Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [276,2,Mod(13,276)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(276, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([0, 0, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("276.13");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 276 = 2^{2} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 276.i (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: | \(2.20387109579\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{11}]$ |
Embedding invariants
Embedding label | 25.2 | ||
Root | \(1.74521 - 2.01408i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 276.25 |
Dual form | 276.2.i.a.265.2 |
$q$-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 \(\left(\mathbb{Z}/276\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(139\) | \(185\) |
\(\chi(n)\) | \(e\left(\frac{1}{11}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.142315 | − | 0.989821i | −0.0821655 | − | 0.571474i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.91931 | + | 1.15081i | 1.75277 | + | 0.514659i | 0.991078 | − | 0.133283i | \(-0.0425519\pi\) |
0.761690 | + | 0.647942i | \(0.224370\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.0825209 | + | 0.0952342i | −0.0311900 | + | 0.0359951i | −0.771130 | − | 0.636677i | \(-0.780308\pi\) |
0.739940 | + | 0.672673i | \(0.234854\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.959493 | + | 0.281733i | −0.319831 | + | 0.0939109i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.03818 | + | 0.667196i | −0.313022 | + | 0.201167i | −0.687713 | − | 0.725983i | \(-0.741385\pi\) |
0.374691 | + | 0.927150i | \(0.377749\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.25227 | + | 1.44519i | 0.347316 | + | 0.400824i | 0.902350 | − | 0.431003i | \(-0.141840\pi\) |
−0.555034 | + | 0.831827i | \(0.687295\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.581323 | − | 4.04319i | 0.150097 | − | 1.04395i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.787312 | − | 1.72397i | 0.190951 | − | 0.418125i | −0.789806 | − | 0.613357i | \(-0.789819\pi\) |
0.980757 | + | 0.195232i | \(0.0625460\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0613378 | + | 0.134311i | 0.0140719 | + | 0.0308131i | 0.916537 | − | 0.399949i | \(-0.130972\pi\) |
−0.902466 | + | 0.430762i | \(0.858245\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.106009 | + | 0.0681277i | 0.0231330 | + | 0.0148667i | ||||
\(22\) | 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 | ||||||||
\(27\) | 0.415415 | + | 0.909632i | 0.0799467 | + | 0.175059i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.11768 | − | 6.82676i | 0.578938 | − | 1.26770i | −0.362962 | − | 0.931804i | \(-0.618234\pi\) |
0.941900 | − | 0.335894i | \(-0.109038\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.335425 | − | 2.33293i | 0.0602441 | − | 0.419007i | −0.937274 | − | 0.348594i | \(-0.886659\pi\) |
0.997518 | − | 0.0704129i | \(-0.0224317\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.808153 | + | 0.932658i | 0.140681 | + | 0.162355i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.433021 | + | 0.278286i | −0.0731940 | + | 0.0470389i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.41275 | + | 2.17658i | −1.21865 | + | 0.357828i | −0.826955 | − | 0.562268i | \(-0.809929\pi\) |
−0.391694 | + | 0.920096i | \(0.628111\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.25227 | − | 1.44519i | 0.200523 | − | 0.231416i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.0522 | − | 2.95160i | −1.56990 | − | 0.460963i | −0.622925 | − | 0.782282i | \(-0.714056\pi\) |
−0.946971 | + | 0.321319i | \(0.895874\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.71801 | + | 11.9490i | 0.261994 | + | 1.82221i | 0.517826 | + | 0.855486i | \(0.326741\pi\) |
−0.255832 | + | 0.966721i | \(0.582350\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.08477 | −0.608921 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.71564 | −0.833712 | −0.416856 | − | 0.908972i | \(-0.636868\pi\) | ||||
−0.416856 | + | 0.908972i | \(0.636868\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.993944 | + | 6.91303i | 0.141992 | + | 0.987576i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.81847 | − | 0.533951i | −0.254637 | − | 0.0747681i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.37352 | + | 5.04731i | −0.600749 | + | 0.693301i | −0.971933 | − | 0.235258i | \(-0.924406\pi\) |
0.371184 | + | 0.928559i | \(0.378952\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.83675 | + | 1.42020i | −0.652188 | + | 0.191500i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.124215 | − | 0.0798279i | 0.0164526 | − | 0.0105735i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.98875 | − | 5.75733i | −0.649480 | − | 0.749540i | 0.331541 | − | 0.943441i | \(-0.392431\pi\) |
−0.981021 | + | 0.193901i | \(0.937886\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.180939 | + | 1.25846i | −0.0231668 | + | 0.161129i | −0.998121 | − | 0.0612782i | \(-0.980482\pi\) |
0.974954 | + | 0.222407i | \(0.0713914\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.0523476 | − | 0.114625i | 0.00659518 | − | 0.0144414i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.24487 | + | 7.10527i | 0.402476 | + | 0.881301i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.94923 | − | 5.75132i | −1.09332 | − | 0.702636i | −0.135726 | − | 0.990746i | \(-0.543337\pi\) |
−0.957597 | + | 0.288111i | \(0.906973\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.93627 | + | 2.73967i | −0.473871 | + | 0.329818i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.77319 | + | 4.99552i | 0.922508 | + | 0.592860i | 0.913384 | − | 0.407099i | \(-0.133460\pi\) |
0.00912348 | + | 0.999958i | \(0.497096\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.25031 | − | 11.4966i | −0.614502 | − | 1.34557i | −0.919451 | − | 0.393204i | \(-0.871367\pi\) |
0.304949 | − | 0.952369i | \(-0.401361\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.85427 | − | 10.6294i | 0.560522 | − | 1.22737i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.0221314 | − | 0.153928i | 0.00252211 | − | 0.0175417i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.44214 | + | 2.81838i | 0.274762 | + | 0.317092i | 0.876313 | − | 0.481742i | \(-0.159996\pi\) |
−0.601551 | + | 0.798834i | \(0.705450\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.841254 | − | 0.540641i | 0.0934726 | − | 0.0600712i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.82984 | − | 2.29905i | 0.859437 | − | 0.252353i | 0.177820 | − | 0.984063i | \(-0.443095\pi\) |
0.681617 | + | 0.731710i | \(0.261277\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.06969 | − | 5.85073i | 0.549885 | − | 0.634601i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.20097 | − | 2.11439i | −0.772025 | − | 0.226687i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.00479 | + | 6.98848i | 0.106508 | + | 0.740778i | 0.971164 | + | 0.238413i | \(0.0766273\pi\) |
−0.864656 | + | 0.502364i | \(0.832464\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.240970 | −0.0252605 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.35692 | −0.244401 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.0858348 | + | 0.596994i | 0.00880647 | + | 0.0612503i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.7100 | + | 3.73198i | 1.29050 | + | 0.378925i | 0.853762 | − | 0.520663i | \(-0.174315\pi\) |
0.436739 | + | 0.899588i | \(0.356133\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.808153 | − | 0.932658i | 0.0812224 | − | 0.0937357i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.47893 | + | 1.90238i | −0.644677 | + | 0.189294i | −0.587697 | − | 0.809081i | \(-0.699965\pi\) |
−0.0569800 | + | 0.998375i | \(0.518147\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.13745 | + | 4.58696i | −0.703274 | + | 0.451967i | −0.842783 | − | 0.538254i | \(-0.819084\pi\) |
0.139509 | + | 0.990221i | \(0.455448\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.337079 | + | 0.389010i | 0.0328955 | + | 0.0379635i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.88329 | − | 13.0986i | 0.182065 | − | 1.26629i | −0.669806 | − | 0.742536i | \(-0.733623\pi\) |
0.851871 | − | 0.523752i | \(-0.175468\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.09393 | − | 6.77476i | 0.296345 | − | 0.648905i | −0.701628 | − | 0.712543i | \(-0.747543\pi\) |
0.997973 | + | 0.0636386i | \(0.0202705\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.20937 | + | 7.02754i | 0.304620 | + | 0.667025i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.67658 | + | 1.72014i | 0.251792 | + | 0.161817i | 0.660448 | − | 0.750871i | \(-0.270366\pi\) |
−0.408657 | + | 0.912688i | \(0.634003\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.50027 | − | 19.2746i | −0.326402 | − | 1.79737i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.60870 | − | 1.03385i | −0.148724 | − | 0.0955792i | ||||
\(118\) | 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 | ||||||||
\(123\) | −1.49098 | + | 10.3700i | −0.134437 | + | 0.935029i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 17.8830 | + | 20.6381i | 1.59950 | + | 1.84593i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.9326 | + | 10.8819i | −1.50252 | + | 0.965614i | −0.507972 | + | 0.861374i | \(0.669605\pi\) |
−0.994552 | + | 0.104240i | \(0.966759\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.5829 | − | 3.40104i | 1.01982 | − | 0.299445i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.33360 | − | 2.69312i | 0.203888 | − | 0.235299i | −0.644592 | − | 0.764527i | \(-0.722973\pi\) |
0.848480 | + | 0.529228i | \(0.177518\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0178526 | − | 0.00524201i | −0.00154802 | − | 0.000454540i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.581323 | + | 4.04319i | 0.0500323 | + | 0.347983i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −20.4210 | −1.74468 | −0.872342 | − | 0.488897i | \(-0.837399\pi\) | ||||
−0.872342 | + | 0.488897i | \(0.837399\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.3307 | 1.21551 | 0.607755 | − | 0.794125i | \(-0.292070\pi\) | ||||
0.607755 | + | 0.794125i | \(0.292070\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.813421 | + | 5.65747i | 0.0685024 | + | 0.476445i | ||||
\(142\) | 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 | ||||||||
\(147\) | 6.70121 | − | 1.96765i | 0.552707 | − | 0.162289i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.1115 | − | 9.71156i | 1.23798 | − | 0.795602i | 0.252866 | − | 0.967501i | \(-0.418627\pi\) |
0.985114 | + | 0.171900i | \(0.0549905\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.03194 | + | 4.65311i | 0.328115 | + | 0.378665i | 0.895707 | − | 0.444645i | \(-0.146670\pi\) |
−0.567592 | + | 0.823310i | \(0.692125\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.269721 | + | 1.87595i | −0.0218056 | + | 0.151662i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.99940 | − | 8.75746i | 0.321240 | − | 0.703416i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.21531 | − | 7.04055i | −0.256610 | − | 0.561897i | 0.736853 | − | 0.676053i | \(-0.236311\pi\) |
−0.993463 | + | 0.114156i | \(0.963584\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.61835 | + | 3.61069i | 0.445564 | + | 0.286347i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.585735 | + | 0.148787i | 0.0461623 | + | 0.0117261i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.7893 | + | 6.93388i | 0.845085 | + | 0.543103i | 0.890038 | − | 0.455886i | \(-0.150678\pi\) |
−0.0449533 | + | 0.998989i | \(0.514314\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.09409 | + | 4.58541i | 0.163024 | + | 0.356973i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.25256 | − | 2.74273i | 0.0969262 | − | 0.212239i | −0.854958 | − | 0.518698i | \(-0.826417\pi\) |
0.951884 | + | 0.306459i | \(0.0991442\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.32968 | − | 9.24815i | 0.102283 | − | 0.711396i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.0966929 | − | 0.111590i | −0.00739429 | − | 0.00853347i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.98890 | − | 1.27819i | 0.151214 | − | 0.0971791i | −0.462846 | − | 0.886439i | \(-0.653172\pi\) |
0.614060 | + | 0.789260i | \(0.289535\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.41286 | + | 0.414852i | −0.106802 | + | 0.0313599i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.98875 | + | 5.75733i | −0.374978 | + | 0.432747i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.0574 | + | 5.88938i | 1.49916 | + | 0.440193i | 0.925451 | − | 0.378867i | \(-0.123686\pi\) |
0.573708 | + | 0.819060i | \(0.305504\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.18165 | − | 15.1737i | −0.162161 | − | 1.12785i | −0.894550 | − | 0.446967i | \(-0.852504\pi\) |
0.732389 | − | 0.680886i | \(-0.238405\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.27140 | 0.0939845 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −31.5577 | −2.32017 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.332858 | + | 2.31508i | 0.0243410 | + | 0.169295i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.120908 | − | 0.0355019i | −0.00879480 | − | 0.00258239i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.93558 | − | 6.85002i | 0.429483 | − | 0.495650i | −0.499219 | − | 0.866476i | \(-0.666380\pi\) |
0.928703 | + | 0.370826i | \(0.120925\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.14918 | − | 2.68644i | 0.658572 | − | 0.193374i | 0.0646640 | − | 0.997907i | \(-0.479402\pi\) |
0.593908 | + | 0.804533i | \(0.297584\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.57116 | − | 4.22303i | 0.470570 | − | 0.302417i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.70078 | − | 1.96280i | −0.121175 | − | 0.139844i | 0.691920 | − | 0.721974i | \(-0.256765\pi\) |
−0.813096 | + | 0.582130i | \(0.802219\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.86746 | + | 19.9437i | −0.203269 | + | 1.41377i | 0.591230 | + | 0.806503i | \(0.298643\pi\) |
−0.794499 | + | 0.607265i | \(0.792267\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.41917 | + | 9.67664i | −0.311705 | + | 0.682538i | ||||
\(202\) | 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 | ||||||||
\(207\) | 3.27197 | + | 3.50631i | 0.227418 | + | 0.243705i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.153291 | − | 0.0985143i | −0.0106034 | − | 0.00681438i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.89338 | − | 21.6635i | −0.681089 | − | 1.49138i | −0.861486 | − | 0.507782i | \(-0.830466\pi\) |
0.180397 | − | 0.983594i | \(-0.442262\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.83844 | − | 8.40501i | 0.263005 | − | 0.575901i | ||||
\(214\) | 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 | ||||||||
\(219\) | −10.6324 | + | 6.83300i | −0.718468 | + | 0.461732i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.47739 | − | 1.02105i | 0.233915 | − | 0.0686836i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.1936 | + | 15.2262i | −0.883507 | + | 1.01962i | 0.116145 | + | 0.993232i | \(0.462946\pi\) |
−0.999652 | + | 0.0263890i | \(0.991599\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.2120 | − | 3.29214i | −0.747467 | − | 0.219476i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.33377 | − | 9.27656i | −0.0885253 | − | 0.615707i | −0.984993 | − | 0.172597i | \(-0.944784\pi\) |
0.896467 | − | 0.443110i | \(-0.146125\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.99434 | 0.197872 | 0.0989359 | − | 0.995094i | \(-0.468456\pi\) | ||||
0.0989359 | + | 0.995094i | \(0.468456\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.155510 | −0.0102318 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.47396 | − | 10.2516i | −0.0965624 | − | 0.671607i | −0.979400 | − | 0.201929i | \(-0.935279\pi\) |
0.882838 | − | 0.469678i | \(-0.155630\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −22.4014 | − | 6.57764i | −1.46130 | − | 0.429078i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.44214 | − | 2.81838i | 0.158634 | − | 0.183073i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.25694 | + | 0.956324i | −0.210674 | + | 0.0618595i | −0.385367 | − | 0.922764i | \(-0.625925\pi\) |
0.174693 | + | 0.984623i | \(0.444107\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.4551 | − | 9.28973i | 0.931135 | − | 0.598404i | 0.0152666 | − | 0.999883i | \(-0.495140\pi\) |
0.915868 | + | 0.401480i | \(0.131504\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.654861 | − | 0.755750i | −0.0420093 | − | 0.0484814i | ||||
\(244\) | 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 | ||||||||
\(249\) | −3.38995 | − | 7.42296i | −0.214829 | − | 0.470411i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.5073 | + | 8.68061i | 0.852572 | + | 0.547915i | 0.892376 | − | 0.451293i | \(-0.149037\pi\) |
−0.0398037 | + | 0.999208i | \(0.512673\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.09341 | + | 3.01419i | 0.320220 | + | 0.189501i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.51267 | − | 4.18544i | −0.407839 | − | 0.262102i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.14370 | − | 20.0219i | −0.570368 | − | 1.24893i | −0.946601 | − | 0.322407i | \(-0.895508\pi\) |
0.376233 | − | 0.926525i | \(-0.377219\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.404422 | − | 0.885560i | 0.0251296 | − | 0.0550260i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.06807 | + | 7.42858i | −0.0661118 | + | 0.459818i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.9296 | + | 17.2297i | 0.920601 | + | 1.06243i | 0.997858 | + | 0.0654188i | \(0.0208383\pi\) |
−0.0772571 | + | 0.997011i | \(0.524616\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −22.9497 | + | 14.7489i | −1.40979 | + | 0.906015i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.77435 | − | 1.98913i | 0.414584 | − | 0.121733i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.55143 | + | 4.09857i | −0.216534 | + | 0.249894i | −0.853617 | − | 0.520902i | \(-0.825596\pi\) |
0.637082 | + | 0.770796i | \(0.280141\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.3625 | + | 7.15346i | 1.47991 | + | 0.434542i | 0.919307 | − | 0.393541i | \(-0.128750\pi\) |
0.560606 | + | 0.828082i | \(0.310568\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.0342936 | + | 0.238517i | 0.00207554 | + | 0.0144357i | ||||
\(274\) | 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 | ||||||||
\(279\) | 0.335425 | + | 2.33293i | 0.0200814 | + | 0.139669i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.14061 | + | 2.09667i | 0.425973 | + | 0.125077i | 0.487690 | − | 0.873017i | \(-0.337840\pi\) |
−0.0617174 | + | 0.998094i | \(0.519658\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.9165 | − | 18.3687i | 0.946141 | − | 1.09190i | −0.0495133 | − | 0.998773i | \(-0.515767\pi\) |
0.995654 | − | 0.0931309i | \(-0.0296875\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.578702 | − | 0.169922i | 0.0342794 | − | 0.0100653i | ||||
\(286\) | 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 | ||||||||
\(291\) | 1.88518 | − | 13.1117i | 0.110511 | − | 0.768622i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.78323 | − | 14.8532i | 0.396281 | − | 0.867733i | −0.601353 | − | 0.798983i | \(-0.705372\pi\) |
0.997634 | − | 0.0687502i | \(-0.0219012\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.9269 | − | 28.3059i | −0.752630 | − | 1.64803i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.03818 | − | 0.667196i | −0.0602412 | − | 0.0387146i | ||||
\(298\) | 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 | ||||||||
\(303\) | 2.80507 | + | 6.14224i | 0.161147 | + | 0.352863i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.15740 | + | 4.72406i | −0.123533 | + | 0.270499i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.54574 | + | 24.6612i | −0.202366 | + | 1.40749i | 0.594871 | + | 0.803821i | \(0.297203\pi\) |
−0.797237 | + | 0.603667i | \(0.793706\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.55604 | + | 6.41201i | 0.316072 | + | 0.364766i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.7744 | + | 15.2789i | −1.34813 | + | 0.866388i | −0.997537 | − | 0.0701421i | \(-0.977655\pi\) |
−0.350588 | + | 0.936530i | \(0.614018\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.29010 | − | 1.55331i | 0.299014 | − | 0.0877985i | −0.128784 | − | 0.991673i | \(-0.541107\pi\) |
0.427798 | + | 0.903874i | \(0.359289\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.337079 | − | 0.389010i | 0.0189922 | − | 0.0219182i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.12306 | + | 0.917014i | 0.175409 | + | 0.0515047i | 0.368258 | − | 0.929724i | \(-0.379954\pi\) |
−0.192849 | + | 0.981228i | \(0.561773\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.31809 | + | 9.16749i | 0.0737987 | + | 0.513281i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.2333 | −0.738610 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.279840 | 0.0155707 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.18009 | + | 22.1180i | 0.176400 | + | 1.22689i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.14612 | − | 2.09829i | −0.395181 | − | 0.116036i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.471660 | − | 0.544325i | 0.0260035 | − | 0.0300096i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.54037 | + | 1.92043i | −0.359491 | + | 0.105556i | −0.456490 | − | 0.889728i | \(-0.650894\pi\) |
0.0969992 | + | 0.995284i | \(0.469076\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.49927 | − | 4.17683i | 0.356158 | − | 0.228889i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −28.4561 | − | 32.8401i | −1.55472 | − | 1.79425i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.655700 | + | 4.56049i | −0.0357183 | + | 0.248426i | −0.999856 | − | 0.0169769i | \(-0.994596\pi\) |
0.964138 | + | 0.265403i | \(0.0855049\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.32171 | − | 2.89414i | 0.0717854 | − | 0.157188i | ||||
\(340\) | 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 | ||||||||
\(345\) | −18.5803 | + | 6.20770i | −1.00033 | + | 0.334212i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.8312 | − | 12.1021i | −1.01091 | − | 0.649674i | −0.0732832 | − | 0.997311i | \(-0.523348\pi\) |
−0.937629 | + | 0.347637i | \(0.886984\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.84062 | + | 19.3583i | 0.473228 | + | 1.03622i | 0.984270 | + | 0.176669i | \(0.0565321\pi\) |
−0.511043 | + | 0.859555i | \(0.670741\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.794382 | + | 1.73945i | −0.0424010 | + | 0.0928452i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.895635 | − | 6.22928i | 0.0476698 | − | 0.331551i | −0.952006 | − | 0.306080i | \(-0.900982\pi\) |
0.999676 | − | 0.0254708i | \(-0.00810848\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 24.7166 | + | 28.5245i | 1.31182 | + | 1.51392i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.200912 | − | 0.129118i | 0.0106334 | − | 0.00683367i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.4027 | − | 4.22900i | 0.760143 | − | 0.223198i | 0.121385 | − | 0.992606i | \(-0.461267\pi\) |
0.638758 | + | 0.769407i | \(0.279448\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.4281 | − | 14.3428i | 0.654109 | − | 0.754882i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.09315 | + | 2.66999i | 0.477267 | + | 0.140138i | ||||
\(364\) | 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 | ||||||||
\(369\) | 10.4766 | 0.545391 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.119770 | − | 0.833016i | −0.00621813 | − | 0.0432481i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.42461 | + | 2.47369i | 0.436210 | + | 0.128083i | 0.492462 | − | 0.870334i | \(-0.336097\pi\) |
−0.0562525 | + | 0.998417i | \(0.517915\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 17.8830 | − | 20.6381i | 0.923474 | − | 1.06575i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.7701 | − | 4.04328i | 0.709198 | − | 0.208239i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.68742 | − | 3.65509i | 0.292143 | − | 0.187749i | −0.386357 | − | 0.922349i | \(-0.626267\pi\) |
0.678500 | + | 0.734600i | \(0.262630\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.1809 | + | 15.2116i | 0.675278 | + | 0.779313i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.0756551 | + | 0.526193i | −0.00386580 | + | 0.0268872i | −0.991663 | − | 0.128858i | \(-0.958869\pi\) |
0.987797 | + | 0.155745i | \(0.0497779\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.263882 | − | 0.577820i | 0.0134487 | − | 0.0294485i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.01484 | − | 10.9810i | −0.254919 | − | 0.558194i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.93689 | − | 2.53008i | −0.199608 | − | 0.128280i | 0.437019 | − | 0.899452i | \(-0.356034\pi\) |
−0.636627 | + | 0.771172i | \(0.719671\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.08309 | + | 0.334795i | −0.459352 | + | 0.0169313i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.99782 | − | 1.92658i | −0.151220 | − | 0.0971831i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.32807 | + | 13.8565i | 0.318400 | + | 0.697198i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.42758 | − | 3.12596i | 0.0716480 | − | 0.156887i | −0.870419 | − | 0.492311i | \(-0.836152\pi\) |
0.942067 | + | 0.335424i | \(0.108880\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.00264796 | + | 0.0184169i | −0.000132564 | + | 0.000922001i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.58668 | + | 9.90955i | 0.428798 | + | 0.494859i | 0.928497 | − | 0.371340i | \(-0.121101\pi\) |
−0.499699 | + | 0.866199i | \(0.666556\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.79157 | − | 2.43670i | 0.188872 | − | 0.121380i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.91931 | − | 1.15081i | 0.194752 | − | 0.0571843i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.24354 | − | 7.20543i | 0.309481 | − | 0.357160i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.93864 | + | 1.15649i | 0.194753 | + | 0.0571848i | 0.377655 | − | 0.925947i | \(-0.376731\pi\) |
−0.182901 | + | 0.983131i | \(0.558549\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.90621 | + | 20.2131i | 0.143353 | + | 0.997040i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.959971 | 0.0472371 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 33.3333 | 1.63627 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.03946 | − | 14.1848i | −0.0998730 | − | 0.694632i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 35.7570 | + | 10.4992i | 1.74684 | + | 0.512919i | 0.990048 | − | 0.140733i | \(-0.0449460\pi\) |
0.756795 | + | 0.653652i | \(0.226764\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.30973 | − | 7.28181i | 0.307517 | − | 0.354894i | −0.580864 | − | 0.814001i | \(-0.697285\pi\) |
0.888381 | + | 0.459107i | \(0.151831\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.48412 | − | 1.61028i | 0.266647 | − | 0.0782946i | ||||
\(424\) | 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 | ||||||||
\(429\) | −0.335848 | + | 2.33587i | −0.0162149 | + | 0.112777i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.3144 | − | 29.1546i | 0.641334 | − | 1.40433i | −0.257604 | − | 0.966251i | \(-0.582933\pi\) |
0.898938 | − | 0.438076i | \(-0.144340\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.2767 | + | 22.5027i | 0.493865 | + | 1.08141i | 0.978415 | + | 0.206649i | \(0.0662559\pi\) |
−0.484551 | + | 0.874763i | \(0.661017\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −25.7895 | − | 16.5739i | −1.23651 | − | 0.794659i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.443696 | − | 0.551883i | 0.0212249 | − | 0.0264001i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.03424 | − | 4.52063i | −0.335726 | − | 0.215758i | 0.361905 | − | 0.932215i | \(-0.382126\pi\) |
−0.697632 | + | 0.716457i | \(0.745763\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.90131 | − | 6.35298i | −0.138158 | − | 0.302523i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.68541 | + | 8.06992i | −0.175099 | + | 0.383413i | −0.976751 | − | 0.214378i | \(-0.931228\pi\) |
0.801652 | + | 0.597791i | \(0.203955\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.10435 | + | 28.5463i | −0.194565 | + | 1.35323i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.7633 | − | 13.5756i | −0.556385 | − | 0.642102i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.42408 | + | 5.41383i | −0.397557 | + | 0.255494i | −0.724110 | − | 0.689685i | \(-0.757749\pi\) |
0.326553 | + | 0.945179i | \(0.394113\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.4053 | − | 3.64253i | 0.584143 | − | 0.171520i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.03194 | − | 4.65311i | 0.189437 | − | 0.218622i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.944434 | − | 0.277311i | −0.0442758 | − | 0.0130005i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.20875 | + | 29.2725i | 0.196877 | + | 1.36931i | 0.813277 | + | 0.581877i | \(0.197681\pi\) |
−0.616400 | + | 0.787433i | \(0.711410\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.89524 | 0.0884623 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.8301 | −0.830430 | −0.415215 | − | 0.909723i | \(-0.636294\pi\) | ||||
−0.415215 | + | 0.909723i | \(0.636294\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.40293 | + | 9.75762i | 0.0651999 | + | 0.453475i | 0.996102 | + | 0.0882069i | \(0.0281137\pi\) |
−0.930902 | + | 0.365268i | \(0.880977\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.23750 | − | 2.71237i | −0.428379 | − | 0.125783i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.2767 | + | 29.1708i | −1.16966 | + | 1.34986i | −0.244797 | + | 0.969574i | \(0.578721\pi\) |
−0.924867 | + | 0.380290i | \(0.875824\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.28622 | − | 0.377669i | 0.0593922 | − | 0.0174391i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.51130 | + | 4.18456i | −0.300025 | + | 0.192814i | ||||
\(472\) | 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 | ||||||||
\(477\) | 2.77437 | − | 6.07502i | 0.127030 | − | 0.278156i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.81750 | + | 6.16945i | 0.128735 | + | 0.281890i | 0.963013 | − | 0.269453i | \(-0.0868430\pi\) |
−0.834279 | + | 0.551343i | \(0.814116\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.4283 | − | 7.98719i | −0.566682 | − | 0.364184i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.0639141 | − | 0.600947i | 0.00290819 | − | 0.0273440i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 45.5195 | + | 29.2536i | 2.06693 | + | 1.32834i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.77299 | − | 6.07200i | −0.125656 | − | 0.275149i | 0.836340 | − | 0.548211i | \(-0.184691\pi\) |
−0.961996 | + | 0.273062i | \(0.911964\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.32782 | − | 11.6663i | 0.240932 | − | 0.527568i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.53163 | − | 17.6079i | 0.114251 | − | 0.794632i | −0.849454 | − | 0.527662i | \(-0.823069\pi\) |
0.963705 | − | 0.266969i | \(-0.0860222\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.31456 | − | 10.7496i | −0.419507 | − | 0.484137i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.24072 | − | 2.72534i | 0.190606 | − | 0.122495i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.11719 | + | 0.328038i | −0.0501130 | + | 0.0147145i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.992242 | − | 1.14511i | 0.0444189 | − | 0.0512621i | −0.733105 | − | 0.680115i | \(-0.761930\pi\) |
0.777524 | + | 0.628853i | \(0.216475\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.89307 | − | 0.849482i | −0.129253 | − | 0.0379521i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.54825 | + | 17.7235i | 0.113621 | + | 0.790250i | 0.964347 | + | 0.264641i | \(0.0852535\pi\) |
−0.850726 | + | 0.525609i | \(0.823837\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27.5822 | −1.22739 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.34325 | −0.414948 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.69998 | + | 18.7788i | 0.119675 | + | 0.832355i | 0.957915 | + | 0.287053i | \(0.0926757\pi\) |
−0.838240 | + | 0.545301i | \(0.816415\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.52813 | + | 0.448699i | 0.0676004 | + | 0.0198493i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.0966929 | + | 0.111590i | −0.00426910 | + | 0.00492680i | ||||
\(514\) | 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 | ||||||||
\(519\) | −1.54823 | − | 1.78675i | −0.0679598 | − | 0.0784298i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.48410 | + | 31.1876i | −0.196452 | + | 1.36635i | 0.618026 | + | 0.786158i | \(0.287933\pi\) |
−0.814478 | + | 0.580195i | \(0.802976\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.15195 | + | 15.6606i | −0.312733 | + | 0.684790i | −0.999098 | − | 0.0424676i | \(-0.986478\pi\) |
0.686365 | + | 0.727257i | \(0.259205\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.611700 | + | 1.33944i | 0.0266968 | + | 0.0584578i | ||||
\(526\) | 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 | ||||||||
\(531\) | 6.40870 | + | 4.11862i | 0.278114 | + | 0.178733i | ||||
\(532\) | 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 | ||||||||
\(537\) | 2.97497 | − | 20.6914i | 0.128379 | − | 0.892899i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.64424 | − | 6.51380i | −0.243115 | − | 0.280569i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.229819 | − | 0.147696i | 0.00988070 | − | 0.00634994i | −0.535691 | − | 0.844414i | \(-0.679949\pi\) |
0.545572 | + | 0.838064i | \(0.316312\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14.7088 | + | 4.31889i | −0.631214 | + | 0.185341i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.9225 | − | 22.9918i | 0.853388 | − | 0.984863i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.3716 | − | 7.44978i | −1.08481 | − | 0.318530i | −0.310010 | − | 0.950733i | \(-0.600332\pi\) |
−0.774802 | + | 0.632203i | \(0.782151\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.180939 | − | 1.25846i | −0.00772228 | − | 0.0537097i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.10814 | 0.0472084 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.469934 | −0.0199836 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.49113 | + | 31.2365i | 0.190638 | + | 1.32591i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −23.7086 | − | 6.96147i | −1.00457 | − | 0.294967i | −0.262237 | − | 0.965003i | \(-0.584460\pi\) |
−0.742328 | + | 0.670036i | \(0.766278\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.1172 | + | 17.4462i | −0.639390 | + | 0.737895i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.24415 | − | 0.658941i | 0.0947479 | − | 0.0278205i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.2024 | − | 9.12730i | 0.598558 | − | 0.384670i | −0.205993 | − | 0.978553i | \(-0.566042\pi\) |
0.804551 | + | 0.593884i | \(0.202406\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.51080 | + | 9.82198i | 0.358052 | + | 0.413214i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.0179335 | + | 0.124730i | −0.000753136 | + | 0.00523818i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.05486 | − | 8.87892i | 0.169989 | − | 0.372223i | −0.805395 | − | 0.592739i | \(-0.798047\pi\) |
0.975384 | + | 0.220515i | \(0.0707739\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.08106 | − | 13.3157i | −0.254484 | − | 0.557243i | 0.738668 | − | 0.674070i | \(-0.235455\pi\) |
−0.993152 | + | 0.116826i | \(0.962728\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.62502 | − | 4.90030i | −0.318540 | − | 0.204713i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.92684 | − | 55.7266i | 0.247166 | − | 2.32396i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.3558 | + | 6.65529i | 0.431119 | + | 0.277063i | 0.738151 | − | 0.674636i | \(-0.235699\pi\) |
−0.307032 | + | 0.951699i | \(0.599336\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.96116 | − | 8.67373i | −0.164620 | − | 0.360468i | ||||
\(580\) | 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 | ||||||||
\(585\) | −5.11522 | − | 5.90327i | −0.211488 | − | 0.244070i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.1633 | − | 6.53159i | 0.419486 | − | 0.269587i | −0.313825 | − | 0.949481i | \(-0.601610\pi\) |
0.733311 | + | 0.679893i | \(0.237974\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.333913 | − | 0.0980456i | 0.0137586 | − | 0.00403990i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.70078 | + | 1.96280i | −0.0699606 | + | 0.0807388i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 41.6427 | + | 12.2274i | 1.71006 | + | 0.502119i | 0.982867 | − | 0.184314i | \(-0.0590063\pi\) |
0.727193 | + | 0.686433i | \(0.240824\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.138834 | + | 0.965615i | 0.00569166 | + | 0.0395863i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.1487 | 0.824633 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −36.5272 | −1.49246 | −0.746230 | − | 0.665688i | \(-0.768138\pi\) | ||||
−0.746230 | + | 0.665688i | \(0.768138\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.0953083 | + | 0.662884i | 0.00388771 | + | 0.0270396i | 0.991673 | − | 0.128782i | \(-0.0411067\pi\) |
−0.987785 | + | 0.155821i | \(0.950198\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.2071 | + | 2.99706i | 0.415664 | + | 0.122050i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −25.3506 | + | 29.2562i | −1.03065 | + | 1.18943i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −34.6753 | + | 10.1816i | −1.40743 | + | 0.413258i | −0.895228 | − | 0.445608i | \(-0.852988\pi\) |
−0.512200 | + | 0.858866i | \(0.671169\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.795593 | − | 0.511296i | 0.0322390 | − | 0.0207188i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.15750 | − | 8.26020i | −0.289562 | − | 0.334172i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.62930 | − | 39.1526i | 0.227365 | − | 1.58136i | −0.481776 | − | 0.876294i | \(-0.660008\pi\) |
0.709142 | − | 0.705066i | \(-0.249083\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −17.7775 | + | 38.9273i | −0.716858 | + | 1.56970i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.38060 | − | 5.21278i | −0.0958393 | − | 0.209859i | 0.855640 | − | 0.517571i | \(-0.173164\pi\) |
−0.951479 | + | 0.307712i | \(0.900437\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.1415 | + | 14.2295i | 0.889942 | + | 0.571931i | 0.903792 | − | 0.427973i | \(-0.140772\pi\) |
−0.0138494 | + | 0.999904i | \(0.504409\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.00497 | − | 3.73767i | 0.120585 | − | 0.149988i | ||||
\(622\) | 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 | ||||||||
\(627\) | −0.0756960 | + | 0.165751i | −0.00302301 | + | 0.00661946i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.08378 | + | 14.4930i | −0.0830858 | + | 0.577875i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.8138 | − | 21.7123i | −0.748967 | − | 0.864354i | 0.245501 | − | 0.969396i | \(-0.421048\pi\) |
−0.994468 | + | 0.105042i | \(0.966502\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.0350 | + | 12.8757i | −0.796320 | + | 0.511764i | ||||
\(634\) | 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 | ||||||||
\(639\) | −8.86572 | − | 2.60321i | −0.350722 | − | 0.102981i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.14585 | + | 21.8799i | 0.124254 | + | 0.864202i | 0.952652 | + | 0.304063i | \(0.0983433\pi\) |
−0.828398 | + | 0.560139i | \(0.810748\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.1875 | −0.441193 | −0.220596 | − | 0.975365i | \(-0.570800\pi\) | ||||
−0.220596 | + | 0.975365i | \(0.570800\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 49.3109 | 1.94161 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.70136 | − | 25.7436i | −0.145516 | − | 1.01208i | −0.923445 | − | 0.383731i | \(-0.874639\pi\) |
0.777929 | − | 0.628352i | \(-0.216270\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.02048 | + | 2.64865i | 0.354085 | + | 0.103969i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.194495 | − | 0.224459i | 0.00762287 | − | 0.00879726i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −43.7741 | + | 12.8532i | −1.71301 | + | 0.502986i | −0.983489 | − | 0.180967i | \(-0.942077\pi\) |
−0.729525 | + | 0.683954i | \(0.760259\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.2454 | − | 7.86963i | 0.478467 | − | 0.307492i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.27660 | + | 9.55170i | 0.322901 | + | 0.372647i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.36052 | − | 30.3281i | 0.169862 | − | 1.18141i | −0.709306 | − | 0.704901i | \(-0.750992\pi\) |
0.879168 | − | 0.476513i | \(-0.158099\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.54464 | − | 14.3308i | 0.254557 | − | 0.557402i | −0.738606 | − | 0.674137i | \(-0.764516\pi\) |
0.993163 | + | 0.116735i | \(0.0372429\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.50555 | − | 3.29669i | −0.0584706 | − | 0.128033i | ||||
\(664\) | 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 | ||||||||
\(669\) | 16.9489 | + | 10.8924i | 0.655280 | + | 0.421123i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.651791 | − | 1.42722i | −0.0251621 | − | 0.0550974i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.20807 | − | 9.21438i | 0.162209 | − | 0.355188i | −0.811023 | − | 0.585015i | \(-0.801089\pi\) |
0.973232 | + | 0.229827i | \(0.0738159\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.66300 | + | 11.5664i | −0.0640088 | + | 0.445191i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.73175 | + | 8.92291i | 0.297155 | + | 0.342935i | 0.884619 | − | 0.466315i | \(-0.154419\pi\) |
−0.587463 | + | 0.809251i | \(0.699873\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.40425 | + | 0.902457i | −0.0538902 | + | 0.0346331i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.99232 | + | 2.64038i | −0.344586 | + | 0.101180i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.85265 | − | 9.06244i | 0.300473 | − | 0.346765i | −0.585356 | − | 0.810777i | \(-0.699045\pi\) |
0.885829 | + | 0.464012i | \(0.153591\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −80.0361 | − | 23.5007i | −3.05802 | − | 0.897917i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.426139 | − | 2.96386i | −0.0162582 | − | 0.113078i | ||||
\(688\) | 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 | ||||||||
\(693\) | 0.0221314 | + | 0.153928i | 0.000840704 | + | 0.00584722i | ||||
\(694\) | 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 | ||||||||
\(699\) | −9.93752 | + | 2.91792i | −0.375871 | + | 0.110366i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.7052 | + | 24.2316i | −1.42410 | + | 0.915216i | −0.424150 | + | 0.905592i | \(0.639427\pi\) |
−0.999954 | + | 0.00962419i | \(0.996936\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.747020 | − | 0.862107i | −0.0281744 | − | 0.0325150i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.32264 | + | 23.1095i | −0.125138 | + | 0.870352i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.353475 | − | 0.774002i | 0.0132938 | − | 0.0291093i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.7599 | + | 34.5095i | 0.591877 | + | 1.29603i | 0.934301 | + | 0.356485i | \(0.116025\pi\) |
−0.342424 | + | 0.939546i | \(0.611248\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.13725 | − | 2.01619i | −0.117656 | − | 0.0756128i | ||||
\(712\) | 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 | ||||||||
\(717\) | 1.41010 | + | 3.08769i | 0.0526612 | + | 0.115312i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.3632 | + | 33.6408i | −0.572952 | + | 1.25459i | 0.372258 | + | 0.928129i | \(0.378584\pi\) |
−0.945210 | + | 0.326462i | \(0.894144\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.152153 | − | 1.05825i | 0.00566648 | − | 0.0394113i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.2523 | − | 12.9859i | −0.418479 | − | 0.482951i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 73.7764 | − | 47.4132i | 2.73999 | − | 1.76088i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 44.6395 | − | 13.1073i | 1.65559 | − | 0.486124i | 0.685336 | − | 0.728227i | \(-0.259655\pi\) |
0.970250 | + | 0.242103i | \(0.0778373\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.654861 | + | 0.755750i | −0.0242541 | + | 0.0279907i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.9524 | + | 6.44580i | 0.811938 | + | 0.238406i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.437796 | + | 3.04494i | 0.0161704 | + | 0.112467i | 0.996308 | − | 0.0858513i | \(-0.0273610\pi\) |
−0.980138 | + | 0.198319i | \(0.936452\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 28.5285 | 1.05229 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.1282 | 0.483582 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.33533 | − | 23.1977i | −0.122692 | − | 0.853341i | −0.954486 | − | 0.298257i | \(-0.903595\pi\) |
0.831794 | − | 0.555085i | \(-0.187314\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.270916 | + | 0.0795482i | 0.00995236 | + | 0.00292228i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.07237 | + | 1.23758i | −0.0393413 | + | 0.0454023i | −0.775079 | − | 0.631864i | \(-0.782290\pi\) |
0.735738 | + | 0.677266i | \(0.236836\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 70.4027 | − | 20.6721i | 2.57936 | − | 0.757367i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.86496 | + | 4.41184i | −0.251176 | + | 0.161421i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.09202 | + | 1.26026i | 0.0399016 | + | 0.0460489i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.05226 | − | 42.0944i | 0.220850 | − | 1.53605i | −0.513984 | − | 0.857800i | \(-0.671831\pi\) |
0.734834 | − | 0.678247i | \(-0.237260\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.66996 | − | 14.6052i | 0.243067 | − | 0.532242i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.4476 | + | 22.8770i | 0.380226 | + | 0.832579i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.49246 | − | 4.81511i | −0.272318 | − | 0.175008i | 0.397353 | − | 0.917666i | \(-0.369929\pi\) |
−0.669671 | + | 0.742657i | \(0.733565\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.25865 | − | 5.47053i | 0.0819837 | − | 0.198568i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.4340 | + | 20.8441i | 1.17573 | + | 0.755597i | 0.974597 | − | 0.223967i | \(-0.0719008\pi\) |
0.201134 | + | 0.979564i | \(0.435537\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.389875 | + | 0.853707i | 0.0141144 | + | 0.0309063i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.21599 | + | 7.04203i | −0.116274 | + | 0.254605i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.07320 | − | 14.4194i | 0.0748588 | − | 0.520654i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.6719 | − | 38.8594i | −1.21424 | − | 1.40131i | −0.890390 | − | 0.455199i | \(-0.849568\pi\) |
−0.323850 | − | 0.946108i | \(-0.604977\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.5168 | + | 11.9000i | −0.666867 | + | 0.428569i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.4813 | − | 7.18835i | 0.880530 | − | 0.258547i | 0.189942 | − | 0.981795i | \(-0.439170\pi\) |
0.690588 | + | 0.723249i | \(0.257352\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.0358 | − | 20.8144i | 0.647865 | − | 0.747676i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.934102 | − | 0.274277i | −0.0335107 | − | 0.00983964i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.220149 | − | 1.53117i | −0.00788766 | − | 0.0548599i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.4029 | −0.408029 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.50497 | 0.268206 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.49944 | − | 31.2943i | −0.160592 | − | 1.11694i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.82123 | + | 2.88377i | 0.350089 | + | 0.102795i | 0.452049 | − | 0.891993i | \(-0.350693\pi\) |
−0.101960 | + | 0.994789i | \(0.532511\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.9296 | − | 17.2297i | 0.531509 | − | 0.613394i | ||||
\(790\) | 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 | ||||||||
\(795\) | 17.8648 | + | 20.6171i | 0.633599 | + | 0.731213i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.236974 | + | 1.64819i | −0.00839403 | + | 0.0583818i | −0.993588 | − | 0.113062i | \(-0.963934\pi\) |
0.985194 | + | 0.171444i | \(0.0548432\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.49999 | + | 9.85361i | −0.159198 | + | 0.348596i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.93297 | − | 6.42232i | −0.103632 | − | 0.226921i | ||||
\(802\) | 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 | ||||||||
\(807\) | 4.56227 | + | 2.93199i | 0.160600 | + | 0.103211i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.33499 | + | 7.30261i | 0.117252 | + | 0.256746i | 0.959154 | − | 0.282884i | \(-0.0912912\pi\) |
−0.841902 | + | 0.539630i | \(0.818564\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.8369 | − | 50.0059i | 0.801912 | − | 1.75594i | 0.163057 | − | 0.986617i | \(-0.447865\pi\) |
0.638856 | − | 0.769326i | \(-0.279408\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.61351 | − | 25.1325i | 0.126731 | − | 0.881436i | ||||
\(814\) | 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 | ||||||||
\(819\) | 0.231209 | − | 0.0678890i | 0.00807909 | − | 0.00237223i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.5323 | + | 14.4630i | −0.437379 | + | 0.504763i | −0.931053 | − | 0.364885i | \(-0.881108\pi\) |
0.493673 | + | 0.869647i | \(0.335654\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.3321 | − | 5.97006i | −0.708734 | − | 0.208103i | −0.0925530 | − | 0.995708i | \(-0.529503\pi\) |
−0.616181 | + | 0.787605i | \(0.711321\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.05228 | + | 14.2739i | 0.0714512 | + | 0.496954i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.2748 | 1.01798 | 0.508992 | − | 0.860771i | \(-0.330018\pi\) | ||||
0.508992 | + | 0.860771i | \(0.330018\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.5164 | −1.09461 | −0.547304 | − | 0.836934i | \(-0.684346\pi\) | ||||
−0.547304 | + | 0.836934i | \(0.684346\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.03513 | + | 28.0650i | 0.139977 | + | 0.973562i | ||||
\(832\) | 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 | ||||||||
\(837\) | 2.26145 | − | 0.664021i | 0.0781671 | − | 0.0229519i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.78578 | + | 5.64628i | −0.303319 | + | 0.194931i | −0.683442 | − | 0.730005i | \(-0.739518\pi\) |
0.380123 | + | 0.924936i | \(0.375882\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.8938 | − | 20.6505i | −0.617027 | − | 0.712087i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.05912 | − | 7.36631i | 0.0364779 | − | 0.253709i | ||||
\(844\) | 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 | ||||||||
\(849\) | −20.4469 | − | 13.1404i | −0.701735 | − | 0.450978i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 25.2783 | + | 27.0887i | 0.866528 | + | 0.928587i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.3790 | − | 9.88346i | −0.526566 | − | 0.338403i | 0.250199 | − | 0.968195i | \(-0.419504\pi\) |
−0.776764 | + | 0.629791i | \(0.783140\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.250551 | − | 0.548629i | −0.00856865 | − | 0.0187627i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.9983 | + | 28.4623i | −0.444014 | + | 0.972255i | 0.546830 | + | 0.837244i | \(0.315834\pi\) |
−0.990844 | + | 0.135012i | \(0.956893\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.37199 | − | 9.54240i | 0.0468117 | − | 0.325582i | −0.952937 | − | 0.303168i | \(-0.901956\pi\) |
0.999749 | − | 0.0224143i | \(-0.00713529\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.864539 | − | 0.997732i | −0.0294634 | − | 0.0340026i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.91655 | + | 5.73032i | −0.303523 | + | 0.195062i | −0.683532 | − | 0.729920i | \(-0.739557\pi\) |
0.380009 | + | 0.924983i | \(0.375921\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.26609 | − | 2.72077i | 0.315056 | − | 0.0925089i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.78041 | − | 10.1331i | 0.298198 | − | 0.344139i | ||||
\(868\) | 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 | ||||||||
\(873\) | −13.2465 | −0.448328 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.44117 | −0.116333 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.805286 | − | 5.60089i | −0.0271926 | − | 0.189129i | 0.971698 | − | 0.236228i | \(-0.0759113\pi\) |
−0.998890 | + | 0.0470996i | \(0.985002\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.6674 | − | 4.60036i | −0.528447 | − | 0.155166i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.9426 | + | 38.0177i | −1.10986 | + | 1.28085i | −0.153667 | + | 0.988123i | \(0.549108\pi\) |
−0.956196 | + | 0.292728i | \(0.905437\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.8285 | + | 4.94130i | −0.566325 | + | 0.166288i | −0.552347 | − | 0.833614i | \(-0.686268\pi\) |
−0.0139782 | + | 0.999902i | \(0.504450\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −26.1781 | + | 16.8236i | −0.879966 | + | 0.565520i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.7918 | + | 20.5329i | 0.597392 | + | 0.689427i | 0.971251 | − | 0.238059i | \(-0.0765111\pi\) |
−0.373859 | + | 0.927486i | \(0.621966\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.360962 | − | 2.51055i | 0.0121063 | − | 0.0842010i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.512657 | + | 1.12256i | −0.0171747 | + | 0.0376072i | ||||
\(892\) | 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 | ||||||||
\(897\) | −8.88860 | − | 2.25787i | −0.296782 | − | 0.0753880i | ||||
\(898\) | 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 | ||||||||
\(903\) | −0.631935 | + | 1.38374i | −0.0210295 | + | 0.0460481i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.91154 | − | 61.9811i | 0.296230 | − | 2.06032i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.7863 | + | 25.1427i | 0.723402 | + | 0.834850i | 0.991712 | − | 0.128483i | \(-0.0410107\pi\) |
−0.268310 | + | 0.963333i | \(0.586465\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.68052 | − | 3.65065i | 0.188411 | − | 0.121084i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.5227 | + | 10.7240i | −1.21005 | + | 0.355303i | −0.823687 | − | 0.567044i | \(-0.808087\pi\) |
−0.386363 | + | 0.922347i | \(0.626269\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.59485 | + | 7.61086i | −0.218258 | + | 0.251883i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.98300 | + | 1.46314i | 0.164733 | + | 0.0483700i | ||||
\(916\) | 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 | ||||||||
\(921\) | 24.9148 | 0.820970 | ||||||||
\(922\) | 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 | ||||||||
\(927\) | 5.55604 | − | 6.41201i | 0.182484 | − | 0.210598i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.8053 | − | 4.64085i | 0.518554 | − | 0.152261i | −0.0119743 | − | 0.999928i | \(-0.503812\pi\) |
0.530529 | + | 0.847667i | \(0.321993\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.867530 | + | 0.557528i | −0.0284321 | + | 0.0182722i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.5069 | + | 21.3580i | 0.605887 | + | 0.699231i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.35965 | + | 9.45657i | −0.0444653 | + | 0.309263i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.43363 | + | 7.51861i | −0.112172 | + | 0.245622i | −0.957389 | − | 0.288800i | \(-0.906744\pi\) |
0.845217 | + | 0.534423i | \(0.179471\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.29036 | − | 5.01520i | −0.0747432 | − | 0.163665i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.74409 | + | 3.04884i | 0.154653 | + | 0.0993894i | 0.615679 | − | 0.787997i | \(-0.288882\pi\) |
−0.461026 | + | 0.887387i | \(0.652518\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.97748 | + | 49.4355i | 0.292347 | + | 1.60984i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.433021 | − | 0.278286i | −0.0140862 | − | 0.00905264i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.3235 | − | 22.6053i | −0.335468 | − | 0.734572i | 0.664451 | − | 0.747332i | \(-0.268666\pi\) |
−0.999919 | + | 0.0127598i | \(0.995938\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.0400 | − | 21.9845i | 0.325911 | − | 0.713646i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.463222 | − | 3.22178i | 0.0150210 | − | 0.104473i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33.0490 | − | 38.1406i | −1.07056 | − | 1.23549i | −0.970650 | − | 0.240497i | \(-0.922689\pi\) |
−0.0999117 | − | 0.994996i | \(-0.531856\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 31.1464 | − | 20.0166i | 1.00788 | − | 0.647722i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.88660 | − | 2.60934i | 0.287263 | − | 0.0843480i | ||||
\(958\) | 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 | ||||||||
\(963\) | 1.88329 | + | 13.0986i | 0.0606883 | + | 0.422096i | ||||
\(964\) | 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 | ||||||||
\(969\) | −0.0398254 | − | 0.276992i | −0.00127938 | − | 0.00889827i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.0575 | − | 6.18304i | −0.675768 | − | 0.198423i | −0.0741980 | − | 0.997244i | \(-0.523640\pi\) |
−0.601570 | + | 0.798820i | \(0.705458\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.18258 | + | 1.36477i | −0.0379117 | + | 0.0437525i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 21.4403 | − | 6.29544i | 0.686639 | − | 0.201615i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.0341 | − | 12.2324i | 0.608953 | − | 0.391351i | −0.199511 | − | 0.979896i | \(-0.563935\pi\) |
0.808465 | + | 0.588545i | \(0.200299\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.70584 | − | 6.58489i | −0.182359 | − | 0.210454i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.05993 | + | 7.37200i | −0.0338411 | + | 0.235370i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.32096 | + | 18.2204i | −0.265398 | + | 0.581140i | −0.994673 | − | 0.103081i | \(-0.967130\pi\) |
0.729275 | + | 0.684220i | \(0.239857\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.40705 | − | 9.65010i | −0.140420 | − | 0.307478i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.605908 | − | 0.389394i | −0.0192863 | − | 0.0123945i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 47.5182 | − | 33.0730i | 1.51099 | − | 1.05166i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46.2705 | − | 29.7363i | −1.46983 | − | 0.944604i | −0.998020 | − | 0.0629045i | \(-0.979964\pi\) |
−0.471812 | − | 0.881699i | \(-0.656400\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.83167 | + | 6.20049i | 0.0898603 | + | 0.196767i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −34.1899 | + | 74.8654i | −1.08389 | + | 2.37339i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.83245 | + | 33.6105i | −0.153045 | + | 1.06445i | 0.758032 | + | 0.652218i | \(0.226161\pi\) |
−0.911077 | + | 0.412236i | \(0.864748\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.05925 | − | 5.83869i | −0.160068 | − | 0.184728i |
(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 | 276.2.i.a.25.2 | ✓ | 20 | |
3.2 | odd | 2 | 828.2.q.c.577.1 | 20 | |||
23.9 | even | 11 | 6348.2.a.s.1.1 | 10 | |||
23.12 | even | 11 | inner | 276.2.i.a.265.2 | yes | 20 | |
23.14 | odd | 22 | 6348.2.a.t.1.10 | 10 | |||
69.35 | odd | 22 | 828.2.q.c.541.1 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
276.2.i.a.25.2 | ✓ | 20 | 1.1 | even | 1 | trivial | |
276.2.i.a.265.2 | yes | 20 | 23.12 | even | 11 | inner | |
828.2.q.c.541.1 | 20 | 69.35 | odd | 22 | |||
828.2.q.c.577.1 | 20 | 3.2 | odd | 2 | |||
6348.2.a.s.1.1 | 10 | 23.9 | even | 11 | |||
6348.2.a.t.1.10 | 10 | 23.14 | odd | 22 |