Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5929,2,Mod(1,5929)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5929, 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("5929.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5929 = 7^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5929.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: | \(47.3433033584\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 847) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.76156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5929.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.76156 | 1.95272 | 0.976358 | − | 0.216160i | \(-0.0693534\pi\) | ||||
0.976358 | + | 0.216160i | \(0.0693534\pi\) | |||||||
\(3\) | −1.76156 | −1.01704 | −0.508518 | − | 0.861052i | \(-0.669806\pi\) | ||||
−0.508518 | + | 0.861052i | \(0.669806\pi\) | |||||||
\(4\) | 5.62620 | 2.81310 | ||||||||
\(5\) | 2.62620 | 1.17447 | 0.587236 | − | 0.809416i | \(-0.300216\pi\) | ||||
0.587236 | + | 0.809416i | \(0.300216\pi\) | |||||||
\(6\) | −4.86464 | −1.98598 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 10.0140 | 3.54047 | ||||||||
\(9\) | 0.103084 | 0.0343612 | ||||||||
\(10\) | 7.25240 | 2.29341 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −9.91087 | −2.86102 | ||||||||
\(13\) | 2.38776 | 0.662244 | 0.331122 | − | 0.943588i | \(-0.392573\pi\) | ||||
0.331122 | + | 0.943588i | \(0.392573\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.62620 | −1.19448 | ||||||||
\(16\) | 16.4017 | 4.10043 | ||||||||
\(17\) | 2.38776 | 0.579116 | 0.289558 | − | 0.957161i | \(-0.406492\pi\) | ||||
0.289558 | + | 0.957161i | \(0.406492\pi\) | |||||||
\(18\) | 0.284672 | 0.0670977 | ||||||||
\(19\) | 1.72928 | 0.396724 | 0.198362 | − | 0.980129i | \(-0.436438\pi\) | ||||
0.198362 | + | 0.980129i | \(0.436438\pi\) | |||||||
\(20\) | 14.7755 | 3.30390 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.626198 | −0.130571 | −0.0652857 | − | 0.997867i | \(-0.520796\pi\) | ||||
−0.0652857 | + | 0.997867i | \(0.520796\pi\) | |||||||
\(24\) | −17.6402 | −3.60078 | ||||||||
\(25\) | 1.89692 | 0.379383 | ||||||||
\(26\) | 6.59392 | 1.29317 | ||||||||
\(27\) | 5.10308 | 0.982089 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.72928 | 0.321120 | 0.160560 | − | 0.987026i | \(-0.448670\pi\) | ||||
0.160560 | + | 0.987026i | \(0.448670\pi\) | |||||||
\(30\) | −12.7755 | −2.33248 | ||||||||
\(31\) | 2.23844 | 0.402036 | 0.201018 | − | 0.979588i | \(-0.435575\pi\) | ||||
0.201018 | + | 0.979588i | \(0.435575\pi\) | |||||||
\(32\) | 25.2663 | 4.46650 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.59392 | 1.13085 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.579969 | 0.0966616 | ||||||||
\(37\) | −6.89692 | −1.13385 | −0.566923 | − | 0.823771i | \(-0.691866\pi\) | ||||
−0.566923 | + | 0.823771i | \(0.691866\pi\) | |||||||
\(38\) | 4.77551 | 0.774690 | ||||||||
\(39\) | −4.20617 | −0.673526 | ||||||||
\(40\) | 26.2986 | 4.15818 | ||||||||
\(41\) | −10.3878 | −1.62229 | −0.811147 | − | 0.584842i | \(-0.801157\pi\) | ||||
−0.811147 | + | 0.584842i | \(0.801157\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.25240 | 1.10598 | 0.552990 | − | 0.833188i | \(-0.313487\pi\) | ||||
0.552990 | + | 0.833188i | \(0.313487\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.270718 | 0.0403563 | ||||||||
\(46\) | −1.72928 | −0.254969 | ||||||||
\(47\) | −6.38776 | −0.931750 | −0.465875 | − | 0.884851i | \(-0.654260\pi\) | ||||
−0.465875 | + | 0.884851i | \(0.654260\pi\) | |||||||
\(48\) | −28.8925 | −4.17028 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 5.23844 | 0.740828 | ||||||||
\(51\) | −4.20617 | −0.588981 | ||||||||
\(52\) | 13.4340 | 1.86296 | ||||||||
\(53\) | −9.25240 | −1.27091 | −0.635457 | − | 0.772136i | \(-0.719188\pi\) | ||||
−0.635457 | + | 0.772136i | \(0.719188\pi\) | |||||||
\(54\) | 14.0925 | 1.91774 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.04623 | −0.403483 | ||||||||
\(58\) | 4.77551 | 0.627055 | ||||||||
\(59\) | 1.76156 | 0.229335 | 0.114668 | − | 0.993404i | \(-0.463420\pi\) | ||||
0.114668 | + | 0.993404i | \(0.463420\pi\) | |||||||
\(60\) | −26.0279 | −3.36019 | ||||||||
\(61\) | 10.3878 | 1.33002 | 0.665008 | − | 0.746836i | \(-0.268428\pi\) | ||||
0.665008 | + | 0.746836i | \(0.268428\pi\) | |||||||
\(62\) | 6.18159 | 0.785062 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 36.9711 | 4.62138 | ||||||||
\(65\) | 6.27072 | 0.777787 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.42003 | −0.784332 | −0.392166 | − | 0.919895i | \(-0.628274\pi\) | ||||
−0.392166 | + | 0.919895i | \(0.628274\pi\) | |||||||
\(68\) | 13.4340 | 1.62911 | ||||||||
\(69\) | 1.10308 | 0.132796 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.08476 | 0.959485 | 0.479742 | − | 0.877409i | \(-0.340730\pi\) | ||||
0.479742 | + | 0.877409i | \(0.340730\pi\) | |||||||
\(72\) | 1.03228 | 0.121655 | ||||||||
\(73\) | −10.3878 | −1.21579 | −0.607897 | − | 0.794016i | \(-0.707987\pi\) | ||||
−0.607897 | + | 0.794016i | \(0.707987\pi\) | |||||||
\(74\) | −19.0462 | −2.21408 | ||||||||
\(75\) | −3.34153 | −0.385846 | ||||||||
\(76\) | 9.72928 | 1.11603 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −11.6156 | −1.31520 | ||||||||
\(79\) | 15.2524 | 1.71603 | 0.858014 | − | 0.513626i | \(-0.171698\pi\) | ||||
0.858014 | + | 0.513626i | \(0.171698\pi\) | |||||||
\(80\) | 43.0741 | 4.81583 | ||||||||
\(81\) | −9.29862 | −1.03318 | ||||||||
\(82\) | −28.6864 | −3.16788 | ||||||||
\(83\) | −12.7755 | −1.40229 | −0.701147 | − | 0.713017i | \(-0.747328\pi\) | ||||
−0.701147 | + | 0.713017i | \(0.747328\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.27072 | 0.680155 | ||||||||
\(86\) | 20.0279 | 2.15966 | ||||||||
\(87\) | −3.04623 | −0.326590 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.1493 | 1.49982 | 0.749912 | − | 0.661538i | \(-0.230096\pi\) | ||||
0.749912 | + | 0.661538i | \(0.230096\pi\) | |||||||
\(90\) | 0.747604 | 0.0788044 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.52311 | −0.367310 | ||||||||
\(93\) | −3.94315 | −0.408885 | ||||||||
\(94\) | −17.6402 | −1.81944 | ||||||||
\(95\) | 4.54144 | 0.465942 | ||||||||
\(96\) | −44.5081 | −4.54259 | ||||||||
\(97\) | 8.35548 | 0.848370 | 0.424185 | − | 0.905575i | \(-0.360561\pi\) | ||||
0.424185 | + | 0.905575i | \(0.360561\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 10.6724 | 1.06724 | ||||||||
\(101\) | 13.8463 | 1.37776 | 0.688880 | − | 0.724875i | \(-0.258103\pi\) | ||||
0.688880 | + | 0.724875i | \(0.258103\pi\) | |||||||
\(102\) | −11.6156 | −1.15011 | ||||||||
\(103\) | 2.92919 | 0.288622 | 0.144311 | − | 0.989532i | \(-0.453903\pi\) | ||||
0.144311 | + | 0.989532i | \(0.453903\pi\) | |||||||
\(104\) | 23.9109 | 2.34465 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −25.5510 | −2.48173 | ||||||||
\(107\) | 3.45856 | 0.334352 | 0.167176 | − | 0.985927i | \(-0.446535\pi\) | ||||
0.167176 | + | 0.985927i | \(0.446535\pi\) | |||||||
\(108\) | 28.7110 | 2.76271 | ||||||||
\(109\) | −16.2341 | −1.55494 | −0.777471 | − | 0.628919i | \(-0.783498\pi\) | ||||
−0.777471 | + | 0.628919i | \(0.783498\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.1493 | 1.15316 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.10308 | 0.668202 | 0.334101 | − | 0.942537i | \(-0.391567\pi\) | ||||
0.334101 | + | 0.942537i | \(0.391567\pi\) | |||||||
\(114\) | −8.41233 | −0.787887 | ||||||||
\(115\) | −1.64452 | −0.153352 | ||||||||
\(116\) | 9.72928 | 0.903341 | ||||||||
\(117\) | 0.246139 | 0.0227555 | ||||||||
\(118\) | 4.86464 | 0.447826 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −46.3265 | −4.22901 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 28.6864 | 2.59714 | ||||||||
\(123\) | 18.2986 | 1.64993 | ||||||||
\(124\) | 12.5939 | 1.13097 | ||||||||
\(125\) | −8.14931 | −0.728897 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.54144 | −0.402987 | −0.201494 | − | 0.979490i | \(-0.564580\pi\) | ||||
−0.201494 | + | 0.979490i | \(0.564580\pi\) | |||||||
\(128\) | 51.5650 | 4.55774 | ||||||||
\(129\) | −12.7755 | −1.12482 | ||||||||
\(130\) | 17.3169 | 1.51880 | ||||||||
\(131\) | 6.27072 | 0.547875 | 0.273938 | − | 0.961747i | \(-0.411674\pi\) | ||||
0.273938 | + | 0.961747i | \(0.411674\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −17.7293 | −1.53158 | ||||||||
\(135\) | 13.4017 | 1.15344 | ||||||||
\(136\) | 23.9109 | 2.05034 | ||||||||
\(137\) | 9.40171 | 0.803242 | 0.401621 | − | 0.915806i | \(-0.368447\pi\) | ||||
0.401621 | + | 0.915806i | \(0.368447\pi\) | |||||||
\(138\) | 3.04623 | 0.259312 | ||||||||
\(139\) | −15.8217 | −1.34198 | −0.670991 | − | 0.741465i | \(-0.734131\pi\) | ||||
−0.670991 | + | 0.741465i | \(0.734131\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.2524 | 0.947623 | ||||||||
\(142\) | 22.3265 | 1.87360 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.69075 | 0.140896 | ||||||||
\(145\) | 4.54144 | 0.377146 | ||||||||
\(146\) | −28.6864 | −2.37410 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −38.8034 | −3.18962 | ||||||||
\(149\) | 3.45856 | 0.283337 | 0.141668 | − | 0.989914i | \(-0.454753\pi\) | ||||
0.141668 | + | 0.989914i | \(0.454753\pi\) | |||||||
\(150\) | −9.22782 | −0.753448 | ||||||||
\(151\) | −10.2986 | −0.838090 | −0.419045 | − | 0.907965i | \(-0.637635\pi\) | ||||
−0.419045 | + | 0.907965i | \(0.637635\pi\) | |||||||
\(152\) | 17.3169 | 1.40459 | ||||||||
\(153\) | 0.246139 | 0.0198991 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.87859 | 0.472180 | ||||||||
\(156\) | −23.6647 | −1.89469 | ||||||||
\(157\) | −11.3372 | −0.904804 | −0.452402 | − | 0.891814i | \(-0.649433\pi\) | ||||
−0.452402 | + | 0.891814i | \(0.649433\pi\) | |||||||
\(158\) | 42.1204 | 3.35092 | ||||||||
\(159\) | 16.2986 | 1.29257 | ||||||||
\(160\) | 66.3544 | 5.24578 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −25.6787 | −2.01751 | ||||||||
\(163\) | −9.72928 | −0.762056 | −0.381028 | − | 0.924563i | \(-0.624430\pi\) | ||||
−0.381028 | + | 0.924563i | \(0.624430\pi\) | |||||||
\(164\) | −58.4436 | −4.56368 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −35.2803 | −2.73828 | ||||||||
\(167\) | −22.5048 | −1.74147 | −0.870737 | − | 0.491750i | \(-0.836357\pi\) | ||||
−0.870737 | + | 0.491750i | \(0.836357\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.29862 | −0.561433 | ||||||||
\(170\) | 17.3169 | 1.32815 | ||||||||
\(171\) | 0.178261 | 0.0136319 | ||||||||
\(172\) | 40.8034 | 3.11123 | ||||||||
\(173\) | −6.92919 | −0.526817 | −0.263408 | − | 0.964684i | \(-0.584847\pi\) | ||||
−0.263408 | + | 0.964684i | \(0.584847\pi\) | |||||||
\(174\) | −8.41233 | −0.637737 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.10308 | −0.233242 | ||||||||
\(178\) | 39.0741 | 2.92873 | ||||||||
\(179\) | 13.9431 | 1.04216 | 0.521080 | − | 0.853508i | \(-0.325529\pi\) | ||||
0.521080 | + | 0.853508i | \(0.325529\pi\) | |||||||
\(180\) | 1.52311 | 0.113526 | ||||||||
\(181\) | −3.16763 | −0.235448 | −0.117724 | − | 0.993046i | \(-0.537560\pi\) | ||||
−0.117724 | + | 0.993046i | \(0.537560\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −18.2986 | −1.35267 | ||||||||
\(184\) | −6.27072 | −0.462283 | ||||||||
\(185\) | −18.1127 | −1.33167 | ||||||||
\(186\) | −10.8892 | −0.798436 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −35.9388 | −2.62110 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.5414 | 0.909851 | ||||||||
\(191\) | 18.3555 | 1.32816 | 0.664078 | − | 0.747663i | \(-0.268824\pi\) | ||||
0.664078 | + | 0.747663i | \(0.268824\pi\) | |||||||
\(192\) | −65.1266 | −4.70011 | ||||||||
\(193\) | −3.04623 | −0.219272 | −0.109636 | − | 0.993972i | \(-0.534969\pi\) | ||||
−0.109636 | + | 0.993972i | \(0.534969\pi\) | |||||||
\(194\) | 23.0741 | 1.65663 | ||||||||
\(195\) | −11.0462 | −0.791037 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.95377 | 0.352942 | 0.176471 | − | 0.984306i | \(-0.443532\pi\) | ||||
0.176471 | + | 0.984306i | \(0.443532\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.7047 | −1.11328 | −0.556638 | − | 0.830755i | \(-0.687909\pi\) | ||||
−0.556638 | + | 0.830755i | \(0.687909\pi\) | |||||||
\(200\) | 18.9956 | 1.34319 | ||||||||
\(201\) | 11.3093 | 0.797693 | ||||||||
\(202\) | 38.2374 | 2.69037 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −23.6647 | −1.65686 | ||||||||
\(205\) | −27.2803 | −1.90534 | ||||||||
\(206\) | 8.08913 | 0.563596 | ||||||||
\(207\) | −0.0645508 | −0.00448659 | ||||||||
\(208\) | 39.1633 | 2.71548 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.5510 | 1.20826 | 0.604131 | − | 0.796885i | \(-0.293520\pi\) | ||||
0.604131 | + | 0.796885i | \(0.293520\pi\) | |||||||
\(212\) | −52.0558 | −3.57521 | ||||||||
\(213\) | −14.2418 | −0.975830 | ||||||||
\(214\) | 9.55102 | 0.652894 | ||||||||
\(215\) | 19.0462 | 1.29894 | ||||||||
\(216\) | 51.1020 | 3.47705 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −44.8313 | −3.03636 | ||||||||
\(219\) | 18.2986 | 1.23651 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.70138 | 0.383516 | ||||||||
\(222\) | 33.5510 | 2.25180 | ||||||||
\(223\) | 22.2943 | 1.49293 | 0.746467 | − | 0.665423i | \(-0.231749\pi\) | ||||
0.746467 | + | 0.665423i | \(0.231749\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.195541 | 0.0130361 | ||||||||
\(226\) | 19.6156 | 1.30481 | ||||||||
\(227\) | −14.2707 | −0.947181 | −0.473590 | − | 0.880745i | \(-0.657042\pi\) | ||||
−0.473590 | + | 0.880745i | \(0.657042\pi\) | |||||||
\(228\) | −17.1387 | −1.13504 | ||||||||
\(229\) | 3.87859 | 0.256305 | 0.128152 | − | 0.991754i | \(-0.459095\pi\) | ||||
0.128152 | + | 0.991754i | \(0.459095\pi\) | |||||||
\(230\) | −4.54144 | −0.299453 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 17.3169 | 1.13691 | ||||||||
\(233\) | 6.68305 | 0.437821 | 0.218911 | − | 0.975745i | \(-0.429750\pi\) | ||||
0.218911 | + | 0.975745i | \(0.429750\pi\) | |||||||
\(234\) | 0.679726 | 0.0444351 | ||||||||
\(235\) | −16.7755 | −1.09431 | ||||||||
\(236\) | 9.91087 | 0.645143 | ||||||||
\(237\) | −26.8680 | −1.74526 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.54144 | −0.293761 | −0.146881 | − | 0.989154i | \(-0.546923\pi\) | ||||
−0.146881 | + | 0.989154i | \(0.546923\pi\) | |||||||
\(240\) | −75.8776 | −4.89787 | ||||||||
\(241\) | 3.70470 | 0.238641 | 0.119320 | − | 0.992856i | \(-0.461928\pi\) | ||||
0.119320 | + | 0.992856i | \(0.461928\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.07081 | 0.0686924 | ||||||||
\(244\) | 58.4436 | 3.74147 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 50.5327 | 3.22185 | ||||||||
\(247\) | 4.12910 | 0.262728 | ||||||||
\(248\) | 22.4157 | 1.42340 | ||||||||
\(249\) | 22.5048 | 1.42618 | ||||||||
\(250\) | −22.5048 | −1.42333 | ||||||||
\(251\) | −8.50916 | −0.537093 | −0.268547 | − | 0.963267i | \(-0.586543\pi\) | ||||
−0.268547 | + | 0.963267i | \(0.586543\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −12.5414 | −0.786920 | ||||||||
\(255\) | −11.0462 | −0.691742 | ||||||||
\(256\) | 68.4575 | 4.27860 | ||||||||
\(257\) | 2.95377 | 0.184251 | 0.0921256 | − | 0.995747i | \(-0.470634\pi\) | ||||
0.0921256 | + | 0.995747i | \(0.470634\pi\) | |||||||
\(258\) | −35.2803 | −2.19646 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 35.2803 | 2.18799 | ||||||||
\(261\) | 0.178261 | 0.0110341 | ||||||||
\(262\) | 17.3169 | 1.06984 | ||||||||
\(263\) | −16.0000 | −0.986602 | −0.493301 | − | 0.869859i | \(-0.664210\pi\) | ||||
−0.493301 | + | 0.869859i | \(0.664210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −24.2986 | −1.49265 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −24.9248 | −1.52537 | ||||||||
\(268\) | −36.1204 | −2.20640 | ||||||||
\(269\) | 6.77551 | 0.413110 | 0.206555 | − | 0.978435i | \(-0.433775\pi\) | ||||
0.206555 | + | 0.978435i | \(0.433775\pi\) | |||||||
\(270\) | 37.0096 | 2.25233 | ||||||||
\(271\) | −3.45856 | −0.210093 | −0.105046 | − | 0.994467i | \(-0.533499\pi\) | ||||
−0.105046 | + | 0.994467i | \(0.533499\pi\) | |||||||
\(272\) | 39.1633 | 2.37462 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 25.9634 | 1.56850 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.20617 | 0.373567 | ||||||||
\(277\) | −11.4586 | −0.688478 | −0.344239 | − | 0.938882i | \(-0.611863\pi\) | ||||
−0.344239 | + | 0.938882i | \(0.611863\pi\) | |||||||
\(278\) | −43.6926 | −2.62051 | ||||||||
\(279\) | 0.230747 | 0.0138145 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.3265 | −1.33189 | −0.665945 | − | 0.746001i | \(-0.731971\pi\) | ||||
−0.665945 | + | 0.746001i | \(0.731971\pi\) | |||||||
\(282\) | 31.0741 | 1.85044 | ||||||||
\(283\) | 12.3632 | 0.734915 | 0.367457 | − | 0.930040i | \(-0.380228\pi\) | ||||
0.367457 | + | 0.930040i | \(0.380228\pi\) | |||||||
\(284\) | 45.4865 | 2.69913 | ||||||||
\(285\) | −8.00000 | −0.473879 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.60455 | 0.153475 | ||||||||
\(289\) | −11.2986 | −0.664625 | ||||||||
\(290\) | 12.5414 | 0.736459 | ||||||||
\(291\) | −14.7187 | −0.862823 | ||||||||
\(292\) | −58.4436 | −3.42015 | ||||||||
\(293\) | −2.15368 | −0.125819 | −0.0629097 | − | 0.998019i | \(-0.520038\pi\) | ||||
−0.0629097 | + | 0.998019i | \(0.520038\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.62620 | 0.269348 | ||||||||
\(296\) | −69.0654 | −4.01434 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.55102 | 0.553276 | ||||||||
\(299\) | −1.49521 | −0.0864701 | ||||||||
\(300\) | −18.8001 | −1.08542 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −28.4402 | −1.63655 | ||||||||
\(303\) | −24.3911 | −1.40123 | ||||||||
\(304\) | 28.3632 | 1.62674 | ||||||||
\(305\) | 27.2803 | 1.56207 | ||||||||
\(306\) | 0.679726 | 0.0388573 | ||||||||
\(307\) | 31.8217 | 1.81616 | 0.908081 | − | 0.418794i | \(-0.137547\pi\) | ||||
0.908081 | + | 0.418794i | \(0.137547\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.15994 | −0.293539 | ||||||||
\(310\) | 16.2341 | 0.922033 | ||||||||
\(311\) | 10.9292 | 0.619738 | 0.309869 | − | 0.950779i | \(-0.399715\pi\) | ||||
0.309869 | + | 0.950779i | \(0.399715\pi\) | |||||||
\(312\) | −42.1204 | −2.38460 | ||||||||
\(313\) | −7.40171 | −0.418369 | −0.209185 | − | 0.977876i | \(-0.567081\pi\) | ||||
−0.209185 | + | 0.977876i | \(0.567081\pi\) | |||||||
\(314\) | −31.3082 | −1.76682 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 85.8130 | 4.82736 | ||||||||
\(317\) | −8.89692 | −0.499701 | −0.249850 | − | 0.968284i | \(-0.580381\pi\) | ||||
−0.249850 | + | 0.968284i | \(0.580381\pi\) | |||||||
\(318\) | 45.0096 | 2.52401 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 97.0933 | 5.42768 | ||||||||
\(321\) | −6.09246 | −0.340048 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.12910 | 0.229749 | ||||||||
\(324\) | −52.3159 | −2.90644 | ||||||||
\(325\) | 4.52937 | 0.251244 | ||||||||
\(326\) | −26.8680 | −1.48808 | ||||||||
\(327\) | 28.5972 | 1.58143 | ||||||||
\(328\) | −104.022 | −5.74368 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.56165 | 0.470591 | 0.235295 | − | 0.971924i | \(-0.424394\pi\) | ||||
0.235295 | + | 0.971924i | \(0.424394\pi\) | |||||||
\(332\) | −71.8776 | −3.94479 | ||||||||
\(333\) | −0.710960 | −0.0389604 | ||||||||
\(334\) | −62.1483 | −3.40060 | ||||||||
\(335\) | −16.8603 | −0.921175 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.72928 | −0.529988 | −0.264994 | − | 0.964250i | \(-0.585370\pi\) | ||||
−0.264994 | + | 0.964250i | \(0.585370\pi\) | |||||||
\(338\) | −20.1556 | −1.09632 | ||||||||
\(339\) | −12.5125 | −0.679585 | ||||||||
\(340\) | 35.2803 | 1.91334 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.492277 | 0.0266193 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 72.6252 | 3.91569 | ||||||||
\(345\) | 2.89692 | 0.155965 | ||||||||
\(346\) | −19.1354 | −1.02872 | ||||||||
\(347\) | 14.8401 | 0.796656 | 0.398328 | − | 0.917243i | \(-0.369591\pi\) | ||||
0.398328 | + | 0.917243i | \(0.369591\pi\) | |||||||
\(348\) | −17.1387 | −0.918730 | ||||||||
\(349\) | −16.2461 | −0.869636 | −0.434818 | − | 0.900518i | \(-0.643187\pi\) | ||||
−0.434818 | + | 0.900518i | \(0.643187\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.1849 | 0.650383 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.8603 | −1.64253 | −0.821263 | − | 0.570549i | \(-0.806730\pi\) | ||||
−0.821263 | + | 0.570549i | \(0.806730\pi\) | |||||||
\(354\) | −8.56934 | −0.455455 | ||||||||
\(355\) | 21.2322 | 1.12689 | ||||||||
\(356\) | 79.6068 | 4.21915 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 38.5048 | 2.03504 | ||||||||
\(359\) | −11.7938 | −0.622455 | −0.311227 | − | 0.950335i | \(-0.600740\pi\) | ||||
−0.311227 | + | 0.950335i | \(0.600740\pi\) | |||||||
\(360\) | 2.71096 | 0.142880 | ||||||||
\(361\) | −16.0096 | −0.842610 | ||||||||
\(362\) | −8.74760 | −0.459764 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −27.2803 | −1.42792 | ||||||||
\(366\) | −50.5327 | −2.64139 | ||||||||
\(367\) | 3.55539 | 0.185590 | 0.0927949 | − | 0.995685i | \(-0.470420\pi\) | ||||
0.0927949 | + | 0.995685i | \(0.470420\pi\) | |||||||
\(368\) | −10.2707 | −0.535398 | ||||||||
\(369\) | −1.07081 | −0.0557441 | ||||||||
\(370\) | −50.0192 | −2.60037 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −22.1849 | −1.15023 | ||||||||
\(373\) | 22.5048 | 1.16525 | 0.582627 | − | 0.812740i | \(-0.302025\pi\) | ||||
0.582627 | + | 0.812740i | \(0.302025\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.3555 | 0.741314 | ||||||||
\(376\) | −63.9667 | −3.29883 | ||||||||
\(377\) | 4.12910 | 0.212660 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.4296 | 1.20350 | 0.601749 | − | 0.798685i | \(-0.294471\pi\) | ||||
0.601749 | + | 0.798685i | \(0.294471\pi\) | |||||||
\(380\) | 25.5510 | 1.31074 | ||||||||
\(381\) | 8.00000 | 0.409852 | ||||||||
\(382\) | 50.6897 | 2.59351 | ||||||||
\(383\) | 3.42629 | 0.175075 | 0.0875376 | − | 0.996161i | \(-0.472100\pi\) | ||||
0.0875376 | + | 0.996161i | \(0.472100\pi\) | |||||||
\(384\) | −90.8347 | −4.63539 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.41233 | −0.428177 | ||||||||
\(387\) | 0.747604 | 0.0380028 | ||||||||
\(388\) | 47.0096 | 2.38655 | ||||||||
\(389\) | 8.05685 | 0.408499 | 0.204249 | − | 0.978919i | \(-0.434525\pi\) | ||||
0.204249 | + | 0.978919i | \(0.434525\pi\) | |||||||
\(390\) | −30.5048 | −1.54467 | ||||||||
\(391\) | −1.49521 | −0.0756159 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.0462 | −0.557209 | ||||||||
\(394\) | 13.6801 | 0.689195 | ||||||||
\(395\) | 40.0558 | 2.01543 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.3632 | 1.32313 | 0.661565 | − | 0.749888i | \(-0.269893\pi\) | ||||
0.661565 | + | 0.749888i | \(0.269893\pi\) | |||||||
\(398\) | −43.3694 | −2.17391 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 31.1127 | 1.55563 | ||||||||
\(401\) | −22.5972 | −1.12845 | −0.564226 | − | 0.825620i | \(-0.690825\pi\) | ||||
−0.564226 | + | 0.825620i | \(0.690825\pi\) | |||||||
\(402\) | 31.2311 | 1.55767 | ||||||||
\(403\) | 5.34485 | 0.266246 | ||||||||
\(404\) | 77.9021 | 3.87578 | ||||||||
\(405\) | −24.4200 | −1.21344 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −42.1204 | −2.08527 | ||||||||
\(409\) | −9.30488 | −0.460097 | −0.230048 | − | 0.973179i | \(-0.573888\pi\) | ||||
−0.230048 | + | 0.973179i | \(0.573888\pi\) | |||||||
\(410\) | −75.3361 | −3.72059 | ||||||||
\(411\) | −16.5616 | −0.816926 | ||||||||
\(412\) | 16.4802 | 0.811922 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.178261 | −0.00876104 | ||||||||
\(415\) | −33.5510 | −1.64695 | ||||||||
\(416\) | 60.3299 | 2.95791 | ||||||||
\(417\) | 27.8709 | 1.36484 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.8463 | 0.676437 | 0.338218 | − | 0.941068i | \(-0.390176\pi\) | ||||
0.338218 | + | 0.941068i | \(0.390176\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.7572 | −1.74270 | −0.871349 | − | 0.490663i | \(-0.836755\pi\) | ||||
−0.871349 | + | 0.490663i | \(0.836755\pi\) | |||||||
\(422\) | 48.4681 | 2.35939 | ||||||||
\(423\) | −0.658473 | −0.0320161 | ||||||||
\(424\) | −92.6531 | −4.49963 | ||||||||
\(425\) | 4.52937 | 0.219707 | ||||||||
\(426\) | −39.3295 | −1.90552 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 19.4586 | 0.940565 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 52.5972 | 2.53646 | ||||||||
\(431\) | −31.3082 | −1.50806 | −0.754032 | − | 0.656838i | \(-0.771894\pi\) | ||||
−0.754032 | + | 0.656838i | \(0.771894\pi\) | |||||||
\(432\) | 83.6993 | 4.02698 | ||||||||
\(433\) | −21.6079 | −1.03841 | −0.519204 | − | 0.854650i | \(-0.673772\pi\) | ||||
−0.519204 | + | 0.854650i | \(0.673772\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.00000 | −0.383571 | ||||||||
\(436\) | −91.3361 | −4.37421 | ||||||||
\(437\) | −1.08287 | −0.0518008 | ||||||||
\(438\) | 50.5327 | 2.41455 | ||||||||
\(439\) | −15.5877 | −0.743959 | −0.371979 | − | 0.928241i | \(-0.621321\pi\) | ||||
−0.371979 | + | 0.928241i | \(0.621321\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 15.7447 | 0.748898 | ||||||||
\(443\) | 23.4942 | 1.11624 | 0.558121 | − | 0.829760i | \(-0.311523\pi\) | ||||
0.558121 | + | 0.829760i | \(0.311523\pi\) | |||||||
\(444\) | 68.3544 | 3.24396 | ||||||||
\(445\) | 37.1589 | 1.76150 | ||||||||
\(446\) | 61.5669 | 2.91528 | ||||||||
\(447\) | −6.09246 | −0.288163 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.7832 | 1.07521 | 0.537603 | − | 0.843198i | \(-0.319330\pi\) | ||||
0.537603 | + | 0.843198i | \(0.319330\pi\) | |||||||
\(450\) | 0.539998 | 0.0254558 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 39.9634 | 1.87972 | ||||||||
\(453\) | 18.1416 | 0.852368 | ||||||||
\(454\) | −39.4094 | −1.84957 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −30.5048 | −1.42852 | ||||||||
\(457\) | −14.5048 | −0.678506 | −0.339253 | − | 0.940695i | \(-0.610174\pi\) | ||||
−0.339253 | + | 0.940695i | \(0.610174\pi\) | |||||||
\(458\) | 10.7110 | 0.500490 | ||||||||
\(459\) | 12.1849 | 0.568743 | ||||||||
\(460\) | −9.25240 | −0.431395 | ||||||||
\(461\) | 31.1633 | 1.45142 | 0.725709 | − | 0.688002i | \(-0.241512\pi\) | ||||
0.725709 | + | 0.688002i | \(0.241512\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.87859 | −0.273201 | −0.136601 | − | 0.990626i | \(-0.543618\pi\) | ||||
−0.136601 | + | 0.990626i | \(0.543618\pi\) | |||||||
\(464\) | 28.3632 | 1.31673 | ||||||||
\(465\) | −10.3555 | −0.480224 | ||||||||
\(466\) | 18.4556 | 0.854941 | ||||||||
\(467\) | 23.7249 | 1.09786 | 0.548929 | − | 0.835869i | \(-0.315036\pi\) | ||||
0.548929 | + | 0.835869i | \(0.315036\pi\) | |||||||
\(468\) | 1.38482 | 0.0640136 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −46.3265 | −2.13688 | ||||||||
\(471\) | 19.9711 | 0.920217 | ||||||||
\(472\) | 17.6402 | 0.811954 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −74.1974 | −3.40800 | ||||||||
\(475\) | 3.28030 | 0.150511 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.953771 | −0.0436702 | ||||||||
\(478\) | −12.5414 | −0.573632 | ||||||||
\(479\) | −8.41233 | −0.384369 | −0.192185 | − | 0.981359i | \(-0.561557\pi\) | ||||
−0.192185 | + | 0.981359i | \(0.561557\pi\) | |||||||
\(480\) | −116.887 | −5.33514 | ||||||||
\(481\) | −16.4681 | −0.750883 | ||||||||
\(482\) | 10.2307 | 0.465998 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.9431 | 0.996387 | ||||||||
\(486\) | 2.95710 | 0.134137 | ||||||||
\(487\) | 24.7957 | 1.12360 | 0.561801 | − | 0.827273i | \(-0.310109\pi\) | ||||
0.561801 | + | 0.827273i | \(0.310109\pi\) | |||||||
\(488\) | 104.022 | 4.70888 | ||||||||
\(489\) | 17.1387 | 0.775038 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.2062 | 0.550857 | 0.275428 | − | 0.961322i | \(-0.411180\pi\) | ||||
0.275428 | + | 0.961322i | \(0.411180\pi\) | |||||||
\(492\) | 102.952 | 4.64142 | ||||||||
\(493\) | 4.12910 | 0.185965 | ||||||||
\(494\) | 11.4028 | 0.513034 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 36.7143 | 1.64852 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 62.1483 | 2.78493 | ||||||||
\(499\) | 22.3265 | 0.999473 | 0.499736 | − | 0.866178i | \(-0.333430\pi\) | ||||
0.499736 | + | 0.866178i | \(0.333430\pi\) | |||||||
\(500\) | −45.8496 | −2.05046 | ||||||||
\(501\) | 39.6435 | 1.77114 | ||||||||
\(502\) | −23.4985 | −1.04879 | ||||||||
\(503\) | 4.54144 | 0.202493 | 0.101246 | − | 0.994861i | \(-0.467717\pi\) | ||||
0.101246 | + | 0.994861i | \(0.467717\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 36.3632 | 1.61814 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.8569 | 0.570997 | ||||||||
\(508\) | −25.5510 | −1.13364 | ||||||||
\(509\) | −4.12141 | −0.182678 | −0.0913391 | − | 0.995820i | \(-0.529115\pi\) | ||||
−0.0913391 | + | 0.995820i | \(0.529115\pi\) | |||||||
\(510\) | −30.5048 | −1.35077 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 85.9194 | 3.79714 | ||||||||
\(513\) | 8.82467 | 0.389619 | ||||||||
\(514\) | 8.15701 | 0.359790 | ||||||||
\(515\) | 7.69264 | 0.338978 | ||||||||
\(516\) | −71.8776 | −3.16423 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.2062 | 0.535791 | ||||||||
\(520\) | 62.7947 | 2.75373 | ||||||||
\(521\) | −39.2880 | −1.72124 | −0.860619 | − | 0.509249i | \(-0.829923\pi\) | ||||
−0.860619 | + | 0.509249i | \(0.829923\pi\) | |||||||
\(522\) | 0.492277 | 0.0215464 | ||||||||
\(523\) | 2.14162 | 0.0936464 | 0.0468232 | − | 0.998903i | \(-0.485090\pi\) | ||||
0.0468232 | + | 0.998903i | \(0.485090\pi\) | |||||||
\(524\) | 35.2803 | 1.54123 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −44.1849 | −1.92655 | ||||||||
\(527\) | 5.34485 | 0.232825 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6079 | −0.982951 | ||||||||
\(530\) | −67.1020 | −2.91473 | ||||||||
\(531\) | 0.181588 | 0.00788024 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −24.8034 | −1.07436 | ||||||||
\(534\) | −68.8313 | −2.97862 | ||||||||
\(535\) | 9.08287 | 0.392687 | ||||||||
\(536\) | −64.2899 | −2.77690 | ||||||||
\(537\) | −24.5616 | −1.05991 | ||||||||
\(538\) | 18.7110 | 0.806687 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 75.4007 | 3.24473 | ||||||||
\(541\) | −43.0462 | −1.85070 | −0.925351 | − | 0.379112i | \(-0.876230\pi\) | ||||
−0.925351 | + | 0.379112i | \(0.876230\pi\) | |||||||
\(542\) | −9.55102 | −0.410251 | ||||||||
\(543\) | 5.57997 | 0.239459 | ||||||||
\(544\) | 60.3299 | 2.58662 | ||||||||
\(545\) | −42.6339 | −1.82624 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.0096 | −1.24036 | −0.620180 | − | 0.784459i | \(-0.712940\pi\) | ||||
−0.620180 | + | 0.784459i | \(0.712940\pi\) | |||||||
\(548\) | 52.8959 | 2.25960 | ||||||||
\(549\) | 1.07081 | 0.0457010 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.99042 | 0.127396 | ||||||||
\(552\) | 11.0462 | 0.470159 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −31.6435 | −1.34440 | ||||||||
\(555\) | 31.9065 | 1.35436 | ||||||||
\(556\) | −89.0162 | −3.77513 | ||||||||
\(557\) | −1.49521 | −0.0633540 | −0.0316770 | − | 0.999498i | \(-0.510085\pi\) | ||||
−0.0316770 | + | 0.999498i | \(0.510085\pi\) | |||||||
\(558\) | 0.637221 | 0.0269757 | ||||||||
\(559\) | 17.3169 | 0.732429 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −61.6560 | −2.60080 | ||||||||
\(563\) | −6.27072 | −0.264279 | −0.132140 | − | 0.991231i | \(-0.542185\pi\) | ||||
−0.132140 | + | 0.991231i | \(0.542185\pi\) | |||||||
\(564\) | 63.3082 | 2.66576 | ||||||||
\(565\) | 18.6541 | 0.784784 | ||||||||
\(566\) | 34.1416 | 1.43508 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 80.9604 | 3.39702 | ||||||||
\(569\) | 7.82174 | 0.327904 | 0.163952 | − | 0.986468i | \(-0.447576\pi\) | ||||
0.163952 | + | 0.986468i | \(0.447576\pi\) | |||||||
\(570\) | −22.0925 | −0.925351 | ||||||||
\(571\) | −15.1753 | −0.635068 | −0.317534 | − | 0.948247i | \(-0.602855\pi\) | ||||
−0.317534 | + | 0.948247i | \(0.602855\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −32.3342 | −1.35078 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.18785 | −0.0495366 | ||||||||
\(576\) | 3.81111 | 0.158796 | ||||||||
\(577\) | −23.6445 | −0.984334 | −0.492167 | − | 0.870501i | \(-0.663795\pi\) | ||||
−0.492167 | + | 0.870501i | \(0.663795\pi\) | |||||||
\(578\) | −31.2018 | −1.29782 | ||||||||
\(579\) | 5.36611 | 0.223008 | ||||||||
\(580\) | 25.5510 | 1.06095 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −40.6464 | −1.68485 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −104.022 | −4.30448 | ||||||||
\(585\) | 0.646409 | 0.0267257 | ||||||||
\(586\) | −5.94751 | −0.245690 | ||||||||
\(587\) | 10.1537 | 0.419087 | 0.209544 | − | 0.977799i | \(-0.432802\pi\) | ||||
0.209544 | + | 0.977799i | \(0.432802\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.87090 | 0.159498 | ||||||||
\(590\) | 12.7755 | 0.525959 | ||||||||
\(591\) | −8.72635 | −0.358954 | ||||||||
\(592\) | −113.121 | −4.64925 | ||||||||
\(593\) | −33.7972 | −1.38788 | −0.693942 | − | 0.720031i | \(-0.744127\pi\) | ||||
−0.693942 | + | 0.720031i | \(0.744127\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19.4586 | 0.797054 | ||||||||
\(597\) | 27.6647 | 1.13224 | ||||||||
\(598\) | −4.12910 | −0.168852 | ||||||||
\(599\) | −18.3265 | −0.748802 | −0.374401 | − | 0.927267i | \(-0.622152\pi\) | ||||
−0.374401 | + | 0.927267i | \(0.622152\pi\) | |||||||
\(600\) | −33.4619 | −1.36608 | ||||||||
\(601\) | −48.4802 | −1.97755 | −0.988775 | − | 0.149415i | \(-0.952261\pi\) | ||||
−0.988775 | + | 0.149415i | \(0.952261\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.661801 | −0.0269506 | ||||||||
\(604\) | −57.9421 | −2.35763 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −67.3574 | −2.73621 | ||||||||
\(607\) | 20.5972 | 0.836017 | 0.418008 | − | 0.908443i | \(-0.362728\pi\) | ||||
0.418008 | + | 0.908443i | \(0.362728\pi\) | |||||||
\(608\) | 43.6926 | 1.77197 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 75.3361 | 3.05027 | ||||||||
\(611\) | −15.2524 | −0.617046 | ||||||||
\(612\) | 1.38482 | 0.0559782 | ||||||||
\(613\) | 18.8122 | 0.759816 | 0.379908 | − | 0.925024i | \(-0.375956\pi\) | ||||
0.379908 | + | 0.925024i | \(0.375956\pi\) | |||||||
\(614\) | 87.8776 | 3.54645 | ||||||||
\(615\) | 48.0558 | 1.93780 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.2062 | −0.571919 | −0.285959 | − | 0.958242i | \(-0.592312\pi\) | ||||
−0.285959 | + | 0.958242i | \(0.592312\pi\) | |||||||
\(618\) | −14.2495 | −0.573198 | ||||||||
\(619\) | 16.0235 | 0.644040 | 0.322020 | − | 0.946733i | \(-0.395638\pi\) | ||||
0.322020 | + | 0.946733i | \(0.395638\pi\) | |||||||
\(620\) | 33.0741 | 1.32829 | ||||||||
\(621\) | −3.19554 | −0.128233 | ||||||||
\(622\) | 30.1816 | 1.21017 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −68.9883 | −2.76174 | ||||||||
\(625\) | −30.8863 | −1.23545 | ||||||||
\(626\) | −20.4402 | −0.816956 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −63.7851 | −2.54530 | ||||||||
\(629\) | −16.4681 | −0.656628 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.1955 | 0.604925 | 0.302462 | − | 0.953161i | \(-0.402191\pi\) | ||||
0.302462 | + | 0.953161i | \(0.402191\pi\) | |||||||
\(632\) | 152.737 | 6.07554 | ||||||||
\(633\) | −30.9171 | −1.22885 | ||||||||
\(634\) | −24.5693 | −0.975773 | ||||||||
\(635\) | −11.9267 | −0.473297 | ||||||||
\(636\) | 91.6993 | 3.63611 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.833407 | 0.0329691 | ||||||||
\(640\) | 135.420 | 5.35294 | ||||||||
\(641\) | −10.2264 | −0.403918 | −0.201959 | − | 0.979394i | \(-0.564731\pi\) | ||||
−0.201959 | + | 0.979394i | \(0.564731\pi\) | |||||||
\(642\) | −16.8247 | −0.664017 | ||||||||
\(643\) | −20.5650 | −0.811003 | −0.405502 | − | 0.914094i | \(-0.632903\pi\) | ||||
−0.405502 | + | 0.914094i | \(0.632903\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −33.5510 | −1.32107 | ||||||||
\(646\) | 11.4028 | 0.448635 | ||||||||
\(647\) | 25.4542 | 1.00071 | 0.500354 | − | 0.865821i | \(-0.333203\pi\) | ||||
0.500354 | + | 0.865821i | \(0.333203\pi\) | |||||||
\(648\) | −93.1160 | −3.65794 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 12.5081 | 0.490609 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −54.7389 | −2.14374 | ||||||||
\(653\) | −45.2514 | −1.77082 | −0.885411 | − | 0.464809i | \(-0.846123\pi\) | ||||
−0.885411 | + | 0.464809i | \(0.846123\pi\) | |||||||
\(654\) | 78.9729 | 3.08809 | ||||||||
\(655\) | 16.4681 | 0.643464 | ||||||||
\(656\) | −170.377 | −6.65210 | ||||||||
\(657\) | −1.07081 | −0.0417762 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −50.3544 | −1.96153 | −0.980765 | − | 0.195191i | \(-0.937467\pi\) | ||||
−0.980765 | + | 0.195191i | \(0.937467\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.2234 | 0.903287 | 0.451644 | − | 0.892198i | \(-0.350838\pi\) | ||||
0.451644 | + | 0.892198i | \(0.350838\pi\) | |||||||
\(662\) | 23.6435 | 0.918930 | ||||||||
\(663\) | −10.0433 | −0.390049 | ||||||||
\(664\) | −127.933 | −4.96478 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.96336 | −0.0760785 | ||||||||
\(667\) | −1.08287 | −0.0419290 | ||||||||
\(668\) | −126.616 | −4.89894 | ||||||||
\(669\) | −39.2726 | −1.51837 | ||||||||
\(670\) | −46.5606 | −1.79879 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.22449 | −0.124295 | −0.0621475 | − | 0.998067i | \(-0.519795\pi\) | ||||
−0.0621475 | + | 0.998067i | \(0.519795\pi\) | |||||||
\(674\) | −26.8680 | −1.03492 | ||||||||
\(675\) | 9.68012 | 0.372588 | ||||||||
\(676\) | −41.0635 | −1.57937 | ||||||||
\(677\) | −42.6218 | −1.63809 | −0.819045 | − | 0.573729i | \(-0.805496\pi\) | ||||
−0.819045 | + | 0.573729i | \(0.805496\pi\) | |||||||
\(678\) | −34.5540 | −1.32704 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 62.7947 | 2.40807 | ||||||||
\(681\) | 25.1387 | 0.963317 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.5877 | 0.596445 | 0.298223 | − | 0.954496i | \(-0.403606\pi\) | ||||
0.298223 | + | 0.954496i | \(0.403606\pi\) | |||||||
\(684\) | 1.00293 | 0.0383480 | ||||||||
\(685\) | 24.6907 | 0.943385 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.83237 | −0.260671 | ||||||||
\(688\) | 118.952 | 4.53499 | ||||||||
\(689\) | −22.0925 | −0.841656 | ||||||||
\(690\) | 8.00000 | 0.304555 | ||||||||
\(691\) | −41.9311 | −1.59513 | −0.797567 | − | 0.603231i | \(-0.793880\pi\) | ||||
−0.797567 | + | 0.603231i | \(0.793880\pi\) | |||||||
\(692\) | −38.9850 | −1.48199 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 40.9817 | 1.55564 | ||||||||
\(695\) | −41.5510 | −1.57612 | ||||||||
\(696\) | −30.5048 | −1.15628 | ||||||||
\(697\) | −24.8034 | −0.939496 | ||||||||
\(698\) | −44.8646 | −1.69815 | ||||||||
\(699\) | −11.7726 | −0.445280 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.4094 | −0.582005 | −0.291003 | − | 0.956722i | \(-0.593989\pi\) | ||||
−0.291003 | + | 0.956722i | \(0.593989\pi\) | |||||||
\(702\) | 33.6493 | 1.27001 | ||||||||
\(703\) | −11.9267 | −0.449824 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 29.5510 | 1.11296 | ||||||||
\(706\) | −85.2224 | −3.20739 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −17.4586 | −0.656133 | ||||||||
\(709\) | 2.86027 | 0.107420 | 0.0537099 | − | 0.998557i | \(-0.482895\pi\) | ||||
0.0537099 | + | 0.998557i | \(0.482895\pi\) | |||||||
\(710\) | 58.6339 | 2.20049 | ||||||||
\(711\) | 1.57227 | 0.0589649 | ||||||||
\(712\) | 141.691 | 5.31008 | ||||||||
\(713\) | −1.40171 | −0.0524944 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 78.4469 | 2.93170 | ||||||||
\(717\) | 8.00000 | 0.298765 | ||||||||
\(718\) | −32.5693 | −1.21548 | ||||||||
\(719\) | 34.4725 | 1.28561 | 0.642804 | − | 0.766031i | \(-0.277771\pi\) | ||||
0.642804 | + | 0.766031i | \(0.277771\pi\) | |||||||
\(720\) | 4.44024 | 0.165478 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −44.2114 | −1.64538 | ||||||||
\(723\) | −6.52604 | −0.242706 | ||||||||
\(724\) | −17.8217 | −0.662340 | ||||||||
\(725\) | 3.28030 | 0.121827 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 40.3309 | 1.49579 | 0.747895 | − | 0.663817i | \(-0.231065\pi\) | ||||
0.747895 | + | 0.663817i | \(0.231065\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.0096 | 0.963318 | ||||||||
\(730\) | −75.3361 | −2.78831 | ||||||||
\(731\) | 17.3169 | 0.640490 | ||||||||
\(732\) | −102.952 | −3.80520 | ||||||||
\(733\) | 28.7634 | 1.06240 | 0.531201 | − | 0.847246i | \(-0.321741\pi\) | ||||
0.531201 | + | 0.847246i | \(0.321741\pi\) | |||||||
\(734\) | 9.81841 | 0.362404 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −15.8217 | −0.583197 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −2.95710 | −0.108852 | ||||||||
\(739\) | 35.1020 | 1.29125 | 0.645625 | − | 0.763655i | \(-0.276597\pi\) | ||||
0.645625 | + | 0.763655i | \(0.276597\pi\) | |||||||
\(740\) | −101.905 | −3.74612 | ||||||||
\(741\) | −7.27365 | −0.267204 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32.4681 | −1.19114 | −0.595570 | − | 0.803303i | \(-0.703074\pi\) | ||||
−0.595570 | + | 0.803303i | \(0.703074\pi\) | |||||||
\(744\) | −39.4865 | −1.44764 | ||||||||
\(745\) | 9.08287 | 0.332771 | ||||||||
\(746\) | 62.1483 | 2.27541 | ||||||||
\(747\) | −1.31695 | −0.0481846 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 39.6435 | 1.44758 | ||||||||
\(751\) | −28.3834 | −1.03572 | −0.517862 | − | 0.855464i | \(-0.673272\pi\) | ||||
−0.517862 | + | 0.855464i | \(0.673272\pi\) | |||||||
\(752\) | −104.770 | −3.82057 | ||||||||
\(753\) | 14.9894 | 0.546243 | ||||||||
\(754\) | 11.4028 | 0.415264 | ||||||||
\(755\) | −27.0462 | −0.984313 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.0462 | −0.619556 | −0.309778 | − | 0.950809i | \(-0.600255\pi\) | ||||
−0.309778 | + | 0.950809i | \(0.600255\pi\) | |||||||
\(758\) | 64.7022 | 2.35009 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 45.4777 | 1.64965 | ||||||||
\(761\) | −27.9388 | −1.01278 | −0.506390 | − | 0.862305i | \(-0.669020\pi\) | ||||
−0.506390 | + | 0.862305i | \(0.669020\pi\) | |||||||
\(762\) | 22.0925 | 0.800325 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 103.272 | 3.73623 | ||||||||
\(765\) | 0.646409 | 0.0233710 | ||||||||
\(766\) | 9.46189 | 0.341872 | ||||||||
\(767\) | 4.20617 | 0.151876 | ||||||||
\(768\) | −120.592 | −4.35148 | ||||||||
\(769\) | −6.69512 | −0.241432 | −0.120716 | − | 0.992687i | \(-0.538519\pi\) | ||||
−0.120716 | + | 0.992687i | \(0.538519\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.20324 | −0.187390 | ||||||||
\(772\) | −17.1387 | −0.616835 | ||||||||
\(773\) | −27.9142 | −1.00400 | −0.502002 | − | 0.864866i | \(-0.667403\pi\) | ||||
−0.502002 | + | 0.864866i | \(0.667403\pi\) | |||||||
\(774\) | 2.06455 | 0.0742087 | ||||||||
\(775\) | 4.24614 | 0.152526 | ||||||||
\(776\) | 83.6714 | 3.00363 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 22.2495 | 0.797682 | ||||||||
\(779\) | −17.9634 | −0.643604 | ||||||||
\(780\) | −62.1483 | −2.22527 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −4.12910 | −0.147656 | ||||||||
\(783\) | 8.82467 | 0.315368 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −29.7736 | −1.06267 | ||||||||
\(786\) | −30.5048 | −1.08807 | ||||||||
\(787\) | −21.8584 | −0.779167 | −0.389584 | − | 0.920991i | \(-0.627381\pi\) | ||||
−0.389584 | + | 0.920991i | \(0.627381\pi\) | |||||||
\(788\) | 27.8709 | 0.992860 | ||||||||
\(789\) | 28.1849 | 1.00341 | ||||||||
\(790\) | 110.616 | 3.93556 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.8034 | 0.880795 | ||||||||
\(794\) | 72.8034 | 2.58370 | ||||||||
\(795\) | 42.8034 | 1.51808 | ||||||||
\(796\) | −88.3578 | −3.13176 | ||||||||
\(797\) | 34.6262 | 1.22652 | 0.613261 | − | 0.789880i | \(-0.289857\pi\) | ||||
0.613261 | + | 0.789880i | \(0.289857\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.2524 | −0.539591 | ||||||||
\(800\) | 47.9282 | 1.69452 | ||||||||
\(801\) | 1.45856 | 0.0515358 | ||||||||
\(802\) | −62.4036 | −2.20355 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 63.6281 | 2.24399 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 14.7601 | 0.519903 | ||||||||
\(807\) | −11.9354 | −0.420148 | ||||||||
\(808\) | 138.656 | 4.87791 | ||||||||
\(809\) | 35.0462 | 1.23216 | 0.616080 | − | 0.787684i | \(-0.288720\pi\) | ||||
0.616080 | + | 0.787684i | \(0.288720\pi\) | |||||||
\(810\) | −67.4373 | −2.36951 | ||||||||
\(811\) | 18.1416 | 0.637038 | 0.318519 | − | 0.947916i | \(-0.396814\pi\) | ||||
0.318519 | + | 0.947916i | \(0.396814\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.09246 | 0.213672 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −25.5510 | −0.895013 | ||||||||
\(816\) | −68.9883 | −2.41507 | ||||||||
\(817\) | 12.5414 | 0.438769 | ||||||||
\(818\) | −25.6960 | −0.898438 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −153.484 | −5.35991 | ||||||||
\(821\) | −3.45856 | −0.120705 | −0.0603524 | − | 0.998177i | \(-0.519222\pi\) | ||||
−0.0603524 | + | 0.998177i | \(0.519222\pi\) | |||||||
\(822\) | −45.7359 | −1.59522 | ||||||||
\(823\) | −33.5308 | −1.16881 | −0.584405 | − | 0.811462i | \(-0.698672\pi\) | ||||
−0.584405 | + | 0.811462i | \(0.698672\pi\) | |||||||
\(824\) | 29.3328 | 1.02186 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.2986 | −0.914493 | −0.457246 | − | 0.889340i | \(-0.651164\pi\) | ||||
−0.457246 | + | 0.889340i | \(0.651164\pi\) | |||||||
\(828\) | −0.363176 | −0.0126212 | ||||||||
\(829\) | 29.0019 | 1.00728 | 0.503639 | − | 0.863914i | \(-0.331994\pi\) | ||||
0.503639 | + | 0.863914i | \(0.331994\pi\) | |||||||
\(830\) | −92.6531 | −3.21603 | ||||||||
\(831\) | 20.1849 | 0.700207 | ||||||||
\(832\) | 88.2778 | 3.06048 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 76.9671 | 2.66515 | ||||||||
\(835\) | −59.1020 | −2.04531 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.4230 | 0.394835 | ||||||||
\(838\) | 38.2374 | 1.32089 | ||||||||
\(839\) | −29.1710 | −1.00709 | −0.503547 | − | 0.863968i | \(-0.667972\pi\) | ||||
−0.503547 | + | 0.863968i | \(0.667972\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0096 | −0.896882 | ||||||||
\(842\) | −98.7455 | −3.40300 | ||||||||
\(843\) | 39.3295 | 1.35458 | ||||||||
\(844\) | 98.7455 | 3.39896 | ||||||||
\(845\) | −19.1676 | −0.659387 | ||||||||
\(846\) | −1.81841 | −0.0625183 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −151.755 | −5.21129 | ||||||||
\(849\) | −21.7784 | −0.747434 | ||||||||
\(850\) | 12.5081 | 0.429025 | ||||||||
\(851\) | 4.31884 | 0.148048 | ||||||||
\(852\) | −80.1270 | −2.74511 | ||||||||
\(853\) | −10.6218 | −0.363685 | −0.181842 | − | 0.983328i | \(-0.558206\pi\) | ||||
−0.181842 | + | 0.983328i | \(0.558206\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.468148 | 0.0160103 | ||||||||
\(856\) | 34.6339 | 1.18376 | ||||||||
\(857\) | −37.8463 | −1.29281 | −0.646403 | − | 0.762996i | \(-0.723727\pi\) | ||||
−0.646403 | + | 0.762996i | \(0.723727\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.0785 | 0.650950 | 0.325475 | − | 0.945551i | \(-0.394476\pi\) | ||||
0.325475 | + | 0.945551i | \(0.394476\pi\) | |||||||
\(860\) | 107.158 | 3.65405 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −86.4594 | −2.94482 | ||||||||
\(863\) | 11.1753 | 0.380413 | 0.190206 | − | 0.981744i | \(-0.439084\pi\) | ||||
0.190206 | + | 0.981744i | \(0.439084\pi\) | |||||||
\(864\) | 128.936 | 4.38650 | ||||||||
\(865\) | −18.1974 | −0.618731 | ||||||||
\(866\) | −59.6714 | −2.02772 | ||||||||
\(867\) | 19.9032 | 0.675947 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −22.0925 | −0.749004 | ||||||||
\(871\) | −15.3295 | −0.519419 | ||||||||
\(872\) | −162.567 | −5.50522 | ||||||||
\(873\) | 0.861314 | 0.0291511 | ||||||||
\(874\) | −2.99042 | −0.101152 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 102.952 | 3.47842 | ||||||||
\(877\) | −5.85838 | −0.197824 | −0.0989118 | − | 0.995096i | \(-0.531536\pi\) | ||||
−0.0989118 | + | 0.995096i | \(0.531536\pi\) | |||||||
\(878\) | −43.0462 | −1.45274 | ||||||||
\(879\) | 3.79383 | 0.127963 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.9065 | 0.872812 | 0.436406 | − | 0.899750i | \(-0.356251\pi\) | ||||
0.436406 | + | 0.899750i | \(0.356251\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.4219 | 0.451684 | 0.225842 | − | 0.974164i | \(-0.427487\pi\) | ||||
0.225842 | + | 0.974164i | \(0.427487\pi\) | |||||||
\(884\) | 32.0771 | 1.07887 | ||||||||
\(885\) | −8.14931 | −0.273936 | ||||||||
\(886\) | 64.8805 | 2.17970 | ||||||||
\(887\) | 49.6068 | 1.66563 | 0.832817 | − | 0.553548i | \(-0.186726\pi\) | ||||
0.832817 | + | 0.553548i | \(0.186726\pi\) | |||||||
\(888\) | 121.663 | 4.08273 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 102.616 | 3.43971 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 125.432 | 4.19977 | ||||||||
\(893\) | −11.0462 | −0.369648 | ||||||||
\(894\) | −16.8247 | −0.562701 | ||||||||
\(895\) | 36.6175 | 1.22399 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.63389 | 0.0879432 | ||||||||
\(898\) | 62.9171 | 2.09957 | ||||||||
\(899\) | 3.87090 | 0.129102 | ||||||||
\(900\) | 1.10015 | 0.0366718 | ||||||||
\(901\) | −22.0925 | −0.736006 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 71.1299 | 2.36575 | ||||||||
\(905\) | −8.31884 | −0.276527 | ||||||||
\(906\) | 50.0991 | 1.66443 | ||||||||
\(907\) | −47.8776 | −1.58975 | −0.794874 | − | 0.606775i | \(-0.792463\pi\) | ||||
−0.794874 | + | 0.606775i | \(0.792463\pi\) | |||||||
\(908\) | −80.2899 | −2.66451 | ||||||||
\(909\) | 1.42733 | 0.0473415 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.8122 | 0.755800 | 0.377900 | − | 0.925846i | \(-0.376646\pi\) | ||||
0.377900 | + | 0.925846i | \(0.376646\pi\) | |||||||
\(912\) | −49.9634 | −1.65445 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −40.0558 | −1.32493 | ||||||||
\(915\) | −48.0558 | −1.58868 | ||||||||
\(916\) | 21.8217 | 0.721011 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 33.6493 | 1.11059 | ||||||||
\(919\) | −40.0000 | −1.31948 | −0.659739 | − | 0.751495i | \(-0.729333\pi\) | ||||
−0.659739 | + | 0.751495i | \(0.729333\pi\) | |||||||
\(920\) | −16.4681 | −0.542939 | ||||||||
\(921\) | −56.0558 | −1.84710 | ||||||||
\(922\) | 86.0591 | 2.83421 | ||||||||
\(923\) | 19.3044 | 0.635413 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.0829 | −0.430162 | ||||||||
\(926\) | −16.2341 | −0.533485 | ||||||||
\(927\) | 0.301952 | 0.00991740 | ||||||||
\(928\) | 43.6926 | 1.43428 | ||||||||
\(929\) | 16.0366 | 0.526145 | 0.263073 | − | 0.964776i | \(-0.415264\pi\) | ||||
0.263073 | + | 0.964776i | \(0.415264\pi\) | |||||||
\(930\) | −28.5972 | −0.937741 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 37.6002 | 1.23163 | ||||||||
\(933\) | −19.2524 | −0.630295 | ||||||||
\(934\) | 65.5177 | 2.14380 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.46482 | 0.0805652 | ||||||||
\(937\) | 25.3049 | 0.826674 | 0.413337 | − | 0.910578i | \(-0.364363\pi\) | ||||
0.413337 | + | 0.910578i | \(0.364363\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.0385 | 0.425496 | ||||||||
\(940\) | −94.3823 | −3.07841 | ||||||||
\(941\) | −20.5294 | −0.669238 | −0.334619 | − | 0.942353i | \(-0.608608\pi\) | ||||
−0.334619 | + | 0.942353i | \(0.608608\pi\) | |||||||
\(942\) | 55.1512 | 1.79692 | ||||||||
\(943\) | 6.50479 | 0.211825 | ||||||||
\(944\) | 28.8925 | 0.940372 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.6907 | −0.542376 | −0.271188 | − | 0.962526i | \(-0.587417\pi\) | ||||
−0.271188 | + | 0.962526i | \(0.587417\pi\) | |||||||
\(948\) | −151.165 | −4.90960 | ||||||||
\(949\) | −24.8034 | −0.805153 | ||||||||
\(950\) | 9.05874 | 0.293904 | ||||||||
\(951\) | 15.6724 | 0.508213 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 56.4681 | 1.82918 | 0.914591 | − | 0.404379i | \(-0.132512\pi\) | ||||
0.914591 | + | 0.404379i | \(0.132512\pi\) | |||||||
\(954\) | −2.63389 | −0.0852755 | ||||||||
\(955\) | 48.2051 | 1.55988 | ||||||||
\(956\) | −25.5510 | −0.826379 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −23.2311 | −0.750564 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −171.035 | −5.52014 | ||||||||
\(961\) | −25.9894 | −0.838367 | ||||||||
\(962\) | −45.4777 | −1.46626 | ||||||||
\(963\) | 0.356522 | 0.0114887 | ||||||||
\(964\) | 20.8434 | 0.671320 | ||||||||
\(965\) | −8.00000 | −0.257529 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.3082 | 1.52133 | 0.760665 | − | 0.649145i | \(-0.224873\pi\) | ||||
0.760665 | + | 0.649145i | \(0.224873\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.27365 | −0.233663 | ||||||||
\(970\) | 60.5972 | 1.94566 | ||||||||
\(971\) | 25.2355 | 0.809846 | 0.404923 | − | 0.914351i | \(-0.367298\pi\) | ||||
0.404923 | + | 0.914351i | \(0.367298\pi\) | |||||||
\(972\) | 6.02458 | 0.193238 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 68.4748 | 2.19407 | ||||||||
\(975\) | −7.97875 | −0.255524 | ||||||||
\(976\) | 170.377 | 5.45363 | ||||||||
\(977\) | 7.10308 | 0.227248 | 0.113624 | − | 0.993524i | \(-0.463754\pi\) | ||||
0.113624 | + | 0.993524i | \(0.463754\pi\) | |||||||
\(978\) | 47.3295 | 1.51343 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.67347 | −0.0534297 | ||||||||
\(982\) | 33.7080 | 1.07567 | ||||||||
\(983\) | 14.1893 | 0.452568 | 0.226284 | − | 0.974061i | \(-0.427342\pi\) | ||||
0.226284 | + | 0.974061i | \(0.427342\pi\) | |||||||
\(984\) | 183.242 | 5.84153 | ||||||||
\(985\) | 13.0096 | 0.414520 | ||||||||
\(986\) | 11.4028 | 0.363138 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 23.2311 | 0.739081 | ||||||||
\(989\) | −4.54144 | −0.144409 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.23407 | 0.134500 | 0.0672499 | − | 0.997736i | \(-0.478578\pi\) | ||||
0.0672499 | + | 0.997736i | \(0.478578\pi\) | |||||||
\(992\) | 56.5573 | 1.79570 | ||||||||
\(993\) | −15.0818 | −0.478607 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −41.2437 | −1.30751 | ||||||||
\(996\) | 126.616 | 4.01199 | ||||||||
\(997\) | 27.7047 | 0.877417 | 0.438708 | − | 0.898629i | \(-0.355436\pi\) | ||||
0.438708 | + | 0.898629i | \(0.355436\pi\) | |||||||
\(998\) | 61.6560 | 1.95169 | ||||||||
\(999\) | −35.1955 | −1.11354 |
(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 | 5929.2.a.y.1.3 | 3 | ||
7.6 | odd | 2 | 847.2.a.j.1.3 | yes | 3 | ||
11.10 | odd | 2 | 5929.2.a.t.1.1 | 3 | |||
21.20 | even | 2 | 7623.2.a.bz.1.1 | 3 | |||
77.6 | even | 10 | 847.2.f.u.729.3 | 12 | |||
77.13 | even | 10 | 847.2.f.u.323.3 | 12 | |||
77.20 | odd | 10 | 847.2.f.t.323.1 | 12 | |||
77.27 | odd | 10 | 847.2.f.t.729.1 | 12 | |||
77.41 | even | 10 | 847.2.f.u.372.1 | 12 | |||
77.48 | odd | 10 | 847.2.f.t.148.3 | 12 | |||
77.62 | even | 10 | 847.2.f.u.148.1 | 12 | |||
77.69 | odd | 10 | 847.2.f.t.372.3 | 12 | |||
77.76 | even | 2 | 847.2.a.i.1.1 | ✓ | 3 | ||
231.230 | odd | 2 | 7623.2.a.ce.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.i.1.1 | ✓ | 3 | 77.76 | even | 2 | ||
847.2.a.j.1.3 | yes | 3 | 7.6 | odd | 2 | ||
847.2.f.t.148.3 | 12 | 77.48 | odd | 10 | |||
847.2.f.t.323.1 | 12 | 77.20 | odd | 10 | |||
847.2.f.t.372.3 | 12 | 77.69 | odd | 10 | |||
847.2.f.t.729.1 | 12 | 77.27 | odd | 10 | |||
847.2.f.u.148.1 | 12 | 77.62 | even | 10 | |||
847.2.f.u.323.3 | 12 | 77.13 | even | 10 | |||
847.2.f.u.372.1 | 12 | 77.41 | even | 10 | |||
847.2.f.u.729.3 | 12 | 77.6 | even | 10 | |||
5929.2.a.t.1.1 | 3 | 11.10 | odd | 2 | |||
5929.2.a.y.1.3 | 3 | 1.1 | even | 1 | trivial | ||
7623.2.a.bz.1.1 | 3 | 21.20 | even | 2 | |||
7623.2.a.ce.1.3 | 3 | 231.230 | odd | 2 |