Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,2,Mod(449,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1792.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.m (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.3091920422\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.18939904.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1345.2 | ||
Root | \(0.500000 - 0.0297061i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.1345 |
Dual form | 1792.2.m.d.449.2 |
$q$-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 \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.236813 | − | 0.236813i | −0.136724 | − | 0.136724i | 0.635432 | − | 0.772156i | \(-0.280822\pi\) |
−0.772156 | + | 0.635432i | \(0.780822\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.98593 | − | 2.98593i | 1.33535 | − | 1.33535i | 0.434842 | − | 0.900507i | \(-0.356804\pi\) |
0.900507 | − | 0.434842i | \(-0.143196\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 2.88784i | − | 0.962613i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.55765 | − | 2.55765i | 0.771160 | − | 0.771160i | −0.207150 | − | 0.978309i | \(-0.566419\pi\) |
0.978309 | + | 0.207150i | \(0.0664187\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.17740 | − | 2.17740i | −0.603902 | − | 0.603902i | 0.337443 | − | 0.941346i | \(-0.390438\pi\) |
−0.941346 | + | 0.337443i | \(0.890438\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.41421 | −0.365148 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.473626 | −0.114871 | −0.0574356 | − | 0.998349i | \(-0.518292\pi\) | ||||
−0.0574356 | + | 0.998349i | \(0.518292\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.12936 | + | 5.12936i | 1.17676 | + | 1.17676i | 0.980566 | + | 0.196191i | \(0.0628573\pi\) |
0.196191 | + | 0.980566i | \(0.437143\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.236813 | + | 0.236813i | −0.0516768 | + | 0.0516768i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.0840215i | 0.0175197i | 0.999962 | + | 0.00875985i | \(0.00278838\pi\) | ||||
−0.999962 | + | 0.00875985i | \(0.997212\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 12.8316i | − | 2.56631i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.39432 | + | 1.39432i | −0.268336 | + | 0.268336i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.35480 | − | 1.35480i | −0.251580 | − | 0.251580i | 0.570038 | − | 0.821618i | \(-0.306928\pi\) |
−0.821618 | + | 0.570038i | \(0.806928\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.196182 | 0.0352354 | 0.0176177 | − | 0.999845i | \(-0.494392\pi\) | ||||
0.0176177 | + | 0.999845i | \(0.494392\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.21137 | −0.210872 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.98593 | − | 2.98593i | −0.504714 | − | 0.504714i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.74441 | − | 1.74441i | 0.286779 | − | 0.286779i | −0.549026 | − | 0.835805i | \(-0.685001\pi\) |
0.835805 | + | 0.549026i | \(0.185001\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.03127i | 0.165136i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.81324i | 0.907876i | 0.891033 | + | 0.453938i | \(0.149981\pi\) | ||||
−0.891033 | + | 0.453938i | \(0.850019\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.30205 | + | 7.30205i | −1.11355 | + | 1.11355i | −0.120886 | + | 0.992666i | \(0.538574\pi\) |
−0.992666 | + | 0.120886i | \(0.961426\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.62289 | − | 8.62289i | −1.28542 | − | 1.28542i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.52637 | 0.514375 | 0.257187 | − | 0.966362i | \(-0.417204\pi\) | ||||
0.257187 | + | 0.966362i | \(0.417204\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.112161 | + | 0.112161i | 0.0157056 | + | 0.0157056i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.88784 | + | 4.88784i | −0.671396 | + | 0.671396i | −0.958038 | − | 0.286642i | \(-0.907461\pi\) |
0.286642 | + | 0.958038i | \(0.407461\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 15.2739i | − | 2.05953i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.42940i | − | 0.321782i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.51230 | + | 7.51230i | −0.978019 | + | 0.978019i | −0.999764 | − | 0.0217448i | \(-0.993078\pi\) |
0.0217448 | + | 0.999764i | \(0.493078\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.77456 | + | 5.77456i | 0.739357 | + | 0.739357i | 0.972454 | − | 0.233097i | \(-0.0748858\pi\) |
−0.233097 | + | 0.972454i | \(0.574886\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.88784 | −0.363834 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −13.0031 | −1.61284 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.77568 | + | 9.77568i | 1.19429 | + | 1.19429i | 0.975851 | + | 0.218439i | \(0.0700963\pi\) |
0.218439 | + | 0.975851i | \(0.429904\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.0198974 | − | 0.0198974i | 0.00239536 | − | 0.00239536i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.95668i | − | 1.06296i | −0.847070 | − | 0.531481i | \(-0.821636\pi\) | ||
0.847070 | − | 0.531481i | \(-0.178364\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.7229i | 1.25502i | 0.778607 | + | 0.627512i | \(0.215927\pi\) | ||||
−0.778607 | + | 0.627512i | \(0.784073\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.03868 | + | 3.03868i | −0.350876 | + | 0.350876i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.55765 | − | 2.55765i | −0.291471 | − | 0.291471i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.51156 | 1.07013 | 0.535067 | − | 0.844810i | \(-0.320286\pi\) | ||||
0.535067 | + | 0.844810i | \(0.320286\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.00313 | −0.889237 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.85387 | − | 5.85387i | −0.642546 | − | 0.642546i | 0.308635 | − | 0.951181i | \(-0.400128\pi\) |
−0.951181 | + | 0.308635i | \(0.900128\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.41421 | + | 1.41421i | −0.153393 | + | 0.153393i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.641669i | 0.0687941i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 15.3231i | − | 1.62425i | −0.583484 | − | 0.812124i | \(-0.698311\pi\) | ||
0.583484 | − | 0.812124i | \(-0.301689\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.17740 | + | 2.17740i | −0.228254 | + | 0.228254i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.0464585 | − | 0.0464585i | −0.00481752 | − | 0.00481752i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 30.6318 | 3.14276 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.2623 | 1.14351 | 0.571755 | − | 0.820425i | \(-0.306263\pi\) | ||||
0.571755 | + | 0.820425i | \(0.306263\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.38607 | − | 7.38607i | −0.742328 | − | 0.742328i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.5947 | − | 10.5947i | 1.05422 | − | 1.05422i | 0.0557734 | − | 0.998443i | \(-0.482238\pi\) |
0.998443 | − | 0.0557734i | \(-0.0177624\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 12.6417i | − | 1.24562i | −0.782373 | − | 0.622810i | \(-0.785991\pi\) | ||
0.782373 | − | 0.622810i | \(-0.214009\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.41421i | 0.138013i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.1371 | + | 12.1371i | −1.17334 | + | 1.17334i | −0.191934 | + | 0.981408i | \(0.561476\pi\) |
−0.981408 | + | 0.191934i | \(0.938524\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.52951 | + | 7.52951i | 0.721196 | + | 0.721196i | 0.968849 | − | 0.247653i | \(-0.0796592\pi\) |
−0.247653 | + | 0.968849i | \(0.579659\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.826195 | −0.0784190 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.00313 | 0.282511 | 0.141256 | − | 0.989973i | \(-0.454886\pi\) | ||||
0.141256 | + | 0.989973i | \(0.454886\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.250882 | + | 0.250882i | 0.0233949 | + | 0.0233949i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.28798 | + | 6.28798i | −0.581324 | + | 0.581324i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.473626i | 0.0434172i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 2.08312i | − | 0.189374i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.37665 | − | 1.37665i | 0.124128 | − | 0.124128i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −23.3845 | − | 23.3845i | −2.09157 | − | 2.09157i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.8562 | −1.67321 | −0.836607 | − | 0.547803i | \(-0.815464\pi\) | ||||
−0.836607 | + | 0.547803i | \(0.815464\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.45844 | 0.304499 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.10280 | − | 1.10280i | −0.0963524 | − | 0.0963524i | 0.657288 | − | 0.753640i | \(-0.271704\pi\) |
−0.753640 | + | 0.657288i | \(0.771704\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.12936 | − | 5.12936i | 0.444772 | − | 0.444772i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.32666i | 0.716645i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 8.04922i | − | 0.687691i | −0.939026 | − | 0.343846i | \(-0.888270\pi\) | ||
0.939026 | − | 0.343846i | \(-0.111730\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.69553 | − | 4.69553i | 0.398270 | − | 0.398270i | −0.479353 | − | 0.877622i | \(-0.659128\pi\) |
0.877622 | + | 0.479353i | \(0.159128\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.835091 | − | 0.835091i | −0.0703273 | − | 0.0703273i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.1380 | −0.931410 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.09069 | −0.671895 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.236813 | + | 0.236813i | 0.0195320 | + | 0.0195320i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.00942 | + | 1.00942i | −0.0826952 | + | 0.0826952i | −0.747244 | − | 0.664549i | \(-0.768624\pi\) |
0.664549 | + | 0.747244i | \(0.268624\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.863230i | 0.0702487i | 0.999383 | + | 0.0351243i | \(0.0111827\pi\) | ||||
−0.999383 | + | 0.0351243i | \(0.988817\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.36776i | 0.110576i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.585786 | − | 0.585786i | 0.0470515 | − | 0.0470515i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.6475 | − | 11.6475i | −0.929571 | − | 0.929571i | 0.0681066 | − | 0.997678i | \(-0.478304\pi\) |
−0.997678 | + | 0.0681066i | \(0.978304\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.31501 | 0.183592 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.0840215 | 0.00662182 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.3861 | + | 11.3861i | 0.891826 | + | 0.891826i | 0.994695 | − | 0.102869i | \(-0.0328022\pi\) |
−0.102869 | + | 0.994695i | \(0.532802\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.61706 | + | 3.61706i | −0.281588 | + | 0.281588i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.47363i | 0.346180i | 0.984906 | + | 0.173090i | \(0.0553751\pi\) | ||||
−0.984906 | + | 0.173090i | \(0.944625\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 3.51785i | − | 0.270604i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 14.8128 | − | 14.8128i | 1.13276 | − | 1.13276i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.71896 | + | 2.71896i | 0.206719 | + | 0.206719i | 0.802871 | − | 0.596152i | \(-0.203305\pi\) |
−0.596152 | + | 0.802871i | \(0.703305\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.8316 | −0.969975 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.55802 | 0.267437 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.8910 | + | 10.8910i | 0.814030 | + | 0.814030i | 0.985235 | − | 0.171206i | \(-0.0547663\pi\) |
−0.171206 | + | 0.985235i | \(0.554766\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.52563 | − | 2.52563i | 0.187729 | − | 0.187729i | −0.606985 | − | 0.794713i | \(-0.707621\pi\) |
0.794713 | + | 0.606985i | \(0.207621\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 2.73498i | − | 0.202176i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 10.4173i | − | 0.765899i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.21137 | + | 1.21137i | −0.0885840 | + | 0.0885840i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.39432 | + | 1.39432i | 0.101422 | + | 0.101422i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.0233 | −1.44884 | −0.724418 | − | 0.689361i | \(-0.757891\pi\) | ||||
−0.724418 | + | 0.689361i | \(0.757891\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.68943 | 0.409534 | 0.204767 | − | 0.978811i | \(-0.434356\pi\) | ||||
0.204767 | + | 0.978811i | \(0.434356\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.07931 | + | 3.07931i | 0.220514 | + | 0.220514i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.7033 | − | 16.7033i | 1.19006 | − | 1.19006i | 0.213012 | − | 0.977050i | \(-0.431673\pi\) |
0.977050 | − | 0.213012i | \(-0.0683274\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 17.7968i | − | 1.26158i | −0.775954 | − | 0.630789i | \(-0.782731\pi\) | ||
0.775954 | − | 0.630789i | \(-0.217269\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 4.63001i | − | 0.326576i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.35480 | + | 1.35480i | −0.0950884 | + | 0.0950884i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.3579 | + | 17.3579i | 1.21233 | + | 1.21233i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.242641 | 0.0168647 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 26.2382 | 1.81493 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.947252 | − | 0.947252i | −0.0652115 | − | 0.0652115i | 0.673749 | − | 0.738960i | \(-0.264683\pi\) |
−0.738960 | + | 0.673749i | \(0.764683\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.12106 | + | 2.12106i | −0.145332 | + | 0.145332i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 43.6068i | 2.97396i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 0.196182i | − | 0.0133177i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.53933 | − | 2.53933i | 0.171592 | − | 0.171592i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.03127 | + | 1.03127i | 0.0693709 | + | 0.0693709i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.64037 | 0.645567 | 0.322783 | − | 0.946473i | \(-0.395381\pi\) | ||||
0.322783 | + | 0.946473i | \(0.395381\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −37.0555 | −2.47037 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.15750 | − | 9.15750i | −0.607805 | − | 0.607805i | 0.334567 | − | 0.942372i | \(-0.391410\pi\) |
−0.942372 | + | 0.334567i | \(0.891410\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.48888 | − | 5.48888i | 0.362715 | − | 0.362715i | −0.502096 | − | 0.864812i | \(-0.667438\pi\) |
0.864812 | + | 0.502096i | \(0.167438\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.21137i | 0.0797021i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 8.67371i | − | 0.568234i | −0.958790 | − | 0.284117i | \(-0.908300\pi\) | ||
0.958790 | − | 0.284117i | \(-0.0917004\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.5295 | − | 10.5295i | 0.686869 | − | 0.686869i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.25246 | − | 2.25246i | −0.146313 | − | 0.146313i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.83286 | 0.441981 | 0.220990 | − | 0.975276i | \(-0.429071\pi\) | ||||
0.220990 | + | 0.975276i | \(0.429071\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.2985 | 1.17871 | 0.589356 | − | 0.807874i | \(-0.299382\pi\) | ||||
0.589356 | + | 0.807874i | \(0.299382\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.07819 | + | 6.07819i | 0.389916 | + | 0.389916i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.98593 | + | 2.98593i | −0.190764 | + | 0.190764i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 22.3374i | − | 1.42129i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.77254i | 0.175703i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.2449 | − | 15.2449i | 0.962252 | − | 0.962252i | −0.0370610 | − | 0.999313i | \(-0.511800\pi\) |
0.999313 | + | 0.0370610i | \(0.0117996\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.214897 | + | 0.214897i | 0.0135105 | + | 0.0135105i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.669808 | 0.0419450 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.4588 | −1.15143 | −0.575715 | − | 0.817651i | \(-0.695276\pi\) | ||||
−0.575715 | + | 0.817651i | \(0.695276\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.74441 | − | 1.74441i | −0.108392 | − | 0.108392i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.91245 | + | 3.91245i | −0.242174 | + | 0.242174i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 9.99684i | − | 0.616432i | −0.951316 | − | 0.308216i | \(-0.900268\pi\) | ||
0.951316 | − | 0.308216i | \(-0.0997319\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 29.1895i | 1.79310i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.62872 | + | 3.62872i | −0.222074 | + | 0.222074i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.5537 | + | 19.5537i | 1.19221 | + | 1.19221i | 0.976446 | + | 0.215761i | \(0.0692233\pi\) |
0.215761 | + | 0.976446i | \(0.430777\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.5947 | −0.765072 | −0.382536 | − | 0.923940i | \(-0.624949\pi\) | ||||
−0.382536 | + | 0.923940i | \(0.624949\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.03127 | 0.0624155 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −32.8186 | − | 32.8186i | −1.97904 | − | 1.97904i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.24707 | − | 1.24707i | 0.0749293 | − | 0.0749293i | −0.668649 | − | 0.743578i | \(-0.733127\pi\) |
0.743578 | + | 0.668649i | \(0.233127\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 0.566543i | − | 0.0339180i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.3459i | 1.39270i | 0.717703 | + | 0.696349i | \(0.245194\pi\) | ||||
−0.717703 | + | 0.696349i | \(0.754806\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.67877 | + | 7.67877i | −0.456455 | + | 0.456455i | −0.897490 | − | 0.441035i | \(-0.854612\pi\) |
0.441035 | + | 0.897490i | \(0.354612\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.25402 | − | 7.25402i | −0.429691 | − | 0.429691i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.81324 | 0.343145 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7757 | −0.986805 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.66705 | − | 2.66705i | −0.156345 | − | 0.156345i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.2002 | + | 14.2002i | −0.829582 | + | 0.829582i | −0.987459 | − | 0.157877i | \(-0.949535\pi\) |
0.157877 | + | 0.987459i | \(0.449535\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 44.8624i | 2.61199i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.13234i | 0.413860i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.182949 | − | 0.182949i | 0.0105802 | − | 0.0105802i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.30205 | + | 7.30205i | 0.420883 | + | 0.420883i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.01795 | −0.288273 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 34.4849 | 1.97460 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.4447 | + | 12.4447i | 0.710254 | + | 0.710254i | 0.966588 | − | 0.256334i | \(-0.0825148\pi\) |
−0.256334 | + | 0.966588i | \(0.582515\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.99371 | + | 2.99371i | −0.170306 | + | 0.170306i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.76978i | 0.157060i | 0.996912 | + | 0.0785300i | \(0.0250227\pi\) | ||||
−0.996912 | + | 0.0785300i | \(0.974977\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.8401i | 0.612718i | 0.951916 | + | 0.306359i | \(0.0991107\pi\) | ||||
−0.951916 | + | 0.306359i | \(0.900889\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.62289 | + | 8.62289i | −0.485845 | + | 0.485845i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.1220 | + | 14.1220i | 0.793168 | + | 0.793168i | 0.982008 | − | 0.188840i | \(-0.0604727\pi\) |
−0.188840 | + | 0.982008i | \(0.560473\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.93021 | −0.388017 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.74846 | 0.320848 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.42940 | − | 2.42940i | −0.135175 | − | 0.135175i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −27.9394 | + | 27.9394i | −1.54980 | + | 1.54980i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 3.56617i | − | 0.197210i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 3.52637i | − | 0.194415i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.0215 | + | 11.0215i | −0.605794 | + | 0.605794i | −0.941844 | − | 0.336050i | \(-0.890909\pi\) |
0.336050 | + | 0.941844i | \(0.390909\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.03756 | − | 5.03756i | −0.276057 | − | 0.276057i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 58.3790 | 3.18959 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.329422 | 0.0179448 | 0.00897239 | − | 0.999960i | \(-0.497144\pi\) | ||||
0.00897239 | + | 0.999960i | \(0.497144\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.711181 | − | 0.711181i | −0.0386260 | − | 0.0386260i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.501765 | − | 0.501765i | 0.0271721 | − | 0.0271721i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 0.118824i | − | 0.00639729i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.0117 | − | 14.0117i | 0.752185 | − | 0.752185i | −0.222702 | − | 0.974887i | \(-0.571488\pi\) |
0.974887 | + | 0.222702i | \(0.0714876\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.68741 | − | 4.68741i | −0.250911 | − | 0.250911i | 0.570433 | − | 0.821344i | \(-0.306775\pi\) |
−0.821344 | + | 0.570433i | \(0.806775\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.07197 | 0.324098 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.89060 | −0.100626 | −0.0503132 | − | 0.998733i | \(-0.516022\pi\) | ||||
−0.0503132 | + | 0.998733i | \(0.516022\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −26.7440 | − | 26.7440i | −1.41942 | − | 1.41942i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.112161 | − | 0.112161i | 0.00593617 | − | 0.00593617i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.4334i | 1.71177i | 0.517165 | + | 0.855886i | \(0.326987\pi\) | ||||
−0.517165 | + | 0.855886i | \(0.673013\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 33.6208i | 1.76951i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.493309 | + | 0.493309i | −0.0258920 | + | 0.0258920i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 32.0179 | + | 32.0179i | 1.67589 | + | 1.67589i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.9992 | 1.04395 | 0.521975 | − | 0.852961i | \(-0.325195\pi\) | ||||
0.521975 | + | 0.852961i | \(0.325195\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 16.7877 | 0.873933 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.88784 | + | 4.88784i | 0.253764 | + | 0.253764i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.10234 | + | 5.10234i | −0.264189 | + | 0.264189i | −0.826754 | − | 0.562564i | \(-0.809815\pi\) |
0.562564 | + | 0.826754i | \(0.309815\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.0755i | 0.571936i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.89989i | 0.303860i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.46067 | + | 9.46067i | −0.485962 | + | 0.485962i | −0.907029 | − | 0.421067i | \(-0.861656\pi\) |
0.421067 | + | 0.907029i | \(0.361656\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.46538 | + | 4.46538i | 0.228769 | + | 0.228769i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.9156 | −0.608858 | −0.304429 | − | 0.952535i | \(-0.598466\pi\) | ||||
−0.304429 | + | 0.952535i | \(0.598466\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15.2739 | −0.778431 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 21.0872 | + | 21.0872i | 1.07192 | + | 1.07192i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.7905 | − | 13.7905i | 0.699204 | − | 0.699204i | −0.265034 | − | 0.964239i | \(-0.585383\pi\) |
0.964239 | + | 0.265034i | \(0.0853833\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 0.0397948i | − | 0.00201251i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.522316i | 0.0263474i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 28.4009 | − | 28.4009i | 1.42900 | − | 1.42900i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.7768 | + | 15.7768i | 0.791815 | + | 0.791815i | 0.981789 | − | 0.189974i | \(-0.0608405\pi\) |
−0.189974 | + | 0.981789i | \(0.560841\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.42940 | −0.121622 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.0166 | 0.500208 | 0.250104 | − | 0.968219i | \(-0.419535\pi\) | ||||
0.250104 | + | 0.968219i | \(0.419535\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.427167 | − | 0.427167i | −0.0212787 | − | 0.0212787i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −23.8968 | + | 23.8968i | −1.18744 | + | 1.18744i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 8.92315i | − | 0.442304i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.54913i | 0.274387i | 0.990544 | + | 0.137193i | \(0.0438082\pi\) | ||||
−0.990544 | + | 0.137193i | \(0.956192\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.90616 | + | 1.90616i | −0.0940239 | + | 0.0940239i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.51230 | + | 7.51230i | 0.369656 | + | 0.369656i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −34.9585 | −1.71605 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.22393 | −0.108906 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.36376 | + | 5.36376i | 0.262037 | + | 0.262037i | 0.825881 | − | 0.563844i | \(-0.190678\pi\) |
−0.563844 | + | 0.825881i | \(0.690678\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.5439 | + | 19.5439i | −0.952513 | + | 0.952513i | −0.998922 | − | 0.0464099i | \(-0.985222\pi\) |
0.0464099 | + | 0.998922i | \(0.485222\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 10.1836i | − | 0.495144i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.07736i | 0.294795i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.77456 | − | 5.77456i | 0.279451 | − | 0.279451i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.63763 | + | 2.63763i | 0.127346 | + | 0.127346i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.6979 | −1.23783 | −0.618913 | − | 0.785460i | \(-0.712427\pi\) | ||||
−0.618913 | + | 0.785460i | \(0.712427\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.47599 | −0.215102 | −0.107551 | − | 0.994200i | \(-0.534301\pi\) | ||||
−0.107551 | + | 0.994200i | \(0.534301\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.91598 | + | 1.91598i | 0.0918641 | + | 0.0918641i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.430977 | + | 0.430977i | −0.0206164 | + | 0.0206164i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 21.2404i | − | 1.01375i | −0.862020 | − | 0.506874i | \(-0.830801\pi\) | ||
0.862020 | − | 0.506874i | \(-0.169199\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.88784i | 0.137516i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.92097 | + | 5.92097i | −0.281314 | + | 0.281314i | −0.833633 | − | 0.552319i | \(-0.813743\pi\) |
0.552319 | + | 0.833633i | \(0.313743\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −45.7538 | − | 45.7538i | −2.16894 | − | 2.16894i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.478089 | 0.0226128 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.63095 | 0.360127 | 0.180063 | − | 0.983655i | \(-0.442370\pi\) | ||||
0.180063 | + | 0.983655i | \(0.442370\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.8682 | + | 14.8682i | 0.700117 | + | 0.700117i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.204424 | − | 0.204424i | 0.00960468 | − | 0.00960468i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.0031i | 0.609596i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.2078i | 1.36628i | 0.730286 | + | 0.683142i | \(0.239387\pi\) | ||||
−0.730286 | + | 0.683142i | \(0.760613\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.660384 | − | 0.660384i | 0.0308241 | − | 0.0308241i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.370169 | − | 0.370169i | −0.0172405 | − | 0.0172405i | 0.698434 | − | 0.715674i | \(-0.253881\pi\) |
−0.715674 | + | 0.698434i | \(0.753881\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −39.2012 | −1.82183 | −0.910916 | − | 0.412592i | \(-0.864624\pi\) | ||||
−0.910916 | + | 0.412592i | \(0.864624\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.277444 | −0.0128661 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.3291 | − | 10.3291i | −0.477973 | − | 0.477973i | 0.426510 | − | 0.904483i | \(-0.359743\pi\) |
−0.904483 | + | 0.426510i | \(0.859743\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.77568 | − | 9.77568i | 0.451399 | − | 0.451399i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.51655i | 0.254189i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 37.3522i | 1.71745i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 65.8177 | − | 65.8177i | 3.01993 | − | 3.01993i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.1153 | + | 14.1153i | 0.646295 | + | 0.646295i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.2528 | 0.971067 | 0.485533 | − | 0.874218i | \(-0.338625\pi\) | ||||
0.485533 | + | 0.874218i | \(0.338625\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.59654 | −0.346372 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.0198974 | − | 0.0198974i | −0.000905362 | − | 0.000905362i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 33.6283 | − | 33.6283i | 1.52698 | − | 1.52698i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.74088i | 0.441401i | 0.975342 | + | 0.220701i | \(0.0708344\pi\) | ||||
−0.975342 | + | 0.220701i | \(0.929166\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 5.39274i | − | 0.243868i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.6931 | + | 14.6931i | −0.663091 | + | 0.663091i | −0.956107 | − | 0.293016i | \(-0.905341\pi\) |
0.293016 | + | 0.956107i | \(0.405341\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.641669 | + | 0.641669i | 0.0288993 | + | 0.0288993i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −44.1086 | −1.98253 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.95668 | −0.401762 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.0868 | − | 29.0868i | −1.30210 | − | 1.30210i | −0.926972 | − | 0.375130i | \(-0.877598\pi\) |
−0.375130 | − | 0.926972i | \(-0.622402\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.05941 | − | 1.05941i | 0.0473310 | − | 0.0473310i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 3.30038i | − | 0.147157i | −0.997289 | − | 0.0735784i | \(-0.976558\pi\) | ||
0.997289 | − | 0.0735784i | \(-0.0234419\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 63.2704i | − | 2.81549i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.833073 | + | 0.833073i | −0.0369981 | + | 0.0369981i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.8519 | + | 11.8519i | 0.525327 | + | 0.525327i | 0.919175 | − | 0.393848i | \(-0.128856\pi\) |
−0.393848 | + | 0.919175i | \(0.628856\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.7229 | 0.474355 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −14.3039 | −0.631533 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −37.7471 | − | 37.7471i | −1.66334 | − | 1.66334i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.01922 | − | 9.01922i | 0.396665 | − | 0.396665i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 1.28777i | − | 0.0565268i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 28.9778i | − | 1.26954i | −0.772702 | − | 0.634769i | \(-0.781095\pi\) | ||
0.772702 | − | 0.634769i | \(-0.218905\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.4747 | − | 17.4747i | 0.764117 | − | 0.764117i | −0.212947 | − | 0.977064i | \(-0.568306\pi\) |
0.977064 | + | 0.212947i | \(0.0683061\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.03868 | + | 3.03868i | 0.132619 | + | 0.132619i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.0929169 | −0.00404753 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.9929 | 0.999693 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 21.6943 | + | 21.6943i | 0.941454 | + | 0.941454i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.6578 | − | 12.6578i | 0.548268 | − | 0.548268i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 72.4813i | 3.13364i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 5.15825i | − | 0.222595i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.55765 | + | 2.55765i | −0.110166 | + | 0.110166i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.22432 | + | 5.22432i | 0.224611 | + | 0.224611i | 0.810437 | − | 0.585826i | \(-0.199230\pi\) |
−0.585826 | + | 0.810437i | \(0.699230\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.19620 | −0.0513340 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 44.9652 | 1.92610 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.2408 | + | 11.2408i | 0.480621 | + | 0.480621i | 0.905330 | − | 0.424709i | \(-0.139624\pi\) |
−0.424709 | + | 0.905330i | \(0.639624\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 16.6760 | − | 16.6760i | 0.711715 | − | 0.711715i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 13.8985i | − | 0.592098i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 9.51156i | − | 0.404473i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.46696 | + | 2.46696i | −0.104717 | + | 0.104717i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.5182 | − | 16.5182i | −0.699900 | − | 0.699900i | 0.264489 | − | 0.964389i | \(-0.414797\pi\) |
−0.964389 | + | 0.264489i | \(0.914797\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.7990 | 1.34495 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.573735 | 0.0242231 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.2728 | + | 18.2728i | 0.770107 | + | 0.770107i | 0.978125 | − | 0.208018i | \(-0.0667014\pi\) |
−0.208018 | + | 0.978125i | \(0.566701\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.96715 | − | 8.96715i | 0.377251 | − | 0.377251i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.00313i | 0.336100i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 18.7351i | − | 0.785417i | −0.919663 | − | 0.392708i | \(-0.871538\pi\) | ||
0.919663 | − | 0.392708i | \(-0.128462\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.0415 | + | 12.0415i | −0.503920 | + | 0.503920i | −0.912654 | − | 0.408734i | \(-0.865970\pi\) |
0.408734 | + | 0.912654i | \(0.365970\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.74178 | + | 4.74178i | 0.198091 | + | 0.198091i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.07813 | 0.0449610 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.96647 | −0.165126 | −0.0825632 | − | 0.996586i | \(-0.526311\pi\) | ||||
−0.0825632 | + | 0.996586i | \(0.526311\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.34733 | − | 1.34733i | −0.0559931 | − | 0.0559931i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.85387 | + | 5.85387i | −0.242860 | + | 0.242860i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25.0027i | 1.03551i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 37.5510i | 1.55254i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.14102 | − | 5.14102i | 0.212193 | − | 0.212193i | −0.593006 | − | 0.805198i | \(-0.702059\pi\) |
0.805198 | + | 0.593006i | \(0.202059\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.00629 | + | 1.00629i | 0.0414635 | + | 0.0414635i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.91112 | −0.325420 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.3463 | 0.753390 | 0.376695 | − | 0.926337i | \(-0.377060\pi\) | ||||
0.376695 | + | 0.926337i | \(0.377060\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.41421 | + | 1.41421i | 0.0579771 | + | 0.0579771i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.21450 | + | 4.21450i | −0.172488 | + | 0.172488i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 35.3692i | − | 1.44515i | −0.691295 | − | 0.722573i | \(-0.742959\pi\) | ||
0.691295 | − | 0.722573i | \(-0.257041\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 34.1275i | − | 1.39209i | −0.717999 | − | 0.696044i | \(-0.754942\pi\) | ||
0.717999 | − | 0.696044i | \(-0.245058\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 28.2306 | − | 28.2306i | 1.14964 | − | 1.14964i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.22005 | − | 6.22005i | −0.252881 | − | 0.252881i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.3626 | −0.501781 | −0.250890 | − | 0.968016i | \(-0.580723\pi\) | ||||
−0.250890 | + | 0.968016i | \(0.580723\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.641669 | 0.0260017 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.67833 | − | 7.67833i | −0.310632 | − | 0.310632i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.6385 | + | 19.6385i | −0.793192 | + | 0.793192i | −0.982012 | − | 0.188820i | \(-0.939534\pi\) |
0.188820 | + | 0.982012i | \(0.439534\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 8.22117i | − | 0.331509i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.01019i | 0.0406689i | 0.999793 | + | 0.0203344i | \(0.00647310\pi\) | ||||
−0.999793 | + | 0.0203344i | \(0.993527\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.818167 | − | 0.818167i | 0.0328849 | − | 0.0328849i | −0.690473 | − | 0.723358i | \(-0.742598\pi\) |
0.723358 | + | 0.690473i | \(0.242598\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.117153 | − | 0.117153i | −0.00470117 | − | 0.00470117i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −15.3231 | −0.613908 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −75.4912 | −3.01965 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.21355 | − | 6.21355i | −0.248145 | − | 0.248145i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.826195 | + | 0.826195i | −0.0329426 | + | 0.0329426i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.6898i | 1.26155i | 0.775966 | + | 0.630775i | \(0.217263\pi\) | ||||
−0.775966 | + | 0.630775i | \(0.782737\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.448643i | 0.0178319i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −56.3032 | + | 56.3032i | −2.23432 | + | 2.23432i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.17740 | + | 2.17740i | 0.0862718 | + | 0.0862718i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −25.8654 | −1.02322 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.2445 | 0.602121 | 0.301061 | − | 0.953605i | \(-0.402659\pi\) | ||||
0.301061 | + | 0.953605i | \(0.402659\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.6030 | + | 21.6030i | 0.851939 | + | 0.851939i | 0.990372 | − | 0.138433i | \(-0.0442066\pi\) |
−0.138433 | + | 0.990372i | \(0.544207\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.3267 | − | 10.3267i | 0.406612 | − | 0.406612i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 22.8048i | − | 0.896547i | −0.893896 | − | 0.448274i | \(-0.852039\pi\) | ||
0.893896 | − | 0.448274i | \(-0.147961\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 38.4277i | 1.50842i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.0464585 | + | 0.0464585i | −0.00182085 | + | 0.00182085i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.3213 | − | 13.3213i | −0.521302 | − | 0.521302i | 0.396663 | − | 0.917964i | \(-0.370168\pi\) |
−0.917964 | + | 0.396663i | \(0.870168\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.58579 | −0.257328 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 30.9661 | 1.20810 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.62688 | − | 9.62688i | −0.375010 | − | 0.375010i | 0.494288 | − | 0.869298i | \(-0.335429\pi\) |
−0.869298 | + | 0.494288i | \(0.835429\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.1305 | + | 18.1305i | −0.705197 | + | 0.705197i | −0.965521 | − | 0.260325i | \(-0.916170\pi\) |
0.260325 | + | 0.965521i | \(0.416170\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 0.488437i | − | 0.0189693i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 30.6318i | − | 1.18785i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.113832 | − | 0.113832i | 0.00440761 | − | 0.00440761i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.28296 | − | 2.28296i | −0.0882645 | − | 0.0882645i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.5386 | 1.14032 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.57745 | −0.176448 | −0.0882239 | − | 0.996101i | \(-0.528119\pi\) | ||||
−0.0882239 | + | 0.996101i | \(0.528119\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 17.8913 | + | 17.8913i | 0.688635 | + | 0.688635i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.1035 | − | 18.1035i | 0.695772 | − | 0.695772i | −0.267723 | − | 0.963496i | \(-0.586271\pi\) |
0.963496 | + | 0.267723i | \(0.0862714\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 11.2623i | − | 0.432206i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.33723i | 0.166203i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.94815 | + | 7.94815i | −0.304128 | + | 0.304128i | −0.842626 | − | 0.538499i | \(-0.818992\pi\) |
0.538499 | + | 0.842626i | \(0.318992\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −24.0344 | − | 24.0344i | −0.918307 | − | 0.918307i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.59967 | −0.0991837 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21.2856 | 0.810916 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.34398 | + | 6.34398i | 0.241336 | + | 0.241336i | 0.817403 | − | 0.576066i | \(-0.195413\pi\) |
−0.576066 | + | 0.817403i | \(0.695413\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.38607 | + | 7.38607i | −0.280574 | + | 0.280574i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 28.0411i | − | 1.06366i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 2.75330i | − | 0.104289i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.05405 | + | 2.05405i | −0.0776912 | + | 0.0776912i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.5173 | + | 19.5173i | 0.737159 | + | 0.737159i | 0.972027 | − | 0.234868i | \(-0.0754658\pi\) |
−0.234868 | + | 0.972027i | \(0.575466\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.8954 | 0.674937 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.98705 | −0.187823 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.5947 | − | 10.5947i | −0.398457 | − | 0.398457i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.30481 | − | 4.30481i | 0.161671 | − | 0.161671i | −0.621636 | − | 0.783306i | \(-0.713532\pi\) |
0.783306 | + | 0.621636i | \(0.213532\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 27.4679i | − | 1.03013i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.0164835i | 0.000617313i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −33.2574 | + | 33.2574i | −1.24376 | + | 1.24376i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.61811 | − | 1.61811i | −0.0604294 | − | 0.0604294i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26.6322 | 0.993215 | 0.496608 | − | 0.867975i | \(-0.334579\pi\) | ||||
0.496608 | + | 0.867975i | \(0.334579\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.6417 | −0.470800 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.33333 | − | 4.33333i | −0.161158 | − | 0.161158i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −17.3842 | + | 17.3842i | −0.645634 | + | 0.645634i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 38.4103i | − | 1.42456i | −0.701896 | − | 0.712279i | \(-0.747663\pi\) | ||
0.701896 | − | 0.712279i | \(-0.252337\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21.1306i | 0.782615i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.45844 | − | 3.45844i | 0.127915 | − | 0.127915i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.64855 | − | 9.64855i | −0.356377 | − | 0.356377i | 0.506099 | − | 0.862476i | \(-0.331087\pi\) |
−0.862476 | + | 0.506099i | \(0.831087\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.41421 | 0.0521641 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 50.0055 | 1.84198 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.3825 | − | 26.3825i | −0.970498 | − | 0.970498i | 0.0290795 | − | 0.999577i | \(-0.490742\pi\) |
−0.999577 | + | 0.0290795i | \(0.990742\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.28978 | + | 5.28978i | −0.194325 | + | 0.194325i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.53540i | 0.0563284i | 0.999603 | + | 0.0281642i | \(0.00896614\pi\) | ||||
−0.999603 | + | 0.0281642i | \(0.991034\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.02814i | 0.220854i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −16.9050 | + | 16.9050i | −0.618523 | + | 0.618523i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.1371 | + | 12.1371i | 0.443482 | + | 0.443482i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.7562 | 0.757404 | 0.378702 | − | 0.925519i | \(-0.376370\pi\) | ||||
0.378702 | + | 0.925519i | \(0.376370\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.22040 | −0.263126 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.57754 | + | 2.57754i | 0.0938065 | + | 0.0938065i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.8405 | + | 20.8405i | −0.757459 | + | 0.757459i | −0.975859 | − | 0.218400i | \(-0.929916\pi\) |
0.218400 | + | 0.975859i | \(0.429916\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 0.101781i | − | 0.00369442i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.3705i | 1.53593i | 0.640492 | + | 0.767965i | \(0.278730\pi\) | ||||
−0.640492 | + | 0.767965i | \(0.721270\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.52951 | − | 7.52951i | 0.272586 | − | 0.272586i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.08402 | + | 4.08402i | 0.147658 | + | 0.147658i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 32.7146 | 1.18126 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.4764 | −0.485970 | −0.242985 | − | 0.970030i | \(-0.578127\pi\) | ||||
−0.242985 | + | 0.970030i | \(0.578127\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.37128 | + | 4.37128i | 0.157428 | + | 0.157428i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.7392 | − | 13.7392i | 0.494166 | − | 0.494166i | −0.415450 | − | 0.909616i | \(-0.636376\pi\) |
0.909616 | + | 0.415450i | \(0.136376\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 2.51732i | − | 0.0904249i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.826195i | 0.0296396i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −29.8182 | + | 29.8182i | −1.06835 | + | 1.06835i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.9080 | − | 22.9080i | −0.819713 | − | 0.819713i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.77804 | 0.135016 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −69.5572 | −2.48260 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.7111 | − | 14.7111i | −0.524394 | − | 0.524394i | 0.394501 | − | 0.918895i | \(-0.370917\pi\) |
−0.918895 | + | 0.394501i | \(0.870917\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.36738 | + | 2.36738i | −0.0842810 | + | 0.0842810i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 3.00313i | − | 0.106779i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 25.1471i | − | 0.892999i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.91245 | − | 6.91245i | 0.245159 | − | 0.245159i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.24496 | − | 3.24496i | −0.114942 | − | 0.114942i | 0.647296 | − | 0.762239i | \(-0.275900\pi\) |
−0.762239 | + | 0.647296i | \(0.775900\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.67018 | −0.0590868 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −44.2507 | −1.56352 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 27.4255 | + | 27.4255i | 0.967824 | + | 0.967824i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.250882 | − | 0.250882i | 0.00884244 | − | 0.00884244i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 9.26111i | − | 0.326007i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 43.9611i | − | 1.54559i | −0.634655 | − | 0.772795i | \(-0.718858\pi\) | ||
0.634655 | − | 0.772795i | \(-0.281142\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.7261 | − | 12.7261i | 0.446875 | − | 0.446875i | −0.447439 | − | 0.894314i | \(-0.647664\pi\) |
0.894314 | + | 0.447439i | \(0.147664\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.98258 | + | 2.98258i | 0.104604 | + | 0.104604i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 67.9961 | 2.38180 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −74.9098 | −2.62076 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.28798 | + | 6.28798i | 0.219720 | + | 0.219720i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.5549 | + | 15.5549i | −0.542869 | + | 0.542869i | −0.924369 | − | 0.381500i | \(-0.875408\pi\) |
0.381500 | + | 0.924369i | \(0.375408\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 26.7572i | − | 0.932698i | −0.884601 | − | 0.466349i | \(-0.845569\pi\) | ||
0.884601 | − | 0.466349i | \(-0.154431\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.5437i | 0.541163i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.47992 | + | 9.47992i | −0.329649 | + | 0.329649i | −0.852453 | − | 0.522804i | \(-0.824886\pi\) |
0.522804 | + | 0.852453i | \(0.324886\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.2500 | − | 11.2500i | −0.390730 | − | 0.390730i | 0.484217 | − | 0.874948i | \(-0.339104\pi\) |
−0.874948 | + | 0.484217i | \(0.839104\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.590646 | −0.0204893 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.473626 | 0.0164102 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.3579 | + | 13.3579i | 0.462270 | + | 0.462270i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.273540 | + | 0.273540i | −0.00945493 | + | 0.00945493i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.4767i | 1.05217i | 0.850431 | + | 0.526087i | \(0.176341\pi\) | ||||
−0.850431 | + | 0.526087i | \(0.823659\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 25.3290i | − | 0.873415i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.52861 | − | 5.52861i | 0.190415 | − | 0.190415i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.5041 | − | 10.5041i | −0.361351 | − | 0.361351i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.08312 | −0.0715768 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.63686 | 0.124817 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.146568 | + | 0.146568i | 0.00502427 | + | 0.00502427i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.9235 | + | 29.9235i | −1.02456 | + | 1.02456i | −0.0248689 | + | 0.999691i | \(0.507917\pi\) |
−0.999691 | + | 0.0248689i | \(0.992083\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 88.4599i | − | 3.02526i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.5515i | 0.599547i | 0.954010 | + | 0.299774i | \(0.0969112\pi\) | ||||
−0.954010 | + | 0.299774i | \(0.903089\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.71986 | − | 6.71986i | 0.229279 | − | 0.229279i | −0.583113 | − | 0.812391i | \(-0.698165\pi\) |
0.812391 | + | 0.583113i | \(0.198165\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.37665 | − | 1.37665i | −0.0469161 | − | 0.0469161i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −52.7588 | −1.79593 | −0.897965 | − | 0.440067i | \(-0.854955\pi\) | ||||
−0.897965 | + | 0.440067i | \(0.854955\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.2373 | 0.552083 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.97270 | + | 3.97270i | 0.134920 | + | 0.134920i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.3272 | − | 24.3272i | 0.825244 | − | 0.825244i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 42.5711i | − | 1.44247i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 32.5236i | − | 1.10076i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −23.3845 | + | 23.3845i | −0.790540 | + | 0.790540i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.1764 | + | 11.1764i | 0.377399 | + | 0.377399i | 0.870163 | − | 0.492764i | \(-0.164013\pi\) |
−0.492764 | + | 0.870163i | \(0.664013\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.72556 | 0.226847 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.6304 | 0.796128 | 0.398064 | − | 0.917358i | \(-0.369682\pi\) | ||||
0.398064 | + | 0.917358i | \(0.369682\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.7140 | + | 18.7140i | 0.629777 | + | 0.629777i | 0.948012 | − | 0.318235i | \(-0.103090\pi\) |
−0.318235 | + | 0.948012i | \(0.603090\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.6240 | − | 10.6240i | 0.357122 | − | 0.357122i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 46.0412i | 1.54591i | 0.634459 | + | 0.772957i | \(0.281223\pi\) | ||||
−0.634459 | + | 0.772957i | \(0.718777\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.8562i | 0.632416i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20.4692 | + | 20.4692i | −0.685744 | + | 0.685744i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.0881 | + | 18.0881i | 0.605294 | + | 0.605294i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 65.0394 | 2.17403 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.0866491 | −0.00289313 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.265788 | − | 0.265788i | −0.00886452 | − | 0.00886452i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.31501 | − | 2.31501i | 0.0771241 | − | 0.0771241i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 3.45844i | − | 0.115090i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 15.0827i | − | 0.501367i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.9531 | − | 19.9531i | 0.662533 | − | 0.662533i | −0.293443 | − | 0.955977i | \(-0.594801\pi\) |
0.955977 | + | 0.293443i | \(0.0948012\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −30.5959 | − | 30.5959i | −1.01480 | − | 1.01480i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.94815 | 0.263334 | 0.131667 | − | 0.991294i | \(-0.457967\pi\) | ||||
0.131667 | + | 0.991294i | \(0.457967\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −29.9443 | −0.991011 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.16647 | − | 8.16647i | −0.269975 | − | 0.269975i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.10280 | + | 1.10280i | −0.0364178 | + | 0.0364178i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.2767i | 0.998735i | 0.866390 | + | 0.499367i | \(0.166434\pi\) | ||||
−0.866390 | + | 0.499367i | \(0.833566\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 5.89411i | − | 0.194217i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −19.5023 | + | 19.5023i | −0.641925 | + | 0.641925i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22.3834 | − | 22.3834i | −0.735963 | − | 0.735963i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −36.5071 | −1.19905 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 50.9720 | 1.67234 | 0.836169 | − | 0.548473i | \(-0.184790\pi\) | ||||
0.836169 | + | 0.548473i | \(0.184790\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.12936 | − | 5.12936i | −0.168108 | − | 0.168108i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.655921 | − | 0.655921i | 0.0214739 | − | 0.0214739i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.23412i | 0.236581i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 6.62686i | − | 0.216490i | −0.994124 | − | 0.108245i | \(-0.965477\pi\) | ||
0.994124 | − | 0.108245i | \(-0.0345231\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.56707 | − | 2.56707i | 0.0837732 | − | 0.0837732i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.5666 | − | 12.5666i | −0.409660 | − | 0.409660i | 0.471960 | − | 0.881620i | \(-0.343547\pi\) |
−0.881620 | + | 0.471960i | \(0.843547\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.488437 | −0.0159057 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.32666 | 0.270866 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.2069 | + | 28.2069i | 0.916601 | + | 0.916601i | 0.996780 | − | 0.0801799i | \(-0.0255495\pi\) |
−0.0801799 | + | 0.996780i | \(0.525549\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23.3481 | − | 23.3481i | 0.757912 | − | 0.757912i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 6.68852i | − | 0.216890i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 38.6729i | − | 1.25274i | −0.779526 | − | 0.626369i | \(-0.784540\pi\) | ||
0.779526 | − | 0.626369i | \(-0.215460\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −59.7882 | + | 59.7882i | −1.93470 | + | 1.93470i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.64116 | + | 1.64116i | 0.0530513 | + | 0.0530513i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.04922 | −0.259923 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9615 | −0.998758 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 35.0501 | + | 35.0501i | 1.12947 | + | 1.12947i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.9882 | − | 16.9882i | 0.546870 | − | 0.546870i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.4567i | 0.529213i | 0.964356 | + | 0.264607i | \(0.0852421\pi\) | ||||
−0.964356 | + | 0.264607i | \(0.914758\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.15063i | 0.0369634i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.05753 | − | 3.05753i | 0.0981207 | − | 0.0981207i | −0.656342 | − | 0.754463i | \(-0.727897\pi\) |
0.754463 | + | 0.656342i | \(0.227897\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.69553 | − | 4.69553i | −0.150532 | − | 0.150532i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.2328 | 0.423790 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.21193 | −0.102759 | −0.0513793 | − | 0.998679i | \(-0.516362\pi\) | ||||
−0.0513793 | + | 0.998679i | \(0.516362\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −39.1912 | − | 39.1912i | −1.25256 | − | 1.25256i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 21.7440 | − | 21.7440i | 0.694233 | − | 0.694233i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 8.33539i | − | 0.265858i | −0.991126 | − | 0.132929i | \(-0.957562\pi\) | ||
0.991126 | − | 0.132929i | \(-0.0424382\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 99.7499i | − | 3.17829i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.835091 | + | 0.835091i | −0.0265812 | + | 0.0265812i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.613530 | − | 0.613530i | −0.0195091 | − | 0.0195091i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.05237 | −0.128728 | −0.0643640 | − | 0.997926i | \(-0.520502\pi\) | ||||
−0.0643640 | + | 0.997926i | \(0.520502\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.22004 | 0.165653 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −53.1399 | − | 53.1399i | −1.68465 | − | 1.68465i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.0203 | + | 11.0203i | −0.349018 | + | 0.349018i | −0.859744 | − | 0.510726i | \(-0.829377\pi\) |
0.510726 | + | 0.859744i | \(0.329377\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.86451i | 0.153906i |
(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 | 1792.2.m.d.1345.2 | yes | 8 | |
4.3 | odd | 2 | 1792.2.m.b.1345.3 | yes | 8 | ||
8.3 | odd | 2 | 1792.2.m.c.1345.2 | yes | 8 | ||
8.5 | even | 2 | 1792.2.m.a.1345.3 | yes | 8 | ||
16.3 | odd | 4 | 1792.2.m.c.449.2 | yes | 8 | ||
16.5 | even | 4 | inner | 1792.2.m.d.449.2 | yes | 8 | |
16.11 | odd | 4 | 1792.2.m.b.449.3 | yes | 8 | ||
16.13 | even | 4 | 1792.2.m.a.449.3 | ✓ | 8 | ||
32.5 | even | 8 | 7168.2.a.x.1.3 | 4 | |||
32.11 | odd | 8 | 7168.2.a.s.1.3 | 4 | |||
32.21 | even | 8 | 7168.2.a.t.1.2 | 4 | |||
32.27 | odd | 8 | 7168.2.a.w.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1792.2.m.a.449.3 | ✓ | 8 | 16.13 | even | 4 | ||
1792.2.m.a.1345.3 | yes | 8 | 8.5 | even | 2 | ||
1792.2.m.b.449.3 | yes | 8 | 16.11 | odd | 4 | ||
1792.2.m.b.1345.3 | yes | 8 | 4.3 | odd | 2 | ||
1792.2.m.c.449.2 | yes | 8 | 16.3 | odd | 4 | ||
1792.2.m.c.1345.2 | yes | 8 | 8.3 | odd | 2 | ||
1792.2.m.d.449.2 | yes | 8 | 16.5 | even | 4 | inner | |
1792.2.m.d.1345.2 | yes | 8 | 1.1 | even | 1 | trivial | |
7168.2.a.s.1.3 | 4 | 32.11 | odd | 8 | |||
7168.2.a.t.1.2 | 4 | 32.21 | even | 8 | |||
7168.2.a.w.1.2 | 4 | 32.27 | odd | 8 | |||
7168.2.a.x.1.3 | 4 | 32.5 | even | 8 |