Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,4,Mod(37,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("144.37");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.49627504083\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - x^{8} + 6x^{7} + 14x^{6} - 80x^{5} + 56x^{4} + 96x^{3} - 64x^{2} - 512x + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 37.3 | ||
Root | \(-1.62580 - 1.16481i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.37 |
Dual form | 144.4.k.a.109.3 |
$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.460984 | + | 2.79061i | −0.162982 | + | 0.986629i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.57499 | − | 2.57285i | −0.946874 | − | 0.321606i | ||||
\(5\) | −8.22587 | − | 8.22587i | −0.735744 | − | 0.735744i | 0.236007 | − | 0.971751i | \(-0.424161\pi\) |
−0.971751 | + | 0.236007i | \(0.924161\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.67171i | 0.144259i | 0.997395 | + | 0.0721293i | \(0.0229794\pi\) | ||||
−0.997395 | + | 0.0721293i | \(0.977021\pi\) | |||||||
\(8\) | 10.6718 | − | 19.9528i | 0.471630 | − | 0.881797i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 26.7472 | − | 19.1632i | 0.845820 | − | 0.605993i | ||||
\(11\) | 45.2213 | + | 45.2213i | 1.23952 | + | 1.23952i | 0.960197 | + | 0.279323i | \(0.0901099\pi\) |
0.279323 | + | 0.960197i | \(0.409890\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 35.3968 | − | 35.3968i | 0.755176 | − | 0.755176i | −0.220264 | − | 0.975440i | \(-0.570692\pi\) |
0.975440 | + | 0.220264i | \(0.0706918\pi\) | |||||||
\(14\) | −7.45568 | − | 1.23161i | −0.142330 | − | 0.0235116i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 50.7609 | + | 38.9786i | 0.793139 | + | 0.609041i | ||||
\(17\) | 72.4991 | 1.03433 | 0.517165 | − | 0.855886i | \(-0.326987\pi\) | ||||
0.517165 | + | 0.855886i | \(0.326987\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 19.4427 | − | 19.4427i | 0.234761 | − | 0.234761i | −0.579916 | − | 0.814676i | \(-0.696915\pi\) |
0.814676 | + | 0.579916i | \(0.196915\pi\) | |||||||
\(20\) | 41.1470 | + | 83.4748i | 0.460037 | + | 0.933277i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −147.041 | + | 105.349i | −1.42497 | + | 1.02093i | ||||
\(23\) | − | 139.462i | − | 1.26434i | −0.774830 | − | 0.632170i | \(-0.782165\pi\) | ||
0.774830 | − | 0.632170i | \(-0.217835\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.3299i | 0.0826390i | ||||||||
\(26\) | 82.4612 | + | 115.096i | 0.621999 | + | 0.868159i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 6.87389 | − | 20.2381i | 0.0463944 | − | 0.136595i | ||||
\(29\) | −66.0434 | + | 66.0434i | −0.422895 | + | 0.422895i | −0.886199 | − | 0.463304i | \(-0.846664\pi\) |
0.463304 | + | 0.886199i | \(0.346664\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 188.682 | 1.09317 | 0.546584 | − | 0.837404i | \(-0.315928\pi\) | ||||
0.546584 | + | 0.837404i | \(0.315928\pi\) | |||||||
\(32\) | −132.174 | + | 123.685i | −0.730165 | + | 0.683271i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −33.4209 | + | 202.317i | −0.168577 | + | 1.02050i | ||||
\(35\) | 21.9771 | − | 21.9771i | 0.106137 | − | 0.106137i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −84.0653 | − | 84.0653i | −0.373520 | − | 0.373520i | 0.495237 | − | 0.868758i | \(-0.335081\pi\) |
−0.868758 | + | 0.495237i | \(0.835081\pi\) | |||||||
\(38\) | 45.2941 | + | 63.2196i | 0.193360 | + | 0.269884i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −251.914 | + | 76.3445i | −0.995776 | + | 0.301778i | ||||
\(41\) | 104.629i | 0.398545i | 0.979944 | + | 0.199272i | \(0.0638578\pi\) | ||||
−0.979944 | + | 0.199272i | \(0.936142\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −31.4857 | − | 31.4857i | −0.111663 | − | 0.111663i | 0.649067 | − | 0.760731i | \(-0.275159\pi\) |
−0.760731 | + | 0.649067i | \(0.775159\pi\) | |||||||
\(44\) | −226.203 | − | 458.898i | −0.775032 | − | 1.57231i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 389.183 | + | 64.2896i | 1.24743 | + | 0.206065i | ||||
\(47\) | 488.151 | 1.51498 | 0.757491 | − | 0.652846i | \(-0.226425\pi\) | ||||
0.757491 | + | 0.652846i | \(0.226425\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 335.862 | 0.979189 | ||||||||
\(50\) | −28.8266 | − | 4.76190i | −0.0815341 | − | 0.0134687i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −359.201 | + | 177.060i | −0.957926 | + | 0.472187i | ||||
\(53\) | −149.560 | − | 149.560i | −0.387617 | − | 0.387617i | 0.486220 | − | 0.873837i | \(-0.338376\pi\) |
−0.873837 | + | 0.486220i | \(0.838376\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 743.968i | − | 1.82394i | ||||||
\(56\) | 53.3080 | + | 28.5118i | 0.127207 | + | 0.0680366i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −153.856 | − | 214.746i | −0.348316 | − | 0.486165i | ||||
\(59\) | −284.698 | − | 284.698i | −0.628212 | − | 0.628212i | 0.319406 | − | 0.947618i | \(-0.396517\pi\) |
−0.947618 | + | 0.319406i | \(0.896517\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −228.069 | + | 228.069i | −0.478709 | + | 0.478709i | −0.904719 | − | 0.426010i | \(-0.859919\pi\) |
0.426010 | + | 0.904719i | \(0.359919\pi\) | |||||||
\(62\) | −86.9792 | + | 526.537i | −0.178167 | + | 1.07855i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −284.227 | − | 425.863i | −0.555131 | − | 0.831763i | ||||
\(65\) | −582.338 | −1.11123 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 139.151 | − | 139.151i | 0.253730 | − | 0.253730i | −0.568768 | − | 0.822498i | \(-0.692580\pi\) |
0.822498 | + | 0.568768i | \(0.192580\pi\) | |||||||
\(68\) | −549.180 | − | 186.529i | −0.979380 | − | 0.332647i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 51.1984 | + | 71.4606i | 0.0874197 | + | 0.122017i | ||||
\(71\) | − | 453.655i | − | 0.758294i | −0.925336 | − | 0.379147i | \(-0.876217\pi\) | ||
0.925336 | − | 0.379147i | \(-0.123783\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 259.747i | 0.416454i | 0.978081 | + | 0.208227i | \(0.0667692\pi\) | ||||
−0.978081 | + | 0.208227i | \(0.933231\pi\) | |||||||
\(74\) | 273.346 | − | 195.841i | 0.429403 | − | 0.307649i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −197.301 | + | 97.2550i | −0.297789 | + | 0.146788i | ||||
\(77\) | −120.818 | + | 120.818i | −0.178811 | + | 0.178811i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 323.190 | 0.460275 | 0.230138 | − | 0.973158i | \(-0.426082\pi\) | ||||
0.230138 | + | 0.973158i | \(0.426082\pi\) | |||||||
\(80\) | −96.9197 | − | 738.185i | −0.135449 | − | 1.03165i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −291.979 | − | 48.2323i | −0.393216 | − | 0.0649557i | ||||
\(83\) | 563.897 | − | 563.897i | 0.745732 | − | 0.745732i | −0.227943 | − | 0.973674i | \(-0.573200\pi\) |
0.973674 | + | 0.227943i | \(0.0732000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −596.368 | − | 596.368i | −0.761002 | − | 0.761002i | ||||
\(86\) | 102.379 | − | 73.3499i | 0.128369 | − | 0.0919711i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1384.88 | − | 419.700i | 1.67760 | − | 0.508411i | ||||
\(89\) | 866.853i | 1.03243i | 0.856459 | + | 0.516215i | \(0.172659\pi\) | ||||
−0.856459 | + | 0.516215i | \(0.827341\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 94.5697 | + | 94.5697i | 0.108941 | + | 0.108941i | ||||
\(92\) | −358.814 | + | 1056.42i | −0.406619 | + | 1.19717i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −225.030 | + | 1362.24i | −0.246915 | + | 1.49472i | ||||
\(95\) | −319.866 | −0.345448 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −936.077 | −0.979837 | −0.489919 | − | 0.871768i | \(-0.662974\pi\) | ||||
−0.489919 | + | 0.871768i | \(0.662974\pi\) | |||||||
\(98\) | −154.827 | + | 937.259i | −0.159591 | + | 0.966097i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 26.5772 | − | 78.2487i | 0.0265772 | − | 0.0782487i | ||||
\(101\) | 1.58844 | + | 1.58844i | 0.00156491 | + | 0.00156491i | 0.707889 | − | 0.706324i | \(-0.249648\pi\) |
−0.706324 | + | 0.707889i | \(0.749648\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1388.28i | 1.32807i | 0.747700 | + | 0.664036i | \(0.231158\pi\) | ||||
−0.747700 | + | 0.664036i | \(0.768842\pi\) | |||||||
\(104\) | −328.518 | − | 1084.01i | −0.309749 | − | 1.02208i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 486.310 | − | 348.420i | 0.445609 | − | 0.319260i | ||||
\(107\) | 821.526 | + | 821.526i | 0.742243 | + | 0.742243i | 0.973009 | − | 0.230767i | \(-0.0741234\pi\) |
−0.230767 | + | 0.973009i | \(0.574123\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 532.797 | − | 532.797i | 0.468190 | − | 0.468190i | −0.433138 | − | 0.901328i | \(-0.642594\pi\) |
0.901328 | + | 0.433138i | \(0.142594\pi\) | |||||||
\(110\) | 2076.12 | + | 342.957i | 1.79955 | + | 0.297270i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −104.139 | + | 135.618i | −0.0878593 | + | 0.114417i | ||||
\(113\) | 67.2680 | 0.0560003 | 0.0280002 | − | 0.999608i | \(-0.491086\pi\) | ||||
0.0280002 | + | 0.999608i | \(0.491086\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1147.19 | + | 1147.19i | −0.930230 | + | 0.930230i | ||||
\(116\) | 670.198 | − | 330.359i | 0.536434 | − | 0.264423i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 925.722 | − | 663.240i | 0.722200 | − | 0.517425i | ||||
\(119\) | 193.696i | 0.149211i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2758.92i | 2.07282i | ||||||||
\(122\) | −531.315 | − | 741.587i | −0.394287 | − | 0.550329i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1429.26 | − | 485.449i | −1.03509 | − | 0.351570i | ||||
\(125\) | −943.262 | + | 943.262i | −0.674943 | + | 0.674943i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1903.59 | 1.33005 | 0.665026 | − | 0.746820i | \(-0.268421\pi\) | ||||
0.665026 | + | 0.746820i | \(0.268421\pi\) | |||||||
\(128\) | 1319.44 | − | 596.851i | 0.911118 | − | 0.412146i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 268.448 | − | 1625.08i | 0.181111 | − | 1.09638i | ||||
\(131\) | −918.430 | + | 918.430i | −0.612546 | + | 0.612546i | −0.943609 | − | 0.331062i | \(-0.892593\pi\) |
0.331062 | + | 0.943609i | \(0.392593\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 51.9451 | + | 51.9451i | 0.0338662 | + | 0.0338662i | ||||
\(134\) | 324.169 | + | 452.461i | 0.208984 | + | 0.291691i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 773.693 | − | 1446.56i | 0.487821 | − | 0.912069i | ||||
\(137\) | 477.234i | 0.297612i | 0.988866 | + | 0.148806i | \(0.0475430\pi\) | ||||
−0.988866 | + | 0.148806i | \(0.952457\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1513.89 | − | 1513.89i | −0.923788 | − | 0.923788i | 0.0735064 | − | 0.997295i | \(-0.476581\pi\) |
−0.997295 | + | 0.0735064i | \(0.976581\pi\) | |||||||
\(140\) | −223.020 | + | 109.933i | −0.134633 | + | 0.0663642i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1265.97 | + | 209.127i | 0.748155 | + | 0.123589i | ||||
\(143\) | 3201.37 | 1.87211 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1086.53 | 0.622285 | ||||||||
\(146\) | −724.853 | − | 119.739i | −0.410885 | − | 0.0678746i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 420.507 | + | 853.081i | 0.233550 | + | 0.473803i | ||||
\(149\) | −375.353 | − | 375.353i | −0.206377 | − | 0.206377i | 0.596349 | − | 0.802725i | \(-0.296618\pi\) |
−0.802725 | + | 0.596349i | \(0.796618\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2997.52i | − | 1.61546i | −0.589553 | − | 0.807730i | \(-0.700696\pi\) | ||
0.589553 | − | 0.807730i | \(-0.299304\pi\) | |||||||
\(152\) | −180.448 | − | 595.423i | −0.0962912 | − | 0.317731i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −281.460 | − | 392.850i | −0.147277 | − | 0.205564i | ||||
\(155\) | −1552.07 | − | 1552.07i | −0.804293 | − | 0.804293i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1509.01 | + | 1509.01i | −0.767082 | + | 0.767082i | −0.977592 | − | 0.210510i | \(-0.932488\pi\) |
0.210510 | + | 0.977592i | \(0.432488\pi\) | |||||||
\(158\) | −148.985 | + | 901.897i | −0.0750167 | + | 0.454121i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2104.66 | + | 69.8265i | 1.03993 | + | 0.0345017i | ||||
\(161\) | 372.601 | 0.182392 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1425.19 | + | 1425.19i | −0.684844 | + | 0.684844i | −0.961088 | − | 0.276244i | \(-0.910910\pi\) |
0.276244 | + | 0.961088i | \(0.410910\pi\) | |||||||
\(164\) | 269.195 | − | 792.565i | 0.128174 | − | 0.377371i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1313.67 | + | 1833.56i | 0.614219 | + | 0.857301i | ||||
\(167\) | − | 792.415i | − | 0.367179i | −0.983003 | − | 0.183590i | \(-0.941228\pi\) | ||
0.983003 | − | 0.183590i | \(-0.0587717\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 308.861i | − | 0.140583i | ||||||
\(170\) | 1939.15 | − | 1389.31i | 0.874857 | − | 0.626797i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 157.496 | + | 319.512i | 0.0698195 | + | 0.141643i | ||||
\(173\) | 773.594 | − | 773.594i | 0.339972 | − | 0.339972i | −0.516384 | − | 0.856357i | \(-0.672722\pi\) |
0.856357 | + | 0.516384i | \(0.172722\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −27.5984 | −0.0119214 | ||||||||
\(176\) | 532.810 | + | 4058.13i | 0.228194 | + | 1.73803i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2419.05 | − | 399.605i | −1.01862 | − | 0.168268i | ||||
\(179\) | −426.050 | + | 426.050i | −0.177902 | + | 0.177902i | −0.790441 | − | 0.612539i | \(-0.790148\pi\) |
0.612539 | + | 0.790441i | \(0.290148\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2618.06 | − | 2618.06i | −1.07513 | − | 1.07513i | −0.996938 | − | 0.0781951i | \(-0.975084\pi\) |
−0.0781951 | − | 0.996938i | \(-0.524916\pi\) | |||||||
\(182\) | −307.502 | + | 220.312i | −0.125239 | + | 0.0897286i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2782.65 | − | 1488.30i | −1.11489 | − | 0.596300i | ||||
\(185\) | 1383.02i | 0.549631i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3278.50 | + | 3278.50i | 1.28207 | + | 1.28207i | ||||
\(188\) | −3697.74 | − | 1255.94i | −1.43450 | − | 0.487227i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 147.453 | − | 892.620i | 0.0563019 | − | 0.340829i | ||||
\(191\) | −3216.39 | −1.21848 | −0.609240 | − | 0.792986i | \(-0.708525\pi\) | ||||
−0.609240 | + | 0.792986i | \(0.708525\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2852.57 | 1.06390 | 0.531950 | − | 0.846776i | \(-0.321459\pi\) | ||||
0.531950 | + | 0.846776i | \(0.321459\pi\) | |||||||
\(194\) | 431.516 | − | 2612.22i | 0.159696 | − | 0.966736i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2544.15 | − | 864.122i | −0.927169 | − | 0.314913i | ||||
\(197\) | −1609.02 | − | 1609.02i | −0.581918 | − | 0.581918i | 0.353512 | − | 0.935430i | \(-0.384987\pi\) |
−0.935430 | + | 0.353512i | \(0.884987\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 747.136i | − | 0.266146i | −0.991106 | − | 0.133073i | \(-0.957516\pi\) | ||
0.991106 | − | 0.133073i | \(-0.0424845\pi\) | |||||||
\(200\) | 206.110 | + | 110.238i | 0.0728708 | + | 0.0389750i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.16496 | + | 3.70047i | −0.00179904 | + | 0.00128893i | ||||
\(203\) | −176.449 | − | 176.449i | −0.0610062 | − | 0.0610062i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 860.666 | − | 860.666i | 0.293227 | − | 0.293227i | ||||
\(206\) | −3874.15 | − | 639.975i | −1.31032 | − | 0.216452i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3176.49 | − | 417.055i | 1.05889 | − | 0.139027i | ||||
\(209\) | 1758.44 | 0.581981 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2227.13 | + | 2227.13i | −0.726645 | + | 0.726645i | −0.969950 | − | 0.243305i | \(-0.921769\pi\) |
0.243305 | + | 0.969950i | \(0.421769\pi\) | |||||||
\(212\) | 748.122 | + | 1517.72i | 0.242364 | + | 0.491684i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2671.27 | + | 1913.85i | −0.853290 | + | 0.611346i | ||||
\(215\) | 517.995i | 0.164311i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 504.102i | 0.157699i | ||||||||
\(218\) | 1241.22 | + | 1732.44i | 0.385623 | + | 0.538237i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1914.12 | + | 5635.55i | −0.586590 | + | 1.72704i | ||||
\(221\) | 2566.23 | − | 2566.23i | 0.781102 | − | 0.781102i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −358.053 | −0.107520 | −0.0537601 | − | 0.998554i | \(-0.517121\pi\) | ||||
−0.0537601 | + | 0.998554i | \(0.517121\pi\) | |||||||
\(224\) | −330.451 | − | 353.130i | −0.0985677 | − | 0.105332i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −31.0094 | + | 187.719i | −0.00912706 | + | 0.0552516i | ||||
\(227\) | −3455.40 | + | 3455.40i | −1.01032 | + | 1.01032i | −0.0103741 | + | 0.999946i | \(0.503302\pi\) |
−0.999946 | + | 0.0103741i | \(0.996698\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1430.03 | − | 1430.03i | −0.412659 | − | 0.412659i | 0.470005 | − | 0.882664i | \(-0.344252\pi\) |
−0.882664 | + | 0.470005i | \(0.844252\pi\) | |||||||
\(230\) | −2672.53 | − | 3730.21i | −0.766181 | − | 1.06940i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 612.951 | + | 2022.55i | 0.173458 | + | 0.572357i | ||||
\(233\) | − | 926.479i | − | 0.260496i | −0.991481 | − | 0.130248i | \(-0.958423\pi\) | ||
0.991481 | − | 0.130248i | \(-0.0415774\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4015.47 | − | 4015.47i | −1.11464 | − | 1.11464i | ||||
\(236\) | 1424.10 | + | 2889.07i | 0.392801 | + | 0.796875i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −540.530 | − | 89.2908i | −0.147216 | − | 0.0243187i | ||||
\(239\) | 792.472 | 0.214480 | 0.107240 | − | 0.994233i | \(-0.465799\pi\) | ||||
0.107240 | + | 0.994233i | \(0.465799\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1449.01 | 0.387299 | 0.193650 | − | 0.981071i | \(-0.437967\pi\) | ||||
0.193650 | + | 0.981071i | \(0.437967\pi\) | |||||||
\(242\) | −7699.07 | − | 1271.82i | −2.04510 | − | 0.337833i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2314.41 | − | 1140.83i | 0.607233 | − | 0.299321i | ||||
\(245\) | −2762.76 | − | 2762.76i | −0.720433 | − | 0.720433i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1376.42i | − | 0.354572i | ||||||
\(248\) | 2013.57 | − | 3764.73i | 0.515571 | − | 0.963953i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2197.45 | − | 3067.10i | −0.555915 | − | 0.775922i | ||||
\(251\) | 3580.04 | + | 3580.04i | 0.900280 | + | 0.900280i | 0.995460 | − | 0.0951802i | \(-0.0303427\pi\) |
−0.0951802 | + | 0.995460i | \(0.530343\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6306.64 | − | 6306.64i | 1.56717 | − | 1.56717i | ||||
\(254\) | −877.525 | + | 5312.18i | −0.216775 | + | 1.31227i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1057.34 | + | 3957.18i | 0.258139 | + | 0.966108i | ||||
\(257\) | 4708.87 | 1.14292 | 0.571461 | − | 0.820629i | \(-0.306377\pi\) | ||||
0.571461 | + | 0.820629i | \(0.306377\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 224.598 | − | 224.598i | 0.0538835 | − | 0.0538835i | ||||
\(260\) | 4411.21 | + | 1498.27i | 1.05220 | + | 0.357379i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2139.60 | − | 2986.36i | −0.504522 | − | 0.704190i | ||||
\(263\) | − | 2967.82i | − | 0.695830i | −0.937526 | − | 0.347915i | \(-0.886890\pi\) | ||
0.937526 | − | 0.347915i | \(-0.113110\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2460.53i | 0.570374i | ||||||||
\(266\) | −168.904 | + | 121.013i | −0.0389330 | + | 0.0278938i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1412.08 | + | 696.050i | −0.321852 | + | 0.158649i | ||||
\(269\) | 663.633 | − | 663.633i | 0.150418 | − | 0.150418i | −0.627887 | − | 0.778305i | \(-0.716080\pi\) |
0.778305 | + | 0.627887i | \(0.216080\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8058.74 | 1.80640 | 0.903199 | − | 0.429223i | \(-0.141212\pi\) | ||||
0.903199 | + | 0.429223i | \(0.141212\pi\) | |||||||
\(272\) | 3680.12 | + | 2825.91i | 0.820368 | + | 0.629949i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1331.77 | − | 219.997i | −0.293633 | − | 0.0485055i | ||||
\(275\) | −467.130 | + | 467.130i | −0.102433 | + | 0.102433i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 482.477 | + | 482.477i | 0.104654 | + | 0.104654i | 0.757495 | − | 0.652841i | \(-0.226423\pi\) |
−0.652841 | + | 0.757495i | \(0.726423\pi\) | |||||||
\(278\) | 4922.56 | − | 3526.80i | 1.06200 | − | 0.760875i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −203.970 | − | 673.039i | −0.0435341 | − | 0.143649i | ||||
\(281\) | − | 5899.10i | − | 1.25235i | −0.779682 | − | 0.626175i | \(-0.784619\pi\) | ||
0.779682 | − | 0.626175i | \(-0.215381\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −679.897 | − | 679.897i | −0.142812 | − | 0.142812i | 0.632086 | − | 0.774898i | \(-0.282199\pi\) |
−0.774898 | + | 0.632086i | \(0.782199\pi\) | |||||||
\(284\) | −1167.18 | + | 3436.43i | −0.243872 | + | 0.718009i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1475.78 | + | 8933.77i | −0.305121 | + | 1.84708i | ||||
\(287\) | −279.538 | −0.0574935 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 343.118 | 0.0698388 | ||||||||
\(290\) | −500.872 | + | 3032.08i | −0.101421 | + | 0.613965i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 668.290 | − | 1967.58i | 0.133934 | − | 0.394329i | ||||
\(293\) | 3552.87 | + | 3552.87i | 0.708398 | + | 0.708398i | 0.966198 | − | 0.257800i | \(-0.0829976\pi\) |
−0.257800 | + | 0.966198i | \(0.582998\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4683.78i | 0.924407i | ||||||||
\(296\) | −2574.46 | + | 780.213i | −0.505532 | + | 0.153206i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1220.49 | − | 874.432i | 0.237253 | − | 0.169981i | ||||
\(299\) | −4936.50 | − | 4936.50i | −0.954799 | − | 0.954799i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 84.1205 | − | 84.1205i | 0.0161084 | − | 0.0161084i | ||||
\(302\) | 8364.89 | + | 1381.81i | 1.59386 | + | 0.263291i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1744.78 | − | 229.079i | 0.329177 | − | 0.0432191i | ||||
\(305\) | 3752.13 | 0.704415 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2735.56 | − | 2735.56i | 0.508556 | − | 0.508556i | −0.405527 | − | 0.914083i | \(-0.632912\pi\) |
0.914083 | + | 0.405527i | \(0.132912\pi\) | |||||||
\(308\) | 1226.04 | − | 604.348i | 0.226819 | − | 0.111805i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5046.70 | − | 3615.74i | 0.924624 | − | 0.662453i | ||||
\(311\) | 5796.70i | 1.05692i | 0.848960 | + | 0.528458i | \(0.177229\pi\) | ||||
−0.848960 | + | 0.528458i | \(0.822771\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 8362.62i | − | 1.51017i | −0.655627 | − | 0.755085i | \(-0.727596\pi\) | ||
0.655627 | − | 0.755085i | \(-0.272404\pi\) | |||||||
\(314\) | −3515.42 | − | 4906.67i | −0.631804 | − | 0.881846i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2448.16 | − | 831.519i | −0.435822 | − | 0.148027i | ||||
\(317\) | 344.406 | − | 344.406i | 0.0610214 | − | 0.0610214i | −0.675938 | − | 0.736959i | \(-0.736261\pi\) |
0.736959 | + | 0.675938i | \(0.236261\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5973.13 | −1.04837 | ||||||||
\(320\) | −1165.07 | + | 5841.11i | −0.203530 | + | 1.02040i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −171.763 | + | 1039.78i | −0.0297266 | + | 0.179953i | ||||
\(323\) | 1409.58 | − | 1409.58i | 0.242820 | − | 0.242820i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 365.644 | + | 365.644i | 0.0624071 | + | 0.0624071i | ||||
\(326\) | −3320.16 | − | 4634.14i | −0.564069 | − | 0.787304i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2087.64 | + | 1116.58i | 0.351435 | + | 0.187965i | ||||
\(329\) | 1304.20i | 0.218549i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2687.86 | + | 2687.86i | 0.446339 | + | 0.446339i | 0.894135 | − | 0.447797i | \(-0.147791\pi\) |
−0.447797 | + | 0.894135i | \(0.647791\pi\) | |||||||
\(332\) | −5722.33 | + | 2820.69i | −0.945945 | + | 0.466282i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2211.32 | + | 365.290i | 0.362270 | + | 0.0598437i | ||||
\(335\) | −2289.27 | −0.373361 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1795.31 | −0.290199 | −0.145099 | − | 0.989417i | \(-0.546350\pi\) | ||||
−0.145099 | + | 0.989417i | \(0.546350\pi\) | |||||||
\(338\) | 861.910 | + | 142.380i | 0.138703 | + | 0.0229125i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2983.12 | + | 6051.85i | 0.475830 | + | 0.965316i | ||||
\(341\) | 8532.42 | + | 8532.42i | 1.35500 | + | 1.35500i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1813.72i | 0.285515i | ||||||||
\(344\) | −964.235 | + | 292.220i | −0.151128 | + | 0.0458007i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1802.18 | + | 2515.41i | 0.280017 | + | 0.390836i | ||||
\(347\) | 1967.33 | + | 1967.33i | 0.304357 | + | 0.304357i | 0.842716 | − | 0.538359i | \(-0.180955\pi\) |
−0.538359 | + | 0.842716i | \(0.680955\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7363.37 | + | 7363.37i | −1.12938 | + | 1.12938i | −0.139097 | + | 0.990279i | \(0.544420\pi\) |
−0.990279 | + | 0.139097i | \(0.955580\pi\) | |||||||
\(350\) | 12.7224 | − | 77.0163i | 0.00194297 | − | 0.0117620i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −11570.3 | − | 383.867i | −1.75198 | − | 0.0581255i | ||||
\(353\) | −10644.3 | −1.60493 | −0.802466 | − | 0.596698i | \(-0.796479\pi\) | ||||
−0.802466 | + | 0.596698i | \(0.796479\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3731.70 | + | 3731.70i | −0.557911 | + | 0.557911i | ||||
\(356\) | 2230.28 | − | 6566.40i | 0.332036 | − | 0.977580i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −992.537 | − | 1385.34i | −0.146529 | − | 0.204518i | ||||
\(359\) | 7459.42i | 1.09664i | 0.836269 | + | 0.548319i | \(0.184732\pi\) | ||||
−0.836269 | + | 0.548319i | \(0.815268\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6102.96i | 0.889775i | ||||||||
\(362\) | 8512.87 | − | 6099.10i | 1.23599 | − | 0.885530i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −473.051 | − | 959.678i | −0.0681170 | − | 0.138189i | ||||
\(365\) | 2136.65 | − | 2136.65i | 0.306403 | − | 0.306403i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6251.35 | −0.889149 | −0.444574 | − | 0.895742i | \(-0.646645\pi\) | ||||
−0.444574 | + | 0.895742i | \(0.646645\pi\) | |||||||
\(368\) | 5436.03 | − | 7079.21i | 0.770034 | − | 1.00280i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3859.47 | − | 637.550i | −0.542282 | − | 0.0895801i | ||||
\(371\) | 399.582 | − | 399.582i | 0.0559171 | − | 0.0559171i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8911.86 | + | 8911.86i | 1.23710 | + | 1.23710i | 0.961180 | + | 0.275921i | \(0.0889827\pi\) |
0.275921 | + | 0.961180i | \(0.411017\pi\) | |||||||
\(374\) | −10660.3 | + | 7637.67i | −1.47389 | + | 1.05598i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5209.43 | − | 9739.97i | 0.714510 | − | 1.33591i | ||||
\(377\) | 4675.45i | 0.638721i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1184.03 | + | 1184.03i | 0.160473 | + | 0.160473i | 0.782776 | − | 0.622303i | \(-0.213803\pi\) |
−0.622303 | + | 0.782776i | \(0.713803\pi\) | |||||||
\(380\) | 2422.98 | + | 822.966i | 0.327095 | + | 0.111098i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1482.70 | − | 8975.67i | 0.198591 | − | 1.20219i | ||||
\(383\) | 2880.38 | 0.384283 | 0.192142 | − | 0.981367i | \(-0.438457\pi\) | ||||
0.192142 | + | 0.981367i | \(0.438457\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1987.66 | 0.263119 | ||||||||
\(386\) | −1314.99 | + | 7960.42i | −0.173397 | + | 1.04968i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7090.77 | + | 2408.38i | 0.927782 | + | 0.315122i | ||||
\(389\) | −9244.24 | − | 9244.24i | −1.20489 | − | 1.20489i | −0.972662 | − | 0.232226i | \(-0.925399\pi\) |
−0.232226 | − | 0.972662i | \(-0.574601\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 10110.9i | − | 1.30774i | ||||||
\(392\) | 3584.24 | − | 6701.38i | 0.461815 | − | 0.863446i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5231.87 | − | 3748.41i | 0.668979 | − | 0.479295i | ||||
\(395\) | −2658.52 | − | 2658.52i | −0.338645 | − | 0.338645i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4257.80 | + | 4257.80i | −0.538270 | + | 0.538270i | −0.923020 | − | 0.384751i | \(-0.874287\pi\) |
0.384751 | + | 0.923020i | \(0.374287\pi\) | |||||||
\(398\) | 2084.96 | + | 344.417i | 0.262587 | + | 0.0433771i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −402.644 | + | 524.354i | −0.0503305 | + | 0.0655442i | ||||
\(401\) | −12722.6 | −1.58437 | −0.792187 | − | 0.610278i | \(-0.791058\pi\) | ||||
−0.792187 | + | 0.610278i | \(0.791058\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6678.72 | − | 6678.72i | 0.825535 | − | 0.825535i | ||||
\(404\) | −7.94560 | − | 16.1192i | −0.000978486 | − | 0.00198505i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 573.739 | − | 411.059i | 0.0701335 | − | 0.0502476i | ||||
\(407\) | − | 7603.08i | − | 0.925972i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 232.991i | − | 0.0281678i | −0.999901 | − | 0.0140839i | \(-0.995517\pi\) | ||
0.999901 | − | 0.0140839i | \(-0.00448320\pi\) | |||||||
\(410\) | 2005.03 | + | 2798.53i | 0.241515 | + | 0.337097i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3571.84 | − | 10516.2i | 0.427116 | − | 1.25752i | ||||
\(413\) | 760.629 | − | 760.629i | 0.0906250 | − | 0.0906250i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9277.08 | −1.09734 | ||||||||
\(416\) | −300.471 | + | 9056.59i | −0.0354129 | + | 1.06739i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −810.614 | + | 4907.13i | −0.0948527 | + | 0.574200i | ||||
\(419\) | 6125.69 | − | 6125.69i | 0.714223 | − | 0.714223i | −0.253193 | − | 0.967416i | \(-0.581481\pi\) |
0.967416 | + | 0.253193i | \(0.0814807\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8308.44 | − | 8308.44i | −0.961825 | − | 0.961825i | 0.0374725 | − | 0.999298i | \(-0.488069\pi\) |
−0.999298 | + | 0.0374725i | \(0.988069\pi\) | |||||||
\(422\) | −5188.38 | − | 7241.73i | −0.598499 | − | 0.835360i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4580.22 | + | 1388.07i | −0.524611 | + | 0.158988i | ||||
\(425\) | 748.907i | 0.0854760i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −609.333 | − | 609.333i | −0.0690579 | − | 0.0690579i | ||||
\(428\) | −4109.39 | − | 8336.72i | −0.464100 | − | 0.941520i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1445.52 | − | 238.787i | −0.162114 | − | 0.0267798i | ||||
\(431\) | −8737.57 | −0.976506 | −0.488253 | − | 0.872702i | \(-0.662366\pi\) | ||||
−0.488253 | + | 0.872702i | \(0.662366\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11627.5 | −1.29049 | −0.645247 | − | 0.763974i | \(-0.723245\pi\) | ||||
−0.645247 | + | 0.763974i | \(0.723245\pi\) | |||||||
\(434\) | −1406.75 | − | 232.383i | −0.155590 | − | 0.0257021i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5406.74 | + | 2665.13i | −0.593890 | + | 0.292744i | ||||
\(437\) | −2711.51 | − | 2711.51i | −0.296817 | − | 0.296817i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17631.8i | 1.91690i | 0.285261 | + | 0.958450i | \(0.407920\pi\) | ||||
−0.285261 | + | 0.958450i | \(0.592080\pi\) | |||||||
\(440\) | −14844.2 | − | 7939.45i | −1.60834 | − | 0.860224i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5978.36 | + | 8344.34i | 0.643352 | + | 0.897963i | ||||
\(443\) | 4549.81 | + | 4549.81i | 0.487964 | + | 0.487964i | 0.907663 | − | 0.419699i | \(-0.137864\pi\) |
−0.419699 | + | 0.907663i | \(0.637864\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7130.62 | − | 7130.62i | 0.759604 | − | 0.759604i | ||||
\(446\) | 165.057 | − | 999.186i | 0.0175239 | − | 0.106083i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1137.78 | − | 759.371i | 0.119989 | − | 0.0800824i | ||||
\(449\) | 12926.5 | 1.35867 | 0.679334 | − | 0.733830i | \(-0.262269\pi\) | ||||
0.679334 | + | 0.733830i | \(0.262269\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4731.46 | + | 4731.46i | −0.494004 | + | 0.494004i | ||||
\(452\) | −509.554 | − | 173.070i | −0.0530252 | − | 0.0180101i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8049.78 | − | 11235.5i | −0.832147 | − | 1.16148i | ||||
\(455\) | − | 1555.84i | − | 0.160305i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 9320.32i | − | 0.954018i | −0.878898 | − | 0.477009i | \(-0.841721\pi\) | ||
0.878898 | − | 0.477009i | \(-0.158279\pi\) | |||||||
\(458\) | 4649.87 | − | 3331.43i | 0.474398 | − | 0.339886i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 11641.5 | − | 5738.43i | 1.17998 | − | 0.581643i | ||||
\(461\) | −12885.0 | + | 12885.0i | −1.30177 | + | 1.30177i | −0.374566 | + | 0.927200i | \(0.622208\pi\) |
−0.927200 | + | 0.374566i | \(0.877792\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7038.37 | 0.706482 | 0.353241 | − | 0.935532i | \(-0.385080\pi\) | ||||
0.353241 | + | 0.935532i | \(0.385080\pi\) | |||||||
\(464\) | −5926.71 | + | 778.144i | −0.592975 | + | 0.0778543i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2585.44 | + | 427.091i | 0.257013 | + | 0.0424563i | ||||
\(467\) | −6001.76 | + | 6001.76i | −0.594707 | + | 0.594707i | −0.938899 | − | 0.344192i | \(-0.888153\pi\) |
0.344192 | + | 0.938899i | \(0.388153\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 371.769 | + | 371.769i | 0.0366028 | + | 0.0366028i | ||||
\(470\) | 13056.7 | − | 9354.53i | 1.28140 | − | 0.918069i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8718.75 | + | 2642.29i | −0.850239 | + | 0.257672i | ||||
\(473\) | − | 2847.65i | − | 0.276818i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 200.840 | + | 200.840i | 0.0194004 | + | 0.0194004i | ||||
\(476\) | 498.351 | − | 1467.25i | 0.0479872 | − | 0.141284i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −365.317 | + | 2211.48i | −0.0349565 | + | 0.211612i | ||||
\(479\) | 587.317 | 0.0560234 | 0.0280117 | − | 0.999608i | \(-0.491082\pi\) | ||||
0.0280117 | + | 0.999608i | \(0.491082\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5951.28 | −0.564148 | ||||||||
\(482\) | −667.971 | + | 4043.63i | −0.0631229 | + | 0.382121i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7098.29 | − | 20898.8i | 0.666631 | − | 1.96270i | ||||
\(485\) | 7700.05 | + | 7700.05i | 0.720910 | + | 0.720910i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8366.45i | 0.778481i | 0.921136 | + | 0.389240i | \(0.127262\pi\) | ||||
−0.921136 | + | 0.389240i | \(0.872738\pi\) | |||||||
\(488\) | 2116.71 | + | 6984.51i | 0.196351 | + | 0.647897i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 8983.36 | − | 6436.19i | 0.828218 | − | 0.593382i | ||||
\(491\) | −1529.30 | − | 1529.30i | −0.140563 | − | 0.140563i | 0.633324 | − | 0.773887i | \(-0.281690\pi\) |
−0.773887 | + | 0.633324i | \(0.781690\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4788.09 | + | 4788.09i | −0.437413 | + | 0.437413i | ||||
\(494\) | 3841.04 | + | 634.505i | 0.349831 | + | 0.0577889i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9577.65 | + | 7354.55i | 0.867035 | + | 0.665784i | ||||
\(497\) | 1212.03 | 0.109390 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11364.5 | − | 11364.5i | 1.01952 | − | 1.01952i | 0.0197191 | − | 0.999806i | \(-0.493723\pi\) |
0.999806 | − | 0.0197191i | \(-0.00627718\pi\) | |||||||
\(500\) | 9572.06 | − | 4718.33i | 0.856151 | − | 0.422020i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −11640.8 | + | 8340.15i | −1.03497 | + | 0.741513i | ||||
\(503\) | − | 12570.2i | − | 1.11427i | −0.830421 | − | 0.557137i | \(-0.811900\pi\) | ||
0.830421 | − | 0.557137i | \(-0.188100\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 26.1326i | − | 0.00230274i | ||||||
\(506\) | 14692.1 | + | 20506.6i | 1.29080 | + | 1.80164i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −14419.7 | − | 4897.66i | −1.25939 | − | 0.427753i | ||||
\(509\) | −11880.4 | + | 11880.4i | −1.03456 | + | 1.03456i | −0.0351750 | + | 0.999381i | \(0.511199\pi\) |
−0.999381 | + | 0.0351750i | \(0.988801\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −693.968 | −0.0600770 | ||||||||
\(512\) | −11530.3 | + | 1126.42i | −0.995262 | + | 0.0972291i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2170.71 | + | 13140.6i | −0.186276 | + | 1.12764i | ||||
\(515\) | 11419.8 | − | 11419.8i | 0.977122 | − | 0.977122i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22074.8 | + | 22074.8i | 1.87785 | + | 1.87785i | ||||
\(518\) | 523.229 | + | 730.300i | 0.0443810 | + | 0.0619451i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6214.57 | + | 11619.3i | −0.524090 | + | 0.979882i | ||||
\(521\) | − | 6612.98i | − | 0.556085i | −0.960569 | − | 0.278042i | \(-0.910314\pi\) | ||
0.960569 | − | 0.278042i | \(-0.0896856\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5129.30 | + | 5129.30i | 0.428850 | + | 0.428850i | 0.888236 | − | 0.459387i | \(-0.151931\pi\) |
−0.459387 | + | 0.888236i | \(0.651931\pi\) | |||||||
\(524\) | 9320.07 | − | 4594.11i | 0.777003 | − | 0.383005i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8282.01 | + | 1368.11i | 0.686526 | + | 0.113408i | ||||
\(527\) | 13679.3 | 1.13070 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7282.60 | −0.598553 | ||||||||
\(530\) | −6866.38 | − | 1134.26i | −0.562748 | − | 0.0929609i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −259.837 | − | 527.130i | −0.0211755 | − | 0.0429586i | ||||
\(533\) | 3703.53 | + | 3703.53i | 0.300972 | + | 0.300972i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 13515.5i | − | 1.09220i | ||||||
\(536\) | −1291.46 | − | 4261.42i | −0.104072 | − | 0.343406i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1546.02 | + | 2157.86i | 0.123891 | + | 0.172922i | ||||
\(539\) | 15188.1 | + | 15188.1i | 1.21372 | + | 1.21372i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10968.5 | + | 10968.5i | −0.871672 | + | 0.871672i | −0.992655 | − | 0.120983i | \(-0.961395\pi\) |
0.120983 | + | 0.992655i | \(0.461395\pi\) | |||||||
\(542\) | −3714.95 | + | 22488.8i | −0.294411 | + | 1.78224i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −9582.49 | + | 8967.07i | −0.755231 | + | 0.706728i | ||||
\(545\) | −8765.44 | −0.688936 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13088.8 | − | 13088.8i | 1.02311 | − | 1.02311i | 0.0233784 | − | 0.999727i | \(-0.492558\pi\) |
0.999727 | − | 0.0233784i | \(-0.00744226\pi\) | |||||||
\(548\) | 1227.85 | − | 3615.04i | 0.0957138 | − | 0.281801i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1088.24 | − | 1518.92i | −0.0843684 | − | 0.117758i | ||||
\(551\) | 2568.12i | 0.198558i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 863.469i | 0.0663986i | ||||||||
\(554\) | −1568.82 | + | 1123.99i | −0.120312 | + | 0.0861981i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7572.70 | + | 15362.7i | 0.577615 | + | 1.17181i | ||||
\(557\) | −5049.87 | + | 5049.87i | −0.384147 | + | 0.384147i | −0.872594 | − | 0.488447i | \(-0.837564\pi\) |
0.488447 | + | 0.872594i | \(0.337564\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2228.98 | −0.168651 | ||||||||
\(560\) | 1972.21 | − | 258.941i | 0.148824 | − | 0.0195397i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16462.1 | + | 2719.39i | 1.23561 | + | 0.204111i | ||||
\(563\) | 3249.06 | − | 3249.06i | 0.243217 | − | 0.243217i | −0.574962 | − | 0.818180i | \(-0.694983\pi\) |
0.818180 | + | 0.574962i | \(0.194983\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −553.338 | − | 553.338i | −0.0412019 | − | 0.0412019i | ||||
\(566\) | 2210.75 | − | 1583.90i | 0.164178 | − | 0.117626i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9051.67 | − | 4841.29i | −0.668661 | − | 0.357634i | ||||
\(569\) | 2806.05i | 0.206741i | 0.994643 | + | 0.103371i | \(0.0329628\pi\) | ||||
−0.994643 | + | 0.103371i | \(0.967037\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12038.8 | − | 12038.8i | −0.882324 | − | 0.882324i | 0.111446 | − | 0.993770i | \(-0.464452\pi\) |
−0.993770 | + | 0.111446i | \(0.964452\pi\) | |||||||
\(572\) | −24250.3 | − | 8236.64i | −1.77265 | − | 0.602083i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 128.863 | − | 780.082i | 0.00937042 | − | 0.0567247i | ||||
\(575\) | 1440.62 | 0.104484 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7206.84 | 0.519973 | 0.259987 | − | 0.965612i | \(-0.416282\pi\) | ||||
0.259987 | + | 0.965612i | \(0.416282\pi\) | |||||||
\(578\) | −158.172 | + | 957.508i | −0.0113825 | + | 0.0689050i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −8230.45 | − | 2795.48i | −0.589226 | − | 0.200131i | ||||
\(581\) | 1506.57 | + | 1506.57i | 0.107578 | + | 0.107578i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 13526.6i | − | 0.960918i | ||||||
\(584\) | 5182.68 | + | 2771.96i | 0.367227 | + | 0.196412i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11552.5 | + | 8276.84i | −0.814382 | + | 0.583470i | ||||
\(587\) | −10377.0 | − | 10377.0i | −0.729647 | − | 0.729647i | 0.240903 | − | 0.970549i | \(-0.422557\pi\) |
−0.970549 | + | 0.240903i | \(0.922557\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3668.48 | − | 3668.48i | 0.256633 | − | 0.256633i | ||||
\(590\) | −13070.6 | − | 2159.14i | −0.912047 | − | 0.150662i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −990.483 | − | 7543.98i | −0.0687645 | − | 0.523743i | ||||
\(593\) | 4758.60 | 0.329531 | 0.164766 | − | 0.986333i | \(-0.447313\pi\) | ||||
0.164766 | + | 0.986333i | \(0.447313\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1593.32 | − | 1593.32i | 0.109781 | − | 0.109781i | ||||
\(596\) | 1877.57 | + | 3809.02i | 0.129041 | + | 0.261785i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 16051.5 | − | 11500.2i | 1.09765 | − | 0.786417i | ||||
\(599\) | 14256.4i | 0.972455i | 0.873832 | + | 0.486227i | \(0.161627\pi\) | ||||
−0.873832 | + | 0.486227i | \(0.838373\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 10385.2i | − | 0.704862i | −0.935838 | − | 0.352431i | \(-0.885355\pi\) | ||
0.935838 | − | 0.352431i | \(-0.114645\pi\) | |||||||
\(602\) | 195.969 | + | 273.526i | 0.0132676 | + | 0.0185184i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7712.16 | + | 22706.2i | −0.519542 | + | 1.52964i | ||||
\(605\) | 22694.5 | − | 22694.5i | 1.52506 | − | 1.52506i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16243.6 | −1.08618 | −0.543088 | − | 0.839676i | \(-0.682745\pi\) | ||||
−0.543088 | + | 0.839676i | \(0.682745\pi\) | |||||||
\(608\) | −165.042 | + | 4974.59i | −0.0110088 | + | 0.331819i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1729.67 | + | 10470.7i | −0.114807 | + | 0.694996i | ||||
\(611\) | 17279.0 | − | 17279.0i | 1.14408 | − | 1.14408i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −500.502 | − | 500.502i | −0.0329773 | − | 0.0329773i | 0.690426 | − | 0.723403i | \(-0.257423\pi\) |
−0.723403 | + | 0.690426i | \(0.757423\pi\) | |||||||
\(614\) | 6372.83 | + | 8894.92i | 0.418870 | + | 0.584642i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1121.31 | + | 3699.99i | 0.0733426 | + | 0.242008i | ||||
\(617\) | 11575.9i | 0.755316i | 0.925945 | + | 0.377658i | \(0.123271\pi\) | ||||
−0.925945 | + | 0.377658i | \(0.876729\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18356.1 | + | 18356.1i | 1.19191 | + | 1.19191i | 0.976530 | + | 0.215380i | \(0.0690992\pi\) |
0.215380 | + | 0.976530i | \(0.430901\pi\) | |||||||
\(620\) | 7763.68 | + | 15750.2i | 0.502898 | + | 1.02023i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −16176.3 | − | 2672.18i | −1.04278 | − | 0.172258i | ||||
\(623\) | −2315.98 | −0.148937 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16809.5 | 1.07581 | ||||||||
\(626\) | 23336.8 | + | 3855.03i | 1.48998 | + | 0.246131i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15313.2 | − | 7548.26i | 0.973027 | − | 0.479631i | ||||
\(629\) | −6094.66 | − | 6094.66i | −0.386343 | − | 0.386343i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10224.8i | 0.645079i | 0.946556 | + | 0.322539i | \(0.104537\pi\) | ||||
−0.946556 | + | 0.322539i | \(0.895463\pi\) | |||||||
\(632\) | 3449.01 | − | 6448.54i | 0.217079 | − | 0.405869i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 802.338 | + | 1119.87i | 0.0502601 | + | 0.0701509i | ||||
\(635\) | −15658.7 | − | 15658.7i | −0.978578 | − | 0.978578i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11888.4 | − | 11888.4i | 0.739461 | − | 0.739461i | ||||
\(638\) | 2753.52 | − | 16668.7i | 0.170866 | − | 1.03436i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −15763.2 | − | 5943.92i | −0.973584 | − | 0.367116i | ||||
\(641\) | −19804.4 | −1.22032 | −0.610162 | − | 0.792277i | \(-0.708896\pi\) | ||||
−0.610162 | + | 0.792277i | \(0.708896\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15680.7 | − | 15680.7i | 0.961723 | − | 0.961723i | −0.0375712 | − | 0.999294i | \(-0.511962\pi\) |
0.999294 | + | 0.0375712i | \(0.0119621\pi\) | |||||||
\(644\) | −2822.45 | − | 958.646i | −0.172702 | − | 0.0586583i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3283.78 | + | 4583.37i | 0.199998 | + | 0.279149i | ||||
\(647\) | − | 9232.26i | − | 0.560985i | −0.959856 | − | 0.280493i | \(-0.909502\pi\) | ||
0.959856 | − | 0.280493i | \(-0.0904978\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 25748.8i | − | 1.55736i | ||||||
\(650\) | −1188.93 | + | 851.814i | −0.0717438 | + | 0.0514014i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14462.6 | − | 7129.00i | 0.868710 | − | 0.428210i | ||||
\(653\) | 19697.9 | − | 19697.9i | 1.18046 | − | 1.18046i | 0.200833 | − | 0.979626i | \(-0.435635\pi\) |
0.979626 | − | 0.200833i | \(-0.0643648\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15109.8 | 0.901355 | ||||||||
\(656\) | −4078.30 | + | 5311.07i | −0.242730 | + | 0.316101i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3639.50 | − | 601.213i | −0.215627 | − | 0.0356196i | ||||
\(659\) | −3888.06 | + | 3888.06i | −0.229829 | + | 0.229829i | −0.812621 | − | 0.582792i | \(-0.801960\pi\) |
0.582792 | + | 0.812621i | \(0.301960\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8110.20 | − | 8110.20i | −0.477232 | − | 0.477232i | 0.427013 | − | 0.904245i | \(-0.359566\pi\) |
−0.904245 | + | 0.427013i | \(0.859566\pi\) | |||||||
\(662\) | −8739.82 | + | 6261.70i | −0.513116 | + | 0.367625i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5233.54 | − | 17269.1i | −0.305875 | − | 1.00929i | ||||
\(665\) | − | 854.587i | − | 0.0498338i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9210.54 | + | 9210.54i | 0.534683 | + | 0.534683i | ||||
\(668\) | −2038.76 | + | 6002.54i | −0.118087 | + | 0.347672i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1055.31 | − | 6388.45i | 0.0608513 | − | 0.368369i | ||||
\(671\) | −20627.1 | −1.18674 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28428.2 | −1.62827 | −0.814135 | − | 0.580676i | \(-0.802788\pi\) | ||||
−0.814135 | + | 0.580676i | \(0.802788\pi\) | |||||||
\(674\) | 827.610 | − | 5010.02i | 0.0472972 | − | 0.286318i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −794.652 | + | 2339.62i | −0.0452124 | + | 0.133114i | ||||
\(677\) | 16967.4 | + | 16967.4i | 0.963235 | + | 0.963235i | 0.999348 | − | 0.0361128i | \(-0.0114975\pi\) |
−0.0361128 | + | 0.999348i | \(0.511498\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 2500.92i | − | 0.141350i | ||||||
\(680\) | −18263.5 | + | 5534.91i | −1.02996 | + | 0.312138i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −27744.0 | + | 19877.3i | −1.55773 | + | 1.11605i | ||||
\(683\) | 9550.16 | + | 9550.16i | 0.535032 | + | 0.535032i | 0.922066 | − | 0.387034i | \(-0.126500\pi\) |
−0.387034 | + | 0.922066i | \(0.626500\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3925.66 | − | 3925.66i | 0.218966 | − | 0.218966i | ||||
\(686\) | −5061.38 | − | 836.095i | −0.281697 | − | 0.0465339i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −370.974 | − | 2825.51i | −0.0205570 | − | 0.156572i | ||||
\(689\) | −10587.9 | −0.585439 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20859.7 | + | 20859.7i | −1.14839 | + | 1.14839i | −0.161527 | + | 0.986868i | \(0.551642\pi\) |
−0.986868 | + | 0.161527i | \(0.948358\pi\) | |||||||
\(692\) | −7850.30 | + | 3869.62i | −0.431248 | + | 0.212574i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6396.96 | + | 4583.14i | −0.349892 | + | 0.250683i | ||||
\(695\) | 24906.1i | 1.35934i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7585.52i | 0.412227i | ||||||||
\(698\) | −17153.9 | − | 23942.7i | −0.930207 | − | 1.29834i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 209.058 | + | 71.0065i | 0.0112880 | + | 0.00383399i | ||||
\(701\) | −23495.4 | + | 23495.4i | −1.26592 | + | 1.26592i | −0.317740 | + | 0.948178i | \(0.602924\pi\) |
−0.948178 | + | 0.317740i | \(0.897076\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3268.91 | −0.175376 | ||||||||
\(704\) | 6404.93 | − | 32111.1i | 0.342890 | − | 1.71908i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4906.86 | − | 29704.2i | 0.261575 | − | 1.58347i | ||||
\(707\) | −4.24384 | + | 4.24384i | −0.000225751 | + | 0.000225751i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4559.45 | + | 4559.45i | 0.241515 | + | 0.241515i | 0.817477 | − | 0.575962i | \(-0.195372\pi\) |
−0.575962 | + | 0.817477i | \(0.695372\pi\) | |||||||
\(710\) | −8693.47 | − | 12134.0i | −0.459521 | − | 0.641380i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 17296.1 | + | 9250.84i | 0.910393 | + | 0.486924i | ||||
\(713\) | − | 26313.9i | − | 1.38214i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −26334.1 | − | 26334.1i | −1.37740 | − | 1.37740i | ||||
\(716\) | 4323.49 | − | 2131.16i | 0.225665 | − | 0.111236i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −20816.3 | − | 3438.67i | −1.08198 | − | 0.178733i | ||||
\(719\) | 6494.67 | 0.336871 | 0.168436 | − | 0.985713i | \(-0.446128\pi\) | ||||
0.168436 | + | 0.985713i | \(0.446128\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3709.08 | −0.191586 | ||||||||
\(722\) | −17031.0 | − | 2813.37i | −0.877878 | − | 0.145018i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13095.9 | + | 26567.7i | 0.672246 | + | 1.36378i | ||||
\(725\) | −682.221 | − | 682.221i | −0.0349476 | − | 0.0349476i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24866.4i | 1.26856i | 0.773103 | + | 0.634280i | \(0.218704\pi\) | ||||
−0.773103 | + | 0.634280i | \(0.781296\pi\) | |||||||
\(728\) | 2896.15 | − | 877.704i | 0.147443 | − | 0.0446839i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4977.59 | + | 6947.50i | 0.252368 | + | 0.352245i | ||||
\(731\) | −2282.68 | − | 2282.68i | −0.115497 | − | 0.115497i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14914.3 | + | 14914.3i | −0.751533 | + | 0.751533i | −0.974765 | − | 0.223232i | \(-0.928339\pi\) |
0.223232 | + | 0.974765i | \(0.428339\pi\) | |||||||
\(734\) | 2881.77 | − | 17445.1i | 0.144916 | − | 0.877260i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 17249.4 | + | 18433.2i | 0.863886 | + | 0.923176i | ||||
\(737\) | 12585.1 | 0.629008 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8451.86 | − | 8451.86i | 0.420713 | − | 0.420713i | −0.464737 | − | 0.885449i | \(-0.653851\pi\) |
0.885449 | + | 0.464737i | \(0.153851\pi\) | |||||||
\(740\) | 3558.30 | − | 10476.4i | 0.176765 | − | 0.520431i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 930.875 | + | 1299.28i | 0.0460559 | + | 0.0642829i | ||||
\(743\) | − | 5622.43i | − | 0.277614i | −0.990319 | − | 0.138807i | \(-0.955673\pi\) | ||
0.990319 | − | 0.138807i | \(-0.0443267\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6175.21i | 0.303681i | ||||||||
\(746\) | −28977.7 | + | 20761.3i | −1.42219 | + | 1.01893i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −16399.5 | − | 33269.7i | −0.801638 | − | 1.62628i | ||||
\(749\) | −2194.88 | + | 2194.88i | −0.107075 | + | 0.107075i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32314.9 | −1.57016 | −0.785079 | − | 0.619396i | \(-0.787378\pi\) | ||||
−0.785079 | + | 0.619396i | \(0.787378\pi\) | |||||||
\(752\) | 24779.0 | + | 19027.4i | 1.20159 | + | 0.922685i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −13047.3 | − | 2155.30i | −0.630181 | − | 0.104100i | ||||
\(755\) | −24657.2 | + | 24657.2i | −1.18857 | + | 1.18857i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12692.8 | + | 12692.8i | 0.609418 | + | 0.609418i | 0.942794 | − | 0.333376i | \(-0.108188\pi\) |
−0.333376 | + | 0.942794i | \(0.608188\pi\) | |||||||
\(758\) | −3849.97 | + | 2758.34i | −0.184482 | + | 0.132173i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3413.53 | + | 6382.21i | −0.162923 | + | 0.304615i | ||||
\(761\) | − | 13108.2i | − | 0.624404i | −0.950016 | − | 0.312202i | \(-0.898933\pi\) | ||
0.950016 | − | 0.312202i | \(-0.101067\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1423.48 | + | 1423.48i | 0.0675404 | + | 0.0675404i | ||||
\(764\) | 24364.1 | + | 8275.27i | 1.15375 | + | 0.391870i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1327.81 | + | 8038.01i | −0.0626314 | + | 0.379145i | ||||
\(767\) | −20154.8 | −0.948822 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23661.2 | 1.10955 | 0.554776 | − | 0.832000i | \(-0.312804\pi\) | ||||
0.554776 | + | 0.832000i | \(0.312804\pi\) | |||||||
\(770\) | −916.280 | + | 5546.79i | −0.0428837 | + | 0.259601i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −21608.2 | − | 7339.24i | −1.00738 | − | 0.342157i | ||||
\(773\) | −21370.5 | − | 21370.5i | −0.994362 | − | 0.994362i | 0.00562228 | − | 0.999984i | \(-0.498210\pi\) |
−0.999984 | + | 0.00562228i | \(0.998210\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1949.06i | 0.0903384i | ||||||||
\(776\) | −9989.59 | + | 18677.3i | −0.462120 | + | 0.864018i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 30058.5 | − | 21535.6i | 1.38515 | − | 0.992402i | ||||
\(779\) | 2034.27 | + | 2034.27i | 0.0935627 | + | 0.0935627i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20514.8 | − | 20514.8i | 0.939921 | − | 0.939921i | ||||
\(782\) | 28215.4 | + | 4660.94i | 1.29026 | + | 0.213139i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 17048.7 | + | 13091.4i | 0.776633 | + | 0.596366i | ||||
\(785\) | 24825.8 | 1.12875 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20890.9 | + | 20890.9i | −0.946226 | + | 0.946226i | −0.998626 | − | 0.0524002i | \(-0.983313\pi\) |
0.0524002 | + | 0.998626i | \(0.483313\pi\) | |||||||
\(788\) | 8048.54 | + | 16328.1i | 0.363854 | + | 0.738151i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8644.42 | − | 6193.35i | 0.389310 | − | 0.278924i | ||||
\(791\) | 179.720i | 0.00807853i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16145.8i | 0.723020i | ||||||||
\(794\) | −9919.09 | − | 13844.6i | −0.443344 | − | 0.618801i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1922.27 | + | 5659.54i | −0.0855942 | + | 0.252007i | ||||
\(797\) | 6834.83 | − | 6834.83i | 0.303767 | − | 0.303767i | −0.538719 | − | 0.842486i | \(-0.681092\pi\) |
0.842486 | + | 0.538719i | \(0.181092\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 35390.5 | 1.56699 | ||||||||
\(800\) | −1277.65 | − | 1365.34i | −0.0564649 | − | 0.0603401i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5864.89 | − | 35503.7i | 0.258225 | − | 1.56319i | ||||
\(803\) | −11746.1 | + | 11746.1i | −0.516203 | + | 0.516203i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3064.97 | − | 3064.97i | −0.134194 | − | 0.134194i | ||||
\(806\) | 15558.9 | + | 21716.5i | 0.679950 | + | 0.949045i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 48.6453 | − | 14.7424i | 0.00211799 | − | 0.000641874i | ||||
\(809\) | − | 15807.0i | − | 0.686952i | −0.939162 | − | 0.343476i | \(-0.888396\pi\) | ||
0.939162 | − | 0.343476i | \(-0.111604\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11522.7 | − | 11522.7i | −0.498910 | − | 0.498910i | 0.412189 | − | 0.911099i | \(-0.364764\pi\) |
−0.911099 | + | 0.412189i | \(0.864764\pi\) | |||||||
\(812\) | 882.621 | + | 1790.57i | 0.0381452 | + | 0.0773852i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 21217.2 | + | 3504.89i | 0.913591 | + | 0.150917i | ||||
\(815\) | 23446.9 | 1.00774 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1224.33 | −0.0524284 | ||||||||
\(818\) | 650.185 | + | 107.405i | 0.0277912 | + | 0.00459086i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8733.90 | + | 4305.17i | −0.371952 | + | 0.183345i | ||||
\(821\) | −308.824 | − | 308.824i | −0.0131279 | − | 0.0131279i | 0.700512 | − | 0.713640i | \(-0.252955\pi\) |
−0.713640 | + | 0.700512i | \(0.752955\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5633.49i | 0.238604i | 0.992858 | + | 0.119302i | \(0.0380656\pi\) | ||||
−0.992858 | + | 0.119302i | \(0.961934\pi\) | |||||||
\(824\) | 27700.1 | + | 14815.4i | 1.17109 | + | 0.626358i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1771.98 | + | 2473.26i | 0.0746430 | + | 0.104184i | ||||
\(827\) | 15835.5 | + | 15835.5i | 0.665844 | + | 0.665844i | 0.956751 | − | 0.290908i | \(-0.0939572\pi\) |
−0.290908 | + | 0.956751i | \(0.593957\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6200.19 | + | 6200.19i | −0.259761 | + | 0.259761i | −0.824957 | − | 0.565196i | \(-0.808801\pi\) |
0.565196 | + | 0.824957i | \(0.308801\pi\) | |||||||
\(830\) | 4276.58 | − | 25888.7i | 0.178846 | − | 1.08266i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −25134.9 | − | 5013.43i | −1.04735 | − | 0.208906i | ||||
\(833\) | 24349.7 | 1.01281 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6518.30 | + | 6518.30i | −0.270150 | + | 0.270150i | ||||
\(836\) | −13320.2 | − | 4524.21i | −0.551063 | − | 0.187169i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 14270.6 | + | 19918.2i | 0.588267 | + | 0.821079i | ||||
\(839\) | − | 30644.3i | − | 1.26098i | −0.776199 | − | 0.630488i | \(-0.782855\pi\) | ||
0.776199 | − | 0.630488i | \(-0.217145\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15665.5i | 0.642319i | ||||||||
\(842\) | 27015.6 | − | 19355.5i | 1.10573 | − | 0.792204i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 22600.6 | − | 11140.4i | 0.921735 | − | 0.454348i | ||||
\(845\) | −2540.65 | + | 2540.65i | −0.103433 | + | 0.103433i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7371.03 | −0.299022 | ||||||||
\(848\) | −1762.17 | − | 13421.5i | −0.0713597 | − | 0.543509i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2089.91 | − | 345.234i | −0.0843331 | − | 0.0139311i | ||||
\(851\) | −11723.9 | + | 11723.9i | −0.472256 | + | 0.472256i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30801.0 | − | 30801.0i | −1.23635 | − | 1.23635i | −0.961482 | − | 0.274869i | \(-0.911365\pi\) |
−0.274869 | − | 0.961482i | \(-0.588635\pi\) | |||||||
\(854\) | 1981.30 | − | 1419.52i | 0.0793897 | − | 0.0568793i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 25158.9 | − | 7624.61i | 1.00457 | − | 0.304444i | ||||
\(857\) | 41788.5i | 1.66566i | 0.553533 | + | 0.832828i | \(0.313279\pi\) | ||||
−0.553533 | + | 0.832828i | \(0.686721\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11914.5 | + | 11914.5i | 0.473243 | + | 0.473243i | 0.902963 | − | 0.429719i | \(-0.141388\pi\) |
−0.429719 | + | 0.902963i | \(0.641388\pi\) | |||||||
\(860\) | 1332.72 | − | 3923.80i | 0.0528435 | − | 0.155582i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4027.88 | − | 24383.1i | 0.159153 | − | 0.963449i | ||||
\(863\) | −27636.7 | −1.09011 | −0.545054 | − | 0.838401i | \(-0.683491\pi\) | ||||
−0.545054 | + | 0.838401i | \(0.683491\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12727.0 | −0.500266 | ||||||||
\(866\) | 5360.10 | − | 32447.9i | 0.210328 | − | 1.27324i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1296.98 | − | 3818.57i | 0.0507169 | − | 0.149321i | ||||
\(869\) | 14615.1 | + | 14615.1i | 0.570520 | + | 0.570520i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 9850.95i | − | 0.383223i | ||||||
\(872\) | −4944.90 | − | 16316.7i | −0.192036 | − | 0.633661i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8816.73 | − | 6316.80i | 0.341224 | − | 0.244473i | ||||
\(875\) | −2520.12 | − | 2520.12i | −0.0973663 | − | 0.0973663i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11918.3 | + | 11918.3i | −0.458896 | + | 0.458896i | −0.898293 | − | 0.439397i | \(-0.855192\pi\) |
0.439397 | + | 0.898293i | \(0.355192\pi\) | |||||||
\(878\) | −49203.4 | − | 8127.96i | −1.89127 | − | 0.312421i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 28998.8 | − | 37764.5i | 1.11085 | − | 1.44664i | ||||
\(881\) | 13330.0 | 0.509759 | 0.254880 | − | 0.966973i | \(-0.417964\pi\) | ||||
0.254880 | + | 0.966973i | \(0.417964\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25172.1 | + | 25172.1i | −0.959353 | + | 0.959353i | −0.999206 | − | 0.0398530i | \(-0.987311\pi\) |
0.0398530 | + | 0.999206i | \(0.487311\pi\) | |||||||
\(884\) | −26041.7 | + | 12836.7i | −0.990812 | + | 0.488398i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14794.1 | + | 10599.4i | −0.560969 | + | 0.401910i | ||||
\(887\) | 48821.3i | 1.84810i | 0.382278 | + | 0.924048i | \(0.375140\pi\) | ||||
−0.382278 | + | 0.924048i | \(0.624860\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5085.84i | 0.191871i | ||||||||
\(890\) | 16611.7 | + | 23185.9i | 0.625645 | + | 0.873249i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2712.25 | + | 921.217i | 0.101808 | + | 0.0345792i | ||||
\(893\) | 9490.96 | − | 9490.96i | 0.355658 | − | 0.355658i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7009.27 | 0.261781 | ||||||||
\(896\) | 1594.61 | + | 3525.15i | 0.0594556 | + | 0.131437i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5958.93 | + | 36072.9i | −0.221439 | + | 1.34050i | ||||
\(899\) | −12461.2 | + | 12461.2i | −0.462296 | + | 0.462296i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10843.0 | − | 10843.0i | −0.400924 | − | 0.400924i | ||||
\(902\) | −11022.5 | − | 15384.8i | −0.406885 | − | 0.567913i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 717.868 | − | 1342.18i | 0.0264114 | − | 0.0493809i | ||||
\(905\) | 43071.7i | 1.58205i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5320.20 | + | 5320.20i | 0.194768 | + | 0.194768i | 0.797753 | − | 0.602985i | \(-0.206022\pi\) |
−0.602985 | + | 0.797753i | \(0.706022\pi\) | |||||||
\(908\) | 35064.8 | − | 17284.4i | 1.28157 | − | 0.631720i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4341.73 | + | 717.215i | 0.158161 | + | 0.0261269i | ||||
\(911\) | 26016.0 | 0.946155 | 0.473077 | − | 0.881021i | \(-0.343143\pi\) | ||||
0.473077 | + | 0.881021i | \(0.343143\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 51000.2 | 1.84870 | ||||||||
\(914\) | 26009.4 | + | 4296.52i | 0.941262 | + | 0.155488i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7153.21 | + | 14511.7i | 0.258023 | + | 0.523450i | ||||
\(917\) | −2453.77 | − | 2453.77i | −0.0883650 | − | 0.0883650i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 24082.1i | − | 0.864413i | −0.901775 | − | 0.432206i | \(-0.857735\pi\) | ||
0.901775 | − | 0.432206i | \(-0.142265\pi\) | |||||||
\(920\) | 10647.1 | + | 35132.3i | 0.381550 | + | 1.25900i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −30017.2 | − | 41896.8i | −1.07220 | − | 1.49653i | ||||
\(923\) | −16057.9 | − | 16057.9i | −0.572646 | − | 0.572646i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 868.385 | − | 868.385i | 0.0308674 | − | 0.0308674i | ||||
\(926\) | −3244.57 | + | 19641.3i | −0.115144 | + | 0.697035i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 560.619 | − | 16897.8i | 0.0198311 | − | 0.597735i | ||||
\(929\) | −9324.93 | −0.329323 | −0.164661 | − | 0.986350i | \(-0.552653\pi\) | ||||
−0.164661 | + | 0.986350i | \(0.552653\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6530.06 | − | 6530.06i | 0.229875 | − | 0.229875i | ||||
\(932\) | −2383.69 | + | 7018.07i | −0.0837772 | + | 0.246657i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −13981.8 | − | 19515.3i | −0.489829 | − | 0.683682i | ||||
\(935\) | − | 53937.0i | − | 1.88656i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15535.2i | 0.541636i | 0.962631 | + | 0.270818i | \(0.0872941\pi\) | ||||
−0.962631 | + | 0.270818i | \(0.912706\pi\) | |||||||
\(938\) | −1208.84 | + | 866.083i | −0.0420790 | + | 0.0301478i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 20085.9 | + | 40748.3i | 0.696947 | + | 1.41390i | ||||
\(941\) | 34024.8 | − | 34024.8i | 1.17872 | − | 1.17872i | 0.198651 | − | 0.980070i | \(-0.436344\pi\) |
0.980070 | − | 0.198651i | \(-0.0636559\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14591.8 | 0.503896 | ||||||||
\(944\) | −3354.40 | − | 25548.7i | −0.115653 | − | 0.880867i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7946.66 | + | 1312.72i | 0.273117 | + | 0.0451164i | ||||
\(947\) | 3816.02 | − | 3816.02i | 0.130944 | − | 0.130944i | −0.638597 | − | 0.769541i | \(-0.720485\pi\) |
0.769541 | + | 0.638597i | \(0.220485\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9194.21 | + | 9194.21i | 0.314496 | + | 0.314496i | ||||
\(950\) | −653.051 | + | 467.883i | −0.0223029 | + | 0.0159791i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3864.78 | + | 2067.08i | 0.131574 | + | 0.0703723i | ||||
\(953\) | − | 21759.7i | − | 0.739629i | −0.929106 | − | 0.369815i | \(-0.879421\pi\) | ||
0.929106 | − | 0.369815i | \(-0.120579\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 26457.6 | + | 26457.6i | 0.896489 | + | 0.896489i | ||||
\(956\) | −6002.97 | − | 2038.91i | −0.203086 | − | 0.0689781i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −270.744 | + | 1638.97i | −0.00913082 | + | 0.0552743i | ||||
\(959\) | −1275.03 | −0.0429331 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5809.78 | 0.195018 | ||||||||
\(962\) | 2743.44 | − | 16607.7i | 0.0919461 | − | 0.556604i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10976.3 | − | 3728.09i | −0.366723 | − | 0.124558i | ||||
\(965\) | −23464.9 | − | 23464.9i | −0.782759 | − | 0.782759i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 19338.5i | − | 0.643108i | −0.946891 | − | 0.321554i | \(-0.895795\pi\) | ||
0.946891 | − | 0.321554i | \(-0.104205\pi\) | |||||||
\(968\) | 55048.2 | + | 29442.6i | 1.82781 | + | 0.977603i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −25037.4 | + | 17938.2i | −0.828766 | + | 0.593775i | ||||
\(971\) | −4184.92 | − | 4184.92i | −0.138311 | − | 0.138311i | 0.634561 | − | 0.772873i | \(-0.281181\pi\) |
−0.772873 | + | 0.634561i | \(0.781181\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4044.67 | − | 4044.67i | 0.133264 | − | 0.133264i | ||||
\(974\) | −23347.5 | − | 3856.80i | −0.768072 | − | 0.126879i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −20466.8 | + | 2687.18i | −0.671236 | + | 0.0881296i | ||||
\(977\) | −17841.9 | −0.584249 | −0.292125 | − | 0.956380i | \(-0.594362\pi\) | ||||
−0.292125 | + | 0.956380i | \(0.594362\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −39200.2 | + | 39200.2i | −1.27972 | + | 1.27972i | ||||
\(980\) | 13819.7 | + | 28036.0i | 0.450463 | + | 0.913855i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4972.66 | − | 3562.69i | 0.161593 | − | 0.115774i | ||||
\(983\) | 61512.0i | 1.99586i | 0.0643304 | + | 0.997929i | \(0.479509\pi\) | ||||
−0.0643304 | + | 0.997929i | \(0.520491\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26471.2i | 0.856286i | ||||||||
\(986\) | −11154.5 | − | 15568.9i | −0.360274 | − | 0.502855i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3541.31 | + | 10426.3i | −0.114032 | + | 0.335735i | ||||
\(989\) | −4391.05 | + | 4391.05i | −0.141180 | + | 0.141180i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1827.73 | 0.0585870 | 0.0292935 | − | 0.999571i | \(-0.490674\pi\) | ||||
0.0292935 | + | 0.999571i | \(0.490674\pi\) | |||||||
\(992\) | −24938.8 | + | 23337.2i | −0.798193 | + | 0.746931i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −558.726 | + | 3382.30i | −0.0178287 | + | 0.107928i | ||||
\(995\) | −6145.84 | + | 6145.84i | −0.195815 | + | 0.195815i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25017.0 | − | 25017.0i | −0.794681 | − | 0.794681i | 0.187570 | − | 0.982251i | \(-0.439939\pi\) |
−0.982251 | + | 0.187570i | \(0.939939\pi\) | |||||||
\(998\) | 26474.9 | + | 36952.6i | 0.839728 | + | 1.17206i | ||||
\(999\) | 0 | 0 |
(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 | 144.4.k.a.37.3 | 10 | ||
3.2 | odd | 2 | 16.4.e.a.5.3 | ✓ | 10 | ||
4.3 | odd | 2 | 576.4.k.a.433.2 | 10 | |||
12.11 | even | 2 | 64.4.e.a.49.3 | 10 | |||
16.3 | odd | 4 | 576.4.k.a.145.2 | 10 | |||
16.13 | even | 4 | inner | 144.4.k.a.109.3 | 10 | ||
24.5 | odd | 2 | 128.4.e.b.97.3 | 10 | |||
24.11 | even | 2 | 128.4.e.a.97.3 | 10 | |||
48.5 | odd | 4 | 128.4.e.b.33.3 | 10 | |||
48.11 | even | 4 | 128.4.e.a.33.3 | 10 | |||
48.29 | odd | 4 | 16.4.e.a.13.3 | yes | 10 | ||
48.35 | even | 4 | 64.4.e.a.17.3 | 10 | |||
96.5 | odd | 8 | 1024.4.b.j.513.6 | 10 | |||
96.11 | even | 8 | 1024.4.b.k.513.6 | 10 | |||
96.29 | odd | 8 | 1024.4.a.n.1.6 | 10 | |||
96.35 | even | 8 | 1024.4.a.m.1.5 | 10 | |||
96.53 | odd | 8 | 1024.4.b.j.513.5 | 10 | |||
96.59 | even | 8 | 1024.4.b.k.513.5 | 10 | |||
96.77 | odd | 8 | 1024.4.a.n.1.5 | 10 | |||
96.83 | even | 8 | 1024.4.a.m.1.6 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.4.e.a.5.3 | ✓ | 10 | 3.2 | odd | 2 | ||
16.4.e.a.13.3 | yes | 10 | 48.29 | odd | 4 | ||
64.4.e.a.17.3 | 10 | 48.35 | even | 4 | |||
64.4.e.a.49.3 | 10 | 12.11 | even | 2 | |||
128.4.e.a.33.3 | 10 | 48.11 | even | 4 | |||
128.4.e.a.97.3 | 10 | 24.11 | even | 2 | |||
128.4.e.b.33.3 | 10 | 48.5 | odd | 4 | |||
128.4.e.b.97.3 | 10 | 24.5 | odd | 2 | |||
144.4.k.a.37.3 | 10 | 1.1 | even | 1 | trivial | ||
144.4.k.a.109.3 | 10 | 16.13 | even | 4 | inner | ||
576.4.k.a.145.2 | 10 | 16.3 | odd | 4 | |||
576.4.k.a.433.2 | 10 | 4.3 | odd | 2 | |||
1024.4.a.m.1.5 | 10 | 96.35 | even | 8 | |||
1024.4.a.m.1.6 | 10 | 96.83 | even | 8 | |||
1024.4.a.n.1.5 | 10 | 96.77 | odd | 8 | |||
1024.4.a.n.1.6 | 10 | 96.29 | odd | 8 | |||
1024.4.b.j.513.5 | 10 | 96.53 | odd | 8 | |||
1024.4.b.j.513.6 | 10 | 96.5 | odd | 8 | |||
1024.4.b.k.513.5 | 10 | 96.59 | even | 8 | |||
1024.4.b.k.513.6 | 10 | 96.11 | even | 8 |