Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(1009,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.1009");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.bb (of order \(6\), 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: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1009.5 | ||
Character | \(\chi\) | \(=\) | 1110.1009 |
Dual form | 1110.2.bb.d.1099.5 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 2.09232 | + | 0.788796i | 0.935714 | + | 0.352760i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0.268117 | − | 0.154798i | 0.101339 | − | 0.0585080i | −0.448474 | − | 0.893796i | \(-0.648032\pi\) |
0.549813 | + | 0.835288i | \(0.314699\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | −1.41760 | − | 1.72928i | −0.448286 | − | 0.546845i | ||||
\(11\) | 4.57198 | 1.37851 | 0.689253 | − | 0.724521i | \(-0.257939\pi\) | ||||
0.689253 | + | 0.724521i | \(0.257939\pi\) | |||||||
\(12\) | −0.866025 | − | 0.500000i | −0.250000 | − | 0.144338i | ||||
\(13\) | 3.32139 | − | 1.91760i | 0.921187 | − | 0.531848i | 0.0371735 | − | 0.999309i | \(-0.488165\pi\) |
0.884014 | + | 0.467461i | \(0.154831\pi\) | |||||||
\(14\) | −0.309595 | −0.0827428 | ||||||||
\(15\) | −2.20640 | + | 0.363043i | −0.569690 | + | 0.0937372i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.86619 | − | 1.65480i | −0.695154 | − | 0.401347i | 0.110386 | − | 0.993889i | \(-0.464791\pi\) |
−0.805540 | + | 0.592541i | \(0.798125\pi\) | |||||||
\(18\) | −0.866025 | + | 0.500000i | −0.204124 | + | 0.117851i | ||||
\(19\) | −0.688327 | − | 1.19222i | −0.157913 | − | 0.273513i | 0.776203 | − | 0.630483i | \(-0.217143\pi\) |
−0.934116 | + | 0.356970i | \(0.883810\pi\) | |||||||
\(20\) | 0.363043 | + | 2.20640i | 0.0811788 | + | 0.493366i | ||||
\(21\) | −0.154798 | + | 0.268117i | −0.0337796 | + | 0.0585080i | ||||
\(22\) | −3.95946 | − | 2.28599i | −0.844159 | − | 0.487375i | ||||
\(23\) | − | 5.47919i | − | 1.14249i | −0.820780 | − | 0.571245i | \(-0.806461\pi\) | ||
0.820780 | − | 0.571245i | \(-0.193539\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | 3.75560 | + | 3.30083i | 0.751120 | + | 0.660165i | ||||
\(26\) | −3.83521 | −0.752146 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0.268117 | + | 0.154798i | 0.0506694 | + | 0.0292540i | ||||
\(29\) | −0.690405 | −0.128205 | −0.0641025 | − | 0.997943i | \(-0.520418\pi\) | ||||
−0.0641025 | + | 0.997943i | \(0.520418\pi\) | |||||||
\(30\) | 2.09232 | + | 0.788796i | 0.382004 | + | 0.144014i | ||||
\(31\) | 2.73678 | 0.491540 | 0.245770 | − | 0.969328i | \(-0.420959\pi\) | ||||
0.245770 | + | 0.969328i | \(0.420959\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | −3.95946 | + | 2.28599i | −0.689253 | + | 0.397940i | ||||
\(34\) | 1.65480 | + | 2.86619i | 0.283795 | + | 0.491548i | ||||
\(35\) | 0.683091 | − | 0.112396i | 0.115463 | − | 0.0189984i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −6.02425 | − | 0.841687i | −0.990380 | − | 0.138372i | ||||
\(38\) | 1.37665i | 0.223323i | ||||||||
\(39\) | −1.91760 | + | 3.32139i | −0.307062 | + | 0.531848i | ||||
\(40\) | 0.788796 | − | 2.09232i | 0.124720 | − | 0.330825i | ||||
\(41\) | 0.175457 | + | 0.303900i | 0.0274017 | + | 0.0474612i | 0.879401 | − | 0.476082i | \(-0.157943\pi\) |
−0.851999 | + | 0.523543i | \(0.824610\pi\) | |||||||
\(42\) | 0.268117 | − | 0.154798i | 0.0413714 | − | 0.0238858i | ||||
\(43\) | − | 5.04831i | − | 0.769860i | −0.922946 | − | 0.384930i | \(-0.874226\pi\) | ||
0.922946 | − | 0.384930i | \(-0.125774\pi\) | |||||||
\(44\) | 2.28599 | + | 3.95946i | 0.344626 | + | 0.596910i | ||||
\(45\) | 1.72928 | − | 1.41760i | 0.257785 | − | 0.211324i | ||||
\(46\) | −2.73959 | + | 4.74511i | −0.403931 | + | 0.699629i | ||||
\(47\) | − | 3.77518i | − | 0.550667i | −0.961349 | − | 0.275333i | \(-0.911212\pi\) | ||
0.961349 | − | 0.275333i | \(-0.0887882\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | −3.45208 | + | 5.97917i | −0.493154 | + | 0.854167i | ||||
\(50\) | −1.60203 | − | 4.73640i | −0.226562 | − | 0.669828i | ||||
\(51\) | 3.30960 | 0.463436 | ||||||||
\(52\) | 3.32139 | + | 1.91760i | 0.460594 | + | 0.265924i | ||||
\(53\) | 11.8620 | + | 6.84854i | 1.62937 | + | 0.940720i | 0.984280 | + | 0.176617i | \(0.0565155\pi\) |
0.645095 | + | 0.764102i | \(0.276818\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 9.56605 | + | 3.60636i | 1.28989 | + | 0.486282i | ||||
\(56\) | −0.154798 | − | 0.268117i | −0.0206857 | − | 0.0358287i | ||||
\(57\) | 1.19222 | + | 0.688327i | 0.157913 | + | 0.0911711i | ||||
\(58\) | 0.597908 | + | 0.345202i | 0.0785092 | + | 0.0453273i | ||||
\(59\) | 5.77406 | − | 10.0010i | 0.751719 | − | 1.30202i | −0.195270 | − | 0.980750i | \(-0.562558\pi\) |
0.946989 | − | 0.321266i | \(-0.104108\pi\) | |||||||
\(60\) | −1.41760 | − | 1.72928i | −0.183012 | − | 0.223249i | ||||
\(61\) | 2.37967 | + | 4.12172i | 0.304686 | + | 0.527732i | 0.977191 | − | 0.212361i | \(-0.0681151\pi\) |
−0.672505 | + | 0.740092i | \(0.734782\pi\) | |||||||
\(62\) | −2.37012 | − | 1.36839i | −0.301005 | − | 0.173786i | ||||
\(63\) | − | 0.309595i | − | 0.0390053i | ||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 8.46200 | − | 1.39234i | 1.04958 | − | 0.172699i | ||||
\(66\) | 4.57198 | 0.562772 | ||||||||
\(67\) | −4.13186 | + | 2.38553i | −0.504787 | + | 0.291439i | −0.730688 | − | 0.682711i | \(-0.760801\pi\) |
0.225901 | + | 0.974150i | \(0.427467\pi\) | |||||||
\(68\) | − | 3.30960i | − | 0.401347i | ||||||
\(69\) | 2.73959 | + | 4.74511i | 0.329808 | + | 0.571245i | ||||
\(70\) | −0.647772 | − | 0.244208i | −0.0774236 | − | 0.0291884i | ||||
\(71\) | −6.67007 | − | 11.5529i | −0.791591 | − | 1.37108i | −0.924981 | − | 0.380013i | \(-0.875920\pi\) |
0.133390 | − | 0.991064i | \(-0.457414\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | 13.3833i | 1.56640i | 0.621769 | + | 0.783201i | \(0.286414\pi\) | ||||
−0.621769 | + | 0.783201i | \(0.713586\pi\) | |||||||
\(74\) | 4.79631 | + | 3.74105i | 0.557560 | + | 0.434888i | ||||
\(75\) | −4.90286 | − | 0.980798i | −0.566133 | − | 0.113253i | ||||
\(76\) | 0.688327 | − | 1.19222i | 0.0789565 | − | 0.136757i | ||||
\(77\) | 1.22583 | − | 0.707733i | 0.139696 | − | 0.0806536i | ||||
\(78\) | 3.32139 | − | 1.91760i | 0.376073 | − | 0.217126i | ||||
\(79\) | 7.63359 | + | 13.2218i | 0.858846 | + | 1.48757i | 0.873030 | + | 0.487666i | \(0.162152\pi\) |
−0.0141837 | + | 0.999899i | \(0.504515\pi\) | |||||||
\(80\) | −1.72928 | + | 1.41760i | −0.193339 | + | 0.158493i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | − | 0.350914i | − | 0.0387519i | ||||||
\(83\) | −2.66210 | − | 1.53697i | −0.292204 | − | 0.168704i | 0.346732 | − | 0.937964i | \(-0.387292\pi\) |
−0.638935 | + | 0.769261i | \(0.720625\pi\) | |||||||
\(84\) | −0.309595 | −0.0337796 | ||||||||
\(85\) | −4.69170 | − | 5.72321i | −0.508886 | − | 0.620769i | ||||
\(86\) | −2.52416 | + | 4.37197i | −0.272187 | + | 0.471441i | ||||
\(87\) | 0.597908 | − | 0.345202i | 0.0641025 | − | 0.0370096i | ||||
\(88\) | − | 4.57198i | − | 0.487375i | ||||||
\(89\) | 5.47776 | − | 9.48775i | 0.580641 | − | 1.00570i | −0.414763 | − | 0.909930i | \(-0.636135\pi\) |
0.995403 | − | 0.0957700i | \(-0.0305313\pi\) | |||||||
\(90\) | −2.20640 | + | 0.363043i | −0.232575 | + | 0.0382680i | ||||
\(91\) | 0.593681 | − | 1.02829i | 0.0622347 | − | 0.107794i | ||||
\(92\) | 4.74511 | − | 2.73959i | 0.494712 | − | 0.285622i | ||||
\(93\) | −2.37012 | + | 1.36839i | −0.245770 | + | 0.141895i | ||||
\(94\) | −1.88759 | + | 3.26940i | −0.194690 | + | 0.337213i | ||||
\(95\) | −0.499784 | − | 3.03745i | −0.0512767 | − | 0.311636i | ||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | − | 0.990093i | − | 0.100529i | −0.998736 | − | 0.0502644i | \(-0.983994\pi\) | ||
0.998736 | − | 0.0502644i | \(-0.0160064\pi\) | |||||||
\(98\) | 5.97917 | − | 3.45208i | 0.603987 | − | 0.348712i | ||||
\(99\) | 2.28599 | − | 3.95946i | 0.229751 | − | 0.397940i | ||||
\(100\) | −0.980798 | + | 4.90286i | −0.0980798 | + | 0.490286i | ||||
\(101\) | 13.4339 | 1.33672 | 0.668360 | − | 0.743838i | \(-0.266997\pi\) | ||||
0.668360 | + | 0.743838i | \(0.266997\pi\) | |||||||
\(102\) | −2.86619 | − | 1.65480i | −0.283795 | − | 0.163849i | ||||
\(103\) | 5.80947i | 0.572424i | 0.958166 | + | 0.286212i | \(0.0923961\pi\) | ||||
−0.958166 | + | 0.286212i | \(0.907604\pi\) | |||||||
\(104\) | −1.91760 | − | 3.32139i | −0.188037 | − | 0.325689i | ||||
\(105\) | −0.535376 | + | 0.438884i | −0.0522474 | + | 0.0428307i | ||||
\(106\) | −6.84854 | − | 11.8620i | −0.665189 | − | 1.15214i | ||||
\(107\) | 6.31907 | − | 3.64832i | 0.610888 | − | 0.352696i | −0.162425 | − | 0.986721i | \(-0.551932\pi\) |
0.773313 | + | 0.634025i | \(0.218598\pi\) | |||||||
\(108\) | −0.866025 | + | 0.500000i | −0.0833333 | + | 0.0481125i | ||||
\(109\) | 6.46495 | − | 11.1976i | 0.619229 | − | 1.07254i | −0.370397 | − | 0.928873i | \(-0.620778\pi\) |
0.989627 | − | 0.143663i | \(-0.0458883\pi\) | |||||||
\(110\) | −6.48126 | − | 7.90623i | −0.617964 | − | 0.753829i | ||||
\(111\) | 5.63800 | − | 2.28320i | 0.535135 | − | 0.216712i | ||||
\(112\) | 0.309595i | 0.0292540i | ||||||||
\(113\) | 2.12749 | + | 1.22831i | 0.200138 | + | 0.115549i | 0.596720 | − | 0.802450i | \(-0.296470\pi\) |
−0.396582 | + | 0.917999i | \(0.629804\pi\) | |||||||
\(114\) | −0.688327 | − | 1.19222i | −0.0644677 | − | 0.111661i | ||||
\(115\) | 4.32196 | − | 11.4642i | 0.403025 | − | 1.06904i | ||||
\(116\) | −0.345202 | − | 0.597908i | −0.0320512 | − | 0.0555144i | ||||
\(117\) | − | 3.83521i | − | 0.354565i | ||||||
\(118\) | −10.0010 | + | 5.77406i | −0.920664 | + | 0.531546i | ||||
\(119\) | −1.02464 | −0.0939282 | ||||||||
\(120\) | 0.363043 | + | 2.20640i | 0.0331411 | + | 0.201416i | ||||
\(121\) | 9.90305 | 0.900277 | ||||||||
\(122\) | − | 4.75935i | − | 0.430891i | ||||||
\(123\) | −0.303900 | − | 0.175457i | −0.0274017 | − | 0.0158204i | ||||
\(124\) | 1.36839 | + | 2.37012i | 0.122885 | + | 0.212843i | ||||
\(125\) | 5.25424 | + | 9.86879i | 0.469954 | + | 0.882691i | ||||
\(126\) | −0.154798 | + | 0.268117i | −0.0137905 | + | 0.0238858i | ||||
\(127\) | 1.18210 | + | 0.682488i | 0.104895 | + | 0.0605610i | 0.551530 | − | 0.834155i | \(-0.314044\pi\) |
−0.446635 | + | 0.894716i | \(0.647378\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 2.52416 | + | 4.37197i | 0.222239 | + | 0.384930i | ||||
\(130\) | −8.02448 | − | 3.02520i | −0.703793 | − | 0.265327i | ||||
\(131\) | 5.74528 | − | 9.95113i | 0.501968 | − | 0.869434i | −0.498030 | − | 0.867160i | \(-0.665943\pi\) |
0.999997 | − | 0.00227379i | \(-0.000723771\pi\) | |||||||
\(132\) | −3.95946 | − | 2.28599i | −0.344626 | − | 0.198970i | ||||
\(133\) | −0.369105 | − | 0.213103i | −0.0320055 | − | 0.0184784i | ||||
\(134\) | 4.77106 | 0.412157 | ||||||||
\(135\) | −0.788796 | + | 2.09232i | −0.0678887 | + | 0.180078i | ||||
\(136\) | −1.65480 | + | 2.86619i | −0.141898 | + | 0.245774i | ||||
\(137\) | 9.54995i | 0.815908i | 0.913003 | + | 0.407954i | \(0.133758\pi\) | ||||
−0.913003 | + | 0.407954i | \(0.866242\pi\) | |||||||
\(138\) | − | 5.47919i | − | 0.466419i | ||||||
\(139\) | −1.30897 | + | 2.26721i | −0.111026 | + | 0.192302i | −0.916184 | − | 0.400758i | \(-0.868747\pi\) |
0.805158 | + | 0.593060i | \(0.202080\pi\) | |||||||
\(140\) | 0.438884 | + | 0.535376i | 0.0370924 | + | 0.0452475i | ||||
\(141\) | 1.88759 | + | 3.26940i | 0.158964 | + | 0.275333i | ||||
\(142\) | 13.3401i | 1.11948i | ||||||||
\(143\) | 15.1853 | − | 8.76726i | 1.26986 | − | 0.733155i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | −1.44455 | − | 0.544588i | −0.119963 | − | 0.0452256i | ||||
\(146\) | 6.69167 | − | 11.5903i | 0.553806 | − | 0.959221i | ||||
\(147\) | − | 6.90415i | − | 0.569445i | ||||||
\(148\) | −2.28320 | − | 5.63800i | −0.187678 | − | 0.463440i | ||||
\(149\) | −6.42401 | −0.526276 | −0.263138 | − | 0.964758i | \(-0.584757\pi\) | ||||
−0.263138 | + | 0.964758i | \(0.584757\pi\) | |||||||
\(150\) | 3.75560 | + | 3.30083i | 0.306644 | + | 0.269511i | ||||
\(151\) | −2.44034 | − | 4.22679i | −0.198592 | − | 0.343972i | 0.749480 | − | 0.662027i | \(-0.230304\pi\) |
−0.948072 | + | 0.318055i | \(0.896970\pi\) | |||||||
\(152\) | −1.19222 | + | 0.688327i | −0.0967016 | + | 0.0558307i | ||||
\(153\) | −2.86619 | + | 1.65480i | −0.231718 | + | 0.133782i | ||||
\(154\) | −1.41547 | −0.114061 | ||||||||
\(155\) | 5.72621 | + | 2.15876i | 0.459940 | + | 0.173396i | ||||
\(156\) | −3.83521 | −0.307062 | ||||||||
\(157\) | −8.03324 | − | 4.63800i | −0.641123 | − | 0.370152i | 0.143924 | − | 0.989589i | \(-0.454028\pi\) |
−0.785047 | + | 0.619436i | \(0.787361\pi\) | |||||||
\(158\) | − | 15.2672i | − | 1.21459i | ||||||
\(159\) | −13.6971 | −1.08625 | ||||||||
\(160\) | 2.20640 | − | 0.363043i | 0.174431 | − | 0.0287010i | ||||
\(161\) | −0.848165 | − | 1.46907i | −0.0668448 | − | 0.115779i | ||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 11.3462 | + | 6.55071i | 0.888700 | + | 0.513091i | 0.873517 | − | 0.486794i | \(-0.161834\pi\) |
0.0151830 | + | 0.999885i | \(0.495167\pi\) | |||||||
\(164\) | −0.175457 | + | 0.303900i | −0.0137009 | + | 0.0237306i | ||||
\(165\) | −10.0876 | + | 1.65982i | −0.785321 | + | 0.129217i | ||||
\(166\) | 1.53697 | + | 2.66210i | 0.119292 | + | 0.206619i | ||||
\(167\) | −18.9448 | + | 10.9378i | −1.46599 | + | 0.846392i | −0.999277 | − | 0.0380142i | \(-0.987897\pi\) |
−0.466717 | + | 0.884407i | \(0.654563\pi\) | |||||||
\(168\) | 0.268117 | + | 0.154798i | 0.0206857 | + | 0.0119429i | ||||
\(169\) | 0.854410 | − | 1.47988i | 0.0657238 | − | 0.113837i | ||||
\(170\) | 1.20152 | + | 7.30229i | 0.0921527 | + | 0.560060i | ||||
\(171\) | −1.37665 | −0.105275 | ||||||||
\(172\) | 4.37197 | − | 2.52416i | 0.333359 | − | 0.192465i | ||||
\(173\) | 3.66596 | + | 2.11655i | 0.278718 | + | 0.160918i | 0.632843 | − | 0.774280i | \(-0.281888\pi\) |
−0.354125 | + | 0.935198i | \(0.615221\pi\) | |||||||
\(174\) | −0.690405 | −0.0523394 | ||||||||
\(175\) | 1.51790 | + | 0.303651i | 0.114743 | + | 0.0229538i | ||||
\(176\) | −2.28599 | + | 3.95946i | −0.172313 | + | 0.298455i | ||||
\(177\) | 11.5481i | 0.868011i | ||||||||
\(178\) | −9.48775 | + | 5.47776i | −0.711137 | + | 0.410575i | ||||
\(179\) | −18.1757 | −1.35852 | −0.679260 | − | 0.733898i | \(-0.737699\pi\) | ||||
−0.679260 | + | 0.733898i | \(0.737699\pi\) | |||||||
\(180\) | 2.09232 | + | 0.788796i | 0.155952 | + | 0.0587934i | ||||
\(181\) | 3.63216 | + | 6.29109i | 0.269977 | + | 0.467613i | 0.968855 | − | 0.247627i | \(-0.0796507\pi\) |
−0.698879 | + | 0.715240i | \(0.746317\pi\) | |||||||
\(182\) | −1.02829 | + | 0.593681i | −0.0762216 | + | 0.0440066i | ||||
\(183\) | −4.12172 | − | 2.37967i | −0.304686 | − | 0.175911i | ||||
\(184\) | −5.47919 | −0.403931 | ||||||||
\(185\) | −11.9407 | − | 6.51298i | −0.877900 | − | 0.478844i | ||||
\(186\) | 2.73678 | 0.200670 | ||||||||
\(187\) | −13.1042 | − | 7.56571i | −0.958274 | − | 0.553260i | ||||
\(188\) | 3.26940 | − | 1.88759i | 0.238446 | − | 0.137667i | ||||
\(189\) | 0.154798 | + | 0.268117i | 0.0112599 | + | 0.0195027i | ||||
\(190\) | −1.08590 | + | 2.88040i | −0.0787794 | + | 0.208966i | ||||
\(191\) | −3.42110 | −0.247542 | −0.123771 | − | 0.992311i | \(-0.539499\pi\) | ||||
−0.123771 | + | 0.992311i | \(0.539499\pi\) | |||||||
\(192\) | 0.866025 | − | 0.500000i | 0.0625000 | − | 0.0360844i | ||||
\(193\) | 19.2854i | 1.38819i | 0.719883 | + | 0.694096i | \(0.244195\pi\) | ||||
−0.719883 | + | 0.694096i | \(0.755805\pi\) | |||||||
\(194\) | −0.495047 | + | 0.857446i | −0.0355423 | + | 0.0615610i | ||||
\(195\) | −6.63214 | + | 5.43681i | −0.474937 | + | 0.389338i | ||||
\(196\) | −6.90415 | −0.493154 | ||||||||
\(197\) | 7.69610 | + | 4.44334i | 0.548324 | + | 0.316575i | 0.748446 | − | 0.663196i | \(-0.230800\pi\) |
−0.200122 | + | 0.979771i | \(0.564134\pi\) | |||||||
\(198\) | −3.95946 | + | 2.28599i | −0.281386 | + | 0.162458i | ||||
\(199\) | −12.5562 | −0.890082 | −0.445041 | − | 0.895510i | \(-0.646811\pi\) | ||||
−0.445041 | + | 0.895510i | \(0.646811\pi\) | |||||||
\(200\) | 3.30083 | − | 3.75560i | 0.233404 | − | 0.265561i | ||||
\(201\) | 2.38553 | − | 4.13186i | 0.168262 | − | 0.291439i | ||||
\(202\) | −11.6341 | − | 6.71693i | −0.818570 | − | 0.472602i | ||||
\(203\) | −0.185110 | + | 0.106873i | −0.0129921 | + | 0.00750102i | ||||
\(204\) | 1.65480 | + | 2.86619i | 0.115859 | + | 0.200674i | ||||
\(205\) | 0.127397 | + | 0.774256i | 0.00889776 | + | 0.0540764i | ||||
\(206\) | 2.90473 | − | 5.03115i | 0.202382 | − | 0.350537i | ||||
\(207\) | −4.74511 | − | 2.73959i | −0.329808 | − | 0.190415i | ||||
\(208\) | 3.83521i | 0.265924i | ||||||||
\(209\) | −3.14702 | − | 5.45080i | −0.217684 | − | 0.377040i | ||||
\(210\) | 0.683091 | − | 0.112396i | 0.0471378 | − | 0.00775608i | ||||
\(211\) | −19.5648 | −1.34689 | −0.673447 | − | 0.739235i | \(-0.735187\pi\) | ||||
−0.673447 | + | 0.739235i | \(0.735187\pi\) | |||||||
\(212\) | 13.6971i | 0.940720i | ||||||||
\(213\) | 11.5529 | + | 6.67007i | 0.791591 | + | 0.457025i | ||||
\(214\) | −7.29664 | −0.498788 | ||||||||
\(215\) | 3.98209 | − | 10.5627i | 0.271576 | − | 0.720369i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0.733778 | − | 0.423647i | 0.0498121 | − | 0.0287590i | ||||
\(218\) | −11.1976 | + | 6.46495i | −0.758398 | + | 0.437861i | ||||
\(219\) | −6.69167 | − | 11.5903i | −0.452181 | − | 0.783201i | ||||
\(220\) | 1.65982 | + | 10.0876i | 0.111905 | + | 0.680108i | ||||
\(221\) | −12.6930 | −0.853823 | ||||||||
\(222\) | −6.02425 | − | 0.841687i | −0.404321 | − | 0.0564903i | ||||
\(223\) | − | 3.99326i | − | 0.267408i | −0.991021 | − | 0.133704i | \(-0.957313\pi\) | ||
0.991021 | − | 0.133704i | \(-0.0426872\pi\) | |||||||
\(224\) | 0.154798 | − | 0.268117i | 0.0103429 | − | 0.0179144i | ||||
\(225\) | 4.73640 | − | 1.60203i | 0.315760 | − | 0.106802i | ||||
\(226\) | −1.22831 | − | 2.12749i | −0.0817058 | − | 0.141519i | ||||
\(227\) | −23.6856 | + | 13.6749i | −1.57207 | + | 0.907633i | −0.576150 | + | 0.817344i | \(0.695446\pi\) |
−0.995916 | + | 0.0902890i | \(0.971221\pi\) | |||||||
\(228\) | 1.37665i | 0.0911711i | ||||||||
\(229\) | 11.8978 | + | 20.6075i | 0.786226 | + | 1.36178i | 0.928264 | + | 0.371922i | \(0.121301\pi\) |
−0.142038 | + | 0.989861i | \(0.545365\pi\) | |||||||
\(230\) | −9.47503 | + | 7.76732i | −0.624765 | + | 0.512162i | ||||
\(231\) | −0.707733 | + | 1.22583i | −0.0465654 | + | 0.0806536i | ||||
\(232\) | 0.690405i | 0.0453273i | ||||||||
\(233\) | 25.6377i | 1.67958i | 0.542910 | + | 0.839791i | \(0.317322\pi\) | ||||
−0.542910 | + | 0.839791i | \(0.682678\pi\) | |||||||
\(234\) | −1.91760 | + | 3.32139i | −0.125358 | + | 0.217126i | ||||
\(235\) | 2.97785 | − | 7.89888i | 0.194253 | − | 0.515266i | ||||
\(236\) | 11.5481 | 0.751719 | ||||||||
\(237\) | −13.2218 | − | 7.63359i | −0.858846 | − | 0.495855i | ||||
\(238\) | 0.887360 | + | 0.512318i | 0.0575190 | + | 0.0332086i | ||||
\(239\) | −3.08398 | + | 5.34161i | −0.199486 | + | 0.345520i | −0.948362 | − | 0.317190i | \(-0.897261\pi\) |
0.748876 | + | 0.662710i | \(0.230594\pi\) | |||||||
\(240\) | 0.788796 | − | 2.09232i | 0.0509166 | − | 0.135059i | ||||
\(241\) | 2.00641 | + | 3.47521i | 0.129244 | + | 0.223858i | 0.923384 | − | 0.383878i | \(-0.125412\pi\) |
−0.794140 | + | 0.607735i | \(0.792078\pi\) | |||||||
\(242\) | −8.57629 | − | 4.95152i | −0.551305 | − | 0.318296i | ||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | −2.37967 | + | 4.12172i | −0.152343 | + | 0.263866i | ||||
\(245\) | −11.9392 | + | 9.78735i | −0.762767 | + | 0.625291i | ||||
\(246\) | 0.175457 | + | 0.303900i | 0.0111867 | + | 0.0193760i | ||||
\(247\) | −4.57240 | − | 2.63988i | −0.290935 | − | 0.167971i | ||||
\(248\) | − | 2.73678i | − | 0.173786i | ||||||
\(249\) | 3.07393 | 0.194803 | ||||||||
\(250\) | 0.384086 | − | 11.1737i | 0.0242917 | − | 0.706689i | ||||
\(251\) | 16.7469 | 1.05706 | 0.528528 | − | 0.848916i | \(-0.322744\pi\) | ||||
0.528528 | + | 0.848916i | \(0.322744\pi\) | |||||||
\(252\) | 0.268117 | − | 0.154798i | 0.0168898 | − | 0.00975134i | ||||
\(253\) | − | 25.0508i | − | 1.57493i | ||||||
\(254\) | −0.682488 | − | 1.18210i | −0.0428231 | − | 0.0741718i | ||||
\(255\) | 6.92473 | + | 2.61060i | 0.433643 | + | 0.163482i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −1.60041 | − | 0.923995i | −0.0998306 | − | 0.0576372i | 0.449253 | − | 0.893404i | \(-0.351690\pi\) |
−0.549084 | + | 0.835767i | \(0.685023\pi\) | |||||||
\(258\) | − | 5.04831i | − | 0.314294i | ||||||
\(259\) | −1.74550 | + | 0.706869i | −0.108460 | + | 0.0439227i | ||||
\(260\) | 5.43681 | + | 6.63214i | 0.337176 | + | 0.411308i | ||||
\(261\) | −0.345202 | + | 0.597908i | −0.0213675 | + | 0.0370096i | ||||
\(262\) | −9.95113 | + | 5.74528i | −0.614783 | + | 0.354945i | ||||
\(263\) | 6.35247 | − | 3.66760i | 0.391710 | − | 0.226154i | −0.291191 | − | 0.956665i | \(-0.594051\pi\) |
0.682901 | + | 0.730511i | \(0.260718\pi\) | |||||||
\(264\) | 2.28599 | + | 3.95946i | 0.140693 | + | 0.243688i | ||||
\(265\) | 19.4170 | + | 23.6861i | 1.19278 | + | 1.45502i | ||||
\(266\) | 0.213103 | + | 0.369105i | 0.0130662 | + | 0.0226313i | ||||
\(267\) | 10.9555i | 0.670466i | ||||||||
\(268\) | −4.13186 | − | 2.38553i | −0.252394 | − | 0.145720i | ||||
\(269\) | −16.3744 | −0.998363 | −0.499181 | − | 0.866498i | \(-0.666366\pi\) | ||||
−0.499181 | + | 0.866498i | \(0.666366\pi\) | |||||||
\(270\) | 1.72928 | − | 1.41760i | 0.105240 | − | 0.0862726i | ||||
\(271\) | −4.72672 | + | 8.18692i | −0.287128 | + | 0.497320i | −0.973123 | − | 0.230286i | \(-0.926034\pi\) |
0.685995 | + | 0.727606i | \(0.259367\pi\) | |||||||
\(272\) | 2.86619 | − | 1.65480i | 0.173789 | − | 0.100337i | ||||
\(273\) | 1.18736i | 0.0718625i | ||||||||
\(274\) | 4.77498 | − | 8.27050i | 0.288467 | − | 0.499639i | ||||
\(275\) | 17.1706 | + | 15.0913i | 1.03542 | + | 0.910041i | ||||
\(276\) | −2.73959 | + | 4.74511i | −0.164904 | + | 0.285622i | ||||
\(277\) | −7.62602 | + | 4.40289i | −0.458203 | + | 0.264544i | −0.711289 | − | 0.702900i | \(-0.751888\pi\) |
0.253085 | + | 0.967444i | \(0.418555\pi\) | |||||||
\(278\) | 2.26721 | − | 1.30897i | 0.135978 | − | 0.0785071i | ||||
\(279\) | 1.36839 | − | 2.37012i | 0.0819233 | − | 0.141895i | ||||
\(280\) | −0.112396 | − | 0.683091i | −0.00671696 | − | 0.0408225i | ||||
\(281\) | −1.60303 | + | 2.77653i | −0.0956286 | + | 0.165634i | −0.909871 | − | 0.414892i | \(-0.863819\pi\) |
0.814242 | + | 0.580525i | \(0.197153\pi\) | |||||||
\(282\) | − | 3.77518i | − | 0.224809i | ||||||
\(283\) | 17.6209 | − | 10.1734i | 1.04745 | − | 0.604748i | 0.125519 | − | 0.992091i | \(-0.459941\pi\) |
0.921936 | + | 0.387343i | \(0.126607\pi\) | |||||||
\(284\) | 6.67007 | − | 11.5529i | 0.395796 | − | 0.685538i | ||||
\(285\) | 1.95155 | + | 2.38062i | 0.115600 | + | 0.141016i | ||||
\(286\) | −17.5345 | −1.03684 | ||||||||
\(287\) | 0.0940861 | + | 0.0543206i | 0.00555372 | + | 0.00320644i | ||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | −3.02329 | − | 5.23649i | −0.177841 | − | 0.308029i | ||||
\(290\) | 0.978720 | + | 1.19390i | 0.0574724 | + | 0.0701083i | ||||
\(291\) | 0.495047 | + | 0.857446i | 0.0290201 | + | 0.0502644i | ||||
\(292\) | −11.5903 | + | 6.69167i | −0.678272 | + | 0.391600i | ||||
\(293\) | 16.0621 | − | 9.27344i | 0.938357 | − | 0.541760i | 0.0489118 | − | 0.998803i | \(-0.484425\pi\) |
0.889445 | + | 0.457043i | \(0.151091\pi\) | |||||||
\(294\) | −3.45208 | + | 5.97917i | −0.201329 | + | 0.348712i | ||||
\(295\) | 19.9699 | − | 16.3707i | 1.16269 | − | 0.953137i | ||||
\(296\) | −0.841687 | + | 6.02425i | −0.0489220 | + | 0.350152i | ||||
\(297\) | 4.57198i | 0.265293i | ||||||||
\(298\) | 5.56336 | + | 3.21201i | 0.322277 | + | 0.186067i | ||||
\(299\) | −10.5069 | − | 18.1985i | −0.607630 | − | 1.05245i | ||||
\(300\) | −1.60203 | − | 4.73640i | −0.0924935 | − | 0.273456i | ||||
\(301\) | −0.781467 | − | 1.35354i | −0.0450430 | − | 0.0780168i | ||||
\(302\) | 4.88068i | 0.280852i | ||||||||
\(303\) | −11.6341 | + | 6.71693i | −0.668360 | + | 0.385878i | ||||
\(304\) | 1.37665 | 0.0789565 | ||||||||
\(305\) | 1.72785 | + | 10.5010i | 0.0989361 | + | 0.601287i | ||||
\(306\) | 3.30960 | 0.189197 | ||||||||
\(307\) | 2.00272i | 0.114301i | 0.998366 | + | 0.0571506i | \(0.0182015\pi\) | ||||
−0.998366 | + | 0.0571506i | \(0.981798\pi\) | |||||||
\(308\) | 1.22583 | + | 0.707733i | 0.0698481 | + | 0.0403268i | ||||
\(309\) | −2.90473 | − | 5.03115i | −0.165245 | − | 0.286212i | ||||
\(310\) | −3.87967 | − | 4.73265i | −0.220350 | − | 0.268796i | ||||
\(311\) | 12.6672 | − | 21.9402i | 0.718290 | − | 1.24411i | −0.243387 | − | 0.969929i | \(-0.578259\pi\) |
0.961677 | − | 0.274185i | \(-0.0884082\pi\) | |||||||
\(312\) | 3.32139 | + | 1.91760i | 0.188037 | + | 0.108563i | ||||
\(313\) | −29.0006 | − | 16.7435i | −1.63921 | − | 0.946398i | −0.981106 | − | 0.193470i | \(-0.938026\pi\) |
−0.658103 | − | 0.752928i | \(-0.728641\pi\) | |||||||
\(314\) | 4.63800 | + | 8.03324i | 0.261737 | + | 0.453342i | ||||
\(315\) | 0.244208 | − | 0.647772i | 0.0137595 | − | 0.0364978i | ||||
\(316\) | −7.63359 | + | 13.2218i | −0.429423 | + | 0.743783i | ||||
\(317\) | −26.9267 | − | 15.5461i | −1.51235 | − | 0.873158i | −0.999896 | − | 0.0144452i | \(-0.995402\pi\) |
−0.512458 | − | 0.858712i | \(-0.671265\pi\) | |||||||
\(318\) | 11.8620 | + | 6.84854i | 0.665189 | + | 0.384047i | ||||
\(319\) | −3.15652 | −0.176731 | ||||||||
\(320\) | −2.09232 | − | 0.788796i | −0.116964 | − | 0.0440950i | ||||
\(321\) | −3.64832 | + | 6.31907i | −0.203629 | + | 0.352696i | ||||
\(322\) | 1.69633i | 0.0945328i | ||||||||
\(323\) | 4.55617i | 0.253512i | ||||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | 18.8035 | + | 3.76156i | 1.04303 | + | 0.208654i | ||||
\(326\) | −6.55071 | − | 11.3462i | −0.362810 | − | 0.628406i | ||||
\(327\) | 12.9299i | 0.715025i | ||||||||
\(328\) | 0.303900 | − | 0.175457i | 0.0167801 | − | 0.00968798i | ||||
\(329\) | −0.584389 | − | 1.01219i | −0.0322184 | − | 0.0558039i | ||||
\(330\) | 9.56605 | + | 3.60636i | 0.526594 | + | 0.198524i | ||||
\(331\) | −15.1793 | + | 26.2913i | −0.834328 | + | 1.44510i | 0.0602485 | + | 0.998183i | \(0.480811\pi\) |
−0.894576 | + | 0.446915i | \(0.852523\pi\) | |||||||
\(332\) | − | 3.07393i | − | 0.168704i | ||||||
\(333\) | −3.74105 | + | 4.79631i | −0.205008 | + | 0.262836i | ||||
\(334\) | 21.8756 | 1.19698 | ||||||||
\(335\) | −10.5269 | + | 1.73210i | −0.575145 | + | 0.0946347i | ||||
\(336\) | −0.154798 | − | 0.268117i | −0.00844491 | − | 0.0146270i | ||||
\(337\) | −10.2584 | + | 5.92268i | −0.558809 | + | 0.322629i | −0.752668 | − | 0.658401i | \(-0.771233\pi\) |
0.193858 | + | 0.981030i | \(0.437900\pi\) | |||||||
\(338\) | −1.47988 | + | 0.854410i | −0.0804949 | + | 0.0464738i | ||||
\(339\) | −2.45662 | −0.133425 | ||||||||
\(340\) | 2.61060 | − | 6.92473i | 0.141579 | − | 0.375546i | ||||
\(341\) | 12.5125 | 0.677590 | ||||||||
\(342\) | 1.19222 | + | 0.688327i | 0.0644677 | + | 0.0372205i | ||||
\(343\) | 4.30466i | 0.232430i | ||||||||
\(344\) | −5.04831 | −0.272187 | ||||||||
\(345\) | 1.98918 | + | 12.0893i | 0.107094 | + | 0.650865i | ||||
\(346\) | −2.11655 | − | 3.66596i | −0.113786 | − | 0.197083i | ||||
\(347\) | 1.18913i | 0.0638360i | 0.999490 | + | 0.0319180i | \(0.0101615\pi\) | ||||
−0.999490 | + | 0.0319180i | \(0.989838\pi\) | |||||||
\(348\) | 0.597908 | + | 0.345202i | 0.0320512 | + | 0.0185048i | ||||
\(349\) | −3.71744 | + | 6.43879i | −0.198990 | + | 0.344660i | −0.948201 | − | 0.317671i | \(-0.897099\pi\) |
0.749211 | + | 0.662331i | \(0.230433\pi\) | |||||||
\(350\) | −1.16272 | − | 1.02192i | −0.0621498 | − | 0.0546239i | ||||
\(351\) | 1.91760 | + | 3.32139i | 0.102354 | + | 0.177283i | ||||
\(352\) | 3.95946 | − | 2.28599i | 0.211040 | − | 0.121844i | ||||
\(353\) | −12.2088 | − | 7.04878i | −0.649811 | − | 0.375169i | 0.138573 | − | 0.990352i | \(-0.455749\pi\) |
−0.788384 | + | 0.615184i | \(0.789082\pi\) | |||||||
\(354\) | 5.77406 | − | 10.0010i | 0.306888 | − | 0.531546i | ||||
\(355\) | −4.84304 | − | 29.4337i | −0.257042 | − | 1.56218i | ||||
\(356\) | 10.9555 | 0.580641 | ||||||||
\(357\) | 0.887360 | − | 0.512318i | 0.0469641 | − | 0.0271147i | ||||
\(358\) | 15.7407 | + | 9.08787i | 0.831920 | + | 0.480309i | ||||
\(359\) | 1.41624 | 0.0747465 | 0.0373733 | − | 0.999301i | \(-0.488101\pi\) | ||||
0.0373733 | + | 0.999301i | \(0.488101\pi\) | |||||||
\(360\) | −1.41760 | − | 1.72928i | −0.0747143 | − | 0.0911409i | ||||
\(361\) | 8.55241 | − | 14.8132i | 0.450127 | − | 0.779643i | ||||
\(362\) | − | 7.26433i | − | 0.381805i | ||||||
\(363\) | −8.57629 | + | 4.95152i | −0.450138 | + | 0.259888i | ||||
\(364\) | 1.18736 | 0.0622347 | ||||||||
\(365\) | −10.5567 | + | 28.0022i | −0.552564 | + | 1.46570i | ||||
\(366\) | 2.37967 | + | 4.12172i | 0.124388 | + | 0.215446i | ||||
\(367\) | 16.3472 | − | 9.43807i | 0.853318 | − | 0.492663i | −0.00845116 | − | 0.999964i | \(-0.502690\pi\) |
0.861769 | + | 0.507301i | \(0.169357\pi\) | |||||||
\(368\) | 4.74511 | + | 2.73959i | 0.247356 | + | 0.142811i | ||||
\(369\) | 0.350914 | 0.0182678 | ||||||||
\(370\) | 7.08449 | + | 11.6108i | 0.368305 | + | 0.603615i | ||||
\(371\) | 4.24055 | 0.220159 | ||||||||
\(372\) | −2.37012 | − | 1.36839i | −0.122885 | − | 0.0709476i | ||||
\(373\) | −19.4504 | + | 11.2297i | −1.00710 | + | 0.581451i | −0.910342 | − | 0.413857i | \(-0.864181\pi\) |
−0.0967600 | + | 0.995308i | \(0.530848\pi\) | |||||||
\(374\) | 7.56571 | + | 13.1042i | 0.391214 | + | 0.677602i | ||||
\(375\) | −9.48470 | − | 5.91950i | −0.489788 | − | 0.305682i | ||||
\(376\) | −3.77518 | −0.194690 | ||||||||
\(377\) | −2.29310 | + | 1.32392i | −0.118101 | + | 0.0681855i | ||||
\(378\) | − | 0.309595i | − | 0.0159239i | ||||||
\(379\) | 17.5279 | − | 30.3592i | 0.900347 | − | 1.55945i | 0.0733034 | − | 0.997310i | \(-0.476646\pi\) |
0.827044 | − | 0.562137i | \(-0.190021\pi\) | |||||||
\(380\) | 2.38062 | − | 1.95155i | 0.122123 | − | 0.100112i | ||||
\(381\) | −1.36498 | −0.0699298 | ||||||||
\(382\) | 2.96276 | + | 1.71055i | 0.151588 | + | 0.0875193i | ||||
\(383\) | 10.7629 | − | 6.21395i | 0.549957 | − | 0.317518i | −0.199148 | − | 0.979969i | \(-0.563817\pi\) |
0.749105 | + | 0.662452i | \(0.230484\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 3.12308 | − | 0.513874i | 0.159167 | − | 0.0261894i | ||||
\(386\) | 9.64268 | − | 16.7016i | 0.490800 | − | 0.850090i | ||||
\(387\) | −4.37197 | − | 2.52416i | −0.222239 | − | 0.128310i | ||||
\(388\) | 0.857446 | − | 0.495047i | 0.0435302 | − | 0.0251322i | ||||
\(389\) | −12.6077 | − | 21.8372i | −0.639235 | − | 1.10719i | −0.985601 | − | 0.169088i | \(-0.945918\pi\) |
0.346366 | − | 0.938100i | \(-0.387416\pi\) | |||||||
\(390\) | 8.46200 | − | 1.39234i | 0.428490 | − | 0.0705041i | ||||
\(391\) | −9.06694 | + | 15.7044i | −0.458535 | + | 0.794206i | ||||
\(392\) | 5.97917 | + | 3.45208i | 0.301994 | + | 0.174356i | ||||
\(393\) | 11.4906i | 0.579623i | ||||||||
\(394\) | −4.44334 | − | 7.69610i | −0.223852 | − | 0.387724i | ||||
\(395\) | 5.54264 | + | 33.6855i | 0.278880 | + | 1.69490i | ||||
\(396\) | 4.57198 | 0.229751 | ||||||||
\(397\) | − | 6.79635i | − | 0.341099i | −0.985349 | − | 0.170550i | \(-0.945446\pi\) | ||
0.985349 | − | 0.170550i | \(-0.0545543\pi\) | |||||||
\(398\) | 10.8739 | + | 6.27808i | 0.545062 | + | 0.314692i | ||||
\(399\) | 0.426206 | 0.0213370 | ||||||||
\(400\) | −4.73640 | + | 1.60203i | −0.236820 | + | 0.0801017i | ||||
\(401\) | −4.27501 | −0.213484 | −0.106742 | − | 0.994287i | \(-0.534042\pi\) | ||||
−0.106742 | + | 0.994287i | \(0.534042\pi\) | |||||||
\(402\) | −4.13186 | + | 2.38553i | −0.206079 | + | 0.118980i | ||||
\(403\) | 9.08990 | − | 5.24805i | 0.452800 | − | 0.261424i | ||||
\(404\) | 6.71693 | + | 11.6341i | 0.334180 | + | 0.578817i | ||||
\(405\) | −0.363043 | − | 2.20640i | −0.0180397 | − | 0.109637i | ||||
\(406\) | 0.213746 | 0.0106080 | ||||||||
\(407\) | −27.5428 | − | 3.84818i | −1.36524 | − | 0.190747i | ||||
\(408\) | − | 3.30960i | − | 0.163849i | ||||||
\(409\) | 4.25865 | − | 7.37620i | 0.210577 | − | 0.364730i | −0.741318 | − | 0.671153i | \(-0.765799\pi\) |
0.951895 | + | 0.306424i | \(0.0991325\pi\) | |||||||
\(410\) | 0.276799 | − | 0.734223i | 0.0136701 | − | 0.0362607i | ||||
\(411\) | −4.77498 | − | 8.27050i | −0.235532 | − | 0.407954i | ||||
\(412\) | −5.03115 | + | 2.90473i | −0.247867 | + | 0.143106i | ||||
\(413\) | − | 3.57525i | − | 0.175926i | ||||||
\(414\) | 2.73959 | + | 4.74511i | 0.134644 | + | 0.233210i | ||||
\(415\) | −4.35762 | − | 5.31568i | −0.213907 | − | 0.260936i | ||||
\(416\) | 1.91760 | − | 3.32139i | 0.0940183 | − | 0.162844i | ||||
\(417\) | − | 2.61795i | − | 0.128202i | ||||||
\(418\) | 6.29404i | 0.307852i | ||||||||
\(419\) | −8.64775 | + | 14.9783i | −0.422470 | + | 0.731740i | −0.996180 | − | 0.0873184i | \(-0.972170\pi\) |
0.573710 | + | 0.819058i | \(0.305504\pi\) | |||||||
\(420\) | −0.647772 | − | 0.244208i | −0.0316081 | − | 0.0119161i | ||||
\(421\) | −14.3686 | −0.700282 | −0.350141 | − | 0.936697i | \(-0.613866\pi\) | ||||
−0.350141 | + | 0.936697i | \(0.613866\pi\) | |||||||
\(422\) | 16.9436 | + | 9.78239i | 0.824801 | + | 0.476199i | ||||
\(423\) | −3.26940 | − | 1.88759i | −0.158964 | − | 0.0917778i | ||||
\(424\) | 6.84854 | − | 11.8620i | 0.332595 | − | 0.576071i | ||||
\(425\) | −5.30208 | − | 15.6756i | −0.257189 | − | 0.760377i | ||||
\(426\) | −6.67007 | − | 11.5529i | −0.323166 | − | 0.559740i | ||||
\(427\) | 1.27606 | + | 0.736736i | 0.0617531 | + | 0.0356532i | ||||
\(428\) | 6.31907 | + | 3.64832i | 0.305444 | + | 0.176348i | ||||
\(429\) | −8.76726 | + | 15.1853i | −0.423287 | + | 0.733155i | ||||
\(430\) | −8.72993 | + | 7.15651i | −0.420995 | + | 0.345117i | ||||
\(431\) | 11.6582 | + | 20.1926i | 0.561557 | + | 0.972645i | 0.997361 | + | 0.0726036i | \(0.0231308\pi\) |
−0.435804 | + | 0.900042i | \(0.643536\pi\) | |||||||
\(432\) | −0.866025 | − | 0.500000i | −0.0416667 | − | 0.0240563i | ||||
\(433\) | − | 30.7382i | − | 1.47718i | −0.674154 | − | 0.738591i | \(-0.735491\pi\) | ||
0.674154 | − | 0.738591i | \(-0.264509\pi\) | |||||||
\(434\) | −0.847293 | −0.0406714 | ||||||||
\(435\) | 1.52331 | − | 0.250646i | 0.0730371 | − | 0.0120176i | ||||
\(436\) | 12.9299 | 0.619229 | ||||||||
\(437\) | −6.53238 | + | 3.77147i | −0.312486 | + | 0.180414i | ||||
\(438\) | 13.3833i | 0.639481i | ||||||||
\(439\) | −18.6368 | − | 32.2798i | −0.889484 | − | 1.54063i | −0.840486 | − | 0.541833i | \(-0.817731\pi\) |
−0.0489981 | − | 0.998799i | \(-0.515603\pi\) | |||||||
\(440\) | 3.60636 | − | 9.56605i | 0.171927 | − | 0.456044i | ||||
\(441\) | 3.45208 | + | 5.97917i | 0.164385 | + | 0.284722i | ||||
\(442\) | 10.9924 | + | 6.34649i | 0.522857 | + | 0.301872i | ||||
\(443\) | − | 15.5587i | − | 0.739218i | −0.929187 | − | 0.369609i | \(-0.879492\pi\) | ||
0.929187 | − | 0.369609i | \(-0.120508\pi\) | |||||||
\(444\) | 4.79631 | + | 3.74105i | 0.227623 | + | 0.177542i | ||||
\(445\) | 18.9451 | − | 15.5306i | 0.898085 | − | 0.736220i | ||||
\(446\) | −1.99663 | + | 3.45826i | −0.0945431 | + | 0.163753i | ||||
\(447\) | 5.56336 | − | 3.21201i | 0.263138 | − | 0.151923i | ||||
\(448\) | −0.268117 | + | 0.154798i | −0.0126674 | + | 0.00731350i | ||||
\(449\) | 0.541729 | + | 0.938301i | 0.0255658 | + | 0.0442812i | 0.878525 | − | 0.477696i | \(-0.158528\pi\) |
−0.852959 | + | 0.521977i | \(0.825195\pi\) | |||||||
\(450\) | −4.90286 | − | 0.980798i | −0.231123 | − | 0.0462353i | ||||
\(451\) | 0.802186 | + | 1.38943i | 0.0377735 | + | 0.0654255i | ||||
\(452\) | 2.45662i | 0.115549i | ||||||||
\(453\) | 4.22679 | + | 2.44034i | 0.198592 | + | 0.114657i | ||||
\(454\) | 27.3497 | 1.28359 | ||||||||
\(455\) | 2.05328 | − | 1.68321i | 0.0962592 | − | 0.0789101i | ||||
\(456\) | 0.688327 | − | 1.19222i | 0.0322339 | − | 0.0558307i | ||||
\(457\) | 21.6972 | − | 12.5269i | 1.01495 | − | 0.585984i | 0.102316 | − | 0.994752i | \(-0.467375\pi\) |
0.912638 | + | 0.408768i | \(0.134042\pi\) | |||||||
\(458\) | − | 23.7955i | − | 1.11189i | ||||||
\(459\) | 1.65480 | − | 2.86619i | 0.0772393 | − | 0.133782i | ||||
\(460\) | 12.0893 | − | 1.98918i | 0.563665 | − | 0.0927459i | ||||
\(461\) | −5.11582 | + | 8.86086i | −0.238267 | + | 0.412691i | −0.960217 | − | 0.279254i | \(-0.909913\pi\) |
0.721950 | + | 0.691945i | \(0.243246\pi\) | |||||||
\(462\) | 1.22583 | − | 0.707733i | 0.0570307 | − | 0.0329267i | ||||
\(463\) | 14.3453 | − | 8.28227i | 0.666683 | − | 0.384910i | −0.128135 | − | 0.991757i | \(-0.540899\pi\) |
0.794819 | + | 0.606847i | \(0.207566\pi\) | |||||||
\(464\) | 0.345202 | − | 0.597908i | 0.0160256 | − | 0.0277572i | ||||
\(465\) | −6.03842 | + | 0.993566i | −0.280025 | + | 0.0460755i | ||||
\(466\) | 12.8189 | − | 22.2029i | 0.593822 | − | 1.02853i | ||||
\(467\) | 26.1213i | 1.20875i | 0.796699 | + | 0.604376i | \(0.206577\pi\) | ||||
−0.796699 | + | 0.604376i | \(0.793423\pi\) | |||||||
\(468\) | 3.32139 | − | 1.91760i | 0.153531 | − | 0.0886413i | ||||
\(469\) | −0.738550 | + | 1.27921i | −0.0341031 | + | 0.0590682i | ||||
\(470\) | −6.52833 | + | 5.35171i | −0.301130 | + | 0.246856i | ||||
\(471\) | 9.27599 | 0.427415 | ||||||||
\(472\) | −10.0010 | − | 5.77406i | −0.460332 | − | 0.265773i | ||||
\(473\) | − | 23.0808i | − | 1.06126i | ||||||
\(474\) | 7.63359 | + | 13.2218i | 0.350623 | + | 0.607296i | ||||
\(475\) | 1.35022 | − | 6.74954i | 0.0619523 | − | 0.309690i | ||||
\(476\) | −0.512318 | − | 0.887360i | −0.0234820 | − | 0.0406721i | ||||
\(477\) | 11.8620 | − | 6.84854i | 0.543125 | − | 0.313573i | ||||
\(478\) | 5.34161 | − | 3.08398i | 0.244319 | − | 0.141058i | ||||
\(479\) | 2.17164 | − | 3.76140i | 0.0992250 | − | 0.171863i | −0.812139 | − | 0.583464i | \(-0.801697\pi\) |
0.911364 | + | 0.411601i | \(0.135030\pi\) | |||||||
\(480\) | −1.72928 | + | 1.41760i | −0.0789303 | + | 0.0647045i | ||||
\(481\) | −21.6229 | + | 8.75655i | −0.985919 | + | 0.399265i | ||||
\(482\) | − | 4.01282i | − | 0.182779i | ||||||
\(483\) | 1.46907 | + | 0.848165i | 0.0668448 | + | 0.0385929i | ||||
\(484\) | 4.95152 | + | 8.57629i | 0.225069 | + | 0.389831i | ||||
\(485\) | 0.780981 | − | 2.07159i | 0.0354625 | − | 0.0940661i | ||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | − | 13.9410i | − | 0.631728i | −0.948804 | − | 0.315864i | \(-0.897706\pi\) | ||
0.948804 | − | 0.315864i | \(-0.102294\pi\) | |||||||
\(488\) | 4.12172 | − | 2.37967i | 0.186581 | − | 0.107723i | ||||
\(489\) | −13.1014 | −0.592467 | ||||||||
\(490\) | 15.2333 | − | 2.50650i | 0.688171 | − | 0.113232i | ||||
\(491\) | −28.8479 | −1.30189 | −0.650943 | − | 0.759127i | \(-0.725626\pi\) | ||||
−0.650943 | + | 0.759127i | \(0.725626\pi\) | |||||||
\(492\) | − | 0.350914i | − | 0.0158204i | ||||||
\(493\) | 1.97883 | + | 1.14248i | 0.0891222 | + | 0.0514547i | ||||
\(494\) | 2.63988 | + | 4.57240i | 0.118774 | + | 0.205722i | ||||
\(495\) | 7.90623 | − | 6.48126i | 0.355359 | − | 0.291311i | ||||
\(496\) | −1.36839 | + | 2.37012i | −0.0614425 | + | 0.106421i | ||||
\(497\) | −3.57672 | − | 2.06502i | −0.160438 | − | 0.0926289i | ||||
\(498\) | −2.66210 | − | 1.53697i | −0.119292 | − | 0.0688731i | ||||
\(499\) | 16.1947 | + | 28.0501i | 0.724976 | + | 1.25570i | 0.958984 | + | 0.283461i | \(0.0914827\pi\) |
−0.234007 | + | 0.972235i | \(0.575184\pi\) | |||||||
\(500\) | −5.91950 | + | 9.48470i | −0.264728 | + | 0.424169i | ||||
\(501\) | 10.9378 | − | 18.9448i | 0.488665 | − | 0.846392i | ||||
\(502\) | −14.5033 | − | 8.37346i | −0.647312 | − | 0.373726i | ||||
\(503\) | 6.88500 | + | 3.97506i | 0.306987 | + | 0.177239i | 0.645577 | − | 0.763695i | \(-0.276617\pi\) |
−0.338590 | + | 0.940934i | \(0.609950\pi\) | |||||||
\(504\) | −0.309595 | −0.0137905 | ||||||||
\(505\) | 28.1079 | + | 10.5966i | 1.25079 | + | 0.471541i | ||||
\(506\) | −12.5254 | + | 21.6946i | −0.556821 | + | 0.964442i | ||||
\(507\) | 1.70882i | 0.0758913i | ||||||||
\(508\) | 1.36498i | 0.0605610i | ||||||||
\(509\) | −18.3769 | + | 31.8297i | −0.814541 | + | 1.41083i | 0.0951156 | + | 0.995466i | \(0.469678\pi\) |
−0.909657 | + | 0.415361i | \(0.863655\pi\) | |||||||
\(510\) | −4.69170 | − | 5.72321i | −0.207752 | − | 0.253428i | ||||
\(511\) | 2.07171 | + | 3.58831i | 0.0916470 | + | 0.158737i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 1.19222 | − | 0.688327i | 0.0526377 | − | 0.0303904i | ||||
\(514\) | 0.923995 | + | 1.60041i | 0.0407557 | + | 0.0705909i | ||||
\(515\) | −4.58248 | + | 12.1553i | −0.201928 | + | 0.535625i | ||||
\(516\) | −2.52416 | + | 4.37197i | −0.111120 | + | 0.192465i | ||||
\(517\) | − | 17.2601i | − | 0.759097i | ||||||
\(518\) | 1.86508 | + | 0.260582i | 0.0819469 | + | 0.0114493i | ||||
\(519\) | −4.23309 | −0.185812 | ||||||||
\(520\) | −1.39234 | − | 8.46200i | −0.0610583 | − | 0.371083i | ||||
\(521\) | 10.8737 | + | 18.8338i | 0.476386 | + | 0.825125i | 0.999634 | − | 0.0270553i | \(-0.00861303\pi\) |
−0.523248 | + | 0.852181i | \(0.675280\pi\) | |||||||
\(522\) | 0.597908 | − | 0.345202i | 0.0261697 | − | 0.0151091i | ||||
\(523\) | −28.0959 | + | 16.2211i | −1.22855 | + | 0.709301i | −0.966726 | − | 0.255815i | \(-0.917656\pi\) |
−0.261820 | + | 0.965117i | \(0.584323\pi\) | |||||||
\(524\) | 11.4906 | 0.501968 | ||||||||
\(525\) | −1.46637 | + | 0.495982i | −0.0639975 | + | 0.0216464i | ||||
\(526\) | −7.33520 | −0.319830 | ||||||||
\(527\) | −7.84413 | − | 4.52881i | −0.341696 | − | 0.197278i | ||||
\(528\) | − | 4.57198i | − | 0.198970i | ||||||
\(529\) | −7.02148 | −0.305282 | ||||||||
\(530\) | −4.97263 | − | 30.2213i | −0.215997 | − | 1.31273i | ||||
\(531\) | −5.77406 | − | 10.0010i | −0.250573 | − | 0.434005i | ||||
\(532\) | − | 0.426206i | − | 0.0184784i | ||||||
\(533\) | 1.16552 | + | 0.672913i | 0.0504843 | + | 0.0291471i | ||||
\(534\) | 5.47776 | − | 9.48775i | 0.237046 | − | 0.410575i | ||||
\(535\) | 16.0993 | − | 2.64899i | 0.696033 | − | 0.114526i | ||||
\(536\) | 2.38553 | + | 4.13186i | 0.103039 | + | 0.178469i | ||||
\(537\) | 15.7407 | − | 9.08787i | 0.679260 | − | 0.392171i | ||||
\(538\) | 14.1806 | + | 8.18718i | 0.611370 | + | 0.352975i | ||||
\(539\) | −15.7828 | + | 27.3367i | −0.679815 | + | 1.17747i | ||||
\(540\) | −2.20640 | + | 0.363043i | −0.0949483 | + | 0.0156229i | ||||
\(541\) | 1.49631 | 0.0643316 | 0.0321658 | − | 0.999483i | \(-0.489760\pi\) | ||||
0.0321658 | + | 0.999483i | \(0.489760\pi\) | |||||||
\(542\) | 8.18692 | − | 4.72672i | 0.351659 | − | 0.203030i | ||||
\(543\) | −6.29109 | − | 3.63216i | −0.269977 | − | 0.155871i | ||||
\(544\) | −3.30960 | −0.141898 | ||||||||
\(545\) | 22.3594 | − | 18.3295i | 0.957770 | − | 0.785148i | ||||
\(546\) | 0.593681 | − | 1.02829i | 0.0254072 | − | 0.0440066i | ||||
\(547\) | − | 18.3785i | − | 0.785806i | −0.919580 | − | 0.392903i | \(-0.871471\pi\) | ||
0.919580 | − | 0.392903i | \(-0.128529\pi\) | |||||||
\(548\) | −8.27050 | + | 4.77498i | −0.353298 | + | 0.203977i | ||||
\(549\) | 4.75935 | 0.203124 | ||||||||
\(550\) | −7.32447 | − | 21.6548i | −0.312317 | − | 0.923362i | ||||
\(551\) | 0.475224 | + | 0.823112i | 0.0202452 | + | 0.0350658i | ||||
\(552\) | 4.74511 | − | 2.73959i | 0.201965 | − | 0.116605i | ||||
\(553\) | 4.09340 | + | 2.36333i | 0.174069 | + | 0.100499i | ||||
\(554\) | 8.80577 | 0.374121 | ||||||||
\(555\) | 13.5975 | − | 0.329961i | 0.577180 | − | 0.0140061i | ||||
\(556\) | −2.61795 | −0.111026 | ||||||||
\(557\) | 6.04437 | + | 3.48972i | 0.256108 | + | 0.147864i | 0.622558 | − | 0.782574i | \(-0.286094\pi\) |
−0.366450 | + | 0.930438i | \(0.619427\pi\) | |||||||
\(558\) | −2.37012 | + | 1.36839i | −0.100335 | + | 0.0579285i | ||||
\(559\) | −9.68066 | − | 16.7674i | −0.409448 | − | 0.709185i | ||||
\(560\) | −0.244208 | + | 0.647772i | −0.0103197 | + | 0.0273734i | ||||
\(561\) | 15.1314 | 0.638849 | ||||||||
\(562\) | 2.77653 | − | 1.60303i | 0.117121 | − | 0.0676197i | ||||
\(563\) | − | 41.0519i | − | 1.73013i | −0.501660 | − | 0.865065i | \(-0.667277\pi\) | ||
0.501660 | − | 0.865065i | \(-0.332723\pi\) | |||||||
\(564\) | −1.88759 | + | 3.26940i | −0.0794819 | + | 0.137667i | ||||
\(565\) | 3.48251 | + | 4.24817i | 0.146510 | + | 0.178722i | ||||
\(566\) | −20.3469 | −0.855243 | ||||||||
\(567\) | −0.268117 | − | 0.154798i | −0.0112599 | − | 0.00650089i | ||||
\(568\) | −11.5529 | + | 6.67007i | −0.484749 | + | 0.279870i | ||||
\(569\) | 2.75954 | 0.115686 | 0.0578429 | − | 0.998326i | \(-0.481578\pi\) | ||||
0.0578429 | + | 0.998326i | \(0.481578\pi\) | |||||||
\(570\) | −0.499784 | − | 3.03745i | −0.0209336 | − | 0.127225i | ||||
\(571\) | −11.4590 | + | 19.8475i | −0.479544 | + | 0.830594i | −0.999725 | − | 0.0234621i | \(-0.992531\pi\) |
0.520181 | + | 0.854056i | \(0.325864\pi\) | |||||||
\(572\) | 15.1853 | + | 8.76726i | 0.634931 | + | 0.366577i | ||||
\(573\) | 2.96276 | − | 1.71055i | 0.123771 | − | 0.0714592i | ||||
\(574\) | −0.0543206 | − | 0.0940861i | −0.00226730 | − | 0.00392708i | ||||
\(575\) | 18.0858 | − | 20.5776i | 0.754232 | − | 0.858147i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −9.23858 | − | 5.33389i | −0.384607 | − | 0.222053i | 0.295214 | − | 0.955431i | \(-0.404609\pi\) |
−0.679821 | + | 0.733378i | \(0.737942\pi\) | |||||||
\(578\) | 6.04658i | 0.251505i | ||||||||
\(579\) | −9.64268 | − | 16.7016i | −0.400736 | − | 0.694096i | ||||
\(580\) | −0.250646 | − | 1.52331i | −0.0104075 | − | 0.0632519i | ||||
\(581\) | −0.951675 | −0.0394821 | ||||||||
\(582\) | − | 0.990093i | − | 0.0410407i | ||||||
\(583\) | 54.2330 | + | 31.3114i | 2.24610 | + | 1.29679i | ||||
\(584\) | 13.3833 | 0.553806 | ||||||||
\(585\) | 3.02520 | − | 8.02448i | 0.125076 | − | 0.331771i | ||||
\(586\) | −18.5469 | −0.766165 | ||||||||
\(587\) | 21.0853 | − | 12.1736i | 0.870284 | − | 0.502459i | 0.00284149 | − | 0.999996i | \(-0.499096\pi\) |
0.867443 | + | 0.497537i | \(0.165762\pi\) | |||||||
\(588\) | 5.97917 | − | 3.45208i | 0.246577 | − | 0.142361i | ||||
\(589\) | −1.88380 | − | 3.26283i | −0.0776205 | − | 0.134443i | ||||
\(590\) | −25.4798 | + | 4.19246i | −1.04899 | + | 0.172601i | ||||
\(591\) | −8.88669 | −0.365550 | ||||||||
\(592\) | 3.74105 | − | 4.79631i | 0.153756 | − | 0.197127i | ||||
\(593\) | 21.9586i | 0.901733i | 0.892591 | + | 0.450867i | \(0.148885\pi\) | ||||
−0.892591 | + | 0.450867i | \(0.851115\pi\) | |||||||
\(594\) | 2.28599 | − | 3.95946i | 0.0937954 | − | 0.162458i | ||||
\(595\) | −2.14386 | − | 0.808228i | −0.0878899 | − | 0.0331341i | ||||
\(596\) | −3.21201 | − | 5.56336i | −0.131569 | − | 0.227884i | ||||
\(597\) | 10.8739 | − | 6.27808i | 0.445041 | − | 0.256945i | ||||
\(598\) | 21.0138i | 0.859319i | ||||||||
\(599\) | −22.2901 | − | 38.6075i | −0.910747 | − | 1.57746i | −0.813012 | − | 0.582247i | \(-0.802173\pi\) |
−0.0977352 | − | 0.995212i | \(-0.531160\pi\) | |||||||
\(600\) | −0.980798 | + | 4.90286i | −0.0400409 | + | 0.200158i | ||||
\(601\) | 10.9231 | − | 18.9193i | 0.445562 | − | 0.771736i | −0.552529 | − | 0.833493i | \(-0.686337\pi\) |
0.998091 | + | 0.0617578i | \(0.0196706\pi\) | |||||||
\(602\) | 1.56293i | 0.0637004i | ||||||||
\(603\) | 4.77106i | 0.194293i | ||||||||
\(604\) | 2.44034 | − | 4.22679i | 0.0992961 | − | 0.171986i | ||||
\(605\) | 20.7203 | + | 7.81148i | 0.842401 | + | 0.317582i | ||||
\(606\) | 13.4339 | 0.545713 | ||||||||
\(607\) | 21.2315 | + | 12.2580i | 0.861762 | + | 0.497539i | 0.864602 | − | 0.502457i | \(-0.167571\pi\) |
−0.00283994 | + | 0.999996i | \(0.500904\pi\) | |||||||
\(608\) | −1.19222 | − | 0.688327i | −0.0483508 | − | 0.0279153i | ||||
\(609\) | 0.106873 | − | 0.185110i | 0.00433071 | − | 0.00750102i | ||||
\(610\) | 3.75415 | − | 9.95808i | 0.152001 | − | 0.403191i | ||||
\(611\) | −7.23930 | − | 12.5388i | −0.292871 | − | 0.507267i | ||||
\(612\) | −2.86619 | − | 1.65480i | −0.115859 | − | 0.0668912i | ||||
\(613\) | −15.8847 | − | 9.17104i | −0.641577 | − | 0.370415i | 0.143645 | − | 0.989629i | \(-0.454118\pi\) |
−0.785222 | + | 0.619215i | \(0.787451\pi\) | |||||||
\(614\) | 1.00136 | − | 1.73440i | 0.0404116 | − | 0.0699949i | ||||
\(615\) | −0.497457 | − | 0.606827i | −0.0200594 | − | 0.0244696i | ||||
\(616\) | −0.707733 | − | 1.22583i | −0.0285154 | − | 0.0493901i | ||||
\(617\) | −24.8079 | − | 14.3229i | −0.998730 | − | 0.576617i | −0.0908575 | − | 0.995864i | \(-0.528961\pi\) |
−0.907872 | + | 0.419247i | \(0.862294\pi\) | |||||||
\(618\) | 5.80947i | 0.233691i | ||||||||
\(619\) | −11.1758 | −0.449193 | −0.224596 | − | 0.974452i | \(-0.572106\pi\) | ||||
−0.224596 | + | 0.974452i | \(0.572106\pi\) | |||||||
\(620\) | 0.993566 | + | 6.03842i | 0.0399026 | + | 0.242509i | ||||
\(621\) | 5.47919 | 0.219872 | ||||||||
\(622\) | −21.9402 | + | 12.6672i | −0.879722 | + | 0.507908i | ||||
\(623\) | − | 3.39178i | − | 0.135889i | ||||||
\(624\) | −1.91760 | − | 3.32139i | −0.0767656 | − | 0.132962i | ||||
\(625\) | 3.20910 | + | 24.7932i | 0.128364 | + | 0.991727i | ||||
\(626\) | 16.7435 | + | 29.0006i | 0.669204 | + | 1.15910i | ||||
\(627\) | 5.45080 | + | 3.14702i | 0.217684 | + | 0.125680i | ||||
\(628\) | − | 9.27599i | − | 0.370152i | ||||||
\(629\) | 15.8738 | + | 12.3813i | 0.632931 | + | 0.493677i | ||||
\(630\) | −0.535376 | + | 0.438884i | −0.0213299 | + | 0.0174855i | ||||
\(631\) | −18.1519 | + | 31.4400i | −0.722615 | + | 1.25161i | 0.237333 | + | 0.971428i | \(0.423727\pi\) |
−0.959948 | + | 0.280178i | \(0.909607\pi\) | |||||||
\(632\) | 13.2218 | − | 7.63359i | 0.525934 | − | 0.303648i | ||||
\(633\) | 16.9436 | − | 9.78239i | 0.673447 | − | 0.388815i | ||||
\(634\) | 15.5461 | + | 26.9267i | 0.617416 | + | 1.06940i | ||||
\(635\) | 1.93500 | + | 2.36042i | 0.0767879 | + | 0.0936705i | ||||
\(636\) | −6.84854 | − | 11.8620i | −0.271562 | − | 0.470360i | ||||
\(637\) | 26.4789i | 1.04913i | ||||||||
\(638\) | 2.73363 | + | 1.57826i | 0.108225 | + | 0.0624839i | ||||
\(639\) | −13.3401 | −0.527728 | ||||||||
\(640\) | 1.41760 | + | 1.72928i | 0.0560357 | + | 0.0683557i | ||||
\(641\) | 20.8852 | − | 36.1742i | 0.824916 | − | 1.42880i | −0.0770677 | − | 0.997026i | \(-0.524556\pi\) |
0.901984 | − | 0.431770i | \(-0.142111\pi\) | |||||||
\(642\) | 6.31907 | − | 3.64832i | 0.249394 | − | 0.143988i | ||||
\(643\) | − | 9.18122i | − | 0.362072i | −0.983476 | − | 0.181036i | \(-0.942055\pi\) | ||
0.983476 | − | 0.181036i | \(-0.0579451\pi\) | |||||||
\(644\) | 0.848165 | − | 1.46907i | 0.0334224 | − | 0.0578893i | ||||
\(645\) | 1.83275 | + | 11.1386i | 0.0721645 | + | 0.438582i | ||||
\(646\) | 2.27808 | − | 3.94576i | 0.0896300 | − | 0.155244i | ||||
\(647\) | −2.25144 | + | 1.29987i | −0.0885133 | + | 0.0511032i | −0.543603 | − | 0.839342i | \(-0.682940\pi\) |
0.455090 | + | 0.890445i | \(0.349607\pi\) | |||||||
\(648\) | −0.866025 | + | 0.500000i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | 26.3989 | − | 45.7243i | 1.03625 | − | 1.79484i | ||||
\(650\) | −14.4035 | − | 12.6594i | −0.564952 | − | 0.496541i | ||||
\(651\) | −0.423647 | + | 0.733778i | −0.0166040 | + | 0.0287590i | ||||
\(652\) | 13.1014i | 0.513091i | ||||||||
\(653\) | −16.7712 | + | 9.68287i | −0.656309 | + | 0.378920i | −0.790869 | − | 0.611985i | \(-0.790371\pi\) |
0.134560 | + | 0.990905i | \(0.457038\pi\) | |||||||
\(654\) | 6.46495 | − | 11.1976i | 0.252799 | − | 0.437861i | ||||
\(655\) | 19.8704 | − | 16.2891i | 0.776400 | − | 0.636467i | ||||
\(656\) | −0.350914 | −0.0137009 | ||||||||
\(657\) | 11.5903 | + | 6.69167i | 0.452181 | + | 0.261067i | ||||
\(658\) | 1.16878i | 0.0455637i | ||||||||
\(659\) | 3.00412 | + | 5.20328i | 0.117024 | + | 0.202691i | 0.918587 | − | 0.395219i | \(-0.129331\pi\) |
−0.801563 | + | 0.597910i | \(0.795998\pi\) | |||||||
\(660\) | −6.48126 | − | 7.90623i | −0.252283 | − | 0.307750i | ||||
\(661\) | 17.0665 | + | 29.5601i | 0.663811 | + | 1.14975i | 0.979606 | + | 0.200927i | \(0.0643953\pi\) |
−0.315796 | + | 0.948827i | \(0.602271\pi\) | |||||||
\(662\) | 26.2913 | − | 15.1793i | 1.02184 | − | 0.589959i | ||||
\(663\) | 10.9924 | − | 6.34649i | 0.426911 | − | 0.246477i | ||||
\(664\) | −1.53697 | + | 2.66210i | −0.0596458 | + | 0.103310i | ||||
\(665\) | −0.604191 | − | 0.737028i | −0.0234295 | − | 0.0285807i | ||||
\(666\) | 5.63800 | − | 2.28320i | 0.218468 | − | 0.0884723i | ||||
\(667\) | 3.78286i | 0.146473i | ||||||||
\(668\) | −18.9448 | − | 10.9378i | −0.732997 | − | 0.423196i | ||||
\(669\) | 1.99663 | + | 3.45826i | 0.0771941 | + | 0.133704i | ||||
\(670\) | 9.98259 | + | 3.76340i | 0.385661 | + | 0.145393i | ||||
\(671\) | 10.8798 | + | 18.8444i | 0.420011 | + | 0.727481i | ||||
\(672\) | 0.309595i | 0.0119429i | ||||||||
\(673\) | 5.77448 | − | 3.33389i | 0.222590 | − | 0.128512i | −0.384559 | − | 0.923100i | \(-0.625647\pi\) |
0.607149 | + | 0.794588i | \(0.292313\pi\) | |||||||
\(674\) | 11.8454 | 0.456266 | ||||||||
\(675\) | −3.30083 | + | 3.75560i | −0.127049 | + | 0.144553i | ||||
\(676\) | 1.70882 | 0.0657238 | ||||||||
\(677\) | 8.18243i | 0.314476i | 0.987561 | + | 0.157238i | \(0.0502590\pi\) | ||||
−0.987561 | + | 0.157238i | \(0.949741\pi\) | |||||||
\(678\) | 2.12749 | + | 1.22831i | 0.0817058 | + | 0.0471729i | ||||
\(679\) | −0.153264 | − | 0.265461i | −0.00588174 | − | 0.0101875i | ||||
\(680\) | −5.72321 | + | 4.69170i | −0.219475 | + | 0.179918i | ||||
\(681\) | 13.6749 | − | 23.6856i | 0.524022 | − | 0.907633i | ||||
\(682\) | −10.8361 | − | 6.25625i | −0.414937 | − | 0.239564i | ||||
\(683\) | −26.9900 | − | 15.5827i | −1.03274 | − | 0.596254i | −0.114974 | − | 0.993369i | \(-0.536678\pi\) |
−0.917769 | + | 0.397114i | \(0.870012\pi\) | |||||||
\(684\) | −0.688327 | − | 1.19222i | −0.0263188 | − | 0.0455856i | ||||
\(685\) | −7.53296 | + | 19.9816i | −0.287820 | + | 0.763456i | ||||
\(686\) | 2.15233 | − | 3.72795i | 0.0821764 | − | 0.142334i | ||||
\(687\) | −20.6075 | − | 11.8978i | −0.786226 | − | 0.453928i | ||||
\(688\) | 4.37197 | + | 2.52416i | 0.166680 | + | 0.0962325i | ||||
\(689\) | 52.5312 | 2.00128 | ||||||||
\(690\) | 4.32196 | − | 11.4642i | 0.164534 | − | 0.436435i | ||||
\(691\) | −20.8249 | + | 36.0698i | −0.792218 | + | 1.37216i | 0.132373 | + | 0.991200i | \(0.457740\pi\) |
−0.924591 | + | 0.380962i | \(0.875593\pi\) | |||||||
\(692\) | 4.23309i | 0.160918i | ||||||||
\(693\) | − | 1.41547i | − | 0.0537691i | ||||||
\(694\) | 0.594567 | − | 1.02982i | 0.0225694 | − | 0.0390914i | ||||
\(695\) | −4.52716 | + | 3.71122i | −0.171725 | + | 0.140774i | ||||
\(696\) | −0.345202 | − | 0.597908i | −0.0130849 | − | 0.0226636i | ||||
\(697\) | − | 1.16138i | − | 0.0439905i | ||||||
\(698\) | 6.43879 | − | 3.71744i | 0.243712 | − | 0.140707i | ||||
\(699\) | −12.8189 | − | 22.2029i | −0.484854 | − | 0.839791i | ||||
\(700\) | 0.495982 | + | 1.46637i | 0.0187464 | + | 0.0554235i | ||||
\(701\) | −24.5191 | + | 42.4683i | −0.926073 | + | 1.60400i | −0.136246 | + | 0.990675i | \(0.543504\pi\) |
−0.789827 | + | 0.613330i | \(0.789830\pi\) | |||||||
\(702\) | − | 3.83521i | − | 0.144751i | ||||||
\(703\) | 3.14318 | + | 7.76157i | 0.118547 | + | 0.292733i | ||||
\(704\) | −4.57198 | −0.172313 | ||||||||
\(705\) | 1.37055 | + | 8.32956i | 0.0516179 | + | 0.313709i | ||||
\(706\) | 7.04878 | + | 12.2088i | 0.265284 | + | 0.459486i | ||||
\(707\) | 3.60185 | − | 2.07953i | 0.135462 | − | 0.0782088i | ||||
\(708\) | −10.0010 | + | 5.77406i | −0.375860 | + | 0.217003i | ||||
\(709\) | −16.7309 | −0.628343 | −0.314171 | − | 0.949366i | \(-0.601727\pi\) | ||||
−0.314171 | + | 0.949366i | \(0.601727\pi\) | |||||||
\(710\) | −10.5226 | + | 27.9118i | −0.394908 | + | 1.04751i | ||||
\(711\) | 15.2672 | 0.572564 | ||||||||
\(712\) | −9.48775 | − | 5.47776i | −0.355569 | − | 0.205288i | ||||
\(713\) | − | 14.9953i | − | 0.561579i | ||||||
\(714\) | −1.02464 | −0.0383460 | ||||||||
\(715\) | 38.6881 | − | 6.36577i | 1.44685 | − | 0.238066i | ||||
\(716\) | −9.08787 | − | 15.7407i | −0.339630 | − | 0.588256i | ||||
\(717\) | − | 6.16796i | − | 0.230347i | ||||||
\(718\) | −1.22650 | − | 0.708122i | −0.0457727 | − | 0.0264269i | ||||
\(719\) | −14.7645 | + | 25.5728i | −0.550622 | + | 0.953705i | 0.447608 | + | 0.894230i | \(0.352276\pi\) |
−0.998230 | + | 0.0594751i | \(0.981057\pi\) | |||||||
\(720\) | 0.363043 | + | 2.20640i | 0.0135298 | + | 0.0822277i | ||||
\(721\) | 0.899292 | + | 1.55762i | 0.0334914 | + | 0.0580088i | ||||
\(722\) | −14.8132 | + | 8.55241i | −0.551291 | + | 0.318288i | ||||
\(723\) | −3.47521 | − | 2.00641i | −0.129244 | − | 0.0746192i | ||||
\(724\) | −3.63216 | + | 6.29109i | −0.134988 | + | 0.233807i | ||||
\(725\) | −2.59289 | − | 2.27891i | −0.0962973 | − | 0.0846364i | ||||
\(726\) | 9.90305 | 0.367537 | ||||||||
\(727\) | 33.7503 | − | 19.4857i | 1.25173 | − | 0.722685i | 0.280275 | − | 0.959920i | \(-0.409574\pi\) |
0.971452 | + | 0.237234i | \(0.0762409\pi\) | |||||||
\(728\) | −1.02829 | − | 0.593681i | −0.0381108 | − | 0.0220033i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 23.1435 | − | 18.9723i | 0.856579 | − | 0.702195i | ||||
\(731\) | −8.35393 | + | 14.4694i | −0.308981 | + | 0.535171i | ||||
\(732\) | − | 4.75935i | − | 0.175911i | ||||||
\(733\) | −29.8567 | + | 17.2377i | −1.10278 | + | 0.636691i | −0.936950 | − | 0.349463i | \(-0.886364\pi\) |
−0.165831 | + | 0.986154i | \(0.553031\pi\) | |||||||
\(734\) | −18.8761 | −0.696731 | ||||||||
\(735\) | 5.44597 | − | 14.4457i | 0.200877 | − | 0.532837i | ||||
\(736\) | −2.73959 | − | 4.74511i | −0.100983 | − | 0.174907i | ||||
\(737\) | −18.8908 | + | 10.9066i | −0.695852 | + | 0.401750i | ||||
\(738\) | −0.303900 | − | 0.175457i | −0.0111867 | − | 0.00645865i | ||||
\(739\) | −9.23484 | −0.339709 | −0.169855 | − | 0.985469i | \(-0.554330\pi\) | ||||
−0.169855 | + | 0.985469i | \(0.554330\pi\) | |||||||
\(740\) | −0.329961 | − | 13.5975i | −0.0121296 | − | 0.499853i | ||||
\(741\) | 5.27975 | 0.193957 | ||||||||
\(742\) | −3.67243 | − | 2.12028i | −0.134819 | − | 0.0778378i | ||||
\(743\) | 24.7745 | − | 14.3036i | 0.908889 | − | 0.524747i | 0.0288154 | − | 0.999585i | \(-0.490827\pi\) |
0.880073 | + | 0.474838i | \(0.157493\pi\) | |||||||
\(744\) | 1.36839 | + | 2.37012i | 0.0501676 | + | 0.0868928i | ||||
\(745\) | −13.4411 | − | 5.06723i | −0.492443 | − | 0.185649i | ||||
\(746\) | 22.4593 | 0.822295 | ||||||||
\(747\) | −2.66210 | + | 1.53697i | −0.0974013 | + | 0.0562346i | ||||
\(748\) | − | 15.1314i | − | 0.553260i | ||||||
\(749\) | 1.12950 | − | 1.95636i | 0.0412711 | − | 0.0714837i | ||||
\(750\) | 5.25424 | + | 9.86879i | 0.191858 | + | 0.360357i | ||||
\(751\) | 13.7813 | 0.502886 | 0.251443 | − | 0.967872i | \(-0.419095\pi\) | ||||
0.251443 | + | 0.967872i | \(0.419095\pi\) | |||||||
\(752\) | 3.26940 | + | 1.88759i | 0.119223 | + | 0.0688333i | ||||
\(753\) | −14.5033 | + | 8.37346i | −0.528528 | + | 0.305146i | ||||
\(754\) | 2.64785 | 0.0964288 | ||||||||
\(755\) | −1.77189 | − | 10.7687i | −0.0644859 | − | 0.391914i | ||||
\(756\) | −0.154798 | + | 0.268117i | −0.00562994 | + | 0.00975134i | ||||
\(757\) | 11.6427 | + | 6.72193i | 0.423162 | + | 0.244313i | 0.696429 | − | 0.717625i | \(-0.254771\pi\) |
−0.273267 | + | 0.961938i | \(0.588104\pi\) | |||||||
\(758\) | −30.3592 | + | 17.5279i | −1.10270 | + | 0.636642i | ||||
\(759\) | 12.5254 | + | 21.6946i | 0.454642 | + | 0.787464i | ||||
\(760\) | −3.03745 | + | 0.499784i | −0.110180 | + | 0.0181291i | ||||
\(761\) | 15.8359 | − | 27.4286i | 0.574051 | − | 0.994286i | −0.422093 | − | 0.906553i | \(-0.638704\pi\) |
0.996144 | − | 0.0877334i | \(-0.0279624\pi\) | |||||||
\(762\) | 1.18210 | + | 0.682488i | 0.0428231 | + | 0.0247239i | ||||
\(763\) | − | 4.00303i | − | 0.144920i | ||||||
\(764\) | −1.71055 | − | 2.96276i | −0.0618855 | − | 0.107189i | ||||
\(765\) | −7.30229 | + | 1.20152i | −0.264015 | + | 0.0434412i | ||||
\(766\) | −12.4279 | −0.449038 | ||||||||
\(767\) | − | 44.2895i | − | 1.59920i | ||||||
\(768\) | 0.866025 | + | 0.500000i | 0.0312500 | + | 0.0180422i | ||||
\(769\) | −8.70963 | −0.314077 | −0.157039 | − | 0.987592i | \(-0.550195\pi\) | ||||
−0.157039 | + | 0.987592i | \(0.550195\pi\) | |||||||
\(770\) | −2.96161 | − | 1.11651i | −0.106729 | − | 0.0402363i | ||||
\(771\) | 1.84799 | 0.0665538 | ||||||||
\(772\) | −16.7016 | + | 9.64268i | −0.601104 | + | 0.347048i | ||||
\(773\) | −2.32166 | + | 1.34041i | −0.0835044 | + | 0.0482113i | −0.541171 | − | 0.840913i | \(-0.682019\pi\) |
0.457666 | + | 0.889124i | \(0.348685\pi\) | |||||||
\(774\) | 2.52416 | + | 4.37197i | 0.0907289 | + | 0.157147i | ||||
\(775\) | 10.2782 | + | 9.03362i | 0.369205 | + | 0.324497i | ||||
\(776\) | −0.990093 | −0.0355423 | ||||||||
\(777\) | 1.15821 | − | 1.48491i | 0.0415506 | − | 0.0532710i | ||||
\(778\) | 25.2154i | 0.904015i | ||||||||
\(779\) | 0.241543 | − | 0.418365i | 0.00865419 | − | 0.0149895i | ||||
\(780\) | −8.02448 | − | 3.02520i | −0.287322 | − | 0.108319i | ||||
\(781\) | −30.4954 | − | 52.8197i | −1.09121 | − | 1.89004i | ||||
\(782\) | 15.7044 | − | 9.06694i | 0.561589 | − | 0.324233i | ||||
\(783\) | − | 0.690405i | − | 0.0246730i | ||||||
\(784\) | −3.45208 | − | 5.97917i | −0.123288 | − | 0.213542i | ||||
\(785\) | −13.1497 | − | 16.0408i | −0.469332 | − | 0.572519i | ||||
\(786\) | 5.74528 | − | 9.95113i | 0.204928 | − | 0.354945i | ||||
\(787\) | 3.44647i | 0.122853i | 0.998112 | + | 0.0614266i | \(0.0195650\pi\) | ||||
−0.998112 | + | 0.0614266i | \(0.980435\pi\) | |||||||
\(788\) | 8.88669i | 0.316575i | ||||||||
\(789\) | −3.66760 | + | 6.35247i | −0.130570 | + | 0.226154i | ||||
\(790\) | 12.0427 | − | 31.9438i | 0.428460 | − | 1.13651i | ||||
\(791\) | 0.760557 | 0.0270423 | ||||||||
\(792\) | −3.95946 | − | 2.28599i | −0.140693 | − | 0.0812292i | ||||
\(793\) | 15.8076 | + | 9.12654i | 0.561346 | + | 0.324093i | ||||
\(794\) | −3.39818 | + | 5.88581i | −0.120597 | + | 0.208880i | ||||
\(795\) | −28.6587 | − | 10.8042i | −1.01642 | − | 0.383186i | ||||
\(796\) | −6.27808 | − | 10.8739i | −0.222520 | − | 0.385417i | ||||
\(797\) | −25.2225 | − | 14.5622i | −0.893426 | − | 0.515820i | −0.0183643 | − | 0.999831i | \(-0.505846\pi\) |
−0.875062 | + | 0.484012i | \(0.839179\pi\) | |||||||
\(798\) | −0.369105 | − | 0.213103i | −0.0130662 | − | 0.00754376i | ||||
\(799\) | −6.24716 | + | 10.8204i | −0.221009 | + | 0.382798i | ||||
\(800\) | 4.90286 | + | 0.980798i | 0.173342 | + | 0.0346764i | ||||
\(801\) | −5.47776 | − | 9.48775i | −0.193547 | − | 0.335233i | ||||
\(802\) | 3.70227 | + | 2.13751i | 0.130732 | + | 0.0754780i | ||||
\(803\) | 61.1884i | 2.15929i | ||||||||
\(804\) | 4.77106 | 0.168262 | ||||||||
\(805\) | −0.615840 | − | 3.74278i | −0.0217055 | − | 0.131916i | ||||
\(806\) | −10.4961 | −0.369710 | ||||||||
\(807\) | 14.1806 | − | 8.18718i | 0.499181 | − | 0.288203i | ||||
\(808\) | − | 13.4339i | − | 0.472602i | ||||||
\(809\) | 20.7139 | + | 35.8775i | 0.728262 | + | 1.26139i | 0.957617 | + | 0.288044i | \(0.0930049\pi\) |
−0.229355 | + | 0.973343i | \(0.573662\pi\) | |||||||
\(810\) | −0.788796 | + | 2.09232i | −0.0277155 | + | 0.0735166i | ||||
\(811\) | −1.58024 | − | 2.73706i | −0.0554897 | − | 0.0961110i | 0.836946 | − | 0.547285i | \(-0.184339\pi\) |
−0.892436 | + | 0.451174i | \(0.851005\pi\) | |||||||
\(812\) | −0.185110 | − | 0.106873i | −0.00649607 | − | 0.00375051i | ||||
\(813\) | − | 9.45345i | − | 0.331547i | ||||||
\(814\) | 21.9286 | + | 17.1040i | 0.768599 | + | 0.599495i | ||||
\(815\) | 18.5726 | + | 22.6560i | 0.650571 | + | 0.793605i | ||||
\(816\) | −1.65480 | + | 2.86619i | −0.0579295 | + | 0.100337i | ||||
\(817\) | −6.01868 | + | 3.47489i | −0.210567 | + | 0.121571i | ||||
\(818\) | −7.37620 | + | 4.25865i | −0.257903 | + | 0.148900i | ||||
\(819\) | −0.593681 | − | 1.02829i | −0.0207449 | − | 0.0359312i | ||||
\(820\) | −0.606827 | + | 0.497457i | −0.0211913 | + | 0.0173719i | ||||
\(821\) | 15.2576 | + | 26.4270i | 0.532495 | + | 0.922308i | 0.999280 | + | 0.0379377i | \(0.0120788\pi\) |
−0.466785 | + | 0.884371i | \(0.654588\pi\) | |||||||
\(822\) | 9.54995i | 0.333093i | ||||||||
\(823\) | 8.61740 | + | 4.97526i | 0.300384 | + | 0.173427i | 0.642615 | − | 0.766189i | \(-0.277849\pi\) |
−0.342232 | + | 0.939616i | \(0.611183\pi\) | |||||||
\(824\) | 5.80947 | 0.202382 | ||||||||
\(825\) | −22.4158 | − | 4.48419i | −0.780418 | − | 0.156120i | ||||
\(826\) | −1.78762 | + | 3.09625i | −0.0621994 | + | 0.107732i | ||||
\(827\) | −4.71088 | + | 2.71983i | −0.163813 | + | 0.0945777i | −0.579665 | − | 0.814855i | \(-0.696817\pi\) |
0.415852 | + | 0.909432i | \(0.363483\pi\) | |||||||
\(828\) | − | 5.47919i | − | 0.190415i | ||||||
\(829\) | 14.9584 | − | 25.9088i | 0.519528 | − | 0.899849i | −0.480214 | − | 0.877151i | \(-0.659441\pi\) |
0.999742 | − | 0.0226976i | \(-0.00722549\pi\) | |||||||
\(830\) | 1.11597 | + | 6.78232i | 0.0387358 | + | 0.235418i | ||||
\(831\) | 4.40289 | − | 7.62602i | 0.152734 | − | 0.264544i | ||||
\(832\) | −3.32139 | + | 1.91760i | −0.115148 | + | 0.0664810i | ||||
\(833\) | 19.7886 | − | 11.4250i | 0.685635 | − | 0.395852i | ||||
\(834\) | −1.30897 | + | 2.26721i | −0.0453261 | + | 0.0785071i | ||||
\(835\) | −48.2663 | + | 7.94177i | −1.67032 | + | 0.274836i | ||||
\(836\) | 3.14702 | − | 5.45080i | 0.108842 | − | 0.188520i | ||||
\(837\) | 2.73678i | 0.0945969i | ||||||||
\(838\) | 14.9783 | − | 8.64775i | 0.517418 | − | 0.298732i | ||||
\(839\) | 15.6157 | − | 27.0471i | 0.539113 | − | 0.933771i | −0.459839 | − | 0.888002i | \(-0.652093\pi\) |
0.998952 | − | 0.0457688i | \(-0.0145738\pi\) | |||||||
\(840\) | 0.438884 | + | 0.535376i | 0.0151429 | + | 0.0184722i | ||||
\(841\) | −28.5233 | −0.983563 | ||||||||
\(842\) | 12.4436 | + | 7.18429i | 0.428833 | + | 0.247587i | ||||
\(843\) | − | 3.20606i | − | 0.110422i | ||||||
\(844\) | −9.78239 | − | 16.9436i | −0.336724 | − | 0.583223i | ||||
\(845\) | 2.95502 | − | 2.42243i | 0.101656 | − | 0.0833341i | ||||
\(846\) | 1.88759 | + | 3.26940i | 0.0648967 | + | 0.112404i | ||||
\(847\) | 2.65518 | − | 1.53297i | 0.0912330 | − | 0.0526734i | ||||
\(848\) | −11.8620 | + | 6.84854i | −0.407344 | + | 0.235180i | ||||
\(849\) | −10.1734 | + | 17.6209i | −0.349151 | + | 0.604748i | ||||
\(850\) | −3.24604 | + | 16.2265i | −0.111338 | + | 0.556564i | ||||
\(851\) | −4.61176 | + | 33.0080i | −0.158089 | + | 1.13150i | ||||
\(852\) | 13.3401i | 0.457025i | ||||||||
\(853\) | −3.38454 | − | 1.95407i | −0.115885 | − | 0.0669060i | 0.440937 | − | 0.897538i | \(-0.354646\pi\) |
−0.556822 | + | 0.830632i | \(0.687979\pi\) | |||||||
\(854\) | −0.736736 | − | 1.27606i | −0.0252106 | − | 0.0436660i | ||||
\(855\) | −2.88040 | − | 1.08590i | −0.0985076 | − | 0.0371370i | ||||
\(856\) | −3.64832 | − | 6.31907i | −0.124697 | − | 0.215981i | ||||
\(857\) | 40.0174i | 1.36697i | 0.729965 | + | 0.683484i | \(0.239536\pi\) | ||||
−0.729965 | + | 0.683484i | \(0.760464\pi\) | |||||||
\(858\) | 15.1853 | − | 8.76726i | 0.518419 | − | 0.299309i | ||||
\(859\) | 25.6649 | 0.875677 | 0.437838 | − | 0.899054i | \(-0.355744\pi\) | ||||
0.437838 | + | 0.899054i | \(0.355744\pi\) | |||||||
\(860\) | 11.1386 | − | 1.83275i | 0.379823 | − | 0.0624963i | ||||
\(861\) | −0.108641 | −0.00370248 | ||||||||
\(862\) | − | 23.3165i | − | 0.794161i | ||||||
\(863\) | −27.5998 | − | 15.9347i | −0.939508 | − | 0.542425i | −0.0497019 | − | 0.998764i | \(-0.515827\pi\) |
−0.889806 | + | 0.456339i | \(0.849160\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 6.00085 | + | 7.32019i | 0.204035 | + | 0.248894i | ||||
\(866\) | −15.3691 | + | 26.6200i | −0.522263 | + | 0.904586i | ||||
\(867\) | 5.23649 | + | 3.02329i | 0.177841 | + | 0.102676i | ||||
\(868\) | 0.733778 | + | 0.423647i | 0.0249060 | + | 0.0143795i | ||||
\(869\) | 34.9007 | + | 60.4497i | 1.18392 | + | 2.05062i | ||||
\(870\) | −1.44455 | − | 0.544588i | −0.0489747 | − | 0.0184633i | ||||
\(871\) | −9.14901 | + | 15.8466i | −0.310002 | + | 0.536940i | ||||
\(872\) | −11.1976 | − | 6.46495i | −0.379199 | − | 0.218931i | ||||
\(873\) | −0.857446 | − | 0.495047i | −0.0290201 | − | 0.0167548i | ||||
\(874\) | 7.54294 | 0.255144 | ||||||||
\(875\) | 2.93642 | + | 1.83265i | 0.0992691 | + | 0.0619549i | ||||
\(876\) | 6.69167 | − | 11.5903i | 0.226091 | − | 0.391600i | ||||
\(877\) | 39.3230i | 1.32784i | 0.747802 | + | 0.663922i | \(0.231109\pi\) | ||||
−0.747802 | + | 0.663922i | \(0.768891\pi\) | |||||||
\(878\) | 37.2735i | 1.25792i | ||||||||
\(879\) | −9.27344 | + | 16.0621i | −0.312786 | + | 0.541760i | ||||
\(880\) | −7.90623 | + | 6.48126i | −0.266519 | + | 0.218483i | ||||
\(881\) | 3.70381 | + | 6.41518i | 0.124784 | + | 0.216133i | 0.921649 | − | 0.388026i | \(-0.126843\pi\) |
−0.796864 | + | 0.604158i | \(0.793509\pi\) | |||||||
\(882\) | − | 6.90415i | − | 0.232475i | ||||||
\(883\) | −24.5241 | + | 14.1590i | −0.825302 | + | 0.476488i | −0.852241 | − | 0.523149i | \(-0.824757\pi\) |
0.0269392 | + | 0.999637i | \(0.491424\pi\) | |||||||
\(884\) | −6.34649 | − | 10.9924i | −0.213456 | − | 0.369716i | ||||
\(885\) | −9.10912 | + | 24.1624i | −0.306200 | + | 0.812209i | ||||
\(886\) | −7.77937 | + | 13.4743i | −0.261353 | + | 0.452677i | ||||
\(887\) | 46.0973i | 1.54780i | 0.633311 | + | 0.773898i | \(0.281695\pi\) | ||||
−0.633311 | + | 0.773898i | \(0.718305\pi\) | |||||||
\(888\) | −2.28320 | − | 5.63800i | −0.0766192 | − | 0.189199i | ||||
\(889\) | 0.422590 | 0.0141732 | ||||||||
\(890\) | −24.1722 | + | 3.97732i | −0.810255 | + | 0.133320i | ||||
\(891\) | −2.28599 | − | 3.95946i | −0.0765836 | − | 0.132647i | ||||
\(892\) | 3.45826 | − | 1.99663i | 0.115791 | − | 0.0668521i | ||||
\(893\) | −4.50084 | + | 2.59856i | −0.150615 | + | 0.0869574i | ||||
\(894\) | −6.42401 | −0.214851 | ||||||||
\(895\) | −38.0295 | − | 14.3370i | −1.27119 | − | 0.479232i | ||||
\(896\) | 0.309595 | 0.0103429 | ||||||||
\(897\) | 18.1985 | + | 10.5069i | 0.607630 | + | 0.350815i | ||||
\(898\) | − | 1.08346i | − | 0.0361554i | ||||||
\(899\) | −1.88948 | −0.0630178 | ||||||||
\(900\) | 3.75560 | + | 3.30083i | 0.125187 | + | 0.110028i | ||||
\(901\) | −22.6659 | − | 39.2585i | −0.755111 | − | 1.30789i | ||||
\(902\) | − | 1.60437i | − | 0.0534197i | ||||||
\(903\) | 1.35354 | + | 0.781467i | 0.0450430 | + | 0.0260056i | ||||
\(904\) | 1.22831 | − | 2.12749i | 0.0408529 | − | 0.0707593i | ||||
\(905\) | 2.63726 | + | 16.0280i | 0.0876655 | + | 0.532789i | ||||
\(906\) | −2.44034 | − | 4.22679i | −0.0810749 | − | 0.140426i | ||||
\(907\) | 25.7386 | − | 14.8602i | 0.854635 | − | 0.493424i | −0.00757682 | − | 0.999971i | \(-0.502412\pi\) |
0.862212 | + | 0.506547i | \(0.169078\pi\) | |||||||
\(908\) | −23.6856 | − | 13.6749i | −0.786033 | − | 0.453816i | ||||
\(909\) | 6.71693 | − | 11.6341i | 0.222787 | − | 0.385878i | ||||
\(910\) | −2.61980 | + | 0.431063i | −0.0868454 | + | 0.0142896i | ||||
\(911\) | −15.4077 | −0.510479 | −0.255239 | − | 0.966878i | \(-0.582154\pi\) | ||||
−0.255239 | + | 0.966878i | \(0.582154\pi\) | |||||||
\(912\) | −1.19222 | + | 0.688327i | −0.0394783 | + | 0.0227928i | ||||
\(913\) | −12.1711 | − | 7.02698i | −0.402804 | − | 0.232559i | ||||
\(914\) | −25.0538 | −0.828706 | ||||||||
\(915\) | −6.74687 | − | 8.23023i | −0.223045 | − | 0.272083i | ||||
\(916\) | −11.8978 | + | 20.6075i | −0.393113 | + | 0.680892i | ||||
\(917\) | − | 3.55743i | − | 0.117477i | ||||||
\(918\) | −2.86619 | + | 1.65480i | −0.0945985 | + | 0.0546165i | ||||
\(919\) | −15.5228 | −0.512048 | −0.256024 | − | 0.966670i | \(-0.582413\pi\) | ||||
−0.256024 | + | 0.966670i | \(0.582413\pi\) | |||||||
\(920\) | −11.4642 | − | 4.32196i | −0.377964 | − | 0.142491i | ||||
\(921\) | −1.00136 | − | 1.73440i | −0.0329959 | − | 0.0571506i | ||||
\(922\) | 8.86086 | − | 5.11582i | 0.291817 | − | 0.168481i | ||||
\(923\) | −44.3078 | − | 25.5811i | −1.45841 | − | 0.842012i | ||||
\(924\) | −1.41547 | −0.0465654 | ||||||||
\(925\) | −19.8464 | − | 23.0460i | −0.652546 | − | 0.757749i | ||||
\(926\) | −16.5645 | −0.544345 | ||||||||
\(927\) | 5.03115 | + | 2.90473i | 0.165245 | + | 0.0954040i | ||||
\(928\) | −0.597908 | + | 0.345202i | −0.0196273 | + | 0.0113318i | ||||
\(929\) | −13.6062 | − | 23.5666i | −0.446405 | − | 0.773196i | 0.551744 | − | 0.834013i | \(-0.313962\pi\) |
−0.998149 | + | 0.0608178i | \(0.980629\pi\) | |||||||
\(930\) | 5.72621 | + | 2.15876i | 0.187770 | + | 0.0707885i | ||||
\(931\) | 9.50463 | 0.311502 | ||||||||
\(932\) | −22.2029 | + | 12.8189i | −0.727280 | + | 0.419895i | ||||
\(933\) | 25.3344i | 0.829410i | ||||||||
\(934\) | 13.0607 | − | 22.6217i | 0.427358 | − | 0.740206i | ||||
\(935\) | −21.4504 | − | 26.1664i | −0.701502 | − | 0.855733i | ||||
\(936\) | −3.83521 | −0.125358 | ||||||||
\(937\) | 30.3829 | + | 17.5416i | 0.992565 | + | 0.573058i | 0.906040 | − | 0.423192i | \(-0.139090\pi\) |
0.0865251 | + | 0.996250i | \(0.472424\pi\) | |||||||
\(938\) | 1.27921 | − | 0.738550i | 0.0417675 | − | 0.0241145i | ||||
\(939\) | 33.4870 | 1.09281 | ||||||||
\(940\) | 8.32956 | − | 1.37055i | 0.271680 | − | 0.0447025i | ||||
\(941\) | 22.3408 | − | 38.6954i | 0.728290 | − | 1.26144i | −0.229315 | − | 0.973352i | \(-0.573649\pi\) |
0.957605 | − | 0.288083i | \(-0.0930180\pi\) | |||||||
\(942\) | −8.03324 | − | 4.63800i | −0.261737 | − | 0.151114i | ||||
\(943\) | 1.66513 | − | 0.961360i | 0.0542239 | − | 0.0313062i | ||||
\(944\) | 5.77406 | + | 10.0010i | 0.187930 | + | 0.325504i | ||||
\(945\) | 0.112396 | + | 0.683091i | 0.00365625 | + | 0.0222210i | ||||
\(946\) | −11.5404 | + | 19.9886i | −0.375211 | + | 0.649884i | ||||
\(947\) | −23.2795 | − | 13.4404i | −0.756483 | − | 0.436756i | 0.0715483 | − | 0.997437i | \(-0.477206\pi\) |
−0.828032 | + | 0.560681i | \(0.810539\pi\) | |||||||
\(948\) | − | 15.2672i | − | 0.495855i | ||||||
\(949\) | 25.6639 | + | 44.4512i | 0.833087 | + | 1.44295i | ||||
\(950\) | −4.54409 | + | 5.17016i | −0.147430 | + | 0.167742i | ||||
\(951\) | 31.0923 | 1.00824 | ||||||||
\(952\) | 1.02464i | 0.0332086i | ||||||||
\(953\) | 32.4670 | + | 18.7448i | 1.05171 | + | 0.607205i | 0.923127 | − | 0.384494i | \(-0.125624\pi\) |
0.128582 | + | 0.991699i | \(0.458957\pi\) | |||||||
\(954\) | −13.6971 | −0.443460 | ||||||||
\(955\) | −7.15803 | − | 2.69855i | −0.231628 | − | 0.0873229i | ||||
\(956\) | −6.16796 | −0.199486 | ||||||||
\(957\) | 2.73363 | − | 1.57826i | 0.0883656 | − | 0.0510179i | ||||
\(958\) | −3.76140 | + | 2.17164i | −0.121525 | + | 0.0701626i | ||||
\(959\) | 1.47831 | + | 2.56051i | 0.0477371 | + | 0.0826832i | ||||
\(960\) | 2.20640 | − | 0.363043i | 0.0712112 | − | 0.0117171i | ||||
\(961\) | −23.5101 | −0.758389 | ||||||||
\(962\) | 23.1042 | + | 3.22804i | 0.744911 | + | 0.104076i | ||||
\(963\) | − | 7.29664i | − | 0.235131i | ||||||
\(964\) | −2.00641 | + | 3.47521i | −0.0646221 | + | 0.111929i | ||||
\(965\) | −15.2122 | + | 40.3512i | −0.489699 | + | 1.29895i | ||||
\(966\) | −0.848165 | − | 1.46907i | −0.0272893 | − | 0.0472664i | ||||
\(967\) | 21.8076 | − | 12.5906i | 0.701285 | − | 0.404887i | −0.106541 | − | 0.994308i | \(-0.533977\pi\) |
0.807826 | + | 0.589421i | \(0.200644\pi\) | |||||||
\(968\) | − | 9.90305i | − | 0.318296i | ||||||
\(969\) | −2.27808 | − | 3.94576i | −0.0731826 | − | 0.126756i | ||||
\(970\) | −1.71215 | + | 1.40356i | −0.0549737 | + | 0.0450656i | ||||
\(971\) | −4.24551 | + | 7.35344i | −0.136245 | + | 0.235983i | −0.926072 | − | 0.377346i | \(-0.876837\pi\) |
0.789827 | + | 0.613329i | \(0.210170\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 0.810505i | 0.0259836i | ||||||||
\(974\) | −6.97051 | + | 12.0733i | −0.223350 | + | 0.386853i | ||||
\(975\) | −18.1651 | + | 6.14413i | −0.581748 | + | 0.196770i | ||||
\(976\) | −4.75935 | −0.152343 | ||||||||
\(977\) | 21.3821 | + | 12.3450i | 0.684075 | + | 0.394951i | 0.801389 | − | 0.598144i | \(-0.204095\pi\) |
−0.117314 | + | 0.993095i | \(0.537428\pi\) | |||||||
\(978\) | 11.3462 | + | 6.55071i | 0.362810 | + | 0.209469i | ||||
\(979\) | 25.0442 | − | 43.3779i | 0.800417 | − | 1.38636i | ||||
\(980\) | −14.4457 | − | 5.44597i | −0.461451 | − | 0.173965i | ||||
\(981\) | −6.46495 | − | 11.1976i | −0.206410 | − | 0.357512i | ||||
\(982\) | 24.9830 | + | 14.4239i | 0.797239 | + | 0.460286i | ||||
\(983\) | −34.3314 | − | 19.8212i | −1.09500 | − | 0.632199i | −0.160097 | − | 0.987101i | \(-0.551181\pi\) |
−0.934903 | + | 0.354903i | \(0.884514\pi\) | |||||||
\(984\) | −0.175457 | + | 0.303900i | −0.00559336 | + | 0.00968798i | ||||
\(985\) | 12.5978 | + | 15.3675i | 0.401399 | + | 0.489651i | ||||
\(986\) | −1.14248 | − | 1.97883i | −0.0363840 | − | 0.0630189i | ||||
\(987\) | 1.01219 | + | 0.584389i | 0.0322184 | + | 0.0186013i | ||||
\(988\) | − | 5.27975i | − | 0.167971i | ||||||
\(989\) | −27.6606 | −0.879557 | ||||||||
\(990\) | −10.0876 | + | 1.65982i | −0.320606 | + | 0.0527527i | ||||
\(991\) | −38.4167 | −1.22035 | −0.610173 | − | 0.792268i | \(-0.708900\pi\) | ||||
−0.610173 | + | 0.792268i | \(0.708900\pi\) | |||||||
\(992\) | 2.37012 | − | 1.36839i | 0.0752513 | − | 0.0434464i | ||||
\(993\) | − | 30.3585i | − | 0.963399i | ||||||
\(994\) | 2.06502 | + | 3.57672i | 0.0654985 | + | 0.113447i | ||||
\(995\) | −26.2715 | − | 9.90424i | −0.832862 | − | 0.313986i | ||||
\(996\) | 1.53697 | + | 2.66210i | 0.0487006 | + | 0.0843520i | ||||
\(997\) | 16.0040 | + | 9.23989i | 0.506850 | + | 0.292630i | 0.731538 | − | 0.681801i | \(-0.238803\pi\) |
−0.224688 | + | 0.974431i | \(0.572136\pi\) | |||||||
\(998\) | − | 32.3895i | − | 1.02527i | ||||||
\(999\) | 0.841687 | − | 6.02425i | 0.0266298 | − | 0.190599i |
(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.bb.d.1009.5 | ✓ | 28 | |
5.4 | even | 2 | inner | 1110.2.bb.d.1009.10 | yes | 28 | |
37.26 | even | 3 | inner | 1110.2.bb.d.1099.10 | yes | 28 | |
185.174 | even | 6 | inner | 1110.2.bb.d.1099.5 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.bb.d.1009.5 | ✓ | 28 | 1.1 | even | 1 | trivial | |
1110.2.bb.d.1009.10 | yes | 28 | 5.4 | even | 2 | inner | |
1110.2.bb.d.1099.5 | yes | 28 | 185.174 | even | 6 | inner | |
1110.2.bb.d.1099.10 | yes | 28 | 37.26 | even | 3 | inner |