Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(191,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.u (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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 191.5 | ||
Character | \(\chi\) | \(=\) | 1110.191 |
Dual form | 1110.2.u.e.401.5 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | −1.08352 | − | 1.35129i | −0.625571 | − | 0.780167i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −0.707107 | + | 0.707107i | −0.316228 | + | 0.316228i | ||||
\(6\) | −0.189341 | + | 1.72167i | −0.0772983 | + | 0.702869i | ||||
\(7\) | −3.77650 | −1.42738 | −0.713691 | − | 0.700461i | \(-0.752978\pi\) | ||||
−0.713691 | + | 0.700461i | \(0.752978\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | −0.651967 | + | 2.92830i | −0.217322 | + | 0.976100i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 1.81549 | 0.547391 | 0.273696 | − | 0.961816i | \(-0.411754\pi\) | ||||
0.273696 | + | 0.961816i | \(0.411754\pi\) | |||||||
\(12\) | 1.35129 | − | 1.08352i | 0.390084 | − | 0.312785i | ||||
\(13\) | −3.90798 | − | 3.90798i | −1.08388 | − | 1.08388i | −0.996144 | − | 0.0877350i | \(-0.972037\pi\) |
−0.0877350 | − | 0.996144i | \(-0.527963\pi\) | |||||||
\(14\) | 2.67039 | + | 2.67039i | 0.713691 | + | 0.713691i | ||||
\(15\) | 1.72167 | + | 0.189341i | 0.444533 | + | 0.0488878i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −1.04463 | + | 1.04463i | −0.253360 | + | 0.253360i | −0.822347 | − | 0.568987i | \(-0.807336\pi\) |
0.568987 | + | 0.822347i | \(0.307336\pi\) | |||||||
\(18\) | 2.53163 | − | 1.60961i | 0.596711 | − | 0.379389i | ||||
\(19\) | −1.01091 | − | 1.01091i | −0.231918 | − | 0.231918i | 0.581575 | − | 0.813493i | \(-0.302437\pi\) |
−0.813493 | + | 0.581575i | \(0.802437\pi\) | |||||||
\(20\) | −0.707107 | − | 0.707107i | −0.158114 | − | 0.158114i | ||||
\(21\) | 4.09191 | + | 5.10314i | 0.892928 | + | 1.11360i | ||||
\(22\) | −1.28375 | − | 1.28375i | −0.273696 | − | 0.273696i | ||||
\(23\) | −5.79126 | + | 5.79126i | −1.20756 | + | 1.20756i | −0.235746 | + | 0.971815i | \(0.575753\pi\) |
−0.971815 | + | 0.235746i | \(0.924247\pi\) | |||||||
\(24\) | −1.72167 | − | 0.189341i | −0.351435 | − | 0.0386492i | ||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | 5.52672i | 1.08388i | ||||||||
\(27\) | 4.66340 | − | 2.29188i | 0.897472 | − | 0.441072i | ||||
\(28\) | − | 3.77650i | − | 0.713691i | ||||||
\(29\) | 3.80924 | + | 3.80924i | 0.707359 | + | 0.707359i | 0.965979 | − | 0.258620i | \(-0.0832678\pi\) |
−0.258620 | + | 0.965979i | \(0.583268\pi\) | |||||||
\(30\) | −1.08352 | − | 1.35129i | −0.197823 | − | 0.246711i | ||||
\(31\) | 4.46840 | − | 4.46840i | 0.802548 | − | 0.802548i | −0.180945 | − | 0.983493i | \(-0.557916\pi\) |
0.983493 | + | 0.180945i | \(0.0579156\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | −1.96712 | − | 2.45325i | −0.342432 | − | 0.427057i | ||||
\(34\) | 1.47733 | 0.253360 | ||||||||
\(35\) | 2.67039 | − | 2.67039i | 0.451378 | − | 0.451378i | ||||
\(36\) | −2.92830 | − | 0.651967i | −0.488050 | − | 0.108661i | ||||
\(37\) | 5.83886 | + | 1.70519i | 0.959903 | + | 0.280332i | ||||
\(38\) | 1.42964i | 0.231918i | ||||||||
\(39\) | −1.04644 | + | 9.51519i | −0.167564 | + | 1.52365i | ||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | 9.74155 | 1.52138 | 0.760688 | − | 0.649118i | \(-0.224862\pi\) | ||||
0.760688 | + | 0.649118i | \(0.224862\pi\) | |||||||
\(42\) | 0.715047 | − | 6.50188i | 0.110334 | − | 1.00326i | ||||
\(43\) | 6.17939 | + | 6.17939i | 0.942348 | + | 0.942348i | 0.998426 | − | 0.0560783i | \(-0.0178596\pi\) |
−0.0560783 | + | 0.998426i | \(0.517860\pi\) | |||||||
\(44\) | 1.81549i | 0.273696i | ||||||||
\(45\) | −1.60961 | − | 2.53163i | −0.239946 | − | 0.377393i | ||||
\(46\) | 8.19007 | 1.20756 | ||||||||
\(47\) | − | 7.59431i | − | 1.10774i | −0.832602 | − | 0.553872i | \(-0.813150\pi\) | ||
0.832602 | − | 0.553872i | \(-0.186850\pi\) | |||||||
\(48\) | 1.08352 | + | 1.35129i | 0.156393 | + | 0.195042i | ||||
\(49\) | 7.26192 | 1.03742 | ||||||||
\(50\) | −0.707107 | + | 0.707107i | −0.100000 | + | 0.100000i | ||||
\(51\) | 2.54347 | + | 0.279720i | 0.356157 | + | 0.0391686i | ||||
\(52\) | 3.90798 | − | 3.90798i | 0.541939 | − | 0.541939i | ||||
\(53\) | 1.46832i | 0.201689i | 0.994902 | + | 0.100844i | \(0.0321544\pi\) | ||||
−0.994902 | + | 0.100844i | \(0.967846\pi\) | |||||||
\(54\) | −4.91812 | − | 1.67692i | −0.669272 | − | 0.228200i | ||||
\(55\) | −1.28375 | + | 1.28375i | −0.173100 | + | 0.173100i | ||||
\(56\) | −2.67039 | + | 2.67039i | −0.356845 | + | 0.356845i | ||||
\(57\) | −0.270690 | + | 2.46137i | −0.0358537 | + | 0.326016i | ||||
\(58\) | − | 5.38709i | − | 0.707359i | ||||||
\(59\) | −3.27282 | + | 3.27282i | −0.426084 | + | 0.426084i | −0.887292 | − | 0.461208i | \(-0.847416\pi\) |
0.461208 | + | 0.887292i | \(0.347416\pi\) | |||||||
\(60\) | −0.189341 | + | 1.72167i | −0.0244439 | + | 0.222267i | ||||
\(61\) | −0.251587 | + | 0.251587i | −0.0322125 | + | 0.0322125i | −0.723030 | − | 0.690817i | \(-0.757251\pi\) |
0.690817 | + | 0.723030i | \(0.257251\pi\) | |||||||
\(62\) | −6.31927 | −0.802548 | ||||||||
\(63\) | 2.46215 | − | 11.0587i | 0.310202 | − | 1.39327i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 5.52672 | 0.685505 | ||||||||
\(66\) | −0.343748 | + | 3.12568i | −0.0423124 | + | 0.384744i | ||||
\(67\) | 1.79916i | 0.219802i | 0.993943 | + | 0.109901i | \(0.0350534\pi\) | ||||
−0.993943 | + | 0.109901i | \(0.964947\pi\) | |||||||
\(68\) | −1.04463 | − | 1.04463i | −0.126680 | − | 0.126680i | ||||
\(69\) | 14.1006 | + | 1.55072i | 1.69751 | + | 0.186685i | ||||
\(70\) | −3.77650 | −0.451378 | ||||||||
\(71\) | − | 14.5030i | − | 1.72119i | −0.509292 | − | 0.860594i | \(-0.670093\pi\) | ||
0.509292 | − | 0.860594i | \(-0.329907\pi\) | |||||||
\(72\) | 1.60961 | + | 2.53163i | 0.189694 | + | 0.298356i | ||||
\(73\) | 7.13983i | 0.835653i | 0.908527 | + | 0.417827i | \(0.137208\pi\) | ||||
−0.908527 | + | 0.417827i | \(0.862792\pi\) | |||||||
\(74\) | −2.92295 | − | 5.33445i | −0.339786 | − | 0.620118i | ||||
\(75\) | −1.35129 | + | 1.08352i | −0.156033 | + | 0.125114i | ||||
\(76\) | 1.01091 | − | 1.01091i | 0.115959 | − | 0.115959i | ||||
\(77\) | −6.85620 | −0.781336 | ||||||||
\(78\) | 7.46820 | − | 5.98831i | 0.845607 | − | 0.678043i | ||||
\(79\) | −8.05198 | − | 8.05198i | −0.905918 | − | 0.905918i | 0.0900218 | − | 0.995940i | \(-0.471306\pi\) |
−0.995940 | + | 0.0900218i | \(0.971306\pi\) | |||||||
\(80\) | 0.707107 | − | 0.707107i | 0.0790569 | − | 0.0790569i | ||||
\(81\) | −8.14988 | − | 3.81831i | −0.905542 | − | 0.424257i | ||||
\(82\) | −6.88832 | − | 6.88832i | −0.760688 | − | 0.760688i | ||||
\(83\) | − | 7.15345i | − | 0.785193i | −0.919711 | − | 0.392597i | \(-0.871577\pi\) | ||
0.919711 | − | 0.392597i | \(-0.128423\pi\) | |||||||
\(84\) | −5.10314 | + | 4.09191i | −0.556798 | + | 0.446464i | ||||
\(85\) | − | 1.47733i | − | 0.160239i | ||||||
\(86\) | − | 8.73898i | − | 0.942348i | ||||||
\(87\) | 1.02000 | − | 9.27479i | 0.109355 | − | 0.994361i | ||||
\(88\) | 1.28375 | − | 1.28375i | 0.136848 | − | 0.136848i | ||||
\(89\) | 7.47158 | + | 7.47158i | 0.791985 | + | 0.791985i | 0.981817 | − | 0.189831i | \(-0.0607941\pi\) |
−0.189831 | + | 0.981817i | \(0.560794\pi\) | |||||||
\(90\) | −0.651967 | + | 2.92830i | −0.0687234 | + | 0.308670i | ||||
\(91\) | 14.7585 | + | 14.7585i | 1.54711 | + | 1.54711i | ||||
\(92\) | −5.79126 | − | 5.79126i | −0.603780 | − | 0.603780i | ||||
\(93\) | −10.8797 | − | 1.19650i | −1.12817 | − | 0.124071i | ||||
\(94\) | −5.36999 | + | 5.36999i | −0.553872 | + | 0.553872i | ||||
\(95\) | 1.42964 | 0.146678 | ||||||||
\(96\) | 0.189341 | − | 1.72167i | 0.0193246 | − | 0.175717i | ||||
\(97\) | 3.22614 | + | 3.22614i | 0.327565 | + | 0.327565i | 0.851660 | − | 0.524095i | \(-0.175596\pi\) |
−0.524095 | + | 0.851660i | \(0.675596\pi\) | |||||||
\(98\) | −5.13495 | − | 5.13495i | −0.518709 | − | 0.518709i | ||||
\(99\) | −1.18364 | + | 5.31630i | −0.118960 | + | 0.534309i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −1.91970 | −0.191017 | −0.0955085 | − | 0.995429i | \(-0.530448\pi\) | ||||
−0.0955085 | + | 0.995429i | \(0.530448\pi\) | |||||||
\(102\) | −1.60072 | − | 1.99630i | −0.158494 | − | 0.197663i | ||||
\(103\) | 11.1661 | − | 11.1661i | 1.10022 | − | 1.10022i | 0.105842 | − | 0.994383i | \(-0.466246\pi\) |
0.994383 | − | 0.105842i | \(-0.0337537\pi\) | |||||||
\(104\) | −5.52672 | −0.541939 | ||||||||
\(105\) | −6.50188 | − | 0.715047i | −0.634519 | − | 0.0697815i | ||||
\(106\) | 1.03826 | − | 1.03826i | 0.100844 | − | 0.100844i | ||||
\(107\) | 16.4971i | 1.59484i | 0.603428 | + | 0.797418i | \(0.293801\pi\) | ||||
−0.603428 | + | 0.797418i | \(0.706199\pi\) | |||||||
\(108\) | 2.29188 | + | 4.66340i | 0.220536 | + | 0.448736i | ||||
\(109\) | 5.92062 | + | 5.92062i | 0.567093 | + | 0.567093i | 0.931313 | − | 0.364220i | \(-0.118664\pi\) |
−0.364220 | + | 0.931313i | \(0.618664\pi\) | |||||||
\(110\) | 1.81549 | 0.173100 | ||||||||
\(111\) | −4.02232 | − | 9.73761i | −0.381782 | − | 0.924253i | ||||
\(112\) | 3.77650 | 0.356845 | ||||||||
\(113\) | 7.61785 | + | 7.61785i | 0.716627 | + | 0.716627i | 0.967913 | − | 0.251286i | \(-0.0808534\pi\) |
−0.251286 | + | 0.967913i | \(0.580853\pi\) | |||||||
\(114\) | 1.93185 | − | 1.54904i | 0.180935 | − | 0.145081i | ||||
\(115\) | − | 8.19007i | − | 0.763728i | ||||||
\(116\) | −3.80924 | + | 3.80924i | −0.353679 | + | 0.353679i | ||||
\(117\) | 13.9916 | − | 8.89586i | 1.29353 | − | 0.822423i | ||||
\(118\) | 4.62846 | 0.426084 | ||||||||
\(119\) | 3.94504 | − | 3.94504i | 0.361641 | − | 0.361641i | ||||
\(120\) | 1.35129 | − | 1.08352i | 0.123355 | − | 0.0989114i | ||||
\(121\) | −7.70399 | −0.700363 | ||||||||
\(122\) | 0.355798 | 0.0322125 | ||||||||
\(123\) | −10.5552 | − | 13.1637i | −0.951728 | − | 1.18693i | ||||
\(124\) | 4.46840 | + | 4.46840i | 0.401274 | + | 0.401274i | ||||
\(125\) | 0.707107 | + | 0.707107i | 0.0632456 | + | 0.0632456i | ||||
\(126\) | −9.56069 | + | 6.07869i | −0.851734 | + | 0.541532i | ||||
\(127\) | 17.1125 | 1.51849 | 0.759245 | − | 0.650805i | \(-0.225568\pi\) | ||||
0.759245 | + | 0.650805i | \(0.225568\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 1.65465 | − | 15.0456i | 0.145684 | − | 1.32469i | ||||
\(130\) | −3.90798 | − | 3.90798i | −0.342753 | − | 0.342753i | ||||
\(131\) | −3.38184 | − | 3.38184i | −0.295473 | − | 0.295473i | 0.543765 | − | 0.839238i | \(-0.316998\pi\) |
−0.839238 | + | 0.543765i | \(0.816998\pi\) | |||||||
\(132\) | 2.45325 | − | 1.96712i | 0.213528 | − | 0.171216i | ||||
\(133\) | 3.81768 | + | 3.81768i | 0.331035 | + | 0.331035i | ||||
\(134\) | 1.27220 | − | 1.27220i | 0.109901 | − | 0.109901i | ||||
\(135\) | −1.67692 | + | 4.91812i | −0.144326 | + | 0.423285i | ||||
\(136\) | 1.47733i | 0.126680i | ||||||||
\(137\) | 4.14104i | 0.353793i | 0.984229 | + | 0.176896i | \(0.0566057\pi\) | ||||
−0.984229 | + | 0.176896i | \(0.943394\pi\) | |||||||
\(138\) | −8.87411 | − | 11.0672i | −0.755414 | − | 0.942099i | ||||
\(139\) | 1.38210i | 0.117229i | 0.998281 | + | 0.0586143i | \(0.0186682\pi\) | ||||
−0.998281 | + | 0.0586143i | \(0.981332\pi\) | |||||||
\(140\) | 2.67039 | + | 2.67039i | 0.225689 | + | 0.225689i | ||||
\(141\) | −10.2621 | + | 8.22859i | −0.864226 | + | 0.692972i | ||||
\(142\) | −10.2552 | + | 10.2552i | −0.860594 | + | 0.860594i | ||||
\(143\) | −7.09491 | − | 7.09491i | −0.593306 | − | 0.593306i | ||||
\(144\) | 0.651967 | − | 2.92830i | 0.0543306 | − | 0.244025i | ||||
\(145\) | −5.38709 | −0.447373 | ||||||||
\(146\) | 5.04862 | − | 5.04862i | 0.417827 | − | 0.417827i | ||||
\(147\) | −7.86844 | − | 9.81296i | −0.648978 | − | 0.809359i | ||||
\(148\) | −1.70519 | + | 5.83886i | −0.140166 | + | 0.479952i | ||||
\(149\) | 10.6466i | 0.872206i | 0.899897 | + | 0.436103i | \(0.143642\pi\) | ||||
−0.899897 | + | 0.436103i | \(0.856358\pi\) | |||||||
\(150\) | 1.72167 | + | 0.189341i | 0.140574 | + | 0.0154597i | ||||
\(151\) | − | 5.50361i | − | 0.447877i | −0.974603 | − | 0.223939i | \(-0.928108\pi\) | ||
0.974603 | − | 0.223939i | \(-0.0718915\pi\) | |||||||
\(152\) | −1.42964 | −0.115959 | ||||||||
\(153\) | −2.37792 | − | 3.74005i | −0.192244 | − | 0.302365i | ||||
\(154\) | 4.84806 | + | 4.84806i | 0.390668 | + | 0.390668i | ||||
\(155\) | 6.31927i | 0.507576i | ||||||||
\(156\) | −9.51519 | − | 1.04644i | −0.761825 | − | 0.0837820i | ||||
\(157\) | −12.5462 | −1.00130 | −0.500649 | − | 0.865650i | \(-0.666905\pi\) | ||||
−0.500649 | + | 0.865650i | \(0.666905\pi\) | |||||||
\(158\) | 11.3872i | 0.905918i | ||||||||
\(159\) | 1.98412 | − | 1.59095i | 0.157351 | − | 0.126171i | ||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 21.8707 | − | 21.8707i | 1.72365 | − | 1.72365i | ||||
\(162\) | 3.06288 | + | 8.46279i | 0.240643 | + | 0.664899i | ||||
\(163\) | 15.7971 | − | 15.7971i | 1.23732 | − | 1.23732i | 0.276233 | − | 0.961091i | \(-0.410914\pi\) |
0.961091 | − | 0.276233i | \(-0.0890863\pi\) | |||||||
\(164\) | 9.74155i | 0.760688i | ||||||||
\(165\) | 3.12568 | + | 0.343748i | 0.243334 | + | 0.0267607i | ||||
\(166\) | −5.05825 | + | 5.05825i | −0.392597 | + | 0.392597i | ||||
\(167\) | 1.29474 | − | 1.29474i | 0.100190 | − | 0.100190i | −0.655235 | − | 0.755425i | \(-0.727430\pi\) |
0.755425 | + | 0.655235i | \(0.227430\pi\) | |||||||
\(168\) | 6.50188 | + | 0.715047i | 0.501631 | + | 0.0551671i | ||||
\(169\) | 17.5446i | 1.34959i | ||||||||
\(170\) | −1.04463 | + | 1.04463i | −0.0801194 | + | 0.0801194i | ||||
\(171\) | 3.61932 | − | 2.30116i | 0.276776 | − | 0.175974i | ||||
\(172\) | −6.17939 | + | 6.17939i | −0.471174 | + | 0.471174i | ||||
\(173\) | 2.17732 | 0.165538 | 0.0827691 | − | 0.996569i | \(-0.473624\pi\) | ||||
0.0827691 | + | 0.996569i | \(0.473624\pi\) | |||||||
\(174\) | −7.27951 | + | 5.83702i | −0.551858 | + | 0.442503i | ||||
\(175\) | 3.77650i | 0.285476i | ||||||||
\(176\) | −1.81549 | −0.136848 | ||||||||
\(177\) | 7.96869 | + | 0.876360i | 0.598963 | + | 0.0658712i | ||||
\(178\) | − | 10.5664i | − | 0.791985i | ||||||
\(179\) | 1.96418 | + | 1.96418i | 0.146810 | + | 0.146810i | 0.776691 | − | 0.629881i | \(-0.216897\pi\) |
−0.629881 | + | 0.776691i | \(0.716897\pi\) | |||||||
\(180\) | 2.53163 | − | 1.60961i | 0.188697 | − | 0.119973i | ||||
\(181\) | 21.1962 | 1.57550 | 0.787749 | − | 0.615997i | \(-0.211247\pi\) | ||||
0.787749 | + | 0.615997i | \(0.211247\pi\) | |||||||
\(182\) | − | 20.8716i | − | 1.54711i | ||||||
\(183\) | 0.612567 | + | 0.0673674i | 0.0452823 | + | 0.00497994i | ||||
\(184\) | 8.19007i | 0.603780i | ||||||||
\(185\) | −5.33445 | + | 2.92295i | −0.392197 | + | 0.214899i | ||||
\(186\) | 6.84706 | + | 8.53917i | 0.502051 | + | 0.626122i | ||||
\(187\) | −1.89651 | + | 1.89651i | −0.138687 | + | 0.138687i | ||||
\(188\) | 7.59431 | 0.553872 | ||||||||
\(189\) | −17.6113 | + | 8.65526i | −1.28103 | + | 0.629577i | ||||
\(190\) | −1.01091 | − | 1.01091i | −0.0733389 | − | 0.0733389i | ||||
\(191\) | −17.7208 | + | 17.7208i | −1.28223 | + | 1.28223i | −0.342832 | + | 0.939397i | \(0.611386\pi\) |
−0.939397 | + | 0.342832i | \(0.888614\pi\) | |||||||
\(192\) | −1.35129 | + | 1.08352i | −0.0975209 | + | 0.0781963i | ||||
\(193\) | 13.8252 | + | 13.8252i | 0.995162 | + | 0.995162i | 0.999988 | − | 0.00482599i | \(-0.00153616\pi\) |
−0.00482599 | + | 0.999988i | \(0.501536\pi\) | |||||||
\(194\) | − | 4.56246i | − | 0.327565i | ||||||
\(195\) | −5.98831 | − | 7.46820i | −0.428832 | − | 0.534809i | ||||
\(196\) | 7.26192i | 0.518709i | ||||||||
\(197\) | 14.5766i | 1.03854i | 0.854610 | + | 0.519271i | \(0.173796\pi\) | ||||
−0.854610 | + | 0.519271i | \(0.826204\pi\) | |||||||
\(198\) | 4.59615 | − | 2.92223i | 0.326635 | − | 0.207674i | ||||
\(199\) | −5.37468 | + | 5.37468i | −0.381001 | + | 0.381001i | −0.871463 | − | 0.490462i | \(-0.836828\pi\) |
0.490462 | + | 0.871463i | \(0.336828\pi\) | |||||||
\(200\) | −0.707107 | − | 0.707107i | −0.0500000 | − | 0.0500000i | ||||
\(201\) | 2.43118 | − | 1.94942i | 0.171482 | − | 0.137502i | ||||
\(202\) | 1.35743 | + | 1.35743i | 0.0955085 | + | 0.0955085i | ||||
\(203\) | −14.3856 | − | 14.3856i | −1.00967 | − | 1.00967i | ||||
\(204\) | −0.279720 | + | 2.54347i | −0.0195843 | + | 0.178079i | ||||
\(205\) | −6.88832 | + | 6.88832i | −0.481101 | + | 0.481101i | ||||
\(206\) | −15.7912 | −1.10022 | ||||||||
\(207\) | −13.1828 | − | 20.7342i | −0.916270 | − | 1.44113i | ||||
\(208\) | 3.90798 | + | 3.90798i | 0.270970 | + | 0.270970i | ||||
\(209\) | −1.83529 | − | 1.83529i | −0.126950 | − | 0.126950i | ||||
\(210\) | 4.09191 | + | 5.10314i | 0.282369 | + | 0.352150i | ||||
\(211\) | −9.97747 | −0.686877 | −0.343439 | − | 0.939175i | \(-0.611592\pi\) | ||||
−0.343439 | + | 0.939175i | \(0.611592\pi\) | |||||||
\(212\) | −1.46832 | −0.100844 | ||||||||
\(213\) | −19.5977 | + | 15.7143i | −1.34281 | + | 1.07672i | ||||
\(214\) | 11.6652 | − | 11.6652i | 0.797418 | − | 0.797418i | ||||
\(215\) | −8.73898 | −0.595993 | ||||||||
\(216\) | 1.67692 | − | 4.91812i | 0.114100 | − | 0.334636i | ||||
\(217\) | −16.8749 | + | 16.8749i | −1.14554 | + | 1.14554i | ||||
\(218\) | − | 8.37303i | − | 0.567093i | ||||||
\(219\) | 9.64797 | − | 7.73615i | 0.651950 | − | 0.522760i | ||||
\(220\) | −1.28375 | − | 1.28375i | −0.0865502 | − | 0.0865502i | ||||
\(221\) | 8.16478 | 0.549222 | ||||||||
\(222\) | −4.04132 | + | 9.72974i | −0.271236 | + | 0.653017i | ||||
\(223\) | 15.2765 | 1.02299 | 0.511493 | − | 0.859287i | \(-0.329092\pi\) | ||||
0.511493 | + | 0.859287i | \(0.329092\pi\) | |||||||
\(224\) | −2.67039 | − | 2.67039i | −0.178423 | − | 0.178423i | ||||
\(225\) | 2.92830 | + | 0.651967i | 0.195220 | + | 0.0434645i | ||||
\(226\) | − | 10.7733i | − | 0.716627i | ||||||
\(227\) | 0.894036 | − | 0.894036i | 0.0593392 | − | 0.0593392i | −0.676814 | − | 0.736154i | \(-0.736640\pi\) |
0.736154 | + | 0.676814i | \(0.236640\pi\) | |||||||
\(228\) | −2.46137 | − | 0.270690i | −0.163008 | − | 0.0179269i | ||||
\(229\) | −22.6190 | −1.49471 | −0.747354 | − | 0.664426i | \(-0.768676\pi\) | ||||
−0.747354 | + | 0.664426i | \(0.768676\pi\) | |||||||
\(230\) | −5.79126 | + | 5.79126i | −0.381864 | + | 0.381864i | ||||
\(231\) | 7.42883 | + | 9.26471i | 0.488781 | + | 0.609573i | ||||
\(232\) | 5.38709 | 0.353679 | ||||||||
\(233\) | −2.55770 | −0.167561 | −0.0837804 | − | 0.996484i | \(-0.526699\pi\) | ||||
−0.0837804 | + | 0.996484i | \(0.526699\pi\) | |||||||
\(234\) | −16.1839 | − | 3.60324i | −1.05797 | − | 0.235551i | ||||
\(235\) | 5.36999 | + | 5.36999i | 0.350299 | + | 0.350299i | ||||
\(236\) | −3.27282 | − | 3.27282i | −0.213042 | − | 0.213042i | ||||
\(237\) | −2.15607 | + | 19.6050i | −0.140052 | + | 1.27348i | ||||
\(238\) | −5.57912 | −0.361641 | ||||||||
\(239\) | −20.5707 | + | 20.5707i | −1.33061 | + | 1.33061i | −0.425785 | + | 0.904825i | \(0.640002\pi\) |
−0.904825 | + | 0.425785i | \(0.859998\pi\) | |||||||
\(240\) | −1.72167 | − | 0.189341i | −0.111133 | − | 0.0122219i | ||||
\(241\) | 4.22260 | + | 4.22260i | 0.272001 | + | 0.272001i | 0.829905 | − | 0.557904i | \(-0.188394\pi\) |
−0.557904 | + | 0.829905i | \(0.688394\pi\) | |||||||
\(242\) | 5.44754 | + | 5.44754i | 0.350181 | + | 0.350181i | ||||
\(243\) | 3.67091 | + | 15.1501i | 0.235489 | + | 0.971877i | ||||
\(244\) | −0.251587 | − | 0.251587i | −0.0161062 | − | 0.0161062i | ||||
\(245\) | −5.13495 | + | 5.13495i | −0.328060 | + | 0.328060i | ||||
\(246\) | −1.84448 | + | 16.7717i | −0.117600 | + | 1.06933i | ||||
\(247\) | 7.90121i | 0.502742i | ||||||||
\(248\) | − | 6.31927i | − | 0.401274i | ||||||
\(249\) | −9.66638 | + | 7.75091i | −0.612582 | + | 0.491194i | ||||
\(250\) | − | 1.00000i | − | 0.0632456i | ||||||
\(251\) | 16.0961 | + | 16.0961i | 1.01597 | + | 1.01597i | 0.999870 | + | 0.0161034i | \(0.00512610\pi\) |
0.0161034 | + | 0.999870i | \(0.494874\pi\) | |||||||
\(252\) | 11.0587 | + | 2.46215i | 0.696633 | + | 0.155101i | ||||
\(253\) | −10.5140 | + | 10.5140i | −0.661008 | + | 0.661008i | ||||
\(254\) | −12.1004 | − | 12.1004i | −0.759245 | − | 0.759245i | ||||
\(255\) | −1.99630 | + | 1.60072i | −0.125013 | + | 0.100241i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.47800 | − | 1.47800i | 0.0921953 | − | 0.0921953i | −0.659505 | − | 0.751700i | \(-0.729234\pi\) |
0.751700 | + | 0.659505i | \(0.229234\pi\) | |||||||
\(258\) | −11.8089 | + | 9.46886i | −0.735189 | + | 0.589505i | ||||
\(259\) | −22.0504 | − | 6.43965i | −1.37015 | − | 0.400140i | ||||
\(260\) | 5.52672i | 0.342753i | ||||||||
\(261\) | −13.6381 | + | 8.67111i | −0.844178 | + | 0.536728i | ||||
\(262\) | 4.78265i | 0.295473i | ||||||||
\(263\) | 10.6468 | 0.656507 | 0.328253 | − | 0.944590i | \(-0.393540\pi\) | ||||
0.328253 | + | 0.944590i | \(0.393540\pi\) | |||||||
\(264\) | −3.12568 | − | 0.343748i | −0.192372 | − | 0.0211562i | ||||
\(265\) | −1.03826 | − | 1.03826i | −0.0637796 | − | 0.0637796i | ||||
\(266\) | − | 5.39902i | − | 0.331035i | ||||||
\(267\) | 2.00066 | − | 18.1919i | 0.122438 | − | 1.11332i | ||||
\(268\) | −1.79916 | −0.109901 | ||||||||
\(269\) | 5.61239i | 0.342194i | 0.985254 | + | 0.171097i | \(0.0547311\pi\) | ||||
−0.985254 | + | 0.171097i | \(0.945269\pi\) | |||||||
\(270\) | 4.66340 | − | 2.29188i | 0.283806 | − | 0.139479i | ||||
\(271\) | 21.9439 | 1.33300 | 0.666499 | − | 0.745506i | \(-0.267792\pi\) | ||||
0.666499 | + | 0.745506i | \(0.267792\pi\) | |||||||
\(272\) | 1.04463 | − | 1.04463i | 0.0633399 | − | 0.0633399i | ||||
\(273\) | 3.95187 | − | 35.9341i | 0.239178 | − | 2.17483i | ||||
\(274\) | 2.92815 | − | 2.92815i | 0.176896 | − | 0.176896i | ||||
\(275\) | − | 1.81549i | − | 0.109478i | ||||||
\(276\) | −1.55072 | + | 14.1006i | −0.0933424 | + | 0.848757i | ||||
\(277\) | 9.61698 | − | 9.61698i | 0.577829 | − | 0.577829i | −0.356476 | − | 0.934305i | \(-0.616022\pi\) |
0.934305 | + | 0.356476i | \(0.116022\pi\) | |||||||
\(278\) | 0.977295 | − | 0.977295i | 0.0586143 | − | 0.0586143i | ||||
\(279\) | 10.1716 | + | 15.9981i | 0.608956 | + | 0.957779i | ||||
\(280\) | − | 3.77650i | − | 0.225689i | ||||||
\(281\) | −0.242604 | + | 0.242604i | −0.0144726 | + | 0.0144726i | −0.714306 | − | 0.699833i | \(-0.753258\pi\) |
0.699833 | + | 0.714306i | \(0.253258\pi\) | |||||||
\(282\) | 13.0749 | + | 1.43792i | 0.778599 | + | 0.0856268i | ||||
\(283\) | −16.6943 | + | 16.6943i | −0.992374 | + | 0.992374i | −0.999971 | − | 0.00759709i | \(-0.997582\pi\) |
0.00759709 | + | 0.999971i | \(0.497582\pi\) | |||||||
\(284\) | 14.5030 | 0.860594 | ||||||||
\(285\) | −1.54904 | − | 1.93185i | −0.0917573 | − | 0.114433i | ||||
\(286\) | 10.0337i | 0.593306i | ||||||||
\(287\) | −36.7889 | −2.17158 | ||||||||
\(288\) | −2.53163 | + | 1.60961i | −0.149178 | + | 0.0948472i | ||||
\(289\) | 14.8175i | 0.871618i | ||||||||
\(290\) | 3.80924 | + | 3.80924i | 0.223687 | + | 0.223687i | ||||
\(291\) | 0.863862 | − | 7.85505i | 0.0506405 | − | 0.460471i | ||||
\(292\) | −7.13983 | −0.417827 | ||||||||
\(293\) | − | 26.8829i | − | 1.57051i | −0.619170 | − | 0.785257i | \(-0.712531\pi\) | ||
0.619170 | − | 0.785257i | \(-0.287469\pi\) | |||||||
\(294\) | −1.37498 | + | 12.5026i | −0.0801906 | + | 0.729169i | ||||
\(295\) | − | 4.62846i | − | 0.269479i | ||||||
\(296\) | 5.33445 | − | 2.92295i | 0.310059 | − | 0.169893i | ||||
\(297\) | 8.46636 | − | 4.16088i | 0.491268 | − | 0.241439i | ||||
\(298\) | 7.52830 | − | 7.52830i | 0.436103 | − | 0.436103i | ||||
\(299\) | 45.2642 | 2.61770 | ||||||||
\(300\) | −1.08352 | − | 1.35129i | −0.0625571 | − | 0.0780167i | ||||
\(301\) | −23.3364 | − | 23.3364i | −1.34509 | − | 1.34509i | ||||
\(302\) | −3.89164 | + | 3.89164i | −0.223939 | + | 0.223939i | ||||
\(303\) | 2.08003 | + | 2.59407i | 0.119495 | + | 0.149025i | ||||
\(304\) | 1.01091 | + | 1.01091i | 0.0579795 | + | 0.0579795i | ||||
\(305\) | − | 0.355798i | − | 0.0203729i | ||||||
\(306\) | −0.963170 | + | 4.32606i | −0.0550608 | + | 0.247304i | ||||
\(307\) | 26.7254i | 1.52530i | 0.646812 | + | 0.762649i | \(0.276102\pi\) | ||||
−0.646812 | + | 0.762649i | \(0.723898\pi\) | |||||||
\(308\) | − | 6.85620i | − | 0.390668i | ||||||
\(309\) | −27.1872 | − | 2.98993i | −1.54663 | − | 0.170091i | ||||
\(310\) | 4.46840 | − | 4.46840i | 0.253788 | − | 0.253788i | ||||
\(311\) | −3.11089 | − | 3.11089i | −0.176403 | − | 0.176403i | 0.613383 | − | 0.789786i | \(-0.289808\pi\) |
−0.789786 | + | 0.613383i | \(0.789808\pi\) | |||||||
\(312\) | 5.98831 | + | 7.46820i | 0.339021 | + | 0.422803i | ||||
\(313\) | 1.42025 | + | 1.42025i | 0.0802770 | + | 0.0802770i | 0.746105 | − | 0.665828i | \(-0.231922\pi\) |
−0.665828 | + | 0.746105i | \(0.731922\pi\) | |||||||
\(314\) | 8.87153 | + | 8.87153i | 0.500649 | + | 0.500649i | ||||
\(315\) | 6.07869 | + | 9.56069i | 0.342495 | + | 0.538684i | ||||
\(316\) | 8.05198 | − | 8.05198i | 0.452959 | − | 0.452959i | ||||
\(317\) | −1.15291 | −0.0647537 | −0.0323768 | − | 0.999476i | \(-0.510308\pi\) | ||||
−0.0323768 | + | 0.999476i | \(0.510308\pi\) | |||||||
\(318\) | −2.52796 | − | 0.278013i | −0.141761 | − | 0.0155902i | ||||
\(319\) | 6.91565 | + | 6.91565i | 0.387202 | + | 0.387202i | ||||
\(320\) | 0.707107 | + | 0.707107i | 0.0395285 | + | 0.0395285i | ||||
\(321\) | 22.2924 | − | 17.8749i | 1.24424 | − | 0.997682i | ||||
\(322\) | −30.9298 | −1.72365 | ||||||||
\(323\) | 2.11204 | 0.117517 | ||||||||
\(324\) | 3.81831 | − | 8.14988i | 0.212128 | − | 0.452771i | ||||
\(325\) | −3.90798 | + | 3.90798i | −0.216776 | + | 0.216776i | ||||
\(326\) | −22.3405 | −1.23732 | ||||||||
\(327\) | 1.58536 | − | 14.4156i | 0.0876707 | − | 0.797184i | ||||
\(328\) | 6.88832 | − | 6.88832i | 0.380344 | − | 0.380344i | ||||
\(329\) | 28.6799i | 1.58117i | ||||||||
\(330\) | −1.96712 | − | 2.45325i | −0.108287 | − | 0.135047i | ||||
\(331\) | −20.7988 | − | 20.7988i | −1.14321 | − | 1.14321i | −0.987860 | − | 0.155348i | \(-0.950350\pi\) |
−0.155348 | − | 0.987860i | \(-0.549650\pi\) | |||||||
\(332\) | 7.15345 | 0.392597 | ||||||||
\(333\) | −8.80006 | + | 15.9862i | −0.482240 | + | 0.876039i | ||||
\(334\) | −1.83104 | −0.100190 | ||||||||
\(335\) | −1.27220 | − | 1.27220i | −0.0695075 | − | 0.0695075i | ||||
\(336\) | −4.09191 | − | 5.10314i | −0.223232 | − | 0.278399i | ||||
\(337\) | − | 30.6964i | − | 1.67214i | −0.548625 | − | 0.836069i | \(-0.684848\pi\) | ||
0.548625 | − | 0.836069i | \(-0.315152\pi\) | |||||||
\(338\) | 12.4059 | − | 12.4059i | 0.674793 | − | 0.674793i | ||||
\(339\) | 2.03983 | − | 18.5480i | 0.110788 | − | 1.00739i | ||||
\(340\) | 1.47733 | 0.0801194 | ||||||||
\(341\) | 8.11234 | − | 8.11234i | 0.439308 | − | 0.439308i | ||||
\(342\) | −4.18641 | − | 0.932077i | −0.226375 | − | 0.0504010i | ||||
\(343\) | −0.989146 | −0.0534088 | ||||||||
\(344\) | 8.73898 | 0.471174 | ||||||||
\(345\) | −11.0672 | + | 8.87411i | −0.595836 | + | 0.477766i | ||||
\(346\) | −1.53960 | − | 1.53960i | −0.0827691 | − | 0.0827691i | ||||
\(347\) | −9.91190 | − | 9.91190i | −0.532099 | − | 0.532099i | 0.389098 | − | 0.921196i | \(-0.372787\pi\) |
−0.921196 | + | 0.389098i | \(0.872787\pi\) | |||||||
\(348\) | 9.27479 | + | 1.02000i | 0.497181 | + | 0.0546777i | ||||
\(349\) | −2.62293 | −0.140402 | −0.0702011 | − | 0.997533i | \(-0.522364\pi\) | ||||
−0.0702011 | + | 0.997533i | \(0.522364\pi\) | |||||||
\(350\) | 2.67039 | − | 2.67039i | 0.142738 | − | 0.142738i | ||||
\(351\) | −27.1811 | − | 9.26788i | −1.45082 | − | 0.494683i | ||||
\(352\) | 1.28375 | + | 1.28375i | 0.0684239 | + | 0.0684239i | ||||
\(353\) | 22.8322 | + | 22.8322i | 1.21523 | + | 1.21523i | 0.969282 | + | 0.245950i | \(0.0791000\pi\) |
0.245950 | + | 0.969282i | \(0.420900\pi\) | |||||||
\(354\) | −5.01503 | − | 6.25439i | −0.266546 | − | 0.332417i | ||||
\(355\) | 10.2552 | + | 10.2552i | 0.544287 | + | 0.544287i | ||||
\(356\) | −7.47158 | + | 7.47158i | −0.395993 | + | 0.395993i | ||||
\(357\) | −9.60541 | − | 1.05636i | −0.508372 | − | 0.0559085i | ||||
\(358\) | − | 2.77777i | − | 0.146810i | ||||||
\(359\) | − | 6.29555i | − | 0.332266i | −0.986103 | − | 0.166133i | \(-0.946872\pi\) | ||
0.986103 | − | 0.166133i | \(-0.0531282\pi\) | |||||||
\(360\) | −2.92830 | − | 0.651967i | −0.154335 | − | 0.0343617i | ||||
\(361\) | − | 16.9561i | − | 0.892428i | ||||||
\(362\) | −14.9879 | − | 14.9879i | −0.787749 | − | 0.787749i | ||||
\(363\) | 8.34743 | + | 10.4103i | 0.438126 | + | 0.546400i | ||||
\(364\) | −14.7585 | + | 14.7585i | −0.773554 | + | 0.773554i | ||||
\(365\) | −5.04862 | − | 5.04862i | −0.264257 | − | 0.264257i | ||||
\(366\) | −0.385515 | − | 0.480787i | −0.0201512 | − | 0.0251311i | ||||
\(367\) | 31.6625 | 1.65277 | 0.826386 | − | 0.563105i | \(-0.190393\pi\) | ||||
0.826386 | + | 0.563105i | \(0.190393\pi\) | |||||||
\(368\) | 5.79126 | − | 5.79126i | 0.301890 | − | 0.301890i | ||||
\(369\) | −6.35118 | + | 28.5262i | −0.330629 | + | 1.48501i | ||||
\(370\) | 5.83886 | + | 1.70519i | 0.303548 | + | 0.0886487i | ||||
\(371\) | − | 5.54509i | − | 0.287887i | ||||||
\(372\) | 1.19650 | − | 10.8797i | 0.0620357 | − | 0.564086i | ||||
\(373\) | 9.39721i | 0.486569i | 0.969955 | + | 0.243284i | \(0.0782248\pi\) | ||||
−0.969955 | + | 0.243284i | \(0.921775\pi\) | |||||||
\(374\) | 2.68208 | 0.138687 | ||||||||
\(375\) | 0.189341 | − | 1.72167i | 0.00977755 | − | 0.0889067i | ||||
\(376\) | −5.36999 | − | 5.36999i | −0.276936 | − | 0.276936i | ||||
\(377\) | − | 29.7729i | − | 1.53338i | ||||||
\(378\) | 18.5733 | + | 6.33289i | 0.955306 | + | 0.325729i | ||||
\(379\) | −10.9284 | −0.561354 | −0.280677 | − | 0.959802i | \(-0.590559\pi\) | ||||
−0.280677 | + | 0.959802i | \(0.590559\pi\) | |||||||
\(380\) | 1.42964i | 0.0733389i | ||||||||
\(381\) | −18.5418 | − | 23.1240i | −0.949923 | − | 1.18468i | ||||
\(382\) | 25.0609 | 1.28223 | ||||||||
\(383\) | 4.41045 | − | 4.41045i | 0.225363 | − | 0.225363i | −0.585389 | − | 0.810752i | \(-0.699058\pi\) |
0.810752 | + | 0.585389i | \(0.199058\pi\) | |||||||
\(384\) | 1.72167 | + | 0.189341i | 0.0878586 | + | 0.00966229i | ||||
\(385\) | 4.84806 | − | 4.84806i | 0.247080 | − | 0.247080i | ||||
\(386\) | − | 19.5518i | − | 0.995162i | ||||||
\(387\) | −22.1239 | + | 14.0663i | −1.12462 | + | 0.715032i | ||||
\(388\) | −3.22614 | + | 3.22614i | −0.163783 | + | 0.163783i | ||||
\(389\) | 6.54945 | − | 6.54945i | 0.332071 | − | 0.332071i | −0.521302 | − | 0.853372i | \(-0.674553\pi\) |
0.853372 | + | 0.521302i | \(0.174553\pi\) | |||||||
\(390\) | −1.04644 | + | 9.51519i | −0.0529884 | + | 0.481820i | ||||
\(391\) | − | 12.0994i | − | 0.611894i | ||||||
\(392\) | 5.13495 | − | 5.13495i | 0.259354 | − | 0.259354i | ||||
\(393\) | −0.905554 | + | 8.23415i | −0.0456792 | + | 0.415358i | ||||
\(394\) | 10.3072 | − | 10.3072i | 0.519271 | − | 0.519271i | ||||
\(395\) | 11.3872 | 0.572953 | ||||||||
\(396\) | −5.31630 | − | 1.18364i | −0.267154 | − | 0.0594802i | ||||
\(397\) | − | 17.8138i | − | 0.894049i | −0.894522 | − | 0.447024i | \(-0.852484\pi\) | ||
0.894522 | − | 0.447024i | \(-0.147516\pi\) | |||||||
\(398\) | 7.60095 | 0.381001 | ||||||||
\(399\) | 1.02226 | − | 9.29534i | 0.0511769 | − | 0.465349i | ||||
\(400\) | 1.00000i | 0.0500000i | ||||||||
\(401\) | −15.1233 | − | 15.1233i | −0.755220 | − | 0.755220i | 0.220229 | − | 0.975448i | \(-0.429320\pi\) |
−0.975448 | + | 0.220229i | \(0.929320\pi\) | |||||||
\(402\) | −3.09756 | − | 0.340655i | −0.154492 | − | 0.0169903i | ||||
\(403\) | −34.9248 | −1.73973 | ||||||||
\(404\) | − | 1.91970i | − | 0.0955085i | ||||||
\(405\) | 8.46279 | − | 3.06288i | 0.420519 | − | 0.152196i | ||||
\(406\) | 20.3443i | 1.00967i | ||||||||
\(407\) | 10.6004 | + | 3.09576i | 0.525443 | + | 0.153451i | ||||
\(408\) | 1.99630 | − | 1.60072i | 0.0988315 | − | 0.0792472i | ||||
\(409\) | −17.1329 | + | 17.1329i | −0.847169 | + | 0.847169i | −0.989779 | − | 0.142610i | \(-0.954451\pi\) |
0.142610 | + | 0.989779i | \(0.454451\pi\) | |||||||
\(410\) | 9.74155 | 0.481101 | ||||||||
\(411\) | 5.59574 | − | 4.48690i | 0.276017 | − | 0.221322i | ||||
\(412\) | 11.1661 | + | 11.1661i | 0.550112 | + | 0.550112i | ||||
\(413\) | 12.3598 | − | 12.3598i | 0.608185 | − | 0.608185i | ||||
\(414\) | −5.33966 | + | 23.9830i | −0.262430 | + | 1.17870i | ||||
\(415\) | 5.05825 | + | 5.05825i | 0.248300 | + | 0.248300i | ||||
\(416\) | − | 5.52672i | − | 0.270970i | ||||||
\(417\) | 1.86762 | − | 1.49754i | 0.0914579 | − | 0.0733347i | ||||
\(418\) | 2.59550i | 0.126950i | ||||||||
\(419\) | 2.98599i | 0.145875i | 0.997337 | + | 0.0729375i | \(0.0232374\pi\) | ||||
−0.997337 | + | 0.0729375i | \(0.976763\pi\) | |||||||
\(420\) | 0.715047 | − | 6.50188i | 0.0348907 | − | 0.317259i | ||||
\(421\) | 22.4754 | − | 22.4754i | 1.09538 | − | 1.09538i | 0.100440 | − | 0.994943i | \(-0.467975\pi\) |
0.994943 | − | 0.100440i | \(-0.0320251\pi\) | |||||||
\(422\) | 7.05514 | + | 7.05514i | 0.343439 | + | 0.343439i | ||||
\(423\) | 22.2384 | + | 4.95124i | 1.08127 | + | 0.240738i | ||||
\(424\) | 1.03826 | + | 1.03826i | 0.0504222 | + | 0.0504222i | ||||
\(425\) | 1.04463 | + | 1.04463i | 0.0506719 | + | 0.0506719i | ||||
\(426\) | 24.9694 | + | 2.74602i | 1.20977 | + | 0.133045i | ||||
\(427\) | 0.950119 | − | 0.950119i | 0.0459795 | − | 0.0459795i | ||||
\(428\) | −16.4971 | −0.797418 | ||||||||
\(429\) | −1.89980 | + | 17.2747i | −0.0917231 | + | 0.834033i | ||||
\(430\) | 6.17939 | + | 6.17939i | 0.297997 | + | 0.297997i | ||||
\(431\) | 3.42819 | + | 3.42819i | 0.165130 | + | 0.165130i | 0.784835 | − | 0.619705i | \(-0.212748\pi\) |
−0.619705 | + | 0.784835i | \(0.712748\pi\) | |||||||
\(432\) | −4.66340 | + | 2.29188i | −0.224368 | + | 0.110268i | ||||
\(433\) | −5.54788 | −0.266614 | −0.133307 | − | 0.991075i | \(-0.542560\pi\) | ||||
−0.133307 | + | 0.991075i | \(0.542560\pi\) | |||||||
\(434\) | 23.8647 | 1.14554 | ||||||||
\(435\) | 5.83702 | + | 7.27951i | 0.279864 | + | 0.349026i | ||||
\(436\) | −5.92062 | + | 5.92062i | −0.283546 | + | 0.283546i | ||||
\(437\) | 11.7088 | 0.560110 | ||||||||
\(438\) | −12.2924 | − | 1.35187i | −0.587355 | − | 0.0645946i | ||||
\(439\) | −19.5185 | + | 19.5185i | −0.931565 | + | 0.931565i | −0.997804 | − | 0.0662388i | \(-0.978900\pi\) |
0.0662388 | + | 0.997804i | \(0.478900\pi\) | |||||||
\(440\) | 1.81549i | 0.0865502i | ||||||||
\(441\) | −4.73454 | + | 21.2651i | −0.225454 | + | 1.01262i | ||||
\(442\) | −5.77337 | − | 5.77337i | −0.274611 | − | 0.274611i | ||||
\(443\) | −34.0155 | −1.61612 | −0.808062 | − | 0.589098i | \(-0.799483\pi\) | ||||
−0.808062 | + | 0.589098i | \(0.799483\pi\) | |||||||
\(444\) | 9.73761 | − | 4.02232i | 0.462126 | − | 0.190891i | ||||
\(445\) | −10.5664 | −0.500896 | ||||||||
\(446\) | −10.8021 | − | 10.8021i | −0.511493 | − | 0.511493i | ||||
\(447\) | 14.3867 | − | 11.5358i | 0.680467 | − | 0.545626i | ||||
\(448\) | 3.77650i | 0.178423i | ||||||||
\(449\) | 13.9432 | − | 13.9432i | 0.658020 | − | 0.658020i | −0.296891 | − | 0.954911i | \(-0.595950\pi\) |
0.954911 | + | 0.296891i | \(0.0959498\pi\) | |||||||
\(450\) | −1.60961 | − | 2.53163i | −0.0758777 | − | 0.119342i | ||||
\(451\) | 17.6857 | 0.832788 | ||||||||
\(452\) | −7.61785 | + | 7.61785i | −0.358314 | + | 0.358314i | ||||
\(453\) | −7.43697 | + | 5.96327i | −0.349419 | + | 0.280179i | ||||
\(454\) | −1.26436 | −0.0593392 | ||||||||
\(455\) | −20.8716 | −0.978477 | ||||||||
\(456\) | 1.54904 | + | 1.93185i | 0.0725405 | + | 0.0904674i | ||||
\(457\) | 22.7546 | + | 22.7546i | 1.06442 | + | 1.06442i | 0.997777 | + | 0.0666382i | \(0.0212273\pi\) |
0.0666382 | + | 0.997777i | \(0.478773\pi\) | |||||||
\(458\) | 15.9941 | + | 15.9941i | 0.747354 | + | 0.747354i | ||||
\(459\) | −2.47736 | + | 7.26568i | −0.115633 | + | 0.339133i | ||||
\(460\) | 8.19007 | 0.381864 | ||||||||
\(461\) | −19.4728 | + | 19.4728i | −0.906938 | + | 0.906938i | −0.996024 | − | 0.0890855i | \(-0.971606\pi\) |
0.0890855 | + | 0.996024i | \(0.471606\pi\) | |||||||
\(462\) | 1.29816 | − | 11.8041i | 0.0603960 | − | 0.549177i | ||||
\(463\) | −5.56886 | − | 5.56886i | −0.258807 | − | 0.258807i | 0.565762 | − | 0.824569i | \(-0.308582\pi\) |
−0.824569 | + | 0.565762i | \(0.808582\pi\) | |||||||
\(464\) | −3.80924 | − | 3.80924i | −0.176840 | − | 0.176840i | ||||
\(465\) | 8.53917 | − | 6.84706i | 0.395994 | − | 0.317525i | ||||
\(466\) | 1.80857 | + | 1.80857i | 0.0837804 | + | 0.0837804i | ||||
\(467\) | −2.99722 | + | 2.99722i | −0.138695 | + | 0.138695i | −0.773045 | − | 0.634351i | \(-0.781268\pi\) |
0.634351 | + | 0.773045i | \(0.281268\pi\) | |||||||
\(468\) | 8.89586 | + | 13.9916i | 0.411211 | + | 0.646763i | ||||
\(469\) | − | 6.79451i | − | 0.313741i | ||||||
\(470\) | − | 7.59431i | − | 0.350299i | ||||||
\(471\) | 13.5941 | + | 16.9536i | 0.626383 | + | 0.781181i | ||||
\(472\) | 4.62846i | 0.213042i | ||||||||
\(473\) | 11.2186 | + | 11.2186i | 0.515833 | + | 0.515833i | ||||
\(474\) | 15.3874 | − | 12.3383i | 0.706768 | − | 0.566716i | ||||
\(475\) | −1.01091 | + | 1.01091i | −0.0463836 | + | 0.0463836i | ||||
\(476\) | 3.94504 | + | 3.94504i | 0.180820 | + | 0.180820i | ||||
\(477\) | −4.29967 | − | 0.957294i | −0.196868 | − | 0.0438315i | ||||
\(478\) | 29.0914 | 1.33061 | ||||||||
\(479\) | 4.22623 | − | 4.22623i | 0.193101 | − | 0.193101i | −0.603933 | − | 0.797035i | \(-0.706401\pi\) |
0.797035 | + | 0.603933i | \(0.206401\pi\) | |||||||
\(480\) | 1.08352 | + | 1.35129i | 0.0494557 | + | 0.0616777i | ||||
\(481\) | −16.1543 | − | 29.4820i | −0.736573 | − | 1.34426i | ||||
\(482\) | − | 5.97165i | − | 0.272001i | ||||||
\(483\) | −53.2509 | − | 5.85629i | −2.42300 | − | 0.266470i | ||||
\(484\) | − | 7.70399i | − | 0.350181i | ||||||
\(485\) | −4.56246 | −0.207170 | ||||||||
\(486\) | 8.11699 | − | 13.3084i | 0.368194 | − | 0.603683i | ||||
\(487\) | 3.09555 | + | 3.09555i | 0.140273 | + | 0.140273i | 0.773756 | − | 0.633483i | \(-0.218376\pi\) |
−0.633483 | + | 0.773756i | \(0.718376\pi\) | |||||||
\(488\) | 0.355798i | 0.0161062i | ||||||||
\(489\) | −38.4629 | − | 4.22998i | −1.73935 | − | 0.191286i | ||||
\(490\) | 7.26192 | 0.328060 | ||||||||
\(491\) | 14.1328i | 0.637804i | 0.947788 | + | 0.318902i | \(0.103314\pi\) | ||||
−0.947788 | + | 0.318902i | \(0.896686\pi\) | |||||||
\(492\) | 13.1637 | − | 10.5552i | 0.593464 | − | 0.475864i | ||||
\(493\) | −7.95849 | −0.358433 | ||||||||
\(494\) | 5.58700 | − | 5.58700i | 0.251371 | − | 0.251371i | ||||
\(495\) | −2.92223 | − | 4.59615i | −0.131345 | − | 0.206582i | ||||
\(496\) | −4.46840 | + | 4.46840i | −0.200637 | + | 0.200637i | ||||
\(497\) | 54.7704i | 2.45679i | ||||||||
\(498\) | 12.3159 | + | 1.35445i | 0.551888 | + | 0.0606941i | ||||
\(499\) | 9.16440 | − | 9.16440i | 0.410255 | − | 0.410255i | −0.471572 | − | 0.881827i | \(-0.656313\pi\) |
0.881827 | + | 0.471572i | \(0.156313\pi\) | |||||||
\(500\) | −0.707107 | + | 0.707107i | −0.0316228 | + | 0.0316228i | ||||
\(501\) | −3.15245 | − | 0.346692i | −0.140841 | − | 0.0154890i | ||||
\(502\) | − | 22.7633i | − | 1.01597i | ||||||
\(503\) | −6.66777 | + | 6.66777i | −0.297301 | + | 0.297301i | −0.839956 | − | 0.542655i | \(-0.817419\pi\) |
0.542655 | + | 0.839956i | \(0.317419\pi\) | |||||||
\(504\) | −6.07869 | − | 9.56069i | −0.270766 | − | 0.425867i | ||||
\(505\) | 1.35743 | − | 1.35743i | 0.0604049 | − | 0.0604049i | ||||
\(506\) | 14.8690 | 0.661008 | ||||||||
\(507\) | 23.7079 | − | 19.0100i | 1.05290 | − | 0.844262i | ||||
\(508\) | 17.1125i | 0.759245i | ||||||||
\(509\) | 7.17963 | 0.318232 | 0.159116 | − | 0.987260i | \(-0.449136\pi\) | ||||
0.159116 | + | 0.987260i | \(0.449136\pi\) | |||||||
\(510\) | 2.54347 | + | 0.279720i | 0.112627 | + | 0.0123862i | ||||
\(511\) | − | 26.9635i | − | 1.19280i | ||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −7.03113 | − | 2.39739i | −0.310432 | − | 0.105847i | ||||
\(514\) | −2.09021 | −0.0921953 | ||||||||
\(515\) | 15.7912i | 0.695843i | ||||||||
\(516\) | 15.0456 | + | 1.65465i | 0.662347 | + | 0.0728419i | ||||
\(517\) | − | 13.7874i | − | 0.606370i | ||||||
\(518\) | 11.0385 | + | 20.1455i | 0.485004 | + | 0.885144i | ||||
\(519\) | −2.35917 | − | 2.94218i | −0.103556 | − | 0.129148i | ||||
\(520\) | 3.90798 | − | 3.90798i | 0.171376 | − | 0.171376i | ||||
\(521\) | 2.92647 | 0.128211 | 0.0641056 | − | 0.997943i | \(-0.479581\pi\) | ||||
0.0641056 | + | 0.997943i | \(0.479581\pi\) | |||||||
\(522\) | 15.7750 | + | 3.51220i | 0.690453 | + | 0.153725i | ||||
\(523\) | 24.4456 | + | 24.4456i | 1.06893 | + | 1.06893i | 0.997441 | + | 0.0714897i | \(0.0227753\pi\) |
0.0714897 | + | 0.997441i | \(0.477225\pi\) | |||||||
\(524\) | 3.38184 | − | 3.38184i | 0.147737 | − | 0.147737i | ||||
\(525\) | 5.10314 | − | 4.09191i | 0.222719 | − | 0.178586i | ||||
\(526\) | −7.52839 | − | 7.52839i | −0.328253 | − | 0.328253i | ||||
\(527\) | 9.33564i | 0.406667i | ||||||||
\(528\) | 1.96712 | + | 2.45325i | 0.0856080 | + | 0.106764i | ||||
\(529\) | − | 44.0773i | − | 1.91640i | ||||||
\(530\) | 1.46832i | 0.0637796i | ||||||||
\(531\) | −7.45002 | − | 11.7176i | −0.323303 | − | 0.508499i | ||||
\(532\) | −3.81768 | + | 3.81768i | −0.165518 | + | 0.165518i | ||||
\(533\) | −38.0698 | − | 38.0698i | −1.64899 | − | 1.64899i | ||||
\(534\) | −14.2783 | + | 11.4489i | −0.617881 | + | 0.495443i | ||||
\(535\) | −11.6652 | − | 11.6652i | −0.504331 | − | 0.504331i | ||||
\(536\) | 1.27220 | + | 1.27220i | 0.0549505 | + | 0.0549505i | ||||
\(537\) | 0.525948 | − | 4.78241i | 0.0226963 | − | 0.206376i | ||||
\(538\) | 3.96856 | − | 3.96856i | 0.171097 | − | 0.171097i | ||||
\(539\) | 13.1840 | 0.567873 | ||||||||
\(540\) | −4.91812 | − | 1.67692i | −0.211642 | − | 0.0721632i | ||||
\(541\) | 4.39040 | + | 4.39040i | 0.188758 | + | 0.188758i | 0.795159 | − | 0.606401i | \(-0.207387\pi\) |
−0.606401 | + | 0.795159i | \(0.707387\pi\) | |||||||
\(542\) | −15.5167 | − | 15.5167i | −0.666499 | − | 0.666499i | ||||
\(543\) | −22.9665 | − | 28.6421i | −0.985585 | − | 1.22915i | ||||
\(544\) | −1.47733 | −0.0633399 | ||||||||
\(545\) | −8.37303 | −0.358661 | ||||||||
\(546\) | −28.2036 | + | 22.6148i | −1.20700 | + | 0.967826i | ||||
\(547\) | 19.6365 | − | 19.6365i | 0.839596 | − | 0.839596i | −0.149210 | − | 0.988806i | \(-0.547673\pi\) |
0.988806 | + | 0.149210i | \(0.0476730\pi\) | |||||||
\(548\) | −4.14104 | −0.176896 | ||||||||
\(549\) | −0.572696 | − | 0.900750i | −0.0244421 | − | 0.0384431i | ||||
\(550\) | −1.28375 | + | 1.28375i | −0.0547391 | + | 0.0547391i | ||||
\(551\) | − | 7.70158i | − | 0.328098i | ||||||
\(552\) | 11.0672 | − | 8.87411i | 0.471050 | − | 0.377707i | ||||
\(553\) | 30.4083 | + | 30.4083i | 1.29309 | + | 1.29309i | ||||
\(554\) | −13.6005 | −0.577829 | ||||||||
\(555\) | 9.72974 | + | 4.04132i | 0.413004 | + | 0.171544i | ||||
\(556\) | −1.38210 | −0.0586143 | ||||||||
\(557\) | 18.2860 | + | 18.2860i | 0.774802 | + | 0.774802i | 0.978942 | − | 0.204139i | \(-0.0654396\pi\) |
−0.204139 | + | 0.978942i | \(0.565440\pi\) | |||||||
\(558\) | 4.11996 | − | 18.5047i | 0.174412 | − | 0.783367i | ||||
\(559\) | − | 48.2979i | − | 2.04278i | ||||||
\(560\) | −2.67039 | + | 2.67039i | −0.112844 | + | 0.112844i | ||||
\(561\) | 4.61765 | + | 0.507829i | 0.194957 | + | 0.0214405i | ||||
\(562\) | 0.343094 | 0.0144726 | ||||||||
\(563\) | 18.2223 | − | 18.2223i | 0.767978 | − | 0.767978i | −0.209772 | − | 0.977750i | \(-0.567272\pi\) |
0.977750 | + | 0.209772i | \(0.0672722\pi\) | |||||||
\(564\) | −8.22859 | − | 10.2621i | −0.346486 | − | 0.432113i | ||||
\(565\) | −10.7733 | −0.453235 | ||||||||
\(566\) | 23.6093 | 0.992374 | ||||||||
\(567\) | 30.7780 | + | 14.4198i | 1.29255 | + | 0.605576i | ||||
\(568\) | −10.2552 | − | 10.2552i | −0.430297 | − | 0.430297i | ||||
\(569\) | 20.9822 | + | 20.9822i | 0.879619 | + | 0.879619i | 0.993495 | − | 0.113876i | \(-0.0363266\pi\) |
−0.113876 | + | 0.993495i | \(0.536327\pi\) | |||||||
\(570\) | −0.270690 | + | 2.46137i | −0.0113379 | + | 0.103095i | ||||
\(571\) | 18.1815 | 0.760873 | 0.380437 | − | 0.924807i | \(-0.375774\pi\) | ||||
0.380437 | + | 0.924807i | \(0.375774\pi\) | |||||||
\(572\) | 7.09491 | − | 7.09491i | 0.296653 | − | 0.296653i | ||||
\(573\) | 43.1467 | + | 4.74507i | 1.80248 | + | 0.198228i | ||||
\(574\) | 26.0137 | + | 26.0137i | 1.08579 | + | 1.08579i | ||||
\(575\) | 5.79126 | + | 5.79126i | 0.241512 | + | 0.241512i | ||||
\(576\) | 2.92830 | + | 0.651967i | 0.122012 | + | 0.0271653i | ||||
\(577\) | −1.13510 | − | 1.13510i | −0.0472550 | − | 0.0472550i | 0.683084 | − | 0.730339i | \(-0.260638\pi\) |
−0.730339 | + | 0.683084i | \(0.760638\pi\) | |||||||
\(578\) | 10.4776 | − | 10.4776i | 0.435809 | − | 0.435809i | ||||
\(579\) | 3.70197 | − | 33.6618i | 0.153849 | − | 1.39894i | ||||
\(580\) | − | 5.38709i | − | 0.223687i | ||||||
\(581\) | 27.0150i | 1.12077i | ||||||||
\(582\) | −6.16520 | + | 4.94351i | −0.255556 | + | 0.204915i | ||||
\(583\) | 2.66571i | 0.110403i | ||||||||
\(584\) | 5.04862 | + | 5.04862i | 0.208913 | + | 0.208913i | ||||
\(585\) | −3.60324 | + | 16.1839i | −0.148976 | + | 0.669122i | ||||
\(586\) | −19.0091 | + | 19.0091i | −0.785257 | + | 0.785257i | ||||
\(587\) | −14.5649 | − | 14.5649i | −0.601156 | − | 0.601156i | 0.339463 | − | 0.940619i | \(-0.389755\pi\) |
−0.940619 | + | 0.339463i | \(0.889755\pi\) | |||||||
\(588\) | 9.81296 | − | 7.86844i | 0.404680 | − | 0.324489i | ||||
\(589\) | −9.03427 | −0.372251 | ||||||||
\(590\) | −3.27282 | + | 3.27282i | −0.134740 | + | 0.134740i | ||||
\(591\) | 19.6972 | − | 15.7941i | 0.810236 | − | 0.649681i | ||||
\(592\) | −5.83886 | − | 1.70519i | −0.239976 | − | 0.0700830i | ||||
\(593\) | 5.14451i | 0.211260i | 0.994406 | + | 0.105630i | \(0.0336859\pi\) | ||||
−0.994406 | + | 0.105630i | \(0.966314\pi\) | |||||||
\(594\) | −8.92881 | − | 3.04444i | −0.366354 | − | 0.124915i | ||||
\(595\) | 5.57912i | 0.228722i | ||||||||
\(596\) | −10.6466 | −0.436103 | ||||||||
\(597\) | 13.0863 | + | 1.43917i | 0.535588 | + | 0.0589015i | ||||
\(598\) | −32.0066 | − | 32.0066i | −1.30885 | − | 1.30885i | ||||
\(599\) | − | 21.5927i | − | 0.882252i | −0.897445 | − | 0.441126i | \(-0.854579\pi\) | ||
0.897445 | − | 0.441126i | \(-0.145421\pi\) | |||||||
\(600\) | −0.189341 | + | 1.72167i | −0.00772983 | + | 0.0702869i | ||||
\(601\) | 26.1906 | 1.06834 | 0.534168 | − | 0.845379i | \(-0.320625\pi\) | ||||
0.534168 | + | 0.845379i | \(0.320625\pi\) | |||||||
\(602\) | 33.0027i | 1.34509i | ||||||||
\(603\) | −5.26847 | − | 1.17299i | −0.214549 | − | 0.0477679i | ||||
\(604\) | 5.50361 | 0.223939 | ||||||||
\(605\) | 5.44754 | − | 5.44754i | 0.221474 | − | 0.221474i | ||||
\(606\) | 0.363478 | − | 3.30509i | 0.0147653 | − | 0.134260i | ||||
\(607\) | −5.21725 | + | 5.21725i | −0.211761 | + | 0.211761i | −0.805015 | − | 0.593254i | \(-0.797843\pi\) |
0.593254 | + | 0.805015i | \(0.297843\pi\) | |||||||
\(608\) | − | 1.42964i | − | 0.0579795i | ||||||
\(609\) | −3.85202 | + | 35.0262i | −0.156092 | + | 1.41933i | ||||
\(610\) | −0.251587 | + | 0.251587i | −0.0101865 | + | 0.0101865i | ||||
\(611\) | −29.6784 | + | 29.6784i | −1.20066 | + | 1.20066i | ||||
\(612\) | 3.74005 | − | 2.37792i | 0.151183 | − | 0.0961218i | ||||
\(613\) | − | 23.3868i | − | 0.944582i | −0.881443 | − | 0.472291i | \(-0.843427\pi\) | ||
0.881443 | − | 0.472291i | \(-0.156573\pi\) | |||||||
\(614\) | 18.8977 | − | 18.8977i | 0.762649 | − | 0.762649i | ||||
\(615\) | 16.7717 | + | 1.84448i | 0.676302 | + | 0.0743766i | ||||
\(616\) | −4.84806 | + | 4.84806i | −0.195334 | + | 0.195334i | ||||
\(617\) | −17.0385 | −0.685946 | −0.342973 | − | 0.939345i | \(-0.611434\pi\) | ||||
−0.342973 | + | 0.939345i | \(0.611434\pi\) | |||||||
\(618\) | 17.1101 | + | 21.3385i | 0.688268 | + | 0.858360i | ||||
\(619\) | − | 37.2757i | − | 1.49824i | −0.662435 | − | 0.749119i | \(-0.730477\pi\) | ||
0.662435 | − | 0.749119i | \(-0.269523\pi\) | |||||||
\(620\) | −6.31927 | −0.253788 | ||||||||
\(621\) | −13.7341 | + | 40.2798i | −0.551131 | + | 1.61637i | ||||
\(622\) | 4.39947i | 0.176403i | ||||||||
\(623\) | −28.2164 | − | 28.2164i | −1.13047 | − | 1.13047i | ||||
\(624\) | 1.04644 | − | 9.51519i | 0.0418910 | − | 0.380912i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | − | 2.00853i | − | 0.0802770i | ||||||
\(627\) | −0.491435 | + | 4.46859i | −0.0196260 | + | 0.178458i | ||||
\(628\) | − | 12.5462i | − | 0.500649i | ||||||
\(629\) | −7.88074 | + | 4.31815i | −0.314226 | + | 0.172176i | ||||
\(630\) | 2.46215 | − | 11.0587i | 0.0980945 | − | 0.440590i | ||||
\(631\) | 16.9809 | − | 16.9809i | 0.676000 | − | 0.676000i | −0.283093 | − | 0.959093i | \(-0.591360\pi\) |
0.959093 | + | 0.283093i | \(0.0913604\pi\) | |||||||
\(632\) | −11.3872 | −0.452959 | ||||||||
\(633\) | 10.8108 | + | 13.4825i | 0.429690 | + | 0.535879i | ||||
\(634\) | 0.815228 | + | 0.815228i | 0.0323768 | + | 0.0323768i | ||||
\(635\) | −12.1004 | + | 12.1004i | −0.480189 | + | 0.480189i | ||||
\(636\) | 1.59095 | + | 1.98412i | 0.0630853 | + | 0.0786755i | ||||
\(637\) | −28.3794 | − | 28.3794i | −1.12443 | − | 1.12443i | ||||
\(638\) | − | 9.78021i | − | 0.387202i | ||||||
\(639\) | 42.4691 | + | 9.45547i | 1.68005 | + | 0.374053i | ||||
\(640\) | − | 1.00000i | − | 0.0395285i | ||||||
\(641\) | 15.5373i | 0.613687i | 0.951760 | + | 0.306844i | \(0.0992729\pi\) | ||||
−0.951760 | + | 0.306844i | \(0.900727\pi\) | |||||||
\(642\) | −28.4026 | − | 3.12359i | −1.12096 | − | 0.123278i | ||||
\(643\) | 17.0643 | − | 17.0643i | 0.672950 | − | 0.672950i | −0.285445 | − | 0.958395i | \(-0.592141\pi\) |
0.958395 | + | 0.285445i | \(0.0921414\pi\) | |||||||
\(644\) | 21.8707 | + | 21.8707i | 0.861825 | + | 0.861825i | ||||
\(645\) | 9.46886 | + | 11.8089i | 0.372836 | + | 0.464975i | ||||
\(646\) | −1.49344 | − | 1.49344i | −0.0587586 | − | 0.0587586i | ||||
\(647\) | 3.54892 | + | 3.54892i | 0.139522 | + | 0.139522i | 0.773418 | − | 0.633896i | \(-0.218545\pi\) |
−0.633896 | + | 0.773418i | \(0.718545\pi\) | |||||||
\(648\) | −8.46279 | + | 3.06288i | −0.332450 | + | 0.120321i | ||||
\(649\) | −5.94177 | + | 5.94177i | −0.233235 | + | 0.233235i | ||||
\(650\) | 5.52672 | 0.216776 | ||||||||
\(651\) | 41.0872 | + | 4.51858i | 1.61033 | + | 0.177097i | ||||
\(652\) | 15.7971 | + | 15.7971i | 0.618662 | + | 0.618662i | ||||
\(653\) | 23.7536 | + | 23.7536i | 0.929549 | + | 0.929549i | 0.997677 | − | 0.0681273i | \(-0.0217024\pi\) |
−0.0681273 | + | 0.997677i | \(0.521702\pi\) | |||||||
\(654\) | −11.3144 | + | 9.07234i | −0.442427 | + | 0.354757i | ||||
\(655\) | 4.78265 | 0.186874 | ||||||||
\(656\) | −9.74155 | −0.380344 | ||||||||
\(657\) | −20.9075 | − | 4.65493i | −0.815681 | − | 0.181606i | ||||
\(658\) | 20.2797 | − | 20.2797i | 0.790587 | − | 0.790587i | ||||
\(659\) | 35.4935 | 1.38263 | 0.691315 | − | 0.722553i | \(-0.257032\pi\) | ||||
0.691315 | + | 0.722553i | \(0.257032\pi\) | |||||||
\(660\) | −0.343748 | + | 3.12568i | −0.0133804 | + | 0.121667i | ||||
\(661\) | 0.325551 | − | 0.325551i | 0.0126625 | − | 0.0126625i | −0.700747 | − | 0.713410i | \(-0.747150\pi\) |
0.713410 | + | 0.700747i | \(0.247150\pi\) | |||||||
\(662\) | 29.4140i | 1.14321i | ||||||||
\(663\) | −8.84670 | − | 11.0330i | −0.343578 | − | 0.428486i | ||||
\(664\) | −5.05825 | − | 5.05825i | −0.196298 | − | 0.196298i | ||||
\(665\) | −5.39902 | −0.209365 | ||||||||
\(666\) | 17.5265 | − | 5.08137i | 0.679140 | − | 0.196899i | ||||
\(667\) | −44.1206 | −1.70836 | ||||||||
\(668\) | 1.29474 | + | 1.29474i | 0.0500950 | + | 0.0500950i | ||||
\(669\) | −16.5523 | − | 20.6429i | −0.639951 | − | 0.798101i | ||||
\(670\) | 1.79916i | 0.0695075i | ||||||||
\(671\) | −0.456755 | + | 0.456755i | −0.0176328 | + | 0.0176328i | ||||
\(672\) | −0.715047 | + | 6.50188i | −0.0275836 | + | 0.250816i | ||||
\(673\) | −38.7813 | −1.49491 | −0.747455 | − | 0.664312i | \(-0.768725\pi\) | ||||
−0.747455 | + | 0.664312i | \(0.768725\pi\) | |||||||
\(674\) | −21.7056 | + | 21.7056i | −0.836069 | + | 0.836069i | ||||
\(675\) | −2.29188 | − | 4.66340i | −0.0882143 | − | 0.179494i | ||||
\(676\) | −17.5446 | −0.674793 | ||||||||
\(677\) | −12.6745 | −0.487122 | −0.243561 | − | 0.969886i | \(-0.578316\pi\) | ||||
−0.243561 | + | 0.969886i | \(0.578316\pi\) | |||||||
\(678\) | −14.5578 | + | 11.6731i | −0.559089 | + | 0.448301i | ||||
\(679\) | −12.1835 | − | 12.1835i | −0.467560 | − | 0.467560i | ||||
\(680\) | −1.04463 | − | 1.04463i | −0.0400597 | − | 0.0400597i | ||||
\(681\) | −2.17681 | − | 0.239395i | −0.0834154 | − | 0.00917365i | ||||
\(682\) | −11.4726 | −0.439308 | ||||||||
\(683\) | 14.3090 | − | 14.3090i | 0.547518 | − | 0.547518i | −0.378204 | − | 0.925722i | \(-0.623458\pi\) |
0.925722 | + | 0.378204i | \(0.123458\pi\) | |||||||
\(684\) | 2.30116 | + | 3.61932i | 0.0879870 | + | 0.138388i | ||||
\(685\) | −2.92815 | − | 2.92815i | −0.111879 | − | 0.111879i | ||||
\(686\) | 0.699432 | + | 0.699432i | 0.0267044 | + | 0.0267044i | ||||
\(687\) | 24.5082 | + | 30.5649i | 0.935045 | + | 1.16612i | ||||
\(688\) | −6.17939 | − | 6.17939i | −0.235587 | − | 0.235587i | ||||
\(689\) | 5.73815 | − | 5.73815i | 0.218606 | − | 0.218606i | ||||
\(690\) | 14.1006 | + | 1.55072i | 0.536801 | + | 0.0590349i | ||||
\(691\) | 40.9622i | 1.55827i | 0.626854 | + | 0.779137i | \(0.284342\pi\) | ||||
−0.626854 | + | 0.779137i | \(0.715658\pi\) | |||||||
\(692\) | 2.17732i | 0.0827691i | ||||||||
\(693\) | 4.47002 | − | 20.0770i | 0.169802 | − | 0.762662i | ||||
\(694\) | 14.0175i | 0.532099i | ||||||||
\(695\) | −0.977295 | − | 0.977295i | −0.0370709 | − | 0.0370709i | ||||
\(696\) | −5.83702 | − | 7.27951i | −0.221252 | − | 0.275929i | ||||
\(697\) | −10.1763 | + | 10.1763i | −0.385455 | + | 0.385455i | ||||
\(698\) | 1.85469 | + | 1.85469i | 0.0702011 | + | 0.0702011i | ||||
\(699\) | 2.77132 | + | 3.45620i | 0.104821 | + | 0.130725i | ||||
\(700\) | −3.77650 | −0.142738 | ||||||||
\(701\) | 28.6764 | − | 28.6764i | 1.08309 | − | 1.08309i | 0.0868723 | − | 0.996219i | \(-0.472313\pi\) |
0.996219 | − | 0.0868723i | \(-0.0276872\pi\) | |||||||
\(702\) | 12.6666 | + | 25.7733i | 0.478068 | + | 0.972751i | ||||
\(703\) | −4.17875 | − | 7.62633i | −0.157605 | − | 0.287633i | ||||
\(704\) | − | 1.81549i | − | 0.0684239i | ||||||
\(705\) | 1.43792 | − | 13.0749i | 0.0541551 | − | 0.492429i | ||||
\(706\) | − | 32.2895i | − | 1.21523i | ||||||
\(707\) | 7.24973 | 0.272654 | ||||||||
\(708\) | −0.876360 | + | 7.96869i | −0.0329356 | + | 0.299482i | ||||
\(709\) | 18.4451 | + | 18.4451i | 0.692722 | + | 0.692722i | 0.962830 | − | 0.270108i | \(-0.0870594\pi\) |
−0.270108 | + | 0.962830i | \(0.587059\pi\) | |||||||
\(710\) | − | 14.5030i | − | 0.544287i | ||||||
\(711\) | 28.8282 | − | 18.3290i | 1.08114 | − | 0.687390i | ||||
\(712\) | 10.5664 | 0.395993 | ||||||||
\(713\) | 51.7553i | 1.93825i | ||||||||
\(714\) | 6.04509 | + | 7.53901i | 0.226232 | + | 0.282140i | ||||
\(715\) | 10.0337 | 0.375240 | ||||||||
\(716\) | −1.96418 | + | 1.96418i | −0.0734050 | + | 0.0734050i | ||||
\(717\) | 50.0858 | + | 5.50821i | 1.87049 | + | 0.205708i | ||||
\(718\) | −4.45163 | + | 4.45163i | −0.166133 | + | 0.166133i | ||||
\(719\) | − | 48.9218i | − | 1.82448i | −0.409660 | − | 0.912238i | \(-0.634353\pi\) | ||
0.409660 | − | 0.912238i | \(-0.365647\pi\) | |||||||
\(720\) | 1.60961 | + | 2.53163i | 0.0599866 | + | 0.0943483i | ||||
\(721\) | −42.1686 | + | 42.1686i | −1.57044 | + | 1.57044i | ||||
\(722\) | −11.9898 | + | 11.9898i | −0.446214 | + | 0.446214i | ||||
\(723\) | 1.13068 | − | 10.2812i | 0.0420505 | − | 0.382363i | ||||
\(724\) | 21.1962i | 0.787749i | ||||||||
\(725\) | 3.80924 | − | 3.80924i | 0.141472 | − | 0.141472i | ||||
\(726\) | 1.45869 | − | 13.2637i | 0.0541369 | − | 0.492263i | ||||
\(727\) | −8.85958 | + | 8.85958i | −0.328584 | + | 0.328584i | −0.852048 | − | 0.523464i | \(-0.824639\pi\) |
0.523464 | + | 0.852048i | \(0.324639\pi\) | |||||||
\(728\) | 20.8716 | 0.773554 | ||||||||
\(729\) | 16.4946 | − | 21.3759i | 0.610912 | − | 0.791699i | ||||
\(730\) | 7.13983i | 0.264257i | ||||||||
\(731\) | −12.9103 | −0.477506 | ||||||||
\(732\) | −0.0673674 | + | 0.612567i | −0.00248997 | + | 0.0226411i | ||||
\(733\) | 8.30705i | 0.306828i | 0.988162 | + | 0.153414i | \(0.0490268\pi\) | ||||
−0.988162 | + | 0.153414i | \(0.950973\pi\) | |||||||
\(734\) | −22.3888 | − | 22.3888i | −0.826386 | − | 0.826386i | ||||
\(735\) | 12.5026 | + | 1.37498i | 0.461167 | + | 0.0507170i | ||||
\(736\) | −8.19007 | −0.301890 | ||||||||
\(737\) | 3.26636i | 0.120318i | ||||||||
\(738\) | 24.6620 | − | 15.6801i | 0.907822 | − | 0.577193i | ||||
\(739\) | − | 17.1146i | − | 0.629569i | −0.949163 | − | 0.314785i | \(-0.898068\pi\) | ||
0.949163 | − | 0.314785i | \(-0.101932\pi\) | |||||||
\(740\) | −2.92295 | − | 5.33445i | −0.107450 | − | 0.196098i | ||||
\(741\) | 10.6768 | − | 8.56112i | 0.392223 | − | 0.314501i | ||||
\(742\) | −3.92097 | + | 3.92097i | −0.143943 | + | 0.143943i | ||||
\(743\) | −12.6952 | −0.465743 | −0.232871 | − | 0.972508i | \(-0.574812\pi\) | ||||
−0.232871 | + | 0.972508i | \(0.574812\pi\) | |||||||
\(744\) | −8.53917 | + | 6.84706i | −0.313061 | + | 0.251025i | ||||
\(745\) | −7.52830 | − | 7.52830i | −0.275816 | − | 0.275816i | ||||
\(746\) | 6.64483 | − | 6.64483i | 0.243284 | − | 0.243284i | ||||
\(747\) | 20.9474 | + | 4.66382i | 0.766427 | + | 0.170640i | ||||
\(748\) | −1.89651 | − | 1.89651i | −0.0693435 | − | 0.0693435i | ||||
\(749\) | − | 62.3012i | − | 2.27644i | ||||||
\(750\) | −1.35129 | + | 1.08352i | −0.0493421 | + | 0.0395646i | ||||
\(751\) | 28.7797i | 1.05018i | 0.851045 | + | 0.525092i | \(0.175969\pi\) | ||||
−0.851045 | + | 0.525092i | \(0.824031\pi\) | |||||||
\(752\) | 7.59431i | 0.276936i | ||||||||
\(753\) | 4.31003 | − | 39.1908i | 0.157066 | − | 1.42819i | ||||
\(754\) | −21.0526 | + | 21.0526i | −0.766691 | + | 0.766691i | ||||
\(755\) | 3.89164 | + | 3.89164i | 0.141631 | + | 0.141631i | ||||
\(756\) | −8.65526 | − | 17.6113i | −0.314789 | − | 0.640517i | ||||
\(757\) | −10.1110 | − | 10.1110i | −0.367489 | − | 0.367489i | 0.499072 | − | 0.866561i | \(-0.333674\pi\) |
−0.866561 | + | 0.499072i | \(0.833674\pi\) | |||||||
\(758\) | 7.72755 | + | 7.72755i | 0.280677 | + | 0.280677i | ||||
\(759\) | 25.5995 | + | 2.81532i | 0.929204 | + | 0.102190i | ||||
\(760\) | 1.01091 | − | 1.01091i | 0.0366694 | − | 0.0366694i | ||||
\(761\) | 47.0638 | 1.70606 | 0.853031 | − | 0.521860i | \(-0.174762\pi\) | ||||
0.853031 | + | 0.521860i | \(0.174762\pi\) | |||||||
\(762\) | −3.24011 | + | 29.4621i | −0.117377 | + | 1.06730i | ||||
\(763\) | −22.3592 | − | 22.3592i | −0.809458 | − | 0.809458i | ||||
\(764\) | −17.7208 | − | 17.7208i | −0.641114 | − | 0.641114i | ||||
\(765\) | 4.32606 | + | 0.963170i | 0.156409 | + | 0.0348235i | ||||
\(766\) | −6.23731 | −0.225363 | ||||||||
\(767\) | 25.5802 | 0.923648 | ||||||||
\(768\) | −1.08352 | − | 1.35129i | −0.0390982 | − | 0.0487605i | ||||
\(769\) | −5.52401 | + | 5.52401i | −0.199201 | + | 0.199201i | −0.799657 | − | 0.600457i | \(-0.794986\pi\) |
0.600457 | + | 0.799657i | \(0.294986\pi\) | |||||||
\(770\) | −6.85620 | −0.247080 | ||||||||
\(771\) | −3.59866 | − | 0.395764i | −0.129602 | − | 0.0142531i | ||||
\(772\) | −13.8252 | + | 13.8252i | −0.497581 | + | 0.497581i | ||||
\(773\) | 1.33377i | 0.0479722i | 0.999712 | + | 0.0239861i | \(0.00763575\pi\) | ||||
−0.999712 | + | 0.0239861i | \(0.992364\pi\) | |||||||
\(774\) | 25.5903 | + | 5.69753i | 0.919826 | + | 0.204793i | ||||
\(775\) | −4.46840 | − | 4.46840i | −0.160510 | − | 0.160510i | ||||
\(776\) | 4.56246 | 0.163783 | ||||||||
\(777\) | 15.1903 | + | 36.7740i | 0.544948 | + | 1.31926i | ||||
\(778\) | −9.26233 | −0.332071 | ||||||||
\(779\) | −9.84780 | − | 9.84780i | −0.352834 | − | 0.352834i | ||||
\(780\) | 7.46820 | − | 5.98831i | 0.267404 | − | 0.214416i | ||||
\(781\) | − | 26.3300i | − | 0.942163i | ||||||
\(782\) | −8.55559 | + | 8.55559i | −0.305947 | + | 0.305947i | ||||
\(783\) | 26.4943 | + | 9.03372i | 0.946831 | + | 0.322839i | ||||
\(784\) | −7.26192 | −0.259354 | ||||||||
\(785\) | 8.87153 | − | 8.87153i | 0.316638 | − | 0.316638i | ||||
\(786\) | 6.46275 | − | 5.18210i | 0.230519 | − | 0.184839i | ||||
\(787\) | −46.5716 | −1.66010 | −0.830049 | − | 0.557690i | \(-0.811688\pi\) | ||||
−0.830049 | + | 0.557690i | \(0.811688\pi\) | |||||||
\(788\) | −14.5766 | −0.519271 | ||||||||
\(789\) | −11.5360 | − | 14.3868i | −0.410691 | − | 0.512185i | ||||
\(790\) | −8.05198 | − | 8.05198i | −0.286476 | − | 0.286476i | ||||
\(791\) | −28.7688 | − | 28.7688i | −1.02290 | − | 1.02290i | ||||
\(792\) | 2.92223 | + | 4.59615i | 0.103837 | + | 0.163317i | ||||
\(793\) | 1.96640 | 0.0698288 | ||||||||
\(794\) | −12.5963 | + | 12.5963i | −0.447024 | + | 0.447024i | ||||
\(795\) | −0.278013 | + | 2.52796i | −0.00986011 | + | 0.0896574i | ||||
\(796\) | −5.37468 | − | 5.37468i | −0.190500 | − | 0.190500i | ||||
\(797\) | 0.503100 | + | 0.503100i | 0.0178207 | + | 0.0178207i | 0.715961 | − | 0.698140i | \(-0.245989\pi\) |
−0.698140 | + | 0.715961i | \(0.745989\pi\) | |||||||
\(798\) | −7.29564 | + | 5.84995i | −0.258263 | + | 0.207086i | ||||
\(799\) | 7.93324 | + | 7.93324i | 0.280658 | + | 0.280658i | ||||
\(800\) | 0.707107 | − | 0.707107i | 0.0250000 | − | 0.0250000i | ||||
\(801\) | −26.7502 | + | 17.0078i | −0.945173 | + | 0.600941i | ||||
\(802\) | 21.3875i | 0.755220i | ||||||||
\(803\) | 12.9623i | 0.457429i | ||||||||
\(804\) | 1.94942 | + | 2.43118i | 0.0687509 | + | 0.0857412i | ||||
\(805\) | 30.9298i | 1.09013i | ||||||||
\(806\) | 24.6956 | + | 24.6956i | 0.869865 | + | 0.869865i | ||||
\(807\) | 7.58397 | − | 6.08114i | 0.266968 | − | 0.214066i | ||||
\(808\) | −1.35743 | + | 1.35743i | −0.0477543 | + | 0.0477543i | ||||
\(809\) | −6.46702 | − | 6.46702i | −0.227368 | − | 0.227368i | 0.584224 | − | 0.811592i | \(-0.301399\pi\) |
−0.811592 | + | 0.584224i | \(0.801399\pi\) | |||||||
\(810\) | −8.14988 | − | 3.81831i | −0.286357 | − | 0.134162i | ||||
\(811\) | −10.3858 | −0.364696 | −0.182348 | − | 0.983234i | \(-0.558370\pi\) | ||||
−0.182348 | + | 0.983234i | \(0.558370\pi\) | |||||||
\(812\) | 14.3856 | − | 14.3856i | 0.504835 | − | 0.504835i | ||||
\(813\) | −23.7767 | − | 29.6526i | −0.833884 | − | 1.03996i | ||||
\(814\) | −5.30658 | − | 9.68465i | −0.185996 | − | 0.339447i | ||||
\(815\) | 22.3405i | 0.782552i | ||||||||
\(816\) | −2.54347 | − | 0.279720i | −0.0890394 | − | 0.00979214i | ||||
\(817\) | − | 12.4936i | − | 0.437095i | ||||||
\(818\) | 24.2296 | 0.847169 | ||||||||
\(819\) | −52.8393 | + | 33.5952i | −1.84635 | + | 1.17391i | ||||
\(820\) | −6.88832 | − | 6.88832i | −0.240551 | − | 0.240551i | ||||
\(821\) | 48.2408i | 1.68361i | 0.539778 | + | 0.841807i | \(0.318508\pi\) | ||||
−0.539778 | + | 0.841807i | \(0.681492\pi\) | |||||||
\(822\) | −7.12950 | − | 0.784070i | −0.248670 | − | 0.0273476i | ||||
\(823\) | 23.2971 | 0.812086 | 0.406043 | − | 0.913854i | \(-0.366908\pi\) | ||||
0.406043 | + | 0.913854i | \(0.366908\pi\) | |||||||
\(824\) | − | 15.7912i | − | 0.550112i | ||||||
\(825\) | −2.45325 | + | 1.96712i | −0.0854114 | + | 0.0684864i | ||||
\(826\) | −17.4794 | −0.608185 | ||||||||
\(827\) | −12.0735 | + | 12.0735i | −0.419837 | + | 0.419837i | −0.885147 | − | 0.465311i | \(-0.845943\pi\) |
0.465311 | + | 0.885147i | \(0.345943\pi\) | |||||||
\(828\) | 20.7342 | − | 13.1828i | 0.720565 | − | 0.458135i | ||||
\(829\) | 21.5000 | − | 21.5000i | 0.746726 | − | 0.746726i | −0.227137 | − | 0.973863i | \(-0.572937\pi\) |
0.973863 | + | 0.227137i | \(0.0729365\pi\) | |||||||
\(830\) | − | 7.15345i | − | 0.248300i | ||||||
\(831\) | −23.4155 | − | 2.57513i | −0.812276 | − | 0.0893304i | ||||
\(832\) | −3.90798 | + | 3.90798i | −0.135485 | + | 0.135485i | ||||
\(833\) | −7.58601 | + | 7.58601i | −0.262840 | + | 0.262840i | ||||
\(834\) | −2.37953 | − | 0.261690i | −0.0823963 | − | 0.00906157i | ||||
\(835\) | 1.83104i | 0.0633657i | ||||||||
\(836\) | 1.83529 | − | 1.83529i | 0.0634749 | − | 0.0634749i | ||||
\(837\) | 10.5969 | − | 31.0790i | 0.366283 | − | 1.07425i | ||||
\(838\) | 2.11141 | − | 2.11141i | 0.0729375 | − | 0.0729375i | ||||
\(839\) | 16.3634 | 0.564928 | 0.282464 | − | 0.959278i | \(-0.408848\pi\) | ||||
0.282464 | + | 0.959278i | \(0.408848\pi\) | |||||||
\(840\) | −5.10314 | + | 4.09191i | −0.176075 | + | 0.141184i | ||||
\(841\) | 0.0206861i | 0.000713315i | ||||||||
\(842\) | −31.7850 | −1.09538 | ||||||||
\(843\) | 0.590696 | + | 0.0649620i | 0.0203446 | + | 0.00223741i | ||||
\(844\) | − | 9.97747i | − | 0.343439i | ||||||
\(845\) | −12.4059 | − | 12.4059i | −0.426777 | − | 0.426777i | ||||
\(846\) | −12.2239 | − | 19.2260i | −0.420266 | − | 0.661003i | ||||
\(847\) | 29.0941 | 0.999685 | ||||||||
\(848\) | − | 1.46832i | − | 0.0504222i | ||||||
\(849\) | 40.6475 | + | 4.47023i | 1.39502 | + | 0.153418i | ||||
\(850\) | − | 1.47733i | − | 0.0506719i | ||||||
\(851\) | −43.6896 | + | 23.9391i | −1.49766 | + | 0.820623i | ||||
\(852\) | −15.7143 | − | 19.5977i | −0.538362 | − | 0.671407i | ||||
\(853\) | −16.6880 | + | 16.6880i | −0.571385 | + | 0.571385i | −0.932515 | − | 0.361130i | \(-0.882391\pi\) |
0.361130 | + | 0.932515i | \(0.382391\pi\) | |||||||
\(854\) | −1.34367 | −0.0459795 | ||||||||
\(855\) | −0.932077 | + | 4.18641i | −0.0318764 | + | 0.143172i | ||||
\(856\) | 11.6652 | + | 11.6652i | 0.398709 | + | 0.398709i | ||||
\(857\) | −6.77996 | + | 6.77996i | −0.231599 | + | 0.231599i | −0.813360 | − | 0.581761i | \(-0.802364\pi\) |
0.581761 | + | 0.813360i | \(0.302364\pi\) | |||||||
\(858\) | 13.5585 | − | 10.8717i | 0.462878 | − | 0.371155i | ||||
\(859\) | 1.71469 | + | 1.71469i | 0.0585046 | + | 0.0585046i | 0.735754 | − | 0.677249i | \(-0.236828\pi\) |
−0.677249 | + | 0.735754i | \(0.736828\pi\) | |||||||
\(860\) | − | 8.73898i | − | 0.297997i | ||||||
\(861\) | 39.8616 | + | 49.7125i | 1.35848 | + | 1.69420i | ||||
\(862\) | − | 4.84819i | − | 0.165130i | ||||||
\(863\) | − | 24.8856i | − | 0.847115i | −0.905869 | − | 0.423558i | \(-0.860781\pi\) | ||
0.905869 | − | 0.423558i | \(-0.139219\pi\) | |||||||
\(864\) | 4.91812 | + | 1.67692i | 0.167318 | + | 0.0570500i | ||||
\(865\) | −1.53960 | + | 1.53960i | −0.0523478 | + | 0.0523478i | ||||
\(866\) | 3.92294 | + | 3.92294i | 0.133307 | + | 0.133307i | ||||
\(867\) | 20.0227 | − | 16.0551i | 0.680008 | − | 0.545259i | ||||
\(868\) | −16.8749 | − | 16.8749i | −0.572771 | − | 0.572771i | ||||
\(869\) | −14.6183 | − | 14.6183i | −0.495892 | − | 0.495892i | ||||
\(870\) | 1.02000 | − | 9.27479i | 0.0345812 | − | 0.314445i | ||||
\(871\) | 7.03107 | − | 7.03107i | 0.238239 | − | 0.238239i | ||||
\(872\) | 8.37303 | 0.283546 | ||||||||
\(873\) | −11.5505 | + | 7.34377i | −0.390924 | + | 0.248549i | ||||
\(874\) | −8.27940 | − | 8.27940i | −0.280055 | − | 0.280055i | ||||
\(875\) | −2.67039 | − | 2.67039i | −0.0902755 | − | 0.0902755i | ||||
\(876\) | 7.73615 | + | 9.64797i | 0.261380 | + | 0.325975i | ||||
\(877\) | −8.12342 | −0.274309 | −0.137154 | − | 0.990550i | \(-0.543796\pi\) | ||||
−0.137154 | + | 0.990550i | \(0.543796\pi\) | |||||||
\(878\) | 27.6033 | 0.931565 | ||||||||
\(879\) | −36.3265 | + | 29.1281i | −1.22526 | + | 0.982468i | ||||
\(880\) | 1.28375 | − | 1.28375i | 0.0432751 | − | 0.0432751i | ||||
\(881\) | 16.6693 | 0.561605 | 0.280802 | − | 0.959766i | \(-0.409399\pi\) | ||||
0.280802 | + | 0.959766i | \(0.409399\pi\) | |||||||
\(882\) | 18.3845 | − | 11.6889i | 0.619039 | − | 0.393584i | ||||
\(883\) | −30.6559 | + | 30.6559i | −1.03165 | + | 1.03165i | −0.0321725 | + | 0.999482i | \(0.510243\pi\) |
−0.999482 | + | 0.0321725i | \(0.989757\pi\) | |||||||
\(884\) | 8.16478i | 0.274611i | ||||||||
\(885\) | −6.25439 | + | 5.01503i | −0.210239 | + | 0.168578i | ||||
\(886\) | 24.0526 | + | 24.0526i | 0.808062 | + | 0.808062i | ||||
\(887\) | −57.7333 | −1.93850 | −0.969248 | − | 0.246087i | \(-0.920855\pi\) | ||||
−0.969248 | + | 0.246087i | \(0.920855\pi\) | |||||||
\(888\) | −9.72974 | − | 4.04132i | −0.326509 | − | 0.135618i | ||||
\(889\) | −64.6253 | −2.16746 | ||||||||
\(890\) | 7.47158 | + | 7.47158i | 0.250448 | + | 0.250448i | ||||
\(891\) | −14.7960 | − | 6.93211i | −0.495686 | − | 0.232235i | ||||
\(892\) | 15.2765i | 0.511493i | ||||||||
\(893\) | −7.67714 | + | 7.67714i | −0.256906 | + | 0.256906i | ||||
\(894\) | −18.3300 | − | 2.01585i | −0.613047 | − | 0.0674201i | ||||
\(895\) | −2.77777 | −0.0928508 | ||||||||
\(896\) | 2.67039 | − | 2.67039i | 0.0892113 | − | 0.0892113i | ||||
\(897\) | −49.0447 | − | 61.1651i | −1.63756 | − | 2.04224i | ||||
\(898\) | −19.7187 | −0.658020 | ||||||||
\(899\) | 34.0425 | 1.13538 | ||||||||
\(900\) | −0.651967 | + | 2.92830i | −0.0217322 | + | 0.0976100i | ||||
\(901\) | −1.53385 | − | 1.53385i | −0.0510998 | − | 0.0510998i | ||||
\(902\) | −12.5057 | − | 12.5057i | −0.416394 | − | 0.416394i | ||||
\(903\) | −6.24878 | + | 56.8198i | −0.207946 | + | 1.89084i | ||||
\(904\) | 10.7733 | 0.358314 | ||||||||
\(905\) | −14.9879 | + | 14.9879i | −0.498216 | + | 0.498216i | ||||
\(906\) | 9.47540 | + | 1.04206i | 0.314799 | + | 0.0346202i | ||||
\(907\) | 15.3616 | + | 15.3616i | 0.510073 | + | 0.510073i | 0.914549 | − | 0.404476i | \(-0.132546\pi\) |
−0.404476 | + | 0.914549i | \(0.632546\pi\) | |||||||
\(908\) | 0.894036 | + | 0.894036i | 0.0296696 | + | 0.0296696i | ||||
\(909\) | 1.25158 | − | 5.62145i | 0.0415123 | − | 0.186452i | ||||
\(910\) | 14.7585 | + | 14.7585i | 0.489239 | + | 0.489239i | ||||
\(911\) | 38.7894 | − | 38.7894i | 1.28515 | − | 1.28515i | 0.347452 | − | 0.937698i | \(-0.387047\pi\) |
0.937698 | − | 0.347452i | \(-0.112953\pi\) | |||||||
\(912\) | 0.270690 | − | 2.46137i | 0.00896343 | − | 0.0815040i | ||||
\(913\) | − | 12.9870i | − | 0.429808i | ||||||
\(914\) | − | 32.1799i | − | 1.06442i | ||||||
\(915\) | −0.480787 | + | 0.385515i | −0.0158943 | + | 0.0127447i | ||||
\(916\) | − | 22.6190i | − | 0.747354i | ||||||
\(917\) | 12.7715 | + | 12.7715i | 0.421753 | + | 0.421753i | ||||
\(918\) | 6.88937 | − | 3.38585i | 0.227383 | − | 0.111750i | ||||
\(919\) | −31.3044 | + | 31.3044i | −1.03264 | + | 1.03264i | −0.0331880 | + | 0.999449i | \(0.510566\pi\) |
−0.999449 | + | 0.0331880i | \(0.989434\pi\) | |||||||
\(920\) | −5.79126 | − | 5.79126i | −0.190932 | − | 0.190932i | ||||
\(921\) | 36.1137 | − | 28.9575i | 1.18999 | − | 0.954182i | ||||
\(922\) | 27.5387 | 0.906938 | ||||||||
\(923\) | −56.6774 | + | 56.6774i | −1.86556 | + | 1.86556i | ||||
\(924\) | −9.26471 | + | 7.42883i | −0.304786 | + | 0.244391i | ||||
\(925\) | 1.70519 | − | 5.83886i | 0.0560664 | − | 0.191981i | ||||
\(926\) | 7.87556i | 0.258807i | ||||||||
\(927\) | 25.4177 | + | 39.9775i | 0.834826 | + | 1.31303i | ||||
\(928\) | 5.38709i | 0.176840i | ||||||||
\(929\) | −21.4506 | −0.703772 | −0.351886 | − | 0.936043i | \(-0.614460\pi\) | ||||
−0.351886 | + | 0.936043i | \(0.614460\pi\) | |||||||
\(930\) | −10.8797 | − | 1.19650i | −0.356760 | − | 0.0392348i | ||||
\(931\) | −7.34112 | − | 7.34112i | −0.240596 | − | 0.240596i | ||||
\(932\) | − | 2.55770i | − | 0.0837804i | ||||||
\(933\) | −0.833002 | + | 7.57443i | −0.0272713 | + | 0.247976i | ||||
\(934\) | 4.23871 | 0.138695 | ||||||||
\(935\) | − | 2.68208i | − | 0.0877133i | ||||||
\(936\) | 3.60324 | − | 16.1839i | 0.117776 | − | 0.528987i | ||||
\(937\) | 32.1470 | 1.05020 | 0.525098 | − | 0.851042i | \(-0.324029\pi\) | ||||
0.525098 | + | 0.851042i | \(0.324029\pi\) | |||||||
\(938\) | −4.80444 | + | 4.80444i | −0.156871 | + | 0.156871i | ||||
\(939\) | 0.380298 | − | 3.45803i | 0.0124106 | − | 0.112848i | ||||
\(940\) | −5.36999 | + | 5.36999i | −0.175150 | + | 0.175150i | ||||
\(941\) | 5.16763i | 0.168460i | 0.996446 | + | 0.0842300i | \(0.0268430\pi\) | ||||
−0.996446 | + | 0.0842300i | \(0.973157\pi\) | |||||||
\(942\) | 2.37552 | − | 21.6005i | 0.0773987 | − | 0.703782i | ||||
\(943\) | −56.4158 | + | 56.4158i | −1.83715 | + | 1.83715i | ||||
\(944\) | 3.27282 | − | 3.27282i | 0.106521 | − | 0.106521i | ||||
\(945\) | 6.33289 | − | 18.5733i | 0.206009 | − | 0.604189i | ||||
\(946\) | − | 15.8655i | − | 0.515833i | ||||||
\(947\) | −5.43912 | + | 5.43912i | −0.176748 | + | 0.176748i | −0.789936 | − | 0.613189i | \(-0.789886\pi\) |
0.613189 | + | 0.789936i | \(0.289886\pi\) | |||||||
\(948\) | −19.6050 | − | 2.15607i | −0.636742 | − | 0.0700260i | ||||
\(949\) | 27.9023 | − | 27.9023i | 0.905747 | − | 0.905747i | ||||
\(950\) | 1.42964 | 0.0463836 | ||||||||
\(951\) | 1.24920 | + | 1.55791i | 0.0405080 | + | 0.0505187i | ||||
\(952\) | − | 5.57912i | − | 0.180820i | ||||||
\(953\) | 42.6988 | 1.38315 | 0.691574 | − | 0.722305i | \(-0.256917\pi\) | ||||
0.691574 | + | 0.722305i | \(0.256917\pi\) | |||||||
\(954\) | 2.36342 | + | 3.71723i | 0.0765184 | + | 0.120350i | ||||
\(955\) | − | 25.0609i | − | 0.810952i | ||||||
\(956\) | −20.5707 | − | 20.5707i | −0.665305 | − | 0.665305i | ||||
\(957\) | 1.85180 | − | 16.8383i | 0.0598602 | − | 0.544305i | ||||
\(958\) | −5.97679 | −0.193101 | ||||||||
\(959\) | − | 15.6386i | − | 0.504997i | ||||||
\(960\) | 0.189341 | − | 1.72167i | 0.00611097 | − | 0.0555667i | ||||
\(961\) | − | 8.93320i | − | 0.288168i | ||||||
\(962\) | −9.42412 | + | 32.2698i | −0.303846 | + | 1.04042i | ||||
\(963\) | −48.3085 | − | 10.7556i | −1.55672 | − | 0.346594i | ||||
\(964\) | −4.22260 | + | 4.22260i | −0.136001 | + | 0.136001i | ||||
\(965\) | −19.5518 | −0.629396 | ||||||||
\(966\) | 33.5130 | + | 41.7951i | 1.07826 | + | 1.34473i | ||||
\(967\) | 41.8337 | + | 41.8337i | 1.34528 | + | 1.34528i | 0.890710 | + | 0.454573i | \(0.150208\pi\) |
0.454573 | + | 0.890710i | \(0.349792\pi\) | |||||||
\(968\) | −5.44754 | + | 5.44754i | −0.175091 | + | 0.175091i | ||||
\(969\) | −2.28844 | − | 2.85398i | −0.0735154 | − | 0.0916832i | ||||
\(970\) | 3.22614 | + | 3.22614i | 0.103585 | + | 0.103585i | ||||
\(971\) | − | 24.5843i | − | 0.788948i | −0.918907 | − | 0.394474i | \(-0.870927\pi\) | ||
0.918907 | − | 0.394474i | \(-0.129073\pi\) | |||||||
\(972\) | −15.1501 | + | 3.67091i | −0.485938 | + | 0.117745i | ||||
\(973\) | − | 5.21951i | − | 0.167330i | ||||||
\(974\) | − | 4.37777i | − | 0.140273i | ||||||
\(975\) | 9.51519 | + | 1.04644i | 0.304730 | + | 0.0335128i | ||||
\(976\) | 0.251587 | − | 0.251587i | 0.00805312 | − | 0.00805312i | ||||
\(977\) | −30.6814 | − | 30.6814i | −0.981584 | − | 0.981584i | 0.0182494 | − | 0.999833i | \(-0.494191\pi\) |
−0.999833 | + | 0.0182494i | \(0.994191\pi\) | |||||||
\(978\) | 24.2063 | + | 30.1884i | 0.774034 | + | 0.965320i | ||||
\(979\) | 13.5646 | + | 13.5646i | 0.433526 | + | 0.433526i | ||||
\(980\) | −5.13495 | − | 5.13495i | −0.164030 | − | 0.164030i | ||||
\(981\) | −21.1974 | + | 13.4773i | −0.676781 | + | 0.430297i | ||||
\(982\) | 9.99339 | − | 9.99339i | 0.318902 | − | 0.318902i | ||||
\(983\) | 46.4725 | 1.48224 | 0.741121 | − | 0.671372i | \(-0.234295\pi\) | ||||
0.741121 | + | 0.671372i | \(0.234295\pi\) | |||||||
\(984\) | −16.7717 | − | 1.84448i | −0.534664 | − | 0.0587999i | ||||
\(985\) | −10.3072 | − | 10.3072i | −0.328416 | − | 0.328416i | ||||
\(986\) | 5.62750 | + | 5.62750i | 0.179216 | + | 0.179216i | ||||
\(987\) | 38.7548 | − | 31.0752i | 1.23358 | − | 0.989136i | ||||
\(988\) | −7.90121 | −0.251371 | ||||||||
\(989\) | −71.5729 | −2.27588 | ||||||||
\(990\) | −1.18364 | + | 5.31630i | −0.0376186 | + | 0.168963i | ||||
\(991\) | 30.0892 | − | 30.0892i | 0.955814 | − | 0.955814i | −0.0432501 | − | 0.999064i | \(-0.513771\pi\) |
0.999064 | + | 0.0432501i | \(0.0137712\pi\) | |||||||
\(992\) | 6.31927 | 0.200637 | ||||||||
\(993\) | −5.56929 | + | 50.6412i | −0.176736 | + | 1.60705i | ||||
\(994\) | 38.7286 | − | 38.7286i | 1.22840 | − | 1.22840i | ||||
\(995\) | − | 7.60095i | − | 0.240966i | ||||||
\(996\) | −7.75091 | − | 9.66638i | −0.245597 | − | 0.306291i | ||||
\(997\) | −43.2407 | − | 43.2407i | −1.36945 | − | 1.36945i | −0.861227 | − | 0.508221i | \(-0.830303\pi\) |
−0.508221 | − | 0.861227i | \(-0.669697\pi\) | |||||||
\(998\) | −12.9604 | −0.410255 | ||||||||
\(999\) | 31.1370 | − | 5.42995i | 0.985133 | − | 0.171796i |
(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 | 1110.2.u.e.191.5 | ✓ | 40 | |
3.2 | odd | 2 | inner | 1110.2.u.e.191.11 | yes | 40 | |
37.31 | odd | 4 | inner | 1110.2.u.e.401.11 | yes | 40 | |
111.68 | even | 4 | inner | 1110.2.u.e.401.5 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.u.e.191.5 | ✓ | 40 | 1.1 | even | 1 | trivial | |
1110.2.u.e.191.11 | yes | 40 | 3.2 | odd | 2 | inner | |
1110.2.u.e.401.5 | yes | 40 | 111.68 | even | 4 | inner | |
1110.2.u.e.401.11 | yes | 40 | 37.31 | odd | 4 | inner |