Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1274,2,Mod(361,1274)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1274, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1274.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1274 = 2 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1274.v (of order \(6\), degree \(2\), not 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: | \(10.1729412175\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + \cdots + 169 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 182) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 667.6 | ||
Root | \(0.500000 + 2.47866i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1274.667 |
Dual form | 1274.2.v.e.361.6 |
$q$-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 \(\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(885\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 3.34469 | 1.93106 | 0.965528 | − | 0.260298i | \(-0.0838210\pi\) | ||||
0.965528 | + | 0.260298i | \(0.0838210\pi\) | |||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −1.35408 | − | 0.781779i | −0.605563 | − | 0.349622i | 0.165664 | − | 0.986182i | \(-0.447023\pi\) |
−0.771227 | + | 0.636560i | \(0.780357\pi\) | |||||||
\(6\) | 2.89658 | − | 1.67234i | 1.18253 | − | 0.682732i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 8.18694 | 2.72898 | ||||||||
\(10\) | −1.56356 | −0.494440 | ||||||||
\(11\) | 2.86614i | 0.864173i | 0.901832 | + | 0.432087i | \(0.142223\pi\) | ||||
−0.901832 | + | 0.432087i | \(0.857777\pi\) | |||||||
\(12\) | 1.67234 | − | 2.89658i | 0.482764 | − | 0.836172i | ||||
\(13\) | 2.99598 | + | 2.00602i | 0.830935 | + | 0.556370i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.52898 | − | 2.61481i | −1.16938 | − | 0.675140i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.11481 | + | 1.93090i | −0.270380 | + | 0.468312i | −0.968959 | − | 0.247221i | \(-0.920483\pi\) |
0.698579 | + | 0.715533i | \(0.253816\pi\) | |||||||
\(18\) | 7.09010 | − | 4.09347i | 1.67115 | − | 0.964840i | ||||
\(19\) | − | 7.23602i | − | 1.66006i | −0.557722 | − | 0.830028i | \(-0.688324\pi\) | ||
0.557722 | − | 0.830028i | \(-0.311676\pi\) | |||||||
\(20\) | −1.35408 | + | 0.781779i | −0.302782 | + | 0.174811i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.43307 | + | 2.48215i | 0.305531 | + | 0.529196i | ||||
\(23\) | −0.833676 | − | 1.44397i | −0.173833 | − | 0.301088i | 0.765924 | − | 0.642932i | \(-0.222282\pi\) |
−0.939757 | + | 0.341843i | \(0.888949\pi\) | |||||||
\(24\) | − | 3.34469i | − | 0.682732i | ||||||
\(25\) | −1.27764 | − | 2.21294i | −0.255529 | − | 0.442589i | ||||
\(26\) | 3.59760 | + | 0.239275i | 0.705548 | + | 0.0469256i | ||||
\(27\) | 17.3487 | 3.33876 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.41379 | + | 4.18080i | −0.448229 | + | 0.776356i | −0.998271 | − | 0.0587816i | \(-0.981278\pi\) |
0.550042 | + | 0.835137i | \(0.314612\pi\) | |||||||
\(30\) | −5.22961 | −0.954792 | ||||||||
\(31\) | −0.517851 | + | 0.298982i | −0.0930088 | + | 0.0536987i | −0.545783 | − | 0.837927i | \(-0.683768\pi\) |
0.452774 | + | 0.891625i | \(0.350434\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 9.58634i | 1.66877i | ||||||||
\(34\) | 2.22961i | 0.382375i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.09347 | − | 7.09010i | 0.682245 | − | 1.18168i | ||||
\(37\) | −0.0333971 | + | 0.0192818i | −0.00549045 | + | 0.00316991i | −0.502743 | − | 0.864436i | \(-0.667676\pi\) |
0.497252 | + | 0.867606i | \(0.334342\pi\) | |||||||
\(38\) | −3.61801 | − | 6.26657i | −0.586918 | − | 1.01657i | ||||
\(39\) | 10.0206 | + | 6.70951i | 1.60458 | + | 1.07438i | ||||
\(40\) | −0.781779 | + | 1.35408i | −0.123610 | + | 0.214099i | ||||
\(41\) | −6.88896 | − | 3.97734i | −1.07588 | − | 0.621157i | −0.146095 | − | 0.989271i | \(-0.546670\pi\) |
−0.929781 | + | 0.368114i | \(0.880004\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.04571 | + | 8.73942i | 0.769463 | + | 1.33275i | 0.937854 | + | 0.347029i | \(0.112809\pi\) |
−0.168391 | + | 0.985720i | \(0.553857\pi\) | |||||||
\(44\) | 2.48215 | + | 1.43307i | 0.374198 | + | 0.216043i | ||||
\(45\) | −11.0858 | − | 6.40037i | −1.65257 | − | 0.954111i | ||||
\(46\) | −1.44397 | − | 0.833676i | −0.212902 | − | 0.122919i | ||||
\(47\) | −6.08501 | − | 3.51318i | −0.887590 | − | 0.512450i | −0.0144363 | − | 0.999896i | \(-0.504595\pi\) |
−0.873153 | + | 0.487446i | \(0.837929\pi\) | |||||||
\(48\) | −1.67234 | − | 2.89658i | −0.241382 | − | 0.418086i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.21294 | − | 1.27764i | −0.312958 | − | 0.180686i | ||||
\(51\) | −3.72868 | + | 6.45826i | −0.522119 | + | 0.904337i | ||||
\(52\) | 3.23525 | − | 1.59158i | 0.448649 | − | 0.220713i | ||||
\(53\) | 2.99202 | + | 5.18233i | 0.410985 | + | 0.711848i | 0.994998 | − | 0.0998972i | \(-0.0318514\pi\) |
−0.584012 | + | 0.811745i | \(0.698518\pi\) | |||||||
\(54\) | 15.0244 | − | 8.67434i | 2.04456 | − | 1.18043i | ||||
\(55\) | 2.24069 | − | 3.88098i | 0.302134 | − | 0.523312i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 24.2022i | − | 3.20566i | ||||||
\(58\) | 4.82757i | 0.633892i | ||||||||
\(59\) | −0.776138 | − | 0.448103i | −0.101044 | − | 0.0583381i | 0.448626 | − | 0.893719i | \(-0.351913\pi\) |
−0.549671 | + | 0.835381i | \(0.685247\pi\) | |||||||
\(60\) | −4.52898 | + | 2.61481i | −0.584688 | + | 0.337570i | ||||
\(61\) | −14.2569 | −1.82541 | −0.912706 | − | 0.408616i | \(-0.866011\pi\) | ||||
−0.912706 | + | 0.408616i | \(0.866011\pi\) | |||||||
\(62\) | −0.298982 | + | 0.517851i | −0.0379707 | + | 0.0657672i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −2.48853 | − | 5.05850i | −0.308664 | − | 0.627430i | ||||
\(66\) | 4.79317 | + | 8.30201i | 0.589998 | + | 1.02191i | ||||
\(67\) | 1.64086i | 0.200464i | 0.994964 | + | 0.100232i | \(0.0319584\pi\) | ||||
−0.994964 | + | 0.100232i | \(0.968042\pi\) | |||||||
\(68\) | 1.11481 | + | 1.93090i | 0.135190 | + | 0.234156i | ||||
\(69\) | −2.78838 | − | 4.82962i | −0.335682 | − | 0.581418i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.98724 | + | 1.14733i | −0.235841 | + | 0.136163i | −0.613264 | − | 0.789878i | \(-0.710144\pi\) |
0.377422 | + | 0.926041i | \(0.376810\pi\) | |||||||
\(72\) | − | 8.18694i | − | 0.964840i | ||||||
\(73\) | 9.72351 | − | 5.61387i | 1.13805 | − | 0.657054i | 0.192104 | − | 0.981375i | \(-0.438469\pi\) |
0.945947 | + | 0.324321i | \(0.105136\pi\) | |||||||
\(74\) | −0.0192818 | + | 0.0333971i | −0.00224147 | + | 0.00388233i | ||||
\(75\) | −4.27332 | − | 7.40161i | −0.493441 | − | 0.854664i | ||||
\(76\) | −6.26657 | − | 3.61801i | −0.718825 | − | 0.415014i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 12.0329 | + | 0.800299i | 1.36245 | + | 0.0906160i | ||||
\(79\) | −2.13049 | + | 3.69011i | −0.239699 | + | 0.415170i | −0.960628 | − | 0.277839i | \(-0.910382\pi\) |
0.720929 | + | 0.693009i | \(0.243715\pi\) | |||||||
\(80\) | 1.56356i | 0.174811i | ||||||||
\(81\) | 33.4651 | 3.71835 | ||||||||
\(82\) | −7.95469 | −0.878449 | ||||||||
\(83\) | − | 4.94829i | − | 0.543145i | −0.962418 | − | 0.271572i | \(-0.912456\pi\) | ||
0.962418 | − | 0.271572i | \(-0.0875437\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.01907 | − | 1.74306i | 0.327465 | − | 0.189062i | ||||
\(86\) | 8.73942 | + | 5.04571i | 0.942396 | + | 0.544092i | ||||
\(87\) | −8.07337 | + | 13.9835i | −0.865556 | + | 1.49919i | ||||
\(88\) | 2.86614 | 0.305531 | ||||||||
\(89\) | −2.09682 | + | 1.21060i | −0.222263 | + | 0.128323i | −0.606997 | − | 0.794704i | \(-0.707626\pi\) |
0.384735 | + | 0.923027i | \(0.374293\pi\) | |||||||
\(90\) | −12.8007 | −1.34932 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.66735 | −0.173833 | ||||||||
\(93\) | −1.73205 | + | 1.00000i | −0.179605 | + | 0.103695i | ||||
\(94\) | −7.02636 | −0.724714 | ||||||||
\(95\) | −5.65696 | + | 9.79815i | −0.580392 | + | 1.00527i | ||||
\(96\) | −2.89658 | − | 1.67234i | −0.295631 | − | 0.170683i | ||||
\(97\) | −4.23338 | + | 2.44414i | −0.429835 | + | 0.248165i | −0.699276 | − | 0.714852i | \(-0.746494\pi\) |
0.269442 | + | 0.963017i | \(0.413161\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 23.4649i | 2.35831i | ||||||||
\(100\) | −2.55529 | −0.255529 | ||||||||
\(101\) | −7.36747 | −0.733091 | −0.366545 | − | 0.930400i | \(-0.619460\pi\) | ||||
−0.366545 | + | 0.930400i | \(0.619460\pi\) | |||||||
\(102\) | 7.45736i | 0.738388i | ||||||||
\(103\) | 2.89263 | − | 5.01017i | 0.285019 | − | 0.493667i | −0.687595 | − | 0.726094i | \(-0.741333\pi\) |
0.972614 | + | 0.232427i | \(0.0746668\pi\) | |||||||
\(104\) | 2.00602 | − | 2.99598i | 0.196706 | − | 0.293780i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.18233 | + | 2.99202i | 0.503352 | + | 0.290611i | ||||
\(107\) | 0.514478 | + | 0.891102i | 0.0497365 | + | 0.0861461i | 0.889822 | − | 0.456308i | \(-0.150829\pi\) |
−0.840085 | + | 0.542454i | \(0.817495\pi\) | |||||||
\(108\) | 8.67434 | − | 15.0244i | 0.834689 | − | 1.44572i | ||||
\(109\) | −12.2573 | + | 7.07674i | −1.17403 | + | 0.677829i | −0.954627 | − | 0.297805i | \(-0.903746\pi\) |
−0.219407 | + | 0.975633i | \(0.570412\pi\) | |||||||
\(110\) | − | 4.48137i | − | 0.427282i | ||||||
\(111\) | −0.111703 | + | 0.0644917i | −0.0106024 | + | 0.00612128i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.77051 | + | 11.7269i | 0.636916 | + | 1.10317i | 0.986106 | + | 0.166119i | \(0.0531237\pi\) |
−0.349189 | + | 0.937052i | \(0.613543\pi\) | |||||||
\(114\) | −12.1011 | − | 20.9597i | −1.13337 | − | 1.96306i | ||||
\(115\) | 2.60700i | 0.243104i | ||||||||
\(116\) | 2.41379 | + | 4.18080i | 0.224115 | + | 0.388178i | ||||
\(117\) | 24.5279 | + | 16.4232i | 2.26760 | + | 1.51832i | ||||
\(118\) | −0.896206 | −0.0825025 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.61481 | + | 4.52898i | −0.238698 | + | 0.413437i | ||||
\(121\) | 2.78525 | 0.253205 | ||||||||
\(122\) | −12.3469 | + | 7.12846i | −1.11783 | + | 0.645381i | ||||
\(123\) | −23.0414 | − | 13.3030i | −2.07758 | − | 1.19949i | ||||
\(124\) | 0.597963i | 0.0536987i | ||||||||
\(125\) | 11.8131i | 1.05660i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.92583 | − | 8.53178i | 0.437096 | − | 0.757073i | −0.560368 | − | 0.828244i | \(-0.689340\pi\) |
0.997464 | + | 0.0711707i | \(0.0226735\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 16.8763 | + | 29.2306i | 1.48588 | + | 2.57361i | ||||
\(130\) | −4.68438 | − | 3.13653i | −0.410848 | − | 0.275092i | ||||
\(131\) | −7.39614 | + | 12.8105i | −0.646204 | + | 1.11926i | 0.337818 | + | 0.941211i | \(0.390311\pi\) |
−0.984022 | + | 0.178047i | \(0.943022\pi\) | |||||||
\(132\) | 8.30201 | + | 4.79317i | 0.722597 | + | 0.417192i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.820432 | + | 1.42103i | 0.0708746 | + | 0.122758i | ||||
\(135\) | −23.4915 | − | 13.5628i | −2.02183 | − | 1.16730i | ||||
\(136\) | 1.93090 | + | 1.11481i | 0.165573 | + | 0.0955938i | ||||
\(137\) | −0.397503 | − | 0.229499i | −0.0339610 | − | 0.0196074i | 0.482923 | − | 0.875663i | \(-0.339575\pi\) |
−0.516884 | + | 0.856055i | \(0.672908\pi\) | |||||||
\(138\) | −4.82962 | − | 2.78838i | −0.411125 | − | 0.237363i | ||||
\(139\) | −7.65731 | − | 13.2628i | −0.649485 | − | 1.12494i | −0.983246 | − | 0.182283i | \(-0.941651\pi\) |
0.333762 | − | 0.942658i | \(-0.391682\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −20.3525 | − | 11.7505i | −1.71399 | − | 0.989570i | ||||
\(142\) | −1.14733 | + | 1.98724i | −0.0962819 | + | 0.166765i | ||||
\(143\) | −5.74953 | + | 8.58689i | −0.480800 | + | 0.718072i | ||||
\(144\) | −4.09347 | − | 7.09010i | −0.341122 | − | 0.590841i | ||||
\(145\) | 6.53693 | − | 3.77410i | 0.542862 | − | 0.313422i | ||||
\(146\) | 5.61387 | − | 9.72351i | 0.464607 | − | 0.804723i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.0385636i | 0.00316991i | ||||||||
\(149\) | 10.2372i | 0.838660i | 0.907834 | + | 0.419330i | \(0.137735\pi\) | ||||
−0.907834 | + | 0.419330i | \(0.862265\pi\) | |||||||
\(150\) | −7.40161 | − | 4.27332i | −0.604339 | − | 0.348915i | ||||
\(151\) | −13.1731 | + | 7.60551i | −1.07201 | + | 0.618927i | −0.928731 | − | 0.370754i | \(-0.879099\pi\) |
−0.143283 | + | 0.989682i | \(0.545766\pi\) | |||||||
\(152\) | −7.23602 | −0.586918 | ||||||||
\(153\) | −9.12684 | + | 15.8082i | −0.737862 | + | 1.27801i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.934950 | 0.0750970 | ||||||||
\(156\) | 10.8209 | − | 5.32335i | 0.866366 | − | 0.426209i | ||||
\(157\) | 1.13709 | + | 1.96950i | 0.0907500 | + | 0.157184i | 0.907827 | − | 0.419345i | \(-0.137740\pi\) |
−0.817077 | + | 0.576529i | \(0.804407\pi\) | |||||||
\(158\) | 4.26098i | 0.338985i | ||||||||
\(159\) | 10.0074 | + | 17.3333i | 0.793636 | + | 1.37462i | ||||
\(160\) | 0.781779 | + | 1.35408i | 0.0618050 | + | 0.107049i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 28.9816 | − | 16.7326i | 2.27701 | − | 1.31463i | ||||
\(163\) | 0.00979262i | 0.000767017i | 1.00000 | 0.000383509i | \(0.000122075\pi\) | |||||
−1.00000 | 0.000383509i | \(0.999878\pi\) | ||||||||
\(164\) | −6.88896 | + | 3.97734i | −0.537938 | + | 0.310578i | ||||
\(165\) | 7.49440 | − | 12.9807i | 0.583438 | − | 1.01054i | ||||
\(166\) | −2.47414 | − | 4.28534i | −0.192031 | − | 0.332607i | ||||
\(167\) | 21.6080 | + | 12.4754i | 1.67208 | + | 0.965376i | 0.966472 | + | 0.256773i | \(0.0826593\pi\) |
0.705608 | + | 0.708603i | \(0.250674\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.95177 | + | 12.0200i | 0.380906 | + | 0.924614i | ||||
\(170\) | 1.74306 | − | 3.01907i | 0.133687 | − | 0.231552i | ||||
\(171\) | − | 59.2408i | − | 4.53026i | ||||||
\(172\) | 10.0914 | 0.769463 | ||||||||
\(173\) | 3.20550 | 0.243709 | 0.121855 | − | 0.992548i | \(-0.461116\pi\) | ||||
0.121855 | + | 0.992548i | \(0.461116\pi\) | |||||||
\(174\) | 16.1467i | 1.22408i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.48215 | − | 1.43307i | 0.187099 | − | 0.108022i | ||||
\(177\) | −2.59594 | − | 1.49877i | −0.195123 | − | 0.112654i | ||||
\(178\) | −1.21060 | + | 2.09682i | −0.0907383 | + | 0.157163i | ||||
\(179\) | 15.8000 | 1.18094 | 0.590472 | − | 0.807058i | \(-0.298942\pi\) | ||||
0.590472 | + | 0.807058i | \(0.298942\pi\) | |||||||
\(180\) | −11.0858 | + | 6.40037i | −0.826285 | + | 0.477056i | ||||
\(181\) | 9.11907 | 0.677815 | 0.338908 | − | 0.940820i | \(-0.389943\pi\) | ||||
0.338908 | + | 0.940820i | \(0.389943\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −47.6850 | −3.52497 | ||||||||
\(184\) | −1.44397 | + | 0.833676i | −0.106451 | + | 0.0614594i | ||||
\(185\) | 0.0602965 | 0.00443308 | ||||||||
\(186\) | −1.00000 | + | 1.73205i | −0.0733236 | + | 0.127000i | ||||
\(187\) | −5.53423 | − | 3.19519i | −0.404703 | − | 0.233655i | ||||
\(188\) | −6.08501 | + | 3.51318i | −0.443795 | + | 0.256225i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 11.3139i | 0.820799i | ||||||||
\(191\) | −3.26137 | −0.235984 | −0.117992 | − | 0.993015i | \(-0.537646\pi\) | ||||
−0.117992 | + | 0.993015i | \(0.537646\pi\) | |||||||
\(192\) | −3.34469 | −0.241382 | ||||||||
\(193\) | − | 22.0730i | − | 1.58885i | −0.607361 | − | 0.794426i | \(-0.707772\pi\) | ||
0.607361 | − | 0.794426i | \(-0.292228\pi\) | |||||||
\(194\) | −2.44414 | + | 4.23338i | −0.175479 | + | 0.303939i | ||||
\(195\) | −8.32336 | − | 16.9191i | −0.596048 | − | 1.21160i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.56660 | − | 2.63653i | −0.325357 | − | 0.187845i | 0.328421 | − | 0.944531i | \(-0.393484\pi\) |
−0.653778 | + | 0.756687i | \(0.726817\pi\) | |||||||
\(198\) | 11.7324 | + | 20.3212i | 0.833789 | + | 1.44416i | ||||
\(199\) | 4.43381 | − | 7.67958i | 0.314304 | − | 0.544391i | −0.664985 | − | 0.746857i | \(-0.731562\pi\) |
0.979289 | + | 0.202466i | \(0.0648954\pi\) | |||||||
\(200\) | −2.21294 | + | 1.27764i | −0.156479 | + | 0.0903431i | ||||
\(201\) | 5.48818i | 0.387106i | ||||||||
\(202\) | −6.38042 | + | 3.68373i | −0.448924 | + | 0.259187i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.72868 | + | 6.45826i | 0.261060 | + | 0.452169i | ||||
\(205\) | 6.21881 | + | 10.7713i | 0.434340 | + | 0.752300i | ||||
\(206\) | − | 5.78525i | − | 0.403077i | ||||||
\(207\) | −6.82525 | − | 11.8217i | −0.474388 | − | 0.821663i | ||||
\(208\) | 0.239275 | − | 3.59760i | 0.0165907 | − | 0.249449i | ||||
\(209\) | 20.7394 | 1.43458 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.28453 | + | 5.68898i | −0.226117 | + | 0.391646i | −0.956654 | − | 0.291227i | \(-0.905936\pi\) |
0.730537 | + | 0.682873i | \(0.239270\pi\) | |||||||
\(212\) | 5.98404 | 0.410985 | ||||||||
\(213\) | −6.64668 | + | 3.83746i | −0.455423 | + | 0.262939i | ||||
\(214\) | 0.891102 | + | 0.514478i | 0.0609145 | + | 0.0351690i | ||||
\(215\) | − | 15.7785i | − | 1.07609i | ||||||
\(216\) | − | 17.3487i | − | 1.18043i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.07674 | + | 12.2573i | −0.479297 | + | 0.830167i | ||||
\(219\) | 32.5221 | − | 18.7766i | 2.19764 | − | 1.26881i | ||||
\(220\) | −2.24069 | − | 3.88098i | −0.151067 | − | 0.261656i | ||||
\(221\) | −7.21336 | + | 3.54861i | −0.485223 | + | 0.238706i | ||||
\(222\) | −0.0644917 | + | 0.111703i | −0.00432840 | + | 0.00749700i | ||||
\(223\) | −14.6463 | − | 8.45606i | −0.980790 | − | 0.566260i | −0.0782817 | − | 0.996931i | \(-0.524943\pi\) |
−0.902509 | + | 0.430672i | \(0.858277\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.4600 | − | 18.1172i | −0.697333 | − | 1.20782i | ||||
\(226\) | 11.7269 | + | 6.77051i | 0.780060 | + | 0.450368i | ||||
\(227\) | 13.9709 | + | 8.06611i | 0.927282 | + | 0.535367i | 0.885951 | − | 0.463779i | \(-0.153507\pi\) |
0.0413312 | + | 0.999146i | \(0.486840\pi\) | |||||||
\(228\) | −20.9597 | − | 12.1011i | −1.38809 | − | 0.801415i | ||||
\(229\) | 5.98583 | + | 3.45592i | 0.395555 | + | 0.228374i | 0.684564 | − | 0.728953i | \(-0.259993\pi\) |
−0.289009 | + | 0.957326i | \(0.593326\pi\) | |||||||
\(230\) | 1.30350 | + | 2.25773i | 0.0859502 | + | 0.148870i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.18080 | + | 2.41379i | 0.274483 | + | 0.158473i | ||||
\(233\) | −3.73702 | + | 6.47272i | −0.244821 | + | 0.424042i | −0.962081 | − | 0.272763i | \(-0.912062\pi\) |
0.717261 | + | 0.696805i | \(0.245396\pi\) | |||||||
\(234\) | 29.4533 | + | 1.95893i | 1.92543 | + | 0.128059i | ||||
\(235\) | 5.49306 | + | 9.51426i | 0.358328 | + | 0.620642i | ||||
\(236\) | −0.776138 | + | 0.448103i | −0.0505222 | + | 0.0291690i | ||||
\(237\) | −7.12582 | + | 12.3423i | −0.462872 | + | 0.801717i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 19.8696i | − | 1.28526i | −0.766179 | − | 0.642628i | \(-0.777844\pi\) | ||
0.766179 | − | 0.642628i | \(-0.222156\pi\) | |||||||
\(240\) | 5.22961i | 0.337570i | ||||||||
\(241\) | 9.21842 | + | 5.32226i | 0.593811 | + | 0.342837i | 0.766603 | − | 0.642121i | \(-0.221946\pi\) |
−0.172792 | + | 0.984958i | \(0.555279\pi\) | |||||||
\(242\) | 2.41210 | − | 1.39263i | 0.155055 | − | 0.0895213i | ||||
\(243\) | 59.8843 | 3.84158 | ||||||||
\(244\) | −7.12846 | + | 12.3469i | −0.456353 | + | 0.790427i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −26.6060 | −1.69633 | ||||||||
\(247\) | 14.5156 | − | 21.6789i | 0.923605 | − | 1.37940i | ||||
\(248\) | 0.298982 | + | 0.517851i | 0.0189853 | + | 0.0328836i | ||||
\(249\) | − | 16.5505i | − | 1.04884i | ||||||
\(250\) | 5.90656 | + | 10.2305i | 0.373564 | + | 0.647032i | ||||
\(251\) | 7.95696 | + | 13.7819i | 0.502239 | + | 0.869904i | 0.999997 | + | 0.00258749i | \(0.000823625\pi\) |
−0.497757 | + | 0.867316i | \(0.665843\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.13861 | − | 2.38943i | 0.260192 | − | 0.150222i | ||||
\(254\) | − | 9.85165i | − | 0.618148i | ||||||
\(255\) | 10.0979 | − | 5.83000i | 0.632352 | − | 0.365089i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −15.5509 | − | 26.9350i | −0.970039 | − | 1.68016i | −0.695420 | − | 0.718603i | \(-0.744782\pi\) |
−0.274619 | − | 0.961553i | \(-0.588552\pi\) | |||||||
\(258\) | 29.2306 | + | 16.8763i | 1.81982 | + | 1.05067i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −5.62506 | − | 0.374120i | −0.348851 | − | 0.0232019i | ||||
\(261\) | −19.7615 | + | 34.2280i | −1.22321 | + | 2.11866i | ||||
\(262\) | 14.7923i | 0.913871i | ||||||||
\(263\) | −28.3747 | −1.74966 | −0.874829 | − | 0.484432i | \(-0.839026\pi\) | ||||
−0.874829 | + | 0.484432i | \(0.839026\pi\) | |||||||
\(264\) | 9.58634 | 0.589998 | ||||||||
\(265\) | − | 9.35639i | − | 0.574758i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.01321 | + | 4.04908i | −0.429202 | + | 0.247800i | ||||
\(268\) | 1.42103 | + | 0.820432i | 0.0868032 | + | 0.0501159i | ||||
\(269\) | 10.7008 | − | 18.5344i | 0.652441 | − | 1.13006i | −0.330088 | − | 0.943950i | \(-0.607078\pi\) |
0.982529 | − | 0.186111i | \(-0.0595883\pi\) | |||||||
\(270\) | −27.1257 | −1.65082 | ||||||||
\(271\) | −4.97667 | + | 2.87328i | −0.302311 | + | 0.174539i | −0.643481 | − | 0.765462i | \(-0.722510\pi\) |
0.341170 | + | 0.940002i | \(0.389177\pi\) | |||||||
\(272\) | 2.22961 | 0.135190 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.458997 | −0.0277290 | ||||||||
\(275\) | 6.34260 | − | 3.66190i | 0.382473 | − | 0.220821i | ||||
\(276\) | −5.57677 | −0.335682 | ||||||||
\(277\) | 13.3010 | − | 23.0380i | 0.799180 | − | 1.38422i | −0.120971 | − | 0.992656i | \(-0.538601\pi\) |
0.920151 | − | 0.391564i | \(-0.128066\pi\) | |||||||
\(278\) | −13.2628 | − | 7.65731i | −0.795453 | − | 0.459255i | ||||
\(279\) | −4.23962 | + | 2.44774i | −0.253819 | + | 0.146543i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6.69143i | − | 0.399177i | −0.979880 | − | 0.199589i | \(-0.936039\pi\) | ||
0.979880 | − | 0.199589i | \(-0.0639606\pi\) | |||||||
\(282\) | −23.5010 | −1.39946 | ||||||||
\(283\) | −19.9338 | −1.18494 | −0.592472 | − | 0.805591i | \(-0.701848\pi\) | ||||
−0.592472 | + | 0.805591i | \(0.701848\pi\) | |||||||
\(284\) | 2.29466i | 0.136163i | ||||||||
\(285\) | −18.9208 | + | 32.7717i | −1.12077 | + | 1.94123i | ||||
\(286\) | −0.685794 | + | 10.3112i | −0.0405519 | + | 0.609716i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −7.09010 | − | 4.09347i | −0.417788 | − | 0.241210i | ||||
\(289\) | 6.01442 | + | 10.4173i | 0.353789 | + | 0.612781i | ||||
\(290\) | 3.77410 | − | 6.53693i | 0.221623 | − | 0.383861i | ||||
\(291\) | −14.1593 | + | 8.17490i | −0.830035 | + | 0.479221i | ||||
\(292\) | − | 11.2277i | − | 0.657054i | ||||||
\(293\) | −7.67375 | + | 4.43044i | −0.448305 | + | 0.258829i | −0.707114 | − | 0.707099i | \(-0.750003\pi\) |
0.258809 | + | 0.965929i | \(0.416670\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.700635 | + | 1.21354i | 0.0407926 | + | 0.0706548i | ||||
\(296\) | 0.0192818 | + | 0.0333971i | 0.00112073 | + | 0.00194117i | ||||
\(297\) | 49.7237i | 2.88526i | ||||||||
\(298\) | 5.11858 | + | 8.86563i | 0.296511 | + | 0.513572i | ||||
\(299\) | 0.398955 | − | 5.99847i | 0.0230722 | − | 0.346900i | ||||
\(300\) | −8.54664 | −0.493441 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −7.60551 | + | 13.1731i | −0.437648 | + | 0.758028i | ||||
\(303\) | −24.6419 | −1.41564 | ||||||||
\(304\) | −6.26657 | + | 3.61801i | −0.359413 | + | 0.207507i | ||||
\(305\) | 19.3050 | + | 11.1458i | 1.10540 | + | 0.638205i | ||||
\(306\) | 18.2537i | 1.04349i | ||||||||
\(307\) | 8.34636i | 0.476352i | 0.971222 | + | 0.238176i | \(0.0765495\pi\) | ||||
−0.971222 | + | 0.238176i | \(0.923450\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.67493 | − | 16.7575i | 0.550387 | − | 0.953299i | ||||
\(310\) | 0.809690 | − | 0.467475i | 0.0459873 | − | 0.0265508i | ||||
\(311\) | 3.34448 | + | 5.79281i | 0.189648 | + | 0.328480i | 0.945133 | − | 0.326686i | \(-0.105932\pi\) |
−0.755485 | + | 0.655166i | \(0.772599\pi\) | |||||||
\(312\) | 6.70951 | − | 10.0206i | 0.379851 | − | 0.567305i | ||||
\(313\) | 10.6894 | − | 18.5145i | 0.604199 | − | 1.04650i | −0.387978 | − | 0.921669i | \(-0.626826\pi\) |
0.992177 | − | 0.124835i | \(-0.0398402\pi\) | |||||||
\(314\) | 1.96950 | + | 1.13709i | 0.111146 | + | 0.0641699i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.13049 | + | 3.69011i | 0.119849 | + | 0.207585i | ||||
\(317\) | −27.4336 | − | 15.8388i | −1.54083 | − | 0.889596i | −0.998787 | − | 0.0492433i | \(-0.984319\pi\) |
−0.542039 | − | 0.840353i | \(-0.682348\pi\) | |||||||
\(318\) | 17.3333 | + | 10.0074i | 0.972002 | + | 0.561185i | ||||
\(319\) | −11.9828 | − | 6.91825i | −0.670906 | − | 0.387348i | ||||
\(320\) | 1.35408 | + | 0.781779i | 0.0756954 | + | 0.0437028i | ||||
\(321\) | 1.72077 | + | 2.98046i | 0.0960439 | + | 0.166353i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.9720 | + | 8.06675i | 0.777424 | + | 0.448846i | ||||
\(324\) | 16.7326 | − | 28.9816i | 0.929587 | − | 1.61009i | ||||
\(325\) | 0.611416 | − | 9.19291i | 0.0339152 | − | 0.509931i | ||||
\(326\) | 0.00489631 | + | 0.00848066i | 0.000271182 | + | 0.000469700i | ||||
\(327\) | −40.9967 | + | 23.6695i | −2.26713 | + | 1.30893i | ||||
\(328\) | −3.97734 | + | 6.88896i | −0.219612 | + | 0.380379i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − | 14.9888i | − | 0.825106i | ||||||
\(331\) | − | 24.6695i | − | 1.35596i | −0.735081 | − | 0.677979i | \(-0.762856\pi\) | ||
0.735081 | − | 0.677979i | \(-0.237144\pi\) | |||||||
\(332\) | −4.28534 | − | 2.47414i | −0.235189 | − | 0.135786i | ||||
\(333\) | −0.273420 | + | 0.157859i | −0.0149833 | + | 0.00865062i | ||||
\(334\) | 24.9508 | 1.36525 | ||||||||
\(335\) | 1.28279 | − | 2.22186i | 0.0700865 | − | 0.121393i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.0871 | 1.53000 | 0.765002 | − | 0.644028i | \(-0.222738\pi\) | ||||
0.765002 | + | 0.644028i | \(0.222738\pi\) | |||||||
\(338\) | 10.2984 | + | 7.93372i | 0.560156 | + | 0.431538i | ||||
\(339\) | 22.6453 | + | 39.2227i | 1.22992 | + | 2.13029i | ||||
\(340\) | − | 3.48613i | − | 0.189062i | ||||||
\(341\) | −0.856923 | − | 1.48423i | −0.0464050 | − | 0.0803757i | ||||
\(342\) | −29.6204 | − | 51.3040i | −1.60169 | − | 2.77420i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 8.73942 | − | 5.04571i | 0.471198 | − | 0.272046i | ||||
\(345\) | 8.71960i | 0.469447i | ||||||||
\(346\) | 2.77604 | − | 1.60275i | 0.149241 | − | 0.0861643i | ||||
\(347\) | 5.05398 | − | 8.75374i | 0.271312 | − | 0.469926i | −0.697886 | − | 0.716209i | \(-0.745876\pi\) |
0.969198 | + | 0.246283i | \(0.0792093\pi\) | |||||||
\(348\) | 8.07337 | + | 13.9835i | 0.432778 | + | 0.749593i | ||||
\(349\) | −15.0596 | − | 8.69465i | −0.806121 | − | 0.465414i | 0.0394863 | − | 0.999220i | \(-0.487428\pi\) |
−0.845607 | + | 0.533806i | \(0.820761\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 51.9763 | + | 34.8018i | 2.77429 | + | 1.85758i | ||||
\(352\) | 1.43307 | − | 2.48215i | 0.0763828 | − | 0.132299i | ||||
\(353\) | − | 3.32659i | − | 0.177056i | −0.996074 | − | 0.0885282i | \(-0.971784\pi\) | ||
0.996074 | − | 0.0885282i | \(-0.0282163\pi\) | |||||||
\(354\) | −2.99753 | −0.159317 | ||||||||
\(355\) | 3.58784 | 0.190423 | ||||||||
\(356\) | 2.42120i | 0.128323i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.6832 | − | 7.89998i | 0.723177 | − | 0.417527i | ||||
\(359\) | 6.94911 | + | 4.01207i | 0.366760 | + | 0.211749i | 0.672042 | − | 0.740513i | \(-0.265417\pi\) |
−0.305282 | + | 0.952262i | \(0.598751\pi\) | |||||||
\(360\) | −6.40037 | + | 11.0858i | −0.337329 | + | 0.584271i | ||||
\(361\) | −33.3599 | −1.75579 | ||||||||
\(362\) | 7.89735 | − | 4.55954i | 0.415075 | − | 0.239644i | ||||
\(363\) | 9.31579 | 0.488952 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −17.5552 | −0.918882 | ||||||||
\(366\) | −41.2964 | + | 23.8425i | −2.15860 | + | 1.24627i | ||||
\(367\) | 1.03908 | 0.0542395 | 0.0271198 | − | 0.999632i | \(-0.491366\pi\) | ||||
0.0271198 | + | 0.999632i | \(0.491366\pi\) | |||||||
\(368\) | −0.833676 | + | 1.44397i | −0.0434583 | + | 0.0752721i | ||||
\(369\) | −56.3995 | − | 32.5623i | −2.93604 | − | 1.69512i | ||||
\(370\) | 0.0522183 | − | 0.0301482i | 0.00271470 | − | 0.00156733i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.00000i | 0.103695i | ||||||||
\(373\) | 27.3124 | 1.41418 | 0.707092 | − | 0.707122i | \(-0.250007\pi\) | ||||
0.707092 | + | 0.707122i | \(0.250007\pi\) | |||||||
\(374\) | −6.39038 | −0.330438 | ||||||||
\(375\) | 39.5112i | 2.04035i | ||||||||
\(376\) | −3.51318 | + | 6.08501i | −0.181178 | + | 0.313810i | ||||
\(377\) | −15.6184 | + | 7.68349i | −0.804390 | + | 0.395720i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.91535 | − | 1.10583i | −0.0983850 | − | 0.0568026i | 0.450000 | − | 0.893028i | \(-0.351424\pi\) |
−0.548385 | + | 0.836226i | \(0.684757\pi\) | |||||||
\(380\) | 5.65696 | + | 9.79815i | 0.290196 | + | 0.502634i | ||||
\(381\) | 16.4754 | − | 28.5361i | 0.844058 | − | 1.46195i | ||||
\(382\) | −2.82443 | + | 1.63068i | −0.144510 | + | 0.0834331i | ||||
\(383\) | 22.3386i | 1.14145i | 0.821142 | + | 0.570724i | \(0.193337\pi\) | ||||
−0.821142 | + | 0.570724i | \(0.806663\pi\) | |||||||
\(384\) | −2.89658 | + | 1.67234i | −0.147816 | + | 0.0853414i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.0365 | − | 19.1158i | −0.561744 | − | 0.972969i | ||||
\(387\) | 41.3089 | + | 71.5491i | 2.09985 | + | 3.63704i | ||||
\(388\) | 4.88829i | 0.248165i | ||||||||
\(389\) | 6.13022 | + | 10.6178i | 0.310814 | + | 0.538346i | 0.978539 | − | 0.206062i | \(-0.0660649\pi\) |
−0.667725 | + | 0.744408i | \(0.732732\pi\) | |||||||
\(390\) | −15.6678 | − | 10.4907i | −0.793370 | − | 0.531217i | ||||
\(391\) | 3.71755 | 0.188004 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −24.7378 | + | 42.8471i | −1.24786 | + | 2.16135i | ||||
\(394\) | −5.27305 | −0.265653 | ||||||||
\(395\) | 5.76971 | − | 3.33114i | 0.290305 | − | 0.167608i | ||||
\(396\) | 20.3212 | + | 11.7324i | 1.02118 | + | 0.589578i | ||||
\(397\) | 2.93517i | 0.147312i | 0.997284 | + | 0.0736561i | \(0.0234667\pi\) | ||||
−0.997284 | + | 0.0736561i | \(0.976533\pi\) | |||||||
\(398\) | − | 8.86762i | − | 0.444493i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.27764 | + | 2.21294i | −0.0638822 | + | 0.110647i | ||||
\(401\) | −18.9229 | + | 10.9251i | −0.944963 | + | 0.545575i | −0.891513 | − | 0.452996i | \(-0.850355\pi\) |
−0.0534502 | + | 0.998571i | \(0.517022\pi\) | |||||||
\(402\) | 2.74409 | + | 4.75290i | 0.136863 | + | 0.237053i | ||||
\(403\) | −2.15123 | − | 0.143077i | −0.107161 | − | 0.00712719i | ||||
\(404\) | −3.68373 | + | 6.38042i | −0.183273 | + | 0.317438i | ||||
\(405\) | −45.3145 | − | 26.1623i | −2.25169 | − | 1.30002i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.0552644 | − | 0.0957207i | −0.00273935 | − | 0.00474470i | ||||
\(408\) | 6.45826 | + | 3.72868i | 0.319731 | + | 0.184597i | ||||
\(409\) | 6.39292 | + | 3.69095i | 0.316109 | + | 0.182506i | 0.649657 | − | 0.760227i | \(-0.274912\pi\) |
−0.333548 | + | 0.942733i | \(0.608246\pi\) | |||||||
\(410\) | 10.7713 | + | 6.21881i | 0.531956 | + | 0.307125i | ||||
\(411\) | −1.32952 | − | 0.767601i | −0.0655806 | − | 0.0378630i | ||||
\(412\) | −2.89263 | − | 5.01017i | −0.142509 | − | 0.246834i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −11.8217 | − | 6.82525i | −0.581004 | − | 0.335443i | ||||
\(415\) | −3.86846 | + | 6.70038i | −0.189895 | + | 0.328909i | ||||
\(416\) | −1.59158 | − | 3.23525i | −0.0780338 | − | 0.158621i | ||||
\(417\) | −25.6113 | − | 44.3601i | −1.25419 | − | 2.17232i | ||||
\(418\) | 17.9609 | − | 10.3697i | 0.878495 | − | 0.507199i | ||||
\(419\) | 4.29137 | − | 7.43287i | 0.209647 | − | 0.363119i | −0.741956 | − | 0.670448i | \(-0.766102\pi\) |
0.951603 | + | 0.307329i | \(0.0994352\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.49525i | 0.365296i | 0.983178 | + | 0.182648i | \(0.0584669\pi\) | ||||
−0.983178 | + | 0.182648i | \(0.941533\pi\) | |||||||
\(422\) | 6.56907i | 0.319777i | ||||||||
\(423\) | −49.8176 | − | 28.7622i | −2.42221 | − | 1.39847i | ||||
\(424\) | 5.18233 | − | 2.99202i | 0.251676 | − | 0.145305i | ||||
\(425\) | 5.69730 | 0.276360 | ||||||||
\(426\) | −3.83746 | + | 6.64668i | −0.185926 | + | 0.322033i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.02896 | 0.0497365 | ||||||||
\(429\) | −19.2304 | + | 28.7205i | −0.928452 | + | 1.38664i | ||||
\(430\) | −7.88925 | − | 13.6646i | −0.380454 | − | 0.658965i | ||||
\(431\) | 16.4791i | 0.793772i | 0.917868 | + | 0.396886i | \(0.129909\pi\) | ||||
−0.917868 | + | 0.396886i | \(0.870091\pi\) | |||||||
\(432\) | −8.67434 | − | 15.0244i | −0.417344 | − | 0.722862i | ||||
\(433\) | −12.7805 | − | 22.1365i | −0.614192 | − | 1.06381i | −0.990526 | − | 0.137328i | \(-0.956149\pi\) |
0.376333 | − | 0.926484i | \(-0.377185\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 21.8640 | − | 12.6232i | 1.04830 | − | 0.605235i | ||||
\(436\) | 14.1535i | 0.677829i | ||||||||
\(437\) | −10.4486 | + | 6.03249i | −0.499823 | + | 0.288573i | ||||
\(438\) | 18.7766 | − | 32.5221i | 0.897183 | − | 1.55397i | ||||
\(439\) | 4.60420 | + | 7.97470i | 0.219746 | + | 0.380612i | 0.954730 | − | 0.297473i | \(-0.0961437\pi\) |
−0.734984 | + | 0.678084i | \(0.762810\pi\) | |||||||
\(440\) | −3.88098 | − | 2.24069i | −0.185019 | − | 0.106821i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.47264 | + | 6.67987i | −0.212742 | + | 0.317729i | ||||
\(443\) | 3.10379 | − | 5.37593i | 0.147466 | − | 0.255418i | −0.782824 | − | 0.622243i | \(-0.786222\pi\) |
0.930290 | + | 0.366825i | \(0.119555\pi\) | |||||||
\(444\) | 0.128983i | 0.00612128i | ||||||||
\(445\) | 3.78569 | 0.179459 | ||||||||
\(446\) | −16.9121 | −0.800812 | ||||||||
\(447\) | 34.2401i | 1.61950i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.51968 | − | 2.60944i | 0.213297 | − | 0.123147i | −0.389546 | − | 0.921007i | \(-0.627368\pi\) |
0.602843 | + | 0.797860i | \(0.294035\pi\) | |||||||
\(450\) | −18.1172 | − | 10.4600i | −0.854055 | − | 0.493089i | ||||
\(451\) | 11.3996 | − | 19.7447i | 0.536787 | − | 0.929743i | ||||
\(452\) | 13.5410 | 0.636916 | ||||||||
\(453\) | −44.0600 | + | 25.4380i | −2.07012 | + | 1.19518i | ||||
\(454\) | 16.1322 | 0.757123 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −24.2022 | −1.13337 | ||||||||
\(457\) | 29.3870 | − | 16.9666i | 1.37467 | − | 0.793664i | 0.383155 | − | 0.923684i | \(-0.374838\pi\) |
0.991511 | + | 0.130021i | \(0.0415043\pi\) | |||||||
\(458\) | 6.91184 | 0.322969 | ||||||||
\(459\) | −19.3404 | + | 33.4986i | −0.902733 | + | 1.56358i | ||||
\(460\) | 2.25773 | + | 1.30350i | 0.105267 | + | 0.0607760i | ||||
\(461\) | 0.731583 | − | 0.422380i | 0.0340732 | − | 0.0196722i | −0.482867 | − | 0.875694i | \(-0.660404\pi\) |
0.516940 | + | 0.856022i | \(0.327071\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 6.50221i | − | 0.302183i | −0.988520 | − | 0.151092i | \(-0.951721\pi\) | ||
0.988520 | − | 0.151092i | \(-0.0482789\pi\) | |||||||
\(464\) | 4.82757 | 0.224115 | ||||||||
\(465\) | 3.12712 | 0.145016 | ||||||||
\(466\) | 7.47405i | 0.346229i | ||||||||
\(467\) | −4.76379 | + | 8.25113i | −0.220442 | + | 0.381817i | −0.954942 | − | 0.296792i | \(-0.904083\pi\) |
0.734500 | + | 0.678608i | \(0.237417\pi\) | |||||||
\(468\) | 26.4868 | − | 13.0302i | 1.22435 | − | 0.602321i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 9.51426 | + | 5.49306i | 0.438860 | + | 0.253376i | ||||
\(471\) | 3.80322 | + | 6.58738i | 0.175243 | + | 0.303530i | ||||
\(472\) | −0.448103 | + | 0.776138i | −0.0206256 | + | 0.0357246i | ||||
\(473\) | −25.0484 | + | 14.4617i | −1.15173 | + | 0.664949i | ||||
\(474\) | 14.2516i | 0.654599i | ||||||||
\(475\) | −16.0129 | + | 9.24505i | −0.734722 | + | 0.424192i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 24.4955 | + | 42.4274i | 1.12157 | + | 1.94262i | ||||
\(478\) | −9.93478 | − | 17.2075i | −0.454406 | − | 0.787055i | ||||
\(479\) | 2.84198i | 0.129854i | 0.997890 | + | 0.0649268i | \(0.0206814\pi\) | ||||
−0.997890 | + | 0.0649268i | \(0.979319\pi\) | |||||||
\(480\) | 2.61481 | + | 4.52898i | 0.119349 | + | 0.206719i | ||||
\(481\) | −0.138737 | − | 0.00922730i | −0.00632585 | − | 0.000420729i | ||||
\(482\) | 10.6445 | 0.484844 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.39263 | − | 2.41210i | 0.0633011 | − | 0.109641i | ||||
\(485\) | 7.64312 | 0.347056 | ||||||||
\(486\) | 51.8613 | − | 29.9422i | 2.35248 | − | 1.35820i | ||||
\(487\) | 4.55853 | + | 2.63187i | 0.206567 | + | 0.119261i | 0.599715 | − | 0.800214i | \(-0.295281\pi\) |
−0.393148 | + | 0.919475i | \(0.628614\pi\) | |||||||
\(488\) | 14.2569i | 0.645381i | ||||||||
\(489\) | 0.0327533i | 0.00148115i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.4457 | − | 19.8245i | 0.516536 | − | 0.894666i | −0.483280 | − | 0.875466i | \(-0.660555\pi\) |
0.999816 | − | 0.0192004i | \(-0.00611205\pi\) | |||||||
\(492\) | −23.0414 | + | 13.3030i | −1.03879 | + | 0.599745i | ||||
\(493\) | −5.38181 | − | 9.32157i | −0.242384 | − | 0.419822i | ||||
\(494\) | 1.73140 | − | 26.0323i | 0.0778992 | − | 1.17125i | ||||
\(495\) | 18.3444 | − | 31.7734i | 0.824517 | − | 1.42811i | ||||
\(496\) | 0.517851 | + | 0.298982i | 0.0232522 | + | 0.0134247i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −8.27524 | − | 14.3331i | −0.370822 | − | 0.642283i | ||||
\(499\) | −5.88791 | − | 3.39938i | −0.263579 | − | 0.152177i | 0.362387 | − | 0.932028i | \(-0.381962\pi\) |
−0.625966 | + | 0.779850i | \(0.715295\pi\) | |||||||
\(500\) | 10.2305 | + | 5.90656i | 0.457520 | + | 0.264150i | ||||
\(501\) | 72.2721 | + | 41.7263i | 3.22888 | + | 1.86419i | ||||
\(502\) | 13.7819 | + | 7.95696i | 0.615115 | + | 0.355137i | ||||
\(503\) | −5.40300 | − | 9.35827i | −0.240908 | − | 0.417265i | 0.720065 | − | 0.693906i | \(-0.244112\pi\) |
−0.960973 | + | 0.276642i | \(0.910779\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.97615 | + | 5.75973i | 0.443933 | + | 0.256305i | ||||
\(506\) | 2.38943 | − | 4.13861i | 0.106223 | − | 0.183984i | ||||
\(507\) | 16.5621 | + | 40.2031i | 0.735550 | + | 1.78548i | ||||
\(508\) | −4.92583 | − | 8.53178i | −0.218548 | − | 0.378537i | ||||
\(509\) | 23.6593 | − | 13.6597i | 1.04868 | − | 0.605455i | 0.126400 | − | 0.991979i | \(-0.459658\pi\) |
0.922279 | + | 0.386524i | \(0.126324\pi\) | |||||||
\(510\) | 5.83000 | − | 10.0979i | 0.258157 | − | 0.447141i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − | 125.535i | − | 5.54252i | ||||||
\(514\) | −26.9350 | − | 15.5509i | −1.18805 | − | 0.685921i | ||||
\(515\) | −7.83369 | + | 4.52279i | −0.345194 | + | 0.199298i | ||||
\(516\) | 33.7526 | 1.48588 | ||||||||
\(517\) | 10.0693 | − | 17.4405i | 0.442846 | − | 0.767031i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.7214 | 0.470616 | ||||||||
\(520\) | −5.05850 | + | 2.48853i | −0.221830 | + | 0.109129i | ||||
\(521\) | 1.81790 | + | 3.14870i | 0.0796437 | + | 0.137947i | 0.903096 | − | 0.429438i | \(-0.141288\pi\) |
−0.823453 | + | 0.567385i | \(0.807955\pi\) | |||||||
\(522\) | 39.5230i | 1.72988i | ||||||||
\(523\) | 3.59223 | + | 6.22193i | 0.157077 | + | 0.272066i | 0.933813 | − | 0.357760i | \(-0.116459\pi\) |
−0.776736 | + | 0.629826i | \(0.783126\pi\) | |||||||
\(524\) | 7.39614 | + | 12.8105i | 0.323102 | + | 0.559629i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.5732 | + | 14.1873i | −1.07144 | + | 0.618597i | ||||
\(527\) | − | 1.33323i | − | 0.0580762i | ||||||
\(528\) | 8.30201 | − | 4.79317i | 0.361299 | − | 0.208596i | ||||
\(529\) | 10.1100 | − | 17.5110i | 0.439564 | − | 0.761347i | ||||
\(530\) | −4.67819 | − | 8.10287i | −0.203208 | − | 0.351966i | ||||
\(531\) | −6.35419 | − | 3.66859i | −0.275748 | − | 0.159203i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.6606 | − | 25.7354i | −0.548389 | − | 1.11473i | ||||
\(534\) | −4.04908 | + | 7.01321i | −0.175221 | + | 0.303491i | ||||
\(535\) | − | 1.60883i | − | 0.0695559i | ||||||
\(536\) | 1.64086 | 0.0708746 | ||||||||
\(537\) | 52.8459 | 2.28047 | ||||||||
\(538\) | − | 21.4017i | − | 0.922691i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −23.4915 | + | 13.5628i | −1.01091 | + | 0.583651i | ||||
\(541\) | −0.385436 | − | 0.222531i | −0.0165712 | − | 0.00956737i | 0.491692 | − | 0.870769i | \(-0.336379\pi\) |
−0.508263 | + | 0.861202i | \(0.669712\pi\) | |||||||
\(542\) | −2.87328 | + | 4.97667i | −0.123418 | + | 0.213766i | ||||
\(543\) | 30.5004 | 1.30890 | ||||||||
\(544\) | 1.93090 | − | 1.11481i | 0.0827867 | − | 0.0477969i | ||||
\(545\) | 22.1298 | 0.947935 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.67129 | −0.242487 | −0.121243 | − | 0.992623i | \(-0.538688\pi\) | ||||
−0.121243 | + | 0.992623i | \(0.538688\pi\) | |||||||
\(548\) | −0.397503 | + | 0.229499i | −0.0169805 | + | 0.00980370i | ||||
\(549\) | −116.721 | −4.98151 | ||||||||
\(550\) | 3.66190 | − | 6.34260i | 0.156144 | − | 0.270450i | ||||
\(551\) | 30.2524 | + | 17.4662i | 1.28879 | + | 0.744085i | ||||
\(552\) | −4.82962 | + | 2.78838i | −0.205562 | + | 0.118682i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 26.6020i | − | 1.13021i | ||||||
\(555\) | 0.201673 | 0.00856054 | ||||||||
\(556\) | −15.3146 | −0.649485 | ||||||||
\(557\) | − | 26.5075i | − | 1.12316i | −0.827423 | − | 0.561579i | \(-0.810194\pi\) | ||
0.827423 | − | 0.561579i | \(-0.189806\pi\) | |||||||
\(558\) | −2.44774 | + | 4.23962i | −0.103621 | + | 0.179477i | ||||
\(559\) | −2.41462 | + | 36.3049i | −0.102128 | + | 1.53553i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.5103 | − | 10.6869i | −0.781504 | − | 0.451202i | ||||
\(562\) | −3.34571 | − | 5.79495i | −0.141130 | − | 0.244445i | ||||
\(563\) | −5.76880 | + | 9.99186i | −0.243126 | + | 0.421107i | −0.961603 | − | 0.274444i | \(-0.911506\pi\) |
0.718477 | + | 0.695551i | \(0.244840\pi\) | |||||||
\(564\) | −20.3525 | + | 11.7505i | −0.856993 | + | 0.494785i | ||||
\(565\) | − | 21.1722i | − | 0.890720i | ||||||
\(566\) | −17.2632 | + | 9.96692i | −0.725627 | + | 0.418941i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.14733 | + | 1.98724i | 0.0481409 | + | 0.0833826i | ||||
\(569\) | −16.0791 | − | 27.8497i | −0.674069 | − | 1.16752i | −0.976740 | − | 0.214427i | \(-0.931212\pi\) |
0.302671 | − | 0.953095i | \(-0.402122\pi\) | |||||||
\(570\) | 37.8416i | 1.58501i | ||||||||
\(571\) | 5.77702 | + | 10.0061i | 0.241761 | + | 0.418742i | 0.961216 | − | 0.275797i | \(-0.0889418\pi\) |
−0.719455 | + | 0.694539i | \(0.755608\pi\) | |||||||
\(572\) | 4.56170 | + | 9.27268i | 0.190734 | + | 0.387710i | ||||
\(573\) | −10.9083 | −0.455699 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.13028 | + | 3.68976i | −0.0888389 | + | 0.153873i | ||||
\(576\) | −8.18694 | −0.341122 | ||||||||
\(577\) | −7.91591 | + | 4.57025i | −0.329543 | + | 0.190262i | −0.655638 | − | 0.755075i | \(-0.727600\pi\) |
0.326095 | + | 0.945337i | \(0.394267\pi\) | |||||||
\(578\) | 10.4173 | + | 6.01442i | 0.433301 | + | 0.250167i | ||||
\(579\) | − | 73.8274i | − | 3.06816i | ||||||
\(580\) | − | 7.54819i | − | 0.313422i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −8.17490 | + | 14.1593i | −0.338860 | + | 0.586923i | ||||
\(583\) | −14.8533 | + | 8.57554i | −0.615160 | + | 0.355163i | ||||
\(584\) | −5.61387 | − | 9.72351i | −0.232304 | − | 0.402362i | ||||
\(585\) | −20.3735 | − | 41.4137i | −0.842339 | − | 1.71224i | ||||
\(586\) | −4.43044 | + | 7.67375i | −0.183020 | + | 0.317000i | ||||
\(587\) | 37.0629 | + | 21.3983i | 1.52975 | + | 0.883201i | 0.999372 | + | 0.0354398i | \(0.0112832\pi\) |
0.530378 | + | 0.847761i | \(0.322050\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.16344 | + | 3.74718i | 0.0891428 | + | 0.154400i | ||||
\(590\) | 1.21354 | + | 0.700635i | 0.0499605 | + | 0.0288447i | ||||
\(591\) | −15.2738 | − | 8.81836i | −0.628282 | − | 0.362739i | ||||
\(592\) | 0.0333971 | + | 0.0192818i | 0.00137261 | + | 0.000792478i | ||||
\(593\) | −12.3356 | − | 7.12195i | −0.506561 | − | 0.292463i | 0.224858 | − | 0.974392i | \(-0.427808\pi\) |
−0.731419 | + | 0.681928i | \(0.761142\pi\) | |||||||
\(594\) | 24.8619 | + | 43.0620i | 1.02009 | + | 1.76686i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.86563 | + | 5.11858i | 0.363150 | + | 0.209665i | ||||
\(597\) | 14.8297 | − | 25.6858i | 0.606939 | − | 1.05125i | ||||
\(598\) | −2.65373 | − | 5.39430i | −0.108519 | − | 0.220589i | ||||
\(599\) | −1.87367 | − | 3.24530i | −0.0765563 | − | 0.132599i | 0.825206 | − | 0.564832i | \(-0.191059\pi\) |
−0.901762 | + | 0.432233i | \(0.857726\pi\) | |||||||
\(600\) | −7.40161 | + | 4.27332i | −0.302169 | + | 0.174458i | ||||
\(601\) | −5.33462 | + | 9.23984i | −0.217604 | + | 0.376901i | −0.954075 | − | 0.299568i | \(-0.903157\pi\) |
0.736471 | + | 0.676469i | \(0.236491\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.4337i | 0.547061i | ||||||||
\(604\) | 15.2110i | 0.618927i | ||||||||
\(605\) | −3.77145 | − | 2.17745i | −0.153331 | − | 0.0885259i | ||||
\(606\) | −21.3405 | + | 12.3209i | −0.866898 | + | 0.500504i | ||||
\(607\) | 9.65256 | 0.391785 | 0.195893 | − | 0.980625i | \(-0.437240\pi\) | ||||
0.195893 | + | 0.980625i | \(0.437240\pi\) | |||||||
\(608\) | −3.61801 | + | 6.26657i | −0.146730 | + | 0.254143i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 22.2915 | 0.902558 | ||||||||
\(611\) | −11.1830 | − | 22.7321i | −0.452417 | − | 0.919641i | ||||
\(612\) | 9.12684 | + | 15.8082i | 0.368931 | + | 0.639007i | ||||
\(613\) | 3.99489i | 0.161352i | 0.996740 | + | 0.0806761i | \(0.0257079\pi\) | ||||
−0.996740 | + | 0.0806761i | \(0.974292\pi\) | |||||||
\(614\) | 4.17318 | + | 7.22816i | 0.168416 | + | 0.291705i | ||||
\(615\) | 20.8000 | + | 36.0266i | 0.838736 | + | 1.45273i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.80199 | − | 1.61773i | 0.112804 | − | 0.0651273i | −0.442537 | − | 0.896750i | \(-0.645921\pi\) |
0.555340 | + | 0.831623i | \(0.312588\pi\) | |||||||
\(618\) | − | 19.3499i | − | 0.778365i | ||||||
\(619\) | 34.0070 | − | 19.6340i | 1.36686 | − | 0.789156i | 0.376333 | − | 0.926485i | \(-0.377185\pi\) |
0.990526 | + | 0.137329i | \(0.0438517\pi\) | |||||||
\(620\) | 0.467475 | − | 0.809690i | 0.0187742 | − | 0.0325179i | ||||
\(621\) | −14.4632 | − | 25.0510i | −0.580387 | − | 1.00526i | ||||
\(622\) | 5.79281 | + | 3.34448i | 0.232270 | + | 0.134101i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.800299 | − | 12.0329i | 0.0320376 | − | 0.481700i | ||||
\(625\) | 2.84703 | − | 4.93120i | 0.113881 | − | 0.197248i | ||||
\(626\) | − | 21.3788i | − | 0.854467i | ||||||
\(627\) | 69.3669 | 2.77025 | ||||||||
\(628\) | 2.27419 | 0.0907500 | ||||||||
\(629\) | − | 0.0859819i | − | 0.00342832i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.4983 | − | 14.7215i | 1.01507 | − | 0.586052i | 0.102400 | − | 0.994743i | \(-0.467348\pi\) |
0.912673 | + | 0.408691i | \(0.134015\pi\) | |||||||
\(632\) | 3.69011 | + | 2.13049i | 0.146785 | + | 0.0847463i | ||||
\(633\) | −10.9857 | + | 19.0279i | −0.436644 | + | 0.756290i | ||||
\(634\) | −31.6776 | −1.25808 | ||||||||
\(635\) | −13.3399 | + | 7.70181i | −0.529379 | + | 0.305637i | ||||
\(636\) | 20.0147 | 0.793636 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −13.8365 | −0.547792 | ||||||||
\(639\) | −16.2694 | + | 9.39313i | −0.643606 | + | 0.371586i | ||||
\(640\) | 1.56356 | 0.0618050 | ||||||||
\(641\) | 2.04559 | − | 3.54307i | 0.0807961 | − | 0.139943i | −0.822796 | − | 0.568337i | \(-0.807587\pi\) |
0.903592 | + | 0.428394i | \(0.140920\pi\) | |||||||
\(642\) | 2.98046 | + | 1.72077i | 0.117629 | + | 0.0679133i | ||||
\(643\) | 19.2672 | − | 11.1239i | 0.759825 | − | 0.438685i | −0.0694080 | − | 0.997588i | \(-0.522111\pi\) |
0.829233 | + | 0.558903i | \(0.188778\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 52.7742i | − | 2.07798i | ||||||
\(646\) | 16.1335 | 0.634764 | ||||||||
\(647\) | 49.8583 | 1.96013 | 0.980066 | − | 0.198670i | \(-0.0636622\pi\) | ||||
0.980066 | + | 0.198670i | \(0.0636622\pi\) | |||||||
\(648\) | − | 33.4651i | − | 1.31463i | ||||||
\(649\) | 1.28433 | − | 2.22452i | 0.0504142 | − | 0.0873200i | ||||
\(650\) | −4.06695 | − | 8.26700i | −0.159519 | − | 0.324259i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.00848066 | + | 0.00489631i | 0.000332128 | + | 0.000191754i | ||||
\(653\) | −3.70177 | − | 6.41165i | −0.144861 | − | 0.250907i | 0.784460 | − | 0.620180i | \(-0.212940\pi\) |
−0.929321 | + | 0.369272i | \(0.879607\pi\) | |||||||
\(654\) | −23.6695 | + | 40.9967i | −0.925550 | + | 1.60310i | ||||
\(655\) | 20.0299 | − | 11.5643i | 0.782635 | − | 0.451854i | ||||
\(656\) | 7.95469i | 0.310578i | ||||||||
\(657\) | 79.6058 | − | 45.9604i | 3.10572 | − | 1.79309i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.0410 | − | 26.0518i | −0.585914 | − | 1.01483i | −0.994761 | − | 0.102230i | \(-0.967402\pi\) |
0.408847 | − | 0.912603i | \(-0.365931\pi\) | |||||||
\(660\) | −7.49440 | − | 12.9807i | −0.291719 | − | 0.505272i | ||||
\(661\) | − | 26.6319i | − | 1.03586i | −0.855423 | − | 0.517931i | \(-0.826702\pi\) | ||
0.855423 | − | 0.517931i | \(-0.173298\pi\) | |||||||
\(662\) | −12.3347 | − | 21.3644i | −0.479404 | − | 0.830351i | ||||
\(663\) | −24.1264 | + | 11.8690i | −0.936993 | + | 0.460954i | ||||
\(664\) | −4.94829 | −0.192031 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.157859 | + | 0.273420i | −0.00611691 | + | 0.0105948i | ||||
\(667\) | 8.04926 | 0.311669 | ||||||||
\(668\) | 21.6080 | − | 12.4754i | 0.836040 | − | 0.482688i | ||||
\(669\) | −48.9874 | − | 28.2829i | −1.89396 | − | 1.09348i | ||||
\(670\) | − | 2.56559i | − | 0.0991172i | ||||||
\(671\) | − | 40.8623i | − | 1.57747i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.84652 | + | 3.19827i | −0.0711783 | + | 0.123284i | −0.899418 | − | 0.437090i | \(-0.856009\pi\) |
0.828240 | + | 0.560374i | \(0.189343\pi\) | |||||||
\(674\) | 24.3242 | − | 14.0436i | 0.936932 | − | 0.540938i | ||||
\(675\) | −22.1654 | − | 38.3917i | −0.853148 | − | 1.47770i | ||||
\(676\) | 12.8855 | + | 1.72163i | 0.495596 | + | 0.0662166i | ||||
\(677\) | 17.8266 | − | 30.8767i | 0.685134 | − | 1.18669i | −0.288261 | − | 0.957552i | \(-0.593077\pi\) |
0.973395 | − | 0.229134i | \(-0.0735896\pi\) | |||||||
\(678\) | 39.2227 | + | 22.6453i | 1.50634 | + | 0.869686i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.74306 | − | 3.01907i | −0.0668434 | − | 0.115776i | ||||
\(681\) | 46.7283 | + | 26.9786i | 1.79063 | + | 1.03382i | ||||
\(682\) | −1.48423 | − | 0.856923i | −0.0568342 | − | 0.0328133i | ||||
\(683\) | 26.2105 | + | 15.1326i | 1.00292 | + | 0.579034i | 0.909110 | − | 0.416557i | \(-0.136763\pi\) |
0.0938062 | + | 0.995590i | \(0.470097\pi\) | |||||||
\(684\) | −51.3040 | − | 29.6204i | −1.96166 | − | 1.13256i | ||||
\(685\) | 0.358834 | + | 0.621519i | 0.0137104 | + | 0.0237470i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.0207 | + | 11.5590i | 0.763838 | + | 0.441002i | ||||
\(688\) | 5.04571 | − | 8.73942i | 0.192366 | − | 0.333187i | ||||
\(689\) | −1.43183 | + | 21.5282i | −0.0545483 | + | 0.820159i | ||||
\(690\) | 4.35980 | + | 7.55139i | 0.165975 | + | 0.287477i | ||||
\(691\) | −3.03377 | + | 1.75155i | −0.115410 | + | 0.0666320i | −0.556594 | − | 0.830785i | \(-0.687892\pi\) |
0.441184 | + | 0.897417i | \(0.354559\pi\) | |||||||
\(692\) | 1.60275 | − | 2.77604i | 0.0609273 | − | 0.105529i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 10.1080i | − | 0.383693i | ||||||
\(695\) | 23.9453i | 0.908297i | ||||||||
\(696\) | 13.9835 | + | 8.07337i | 0.530042 | + | 0.306020i | ||||
\(697\) | 15.3597 | − | 8.86793i | 0.581791 | − | 0.335897i | ||||
\(698\) | −17.3893 | −0.658195 | ||||||||
\(699\) | −12.4992 | + | 21.6492i | −0.472762 | + | 0.818849i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −45.2243 | −1.70810 | −0.854048 | − | 0.520194i | \(-0.825860\pi\) | ||||
−0.854048 | + | 0.520194i | \(0.825860\pi\) | |||||||
\(702\) | 62.4137 | + | 4.15110i | 2.35565 | + | 0.156673i | ||||
\(703\) | 0.139524 | + | 0.241662i | 0.00526223 | + | 0.00911445i | ||||
\(704\) | − | 2.86614i | − | 0.108022i | ||||||
\(705\) | 18.3726 | + | 31.8222i | 0.691951 | + | 1.19849i | ||||
\(706\) | −1.66329 | − | 2.88091i | −0.0625989 | − | 0.108424i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.59594 | + | 1.49877i | −0.0975613 | + | 0.0563270i | ||||
\(709\) | 2.99826i | 0.112602i | 0.998414 | + | 0.0563009i | \(0.0179306\pi\) | ||||
−0.998414 | + | 0.0563009i | \(0.982069\pi\) | |||||||
\(710\) | 3.10716 | − | 1.79392i | 0.116610 | − | 0.0673245i | ||||
\(711\) | −17.4422 | + | 30.2107i | −0.654133 | + | 1.13299i | ||||
\(712\) | 1.21060 | + | 2.09682i | 0.0453692 | + | 0.0785817i | ||||
\(713\) | 0.863440 | + | 0.498507i | 0.0323361 | + | 0.0186692i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.4984 | − | 7.13248i | 0.542208 | − | 0.266740i | ||||
\(716\) | 7.89998 | − | 13.6832i | 0.295236 | − | 0.511364i | ||||
\(717\) | − | 66.4575i | − | 2.48190i | ||||||
\(718\) | 8.02414 | 0.299458 | ||||||||
\(719\) | 20.0794 | 0.748834 | 0.374417 | − | 0.927260i | \(-0.377843\pi\) | ||||
0.374417 | + | 0.927260i | \(0.377843\pi\) | |||||||
\(720\) | 12.8007i | 0.477056i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −28.8905 | + | 16.6800i | −1.07519 | + | 0.620764i | ||||
\(723\) | 30.8327 | + | 17.8013i | 1.14668 | + | 0.662037i | ||||
\(724\) | 4.55954 | − | 7.89735i | 0.169454 | − | 0.293503i | ||||
\(725\) | 12.3358 | 0.458142 | ||||||||
\(726\) | 8.06771 | − | 4.65790i | 0.299421 | − | 0.172871i | ||||
\(727\) | −32.5895 | −1.20868 | −0.604338 | − | 0.796728i | \(-0.706562\pi\) | ||||
−0.604338 | + | 0.796728i | \(0.706562\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 99.8990 | 3.69996 | ||||||||
\(730\) | −15.2033 | + | 8.77761i | −0.562698 | + | 0.324874i | ||||
\(731\) | −22.4999 | −0.832190 | ||||||||
\(732\) | −23.8425 | + | 41.2964i | −0.881244 | + | 1.52636i | ||||
\(733\) | 16.0380 | + | 9.25952i | 0.592376 | + | 0.342008i | 0.766036 | − | 0.642797i | \(-0.222226\pi\) |
−0.173661 | + | 0.984806i | \(0.555560\pi\) | |||||||
\(734\) | 0.899869 | − | 0.519540i | 0.0332148 | − | 0.0191766i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.66735i | 0.0614594i | ||||||||
\(737\) | −4.70294 | −0.173235 | ||||||||
\(738\) | −65.1245 | −2.39727 | ||||||||
\(739\) | − | 15.9312i | − | 0.586038i | −0.956107 | − | 0.293019i | \(-0.905340\pi\) | ||
0.956107 | − | 0.293019i | \(-0.0946600\pi\) | |||||||
\(740\) | 0.0301482 | − | 0.0522183i | 0.00110827 | − | 0.00191958i | ||||
\(741\) | 48.5501 | − | 72.5093i | 1.78353 | − | 2.66370i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.5962 | + | 6.11773i | 0.388738 | + | 0.224438i | 0.681613 | − | 0.731713i | \(-0.261279\pi\) |
−0.292875 | + | 0.956151i | \(0.594612\pi\) | |||||||
\(744\) | 1.00000 | + | 1.73205i | 0.0366618 | + | 0.0635001i | ||||
\(745\) | 8.00319 | − | 13.8619i | 0.293214 | − | 0.507862i | ||||
\(746\) | 23.6532 | − | 13.6562i | 0.866007 | − | 0.499989i | ||||
\(747\) | − | 40.5113i | − | 1.48223i | ||||||
\(748\) | −5.53423 | + | 3.19519i | −0.202351 | + | 0.116828i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 19.7556 | + | 34.2177i | 0.721373 | + | 1.24945i | ||||
\(751\) | −10.4107 | − | 18.0318i | −0.379891 | − | 0.657990i | 0.611155 | − | 0.791511i | \(-0.290705\pi\) |
−0.991046 | + | 0.133521i | \(0.957372\pi\) | |||||||
\(752\) | 7.02636i | 0.256225i | ||||||||
\(753\) | 26.6136 | + | 46.0960i | 0.969852 | + | 1.67983i | ||||
\(754\) | −9.68421 | + | 14.4633i | −0.352678 | + | 0.526723i | ||||
\(755\) | 23.7833 | 0.865563 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.5575 | + | 23.4823i | −0.492757 | + | 0.853480i | −0.999965 | − | 0.00834344i | \(-0.997344\pi\) |
0.507208 | + | 0.861824i | \(0.330678\pi\) | |||||||
\(758\) | −2.21166 | −0.0803310 | ||||||||
\(759\) | 13.8424 | − | 7.99190i | 0.502446 | − | 0.290087i | ||||
\(760\) | 9.79815 | + | 5.65696i | 0.355416 | + | 0.205200i | ||||
\(761\) | 48.3727i | 1.75351i | 0.480937 | + | 0.876755i | \(0.340297\pi\) | ||||
−0.480937 | + | 0.876755i | \(0.659703\pi\) | |||||||
\(762\) | − | 32.9507i | − | 1.19368i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1.63068 | + | 2.82443i | −0.0589961 | + | 0.102184i | ||||
\(765\) | 24.7170 | − | 14.2703i | 0.893644 | − | 0.515945i | ||||
\(766\) | 11.1693 | + | 19.3458i | 0.403563 | + | 0.698991i | ||||
\(767\) | −1.42639 | − | 2.89945i | −0.0515039 | − | 0.104693i | ||||
\(768\) | −1.67234 | + | 2.89658i | −0.0603455 | + | 0.104521i | ||||
\(769\) | −15.0214 | − | 8.67264i | −0.541687 | − | 0.312743i | 0.204075 | − | 0.978955i | \(-0.434581\pi\) |
−0.745762 | + | 0.666212i | \(0.767915\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −52.0129 | − | 90.0890i | −1.87320 | − | 3.24448i | ||||
\(772\) | −19.1158 | − | 11.0365i | −0.687993 | − | 0.397213i | ||||
\(773\) | 12.1659 | + | 7.02398i | 0.437576 | + | 0.252635i | 0.702569 | − | 0.711616i | \(-0.252036\pi\) |
−0.264993 | + | 0.964250i | \(0.585370\pi\) | |||||||
\(774\) | 71.5491 | + | 41.3089i | 2.57178 | + | 1.48482i | ||||
\(775\) | 1.32326 | + | 0.763984i | 0.0475329 | + | 0.0274431i | ||||
\(776\) | 2.44414 | + | 4.23338i | 0.0877396 | + | 0.151970i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.6178 | + | 6.13022i | 0.380668 | + | 0.219779i | ||||
\(779\) | −28.7801 | + | 49.8487i | −1.03116 | + | 1.78601i | ||||
\(780\) | −18.8141 | − | 1.25131i | −0.673652 | − | 0.0448042i | ||||
\(781\) | −3.28841 | − | 5.69569i | −0.117669 | − | 0.203808i | ||||
\(782\) | 3.21949 | − | 1.85877i | 0.115129 | − | 0.0664696i | ||||
\(783\) | −41.8760 | + | 72.5314i | −1.49653 | + | 2.59206i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 3.55582i | − | 0.126913i | ||||||
\(786\) | 49.4756i | 1.76474i | ||||||||
\(787\) | 6.71670 | + | 3.87789i | 0.239424 | + | 0.138232i | 0.614912 | − | 0.788596i | \(-0.289191\pi\) |
−0.375488 | + | 0.926827i | \(0.622525\pi\) | |||||||
\(788\) | −4.56660 | + | 2.63653i | −0.162678 | + | 0.0939224i | ||||
\(789\) | −94.9044 | −3.37869 | ||||||||
\(790\) | 3.33114 | − | 5.76971i | 0.118517 | − | 0.205277i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 23.4649 | 0.833789 | ||||||||
\(793\) | −42.7134 | − | 28.5997i | −1.51680 | − | 1.01560i | ||||
\(794\) | 1.46759 | + | 2.54193i | 0.0520827 | + | 0.0902099i | ||||
\(795\) | − | 31.2942i | − | 1.10989i | ||||||
\(796\) | −4.43381 | − | 7.67958i | −0.157152 | − | 0.272195i | ||||
\(797\) | −16.9246 | − | 29.3143i | −0.599500 | − | 1.03836i | −0.992895 | − | 0.118995i | \(-0.962033\pi\) |
0.393395 | − | 0.919370i | \(-0.371301\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.5672 | − | 7.83303i | 0.479973 | − | 0.277113i | ||||
\(800\) | 2.55529i | 0.0903431i | ||||||||
\(801\) | −17.1665 | + | 9.91111i | −0.606550 | + | 0.350192i | ||||
\(802\) | −10.9251 | + | 18.9229i | −0.385779 | + | 0.668190i | ||||
\(803\) | 16.0901 | + | 27.8689i | 0.567808 | + | 0.983473i | ||||
\(804\) | 4.75290 | + | 2.74409i | 0.167622 | + | 0.0967766i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.93456 | + | 0.951708i | −0.0681420 | + | 0.0335225i | ||||
\(807\) | 35.7909 | − | 61.9917i | 1.25990 | − | 2.18221i | ||||
\(808\) | 7.36747i | 0.259187i | ||||||||
\(809\) | −32.8340 | −1.15438 | −0.577191 | − | 0.816609i | \(-0.695851\pi\) | ||||
−0.577191 | + | 0.816609i | \(0.695851\pi\) | |||||||
\(810\) | −52.3246 | −1.83850 | ||||||||
\(811\) | 12.2083i | 0.428690i | 0.976758 | + | 0.214345i | \(0.0687617\pi\) | ||||
−0.976758 | + | 0.214345i | \(0.931238\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.6454 | + | 9.61023i | −0.583780 | + | 0.337045i | ||||
\(814\) | −0.0957207 | − | 0.0552644i | −0.00335501 | − | 0.00193701i | ||||
\(815\) | 0.00765566 | − | 0.0132600i | 0.000268166 | − | 0.000464477i | ||||
\(816\) | 7.45736 | 0.261060 | ||||||||
\(817\) | 63.2386 | − | 36.5108i | 2.21244 | − | 1.27735i | ||||
\(818\) | 7.38191 | 0.258102 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.4376 | 0.434340 | ||||||||
\(821\) | −41.1248 | + | 23.7434i | −1.43526 | + | 0.828650i | −0.997516 | − | 0.0704470i | \(-0.977557\pi\) |
−0.437749 | + | 0.899097i | \(0.644224\pi\) | |||||||
\(822\) | −1.53520 | −0.0535463 | ||||||||
\(823\) | 11.0229 | − | 19.0923i | 0.384235 | − | 0.665515i | −0.607427 | − | 0.794375i | \(-0.707798\pi\) |
0.991663 | + | 0.128860i | \(0.0411317\pi\) | |||||||
\(824\) | −5.01017 | − | 2.89263i | −0.174538 | − | 0.100769i | ||||
\(825\) | 21.2140 | − | 12.2479i | 0.738578 | − | 0.426418i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 45.9092i | 1.59642i | 0.602380 | + | 0.798209i | \(0.294219\pi\) | ||||
−0.602380 | + | 0.798209i | \(0.705781\pi\) | |||||||
\(828\) | −13.6505 | −0.474388 | ||||||||
\(829\) | −26.7766 | −0.929991 | −0.464996 | − | 0.885313i | \(-0.653944\pi\) | ||||
−0.464996 | + | 0.885313i | \(0.653944\pi\) | |||||||
\(830\) | 7.73693i | 0.268553i | ||||||||
\(831\) | 44.4877 | − | 77.0550i | 1.54326 | − | 2.67301i | ||||
\(832\) | −2.99598 | − | 2.00602i | −0.103867 | − | 0.0695462i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −44.3601 | − | 25.6113i | −1.53606 | − | 0.886847i | ||||
\(835\) | −19.5060 | − | 33.7854i | −0.675033 | − | 1.16919i | ||||
\(836\) | 10.3697 | − | 17.9609i | 0.358644 | − | 0.621190i | ||||
\(837\) | −8.98404 | + | 5.18694i | −0.310534 | + | 0.179287i | ||||
\(838\) | − | 8.58273i | − | 0.296486i | ||||||
\(839\) | −24.5960 | + | 14.2005i | −0.849147 | + | 0.490255i | −0.860363 | − | 0.509682i | \(-0.829763\pi\) |
0.0112158 | + | 0.999937i | \(0.496430\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.84726 | + | 4.93160i | 0.0981814 | + | 0.170055i | ||||
\(842\) | 3.74763 | + | 6.49108i | 0.129152 | + | 0.223697i | ||||
\(843\) | − | 22.3807i | − | 0.770834i | ||||||
\(844\) | 3.28453 | + | 5.68898i | 0.113058 | + | 0.195823i | ||||
\(845\) | 2.69187 | − | 20.1472i | 0.0926031 | − | 0.693085i | ||||
\(846\) | −57.5244 | −1.97773 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.99202 | − | 5.18233i | 0.102746 | − | 0.177962i | ||||
\(849\) | −66.6725 | −2.28819 | ||||||||
\(850\) | 4.93401 | − | 2.84865i | 0.169235 | − | 0.0977079i | ||||
\(851\) | 0.0556847 | + | 0.0321496i | 0.00190885 | + | 0.00110207i | ||||
\(852\) | 7.67493i | 0.262939i | ||||||||
\(853\) | 21.3316i | 0.730379i | 0.930933 | + | 0.365189i | \(0.118996\pi\) | ||||
−0.930933 | + | 0.365189i | \(0.881004\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −46.3132 | + | 80.2168i | −1.58388 | + | 2.74336i | ||||
\(856\) | 0.891102 | − | 0.514478i | 0.0304572 | − | 0.0175845i | ||||
\(857\) | 20.5412 | + | 35.5784i | 0.701673 | + | 1.21533i | 0.967879 | + | 0.251417i | \(0.0808966\pi\) |
−0.266206 | + | 0.963916i | \(0.585770\pi\) | |||||||
\(858\) | −2.29377 | + | 34.4878i | −0.0783079 | + | 1.17740i | ||||
\(859\) | −14.4309 | + | 24.9951i | −0.492376 | + | 0.852820i | −0.999961 | − | 0.00878126i | \(-0.997205\pi\) |
0.507586 | + | 0.861601i | \(0.330538\pi\) | |||||||
\(860\) | −13.6646 | − | 7.88925i | −0.465958 | − | 0.269021i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.23956 | + | 14.2713i | 0.280641 | + | 0.486084i | ||||
\(863\) | −19.6875 | − | 11.3666i | −0.670171 | − | 0.386923i | 0.125970 | − | 0.992034i | \(-0.459796\pi\) |
−0.796141 | + | 0.605111i | \(0.793129\pi\) | |||||||
\(864\) | −15.0244 | − | 8.67434i | −0.511140 | − | 0.295107i | ||||
\(865\) | −4.34050 | − | 2.50599i | −0.147581 | − | 0.0852062i | ||||
\(866\) | −22.1365 | − | 12.7805i | −0.752229 | − | 0.434300i | ||||
\(867\) | 20.1163 | + | 34.8425i | 0.683187 | + | 1.18331i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.5764 | − | 6.10627i | −0.358779 | − | 0.207141i | ||||
\(870\) | 12.6232 | − | 21.8640i | 0.427966 | − | 0.741258i | ||||
\(871\) | −3.29161 | + | 4.91599i | −0.111532 | + | 0.166572i | ||||
\(872\) | 7.07674 | + | 12.2573i | 0.239649 | + | 0.415084i | ||||
\(873\) | −34.6584 | + | 20.0100i | −1.17301 | + | 0.677238i | ||||
\(874\) | −6.03249 | + | 10.4486i | −0.204052 | + | 0.353428i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 37.5533i | − | 1.26881i | ||||||
\(877\) | 29.4178i | 0.993368i | 0.867932 | + | 0.496684i | \(0.165449\pi\) | ||||
−0.867932 | + | 0.496684i | \(0.834551\pi\) | |||||||
\(878\) | 7.97470 | + | 4.60420i | 0.269133 | + | 0.155384i | ||||
\(879\) | −25.6663 | + | 14.8184i | −0.865703 | + | 0.499814i | ||||
\(880\) | −4.48137 | −0.151067 | ||||||||
\(881\) | 2.11104 | − | 3.65644i | 0.0711229 | − | 0.123188i | −0.828271 | − | 0.560328i | \(-0.810675\pi\) |
0.899394 | + | 0.437140i | \(0.144008\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.1982 | 1.25182 | 0.625910 | − | 0.779895i | \(-0.284728\pi\) | ||||
0.625910 | + | 0.779895i | \(0.284728\pi\) | |||||||
\(884\) | −0.533490 | + | 8.02126i | −0.0179432 | + | 0.269784i | ||||
\(885\) | 2.34341 | + | 4.05890i | 0.0787727 | + | 0.136438i | ||||
\(886\) | − | 6.20759i | − | 0.208548i | ||||||
\(887\) | 28.0947 | + | 48.6614i | 0.943327 | + | 1.63389i | 0.759067 | + | 0.651013i | \(0.225656\pi\) |
0.184260 | + | 0.982878i | \(0.441011\pi\) | |||||||
\(888\) | 0.0644917 | + | 0.111703i | 0.00216420 | + | 0.00374850i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 3.27850 | − | 1.89284i | 0.109896 | − | 0.0634482i | ||||
\(891\) | 95.9157i | 3.21330i | ||||||||
\(892\) | −14.6463 | + | 8.45606i | −0.490395 | + | 0.283130i | ||||
\(893\) | −25.4214 | + | 44.0312i | −0.850696 | + | 1.47345i | ||||
\(894\) | 17.1200 | + | 29.6528i | 0.572580 | + | 0.991737i | ||||
\(895\) | −21.3944 | − | 12.3521i | −0.715136 | − | 0.412884i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.33438 | − | 20.0630i | 0.0445536 | − | 0.669884i | ||||
\(898\) | 2.60944 | − | 4.51968i | 0.0870781 | − | 0.150824i | ||||
\(899\) | − | 2.88671i | − | 0.0962772i | ||||||
\(900\) | −20.9200 | −0.697333 | ||||||||
\(901\) | −13.3421 | −0.444489 | ||||||||
\(902\) | − | 22.7992i | − | 0.759132i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.7269 | − | 6.77051i | 0.390030 | − | 0.225184i | ||||
\(905\) | −12.3480 | − | 7.12910i | −0.410460 | − | 0.236979i | ||||
\(906\) | −25.4380 | + | 44.0600i | −0.845123 | + | 1.46380i | ||||
\(907\) | 0.653612 | 0.0217028 | 0.0108514 | − | 0.999941i | \(-0.496546\pi\) | ||||
0.0108514 | + | 0.999941i | \(0.496546\pi\) | |||||||
\(908\) | 13.9709 | − | 8.06611i | 0.463641 | − | 0.267683i | ||||
\(909\) | −60.3170 | −2.00059 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.7806 | 1.31799 | 0.658995 | − | 0.752147i | \(-0.270982\pi\) | ||||
0.658995 | + | 0.752147i | \(0.270982\pi\) | |||||||
\(912\) | −20.9597 | + | 12.1011i | −0.694046 | + | 0.400708i | ||||
\(913\) | 14.1825 | 0.469371 | ||||||||
\(914\) | 16.9666 | − | 29.3870i | 0.561205 | − | 0.972036i | ||||
\(915\) | 64.5693 | + | 37.2791i | 2.13460 | + | 1.23241i | ||||
\(916\) | 5.98583 | − | 3.45592i | 0.197777 | − | 0.114187i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 38.6808i | 1.27666i | ||||||||
\(919\) | 34.6056 | 1.14153 | 0.570767 | − | 0.821112i | \(-0.306646\pi\) | ||||
0.570767 | + | 0.821112i | \(0.306646\pi\) | |||||||
\(920\) | 2.60700 | 0.0859502 | ||||||||
\(921\) | 27.9160i | 0.919863i | ||||||||
\(922\) | 0.422380 | − | 0.731583i | 0.0139103 | − | 0.0240934i | ||||
\(923\) | −8.25528 | − | 0.549054i | −0.271726 | − | 0.0180723i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.0853392 | + | 0.0492706i | 0.00280593 | + | 0.00162001i | ||||
\(926\) | −3.25111 | − | 5.63108i | −0.106838 | − | 0.185049i | ||||
\(927\) | 23.6817 | − | 41.0180i | 0.777810 | − | 1.34721i | ||||
\(928\) | 4.18080 | − | 2.41379i | 0.137242 | − | 0.0792365i | ||||
\(929\) | 19.2707i | 0.632252i | 0.948717 | + | 0.316126i | \(0.102382\pi\) | ||||
−0.948717 | + | 0.316126i | \(0.897618\pi\) | |||||||
\(930\) | 2.70816 | − | 1.56356i | 0.0888041 | − | 0.0512711i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 3.73702 | + | 6.47272i | 0.122410 | + | 0.212021i | ||||
\(933\) | 11.1862 | + | 19.3751i | 0.366221 | + | 0.634314i | ||||
\(934\) | 9.52759i | 0.311752i | ||||||||
\(935\) | 4.99586 | + | 8.65308i | 0.163382 | + | 0.282986i | ||||
\(936\) | 16.4232 | − | 24.5279i | 0.536808 | − | 0.801719i | ||||
\(937\) | −50.9507 | −1.66449 | −0.832244 | − | 0.554410i | \(-0.812944\pi\) | ||||
−0.832244 | + | 0.554410i | \(0.812944\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 35.7526 | − | 61.9254i | 1.16674 | − | 2.02086i | ||||
\(940\) | 10.9861 | 0.358328 | ||||||||
\(941\) | −21.0456 | + | 12.1507i | −0.686068 | + | 0.396102i | −0.802138 | − | 0.597139i | \(-0.796304\pi\) |
0.116069 | + | 0.993241i | \(0.462971\pi\) | |||||||
\(942\) | 6.58738 | + | 3.80322i | 0.214628 | + | 0.123916i | ||||
\(943\) | 13.2633i | 0.431911i | ||||||||
\(944\) | 0.896206i | 0.0291690i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14.4617 | + | 25.0484i | −0.470190 | + | 0.814393i | ||||
\(947\) | −22.2278 | + | 12.8332i | −0.722307 | + | 0.417024i | −0.815601 | − | 0.578614i | \(-0.803594\pi\) |
0.0932940 | + | 0.995639i | \(0.470260\pi\) | |||||||
\(948\) | 7.12582 | + | 12.3423i | 0.231436 | + | 0.400859i | ||||
\(949\) | 40.3930 | + | 2.68651i | 1.31121 | + | 0.0872080i | ||||
\(950\) | −9.24505 | + | 16.0129i | −0.299949 | + | 0.519527i | ||||
\(951\) | −91.7569 | − | 52.9759i | −2.97542 | − | 1.71786i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.40492 | + | 4.16544i | 0.0779029 | + | 0.134932i | 0.902345 | − | 0.431015i | \(-0.141844\pi\) |
−0.824442 | + | 0.565946i | \(0.808511\pi\) | |||||||
\(954\) | 42.4274 | + | 24.4955i | 1.37364 | + | 0.793070i | ||||
\(955\) | 4.41616 | + | 2.54967i | 0.142903 | + | 0.0825053i | ||||
\(956\) | −17.2075 | − | 9.93478i | −0.556532 | − | 0.321314i | ||||
\(957\) | −40.0786 | − | 23.1394i | −1.29556 | − | 0.747990i | ||||
\(958\) | 1.42099 | + | 2.46123i | 0.0459102 | + | 0.0795188i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 4.52898 | + | 2.61481i | 0.146172 | + | 0.0843925i | ||||
\(961\) | −15.3212 | + | 26.5371i | −0.494233 | + | 0.856037i | ||||
\(962\) | −0.124763 | + | 0.0613773i | −0.00402252 | + | 0.00197888i | ||||
\(963\) | 4.21200 | + | 7.29540i | 0.135730 | + | 0.235091i | ||||
\(964\) | 9.21842 | − | 5.32226i | 0.296905 | − | 0.171418i | ||||
\(965\) | −17.2562 | + | 29.8887i | −0.555498 | + | 0.962150i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 58.2044i | 1.87173i | 0.352362 | + | 0.935864i | \(0.385378\pi\) | ||||
−0.352362 | + | 0.935864i | \(0.614622\pi\) | |||||||
\(968\) | − | 2.78525i | − | 0.0895213i | ||||||
\(969\) | 46.7321 | + | 26.9808i | 1.50125 | + | 0.866747i | ||||
\(970\) | 6.61913 | − | 3.82156i | 0.212528 | − | 0.122703i | ||||
\(971\) | −36.1337 | −1.15959 | −0.579793 | − | 0.814764i | \(-0.696867\pi\) | ||||
−0.579793 | + | 0.814764i | \(0.696867\pi\) | |||||||
\(972\) | 29.9422 | − | 51.8613i | 0.960395 | − | 1.66345i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 5.26374 | 0.168661 | ||||||||
\(975\) | 2.04499 | − | 30.7474i | 0.0654922 | − | 0.984706i | ||||
\(976\) | 7.12846 | + | 12.3469i | 0.228177 | + | 0.395213i | ||||
\(977\) | − | 16.7194i | − | 0.534901i | −0.963572 | − | 0.267451i | \(-0.913819\pi\) | ||
0.963572 | − | 0.267451i | \(-0.0861812\pi\) | |||||||
\(978\) | 0.0163766 | + | 0.0283652i | 0.000523667 | + | 0.000907018i | ||||
\(979\) | −3.46975 | − | 6.00978i | −0.110894 | − | 0.192073i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −100.349 | + | 57.9368i | −3.20391 | + | 1.84978i | ||||
\(982\) | − | 22.8913i | − | 0.730492i | ||||||
\(983\) | −40.2497 | + | 23.2382i | −1.28377 | + | 0.741183i | −0.977535 | − | 0.210774i | \(-0.932402\pi\) |
−0.306232 | + | 0.951957i | \(0.599068\pi\) | |||||||
\(984\) | −13.3030 | + | 23.0414i | −0.424083 | + | 0.734534i | ||||
\(985\) | 4.12236 | + | 7.14014i | 0.131349 | + | 0.227504i | ||||
\(986\) | −9.32157 | − | 5.38181i | −0.296859 | − | 0.171392i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −11.5167 | − | 23.4103i | −0.366396 | − | 0.744782i | ||||
\(989\) | 8.41296 | − | 14.5717i | 0.267517 | − | 0.463352i | ||||
\(990\) | − | 36.6887i | − | 1.16604i | ||||||
\(991\) | 35.3510 | 1.12296 | 0.561480 | − | 0.827490i | \(-0.310232\pi\) | ||||
0.561480 | + | 0.827490i | \(0.310232\pi\) | |||||||
\(992\) | 0.597963 | 0.0189853 | ||||||||
\(993\) | − | 82.5118i | − | 2.61843i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.0075 | + | 6.93251i | −0.380662 | + | 0.219775i | ||||
\(996\) | −14.3331 | − | 8.27524i | −0.454163 | − | 0.262211i | ||||
\(997\) | −0.743899 | + | 1.28847i | −0.0235595 | + | 0.0408063i | −0.877565 | − | 0.479458i | \(-0.840833\pi\) |
0.854005 | + | 0.520264i | \(0.174167\pi\) | |||||||
\(998\) | −6.79877 | −0.215211 | ||||||||
\(999\) | −0.579396 | + | 0.334514i | −0.0183313 | + | 0.0105836i |
(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 | 1274.2.v.e.667.6 | 12 | ||
7.2 | even | 3 | 182.2.m.b.43.1 | ✓ | 12 | ||
7.3 | odd | 6 | 1274.2.o.e.459.6 | 12 | |||
7.4 | even | 3 | 1274.2.o.d.459.4 | 12 | |||
7.5 | odd | 6 | 1274.2.m.c.589.3 | 12 | |||
7.6 | odd | 2 | 1274.2.v.d.667.4 | 12 | |||
13.10 | even | 6 | 1274.2.o.d.569.1 | 12 | |||
21.2 | odd | 6 | 1638.2.bj.g.1135.4 | 12 | |||
28.23 | odd | 6 | 1456.2.cc.d.225.6 | 12 | |||
91.9 | even | 3 | 2366.2.d.r.337.12 | 12 | |||
91.10 | odd | 6 | 1274.2.v.d.361.4 | 12 | |||
91.23 | even | 6 | 182.2.m.b.127.1 | yes | 12 | ||
91.30 | even | 6 | 2366.2.d.r.337.6 | 12 | |||
91.58 | odd | 12 | 2366.2.a.bh.1.6 | 6 | |||
91.62 | odd | 6 | 1274.2.o.e.569.3 | 12 | |||
91.72 | odd | 12 | 2366.2.a.bf.1.6 | 6 | |||
91.75 | odd | 6 | 1274.2.m.c.491.3 | 12 | |||
91.88 | even | 6 | inner | 1274.2.v.e.361.6 | 12 | ||
273.23 | odd | 6 | 1638.2.bj.g.127.6 | 12 | |||
364.23 | odd | 6 | 1456.2.cc.d.673.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
182.2.m.b.43.1 | ✓ | 12 | 7.2 | even | 3 | ||
182.2.m.b.127.1 | yes | 12 | 91.23 | even | 6 | ||
1274.2.m.c.491.3 | 12 | 91.75 | odd | 6 | |||
1274.2.m.c.589.3 | 12 | 7.5 | odd | 6 | |||
1274.2.o.d.459.4 | 12 | 7.4 | even | 3 | |||
1274.2.o.d.569.1 | 12 | 13.10 | even | 6 | |||
1274.2.o.e.459.6 | 12 | 7.3 | odd | 6 | |||
1274.2.o.e.569.3 | 12 | 91.62 | odd | 6 | |||
1274.2.v.d.361.4 | 12 | 91.10 | odd | 6 | |||
1274.2.v.d.667.4 | 12 | 7.6 | odd | 2 | |||
1274.2.v.e.361.6 | 12 | 91.88 | even | 6 | inner | ||
1274.2.v.e.667.6 | 12 | 1.1 | even | 1 | trivial | ||
1456.2.cc.d.225.6 | 12 | 28.23 | odd | 6 | |||
1456.2.cc.d.673.6 | 12 | 364.23 | odd | 6 | |||
1638.2.bj.g.127.6 | 12 | 273.23 | odd | 6 | |||
1638.2.bj.g.1135.4 | 12 | 21.2 | odd | 6 | |||
2366.2.a.bf.1.6 | 6 | 91.72 | odd | 12 | |||
2366.2.a.bh.1.6 | 6 | 91.58 | odd | 12 | |||
2366.2.d.r.337.6 | 12 | 91.30 | even | 6 | |||
2366.2.d.r.337.12 | 12 | 91.9 | even | 3 |