Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(19,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([10, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.x (of order \(12\), degree \(4\), 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 215.2 | ||
Character | \(\chi\) | \(=\) | 637.215 |
Dual form | 637.2.x.b.80.1 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.433802 | + | 1.61897i | −0.306744 | + | 1.14479i | 0.624689 | + | 0.780873i | \(0.285226\pi\) |
−0.931433 | + | 0.363912i | \(0.881441\pi\) | |||||||
\(3\) | 0.637748i | 0.368204i | 0.982907 | + | 0.184102i | \(0.0589377\pi\) | ||||
−0.982907 | + | 0.184102i | \(0.941062\pi\) | |||||||
\(4\) | −0.700831 | − | 0.404625i | −0.350416 | − | 0.202313i | ||||
\(5\) | 0.520288 | + | 1.94174i | 0.232680 | + | 0.868373i | 0.979181 | + | 0.202989i | \(0.0650656\pi\) |
−0.746501 | + | 0.665384i | \(0.768268\pi\) | |||||||
\(6\) | −1.03250 | − | 0.276656i | −0.421515 | − | 0.112945i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.41124 | + | 1.41124i | −0.498948 | + | 0.498948i | ||||
\(9\) | 2.59328 | 0.864426 | ||||||||
\(10\) | −3.36932 | −1.06547 | ||||||||
\(11\) | 0.694217 | − | 0.694217i | 0.209314 | − | 0.209314i | −0.594662 | − | 0.803976i | \(-0.702714\pi\) |
0.803976 | + | 0.594662i | \(0.202714\pi\) | |||||||
\(12\) | 0.258049 | − | 0.446954i | 0.0744924 | − | 0.129025i | ||||
\(13\) | 1.60977 | + | 3.22624i | 0.446471 | + | 0.894798i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.23834 | + | 0.331813i | −0.319739 | + | 0.0856737i | ||||
\(16\) | −2.48181 | − | 4.29862i | −0.620452 | − | 1.07465i | ||||
\(17\) | −2.99281 | + | 5.18370i | −0.725863 | + | 1.25723i | 0.232755 | + | 0.972535i | \(0.425226\pi\) |
−0.958618 | + | 0.284696i | \(0.908107\pi\) | |||||||
\(18\) | −1.12497 | + | 4.19844i | −0.265158 | + | 0.989582i | ||||
\(19\) | 1.98532 | − | 1.98532i | 0.455464 | − | 0.455464i | −0.441699 | − | 0.897163i | \(-0.645624\pi\) |
0.897163 | + | 0.441699i | \(0.145624\pi\) | |||||||
\(20\) | 0.421043 | − | 1.57135i | 0.0941481 | − | 0.351366i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.822765 | + | 1.42507i | 0.175414 | + | 0.303826i | ||||
\(23\) | −2.58851 | + | 1.49448i | −0.539742 | + | 0.311620i | −0.744974 | − | 0.667093i | \(-0.767538\pi\) |
0.205233 | + | 0.978713i | \(0.434205\pi\) | |||||||
\(24\) | −0.900016 | − | 0.900016i | −0.183715 | − | 0.183715i | ||||
\(25\) | 0.830467 | − | 0.479471i | 0.166093 | − | 0.0958941i | ||||
\(26\) | −5.92151 | + | 1.20663i | −1.16130 | + | 0.236639i | ||||
\(27\) | 3.56710i | 0.686489i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.65708 | − | 6.33425i | 0.679103 | − | 1.17624i | −0.296148 | − | 0.955142i | \(-0.595702\pi\) |
0.975251 | − | 0.221099i | \(-0.0709645\pi\) | |||||||
\(30\) | − | 2.14878i | − | 0.392312i | ||||||
\(31\) | −8.34708 | − | 2.23659i | −1.49918 | − | 0.401704i | −0.586354 | − | 0.810055i | \(-0.699437\pi\) |
−0.912825 | + | 0.408351i | \(0.866104\pi\) | |||||||
\(32\) | 4.18037 | − | 1.12013i | 0.738992 | − | 0.198012i | ||||
\(33\) | 0.442736 | + | 0.442736i | 0.0770704 | + | 0.0770704i | ||||
\(34\) | −7.09397 | − | 7.09397i | −1.21661 | − | 1.21661i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.81745 | − | 1.04931i | −0.302908 | − | 0.174884i | ||||
\(37\) | 4.63309 | + | 1.24143i | 0.761675 | + | 0.204090i | 0.618690 | − | 0.785635i | \(-0.287664\pi\) |
0.142984 | + | 0.989725i | \(0.454330\pi\) | |||||||
\(38\) | 2.35294 | + | 4.07541i | 0.381697 | + | 0.661119i | ||||
\(39\) | −2.05753 | + | 1.02663i | −0.329468 | + | 0.164393i | ||||
\(40\) | −3.47451 | − | 2.00601i | −0.549369 | − | 0.317178i | ||||
\(41\) | 0.886060 | + | 3.30682i | 0.138379 | + | 0.516439i | 0.999961 | + | 0.00881984i | \(0.00280748\pi\) |
−0.861582 | + | 0.507619i | \(0.830526\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.748633 | + | 0.432224i | −0.114165 | + | 0.0659135i | −0.555995 | − | 0.831185i | \(-0.687663\pi\) |
0.441830 | + | 0.897099i | \(0.354329\pi\) | |||||||
\(44\) | −0.767427 | + | 0.205631i | −0.115694 | + | 0.0310001i | ||||
\(45\) | 1.34925 | + | 5.03547i | 0.201134 | + | 0.750644i | ||||
\(46\) | −1.29661 | − | 4.83903i | −0.191175 | − | 0.713476i | ||||
\(47\) | −2.96429 | + | 0.794280i | −0.432387 | + | 0.115858i | −0.468446 | − | 0.883492i | \(-0.655186\pi\) |
0.0360596 | + | 0.999350i | \(0.488519\pi\) | |||||||
\(48\) | 2.74144 | − | 1.58277i | 0.395692 | − | 0.228453i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.415990 | + | 1.55250i | 0.0588299 | + | 0.219556i | ||||
\(51\) | −3.30589 | − | 1.90866i | −0.462918 | − | 0.267266i | ||||
\(52\) | 0.177238 | − | 2.91241i | 0.0245784 | − | 0.403878i | ||||
\(53\) | −3.16223 | − | 5.47715i | −0.434366 | − | 0.752344i | 0.562878 | − | 0.826540i | \(-0.309694\pi\) |
−0.997244 | + | 0.0741963i | \(0.976361\pi\) | |||||||
\(54\) | −5.77504 | − | 1.54742i | −0.785883 | − | 0.210577i | ||||
\(55\) | 1.70918 | + | 0.986797i | 0.230466 | + | 0.133060i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.26614 | + | 1.26614i | 0.167704 | + | 0.167704i | ||||
\(58\) | 8.66852 | + | 8.66852i | 1.13823 | + | 1.13823i | ||||
\(59\) | −0.491481 | + | 0.131692i | −0.0639854 | + | 0.0171448i | −0.290670 | − | 0.956823i | \(-0.593878\pi\) |
0.226684 | + | 0.973968i | \(0.427211\pi\) | |||||||
\(60\) | 1.00213 | + | 0.268520i | 0.129374 | + | 0.0346657i | ||||
\(61\) | − | 13.0284i | − | 1.66811i | −0.551679 | − | 0.834057i | \(-0.686012\pi\) | ||
0.551679 | − | 0.834057i | \(-0.313988\pi\) | |||||||
\(62\) | 7.24196 | − | 12.5434i | 0.919729 | − | 1.59302i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 2.67342i | − | 0.334178i | ||||||
\(65\) | −5.42698 | + | 4.80434i | −0.673134 | + | 0.595905i | ||||
\(66\) | −0.908836 | + | 0.524717i | −0.111870 | + | 0.0645882i | ||||
\(67\) | 0.606011 | + | 0.606011i | 0.0740361 | + | 0.0740361i | 0.743155 | − | 0.669119i | \(-0.233328\pi\) |
−0.669119 | + | 0.743155i | \(0.733328\pi\) | |||||||
\(68\) | 4.19491 | − | 2.42193i | 0.508707 | − | 0.293702i | ||||
\(69\) | −0.953100 | − | 1.65082i | −0.114740 | − | 0.198735i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.01121 | + | 11.2380i | −0.357365 | + | 1.33370i | 0.520117 | + | 0.854095i | \(0.325888\pi\) |
−0.877482 | + | 0.479609i | \(0.840778\pi\) | |||||||
\(72\) | −3.65973 | + | 3.65973i | −0.431304 | + | 0.431304i | ||||
\(73\) | 0.377014 | − | 1.40704i | 0.0441262 | − | 0.164681i | −0.940347 | − | 0.340217i | \(-0.889499\pi\) |
0.984473 | + | 0.175536i | \(0.0561660\pi\) | |||||||
\(74\) | −4.01968 | + | 6.96230i | −0.467279 | + | 0.809350i | ||||
\(75\) | 0.305782 | + | 0.529629i | 0.0353086 | + | 0.0611563i | ||||
\(76\) | −2.19469 | + | 0.588064i | −0.251748 | + | 0.0674556i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.769526 | − | 3.77644i | −0.0871316 | − | 0.427597i | ||||
\(79\) | 5.80137 | − | 10.0483i | 0.652705 | − | 1.13052i | −0.329758 | − | 0.944065i | \(-0.606967\pi\) |
0.982464 | − | 0.186454i | \(-0.0596994\pi\) | |||||||
\(80\) | 7.05555 | − | 7.05555i | 0.788834 | − | 0.788834i | ||||
\(81\) | 5.50492 | 0.611657 | ||||||||
\(82\) | −5.73802 | −0.633658 | ||||||||
\(83\) | 1.23779 | − | 1.23779i | 0.135865 | − | 0.135865i | −0.635904 | − | 0.771768i | \(-0.719372\pi\) |
0.771768 | + | 0.635904i | \(0.219372\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.6225 | − | 3.11424i | −1.26064 | − | 0.337787i | ||||
\(86\) | −0.374999 | − | 1.39951i | −0.0404372 | − | 0.150914i | ||||
\(87\) | 4.03966 | + | 2.33230i | 0.433097 | + | 0.250049i | ||||
\(88\) | 1.95941i | 0.208874i | ||||||||
\(89\) | −2.07729 | + | 7.75255i | −0.220192 | + | 0.821769i | 0.764082 | + | 0.645120i | \(0.223193\pi\) |
−0.984274 | + | 0.176649i | \(0.943474\pi\) | |||||||
\(90\) | −8.73759 | −0.921023 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.41881 | 0.252179 | ||||||||
\(93\) | 1.42638 | − | 5.32334i | 0.147909 | − | 0.552004i | ||||
\(94\) | − | 5.14367i | − | 0.530529i | ||||||
\(95\) | 4.88792 | + | 2.82204i | 0.501490 | + | 0.289535i | ||||
\(96\) | 0.714359 | + | 2.66602i | 0.0729090 | + | 0.272100i | ||||
\(97\) | 12.0756 | + | 3.23566i | 1.22609 | + | 0.328531i | 0.813058 | − | 0.582183i | \(-0.197801\pi\) |
0.413037 | + | 0.910714i | \(0.364468\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.80030 | − | 1.80030i | 0.180937 | − | 0.180937i | ||||
\(100\) | −0.776023 | −0.0776023 | ||||||||
\(101\) | 7.99635 | 0.795667 | 0.397833 | − | 0.917458i | \(-0.369762\pi\) | ||||
0.397833 | + | 0.917458i | \(0.369762\pi\) | |||||||
\(102\) | 4.52417 | − | 4.52417i | 0.447959 | − | 0.447959i | ||||
\(103\) | 5.16928 | − | 8.95345i | 0.509344 | − | 0.882210i | −0.490597 | − | 0.871386i | \(-0.663221\pi\) |
0.999941 | − | 0.0108235i | \(-0.00344528\pi\) | |||||||
\(104\) | −6.82477 | − | 2.28122i | −0.669224 | − | 0.223692i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.2391 | − | 2.74356i | 0.994511 | − | 0.266479i | ||||
\(107\) | −6.52593 | − | 11.3032i | −0.630885 | − | 1.09273i | −0.987371 | − | 0.158425i | \(-0.949358\pi\) |
0.356486 | − | 0.934301i | \(-0.383975\pi\) | |||||||
\(108\) | 1.44334 | − | 2.49994i | 0.138885 | − | 0.240557i | ||||
\(109\) | −3.03074 | + | 11.3109i | −0.290292 | + | 1.08339i | 0.654592 | + | 0.755982i | \(0.272840\pi\) |
−0.944885 | + | 0.327403i | \(0.893826\pi\) | |||||||
\(110\) | −2.33904 | + | 2.33904i | −0.223019 | + | 0.223019i | ||||
\(111\) | −0.791721 | + | 2.95474i | −0.0751468 | + | 0.280452i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.05748 | + | 7.02777i | 0.381696 | + | 0.661117i | 0.991305 | − | 0.131586i | \(-0.0420069\pi\) |
−0.609609 | + | 0.792702i | \(0.708674\pi\) | |||||||
\(114\) | −2.59909 | + | 1.50058i | −0.243427 | + | 0.140543i | ||||
\(115\) | −4.24866 | − | 4.24866i | −0.396189 | − | 0.396189i | ||||
\(116\) | −5.12600 | + | 2.95950i | −0.475937 | + | 0.274782i | ||||
\(117\) | 4.17459 | + | 8.36653i | 0.385941 | + | 0.773486i | ||||
\(118\) | − | 0.852822i | − | 0.0785086i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.27933 | − | 2.21587i | 0.116786 | − | 0.202280i | ||||
\(121\) | 10.0361i | 0.912375i | ||||||||
\(122\) | 21.0926 | + | 5.65174i | 1.90963 | + | 0.511684i | ||||
\(123\) | −2.10892 | + | 0.565083i | −0.190155 | + | 0.0509518i | ||||
\(124\) | 4.94491 | + | 4.94491i | 0.444066 | + | 0.444066i | ||||
\(125\) | 8.47036 | + | 8.47036i | 0.757612 | + | 0.757612i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.81853 | + | 3.93668i | 0.605047 | + | 0.349324i | 0.771024 | − | 0.636805i | \(-0.219745\pi\) |
−0.165977 | + | 0.986130i | \(0.553078\pi\) | |||||||
\(128\) | 12.6889 | + | 3.39999i | 1.12155 | + | 0.300519i | ||||
\(129\) | −0.275650 | − | 0.477440i | −0.0242696 | − | 0.0420362i | ||||
\(130\) | −5.42385 | − | 10.8702i | −0.475703 | − | 0.953384i | ||||
\(131\) | 17.2856 | + | 9.97987i | 1.51025 | + | 0.871945i | 0.999928 | + | 0.0119634i | \(0.00380815\pi\) |
0.510325 | + | 0.859982i | \(0.329525\pi\) | |||||||
\(132\) | −0.131141 | − | 0.489425i | −0.0114144 | − | 0.0425990i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.24400 | + | 0.718226i | −0.107466 | + | 0.0620452i | ||||
\(135\) | −6.92639 | + | 1.85592i | −0.596129 | + | 0.159732i | ||||
\(136\) | −3.09187 | − | 11.5390i | −0.265125 | − | 0.989461i | ||||
\(137\) | −2.78324 | − | 10.3872i | −0.237788 | − | 0.887437i | −0.976872 | − | 0.213824i | \(-0.931408\pi\) |
0.739084 | − | 0.673613i | \(-0.235259\pi\) | |||||||
\(138\) | 3.08608 | − | 0.826913i | 0.262705 | − | 0.0703915i | ||||
\(139\) | −14.1096 | + | 8.14616i | −1.19676 | + | 0.690949i | −0.959831 | − | 0.280579i | \(-0.909474\pi\) |
−0.236927 | + | 0.971527i | \(0.576140\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.506551 | − | 1.89047i | −0.0426593 | − | 0.159207i | ||||
\(142\) | −16.8877 | − | 9.75012i | −1.41719 | − | 0.818212i | ||||
\(143\) | 3.35724 | + | 1.12218i | 0.280747 | + | 0.0938413i | ||||
\(144\) | −6.43601 | − | 11.1475i | −0.536334 | − | 0.928959i | ||||
\(145\) | 14.2022 | + | 3.80547i | 1.17943 | + | 0.316027i | ||||
\(146\) | 2.11440 | + | 1.22075i | 0.174989 | + | 0.101030i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.74470 | − | 2.74470i | −0.225613 | − | 0.225613i | ||||
\(149\) | 13.2274 | + | 13.2274i | 1.08363 | + | 1.08363i | 0.996168 | + | 0.0874634i | \(0.0278761\pi\) |
0.0874634 | + | 0.996168i | \(0.472124\pi\) | |||||||
\(150\) | −0.990103 | + | 0.265297i | −0.0808416 | + | 0.0216614i | ||||
\(151\) | 0.0351934 | + | 0.00943004i | 0.00286400 | + | 0.000767406i | 0.260251 | − | 0.965541i | \(-0.416195\pi\) |
−0.257387 | + | 0.966308i | \(0.582861\pi\) | |||||||
\(152\) | 5.60353i | 0.454506i | ||||||||
\(153\) | −7.76118 | + | 13.4428i | −0.627454 | + | 1.08678i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 17.3715i | − | 1.39532i | ||||||
\(156\) | 1.85738 | + | 0.113033i | 0.148710 | + | 0.00904988i | ||||
\(157\) | −6.22554 | + | 3.59432i | −0.496852 | + | 0.286858i | −0.727413 | − | 0.686200i | \(-0.759277\pi\) |
0.230560 | + | 0.973058i | \(0.425944\pi\) | |||||||
\(158\) | 13.7512 | + | 13.7512i | 1.09399 | + | 1.09399i | ||||
\(159\) | 3.49304 | − | 2.01671i | 0.277016 | − | 0.159935i | ||||
\(160\) | 4.34999 | + | 7.53441i | 0.343897 | + | 0.595647i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.38804 | + | 8.91230i | −0.187622 | + | 0.700216i | ||||
\(163\) | −11.6359 | + | 11.6359i | −0.911397 | + | 0.911397i | −0.996382 | − | 0.0849855i | \(-0.972916\pi\) |
0.0849855 | + | 0.996382i | \(0.472916\pi\) | |||||||
\(164\) | 0.717044 | − | 2.67605i | 0.0559918 | − | 0.208964i | ||||
\(165\) | −0.629328 | + | 1.09003i | −0.0489932 | + | 0.0848586i | ||||
\(166\) | 1.46699 | + | 2.54090i | 0.113860 | + | 0.197212i | ||||
\(167\) | 6.49344 | − | 1.73991i | 0.502478 | − | 0.134638i | 0.00132801 | − | 0.999999i | \(-0.499577\pi\) |
0.501150 | + | 0.865361i | \(0.332911\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.81725 | + | 10.3870i | −0.601327 | + | 0.799003i | ||||
\(170\) | 10.0837 | − | 17.4656i | 0.773388 | − | 1.33955i | ||||
\(171\) | 5.14849 | − | 5.14849i | 0.393715 | − | 0.393715i | ||||
\(172\) | 0.699554 | 0.0533405 | ||||||||
\(173\) | 9.51731 | 0.723587 | 0.361794 | − | 0.932258i | \(-0.382164\pi\) | ||||
0.361794 | + | 0.932258i | \(0.382164\pi\) | |||||||
\(174\) | −5.52834 | + | 5.52834i | −0.419102 | + | 0.419102i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.70709 | − | 1.26126i | −0.354810 | − | 0.0950711i | ||||
\(177\) | −0.0839864 | − | 0.313441i | −0.00631280 | − | 0.0235597i | ||||
\(178\) | −11.6500 | − | 6.72614i | −0.873206 | − | 0.504146i | ||||
\(179\) | 6.00707i | 0.448989i | 0.974475 | + | 0.224495i | \(0.0720731\pi\) | ||||
−0.974475 | + | 0.224495i | \(0.927927\pi\) | |||||||
\(180\) | 1.09188 | − | 4.07496i | 0.0813841 | − | 0.303729i | ||||
\(181\) | 6.05960 | 0.450407 | 0.225203 | − | 0.974312i | \(-0.427695\pi\) | ||||
0.225203 | + | 0.974312i | \(0.427695\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.30883 | 0.614207 | ||||||||
\(184\) | 1.54394 | − | 5.76207i | 0.113821 | − | 0.424786i | ||||
\(185\) | 9.64216i | 0.708905i | ||||||||
\(186\) | 7.99956 | + | 4.61855i | 0.586556 | + | 0.338648i | ||||
\(187\) | 1.52095 | + | 5.67627i | 0.111223 | + | 0.415090i | ||||
\(188\) | 2.39886 | + | 0.642771i | 0.174955 | + | 0.0468789i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.68919 | + | 6.68919i | −0.485285 | + | 0.485285i | ||||
\(191\) | 21.6273 | 1.56490 | 0.782449 | − | 0.622715i | \(-0.213970\pi\) | ||||
0.782449 | + | 0.622715i | \(0.213970\pi\) | |||||||
\(192\) | 1.70497 | 0.123046 | ||||||||
\(193\) | 6.85258 | − | 6.85258i | 0.493260 | − | 0.493260i | −0.416072 | − | 0.909332i | \(-0.636594\pi\) |
0.909332 | + | 0.416072i | \(0.136594\pi\) | |||||||
\(194\) | −10.4769 | + | 18.1465i | −0.752195 | + | 1.30284i | ||||
\(195\) | −3.06396 | − | 3.46105i | −0.219415 | − | 0.247851i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.47322 | + | 1.19859i | −0.318704 | + | 0.0853964i | −0.414624 | − | 0.909993i | \(-0.636087\pi\) |
0.0959210 | + | 0.995389i | \(0.469420\pi\) | |||||||
\(198\) | 2.13366 | + | 3.69560i | 0.151632 | + | 0.262635i | ||||
\(199\) | 10.7801 | − | 18.6717i | 0.764182 | − | 1.32360i | −0.176496 | − | 0.984301i | \(-0.556476\pi\) |
0.940678 | − | 0.339300i | \(-0.110190\pi\) | |||||||
\(200\) | −0.495341 | + | 1.84864i | −0.0350259 | + | 0.130718i | ||||
\(201\) | −0.386483 | + | 0.386483i | −0.0272604 | + | 0.0272604i | ||||
\(202\) | −3.46883 | + | 12.9459i | −0.244066 | + | 0.910868i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.54458 | + | 2.67530i | 0.108142 | + | 0.187308i | ||||
\(205\) | −5.95998 | + | 3.44100i | −0.416263 | + | 0.240330i | ||||
\(206\) | 12.2529 | + | 12.2529i | 0.853702 | + | 0.853702i | ||||
\(207\) | −6.71272 | + | 3.87559i | −0.466566 | + | 0.269372i | ||||
\(208\) | 9.87322 | − | 14.9267i | 0.684585 | − | 1.03498i | ||||
\(209\) | − | 2.75649i | − | 0.190670i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.39505 | − | 12.8086i | 0.509096 | − | 0.881780i | −0.490848 | − | 0.871245i | \(-0.663313\pi\) |
0.999945 | − | 0.0105352i | \(-0.00335353\pi\) | |||||||
\(212\) | 5.11807i | 0.351511i | ||||||||
\(213\) | −7.16701 | − | 1.92039i | −0.491076 | − | 0.131583i | ||||
\(214\) | 21.1306 | − | 5.66192i | 1.44446 | − | 0.387041i | ||||
\(215\) | −1.22877 | − | 1.22877i | −0.0838015 | − | 0.0838015i | ||||
\(216\) | −5.03404 | − | 5.03404i | −0.342523 | − | 0.342523i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −16.9972 | − | 9.81336i | −1.15120 | − | 0.664644i | ||||
\(219\) | 0.897335 | + | 0.240440i | 0.0606363 | + | 0.0162474i | ||||
\(220\) | −0.798566 | − | 1.38316i | −0.0538393 | − | 0.0932524i | ||||
\(221\) | −21.5416 | − | 1.31094i | −1.44904 | − | 0.0881832i | ||||
\(222\) | −4.44019 | − | 2.56355i | −0.298006 | − | 0.172054i | ||||
\(223\) | −5.52568 | − | 20.6221i | −0.370027 | − | 1.38096i | −0.860477 | − | 0.509490i | \(-0.829834\pi\) |
0.490450 | − | 0.871469i | \(-0.336832\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.15363 | − | 1.24340i | 0.143575 | − | 0.0828933i | ||||
\(226\) | −13.1379 | + | 3.52029i | −0.873919 | + | 0.234166i | ||||
\(227\) | 3.49849 | + | 13.0566i | 0.232203 | + | 0.866594i | 0.979390 | + | 0.201980i | \(0.0647375\pi\) |
−0.747186 | + | 0.664615i | \(0.768596\pi\) | |||||||
\(228\) | −0.375037 | − | 1.39966i | −0.0248374 | − | 0.0926946i | ||||
\(229\) | −6.94692 | + | 1.86142i | −0.459066 | + | 0.123006i | −0.480938 | − | 0.876755i | \(-0.659704\pi\) |
0.0218726 | + | 0.999761i | \(0.493037\pi\) | |||||||
\(230\) | 8.72153 | − | 5.03538i | 0.575081 | − | 0.332023i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.77813 | + | 14.1002i | 0.248046 | + | 0.925721i | ||||
\(233\) | −20.0959 | − | 11.6024i | −1.31653 | − | 0.760097i | −0.333359 | − | 0.942800i | \(-0.608182\pi\) |
−0.983168 | + | 0.182702i | \(0.941515\pi\) | |||||||
\(234\) | −15.3561 | + | 3.12912i | −1.00386 | + | 0.204557i | ||||
\(235\) | −3.08457 | − | 5.34264i | −0.201215 | − | 0.348515i | ||||
\(236\) | 0.397731 | + | 0.106572i | 0.0258901 | + | 0.00693723i | ||||
\(237\) | 6.40827 | + | 3.69982i | 0.416262 | + | 0.240329i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.77302 | − | 2.77302i | −0.179372 | − | 0.179372i | 0.611710 | − | 0.791082i | \(-0.290482\pi\) |
−0.791082 | + | 0.611710i | \(0.790482\pi\) | |||||||
\(240\) | 4.49966 | + | 4.49966i | 0.290452 | + | 0.290452i | ||||
\(241\) | 3.08037 | − | 0.825382i | 0.198424 | − | 0.0531675i | −0.158238 | − | 0.987401i | \(-0.550581\pi\) |
0.356662 | + | 0.934233i | \(0.383915\pi\) | |||||||
\(242\) | −16.2482 | − | 4.35369i | −1.04447 | − | 0.279866i | ||||
\(243\) | 14.2121i | 0.911704i | ||||||||
\(244\) | −5.27161 | + | 9.13070i | −0.337480 | + | 0.584533i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 3.65941i | − | 0.233316i | ||||||
\(247\) | 9.60104 | + | 3.20920i | 0.610900 | + | 0.204197i | ||||
\(248\) | 14.9361 | − | 8.62336i | 0.948443 | − | 0.547584i | ||||
\(249\) | 0.789397 | + | 0.789397i | 0.0500260 | + | 0.0500260i | ||||
\(250\) | −17.3877 | + | 10.0388i | −1.09970 | + | 0.634910i | ||||
\(251\) | −5.89697 | − | 10.2138i | −0.372213 | − | 0.644692i | 0.617692 | − | 0.786420i | \(-0.288068\pi\) |
−0.989906 | + | 0.141727i | \(0.954734\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.759496 | + | 2.83448i | −0.0477491 | + | 0.178202i | ||||
\(254\) | −9.33127 | + | 9.33127i | −0.585496 | + | 0.585496i | ||||
\(255\) | 1.98610 | − | 7.41224i | 0.124375 | − | 0.464173i | ||||
\(256\) | −8.33554 | + | 14.4376i | −0.520971 | + | 0.902349i | ||||
\(257\) | −8.34519 | − | 14.4543i | −0.520559 | − | 0.901634i | −0.999714 | − | 0.0239041i | \(-0.992390\pi\) |
0.479156 | − | 0.877730i | \(-0.340943\pi\) | |||||||
\(258\) | 0.892538 | − | 0.239155i | 0.0555670 | − | 0.0148891i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 5.74735 | − | 1.17114i | 0.356436 | − | 0.0726310i | ||||
\(261\) | 9.48383 | − | 16.4265i | 0.587034 | − | 1.01677i | ||||
\(262\) | −23.6557 | + | 23.6557i | −1.46145 | + | 1.46145i | ||||
\(263\) | 9.51537 | 0.586743 | 0.293371 | − | 0.955999i | \(-0.405223\pi\) | ||||
0.293371 | + | 0.955999i | \(0.405223\pi\) | |||||||
\(264\) | −1.24961 | −0.0769083 | ||||||||
\(265\) | 8.98993 | − | 8.98993i | 0.552247 | − | 0.552247i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.94418 | − | 1.32479i | −0.302579 | − | 0.0810758i | ||||
\(268\) | −0.179504 | − | 0.669919i | −0.0109650 | − | 0.0409218i | ||||
\(269\) | 0.275945 | + | 0.159317i | 0.0168247 | + | 0.00971373i | 0.508389 | − | 0.861128i | \(-0.330241\pi\) |
−0.491564 | + | 0.870841i | \(0.663575\pi\) | |||||||
\(270\) | − | 12.0187i | − | 0.731437i | ||||||
\(271\) | 6.94654 | − | 25.9248i | 0.421972 | − | 1.57482i | −0.348475 | − | 0.937318i | \(-0.613300\pi\) |
0.770447 | − | 0.637504i | \(-0.220033\pi\) | |||||||
\(272\) | 29.7103 | 1.80145 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 18.0239 | 1.08886 | ||||||||
\(275\) | 0.243668 | − | 0.909381i | 0.0146937 | − | 0.0548378i | ||||
\(276\) | 1.54259i | 0.0928532i | ||||||||
\(277\) | 13.1218 | + | 7.57587i | 0.788412 | + | 0.455190i | 0.839403 | − | 0.543509i | \(-0.182905\pi\) |
−0.0509909 | + | 0.998699i | \(0.516238\pi\) | |||||||
\(278\) | −7.06764 | − | 26.3768i | −0.423889 | − | 1.58198i | ||||
\(279\) | −21.6463 | − | 5.80010i | −1.29593 | − | 0.347243i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.40600 | − | 5.40600i | 0.322495 | − | 0.322495i | −0.527228 | − | 0.849724i | \(-0.676769\pi\) |
0.849724 | + | 0.527228i | \(0.176769\pi\) | |||||||
\(282\) | 3.28036 | 0.195343 | ||||||||
\(283\) | −1.79244 | −0.106549 | −0.0532746 | − | 0.998580i | \(-0.516966\pi\) | ||||
−0.0532746 | + | 0.998580i | \(0.516966\pi\) | |||||||
\(284\) | 6.65752 | − | 6.65752i | 0.395051 | − | 0.395051i | ||||
\(285\) | −1.79975 | + | 3.11726i | −0.106608 | + | 0.184651i | ||||
\(286\) | −3.27315 | + | 4.94848i | −0.193546 | + | 0.292610i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 10.8409 | − | 2.90480i | 0.638803 | − | 0.171167i | ||||
\(289\) | −9.41380 | − | 16.3052i | −0.553753 | − | 0.959128i | ||||
\(290\) | −12.3219 | + | 21.3422i | −0.723567 | + | 1.25325i | ||||
\(291\) | −2.06353 | + | 7.70122i | −0.120967 | + | 0.451453i | ||||
\(292\) | −0.833545 | + | 0.833545i | −0.0487796 | + | 0.0487796i | ||||
\(293\) | 6.85691 | − | 25.5903i | 0.400585 | − | 1.49500i | −0.411471 | − | 0.911423i | \(-0.634985\pi\) |
0.812055 | − | 0.583580i | \(-0.198349\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.511424 | − | 0.885812i | −0.0297762 | − | 0.0515739i | ||||
\(296\) | −8.29035 | + | 4.78644i | −0.481867 | + | 0.278206i | ||||
\(297\) | 2.47634 | + | 2.47634i | 0.143692 | + | 0.143692i | ||||
\(298\) | −27.1529 | + | 15.6767i | −1.57292 | + | 0.908127i | ||||
\(299\) | −8.98846 | − | 5.94538i | −0.519816 | − | 0.343830i | ||||
\(300\) | − | 0.494908i | − | 0.0285735i | ||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.0305339 | + | 0.0528863i | −0.00175703 | + | 0.00304327i | ||||
\(303\) | 5.09966i | 0.292968i | ||||||||
\(304\) | −13.4613 | − | 3.60695i | −0.772059 | − | 0.206873i | ||||
\(305\) | 25.2978 | − | 6.77851i | 1.44855 | − | 0.388136i | ||||
\(306\) | −18.3966 | − | 18.3966i | −1.05166 | − | 1.05166i | ||||
\(307\) | −1.54710 | − | 1.54710i | −0.0882978 | − | 0.0882978i | 0.661578 | − | 0.749876i | \(-0.269887\pi\) |
−0.749876 | + | 0.661578i | \(0.769887\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.71005 | + | 3.29670i | 0.324833 | + | 0.187543i | ||||
\(310\) | 28.1240 | + | 7.53581i | 1.59734 | + | 0.428005i | ||||
\(311\) | −14.6672 | − | 25.4043i | −0.831699 | − | 1.44055i | −0.896690 | − | 0.442660i | \(-0.854035\pi\) |
0.0649904 | − | 0.997886i | \(-0.479298\pi\) | |||||||
\(312\) | 1.45484 | − | 4.35249i | 0.0823644 | − | 0.246411i | ||||
\(313\) | −24.2354 | − | 13.9923i | −1.36987 | − | 0.790893i | −0.378957 | − | 0.925414i | \(-0.623717\pi\) |
−0.990911 | + | 0.134521i | \(0.957050\pi\) | |||||||
\(314\) | −3.11844 | − | 11.6382i | −0.175984 | − | 0.656781i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.13157 | + | 4.69476i | −0.457436 | + | 0.264101i | ||||
\(317\) | −7.59654 | + | 2.03549i | −0.426664 | + | 0.114324i | −0.465760 | − | 0.884911i | \(-0.654219\pi\) |
0.0390957 | + | 0.999235i | \(0.487552\pi\) | |||||||
\(318\) | 1.74970 | + | 6.52998i | 0.0981185 | + | 0.366183i | ||||
\(319\) | −1.85854 | − | 6.93616i | −0.104058 | − | 0.388350i | ||||
\(320\) | 5.19109 | − | 1.39095i | 0.290191 | − | 0.0777564i | ||||
\(321\) | 7.20862 | − | 4.16190i | 0.402346 | − | 0.232295i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.34961 | + | 16.2330i | 0.242019 | + | 0.903227i | ||||
\(324\) | −3.85802 | − | 2.22743i | −0.214334 | − | 0.123746i | ||||
\(325\) | 2.88375 | + | 1.90745i | 0.159962 | + | 0.105806i | ||||
\(326\) | −13.7905 | − | 23.8859i | −0.763788 | − | 1.32292i | ||||
\(327\) | −7.21349 | − | 1.93285i | −0.398907 | − | 0.106887i | ||||
\(328\) | −5.91716 | − | 3.41627i | −0.326720 | − | 0.188632i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.49172 | − | 1.49172i | −0.0821165 | − | 0.0821165i | ||||
\(331\) | 11.5133 | + | 11.5133i | 0.632826 | + | 0.632826i | 0.948776 | − | 0.315950i | \(-0.102323\pi\) |
−0.315950 | + | 0.948776i | \(0.602323\pi\) | |||||||
\(332\) | −1.36832 | + | 0.366640i | −0.0750963 | + | 0.0201220i | ||||
\(333\) | 12.0149 | + | 3.21938i | 0.658411 | + | 0.176421i | ||||
\(334\) | 11.2675i | 0.616529i | ||||||||
\(335\) | −0.861417 | + | 1.49202i | −0.0470642 | + | 0.0815176i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 11.0114i | − | 0.599827i | −0.953966 | − | 0.299913i | \(-0.903042\pi\) | ||
0.953966 | − | 0.299913i | \(-0.0969578\pi\) | |||||||
\(338\) | −13.4252 | − | 17.1618i | −0.730233 | − | 0.933480i | ||||
\(339\) | −4.48195 | + | 2.58765i | −0.243426 | + | 0.140542i | ||||
\(340\) | 6.88532 | + | 6.88532i | 0.373409 | + | 0.373409i | ||||
\(341\) | −7.34737 | + | 4.24200i | −0.397882 | + | 0.229717i | ||||
\(342\) | 6.10183 | + | 10.5687i | 0.329949 | + | 0.571488i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.446530 | − | 1.66647i | 0.0240753 | − | 0.0898501i | ||||
\(345\) | 2.70957 | − | 2.70957i | 0.145879 | − | 0.145879i | ||||
\(346\) | −4.12863 | + | 15.4082i | −0.221956 | + | 0.828352i | ||||
\(347\) | −2.36362 | + | 4.09391i | −0.126886 | + | 0.219772i | −0.922468 | − | 0.386073i | \(-0.873831\pi\) |
0.795583 | + | 0.605845i | \(0.207165\pi\) | |||||||
\(348\) | −1.88741 | − | 3.26910i | −0.101176 | − | 0.175242i | ||||
\(349\) | −22.4353 | + | 6.01151i | −1.20093 | + | 0.321789i | −0.803198 | − | 0.595712i | \(-0.796870\pi\) |
−0.397734 | + | 0.917501i | \(0.630203\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.5083 | + | 5.74223i | −0.614269 | + | 0.306498i | ||||
\(352\) | 2.12447 | − | 3.67970i | 0.113235 | − | 0.196128i | ||||
\(353\) | −9.29908 | + | 9.29908i | −0.494940 | + | 0.494940i | −0.909859 | − | 0.414919i | \(-0.863810\pi\) |
0.414919 | + | 0.909859i | \(0.363810\pi\) | |||||||
\(354\) | 0.543886 | 0.0289072 | ||||||||
\(355\) | −23.3880 | −1.24130 | ||||||||
\(356\) | 4.59271 | − | 4.59271i | 0.243413 | − | 0.243413i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.72526 | − | 2.60588i | −0.513996 | − | 0.137725i | ||||
\(359\) | 2.43301 | + | 9.08010i | 0.128409 | + | 0.479229i | 0.999938 | − | 0.0111144i | \(-0.00353790\pi\) |
−0.871529 | + | 0.490344i | \(0.836871\pi\) | |||||||
\(360\) | −9.01037 | − | 5.20214i | −0.474888 | − | 0.274177i | ||||
\(361\) | 11.1170i | 0.585105i | ||||||||
\(362\) | −2.62867 | + | 9.81032i | −0.138160 | + | 0.515619i | ||||
\(363\) | −6.40052 | −0.335940 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.92826 | 0.153272 | ||||||||
\(366\) | −3.60439 | + | 13.4518i | −0.188404 | + | 0.703135i | ||||
\(367\) | 7.31961i | 0.382081i | 0.981582 | + | 0.191040i | \(0.0611861\pi\) | ||||
−0.981582 | + | 0.191040i | \(0.938814\pi\) | |||||||
\(368\) | 12.8484 | + | 7.41801i | 0.669767 | + | 0.386690i | ||||
\(369\) | 2.29780 | + | 8.57550i | 0.119619 | + | 0.446423i | ||||
\(370\) | −15.6104 | − | 4.18279i | −0.811544 | − | 0.217453i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −3.15361 | + | 3.15361i | −0.163507 | + | 0.163507i | ||||
\(373\) | −1.08512 | −0.0561856 | −0.0280928 | − | 0.999605i | \(-0.508943\pi\) | ||||
−0.0280928 | + | 0.999605i | \(0.508943\pi\) | |||||||
\(374\) | −9.84951 | −0.509306 | ||||||||
\(375\) | −5.40196 | + | 5.40196i | −0.278956 | + | 0.278956i | ||||
\(376\) | 3.06241 | − | 5.30425i | 0.157932 | − | 0.273546i | ||||
\(377\) | 26.3229 | + | 1.60191i | 1.35570 | + | 0.0825025i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.1695 | + | 6.74414i | −1.29287 | + | 0.346423i | −0.838749 | − | 0.544518i | \(-0.816713\pi\) |
−0.454119 | + | 0.890941i | \(0.650046\pi\) | |||||||
\(380\) | −2.28374 | − | 3.95555i | −0.117153 | − | 0.202915i | ||||
\(381\) | −2.51061 | + | 4.34851i | −0.128623 | + | 0.222781i | ||||
\(382\) | −9.38197 | + | 35.0140i | −0.480023 | + | 1.79147i | ||||
\(383\) | 3.76918 | − | 3.76918i | 0.192596 | − | 0.192596i | −0.604221 | − | 0.796817i | \(-0.706516\pi\) |
0.796817 | + | 0.604221i | \(0.206516\pi\) | |||||||
\(384\) | −2.16834 | + | 8.09234i | −0.110652 | + | 0.412961i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.12146 | + | 14.0668i | 0.413372 | + | 0.715981i | ||||
\(387\) | −1.94141 | + | 1.12088i | −0.0986876 | + | 0.0569773i | ||||
\(388\) | −7.15375 | − | 7.15375i | −0.363177 | − | 0.363177i | ||||
\(389\) | −2.97841 | + | 1.71958i | −0.151011 | + | 0.0871864i | −0.573602 | − | 0.819134i | \(-0.694454\pi\) |
0.422590 | + | 0.906321i | \(0.361121\pi\) | |||||||
\(390\) | 6.93249 | − | 3.45905i | 0.351040 | − | 0.175156i | ||||
\(391\) | − | 17.8907i | − | 0.904773i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.36465 | + | 11.0239i | −0.321054 | + | 0.556082i | ||||
\(394\) | − | 7.76196i | − | 0.391042i | ||||||
\(395\) | 22.5295 | + | 6.03677i | 1.13358 | + | 0.303743i | ||||
\(396\) | −1.99015 | + | 0.533259i | −0.100009 | + | 0.0267973i | ||||
\(397\) | 0.424872 | + | 0.424872i | 0.0213237 | + | 0.0213237i | 0.717688 | − | 0.696365i | \(-0.245200\pi\) |
−0.696365 | + | 0.717688i | \(0.745200\pi\) | |||||||
\(398\) | 25.5525 | + | 25.5525i | 1.28083 | + | 1.28083i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.12212 | − | 2.37991i | −0.206106 | − | 0.118995i | ||||
\(401\) | −11.5834 | − | 3.10377i | −0.578448 | − | 0.154995i | −0.0422800 | − | 0.999106i | \(-0.513462\pi\) |
−0.536168 | + | 0.844111i | \(0.680129\pi\) | |||||||
\(402\) | −0.458047 | − | 0.793361i | −0.0228453 | − | 0.0395693i | ||||
\(403\) | −6.22113 | − | 30.5301i | −0.309896 | − | 1.52081i | ||||
\(404\) | −5.60409 | − | 3.23553i | −0.278814 | − | 0.160973i | ||||
\(405\) | 2.86414 | + | 10.6891i | 0.142320 | + | 0.531147i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.07819 | − | 2.35454i | 0.202148 | − | 0.116710i | ||||
\(408\) | 7.35898 | − | 1.97183i | 0.364324 | − | 0.0976203i | ||||
\(409\) | −3.00424 | − | 11.2120i | −0.148550 | − | 0.554396i | −0.999572 | − | 0.0292657i | \(-0.990683\pi\) |
0.851022 | − | 0.525131i | \(-0.175984\pi\) | |||||||
\(410\) | −2.98542 | − | 11.1418i | −0.147440 | − | 0.550252i | ||||
\(411\) | 6.62441 | − | 1.77501i | 0.326758 | − | 0.0875546i | ||||
\(412\) | −7.24558 | + | 4.18324i | −0.356964 | + | 0.206093i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.36248 | − | 12.5489i | −0.165257 | − | 0.616747i | ||||
\(415\) | 3.04747 | + | 1.75946i | 0.149594 | + | 0.0863683i | ||||
\(416\) | 10.3432 | + | 11.6837i | 0.507119 | + | 0.572842i | ||||
\(417\) | −5.19520 | − | 8.99836i | −0.254410 | − | 0.440651i | ||||
\(418\) | 4.46267 | + | 1.19577i | 0.218276 | + | 0.0584870i | ||||
\(419\) | −30.9881 | − | 17.8910i | −1.51387 | − | 0.874032i | −0.999868 | − | 0.0162408i | \(-0.994830\pi\) |
−0.513999 | − | 0.857791i | \(-0.671836\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.47255 | − | 3.47255i | −0.169242 | − | 0.169242i | 0.617404 | − | 0.786646i | \(-0.288184\pi\) |
−0.786646 | + | 0.617404i | \(0.788184\pi\) | |||||||
\(422\) | 17.5288 | + | 17.5288i | 0.853287 | + | 0.853287i | ||||
\(423\) | −7.68723 | + | 2.05979i | −0.373766 | + | 0.100150i | ||||
\(424\) | 12.1922 | + | 3.26690i | 0.592107 | + | 0.158655i | ||||
\(425\) | 5.73985i | 0.278424i | ||||||||
\(426\) | 6.21813 | − | 10.7701i | 0.301269 | − | 0.521814i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 10.5622i | 0.510544i | ||||||||
\(429\) | −0.715668 | + | 2.14108i | −0.0345528 | + | 0.103372i | ||||
\(430\) | 2.52239 | − | 1.45630i | 0.121640 | − | 0.0702291i | ||||
\(431\) | 0.347144 | + | 0.347144i | 0.0167213 | + | 0.0167213i | 0.715418 | − | 0.698697i | \(-0.246236\pi\) |
−0.698697 | + | 0.715418i | \(0.746236\pi\) | |||||||
\(432\) | 15.3336 | − | 8.85286i | 0.737739 | − | 0.425934i | ||||
\(433\) | 8.89347 | + | 15.4039i | 0.427393 | + | 0.740266i | 0.996641 | − | 0.0818999i | \(-0.0260988\pi\) |
−0.569248 | + | 0.822166i | \(0.692765\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.42693 | + | 9.05744i | −0.116363 | + | 0.434271i | ||||
\(436\) | 6.70070 | − | 6.70070i | 0.320905 | − | 0.320905i | ||||
\(437\) | −2.17201 | + | 8.10604i | −0.103901 | + | 0.387764i | ||||
\(438\) | −0.778531 | + | 1.34846i | −0.0371997 | + | 0.0644317i | ||||
\(439\) | 14.3012 | + | 24.7704i | 0.682559 | + | 1.18223i | 0.974197 | + | 0.225698i | \(0.0724662\pi\) |
−0.291639 | + | 0.956529i | \(0.594200\pi\) | |||||||
\(440\) | −3.80467 | + | 1.01946i | −0.181381 | + | 0.0486008i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.4672 | − | 34.3065i | 0.545437 | − | 1.63179i | ||||
\(443\) | 3.68575 | − | 6.38391i | 0.175115 | − | 0.303309i | −0.765086 | − | 0.643928i | \(-0.777304\pi\) |
0.940201 | + | 0.340620i | \(0.110637\pi\) | |||||||
\(444\) | 1.75043 | − | 1.75043i | 0.0830716 | − | 0.0830716i | ||||
\(445\) | −16.1342 | −0.764836 | ||||||||
\(446\) | 35.7837 | 1.69441 | ||||||||
\(447\) | −8.43576 | + | 8.43576i | −0.398998 | + | 0.398998i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.5220 | + | 6.03476i | 1.06288 | + | 0.284798i | 0.747565 | − | 0.664189i | \(-0.231223\pi\) |
0.315315 | + | 0.948987i | \(0.397890\pi\) | |||||||
\(450\) | 1.07878 | + | 4.02606i | 0.0508541 | + | 0.189790i | ||||
\(451\) | 2.91077 | + | 1.68053i | 0.137063 | + | 0.0791332i | ||||
\(452\) | − | 6.56704i | − | 0.308887i | ||||||
\(453\) | −0.00601399 | + | 0.0224445i | −0.000282562 | + | 0.00105454i | ||||
\(454\) | −22.6558 | −1.06329 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.57364 | −0.167351 | ||||||||
\(457\) | −1.16783 | + | 4.35841i | −0.0546289 | + | 0.203878i | −0.987846 | − | 0.155435i | \(-0.950322\pi\) |
0.933217 | + | 0.359313i | \(0.116989\pi\) | |||||||
\(458\) | − | 12.0544i | − | 0.563263i | ||||||
\(459\) | −18.4908 | − | 10.6757i | −0.863076 | − | 0.498297i | ||||
\(460\) | 1.25848 | + | 4.69671i | 0.0586769 | + | 0.218985i | ||||
\(461\) | 32.1809 | + | 8.62285i | 1.49882 | + | 0.401606i | 0.912703 | − | 0.408623i | \(-0.133991\pi\) |
0.586112 | + | 0.810230i | \(0.300658\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.0991 | − | 29.0991i | 1.35235 | − | 1.35235i | 0.469321 | − | 0.883028i | \(-0.344499\pi\) |
0.883028 | − | 0.469321i | \(-0.155501\pi\) | |||||||
\(464\) | −36.3047 | −1.68540 | ||||||||
\(465\) | 11.0787 | 0.513761 | ||||||||
\(466\) | 27.5016 | − | 27.5016i | 1.27399 | − | 1.27399i | ||||
\(467\) | −2.85866 | + | 4.95135i | −0.132283 | + | 0.229121i | −0.924556 | − | 0.381045i | \(-0.875564\pi\) |
0.792273 | + | 0.610167i | \(0.208897\pi\) | |||||||
\(468\) | 0.459626 | − | 7.55267i | 0.0212462 | − | 0.349122i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 9.98767 | − | 2.67619i | 0.460697 | − | 0.123443i | ||||
\(471\) | −2.29227 | − | 3.97033i | −0.105622 | − | 0.182943i | ||||
\(472\) | 0.507749 | − | 0.879447i | 0.0233710 | − | 0.0404798i | ||||
\(473\) | −0.219657 | + | 0.819771i | −0.0100998 | + | 0.0376931i | ||||
\(474\) | −8.76981 | + | 8.76981i | −0.402811 | + | 0.402811i | ||||
\(475\) | 0.696841 | − | 2.60065i | 0.0319733 | − | 0.119326i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.20054 | − | 14.2038i | −0.375477 | − | 0.650345i | ||||
\(478\) | 5.69239 | − | 3.28650i | 0.260364 | − | 0.150321i | ||||
\(479\) | −23.5643 | − | 23.5643i | −1.07668 | − | 1.07668i | −0.996805 | − | 0.0798746i | \(-0.974548\pi\) |
−0.0798746 | − | 0.996805i | \(-0.525452\pi\) | |||||||
\(480\) | −4.80506 | + | 2.77420i | −0.219320 | + | 0.126624i | ||||
\(481\) | 3.45307 | + | 16.9459i | 0.157446 | + | 0.772665i | ||||
\(482\) | 5.34507i | 0.243461i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.06087 | − | 7.03363i | 0.184585 | − | 0.319711i | ||||
\(485\) | 25.1312i | 1.14115i | ||||||||
\(486\) | −23.0089 | − | 6.16522i | −1.04371 | − | 0.279660i | ||||
\(487\) | 14.6038 | − | 3.91309i | 0.661763 | − | 0.177319i | 0.0877214 | − | 0.996145i | \(-0.472041\pi\) |
0.574041 | + | 0.818826i | \(0.305375\pi\) | |||||||
\(488\) | 18.3862 | + | 18.3862i | 0.832303 | + | 0.832303i | ||||
\(489\) | −7.42080 | − | 7.42080i | −0.335580 | − | 0.335580i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.79911 | − | 2.19342i | −0.171451 | − | 0.0989875i | 0.411819 | − | 0.911266i | \(-0.364894\pi\) |
−0.583270 | + | 0.812278i | \(0.698227\pi\) | |||||||
\(492\) | 1.70664 | + | 0.457294i | 0.0769415 | + | 0.0206164i | ||||
\(493\) | 21.8899 | + | 37.9144i | 0.985871 | + | 1.70758i | ||||
\(494\) | −9.36056 | + | 14.1516i | −0.421151 | + | 0.636713i | ||||
\(495\) | 4.43238 | + | 2.55904i | 0.199221 | + | 0.115020i | ||||
\(496\) | 11.1016 | + | 41.4317i | 0.498476 | + | 1.86034i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.62045 | + | 0.935569i | −0.0726142 | + | 0.0419238i | ||||
\(499\) | −19.3575 | + | 5.18682i | −0.866560 | + | 0.232194i | −0.664599 | − | 0.747200i | \(-0.731398\pi\) |
−0.201960 | + | 0.979394i | \(0.564731\pi\) | |||||||
\(500\) | −2.50897 | − | 9.36361i | −0.112205 | − | 0.418753i | ||||
\(501\) | 1.10963 | + | 4.14118i | 0.0495745 | + | 0.185014i | ||||
\(502\) | 19.0940 | − | 5.11623i | 0.852209 | − | 0.228349i | ||||
\(503\) | −0.917016 | + | 0.529439i | −0.0408877 | + | 0.0236065i | −0.520305 | − | 0.853981i | \(-0.674182\pi\) |
0.479417 | + | 0.877587i | \(0.340848\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.16041 | + | 15.5268i | 0.185136 | + | 0.690936i | ||||
\(506\) | −4.25947 | − | 2.45920i | −0.189356 | − | 0.109325i | ||||
\(507\) | −6.62432 | − | 4.98544i | −0.294196 | − | 0.221411i | ||||
\(508\) | −3.18576 | − | 5.51790i | −0.141345 | − | 0.244817i | ||||
\(509\) | −10.8606 | − | 2.91008i | −0.481387 | − | 0.128987i | 0.00996149 | − | 0.999950i | \(-0.496829\pi\) |
−0.491348 | + | 0.870963i | \(0.663496\pi\) | |||||||
\(510\) | 11.1386 | + | 6.43089i | 0.493227 | + | 0.284765i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.18017 | − | 1.18017i | −0.0521565 | − | 0.0521565i | ||||
\(513\) | 7.08184 | + | 7.08184i | 0.312671 | + | 0.312671i | ||||
\(514\) | 27.0212 | − | 7.24032i | 1.19186 | − | 0.319357i | ||||
\(515\) | 20.0748 | + | 5.37903i | 0.884601 | + | 0.237028i | ||||
\(516\) | 0.446140i | 0.0196402i | ||||||||
\(517\) | −1.50646 | + | 2.60927i | −0.0662541 | + | 0.114755i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.06965i | 0.266428i | ||||||||
\(520\) | 0.878691 | − | 14.4388i | 0.0385332 | − | 0.633185i | ||||
\(521\) | −14.6510 | + | 8.45874i | −0.641871 | + | 0.370584i | −0.785335 | − | 0.619071i | \(-0.787509\pi\) |
0.143464 | + | 0.989656i | \(0.454176\pi\) | |||||||
\(522\) | 22.4799 | + | 22.4799i | 0.983917 | + | 0.983917i | ||||
\(523\) | 0.268849 | − | 0.155220i | 0.0117560 | − | 0.00678731i | −0.494111 | − | 0.869399i | \(-0.664506\pi\) |
0.505866 | + | 0.862612i | \(0.331173\pi\) | |||||||
\(524\) | −8.07621 | − | 13.9884i | −0.352811 | − | 0.611086i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.12779 | + | 15.4051i | −0.179980 | + | 0.671695i | ||||
\(527\) | 36.5750 | − | 36.5750i | 1.59323 | − | 1.59323i | ||||
\(528\) | 0.804367 | − | 3.00194i | 0.0350056 | − | 0.130643i | ||||
\(529\) | −7.03308 | + | 12.1816i | −0.305786 | + | 0.529637i | ||||
\(530\) | 10.6546 | + | 18.4543i | 0.462806 | + | 0.801603i | ||||
\(531\) | −1.27455 | + | 0.341514i | −0.0553106 | + | 0.0148204i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.24224 | + | 8.18188i | −0.400326 | + | 0.354396i | ||||
\(534\) | 4.28959 | − | 7.42978i | 0.185629 | − | 0.321518i | ||||
\(535\) | 18.5526 | − | 18.5526i | 0.802099 | − | 0.802099i | ||||
\(536\) | −1.71045 | −0.0738803 | ||||||||
\(537\) | −3.83100 | −0.165320 | ||||||||
\(538\) | −0.377635 | + | 0.377635i | −0.0162810 | + | 0.0162810i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5.60519 | + | 1.50190i | 0.241209 | + | 0.0646317i | ||||
\(541\) | −8.05676 | − | 30.0682i | −0.346387 | − | 1.29273i | −0.890984 | − | 0.454036i | \(-0.849984\pi\) |
0.544597 | − | 0.838698i | \(-0.316683\pi\) | |||||||
\(542\) | 38.9581 | + | 22.4925i | 1.67340 | + | 0.966135i | ||||
\(543\) | 3.86450i | 0.165842i | ||||||||
\(544\) | −6.70465 | + | 25.0221i | −0.287459 | + | 1.07281i | ||||
\(545\) | −23.5396 | −1.00833 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.8672 | −0.592920 | −0.296460 | − | 0.955045i | \(-0.595806\pi\) | ||||
−0.296460 | + | 0.955045i | \(0.595806\pi\) | |||||||
\(548\) | −2.25234 | + | 8.40583i | −0.0962150 | + | 0.359079i | ||||
\(549\) | − | 33.7862i | − | 1.44196i | ||||||
\(550\) | 1.36656 | + | 0.788983i | 0.0582702 | + | 0.0336423i | ||||
\(551\) | −5.31504 | − | 19.8360i | −0.226428 | − | 0.845042i | ||||
\(552\) | 3.67475 | + | 0.984647i | 0.156408 | + | 0.0419094i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −17.9574 | + | 17.9574i | −0.762936 | + | 0.762936i | ||||
\(555\) | −6.14927 | −0.261022 | ||||||||
\(556\) | 13.1846 | 0.559150 | ||||||||
\(557\) | −16.0453 | + | 16.0453i | −0.679860 | + | 0.679860i | −0.959968 | − | 0.280108i | \(-0.909630\pi\) |
0.280108 | + | 0.959968i | \(0.409630\pi\) | |||||||
\(558\) | 18.7804 | − | 32.5286i | 0.795038 | − | 1.37705i | ||||
\(559\) | −2.59959 | − | 1.71949i | −0.109951 | − | 0.0727266i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.62003 | + | 0.969985i | −0.152838 | + | 0.0409528i | ||||
\(562\) | 6.40703 | + | 11.0973i | 0.270264 | + | 0.468111i | ||||
\(563\) | 11.2217 | − | 19.4366i | 0.472940 | − | 0.819156i | −0.526580 | − | 0.850125i | \(-0.676526\pi\) |
0.999520 | + | 0.0309690i | \(0.00985932\pi\) | |||||||
\(564\) | −0.409927 | + | 1.52987i | −0.0172610 | + | 0.0644190i | ||||
\(565\) | −11.5350 | + | 11.5350i | −0.485283 | + | 0.485283i | ||||
\(566\) | 0.777562 | − | 2.90190i | 0.0326834 | − | 0.121976i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.6100 | − | 20.1090i | −0.487143 | − | 0.843756i | ||||
\(569\) | 11.1921 | − | 6.46175i | 0.469196 | − | 0.270891i | −0.246707 | − | 0.969090i | \(-0.579349\pi\) |
0.715903 | + | 0.698200i | \(0.246015\pi\) | |||||||
\(570\) | −4.26602 | − | 4.26602i | −0.178684 | − | 0.178684i | ||||
\(571\) | 15.1053 | − | 8.72106i | 0.632138 | − | 0.364965i | −0.149442 | − | 0.988771i | \(-0.547748\pi\) |
0.781580 | + | 0.623805i | \(0.214414\pi\) | |||||||
\(572\) | −1.89880 | − | 2.14488i | −0.0793928 | − | 0.0896821i | ||||
\(573\) | 13.7928i | 0.576202i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.43312 | + | 2.48223i | −0.0597650 | + | 0.103516i | ||||
\(576\) | − | 6.93292i | − | 0.288872i | ||||||
\(577\) | 13.9338 | + | 3.73355i | 0.580071 | + | 0.155430i | 0.536912 | − | 0.843639i | \(-0.319591\pi\) |
0.0431598 | + | 0.999068i | \(0.486258\pi\) | |||||||
\(578\) | 30.4813 | − | 8.16745i | 1.26786 | − | 0.339721i | ||||
\(579\) | 4.37022 | + | 4.37022i | 0.181620 | + | 0.181620i | ||||
\(580\) | −8.41357 | − | 8.41357i | −0.349354 | − | 0.349354i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −11.5729 | − | 6.68160i | −0.479711 | − | 0.276961i | ||||
\(583\) | −5.99760 | − | 1.60705i | −0.248395 | − | 0.0665573i | ||||
\(584\) | 1.45361 | + | 2.51772i | 0.0601507 | + | 0.104184i | ||||
\(585\) | −14.0737 | + | 12.4590i | −0.581874 | + | 0.515116i | ||||
\(586\) | 38.4555 | + | 22.2023i | 1.58858 | + | 0.917167i | ||||
\(587\) | 4.97130 | + | 18.5532i | 0.205188 | + | 0.765771i | 0.989392 | + | 0.145268i | \(0.0464046\pi\) |
−0.784205 | + | 0.620502i | \(0.786929\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.0120 | + | 12.1313i | −0.865783 | + | 0.499860i | ||||
\(590\) | 1.65596 | − | 0.443713i | 0.0681748 | − | 0.0182674i | ||||
\(591\) | −0.764402 | − | 2.85279i | −0.0314433 | − | 0.117348i | ||||
\(592\) | −6.16199 | − | 22.9969i | −0.253256 | − | 0.945165i | ||||
\(593\) | −2.51561 | + | 0.674056i | −0.103304 | + | 0.0276802i | −0.310101 | − | 0.950704i | \(-0.600363\pi\) |
0.206797 | + | 0.978384i | \(0.433696\pi\) | |||||||
\(594\) | −5.08337 | + | 2.93489i | −0.208573 | + | 0.120420i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.91804 | − | 14.6223i | −0.160489 | − | 0.598954i | ||||
\(597\) | 11.9078 | + | 6.87500i | 0.487356 | + | 0.281375i | ||||
\(598\) | 13.5246 | − | 11.9729i | 0.553063 | − | 0.489610i | ||||
\(599\) | −12.4050 | − | 21.4861i | −0.506855 | − | 0.877898i | −0.999969 | − | 0.00793343i | \(-0.997475\pi\) |
0.493114 | − | 0.869965i | \(-0.335859\pi\) | |||||||
\(600\) | −1.17896 | − | 0.315903i | −0.0481310 | − | 0.0128967i | ||||
\(601\) | 15.2889 | + | 8.82708i | 0.623649 | + | 0.360064i | 0.778288 | − | 0.627907i | \(-0.216088\pi\) |
−0.154639 | + | 0.987971i | \(0.549422\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.57155 | + | 1.57155i | 0.0639987 | + | 0.0639987i | ||||
\(604\) | −0.0208490 | − | 0.0208490i | −0.000848334 | − | 0.000848334i | ||||
\(605\) | −19.4876 | + | 5.22168i | −0.792282 | + | 0.212291i | ||||
\(606\) | −8.25620 | − | 2.21224i | −0.335385 | − | 0.0898662i | ||||
\(607\) | − | 15.0740i | − | 0.611835i | −0.952058 | − | 0.305917i | \(-0.901037\pi\) | ||
0.952058 | − | 0.305917i | \(-0.0989631\pi\) | |||||||
\(608\) | 6.07556 | − | 10.5232i | 0.246397 | − | 0.426771i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 43.8969i | 1.77733i | ||||||||
\(611\) | −7.33438 | − | 8.28491i | −0.296717 | − | 0.335172i | ||||
\(612\) | 10.8786 | − | 6.28074i | 0.439740 | − | 0.253884i | ||||
\(613\) | −24.8050 | − | 24.8050i | −1.00186 | − | 1.00186i | −0.999998 | − | 0.00186450i | \(-0.999407\pi\) |
−0.00186450 | − | 0.999998i | \(-0.500593\pi\) | |||||||
\(614\) | 3.17585 | − | 1.83358i | 0.128167 | − | 0.0739972i | ||||
\(615\) | −2.19449 | − | 3.80097i | −0.0884904 | − | 0.153270i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.01921 | − | 33.6601i | 0.363100 | − | 1.35511i | −0.506879 | − | 0.862017i | \(-0.669201\pi\) |
0.869979 | − | 0.493089i | \(-0.164132\pi\) | |||||||
\(618\) | −7.81429 | + | 7.81429i | −0.314337 | + | 0.314337i | ||||
\(619\) | −2.05655 | + | 7.67515i | −0.0826597 | + | 0.308490i | −0.994861 | − | 0.101253i | \(-0.967715\pi\) |
0.912201 | + | 0.409743i | \(0.134382\pi\) | |||||||
\(620\) | −7.02896 | + | 12.1745i | −0.282290 | + | 0.488940i | ||||
\(621\) | −5.33095 | − | 9.23348i | −0.213924 | − | 0.370527i | ||||
\(622\) | 47.4915 | − | 12.7253i | 1.90423 | − | 0.510238i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 9.51949 | + | 6.29663i | 0.381084 | + | 0.252067i | ||||
\(625\) | −9.64286 | + | 16.7019i | −0.385715 | + | 0.668077i | ||||
\(626\) | 33.1665 | − | 33.1665i | 1.32560 | − | 1.32560i | ||||
\(627\) | 1.75795 | 0.0702056 | ||||||||
\(628\) | 5.81741 | 0.232140 | ||||||||
\(629\) | −20.3011 | + | 20.3011i | −0.809460 | + | 0.809460i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.9973 | + | 10.9852i | 1.63208 | + | 0.437314i | 0.954517 | − | 0.298155i | \(-0.0963713\pi\) |
0.677559 | + | 0.735469i | \(0.263038\pi\) | |||||||
\(632\) | 5.99339 | + | 22.3676i | 0.238404 | + | 0.889737i | ||||
\(633\) | 8.16866 | + | 4.71618i | 0.324675 | + | 0.187451i | ||||
\(634\) | − | 13.1816i | − | 0.523507i | ||||||
\(635\) | −4.09642 | + | 15.2880i | −0.162561 | + | 0.606687i | ||||
\(636\) | −3.26404 | −0.129428 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 12.0357 | 0.476497 | ||||||||
\(639\) | −7.80890 | + | 29.1432i | −0.308915 | + | 1.15289i | ||||
\(640\) | 26.4076i | 1.04385i | ||||||||
\(641\) | 17.7415 | + | 10.2431i | 0.700748 | + | 0.404577i | 0.807626 | − | 0.589695i | \(-0.200752\pi\) |
−0.106878 | + | 0.994272i | \(0.534085\pi\) | |||||||
\(642\) | 3.61088 | + | 13.4760i | 0.142510 | + | 0.531855i | ||||
\(643\) | −20.9593 | − | 5.61604i | −0.826556 | − | 0.221475i | −0.179345 | − | 0.983786i | \(-0.557398\pi\) |
−0.647211 | + | 0.762311i | \(0.724065\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.783647 | − | 0.783647i | 0.0308561 | − | 0.0308561i | ||||
\(646\) | −28.1676 | −1.10824 | ||||||||
\(647\) | −39.1337 | −1.53850 | −0.769252 | − | 0.638945i | \(-0.779371\pi\) | ||||
−0.769252 | + | 0.638945i | \(0.779371\pi\) | |||||||
\(648\) | −7.76875 | + | 7.76875i | −0.305185 | + | 0.305185i | ||||
\(649\) | −0.249772 | + | 0.432618i | −0.00980440 | + | 0.0169817i | ||||
\(650\) | −4.33908 | + | 3.84126i | −0.170193 | + | 0.150666i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.8630 | − | 3.44664i | 0.503755 | − | 0.134981i | ||||
\(653\) | 14.8092 | + | 25.6503i | 0.579528 | + | 1.00377i | 0.995533 | + | 0.0944103i | \(0.0300966\pi\) |
−0.416005 | + | 0.909362i | \(0.636570\pi\) | |||||||
\(654\) | 6.25845 | − | 10.8400i | 0.244725 | − | 0.423876i | ||||
\(655\) | −10.3848 | + | 38.7566i | −0.405768 | + | 1.51435i | ||||
\(656\) | 12.0157 | − | 12.0157i | 0.469135 | − | 0.469135i | ||||
\(657\) | 0.977702 | − | 3.64883i | 0.0381438 | − | 0.142355i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.87682 | + | 3.25074i | 0.0731104 | + | 0.126631i | 0.900263 | − | 0.435346i | \(-0.143374\pi\) |
−0.827153 | + | 0.561977i | \(0.810041\pi\) | |||||||
\(660\) | 0.882106 | − | 0.509284i | 0.0343359 | − | 0.0198239i | ||||
\(661\) | 30.7260 | + | 30.7260i | 1.19510 | + | 1.19510i | 0.975615 | + | 0.219487i | \(0.0704385\pi\) |
0.219487 | + | 0.975615i | \(0.429562\pi\) | |||||||
\(662\) | −23.6341 | + | 13.6452i | −0.918566 | + | 0.530334i | ||||
\(663\) | 0.836048 | − | 13.7381i | 0.0324694 | − | 0.533544i | ||||
\(664\) | 3.49363i | 0.135579i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10.4242 | + | 18.0552i | −0.403928 | + | 0.699623i | ||||
\(667\) | 21.8617i | 0.846488i | ||||||||
\(668\) | −5.25482 | − | 1.40802i | −0.203315 | − | 0.0544781i | ||||
\(669\) | 13.1517 | − | 3.52399i | 0.508475 | − | 0.136245i | ||||
\(670\) | −2.04185 | − | 2.04185i | −0.0788835 | − | 0.0788835i | ||||
\(671\) | −9.04453 | − | 9.04453i | −0.349160 | − | 0.349160i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.1880 | + | 13.3876i | 0.893833 | + | 0.516055i | 0.875194 | − | 0.483771i | \(-0.160733\pi\) |
0.0186390 | + | 0.999826i | \(0.494067\pi\) | |||||||
\(674\) | 17.8271 | + | 4.77675i | 0.686673 | + | 0.183993i | ||||
\(675\) | 1.71032 | + | 2.96236i | 0.0658303 | + | 0.114021i | ||||
\(676\) | 9.68143 | − | 4.11651i | 0.372363 | − | 0.158327i | ||||
\(677\) | −18.0711 | − | 10.4333i | −0.694527 | − | 0.400985i | 0.110779 | − | 0.993845i | \(-0.464666\pi\) |
−0.805306 | + | 0.592860i | \(0.797999\pi\) | |||||||
\(678\) | −2.24506 | − | 8.37867i | −0.0862209 | − | 0.321781i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 20.7971 | − | 12.0072i | 0.797532 | − | 0.460456i | ||||
\(681\) | −8.32680 | + | 2.23116i | −0.319084 | + | 0.0854982i | ||||
\(682\) | −3.68038 | − | 13.7354i | −0.140929 | − | 0.525954i | ||||
\(683\) | 8.48852 | + | 31.6796i | 0.324804 | + | 1.21219i | 0.914509 | + | 0.404567i | \(0.132578\pi\) |
−0.589704 | + | 0.807619i | \(0.700756\pi\) | |||||||
\(684\) | −5.69143 | + | 1.52501i | −0.217617 | + | 0.0583103i | ||||
\(685\) | 18.7211 | − | 10.8087i | 0.715298 | − | 0.412977i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.18712 | − | 4.43039i | −0.0452914 | − | 0.169030i | ||||
\(688\) | 3.71593 | + | 2.14539i | 0.141668 | + | 0.0817923i | ||||
\(689\) | 12.5801 | − | 19.0191i | 0.479264 | − | 0.724570i | ||||
\(690\) | 3.21130 | + | 5.56214i | 0.122252 | + | 0.211747i | ||||
\(691\) | −43.4491 | − | 11.6421i | −1.65288 | − | 0.442888i | −0.692464 | − | 0.721453i | \(-0.743475\pi\) |
−0.960418 | + | 0.278564i | \(0.910141\pi\) | |||||||
\(692\) | −6.67003 | − | 3.85094i | −0.253556 | − | 0.146391i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.60257 | − | 5.60257i | −0.212671 | − | 0.212671i | ||||
\(695\) | −23.1588 | − | 23.1588i | −0.878463 | − | 0.878463i | ||||
\(696\) | −8.99236 | + | 2.40950i | −0.340855 | + | 0.0913317i | ||||
\(697\) | −19.7934 | − | 5.30361i | −0.749727 | − | 0.200889i | ||||
\(698\) | − | 38.9298i | − | 1.47352i | ||||||
\(699\) | 7.39940 | − | 12.8161i | 0.279871 | − | 0.484751i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 38.7293i | − | 1.46279i | −0.681956 | − | 0.731393i | \(-0.738871\pi\) | ||
0.681956 | − | 0.731393i | \(-0.261129\pi\) | |||||||
\(702\) | −4.30417 | − | 21.1226i | −0.162450 | − | 0.797223i | ||||
\(703\) | 11.6628 | − | 6.73352i | 0.439871 | − | 0.253960i | ||||
\(704\) | −1.85593 | − | 1.85593i | −0.0699482 | − | 0.0699482i | ||||
\(705\) | 3.40726 | − | 1.96718i | 0.128325 | − | 0.0740884i | ||||
\(706\) | −11.0210 | − | 19.0889i | −0.414780 | − | 0.718420i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.0679660 | + | 0.253653i | −0.00255432 | + | 0.00953285i | ||||
\(709\) | 20.8624 | − | 20.8624i | 0.783504 | − | 0.783504i | −0.196917 | − | 0.980420i | \(-0.563093\pi\) |
0.980420 | + | 0.196917i | \(0.0630928\pi\) | |||||||
\(710\) | 10.1457 | − | 37.8644i | 0.380763 | − | 1.42103i | ||||
\(711\) | 15.0446 | − | 26.0580i | 0.564215 | − | 0.977250i | ||||
\(712\) | −8.00915 | − | 13.8723i | −0.300156 | − | 0.519885i | ||||
\(713\) | 24.9490 | − | 6.68507i | 0.934348 | − | 0.250358i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.432246 | + | 7.10276i | −0.0161651 | + | 0.265628i | ||||
\(716\) | 2.43061 | − | 4.20994i | 0.0908362 | − | 0.157333i | ||||
\(717\) | 1.76849 | − | 1.76849i | 0.0660455 | − | 0.0660455i | ||||
\(718\) | −15.7559 | −0.588003 | ||||||||
\(719\) | −8.46228 | −0.315590 | −0.157795 | − | 0.987472i | \(-0.550438\pi\) | ||||
−0.157795 | + | 0.987472i | \(0.550438\pi\) | |||||||
\(720\) | 18.2970 | − | 18.2970i | 0.681888 | − | 0.681888i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −17.9981 | − | 4.82258i | −0.669820 | − | 0.179478i | ||||
\(723\) | 0.526386 | + | 1.96450i | 0.0195765 | + | 0.0730605i | ||||
\(724\) | −4.24676 | − | 2.45187i | −0.157830 | − | 0.0911229i | ||||
\(725\) | − | 7.01385i | − | 0.260488i | ||||||
\(726\) | 2.77656 | − | 10.3623i | 0.103048 | − | 0.384580i | ||||
\(727\) | 3.27056 | 0.121299 | 0.0606493 | − | 0.998159i | \(-0.480683\pi\) | ||||
0.0606493 | + | 0.998159i | \(0.480683\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.45103 | 0.275964 | ||||||||
\(730\) | −1.27028 | + | 4.74076i | −0.0470153 | + | 0.175463i | ||||
\(731\) | − | 5.17425i | − | 0.191376i | ||||||
\(732\) | −5.82309 | − | 3.36196i | −0.215228 | − | 0.124262i | ||||
\(733\) | 3.57318 | + | 13.3353i | 0.131979 | + | 0.492551i | 0.999992 | − | 0.00399003i | \(-0.00127007\pi\) |
−0.868014 | + | 0.496541i | \(0.834603\pi\) | |||||||
\(734\) | −11.8502 | − | 3.17526i | −0.437400 | − | 0.117201i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.14692 | + | 9.14692i | −0.337160 | + | 0.337160i | ||||
\(737\) | 0.841407 | 0.0309936 | ||||||||
\(738\) | −14.8803 | −0.547750 | ||||||||
\(739\) | 30.0608 | − | 30.0608i | 1.10580 | − | 1.10580i | 0.112109 | − | 0.993696i | \(-0.464240\pi\) |
0.993696 | − | 0.112109i | \(-0.0357605\pi\) | |||||||
\(740\) | 3.90146 | − | 6.75753i | 0.143420 | − | 0.248412i | ||||
\(741\) | −2.04666 | + | 6.12305i | −0.0751861 | + | 0.224936i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −47.1919 | + | 12.6450i | −1.73130 | + | 0.463901i | −0.980482 | − | 0.196606i | \(-0.937008\pi\) |
−0.750820 | + | 0.660507i | \(0.770341\pi\) | |||||||
\(744\) | 5.49953 | + | 9.52547i | 0.201623 | + | 0.349221i | ||||
\(745\) | −18.8021 | + | 32.5663i | −0.688857 | + | 1.19314i | ||||
\(746\) | 0.470729 | − | 1.75678i | 0.0172346 | − | 0.0643204i | ||||
\(747\) | 3.20993 | − | 3.20993i | 0.117445 | − | 0.117445i | ||||
\(748\) | 1.23083 | − | 4.59352i | 0.0450036 | − | 0.167956i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −6.40223 | − | 11.0890i | −0.233776 | − | 0.404913i | ||||
\(751\) | 9.96838 | − | 5.75525i | 0.363751 | − | 0.210012i | −0.306974 | − | 0.951718i | \(-0.599316\pi\) |
0.670725 | + | 0.741706i | \(0.265983\pi\) | |||||||
\(752\) | 10.7711 | + | 10.7711i | 0.392782 | + | 0.392782i | ||||
\(753\) | 6.51387 | − | 3.76078i | 0.237379 | − | 0.137051i | ||||
\(754\) | −14.0124 | + | 41.9211i | −0.510300 | + | 1.52668i | ||||
\(755\) | 0.0732428i | 0.00266558i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.97468 | + | 15.5446i | −0.326190 | + | 0.564978i | −0.981753 | − | 0.190163i | \(-0.939098\pi\) |
0.655562 | + | 0.755141i | \(0.272432\pi\) | |||||||
\(758\) | − | 43.6743i | − | 1.58632i | ||||||
\(759\) | −1.80768 | − | 0.484368i | −0.0656148 | − | 0.0175814i | ||||
\(760\) | −10.8806 | + | 2.91545i | −0.394681 | + | 0.105754i | ||||
\(761\) | −7.83029 | − | 7.83029i | −0.283848 | − | 0.283848i | 0.550794 | − | 0.834641i | \(-0.314325\pi\) |
−0.834641 | + | 0.550794i | \(0.814325\pi\) | |||||||
\(762\) | −5.95100 | − | 5.95100i | −0.215582 | − | 0.215582i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −15.1571 | − | 8.75096i | −0.548365 | − | 0.316599i | ||||
\(765\) | −30.1404 | − | 8.07610i | −1.08973 | − | 0.291992i | ||||
\(766\) | 4.46711 | + | 7.73726i | 0.161403 | + | 0.279559i | ||||
\(767\) | −1.21604 | − | 1.37364i | −0.0439088 | − | 0.0495993i | ||||
\(768\) | −9.20755 | − | 5.31598i | −0.332249 | − | 0.191824i | ||||
\(769\) | −2.87361 | − | 10.7245i | −0.103625 | − | 0.386734i | 0.894561 | − | 0.446947i | \(-0.147489\pi\) |
−0.998186 | + | 0.0602130i | \(0.980822\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.21820 | − | 5.32213i | 0.331986 | − | 0.191672i | ||||
\(772\) | −7.57523 | + | 2.02978i | −0.272638 | + | 0.0730533i | ||||
\(773\) | −0.718001 | − | 2.67962i | −0.0258247 | − | 0.0963792i | 0.951811 | − | 0.306686i | \(-0.0992203\pi\) |
−0.977635 | + | 0.210307i | \(0.932554\pi\) | |||||||
\(774\) | −0.972476 | − | 3.62933i | −0.0349549 | − | 0.130454i | ||||
\(775\) | −8.00436 | + | 2.14476i | −0.287525 | + | 0.0770421i | ||||
\(776\) | −21.6079 | + | 12.4753i | −0.775678 | + | 0.447838i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.49192 | − | 5.56791i | −0.0534879 | − | 0.199619i | ||||
\(779\) | 8.32421 | + | 4.80599i | 0.298246 | + | 0.172192i | ||||
\(780\) | 0.746893 | + | 3.66537i | 0.0267431 | + | 0.131241i | ||||
\(781\) | 5.71117 | + | 9.89204i | 0.204362 | + | 0.353965i | ||||
\(782\) | 28.9646 | + | 7.76103i | 1.03577 | + | 0.277534i | ||||
\(783\) | 22.5949 | + | 13.0452i | 0.807477 | + | 0.466197i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.2183 | − | 10.2183i | −0.364707 | − | 0.364707i | ||||
\(786\) | −15.0864 | − | 15.0864i | −0.538113 | − | 0.538113i | ||||
\(787\) | 37.6817 | − | 10.0968i | 1.34321 | − | 0.359912i | 0.485585 | − | 0.874189i | \(-0.338607\pi\) |
0.857624 | + | 0.514278i | \(0.171940\pi\) | |||||||
\(788\) | 3.61995 | + | 0.969963i | 0.128955 | + | 0.0345535i | ||||
\(789\) | 6.06841i | 0.216041i | ||||||||
\(790\) | −19.5467 | + | 33.8559i | −0.695441 | + | 1.20454i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 5.08130i | 0.180556i | ||||||||
\(793\) | 42.0327 | − | 20.9728i | 1.49262 | − | 0.744765i | ||||
\(794\) | −0.872166 | + | 0.503545i | −0.0309520 | + | 0.0178701i | ||||
\(795\) | 5.73331 | + | 5.73331i | 0.203340 | + | 0.203340i | ||||
\(796\) | −15.1101 | + | 8.72381i | −0.535563 | + | 0.309207i | ||||
\(797\) | −16.0998 | − | 27.8857i | −0.570285 | − | 0.987763i | −0.996536 | − | 0.0831583i | \(-0.973499\pi\) |
0.426251 | − | 0.904605i | \(-0.359834\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.75426 | − | 17.7431i | 0.168193 | − | 0.627707i | ||||
\(800\) | 2.93459 | − | 2.93459i | 0.103754 | − | 0.103754i | ||||
\(801\) | −5.38699 | + | 20.1045i | −0.190340 | + | 0.710358i | ||||
\(802\) | 10.0498 | − | 17.4068i | 0.354871 | − | 0.614655i | ||||
\(803\) | −0.715059 | − | 1.23852i | −0.0252339 | − | 0.0437064i | ||||
\(804\) | 0.427240 | − | 0.114479i | 0.0150676 | − | 0.00403735i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 52.1261 | + | 3.17219i | 1.83606 | + | 0.111736i | ||||
\(807\) | −0.101604 | + | 0.175984i | −0.00357664 | + | 0.00619492i | ||||
\(808\) | −11.2848 | + | 11.2848i | −0.396997 | + | 0.396997i | ||||
\(809\) | 11.7932 | 0.414629 | 0.207314 | − | 0.978274i | \(-0.433528\pi\) | ||||
0.207314 | + | 0.978274i | \(0.433528\pi\) | |||||||
\(810\) | −18.5478 | −0.651705 | ||||||||
\(811\) | 14.4330 | − | 14.4330i | 0.506811 | − | 0.506811i | −0.406735 | − | 0.913546i | \(-0.633333\pi\) |
0.913546 | + | 0.406735i | \(0.133333\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.5335 | + | 4.43015i | 0.579856 | + | 0.155372i | ||||
\(814\) | 2.04281 | + | 7.62388i | 0.0716005 | + | 0.267217i | ||||
\(815\) | −28.6480 | − | 16.5399i | −1.00350 | − | 0.579369i | ||||
\(816\) | 18.9477i | 0.663302i | ||||||||
\(817\) | −0.628174 | + | 2.34438i | −0.0219770 | + | 0.0820194i | ||||
\(818\) | 19.4551 | 0.680232 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.56926 | 0.194487 | ||||||||
\(821\) | −2.34685 | + | 8.75856i | −0.0819056 | + | 0.305676i | −0.994710 | − | 0.102721i | \(-0.967245\pi\) |
0.912805 | + | 0.408396i | \(0.133912\pi\) | |||||||
\(822\) | 11.4947i | 0.400925i | ||||||||
\(823\) | 14.1019 | + | 8.14175i | 0.491562 | + | 0.283804i | 0.725222 | − | 0.688515i | \(-0.241737\pi\) |
−0.233660 | + | 0.972318i | \(0.575070\pi\) | |||||||
\(824\) | 5.34038 | + | 19.9306i | 0.186041 | + | 0.694314i | ||||
\(825\) | 0.579957 | + | 0.155399i | 0.0201915 | + | 0.00541030i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.1227 | + | 27.1227i | −0.943148 | + | 0.943148i | −0.998469 | − | 0.0553203i | \(-0.982382\pi\) |
0.0553203 | + | 0.998469i | \(0.482382\pi\) | |||||||
\(828\) | 6.27265 | 0.217990 | ||||||||
\(829\) | 2.81059 | 0.0976158 | 0.0488079 | − | 0.998808i | \(-0.484458\pi\) | ||||
0.0488079 | + | 0.998808i | \(0.484458\pi\) | |||||||
\(830\) | −4.17051 | + | 4.17051i | −0.144760 | + | 0.144760i | ||||
\(831\) | −4.83150 | + | 8.36841i | −0.167603 | + | 0.290297i | ||||
\(832\) | 8.62510 | − | 4.30360i | 0.299021 | − | 0.149201i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 16.8218 | − | 4.50738i | 0.582490 | − | 0.156078i | ||||
\(835\) | 6.75692 | + | 11.7033i | 0.233833 | + | 0.405010i | ||||
\(836\) | −1.11534 | + | 1.93183i | −0.0385750 | + | 0.0668138i | ||||
\(837\) | 7.97816 | − | 29.7749i | 0.275765 | − | 1.02917i | ||||
\(838\) | 42.4077 | − | 42.4077i | 1.46495 | − | 1.46495i | ||||
\(839\) | −9.79321 | + | 36.5488i | −0.338099 | + | 1.26180i | 0.562371 | + | 0.826885i | \(0.309889\pi\) |
−0.900470 | + | 0.434918i | \(0.856777\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.2485 | − | 21.2150i | −0.422363 | − | 0.731553i | ||||
\(842\) | 7.12836 | − | 4.11556i | 0.245660 | − | 0.141832i | ||||
\(843\) | 3.44767 | + | 3.44767i | 0.118744 | + | 0.118744i | ||||
\(844\) | −10.3654 | + | 5.98444i | −0.356790 | + | 0.205993i | ||||
\(845\) | −24.2362 | − | 9.77483i | −0.833749 | − | 0.336264i | ||||
\(846\) | − | 13.3389i | − | 0.458602i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −15.6961 | + | 27.1864i | −0.539006 | + | 0.933586i | ||||
\(849\) | − | 1.14312i | − | 0.0392319i | ||||||
\(850\) | −9.29265 | − | 2.48996i | −0.318735 | − | 0.0854049i | ||||
\(851\) | −13.8481 | + | 3.71058i | −0.474706 | + | 0.127197i | ||||
\(852\) | 4.24583 | + | 4.24583i | 0.145460 | + | 0.145460i | ||||
\(853\) | 7.88711 | + | 7.88711i | 0.270050 | + | 0.270050i | 0.829120 | − | 0.559070i | \(-0.188842\pi\) |
−0.559070 | + | 0.829120i | \(0.688842\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.6757 | + | 7.31833i | 0.433501 | + | 0.250282i | ||||
\(856\) | 25.1612 | + | 6.74193i | 0.859993 | + | 0.230434i | ||||
\(857\) | −8.86465 | − | 15.3540i | −0.302811 | − | 0.524483i | 0.673961 | − | 0.738767i | \(-0.264592\pi\) |
−0.976771 | + | 0.214284i | \(0.931258\pi\) | |||||||
\(858\) | −3.15588 | − | 2.08745i | −0.107740 | − | 0.0712643i | ||||
\(859\) | −3.20832 | − | 1.85233i | −0.109467 | − | 0.0632005i | 0.444267 | − | 0.895894i | \(-0.353464\pi\) |
−0.553734 | + | 0.832694i | \(0.686797\pi\) | |||||||
\(860\) | 0.363970 | + | 1.35835i | 0.0124113 | + | 0.0463195i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.712607 | + | 0.411424i | −0.0242715 | + | 0.0140132i | ||||
\(863\) | −38.0906 | + | 10.2063i | −1.29662 | + | 0.347428i | −0.840171 | − | 0.542322i | \(-0.817545\pi\) |
−0.456448 | + | 0.889750i | \(0.650879\pi\) | |||||||
\(864\) | 3.99561 | + | 14.9118i | 0.135933 | + | 0.507310i | ||||
\(865\) | 4.95174 | + | 18.4801i | 0.168364 | + | 0.628344i | ||||
\(866\) | −28.7965 | + | 7.71601i | −0.978546 | + | 0.262201i | ||||
\(867\) | 10.3986 | − | 6.00364i | 0.353155 | − | 0.203894i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.94827 | − | 11.0031i | −0.100013 | − | 0.373254i | ||||
\(870\) | −13.6109 | − | 7.85827i | −0.461454 | − | 0.266420i | ||||
\(871\) | −0.979596 | + | 2.93068i | −0.0331924 | + | 0.0993023i | ||||
\(872\) | −11.6853 | − | 20.2395i | −0.395713 | − | 0.685394i | ||||
\(873\) | 31.3155 | + | 8.39095i | 1.05987 | + | 0.283991i | ||||
\(874\) | −12.1812 | − | 7.03283i | −0.412036 | − | 0.237889i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.531592 | − | 0.531592i | −0.0179608 | − | 0.0179608i | ||||
\(877\) | −28.1504 | − | 28.1504i | −0.950570 | − | 0.950570i | 0.0482643 | − | 0.998835i | \(-0.484631\pi\) |
−0.998835 | + | 0.0482643i | \(0.984631\pi\) | |||||||
\(878\) | −46.3064 | + | 12.4078i | −1.56277 | + | 0.418742i | ||||
\(879\) | 16.3202 | + | 4.37298i | 0.550467 | + | 0.147497i | ||||
\(880\) | − | 9.79616i | − | 0.330229i | ||||||
\(881\) | −1.49665 | + | 2.59227i | −0.0504233 | + | 0.0873357i | −0.890135 | − | 0.455696i | \(-0.849390\pi\) |
0.839712 | + | 0.543032i | \(0.182724\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1.38623i | − | 0.0466504i | −0.999728 | − | 0.0233252i | \(-0.992575\pi\) | ||
0.999728 | − | 0.0233252i | \(-0.00742531\pi\) | |||||||
\(884\) | 14.5666 | + | 9.63502i | 0.489927 | + | 0.324061i | ||||
\(885\) | 0.564925 | − | 0.326160i | 0.0189897 | − | 0.0109637i | ||||
\(886\) | 8.73647 | + | 8.73647i | 0.293508 | + | 0.293508i | ||||
\(887\) | 30.8094 | − | 17.7878i | 1.03448 | − | 0.597256i | 0.116214 | − | 0.993224i | \(-0.462924\pi\) |
0.918264 | + | 0.395968i | \(0.129591\pi\) | |||||||
\(888\) | −3.05254 | − | 5.28716i | −0.102437 | − | 0.177425i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 6.99906 | − | 26.1209i | 0.234609 | − | 0.875573i | ||||
\(891\) | 3.82161 | − | 3.82161i | 0.128029 | − | 0.128029i | ||||
\(892\) | −4.47166 | + | 16.6885i | −0.149722 | + | 0.558771i | ||||
\(893\) | −4.30817 | + | 7.46197i | −0.144168 | + | 0.249705i | ||||
\(894\) | −9.99780 | − | 17.3167i | −0.334376 | − | 0.579157i | ||||
\(895\) | −11.6642 | + | 3.12540i | −0.389890 | + | 0.104471i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.79166 | − | 5.73238i | 0.126600 | − | 0.191398i | ||||
\(898\) | −19.5402 | + | 33.8446i | −0.652065 | + | 1.12941i | ||||
\(899\) | −44.6931 | + | 44.6931i | −1.49060 | + | 1.49060i | ||||
\(900\) | −2.01244 | −0.0670815 | ||||||||
\(901\) | 37.8558 | 1.26116 | ||||||||
\(902\) | −3.98343 | + | 3.98343i | −0.132634 | + | 0.132634i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −15.6439 | − | 4.19178i | −0.520310 | − | 0.139417i | ||||
\(905\) | 3.15274 | + | 11.7662i | 0.104801 | + | 0.391121i | ||||
\(906\) | −0.0337282 | − | 0.0194730i | −0.00112054 | − | 0.000646946i | ||||
\(907\) | 49.8113i | 1.65396i | 0.562233 | + | 0.826979i | \(0.309942\pi\) | ||||
−0.562233 | + | 0.826979i | \(0.690058\pi\) | |||||||
\(908\) | 2.83116 | − | 10.5660i | 0.0939553 | − | 0.350646i | ||||
\(909\) | 20.7368 | 0.687795 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −55.7036 | −1.84554 | −0.922772 | − | 0.385347i | \(-0.874082\pi\) | ||||
−0.922772 | + | 0.385347i | \(0.874082\pi\) | |||||||
\(912\) | 2.30033 | − | 8.58493i | 0.0761714 | − | 0.284276i | ||||
\(913\) | − | 1.71859i | − | 0.0568769i | ||||||
\(914\) | −6.54953 | − | 3.78137i | −0.216639 | − | 0.125077i | ||||
\(915\) | 4.32299 | + | 16.1336i | 0.142914 | + | 0.533360i | ||||
\(916\) | 5.62180 | + | 1.50636i | 0.185749 | + | 0.0497714i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 25.3049 | − | 25.3049i | 0.835187 | − | 0.835187i | ||||
\(919\) | −20.0645 | −0.661867 | −0.330934 | − | 0.943654i | \(-0.607364\pi\) | ||||
−0.330934 | + | 0.943654i | \(0.607364\pi\) | |||||||
\(920\) | 11.9917 | 0.395356 | ||||||||
\(921\) | 0.986663 | − | 0.986663i | 0.0325116 | − | 0.0325116i | ||||
\(922\) | −27.9203 | + | 48.3594i | −0.919506 | + | 1.59263i | ||||
\(923\) | −41.1038 | + | 8.37574i | −1.35295 | + | 0.275691i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.44286 | − | 1.19046i | 0.146080 | − | 0.0391421i | ||||
\(926\) | 34.4873 | + | 59.7338i | 1.13332 | + | 1.96297i | ||||
\(927\) | 13.4054 | − | 23.2188i | 0.440290 | − | 0.762605i | ||||
\(928\) | 8.19279 | − | 30.5759i | 0.268942 | − | 1.00370i | ||||
\(929\) | −22.3969 | + | 22.3969i | −0.734818 | + | 0.734818i | −0.971570 | − | 0.236752i | \(-0.923917\pi\) |
0.236752 | + | 0.971570i | \(0.423917\pi\) | |||||||
\(930\) | −4.80595 | + | 17.9360i | −0.157593 | + | 0.588146i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 9.38923 | + | 16.2626i | 0.307555 | + | 0.532700i | ||||
\(933\) | 16.2016 | − | 9.35397i | 0.530415 | − | 0.306235i | ||||
\(934\) | −6.77600 | − | 6.77600i | −0.221717 | − | 0.221717i | ||||
\(935\) | −10.2305 | + | 5.90659i | −0.334574 | + | 0.193166i | ||||
\(936\) | −17.6985 | − | 5.91584i | −0.578495 | − | 0.193365i | ||||
\(937\) | 43.3600i | 1.41651i | 0.705957 | + | 0.708255i | \(0.250517\pi\) | ||||
−0.705957 | + | 0.708255i | \(0.749483\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.92359 | − | 15.4561i | 0.291210 | − | 0.504391i | ||||
\(940\) | 4.99238i | 0.162834i | ||||||||
\(941\) | −37.4931 | − | 10.0463i | −1.22224 | − | 0.327499i | −0.410688 | − | 0.911776i | \(-0.634711\pi\) |
−0.811554 | + | 0.584277i | \(0.801378\pi\) | |||||||
\(942\) | 7.42224 | − | 1.98878i | 0.241830 | − | 0.0647980i | ||||
\(943\) | −7.23554 | − | 7.23554i | −0.235622 | − | 0.235622i | ||||
\(944\) | 1.78586 | + | 1.78586i | 0.0581246 | + | 0.0581246i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.23190 | − | 0.711236i | −0.0400524 | − | 0.0231243i | ||||
\(947\) | −39.8444 | − | 10.6763i | −1.29477 | − | 0.346932i | −0.455299 | − | 0.890339i | \(-0.650468\pi\) |
−0.839470 | + | 0.543406i | \(0.817134\pi\) | |||||||
\(948\) | −2.99408 | − | 5.18590i | −0.0972431 | − | 0.168430i | ||||
\(949\) | 5.14634 | − | 1.04867i | 0.167057 | − | 0.0340413i | ||||
\(950\) | 3.90808 | + | 2.25633i | 0.126795 | + | 0.0732050i | ||||
\(951\) | −1.29813 | − | 4.84468i | −0.0420947 | − | 0.157100i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.00364 | + | 5.19825i | −0.291656 | + | 0.168388i | −0.638689 | − | 0.769465i | \(-0.720523\pi\) |
0.347032 | + | 0.937853i | \(0.387189\pi\) | |||||||
\(954\) | 26.5529 | − | 7.11482i | 0.859681 | − | 0.230351i | ||||
\(955\) | 11.2524 | + | 41.9947i | 0.364120 | + | 1.35892i | ||||
\(956\) | 0.821387 | + | 3.06546i | 0.0265655 | + | 0.0991439i | ||||
\(957\) | 4.42352 | − | 1.18528i | 0.142992 | − | 0.0383146i | ||||
\(958\) | 48.3721 | − | 27.9277i | 1.56283 | − | 0.902301i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.887075 | + | 3.31061i | 0.0286302 | + | 0.106850i | ||||
\(961\) | 37.8246 | + | 21.8380i | 1.22015 | + | 0.704452i | ||||
\(962\) | −28.9328 | − | 1.76074i | −0.932832 | − | 0.0567685i | ||||
\(963\) | −16.9235 | − | 29.3124i | −0.545353 | − | 0.944580i | ||||
\(964\) | −2.49279 | − | 0.667940i | −0.0802873 | − | 0.0215129i | ||||
\(965\) | 16.8713 | + | 9.74062i | 0.543105 | + | 0.313562i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.1251 | + | 15.1251i | 0.486390 | + | 0.486390i | 0.907165 | − | 0.420775i | \(-0.138242\pi\) |
−0.420775 | + | 0.907165i | \(0.638242\pi\) | |||||||
\(968\) | −14.1634 | − | 14.1634i | −0.455228 | − | 0.455228i | ||||
\(969\) | −10.3526 | + | 2.77396i | −0.332572 | + | 0.0891124i | ||||
\(970\) | −40.6867 | − | 10.9020i | −1.30637 | − | 0.350041i | ||||
\(971\) | 17.4624i | 0.560396i | 0.959942 | + | 0.280198i | \(0.0904002\pi\) | ||||
−0.959942 | + | 0.280198i | \(0.909600\pi\) | |||||||
\(972\) | 5.75056 | − | 9.96026i | 0.184449 | − | 0.319475i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 25.3407i | 0.811968i | ||||||||
\(975\) | −1.21647 | + | 1.83911i | −0.0389583 | + | 0.0588986i | ||||
\(976\) | −56.0040 | + | 32.3339i | −1.79265 | + | 1.03498i | ||||
\(977\) | −8.45756 | − | 8.45756i | −0.270581 | − | 0.270581i | 0.558753 | − | 0.829334i | \(-0.311280\pi\) |
−0.829334 | + | 0.558753i | \(0.811280\pi\) | |||||||
\(978\) | 15.2332 | − | 8.79490i | 0.487104 | − | 0.281230i | ||||
\(979\) | 3.93986 | + | 6.82405i | 0.125919 | + | 0.218097i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.85955 | + | 29.3322i | −0.250936 | + | 0.936506i | ||||
\(982\) | 5.19914 | − | 5.19914i | 0.165911 | − | 0.165911i | ||||
\(983\) | −3.18140 | + | 11.8732i | −0.101471 | + | 0.378695i | −0.997921 | − | 0.0644501i | \(-0.979471\pi\) |
0.896450 | + | 0.443145i | \(0.146137\pi\) | |||||||
\(984\) | 2.17872 | − | 3.77366i | 0.0694551 | − | 0.120300i | ||||
\(985\) | −4.65472 | − | 8.06222i | −0.148312 | − | 0.256884i | ||||
\(986\) | −70.8782 | + | 18.9918i | −2.25722 | + | 0.604821i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.43019 | − | 6.13393i | −0.172757 | − | 0.195146i | ||||
\(989\) | 1.29190 | − | 2.23763i | 0.0410799 | − | 0.0711525i | ||||
\(990\) | −6.06579 | + | 6.06579i | −0.192783 | + | 0.192783i | ||||
\(991\) | −38.3547 | −1.21838 | −0.609189 | − | 0.793025i | \(-0.708505\pi\) | ||||
−0.609189 | + | 0.793025i | \(0.708505\pi\) | |||||||
\(992\) | −37.3991 | −1.18742 | ||||||||
\(993\) | −7.34257 | + | 7.34257i | −0.233009 | + | 0.233009i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 41.8644 | + | 11.2175i | 1.32719 | + | 0.355619i | ||||
\(996\) | −0.233824 | − | 0.872644i | −0.00740901 | − | 0.0276508i | ||||
\(997\) | −33.1334 | − | 19.1296i | −1.04935 | − | 0.605840i | −0.126879 | − | 0.991918i | \(-0.540496\pi\) |
−0.922466 | + | 0.386078i | \(0.873829\pi\) | |||||||
\(998\) | − | 33.5892i | − | 1.06325i | ||||||
\(999\) | −4.42832 | + | 16.5267i | −0.140106 | + | 0.522882i |
(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 | 637.2.x.b.215.2 | 32 | ||
7.2 | even | 3 | 91.2.bc.a.20.7 | ✓ | 32 | ||
7.3 | odd | 6 | 637.2.bb.b.423.1 | 32 | |||
7.4 | even | 3 | 637.2.bb.b.423.2 | 32 | |||
7.5 | odd | 6 | 91.2.bc.a.20.8 | yes | 32 | ||
7.6 | odd | 2 | inner | 637.2.x.b.215.1 | 32 | ||
13.2 | odd | 12 | 637.2.bb.b.509.1 | 32 | |||
21.2 | odd | 6 | 819.2.fm.g.748.1 | 32 | |||
21.5 | even | 6 | 819.2.fm.g.748.2 | 32 | |||
91.2 | odd | 12 | 91.2.bc.a.41.8 | yes | 32 | ||
91.41 | even | 12 | 637.2.bb.b.509.2 | 32 | |||
91.54 | even | 12 | 91.2.bc.a.41.7 | yes | 32 | ||
91.67 | odd | 12 | inner | 637.2.x.b.80.2 | 32 | ||
91.80 | even | 12 | inner | 637.2.x.b.80.1 | 32 | ||
273.2 | even | 12 | 819.2.fm.g.496.2 | 32 | |||
273.236 | odd | 12 | 819.2.fm.g.496.1 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.bc.a.20.7 | ✓ | 32 | 7.2 | even | 3 | ||
91.2.bc.a.20.8 | yes | 32 | 7.5 | odd | 6 | ||
91.2.bc.a.41.7 | yes | 32 | 91.54 | even | 12 | ||
91.2.bc.a.41.8 | yes | 32 | 91.2 | odd | 12 | ||
637.2.x.b.80.1 | 32 | 91.80 | even | 12 | inner | ||
637.2.x.b.80.2 | 32 | 91.67 | odd | 12 | inner | ||
637.2.x.b.215.1 | 32 | 7.6 | odd | 2 | inner | ||
637.2.x.b.215.2 | 32 | 1.1 | even | 1 | trivial | ||
637.2.bb.b.423.1 | 32 | 7.3 | odd | 6 | |||
637.2.bb.b.423.2 | 32 | 7.4 | even | 3 | |||
637.2.bb.b.509.1 | 32 | 13.2 | odd | 12 | |||
637.2.bb.b.509.2 | 32 | 91.41 | even | 12 | |||
819.2.fm.g.496.1 | 32 | 273.236 | odd | 12 | |||
819.2.fm.g.496.2 | 32 | 273.2 | even | 12 | |||
819.2.fm.g.748.1 | 32 | 21.2 | odd | 6 | |||
819.2.fm.g.748.2 | 32 | 21.5 | even | 6 |