Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,2,Mod(1077,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1078.1077");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(8.60787333789\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 154) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1077.9 | ||
Root | \(-0.0499037 - 0.186243i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1078.1077 |
Dual form | 1078.2.c.b.1077.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(981\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | − | 3.12703i | − | 1.80539i | −0.430279 | − | 0.902696i | \(-0.641585\pi\) | ||
0.430279 | − | 0.902696i | \(-0.358415\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 2.20288i | 0.985157i | 0.870268 | + | 0.492579i | \(0.163946\pi\) | ||||
−0.870268 | + | 0.492579i | \(0.836054\pi\) | |||||||
\(6\) | 3.12703 | 1.27660 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −6.77832 | −2.25944 | ||||||||
\(10\) | −2.20288 | −0.696611 | ||||||||
\(11\) | −1.49053 | + | 2.96282i | −0.449412 | + | 0.893325i | ||||
\(12\) | 3.12703i | 0.902696i | ||||||||
\(13\) | 1.45937 | 0.404757 | 0.202378 | − | 0.979307i | \(-0.435133\pi\) | ||||
0.202378 | + | 0.979307i | \(0.435133\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.88847 | 1.77860 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.60732 | 1.84505 | 0.922523 | − | 0.385943i | \(-0.126124\pi\) | ||||
0.922523 | + | 0.385943i | \(0.126124\pi\) | |||||||
\(18\) | − | 6.77832i | − | 1.59767i | ||||||
\(19\) | 0.180645 | 0.0414429 | 0.0207214 | − | 0.999785i | \(-0.493404\pi\) | ||||
0.0207214 | + | 0.999785i | \(0.493404\pi\) | |||||||
\(20\) | − | 2.20288i | − | 0.492579i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.96282 | − | 1.49053i | −0.631676 | − | 0.317782i | ||||
\(23\) | 2.28779 | 0.477037 | 0.238519 | − | 0.971138i | \(-0.423338\pi\) | ||||
0.238519 | + | 0.971138i | \(0.423338\pi\) | |||||||
\(24\) | −3.12703 | −0.638302 | ||||||||
\(25\) | 0.147325 | 0.0294651 | ||||||||
\(26\) | 1.45937i | 0.286206i | ||||||||
\(27\) | 11.8149i | 2.27378i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.45335i | − | 0.826967i | −0.910512 | − | 0.413483i | \(-0.864312\pi\) | ||
0.910512 | − | 0.413483i | \(-0.135688\pi\) | |||||||
\(30\) | 6.88847i | 1.25766i | ||||||||
\(31\) | 8.54897i | 1.53544i | 0.640785 | + | 0.767720i | \(0.278609\pi\) | ||||
−0.640785 | + | 0.767720i | \(0.721391\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 9.26484 | + | 4.66093i | 1.61280 | + | 0.811364i | ||||
\(34\) | 7.60732i | 1.30464i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.77832 | 1.12972 | ||||||||
\(37\) | 1.50947 | 0.248155 | 0.124078 | − | 0.992273i | \(-0.460403\pi\) | ||||
0.124078 | + | 0.992273i | \(0.460403\pi\) | |||||||
\(38\) | 0.180645i | 0.0293045i | ||||||||
\(39\) | − | 4.56350i | − | 0.730745i | ||||||
\(40\) | 2.20288 | 0.348306 | ||||||||
\(41\) | 7.10368 | 1.10941 | 0.554705 | − | 0.832047i | \(-0.312831\pi\) | ||||
0.554705 | + | 0.832047i | \(0.312831\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.58174i | − | 0.241213i | −0.992700 | − | 0.120606i | \(-0.961516\pi\) | ||
0.992700 | − | 0.120606i | \(-0.0384839\pi\) | |||||||
\(44\) | 1.49053 | − | 2.96282i | 0.224706 | − | 0.446662i | ||||
\(45\) | − | 14.9318i | − | 2.22590i | ||||||
\(46\) | 2.28779i | 0.337316i | ||||||||
\(47\) | 0.545357i | 0.0795486i | 0.999209 | + | 0.0397743i | \(0.0126639\pi\) | ||||
−0.999209 | + | 0.0397743i | \(0.987336\pi\) | |||||||
\(48\) | − | 3.12703i | − | 0.451348i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.147325i | 0.0208349i | ||||||||
\(51\) | − | 23.7883i | − | 3.33103i | ||||||
\(52\) | −1.45937 | −0.202378 | ||||||||
\(53\) | 4.83444 | 0.664061 | 0.332031 | − | 0.943269i | \(-0.392266\pi\) | ||||
0.332031 | + | 0.943269i | \(0.392266\pi\) | |||||||
\(54\) | −11.8149 | −1.60781 | ||||||||
\(55\) | −6.52674 | − | 3.28346i | −0.880065 | − | 0.442741i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.564883i | − | 0.0748206i | ||||||
\(58\) | 4.45335 | 0.584754 | ||||||||
\(59\) | − | 6.18967i | − | 0.805826i | −0.915238 | − | 0.402913i | \(-0.867998\pi\) | ||
0.915238 | − | 0.402913i | \(-0.132002\pi\) | |||||||
\(60\) | −6.88847 | −0.889298 | ||||||||
\(61\) | 5.72621 | 0.733166 | 0.366583 | − | 0.930385i | \(-0.380528\pi\) | ||||
0.366583 | + | 0.930385i | \(0.380528\pi\) | |||||||
\(62\) | −8.54897 | −1.08572 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 3.21482i | 0.398749i | ||||||||
\(66\) | −4.66093 | + | 9.26484i | −0.573721 | + | 1.14042i | ||||
\(67\) | −2.98176 | −0.364280 | −0.182140 | − | 0.983273i | \(-0.558302\pi\) | ||||
−0.182140 | + | 0.983273i | \(0.558302\pi\) | |||||||
\(68\) | −7.60732 | −0.922523 | ||||||||
\(69\) | − | 7.15399i | − | 0.861240i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.57488 | −0.898973 | −0.449486 | − | 0.893287i | \(-0.648393\pi\) | ||||
−0.449486 | + | 0.893287i | \(0.648393\pi\) | |||||||
\(72\) | 6.77832i | 0.798833i | ||||||||
\(73\) | 9.67644 | 1.13254 | 0.566271 | − | 0.824219i | \(-0.308386\pi\) | ||||
0.566271 | + | 0.824219i | \(0.308386\pi\) | |||||||
\(74\) | 1.50947i | 0.175472i | ||||||||
\(75\) | − | 0.460691i | − | 0.0531960i | ||||||
\(76\) | −0.180645 | −0.0207214 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.56350 | 0.516715 | ||||||||
\(79\) | 6.91879i | 0.778424i | 0.921148 | + | 0.389212i | \(0.127253\pi\) | ||||
−0.921148 | + | 0.389212i | \(0.872747\pi\) | |||||||
\(80\) | 2.20288i | 0.246289i | ||||||||
\(81\) | 16.6107 | 1.84563 | ||||||||
\(82\) | 7.10368i | 0.784471i | ||||||||
\(83\) | 5.84246 | 0.641293 | 0.320647 | − | 0.947199i | \(-0.396100\pi\) | ||||
0.320647 | + | 0.947199i | \(0.396100\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.7580i | 1.81766i | ||||||||
\(86\) | 1.58174 | 0.170563 | ||||||||
\(87\) | −13.9258 | −1.49300 | ||||||||
\(88\) | 2.96282 | + | 1.49053i | 0.315838 | + | 0.158891i | ||||
\(89\) | − | 16.1111i | − | 1.70778i | −0.520455 | − | 0.853889i | \(-0.674238\pi\) | ||
0.520455 | − | 0.853889i | \(-0.325762\pi\) | |||||||
\(90\) | 14.9318 | 1.57395 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.28779 | −0.238519 | ||||||||
\(93\) | 26.7329 | 2.77207 | ||||||||
\(94\) | −0.545357 | −0.0562493 | ||||||||
\(95\) | 0.397940i | 0.0408278i | ||||||||
\(96\) | 3.12703 | 0.319151 | ||||||||
\(97\) | 11.3012i | 1.14746i | 0.819045 | + | 0.573729i | \(0.194504\pi\) | ||||
−0.819045 | + | 0.573729i | \(0.805496\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.1033 | − | 20.0830i | 1.01542 | − | 2.01841i | ||||
\(100\) | −0.147325 | −0.0147325 | ||||||||
\(101\) | 0.517716 | 0.0515147 | 0.0257573 | − | 0.999668i | \(-0.491800\pi\) | ||||
0.0257573 | + | 0.999668i | \(0.491800\pi\) | |||||||
\(102\) | 23.7883 | 2.35539 | ||||||||
\(103\) | 2.88716i | 0.284480i | 0.989832 | + | 0.142240i | \(0.0454305\pi\) | ||||
−0.989832 | + | 0.142240i | \(0.954570\pi\) | |||||||
\(104\) | − | 1.45937i | − | 0.143103i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.83444i | 0.469562i | ||||||||
\(107\) | 5.21959i | 0.504597i | 0.967649 | + | 0.252299i | \(0.0811865\pi\) | ||||
−0.967649 | + | 0.252299i | \(0.918814\pi\) | |||||||
\(108\) | − | 11.8149i | − | 1.13689i | ||||||
\(109\) | 10.0540i | 0.963002i | 0.876446 | + | 0.481501i | \(0.159908\pi\) | ||||
−0.876446 | + | 0.481501i | \(0.840092\pi\) | |||||||
\(110\) | 3.28346 | − | 6.52674i | 0.313065 | − | 0.622300i | ||||
\(111\) | − | 4.72016i | − | 0.448018i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.83235 | 0.736806 | 0.368403 | − | 0.929666i | \(-0.379905\pi\) | ||||
0.368403 | + | 0.929666i | \(0.379905\pi\) | |||||||
\(114\) | 0.564883 | 0.0529062 | ||||||||
\(115\) | 5.03973i | 0.469957i | ||||||||
\(116\) | 4.45335i | 0.413483i | ||||||||
\(117\) | −9.89209 | −0.914524 | ||||||||
\(118\) | 6.18967 | 0.569805 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | − | 6.88847i | − | 0.628828i | ||||||
\(121\) | −6.55664 | − | 8.83235i | −0.596058 | − | 0.802941i | ||||
\(122\) | 5.72621i | 0.518427i | ||||||||
\(123\) | − | 22.2134i | − | 2.00292i | ||||||
\(124\) | − | 8.54897i | − | 0.767720i | ||||||
\(125\) | 11.3389i | 1.01419i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.4702i | 1.19529i | 0.801762 | + | 0.597644i | \(0.203896\pi\) | ||||
−0.801762 | + | 0.597644i | \(0.796104\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −4.94614 | −0.435484 | ||||||||
\(130\) | −3.21482 | −0.281958 | ||||||||
\(131\) | 2.62462 | 0.229314 | 0.114657 | − | 0.993405i | \(-0.463423\pi\) | ||||
0.114657 | + | 0.993405i | \(0.463423\pi\) | |||||||
\(132\) | −9.26484 | − | 4.66093i | −0.806401 | − | 0.405682i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 2.98176i | − | 0.257585i | ||||||
\(135\) | −26.0268 | −2.24003 | ||||||||
\(136\) | − | 7.60732i | − | 0.652322i | ||||||
\(137\) | −8.72291 | −0.745248 | −0.372624 | − | 0.927982i | \(-0.621542\pi\) | ||||
−0.372624 | + | 0.927982i | \(0.621542\pi\) | |||||||
\(138\) | 7.15399 | 0.608988 | ||||||||
\(139\) | −4.09291 | −0.347156 | −0.173578 | − | 0.984820i | \(-0.555533\pi\) | ||||
−0.173578 | + | 0.984820i | \(0.555533\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.70535 | 0.143616 | ||||||||
\(142\) | − | 7.57488i | − | 0.635670i | ||||||
\(143\) | −2.17524 | + | 4.32386i | −0.181902 | + | 0.361579i | ||||
\(144\) | −6.77832 | −0.564860 | ||||||||
\(145\) | 9.81020 | 0.814692 | ||||||||
\(146\) | 9.67644i | 0.800828i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.50947 | −0.124078 | ||||||||
\(149\) | 18.5917i | 1.52309i | 0.648110 | + | 0.761547i | \(0.275560\pi\) | ||||
−0.648110 | + | 0.761547i | \(0.724440\pi\) | |||||||
\(150\) | 0.460691 | 0.0376152 | ||||||||
\(151\) | − | 13.2045i | − | 1.07457i | −0.843402 | − | 0.537283i | \(-0.819451\pi\) | ||
0.843402 | − | 0.537283i | \(-0.180549\pi\) | |||||||
\(152\) | − | 0.180645i | − | 0.0146523i | ||||||
\(153\) | −51.5648 | −4.16877 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.8324 | −1.51265 | ||||||||
\(156\) | 4.56350i | 0.365373i | ||||||||
\(157\) | 5.75901i | 0.459619i | 0.973236 | + | 0.229810i | \(0.0738104\pi\) | ||||
−0.973236 | + | 0.229810i | \(0.926190\pi\) | |||||||
\(158\) | −6.91879 | −0.550429 | ||||||||
\(159\) | − | 15.1174i | − | 1.19889i | ||||||
\(160\) | −2.20288 | −0.174153 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 16.6107i | 1.30506i | ||||||||
\(163\) | −5.31289 | −0.416137 | −0.208069 | − | 0.978114i | \(-0.566718\pi\) | ||||
−0.208069 | + | 0.978114i | \(0.566718\pi\) | |||||||
\(164\) | −7.10368 | −0.554705 | ||||||||
\(165\) | −10.2675 | + | 20.4093i | −0.799321 | + | 1.58886i | ||||
\(166\) | 5.84246i | 0.453463i | ||||||||
\(167\) | 16.0519 | 1.24213 | 0.621067 | − | 0.783757i | \(-0.286699\pi\) | ||||
0.621067 | + | 0.783757i | \(0.286699\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.8702 | −0.836172 | ||||||||
\(170\) | −16.7580 | −1.28528 | ||||||||
\(171\) | −1.22447 | −0.0936377 | ||||||||
\(172\) | 1.58174i | 0.120606i | ||||||||
\(173\) | 7.09477 | 0.539405 | 0.269703 | − | 0.962944i | \(-0.413075\pi\) | ||||
0.269703 | + | 0.962944i | \(0.413075\pi\) | |||||||
\(174\) | − | 13.9258i | − | 1.05571i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.49053 | + | 2.96282i | −0.112353 | + | 0.223331i | ||||
\(177\) | −19.3553 | −1.45483 | ||||||||
\(178\) | 16.1111 | 1.20758 | ||||||||
\(179\) | −24.9728 | −1.86656 | −0.933278 | − | 0.359155i | \(-0.883065\pi\) | ||||
−0.933278 | + | 0.359155i | \(0.883065\pi\) | |||||||
\(180\) | 14.9318i | 1.11295i | ||||||||
\(181\) | − | 19.3579i | − | 1.43886i | −0.694566 | − | 0.719429i | \(-0.744404\pi\) | ||
0.694566 | − | 0.719429i | \(-0.255596\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 17.9060i | − | 1.32365i | ||||||
\(184\) | − | 2.28779i | − | 0.168658i | ||||||
\(185\) | 3.32518i | 0.244472i | ||||||||
\(186\) | 26.7329i | 1.96015i | ||||||||
\(187\) | −11.3389 | + | 22.5391i | −0.829185 | + | 1.64822i | ||||
\(188\) | − | 0.545357i | − | 0.0397743i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.397940 | −0.0288696 | ||||||||
\(191\) | 6.00000 | 0.434145 | 0.217072 | − | 0.976156i | \(-0.430349\pi\) | ||||
0.217072 | + | 0.976156i | \(0.430349\pi\) | |||||||
\(192\) | 3.12703i | 0.225674i | ||||||||
\(193\) | 16.6114i | 1.19571i | 0.801603 | + | 0.597857i | \(0.203981\pi\) | ||||
−0.801603 | + | 0.597857i | \(0.796019\pi\) | |||||||
\(194\) | −11.3012 | −0.811376 | ||||||||
\(195\) | 10.0528 | 0.719899 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 20.6396i | − | 1.47051i | −0.677790 | − | 0.735256i | \(-0.737062\pi\) | ||
0.677790 | − | 0.735256i | \(-0.262938\pi\) | |||||||
\(198\) | 20.0830 | + | 10.1033i | 1.42723 | + | 0.718009i | ||||
\(199\) | 0.726003i | 0.0514650i | 0.999669 | + | 0.0257325i | \(0.00819181\pi\) | ||||
−0.999669 | + | 0.0257325i | \(0.991808\pi\) | |||||||
\(200\) | − | 0.147325i | − | 0.0104175i | ||||||
\(201\) | 9.32407i | 0.657669i | ||||||||
\(202\) | 0.517716i | 0.0364264i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 23.7883i | 1.66552i | ||||||||
\(205\) | 15.6486i | 1.09294i | ||||||||
\(206\) | −2.88716 | −0.201158 | ||||||||
\(207\) | −15.5074 | −1.07784 | ||||||||
\(208\) | 1.45937 | 0.101189 | ||||||||
\(209\) | −0.269257 | + | 0.535220i | −0.0186249 | + | 0.0370219i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 10.2878i | − | 0.708241i | −0.935200 | − | 0.354120i | \(-0.884780\pi\) | ||
0.935200 | − | 0.354120i | \(-0.115220\pi\) | |||||||
\(212\) | −4.83444 | −0.332031 | ||||||||
\(213\) | 23.6869i | 1.62300i | ||||||||
\(214\) | −5.21959 | −0.356804 | ||||||||
\(215\) | 3.48438 | 0.237632 | ||||||||
\(216\) | 11.8149 | 0.803904 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −10.0540 | −0.680945 | ||||||||
\(219\) | − | 30.2585i | − | 2.04468i | ||||||
\(220\) | 6.52674 | + | 3.28346i | 0.440033 | + | 0.221371i | ||||
\(221\) | 11.1019 | 0.746795 | ||||||||
\(222\) | 4.72016 | 0.316796 | ||||||||
\(223\) | 0.894768i | 0.0599181i | 0.999551 | + | 0.0299590i | \(0.00953768\pi\) | ||||
−0.999551 | + | 0.0299590i | \(0.990462\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.998618 | −0.0665745 | ||||||||
\(226\) | 7.83235i | 0.521000i | ||||||||
\(227\) | −13.4848 | −0.895017 | −0.447508 | − | 0.894280i | \(-0.647689\pi\) | ||||
−0.447508 | + | 0.894280i | \(0.647689\pi\) | |||||||
\(228\) | 0.564883i | 0.0374103i | ||||||||
\(229\) | 4.88550i | 0.322843i | 0.986886 | + | 0.161422i | \(0.0516079\pi\) | ||||
−0.986886 | + | 0.161422i | \(0.948392\pi\) | |||||||
\(230\) | −5.03973 | −0.332310 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.45335 | −0.292377 | ||||||||
\(233\) | − | 22.6606i | − | 1.48455i | −0.670097 | − | 0.742274i | \(-0.733747\pi\) | ||
0.670097 | − | 0.742274i | \(-0.266253\pi\) | |||||||
\(234\) | − | 9.89209i | − | 0.646666i | ||||||
\(235\) | −1.20136 | −0.0783678 | ||||||||
\(236\) | 6.18967i | 0.402913i | ||||||||
\(237\) | 21.6353 | 1.40536 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.2410i | 1.63270i | 0.577556 | + | 0.816351i | \(0.304007\pi\) | ||||
−0.577556 | + | 0.816351i | \(0.695993\pi\) | |||||||
\(240\) | 6.88847 | 0.444649 | ||||||||
\(241\) | 14.0669 | 0.906128 | 0.453064 | − | 0.891478i | \(-0.350331\pi\) | ||||
0.453064 | + | 0.891478i | \(0.350331\pi\) | |||||||
\(242\) | 8.83235 | − | 6.55664i | 0.567765 | − | 0.421477i | ||||
\(243\) | − | 16.4973i | − | 1.05830i | ||||||
\(244\) | −5.72621 | −0.366583 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 22.2134 | 1.41628 | ||||||||
\(247\) | 0.263629 | 0.0167743 | ||||||||
\(248\) | 8.54897 | 0.542860 | ||||||||
\(249\) | − | 18.2696i | − | 1.15779i | ||||||
\(250\) | −11.3389 | −0.717137 | ||||||||
\(251\) | − | 3.03720i | − | 0.191706i | −0.995395 | − | 0.0958532i | \(-0.969442\pi\) | ||
0.995395 | − | 0.0958532i | \(-0.0305579\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.41002 | + | 6.77832i | −0.214386 | + | 0.426149i | ||||
\(254\) | −13.4702 | −0.845196 | ||||||||
\(255\) | 52.4028 | 3.28159 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 25.7683i | − | 1.60738i | −0.595045 | − | 0.803692i | \(-0.702866\pi\) | ||
0.595045 | − | 0.803692i | \(-0.297134\pi\) | |||||||
\(258\) | − | 4.94614i | − | 0.307933i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 3.21482i | − | 0.199375i | ||||||
\(261\) | 30.1863i | 1.86848i | ||||||||
\(262\) | 2.62462i | 0.162149i | ||||||||
\(263\) | − | 6.41002i | − | 0.395259i | −0.980277 | − | 0.197629i | \(-0.936676\pi\) | ||
0.980277 | − | 0.197629i | \(-0.0633243\pi\) | |||||||
\(264\) | 4.66093 | − | 9.26484i | 0.286861 | − | 0.570211i | ||||
\(265\) | 10.6497i | 0.654205i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −50.3800 | −3.08321 | ||||||||
\(268\) | 2.98176 | 0.182140 | ||||||||
\(269\) | 2.74152i | 0.167153i | 0.996501 | + | 0.0835767i | \(0.0266344\pi\) | ||||
−0.996501 | + | 0.0835767i | \(0.973366\pi\) | |||||||
\(270\) | − | 26.0268i | − | 1.58394i | ||||||
\(271\) | −28.6002 | −1.73734 | −0.868670 | − | 0.495392i | \(-0.835024\pi\) | ||||
−0.868670 | + | 0.495392i | \(0.835024\pi\) | |||||||
\(272\) | 7.60732 | 0.461261 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 8.72291i | − | 0.526970i | ||||||
\(275\) | −0.219593 | + | 0.436499i | −0.0132419 | + | 0.0263219i | ||||
\(276\) | 7.15399i | 0.430620i | ||||||||
\(277\) | − | 10.7683i | − | 0.647006i | −0.946227 | − | 0.323503i | \(-0.895139\pi\) | ||
0.946227 | − | 0.323503i | \(-0.104861\pi\) | |||||||
\(278\) | − | 4.09291i | − | 0.245476i | ||||||
\(279\) | − | 57.9477i | − | 3.46924i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.6289i | 1.17096i | 0.810686 | + | 0.585481i | \(0.199094\pi\) | ||||
−0.810686 | + | 0.585481i | \(0.800906\pi\) | |||||||
\(282\) | 1.70535i | 0.101552i | ||||||||
\(283\) | −10.6233 | −0.631487 | −0.315744 | − | 0.948845i | \(-0.602254\pi\) | ||||
−0.315744 | + | 0.948845i | \(0.602254\pi\) | |||||||
\(284\) | 7.57488 | 0.449486 | ||||||||
\(285\) | 1.24437 | 0.0737101 | ||||||||
\(286\) | −4.32386 | − | 2.17524i | −0.255675 | − | 0.128624i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 6.77832i | − | 0.399416i | ||||||
\(289\) | 40.8713 | 2.40419 | ||||||||
\(290\) | 9.81020i | 0.576075i | ||||||||
\(291\) | 35.3391 | 2.07161 | ||||||||
\(292\) | −9.67644 | −0.566271 | ||||||||
\(293\) | −0.277651 | −0.0162206 | −0.00811028 | − | 0.999967i | \(-0.502582\pi\) | ||||
−0.00811028 | + | 0.999967i | \(0.502582\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.6351 | 0.793866 | ||||||||
\(296\) | − | 1.50947i | − | 0.0877362i | ||||||
\(297\) | −35.0055 | − | 17.6105i | −2.03123 | − | 1.02186i | ||||
\(298\) | −18.5917 | −1.07699 | ||||||||
\(299\) | 3.33874 | 0.193084 | ||||||||
\(300\) | 0.460691i | 0.0265980i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 13.2045 | 0.759833 | ||||||||
\(303\) | − | 1.61891i | − | 0.0930042i | ||||||
\(304\) | 0.180645 | 0.0103607 | ||||||||
\(305\) | 12.6141i | 0.722284i | ||||||||
\(306\) | − | 51.5648i | − | 2.94777i | ||||||
\(307\) | −6.41443 | −0.366091 | −0.183045 | − | 0.983104i | \(-0.558596\pi\) | ||||
−0.183045 | + | 0.983104i | \(0.558596\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.02823 | 0.513598 | ||||||||
\(310\) | − | 18.8324i | − | 1.06961i | ||||||
\(311\) | − | 11.3024i | − | 0.640899i | −0.947266 | − | 0.320449i | \(-0.896166\pi\) | ||
0.947266 | − | 0.320449i | \(-0.103834\pi\) | |||||||
\(312\) | −4.56350 | −0.258357 | ||||||||
\(313\) | 16.4467i | 0.929621i | 0.885410 | + | 0.464810i | \(0.153877\pi\) | ||||
−0.885410 | + | 0.464810i | \(0.846123\pi\) | |||||||
\(314\) | −5.75901 | −0.325000 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 6.91879i | − | 0.389212i | ||||||
\(317\) | −28.1910 | −1.58337 | −0.791683 | − | 0.610932i | \(-0.790795\pi\) | ||||
−0.791683 | + | 0.610932i | \(0.790795\pi\) | |||||||
\(318\) | 15.1174 | 0.847744 | ||||||||
\(319\) | 13.1945 | + | 6.63786i | 0.738750 | + | 0.371649i | ||||
\(320\) | − | 2.20288i | − | 0.123145i | ||||||
\(321\) | 16.3218 | 0.910996 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.37423 | 0.0764640 | ||||||||
\(324\) | −16.6107 | −0.922815 | ||||||||
\(325\) | 0.215002 | 0.0119262 | ||||||||
\(326\) | − | 5.31289i | − | 0.294254i | ||||||
\(327\) | 31.4393 | 1.73860 | ||||||||
\(328\) | − | 7.10368i | − | 0.392235i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −20.4093 | − | 10.2675i | −1.12350 | − | 0.565206i | ||||
\(331\) | 19.1126 | 1.05052 | 0.525261 | − | 0.850941i | \(-0.323968\pi\) | ||||
0.525261 | + | 0.850941i | \(0.323968\pi\) | |||||||
\(332\) | −5.84246 | −0.320647 | ||||||||
\(333\) | −10.2317 | −0.560692 | ||||||||
\(334\) | 16.0519i | 0.878322i | ||||||||
\(335\) | − | 6.56846i | − | 0.358874i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.0358i | 0.873525i | 0.899577 | + | 0.436763i | \(0.143875\pi\) | ||||
−0.899577 | + | 0.436763i | \(0.856125\pi\) | |||||||
\(338\) | − | 10.8702i | − | 0.591263i | ||||||
\(339\) | − | 24.4920i | − | 1.33022i | ||||||
\(340\) | − | 16.7580i | − | 0.908830i | ||||||
\(341\) | −25.3291 | − | 12.7425i | −1.37165 | − | 0.690045i | ||||
\(342\) | − | 1.22447i | − | 0.0662119i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.58174 | −0.0852816 | ||||||||
\(345\) | 15.7594 | 0.848457 | ||||||||
\(346\) | 7.09477i | 0.381417i | ||||||||
\(347\) | − | 9.87094i | − | 0.529900i | −0.964262 | − | 0.264950i | \(-0.914645\pi\) | ||
0.964262 | − | 0.264950i | \(-0.0853554\pi\) | |||||||
\(348\) | 13.9258 | 0.746500 | ||||||||
\(349\) | −31.1871 | −1.66940 | −0.834702 | − | 0.550701i | \(-0.814360\pi\) | ||||
−0.834702 | + | 0.550701i | \(0.814360\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.2424i | 0.920330i | ||||||||
\(352\) | −2.96282 | − | 1.49053i | −0.157919 | − | 0.0794455i | ||||
\(353\) | − | 25.9682i | − | 1.38215i | −0.722783 | − | 0.691075i | \(-0.757138\pi\) | ||
0.722783 | − | 0.691075i | \(-0.242862\pi\) | |||||||
\(354\) | − | 19.3553i | − | 1.02872i | ||||||
\(355\) | − | 16.6865i | − | 0.885630i | ||||||
\(356\) | 16.1111i | 0.853889i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 24.9728i | − | 1.31985i | ||||||
\(359\) | 4.01067i | 0.211675i | 0.994383 | + | 0.105838i | \(0.0337524\pi\) | ||||
−0.994383 | + | 0.105838i | \(0.966248\pi\) | |||||||
\(360\) | −14.9318 | −0.786976 | ||||||||
\(361\) | −18.9674 | −0.998282 | ||||||||
\(362\) | 19.3579 | 1.01743 | ||||||||
\(363\) | −27.6190 | + | 20.5028i | −1.44962 | + | 1.07612i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 21.3160i | 1.11573i | ||||||||
\(366\) | 17.9060 | 0.935963 | ||||||||
\(367\) | 19.1851i | 1.00145i | 0.865605 | + | 0.500727i | \(0.166934\pi\) | ||||
−0.865605 | + | 0.500727i | \(0.833066\pi\) | |||||||
\(368\) | 2.28779 | 0.119259 | ||||||||
\(369\) | −48.1510 | −2.50664 | ||||||||
\(370\) | −3.32518 | −0.172868 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −26.7329 | −1.38604 | ||||||||
\(373\) | − | 21.0289i | − | 1.08884i | −0.838814 | − | 0.544419i | \(-0.816750\pi\) | ||
0.838814 | − | 0.544419i | \(-0.183250\pi\) | |||||||
\(374\) | −22.5391 | − | 11.3389i | −1.16547 | − | 0.586322i | ||||
\(375\) | 35.4572 | 1.83100 | ||||||||
\(376\) | 0.545357 | 0.0281247 | ||||||||
\(377\) | − | 6.49910i | − | 0.334721i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.7525 | 1.06599 | 0.532993 | − | 0.846120i | \(-0.321067\pi\) | ||||
0.532993 | + | 0.846120i | \(0.321067\pi\) | |||||||
\(380\) | − | 0.397940i | − | 0.0204139i | ||||||
\(381\) | 42.1218 | 2.15796 | ||||||||
\(382\) | 6.00000i | 0.306987i | ||||||||
\(383\) | 1.25606i | 0.0641816i | 0.999485 | + | 0.0320908i | \(0.0102166\pi\) | ||||
−0.999485 | + | 0.0320908i | \(0.989783\pi\) | |||||||
\(384\) | −3.12703 | −0.159576 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.6114 | −0.845497 | ||||||||
\(387\) | 10.7215i | 0.545006i | ||||||||
\(388\) | − | 11.3012i | − | 0.573729i | ||||||
\(389\) | −16.6479 | −0.844080 | −0.422040 | − | 0.906577i | \(-0.638686\pi\) | ||||
−0.422040 | + | 0.906577i | \(0.638686\pi\) | |||||||
\(390\) | 10.0528i | 0.509045i | ||||||||
\(391\) | 17.4040 | 0.880156 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 8.20726i | − | 0.414001i | ||||||
\(394\) | 20.6396 | 1.03981 | ||||||||
\(395\) | −15.2412 | −0.766870 | ||||||||
\(396\) | −10.1033 | + | 20.0830i | −0.507709 | + | 1.00921i | ||||
\(397\) | − | 14.1742i | − | 0.711384i | −0.934603 | − | 0.355692i | \(-0.884245\pi\) | ||
0.934603 | − | 0.355692i | \(-0.115755\pi\) | |||||||
\(398\) | −0.726003 | −0.0363912 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.147325 | 0.00736626 | ||||||||
\(401\) | −4.85270 | −0.242332 | −0.121166 | − | 0.992632i | \(-0.538663\pi\) | ||||
−0.121166 | + | 0.992632i | \(0.538663\pi\) | |||||||
\(402\) | −9.32407 | −0.465042 | ||||||||
\(403\) | 12.4761i | 0.621480i | ||||||||
\(404\) | −0.517716 | −0.0257573 | ||||||||
\(405\) | 36.5913i | 1.81824i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.24991 | + | 4.47229i | −0.111524 | + | 0.221683i | ||||
\(408\) | −23.7883 | −1.17770 | ||||||||
\(409\) | −10.6280 | −0.525523 | −0.262761 | − | 0.964861i | \(-0.584633\pi\) | ||||
−0.262761 | + | 0.964861i | \(0.584633\pi\) | |||||||
\(410\) | −15.6486 | −0.772827 | ||||||||
\(411\) | 27.2768i | 1.34547i | ||||||||
\(412\) | − | 2.88716i | − | 0.142240i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 15.5074i | − | 0.762146i | ||||||
\(415\) | 12.8702i | 0.631775i | ||||||||
\(416\) | 1.45937i | 0.0715516i | ||||||||
\(417\) | 12.7986i | 0.626752i | ||||||||
\(418\) | −0.535220 | − | 0.269257i | −0.0261785 | − | 0.0131698i | ||||
\(419\) | − | 11.3690i | − | 0.555410i | −0.960666 | − | 0.277705i | \(-0.910426\pi\) | ||
0.960666 | − | 0.277705i | \(-0.0895739\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.2464 | 1.32791 | 0.663955 | − | 0.747772i | \(-0.268877\pi\) | ||||
0.663955 | + | 0.747772i | \(0.268877\pi\) | |||||||
\(422\) | 10.2878 | 0.500802 | ||||||||
\(423\) | − | 3.69661i | − | 0.179735i | ||||||
\(424\) | − | 4.83444i | − | 0.234781i | ||||||
\(425\) | 1.12075 | 0.0543644 | ||||||||
\(426\) | −23.6869 | −1.14763 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 5.21959i | − | 0.252299i | ||||||
\(429\) | 13.5208 | + | 6.80203i | 0.652793 | + | 0.328405i | ||||
\(430\) | 3.48438i | 0.168032i | ||||||||
\(431\) | − | 15.2210i | − | 0.733169i | −0.930385 | − | 0.366584i | \(-0.880527\pi\) | ||
0.930385 | − | 0.366584i | \(-0.119473\pi\) | |||||||
\(432\) | 11.8149i | 0.568446i | ||||||||
\(433\) | − | 1.85534i | − | 0.0891619i | −0.999006 | − | 0.0445810i | \(-0.985805\pi\) | ||
0.999006 | − | 0.0445810i | \(-0.0141953\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 30.6768i | − | 1.47084i | ||||||
\(436\) | − | 10.0540i | − | 0.481501i | ||||||
\(437\) | 0.413279 | 0.0197698 | ||||||||
\(438\) | 30.2585 | 1.44581 | ||||||||
\(439\) | 32.9404 | 1.57216 | 0.786079 | − | 0.618126i | \(-0.212108\pi\) | ||||
0.786079 | + | 0.618126i | \(0.212108\pi\) | |||||||
\(440\) | −3.28346 | + | 6.52674i | −0.156533 | + | 0.311150i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.1019i | 0.528064i | ||||||||
\(443\) | −32.8613 | −1.56129 | −0.780643 | − | 0.624977i | \(-0.785108\pi\) | ||||
−0.780643 | + | 0.624977i | \(0.785108\pi\) | |||||||
\(444\) | 4.72016i | 0.224009i | ||||||||
\(445\) | 35.4909 | 1.68243 | ||||||||
\(446\) | −0.894768 | −0.0423685 | ||||||||
\(447\) | 58.1369 | 2.74978 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.62716 | 0.171176 | 0.0855880 | − | 0.996331i | \(-0.472723\pi\) | ||||
0.0855880 | + | 0.996331i | \(0.472723\pi\) | |||||||
\(450\) | − | 0.998618i | − | 0.0470753i | ||||||
\(451\) | −10.5883 | + | 21.0470i | −0.498581 | + | 0.991063i | ||||
\(452\) | −7.83235 | −0.368403 | ||||||||
\(453\) | −41.2909 | −1.94001 | ||||||||
\(454\) | − | 13.4848i | − | 0.632872i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.564883 | −0.0264531 | ||||||||
\(457\) | − | 2.73567i | − | 0.127969i | −0.997951 | − | 0.0639846i | \(-0.979619\pi\) | ||
0.997951 | − | 0.0639846i | \(-0.0203808\pi\) | |||||||
\(458\) | −4.88550 | −0.228285 | ||||||||
\(459\) | 89.8799i | 4.19523i | ||||||||
\(460\) | − | 5.03973i | − | 0.234978i | ||||||
\(461\) | 20.4439 | 0.952169 | 0.476084 | − | 0.879400i | \(-0.342056\pi\) | ||||
0.476084 | + | 0.879400i | \(0.342056\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.1701 | 1.40212 | 0.701062 | − | 0.713100i | \(-0.252710\pi\) | ||||
0.701062 | + | 0.713100i | \(0.252710\pi\) | |||||||
\(464\) | − | 4.45335i | − | 0.206742i | ||||||
\(465\) | 58.8893i | 2.73093i | ||||||||
\(466\) | 22.6606 | 1.04973 | ||||||||
\(467\) | − | 27.1722i | − | 1.25738i | −0.777656 | − | 0.628691i | \(-0.783591\pi\) | ||
0.777656 | − | 0.628691i | \(-0.216409\pi\) | |||||||
\(468\) | 9.89209 | 0.457262 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 1.20136i | − | 0.0554144i | ||||||
\(471\) | 18.0086 | 0.829793 | ||||||||
\(472\) | −6.18967 | −0.284903 | ||||||||
\(473\) | 4.68641 | + | 2.35763i | 0.215481 | + | 0.108404i | ||||
\(474\) | 21.6353i | 0.993740i | ||||||||
\(475\) | 0.0266136 | 0.00122112 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −32.7694 | −1.50041 | ||||||||
\(478\) | −25.2410 | −1.15449 | ||||||||
\(479\) | 21.6184 | 0.987770 | 0.493885 | − | 0.869527i | \(-0.335576\pi\) | ||||
0.493885 | + | 0.869527i | \(0.335576\pi\) | |||||||
\(480\) | 6.88847i | 0.314414i | ||||||||
\(481\) | 2.20288 | 0.100443 | ||||||||
\(482\) | 14.0669i | 0.640730i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.55664 | + | 8.83235i | 0.298029 | + | 0.401471i | ||||
\(485\) | −24.8951 | −1.13043 | ||||||||
\(486\) | 16.4973 | 0.748333 | ||||||||
\(487\) | 2.08573 | 0.0945135 | 0.0472567 | − | 0.998883i | \(-0.484952\pi\) | ||||
0.0472567 | + | 0.998883i | \(0.484952\pi\) | |||||||
\(488\) | − | 5.72621i | − | 0.259213i | ||||||
\(489\) | 16.6136i | 0.751291i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 2.47983i | − | 0.111913i | −0.998433 | − | 0.0559566i | \(-0.982179\pi\) | ||
0.998433 | − | 0.0559566i | \(-0.0178208\pi\) | |||||||
\(492\) | 22.2134i | 1.00146i | ||||||||
\(493\) | − | 33.8781i | − | 1.52579i | ||||||
\(494\) | 0.263629i | 0.0118612i | ||||||||
\(495\) | 44.2403 | + | 22.2563i | 1.98846 | + | 1.00035i | ||||
\(496\) | 8.54897i | 0.383860i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 18.2696 | 0.818678 | ||||||||
\(499\) | 15.3838 | 0.688672 | 0.344336 | − | 0.938846i | \(-0.388104\pi\) | ||||
0.344336 | + | 0.938846i | \(0.388104\pi\) | |||||||
\(500\) | − | 11.3389i | − | 0.507093i | ||||||
\(501\) | − | 50.1948i | − | 2.24254i | ||||||
\(502\) | 3.03720 | 0.135557 | ||||||||
\(503\) | 15.5714 | 0.694295 | 0.347147 | − | 0.937811i | \(-0.387150\pi\) | ||||
0.347147 | + | 0.937811i | \(0.387150\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.14047i | 0.0507501i | ||||||||
\(506\) | −6.77832 | − | 3.41002i | −0.301333 | − | 0.151594i | ||||
\(507\) | 33.9916i | 1.50962i | ||||||||
\(508\) | − | 13.4702i | − | 0.597644i | ||||||
\(509\) | 30.7550i | 1.36319i | 0.731729 | + | 0.681595i | \(0.238714\pi\) | ||||
−0.731729 | + | 0.681595i | \(0.761286\pi\) | |||||||
\(510\) | 52.4028i | 2.32043i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 2.13431i | 0.0942321i | ||||||||
\(514\) | 25.7683 | 1.13659 | ||||||||
\(515\) | −6.36006 | −0.280258 | ||||||||
\(516\) | 4.94614 | 0.217742 | ||||||||
\(517\) | −1.61580 | − | 0.812872i | −0.0710627 | − | 0.0357500i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 22.1856i | − | 0.973838i | ||||||
\(520\) | 3.21482 | 0.140979 | ||||||||
\(521\) | − | 3.69331i | − | 0.161807i | −0.996722 | − | 0.0809035i | \(-0.974219\pi\) | ||
0.996722 | − | 0.0809035i | \(-0.0257806\pi\) | |||||||
\(522\) | −30.1863 | −1.32122 | ||||||||
\(523\) | 29.2014 | 1.27689 | 0.638444 | − | 0.769669i | \(-0.279579\pi\) | ||||
0.638444 | + | 0.769669i | \(0.279579\pi\) | |||||||
\(524\) | −2.62462 | −0.114657 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.41002 | 0.279490 | ||||||||
\(527\) | 65.0348i | 2.83296i | ||||||||
\(528\) | 9.26484 | + | 4.66093i | 0.403200 | + | 0.202841i | ||||
\(529\) | −17.7660 | −0.772435 | ||||||||
\(530\) | −10.6497 | −0.462593 | ||||||||
\(531\) | 41.9556i | 1.82072i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.3669 | 0.449041 | ||||||||
\(534\) | − | 50.3800i | − | 2.18016i | ||||||
\(535\) | −11.4981 | −0.497107 | ||||||||
\(536\) | 2.98176i | 0.128793i | ||||||||
\(537\) | 78.0908i | 3.36987i | ||||||||
\(538\) | −2.74152 | −0.118195 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 26.0268 | 1.12002 | ||||||||
\(541\) | − | 16.1749i | − | 0.695411i | −0.937604 | − | 0.347706i | \(-0.886961\pi\) | ||
0.937604 | − | 0.347706i | \(-0.113039\pi\) | |||||||
\(542\) | − | 28.6002i | − | 1.22848i | ||||||
\(543\) | −60.5326 | −2.59770 | ||||||||
\(544\) | 7.60732i | 0.326161i | ||||||||
\(545\) | −22.1478 | −0.948708 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 34.0719i | − | 1.45681i | −0.685146 | − | 0.728405i | \(-0.740262\pi\) | ||
0.685146 | − | 0.728405i | \(-0.259738\pi\) | |||||||
\(548\) | 8.72291 | 0.372624 | ||||||||
\(549\) | −38.8141 | −1.65654 | ||||||||
\(550\) | −0.436499 | − | 0.219593i | −0.0186124 | − | 0.00936346i | ||||
\(551\) | − | 0.804477i | − | 0.0342719i | ||||||
\(552\) | −7.15399 | −0.304494 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 10.7683 | 0.457502 | ||||||||
\(555\) | 10.3979 | 0.441368 | ||||||||
\(556\) | 4.09291 | 0.173578 | ||||||||
\(557\) | − | 25.6864i | − | 1.08837i | −0.838966 | − | 0.544185i | \(-0.816839\pi\) | ||
0.838966 | − | 0.544185i | \(-0.183161\pi\) | |||||||
\(558\) | 57.9477 | 2.45312 | ||||||||
\(559\) | − | 2.30834i | − | 0.0976325i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 70.4806 | + | 35.4572i | 2.97569 | + | 1.49700i | ||||
\(562\) | −19.6289 | −0.827996 | ||||||||
\(563\) | −21.9366 | −0.924516 | −0.462258 | − | 0.886746i | \(-0.652961\pi\) | ||||
−0.462258 | + | 0.886746i | \(0.652961\pi\) | |||||||
\(564\) | −1.70535 | −0.0718082 | ||||||||
\(565\) | 17.2537i | 0.725870i | ||||||||
\(566\) | − | 10.6233i | − | 0.446529i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.57488i | 0.317835i | ||||||||
\(569\) | 2.56697i | 0.107613i | 0.998551 | + | 0.0538065i | \(0.0171354\pi\) | ||||
−0.998551 | + | 0.0538065i | \(0.982865\pi\) | |||||||
\(570\) | 1.24437i | 0.0521209i | ||||||||
\(571\) | 34.3092i | 1.43579i | 0.696149 | + | 0.717897i | \(0.254895\pi\) | ||||
−0.696149 | + | 0.717897i | \(0.745105\pi\) | |||||||
\(572\) | 2.17524 | − | 4.32386i | 0.0909512 | − | 0.180790i | ||||
\(573\) | − | 18.7622i | − | 0.783801i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.337049 | 0.0140559 | ||||||||
\(576\) | 6.77832 | 0.282430 | ||||||||
\(577\) | − | 20.6988i | − | 0.861701i | −0.902423 | − | 0.430851i | \(-0.858214\pi\) | ||
0.902423 | − | 0.430851i | \(-0.141786\pi\) | |||||||
\(578\) | 40.8713i | 1.70002i | ||||||||
\(579\) | 51.9443 | 2.15873 | ||||||||
\(580\) | −9.81020 | −0.407346 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 35.3391i | 1.46485i | ||||||||
\(583\) | −7.20587 | + | 14.3236i | −0.298437 | + | 0.593222i | ||||
\(584\) | − | 9.67644i | − | 0.400414i | ||||||
\(585\) | − | 21.7911i | − | 0.900950i | ||||||
\(586\) | − | 0.277651i | − | 0.0114697i | ||||||
\(587\) | 16.0435i | 0.662184i | 0.943598 | + | 0.331092i | \(0.107417\pi\) | ||||
−0.943598 | + | 0.331092i | \(0.892583\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.54433i | 0.0636331i | ||||||||
\(590\) | 13.6351i | 0.561348i | ||||||||
\(591\) | −64.5407 | −2.65485 | ||||||||
\(592\) | 1.50947 | 0.0620388 | ||||||||
\(593\) | −35.4872 | −1.45728 | −0.728641 | − | 0.684895i | \(-0.759848\pi\) | ||||
−0.728641 | + | 0.684895i | \(0.759848\pi\) | |||||||
\(594\) | 17.6105 | − | 35.0055i | 0.722568 | − | 1.43629i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 18.5917i | − | 0.761547i | ||||||
\(597\) | 2.27023 | 0.0929144 | ||||||||
\(598\) | 3.33874i | 0.136531i | ||||||||
\(599\) | 0.749386 | 0.0306191 | 0.0153095 | − | 0.999883i | \(-0.495127\pi\) | ||||
0.0153095 | + | 0.999883i | \(0.495127\pi\) | |||||||
\(600\) | −0.460691 | −0.0188076 | ||||||||
\(601\) | −18.5168 | −0.755317 | −0.377658 | − | 0.925945i | \(-0.623271\pi\) | ||||
−0.377658 | + | 0.925945i | \(0.623271\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 20.2114 | 0.823070 | ||||||||
\(604\) | 13.2045i | 0.537283i | ||||||||
\(605\) | 19.4566 | − | 14.4435i | 0.791023 | − | 0.587211i | ||||
\(606\) | 1.61891 | 0.0657639 | ||||||||
\(607\) | −36.9910 | −1.50142 | −0.750710 | − | 0.660632i | \(-0.770288\pi\) | ||||
−0.750710 | + | 0.660632i | \(0.770288\pi\) | |||||||
\(608\) | 0.180645i | 0.00732613i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.6141 | −0.510732 | ||||||||
\(611\) | 0.795879i | 0.0321978i | ||||||||
\(612\) | 51.5648 | 2.08439 | ||||||||
\(613\) | − | 3.22552i | − | 0.130277i | −0.997876 | − | 0.0651387i | \(-0.979251\pi\) | ||
0.997876 | − | 0.0651387i | \(-0.0207490\pi\) | |||||||
\(614\) | − | 6.41443i | − | 0.258865i | ||||||
\(615\) | 48.9335 | 1.97319 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.8351 | −0.436206 | −0.218103 | − | 0.975926i | \(-0.569987\pi\) | ||||
−0.218103 | + | 0.975926i | \(0.569987\pi\) | |||||||
\(618\) | 9.02823i | 0.363169i | ||||||||
\(619\) | 5.12834i | 0.206125i | 0.994675 | + | 0.103063i | \(0.0328642\pi\) | ||||
−0.994675 | + | 0.103063i | \(0.967136\pi\) | |||||||
\(620\) | 18.8324 | 0.756325 | ||||||||
\(621\) | 27.0301i | 1.08468i | ||||||||
\(622\) | 11.3024 | 0.453184 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 4.56350i | − | 0.182686i | ||||||
\(625\) | −24.2417 | −0.969667 | ||||||||
\(626\) | −16.4467 | −0.657341 | ||||||||
\(627\) | 1.67365 | + | 0.841976i | 0.0668391 | + | 0.0336253i | ||||
\(628\) | − | 5.75901i | − | 0.229810i | ||||||
\(629\) | 11.4830 | 0.457858 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.9567 | −1.19256 | −0.596278 | − | 0.802778i | \(-0.703354\pi\) | ||||
−0.596278 | + | 0.802778i | \(0.703354\pi\) | |||||||
\(632\) | 6.91879 | 0.275215 | ||||||||
\(633\) | −32.1702 | −1.27865 | ||||||||
\(634\) | − | 28.1910i | − | 1.11961i | ||||||
\(635\) | −29.6732 | −1.17755 | ||||||||
\(636\) | 15.1174i | 0.599445i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −6.63786 | + | 13.1945i | −0.262795 | + | 0.522375i | ||||
\(639\) | 51.3450 | 2.03118 | ||||||||
\(640\) | 2.20288 | 0.0870764 | ||||||||
\(641\) | 9.22690 | 0.364441 | 0.182220 | − | 0.983258i | \(-0.441672\pi\) | ||||
0.182220 | + | 0.983258i | \(0.441672\pi\) | |||||||
\(642\) | 16.3218i | 0.644171i | ||||||||
\(643\) | 1.79941i | 0.0709616i | 0.999370 | + | 0.0354808i | \(0.0112963\pi\) | ||||
−0.999370 | + | 0.0354808i | \(0.988704\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 10.8958i | − | 0.429020i | ||||||
\(646\) | 1.37423i | 0.0540682i | ||||||||
\(647\) | − | 40.7244i | − | 1.60104i | −0.599306 | − | 0.800520i | \(-0.704557\pi\) | ||
0.599306 | − | 0.800520i | \(-0.295443\pi\) | |||||||
\(648\) | − | 16.6107i | − | 0.652529i | ||||||
\(649\) | 18.3389 | + | 9.22589i | 0.719865 | + | 0.362148i | ||||
\(650\) | 0.215002i | 0.00843309i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.31289 | 0.208069 | ||||||||
\(653\) | −37.7384 | −1.47682 | −0.738408 | − | 0.674354i | \(-0.764422\pi\) | ||||
−0.738408 | + | 0.674354i | \(0.764422\pi\) | |||||||
\(654\) | 31.4393i | 1.22937i | ||||||||
\(655\) | 5.78171i | 0.225910i | ||||||||
\(656\) | 7.10368 | 0.277352 | ||||||||
\(657\) | −65.5900 | −2.55891 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 32.5997i | − | 1.26991i | −0.772551 | − | 0.634953i | \(-0.781019\pi\) | ||
0.772551 | − | 0.634953i | \(-0.218981\pi\) | |||||||
\(660\) | 10.2675 | − | 20.4093i | 0.399661 | − | 0.794432i | ||||
\(661\) | 12.6725i | 0.492902i | 0.969155 | + | 0.246451i | \(0.0792645\pi\) | ||||
−0.969155 | + | 0.246451i | \(0.920735\pi\) | |||||||
\(662\) | 19.1126i | 0.742832i | ||||||||
\(663\) | − | 34.7160i | − | 1.34826i | ||||||
\(664\) | − | 5.84246i | − | 0.226731i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − | 10.2317i | − | 0.396469i | ||||||
\(667\) | − | 10.1883i | − | 0.394494i | ||||||
\(668\) | −16.0519 | −0.621067 | ||||||||
\(669\) | 2.79797 | 0.108176 | ||||||||
\(670\) | 6.56846 | 0.253762 | ||||||||
\(671\) | −8.53508 | + | 16.9657i | −0.329493 | + | 0.654955i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1.20344i | − | 0.0463893i | −0.999731 | − | 0.0231947i | \(-0.992616\pi\) | ||
0.999731 | − | 0.0231947i | \(-0.00738375\pi\) | |||||||
\(674\) | −16.0358 | −0.617676 | ||||||||
\(675\) | 1.74064i | 0.0669971i | ||||||||
\(676\) | 10.8702 | 0.418086 | ||||||||
\(677\) | 26.3159 | 1.01140 | 0.505701 | − | 0.862709i | \(-0.331234\pi\) | ||||
0.505701 | + | 0.862709i | \(0.331234\pi\) | |||||||
\(678\) | 24.4920 | 0.940610 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 16.7580 | 0.642640 | ||||||||
\(681\) | 42.1673i | 1.61586i | ||||||||
\(682\) | 12.7425 | − | 25.3291i | 0.487936 | − | 0.969901i | ||||
\(683\) | 32.9274 | 1.25993 | 0.629966 | − | 0.776623i | \(-0.283069\pi\) | ||||
0.629966 | + | 0.776623i | \(0.283069\pi\) | |||||||
\(684\) | 1.22447 | 0.0468189 | ||||||||
\(685\) | − | 19.2155i | − | 0.734187i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.2771 | 0.582858 | ||||||||
\(688\) | − | 1.58174i | − | 0.0603032i | ||||||
\(689\) | 7.05524 | 0.268783 | ||||||||
\(690\) | 15.7594i | 0.599949i | ||||||||
\(691\) | − | 28.2336i | − | 1.07406i | −0.843565 | − | 0.537028i | \(-0.819547\pi\) | ||
0.843565 | − | 0.537028i | \(-0.180453\pi\) | |||||||
\(692\) | −7.09477 | −0.269703 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.87094 | 0.374696 | ||||||||
\(695\) | − | 9.01618i | − | 0.342003i | ||||||
\(696\) | 13.9258i | 0.527855i | ||||||||
\(697\) | 54.0400 | 2.04691 | ||||||||
\(698\) | − | 31.1871i | − | 1.18045i | ||||||
\(699\) | −70.8605 | −2.68019 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 24.2464i | − | 0.915775i | −0.889010 | − | 0.457888i | \(-0.848606\pi\) | ||
0.889010 | − | 0.457888i | \(-0.151394\pi\) | |||||||
\(702\) | −17.2424 | −0.650771 | ||||||||
\(703\) | 0.272679 | 0.0102843 | ||||||||
\(704\) | 1.49053 | − | 2.96282i | 0.0561765 | − | 0.111666i | ||||
\(705\) | 3.75668i | 0.141485i | ||||||||
\(706\) | 25.9682 | 0.977327 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 19.3553 | 0.727416 | ||||||||
\(709\) | 43.2699 | 1.62504 | 0.812518 | − | 0.582936i | \(-0.198096\pi\) | ||||
0.812518 | + | 0.582936i | \(0.198096\pi\) | |||||||
\(710\) | 16.6865 | 0.626235 | ||||||||
\(711\) | − | 46.8978i | − | 1.75880i | ||||||
\(712\) | −16.1111 | −0.603791 | ||||||||
\(713\) | 19.5583i | 0.732463i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.52494 | − | 4.79178i | −0.356213 | − | 0.179203i | ||||
\(716\) | 24.9728 | 0.933278 | ||||||||
\(717\) | 78.9293 | 2.94767 | ||||||||
\(718\) | −4.01067 | −0.149677 | ||||||||
\(719\) | − | 23.0095i | − | 0.858110i | −0.903278 | − | 0.429055i | \(-0.858847\pi\) | ||
0.903278 | − | 0.429055i | \(-0.141153\pi\) | |||||||
\(720\) | − | 14.9318i | − | 0.556476i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 18.9674i | − | 0.705892i | ||||||
\(723\) | − | 43.9876i | − | 1.63592i | ||||||
\(724\) | 19.3579i | 0.719429i | ||||||||
\(725\) | − | 0.656091i | − | 0.0243666i | ||||||
\(726\) | −20.5028 | − | 27.6190i | −0.760931 | − | 1.02504i | ||||
\(727\) | 39.3745i | 1.46032i | 0.683276 | + | 0.730160i | \(0.260555\pi\) | ||||
−0.683276 | + | 0.730160i | \(0.739445\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.75557 | −0.0650210 | ||||||||
\(730\) | −21.3160 | −0.788941 | ||||||||
\(731\) | − | 12.0328i | − | 0.445048i | ||||||
\(732\) | 17.9060i | 0.661826i | ||||||||
\(733\) | 8.18529 | 0.302331 | 0.151165 | − | 0.988509i | \(-0.451697\pi\) | ||||
0.151165 | + | 0.988509i | \(0.451697\pi\) | |||||||
\(734\) | −19.1851 | −0.708135 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.28779i | 0.0843291i | ||||||||
\(737\) | 4.44441 | − | 8.83444i | 0.163712 | − | 0.325421i | ||||
\(738\) | − | 48.1510i | − | 1.77246i | ||||||
\(739\) | − | 38.1924i | − | 1.40493i | −0.711718 | − | 0.702466i | \(-0.752082\pi\) | ||
0.711718 | − | 0.702466i | \(-0.247918\pi\) | |||||||
\(740\) | − | 3.32518i | − | 0.122236i | ||||||
\(741\) | − | 0.824375i | − | 0.0302842i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 27.3005i | − | 1.00156i | −0.865575 | − | 0.500779i | \(-0.833047\pi\) | ||
0.865575 | − | 0.500779i | \(-0.166953\pi\) | |||||||
\(744\) | − | 26.7329i | − | 0.980076i | ||||||
\(745\) | −40.9553 | −1.50049 | ||||||||
\(746\) | 21.0289 | 0.769924 | ||||||||
\(747\) | −39.6021 | −1.44896 | ||||||||
\(748\) | 11.3389 | − | 22.5391i | 0.414592 | − | 0.824112i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 35.4572i | 1.29471i | ||||||||
\(751\) | −2.23167 | −0.0814349 | −0.0407175 | − | 0.999171i | \(-0.512964\pi\) | ||||
−0.0407175 | + | 0.999171i | \(0.512964\pi\) | |||||||
\(752\) | 0.545357i | 0.0198871i | ||||||||
\(753\) | −9.49742 | −0.346105 | ||||||||
\(754\) | 6.49910 | 0.236683 | ||||||||
\(755\) | 29.0879 | 1.05862 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.6709 | −0.605913 | −0.302956 | − | 0.953004i | \(-0.597974\pi\) | ||||
−0.302956 | + | 0.953004i | \(0.597974\pi\) | |||||||
\(758\) | 20.7525i | 0.753766i | ||||||||
\(759\) | 21.1960 | + | 10.6632i | 0.769367 | + | 0.387051i | ||||
\(760\) | 0.397940 | 0.0144348 | ||||||||
\(761\) | −45.6321 | −1.65416 | −0.827081 | − | 0.562083i | \(-0.810000\pi\) | ||||
−0.827081 | + | 0.562083i | \(0.810000\pi\) | |||||||
\(762\) | 42.1218i | 1.52591i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −6.00000 | −0.217072 | ||||||||
\(765\) | − | 113.591i | − | 4.10689i | ||||||
\(766\) | −1.25606 | −0.0453832 | ||||||||
\(767\) | − | 9.03303i | − | 0.326164i | ||||||
\(768\) | − | 3.12703i | − | 0.112837i | ||||||
\(769\) | 51.3570 | 1.85198 | 0.925991 | − | 0.377546i | \(-0.123232\pi\) | ||||
0.925991 | + | 0.377546i | \(0.123232\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −80.5784 | −2.90196 | ||||||||
\(772\) | − | 16.6114i | − | 0.597857i | ||||||
\(773\) | − | 21.8478i | − | 0.785812i | −0.919579 | − | 0.392906i | \(-0.871470\pi\) | ||
0.919579 | − | 0.392906i | \(-0.128530\pi\) | |||||||
\(774\) | −10.7215 | −0.385377 | ||||||||
\(775\) | 1.25948i | 0.0452418i | ||||||||
\(776\) | 11.3012 | 0.405688 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 16.6479i | − | 0.596854i | ||||||
\(779\) | 1.28325 | 0.0459771 | ||||||||
\(780\) | −10.0528 | −0.359949 | ||||||||
\(781\) | 11.2906 | − | 22.4430i | 0.404009 | − | 0.803075i | ||||
\(782\) | 17.4040i | 0.622364i | ||||||||
\(783\) | 52.6160 | 1.88034 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.6864 | −0.452797 | ||||||||
\(786\) | 8.20726 | 0.292743 | ||||||||
\(787\) | −20.4402 | −0.728613 | −0.364307 | − | 0.931279i | \(-0.618694\pi\) | ||||
−0.364307 | + | 0.931279i | \(0.618694\pi\) | |||||||
\(788\) | 20.6396i | 0.735256i | ||||||||
\(789\) | −20.0443 | −0.713597 | ||||||||
\(790\) | − | 15.2412i | − | 0.542259i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −20.0830 | − | 10.1033i | −0.713617 | − | 0.359005i | ||||
\(793\) | 8.35667 | 0.296754 | ||||||||
\(794\) | 14.1742 | 0.503025 | ||||||||
\(795\) | 33.3019 | 1.18110 | ||||||||
\(796\) | − | 0.726003i | − | 0.0257325i | ||||||
\(797\) | 6.09214i | 0.215795i | 0.994162 | + | 0.107897i | \(0.0344118\pi\) | ||||
−0.994162 | + | 0.107897i | \(0.965588\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.14871i | 0.146771i | ||||||||
\(800\) | 0.147325i | 0.00520873i | ||||||||
\(801\) | 109.207i | 3.85862i | ||||||||
\(802\) | − | 4.85270i | − | 0.171355i | ||||||
\(803\) | −14.4230 | + | 28.6696i | −0.508977 | + | 1.01173i | ||||
\(804\) | − | 9.32407i | − | 0.328834i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12.4761 | −0.439453 | ||||||||
\(807\) | 8.57282 | 0.301777 | ||||||||
\(808\) | − | 0.517716i | − | 0.0182132i | ||||||
\(809\) | 34.7780i | 1.22273i | 0.791349 | + | 0.611364i | \(0.209379\pi\) | ||||
−0.791349 | + | 0.611364i | \(0.790621\pi\) | |||||||
\(810\) | −36.5913 | −1.28569 | ||||||||
\(811\) | −26.6602 | −0.936167 | −0.468083 | − | 0.883684i | \(-0.655055\pi\) | ||||
−0.468083 | + | 0.883684i | \(0.655055\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 89.4337i | 3.13658i | ||||||||
\(814\) | −4.47229 | − | 2.24991i | −0.156754 | − | 0.0788593i | ||||
\(815\) | − | 11.7036i | − | 0.409961i | ||||||
\(816\) | − | 23.7883i | − | 0.832758i | ||||||
\(817\) | − | 0.285733i | − | 0.00999655i | ||||||
\(818\) | − | 10.6280i | − | 0.371601i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 15.6486i | − | 0.546471i | ||||||
\(821\) | 12.7504i | 0.444993i | 0.974933 | + | 0.222497i | \(0.0714206\pi\) | ||||
−0.974933 | + | 0.222497i | \(0.928579\pi\) | |||||||
\(822\) | −27.2768 | −0.951388 | ||||||||
\(823\) | −15.8764 | −0.553416 | −0.276708 | − | 0.960954i | \(-0.589243\pi\) | ||||
−0.276708 | + | 0.960954i | \(0.589243\pi\) | |||||||
\(824\) | 2.88716 | 0.100579 | ||||||||
\(825\) | 1.36494 | + | 0.686673i | 0.0475213 | + | 0.0239069i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.9639i | 1.25059i | 0.780390 | + | 0.625293i | \(0.215021\pi\) | ||||
−0.780390 | + | 0.625293i | \(0.784979\pi\) | |||||||
\(828\) | 15.5074 | 0.538919 | ||||||||
\(829\) | − | 35.9072i | − | 1.24711i | −0.781780 | − | 0.623555i | \(-0.785688\pi\) | ||
0.781780 | − | 0.623555i | \(-0.214312\pi\) | |||||||
\(830\) | −12.8702 | −0.446732 | ||||||||
\(831\) | −33.6729 | −1.16810 | ||||||||
\(832\) | −1.45937 | −0.0505946 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −12.7986 | −0.443181 | ||||||||
\(835\) | 35.3604i | 1.22370i | ||||||||
\(836\) | 0.269257 | − | 0.535220i | 0.00931246 | − | 0.0185110i | ||||
\(837\) | −101.005 | −3.49126 | ||||||||
\(838\) | 11.3690 | 0.392735 | ||||||||
\(839\) | − | 39.5137i | − | 1.36416i | −0.731276 | − | 0.682081i | \(-0.761075\pi\) | ||
0.731276 | − | 0.682081i | \(-0.238925\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.16765 | 0.316126 | ||||||||
\(842\) | 27.2464i | 0.938974i | ||||||||
\(843\) | 61.3802 | 2.11405 | ||||||||
\(844\) | 10.2878i | 0.354120i | ||||||||
\(845\) | − | 23.9458i | − | 0.823761i | ||||||
\(846\) | 3.69661 | 0.127092 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.83444 | 0.166015 | ||||||||
\(849\) | 33.2193i | 1.14008i | ||||||||
\(850\) | 1.12075i | 0.0384414i | ||||||||
\(851\) | 3.45335 | 0.118379 | ||||||||
\(852\) | − | 23.6869i | − | 0.811499i | ||||||
\(853\) | 8.92246 | 0.305499 | 0.152750 | − | 0.988265i | \(-0.451187\pi\) | ||||
0.152750 | + | 0.988265i | \(0.451187\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 2.69736i | − | 0.0922479i | ||||||
\(856\) | 5.21959 | 0.178402 | ||||||||
\(857\) | −8.74093 | −0.298584 | −0.149292 | − | 0.988793i | \(-0.547700\pi\) | ||||
−0.149292 | + | 0.988793i | \(0.547700\pi\) | |||||||
\(858\) | −6.80203 | + | 13.5208i | −0.232218 | + | 0.461594i | ||||
\(859\) | − | 29.7711i | − | 1.01578i | −0.861423 | − | 0.507888i | \(-0.830426\pi\) | ||
0.861423 | − | 0.507888i | \(-0.169574\pi\) | |||||||
\(860\) | −3.48438 | −0.118816 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.2210 | 0.518428 | ||||||||
\(863\) | 22.9728 | 0.782005 | 0.391002 | − | 0.920390i | \(-0.372128\pi\) | ||||
0.391002 | + | 0.920390i | \(0.372128\pi\) | |||||||
\(864\) | −11.8149 | −0.401952 | ||||||||
\(865\) | 15.6289i | 0.531399i | ||||||||
\(866\) | 1.85534 | 0.0630470 | ||||||||
\(867\) | − | 127.806i | − | 4.34051i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20.4991 | − | 10.3127i | −0.695386 | − | 0.349833i | ||||
\(870\) | 30.6768 | 1.04004 | ||||||||
\(871\) | −4.35150 | −0.147445 | ||||||||
\(872\) | 10.0540 | 0.340472 | ||||||||
\(873\) | − | 76.6029i | − | 2.59261i | ||||||
\(874\) | 0.413279i | 0.0139794i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 30.2585i | 1.02234i | ||||||||
\(877\) | − | 33.2451i | − | 1.12261i | −0.827610 | − | 0.561303i | \(-0.810300\pi\) | ||
0.827610 | − | 0.561303i | \(-0.189700\pi\) | |||||||
\(878\) | 32.9404i | 1.11168i | ||||||||
\(879\) | 0.868224i | 0.0292845i | ||||||||
\(880\) | −6.52674 | − | 3.28346i | −0.220016 | − | 0.110685i | ||||
\(881\) | − | 2.73248i | − | 0.0920594i | −0.998940 | − | 0.0460297i | \(-0.985343\pi\) | ||
0.998940 | − | 0.0460297i | \(-0.0146569\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.7473 | −0.664550 | −0.332275 | − | 0.943183i | \(-0.607816\pi\) | ||||
−0.332275 | + | 0.943183i | \(0.607816\pi\) | |||||||
\(884\) | −11.1019 | −0.373398 | ||||||||
\(885\) | − | 42.6373i | − | 1.43324i | ||||||
\(886\) | − | 32.8613i | − | 1.10400i | ||||||
\(887\) | 24.4620 | 0.821353 | 0.410676 | − | 0.911781i | \(-0.365293\pi\) | ||||
0.410676 | + | 0.911781i | \(0.365293\pi\) | |||||||
\(888\) | −4.72016 | −0.158398 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 35.4909i | 1.18966i | ||||||||
\(891\) | −24.7587 | + | 49.2145i | −0.829448 | + | 1.64875i | ||||
\(892\) | − | 0.894768i | − | 0.0299590i | ||||||
\(893\) | 0.0985163i | 0.00329672i | ||||||||
\(894\) | 58.1369i | 1.94439i | ||||||||
\(895\) | − | 55.0121i | − | 1.83885i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 10.4403i | − | 0.348593i | ||||||
\(898\) | 3.62716i | 0.121040i | ||||||||
\(899\) | 38.0716 | 1.26976 | ||||||||
\(900\) | 0.998618 | 0.0332873 | ||||||||
\(901\) | 36.7771 | 1.22522 | ||||||||
\(902\) | −21.0470 | − | 10.5883i | −0.700787 | − | 0.352550i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 7.83235i | − | 0.260500i | ||||||
\(905\) | 42.6430 | 1.41750 | ||||||||
\(906\) | − | 41.2909i | − | 1.37180i | ||||||
\(907\) | −44.6217 | −1.48164 | −0.740820 | − | 0.671703i | \(-0.765563\pi\) | ||||
−0.740820 | + | 0.671703i | \(0.765563\pi\) | |||||||
\(908\) | 13.4848 | 0.447508 | ||||||||
\(909\) | −3.50925 | −0.116394 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.0868 | 1.22874 | 0.614370 | − | 0.789018i | \(-0.289410\pi\) | ||||
0.614370 | + | 0.789018i | \(0.289410\pi\) | |||||||
\(912\) | − | 0.564883i | − | 0.0187052i | ||||||
\(913\) | −8.70836 | + | 17.3102i | −0.288205 | + | 0.572883i | ||||
\(914\) | 2.73567 | 0.0904878 | ||||||||
\(915\) | 39.4448 | 1.30401 | ||||||||
\(916\) | − | 4.88550i | − | 0.161422i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −89.8799 | −2.96648 | ||||||||
\(919\) | 50.9873i | 1.68192i | 0.541100 | + | 0.840958i | \(0.318008\pi\) | ||||
−0.541100 | + | 0.840958i | \(0.681992\pi\) | |||||||
\(920\) | 5.03973 | 0.166155 | ||||||||
\(921\) | 20.0581i | 0.660938i | ||||||||
\(922\) | 20.4439i | 0.673285i | ||||||||
\(923\) | −11.0546 | −0.363865 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.222383 | 0.00731191 | ||||||||
\(926\) | 30.1701i | 0.991451i | ||||||||
\(927\) | − | 19.5701i | − | 0.642766i | ||||||
\(928\) | 4.45335 | 0.146188 | ||||||||
\(929\) | − | 12.1898i | − | 0.399934i | −0.979803 | − | 0.199967i | \(-0.935917\pi\) | ||
0.979803 | − | 0.199967i | \(-0.0640834\pi\) | |||||||
\(930\) | −58.8893 | −1.93106 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 22.6606i | 0.742274i | ||||||||
\(933\) | −35.3429 | −1.15707 | ||||||||
\(934\) | 27.1722 | 0.889103 | ||||||||
\(935\) | −49.6510 | − | 24.9783i | −1.62376 | − | 0.816878i | ||||
\(936\) | 9.89209i | 0.323333i | ||||||||
\(937\) | −17.0188 | −0.555979 | −0.277990 | − | 0.960584i | \(-0.589668\pi\) | ||||
−0.277990 | + | 0.960584i | \(0.589668\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 51.4292 | 1.67833 | ||||||||
\(940\) | 1.20136 | 0.0391839 | ||||||||
\(941\) | −13.5983 | −0.443292 | −0.221646 | − | 0.975127i | \(-0.571143\pi\) | ||||
−0.221646 | + | 0.975127i | \(0.571143\pi\) | |||||||
\(942\) | 18.0086i | 0.586752i | ||||||||
\(943\) | 16.2517 | 0.529230 | ||||||||
\(944\) | − | 6.18967i | − | 0.201457i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.35763 | + | 4.68641i | −0.0766531 | + | 0.152368i | ||||
\(947\) | −33.0849 | −1.07512 | −0.537558 | − | 0.843227i | \(-0.680653\pi\) | ||||
−0.537558 | + | 0.843227i | \(0.680653\pi\) | |||||||
\(948\) | −21.6353 | −0.702681 | ||||||||
\(949\) | 14.1215 | 0.458404 | ||||||||
\(950\) | 0.0266136i | 0.000863460i | ||||||||
\(951\) | 88.1542i | 2.85860i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.427553i | 0.0138498i | 0.999976 | + | 0.00692490i | \(0.00220428\pi\) | ||||
−0.999976 | + | 0.00692490i | \(0.997796\pi\) | |||||||
\(954\) | − | 32.7694i | − | 1.06095i | ||||||
\(955\) | 13.2173i | 0.427701i | ||||||||
\(956\) | − | 25.2410i | − | 0.816351i | ||||||
\(957\) | 20.7568 | − | 41.2596i | 0.670971 | − | 1.33373i | ||||
\(958\) | 21.6184i | 0.698459i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −6.88847 | −0.222324 | ||||||||
\(961\) | −42.0849 | −1.35758 | ||||||||
\(962\) | 2.20288i | 0.0710237i | ||||||||
\(963\) | − | 35.3801i | − | 1.14011i | ||||||
\(964\) | −14.0669 | −0.453064 | ||||||||
\(965\) | −36.5928 | −1.17797 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.75935i | 0.217366i | 0.994076 | + | 0.108683i | \(0.0346634\pi\) | ||||
−0.994076 | + | 0.108683i | \(0.965337\pi\) | |||||||
\(968\) | −8.83235 | + | 6.55664i | −0.283883 | + | 0.210738i | ||||
\(969\) | − | 4.29725i | − | 0.138047i | ||||||
\(970\) | − | 24.8951i | − | 0.799333i | ||||||
\(971\) | − | 21.4878i | − | 0.689575i | −0.938681 | − | 0.344787i | \(-0.887951\pi\) | ||
0.938681 | − | 0.344787i | \(-0.112049\pi\) | |||||||
\(972\) | 16.4973i | 0.529151i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.08573i | 0.0668311i | ||||||||
\(975\) | − | 0.672319i | − | 0.0215314i | ||||||
\(976\) | 5.72621 | 0.183291 | ||||||||
\(977\) | 43.2933 | 1.38507 | 0.692537 | − | 0.721382i | \(-0.256493\pi\) | ||||
0.692537 | + | 0.721382i | \(0.256493\pi\) | |||||||
\(978\) | −16.6136 | −0.531243 | ||||||||
\(979\) | 47.7345 | + | 24.0141i | 1.52560 | + | 0.767495i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 68.1495i | − | 2.17584i | ||||||
\(982\) | 2.47983 | 0.0791346 | ||||||||
\(983\) | 20.9608i | 0.668545i | 0.942476 | + | 0.334273i | \(0.108491\pi\) | ||||
−0.942476 | + | 0.334273i | \(0.891509\pi\) | |||||||
\(984\) | −22.2134 | −0.708139 | ||||||||
\(985\) | 45.4666 | 1.44868 | ||||||||
\(986\) | 33.8781 | 1.07890 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.263629 | −0.00838715 | ||||||||
\(989\) | − | 3.61869i | − | 0.115068i | ||||||
\(990\) | −22.2563 | + | 44.2403i | −0.707352 | + | 1.40605i | ||||
\(991\) | 38.5404 | 1.22428 | 0.612138 | − | 0.790751i | \(-0.290310\pi\) | ||||
0.612138 | + | 0.790751i | \(0.290310\pi\) | |||||||
\(992\) | −8.54897 | −0.271430 | ||||||||
\(993\) | − | 59.7656i | − | 1.89660i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.59930 | −0.0507011 | ||||||||
\(996\) | 18.2696i | 0.578893i | ||||||||
\(997\) | 19.4465 | 0.615876 | 0.307938 | − | 0.951406i | \(-0.400361\pi\) | ||||
0.307938 | + | 0.951406i | \(0.400361\pi\) | |||||||
\(998\) | 15.3838i | 0.486965i | ||||||||
\(999\) | 17.8343i | 0.564252i |
(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 | 1078.2.c.b.1077.9 | 16 | ||
7.2 | even | 3 | 1078.2.i.c.1011.8 | 16 | |||
7.3 | odd | 6 | 1078.2.i.c.901.4 | 16 | |||
7.4 | even | 3 | 154.2.i.a.131.1 | yes | 16 | ||
7.5 | odd | 6 | 154.2.i.a.87.5 | yes | 16 | ||
7.6 | odd | 2 | inner | 1078.2.c.b.1077.16 | 16 | ||
11.10 | odd | 2 | inner | 1078.2.c.b.1077.1 | 16 | ||
21.5 | even | 6 | 1386.2.bk.c.703.3 | 16 | |||
21.11 | odd | 6 | 1386.2.bk.c.901.7 | 16 | |||
28.11 | odd | 6 | 1232.2.bn.b.593.7 | 16 | |||
28.19 | even | 6 | 1232.2.bn.b.241.8 | 16 | |||
77.10 | even | 6 | 1078.2.i.c.901.8 | 16 | |||
77.32 | odd | 6 | 154.2.i.a.131.5 | yes | 16 | ||
77.54 | even | 6 | 154.2.i.a.87.1 | ✓ | 16 | ||
77.65 | odd | 6 | 1078.2.i.c.1011.4 | 16 | |||
77.76 | even | 2 | inner | 1078.2.c.b.1077.8 | 16 | ||
231.32 | even | 6 | 1386.2.bk.c.901.3 | 16 | |||
231.131 | odd | 6 | 1386.2.bk.c.703.7 | 16 | |||
308.131 | odd | 6 | 1232.2.bn.b.241.7 | 16 | |||
308.263 | even | 6 | 1232.2.bn.b.593.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.i.a.87.1 | ✓ | 16 | 77.54 | even | 6 | ||
154.2.i.a.87.5 | yes | 16 | 7.5 | odd | 6 | ||
154.2.i.a.131.1 | yes | 16 | 7.4 | even | 3 | ||
154.2.i.a.131.5 | yes | 16 | 77.32 | odd | 6 | ||
1078.2.c.b.1077.1 | 16 | 11.10 | odd | 2 | inner | ||
1078.2.c.b.1077.8 | 16 | 77.76 | even | 2 | inner | ||
1078.2.c.b.1077.9 | 16 | 1.1 | even | 1 | trivial | ||
1078.2.c.b.1077.16 | 16 | 7.6 | odd | 2 | inner | ||
1078.2.i.c.901.4 | 16 | 7.3 | odd | 6 | |||
1078.2.i.c.901.8 | 16 | 77.10 | even | 6 | |||
1078.2.i.c.1011.4 | 16 | 77.65 | odd | 6 | |||
1078.2.i.c.1011.8 | 16 | 7.2 | even | 3 | |||
1232.2.bn.b.241.7 | 16 | 308.131 | odd | 6 | |||
1232.2.bn.b.241.8 | 16 | 28.19 | even | 6 | |||
1232.2.bn.b.593.7 | 16 | 28.11 | odd | 6 | |||
1232.2.bn.b.593.8 | 16 | 308.263 | even | 6 | |||
1386.2.bk.c.703.3 | 16 | 21.5 | even | 6 | |||
1386.2.bk.c.703.7 | 16 | 231.131 | odd | 6 | |||
1386.2.bk.c.901.3 | 16 | 231.32 | even | 6 | |||
1386.2.bk.c.901.7 | 16 | 21.11 | odd | 6 |