Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,2,Mod(113,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 0, 10, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("360.113");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.bs (of order \(12\), degree \(4\), 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: | \(2.87461447277\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 113.16 | ||
Character | \(\chi\) | \(=\) | 360.113 |
Dual form | 360.2.bs.a.137.16 |
$q$-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 \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(217\) | \(271\) | \(281\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.60229 | − | 0.657781i | 0.925081 | − | 0.379770i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.22211 | − | 0.249468i | 0.993757 | − | 0.111566i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.85561 | + | 0.765158i | 1.07932 | + | 0.289202i | 0.754316 | − | 0.656511i | \(-0.227968\pi\) |
0.325002 | + | 0.945713i | \(0.394635\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.13465 | − | 2.10791i | 0.711549 | − | 0.702636i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.16595 | + | 1.82786i | −0.954569 | + | 0.551121i | −0.894497 | − | 0.447073i | \(-0.852466\pi\) |
−0.0600718 | + | 0.998194i | \(0.519133\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.61711 | + | 1.50510i | −1.55790 | + | 0.417439i | −0.931999 | − | 0.362460i | \(-0.881937\pi\) |
−0.625905 | + | 0.779899i | \(0.715270\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.39636 | − | 1.86138i | 0.876936 | − | 0.480606i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.79242 | − | 2.79242i | −0.677261 | − | 0.677261i | 0.282119 | − | 0.959379i | \(-0.408963\pi\) |
−0.959379 | + | 0.282119i | \(0.908963\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.15582i | 0.723994i | 0.932179 | + | 0.361997i | \(0.117905\pi\) | ||||
−0.932179 | + | 0.361997i | \(0.882095\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.07881 | − | 0.652362i | 1.10829 | − | 0.142357i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.00442531 | + | 0.0165155i | 0.000922741 | + | 0.00344371i | 0.966386 | − | 0.257097i | \(-0.0827659\pi\) |
−0.965463 | + | 0.260540i | \(0.916099\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.87553 | − | 1.10869i | 0.975106 | − | 0.221738i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.03378 | − | 4.78161i | 0.391401 | − | 0.920220i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.867889 | − | 1.50323i | −0.161163 | − | 0.279143i | 0.774123 | − | 0.633035i | \(-0.218191\pi\) |
−0.935286 | + | 0.353893i | \(0.884858\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.0235550 | − | 0.0407985i | 0.00423061 | − | 0.00732762i | −0.863902 | − | 0.503659i | \(-0.831987\pi\) |
0.868133 | + | 0.496332i | \(0.165320\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.87043 | + | 5.01126i | −0.673755 | + | 0.872348i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.53635 | + | 0.987880i | 1.10485 | + | 0.166982i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.93650 | − | 5.93650i | 0.975955 | − | 0.975955i | −0.0237623 | − | 0.999718i | \(-0.507564\pi\) |
0.999718 | + | 0.0237623i | \(0.00756450\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.01019 | + | 6.10643i | −1.28266 | + | 0.977811i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.7692 | − | 6.21760i | −1.68187 | − | 0.971027i | −0.960419 | − | 0.278558i | \(-0.910143\pi\) |
−0.721448 | − | 0.692468i | \(-0.756523\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.95353 | + | 11.0227i | −0.450409 | + | 1.68095i | 0.250837 | + | 0.968029i | \(0.419294\pi\) |
−0.701246 | + | 0.712920i | \(0.747372\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.21756 | − | 5.21653i | 0.628717 | − | 0.777634i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.133675 | − | 0.498880i | 0.0194984 | − | 0.0727691i | −0.955491 | − | 0.295020i | \(-0.904674\pi\) |
0.974990 | + | 0.222251i | \(0.0713404\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.50685 | + | 0.869979i | 0.215264 | + | 0.124283i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.31105 | − | 2.63746i | −0.883724 | − | 0.369318i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.87002 | − | 4.87002i | 0.668949 | − | 0.668949i | −0.288524 | − | 0.957473i | \(-0.593164\pi\) |
0.957473 | + | 0.288524i | \(0.0931643\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.57909 | + | 4.85151i | −0.887124 | + | 0.654177i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.07584 | + | 5.05652i | 0.274951 | + | 0.669753i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.07064 | + | 1.85441i | −0.139386 | + | 0.241424i | −0.927264 | − | 0.374407i | \(-0.877846\pi\) |
0.787878 | + | 0.615831i | \(0.211180\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.16162 | + | 2.01199i | 0.148731 | + | 0.257609i | 0.930759 | − | 0.365634i | \(-0.119148\pi\) |
−0.782028 | + | 0.623244i | \(0.785815\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.70860 | − | 4.38602i | 0.971192 | − | 0.552586i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12.1063 | + | 4.74578i | −1.50161 | + | 0.588642i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.05975 | + | 11.4191i | 0.373808 | + | 1.39507i | 0.855078 | + | 0.518499i | \(0.173509\pi\) |
−0.481270 | + | 0.876572i | \(0.659824\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.0179542 | + | 0.0235517i | 0.00216143 | + | 0.00283529i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.67122i | − | 0.910406i | −0.890388 | − | 0.455203i | \(-0.849567\pi\) | ||
0.890388 | − | 0.455203i | \(-0.150433\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.97978 | + | 7.97978i | 0.933962 | + | 0.933962i | 0.997951 | − | 0.0639883i | \(-0.0203820\pi\) |
−0.0639883 | + | 0.997951i | \(0.520382\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.08273 | − | 4.98347i | 0.817843 | − | 0.575442i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.4393 | + | 2.79720i | −1.18967 | + | 0.318771i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.452608 | − | 0.261313i | 0.0509223 | − | 0.0294000i | −0.474323 | − | 0.880351i | \(-0.657307\pi\) |
0.525245 | + | 0.850951i | \(0.323974\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.113447 | − | 8.99928i | 0.0126052 | − | 0.999921i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.28798 | − | 2.48871i | −1.01949 | − | 0.273171i | −0.289900 | − | 0.957057i | \(-0.593622\pi\) |
−0.729589 | + | 0.683886i | \(0.760289\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.90167 | − | 5.50843i | −0.748592 | − | 0.597474i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.37940 | − | 1.83772i | −0.255099 | − | 0.197025i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.16365 | −0.759346 | −0.379673 | − | 0.925121i | \(-0.623963\pi\) | ||||
−0.379673 | + | 0.925121i | \(0.623963\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17.1919 | −1.80220 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.0109054 | − | 0.0808649i | 0.00113084 | − | 0.00838530i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.787276 | + | 7.01257i | 0.0807728 | + | 0.719474i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.80611 | − | 1.82369i | −0.691056 | − | 0.185168i | −0.103835 | − | 0.994595i | \(-0.533111\pi\) |
−0.587221 | + | 0.809427i | \(0.699778\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.90522 | + | 10.5754i | −0.291986 | + | 1.06286i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.95553 | + | 1.70638i | −0.294086 | + | 0.169791i | −0.639783 | − | 0.768555i | \(-0.720976\pi\) |
0.345697 | + | 0.938346i | \(0.387643\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.63782 | − | 0.974751i | 0.358445 | − | 0.0960451i | −0.0751023 | − | 0.997176i | \(-0.523928\pi\) |
0.433547 | + | 0.901131i | \(0.357262\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 11.1229 | − | 2.71662i | 1.08549 | − | 0.265115i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.18949 | + | 6.18949i | 0.598360 | + | 0.598360i | 0.939876 | − | 0.341516i | \(-0.110940\pi\) |
−0.341516 | + | 0.939876i | \(0.610940\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 7.51076i | − | 0.719400i | −0.933068 | − | 0.359700i | \(-0.882879\pi\) | ||
0.933068 | − | 0.359700i | \(-0.117121\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.60706 | − | 13.4169i | 0.532199 | − | 1.27348i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.25011 | + | 15.8616i | 0.399817 | + | 1.49214i | 0.813419 | + | 0.581679i | \(0.197604\pi\) |
−0.413602 | + | 0.910458i | \(0.635729\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.0139536 | + | 0.0355952i | 0.00130118 | + | 0.00331927i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.81793 | + | 15.0532i | −0.815218 | + | 1.39167i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.83741 | − | 10.1107i | −0.535114 | − | 0.926845i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.18215 | − | 2.04754i | 0.107468 | − | 0.186140i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −21.3452 | − | 2.87861i | −1.92463 | − | 0.259555i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.5574 | − | 3.67992i | 0.944280 | − | 0.329142i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.64093 | − | 9.64093i | 0.855495 | − | 0.855495i | −0.135309 | − | 0.990803i | \(-0.543203\pi\) |
0.990803 | + | 0.135309i | \(0.0432027\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.51813 | + | 19.6043i | 0.221709 | + | 1.72607i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.8254 | + | 7.98211i | 1.20793 | + | 0.697400i | 0.962307 | − | 0.271965i | \(-0.0876733\pi\) |
0.245625 | + | 0.969365i | \(0.421007\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.41470 | + | 9.01177i | −0.209381 | + | 0.781420i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.32642 | − | 11.1326i | 0.286292 | − | 0.958142i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.93154 | − | 7.20862i | 0.165023 | − | 0.615874i | −0.833014 | − | 0.553251i | \(-0.813387\pi\) |
0.998037 | − | 0.0626224i | \(-0.0199464\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.7638 | − | 6.21447i | −0.912971 | − | 0.527104i | −0.0315853 | − | 0.999501i | \(-0.510056\pi\) |
−0.881386 | + | 0.472397i | \(0.843389\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.113969 | − | 0.887278i | −0.00959791 | − | 0.0747223i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.0324 | − | 15.0324i | 1.25707 | − | 1.25707i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.30355 | − | 3.12383i | −0.191300 | − | 0.259420i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.98666 | + | 0.402781i | 0.246336 | + | 0.0332208i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.40866 | + | 16.2963i | −0.770787 | + | 1.33504i | 0.166345 | + | 0.986068i | \(0.446803\pi\) |
−0.937132 | + | 0.348975i | \(0.886530\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.5767 | − | 18.3195i | −0.860724 | − | 1.49082i | −0.871232 | − | 0.490872i | \(-0.836678\pi\) |
0.0105079 | − | 0.999945i | \(-0.496655\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.8470 | − | 0.0746697i | −0.957772 | − | 0.00603669i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.0421639 | − | 0.0965349i | 0.00338668 | − | 0.00775387i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.00602 | + | 14.9507i | 0.319716 | + | 1.19319i | 0.919518 | + | 0.393047i | \(0.128579\pi\) |
−0.599803 | + | 0.800148i | \(0.704754\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.59977 | − | 11.0066i | 0.364785 | − | 0.872879i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.0505478i | 0.00398372i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.05208 | − | 3.05208i | −0.239057 | − | 0.239057i | 0.577402 | − | 0.816460i | \(-0.304066\pi\) |
−0.816460 | + | 0.577402i | \(0.804066\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.35036 | + | 12.1011i | −0.572224 | + | 0.942070i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.5890 | − | 5.24886i | 1.51584 | − | 0.406169i | 0.597473 | − | 0.801889i | \(-0.296172\pi\) |
0.918371 | + | 0.395720i | \(0.129505\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18.0282 | − | 10.4086i | 1.38679 | − | 0.800661i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.65217 | + | 6.73656i | 0.508704 | + | 0.515158i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.0750 | + | 4.03932i | 1.14613 | + | 0.307104i | 0.781412 | − | 0.624015i | \(-0.214500\pi\) |
0.364715 | + | 0.931119i | \(0.381166\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.7709 | + | 0.564566i | 1.11658 | + | 0.0426771i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.495684 | + | 3.67555i | −0.0372579 | + | 0.276271i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.89096 | −0.290824 | −0.145412 | − | 0.989371i | \(-0.546451\pi\) | ||||
−0.145412 | + | 0.989371i | \(0.546451\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.5521 | 1.08165 | 0.540826 | − | 0.841134i | \(-0.318112\pi\) | ||||
0.540826 | + | 0.841134i | \(0.318112\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.18471 | + | 2.45970i | 0.235420 | + | 0.181826i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 11.7106 | − | 14.6725i | 0.860980 | − | 1.07875i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.9448 | + | 3.73650i | 1.01974 | + | 0.273240i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.46635 | − | 12.0982i | 0.688576 | − | 0.880016i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.08036 | + | 3.51050i | −0.439960 | + | 0.254011i | −0.703580 | − | 0.710616i | \(-0.748417\pi\) |
0.263621 | + | 0.964626i | \(0.415083\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.7922 | − | 3.69562i | 0.992787 | − | 0.266017i | 0.274366 | − | 0.961625i | \(-0.411532\pi\) |
0.718421 | + | 0.695609i | \(0.244865\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −16.2762 | + | 15.5674i | −1.16556 | + | 1.11481i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.76470 | − | 2.76470i | −0.196977 | − | 0.196977i | 0.601726 | − | 0.798703i | \(-0.294480\pi\) |
−0.798703 | + | 0.601726i | \(0.794480\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.66540i | 0.543386i | 0.962384 | + | 0.271693i | \(0.0875835\pi\) | ||||
−0.962384 | + | 0.271693i | \(0.912416\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.4139 | + | 16.2841i | 0.875609 | + | 1.14859i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.32814 | − | 4.95670i | −0.0932175 | − | 0.347892i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −25.4814 | − | 11.1296i | −1.77970 | − | 0.777326i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.0442596 | + | 0.0259266i | 0.00307625 | + | 0.00180202i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.76839 | − | 9.99115i | −0.399008 | − | 0.691102i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.56336 | − | 16.5642i | 0.658369 | − | 1.14033i | −0.322669 | − | 0.946512i | \(-0.604580\pi\) |
0.981038 | − | 0.193816i | \(-0.0620866\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.04598 | − | 12.2915i | −0.345745 | − | 0.842199i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.81324 | + | 25.2305i | −0.260061 | + | 1.72070i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.0984811 | − | 0.0984811i | 0.00668533 | − | 0.00668533i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.0348 | + | 7.53695i | 1.21868 | + | 0.509300i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.8882 | + | 11.4824i | 1.33782 | + | 0.772392i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.72248 | + | 25.0887i | −0.450171 | + | 1.68006i | 0.251740 | + | 0.967795i | \(0.418997\pi\) |
−0.701910 | + | 0.712265i | \(0.747669\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.07053 | − | 12.6438i | 0.538035 | − | 0.842922i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.17675 | − | 15.5878i | 0.277221 | − | 1.03460i | −0.677118 | − | 0.735874i | \(-0.736771\pi\) |
0.954339 | − | 0.298727i | \(-0.0965620\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.20334 | − | 4.73620i | −0.542092 | − | 0.312977i | 0.203834 | − | 0.979005i | \(-0.434660\pi\) |
−0.745926 | + | 0.666028i | \(0.767993\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.8868 | + | 11.3487i | −0.979481 | + | 0.746690i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.35560 | − | 8.35560i | 0.547393 | − | 0.547393i | −0.378293 | − | 0.925686i | \(-0.623489\pi\) |
0.925686 | + | 0.378293i | \(0.123489\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.172585 | − | 1.14191i | 0.0112582 | − | 0.0744902i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.553321 | − | 0.716416i | 0.0359420 | − | 0.0465362i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.475159 | + | 0.823000i | −0.0307355 | + | 0.0532355i | −0.880984 | − | 0.473146i | \(-0.843118\pi\) |
0.850249 | + | 0.526382i | \(0.176452\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.38145 | − | 11.0530i | −0.411065 | − | 0.711986i | 0.583941 | − | 0.811796i | \(-0.301510\pi\) |
−0.995007 | + | 0.0998100i | \(0.968177\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.73778 | − | 14.4941i | −0.368079 | − | 0.929794i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.56541 | + | 1.55728i | 0.227786 | + | 0.0994908i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.74982 | − | 17.7266i | −0.302224 | − | 1.12791i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −16.5190 | + | 2.12183i | −1.04685 | + | 0.134466i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.7575i | 1.18396i | 0.805951 | + | 0.591982i | \(0.201654\pi\) | ||||
−0.805951 | + | 0.591982i | \(0.798346\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.0441983 | − | 0.0441983i | −0.00277872 | − | 0.00277872i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −14.6818 | − | 4.28630i | −0.919410 | − | 0.268419i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.78980 | − | 1.01547i | 0.236401 | − | 0.0633435i | −0.138673 | − | 0.990338i | \(-0.544284\pi\) |
0.375074 | + | 0.926995i | \(0.377617\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.4947 | − | 12.4100i | 1.33561 | − | 0.771118i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.02131 | − | 1.37943i | −0.310811 | − | 0.0853848i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.2488 | + | 5.42565i | 1.24860 | + | 0.334560i | 0.821794 | − | 0.569785i | \(-0.192974\pi\) |
0.426802 | + | 0.904345i | \(0.359640\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.60681 | − | 12.0366i | 0.590141 | − | 0.739405i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.4782 | + | 4.71212i | −0.702456 | + | 0.288377i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.04943 | −0.124956 | −0.0624778 | − | 0.998046i | \(-0.519900\pi\) | ||||
−0.0624778 | + | 0.998046i | \(0.519900\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.06017 | −0.428875 | −0.214437 | − | 0.976738i | \(-0.568792\pi\) | ||||
−0.214437 | + | 0.976738i | \(0.568792\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −27.5463 | + | 11.3085i | −1.66718 | + | 0.684421i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13.4091 | + | 12.4218i | −0.808602 | + | 0.749066i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.2827 | − | 5.16678i | −1.15858 | − | 0.310442i | −0.372184 | − | 0.928159i | \(-0.621391\pi\) |
−0.786400 | + | 0.617717i | \(0.788058\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.0357178 | − | 0.136742i | −0.00213837 | − | 0.00818654i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.8727 | + | 6.27735i | −0.648610 | + | 0.374475i | −0.787923 | − | 0.615773i | \(-0.788844\pi\) |
0.139313 | + | 0.990248i | \(0.455510\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.70224 | + | 1.52791i | −0.338963 | + | 0.0908248i | −0.424285 | − | 0.905529i | \(-0.639475\pi\) |
0.0853225 | + | 0.996353i | \(0.472808\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.87417 | + | 10.7183i | 0.347956 | + | 0.634897i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −25.9952 | − | 25.9952i | −1.53445 | − | 1.53445i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 1.40481i | − | 0.0826359i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.1049 | + | 1.55485i | −0.709604 | + | 0.0911470i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.11779 | + | 7.90371i | 0.123723 | + | 0.461740i | 0.999791 | − | 0.0204476i | \(-0.00650912\pi\) |
−0.876068 | + | 0.482187i | \(0.839842\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.91647 | + | 4.38779i | −0.111581 | + | 0.255467i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.30128 | + | 18.8558i | 0.133534 | + | 1.09412i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.0497148 | − | 0.0861086i | −0.00287508 | − | 0.00497979i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.8682 | + | 29.2166i | −0.972269 | + | 1.68402i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.61319 | + | 4.67820i | −0.207572 | + | 0.268756i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.08318 | + | 4.18108i | 0.176543 | + | 0.239408i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.0523 | + | 11.0523i | −0.630790 | + | 0.630790i | −0.948266 | − | 0.317477i | \(-0.897165\pi\) |
0.317477 | + | 0.948266i | \(0.397165\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.18766 | − | 3.95472i | 0.295116 | − | 0.224976i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.0045 | + | 5.77608i | 0.567301 | + | 0.327532i | 0.756071 | − | 0.654490i | \(-0.227117\pi\) |
−0.188769 | + | 0.982021i | \(0.560450\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.94044 | − | 14.7059i | 0.222727 | − | 0.831228i | −0.760576 | − | 0.649249i | \(-0.775083\pi\) |
0.983302 | − | 0.181979i | \(-0.0582502\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 16.0352 | − | 11.6693i | 0.903480 | − | 0.657488i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.65400 | − | 6.17280i | 0.0928977 | − | 0.346699i | −0.903795 | − | 0.427967i | \(-0.859230\pi\) |
0.996692 | + | 0.0812674i | \(0.0258968\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.49539 | + | 3.17276i | 0.307683 | + | 0.177641i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.9887 | + | 5.84601i | 0.780771 | + | 0.326292i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.81236 | − | 8.81236i | 0.490333 | − | 0.490333i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −25.7177 | + | 13.5658i | −1.42656 | + | 0.752495i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.94043 | − | 12.0344i | −0.273207 | − | 0.665503i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.763444 | − | 1.32232i | 0.0420900 | − | 0.0729020i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.76353 | − | 11.7148i | −0.371757 | − | 0.643903i | 0.618079 | − | 0.786116i | \(-0.287911\pi\) |
−0.989836 | + | 0.142214i | \(0.954578\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.158743 | − | 25.1860i | 0.00869907 | − | 1.38018i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.64781 | + | 24.6113i | 0.527116 | + | 1.34466i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.82116 | − | 6.79666i | −0.0992048 | − | 0.370237i | 0.898419 | − | 0.439140i | \(-0.144717\pi\) |
−0.997623 | + | 0.0689028i | \(0.978050\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.2434 | + | 22.6192i | 0.936532 | + | 1.22851i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.172221i | 0.00932630i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.9959 | − | 10.9959i | −0.593720 | − | 0.593720i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.0457715 | + | 0.0478553i | 0.00246426 | + | 0.00257644i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −29.5309 | + | 7.91278i | −1.58530 | + | 0.424780i | −0.940562 | − | 0.339622i | \(-0.889701\pi\) |
−0.644739 | + | 0.764403i | \(0.723034\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.7285 | − | 15.4317i | 1.43074 | − | 0.826039i | 0.433565 | − | 0.901122i | \(-0.357255\pi\) |
0.997177 | + | 0.0750829i | \(0.0239221\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.22715 | + | 29.9198i | −0.225629 | + | 1.59700i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.0664 | − | 4.03704i | −0.801905 | − | 0.214870i | −0.165485 | − | 0.986212i | \(-0.552919\pi\) |
−0.636420 | + | 0.771342i | \(0.719586\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.91372 | − | 17.0463i | −0.101570 | − | 0.904723i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −16.0038 | − | 12.3605i | −0.847012 | − | 0.654186i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.34799 | 0.282256 | 0.141128 | − | 0.989991i | \(-0.454927\pi\) | ||||
0.141128 | + | 0.989991i | \(0.454927\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.04082 | 0.475833 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.547308 | − | 4.05835i | 0.0287262 | − | 0.213008i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.7226 | + | 15.7412i | 1.03233 | + | 0.823934i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.30973 | + | 0.886840i | 0.172767 | + | 0.0462927i | 0.344165 | − | 0.938909i | \(-0.388162\pi\) |
−0.171399 | + | 0.985202i | \(0.554829\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −36.0946 | + | 9.42810i | −1.87901 | + | 0.490807i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 17.6332 | − | 10.1805i | 0.915471 | − | 0.528547i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.26293 | + | 2.21404i | −0.427838 | + | 0.114639i | −0.466311 | − | 0.884621i | \(-0.654417\pi\) |
0.0384731 | + | 0.999260i | \(0.487751\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.4954 | − | 12.8407i | 0.748538 | − | 0.663092i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.13753 | + | 7.13753i | 0.367602 | + | 0.367602i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.4965i | 0.898737i | 0.893346 | + | 0.449369i | \(0.148351\pi\) | ||||
−0.893346 | + | 0.449369i | \(0.851649\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.10592 | − | 21.7892i | 0.466510 | − | 1.11629i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.59627 | − | 13.4215i | −0.183761 | − | 0.685805i | −0.994892 | − | 0.100941i | \(-0.967815\pi\) |
0.811132 | − | 0.584864i | \(-0.198852\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −22.4995 | + | 8.81996i | −1.14668 | + | 0.449507i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 16.9301 | + | 29.7554i | 0.860607 | + | 1.51255i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.179116 | − | 0.310238i | −0.00908155 | − | 0.0157297i | 0.861449 | − | 0.507844i | \(-0.169557\pi\) |
−0.870530 | + | 0.492115i | \(0.836224\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.0337608 | − | 0.0584754i | 0.00170736 | − | 0.00295723i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 27.4028 | + | 3.69553i | 1.38229 | + | 0.186415i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.940554 | − | 0.693577i | 0.0473244 | − | 0.0348977i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.2262 | − | 17.2262i | 0.864557 | − | 0.864557i | −0.127306 | − | 0.991863i | \(-0.540633\pi\) |
0.991863 | + | 0.127306i | \(0.0406332\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.05873 | + | 16.0278i | 0.103066 | + | 0.802393i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.61875 | − | 4.39869i | −0.380462 | − | 0.219660i | 0.297557 | − | 0.954704i | \(-0.403828\pi\) |
−0.678019 | + | 0.735044i | \(0.737161\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0709052 | + | 0.264622i | −0.00353204 | + | 0.0131818i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.99294 | − | 20.0257i | −0.0990302 | − | 0.995084i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.94356 | + | 29.6458i | −0.393748 | + | 1.46949i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.59212 | + | 3.80596i | 0.325959 | + | 0.188193i | 0.654046 | − | 0.756455i | \(-0.273070\pi\) |
−0.328086 | + | 0.944648i | \(0.606404\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.64680 | − | 12.8208i | −0.0812309 | − | 0.632404i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.47625 | + | 4.47625i | −0.220262 | + | 0.220262i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21.2598 | − | 3.21312i | −1.04360 | − | 0.157726i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −21.3344 | − | 2.87716i | −1.04475 | − | 0.140895i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.80742 | − | 11.7908i | 0.332564 | − | 0.576018i | −0.650450 | − | 0.759549i | \(-0.725420\pi\) |
0.983014 | + | 0.183531i | \(0.0587529\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.75046 | + | 15.1562i | 0.426471 | + | 0.738670i | 0.996557 | − | 0.0829155i | \(-0.0264231\pi\) |
−0.570085 | + | 0.821586i | \(0.693090\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.766245 | − | 1.34671i | −0.0372561 | − | 0.0654791i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −16.7104 | − | 10.5186i | −0.810576 | − | 0.510227i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.77765 | + | 6.63429i | 0.0860266 | + | 0.321056i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14.1981 | − | 33.9741i | 0.685493 | − | 1.64029i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.51527i | 0.313830i | 0.987612 | + | 0.156915i | \(0.0501548\pi\) | ||||
−0.987612 | + | 0.156915i | \(0.949845\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.3750 | + | 11.3750i | 0.546646 | + | 0.546646i | 0.925469 | − | 0.378823i | \(-0.123671\pi\) |
−0.378823 | + | 0.925469i | \(0.623671\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.74575 | − | 3.49003i | −0.275487 | − | 0.167334i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.0521198 | + | 0.0139655i | −0.00249323 | + | 0.000668059i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.7213 | + | 9.07671i | −0.750338 | + | 0.433208i | −0.825816 | − | 0.563940i | \(-0.809285\pi\) |
0.0754782 | + | 0.997147i | \(0.475952\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.05043 | − | 1.31920i | 0.240497 | − | 0.0628190i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.6627 | − | 4.73270i | −0.839179 | − | 0.224857i | −0.186465 | − | 0.982462i | \(-0.559703\pi\) |
−0.652714 | + | 0.757604i | \(0.726370\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.9184 | + | 1.78710i | −0.754605 | + | 0.0847168i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.35599 | + | 32.3001i | −0.206031 | + | 1.52774i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.4573 | 1.01263 | 0.506317 | − | 0.862347i | \(-0.331006\pi\) | ||||
0.506317 | + | 0.862347i | \(0.331006\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 45.4597 | 2.14061 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −28.9972 | − | 22.3959i | −1.36241 | − | 1.05225i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −38.2022 | + | 4.28883i | −1.79095 | + | 0.201063i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.1591 | + | 3.25801i | 0.568778 | + | 0.152404i | 0.531736 | − | 0.846910i | \(-0.321540\pi\) |
0.0370417 | + | 0.999314i | \(0.488207\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −19.0314 | + | 7.67308i | −0.888309 | + | 0.358149i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.8369 | + | 6.83406i | −0.551301 | + | 0.318294i | −0.749647 | − | 0.661838i | \(-0.769777\pi\) |
0.198346 | + | 0.980132i | \(0.436443\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.2066 | − | 5.95025i | 1.03203 | − | 0.276531i | 0.297223 | − | 0.954808i | \(-0.403940\pi\) |
0.734807 | + | 0.678277i | \(0.237273\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.00405983 | − | 0.182411i | 0.000188270 | − | 0.00845912i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.8793 | − | 20.8793i | −0.966177 | − | 0.966177i | 0.0332691 | − | 0.999446i | \(-0.489408\pi\) |
−0.999446 | + | 0.0332691i | \(0.989408\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 34.9498i | 1.61383i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.2531 | + | 21.3202i | 0.748902 | + | 0.982383i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.7973 | − | 40.2960i | −0.496459 | − | 1.85281i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.49882 | + | 15.3863i | 0.160537 | + | 0.705971i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.130225 | − | 20.6614i | 0.00596260 | − | 0.946018i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.0800 | − | 31.3155i | −0.826096 | − | 1.43084i | −0.901078 | − | 0.433656i | \(-0.857223\pi\) |
0.0749821 | − | 0.997185i | \(-0.476110\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.4109 | + | 42.2810i | −1.11304 | + | 1.92785i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.0332494 | + | 0.0809920i | 0.00151290 | + | 0.00368527i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.5789 | − | 2.35453i | −0.707400 | − | 0.106914i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.8415 | − | 19.8415i | 0.899103 | − | 0.899103i | −0.0962539 | − | 0.995357i | \(-0.530686\pi\) |
0.995357 | + | 0.0962539i | \(0.0306861\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.89791 | − | 2.88271i | −0.311934 | − | 0.130361i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.8519 | − | 8.57477i | −0.670259 | − | 0.386974i | 0.125916 | − | 0.992041i | \(-0.459813\pi\) |
−0.796175 | + | 0.605067i | \(0.793146\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.77413 | + | 6.62115i | −0.0799029 | + | 0.298202i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.81750 | + | 24.2244i | −0.171584 | + | 1.08880i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.86969 | − | 21.9060i | 0.263292 | − | 0.982618i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.8823 | − | 11.4791i | −0.890056 | − | 0.513874i | −0.0160952 | − | 0.999870i | \(-0.505123\pi\) |
−0.873961 | + | 0.485996i | \(0.838457\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 27.9346 | − | 21.2955i | 1.24803 | − | 0.951412i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.820890 | + | 0.820890i | −0.0366017 | + | 0.0366017i | −0.725171 | − | 0.688569i | \(-0.758239\pi\) |
0.688569 | + | 0.725171i | \(0.258239\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.14183 | + | 4.52907i | −0.273308 | + | 0.201541i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 22.0398 | − | 28.5362i | 0.978822 | − | 1.26734i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.1122 | − | 22.7110i | 0.581188 | − | 1.00665i | −0.414151 | − | 0.910208i | \(-0.635921\pi\) |
0.995339 | − | 0.0964388i | \(-0.0307452\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.6813 | + | 28.8929i | 0.737938 | + | 1.27815i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 15.0899 | + | 6.41823i | 0.666234 | + | 0.283372i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.84046 | − | 3.07352i | 0.345492 | − | 0.135436i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.488677 | + | 1.82377i | 0.0214920 | + | 0.0802092i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 26.8114 | − | 3.44386i | 1.17689 | − | 0.151169i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.8958i | 0.521166i | 0.965451 | + | 0.260583i | \(0.0839147\pi\) | ||||
−0.965451 | + | 0.260583i | \(0.916085\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.6324 | + | 10.6324i | 0.464923 | + | 0.464923i | 0.900265 | − | 0.435342i | \(-0.143373\pi\) |
−0.435342 | + | 0.900265i | \(0.643373\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 24.0386 | − | 8.81144i | 1.04913 | − | 0.384563i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.179702 | + | 0.0481510i | −0.00782793 | + | 0.00209749i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.9183 | − | 11.4999i | 0.866014 | − | 0.499994i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.62348 | + | 6.21533i | 0.0704529 | + | 0.269722i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 69.8499 | + | 18.7162i | 3.02553 | + | 0.810689i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.2978 | + | 12.2096i | 0.661381 | + | 0.527869i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.23444 | + | 2.55940i | −0.269036 | + | 0.110446i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.36081 | −0.273979 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.59421 | 0.412487 | 0.206244 | − | 0.978501i | \(-0.433876\pi\) | ||||
0.206244 | + | 0.978501i | \(0.433876\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 23.3167 | − | 9.57212i | 1.00062 | − | 0.410779i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.87369 | − | 16.6897i | −0.0802603 | − | 0.714909i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.9852 | + | 3.74733i | 0.597965 | + | 0.160224i | 0.545091 | − | 0.838377i | \(-0.316495\pi\) |
0.0528744 | + | 0.998601i | \(0.483162\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.72076 | + | 1.84630i | 0.286835 | + | 0.0787981i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.74391 | − | 2.73890i | 0.202098 | − | 0.116681i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.49242 | − | 0.399892i | 0.0634640 | − | 0.0170051i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.11242 | − | 31.2126i | 0.386801 | − | 1.32490i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.1923 | + | 25.1923i | 1.06743 | + | 1.06743i | 0.997556 | + | 0.0698778i | \(0.0222609\pi\) |
0.0698778 | + | 0.997556i | \(0.477739\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 66.3611i | − | 2.80678i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.8014 | − | 3.18568i | 1.04711 | − | 0.134500i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.362891 | + | 1.35433i | 0.0152940 | + | 0.0570781i | 0.973151 | − | 0.230167i | \(-0.0739272\pi\) |
−0.957857 | + | 0.287245i | \(0.907261\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.4012 | + | 34.1860i | 0.563792 | + | 1.43822i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.20983 | − | 25.6116i | 0.302784 | − | 1.07559i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.3719 | + | 21.4287i | 0.518657 | + | 0.898339i | 0.999765 | + | 0.0216784i | \(0.00690098\pi\) |
−0.481108 | + | 0.876661i | \(0.659766\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.92196 | − | 15.4533i | 0.373373 | − | 0.646700i | −0.616709 | − | 0.787191i | \(-0.711535\pi\) |
0.990082 | + | 0.140491i | \(0.0448680\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.43335 | + | 9.62437i | −0.310532 | + | 0.402064i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.0398863 | + | 0.0756154i | 0.00166337 | + | 0.00315338i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.2195 | + | 16.2195i | −0.675226 | + | 0.675226i | −0.958916 | − | 0.283690i | \(-0.908441\pi\) |
0.283690 | + | 0.958916i | \(0.408441\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.6682 | − | 14.9937i | 0.817383 | − | 0.623118i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.6186 | − | 14.2135i | −1.02135 | − | 0.589677i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.51652 | + | 24.3200i | −0.269887 | + | 1.00723i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −15.8391 | + | 35.6496i | −0.654867 | + | 1.47393i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.45896 | + | 35.3013i | −0.390413 | + | 1.45704i | 0.439041 | + | 0.898467i | \(0.355318\pi\) |
−0.829454 | + | 0.558574i | \(0.811348\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.128753 | + | 0.0743353i | 0.00530516 | + | 0.00306293i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.24842 | − | 2.61128i | −0.257026 | − | 0.107414i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.8715 | + | 21.8715i | −0.898153 | + | 0.898153i | −0.995273 | − | 0.0971194i | \(-0.969037\pi\) |
0.0971194 | + | 0.995273i | \(0.469037\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15.4936 | − | 21.0108i | −0.635178 | − | 0.861359i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.04216 | + | 12.2822i | 0.206362 | + | 0.502676i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.01176 | − | 5.21653i | 0.123057 | − | 0.213142i | −0.797915 | − | 0.602771i | \(-0.794063\pi\) |
0.920972 | + | 0.389629i | \(0.127397\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.1359 | − | 38.3405i | −0.902942 | − | 1.56394i | −0.823656 | − | 0.567090i | \(-0.808069\pi\) |
−0.0792867 | − | 0.996852i | \(-0.525264\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 30.6020 | + | 17.9262i | 1.24621 | + | 0.730011i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.11607 | − | 4.84477i | 0.0860304 | − | 0.196968i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.40334 | + | 35.0937i | 0.381670 | + | 1.42441i | 0.843350 | + | 0.537365i | \(0.180580\pi\) |
−0.461680 | + | 0.887046i | \(0.652753\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.38849 | − | 7.06843i | −0.218353 | − | 0.286427i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.00346i | 0.121507i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.6310 | − | 22.6310i | −0.914056 | − | 0.914056i | 0.0825324 | − | 0.996588i | \(-0.473699\pi\) |
−0.996588 | + | 0.0825324i | \(0.973699\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −48.1494 | − | 1.07164i | −1.94157 | − | 0.0432125i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.6990 | − | 4.74243i | 0.712535 | − | 0.190923i | 0.115697 | − | 0.993285i | \(-0.463090\pi\) |
0.596838 | + | 0.802361i | \(0.296423\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.246643 | + | 0.142399i | −0.00991341 | + | 0.00572351i | −0.504949 | − | 0.863149i | \(-0.668489\pi\) |
0.495035 | + | 0.868873i | \(0.335155\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.0879706 | + | 0.0124287i | 0.00353014 | + | 0.000498748i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −20.4566 | − | 5.48132i | −0.819576 | − | 0.219605i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.5416 | − | 10.8109i | 0.901664 | − | 0.432436i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −15.8146 | − | 12.2144i | −0.631575 | − | 0.487794i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −33.1544 | −1.32195 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.6964 | −0.465625 | −0.232813 | − | 0.972522i | \(-0.574793\pi\) | ||||
−0.232813 | + | 0.972522i | \(0.574793\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.42762 | − | 32.8312i | 0.175982 | − | 1.30492i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.0181 | − | 23.8283i | 0.754710 | − | 0.945597i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.77353 | − | 2.61881i | −0.387241 | − | 0.103761i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16.1702 | − | 16.3754i | −0.639684 | − | 0.647799i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.50621 | + | 4.33372i | −0.296478 | + | 0.171171i | −0.640859 | − | 0.767658i | \(-0.721422\pi\) |
0.344382 | + | 0.938830i | \(0.388089\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −46.4536 | + | 12.4472i | −1.83195 | + | 0.490870i | −0.998128 | − | 0.0611592i | \(-0.980520\pi\) |
−0.833825 | + | 0.552029i | \(0.813854\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.4862 | + | 42.9348i | 0.412895 | + | 1.69055i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.10316 | + | 8.10316i | 0.318568 | + | 0.318568i | 0.848217 | − | 0.529649i | \(-0.177676\pi\) |
−0.529649 | + | 0.848217i | \(0.677676\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 7.82795i | − | 0.307274i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.0930160 | − | 0.222574i | 0.00364559 | − | 0.00872337i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.32971 | − | 16.1587i | −0.169435 | − | 0.632338i | −0.997433 | − | 0.0716077i | \(-0.977187\pi\) |
0.827998 | − | 0.560731i | \(-0.189480\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 32.7129 | + | 14.2881i | 1.27820 | + | 0.558283i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 33.8547 | + | 0.213380i | 1.32080 | + | 0.00832477i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.1363 | + | 41.8053i | 0.940218 | + | 1.62850i | 0.765055 | + | 0.643965i | \(0.222712\pi\) |
0.175163 | + | 0.984540i | \(0.443955\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.548876 | − | 0.950681i | 0.0213488 | − | 0.0369772i | −0.855154 | − | 0.518375i | \(-0.826537\pi\) |
0.876502 | + | 0.481397i | \(0.159871\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 39.4195 | + | 5.31611i | 1.53093 | + | 0.206460i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.11757 | + | 20.6275i | −0.120894 | + | 0.799901i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.0209859 | − | 0.0209859i | 0.000812576 | − | 0.000812576i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.73149 | + | 44.6211i | 0.221592 | + | 1.72515i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.35529 | − | 4.24658i | −0.283948 | − | 0.163937i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.0180520 | + | 0.0673708i | −0.000695852 | + | 0.00259695i | −0.966273 | − | 0.257520i | \(-0.917095\pi\) |
0.965577 | + | 0.260117i | \(0.0837612\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.61443 | − | 25.5677i | 0.177609 | − | 0.984101i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.177161 | − | 0.661175i | 0.00680886 | − | 0.0254110i | −0.962438 | − | 0.271502i | \(-0.912480\pi\) |
0.969247 | + | 0.246091i | \(0.0791463\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.0402 | − | 10.4155i | −0.692318 | − | 0.399710i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.56103 | − | 27.7236i | −0.136459 | − | 1.06237i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.5217 | − | 17.5217i | 0.670448 | − | 0.670448i | −0.287371 | − | 0.957819i | \(-0.592781\pi\) |
0.957819 | + | 0.287371i | \(0.0927813\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.49378 | − | 16.5002i | 0.0952823 | − | 0.630440i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.2595 | − | 2.19275i | −0.620338 | − | 0.0836587i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −20.0256 | + | 34.6853i | −0.762914 | + | 1.32141i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.48505 | − | 6.03629i | −0.132578 | − | 0.229631i | 0.792092 | − | 0.610402i | \(-0.208992\pi\) |
−0.924670 | + | 0.380771i | \(0.875659\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −16.3880 | + | 27.9761i | −0.622529 | + | 1.06273i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −25.4686 | − | 11.1240i | −0.966078 | − | 0.421957i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.7100 | + | 47.4343i | 0.481425 | + | 1.79670i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.89191 | − | 18.8842i | 0.298499 | − | 0.714267i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 27.7664i | − | 1.04872i | −0.851496 | − | 0.524362i | \(-0.824304\pi\) | ||
0.851496 | − | 0.524362i | \(-0.175696\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.7345 | + | 18.7345i | 0.706586 | + | 0.706586i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.474599 | − | 1.94320i | −0.0178744 | − | 0.0731850i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.74549 | + | 2.61130i | −0.366517 | + | 0.0982079i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −39.1415 | + | 22.5984i | −1.46999 | + | 0.848700i | −0.999433 | − | 0.0336686i | \(-0.989281\pi\) |
−0.470559 | + | 0.882369i | \(0.655948\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.415334 | − | 1.51187i | 0.0155762 | − | 0.0566995i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.000778044 | 0 | 0.000208476i | 2.91380e−5 | 0 | 7.80750e-6i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 29.6534 | − | 37.1536i | 1.10898 | − | 1.38947i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.219988 | + | 1.63123i | −0.00821560 | + | 0.0609195i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −47.7179 | −1.77958 | −0.889789 | − | 0.456372i | \(-0.849149\pi\) | ||||
−0.889789 | + | 0.456372i | \(0.849149\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.1340 | 0.414653 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17.4954 | − | 13.5125i | −0.650660 | − | 0.502534i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.89804 | − | 6.36682i | −0.219048 | − | 0.236458i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.9083 | − | 7.21005i | −0.997972 | − | 0.267406i | −0.277377 | − | 0.960761i | \(-0.589465\pi\) |
−0.720596 | + | 0.693355i | \(0.756132\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.7275 | − | 19.4494i | −0.693611 | − | 0.720350i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 39.0275 | − | 22.5325i | 1.44348 | − | 0.833396i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.53774 | − | 2.28768i | 0.315348 | − | 0.0844974i | −0.0976733 | − | 0.995219i | \(-0.531140\pi\) |
0.413022 | + | 0.910721i | \(0.364473\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.73716 | + | 0.149945i | 0.248504 | + | 0.00553082i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −30.5596 | − | 30.5596i | −1.12568 | − | 1.12568i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.7202i | 1.60827i | 0.594444 | + | 0.804137i | \(0.297372\pi\) | ||||
−0.594444 | + | 0.804137i | \(0.702628\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −19.2708 | − | 25.2787i | −0.707929 | − | 0.928636i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.33009 | − | 4.96395i | −0.0487962 | − | 0.182110i | 0.937226 | − | 0.348721i | \(-0.113384\pi\) |
−0.986023 | + | 0.166612i | \(0.946717\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.8417 | + | 38.5592i | −0.617030 | + | 1.41270i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −25.0725 | + | 14.2657i | −0.917356 | + | 0.521955i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.9388 | + | 22.4107i | 0.472774 | + | 0.818869i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.7247 | + | 25.5039i | −0.537311 | + | 0.930650i | 0.461737 | + | 0.887017i | \(0.347227\pi\) |
−0.999048 | + | 0.0436330i | \(0.986107\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.3383 | + | 30.0549i | 0.449634 | + | 1.09526i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −28.0728 | − | 38.0693i | −1.02167 | − | 1.38548i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.41487 | + | 6.41487i | −0.233152 | + | 0.233152i | −0.814007 | − | 0.580855i | \(-0.802718\pi\) |
0.580855 | + | 0.814007i | \(0.302718\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.0998911 | − | 0.0417456i | −0.00362582 | − | 0.00151527i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.4480 | − | 7.18686i | −0.451240 | − | 0.260524i | 0.257114 | − | 0.966381i | \(-0.417228\pi\) |
−0.708354 | + | 0.705858i | \(0.750562\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.74691 | − | 21.4478i | 0.208052 | − | 0.776462i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −26.3439 | + | 2.78952i | −0.952466 | + | 0.100855i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.22285 | − | 12.0278i | 0.116370 | − | 0.434300i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.51296 | + | 4.33761i | 0.270924 | + | 0.156418i | 0.629308 | − | 0.777156i | \(-0.283339\pi\) |
−0.358383 | + | 0.933575i | \(0.616672\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.40438 | − | 4.11993i | 0.194634 | − | 0.148376i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.7586 | + | 27.7586i | −0.998407 | + | 0.998407i | −0.999999 | − | 0.00159176i | \(-0.999493\pi\) |
0.00159176 | + | 0.999999i | \(0.499493\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.0696103 | − | 0.225029i | 0.00250048 | − | 0.00808330i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 26.2776 | − | 34.0231i | 0.942704 | − | 1.22057i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19.6216 | − | 33.9856i | 0.703018 | − | 1.21766i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.0219 | + | 24.2867i | 0.501744 | + | 0.869046i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.95294 | + | 1.09267i | −0.319952 | + | 0.0390489i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.6315 | + | 32.2227i | 0.450839 | + | 1.15008i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.08276 | − | 22.7012i | −0.216827 | − | 0.809209i | −0.985515 | − | 0.169586i | \(-0.945757\pi\) |
0.768689 | − | 0.639623i | \(-0.220910\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 36.0133 | − | 4.62583i | 1.28211 | − | 0.164684i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 48.5466i | 1.72612i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.55322 | − | 9.55322i | −0.339245 | − | 0.339245i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.47539 | − | 25.6053i | 0.265125 | − | 0.908127i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.512177 | + | 0.137238i | −0.0181423 | + | 0.00486120i | −0.267879 | − | 0.963453i | \(-0.586323\pi\) |
0.249737 | + | 0.968314i | \(0.419656\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.76636 | + | 1.01981i | −0.0624892 | + | 0.0360782i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.2919 | + | 15.1003i | −0.540312 | + | 0.533544i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −39.8495 | − | 10.6776i | −1.40626 | − | 0.376806i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.0126101 | + | 0.112323i | 0.000444446 | + | 0.00395885i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.28377 | + | 1.34807i | −0.115594 | + | 0.0474544i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.8852 | 0.382705 | 0.191352 | − | 0.981521i | \(-0.438713\pi\) | ||||
0.191352 | + | 0.981521i | \(0.438713\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.7758 | −0.799767 | −0.399884 | − | 0.916566i | \(-0.630949\pi\) | ||||
−0.399884 | + | 0.916566i | \(0.630949\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.3124 | + | 4.64405i | −0.396744 | + | 0.162874i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.54345 | − | 6.02066i | −0.264236 | − | 0.210894i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −34.7857 | − | 9.32079i | −1.21700 | − | 0.326093i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −36.6986 | + | 36.2389i | −1.28235 | + | 1.26629i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.1402 | + | 13.9374i | −0.842499 | + | 0.486417i | −0.858113 | − | 0.513461i | \(-0.828363\pi\) |
0.0156138 | + | 0.999878i | \(0.495030\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.15599 | − | 0.577696i | 0.0751531 | − | 0.0201372i | −0.221047 | − | 0.975263i | \(-0.570947\pi\) |
0.296200 | + | 0.955126i | \(0.404281\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −13.3144 | + | 28.7237i | −0.463550 | + | 1.00003i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.5100 | + | 29.5100i | 1.02616 | + | 1.02616i | 0.999648 | + | 0.0265159i | \(0.00844126\pi\) |
0.0265159 | + | 0.999648i | \(0.491559\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 42.1717i | 1.46468i | 0.680938 | + | 0.732341i | \(0.261573\pi\) | ||||
−0.680938 | + | 0.732341i | \(0.738427\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −34.2950 | + | 4.40512i | −1.18968 | + | 0.152812i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.77840 | − | 6.63710i | −0.0616181 | − | 0.229962i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 42.2195 | − | 16.5504i | 1.46107 | − | 0.572749i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.147177 | − | 0.195606i | −0.00508717 | − | 0.00676113i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.7092 | + | 28.9412i | 0.576866 | + | 0.999162i | 0.995836 | + | 0.0911617i | \(0.0290580\pi\) |
−0.418970 | + | 0.908000i | \(0.637609\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.9935 | − | 22.5055i | 0.448053 | − | 0.776050i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.2920 | + | 17.2100i | −0.457802 | + | 0.592742i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 37.4640 | − | 27.6265i | 1.28880 | − | 0.950381i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.94245 | − | 4.94245i | 0.169825 | − | 0.169825i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.13159 | + | 6.19897i | −0.279075 | + | 0.212748i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.124315 | + | 0.0717733i | 0.00426147 | + | 0.00246036i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.4930 | − | 39.1602i | 0.359272 | − | 1.34082i | −0.515750 | − | 0.856739i | \(-0.672487\pi\) |
0.875022 | − | 0.484082i | \(-0.160847\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 16.4624 | + | 13.3099i | 0.563002 | + | 0.455188i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.08925 | − | 7.79718i | 0.0713673 | − | 0.266346i | −0.921018 | − | 0.389521i | \(-0.872641\pi\) |
0.992385 | + | 0.123174i | \(0.0393074\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.136572 | + | 0.0788501i | 0.00465979 | + | 0.00269033i | 0.502328 | − | 0.864677i | \(-0.332477\pi\) |
−0.497668 | + | 0.867367i | \(0.665810\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −58.7509 | − | 24.5526i | −2.00222 | − | 0.836751i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14.5279 | + | 14.5279i | −0.494536 | + | 0.494536i | −0.909732 | − | 0.415196i | \(-0.863713\pi\) |
0.415196 | + | 0.909732i | \(0.363713\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 34.5059 | + | 5.21509i | 1.17323 | + | 0.177318i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.924058 | − | 2.25091i | −0.0313826 | − | 0.0764449i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.955288 | + | 1.65461i | −0.0324059 | + | 0.0561287i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34.3739 | − | 59.5373i | −1.16471 | − | 2.01735i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −18.3728 | + | 10.4537i | −0.621826 | + | 0.353805i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 32.9634 | − | 2.43035i | 1.11437 | − | 0.0821608i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.3564 | − | 38.6505i | −0.349710 | − | 1.30513i | −0.887013 | − | 0.461745i | \(-0.847223\pi\) |
0.537303 | − | 0.843389i | \(-0.319443\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.59222 | + | 11.2710i | 0.289809 | + | 0.380160i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 18.9638i | − | 0.638908i | −0.947602 | − | 0.319454i | \(-0.896500\pi\) | ||
0.947602 | − | 0.319454i | \(-0.103500\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.93666 | + | 1.93666i | 0.0651736 | + | 0.0651736i | 0.738942 | − | 0.673769i | \(-0.235326\pi\) |
−0.673769 | + | 0.738942i | \(0.735326\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.184531 | + | 8.29112i | −0.00620294 | + | 0.278703i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.573135 | + | 0.153571i | −0.0192440 | + | 0.00515641i | −0.268428 | − | 0.963300i | \(-0.586504\pi\) |
0.249184 | + | 0.968456i | \(0.419838\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 34.9076 | − | 20.1539i | 1.17076 | − | 0.675940i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 16.0903 | + | 28.6986i | 0.539044 | + | 0.961440i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.57437 | + | 0.421852i | 0.0526844 | + | 0.0141167i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.64614 | + | 0.970671i | −0.289009 | + | 0.0324460i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.136298 | − | 0.105269i | −0.00455086 | − | 0.00351484i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.0817726 | −0.00272727 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −27.1983 | −0.906106 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.80961 | + | 57.9091i | −0.259887 | + | 1.92709i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 32.3364 | − | 3.63030i | 1.07490 | − | 0.120675i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −44.1094 | − | 11.8191i | −1.46463 | − | 0.392446i | −0.563543 | − | 0.826087i | \(-0.690562\pi\) |
−0.901086 | + | 0.433640i | \(0.857229\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.71214 | + | 9.87251i | −0.0899559 | + | 0.327450i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.8735 | − | 16.0928i | 0.923491 | − | 0.533177i | 0.0387436 | − | 0.999249i | \(-0.487664\pi\) |
0.884747 | + | 0.466072i | \(0.154331\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 33.9543 | − | 9.09802i | 1.12372 | − | 0.301101i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.69038 | + | 4.67123i | 0.254236 | + | 0.154426i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 33.3724 | + | 33.3724i | 1.10205 | + | 1.10205i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 51.4113i | 1.69590i | 0.530074 | + | 0.847951i | \(0.322164\pi\) | ||||
−0.530074 | + | 0.847951i | \(0.677836\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.4390 | + | 24.9790i | −0.343976 | + | 0.823086i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.5459 | + | 43.0901i | 0.380039 | + | 1.41833i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.3619 | − | 35.5254i | 0.735254 | − | 1.16807i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.71078 | − | 9.74894i | 0.187567 | − | 0.320197i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.8456 | − | 23.9813i | −0.454260 | − | 0.786802i | 0.544385 | − | 0.838835i | \(-0.316763\pi\) |
−0.998645 | + | 0.0520338i | \(0.983430\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.74550 | + | 4.75534i | −0.0899800 | + | 0.155850i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 19.8294 | + | 2.67419i | 0.649186 | + | 0.0875492i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 31.9190 | + | 4.82412i | 1.04386 | + | 0.157766i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.9248 | − | 26.9248i | 0.879596 | − | 0.879596i | −0.113896 | − | 0.993493i | \(-0.536333\pi\) |
0.993493 | + | 0.113896i | \(0.0363332\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.35956 | − | 26.1551i | −0.109635 | − | 0.853538i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.32622 | − | 0.765694i | −0.0432336 | − | 0.0249609i | 0.478227 | − | 0.878236i | \(-0.341279\pi\) |
−0.521461 | + | 0.853275i | \(0.674613\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.0550296 | − | 0.205373i | 0.00179201 | − | 0.00668788i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 18.0171 | − | 29.2451i | 0.586098 | − | 0.951344i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.61913 | − | 17.2388i | 0.150102 | − | 0.560187i | −0.849373 | − | 0.527792i | \(-0.823020\pi\) |
0.999475 | − | 0.0323948i | \(-0.0103134\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −56.8336 | − | 32.8129i | −1.84490 | − | 1.06515i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.41017 | − | 10.9786i | −0.0457280 | − | 0.356004i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28.0955 | + | 28.0955i | −0.910103 | + | 0.910103i | −0.996280 | − | 0.0861773i | \(-0.972535\pi\) |
0.0861773 | + | 0.996280i | \(0.472535\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.6355 | + | 9.31756i | −0.408874 | + | 0.301509i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.8922 | + | 1.46892i | 0.352094 | + | 0.0474833i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.0315 | − | 19.1070i | 0.356224 | − | 0.616999i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.4989 | + | 26.8449i | 0.499964 | + | 0.865963i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 26.2593 | + | 0.165508i | 0.846193 | + | 0.00533342i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 29.7259 | − | 11.6528i | 0.956911 | − | 0.375117i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.6150 | + | 47.0797i | 0.405670 | + | 1.51398i | 0.802817 | + | 0.596225i | \(0.203333\pi\) |
−0.397148 | + | 0.917755i | \(0.630000\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.32333 | − | 19.9165i | 0.267384 | − | 0.639811i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 27.3898i | − | 0.878981i | −0.898247 | − | 0.439490i | \(-0.855159\pi\) | ||
0.898247 | − | 0.439490i | \(-0.144841\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25.9821 | − | 25.9821i | −0.832947 | − | 0.832947i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −32.2838 | + | 38.6529i | −1.03391 | + | 1.23788i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.51332 | + | 0.405493i | −0.0484155 | + | 0.0129729i | −0.282945 | − | 0.959136i | \(-0.591312\pi\) |
0.234530 | + | 0.972109i | \(0.424645\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.6798 | − | 13.0942i | 0.724848 | − | 0.418491i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.8320 | − | 16.0328i | −0.505476 | − | 0.511889i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.9807 | + | 6.96151i | 0.828656 | + | 0.222038i | 0.648127 | − | 0.761532i | \(-0.275553\pi\) |
0.180529 | + | 0.983570i | \(0.442219\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.83317 | − | 5.45376i | −0.217723 | − | 0.173771i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.353457 | − | 2.62092i | 0.0112507 | − | 0.0834248i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.195116 | −0.00620432 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.3249 | 0.709175 | 0.354588 | − | 0.935023i | \(-0.384621\pi\) | ||||
0.354588 | + | 0.935023i | \(0.384621\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −18.5429 | − | 14.3215i | −0.588440 | − | 0.454480i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.91227 | + | 17.0334i | 0.0606232 | + | 0.539994i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.1763 | + | 11.3011i | 1.33574 | + | 0.357909i | 0.854850 | − | 0.518874i | \(-0.173649\pi\) |
0.480885 | + | 0.876784i | \(0.340315\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −16.3125 | − | 40.4595i | −0.516104 | − | 1.28008i |
(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 | 360.2.bs.a.113.16 | ✓ | 72 | |
3.2 | odd | 2 | 1080.2.bt.a.233.1 | 72 | |||
4.3 | odd | 2 | 720.2.cu.e.113.3 | 72 | |||
5.2 | odd | 4 | inner | 360.2.bs.a.257.7 | yes | 72 | |
9.2 | odd | 6 | inner | 360.2.bs.a.353.7 | yes | 72 | |
9.7 | even | 3 | 1080.2.bt.a.953.7 | 72 | |||
15.2 | even | 4 | 1080.2.bt.a.17.7 | 72 | |||
20.7 | even | 4 | 720.2.cu.e.257.12 | 72 | |||
36.11 | even | 6 | 720.2.cu.e.353.12 | 72 | |||
45.2 | even | 12 | inner | 360.2.bs.a.137.16 | yes | 72 | |
45.7 | odd | 12 | 1080.2.bt.a.737.1 | 72 | |||
180.47 | odd | 12 | 720.2.cu.e.497.3 | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.bs.a.113.16 | ✓ | 72 | 1.1 | even | 1 | trivial | |
360.2.bs.a.137.16 | yes | 72 | 45.2 | even | 12 | inner | |
360.2.bs.a.257.7 | yes | 72 | 5.2 | odd | 4 | inner | |
360.2.bs.a.353.7 | yes | 72 | 9.2 | odd | 6 | inner | |
720.2.cu.e.113.3 | 72 | 4.3 | odd | 2 | |||
720.2.cu.e.257.12 | 72 | 20.7 | even | 4 | |||
720.2.cu.e.353.12 | 72 | 36.11 | even | 6 | |||
720.2.cu.e.497.3 | 72 | 180.47 | odd | 12 | |||
1080.2.bt.a.17.7 | 72 | 15.2 | even | 4 | |||
1080.2.bt.a.233.1 | 72 | 3.2 | odd | 2 | |||
1080.2.bt.a.737.1 | 72 | 45.7 | odd | 12 | |||
1080.2.bt.a.953.7 | 72 | 9.7 | even | 3 |