Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2009,2,Mod(1,2009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2009, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2009 = 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2009.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: | \(16.0419457661\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.633117.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 6x^{3} + 4x^{2} + 6x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 287) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.460315\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.460315 | −0.325492 | −0.162746 | − | 0.986668i | \(-0.552035\pi\) | ||||
−0.162746 | + | 0.986668i | \(0.552035\pi\) | |||||||
\(3\) | −0.539685 | −0.311588 | −0.155794 | − | 0.987790i | \(-0.549794\pi\) | ||||
−0.155794 | + | 0.987790i | \(0.549794\pi\) | |||||||
\(4\) | −1.78811 | −0.894055 | ||||||||
\(5\) | −4.10136 | −1.83418 | −0.917091 | − | 0.398678i | \(-0.869469\pi\) | ||||
−0.917091 | + | 0.398678i | \(0.869469\pi\) | |||||||
\(6\) | 0.248425 | 0.101419 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.74372 | 0.616499 | ||||||||
\(9\) | −2.70874 | −0.902913 | ||||||||
\(10\) | 1.88791 | 0.597011 | ||||||||
\(11\) | 2.76768 | 0.834486 | 0.417243 | − | 0.908795i | \(-0.362996\pi\) | ||||
0.417243 | + | 0.908795i | \(0.362996\pi\) | |||||||
\(12\) | 0.965017 | 0.278576 | ||||||||
\(13\) | 4.05697 | 1.12520 | 0.562600 | − | 0.826729i | \(-0.309801\pi\) | ||||
0.562600 | + | 0.826729i | \(0.309801\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.21344 | 0.571508 | ||||||||
\(16\) | 2.77356 | 0.693390 | ||||||||
\(17\) | −5.22447 | −1.26712 | −0.633560 | − | 0.773694i | \(-0.718407\pi\) | ||||
−0.633560 | + | 0.773694i | \(0.718407\pi\) | |||||||
\(18\) | 1.24687 | 0.293891 | ||||||||
\(19\) | 0.109209 | 0.0250542 | 0.0125271 | − | 0.999922i | \(-0.496012\pi\) | ||||
0.0125271 | + | 0.999922i | \(0.496012\pi\) | |||||||
\(20\) | 7.33368 | 1.63986 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.27400 | −0.271618 | ||||||||
\(23\) | 6.08681 | 1.26919 | 0.634593 | − | 0.772846i | \(-0.281168\pi\) | ||||
0.634593 | + | 0.772846i | \(0.281168\pi\) | |||||||
\(24\) | −0.941062 | −0.192093 | ||||||||
\(25\) | 11.8211 | 2.36422 | ||||||||
\(26\) | −1.86748 | −0.366243 | ||||||||
\(27\) | 3.08092 | 0.592924 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.25431 | 0.418614 | 0.209307 | − | 0.977850i | \(-0.432879\pi\) | ||||
0.209307 | + | 0.977850i | \(0.432879\pi\) | |||||||
\(30\) | −1.01888 | −0.186021 | ||||||||
\(31\) | 1.18073 | 0.212065 | 0.106032 | − | 0.994363i | \(-0.466185\pi\) | ||||
0.106032 | + | 0.994363i | \(0.466185\pi\) | |||||||
\(32\) | −4.76415 | −0.842192 | ||||||||
\(33\) | −1.49368 | −0.260016 | ||||||||
\(34\) | 2.40490 | 0.412437 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.84353 | 0.807254 | ||||||||
\(37\) | −8.95429 | −1.47208 | −0.736038 | − | 0.676940i | \(-0.763305\pi\) | ||||
−0.736038 | + | 0.676940i | \(0.763305\pi\) | |||||||
\(38\) | −0.0502704 | −0.00815494 | ||||||||
\(39\) | −2.18949 | −0.350598 | ||||||||
\(40\) | −7.15163 | −1.13077 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.93974 | −1.21080 | −0.605399 | − | 0.795922i | \(-0.706987\pi\) | ||||
−0.605399 | + | 0.795922i | \(0.706987\pi\) | |||||||
\(44\) | −4.94891 | −0.746077 | ||||||||
\(45\) | 11.1095 | 1.65611 | ||||||||
\(46\) | −2.80185 | −0.413110 | ||||||||
\(47\) | 10.5714 | 1.54199 | 0.770997 | − | 0.636839i | \(-0.219758\pi\) | ||||
0.770997 | + | 0.636839i | \(0.219758\pi\) | |||||||
\(48\) | −1.49685 | −0.216052 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.44143 | −0.769535 | ||||||||
\(51\) | 2.81957 | 0.394819 | ||||||||
\(52\) | −7.25431 | −1.00599 | ||||||||
\(53\) | 6.23100 | 0.855893 | 0.427947 | − | 0.903804i | \(-0.359237\pi\) | ||||
0.427947 | + | 0.903804i | \(0.359237\pi\) | |||||||
\(54\) | −1.41819 | −0.192992 | ||||||||
\(55\) | −11.3512 | −1.53060 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.0589384 | −0.00780658 | ||||||||
\(58\) | −1.03769 | −0.136255 | ||||||||
\(59\) | 9.43006 | 1.22769 | 0.613845 | − | 0.789427i | \(-0.289622\pi\) | ||||
0.613845 | + | 0.789427i | \(0.289622\pi\) | |||||||
\(60\) | −3.95788 | −0.510960 | ||||||||
\(61\) | −6.89732 | −0.883111 | −0.441556 | − | 0.897234i | \(-0.645573\pi\) | ||||
−0.441556 | + | 0.897234i | \(0.645573\pi\) | |||||||
\(62\) | −0.543506 | −0.0690253 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.35411 | −0.419264 | ||||||||
\(65\) | −16.6391 | −2.06382 | ||||||||
\(66\) | 0.687561 | 0.0846329 | ||||||||
\(67\) | −1.35699 | −0.165782 | −0.0828912 | − | 0.996559i | \(-0.526415\pi\) | ||||
−0.0828912 | + | 0.996559i | \(0.526415\pi\) | |||||||
\(68\) | 9.34193 | 1.13288 | ||||||||
\(69\) | −3.28496 | −0.395463 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.90672 | −0.938356 | −0.469178 | − | 0.883104i | \(-0.655450\pi\) | ||||
−0.469178 | + | 0.883104i | \(0.655450\pi\) | |||||||
\(72\) | −4.72329 | −0.556645 | ||||||||
\(73\) | −9.88791 | −1.15729 | −0.578646 | − | 0.815579i | \(-0.696419\pi\) | ||||
−0.578646 | + | 0.815579i | \(0.696419\pi\) | |||||||
\(74\) | 4.12179 | 0.479148 | ||||||||
\(75\) | −6.37969 | −0.736663 | ||||||||
\(76\) | −0.195277 | −0.0223999 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.00785 | 0.114117 | ||||||||
\(79\) | −12.5668 | −1.41388 | −0.706939 | − | 0.707275i | \(-0.749924\pi\) | ||||
−0.706939 | + | 0.707275i | \(0.749924\pi\) | |||||||
\(80\) | −11.3754 | −1.27180 | ||||||||
\(81\) | 6.46349 | 0.718165 | ||||||||
\(82\) | −0.460315 | −0.0508332 | ||||||||
\(83\) | 14.9633 | 1.64244 | 0.821220 | − | 0.570611i | \(-0.193294\pi\) | ||||
0.821220 | + | 0.570611i | \(0.193294\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 21.4274 | 2.32413 | ||||||||
\(86\) | 3.65478 | 0.394105 | ||||||||
\(87\) | −1.21662 | −0.130435 | ||||||||
\(88\) | 4.82606 | 0.514460 | ||||||||
\(89\) | 0.852931 | 0.0904105 | 0.0452053 | − | 0.998978i | \(-0.485606\pi\) | ||||
0.0452053 | + | 0.998978i | \(0.485606\pi\) | |||||||
\(90\) | −5.11387 | −0.539049 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −10.8839 | −1.13472 | ||||||||
\(93\) | −0.637221 | −0.0660768 | ||||||||
\(94\) | −4.86616 | −0.501906 | ||||||||
\(95\) | −0.447904 | −0.0459540 | ||||||||
\(96\) | 2.57115 | 0.262416 | ||||||||
\(97\) | −9.92806 | −1.00804 | −0.504021 | − | 0.863691i | \(-0.668147\pi\) | ||||
−0.504021 | + | 0.863691i | \(0.668147\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.49692 | −0.753469 | ||||||||
\(100\) | −21.1375 | −2.11375 | ||||||||
\(101\) | −11.2908 | −1.12348 | −0.561740 | − | 0.827314i | \(-0.689868\pi\) | ||||
−0.561740 | + | 0.827314i | \(0.689868\pi\) | |||||||
\(102\) | −1.29789 | −0.128510 | ||||||||
\(103\) | 10.8690 | 1.07096 | 0.535479 | − | 0.844549i | \(-0.320131\pi\) | ||||
0.535479 | + | 0.844549i | \(0.320131\pi\) | |||||||
\(104\) | 7.07423 | 0.693685 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.86822 | −0.278586 | ||||||||
\(107\) | 1.99215 | 0.192588 | 0.0962941 | − | 0.995353i | \(-0.469301\pi\) | ||||
0.0962941 | + | 0.995353i | \(0.469301\pi\) | |||||||
\(108\) | −5.50903 | −0.530107 | ||||||||
\(109\) | −17.8607 | −1.71074 | −0.855371 | − | 0.518016i | \(-0.826671\pi\) | ||||
−0.855371 | + | 0.518016i | \(0.826671\pi\) | |||||||
\(110\) | 5.22514 | 0.498197 | ||||||||
\(111\) | 4.83250 | 0.458680 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.2536 | −1.52901 | −0.764506 | − | 0.644616i | \(-0.777017\pi\) | ||||
−0.764506 | + | 0.644616i | \(0.777017\pi\) | |||||||
\(114\) | 0.0271302 | 0.00254098 | ||||||||
\(115\) | −24.9642 | −2.32792 | ||||||||
\(116\) | −4.03095 | −0.374264 | ||||||||
\(117\) | −10.9893 | −1.01596 | ||||||||
\(118\) | −4.34079 | −0.399602 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.85963 | 0.352334 | ||||||||
\(121\) | −3.33996 | −0.303633 | ||||||||
\(122\) | 3.17494 | 0.287445 | ||||||||
\(123\) | −0.539685 | −0.0486618 | ||||||||
\(124\) | −2.11127 | −0.189598 | ||||||||
\(125\) | −27.9759 | −2.50224 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.3566 | 1.54015 | 0.770073 | − | 0.637955i | \(-0.220220\pi\) | ||||
0.770073 | + | 0.637955i | \(0.220220\pi\) | |||||||
\(128\) | 11.0723 | 0.978658 | ||||||||
\(129\) | 4.28496 | 0.377270 | ||||||||
\(130\) | 7.65921 | 0.671757 | ||||||||
\(131\) | 0.803568 | 0.0702080 | 0.0351040 | − | 0.999384i | \(-0.488824\pi\) | ||||
0.0351040 | + | 0.999384i | \(0.488824\pi\) | |||||||
\(132\) | 2.67086 | 0.232468 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.624641 | 0.0539608 | ||||||||
\(135\) | −12.6360 | −1.08753 | ||||||||
\(136\) | −9.11002 | −0.781178 | ||||||||
\(137\) | −4.63907 | −0.396343 | −0.198171 | − | 0.980167i | \(-0.563500\pi\) | ||||
−0.198171 | + | 0.980167i | \(0.563500\pi\) | |||||||
\(138\) | 1.51212 | 0.128720 | ||||||||
\(139\) | 0.0641748 | 0.00544323 | 0.00272162 | − | 0.999996i | \(-0.499134\pi\) | ||||
0.00272162 | + | 0.999996i | \(0.499134\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.70522 | −0.480466 | ||||||||
\(142\) | 3.63958 | 0.305427 | ||||||||
\(143\) | 11.2284 | 0.938964 | ||||||||
\(144\) | −7.51285 | −0.626071 | ||||||||
\(145\) | −9.24572 | −0.767815 | ||||||||
\(146\) | 4.55155 | 0.376689 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 16.0113 | 1.31612 | ||||||||
\(149\) | 14.2436 | 1.16688 | 0.583440 | − | 0.812156i | \(-0.301706\pi\) | ||||
0.583440 | + | 0.812156i | \(0.301706\pi\) | |||||||
\(150\) | 2.93666 | 0.239778 | ||||||||
\(151\) | 12.8350 | 1.04450 | 0.522249 | − | 0.852793i | \(-0.325093\pi\) | ||||
0.522249 | + | 0.852793i | \(0.325093\pi\) | |||||||
\(152\) | 0.190430 | 0.0154459 | ||||||||
\(153\) | 14.1517 | 1.14410 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.84258 | −0.388966 | ||||||||
\(156\) | 3.91504 | 0.313454 | ||||||||
\(157\) | −14.3051 | −1.14167 | −0.570835 | − | 0.821064i | \(-0.693381\pi\) | ||||
−0.570835 | + | 0.821064i | \(0.693381\pi\) | |||||||
\(158\) | 5.78469 | 0.460205 | ||||||||
\(159\) | −3.36278 | −0.266686 | ||||||||
\(160\) | 19.5395 | 1.54473 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.97524 | −0.233757 | ||||||||
\(163\) | 5.60958 | 0.439376 | 0.219688 | − | 0.975570i | \(-0.429496\pi\) | ||||
0.219688 | + | 0.975570i | \(0.429496\pi\) | |||||||
\(164\) | −1.78811 | −0.139628 | ||||||||
\(165\) | 6.12610 | 0.476916 | ||||||||
\(166\) | −6.88785 | −0.534600 | ||||||||
\(167\) | −4.49350 | −0.347717 | −0.173859 | − | 0.984771i | \(-0.555624\pi\) | ||||
−0.173859 | + | 0.984771i | \(0.555624\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.45899 | 0.266076 | ||||||||
\(170\) | −9.86335 | −0.756484 | ||||||||
\(171\) | −0.295818 | −0.0226218 | ||||||||
\(172\) | 14.1971 | 1.08252 | ||||||||
\(173\) | −14.2512 | −1.08350 | −0.541749 | − | 0.840541i | \(-0.682238\pi\) | ||||
−0.541749 | + | 0.840541i | \(0.682238\pi\) | |||||||
\(174\) | 0.560026 | 0.0424555 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.67632 | 0.578625 | ||||||||
\(177\) | −5.08927 | −0.382533 | ||||||||
\(178\) | −0.392617 | −0.0294279 | ||||||||
\(179\) | 5.78841 | 0.432646 | 0.216323 | − | 0.976322i | \(-0.430594\pi\) | ||||
0.216323 | + | 0.976322i | \(0.430594\pi\) | |||||||
\(180\) | −19.8650 | −1.48065 | ||||||||
\(181\) | 14.6662 | 1.09013 | 0.545065 | − | 0.838394i | \(-0.316505\pi\) | ||||
0.545065 | + | 0.838394i | \(0.316505\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.72238 | 0.275166 | ||||||||
\(184\) | 10.6137 | 0.782452 | ||||||||
\(185\) | 36.7247 | 2.70006 | ||||||||
\(186\) | 0.293322 | 0.0215074 | ||||||||
\(187\) | −14.4596 | −1.05739 | ||||||||
\(188\) | −18.9028 | −1.37863 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.206177 | 0.0149576 | ||||||||
\(191\) | 8.41984 | 0.609238 | 0.304619 | − | 0.952474i | \(-0.401471\pi\) | ||||
0.304619 | + | 0.952474i | \(0.401471\pi\) | |||||||
\(192\) | 1.81016 | 0.130637 | ||||||||
\(193\) | −8.76374 | −0.630828 | −0.315414 | − | 0.948954i | \(-0.602143\pi\) | ||||
−0.315414 | + | 0.948954i | \(0.602143\pi\) | |||||||
\(194\) | 4.57003 | 0.328109 | ||||||||
\(195\) | 8.97986 | 0.643061 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.9953 | −1.35336 | −0.676680 | − | 0.736277i | \(-0.736582\pi\) | ||||
−0.676680 | + | 0.736277i | \(0.736582\pi\) | |||||||
\(198\) | 3.45094 | 0.245248 | ||||||||
\(199\) | 6.81886 | 0.483376 | 0.241688 | − | 0.970354i | \(-0.422299\pi\) | ||||
0.241688 | + | 0.970354i | \(0.422299\pi\) | |||||||
\(200\) | 20.6128 | 1.45754 | ||||||||
\(201\) | 0.732347 | 0.0516558 | ||||||||
\(202\) | 5.19734 | 0.365684 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −5.04170 | −0.352990 | ||||||||
\(205\) | −4.10136 | −0.286451 | ||||||||
\(206\) | −5.00317 | −0.348588 | ||||||||
\(207\) | −16.4876 | −1.14597 | ||||||||
\(208\) | 11.2522 | 0.780203 | ||||||||
\(209\) | 0.302255 | 0.0209074 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.02073 | 0.345641 | 0.172821 | − | 0.984953i | \(-0.444712\pi\) | ||||
0.172821 | + | 0.984953i | \(0.444712\pi\) | |||||||
\(212\) | −11.1417 | −0.765216 | ||||||||
\(213\) | 4.26714 | 0.292380 | ||||||||
\(214\) | −0.917014 | −0.0626858 | ||||||||
\(215\) | 32.5637 | 2.22083 | ||||||||
\(216\) | 5.37228 | 0.365537 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.22152 | 0.556832 | ||||||||
\(219\) | 5.33636 | 0.360598 | ||||||||
\(220\) | 20.2973 | 1.36844 | ||||||||
\(221\) | −21.1955 | −1.42576 | ||||||||
\(222\) | −2.22447 | −0.149297 | ||||||||
\(223\) | −6.96231 | −0.466231 | −0.233115 | − | 0.972449i | \(-0.574892\pi\) | ||||
−0.233115 | + | 0.972449i | \(0.574892\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −32.0203 | −2.13469 | ||||||||
\(226\) | 7.48178 | 0.497681 | ||||||||
\(227\) | −10.1094 | −0.670987 | −0.335493 | − | 0.942043i | \(-0.608903\pi\) | ||||
−0.335493 | + | 0.942043i | \(0.608903\pi\) | |||||||
\(228\) | 0.105388 | 0.00697952 | ||||||||
\(229\) | 2.32356 | 0.153545 | 0.0767725 | − | 0.997049i | \(-0.475538\pi\) | ||||
0.0767725 | + | 0.997049i | \(0.475538\pi\) | |||||||
\(230\) | 11.4914 | 0.757718 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.93089 | 0.258075 | ||||||||
\(233\) | 17.5655 | 1.15075 | 0.575377 | − | 0.817888i | \(-0.304855\pi\) | ||||
0.575377 | + | 0.817888i | \(0.304855\pi\) | |||||||
\(234\) | 5.05852 | 0.330686 | ||||||||
\(235\) | −43.3570 | −2.82830 | ||||||||
\(236\) | −16.8620 | −1.09762 | ||||||||
\(237\) | 6.78213 | 0.440547 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.0063 | −1.48815 | −0.744077 | − | 0.668093i | \(-0.767111\pi\) | ||||
−0.744077 | + | 0.668093i | \(0.767111\pi\) | |||||||
\(240\) | 6.13912 | 0.396278 | ||||||||
\(241\) | 12.6808 | 0.816839 | 0.408420 | − | 0.912794i | \(-0.366080\pi\) | ||||
0.408420 | + | 0.912794i | \(0.366080\pi\) | |||||||
\(242\) | 1.53743 | 0.0988298 | ||||||||
\(243\) | −12.7310 | −0.816695 | ||||||||
\(244\) | 12.3332 | 0.789550 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.248425 | 0.0158390 | ||||||||
\(247\) | 0.443057 | 0.0281910 | ||||||||
\(248\) | 2.05886 | 0.130738 | ||||||||
\(249\) | −8.07550 | −0.511764 | ||||||||
\(250\) | 12.8777 | 0.814457 | ||||||||
\(251\) | 18.5629 | 1.17168 | 0.585840 | − | 0.810427i | \(-0.300765\pi\) | ||||
0.585840 | + | 0.810427i | \(0.300765\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.8463 | 1.05912 | ||||||||
\(254\) | −7.98948 | −0.501305 | ||||||||
\(255\) | −11.5641 | −0.724170 | ||||||||
\(256\) | 1.61150 | 0.100719 | ||||||||
\(257\) | −18.1358 | −1.13128 | −0.565639 | − | 0.824653i | \(-0.691370\pi\) | ||||
−0.565639 | + | 0.824653i | \(0.691370\pi\) | |||||||
\(258\) | −1.97243 | −0.122798 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 29.7525 | 1.84517 | ||||||||
\(261\) | −6.10633 | −0.377972 | ||||||||
\(262\) | −0.369894 | −0.0228521 | ||||||||
\(263\) | 4.24808 | 0.261948 | 0.130974 | − | 0.991386i | \(-0.458190\pi\) | ||||
0.130974 | + | 0.991386i | \(0.458190\pi\) | |||||||
\(264\) | −2.60456 | −0.160299 | ||||||||
\(265\) | −25.5555 | −1.56986 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.460315 | −0.0281708 | ||||||||
\(268\) | 2.42644 | 0.148219 | ||||||||
\(269\) | 1.31427 | 0.0801326 | 0.0400663 | − | 0.999197i | \(-0.487243\pi\) | ||||
0.0400663 | + | 0.999197i | \(0.487243\pi\) | |||||||
\(270\) | 5.81652 | 0.353982 | ||||||||
\(271\) | 7.91618 | 0.480874 | 0.240437 | − | 0.970665i | \(-0.422709\pi\) | ||||
0.240437 | + | 0.970665i | \(0.422709\pi\) | |||||||
\(272\) | −14.4904 | −0.878608 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.13543 | 0.129006 | ||||||||
\(275\) | 32.7171 | 1.97291 | ||||||||
\(276\) | 5.87387 | 0.353566 | ||||||||
\(277\) | 0.0684353 | 0.00411188 | 0.00205594 | − | 0.999998i | \(-0.499346\pi\) | ||||
0.00205594 | + | 0.999998i | \(0.499346\pi\) | |||||||
\(278\) | −0.0295406 | −0.00177173 | ||||||||
\(279\) | −3.19828 | −0.191476 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.33050 | 0.496956 | 0.248478 | − | 0.968638i | \(-0.420070\pi\) | ||||
0.248478 | + | 0.968638i | \(0.420070\pi\) | |||||||
\(282\) | 2.62619 | 0.156388 | ||||||||
\(283\) | −3.09424 | −0.183934 | −0.0919668 | − | 0.995762i | \(-0.529315\pi\) | ||||
−0.0919668 | + | 0.995762i | \(0.529315\pi\) | |||||||
\(284\) | 14.1381 | 0.838942 | ||||||||
\(285\) | 0.241727 | 0.0143187 | ||||||||
\(286\) | −5.16859 | −0.305625 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 12.9049 | 0.760426 | ||||||||
\(289\) | 10.2951 | 0.605593 | ||||||||
\(290\) | 4.25594 | 0.249917 | ||||||||
\(291\) | 5.35803 | 0.314093 | ||||||||
\(292\) | 17.6807 | 1.03468 | ||||||||
\(293\) | −4.47354 | −0.261347 | −0.130674 | − | 0.991425i | \(-0.541714\pi\) | ||||
−0.130674 | + | 0.991425i | \(0.541714\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −38.6760 | −2.25181 | ||||||||
\(296\) | −15.6138 | −0.907533 | ||||||||
\(297\) | 8.52700 | 0.494787 | ||||||||
\(298\) | −6.55653 | −0.379809 | ||||||||
\(299\) | 24.6940 | 1.42809 | ||||||||
\(300\) | 11.4076 | 0.658617 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5.90813 | −0.339975 | ||||||||
\(303\) | 6.09350 | 0.350063 | ||||||||
\(304\) | 0.302897 | 0.0173723 | ||||||||
\(305\) | 28.2884 | 1.61979 | ||||||||
\(306\) | −6.51425 | −0.372395 | ||||||||
\(307\) | −25.8316 | −1.47429 | −0.737143 | − | 0.675737i | \(-0.763825\pi\) | ||||
−0.737143 | + | 0.675737i | \(0.763825\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.86586 | −0.333697 | ||||||||
\(310\) | 2.22911 | 0.126605 | ||||||||
\(311\) | −13.6802 | −0.775735 | −0.387867 | − | 0.921715i | \(-0.626788\pi\) | ||||
−0.387867 | + | 0.921715i | \(0.626788\pi\) | |||||||
\(312\) | −3.81786 | −0.216144 | ||||||||
\(313\) | −24.0537 | −1.35959 | −0.679797 | − | 0.733400i | \(-0.737932\pi\) | ||||
−0.679797 | + | 0.733400i | \(0.737932\pi\) | |||||||
\(314\) | 6.58484 | 0.371604 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 22.4709 | 1.26408 | ||||||||
\(317\) | 3.80766 | 0.213859 | 0.106930 | − | 0.994267i | \(-0.465898\pi\) | ||||
0.106930 | + | 0.994267i | \(0.465898\pi\) | |||||||
\(318\) | 1.54794 | 0.0868039 | ||||||||
\(319\) | 6.23920 | 0.349328 | ||||||||
\(320\) | 13.7564 | 0.769006 | ||||||||
\(321\) | −1.07513 | −0.0600081 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.570558 | −0.0317467 | ||||||||
\(324\) | −11.5574 | −0.642080 | ||||||||
\(325\) | 47.9579 | 2.66023 | ||||||||
\(326\) | −2.58217 | −0.143013 | ||||||||
\(327\) | 9.63914 | 0.533046 | ||||||||
\(328\) | 1.74372 | 0.0962810 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.81993 | −0.155232 | ||||||||
\(331\) | −21.1336 | −1.16161 | −0.580805 | − | 0.814043i | \(-0.697262\pi\) | ||||
−0.580805 | + | 0.814043i | \(0.697262\pi\) | |||||||
\(332\) | −26.7561 | −1.46843 | ||||||||
\(333\) | 24.2548 | 1.32916 | ||||||||
\(334\) | 2.06842 | 0.113179 | ||||||||
\(335\) | 5.56549 | 0.304075 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.7801 | −1.13197 | −0.565983 | − | 0.824417i | \(-0.691503\pi\) | ||||
−0.565983 | + | 0.824417i | \(0.691503\pi\) | |||||||
\(338\) | −1.59222 | −0.0866055 | ||||||||
\(339\) | 8.77185 | 0.476421 | ||||||||
\(340\) | −38.3146 | −2.07790 | ||||||||
\(341\) | 3.26787 | 0.176965 | ||||||||
\(342\) | 0.136169 | 0.00736320 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −13.8447 | −0.746456 | ||||||||
\(345\) | 13.4728 | 0.725351 | ||||||||
\(346\) | 6.56003 | 0.352669 | ||||||||
\(347\) | 21.8355 | 1.17219 | 0.586096 | − | 0.810242i | \(-0.300664\pi\) | ||||
0.586096 | + | 0.810242i | \(0.300664\pi\) | |||||||
\(348\) | 2.17545 | 0.116616 | ||||||||
\(349\) | 6.23178 | 0.333579 | 0.166790 | − | 0.985992i | \(-0.446660\pi\) | ||||
0.166790 | + | 0.985992i | \(0.446660\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.4992 | 0.667158 | ||||||||
\(352\) | −13.1856 | −0.702797 | ||||||||
\(353\) | −28.5933 | −1.52187 | −0.760933 | − | 0.648830i | \(-0.775258\pi\) | ||||
−0.760933 | + | 0.648830i | \(0.775258\pi\) | |||||||
\(354\) | 2.34266 | 0.124511 | ||||||||
\(355\) | 32.4283 | 1.72112 | ||||||||
\(356\) | −1.52514 | −0.0808320 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.66449 | −0.140823 | ||||||||
\(359\) | 6.89008 | 0.363644 | 0.181822 | − | 0.983331i | \(-0.441800\pi\) | ||||
0.181822 | + | 0.983331i | \(0.441800\pi\) | |||||||
\(360\) | 19.3719 | 1.02099 | ||||||||
\(361\) | −18.9881 | −0.999372 | ||||||||
\(362\) | −6.75107 | −0.354828 | ||||||||
\(363\) | 1.80253 | 0.0946081 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 40.5539 | 2.12269 | ||||||||
\(366\) | −1.71347 | −0.0895644 | ||||||||
\(367\) | −27.9358 | −1.45824 | −0.729119 | − | 0.684387i | \(-0.760070\pi\) | ||||
−0.729119 | + | 0.684387i | \(0.760070\pi\) | |||||||
\(368\) | 16.8821 | 0.880042 | ||||||||
\(369\) | −2.70874 | −0.141011 | ||||||||
\(370\) | −16.9049 | −0.878845 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.13942 | 0.0590763 | ||||||||
\(373\) | 6.20063 | 0.321057 | 0.160528 | − | 0.987031i | \(-0.448680\pi\) | ||||
0.160528 | + | 0.987031i | \(0.448680\pi\) | |||||||
\(374\) | 6.65599 | 0.344173 | ||||||||
\(375\) | 15.0982 | 0.779666 | ||||||||
\(376\) | 18.4335 | 0.950637 | ||||||||
\(377\) | 9.14565 | 0.471025 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.4006 | −0.945174 | −0.472587 | − | 0.881284i | \(-0.656680\pi\) | ||||
−0.472587 | + | 0.881284i | \(0.656680\pi\) | |||||||
\(380\) | 0.800902 | 0.0410854 | ||||||||
\(381\) | −9.36709 | −0.479890 | ||||||||
\(382\) | −3.87577 | −0.198302 | ||||||||
\(383\) | 34.2322 | 1.74918 | 0.874591 | − | 0.484861i | \(-0.161130\pi\) | ||||
0.874591 | + | 0.484861i | \(0.161130\pi\) | |||||||
\(384\) | −5.97554 | −0.304938 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.03408 | 0.205329 | ||||||||
\(387\) | 21.5067 | 1.09325 | ||||||||
\(388\) | 17.7525 | 0.901245 | ||||||||
\(389\) | −23.0399 | −1.16817 | −0.584085 | − | 0.811693i | \(-0.698546\pi\) | ||||
−0.584085 | + | 0.811693i | \(0.698546\pi\) | |||||||
\(390\) | −4.13356 | −0.209311 | ||||||||
\(391\) | −31.8003 | −1.60821 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.433674 | −0.0218760 | ||||||||
\(394\) | 8.74382 | 0.440507 | ||||||||
\(395\) | 51.5410 | 2.59331 | ||||||||
\(396\) | 13.4053 | 0.673643 | ||||||||
\(397\) | −1.35123 | −0.0678165 | −0.0339082 | − | 0.999425i | \(-0.510795\pi\) | ||||
−0.0339082 | + | 0.999425i | \(0.510795\pi\) | |||||||
\(398\) | −3.13882 | −0.157335 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 32.7866 | 1.63933 | ||||||||
\(401\) | 1.54256 | 0.0770319 | 0.0385160 | − | 0.999258i | \(-0.487737\pi\) | ||||
0.0385160 | + | 0.999258i | \(0.487737\pi\) | |||||||
\(402\) | −0.337110 | −0.0168135 | ||||||||
\(403\) | 4.79017 | 0.238615 | ||||||||
\(404\) | 20.1893 | 1.00445 | ||||||||
\(405\) | −26.5091 | −1.31725 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.7826 | −1.22843 | ||||||||
\(408\) | 4.91655 | 0.243405 | ||||||||
\(409\) | −4.34571 | −0.214882 | −0.107441 | − | 0.994211i | \(-0.534266\pi\) | ||||
−0.107441 | + | 0.994211i | \(0.534266\pi\) | |||||||
\(410\) | 1.88791 | 0.0932374 | ||||||||
\(411\) | 2.50364 | 0.123495 | ||||||||
\(412\) | −19.4350 | −0.957495 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 7.58947 | 0.373002 | ||||||||
\(415\) | −61.3700 | −3.01254 | ||||||||
\(416\) | −19.3280 | −0.947634 | ||||||||
\(417\) | −0.0346342 | −0.00169604 | ||||||||
\(418\) | −0.139132 | −0.00680518 | ||||||||
\(419\) | −27.2835 | −1.33288 | −0.666442 | − | 0.745557i | \(-0.732184\pi\) | ||||
−0.666442 | + | 0.745557i | \(0.732184\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.6168 | −0.809853 | −0.404927 | − | 0.914349i | \(-0.632703\pi\) | ||||
−0.404927 | + | 0.914349i | \(0.632703\pi\) | |||||||
\(422\) | −2.31111 | −0.112503 | ||||||||
\(423\) | −28.6351 | −1.39229 | ||||||||
\(424\) | 10.8651 | 0.527657 | ||||||||
\(425\) | −61.7591 | −2.99576 | ||||||||
\(426\) | −1.96423 | −0.0951672 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.56218 | −0.172184 | ||||||||
\(429\) | −6.05979 | −0.292570 | ||||||||
\(430\) | −14.9895 | −0.722860 | ||||||||
\(431\) | −9.36507 | −0.451099 | −0.225550 | − | 0.974232i | \(-0.572418\pi\) | ||||
−0.225550 | + | 0.974232i | \(0.572418\pi\) | |||||||
\(432\) | 8.54513 | 0.411128 | ||||||||
\(433\) | 3.87136 | 0.186046 | 0.0930228 | − | 0.995664i | \(-0.470347\pi\) | ||||
0.0930228 | + | 0.995664i | \(0.470347\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.98978 | 0.239242 | ||||||||
\(436\) | 31.9368 | 1.52950 | ||||||||
\(437\) | 0.664733 | 0.0317985 | ||||||||
\(438\) | −2.45641 | −0.117372 | ||||||||
\(439\) | −29.6011 | −1.41279 | −0.706393 | − | 0.707820i | \(-0.749679\pi\) | ||||
−0.706393 | + | 0.707820i | \(0.749679\pi\) | |||||||
\(440\) | −19.7934 | −0.943613 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.75660 | 0.464074 | ||||||||
\(443\) | −0.570558 | −0.0271080 | −0.0135540 | − | 0.999908i | \(-0.504315\pi\) | ||||
−0.0135540 | + | 0.999908i | \(0.504315\pi\) | |||||||
\(444\) | −8.64104 | −0.410086 | ||||||||
\(445\) | −3.49817 | −0.165829 | ||||||||
\(446\) | 3.20485 | 0.151754 | ||||||||
\(447\) | −7.68705 | −0.363585 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.8280 | 0.888551 | 0.444275 | − | 0.895890i | \(-0.353461\pi\) | ||||
0.444275 | + | 0.895890i | \(0.353461\pi\) | |||||||
\(450\) | 14.7394 | 0.694823 | ||||||||
\(451\) | 2.76768 | 0.130325 | ||||||||
\(452\) | 29.0633 | 1.36702 | ||||||||
\(453\) | −6.92686 | −0.325452 | ||||||||
\(454\) | 4.65352 | 0.218401 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.102772 | −0.00481275 | ||||||||
\(457\) | 22.2732 | 1.04190 | 0.520949 | − | 0.853588i | \(-0.325578\pi\) | ||||
0.520949 | + | 0.853588i | \(0.325578\pi\) | |||||||
\(458\) | −1.06957 | −0.0499776 | ||||||||
\(459\) | −16.0962 | −0.751306 | ||||||||
\(460\) | 44.6387 | 2.08129 | ||||||||
\(461\) | −4.47354 | −0.208354 | −0.104177 | − | 0.994559i | \(-0.533221\pi\) | ||||
−0.104177 | + | 0.994559i | \(0.533221\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.62240 | −0.168347 | −0.0841736 | − | 0.996451i | \(-0.526825\pi\) | ||||
−0.0841736 | + | 0.996451i | \(0.526825\pi\) | |||||||
\(464\) | 6.25246 | 0.290263 | ||||||||
\(465\) | 2.61347 | 0.121197 | ||||||||
\(466\) | −8.08565 | −0.374561 | ||||||||
\(467\) | 1.54346 | 0.0714226 | 0.0357113 | − | 0.999362i | \(-0.488630\pi\) | ||||
0.0357113 | + | 0.999362i | \(0.488630\pi\) | |||||||
\(468\) | 19.6500 | 0.908323 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 19.9578 | 0.920587 | ||||||||
\(471\) | 7.72025 | 0.355730 | ||||||||
\(472\) | 16.4434 | 0.756869 | ||||||||
\(473\) | −21.9746 | −1.01039 | ||||||||
\(474\) | −3.12191 | −0.143394 | ||||||||
\(475\) | 1.29097 | 0.0592338 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −16.8781 | −0.772797 | ||||||||
\(478\) | 10.5901 | 0.484382 | ||||||||
\(479\) | 14.5913 | 0.666693 | 0.333347 | − | 0.942804i | \(-0.391822\pi\) | ||||
0.333347 | + | 0.942804i | \(0.391822\pi\) | |||||||
\(480\) | −10.5452 | −0.481320 | ||||||||
\(481\) | −36.3273 | −1.65638 | ||||||||
\(482\) | −5.83713 | −0.265874 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.97221 | 0.271464 | ||||||||
\(485\) | 40.7185 | 1.84893 | ||||||||
\(486\) | 5.86027 | 0.265827 | ||||||||
\(487\) | −1.52440 | −0.0690771 | −0.0345385 | − | 0.999403i | \(-0.510996\pi\) | ||||
−0.0345385 | + | 0.999403i | \(0.510996\pi\) | |||||||
\(488\) | −12.0270 | −0.544437 | ||||||||
\(489\) | −3.02741 | −0.136904 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.8827 | −1.57424 | −0.787118 | − | 0.616802i | \(-0.788428\pi\) | ||||
−0.787118 | + | 0.616802i | \(0.788428\pi\) | |||||||
\(492\) | 0.965017 | 0.0435063 | ||||||||
\(493\) | −11.7776 | −0.530435 | ||||||||
\(494\) | −0.203945 | −0.00917594 | ||||||||
\(495\) | 30.7475 | 1.38200 | ||||||||
\(496\) | 3.27482 | 0.147044 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 3.71727 | 0.166575 | ||||||||
\(499\) | 14.7766 | 0.661490 | 0.330745 | − | 0.943720i | \(-0.392700\pi\) | ||||
0.330745 | + | 0.943720i | \(0.392700\pi\) | |||||||
\(500\) | 50.0239 | 2.23714 | ||||||||
\(501\) | 2.42507 | 0.108344 | ||||||||
\(502\) | −8.54478 | −0.381372 | ||||||||
\(503\) | −18.9590 | −0.845338 | −0.422669 | − | 0.906284i | \(-0.638907\pi\) | ||||
−0.422669 | + | 0.906284i | \(0.638907\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 46.3078 | 2.06067 | ||||||||
\(506\) | −7.75461 | −0.344734 | ||||||||
\(507\) | −1.86677 | −0.0829060 | ||||||||
\(508\) | −31.0355 | −1.37698 | ||||||||
\(509\) | 17.0790 | 0.757011 | 0.378506 | − | 0.925599i | \(-0.376438\pi\) | ||||
0.378506 | + | 0.925599i | \(0.376438\pi\) | |||||||
\(510\) | 5.32311 | 0.235711 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.8863 | −1.01144 | ||||||||
\(513\) | 0.336464 | 0.0148552 | ||||||||
\(514\) | 8.34815 | 0.368221 | ||||||||
\(515\) | −44.5778 | −1.96433 | ||||||||
\(516\) | −7.66198 | −0.337300 | ||||||||
\(517\) | 29.2582 | 1.28677 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.69116 | 0.337604 | ||||||||
\(520\) | −29.0139 | −1.27234 | ||||||||
\(521\) | −25.3095 | −1.10883 | −0.554415 | − | 0.832240i | \(-0.687058\pi\) | ||||
−0.554415 | + | 0.832240i | \(0.687058\pi\) | |||||||
\(522\) | 2.81083 | 0.123027 | ||||||||
\(523\) | 4.43499 | 0.193928 | 0.0969642 | − | 0.995288i | \(-0.469087\pi\) | ||||
0.0969642 | + | 0.995288i | \(0.469087\pi\) | |||||||
\(524\) | −1.43687 | −0.0627699 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.95545 | −0.0852617 | ||||||||
\(527\) | −6.16867 | −0.268712 | ||||||||
\(528\) | −4.14280 | −0.180292 | ||||||||
\(529\) | 14.0492 | 0.610835 | ||||||||
\(530\) | 11.7636 | 0.510978 | ||||||||
\(531\) | −25.5436 | −1.10850 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.05697 | 0.175727 | ||||||||
\(534\) | 0.211889 | 0.00916935 | ||||||||
\(535\) | −8.17051 | −0.353242 | ||||||||
\(536\) | −2.36621 | −0.102205 | ||||||||
\(537\) | −3.12392 | −0.134807 | ||||||||
\(538\) | −0.604979 | −0.0260825 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 22.5945 | 0.972313 | ||||||||
\(541\) | −5.57149 | −0.239537 | −0.119769 | − | 0.992802i | \(-0.538215\pi\) | ||||
−0.119769 | + | 0.992802i | \(0.538215\pi\) | |||||||
\(542\) | −3.64393 | −0.156520 | ||||||||
\(543\) | −7.91514 | −0.339671 | ||||||||
\(544\) | 24.8902 | 1.06716 | ||||||||
\(545\) | 73.2529 | 3.13781 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.0432 | 1.62661 | 0.813304 | − | 0.581839i | \(-0.197666\pi\) | ||||
0.813304 | + | 0.581839i | \(0.197666\pi\) | |||||||
\(548\) | 8.29517 | 0.354352 | ||||||||
\(549\) | 18.6830 | 0.797373 | ||||||||
\(550\) | −15.0601 | −0.642167 | ||||||||
\(551\) | 0.246190 | 0.0104881 | ||||||||
\(552\) | −5.72806 | −0.243802 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −0.0315018 | −0.00133838 | ||||||||
\(555\) | −19.8198 | −0.841304 | ||||||||
\(556\) | −0.114752 | −0.00486655 | ||||||||
\(557\) | −19.0835 | −0.808594 | −0.404297 | − | 0.914628i | \(-0.632484\pi\) | ||||
−0.404297 | + | 0.914628i | \(0.632484\pi\) | |||||||
\(558\) | 1.47222 | 0.0623239 | ||||||||
\(559\) | −32.2113 | −1.36239 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.80366 | 0.329471 | ||||||||
\(562\) | −3.83465 | −0.161755 | ||||||||
\(563\) | 19.1867 | 0.808621 | 0.404311 | − | 0.914622i | \(-0.367511\pi\) | ||||
0.404311 | + | 0.914622i | \(0.367511\pi\) | |||||||
\(564\) | 10.2016 | 0.429563 | ||||||||
\(565\) | 66.6619 | 2.80449 | ||||||||
\(566\) | 1.42432 | 0.0598688 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −13.7871 | −0.578495 | ||||||||
\(569\) | 29.3295 | 1.22956 | 0.614778 | − | 0.788700i | \(-0.289246\pi\) | ||||
0.614778 | + | 0.788700i | \(0.289246\pi\) | |||||||
\(570\) | −0.111271 | −0.00466061 | ||||||||
\(571\) | −21.5864 | −0.903362 | −0.451681 | − | 0.892180i | \(-0.649175\pi\) | ||||
−0.451681 | + | 0.892180i | \(0.649175\pi\) | |||||||
\(572\) | −20.0776 | −0.839486 | ||||||||
\(573\) | −4.54406 | −0.189831 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 71.9529 | 3.00064 | ||||||||
\(576\) | 9.08541 | 0.378559 | ||||||||
\(577\) | −5.28198 | −0.219892 | −0.109946 | − | 0.993938i | \(-0.535068\pi\) | ||||
−0.109946 | + | 0.993938i | \(0.535068\pi\) | |||||||
\(578\) | −4.73898 | −0.197115 | ||||||||
\(579\) | 4.72966 | 0.196558 | ||||||||
\(580\) | 16.5324 | 0.686469 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2.46638 | −0.102235 | ||||||||
\(583\) | 17.2454 | 0.714231 | ||||||||
\(584\) | −17.2418 | −0.713470 | ||||||||
\(585\) | 45.0709 | 1.86345 | ||||||||
\(586\) | 2.05924 | 0.0850662 | ||||||||
\(587\) | 41.8869 | 1.72886 | 0.864428 | − | 0.502757i | \(-0.167681\pi\) | ||||
0.864428 | + | 0.502757i | \(0.167681\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.128946 | 0.00531312 | ||||||||
\(590\) | 17.8031 | 0.732944 | ||||||||
\(591\) | 10.2515 | 0.421690 | ||||||||
\(592\) | −24.8353 | −1.02072 | ||||||||
\(593\) | −25.8605 | −1.06196 | −0.530982 | − | 0.847383i | \(-0.678177\pi\) | ||||
−0.530982 | + | 0.847383i | \(0.678177\pi\) | |||||||
\(594\) | −3.92510 | −0.161049 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −25.4691 | −1.04325 | ||||||||
\(597\) | −3.68004 | −0.150614 | ||||||||
\(598\) | −11.3670 | −0.464831 | ||||||||
\(599\) | −39.4470 | −1.61176 | −0.805881 | − | 0.592078i | \(-0.798308\pi\) | ||||
−0.805881 | + | 0.592078i | \(0.798308\pi\) | |||||||
\(600\) | −11.1244 | −0.454152 | ||||||||
\(601\) | −40.0435 | −1.63341 | −0.816704 | − | 0.577056i | \(-0.804201\pi\) | ||||
−0.816704 | + | 0.577056i | \(0.804201\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.67573 | 0.149687 | ||||||||
\(604\) | −22.9504 | −0.933838 | ||||||||
\(605\) | 13.6984 | 0.556918 | ||||||||
\(606\) | −2.80493 | −0.113942 | ||||||||
\(607\) | 10.7580 | 0.436653 | 0.218327 | − | 0.975876i | \(-0.429940\pi\) | ||||
0.218327 | + | 0.975876i | \(0.429940\pi\) | |||||||
\(608\) | −0.520288 | −0.0211004 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −13.0215 | −0.527227 | ||||||||
\(611\) | 42.8877 | 1.73505 | ||||||||
\(612\) | −25.3049 | −1.02289 | ||||||||
\(613\) | 16.7220 | 0.675393 | 0.337697 | − | 0.941255i | \(-0.390352\pi\) | ||||
0.337697 | + | 0.941255i | \(0.390352\pi\) | |||||||
\(614\) | 11.8906 | 0.479867 | ||||||||
\(615\) | 2.21344 | 0.0892546 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −42.3381 | −1.70447 | −0.852234 | − | 0.523160i | \(-0.824753\pi\) | ||||
−0.852234 | + | 0.523160i | \(0.824753\pi\) | |||||||
\(618\) | 2.70014 | 0.108616 | ||||||||
\(619\) | −32.0830 | −1.28952 | −0.644762 | − | 0.764384i | \(-0.723043\pi\) | ||||
−0.644762 | + | 0.764384i | \(0.723043\pi\) | |||||||
\(620\) | 8.65907 | 0.347757 | ||||||||
\(621\) | 18.7530 | 0.752531 | ||||||||
\(622\) | 6.29721 | 0.252495 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −6.07267 | −0.243101 | ||||||||
\(625\) | 55.6333 | 2.22533 | ||||||||
\(626\) | 11.0723 | 0.442536 | ||||||||
\(627\) | −0.163123 | −0.00651449 | ||||||||
\(628\) | 25.5791 | 1.02072 | ||||||||
\(629\) | 46.7814 | 1.86530 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.9458 | −1.78927 | −0.894633 | − | 0.446802i | \(-0.852563\pi\) | ||||
−0.894633 | + | 0.446802i | \(0.852563\pi\) | |||||||
\(632\) | −21.9130 | −0.871654 | ||||||||
\(633\) | −2.70961 | −0.107698 | ||||||||
\(634\) | −1.75272 | −0.0696094 | ||||||||
\(635\) | −71.1855 | −2.82491 | ||||||||
\(636\) | 6.01302 | 0.238432 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.87199 | −0.113703 | ||||||||
\(639\) | 21.4173 | 0.847254 | ||||||||
\(640\) | −45.4113 | −1.79504 | ||||||||
\(641\) | 10.4353 | 0.412171 | 0.206085 | − | 0.978534i | \(-0.433928\pi\) | ||||
0.206085 | + | 0.978534i | \(0.433928\pi\) | |||||||
\(642\) | 0.494899 | 0.0195321 | ||||||||
\(643\) | 33.1360 | 1.30676 | 0.653378 | − | 0.757032i | \(-0.273351\pi\) | ||||
0.653378 | + | 0.757032i | \(0.273351\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17.5742 | −0.691981 | ||||||||
\(646\) | 0.262636 | 0.0103333 | ||||||||
\(647\) | 29.4094 | 1.15620 | 0.578101 | − | 0.815965i | \(-0.303794\pi\) | ||||
0.578101 | + | 0.815965i | \(0.303794\pi\) | |||||||
\(648\) | 11.2705 | 0.442748 | ||||||||
\(649\) | 26.0994 | 1.02449 | ||||||||
\(650\) | −22.0757 | −0.865881 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.0306 | −0.392827 | ||||||||
\(653\) | −41.0121 | −1.60493 | −0.802464 | − | 0.596701i | \(-0.796478\pi\) | ||||
−0.802464 | + | 0.596701i | \(0.796478\pi\) | |||||||
\(654\) | −4.43704 | −0.173502 | ||||||||
\(655\) | −3.29572 | −0.128774 | ||||||||
\(656\) | 2.77356 | 0.108289 | ||||||||
\(657\) | 26.7838 | 1.04493 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.6194 | 1.62126 | 0.810631 | − | 0.585558i | \(-0.199124\pi\) | ||||
0.810631 | + | 0.585558i | \(0.199124\pi\) | |||||||
\(660\) | −10.9541 | −0.426389 | ||||||||
\(661\) | 43.0712 | 1.67527 | 0.837637 | − | 0.546227i | \(-0.183936\pi\) | ||||
0.837637 | + | 0.546227i | \(0.183936\pi\) | |||||||
\(662\) | 9.72812 | 0.378094 | ||||||||
\(663\) | 11.4389 | 0.444250 | ||||||||
\(664\) | 26.0919 | 1.01256 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −11.1649 | −0.432629 | ||||||||
\(667\) | 13.7215 | 0.531300 | ||||||||
\(668\) | 8.03487 | 0.310878 | ||||||||
\(669\) | 3.75746 | 0.145272 | ||||||||
\(670\) | −2.56188 | −0.0989739 | ||||||||
\(671\) | −19.0896 | −0.736944 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 44.0679 | 1.69869 | 0.849346 | − | 0.527837i | \(-0.176997\pi\) | ||||
0.849346 | + | 0.527837i | \(0.176997\pi\) | |||||||
\(674\) | 9.56540 | 0.368445 | ||||||||
\(675\) | 36.4200 | 1.40181 | ||||||||
\(676\) | −6.18506 | −0.237887 | ||||||||
\(677\) | −5.02017 | −0.192941 | −0.0964704 | − | 0.995336i | \(-0.530755\pi\) | ||||
−0.0964704 | + | 0.995336i | \(0.530755\pi\) | |||||||
\(678\) | −4.03781 | −0.155071 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 37.3635 | 1.43282 | ||||||||
\(681\) | 5.45592 | 0.209071 | ||||||||
\(682\) | −1.50425 | −0.0576007 | ||||||||
\(683\) | 24.9476 | 0.954595 | 0.477297 | − | 0.878742i | \(-0.341616\pi\) | ||||
0.477297 | + | 0.878742i | \(0.341616\pi\) | |||||||
\(684\) | 0.528956 | 0.0202251 | ||||||||
\(685\) | 19.0265 | 0.726965 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.25399 | −0.0478427 | ||||||||
\(688\) | −22.0213 | −0.839556 | ||||||||
\(689\) | 25.2790 | 0.963052 | ||||||||
\(690\) | −6.20172 | −0.236096 | ||||||||
\(691\) | −42.8508 | −1.63012 | −0.815061 | − | 0.579375i | \(-0.803297\pi\) | ||||
−0.815061 | + | 0.579375i | \(0.803297\pi\) | |||||||
\(692\) | 25.4827 | 0.968706 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.0512 | −0.381538 | ||||||||
\(695\) | −0.263204 | −0.00998389 | ||||||||
\(696\) | −2.12144 | −0.0804131 | ||||||||
\(697\) | −5.22447 | −0.197891 | ||||||||
\(698\) | −2.86858 | −0.108577 | ||||||||
\(699\) | −9.47984 | −0.358560 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −46.3548 | −1.75079 | −0.875397 | − | 0.483404i | \(-0.839400\pi\) | ||||
−0.875397 | + | 0.483404i | \(0.839400\pi\) | |||||||
\(702\) | −5.75357 | −0.217154 | ||||||||
\(703\) | −0.977887 | −0.0368817 | ||||||||
\(704\) | −9.28310 | −0.349870 | ||||||||
\(705\) | 23.3991 | 0.881262 | ||||||||
\(706\) | 13.1619 | 0.495355 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 9.10017 | 0.342005 | ||||||||
\(709\) | 10.9521 | 0.411316 | 0.205658 | − | 0.978624i | \(-0.434067\pi\) | ||||
0.205658 | + | 0.978624i | \(0.434067\pi\) | |||||||
\(710\) | −14.9272 | −0.560208 | ||||||||
\(711\) | 34.0402 | 1.27661 | ||||||||
\(712\) | 1.48728 | 0.0557380 | ||||||||
\(713\) | 7.18686 | 0.269150 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −46.0516 | −1.72223 | ||||||||
\(716\) | −10.3503 | −0.386809 | ||||||||
\(717\) | 12.4162 | 0.463691 | ||||||||
\(718\) | −3.17160 | −0.118363 | ||||||||
\(719\) | −7.62700 | −0.284439 | −0.142220 | − | 0.989835i | \(-0.545424\pi\) | ||||
−0.142220 | + | 0.989835i | \(0.545424\pi\) | |||||||
\(720\) | 30.8129 | 1.14833 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 8.74049 | 0.325287 | ||||||||
\(723\) | −6.84362 | −0.254517 | ||||||||
\(724\) | −26.2248 | −0.974637 | ||||||||
\(725\) | 26.6484 | 0.989698 | ||||||||
\(726\) | −0.829729 | −0.0307941 | ||||||||
\(727\) | 37.2537 | 1.38166 | 0.690832 | − | 0.723015i | \(-0.257244\pi\) | ||||
0.690832 | + | 0.723015i | \(0.257244\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.5197 | −0.463693 | ||||||||
\(730\) | −18.6675 | −0.690916 | ||||||||
\(731\) | 41.4809 | 1.53423 | ||||||||
\(732\) | −6.65603 | −0.246014 | ||||||||
\(733\) | −7.99745 | −0.295393 | −0.147696 | − | 0.989033i | \(-0.547186\pi\) | ||||
−0.147696 | + | 0.989033i | \(0.547186\pi\) | |||||||
\(734\) | 12.8593 | 0.474644 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −28.9985 | −1.06890 | ||||||||
\(737\) | −3.75571 | −0.138343 | ||||||||
\(738\) | 1.24687 | 0.0458980 | ||||||||
\(739\) | 19.7183 | 0.725350 | 0.362675 | − | 0.931916i | \(-0.381864\pi\) | ||||
0.362675 | + | 0.931916i | \(0.381864\pi\) | |||||||
\(740\) | −65.6679 | −2.41400 | ||||||||
\(741\) | −0.239111 | −0.00878397 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.1345 | 1.14221 | 0.571106 | − | 0.820876i | \(-0.306514\pi\) | ||||
0.571106 | + | 0.820876i | \(0.306514\pi\) | |||||||
\(744\) | −1.11114 | −0.0407363 | ||||||||
\(745\) | −58.4180 | −2.14027 | ||||||||
\(746\) | −2.85424 | −0.104501 | ||||||||
\(747\) | −40.5318 | −1.48298 | ||||||||
\(748\) | 25.8555 | 0.945369 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −6.94990 | −0.253775 | ||||||||
\(751\) | −40.7231 | −1.48601 | −0.743004 | − | 0.669287i | \(-0.766600\pi\) | ||||
−0.743004 | + | 0.669287i | \(0.766600\pi\) | |||||||
\(752\) | 29.3203 | 1.06920 | ||||||||
\(753\) | −10.0181 | −0.365081 | ||||||||
\(754\) | −4.20988 | −0.153315 | ||||||||
\(755\) | −52.6409 | −1.91580 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.9086 | 1.26878 | 0.634388 | − | 0.773015i | \(-0.281252\pi\) | ||||
0.634388 | + | 0.773015i | \(0.281252\pi\) | |||||||
\(758\) | 8.47005 | 0.307646 | ||||||||
\(759\) | −9.09171 | −0.330008 | ||||||||
\(760\) | −0.781021 | −0.0283306 | ||||||||
\(761\) | −4.76771 | −0.172830 | −0.0864148 | − | 0.996259i | \(-0.527541\pi\) | ||||
−0.0864148 | + | 0.996259i | \(0.527541\pi\) | |||||||
\(762\) | 4.31181 | 0.156200 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −15.0556 | −0.544693 | ||||||||
\(765\) | −58.0413 | −2.09849 | ||||||||
\(766\) | −15.7576 | −0.569344 | ||||||||
\(767\) | 38.2574 | 1.38140 | ||||||||
\(768\) | −0.869704 | −0.0313827 | ||||||||
\(769\) | −51.9550 | −1.87354 | −0.936772 | − | 0.349941i | \(-0.886202\pi\) | ||||
−0.936772 | + | 0.349941i | \(0.886202\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.78760 | 0.352492 | ||||||||
\(772\) | 15.6705 | 0.563995 | ||||||||
\(773\) | −19.6577 | −0.707038 | −0.353519 | − | 0.935427i | \(-0.615015\pi\) | ||||
−0.353519 | + | 0.935427i | \(0.615015\pi\) | |||||||
\(774\) | −9.89984 | −0.355842 | ||||||||
\(775\) | 13.9575 | 0.501369 | ||||||||
\(776\) | −17.3118 | −0.621457 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.6056 | 0.380229 | ||||||||
\(779\) | 0.109209 | 0.00391281 | ||||||||
\(780\) | −16.0570 | −0.574932 | ||||||||
\(781\) | −21.8833 | −0.783045 | ||||||||
\(782\) | 14.6382 | 0.523459 | ||||||||
\(783\) | 6.94535 | 0.248207 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 58.6703 | 2.09403 | ||||||||
\(786\) | 0.199626 | 0.00712044 | ||||||||
\(787\) | −16.1094 | −0.574238 | −0.287119 | − | 0.957895i | \(-0.592698\pi\) | ||||
−0.287119 | + | 0.957895i | \(0.592698\pi\) | |||||||
\(788\) | 33.9657 | 1.20998 | ||||||||
\(789\) | −2.29263 | −0.0816196 | ||||||||
\(790\) | −23.7251 | −0.844100 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −13.0725 | −0.464513 | ||||||||
\(793\) | −27.9822 | −0.993677 | ||||||||
\(794\) | 0.621992 | 0.0220737 | ||||||||
\(795\) | 13.7920 | 0.489150 | ||||||||
\(796\) | −12.1929 | −0.432165 | ||||||||
\(797\) | −20.3109 | −0.719447 | −0.359724 | − | 0.933059i | \(-0.617129\pi\) | ||||
−0.359724 | + | 0.933059i | \(0.617129\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −55.2298 | −1.95389 | ||||||||
\(800\) | −56.3177 | −1.99113 | ||||||||
\(801\) | −2.31037 | −0.0816329 | ||||||||
\(802\) | −0.710064 | −0.0250732 | ||||||||
\(803\) | −27.3666 | −0.965745 | ||||||||
\(804\) | −1.30952 | −0.0461831 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.20499 | −0.0776673 | ||||||||
\(807\) | −0.709294 | −0.0249683 | ||||||||
\(808\) | −19.6881 | −0.692625 | ||||||||
\(809\) | 3.62656 | 0.127503 | 0.0637515 | − | 0.997966i | \(-0.479693\pi\) | ||||
0.0637515 | + | 0.997966i | \(0.479693\pi\) | |||||||
\(810\) | 12.2025 | 0.428753 | ||||||||
\(811\) | −10.2870 | −0.361225 | −0.180613 | − | 0.983554i | \(-0.557808\pi\) | ||||
−0.180613 | + | 0.983554i | \(0.557808\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.27225 | −0.149834 | ||||||||
\(814\) | 11.4078 | 0.399843 | ||||||||
\(815\) | −23.0069 | −0.805896 | ||||||||
\(816\) | 7.82025 | 0.273763 | ||||||||
\(817\) | −0.867089 | −0.0303356 | ||||||||
\(818\) | 2.00039 | 0.0699422 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.33368 | 0.256103 | ||||||||
\(821\) | 6.42929 | 0.224384 | 0.112192 | − | 0.993687i | \(-0.464213\pi\) | ||||
0.112192 | + | 0.993687i | \(0.464213\pi\) | |||||||
\(822\) | −1.15246 | −0.0401967 | ||||||||
\(823\) | 4.04441 | 0.140979 | 0.0704896 | − | 0.997513i | \(-0.477544\pi\) | ||||
0.0704896 | + | 0.997513i | \(0.477544\pi\) | |||||||
\(824\) | 18.9526 | 0.660244 | ||||||||
\(825\) | −17.6569 | −0.614735 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.70225 | 0.163513 | 0.0817566 | − | 0.996652i | \(-0.473947\pi\) | ||||
0.0817566 | + | 0.996652i | \(0.473947\pi\) | |||||||
\(828\) | 29.4816 | 1.02456 | ||||||||
\(829\) | 6.74357 | 0.234214 | 0.117107 | − | 0.993119i | \(-0.462638\pi\) | ||||
0.117107 | + | 0.993119i | \(0.462638\pi\) | |||||||
\(830\) | 28.2495 | 0.980555 | ||||||||
\(831\) | −0.0369335 | −0.00128121 | ||||||||
\(832\) | −13.6075 | −0.471756 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0.0159426 | 0.000552048 0 | ||||||||
\(835\) | 18.4294 | 0.637777 | ||||||||
\(836\) | −0.540465 | −0.0186924 | ||||||||
\(837\) | 3.63773 | 0.125738 | ||||||||
\(838\) | 12.5590 | 0.433842 | ||||||||
\(839\) | −50.7412 | −1.75178 | −0.875890 | − | 0.482511i | \(-0.839725\pi\) | ||||
−0.875890 | + | 0.482511i | \(0.839725\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.9181 | −0.824762 | ||||||||
\(842\) | 7.64895 | 0.263600 | ||||||||
\(843\) | −4.49585 | −0.154845 | ||||||||
\(844\) | −8.97762 | −0.309022 | ||||||||
\(845\) | −14.1866 | −0.488032 | ||||||||
\(846\) | 13.1812 | 0.453177 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 17.2820 | 0.593468 | ||||||||
\(849\) | 1.66992 | 0.0573114 | ||||||||
\(850\) | 28.4286 | 0.975093 | ||||||||
\(851\) | −54.5030 | −1.86834 | ||||||||
\(852\) | −7.63013 | −0.261404 | ||||||||
\(853\) | −9.55166 | −0.327042 | −0.163521 | − | 0.986540i | \(-0.552285\pi\) | ||||
−0.163521 | + | 0.986540i | \(0.552285\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.21326 | 0.0414925 | ||||||||
\(856\) | 3.47375 | 0.118730 | ||||||||
\(857\) | 25.8962 | 0.884598 | 0.442299 | − | 0.896868i | \(-0.354163\pi\) | ||||
0.442299 | + | 0.896868i | \(0.354163\pi\) | |||||||
\(858\) | 2.78941 | 0.0952289 | ||||||||
\(859\) | 41.3258 | 1.41002 | 0.705010 | − | 0.709198i | \(-0.250943\pi\) | ||||
0.705010 | + | 0.709198i | \(0.250943\pi\) | |||||||
\(860\) | −58.2275 | −1.98554 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.31088 | 0.146829 | ||||||||
\(863\) | −1.76472 | −0.0600719 | −0.0300360 | − | 0.999549i | \(-0.509562\pi\) | ||||
−0.0300360 | + | 0.999549i | \(0.509562\pi\) | |||||||
\(864\) | −14.6780 | −0.499356 | ||||||||
\(865\) | 58.4492 | 1.98733 | ||||||||
\(866\) | −1.78204 | −0.0605563 | ||||||||
\(867\) | −5.55611 | −0.188695 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −34.7809 | −1.17986 | ||||||||
\(870\) | −2.29687 | −0.0778711 | ||||||||
\(871\) | −5.50526 | −0.186539 | ||||||||
\(872\) | −31.1440 | −1.05467 | ||||||||
\(873\) | 26.8925 | 0.910175 | ||||||||
\(874\) | −0.305986 | −0.0103501 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −9.54201 | −0.322395 | ||||||||
\(877\) | −37.4713 | −1.26532 | −0.632658 | − | 0.774432i | \(-0.718036\pi\) | ||||
−0.632658 | + | 0.774432i | \(0.718036\pi\) | |||||||
\(878\) | 13.6258 | 0.459850 | ||||||||
\(879\) | 2.41430 | 0.0814325 | ||||||||
\(880\) | −31.4833 | −1.06130 | ||||||||
\(881\) | 14.9319 | 0.503068 | 0.251534 | − | 0.967849i | \(-0.419065\pi\) | ||||
0.251534 | + | 0.967849i | \(0.419065\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.3025 | 1.18802 | 0.594012 | − | 0.804456i | \(-0.297543\pi\) | ||||
0.594012 | + | 0.804456i | \(0.297543\pi\) | |||||||
\(884\) | 37.8999 | 1.27471 | ||||||||
\(885\) | 20.8729 | 0.701635 | ||||||||
\(886\) | 0.262636 | 0.00882343 | ||||||||
\(887\) | 6.34513 | 0.213049 | 0.106524 | − | 0.994310i | \(-0.466028\pi\) | ||||
0.106524 | + | 0.994310i | \(0.466028\pi\) | |||||||
\(888\) | 8.42654 | 0.282776 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.61026 | 0.0539761 | ||||||||
\(891\) | 17.8889 | 0.599299 | ||||||||
\(892\) | 12.4494 | 0.416836 | ||||||||
\(893\) | 1.15449 | 0.0386334 | ||||||||
\(894\) | 3.53846 | 0.118344 | ||||||||
\(895\) | −23.7403 | −0.793551 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −13.3270 | −0.444975 | ||||||||
\(898\) | −8.66682 | −0.289216 | ||||||||
\(899\) | 2.66172 | 0.0887734 | ||||||||
\(900\) | 57.2559 | 1.90853 | ||||||||
\(901\) | −32.5537 | −1.08452 | ||||||||
\(902\) | −1.27400 | −0.0424196 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −28.3418 | −0.942635 | ||||||||
\(905\) | −60.1513 | −1.99950 | ||||||||
\(906\) | 3.18853 | 0.105932 | ||||||||
\(907\) | −21.6718 | −0.719599 | −0.359800 | − | 0.933030i | \(-0.617155\pi\) | ||||
−0.359800 | + | 0.933030i | \(0.617155\pi\) | |||||||
\(908\) | 18.0768 | 0.599899 | ||||||||
\(909\) | 30.5840 | 1.01441 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.13876 | −0.170255 | −0.0851274 | − | 0.996370i | \(-0.527130\pi\) | ||||
−0.0851274 | + | 0.996370i | \(0.527130\pi\) | |||||||
\(912\) | −0.163469 | −0.00541301 | ||||||||
\(913\) | 41.4137 | 1.37059 | ||||||||
\(914\) | −10.2527 | −0.339129 | ||||||||
\(915\) | −15.2668 | −0.504705 | ||||||||
\(916\) | −4.15478 | −0.137278 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 7.40931 | 0.244544 | ||||||||
\(919\) | −34.5055 | −1.13823 | −0.569116 | − | 0.822257i | \(-0.692715\pi\) | ||||
−0.569116 | + | 0.822257i | \(0.692715\pi\) | |||||||
\(920\) | −43.5306 | −1.43516 | ||||||||
\(921\) | 13.9409 | 0.459369 | ||||||||
\(922\) | 2.05924 | 0.0678173 | ||||||||
\(923\) | −32.0773 | −1.05584 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −105.850 | −3.48032 | ||||||||
\(926\) | 1.66744 | 0.0547956 | ||||||||
\(927\) | −29.4414 | −0.966982 | ||||||||
\(928\) | −10.7399 | −0.352553 | ||||||||
\(929\) | 5.42071 | 0.177848 | 0.0889238 | − | 0.996038i | \(-0.471657\pi\) | ||||
0.0889238 | + | 0.996038i | \(0.471657\pi\) | |||||||
\(930\) | −1.20302 | −0.0394485 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −31.4090 | −1.02884 | ||||||||
\(933\) | 7.38302 | 0.241709 | ||||||||
\(934\) | −0.710475 | −0.0232475 | ||||||||
\(935\) | 59.3042 | 1.93945 | ||||||||
\(936\) | −19.1622 | −0.626337 | ||||||||
\(937\) | −46.9692 | −1.53442 | −0.767208 | − | 0.641398i | \(-0.778355\pi\) | ||||
−0.767208 | + | 0.641398i | \(0.778355\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.9814 | 0.423633 | ||||||||
\(940\) | 77.5271 | 2.52865 | ||||||||
\(941\) | −3.58221 | −0.116777 | −0.0583884 | − | 0.998294i | \(-0.518596\pi\) | ||||
−0.0583884 | + | 0.998294i | \(0.518596\pi\) | |||||||
\(942\) | −3.55374 | −0.115787 | ||||||||
\(943\) | 6.08681 | 0.198214 | ||||||||
\(944\) | 26.1548 | 0.851267 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.1152 | 0.328875 | ||||||||
\(947\) | −35.5839 | −1.15632 | −0.578161 | − | 0.815923i | \(-0.696229\pi\) | ||||
−0.578161 | + | 0.815923i | \(0.696229\pi\) | |||||||
\(948\) | −12.1272 | −0.393873 | ||||||||
\(949\) | −40.1150 | −1.30219 | ||||||||
\(950\) | −0.594253 | −0.0192801 | ||||||||
\(951\) | −2.05494 | −0.0666359 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −43.5164 | −1.40963 | −0.704817 | − | 0.709389i | \(-0.748971\pi\) | ||||
−0.704817 | + | 0.709389i | \(0.748971\pi\) | |||||||
\(954\) | 7.76926 | 0.251539 | ||||||||
\(955\) | −34.5328 | −1.11745 | ||||||||
\(956\) | 41.1378 | 1.33049 | ||||||||
\(957\) | −3.36720 | −0.108846 | ||||||||
\(958\) | −6.71659 | −0.217003 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −7.42413 | −0.239613 | ||||||||
\(961\) | −29.6059 | −0.955028 | ||||||||
\(962\) | 16.7220 | 0.539138 | ||||||||
\(963\) | −5.39621 | −0.173890 | ||||||||
\(964\) | −22.6746 | −0.730299 | ||||||||
\(965\) | 35.9432 | 1.15705 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.2431 | −0.715289 | −0.357645 | − | 0.933858i | \(-0.616420\pi\) | ||||
−0.357645 | + | 0.933858i | \(0.616420\pi\) | |||||||
\(968\) | −5.82396 | −0.187189 | ||||||||
\(969\) | 0.307922 | 0.00989188 | ||||||||
\(970\) | −18.7433 | −0.601812 | ||||||||
\(971\) | −10.0764 | −0.323366 | −0.161683 | − | 0.986843i | \(-0.551692\pi\) | ||||
−0.161683 | + | 0.986843i | \(0.551692\pi\) | |||||||
\(972\) | 22.7645 | 0.730171 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.701702 | 0.0224840 | ||||||||
\(975\) | −25.8822 | −0.828893 | ||||||||
\(976\) | −19.1301 | −0.612341 | ||||||||
\(977\) | 60.5914 | 1.93849 | 0.969245 | − | 0.246097i | \(-0.0791481\pi\) | ||||
0.969245 | + | 0.246097i | \(0.0791481\pi\) | |||||||
\(978\) | 1.39356 | 0.0445612 | ||||||||
\(979\) | 2.36064 | 0.0754463 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 48.3799 | 1.54465 | ||||||||
\(982\) | 16.0570 | 0.512401 | ||||||||
\(983\) | −41.9563 | −1.33820 | −0.669100 | − | 0.743173i | \(-0.733320\pi\) | ||||
−0.669100 | + | 0.743173i | \(0.733320\pi\) | |||||||
\(984\) | −0.941062 | −0.0299999 | ||||||||
\(985\) | 77.9066 | 2.48231 | ||||||||
\(986\) | 5.42138 | 0.172652 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.792234 | −0.0252043 | ||||||||
\(989\) | −48.3276 | −1.53673 | ||||||||
\(990\) | −14.1535 | −0.449829 | ||||||||
\(991\) | 40.0186 | 1.27123 | 0.635616 | − | 0.772005i | \(-0.280746\pi\) | ||||
0.635616 | + | 0.772005i | \(0.280746\pi\) | |||||||
\(992\) | −5.62517 | −0.178599 | ||||||||
\(993\) | 11.4055 | 0.361943 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −27.9666 | −0.886599 | ||||||||
\(996\) | 14.4399 | 0.457545 | ||||||||
\(997\) | −6.59339 | −0.208815 | −0.104407 | − | 0.994535i | \(-0.533295\pi\) | ||||
−0.104407 | + | 0.994535i | \(0.533295\pi\) | |||||||
\(998\) | −6.80187 | −0.215310 | ||||||||
\(999\) | −27.5875 | −0.872829 |
(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 | 2009.2.a.n.1.3 | 5 | ||
7.6 | odd | 2 | 287.2.a.e.1.3 | ✓ | 5 | ||
21.20 | even | 2 | 2583.2.a.r.1.3 | 5 | |||
28.27 | even | 2 | 4592.2.a.bb.1.3 | 5 | |||
35.34 | odd | 2 | 7175.2.a.n.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.2.a.e.1.3 | ✓ | 5 | 7.6 | odd | 2 | ||
2009.2.a.n.1.3 | 5 | 1.1 | even | 1 | trivial | ||
2583.2.a.r.1.3 | 5 | 21.20 | even | 2 | |||
4592.2.a.bb.1.3 | 5 | 28.27 | even | 2 | |||
7175.2.a.n.1.3 | 5 | 35.34 | odd | 2 |