Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8281,2,Mod(1,8281)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8281, 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("8281.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8281 = 7^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8281.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: | \(66.1241179138\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 16x^{10} + 88x^{8} - 197x^{6} + 172x^{4} - 36x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(1.37905\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8281.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.37905 | 0.975139 | 0.487570 | − | 0.873084i | \(-0.337884\pi\) | ||||
0.487570 | + | 0.873084i | \(0.337884\pi\) | |||||||
\(3\) | 2.88120 | 1.66346 | 0.831732 | − | 0.555178i | \(-0.187350\pi\) | ||||
0.831732 | + | 0.555178i | \(0.187350\pi\) | |||||||
\(4\) | −0.0982074 | −0.0491037 | ||||||||
\(5\) | 0.805948 | 0.360431 | 0.180216 | − | 0.983627i | \(-0.442320\pi\) | ||||
0.180216 | + | 0.983627i | \(0.442320\pi\) | |||||||
\(6\) | 3.97334 | 1.62211 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.89354 | −1.02302 | ||||||||
\(9\) | 5.30133 | 1.76711 | ||||||||
\(10\) | 1.11145 | 0.351470 | ||||||||
\(11\) | 5.27158 | 1.58944 | 0.794720 | − | 0.606976i | \(-0.207618\pi\) | ||||
0.794720 | + | 0.606976i | \(0.207618\pi\) | |||||||
\(12\) | −0.282955 | −0.0816822 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.32210 | 0.599564 | ||||||||
\(16\) | −3.79394 | −0.948485 | ||||||||
\(17\) | −0.560102 | −0.135845 | −0.0679223 | − | 0.997691i | \(-0.521637\pi\) | ||||
−0.0679223 | + | 0.997691i | \(0.521637\pi\) | |||||||
\(18\) | 7.31083 | 1.72318 | ||||||||
\(19\) | 5.84469 | 1.34086 | 0.670431 | − | 0.741972i | \(-0.266109\pi\) | ||||
0.670431 | + | 0.741972i | \(0.266109\pi\) | |||||||
\(20\) | −0.0791501 | −0.0176985 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.26980 | 1.54993 | ||||||||
\(23\) | −1.60488 | −0.334640 | −0.167320 | − | 0.985903i | \(-0.553511\pi\) | ||||
−0.167320 | + | 0.985903i | \(0.553511\pi\) | |||||||
\(24\) | −8.33689 | −1.70176 | ||||||||
\(25\) | −4.35045 | −0.870089 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 6.63060 | 1.27606 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.28015 | 0.423414 | 0.211707 | − | 0.977333i | \(-0.432098\pi\) | ||||
0.211707 | + | 0.977333i | \(0.432098\pi\) | |||||||
\(30\) | 3.20230 | 0.584658 | ||||||||
\(31\) | 3.47590 | 0.624290 | 0.312145 | − | 0.950034i | \(-0.398952\pi\) | ||||
0.312145 | + | 0.950034i | \(0.398952\pi\) | |||||||
\(32\) | 0.555034 | 0.0981171 | ||||||||
\(33\) | 15.1885 | 2.64398 | ||||||||
\(34\) | −0.772411 | −0.132467 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.520630 | −0.0867716 | ||||||||
\(37\) | 1.24196 | 0.204177 | 0.102088 | − | 0.994775i | \(-0.467448\pi\) | ||||
0.102088 | + | 0.994775i | \(0.467448\pi\) | |||||||
\(38\) | 8.06014 | 1.30753 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.33205 | −0.368729 | ||||||||
\(41\) | 0.927702 | 0.144883 | 0.0724413 | − | 0.997373i | \(-0.476921\pi\) | ||||
0.0724413 | + | 0.997373i | \(0.476921\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.44711 | 0.678179 | 0.339089 | − | 0.940754i | \(-0.389881\pi\) | ||||
0.339089 | + | 0.940754i | \(0.389881\pi\) | |||||||
\(44\) | −0.517708 | −0.0780474 | ||||||||
\(45\) | 4.27260 | 0.636921 | ||||||||
\(46\) | −2.21321 | −0.326320 | ||||||||
\(47\) | −3.84418 | −0.560731 | −0.280365 | − | 0.959893i | \(-0.590456\pi\) | ||||
−0.280365 | + | 0.959893i | \(0.590456\pi\) | |||||||
\(48\) | −10.9311 | −1.57777 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.99951 | −0.848458 | ||||||||
\(51\) | −1.61377 | −0.225973 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.45454 | 0.749239 | 0.374620 | − | 0.927179i | \(-0.377773\pi\) | ||||
0.374620 | + | 0.927179i | \(0.377773\pi\) | |||||||
\(54\) | 9.14396 | 1.24434 | ||||||||
\(55\) | 4.24862 | 0.572884 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 16.8397 | 2.23048 | ||||||||
\(58\) | 3.14446 | 0.412887 | ||||||||
\(59\) | −10.9940 | −1.43129 | −0.715646 | − | 0.698463i | \(-0.753868\pi\) | ||||
−0.715646 | + | 0.698463i | \(0.753868\pi\) | |||||||
\(60\) | −0.228047 | −0.0294408 | ||||||||
\(61\) | 7.30215 | 0.934944 | 0.467472 | − | 0.884008i | \(-0.345165\pi\) | ||||
0.467472 | + | 0.884008i | \(0.345165\pi\) | |||||||
\(62\) | 4.79346 | 0.608770 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.35330 | 1.04416 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 20.9458 | 2.57824 | ||||||||
\(67\) | −7.34556 | −0.897403 | −0.448701 | − | 0.893682i | \(-0.648113\pi\) | ||||
−0.448701 | + | 0.893682i | \(0.648113\pi\) | |||||||
\(68\) | 0.0550061 | 0.00667047 | ||||||||
\(69\) | −4.62397 | −0.556661 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.31460 | 1.10544 | 0.552720 | − | 0.833367i | \(-0.313590\pi\) | ||||
0.552720 | + | 0.833367i | \(0.313590\pi\) | |||||||
\(72\) | −15.3396 | −1.80779 | ||||||||
\(73\) | −5.00146 | −0.585376 | −0.292688 | − | 0.956208i | \(-0.594550\pi\) | ||||
−0.292688 | + | 0.956208i | \(0.594550\pi\) | |||||||
\(74\) | 1.71273 | 0.199101 | ||||||||
\(75\) | −12.5345 | −1.44736 | ||||||||
\(76\) | −0.573991 | −0.0658413 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.3687 | 1.27908 | 0.639542 | − | 0.768756i | \(-0.279124\pi\) | ||||
0.639542 | + | 0.768756i | \(0.279124\pi\) | |||||||
\(80\) | −3.05772 | −0.341863 | ||||||||
\(81\) | 3.20012 | 0.355568 | ||||||||
\(82\) | 1.27935 | 0.141281 | ||||||||
\(83\) | −5.81962 | −0.638786 | −0.319393 | − | 0.947622i | \(-0.603479\pi\) | ||||
−0.319393 | + | 0.947622i | \(0.603479\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.451413 | −0.0489626 | ||||||||
\(86\) | 6.13281 | 0.661318 | ||||||||
\(87\) | 6.56959 | 0.704334 | ||||||||
\(88\) | −15.2535 | −1.62603 | ||||||||
\(89\) | 5.00946 | 0.531001 | 0.265501 | − | 0.964111i | \(-0.414463\pi\) | ||||
0.265501 | + | 0.964111i | \(0.414463\pi\) | |||||||
\(90\) | 5.89215 | 0.621087 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.157611 | 0.0164320 | ||||||||
\(93\) | 10.0148 | 1.03848 | ||||||||
\(94\) | −5.30133 | −0.546791 | ||||||||
\(95\) | 4.71051 | 0.483289 | ||||||||
\(96\) | 1.59917 | 0.163214 | ||||||||
\(97\) | −10.6483 | −1.08117 | −0.540586 | − | 0.841289i | \(-0.681798\pi\) | ||||
−0.540586 | + | 0.841289i | \(0.681798\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 27.9464 | 2.80872 | ||||||||
\(100\) | 0.427246 | 0.0427246 | ||||||||
\(101\) | 3.91554 | 0.389611 | 0.194805 | − | 0.980842i | \(-0.437592\pi\) | ||||
0.194805 | + | 0.980842i | \(0.437592\pi\) | |||||||
\(102\) | −2.22547 | −0.220355 | ||||||||
\(103\) | 8.45379 | 0.832977 | 0.416488 | − | 0.909141i | \(-0.363261\pi\) | ||||
0.416488 | + | 0.909141i | \(0.363261\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.52212 | 0.730613 | ||||||||
\(107\) | −9.67522 | −0.935339 | −0.467670 | − | 0.883903i | \(-0.654906\pi\) | ||||
−0.467670 | + | 0.883903i | \(0.654906\pi\) | |||||||
\(108\) | −0.651174 | −0.0626592 | ||||||||
\(109\) | −14.5638 | −1.39496 | −0.697478 | − | 0.716606i | \(-0.745695\pi\) | ||||
−0.697478 | + | 0.716606i | \(0.745695\pi\) | |||||||
\(110\) | 5.85908 | 0.558641 | ||||||||
\(111\) | 3.57833 | 0.339640 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.5114 | 1.83548 | 0.917741 | − | 0.397180i | \(-0.130011\pi\) | ||||
0.917741 | + | 0.397180i | \(0.130011\pi\) | |||||||
\(114\) | 23.2229 | 2.17502 | ||||||||
\(115\) | −1.29345 | −0.120615 | ||||||||
\(116\) | −0.223928 | −0.0207912 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −15.1613 | −1.39571 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −6.71910 | −0.613367 | ||||||||
\(121\) | 16.7895 | 1.52632 | ||||||||
\(122\) | 10.0701 | 0.911701 | ||||||||
\(123\) | 2.67290 | 0.241007 | ||||||||
\(124\) | −0.341359 | −0.0306550 | ||||||||
\(125\) | −7.53598 | −0.674038 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.91731 | −0.170134 | −0.0850670 | − | 0.996375i | \(-0.527110\pi\) | ||||
−0.0850670 | + | 0.996375i | \(0.527110\pi\) | |||||||
\(128\) | 10.4096 | 0.920087 | ||||||||
\(129\) | 12.8130 | 1.12813 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.5816 | 1.36137 | 0.680684 | − | 0.732577i | \(-0.261683\pi\) | ||||
0.680684 | + | 0.732577i | \(0.261683\pi\) | |||||||
\(132\) | −1.49162 | −0.129829 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −10.1299 | −0.875093 | ||||||||
\(135\) | 5.34392 | 0.459932 | ||||||||
\(136\) | 1.62068 | 0.138972 | ||||||||
\(137\) | −7.85105 | −0.670761 | −0.335380 | − | 0.942083i | \(-0.608865\pi\) | ||||
−0.335380 | + | 0.942083i | \(0.608865\pi\) | |||||||
\(138\) | −6.37671 | −0.542822 | ||||||||
\(139\) | 9.92481 | 0.841812 | 0.420906 | − | 0.907104i | \(-0.361712\pi\) | ||||
0.420906 | + | 0.907104i | \(0.361712\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.0759 | −0.932755 | ||||||||
\(142\) | 12.8453 | 1.07796 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −20.1129 | −1.67608 | ||||||||
\(145\) | 1.83769 | 0.152612 | ||||||||
\(146\) | −6.89728 | −0.570823 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.121969 | −0.0100258 | ||||||||
\(149\) | 7.91925 | 0.648770 | 0.324385 | − | 0.945925i | \(-0.394843\pi\) | ||||
0.324385 | + | 0.945925i | \(0.394843\pi\) | |||||||
\(150\) | −17.2858 | −1.41138 | ||||||||
\(151\) | −1.50116 | −0.122163 | −0.0610815 | − | 0.998133i | \(-0.519455\pi\) | ||||
−0.0610815 | + | 0.998133i | \(0.519455\pi\) | |||||||
\(152\) | −16.9118 | −1.37173 | ||||||||
\(153\) | −2.96928 | −0.240052 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.80140 | 0.225014 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.85692 | 0.307816 | 0.153908 | − | 0.988085i | \(-0.450814\pi\) | ||||
0.153908 | + | 0.988085i | \(0.450814\pi\) | |||||||
\(158\) | 15.6781 | 1.24728 | ||||||||
\(159\) | 15.7156 | 1.24633 | ||||||||
\(160\) | 0.447329 | 0.0353644 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 4.41314 | 0.346729 | ||||||||
\(163\) | −14.3608 | −1.12483 | −0.562414 | − | 0.826856i | \(-0.690127\pi\) | ||||
−0.562414 | + | 0.826856i | \(0.690127\pi\) | |||||||
\(164\) | −0.0911072 | −0.00711427 | ||||||||
\(165\) | 12.2411 | 0.952971 | ||||||||
\(166\) | −8.02557 | −0.622905 | ||||||||
\(167\) | 4.52138 | 0.349875 | 0.174937 | − | 0.984580i | \(-0.444028\pi\) | ||||
0.174937 | + | 0.984580i | \(0.444028\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −0.622523 | −0.0477454 | ||||||||
\(171\) | 30.9846 | 2.36945 | ||||||||
\(172\) | −0.436739 | −0.0333011 | ||||||||
\(173\) | −19.5179 | −1.48392 | −0.741960 | − | 0.670444i | \(-0.766104\pi\) | ||||
−0.741960 | + | 0.670444i | \(0.766104\pi\) | |||||||
\(174\) | 9.05982 | 0.686823 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −20.0001 | −1.50756 | ||||||||
\(177\) | −31.6759 | −2.38090 | ||||||||
\(178\) | 6.90832 | 0.517800 | ||||||||
\(179\) | 20.8196 | 1.55613 | 0.778065 | − | 0.628183i | \(-0.216201\pi\) | ||||
0.778065 | + | 0.628183i | \(0.216201\pi\) | |||||||
\(180\) | −0.419601 | −0.0312752 | ||||||||
\(181\) | −16.5522 | −1.23031 | −0.615157 | − | 0.788405i | \(-0.710907\pi\) | ||||
−0.615157 | + | 0.788405i | \(0.710907\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 21.0390 | 1.55525 | ||||||||
\(184\) | 4.64378 | 0.342344 | ||||||||
\(185\) | 1.00095 | 0.0735916 | ||||||||
\(186\) | 13.8109 | 1.01267 | ||||||||
\(187\) | −2.95262 | −0.215917 | ||||||||
\(188\) | 0.377527 | 0.0275340 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.49606 | 0.471274 | ||||||||
\(191\) | −4.25008 | −0.307525 | −0.153762 | − | 0.988108i | \(-0.549139\pi\) | ||||
−0.153762 | + | 0.988108i | \(0.549139\pi\) | |||||||
\(192\) | 24.0676 | 1.73693 | ||||||||
\(193\) | −11.5972 | −0.834787 | −0.417393 | − | 0.908726i | \(-0.637056\pi\) | ||||
−0.417393 | + | 0.908726i | \(0.637056\pi\) | |||||||
\(194\) | −14.6846 | −1.05429 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.4213 | −1.02748 | −0.513738 | − | 0.857947i | \(-0.671740\pi\) | ||||
−0.513738 | + | 0.857947i | \(0.671740\pi\) | |||||||
\(198\) | 38.5396 | 2.73889 | ||||||||
\(199\) | 7.05924 | 0.500416 | 0.250208 | − | 0.968192i | \(-0.419501\pi\) | ||||
0.250208 | + | 0.968192i | \(0.419501\pi\) | |||||||
\(200\) | 12.5882 | 0.890121 | ||||||||
\(201\) | −21.1640 | −1.49280 | ||||||||
\(202\) | 5.39974 | 0.379925 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.158484 | 0.0110961 | ||||||||
\(205\) | 0.747680 | 0.0522202 | ||||||||
\(206\) | 11.6582 | 0.812268 | ||||||||
\(207\) | −8.50798 | −0.591345 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 30.8107 | 2.13122 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.4226 | −1.81901 | −0.909505 | − | 0.415693i | \(-0.863539\pi\) | ||||
−0.909505 | + | 0.415693i | \(0.863539\pi\) | |||||||
\(212\) | −0.535677 | −0.0367904 | ||||||||
\(213\) | 26.8372 | 1.83886 | ||||||||
\(214\) | −13.3427 | −0.912086 | ||||||||
\(215\) | 3.58414 | 0.244437 | ||||||||
\(216\) | −19.1859 | −1.30544 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −20.0842 | −1.36028 | ||||||||
\(219\) | −14.4102 | −0.973752 | ||||||||
\(220\) | −0.417246 | −0.0281307 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 4.93472 | 0.331197 | ||||||||
\(223\) | 23.0005 | 1.54023 | 0.770115 | − | 0.637905i | \(-0.220199\pi\) | ||||
0.770115 | + | 0.637905i | \(0.220199\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −23.0632 | −1.53754 | ||||||||
\(226\) | 26.9073 | 1.78985 | ||||||||
\(227\) | −0.453367 | −0.0300911 | −0.0150455 | − | 0.999887i | \(-0.504789\pi\) | ||||
−0.0150455 | + | 0.999887i | \(0.504789\pi\) | |||||||
\(228\) | −1.65379 | −0.109525 | ||||||||
\(229\) | 17.3335 | 1.14543 | 0.572714 | − | 0.819755i | \(-0.305890\pi\) | ||||
0.572714 | + | 0.819755i | \(0.305890\pi\) | |||||||
\(230\) | −1.78373 | −0.117616 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.59772 | −0.433162 | ||||||||
\(233\) | 7.81511 | 0.511985 | 0.255992 | − | 0.966679i | \(-0.417598\pi\) | ||||
0.255992 | + | 0.966679i | \(0.417598\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.09821 | −0.202105 | ||||||||
\(236\) | 1.07969 | 0.0702818 | ||||||||
\(237\) | 32.7557 | 2.12771 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.5314 | −0.875276 | −0.437638 | − | 0.899151i | \(-0.644185\pi\) | ||||
−0.437638 | + | 0.899151i | \(0.644185\pi\) | |||||||
\(240\) | −8.80991 | −0.568677 | ||||||||
\(241\) | 22.5592 | 1.45317 | 0.726583 | − | 0.687078i | \(-0.241107\pi\) | ||||
0.726583 | + | 0.687078i | \(0.241107\pi\) | |||||||
\(242\) | 23.1537 | 1.48838 | ||||||||
\(243\) | −10.6716 | −0.684585 | ||||||||
\(244\) | −0.717125 | −0.0459092 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.68607 | 0.235015 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −10.0577 | −0.638663 | ||||||||
\(249\) | −16.7675 | −1.06260 | ||||||||
\(250\) | −10.3925 | −0.657281 | ||||||||
\(251\) | −6.73236 | −0.424943 | −0.212471 | − | 0.977167i | \(-0.568151\pi\) | ||||
−0.212471 | + | 0.977167i | \(0.568151\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.46023 | −0.531890 | ||||||||
\(254\) | −2.64408 | −0.165904 | ||||||||
\(255\) | −1.30061 | −0.0814475 | ||||||||
\(256\) | −2.35120 | −0.146950 | ||||||||
\(257\) | 16.5381 | 1.03162 | 0.515811 | − | 0.856703i | \(-0.327491\pi\) | ||||
0.515811 | + | 0.856703i | \(0.327491\pi\) | |||||||
\(258\) | 17.6699 | 1.10008 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.0878 | 0.748219 | ||||||||
\(262\) | 21.4878 | 1.32752 | ||||||||
\(263\) | −10.0227 | −0.618028 | −0.309014 | − | 0.951057i | \(-0.599999\pi\) | ||||
−0.309014 | + | 0.951057i | \(0.599999\pi\) | |||||||
\(264\) | −43.9485 | −2.70485 | ||||||||
\(265\) | 4.39608 | 0.270049 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.4333 | 0.883302 | ||||||||
\(268\) | 0.721388 | 0.0440658 | ||||||||
\(269\) | −15.7230 | −0.958647 | −0.479323 | − | 0.877638i | \(-0.659118\pi\) | ||||
−0.479323 | + | 0.877638i | \(0.659118\pi\) | |||||||
\(270\) | 7.36956 | 0.448497 | ||||||||
\(271\) | −5.21618 | −0.316860 | −0.158430 | − | 0.987370i | \(-0.550643\pi\) | ||||
−0.158430 | + | 0.987370i | \(0.550643\pi\) | |||||||
\(272\) | 2.12499 | 0.128847 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.8270 | −0.654085 | ||||||||
\(275\) | −22.9337 | −1.38296 | ||||||||
\(276\) | 0.454108 | 0.0273341 | ||||||||
\(277\) | −19.2724 | −1.15797 | −0.578983 | − | 0.815340i | \(-0.696550\pi\) | ||||
−0.578983 | + | 0.815340i | \(0.696550\pi\) | |||||||
\(278\) | 13.6869 | 0.820884 | ||||||||
\(279\) | 18.4269 | 1.10319 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.14283 | 0.127831 | 0.0639153 | − | 0.997955i | \(-0.479641\pi\) | ||||
0.0639153 | + | 0.997955i | \(0.479641\pi\) | |||||||
\(282\) | −15.2742 | −0.909566 | ||||||||
\(283\) | −15.7502 | −0.936255 | −0.468127 | − | 0.883661i | \(-0.655071\pi\) | ||||
−0.468127 | + | 0.883661i | \(0.655071\pi\) | |||||||
\(284\) | −0.914762 | −0.0542812 | ||||||||
\(285\) | 13.5719 | 0.803933 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.94242 | 0.173384 | ||||||||
\(289\) | −16.6863 | −0.981546 | ||||||||
\(290\) | 2.53427 | 0.148817 | ||||||||
\(291\) | −30.6800 | −1.79849 | ||||||||
\(292\) | 0.491180 | 0.0287441 | ||||||||
\(293\) | −23.1487 | −1.35236 | −0.676182 | − | 0.736735i | \(-0.736367\pi\) | ||||
−0.676182 | + | 0.736735i | \(0.736367\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.86057 | −0.515882 | ||||||||
\(296\) | −3.59366 | −0.208877 | ||||||||
\(297\) | 34.9537 | 2.02822 | ||||||||
\(298\) | 10.9211 | 0.632641 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.23098 | 0.0710708 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.07019 | −0.119126 | ||||||||
\(303\) | 11.2815 | 0.648103 | ||||||||
\(304\) | −22.1744 | −1.27179 | ||||||||
\(305\) | 5.88515 | 0.336983 | ||||||||
\(306\) | −4.09481 | −0.234085 | ||||||||
\(307\) | −4.23590 | −0.241756 | −0.120878 | − | 0.992667i | \(-0.538571\pi\) | ||||
−0.120878 | + | 0.992667i | \(0.538571\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 24.3571 | 1.38563 | ||||||||
\(310\) | 3.86328 | 0.219420 | ||||||||
\(311\) | 27.2501 | 1.54521 | 0.772606 | − | 0.634885i | \(-0.218953\pi\) | ||||
0.772606 | + | 0.634885i | \(0.218953\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.69697 | 0.152442 | 0.0762209 | − | 0.997091i | \(-0.475715\pi\) | ||||
0.0762209 | + | 0.997091i | \(0.475715\pi\) | |||||||
\(314\) | 5.31891 | 0.300163 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.11649 | −0.0628077 | ||||||||
\(317\) | −24.0705 | −1.35193 | −0.675966 | − | 0.736933i | \(-0.736273\pi\) | ||||
−0.675966 | + | 0.736933i | \(0.736273\pi\) | |||||||
\(318\) | 21.6727 | 1.21535 | ||||||||
\(319\) | 12.0200 | 0.672991 | ||||||||
\(320\) | 6.73233 | 0.376349 | ||||||||
\(321\) | −27.8763 | −1.55590 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.27362 | −0.182149 | ||||||||
\(324\) | −0.314275 | −0.0174597 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −19.8044 | −1.09686 | ||||||||
\(327\) | −41.9612 | −2.32046 | ||||||||
\(328\) | −2.68434 | −0.148218 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 16.8812 | 0.929279 | ||||||||
\(331\) | 0.619723 | 0.0340631 | 0.0170315 | − | 0.999855i | \(-0.494578\pi\) | ||||
0.0170315 | + | 0.999855i | \(0.494578\pi\) | |||||||
\(332\) | 0.571530 | 0.0313668 | ||||||||
\(333\) | 6.58403 | 0.360803 | ||||||||
\(334\) | 6.23523 | 0.341177 | ||||||||
\(335\) | −5.92014 | −0.323452 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.72118 | 0.311652 | 0.155826 | − | 0.987784i | \(-0.450196\pi\) | ||||
0.155826 | + | 0.987784i | \(0.450196\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 56.2164 | 3.05326 | ||||||||
\(340\) | 0.0443321 | 0.00240425 | ||||||||
\(341\) | 18.3235 | 0.992272 | ||||||||
\(342\) | 42.7295 | 2.31055 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −12.8679 | −0.693792 | ||||||||
\(345\) | −3.72668 | −0.200638 | ||||||||
\(346\) | −26.9163 | −1.44703 | ||||||||
\(347\) | −1.86486 | −0.100111 | −0.0500554 | − | 0.998746i | \(-0.515940\pi\) | ||||
−0.0500554 | + | 0.998746i | \(0.515940\pi\) | |||||||
\(348\) | −0.645182 | −0.0345854 | ||||||||
\(349\) | 22.3172 | 1.19461 | 0.597307 | − | 0.802012i | \(-0.296237\pi\) | ||||
0.597307 | + | 0.802012i | \(0.296237\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.92591 | 0.155951 | ||||||||
\(353\) | −2.33199 | −0.124119 | −0.0620597 | − | 0.998072i | \(-0.519767\pi\) | ||||
−0.0620597 | + | 0.998072i | \(0.519767\pi\) | |||||||
\(354\) | −43.6827 | −2.32171 | ||||||||
\(355\) | 7.50708 | 0.398435 | ||||||||
\(356\) | −0.491966 | −0.0260741 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 28.7114 | 1.51744 | ||||||||
\(359\) | −3.27105 | −0.172639 | −0.0863197 | − | 0.996267i | \(-0.527511\pi\) | ||||
−0.0863197 | + | 0.996267i | \(0.527511\pi\) | |||||||
\(360\) | −12.3629 | −0.651585 | ||||||||
\(361\) | 15.1603 | 0.797913 | ||||||||
\(362\) | −22.8264 | −1.19973 | ||||||||
\(363\) | 48.3741 | 2.53898 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.03092 | −0.210988 | ||||||||
\(366\) | 29.0139 | 1.51658 | ||||||||
\(367\) | 4.15290 | 0.216780 | 0.108390 | − | 0.994108i | \(-0.465431\pi\) | ||||
0.108390 | + | 0.994108i | \(0.465431\pi\) | |||||||
\(368\) | 6.08880 | 0.317401 | ||||||||
\(369\) | 4.91805 | 0.256024 | ||||||||
\(370\) | 1.38037 | 0.0717620 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.983525 | −0.0509934 | ||||||||
\(373\) | −11.1089 | −0.575198 | −0.287599 | − | 0.957751i | \(-0.592857\pi\) | ||||
−0.287599 | + | 0.957751i | \(0.592857\pi\) | |||||||
\(374\) | −4.07183 | −0.210549 | ||||||||
\(375\) | −21.7127 | −1.12124 | ||||||||
\(376\) | 11.1233 | 0.573640 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.64030 | −0.238356 | −0.119178 | − | 0.992873i | \(-0.538026\pi\) | ||||
−0.119178 | + | 0.992873i | \(0.538026\pi\) | |||||||
\(380\) | −0.462607 | −0.0237312 | ||||||||
\(381\) | −5.52416 | −0.283012 | ||||||||
\(382\) | −5.86109 | −0.299880 | ||||||||
\(383\) | −3.66933 | −0.187494 | −0.0937469 | − | 0.995596i | \(-0.529884\pi\) | ||||
−0.0937469 | + | 0.995596i | \(0.529884\pi\) | |||||||
\(384\) | 29.9922 | 1.53053 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −15.9932 | −0.814033 | ||||||||
\(387\) | 23.5756 | 1.19842 | ||||||||
\(388\) | 1.04574 | 0.0530896 | ||||||||
\(389\) | 16.8831 | 0.856008 | 0.428004 | − | 0.903777i | \(-0.359217\pi\) | ||||
0.428004 | + | 0.903777i | \(0.359217\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.898894 | 0.0454590 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 44.8937 | 2.26459 | ||||||||
\(394\) | −19.8878 | −1.00193 | ||||||||
\(395\) | 9.16262 | 0.461021 | ||||||||
\(396\) | −2.74454 | −0.137918 | ||||||||
\(397\) | 16.7086 | 0.838578 | 0.419289 | − | 0.907853i | \(-0.362279\pi\) | ||||
0.419289 | + | 0.907853i | \(0.362279\pi\) | |||||||
\(398\) | 9.73508 | 0.487976 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.5053 | 0.825267 | ||||||||
\(401\) | 25.3134 | 1.26409 | 0.632046 | − | 0.774931i | \(-0.282215\pi\) | ||||
0.632046 | + | 0.774931i | \(0.282215\pi\) | |||||||
\(402\) | −29.1864 | −1.45568 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −0.384535 | −0.0191313 | ||||||||
\(405\) | 2.57913 | 0.128158 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.54708 | 0.324527 | ||||||||
\(408\) | 4.66950 | 0.231175 | ||||||||
\(409\) | 5.73343 | 0.283500 | 0.141750 | − | 0.989903i | \(-0.454727\pi\) | ||||
0.141750 | + | 0.989903i | \(0.454727\pi\) | |||||||
\(410\) | 1.03109 | 0.0509220 | ||||||||
\(411\) | −22.6205 | −1.11579 | ||||||||
\(412\) | −0.830225 | −0.0409022 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −11.7330 | −0.576644 | ||||||||
\(415\) | −4.69031 | −0.230238 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 28.5954 | 1.40032 | ||||||||
\(418\) | 42.4897 | 2.07824 | ||||||||
\(419\) | −34.3458 | −1.67790 | −0.838950 | − | 0.544208i | \(-0.816830\pi\) | ||||
−0.838950 | + | 0.544208i | \(0.816830\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.94167 | −0.143368 | −0.0716842 | − | 0.997427i | \(-0.522837\pi\) | ||||
−0.0716842 | + | 0.997427i | \(0.522837\pi\) | |||||||
\(422\) | −36.4383 | −1.77379 | ||||||||
\(423\) | −20.3793 | −0.990873 | ||||||||
\(424\) | −15.7830 | −0.766488 | ||||||||
\(425\) | 2.43669 | 0.118197 | ||||||||
\(426\) | 37.0100 | 1.79314 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.950178 | 0.0459286 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.94273 | 0.238360 | ||||||||
\(431\) | −39.6955 | −1.91207 | −0.956033 | − | 0.293258i | \(-0.905261\pi\) | ||||
−0.956033 | + | 0.293258i | \(0.905261\pi\) | |||||||
\(432\) | −25.1561 | −1.21032 | ||||||||
\(433\) | −9.83653 | −0.472714 | −0.236357 | − | 0.971666i | \(-0.575953\pi\) | ||||
−0.236357 | + | 0.971666i | \(0.575953\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.29475 | 0.253864 | ||||||||
\(436\) | 1.43027 | 0.0684975 | ||||||||
\(437\) | −9.37999 | −0.448706 | ||||||||
\(438\) | −19.8725 | −0.949544 | ||||||||
\(439\) | 28.5465 | 1.36245 | 0.681226 | − | 0.732073i | \(-0.261447\pi\) | ||||
0.681226 | + | 0.732073i | \(0.261447\pi\) | |||||||
\(440\) | −12.2936 | −0.586073 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.33901 | 0.158641 | 0.0793207 | − | 0.996849i | \(-0.474725\pi\) | ||||
0.0793207 | + | 0.996849i | \(0.474725\pi\) | |||||||
\(444\) | −0.351419 | −0.0166776 | ||||||||
\(445\) | 4.03736 | 0.191389 | ||||||||
\(446\) | 31.7190 | 1.50194 | ||||||||
\(447\) | 22.8170 | 1.07921 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.1851 | 0.858206 | 0.429103 | − | 0.903256i | \(-0.358830\pi\) | ||||
0.429103 | + | 0.903256i | \(0.358830\pi\) | |||||||
\(450\) | −31.8054 | −1.49932 | ||||||||
\(451\) | 4.89045 | 0.230282 | ||||||||
\(452\) | −1.91617 | −0.0901289 | ||||||||
\(453\) | −4.32516 | −0.203214 | ||||||||
\(454\) | −0.625219 | −0.0293430 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −48.7265 | −2.28183 | ||||||||
\(457\) | −8.72932 | −0.408341 | −0.204170 | − | 0.978935i | \(-0.565450\pi\) | ||||
−0.204170 | + | 0.978935i | \(0.565450\pi\) | |||||||
\(458\) | 23.9038 | 1.11695 | ||||||||
\(459\) | −3.71381 | −0.173346 | ||||||||
\(460\) | 0.127026 | 0.00592262 | ||||||||
\(461\) | 2.27124 | 0.105782 | 0.0528910 | − | 0.998600i | \(-0.483156\pi\) | ||||
0.0528910 | + | 0.998600i | \(0.483156\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.48326 | 0.254829 | 0.127414 | − | 0.991850i | \(-0.459332\pi\) | ||||
0.127414 | + | 0.991850i | \(0.459332\pi\) | |||||||
\(464\) | −8.65077 | −0.401602 | ||||||||
\(465\) | 8.07139 | 0.374302 | ||||||||
\(466\) | 10.7775 | 0.499257 | ||||||||
\(467\) | 18.8819 | 0.873750 | 0.436875 | − | 0.899522i | \(-0.356085\pi\) | ||||
0.436875 | + | 0.899522i | \(0.356085\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4.27260 | −0.197080 | ||||||||
\(471\) | 11.1126 | 0.512040 | ||||||||
\(472\) | 31.8115 | 1.46424 | ||||||||
\(473\) | 23.4433 | 1.07792 | ||||||||
\(474\) | 45.1718 | 2.07481 | ||||||||
\(475\) | −25.4270 | −1.16667 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 28.9163 | 1.32399 | ||||||||
\(478\) | −18.6606 | −0.853516 | ||||||||
\(479\) | −33.1354 | −1.51399 | −0.756997 | − | 0.653418i | \(-0.773334\pi\) | ||||
−0.756997 | + | 0.653418i | \(0.773334\pi\) | |||||||
\(480\) | 1.28884 | 0.0588275 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 31.1104 | 1.41704 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.64886 | −0.0749480 | ||||||||
\(485\) | −8.58199 | −0.389688 | ||||||||
\(486\) | −14.7168 | −0.667565 | ||||||||
\(487\) | −15.9563 | −0.723048 | −0.361524 | − | 0.932363i | \(-0.617743\pi\) | ||||
−0.361524 | + | 0.932363i | \(0.617743\pi\) | |||||||
\(488\) | −21.1291 | −0.956469 | ||||||||
\(489\) | −41.3765 | −1.87111 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −31.6928 | −1.43028 | −0.715138 | − | 0.698983i | \(-0.753636\pi\) | ||||
−0.715138 | + | 0.698983i | \(0.753636\pi\) | |||||||
\(492\) | −0.262498 | −0.0118343 | ||||||||
\(493\) | −1.27712 | −0.0575185 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 22.5233 | 1.01235 | ||||||||
\(496\) | −13.1874 | −0.592130 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −23.1233 | −1.03618 | ||||||||
\(499\) | −24.2184 | −1.08417 | −0.542083 | − | 0.840325i | \(-0.682364\pi\) | ||||
−0.542083 | + | 0.840325i | \(0.682364\pi\) | |||||||
\(500\) | 0.740089 | 0.0330978 | ||||||||
\(501\) | 13.0270 | 0.582004 | ||||||||
\(502\) | −9.28429 | −0.414378 | ||||||||
\(503\) | 0.854498 | 0.0381002 | 0.0190501 | − | 0.999819i | \(-0.493936\pi\) | ||||
0.0190501 | + | 0.999819i | \(0.493936\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.15572 | 0.140428 | ||||||||
\(506\) | −11.6671 | −0.518667 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.188294 | 0.00835420 | ||||||||
\(509\) | 1.30000 | 0.0576215 | 0.0288108 | − | 0.999585i | \(-0.490828\pi\) | ||||
0.0288108 | + | 0.999585i | \(0.490828\pi\) | |||||||
\(510\) | −1.79362 | −0.0794227 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −24.0616 | −1.06338 | ||||||||
\(513\) | 38.7538 | 1.71102 | ||||||||
\(514\) | 22.8070 | 1.00597 | ||||||||
\(515\) | 6.81332 | 0.300231 | ||||||||
\(516\) | −1.25833 | −0.0553951 | ||||||||
\(517\) | −20.2649 | −0.891248 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −56.2351 | −2.46845 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.0455 | −1.09726 | −0.548632 | − | 0.836064i | \(-0.684851\pi\) | ||||
−0.548632 | + | 0.836064i | \(0.684851\pi\) | |||||||
\(522\) | 16.6698 | 0.729618 | ||||||||
\(523\) | 12.8239 | 0.560752 | 0.280376 | − | 0.959890i | \(-0.409541\pi\) | ||||
0.280376 | + | 0.959890i | \(0.409541\pi\) | |||||||
\(524\) | −1.53022 | −0.0668482 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.8219 | −0.602664 | ||||||||
\(527\) | −1.94686 | −0.0848065 | ||||||||
\(528\) | −57.6242 | −2.50777 | ||||||||
\(529\) | −20.4244 | −0.888016 | ||||||||
\(530\) | 6.06244 | 0.263335 | ||||||||
\(531\) | −58.2827 | −2.52925 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 19.9043 | 0.861342 | ||||||||
\(535\) | −7.79773 | −0.337125 | ||||||||
\(536\) | 21.2547 | 0.918063 | ||||||||
\(537\) | 59.9855 | 2.58857 | ||||||||
\(538\) | −21.6828 | −0.934814 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.524813 | −0.0225843 | ||||||||
\(541\) | −28.7449 | −1.23584 | −0.617920 | − | 0.786241i | \(-0.712025\pi\) | ||||
−0.617920 | + | 0.786241i | \(0.712025\pi\) | |||||||
\(542\) | −7.19340 | −0.308983 | ||||||||
\(543\) | −47.6902 | −2.04658 | ||||||||
\(544\) | −0.310876 | −0.0133287 | ||||||||
\(545\) | −11.7376 | −0.502785 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.88085 | −0.379718 | −0.189859 | − | 0.981811i | \(-0.560803\pi\) | ||||
−0.189859 | + | 0.981811i | \(0.560803\pi\) | |||||||
\(548\) | 0.771031 | 0.0329368 | ||||||||
\(549\) | 38.7111 | 1.65215 | ||||||||
\(550\) | −31.6269 | −1.34857 | ||||||||
\(551\) | 13.3268 | 0.567740 | ||||||||
\(552\) | 13.3797 | 0.569476 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −26.5777 | −1.12918 | ||||||||
\(555\) | 2.88395 | 0.122417 | ||||||||
\(556\) | −0.974690 | −0.0413361 | ||||||||
\(557\) | 38.7273 | 1.64093 | 0.820465 | − | 0.571696i | \(-0.193714\pi\) | ||||
0.820465 | + | 0.571696i | \(0.193714\pi\) | |||||||
\(558\) | 25.4117 | 1.07576 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.50710 | −0.359170 | ||||||||
\(562\) | 2.95508 | 0.124653 | ||||||||
\(563\) | 6.90882 | 0.291172 | 0.145586 | − | 0.989346i | \(-0.453493\pi\) | ||||
0.145586 | + | 0.989346i | \(0.453493\pi\) | |||||||
\(564\) | 1.08773 | 0.0458017 | ||||||||
\(565\) | 15.7252 | 0.661565 | ||||||||
\(566\) | −21.7205 | −0.912979 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −26.9522 | −1.13089 | ||||||||
\(569\) | −2.83745 | −0.118952 | −0.0594759 | − | 0.998230i | \(-0.518943\pi\) | ||||
−0.0594759 | + | 0.998230i | \(0.518943\pi\) | |||||||
\(570\) | 18.7165 | 0.783946 | ||||||||
\(571\) | −46.6724 | −1.95318 | −0.976589 | − | 0.215113i | \(-0.930988\pi\) | ||||
−0.976589 | + | 0.215113i | \(0.930988\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.2453 | −0.511557 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.98193 | 0.291167 | ||||||||
\(576\) | 44.2836 | 1.84515 | ||||||||
\(577\) | −11.4088 | −0.474955 | −0.237478 | − | 0.971393i | \(-0.576321\pi\) | ||||
−0.237478 | + | 0.971393i | \(0.576321\pi\) | |||||||
\(578\) | −23.0113 | −0.957144 | ||||||||
\(579\) | −33.4140 | −1.38864 | ||||||||
\(580\) | −0.180474 | −0.00749379 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −42.3094 | −1.75378 | ||||||||
\(583\) | 28.7541 | 1.19087 | ||||||||
\(584\) | 14.4719 | 0.598853 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −31.9234 | −1.31874 | ||||||||
\(587\) | −46.4410 | −1.91683 | −0.958413 | − | 0.285384i | \(-0.907879\pi\) | ||||
−0.958413 | + | 0.285384i | \(0.907879\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.3156 | 0.837088 | ||||||||
\(590\) | −12.2192 | −0.503057 | ||||||||
\(591\) | −41.5508 | −1.70917 | ||||||||
\(592\) | −4.71191 | −0.193658 | ||||||||
\(593\) | 20.2606 | 0.832002 | 0.416001 | − | 0.909364i | \(-0.363431\pi\) | ||||
0.416001 | + | 0.909364i | \(0.363431\pi\) | |||||||
\(594\) | 48.2031 | 1.97780 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.777728 | −0.0318570 | ||||||||
\(597\) | 20.3391 | 0.832424 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −38.9876 | −1.59299 | −0.796494 | − | 0.604646i | \(-0.793315\pi\) | ||||
−0.796494 | + | 0.604646i | \(0.793315\pi\) | |||||||
\(600\) | 36.2692 | 1.48068 | ||||||||
\(601\) | 19.1390 | 0.780697 | 0.390348 | − | 0.920667i | \(-0.372355\pi\) | ||||
0.390348 | + | 0.920667i | \(0.372355\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −38.9412 | −1.58581 | ||||||||
\(604\) | 0.147425 | 0.00599865 | ||||||||
\(605\) | 13.5315 | 0.550134 | ||||||||
\(606\) | 15.5578 | 0.631991 | ||||||||
\(607\) | 43.3336 | 1.75886 | 0.879428 | − | 0.476033i | \(-0.157926\pi\) | ||||
0.879428 | + | 0.476033i | \(0.157926\pi\) | |||||||
\(608\) | 3.24400 | 0.131562 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.11595 | 0.328605 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.291606 | 0.0117875 | ||||||||
\(613\) | −10.3096 | −0.416399 | −0.208200 | − | 0.978086i | \(-0.566760\pi\) | ||||
−0.208200 | + | 0.978086i | \(0.566760\pi\) | |||||||
\(614\) | −5.84154 | −0.235745 | ||||||||
\(615\) | 2.15422 | 0.0868664 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.0699 | 0.445659 | 0.222829 | − | 0.974857i | \(-0.428471\pi\) | ||||
0.222829 | + | 0.974857i | \(0.428471\pi\) | |||||||
\(618\) | 33.5898 | 1.35118 | ||||||||
\(619\) | −33.7616 | −1.35700 | −0.678498 | − | 0.734603i | \(-0.737369\pi\) | ||||
−0.678498 | + | 0.734603i | \(0.737369\pi\) | |||||||
\(620\) | −0.275118 | −0.0110490 | ||||||||
\(621\) | −10.6413 | −0.427020 | ||||||||
\(622\) | 37.5794 | 1.50680 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.6786 | 0.627145 | ||||||||
\(626\) | 3.71927 | 0.148652 | ||||||||
\(627\) | 88.7719 | 3.54521 | ||||||||
\(628\) | −0.378778 | −0.0151149 | ||||||||
\(629\) | −0.695623 | −0.0277363 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.5975 | 1.53654 | 0.768271 | − | 0.640125i | \(-0.221117\pi\) | ||||
0.768271 | + | 0.640125i | \(0.221117\pi\) | |||||||
\(632\) | −32.8959 | −1.30853 | ||||||||
\(633\) | −76.1290 | −3.02586 | ||||||||
\(634\) | −33.1945 | −1.31832 | ||||||||
\(635\) | −1.54525 | −0.0613215 | ||||||||
\(636\) | −1.54339 | −0.0611995 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 16.5763 | 0.656260 | ||||||||
\(639\) | 49.3798 | 1.95343 | ||||||||
\(640\) | 8.38960 | 0.331628 | ||||||||
\(641\) | 19.5228 | 0.771105 | 0.385553 | − | 0.922686i | \(-0.374011\pi\) | ||||
0.385553 | + | 0.922686i | \(0.374011\pi\) | |||||||
\(642\) | −38.4429 | −1.51722 | ||||||||
\(643\) | −12.4718 | −0.491839 | −0.245920 | − | 0.969290i | \(-0.579090\pi\) | ||||
−0.245920 | + | 0.969290i | \(0.579090\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.3266 | 0.406611 | ||||||||
\(646\) | −4.51450 | −0.177621 | ||||||||
\(647\) | 35.9391 | 1.41291 | 0.706455 | − | 0.707758i | \(-0.250293\pi\) | ||||
0.706455 | + | 0.707758i | \(0.250293\pi\) | |||||||
\(648\) | −9.25967 | −0.363754 | ||||||||
\(649\) | −57.9556 | −2.27496 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.41034 | 0.0552332 | ||||||||
\(653\) | 4.85888 | 0.190143 | 0.0950713 | − | 0.995470i | \(-0.469692\pi\) | ||||
0.0950713 | + | 0.995470i | \(0.469692\pi\) | |||||||
\(654\) | −57.8668 | −2.26277 | ||||||||
\(655\) | 12.5579 | 0.490679 | ||||||||
\(656\) | −3.51964 | −0.137419 | ||||||||
\(657\) | −26.5144 | −1.03442 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.6206 | −0.920127 | −0.460063 | − | 0.887886i | \(-0.652173\pi\) | ||||
−0.460063 | + | 0.887886i | \(0.652173\pi\) | |||||||
\(660\) | −1.20217 | −0.0467944 | ||||||||
\(661\) | 16.3932 | 0.637623 | 0.318812 | − | 0.947818i | \(-0.396716\pi\) | ||||
0.318812 | + | 0.947818i | \(0.396716\pi\) | |||||||
\(662\) | 0.854633 | 0.0332162 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 16.8393 | 0.653492 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.07974 | 0.351833 | ||||||||
\(667\) | −3.65936 | −0.141691 | ||||||||
\(668\) | −0.444033 | −0.0171801 | ||||||||
\(669\) | 66.2692 | 2.56212 | ||||||||
\(670\) | −8.16420 | −0.315410 | ||||||||
\(671\) | 38.4939 | 1.48604 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.2536 | −0.549434 | −0.274717 | − | 0.961525i | \(-0.588584\pi\) | ||||
−0.274717 | + | 0.961525i | \(0.588584\pi\) | |||||||
\(674\) | 7.88982 | 0.303904 | ||||||||
\(675\) | −28.8461 | −1.11029 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.2715 | −0.394765 | −0.197383 | − | 0.980327i | \(-0.563244\pi\) | ||||
−0.197383 | + | 0.980327i | \(0.563244\pi\) | |||||||
\(678\) | 77.5255 | 2.97735 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.30618 | 0.0500898 | ||||||||
\(681\) | −1.30624 | −0.0500554 | ||||||||
\(682\) | 25.2691 | 0.967604 | ||||||||
\(683\) | −2.22201 | −0.0850230 | −0.0425115 | − | 0.999096i | \(-0.513536\pi\) | ||||
−0.0425115 | + | 0.999096i | \(0.513536\pi\) | |||||||
\(684\) | −3.04292 | −0.116349 | ||||||||
\(685\) | −6.32754 | −0.241763 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 49.9413 | 1.90538 | ||||||||
\(688\) | −16.8721 | −0.643242 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −5.13930 | −0.195650 | ||||||||
\(691\) | −2.64015 | −0.100436 | −0.0502179 | − | 0.998738i | \(-0.515992\pi\) | ||||
−0.0502179 | + | 0.998738i | \(0.515992\pi\) | |||||||
\(692\) | 1.91680 | 0.0728659 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.57174 | −0.0976220 | ||||||||
\(695\) | 7.99889 | 0.303415 | ||||||||
\(696\) | −19.0094 | −0.720549 | ||||||||
\(697\) | −0.519607 | −0.0196815 | ||||||||
\(698\) | 30.7767 | 1.16492 | ||||||||
\(699\) | 22.5169 | 0.851668 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.89991 | 0.336145 | 0.168072 | − | 0.985775i | \(-0.446246\pi\) | ||||
0.168072 | + | 0.985775i | \(0.446246\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.25885 | 0.273773 | ||||||||
\(704\) | 44.0351 | 1.65964 | ||||||||
\(705\) | −8.92656 | −0.336194 | ||||||||
\(706\) | −3.21594 | −0.121034 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 3.11080 | 0.116911 | ||||||||
\(709\) | 40.5944 | 1.52456 | 0.762278 | − | 0.647250i | \(-0.224081\pi\) | ||||
0.762278 | + | 0.647250i | \(0.224081\pi\) | |||||||
\(710\) | 10.3527 | 0.388529 | ||||||||
\(711\) | 60.2695 | 2.26028 | ||||||||
\(712\) | −14.4951 | −0.543226 | ||||||||
\(713\) | −5.57839 | −0.208912 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.04464 | −0.0764118 | ||||||||
\(717\) | −38.9868 | −1.45599 | ||||||||
\(718\) | −4.51096 | −0.168348 | ||||||||
\(719\) | 14.5135 | 0.541262 | 0.270631 | − | 0.962683i | \(-0.412768\pi\) | ||||
0.270631 | + | 0.962683i | \(0.412768\pi\) | |||||||
\(720\) | −16.2100 | −0.604110 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 20.9069 | 0.778076 | ||||||||
\(723\) | 64.9977 | 2.41729 | ||||||||
\(724\) | 1.62555 | 0.0604129 | ||||||||
\(725\) | −9.91969 | −0.368408 | ||||||||
\(726\) | 66.7105 | 2.47586 | ||||||||
\(727\) | −30.6942 | −1.13839 | −0.569193 | − | 0.822204i | \(-0.692744\pi\) | ||||
−0.569193 | + | 0.822204i | \(0.692744\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −40.3475 | −1.49435 | ||||||||
\(730\) | −5.55885 | −0.205742 | ||||||||
\(731\) | −2.49084 | −0.0921269 | ||||||||
\(732\) | −2.06618 | −0.0763683 | ||||||||
\(733\) | 13.2644 | 0.489930 | 0.244965 | − | 0.969532i | \(-0.421223\pi\) | ||||
0.244965 | + | 0.969532i | \(0.421223\pi\) | |||||||
\(734\) | 5.72708 | 0.211390 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.890761 | −0.0328339 | ||||||||
\(737\) | −38.7227 | −1.42637 | ||||||||
\(738\) | 6.78227 | 0.249659 | ||||||||
\(739\) | −7.25474 | −0.266870 | −0.133435 | − | 0.991058i | \(-0.542601\pi\) | ||||
−0.133435 | + | 0.991058i | \(0.542601\pi\) | |||||||
\(740\) | −0.0983010 | −0.00361362 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −46.2694 | −1.69746 | −0.848730 | − | 0.528827i | \(-0.822632\pi\) | ||||
−0.848730 | + | 0.528827i | \(0.822632\pi\) | |||||||
\(744\) | −28.9782 | −1.06239 | ||||||||
\(745\) | 6.38250 | 0.233837 | ||||||||
\(746\) | −15.3198 | −0.560898 | ||||||||
\(747\) | −30.8517 | −1.12881 | ||||||||
\(748\) | 0.289969 | 0.0106023 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −29.9430 | −1.09336 | ||||||||
\(751\) | −36.0260 | −1.31461 | −0.657305 | − | 0.753625i | \(-0.728303\pi\) | ||||
−0.657305 | + | 0.753625i | \(0.728303\pi\) | |||||||
\(752\) | 14.5846 | 0.531845 | ||||||||
\(753\) | −19.3973 | −0.706877 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.20986 | −0.0440313 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.5626 | −0.383906 | −0.191953 | − | 0.981404i | \(-0.561482\pi\) | ||||
−0.191953 | + | 0.981404i | \(0.561482\pi\) | |||||||
\(758\) | −6.39923 | −0.232430 | ||||||||
\(759\) | −24.3756 | −0.884780 | ||||||||
\(760\) | −13.6301 | −0.494415 | ||||||||
\(761\) | −7.81202 | −0.283185 | −0.141593 | − | 0.989925i | \(-0.545222\pi\) | ||||
−0.141593 | + | 0.989925i | \(0.545222\pi\) | |||||||
\(762\) | −7.61813 | −0.275976 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.417389 | 0.0151006 | ||||||||
\(765\) | −2.39309 | −0.0865223 | ||||||||
\(766\) | −5.06020 | −0.182833 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −6.77429 | −0.244446 | ||||||||
\(769\) | 25.2915 | 0.912033 | 0.456017 | − | 0.889971i | \(-0.349276\pi\) | ||||
0.456017 | + | 0.889971i | \(0.349276\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 47.6497 | 1.71606 | ||||||||
\(772\) | 1.13893 | 0.0409911 | ||||||||
\(773\) | −46.6004 | −1.67610 | −0.838051 | − | 0.545592i | \(-0.816305\pi\) | ||||
−0.838051 | + | 0.545592i | \(0.816305\pi\) | |||||||
\(774\) | 32.5121 | 1.16862 | ||||||||
\(775\) | −15.1217 | −0.543188 | ||||||||
\(776\) | 30.8114 | 1.10606 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 23.2827 | 0.834727 | ||||||||
\(779\) | 5.42212 | 0.194268 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 49.1026 | 1.75703 | ||||||||
\(782\) | 1.23962 | 0.0443289 | ||||||||
\(783\) | 15.1188 | 0.540302 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.10848 | 0.110946 | ||||||||
\(786\) | 61.9108 | 2.20829 | ||||||||
\(787\) | −39.7332 | −1.41633 | −0.708167 | − | 0.706045i | \(-0.750478\pi\) | ||||
−0.708167 | + | 0.706045i | \(0.750478\pi\) | |||||||
\(788\) | 1.41628 | 0.0504529 | ||||||||
\(789\) | −28.8775 | −1.02807 | ||||||||
\(790\) | 12.6358 | 0.449560 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −80.8641 | −2.87338 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 23.0420 | 0.817730 | ||||||||
\(795\) | 12.6660 | 0.449217 | ||||||||
\(796\) | −0.693270 | −0.0245723 | ||||||||
\(797\) | −2.78598 | −0.0986844 | −0.0493422 | − | 0.998782i | \(-0.515712\pi\) | ||||
−0.0493422 | + | 0.998782i | \(0.515712\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.15313 | 0.0761723 | ||||||||
\(800\) | −2.41465 | −0.0853706 | ||||||||
\(801\) | 26.5568 | 0.938338 | ||||||||
\(802\) | 34.9086 | 1.23267 | ||||||||
\(803\) | −26.3656 | −0.930421 | ||||||||
\(804\) | 2.07847 | 0.0733018 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −45.3011 | −1.59467 | ||||||||
\(808\) | −11.3298 | −0.398580 | ||||||||
\(809\) | −41.4586 | −1.45761 | −0.728803 | − | 0.684723i | \(-0.759923\pi\) | ||||
−0.728803 | + | 0.684723i | \(0.759923\pi\) | |||||||
\(810\) | 3.55676 | 0.124972 | ||||||||
\(811\) | 27.8622 | 0.978375 | 0.489188 | − | 0.872179i | \(-0.337293\pi\) | ||||
0.489188 | + | 0.872179i | \(0.337293\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15.0289 | −0.527085 | ||||||||
\(814\) | 9.02878 | 0.316459 | ||||||||
\(815\) | −11.5741 | −0.405423 | ||||||||
\(816\) | 6.12254 | 0.214332 | ||||||||
\(817\) | 25.9920 | 0.909344 | ||||||||
\(818\) | 7.90671 | 0.276452 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.0734276 | −0.00256420 | ||||||||
\(821\) | 22.4202 | 0.782469 | 0.391235 | − | 0.920291i | \(-0.372048\pi\) | ||||
0.391235 | + | 0.920291i | \(0.372048\pi\) | |||||||
\(822\) | −31.1949 | −1.08805 | ||||||||
\(823\) | −2.36166 | −0.0823221 | −0.0411611 | − | 0.999153i | \(-0.513106\pi\) | ||||
−0.0411611 | + | 0.999153i | \(0.513106\pi\) | |||||||
\(824\) | −24.4614 | −0.852154 | ||||||||
\(825\) | −66.0767 | −2.30050 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −43.3148 | −1.50620 | −0.753102 | − | 0.657904i | \(-0.771443\pi\) | ||||
−0.753102 | + | 0.657904i | \(0.771443\pi\) | |||||||
\(828\) | 0.835546 | 0.0290372 | ||||||||
\(829\) | −54.9280 | −1.90773 | −0.953864 | − | 0.300239i | \(-0.902933\pi\) | ||||
−0.953864 | + | 0.300239i | \(0.902933\pi\) | |||||||
\(830\) | −6.46820 | −0.224514 | ||||||||
\(831\) | −55.5277 | −1.92623 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 39.4346 | 1.36551 | ||||||||
\(835\) | 3.64400 | 0.126106 | ||||||||
\(836\) | −3.02584 | −0.104651 | ||||||||
\(837\) | 23.0473 | 0.796632 | ||||||||
\(838\) | −47.3647 | −1.63619 | ||||||||
\(839\) | −14.7410 | −0.508917 | −0.254459 | − | 0.967084i | \(-0.581897\pi\) | ||||
−0.254459 | + | 0.967084i | \(0.581897\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.8009 | −0.820721 | ||||||||
\(842\) | −4.05673 | −0.139804 | ||||||||
\(843\) | 6.17393 | 0.212642 | ||||||||
\(844\) | 2.59490 | 0.0893201 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −28.1041 | −0.966239 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −20.6942 | −0.710642 | ||||||||
\(849\) | −45.3796 | −1.55743 | ||||||||
\(850\) | 3.36033 | 0.115258 | ||||||||
\(851\) | −1.99319 | −0.0683256 | ||||||||
\(852\) | −2.63562 | −0.0902947 | ||||||||
\(853\) | −24.1038 | −0.825297 | −0.412649 | − | 0.910890i | \(-0.635396\pi\) | ||||
−0.412649 | + | 0.910890i | \(0.635396\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 24.9720 | 0.854024 | ||||||||
\(856\) | 27.9957 | 0.956873 | ||||||||
\(857\) | −18.5850 | −0.634851 | −0.317425 | − | 0.948283i | \(-0.602818\pi\) | ||||
−0.317425 | + | 0.948283i | \(0.602818\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.4975 | 1.00644 | 0.503221 | − | 0.864158i | \(-0.332148\pi\) | ||||
0.503221 | + | 0.864158i | \(0.332148\pi\) | |||||||
\(860\) | −0.351989 | −0.0120027 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −54.7423 | −1.86453 | ||||||||
\(863\) | 18.6435 | 0.634631 | 0.317315 | − | 0.948320i | \(-0.397219\pi\) | ||||
0.317315 | + | 0.948320i | \(0.397219\pi\) | |||||||
\(864\) | 3.68021 | 0.125203 | ||||||||
\(865\) | −15.7304 | −0.534851 | ||||||||
\(866\) | −13.5651 | −0.460961 | ||||||||
\(867\) | −48.0766 | −1.63277 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 59.9312 | 2.03303 | ||||||||
\(870\) | 7.30175 | 0.247552 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 42.1409 | 1.42707 | ||||||||
\(873\) | −56.4502 | −1.91055 | ||||||||
\(874\) | −12.9355 | −0.437551 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.41519 | 0.0478148 | ||||||||
\(877\) | −37.7518 | −1.27479 | −0.637395 | − | 0.770538i | \(-0.719988\pi\) | ||||
−0.637395 | + | 0.770538i | \(0.719988\pi\) | |||||||
\(878\) | 39.3673 | 1.32858 | ||||||||
\(879\) | −66.6962 | −2.24961 | ||||||||
\(880\) | −16.1190 | −0.543372 | ||||||||
\(881\) | 29.8298 | 1.00499 | 0.502497 | − | 0.864579i | \(-0.332415\pi\) | ||||
0.502497 | + | 0.864579i | \(0.332415\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.3979 | 1.09028 | 0.545138 | − | 0.838346i | \(-0.316477\pi\) | ||||
0.545138 | + | 0.838346i | \(0.316477\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −25.5291 | −0.858151 | ||||||||
\(886\) | 4.60468 | 0.154697 | ||||||||
\(887\) | −25.9198 | −0.870302 | −0.435151 | − | 0.900358i | \(-0.643305\pi\) | ||||
−0.435151 | + | 0.900358i | \(0.643305\pi\) | |||||||
\(888\) | −10.3541 | −0.347459 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 5.56775 | 0.186631 | ||||||||
\(891\) | 16.8697 | 0.565155 | ||||||||
\(892\) | −2.25882 | −0.0756310 | ||||||||
\(893\) | −22.4680 | −0.751863 | ||||||||
\(894\) | 31.4658 | 1.05238 | ||||||||
\(895\) | 16.7795 | 0.560878 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 25.0782 | 0.836870 | ||||||||
\(899\) | 7.92559 | 0.264333 | ||||||||
\(900\) | 2.26497 | 0.0754991 | ||||||||
\(901\) | −3.05510 | −0.101780 | ||||||||
\(902\) | 6.74420 | 0.224557 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −56.4572 | −1.87774 | ||||||||
\(905\) | −13.3402 | −0.443443 | ||||||||
\(906\) | −5.96463 | −0.198162 | ||||||||
\(907\) | 15.5423 | 0.516072 | 0.258036 | − | 0.966135i | \(-0.416925\pi\) | ||||
0.258036 | + | 0.966135i | \(0.416925\pi\) | |||||||
\(908\) | 0.0445240 | 0.00147758 | ||||||||
\(909\) | 20.7576 | 0.688485 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.6358 | 0.783090 | 0.391545 | − | 0.920159i | \(-0.371941\pi\) | ||||
0.391545 | + | 0.920159i | \(0.371941\pi\) | |||||||
\(912\) | −63.8889 | −2.11557 | ||||||||
\(913\) | −30.6786 | −1.01531 | ||||||||
\(914\) | −12.0382 | −0.398189 | ||||||||
\(915\) | 16.9563 | 0.560559 | ||||||||
\(916\) | −1.70228 | −0.0562448 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −5.12155 | −0.169036 | ||||||||
\(919\) | 44.4817 | 1.46732 | 0.733659 | − | 0.679518i | \(-0.237811\pi\) | ||||
0.733659 | + | 0.679518i | \(0.237811\pi\) | |||||||
\(920\) | 3.74264 | 0.123391 | ||||||||
\(921\) | −12.2045 | −0.402151 | ||||||||
\(922\) | 3.13216 | 0.103152 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.40307 | −0.177652 | ||||||||
\(926\) | 7.56171 | 0.248493 | ||||||||
\(927\) | 44.8163 | 1.47196 | ||||||||
\(928\) | 1.26556 | 0.0415441 | ||||||||
\(929\) | −2.94270 | −0.0965470 | −0.0482735 | − | 0.998834i | \(-0.515372\pi\) | ||||
−0.0482735 | + | 0.998834i | \(0.515372\pi\) | |||||||
\(930\) | 11.1309 | 0.364996 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.767502 | −0.0251404 | ||||||||
\(933\) | 78.5131 | 2.57040 | ||||||||
\(934\) | 26.0392 | 0.852028 | ||||||||
\(935\) | −2.37966 | −0.0778232 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.951020 | −0.0310685 | −0.0155342 | − | 0.999879i | \(-0.504945\pi\) | ||||
−0.0155342 | + | 0.999879i | \(0.504945\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.77052 | 0.253581 | ||||||||
\(940\) | 0.304267 | 0.00992409 | ||||||||
\(941\) | −22.0692 | −0.719436 | −0.359718 | − | 0.933061i | \(-0.617127\pi\) | ||||
−0.359718 | + | 0.933061i | \(0.617127\pi\) | |||||||
\(942\) | 15.3248 | 0.499311 | ||||||||
\(943\) | −1.48885 | −0.0484835 | ||||||||
\(944\) | 41.7105 | 1.35756 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 32.3296 | 1.05113 | ||||||||
\(947\) | −51.1717 | −1.66286 | −0.831429 | − | 0.555631i | \(-0.812477\pi\) | ||||
−0.831429 | + | 0.555631i | \(0.812477\pi\) | |||||||
\(948\) | −3.21685 | −0.104478 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −35.0652 | −1.13767 | ||||||||
\(951\) | −69.3519 | −2.24889 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45.8470 | 1.48513 | 0.742565 | − | 0.669773i | \(-0.233609\pi\) | ||||
0.742565 | + | 0.669773i | \(0.233609\pi\) | |||||||
\(954\) | 39.8772 | 1.29107 | ||||||||
\(955\) | −3.42534 | −0.110842 | ||||||||
\(956\) | 1.32889 | 0.0429793 | ||||||||
\(957\) | 34.6321 | 1.11950 | ||||||||
\(958\) | −45.6955 | −1.47635 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 19.3972 | 0.626042 | ||||||||
\(961\) | −18.9181 | −0.610262 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −51.2916 | −1.65285 | ||||||||
\(964\) | −2.21548 | −0.0713559 | ||||||||
\(965\) | −9.34676 | −0.300883 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.2609 | 0.619387 | 0.309694 | − | 0.950836i | \(-0.399773\pi\) | ||||
0.309694 | + | 0.950836i | \(0.399773\pi\) | |||||||
\(968\) | −48.5813 | −1.56146 | ||||||||
\(969\) | −9.43196 | −0.302998 | ||||||||
\(970\) | −11.8350 | −0.380000 | ||||||||
\(971\) | 47.3326 | 1.51897 | 0.759487 | − | 0.650522i | \(-0.225450\pi\) | ||||
0.759487 | + | 0.650522i | \(0.225450\pi\) | |||||||
\(972\) | 1.04803 | 0.0336156 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −22.0046 | −0.705072 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −27.7039 | −0.886781 | ||||||||
\(977\) | −47.8571 | −1.53108 | −0.765541 | − | 0.643387i | \(-0.777529\pi\) | ||||
−0.765541 | + | 0.643387i | \(0.777529\pi\) | |||||||
\(978\) | −57.0605 | −1.82459 | ||||||||
\(979\) | 26.4078 | 0.843995 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −77.2074 | −2.46504 | ||||||||
\(982\) | −43.7061 | −1.39472 | ||||||||
\(983\) | −15.7686 | −0.502941 | −0.251471 | − | 0.967865i | \(-0.580914\pi\) | ||||
−0.251471 | + | 0.967865i | \(0.580914\pi\) | |||||||
\(984\) | −7.73414 | −0.246555 | ||||||||
\(985\) | −11.6228 | −0.370335 | ||||||||
\(986\) | −1.76122 | −0.0560885 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.13707 | −0.226945 | ||||||||
\(990\) | 31.0609 | 0.987181 | ||||||||
\(991\) | −12.1378 | −0.385571 | −0.192786 | − | 0.981241i | \(-0.561752\pi\) | ||||
−0.192786 | + | 0.981241i | \(0.561752\pi\) | |||||||
\(992\) | 1.92924 | 0.0612536 | ||||||||
\(993\) | 1.78555 | 0.0566627 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.68938 | 0.180366 | ||||||||
\(996\) | 1.64669 | 0.0521775 | ||||||||
\(997\) | 33.7876 | 1.07006 | 0.535032 | − | 0.844832i | \(-0.320299\pi\) | ||||
0.535032 | + | 0.844832i | \(0.320299\pi\) | |||||||
\(998\) | −33.3986 | −1.05721 | ||||||||
\(999\) | 8.23493 | 0.260542 |
(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 | 8281.2.a.cp.1.10 | 12 | ||
7.2 | even | 3 | 1183.2.e.j.508.3 | 24 | |||
7.4 | even | 3 | 1183.2.e.j.170.3 | 24 | |||
7.6 | odd | 2 | 8281.2.a.co.1.10 | 12 | |||
13.2 | odd | 12 | 637.2.q.g.589.5 | 12 | |||
13.7 | odd | 12 | 637.2.q.g.491.5 | 12 | |||
13.12 | even | 2 | inner | 8281.2.a.cp.1.3 | 12 | ||
91.2 | odd | 12 | 91.2.k.b.4.2 | ✓ | 12 | ||
91.20 | even | 12 | 637.2.q.i.491.5 | 12 | |||
91.25 | even | 6 | 1183.2.e.j.170.10 | 24 | |||
91.33 | even | 12 | 637.2.u.g.361.2 | 12 | |||
91.41 | even | 12 | 637.2.q.i.589.5 | 12 | |||
91.46 | odd | 12 | 91.2.k.b.23.5 | yes | 12 | ||
91.51 | even | 6 | 1183.2.e.j.508.10 | 24 | |||
91.54 | even | 12 | 637.2.k.i.459.2 | 12 | |||
91.59 | even | 12 | 637.2.k.i.569.5 | 12 | |||
91.67 | odd | 12 | 91.2.u.b.30.2 | yes | 12 | ||
91.72 | odd | 12 | 91.2.u.b.88.2 | yes | 12 | ||
91.80 | even | 12 | 637.2.u.g.30.2 | 12 | |||
91.90 | odd | 2 | 8281.2.a.co.1.3 | 12 | |||
273.2 | even | 12 | 819.2.bm.f.550.5 | 12 | |||
273.137 | even | 12 | 819.2.bm.f.478.2 | 12 | |||
273.158 | even | 12 | 819.2.do.e.667.5 | 12 | |||
273.254 | even | 12 | 819.2.do.e.361.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.b.4.2 | ✓ | 12 | 91.2 | odd | 12 | ||
91.2.k.b.23.5 | yes | 12 | 91.46 | odd | 12 | ||
91.2.u.b.30.2 | yes | 12 | 91.67 | odd | 12 | ||
91.2.u.b.88.2 | yes | 12 | 91.72 | odd | 12 | ||
637.2.k.i.459.2 | 12 | 91.54 | even | 12 | |||
637.2.k.i.569.5 | 12 | 91.59 | even | 12 | |||
637.2.q.g.491.5 | 12 | 13.7 | odd | 12 | |||
637.2.q.g.589.5 | 12 | 13.2 | odd | 12 | |||
637.2.q.i.491.5 | 12 | 91.20 | even | 12 | |||
637.2.q.i.589.5 | 12 | 91.41 | even | 12 | |||
637.2.u.g.30.2 | 12 | 91.80 | even | 12 | |||
637.2.u.g.361.2 | 12 | 91.33 | even | 12 | |||
819.2.bm.f.478.2 | 12 | 273.137 | even | 12 | |||
819.2.bm.f.550.5 | 12 | 273.2 | even | 12 | |||
819.2.do.e.361.5 | 12 | 273.254 | even | 12 | |||
819.2.do.e.667.5 | 12 | 273.158 | even | 12 | |||
1183.2.e.j.170.3 | 24 | 7.4 | even | 3 | |||
1183.2.e.j.170.10 | 24 | 91.25 | even | 6 | |||
1183.2.e.j.508.3 | 24 | 7.2 | even | 3 | |||
1183.2.e.j.508.10 | 24 | 91.51 | even | 6 | |||
8281.2.a.co.1.3 | 12 | 91.90 | odd | 2 | |||
8281.2.a.co.1.10 | 12 | 7.6 | odd | 2 | |||
8281.2.a.cp.1.3 | 12 | 13.12 | even | 2 | inner | ||
8281.2.a.cp.1.10 | 12 | 1.1 | even | 1 | trivial |