Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(79,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.4868829729.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - x^{6} + 5x^{5} - 8x^{4} + 15x^{3} - 9x^{2} - 54x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 235.1 | ||
Root | \(-1.70103 + 0.326320i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.235 |
Dual form | 273.2.i.d.79.1 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.13312 | − | 1.96262i | −0.801236 | − | 1.38778i | −0.918803 | − | 0.394716i | \(-0.870843\pi\) |
0.117567 | − | 0.993065i | \(-0.462490\pi\) | |||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | −1.56792 | + | 2.71571i | −0.783958 | + | 1.35785i | ||||
\(5\) | −1.63312 | − | 2.82864i | −0.730353 | − | 1.26501i | −0.956732 | − | 0.290969i | \(-0.906022\pi\) |
0.226380 | − | 0.974039i | \(-0.427311\pi\) | |||||||
\(6\) | 2.26624 | 0.925187 | ||||||||
\(7\) | −0.133118 | + | 2.64240i | −0.0503141 | + | 0.998733i | ||||
\(8\) | 2.57406 | 0.910068 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −3.70103 | + | 6.41038i | −1.17037 | + | 2.02714i | ||||
\(11\) | −1.06520 | + | 1.84499i | −0.321171 | + | 0.556284i | −0.980730 | − | 0.195368i | \(-0.937410\pi\) |
0.659559 | + | 0.751653i | \(0.270743\pi\) | |||||||
\(12\) | −1.56792 | − | 2.71571i | −0.452618 | − | 0.783958i | ||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 5.33686 | − | 2.73289i | 1.42634 | − | 0.730396i | ||||
\(15\) | 3.26624 | 0.843339 | ||||||||
\(16\) | 0.219115 | + | 0.379518i | 0.0547788 | + | 0.0948796i | ||||
\(17\) | −1.72183 | + | 2.98229i | −0.417604 | + | 0.723312i | −0.995698 | − | 0.0926586i | \(-0.970463\pi\) |
0.578094 | + | 0.815970i | \(0.303797\pi\) | |||||||
\(18\) | −1.13312 | + | 1.96262i | −0.267079 | + | 0.462594i | ||||
\(19\) | 0.635830 | + | 1.10129i | 0.145869 | + | 0.252653i | 0.929697 | − | 0.368325i | \(-0.120069\pi\) |
−0.783828 | + | 0.620979i | \(0.786735\pi\) | |||||||
\(20\) | 10.2424 | 2.29026 | ||||||||
\(21\) | −2.22183 | − | 1.43648i | −0.484842 | − | 0.313467i | ||||
\(22\) | 4.82801 | 1.02933 | ||||||||
\(23\) | 4.48806 | + | 7.77355i | 0.935826 | + | 1.62090i | 0.773154 | + | 0.634218i | \(0.218678\pi\) |
0.162671 | + | 0.986680i | \(0.447989\pi\) | |||||||
\(24\) | −1.28703 | + | 2.22920i | −0.262714 | + | 0.455034i | ||||
\(25\) | −2.83415 | + | 4.90890i | −0.566830 | + | 0.981779i | ||||
\(26\) | 1.13312 | + | 1.96262i | 0.222223 | + | 0.384901i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −6.96727 | − | 4.50457i | −1.31669 | − | 0.851284i | ||||
\(29\) | −8.53790 | −1.58545 | −0.792724 | − | 0.609581i | \(-0.791338\pi\) | ||||
−0.792724 | + | 0.609581i | \(0.791338\pi\) | |||||||
\(30\) | −3.70103 | − | 6.41038i | −0.675713 | − | 1.17037i | ||||
\(31\) | 1.78703 | − | 3.09523i | 0.320960 | − | 0.555919i | −0.659726 | − | 0.751506i | \(-0.729328\pi\) |
0.980686 | + | 0.195587i | \(0.0626611\pi\) | |||||||
\(32\) | 3.07063 | − | 5.31848i | 0.542815 | − | 0.940184i | ||||
\(33\) | −1.06520 | − | 1.84499i | −0.185428 | − | 0.321171i | ||||
\(34\) | 7.80413 | 1.33840 | ||||||||
\(35\) | 7.69181 | − | 3.93881i | 1.30015 | − | 0.665780i | ||||
\(36\) | 3.13583 | 0.522638 | ||||||||
\(37\) | 0.890499 | + | 1.54239i | 0.146397 | + | 0.253567i | 0.929893 | − | 0.367829i | \(-0.119899\pi\) |
−0.783496 | + | 0.621397i | \(0.786566\pi\) | |||||||
\(38\) | 1.44094 | − | 2.49578i | 0.233752 | − | 0.404870i | ||||
\(39\) | 0.500000 | − | 0.866025i | 0.0800641 | − | 0.138675i | ||||
\(40\) | −4.20375 | − | 7.28110i | −0.664670 | − | 1.15124i | ||||
\(41\) | 2.95841 | 0.462027 | 0.231013 | − | 0.972951i | \(-0.425796\pi\) | ||||
0.231013 | + | 0.972951i | \(0.425796\pi\) | |||||||
\(42\) | −0.301678 | + | 5.98831i | −0.0465499 | + | 0.924016i | ||||
\(43\) | −11.7803 | −1.79647 | −0.898236 | − | 0.439512i | \(-0.855151\pi\) | ||||
−0.898236 | + | 0.439512i | \(0.855151\pi\) | |||||||
\(44\) | −3.34030 | − | 5.78556i | −0.503569 | − | 0.872207i | ||||
\(45\) | −1.63312 | + | 2.82864i | −0.243451 | + | 0.421669i | ||||
\(46\) | 10.1710 | − | 17.6167i | 1.49963 | − | 2.59744i | ||||
\(47\) | −3.61233 | − | 6.25673i | −0.526912 | − | 0.912638i | −0.999508 | − | 0.0313590i | \(-0.990016\pi\) |
0.472596 | − | 0.881279i | \(-0.343317\pi\) | |||||||
\(48\) | −0.438230 | −0.0632531 | ||||||||
\(49\) | −6.96456 | − | 0.703505i | −0.994937 | − | 0.100501i | ||||
\(50\) | 12.8457 | 1.81666 | ||||||||
\(51\) | −1.72183 | − | 2.98229i | −0.241104 | − | 0.417604i | ||||
\(52\) | 1.56792 | − | 2.71571i | 0.217431 | − | 0.376601i | ||||
\(53\) | −5.60310 | + | 9.70485i | −0.769645 | + | 1.33306i | 0.168110 | + | 0.985768i | \(0.446233\pi\) |
−0.937755 | + | 0.347296i | \(0.887100\pi\) | |||||||
\(54\) | −1.13312 | − | 1.96262i | −0.154198 | − | 0.267079i | ||||
\(55\) | 6.95841 | 0.938272 | ||||||||
\(56\) | −0.342655 | + | 6.80170i | −0.0457892 | + | 0.908915i | ||||
\(57\) | −1.27166 | −0.168435 | ||||||||
\(58\) | 9.67445 | + | 16.7566i | 1.27032 | + | 2.20025i | ||||
\(59\) | −2.97921 | + | 5.16014i | −0.387860 | + | 0.671793i | −0.992161 | − | 0.124963i | \(-0.960119\pi\) |
0.604302 | + | 0.796756i | \(0.293452\pi\) | |||||||
\(60\) | −5.12118 | + | 8.87015i | −0.661142 | + | 1.14513i | ||||
\(61\) | −1.45559 | − | 2.52116i | −0.186369 | − | 0.322801i | 0.757668 | − | 0.652640i | \(-0.226339\pi\) |
−0.944037 | + | 0.329839i | \(0.893005\pi\) | |||||||
\(62\) | −8.09967 | −1.02866 | ||||||||
\(63\) | 2.35495 | − | 1.20592i | 0.296695 | − | 0.151931i | ||||
\(64\) | −13.0411 | −1.63013 | ||||||||
\(65\) | 1.63312 | + | 2.82864i | 0.202563 | + | 0.350850i | ||||
\(66\) | −2.41400 | + | 4.18118i | −0.297143 | + | 0.514667i | ||||
\(67\) | −3.20103 | + | 5.54435i | −0.391068 | + | 0.677350i | −0.992591 | − | 0.121506i | \(-0.961228\pi\) |
0.601522 | + | 0.798856i | \(0.294561\pi\) | |||||||
\(68\) | −5.39936 | − | 9.35196i | −0.654768 | − | 1.13409i | ||||
\(69\) | −8.97613 | −1.08060 | ||||||||
\(70\) | −16.4461 | − | 10.6330i | −1.96569 | − | 1.27088i | ||||
\(71\) | 4.23007 | 0.502017 | 0.251009 | − | 0.967985i | \(-0.419238\pi\) | ||||
0.251009 | + | 0.967985i | \(0.419238\pi\) | |||||||
\(72\) | −1.28703 | − | 2.22920i | −0.151678 | − | 0.262714i | ||||
\(73\) | 0.479207 | − | 0.830011i | 0.0560869 | − | 0.0971454i | −0.836619 | − | 0.547786i | \(-0.815471\pi\) |
0.892706 | + | 0.450640i | \(0.148804\pi\) | |||||||
\(74\) | 2.01808 | − | 3.49542i | 0.234597 | − | 0.406334i | ||||
\(75\) | −2.83415 | − | 4.90890i | −0.327260 | − | 0.566830i | ||||
\(76\) | −3.98771 | −0.457422 | ||||||||
\(77\) | −4.73339 | − | 3.06030i | −0.539420 | − | 0.348753i | ||||
\(78\) | −2.26624 | −0.256601 | ||||||||
\(79\) | −1.65662 | − | 2.86936i | −0.186385 | − | 0.322828i | 0.757658 | − | 0.652652i | \(-0.226344\pi\) |
−0.944042 | + | 0.329825i | \(0.893010\pi\) | |||||||
\(80\) | 0.715682 | − | 1.23960i | 0.0800156 | − | 0.138591i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −3.35223 | − | 5.80624i | −0.370192 | − | 0.641192i | ||||
\(83\) | −10.4779 | −1.15009 | −0.575047 | − | 0.818120i | \(-0.695016\pi\) | ||||
−0.575047 | + | 0.818120i | \(0.695016\pi\) | |||||||
\(84\) | 7.38471 | − | 3.78155i | 0.805738 | − | 0.412601i | ||||
\(85\) | 11.2478 | 1.21999 | ||||||||
\(86\) | 13.3484 | + | 23.1202i | 1.43940 | + | 2.49311i | ||||
\(87\) | 4.26895 | − | 7.39404i | 0.457679 | − | 0.792724i | ||||
\(88\) | −2.74190 | + | 4.74911i | −0.292287 | + | 0.506256i | ||||
\(89\) | −7.54712 | − | 13.0720i | −0.799993 | − | 1.38563i | −0.919620 | − | 0.392810i | \(-0.871503\pi\) |
0.119626 | − | 0.992819i | \(-0.461830\pi\) | |||||||
\(90\) | 7.40207 | 0.780246 | ||||||||
\(91\) | 0.133118 | − | 2.64240i | 0.0139546 | − | 0.276999i | ||||
\(92\) | −28.1476 | −2.93459 | ||||||||
\(93\) | 1.78703 | + | 3.09523i | 0.185306 | + | 0.320960i | ||||
\(94\) | −8.18639 | + | 14.1792i | −0.844361 | + | 1.46248i | ||||
\(95\) | 2.07677 | − | 3.59707i | 0.213072 | − | 0.369052i | ||||
\(96\) | 3.07063 | + | 5.31848i | 0.313395 | + | 0.542815i | ||||
\(97\) | 3.78100 | 0.383902 | 0.191951 | − | 0.981404i | \(-0.438519\pi\) | ||||
0.191951 | + | 0.981404i | \(0.438519\pi\) | |||||||
\(98\) | 6.51096 | + | 14.4659i | 0.657706 | + | 1.46128i | ||||
\(99\) | 2.13041 | 0.214114 | ||||||||
\(100\) | −8.88742 | − | 15.3935i | −0.888742 | − | 1.53935i | ||||
\(101\) | 4.85777 | − | 8.41390i | 0.483366 | − | 0.837215i | −0.516451 | − | 0.856316i | \(-0.672747\pi\) |
0.999818 | + | 0.0191018i | \(0.00608066\pi\) | |||||||
\(102\) | −3.90207 | + | 6.75858i | −0.386362 | + | 0.669199i | ||||
\(103\) | 6.24816 | + | 10.8221i | 0.615649 | + | 1.06634i | 0.990270 | + | 0.139157i | \(0.0444394\pi\) |
−0.374621 | + | 0.927178i | \(0.622227\pi\) | |||||||
\(104\) | −2.57406 | −0.252407 | ||||||||
\(105\) | −0.434797 | + | 8.63071i | −0.0424318 | + | 0.842271i | ||||
\(106\) | 25.3959 | 2.46667 | ||||||||
\(107\) | 6.44648 | + | 11.1656i | 0.623204 | + | 1.07942i | 0.988885 | + | 0.148681i | \(0.0475029\pi\) |
−0.365681 | + | 0.930740i | \(0.619164\pi\) | |||||||
\(108\) | −1.56792 | + | 2.71571i | −0.150873 | + | 0.261319i | ||||
\(109\) | 3.68295 | − | 6.37906i | 0.352763 | − | 0.611003i | −0.633970 | − | 0.773358i | \(-0.718576\pi\) |
0.986732 | + | 0.162355i | \(0.0519089\pi\) | |||||||
\(110\) | −7.88471 | − | 13.6567i | −0.751777 | − | 1.30212i | ||||
\(111\) | −1.78100 | −0.169045 | ||||||||
\(112\) | −1.03201 | + | 0.528469i | −0.0975156 | + | 0.0499356i | ||||
\(113\) | 12.7333 | 1.19784 | 0.598922 | − | 0.800808i | \(-0.295596\pi\) | ||||
0.598922 | + | 0.800808i | \(0.295596\pi\) | |||||||
\(114\) | 1.44094 | + | 2.49578i | 0.134957 | + | 0.233752i | ||||
\(115\) | 14.6591 | − | 25.3903i | 1.36697 | − | 2.36765i | ||||
\(116\) | 13.3867 | − | 23.1864i | 1.24292 | − | 2.15281i | ||||
\(117\) | 0.500000 | + | 0.866025i | 0.0462250 | + | 0.0800641i | ||||
\(118\) | 13.5032 | 1.24307 | ||||||||
\(119\) | −7.65120 | − | 4.94675i | −0.701384 | − | 0.453468i | ||||
\(120\) | 8.40749 | 0.767495 | ||||||||
\(121\) | 3.23068 | + | 5.59571i | 0.293698 | + | 0.508701i | ||||
\(122\) | −3.29871 | + | 5.71353i | −0.298651 | + | 0.517279i | ||||
\(123\) | −1.47921 | + | 2.56206i | −0.133376 | + | 0.231013i | ||||
\(124\) | 5.60382 | + | 9.70611i | 0.503238 | + | 0.871634i | ||||
\(125\) | 2.18284 | 0.195239 | ||||||||
\(126\) | −5.03519 | − | 3.25541i | −0.448570 | − | 0.290015i | ||||
\(127\) | 10.5972 | 0.940349 | 0.470175 | − | 0.882573i | \(-0.344191\pi\) | ||||
0.470175 | + | 0.882573i | \(0.344191\pi\) | |||||||
\(128\) | 8.63583 | + | 14.9577i | 0.763307 | + | 1.32209i | ||||
\(129\) | 5.89013 | − | 10.2020i | 0.518597 | − | 0.898236i | ||||
\(130\) | 3.70103 | − | 6.41038i | 0.324602 | − | 0.562227i | ||||
\(131\) | −8.64198 | − | 14.9683i | −0.755053 | − | 1.30779i | −0.945348 | − | 0.326063i | \(-0.894278\pi\) |
0.190295 | − | 0.981727i | \(-0.439055\pi\) | |||||||
\(132\) | 6.68059 | 0.581471 | ||||||||
\(133\) | −2.99469 | + | 1.53352i | −0.259673 | + | 0.132973i | ||||
\(134\) | 14.5086 | 1.25335 | ||||||||
\(135\) | −1.63312 | − | 2.82864i | −0.140556 | − | 0.243451i | ||||
\(136\) | −4.43208 | + | 7.67660i | −0.380048 | + | 0.658263i | ||||
\(137\) | −8.06755 | + | 13.9734i | −0.689257 | + | 1.19383i | 0.282822 | + | 0.959173i | \(0.408730\pi\) |
−0.972079 | + | 0.234656i | \(0.924604\pi\) | |||||||
\(138\) | 10.1710 | + | 17.6167i | 0.865814 | + | 1.49963i | ||||
\(139\) | 1.31325 | 0.111388 | 0.0556940 | − | 0.998448i | \(-0.482263\pi\) | ||||
0.0556940 | + | 0.998448i | \(0.482263\pi\) | |||||||
\(140\) | −1.36345 | + | 27.0644i | −0.115232 | + | 2.28736i | ||||
\(141\) | 7.22465 | 0.608425 | ||||||||
\(142\) | −4.79318 | − | 8.30202i | −0.402234 | − | 0.696690i | ||||
\(143\) | 1.06520 | − | 1.84499i | 0.0890768 | − | 0.154286i | ||||
\(144\) | 0.219115 | − | 0.379518i | 0.0182596 | − | 0.0316265i | ||||
\(145\) | 13.9434 | + | 24.1507i | 1.15794 | + | 2.00560i | ||||
\(146\) | −2.17199 | −0.179755 | ||||||||
\(147\) | 4.09153 | − | 5.67973i | 0.337464 | − | 0.468456i | ||||
\(148\) | −5.58491 | −0.459076 | ||||||||
\(149\) | −2.82801 | − | 4.89825i | −0.231679 | − | 0.401280i | 0.726623 | − | 0.687036i | \(-0.241089\pi\) |
−0.958302 | + | 0.285756i | \(0.907755\pi\) | |||||||
\(150\) | −6.42286 | + | 11.1247i | −0.524424 | + | 0.908330i | ||||
\(151\) | 4.19181 | − | 7.26043i | 0.341125 | − | 0.590845i | −0.643517 | − | 0.765432i | \(-0.722526\pi\) |
0.984642 | + | 0.174587i | \(0.0558589\pi\) | |||||||
\(152\) | 1.63666 | + | 2.83479i | 0.132751 | + | 0.229932i | ||||
\(153\) | 3.44365 | 0.278403 | ||||||||
\(154\) | −0.642697 | + | 12.7575i | −0.0517900 | + | 1.02803i | ||||
\(155\) | −11.6737 | −0.937656 | ||||||||
\(156\) | 1.56792 | + | 2.71571i | 0.125534 | + | 0.217431i | ||||
\(157\) | 1.24544 | − | 2.15717i | 0.0993972 | − | 0.172161i | −0.812038 | − | 0.583604i | \(-0.801642\pi\) |
0.911435 | + | 0.411443i | \(0.134975\pi\) | |||||||
\(158\) | −3.75430 | + | 6.50264i | −0.298676 | + | 0.517322i | ||||
\(159\) | −5.60310 | − | 9.70485i | −0.444355 | − | 0.769645i | ||||
\(160\) | −20.0588 | −1.58579 | ||||||||
\(161\) | −21.1383 | + | 10.8245i | −1.66593 | + | 0.853087i | ||||
\(162\) | 2.26624 | 0.178052 | ||||||||
\(163\) | −5.64209 | − | 9.77238i | −0.441922 | − | 0.765432i | 0.555910 | − | 0.831243i | \(-0.312370\pi\) |
−0.997832 | + | 0.0658106i | \(0.979037\pi\) | |||||||
\(164\) | −4.63854 | + | 8.03419i | −0.362209 | + | 0.627365i | ||||
\(165\) | −3.47921 | + | 6.02616i | −0.270856 | + | 0.469136i | ||||
\(166\) | 11.8727 | + | 20.5640i | 0.921497 | + | 1.59608i | ||||
\(167\) | 3.27166 | 0.253169 | 0.126584 | − | 0.991956i | \(-0.459599\pi\) | ||||
0.126584 | + | 0.991956i | \(0.459599\pi\) | |||||||
\(168\) | −5.71912 | − | 3.69760i | −0.441239 | − | 0.285276i | ||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −12.7451 | − | 22.0751i | −0.977503 | − | 1.69308i | ||||
\(171\) | 0.635830 | − | 1.10129i | 0.0486231 | − | 0.0842177i | ||||
\(172\) | 18.4704 | − | 31.9918i | 1.40836 | − | 2.43935i | ||||
\(173\) | 9.90207 | + | 17.1509i | 0.752840 | + | 1.30396i | 0.946441 | + | 0.322877i | \(0.104650\pi\) |
−0.193601 | + | 0.981080i | \(0.562017\pi\) | |||||||
\(174\) | −19.3489 | −1.46684 | ||||||||
\(175\) | −12.5940 | − | 8.14243i | −0.952016 | − | 0.615510i | ||||
\(176\) | −0.933608 | −0.0703734 | ||||||||
\(177\) | −2.97921 | − | 5.16014i | −0.223931 | − | 0.387860i | ||||
\(178\) | −17.1036 | + | 29.6242i | −1.28197 | + | 2.22043i | ||||
\(179\) | 1.52362 | − | 2.63898i | 0.113881 | − | 0.197247i | −0.803451 | − | 0.595371i | \(-0.797005\pi\) |
0.917332 | + | 0.398124i | \(0.130339\pi\) | |||||||
\(180\) | −5.12118 | − | 8.87015i | −0.381710 | − | 0.661142i | ||||
\(181\) | 10.7931 | 0.802242 | 0.401121 | − | 0.916025i | \(-0.368621\pi\) | ||||
0.401121 | + | 0.916025i | \(0.368621\pi\) | |||||||
\(182\) | −5.33686 | + | 2.73289i | −0.395595 | + | 0.202575i | ||||
\(183\) | 2.91118 | 0.215201 | ||||||||
\(184\) | 11.5525 | + | 20.0096i | 0.851665 | + | 1.47513i | ||||
\(185\) | 2.90858 | − | 5.03781i | 0.213843 | − | 0.370387i | ||||
\(186\) | 4.04983 | − | 7.01452i | 0.296948 | − | 0.514329i | ||||
\(187\) | −3.66819 | − | 6.35349i | −0.268245 | − | 0.464613i | ||||
\(188\) | 22.6553 | 1.65231 | ||||||||
\(189\) | −0.133118 | + | 2.64240i | −0.00968295 | + | 0.192206i | ||||
\(190\) | −9.41291 | −0.682885 | ||||||||
\(191\) | 9.07135 | + | 15.7120i | 0.656380 | + | 1.13688i | 0.981546 | + | 0.191226i | \(0.0612464\pi\) |
−0.325166 | + | 0.945657i | \(0.605420\pi\) | |||||||
\(192\) | 6.52054 | − | 11.2939i | 0.470579 | − | 0.815067i | ||||
\(193\) | −3.90195 | + | 6.75838i | −0.280869 | + | 0.486479i | −0.971599 | − | 0.236634i | \(-0.923956\pi\) |
0.690730 | + | 0.723113i | \(0.257289\pi\) | |||||||
\(194\) | −4.28432 | − | 7.42066i | −0.307596 | − | 0.532772i | ||||
\(195\) | −3.26624 | −0.233900 | ||||||||
\(196\) | 12.8304 | − | 17.8107i | 0.916454 | − | 1.27219i | ||||
\(197\) | −5.12476 | −0.365124 | −0.182562 | − | 0.983194i | \(-0.558439\pi\) | ||||
−0.182562 | + | 0.983194i | \(0.558439\pi\) | |||||||
\(198\) | −2.41400 | − | 4.18118i | −0.171556 | − | 0.297143i | ||||
\(199\) | −4.52904 | + | 7.84453i | −0.321055 | + | 0.556084i | −0.980706 | − | 0.195488i | \(-0.937371\pi\) |
0.659651 | + | 0.751572i | \(0.270704\pi\) | |||||||
\(200\) | −7.29528 | + | 12.6358i | −0.515854 | + | 0.893485i | ||||
\(201\) | −3.20103 | − | 5.54435i | −0.225783 | − | 0.391068i | ||||
\(202\) | −22.0177 | −1.54916 | ||||||||
\(203\) | 1.13655 | − | 22.5605i | 0.0797703 | − | 1.58344i | ||||
\(204\) | 10.7987 | 0.756061 | ||||||||
\(205\) | −4.83144 | − | 8.36830i | −0.337442 | − | 0.584467i | ||||
\(206\) | 14.1598 | − | 24.5255i | 0.986560 | − | 1.70877i | ||||
\(207\) | 4.48806 | − | 7.77355i | 0.311942 | − | 0.540299i | ||||
\(208\) | −0.219115 | − | 0.379518i | −0.0151929 | − | 0.0263149i | ||||
\(209\) | −2.70915 | −0.187396 | ||||||||
\(210\) | 17.4315 | − | 8.92627i | 1.20289 | − | 0.615971i | ||||
\(211\) | −5.28960 | −0.364151 | −0.182075 | − | 0.983285i | \(-0.558282\pi\) | ||||
−0.182075 | + | 0.983285i | \(0.558282\pi\) | |||||||
\(212\) | −17.5704 | − | 30.4328i | −1.20674 | − | 2.09013i | ||||
\(213\) | −2.11504 | + | 3.66335i | −0.144920 | + | 0.251009i | ||||
\(214\) | 14.6092 | − | 25.3040i | 0.998667 | − | 1.72974i | ||||
\(215\) | 19.2386 | + | 33.3222i | 1.31206 | + | 2.27255i | ||||
\(216\) | 2.57406 | 0.175143 | ||||||||
\(217\) | 7.94094 | + | 5.13408i | 0.539066 | + | 0.348524i | ||||
\(218\) | −16.6929 | −1.13058 | ||||||||
\(219\) | 0.479207 | + | 0.830011i | 0.0323818 | + | 0.0560869i | ||||
\(220\) | −10.9102 | + | 18.8970i | −0.735566 | + | 1.27404i | ||||
\(221\) | 1.72183 | − | 2.98229i | 0.115823 | − | 0.200611i | ||||
\(222\) | 2.01808 | + | 3.49542i | 0.135445 | + | 0.234597i | ||||
\(223\) | −23.5197 | −1.57499 | −0.787497 | − | 0.616319i | \(-0.788623\pi\) | ||||
−0.787497 | + | 0.616319i | \(0.788623\pi\) | |||||||
\(224\) | 13.6448 | + | 8.82181i | 0.911682 | + | 0.589432i | ||||
\(225\) | 5.66830 | 0.377887 | ||||||||
\(226\) | −14.4283 | − | 24.9905i | −0.959755 | − | 1.66234i | ||||
\(227\) | −5.40207 | + | 9.35665i | −0.358548 | + | 0.621023i | −0.987718 | − | 0.156244i | \(-0.950061\pi\) |
0.629171 | + | 0.777267i | \(0.283395\pi\) | |||||||
\(228\) | 1.99385 | − | 3.45346i | 0.132046 | − | 0.228711i | ||||
\(229\) | 14.9342 | + | 25.8667i | 0.986878 | + | 1.70932i | 0.633275 | + | 0.773927i | \(0.281710\pi\) |
0.353603 | + | 0.935395i | \(0.384956\pi\) | |||||||
\(230\) | −66.4419 | −4.38105 | ||||||||
\(231\) | 5.01699 | − | 2.56909i | 0.330094 | − | 0.169034i | ||||
\(232\) | −21.9771 | −1.44286 | ||||||||
\(233\) | −5.47330 | − | 9.48004i | −0.358568 | − | 0.621058i | 0.629154 | − | 0.777281i | \(-0.283402\pi\) |
−0.987722 | + | 0.156223i | \(0.950068\pi\) | |||||||
\(234\) | 1.13312 | − | 1.96262i | 0.0740743 | − | 0.128300i | ||||
\(235\) | −11.7987 | + | 20.4360i | −0.769663 | + | 1.33310i | ||||
\(236\) | −9.34229 | − | 16.1813i | −0.608131 | − | 1.05331i | ||||
\(237\) | 3.31325 | 0.215218 | ||||||||
\(238\) | −1.03887 | + | 20.6216i | −0.0673402 | + | 1.33670i | ||||
\(239\) | 30.2945 | 1.95959 | 0.979795 | − | 0.200007i | \(-0.0640964\pi\) | ||||
0.979795 | + | 0.200007i | \(0.0640964\pi\) | |||||||
\(240\) | 0.715682 | + | 1.23960i | 0.0461970 | + | 0.0800156i | ||||
\(241\) | −11.9048 | + | 20.6197i | −0.766854 | + | 1.32823i | 0.172406 | + | 0.985026i | \(0.444846\pi\) |
−0.939261 | + | 0.343205i | \(0.888488\pi\) | |||||||
\(242\) | 7.32149 | − | 12.6812i | 0.470643 | − | 0.815178i | ||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 9.12896 | 0.584422 | ||||||||
\(245\) | 9.38399 | + | 20.8492i | 0.599521 | + | 1.33200i | ||||
\(246\) | 6.70447 | 0.427461 | ||||||||
\(247\) | −0.635830 | − | 1.10129i | −0.0404569 | − | 0.0700734i | ||||
\(248\) | 4.59992 | − | 7.96730i | 0.292095 | − | 0.505924i | ||||
\(249\) | 5.23893 | − | 9.07409i | 0.332004 | − | 0.575047i | ||||
\(250\) | −2.47342 | − | 4.28408i | −0.156433 | − | 0.270949i | ||||
\(251\) | 20.5084 | 1.29448 | 0.647239 | − | 0.762287i | \(-0.275924\pi\) | ||||
0.647239 | + | 0.762287i | \(0.275924\pi\) | |||||||
\(252\) | −0.417437 | + | 8.28612i | −0.0262961 | + | 0.521976i | ||||
\(253\) | −19.1228 | −1.20224 | ||||||||
\(254\) | −12.0079 | − | 20.7983i | −0.753441 | − | 1.30500i | ||||
\(255\) | −5.62389 | + | 9.74087i | −0.352182 | + | 0.609997i | ||||
\(256\) | 6.52976 | − | 11.3099i | 0.408110 | − | 0.706868i | ||||
\(257\) | −1.34598 | − | 2.33130i | −0.0839597 | − | 0.145422i | 0.820988 | − | 0.570946i | \(-0.193423\pi\) |
−0.904947 | + | 0.425523i | \(0.860090\pi\) | |||||||
\(258\) | −26.6969 | −1.66207 | ||||||||
\(259\) | −4.19415 | + | 2.14773i | −0.260612 | + | 0.133454i | ||||
\(260\) | −10.2424 | −0.635204 | ||||||||
\(261\) | 4.26895 | + | 7.39404i | 0.264241 | + | 0.457679i | ||||
\(262\) | −19.5848 | + | 33.9218i | −1.20995 | + | 2.09570i | ||||
\(263\) | 1.33415 | − | 2.31082i | 0.0822673 | − | 0.142491i | −0.821956 | − | 0.569551i | \(-0.807117\pi\) |
0.904224 | + | 0.427060i | \(0.140451\pi\) | |||||||
\(264\) | −2.74190 | − | 4.74911i | −0.168752 | − | 0.292287i | ||||
\(265\) | 36.6021 | 2.24845 | ||||||||
\(266\) | 6.40304 | + | 4.13978i | 0.392596 | + | 0.253826i | ||||
\(267\) | 15.0942 | 0.923753 | ||||||||
\(268\) | −10.0379 | − | 17.3861i | −0.613162 | − | 1.06203i | ||||
\(269\) | −0.449557 | + | 0.778656i | −0.0274100 | + | 0.0474755i | −0.879405 | − | 0.476074i | \(-0.842059\pi\) |
0.851995 | + | 0.523550i | \(0.175393\pi\) | |||||||
\(270\) | −3.70103 | + | 6.41038i | −0.225238 | + | 0.390123i | ||||
\(271\) | −11.0287 | − | 19.1022i | −0.669944 | − | 1.16038i | −0.977919 | − | 0.208983i | \(-0.932985\pi\) |
0.307975 | − | 0.951394i | \(-0.400349\pi\) | |||||||
\(272\) | −1.50911 | −0.0915034 | ||||||||
\(273\) | 2.22183 | + | 1.43648i | 0.134471 | + | 0.0869400i | ||||
\(274\) | 36.5659 | 2.20903 | ||||||||
\(275\) | −6.03790 | − | 10.4579i | −0.364099 | − | 0.630638i | ||||
\(276\) | 14.0738 | − | 24.3765i | 0.847143 | − | 1.46730i | ||||
\(277\) | −4.83415 | + | 8.37300i | −0.290456 | + | 0.503085i | −0.973918 | − | 0.226902i | \(-0.927140\pi\) |
0.683462 | + | 0.729986i | \(0.260474\pi\) | |||||||
\(278\) | −1.48806 | − | 2.57740i | −0.0892481 | − | 0.154582i | ||||
\(279\) | −3.57406 | −0.213973 | ||||||||
\(280\) | 19.7992 | − | 10.1387i | 1.18323 | − | 0.605905i | ||||
\(281\) | −27.1538 | −1.61986 | −0.809929 | − | 0.586528i | \(-0.800494\pi\) | ||||
−0.809929 | + | 0.586528i | \(0.800494\pi\) | |||||||
\(282\) | −8.18639 | − | 14.1792i | −0.487492 | − | 0.844361i | ||||
\(283\) | 13.7949 | − | 23.8935i | 0.820022 | − | 1.42032i | −0.0856426 | − | 0.996326i | \(-0.527294\pi\) |
0.905665 | − | 0.423994i | \(-0.139372\pi\) | |||||||
\(284\) | −6.63240 | + | 11.4876i | −0.393560 | + | 0.681666i | ||||
\(285\) | 2.07677 | + | 3.59707i | 0.123017 | + | 0.213072i | ||||
\(286\) | −4.82801 | −0.285486 | ||||||||
\(287\) | −0.393820 | + | 7.81731i | −0.0232464 | + | 0.461441i | ||||
\(288\) | −6.14125 | −0.361877 | ||||||||
\(289\) | 2.57063 | + | 4.45246i | 0.151213 | + | 0.261909i | ||||
\(290\) | 31.5990 | − | 54.7311i | 1.85556 | − | 3.21392i | ||||
\(291\) | −1.89050 | + | 3.27444i | −0.110823 | + | 0.191951i | ||||
\(292\) | 1.50271 | + | 2.60277i | 0.0879395 | + | 0.152316i | ||||
\(293\) | 0.331470 | 0.0193647 | 0.00968236 | − | 0.999953i | \(-0.496918\pi\) | ||||
0.00968236 | + | 0.999953i | \(0.496918\pi\) | |||||||
\(294\) | −15.7833 | − | 1.59431i | −0.920503 | − | 0.0929819i | ||||
\(295\) | 19.4616 | 1.13310 | ||||||||
\(296\) | 2.29220 | + | 3.97020i | 0.133231 | + | 0.230763i | ||||
\(297\) | −1.06520 | + | 1.84499i | −0.0618094 | + | 0.107057i | ||||
\(298\) | −6.40893 | + | 11.1006i | −0.371260 | + | 0.643040i | ||||
\(299\) | −4.48806 | − | 7.77355i | −0.259551 | − | 0.449556i | ||||
\(300\) | 17.7748 | 1.02623 | ||||||||
\(301\) | 1.56817 | − | 31.1282i | 0.0903878 | − | 1.79420i | ||||
\(302\) | −18.9993 | −1.09328 | ||||||||
\(303\) | 4.85777 | + | 8.41390i | 0.279072 | + | 0.483366i | ||||
\(304\) | −0.278640 | + | 0.482618i | −0.0159811 | + | 0.0276801i | ||||
\(305\) | −4.75430 | + | 8.23469i | −0.272230 | + | 0.471517i | ||||
\(306\) | −3.90207 | − | 6.75858i | −0.223066 | − | 0.386362i | ||||
\(307\) | 2.21236 | 0.126266 | 0.0631331 | − | 0.998005i | \(-0.479891\pi\) | ||||
0.0631331 | + | 0.998005i | \(0.479891\pi\) | |||||||
\(308\) | 15.7324 | − | 8.05624i | 0.896439 | − | 0.459047i | ||||
\(309\) | −12.4963 | −0.710890 | ||||||||
\(310\) | 13.2277 | + | 22.9111i | 0.751284 | + | 1.30126i | ||||
\(311\) | 4.35162 | − | 7.53723i | 0.246758 | − | 0.427397i | −0.715866 | − | 0.698237i | \(-0.753968\pi\) |
0.962624 | + | 0.270840i | \(0.0873014\pi\) | |||||||
\(312\) | 1.28703 | − | 2.22920i | 0.0728637 | − | 0.126204i | ||||
\(313\) | −17.2034 | − | 29.7971i | −0.972392 | − | 1.68423i | −0.688285 | − | 0.725441i | \(-0.741636\pi\) |
−0.284107 | − | 0.958792i | \(-0.591697\pi\) | |||||||
\(314\) | −5.64494 | −0.318563 | ||||||||
\(315\) | −7.25701 | − | 4.69190i | −0.408886 | − | 0.264358i | ||||
\(316\) | 10.3898 | 0.584471 | ||||||||
\(317\) | 4.74164 | + | 8.21277i | 0.266317 | + | 0.461275i | 0.967908 | − | 0.251305i | \(-0.0808598\pi\) |
−0.701591 | + | 0.712580i | \(0.747526\pi\) | |||||||
\(318\) | −12.6980 | + | 21.9935i | −0.712066 | + | 1.23333i | ||||
\(319\) | 9.09460 | − | 15.7523i | 0.509200 | − | 0.881960i | ||||
\(320\) | 21.2976 | + | 36.8886i | 1.19057 | + | 2.06213i | ||||
\(321\) | −12.8930 | −0.719615 | ||||||||
\(322\) | 45.1965 | + | 29.2210i | 2.51870 | + | 1.62842i | ||||
\(323\) | −4.37916 | −0.243663 | ||||||||
\(324\) | −1.56792 | − | 2.71571i | −0.0871064 | − | 0.150873i | ||||
\(325\) | 2.83415 | − | 4.90890i | 0.157210 | − | 0.272297i | ||||
\(326\) | −12.7863 | + | 22.1465i | −0.708168 | + | 1.22658i | ||||
\(327\) | 3.68295 | + | 6.37906i | 0.203668 | + | 0.352763i | ||||
\(328\) | 7.61514 | 0.420475 | ||||||||
\(329\) | 17.0137 | − | 8.71232i | 0.937993 | − | 0.480326i | ||||
\(330\) | 15.7694 | 0.868078 | ||||||||
\(331\) | 4.06188 | + | 7.03539i | 0.223261 | + | 0.386700i | 0.955796 | − | 0.294029i | \(-0.0949964\pi\) |
−0.732535 | + | 0.680729i | \(0.761663\pi\) | |||||||
\(332\) | 16.4284 | − | 28.4548i | 0.901625 | − | 1.56166i | ||||
\(333\) | 0.890499 | − | 1.54239i | 0.0487990 | − | 0.0845224i | ||||
\(334\) | −3.70718 | − | 6.42102i | −0.202848 | − | 0.351343i | ||||
\(335\) | 20.9107 | 1.14247 | ||||||||
\(336\) | 0.0583365 | − | 1.15798i | 0.00318252 | − | 0.0631729i | ||||
\(337\) | −31.5558 | −1.71896 | −0.859478 | − | 0.511173i | \(-0.829211\pi\) | ||||
−0.859478 | + | 0.511173i | \(0.829211\pi\) | |||||||
\(338\) | −1.13312 | − | 1.96262i | −0.0616335 | − | 0.106752i | ||||
\(339\) | −6.36663 | + | 11.0273i | −0.345788 | + | 0.598922i | ||||
\(340\) | −17.6356 | + | 30.5457i | −0.956423 | + | 1.65657i | ||||
\(341\) | 3.80710 | + | 6.59409i | 0.206166 | + | 0.357090i | ||||
\(342\) | −2.88188 | −0.155834 | ||||||||
\(343\) | 2.78605 | − | 18.3095i | 0.150433 | − | 0.988620i | ||||
\(344\) | −30.3231 | −1.63491 | ||||||||
\(345\) | 14.6591 | + | 25.3903i | 0.789218 | + | 1.36697i | ||||
\(346\) | 22.4404 | − | 38.8680i | 1.20641 | − | 2.08955i | ||||
\(347\) | 1.27546 | − | 2.20916i | 0.0684704 | − | 0.118594i | −0.829758 | − | 0.558124i | \(-0.811521\pi\) |
0.898228 | + | 0.439529i | \(0.144855\pi\) | |||||||
\(348\) | 13.3867 | + | 23.1864i | 0.717602 | + | 1.24292i | ||||
\(349\) | −7.54309 | −0.403773 | −0.201886 | − | 0.979409i | \(-0.564707\pi\) | ||||
−0.201886 | + | 0.979409i | \(0.564707\pi\) | |||||||
\(350\) | −1.71000 | + | 33.9435i | −0.0914035 | + | 1.81436i | ||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 6.54168 | + | 11.3305i | 0.348673 | + | 0.603919i | ||||
\(353\) | −1.28334 | + | 2.22281i | −0.0683053 | + | 0.118308i | −0.898155 | − | 0.439678i | \(-0.855093\pi\) |
0.829850 | + | 0.557986i | \(0.188426\pi\) | |||||||
\(354\) | −6.75159 | + | 11.6941i | −0.358843 | + | 0.621534i | ||||
\(355\) | −6.90821 | − | 11.9654i | −0.366650 | − | 0.635056i | ||||
\(356\) | 47.3330 | 2.50864 | ||||||||
\(357\) | 8.10961 | − | 4.15276i | 0.429206 | − | 0.219787i | ||||
\(358\) | −6.90576 | −0.364981 | ||||||||
\(359\) | 14.8495 | + | 25.7201i | 0.783728 | + | 1.35746i | 0.929756 | + | 0.368176i | \(0.120018\pi\) |
−0.146028 | + | 0.989280i | \(0.546649\pi\) | |||||||
\(360\) | −4.20375 | + | 7.28110i | −0.221557 | + | 0.383748i | ||||
\(361\) | 8.69144 | − | 15.0540i | 0.457444 | − | 0.792317i | ||||
\(362\) | −12.2298 | − | 21.1827i | −0.642785 | − | 1.11334i | ||||
\(363\) | −6.46137 | −0.339134 | ||||||||
\(364\) | 6.96727 | + | 4.50457i | 0.365184 | + | 0.236104i | ||||
\(365\) | −3.13041 | −0.163853 | ||||||||
\(366\) | −3.29871 | − | 5.71353i | −0.172426 | − | 0.298651i | ||||
\(367\) | 1.49187 | − | 2.58399i | 0.0778747 | − | 0.134883i | −0.824458 | − | 0.565923i | \(-0.808520\pi\) |
0.902333 | + | 0.431040i | \(0.141853\pi\) | |||||||
\(368\) | −1.96680 | + | 3.40660i | −0.102527 | + | 0.177582i | ||||
\(369\) | −1.47921 | − | 2.56206i | −0.0770044 | − | 0.133376i | ||||
\(370\) | −13.1831 | −0.685355 | ||||||||
\(371\) | −24.8982 | − | 16.0975i | −1.29265 | − | 0.835742i | ||||
\(372\) | −11.2076 | −0.581089 | ||||||||
\(373\) | −17.4579 | − | 30.2380i | −0.903936 | − | 1.56566i | −0.822339 | − | 0.568998i | \(-0.807331\pi\) |
−0.0815967 | − | 0.996665i | \(-0.526002\pi\) | |||||||
\(374\) | −8.31299 | + | 14.3985i | −0.429855 | + | 0.744530i | ||||
\(375\) | −1.09142 | + | 1.89039i | −0.0563607 | + | 0.0976195i | ||||
\(376\) | −9.29834 | − | 16.1052i | −0.479525 | − | 0.830562i | ||||
\(377\) | 8.53790 | 0.439724 | ||||||||
\(378\) | 5.33686 | − | 2.73289i | 0.274499 | − | 0.140565i | ||||
\(379\) | −13.1172 | −0.673783 | −0.336891 | − | 0.941543i | \(-0.609376\pi\) | ||||
−0.336891 | + | 0.941543i | \(0.609376\pi\) | |||||||
\(380\) | 6.51240 | + | 11.2798i | 0.334079 | + | 0.578642i | ||||
\(381\) | −5.29860 | + | 9.17744i | −0.271455 | + | 0.470175i | ||||
\(382\) | 20.5578 | − | 35.6072i | 1.05183 | − | 1.82182i | ||||
\(383\) | 8.66548 | + | 15.0091i | 0.442785 | + | 0.766927i | 0.997895 | − | 0.0648505i | \(-0.0206570\pi\) |
−0.555110 | + | 0.831777i | \(0.687324\pi\) | |||||||
\(384\) | −17.2717 | −0.881391 | ||||||||
\(385\) | −0.926294 | + | 18.3869i | −0.0472083 | + | 0.937084i | ||||
\(386\) | 17.6855 | 0.900169 | ||||||||
\(387\) | 5.89013 | + | 10.2020i | 0.299412 | + | 0.518597i | ||||
\(388\) | −5.92828 | + | 10.2681i | −0.300963 | + | 0.521283i | ||||
\(389\) | 10.1952 | − | 17.6587i | 0.516919 | − | 0.895330i | −0.482888 | − | 0.875682i | \(-0.660412\pi\) |
0.999807 | − | 0.0196482i | \(-0.00625461\pi\) | |||||||
\(390\) | 3.70103 | + | 6.41038i | 0.187409 | + | 0.324602i | ||||
\(391\) | −30.9107 | −1.56322 | ||||||||
\(392\) | −17.9272 | − | 1.81086i | −0.905460 | − | 0.0914624i | ||||
\(393\) | 17.2840 | 0.871860 | ||||||||
\(394\) | 5.80696 | + | 10.0579i | 0.292550 | + | 0.506712i | ||||
\(395\) | −5.41092 | + | 9.37199i | −0.272253 | + | 0.471556i | ||||
\(396\) | −3.34030 | + | 5.78556i | −0.167856 | + | 0.290736i | ||||
\(397\) | −5.17644 | − | 8.96585i | −0.259798 | − | 0.449983i | 0.706390 | − | 0.707823i | \(-0.250323\pi\) |
−0.966188 | + | 0.257840i | \(0.916989\pi\) | |||||||
\(398\) | 20.5278 | 1.02896 | ||||||||
\(399\) | 0.169281 | − | 3.36024i | 0.00847467 | − | 0.168222i | ||||
\(400\) | −2.48402 | −0.124201 | ||||||||
\(401\) | −0.809925 | − | 1.40283i | −0.0404457 | − | 0.0700541i | 0.845094 | − | 0.534618i | \(-0.179544\pi\) |
−0.885540 | + | 0.464564i | \(0.846211\pi\) | |||||||
\(402\) | −7.25430 | + | 12.5648i | −0.361812 | + | 0.626676i | ||||
\(403\) | −1.78703 | + | 3.09523i | −0.0890183 | + | 0.154184i | ||||
\(404\) | 15.2331 | + | 26.3846i | 0.757877 | + | 1.31268i | ||||
\(405\) | 3.26624 | 0.162301 | ||||||||
\(406\) | −45.5656 | + | 23.3331i | −2.26138 | + | 1.15800i | ||||
\(407\) | −3.79425 | −0.188074 | ||||||||
\(408\) | −4.43208 | − | 7.67660i | −0.219421 | − | 0.380048i | ||||
\(409\) | −5.12758 | + | 8.88123i | −0.253543 | + | 0.439149i | −0.964499 | − | 0.264088i | \(-0.914929\pi\) |
0.710956 | + | 0.703236i | \(0.248262\pi\) | |||||||
\(410\) | −10.9492 | + | 18.9646i | −0.540742 | + | 0.936592i | ||||
\(411\) | −8.06755 | − | 13.9734i | −0.397943 | − | 0.689257i | ||||
\(412\) | −39.1863 | −1.93057 | ||||||||
\(413\) | −13.2386 | − | 8.55917i | −0.651427 | − | 0.421169i | ||||
\(414\) | −20.3420 | −0.999756 | ||||||||
\(415\) | 17.1116 | + | 29.6381i | 0.839975 | + | 1.45488i | ||||
\(416\) | −3.07063 | + | 5.31848i | −0.150550 | + | 0.260760i | ||||
\(417\) | −0.656623 | + | 1.13730i | −0.0321550 | + | 0.0556940i | ||||
\(418\) | 3.06979 | + | 5.31704i | 0.150148 | + | 0.260065i | ||||
\(419\) | −34.2709 | −1.67424 | −0.837122 | − | 0.547016i | \(-0.815764\pi\) | ||||
−0.837122 | + | 0.547016i | \(0.815764\pi\) | |||||||
\(420\) | −22.7568 | − | 14.7130i | −1.11042 | − | 0.717921i | ||||
\(421\) | 22.8979 | 1.11597 | 0.557987 | − | 0.829850i | \(-0.311574\pi\) | ||||
0.557987 | + | 0.829850i | \(0.311574\pi\) | |||||||
\(422\) | 5.99374 | + | 10.3815i | 0.291771 | + | 0.505362i | ||||
\(423\) | −3.61233 | + | 6.25673i | −0.175637 | + | 0.304213i | ||||
\(424\) | −14.4227 | + | 24.9809i | −0.700429 | + | 1.21318i | ||||
\(425\) | −9.75984 | − | 16.9045i | −0.473422 | − | 0.819990i | ||||
\(426\) | 9.58635 | 0.464460 | ||||||||
\(427\) | 6.85567 | − | 3.51064i | 0.331769 | − | 0.169892i | ||||
\(428\) | −40.4301 | −1.95426 | ||||||||
\(429\) | 1.06520 | + | 1.84499i | 0.0514285 | + | 0.0890768i | ||||
\(430\) | 43.5991 | − | 75.5159i | 2.10254 | − | 3.64170i | ||||
\(431\) | −2.05869 | + | 3.56576i | −0.0991636 | + | 0.171756i | −0.911339 | − | 0.411657i | \(-0.864950\pi\) |
0.812175 | + | 0.583414i | \(0.198283\pi\) | |||||||
\(432\) | 0.219115 | + | 0.379518i | 0.0105422 | + | 0.0182596i | ||||
\(433\) | 25.2549 | 1.21367 | 0.606836 | − | 0.794827i | \(-0.292438\pi\) | ||||
0.606836 | + | 0.794827i | \(0.292438\pi\) | |||||||
\(434\) | 1.07822 | − | 21.4026i | 0.0517560 | − | 1.02736i | ||||
\(435\) | −27.8868 | −1.33707 | ||||||||
\(436\) | 11.5491 | + | 20.0036i | 0.553102 | + | 0.958001i | ||||
\(437\) | −5.70729 | + | 9.88532i | −0.273017 | + | 0.472879i | ||||
\(438\) | 1.08600 | − | 1.88100i | 0.0518909 | − | 0.0898777i | ||||
\(439\) | −0.819150 | − | 1.41881i | −0.0390959 | − | 0.0677161i | 0.845815 | − | 0.533476i | \(-0.179114\pi\) |
−0.884911 | + | 0.465760i | \(0.845781\pi\) | |||||||
\(440\) | 17.9114 | 0.853891 | ||||||||
\(441\) | 2.87303 | + | 6.38324i | 0.136811 | + | 0.303964i | ||||
\(442\) | −7.80413 | −0.371205 | ||||||||
\(443\) | 14.5940 | + | 25.2775i | 0.693381 | + | 1.20097i | 0.970723 | + | 0.240200i | \(0.0772132\pi\) |
−0.277342 | + | 0.960771i | \(0.589454\pi\) | |||||||
\(444\) | 2.79245 | − | 4.83667i | 0.132524 | − | 0.229538i | ||||
\(445\) | −24.6507 | + | 42.6962i | −1.16855 | + | 2.02400i | ||||
\(446\) | 26.6506 | + | 46.1602i | 1.26194 | + | 2.18575i | ||||
\(447\) | 5.65601 | 0.267520 | ||||||||
\(448\) | 1.73601 | − | 34.4597i | 0.0820187 | − | 1.62807i | ||||
\(449\) | −8.63336 | −0.407433 | −0.203717 | − | 0.979030i | \(-0.565302\pi\) | ||||
−0.203717 | + | 0.979030i | \(0.565302\pi\) | |||||||
\(450\) | −6.42286 | − | 11.1247i | −0.302777 | − | 0.524424i | ||||
\(451\) | −3.15131 | + | 5.45823i | −0.148390 | + | 0.257018i | ||||
\(452\) | −19.9647 | + | 34.5798i | −0.939058 | + | 1.62650i | ||||
\(453\) | 4.19181 | + | 7.26043i | 0.196948 | + | 0.341125i | ||||
\(454\) | 24.4847 | 1.14913 | ||||||||
\(455\) | −7.69181 | + | 3.93881i | −0.360598 | + | 0.184654i | ||||
\(456\) | −3.27333 | −0.153288 | ||||||||
\(457\) | −3.72736 | − | 6.45598i | −0.174359 | − | 0.301998i | 0.765580 | − | 0.643340i | \(-0.222452\pi\) |
−0.939939 | + | 0.341342i | \(0.889119\pi\) | |||||||
\(458\) | 33.8444 | − | 58.6202i | 1.58144 | − | 2.73914i | ||||
\(459\) | −1.72183 | + | 2.98229i | −0.0803680 | + | 0.139201i | ||||
\(460\) | 45.9684 | + | 79.6196i | 2.14329 | + | 3.71228i | ||||
\(461\) | 13.8405 | 0.644617 | 0.322309 | − | 0.946635i | \(-0.395541\pi\) | ||||
0.322309 | + | 0.946635i | \(0.395541\pi\) | |||||||
\(462\) | −10.7270 | − | 6.93536i | −0.499065 | − | 0.322662i | ||||
\(463\) | 23.3893 | 1.08699 | 0.543496 | − | 0.839412i | \(-0.317100\pi\) | ||||
0.543496 | + | 0.839412i | \(0.317100\pi\) | |||||||
\(464\) | −1.87078 | − | 3.24029i | −0.0868488 | − | 0.150427i | ||||
\(465\) | 5.83686 | − | 10.1097i | 0.270678 | − | 0.468828i | ||||
\(466\) | −12.4038 | + | 21.4840i | −0.574595 | + | 0.995228i | ||||
\(467\) | 13.0768 | + | 22.6496i | 0.605121 | + | 1.04810i | 0.992032 | + | 0.125983i | \(0.0402085\pi\) |
−0.386912 | + | 0.922117i | \(0.626458\pi\) | |||||||
\(468\) | −3.13583 | −0.144954 | ||||||||
\(469\) | −14.2243 | − | 9.19647i | −0.656816 | − | 0.424653i | ||||
\(470\) | 53.4774 | 2.46673 | ||||||||
\(471\) | 1.24544 | + | 2.15717i | 0.0573870 | + | 0.0993972i | ||||
\(472\) | −7.66866 | + | 13.2825i | −0.352979 | + | 0.611377i | ||||
\(473\) | 12.5484 | − | 21.7344i | 0.576975 | − | 0.999350i | ||||
\(474\) | −3.75430 | − | 6.50264i | −0.172441 | − | 0.298676i | ||||
\(475\) | −7.20816 | −0.330733 | ||||||||
\(476\) | 25.4304 | − | 13.0223i | 1.16560 | − | 0.596878i | ||||
\(477\) | 11.2062 | 0.513097 | ||||||||
\(478\) | −34.3273 | − | 59.4566i | −1.57009 | − | 2.71948i | ||||
\(479\) | −7.45559 | + | 12.9135i | −0.340655 | + | 0.590031i | −0.984554 | − | 0.175079i | \(-0.943982\pi\) |
0.643900 | + | 0.765110i | \(0.277315\pi\) | |||||||
\(480\) | 10.0294 | − | 17.3714i | 0.457777 | − | 0.792893i | ||||
\(481\) | −0.890499 | − | 1.54239i | −0.0406033 | − | 0.0703269i | ||||
\(482\) | 53.9581 | 2.45772 | ||||||||
\(483\) | 1.19489 | − | 23.7185i | 0.0543693 | − | 1.07923i | ||||
\(484\) | −20.2617 | −0.920988 | ||||||||
\(485\) | −6.17482 | − | 10.6951i | −0.280384 | − | 0.485639i | ||||
\(486\) | −1.13312 | + | 1.96262i | −0.0513993 | + | 0.0890262i | ||||
\(487\) | 1.65970 | − | 2.87469i | 0.0752083 | − | 0.130265i | −0.825969 | − | 0.563716i | \(-0.809371\pi\) |
0.901177 | + | 0.433452i | \(0.142704\pi\) | |||||||
\(488\) | −3.74678 | − | 6.48960i | −0.169609 | − | 0.293771i | ||||
\(489\) | 11.2842 | 0.510288 | ||||||||
\(490\) | 30.2858 | − | 42.0418i | 1.36817 | − | 1.89925i | ||||
\(491\) | 20.7495 | 0.936413 | 0.468206 | − | 0.883619i | \(-0.344900\pi\) | ||||
0.468206 | + | 0.883619i | \(0.344900\pi\) | |||||||
\(492\) | −4.63854 | − | 8.03419i | −0.209122 | − | 0.362209i | ||||
\(493\) | 14.7008 | − | 25.4625i | 0.662090 | − | 1.14677i | ||||
\(494\) | −1.44094 | + | 2.49578i | −0.0648310 | + | 0.112291i | ||||
\(495\) | −3.47921 | − | 6.02616i | −0.156379 | − | 0.270856i | ||||
\(496\) | 1.56626 | 0.0703272 | ||||||||
\(497\) | −0.563101 | + | 11.1775i | −0.0252585 | + | 0.501382i | ||||
\(498\) | −23.7453 | −1.06405 | ||||||||
\(499\) | −12.4855 | − | 21.6255i | −0.558926 | − | 0.968089i | −0.997586 | − | 0.0694355i | \(-0.977880\pi\) |
0.438660 | − | 0.898653i | \(-0.355453\pi\) | |||||||
\(500\) | −3.42251 | + | 5.92796i | −0.153059 | + | 0.265106i | ||||
\(501\) | −1.63583 | + | 2.83334i | −0.0730835 | + | 0.126584i | ||||
\(502\) | −23.2384 | − | 40.2501i | −1.03718 | − | 1.79645i | ||||
\(503\) | −9.50934 | −0.424000 | −0.212000 | − | 0.977270i | \(-0.567998\pi\) | ||||
−0.212000 | + | 0.977270i | \(0.567998\pi\) | |||||||
\(504\) | 6.06177 | − | 3.10410i | 0.270013 | − | 0.138268i | ||||
\(505\) | −31.7333 | −1.41211 | ||||||||
\(506\) | 21.6684 | + | 37.5308i | 0.963278 | + | 1.66845i | ||||
\(507\) | −0.500000 | + | 0.866025i | −0.0222058 | + | 0.0384615i | ||||
\(508\) | −16.6155 | + | 28.7789i | −0.737194 | + | 1.27686i | ||||
\(509\) | −4.64457 | − | 8.04464i | −0.205867 | − | 0.356572i | 0.744542 | − | 0.667576i | \(-0.232668\pi\) |
−0.950409 | + | 0.311004i | \(0.899335\pi\) | |||||||
\(510\) | 25.4902 | 1.12872 | ||||||||
\(511\) | 2.12943 | + | 1.37675i | 0.0942004 | + | 0.0609037i | ||||
\(512\) | 4.94734 | 0.218644 | ||||||||
\(513\) | 0.635830 | + | 1.10129i | 0.0280726 | + | 0.0486231i | ||||
\(514\) | −3.05030 | + | 5.28327i | −0.134543 | + | 0.233035i | ||||
\(515\) | 20.4080 | − | 35.3476i | 0.899282 | − | 1.55760i | ||||
\(516\) | 18.4704 | + | 31.9918i | 0.813116 | + | 1.40836i | ||||
\(517\) | 15.3914 | 0.676915 | ||||||||
\(518\) | 8.96765 | + | 5.79788i | 0.394016 | + | 0.254744i | ||||
\(519\) | −19.8041 | −0.869305 | ||||||||
\(520\) | 4.20375 | + | 7.28110i | 0.184346 | + | 0.319297i | ||||
\(521\) | −5.85434 | + | 10.1400i | −0.256483 | + | 0.444242i | −0.965297 | − | 0.261153i | \(-0.915897\pi\) |
0.708814 | + | 0.705395i | \(0.249230\pi\) | |||||||
\(522\) | 9.67445 | − | 16.7566i | 0.423439 | − | 0.733418i | ||||
\(523\) | 14.4198 | + | 24.9758i | 0.630533 | + | 1.09212i | 0.987443 | + | 0.157976i | \(0.0504970\pi\) |
−0.356910 | + | 0.934139i | \(0.616170\pi\) | |||||||
\(524\) | 54.1995 | 2.36772 | ||||||||
\(525\) | 13.3485 | − | 6.83550i | 0.582578 | − | 0.298326i | ||||
\(526\) | −6.04701 | −0.263662 | ||||||||
\(527\) | 6.15391 | + | 10.6589i | 0.268069 | + | 0.464308i | ||||
\(528\) | 0.466804 | − | 0.808528i | 0.0203150 | − | 0.0351867i | ||||
\(529\) | −28.7854 | + | 49.8578i | −1.25154 | + | 2.16773i | ||||
\(530\) | −41.4745 | − | 71.8360i | −1.80154 | − | 3.12036i | ||||
\(531\) | 5.95841 | 0.258573 | ||||||||
\(532\) | 0.530838 | − | 10.5371i | 0.0230147 | − | 0.456842i | ||||
\(533\) | −2.95841 | −0.128143 | ||||||||
\(534\) | −17.1036 | − | 29.6242i | −0.740144 | − | 1.28197i | ||||
\(535\) | 21.0557 | − | 36.4696i | 0.910318 | − | 1.57672i | ||||
\(536\) | −8.23965 | + | 14.2715i | −0.355899 | + | 0.616435i | ||||
\(537\) | 1.52362 | + | 2.63898i | 0.0657489 | + | 0.113881i | ||||
\(538\) | 2.03761 | 0.0878475 | ||||||||
\(539\) | 8.71663 | − | 12.1001i | 0.375452 | − | 0.521190i | ||||
\(540\) | 10.2424 | 0.440761 | ||||||||
\(541\) | −2.10125 | − | 3.63948i | −0.0903400 | − | 0.156473i | 0.817314 | − | 0.576192i | \(-0.195462\pi\) |
−0.907654 | + | 0.419719i | \(0.862129\pi\) | |||||||
\(542\) | −24.9936 | + | 43.2902i | −1.07357 | + | 1.85947i | ||||
\(543\) | −5.39653 | + | 9.34707i | −0.231587 | + | 0.401121i | ||||
\(544\) | 10.5742 | + | 18.3150i | 0.453364 | + | 0.785249i | ||||
\(545\) | −24.0588 | −1.03057 | ||||||||
\(546\) | 0.301678 | − | 5.98831i | 0.0129106 | − | 0.256276i | ||||
\(547\) | 26.1238 | 1.11697 | 0.558486 | − | 0.829514i | \(-0.311383\pi\) | ||||
0.558486 | + | 0.829514i | \(0.311383\pi\) | |||||||
\(548\) | −25.2985 | − | 43.8182i | −1.08070 | − | 1.87182i | ||||
\(549\) | −1.45559 | + | 2.52116i | −0.0621230 | + | 0.107600i | ||||
\(550\) | −13.6833 | + | 23.7002i | −0.583458 | + | 1.01058i | ||||
\(551\) | −5.42865 | − | 9.40270i | −0.231268 | − | 0.400568i | ||||
\(552\) | −23.1051 | −0.983418 | ||||||||
\(553\) | 7.80251 | − | 3.99550i | 0.331797 | − | 0.169906i | ||||
\(554\) | 21.9107 | 0.930895 | ||||||||
\(555\) | 2.90858 | + | 5.03781i | 0.123462 | + | 0.213843i | ||||
\(556\) | −2.05906 | + | 3.56639i | −0.0873235 | + | 0.151249i | ||||
\(557\) | 19.0885 | − | 33.0622i | 0.808804 | − | 1.40089i | −0.104889 | − | 0.994484i | \(-0.533449\pi\) |
0.913693 | − | 0.406405i | \(-0.133218\pi\) | |||||||
\(558\) | 4.04983 | + | 7.01452i | 0.171443 | + | 0.296948i | ||||
\(559\) | 11.7803 | 0.498252 | ||||||||
\(560\) | 3.18024 | + | 2.05613i | 0.134390 | + | 0.0868874i | ||||
\(561\) | 7.33638 | 0.309742 | ||||||||
\(562\) | 30.7684 | + | 53.2925i | 1.29789 | + | 2.24801i | ||||
\(563\) | 13.7658 | − | 23.8430i | 0.580157 | − | 1.00486i | −0.415303 | − | 0.909683i | \(-0.636324\pi\) |
0.995460 | − | 0.0951789i | \(-0.0303423\pi\) | |||||||
\(564\) | −11.3276 | + | 19.6200i | −0.476980 | + | 0.826153i | ||||
\(565\) | −20.7949 | − | 36.0178i | −0.874848 | − | 1.51528i | ||||
\(566\) | −62.5251 | −2.62812 | ||||||||
\(567\) | −2.22183 | − | 1.43648i | −0.0933079 | − | 0.0603267i | ||||
\(568\) | 10.8885 | 0.456870 | ||||||||
\(569\) | −10.7777 | − | 18.6675i | −0.451824 | − | 0.782583i | 0.546675 | − | 0.837345i | \(-0.315893\pi\) |
−0.998499 | + | 0.0547621i | \(0.982560\pi\) | |||||||
\(570\) | 4.70646 | − | 8.15182i | 0.197132 | − | 0.341442i | ||||
\(571\) | −9.16017 | + | 15.8659i | −0.383341 | + | 0.663966i | −0.991538 | − | 0.129820i | \(-0.958560\pi\) |
0.608196 | + | 0.793787i | \(0.291893\pi\) | |||||||
\(572\) | 3.34030 | + | 5.78556i | 0.139665 | + | 0.241907i | ||||
\(573\) | −18.1427 | −0.757922 | ||||||||
\(574\) | 15.7887 | − | 8.08503i | 0.659006 | − | 0.337462i | ||||
\(575\) | −50.8794 | −2.12182 | ||||||||
\(576\) | 6.52054 | + | 11.2939i | 0.271689 | + | 0.470579i | ||||
\(577\) | −6.10310 | + | 10.5709i | −0.254075 | + | 0.440072i | −0.964644 | − | 0.263556i | \(-0.915104\pi\) |
0.710569 | + | 0.703628i | \(0.248438\pi\) | |||||||
\(578\) | 5.82565 | − | 10.0903i | 0.242315 | − | 0.419702i | ||||
\(579\) | −3.90195 | − | 6.75838i | −0.162160 | − | 0.280869i | ||||
\(580\) | −87.4483 | −3.63109 | ||||||||
\(581\) | 1.39480 | − | 27.6867i | 0.0578659 | − | 1.14864i | ||||
\(582\) | 8.56864 | 0.355181 | ||||||||
\(583\) | −11.9369 | − | 20.6753i | −0.494375 | − | 0.856283i | ||||
\(584\) | 1.23351 | − | 2.13650i | 0.0510429 | − | 0.0884089i | ||||
\(585\) | 1.63312 | − | 2.82864i | 0.0675211 | − | 0.116950i | ||||
\(586\) | −0.375595 | − | 0.650550i | −0.0155157 | − | 0.0268740i | ||||
\(587\) | 13.9272 | 0.574836 | 0.287418 | − | 0.957805i | \(-0.407203\pi\) | ||||
0.287418 | + | 0.957805i | \(0.407203\pi\) | |||||||
\(588\) | 9.00932 | + | 20.0167i | 0.371538 | + | 0.825477i | ||||
\(589\) | 4.54499 | 0.187273 | ||||||||
\(590\) | −22.0523 | − | 38.1957i | −0.907878 | − | 1.57249i | ||||
\(591\) | 2.56238 | − | 4.43817i | 0.105402 | − | 0.182562i | ||||
\(592\) | −0.390243 | + | 0.675921i | −0.0160389 | + | 0.0277802i | ||||
\(593\) | −11.0999 | − | 19.2256i | −0.455819 | − | 0.789501i | 0.542916 | − | 0.839787i | \(-0.317320\pi\) |
−0.998735 | + | 0.0502859i | \(0.983987\pi\) | |||||||
\(594\) | 4.82801 | 0.198096 | ||||||||
\(595\) | −1.49729 | + | 29.7212i | −0.0613828 | + | 1.21845i | ||||
\(596\) | 17.7363 | 0.726507 | ||||||||
\(597\) | −4.52904 | − | 7.84453i | −0.185361 | − | 0.321055i | ||||
\(598\) | −10.1710 | + | 17.6167i | −0.415924 | + | 0.720401i | ||||
\(599\) | −11.9406 | + | 20.6817i | −0.487879 | + | 0.845031i | −0.999903 | − | 0.0139405i | \(-0.995562\pi\) |
0.512024 | + | 0.858971i | \(0.328896\pi\) | |||||||
\(600\) | −7.29528 | − | 12.6358i | −0.297828 | − | 0.515854i | ||||
\(601\) | 40.0534 | 1.63381 | 0.816905 | − | 0.576772i | \(-0.195688\pi\) | ||||
0.816905 | + | 0.576772i | \(0.195688\pi\) | |||||||
\(602\) | −62.8696 | + | 32.1942i | −2.56238 | + | 1.31214i | ||||
\(603\) | 6.40207 | 0.260712 | ||||||||
\(604\) | 13.1448 | + | 22.7675i | 0.534854 | + | 0.926395i | ||||
\(605\) | 10.5522 | − | 18.2769i | 0.429007 | − | 0.743062i | ||||
\(606\) | 11.0089 | − | 19.0679i | 0.447204 | − | 0.774580i | ||||
\(607\) | 9.76515 | + | 16.9137i | 0.396355 | + | 0.686507i | 0.993273 | − | 0.115795i | \(-0.0369416\pi\) |
−0.596918 | + | 0.802302i | \(0.703608\pi\) | |||||||
\(608\) | 7.80959 | 0.316721 | ||||||||
\(609\) | 18.9697 | + | 12.2646i | 0.768692 | + | 0.496985i | ||||
\(610\) | 21.5487 | 0.872483 | ||||||||
\(611\) | 3.61233 | + | 6.25673i | 0.146139 | + | 0.253120i | ||||
\(612\) | −5.39936 | + | 9.35196i | −0.218256 | + | 0.378030i | ||||
\(613\) | −8.96124 | + | 15.5213i | −0.361941 | + | 0.626900i | −0.988280 | − | 0.152650i | \(-0.951219\pi\) |
0.626339 | + | 0.779551i | \(0.284552\pi\) | |||||||
\(614\) | −2.50687 | − | 4.34202i | −0.101169 | − | 0.175230i | ||||
\(615\) | 9.66288 | 0.389645 | ||||||||
\(616\) | −12.1840 | − | 7.87739i | −0.490909 | − | 0.317389i | ||||
\(617\) | −23.8703 | −0.960982 | −0.480491 | − | 0.877000i | \(-0.659542\pi\) | ||||
−0.480491 | + | 0.877000i | \(0.659542\pi\) | |||||||
\(618\) | 14.1598 | + | 24.5255i | 0.569591 | + | 0.986560i | ||||
\(619\) | −22.3244 | + | 38.6670i | −0.897294 | + | 1.55416i | −0.0663545 | + | 0.997796i | \(0.521137\pi\) |
−0.830940 | + | 0.556363i | \(0.812197\pi\) | |||||||
\(620\) | 18.3034 | − | 31.7024i | 0.735083 | − | 1.27320i | ||||
\(621\) | 4.48806 | + | 7.77355i | 0.180100 | + | 0.311942i | ||||
\(622\) | −19.7236 | −0.790845 | ||||||||
\(623\) | 35.5461 | − | 18.2024i | 1.42413 | − | 0.729263i | ||||
\(624\) | 0.438230 | 0.0175432 | ||||||||
\(625\) | 10.6059 | + | 18.3700i | 0.424237 | + | 0.734800i | ||||
\(626\) | −38.9869 | + | 67.5273i | −1.55823 | + | 2.69894i | ||||
\(627\) | 1.35458 | − | 2.34620i | 0.0540966 | − | 0.0936980i | ||||
\(628\) | 3.90550 | + | 6.76453i | 0.155846 | + | 0.269934i | ||||
\(629\) | −6.13314 | −0.244544 | ||||||||
\(630\) | −0.985352 | + | 19.5592i | −0.0392574 | + | 0.779258i | ||||
\(631\) | 10.5992 | 0.421946 | 0.210973 | − | 0.977492i | \(-0.432337\pi\) | ||||
0.210973 | + | 0.977492i | \(0.432337\pi\) | |||||||
\(632\) | −4.26425 | − | 7.38589i | −0.169623 | − | 0.293795i | ||||
\(633\) | 2.64480 | − | 4.58093i | 0.105121 | − | 0.182075i | ||||
\(634\) | 10.7457 | − | 18.6121i | 0.426766 | − | 0.739180i | ||||
\(635\) | −17.3065 | − | 29.9757i | −0.686787 | − | 1.18955i | ||||
\(636\) | 35.1407 | 1.39342 | ||||||||
\(637\) | 6.96456 | + | 0.703505i | 0.275946 | + | 0.0278739i | ||||
\(638\) | −41.2210 | −1.63196 | ||||||||
\(639\) | −2.11504 | − | 3.66335i | −0.0836696 | − | 0.144920i | ||||
\(640\) | 28.2067 | − | 48.8554i | 1.11497 | − | 1.93118i | ||||
\(641\) | 0.760092 | − | 1.31652i | 0.0300218 | − | 0.0519993i | −0.850624 | − | 0.525774i | \(-0.823776\pi\) |
0.880646 | + | 0.473775i | \(0.157109\pi\) | |||||||
\(642\) | 14.6092 | + | 25.3040i | 0.576581 | + | 0.998667i | ||||
\(643\) | 6.86343 | 0.270667 | 0.135334 | − | 0.990800i | \(-0.456789\pi\) | ||||
0.135334 | + | 0.990800i | \(0.456789\pi\) | |||||||
\(644\) | 3.74697 | − | 74.3773i | 0.147651 | − | 2.93087i | ||||
\(645\) | −38.4771 | −1.51504 | ||||||||
\(646\) | 4.96210 | + | 8.59461i | 0.195231 | + | 0.338151i | ||||
\(647\) | −22.1345 | + | 38.3381i | −0.870196 | + | 1.50722i | −0.00840308 | + | 0.999965i | \(0.502675\pi\) |
−0.861793 | + | 0.507260i | \(0.830659\pi\) | |||||||
\(648\) | −1.28703 | + | 2.22920i | −0.0505593 | + | 0.0875713i | ||||
\(649\) | −6.34692 | − | 10.9932i | −0.249139 | − | 0.431521i | ||||
\(650\) | −12.8457 | −0.503851 | ||||||||
\(651\) | −8.41672 | + | 4.31002i | −0.329877 | + | 0.168923i | ||||
\(652\) | 35.3853 | 1.38579 | ||||||||
\(653\) | 3.88127 | + | 6.72256i | 0.151886 | + | 0.263074i | 0.931921 | − | 0.362662i | \(-0.118132\pi\) |
−0.780035 | + | 0.625736i | \(0.784799\pi\) | |||||||
\(654\) | 8.34644 | − | 14.4565i | 0.326372 | − | 0.565292i | ||||
\(655\) | −28.2267 | + | 48.8901i | −1.10291 | + | 1.91030i | ||||
\(656\) | 0.648233 | + | 1.12277i | 0.0253092 | + | 0.0438369i | ||||
\(657\) | −0.958414 | −0.0373913 | ||||||||
\(658\) | −36.3775 | − | 23.5192i | −1.41814 | − | 0.916875i | ||||
\(659\) | −3.76377 | −0.146616 | −0.0733078 | − | 0.997309i | \(-0.523356\pi\) | ||||
−0.0733078 | + | 0.997309i | \(0.523356\pi\) | |||||||
\(660\) | −10.9102 | − | 18.8970i | −0.424679 | − | 0.735566i | ||||
\(661\) | −15.5918 | + | 27.0057i | −0.606450 | + | 1.05040i | 0.385371 | + | 0.922762i | \(0.374074\pi\) |
−0.991821 | + | 0.127640i | \(0.959260\pi\) | |||||||
\(662\) | 9.20519 | − | 15.9439i | 0.357770 | − | 0.619676i | ||||
\(663\) | 1.72183 | + | 2.98229i | 0.0668702 | + | 0.115823i | ||||
\(664\) | −26.9706 | −1.04666 | ||||||||
\(665\) | 9.22845 | + | 5.96650i | 0.357864 | + | 0.231371i | ||||
\(666\) | −4.03616 | −0.156398 | ||||||||
\(667\) | −38.3186 | − | 66.3698i | −1.48370 | − | 2.56985i | ||||
\(668\) | −5.12969 | + | 8.88488i | −0.198473 | + | 0.343766i | ||||
\(669\) | 11.7598 | − | 20.3686i | 0.454662 | − | 0.787497i | ||||
\(670\) | −23.6943 | − | 41.0397i | −0.915389 | − | 1.58550i | ||||
\(671\) | 6.20200 | 0.239425 | ||||||||
\(672\) | −14.4623 | + | 7.40584i | −0.557896 | + | 0.285686i | ||||
\(673\) | −29.1587 | −1.12398 | −0.561992 | − | 0.827142i | \(-0.689965\pi\) | ||||
−0.561992 | + | 0.827142i | \(0.689965\pi\) | |||||||
\(674\) | 35.7565 | + | 61.9321i | 1.37729 | + | 2.38553i | ||||
\(675\) | −2.83415 | + | 4.90890i | −0.109087 | + | 0.188943i | ||||
\(676\) | −1.56792 | + | 2.71571i | −0.0603044 | + | 0.104450i | ||||
\(677\) | 10.3784 | + | 17.9760i | 0.398876 | + | 0.690874i | 0.993588 | − | 0.113065i | \(-0.0360670\pi\) |
−0.594711 | + | 0.803939i | \(0.702734\pi\) | |||||||
\(678\) | 28.8566 | 1.10823 | ||||||||
\(679\) | −0.503321 | + | 9.99091i | −0.0193157 | + | 0.383416i | ||||
\(680\) | 28.9525 | 1.11028 | ||||||||
\(681\) | −5.40207 | − | 9.35665i | −0.207008 | − | 0.358548i | ||||
\(682\) | 8.62779 | − | 14.9438i | 0.330375 | − | 0.572227i | ||||
\(683\) | 12.9259 | − | 22.3884i | 0.494597 | − | 0.856667i | −0.505384 | − | 0.862895i | \(-0.668649\pi\) |
0.999981 | + | 0.00622790i | \(0.00198241\pi\) | |||||||
\(684\) | 1.99385 | + | 3.45346i | 0.0762370 | + | 0.132046i | ||||
\(685\) | 52.7010 | 2.01360 | ||||||||
\(686\) | −39.0915 | + | 15.2789i | −1.49252 | + | 0.583350i | ||||
\(687\) | −29.8683 | −1.13955 | ||||||||
\(688\) | −2.58123 | − | 4.47082i | −0.0984085 | − | 0.170449i | ||||
\(689\) | 5.60310 | − | 9.70485i | 0.213461 | − | 0.369726i | ||||
\(690\) | 33.2209 | − | 57.5404i | 1.26470 | − | 2.19052i | ||||
\(691\) | 1.02988 | + | 1.78380i | 0.0391783 | + | 0.0678588i | 0.884950 | − | 0.465687i | \(-0.154193\pi\) |
−0.845771 | + | 0.533546i | \(0.820859\pi\) | |||||||
\(692\) | −62.1024 | −2.36078 | ||||||||
\(693\) | −0.283597 | + | 5.62939i | −0.0107729 | + | 0.213843i | ||||
\(694\) | −5.78100 | −0.219444 | ||||||||
\(695\) | −2.14469 | − | 3.71471i | −0.0813526 | − | 0.140907i | ||||
\(696\) | 10.9885 | − | 19.0327i | 0.416519 | − | 0.721432i | ||||
\(697\) | −5.09388 | + | 8.82285i | −0.192944 | + | 0.334189i | ||||
\(698\) | 8.54722 | + | 14.8042i | 0.323517 | + | 0.560348i | ||||
\(699\) | 10.9466 | 0.414039 | ||||||||
\(700\) | 41.8588 | − | 21.4350i | 1.58211 | − | 0.810166i | ||||
\(701\) | 2.70966 | 0.102343 | 0.0511713 | − | 0.998690i | \(-0.483705\pi\) | ||||
0.0511713 | + | 0.998690i | \(0.483705\pi\) | |||||||
\(702\) | 1.13312 | + | 1.96262i | 0.0427668 | + | 0.0740743i | ||||
\(703\) | −1.13241 | + | 1.96139i | −0.0427097 | + | 0.0739754i | ||||
\(704\) | 13.8914 | − | 24.0606i | 0.523552 | − | 0.906818i | ||||
\(705\) | −11.7987 | − | 20.4360i | −0.444365 | − | 0.769663i | ||||
\(706\) | 5.81671 | 0.218915 | ||||||||
\(707\) | 21.5862 | + | 13.9562i | 0.811834 | + | 0.524878i | ||||
\(708\) | 18.6846 | 0.702209 | ||||||||
\(709\) | −3.98094 | − | 6.89519i | −0.149507 | − | 0.258954i | 0.781538 | − | 0.623857i | \(-0.214435\pi\) |
−0.931045 | + | 0.364903i | \(0.881102\pi\) | |||||||
\(710\) | −15.6556 | + | 27.1164i | −0.587546 | + | 1.01766i | ||||
\(711\) | −1.65662 | + | 2.86936i | −0.0621282 | + | 0.107609i | ||||
\(712\) | −19.4267 | − | 33.6481i | −0.728048 | − | 1.26102i | ||||
\(713\) | 32.0812 | 1.20145 | ||||||||
\(714\) | −17.3394 | − | 11.2105i | −0.648912 | − | 0.419543i | ||||
\(715\) | −6.95841 | −0.260230 | ||||||||
\(716\) | 4.77781 | + | 8.27540i | 0.178555 | + | 0.309266i | ||||
\(717\) | −15.1473 | + | 26.2358i | −0.565685 | + | 0.979795i | ||||
\(718\) | 33.6525 | − | 58.2879i | 1.25590 | − | 2.17529i | ||||
\(719\) | −4.49334 | − | 7.78270i | −0.167573 | − | 0.290246i | 0.769993 | − | 0.638053i | \(-0.220260\pi\) |
−0.937566 | + | 0.347807i | \(0.886926\pi\) | |||||||
\(720\) | −1.43136 | −0.0533438 | ||||||||
\(721\) | −29.4281 | + | 15.0695i | −1.09596 | + | 0.561218i | ||||
\(722\) | −39.3937 | −1.46608 | ||||||||
\(723\) | −11.9048 | − | 20.6197i | −0.442743 | − | 0.766854i | ||||
\(724\) | −16.9226 | + | 29.3108i | −0.628924 | + | 1.08933i | ||||
\(725\) | 24.1977 | − | 41.9116i | 0.898680 | − | 1.55656i | ||||
\(726\) | 7.32149 | + | 12.6812i | 0.271726 | + | 0.470643i | ||||
\(727\) | −12.1319 | −0.449945 | −0.224973 | − | 0.974365i | \(-0.572229\pi\) | ||||
−0.224973 | + | 0.974365i | \(0.572229\pi\) | |||||||
\(728\) | 0.342655 | − | 6.80170i | 0.0126996 | − | 0.252088i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 3.54712 | + | 6.14380i | 0.131285 | + | 0.227392i | ||||
\(731\) | 20.2836 | − | 35.1322i | 0.750215 | − | 1.29941i | ||||
\(732\) | −4.56448 | + | 7.90591i | −0.168708 | + | 0.292211i | ||||
\(733\) | −0.780629 | − | 1.35209i | −0.0288332 | − | 0.0499406i | 0.851249 | − | 0.524762i | \(-0.175846\pi\) |
−0.880082 | + | 0.474822i | \(0.842513\pi\) | |||||||
\(734\) | −6.76184 | −0.249584 | ||||||||
\(735\) | −22.7479 | − | 2.29781i | −0.839069 | − | 0.0847561i | ||||
\(736\) | 55.1247 | 2.03192 | ||||||||
\(737\) | −6.81950 | − | 11.8117i | −0.251200 | − | 0.435091i | ||||
\(738\) | −3.35223 | + | 5.80624i | −0.123397 | + | 0.213731i | ||||
\(739\) | 17.3246 | − | 30.0070i | 0.637294 | − | 1.10383i | −0.348730 | − | 0.937223i | \(-0.613387\pi\) |
0.986024 | − | 0.166603i | \(-0.0532797\pi\) | |||||||
\(740\) | 9.12081 | + | 15.7977i | 0.335288 | + | 0.580735i | ||||
\(741\) | 1.27166 | 0.0467156 | ||||||||
\(742\) | −3.38066 | + | 67.1062i | −0.124108 | + | 2.46354i | ||||
\(743\) | −5.28770 | −0.193987 | −0.0969935 | − | 0.995285i | \(-0.530923\pi\) | ||||
−0.0969935 | + | 0.995285i | \(0.530923\pi\) | |||||||
\(744\) | 4.59992 | + | 7.96730i | 0.168641 | + | 0.292095i | ||||
\(745\) | −9.23694 | + | 15.9989i | −0.338415 | + | 0.586153i | ||||
\(746\) | −39.5637 | + | 68.5264i | −1.44853 | + | 2.50893i | ||||
\(747\) | 5.23893 | + | 9.07409i | 0.191682 | + | 0.332004i | ||||
\(748\) | 23.0056 | 0.841170 | ||||||||
\(749\) | −30.3622 | + | 15.5478i | −1.10941 | + | 0.568105i | ||||
\(750\) | 4.94683 | 0.180633 | ||||||||
\(751\) | 17.2297 | + | 29.8427i | 0.628721 | + | 1.08898i | 0.987809 | + | 0.155673i | \(0.0497545\pi\) |
−0.359088 | + | 0.933304i | \(0.616912\pi\) | |||||||
\(752\) | 1.58303 | − | 2.74189i | 0.0577271 | − | 0.0999863i | ||||
\(753\) | −10.2542 | + | 17.7608i | −0.373683 | + | 0.647239i | ||||
\(754\) | −9.67445 | − | 16.7566i | −0.352323 | − | 0.610241i | ||||
\(755\) | −27.3829 | −0.996565 | ||||||||
\(756\) | −6.96727 | − | 4.50457i | −0.253397 | − | 0.163830i | ||||
\(757\) | 19.7567 | 0.718069 | 0.359034 | − | 0.933324i | \(-0.383106\pi\) | ||||
0.359034 | + | 0.933324i | \(0.383106\pi\) | |||||||
\(758\) | 14.8633 | + | 25.7440i | 0.539859 | + | 0.935063i | ||||
\(759\) | 9.56140 | − | 16.5608i | 0.347057 | − | 0.601120i | ||||
\(760\) | 5.34573 | − | 9.25908i | 0.193910 | − | 0.335862i | ||||
\(761\) | 7.94858 | + | 13.7673i | 0.288136 | + | 0.499066i | 0.973365 | − | 0.229262i | \(-0.0736312\pi\) |
−0.685229 | + | 0.728328i | \(0.740298\pi\) | |||||||
\(762\) | 24.0158 | 0.869999 | ||||||||
\(763\) | 16.3658 | + | 10.5810i | 0.592480 | + | 0.383058i | ||||
\(764\) | −56.8924 | −2.05830 | ||||||||
\(765\) | −5.62389 | − | 9.74087i | −0.203332 | − | 0.352182i | ||||
\(766\) | 19.6380 | − | 34.0141i | 0.709551 | − | 1.22898i | ||||
\(767\) | 2.97921 | − | 5.16014i | 0.107573 | − | 0.186322i | ||||
\(768\) | 6.52976 | + | 11.3099i | 0.235623 | + | 0.408110i | ||||
\(769\) | −29.1892 | −1.05259 | −0.526295 | − | 0.850302i | \(-0.676419\pi\) | ||||
−0.526295 | + | 0.850302i | \(0.676419\pi\) | |||||||
\(770\) | 37.1361 | − | 19.0166i | 1.33829 | − | 0.685310i | ||||
\(771\) | 2.69195 | 0.0969483 | ||||||||
\(772\) | −12.2359 | − | 21.1931i | −0.440378 | − | 0.762758i | ||||
\(773\) | −19.9770 | + | 34.6011i | −0.718521 | + | 1.24452i | 0.243064 | + | 0.970010i | \(0.421847\pi\) |
−0.961586 | + | 0.274505i | \(0.911486\pi\) | |||||||
\(774\) | 13.3484 | − | 23.1202i | 0.479799 | − | 0.831037i | ||||
\(775\) | 10.1294 | + | 17.5447i | 0.363860 | + | 0.630224i | ||||
\(776\) | 9.73252 | 0.349377 | ||||||||
\(777\) | 0.237084 | − | 4.70611i | 0.00850533 | − | 0.168831i | ||||
\(778\) | −46.2097 | −1.65670 | ||||||||
\(779\) | 1.88105 | + | 3.25807i | 0.0673956 | + | 0.116733i | ||||
\(780\) | 5.12118 | − | 8.87015i | 0.183368 | − | 0.317602i | ||||
\(781\) | −4.50589 | + | 7.80443i | −0.161233 | + | 0.279264i | ||||
\(782\) | 35.0254 | + | 60.6659i | 1.25251 | + | 2.16941i | ||||
\(783\) | −8.53790 | −0.305120 | ||||||||
\(784\) | −1.25905 | − | 2.79733i | −0.0449659 | − | 0.0999045i | ||||
\(785\) | −8.13583 | −0.290380 | ||||||||
\(786\) | −19.5848 | − | 33.9218i | −0.698565 | − | 1.20995i | ||||
\(787\) | −16.6801 | + | 28.8908i | −0.594581 | + | 1.02984i | 0.399025 | + | 0.916940i | \(0.369349\pi\) |
−0.993606 | + | 0.112905i | \(0.963985\pi\) | |||||||
\(788\) | 8.03519 | − | 13.9173i | 0.286242 | − | 0.495785i | ||||
\(789\) | 1.33415 | + | 2.31082i | 0.0474971 | + | 0.0822673i | ||||
\(790\) | 24.5249 | 0.872556 | ||||||||
\(791\) | −1.69503 | + | 33.6463i | −0.0602684 | + | 1.19633i | ||||
\(792\) | 5.48380 | 0.194858 | ||||||||
\(793\) | 1.45559 | + | 2.52116i | 0.0516895 | + | 0.0895288i | ||||
\(794\) | −11.7310 | + | 20.3188i | −0.416319 | + | 0.721086i | ||||
\(795\) | −18.3011 | + | 31.6984i | −0.649072 | + | 1.12422i | ||||
\(796\) | −14.2023 | − | 24.5991i | −0.503387 | − | 0.871892i | ||||
\(797\) | 1.65037 | 0.0584589 | 0.0292295 | − | 0.999573i | \(-0.490695\pi\) | ||||
0.0292295 | + | 0.999573i | \(0.490695\pi\) | |||||||
\(798\) | −6.78668 | + | 3.47531i | −0.240246 | + | 0.123025i | ||||
\(799\) | 24.8792 | 0.880163 | ||||||||
\(800\) | 17.4052 | + | 30.1468i | 0.615368 | + | 1.06585i | ||||
\(801\) | −7.54712 | + | 13.0720i | −0.266664 | + | 0.461876i | ||||
\(802\) | −1.83548 | + | 3.17915i | −0.0648132 | + | 0.112260i | ||||
\(803\) | 1.02091 | + | 1.76826i | 0.0360270 | + | 0.0624006i | ||||
\(804\) | 20.0758 | 0.708019 | ||||||||
\(805\) | 65.1399 | + | 42.1151i | 2.29588 | + | 1.48436i | ||||
\(806\) | 8.09967 | 0.285299 | ||||||||
\(807\) | −0.449557 | − | 0.778656i | −0.0158252 | − | 0.0274100i | ||||
\(808\) | 12.5042 | − | 21.6579i | 0.439896 | − | 0.761922i | ||||
\(809\) | −11.5637 | + | 20.0290i | −0.406560 | + | 0.704182i | −0.994502 | − | 0.104721i | \(-0.966605\pi\) |
0.587942 | + | 0.808903i | \(0.299938\pi\) | |||||||
\(810\) | −3.70103 | − | 6.41038i | −0.130041 | − | 0.225238i | ||||
\(811\) | −43.9914 | −1.54475 | −0.772373 | − | 0.635169i | \(-0.780930\pi\) | ||||
−0.772373 | + | 0.635169i | \(0.780930\pi\) | |||||||
\(812\) | 59.4858 | + | 38.4596i | 2.08754 | + | 1.34967i | ||||
\(813\) | 22.0573 | 0.773585 | ||||||||
\(814\) | 4.29933 | + | 7.44667i | 0.150692 | + | 0.261006i | ||||
\(815\) | −18.4284 | + | 31.9189i | −0.645519 | + | 1.11807i | ||||
\(816\) | 0.754556 | − | 1.30693i | 0.0264147 | − | 0.0457517i | ||||
\(817\) | −7.49024 | − | 12.9735i | −0.262050 | − | 0.453885i | ||||
\(818\) | 23.2406 | 0.812590 | ||||||||
\(819\) | −2.35495 | + | 1.20592i | −0.0822884 | + | 0.0421381i | ||||
\(820\) | 30.3012 | 1.05816 | ||||||||
\(821\) | 7.98474 | + | 13.8300i | 0.278669 | + | 0.482670i | 0.971054 | − | 0.238859i | \(-0.0767733\pi\) |
−0.692385 | + | 0.721528i | \(0.743440\pi\) | |||||||
\(822\) | −18.2830 | + | 31.6670i | −0.637692 | + | 1.10451i | ||||
\(823\) | −9.84326 | + | 17.0490i | −0.343115 | + | 0.594292i | −0.985009 | − | 0.172501i | \(-0.944815\pi\) |
0.641895 | + | 0.766793i | \(0.278149\pi\) | |||||||
\(824\) | 16.0831 | + | 27.8568i | 0.560282 | + | 0.970437i | ||||
\(825\) | 12.0758 | 0.420425 | ||||||||
\(826\) | −1.79752 | + | 35.6808i | −0.0625438 | + | 1.24149i | ||||
\(827\) | −8.49580 | −0.295428 | −0.147714 | − | 0.989030i | \(-0.547192\pi\) | ||||
−0.147714 | + | 0.989030i | \(0.547192\pi\) | |||||||
\(828\) | 14.0738 | + | 24.3765i | 0.489099 | + | 0.847143i | ||||
\(829\) | 9.58661 | − | 16.6045i | 0.332957 | − | 0.576698i | −0.650134 | − | 0.759820i | \(-0.725287\pi\) |
0.983090 | + | 0.183122i | \(0.0586204\pi\) | |||||||
\(830\) | 38.7789 | − | 67.1671i | 1.34604 | − | 2.33140i | ||||
\(831\) | −4.83415 | − | 8.37300i | −0.167695 | − | 0.290456i | ||||
\(832\) | 13.0411 | 0.452118 | ||||||||
\(833\) | 14.0898 | − | 19.5590i | 0.488183 | − | 0.677680i | ||||
\(834\) | 2.97613 | 0.103055 | ||||||||
\(835\) | −5.34301 | − | 9.25436i | −0.184902 | − | 0.320260i | ||||
\(836\) | 4.24772 | − | 7.35727i | 0.146911 | − | 0.254457i | ||||
\(837\) | 1.78703 | − | 3.09523i | 0.0617688 | − | 0.106987i | ||||
\(838\) | 38.8330 | + | 67.2608i | 1.34146 | + | 2.32348i | ||||
\(839\) | 24.1587 | 0.834050 | 0.417025 | − | 0.908895i | \(-0.363073\pi\) | ||||
0.417025 | + | 0.908895i | \(0.363073\pi\) | |||||||
\(840\) | −1.11919 | + | 22.2160i | −0.0386158 | + | 0.766523i | ||||
\(841\) | 43.8957 | 1.51364 | ||||||||
\(842\) | −25.9460 | − | 44.9398i | −0.894158 | − | 1.54873i | ||||
\(843\) | 13.5769 | − | 23.5159i | 0.467613 | − | 0.809929i | ||||
\(844\) | 8.29364 | − | 14.3650i | 0.285479 | − | 0.494464i | ||||
\(845\) | −1.63312 | − | 2.82864i | −0.0561810 | − | 0.0973083i | ||||
\(846\) | 16.3728 | 0.562907 | ||||||||
\(847\) | −15.2162 | + | 7.79187i | −0.522834 | + | 0.267732i | ||||
\(848\) | −4.91089 | −0.168641 | ||||||||
\(849\) | 13.7949 | + | 23.8935i | 0.473440 | + | 0.820022i | ||||
\(850\) | −22.1181 | + | 38.3097i | −0.758645 | + | 1.31401i | ||||
\(851\) | −7.99323 | + | 13.8447i | −0.274004 | + | 0.474590i | ||||
\(852\) | −6.63240 | − | 11.4876i | −0.227222 | − | 0.393560i | ||||
\(853\) | 4.75591 | 0.162839 | 0.0814196 | − | 0.996680i | \(-0.474055\pi\) | ||||
0.0814196 | + | 0.996680i | \(0.474055\pi\) | |||||||
\(854\) | −14.6583 | − | 9.47709i | −0.501598 | − | 0.324299i | ||||
\(855\) | −4.15354 | −0.142048 | ||||||||
\(856\) | 16.5936 | + | 28.7410i | 0.567158 | + | 0.982347i | ||||
\(857\) | 11.1127 | − | 19.2477i | 0.379602 | − | 0.657490i | −0.611402 | − | 0.791320i | \(-0.709394\pi\) |
0.991004 | + | 0.133830i | \(0.0427276\pi\) | |||||||
\(858\) | 2.41400 | − | 4.18118i | 0.0824127 | − | 0.142743i | ||||
\(859\) | −12.3227 | − | 21.3435i | −0.420445 | − | 0.728232i | 0.575538 | − | 0.817775i | \(-0.304793\pi\) |
−0.995983 | + | 0.0895430i | \(0.971459\pi\) | |||||||
\(860\) | −120.658 | −4.11439 | ||||||||
\(861\) | −6.57308 | − | 4.24971i | −0.224010 | − | 0.144830i | ||||
\(862\) | 9.33096 | 0.317814 | ||||||||
\(863\) | −7.77543 | − | 13.4674i | −0.264679 | − | 0.458437i | 0.702801 | − | 0.711387i | \(-0.251933\pi\) |
−0.967479 | + | 0.252950i | \(0.918599\pi\) | |||||||
\(864\) | 3.07063 | − | 5.31848i | 0.104465 | − | 0.180938i | ||||
\(865\) | 32.3425 | − | 56.0188i | 1.09968 | − | 1.90470i | ||||
\(866\) | −28.6168 | − | 49.5657i | −0.972437 | − | 1.68431i | ||||
\(867\) | −5.14125 | −0.174606 | ||||||||
\(868\) | −26.3934 | + | 13.5155i | −0.895850 | + | 0.458745i | ||||
\(869\) | 7.05856 | 0.239445 | ||||||||
\(870\) | 31.5990 | + | 54.7311i | 1.07131 | + | 1.85556i | ||||
\(871\) | 3.20103 | − | 5.54435i | 0.108463 | − | 0.187863i | ||||
\(872\) | 9.48014 | − | 16.4201i | 0.321038 | − | 0.556054i | ||||
\(873\) | −1.89050 | − | 3.27444i | −0.0639837 | − | 0.110823i | ||||
\(874\) | 25.8681 | 0.875003 | ||||||||
\(875\) | −0.290576 | + | 5.76794i | −0.00982327 | + | 0.194992i | ||||
\(876\) | −3.00542 | −0.101544 | ||||||||
\(877\) | −10.1085 | − | 17.5085i | −0.341341 | − | 0.591219i | 0.643341 | − | 0.765579i | \(-0.277548\pi\) |
−0.984682 | + | 0.174360i | \(0.944214\pi\) | |||||||
\(878\) | −1.85639 | + | 3.21536i | −0.0626501 | + | 0.108513i | ||||
\(879\) | −0.165735 | + | 0.287062i | −0.00559011 | + | 0.00968236i | ||||
\(880\) | 1.52469 | + | 2.64085i | 0.0513974 | + | 0.0890229i | ||||
\(881\) | −16.1927 | −0.545545 | −0.272772 | − | 0.962079i | \(-0.587941\pi\) | ||||
−0.272772 | + | 0.962079i | \(0.587941\pi\) | |||||||
\(882\) | 9.27238 | − | 12.8716i | 0.312217 | − | 0.433410i | ||||
\(883\) | 37.3295 | 1.25624 | 0.628118 | − | 0.778118i | \(-0.283825\pi\) | ||||
0.628118 | + | 0.778118i | \(0.283825\pi\) | |||||||
\(884\) | 5.39936 | + | 9.35196i | 0.181600 | + | 0.314540i | ||||
\(885\) | −9.73080 | + | 16.8542i | −0.327097 | + | 0.566549i | ||||
\(886\) | 33.0734 | − | 57.2849i | 1.11112 | − | 1.92452i | ||||
\(887\) | 20.3137 | + | 35.1844i | 0.682068 | + | 1.18138i | 0.974349 | + | 0.225043i | \(0.0722524\pi\) |
−0.292281 | + | 0.956332i | \(0.594414\pi\) | |||||||
\(888\) | −4.58440 | −0.153842 | ||||||||
\(889\) | −1.41068 | + | 28.0020i | −0.0473128 | + | 0.939158i | ||||
\(890\) | 111.729 | 3.74515 | ||||||||
\(891\) | −1.06520 | − | 1.84499i | −0.0356857 | − | 0.0618094i | ||||
\(892\) | 36.8768 | − | 63.8726i | 1.23473 | − | 2.13861i | ||||
\(893\) | 4.59365 | − | 7.95644i | 0.153721 | − | 0.266252i | ||||
\(894\) | −6.40893 | − | 11.1006i | −0.214347 | − | 0.371260i | ||||
\(895\) | −9.95299 | −0.332692 | ||||||||
\(896\) | −40.6738 | + | 20.8282i | −1.35882 | + | 0.695820i | ||||
\(897\) | 8.97613 | 0.299704 | ||||||||
\(898\) | 9.78262 | + | 16.9440i | 0.326450 | + | 0.565428i | ||||
\(899\) | −15.2575 | + | 26.4267i | −0.508865 | + | 0.881381i | ||||
\(900\) | −8.88742 | + | 15.3935i | −0.296247 | + | 0.513115i | ||||
\(901\) | −19.2951 | − | 33.4202i | −0.642814 | − | 1.11339i | ||||
\(902\) | 14.2832 | 0.475580 | ||||||||
\(903\) | 26.1737 | + | 16.9222i | 0.871006 | + | 0.563134i | ||||
\(904\) | 32.7762 | 1.09012 | ||||||||
\(905\) | −17.6263 | − | 30.5297i | −0.585920 | − | 1.01484i | ||||
\(906\) | 9.49963 | − | 16.4538i | 0.315604 | − | 0.546642i | ||||
\(907\) | −4.42854 | + | 7.67045i | −0.147047 | + | 0.254693i | −0.930135 | − | 0.367218i | \(-0.880310\pi\) |
0.783088 | + | 0.621911i | \(0.213644\pi\) | |||||||
\(908\) | −16.9400 | − | 29.3409i | −0.562172 | − | 0.973711i | ||||
\(909\) | −9.71554 | −0.322244 | ||||||||
\(910\) | 16.4461 | + | 10.6330i | 0.545183 | + | 0.352479i | ||||
\(911\) | 4.01325 | 0.132965 | 0.0664825 | − | 0.997788i | \(-0.478822\pi\) | ||||
0.0664825 | + | 0.997788i | \(0.478822\pi\) | |||||||
\(912\) | −0.278640 | − | 0.482618i | −0.00922669 | − | 0.0159811i | ||||
\(913\) | 11.1611 | − | 19.3315i | 0.369377 | − | 0.639780i | ||||
\(914\) | −8.44709 | + | 14.6308i | −0.279405 | + | 0.483943i | ||||
\(915\) | −4.75430 | − | 8.23469i | −0.157172 | − | 0.272230i | ||||
\(916\) | −93.6621 | −3.09468 | ||||||||
\(917\) | 40.7028 | − | 20.8430i | 1.34412 | − | 0.688296i | ||||
\(918\) | 7.80413 | 0.257575 | ||||||||
\(919\) | 17.1415 | + | 29.6899i | 0.565446 | + | 0.979381i | 0.997008 | + | 0.0772976i | \(0.0246292\pi\) |
−0.431562 | + | 0.902083i | \(0.642038\pi\) | |||||||
\(920\) | 37.7333 | − | 65.3561i | 1.24403 | − | 2.15473i | ||||
\(921\) | −1.10618 | + | 1.91596i | −0.0364499 | + | 0.0631331i | ||||
\(922\) | −15.6830 | − | 27.1637i | −0.516491 | − | 0.894588i | ||||
\(923\) | −4.23007 | −0.139235 | ||||||||
\(924\) | −0.889311 | + | 17.6528i | −0.0292562 | + | 0.580735i | ||||
\(925\) | −10.0952 | −0.331929 | ||||||||
\(926\) | −26.5028 | − | 45.9042i | −0.870936 | − | 1.50851i | ||||
\(927\) | 6.24816 | − | 10.8221i | 0.205216 | − | 0.355445i | ||||
\(928\) | −26.2167 | + | 45.4086i | −0.860605 | + | 1.49061i | ||||
\(929\) | 2.60864 | + | 4.51829i | 0.0855866 | + | 0.148240i | 0.905641 | − | 0.424045i | \(-0.139390\pi\) |
−0.820054 | + | 0.572286i | \(0.806057\pi\) | |||||||
\(930\) | −26.4554 | −0.867508 | ||||||||
\(931\) | −3.65351 | − | 8.11731i | −0.119739 | − | 0.266034i | ||||
\(932\) | 34.3267 | 1.12441 | ||||||||
\(933\) | 4.35162 | + | 7.53723i | 0.142466 | + | 0.246758i | ||||
\(934\) | 29.6351 | − | 51.3294i | 0.969689 | − | 1.67955i | ||||
\(935\) | −11.9812 | + | 20.7520i | −0.391827 | + | 0.678663i | ||||
\(936\) | 1.28703 | + | 2.22920i | 0.0420679 | + | 0.0728637i | ||||
\(937\) | 12.6090 | 0.411919 | 0.205960 | − | 0.978560i | \(-0.433968\pi\) | ||||
0.205960 | + | 0.978560i | \(0.433968\pi\) | |||||||
\(938\) | −1.93136 | + | 38.3375i | −0.0630612 | + | 1.25176i | ||||
\(939\) | 34.4068 | 1.12282 | ||||||||
\(940\) | −36.9988 | − | 64.0837i | −1.20677 | − | 2.09018i | ||||
\(941\) | −4.91020 | + | 8.50472i | −0.160068 | + | 0.277246i | −0.934893 | − | 0.354930i | \(-0.884505\pi\) |
0.774825 | + | 0.632176i | \(0.217838\pi\) | |||||||
\(942\) | 2.82247 | − | 4.88866i | 0.0919611 | − | 0.159281i | ||||
\(943\) | 13.2775 | + | 22.9974i | 0.432377 | + | 0.748898i | ||||
\(944\) | −2.61116 | −0.0849859 | ||||||||
\(945\) | 7.69181 | − | 3.93881i | 0.250215 | − | 0.128129i | ||||
\(946\) | −56.8752 | −1.84917 | ||||||||
\(947\) | 14.9545 | + | 25.9020i | 0.485956 | + | 0.841700i | 0.999870 | − | 0.0161415i | \(-0.00513821\pi\) |
−0.513914 | + | 0.857842i | \(0.671805\pi\) | |||||||
\(948\) | −5.19489 | + | 8.99781i | −0.168722 | + | 0.292235i | ||||
\(949\) | −0.479207 | + | 0.830011i | −0.0155557 | + | 0.0269433i | ||||
\(950\) | 8.16769 | + | 14.1469i | 0.264995 | + | 0.458985i | ||||
\(951\) | −9.48328 | −0.307517 | ||||||||
\(952\) | −19.6946 | − | 12.7332i | −0.638307 | − | 0.412687i | ||||
\(953\) | −40.0603 | −1.29768 | −0.648840 | − | 0.760925i | \(-0.724746\pi\) | ||||
−0.648840 | + | 0.760925i | \(0.724746\pi\) | |||||||
\(954\) | −12.6980 | − | 21.9935i | −0.411111 | − | 0.712066i | ||||
\(955\) | 29.6292 | − | 51.3192i | 0.958778 | − | 1.66065i | ||||
\(956\) | −47.4992 | + | 82.2711i | −1.53623 | + | 2.66084i | ||||
\(957\) | 9.09460 | + | 15.7523i | 0.293987 | + | 0.509200i | ||||
\(958\) | 33.7923 | 1.09178 | ||||||||
\(959\) | −35.8494 | − | 23.1778i | −1.15764 | − | 0.748450i | ||||
\(960\) | −42.5952 | −1.37476 | ||||||||
\(961\) | 9.11305 | + | 15.7843i | 0.293969 | + | 0.509170i | ||||
\(962\) | −2.01808 | + | 3.49542i | −0.0650656 | + | 0.112697i | ||||
\(963\) | 6.44648 | − | 11.1656i | 0.207735 | − | 0.359807i | ||||
\(964\) | −37.3314 | − | 64.6598i | −1.20236 | − | 2.08255i | ||||
\(965\) | 25.4894 | 0.820533 | ||||||||
\(966\) | −47.9044 | + | 24.5308i | −1.54130 | + | 0.789265i | ||||
\(967\) | −20.8069 | −0.669104 | −0.334552 | − | 0.942377i | \(-0.608585\pi\) | ||||
−0.334552 | + | 0.942377i | \(0.608585\pi\) | |||||||
\(968\) | 8.31597 | + | 14.4037i | 0.267285 | + | 0.462952i | ||||
\(969\) | 2.18958 | − | 3.79246i | 0.0703394 | − | 0.121831i | ||||
\(970\) | −13.9936 | + | 24.2376i | −0.449307 | + | 0.778223i | ||||
\(971\) | 5.61948 | + | 9.73323i | 0.180338 | + | 0.312354i | 0.941996 | − | 0.335625i | \(-0.108948\pi\) |
−0.761658 | + | 0.647979i | \(0.775614\pi\) | |||||||
\(972\) | 3.13583 | 0.100582 | ||||||||
\(973\) | −0.174817 | + | 3.47012i | −0.00560439 | + | 0.111247i | ||||
\(974\) | −7.52256 | −0.241038 | ||||||||
\(975\) | 2.83415 | + | 4.90890i | 0.0907655 | + | 0.157210i | ||||
\(976\) | 0.637883 | − | 1.10485i | 0.0204181 | − | 0.0353653i | ||||
\(977\) | 17.3199 | − | 29.9989i | 0.554112 | − | 0.959750i | −0.443860 | − | 0.896096i | \(-0.646391\pi\) |
0.997972 | − | 0.0636538i | \(-0.0202753\pi\) | |||||||
\(978\) | −12.7863 | − | 22.1465i | −0.408861 | − | 0.708168i | ||||
\(979\) | 32.1569 | 1.02774 | ||||||||
\(980\) | −71.3335 | − | 7.20555i | −2.27867 | − | 0.230173i | ||||
\(981\) | −7.36590 | −0.235175 | ||||||||
\(982\) | −23.5117 | − | 40.7234i | −0.750287 | − | 1.29954i | ||||
\(983\) | 23.4095 | − | 40.5464i | 0.746646 | − | 1.29323i | −0.202776 | − | 0.979225i | \(-0.564996\pi\) |
0.949422 | − | 0.314004i | \(-0.101670\pi\) | |||||||
\(984\) | −3.80757 | + | 6.59490i | −0.121381 | + | 0.210238i | ||||
\(985\) | 8.36934 | + | 14.4961i | 0.266669 | + | 0.461885i | ||||
\(986\) | −66.6309 | −2.12196 | ||||||||
\(987\) | −0.961735 | + | 19.0904i | −0.0306124 | + | 0.607655i | ||||
\(988\) | 3.98771 | 0.126866 | ||||||||
\(989\) | −52.8706 | − | 91.5745i | −1.68119 | − | 2.91190i | ||||
\(990\) | −7.88471 | + | 13.6567i | −0.250592 | + | 0.434039i | ||||
\(991\) | 7.67373 | − | 13.2913i | 0.243764 | − | 0.422212i | −0.718019 | − | 0.696023i | \(-0.754951\pi\) |
0.961783 | + | 0.273811i | \(0.0882844\pi\) | |||||||
\(992\) | −10.9746 | − | 19.0086i | −0.348444 | − | 0.603523i | ||||
\(993\) | −8.12377 | −0.257800 | ||||||||
\(994\) | 22.5753 | − | 11.5603i | 0.716046 | − | 0.366672i | ||||
\(995\) | 29.5858 | 0.937934 | ||||||||
\(996\) | 16.4284 | + | 28.4548i | 0.520554 | + | 0.901625i | ||||
\(997\) | −25.5823 | + | 44.3098i | −0.810199 | + | 1.40331i | 0.102526 | + | 0.994730i | \(0.467308\pi\) |
−0.912725 | + | 0.408575i | \(0.866026\pi\) | |||||||
\(998\) | −28.2950 | + | 49.0084i | −0.895663 | + | 1.55133i | ||||
\(999\) | 0.890499 | + | 1.54239i | 0.0281741 | + | 0.0487990i |
(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 | 273.2.i.d.235.1 | yes | 8 | |
3.2 | odd | 2 | 819.2.j.f.235.4 | 8 | |||
7.2 | even | 3 | inner | 273.2.i.d.79.1 | ✓ | 8 | |
7.3 | odd | 6 | 1911.2.a.q.1.4 | 4 | |||
7.4 | even | 3 | 1911.2.a.r.1.4 | 4 | |||
21.2 | odd | 6 | 819.2.j.f.352.4 | 8 | |||
21.11 | odd | 6 | 5733.2.a.bj.1.1 | 4 | |||
21.17 | even | 6 | 5733.2.a.bk.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.i.d.79.1 | ✓ | 8 | 7.2 | even | 3 | inner | |
273.2.i.d.235.1 | yes | 8 | 1.1 | even | 1 | trivial | |
819.2.j.f.235.4 | 8 | 3.2 | odd | 2 | |||
819.2.j.f.352.4 | 8 | 21.2 | odd | 6 | |||
1911.2.a.q.1.4 | 4 | 7.3 | odd | 6 | |||
1911.2.a.r.1.4 | 4 | 7.4 | even | 3 | |||
5733.2.a.bj.1.1 | 4 | 21.11 | odd | 6 | |||
5733.2.a.bk.1.1 | 4 | 21.17 | even | 6 |