Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [828,2,Mod(73,828)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(828, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([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("828.73");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 828 = 2^{2} \cdot 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 828.q (of order \(11\), degree \(10\), 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: | \(6.61161328736\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{11})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 8 x^{19} + 43 x^{18} - 165 x^{17} + 538 x^{16} - 1433 x^{15} + 3444 x^{14} - 7370 x^{13} + \cdots + 529 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 276) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{11}]$ |
Embedding invariants
Embedding label | 541.1 | ||
Root | \(1.74521 - 2.01408i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 828.541 |
Dual form | 828.2.q.c.577.1 |
$q$-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 \(\left(\mathbb{Z}/828\mathbb{Z}\right)^\times\).
\(n\) | \(415\) | \(461\) | \(649\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{10}{11}\right)\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.91931 | + | 1.15081i | −1.75277 | + | 0.514659i | −0.991078 | − | 0.133283i | \(-0.957448\pi\) |
−0.761690 | + | 0.647942i | \(0.775630\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.0825209 | − | 0.0952342i | −0.0311900 | − | 0.0359951i | 0.739940 | − | 0.672673i | \(-0.234854\pi\) |
−0.771130 | + | 0.636677i | \(0.780308\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.03818 | + | 0.667196i | 0.313022 | + | 0.201167i | 0.687713 | − | 0.725983i | \(-0.258615\pi\) |
−0.374691 | + | 0.927150i | \(0.622251\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.25227 | − | 1.44519i | 0.347316 | − | 0.400824i | −0.555034 | − | 0.831827i | \(-0.687295\pi\) |
0.902350 | + | 0.431003i | \(0.141840\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.787312 | − | 1.72397i | −0.190951 | − | 0.418125i | 0.789806 | − | 0.613357i | \(-0.210181\pi\) |
−0.980757 | + | 0.195232i | \(0.937454\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0613378 | − | 0.134311i | 0.0140719 | − | 0.0308131i | −0.902466 | − | 0.430762i | \(-0.858245\pi\) |
0.916537 | + | 0.399949i | \(0.130972\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.15160 | − | 4.28610i | 0.448639 | − | 0.893713i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.83034 | − | 6.31757i | 1.96607 | − | 1.26351i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.11768 | − | 6.82676i | −0.578938 | − | 1.26770i | −0.941900 | − | 0.335894i | \(-0.890962\pi\) |
0.362962 | − | 0.931804i | \(-0.381766\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.335425 | + | 2.33293i | 0.0602441 | + | 0.419007i | 0.997518 | + | 0.0704129i | \(0.0224317\pi\) |
−0.937274 | + | 0.348594i | \(0.886659\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.433021 | + | 0.278286i | 0.0731940 | + | 0.0470389i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.41275 | − | 2.17658i | −1.21865 | − | 0.357828i | −0.391694 | − | 0.920096i | \(-0.628111\pi\) |
−0.826955 | + | 0.562268i | \(0.809929\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.0522 | − | 2.95160i | 1.56990 | − | 0.460963i | 0.622925 | − | 0.782282i | \(-0.285944\pi\) |
0.946971 | + | 0.321319i | \(0.104126\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.71801 | − | 11.9490i | 0.261994 | − | 1.82221i | −0.255832 | − | 0.966721i | \(-0.582350\pi\) |
0.517826 | − | 0.855486i | \(-0.326741\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.71564 | 0.833712 | 0.416856 | − | 0.908972i | \(-0.363132\pi\) | ||||
0.416856 | + | 0.908972i | \(0.363132\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.993944 | − | 6.91303i | 0.141992 | − | 0.987576i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.37352 | + | 5.04731i | 0.600749 | + | 0.693301i | 0.971933 | − | 0.235258i | \(-0.0755936\pi\) |
−0.371184 | + | 0.928559i | \(0.621048\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.83675 | − | 1.42020i | −0.652188 | − | 0.191500i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.98875 | − | 5.75733i | 0.649480 | − | 0.749540i | −0.331541 | − | 0.943441i | \(-0.607569\pi\) |
0.981021 | + | 0.193901i | \(0.0621140\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.180939 | − | 1.25846i | −0.0231668 | − | 0.161129i | 0.974954 | − | 0.222407i | \(-0.0713914\pi\) |
−0.998121 | + | 0.0612782i | \(0.980482\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.24487 | + | 7.10527i | −0.402476 | + | 0.881301i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.94923 | + | 5.75132i | −1.09332 | + | 0.702636i | −0.957597 | − | 0.288111i | \(-0.906973\pi\) |
−0.135726 | + | 0.990746i | \(0.543337\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.77319 | + | 4.99552i | −0.922508 | + | 0.592860i | −0.913384 | − | 0.407099i | \(-0.866540\pi\) |
−0.00912348 | + | 0.999958i | \(0.502904\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.25031 | + | 11.4966i | −0.614502 | + | 1.34557i | 0.304949 | + | 0.952369i | \(0.401361\pi\) |
−0.919451 | + | 0.393204i | \(0.871367\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.0221314 | − | 0.153928i | −0.00252211 | − | 0.0175417i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.44214 | − | 2.81838i | 0.274762 | − | 0.317092i | −0.601551 | − | 0.798834i | \(-0.705450\pi\) |
0.876313 | + | 0.481742i | \(0.159996\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.82984 | − | 2.29905i | −0.859437 | − | 0.252353i | −0.177820 | − | 0.984063i | \(-0.556905\pi\) |
−0.681617 | + | 0.731710i | \(0.738723\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.06969 | + | 5.85073i | 0.549885 | + | 0.634601i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.00479 | + | 6.98848i | −0.106508 | + | 0.740778i | 0.864656 | + | 0.502364i | \(0.167536\pi\) |
−0.971164 | + | 0.238413i | \(0.923373\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.240970 | −0.0252605 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.0858348 | + | 0.596994i | −0.00880647 | + | 0.0612503i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.7100 | − | 3.73198i | 1.29050 | − | 0.378925i | 0.436739 | − | 0.899588i | \(-0.356133\pi\) |
0.853762 | + | 0.520663i | \(0.174315\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.47893 | + | 1.90238i | 0.644677 | + | 0.189294i | 0.587697 | − | 0.809081i | \(-0.300035\pi\) |
0.0569800 | + | 0.998375i | \(0.481853\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.13745 | − | 4.58696i | −0.703274 | − | 0.451967i | 0.139509 | − | 0.990221i | \(-0.455448\pi\) |
−0.842783 | + | 0.538254i | \(0.819084\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.88329 | − | 13.0986i | −0.182065 | − | 1.26629i | −0.851871 | − | 0.523752i | \(-0.824532\pi\) |
0.669806 | − | 0.742536i | \(-0.266377\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.09393 | + | 6.77476i | 0.296345 | + | 0.648905i | 0.997973 | − | 0.0636386i | \(-0.0202705\pi\) |
−0.701628 | + | 0.712543i | \(0.747543\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.67658 | + | 1.72014i | −0.251792 | + | 0.161817i | −0.660448 | − | 0.750871i | \(-0.729634\pi\) |
0.408657 | + | 0.912688i | \(0.365997\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.50027 | + | 19.2746i | −0.326402 | + | 1.79737i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.0992114 | + | 0.217243i | −0.00909470 | + | 0.0199146i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.93690 | − | 8.62062i | −0.357900 | − | 0.783692i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −17.8830 | + | 20.6381i | −1.59950 | + | 1.84593i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.9326 | − | 10.8819i | −1.50252 | − | 0.965614i | −0.994552 | − | 0.104240i | \(-0.966759\pi\) |
−0.507972 | − | 0.861374i | \(-0.669605\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.33360 | − | 2.69312i | −0.203888 | − | 0.235299i | 0.644592 | − | 0.764527i | \(-0.277027\pi\) |
−0.848480 | + | 0.529228i | \(0.822482\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0178526 | + | 0.00524201i | −0.00154802 | + | 0.000454540i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.4210 | 1.74468 | 0.872342 | − | 0.488897i | \(-0.162601\pi\) | ||||
0.872342 | + | 0.488897i | \(0.162601\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.3307 | 1.21551 | 0.607755 | − | 0.794125i | \(-0.292070\pi\) | ||||
0.607755 | + | 0.794125i | \(0.292070\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.26430 | − | 0.664858i | 0.189350 | − | 0.0555982i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20.0755 | + | 23.1683i | 1.66718 | + | 1.92402i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.1115 | − | 9.71156i | −1.23798 | − | 0.795602i | −0.252866 | − | 0.967501i | \(-0.581373\pi\) |
−0.985114 | + | 0.171900i | \(0.945009\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.03194 | − | 4.65311i | 0.328115 | − | 0.378665i | −0.567592 | − | 0.823310i | \(-0.692125\pi\) |
0.895707 | + | 0.444645i | \(0.146670\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.99940 | − | 8.75746i | −0.321240 | − | 0.703416i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.21531 | + | 7.04055i | −0.256610 | + | 0.561897i | −0.993463 | − | 0.114156i | \(-0.963584\pi\) |
0.736853 | + | 0.676053i | \(0.236311\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.585735 | + | 0.148787i | −0.0461623 | + | 0.0117261i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.7893 | − | 6.93388i | 0.845085 | − | 0.543103i | −0.0449533 | − | 0.998989i | \(-0.514314\pi\) |
0.890038 | + | 0.455886i | \(0.150678\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.25256 | − | 2.74273i | −0.0969262 | − | 0.212239i | 0.854958 | − | 0.518698i | \(-0.173583\pi\) |
−0.951884 | + | 0.306459i | \(0.900856\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.32968 | + | 9.24815i | 0.102283 | + | 0.711396i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.98890 | − | 1.27819i | −0.151214 | − | 0.0971791i | 0.462846 | − | 0.886439i | \(-0.346828\pi\) |
−0.614060 | + | 0.789260i | \(0.710465\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.41286 | − | 0.414852i | −0.106802 | − | 0.0313599i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.0574 | + | 5.88938i | −1.49916 | + | 0.440193i | −0.925451 | − | 0.378867i | \(-0.876314\pi\) |
−0.573708 | + | 0.819060i | \(0.694496\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.18165 | + | 15.1737i | −0.162161 | + | 1.12785i | 0.732389 | + | 0.680886i | \(0.238405\pi\) |
−0.894550 | + | 0.446967i | \(0.852504\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 31.5577 | 2.32017 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.332858 | − | 2.31508i | 0.0243410 | − | 0.169295i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.93558 | − | 6.85002i | −0.429483 | − | 0.495650i | 0.499219 | − | 0.866476i | \(-0.333620\pi\) |
−0.928703 | + | 0.370826i | \(0.879075\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.14918 | + | 2.68644i | 0.658572 | + | 0.193374i | 0.593908 | − | 0.804533i | \(-0.297584\pi\) |
0.0646640 | + | 0.997907i | \(0.479402\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.70078 | − | 1.96280i | 0.121175 | − | 0.139844i | −0.691920 | − | 0.721974i | \(-0.743235\pi\) |
0.813096 | + | 0.582130i | \(0.197781\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.86746 | − | 19.9437i | −0.203269 | − | 1.41377i | −0.794499 | − | 0.607265i | \(-0.792267\pi\) |
0.591230 | − | 0.806503i | \(-0.298643\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.392867 | + | 0.860260i | −0.0275739 | + | 0.0603784i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −36.0011 | + | 23.1365i | −2.51442 | + | 1.61592i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.153291 | − | 0.0985143i | 0.0106034 | − | 0.00681438i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.89338 | + | 21.6635i | −0.681089 | + | 1.49138i | 0.180397 | + | 0.983594i | \(0.442262\pi\) |
−0.861486 | + | 0.507782i | \(0.830466\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.01767 | + | 48.8090i | 0.478601 | + | 3.32874i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.194495 | − | 0.224459i | 0.0132032 | − | 0.0152373i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.47739 | − | 1.02105i | −0.233915 | − | 0.0686836i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.1936 | − | 15.2262i | −0.883507 | − | 1.01962i | −0.999652 | − | 0.0263890i | \(-0.991599\pi\) |
0.116145 | − | 0.993232i | \(-0.462946\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.33377 | − | 9.27656i | 0.0885253 | − | 0.615707i | −0.896467 | − | 0.443110i | \(-0.853875\pi\) |
0.984993 | − | 0.172597i | \(-0.0552158\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.99434 | 0.197872 | 0.0989359 | − | 0.995094i | \(-0.468456\pi\) | ||||
0.0989359 | + | 0.995094i | \(0.468456\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.47396 | − | 10.2516i | 0.0965624 | − | 0.671607i | −0.882838 | − | 0.469678i | \(-0.844370\pi\) |
0.979400 | − | 0.201929i | \(-0.0647209\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −22.4014 | + | 6.57764i | −1.46130 | + | 0.429078i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.25694 | + | 0.956324i | 0.210674 | + | 0.0618595i | 0.385367 | − | 0.922764i | \(-0.374075\pi\) |
−0.174693 | + | 0.984623i | \(0.555893\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.4551 | + | 9.28973i | 0.931135 | + | 0.598404i | 0.915868 | − | 0.401480i | \(-0.131504\pi\) |
0.0152666 | + | 0.999883i | \(0.495140\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.06003 | + | 28.2381i | 0.259386 | + | 1.80407i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.117294 | − | 0.256838i | −0.00746323 | − | 0.0163422i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.5073 | + | 8.68061i | −0.852572 | + | 0.547915i | −0.892376 | − | 0.451293i | \(-0.850963\pi\) |
0.0398037 | + | 0.999208i | \(0.487327\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.09341 | − | 3.01419i | 0.320220 | − | 0.189501i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.14370 | − | 20.0219i | 0.570368 | − | 1.24893i | −0.376233 | − | 0.926525i | \(-0.622781\pi\) |
0.946601 | − | 0.322407i | \(-0.104492\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.404422 | + | 0.885560i | 0.0251296 | + | 0.0550260i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.9296 | + | 17.2297i | −0.920601 | + | 1.06243i | 0.0772571 | + | 0.997011i | \(0.475384\pi\) |
−0.997858 | + | 0.0654188i | \(0.979162\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −22.9497 | − | 14.7489i | −1.40979 | − | 0.906015i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.55143 | + | 4.09857i | 0.216534 | + | 0.249894i | 0.853617 | − | 0.520902i | \(-0.174404\pi\) |
−0.637082 | + | 0.770796i | \(0.719859\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.3625 | − | 7.15346i | 1.47991 | − | 0.434542i | 0.560606 | − | 0.828082i | \(-0.310568\pi\) |
0.919307 | + | 0.393541i | \(0.128750\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14.4207 | 0.869600 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −28.3536 | −1.70360 | −0.851800 | − | 0.523867i | \(-0.824489\pi\) | ||||
−0.851800 | + | 0.523867i | \(0.824489\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.14061 | + | 2.09667i | −0.425973 | + | 0.125077i | −0.487690 | − | 0.873017i | \(-0.662160\pi\) |
0.0617174 | + | 0.998094i | \(0.480342\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.9165 | + | 18.3687i | 0.946141 | + | 1.09190i | 0.995654 | + | 0.0931309i | \(0.0296875\pi\) |
−0.0495133 | + | 0.998773i | \(0.515767\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.11061 | − | 0.713748i | −0.0655574 | − | 0.0421312i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.78041 | − | 10.1331i | 0.516495 | − | 0.596067i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.78323 | − | 14.8532i | −0.396281 | − | 0.867733i | −0.997634 | − | 0.0687502i | \(-0.978099\pi\) |
0.601353 | − | 0.798983i | \(-0.294628\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.9269 | + | 28.3059i | −0.752630 | + | 1.64803i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.49986 | − | 8.47680i | −0.202402 | − | 0.490226i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.27973 | + | 0.822430i | −0.0737622 | + | 0.0474041i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.15740 | + | 4.72406i | 0.123533 | + | 0.270499i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.54574 | − | 24.6612i | −0.202366 | − | 1.40749i | −0.797237 | − | 0.603667i | \(-0.793706\pi\) |
0.594871 | − | 0.803821i | \(-0.297203\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.7744 | + | 15.2789i | 1.34813 | + | 0.866388i | 0.997537 | − | 0.0701421i | \(-0.0223453\pi\) |
0.350588 | + | 0.936530i | \(0.385982\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.29010 | + | 1.55331i | 0.299014 | + | 0.0877985i | 0.427798 | − | 0.903874i | \(-0.359289\pi\) |
−0.128784 | + | 0.991673i | \(0.541107\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.12306 | + | 0.917014i | −0.175409 | + | 0.0515047i | −0.368258 | − | 0.929724i | \(-0.620046\pi\) |
0.192849 | + | 0.981228i | \(0.438227\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.31809 | − | 9.16749i | 0.0737987 | − | 0.513281i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.279840 | −0.0155707 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.18009 | − | 22.1180i | 0.176400 | − | 1.22689i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.471660 | − | 0.544325i | −0.0260035 | − | 0.0300096i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.54037 | − | 1.92043i | −0.359491 | − | 0.105556i | 0.0969992 | − | 0.995284i | \(-0.469076\pi\) |
−0.456490 | + | 0.889728i | \(0.650894\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 28.4561 | − | 32.8401i | 1.55472 | − | 1.79425i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.655700 | − | 4.56049i | −0.0357183 | − | 0.248426i | 0.964138 | − | 0.265403i | \(-0.0855049\pi\) |
−0.999856 | + | 0.0169769i | \(0.994596\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.20829 | + | 2.64579i | −0.0654327 | + | 0.143278i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.48244 | + | 0.952706i | −0.0800442 | + | 0.0514413i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.8312 | − | 12.1021i | 1.01091 | − | 0.649674i | 0.0732832 | − | 0.997311i | \(-0.476652\pi\) |
0.937629 | + | 0.347637i | \(0.113016\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.84062 | − | 19.3583i | 0.473228 | − | 1.03622i | −0.511043 | − | 0.859555i | \(-0.670741\pi\) |
0.984270 | − | 0.176669i | \(-0.0565321\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.895635 | − | 6.22928i | −0.0476698 | − | 0.331551i | −0.999676 | − | 0.0254708i | \(-0.991892\pi\) |
0.952006 | − | 0.306080i | \(-0.0990176\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 24.7166 | − | 28.5245i | 1.31182 | − | 1.51392i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.4027 | − | 4.22900i | −0.760143 | − | 0.223198i | −0.121385 | − | 0.992606i | \(-0.538733\pi\) |
−0.638758 | + | 0.769407i | \(0.720552\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.4281 | + | 14.3428i | 0.654109 | + | 0.754882i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.34718 | − | 51.1007i | 0.384569 | − | 2.67474i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.18117 | 0.427053 | 0.213527 | − | 0.976937i | \(-0.431505\pi\) | ||||
0.213527 | + | 0.976937i | \(0.431505\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.119770 | − | 0.833016i | 0.00621813 | − | 0.0432481i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.42461 | − | 2.47369i | 0.436210 | − | 0.128083i | −0.0562525 | − | 0.998417i | \(-0.517915\pi\) |
0.492462 | + | 0.870334i | \(0.336097\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.7701 | − | 4.04328i | −0.709198 | − | 0.208239i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.68742 | + | 3.65509i | 0.292143 | + | 0.187749i | 0.678500 | − | 0.734600i | \(-0.262630\pi\) |
−0.386357 | + | 0.922349i | \(0.626267\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.0756551 | + | 0.526193i | 0.00386580 | + | 0.0268872i | 0.991663 | − | 0.128858i | \(-0.0411312\pi\) |
−0.987797 | + | 0.155745i | \(0.950222\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.263882 | + | 0.577820i | 0.0134487 | + | 0.0294485i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.93689 | − | 2.53008i | 0.199608 | − | 0.128280i | −0.437019 | − | 0.899452i | \(-0.643966\pi\) |
0.636627 | + | 0.771172i | \(0.280329\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.08309 | − | 0.334795i | −0.459352 | − | 0.0169313i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.32807 | + | 13.8565i | −0.318400 | + | 0.697198i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.42758 | + | 3.12596i | 0.0716480 | + | 0.156887i | 0.942067 | − | 0.335424i | \(-0.108880\pi\) |
−0.870419 | + | 0.492311i | \(0.836152\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.58668 | + | 9.90955i | −0.428798 | + | 0.494859i | −0.928497 | − | 0.371340i | \(-0.878899\pi\) |
0.499699 | + | 0.866199i | \(0.333444\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.79157 | + | 2.43670i | 0.188872 | + | 0.121380i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.24354 | − | 7.20543i | −0.309481 | − | 0.357160i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.93864 | − | 1.15649i | 0.194753 | − | 0.0571848i | −0.182901 | − | 0.983131i | \(-0.558549\pi\) |
0.377655 | + | 0.925947i | \(0.376731\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.959971 | −0.0472371 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 33.3333 | 1.63627 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −35.7570 | + | 10.4992i | −1.74684 | + | 0.512919i | −0.990048 | − | 0.140733i | \(-0.955054\pi\) |
−0.756795 | + | 0.653652i | \(0.773236\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.30973 | + | 7.28181i | 0.307517 | + | 0.354894i | 0.888381 | − | 0.459107i | \(-0.151831\pi\) |
−0.580864 | + | 0.814001i | \(0.697285\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −18.6309 | − | 11.9733i | −0.903729 | − | 0.580792i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.104917 | + | 0.121081i | −0.00507729 | + | 0.00585950i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.3144 | − | 29.1546i | −0.641334 | − | 1.40433i | −0.898938 | − | 0.438076i | \(-0.855660\pi\) |
0.257604 | − | 0.966251i | \(-0.417067\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.2767 | − | 22.5027i | 0.493865 | − | 1.08141i | −0.484551 | − | 0.874763i | \(-0.661017\pi\) |
0.978415 | − | 0.206649i | \(-0.0662559\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.443696 | − | 0.551883i | −0.0212249 | − | 0.0264001i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.03424 | + | 4.52063i | −0.335726 | + | 0.215758i | −0.697632 | − | 0.716457i | \(-0.745763\pi\) |
0.361905 | + | 0.932215i | \(0.382126\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.68541 | + | 8.06992i | 0.175099 | + | 0.383413i | 0.976751 | − | 0.214378i | \(-0.0687724\pi\) |
−0.801652 | + | 0.597791i | \(0.796045\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.10435 | − | 28.5463i | −0.194565 | − | 1.35323i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.42408 | + | 5.41383i | 0.397557 | + | 0.255494i | 0.724110 | − | 0.689685i | \(-0.242251\pi\) |
−0.326553 | + | 0.945179i | \(0.605887\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.4053 | + | 3.64253i | 0.584143 | + | 0.171520i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.944434 | − | 0.277311i | 0.0442758 | − | 0.0130005i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.20875 | − | 29.2725i | 0.196877 | − | 1.36931i | −0.616400 | − | 0.787433i | \(-0.711410\pi\) |
0.813277 | − | 0.581877i | \(-0.197681\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.8301 | 0.830430 | 0.415215 | − | 0.909723i | \(-0.363706\pi\) | ||||
0.415215 | + | 0.909723i | \(0.363706\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.40293 | − | 9.75762i | 0.0651999 | − | 0.453475i | −0.930902 | − | 0.365268i | \(-0.880977\pi\) |
0.996102 | − | 0.0882069i | \(-0.0281137\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.2767 | + | 29.1708i | 1.16966 | + | 1.34986i | 0.924867 | + | 0.380290i | \(0.124176\pi\) |
0.244797 | + | 0.969574i | \(0.421279\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.28622 | + | 0.377669i | 0.0593922 | + | 0.0174391i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.75593 | − | 11.2589i | 0.448578 | − | 0.517687i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.245549 | − | 1.70783i | −0.0112665 | − | 0.0783605i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.81750 | + | 6.16945i | −0.128735 | + | 0.281890i | −0.963013 | − | 0.269453i | \(-0.913157\pi\) |
0.834279 | + | 0.551343i | \(0.185884\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.4283 | + | 7.98719i | −0.566682 | + | 0.364184i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −45.5195 | + | 29.2536i | −2.06693 | + | 1.32834i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.77299 | + | 6.07200i | −0.125656 | + | 0.275149i | −0.961996 | − | 0.273062i | \(-0.911964\pi\) |
0.836340 | + | 0.548211i | \(0.184691\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.53163 | − | 17.6079i | −0.114251 | − | 0.794632i | −0.963705 | − | 0.266969i | \(-0.913978\pi\) |
0.849454 | − | 0.527662i | \(-0.176931\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.31456 | + | 10.7496i | −0.419507 | + | 0.484137i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.11719 | + | 0.328038i | 0.0501130 | + | 0.0147145i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.992242 | + | 1.14511i | 0.0444189 | + | 0.0512621i | 0.777524 | − | 0.628853i | \(-0.216475\pi\) |
−0.733105 | + | 0.680115i | \(0.761930\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.54825 | + | 17.7235i | −0.113621 | + | 0.790250i | 0.850726 | + | 0.525609i | \(0.176163\pi\) |
−0.964347 | + | 0.264641i | \(0.914747\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27.5822 | −1.22739 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.69998 | + | 18.7788i | −0.119675 | + | 0.832355i | 0.838240 | + | 0.545301i | \(0.183585\pi\) |
−0.957915 | + | 0.287053i | \(0.907324\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.52813 | − | 0.448699i | 0.0676004 | − | 0.0198493i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 33.2526 | + | 9.76384i | 1.46528 | + | 0.430246i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.93385 | + | 3.81346i | 0.260971 | + | 0.167716i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.48410 | + | 31.1876i | 0.196452 | + | 1.36635i | 0.814478 | + | 0.580195i | \(0.197024\pi\) |
−0.618026 | + | 0.786158i | \(0.712067\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.15195 | − | 15.6606i | −0.312733 | − | 0.684790i | 0.686365 | − | 0.727257i | \(-0.259205\pi\) |
−0.999098 | + | 0.0424676i | \(0.986478\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.75783 | − | 2.41501i | 0.163693 | − | 0.105199i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.7413 | − | 18.4439i | −0.597447 | − | 0.801909i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.32244 | − | 18.2236i | 0.360485 | − | 0.789352i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.4552 | + | 49.1701i | 0.970824 | + | 2.12581i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.64424 | − | 6.51380i | 0.243115 | − | 0.280569i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.229819 | + | 0.147696i | 0.00988070 | + | 0.00634994i | 0.545572 | − | 0.838064i | \(-0.316312\pi\) |
−0.535691 | + | 0.844414i | \(0.679949\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −19.9225 | − | 22.9918i | −0.853388 | − | 0.984863i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.3716 | + | 7.44978i | −1.08481 | + | 0.318530i | −0.774802 | − | 0.632203i | \(-0.782151\pi\) |
−0.310010 | + | 0.950733i | \(0.600332\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.10814 | −0.0472084 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.469934 | −0.0199836 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.7086 | − | 6.96147i | 1.00457 | − | 0.294967i | 0.262237 | − | 0.965003i | \(-0.415540\pi\) |
0.742328 | + | 0.670036i | \(0.233722\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.1172 | − | 17.4462i | −0.639390 | − | 0.737895i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.2024 | − | 9.12730i | −0.598558 | − | 0.384670i | 0.205993 | − | 0.978553i | \(-0.433958\pi\) |
−0.804551 | + | 0.593884i | \(0.797594\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.51080 | − | 9.82198i | 0.358052 | − | 0.413214i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.05486 | − | 8.87892i | −0.169989 | − | 0.372223i | 0.805395 | − | 0.592739i | \(-0.201953\pi\) |
−0.975384 | + | 0.220515i | \(0.929226\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.08106 | + | 13.3157i | −0.254484 | + | 0.557243i | −0.993152 | − | 0.116826i | \(-0.962728\pi\) |
0.738668 | + | 0.674070i | \(0.235455\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.92684 | − | 55.7266i | −0.247166 | − | 2.32396i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.3558 | − | 6.65529i | 0.431119 | − | 0.277063i | −0.307032 | − | 0.951699i | \(-0.599336\pi\) |
0.738151 | + | 0.674636i | \(0.235699\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.427177 | + | 0.935388i | 0.0177223 | + | 0.0388064i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.17294 | + | 8.15799i | 0.0485783 | + | 0.337870i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.1633 | − | 6.53159i | −0.419486 | − | 0.269587i | 0.313825 | − | 0.949481i | \(-0.398390\pi\) |
−0.733311 | + | 0.679893i | \(0.762026\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.333913 | + | 0.0980456i | 0.0137586 | + | 0.00403990i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −41.6427 | + | 12.2274i | −1.71006 | + | 0.502119i | −0.982867 | − | 0.184314i | \(-0.940994\pi\) |
−0.727193 | + | 0.686433i | \(0.759176\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.138834 | − | 0.965615i | 0.00569166 | − | 0.0395863i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.5272 | 1.49246 | 0.746230 | − | 0.665688i | \(-0.231862\pi\) | ||||
0.746230 | + | 0.665688i | \(0.231862\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.0953083 | − | 0.662884i | 0.00388771 | − | 0.0270396i | −0.987785 | − | 0.155821i | \(-0.950198\pi\) |
0.991673 | + | 0.128782i | \(0.0411067\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 25.3506 | + | 29.2562i | 1.03065 | + | 1.18943i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −34.6753 | − | 10.1816i | −1.40743 | − | 0.413258i | −0.512200 | − | 0.858866i | \(-0.671169\pi\) |
−0.895228 | + | 0.445608i | \(0.852988\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.15750 | − | 8.26020i | 0.289562 | − | 0.334172i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.62930 | + | 39.1526i | 0.227365 | + | 1.58136i | 0.709142 | + | 0.705066i | \(0.249083\pi\) |
−0.481776 | + | 0.876294i | \(0.660008\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.38060 | − | 5.21278i | 0.0958393 | − | 0.209859i | −0.855640 | − | 0.517571i | \(-0.826836\pi\) |
0.951479 | + | 0.307712i | \(0.0995635\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.1415 | − | 14.2295i | 0.889942 | − | 0.571931i | −0.0138494 | − | 0.999904i | \(-0.504409\pi\) |
0.903792 | + | 0.427973i | \(0.140772\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.748459 | − | 0.481005i | 0.0299864 | − | 0.0192711i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.0671 | − | 48.3201i | 0.882682 | − | 1.93280i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.08378 | + | 14.4930i | 0.0830858 | + | 0.577875i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.8138 | + | 21.7123i | −0.748967 | + | 0.864354i | −0.994468 | − | 0.105042i | \(-0.966502\pi\) |
0.245501 | + | 0.969396i | \(0.421048\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 78.8871 | + | 23.1633i | 3.13054 | + | 0.919209i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.74597 | − | 10.0934i | −0.346528 | − | 0.399915i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.14585 | + | 21.8799i | −0.124254 | + | 0.864202i | 0.828398 | + | 0.560139i | \(0.189252\pi\) |
−0.952652 | + | 0.304063i | \(0.901657\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.1875 | −0.441193 | −0.220596 | − | 0.975365i | \(-0.570800\pi\) | ||||
−0.220596 | + | 0.975365i | \(0.570800\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.70136 | − | 25.7436i | 0.145516 | − | 1.01208i | −0.777929 | − | 0.628352i | \(-0.783730\pi\) |
0.923445 | − | 0.383731i | \(-0.125361\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.02048 | − | 2.64865i | 0.354085 | − | 0.103969i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 43.7741 | + | 12.8532i | 1.71301 | + | 0.502986i | 0.983489 | − | 0.180967i | \(-0.0579228\pi\) |
0.729525 | + | 0.683954i | \(0.239741\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.2454 | + | 7.86963i | 0.478467 | + | 0.307492i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.36052 | − | 30.3281i | −0.169862 | − | 1.18141i | −0.879168 | − | 0.476513i | \(-0.841901\pi\) |
0.709306 | − | 0.704901i | \(-0.249008\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.54464 | + | 14.3308i | 0.254557 | + | 0.557402i | 0.993163 | − | 0.116735i | \(-0.0372429\pi\) |
−0.738606 | + | 0.674137i | \(0.764516\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.0639374 | − | 0.0410901i | 0.00247939 | − | 0.00159341i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −35.9681 | − | 1.32575i | −1.39269 | − | 0.0513334i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.651791 | − | 1.42722i | 0.0251621 | − | 0.0550974i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.20807 | + | 9.21438i | 0.162209 | + | 0.355188i | 0.973232 | − | 0.229827i | \(-0.0738159\pi\) |
−0.811023 | + | 0.585015i | \(0.801089\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.73175 | + | 8.92291i | −0.297155 | + | 0.342935i | −0.884619 | − | 0.466315i | \(-0.845581\pi\) |
0.587463 | + | 0.809251i | \(0.300127\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.40425 | − | 0.902457i | −0.0538902 | − | 0.0346331i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.85265 | − | 9.06244i | −0.300473 | − | 0.346765i | 0.585356 | − | 0.810777i | \(-0.300955\pi\) |
−0.885829 | + | 0.464012i | \(0.846409\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −80.0361 | + | 23.5007i | −3.05802 | + | 0.897917i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.7711 | 0.486541 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.6233 | 0.784548 | 0.392274 | − | 0.919848i | \(-0.371689\pi\) | ||||
0.392274 | + | 0.919848i | \(0.371689\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −56.1662 | + | 16.4919i | −2.13051 | + | 0.625573i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.0027 | − | 15.0059i | −0.492513 | − | 0.568391i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37.7052 | + | 24.2316i | 1.42410 | + | 0.915216i | 0.999954 | + | 0.00962419i | \(0.00306352\pi\) |
0.424150 | + | 0.905592i | \(0.360573\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.747020 | + | 0.862107i | −0.0281744 | + | 0.0325150i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.353475 | − | 0.774002i | −0.0132938 | − | 0.0291093i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.7599 | − | 34.5095i | 0.591877 | − | 1.29603i | −0.342424 | − | 0.939546i | \(-0.611248\pi\) |
0.934301 | − | 0.356485i | \(-0.116025\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.7209 | + | 3.58186i | 0.401500 | + | 0.134142i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.10936 | + | 5.21157i | −0.303273 | + | 0.194902i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.3632 | + | 33.6408i | 0.572952 | + | 1.25459i | 0.945210 | + | 0.326462i | \(0.105856\pi\) |
−0.372258 | + | 0.928129i | \(0.621416\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.152153 | + | 1.05825i | 0.00566648 | + | 0.0394113i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −73.7764 | − | 47.4132i | −2.73999 | − | 1.76088i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 44.6395 | + | 13.1073i | 1.65559 | + | 0.486124i | 0.970250 | − | 0.242103i | \(-0.0778373\pi\) |
0.685336 | + | 0.728227i | \(0.259655\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21.9524 | + | 6.44580i | −0.811938 | + | 0.238406i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.437796 | − | 3.04494i | 0.0161704 | − | 0.112467i | −0.980138 | − | 0.198319i | \(-0.936452\pi\) |
0.996308 | + | 0.0858513i | \(0.0273610\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.1282 | −0.483582 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.33533 | + | 23.1977i | −0.122692 | + | 0.853341i | 0.831794 | + | 0.555085i | \(0.187314\pi\) |
−0.954486 | + | 0.298257i | \(0.903595\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.07237 | + | 1.23758i | 0.0393413 | + | 0.0454023i | 0.775079 | − | 0.631864i | \(-0.217710\pi\) |
−0.735738 | + | 0.677266i | \(0.763164\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 70.4027 | + | 20.6721i | 2.57936 | + | 0.757367i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.09202 | + | 1.26026i | −0.0399016 | + | 0.0460489i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.05226 | + | 42.0944i | 0.220850 | + | 1.53605i | 0.734834 | + | 0.678247i | \(0.237260\pi\) |
−0.513984 | + | 0.857800i | \(0.671831\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.4476 | + | 22.8770i | −0.380226 | + | 0.832579i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.49246 | + | 4.81511i | −0.272318 | + | 0.175008i | −0.669671 | − | 0.742657i | \(-0.733565\pi\) |
0.397353 | + | 0.917666i | \(0.369929\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32.4340 | + | 20.8441i | −1.17573 | + | 0.755597i | −0.974597 | − | 0.223967i | \(-0.928099\pi\) |
−0.201134 | + | 0.979564i | \(0.564463\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.389875 | − | 0.853707i | 0.0141144 | − | 0.0309063i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.07320 | − | 14.4194i | −0.0748588 | − | 0.520654i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.6719 | + | 38.8594i | −1.21424 | + | 1.40131i | −0.323850 | + | 0.946108i | \(0.604977\pi\) |
−0.890390 | + | 0.455199i | \(0.849568\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.4813 | − | 7.18835i | −0.880530 | − | 0.258547i | −0.189942 | − | 0.981795i | \(-0.560830\pi\) |
−0.690588 | + | 0.723249i | \(0.742648\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.0358 | + | 20.8144i | 0.647865 | + | 0.747676i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.220149 | − | 1.53117i | 0.00788766 | − | 0.0548599i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.4029 | −0.408029 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.49944 | − | 31.2943i | 0.160592 | − | 1.11694i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.82123 | − | 2.88377i | 0.350089 | − | 0.102795i | −0.101960 | − | 0.994789i | \(-0.532511\pi\) |
0.452049 | + | 0.891993i | \(0.350693\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.384690 | + | 0.112955i | 0.0136780 | + | 0.00401622i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.04530 | − | 1.31443i | −0.0726306 | − | 0.0466768i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.236974 | + | 1.64819i | 0.00839403 | + | 0.0583818i | 0.993588 | − | 0.113062i | \(-0.0360659\pi\) |
−0.985194 | + | 0.171444i | \(0.945157\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.49999 | − | 9.85361i | −0.159198 | − | 0.348596i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.1212 | + | 8.43250i | −0.463038 | + | 0.297576i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.12445 | − | 1.25721i | 0.0748769 | − | 0.0443110i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.33499 | + | 7.30261i | −0.117252 | + | 0.256746i | −0.959154 | − | 0.282884i | \(-0.908709\pi\) |
0.841902 | + | 0.539630i | \(0.181436\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.8369 | + | 50.0059i | 0.801912 | + | 1.75594i | 0.638856 | + | 0.769326i | \(0.279408\pi\) |
0.163057 | + | 0.986617i | \(0.447865\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −34.3071 | + | 39.5925i | −1.20172 | + | 1.38686i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.49950 | − | 0.963673i | −0.0524610 | − | 0.0337147i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.5323 | + | 14.4630i | 0.437379 | + | 0.504763i | 0.931053 | − | 0.364885i | \(-0.118892\pi\) |
−0.493673 | + | 0.869647i | \(0.664346\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.3321 | + | 5.97006i | −0.708734 | + | 0.208103i | −0.616181 | − | 0.787605i | \(-0.711321\pi\) |
−0.0925530 | + | 0.995708i | \(0.529503\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −29.2748 | −1.01798 | −0.508992 | − | 0.860771i | \(-0.669982\pi\) | ||||
−0.508992 | + | 0.860771i | \(0.669982\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.5164 | −1.09461 | −0.547304 | − | 0.836934i | \(-0.684346\pi\) | ||||
−0.547304 | + | 0.836934i | \(0.684346\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12.7004 | + | 3.72918i | −0.440043 | + | 0.129208i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.06555 | + | 9.30814i | 0.279120 | + | 0.322121i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.78578 | + | 5.64628i | 0.303319 | + | 0.194931i | 0.683442 | − | 0.730005i | \(-0.260482\pi\) |
−0.380123 | + | 0.924936i | \(0.624118\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.8938 | + | 20.6505i | −0.617027 | + | 0.712087i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −15.8543 | − | 34.7161i | −0.545405 | − | 1.19427i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.496101 | + | 1.08631i | −0.0170462 | + | 0.0373260i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.2783 | + | 27.0887i | −0.866528 | + | 0.928587i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.3790 | + | 9.88346i | −0.526566 | + | 0.338403i | −0.776764 | − | 0.629791i | \(-0.783140\pi\) |
0.250199 | + | 0.968195i | \(0.419504\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.9983 | + | 28.4623i | 0.444014 | + | 0.972255i | 0.990844 | + | 0.135012i | \(0.0431072\pi\) |
−0.546830 | + | 0.837244i | \(0.684166\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.37199 | + | 9.54240i | 0.0468117 | + | 0.325582i | 0.999749 | + | 0.0224143i | \(0.00713529\pi\) |
−0.952937 | + | 0.303168i | \(0.901956\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.91655 | + | 5.73032i | 0.303523 | + | 0.195062i | 0.683532 | − | 0.729920i | \(-0.260443\pi\) |
−0.380009 | + | 0.924983i | \(0.624079\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.26609 | + | 2.72077i | 0.315056 | + | 0.0925089i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.41579 | − | 1.29659i | 0.149795 | − | 0.0439839i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.89505 | + | 20.1355i | −0.0980951 | + | 0.682267i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.44117 | 0.116333 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.805286 | + | 5.60089i | −0.0271926 | + | 0.189129i | −0.998890 | − | 0.0470996i | \(-0.985002\pi\) |
0.971698 | + | 0.236228i | \(0.0759113\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.9426 | + | 38.0177i | 1.10986 | + | 1.28085i | 0.956196 | + | 0.292728i | \(0.0945629\pi\) |
0.153667 | + | 0.988123i | \(0.450892\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.8285 | − | 4.94130i | −0.566325 | − | 0.166288i | −0.0139782 | − | 0.999902i | \(-0.504450\pi\) |
−0.552347 | + | 0.833614i | \(0.686268\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.7918 | + | 20.5329i | −0.597392 | + | 0.689427i | −0.971251 | − | 0.238059i | \(-0.923489\pi\) |
0.373859 | + | 0.927486i | \(0.378034\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.360962 | + | 2.51055i | 0.0121063 | + | 0.0842010i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.350585 | − | 0.767674i | 0.0117319 | − | 0.0256892i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 71.8335 | − | 46.1646i | 2.40113 | − | 1.54311i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.8806 | − | 9.56319i | 0.496296 | − | 0.318950i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.25810 | − | 11.5136i | 0.175173 | − | 0.383574i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.91154 | − | 61.9811i | −0.296230 | − | 2.06032i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.7863 | − | 25.1427i | 0.723402 | − | 0.834850i | −0.268310 | − | 0.963333i | \(-0.586465\pi\) |
0.991712 | + | 0.128483i | \(0.0410107\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36.5227 | + | 10.7240i | 1.21005 | + | 0.355303i | 0.823687 | − | 0.567044i | \(-0.191913\pi\) |
0.386363 | + | 0.922347i | \(0.373731\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.59485 | − | 7.61086i | −0.218258 | − | 0.251883i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.0639062 | + | 0.444477i | −0.00211037 | + | 0.0146779i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.8732 | 0.820491 | 0.410246 | − | 0.911975i | \(-0.365443\pi\) | ||||
0.410246 | + | 0.911975i | \(0.365443\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.51461 | + | 17.4895i | −0.0827693 | + | 0.575673i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −86.6205 | + | 25.4341i | −2.84807 | + | 0.836267i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.8053 | − | 4.64085i | −0.518554 | − | 0.152261i | 0.0119743 | − | 0.999928i | \(-0.496188\pi\) |
−0.530529 | + | 0.847667i | \(0.678007\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.867530 | − | 0.557528i | −0.0284321 | − | 0.0182722i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.35965 | + | 9.45657i | 0.0444653 | + | 0.309263i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.43363 | − | 7.51861i | −0.112172 | − | 0.245622i | 0.845217 | − | 0.534423i | \(-0.179471\pi\) |
−0.957389 | + | 0.288800i | \(0.906744\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.74409 | + | 3.04884i | −0.154653 | + | 0.0993894i | −0.615679 | − | 0.787997i | \(-0.711118\pi\) |
0.461026 | + | 0.887387i | \(0.347482\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.97748 | − | 49.4355i | 0.292347 | − | 1.60984i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.3235 | − | 22.6053i | 0.335468 | − | 0.734572i | −0.664451 | − | 0.747332i | \(-0.731334\pi\) |
0.999919 | + | 0.0127598i | \(0.00406168\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.0400 | + | 21.9845i | 0.325911 | + | 0.713646i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.0490 | − | 38.1406i | 1.07056 | − | 1.23549i | 0.0999117 | − | 0.994996i | \(-0.468144\pi\) |
0.970650 | − | 0.240497i | \(-0.0773106\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 31.1464 | + | 20.0166i | 1.00788 | + | 0.647722i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.68516 | − | 1.94478i | −0.0544166 | − | 0.0628001i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.4142 | − | 7.16866i | 0.787556 | − | 0.231247i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −38.9500 | −1.25385 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.31499 | 0.0422872 | 0.0211436 | − | 0.999776i | \(-0.493269\pi\) | ||||
0.0211436 | + | 0.999776i | \(0.493269\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.0575 | − | 6.18304i | 0.675768 | − | 0.198423i | 0.0741980 | − | 0.997244i | \(-0.476360\pi\) |
0.601570 | + | 0.798820i | \(0.294542\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.18258 | − | 1.36477i | −0.0379117 | − | 0.0437525i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.0341 | − | 12.2324i | −0.608953 | − | 0.391351i | 0.199511 | − | 0.979896i | \(-0.436065\pi\) |
−0.808465 | + | 0.588545i | \(0.799701\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.70584 | + | 6.58489i | −0.182359 | + | 0.210454i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.32096 | + | 18.2204i | 0.265398 | + | 0.581140i | 0.994673 | − | 0.103081i | \(-0.0328700\pi\) |
−0.729275 | + | 0.684220i | \(0.760143\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.40705 | + | 9.65010i | −0.140420 | + | 0.307478i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −47.5182 | − | 33.0730i | −1.51099 | − | 1.05166i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46.2705 | + | 29.7363i | −1.46983 | + | 0.944604i | −0.471812 | + | 0.881699i | \(0.656400\pi\) |
−0.998020 | + | 0.0629045i | \(0.979964\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 34.1899 | + | 74.8654i | 1.08389 | + | 2.37339i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.83245 | − | 33.6105i | −0.153045 | − | 1.06445i | −0.911077 | − | 0.412236i | \(-0.864748\pi\) |
0.758032 | − | 0.652218i | \(-0.226161\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 828.2.q.c.541.1 | 20 | ||
3.2 | odd | 2 | 276.2.i.a.265.2 | yes | 20 | ||
23.2 | even | 11 | inner | 828.2.q.c.577.1 | 20 | ||
69.2 | odd | 22 | 276.2.i.a.25.2 | ✓ | 20 | ||
69.5 | even | 22 | 6348.2.a.t.1.10 | 10 | |||
69.41 | odd | 22 | 6348.2.a.s.1.1 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
276.2.i.a.25.2 | ✓ | 20 | 69.2 | odd | 22 | ||
276.2.i.a.265.2 | yes | 20 | 3.2 | odd | 2 | ||
828.2.q.c.541.1 | 20 | 1.1 | even | 1 | trivial | ||
828.2.q.c.577.1 | 20 | 23.2 | even | 11 | inner | ||
6348.2.a.s.1.1 | 10 | 69.41 | odd | 22 | |||
6348.2.a.t.1.10 | 10 | 69.5 | even | 22 |