Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,2,Mod(1133,1134)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1134, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1134.1133");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.05503558921\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 56 x^{14} - 252 x^{13} + 962 x^{12} - 2860 x^{11} + 7240 x^{10} - 15036 x^{9} + 26533 x^{8} - 38796 x^{7} + 47500 x^{6} - 47396 x^{5} + 38144 x^{4} + \cdots + 457 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1133.9 | ||
Root | \(0.500000 + 2.18553i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.1133 |
Dual form | 1134.2.d.b.1133.1 |
$q$-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 \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −3.79792 | −1.69848 | −0.849240 | − | 0.528007i | \(-0.822940\pi\) | ||||
−0.849240 | + | 0.528007i | \(0.822940\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.59077 | − | 0.536572i | 0.979219 | − | 0.202805i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 3.79792i | − | 1.20101i | ||||||
\(11\) | 1.61401i | 0.486644i | 0.969946 | + | 0.243322i | \(0.0782371\pi\) | ||||
−0.969946 | + | 0.243322i | \(0.921763\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.11225i | − | 1.41788i | −0.705268 | − | 0.708941i | \(-0.749173\pi\) | ||
0.705268 | − | 0.708941i | \(-0.250827\pi\) | |||||||
\(14\) | 0.536572 | + | 2.59077i | 0.143405 | + | 0.692412i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.33198 | 0.565587 | 0.282794 | − | 0.959181i | \(-0.408739\pi\) | ||||
0.282794 | + | 0.959181i | \(0.408739\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.24621i | 0.974148i | 0.873361 | + | 0.487074i | \(0.161936\pi\) | ||||
−0.873361 | + | 0.487074i | \(0.838064\pi\) | |||||||
\(20\) | 3.79792 | 0.849240 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.61401 | −0.344109 | ||||||||
\(23\) | 2.62863i | 0.548106i | 0.961715 | + | 0.274053i | \(0.0883645\pi\) | ||||
−0.961715 | + | 0.274053i | \(0.911636\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.42418 | 1.88484 | ||||||||
\(26\) | 5.11225 | 1.00259 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.59077 | + | 0.536572i | −0.489610 | + | 0.101403i | ||||
\(29\) | 4.01461i | 0.745495i | 0.927933 | + | 0.372747i | \(0.121584\pi\) | ||||
−0.927933 | + | 0.372747i | \(0.878416\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.98863i | 1.43480i | 0.696661 | + | 0.717401i | \(0.254668\pi\) | ||||
−0.696661 | + | 0.717401i | \(0.745332\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.33198i | 0.399931i | ||||||||
\(35\) | −9.83953 | + | 2.03786i | −1.66318 | + | 0.344461i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.74907 | −0.945141 | −0.472570 | − | 0.881293i | \(-0.656674\pi\) | ||||
−0.472570 | + | 0.881293i | \(0.656674\pi\) | |||||||
\(38\) | −4.24621 | −0.688826 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.79792i | 0.600504i | ||||||||
\(41\) | 8.51737 | 1.33019 | 0.665095 | − | 0.746759i | \(-0.268391\pi\) | ||||
0.665095 | + | 0.746759i | \(0.268391\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.25725 | 1.41172 | 0.705859 | − | 0.708352i | \(-0.250561\pi\) | ||||
0.705859 | + | 0.708352i | \(0.250561\pi\) | |||||||
\(44\) | − | 1.61401i | − | 0.243322i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.62863 | −0.387570 | ||||||||
\(47\) | −9.69576 | −1.41427 | −0.707136 | − | 0.707078i | \(-0.750013\pi\) | ||||
−0.707136 | + | 0.707078i | \(0.750013\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.42418 | − | 2.78027i | 0.917740 | − | 0.397181i | ||||
\(50\) | 9.42418i | 1.33278i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.11225i | 0.708941i | ||||||||
\(53\) | − | 2.19615i | − | 0.301665i | −0.988559 | − | 0.150832i | \(-0.951805\pi\) | ||
0.988559 | − | 0.150832i | \(-0.0481954\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 6.12989i | − | 0.826555i | ||||||
\(56\) | −0.536572 | − | 2.59077i | −0.0717024 | − | 0.346206i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.01461 | −0.527144 | ||||||||
\(59\) | −1.46594 | −0.190849 | −0.0954247 | − | 0.995437i | \(-0.530421\pi\) | ||||
−0.0954247 | + | 0.995437i | \(0.530421\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.4152i | 1.84568i | 0.385186 | + | 0.922839i | \(0.374137\pi\) | ||||
−0.385186 | + | 0.922839i | \(0.625863\pi\) | |||||||
\(62\) | −7.98863 | −1.01456 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 19.4159i | 2.40824i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.78094 | −0.706255 | −0.353127 | − | 0.935575i | \(-0.614882\pi\) | ||||
−0.353127 | + | 0.935575i | \(0.614882\pi\) | |||||||
\(68\) | −2.33198 | −0.282794 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.03786 | − | 9.83953i | −0.243570 | − | 1.17605i | ||||
\(71\) | 15.6668i | 1.85931i | 0.368432 | + | 0.929655i | \(0.379895\pi\) | ||||
−0.368432 | + | 0.929655i | \(0.620105\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.65133i | 0.895521i | 0.894154 | + | 0.447760i | \(0.147778\pi\) | ||||
−0.894154 | + | 0.447760i | \(0.852222\pi\) | |||||||
\(74\) | − | 5.74907i | − | 0.668315i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 4.24621i | − | 0.487074i | ||||||
\(77\) | 0.866035 | + | 4.18154i | 0.0986938 | + | 0.476531i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.64324 | −0.184879 | −0.0924394 | − | 0.995718i | \(-0.529466\pi\) | ||||
−0.0924394 | + | 0.995718i | \(0.529466\pi\) | |||||||
\(80\) | −3.79792 | −0.424620 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.51737i | 0.940586i | ||||||||
\(83\) | 3.02145 | 0.331647 | 0.165824 | − | 0.986155i | \(-0.446972\pi\) | ||||
0.165824 | + | 0.986155i | \(0.446972\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.85666 | −0.960639 | ||||||||
\(86\) | 9.25725i | 0.998235i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.61401 | 0.172055 | ||||||||
\(89\) | 17.5236 | 1.85750 | 0.928752 | − | 0.370703i | \(-0.120883\pi\) | ||||
0.928752 | + | 0.370703i | \(0.120883\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.74309 | − | 13.2447i | −0.287554 | − | 1.38842i | ||||
\(92\) | − | 2.62863i | − | 0.274053i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 9.69576i | − | 1.00004i | ||||||
\(95\) | − | 16.1268i | − | 1.65457i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10.3761i | − | 1.05353i | −0.850010 | − | 0.526767i | \(-0.823404\pi\) | ||
0.850010 | − | 0.526767i | \(-0.176596\pi\) | |||||||
\(98\) | 2.78027 | + | 6.42418i | 0.280850 | + | 0.648940i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9.42418 | −0.942418 | ||||||||
\(101\) | 7.70683 | 0.766858 | 0.383429 | − | 0.923570i | \(-0.374743\pi\) | ||||
0.383429 | + | 0.923570i | \(0.374743\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.93188i | 0.288887i | 0.989513 | + | 0.144444i | \(0.0461392\pi\) | ||||
−0.989513 | + | 0.144444i | \(0.953861\pi\) | |||||||
\(104\) | −5.11225 | −0.501297 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.19615 | 0.213309 | ||||||||
\(107\) | 12.3166i | 1.19069i | 0.803470 | + | 0.595345i | \(0.202985\pi\) | ||||
−0.803470 | + | 0.595345i | \(0.797015\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.47720 | 0.141490 | 0.0707452 | − | 0.997494i | \(-0.477462\pi\) | ||||
0.0707452 | + | 0.997494i | \(0.477462\pi\) | |||||||
\(110\) | 6.12989 | 0.584462 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.59077 | − | 0.536572i | 0.244805 | − | 0.0507013i | ||||
\(113\) | − | 6.93237i | − | 0.652142i | −0.945345 | − | 0.326071i | \(-0.894275\pi\) | ||
0.945345 | − | 0.326071i | \(-0.105725\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 9.98331i | − | 0.930948i | ||||||
\(116\) | − | 4.01461i | − | 0.372747i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 1.46594i | − | 0.134951i | ||||||
\(119\) | 6.04162 | − | 1.25127i | 0.553834 | − | 0.114704i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.39496 | 0.763178 | ||||||||
\(122\) | −14.4152 | −1.30509 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 7.98863i | − | 0.717401i | ||||||
\(125\) | −16.8027 | −1.50288 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.7727 | 1.31086 | 0.655430 | − | 0.755256i | \(-0.272487\pi\) | ||||
0.655430 | + | 0.755256i | \(0.272487\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −19.4159 | −1.70289 | ||||||||
\(131\) | −7.70683 | −0.673348 | −0.336674 | − | 0.941621i | \(-0.609302\pi\) | ||||
−0.336674 | + | 0.941621i | \(0.609302\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.27840 | + | 11.0010i | 0.197562 | + | 0.953904i | ||||
\(134\) | − | 5.78094i | − | 0.499397i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 2.33198i | − | 0.199965i | ||||||
\(137\) | − | 0.476309i | − | 0.0406939i | −0.999793 | − | 0.0203469i | \(-0.993523\pi\) | ||
0.999793 | − | 0.0203469i | \(-0.00647708\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.83702i | 0.664727i | 0.943151 | + | 0.332364i | \(0.107846\pi\) | ||||
−0.943151 | + | 0.332364i | \(0.892154\pi\) | |||||||
\(140\) | 9.83953 | − | 2.03786i | 0.831592 | − | 0.172230i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −15.6668 | −1.31473 | ||||||||
\(143\) | 8.25124 | 0.690003 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 15.2472i | − | 1.26621i | ||||||
\(146\) | −7.65133 | −0.633229 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.74907 | 0.472570 | ||||||||
\(149\) | − | 19.7434i | − | 1.61744i | −0.588191 | − | 0.808722i | \(-0.700160\pi\) | ||
0.588191 | − | 0.808722i | \(-0.299840\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.1750 | 0.990788 | 0.495394 | − | 0.868668i | \(-0.335024\pi\) | ||||
0.495394 | + | 0.868668i | \(0.335024\pi\) | |||||||
\(152\) | 4.24621 | 0.344413 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.18154 | + | 0.866035i | −0.336958 | + | 0.0697871i | ||||
\(155\) | − | 30.3402i | − | 2.43698i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 10.0794i | − | 0.804426i | −0.915546 | − | 0.402213i | \(-0.868241\pi\) | ||
0.915546 | − | 0.402213i | \(-0.131759\pi\) | |||||||
\(158\) | − | 1.64324i | − | 0.130729i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 3.79792i | − | 0.300252i | ||||||
\(161\) | 1.41045 | + | 6.81017i | 0.111159 | + | 0.536716i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.05934 | −0.396278 | −0.198139 | − | 0.980174i | \(-0.563490\pi\) | ||||
−0.198139 | + | 0.980174i | \(0.563490\pi\) | |||||||
\(164\) | −8.51737 | −0.665095 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.02145i | 0.234510i | ||||||||
\(167\) | −2.38747 | −0.184748 | −0.0923740 | − | 0.995724i | \(-0.529446\pi\) | ||||
−0.0923740 | + | 0.995724i | \(0.529446\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.1351 | −1.01039 | ||||||||
\(170\) | − | 8.85666i | − | 0.679274i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.25725 | −0.705859 | ||||||||
\(173\) | −0.232053 | −0.0176427 | −0.00882134 | − | 0.999961i | \(-0.502808\pi\) | ||||
−0.00882134 | + | 0.999961i | \(0.502808\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 24.4159 | − | 5.05675i | 1.84567 | − | 0.382254i | ||||
\(176\) | 1.61401i | 0.121661i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 17.5236i | 1.31345i | ||||||||
\(179\) | − | 24.4451i | − | 1.82711i | −0.406711 | − | 0.913557i | \(-0.633325\pi\) | ||
0.406711 | − | 0.913557i | \(-0.366675\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.5527i | 0.784373i | 0.919886 | + | 0.392187i | \(0.128281\pi\) | ||||
−0.919886 | + | 0.392187i | \(0.871719\pi\) | |||||||
\(182\) | 13.2447 | − | 2.74309i | 0.981759 | − | 0.203331i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.62863 | 0.193785 | ||||||||
\(185\) | 21.8345 | 1.60530 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.76384i | 0.275239i | ||||||||
\(188\) | 9.69576 | 0.707136 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 16.1268 | 1.16996 | ||||||||
\(191\) | 12.1732i | 0.880825i | 0.897795 | + | 0.440413i | \(0.145168\pi\) | ||||
−0.897795 | + | 0.440413i | \(0.854832\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24.3784 | −1.75479 | −0.877397 | − | 0.479765i | \(-0.840722\pi\) | ||||
−0.877397 | + | 0.479765i | \(0.840722\pi\) | |||||||
\(194\) | 10.3761 | 0.744961 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.42418 | + | 2.78027i | −0.458870 | + | 0.198591i | ||||
\(197\) | 2.10759i | 0.150159i | 0.997178 | + | 0.0750797i | \(0.0239211\pi\) | ||||
−0.997178 | + | 0.0750797i | \(0.976079\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.1753i | 1.35930i | 0.733537 | + | 0.679650i | \(0.237868\pi\) | ||||
−0.733537 | + | 0.679650i | \(0.762132\pi\) | |||||||
\(200\) | − | 9.42418i | − | 0.666390i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.70683i | 0.542250i | ||||||||
\(203\) | 2.15413 | + | 10.4009i | 0.151190 | + | 0.730003i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −32.3483 | −2.25930 | ||||||||
\(206\) | −2.93188 | −0.204274 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 5.11225i | − | 0.354470i | ||||||
\(209\) | −6.85345 | −0.474063 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.67511 | 0.597220 | 0.298610 | − | 0.954375i | \(-0.403477\pi\) | ||||
0.298610 | + | 0.954375i | \(0.403477\pi\) | |||||||
\(212\) | 2.19615i | 0.150832i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −12.3166 | −0.841945 | ||||||||
\(215\) | −35.1583 | −2.39778 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.28648 | + | 20.6967i | 0.290985 | + | 1.40498i | ||||
\(218\) | 1.47720i | 0.100049i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.12989i | 0.413277i | ||||||||
\(221\) | − | 11.9216i | − | 0.801936i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.71748i | 0.248941i | 0.992223 | + | 0.124470i | \(0.0397232\pi\) | ||||
−0.992223 | + | 0.124470i | \(0.960277\pi\) | |||||||
\(224\) | 0.536572 | + | 2.59077i | 0.0358512 | + | 0.173103i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.93237 | 0.461134 | ||||||||
\(227\) | −3.21943 | −0.213681 | −0.106841 | − | 0.994276i | \(-0.534073\pi\) | ||||
−0.106841 | + | 0.994276i | \(0.534073\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.99060i | 0.594116i | 0.954859 | + | 0.297058i | \(0.0960054\pi\) | ||||
−0.954859 | + | 0.297058i | \(0.903995\pi\) | |||||||
\(230\) | 9.98331 | 0.658280 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.01461 | 0.263572 | ||||||||
\(233\) | − | 10.1604i | − | 0.665630i | −0.942992 | − | 0.332815i | \(-0.892002\pi\) | ||
0.942992 | − | 0.332815i | \(-0.107998\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 36.8237 | 2.40211 | ||||||||
\(236\) | 1.46594 | 0.0954247 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.25127 | + | 6.04162i | 0.0811080 | + | 0.391620i | ||||
\(239\) | − | 3.59851i | − | 0.232768i | −0.993204 | − | 0.116384i | \(-0.962870\pi\) | ||
0.993204 | − | 0.116384i | \(-0.0371304\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 23.2144i | − | 1.49537i | −0.664054 | − | 0.747685i | \(-0.731165\pi\) | ||
0.664054 | − | 0.747685i | \(-0.268835\pi\) | |||||||
\(242\) | 8.39496i | 0.539648i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 14.4152i | − | 0.922839i | ||||||
\(245\) | −24.3985 | + | 10.5592i | −1.55876 | + | 0.674605i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.7077 | 1.38123 | ||||||||
\(248\) | 7.98863 | 0.507279 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 16.8027i | − | 1.06269i | ||||||
\(251\) | 25.9199 | 1.63605 | 0.818026 | − | 0.575181i | \(-0.195068\pi\) | ||||
0.818026 | + | 0.575181i | \(0.195068\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.24264 | −0.266733 | ||||||||
\(254\) | 14.7727i | 0.926919i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.29638 | 0.392757 | 0.196379 | − | 0.980528i | \(-0.437082\pi\) | ||||
0.196379 | + | 0.980528i | \(0.437082\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.8945 | + | 3.08479i | −0.925500 | + | 0.191679i | ||||
\(260\) | − | 19.4159i | − | 1.20412i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 7.70683i | − | 0.476129i | ||||||
\(263\) | − | 26.6413i | − | 1.64277i | −0.570374 | − | 0.821385i | \(-0.693202\pi\) | ||
0.570374 | − | 0.821385i | \(-0.306798\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.34081i | 0.512372i | ||||||||
\(266\) | −11.0010 | + | 2.27840i | −0.674512 | + | 0.139697i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.78094 | 0.353127 | ||||||||
\(269\) | −3.27493 | −0.199676 | −0.0998379 | − | 0.995004i | \(-0.531832\pi\) | ||||
−0.0998379 | + | 0.995004i | \(0.531832\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.5466i | 1.00514i | 0.864538 | + | 0.502568i | \(0.167611\pi\) | ||||
−0.864538 | + | 0.502568i | \(0.832389\pi\) | |||||||
\(272\) | 2.33198 | 0.141397 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.476309 | 0.0287749 | ||||||||
\(275\) | 15.2108i | 0.917244i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.98363 | −0.419606 | −0.209803 | − | 0.977744i | \(-0.567282\pi\) | ||||
−0.209803 | + | 0.977744i | \(0.567282\pi\) | |||||||
\(278\) | −7.83702 | −0.470033 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.03786 | + | 9.83953i | 0.121785 | + | 0.588025i | ||||
\(281\) | − | 2.15864i | − | 0.128773i | −0.997925 | − | 0.0643867i | \(-0.979491\pi\) | ||
0.997925 | − | 0.0643867i | \(-0.0205091\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.34613i | 0.377238i | 0.982050 | + | 0.188619i | \(0.0604012\pi\) | ||||
−0.982050 | + | 0.188619i | \(0.939599\pi\) | |||||||
\(284\) | − | 15.6668i | − | 0.929655i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.25124i | 0.487906i | ||||||||
\(287\) | 22.0665 | − | 4.57018i | 1.30255 | − | 0.269769i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.5619 | −0.680111 | ||||||||
\(290\) | 15.2472 | 0.895344 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 7.65133i | − | 0.447760i | ||||||
\(293\) | −27.7945 | −1.62377 | −0.811886 | − | 0.583816i | \(-0.801559\pi\) | ||||
−0.811886 | + | 0.583816i | \(0.801559\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.56753 | 0.324154 | ||||||||
\(296\) | 5.74907i | 0.334158i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 19.7434 | 1.14371 | ||||||||
\(299\) | 13.4382 | 0.777150 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.9834 | − | 4.96718i | 1.38238 | − | 0.286304i | ||||
\(302\) | 12.1750i | 0.700593i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.24621i | 0.243537i | ||||||||
\(305\) | − | 54.7478i | − | 3.13485i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.30829i | 0.417106i | 0.978011 | + | 0.208553i | \(0.0668754\pi\) | ||||
−0.978011 | + | 0.208553i | \(0.933125\pi\) | |||||||
\(308\) | −0.866035 | − | 4.18154i | −0.0493469 | − | 0.238265i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 30.3402 | 1.72321 | ||||||||
\(311\) | −3.65543 | −0.207281 | −0.103640 | − | 0.994615i | \(-0.533049\pi\) | ||||
−0.103640 | + | 0.994615i | \(0.533049\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 20.1737i | − | 1.14029i | −0.821545 | − | 0.570143i | \(-0.806888\pi\) | ||
0.821545 | − | 0.570143i | \(-0.193112\pi\) | |||||||
\(314\) | 10.0794 | 0.568815 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.64324 | 0.0924394 | ||||||||
\(317\) | 12.3330i | 0.692688i | 0.938108 | + | 0.346344i | \(0.112577\pi\) | ||||
−0.938108 | + | 0.346344i | \(0.887423\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.47964 | −0.362790 | ||||||||
\(320\) | 3.79792 | 0.212310 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.81017 | + | 1.41045i | −0.379516 | + | 0.0786011i | ||||
\(323\) | 9.90206i | 0.550966i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 48.1787i | − | 2.67247i | ||||||
\(326\) | − | 5.05934i | − | 0.280211i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 8.51737i | − | 0.470293i | ||||||
\(329\) | −25.1195 | + | 5.20247i | −1.38488 | + | 0.286822i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.5152 | −1.23755 | −0.618773 | − | 0.785570i | \(-0.712370\pi\) | ||||
−0.618773 | + | 0.785570i | \(0.712370\pi\) | |||||||
\(332\) | −3.02145 | −0.165824 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 2.38747i | − | 0.130637i | ||||||
\(335\) | 21.9555 | 1.19956 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.78726 | −0.533146 | −0.266573 | − | 0.963815i | \(-0.585891\pi\) | ||||
−0.266573 | + | 0.963815i | \(0.585891\pi\) | |||||||
\(338\) | − | 13.1351i | − | 0.714453i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8.85666 | 0.480320 | ||||||||
\(341\) | −12.8938 | −0.698237 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.1518 | − | 10.6501i | 0.818118 | − | 0.575050i | ||||
\(344\) | − | 9.25725i | − | 0.499118i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 0.232053i | − | 0.0124753i | ||||||
\(347\) | 10.8185i | 0.580765i | 0.956911 | + | 0.290383i | \(0.0937826\pi\) | ||||
−0.956911 | + | 0.290383i | \(0.906217\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.87806i | 0.528760i | 0.964419 | + | 0.264380i | \(0.0851674\pi\) | ||||
−0.964419 | + | 0.264380i | \(0.914833\pi\) | |||||||
\(350\) | 5.05675 | + | 24.4159i | 0.270295 | + | 1.30508i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.61401 | −0.0860273 | ||||||||
\(353\) | 10.4167 | 0.554427 | 0.277213 | − | 0.960808i | \(-0.410589\pi\) | ||||
0.277213 | + | 0.960808i | \(0.410589\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 59.5013i | − | 3.15800i | ||||||
\(356\) | −17.5236 | −0.928752 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 24.4451 | 1.29196 | ||||||||
\(359\) | − | 9.97078i | − | 0.526237i | −0.964763 | − | 0.263119i | \(-0.915249\pi\) | ||
0.964763 | − | 0.263119i | \(-0.0847511\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.969696 | 0.0510366 | ||||||||
\(362\) | −10.5527 | −0.554636 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.74309 | + | 13.2447i | 0.143777 | + | 0.694208i | ||||
\(365\) | − | 29.0591i | − | 1.52102i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.2534i | 1.26602i | 0.774144 | + | 0.633010i | \(0.218181\pi\) | ||||
−0.774144 | + | 0.633010i | \(0.781819\pi\) | |||||||
\(368\) | 2.62863i | 0.137027i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 21.8345i | 1.13512i | ||||||||
\(371\) | −1.17839 | − | 5.68973i | −0.0611791 | − | 0.295396i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.65153 | −0.137291 | −0.0686455 | − | 0.997641i | \(-0.521868\pi\) | ||||
−0.0686455 | + | 0.997641i | \(0.521868\pi\) | |||||||
\(374\) | −3.76384 | −0.194624 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.69576i | 0.500021i | ||||||||
\(377\) | 20.5237 | 1.05702 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.4305 | −0.998078 | −0.499039 | − | 0.866580i | \(-0.666314\pi\) | ||||
−0.499039 | + | 0.866580i | \(0.666314\pi\) | |||||||
\(380\) | 16.1268i | 0.827285i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12.1732 | −0.622838 | ||||||||
\(383\) | 21.2320 | 1.08490 | 0.542452 | − | 0.840087i | \(-0.317496\pi\) | ||||
0.542452 | + | 0.840087i | \(0.317496\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.28913 | − | 15.8811i | −0.167630 | − | 0.809378i | ||||
\(386\) | − | 24.3784i | − | 1.24083i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10.3761i | 0.526767i | ||||||||
\(389\) | 4.47156i | 0.226717i | 0.993554 | + | 0.113359i | \(0.0361609\pi\) | ||||
−0.993554 | + | 0.113359i | \(0.963839\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.12989i | 0.310002i | ||||||||
\(392\) | −2.78027 | − | 6.42418i | −0.140425 | − | 0.324470i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.10759 | −0.106179 | ||||||||
\(395\) | 6.24088 | 0.314013 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 35.0315i | − | 1.75818i | −0.476656 | − | 0.879090i | \(-0.658151\pi\) | ||
0.476656 | − | 0.879090i | \(-0.341849\pi\) | |||||||
\(398\) | −19.1753 | −0.961170 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.42418 | 0.471209 | ||||||||
\(401\) | 21.3229i | 1.06482i | 0.846488 | + | 0.532408i | \(0.178713\pi\) | ||||
−0.846488 | + | 0.532408i | \(0.821287\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 40.8399 | 2.03438 | ||||||||
\(404\) | −7.70683 | −0.383429 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.4009 | + | 2.15413i | −0.516190 | + | 0.106908i | ||||
\(407\) | − | 9.27908i | − | 0.459947i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.0927i | 1.19131i | 0.803241 | + | 0.595654i | \(0.203107\pi\) | ||||
−0.803241 | + | 0.595654i | \(0.796893\pi\) | |||||||
\(410\) | − | 32.3483i | − | 1.59757i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 2.93188i | − | 0.144444i | ||||||
\(413\) | −3.79792 | + | 0.786583i | −0.186883 | + | 0.0387052i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.4752 | −0.563297 | ||||||||
\(416\) | 5.11225 | 0.250648 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 6.85345i | − | 0.335213i | ||||||
\(419\) | 25.8304 | 1.26190 | 0.630948 | − | 0.775825i | \(-0.282666\pi\) | ||||
0.630948 | + | 0.775825i | \(0.282666\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.0648 | −0.831686 | −0.415843 | − | 0.909436i | \(-0.636513\pi\) | ||||
−0.415843 | + | 0.909436i | \(0.636513\pi\) | |||||||
\(422\) | 8.67511i | 0.422298i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.19615 | −0.106655 | ||||||||
\(425\) | 21.9770 | 1.06604 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.73479 | + | 37.3465i | 0.374313 | + | 1.80732i | ||||
\(428\) | − | 12.3166i | − | 0.595345i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 35.1583i | − | 1.69548i | ||||||
\(431\) | 27.4224i | 1.32089i | 0.750874 | + | 0.660446i | \(0.229633\pi\) | ||||
−0.750874 | + | 0.660446i | \(0.770367\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.1385i | 1.01585i | 0.861401 | + | 0.507925i | \(0.169587\pi\) | ||||
−0.861401 | + | 0.507925i | \(0.830413\pi\) | |||||||
\(434\) | −20.6967 | + | 4.28648i | −0.993474 | + | 0.205757i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.47720 | −0.0707452 | ||||||||
\(437\) | −11.1617 | −0.533937 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 25.5428i | − | 1.21909i | −0.792750 | − | 0.609546i | \(-0.791352\pi\) | ||
0.792750 | − | 0.609546i | \(-0.208648\pi\) | |||||||
\(440\) | −6.12989 | −0.292231 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.9216 | 0.567054 | ||||||||
\(443\) | − | 30.9184i | − | 1.46898i | −0.678620 | − | 0.734490i | \(-0.737422\pi\) | ||
0.678620 | − | 0.734490i | \(-0.262578\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −66.5534 | −3.15493 | ||||||||
\(446\) | −3.71748 | −0.176028 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.59077 | + | 0.536572i | −0.122402 | + | 0.0253506i | ||||
\(449\) | − | 1.16428i | − | 0.0549456i | −0.999623 | − | 0.0274728i | \(-0.991254\pi\) | ||
0.999623 | − | 0.0274728i | \(-0.00874596\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.7472i | 0.647328i | ||||||||
\(452\) | 6.93237i | 0.326071i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 3.21943i | − | 0.151095i | ||||||
\(455\) | 10.4180 | + | 50.3021i | 0.488404 | + | 2.35820i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.21166 | 0.337347 | 0.168674 | − | 0.985672i | \(-0.446052\pi\) | ||||
0.168674 | + | 0.985672i | \(0.446052\pi\) | |||||||
\(458\) | −8.99060 | −0.420103 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9.98331i | 0.465474i | ||||||||
\(461\) | −28.6513 | −1.33442 | −0.667211 | − | 0.744868i | \(-0.732512\pi\) | ||||
−0.667211 | + | 0.744868i | \(0.732512\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.3402 | −1.31708 | −0.658540 | − | 0.752546i | \(-0.728826\pi\) | ||||
−0.658540 | + | 0.752546i | \(0.728826\pi\) | |||||||
\(464\) | 4.01461i | 0.186374i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.1604 | 0.470671 | ||||||||
\(467\) | −10.2188 | −0.472867 | −0.236434 | − | 0.971648i | \(-0.575979\pi\) | ||||
−0.236434 | + | 0.971648i | \(0.575979\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.9771 | + | 3.10189i | −0.691578 | + | 0.143232i | ||||
\(470\) | 36.8237i | 1.69855i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.46594i | 0.0674754i | ||||||||
\(473\) | 14.9413i | 0.687003i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 40.0171i | 1.83611i | ||||||||
\(476\) | −6.04162 | + | 1.25127i | −0.276917 | + | 0.0573520i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.59851 | 0.164592 | ||||||||
\(479\) | −12.6276 | −0.576972 | −0.288486 | − | 0.957484i | \(-0.593152\pi\) | ||||
−0.288486 | + | 0.957484i | \(0.593152\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.3906i | 1.34010i | ||||||||
\(482\) | 23.2144 | 1.05739 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.39496 | −0.381589 | ||||||||
\(485\) | 39.4076i | 1.78941i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.8841 | 0.991664 | 0.495832 | − | 0.868418i | \(-0.334863\pi\) | ||||
0.495832 | + | 0.868418i | \(0.334863\pi\) | |||||||
\(488\) | 14.4152 | 0.652546 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −10.5592 | − | 24.3985i | −0.477018 | − | 1.10221i | ||||
\(491\) | 7.60770i | 0.343330i | 0.985155 | + | 0.171665i | \(0.0549147\pi\) | ||||
−0.985155 | + | 0.171665i | \(0.945085\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.36198i | 0.421642i | ||||||||
\(494\) | 21.7077i | 0.976674i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.98863i | 0.358700i | ||||||||
\(497\) | 8.40638 | + | 40.5891i | 0.377078 | + | 1.82067i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.85666 | 0.172648 | 0.0863238 | − | 0.996267i | \(-0.472488\pi\) | ||||
0.0863238 | + | 0.996267i | \(0.472488\pi\) | |||||||
\(500\) | 16.8027 | 0.751439 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 25.9199i | 1.15686i | ||||||||
\(503\) | −2.16549 | −0.0965545 | −0.0482773 | − | 0.998834i | \(-0.515373\pi\) | ||||
−0.0482773 | + | 0.998834i | \(0.515373\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −29.2699 | −1.30249 | ||||||||
\(506\) | − | 4.24264i | − | 0.188608i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −14.7727 | −0.655430 | ||||||||
\(509\) | 25.8985 | 1.14793 | 0.573966 | − | 0.818879i | \(-0.305404\pi\) | ||||
0.573966 | + | 0.818879i | \(0.305404\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.10549 | + | 19.8228i | 0.181616 | + | 0.876911i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.29638i | 0.277721i | ||||||||
\(515\) | − | 11.1351i | − | 0.490669i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 15.6491i | − | 0.688246i | ||||||
\(518\) | −3.08479 | − | 14.8945i | −0.135538 | − | 0.654427i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 19.4159 | 0.851443 | ||||||||
\(521\) | −29.9192 | −1.31079 | −0.655393 | − | 0.755288i | \(-0.727497\pi\) | ||||
−0.655393 | + | 0.755288i | \(0.727497\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.7497i | 0.601234i | 0.953745 | + | 0.300617i | \(0.0971925\pi\) | ||||
−0.953745 | + | 0.300617i | \(0.902807\pi\) | |||||||
\(524\) | 7.70683 | 0.336674 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 26.6413 | 1.16161 | ||||||||
\(527\) | 18.6293i | 0.811505i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.0903 | 0.699579 | ||||||||
\(530\) | −8.34081 | −0.362301 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.27840 | − | 11.0010i | −0.0987810 | − | 0.476952i | ||||
\(533\) | − | 43.5429i | − | 1.88605i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 46.7774i | − | 2.02236i | ||||||
\(536\) | 5.78094i | 0.249699i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 3.27493i | − | 0.141192i | ||||||
\(539\) | 4.48739 | + | 10.3687i | 0.193286 | + | 0.446612i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −37.3402 | −1.60538 | −0.802690 | − | 0.596397i | \(-0.796599\pi\) | ||||
−0.802690 | + | 0.596397i | \(0.796599\pi\) | |||||||
\(542\) | −16.5466 | −0.710738 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.33198i | 0.0999827i | ||||||||
\(545\) | −5.61029 | −0.240319 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.35411 | −0.0578975 | −0.0289488 | − | 0.999581i | \(-0.509216\pi\) | ||||
−0.0289488 | + | 0.999581i | \(0.509216\pi\) | |||||||
\(548\) | 0.476309i | 0.0203469i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −15.2108 | −0.648589 | ||||||||
\(551\) | −17.0469 | −0.726222 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.25725 | + | 0.881715i | −0.181037 | + | 0.0374944i | ||||
\(554\) | − | 6.98363i | − | 0.296706i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 7.83702i | − | 0.332364i | ||||||
\(557\) | − | 21.1944i | − | 0.898035i | −0.893523 | − | 0.449018i | \(-0.851774\pi\) | ||
0.893523 | − | 0.449018i | \(-0.148226\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 47.3253i | − | 2.00165i | ||||||
\(560\) | −9.83953 | + | 2.03786i | −0.415796 | + | 0.0861151i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.15864 | 0.0910566 | ||||||||
\(563\) | −32.1608 | −1.35542 | −0.677709 | − | 0.735330i | \(-0.737027\pi\) | ||||
−0.677709 | + | 0.735330i | \(0.737027\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 26.3286i | 1.10765i | ||||||||
\(566\) | −6.34613 | −0.266748 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 15.6668 | 0.657365 | ||||||||
\(569\) | 28.3101i | 1.18682i | 0.804901 | + | 0.593410i | \(0.202219\pi\) | ||||
−0.804901 | + | 0.593410i | \(0.797781\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.6999 | 0.573324 | 0.286662 | − | 0.958032i | \(-0.407454\pi\) | ||||
0.286662 | + | 0.958032i | \(0.407454\pi\) | |||||||
\(572\) | −8.25124 | −0.345002 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.57018 | + | 22.0665i | 0.190756 | + | 0.921039i | ||||
\(575\) | 24.7727i | 1.03309i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.1791i | 0.756804i | 0.925641 | + | 0.378402i | \(0.123526\pi\) | ||||
−0.925641 | + | 0.378402i | \(0.876474\pi\) | |||||||
\(578\) | − | 11.5619i | − | 0.480911i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 15.2472i | 0.633104i | ||||||||
\(581\) | 7.82789 | − | 1.62123i | 0.324756 | − | 0.0672598i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.54462 | 0.146803 | ||||||||
\(584\) | 7.65133 | 0.316614 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 27.7945i | − | 1.14818i | ||||||
\(587\) | 11.0814 | 0.457378 | 0.228689 | − | 0.973500i | \(-0.426556\pi\) | ||||
0.228689 | + | 0.973500i | \(0.426556\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −33.9214 | −1.39771 | ||||||||
\(590\) | 5.56753i | 0.229211i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.74907 | −0.236285 | ||||||||
\(593\) | 32.4304 | 1.33175 | 0.665877 | − | 0.746061i | \(-0.268057\pi\) | ||||
0.665877 | + | 0.746061i | \(0.268057\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22.9456 | + | 4.75223i | −0.940676 | + | 0.194823i | ||||
\(596\) | 19.7434i | 0.808722i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 13.4382i | 0.549528i | ||||||||
\(599\) | − | 12.7938i | − | 0.522740i | −0.965239 | − | 0.261370i | \(-0.915826\pi\) | ||
0.965239 | − | 0.261370i | \(-0.0841743\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 31.2244i | − | 1.27367i | −0.771000 | − | 0.636836i | \(-0.780243\pi\) | ||
0.771000 | − | 0.636836i | \(-0.219757\pi\) | |||||||
\(602\) | 4.96718 | + | 23.9834i | 0.202447 | + | 0.977491i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −12.1750 | −0.495394 | ||||||||
\(605\) | −31.8834 | −1.29624 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.1607i | 0.980653i | 0.871539 | + | 0.490327i | \(0.163123\pi\) | ||||
−0.871539 | + | 0.490327i | \(0.836877\pi\) | |||||||
\(608\) | −4.24621 | −0.172207 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 54.7478 | 2.21667 | ||||||||
\(611\) | 49.5671i | 2.00527i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.99979 | −0.201939 | −0.100970 | − | 0.994889i | \(-0.532195\pi\) | ||||
−0.100970 | + | 0.994889i | \(0.532195\pi\) | |||||||
\(614\) | −7.30829 | −0.294939 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.18154 | − | 0.866035i | 0.168479 | − | 0.0348935i | ||||
\(617\) | 18.0949i | 0.728473i | 0.931307 | + | 0.364236i | \(0.118670\pi\) | ||||
−0.931307 | + | 0.364236i | \(0.881330\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 8.97221i | − | 0.360624i | −0.983610 | − | 0.180312i | \(-0.942289\pi\) | ||
0.983610 | − | 0.180312i | \(-0.0577107\pi\) | |||||||
\(620\) | 30.3402i | 1.21849i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 3.65543i | − | 0.146570i | ||||||
\(623\) | 45.3997 | − | 9.40270i | 1.81890 | − | 0.376711i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.6943 | 0.667771 | ||||||||
\(626\) | 20.1737 | 0.806304 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.0794i | 0.402213i | ||||||||
\(629\) | −13.4067 | −0.534560 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.6267 | −1.41827 | −0.709137 | − | 0.705070i | \(-0.750915\pi\) | ||||
−0.709137 | + | 0.705070i | \(0.750915\pi\) | |||||||
\(632\) | 1.64324i | 0.0653645i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −12.3330 | −0.489805 | ||||||||
\(635\) | −56.1053 | −2.22647 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.2134 | − | 32.8420i | −0.563156 | − | 1.30125i | ||||
\(638\) | − | 6.47964i | − | 0.256531i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.79792i | 0.150126i | ||||||||
\(641\) | 16.7338i | 0.660944i | 0.943816 | + | 0.330472i | \(0.107208\pi\) | ||||
−0.943816 | + | 0.330472i | \(0.892792\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 17.4707i | − | 0.688978i | −0.938790 | − | 0.344489i | \(-0.888052\pi\) | ||
0.938790 | − | 0.344489i | \(-0.111948\pi\) | |||||||
\(644\) | −1.41045 | − | 6.81017i | −0.0555794 | − | 0.268358i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.90206 | −0.389591 | ||||||||
\(647\) | −21.0554 | −0.827775 | −0.413887 | − | 0.910328i | \(-0.635829\pi\) | ||||
−0.413887 | + | 0.910328i | \(0.635829\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 2.36605i | − | 0.0928756i | ||||||
\(650\) | 48.1787 | 1.88973 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.05934 | 0.198139 | ||||||||
\(653\) | 1.19637i | 0.0468174i | 0.999726 | + | 0.0234087i | \(0.00745190\pi\) | ||||
−0.999726 | + | 0.0234087i | \(0.992548\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 29.2699 | 1.14367 | ||||||||
\(656\) | 8.51737 | 0.332547 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.20247 | − | 25.1195i | −0.202813 | − | 0.979259i | ||||
\(659\) | 32.1986i | 1.25428i | 0.778907 | + | 0.627140i | \(0.215774\pi\) | ||||
−0.778907 | + | 0.627140i | \(0.784226\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 23.2109i | − | 0.902798i | −0.892322 | − | 0.451399i | \(-0.850925\pi\) | ||
0.892322 | − | 0.451399i | \(-0.149075\pi\) | |||||||
\(662\) | − | 22.5152i | − | 0.875077i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 3.02145i | − | 0.117255i | ||||||
\(665\) | −8.65317 | − | 41.7807i | −0.335555 | − | 1.62019i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.5529 | −0.408610 | ||||||||
\(668\) | 2.38747 | 0.0923740 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 21.9555i | 0.848217i | ||||||||
\(671\) | −23.2664 | −0.898188 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.0153 | 0.925721 | 0.462861 | − | 0.886431i | \(-0.346823\pi\) | ||||
0.462861 | + | 0.886431i | \(0.346823\pi\) | |||||||
\(674\) | − | 9.78726i | − | 0.376991i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.1351 | 0.505194 | ||||||||
\(677\) | −3.45488 | −0.132782 | −0.0663908 | − | 0.997794i | \(-0.521148\pi\) | ||||
−0.0663908 | + | 0.997794i | \(0.521148\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.56753 | − | 26.8821i | −0.213662 | − | 1.03164i | ||||
\(680\) | 8.85666i | 0.339637i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 12.8938i | − | 0.493728i | ||||||
\(683\) | − | 20.4853i | − | 0.783848i | −0.919998 | − | 0.391924i | \(-0.871810\pi\) | ||
0.919998 | − | 0.391924i | \(-0.128190\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.80898i | 0.0691177i | ||||||||
\(686\) | 10.6501 | + | 15.1518i | 0.406622 | + | 0.578497i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9.25725 | 0.352929 | ||||||||
\(689\) | −11.2273 | −0.427725 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 40.4968i | − | 1.54057i | −0.637698 | − | 0.770286i | \(-0.720113\pi\) | ||
0.637698 | − | 0.770286i | \(-0.279887\pi\) | |||||||
\(692\) | 0.232053 | 0.00882134 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.8185 | −0.410663 | ||||||||
\(695\) | − | 29.7644i | − | 1.12903i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.8623 | 0.752338 | ||||||||
\(698\) | −9.87806 | −0.373890 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −24.4159 | + | 5.05675i | −0.922834 | + | 0.191127i | ||||
\(701\) | 17.2261i | 0.650619i | 0.945608 | + | 0.325310i | \(0.105469\pi\) | ||||
−0.945608 | + | 0.325310i | \(0.894531\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 24.4117i | − | 0.920707i | ||||||
\(704\) | − | 1.61401i | − | 0.0608305i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.4167i | 0.392039i | ||||||||
\(707\) | 19.9666 | − | 4.13527i | 0.750922 | − | 0.155523i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.2472 | 1.02329 | 0.511645 | − | 0.859197i | \(-0.329036\pi\) | ||||
0.511645 | + | 0.859197i | \(0.329036\pi\) | |||||||
\(710\) | 59.5013 | 2.23304 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 17.5236i | − | 0.656726i | ||||||
\(713\) | −20.9991 | −0.786424 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31.3375 | −1.17196 | ||||||||
\(716\) | 24.4451i | 0.913557i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.97078 | 0.372106 | ||||||||
\(719\) | 33.6709 | 1.25571 | 0.627857 | − | 0.778329i | \(-0.283932\pi\) | ||||
0.627857 | + | 0.778329i | \(0.283932\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.57317 | + | 7.59584i | 0.0585878 | + | 0.282884i | ||||
\(722\) | 0.969696i | 0.0360883i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 10.5527i | − | 0.392187i | ||||||
\(725\) | 37.8344i | 1.40514i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 44.4862i | − | 1.64990i | −0.565205 | − | 0.824951i | \(-0.691203\pi\) | ||
0.565205 | − | 0.824951i | \(-0.308797\pi\) | |||||||
\(728\) | −13.2447 | + | 2.74309i | −0.490880 | + | 0.101666i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 29.0591 | 1.07553 | ||||||||
\(731\) | 21.5877 | 0.798450 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.7418i | 0.581438i | 0.956809 | + | 0.290719i | \(0.0938944\pi\) | ||||
−0.956809 | + | 0.290719i | \(0.906106\pi\) | |||||||
\(734\) | −24.2534 | −0.895211 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.62863 | −0.0968925 | ||||||||
\(737\) | − | 9.33053i | − | 0.343694i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.27818 | 0.0838043 | 0.0419022 | − | 0.999122i | \(-0.486658\pi\) | ||||
0.0419022 | + | 0.999122i | \(0.486658\pi\) | |||||||
\(740\) | −21.8345 | −0.802652 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.68973 | − | 1.17839i | 0.208876 | − | 0.0432602i | ||||
\(743\) | − | 34.8955i | − | 1.28019i | −0.768295 | − | 0.640096i | \(-0.778894\pi\) | ||
0.768295 | − | 0.640096i | \(-0.221106\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 74.9839i | 2.74720i | ||||||||
\(746\) | − | 2.65153i | − | 0.0970794i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 3.76384i | − | 0.137620i | ||||||
\(749\) | 6.60874 | + | 31.9095i | 0.241478 | + | 1.16595i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.2409 | 0.446676 | 0.223338 | − | 0.974741i | \(-0.428305\pi\) | ||||
0.223338 | + | 0.974741i | \(0.428305\pi\) | |||||||
\(752\) | −9.69576 | −0.353568 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 20.5237i | 0.747428i | ||||||||
\(755\) | −46.2397 | −1.68283 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.4361 | −0.561036 | −0.280518 | − | 0.959849i | \(-0.590506\pi\) | ||||
−0.280518 | + | 0.959849i | \(0.590506\pi\) | |||||||
\(758\) | − | 19.4305i | − | 0.705748i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −16.1268 | −0.584979 | ||||||||
\(761\) | 10.4962 | 0.380488 | 0.190244 | − | 0.981737i | \(-0.439072\pi\) | ||||
0.190244 | + | 0.981737i | \(0.439072\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.82709 | − | 0.792625i | 0.138550 | − | 0.0286950i | ||||
\(764\) | − | 12.1732i | − | 0.440413i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21.2320i | 0.767143i | ||||||||
\(767\) | 7.49425i | 0.270602i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 42.4382i | − | 1.53036i | −0.643815 | − | 0.765181i | \(-0.722649\pi\) | ||
0.643815 | − | 0.765181i | \(-0.277351\pi\) | |||||||
\(770\) | 15.8811 | − | 3.28913i | 0.572317 | − | 0.118532i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 24.3784 | 0.877397 | ||||||||
\(773\) | 27.7852 | 0.999366 | 0.499683 | − | 0.866208i | \(-0.333450\pi\) | ||||
0.499683 | + | 0.866208i | \(0.333450\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 75.2863i | 2.70436i | ||||||||
\(776\) | −10.3761 | −0.372480 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.47156 | −0.160313 | ||||||||
\(779\) | 36.1665i | 1.29580i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25.2865 | −0.904821 | ||||||||
\(782\) | −6.12989 | −0.219205 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.42418 | − | 2.78027i | 0.229435 | − | 0.0992953i | ||||
\(785\) | 38.2808i | 1.36630i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.1387i | 1.18127i | 0.806940 | + | 0.590633i | \(0.201122\pi\) | ||||
−0.806940 | + | 0.590633i | \(0.798878\pi\) | |||||||
\(788\) | − | 2.10759i | − | 0.0750797i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.24088i | 0.222041i | ||||||||
\(791\) | −3.71971 | − | 17.9602i | −0.132258 | − | 0.638590i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 73.6941 | 2.61695 | ||||||||
\(794\) | 35.0315 | 1.24322 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 19.1753i | − | 0.679650i | ||||||
\(797\) | 0.232053 | 0.00821975 | 0.00410987 | − | 0.999992i | \(-0.498692\pi\) | ||||
0.00410987 | + | 0.999992i | \(0.498692\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.6103 | −0.799894 | ||||||||
\(800\) | 9.42418i | 0.333195i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −21.3229 | −0.752938 | ||||||||
\(803\) | −12.3494 | −0.435799 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.35676 | − | 25.8645i | −0.188801 | − | 0.911602i | ||||
\(806\) | 40.8399i | 1.43852i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 7.70683i | − | 0.271125i | ||||||
\(809\) | − | 31.8244i | − | 1.11889i | −0.828869 | − | 0.559443i | \(-0.811015\pi\) | ||
0.828869 | − | 0.559443i | \(-0.188985\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 28.9878i | − | 1.01790i | −0.860797 | − | 0.508949i | \(-0.830034\pi\) | ||
0.860797 | − | 0.508949i | \(-0.169966\pi\) | |||||||
\(812\) | −2.15413 | − | 10.4009i | −0.0755951 | − | 0.365001i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9.27908 | 0.325231 | ||||||||
\(815\) | 19.2150 | 0.673071 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 39.3082i | 1.37522i | ||||||||
\(818\) | −24.0927 | −0.842382 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 32.3483 | 1.12965 | ||||||||
\(821\) | − | 11.9562i | − | 0.417273i | −0.977993 | − | 0.208637i | \(-0.933097\pi\) | ||
0.977993 | − | 0.208637i | \(-0.0669026\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.7729 | −0.549807 | −0.274904 | − | 0.961472i | \(-0.588646\pi\) | ||||
−0.274904 | + | 0.961472i | \(0.588646\pi\) | |||||||
\(824\) | 2.93188 | 0.102137 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.786583 | − | 3.79792i | −0.0273687 | − | 0.132146i | ||||
\(827\) | 13.4682i | 0.468336i | 0.972196 | + | 0.234168i | \(0.0752366\pi\) | ||||
−0.972196 | + | 0.234168i | \(0.924763\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.7775i | 0.513242i | 0.966512 | + | 0.256621i | \(0.0826092\pi\) | ||||
−0.966512 | + | 0.256621i | \(0.917391\pi\) | |||||||
\(830\) | − | 11.4752i | − | 0.398311i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.11225i | 0.177235i | ||||||||
\(833\) | 14.9810 | − | 6.48352i | 0.519062 | − | 0.224641i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.06742 | 0.313791 | ||||||||
\(836\) | 6.85345 | 0.237031 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 25.8304i | 0.892296i | ||||||||
\(839\) | −41.3777 | −1.42852 | −0.714259 | − | 0.699881i | \(-0.753236\pi\) | ||||
−0.714259 | + | 0.699881i | \(0.753236\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.8829 | 0.444238 | ||||||||
\(842\) | − | 17.0648i | − | 0.588091i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −8.67511 | −0.298610 | ||||||||
\(845\) | 49.8859 | 1.71613 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.7494 | − | 4.50450i | 0.747318 | − | 0.154776i | ||||
\(848\) | − | 2.19615i | − | 0.0754162i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 21.9770i | 0.753804i | ||||||||
\(851\) | − | 15.1121i | − | 0.518038i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 9.08578i | − | 0.311091i | −0.987829 | − | 0.155546i | \(-0.950286\pi\) | ||
0.987829 | − | 0.155546i | \(-0.0497135\pi\) | |||||||
\(854\) | −37.3465 | + | 7.73479i | −1.27797 | + | 0.264679i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.3166 | 0.420972 | ||||||||
\(857\) | 0.0314947 | 0.00107584 | 0.000537919 | − | 1.00000i | \(-0.499829\pi\) | ||||
0.000537919 | 1.00000i | \(0.499829\pi\) | ||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.8682i | 0.848493i | 0.905547 | + | 0.424246i | \(0.139461\pi\) | ||||
−0.905547 | + | 0.424246i | \(0.860539\pi\) | |||||||
\(860\) | 35.1583 | 1.19889 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −27.4224 | −0.934011 | ||||||||
\(863\) | − | 13.7637i | − | 0.468521i | −0.972174 | − | 0.234261i | \(-0.924733\pi\) | ||
0.972174 | − | 0.234261i | \(-0.0752669\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.881319 | 0.0299658 | ||||||||
\(866\) | −21.1385 | −0.718314 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.28648 | − | 20.6967i | −0.145492 | − | 0.702492i | ||||
\(869\) | − | 2.65221i | − | 0.0899701i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.5536i | 1.00139i | ||||||||
\(872\) | − | 1.47720i | − | 0.0500244i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 11.1617i | − | 0.377550i | ||||||
\(875\) | −43.5319 | + | 9.01584i | −1.47165 | + | 0.304791i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.5812 | 0.492374 | 0.246187 | − | 0.969222i | \(-0.420822\pi\) | ||||
0.246187 | + | 0.969222i | \(0.420822\pi\) | |||||||
\(878\) | 25.5428 | 0.862029 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 6.12989i | − | 0.206639i | ||||||
\(881\) | −24.9089 | −0.839201 | −0.419600 | − | 0.907709i | \(-0.637830\pi\) | ||||
−0.419600 | + | 0.907709i | \(0.637830\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 53.0681 | 1.78588 | 0.892942 | − | 0.450172i | \(-0.148637\pi\) | ||||
0.892942 | + | 0.450172i | \(0.148637\pi\) | |||||||
\(884\) | 11.9216i | 0.400968i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 30.9184 | 1.03873 | ||||||||
\(887\) | −39.1668 | −1.31509 | −0.657547 | − | 0.753414i | \(-0.728406\pi\) | ||||
−0.657547 | + | 0.753414i | \(0.728406\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 38.2725 | − | 7.92659i | 1.28362 | − | 0.265849i | ||||
\(890\) | − | 66.5534i | − | 2.23087i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 3.71748i | − | 0.124470i | ||||||
\(893\) | − | 41.1702i | − | 1.37771i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 92.8405i | 3.10332i | ||||||||
\(896\) | −0.536572 | − | 2.59077i | −0.0179256 | − | 0.0865516i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.16428 | 0.0388524 | ||||||||
\(899\) | −32.0713 | −1.06964 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 5.12138i | − | 0.170618i | ||||||
\(902\) | −13.7472 | −0.457730 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.93237 | −0.230567 | ||||||||
\(905\) | − | 40.0782i | − | 1.33224i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.8605 | 0.925094 | 0.462547 | − | 0.886595i | \(-0.346936\pi\) | ||||
0.462547 | + | 0.886595i | \(0.346936\pi\) | |||||||
\(908\) | 3.21943 | 0.106841 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −50.3021 | + | 10.4180i | −1.66750 | + | 0.345354i | ||||
\(911\) | − | 37.5327i | − | 1.24351i | −0.783211 | − | 0.621756i | \(-0.786419\pi\) | ||
0.783211 | − | 0.621756i | \(-0.213581\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.87667i | 0.161394i | ||||||||
\(914\) | 7.21166i | 0.238540i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 8.99060i | − | 0.297058i | ||||||
\(917\) | −19.9666 | + | 4.13527i | −0.659356 | + | 0.136559i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.4325 | −0.476083 | −0.238042 | − | 0.971255i | \(-0.576505\pi\) | ||||
−0.238042 | + | 0.971255i | \(0.576505\pi\) | |||||||
\(920\) | −9.98331 | −0.329140 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 28.6513i | − | 0.943579i | ||||||
\(923\) | 80.0926 | 2.63628 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −54.1802 | −1.78144 | ||||||||
\(926\) | − | 28.3402i | − | 0.931316i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.01461 | −0.131786 | ||||||||
\(929\) | 6.00625 | 0.197059 | 0.0985293 | − | 0.995134i | \(-0.468586\pi\) | ||||
0.0985293 | + | 0.995134i | \(0.468586\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.8056 | + | 27.2784i | 0.386913 | + | 0.894014i | ||||
\(932\) | 10.1604i | 0.332815i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 10.2188i | − | 0.334368i | ||||||
\(935\) | − | 14.2948i | − | 0.467489i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.11686i | 0.232498i | 0.993220 | + | 0.116249i | \(0.0370870\pi\) | ||||
−0.993220 | + | 0.116249i | \(0.962913\pi\) | |||||||
\(938\) | −3.10189 | − | 14.9771i | −0.101280 | − | 0.489020i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −36.8237 | −1.20106 | ||||||||
\(941\) | 1.74214 | 0.0567923 | 0.0283961 | − | 0.999597i | \(-0.490960\pi\) | ||||
0.0283961 | + | 0.999597i | \(0.490960\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.3890i | 0.729085i | ||||||||
\(944\) | −1.46594 | −0.0477123 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14.9413 | −0.485785 | ||||||||
\(947\) | − | 40.4694i | − | 1.31508i | −0.753421 | − | 0.657539i | \(-0.771597\pi\) | ||
0.753421 | − | 0.657539i | \(-0.228403\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 39.1155 | 1.26974 | ||||||||
\(950\) | −40.0171 | −1.29832 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.25127 | − | 6.04162i | −0.0405540 | − | 0.195810i | ||||
\(953\) | − | 14.0692i | − | 0.455745i | −0.973691 | − | 0.227873i | \(-0.926823\pi\) | ||
0.973691 | − | 0.227873i | \(-0.0731770\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 46.2330i | − | 1.49606i | ||||||
\(956\) | 3.59851i | 0.116384i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 12.6276i | − | 0.407981i | ||||||
\(959\) | −0.255574 | − | 1.23401i | −0.00825292 | − | 0.0398482i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −32.8183 | −1.05865 | ||||||||
\(962\) | −29.3906 | −0.947592 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 23.2144i | 0.747685i | ||||||||
\(965\) | 92.5871 | 2.98048 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.6269 | 1.04921 | 0.524605 | − | 0.851346i | \(-0.324213\pi\) | ||||
0.524605 | + | 0.851346i | \(0.324213\pi\) | |||||||
\(968\) | − | 8.39496i | − | 0.269824i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −39.4076 | −1.26530 | ||||||||
\(971\) | 35.0687 | 1.12541 | 0.562704 | − | 0.826658i | \(-0.309761\pi\) | ||||
0.562704 | + | 0.826658i | \(0.309761\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.20512 | + | 20.3039i | 0.134810 | + | 0.650914i | ||||
\(974\) | 21.8841i | 0.701212i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.4152i | 0.461420i | ||||||||
\(977\) | 26.7096i | 0.854515i | 0.904130 | + | 0.427258i | \(0.140520\pi\) | ||||
−0.904130 | + | 0.427258i | \(0.859480\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.2834i | 0.903942i | ||||||||
\(980\) | 24.3985 | − | 10.5592i | 0.779382 | − | 0.337302i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.60770 | −0.242771 | ||||||||
\(983\) | 17.9470 | 0.572420 | 0.286210 | − | 0.958167i | \(-0.407604\pi\) | ||||
0.286210 | + | 0.958167i | \(0.407604\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 8.00445i | − | 0.255043i | ||||||
\(986\) | −9.36198 | −0.298146 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −21.7077 | −0.690613 | ||||||||
\(989\) | 24.3339i | 0.773772i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.9725 | 0.825043 | 0.412521 | − | 0.910948i | \(-0.364648\pi\) | ||||
0.412521 | + | 0.910948i | \(0.364648\pi\) | |||||||
\(992\) | −7.98863 | −0.253639 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −40.5891 | + | 8.40638i | −1.28741 | + | 0.266634i | ||||
\(995\) | − | 72.8261i | − | 2.30874i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 22.7106i | − | 0.719252i | −0.933097 | − | 0.359626i | \(-0.882904\pi\) | ||
0.933097 | − | 0.359626i | \(-0.117096\pi\) | |||||||
\(998\) | 3.85666i | 0.122080i | ||||||||
\(999\) | 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 | 1134.2.d.b.1133.9 | yes | 16 | |
3.2 | odd | 2 | inner | 1134.2.d.b.1133.8 | yes | 16 | |
7.6 | odd | 2 | inner | 1134.2.d.b.1133.16 | yes | 16 | |
9.2 | odd | 6 | 1134.2.m.i.377.1 | 16 | |||
9.4 | even | 3 | 1134.2.m.i.755.4 | 16 | |||
9.5 | odd | 6 | 1134.2.m.h.755.5 | 16 | |||
9.7 | even | 3 | 1134.2.m.h.377.8 | 16 | |||
21.20 | even | 2 | inner | 1134.2.d.b.1133.1 | ✓ | 16 | |
63.13 | odd | 6 | 1134.2.m.i.755.1 | 16 | |||
63.20 | even | 6 | 1134.2.m.i.377.4 | 16 | |||
63.34 | odd | 6 | 1134.2.m.h.377.5 | 16 | |||
63.41 | even | 6 | 1134.2.m.h.755.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1134.2.d.b.1133.1 | ✓ | 16 | 21.20 | even | 2 | inner | |
1134.2.d.b.1133.8 | yes | 16 | 3.2 | odd | 2 | inner | |
1134.2.d.b.1133.9 | yes | 16 | 1.1 | even | 1 | trivial | |
1134.2.d.b.1133.16 | yes | 16 | 7.6 | odd | 2 | inner | |
1134.2.m.h.377.5 | 16 | 63.34 | odd | 6 | |||
1134.2.m.h.377.8 | 16 | 9.7 | even | 3 | |||
1134.2.m.h.755.5 | 16 | 9.5 | odd | 6 | |||
1134.2.m.h.755.8 | 16 | 63.41 | even | 6 | |||
1134.2.m.i.377.1 | 16 | 9.2 | odd | 6 | |||
1134.2.m.i.377.4 | 16 | 63.20 | even | 6 | |||
1134.2.m.i.755.1 | 16 | 63.13 | odd | 6 | |||
1134.2.m.i.755.4 | 16 | 9.4 | even | 3 |