Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(251,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.251");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.38429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | 16.0.101415451701035401216.7 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 18x^{12} + 145x^{8} - 72x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 251.13 | ||
Root | \(0.332046 - 1.81768i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.251 |
Dual form | 1050.2.b.f.251.6 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0.420861 | − | 1.68014i | 0.242984 | − | 0.970030i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.68014 | + | 0.420861i | 0.685915 | + | 0.171816i | ||||
\(7\) | −2.57794 | − | 0.595188i | −0.974368 | − | 0.224960i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −2.64575 | − | 1.41421i | −0.881917 | − | 0.471405i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.82843i | − | 0.852803i | −0.904534 | − | 0.426401i | \(-0.859781\pi\) | ||
0.904534 | − | 0.426401i | \(-0.140219\pi\) | |||||||
\(12\) | −0.420861 | + | 1.68014i | −0.121492 | + | 0.485015i | ||||
\(13\) | 3.36028i | 0.931975i | 0.884791 | + | 0.465987i | \(0.154301\pi\) | ||||
−0.884791 | + | 0.465987i | \(0.845699\pi\) | |||||||
\(14\) | 0.595188 | − | 2.57794i | 0.159071 | − | 0.688982i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.75216 | −1.15257 | −0.576284 | − | 0.817250i | \(-0.695498\pi\) | ||||
−0.576284 | + | 0.817250i | \(0.695498\pi\) | |||||||
\(18\) | 1.41421 | − | 2.64575i | 0.333333 | − | 0.623610i | ||||
\(19\) | 5.59388i | 1.28332i | 0.766987 | + | 0.641662i | \(0.221755\pi\) | ||||
−0.766987 | + | 0.641662i | \(0.778245\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.08495 | + | 4.08080i | −0.454974 | + | 0.890505i | ||||
\(22\) | 2.82843 | 0.603023 | ||||||||
\(23\) | 7.29150i | 1.52038i | 0.649699 | + | 0.760192i | \(0.274895\pi\) | ||||
−0.649699 | + | 0.760192i | \(0.725105\pi\) | |||||||
\(24\) | −1.68014 | − | 0.420861i | −0.342957 | − | 0.0859080i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.36028 | −0.659006 | ||||||||
\(27\) | −3.48957 | + | 3.85005i | −0.671569 | + | 0.740942i | ||||
\(28\) | 2.57794 | + | 0.595188i | 0.487184 | + | 0.112480i | ||||
\(29\) | − | 0.500983i | − | 0.0930303i | −0.998918 | − | 0.0465151i | \(-0.985188\pi\) | ||
0.998918 | − | 0.0465151i | \(-0.0148116\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.06871i | 0.551157i | 0.961279 | + | 0.275578i | \(0.0888694\pi\) | ||||
−0.961279 | + | 0.275578i | \(0.911131\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −4.75216 | − | 1.19038i | −0.827245 | − | 0.207218i | ||||
\(34\) | − | 4.75216i | − | 0.814988i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.64575 | + | 1.41421i | 0.440959 | + | 0.235702i | ||||
\(37\) | 3.32941 | 0.547352 | 0.273676 | − | 0.961822i | \(-0.411760\pi\) | ||||
0.273676 | + | 0.961822i | \(0.411760\pi\) | |||||||
\(38\) | −5.59388 | −0.907447 | ||||||||
\(39\) | 5.64575 | + | 1.41421i | 0.904044 | + | 0.226455i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.33981 | 0.677765 | 0.338883 | − | 0.940829i | \(-0.389951\pi\) | ||||
0.338883 | + | 0.940829i | \(0.389951\pi\) | |||||||
\(42\) | −4.08080 | − | 2.08495i | −0.629682 | − | 0.321715i | ||||
\(43\) | −10.3117 | −1.57253 | −0.786263 | − | 0.617892i | \(-0.787987\pi\) | ||||
−0.786263 | + | 0.617892i | \(0.787987\pi\) | |||||||
\(44\) | 2.82843i | 0.426401i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.29150 | −1.07507 | ||||||||
\(47\) | −7.82087 | −1.14079 | −0.570396 | − | 0.821370i | \(-0.693210\pi\) | ||||
−0.570396 | + | 0.821370i | \(0.693210\pi\) | |||||||
\(48\) | 0.420861 | − | 1.68014i | 0.0607461 | − | 0.242508i | ||||
\(49\) | 6.29150 | + | 3.06871i | 0.898786 | + | 0.438387i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | + | 7.98430i | −0.280056 | + | 1.11803i | ||||
\(52\) | − | 3.36028i | − | 0.465987i | ||||||
\(53\) | − | 8.58301i | − | 1.17897i | −0.807781 | − | 0.589483i | \(-0.799331\pi\) | ||
0.807781 | − | 0.589483i | \(-0.200669\pi\) | |||||||
\(54\) | −3.85005 | − | 3.48957i | −0.523925 | − | 0.474871i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.595188 | + | 2.57794i | −0.0795353 | + | 0.344491i | ||||
\(57\) | 9.39851 | + | 2.35425i | 1.24486 | + | 0.311828i | ||||
\(58\) | 0.500983 | 0.0657823 | ||||||||
\(59\) | 2.16991 | 0.282498 | 0.141249 | − | 0.989974i | \(-0.454888\pi\) | ||||
0.141249 | + | 0.989974i | \(0.454888\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.52517i | 0.323315i | 0.986847 | + | 0.161657i | \(0.0516839\pi\) | ||||
−0.986847 | + | 0.161657i | \(0.948316\pi\) | |||||||
\(62\) | −3.06871 | −0.389727 | ||||||||
\(63\) | 5.97885 | + | 5.22047i | 0.753265 | + | 0.657717i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.19038 | − | 4.75216i | 0.146525 | − | 0.584950i | ||||
\(67\) | −10.3117 | −1.25978 | −0.629890 | − | 0.776684i | \(-0.716900\pi\) | ||||
−0.629890 | + | 0.776684i | \(0.716900\pi\) | |||||||
\(68\) | 4.75216 | 0.576284 | ||||||||
\(69\) | 12.2508 | + | 3.06871i | 1.47482 | + | 0.369430i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.81076i | − | 1.16432i | −0.813073 | − | 0.582161i | \(-0.802207\pi\) | ||
0.813073 | − | 0.582161i | \(-0.197793\pi\) | |||||||
\(72\) | −1.41421 | + | 2.64575i | −0.166667 | + | 0.311805i | ||||
\(73\) | 5.53019i | 0.647260i | 0.946184 | + | 0.323630i | \(0.104903\pi\) | ||||
−0.946184 | + | 0.323630i | \(0.895097\pi\) | |||||||
\(74\) | 3.32941i | 0.387036i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 5.59388i | − | 0.641662i | ||||||
\(77\) | −1.68345 | + | 7.29150i | −0.191846 | + | 0.830944i | ||||
\(78\) | −1.41421 | + | 5.64575i | −0.160128 | + | 0.639255i | ||||
\(79\) | −3.29150 | −0.370323 | −0.185161 | − | 0.982708i | \(-0.559281\pi\) | ||||
−0.185161 | + | 0.982708i | \(0.559281\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.00000 | + | 7.48331i | 0.555556 | + | 0.831479i | ||||
\(82\) | 4.33981i | 0.479252i | ||||||||
\(83\) | −6.97915 | −0.766061 | −0.383030 | − | 0.923736i | \(-0.625120\pi\) | ||||
−0.383030 | + | 0.923736i | \(0.625120\pi\) | |||||||
\(84\) | 2.08495 | − | 4.08080i | 0.227487 | − | 0.445252i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 10.3117i | − | 1.11194i | ||||||
\(87\) | −0.841723 | − | 0.210845i | −0.0902422 | − | 0.0226049i | ||||
\(88\) | −2.82843 | −0.301511 | ||||||||
\(89\) | −15.8219 | −1.67712 | −0.838558 | − | 0.544812i | \(-0.816601\pi\) | ||||
−0.838558 | + | 0.544812i | \(0.816601\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | − | 8.66259i | 0.209657 | − | 0.908086i | ||||
\(92\) | − | 7.29150i | − | 0.760192i | ||||||
\(93\) | 5.15587 | + | 1.29150i | 0.534639 | + | 0.133923i | ||||
\(94\) | − | 7.82087i | − | 0.806661i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.68014 | + | 0.420861i | 0.171479 | + | 0.0429540i | ||||
\(97\) | 14.6315i | 1.48560i | 0.669511 | + | 0.742802i | \(0.266504\pi\) | ||||
−0.669511 | + | 0.742802i | \(0.733496\pi\) | |||||||
\(98\) | −3.06871 | + | 6.29150i | −0.309987 | + | 0.635538i | ||||
\(99\) | −4.00000 | + | 7.48331i | −0.402015 | + | 0.752101i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.16991 | 0.215914 | 0.107957 | − | 0.994156i | \(-0.465569\pi\) | ||||
0.107957 | + | 0.994156i | \(0.465569\pi\) | |||||||
\(102\) | −7.98430 | − | 2.00000i | −0.790563 | − | 0.198030i | ||||
\(103\) | − | 3.14944i | − | 0.310323i | −0.987889 | − | 0.155162i | \(-0.950410\pi\) | ||
0.987889 | − | 0.155162i | \(-0.0495899\pi\) | |||||||
\(104\) | 3.36028 | 0.329503 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.58301 | 0.833655 | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | 3.48957 | − | 3.85005i | 0.335784 | − | 0.370471i | ||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.40122 | − | 5.59388i | 0.132998 | − | 0.530948i | ||||
\(112\) | −2.57794 | − | 0.595188i | −0.243592 | − | 0.0562400i | ||||
\(113\) | − | 6.00000i | − | 0.564433i | −0.959351 | − | 0.282216i | \(-0.908930\pi\) | ||
0.959351 | − | 0.282216i | \(-0.0910696\pi\) | |||||||
\(114\) | −2.35425 | + | 9.39851i | −0.220496 | + | 0.880251i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.500983i | 0.0465151i | ||||||||
\(117\) | 4.75216 | − | 8.89047i | 0.439337 | − | 0.821925i | ||||
\(118\) | 2.16991i | 0.199756i | ||||||||
\(119\) | 12.2508 | + | 2.82843i | 1.12303 | + | 0.259281i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.00000 | 0.272727 | ||||||||
\(122\) | −2.52517 | −0.228618 | ||||||||
\(123\) | 1.82646 | − | 7.29150i | 0.164686 | − | 0.657453i | ||||
\(124\) | − | 3.06871i | − | 0.275578i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −5.22047 | + | 5.97885i | −0.465076 | + | 0.532639i | ||||
\(127\) | −3.32941 | −0.295437 | −0.147719 | − | 0.989029i | \(-0.547193\pi\) | ||||
−0.147719 | + | 0.989029i | \(0.547193\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −4.33981 | + | 17.3252i | −0.382099 | + | 1.52540i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.9918 | −1.57195 | −0.785975 | − | 0.618258i | \(-0.787839\pi\) | ||||
−0.785975 | + | 0.618258i | \(0.787839\pi\) | |||||||
\(132\) | 4.75216 | + | 1.19038i | 0.413622 | + | 0.103609i | ||||
\(133\) | 3.32941 | − | 14.4207i | 0.288696 | − | 1.25043i | ||||
\(134\) | − | 10.3117i | − | 0.890799i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.75216i | 0.407494i | ||||||||
\(137\) | − | 1.29150i | − | 0.110341i | −0.998477 | − | 0.0551703i | \(-0.982430\pi\) | ||
0.998477 | − | 0.0551703i | \(-0.0175702\pi\) | |||||||
\(138\) | −3.06871 | + | 12.2508i | −0.261226 | + | 1.04285i | ||||
\(139\) | 0.543544i | 0.0461028i | 0.999734 | + | 0.0230514i | \(0.00733813\pi\) | ||||
−0.999734 | + | 0.0230514i | \(0.992662\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.29150 | + | 13.1402i | −0.277195 | + | 1.10660i | ||||
\(142\) | 9.81076 | 0.823301 | ||||||||
\(143\) | 9.50432 | 0.794791 | ||||||||
\(144\) | −2.64575 | − | 1.41421i | −0.220479 | − | 0.117851i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.53019 | −0.457682 | ||||||||
\(147\) | 7.80372 | − | 9.27911i | 0.643640 | − | 0.765328i | ||||
\(148\) | −3.32941 | −0.273676 | ||||||||
\(149\) | − | 10.8127i | − | 0.885813i | −0.896568 | − | 0.442906i | \(-0.853947\pi\) | ||
0.896568 | − | 0.442906i | \(-0.146053\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.41699 | −0.115313 | −0.0576567 | − | 0.998336i | \(-0.518363\pi\) | ||||
−0.0576567 | + | 0.998336i | \(0.518363\pi\) | |||||||
\(152\) | 5.59388 | 0.453724 | ||||||||
\(153\) | 12.5730 | + | 6.72057i | 1.01647 | + | 0.543326i | ||||
\(154\) | −7.29150 | − | 1.68345i | −0.587566 | − | 0.135656i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.64575 | − | 1.41421i | −0.452022 | − | 0.113228i | ||||
\(157\) | − | 16.3797i | − | 1.30724i | −0.756821 | − | 0.653622i | \(-0.773249\pi\) | ||
0.756821 | − | 0.653622i | \(-0.226751\pi\) | |||||||
\(158\) | − | 3.29150i | − | 0.261858i | ||||||
\(159\) | −14.4207 | − | 3.61226i | −1.14363 | − | 0.286471i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.33981 | − | 18.7970i | 0.342025 | − | 1.48141i | ||||
\(162\) | −7.48331 | + | 5.00000i | −0.587945 | + | 0.392837i | ||||
\(163\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(164\) | −4.33981 | −0.338883 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 6.97915i | − | 0.541687i | ||||||
\(167\) | 20.6921 | 1.60120 | 0.800601 | − | 0.599198i | \(-0.204514\pi\) | ||||
0.800601 | + | 0.599198i | \(0.204514\pi\) | |||||||
\(168\) | 4.08080 | + | 2.08495i | 0.314841 | + | 0.160858i | ||||
\(169\) | 1.70850 | 0.131423 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.91094 | − | 14.8000i | 0.604965 | − | 1.13179i | ||||
\(172\) | 10.3117 | 0.786263 | ||||||||
\(173\) | 2.22699 | 0.169315 | 0.0846574 | − | 0.996410i | \(-0.473020\pi\) | ||||
0.0846574 | + | 0.996410i | \(0.473020\pi\) | |||||||
\(174\) | 0.210845 | − | 0.841723i | 0.0159841 | − | 0.0638108i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 2.82843i | − | 0.213201i | ||||||
\(177\) | 0.913230 | − | 3.64575i | 0.0686426 | − | 0.274031i | ||||
\(178\) | − | 15.8219i | − | 1.18590i | ||||||
\(179\) | − | 24.4539i | − | 1.82777i | −0.405975 | − | 0.913884i | \(-0.633068\pi\) | ||
0.405975 | − | 0.913884i | \(-0.366932\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.8000i | 1.10008i | 0.835139 | + | 0.550038i | \(0.185387\pi\) | ||||
−0.835139 | + | 0.550038i | \(0.814613\pi\) | |||||||
\(182\) | 8.66259 | + | 2.00000i | 0.642114 | + | 0.148250i | ||||
\(183\) | 4.24264 | + | 1.06275i | 0.313625 | + | 0.0785604i | ||||
\(184\) | 7.29150 | 0.537537 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.29150 | + | 5.15587i | −0.0946976 | + | 0.378047i | ||||
\(187\) | 13.4411i | 0.982913i | ||||||||
\(188\) | 7.82087 | 0.570396 | ||||||||
\(189\) | 11.2874 | − | 7.84823i | 0.821037 | − | 0.570874i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.500983i | 0.0362499i | 0.999836 | + | 0.0181249i | \(0.00576966\pi\) | ||||
−0.999836 | + | 0.0181249i | \(0.994230\pi\) | |||||||
\(192\) | −0.420861 | + | 1.68014i | −0.0303731 | + | 0.121254i | ||||
\(193\) | −8.48528 | −0.610784 | −0.305392 | − | 0.952227i | \(-0.598787\pi\) | ||||
−0.305392 | + | 0.952227i | \(0.598787\pi\) | |||||||
\(194\) | −14.6315 | −1.05048 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.29150 | − | 3.06871i | −0.449393 | − | 0.219194i | ||||
\(197\) | − | 18.0000i | − | 1.28245i | −0.767354 | − | 0.641223i | \(-0.778427\pi\) | ||
0.767354 | − | 0.641223i | \(-0.221573\pi\) | |||||||
\(198\) | −7.48331 | − | 4.00000i | −0.531816 | − | 0.284268i | ||||
\(199\) | − | 9.20614i | − | 0.652606i | −0.945265 | − | 0.326303i | \(-0.894197\pi\) | ||
0.945265 | − | 0.326303i | \(-0.105803\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.33981 | + | 17.3252i | −0.306107 | + | 1.22202i | ||||
\(202\) | 2.16991i | 0.152674i | ||||||||
\(203\) | −0.298179 | + | 1.29150i | −0.0209281 | + | 0.0906457i | ||||
\(204\) | 2.00000 | − | 7.98430i | 0.140028 | − | 0.559013i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.14944 | 0.219432 | ||||||||
\(207\) | 10.3117 | − | 19.2915i | 0.716716 | − | 1.34085i | ||||
\(208\) | 3.36028i | 0.232994i | ||||||||
\(209\) | 15.8219 | 1.09442 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.1660 | −1.45713 | −0.728564 | − | 0.684978i | \(-0.759812\pi\) | ||||
−0.728564 | + | 0.684978i | \(0.759812\pi\) | |||||||
\(212\) | 8.58301i | 0.589483i | ||||||||
\(213\) | −16.4835 | − | 4.12897i | −1.12943 | − | 0.282912i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.85005 | + | 3.48957i | 0.261963 | + | 0.237435i | ||||
\(217\) | 1.82646 | − | 7.91094i | 0.123988 | − | 0.537030i | ||||
\(218\) | − | 2.00000i | − | 0.135457i | ||||||
\(219\) | 9.29150 | + | 2.32744i | 0.627862 | + | 0.157274i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 15.9686i | − | 1.07416i | ||||||
\(222\) | 5.59388 | + | 1.40122i | 0.375437 | + | 0.0940438i | ||||
\(223\) | 1.19038i | 0.0797135i | 0.999205 | + | 0.0398567i | \(0.0126902\pi\) | ||||
−0.999205 | + | 0.0398567i | \(0.987310\pi\) | |||||||
\(224\) | 0.595188 | − | 2.57794i | 0.0397677 | − | 0.172246i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.00000 | 0.399114 | ||||||||
\(227\) | 18.1669 | 1.20578 | 0.602890 | − | 0.797824i | \(-0.294016\pi\) | ||||
0.602890 | + | 0.797824i | \(0.294016\pi\) | |||||||
\(228\) | −9.39851 | − | 2.35425i | −0.622432 | − | 0.155914i | ||||
\(229\) | 24.9007i | 1.64548i | 0.568415 | + | 0.822742i | \(0.307557\pi\) | ||||
−0.568415 | + | 0.822742i | \(0.692443\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.5423 | + | 5.89714i | 0.759425 | + | 0.388003i | ||||
\(232\) | −0.500983 | −0.0328912 | ||||||||
\(233\) | 13.2915i | 0.870755i | 0.900248 | + | 0.435378i | \(0.143385\pi\) | ||||
−0.900248 | + | 0.435378i | \(0.856615\pi\) | |||||||
\(234\) | 8.89047 | + | 4.75216i | 0.581188 | + | 0.310658i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.16991 | −0.141249 | ||||||||
\(237\) | −1.38527 | + | 5.53019i | −0.0899827 | + | 0.359224i | ||||
\(238\) | −2.82843 | + | 12.2508i | −0.183340 | + | 0.794099i | ||||
\(239\) | 14.6431i | 0.947185i | 0.880744 | + | 0.473592i | \(0.157043\pi\) | ||||
−0.880744 | + | 0.473592i | \(0.842957\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.3252i | 1.11601i | 0.829836 | + | 0.558007i | \(0.188434\pi\) | ||||
−0.829836 | + | 0.558007i | \(0.811566\pi\) | |||||||
\(242\) | 3.00000i | 0.192847i | ||||||||
\(243\) | 14.6773 | − | 5.25127i | 0.941551 | − | 0.336869i | ||||
\(244\) | − | 2.52517i | − | 0.161657i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.29150 | + | 1.82646i | 0.464889 | + | 0.116451i | ||||
\(247\) | −18.7970 | −1.19603 | ||||||||
\(248\) | 3.06871 | 0.194863 | ||||||||
\(249\) | −2.93725 | + | 11.7260i | −0.186141 | + | 0.743102i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.50972 | 0.410890 | 0.205445 | − | 0.978669i | \(-0.434136\pi\) | ||||
0.205445 | + | 0.978669i | \(0.434136\pi\) | |||||||
\(252\) | −5.97885 | − | 5.22047i | −0.376632 | − | 0.328859i | ||||
\(253\) | 20.6235 | 1.29659 | ||||||||
\(254\) | − | 3.32941i | − | 0.208906i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.7105 | 1.16713 | 0.583563 | − | 0.812068i | \(-0.301658\pi\) | ||||
0.583563 | + | 0.812068i | \(0.301658\pi\) | |||||||
\(258\) | −17.3252 | − | 4.33981i | −1.07862 | − | 0.270185i | ||||
\(259\) | −8.58301 | − | 1.98162i | −0.533322 | − | 0.123132i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.708497 | + | 1.32548i | −0.0438549 | + | 0.0820450i | ||||
\(262\) | − | 17.9918i | − | 1.11154i | ||||||
\(263\) | 14.5830i | 0.899227i | 0.893223 | + | 0.449613i | \(0.148438\pi\) | ||||
−0.893223 | + | 0.449613i | \(0.851562\pi\) | |||||||
\(264\) | −1.19038 | + | 4.75216i | −0.0732626 | + | 0.292475i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 14.4207 | + | 3.32941i | 0.884188 | + | 0.204139i | ||||
\(267\) | −6.65882 | + | 26.5830i | −0.407513 | + | 1.62685i | ||||
\(268\) | 10.3117 | 0.629890 | ||||||||
\(269\) | −9.31216 | −0.567773 | −0.283886 | − | 0.958858i | \(-0.591624\pi\) | ||||
−0.283886 | + | 0.958858i | \(0.591624\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 20.3939i | − | 1.23884i | −0.785059 | − | 0.619421i | \(-0.787368\pi\) | ||
0.785059 | − | 0.619421i | \(-0.212632\pi\) | |||||||
\(272\) | −4.75216 | −0.288142 | ||||||||
\(273\) | −13.7127 | − | 7.00603i | −0.829928 | − | 0.424024i | ||||
\(274\) | 1.29150 | 0.0780225 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −12.2508 | − | 3.06871i | −0.737409 | − | 0.184715i | ||||
\(277\) | 6.98233 | 0.419528 | 0.209764 | − | 0.977752i | \(-0.432730\pi\) | ||||
0.209764 | + | 0.977752i | \(0.432730\pi\) | |||||||
\(278\) | −0.543544 | −0.0325996 | ||||||||
\(279\) | 4.33981 | − | 8.11905i | 0.259818 | − | 0.486075i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.30978i | 0.555375i | 0.960672 | + | 0.277687i | \(0.0895679\pi\) | ||||
−0.960672 | + | 0.277687i | \(0.910432\pi\) | |||||||
\(282\) | −13.1402 | − | 3.29150i | −0.782486 | − | 0.196006i | ||||
\(283\) | 32.2016i | 1.91419i | 0.289779 | + | 0.957094i | \(0.406418\pi\) | ||||
−0.289779 | + | 0.957094i | \(0.593582\pi\) | |||||||
\(284\) | 9.81076i | 0.582161i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.50432i | 0.562002i | ||||||||
\(287\) | −11.1878 | − | 2.58301i | −0.660393 | − | 0.152470i | ||||
\(288\) | 1.41421 | − | 2.64575i | 0.0833333 | − | 0.155902i | ||||
\(289\) | 5.58301 | 0.328412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 24.5830 | + | 6.15784i | 1.44108 | + | 0.360979i | ||||
\(292\) | − | 5.53019i | − | 0.323630i | ||||||
\(293\) | 7.27733 | 0.425146 | 0.212573 | − | 0.977145i | \(-0.431816\pi\) | ||||
0.212573 | + | 0.977145i | \(0.431816\pi\) | |||||||
\(294\) | 9.27911 | + | 7.80372i | 0.541169 | + | 0.455122i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 3.32941i | − | 0.193518i | ||||||
\(297\) | 10.8896 | + | 9.87000i | 0.631878 | + | 0.572716i | ||||
\(298\) | 10.8127 | 0.626364 | ||||||||
\(299\) | −24.5015 | −1.41696 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.5830 | + | 6.13742i | 1.53222 | + | 0.353755i | ||||
\(302\) | − | 1.41699i | − | 0.0815389i | ||||||
\(303\) | 0.913230 | − | 3.64575i | 0.0524637 | − | 0.209443i | ||||
\(304\) | 5.59388i | 0.320831i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6.72057 | + | 12.5730i | −0.384189 | + | 0.718752i | ||||
\(307\) | − | 12.0399i | − | 0.687154i | −0.939124 | − | 0.343577i | \(-0.888361\pi\) | ||
0.939124 | − | 0.343577i | \(-0.111639\pi\) | |||||||
\(308\) | 1.68345 | − | 7.29150i | 0.0959232 | − | 0.415472i | ||||
\(309\) | −5.29150 | − | 1.32548i | −0.301023 | − | 0.0754038i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.5015 | −1.38935 | −0.694677 | − | 0.719322i | \(-0.744453\pi\) | ||||
−0.694677 | + | 0.719322i | \(0.744453\pi\) | |||||||
\(312\) | 1.41421 | − | 5.64575i | 0.0800641 | − | 0.319628i | ||||
\(313\) | − | 14.6315i | − | 0.827022i | −0.910499 | − | 0.413511i | \(-0.864302\pi\) | ||
0.910499 | − | 0.413511i | \(-0.135698\pi\) | |||||||
\(314\) | 16.3797 | 0.924361 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.29150 | 0.185161 | ||||||||
\(317\) | − | 6.00000i | − | 0.336994i | −0.985702 | − | 0.168497i | \(-0.946109\pi\) | ||
0.985702 | − | 0.168497i | \(-0.0538913\pi\) | |||||||
\(318\) | 3.61226 | − | 14.4207i | 0.202565 | − | 0.808671i | ||||
\(319\) | −1.41699 | −0.0793365 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 18.7970 | + | 4.33981i | 1.04752 | + | 0.241848i | ||||
\(323\) | − | 26.5830i | − | 1.47912i | ||||||
\(324\) | −5.00000 | − | 7.48331i | −0.277778 | − | 0.415740i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.841723 | + | 3.36028i | −0.0465474 | + | 0.185824i | ||||
\(328\) | − | 4.33981i | − | 0.239626i | ||||||
\(329\) | 20.1617 | + | 4.65489i | 1.11155 | + | 0.256632i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.00000 | 0.439720 | 0.219860 | − | 0.975531i | \(-0.429440\pi\) | ||||
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(332\) | 6.97915 | 0.383030 | ||||||||
\(333\) | −8.80879 | − | 4.70850i | −0.482719 | − | 0.258024i | ||||
\(334\) | 20.6921i | 1.13222i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.08495 | + | 4.08080i | −0.113744 | + | 0.222626i | ||||
\(337\) | −22.4499 | −1.22293 | −0.611463 | − | 0.791273i | \(-0.709419\pi\) | ||||
−0.611463 | + | 0.791273i | \(0.709419\pi\) | |||||||
\(338\) | 1.70850i | 0.0929300i | ||||||||
\(339\) | −10.0808 | − | 2.52517i | −0.547517 | − | 0.137148i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.67963 | 0.470028 | ||||||||
\(342\) | 14.8000 | + | 7.91094i | 0.800293 | + | 0.427775i | ||||
\(343\) | −14.3926 | − | 11.6556i | −0.777129 | − | 0.629342i | ||||
\(344\) | 10.3117i | 0.555972i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.22699i | 0.119724i | ||||||||
\(347\) | 24.0000i | 1.28839i | 0.764862 | + | 0.644194i | \(0.222807\pi\) | ||||
−0.764862 | + | 0.644194i | \(0.777193\pi\) | |||||||
\(348\) | 0.841723 | + | 0.210845i | 0.0451211 | + | 0.0113025i | ||||
\(349\) | − | 13.7129i | − | 0.734036i | −0.930214 | − | 0.367018i | \(-0.880379\pi\) | ||
0.930214 | − | 0.367018i | \(-0.119621\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.9373 | − | 11.7260i | −0.690540 | − | 0.625885i | ||||
\(352\) | 2.82843 | 0.150756 | ||||||||
\(353\) | 9.80250 | 0.521734 | 0.260867 | − | 0.965375i | \(-0.415992\pi\) | ||||
0.260867 | + | 0.965375i | \(0.415992\pi\) | |||||||
\(354\) | 3.64575 | + | 0.913230i | 0.193769 | + | 0.0485376i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 15.8219 | 0.838558 | ||||||||
\(357\) | 9.90803 | − | 19.3926i | 0.524388 | − | 1.02637i | ||||
\(358\) | 24.4539 | 1.29243 | ||||||||
\(359\) | 4.33138i | 0.228601i | 0.993446 | + | 0.114301i | \(0.0364627\pi\) | ||||
−0.993446 | + | 0.114301i | \(0.963537\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.2915 | −0.646921 | ||||||||
\(362\) | −14.8000 | −0.777872 | ||||||||
\(363\) | 1.26258 | − | 5.04042i | 0.0662685 | − | 0.264554i | ||||
\(364\) | −2.00000 | + | 8.66259i | −0.104828 | + | 0.454043i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.06275 | + | 4.24264i | −0.0555506 | + | 0.221766i | ||||
\(367\) | 14.6315i | 0.763759i | 0.924212 | + | 0.381879i | \(0.124723\pi\) | ||||
−0.924212 | + | 0.381879i | \(0.875277\pi\) | |||||||
\(368\) | 7.29150i | 0.380096i | ||||||||
\(369\) | −11.4821 | − | 6.13742i | −0.597733 | − | 0.319502i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.10850 | + | 22.1264i | −0.265220 | + | 1.14875i | ||||
\(372\) | −5.15587 | − | 1.29150i | −0.267319 | − | 0.0669613i | ||||
\(373\) | 6.98233 | 0.361531 | 0.180766 | − | 0.983526i | \(-0.442142\pi\) | ||||
0.180766 | + | 0.983526i | \(0.442142\pi\) | |||||||
\(374\) | −13.4411 | −0.695024 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.82087i | 0.403331i | ||||||||
\(377\) | 1.68345 | 0.0867019 | ||||||||
\(378\) | 7.84823 | + | 11.2874i | 0.403669 | + | 0.580561i | ||||
\(379\) | 6.58301 | 0.338146 | 0.169073 | − | 0.985604i | \(-0.445923\pi\) | ||||
0.169073 | + | 0.985604i | \(0.445923\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.40122 | + | 5.59388i | −0.0717867 | + | 0.286583i | ||||
\(382\) | −0.500983 | −0.0256325 | ||||||||
\(383\) | −20.6921 | −1.05732 | −0.528658 | − | 0.848835i | \(-0.677305\pi\) | ||||
−0.528658 | + | 0.848835i | \(0.677305\pi\) | |||||||
\(384\) | −1.68014 | − | 0.420861i | −0.0857394 | − | 0.0214770i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 8.48528i | − | 0.431889i | ||||||
\(387\) | 27.2823 | + | 14.5830i | 1.38684 | + | 0.741296i | ||||
\(388\) | − | 14.6315i | − | 0.742802i | ||||||
\(389\) | 37.0931i | 1.88069i | 0.340218 | + | 0.940346i | \(0.389499\pi\) | ||||
−0.340218 | + | 0.940346i | \(0.610501\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 34.6504i | − | 1.75234i | ||||||
\(392\) | 3.06871 | − | 6.29150i | 0.154993 | − | 0.317769i | ||||
\(393\) | −7.57205 | + | 30.2288i | −0.381959 | + | 1.52484i | ||||
\(394\) | 18.0000 | 0.906827 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.00000 | − | 7.48331i | 0.201008 | − | 0.376051i | ||||
\(397\) | − | 14.8424i | − | 0.744916i | −0.928049 | − | 0.372458i | \(-0.878515\pi\) | ||
0.928049 | − | 0.372458i | \(-0.121485\pi\) | |||||||
\(398\) | 9.20614 | 0.461462 | ||||||||
\(399\) | −22.8275 | − | 11.6630i | −1.14281 | − | 0.583879i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.48331i | 0.373699i | 0.982389 | + | 0.186849i | \(0.0598277\pi\) | ||||
−0.982389 | + | 0.186849i | \(0.940172\pi\) | |||||||
\(402\) | −17.3252 | − | 4.33981i | −0.864102 | − | 0.216450i | ||||
\(403\) | −10.3117 | −0.513664 | ||||||||
\(404\) | −2.16991 | −0.107957 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.29150 | − | 0.298179i | −0.0640962 | − | 0.0147984i | ||||
\(407\) | − | 9.41699i | − | 0.466783i | ||||||
\(408\) | 7.98430 | + | 2.00000i | 0.395282 | + | 0.0990148i | ||||
\(409\) | − | 23.4626i | − | 1.16015i | −0.814563 | − | 0.580076i | \(-0.803023\pi\) | ||
0.814563 | − | 0.580076i | \(-0.196977\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.16991 | − | 0.543544i | −0.107034 | − | 0.0268110i | ||||
\(412\) | 3.14944i | 0.155162i | ||||||||
\(413\) | −5.59388 | − | 1.29150i | −0.275257 | − | 0.0635507i | ||||
\(414\) | 19.2915 | + | 10.3117i | 0.948126 | + | 0.506794i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.36028 | −0.164751 | ||||||||
\(417\) | 0.913230 | + | 0.228757i | 0.0447211 | + | 0.0112023i | ||||
\(418\) | 15.8219i | 0.773874i | ||||||||
\(419\) | 33.8137 | 1.65191 | 0.825953 | − | 0.563739i | \(-0.190638\pi\) | ||||
0.825953 | + | 0.563739i | \(0.190638\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | − | 21.1660i | − | 1.03035i | ||||||
\(423\) | 20.6921 | + | 11.0604i | 1.00608 | + | 0.537774i | ||||
\(424\) | −8.58301 | −0.416828 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.12897 | − | 16.4835i | 0.200049 | − | 0.798626i | ||||
\(427\) | 1.50295 | − | 6.50972i | 0.0727328 | − | 0.315028i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.00000 | − | 15.9686i | 0.193122 | − | 0.770971i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.98626i | 0.432853i | 0.976299 | + | 0.216427i | \(0.0694402\pi\) | ||||
−0.976299 | + | 0.216427i | \(0.930560\pi\) | |||||||
\(432\) | −3.48957 | + | 3.85005i | −0.167892 | + | 0.185236i | ||||
\(433\) | 18.5496i | 0.891439i | 0.895173 | + | 0.445719i | \(0.147052\pi\) | ||||
−0.895173 | + | 0.445719i | \(0.852948\pi\) | |||||||
\(434\) | 7.91094 | + | 1.82646i | 0.379737 | + | 0.0876729i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | 0.0957826 | ||||||||
\(437\) | −40.7878 | −1.95114 | ||||||||
\(438\) | −2.32744 | + | 9.29150i | −0.111210 | + | 0.443965i | ||||
\(439\) | − | 26.5313i | − | 1.26627i | −0.774041 | − | 0.633135i | \(-0.781768\pi\) | ||
0.774041 | − | 0.633135i | \(-0.218232\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.3059 | − | 17.0166i | −0.585997 | − | 0.810313i | ||||
\(442\) | 15.9686 | 0.759549 | ||||||||
\(443\) | − | 29.1660i | − | 1.38572i | −0.721073 | − | 0.692859i | \(-0.756351\pi\) | ||
0.721073 | − | 0.692859i | \(-0.243649\pi\) | |||||||
\(444\) | −1.40122 | + | 5.59388i | −0.0664990 | + | 0.265474i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.19038 | −0.0563659 | ||||||||
\(447\) | −18.1669 | − | 4.55066i | −0.859265 | − | 0.215239i | ||||
\(448\) | 2.57794 | + | 0.595188i | 0.121796 | + | 0.0281200i | ||||
\(449\) | − | 36.5921i | − | 1.72689i | −0.504446 | − | 0.863444i | \(-0.668303\pi\) | ||
0.504446 | − | 0.863444i | \(-0.331697\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 12.2748i | − | 0.578000i | ||||||
\(452\) | 6.00000i | 0.282216i | ||||||||
\(453\) | −0.596358 | + | 2.38075i | −0.0280194 | + | 0.111857i | ||||
\(454\) | 18.1669i | 0.852615i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.35425 | − | 9.39851i | 0.110248 | − | 0.440126i | ||||
\(457\) | −8.48528 | −0.396925 | −0.198462 | − | 0.980109i | \(-0.563595\pi\) | ||||
−0.198462 | + | 0.980109i | \(0.563595\pi\) | |||||||
\(458\) | −24.9007 | −1.16353 | ||||||||
\(459\) | 16.5830 | − | 18.2960i | 0.774028 | − | 0.853986i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.9918 | 0.837961 | 0.418981 | − | 0.907995i | \(-0.362388\pi\) | ||||
0.418981 | + | 0.907995i | \(0.362388\pi\) | |||||||
\(462\) | −5.89714 | + | 11.5423i | −0.274360 | + | 0.536994i | ||||
\(463\) | 1.50295 | 0.0698480 | 0.0349240 | − | 0.999390i | \(-0.488881\pi\) | ||||
0.0349240 | + | 0.999390i | \(0.488881\pi\) | |||||||
\(464\) | − | 0.500983i | − | 0.0232576i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.2915 | −0.615717 | ||||||||
\(467\) | 0.841723 | 0.0389503 | 0.0194751 | − | 0.999810i | \(-0.493800\pi\) | ||||
0.0194751 | + | 0.999810i | \(0.493800\pi\) | |||||||
\(468\) | −4.75216 | + | 8.89047i | −0.219669 | + | 0.410962i | ||||
\(469\) | 26.5830 | + | 6.13742i | 1.22749 | + | 0.283400i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −27.5203 | − | 6.89360i | −1.26807 | − | 0.317640i | ||||
\(472\) | − | 2.16991i | − | 0.0998781i | ||||||
\(473\) | 29.1660i | 1.34105i | ||||||||
\(474\) | −5.53019 | − | 1.38527i | −0.254010 | − | 0.0636274i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −12.2508 | − | 2.82843i | −0.561513 | − | 0.129641i | ||||
\(477\) | −12.1382 | + | 22.7085i | −0.555770 | + | 1.03975i | ||||
\(478\) | −14.6431 | −0.669761 | ||||||||
\(479\) | −21.6991 | −0.991456 | −0.495728 | − | 0.868478i | \(-0.665099\pi\) | ||||
−0.495728 | + | 0.868478i | \(0.665099\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.1878i | 0.510118i | ||||||||
\(482\) | −17.3252 | −0.789141 | ||||||||
\(483\) | −29.7552 | − | 15.2024i | −1.35391 | − | 0.691735i | ||||
\(484\) | −3.00000 | −0.136364 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 5.25127 | + | 14.6773i | 0.238202 | + | 0.665777i | ||||
\(487\) | 9.98823 | 0.452610 | 0.226305 | − | 0.974056i | \(-0.427335\pi\) | ||||
0.226305 | + | 0.974056i | \(0.427335\pi\) | |||||||
\(488\) | 2.52517 | 0.114309 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.1421i | 0.638226i | 0.947717 | + | 0.319113i | \(0.103385\pi\) | ||||
−0.947717 | + | 0.319113i | \(0.896615\pi\) | |||||||
\(492\) | −1.82646 | + | 7.29150i | −0.0823432 | + | 0.328726i | ||||
\(493\) | 2.38075i | 0.107224i | ||||||||
\(494\) | − | 18.7970i | − | 0.845718i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.06871i | 0.137789i | ||||||||
\(497\) | −5.83925 | + | 25.2915i | −0.261926 | + | 1.13448i | ||||
\(498\) | −11.7260 | − | 2.93725i | −0.525453 | − | 0.131621i | ||||
\(499\) | −22.5830 | −1.01095 | −0.505477 | − | 0.862840i | \(-0.668683\pi\) | ||||
−0.505477 | + | 0.862840i | \(0.668683\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.70850 | − | 34.7656i | 0.389067 | − | 1.55321i | ||||
\(502\) | 6.50972i | 0.290543i | ||||||||
\(503\) | −15.6417 | −0.697431 | −0.348715 | − | 0.937229i | \(-0.613382\pi\) | ||||
−0.348715 | + | 0.937229i | \(0.613382\pi\) | |||||||
\(504\) | 5.22047 | − | 5.97885i | 0.232538 | − | 0.266319i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 20.6235i | 0.916826i | ||||||||
\(507\) | 0.719041 | − | 2.87052i | 0.0319337 | − | 0.127484i | ||||
\(508\) | 3.32941 | 0.147719 | ||||||||
\(509\) | −39.6909 | −1.75927 | −0.879633 | − | 0.475652i | \(-0.842212\pi\) | ||||
−0.879633 | + | 0.475652i | \(0.842212\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.29150 | − | 14.2565i | 0.145608 | − | 0.630669i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −21.5367 | − | 19.5203i | −0.950869 | − | 0.861840i | ||||
\(514\) | 18.7105i | 0.825283i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.33981 | − | 17.3252i | 0.191050 | − | 0.762699i | ||||
\(517\) | 22.1208i | 0.972870i | ||||||||
\(518\) | 1.98162 | − | 8.58301i | 0.0870676 | − | 0.377116i | ||||
\(519\) | 0.937254 | − | 3.74166i | 0.0411409 | − | 0.164241i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.0194 | −0.570392 | −0.285196 | − | 0.958469i | \(-0.592059\pi\) | ||||
−0.285196 | + | 0.958469i | \(0.592059\pi\) | |||||||
\(522\) | −1.32548 | − | 0.708497i | −0.0580146 | − | 0.0310101i | ||||
\(523\) | − | 16.8014i | − | 0.734675i | −0.930088 | − | 0.367337i | \(-0.880269\pi\) | ||
0.930088 | − | 0.367337i | \(-0.119731\pi\) | |||||||
\(524\) | 17.9918 | 0.785975 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.5830 | −0.635849 | ||||||||
\(527\) | − | 14.5830i | − | 0.635246i | ||||||
\(528\) | −4.75216 | − | 1.19038i | −0.206811 | − | 0.0518045i | ||||
\(529\) | −30.1660 | −1.31157 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.74103 | − | 3.06871i | −0.249140 | − | 0.133171i | ||||
\(532\) | −3.32941 | + | 14.4207i | −0.144348 | + | 0.625215i | ||||
\(533\) | 14.5830i | 0.631660i | ||||||||
\(534\) | −26.5830 | − | 6.65882i | −1.15036 | − | 0.288155i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 10.3117i | 0.445399i | ||||||||
\(537\) | −41.0860 | − | 10.2917i | −1.77299 | − | 0.444119i | ||||
\(538\) | − | 9.31216i | − | 0.401476i | ||||||
\(539\) | 8.67963 | − | 17.7951i | 0.373858 | − | 0.766487i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.00000 | 0.0859867 | 0.0429934 | − | 0.999075i | \(-0.486311\pi\) | ||||
0.0429934 | + | 0.999075i | \(0.486311\pi\) | |||||||
\(542\) | 20.3939 | 0.875993 | ||||||||
\(543\) | 24.8661 | + | 6.22876i | 1.06711 | + | 0.267302i | ||||
\(544\) | − | 4.75216i | − | 0.203747i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 7.00603 | − | 13.7127i | 0.299831 | − | 0.586848i | ||||
\(547\) | 16.9706 | 0.725609 | 0.362804 | − | 0.931865i | \(-0.381819\pi\) | ||||
0.362804 | + | 0.931865i | \(0.381819\pi\) | |||||||
\(548\) | 1.29150i | 0.0551703i | ||||||||
\(549\) | 3.57113 | − | 6.68097i | 0.152412 | − | 0.285137i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.80244 | 0.119388 | ||||||||
\(552\) | 3.06871 | − | 12.2508i | 0.130613 | − | 0.521427i | ||||
\(553\) | 8.48528 | + | 1.95906i | 0.360831 | + | 0.0833078i | ||||
\(554\) | 6.98233i | 0.296651i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 0.543544i | − | 0.0230514i | ||||||
\(557\) | 35.1660i | 1.49003i | 0.667047 | + | 0.745016i | \(0.267558\pi\) | ||||
−0.667047 | + | 0.745016i | \(0.732442\pi\) | |||||||
\(558\) | 8.11905 | + | 4.33981i | 0.343707 | + | 0.183719i | ||||
\(559\) | − | 34.6504i | − | 1.46555i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 22.5830 | + | 5.65685i | 0.953455 | + | 0.238833i | ||||
\(562\) | −9.30978 | −0.392709 | ||||||||
\(563\) | −13.1166 | −0.552798 | −0.276399 | − | 0.961043i | \(-0.589141\pi\) | ||||
−0.276399 | + | 0.961043i | \(0.589141\pi\) | |||||||
\(564\) | 3.29150 | − | 13.1402i | 0.138597 | − | 0.553301i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −32.2016 | −1.35353 | ||||||||
\(567\) | −8.43570 | − | 22.2674i | −0.354266 | − | 0.935145i | ||||
\(568\) | −9.81076 | −0.411650 | ||||||||
\(569\) | 33.7637i | 1.41545i | 0.706490 | + | 0.707723i | \(0.250278\pi\) | ||||
−0.706490 | + | 0.707723i | \(0.749722\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.4170 | −0.561484 | −0.280742 | − | 0.959783i | \(-0.590580\pi\) | ||||
−0.280742 | + | 0.959783i | \(0.590580\pi\) | |||||||
\(572\) | −9.50432 | −0.397395 | ||||||||
\(573\) | 0.841723 | + | 0.210845i | 0.0351635 | + | 0.00880816i | ||||
\(574\) | 2.58301 | − | 11.1878i | 0.107813 | − | 0.466968i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.64575 | + | 1.41421i | 0.110240 | + | 0.0589256i | ||||
\(577\) | 36.3306i | 1.51246i | 0.654305 | + | 0.756231i | \(0.272961\pi\) | ||||
−0.654305 | + | 0.756231i | \(0.727039\pi\) | |||||||
\(578\) | 5.58301i | 0.232222i | ||||||||
\(579\) | −3.57113 | + | 14.2565i | −0.148411 | + | 0.592479i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.9918 | + | 4.15390i | 0.746425 | + | 0.172333i | ||||
\(582\) | −6.15784 | + | 24.5830i | −0.255251 | + | 1.01900i | ||||
\(583\) | −24.2764 | −1.00543 | ||||||||
\(584\) | 5.53019 | 0.228841 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.27733i | 0.300624i | ||||||||
\(587\) | −37.7719 | −1.55901 | −0.779507 | − | 0.626394i | \(-0.784530\pi\) | ||||
−0.779507 | + | 0.626394i | \(0.784530\pi\) | |||||||
\(588\) | −7.80372 | + | 9.27911i | −0.321820 | + | 0.382664i | ||||
\(589\) | −17.1660 | −0.707313 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −30.2425 | − | 7.57551i | −1.24401 | − | 0.311615i | ||||
\(592\) | 3.32941 | 0.136838 | ||||||||
\(593\) | −6.43560 | −0.264279 | −0.132139 | − | 0.991231i | \(-0.542185\pi\) | ||||
−0.132139 | + | 0.991231i | \(0.542185\pi\) | |||||||
\(594\) | −9.87000 | + | 10.8896i | −0.404971 | + | 0.446805i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.8127i | 0.442906i | ||||||||
\(597\) | −15.4676 | − | 3.87451i | −0.633047 | − | 0.158573i | ||||
\(598\) | − | 24.5015i | − | 1.00194i | ||||||
\(599\) | − | 4.15390i | − | 0.169724i | −0.996393 | − | 0.0848620i | \(-0.972955\pi\) | ||
0.996393 | − | 0.0848620i | \(-0.0270449\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.13742i | 0.250351i | 0.992135 | + | 0.125175i | \(0.0399494\pi\) | ||||
−0.992135 | + | 0.125175i | \(0.960051\pi\) | |||||||
\(602\) | −6.13742 | + | 26.5830i | −0.250143 | + | 1.08344i | ||||
\(603\) | 27.2823 | + | 14.5830i | 1.11102 | + | 0.593866i | ||||
\(604\) | 1.41699 | 0.0576567 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.64575 | + | 0.913230i | 0.148099 | + | 0.0370974i | ||||
\(607\) | 5.95188i | 0.241579i | 0.992678 | + | 0.120790i | \(0.0385427\pi\) | ||||
−0.992678 | + | 0.120790i | \(0.961457\pi\) | |||||||
\(608\) | −5.59388 | −0.226862 | ||||||||
\(609\) | 2.04442 | + | 1.04453i | 0.0828439 | + | 0.0423264i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 26.2803i | − | 1.06319i | ||||||
\(612\) | −12.5730 | − | 6.72057i | −0.508235 | − | 0.271663i | ||||
\(613\) | 47.5823 | 1.92183 | 0.960915 | − | 0.276843i | \(-0.0892883\pi\) | ||||
0.960915 | + | 0.276843i | \(0.0892883\pi\) | |||||||
\(614\) | 12.0399 | 0.485891 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.29150 | + | 1.68345i | 0.293783 | + | 0.0678280i | ||||
\(617\) | − | 47.1660i | − | 1.89883i | −0.314021 | − | 0.949416i | \(-0.601676\pi\) | ||
0.314021 | − | 0.949416i | \(-0.398324\pi\) | |||||||
\(618\) | 1.32548 | − | 5.29150i | 0.0533185 | − | 0.212855i | ||||
\(619\) | 40.2443i | 1.61755i | 0.588116 | + | 0.808777i | \(0.299870\pi\) | ||||
−0.588116 | + | 0.808777i | \(0.700130\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −28.0726 | − | 25.4442i | −1.12652 | − | 1.02104i | ||||
\(622\) | − | 24.5015i | − | 0.982421i | ||||||
\(623\) | 40.7878 | + | 9.41699i | 1.63413 | + | 0.377284i | ||||
\(624\) | 5.64575 | + | 1.41421i | 0.226011 | + | 0.0566139i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 14.6315 | 0.584793 | ||||||||
\(627\) | 6.65882 | − | 26.5830i | 0.265928 | − | 1.06162i | ||||
\(628\) | 16.3797i | 0.653622i | ||||||||
\(629\) | −15.8219 | −0.630860 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.4575 | 1.29211 | 0.646057 | − | 0.763290i | \(-0.276417\pi\) | ||||
0.646057 | + | 0.763290i | \(0.276417\pi\) | |||||||
\(632\) | 3.29150i | 0.130929i | ||||||||
\(633\) | −8.90796 | + | 35.5619i | −0.354060 | + | 1.41346i | ||||
\(634\) | 6.00000 | 0.238290 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 14.4207 | + | 3.61226i | 0.571817 | + | 0.143235i | ||||
\(637\) | −10.3117 | + | 21.1412i | −0.408566 | + | 0.837646i | ||||
\(638\) | − | 1.41699i | − | 0.0560994i | ||||||
\(639\) | −13.8745 | + | 25.9568i | −0.548867 | + | 1.02684i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.1068i | 1.11015i | 0.831800 | + | 0.555076i | \(0.187311\pi\) | ||||
−0.831800 | + | 0.555076i | \(0.812689\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 22.6786i | − | 0.894357i | −0.894445 | − | 0.447178i | \(-0.852429\pi\) | ||
0.894445 | − | 0.447178i | \(-0.147571\pi\) | |||||||
\(644\) | −4.33981 | + | 18.7970i | −0.171013 | + | 0.740706i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 26.5830 | 1.04589 | ||||||||
\(647\) | −13.9583 | −0.548757 | −0.274379 | − | 0.961622i | \(-0.588472\pi\) | ||||
−0.274379 | + | 0.961622i | \(0.588472\pi\) | |||||||
\(648\) | 7.48331 | − | 5.00000i | 0.293972 | − | 0.196419i | ||||
\(649\) | − | 6.13742i | − | 0.240915i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.5228 | − | 6.39812i | −0.490808 | − | 0.250762i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 23.1660i | − | 0.906556i | −0.891369 | − | 0.453278i | \(-0.850254\pi\) | ||
0.891369 | − | 0.453278i | \(-0.149746\pi\) | |||||||
\(654\) | −3.36028 | − | 0.841723i | −0.131397 | − | 0.0329140i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.33981 | 0.169441 | ||||||||
\(657\) | 7.82087 | − | 14.6315i | 0.305121 | − | 0.570830i | ||||
\(658\) | −4.65489 | + | 20.1617i | −0.181466 | + | 0.785985i | ||||
\(659\) | 27.1048i | 1.05585i | 0.849290 | + | 0.527927i | \(0.177031\pi\) | ||||
−0.849290 | + | 0.527927i | \(0.822969\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.66259i | 0.336936i | 0.985707 | + | 0.168468i | \(0.0538820\pi\) | ||||
−0.985707 | + | 0.168468i | \(0.946118\pi\) | |||||||
\(662\) | 8.00000i | 0.310929i | ||||||||
\(663\) | −26.8295 | − | 6.72057i | −1.04197 | − | 0.261005i | ||||
\(664\) | 6.97915i | 0.270843i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.70850 | − | 8.80879i | 0.182451 | − | 0.341334i | ||||
\(667\) | 3.65292 | 0.141442 | ||||||||
\(668\) | −20.6921 | −0.800601 | ||||||||
\(669\) | 2.00000 | + | 0.500983i | 0.0773245 | + | 0.0193691i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.14226 | 0.275724 | ||||||||
\(672\) | −4.08080 | − | 2.08495i | −0.157420 | − | 0.0804288i | ||||
\(673\) | −23.6294 | −0.910846 | −0.455423 | − | 0.890275i | \(-0.650512\pi\) | ||||
−0.455423 | + | 0.890275i | \(0.650512\pi\) | |||||||
\(674\) | − | 22.4499i | − | 0.864740i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.70850 | −0.0657114 | ||||||||
\(677\) | −6.19024 | −0.237910 | −0.118955 | − | 0.992900i | \(-0.537954\pi\) | ||||
−0.118955 | + | 0.992900i | \(0.537954\pi\) | |||||||
\(678\) | 2.52517 | − | 10.0808i | 0.0969785 | − | 0.387153i | ||||
\(679\) | 8.70850 | − | 37.7191i | 0.334201 | − | 1.44753i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.64575 | − | 30.5230i | 0.292986 | − | 1.16964i | ||||
\(682\) | 8.67963i | 0.332360i | ||||||||
\(683\) | 26.5830i | 1.01717i | 0.861012 | + | 0.508585i | \(0.169831\pi\) | ||||
−0.861012 | + | 0.508585i | \(0.830169\pi\) | |||||||
\(684\) | −7.91094 | + | 14.8000i | −0.302482 | + | 0.565893i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 11.6556 | − | 14.3926i | 0.445012 | − | 0.549513i | ||||
\(687\) | 41.8367 | + | 10.4797i | 1.59617 | + | 0.399827i | ||||
\(688\) | −10.3117 | −0.393131 | ||||||||
\(689\) | 28.8413 | 1.09877 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.7313i | 0.446280i | 0.974786 | + | 0.223140i | \(0.0716307\pi\) | ||||
−0.974786 | + | 0.223140i | \(0.928369\pi\) | |||||||
\(692\) | −2.22699 | −0.0846574 | ||||||||
\(693\) | 14.7657 | − | 16.9108i | 0.560903 | − | 0.642386i | ||||
\(694\) | −24.0000 | −0.911028 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.210845 | + | 0.841723i | −0.00799204 | + | 0.0319054i | ||||
\(697\) | −20.6235 | −0.781170 | ||||||||
\(698\) | 13.7129 | 0.519042 | ||||||||
\(699\) | 22.3316 | + | 5.59388i | 0.844659 | + | 0.211580i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.1245i | 0.797860i | 0.916981 | + | 0.398930i | \(0.130618\pi\) | ||||
−0.916981 | + | 0.398930i | \(0.869382\pi\) | |||||||
\(702\) | 11.7260 | − | 12.9373i | 0.442568 | − | 0.488285i | ||||
\(703\) | 18.6243i | 0.702430i | ||||||||
\(704\) | 2.82843i | 0.106600i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.80250i | 0.368922i | ||||||||
\(707\) | −5.59388 | − | 1.29150i | −0.210380 | − | 0.0485720i | ||||
\(708\) | −0.913230 | + | 3.64575i | −0.0343213 | + | 0.137016i | ||||
\(709\) | 0.583005 | 0.0218952 | 0.0109476 | − | 0.999940i | \(-0.496515\pi\) | ||||
0.0109476 | + | 0.999940i | \(0.496515\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.70850 | + | 4.65489i | 0.326594 | + | 0.174572i | ||||
\(712\) | 15.8219i | 0.592950i | ||||||||
\(713\) | −22.3755 | −0.837970 | ||||||||
\(714\) | 19.3926 | + | 9.90803i | 0.725751 | + | 0.370799i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 24.4539i | 0.913884i | ||||||||
\(717\) | 24.6025 | + | 6.16272i | 0.918798 | + | 0.230151i | ||||
\(718\) | −4.33138 | −0.161646 | ||||||||
\(719\) | −2.80244 | −0.104513 | −0.0522567 | − | 0.998634i | \(-0.516641\pi\) | ||||
−0.0522567 | + | 0.998634i | \(0.516641\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.87451 | + | 8.11905i | −0.0698103 | + | 0.302369i | ||||
\(722\) | − | 12.2915i | − | 0.457442i | ||||||
\(723\) | 29.1088 | + | 7.29150i | 1.08257 | + | 0.271174i | ||||
\(724\) | − | 14.8000i | − | 0.550038i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.04042 | + | 1.26258i | 0.187068 | + | 0.0468589i | ||||
\(727\) | − | 45.8536i | − | 1.70062i | −0.526286 | − | 0.850308i | \(-0.676416\pi\) | ||
0.526286 | − | 0.850308i | \(-0.323584\pi\) | |||||||
\(728\) | −8.66259 | − | 2.00000i | −0.321057 | − | 0.0741249i | ||||
\(729\) | −2.64575 | − | 26.8701i | −0.0979908 | − | 0.995187i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 49.0030 | 1.81244 | ||||||||
\(732\) | −4.24264 | − | 1.06275i | −0.156813 | − | 0.0392802i | ||||
\(733\) | − | 28.2835i | − | 1.04467i | −0.852739 | − | 0.522337i | \(-0.825060\pi\) | ||
0.852739 | − | 0.522337i | \(-0.174940\pi\) | |||||||
\(734\) | −14.6315 | −0.540059 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.29150 | −0.268768 | ||||||||
\(737\) | 29.1660i | 1.07434i | ||||||||
\(738\) | 6.13742 | − | 11.4821i | 0.225922 | − | 0.422661i | ||||
\(739\) | 33.1660 | 1.22003 | 0.610016 | − | 0.792389i | \(-0.291163\pi\) | ||||
0.610016 | + | 0.792389i | \(0.291163\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.91094 | + | 31.5817i | −0.290616 | + | 1.16018i | ||||
\(742\) | −22.1264 | − | 5.10850i | −0.812287 | − | 0.187539i | ||||
\(743\) | − | 2.12549i | − | 0.0779767i | −0.999240 | − | 0.0389884i | \(-0.987586\pi\) | ||
0.999240 | − | 0.0389884i | \(-0.0124135\pi\) | |||||||
\(744\) | 1.29150 | − | 5.15587i | 0.0473488 | − | 0.189023i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6.98233i | 0.255641i | ||||||||
\(747\) | 18.4651 | + | 9.87000i | 0.675602 | + | 0.361125i | ||||
\(748\) | − | 13.4411i | − | 0.491456i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.1660 | −0.772359 | −0.386179 | − | 0.922424i | \(-0.626205\pi\) | ||||
−0.386179 | + | 0.922424i | \(0.626205\pi\) | |||||||
\(752\) | −7.82087 | −0.285198 | ||||||||
\(753\) | 2.73969 | − | 10.9373i | 0.0998399 | − | 0.398576i | ||||
\(754\) | 1.68345i | 0.0613075i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −11.2874 | + | 7.84823i | −0.410519 | + | 0.285437i | ||||
\(757\) | 34.2646 | 1.24537 | 0.622685 | − | 0.782473i | \(-0.286042\pi\) | ||||
0.622685 | + | 0.782473i | \(0.286042\pi\) | |||||||
\(758\) | 6.58301i | 0.239106i | ||||||||
\(759\) | 8.67963 | − | 34.6504i | 0.315051 | − | 1.25773i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.4821 | −0.416225 | −0.208112 | − | 0.978105i | \(-0.566732\pi\) | ||||
−0.208112 | + | 0.978105i | \(0.566732\pi\) | |||||||
\(762\) | −5.59388 | − | 1.40122i | −0.202645 | − | 0.0507609i | ||||
\(763\) | 5.15587 | + | 1.19038i | 0.186655 | + | 0.0430945i | ||||
\(764\) | − | 0.500983i | − | 0.0181249i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 20.6921i | − | 0.747635i | ||||||
\(767\) | 7.29150i | 0.263281i | ||||||||
\(768\) | 0.420861 | − | 1.68014i | 0.0151865 | − | 0.0606269i | ||||
\(769\) | 35.7375i | 1.28873i | 0.764720 | + | 0.644363i | \(0.222877\pi\) | ||||
−0.764720 | + | 0.644363i | \(0.777123\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.87451 | − | 31.4362i | 0.283593 | − | 1.13215i | ||||
\(772\) | 8.48528 | 0.305392 | ||||||||
\(773\) | 41.9277 | 1.50803 | 0.754017 | − | 0.656855i | \(-0.228113\pi\) | ||||
0.754017 | + | 0.656855i | \(0.228113\pi\) | |||||||
\(774\) | −14.5830 | + | 27.2823i | −0.524175 | + | 0.980642i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 14.6315 | 0.525241 | ||||||||
\(777\) | −6.94167 | + | 13.5867i | −0.249031 | + | 0.487419i | ||||
\(778\) | −37.0931 | −1.32985 | ||||||||
\(779\) | 24.2764i | 0.869792i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.7490 | −0.992938 | ||||||||
\(782\) | 34.6504 | 1.23909 | ||||||||
\(783\) | 1.92881 | + | 1.74822i | 0.0689301 | + | 0.0624762i | ||||
\(784\) | 6.29150 | + | 3.06871i | 0.224697 | + | 0.109597i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −30.2288 | − | 7.57205i | −1.07822 | − | 0.270086i | ||||
\(787\) | 28.2835i | 1.00820i | 0.863646 | + | 0.504099i | \(0.168175\pi\) | ||||
−0.863646 | + | 0.504099i | \(0.831825\pi\) | |||||||
\(788\) | 18.0000i | 0.641223i | ||||||||
\(789\) | 24.5015 | + | 6.13742i | 0.872277 | + | 0.218498i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.57113 | + | 15.4676i | −0.126975 | + | 0.549965i | ||||
\(792\) | 7.48331 | + | 4.00000i | 0.265908 | + | 0.142134i | ||||
\(793\) | −8.48528 | −0.301321 | ||||||||
\(794\) | 14.8424 | 0.526735 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.20614i | 0.326303i | ||||||||
\(797\) | 15.0982 | 0.534806 | 0.267403 | − | 0.963585i | \(-0.413835\pi\) | ||||
0.267403 | + | 0.963585i | \(0.413835\pi\) | |||||||
\(798\) | 11.6630 | − | 22.8275i | 0.412865 | − | 0.808086i | ||||
\(799\) | 37.1660 | 1.31484 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 41.8608 | + | 22.3755i | 1.47908 | + | 0.790600i | ||||
\(802\) | −7.48331 | −0.264245 | ||||||||
\(803\) | 15.6417 | 0.551985 | ||||||||
\(804\) | 4.33981 | − | 17.3252i | 0.153053 | − | 0.611012i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 10.3117i | − | 0.363216i | ||||||
\(807\) | −3.91913 | + | 15.6458i | −0.137960 | + | 0.550757i | ||||
\(808\) | − | 2.16991i | − | 0.0763371i | ||||||
\(809\) | − | 11.1362i | − | 0.391529i | −0.980651 | − | 0.195765i | \(-0.937281\pi\) | ||
0.980651 | − | 0.195765i | \(-0.0627188\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.0062i | 0.842970i | 0.906835 | + | 0.421485i | \(0.138491\pi\) | ||||
−0.906835 | + | 0.421485i | \(0.861509\pi\) | |||||||
\(812\) | 0.298179 | − | 1.29150i | 0.0104640 | − | 0.0453229i | ||||
\(813\) | −34.2646 | − | 8.58301i | −1.20171 | − | 0.301019i | ||||
\(814\) | 9.41699 | 0.330065 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.00000 | + | 7.98430i | −0.0700140 | + | 0.279506i | ||||
\(817\) | − | 57.6827i | − | 2.01806i | ||||||
\(818\) | 23.4626 | 0.820351 | ||||||||
\(819\) | −17.5423 | + | 20.0906i | −0.612976 | + | 0.702024i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.4362i | 1.09713i | 0.836107 | + | 0.548566i | \(0.184826\pi\) | ||||
−0.836107 | + | 0.548566i | \(0.815174\pi\) | |||||||
\(822\) | 0.543544 | − | 2.16991i | 0.0189583 | − | 0.0756842i | ||||
\(823\) | −11.8147 | −0.411834 | −0.205917 | − | 0.978569i | \(-0.566018\pi\) | ||||
−0.205917 | + | 0.978569i | \(0.566018\pi\) | |||||||
\(824\) | −3.14944 | −0.109716 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.29150 | − | 5.59388i | 0.0449371 | − | 0.194636i | ||||
\(827\) | − | 36.0000i | − | 1.25184i | −0.779886 | − | 0.625921i | \(-0.784723\pi\) | ||
0.779886 | − | 0.625921i | \(-0.215277\pi\) | |||||||
\(828\) | −10.3117 | + | 19.2915i | −0.358358 | + | 0.670426i | ||||
\(829\) | 33.2123i | 1.15351i | 0.816917 | + | 0.576755i | \(0.195681\pi\) | ||||
−0.816917 | + | 0.576755i | \(0.804319\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.93859 | − | 11.7313i | 0.101939 | − | 0.406954i | ||||
\(832\) | − | 3.36028i | − | 0.116497i | ||||||
\(833\) | −29.8982 | − | 14.5830i | −1.03591 | − | 0.505271i | ||||
\(834\) | −0.228757 | + | 0.913230i | −0.00792119 | + | 0.0316226i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −15.8219 | −0.547211 | ||||||||
\(837\) | −11.8147 | − | 10.7085i | −0.408375 | − | 0.370140i | ||||
\(838\) | 33.8137i | 1.16807i | ||||||||
\(839\) | −37.5210 | −1.29537 | −0.647684 | − | 0.761909i | \(-0.724262\pi\) | ||||
−0.647684 | + | 0.761909i | \(0.724262\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.7490 | 0.991345 | ||||||||
\(842\) | − | 10.0000i | − | 0.344623i | ||||||
\(843\) | 15.6417 | + | 3.91813i | 0.538730 | + | 0.134947i | ||||
\(844\) | 21.1660 | 0.728564 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −11.0604 | + | 20.6921i | −0.380264 | + | 0.711408i | ||||
\(847\) | −7.73381 | − | 1.78556i | −0.265737 | − | 0.0613527i | ||||
\(848\) | − | 8.58301i | − | 0.294742i | ||||||
\(849\) | 54.1033 | + | 13.5524i | 1.85682 | + | 0.465118i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.2764i | 0.832184i | ||||||||
\(852\) | 16.4835 | + | 4.12897i | 0.564714 | + | 0.141456i | ||||
\(853\) | 23.5220i | 0.805377i | 0.915337 | + | 0.402689i | \(0.131924\pi\) | ||||
−0.915337 | + | 0.402689i | \(0.868076\pi\) | |||||||
\(854\) | 6.50972 | + | 1.50295i | 0.222758 | + | 0.0514299i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 46.1363 | 1.57599 | 0.787993 | − | 0.615684i | \(-0.211120\pi\) | ||||
0.787993 | + | 0.615684i | \(0.211120\pi\) | |||||||
\(858\) | 15.9686 | + | 4.00000i | 0.545159 | + | 0.136558i | ||||
\(859\) | 22.9191i | 0.781988i | 0.920393 | + | 0.390994i | \(0.127869\pi\) | ||||
−0.920393 | + | 0.390994i | \(0.872131\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.04831 | + | 17.7099i | −0.308366 | + | 0.603553i | ||||
\(862\) | −8.98626 | −0.306073 | ||||||||
\(863\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(864\) | −3.85005 | − | 3.48957i | −0.130981 | − | 0.118718i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −18.5496 | −0.630342 | ||||||||
\(867\) | 2.34967 | − | 9.38024i | 0.0797990 | − | 0.318570i | ||||
\(868\) | −1.82646 | + | 7.91094i | −0.0619941 | + | 0.268515i | ||||
\(869\) | 9.30978i | 0.315812i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 34.6504i | − | 1.17408i | ||||||
\(872\) | 2.00000i | 0.0677285i | ||||||||
\(873\) | 20.6921 | − | 38.7113i | 0.700321 | − | 1.31018i | ||||
\(874\) | − | 40.7878i | − | 1.37967i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −9.29150 | − | 2.32744i | −0.313931 | − | 0.0786370i | ||||
\(877\) | 23.9529 | 0.808832 | 0.404416 | − | 0.914575i | \(-0.367475\pi\) | ||||
0.404416 | + | 0.914575i | \(0.367475\pi\) | |||||||
\(878\) | 26.5313 | 0.895389 | ||||||||
\(879\) | 3.06275 | − | 12.2269i | 0.103304 | − | 0.412404i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.8219 | −0.533053 | −0.266526 | − | 0.963828i | \(-0.585876\pi\) | ||||
−0.266526 | + | 0.963828i | \(0.585876\pi\) | |||||||
\(882\) | 17.0166 | − | 12.3059i | 0.572978 | − | 0.414362i | ||||
\(883\) | −30.9352 | −1.04105 | −0.520527 | − | 0.853845i | \(-0.674264\pi\) | ||||
−0.520527 | + | 0.853845i | \(0.674264\pi\) | |||||||
\(884\) | 15.9686i | 0.537082i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 29.1660 | 0.979851 | ||||||||
\(887\) | 2.27980 | 0.0765483 | 0.0382742 | − | 0.999267i | \(-0.487814\pi\) | ||||
0.0382742 | + | 0.999267i | \(0.487814\pi\) | |||||||
\(888\) | −5.59388 | − | 1.40122i | −0.187718 | − | 0.0470219i | ||||
\(889\) | 8.58301 | + | 1.98162i | 0.287865 | + | 0.0664616i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 21.1660 | − | 14.1421i | 0.709088 | − | 0.473779i | ||||
\(892\) | − | 1.19038i | − | 0.0398567i | ||||||
\(893\) | − | 43.7490i | − | 1.46400i | ||||||
\(894\) | 4.55066 | − | 18.1669i | 0.152197 | − | 0.607592i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.595188 | + | 2.57794i | −0.0198838 | + | 0.0861228i | ||||
\(897\) | −10.3117 | + | 41.1660i | −0.344299 | + | 1.37449i | ||||
\(898\) | 36.5921 | 1.22109 | ||||||||
\(899\) | 1.53737 | 0.0512743 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 40.7878i | 1.35884i | ||||||||
\(902\) | 12.2748 | 0.408708 | ||||||||
\(903\) | 21.4995 | − | 42.0802i | 0.715459 | − | 1.40034i | ||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.38075 | − | 0.596358i | −0.0790952 | − | 0.0198127i | ||||
\(907\) | −33.9411 | −1.12700 | −0.563498 | − | 0.826117i | \(-0.690545\pi\) | ||||
−0.563498 | + | 0.826117i | \(0.690545\pi\) | |||||||
\(908\) | −18.1669 | −0.602890 | ||||||||
\(909\) | −5.74103 | − | 3.06871i | −0.190418 | − | 0.101783i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 18.2960i | − | 0.606175i | −0.952963 | − | 0.303087i | \(-0.901983\pi\) | ||
0.952963 | − | 0.303087i | \(-0.0980174\pi\) | |||||||
\(912\) | 9.39851 | + | 2.35425i | 0.311216 | + | 0.0779570i | ||||
\(913\) | 19.7400i | 0.653299i | ||||||||
\(914\) | − | 8.48528i | − | 0.280668i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 24.9007i | − | 0.822742i | ||||||
\(917\) | 46.3817 | + | 10.7085i | 1.53166 | + | 0.353626i | ||||
\(918\) | 18.2960 | + | 16.5830i | 0.603859 | + | 0.547321i | ||||
\(919\) | −41.8745 | −1.38131 | −0.690656 | − | 0.723183i | \(-0.742678\pi\) | ||||
−0.690656 | + | 0.723183i | \(0.742678\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.2288 | − | 5.06713i | −0.666560 | − | 0.166968i | ||||
\(922\) | 17.9918i | 0.592528i | ||||||||
\(923\) | 32.9669 | 1.08512 | ||||||||
\(924\) | −11.5423 | − | 5.89714i | −0.379712 | − | 0.194002i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.50295i | 0.0493900i | ||||||||
\(927\) | −4.45398 | + | 8.33263i | −0.146288 | + | 0.273680i | ||||
\(928\) | 0.500983 | 0.0164456 | ||||||||
\(929\) | 51.8055 | 1.69968 | 0.849841 | − | 0.527039i | \(-0.176698\pi\) | ||||
0.849841 | + | 0.527039i | \(0.176698\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.1660 | + | 35.1939i | −0.562593 | + | 1.15343i | ||||
\(932\) | − | 13.2915i | − | 0.435378i | ||||||
\(933\) | −10.3117 | + | 41.1660i | −0.337591 | + | 1.34771i | ||||
\(934\) | 0.841723i | 0.0275420i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −8.89047 | − | 4.75216i | −0.290594 | − | 0.155329i | ||||
\(937\) | − | 5.53019i | − | 0.180663i | −0.995912 | − | 0.0903317i | \(-0.971207\pi\) | ||
0.995912 | − | 0.0903317i | \(-0.0287927\pi\) | |||||||
\(938\) | −6.13742 | + | 26.5830i | −0.200394 | + | 0.867966i | ||||
\(939\) | −24.5830 | − | 6.15784i | −0.802236 | − | 0.200953i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.632534 | 0.0206200 | 0.0103100 | − | 0.999947i | \(-0.496718\pi\) | ||||
0.0103100 | + | 0.999947i | \(0.496718\pi\) | |||||||
\(942\) | 6.89360 | − | 27.5203i | 0.224605 | − | 0.896658i | ||||
\(943\) | 31.6438i | 1.03046i | ||||||||
\(944\) | 2.16991 | 0.0706245 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −29.1660 | −0.948269 | ||||||||
\(947\) | − | 24.0000i | − | 0.779895i | −0.920837 | − | 0.389948i | \(-0.872493\pi\) | ||
0.920837 | − | 0.389948i | \(-0.127507\pi\) | |||||||
\(948\) | 1.38527 | − | 5.53019i | 0.0449914 | − | 0.179612i | ||||
\(949\) | −18.5830 | −0.603230 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.0808 | − | 2.52517i | −0.326894 | − | 0.0818842i | ||||
\(952\) | 2.82843 | − | 12.2508i | 0.0916698 | − | 0.397049i | ||||
\(953\) | 3.87451i | 0.125508i | 0.998029 | + | 0.0627538i | \(0.0199883\pi\) | ||||
−0.998029 | + | 0.0627538i | \(0.980012\pi\) | |||||||
\(954\) | −22.7085 | − | 12.1382i | −0.735215 | − | 0.392989i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 14.6431i | − | 0.473592i | ||||||
\(957\) | −0.596358 | + | 2.38075i | −0.0192775 | + | 0.0769588i | ||||
\(958\) | − | 21.6991i | − | 0.701065i | ||||||
\(959\) | −0.768687 | + | 3.32941i | −0.0248222 | + | 0.107512i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.5830 | 0.696226 | ||||||||
\(962\) | −11.1878 | −0.360708 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 17.3252i | − | 0.558007i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 15.2024 | − | 29.7552i | 0.489131 | − | 0.957358i | ||||
\(967\) | −26.9588 | −0.866936 | −0.433468 | − | 0.901169i | \(-0.642710\pi\) | ||||
−0.433468 | + | 0.901169i | \(0.642710\pi\) | |||||||
\(968\) | − | 3.00000i | − | 0.0964237i | ||||||
\(969\) | −44.6632 | − | 11.1878i | −1.43479 | − | 0.359403i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.31216 | 0.298842 | 0.149421 | − | 0.988774i | \(-0.452259\pi\) | ||||
0.149421 | + | 0.988774i | \(0.452259\pi\) | |||||||
\(972\) | −14.6773 | + | 5.25127i | −0.470776 | + | 0.168435i | ||||
\(973\) | 0.323511 | − | 1.40122i | 0.0103713 | − | 0.0449211i | ||||
\(974\) | 9.98823i | 0.320044i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.52517i | 0.0808287i | ||||||||
\(977\) | 20.1255i | 0.643872i | 0.946762 | + | 0.321936i | \(0.104334\pi\) | ||||
−0.946762 | + | 0.321936i | \(0.895666\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 44.7510i | 1.43025i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.29150 | + | 2.82843i | 0.168945 | + | 0.0903047i | ||||
\(982\) | −14.1421 | −0.451294 | ||||||||
\(983\) | −29.0037 | −0.925074 | −0.462537 | − | 0.886600i | \(-0.653061\pi\) | ||||
−0.462537 | + | 0.886600i | \(0.653061\pi\) | |||||||
\(984\) | −7.29150 | − | 1.82646i | −0.232445 | − | 0.0582254i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.38075 | −0.0758186 | ||||||||
\(987\) | 16.3062 | − | 31.9154i | 0.519031 | − | 1.01588i | ||||
\(988\) | 18.7970 | 0.598013 | ||||||||
\(989\) | − | 75.1881i | − | 2.39084i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.2915 | −0.358686 | −0.179343 | − | 0.983787i | \(-0.557397\pi\) | ||||
−0.179343 | + | 0.983787i | \(0.557397\pi\) | |||||||
\(992\) | −3.06871 | −0.0974317 | ||||||||
\(993\) | 3.36689 | − | 13.4411i | 0.106845 | − | 0.426541i | ||||
\(994\) | −25.2915 | − | 5.83925i | −0.802198 | − | 0.185210i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.93725 | − | 11.7260i | 0.0930705 | − | 0.371551i | ||||
\(997\) | − | 26.3244i | − | 0.833703i | −0.908975 | − | 0.416851i | \(-0.863134\pi\) | ||
0.908975 | − | 0.416851i | \(-0.136866\pi\) | |||||||
\(998\) | − | 22.5830i | − | 0.714853i | ||||||
\(999\) | −11.6182 | + | 12.8184i | −0.367584 | + | 0.405556i |
(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 | 1050.2.b.f.251.13 | 16 | ||
3.2 | odd | 2 | inner | 1050.2.b.f.251.3 | 16 | ||
5.2 | odd | 4 | 210.2.d.a.209.1 | ✓ | 8 | ||
5.3 | odd | 4 | 210.2.d.b.209.8 | yes | 8 | ||
5.4 | even | 2 | inner | 1050.2.b.f.251.4 | 16 | ||
7.6 | odd | 2 | inner | 1050.2.b.f.251.12 | 16 | ||
15.2 | even | 4 | 210.2.d.b.209.2 | yes | 8 | ||
15.8 | even | 4 | 210.2.d.a.209.7 | yes | 8 | ||
15.14 | odd | 2 | inner | 1050.2.b.f.251.14 | 16 | ||
20.3 | even | 4 | 1680.2.k.f.209.1 | 8 | |||
20.7 | even | 4 | 1680.2.k.e.209.8 | 8 | |||
21.20 | even | 2 | inner | 1050.2.b.f.251.6 | 16 | ||
35.13 | even | 4 | 210.2.d.b.209.1 | yes | 8 | ||
35.27 | even | 4 | 210.2.d.a.209.8 | yes | 8 | ||
35.34 | odd | 2 | inner | 1050.2.b.f.251.5 | 16 | ||
60.23 | odd | 4 | 1680.2.k.e.209.2 | 8 | |||
60.47 | odd | 4 | 1680.2.k.f.209.7 | 8 | |||
105.62 | odd | 4 | 210.2.d.b.209.7 | yes | 8 | ||
105.83 | odd | 4 | 210.2.d.a.209.2 | yes | 8 | ||
105.104 | even | 2 | inner | 1050.2.b.f.251.11 | 16 | ||
140.27 | odd | 4 | 1680.2.k.e.209.1 | 8 | |||
140.83 | odd | 4 | 1680.2.k.f.209.8 | 8 | |||
420.83 | even | 4 | 1680.2.k.e.209.7 | 8 | |||
420.167 | even | 4 | 1680.2.k.f.209.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.d.a.209.1 | ✓ | 8 | 5.2 | odd | 4 | ||
210.2.d.a.209.2 | yes | 8 | 105.83 | odd | 4 | ||
210.2.d.a.209.7 | yes | 8 | 15.8 | even | 4 | ||
210.2.d.a.209.8 | yes | 8 | 35.27 | even | 4 | ||
210.2.d.b.209.1 | yes | 8 | 35.13 | even | 4 | ||
210.2.d.b.209.2 | yes | 8 | 15.2 | even | 4 | ||
210.2.d.b.209.7 | yes | 8 | 105.62 | odd | 4 | ||
210.2.d.b.209.8 | yes | 8 | 5.3 | odd | 4 | ||
1050.2.b.f.251.3 | 16 | 3.2 | odd | 2 | inner | ||
1050.2.b.f.251.4 | 16 | 5.4 | even | 2 | inner | ||
1050.2.b.f.251.5 | 16 | 35.34 | odd | 2 | inner | ||
1050.2.b.f.251.6 | 16 | 21.20 | even | 2 | inner | ||
1050.2.b.f.251.11 | 16 | 105.104 | even | 2 | inner | ||
1050.2.b.f.251.12 | 16 | 7.6 | odd | 2 | inner | ||
1050.2.b.f.251.13 | 16 | 1.1 | even | 1 | trivial | ||
1050.2.b.f.251.14 | 16 | 15.14 | odd | 2 | inner | ||
1680.2.k.e.209.1 | 8 | 140.27 | odd | 4 | |||
1680.2.k.e.209.2 | 8 | 60.23 | odd | 4 | |||
1680.2.k.e.209.7 | 8 | 420.83 | even | 4 | |||
1680.2.k.e.209.8 | 8 | 20.7 | even | 4 | |||
1680.2.k.f.209.1 | 8 | 20.3 | even | 4 | |||
1680.2.k.f.209.2 | 8 | 420.167 | even | 4 | |||
1680.2.k.f.209.7 | 8 | 60.47 | odd | 4 | |||
1680.2.k.f.209.8 | 8 | 140.83 | odd | 4 |