Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8512,2,Mod(1,8512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8512, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8512.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8512 = 2^{6} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8512.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: | \(67.9686622005\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 10x^{5} + 31x^{4} + 12x^{3} - 45x^{2} - 15x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 4256) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.838827\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8512.1 |
$q$-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 | 0 | ||||||||
\(3\) | 0.838827 | 0.484297 | 0.242149 | − | 0.970239i | \(-0.422148\pi\) | ||||
0.242149 | + | 0.970239i | \(0.422148\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.50991 | 1.12247 | 0.561233 | − | 0.827658i | \(-0.310327\pi\) | ||||
0.561233 | + | 0.827658i | \(0.310327\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.29637 | −0.765456 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.46016 | 1.04328 | 0.521639 | − | 0.853167i | \(-0.325321\pi\) | ||||
0.521639 | + | 0.853167i | \(0.325321\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.36062 | 1.76412 | 0.882059 | − | 0.471139i | \(-0.156157\pi\) | ||||
0.882059 | + | 0.471139i | \(0.156157\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.10538 | 0.543608 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.34077 | 1.53786 | 0.768931 | − | 0.639332i | \(-0.220789\pi\) | ||||
0.768931 | + | 0.639332i | \(0.220789\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.838827 | −0.183047 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.29877 | −1.10487 | −0.552435 | − | 0.833556i | \(-0.686301\pi\) | ||||
−0.552435 | + | 0.833556i | \(0.686301\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.29966 | 0.259932 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.44274 | −0.855006 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.1298 | 1.88106 | 0.940532 | − | 0.339704i | \(-0.110327\pi\) | ||||
0.940532 | + | 0.339704i | \(0.110327\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.39225 | −1.68690 | −0.843449 | − | 0.537209i | \(-0.819479\pi\) | ||||
−0.843449 | + | 0.537209i | \(0.819479\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.90248 | 0.505256 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.50991 | −0.424253 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.14446 | −0.352546 | −0.176273 | − | 0.984341i | \(-0.556404\pi\) | ||||
−0.176273 | + | 0.984341i | \(0.556404\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.33546 | 0.854357 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.43345 | −1.16091 | −0.580455 | − | 0.814292i | \(-0.697125\pi\) | ||||
−0.580455 | + | 0.814292i | \(0.697125\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.15432 | 0.176032 | 0.0880159 | − | 0.996119i | \(-0.471947\pi\) | ||||
0.0880159 | + | 0.996119i | \(0.471947\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.76368 | −0.859199 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.96586 | 0.870211 | 0.435105 | − | 0.900380i | \(-0.356711\pi\) | ||||
0.435105 | + | 0.900380i | \(0.356711\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.31881 | 0.744782 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.50168 | 0.893074 | 0.446537 | − | 0.894765i | \(-0.352657\pi\) | ||||
0.446537 | + | 0.894765i | \(0.352657\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.68469 | 1.17104 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.838827 | 0.111105 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.26281 | 1.20591 | 0.602957 | − | 0.797773i | \(-0.293989\pi\) | ||||
0.602957 | + | 0.797773i | \(0.293989\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.12100 | 0.911751 | 0.455875 | − | 0.890044i | \(-0.349326\pi\) | ||||
0.455875 | + | 0.890044i | \(0.349326\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.29637 | 0.289315 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 15.9646 | 1.98016 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.54487 | 0.921753 | 0.460876 | − | 0.887464i | \(-0.347535\pi\) | ||||
0.460876 | + | 0.887464i | \(0.347535\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.44476 | −0.535086 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.10596 | 0.131254 | 0.0656269 | − | 0.997844i | \(-0.479095\pi\) | ||||
0.0656269 | + | 0.997844i | \(0.479095\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.0584070 | 0.00683603 | 0.00341801 | − | 0.999994i | \(-0.498912\pi\) | ||||
0.00341801 | + | 0.999994i | \(0.498912\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.09019 | 0.125884 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.46016 | −0.394322 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.5650 | 1.86371 | 0.931857 | − | 0.362827i | \(-0.118188\pi\) | ||||
0.931857 | + | 0.362827i | \(0.118188\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.16241 | 0.351379 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.59617 | −0.614260 | −0.307130 | − | 0.951668i | \(-0.599369\pi\) | ||||
−0.307130 | + | 0.951668i | \(0.599369\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 15.9148 | 1.72620 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.49719 | 0.910994 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.8293 | −1.57191 | −0.785953 | − | 0.618286i | \(-0.787827\pi\) | ||||
−0.785953 | + | 0.618286i | \(0.787827\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.36062 | −0.666774 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.87848 | −0.816960 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.50991 | 0.257512 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.89047 | −0.191948 | −0.0959741 | − | 0.995384i | \(-0.530597\pi\) | ||||
−0.0959741 | + | 0.995384i | \(0.530597\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.94580 | −0.798583 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.59919 | 0.358132 | 0.179066 | − | 0.983837i | \(-0.442692\pi\) | ||||
0.179066 | + | 0.983837i | \(0.442692\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.29050 | 0.915420 | 0.457710 | − | 0.889101i | \(-0.348670\pi\) | ||||
0.457710 | + | 0.889101i | \(0.348670\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.10538 | −0.205464 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −19.8956 | −1.92338 | −0.961690 | − | 0.274138i | \(-0.911608\pi\) | ||||
−0.961690 | + | 0.274138i | \(0.911608\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.787338 | −0.0754133 | −0.0377067 | − | 0.999289i | \(-0.512005\pi\) | ||||
−0.0377067 | + | 0.999289i | \(0.512005\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.79883 | −0.170737 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.5592 | −0.993324 | −0.496662 | − | 0.867944i | \(-0.665441\pi\) | ||||
−0.496662 | + | 0.867944i | \(0.665441\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.2995 | −1.24018 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −14.6063 | −1.35035 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.34077 | −0.581257 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.972699 | 0.0884272 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.23539 | −0.562226 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.28753 | −0.830702 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.27500 | −0.113138 | −0.0565688 | − | 0.998399i | \(-0.518016\pi\) | ||||
−0.0565688 | + | 0.998399i | \(0.518016\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.968273 | 0.0852517 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.07361 | 0.705394 | 0.352697 | − | 0.935738i | \(-0.385265\pi\) | ||||
0.352697 | + | 0.935738i | \(0.385265\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.00000 | −0.0867110 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.1509 | −0.959715 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.8874 | 0.930172 | 0.465086 | − | 0.885265i | \(-0.346023\pi\) | ||||
0.465086 | + | 0.885265i | \(0.346023\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.1523 | −1.03075 | −0.515374 | − | 0.856966i | \(-0.672347\pi\) | ||||
−0.515374 | + | 0.856966i | \(0.672347\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.00433 | 0.421441 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 22.0087 | 1.84046 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 25.4250 | 2.11143 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.838827 | 0.0691853 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.5985 | −1.11403 | −0.557014 | − | 0.830503i | \(-0.688053\pi\) | ||||
−0.557014 | + | 0.830503i | \(0.688053\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.4025 | −1.33482 | −0.667409 | − | 0.744692i | \(-0.732597\pi\) | ||||
−0.667409 | + | 0.744692i | \(0.732597\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14.5607 | −1.17717 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −23.5737 | −1.89349 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.2552 | 1.37711 | 0.688557 | − | 0.725183i | \(-0.258245\pi\) | ||||
0.688557 | + | 0.725183i | \(0.258245\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.45379 | 0.432514 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.29877 | 0.417602 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.9989 | −1.17480 | −0.587401 | − | 0.809296i | \(-0.699849\pi\) | ||||
−0.587401 | + | 0.809296i | \(0.699849\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.28496 | 0.567133 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.30131 | 0.332845 | 0.166423 | − | 0.986055i | \(-0.446778\pi\) | ||||
0.166423 | + | 0.986055i | \(0.446778\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27.4575 | 2.11211 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.29637 | −0.175608 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 24.4226 | 1.85682 | 0.928410 | − | 0.371558i | \(-0.121176\pi\) | ||||
0.928410 | + | 0.371558i | \(0.121176\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.29966 | −0.0982450 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.76990 | 0.584021 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.51414 | −0.636377 | −0.318188 | − | 0.948028i | \(-0.603074\pi\) | ||||
−0.318188 | + | 0.948028i | \(0.603074\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.5481 | 1.23001 | 0.615004 | − | 0.788524i | \(-0.289154\pi\) | ||||
0.615004 | + | 0.788524i | \(0.289154\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.97329 | 0.441558 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.38240 | −0.395722 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 21.9401 | 1.60442 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.44274 | 0.323162 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.6296 | −1.13092 | −0.565459 | − | 0.824776i | \(-0.691301\pi\) | ||||
−0.565459 | + | 0.824776i | \(0.691301\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.4908 | −0.971089 | −0.485545 | − | 0.874212i | \(-0.661379\pi\) | ||||
−0.485545 | + | 0.874212i | \(0.661379\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 13.3915 | 0.958988 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.3172 | −0.948811 | −0.474405 | − | 0.880306i | \(-0.657337\pi\) | ||||
−0.474405 | + | 0.880306i | \(0.657337\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.56699 | 0.607298 | 0.303649 | − | 0.952784i | \(-0.401795\pi\) | ||||
0.303649 | + | 0.952784i | \(0.401795\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.32885 | 0.446402 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.1298 | −0.710976 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.6573 | −1.30308 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.1679 | 0.845730 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.46016 | 0.239344 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.06901 | −0.624337 | −0.312168 | − | 0.950027i | \(-0.601055\pi\) | ||||
−0.312168 | + | 0.950027i | \(0.601055\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.927714 | 0.0635659 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.89723 | 0.197590 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.39225 | 0.637588 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.0489934 | 0.00331067 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 40.3312 | 2.71297 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.44936 | −0.164021 | −0.0820105 | − | 0.996631i | \(-0.526134\pi\) | ||||
−0.0820105 | + | 0.996631i | \(0.526134\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.98450 | −0.198966 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.5126 | 0.764117 | 0.382058 | − | 0.924138i | \(-0.375215\pi\) | ||||
0.382058 | + | 0.924138i | \(0.375215\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.76061 | 0.578918 | 0.289459 | − | 0.957190i | \(-0.406525\pi\) | ||||
0.289459 | + | 0.957190i | \(0.406525\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.90248 | −0.190969 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.1559 | 0.665333 | 0.332666 | − | 0.943045i | \(-0.392052\pi\) | ||||
0.332666 | + | 0.943045i | \(0.392052\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.9738 | 0.976783 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.8952 | 0.902591 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.4419 | −1.06354 | −0.531770 | − | 0.846889i | \(-0.678473\pi\) | ||||
−0.531770 | + | 0.846889i | \(0.678473\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.10981 | −0.329152 | −0.164576 | − | 0.986364i | \(-0.552626\pi\) | ||||
−0.164576 | + | 0.986364i | \(0.552626\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.9809 | 1.02518 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.50991 | 0.160352 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.36062 | 0.404716 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.69422 | −0.297484 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.82819 | −0.430992 | −0.215496 | − | 0.976505i | \(-0.569137\pi\) | ||||
−0.215496 | + | 0.976505i | \(0.569137\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.3346 | −1.15269 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 13.3497 | 0.835994 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.2450 | −0.826202 | −0.413101 | − | 0.910685i | \(-0.635554\pi\) | ||||
−0.413101 | + | 0.910685i | \(0.635554\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.14446 | 0.133250 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −23.2619 | −1.43987 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.19868 | 0.0739139 | 0.0369569 | − | 0.999317i | \(-0.488234\pi\) | ||||
0.0369569 | + | 0.999317i | \(0.488234\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.3186 | 1.00245 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.4393 | −0.761270 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 29.0920 | 1.77377 | 0.886885 | − | 0.461989i | \(-0.152864\pi\) | ||||
0.886885 | + | 0.461989i | \(0.152864\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.7017 | 0.771572 | 0.385786 | − | 0.922588i | \(-0.373930\pi\) | ||||
0.385786 | + | 0.922588i | \(0.373930\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.33546 | −0.322917 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.49703 | 0.271181 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.98143 | −0.479558 | −0.239779 | − | 0.970828i | \(-0.577075\pi\) | ||||
−0.239779 | + | 0.970828i | \(0.577075\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 21.5681 | 1.29125 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.4089 | 1.21749 | 0.608745 | − | 0.793366i | \(-0.291673\pi\) | ||||
0.608745 | + | 0.793366i | \(0.291673\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.9925 | 1.12899 | 0.564493 | − | 0.825438i | \(-0.309072\pi\) | ||||
0.564493 | + | 0.825438i | \(0.309072\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.10538 | 0.124712 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.43345 | 0.438783 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 23.2053 | 1.36502 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.58578 | −0.0929600 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.2730 | −1.12594 | −0.562971 | − | 0.826476i | \(-0.690342\pi\) | ||||
−0.562971 | + | 0.826476i | \(0.690342\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 23.2488 | 1.35360 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −15.3726 | −0.892008 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −33.7035 | −1.94912 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.15432 | −0.0665337 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.01910 | 0.173443 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 17.8731 | 1.02341 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.77122 | −0.500600 | −0.250300 | − | 0.968168i | \(-0.580529\pi\) | ||||
−0.250300 | + | 0.968168i | \(0.580529\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.79313 | 0.443336 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.49554 | 0.311623 | 0.155812 | − | 0.987787i | \(-0.450201\pi\) | ||||
0.155812 | + | 0.987787i | \(0.450201\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.2854 | −1.42922 | −0.714608 | − | 0.699526i | \(-0.753395\pi\) | ||||
−0.714608 | + | 0.699526i | \(0.753395\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.76368 | 0.324747 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.49512 | 0.364802 | 0.182401 | − | 0.983224i | \(-0.441613\pi\) | ||||
0.182401 | + | 0.983224i | \(0.441613\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 35.0509 | 1.96247 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.6890 | −0.931488 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.34077 | 0.352810 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.26663 | 0.458550 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.660441 | −0.0365225 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.96586 | −0.328909 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.1880 | 0.669914 | 0.334957 | − | 0.942233i | \(-0.391278\pi\) | ||||
0.334957 | + | 0.942233i | \(0.391278\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.92446 | 0.269859 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 18.9370 | 1.03464 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.73440 | 0.530267 | 0.265133 | − | 0.964212i | \(-0.414584\pi\) | ||||
0.265133 | + | 0.964212i | \(0.414584\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.85733 | −0.481064 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −32.4987 | −1.75990 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −11.1559 | −0.600616 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.90135 | −0.209435 | −0.104718 | − | 0.994502i | \(-0.533394\pi\) | ||||
−0.104718 | + | 0.994502i | \(0.533394\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.55550 | 0.190322 | 0.0951608 | − | 0.995462i | \(-0.469663\pi\) | ||||
0.0951608 | + | 0.995462i | \(0.469663\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −28.2586 | −1.50833 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.90189 | 0.154452 | 0.0772261 | − | 0.997014i | \(-0.475394\pi\) | ||||
0.0772261 | + | 0.997014i | \(0.475394\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.77587 | 0.147328 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.31881 | −0.281501 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.40056 | 0.0739185 | 0.0369592 | − | 0.999317i | \(-0.488233\pi\) | ||||
0.0369592 | + | 0.999317i | \(0.488233\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.815926 | 0.0428250 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.146597 | 0.00767321 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.1574 | 0.530213 | 0.265106 | − | 0.964219i | \(-0.414593\pi\) | ||||
0.265106 | + | 0.964219i | \(0.414593\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 17.0700 | 0.888626 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.50168 | −0.337550 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.10281 | 0.0571012 | 0.0285506 | − | 0.999592i | \(-0.490911\pi\) | ||||
0.0285506 | + | 0.999592i | \(0.490911\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.79064 | −0.402307 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 64.4321 | 3.31842 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.6517 | −0.958071 | −0.479036 | − | 0.877795i | \(-0.659014\pi\) | ||||
−0.479036 | + | 0.877795i | \(0.659014\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.06950 | −0.0547923 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.13654 | −0.160270 | −0.0801348 | − | 0.996784i | \(-0.525535\pi\) | ||||
−0.0801348 | + | 0.996784i | \(0.525535\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.68469 | −0.442613 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.65074 | −0.134745 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 33.4216 | 1.69454 | 0.847270 | − | 0.531162i | \(-0.178244\pi\) | ||||
0.847270 | + | 0.531162i | \(0.178244\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −33.5983 | −1.69914 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.77236 | 0.341620 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 41.5768 | 2.09196 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.9045 | 0.547283 | 0.273642 | − | 0.961832i | \(-0.411772\pi\) | ||||
0.273642 | + | 0.961832i | \(0.411772\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.838827 | −0.0419939 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.52313 | 0.275812 | 0.137906 | − | 0.990445i | \(-0.455963\pi\) | ||||
0.137906 | + | 0.990445i | \(0.455963\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −59.7405 | −2.97589 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.93738 | 0.394412 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.42016 | −0.367804 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.7459 | 0.729137 | 0.364568 | − | 0.931177i | \(-0.381217\pi\) | ||||
0.364568 | + | 0.931177i | \(0.381217\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.13264 | 0.450480 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.26281 | −0.455793 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.0459 | −0.689486 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.1937 | −0.499188 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.1788 | 0.790386 | 0.395193 | − | 0.918598i | \(-0.370678\pi\) | ||||
0.395193 | + | 0.918598i | \(0.370678\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.24074 | −0.352892 | −0.176446 | − | 0.984310i | \(-0.556460\pi\) | ||||
−0.176446 | + | 0.984310i | \(0.556460\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.6998 | −0.666108 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.24084 | 0.399739 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.12100 | −0.344609 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 18.4615 | 0.891332 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.6634 | −0.561807 | −0.280903 | − | 0.959736i | \(-0.590634\pi\) | ||||
−0.280903 | + | 0.959736i | \(0.590634\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.52522 | 0.265525 | 0.132762 | − | 0.991148i | \(-0.457615\pi\) | ||||
0.132762 | + | 0.991148i | \(0.457615\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 21.3272 | 1.02256 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.29877 | −0.253475 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.9712 | 1.66908 | 0.834542 | − | 0.550945i | \(-0.185733\pi\) | ||||
0.834542 | + | 0.550945i | \(0.185733\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.29637 | −0.109351 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.2216 | 1.48338 | 0.741691 | − | 0.670742i | \(-0.234024\pi\) | ||||
0.741691 | + | 0.670742i | \(0.234024\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −37.2203 | −1.76441 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.4068 | −0.539521 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.5208 | −0.496508 | −0.248254 | − | 0.968695i | \(-0.579857\pi\) | ||||
−0.248254 | + | 0.968695i | \(0.579857\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.7209 | −1.21115 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13.7589 | −0.646448 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −15.9646 | −0.748432 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.0833 | 0.752346 | 0.376173 | − | 0.926550i | \(-0.377240\pi\) | ||||
0.376173 | + | 0.926550i | \(0.377240\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −28.1704 | −1.31488 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.7877 | 1.34078 | 0.670388 | − | 0.742011i | \(-0.266128\pi\) | ||||
0.670388 | + | 0.742011i | \(0.266128\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.7307 | 0.824017 | 0.412009 | − | 0.911180i | \(-0.364827\pi\) | ||||
0.412009 | + | 0.911180i | \(0.364827\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −19.7743 | −0.917011 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.9193 | 1.33823 | 0.669114 | − | 0.743160i | \(-0.266674\pi\) | ||||
0.669114 | + | 0.743160i | \(0.266674\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.54487 | −0.348390 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.4741 | 0.666932 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.99412 | 0.183650 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.29966 | 0.0596325 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14.9303 | −0.683609 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −39.4956 | −1.80460 | −0.902300 | − | 0.431109i | \(-0.858122\pi\) | ||||
−0.902300 | + | 0.431109i | \(0.858122\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.6401 | −0.621934 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.44476 | 0.202243 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.74491 | −0.215455 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.43774 | 0.110464 | 0.0552322 | − | 0.998474i | \(-0.482410\pi\) | ||||
0.0552322 | + | 0.998474i | \(0.482410\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.5815 | −0.568954 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.5143 | 1.28683 | 0.643416 | − | 0.765516i | \(-0.277516\pi\) | ||||
0.643416 | + | 0.765516i | \(0.277516\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 64.2310 | 2.89282 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −19.9433 | −0.896383 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.10596 | −0.0496093 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.7694 | −1.10883 | −0.554416 | − | 0.832240i | \(-0.687058\pi\) | ||||
−0.554416 | + | 0.832240i | \(0.687058\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.60805 | 0.161196 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.3299 | −1.12940 | −0.564702 | − | 0.825295i | \(-0.691009\pi\) | ||||
−0.564702 | + | 0.825295i | \(0.691009\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.03364 | 0.401992 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 23.0321 | 1.02289 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −27.6943 | −1.22753 | −0.613764 | − | 0.789490i | \(-0.710345\pi\) | ||||
−0.613764 | + | 0.789490i | \(0.710345\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.0584070 | −0.00258377 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.44274 | −0.196152 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 23.3183 | 1.02753 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.6428 | 0.907871 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.4864 | 0.899253 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.6577 | 0.598353 | 0.299177 | − | 0.954198i | \(-0.403288\pi\) | ||||
0.299177 | + | 0.954198i | \(0.403288\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.2806 | 1.14917 | 0.574586 | − | 0.818444i | \(-0.305163\pi\) | ||||
0.574586 | + | 0.818444i | \(0.305163\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.09019 | −0.0475798 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −59.5541 | −2.59422 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.07700 | 0.220739 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −21.2708 | −0.923075 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −47.2814 | −2.04798 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −49.9362 | −2.15893 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.14189 | −0.308195 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.46016 | 0.149040 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.56729 | −0.153370 | −0.0766849 | − | 0.997055i | \(-0.524434\pi\) | ||||
−0.0766849 | + | 0.997055i | \(0.524434\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.8810 | 0.595690 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.97615 | −0.0846490 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.75085 | −0.331402 | −0.165701 | − | 0.986176i | \(-0.552989\pi\) | ||||
−0.165701 | + | 0.986176i | \(0.552989\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.3524 | −0.697905 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.1298 | 0.431546 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.5650 | −0.704417 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.51490 | −0.191647 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.922909 | −0.0391049 | −0.0195524 | − | 0.999809i | \(-0.506224\pi\) | ||||
−0.0195524 | + | 0.999809i | \(0.506224\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.34217 | 0.310541 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.4039 | 0.777014 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −30.6656 | −1.29240 | −0.646201 | − | 0.763168i | \(-0.723643\pi\) | ||||
−0.646201 | + | 0.763168i | \(0.723643\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −26.5026 | −1.11497 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.16241 | −0.132809 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.5203 | −0.482955 | −0.241477 | − | 0.970406i | \(-0.577632\pi\) | ||||
−0.241477 | + | 0.970406i | \(0.577632\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.4530 | 0.646689 | 0.323344 | − | 0.946281i | \(-0.395193\pi\) | ||||
0.323344 | + | 0.946281i | \(0.395193\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.1105 | −0.547701 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.88660 | −0.287191 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.0625 | −1.62619 | −0.813097 | − | 0.582128i | \(-0.802220\pi\) | ||||
−0.813097 | + | 0.582128i | \(0.802220\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.3165 | −0.470296 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.59617 | 0.232168 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.4968 | 0.931724 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −36.6606 | −1.51573 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.2106 | 0.958003 | 0.479001 | − | 0.877814i | \(-0.340999\pi\) | ||||
0.479001 | + | 0.877814i | \(0.340999\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.39225 | −0.387001 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.1708 | −0.459507 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −25.4167 | −1.04374 | −0.521870 | − | 0.853025i | \(-0.674765\pi\) | ||||
−0.521870 | + | 0.853025i | \(0.674765\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15.9148 | −0.652442 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.18623 | 0.294113 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −47.0201 | −1.92119 | −0.960594 | − | 0.277955i | \(-0.910343\pi\) | ||||
−0.960594 | + | 0.277955i | \(0.910343\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.46252 | −0.222821 | −0.111410 | − | 0.993774i | \(-0.535537\pi\) | ||||
−0.111410 | + | 0.993774i | \(0.535537\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17.3258 | −0.705562 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.44139 | 0.0992565 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.7810 | 0.518766 | 0.259383 | − | 0.965775i | \(-0.416481\pi\) | ||||
0.259383 | + | 0.965775i | \(0.416481\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.49719 | −0.344324 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 37.9466 | 1.53515 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.8772 | 0.439328 | 0.219664 | − | 0.975576i | \(-0.429504\pi\) | ||||
0.219664 | + | 0.975576i | \(0.429504\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −15.6503 | −0.631080 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −38.7821 | −1.56131 | −0.780655 | − | 0.624962i | \(-0.785114\pi\) | ||||
−0.780655 | + | 0.624962i | \(0.785114\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.9373 | −1.00232 | −0.501158 | − | 0.865356i | \(-0.667092\pi\) | ||||
−0.501158 | + | 0.865356i | \(0.667092\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 23.5411 | 0.944671 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.8293 | 0.594125 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.8092 | −1.19237 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.90248 | 0.115914 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13.5975 | −0.542168 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.7661 | 1.82192 | 0.910959 | − | 0.412496i | \(-0.135343\pi\) | ||||
0.910959 | + | 0.412496i | \(0.135343\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.60734 | −0.302364 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.20013 | −0.126993 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.36062 | 0.252017 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.53970 | −0.100469 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.7497 | 1.37253 | 0.686265 | − | 0.727351i | \(-0.259249\pi\) | ||||
0.686265 | + | 0.727351i | \(0.259249\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.0973 | −0.477070 | −0.238535 | − | 0.971134i | \(-0.576667\pi\) | ||||
−0.238535 | + | 0.971134i | \(0.576667\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.43028 | 0.0956922 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −40.1375 | −1.57797 | −0.788985 | − | 0.614413i | \(-0.789393\pi\) | ||||
−0.788985 | + | 0.614413i | \(0.789393\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32.0508 | 1.25810 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.87848 | 0.308782 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.1580 | 1.02364 | 0.511820 | − | 0.859093i | \(-0.328971\pi\) | ||||
0.511820 | + | 0.859093i | \(0.328971\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.2640 | 0.791782 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.134124 | −0.00523268 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.5535 | 1.26810 | 0.634052 | − | 0.773290i | \(-0.281390\pi\) | ||||
0.634052 | + | 0.773290i | \(0.281390\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.6399 | 0.491634 | 0.245817 | − | 0.969316i | \(-0.420944\pi\) | ||||
0.245817 | + | 0.969316i | \(0.420944\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 33.8309 | 1.31388 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.50991 | −0.0973302 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −53.6757 | −2.07833 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.05459 | −0.0794350 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.6398 | 0.951209 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.2360 | 0.471665 | 0.235832 | − | 0.971794i | \(-0.424218\pi\) | ||||
0.235832 | + | 0.971794i | \(0.424218\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.77405 | −0.222243 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.7535 | 1.29725 | 0.648626 | − | 0.761107i | \(-0.275344\pi\) | ||||
0.648626 | + | 0.761107i | \(0.275344\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.89047 | 0.0725496 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.65707 | 0.370060 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.4124 | −0.513212 | −0.256606 | − | 0.966516i | \(-0.582604\pi\) | ||||
−0.256606 | + | 0.966516i | \(0.582604\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 27.3264 | 1.04409 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.34864 | 0.280368 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 41.3547 | 1.57549 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.6257 | −0.480304 | −0.240152 | − | 0.970735i | \(-0.577197\pi\) | ||||
−0.240152 | + | 0.970735i | \(0.577197\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.94580 | 0.301836 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −30.5013 | −1.15698 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −47.1338 | −1.78532 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.51902 | 0.322219 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.500105 | −0.0188887 | −0.00944435 | − | 0.999955i | \(-0.503006\pi\) | ||||
−0.00944435 | + | 0.999955i | \(0.503006\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.14446 | −0.0808797 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.5604 | 0.473053 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.59919 | −0.135361 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.59561 | 0.135036 | 0.0675180 | − | 0.997718i | \(-0.478492\pi\) | ||||
0.0675180 | + | 0.997718i | \(0.478492\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −38.0394 | −1.42659 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 49.7674 | 1.86380 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 55.2400 | 2.06586 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.7919 | −0.515069 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.2473 | 0.605923 | 0.302961 | − | 0.953003i | \(-0.402025\pi\) | ||||
0.302961 | + | 0.953003i | \(0.402025\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.29050 | −0.345996 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.28625 | −0.159407 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.1653 | 0.488949 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.4012 | −0.497022 | −0.248511 | − | 0.968629i | \(-0.579941\pi\) | ||||
−0.248511 | + | 0.968629i | \(0.579941\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.91801 | 0.145111 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.31926 | 0.270713 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.33243 | −0.344701 | −0.172351 | − | 0.985036i | \(-0.555136\pi\) | ||||
−0.172351 | + | 0.985036i | \(0.555136\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.10538 | 0.0776582 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 26.1065 | 0.961644 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.7733 | −0.396303 | −0.198151 | − | 0.980171i | \(-0.563494\pi\) | ||||
−0.198151 | + | 0.980171i | \(0.563494\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.33546 | 0.196003 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −51.2919 | −1.88172 | −0.940859 | − | 0.338797i | \(-0.889980\pi\) | ||||
−0.940859 | + | 0.338797i | \(0.889980\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −34.1309 | −1.25046 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.8509 | 0.470189 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19.8956 | 0.726970 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.58651 | 0.0578926 | 0.0289463 | − | 0.999581i | \(-0.490785\pi\) | ||||
0.0289463 | + | 0.999581i | \(0.490785\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.72767 | −0.208728 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −41.1689 | −1.49829 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.36632 | −0.122351 | −0.0611755 | − | 0.998127i | \(-0.519485\pi\) | ||||
−0.0611755 | + | 0.998127i | \(0.519485\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −15.3796 | −0.558243 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.5896 | −0.383874 | −0.191937 | − | 0.981407i | \(-0.561477\pi\) | ||||
−0.191937 | + | 0.981407i | \(0.561477\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.787338 | 0.0285036 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −36.5462 | −1.32133 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 58.9172 | 2.12738 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.9476 | 0.935695 | 0.467847 | − | 0.883809i | \(-0.345030\pi\) | ||||
0.467847 | + | 0.883809i | \(0.345030\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.1103 | −0.400127 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.86293 | −0.210875 | −0.105438 | − | 0.994426i | \(-0.533624\pi\) | ||||
−0.105438 | + | 0.994426i | \(0.533624\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12.2067 | −0.438479 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.79883 | 0.0645326 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.43345 | −0.266331 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.82681 | 0.136934 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −45.0042 | −1.60832 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 43.3090 | 1.54576 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.0191 | 0.927480 | 0.463740 | − | 0.885971i | \(-0.346507\pi\) | ||||
0.463740 | + | 0.885971i | \(0.346507\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.00549 | 0.0357963 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.5592 | 0.375441 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 45.2940 | 1.60844 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13.6885 | 0.485482 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.96085 | −0.175722 | −0.0878611 | − | 0.996133i | \(-0.528003\pi\) | ||||
−0.0878611 | + | 0.996133i | \(0.528003\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 37.8282 | 1.33826 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 34.0536 | 1.20323 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.202098 | 0.00713187 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.2995 | 0.468744 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.4032 | 0.859032 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36.8839 | −1.29677 | −0.648385 | − | 0.761313i | \(-0.724555\pi\) | ||||
−0.648385 | + | 0.761313i | \(0.724555\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −46.2723 | −1.62484 | −0.812421 | − | 0.583072i | \(-0.801851\pi\) | ||||
−0.812421 | + | 0.583072i | \(0.801851\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.6545 | 0.373670 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −37.6459 | −1.31868 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.15432 | 0.0403844 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 14.6063 | 0.510386 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35.3927 | −1.23521 | −0.617607 | − | 0.786487i | \(-0.711898\pi\) | ||||
−0.617607 | + | 0.786487i | \(0.711898\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.4699 | −0.399815 | −0.199907 | − | 0.979815i | \(-0.564064\pi\) | ||||
−0.199907 | + | 0.979815i | \(0.564064\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.77223 | 0.131332 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.4282 | −0.779905 | −0.389953 | − | 0.920835i | \(-0.627509\pi\) | ||||
−0.389953 | + | 0.920835i | \(0.627509\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 53.8294 | 1.86957 | 0.934786 | − | 0.355211i | \(-0.115591\pi\) | ||||
0.934786 | + | 0.355211i | \(0.115591\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.69504 | −0.232248 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.34077 | 0.219695 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.7959 | 0.373608 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 41.7273 | 1.44231 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.60165 | 0.0552952 | 0.0276476 | − | 0.999618i | \(-0.491198\pi\) | ||||
0.0276476 | + | 0.999618i | \(0.491198\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 73.6137 | 2.53840 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.1195 | 0.589627 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 68.9158 | 2.37078 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.972699 | −0.0334223 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.9314 | 0.546765 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.3630 | 0.389518 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −37.7120 | −1.29123 | −0.645617 | − | 0.763662i | \(-0.723400\pi\) | ||||
−0.645617 | + | 0.763662i | \(0.723400\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.76368 | −0.197114 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.3095 | 0.967035 | 0.483517 | − | 0.875335i | \(-0.339359\pi\) | ||||
0.483517 | + | 0.875335i | \(0.339359\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.40350 | 0.116126 | 0.0580629 | − | 0.998313i | \(-0.481508\pi\) | ||||
0.0580629 | + | 0.998313i | \(0.481508\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.23539 | 0.212501 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.3494 | 0.488458 | 0.244229 | − | 0.969718i | \(-0.421465\pi\) | ||||
0.244229 | + | 0.969718i | \(0.421465\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 61.2987 | 2.08422 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 19.4653 | 0.661076 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 57.3177 | 1.94437 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 47.9901 | 1.62608 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.34122 | 0.146928 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.28753 | 0.313976 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41.1281 | −1.38880 | −0.694398 | − | 0.719591i | \(-0.744329\pi\) | ||||
−0.694398 | + | 0.719591i | \(0.744329\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.1667 | −0.545291 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.2298 | −0.479416 | −0.239708 | − | 0.970845i | \(-0.577052\pi\) | ||||
−0.239708 | + | 0.970845i | \(0.577052\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.2550 | 1.18643 | 0.593213 | − | 0.805046i | \(-0.297859\pi\) | ||||
0.593213 | + | 0.805046i | \(0.297859\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 19.5018 | 0.655545 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −30.0916 | −1.01038 | −0.505189 | − | 0.863009i | \(-0.668577\pi\) | ||||
−0.505189 | + | 0.863009i | \(0.668577\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.27500 | 0.0427620 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.9425 | 0.366586 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.96586 | 0.199640 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.3697 | −0.714312 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −28.2714 | −0.943954 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −95.1421 | −3.17317 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 41.2257 | 1.37343 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.968273 | −0.0322221 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 41.5342 | 1.38064 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 49.2512 | 1.63536 | 0.817680 | − | 0.575674i | \(-0.195260\pi\) | ||||
0.817680 | + | 0.575674i | \(0.195260\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.26506 | −0.274135 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.2177 | −1.33247 | −0.666236 | − | 0.745741i | \(-0.732096\pi\) | ||||
−0.666236 | + | 0.745741i | \(0.732096\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19.3637 | −0.640843 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 14.9924 | 0.495635 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.07361 | −0.266614 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35.3387 | −1.16572 | −0.582859 | − | 0.812573i | \(-0.698066\pi\) | ||||
−0.582859 | + | 0.812573i | \(0.698066\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.35754 | −0.242439 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.03462 | 0.231547 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.78706 | −0.0916380 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −21.3344 | −0.700714 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −37.5422 | −1.23172 | −0.615860 | − | 0.787856i | \(-0.711191\pi\) | ||||
−0.615860 | + | 0.787856i | \(0.711191\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.00000 | 0.0327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.60981 | 0.150918 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 55.0676 | 1.80090 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.3138 | −1.08831 | −0.544157 | − | 0.838983i | \(-0.683150\pi\) | ||||
−0.544157 | + | 0.838983i | \(0.683150\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21.2101 | −0.692165 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −51.7592 | −1.68730 | −0.843650 | − | 0.536893i | \(-0.819598\pi\) | ||||
−0.843650 | + | 0.536893i | \(0.819598\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 39.3882 | 1.28266 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.1509 | 0.362738 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33.8775 | −1.10087 | −0.550435 | − | 0.834878i | \(-0.685538\pi\) | ||||
−0.550435 | + | 0.834878i | \(0.685538\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.371505 | 0.0120596 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.44828 | 0.176673 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −55.7038 | −1.80442 | −0.902211 | − | 0.431295i | \(-0.858057\pi\) | ||||
−0.902211 | + | 0.431295i | \(0.858057\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −39.2289 | −1.26942 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 29.4016 | 0.950420 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.8874 | −0.351572 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 57.2144 | 1.84563 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 45.6876 | 1.47226 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −33.8607 | −1.09002 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.96518 | −0.0953536 | −0.0476768 | − | 0.998863i | \(-0.515182\pi\) | ||||
−0.0476768 | + | 0.998863i | \(0.515182\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.31881 | 0.170865 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.53029 | −0.0491093 | −0.0245547 | − | 0.999698i | \(-0.507817\pi\) | ||||
−0.0245547 | + | 0.999698i | \(0.507817\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.1523 | 0.389586 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.93428 | 0.222075 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23.1611 | −0.740988 | −0.370494 | − | 0.928835i | \(-0.620812\pi\) | ||||
−0.370494 | + | 0.928835i | \(0.620812\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −51.3119 | −1.63993 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.80802 | 0.0577256 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −53.1318 | −1.69464 | −0.847320 | − | 0.531082i | \(-0.821786\pi\) | ||||
−0.847320 | + | 0.531082i | \(0.821786\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −33.4250 | −1.06501 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.00433 | −0.159290 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.11646 | −0.194492 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35.2726 | 1.12047 | 0.560236 | − | 0.828333i | \(-0.310711\pi\) | ||||
0.560236 | + | 0.828333i | \(0.310711\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10.2236 | 0.324438 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21.5024 | 0.681672 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.2627 | −1.24346 | −0.621731 | − | 0.783230i | \(-0.713570\pi\) | ||||
−0.621731 | + | 0.783230i | \(0.713570\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.52726 | 0.301429 |
(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 | 8512.2.a.ch.1.6 | 7 | ||
4.3 | odd | 2 | 8512.2.a.ci.1.2 | 7 | |||
8.3 | odd | 2 | 4256.2.a.p.1.6 | ✓ | 7 | ||
8.5 | even | 2 | 4256.2.a.q.1.2 | yes | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4256.2.a.p.1.6 | ✓ | 7 | 8.3 | odd | 2 | ||
4256.2.a.q.1.2 | yes | 7 | 8.5 | even | 2 | ||
8512.2.a.ch.1.6 | 7 | 1.1 | even | 1 | trivial | ||
8512.2.a.ci.1.2 | 7 | 4.3 | odd | 2 |