Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [260,2,Mod(103,260)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(260, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("260.103");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 260 = 2^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 260.p (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.07611045255\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(32\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 207.17 | ||
Character | \(\chi\) | \(=\) | 260.207 |
Dual form | 260.2.p.d.103.17 |
$q$-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 \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).
\(n\) | \(41\) | \(131\) | \(157\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0324895 | − | 1.41384i | 0.0229736 | − | 0.999736i | ||||
\(3\) | 2.32949 | + | 2.32949i | 1.34493 | + | 1.34493i | 0.891075 | + | 0.453856i | \(0.149952\pi\) |
0.453856 | + | 0.891075i | \(0.350048\pi\) | |||||||
\(4\) | −1.99789 | − | 0.0918700i | −0.998944 | − | 0.0459350i | ||||
\(5\) | −2.23599 | + | 0.0191440i | −0.999963 | + | 0.00856145i | ||||
\(6\) | 3.36921 | − | 3.21784i | 1.37547 | − | 1.31368i | ||||
\(7\) | 1.97121 | + | 1.97121i | 0.745047 | + | 0.745047i | 0.973544 | − | 0.228498i | \(-0.0733814\pi\) |
−0.228498 | + | 0.973544i | \(0.573381\pi\) | |||||||
\(8\) | −0.194800 | + | 2.82171i | −0.0688722 | + | 0.997625i | ||||
\(9\) | 7.85303i | 2.61768i | ||||||||
\(10\) | −0.0455796 | + | 3.16195i | −0.0144135 | + | 0.999896i | ||||
\(11\) | 2.76564 | 0.833871 | 0.416935 | − | 0.908936i | \(-0.363104\pi\) | ||||
0.416935 | + | 0.908936i | \(0.363104\pi\) | |||||||
\(12\) | −4.44005 | − | 4.86807i | −1.28173 | − | 1.40529i | ||||
\(13\) | 0.543628 | − | 3.56433i | 0.150775 | − | 0.988568i | ||||
\(14\) | 2.85102 | − | 2.72293i | 0.761966 | − | 0.727734i | ||||
\(15\) | −5.25330 | − | 5.16411i | −1.35640 | − | 1.33337i | ||||
\(16\) | 3.98312 | + | 0.367092i | 0.995780 | + | 0.0917730i | ||||
\(17\) | −1.79865 | − | 1.79865i | −0.436237 | − | 0.436237i | 0.454506 | − | 0.890744i | \(-0.349816\pi\) |
−0.890744 | + | 0.454506i | \(0.849816\pi\) | |||||||
\(18\) | 11.1029 | + | 0.255141i | 2.61699 | + | 0.0601374i | ||||
\(19\) | 2.06756i | 0.474330i | 0.971469 | + | 0.237165i | \(0.0762182\pi\) | ||||
−0.971469 | + | 0.237165i | \(0.923782\pi\) | |||||||
\(20\) | 4.46901 | + | 0.167172i | 0.999301 | + | 0.0373809i | ||||
\(21\) | 9.18381i | 2.00407i | ||||||||
\(22\) | 0.0898542 | − | 3.91017i | 0.0191570 | − | 0.833651i | ||||
\(23\) | −1.07900 | − | 1.07900i | −0.224988 | − | 0.224988i | 0.585607 | − | 0.810595i | \(-0.300856\pi\) |
−0.810595 | + | 0.585607i | \(0.800856\pi\) | |||||||
\(24\) | −7.02693 | + | 6.11936i | −1.43437 | + | 1.24911i | ||||
\(25\) | 4.99927 | − | 0.0856113i | 0.999853 | − | 0.0171223i | ||||
\(26\) | −5.02174 | − | 0.884407i | −0.984843 | − | 0.173446i | ||||
\(27\) | −11.3051 | + | 11.3051i | −2.17567 | + | 2.17567i | ||||
\(28\) | −3.75716 | − | 4.11935i | −0.710036 | − | 0.778484i | ||||
\(29\) | − | 7.19247i | − | 1.33561i | −0.744337 | − | 0.667804i | \(-0.767234\pi\) | ||
0.744337 | − | 0.667804i | \(-0.232766\pi\) | |||||||
\(30\) | −7.47190 | + | 7.25955i | −1.36418 | + | 1.32541i | ||||
\(31\) | −2.08767 | −0.374957 | −0.187478 | − | 0.982269i | \(-0.560031\pi\) | ||||
−0.187478 | + | 0.982269i | \(0.560031\pi\) | |||||||
\(32\) | 0.648419 | − | 5.61957i | 0.114625 | − | 0.993409i | ||||
\(33\) | 6.44252 | + | 6.44252i | 1.12150 | + | 1.12150i | ||||
\(34\) | −2.60144 | + | 2.48457i | −0.446144 | + | 0.426100i | ||||
\(35\) | −4.44533 | − | 4.36986i | −0.751398 | − | 0.738641i | ||||
\(36\) | 0.721458 | − | 15.6895i | 0.120243 | − | 2.61491i | ||||
\(37\) | 2.10529 | − | 2.10529i | 0.346108 | − | 0.346108i | −0.512549 | − | 0.858658i | \(-0.671299\pi\) |
0.858658 | + | 0.512549i | \(0.171299\pi\) | |||||||
\(38\) | 2.92320 | + | 0.0671739i | 0.474205 | + | 0.0108971i | ||||
\(39\) | 9.56945 | − | 7.03670i | 1.53234 | − | 1.12677i | ||||
\(40\) | 0.381551 | − | 6.31304i | 0.0603285 | − | 0.998179i | ||||
\(41\) | − | 2.07353i | − | 0.323831i | −0.986805 | − | 0.161915i | \(-0.948233\pi\) | ||
0.986805 | − | 0.161915i | \(-0.0517671\pi\) | |||||||
\(42\) | 12.9844 | + | 0.298378i | 2.00354 | + | 0.0460407i | ||||
\(43\) | −1.37442 | − | 1.37442i | −0.209596 | − | 0.209596i | 0.594500 | − | 0.804096i | \(-0.297350\pi\) |
−0.804096 | + | 0.594500i | \(0.797350\pi\) | |||||||
\(44\) | −5.52543 | − | 0.254079i | −0.832991 | − | 0.0383038i | ||||
\(45\) | −0.150338 | − | 17.5593i | −0.0224111 | − | 2.61758i | ||||
\(46\) | −1.56059 | + | 1.49048i | −0.230097 | + | 0.219760i | ||||
\(47\) | −3.03509 | − | 3.03509i | −0.442713 | − | 0.442713i | 0.450210 | − | 0.892923i | \(-0.351349\pi\) |
−0.892923 | + | 0.450210i | \(0.851349\pi\) | |||||||
\(48\) | 8.42350 | + | 10.1338i | 1.21583 | + | 1.46268i | ||||
\(49\) | 0.771320i | 0.110189i | ||||||||
\(50\) | 0.0413830 | − | 7.07095i | 0.00585244 | − | 0.999983i | ||||
\(51\) | − | 8.37988i | − | 1.17342i | ||||||
\(52\) | −1.41356 | + | 7.07120i | −0.196026 | + | 0.980599i | ||||
\(53\) | −4.80760 | + | 4.80760i | −0.660375 | + | 0.660375i | −0.955468 | − | 0.295093i | \(-0.904649\pi\) |
0.295093 | + | 0.955468i | \(0.404649\pi\) | |||||||
\(54\) | 15.6163 | + | 16.3509i | 2.12511 | + | 2.22507i | ||||
\(55\) | −6.18392 | + | 0.0529453i | −0.833840 | + | 0.00713914i | ||||
\(56\) | −5.94617 | + | 5.17819i | −0.794590 | + | 0.691964i | ||||
\(57\) | −4.81635 | + | 4.81635i | −0.637941 | + | 0.637941i | ||||
\(58\) | −10.1690 | − | 0.233680i | −1.33526 | − | 0.0306837i | ||||
\(59\) | − | 9.65260i | − | 1.25666i | −0.777947 | − | 0.628330i | \(-0.783739\pi\) | ||
0.777947 | − | 0.628330i | \(-0.216261\pi\) | |||||||
\(60\) | 10.0211 | + | 10.7999i | 1.29372 | + | 1.39427i | ||||
\(61\) | 6.83718 | 0.875412 | 0.437706 | − | 0.899118i | \(-0.355791\pi\) | ||||
0.437706 | + | 0.899118i | \(0.355791\pi\) | |||||||
\(62\) | −0.0678274 | + | 2.95163i | −0.00861409 | + | 0.374858i | ||||
\(63\) | −15.4800 | + | 15.4800i | −1.95029 | + | 1.95029i | ||||
\(64\) | −7.92411 | − | 1.09934i | −0.990513 | − | 0.137417i | ||||
\(65\) | −1.14731 | + | 7.98021i | −0.142306 | + | 0.989823i | ||||
\(66\) | 9.31801 | − | 8.89938i | 1.14697 | − | 1.09544i | ||||
\(67\) | 10.5309 | + | 10.5309i | 1.28656 | + | 1.28656i | 0.936864 | + | 0.349695i | \(0.113715\pi\) |
0.349695 | + | 0.936864i | \(0.386285\pi\) | |||||||
\(68\) | 3.42827 | + | 3.75875i | 0.415738 | + | 0.455815i | ||||
\(69\) | − | 5.02705i | − | 0.605186i | ||||||
\(70\) | −6.32271 | + | 6.14301i | −0.755708 | + | 0.734230i | ||||
\(71\) | −3.76638 | −0.446987 | −0.223493 | − | 0.974705i | \(-0.571746\pi\) | ||||
−0.223493 | + | 0.974705i | \(0.571746\pi\) | |||||||
\(72\) | −22.1590 | − | 1.52977i | −2.61146 | − | 0.180285i | ||||
\(73\) | −0.228478 | − | 0.228478i | −0.0267413 | − | 0.0267413i | 0.693610 | − | 0.720351i | \(-0.256019\pi\) |
−0.720351 | + | 0.693610i | \(0.756019\pi\) | |||||||
\(74\) | −2.90815 | − | 3.04495i | −0.338066 | − | 0.353968i | ||||
\(75\) | 11.8452 | + | 11.4463i | 1.36776 | + | 1.32171i | ||||
\(76\) | 0.189946 | − | 4.13075i | 0.0217884 | − | 0.473830i | ||||
\(77\) | 5.45164 | + | 5.45164i | 0.621273 | + | 0.621273i | ||||
\(78\) | −9.63786 | − | 13.7583i | −1.09127 | − | 1.55782i | ||||
\(79\) | 3.36550 | 0.378648 | 0.189324 | − | 0.981915i | \(-0.439370\pi\) | ||||
0.189324 | + | 0.981915i | \(0.439370\pi\) | |||||||
\(80\) | −8.91323 | − | 0.744560i | −0.996529 | − | 0.0832443i | ||||
\(81\) | −29.1110 | −3.23456 | ||||||||
\(82\) | −2.93164 | − | 0.0673679i | −0.323745 | − | 0.00743954i | ||||
\(83\) | 2.38904 | − | 2.38904i | 0.262232 | − | 0.262232i | −0.563729 | − | 0.825960i | \(-0.690634\pi\) |
0.825960 | + | 0.563729i | \(0.190634\pi\) | |||||||
\(84\) | 0.843717 | − | 18.3482i | 0.0920570 | − | 2.00196i | ||||
\(85\) | 4.05619 | + | 3.98733i | 0.439956 | + | 0.432486i | ||||
\(86\) | −1.98786 | + | 1.89855i | −0.214356 | + | 0.204726i | ||||
\(87\) | 16.7548 | − | 16.7548i | 1.79630 | − | 1.79630i | ||||
\(88\) | −0.538746 | + | 7.80383i | −0.0574305 | + | 0.831891i | ||||
\(89\) | −3.39594 | −0.359969 | −0.179985 | − | 0.983669i | \(-0.557605\pi\) | ||||
−0.179985 | + | 0.983669i | \(0.557605\pi\) | |||||||
\(90\) | −24.8309 | − | 0.357938i | −2.61741 | − | 0.0377300i | ||||
\(91\) | 8.09764 | − | 5.95444i | 0.848864 | − | 0.624195i | ||||
\(92\) | 2.05660 | + | 2.25486i | 0.214415 | + | 0.235085i | ||||
\(93\) | −4.86321 | − | 4.86321i | −0.504291 | − | 0.504291i | ||||
\(94\) | −4.38974 | + | 4.19252i | −0.452767 | + | 0.432426i | ||||
\(95\) | −0.0395813 | − | 4.62303i | −0.00406095 | − | 0.474313i | ||||
\(96\) | 14.6012 | − | 11.5802i | 1.49023 | − | 1.18190i | ||||
\(97\) | −5.33246 | + | 5.33246i | −0.541430 | + | 0.541430i | −0.923948 | − | 0.382518i | \(-0.875057\pi\) |
0.382518 | + | 0.923948i | \(0.375057\pi\) | |||||||
\(98\) | 1.09052 | + | 0.0250598i | 0.110160 | + | 0.00253142i | ||||
\(99\) | 21.7186i | 2.18281i | ||||||||
\(100\) | −9.99585 | − | 0.288241i | −0.999585 | − | 0.0288241i | ||||
\(101\) | 2.70868 | 0.269524 | 0.134762 | − | 0.990878i | \(-0.456973\pi\) | ||||
0.134762 | + | 0.990878i | \(0.456973\pi\) | |||||||
\(102\) | −11.8478 | − | 0.272258i | −1.17311 | − | 0.0269576i | ||||
\(103\) | −2.34247 | − | 2.34247i | −0.230810 | − | 0.230810i | 0.582221 | − | 0.813031i | \(-0.302184\pi\) |
−0.813031 | + | 0.582221i | \(0.802184\pi\) | |||||||
\(104\) | 9.95162 | + | 2.22829i | 0.975836 | + | 0.218502i | ||||
\(105\) | −0.175815 | − | 20.5349i | −0.0171578 | − | 2.00400i | ||||
\(106\) | 6.64098 | + | 6.95338i | 0.645029 | + | 0.675372i | ||||
\(107\) | −4.03232 | + | 4.03232i | −0.389819 | + | 0.389819i | −0.874623 | − | 0.484804i | \(-0.838891\pi\) |
0.484804 | + | 0.874623i | \(0.338891\pi\) | |||||||
\(108\) | 23.6249 | − | 21.5477i | 2.27331 | − | 2.07343i | ||||
\(109\) | 13.2900 | 1.27295 | 0.636477 | − | 0.771296i | \(-0.280391\pi\) | ||||
0.636477 | + | 0.771296i | \(0.280391\pi\) | |||||||
\(110\) | −0.126057 | + | 8.74480i | −0.0120190 | + | 0.833784i | ||||
\(111\) | 9.80852 | 0.930984 | ||||||||
\(112\) | 7.12794 | + | 8.57517i | 0.673527 | + | 0.810278i | ||||
\(113\) | −8.26021 | + | 8.26021i | −0.777055 | + | 0.777055i | −0.979329 | − | 0.202274i | \(-0.935167\pi\) |
0.202274 | + | 0.979329i | \(0.435167\pi\) | |||||||
\(114\) | 6.65307 | + | 6.96603i | 0.623117 | + | 0.652429i | ||||
\(115\) | 2.43329 | + | 2.39198i | 0.226906 | + | 0.223053i | ||||
\(116\) | −0.660772 | + | 14.3698i | −0.0613511 | + | 1.33420i | ||||
\(117\) | 27.9908 | + | 4.26913i | 2.58775 | + | 0.394681i | ||||
\(118\) | −13.6472 | − | 0.313608i | −1.25633 | − | 0.0288700i | ||||
\(119\) | − | 7.09103i | − | 0.650034i | ||||||
\(120\) | 15.5950 | − | 13.8173i | 1.42362 | − | 1.26134i | ||||
\(121\) | −3.35125 | −0.304659 | ||||||||
\(122\) | 0.222137 | − | 9.66669i | 0.0201113 | − | 0.875181i | ||||
\(123\) | 4.83026 | − | 4.83026i | 0.435530 | − | 0.435530i | ||||
\(124\) | 4.17094 | + | 0.191794i | 0.374561 | + | 0.0172236i | ||||
\(125\) | −11.1767 | + | 0.287132i | −0.999670 | + | 0.0256818i | ||||
\(126\) | 21.3833 | + | 22.3891i | 1.90497 | + | 1.99458i | ||||
\(127\) | −11.0132 | + | 11.0132i | −0.977260 | + | 0.977260i | −0.999747 | − | 0.0224874i | \(-0.992841\pi\) |
0.0224874 | + | 0.999747i | \(0.492841\pi\) | |||||||
\(128\) | −1.81174 | + | 11.1677i | −0.160137 | + | 0.987095i | ||||
\(129\) | − | 6.40337i | − | 0.563785i | ||||||
\(130\) | 11.2455 | + | 1.88139i | 0.986292 | + | 0.165008i | ||||
\(131\) | − | 0.116373i | − | 0.0101676i | −0.999987 | − | 0.00508378i | \(-0.998382\pi\) | ||
0.999987 | − | 0.00508378i | \(-0.00161822\pi\) | |||||||
\(132\) | −12.2796 | − | 13.4633i | −1.06880 | − | 1.17183i | ||||
\(133\) | −4.07559 | + | 4.07559i | −0.353398 | + | 0.353398i | ||||
\(134\) | 15.2312 | − | 14.5469i | 1.31578 | − | 1.25666i | ||||
\(135\) | 25.0616 | − | 25.4944i | 2.15696 | − | 2.19421i | ||||
\(136\) | 5.42565 | − | 4.72490i | 0.465246 | − | 0.405157i | ||||
\(137\) | 11.3786 | − | 11.3786i | 0.972143 | − | 0.972143i | −0.0274794 | − | 0.999622i | \(-0.508748\pi\) |
0.999622 | + | 0.0274794i | \(0.00874807\pi\) | |||||||
\(138\) | −7.10745 | − | 0.163326i | −0.605026 | − | 0.0139033i | ||||
\(139\) | 13.9762 | 1.18545 | 0.592725 | − | 0.805405i | \(-0.298052\pi\) | ||||
0.592725 | + | 0.805405i | \(0.298052\pi\) | |||||||
\(140\) | 8.47982 | + | 9.13888i | 0.716675 | + | 0.772376i | ||||
\(141\) | − | 14.1404i | − | 1.19084i | ||||||
\(142\) | −0.122368 | + | 5.32506i | −0.0102689 | + | 0.446869i | ||||
\(143\) | 1.50348 | − | 9.85765i | 0.125727 | − | 0.824338i | ||||
\(144\) | −2.88279 | + | 31.2796i | −0.240232 | + | 2.60663i | ||||
\(145\) | 0.137692 | + | 16.0823i | 0.0114347 | + | 1.33556i | ||||
\(146\) | −0.330454 | + | 0.315608i | −0.0273486 | + | 0.0261199i | ||||
\(147\) | −1.79678 | + | 1.79678i | −0.148196 | + | 0.148196i | ||||
\(148\) | −4.39956 | + | 4.01273i | −0.361641 | + | 0.329845i | ||||
\(149\) | 10.9656 | 0.898337 | 0.449169 | − | 0.893447i | \(-0.351720\pi\) | ||||
0.449169 | + | 0.893447i | \(0.351720\pi\) | |||||||
\(150\) | 16.5681 | − | 16.3753i | 1.35278 | − | 1.33704i | ||||
\(151\) | −17.6591 | −1.43708 | −0.718540 | − | 0.695486i | \(-0.755189\pi\) | ||||
−0.718540 | + | 0.695486i | \(0.755189\pi\) | |||||||
\(152\) | −5.83405 | − | 0.402760i | −0.473204 | − | 0.0326682i | ||||
\(153\) | 14.1249 | − | 14.1249i | 1.14193 | − | 1.14193i | ||||
\(154\) | 7.88488 | − | 7.53063i | 0.635381 | − | 0.606836i | ||||
\(155\) | 4.66800 | − | 0.0399663i | 0.374943 | − | 0.00321017i | ||||
\(156\) | −19.7652 | + | 13.1794i | −1.58248 | + | 1.05520i | ||||
\(157\) | −13.6301 | − | 13.6301i | −1.08780 | − | 1.08780i | −0.995754 | − | 0.0920491i | \(-0.970658\pi\) |
−0.0920491 | − | 0.995754i | \(-0.529342\pi\) | |||||||
\(158\) | 0.109344 | − | 4.75828i | 0.00869890 | − | 0.378549i | ||||
\(159\) | −22.3985 | −1.77632 | ||||||||
\(160\) | −1.34228 | + | 12.5777i | −0.106116 | + | 0.994354i | ||||
\(161\) | − | 4.25388i | − | 0.335253i | ||||||
\(162\) | −0.945804 | + | 41.1584i | −0.0743094 | + | 3.23371i | ||||
\(163\) | −4.50085 | + | 4.50085i | −0.352534 | + | 0.352534i | −0.861052 | − | 0.508518i | \(-0.830194\pi\) |
0.508518 | + | 0.861052i | \(0.330194\pi\) | |||||||
\(164\) | −0.190495 | + | 4.14268i | −0.0148752 | + | 0.323489i | ||||
\(165\) | −14.5287 | − | 14.2820i | −1.13106 | − | 1.11186i | ||||
\(166\) | −3.30011 | − | 3.45535i | −0.256138 | − | 0.268187i | ||||
\(167\) | 7.06397 | + | 7.06397i | 0.546626 | + | 0.546626i | 0.925463 | − | 0.378837i | \(-0.123676\pi\) |
−0.378837 | + | 0.925463i | \(0.623676\pi\) | |||||||
\(168\) | −25.9141 | − | 1.78901i | −1.99931 | − | 0.138025i | ||||
\(169\) | −12.4089 | − | 3.87534i | −0.954534 | − | 0.298103i | ||||
\(170\) | 5.76923 | − | 5.60527i | 0.442480 | − | 0.429904i | ||||
\(171\) | −16.2366 | −1.24164 | ||||||||
\(172\) | 2.61966 | + | 2.87220i | 0.199747 | + | 0.219003i | ||||
\(173\) | 2.54024 | − | 2.54024i | 0.193131 | − | 0.193131i | −0.603917 | − | 0.797047i | \(-0.706394\pi\) |
0.797047 | + | 0.603917i | \(0.206394\pi\) | |||||||
\(174\) | −23.1442 | − | 24.2329i | −1.75456 | − | 1.83709i | ||||
\(175\) | 10.0234 | + | 9.68584i | 0.757694 | + | 0.732180i | ||||
\(176\) | 11.0159 | + | 1.01524i | 0.830352 | + | 0.0765268i | ||||
\(177\) | 22.4856 | − | 22.4856i | 1.69012 | − | 1.69012i | ||||
\(178\) | −0.110333 | + | 4.80132i | −0.00826978 | + | 0.359874i | ||||
\(179\) | 0.176655 | 0.0132038 | 0.00660192 | − | 0.999978i | \(-0.497899\pi\) | ||||
0.00660192 | + | 0.999978i | \(0.497899\pi\) | |||||||
\(180\) | −1.31281 | + | 35.0953i | −0.0978511 | + | 2.61585i | ||||
\(181\) | 13.6105 | 1.01166 | 0.505828 | − | 0.862634i | \(-0.331187\pi\) | ||||
0.505828 | + | 0.862634i | \(0.331187\pi\) | |||||||
\(182\) | −8.15553 | − | 11.6422i | −0.604528 | − | 0.862980i | ||||
\(183\) | 15.9271 | + | 15.9271i | 1.17737 | + | 1.17737i | ||||
\(184\) | 3.25482 | − | 2.83444i | 0.239949 | − | 0.208958i | ||||
\(185\) | −4.66711 | + | 4.74771i | −0.343132 | + | 0.349059i | ||||
\(186\) | −7.03380 | + | 6.71779i | −0.515743 | + | 0.492573i | ||||
\(187\) | −4.97442 | − | 4.97442i | −0.363765 | − | 0.363765i | ||||
\(188\) | 5.78494 | + | 6.34261i | 0.421910 | + | 0.462582i | ||||
\(189\) | −44.5694 | −3.24194 | ||||||||
\(190\) | −6.53751 | − | 0.0942384i | −0.474281 | − | 0.00683677i | ||||
\(191\) | − | 13.9159i | − | 1.00692i | −0.864020 | − | 0.503458i | \(-0.832061\pi\) | ||
0.864020 | − | 0.503458i | \(-0.167939\pi\) | |||||||
\(192\) | −15.8982 | − | 21.0200i | −1.14736 | − | 1.51699i | ||||
\(193\) | 17.4956 | + | 17.4956i | 1.25936 | + | 1.25936i | 0.951398 | + | 0.307964i | \(0.0996478\pi\) |
0.307964 | + | 0.951398i | \(0.400352\pi\) | |||||||
\(194\) | 7.36600 | + | 7.71250i | 0.528848 | + | 0.553725i | ||||
\(195\) | −21.2624 | + | 15.9172i | −1.52264 | + | 1.13985i | ||||
\(196\) | 0.0708612 | − | 1.54101i | 0.00506151 | − | 0.110072i | ||||
\(197\) | −1.46918 | + | 1.46918i | −0.104675 | + | 0.104675i | −0.757505 | − | 0.652830i | \(-0.773582\pi\) |
0.652830 | + | 0.757505i | \(0.273582\pi\) | |||||||
\(198\) | 30.7067 | + | 0.705628i | 2.18223 | + | 0.0501468i | ||||
\(199\) | −12.6116 | −0.894010 | −0.447005 | − | 0.894531i | \(-0.647509\pi\) | ||||
−0.447005 | + | 0.894531i | \(0.647509\pi\) | |||||||
\(200\) | −0.732286 | + | 14.1232i | −0.0517805 | + | 0.998658i | ||||
\(201\) | 49.0634i | 3.46066i | ||||||||
\(202\) | 0.0880037 | − | 3.82964i | 0.00619192 | − | 0.269453i | ||||
\(203\) | 14.1778 | − | 14.1778i | 0.995090 | − | 0.995090i | ||||
\(204\) | −0.769859 | + | 16.7421i | −0.0539009 | + | 1.17218i | ||||
\(205\) | 0.0396956 | + | 4.63638i | 0.00277246 | + | 0.323819i | ||||
\(206\) | −3.38798 | + | 3.23577i | −0.236052 | + | 0.225447i | ||||
\(207\) | 8.47345 | − | 8.47345i | 0.588945 | − | 0.588945i | ||||
\(208\) | 3.47377 | − | 13.9976i | 0.240863 | − | 0.970559i | ||||
\(209\) | 5.71811i | 0.395530i | ||||||||
\(210\) | −29.0387 | − | 0.418594i | −2.00386 | − | 0.0288857i | ||||
\(211\) | − | 1.88981i | − | 0.130100i | −0.997882 | − | 0.0650498i | \(-0.979279\pi\) | ||
0.997882 | − | 0.0650498i | \(-0.0207206\pi\) | |||||||
\(212\) | 10.0467 | − | 9.16338i | 0.690012 | − | 0.629344i | ||||
\(213\) | −8.77373 | − | 8.77373i | −0.601166 | − | 0.601166i | ||||
\(214\) | 5.57005 | + | 5.83206i | 0.380760 | + | 0.398671i | ||||
\(215\) | 3.09949 | + | 3.04686i | 0.211383 | + | 0.207794i | ||||
\(216\) | −29.6975 | − | 34.1019i | −2.02066 | − | 2.32034i | ||||
\(217\) | −4.11523 | − | 4.11523i | −0.279360 | − | 0.279360i | ||||
\(218\) | 0.431787 | − | 18.7900i | 0.0292443 | − | 1.27262i | ||||
\(219\) | − | 1.06447i | − | 0.0719305i | ||||||
\(220\) | 12.3597 | + | 0.462338i | 0.833288 | + | 0.0311708i | ||||
\(221\) | −7.38879 | + | 5.43320i | −0.497024 | + | 0.365476i | ||||
\(222\) | 0.318674 | − | 13.8677i | 0.0213880 | − | 0.930738i | ||||
\(223\) | −16.9564 | + | 16.9564i | −1.13548 | + | 1.13548i | −0.146235 | + | 0.989250i | \(0.546715\pi\) |
−0.989250 | + | 0.146235i | \(0.953285\pi\) | |||||||
\(224\) | 12.3555 | − | 9.79917i | 0.825537 | − | 0.654735i | ||||
\(225\) | 0.672309 | + | 39.2594i | 0.0448206 | + | 2.61729i | ||||
\(226\) | 11.4102 | + | 11.9470i | 0.758998 | + | 0.794702i | ||||
\(227\) | −11.9034 | − | 11.9034i | −0.790053 | − | 0.790053i | 0.191449 | − | 0.981502i | \(-0.438681\pi\) |
−0.981502 | + | 0.191449i | \(0.938681\pi\) | |||||||
\(228\) | 10.0650 | − | 9.18006i | 0.666572 | − | 0.607964i | ||||
\(229\) | −11.3479 | −0.749888 | −0.374944 | − | 0.927048i | \(-0.622338\pi\) | ||||
−0.374944 | + | 0.927048i | \(0.622338\pi\) | |||||||
\(230\) | 3.46093 | − | 3.36257i | 0.228207 | − | 0.221721i | ||||
\(231\) | 25.3991i | 1.67114i | ||||||||
\(232\) | 20.2951 | + | 1.40109i | 1.33244 | + | 0.0919862i | ||||
\(233\) | −13.9055 | + | 13.9055i | −0.910979 | + | 0.910979i | −0.996349 | − | 0.0853703i | \(-0.972793\pi\) |
0.0853703 | + | 0.996349i | \(0.472793\pi\) | |||||||
\(234\) | 6.94528 | − | 39.4359i | 0.454027 | − | 2.57800i | ||||
\(235\) | 6.84452 | + | 6.72832i | 0.446487 | + | 0.438907i | ||||
\(236\) | −0.886784 | + | 19.2848i | −0.0577247 | + | 1.25533i | ||||
\(237\) | 7.83990 | + | 7.83990i | 0.509256 | + | 0.509256i | ||||
\(238\) | −10.0256 | − | 0.230384i | −0.649862 | − | 0.0149336i | ||||
\(239\) | 14.6554i | 0.947981i | 0.880530 | + | 0.473991i | \(0.157187\pi\) | ||||
−0.880530 | + | 0.473991i | \(0.842813\pi\) | |||||||
\(240\) | −19.0288 | − | 22.4977i | −1.22830 | − | 1.45222i | ||||
\(241\) | − | 21.9420i | − | 1.41341i | −0.707511 | − | 0.706703i | \(-0.750182\pi\) | ||
0.707511 | − | 0.706703i | \(-0.249818\pi\) | |||||||
\(242\) | −0.108881 | + | 4.73814i | −0.00699911 | + | 0.304579i | ||||
\(243\) | −33.8986 | − | 33.8986i | −2.17460 | − | 2.17460i | ||||
\(244\) | −13.6599 | − | 0.628132i | −0.874488 | − | 0.0402120i | ||||
\(245\) | −0.0147661 | − | 1.72466i | −0.000943374 | − | 0.110185i | ||||
\(246\) | −6.67228 | − | 6.98615i | −0.425409 | − | 0.445421i | ||||
\(247\) | 7.36946 | + | 1.12398i | 0.468908 | + | 0.0715173i | ||||
\(248\) | 0.406678 | − | 5.89081i | 0.0258241 | − | 0.374066i | ||||
\(249\) | 11.1305 | 0.705367 | ||||||||
\(250\) | 0.0428343 | + | 15.8113i | 0.00270908 | + | 0.999996i | ||||
\(251\) | − | 17.7075i | − | 1.11769i | −0.829273 | − | 0.558843i | \(-0.811245\pi\) | ||
0.829273 | − | 0.558843i | \(-0.188755\pi\) | |||||||
\(252\) | 32.3494 | − | 29.5051i | 2.03782 | − | 1.85865i | ||||
\(253\) | −2.98413 | − | 2.98413i | −0.187611 | − | 0.187611i | ||||
\(254\) | 15.2130 | + | 15.9287i | 0.954551 | + | 0.999453i | ||||
\(255\) | 0.160424 | + | 18.7373i | 0.0100462 | + | 1.17337i | ||||
\(256\) | 15.7305 | + | 2.92434i | 0.983155 | + | 0.182771i | ||||
\(257\) | 9.61099 | + | 9.61099i | 0.599517 | + | 0.599517i | 0.940184 | − | 0.340667i | \(-0.110653\pi\) |
−0.340667 | + | 0.940184i | \(0.610653\pi\) | |||||||
\(258\) | −9.05334 | − | 0.208042i | −0.563637 | − | 0.0129522i | ||||
\(259\) | 8.29995 | 0.515734 | ||||||||
\(260\) | 3.02534 | − | 15.8382i | 0.187624 | − | 0.982241i | ||||
\(261\) | 56.4827 | 3.49619 | ||||||||
\(262\) | −0.164533 | − | 0.00378090i | −0.0101649 | − | 0.000233585i | ||||
\(263\) | −0.442921 | − | 0.442921i | −0.0273117 | − | 0.0273117i | 0.693319 | − | 0.720631i | \(-0.256148\pi\) |
−0.720631 | + | 0.693319i | \(0.756148\pi\) | |||||||
\(264\) | −19.4339 | + | 16.9239i | −1.19608 | + | 1.04160i | ||||
\(265\) | 10.6577 | − | 10.8418i | 0.654697 | − | 0.666004i | ||||
\(266\) | 5.62981 | + | 5.89464i | 0.345186 | + | 0.361424i | ||||
\(267\) | −7.91081 | − | 7.91081i | −0.484134 | − | 0.484134i | ||||
\(268\) | −20.0722 | − | 22.0071i | −1.22610 | − | 1.34430i | ||||
\(269\) | 19.9649i | 1.21728i | 0.793446 | + | 0.608641i | \(0.208285\pi\) | ||||
−0.793446 | + | 0.608641i | \(0.791715\pi\) | |||||||
\(270\) | −35.2308 | − | 36.2614i | −2.14408 | − | 2.20680i | ||||
\(271\) | −19.6206 | −1.19186 | −0.595932 | − | 0.803035i | \(-0.703217\pi\) | ||||
−0.595932 | + | 0.803035i | \(0.703217\pi\) | |||||||
\(272\) | −6.50398 | − | 7.82452i | −0.394361 | − | 0.474431i | ||||
\(273\) | 32.7342 | + | 4.99258i | 1.98116 | + | 0.302165i | ||||
\(274\) | −15.7179 | − | 16.4573i | −0.949553 | − | 0.994220i | ||||
\(275\) | 13.8262 | − | 0.236770i | 0.833749 | − | 0.0142778i | ||||
\(276\) | −0.461835 | + | 10.0435i | −0.0277992 | + | 0.604547i | ||||
\(277\) | −2.71322 | − | 2.71322i | −0.163022 | − | 0.163022i | 0.620882 | − | 0.783904i | \(-0.286775\pi\) |
−0.783904 | + | 0.620882i | \(0.786775\pi\) | |||||||
\(278\) | 0.454081 | − | 19.7602i | 0.0272340 | − | 1.18514i | ||||
\(279\) | − | 16.3946i | − | 0.981516i | ||||||
\(280\) | 13.1964 | − | 11.6922i | 0.788637 | − | 0.698742i | ||||
\(281\) | − | 10.7683i | − | 0.642383i | −0.947014 | − | 0.321191i | \(-0.895917\pi\) | ||
0.947014 | − | 0.321191i | \(-0.104083\pi\) | |||||||
\(282\) | −19.9923 | − | 0.459415i | −1.19052 | − | 0.0273578i | ||||
\(283\) | 9.22116 | + | 9.22116i | 0.548141 | + | 0.548141i | 0.925903 | − | 0.377762i | \(-0.123306\pi\) |
−0.377762 | + | 0.925903i | \(0.623306\pi\) | |||||||
\(284\) | 7.52480 | + | 0.346017i | 0.446515 | + | 0.0205323i | ||||
\(285\) | 10.6771 | − | 10.8615i | 0.632456 | − | 0.643380i | ||||
\(286\) | −13.8883 | − | 2.44595i | −0.821232 | − | 0.144632i | ||||
\(287\) | 4.08735 | − | 4.08735i | 0.241269 | − | 0.241269i | ||||
\(288\) | 44.1307 | + | 5.09206i | 2.60042 | + | 0.300052i | ||||
\(289\) | − | 10.5297i | − | 0.619394i | ||||||
\(290\) | 22.7422 | + | 0.327830i | 1.33547 | + | 0.0192508i | ||||
\(291\) | −24.8438 | −1.45637 | ||||||||
\(292\) | 0.435483 | + | 0.477464i | 0.0254847 | + | 0.0279415i | ||||
\(293\) | −1.67405 | − | 1.67405i | −0.0977990 | − | 0.0977990i | 0.656514 | − | 0.754313i | \(-0.272030\pi\) |
−0.754313 | + | 0.656514i | \(0.772030\pi\) | |||||||
\(294\) | 2.48199 | + | 2.59874i | 0.144752 | + | 0.151562i | ||||
\(295\) | 0.184789 | + | 21.5831i | 0.0107588 | + | 1.25661i | ||||
\(296\) | 5.53042 | + | 6.35064i | 0.321449 | + | 0.369124i | ||||
\(297\) | −31.2658 | + | 31.2658i | −1.81422 | + | 1.81422i | ||||
\(298\) | 0.356267 | − | 15.5036i | 0.0206380 | − | 0.898100i | ||||
\(299\) | −4.43250 | + | 3.25935i | −0.256338 | + | 0.188493i | ||||
\(300\) | −22.6138 | − | 23.9567i | −1.30561 | − | 1.38314i | ||||
\(301\) | − | 5.41852i | − | 0.312318i | ||||||
\(302\) | −0.573736 | + | 24.9672i | −0.0330148 | + | 1.43670i | ||||
\(303\) | 6.30984 | + | 6.30984i | 0.362491 | + | 0.362491i | ||||
\(304\) | −0.758984 | + | 8.23533i | −0.0435307 | + | 0.472329i | ||||
\(305\) | −15.2878 | + | 0.130891i | −0.875380 | + | 0.00749479i | ||||
\(306\) | −19.5114 | − | 20.4292i | −1.11539 | − | 1.16786i | ||||
\(307\) | −19.6500 | − | 19.6500i | −1.12149 | − | 1.12149i | −0.991518 | − | 0.129968i | \(-0.958513\pi\) |
−0.129968 | − | 0.991518i | \(-0.541487\pi\) | |||||||
\(308\) | −10.3909 | − | 11.3926i | −0.592079 | − | 0.649155i | ||||
\(309\) | − | 10.9135i | − | 0.620847i | ||||||
\(310\) | 0.0951552 | − | 6.60111i | 0.00540445 | − | 0.374918i | ||||
\(311\) | 33.7067i | 1.91133i | 0.294458 | + | 0.955664i | \(0.404861\pi\) | ||||
−0.294458 | + | 0.955664i | \(0.595139\pi\) | |||||||
\(312\) | 17.9914 | + | 28.3730i | 1.01856 | + | 1.60630i | ||||
\(313\) | −14.3198 | + | 14.3198i | −0.809405 | + | 0.809405i | −0.984544 | − | 0.175139i | \(-0.943963\pi\) |
0.175139 | + | 0.984544i | \(0.443963\pi\) | |||||||
\(314\) | −19.7137 | + | 18.8280i | −1.11251 | + | 1.06253i | ||||
\(315\) | 34.3166 | − | 34.9093i | 1.93352 | − | 1.96692i | ||||
\(316\) | −6.72390 | − | 0.309189i | −0.378249 | − | 0.0173932i | ||||
\(317\) | −19.1858 | + | 19.1858i | −1.07758 | + | 1.07758i | −0.0808584 | + | 0.996726i | \(0.525766\pi\) |
−0.996726 | + | 0.0808584i | \(0.974234\pi\) | |||||||
\(318\) | −0.727717 | + | 31.6679i | −0.0408083 | + | 1.77585i | ||||
\(319\) | − | 19.8918i | − | 1.11372i | ||||||
\(320\) | 17.7392 | + | 2.30641i | 0.991653 | + | 0.128932i | ||||
\(321\) | −18.7865 | −1.04856 | ||||||||
\(322\) | −6.01430 | − | 0.138206i | −0.335164 | − | 0.00770194i | ||||
\(323\) | 3.71882 | − | 3.71882i | 0.206921 | − | 0.206921i | ||||
\(324\) | 58.1606 | + | 2.67443i | 3.23115 | + | 0.148579i | ||||
\(325\) | 2.41260 | − | 17.8656i | 0.133827 | − | 0.991005i | ||||
\(326\) | 6.21725 | + | 6.50971i | 0.344342 | + | 0.360540i | ||||
\(327\) | 30.9590 | + | 30.9590i | 1.71204 | + | 1.71204i | ||||
\(328\) | 5.85090 | + | 0.403923i | 0.323062 | + | 0.0223029i | ||||
\(329\) | − | 11.9656i | − | 0.659684i | ||||||
\(330\) | −20.6646 | + | 20.0773i | −1.13755 | + | 1.10522i | ||||
\(331\) | 13.7338 | 0.754877 | 0.377439 | − | 0.926035i | \(-0.376805\pi\) | ||||
0.377439 | + | 0.926035i | \(0.376805\pi\) | |||||||
\(332\) | −4.99253 | + | 4.55356i | −0.274000 | + | 0.249909i | ||||
\(333\) | 16.5330 | + | 16.5330i | 0.906000 | + | 0.906000i | ||||
\(334\) | 10.2168 | − | 9.75782i | 0.559040 | − | 0.533924i | ||||
\(335\) | −23.7486 | − | 23.3454i | −1.29753 | − | 1.27550i | ||||
\(336\) | −3.37130 | + | 36.5802i | −0.183920 | + | 1.99561i | ||||
\(337\) | −7.13548 | − | 7.13548i | −0.388694 | − | 0.388694i | 0.485527 | − | 0.874221i | \(-0.338628\pi\) |
−0.874221 | + | 0.485527i | \(0.838628\pi\) | |||||||
\(338\) | −5.88228 | + | 17.4183i | −0.319954 | + | 0.947433i | ||||
\(339\) | −38.4841 | −2.09017 | ||||||||
\(340\) | −7.73751 | − | 8.33888i | −0.419625 | − | 0.452239i | ||||
\(341\) | −5.77374 | −0.312666 | ||||||||
\(342\) | −0.527519 | + | 22.9560i | −0.0285250 | + | 1.24132i | ||||
\(343\) | 12.2780 | − | 12.2780i | 0.662951 | − | 0.662951i | ||||
\(344\) | 4.14594 | − | 3.61047i | 0.223534 | − | 0.194663i | ||||
\(345\) | 0.0962377 | + | 11.2404i | 0.00518127 | + | 0.605164i | ||||
\(346\) | −3.50896 | − | 3.67402i | −0.188643 | − | 0.197517i | ||||
\(347\) | −22.6909 | + | 22.6909i | −1.21811 | + | 1.21811i | −0.249817 | + | 0.968293i | \(0.580370\pi\) |
−0.968293 | + | 0.249817i | \(0.919630\pi\) | |||||||
\(348\) | −35.0134 | + | 31.9349i | −1.87692 | + | 1.71189i | ||||
\(349\) | 17.6400 | 0.944247 | 0.472124 | − | 0.881532i | \(-0.343488\pi\) | ||||
0.472124 | + | 0.881532i | \(0.343488\pi\) | |||||||
\(350\) | 14.0199 | − | 13.8567i | 0.749394 | − | 0.740673i | ||||
\(351\) | 34.1493 | + | 46.4409i | 1.82276 | + | 2.47883i | ||||
\(352\) | 1.79329 | − | 15.5417i | 0.0955828 | − | 0.828375i | ||||
\(353\) | −24.4668 | − | 24.4668i | −1.30224 | − | 1.30224i | −0.926879 | − | 0.375359i | \(-0.877519\pi\) |
−0.375359 | − | 0.926879i | \(-0.622481\pi\) | |||||||
\(354\) | −31.0605 | − | 32.5216i | −1.65085 | − | 1.72850i | ||||
\(355\) | 8.42157 | − | 0.0721034i | 0.446970 | − | 0.00382685i | ||||
\(356\) | 6.78472 | + | 0.311985i | 0.359589 | + | 0.0165352i | ||||
\(357\) | 16.5185 | − | 16.5185i | 0.874251 | − | 0.874251i | ||||
\(358\) | 0.00573945 | − | 0.249762i | 0.000303339 | − | 0.0132004i | ||||
\(359\) | 26.5212i | 1.39973i | 0.714273 | + | 0.699867i | \(0.246757\pi\) | ||||
−0.714273 | + | 0.699867i | \(0.753243\pi\) | |||||||
\(360\) | 49.5765 | + | 2.99633i | 2.61291 | + | 0.157921i | ||||
\(361\) | 14.7252 | 0.775011 | ||||||||
\(362\) | 0.442197 | − | 19.2430i | 0.0232414 | − | 1.01139i | ||||
\(363\) | −7.80671 | − | 7.80671i | −0.409746 | − | 0.409746i | ||||
\(364\) | −16.7252 | + | 11.1524i | −0.876640 | + | 0.584543i | ||||
\(365\) | 0.515247 | + | 0.506499i | 0.0269693 | + | 0.0265114i | ||||
\(366\) | 23.0359 | − | 22.0010i | 1.20411 | − | 1.15001i | ||||
\(367\) | 5.52850 | − | 5.52850i | 0.288586 | − | 0.288586i | −0.547935 | − | 0.836521i | \(-0.684586\pi\) |
0.836521 | + | 0.547935i | \(0.184586\pi\) | |||||||
\(368\) | −3.90170 | − | 4.69389i | −0.203390 | − | 0.244686i | ||||
\(369\) | 16.2835 | 0.847684 | ||||||||
\(370\) | 6.56088 | + | 6.75279i | 0.341084 | + | 0.351061i | ||||
\(371\) | −18.9536 | −0.984020 | ||||||||
\(372\) | 9.26936 | + | 10.1629i | 0.480594 | + | 0.526923i | ||||
\(373\) | −13.6242 | + | 13.6242i | −0.705432 | + | 0.705432i | −0.965571 | − | 0.260139i | \(-0.916232\pi\) |
0.260139 | + | 0.965571i | \(0.416232\pi\) | |||||||
\(374\) | −7.19465 | + | 6.87142i | −0.372026 | + | 0.355312i | ||||
\(375\) | −26.7048 | − | 25.3670i | −1.37903 | − | 1.30995i | ||||
\(376\) | 9.15538 | − | 7.97291i | 0.472153 | − | 0.411172i | ||||
\(377\) | −25.6364 | − | 3.91003i | −1.32034 | − | 0.201377i | ||||
\(378\) | −1.44804 | + | 63.0140i | −0.0744790 | + | 3.24109i | ||||
\(379\) | − | 26.5880i | − | 1.36574i | −0.730542 | − | 0.682868i | \(-0.760732\pi\) | ||
0.730542 | − | 0.682868i | \(-0.239268\pi\) | |||||||
\(380\) | −0.345639 | + | 9.23994i | −0.0177309 | + | 0.473999i | ||||
\(381\) | −51.3101 | −2.62869 | ||||||||
\(382\) | −19.6748 | − | 0.452119i | −1.00665 | − | 0.0231324i | ||||
\(383\) | 8.03967 | − | 8.03967i | 0.410808 | − | 0.410808i | −0.471212 | − | 0.882020i | \(-0.656183\pi\) |
0.882020 | + | 0.471212i | \(0.156183\pi\) | |||||||
\(384\) | −30.2355 | + | 21.7946i | −1.54295 | + | 1.11220i | ||||
\(385\) | −12.2942 | − | 12.0854i | −0.626569 | − | 0.615931i | ||||
\(386\) | 25.3044 | − | 24.1676i | 1.28796 | − | 1.23010i | ||||
\(387\) | 10.7933 | − | 10.7933i | 0.548656 | − | 0.548656i | ||||
\(388\) | 11.1436 | − | 10.1638i | 0.565729 | − | 0.515988i | ||||
\(389\) | 15.3855i | 0.780076i | 0.920799 | + | 0.390038i | \(0.127538\pi\) | ||||
−0.920799 | + | 0.390038i | \(0.872462\pi\) | |||||||
\(390\) | 21.8135 | + | 30.5788i | 1.10457 | + | 1.54842i | ||||
\(391\) | 3.88150i | 0.196296i | ||||||||
\(392\) | −2.17644 | − | 0.150253i | −0.109927 | − | 0.00758893i | ||||
\(393\) | 0.271090 | − | 0.271090i | 0.0136747 | − | 0.0136747i | ||||
\(394\) | 2.02945 | + | 2.12492i | 0.102242 | + | 0.107052i | ||||
\(395\) | −7.52521 | + | 0.0644291i | −0.378635 | + | 0.00324178i | ||||
\(396\) | 1.99529 | − | 43.3914i | 0.100267 | − | 2.18050i | ||||
\(397\) | 0.850203 | − | 0.850203i | 0.0426705 | − | 0.0426705i | −0.685450 | − | 0.728120i | \(-0.740394\pi\) |
0.728120 | + | 0.685450i | \(0.240394\pi\) | |||||||
\(398\) | −0.409744 | + | 17.8307i | −0.0205386 | + | 0.893774i | ||||
\(399\) | −18.9881 | −0.950592 | ||||||||
\(400\) | 19.9441 | + | 1.49419i | 0.997205 | + | 0.0747095i | ||||
\(401\) | 2.07340i | 0.103541i | 0.998659 | + | 0.0517704i | \(0.0164864\pi\) | ||||
−0.998659 | + | 0.0517704i | \(0.983514\pi\) | |||||||
\(402\) | 69.3678 | + | 1.59405i | 3.45975 | + | 0.0795038i | ||||
\(403\) | −1.13492 | + | 7.44116i | −0.0565342 | + | 0.370670i | ||||
\(404\) | −5.41164 | − | 0.248846i | −0.269239 | − | 0.0123806i | ||||
\(405\) | 65.0919 | − | 0.557301i | 3.23444 | − | 0.0276925i | ||||
\(406\) | −19.5846 | − | 20.5058i | −0.971967 | − | 1.01769i | ||||
\(407\) | 5.82248 | − | 5.82248i | 0.288610 | − | 0.288610i | ||||
\(408\) | 23.6456 | + | 1.63240i | 1.17063 | + | 0.0808158i | ||||
\(409\) | 5.67158 | 0.280442 | 0.140221 | − | 0.990120i | \(-0.455219\pi\) | ||||
0.140221 | + | 0.990120i | \(0.455219\pi\) | |||||||
\(410\) | 6.55639 | + | 0.0945105i | 0.323797 | + | 0.00466754i | ||||
\(411\) | 53.0128 | 2.61493 | ||||||||
\(412\) | 4.46479 | + | 4.89519i | 0.219964 | + | 0.241169i | ||||
\(413\) | 19.0273 | − | 19.0273i | 0.936271 | − | 0.936271i | ||||
\(414\) | −11.7048 | − | 12.2554i | −0.575260 | − | 0.602320i | ||||
\(415\) | −5.29613 | + | 5.38760i | −0.259977 | + | 0.264467i | ||||
\(416\) | −19.6775 | − | 5.36614i | −0.964770 | − | 0.263097i | ||||
\(417\) | 32.5575 | + | 32.5575i | 1.59435 | + | 1.59435i | ||||
\(418\) | 8.08450 | + | 0.185779i | 0.395426 | + | 0.00908673i | ||||
\(419\) | 19.1062 | 0.933399 | 0.466699 | − | 0.884416i | \(-0.345443\pi\) | ||||
0.466699 | + | 0.884416i | \(0.345443\pi\) | |||||||
\(420\) | −1.53528 | + | 41.0426i | −0.0749140 | + | 2.00267i | ||||
\(421\) | − | 20.3290i | − | 0.990773i | −0.868673 | − | 0.495387i | \(-0.835026\pi\) | ||
0.868673 | − | 0.495387i | \(-0.164974\pi\) | |||||||
\(422\) | −2.67188 | − | 0.0613989i | −0.130065 | − | 0.00298885i | ||||
\(423\) | 23.8347 | − | 23.8347i | 1.15888 | − | 1.15888i | ||||
\(424\) | −12.6291 | − | 14.5022i | −0.613325 | − | 0.704288i | ||||
\(425\) | −9.14593 | − | 8.83796i | −0.443643 | − | 0.428704i | ||||
\(426\) | −12.6897 | + | 12.1196i | −0.614818 | + | 0.587197i | ||||
\(427\) | 13.4775 | + | 13.4775i | 0.652222 | + | 0.652222i | ||||
\(428\) | 8.42657 | − | 7.68567i | 0.407314 | − | 0.371501i | ||||
\(429\) | 26.4656 | − | 19.4609i | 1.27777 | − | 0.939583i | ||||
\(430\) | 4.40848 | − | 4.28319i | 0.212596 | − | 0.206554i | ||||
\(431\) | −34.3570 | −1.65492 | −0.827460 | − | 0.561524i | \(-0.810215\pi\) | ||||
−0.827460 | + | 0.561524i | \(0.810215\pi\) | |||||||
\(432\) | −49.1795 | + | 40.8795i | −2.36615 | + | 1.96682i | ||||
\(433\) | 20.9912 | − | 20.9912i | 1.00877 | − | 1.00877i | 0.00881105 | − | 0.999961i | \(-0.497195\pi\) |
0.999961 | − | 0.00881105i | \(-0.00280468\pi\) | |||||||
\(434\) | −5.95199 | + | 5.68458i | −0.285704 | + | 0.272869i | ||||
\(435\) | −37.1427 | + | 37.7842i | −1.78086 | + | 1.81161i | ||||
\(436\) | −26.5520 | − | 1.22095i | −1.27161 | − | 0.0584731i | ||||
\(437\) | 2.23090 | − | 2.23090i | 0.106718 | − | 0.106718i | ||||
\(438\) | −1.50500 | − | 0.0345842i | −0.0719115 | − | 0.00165250i | ||||
\(439\) | 16.6708 | 0.795656 | 0.397828 | − | 0.917460i | \(-0.369764\pi\) | ||||
0.397828 | + | 0.917460i | \(0.369764\pi\) | |||||||
\(440\) | 1.05523 | − | 17.4596i | 0.0503062 | − | 0.832352i | ||||
\(441\) | −6.05720 | −0.288438 | ||||||||
\(442\) | 7.44161 | + | 10.6231i | 0.353962 | + | 0.505289i | ||||
\(443\) | 21.7096 | + | 21.7096i | 1.03146 | + | 1.03146i | 0.999489 | + | 0.0319665i | \(0.0101770\pi\) |
0.0319665 | + | 0.999489i | \(0.489823\pi\) | |||||||
\(444\) | −19.5963 | − | 0.901108i | −0.930001 | − | 0.0427647i | ||||
\(445\) | 7.59328 | − | 0.0650119i | 0.359956 | − | 0.00308186i | ||||
\(446\) | 23.4227 | + | 24.5246i | 1.10910 | + | 1.16127i | ||||
\(447\) | 25.5443 | + | 25.5443i | 1.20820 | + | 1.20820i | ||||
\(448\) | −13.4530 | − | 17.7871i | −0.635596 | − | 0.840361i | ||||
\(449\) | 31.2426 | 1.47443 | 0.737215 | − | 0.675658i | \(-0.236140\pi\) | ||||
0.737215 | + | 0.675658i | \(0.236140\pi\) | |||||||
\(450\) | 55.5284 | + | 0.324982i | 2.61763 | + | 0.0153198i | ||||
\(451\) | − | 5.73462i | − | 0.270033i | ||||||
\(452\) | 17.2618 | − | 15.7441i | 0.811929 | − | 0.740541i | ||||
\(453\) | −41.1367 | − | 41.1367i | −1.93277 | − | 1.93277i | ||||
\(454\) | −17.2162 | + | 16.4427i | −0.807995 | + | 0.771694i | ||||
\(455\) | −17.9922 | + | 13.4691i | −0.843489 | + | 0.631439i | ||||
\(456\) | −12.6521 | − | 14.5286i | −0.592490 | − | 0.680363i | ||||
\(457\) | −22.4089 | + | 22.4089i | −1.04824 | + | 1.04824i | −0.0494661 | + | 0.998776i | \(0.515752\pi\) |
−0.998776 | + | 0.0494661i | \(0.984248\pi\) | |||||||
\(458\) | −0.368686 | + | 16.0441i | −0.0172276 | + | 0.749690i | ||||
\(459\) | 40.6678 | 1.89821 | ||||||||
\(460\) | −4.64170 | − | 5.00245i | −0.216420 | − | 0.233241i | ||||
\(461\) | − | 14.9213i | − | 0.694953i | −0.937689 | − | 0.347477i | \(-0.887039\pi\) | ||
0.937689 | − | 0.347477i | \(-0.112961\pi\) | |||||||
\(462\) | 35.9103 | + | 0.825204i | 1.67070 | + | 0.0383920i | ||||
\(463\) | −12.5507 | + | 12.5507i | −0.583282 | + | 0.583282i | −0.935804 | − | 0.352522i | \(-0.885324\pi\) |
0.352522 | + | 0.935804i | \(0.385324\pi\) | |||||||
\(464\) | 2.64030 | − | 28.6485i | 0.122573 | − | 1.32997i | ||||
\(465\) | 10.9672 | + | 10.7810i | 0.508590 | + | 0.499955i | ||||
\(466\) | 19.2084 | + | 20.1119i | 0.889810 | + | 0.931667i | ||||
\(467\) | −14.2920 | + | 14.2920i | −0.661354 | + | 0.661354i | −0.955699 | − | 0.294346i | \(-0.904898\pi\) |
0.294346 | + | 0.955699i | \(0.404898\pi\) | |||||||
\(468\) | −55.5304 | − | 11.1008i | −2.56689 | − | 0.513133i | ||||
\(469\) | 41.5173i | 1.91709i | ||||||||
\(470\) | 9.73514 | − | 9.45846i | 0.449048 | − | 0.436286i | ||||
\(471\) | − | 63.5025i | − | 2.92604i | ||||||
\(472\) | 27.2368 | + | 1.88032i | 1.25368 | + | 0.0865490i | ||||
\(473\) | −3.80113 | − | 3.80113i | −0.174776 | − | 0.174776i | ||||
\(474\) | 11.3391 | − | 10.8296i | 0.520821 | − | 0.497422i | ||||
\(475\) | 0.177006 | + | 10.3363i | 0.00812161 | + | 0.474261i | ||||
\(476\) | −0.651453 | + | 14.1671i | −0.0298593 | + | 0.649348i | ||||
\(477\) | −37.7543 | − | 37.7543i | −1.72865 | − | 1.72865i | ||||
\(478\) | 20.7204 | + | 0.476148i | 0.947731 | + | 0.0217785i | ||||
\(479\) | 0.392894i | 0.0179518i | 0.999960 | + | 0.00897588i | \(0.00285715\pi\) | ||||
−0.999960 | + | 0.00897588i | \(0.997143\pi\) | |||||||
\(480\) | −32.4264 | + | 26.1728i | −1.48006 | + | 1.19462i | ||||
\(481\) | −6.35947 | − | 8.64847i | −0.289967 | − | 0.394336i | ||||
\(482\) | −31.0224 | − | 0.712883i | −1.41303 | − | 0.0324709i | ||||
\(483\) | 9.90936 | − | 9.90936i | 0.450891 | − | 0.450891i | ||||
\(484\) | 6.69543 | + | 0.307880i | 0.304338 | + | 0.0139945i | ||||
\(485\) | 11.8212 | − | 12.0254i | 0.536775 | − | 0.546045i | ||||
\(486\) | −49.0285 | + | 46.8258i | −2.22398 | + | 2.12406i | ||||
\(487\) | 8.76391 | + | 8.76391i | 0.397131 | + | 0.397131i | 0.877220 | − | 0.480089i | \(-0.159396\pi\) |
−0.480089 | + | 0.877220i | \(0.659396\pi\) | |||||||
\(488\) | −1.33188 | + | 19.2926i | −0.0602915 | + | 0.873333i | ||||
\(489\) | −20.9694 | −0.948267 | ||||||||
\(490\) | −2.43888 | − | 0.0351564i | −0.110177 | − | 0.00158821i | ||||
\(491\) | 2.47325i | 0.111616i | 0.998442 | + | 0.0558081i | \(0.0177735\pi\) | ||||
−0.998442 | + | 0.0558081i | \(0.982226\pi\) | |||||||
\(492\) | −10.0941 | + | 9.20657i | −0.455076 | + | 0.415064i | ||||
\(493\) | −12.9367 | + | 12.9367i | −0.582642 | + | 0.582642i | ||||
\(494\) | 1.82856 | − | 10.3827i | 0.0822709 | − | 0.467141i | ||||
\(495\) | −0.415781 | − | 48.5626i | −0.0186880 | − | 2.18273i | ||||
\(496\) | −8.31544 | − | 0.766367i | −0.373374 | − | 0.0344109i | ||||
\(497\) | −7.42431 | − | 7.42431i | −0.333026 | − | 0.333026i | ||||
\(498\) | 0.361625 | − | 15.7368i | 0.0162048 | − | 0.705181i | ||||
\(499\) | − | 17.6033i | − | 0.788032i | −0.919104 | − | 0.394016i | \(-0.871085\pi\) | ||
0.919104 | − | 0.394016i | \(-0.128915\pi\) | |||||||
\(500\) | 22.3561 | + | 0.453142i | 0.999795 | + | 0.0202651i | ||||
\(501\) | 32.9109i | 1.47035i | ||||||||
\(502\) | −25.0356 | − | 0.575308i | −1.11739 | − | 0.0256772i | ||||
\(503\) | −5.95062 | − | 5.95062i | −0.265325 | − | 0.265325i | 0.561888 | − | 0.827213i | \(-0.310075\pi\) |
−0.827213 | + | 0.561888i | \(0.810075\pi\) | |||||||
\(504\) | −40.6645 | − | 46.6955i | −1.81134 | − | 2.07998i | ||||
\(505\) | −6.05657 | + | 0.0518549i | −0.269514 | + | 0.00230751i | ||||
\(506\) | −4.31604 | + | 4.12213i | −0.191871 | + | 0.183251i | ||||
\(507\) | −19.8789 | − | 37.9340i | −0.882853 | − | 1.68471i | ||||
\(508\) | 23.0148 | − | 20.9913i | 1.02112 | − | 0.931338i | ||||
\(509\) | −18.7434 | −0.830785 | −0.415392 | − | 0.909642i | \(-0.636356\pi\) | ||||
−0.415392 | + | 0.909642i | \(0.636356\pi\) | |||||||
\(510\) | 26.4968 | + | 0.381951i | 1.17330 | + | 0.0169131i | ||||
\(511\) | − | 0.900755i | − | 0.0398471i | ||||||
\(512\) | 4.64563 | − | 22.1454i | 0.205310 | − | 0.978697i | ||||
\(513\) | −23.3739 | − | 23.3739i | −1.03198 | − | 1.03198i | ||||
\(514\) | 13.9007 | − | 13.2762i | 0.613132 | − | 0.585586i | ||||
\(515\) | 5.28257 | + | 5.19288i | 0.232778 | + | 0.228826i | ||||
\(516\) | −0.588277 | + | 12.7932i | −0.0258975 | + | 0.563190i | ||||
\(517\) | −8.39396 | − | 8.39396i | −0.369166 | − | 0.369166i | ||||
\(518\) | 0.269661 | − | 11.7348i | 0.0118482 | − | 0.515597i | ||||
\(519\) | 11.8349 | 0.519495 | ||||||||
\(520\) | −22.2943 | − | 4.79192i | −0.977671 | − | 0.210140i | ||||
\(521\) | −12.6489 | −0.554157 | −0.277078 | − | 0.960847i | \(-0.589366\pi\) | ||||
−0.277078 | + | 0.960847i | \(0.589366\pi\) | |||||||
\(522\) | 1.83510 | − | 79.8575i | 0.0803199 | − | 3.49527i | ||||
\(523\) | −14.7541 | − | 14.7541i | −0.645150 | − | 0.645150i | 0.306667 | − | 0.951817i | \(-0.400786\pi\) |
−0.951817 | + | 0.306667i | \(0.900786\pi\) | |||||||
\(524\) | −0.0106912 | + | 0.232500i | −0.000467047 | + | 0.0101568i | ||||
\(525\) | 0.786238 | + | 45.9123i | 0.0343143 | + | 2.00378i | ||||
\(526\) | −0.640610 | + | 0.611829i | −0.0279319 | + | 0.0266770i | ||||
\(527\) | 3.75499 | + | 3.75499i | 0.163570 | + | 0.163570i | ||||
\(528\) | 23.2963 | + | 28.0263i | 1.01384 | + | 1.21969i | ||||
\(529\) | − | 20.6715i | − | 0.898761i | ||||||
\(530\) | −14.9823 | − | 15.4205i | −0.650788 | − | 0.669825i | ||||
\(531\) | 75.8022 | 3.28953 | ||||||||
\(532\) | 8.51699 | − | 7.76814i | 0.369258 | − | 0.336792i | ||||
\(533\) | −7.39074 | − | 1.12723i | −0.320129 | − | 0.0488257i | ||||
\(534\) | −11.4416 | + | 10.9276i | −0.495128 | + | 0.472884i | ||||
\(535\) | 8.93901 | − | 9.09340i | 0.386467 | − | 0.393142i | ||||
\(536\) | −31.7667 | + | 27.6638i | −1.37211 | + | 1.19490i | ||||
\(537\) | 0.411517 | + | 0.411517i | 0.0177583 | + | 0.0177583i | ||||
\(538\) | 28.2272 | + | 0.648650i | 1.21696 | + | 0.0279653i | ||||
\(539\) | 2.13319i | 0.0918830i | ||||||||
\(540\) | −52.4125 | + | 48.6327i | −2.25547 | + | 2.09282i | ||||
\(541\) | 30.7974i | 1.32408i | 0.749467 | + | 0.662042i | \(0.230310\pi\) | ||||
−0.749467 | + | 0.662042i | \(0.769690\pi\) | |||||||
\(542\) | −0.637463 | + | 27.7403i | −0.0273814 | + | 1.19155i | ||||
\(543\) | 31.7054 | + | 31.7054i | 1.36061 | + | 1.36061i | ||||
\(544\) | −11.2739 | + | 8.94137i | −0.483366 | + | 0.383358i | ||||
\(545\) | −29.7163 | + | 0.254424i | −1.27291 | + | 0.0108983i | ||||
\(546\) | 8.12223 | − | 46.1187i | 0.347599 | − | 1.97370i | ||||
\(547\) | 17.8667 | − | 17.8667i | 0.763927 | − | 0.763927i | −0.213103 | − | 0.977030i | \(-0.568357\pi\) |
0.977030 | + | 0.213103i | \(0.0683570\pi\) | |||||||
\(548\) | −23.7786 | + | 21.6879i | −1.01577 | + | 0.926461i | ||||
\(549\) | 53.6926i | 2.29155i | ||||||||
\(550\) | 0.114450 | − | 19.5557i | 0.00488018 | − | 0.833857i | ||||
\(551\) | 14.8708 | 0.633519 | ||||||||
\(552\) | 14.1849 | + | 0.979269i | 0.603749 | + | 0.0416805i | ||||
\(553\) | 6.63410 | + | 6.63410i | 0.282111 | + | 0.282111i | ||||
\(554\) | −3.92421 | + | 3.74791i | −0.166724 | + | 0.159234i | ||||
\(555\) | −21.9317 | + | 0.187774i | −0.930949 | + | 0.00797057i | ||||
\(556\) | −27.9230 | − | 1.28400i | −1.18420 | − | 0.0544536i | ||||
\(557\) | 10.5065 | − | 10.5065i | 0.445173 | − | 0.445173i | −0.448573 | − | 0.893746i | \(-0.648068\pi\) |
0.893746 | + | 0.448573i | \(0.148068\pi\) | |||||||
\(558\) | −23.1793 | − | 0.532651i | −0.981257 | − | 0.0225489i | ||||
\(559\) | −5.64605 | + | 4.15170i | −0.238802 | + | 0.175598i | ||||
\(560\) | −16.1021 | − | 19.0375i | −0.680440 | − | 0.804481i | ||||
\(561\) | − | 23.1757i | − | 0.978479i | ||||||
\(562\) | −15.2246 | − | 0.349857i | −0.642213 | − | 0.0147578i | ||||
\(563\) | −13.5627 | − | 13.5627i | −0.571601 | − | 0.571601i | 0.360974 | − | 0.932576i | \(-0.382444\pi\) |
−0.932576 | + | 0.360974i | \(0.882444\pi\) | |||||||
\(564\) | −1.29908 | + | 28.2510i | −0.0547011 | + | 1.18958i | ||||
\(565\) | 18.3116 | − | 18.6278i | 0.770374 | − | 0.783679i | ||||
\(566\) | 13.3368 | − | 12.7377i | 0.560589 | − | 0.535404i | ||||
\(567\) | −57.3839 | − | 57.3839i | −2.40990 | − | 2.40990i | ||||
\(568\) | 0.733690 | − | 10.6276i | 0.0307849 | − | 0.445925i | ||||
\(569\) | 18.7390i | 0.785582i | 0.919628 | + | 0.392791i | \(0.128490\pi\) | ||||
−0.919628 | + | 0.392791i | \(0.871510\pi\) | |||||||
\(570\) | −15.0095 | − | 15.4486i | −0.628680 | − | 0.647070i | ||||
\(571\) | 8.09676i | 0.338839i | 0.985544 | + | 0.169419i | \(0.0541892\pi\) | ||||
−0.985544 | + | 0.169419i | \(0.945811\pi\) | |||||||
\(572\) | −3.90940 | + | 19.5564i | −0.163460 | + | 0.817693i | ||||
\(573\) | 32.4168 | − | 32.4168i | 1.35423 | − | 1.35423i | ||||
\(574\) | −5.64607 | − | 5.91166i | −0.235662 | − | 0.246748i | ||||
\(575\) | −5.48660 | − | 5.30185i | −0.228807 | − | 0.221102i | ||||
\(576\) | 8.63314 | − | 62.2283i | 0.359714 | − | 2.59284i | ||||
\(577\) | −19.0166 | + | 19.0166i | −0.791673 | + | 0.791673i | −0.981766 | − | 0.190093i | \(-0.939121\pi\) |
0.190093 | + | 0.981766i | \(0.439121\pi\) | |||||||
\(578\) | −14.8873 | − | 0.342105i | −0.619231 | − | 0.0142297i | ||||
\(579\) | 81.5117i | 3.38751i | ||||||||
\(580\) | 1.20238 | − | 32.1432i | 0.0499262 | − | 1.33467i | ||||
\(581\) | 9.41860 | 0.390750 | ||||||||
\(582\) | −0.807164 | + | 35.1252i | −0.0334580 | + | 1.45599i | ||||
\(583\) | −13.2961 | + | 13.2961i | −0.550667 | + | 0.550667i | ||||
\(584\) | 0.689206 | − | 0.600191i | 0.0285196 | − | 0.0248361i | ||||
\(585\) | −62.6688 | − | 9.00986i | −2.59104 | − | 0.372512i | ||||
\(586\) | −2.42123 | + | 2.31245i | −0.100020 | + | 0.0955264i | ||||
\(587\) | −6.97520 | − | 6.97520i | −0.287897 | − | 0.287897i | 0.548351 | − | 0.836248i | \(-0.315256\pi\) |
−0.836248 | + | 0.548351i | \(0.815256\pi\) | |||||||
\(588\) | 3.75484 | − | 3.42470i | 0.154847 | − | 0.141232i | ||||
\(589\) | − | 4.31638i | − | 0.177853i | ||||||
\(590\) | 30.5210 | + | 0.439961i | 1.25653 | + | 0.0181129i | ||||
\(591\) | −6.84487 | −0.281560 | ||||||||
\(592\) | 9.15848 | − | 7.61280i | 0.376411 | − | 0.312884i | ||||
\(593\) | 26.5561 | + | 26.5561i | 1.09053 | + | 1.09053i | 0.995472 | + | 0.0950558i | \(0.0303029\pi\) |
0.0950558 | + | 0.995472i | \(0.469697\pi\) | |||||||
\(594\) | 43.1890 | + | 45.2206i | 1.77207 | + | 1.85542i | ||||
\(595\) | 0.135751 | + | 15.8555i | 0.00556523 | + | 0.650010i | ||||
\(596\) | −21.9081 | − | 1.00741i | −0.897389 | − | 0.0412651i | ||||
\(597\) | −29.3785 | − | 29.3785i | −1.20238 | − | 1.20238i | ||||
\(598\) | 4.46419 | + | 6.37274i | 0.182554 | + | 0.260601i | ||||
\(599\) | 35.1399 | 1.43578 | 0.717889 | − | 0.696157i | \(-0.245108\pi\) | ||||
0.717889 | + | 0.696157i | \(0.245108\pi\) | |||||||
\(600\) | −34.6056 | + | 31.1939i | −1.41277 | + | 1.27349i | ||||
\(601\) | 23.8391 | 0.972417 | 0.486209 | − | 0.873843i | \(-0.338380\pi\) | ||||
0.486209 | + | 0.873843i | \(0.338380\pi\) | |||||||
\(602\) | −7.66092 | − | 0.176045i | −0.312236 | − | 0.00717506i | ||||
\(603\) | −82.6998 | + | 82.6998i | −3.36780 | + | 3.36780i | ||||
\(604\) | 35.2810 | + | 1.62234i | 1.43556 | + | 0.0660122i | ||||
\(605\) | 7.49336 | − | 0.0641563i | 0.304648 | − | 0.00260833i | ||||
\(606\) | 9.12611 | − | 8.71610i | 0.370723 | − | 0.354067i | ||||
\(607\) | 21.1327 | − | 21.1327i | 0.857750 | − | 0.857750i | −0.133323 | − | 0.991073i | \(-0.542565\pi\) |
0.991073 | + | 0.133323i | \(0.0425646\pi\) | |||||||
\(608\) | 11.6188 | + | 1.34064i | 0.471204 | + | 0.0543703i | ||||
\(609\) | 66.0543 | 2.67665 | ||||||||
\(610\) | −0.311636 | + | 21.6188i | −0.0126178 | + | 0.875321i | ||||
\(611\) | −12.4680 | + | 9.16811i | −0.504403 | + | 0.370902i | ||||
\(612\) | −29.5176 | + | 26.9223i | −1.19318 | + | 1.08827i | ||||
\(613\) | 13.5802 | + | 13.5802i | 0.548499 | + | 0.548499i | 0.926007 | − | 0.377507i | \(-0.123219\pi\) |
−0.377507 | + | 0.926007i | \(0.623219\pi\) | |||||||
\(614\) | −28.4204 | + | 27.1436i | −1.14695 | + | 1.09543i | ||||
\(615\) | −10.7079 | + | 10.8929i | −0.431785 | + | 0.439243i | ||||
\(616\) | −16.4449 | + | 14.3210i | −0.662586 | + | 0.577009i | ||||
\(617\) | 27.8314 | − | 27.8314i | 1.12045 | − | 1.12045i | 0.128779 | − | 0.991673i | \(-0.458894\pi\) |
0.991673 | − | 0.128779i | \(-0.0411056\pi\) | |||||||
\(618\) | −15.4300 | − | 0.354574i | −0.620684 | − | 0.0142631i | ||||
\(619\) | − | 18.4469i | − | 0.741443i | −0.928744 | − | 0.370721i | \(-0.879110\pi\) | ||
0.928744 | − | 0.370721i | \(-0.120890\pi\) | |||||||
\(620\) | −9.32982 | − | 0.349001i | −0.374695 | − | 0.0140162i | ||||
\(621\) | 24.3964 | 0.978996 | ||||||||
\(622\) | 47.6558 | + | 1.09511i | 1.91082 | + | 0.0439100i | ||||
\(623\) | −6.69411 | − | 6.69411i | −0.268194 | − | 0.268194i | ||||
\(624\) | 40.6994 | − | 24.5151i | 1.62928 | − | 0.981391i | ||||
\(625\) | 24.9853 | − | 0.855988i | 0.999414 | − | 0.0342395i | ||||
\(626\) | 19.7807 | + | 20.7112i | 0.790596 | + | 0.827786i | ||||
\(627\) | −13.3203 | + | 13.3203i | −0.531961 | + | 0.531961i | ||||
\(628\) | 25.9793 | + | 28.4837i | 1.03669 | + | 1.13662i | ||||
\(629\) | −7.57339 | −0.301971 | ||||||||
\(630\) | −48.2413 | − | 49.6524i | −1.92198 | − | 1.97820i | ||||
\(631\) | −2.29587 | −0.0913973 | −0.0456986 | − | 0.998955i | \(-0.514551\pi\) | ||||
−0.0456986 | + | 0.998955i | \(0.514551\pi\) | |||||||
\(632\) | −0.655599 | + | 9.49647i | −0.0260783 | + | 0.377749i | ||||
\(633\) | 4.40228 | − | 4.40228i | 0.174975 | − | 0.174975i | ||||
\(634\) | 26.5024 | + | 27.7490i | 1.05254 | + | 1.10206i | ||||
\(635\) | 24.4144 | − | 24.8361i | 0.968857 | − | 0.985591i | ||||
\(636\) | 44.7497 | + | 2.05775i | 1.77444 | + | 0.0815951i | ||||
\(637\) | 2.74924 | + | 0.419311i | 0.108929 | + | 0.0166137i | ||||
\(638\) | −28.1238 | − | 0.646273i | −1.11343 | − | 0.0255862i | ||||
\(639\) | − | 29.5775i | − | 1.17007i | ||||||
\(640\) | 3.83723 | − | 25.0055i | 0.151680 | − | 0.988430i | ||||
\(641\) | 38.1507 | 1.50686 | 0.753431 | − | 0.657527i | \(-0.228397\pi\) | ||||
0.753431 | + | 0.657527i | \(0.228397\pi\) | |||||||
\(642\) | −0.610363 | + | 26.5611i | −0.0240891 | + | 1.04828i | ||||
\(643\) | 23.1735 | − | 23.1735i | 0.913875 | − | 0.913875i | −0.0826995 | − | 0.996575i | \(-0.526354\pi\) |
0.996575 | + | 0.0826995i | \(0.0263542\pi\) | |||||||
\(644\) | −0.390804 | + | 8.49878i | −0.0153998 | + | 0.334899i | ||||
\(645\) | 0.122586 | + | 14.3178i | 0.00482682 | + | 0.563765i | ||||
\(646\) | −5.13699 | − | 5.37864i | −0.202112 | − | 0.211620i | ||||
\(647\) | 2.29915 | − | 2.29915i | 0.0903891 | − | 0.0903891i | −0.660466 | − | 0.750856i | \(-0.729641\pi\) |
0.750856 | + | 0.660466i | \(0.229641\pi\) | |||||||
\(648\) | 5.67083 | − | 82.1430i | 0.222771 | − | 3.22688i | ||||
\(649\) | − | 26.6956i | − | 1.04789i | ||||||
\(650\) | −25.1807 | − | 3.99147i | −0.987669 | − | 0.156558i | ||||
\(651\) | − | 19.1728i | − | 0.751441i | ||||||
\(652\) | 9.40569 | − | 8.57870i | 0.368355 | − | 0.335968i | ||||
\(653\) | 4.75371 | − | 4.75371i | 0.186027 | − | 0.186027i | −0.607949 | − | 0.793976i | \(-0.708008\pi\) |
0.793976 | + | 0.607949i | \(0.208008\pi\) | |||||||
\(654\) | 44.7769 | − | 42.7652i | 1.75092 | − | 1.67225i | ||||
\(655\) | 0.00222784 | + | 0.260208i | 8.70490e−5 | + | 0.0101672i | ||||
\(656\) | 0.761175 | − | 8.25911i | 0.0297189 | − | 0.322464i | ||||
\(657\) | 1.79425 | − | 1.79425i | 0.0700002 | − | 0.0700002i | ||||
\(658\) | −16.9174 | − | 0.388756i | −0.659510 | − | 0.0151553i | ||||
\(659\) | 35.0519 | 1.36543 | 0.682715 | − | 0.730685i | \(-0.260799\pi\) | ||||
0.682715 | + | 0.730685i | \(0.260799\pi\) | |||||||
\(660\) | 27.7147 | + | 29.8687i | 1.07879 | + | 1.16264i | ||||
\(661\) | − | 6.89099i | − | 0.268028i | −0.990979 | − | 0.134014i | \(-0.957213\pi\) | ||
0.990979 | − | 0.134014i | \(-0.0427868\pi\) | |||||||
\(662\) | 0.446204 | − | 19.4174i | 0.0173422 | − | 0.754678i | ||||
\(663\) | −29.8687 | − | 4.55554i | −1.16000 | − | 0.176922i | ||||
\(664\) | 6.27581 | + | 7.20658i | 0.243549 | + | 0.279669i | ||||
\(665\) | 9.03493 | − | 9.19098i | 0.350360 | − | 0.356411i | ||||
\(666\) | 23.9121 | − | 22.8378i | 0.926575 | − | 0.884947i | ||||
\(667\) | −7.76069 | + | 7.76069i | −0.300495 | + | 0.300495i | ||||
\(668\) | −13.4641 | − | 14.7620i | −0.520940 | − | 0.571159i | ||||
\(669\) | −78.9995 | −3.05430 | ||||||||
\(670\) | −33.7783 | + | 32.8183i | −1.30497 | + | 1.26788i | ||||
\(671\) | 18.9092 | 0.729980 | ||||||||
\(672\) | 51.6091 | + | 5.95496i | 1.99086 | + | 0.229718i | ||||
\(673\) | −10.4035 | + | 10.4035i | −0.401024 | + | 0.401024i | −0.878594 | − | 0.477570i | \(-0.841518\pi\) |
0.477570 | + | 0.878594i | \(0.341518\pi\) | |||||||
\(674\) | −10.3203 | + | 9.85659i | −0.397521 | + | 0.379662i | ||||
\(675\) | −55.5493 | + | 57.4850i | −2.13809 | + | 2.21260i | ||||
\(676\) | 24.4356 | + | 8.88251i | 0.939833 | + | 0.341635i | ||||
\(677\) | −29.5371 | − | 29.5371i | −1.13520 | − | 1.13520i | −0.989299 | − | 0.145903i | \(-0.953391\pi\) |
−0.145903 | − | 0.989299i | \(-0.546609\pi\) | |||||||
\(678\) | −1.25033 | + | 54.4104i | −0.0480187 | + | 2.08962i | ||||
\(679\) | −21.0228 | −0.806781 | ||||||||
\(680\) | −12.0412 | + | 10.6687i | −0.461760 | + | 0.409125i | ||||
\(681\) | − | 55.4574i | − | 2.12513i | ||||||
\(682\) | −0.187586 | + | 8.16315i | −0.00718304 | + | 0.312583i | ||||
\(683\) | 6.74455 | − | 6.74455i | 0.258073 | − | 0.258073i | −0.566197 | − | 0.824270i | \(-0.691586\pi\) |
0.824270 | + | 0.566197i | \(0.191586\pi\) | |||||||
\(684\) | 32.4389 | + | 1.49166i | 1.24033 | + | 0.0570349i | ||||
\(685\) | −25.2247 | + | 25.6603i | −0.963784 | + | 0.980430i | ||||
\(686\) | −16.9603 | − | 17.7581i | −0.647546 | − | 0.678006i | ||||
\(687\) | −26.4347 | − | 26.4347i | −1.00855 | − | 1.00855i | ||||
\(688\) | −4.96992 | − | 5.97900i | −0.189477 | − | 0.227947i | ||||
\(689\) | 14.5223 | + | 19.7494i | 0.553257 | + | 0.752394i | ||||
\(690\) | 15.8953 | + | 0.229131i | 0.605123 | + | 0.00872286i | ||||
\(691\) | 10.6205 | 0.404021 | 0.202010 | − | 0.979383i | \(-0.435252\pi\) | ||||
0.202010 | + | 0.979383i | \(0.435252\pi\) | |||||||
\(692\) | −5.30849 | + | 4.84174i | −0.201798 | + | 0.184055i | ||||
\(693\) | −42.8119 | + | 42.8119i | −1.62629 | + | 1.62629i | ||||
\(694\) | 31.3441 | + | 32.8185i | 1.18980 | + | 1.24577i | ||||
\(695\) | −31.2507 | + | 0.267561i | −1.18541 | + | 0.0101492i | ||||
\(696\) | 44.0133 | + | 50.5410i | 1.66832 | + | 1.91575i | ||||
\(697\) | −3.72956 | + | 3.72956i | −0.141267 | + | 0.141267i | ||||
\(698\) | 0.573115 | − | 24.9401i | 0.0216927 | − | 0.943998i | ||||
\(699\) | −64.7854 | −2.45041 | ||||||||
\(700\) | −19.1357 | − | 20.2721i | −0.723262 | − | 0.766212i | ||||
\(701\) | 6.12695 | 0.231412 | 0.115706 | − | 0.993284i | \(-0.463087\pi\) | ||||
0.115706 | + | 0.993284i | \(0.463087\pi\) | |||||||
\(702\) | 66.7695 | − | 46.7729i | 2.52005 | − | 1.76533i | ||||
\(703\) | 4.35282 | + | 4.35282i | 0.164170 | + | 0.164170i | ||||
\(704\) | −21.9152 | − | 3.04037i | −0.825960 | − | 0.114588i | ||||
\(705\) | 0.270704 | + | 31.6178i | 0.0101953 | + | 1.19079i | ||||
\(706\) | −35.3871 | + | 33.7973i | −1.33181 | + | 1.27198i | ||||
\(707\) | 5.33937 | + | 5.33937i | 0.200808 | + | 0.200808i | ||||
\(708\) | −46.9895 | + | 42.8580i | −1.76597 | + | 1.61070i | ||||
\(709\) | 23.2312 | 0.872467 | 0.436233 | − | 0.899834i | \(-0.356312\pi\) | ||||
0.436233 | + | 0.899834i | \(0.356312\pi\) | |||||||
\(710\) | 0.171670 | − | 11.9091i | 0.00644265 | − | 0.446940i | ||||
\(711\) | 26.4294i | 0.991180i | ||||||||
\(712\) | 0.661530 | − | 9.58237i | 0.0247919 | − | 0.359115i | ||||
\(713\) | 2.25260 | + | 2.25260i | 0.0843607 | + | 0.0843607i | ||||
\(714\) | −22.8178 | − | 23.8912i | −0.853935 | − | 0.894105i | ||||
\(715\) | −3.17304 | + | 22.0703i | −0.118665 | + | 0.825384i | ||||
\(716\) | −0.352938 | − | 0.0162293i | −0.0131899 | − | 0.000606518i | ||||
\(717\) | −34.1397 | + | 34.1397i | −1.27497 | + | 1.27497i | ||||
\(718\) | 37.4967 | + | 0.861660i | 1.39936 | + | 0.0321569i | ||||
\(719\) | −49.2456 | −1.83655 | −0.918276 | − | 0.395940i | \(-0.870419\pi\) | ||||
−0.918276 | + | 0.395940i | \(0.870419\pi\) | |||||||
\(720\) | 5.84705 | − | 69.9959i | 0.217907 | − | 2.60859i | ||||
\(721\) | − | 9.23498i | − | 0.343929i | ||||||
\(722\) | 0.478415 | − | 20.8191i | 0.0178048 | − | 0.774806i | ||||
\(723\) | 51.1135 | − | 51.1135i | 1.90093 | − | 1.90093i | ||||
\(724\) | −27.1922 | − | 1.25039i | −1.01059 | − | 0.0464704i | ||||
\(725\) | −0.615757 | − | 35.9571i | −0.0228686 | − | 1.33541i | ||||
\(726\) | −11.2911 | + | 10.7838i | −0.419051 | + | 0.400224i | ||||
\(727\) | 25.1121 | − | 25.1121i | 0.931356 | − | 0.931356i | −0.0664346 | − | 0.997791i | \(-0.521162\pi\) |
0.997791 | + | 0.0664346i | \(0.0211624\pi\) | |||||||
\(728\) | 15.2243 | + | 24.0091i | 0.564249 | + | 0.889838i | ||||
\(729\) | − | 70.5996i | − | 2.61480i | ||||||
\(730\) | 0.732850 | − | 0.712022i | 0.0271240 | − | 0.0263531i | ||||
\(731\) | 4.94419i | 0.182867i | ||||||||
\(732\) | −30.3574 | − | 33.2839i | −1.12204 | − | 1.23021i | ||||
\(733\) | 7.99950 | + | 7.99950i | 0.295468 | + | 0.295468i | 0.839236 | − | 0.543768i | \(-0.183003\pi\) |
−0.543768 | + | 0.839236i | \(0.683003\pi\) | |||||||
\(734\) | −7.63680 | − | 7.99604i | −0.281880 | − | 0.295139i | ||||
\(735\) | 3.98318 | − | 4.05198i | 0.146922 | − | 0.149459i | ||||
\(736\) | −6.76318 | + | 5.36389i | −0.249294 | + | 0.197715i | ||||
\(737\) | 29.1247 | + | 29.1247i | 1.07282 | + | 1.07282i | ||||
\(738\) | 0.529043 | − | 23.0222i | 0.0194743 | − | 0.847461i | ||||
\(739\) | − | 22.0584i | − | 0.811432i | −0.913999 | − | 0.405716i | \(-0.867022\pi\) | ||
0.913999 | − | 0.405716i | \(-0.132978\pi\) | |||||||
\(740\) | 9.76053 | − | 9.05664i | 0.358804 | − | 0.332929i | ||||
\(741\) | 14.5488 | + | 19.7854i | 0.534463 | + | 0.726834i | ||||
\(742\) | −0.615792 | + | 26.7973i | −0.0226064 | + | 0.983760i | ||||
\(743\) | 7.61946 | − | 7.61946i | 0.279531 | − | 0.279531i | −0.553391 | − | 0.832922i | \(-0.686666\pi\) |
0.832922 | + | 0.553391i | \(0.186666\pi\) | |||||||
\(744\) | 14.6699 | − | 12.7752i | 0.537825 | − | 0.468362i | ||||
\(745\) | −24.5189 | + | 0.209925i | −0.898305 | + | 0.00769107i | ||||
\(746\) | 18.8197 | + | 19.7050i | 0.689040 | + | 0.721453i | ||||
\(747\) | 18.7612 | + | 18.7612i | 0.686438 | + | 0.686438i | ||||
\(748\) | 9.48134 | + | 10.3953i | 0.346672 | + | 0.380091i | ||||
\(749\) | −15.8971 | −0.580866 | ||||||||
\(750\) | −36.7325 | + | 36.9321i | −1.34128 | + | 1.34857i | ||||
\(751\) | − | 44.8924i | − | 1.63815i | −0.573687 | − | 0.819074i | \(-0.694488\pi\) | ||
0.573687 | − | 0.819074i | \(-0.305512\pi\) | |||||||
\(752\) | −10.9750 | − | 13.2033i | −0.400216 | − | 0.481474i | ||||
\(753\) | 41.2494 | − | 41.2494i | 1.50321 | − | 1.50321i | ||||
\(754\) | −6.36107 | + | 36.1187i | −0.231656 | + | 1.31536i | ||||
\(755\) | 39.4856 | − | 0.338066i | 1.43703 | − | 0.0123035i | ||||
\(756\) | 89.0446 | + | 4.09459i | 3.23852 | + | 0.148919i | ||||
\(757\) | 23.9690 | + | 23.9690i | 0.871169 | + | 0.871169i | 0.992600 | − | 0.121431i | \(-0.0387483\pi\) |
−0.121431 | + | 0.992600i | \(0.538748\pi\) | |||||||
\(758\) | −37.5912 | − | 0.863833i | −1.36538 | − | 0.0313758i | ||||
\(759\) | − | 13.9030i | − | 0.504647i | ||||||
\(760\) | 13.0526 | + | 0.788879i | 0.473466 | + | 0.0286156i | ||||
\(761\) | 38.3827i | 1.39137i | 0.718347 | + | 0.695685i | \(0.244899\pi\) | ||||
−0.718347 | + | 0.695685i | \(0.755101\pi\) | |||||||
\(762\) | −1.66704 | + | 72.5442i | −0.0603904 | + | 2.62800i | ||||
\(763\) | 26.1974 | + | 26.1974i | 0.948410 | + | 0.948410i | ||||
\(764\) | −1.27845 | + | 27.8023i | −0.0462527 | + | 1.00585i | ||||
\(765\) | −31.3126 | + | 31.8534i | −1.13211 | + | 1.15166i | ||||
\(766\) | −11.1056 | − | 11.6280i | −0.401262 | − | 0.420137i | ||||
\(767\) | −34.4051 | − | 5.24742i | −1.24229 | − | 0.189473i | ||||
\(768\) | 29.8318 | + | 43.4562i | 1.07646 | + | 1.56809i | ||||
\(769\) | −22.2289 | −0.801594 | −0.400797 | − | 0.916167i | \(-0.631267\pi\) | ||||
−0.400797 | + | 0.916167i | \(0.631267\pi\) | |||||||
\(770\) | −17.4863 | + | 16.9893i | −0.630163 | + | 0.612253i | ||||
\(771\) | 44.7774i | 1.61262i | ||||||||
\(772\) | −33.3470 | − | 36.5616i | −1.20018 | − | 1.31588i | ||||
\(773\) | 29.7075 | + | 29.7075i | 1.06850 | + | 1.06850i | 0.997474 | + | 0.0710290i | \(0.0226283\pi\) |
0.0710290 | + | 0.997474i | \(0.477372\pi\) | |||||||
\(774\) | −14.9094 | − | 15.6107i | −0.535906 | − | 0.561116i | ||||
\(775\) | −10.4368 | + | 0.178728i | −0.374902 | + | 0.00642011i | ||||
\(776\) | −14.0079 | − | 16.0854i | −0.502855 | − | 0.577434i | ||||
\(777\) | 19.3346 | + | 19.3346i | 0.693626 | + | 0.693626i | ||||
\(778\) | 21.7526 | + | 0.499867i | 0.779870 | + | 0.0179211i | ||||
\(779\) | 4.28714 | 0.153603 | ||||||||
\(780\) | 43.9423 | − | 29.8473i | 1.57339 | − | 1.06871i | ||||
\(781\) | −10.4164 | −0.372729 | ||||||||
\(782\) | 5.48782 | + | 0.126108i | 0.196244 | + | 0.00450962i | ||||
\(783\) | 81.3115 | + | 81.3115i | 2.90584 | + | 2.90584i | ||||
\(784\) | −0.283145 | + | 3.07226i | −0.0101123 | + | 0.109724i | ||||
\(785\) | 30.7377 | + | 30.2159i | 1.09708 | + | 1.07845i | ||||
\(786\) | −0.374470 | − | 0.392085i | −0.0133569 | − | 0.0139852i | ||||
\(787\) | −29.9253 | − | 29.9253i | −1.06672 | − | 1.06672i | −0.997609 | − | 0.0691119i | \(-0.977983\pi\) |
−0.0691119 | − | 0.997609i | \(-0.522017\pi\) | |||||||
\(788\) | 3.07023 | − | 2.80028i | 0.109372 | − | 0.0997559i | ||||
\(789\) | − | 2.06356i | − | 0.0734646i | ||||||
\(790\) | −0.153398 | + | 10.6415i | −0.00545766 | + | 0.378609i | ||||
\(791\) | −32.5652 | −1.15788 | ||||||||
\(792\) | −61.2837 | − | 4.23079i | −2.17762 | − | 0.150335i | ||||
\(793\) | 3.71689 | − | 24.3700i | 0.131990 | − | 0.865404i | ||||
\(794\) | −1.17443 | − | 1.22967i | −0.0416789 | − | 0.0436395i | ||||
\(795\) | 50.0827 | − | 0.428797i | 1.77625 | − | 0.0152078i | ||||
\(796\) | 25.1965 | + | 1.15862i | 0.893066 | + | 0.0410663i | ||||
\(797\) | 23.3434 | + | 23.3434i | 0.826866 | + | 0.826866i | 0.987082 | − | 0.160216i | \(-0.0512190\pi\) |
−0.160216 | + | 0.987082i | \(0.551219\pi\) | |||||||
\(798\) | −0.616913 | + | 26.8461i | −0.0218385 | + | 0.950341i | ||||
\(799\) | 10.9181i | 0.386256i | ||||||||
\(800\) | 2.76052 | − | 28.1492i | 0.0975992 | − | 0.995226i | ||||
\(801\) | − | 26.6685i | − | 0.942284i | ||||||
\(802\) | 2.93146 | + | 0.0673638i | 0.103513 | + | 0.00237870i | ||||
\(803\) | −0.631887 | − | 0.631887i | −0.0222988 | − | 0.0222988i | ||||
\(804\) | 4.50745 | − | 98.0232i | 0.158966 | − | 3.45701i | ||||
\(805\) | 0.0814362 | + | 9.51161i | 0.00287025 | + | 0.335240i | ||||
\(806\) | 10.4837 | + | 1.84635i | 0.369274 | + | 0.0650349i | ||||
\(807\) | −46.5080 | + | 46.5080i | −1.63716 | + | 1.63716i | ||||
\(808\) | −0.527650 | + | 7.64311i | −0.0185627 | + | 0.268884i | ||||
\(809\) | − | 33.0140i | − | 1.16071i | −0.814364 | − | 0.580355i | \(-0.802914\pi\) | ||
0.814364 | − | 0.580355i | \(-0.197086\pi\) | |||||||
\(810\) | 1.32687 | − | 92.0476i | 0.0466214 | − | 3.23422i | ||||
\(811\) | 6.20729 | 0.217967 | 0.108984 | − | 0.994044i | \(-0.465240\pi\) | ||||
0.108984 | + | 0.994044i | \(0.465240\pi\) | |||||||
\(812\) | −29.6283 | + | 27.0232i | −1.03975 | + | 0.948330i | ||||
\(813\) | −45.7059 | − | 45.7059i | −1.60298 | − | 1.60298i | ||||
\(814\) | −8.04289 | − | 8.42123i | −0.281903 | − | 0.295164i | ||||
\(815\) | 9.97767 | − | 10.1500i | 0.349503 | − | 0.355539i | ||||
\(816\) | 3.07619 | − | 33.3781i | 0.107688 | − | 1.16847i | ||||
\(817\) | 2.84168 | − | 2.84168i | 0.0994179 | − | 0.0994179i | ||||
\(818\) | 0.184267 | − | 8.01871i | 0.00644274 | − | 0.280368i | ||||
\(819\) | 46.7604 | + | 63.5911i | 1.63394 | + | 2.22205i | ||||
\(820\) | 0.346637 | − | 9.26662i | 0.0121051 | − | 0.323604i | ||||
\(821\) | 33.2987i | 1.16213i | 0.813856 | + | 0.581067i | \(0.197364\pi\) | ||||
−0.813856 | + | 0.581067i | \(0.802636\pi\) | |||||||
\(822\) | 1.72236 | − | 74.9517i | 0.0600742 | − | 2.61424i | ||||
\(823\) | −24.2581 | − | 24.2581i | −0.845585 | − | 0.845585i | 0.143994 | − | 0.989579i | \(-0.454005\pi\) |
−0.989579 | + | 0.143994i | \(0.954005\pi\) | |||||||
\(824\) | 7.06608 | − | 6.15345i | 0.246159 | − | 0.214366i | ||||
\(825\) | 32.7594 | + | 31.6563i | 1.14054 | + | 1.10213i | ||||
\(826\) | −26.2833 | − | 27.5197i | −0.914514 | − | 0.957533i | ||||
\(827\) | 34.2425 | + | 34.2425i | 1.19073 | + | 1.19073i | 0.976863 | + | 0.213864i | \(0.0686050\pi\) |
0.213864 | + | 0.976863i | \(0.431395\pi\) | |||||||
\(828\) | −17.7075 | + | 16.1506i | −0.615377 | + | 0.561270i | ||||
\(829\) | 4.60028i | 0.159774i | 0.996804 | + | 0.0798872i | \(0.0254560\pi\) | ||||
−0.996804 | + | 0.0798872i | \(0.974544\pi\) | |||||||
\(830\) | 7.44514 | + | 7.66293i | 0.258425 | + | 0.265984i | ||||
\(831\) | − | 12.6408i | − | 0.438506i | ||||||
\(832\) | −8.22617 | + | 27.6465i | −0.285191 | + | 0.958471i | ||||
\(833\) | 1.38734 | − | 1.38734i | 0.0480684 | − | 0.0480684i | ||||
\(834\) | 47.0889 | − | 44.9733i | 1.63055 | − | 1.55730i | ||||
\(835\) | −15.9302 | − | 15.6597i | −0.551286 | − | 0.541926i | ||||
\(836\) | 0.525323 | − | 11.4242i | 0.0181687 | − | 0.395113i | ||||
\(837\) | 23.6013 | − | 23.6013i | 0.815781 | − | 0.815781i | ||||
\(838\) | 0.620751 | − | 27.0131i | 0.0214435 | − | 0.933153i | ||||
\(839\) | 55.0950i | 1.90209i | 0.309049 | + | 0.951046i | \(0.399989\pi\) | ||||
−0.309049 | + | 0.951046i | \(0.600011\pi\) | |||||||
\(840\) | 57.9777 | + | 3.50409i | 2.00042 | + | 0.120903i | ||||
\(841\) | −22.7316 | −0.783848 | ||||||||
\(842\) | −28.7419 | − | 0.660478i | −0.990512 | − | 0.0227616i | ||||
\(843\) | 25.0846 | − | 25.0846i | 0.863960 | − | 0.863960i | ||||
\(844\) | −0.173616 | + | 3.77562i | −0.00597612 | + | 0.129962i | ||||
\(845\) | 27.8204 | + | 8.42766i | 0.957051 | + | 0.289920i | ||||
\(846\) | −32.9240 | − | 34.4728i | −1.13195 | − | 1.18520i | ||||
\(847\) | −6.60602 | − | 6.60602i | −0.226985 | − | 0.226985i | ||||
\(848\) | −20.9141 | + | 17.3844i | −0.718193 | + | 0.596984i | ||||
\(849\) | 42.9612i | 1.47442i | ||||||||
\(850\) | −12.7926 | + | 12.6437i | −0.438783 | + | 0.433677i | ||||
\(851\) | −4.54324 | −0.155740 | ||||||||
\(852\) | 16.7229 | + | 18.3350i | 0.572917 | + | 0.628146i | ||||
\(853\) | 14.2077 | + | 14.2077i | 0.486464 | + | 0.486464i | 0.907188 | − | 0.420724i | \(-0.138224\pi\) |
−0.420724 | + | 0.907188i | \(0.638224\pi\) | |||||||
\(854\) | 19.4929 | − | 18.6172i | 0.667034 | − | 0.637066i | ||||
\(855\) | 36.3048 | − | 0.310833i | 1.24160 | − | 0.0106303i | ||||
\(856\) | −10.5925 | − | 12.1635i | −0.362046 | − | 0.415741i | ||||
\(857\) | 21.8873 | + | 21.8873i | 0.747654 | + | 0.747654i | 0.974038 | − | 0.226384i | \(-0.0726903\pi\) |
−0.226384 | + | 0.974038i | \(0.572690\pi\) | |||||||
\(858\) | −26.6548 | − | 38.0504i | −0.909980 | − | 1.29902i | ||||
\(859\) | −12.7489 | −0.434987 | −0.217494 | − | 0.976062i | \(-0.569788\pi\) | ||||
−0.217494 | + | 0.976062i | \(0.569788\pi\) | |||||||
\(860\) | −5.91251 | − | 6.37204i | −0.201615 | − | 0.217285i | ||||
\(861\) | 19.0429 | 0.648980 | ||||||||
\(862\) | −1.11624 | + | 48.5754i | −0.0380194 | + | 1.65448i | ||||
\(863\) | 10.9472 | − | 10.9472i | 0.372647 | − | 0.372647i | −0.495794 | − | 0.868440i | \(-0.665123\pi\) |
0.868440 | + | 0.495794i | \(0.165123\pi\) | |||||||
\(864\) | 56.1993 | + | 70.8602i | 1.91194 | + | 2.41071i | ||||
\(865\) | −5.63131 | + | 5.72857i | −0.191470 | + | 0.194777i | ||||
\(866\) | −28.9962 | − | 30.3602i | −0.985331 | − | 1.03168i | ||||
\(867\) | 24.5288 | − | 24.5288i | 0.833042 | − | 0.833042i | ||||
\(868\) | 7.84371 | + | 8.59985i | 0.266233 | + | 0.291898i | ||||
\(869\) | 9.30775 | 0.315744 | ||||||||
\(870\) | 52.2141 | + | 53.7414i | 1.77022 | + | 1.82200i | ||||
\(871\) | 43.2607 | − | 31.8108i | 1.46583 | − | 1.07787i | ||||
\(872\) | −2.58890 | + | 37.5006i | −0.0876711 | + | 1.26993i | ||||
\(873\) | −41.8760 | − | 41.8760i | −1.41729 | − | 1.41729i | ||||
\(874\) | −3.08166 | − | 3.22662i | −0.104239 | − | 0.109142i | ||||
\(875\) | −22.5975 | − | 21.4655i | −0.763935 | − | 0.725667i | ||||
\(876\) | −0.0977931 | + | 2.12670i | −0.00330412 | + | 0.0718545i | ||||
\(877\) | −12.5512 | + | 12.5512i | −0.423825 | + | 0.423825i | −0.886519 | − | 0.462693i | \(-0.846883\pi\) |
0.462693 | + | 0.886519i | \(0.346883\pi\) | |||||||
\(878\) | 0.541628 | − | 23.5699i | 0.0182791 | − | 0.795446i | ||||
\(879\) | − | 7.79935i | − | 0.263066i | ||||||
\(880\) | −24.6507 | − | 2.05918i | −0.830977 | − | 0.0694150i | ||||
\(881\) | −24.6194 | −0.829449 | −0.414724 | − | 0.909947i | \(-0.636122\pi\) | ||||
−0.414724 | + | 0.909947i | \(0.636122\pi\) | |||||||
\(882\) | −0.196796 | + | 8.56392i | −0.00662645 | + | 0.288362i | ||||
\(883\) | −5.17226 | − | 5.17226i | −0.174060 | − | 0.174060i | 0.614700 | − | 0.788761i | \(-0.289277\pi\) |
−0.788761 | + | 0.614700i | \(0.789277\pi\) | |||||||
\(884\) | 15.2611 | − | 10.1761i | 0.513288 | − | 0.342260i | ||||
\(885\) | −49.8470 | + | 50.7080i | −1.67559 | + | 1.70453i | ||||
\(886\) | 31.3993 | − | 29.9886i | 1.05488 | − | 1.00749i | ||||
\(887\) | −4.95615 | + | 4.95615i | −0.166411 | + | 0.166411i | −0.785400 | − | 0.618989i | \(-0.787543\pi\) |
0.618989 | + | 0.785400i | \(0.287543\pi\) | |||||||
\(888\) | −1.91070 | + | 27.6768i | −0.0641189 | + | 0.928773i | ||||
\(889\) | −43.4184 | −1.45621 | ||||||||
\(890\) | 0.154786 | − | 10.7378i | 0.00518843 | − | 0.359932i | ||||
\(891\) | −80.5106 | −2.69721 | ||||||||
\(892\) | 35.4348 | − | 32.3192i | 1.18644 | − | 1.08213i | ||||
\(893\) | 6.27522 | − | 6.27522i | 0.209992 | − | 0.209992i | ||||
\(894\) | 36.9454 | − | 35.2856i | 1.23564 | − | 1.18013i | ||||
\(895\) | −0.394999 | + | 0.00338189i | −0.0132034 | + | 0.000113044i | ||||
\(896\) | −25.5852 | + | 18.4426i | −0.854741 | + | 0.616122i | ||||
\(897\) | −17.9181 | − | 2.73285i | −0.598267 | − | 0.0912471i | ||||
\(898\) | 1.01506 | − | 44.1721i | 0.0338729 | − | 1.47404i | ||||
\(899\) | 15.0155i | 0.500795i | ||||||||
\(900\) | 2.26356 | − | 78.4977i | 0.0754521 | − | 2.61659i | ||||
\(901\) | 17.2944 | 0.576160 | ||||||||
\(902\) | −8.10784 | − | 0.186315i | −0.269962 | − | 0.00620362i | ||||
\(903\) | 12.6224 | − | 12.6224i | 0.420046 | − | 0.420046i | ||||
\(904\) | −21.6988 | − | 24.9170i | −0.721693 | − | 0.828728i | ||||
\(905\) | −30.4328 | + | 0.260558i | −1.01162 | + | 0.00866125i | ||||
\(906\) | −59.4973 | + | 56.8243i | −1.97667 | + | 1.88786i | ||||
\(907\) | −19.1464 | + | 19.1464i | −0.635747 | + | 0.635747i | −0.949503 | − | 0.313757i | \(-0.898412\pi\) |
0.313757 | + | 0.949503i | \(0.398412\pi\) | |||||||
\(908\) | 22.6880 | + | 24.8751i | 0.752928 | + | 0.825510i | ||||
\(909\) | 21.2714i | 0.705526i | ||||||||
\(910\) | 18.4585 | + | 25.8757i | 0.611895 | + | 0.857772i | ||||
\(911\) | − | 7.23745i | − | 0.239787i | −0.992787 | − | 0.119894i | \(-0.961745\pi\) | ||
0.992787 | − | 0.119894i | \(-0.0382554\pi\) | |||||||
\(912\) | −20.9522 | + | 17.4161i | −0.693795 | + | 0.576703i | ||||
\(913\) | 6.60723 | − | 6.60723i | 0.218667 | − | 0.218667i | ||||
\(914\) | 30.9545 | + | 32.4106i | 1.02388 | + | 1.07205i | ||||
\(915\) | −35.9178 | − | 35.3080i | −1.18741 | − | 1.16725i | ||||
\(916\) | 22.6718 | + | 1.04253i | 0.749096 | + | 0.0344461i | ||||
\(917\) | 0.229395 | − | 0.229395i | 0.00757530 | − | 0.00757530i | ||||
\(918\) | 1.32128 | − | 57.4978i | 0.0436087 | − | 1.89771i | ||||
\(919\) | −10.7419 | −0.354342 | −0.177171 | − | 0.984180i | \(-0.556695\pi\) | ||||
−0.177171 | + | 0.984180i | \(0.556695\pi\) | |||||||
\(920\) | −7.22348 | + | 6.40009i | −0.238151 | + | 0.211005i | ||||
\(921\) | − | 91.5490i | − | 3.01664i | ||||||
\(922\) | −21.0963 | − | 0.484785i | −0.694770 | − | 0.0159656i | ||||
\(923\) | −2.04751 | + | 13.4246i | −0.0673946 | + | 0.441877i | ||||
\(924\) | 2.33341 | − | 50.7446i | 0.0767637 | − | 1.66937i | ||||
\(925\) | 10.3447 | − | 10.7052i | 0.340131 | − | 0.351984i | ||||
\(926\) | 17.3369 | + | 18.1525i | 0.569728 | + | 0.596528i | ||||
\(927\) | 18.3955 | − | 18.3955i | 0.604187 | − | 0.604187i | ||||
\(928\) | −40.4186 | − | 4.66373i | −1.32680 | − | 0.153095i | ||||
\(929\) | −8.77452 | −0.287883 | −0.143941 | − | 0.989586i | \(-0.545978\pi\) | ||||
−0.143941 | + | 0.989586i | \(0.545978\pi\) | |||||||
\(930\) | 15.5989 | − | 15.1555i | 0.511507 | − | 0.496970i | ||||
\(931\) | −1.59475 | −0.0522658 | ||||||||
\(932\) | 29.0591 | − | 26.5041i | 0.951863 | − | 0.868172i | ||||
\(933\) | −78.5193 | + | 78.5193i | −2.57061 | + | 2.57061i | ||||
\(934\) | 19.7422 | + | 20.6709i | 0.645985 | + | 0.676373i | ||||
\(935\) | 11.2180 | + | 11.0275i | 0.366867 | + | 0.360638i | ||||
\(936\) | −17.4989 | + | 78.1504i | −0.571968 | + | 2.55443i | ||||
\(937\) | 32.7992 | + | 32.7992i | 1.07150 | + | 1.07150i | 0.997238 | + | 0.0742661i | \(0.0236614\pi\) |
0.0742661 | + | 0.997238i | \(0.476339\pi\) | |||||||
\(938\) | 58.6989 | + | 1.34888i | 1.91659 | + | 0.0440424i | ||||
\(939\) | −66.7158 | −2.17719 | ||||||||
\(940\) | −13.0565 | − | 14.0712i | −0.425855 | − | 0.458953i | ||||
\(941\) | − | 19.2482i | − | 0.627473i | −0.949510 | − | 0.313736i | \(-0.898419\pi\) | ||
0.949510 | − | 0.313736i | \(-0.101581\pi\) | |||||||
\(942\) | −89.7824 | − | 2.06317i | −2.92527 | − | 0.0672216i | ||||
\(943\) | −2.23734 | + | 2.23734i | −0.0728579 | + | 0.0728579i | ||||
\(944\) | 3.54339 | − | 38.4474i | 0.115328 | − | 1.25136i | ||||
\(945\) | 99.6565 | − | 0.853235i | 3.24182 | − | 0.0277557i | ||||
\(946\) | −5.49769 | + | 5.25070i | −0.178745 | + | 0.170715i | ||||
\(947\) | 6.83224 | + | 6.83224i | 0.222018 | + | 0.222018i | 0.809348 | − | 0.587330i | \(-0.199821\pi\) |
−0.587330 | + | 0.809348i | \(0.699821\pi\) | |||||||
\(948\) | −14.9430 | − | 16.3835i | −0.485326 | − | 0.532111i | ||||
\(949\) | −0.938578 | + | 0.690164i | −0.0304675 | + | 0.0224037i | ||||
\(950\) | 14.6196 | + | 0.0855617i | 0.474322 | + | 0.00277599i | ||||
\(951\) | −89.3864 | −2.89855 | ||||||||
\(952\) | 20.0088 | + | 1.38133i | 0.648491 | + | 0.0447693i | ||||
\(953\) | 15.3847 | − | 15.3847i | 0.498360 | − | 0.498360i | −0.412567 | − | 0.910927i | \(-0.635368\pi\) |
0.910927 | + | 0.412567i | \(0.135368\pi\) | |||||||
\(954\) | −54.6051 | + | 52.1519i | −1.76791 | + | 1.68848i | ||||
\(955\) | 0.266405 | + | 31.1157i | 0.00862066 | + | 1.00688i | ||||
\(956\) | 1.34639 | − | 29.2799i | 0.0435455 | − | 0.946981i | ||||
\(957\) | 46.3376 | − | 46.3376i | 1.49788 | − | 1.49788i | ||||
\(958\) | 0.555489 | + | 0.0127649i | 0.0179470 | + | 0.000412416i | ||||
\(959\) | 44.8593 | 1.44858 | ||||||||
\(960\) | 35.9506 | + | 46.6961i | 1.16030 | + | 1.50711i | ||||
\(961\) | −26.6416 | −0.859407 | ||||||||
\(962\) | −12.4342 | + | 8.71030i | −0.400894 | + | 0.280831i | ||||
\(963\) | −31.6659 | − | 31.6659i | −1.02042 | − | 1.02042i | ||||
\(964\) | −2.01581 | + | 43.8376i | −0.0649247 | + | 1.41191i | ||||
\(965\) | −39.4549 | − | 38.7850i | −1.27010 | − | 1.24853i | ||||
\(966\) | −13.6883 | − | 14.3322i | −0.440414 | − | 0.461131i | ||||
\(967\) | 8.30264 | + | 8.30264i | 0.266995 | + | 0.266995i | 0.827888 | − | 0.560893i | \(-0.189542\pi\) |
−0.560893 | + | 0.827888i | \(0.689542\pi\) | |||||||
\(968\) | 0.652824 | − | 9.45627i | 0.0209826 | − | 0.303936i | ||||
\(969\) | 17.3259 | 0.556588 | ||||||||
\(970\) | −16.6179 | − | 17.1040i | −0.533570 | − | 0.549177i | ||||
\(971\) | 18.4848i | 0.593205i | 0.955001 | + | 0.296603i | \(0.0958537\pi\) | ||||
−0.955001 | + | 0.296603i | \(0.904146\pi\) | |||||||
\(972\) | 64.6113 | + | 70.8399i | 2.07241 | + | 2.27219i | ||||
\(973\) | 27.5501 | + | 27.5501i | 0.883215 | + | 0.883215i | ||||
\(974\) | 12.6755 | − | 12.1060i | 0.406150 | − | 0.387902i | ||||
\(975\) | 47.2378 | − | 35.9976i | 1.51282 | − | 1.15285i | ||||
\(976\) | 27.2333 | + | 2.50988i | 0.871717 | + | 0.0803392i | ||||
\(977\) | −2.64245 | + | 2.64245i | −0.0845395 | + | 0.0845395i | −0.748112 | − | 0.663572i | \(-0.769039\pi\) |
0.663572 | + | 0.748112i | \(0.269039\pi\) | |||||||
\(978\) | −0.681284 | + | 29.6473i | −0.0217851 | + | 0.948017i | ||||
\(979\) | −9.39195 | −0.300168 | ||||||||
\(980\) | −0.128943 | + | 3.44704i | −0.00411895 | + | 0.110112i | ||||
\(981\) | 104.367i | 3.33218i | ||||||||
\(982\) | 3.49678 | + | 0.0803547i | 0.111587 | + | 0.00256422i | ||||
\(983\) | −2.55748 | + | 2.55748i | −0.0815708 | + | 0.0815708i | −0.746715 | − | 0.665144i | \(-0.768370\pi\) |
0.665144 | + | 0.746715i | \(0.268370\pi\) | |||||||
\(984\) | 12.6887 | + | 14.5705i | 0.404500 | + | 0.464492i | ||||
\(985\) | 3.25694 | − | 3.31319i | 0.103775 | − | 0.105567i | ||||
\(986\) | 17.8702 | + | 18.7108i | 0.569103 | + | 0.595873i | ||||
\(987\) | 27.8737 | − | 27.8737i | 0.887230 | − | 0.887230i | ||||
\(988\) | −14.6201 | − | 2.92262i | −0.465128 | − | 0.0929811i | ||||
\(989\) | 2.96600i | 0.0943132i | ||||||||
\(990\) | −68.6732 | − | 0.989926i | −2.18258 | − | 0.0314619i | ||||
\(991\) | 4.79719i | 0.152388i | 0.997093 | + | 0.0761939i | \(0.0242768\pi\) | ||||
−0.997093 | + | 0.0761939i | \(0.975723\pi\) | |||||||
\(992\) | −1.35369 | + | 11.7318i | −0.0429796 | + | 0.372485i | ||||
\(993\) | 31.9927 | + | 31.9927i | 1.01526 | + | 1.01526i | ||||
\(994\) | −10.7380 | + | 10.2556i | −0.340589 | + | 0.325287i | ||||
\(995\) | 28.1993 | − | 0.241435i | 0.893977 | − | 0.00765402i | ||||
\(996\) | −22.2375 | − | 1.02256i | −0.704622 | − | 0.0324010i | ||||
\(997\) | 24.0505 | + | 24.0505i | 0.761686 | + | 0.761686i | 0.976627 | − | 0.214941i | \(-0.0689560\pi\) |
−0.214941 | + | 0.976627i | \(0.568956\pi\) | |||||||
\(998\) | −24.8883 | − | 0.571923i | −0.787824 | − | 0.0181039i | ||||
\(999\) | 47.6011i | 1.50603i |
(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 | 260.2.p.d.207.17 | yes | 64 | |
4.3 | odd | 2 | inner | 260.2.p.d.207.32 | yes | 64 | |
5.3 | odd | 4 | inner | 260.2.p.d.103.1 | ✓ | 64 | |
13.12 | even | 2 | inner | 260.2.p.d.207.16 | yes | 64 | |
20.3 | even | 4 | inner | 260.2.p.d.103.16 | yes | 64 | |
52.51 | odd | 2 | inner | 260.2.p.d.207.1 | yes | 64 | |
65.38 | odd | 4 | inner | 260.2.p.d.103.32 | yes | 64 | |
260.103 | even | 4 | inner | 260.2.p.d.103.17 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.p.d.103.1 | ✓ | 64 | 5.3 | odd | 4 | inner | |
260.2.p.d.103.16 | yes | 64 | 20.3 | even | 4 | inner | |
260.2.p.d.103.17 | yes | 64 | 260.103 | even | 4 | inner | |
260.2.p.d.103.32 | yes | 64 | 65.38 | odd | 4 | inner | |
260.2.p.d.207.1 | yes | 64 | 52.51 | odd | 2 | inner | |
260.2.p.d.207.16 | yes | 64 | 13.12 | even | 2 | inner | |
260.2.p.d.207.17 | yes | 64 | 1.1 | even | 1 | trivial | |
260.2.p.d.207.32 | yes | 64 | 4.3 | odd | 2 | inner |