |||||||
\(702\) | 9.82483 | 0.370814 | ||||||||
\(703\) | −3.41761 | −0.128898 | ||||||||
\(704\) | 19.4574 | 0.733328 | ||||||||
\(705\) | −18.5904 | −0.700157 | ||||||||
\(706\) | 10.3981 | 0.391338 | ||||||||
\(707\) | 1.20443 | 0.0452972 | ||||||||
\(708\) | −5.22026 | −0.196189 | ||||||||
\(709\) | −17.3105 | −0.650109 | −0.325055 | − | 0.945695i | \(-0.605383\pi\) | ||||
−0.325055 | + | 0.945695i | \(0.605383\pi\) | |||||||
\(710\) | −62.6510 | −2.35125 | ||||||||
\(711\) | 11.8246 | 0.443456 | ||||||||
\(712\) | 28.3164 | 1.06120 | ||||||||
\(713\) | −2.39031 | −0.0895177 | ||||||||
\(714\) | −0.347446 | −0.0130029 | ||||||||
\(715\) | 99.1242 | 3.70704 | ||||||||
\(716\) | −11.9615 | −0.447024 | ||||||||
\(717\) | −7.22761 | −0.269920 | ||||||||
\(718\) | 44.4799 | 1.65997 | ||||||||
\(719\) | 42.5723 | 1.58768 | 0.793840 | − | 0.608127i | \(-0.208079\pi\) | ||||
0.793840 | + | 0.608127i | \(0.208079\pi\) | |||||||
\(720\) | −14.0291 | −0.522835 | ||||||||
\(721\) | −0.567261 | −0.0211259 | ||||||||
\(722\) | −28.1247 | −1.04669 | ||||||||
\(723\) | −7.00840 | −0.260645 | ||||||||
\(724\) | −13.7103 | −0.509538 | ||||||||
\(725\) | 12.6066 | 0.468198 | ||||||||
\(726\) | 38.5360 | 1.43020 | ||||||||
\(727\) | 43.8139 | 1.62497 | 0.812484 | − | 0.582984i | \(-0.198115\pi\) | ||||
0.812484 | + | 0.582984i | \(0.198115\pi\) | |||||||
\(728\) | −2.61893 | −0.0970642 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 51.4712 | 1.90504 | ||||||||
\(731\) | −11.8990 | −0.440100 | ||||||||
\(732\) | 0.879143 | 0.0324941 | ||||||||
\(733\) | 28.5615 | 1.05494 | 0.527472 | − | 0.849573i | \(-0.323140\pi\) | ||||
0.527472 | + | 0.849573i | \(0.323140\pi\) | |||||||
\(734\) | −61.4056 | −2.26652 | ||||||||
\(735\) | 19.8014 | 0.730386 | ||||||||
\(736\) | −6.08310 | −0.224226 | ||||||||
\(737\) | 43.2624 | 1.59359 | ||||||||
\(738\) | 0.828070 | 0.0304817 | ||||||||
\(739\) | 12.1462 | 0.446804 | 0.223402 | − | 0.974726i | \(-0.428284\pi\) | ||||
0.223402 | + | 0.974726i | \(0.428284\pi\) | |||||||
\(740\) | 1.18656 | 0.0436187 | ||||||||
\(741\) | 35.6728 | 1.31047 | ||||||||
\(742\) | 2.48271 | 0.0911431 | ||||||||
\(743\) | 17.7516 | 0.651243 | 0.325621 | − | 0.945500i | \(-0.394427\pi\) | ||||
0.325621 | + | 0.945500i | \(0.394427\pi\) | |||||||
\(744\) | −3.25612 | −0.119375 | ||||||||
\(745\) | −36.1528 | −1.32453 | ||||||||
\(746\) | −42.8614 | −1.56927 | ||||||||
\(747\) | −14.1343 | −0.517148 | ||||||||
\(748\) | 4.28751 | 0.156767 | ||||||||
\(749\) | 0.0780108 | 0.00285045 | ||||||||
\(750\) | −8.92144 | −0.325765 | ||||||||
\(751\) | −15.6226 | −0.570077 | −0.285039 | − | 0.958516i | \(-0.592006\pi\) | ||||
−0.285039 | + | 0.958516i | \(0.592006\pi\) | |||||||
\(752\) | −32.1828 | −1.17359 | ||||||||
\(753\) | 6.24384 | 0.227538 | ||||||||
\(754\) | −39.9035 | −1.45320 | ||||||||
\(755\) | −19.7458 | −0.718621 | ||||||||
\(756\) | 0.153857 | 0.00559574 | ||||||||
\(757\) | 22.9539 | 0.834273 | 0.417136 | − | 0.908844i | \(-0.363034\pi\) | ||||
0.417136 | + | 0.908844i | \(0.363034\pi\) | |||||||
\(758\) | 16.9222 | 0.614643 | ||||||||
\(759\) | 9.01312 | 0.327155 | ||||||||
\(760\) | −35.8076 | −1.29888 | ||||||||
\(761\) | 25.4760 | 0.923505 | 0.461753 | − | 0.887009i | \(-0.347221\pi\) | ||||
0.461753 | + | 0.887009i | \(0.347221\pi\) | |||||||
\(762\) | −2.44386 | −0.0885317 | ||||||||
\(763\) | 3.28233 | 0.118828 | ||||||||
\(764\) | 5.98649 | 0.216584 | ||||||||
\(765\) | 2.84674 | 0.102924 | ||||||||
\(766\) | 25.1726 | 0.909522 | ||||||||
\(767\) | 42.3954 | 1.53081 | ||||||||
\(768\) | −15.5005 | −0.559327 | ||||||||
\(769\) | −39.6679 | −1.43046 | −0.715230 | − | 0.698889i | \(-0.753678\pi\) | ||||
−0.715230 | + | 0.698889i | \(0.753678\pi\) | |||||||
\(770\) | 5.79398 | 0.208800 | ||||||||
\(771\) | −20.5485 | −0.740036 | ||||||||
\(772\) | 2.75251 | 0.0990651 | ||||||||
\(773\) | −8.15404 | −0.293280 | −0.146640 | − | 0.989190i | \(-0.546846\pi\) | ||||
−0.146640 | + | 0.989190i | \(0.546846\pi\) | |||||||
\(774\) | 19.6673 | 0.706926 | ||||||||
\(775\) | 4.82206 | 0.173213 | ||||||||
\(776\) | 36.1644 | 1.29823 | ||||||||
\(777\) | 0.119710 | 0.00429456 | ||||||||
\(778\) | −16.4897 | −0.591184 | ||||||||
\(779\) | 3.00663 | 0.107724 | ||||||||
\(780\) | −12.3852 | −0.443462 | ||||||||
\(781\) | 77.9986 | 2.79101 | ||||||||
\(782\) | 2.54313 | 0.0909421 | ||||||||
\(783\) | −4.06149 | −0.145146 | ||||||||
\(784\) | 34.2792 | 1.22426 | ||||||||
\(785\) | −2.84674 | −0.101605 | ||||||||
\(786\) | 6.94259 | 0.247634 | ||||||||
\(787\) | −14.5143 | −0.517379 | −0.258690 | − | 0.965960i | \(-0.583291\pi\) | ||||
−0.258690 | + | 0.965960i | \(0.583291\pi\) | |||||||
\(788\) | 2.73907 | 0.0975752 | ||||||||
\(789\) | 11.0544 | 0.393547 | ||||||||
\(790\) | −55.6375 | −1.97949 | ||||||||
\(791\) | −4.41506 | −0.156981 | ||||||||
\(792\) | 12.2778 | 0.436273 | ||||||||
\(793\) | −7.13980 | −0.253542 | ||||||||
\(794\) | −36.6209 | −1.29963 | ||||||||
\(795\) | −20.3416 | −0.721444 | ||||||||
\(796\) | 3.77600 | 0.133837 | ||||||||
\(797\) | 42.1463 | 1.49290 | 0.746449 | − | 0.665442i | \(-0.231757\pi\) | ||||
0.746449 | + | 0.665442i | \(0.231757\pi\) | |||||||
\(798\) | 2.08514 | 0.0738130 | ||||||||
\(799\) | 6.53043 | 0.231030 | ||||||||
\(800\) | 12.2717 | 0.433870 | ||||||||
\(801\) | 13.5101 | 0.477356 | ||||||||
\(802\) | 41.6550 | 1.47089 | ||||||||
\(803\) | −64.0801 | −2.26134 | ||||||||
\(804\) | −5.40548 | −0.190636 | ||||||||
\(805\) | 0.920737 | 0.0324517 | ||||||||
\(806\) | −15.2632 | −0.537622 | ||||||||
\(807\) | 6.38068 | 0.224611 | ||||||||
\(808\) | −12.0090 | −0.422476 | ||||||||
\(809\) | −11.4192 | −0.401477 | −0.200739 | − | 0.979645i | \(-0.564334\pi\) | ||||
−0.200739 | + | 0.979645i | \(0.564334\pi\) | |||||||
\(810\) | −4.70524 | −0.165325 | ||||||||
\(811\) | −48.2942 | −1.69584 | −0.847919 | − | 0.530125i | \(-0.822145\pi\) | ||||
−0.847919 | + | 0.530125i | \(0.822145\pi\) | |||||||
\(812\) | −0.624891 | −0.0219294 | ||||||||
\(813\) | 7.66461 | 0.268809 | ||||||||
\(814\) | −5.51380 | −0.193259 | ||||||||
\(815\) | 19.9836 | 0.699996 | ||||||||
\(816\) | 4.92813 | 0.172519 | ||||||||
\(817\) | 71.4096 | 2.49831 | ||||||||
\(818\) | 41.3669 | 1.44636 | ||||||||
\(819\) | −1.24952 | −0.0436619 | ||||||||
\(820\) | −1.04387 | −0.0364534 | ||||||||
\(821\) | 2.29552 | 0.0801144 | 0.0400572 | − | 0.999197i | \(-0.487246\pi\) | ||||
0.0400572 | + | 0.999197i | \(0.487246\pi\) | |||||||
\(822\) | −2.07240 | −0.0722833 | ||||||||
\(823\) | 9.17424 | 0.319794 | 0.159897 | − | 0.987134i | \(-0.448884\pi\) | ||||
0.159897 | + | 0.987134i | \(0.448884\pi\) | |||||||
\(824\) | 5.65600 | 0.197036 | ||||||||
\(825\) | −18.1825 | −0.633034 | ||||||||
\(826\) | 2.47808 | 0.0862234 | ||||||||
\(827\) | 47.9175 | 1.66625 | 0.833127 | − | 0.553082i | \(-0.186549\pi\) | ||||
0.833127 | + | 0.553082i | \(0.186549\pi\) | |||||||
\(828\) | −1.12616 | −0.0391366 | ||||||||
\(829\) | 39.4460 | 1.37002 | 0.685008 | − | 0.728535i | \(-0.259799\pi\) | ||||
0.685008 | + | 0.728535i | \(0.259799\pi\) | |||||||
\(830\) | 66.5054 | 2.30844 | ||||||||
\(831\) | −5.75758 | −0.199728 | ||||||||
\(832\) | 19.7440 | 0.684499 | ||||||||
\(833\) | −6.95581 | −0.241005 | ||||||||
\(834\) | −15.5763 | −0.539364 | ||||||||
\(835\) | −1.61800 | −0.0559933 | ||||||||
\(836\) | −25.7307 | −0.889916 | ||||||||
\(837\) | −1.55353 | −0.0536978 | ||||||||
\(838\) | −6.52213 | −0.225303 | ||||||||
\(839\) | 34.3489 | 1.18586 | 0.592929 | − | 0.805255i | \(-0.297972\pi\) | ||||
0.592929 | + | 0.805255i | \(0.297972\pi\) | |||||||
\(840\) | 1.25424 | 0.0432755 | ||||||||
\(841\) | −12.5043 | −0.431182 | ||||||||
\(842\) | −9.38273 | −0.323350 | ||||||||
\(843\) | −17.7636 | −0.611812 | ||||||||
\(844\) | 6.63154 | 0.228267 | ||||||||
\(845\) | 63.5765 | 2.18710 | ||||||||
\(846\) | −10.7938 | −0.371100 | ||||||||
\(847\) | −4.90101 | −0.168401 | ||||||||
\(848\) | −35.2144 | −1.20927 | ||||||||
\(849\) | 30.0100 | 1.02994 | ||||||||
\(850\) | −5.13035 | −0.175970 | ||||||||
\(851\) | −0.876213 | −0.0300362 | ||||||||
\(852\) | −9.74564 | −0.333880 | ||||||||
\(853\) | −53.6133 | −1.83568 | −0.917842 | − | 0.396945i | \(-0.870070\pi\) | ||||
−0.917842 | + | 0.396945i | \(0.870070\pi\) | |||||||
\(854\) | −0.417333 | −0.0142808 | ||||||||
\(855\) | −17.0842 | −0.584267 | ||||||||
\(856\) | −0.777824 | −0.0265855 | ||||||||
\(857\) | −17.1709 | −0.586546 | −0.293273 | − | 0.956029i | \(-0.594744\pi\) | ||||
−0.293273 | + | 0.956029i | \(0.594744\pi\) | |||||||
\(858\) | 57.5527 | 1.96482 | ||||||||
\(859\) | −54.5231 | −1.86030 | −0.930152 | − | 0.367174i | \(-0.880325\pi\) | ||||
−0.930152 | + | 0.367174i | \(0.880325\pi\) | |||||||
\(860\) | −24.7926 | −0.845422 | ||||||||
\(861\) | −0.105314 | −0.00358909 | ||||||||
\(862\) | −31.1052 | −1.05945 | ||||||||
\(863\) | −10.8298 | −0.368651 | −0.184326 | − | 0.982865i | \(-0.559010\pi\) | ||||
−0.184326 | + | 0.982865i | \(0.559010\pi\) | |||||||
\(864\) | −3.95359 | −0.134504 | ||||||||
\(865\) | 44.1859 | 1.50237 | ||||||||
\(866\) | 33.7951 | 1.14840 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −0.239022 | −0.00811293 | ||||||||
\(869\) | 69.2670 | 2.34972 | ||||||||
\(870\) | 19.1103 | 0.647901 | ||||||||
\(871\) | 43.8996 | 1.48748 | ||||||||
\(872\) | −32.7272 | −1.10828 | ||||||||
\(873\) | 17.2545 | 0.583975 | ||||||||
\(874\) | −15.2621 | −0.516249 | ||||||||
\(875\) | 1.13463 | 0.0383575 | ||||||||
\(876\) | 8.00658 | 0.270517 | ||||||||
\(877\) | 13.9853 | 0.472250 | 0.236125 | − | 0.971723i | \(-0.424123\pi\) | ||||
0.236125 | + | 0.971723i | \(0.424123\pi\) | |||||||
\(878\) | −19.4311 | −0.655770 | ||||||||
\(879\) | 2.13300 | 0.0719442 | ||||||||
\(880\) | −82.1810 | −2.77032 | ||||||||
\(881\) | 40.7496 | 1.37289 | 0.686445 | − | 0.727182i | \(-0.259170\pi\) | ||||
0.686445 | + | 0.727182i | \(0.259170\pi\) | |||||||
\(882\) | 11.4969 | 0.387122 | ||||||||
\(883\) | 50.6880 | 1.70579 | 0.852894 | − | 0.522084i | \(-0.174845\pi\) | ||||
0.852894 | + | 0.522084i | \(0.174845\pi\) | |||||||
\(884\) | 4.35066 | 0.146329 | ||||||||
\(885\) | −20.3037 | −0.682502 | ||||||||
\(886\) | 60.6638 | 2.03804 | ||||||||
\(887\) | 14.8357 | 0.498136 | 0.249068 | − | 0.968486i | \(-0.419876\pi\) | ||||
0.249068 | + | 0.968486i | \(0.419876\pi\) | |||||||
\(888\) | −1.19359 | −0.0400543 | ||||||||
\(889\) | 0.310811 | 0.0104243 | ||||||||
\(890\) | −63.5683 | −2.13081 | ||||||||
\(891\) | 5.85789 | 0.196247 | ||||||||
\(892\) | −15.1920 | −0.508666 | ||||||||
\(893\) | −39.1912 | −1.31148 | ||||||||
\(894\) | −20.9907 | −0.702035 | ||||||||
\(895\) | −46.5233 | −1.55510 | ||||||||
\(896\) | 2.81624 | 0.0940838 | ||||||||
\(897\) | 9.14587 | 0.305372 | ||||||||
\(898\) | 6.31712 | 0.210805 | ||||||||
\(899\) | 6.30965 | 0.210439 | ||||||||
\(900\) | 2.27184 | 0.0757280 | ||||||||
\(901\) | 7.14559 | 0.238054 | ||||||||
\(902\) | 4.85074 | 0.161512 | ||||||||
\(903\) | −2.50129 | −0.0832377 | ||||||||
\(904\) | 44.0213 | 1.46413 | ||||||||
\(905\) | −53.3248 | −1.77258 | ||||||||
\(906\) | −11.4646 | −0.380887 | ||||||||
\(907\) | 11.8684 | 0.394083 | 0.197041 | − | 0.980395i | \(-0.436867\pi\) | ||||
0.197041 | + | 0.980395i | \(0.436867\pi\) | |||||||
\(908\) | 1.83601 | 0.0609300 | ||||||||
\(909\) | −5.72965 | −0.190040 | ||||||||
\(910\) | 5.87931 | 0.194897 | ||||||||
\(911\) | 21.1556 | 0.700916 | 0.350458 | − | 0.936578i | \(-0.386026\pi\) | ||||
0.350458 | + | 0.936578i | \(0.386026\pi\) | |||||||
\(912\) | −29.5753 | −0.979336 | ||||||||
\(913\) | −82.7972 | −2.74019 | ||||||||
\(914\) | −0.739763 | −0.0244692 | ||||||||
\(915\) | 3.41935 | 0.113040 | ||||||||
\(916\) | 19.4394 | 0.642295 | ||||||||
\(917\) | −0.882960 | −0.0291579 | ||||||||
\(918\) | 1.65285 | 0.0545523 | ||||||||
\(919\) | 45.0715 | 1.48677 | 0.743386 | − | 0.668862i | \(-0.233218\pi\) | ||||
0.743386 | + | 0.668862i | \(0.233218\pi\) | |||||||
\(920\) | −9.18042 | −0.302669 | ||||||||
\(921\) | 29.6255 | 0.976194 | ||||||||
\(922\) | 20.5661 | 0.677307 | ||||||||
\(923\) | 79.1474 | 2.60517 | ||||||||
\(924\) | 0.901279 | 0.0296499 | ||||||||
\(925\) | 1.76762 | 0.0581190 | ||||||||
\(926\) | −34.7522 | −1.14203 | ||||||||
\(927\) | 2.69854 | 0.0886318 | ||||||||
\(928\) | 16.0575 | 0.527112 | ||||||||
\(929\) | −5.47683 | −0.179689 | −0.0898444 | − | 0.995956i | \(-0.528637\pi\) | ||||
−0.0898444 | + | 0.995956i | \(0.528637\pi\) | |||||||
\(930\) | 7.30974 | 0.239696 | ||||||||
\(931\) | 41.7440 | 1.36811 | ||||||||
\(932\) | 16.3481 | 0.535500 | ||||||||
\(933\) | 10.9032 | 0.356954 | ||||||||
\(934\) | 43.5406 | 1.42469 | ||||||||
\(935\) | 16.6759 | 0.545360 | ||||||||
\(936\) | 12.4587 | 0.407224 | ||||||||
\(937\) | −21.1231 | −0.690061 | −0.345030 | − | 0.938592i | \(-0.612131\pi\) | ||||
−0.345030 | + | 0.938592i | \(0.612131\pi\) | |||||||
\(938\) | 2.56600 | 0.0837829 | ||||||||
\(939\) | 6.91690 | 0.225725 | ||||||||
\(940\) | 13.6067 | 0.443803 | ||||||||
\(941\) | −0.116854 | −0.00380933 | −0.00190466 | − | 0.999998i | \(-0.500606\pi\) | ||||
−0.00190466 | + | 0.999998i | \(0.500606\pi\) | |||||||
\(942\) | −1.65285 | −0.0538528 | ||||||||
\(943\) | 0.770845 | 0.0251022 | ||||||||
\(944\) | −35.1488 | −1.14399 | ||||||||
\(945\) | 0.598414 | 0.0194664 | ||||||||
\(946\) | 115.209 | 3.74576 | ||||||||
\(947\) | 54.3483 | 1.76608 | 0.883041 | − | 0.469297i | \(-0.155492\pi\) | ||||
0.883041 | + | 0.469297i | \(0.155492\pi\) | |||||||
\(948\) | −8.65466 | −0.281090 | ||||||||
\(949\) | −65.0239 | −2.11077 | ||||||||
\(950\) | 30.7889 | 0.998923 | ||||||||
\(951\) | 11.9804 | 0.388491 | ||||||||
\(952\) | −0.440589 | −0.0142796 | ||||||||
\(953\) | 40.8873 | 1.32447 | 0.662235 | − | 0.749296i | \(-0.269608\pi\) | ||||
0.662235 | + | 0.749296i | \(0.269608\pi\) | |||||||
\(954\) | −11.8106 | −0.382382 | ||||||||
\(955\) | 23.2839 | 0.753449 | ||||||||
\(956\) | 5.29004 | 0.171092 | ||||||||
\(957\) | −23.7918 | −0.769079 | ||||||||
\(958\) | −0.767449 | −0.0247951 | ||||||||
\(959\) | 0.263568 | 0.00851107 | ||||||||
\(960\) | −9.45566 | −0.305180 | ||||||||
\(961\) | −28.5865 | −0.922147 | ||||||||
\(962\) | −5.59501 | −0.180390 | ||||||||
\(963\) | −0.371109 | −0.0119588 | ||||||||
\(964\) | 5.12960 | 0.165213 | ||||||||
\(965\) | 10.7056 | 0.344627 | ||||||||
\(966\) | 0.534591 | 0.0172002 | ||||||||
\(967\) | 18.4373 | 0.592905 | 0.296453 | − | 0.955048i | \(-0.404196\pi\) | ||||
0.296453 | + | 0.955048i | \(0.404196\pi\) | |||||||
\(968\) | 48.8666 | 1.57063 | ||||||||
\(969\) | 6.00132 | 0.192790 | ||||||||
\(970\) | −81.1865 | −2.60674 | ||||||||
\(971\) | −20.8773 | −0.669985 | −0.334993 | − | 0.942221i | \(-0.608734\pi\) | ||||
−0.334993 | + | 0.942221i | \(0.608734\pi\) | |||||||
\(972\) | −0.731922 | −0.0234764 | ||||||||
\(973\) | 1.98100 | 0.0635080 | ||||||||
\(974\) | −68.7526 | −2.20297 | ||||||||
\(975\) | −18.4503 | −0.590883 | ||||||||
\(976\) | 5.91940 | 0.189475 | ||||||||
\(977\) | −11.9099 | −0.381033 | −0.190517 | − | 0.981684i | \(-0.561016\pi\) | ||||
−0.190517 | + | 0.981684i | \(0.561016\pi\) | |||||||
\(978\) | 11.6027 | 0.371015 | ||||||||
\(979\) | 79.1406 | 2.52934 | ||||||||
\(980\) | −14.4931 | −0.462964 | ||||||||
\(981\) | −15.6145 | −0.498533 | ||||||||
\(982\) | 58.8364 | 1.87755 | ||||||||
\(983\) | −12.6322 | −0.402904 | −0.201452 | − | 0.979498i | \(-0.564566\pi\) | ||||
−0.201452 | + | 0.979498i | \(0.564566\pi\) | |||||||
\(984\) | 1.05006 | 0.0334746 | ||||||||
\(985\) | 10.6533 | 0.339444 | ||||||||
\(986\) | −6.71305 | −0.213787 | ||||||||
\(987\) | 1.37276 | 0.0436955 | ||||||||
\(988\) | −26.1097 | −0.830661 | ||||||||
\(989\) | 18.3081 | 0.582165 | ||||||||
\(990\) | −27.5628 | −0.876003 | ||||||||
\(991\) | −16.5903 | −0.527009 | −0.263504 | − | 0.964658i | \(-0.584878\pi\) | ||||
−0.263504 | + | 0.964658i | \(0.584878\pi\) | |||||||
\(992\) | 6.14201 | 0.195009 | ||||||||
\(993\) | −24.3174 | −0.771689 | ||||||||
\(994\) | 4.62630 | 0.146737 | ||||||||
\(995\) | 14.6864 | 0.465591 | ||||||||
\(996\) | 10.3452 | 0.327801 | ||||||||
\(997\) | 46.0986 | 1.45996 | 0.729978 | − | 0.683470i | \(-0.239530\pi\) | ||||
0.729978 | + | 0.683470i | \(0.239530\pi\) | |||||||
\(998\) | 23.4953 | 0.743731 | ||||||||
\(999\) | −0.569477 | −0.0180174 |
(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 | 8007.2.a.j.1.15 | ✓ | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.j.1.15 | ✓ | 64 | 1.1 | even | 1 | trivial |