Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,2,Mod(47,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.y (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: | \(4.59938315643\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 239.15 | ||
Character | \(\chi\) | \(=\) | 576.239 |
Dual form | 576.2.y.a.335.15 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 | 0 | ||||||||
\(3\) | 0.800065 | + | 1.53620i | 0.461918 | + | 0.886923i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.73424 | − | 1.00059i | 1.67000 | − | 0.447476i | 0.704891 | − | 0.709315i | \(-0.250996\pi\) |
0.965111 | + | 0.261839i | \(0.0843291\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.68236 | + | 2.91393i | 0.635872 | + | 1.10136i | 0.986330 | + | 0.164785i | \(0.0526929\pi\) |
−0.350457 | + | 0.936579i | \(0.613974\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.71979 | + | 2.45811i | −0.573264 | + | 0.819371i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.211428 | − | 0.0566521i | −0.0637480 | − | 0.0170812i | 0.226804 | − | 0.973940i | \(-0.427172\pi\) |
−0.290552 | + | 0.956859i | \(0.593839\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.71526 | + | 0.727551i | −0.753076 | + | 0.201786i | −0.614882 | − | 0.788619i | \(-0.710796\pi\) |
−0.138194 | + | 0.990405i | \(0.544130\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.52473 | + | 4.93599i | 1.16828 | + | 1.27447i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.23937i | − | 1.02820i | −0.857731 | − | 0.514100i | \(-0.828126\pi\) | ||
0.857731 | − | 0.514100i | \(-0.171874\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.12365 | − | 1.12365i | 0.257782 | − | 0.257782i | −0.566369 | − | 0.824152i | \(-0.691652\pi\) |
0.824152 | + | 0.566369i | \(0.191652\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.13037 | + | 4.91577i | −0.683104 | + | 1.07271i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.33369 | − | 1.92471i | −0.695123 | − | 0.401329i | 0.110405 | − | 0.993887i | \(-0.464785\pi\) |
−0.805528 | + | 0.592557i | \(0.798118\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.61325 | − | 4.97286i | 1.72265 | − | 0.994572i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.15209 | − | 0.675290i | −0.991519 | − | 0.129960i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.03634 | + | 0.545635i | 0.378138 | + | 0.101322i | 0.442882 | − | 0.896580i | \(-0.353956\pi\) |
−0.0647434 | + | 0.997902i | \(0.520623\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.21206 | − | 4.16388i | −1.29532 | − | 0.747856i | −0.315731 | − | 0.948849i | \(-0.602250\pi\) |
−0.979593 | + | 0.200993i | \(0.935583\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.0821277 | − | 0.370121i | −0.0142966 | − | 0.0644297i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.19798 | + | 9.19798i | 1.55474 | + | 1.55474i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.66564 | + | 2.66564i | −0.438229 | + | 0.438229i | −0.891416 | − | 0.453187i | \(-0.850287\pi\) |
0.453187 | + | 0.891416i | \(0.350287\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.29004 | − | 3.58908i | −0.526828 | − | 0.574712i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.70386 | − | 2.95117i | 0.266098 | − | 0.460895i | −0.701753 | − | 0.712420i | \(-0.747599\pi\) |
0.967851 | + | 0.251526i | \(0.0809323\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.25664 | − | 4.68985i | 0.191636 | − | 0.715195i | −0.801476 | − | 0.598027i | \(-0.795952\pi\) |
0.993112 | − | 0.117168i | \(-0.0373817\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.96257 | + | 10.9000i | −0.590704 | + | 1.62487i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.34998 | + | 4.07028i | 0.342779 | + | 0.593711i | 0.984948 | − | 0.172852i | \(-0.0552984\pi\) |
−0.642168 | + | 0.766564i | \(0.721965\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.16067 | + | 3.74239i | −0.308667 | + | 0.534628i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.51251 | − | 3.39177i | 0.911933 | − | 0.474943i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.58271 | + | 7.58271i | 1.04157 | + | 1.04157i | 0.999098 | + | 0.0424680i | \(0.0135220\pi\) |
0.0424680 | + | 0.999098i | \(0.486478\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.846209 | −0.114103 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.62513 | + | 0.827151i | 0.347707 | + | 0.109559i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.43167 | + | 5.34305i | 0.186387 | + | 0.695605i | 0.994329 | + | 0.106344i | \(0.0339145\pi\) |
−0.807942 | + | 0.589261i | \(0.799419\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.33105 | + | 8.69958i | −0.298460 | + | 1.11387i | 0.639971 | + | 0.768399i | \(0.278946\pi\) |
−0.938431 | + | 0.345468i | \(0.887720\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.0561 | − | 0.875933i | −1.26695 | − | 0.110357i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.41144 | + | 5.43370i | −1.16735 | + | 0.673967i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.38665 | − | 5.17504i | −0.169406 | − | 0.632231i | −0.997437 | − | 0.0715493i | \(-0.977206\pi\) |
0.828031 | − | 0.560682i | \(-0.189461\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.289558 | − | 6.66110i | 0.0348587 | − | 0.801902i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.53614i | − | 0.894375i | −0.894440 | − | 0.447187i | \(-0.852426\pi\) | ||
0.894440 | − | 0.447187i | \(-0.147574\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 3.22646i | − | 0.377629i | −0.982013 | − | 0.188814i | \(-0.939536\pi\) | ||
0.982013 | − | 0.188814i | \(-0.0604644\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 14.5304 | + | 9.25302i | 1.67783 | + | 1.06845i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.190618 | − | 0.711397i | −0.0217230 | − | 0.0810712i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.98587 | + | 2.87859i | −0.560954 | + | 0.323867i | −0.753528 | − | 0.657415i | \(-0.771650\pi\) |
0.192574 | + | 0.981282i | \(0.438316\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.08462 | − | 8.45489i | −0.342736 | − | 0.939432i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.20739 | + | 4.50604i | −0.132528 | + | 0.494602i | −0.999996 | − | 0.00289160i | \(-0.999080\pi\) |
0.867468 | + | 0.497494i | \(0.165746\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.24186 | − | 15.8308i | −0.460094 | − | 1.71710i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.790999 | + | 3.56475i | 0.0848040 | + | 0.382182i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.96157 | 0.313926 | 0.156963 | − | 0.987605i | \(-0.449830\pi\) | ||||
0.156963 | + | 0.987605i | \(0.449830\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.68807 | − | 6.68807i | −0.701100 | − | 0.701100i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.626426 | − | 14.4105i | 0.0649573 | − | 1.49430i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.07166 | − | 5.32027i | 0.315146 | − | 0.545849i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.63883 | − | 13.2308i | −0.775606 | − | 1.34339i | −0.934453 | − | 0.356085i | \(-0.884111\pi\) |
0.158848 | − | 0.987303i | \(-0.449222\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.502870 | − | 0.422285i | 0.0505403 | − | 0.0424412i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.0347486 | − | 0.129684i | 0.00345762 | − | 0.0129040i | −0.964175 | − | 0.265265i | \(-0.914540\pi\) |
0.967633 | + | 0.252361i | \(0.0812071\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.09117 | − | 7.08611i | 0.403115 | − | 0.698215i | −0.590985 | − | 0.806682i | \(-0.701261\pi\) |
0.994100 | + | 0.108467i | \(0.0345942\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.77091 | + | 21.4889i | −0.660774 | + | 2.09710i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.28837 | − | 8.28837i | 0.801267 | − | 0.801267i | −0.182027 | − | 0.983294i | \(-0.558266\pi\) |
0.983294 | + | 0.182027i | \(0.0582658\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.31291 | + | 6.31291i | 0.604667 | + | 0.604667i | 0.941547 | − | 0.336881i | \(-0.109372\pi\) |
−0.336881 | + | 0.941547i | \(0.609372\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.22764 | − | 1.96226i | −0.591101 | − | 0.186250i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.6562 | + | 8.46178i | 1.37874 | + | 0.796017i | 0.992008 | − | 0.126174i | \(-0.0402696\pi\) |
0.386735 | + | 0.922191i | \(0.373603\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.3746 | − | 3.85167i | −1.34044 | − | 0.359171i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.88128 | − | 7.92564i | 0.266374 | − | 0.732725i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.3533 | − | 7.13215i | 1.13242 | − | 0.653803i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.48479 | − | 5.47604i | −0.862253 | − | 0.497822i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.89676 | + | 0.256333i | 0.531693 | + | 0.0231128i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 13.5199 | − | 13.5199i | 1.20926 | − | 1.20926i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 13.4028i | − | 1.18931i | −0.803981 | − | 0.594654i | \(-0.797289\pi\) | ||
0.803981 | − | 0.594654i | \(-0.202711\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.20992 | − | 1.82174i | 0.722843 | − | 0.160395i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.632708 | + | 0.169534i | −0.0552800 | + | 0.0148122i | −0.286353 | − | 0.958124i | \(-0.592443\pi\) |
0.231073 | + | 0.972936i | \(0.425776\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.16461 | + | 1.38385i | 0.447829 | + | 0.119995i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −19.9148 | + | 2.63341i | −1.71399 | + | 0.226648i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.5230 | − | 18.2263i | −0.899037 | − | 1.55718i | −0.828727 | − | 0.559652i | \(-0.810935\pi\) |
−0.0703095 | − | 0.997525i | \(-0.522399\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.44400 | + | 1.72666i | −0.546573 | + | 0.146454i | −0.521530 | − | 0.853233i | \(-0.674639\pi\) |
−0.0250423 | + | 0.999686i | \(0.507972\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.37261 | + | 6.86651i | −0.368240 | + | 0.578264i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.615299 | 0.0514539 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.15012 | 0.676831 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.47772 | − | 0.325057i | −0.616752 | − | 0.0268103i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −21.5773 | + | 5.78161i | −1.76768 | + | 0.473648i | −0.988250 | − | 0.152844i | \(-0.951157\pi\) |
−0.779428 | + | 0.626492i | \(0.784490\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.97506 | + | 17.2773i | 0.811759 | + | 1.40601i | 0.911632 | + | 0.411007i | \(0.134823\pi\) |
−0.0998734 | + | 0.995000i | \(0.531844\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.4209 | + | 7.29084i | 0.842476 | + | 0.589430i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −31.0979 | − | 8.33265i | −2.49784 | − | 0.669295i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.3943 | + | 3.85693i | −1.14879 | + | 0.307817i | −0.782479 | − | 0.622677i | \(-0.786045\pi\) |
−0.366308 | + | 0.930494i | \(0.619378\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.58187 | + | 17.7152i | −0.442671 | + | 1.40491i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 12.9522i | − | 1.02078i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.35766 | − | 4.35766i | 0.341318 | − | 0.341318i | −0.515545 | − | 0.856863i | \(-0.672410\pi\) |
0.856863 | + | 0.515545i | \(0.172410\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.677022 | − | 1.29994i | −0.0527061 | − | 0.101200i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.8952 | + | 6.86770i | 0.920479 | + | 0.531439i | 0.883788 | − | 0.467888i | \(-0.154985\pi\) |
0.0366910 | + | 0.999327i | \(0.488318\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.41505 | + | 2.54903i | −0.339619 | + | 0.196079i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.829610 | + | 4.69449i | 0.0634418 | + | 0.358997i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.24342 | + | 1.40497i | 0.398650 | + | 0.106818i | 0.452573 | − | 0.891727i | \(-0.350506\pi\) |
−0.0539235 | + | 0.998545i | \(0.517173\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 28.9812 | + | 16.7323i | 2.19077 | + | 1.26484i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.06254 | + | 6.47410i | −0.530853 | + | 0.486623i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.380130 | + | 0.380130i | 0.0284123 | + | 0.0284123i | 0.721170 | − | 0.692758i | \(-0.243605\pi\) |
−0.692758 | + | 0.721170i | \(0.743605\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.98992 | + | 4.98992i | −0.370898 | + | 0.370898i | −0.867804 | − | 0.496906i | \(-0.834469\pi\) |
0.496906 | + | 0.867804i | \(0.334469\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −15.2292 | + | 3.37929i | −1.12578 | + | 0.249804i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.28695 | + | 12.6214i | −0.535747 | + | 0.927941i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.240169 | + | 0.896324i | −0.0175629 | + | 0.0655457i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.69991 | − | 16.1489i | −0.487347 | − | 1.17466i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.40555 | − | 9.36269i | −0.391132 | − | 0.677461i | 0.601467 | − | 0.798898i | \(-0.294583\pi\) |
−0.992599 | + | 0.121437i | \(0.961250\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.60044 | − | 4.50410i | 0.187184 | − | 0.324212i | −0.757126 | − | 0.653268i | \(-0.773397\pi\) |
0.944310 | + | 0.329056i | \(0.106731\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −15.8770 | − | 10.1105i | −1.13697 | − | 0.724028i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.94550 | + | 2.94550i | 0.209858 | + | 0.209858i | 0.804207 | − | 0.594349i | \(-0.202590\pi\) |
−0.594349 | + | 0.804207i | \(0.702590\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.57285 | −0.182384 | −0.0911921 | − | 0.995833i | \(-0.529068\pi\) | ||||
−0.0911921 | + | 0.995833i | \(0.529068\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.84046 | − | 6.27053i | 0.482489 | − | 0.442289i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.83591 | + | 6.85170i | 0.128856 | + | 0.480895i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.40971 | − | 12.7252i | 0.238145 | − | 0.888768i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.4644 | − | 4.88449i | 0.727327 | − | 0.339495i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.301228 | + | 0.173914i | −0.0208364 | + | 0.0120299i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.70786 | + | 17.5700i | 0.324103 | + | 1.20957i | 0.915211 | + | 0.402975i | \(0.132024\pi\) |
−0.591108 | + | 0.806592i | \(0.701309\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.5770 | − | 6.02940i | 0.793242 | − | 0.413127i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 18.7704i | − | 1.28013i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 28.0206i | − | 1.90216i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.95647 | − | 2.58138i | 0.334927 | − | 0.174433i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.08436 | + | 11.5110i | 0.207476 | + | 0.774312i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.82059 | − | 1.62847i | 0.188881 | − | 0.109050i | −0.402578 | − | 0.915386i | \(-0.631886\pi\) |
0.591458 | + | 0.806336i | \(0.298552\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.58916 | + | 29.7246i | −0.172610 | + | 1.98164i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.36663 | − | 8.83238i | 0.157079 | − | 0.586226i | −0.841840 | − | 0.539728i | \(-0.818527\pi\) |
0.998918 | − | 0.0464979i | \(-0.0148061\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.36053 | + | 5.07755i | 0.0899061 | + | 0.335534i | 0.996198 | − | 0.0871183i | \(-0.0277658\pi\) |
−0.906292 | + | 0.422652i | \(0.861099\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.940338 | − | 0.861991i | 0.0618697 | − | 0.0567148i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.1506 | −0.927034 | −0.463517 | − | 0.886088i | \(-0.653413\pi\) | ||||
−0.463517 | + | 0.886088i | \(0.653413\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.8480 | + | 12.8480i | 0.838114 | + | 0.838114i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.41110 | − | 5.35621i | −0.546360 | − | 0.347923i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.51536 | + | 13.0170i | −0.486128 | + | 0.841999i | −0.999873 | − | 0.0159444i | \(-0.994925\pi\) |
0.513745 | + | 0.857943i | \(0.328258\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.18920 | + | 12.4521i | 0.463097 | + | 0.802108i | 0.999113 | − | 0.0420996i | \(-0.0134047\pi\) |
−0.536016 | + | 0.844208i | \(0.680071\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.5205 | − | 11.5030i | 0.674888 | − | 0.737921i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.32388 | + | 16.1369i | −0.276242 | + | 1.03095i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.23348 | + | 3.86850i | −0.142113 | + | 0.246147i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.88815 | + | 1.75034i | −0.499891 | + | 0.110923i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.59758 | + | 3.59758i | −0.227077 | + | 0.227077i | −0.811471 | − | 0.584393i | \(-0.801333\pi\) |
0.584393 | + | 0.811471i | \(0.301333\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.595798 | + | 0.595798i | 0.0374575 | + | 0.0374575i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 20.9255 | − | 19.1820i | 1.31041 | − | 1.20122i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.92640 | − | 2.84426i | −0.307300 | − | 0.177420i | 0.338418 | − | 0.940996i | \(-0.390108\pi\) |
−0.645718 | + | 0.763576i | \(0.723442\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.2521 | − | 3.28294i | −0.761307 | − | 0.203992i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.84331 | + | 4.06716i | −0.299793 | + | 0.251751i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.8392 | + | 10.8768i | −1.16167 | + | 0.670693i | −0.951705 | − | 0.307015i | \(-0.900670\pi\) |
−0.209970 | + | 0.977708i | \(0.567337\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 35.9028 | + | 20.7285i | 2.20549 | + | 1.27334i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.36945 | + | 4.54955i | 0.145008 | + | 0.278428i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.43467 | − | 7.43467i | 0.453300 | − | 0.453300i | −0.443148 | − | 0.896448i | \(-0.646139\pi\) |
0.896448 | + | 0.443148i | \(0.146139\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 11.8875i | − | 0.722111i | −0.932544 | − | 0.361056i | \(-0.882416\pi\) | ||
0.932544 | − | 0.361056i | \(-0.117584\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.92329 | − | 15.6251i | 0.297971 | − | 0.945673i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.10281 | + | 0.563445i | −0.126804 | + | 0.0339770i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.0081 | − | 2.68166i | −0.601329 | − | 0.161126i | −0.0547032 | − | 0.998503i | \(-0.517421\pi\) |
−0.546626 | + | 0.837377i | \(0.684088\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 22.6385 | − | 10.5670i | 1.35533 | − | 0.632631i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.05630 | + | 12.2219i | 0.420944 | + | 0.729096i | 0.996032 | − | 0.0889955i | \(-0.0283657\pi\) |
−0.575088 | + | 0.818091i | \(0.695032\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.7951 | − | 3.42843i | 0.760588 | − | 0.203799i | 0.142378 | − | 0.989812i | \(-0.454525\pi\) |
0.618209 | + | 0.786013i | \(0.287858\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.6305 | + | 0.462109i | 0.629697 | + | 0.0273730i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.4660 | 0.676817 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.972286 | −0.0571933 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.2136 | − | 22.3203i | 0.833216 | − | 1.30844i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 29.7073 | − | 7.96005i | 1.73552 | − | 0.465031i | 0.754077 | − | 0.656787i | \(-0.228085\pi\) |
0.981443 | + | 0.191756i | \(0.0614181\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.6924 | + | 18.5197i | 0.622533 | + | 1.07826i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.05104 | + | 0.434652i | 0.0609875 | + | 0.0252210i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.4522 | + | 2.80065i | 0.604463 | + | 0.161965i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.7800 | − | 4.22825i | 0.909546 | − | 0.243712i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.227020 | − | 0.0503746i | 0.0130420 | − | 0.00289395i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 34.8187i | 1.99371i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.8109 | + | 23.8109i | −1.35896 | + | 1.35896i | −0.483758 | + | 0.875202i | \(0.660728\pi\) |
−0.875202 | + | 0.483758i | \(0.839272\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.1588 | + | 0.615486i | 0.805469 | + | 0.0350138i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.20941 | + | 5.31706i | 0.522218 | + | 0.301503i | 0.737842 | − | 0.674974i | \(-0.235845\pi\) |
−0.215624 | + | 0.976477i | \(0.569178\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.4634 | + | 9.50514i | −0.930565 | + | 0.537262i | −0.886990 | − | 0.461788i | \(-0.847208\pi\) |
−0.0435750 | + | 0.999050i | \(0.513875\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −38.4283 | + | 6.79104i | −2.16519 | + | 0.382632i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.8751 | − | 3.18193i | −0.666972 | − | 0.178715i | −0.0905818 | − | 0.995889i | \(-0.528873\pi\) |
−0.576391 | + | 0.817174i | \(0.695539\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.399628 | − | 0.230725i | −0.0223749 | − | 0.0129181i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.3638 | + | 6.10132i | 1.08078 | + | 0.340543i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.76356 | − | 4.76356i | −0.265052 | − | 0.265052i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −19.7692 | + | 19.7692i | −1.09660 | + | 1.09660i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.64712 | + | 14.7486i | −0.256987 | + | 0.815599i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.90701 | + | 13.6953i | −0.435928 | + | 0.755049i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.94844 | − | 33.3960i | 0.491851 | − | 1.83561i | −0.0551468 | − | 0.998478i | \(-0.517563\pi\) |
0.546998 | − | 0.837134i | \(-0.315771\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.96809 | − | 11.1368i | −0.107851 | − | 0.610293i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.3561 | − | 17.9374i | −0.565817 | − | 0.980023i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.3693 | + | 24.8884i | −0.782746 | + | 1.35576i | 0.147591 | + | 0.989049i | \(0.452848\pi\) |
−0.930336 | + | 0.366707i | \(0.880485\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.27301 | + | 29.2848i | −0.0691406 | + | 1.59053i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.28894 | + | 1.28894i | 0.0698001 | + | 0.0698001i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.01293 | 0.486653 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.58372 | − | 25.1639i | −0.300617 | − | 1.35478i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.92992 | + | 10.9346i | 0.157287 | + | 0.587002i | 0.998899 | + | 0.0469191i | \(0.0149403\pi\) |
−0.841612 | + | 0.540082i | \(0.818393\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.90715 | + | 10.8496i | −0.155616 | + | 0.580767i | 0.843436 | + | 0.537230i | \(0.180529\pi\) |
−0.999052 | + | 0.0435372i | \(0.986137\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.4805 | − | 1.91482i | 0.772914 | − | 0.102205i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.85946 | − | 1.07356i | 0.0989689 | − | 0.0571397i | −0.449699 | − | 0.893180i | \(-0.648469\pi\) |
0.548668 | + | 0.836041i | \(0.315135\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.54056 | − | 28.1417i | −0.400211 | − | 1.49361i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 20.8398 | + | 13.2708i | 1.10296 | + | 0.702366i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.0166i | 0.581435i | 0.956809 | + | 0.290718i | \(0.0938941\pi\) | ||||
−0.956809 | + | 0.290718i | \(0.906106\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.4748i | 0.867097i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.823831 | − | 18.9517i | 0.0432399 | − | 0.994705i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.22835 | − | 12.0484i | −0.168980 | − | 0.630641i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.1365 | + | 11.6258i | −1.05112 | + | 0.606863i | −0.922962 | − | 0.384891i | \(-0.874239\pi\) |
−0.128156 | + | 0.991754i | \(0.540906\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.32402 | + | 9.26366i | 0.225099 | + | 0.482247i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.33867 | + | 34.8524i | −0.484839 | + | 1.80945i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.66079 | − | 9.93021i | −0.137771 | − | 0.514167i | −0.999971 | − | 0.00759967i | \(-0.997581\pi\) |
0.862201 | − | 0.506567i | \(-0.169086\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 31.5860 | + | 9.95240i | 1.63109 | + | 0.513940i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.92615 | −0.305212 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.14819 | + | 6.14819i | 0.315811 | + | 0.315811i | 0.847156 | − | 0.531345i | \(-0.178313\pi\) |
−0.531345 | + | 0.847156i | \(0.678313\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.5894 | − | 10.7231i | 1.05483 | − | 0.549363i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.40170 | + | 2.42782i | −0.0716238 | + | 0.124056i | −0.899613 | − | 0.436688i | \(-0.856151\pi\) |
0.827989 | + | 0.560744i | \(0.189485\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.42363 | − | 2.46580i | −0.0725548 | − | 0.125669i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.36701 | + | 11.1545i | 0.476152 | + | 0.567017i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.82350 | − | 29.1977i | 0.396667 | − | 1.48038i | −0.422255 | − | 0.906477i | \(-0.638761\pi\) |
0.818922 | − | 0.573905i | \(-0.194572\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.15956 | + | 14.1328i | −0.412647 | + | 0.714725i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.766644 | − | 0.836325i | −0.0386721 | − | 0.0421870i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.7382 | + | 15.7382i | −0.791873 | + | 0.791873i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.95789 | + | 1.95789i | 0.0982636 | + | 0.0982636i | 0.754530 | − | 0.656266i | \(-0.227865\pi\) |
−0.656266 | + | 0.754530i | \(0.727865\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.00615 | + | 9.04103i | 0.100433 | + | 0.452617i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.7356 | − | 16.5905i | −1.43499 | − | 0.828489i | −0.437490 | − | 0.899223i | \(-0.644133\pi\) |
−0.997495 | + | 0.0707337i | \(0.977466\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.6120 | + | 6.05887i | 1.12638 | + | 0.301814i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −19.9786 | − | 28.4861i | −0.992743 | − | 1.41549i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.714607 | − | 0.412578i | 0.0354217 | − | 0.0204508i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.8959 | + | 13.2190i | 1.13213 | + | 0.653636i | 0.944470 | − | 0.328598i | \(-0.106576\pi\) |
0.187660 | + | 0.982234i | \(0.439910\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.5801 | − | 30.7475i | 0.965816 | − | 1.51666i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.1607 | + | 13.1607i | −0.647596 | + | 0.647596i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.0347i | 0.885290i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.80811 | − | 8.51780i | −0.382365 | − | 0.417118i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.499479 | − | 0.133835i | 0.0244012 | − | 0.00653827i | −0.246598 | − | 0.969118i | \(-0.579313\pi\) |
0.270999 | + | 0.962580i | \(0.412646\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.8514 | + | 3.44352i | 0.626339 | + | 0.167827i | 0.558008 | − | 0.829836i | \(-0.311566\pi\) |
0.0683313 | + | 0.997663i | \(0.478233\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −14.0467 | − | 1.22353i | −0.682972 | − | 0.0594902i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −21.0818 | − | 36.5148i | −1.02262 | − | 1.77123i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −29.2717 | + | 7.84332i | −1.41655 | + | 0.379565i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.492279 | + | 0.945220i | 0.0237675 | + | 0.0456356i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.61129 | 0.414791 | 0.207396 | − | 0.978257i | \(-0.433501\pi\) | ||||
0.207396 | + | 0.978257i | \(0.433501\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.43973 | 0.309474 | 0.154737 | − | 0.987956i | \(-0.450547\pi\) | ||||
0.154737 | + | 0.987956i | \(0.450547\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.52063 | + | 12.5202i | 0.312640 | + | 0.600297i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.90859 | + | 1.58320i | −0.282646 | + | 0.0757348i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.4510 | − | 25.0298i | −0.689707 | − | 1.19461i | −0.971933 | − | 0.235260i | \(-0.924406\pi\) |
0.282225 | − | 0.959348i | \(-0.408927\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.48331 | − | 11.7473i | −0.261110 | − | 0.559396i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.1860 | + | 8.35627i | 1.48169 | + | 0.397018i | 0.906923 | − | 0.421297i | \(-0.138425\pi\) |
0.574770 | + | 0.818315i | \(0.305092\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.0592 | − | 2.96330i | 0.524257 | − | 0.140474i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −26.1449 | − | 28.5212i | −1.23661 | − | 1.34901i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 10.7097i | − | 0.505423i | −0.967542 | − | 0.252711i | \(-0.918678\pi\) | ||
0.967542 | − | 0.252711i | \(-0.0813223\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.527433 | + | 0.527433i | −0.0248359 | + | 0.0248359i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.5606 | + | 29.1466i | −0.872054 | + | 1.36943i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −31.6669 | − | 18.2829i | −1.48457 | − | 0.857114i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.1358 | − | 7.58393i | 0.614465 | − | 0.354761i | −0.160246 | − | 0.987077i | \(-0.551229\pi\) |
0.774711 | + | 0.632316i | \(0.217895\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.86281 | + | 21.8416i | −0.133624 | + | 1.01948i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.5696 | − | 3.10006i | −0.538849 | − | 0.144384i | −0.0208774 | − | 0.999782i | \(-0.506646\pi\) |
−0.517971 | + | 0.855398i | \(0.673313\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.03363 | + | 1.17412i | 0.0945107 | + | 0.0545658i | 0.546510 | − | 0.837452i | \(-0.315956\pi\) |
−0.452000 | + | 0.892018i | \(0.649289\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12.0797 | − | 54.4391i | −0.560184 | − | 2.52455i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.1509 | − | 24.1509i | −1.11757 | − | 1.11757i | −0.992097 | − | 0.125473i | \(-0.959955\pi\) |
−0.125473 | − | 0.992097i | \(-0.540045\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.7469 | − | 12.7469i | 0.588596 | − | 0.588596i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.4413 | − | 19.0266i | −0.803654 | − | 0.876700i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.531379 | + | 0.920376i | −0.0244328 | + | 0.0423189i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.09051 | − | 15.2660i | 0.187685 | − | 0.700452i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −31.6799 | + | 5.59846i | −1.45052 | + | 0.256336i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.40917 | + | 4.17281i | 0.110078 | + | 0.190660i | 0.915801 | − | 0.401631i | \(-0.131557\pi\) |
−0.805724 | + | 0.592292i | \(0.798223\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.29851 | − | 9.17730i | 0.241591 | − | 0.418449i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 19.8971 | − | 10.3626i | 0.905351 | − | 0.471515i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −41.7638 | − | 41.7638i | −1.89640 | − | 1.89640i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −37.5042 | −1.69948 | −0.849739 | − | 0.527204i | \(-0.823240\pi\) | ||||
−0.849739 | + | 0.527204i | \(0.823240\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.1806 | + | 3.20781i | 0.460384 | + | 0.145062i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.504576 | + | 1.88310i | 0.0227712 | + | 0.0849832i | 0.976376 | − | 0.216077i | \(-0.0693262\pi\) |
−0.953605 | + | 0.301060i | \(0.902660\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.31315 | − | 8.63279i | 0.104179 | − | 0.388801i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.45530 | − | 2.08008i | 0.0654111 | − | 0.0934925i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 21.9598 | − | 12.6785i | 0.985032 | − | 0.568708i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.91509 | + | 10.8793i | 0.130497 | + | 0.487023i | 0.999976 | − | 0.00694794i | \(-0.00221162\pi\) |
−0.869478 | + | 0.493971i | \(0.835545\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.03320 | + | 23.7680i | −0.0461598 | + | 1.06187i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 15.3339i | − | 0.683706i | −0.939753 | − | 0.341853i | \(-0.888945\pi\) | ||
0.939753 | − | 0.341853i | \(-0.111055\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 0.519039i | − | 0.0230969i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.44813 | − | 4.74299i | −0.330783 | − | 0.210644i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.59758 | + | 32.0866i | 0.381081 | + | 1.42221i | 0.844253 | + | 0.535945i | \(0.180045\pi\) |
−0.463172 | + | 0.886269i | \(0.653289\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.40169 | − | 5.42807i | 0.415906 | − | 0.240124i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.54791 | + | 5.03034i | −0.289097 | + | 0.222095i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.18713 | − | 30.5548i | 0.360768 | − | 1.34641i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.266262 | − | 0.993703i | −0.0117102 | − | 0.0437030i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.03677 | + | 9.17899i | 0.0894042 | + | 0.402913i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.5032 | 0.898262 | 0.449131 | − | 0.893466i | \(-0.351734\pi\) | ||||
0.449131 | + | 0.893466i | \(0.351734\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.2406 | + | 29.2406i | 1.27860 | + | 1.27860i | 0.941451 | + | 0.337151i | \(0.109463\pi\) |
0.337151 | + | 0.941451i | \(0.390537\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.51725 | + | 57.9076i | −0.109862 | + | 2.52730i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.6523 | + | 30.5746i | −0.768944 | + | 1.33185i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.09099 | − | 7.08581i | −0.177869 | − | 0.308079i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −15.5960 | − | 5.66974i | −0.676808 | − | 0.246046i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.47928 | + | 9.25281i | −0.107390 | + | 0.400784i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.6575 | − | 39.2440i | 0.979570 | − | 1.69667i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.279825 | + | 0.888083i | −0.0120754 | + | 0.0383236i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.668841 | − | 0.668841i | 0.0288090 | − | 0.0288090i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.5836 | + | 20.5836i | 0.884956 | + | 0.884956i | 0.994033 | − | 0.109077i | \(-0.0347895\pi\) |
−0.109077 | + | 0.994033i | \(0.534790\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.6578 | − | 3.67324i | −0.500282 | − | 0.157634i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 29.8905 | + | 17.2573i | 1.28037 | + | 0.739221i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.0779 | + | 10.2029i | 1.62809 | + | 0.436246i | 0.953365 | − | 0.301821i | \(-0.0975945\pi\) |
0.674728 | + | 0.738067i | \(0.264261\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −17.3756 | − | 20.6914i | −0.741574 | − | 0.883089i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.90122 | − | 1.67502i | 0.123596 | − | 0.0713584i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.7761 | − | 9.68566i | −0.713391 | − | 0.411876i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −25.2189 | − | 1.09627i | −1.07048 | − | 0.0465340i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.52288 | − | 1.52288i | 0.0645265 | − | 0.0645265i | −0.674107 | − | 0.738634i | \(-0.735471\pi\) |
0.738634 | + | 0.674107i | \(0.235471\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.6484i | 0.577266i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.56908 | + | 0.348170i | −0.0662466 | + | 0.0146998i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.85715 | − | 1.30147i | 0.204705 | − | 0.0548504i | −0.155010 | − | 0.987913i | \(-0.549541\pi\) |
0.359714 | + | 0.933063i | \(0.382874\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 63.1966 | + | 16.9335i | 2.65870 | + | 0.712397i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 19.4475 | − | 23.2126i | 0.816719 | − | 0.974836i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.4710 | + | 30.2606i | 0.732421 | + | 1.26859i | 0.955846 | + | 0.293869i | \(0.0949430\pi\) |
−0.223425 | + | 0.974721i | \(0.571724\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.1869 | + | 9.16034i | −1.43068 | + | 0.383348i | −0.889258 | − | 0.457406i | \(-0.848779\pi\) |
−0.541417 | + | 0.840754i | \(0.682112\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.0581 | − | 15.7947i | 0.420185 | − | 0.659835i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −38.2852 | −1.59660 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.4865 | −0.727972 | −0.363986 | − | 0.931404i | \(-0.618584\pi\) | ||||
−0.363986 | + | 0.931404i | \(0.618584\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.99970 | + | 0.391218i | 0.374015 | + | 0.0162584i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.1616 | + | 4.06253i | −0.629008 | + | 0.168542i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.17362 | − | 2.03278i | −0.0486065 | − | 0.0841890i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.82909 | − | 32.4792i | 0.116969 | − | 1.34285i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.3561 | − | 3.31081i | −0.509991 | − | 0.136652i | −0.00535825 | − | 0.999986i | \(-0.501706\pi\) |
−0.504633 | + | 0.863334i | \(0.668372\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.7825 | + | 3.42507i | −0.526696 | + | 0.141128i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.16827 | + | 6.88145i | −0.0891907 | + | 0.283065i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 25.7816i | − | 1.05872i | −0.848397 | − | 0.529361i | \(-0.822432\pi\) | ||
0.848397 | − | 0.529361i | \(-0.177568\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 38.9937 | − | 38.9937i | 1.59858 | − | 1.59858i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.05844 | − | 3.95239i | −0.0842465 | − | 0.161761i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.3647 | + | 15.7990i | 1.11809 | + | 0.645531i | 0.940913 | − | 0.338647i | \(-0.109969\pi\) |
0.177180 | + | 0.984179i | \(0.443303\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.3729 | + | 13.4944i | −0.953401 | + | 0.550447i | −0.894136 | − | 0.447796i | \(-0.852209\pi\) |
−0.0592656 | + | 0.998242i | \(0.518876\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.1056 | + | 5.49146i | 0.615146 | + | 0.223630i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −40.8977 | − | 10.9585i | −1.66273 | − | 0.445527i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.2314 | − | 12.2579i | −0.861755 | − | 0.497534i | 0.00284471 | − | 0.999996i | \(-0.499095\pi\) |
−0.864600 | + | 0.502462i | \(0.832428\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.05671 | + | 8.30212i | −0.366996 | + | 0.336419i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.34212 | − | 9.34212i | −0.377942 | − | 0.377942i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −30.3894 | + | 30.3894i | −1.22742 | + | 1.22742i | −0.262481 | + | 0.964937i | \(0.584541\pi\) |
−0.964937 | + | 0.262481i | \(0.915459\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 22.2764 | − | 4.94301i | 0.898272 | − | 0.199322i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.8393 | − | 27.4345i | 0.637668 | − | 1.10447i | −0.348275 | − | 0.937392i | \(-0.613233\pi\) |
0.985943 | − | 0.167081i | \(-0.0534341\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.39413 | + | 20.1312i | −0.216809 | + | 0.809141i | 0.768713 | + | 0.639593i | \(0.220897\pi\) |
−0.985522 | + | 0.169547i | \(0.945769\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.8757 | + | 12.1675i | 0.637071 | + | 0.488264i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.98242 | + | 8.62981i | 0.199617 | + | 0.345746i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.0944 | − | 20.9481i | 0.483775 | − | 0.837923i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.508167 | − | 0.323602i | −0.0202943 | − | 0.0129234i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.3007 | + | 11.3007i | 0.450587 | + | 0.450587i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.9953 | 0.796002 | 0.398001 | − | 0.917385i | \(-0.369704\pi\) | ||||
0.398001 | + | 0.917385i | \(0.369704\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23.2243 | + | 21.2893i | −0.923084 | + | 0.846174i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.4107 | − | 50.0494i | −0.532187 | − | 1.98615i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.14400 | − | 11.7335i | 0.124570 | − | 0.464900i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 18.5247 | + | 12.9606i | 0.732824 | + | 0.512713i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.6976 | − | 7.33098i | 0.501526 | − | 0.289556i | −0.227818 | − | 0.973704i | \(-0.573159\pi\) |
0.729344 | + | 0.684148i | \(0.239826\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.45056 | + | 12.8777i | 0.136077 | + | 0.507846i | 0.999991 | + | 0.00420705i | \(0.00133915\pi\) |
−0.863914 | + | 0.503639i | \(0.831994\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 28.8350 | − | 15.0175i | 1.13538 | − | 0.591315i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.5078i | 1.19939i | 0.800231 | + | 0.599693i | \(0.204710\pi\) | ||||
−0.800231 | + | 0.599693i | \(0.795290\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.21078i | − | 0.0475272i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 43.0451 | − | 22.4183i | 1.68707 | − | 0.878642i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.39824 | + | 20.1465i | 0.211249 | + | 0.788394i | 0.987453 | + | 0.157912i | \(0.0504761\pi\) |
−0.776204 | + | 0.630482i | \(0.782857\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.19305 | + | 1.26616i | −0.0856896 | + | 0.0494729i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.93100 | + | 5.54884i | 0.309418 | + | 0.216481i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.90477 | − | 14.5728i | 0.152108 | − | 0.567676i | −0.847227 | − | 0.531230i | \(-0.821730\pi\) |
0.999336 | − | 0.0364452i | \(-0.0116034\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.44325 | + | 9.11835i | 0.0950316 | + | 0.354663i | 0.997024 | − | 0.0770887i | \(-0.0245625\pi\) |
−0.901993 | + | 0.431751i | \(0.857896\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −15.2154 | + | 13.9477i | −0.590918 | + | 0.541684i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 20.6706 | 0.801570 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.73833 | − | 5.73833i | −0.222189 | − | 0.222189i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.75830 | + | 3.03010i | 0.183966 | + | 0.117150i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.985698 | − | 1.70728i | 0.0380525 | − | 0.0659088i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.1140 | − | 27.9103i | −0.621149 | − | 1.07586i | −0.989272 | − | 0.146085i | \(-0.953333\pi\) |
0.368123 | − | 0.929777i | \(-0.380001\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −47.7343 | + | 19.8042i | −1.83729 | + | 0.762263i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.16296 | + | 15.5364i | −0.159996 | + | 0.597111i | 0.838630 | + | 0.544701i | \(0.183357\pi\) |
−0.998626 | + | 0.0524101i | \(0.983310\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25.7025 | − | 44.5181i | 0.986372 | − | 1.70845i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.4617 | − | 3.43087i | 0.592494 | − | 0.131471i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.6734 | − | 28.6734i | 1.09716 | − | 1.09716i | 0.102416 | − | 0.994742i | \(-0.467343\pi\) |
0.994742 | − | 0.102416i | \(-0.0326571\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −57.5322 | − | 57.5322i | −2.19819 | − | 2.19819i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.71160 | + | 6.15240i | −0.256064 | + | 0.234729i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −26.1058 | − | 15.0722i | −0.994552 | − | 0.574205i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.0504 | − | 11.8033i | −1.67575 | − | 0.449017i | −0.709102 | − | 0.705106i | \(-0.750899\pi\) |
−0.966653 | + | 0.256089i | \(0.917566\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.07652 | + | 0.754895i | 0.0788804 | + | 0.0286761i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22.3358 | + | 12.8956i | −0.847243 | + | 0.489156i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.5111 | − | 7.22328i | −0.473892 | − | 0.273601i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.3214 | − | 21.7380i | −0.428213 | − | 0.822208i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.0178 | + | 13.0178i | −0.491676 | + | 0.491676i | −0.908834 | − | 0.417158i | \(-0.863026\pi\) |
0.417158 | + | 0.908834i | \(0.363026\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.99049i | 0.225935i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.45784 | + | 30.0164i | −0.356203 | + | 1.13048i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.436349 | − | 0.116919i | 0.0164106 | − | 0.00439721i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.3841 | − | 4.39011i | −0.615319 | − | 0.164874i | −0.0623199 | − | 0.998056i | \(-0.519850\pi\) |
−0.552999 | + | 0.833182i | \(0.686517\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.49876 | − | 17.2064i | 0.0562079 | − | 0.645291i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.0285 | + | 27.7622i | 0.600273 | + | 1.03970i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.29767 | − | 0.615660i | 0.0859282 | − | 0.0230244i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −26.0094 | − | 1.13063i | −0.971339 | − | 0.0422242i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 43.0731 | 1.60635 | 0.803177 | − | 0.595740i | \(-0.203141\pi\) | ||||
0.803177 | + | 0.595740i | \(0.203141\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.5313 | 1.02532 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.3770 | + | 21.0065i | −0.497495 | + | 0.781240i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 20.2528 | − | 5.42673i | 0.752171 | − | 0.201544i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.3101 | − | 26.5179i | −0.567821 | − | 0.983495i | −0.996781 | − | 0.0801716i | \(-0.974453\pi\) |
0.428960 | − | 0.903324i | \(-0.358880\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.0880 | + | 6.95830i | 0.966221 | + | 0.257715i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19.8820 | − | 5.32737i | −0.735363 | − | 0.197040i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.53658 | + | 0.679676i | −0.0936909 | + | 0.0251044i | −0.305360 | − | 0.952237i | \(-0.598777\pi\) |
0.211669 | + | 0.977341i | \(0.432110\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −28.2489 | + | 6.26827i | −1.04197 | + | 0.231209i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.17271i | 0.0431972i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.1402 | + | 13.1402i | −0.483370 | + | 0.483370i | −0.906206 | − | 0.422836i | \(-0.861035\pi\) |
0.422836 | + | 0.906206i | \(0.361035\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.72970 | − | 0.336011i | −0.283958 | − | 0.0123437i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.79055 | + | 1.03378i | 0.0656890 | + | 0.0379255i | 0.532485 | − | 0.846440i | \(-0.321258\pi\) |
−0.466796 | + | 0.884365i | \(0.654592\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −74.7897 | + | 43.1798i | −2.74008 | + | 1.58199i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.99989 | − | 10.7174i | −0.329289 | − | 0.392127i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 38.0958 | + | 10.2077i | 1.39199 | + | 0.372982i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.86676 | − | 4.54188i | −0.287062 | − | 0.165735i | 0.349554 | − | 0.936916i | \(-0.386333\pi\) |
−0.636616 | + | 0.771181i | \(0.719666\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.40489 | − | 2.64829i | −0.306291 | − | 0.0965091i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 54.5367 | + | 54.5367i | 1.98479 | + | 1.98479i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.3910 | − | 18.3910i | 0.668433 | − | 0.668433i | −0.288920 | − | 0.957353i | \(-0.593296\pi\) |
0.957353 | + | 0.288920i | \(0.0932961\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.438586 | + | 1.39194i | −0.0159196 | + | 0.0505242i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.1080 | − | 24.4358i | 0.511415 | − | 0.885797i | −0.488497 | − | 0.872565i | \(-0.662455\pi\) |
0.999912 | − | 0.0132318i | \(-0.00421194\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.77481 | + | 29.0160i | −0.281467 | + | 1.05045i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 46.2091 | + | 16.7988i | 1.67069 | + | 0.607362i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.77467 | − | 13.4661i | −0.280727 | − | 0.486234i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.6064 | + | 25.2991i | −0.526722 | + | 0.912309i | 0.472794 | + | 0.881173i | \(0.343246\pi\) |
−0.999515 | + | 0.0311354i | \(0.990088\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.427898 | − | 9.84350i | 0.0154104 | − | 0.354505i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.5491 | + | 10.5491i | 0.379425 | + | 0.379425i | 0.870895 | − | 0.491470i | \(-0.163540\pi\) |
−0.491470 | + | 0.870895i | \(0.663540\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −82.8256 | −2.97518 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.75923 | − | 21.4482i | −0.170736 | − | 0.769448i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.40154 | − | 5.23060i | −0.0502152 | − | 0.187406i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.426938 | + | 1.59335i | −0.0152770 | + | 0.0570146i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.1229 | − | 4.18627i | −0.361764 | − | 0.149605i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −49.8924 | + | 28.8054i | −1.78074 | + | 1.02811i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.05729 | + | 33.8023i | 0.322857 | + | 1.20492i | 0.916448 | + | 0.400153i | \(0.131043\pi\) |
−0.593591 | + | 0.804767i | \(0.702290\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −31.7815 | − | 20.2385i | −1.13145 | − | 0.720511i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 56.9431i | 2.02466i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 25.3175i | − | 0.899052i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.11845 | + | 71.7379i | −0.110600 | + | 2.54428i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.41329 | − | 27.6668i | −0.262592 | − | 0.980007i | −0.963708 | − | 0.266959i | \(-0.913981\pi\) |
0.701116 | − | 0.713048i | \(-0.252686\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.2554 | − | 9.96243i | 0.610453 | − | 0.352445i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.09328 | + | 7.27986i | −0.179962 | + | 0.257221i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.182786 | + | 0.682165i | −0.00645036 | + | 0.0240731i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.9598 | − | 48.3667i | −0.456773 | − | 1.70470i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17.3693 | + | 5.47289i | 0.611429 | + | 0.192655i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39.9831 | 1.40573 | 0.702865 | − | 0.711323i | \(-0.251904\pi\) | ||||
0.702865 | + | 0.711323i | \(0.251904\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.5121 | + | 33.5121i | 1.17677 | + | 1.17677i | 0.980563 | + | 0.196204i | \(0.0628616\pi\) |
0.196204 | + | 0.980563i | \(0.437138\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.2614 | − | 9.51073i | 0.640457 | − | 0.333556i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.9123 | − | 20.6328i | 0.417271 | − | 0.722734i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.85771 | − | 6.68176i | −0.134964 | − | 0.233765i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 27.9421 | − | 4.93793i | 0.976377 | − | 0.172545i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.91908 | + | 10.8942i | −0.101877 | + | 0.380209i | −0.997972 | − | 0.0636527i | \(-0.979725\pi\) |
0.896096 | + | 0.443861i | \(0.146392\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.4702 | + | 47.5798i | −0.957551 | + | 1.65853i | −0.229131 | + | 0.973396i | \(0.573588\pi\) |
−0.728420 | + | 0.685131i | \(0.759745\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.54794 | − | 2.77953i | −0.0887080 | − | 0.0967708i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.2104 | − | 14.2104i | 0.494144 | − | 0.494144i | −0.415465 | − | 0.909609i | \(-0.636381\pi\) |
0.909609 | + | 0.415465i | \(0.136381\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.15512 | + | 6.15512i | 0.213776 | + | 0.213776i | 0.805869 | − | 0.592093i | \(-0.201698\pi\) |
−0.592093 | + | 0.805869i | \(0.701698\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.88757 | − | 17.5199i | −0.134858 | − | 0.607759i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.8654 | + | 9.15989i | 0.549704 | + | 0.317371i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 51.2913 | + | 13.7435i | 1.77501 | + | 0.475612i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 34.3453 | + | 26.3229i | 1.18715 | + | 0.909853i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.5384 | − | 12.4352i | 0.743590 | − | 0.429312i | −0.0797833 | − | 0.996812i | \(-0.525423\pi\) |
0.823373 | + | 0.567500i | \(0.192089\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.2658 | − | 12.2778i | −0.733303 | − | 0.423373i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.1297 | + | 20.6181i | −0.452210 | + | 0.710127i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13.9363 | + | 13.9363i | −0.479424 | + | 0.479424i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 36.8507i | − | 1.26621i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.5036 | + | 16.9128i | 0.532083 | + | 0.580444i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.0170 | − | 3.75585i | 0.480497 | − | 0.128749i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.8477 | + | 5.05023i | 0.645334 | + | 0.172917i | 0.566618 | − | 0.823980i | \(-0.308251\pi\) |
0.0787157 | + | 0.996897i | \(0.474918\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.79521 | + | 16.7003i | 0.266590 | + | 0.571137i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.6982 | + | 32.3862i | 0.638717 | + | 1.10629i | 0.985715 | + | 0.168424i | \(0.0538679\pi\) |
−0.346998 | + | 0.937866i | \(0.612799\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.5180 | + | 7.10549i | −0.904784 | + | 0.242436i | −0.681070 | − | 0.732219i | \(-0.738485\pi\) |
−0.223714 | + | 0.974655i | \(0.571818\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.17354 | + | 17.6140i | 0.312634 | + | 0.600284i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.1797 | −0.346520 | −0.173260 | − | 0.984876i | \(-0.555430\pi\) | ||||
−0.173260 | + | 0.984876i | \(0.555430\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.9860 | 0.713545 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.777892 | − | 1.49362i | −0.0264186 | − | 0.0507261i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.21723 | − | 0.326156i | 0.0412918 | − | 0.0110641i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.53020 | + | 13.0427i | 0.255151 | + | 0.441935i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 45.6601 | + | 3.97721i | 1.54536 | + | 0.134608i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 62.1414 | + | 16.6507i | 2.10076 | + | 0.562897i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.7779 | − | 6.90717i | 0.870458 | − | 0.233239i | 0.204172 | − | 0.978935i | \(-0.434550\pi\) |
0.666286 | + | 0.745696i | \(0.267883\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 35.9960 | + | 39.2677i | 1.21411 | + | 1.32447i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.7798i | 1.03700i | 0.855078 | + | 0.518499i | \(0.173509\pi\) | ||||
−0.855078 | + | 0.518499i | \(0.826491\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.8089 | − | 19.8089i | 0.666622 | − | 0.666622i | −0.290310 | − | 0.956933i | \(-0.593759\pi\) |
0.956933 | + | 0.290310i | \(0.0937586\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −19.8953 | + | 31.2425i | −0.668774 | + | 1.05021i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.0940 | − | 12.1786i | −0.708266 | − | 0.408918i | 0.102153 | − | 0.994769i | \(-0.467427\pi\) |
−0.810419 | + | 0.585851i | \(0.800760\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 39.0550 | − | 22.5484i | 1.30986 | − | 0.756249i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.173190 | + | 1.96235i | 0.00580210 | + | 0.0657413i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.21410 | + | 1.93301i | 0.241411 | + | 0.0646858i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.79985 | + | 1.03914i | 0.0601624 | + | 0.0347348i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.06006 | + | 18.2972i | 0.135561 | + | 0.610927i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.4142 | − | 12.4142i | −0.414037 | − | 0.414037i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.1460 | − | 32.1460i | 1.07094 | − | 1.07094i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 19.1205 | + | 20.8583i | 0.636289 | + | 0.694122i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.6407 | + | 23.6264i | −0.453433 | + | 0.785369i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.0239 | − | 56.0698i | 0.498859 | − | 1.86177i | −0.00838605 | − | 0.999965i | \(-0.502669\pi\) |
0.507245 | − | 0.861802i | \(-0.330664\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.259016 | + | 0.308445i | 0.00859103 | + | 0.0102305i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.9347 | + | 20.6715i | 0.395414 | + | 0.684877i | 0.993154 | − | 0.116813i | \(-0.0372678\pi\) |
−0.597740 | + | 0.801690i | \(0.703934\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.510553 | − | 0.884303i | 0.0168968 | − | 0.0292662i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −53.4884 | + | 27.8572i | −1.76827 | + | 0.920932i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.55845 | − | 1.55845i | −0.0514646 | − | 0.0514646i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.7779 | 0.520466 | 0.260233 | − | 0.965546i | \(-0.416201\pi\) | ||||
0.260233 | + | 0.965546i | \(0.416201\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −55.6284 | − | 17.5279i | −1.83302 | − | 0.577565i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.48292 | + | 20.4625i | 0.180473 | + | 0.673533i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.70397 | + | 36.2157i | −0.319065 | + | 1.19077i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.3825 | + | 22.2432i | 0.341006 | + | 0.730562i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.3132 | − | 8.26371i | 0.469600 | − | 0.271123i | −0.246472 | − | 0.969150i | \(-0.579271\pi\) |
0.716072 | + | 0.698026i | \(0.245938\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.77730 | + | 6.63296i | 0.0582485 | + | 0.217387i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.799912 | + | 18.4014i | −0.0261879 | + | 0.602436i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.58740i | 0.117320i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.92940i | 0.193705i | 0.995299 | + | 0.0968526i | \(0.0308775\pi\) | ||||
−0.995299 | + | 0.0968526i | \(0.969122\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −27.7735 | − | 17.6862i | −0.906354 | − | 0.577169i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.52232 | − | 20.6096i | −0.180022 | − | 0.671853i | −0.995641 | − | 0.0932635i | \(-0.970270\pi\) |
0.815619 | − | 0.578589i | \(-0.196397\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.3603 | + | 6.55886i | −0.369941 | + | 0.213586i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −41.1775 | − | 53.6001i | −1.33950 | − | 1.74361i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.57071 | − | 31.9863i | 0.278511 | − | 1.03942i | −0.674941 | − | 0.737871i | \(-0.735831\pi\) |
0.953452 | − | 0.301545i | \(-0.0975022\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.34741 | + | 8.76066i | 0.0762002 | + | 0.284383i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.61279 | − | 20.7882i | −0.149580 | − | 0.674105i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.546564 | 0.0177049 | 0.00885247 | − | 0.999961i | \(-0.497182\pi\) | ||||
0.00885247 | + | 0.999961i | \(0.497182\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −29.5538 | − | 29.5538i | −0.956339 | − | 0.956339i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.0347109 | − | 0.798502i | 0.00112205 | − | 0.0258119i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 35.4068 | − | 61.3264i | 1.14335 | − | 1.98033i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.1758 | + | 33.2135i | 0.618576 | + | 1.07140i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.11946 | + | 34.6280i | 0.197197 | + | 1.11587i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.20393 | − | 19.4213i | 0.167521 | − | 0.625195i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.49046 | − | 12.9739i | 0.240877 | − | 0.417211i | −0.720087 | − | 0.693883i | \(-0.755898\pi\) |
0.960964 | + | 0.276672i | \(0.0892316\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.50660 | − | 11.1289i | 0.112648 | − | 0.357512i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29.4725 | + | 29.4725i | −0.945816 | + | 0.945816i | −0.998606 | − | 0.0527896i | \(-0.983189\pi\) |
0.0527896 | + | 0.998606i | \(0.483189\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.8725 | − | 15.8725i | −0.508849 | − | 0.508849i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −46.1859 | − | 14.5527i | −1.47913 | − | 0.466059i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.02199 | + | 1.16740i | 0.0646892 | + | 0.0373483i | 0.531996 | − | 0.846747i | \(-0.321442\pi\) |
−0.467307 | + | 0.884095i | \(0.654776\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.626159 | − | 0.167779i | −0.0200121 | − | 0.00536224i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −26.3747 | + | 4.66094i | −0.842080 | + | 0.148812i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.5089 | + | 12.4182i | −0.686029 | + | 0.396079i | −0.802123 | − | 0.597159i | \(-0.796296\pi\) |
0.116094 | + | 0.993238i | \(0.462963\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.9464 | + | 8.05197i | 0.444370 | + | 0.256557i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −27.3649 | − | 1.18955i | −0.871033 | − | 0.0378639i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.2158 | + | 13.2158i | −0.420240 | + | 0.420240i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 7.12527i | − | 0.226342i | −0.993576 | − | 0.113171i | \(-0.963899\pi\) | ||
0.993576 | − | 0.113171i | \(-0.0361008\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 58.4622 | − | 12.9724i | 1.85524 | − | 0.411668i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.60763 | + | 2.57436i | −0.304582 | + | 0.0816126i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −47.5897 | − | 12.7516i | −1.50718 | − | 0.403848i | −0.591684 | − | 0.806170i | \(-0.701537\pi\) |
−0.915498 | + | 0.402322i | \(0.868203\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 15.5337 | − | 11.9335i | 0.491465 | − | 0.377561i |
(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 | 576.2.y.a.239.15 | 88 | ||
3.2 | odd | 2 | 1728.2.z.a.1583.1 | 88 | |||
4.3 | odd | 2 | 144.2.u.a.131.7 | yes | 88 | ||
9.2 | odd | 6 | inner | 576.2.y.a.47.3 | 88 | ||
9.7 | even | 3 | 1728.2.z.a.1007.1 | 88 | |||
12.11 | even | 2 | 432.2.v.a.179.16 | 88 | |||
16.5 | even | 4 | 144.2.u.a.59.14 | yes | 88 | ||
16.11 | odd | 4 | inner | 576.2.y.a.527.3 | 88 | ||
36.7 | odd | 6 | 432.2.v.a.35.9 | 88 | |||
36.11 | even | 6 | 144.2.u.a.83.14 | yes | 88 | ||
48.5 | odd | 4 | 432.2.v.a.395.9 | 88 | |||
48.11 | even | 4 | 1728.2.z.a.719.1 | 88 | |||
144.11 | even | 12 | inner | 576.2.y.a.335.15 | 88 | ||
144.43 | odd | 12 | 1728.2.z.a.143.1 | 88 | |||
144.101 | odd | 12 | 144.2.u.a.11.7 | ✓ | 88 | ||
144.133 | even | 12 | 432.2.v.a.251.16 | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.u.a.11.7 | ✓ | 88 | 144.101 | odd | 12 | ||
144.2.u.a.59.14 | yes | 88 | 16.5 | even | 4 | ||
144.2.u.a.83.14 | yes | 88 | 36.11 | even | 6 | ||
144.2.u.a.131.7 | yes | 88 | 4.3 | odd | 2 | ||
432.2.v.a.35.9 | 88 | 36.7 | odd | 6 | |||
432.2.v.a.179.16 | 88 | 12.11 | even | 2 | |||
432.2.v.a.251.16 | 88 | 144.133 | even | 12 | |||
432.2.v.a.395.9 | 88 | 48.5 | odd | 4 | |||
576.2.y.a.47.3 | 88 | 9.2 | odd | 6 | inner | ||
576.2.y.a.239.15 | 88 | 1.1 | even | 1 | trivial | ||
576.2.y.a.335.15 | 88 | 144.11 | even | 12 | inner | ||
576.2.y.a.527.3 | 88 | 16.11 | odd | 4 | inner | ||
1728.2.z.a.143.1 | 88 | 144.43 | odd | 12 | |||
1728.2.z.a.719.1 | 88 | 48.11 | even | 4 | |||
1728.2.z.a.1007.1 | 88 | 9.7 | even | 3 | |||
1728.2.z.a.1583.1 | 88 | 3.2 | odd | 2 |