Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3850,2,Mod(1849,3850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3850, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("3850.1849");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3850.c (of order \(2\), degree \(1\), not 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: | \(30.7424047782\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 770) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1849.4 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3850.1849 |
Dual form | 3850.2.c.x.1849.1 |
$q$-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 \(\left(\mathbb{Z}/3850\mathbb{Z}\right)^\times\).
\(n\) | \(1751\) | \(2201\) | \(2927\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0.732051i | 0.422650i | 0.977416 | + | 0.211325i | \(0.0677778\pi\) | ||||
−0.977416 | + | 0.211325i | \(0.932222\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.732051 | −0.298858 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 2.46410 | 0.821367 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | − 0.732051i | − 0.211325i | ||||||||
\(13\) | − 5.46410i | − 1.51547i | −0.652563 | − | 0.757735i | \(-0.726306\pi\) | ||||
0.652563 | − | 0.757735i | \(-0.273694\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.46410i | 0.840168i | 0.907485 | + | 0.420084i | \(0.137999\pi\) | ||||
−0.907485 | + | 0.420084i | \(0.862001\pi\) | |||||||
\(18\) | 2.46410i | 0.580794i | ||||||||
\(19\) | −3.26795 | −0.749719 | −0.374859 | − | 0.927082i | \(-0.622309\pi\) | ||||
−0.374859 | + | 0.927082i | \(0.622309\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.732051 | −0.159747 | ||||||||
\(22\) | 1.00000i | 0.213201i | ||||||||
\(23\) | − 2.19615i | − 0.457929i | −0.973435 | − | 0.228965i | \(-0.926466\pi\) | ||||
0.973435 | − | 0.228965i | \(-0.0735340\pi\) | |||||||
\(24\) | 0.732051 | 0.149429 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.46410 | 1.07160 | ||||||||
\(27\) | 4.00000i | 0.769800i | ||||||||
\(28\) | − 1.00000i | − 0.188982i | ||||||||
\(29\) | 1.26795 | 0.235452 | 0.117726 | − | 0.993046i | \(-0.462440\pi\) | ||||
0.117726 | + | 0.993046i | \(0.462440\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0.732051i | 0.127434i | ||||||||
\(34\) | −3.46410 | −0.594089 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.46410 | −0.410684 | ||||||||
\(37\) | − 2.73205i | − 0.449146i | −0.974457 | − | 0.224573i | \(-0.927901\pi\) | ||||
0.974457 | − | 0.224573i | \(-0.0720988\pi\) | |||||||
\(38\) | − 3.26795i | − 0.530131i | ||||||||
\(39\) | 4.00000 | 0.640513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.19615 | 1.28002 | 0.640012 | − | 0.768365i | \(-0.278929\pi\) | ||||
0.640012 | + | 0.768365i | \(0.278929\pi\) | |||||||
\(42\) | − 0.732051i | − 0.112958i | ||||||||
\(43\) | − 2.00000i | − 0.304997i | −0.988304 | − | 0.152499i | \(-0.951268\pi\) | ||||
0.988304 | − | 0.152499i | \(-0.0487319\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.19615 | 0.323805 | ||||||||
\(47\) | − 6.92820i | − 1.01058i | −0.862949 | − | 0.505291i | \(-0.831385\pi\) | ||||
0.862949 | − | 0.505291i | \(-0.168615\pi\) | |||||||
\(48\) | 0.732051i | 0.105662i | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.53590 | −0.355097 | ||||||||
\(52\) | 5.46410i | 0.757735i | ||||||||
\(53\) | 10.7321i | 1.47416i | 0.675805 | + | 0.737080i | \(0.263796\pi\) | ||||
−0.675805 | + | 0.737080i | \(0.736204\pi\) | |||||||
\(54\) | −4.00000 | −0.544331 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | − 2.39230i | − 0.316869i | ||||||||
\(58\) | 1.26795i | 0.166490i | ||||||||
\(59\) | 6.92820 | 0.901975 | 0.450988 | − | 0.892530i | \(-0.351072\pi\) | ||||
0.450988 | + | 0.892530i | \(0.351072\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.92820 | 1.14314 | 0.571570 | − | 0.820554i | \(-0.306335\pi\) | ||||
0.571570 | + | 0.820554i | \(0.306335\pi\) | |||||||
\(62\) | 2.00000i | 0.254000i | ||||||||
\(63\) | 2.46410i | 0.310448i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.732051 | −0.0901092 | ||||||||
\(67\) | − 4.00000i | − 0.488678i | −0.969690 | − | 0.244339i | \(-0.921429\pi\) | ||||
0.969690 | − | 0.244339i | \(-0.0785709\pi\) | |||||||
\(68\) | − 3.46410i | − 0.420084i | ||||||||
\(69\) | 1.60770 | 0.193544 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.53590 | 0.300956 | 0.150478 | − | 0.988613i | \(-0.451919\pi\) | ||||
0.150478 | + | 0.988613i | \(0.451919\pi\) | |||||||
\(72\) | − 2.46410i | − 0.290397i | ||||||||
\(73\) | − 6.39230i | − 0.748163i | −0.927396 | − | 0.374081i | \(-0.877958\pi\) | ||||
0.927396 | − | 0.374081i | \(-0.122042\pi\) | |||||||
\(74\) | 2.73205 | 0.317594 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.26795 | 0.374859 | ||||||||
\(77\) | 1.00000i | 0.113961i | ||||||||
\(78\) | 4.00000i | 0.452911i | ||||||||
\(79\) | 1.80385 | 0.202949 | 0.101474 | − | 0.994838i | \(-0.467644\pi\) | ||||
0.101474 | + | 0.994838i | \(0.467644\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.46410 | 0.496011 | ||||||||
\(82\) | 8.19615i | 0.905114i | ||||||||
\(83\) | − 4.39230i | − 0.482118i | −0.970510 | − | 0.241059i | \(-0.922505\pi\) | ||||
0.970510 | − | 0.241059i | \(-0.0774947\pi\) | |||||||
\(84\) | 0.732051 | 0.0798733 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.00000 | 0.215666 | ||||||||
\(87\) | 0.928203i | 0.0995138i | ||||||||
\(88\) | − 1.00000i | − 0.106600i | ||||||||
\(89\) | 3.46410 | 0.367194 | 0.183597 | − | 0.983002i | \(-0.441226\pi\) | ||||
0.183597 | + | 0.983002i | \(0.441226\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.46410 | 0.572793 | ||||||||
\(92\) | 2.19615i | 0.228965i | ||||||||
\(93\) | 1.46410i | 0.151820i | ||||||||
\(94\) | 6.92820 | 0.714590 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.732051 | −0.0747146 | ||||||||
\(97\) | − 16.5885i | − 1.68430i | −0.539241 | − | 0.842151i | \(-0.681289\pi\) | ||||
0.539241 | − | 0.842151i | \(-0.318711\pi\) | |||||||
\(98\) | − 1.00000i | − 0.101015i | ||||||||
\(99\) | 2.46410 | 0.247652 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 19.8564 | 1.97579 | 0.987893 | − | 0.155136i | \(-0.0495815\pi\) | ||||
0.987893 | + | 0.155136i | \(0.0495815\pi\) | |||||||
\(102\) | − 2.53590i | − 0.251091i | ||||||||
\(103\) | 8.39230i | 0.826918i | 0.910523 | + | 0.413459i | \(0.135680\pi\) | ||||
−0.910523 | + | 0.413459i | \(0.864320\pi\) | |||||||
\(104\) | −5.46410 | −0.535799 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.7321 | −1.04239 | ||||||||
\(107\) | − 19.8564i | − 1.91959i | −0.280700 | − | 0.959796i | \(-0.590567\pi\) | ||||
0.280700 | − | 0.959796i | \(-0.409433\pi\) | |||||||
\(108\) | − 4.00000i | − 0.384900i | ||||||||
\(109\) | −1.66025 | −0.159023 | −0.0795117 | − | 0.996834i | \(-0.525336\pi\) | ||||
−0.0795117 | + | 0.996834i | \(0.525336\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.00000 | 0.189832 | ||||||||
\(112\) | 1.00000i | 0.0944911i | ||||||||
\(113\) | 19.8564i | 1.86793i | 0.357360 | + | 0.933967i | \(0.383677\pi\) | ||||
−0.357360 | + | 0.933967i | \(0.616323\pi\) | |||||||
\(114\) | 2.39230 | 0.224060 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.26795 | −0.117726 | ||||||||
\(117\) | − 13.4641i | − 1.24476i | ||||||||
\(118\) | 6.92820i | 0.637793i | ||||||||
\(119\) | −3.46410 | −0.317554 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 8.92820i | 0.808322i | ||||||||
\(123\) | 6.00000i | 0.541002i | ||||||||
\(124\) | −2.00000 | −0.179605 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.46410 | −0.219520 | ||||||||
\(127\) | 14.9282i | 1.32466i | 0.749211 | + | 0.662332i | \(0.230433\pi\) | ||||
−0.749211 | + | 0.662332i | \(0.769567\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | 1.46410 | 0.128907 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.6603 | −1.01876 | −0.509381 | − | 0.860541i | \(-0.670125\pi\) | ||||
−0.509381 | + | 0.860541i | \(0.670125\pi\) | |||||||
\(132\) | − 0.732051i | − 0.0637168i | ||||||||
\(133\) | − 3.26795i | − 0.283367i | ||||||||
\(134\) | 4.00000 | 0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.46410 | 0.297044 | ||||||||
\(137\) | 12.9282i | 1.10453i | 0.833668 | + | 0.552265i | \(0.186237\pi\) | ||||
−0.833668 | + | 0.552265i | \(0.813763\pi\) | |||||||
\(138\) | 1.60770i | 0.136856i | ||||||||
\(139\) | 3.66025 | 0.310459 | 0.155229 | − | 0.987878i | \(-0.450388\pi\) | ||||
0.155229 | + | 0.987878i | \(0.450388\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.07180 | 0.427122 | ||||||||
\(142\) | 2.53590i | 0.212808i | ||||||||
\(143\) | − 5.46410i | − 0.456931i | ||||||||
\(144\) | 2.46410 | 0.205342 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.39230 | 0.529031 | ||||||||
\(147\) | − 0.732051i | − 0.0603785i | ||||||||
\(148\) | 2.73205i | 0.224573i | ||||||||
\(149\) | 10.7321 | 0.879204 | 0.439602 | − | 0.898193i | \(-0.355120\pi\) | ||||
0.439602 | + | 0.898193i | \(0.355120\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.1244 | −1.06804 | −0.534022 | − | 0.845470i | \(-0.679320\pi\) | ||||
−0.534022 | + | 0.845470i | \(0.679320\pi\) | |||||||
\(152\) | 3.26795i | 0.265066i | ||||||||
\(153\) | 8.53590i | 0.690086i | ||||||||
\(154\) | −1.00000 | −0.0805823 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.00000 | −0.320256 | ||||||||
\(157\) | 11.4641i | 0.914935i | 0.889226 | + | 0.457467i | \(0.151243\pi\) | ||||
−0.889226 | + | 0.457467i | \(0.848757\pi\) | |||||||
\(158\) | 1.80385i | 0.143506i | ||||||||
\(159\) | −7.85641 | −0.623054 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.19615 | 0.173081 | ||||||||
\(162\) | 4.46410i | 0.350733i | ||||||||
\(163\) | 4.00000i | 0.313304i | 0.987654 | + | 0.156652i | \(0.0500701\pi\) | ||||
−0.987654 | + | 0.156652i | \(0.949930\pi\) | |||||||
\(164\) | −8.19615 | −0.640012 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.39230 | 0.340909 | ||||||||
\(167\) | − 13.8564i | − 1.07224i | −0.844141 | − | 0.536120i | \(-0.819889\pi\) | ||||
0.844141 | − | 0.536120i | \(-0.180111\pi\) | |||||||
\(168\) | 0.732051i | 0.0564789i | ||||||||
\(169\) | −16.8564 | −1.29665 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.05256 | −0.615795 | ||||||||
\(172\) | 2.00000i | 0.152499i | ||||||||
\(173\) | 12.9282i | 0.982913i | 0.870902 | + | 0.491457i | \(0.163535\pi\) | ||||
−0.870902 | + | 0.491457i | \(0.836465\pi\) | |||||||
\(174\) | −0.928203 | −0.0703669 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 5.07180i | 0.381220i | ||||||||
\(178\) | 3.46410i | 0.259645i | ||||||||
\(179\) | 6.00000 | 0.448461 | 0.224231 | − | 0.974536i | \(-0.428013\pi\) | ||||
0.224231 | + | 0.974536i | \(0.428013\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.0000 | 1.04061 | 0.520306 | − | 0.853980i | \(-0.325818\pi\) | ||||
0.520306 | + | 0.853980i | \(0.325818\pi\) | |||||||
\(182\) | 5.46410i | 0.405026i | ||||||||
\(183\) | 6.53590i | 0.483148i | ||||||||
\(184\) | −2.19615 | −0.161903 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.46410 | −0.107353 | ||||||||
\(187\) | 3.46410i | 0.253320i | ||||||||
\(188\) | 6.92820i | 0.505291i | ||||||||
\(189\) | −4.00000 | −0.290957 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.0000 | −0.868290 | −0.434145 | − | 0.900843i | \(-0.642949\pi\) | ||||
−0.434145 | + | 0.900843i | \(0.642949\pi\) | |||||||
\(192\) | − 0.732051i | − 0.0528312i | ||||||||
\(193\) | 8.39230i | 0.604091i | 0.953293 | + | 0.302046i | \(0.0976695\pi\) | ||||
−0.953293 | + | 0.302046i | \(0.902330\pi\) | |||||||
\(194\) | 16.5885 | 1.19098 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 24.2487i | 1.72765i | 0.503793 | + | 0.863825i | \(0.331938\pi\) | ||||
−0.503793 | + | 0.863825i | \(0.668062\pi\) | |||||||
\(198\) | 2.46410i | 0.175116i | ||||||||
\(199\) | 10.9282 | 0.774680 | 0.387340 | − | 0.921937i | \(-0.373394\pi\) | ||||
0.387340 | + | 0.921937i | \(0.373394\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.92820 | 0.206540 | ||||||||
\(202\) | 19.8564i | 1.39709i | ||||||||
\(203\) | 1.26795i | 0.0889926i | ||||||||
\(204\) | 2.53590 | 0.177548 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8.39230 | −0.584720 | ||||||||
\(207\) | − 5.41154i | − 0.376128i | ||||||||
\(208\) | − 5.46410i | − 0.378867i | ||||||||
\(209\) | −3.26795 | −0.226049 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.0718 | 0.899900 | 0.449950 | − | 0.893054i | \(-0.351442\pi\) | ||||
0.449950 | + | 0.893054i | \(0.351442\pi\) | |||||||
\(212\) | − 10.7321i | − 0.737080i | ||||||||
\(213\) | 1.85641i | 0.127199i | ||||||||
\(214\) | 19.8564 | 1.35736 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.00000 | 0.272166 | ||||||||
\(217\) | 2.00000i | 0.135769i | ||||||||
\(218\) | − 1.66025i | − 0.112447i | ||||||||
\(219\) | 4.67949 | 0.316211 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.9282 | 1.27325 | ||||||||
\(222\) | 2.00000i | 0.134231i | ||||||||
\(223\) | 18.5359i | 1.24126i | 0.784105 | + | 0.620628i | \(0.213122\pi\) | ||||
−0.784105 | + | 0.620628i | \(0.786878\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −19.8564 | −1.32083 | ||||||||
\(227\) | − 6.92820i | − 0.459841i | −0.973209 | − | 0.229920i | \(-0.926153\pi\) | ||||
0.973209 | − | 0.229920i | \(-0.0738466\pi\) | |||||||
\(228\) | 2.39230i | 0.158434i | ||||||||
\(229\) | −3.60770 | −0.238403 | −0.119202 | − | 0.992870i | \(-0.538033\pi\) | ||||
−0.119202 | + | 0.992870i | \(0.538033\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.732051 | −0.0481654 | ||||||||
\(232\) | − 1.26795i | − 0.0832449i | ||||||||
\(233\) | − 19.8564i | − 1.30084i | −0.759576 | − | 0.650418i | \(-0.774594\pi\) | ||||
0.759576 | − | 0.650418i | \(-0.225406\pi\) | |||||||
\(234\) | 13.4641 | 0.880176 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.92820 | −0.450988 | ||||||||
\(237\) | 1.32051i | 0.0857762i | ||||||||
\(238\) | − 3.46410i | − 0.224544i | ||||||||
\(239\) | −4.73205 | −0.306091 | −0.153045 | − | 0.988219i | \(-0.548908\pi\) | ||||
−0.153045 | + | 0.988219i | \(0.548908\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.73205 | 0.433650 | 0.216825 | − | 0.976211i | \(-0.430430\pi\) | ||||
0.216825 | + | 0.976211i | \(0.430430\pi\) | |||||||
\(242\) | 1.00000i | 0.0642824i | ||||||||
\(243\) | 15.2679i | 0.979439i | ||||||||
\(244\) | −8.92820 | −0.571570 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.00000 | −0.382546 | ||||||||
\(247\) | 17.8564i | 1.13618i | ||||||||
\(248\) | − 2.00000i | − 0.127000i | ||||||||
\(249\) | 3.21539 | 0.203767 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | − 2.46410i | − 0.155224i | ||||||||
\(253\) | − 2.19615i | − 0.138071i | ||||||||
\(254\) | −14.9282 | −0.936679 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − 6.33975i | − 0.395462i | −0.980256 | − | 0.197731i | \(-0.936643\pi\) | ||||
0.980256 | − | 0.197731i | \(-0.0633573\pi\) | |||||||
\(258\) | 1.46410i | 0.0911510i | ||||||||
\(259\) | 2.73205 | 0.169761 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.12436 | 0.193393 | ||||||||
\(262\) | − 11.6603i | − 0.720373i | ||||||||
\(263\) | 24.0000i | 1.47990i | 0.672660 | + | 0.739952i | \(0.265152\pi\) | ||||
−0.672660 | + | 0.739952i | \(0.734848\pi\) | |||||||
\(264\) | 0.732051 | 0.0450546 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.26795 | 0.200371 | ||||||||
\(267\) | 2.53590i | 0.155194i | ||||||||
\(268\) | 4.00000i | 0.244339i | ||||||||
\(269\) | −7.60770 | −0.463849 | −0.231925 | − | 0.972734i | \(-0.574502\pi\) | ||||
−0.231925 | + | 0.972734i | \(0.574502\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.3923 | −1.23874 | −0.619372 | − | 0.785098i | \(-0.712613\pi\) | ||||
−0.619372 | + | 0.785098i | \(0.712613\pi\) | |||||||
\(272\) | 3.46410i | 0.210042i | ||||||||
\(273\) | 4.00000i | 0.242091i | ||||||||
\(274\) | −12.9282 | −0.781021 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.60770 | −0.0967719 | ||||||||
\(277\) | 20.9282i | 1.25745i | 0.777626 | + | 0.628727i | \(0.216424\pi\) | ||||
−0.777626 | + | 0.628727i | \(0.783576\pi\) | |||||||
\(278\) | 3.66025i | 0.219527i | ||||||||
\(279\) | 4.92820 | 0.295044 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.60770 | 0.0959071 | 0.0479535 | − | 0.998850i | \(-0.484730\pi\) | ||||
0.0479535 | + | 0.998850i | \(0.484730\pi\) | |||||||
\(282\) | 5.07180i | 0.302021i | ||||||||
\(283\) | − 23.7128i | − 1.40958i | −0.709416 | − | 0.704790i | \(-0.751041\pi\) | ||||
0.709416 | − | 0.704790i | \(-0.248959\pi\) | |||||||
\(284\) | −2.53590 | −0.150478 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.46410 | 0.323099 | ||||||||
\(287\) | 8.19615i | 0.483804i | ||||||||
\(288\) | 2.46410i | 0.145199i | ||||||||
\(289\) | 5.00000 | 0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.1436 | 0.711870 | ||||||||
\(292\) | 6.39230i | 0.374081i | ||||||||
\(293\) | − 14.5359i | − 0.849196i | −0.905382 | − | 0.424598i | \(-0.860415\pi\) | ||||
0.905382 | − | 0.424598i | \(-0.139585\pi\) | |||||||
\(294\) | 0.732051 | 0.0426941 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.73205 | −0.158797 | ||||||||
\(297\) | 4.00000i | 0.232104i | ||||||||
\(298\) | 10.7321i | 0.621691i | ||||||||
\(299\) | −12.0000 | −0.693978 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.00000 | 0.115278 | ||||||||
\(302\) | − 13.1244i | − 0.755222i | ||||||||
\(303\) | 14.5359i | 0.835066i | ||||||||
\(304\) | −3.26795 | −0.187430 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −8.53590 | −0.487965 | ||||||||
\(307\) | 3.60770i | 0.205902i | 0.994686 | + | 0.102951i | \(0.0328285\pi\) | ||||
−0.994686 | + | 0.102951i | \(0.967172\pi\) | |||||||
\(308\) | − 1.00000i | − 0.0569803i | ||||||||
\(309\) | −6.14359 | −0.349497 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.0718 | 0.627824 | 0.313912 | − | 0.949452i | \(-0.398360\pi\) | ||||
0.313912 | + | 0.949452i | \(0.398360\pi\) | |||||||
\(312\) | − 4.00000i | − 0.226455i | ||||||||
\(313\) | − 11.8038i | − 0.667193i | −0.942716 | − | 0.333596i | \(-0.891738\pi\) | ||||
0.942716 | − | 0.333596i | \(-0.108262\pi\) | |||||||
\(314\) | −11.4641 | −0.646957 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.80385 | −0.101474 | ||||||||
\(317\) | − 0.588457i | − 0.0330511i | −0.999863 | − | 0.0165255i | \(-0.994740\pi\) | ||||
0.999863 | − | 0.0165255i | \(-0.00526048\pi\) | |||||||
\(318\) | − 7.85641i | − 0.440565i | ||||||||
\(319\) | 1.26795 | 0.0709915 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.5359 | 0.811315 | ||||||||
\(322\) | 2.19615i | 0.122387i | ||||||||
\(323\) | − 11.3205i | − 0.629890i | ||||||||
\(324\) | −4.46410 | −0.248006 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.00000 | −0.221540 | ||||||||
\(327\) | − 1.21539i | − 0.0672112i | ||||||||
\(328\) | − 8.19615i | − 0.452557i | ||||||||
\(329\) | 6.92820 | 0.381964 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.7846 | 1.25236 | 0.626178 | − | 0.779680i | \(-0.284618\pi\) | ||||
0.626178 | + | 0.779680i | \(0.284618\pi\) | |||||||
\(332\) | 4.39230i | 0.241059i | ||||||||
\(333\) | − 6.73205i | − 0.368914i | ||||||||
\(334\) | 13.8564 | 0.758189 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.732051 | −0.0399366 | ||||||||
\(337\) | − 18.7846i | − 1.02326i | −0.859205 | − | 0.511631i | \(-0.829041\pi\) | ||||
0.859205 | − | 0.511631i | \(-0.170959\pi\) | |||||||
\(338\) | − 16.8564i | − 0.916868i | ||||||||
\(339\) | −14.5359 | −0.789482 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.00000 | 0.108306 | ||||||||
\(342\) | − 8.05256i | − 0.435433i | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | −2.00000 | −0.107833 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.9282 | −0.695025 | ||||||||
\(347\) | − 36.9282i | − 1.98241i | −0.132336 | − | 0.991205i | \(-0.542248\pi\) | ||||
0.132336 | − | 0.991205i | \(-0.457752\pi\) | |||||||
\(348\) | − 0.928203i | − 0.0497569i | ||||||||
\(349\) | 26.3923 | 1.41275 | 0.706374 | − | 0.707839i | \(-0.250330\pi\) | ||||
0.706374 | + | 0.707839i | \(0.250330\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 21.8564 | 1.16661 | ||||||||
\(352\) | 1.00000i | 0.0533002i | ||||||||
\(353\) | − 3.80385i | − 0.202458i | −0.994863 | − | 0.101229i | \(-0.967722\pi\) | ||||
0.994863 | − | 0.101229i | \(-0.0322775\pi\) | |||||||
\(354\) | −5.07180 | −0.269563 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.46410 | −0.183597 | ||||||||
\(357\) | − 2.53590i | − 0.134214i | ||||||||
\(358\) | 6.00000i | 0.317110i | ||||||||
\(359\) | −4.05256 | −0.213886 | −0.106943 | − | 0.994265i | \(-0.534106\pi\) | ||||
−0.106943 | + | 0.994265i | \(0.534106\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.32051 | −0.437921 | ||||||||
\(362\) | 14.0000i | 0.735824i | ||||||||
\(363\) | 0.732051i | 0.0384227i | ||||||||
\(364\) | −5.46410 | −0.286397 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −6.53590 | −0.341637 | ||||||||
\(367\) | − 8.39230i | − 0.438075i | −0.975716 | − | 0.219037i | \(-0.929708\pi\) | ||||
0.975716 | − | 0.219037i | \(-0.0702917\pi\) | |||||||
\(368\) | − 2.19615i | − 0.114482i | ||||||||
\(369\) | 20.1962 | 1.05137 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.7321 | −0.557180 | ||||||||
\(372\) | − 1.46410i | − 0.0759101i | ||||||||
\(373\) | 2.39230i | 0.123869i | 0.998080 | + | 0.0619344i | \(0.0197270\pi\) | ||||
−0.998080 | + | 0.0619344i | \(0.980273\pi\) | |||||||
\(374\) | −3.46410 | −0.179124 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.92820 | −0.357295 | ||||||||
\(377\) | − 6.92820i | − 0.356821i | ||||||||
\(378\) | − 4.00000i | − 0.205738i | ||||||||
\(379\) | −33.8564 | −1.73909 | −0.869543 | − | 0.493857i | \(-0.835587\pi\) | ||||
−0.869543 | + | 0.493857i | \(0.835587\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.9282 | −0.559869 | ||||||||
\(382\) | − 12.0000i | − 0.613973i | ||||||||
\(383\) | 26.5359i | 1.35592i | 0.735098 | + | 0.677961i | \(0.237136\pi\) | ||||
−0.735098 | + | 0.677961i | \(0.762864\pi\) | |||||||
\(384\) | 0.732051 | 0.0373573 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.39230 | −0.427157 | ||||||||
\(387\) | − 4.92820i | − 0.250515i | ||||||||
\(388\) | 16.5885i | 0.842151i | ||||||||
\(389\) | 22.3923 | 1.13533 | 0.567667 | − | 0.823258i | \(-0.307846\pi\) | ||||
0.567667 | + | 0.823258i | \(0.307846\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.60770 | 0.384738 | ||||||||
\(392\) | 1.00000i | 0.0505076i | ||||||||
\(393\) | − 8.53590i | − 0.430579i | ||||||||
\(394\) | −24.2487 | −1.22163 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.46410 | −0.123826 | ||||||||
\(397\) | 9.60770i | 0.482196i | 0.970501 | + | 0.241098i | \(0.0775076\pi\) | ||||
−0.970501 | + | 0.241098i | \(0.922492\pi\) | |||||||
\(398\) | 10.9282i | 0.547781i | ||||||||
\(399\) | 2.39230 | 0.119765 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.46410 | 0.472615 | 0.236307 | − | 0.971678i | \(-0.424063\pi\) | ||||
0.236307 | + | 0.971678i | \(0.424063\pi\) | |||||||
\(402\) | 2.92820i | 0.146046i | ||||||||
\(403\) | − 10.9282i | − 0.544373i | ||||||||
\(404\) | −19.8564 | −0.987893 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.26795 | −0.0629273 | ||||||||
\(407\) | − 2.73205i | − 0.135423i | ||||||||
\(408\) | 2.53590i | 0.125546i | ||||||||
\(409\) | −35.1244 | −1.73679 | −0.868394 | − | 0.495875i | \(-0.834847\pi\) | ||||
−0.868394 | + | 0.495875i | \(0.834847\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.46410 | −0.466830 | ||||||||
\(412\) | − 8.39230i | − 0.413459i | ||||||||
\(413\) | 6.92820i | 0.340915i | ||||||||
\(414\) | 5.41154 | 0.265963 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.46410 | 0.267900 | ||||||||
\(417\) | 2.67949i | 0.131215i | ||||||||
\(418\) | − 3.26795i | − 0.159841i | ||||||||
\(419\) | −17.0718 | −0.834012 | −0.417006 | − | 0.908904i | \(-0.636921\pi\) | ||||
−0.417006 | + | 0.908904i | \(0.636921\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.14359 | −0.396894 | −0.198447 | − | 0.980112i | \(-0.563590\pi\) | ||||
−0.198447 | + | 0.980112i | \(0.563590\pi\) | |||||||
\(422\) | 13.0718i | 0.636325i | ||||||||
\(423\) | − 17.0718i | − 0.830059i | ||||||||
\(424\) | 10.7321 | 0.521194 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.85641 | −0.0899432 | ||||||||
\(427\) | 8.92820i | 0.432066i | ||||||||
\(428\) | 19.8564i | 0.959796i | ||||||||
\(429\) | 4.00000 | 0.193122 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.1244 | −1.01752 | −0.508762 | − | 0.860907i | \(-0.669897\pi\) | ||||
−0.508762 | + | 0.860907i | \(0.669897\pi\) | |||||||
\(432\) | 4.00000i | 0.192450i | ||||||||
\(433\) | 7.80385i | 0.375029i | 0.982262 | + | 0.187514i | \(0.0600432\pi\) | ||||
−0.982262 | + | 0.187514i | \(0.939957\pi\) | |||||||
\(434\) | −2.00000 | −0.0960031 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.66025 | 0.0795117 | ||||||||
\(437\) | 7.17691i | 0.343318i | ||||||||
\(438\) | 4.67949i | 0.223595i | ||||||||
\(439\) | 22.2487 | 1.06187 | 0.530937 | − | 0.847412i | \(-0.321840\pi\) | ||||
0.530937 | + | 0.847412i | \(0.321840\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.46410 | −0.117338 | ||||||||
\(442\) | 18.9282i | 0.900323i | ||||||||
\(443\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(444\) | −2.00000 | −0.0949158 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −18.5359 | −0.877700 | ||||||||
\(447\) | 7.85641i | 0.371595i | ||||||||
\(448\) | − 1.00000i | − 0.0472456i | ||||||||
\(449\) | −19.6077 | −0.925344 | −0.462672 | − | 0.886529i | \(-0.653109\pi\) | ||||
−0.462672 | + | 0.886529i | \(0.653109\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.19615 | 0.385942 | ||||||||
\(452\) | − 19.8564i | − 0.933967i | ||||||||
\(453\) | − 9.60770i | − 0.451409i | ||||||||
\(454\) | 6.92820 | 0.325157 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.39230 | −0.112030 | ||||||||
\(457\) | 2.00000i | 0.0935561i | 0.998905 | + | 0.0467780i | \(0.0148953\pi\) | ||||
−0.998905 | + | 0.0467780i | \(0.985105\pi\) | |||||||
\(458\) | − 3.60770i | − 0.168577i | ||||||||
\(459\) | −13.8564 | −0.646762 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.60770 | 0.0748778 | 0.0374389 | − | 0.999299i | \(-0.488080\pi\) | ||||
0.0374389 | + | 0.999299i | \(0.488080\pi\) | |||||||
\(462\) | − 0.732051i | − 0.0340581i | ||||||||
\(463\) | 17.5167i | 0.814068i | 0.913413 | + | 0.407034i | \(0.133437\pi\) | ||||
−0.913413 | + | 0.407034i | \(0.866563\pi\) | |||||||
\(464\) | 1.26795 | 0.0588631 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 19.8564 | 0.919830 | ||||||||
\(467\) | 4.05256i | 0.187530i | 0.995594 | + | 0.0937650i | \(0.0298902\pi\) | ||||
−0.995594 | + | 0.0937650i | \(0.970110\pi\) | |||||||
\(468\) | 13.4641i | 0.622378i | ||||||||
\(469\) | 4.00000 | 0.184703 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.39230 | −0.386697 | ||||||||
\(472\) | − 6.92820i | − 0.318896i | ||||||||
\(473\) | − 2.00000i | − 0.0919601i | ||||||||
\(474\) | −1.32051 | −0.0606529 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.46410 | 0.158777 | ||||||||
\(477\) | 26.4449i | 1.21083i | ||||||||
\(478\) | − 4.73205i | − 0.216439i | ||||||||
\(479\) | −8.78461 | −0.401379 | −0.200690 | − | 0.979655i | \(-0.564318\pi\) | ||||
−0.200690 | + | 0.979655i | \(0.564318\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.9282 | −0.680667 | ||||||||
\(482\) | 6.73205i | 0.306637i | ||||||||
\(483\) | 1.60770i | 0.0731527i | ||||||||
\(484\) | −1.00000 | −0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −15.2679 | −0.692568 | ||||||||
\(487\) | − 6.19615i | − 0.280774i | −0.990097 | − | 0.140387i | \(-0.955165\pi\) | ||||
0.990097 | − | 0.140387i | \(-0.0448347\pi\) | |||||||
\(488\) | − 8.92820i | − 0.404161i | ||||||||
\(489\) | −2.92820 | −0.132418 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.7128 | 1.25066 | 0.625331 | − | 0.780360i | \(-0.284964\pi\) | ||||
0.625331 | + | 0.780360i | \(0.284964\pi\) | |||||||
\(492\) | − 6.00000i | − 0.270501i | ||||||||
\(493\) | 4.39230i | 0.197819i | ||||||||
\(494\) | −17.8564 | −0.803398 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | 2.53590i | 0.113751i | ||||||||
\(498\) | 3.21539i | 0.144085i | ||||||||
\(499\) | −39.8564 | −1.78422 | −0.892109 | − | 0.451820i | \(-0.850775\pi\) | ||||
−0.892109 | + | 0.451820i | \(0.850775\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.1436 | 0.453182 | ||||||||
\(502\) | 12.0000i | 0.535586i | ||||||||
\(503\) | 32.7846i | 1.46179i | 0.682488 | + | 0.730897i | \(0.260898\pi\) | ||||
−0.682488 | + | 0.730897i | \(0.739102\pi\) | |||||||
\(504\) | 2.46410 | 0.109760 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.19615 | 0.0976309 | ||||||||
\(507\) | − 12.3397i | − 0.548027i | ||||||||
\(508\) | − 14.9282i | − 0.662332i | ||||||||
\(509\) | −24.9282 | −1.10492 | −0.552462 | − | 0.833538i | \(-0.686311\pi\) | ||||
−0.552462 | + | 0.833538i | \(0.686311\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.39230 | 0.282779 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − 13.0718i | − 0.577134i | ||||||||
\(514\) | 6.33975 | 0.279634 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.46410 | −0.0644535 | ||||||||
\(517\) | − 6.92820i | − 0.304702i | ||||||||
\(518\) | 2.73205i | 0.120039i | ||||||||
\(519\) | −9.46410 | −0.415428 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.3923 | −0.455295 | −0.227648 | − | 0.973744i | \(-0.573103\pi\) | ||||
−0.227648 | + | 0.973744i | \(0.573103\pi\) | |||||||
\(522\) | 3.12436i | 0.136749i | ||||||||
\(523\) | − 33.1769i | − 1.45073i | −0.688367 | − | 0.725363i | \(-0.741672\pi\) | ||||
0.688367 | − | 0.725363i | \(-0.258328\pi\) | |||||||
\(524\) | 11.6603 | 0.509381 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.0000 | −1.04645 | ||||||||
\(527\) | 6.92820i | 0.301797i | ||||||||
\(528\) | 0.732051i | 0.0318584i | ||||||||
\(529\) | 18.1769 | 0.790301 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.0718 | 0.740853 | ||||||||
\(532\) | 3.26795i | 0.141684i | ||||||||
\(533\) | − 44.7846i | − 1.93984i | ||||||||
\(534\) | −2.53590 | −0.109739 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.00000 | −0.172774 | ||||||||
\(537\) | 4.39230i | 0.189542i | ||||||||
\(538\) | − 7.60770i | − 0.327991i | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.2679 | −0.742407 | −0.371204 | − | 0.928552i | \(-0.621055\pi\) | ||||
−0.371204 | + | 0.928552i | \(0.621055\pi\) | |||||||
\(542\) | − 20.3923i | − 0.875924i | ||||||||
\(543\) | 10.2487i | 0.439814i | ||||||||
\(544\) | −3.46410 | −0.148522 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.00000 | −0.171184 | ||||||||
\(547\) | − 12.7846i | − 0.546630i | −0.961925 | − | 0.273315i | \(-0.911880\pi\) | ||||
0.961925 | − | 0.273315i | \(-0.0881202\pi\) | |||||||
\(548\) | − 12.9282i | − 0.552265i | ||||||||
\(549\) | 22.0000 | 0.938937 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.14359 | −0.176523 | ||||||||
\(552\) | − 1.60770i | − 0.0684280i | ||||||||
\(553\) | 1.80385i | 0.0767074i | ||||||||
\(554\) | −20.9282 | −0.889154 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.66025 | −0.155229 | ||||||||
\(557\) | − 46.3923i | − 1.96571i | −0.184393 | − | 0.982853i | \(-0.559032\pi\) | ||||
0.184393 | − | 0.982853i | \(-0.440968\pi\) | |||||||
\(558\) | 4.92820i | 0.208627i | ||||||||
\(559\) | −10.9282 | −0.462214 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.53590 | −0.107066 | ||||||||
\(562\) | 1.60770i | 0.0678165i | ||||||||
\(563\) | − 18.9282i | − 0.797729i | −0.917010 | − | 0.398864i | \(-0.869404\pi\) | ||||
0.917010 | − | 0.398864i | \(-0.130596\pi\) | |||||||
\(564\) | −5.07180 | −0.213561 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 23.7128 | 0.996724 | ||||||||
\(567\) | 4.46410i | 0.187475i | ||||||||
\(568\) | − 2.53590i | − 0.106404i | ||||||||
\(569\) | 6.00000 | 0.251533 | 0.125767 | − | 0.992060i | \(-0.459861\pi\) | ||||
0.125767 | + | 0.992060i | \(0.459861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.3923 | 1.02079 | 0.510393 | − | 0.859941i | \(-0.329500\pi\) | ||||
0.510393 | + | 0.859941i | \(0.329500\pi\) | |||||||
\(572\) | 5.46410i | 0.228466i | ||||||||
\(573\) | − 8.78461i | − 0.366982i | ||||||||
\(574\) | −8.19615 | −0.342101 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.46410 | −0.102671 | ||||||||
\(577\) | − 3.41154i | − 0.142024i | −0.997475 | − | 0.0710122i | \(-0.977377\pi\) | ||||
0.997475 | − | 0.0710122i | \(-0.0226229\pi\) | |||||||
\(578\) | 5.00000i | 0.207973i | ||||||||
\(579\) | −6.14359 | −0.255319 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.39230 | 0.182224 | ||||||||
\(582\) | 12.1436i | 0.503368i | ||||||||
\(583\) | 10.7321i | 0.444476i | ||||||||
\(584\) | −6.39230 | −0.264515 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.5359 | 0.600472 | ||||||||
\(587\) | − 42.5885i | − 1.75781i | −0.476993 | − | 0.878907i | \(-0.658273\pi\) | ||||
0.476993 | − | 0.878907i | \(-0.341727\pi\) | |||||||
\(588\) | 0.732051i | 0.0301893i | ||||||||
\(589\) | −6.53590 | −0.269307 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.7513 | −0.730190 | ||||||||
\(592\) | − 2.73205i | − 0.112287i | ||||||||
\(593\) | 48.2487i | 1.98134i | 0.136293 | + | 0.990669i | \(0.456481\pi\) | ||||
−0.136293 | + | 0.990669i | \(0.543519\pi\) | |||||||
\(594\) | −4.00000 | −0.164122 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10.7321 | −0.439602 | ||||||||
\(597\) | 8.00000i | 0.327418i | ||||||||
\(598\) | − 12.0000i | − 0.490716i | ||||||||
\(599\) | 25.1769 | 1.02870 | 0.514350 | − | 0.857580i | \(-0.328033\pi\) | ||||
0.514350 | + | 0.857580i | \(0.328033\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.5167 | 1.61192 | 0.805959 | − | 0.591971i | \(-0.201650\pi\) | ||||
0.805959 | + | 0.591971i | \(0.201650\pi\) | |||||||
\(602\) | 2.00000i | 0.0815139i | ||||||||
\(603\) | − 9.85641i | − 0.401384i | ||||||||
\(604\) | 13.1244 | 0.534022 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −14.5359 | −0.590481 | ||||||||
\(607\) | 7.07180i | 0.287035i | 0.989648 | + | 0.143518i | \(0.0458414\pi\) | ||||
−0.989648 | + | 0.143518i | \(0.954159\pi\) | |||||||
\(608\) | − 3.26795i | − 0.132533i | ||||||||
\(609\) | −0.928203 | −0.0376127 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −37.8564 | −1.53151 | ||||||||
\(612\) | − 8.53590i | − 0.345043i | ||||||||
\(613\) | − 27.1769i | − 1.09767i | −0.835932 | − | 0.548833i | \(-0.815072\pi\) | ||||
0.835932 | − | 0.548833i | \(-0.184928\pi\) | |||||||
\(614\) | −3.60770 | −0.145595 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.00000 | 0.0402911 | ||||||||
\(617\) | − 17.3205i | − 0.697297i | −0.937253 | − | 0.348649i | \(-0.886641\pi\) | ||||
0.937253 | − | 0.348649i | \(-0.113359\pi\) | |||||||
\(618\) | − 6.14359i | − 0.247132i | ||||||||
\(619\) | 12.7846 | 0.513857 | 0.256928 | − | 0.966430i | \(-0.417290\pi\) | ||||
0.256928 | + | 0.966430i | \(0.417290\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.78461 | 0.352514 | ||||||||
\(622\) | 11.0718i | 0.443939i | ||||||||
\(623\) | 3.46410i | 0.138786i | ||||||||
\(624\) | 4.00000 | 0.160128 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 11.8038 | 0.471777 | ||||||||
\(627\) | − 2.39230i | − 0.0955395i | ||||||||
\(628\) | − 11.4641i | − 0.457467i | ||||||||
\(629\) | 9.46410 | 0.377358 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.0718 | −1.31657 | −0.658284 | − | 0.752770i | \(-0.728717\pi\) | ||||
−0.658284 | + | 0.752770i | \(0.728717\pi\) | |||||||
\(632\) | − 1.80385i | − 0.0717532i | ||||||||
\(633\) | 9.56922i | 0.380342i | ||||||||
\(634\) | 0.588457 | 0.0233706 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 7.85641 | 0.311527 | ||||||||
\(637\) | 5.46410i | 0.216496i | ||||||||
\(638\) | 1.26795i | 0.0501986i | ||||||||
\(639\) | 6.24871 | 0.247195 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 47.5692 | 1.87887 | 0.939436 | − | 0.342725i | \(-0.111350\pi\) | ||||
0.939436 | + | 0.342725i | \(0.111350\pi\) | |||||||
\(642\) | 14.5359i | 0.573686i | ||||||||
\(643\) | − 36.7321i | − 1.44857i | −0.689500 | − | 0.724285i | \(-0.742170\pi\) | ||||
0.689500 | − | 0.724285i | \(-0.257830\pi\) | |||||||
\(644\) | −2.19615 | −0.0865405 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.3205 | 0.445399 | ||||||||
\(647\) | − 33.4641i | − 1.31561i | −0.753188 | − | 0.657805i | \(-0.771485\pi\) | ||||
0.753188 | − | 0.657805i | \(-0.228515\pi\) | |||||||
\(648\) | − 4.46410i | − 0.175366i | ||||||||
\(649\) | 6.92820 | 0.271956 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.46410 | −0.0573827 | ||||||||
\(652\) | − 4.00000i | − 0.156652i | ||||||||
\(653\) | 5.66025i | 0.221503i | 0.993848 | + | 0.110751i | \(0.0353257\pi\) | ||||
−0.993848 | + | 0.110751i | \(0.964674\pi\) | |||||||
\(654\) | 1.21539 | 0.0475255 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 8.19615 | 0.320006 | ||||||||
\(657\) | − 15.7513i | − 0.614516i | ||||||||
\(658\) | 6.92820i | 0.270089i | ||||||||
\(659\) | 18.2487 | 0.710869 | 0.355434 | − | 0.934701i | \(-0.384333\pi\) | ||||
0.355434 | + | 0.934701i | \(0.384333\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.0000 | −1.78919 | −0.894596 | − | 0.446875i | \(-0.852537\pi\) | ||||
−0.894596 | + | 0.446875i | \(0.852537\pi\) | |||||||
\(662\) | 22.7846i | 0.885549i | ||||||||
\(663\) | 13.8564i | 0.538138i | ||||||||
\(664\) | −4.39230 | −0.170454 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.73205 | 0.260862 | ||||||||
\(667\) | − 2.78461i | − 0.107821i | ||||||||
\(668\) | 13.8564i | 0.536120i | ||||||||
\(669\) | −13.5692 | −0.524616 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.92820 | 0.344669 | ||||||||
\(672\) | − 0.732051i | − 0.0282395i | ||||||||
\(673\) | − 2.00000i | − 0.0770943i | −0.999257 | − | 0.0385472i | \(-0.987727\pi\) | ||||
0.999257 | − | 0.0385472i | \(-0.0122730\pi\) | |||||||
\(674\) | 18.7846 | 0.723556 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.8564 | 0.648323 | ||||||||
\(677\) | − 31.8564i | − 1.22434i | −0.790726 | − | 0.612171i | \(-0.790297\pi\) | ||||
0.790726 | − | 0.612171i | \(-0.209703\pi\) | |||||||
\(678\) | − 14.5359i | − 0.558248i | ||||||||
\(679\) | 16.5885 | 0.636607 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.07180 | 0.194352 | ||||||||
\(682\) | 2.00000i | 0.0765840i | ||||||||
\(683\) | 42.2487i | 1.61660i | 0.588769 | + | 0.808301i | \(0.299613\pi\) | ||||
−0.588769 | + | 0.808301i | \(0.700387\pi\) | |||||||
\(684\) | 8.05256 | 0.307897 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | − 2.64102i | − 0.100761i | ||||||||
\(688\) | − 2.00000i | − 0.0762493i | ||||||||
\(689\) | 58.6410 | 2.23404 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.53590 | −0.248637 | −0.124319 | − | 0.992242i | \(-0.539675\pi\) | ||||
−0.124319 | + | 0.992242i | \(0.539675\pi\) | |||||||
\(692\) | − 12.9282i | − 0.491457i | ||||||||
\(693\) | 2.46410i | 0.0936035i | ||||||||
\(694\) | 36.9282 | 1.40178 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.928203 | 0.0351835 | ||||||||
\(697\) | 28.3923i | 1.07544i | ||||||||
\(698\) | 26.3923i | 0.998963i | ||||||||
\(699\) | 14.5359 | 0.549798 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.9090 | −0.903029 | −0.451515 | − | 0.892264i | \(-0.649116\pi\) | ||||
−0.451515 | + | 0.892264i | \(0.649116\pi\) | |||||||
\(702\) | 21.8564i | 0.824917i | ||||||||
\(703\) | 8.92820i | 0.336734i | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.80385 | 0.143160 | ||||||||
\(707\) | 19.8564i | 0.746777i | ||||||||
\(708\) | − 5.07180i | − 0.190610i | ||||||||
\(709\) | 9.32051 | 0.350039 | 0.175020 | − | 0.984565i | \(-0.444001\pi\) | ||||
0.175020 | + | 0.984565i | \(0.444001\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.44486 | 0.166695 | ||||||||
\(712\) | − 3.46410i | − 0.129823i | ||||||||
\(713\) | − 4.39230i | − 0.164493i | ||||||||
\(714\) | 2.53590 | 0.0949036 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.00000 | −0.224231 | ||||||||
\(717\) | − 3.46410i | − 0.129369i | ||||||||
\(718\) | − 4.05256i | − 0.151240i | ||||||||
\(719\) | −27.7128 | −1.03351 | −0.516757 | − | 0.856132i | \(-0.672861\pi\) | ||||
−0.516757 | + | 0.856132i | \(0.672861\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.39230 | −0.312546 | ||||||||
\(722\) | − 8.32051i | − 0.309657i | ||||||||
\(723\) | 4.92820i | 0.183282i | ||||||||
\(724\) | −14.0000 | −0.520306 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.732051 | −0.0271690 | ||||||||
\(727\) | − 4.00000i | − 0.148352i | −0.997245 | − | 0.0741759i | \(-0.976367\pi\) | ||||
0.997245 | − | 0.0741759i | \(-0.0236326\pi\) | |||||||
\(728\) | − 5.46410i | − 0.202513i | ||||||||
\(729\) | 2.21539 | 0.0820515 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.92820 | 0.256249 | ||||||||
\(732\) | − 6.53590i | − 0.241574i | ||||||||
\(733\) | − 26.0000i | − 0.960332i | −0.877178 | − | 0.480166i | \(-0.840576\pi\) | ||||
0.877178 | − | 0.480166i | \(-0.159424\pi\) | |||||||
\(734\) | 8.39230 | 0.309766 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.19615 | 0.0809513 | ||||||||
\(737\) | − 4.00000i | − 0.147342i | ||||||||
\(738\) | 20.1962i | 0.743431i | ||||||||
\(739\) | 43.7128 | 1.60800 | 0.804001 | − | 0.594628i | \(-0.202701\pi\) | ||||
0.804001 | + | 0.594628i | \(0.202701\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.0718 | −0.480204 | ||||||||
\(742\) | − 10.7321i | − 0.393986i | ||||||||
\(743\) | − 8.78461i | − 0.322276i | −0.986932 | − | 0.161138i | \(-0.948484\pi\) | ||||
0.986932 | − | 0.161138i | \(-0.0515164\pi\) | |||||||
\(744\) | 1.46410 | 0.0536766 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.39230 | −0.0875885 | ||||||||
\(747\) | − 10.8231i | − 0.395996i | ||||||||
\(748\) | − 3.46410i | − 0.126660i | ||||||||
\(749\) | 19.8564 | 0.725537 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.3923 | −1.18201 | −0.591006 | − | 0.806667i | \(-0.701269\pi\) | ||||
−0.591006 | + | 0.806667i | \(0.701269\pi\) | |||||||
\(752\) | − 6.92820i | − 0.252646i | ||||||||
\(753\) | 8.78461i | 0.320129i | ||||||||
\(754\) | 6.92820 | 0.252310 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.00000 | 0.145479 | ||||||||
\(757\) | 29.3731i | 1.06758i | 0.845616 | + | 0.533791i | \(0.179233\pi\) | ||||
−0.845616 | + | 0.533791i | \(0.820767\pi\) | |||||||
\(758\) | − 33.8564i | − 1.22972i | ||||||||
\(759\) | 1.60770 | 0.0583556 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.6603 | −1.07518 | −0.537592 | − | 0.843205i | \(-0.680666\pi\) | ||||
−0.537592 | + | 0.843205i | \(0.680666\pi\) | |||||||
\(762\) | − 10.9282i | − 0.395887i | ||||||||
\(763\) | − 1.66025i | − 0.0601052i | ||||||||
\(764\) | 12.0000 | 0.434145 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −26.5359 | −0.958781 | ||||||||
\(767\) | − 37.8564i | − 1.36692i | ||||||||
\(768\) | 0.732051i | 0.0264156i | ||||||||
\(769\) | 7.80385 | 0.281414 | 0.140707 | − | 0.990051i | \(-0.455062\pi\) | ||||
0.140707 | + | 0.990051i | \(0.455062\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.64102 | 0.167142 | ||||||||
\(772\) | − 8.39230i | − 0.302046i | ||||||||
\(773\) | − 12.9282i | − 0.464995i | −0.972597 | − | 0.232498i | \(-0.925310\pi\) | ||||
0.972597 | − | 0.232498i | \(-0.0746898\pi\) | |||||||
\(774\) | 4.92820 | 0.177141 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −16.5885 | −0.595491 | ||||||||
\(777\) | 2.00000i | 0.0717496i | ||||||||
\(778\) | 22.3923i | 0.802803i | ||||||||
\(779\) | −26.7846 | −0.959658 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.53590 | 0.0907416 | ||||||||
\(782\) | 7.60770i | 0.272051i | ||||||||
\(783\) | 5.07180i | 0.181251i | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 8.53590 | 0.304465 | ||||||||
\(787\) | 45.8564i | 1.63460i | 0.576209 | + | 0.817302i | \(0.304531\pi\) | ||||
−0.576209 | + | 0.817302i | \(0.695469\pi\) | |||||||
\(788\) | − 24.2487i | − 0.863825i | ||||||||
\(789\) | −17.5692 | −0.625481 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.8564 | −0.706013 | ||||||||
\(792\) | − 2.46410i | − 0.0875580i | ||||||||
\(793\) | − 48.7846i | − 1.73239i | ||||||||
\(794\) | −9.60770 | −0.340964 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.9282 | −0.387340 | ||||||||
\(797\) | − 46.3923i | − 1.64330i | −0.569993 | − | 0.821650i | \(-0.693054\pi\) | ||||
0.569993 | − | 0.821650i | \(-0.306946\pi\) | |||||||
\(798\) | 2.39230i | 0.0846867i | ||||||||
\(799\) | 24.0000 | 0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.53590 | 0.301601 | ||||||||
\(802\) | 9.46410i | 0.334189i | ||||||||
\(803\) | − 6.39230i | − 0.225580i | ||||||||
\(804\) | −2.92820 | −0.103270 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10.9282 | 0.384930 | ||||||||
\(807\) | − 5.56922i | − 0.196046i | ||||||||
\(808\) | − 19.8564i | − 0.698546i | ||||||||
\(809\) | −31.1769 | −1.09612 | −0.548061 | − | 0.836438i | \(-0.684634\pi\) | ||||
−0.548061 | + | 0.836438i | \(0.684634\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.8756 | −0.662814 | −0.331407 | − | 0.943488i | \(-0.607523\pi\) | ||||
−0.331407 | + | 0.943488i | \(0.607523\pi\) | |||||||
\(812\) | − 1.26795i | − 0.0444963i | ||||||||
\(813\) | − 14.9282i | − 0.523555i | ||||||||
\(814\) | 2.73205 | 0.0957583 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.53590 | −0.0887742 | ||||||||
\(817\) | 6.53590i | 0.228662i | ||||||||
\(818\) | − 35.1244i | − 1.22809i | ||||||||
\(819\) | 13.4641 | 0.470474 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −47.9090 | −1.67203 | −0.836017 | − | 0.548703i | \(-0.815122\pi\) | ||||
−0.836017 | + | 0.548703i | \(0.815122\pi\) | |||||||
\(822\) | − 9.46410i | − 0.330098i | ||||||||
\(823\) | 25.1244i | 0.875780i | 0.899029 | + | 0.437890i | \(0.144274\pi\) | ||||
−0.899029 | + | 0.437890i | \(0.855726\pi\) | |||||||
\(824\) | 8.39230 | 0.292360 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.92820 | −0.241063 | ||||||||
\(827\) | 1.85641i | 0.0645536i | 0.999479 | + | 0.0322768i | \(0.0102758\pi\) | ||||
−0.999479 | + | 0.0322768i | \(0.989724\pi\) | |||||||
\(828\) | 5.41154i | 0.188064i | ||||||||
\(829\) | 46.2487 | 1.60628 | 0.803142 | − | 0.595788i | \(-0.203160\pi\) | ||||
0.803142 | + | 0.595788i | \(0.203160\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.3205 | −0.531463 | ||||||||
\(832\) | 5.46410i | 0.189434i | ||||||||
\(833\) | − 3.46410i | − 0.120024i | ||||||||
\(834\) | −2.67949 | −0.0927832 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.26795 | 0.113024 | ||||||||
\(837\) | 8.00000i | 0.276520i | ||||||||
\(838\) | − 17.0718i | − 0.589735i | ||||||||
\(839\) | 4.14359 | 0.143053 | 0.0715264 | − | 0.997439i | \(-0.477213\pi\) | ||||
0.0715264 | + | 0.997439i | \(0.477213\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.3923 | −0.944562 | ||||||||
\(842\) | − 8.14359i | − 0.280647i | ||||||||
\(843\) | 1.17691i | 0.0405351i | ||||||||
\(844\) | −13.0718 | −0.449950 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 17.0718 | 0.586940 | ||||||||
\(847\) | 1.00000i | 0.0343604i | ||||||||
\(848\) | 10.7321i | 0.368540i | ||||||||
\(849\) | 17.3590 | 0.595759 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.00000 | −0.205677 | ||||||||
\(852\) | − 1.85641i | − 0.0635994i | ||||||||
\(853\) | 13.2154i | 0.452486i | 0.974071 | + | 0.226243i | \(0.0726444\pi\) | ||||
−0.974071 | + | 0.226243i | \(0.927356\pi\) | |||||||
\(854\) | −8.92820 | −0.305517 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −19.8564 | −0.678678 | ||||||||
\(857\) | − 20.5359i | − 0.701493i | −0.936470 | − | 0.350746i | \(-0.885928\pi\) | ||||
0.936470 | − | 0.350746i | \(-0.114072\pi\) | |||||||
\(858\) | 4.00000i | 0.136558i | ||||||||
\(859\) | −28.7846 | −0.982118 | −0.491059 | − | 0.871126i | \(-0.663390\pi\) | ||||
−0.491059 | + | 0.871126i | \(0.663390\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.00000 | −0.204479 | ||||||||
\(862\) | − 21.1244i | − 0.719498i | ||||||||
\(863\) | − 37.5167i | − 1.27708i | −0.769588 | − | 0.638541i | \(-0.779538\pi\) | ||||
0.769588 | − | 0.638541i | \(-0.220462\pi\) | |||||||
\(864\) | −4.00000 | −0.136083 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −7.80385 | −0.265186 | ||||||||
\(867\) | 3.66025i | 0.124309i | ||||||||
\(868\) | − 2.00000i | − 0.0678844i | ||||||||
\(869\) | 1.80385 | 0.0611913 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.8564 | −0.740576 | ||||||||
\(872\) | 1.66025i | 0.0562233i | ||||||||
\(873\) | − 40.8756i | − 1.38343i | ||||||||
\(874\) | −7.17691 | −0.242763 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.67949 | −0.158105 | ||||||||
\(877\) | 13.3205i | 0.449802i | 0.974382 | + | 0.224901i | \(0.0722058\pi\) | ||||
−0.974382 | + | 0.224901i | \(0.927794\pi\) | |||||||
\(878\) | 22.2487i | 0.750858i | ||||||||
\(879\) | 10.6410 | 0.358913 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.9282 | 0.839853 | 0.419926 | − | 0.907558i | \(-0.362056\pi\) | ||||
0.419926 | + | 0.907558i | \(0.362056\pi\) | |||||||
\(882\) | − 2.46410i | − 0.0829706i | ||||||||
\(883\) | 56.3923i | 1.89775i | 0.315649 | + | 0.948876i | \(0.397778\pi\) | ||||
−0.315649 | + | 0.948876i | \(0.602222\pi\) | |||||||
\(884\) | −18.9282 | −0.636624 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 13.8564i | − 0.465253i | −0.972566 | − | 0.232626i | \(-0.925268\pi\) | ||||
0.972566 | − | 0.232626i | \(-0.0747319\pi\) | |||||||
\(888\) | − 2.00000i | − 0.0671156i | ||||||||
\(889\) | −14.9282 | −0.500676 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.46410 | 0.149553 | ||||||||
\(892\) | − 18.5359i | − 0.620628i | ||||||||
\(893\) | 22.6410i | 0.757653i | ||||||||
\(894\) | −7.85641 | −0.262758 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | − 8.78461i | − 0.293310i | ||||||||
\(898\) | − 19.6077i | − 0.654317i | ||||||||
\(899\) | 2.53590 | 0.0845769 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37.1769 | −1.23854 | ||||||||
\(902\) | 8.19615i | 0.272902i | ||||||||
\(903\) | 1.46410i | 0.0487223i | ||||||||
\(904\) | 19.8564 | 0.660414 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 9.60770 | 0.319194 | ||||||||
\(907\) | 59.0333i | 1.96017i | 0.198580 | + | 0.980085i | \(0.436367\pi\) | ||||
−0.198580 | + | 0.980085i | \(0.563633\pi\) | |||||||
\(908\) | 6.92820i | 0.229920i | ||||||||
\(909\) | 48.9282 | 1.62285 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.53590 | 0.0840181 | 0.0420090 | − | 0.999117i | \(-0.486624\pi\) | ||||
0.0420090 | + | 0.999117i | \(0.486624\pi\) | |||||||
\(912\) | − 2.39230i | − 0.0792171i | ||||||||
\(913\) | − 4.39230i | − 0.145364i | ||||||||
\(914\) | −2.00000 | −0.0661541 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.60770 | 0.119202 | ||||||||
\(917\) | − 11.6603i | − 0.385056i | ||||||||
\(918\) | − 13.8564i | − 0.457330i | ||||||||
\(919\) | −47.3731 | −1.56269 | −0.781347 | − | 0.624097i | \(-0.785467\pi\) | ||||
−0.781347 | + | 0.624097i | \(0.785467\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.64102 | −0.0870244 | ||||||||
\(922\) | 1.60770i | 0.0529466i | ||||||||
\(923\) | − 13.8564i | − 0.456089i | ||||||||
\(924\) | 0.732051 | 0.0240827 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −17.5167 | −0.575633 | ||||||||
\(927\) | 20.6795i | 0.679204i | ||||||||
\(928\) | 1.26795i | 0.0416225i | ||||||||
\(929\) | 46.3923 | 1.52208 | 0.761041 | − | 0.648704i | \(-0.224689\pi\) | ||||
0.761041 | + | 0.648704i | \(0.224689\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.26795 | 0.107103 | ||||||||
\(932\) | 19.8564i | 0.650418i | ||||||||
\(933\) | 8.10512i | 0.265350i | ||||||||
\(934\) | −4.05256 | −0.132604 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −13.4641 | −0.440088 | ||||||||
\(937\) | − 42.7846i | − 1.39771i | −0.715262 | − | 0.698856i | \(-0.753693\pi\) | ||||
0.715262 | − | 0.698856i | \(-0.246307\pi\) | |||||||
\(938\) | 4.00000i | 0.130605i | ||||||||
\(939\) | 8.64102 | 0.281989 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.7846 | 0.873153 | 0.436577 | − | 0.899667i | \(-0.356191\pi\) | ||||
0.436577 | + | 0.899667i | \(0.356191\pi\) | |||||||
\(942\) | − 8.39230i | − 0.273436i | ||||||||
\(943\) | − 18.0000i | − 0.586161i | ||||||||
\(944\) | 6.92820 | 0.225494 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.00000 | 0.0650256 | ||||||||
\(947\) | 12.6795i | 0.412028i | 0.978549 | + | 0.206014i | \(0.0660493\pi\) | ||||
−0.978549 | + | 0.206014i | \(0.933951\pi\) | |||||||
\(948\) | − 1.32051i | − 0.0428881i | ||||||||
\(949\) | −34.9282 | −1.13382 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.430781 | 0.0139690 | ||||||||
\(952\) | 3.46410i | 0.112272i | ||||||||
\(953\) | − 33.4641i | − 1.08401i | −0.840376 | − | 0.542004i | \(-0.817666\pi\) | ||||
0.840376 | − | 0.542004i | \(-0.182334\pi\) | |||||||
\(954\) | −26.4449 | −0.856184 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4.73205 | 0.153045 | ||||||||
\(957\) | 0.928203i | 0.0300045i | ||||||||
\(958\) | − 8.78461i | − 0.283818i | ||||||||
\(959\) | −12.9282 | −0.417473 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | − 14.9282i | − 0.481305i | ||||||||
\(963\) | − 48.9282i | − 1.57669i | ||||||||
\(964\) | −6.73205 | −0.216825 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.60770 | −0.0517267 | ||||||||
\(967\) | 13.0718i | 0.420361i | 0.977663 | + | 0.210180i | \(0.0674051\pi\) | ||||
−0.977663 | + | 0.210180i | \(0.932595\pi\) | |||||||
\(968\) | − 1.00000i | − 0.0321412i | ||||||||
\(969\) | 8.28719 | 0.266223 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.0718 | 0.932958 | 0.466479 | − | 0.884532i | \(-0.345522\pi\) | ||||
0.466479 | + | 0.884532i | \(0.345522\pi\) | |||||||
\(972\) | − 15.2679i | − 0.489720i | ||||||||
\(973\) | 3.66025i | 0.117342i | ||||||||
\(974\) | 6.19615 | 0.198538 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.92820 | 0.285785 | ||||||||
\(977\) | 21.7128i | 0.694654i | 0.937744 | + | 0.347327i | \(0.112911\pi\) | ||||
−0.937744 | + | 0.347327i | \(0.887089\pi\) | |||||||
\(978\) | − 2.92820i | − 0.0936336i | ||||||||
\(979\) | 3.46410 | 0.110713 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.09103 | −0.130617 | ||||||||
\(982\) | 27.7128i | 0.884351i | ||||||||
\(983\) | − 25.1769i | − 0.803019i | −0.915855 | − | 0.401509i | \(-0.868486\pi\) | ||||
0.915855 | − | 0.401509i | \(-0.131514\pi\) | |||||||
\(984\) | 6.00000 | 0.191273 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.39230 | −0.139879 | ||||||||
\(987\) | 5.07180i | 0.161437i | ||||||||
\(988\) | − 17.8564i | − 0.568088i | ||||||||
\(989\) | −4.39230 | −0.139667 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.00000 | −0.127064 | −0.0635321 | − | 0.997980i | \(-0.520237\pi\) | ||||
−0.0635321 | + | 0.997980i | \(0.520237\pi\) | |||||||
\(992\) | 2.00000i | 0.0635001i | ||||||||
\(993\) | 16.6795i | 0.529308i | ||||||||
\(994\) | −2.53590 | −0.0804338 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.21539 | −0.101884 | ||||||||
\(997\) | − 37.7128i | − 1.19438i | −0.802101 | − | 0.597188i | \(-0.796284\pi\) | ||||
0.802101 | − | 0.597188i | \(-0.203716\pi\) | |||||||
\(998\) | − 39.8564i | − 1.26163i | ||||||||
\(999\) | 10.9282 | 0.345753 |
(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 | 3850.2.c.x.1849.4 | 4 | ||
5.2 | odd | 4 | 3850.2.a.bd.1.2 | 2 | |||
5.3 | odd | 4 | 770.2.a.j.1.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 3850.2.c.x.1849.1 | 4 | ||
15.8 | even | 4 | 6930.2.a.bv.1.2 | 2 | |||
20.3 | even | 4 | 6160.2.a.t.1.2 | 2 | |||
35.13 | even | 4 | 5390.2.a.bs.1.2 | 2 | |||
55.43 | even | 4 | 8470.2.a.br.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.a.j.1.1 | ✓ | 2 | 5.3 | odd | 4 | ||
3850.2.a.bd.1.2 | 2 | 5.2 | odd | 4 | |||
3850.2.c.x.1849.1 | 4 | 5.4 | even | 2 | inner | ||
3850.2.c.x.1849.4 | 4 | 1.1 | even | 1 | trivial | ||
5390.2.a.bs.1.2 | 2 | 35.13 | even | 4 | |||
6160.2.a.t.1.2 | 2 | 20.3 | even | 4 | |||
6930.2.a.bv.1.2 | 2 | 15.8 | even | 4 | |||
8470.2.a.br.1.1 | 2 | 55.43 | even | 4 |