Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1201,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.1201");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.q (of order \(3\), degree \(2\), 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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.17819046144.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 10x^{6} + 8x^{5} + 38x^{4} - 4x^{3} + 16x^{2} + 4x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1201.1 | ||
Root | \(-0.868255 + 1.50386i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1201 |
Dual form | 2100.2.q.m.1801.1 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.61250 | − | 0.418148i | −0.987432 | − | 0.158045i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.292387 | − | 0.506430i | 0.0881581 | − | 0.152694i | −0.818574 | − | 0.574400i | \(-0.805235\pi\) |
0.906733 | + | 0.421706i | \(0.138569\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.75198 | 0.485911 | 0.242956 | − | 0.970037i | \(-0.421883\pi\) | ||||
0.242956 | + | 0.970037i | \(0.421883\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.11250 | + | 5.39101i | −0.754892 | + | 1.30751i | 0.190536 | + | 0.981680i | \(0.438977\pi\) |
−0.945428 | + | 0.325831i | \(0.894356\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.48075 | + | 6.02884i | 0.798540 | + | 1.38311i | 0.920567 | + | 0.390585i | \(0.127727\pi\) |
−0.122027 | + | 0.992527i | \(0.538940\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.66838 | + | 2.05342i | −0.364070 | + | 0.448092i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.37599 | + | 2.38328i | 0.286914 | + | 0.496949i | 0.973071 | − | 0.230504i | \(-0.0740374\pi\) |
−0.686158 | + | 0.727453i | \(0.740704\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.24047 | 0.601739 | 0.300870 | − | 0.953665i | \(-0.402723\pi\) | ||||
0.300870 | + | 0.953665i | \(0.402723\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.25198 | − | 2.16849i | 0.224862 | − | 0.389472i | −0.731416 | − | 0.681931i | \(-0.761140\pi\) |
0.956278 | + | 0.292459i | \(0.0944736\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.292387 | − | 0.506430i | −0.0508981 | − | 0.0881581i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.94412 | + | 3.36732i | 0.319612 | + | 0.553584i | 0.980407 | − | 0.196982i | \(-0.0631142\pi\) |
−0.660795 | + | 0.750566i | \(0.729781\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.875989 | − | 1.51726i | 0.140271 | − | 0.242956i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.58477 | 0.716022 | 0.358011 | − | 0.933717i | \(-0.383455\pi\) | ||||
0.358011 | + | 0.933717i | \(0.383455\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.754325 | 0.115033 | 0.0575167 | − | 0.998345i | \(-0.481682\pi\) | ||||
0.0575167 | + | 0.998345i | \(0.481682\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.727603 | − | 1.26025i | −0.106132 | − | 0.183826i | 0.808068 | − | 0.589089i | \(-0.200513\pi\) |
−0.914200 | + | 0.405263i | \(0.867180\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.65030 | + | 2.18482i | 0.950043 | + | 0.312118i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.11250 | + | 5.39101i | 0.435837 | + | 0.754892i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.263490 | − | 0.456378i | 0.0361931 | − | 0.0626883i | −0.847361 | − | 0.531017i | \(-0.821810\pi\) |
0.883555 | + | 0.468328i | \(0.155144\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.96151 | 0.922074 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.05327 | − | 8.75253i | 0.657880 | − | 1.13948i | −0.323283 | − | 0.946302i | \(-0.604787\pi\) |
0.981163 | − | 0.193180i | \(-0.0618800\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.07704 | − | 7.06164i | −0.522012 | − | 0.904151i | −0.999672 | − | 0.0256061i | \(-0.991848\pi\) |
0.477660 | − | 0.878545i | \(-0.341485\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.944123 | + | 2.47156i | 0.118948 | + | 0.311388i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.34901 | − | 12.7289i | 0.897824 | − | 1.55508i | 0.0675547 | − | 0.997716i | \(-0.478480\pi\) |
0.830270 | − | 0.557362i | \(-0.188186\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.75198 | 0.331299 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.3561 | 1.58507 | 0.792536 | − | 0.609825i | \(-0.208760\pi\) | ||||
0.792536 | + | 0.609825i | \(0.208760\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.37716 | + | 5.84942i | −0.395267 | + | 0.684622i | −0.993135 | − | 0.116972i | \(-0.962681\pi\) |
0.597868 | + | 0.801594i | \(0.296015\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.975625 | + | 1.20079i | −0.111183 | + | 0.136842i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.04771 | + | 7.01085i | 0.455403 | + | 0.788782i | 0.998711 | − | 0.0507516i | \(-0.0161617\pi\) |
−0.543308 | + | 0.839534i | \(0.682828\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.72895 | −0.628834 | −0.314417 | − | 0.949285i | \(-0.601809\pi\) | ||||
−0.314417 | + | 0.949285i | \(0.601809\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.62023 | − | 2.80633i | 0.173707 | − | 0.300870i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.50192 | + | 14.7258i | 0.901202 | + | 1.56093i | 0.825936 | + | 0.563763i | \(0.190647\pi\) |
0.0752651 | + | 0.997164i | \(0.476020\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.57704 | − | 0.732586i | −0.479804 | − | 0.0767959i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.25198 | − | 2.16849i | −0.129824 | − | 0.224862i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.1132 | 1.12838 | 0.564189 | − | 0.825645i | \(-0.309189\pi\) | ||||
0.564189 | + | 0.825645i | \(0.309189\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.584775 | −0.0587721 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.67803 | + | 15.0308i | −0.863496 | + | 1.49562i | 0.00503661 | + | 0.999987i | \(0.498397\pi\) |
−0.868533 | + | 0.495632i | \(0.834937\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.68063 | + | 11.5712i | 0.658262 | + | 1.14014i | 0.981065 | + | 0.193678i | \(0.0620416\pi\) |
−0.322803 | + | 0.946466i | \(0.604625\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.06361 | + | 1.84223i | 0.102823 | + | 0.178095i | 0.912847 | − | 0.408302i | \(-0.133879\pi\) |
−0.810024 | + | 0.586397i | \(0.800546\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.14400 | + | 1.98147i | −0.109575 | + | 0.189790i | −0.915598 | − | 0.402094i | \(-0.868282\pi\) |
0.806023 | + | 0.591884i | \(0.201616\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.88825 | 0.369056 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.7765 | −1.10784 | −0.553920 | − | 0.832570i | \(-0.686868\pi\) | ||||
−0.553920 | + | 0.832570i | \(0.686868\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.875989 | − | 1.51726i | −0.0809852 | − | 0.140271i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.3856 | − | 12.7825i | 0.952050 | − | 1.17177i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.32902 | + | 9.23013i | 0.484456 | + | 0.839103i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.29239 | − | 3.97053i | 0.206698 | − | 0.358011i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.2606 | −1.35416 | −0.677081 | − | 0.735909i | \(-0.736755\pi\) | ||||
−0.677081 | + | 0.735909i | \(0.736755\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.377162 | − | 0.653265i | 0.0332073 | − | 0.0575167i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.00891 | − | 6.94363i | −0.350260 | − | 0.606668i | 0.636035 | − | 0.771660i | \(-0.280573\pi\) |
−0.986295 | + | 0.164992i | \(0.947240\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.57252 | − | 17.2058i | −0.569910 | − | 1.49193i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.34641 | + | 12.7243i | −0.627646 | + | 1.08711i | 0.360377 | + | 0.932807i | \(0.382648\pi\) |
−0.988023 | + | 0.154308i | \(0.950685\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.1080 | 1.62072 | 0.810361 | − | 0.585931i | \(-0.199271\pi\) | ||||
0.810361 | + | 0.585931i | \(0.199271\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.45521 | −0.122550 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.512256 | − | 0.887254i | 0.0428370 | − | 0.0741959i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.21726 | − | 4.66692i | 0.430313 | − | 0.384921i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.912621 | + | 1.58071i | 0.0747648 | + | 0.129496i | 0.900984 | − | 0.433852i | \(-0.142846\pi\) |
−0.826219 | + | 0.563349i | \(0.809513\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.41379 | − | 4.18081i | 0.196432 | − | 0.340230i | −0.750937 | − | 0.660374i | \(-0.770398\pi\) |
0.947369 | + | 0.320144i | \(0.103731\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.22500 | 0.503261 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.24281 | − | 12.5449i | 0.578039 | − | 1.00119i | −0.417665 | − | 0.908601i | \(-0.637151\pi\) |
0.995704 | − | 0.0925924i | \(-0.0295154\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.263490 | − | 0.456378i | −0.0208961 | − | 0.0361931i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.59820 | − | 6.80169i | −0.204767 | − | 0.536048i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.80977 | − | 10.0628i | −0.455057 | − | 0.788181i | 0.543635 | − | 0.839322i | \(-0.317048\pi\) |
−0.998691 | + | 0.0511407i | \(0.983714\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.2998 | −1.64822 | −0.824112 | − | 0.566427i | \(-0.808325\pi\) | ||||
−0.824112 | + | 0.566427i | \(0.808325\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.93057 | −0.763890 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.48075 | − | 6.02884i | 0.266180 | − | 0.461037i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.99109 | + | 10.3769i | 0.455494 | + | 0.788939i | 0.998716 | − | 0.0506497i | \(-0.0161292\pi\) |
−0.543222 | + | 0.839589i | \(0.682796\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.05327 | − | 8.75253i | −0.379827 | − | 0.657880i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.2095 | + | 17.6834i | −0.763096 | + | 1.32172i | 0.178151 | + | 0.984003i | \(0.442988\pi\) |
−0.941247 | + | 0.337718i | \(0.890345\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.8276 | 1.47377 | 0.736887 | − | 0.676016i | \(-0.236295\pi\) | ||||
0.736887 | + | 0.676016i | \(0.236295\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.15408 | −0.602767 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.82011 | + | 3.15253i | 0.133100 | + | 0.230536i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.61250 | + | 0.418148i | 0.190031 | + | 0.0304158i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.39976 | + | 2.42445i | 0.101283 | + | 0.175427i | 0.912213 | − | 0.409715i | \(-0.134372\pi\) |
−0.810931 | + | 0.585142i | \(0.801039\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.5289 | − | 18.2366i | 0.757887 | − | 1.31270i | −0.186040 | − | 0.982542i | \(-0.559565\pi\) |
0.943926 | − | 0.330156i | \(-0.107101\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.18416 | −0.511850 | −0.255925 | − | 0.966697i | \(-0.582380\pi\) | ||||
−0.255925 | + | 0.966697i | \(0.582380\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.54771 | − | 9.60892i | 0.393267 | − | 0.681159i | −0.599611 | − | 0.800291i | \(-0.704678\pi\) |
0.992878 | + | 0.119133i | \(0.0380115\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.34901 | − | 12.7289i | −0.518359 | − | 0.897824i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.46572 | − | 1.35499i | −0.594177 | − | 0.0951020i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.37599 | − | 2.38328i | 0.0956378 | − | 0.165650i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.07092 | 0.281591 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.2340 | 0.842226 | 0.421113 | − | 0.907008i | \(-0.361640\pi\) | ||||
0.421113 | + | 0.907008i | \(0.361640\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.67803 | − | 11.5667i | 0.457571 | − | 0.792536i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.17754 | + | 5.14166i | −0.283590 | + | 0.349039i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.37716 | + | 5.84942i | 0.228207 | + | 0.395267i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.45303 | + | 9.44493i | −0.366810 | + | 0.635334i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.8074 | 0.790684 | 0.395342 | − | 0.918534i | \(-0.370626\pi\) | ||||
0.395342 | + | 0.918534i | \(0.370626\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.0984 | + | 22.6871i | −0.869370 | + | 1.50579i | −0.00672884 | + | 0.999977i | \(0.502142\pi\) |
−0.862641 | + | 0.505816i | \(0.831191\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.97067 | − | 8.60946i | −0.328471 | − | 0.568929i | 0.653737 | − | 0.756721i | \(-0.273200\pi\) |
−0.982209 | + | 0.187792i | \(0.939867\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.552099 | + | 1.44531i | 0.0363255 | + | 0.0950944i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.68241 | + | 13.3063i | 0.503292 | + | 0.871727i | 0.999993 | + | 0.00380503i | \(0.00121118\pi\) |
−0.496701 | + | 0.867922i | \(0.665455\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.09543 | 0.525855 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.2183 | −0.984390 | −0.492195 | − | 0.870485i | \(-0.663805\pi\) | ||||
−0.492195 | + | 0.870485i | \(0.663805\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.3730 | + | 23.1626i | −0.861428 | + | 1.49204i | 0.00912311 | + | 0.999958i | \(0.497096\pi\) |
−0.870551 | + | 0.492078i | \(0.836237\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.09820 | + | 10.5624i | 0.388019 | + | 0.672069i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.86448 | + | 4.96142i | −0.181529 | + | 0.314417i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.05310 | 0.508307 | 0.254154 | − | 0.967164i | \(-0.418203\pi\) | ||||
0.254154 | + | 0.967164i | \(0.418203\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.60929 | 0.101175 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.98514 | + | 13.8307i | 0.498099 | + | 0.862733i | 0.999998 | − | 0.00219336i | \(-0.000698168\pi\) |
−0.501898 | + | 0.864927i | \(0.667365\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.67098 | − | 9.61005i | −0.228104 | − | 0.597139i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.62023 | − | 2.80633i | −0.100290 | − | 0.173707i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.7454 | − | 20.3437i | 0.724253 | − | 1.25444i | −0.235027 | − | 0.971989i | \(-0.575518\pi\) |
0.959281 | − | 0.282455i | \(-0.0911488\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.0038 | 1.04062 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.56831 | + | 11.3766i | −0.400477 | + | 0.693647i | −0.993783 | − | 0.111330i | \(-0.964489\pi\) |
0.593306 | + | 0.804977i | \(0.297822\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.69275 | − | 4.66398i | −0.163573 | − | 0.283317i | 0.772575 | − | 0.634924i | \(-0.218969\pi\) |
−0.936148 | + | 0.351607i | \(0.885635\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.92296 | + | 3.59754i | −0.176906 | + | 0.217733i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.03285 | − | 8.71716i | 0.302395 | − | 0.523763i | −0.674283 | − | 0.738473i | \(-0.735547\pi\) |
0.976678 | + | 0.214710i | \(0.0688805\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.50396 | −0.149908 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.8822 | −1.60366 | −0.801828 | − | 0.597555i | \(-0.796139\pi\) | ||||
−0.801828 | + | 0.597555i | \(0.796139\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.92865 | + | 10.2687i | −0.352422 | + | 0.610413i | −0.986673 | − | 0.162714i | \(-0.947975\pi\) |
0.634251 | + | 0.773127i | \(0.281308\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.9777 | − | 1.91711i | −0.707023 | − | 0.113164i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.8753 | − | 18.8366i | −0.639724 | − | 1.10803i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.55662 | − | 9.62435i | 0.325735 | − | 0.564189i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.3879 | 0.957388 | 0.478694 | − | 0.877982i | \(-0.341110\pi\) | ||||
0.478694 | + | 0.877982i | \(0.341110\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.292387 | + | 0.506430i | −0.0169660 | + | 0.0293860i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.41070 | + | 4.17546i | 0.139415 | + | 0.241473i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.97067 | − | 0.315420i | −0.113588 | − | 0.0181805i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.67803 | + | 15.0308i | 0.498540 | + | 0.863496i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.0141 | 1.14226 | 0.571132 | − | 0.820858i | \(-0.306504\pi\) | ||||
0.571132 | + | 0.820858i | \(0.306504\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.3613 | 0.760096 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.3183 | − | 24.7999i | 0.811914 | − | 1.40628i | −0.0996095 | − | 0.995027i | \(-0.531759\pi\) |
0.911523 | − | 0.411249i | \(-0.134907\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.6806 | + | 23.6956i | 0.773275 | + | 1.33935i | 0.935759 | + | 0.352641i | \(0.114716\pi\) |
−0.162484 | + | 0.986711i | \(0.551951\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.00830 | − | 6.94258i | −0.225129 | − | 0.389934i | 0.731229 | − | 0.682132i | \(-0.238947\pi\) |
−0.956358 | + | 0.292197i | \(0.905614\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.947472 | − | 1.64107i | 0.0530482 | − | 0.0918822i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.12722 | 0.118730 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −43.3354 | −2.41125 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.14400 | + | 1.98147i | 0.0632634 | + | 0.109575i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.37389 | + | 3.59664i | 0.0757452 | + | 0.198289i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.98849 | − | 8.64032i | −0.274192 | − | 0.474915i | 0.695739 | − | 0.718295i | \(-0.255077\pi\) |
−0.969931 | + | 0.243380i | \(0.921744\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.94412 | − | 3.36732i | 0.106537 | − | 0.184528i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.936640 | −0.0510220 | −0.0255110 | − | 0.999675i | \(-0.508121\pi\) | ||||
−0.0255110 | + | 0.999675i | \(0.508121\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.88825 | + | 10.1987i | −0.319806 | + | 0.553920i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.732125 | − | 1.26808i | −0.0396468 | − | 0.0686703i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.4603 | − | 8.48866i | −0.888775 | − | 0.458345i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.0887310 | + | 0.153687i | −0.00476333 | + | 0.00825033i | −0.868397 | − | 0.495869i | \(-0.834850\pi\) |
0.863634 | + | 0.504119i | \(0.168183\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −31.6891 | −1.69628 | −0.848139 | − | 0.529774i | \(-0.822277\pi\) | ||||
−0.848139 | + | 0.529774i | \(0.822277\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.75198 | −0.0935137 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.2323 | + | 21.1870i | −0.651060 | + | 1.12767i | 0.331806 | + | 0.943348i | \(0.392342\pi\) |
−0.982866 | + | 0.184321i | \(0.940991\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.87716 | − | 15.3855i | −0.311052 | − | 0.814286i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.01243 | − | 13.8779i | −0.422880 | − | 0.732450i | 0.573340 | − | 0.819318i | \(-0.305648\pi\) |
−0.996220 | + | 0.0868679i | \(0.972314\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.7313 | + | 25.5154i | −0.775332 | + | 1.34291i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.6580 | 0.559402 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.67029 | − | 13.2853i | 0.400386 | − | 0.693489i | −0.593386 | − | 0.804918i | \(-0.702209\pi\) |
0.993772 | + | 0.111429i | \(0.0355427\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.29239 | − | 3.97053i | −0.119337 | − | 0.206698i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.879200 | + | 1.08211i | −0.0456458 | + | 0.0561803i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.82054 | − | 3.15327i | −0.0942640 | − | 0.163270i | 0.815037 | − | 0.579409i | \(-0.196716\pi\) |
−0.909301 | + | 0.416139i | \(0.863383\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.67723 | 0.292392 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.08959 | 0.210068 | 0.105034 | − | 0.994469i | \(-0.466505\pi\) | ||||
0.105034 | + | 0.994469i | \(0.466505\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.63031 | + | 13.2161i | −0.390913 | + | 0.677081i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.96002 | + | 6.85895i | 0.202348 | + | 0.350476i | 0.949284 | − | 0.314419i | \(-0.101810\pi\) |
−0.746937 | + | 0.664895i | \(0.768476\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.377162 | − | 0.653265i | −0.0191722 | − | 0.0332073i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.3028 | − | 19.5770i | 0.573074 | − | 0.992593i | −0.423174 | − | 0.906048i | \(-0.639084\pi\) |
0.996248 | − | 0.0865447i | \(-0.0275825\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.1311 | −0.866355 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.01781 | −0.404445 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.1484 | − | 19.3097i | −0.559524 | − | 0.969125i | −0.997536 | − | 0.0701554i | \(-0.977650\pi\) |
0.438012 | − | 0.898969i | \(-0.355683\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −18.1869 | − | 2.91094i | −0.910486 | − | 0.145729i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.52177 | + | 6.09989i | 0.175869 | + | 0.304614i | 0.940462 | − | 0.339900i | \(-0.110393\pi\) |
−0.764593 | + | 0.644514i | \(0.777060\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.19344 | − | 3.79915i | 0.109263 | − | 0.189249i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.27375 | 0.112706 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.62957 | + | 8.01865i | −0.228917 | + | 0.396497i | −0.957488 | − | 0.288475i | \(-0.906852\pi\) |
0.728570 | + | 0.684971i | \(0.240185\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.34641 | + | 12.7243i | 0.362371 | + | 0.627646i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −16.8615 | + | 20.7529i | −0.829701 | + | 1.02119i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.55402 | − | 16.5480i | 0.467862 | − | 0.810361i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.9183 | −0.582248 | −0.291124 | − | 0.956685i | \(-0.594029\pi\) | ||||
−0.291124 | + | 0.956685i | \(0.594029\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.68576 | −0.277107 | −0.138553 | − | 0.990355i | \(-0.544245\pi\) | ||||
−0.138553 | + | 0.990355i | \(0.544245\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.727603 | + | 1.26025i | −0.0353773 | + | 0.0612752i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.69845 | + | 20.1533i | 0.372554 | + | 0.975289i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.512256 | − | 0.887254i | −0.0247320 | − | 0.0428370i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.85866 | − | 11.8796i | 0.330370 | − | 0.572218i | −0.652214 | − | 0.758035i | \(-0.726160\pi\) |
0.982584 | + | 0.185817i | \(0.0594931\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.8294 | −1.09711 | −0.548556 | − | 0.836114i | \(-0.684822\pi\) | ||||
−0.548556 | + | 0.836114i | \(0.684822\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.57896 | + | 16.5912i | −0.458224 | + | 0.793667i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.6966 | − | 34.1155i | −0.940067 | − | 1.62824i | −0.765340 | − | 0.643627i | \(-0.777429\pi\) |
−0.174727 | − | 0.984617i | \(-0.555904\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.43304 | − | 6.85174i | −0.0682400 | − | 0.326274i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.58342 | + | 4.47462i | 0.122742 | + | 0.212596i | 0.920848 | − | 0.389921i | \(-0.127498\pi\) |
−0.798106 | + | 0.602517i | \(0.794165\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.82524 | 0.0863309 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −36.7384 | −1.73379 | −0.866895 | − | 0.498491i | \(-0.833888\pi\) | ||||
−0.866895 | + | 0.498491i | \(0.833888\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.34053 | − | 2.32187i | 0.0631231 | − | 0.109332i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.41379 | − | 4.18081i | −0.113410 | − | 0.196432i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.597031 | + | 1.03409i | 0.0279280 | + | 0.0483726i | 0.879652 | − | 0.475619i | \(-0.157776\pi\) |
−0.851724 | + | 0.523991i | \(0.824442\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.11250 | − | 5.39101i | 0.145279 | − | 0.251631i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.5340 | −0.676917 | −0.338459 | − | 0.940981i | \(-0.609906\pi\) | ||||
−0.338459 | + | 0.940981i | \(0.609906\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.2762 | 1.50000 | 0.750001 | − | 0.661436i | \(-0.230053\pi\) | ||||
0.750001 | + | 0.661436i | \(0.230053\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.15174 | + | 10.6551i | 0.284668 | + | 0.493060i | 0.972529 | − | 0.232783i | \(-0.0747832\pi\) |
−0.687860 | + | 0.725843i | \(0.741450\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −24.5218 | + | 30.1812i | −1.13231 | + | 1.39364i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.24281 | − | 12.5449i | −0.333731 | − | 0.578039i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.220555 | − | 0.382013i | 0.0101411 | − | 0.0175650i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.526980 | −0.0241287 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.5196 | − | 19.9525i | 0.526342 | − | 0.911651i | −0.473187 | − | 0.880962i | \(-0.656896\pi\) |
0.999529 | − | 0.0306893i | \(-0.00977024\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.40606 | + | 5.89947i | 0.155303 | + | 0.268993i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.18954 | − | 1.15073i | −0.327135 | − | 0.0523602i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.80507 | − | 15.2508i | 0.398996 | − | 0.691081i | −0.594606 | − | 0.804017i | \(-0.702692\pi\) |
0.993602 | + | 0.112936i | \(0.0360254\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.6195 | −0.525454 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.7403 | −0.845740 | −0.422870 | − | 0.906190i | \(-0.638977\pi\) | ||||
−0.422870 | + | 0.906190i | \(0.638977\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.0859 | + | 17.4694i | −0.454248 | + | 0.786781i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −34.8927 | − | 5.58481i | −1.56515 | − | 0.250513i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.0063 | + | 24.2596i | 0.627008 | + | 1.08601i | 0.988149 | + | 0.153499i | \(0.0490541\pi\) |
−0.361141 | + | 0.932511i | \(0.617613\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.6499 | + | 18.4461i | −0.475801 | + | 0.824112i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.7178 | 0.745412 | 0.372706 | − | 0.927950i | \(-0.378430\pi\) | ||||
0.372706 | + | 0.927950i | \(0.378430\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.96529 | + | 8.60013i | −0.220516 | + | 0.381945i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.131059 | − | 0.227000i | −0.00580907 | − | 0.0100616i | 0.863106 | − | 0.505022i | \(-0.168516\pi\) |
−0.868915 | + | 0.494961i | \(0.835182\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.2688 | − | 13.8694i | 0.498500 | − | 0.613548i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.48075 | − | 6.02884i | −0.153679 | − | 0.266180i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.850968 | −0.0374255 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.9822 | 0.525960 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.1710 | − | 33.2052i | 0.839898 | − | 1.45475i | −0.0500804 | − | 0.998745i | \(-0.515948\pi\) |
0.889979 | − | 0.456002i | \(-0.150719\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.79603 | + | 3.11081i | 0.0785348 | + | 0.136026i | 0.902618 | − | 0.430443i | \(-0.141642\pi\) |
−0.824083 | + | 0.566469i | \(0.808309\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.79356 | + | 13.4988i | 0.339493 | + | 0.588019i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.71331 | − | 13.3598i | 0.335361 | − | 0.580863i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.1065 | −0.438587 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.03242 | 0.347923 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.2095 | + | 17.6834i | 0.440574 | + | 0.763096i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.05093 | − | 2.72910i | 0.131413 | − | 0.117551i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.48602 | − | 14.6982i | −0.364843 | − | 0.631926i | 0.623908 | − | 0.781498i | \(-0.285544\pi\) |
−0.988751 | + | 0.149572i | \(0.952211\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.91379 | − | 17.1712i | 0.425442 | − | 0.736887i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.0926 | −1.24391 | −0.621954 | − | 0.783054i | \(-0.713661\pi\) | ||||
−0.621954 | + | 0.783054i | \(0.713661\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.07704 | + | 7.06164i | −0.174004 | + | 0.301384i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.2793 | + | 19.5363i | 0.480513 | + | 0.832273i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.64308 | − | 20.0084i | −0.325017 | − | 0.850843i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.705437 | − | 1.22185i | 0.0298903 | − | 0.0517716i | −0.850693 | − | 0.525662i | \(-0.823818\pi\) |
0.880584 | + | 0.473891i | \(0.157151\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.32156 | 0.0558961 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.64022 | 0.153690 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.39455 | − | 7.61158i | 0.185208 | − | 0.320790i | −0.758439 | − | 0.651745i | \(-0.774037\pi\) |
0.943647 | + | 0.330955i | \(0.107371\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.66838 | − | 2.05342i | 0.0700652 | − | 0.0862354i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.0534 | − | 26.0733i | −0.631072 | − | 1.09305i | −0.987333 | − | 0.158662i | \(-0.949282\pi\) |
0.356261 | − | 0.934386i | \(-0.384051\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.0025 | − | 22.5210i | 0.544139 | − | 0.942476i | −0.454522 | − | 0.890736i | \(-0.650190\pi\) |
0.998661 | − | 0.0517403i | \(-0.0164768\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.79951 | 0.116951 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.6370 | − | 21.8879i | 0.526086 | − | 0.911207i | −0.473452 | − | 0.880819i | \(-0.656992\pi\) |
0.999538 | − | 0.0303878i | \(-0.00967423\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.5289 | − | 18.2366i | −0.437566 | − | 0.757887i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.9669 | + | 2.39555i | 0.620931 | + | 0.0993842i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.154082 | − | 0.266878i | −0.00638143 | − | 0.0110530i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.75719 | −0.237625 | −0.118812 | − | 0.992917i | \(-0.537909\pi\) | ||||
−0.118812 | + | 0.992917i | \(0.537909\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.4313 | 0.718245 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.59208 | + | 6.22167i | −0.147758 | + | 0.255925i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.98514 | + | 13.8307i | 0.327910 | + | 0.567957i | 0.982097 | − | 0.188376i | \(-0.0603223\pi\) |
−0.654187 | + | 0.756333i | \(0.726989\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.54771 | − | 9.60892i | −0.227053 | − | 0.393267i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.0976 | + | 22.6858i | −0.535155 | + | 0.926916i | 0.464001 | + | 0.885835i | \(0.346413\pi\) |
−0.999156 | + | 0.0410809i | \(0.986920\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.8615 | −0.891749 | −0.445875 | − | 0.895095i | \(-0.647107\pi\) | ||||
−0.445875 | + | 0.895095i | \(0.647107\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.6980 | −0.598550 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.30026 | + | 7.44827i | 0.174542 | + | 0.302316i | 0.940003 | − | 0.341167i | \(-0.110822\pi\) |
−0.765461 | + | 0.643483i | \(0.777489\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.40632 | + | 6.65403i | −0.219075 | + | 0.269635i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.27474 | − | 2.20792i | −0.0515706 | − | 0.0893229i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.1251 | − | 38.3217i | 0.893623 | − | 1.54780i | 0.0581239 | − | 0.998309i | \(-0.481488\pi\) |
0.835499 | − | 0.549491i | \(-0.185179\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −32.3683 | −1.30310 | −0.651550 | − | 0.758606i | \(-0.725881\pi\) | ||||
−0.651550 | + | 0.758606i | \(0.725881\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.0233 | + | 36.4134i | −0.844996 | + | 1.46358i | 0.0406284 | + | 0.999174i | \(0.487064\pi\) |
−0.885625 | + | 0.464402i | \(0.846269\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.37599 | − | 2.38328i | −0.0552165 | − | 0.0956378i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −16.0537 | − | 42.0261i | −0.643178 | − | 1.68374i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.03546 | − | 3.52552i | 0.0812884 | − | 0.140796i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −24.2043 | −0.965090 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.74086 | 0.148921 | 0.0744607 | − | 0.997224i | \(-0.476276\pi\) | ||||
0.0744607 | + | 0.997224i | \(0.476276\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.11702 | − | 10.5950i | 0.243130 | − | 0.421113i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.6512 | + | 3.82776i | 0.461637 | + | 0.151661i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.67803 | − | 11.5667i | −0.264179 | − | 0.457571i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.4004 | + | 30.1384i | −0.687275 | + | 1.19040i | 0.285441 | + | 0.958396i | \(0.407860\pi\) |
−0.972716 | + | 0.231999i | \(0.925473\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.9864 | 0.906494 | 0.453247 | − | 0.891385i | \(-0.350266\pi\) | ||||
0.453247 | + | 0.891385i | \(0.350266\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.31312 | − | 5.73850i | 0.130252 | − | 0.225604i | −0.793521 | − | 0.608542i | \(-0.791755\pi\) |
0.923774 | + | 0.382939i | \(0.125088\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.95503 | − | 5.11826i | −0.115995 | − | 0.200909i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.36404 | + | 6.18869i | 0.0926541 | + | 0.242554i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.24207 | − | 9.07953i | −0.205138 | − | 0.355309i | 0.745039 | − | 0.667021i | \(-0.232431\pi\) |
−0.950177 | + | 0.311712i | \(0.899098\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.75432 | 0.263511 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.2344 | 0.515539 | 0.257770 | − | 0.966206i | \(-0.417012\pi\) | ||||
0.257770 | + | 0.966206i | \(0.417012\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.75450 | − | 11.6991i | 0.262720 | − | 0.455044i | −0.704244 | − | 0.709958i | \(-0.748714\pi\) |
0.966964 | + | 0.254914i | \(0.0820472\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.45303 | + | 9.44493i | 0.211778 | + | 0.366810i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.45885 | + | 7.72295i | 0.172647 | + | 0.299034i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.90371 | − | 10.2255i | 0.228251 | − | 0.395342i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.76830 | −0.184078 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.8059 | −0.570727 | −0.285363 | − | 0.958419i | \(-0.592114\pi\) | ||||
−0.285363 | + | 0.958419i | \(0.592114\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.4531 | + | 37.1578i | 0.824509 | + | 1.42809i | 0.902294 | + | 0.431122i | \(0.141882\pi\) |
−0.0777847 | + | 0.996970i | \(0.524785\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −29.0333 | − | 4.64698i | −1.11420 | − | 0.178335i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.0984 | + | 22.6871i | 0.501931 | + | 0.869370i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.8824 | − | 41.3656i | 0.913836 | − | 1.58281i | 0.105239 | − | 0.994447i | \(-0.466439\pi\) |
0.808597 | − | 0.588363i | \(-0.200227\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.94135 | −0.379286 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.461628 | − | 0.799564i | 0.0175866 | − | 0.0304609i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.4948 | + | 18.1775i | 0.399241 | + | 0.691505i | 0.993632 | − | 0.112671i | \(-0.0359405\pi\) |
−0.594392 | + | 0.804176i | \(0.702607\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.52772 | + | 0.244523i | 0.0580334 | + | 0.00928864i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.2701 | + | 24.7166i | −0.540519 | + | 0.936206i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.3648 | 0.581151 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33.1194 | −1.25090 | −0.625452 | − | 0.780263i | \(-0.715085\pi\) | ||||
−0.625452 | + | 0.780263i | \(0.715085\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.5340 | + | 23.4416i | −0.510446 | + | 0.884118i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 28.9564 | − | 35.6392i | 1.08902 | − | 1.34035i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.7366 | + | 28.9886i | 0.628555 | + | 1.08869i | 0.987842 | + | 0.155462i | \(0.0496866\pi\) |
−0.359287 | + | 0.933227i | \(0.616980\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.04771 | − | 7.01085i | 0.151801 | − | 0.262927i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.89083 | 0.258064 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.60915 | + | 13.1794i | −0.284169 | + | 0.492195i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.43588 | − | 12.8793i | −0.277312 | − | 0.480318i | 0.693404 | − | 0.720549i | \(-0.256110\pi\) |
−0.970716 | + | 0.240231i | \(0.922777\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.6147 | − | 33.0232i | −0.469795 | − | 1.22985i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.3730 | + | 23.1626i | 0.497346 | + | 0.861428i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.9682 | −0.443876 | −0.221938 | − | 0.975061i | \(-0.571238\pi\) | ||||
−0.221938 | + | 0.975061i | \(0.571238\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.34784 | + | 4.06657i | −0.0868378 | + | 0.150408i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.8474 | + | 22.2524i | 0.474530 | + | 0.821909i | 0.999575 | − | 0.0291651i | \(-0.00928486\pi\) |
−0.525045 | + | 0.851074i | \(0.675952\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.29752 | − | 7.44352i | −0.158301 | − | 0.274185i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.38298 | − | 4.12744i | 0.0876593 | − | 0.151830i | −0.818862 | − | 0.573990i | \(-0.805395\pi\) |
0.906521 | + | 0.422160i | \(0.138728\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.1964 | 0.448046 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.9703 | −1.02613 | −0.513065 | − | 0.858350i | \(-0.671490\pi\) | ||||
−0.513065 | + | 0.858350i | \(0.671490\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.86448 | + | 4.96142i | 0.104806 | + | 0.181529i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.00836 | − | 5.25757i | −0.0733838 | − | 0.192107i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.8613 | − | 18.8123i | −0.396333 | − | 0.686469i | 0.596937 | − | 0.802288i | \(-0.296384\pi\) |
−0.993270 | + | 0.115819i | \(0.963051\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.02655 | − | 6.97419i | 0.146736 | − | 0.254154i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.2574 | −0.372812 | −0.186406 | − | 0.982473i | \(-0.559684\pi\) | ||||
−0.186406 | + | 0.982473i | \(0.559684\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.804644 | − | 1.39368i | 0.0292067 | − | 0.0505875i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.1717 | + | 26.2782i | 0.549975 | + | 0.952584i | 0.998276 | + | 0.0587013i | \(0.0186960\pi\) |
−0.448301 | + | 0.893883i | \(0.647971\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.81725 | − | 4.69822i | 0.138194 | − | 0.170087i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.85322 | − | 15.3342i | 0.319671 | − | 0.553687i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.8125 | 1.21931 | 0.609655 | − | 0.792667i | \(-0.291308\pi\) | ||||
0.609655 | + | 0.792667i | \(0.291308\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.9703 | 0.575156 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.52017 | − | 13.0253i | 0.270482 | − | 0.468488i | −0.698504 | − | 0.715607i | \(-0.746150\pi\) |
0.968985 | + | 0.247119i | \(0.0794837\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.1580 | − | 1.62586i | −0.364418 | − | 0.0583275i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15.9585 | + | 27.6409i | 0.571772 | + | 0.990338i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.90514 | − | 6.76391i | 0.139737 | − | 0.242032i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.24047 | −0.115805 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.911269 | + | 1.57836i | −0.0324832 | + | 0.0562626i | −0.881810 | − | 0.471605i | \(-0.843675\pi\) |
0.849327 | + | 0.527867i | \(0.177008\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.7454 | − | 20.3437i | −0.418148 | − | 0.724253i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 30.7661 | + | 4.92432i | 1.09392 | + | 0.175089i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.14289 | − | 12.3718i | −0.253651 | − | 0.439337i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.7990 | 0.949270 | 0.474635 | − | 0.880183i | \(-0.342580\pi\) | ||||
0.474635 | + | 0.880183i | \(0.342580\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.05865 | 0.320472 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.50192 | − | 14.7258i | 0.300401 | − | 0.520309i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.97488 | + | 3.42059i | 0.0696920 | + | 0.120710i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.56831 | + | 11.3766i | 0.231216 | + | 0.400477i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.01125 | − | 1.75154i | 0.0355538 | − | 0.0615810i | −0.847701 | − | 0.530474i | \(-0.822014\pi\) |
0.883255 | + | 0.468893i | \(0.155347\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.357073 | −0.0125385 | −0.00626927 | − | 0.999980i | \(-0.501996\pi\) | ||||
−0.00626927 | + | 0.999980i | \(0.501996\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.38550 | −0.188878 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.62562 | + | 4.54771i | 0.0918588 | + | 0.159104i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.65408 | + | 4.33013i | 0.0577983 | + | 0.151307i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.37963 | − | 4.12164i | −0.0830496 | − | 0.143846i | 0.821509 | − | 0.570196i | \(-0.193133\pi\) |
−0.904558 | + | 0.426350i | \(0.859799\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.3679 | + | 19.6898i | −0.396260 | + | 0.686342i | −0.993261 | − | 0.115898i | \(-0.963025\pi\) |
0.597002 | + | 0.802240i | \(0.296359\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.46781 | 0.224908 | 0.112454 | − | 0.993657i | \(-0.464129\pi\) | ||||
0.112454 | + | 0.993657i | \(0.464129\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.18015 | + | 2.04407i | −0.0409882 | + | 0.0709936i | −0.885792 | − | 0.464083i | \(-0.846384\pi\) |
0.844804 | + | 0.535077i | \(0.179717\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.03285 | − | 8.71716i | −0.174588 | − | 0.302395i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −32.4775 | + | 29.0516i | −1.12528 | + | 1.00658i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.25198 | + | 2.16849i | −0.0432747 | + | 0.0749540i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31.3590 | 1.08263 | 0.541317 | − | 0.840819i | \(-0.317926\pi\) | ||||
0.541317 | + | 0.840819i | \(0.317926\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.4994 | −0.637910 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.4411 | + | 23.2806i | −0.462936 | + | 0.801828i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.0625 | − | 26.3420i | −0.345751 | − | 0.905123i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.92865 | + | 10.2687i | 0.203471 | + | 0.352422i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.35018 | + | 9.26679i | −0.183402 | + | 0.317661i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.4278 | 0.596718 | 0.298359 | − | 0.954454i | \(-0.403561\pi\) | ||||
0.298359 | + | 0.954454i | \(0.403561\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.35161 | − | 4.07311i | 0.0803296 | − | 0.139135i | −0.823062 | − | 0.567952i | \(-0.807736\pi\) |
0.903392 | + | 0.428817i | \(0.141069\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.99708 | − | 6.92315i | −0.136379 | − | 0.236215i | 0.789745 | − | 0.613436i | \(-0.210213\pi\) |
−0.926123 | + | 0.377221i | \(0.876880\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.64913 | + | 9.41445i | −0.260682 | + | 0.320844i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.3547 | + | 17.9349i | 0.352478 | + | 0.610510i | 0.986683 | − | 0.162655i | \(-0.0520057\pi\) |
−0.634205 | + | 0.773165i | \(0.718672\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −21.7506 | −0.738689 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.73400 | 0.160590 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.8753 | − | 22.3007i | 0.436263 | − | 0.755630i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.55662 | − | 9.62435i | −0.188063 | − | 0.325735i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.15174 | − | 14.1192i | −0.275265 | − | 0.476772i | 0.694937 | − | 0.719070i | \(-0.255432\pi\) |
−0.970202 | + | 0.242298i | \(0.922099\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.19393 | − | 14.1923i | 0.276374 | − | 0.478694i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.44801 | 0.284621 | 0.142310 | − | 0.989822i | \(-0.454547\pi\) | ||||
0.142310 | + | 0.989822i | \(0.454547\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.6622 | −1.36839 | −0.684197 | − | 0.729298i | \(-0.739847\pi\) | ||||
−0.684197 | + | 0.729298i | \(0.739847\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.8781 | − | 18.8414i | −0.365250 | − | 0.632632i | 0.623566 | − | 0.781771i | \(-0.285683\pi\) |
−0.988816 | + | 0.149139i | \(0.952350\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 39.8684 | + | 6.38120i | 1.33714 | + | 0.214019i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.292387 | + | 0.506430i | 0.00979535 | + | 0.0169660i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.06521 | − | 8.77321i | 0.169501 | − | 0.293584i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.82140 | 0.160982 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.05699 | − | 7.02692i | 0.135308 | − | 0.234361i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.64022 | + | 2.84095i | 0.0546438 | + | 0.0946458i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.25850 | + | 1.54894i | −0.0418802 | + | 0.0515456i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.5598 | − | 21.7543i | 0.417042 | − | 0.722339i | −0.578598 | − | 0.815613i | \(-0.696400\pi\) |
0.995640 | + | 0.0932742i | \(0.0297333\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.3561 | 0.575664 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.33526 | −0.309291 | −0.154646 | − | 0.987970i | \(-0.549424\pi\) | ||||
−0.154646 | + | 0.987970i | \(0.549424\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.67507 | + | 2.90131i | −0.0554369 | + | 0.0960195i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.56980 | + | 19.8165i | 0.249977 | + | 0.654400i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.5657 | − | 18.3003i | −0.348531 | − | 0.603673i | 0.637458 | − | 0.770485i | \(-0.279986\pi\) |
−0.985989 | + | 0.166812i | \(0.946653\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.0070 | − | 17.3327i | 0.329743 | − | 0.571132i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 23.3995 | 0.770205 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.68063 | − | 11.5712i | 0.219421 | − | 0.380048i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.4611 | + | 49.2960i | 0.933778 | + | 1.61735i | 0.776799 | + | 0.629748i | \(0.216842\pi\) |
0.156979 | + | 0.987602i | \(0.449825\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.97612 | + | 47.6985i | 0.326954 | + | 1.56325i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14.3183 | − | 24.7999i | −0.468759 | − | 0.811914i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.1734 | −0.365019 | −0.182509 | − | 0.983204i | \(-0.558422\pi\) | ||||
−0.182509 | + | 0.983204i | \(0.558422\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.3613 | 0.892901 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.9941 | + | 25.9706i | −0.488794 | + | 0.846616i | −0.999917 | − | 0.0128918i | \(-0.995896\pi\) |
0.511123 | + | 0.859508i | \(0.329230\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.30860 | + | 10.9268i | 0.205436 | + | 0.355826i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.8297 | − | 34.3460i | −0.644378 | − | 1.11610i | −0.984445 | − | 0.175694i | \(-0.943783\pi\) |
0.340067 | − | 0.940401i | \(-0.389550\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.91671 | + | 10.2480i | −0.192065 | + | 0.332666i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.01660 | −0.259956 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.9334 | −0.580921 | −0.290460 | − | 0.956887i | \(-0.593808\pi\) | ||||
−0.290460 | + | 0.956887i | \(0.593808\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.947472 | − | 1.64107i | −0.0306274 | − | 0.0530482i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 24.5131 | − | 30.1705i | 0.791571 | − | 0.974255i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.3651 | + | 21.4170i | 0.398874 | + | 0.690870i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.06361 | − | 1.84223i | 0.0342744 | − | 0.0593650i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.2432 | 0.329398 | 0.164699 | − | 0.986344i | \(-0.447335\pi\) | ||||
0.164699 | + | 0.986344i | \(0.447335\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −21.6677 | + | 37.5295i | −0.696066 | + | 1.20562i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.3547 | + | 17.9349i | 0.332298 | + | 0.575558i | 0.982962 | − | 0.183808i | \(-0.0588426\pi\) |
−0.650664 | + | 0.759366i | \(0.725509\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −49.9197 | − | 7.98999i | −1.60035 | − | 0.256147i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.1674 | − | 31.4669i | 0.581228 | − | 1.00672i | −0.414107 | − | 0.910228i | \(-0.635906\pi\) |
0.995334 | − | 0.0964874i | \(-0.0307608\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.94342 | 0.317793 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.28800 | 0.0730503 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15.9387 | + | 27.6067i | −0.508367 | + | 0.880517i | 0.491586 | + | 0.870829i | \(0.336417\pi\) |
−0.999953 | + | 0.00968816i | \(0.996916\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.80172 | + | 0.608492i | 0.121010 | + | 0.0193685i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.03794 | + | 1.79777i | 0.0330047 | + | 0.0571658i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.30365 | + | 9.18619i | −0.168476 | + | 0.291809i | −0.937884 | − | 0.346948i | \(-0.887218\pi\) |
0.769408 | + | 0.638757i | \(0.220551\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.97698 | −0.316610 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.8248 | + | 18.7491i | −0.342825 | + | 0.593791i | −0.984956 | − | 0.172804i | \(-0.944717\pi\) |
0.642131 | + | 0.766595i | \(0.278051\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.94412 | − | 3.36732i | −0.0615093 | − | 0.106537i |
(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 | 2100.2.q.m.1201.1 | 8 | ||
5.2 | odd | 4 | 420.2.bb.a.109.2 | ✓ | 16 | ||
5.3 | odd | 4 | 420.2.bb.a.109.8 | yes | 16 | ||
5.4 | even | 2 | 2100.2.q.l.1201.4 | 8 | |||
7.2 | even | 3 | inner | 2100.2.q.m.1801.1 | 8 | ||
15.2 | even | 4 | 1260.2.bm.c.109.6 | 16 | |||
15.8 | even | 4 | 1260.2.bm.c.109.1 | 16 | |||
20.3 | even | 4 | 1680.2.di.e.529.4 | 16 | |||
20.7 | even | 4 | 1680.2.di.e.529.6 | 16 | |||
35.2 | odd | 12 | 420.2.bb.a.289.8 | yes | 16 | ||
35.3 | even | 12 | 2940.2.k.g.589.7 | 8 | |||
35.9 | even | 6 | 2100.2.q.l.1801.4 | 8 | |||
35.12 | even | 12 | 2940.2.bb.i.1549.1 | 16 | |||
35.13 | even | 4 | 2940.2.bb.i.949.1 | 16 | |||
35.17 | even | 12 | 2940.2.k.g.589.3 | 8 | |||
35.18 | odd | 12 | 2940.2.k.f.589.2 | 8 | |||
35.23 | odd | 12 | 420.2.bb.a.289.2 | yes | 16 | ||
35.27 | even | 4 | 2940.2.bb.i.949.7 | 16 | |||
35.32 | odd | 12 | 2940.2.k.f.589.6 | 8 | |||
35.33 | even | 12 | 2940.2.bb.i.1549.7 | 16 | |||
105.2 | even | 12 | 1260.2.bm.c.289.1 | 16 | |||
105.23 | even | 12 | 1260.2.bm.c.289.6 | 16 | |||
140.23 | even | 12 | 1680.2.di.e.289.6 | 16 | |||
140.107 | even | 12 | 1680.2.di.e.289.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.bb.a.109.2 | ✓ | 16 | 5.2 | odd | 4 | ||
420.2.bb.a.109.8 | yes | 16 | 5.3 | odd | 4 | ||
420.2.bb.a.289.2 | yes | 16 | 35.23 | odd | 12 | ||
420.2.bb.a.289.8 | yes | 16 | 35.2 | odd | 12 | ||
1260.2.bm.c.109.1 | 16 | 15.8 | even | 4 | |||
1260.2.bm.c.109.6 | 16 | 15.2 | even | 4 | |||
1260.2.bm.c.289.1 | 16 | 105.2 | even | 12 | |||
1260.2.bm.c.289.6 | 16 | 105.23 | even | 12 | |||
1680.2.di.e.289.4 | 16 | 140.107 | even | 12 | |||
1680.2.di.e.289.6 | 16 | 140.23 | even | 12 | |||
1680.2.di.e.529.4 | 16 | 20.3 | even | 4 | |||
1680.2.di.e.529.6 | 16 | 20.7 | even | 4 | |||
2100.2.q.l.1201.4 | 8 | 5.4 | even | 2 | |||
2100.2.q.l.1801.4 | 8 | 35.9 | even | 6 | |||
2100.2.q.m.1201.1 | 8 | 1.1 | even | 1 | trivial | ||
2100.2.q.m.1801.1 | 8 | 7.2 | even | 3 | inner | ||
2940.2.k.f.589.2 | 8 | 35.18 | odd | 12 | |||
2940.2.k.f.589.6 | 8 | 35.32 | odd | 12 | |||
2940.2.k.g.589.3 | 8 | 35.17 | even | 12 | |||
2940.2.k.g.589.7 | 8 | 35.3 | even | 12 | |||
2940.2.bb.i.949.1 | 16 | 35.13 | even | 4 | |||
2940.2.bb.i.949.7 | 16 | 35.27 | even | 4 | |||
2940.2.bb.i.1549.1 | 16 | 35.12 | even | 12 | |||
2940.2.bb.i.1549.7 | 16 | 35.33 | even | 12 |