Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5290,2,Mod(1,5290)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5290, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5290.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5290 = 2 \cdot 5 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5290.a (trivial) |
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: | yes |
Analytic conductor: | \(42.2408626693\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 5 x^{14} - 24 x^{13} + 142 x^{12} + 184 x^{11} - 1488 x^{10} - 426 x^{9} + 7165 x^{8} + \cdots - 32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(2.78829\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5290.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 2.78829 | 1.60982 | 0.804911 | − | 0.593396i | \(-0.202213\pi\) | ||||
0.804911 | + | 0.593396i | \(0.202213\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 2.78829 | 1.13832 | ||||||||
\(7\) | −0.104808 | −0.0396136 | −0.0198068 | − | 0.999804i | \(-0.506305\pi\) | ||||
−0.0198068 | + | 0.999804i | \(0.506305\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 4.77457 | 1.59152 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 1.61337 | 0.486450 | 0.243225 | − | 0.969970i | \(-0.421795\pi\) | ||||
0.243225 | + | 0.969970i | \(0.421795\pi\) | |||||||
\(12\) | 2.78829 | 0.804911 | ||||||||
\(13\) | −0.820624 | −0.227600 | −0.113800 | − | 0.993504i | \(-0.536302\pi\) | ||||
−0.113800 | + | 0.993504i | \(0.536302\pi\) | |||||||
\(14\) | −0.104808 | −0.0280111 | ||||||||
\(15\) | 2.78829 | 0.719934 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.39546 | 0.580984 | 0.290492 | − | 0.956877i | \(-0.406181\pi\) | ||||
0.290492 | + | 0.956877i | \(0.406181\pi\) | |||||||
\(18\) | 4.77457 | 1.12538 | ||||||||
\(19\) | −5.04341 | −1.15704 | −0.578518 | − | 0.815669i | \(-0.696369\pi\) | ||||
−0.578518 | + | 0.815669i | \(0.696369\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −0.292235 | −0.0637709 | ||||||||
\(22\) | 1.61337 | 0.343972 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | 2.78829 | 0.569158 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.820624 | −0.160938 | ||||||||
\(27\) | 4.94803 | 0.952250 | ||||||||
\(28\) | −0.104808 | −0.0198068 | ||||||||
\(29\) | 9.29479 | 1.72600 | 0.863000 | − | 0.505204i | \(-0.168583\pi\) | ||||
0.863000 | + | 0.505204i | \(0.168583\pi\) | |||||||
\(30\) | 2.78829 | 0.509070 | ||||||||
\(31\) | 6.93969 | 1.24641 | 0.623203 | − | 0.782060i | \(-0.285831\pi\) | ||||
0.623203 | + | 0.782060i | \(0.285831\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.49855 | 0.783097 | ||||||||
\(34\) | 2.39546 | 0.410817 | ||||||||
\(35\) | −0.104808 | −0.0177158 | ||||||||
\(36\) | 4.77457 | 0.795762 | ||||||||
\(37\) | −3.78260 | −0.621856 | −0.310928 | − | 0.950433i | \(-0.600640\pi\) | ||||
−0.310928 | + | 0.950433i | \(0.600640\pi\) | |||||||
\(38\) | −5.04341 | −0.818149 | ||||||||
\(39\) | −2.28814 | −0.366396 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 10.1328 | 1.58248 | 0.791240 | − | 0.611505i | \(-0.209436\pi\) | ||||
0.791240 | + | 0.611505i | \(0.209436\pi\) | |||||||
\(42\) | −0.292235 | −0.0450928 | ||||||||
\(43\) | −1.06696 | −0.162709 | −0.0813547 | − | 0.996685i | \(-0.525925\pi\) | ||||
−0.0813547 | + | 0.996685i | \(0.525925\pi\) | |||||||
\(44\) | 1.61337 | 0.243225 | ||||||||
\(45\) | 4.77457 | 0.711752 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.70310 | −1.26948 | −0.634739 | − | 0.772727i | \(-0.718892\pi\) | ||||
−0.634739 | + | 0.772727i | \(0.718892\pi\) | |||||||
\(48\) | 2.78829 | 0.402455 | ||||||||
\(49\) | −6.98902 | −0.998431 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 6.67923 | 0.935280 | ||||||||
\(52\) | −0.820624 | −0.113800 | ||||||||
\(53\) | −10.1839 | −1.39887 | −0.699436 | − | 0.714696i | \(-0.746565\pi\) | ||||
−0.699436 | + | 0.714696i | \(0.746565\pi\) | |||||||
\(54\) | 4.94803 | 0.673342 | ||||||||
\(55\) | 1.61337 | 0.217547 | ||||||||
\(56\) | −0.104808 | −0.0140055 | ||||||||
\(57\) | −14.0625 | −1.86262 | ||||||||
\(58\) | 9.29479 | 1.22047 | ||||||||
\(59\) | −1.88759 | −0.245744 | −0.122872 | − | 0.992423i | \(-0.539210\pi\) | ||||
−0.122872 | + | 0.992423i | \(0.539210\pi\) | |||||||
\(60\) | 2.78829 | 0.359967 | ||||||||
\(61\) | 0.718868 | 0.0920417 | 0.0460208 | − | 0.998940i | \(-0.485346\pi\) | ||||
0.0460208 | + | 0.998940i | \(0.485346\pi\) | |||||||
\(62\) | 6.93969 | 0.881342 | ||||||||
\(63\) | −0.500413 | −0.0630461 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.820624 | −0.101786 | ||||||||
\(66\) | 4.49855 | 0.553733 | ||||||||
\(67\) | −3.50684 | −0.428429 | −0.214215 | − | 0.976787i | \(-0.568719\pi\) | ||||
−0.214215 | + | 0.976787i | \(0.568719\pi\) | |||||||
\(68\) | 2.39546 | 0.290492 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.104808 | −0.0125269 | ||||||||
\(71\) | −1.31155 | −0.155652 | −0.0778259 | − | 0.996967i | \(-0.524798\pi\) | ||||
−0.0778259 | + | 0.996967i | \(0.524798\pi\) | |||||||
\(72\) | 4.77457 | 0.562689 | ||||||||
\(73\) | 11.3521 | 1.32867 | 0.664333 | − | 0.747437i | \(-0.268716\pi\) | ||||
0.664333 | + | 0.747437i | \(0.268716\pi\) | |||||||
\(74\) | −3.78260 | −0.439719 | ||||||||
\(75\) | 2.78829 | 0.321964 | ||||||||
\(76\) | −5.04341 | −0.578518 | ||||||||
\(77\) | −0.169094 | −0.0192700 | ||||||||
\(78\) | −2.28814 | −0.259081 | ||||||||
\(79\) | 13.5089 | 1.51987 | 0.759933 | − | 0.650002i | \(-0.225232\pi\) | ||||
0.759933 | + | 0.650002i | \(0.225232\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −0.527159 | −0.0585732 | ||||||||
\(82\) | 10.1328 | 1.11898 | ||||||||
\(83\) | −12.0038 | −1.31759 | −0.658794 | − | 0.752324i | \(-0.728933\pi\) | ||||
−0.658794 | + | 0.752324i | \(0.728933\pi\) | |||||||
\(84\) | −0.292235 | −0.0318854 | ||||||||
\(85\) | 2.39546 | 0.259824 | ||||||||
\(86\) | −1.06696 | −0.115053 | ||||||||
\(87\) | 25.9166 | 2.77855 | ||||||||
\(88\) | 1.61337 | 0.171986 | ||||||||
\(89\) | 12.3656 | 1.31075 | 0.655373 | − | 0.755305i | \(-0.272511\pi\) | ||||
0.655373 | + | 0.755305i | \(0.272511\pi\) | |||||||
\(90\) | 4.77457 | 0.503284 | ||||||||
\(91\) | 0.0860079 | 0.00901607 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 19.3499 | 2.00649 | ||||||||
\(94\) | −8.70310 | −0.897656 | ||||||||
\(95\) | −5.04341 | −0.517443 | ||||||||
\(96\) | 2.78829 | 0.284579 | ||||||||
\(97\) | 18.1600 | 1.84387 | 0.921936 | − | 0.387341i | \(-0.126606\pi\) | ||||
0.921936 | + | 0.387341i | \(0.126606\pi\) | |||||||
\(98\) | −6.98902 | −0.705997 | ||||||||
\(99\) | 7.70316 | 0.774197 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 10.7972 | 1.07437 | 0.537183 | − | 0.843466i | \(-0.319488\pi\) | ||||
0.537183 | + | 0.843466i | \(0.319488\pi\) | |||||||
\(102\) | 6.67923 | 0.661343 | ||||||||
\(103\) | −3.49218 | −0.344094 | −0.172047 | − | 0.985089i | \(-0.555038\pi\) | ||||
−0.172047 | + | 0.985089i | \(0.555038\pi\) | |||||||
\(104\) | −0.820624 | −0.0804688 | ||||||||
\(105\) | −0.292235 | −0.0285192 | ||||||||
\(106\) | −10.1839 | −0.989151 | ||||||||
\(107\) | −8.04757 | −0.777988 | −0.388994 | − | 0.921240i | \(-0.627177\pi\) | ||||
−0.388994 | + | 0.921240i | \(0.627177\pi\) | |||||||
\(108\) | 4.94803 | 0.476125 | ||||||||
\(109\) | −4.75271 | −0.455227 | −0.227614 | − | 0.973752i | \(-0.573092\pi\) | ||||
−0.227614 | + | 0.973752i | \(0.573092\pi\) | |||||||
\(110\) | 1.61337 | 0.153829 | ||||||||
\(111\) | −10.5470 | −1.00108 | ||||||||
\(112\) | −0.104808 | −0.00990341 | ||||||||
\(113\) | −12.0649 | −1.13497 | −0.567487 | − | 0.823383i | \(-0.692084\pi\) | ||||
−0.567487 | + | 0.823383i | \(0.692084\pi\) | |||||||
\(114\) | −14.0625 | −1.31707 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 9.29479 | 0.863000 | ||||||||
\(117\) | −3.91813 | −0.362232 | ||||||||
\(118\) | −1.88759 | −0.173767 | ||||||||
\(119\) | −0.251063 | −0.0230149 | ||||||||
\(120\) | 2.78829 | 0.254535 | ||||||||
\(121\) | −8.39703 | −0.763367 | ||||||||
\(122\) | 0.718868 | 0.0650833 | ||||||||
\(123\) | 28.2533 | 2.54751 | ||||||||
\(124\) | 6.93969 | 0.623203 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −0.500413 | −0.0445803 | ||||||||
\(127\) | −7.72617 | −0.685587 | −0.342793 | − | 0.939411i | \(-0.611373\pi\) | ||||
−0.342793 | + | 0.939411i | \(0.611373\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −2.97499 | −0.261933 | ||||||||
\(130\) | −0.820624 | −0.0719735 | ||||||||
\(131\) | −15.9385 | −1.39255 | −0.696276 | − | 0.717774i | \(-0.745161\pi\) | ||||
−0.696276 | + | 0.717774i | \(0.745161\pi\) | |||||||
\(132\) | 4.49855 | 0.391548 | ||||||||
\(133\) | 0.528588 | 0.0458344 | ||||||||
\(134\) | −3.50684 | −0.302945 | ||||||||
\(135\) | 4.94803 | 0.425859 | ||||||||
\(136\) | 2.39546 | 0.205409 | ||||||||
\(137\) | 1.42400 | 0.121661 | 0.0608305 | − | 0.998148i | \(-0.480625\pi\) | ||||
0.0608305 | + | 0.998148i | \(0.480625\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.21002 | 0.611546 | 0.305773 | − | 0.952104i | \(-0.401085\pi\) | ||||
0.305773 | + | 0.952104i | \(0.401085\pi\) | |||||||
\(140\) | −0.104808 | −0.00885788 | ||||||||
\(141\) | −24.2668 | −2.04363 | ||||||||
\(142\) | −1.31155 | −0.110062 | ||||||||
\(143\) | −1.32397 | −0.110716 | ||||||||
\(144\) | 4.77457 | 0.397881 | ||||||||
\(145\) | 9.29479 | 0.771890 | ||||||||
\(146\) | 11.3521 | 0.939509 | ||||||||
\(147\) | −19.4874 | −1.60730 | ||||||||
\(148\) | −3.78260 | −0.310928 | ||||||||
\(149\) | −18.4817 | −1.51408 | −0.757038 | − | 0.653371i | \(-0.773354\pi\) | ||||
−0.757038 | + | 0.653371i | \(0.773354\pi\) | |||||||
\(150\) | 2.78829 | 0.227663 | ||||||||
\(151\) | 7.08884 | 0.576881 | 0.288441 | − | 0.957498i | \(-0.406863\pi\) | ||||
0.288441 | + | 0.957498i | \(0.406863\pi\) | |||||||
\(152\) | −5.04341 | −0.409074 | ||||||||
\(153\) | 11.4373 | 0.924650 | ||||||||
\(154\) | −0.169094 | −0.0136260 | ||||||||
\(155\) | 6.93969 | 0.557410 | ||||||||
\(156\) | −2.28814 | −0.183198 | ||||||||
\(157\) | 7.01390 | 0.559770 | 0.279885 | − | 0.960034i | \(-0.409704\pi\) | ||||
0.279885 | + | 0.960034i | \(0.409704\pi\) | |||||||
\(158\) | 13.5089 | 1.07471 | ||||||||
\(159\) | −28.3958 | −2.25193 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.527159 | −0.0414175 | ||||||||
\(163\) | −12.3924 | −0.970649 | −0.485325 | − | 0.874334i | \(-0.661299\pi\) | ||||
−0.485325 | + | 0.874334i | \(0.661299\pi\) | |||||||
\(164\) | 10.1328 | 0.791240 | ||||||||
\(165\) | 4.49855 | 0.350212 | ||||||||
\(166\) | −12.0038 | −0.931675 | ||||||||
\(167\) | −8.43589 | −0.652789 | −0.326395 | − | 0.945234i | \(-0.605834\pi\) | ||||
−0.326395 | + | 0.945234i | \(0.605834\pi\) | |||||||
\(168\) | −0.292235 | −0.0225464 | ||||||||
\(169\) | −12.3266 | −0.948198 | ||||||||
\(170\) | 2.39546 | 0.183723 | ||||||||
\(171\) | −24.0801 | −1.84145 | ||||||||
\(172\) | −1.06696 | −0.0813547 | ||||||||
\(173\) | −20.9993 | −1.59655 | −0.798273 | − | 0.602295i | \(-0.794253\pi\) | ||||
−0.798273 | + | 0.602295i | \(0.794253\pi\) | |||||||
\(174\) | 25.9166 | 1.96473 | ||||||||
\(175\) | −0.104808 | −0.00792273 | ||||||||
\(176\) | 1.61337 | 0.121612 | ||||||||
\(177\) | −5.26316 | −0.395604 | ||||||||
\(178\) | 12.3656 | 0.926838 | ||||||||
\(179\) | −14.6536 | −1.09526 | −0.547629 | − | 0.836721i | \(-0.684470\pi\) | ||||
−0.547629 | + | 0.836721i | \(0.684470\pi\) | |||||||
\(180\) | 4.77457 | 0.355876 | ||||||||
\(181\) | 16.3855 | 1.21793 | 0.608964 | − | 0.793198i | \(-0.291585\pi\) | ||||
0.608964 | + | 0.793198i | \(0.291585\pi\) | |||||||
\(182\) | 0.0860079 | 0.00637533 | ||||||||
\(183\) | 2.00442 | 0.148171 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.78260 | −0.278102 | ||||||||
\(186\) | 19.3499 | 1.41880 | ||||||||
\(187\) | 3.86476 | 0.282619 | ||||||||
\(188\) | −8.70310 | −0.634739 | ||||||||
\(189\) | −0.518593 | −0.0377221 | ||||||||
\(190\) | −5.04341 | −0.365887 | ||||||||
\(191\) | 19.0662 | 1.37959 | 0.689793 | − | 0.724007i | \(-0.257702\pi\) | ||||
0.689793 | + | 0.724007i | \(0.257702\pi\) | |||||||
\(192\) | 2.78829 | 0.201228 | ||||||||
\(193\) | −3.51113 | −0.252737 | −0.126368 | − | 0.991983i | \(-0.540332\pi\) | ||||
−0.126368 | + | 0.991983i | \(0.540332\pi\) | |||||||
\(194\) | 18.1600 | 1.30382 | ||||||||
\(195\) | −2.28814 | −0.163857 | ||||||||
\(196\) | −6.98902 | −0.499215 | ||||||||
\(197\) | 16.3731 | 1.16654 | 0.583268 | − | 0.812280i | \(-0.301774\pi\) | ||||
0.583268 | + | 0.812280i | \(0.301774\pi\) | |||||||
\(198\) | 7.70316 | 0.547440 | ||||||||
\(199\) | 24.3835 | 1.72850 | 0.864252 | − | 0.503059i | \(-0.167792\pi\) | ||||
0.864252 | + | 0.503059i | \(0.167792\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −9.77811 | −0.689695 | ||||||||
\(202\) | 10.7972 | 0.759692 | ||||||||
\(203\) | −0.974167 | −0.0683731 | ||||||||
\(204\) | 6.67923 | 0.467640 | ||||||||
\(205\) | 10.1328 | 0.707707 | ||||||||
\(206\) | −3.49218 | −0.243311 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.820624 | −0.0569001 | ||||||||
\(209\) | −8.13689 | −0.562840 | ||||||||
\(210\) | −0.292235 | −0.0201661 | ||||||||
\(211\) | −3.50940 | −0.241597 | −0.120799 | − | 0.992677i | \(-0.538546\pi\) | ||||
−0.120799 | + | 0.992677i | \(0.538546\pi\) | |||||||
\(212\) | −10.1839 | −0.699436 | ||||||||
\(213\) | −3.65697 | −0.250572 | ||||||||
\(214\) | −8.04757 | −0.550120 | ||||||||
\(215\) | −1.06696 | −0.0727659 | ||||||||
\(216\) | 4.94803 | 0.336671 | ||||||||
\(217\) | −0.727334 | −0.0493747 | ||||||||
\(218\) | −4.75271 | −0.321894 | ||||||||
\(219\) | 31.6530 | 2.13891 | ||||||||
\(220\) | 1.61337 | 0.108773 | ||||||||
\(221\) | −1.96577 | −0.132232 | ||||||||
\(222\) | −10.5470 | −0.707868 | ||||||||
\(223\) | 0.760922 | 0.0509551 | 0.0254776 | − | 0.999675i | \(-0.491889\pi\) | ||||
0.0254776 | + | 0.999675i | \(0.491889\pi\) | |||||||
\(224\) | −0.104808 | −0.00700277 | ||||||||
\(225\) | 4.77457 | 0.318305 | ||||||||
\(226\) | −12.0649 | −0.802547 | ||||||||
\(227\) | −22.1110 | −1.46756 | −0.733780 | − | 0.679388i | \(-0.762246\pi\) | ||||
−0.733780 | + | 0.679388i | \(0.762246\pi\) | |||||||
\(228\) | −14.0625 | −0.931311 | ||||||||
\(229\) | −18.3056 | −1.20967 | −0.604833 | − | 0.796352i | \(-0.706760\pi\) | ||||
−0.604833 | + | 0.796352i | \(0.706760\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.471483 | −0.0310213 | ||||||||
\(232\) | 9.29479 | 0.610233 | ||||||||
\(233\) | −8.93455 | −0.585322 | −0.292661 | − | 0.956216i | \(-0.594541\pi\) | ||||
−0.292661 | + | 0.956216i | \(0.594541\pi\) | |||||||
\(234\) | −3.91813 | −0.256136 | ||||||||
\(235\) | −8.70310 | −0.567727 | ||||||||
\(236\) | −1.88759 | −0.122872 | ||||||||
\(237\) | 37.6667 | 2.44671 | ||||||||
\(238\) | −0.251063 | −0.0162740 | ||||||||
\(239\) | −15.4332 | −0.998289 | −0.499145 | − | 0.866519i | \(-0.666352\pi\) | ||||
−0.499145 | + | 0.866519i | \(0.666352\pi\) | |||||||
\(240\) | 2.78829 | 0.179984 | ||||||||
\(241\) | 24.2931 | 1.56486 | 0.782429 | − | 0.622740i | \(-0.213981\pi\) | ||||
0.782429 | + | 0.622740i | \(0.213981\pi\) | |||||||
\(242\) | −8.39703 | −0.539782 | ||||||||
\(243\) | −16.3140 | −1.04654 | ||||||||
\(244\) | 0.718868 | 0.0460208 | ||||||||
\(245\) | −6.98902 | −0.446512 | ||||||||
\(246\) | 28.2533 | 1.80136 | ||||||||
\(247\) | 4.13874 | 0.263342 | ||||||||
\(248\) | 6.93969 | 0.440671 | ||||||||
\(249\) | −33.4701 | −2.12108 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 5.22097 | 0.329545 | 0.164772 | − | 0.986332i | \(-0.447311\pi\) | ||||
0.164772 | + | 0.986332i | \(0.447311\pi\) | |||||||
\(252\) | −0.500413 | −0.0315230 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −7.72617 | −0.484783 | ||||||||
\(255\) | 6.67923 | 0.418270 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 25.4108 | 1.58508 | 0.792542 | − | 0.609817i | \(-0.208757\pi\) | ||||
0.792542 | + | 0.609817i | \(0.208757\pi\) | |||||||
\(258\) | −2.97499 | −0.185215 | ||||||||
\(259\) | 0.396446 | 0.0246340 | ||||||||
\(260\) | −0.820624 | −0.0508930 | ||||||||
\(261\) | 44.3787 | 2.74697 | ||||||||
\(262\) | −15.9385 | −0.984682 | ||||||||
\(263\) | −13.4327 | −0.828296 | −0.414148 | − | 0.910210i | \(-0.635920\pi\) | ||||
−0.414148 | + | 0.910210i | \(0.635920\pi\) | |||||||
\(264\) | 4.49855 | 0.276867 | ||||||||
\(265\) | −10.1839 | −0.625594 | ||||||||
\(266\) | 0.528588 | 0.0324098 | ||||||||
\(267\) | 34.4788 | 2.11007 | ||||||||
\(268\) | −3.50684 | −0.214215 | ||||||||
\(269\) | 7.33351 | 0.447132 | 0.223566 | − | 0.974689i | \(-0.428230\pi\) | ||||
0.223566 | + | 0.974689i | \(0.428230\pi\) | |||||||
\(270\) | 4.94803 | 0.301128 | ||||||||
\(271\) | −3.57309 | −0.217050 | −0.108525 | − | 0.994094i | \(-0.534613\pi\) | ||||
−0.108525 | + | 0.994094i | \(0.534613\pi\) | |||||||
\(272\) | 2.39546 | 0.145246 | ||||||||
\(273\) | 0.239815 | 0.0145143 | ||||||||
\(274\) | 1.42400 | 0.0860273 | ||||||||
\(275\) | 1.61337 | 0.0972899 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.3045 | −0.859474 | −0.429737 | − | 0.902954i | \(-0.641394\pi\) | ||||
−0.429737 | + | 0.902954i | \(0.641394\pi\) | |||||||
\(278\) | 7.21002 | 0.432428 | ||||||||
\(279\) | 33.1341 | 1.98369 | ||||||||
\(280\) | −0.104808 | −0.00626347 | ||||||||
\(281\) | 20.0779 | 1.19775 | 0.598873 | − | 0.800844i | \(-0.295615\pi\) | ||||
0.598873 | + | 0.800844i | \(0.295615\pi\) | |||||||
\(282\) | −24.2668 | −1.44507 | ||||||||
\(283\) | −12.5198 | −0.744225 | −0.372112 | − | 0.928188i | \(-0.621366\pi\) | ||||
−0.372112 | + | 0.928188i | \(0.621366\pi\) | |||||||
\(284\) | −1.31155 | −0.0778259 | ||||||||
\(285\) | −14.0625 | −0.832990 | ||||||||
\(286\) | −1.32397 | −0.0782881 | ||||||||
\(287\) | −1.06200 | −0.0626878 | ||||||||
\(288\) | 4.77457 | 0.281345 | ||||||||
\(289\) | −11.2618 | −0.662458 | ||||||||
\(290\) | 9.29479 | 0.545809 | ||||||||
\(291\) | 50.6355 | 2.96831 | ||||||||
\(292\) | 11.3521 | 0.664333 | ||||||||
\(293\) | −4.15264 | −0.242600 | −0.121300 | − | 0.992616i | \(-0.538706\pi\) | ||||
−0.121300 | + | 0.992616i | \(0.538706\pi\) | |||||||
\(294\) | −19.4874 | −1.13653 | ||||||||
\(295\) | −1.88759 | −0.109900 | ||||||||
\(296\) | −3.78260 | −0.219859 | ||||||||
\(297\) | 7.98301 | 0.463221 | ||||||||
\(298\) | −18.4817 | −1.07061 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 2.78829 | 0.160982 | ||||||||
\(301\) | 0.111825 | 0.00644551 | ||||||||
\(302\) | 7.08884 | 0.407917 | ||||||||
\(303\) | 30.1059 | 1.72954 | ||||||||
\(304\) | −5.04341 | −0.289259 | ||||||||
\(305\) | 0.718868 | 0.0411623 | ||||||||
\(306\) | 11.4373 | 0.653826 | ||||||||
\(307\) | −16.8331 | −0.960718 | −0.480359 | − | 0.877072i | \(-0.659494\pi\) | ||||
−0.480359 | + | 0.877072i | \(0.659494\pi\) | |||||||
\(308\) | −0.169094 | −0.00963502 | ||||||||
\(309\) | −9.73721 | −0.553930 | ||||||||
\(310\) | 6.93969 | 0.394148 | ||||||||
\(311\) | 3.68661 | 0.209048 | 0.104524 | − | 0.994522i | \(-0.466668\pi\) | ||||
0.104524 | + | 0.994522i | \(0.466668\pi\) | |||||||
\(312\) | −2.28814 | −0.129540 | ||||||||
\(313\) | 5.63837 | 0.318700 | 0.159350 | − | 0.987222i | \(-0.449060\pi\) | ||||
0.159350 | + | 0.987222i | \(0.449060\pi\) | |||||||
\(314\) | 7.01390 | 0.395817 | ||||||||
\(315\) | −0.500413 | −0.0281951 | ||||||||
\(316\) | 13.5089 | 0.759933 | ||||||||
\(317\) | 20.4608 | 1.14919 | 0.574595 | − | 0.818438i | \(-0.305159\pi\) | ||||
0.574595 | + | 0.818438i | \(0.305159\pi\) | |||||||
\(318\) | −28.3958 | −1.59236 | ||||||||
\(319\) | 14.9959 | 0.839612 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −22.4390 | −1.25242 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.0813 | −0.672219 | ||||||||
\(324\) | −0.527159 | −0.0292866 | ||||||||
\(325\) | −0.820624 | −0.0455201 | ||||||||
\(326\) | −12.3924 | −0.686353 | ||||||||
\(327\) | −13.2520 | −0.732835 | ||||||||
\(328\) | 10.1328 | 0.559491 | ||||||||
\(329\) | 0.912153 | 0.0502886 | ||||||||
\(330\) | 4.49855 | 0.247637 | ||||||||
\(331\) | −8.99155 | −0.494220 | −0.247110 | − | 0.968987i | \(-0.579481\pi\) | ||||
−0.247110 | + | 0.968987i | \(0.579481\pi\) | |||||||
\(332\) | −12.0038 | −0.658794 | ||||||||
\(333\) | −18.0603 | −0.989699 | ||||||||
\(334\) | −8.43589 | −0.461592 | ||||||||
\(335\) | −3.50684 | −0.191599 | ||||||||
\(336\) | −0.292235 | −0.0159427 | ||||||||
\(337\) | −17.6675 | −0.962409 | −0.481204 | − | 0.876608i | \(-0.659801\pi\) | ||||
−0.481204 | + | 0.876608i | \(0.659801\pi\) | |||||||
\(338\) | −12.3266 | −0.670477 | ||||||||
\(339\) | −33.6406 | −1.82710 | ||||||||
\(340\) | 2.39546 | 0.129912 | ||||||||
\(341\) | 11.1963 | 0.606314 | ||||||||
\(342\) | −24.0801 | −1.30210 | ||||||||
\(343\) | 1.46616 | 0.0791651 | ||||||||
\(344\) | −1.06696 | −0.0575265 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −20.9993 | −1.12893 | ||||||||
\(347\) | 0.101431 | 0.00544510 | 0.00272255 | − | 0.999996i | \(-0.499133\pi\) | ||||
0.00272255 | + | 0.999996i | \(0.499133\pi\) | |||||||
\(348\) | 25.9166 | 1.38928 | ||||||||
\(349\) | −15.8436 | −0.848087 | −0.424043 | − | 0.905642i | \(-0.639390\pi\) | ||||
−0.424043 | + | 0.905642i | \(0.639390\pi\) | |||||||
\(350\) | −0.104808 | −0.00560221 | ||||||||
\(351\) | −4.06048 | −0.216732 | ||||||||
\(352\) | 1.61337 | 0.0859930 | ||||||||
\(353\) | −11.0240 | −0.586748 | −0.293374 | − | 0.955998i | \(-0.594778\pi\) | ||||
−0.293374 | + | 0.955998i | \(0.594778\pi\) | |||||||
\(354\) | −5.26316 | −0.279734 | ||||||||
\(355\) | −1.31155 | −0.0696096 | ||||||||
\(356\) | 12.3656 | 0.655373 | ||||||||
\(357\) | −0.700036 | −0.0370498 | ||||||||
\(358\) | −14.6536 | −0.774465 | ||||||||
\(359\) | −35.3001 | −1.86307 | −0.931534 | − | 0.363655i | \(-0.881529\pi\) | ||||
−0.931534 | + | 0.363655i | \(0.881529\pi\) | |||||||
\(360\) | 4.77457 | 0.251642 | ||||||||
\(361\) | 6.43595 | 0.338734 | ||||||||
\(362\) | 16.3855 | 0.861205 | ||||||||
\(363\) | −23.4134 | −1.22888 | ||||||||
\(364\) | 0.0860079 | 0.00450804 | ||||||||
\(365\) | 11.3521 | 0.594197 | ||||||||
\(366\) | 2.00442 | 0.104772 | ||||||||
\(367\) | −24.1075 | −1.25840 | −0.629202 | − | 0.777242i | \(-0.716618\pi\) | ||||
−0.629202 | + | 0.777242i | \(0.716618\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 48.3799 | 2.51856 | ||||||||
\(370\) | −3.78260 | −0.196648 | ||||||||
\(371\) | 1.06736 | 0.0554144 | ||||||||
\(372\) | 19.3499 | 1.00325 | ||||||||
\(373\) | −2.20688 | −0.114268 | −0.0571341 | − | 0.998367i | \(-0.518196\pi\) | ||||
−0.0571341 | + | 0.998367i | \(0.518196\pi\) | |||||||
\(374\) | 3.86476 | 0.199842 | ||||||||
\(375\) | 2.78829 | 0.143987 | ||||||||
\(376\) | −8.70310 | −0.448828 | ||||||||
\(377\) | −7.62753 | −0.392838 | ||||||||
\(378\) | −0.518593 | −0.0266735 | ||||||||
\(379\) | 32.3416 | 1.66128 | 0.830639 | − | 0.556811i | \(-0.187975\pi\) | ||||
0.830639 | + | 0.556811i | \(0.187975\pi\) | |||||||
\(380\) | −5.04341 | −0.258721 | ||||||||
\(381\) | −21.5428 | −1.10367 | ||||||||
\(382\) | 19.0662 | 0.975514 | ||||||||
\(383\) | 35.7304 | 1.82574 | 0.912869 | − | 0.408254i | \(-0.133862\pi\) | ||||
0.912869 | + | 0.408254i | \(0.133862\pi\) | |||||||
\(384\) | 2.78829 | 0.142289 | ||||||||
\(385\) | −0.169094 | −0.00861782 | ||||||||
\(386\) | −3.51113 | −0.178712 | ||||||||
\(387\) | −5.09427 | −0.258956 | ||||||||
\(388\) | 18.1600 | 0.921936 | ||||||||
\(389\) | −27.9098 | −1.41508 | −0.707542 | − | 0.706671i | \(-0.750196\pi\) | ||||
−0.707542 | + | 0.706671i | \(0.750196\pi\) | |||||||
\(390\) | −2.28814 | −0.115865 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −6.98902 | −0.352999 | ||||||||
\(393\) | −44.4411 | −2.24176 | ||||||||
\(394\) | 16.3731 | 0.824865 | ||||||||
\(395\) | 13.5089 | 0.679704 | ||||||||
\(396\) | 7.70316 | 0.387098 | ||||||||
\(397\) | −28.5928 | −1.43503 | −0.717515 | − | 0.696544i | \(-0.754720\pi\) | ||||
−0.717515 | + | 0.696544i | \(0.754720\pi\) | |||||||
\(398\) | 24.3835 | 1.22224 | ||||||||
\(399\) | 1.47386 | 0.0737853 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −14.0942 | −0.703830 | −0.351915 | − | 0.936032i | \(-0.614469\pi\) | ||||
−0.351915 | + | 0.936032i | \(0.614469\pi\) | |||||||
\(402\) | −9.77811 | −0.487688 | ||||||||
\(403\) | −5.69488 | −0.283682 | ||||||||
\(404\) | 10.7972 | 0.537183 | ||||||||
\(405\) | −0.527159 | −0.0261947 | ||||||||
\(406\) | −0.974167 | −0.0483471 | ||||||||
\(407\) | −6.10274 | −0.302502 | ||||||||
\(408\) | 6.67923 | 0.330671 | ||||||||
\(409\) | 3.26948 | 0.161665 | 0.0808327 | − | 0.996728i | \(-0.474242\pi\) | ||||
0.0808327 | + | 0.996728i | \(0.474242\pi\) | |||||||
\(410\) | 10.1328 | 0.500424 | ||||||||
\(411\) | 3.97054 | 0.195852 | ||||||||
\(412\) | −3.49218 | −0.172047 | ||||||||
\(413\) | 0.197835 | 0.00973481 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.0038 | −0.589243 | ||||||||
\(416\) | −0.820624 | −0.0402344 | ||||||||
\(417\) | 20.1037 | 0.984480 | ||||||||
\(418\) | −8.13689 | −0.397988 | ||||||||
\(419\) | −19.2547 | −0.940654 | −0.470327 | − | 0.882492i | \(-0.655864\pi\) | ||||
−0.470327 | + | 0.882492i | \(0.655864\pi\) | |||||||
\(420\) | −0.292235 | −0.0142596 | ||||||||
\(421\) | −35.2902 | −1.71994 | −0.859970 | − | 0.510344i | \(-0.829518\pi\) | ||||
−0.859970 | + | 0.510344i | \(0.829518\pi\) | |||||||
\(422\) | −3.50940 | −0.170835 | ||||||||
\(423\) | −41.5536 | −2.02040 | ||||||||
\(424\) | −10.1839 | −0.494576 | ||||||||
\(425\) | 2.39546 | 0.116197 | ||||||||
\(426\) | −3.65697 | −0.177181 | ||||||||
\(427\) | −0.0753430 | −0.00364611 | ||||||||
\(428\) | −8.04757 | −0.388994 | ||||||||
\(429\) | −3.69162 | −0.178233 | ||||||||
\(430\) | −1.06696 | −0.0514532 | ||||||||
\(431\) | 32.6180 | 1.57116 | 0.785578 | − | 0.618763i | \(-0.212366\pi\) | ||||
0.785578 | + | 0.618763i | \(0.212366\pi\) | |||||||
\(432\) | 4.94803 | 0.238062 | ||||||||
\(433\) | 4.24030 | 0.203776 | 0.101888 | − | 0.994796i | \(-0.467512\pi\) | ||||
0.101888 | + | 0.994796i | \(0.467512\pi\) | |||||||
\(434\) | −0.727334 | −0.0349132 | ||||||||
\(435\) | 25.9166 | 1.24261 | ||||||||
\(436\) | −4.75271 | −0.227614 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 31.6530 | 1.51244 | ||||||||
\(439\) | 17.7359 | 0.846487 | 0.423244 | − | 0.906016i | \(-0.360891\pi\) | ||||
0.423244 | + | 0.906016i | \(0.360891\pi\) | |||||||
\(440\) | 1.61337 | 0.0769144 | ||||||||
\(441\) | −33.3696 | −1.58903 | ||||||||
\(442\) | −1.96577 | −0.0935022 | ||||||||
\(443\) | 33.2025 | 1.57750 | 0.788750 | − | 0.614714i | \(-0.210728\pi\) | ||||
0.788750 | + | 0.614714i | \(0.210728\pi\) | |||||||
\(444\) | −10.5470 | −0.500538 | ||||||||
\(445\) | 12.3656 | 0.586184 | ||||||||
\(446\) | 0.760922 | 0.0360307 | ||||||||
\(447\) | −51.5323 | −2.43739 | ||||||||
\(448\) | −0.104808 | −0.00495170 | ||||||||
\(449\) | −15.8541 | −0.748201 | −0.374101 | − | 0.927388i | \(-0.622049\pi\) | ||||
−0.374101 | + | 0.927388i | \(0.622049\pi\) | |||||||
\(450\) | 4.77457 | 0.225076 | ||||||||
\(451\) | 16.3480 | 0.769797 | ||||||||
\(452\) | −12.0649 | −0.567487 | ||||||||
\(453\) | 19.7658 | 0.928676 | ||||||||
\(454\) | −22.1110 | −1.03772 | ||||||||
\(455\) | 0.0860079 | 0.00403211 | ||||||||
\(456\) | −14.0625 | −0.658537 | ||||||||
\(457\) | 23.3208 | 1.09090 | 0.545451 | − | 0.838143i | \(-0.316358\pi\) | ||||
0.545451 | + | 0.838143i | \(0.316358\pi\) | |||||||
\(458\) | −18.3056 | −0.855363 | ||||||||
\(459\) | 11.8528 | 0.553241 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 35.0520 | 1.63254 | 0.816268 | − | 0.577673i | \(-0.196039\pi\) | ||||
0.816268 | + | 0.577673i | \(0.196039\pi\) | |||||||
\(462\) | −0.471483 | −0.0219354 | ||||||||
\(463\) | 21.7943 | 1.01287 | 0.506434 | − | 0.862279i | \(-0.330963\pi\) | ||||
0.506434 | + | 0.862279i | \(0.330963\pi\) | |||||||
\(464\) | 9.29479 | 0.431500 | ||||||||
\(465\) | 19.3499 | 0.897330 | ||||||||
\(466\) | −8.93455 | −0.413885 | ||||||||
\(467\) | −4.79248 | −0.221770 | −0.110885 | − | 0.993833i | \(-0.535368\pi\) | ||||
−0.110885 | + | 0.993833i | \(0.535368\pi\) | |||||||
\(468\) | −3.91813 | −0.181116 | ||||||||
\(469\) | 0.367545 | 0.0169716 | ||||||||
\(470\) | −8.70310 | −0.401444 | ||||||||
\(471\) | 19.5568 | 0.901130 | ||||||||
\(472\) | −1.88759 | −0.0868836 | ||||||||
\(473\) | −1.72140 | −0.0791499 | ||||||||
\(474\) | 37.6667 | 1.73009 | ||||||||
\(475\) | −5.04341 | −0.231407 | ||||||||
\(476\) | −0.251063 | −0.0115074 | ||||||||
\(477\) | −48.6240 | −2.22634 | ||||||||
\(478\) | −15.4332 | −0.705897 | ||||||||
\(479\) | −18.4300 | −0.842088 | −0.421044 | − | 0.907040i | \(-0.638336\pi\) | ||||
−0.421044 | + | 0.907040i | \(0.638336\pi\) | |||||||
\(480\) | 2.78829 | 0.127268 | ||||||||
\(481\) | 3.10410 | 0.141535 | ||||||||
\(482\) | 24.2931 | 1.10652 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.39703 | −0.381683 | ||||||||
\(485\) | 18.1600 | 0.824605 | ||||||||
\(486\) | −16.3140 | −0.740017 | ||||||||
\(487\) | 18.5292 | 0.839640 | 0.419820 | − | 0.907607i | \(-0.362093\pi\) | ||||
0.419820 | + | 0.907607i | \(0.362093\pi\) | |||||||
\(488\) | 0.718868 | 0.0325416 | ||||||||
\(489\) | −34.5537 | −1.56257 | ||||||||
\(490\) | −6.98902 | −0.315732 | ||||||||
\(491\) | −42.7858 | −1.93090 | −0.965448 | − | 0.260594i | \(-0.916082\pi\) | ||||
−0.965448 | + | 0.260594i | \(0.916082\pi\) | |||||||
\(492\) | 28.2533 | 1.27376 | ||||||||
\(493\) | 22.2653 | 1.00278 | ||||||||
\(494\) | 4.13874 | 0.186211 | ||||||||
\(495\) | 7.70316 | 0.346231 | ||||||||
\(496\) | 6.93969 | 0.311601 | ||||||||
\(497\) | 0.137460 | 0.00616593 | ||||||||
\(498\) | −33.4701 | −1.49983 | ||||||||
\(499\) | −3.23317 | −0.144737 | −0.0723684 | − | 0.997378i | \(-0.523056\pi\) | ||||
−0.0723684 | + | 0.997378i | \(0.523056\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −23.5217 | −1.05087 | ||||||||
\(502\) | 5.22097 | 0.233023 | ||||||||
\(503\) | 33.8588 | 1.50969 | 0.754846 | − | 0.655902i | \(-0.227712\pi\) | ||||
0.754846 | + | 0.655902i | \(0.227712\pi\) | |||||||
\(504\) | −0.500413 | −0.0222902 | ||||||||
\(505\) | 10.7972 | 0.480471 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −34.3701 | −1.52643 | ||||||||
\(508\) | −7.72617 | −0.342793 | ||||||||
\(509\) | −10.1320 | −0.449093 | −0.224547 | − | 0.974463i | \(-0.572090\pi\) | ||||
−0.224547 | + | 0.974463i | \(0.572090\pi\) | |||||||
\(510\) | 6.67923 | 0.295761 | ||||||||
\(511\) | −1.18979 | −0.0526333 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −24.9549 | −1.10179 | ||||||||
\(514\) | 25.4108 | 1.12082 | ||||||||
\(515\) | −3.49218 | −0.153884 | ||||||||
\(516\) | −2.97499 | −0.130967 | ||||||||
\(517\) | −14.0413 | −0.617537 | ||||||||
\(518\) | 0.396446 | 0.0174188 | ||||||||
\(519\) | −58.5522 | −2.57016 | ||||||||
\(520\) | −0.820624 | −0.0359868 | ||||||||
\(521\) | 3.51501 | 0.153995 | 0.0769976 | − | 0.997031i | \(-0.475467\pi\) | ||||
0.0769976 | + | 0.997031i | \(0.475467\pi\) | |||||||
\(522\) | 44.3787 | 1.94240 | ||||||||
\(523\) | −17.6643 | −0.772407 | −0.386204 | − | 0.922414i | \(-0.626214\pi\) | ||||
−0.386204 | + | 0.922414i | \(0.626214\pi\) | |||||||
\(524\) | −15.9385 | −0.696276 | ||||||||
\(525\) | −0.292235 | −0.0127542 | ||||||||
\(526\) | −13.4327 | −0.585694 | ||||||||
\(527\) | 16.6237 | 0.724141 | ||||||||
\(528\) | 4.49855 | 0.195774 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | −10.1839 | −0.442362 | ||||||||
\(531\) | −9.01246 | −0.391107 | ||||||||
\(532\) | 0.528588 | 0.0229172 | ||||||||
\(533\) | −8.31524 | −0.360173 | ||||||||
\(534\) | 34.4788 | 1.49204 | ||||||||
\(535\) | −8.04757 | −0.347927 | ||||||||
\(536\) | −3.50684 | −0.151473 | ||||||||
\(537\) | −40.8584 | −1.76317 | ||||||||
\(538\) | 7.33351 | 0.316170 | ||||||||
\(539\) | −11.2759 | −0.485686 | ||||||||
\(540\) | 4.94803 | 0.212929 | ||||||||
\(541\) | 4.93503 | 0.212174 | 0.106087 | − | 0.994357i | \(-0.466168\pi\) | ||||
0.106087 | + | 0.994357i | \(0.466168\pi\) | |||||||
\(542\) | −3.57309 | −0.153477 | ||||||||
\(543\) | 45.6877 | 1.96065 | ||||||||
\(544\) | 2.39546 | 0.102704 | ||||||||
\(545\) | −4.75271 | −0.203584 | ||||||||
\(546\) | 0.239815 | 0.0102631 | ||||||||
\(547\) | 44.2402 | 1.89158 | 0.945788 | − | 0.324786i | \(-0.105292\pi\) | ||||
0.945788 | + | 0.324786i | \(0.105292\pi\) | |||||||
\(548\) | 1.42400 | 0.0608305 | ||||||||
\(549\) | 3.43229 | 0.146487 | ||||||||
\(550\) | 1.61337 | 0.0687944 | ||||||||
\(551\) | −46.8774 | −1.99704 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.41583 | −0.0602074 | ||||||||
\(554\) | −14.3045 | −0.607740 | ||||||||
\(555\) | −10.5470 | −0.447695 | ||||||||
\(556\) | 7.21002 | 0.305773 | ||||||||
\(557\) | 20.9490 | 0.887637 | 0.443818 | − | 0.896117i | \(-0.353624\pi\) | ||||
0.443818 | + | 0.896117i | \(0.353624\pi\) | |||||||
\(558\) | 33.1341 | 1.40268 | ||||||||
\(559\) | 0.875571 | 0.0370327 | ||||||||
\(560\) | −0.104808 | −0.00442894 | ||||||||
\(561\) | 10.7761 | 0.454966 | ||||||||
\(562\) | 20.0779 | 0.846934 | ||||||||
\(563\) | 14.4921 | 0.610767 | 0.305384 | − | 0.952229i | \(-0.401215\pi\) | ||||
0.305384 | + | 0.952229i | \(0.401215\pi\) | |||||||
\(564\) | −24.2668 | −1.02182 | ||||||||
\(565\) | −12.0649 | −0.507575 | ||||||||
\(566\) | −12.5198 | −0.526246 | ||||||||
\(567\) | 0.0552504 | 0.00232030 | ||||||||
\(568\) | −1.31155 | −0.0550312 | ||||||||
\(569\) | 17.0313 | 0.713987 | 0.356994 | − | 0.934107i | \(-0.383802\pi\) | ||||
0.356994 | + | 0.934107i | \(0.383802\pi\) | |||||||
\(570\) | −14.0625 | −0.589013 | ||||||||
\(571\) | 16.6349 | 0.696150 | 0.348075 | − | 0.937467i | \(-0.386836\pi\) | ||||
0.348075 | + | 0.937467i | \(0.386836\pi\) | |||||||
\(572\) | −1.32397 | −0.0553580 | ||||||||
\(573\) | 53.1623 | 2.22089 | ||||||||
\(574\) | −1.06200 | −0.0443270 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.77457 | 0.198941 | ||||||||
\(577\) | −13.1663 | −0.548119 | −0.274059 | − | 0.961713i | \(-0.588367\pi\) | ||||
−0.274059 | + | 0.961713i | \(0.588367\pi\) | |||||||
\(578\) | −11.2618 | −0.468429 | ||||||||
\(579\) | −9.79006 | −0.406861 | ||||||||
\(580\) | 9.29479 | 0.385945 | ||||||||
\(581\) | 1.25809 | 0.0521944 | ||||||||
\(582\) | 50.6355 | 2.09891 | ||||||||
\(583\) | −16.4305 | −0.680480 | ||||||||
\(584\) | 11.3521 | 0.469754 | ||||||||
\(585\) | −3.91813 | −0.161995 | ||||||||
\(586\) | −4.15264 | −0.171544 | ||||||||
\(587\) | −42.1135 | −1.73821 | −0.869104 | − | 0.494629i | \(-0.835304\pi\) | ||||
−0.869104 | + | 0.494629i | \(0.835304\pi\) | |||||||
\(588\) | −19.4874 | −0.803648 | ||||||||
\(589\) | −34.9997 | −1.44214 | ||||||||
\(590\) | −1.88759 | −0.0777110 | ||||||||
\(591\) | 45.6530 | 1.87791 | ||||||||
\(592\) | −3.78260 | −0.155464 | ||||||||
\(593\) | 4.53513 | 0.186236 | 0.0931178 | − | 0.995655i | \(-0.470317\pi\) | ||||
0.0931178 | + | 0.995655i | \(0.470317\pi\) | |||||||
\(594\) | 7.98301 | 0.327547 | ||||||||
\(595\) | −0.251063 | −0.0102926 | ||||||||
\(596\) | −18.4817 | −0.757038 | ||||||||
\(597\) | 67.9885 | 2.78258 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.2169 | 1.23463 | 0.617314 | − | 0.786717i | \(-0.288221\pi\) | ||||
0.617314 | + | 0.786717i | \(0.288221\pi\) | |||||||
\(600\) | 2.78829 | 0.113832 | ||||||||
\(601\) | −30.8107 | −1.25679 | −0.628397 | − | 0.777893i | \(-0.716289\pi\) | ||||
−0.628397 | + | 0.777893i | \(0.716289\pi\) | |||||||
\(602\) | 0.111825 | 0.00455766 | ||||||||
\(603\) | −16.7437 | −0.681856 | ||||||||
\(604\) | 7.08884 | 0.288441 | ||||||||
\(605\) | −8.39703 | −0.341388 | ||||||||
\(606\) | 30.1059 | 1.22297 | ||||||||
\(607\) | −9.83550 | −0.399211 | −0.199605 | − | 0.979876i | \(-0.563966\pi\) | ||||
−0.199605 | + | 0.979876i | \(0.563966\pi\) | |||||||
\(608\) | −5.04341 | −0.204537 | ||||||||
\(609\) | −2.71626 | −0.110068 | ||||||||
\(610\) | 0.718868 | 0.0291061 | ||||||||
\(611\) | 7.14197 | 0.288933 | ||||||||
\(612\) | 11.4373 | 0.462325 | ||||||||
\(613\) | −17.5242 | −0.707794 | −0.353897 | − | 0.935284i | \(-0.615144\pi\) | ||||
−0.353897 | + | 0.935284i | \(0.615144\pi\) | |||||||
\(614\) | −16.8331 | −0.679330 | ||||||||
\(615\) | 28.2533 | 1.13928 | ||||||||
\(616\) | −0.169094 | −0.00681299 | ||||||||
\(617\) | 13.1614 | 0.529859 | 0.264930 | − | 0.964268i | \(-0.414651\pi\) | ||||
0.264930 | + | 0.964268i | \(0.414651\pi\) | |||||||
\(618\) | −9.73721 | −0.391688 | ||||||||
\(619\) | −11.3157 | −0.454818 | −0.227409 | − | 0.973799i | \(-0.573025\pi\) | ||||
−0.227409 | + | 0.973799i | \(0.573025\pi\) | |||||||
\(620\) | 6.93969 | 0.278705 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.68661 | 0.147820 | ||||||||
\(623\) | −1.29601 | −0.0519234 | ||||||||
\(624\) | −2.28814 | −0.0915989 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 5.63837 | 0.225355 | ||||||||
\(627\) | −22.6880 | −0.906072 | ||||||||
\(628\) | 7.01390 | 0.279885 | ||||||||
\(629\) | −9.06106 | −0.361288 | ||||||||
\(630\) | −0.500413 | −0.0199369 | ||||||||
\(631\) | 7.97357 | 0.317423 | 0.158711 | − | 0.987325i | \(-0.449266\pi\) | ||||
0.158711 | + | 0.987325i | \(0.449266\pi\) | |||||||
\(632\) | 13.5089 | 0.537354 | ||||||||
\(633\) | −9.78523 | −0.388928 | ||||||||
\(634\) | 20.4608 | 0.812601 | ||||||||
\(635\) | −7.72617 | −0.306604 | ||||||||
\(636\) | −28.3958 | −1.12597 | ||||||||
\(637\) | 5.73536 | 0.227243 | ||||||||
\(638\) | 14.9959 | 0.593695 | ||||||||
\(639\) | −6.26207 | −0.247724 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 16.7615 | 0.662041 | 0.331020 | − | 0.943624i | \(-0.392607\pi\) | ||||
0.331020 | + | 0.943624i | \(0.392607\pi\) | |||||||
\(642\) | −22.4390 | −0.885595 | ||||||||
\(643\) | −38.3427 | −1.51209 | −0.756044 | − | 0.654521i | \(-0.772870\pi\) | ||||
−0.756044 | + | 0.654521i | \(0.772870\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.97499 | −0.117140 | ||||||||
\(646\) | −12.0813 | −0.475331 | ||||||||
\(647\) | 24.4928 | 0.962913 | 0.481456 | − | 0.876470i | \(-0.340108\pi\) | ||||
0.481456 | + | 0.876470i | \(0.340108\pi\) | |||||||
\(648\) | −0.527159 | −0.0207088 | ||||||||
\(649\) | −3.04539 | −0.119542 | ||||||||
\(650\) | −0.820624 | −0.0321875 | ||||||||
\(651\) | −2.02802 | −0.0794844 | ||||||||
\(652\) | −12.3924 | −0.485325 | ||||||||
\(653\) | 20.8273 | 0.815037 | 0.407519 | − | 0.913197i | \(-0.366394\pi\) | ||||
0.407519 | + | 0.913197i | \(0.366394\pi\) | |||||||
\(654\) | −13.2520 | −0.518192 | ||||||||
\(655\) | −15.9385 | −0.622768 | ||||||||
\(656\) | 10.1328 | 0.395620 | ||||||||
\(657\) | 54.2016 | 2.11460 | ||||||||
\(658\) | 0.912153 | 0.0355594 | ||||||||
\(659\) | −33.2234 | −1.29420 | −0.647100 | − | 0.762405i | \(-0.724019\pi\) | ||||
−0.647100 | + | 0.762405i | \(0.724019\pi\) | |||||||
\(660\) | 4.49855 | 0.175106 | ||||||||
\(661\) | 7.64158 | 0.297223 | 0.148612 | − | 0.988896i | \(-0.452520\pi\) | ||||
0.148612 | + | 0.988896i | \(0.452520\pi\) | |||||||
\(662\) | −8.99155 | −0.349466 | ||||||||
\(663\) | −5.48114 | −0.212870 | ||||||||
\(664\) | −12.0038 | −0.465837 | ||||||||
\(665\) | 0.528588 | 0.0204978 | ||||||||
\(666\) | −18.0603 | −0.699823 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −8.43589 | −0.326395 | ||||||||
\(669\) | 2.12167 | 0.0820286 | ||||||||
\(670\) | −3.50684 | −0.135481 | ||||||||
\(671\) | 1.15980 | 0.0447736 | ||||||||
\(672\) | −0.292235 | −0.0112732 | ||||||||
\(673\) | −2.98332 | −0.114999 | −0.0574993 | − | 0.998346i | \(-0.518313\pi\) | ||||
−0.0574993 | + | 0.998346i | \(0.518313\pi\) | |||||||
\(674\) | −17.6675 | −0.680526 | ||||||||
\(675\) | 4.94803 | 0.190450 | ||||||||
\(676\) | −12.3266 | −0.474099 | ||||||||
\(677\) | 17.0692 | 0.656023 | 0.328012 | − | 0.944674i | \(-0.393621\pi\) | ||||
0.328012 | + | 0.944674i | \(0.393621\pi\) | |||||||
\(678\) | −33.6406 | −1.29196 | ||||||||
\(679\) | −1.90331 | −0.0730425 | ||||||||
\(680\) | 2.39546 | 0.0918616 | ||||||||
\(681\) | −61.6520 | −2.36251 | ||||||||
\(682\) | 11.1963 | 0.428728 | ||||||||
\(683\) | −11.1574 | −0.426927 | −0.213464 | − | 0.976951i | \(-0.568474\pi\) | ||||
−0.213464 | + | 0.976951i | \(0.568474\pi\) | |||||||
\(684\) | −24.0801 | −0.920727 | ||||||||
\(685\) | 1.42400 | 0.0544084 | ||||||||
\(686\) | 1.46616 | 0.0559782 | ||||||||
\(687\) | −51.0413 | −1.94735 | ||||||||
\(688\) | −1.06696 | −0.0406774 | ||||||||
\(689\) | 8.35719 | 0.318383 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.1266 | −1.14607 | −0.573036 | − | 0.819530i | \(-0.694234\pi\) | ||||
−0.573036 | + | 0.819530i | \(0.694234\pi\) | |||||||
\(692\) | −20.9993 | −0.798273 | ||||||||
\(693\) | −0.807351 | −0.0306687 | ||||||||
\(694\) | 0.101431 | 0.00385026 | ||||||||
\(695\) | 7.21002 | 0.273492 | ||||||||
\(696\) | 25.9166 | 0.982366 | ||||||||
\(697\) | 24.2727 | 0.919395 | ||||||||
\(698\) | −15.8436 | −0.599688 | ||||||||
\(699\) | −24.9121 | −0.942263 | ||||||||
\(700\) | −0.104808 | −0.00396136 | ||||||||
\(701\) | 14.6121 | 0.551892 | 0.275946 | − | 0.961173i | \(-0.411009\pi\) | ||||
0.275946 | + | 0.961173i | \(0.411009\pi\) | |||||||
\(702\) | −4.06048 | −0.153253 | ||||||||
\(703\) | 19.0772 | 0.719510 | ||||||||
\(704\) | 1.61337 | 0.0608062 | ||||||||
\(705\) | −24.2668 | −0.913940 | ||||||||
\(706\) | −11.0240 | −0.414894 | ||||||||
\(707\) | −1.13164 | −0.0425596 | ||||||||
\(708\) | −5.26316 | −0.197802 | ||||||||
\(709\) | −9.76279 | −0.366649 | −0.183325 | − | 0.983052i | \(-0.558686\pi\) | ||||
−0.183325 | + | 0.983052i | \(0.558686\pi\) | |||||||
\(710\) | −1.31155 | −0.0492214 | ||||||||
\(711\) | 64.4991 | 2.41890 | ||||||||
\(712\) | 12.3656 | 0.463419 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −0.700036 | −0.0261982 | ||||||||
\(715\) | −1.32397 | −0.0495137 | ||||||||
\(716\) | −14.6536 | −0.547629 | ||||||||
\(717\) | −43.0322 | −1.60707 | ||||||||
\(718\) | −35.3001 | −1.31739 | ||||||||
\(719\) | 14.8218 | 0.552761 | 0.276381 | − | 0.961048i | \(-0.410865\pi\) | ||||
0.276381 | + | 0.961048i | \(0.410865\pi\) | |||||||
\(720\) | 4.77457 | 0.177938 | ||||||||
\(721\) | 0.366007 | 0.0136308 | ||||||||
\(722\) | 6.43595 | 0.239521 | ||||||||
\(723\) | 67.7363 | 2.51914 | ||||||||
\(724\) | 16.3855 | 0.608964 | ||||||||
\(725\) | 9.29479 | 0.345200 | ||||||||
\(726\) | −23.4134 | −0.868952 | ||||||||
\(727\) | −29.0598 | −1.07777 | −0.538885 | − | 0.842379i | \(-0.681154\pi\) | ||||
−0.538885 | + | 0.842379i | \(0.681154\pi\) | |||||||
\(728\) | 0.0860079 | 0.00318766 | ||||||||
\(729\) | −43.9067 | −1.62617 | ||||||||
\(730\) | 11.3521 | 0.420161 | ||||||||
\(731\) | −2.55585 | −0.0945315 | ||||||||
\(732\) | 2.00442 | 0.0740853 | ||||||||
\(733\) | 8.23520 | 0.304174 | 0.152087 | − | 0.988367i | \(-0.451401\pi\) | ||||
0.152087 | + | 0.988367i | \(0.451401\pi\) | |||||||
\(734\) | −24.1075 | −0.889826 | ||||||||
\(735\) | −19.4874 | −0.718804 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.65784 | −0.208409 | ||||||||
\(738\) | 48.3799 | 1.78089 | ||||||||
\(739\) | 3.77121 | 0.138726 | 0.0693631 | − | 0.997591i | \(-0.477903\pi\) | ||||
0.0693631 | + | 0.997591i | \(0.477903\pi\) | |||||||
\(740\) | −3.78260 | −0.139051 | ||||||||
\(741\) | 11.5400 | 0.423933 | ||||||||
\(742\) | 1.06736 | 0.0391839 | ||||||||
\(743\) | 1.77452 | 0.0651007 | 0.0325503 | − | 0.999470i | \(-0.489637\pi\) | ||||
0.0325503 | + | 0.999470i | \(0.489637\pi\) | |||||||
\(744\) | 19.3499 | 0.709402 | ||||||||
\(745\) | −18.4817 | −0.677115 | ||||||||
\(746\) | −2.20688 | −0.0807998 | ||||||||
\(747\) | −57.3130 | −2.09697 | ||||||||
\(748\) | 3.86476 | 0.141310 | ||||||||
\(749\) | 0.843448 | 0.0308189 | ||||||||
\(750\) | 2.78829 | 0.101814 | ||||||||
\(751\) | 0.476437 | 0.0173854 | 0.00869272 | − | 0.999962i | \(-0.497233\pi\) | ||||
0.00869272 | + | 0.999962i | \(0.497233\pi\) | |||||||
\(752\) | −8.70310 | −0.317369 | ||||||||
\(753\) | 14.5576 | 0.530508 | ||||||||
\(754\) | −7.62753 | −0.277778 | ||||||||
\(755\) | 7.08884 | 0.257989 | ||||||||
\(756\) | −0.518593 | −0.0188610 | ||||||||
\(757\) | 49.6224 | 1.80356 | 0.901779 | − | 0.432198i | \(-0.142262\pi\) | ||||
0.901779 | + | 0.432198i | \(0.142262\pi\) | |||||||
\(758\) | 32.3416 | 1.17470 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.04341 | −0.182944 | ||||||||
\(761\) | 3.12436 | 0.113258 | 0.0566291 | − | 0.998395i | \(-0.481965\pi\) | ||||
0.0566291 | + | 0.998395i | \(0.481965\pi\) | |||||||
\(762\) | −21.5428 | −0.780414 | ||||||||
\(763\) | 0.498122 | 0.0180332 | ||||||||
\(764\) | 19.0662 | 0.689793 | ||||||||
\(765\) | 11.4373 | 0.413516 | ||||||||
\(766\) | 35.7304 | 1.29099 | ||||||||
\(767\) | 1.54901 | 0.0559314 | ||||||||
\(768\) | 2.78829 | 0.100614 | ||||||||
\(769\) | 33.8619 | 1.22109 | 0.610545 | − | 0.791982i | \(-0.290950\pi\) | ||||
0.610545 | + | 0.791982i | \(0.290950\pi\) | |||||||
\(770\) | −0.169094 | −0.00609372 | ||||||||
\(771\) | 70.8528 | 2.55170 | ||||||||
\(772\) | −3.51113 | −0.126368 | ||||||||
\(773\) | 0.401860 | 0.0144539 | 0.00722695 | − | 0.999974i | \(-0.497700\pi\) | ||||
0.00722695 | + | 0.999974i | \(0.497700\pi\) | |||||||
\(774\) | −5.09427 | −0.183110 | ||||||||
\(775\) | 6.93969 | 0.249281 | ||||||||
\(776\) | 18.1600 | 0.651908 | ||||||||
\(777\) | 1.10541 | 0.0396563 | ||||||||
\(778\) | −27.9098 | −1.00062 | ||||||||
\(779\) | −51.1039 | −1.83099 | ||||||||
\(780\) | −2.28814 | −0.0819286 | ||||||||
\(781\) | −2.11601 | −0.0757168 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 45.9909 | 1.64358 | ||||||||
\(784\) | −6.98902 | −0.249608 | ||||||||
\(785\) | 7.01390 | 0.250337 | ||||||||
\(786\) | −44.4411 | −1.58516 | ||||||||
\(787\) | −25.0932 | −0.894477 | −0.447238 | − | 0.894415i | \(-0.647592\pi\) | ||||
−0.447238 | + | 0.894415i | \(0.647592\pi\) | |||||||
\(788\) | 16.3731 | 0.583268 | ||||||||
\(789\) | −37.4543 | −1.33341 | ||||||||
\(790\) | 13.5089 | 0.480624 | ||||||||
\(791\) | 1.26450 | 0.0449604 | ||||||||
\(792\) | 7.70316 | 0.273720 | ||||||||
\(793\) | −0.589921 | −0.0209487 | ||||||||
\(794\) | −28.5928 | −1.01472 | ||||||||
\(795\) | −28.3958 | −1.00710 | ||||||||
\(796\) | 24.3835 | 0.864252 | ||||||||
\(797\) | 6.68778 | 0.236893 | 0.118447 | − | 0.992960i | \(-0.462209\pi\) | ||||
0.118447 | + | 0.992960i | \(0.462209\pi\) | |||||||
\(798\) | 1.47386 | 0.0521741 | ||||||||
\(799\) | −20.8479 | −0.737545 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 59.0403 | 2.08609 | ||||||||
\(802\) | −14.0942 | −0.497683 | ||||||||
\(803\) | 18.3152 | 0.646329 | ||||||||
\(804\) | −9.77811 | −0.344847 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.69488 | −0.200594 | ||||||||
\(807\) | 20.4480 | 0.719803 | ||||||||
\(808\) | 10.7972 | 0.379846 | ||||||||
\(809\) | −4.38696 | −0.154237 | −0.0771187 | − | 0.997022i | \(-0.524572\pi\) | ||||
−0.0771187 | + | 0.997022i | \(0.524572\pi\) | |||||||
\(810\) | −0.527159 | −0.0185225 | ||||||||
\(811\) | 27.1184 | 0.952257 | 0.476129 | − | 0.879376i | \(-0.342040\pi\) | ||||
0.476129 | + | 0.879376i | \(0.342040\pi\) | |||||||
\(812\) | −0.974167 | −0.0341866 | ||||||||
\(813\) | −9.96281 | −0.349411 | ||||||||
\(814\) | −6.10274 | −0.213901 | ||||||||
\(815\) | −12.3924 | −0.434088 | ||||||||
\(816\) | 6.67923 | 0.233820 | ||||||||
\(817\) | 5.38110 | 0.188261 | ||||||||
\(818\) | 3.26948 | 0.114315 | ||||||||
\(819\) | 0.410651 | 0.0143493 | ||||||||
\(820\) | 10.1328 | 0.353853 | ||||||||
\(821\) | −24.6081 | −0.858827 | −0.429414 | − | 0.903108i | \(-0.641280\pi\) | ||||
−0.429414 | + | 0.903108i | \(0.641280\pi\) | |||||||
\(822\) | 3.97054 | 0.138489 | ||||||||
\(823\) | 10.2736 | 0.358116 | 0.179058 | − | 0.983838i | \(-0.442695\pi\) | ||||
0.179058 | + | 0.983838i | \(0.442695\pi\) | |||||||
\(824\) | −3.49218 | −0.121656 | ||||||||
\(825\) | 4.49855 | 0.156619 | ||||||||
\(826\) | 0.197835 | 0.00688355 | ||||||||
\(827\) | 21.4151 | 0.744675 | 0.372337 | − | 0.928097i | \(-0.378556\pi\) | ||||
0.372337 | + | 0.928097i | \(0.378556\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.6204 | 0.646712 | 0.323356 | − | 0.946277i | \(-0.395189\pi\) | ||||
0.323356 | + | 0.946277i | \(0.395189\pi\) | |||||||
\(830\) | −12.0038 | −0.416658 | ||||||||
\(831\) | −39.8851 | −1.38360 | ||||||||
\(832\) | −0.820624 | −0.0284500 | ||||||||
\(833\) | −16.7419 | −0.580072 | ||||||||
\(834\) | 20.1037 | 0.696133 | ||||||||
\(835\) | −8.43589 | −0.291936 | ||||||||
\(836\) | −8.13689 | −0.281420 | ||||||||
\(837\) | 34.3378 | 1.18689 | ||||||||
\(838\) | −19.2547 | −0.665143 | ||||||||
\(839\) | 16.1518 | 0.557621 | 0.278811 | − | 0.960346i | \(-0.410060\pi\) | ||||
0.278811 | + | 0.960346i | \(0.410060\pi\) | |||||||
\(840\) | −0.292235 | −0.0100831 | ||||||||
\(841\) | 57.3931 | 1.97907 | ||||||||
\(842\) | −35.2902 | −1.21618 | ||||||||
\(843\) | 55.9830 | 1.92816 | ||||||||
\(844\) | −3.50940 | −0.120799 | ||||||||
\(845\) | −12.3266 | −0.424047 | ||||||||
\(846\) | −41.5536 | −1.42864 | ||||||||
\(847\) | 0.880075 | 0.0302397 | ||||||||
\(848\) | −10.1839 | −0.349718 | ||||||||
\(849\) | −34.9089 | −1.19807 | ||||||||
\(850\) | 2.39546 | 0.0821635 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −3.65697 | −0.125286 | ||||||||
\(853\) | −40.8774 | −1.39961 | −0.699807 | − | 0.714332i | \(-0.746731\pi\) | ||||
−0.699807 | + | 0.714332i | \(0.746731\pi\) | |||||||
\(854\) | −0.0753430 | −0.00257819 | ||||||||
\(855\) | −24.0801 | −0.823523 | ||||||||
\(856\) | −8.04757 | −0.275060 | ||||||||
\(857\) | 38.1768 | 1.30409 | 0.652047 | − | 0.758179i | \(-0.273911\pi\) | ||||
0.652047 | + | 0.758179i | \(0.273911\pi\) | |||||||
\(858\) | −3.69162 | −0.126030 | ||||||||
\(859\) | −54.2939 | −1.85248 | −0.926241 | − | 0.376931i | \(-0.876979\pi\) | ||||
−0.926241 | + | 0.376931i | \(0.876979\pi\) | |||||||
\(860\) | −1.06696 | −0.0363829 | ||||||||
\(861\) | −2.96116 | −0.100916 | ||||||||
\(862\) | 32.6180 | 1.11097 | ||||||||
\(863\) | 38.0704 | 1.29593 | 0.647966 | − | 0.761669i | \(-0.275620\pi\) | ||||
0.647966 | + | 0.761669i | \(0.275620\pi\) | |||||||
\(864\) | 4.94803 | 0.168336 | ||||||||
\(865\) | −20.9993 | −0.713997 | ||||||||
\(866\) | 4.24030 | 0.144091 | ||||||||
\(867\) | −31.4012 | −1.06644 | ||||||||
\(868\) | −0.727334 | −0.0246873 | ||||||||
\(869\) | 21.7948 | 0.739338 | ||||||||
\(870\) | 25.9166 | 0.878655 | ||||||||
\(871\) | 2.87780 | 0.0975106 | ||||||||
\(872\) | −4.75271 | −0.160947 | ||||||||
\(873\) | 86.7065 | 2.93457 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.104808 | −0.00354315 | ||||||||
\(876\) | 31.6530 | 1.06946 | ||||||||
\(877\) | −10.6650 | −0.360131 | −0.180066 | − | 0.983655i | \(-0.557631\pi\) | ||||
−0.180066 | + | 0.983655i | \(0.557631\pi\) | |||||||
\(878\) | 17.7359 | 0.598557 | ||||||||
\(879\) | −11.5788 | −0.390542 | ||||||||
\(880\) | 1.61337 | 0.0543867 | ||||||||
\(881\) | −29.7448 | −1.00213 | −0.501064 | − | 0.865411i | \(-0.667058\pi\) | ||||
−0.501064 | + | 0.865411i | \(0.667058\pi\) | |||||||
\(882\) | −33.3696 | −1.12361 | ||||||||
\(883\) | 33.4709 | 1.12639 | 0.563193 | − | 0.826326i | \(-0.309573\pi\) | ||||
0.563193 | + | 0.826326i | \(0.309573\pi\) | |||||||
\(884\) | −1.96577 | −0.0661160 | ||||||||
\(885\) | −5.26316 | −0.176919 | ||||||||
\(886\) | 33.2025 | 1.11546 | ||||||||
\(887\) | 0.763899 | 0.0256492 | 0.0128246 | − | 0.999918i | \(-0.495918\pi\) | ||||
0.0128246 | + | 0.999918i | \(0.495918\pi\) | |||||||
\(888\) | −10.5470 | −0.353934 | ||||||||
\(889\) | 0.809763 | 0.0271586 | ||||||||
\(890\) | 12.3656 | 0.414495 | ||||||||
\(891\) | −0.850503 | −0.0284929 | ||||||||
\(892\) | 0.760922 | 0.0254776 | ||||||||
\(893\) | 43.8933 | 1.46883 | ||||||||
\(894\) | −51.5323 | −1.72350 | ||||||||
\(895\) | −14.6536 | −0.489814 | ||||||||
\(896\) | −0.104808 | −0.00350138 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15.8541 | −0.529058 | ||||||||
\(899\) | 64.5030 | 2.15130 | ||||||||
\(900\) | 4.77457 | 0.159152 | ||||||||
\(901\) | −24.3952 | −0.812721 | ||||||||
\(902\) | 16.3480 | 0.544329 | ||||||||
\(903\) | 0.311802 | 0.0103761 | ||||||||
\(904\) | −12.0649 | −0.401274 | ||||||||
\(905\) | 16.3855 | 0.544674 | ||||||||
\(906\) | 19.7658 | 0.656673 | ||||||||
\(907\) | −18.7122 | −0.621329 | −0.310664 | − | 0.950520i | \(-0.600551\pi\) | ||||
−0.310664 | + | 0.950520i | \(0.600551\pi\) | |||||||
\(908\) | −22.1110 | −0.733780 | ||||||||
\(909\) | 51.5523 | 1.70988 | ||||||||
\(910\) | 0.0860079 | 0.00285113 | ||||||||
\(911\) | −39.5665 | −1.31090 | −0.655448 | − | 0.755241i | \(-0.727520\pi\) | ||||
−0.655448 | + | 0.755241i | \(0.727520\pi\) | |||||||
\(912\) | −14.0625 | −0.465656 | ||||||||
\(913\) | −19.3666 | −0.640940 | ||||||||
\(914\) | 23.3208 | 0.771385 | ||||||||
\(915\) | 2.00442 | 0.0662639 | ||||||||
\(916\) | −18.3056 | −0.604833 | ||||||||
\(917\) | 1.67048 | 0.0551640 | ||||||||
\(918\) | 11.8528 | 0.391201 | ||||||||
\(919\) | 39.1397 | 1.29110 | 0.645549 | − | 0.763719i | \(-0.276629\pi\) | ||||
0.645549 | + | 0.763719i | \(0.276629\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −46.9357 | −1.54659 | ||||||||
\(922\) | 35.0520 | 1.15438 | ||||||||
\(923\) | 1.07629 | 0.0354264 | ||||||||
\(924\) | −0.471483 | −0.0155107 | ||||||||
\(925\) | −3.78260 | −0.124371 | ||||||||
\(926\) | 21.7943 | 0.716206 | ||||||||
\(927\) | −16.6737 | −0.547635 | ||||||||
\(928\) | 9.29479 | 0.305116 | ||||||||
\(929\) | 34.4775 | 1.13117 | 0.565584 | − | 0.824690i | \(-0.308651\pi\) | ||||
0.565584 | + | 0.824690i | \(0.308651\pi\) | |||||||
\(930\) | 19.3499 | 0.634508 | ||||||||
\(931\) | 35.2484 | 1.15522 | ||||||||
\(932\) | −8.93455 | −0.292661 | ||||||||
\(933\) | 10.2793 | 0.336531 | ||||||||
\(934\) | −4.79248 | −0.156815 | ||||||||
\(935\) | 3.86476 | 0.126391 | ||||||||
\(936\) | −3.91813 | −0.128068 | ||||||||
\(937\) | −46.1403 | −1.50734 | −0.753670 | − | 0.657253i | \(-0.771718\pi\) | ||||
−0.753670 | + | 0.657253i | \(0.771718\pi\) | |||||||
\(938\) | 0.367545 | 0.0120008 | ||||||||
\(939\) | 15.7214 | 0.513050 | ||||||||
\(940\) | −8.70310 | −0.283864 | ||||||||
\(941\) | −0.749900 | −0.0244460 | −0.0122230 | − | 0.999925i | \(-0.503891\pi\) | ||||
−0.0122230 | + | 0.999925i | \(0.503891\pi\) | |||||||
\(942\) | 19.5568 | 0.637195 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −1.88759 | −0.0614360 | ||||||||
\(945\) | −0.518593 | −0.0168698 | ||||||||
\(946\) | −1.72140 | −0.0559674 | ||||||||
\(947\) | −4.32198 | −0.140446 | −0.0702228 | − | 0.997531i | \(-0.522371\pi\) | ||||
−0.0702228 | + | 0.997531i | \(0.522371\pi\) | |||||||
\(948\) | 37.6667 | 1.22336 | ||||||||
\(949\) | −9.31583 | −0.302405 | ||||||||
\(950\) | −5.04341 | −0.163630 | ||||||||
\(951\) | 57.0506 | 1.84999 | ||||||||
\(952\) | −0.251063 | −0.00813699 | ||||||||
\(953\) | −18.8602 | −0.610942 | −0.305471 | − | 0.952201i | \(-0.598814\pi\) | ||||
−0.305471 | + | 0.952201i | \(0.598814\pi\) | |||||||
\(954\) | −48.6240 | −1.57426 | ||||||||
\(955\) | 19.0662 | 0.616969 | ||||||||
\(956\) | −15.4332 | −0.499145 | ||||||||
\(957\) | 41.8131 | 1.35162 | ||||||||
\(958\) | −18.4300 | −0.595446 | ||||||||
\(959\) | −0.149247 | −0.00481943 | ||||||||
\(960\) | 2.78829 | 0.0899918 | ||||||||
\(961\) | 17.1593 | 0.553527 | ||||||||
\(962\) | 3.10410 | 0.100080 | ||||||||
\(963\) | −38.4237 | −1.23819 | ||||||||
\(964\) | 24.2931 | 0.782429 | ||||||||
\(965\) | −3.51113 | −0.113027 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.7430 | 0.827840 | 0.413920 | − | 0.910313i | \(-0.364159\pi\) | ||||
0.413920 | + | 0.910313i | \(0.364159\pi\) | |||||||
\(968\) | −8.39703 | −0.269891 | ||||||||
\(969\) | −33.6861 | −1.08215 | ||||||||
\(970\) | 18.1600 | 0.583084 | ||||||||
\(971\) | 22.0733 | 0.708365 | 0.354182 | − | 0.935176i | \(-0.384759\pi\) | ||||
0.354182 | + | 0.935176i | \(0.384759\pi\) | |||||||
\(972\) | −16.3140 | −0.523271 | ||||||||
\(973\) | −0.755667 | −0.0242256 | ||||||||
\(974\) | 18.5292 | 0.593715 | ||||||||
\(975\) | −2.28814 | −0.0732792 | ||||||||
\(976\) | 0.718868 | 0.0230104 | ||||||||
\(977\) | 4.11932 | 0.131789 | 0.0658944 | − | 0.997827i | \(-0.479010\pi\) | ||||
0.0658944 | + | 0.997827i | \(0.479010\pi\) | |||||||
\(978\) | −34.5537 | −1.10491 | ||||||||
\(979\) | 19.9502 | 0.637612 | ||||||||
\(980\) | −6.98902 | −0.223256 | ||||||||
\(981\) | −22.6922 | −0.724506 | ||||||||
\(982\) | −42.7858 | −1.36535 | ||||||||
\(983\) | −12.9570 | −0.413263 | −0.206631 | − | 0.978419i | \(-0.566250\pi\) | ||||
−0.206631 | + | 0.978419i | \(0.566250\pi\) | |||||||
\(984\) | 28.2533 | 0.900681 | ||||||||
\(985\) | 16.3731 | 0.521691 | ||||||||
\(986\) | 22.2653 | 0.709071 | ||||||||
\(987\) | 2.54335 | 0.0809557 | ||||||||
\(988\) | 4.13874 | 0.131671 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 7.70316 | 0.244822 | ||||||||
\(991\) | 9.28169 | 0.294842 | 0.147421 | − | 0.989074i | \(-0.452903\pi\) | ||||
0.147421 | + | 0.989074i | \(0.452903\pi\) | |||||||
\(992\) | 6.93969 | 0.220335 | ||||||||
\(993\) | −25.0711 | −0.795606 | ||||||||
\(994\) | 0.137460 | 0.00435997 | ||||||||
\(995\) | 24.3835 | 0.773010 | ||||||||
\(996\) | −33.4701 | −1.06054 | ||||||||
\(997\) | −12.6283 | −0.399941 | −0.199971 | − | 0.979802i | \(-0.564085\pi\) | ||||
−0.199971 | + | 0.979802i | \(0.564085\pi\) | |||||||
\(998\) | −3.23317 | −0.102344 | ||||||||
\(999\) | −18.7164 | −0.592162 |
(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 | 5290.2.a.bl.1.13 | 15 | ||
23.17 | odd | 22 | 230.2.g.d.151.3 | yes | 30 | ||
23.19 | odd | 22 | 230.2.g.d.131.3 | ✓ | 30 | ||
23.22 | odd | 2 | 5290.2.a.bk.1.13 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.2.g.d.131.3 | ✓ | 30 | 23.19 | odd | 22 | ||
230.2.g.d.151.3 | yes | 30 | 23.17 | odd | 22 | ||
5290.2.a.bk.1.13 | 15 | 23.22 | odd | 2 | |||
5290.2.a.bl.1.13 | 15 | 1.1 | even | 1 | trivial |