Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1040,2,Mod(177,1040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1040, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 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("1040.177");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1040 = 2^{4} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1040.cd (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.30444181021\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 41 x^{18} + 640 x^{16} + 4888 x^{14} + 19956 x^{12} + 45364 x^{10} + 57952 x^{8} + 41120 x^{6} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 520) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 177.2 | ||
Root | \(1.79929i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1040.177 |
Dual form | 1040.2.cd.p.993.2 |
$q$-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 \(\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(417\) | \(561\) | \(911\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.75903 | + | 1.75903i | −1.01558 | + | 1.01558i | −0.0157021 | + | 0.999877i | \(0.504998\pi\) |
−0.999877 | + | 0.0157021i | \(0.995002\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.831197 | − | 2.07584i | 0.371723 | − | 0.928344i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.71535 | 1.78223 | 0.891117 | − | 0.453774i | \(-0.149922\pi\) | ||||
0.891117 | + | 0.453774i | \(0.149922\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 3.18840i | − | 1.06280i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.281047 | − | 0.281047i | 0.0847389 | − | 0.0847389i | −0.663467 | − | 0.748206i | \(-0.730916\pi\) |
0.748206 | + | 0.663467i | \(0.230916\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.26501 | − | 1.52961i | −0.905551 | − | 0.424237i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.18937 | + | 5.11358i | 0.565293 | + | 1.32032i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.84321 | − | 4.84321i | 1.17465 | − | 1.17465i | 0.193564 | − | 0.981088i | \(-0.437995\pi\) |
0.981088 | − | 0.193564i | \(-0.0620048\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.782284 | + | 0.782284i | −0.179468 | + | 0.179468i | −0.791124 | − | 0.611656i | \(-0.790504\pi\) |
0.611656 | + | 0.791124i | \(0.290504\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.29446 | + | 8.29446i | −1.81000 | + | 1.81000i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.30324 | − | 2.30324i | −0.480259 | − | 0.480259i | 0.424955 | − | 0.905214i | \(-0.360290\pi\) |
−0.905214 | + | 0.424955i | \(0.860290\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.61822 | − | 3.45086i | −0.723644 | − | 0.690173i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.331406 | + | 0.331406i | 0.0637792 | + | 0.0637792i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 6.24720i | − | 1.16008i | −0.814590 | − | 0.580038i | \(-0.803038\pi\) | ||
0.814590 | − | 0.580038i | \(-0.196962\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.66847 | − | 6.66847i | −1.19769 | − | 1.19769i | −0.974856 | − | 0.222837i | \(-0.928468\pi\) |
−0.222837 | − | 0.974856i | \(-0.571532\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.988743i | 0.172118i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.91938 | − | 9.78831i | 0.662497 | − | 1.65453i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.15078 | −0.517985 | −0.258993 | − | 0.965879i | \(-0.583391\pi\) | ||||
−0.258993 | + | 0.965879i | \(0.583391\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.43390 | − | 3.05264i | 1.35050 | − | 0.488813i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.37025 | + | 8.37025i | 1.30721 | + | 1.30721i | 0.923418 | + | 0.383795i | \(0.125383\pi\) |
0.383795 | + | 0.923418i | \(0.374617\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.55538 | + | 3.55538i | 0.542190 | + | 0.542190i | 0.924170 | − | 0.381980i | \(-0.124758\pi\) |
−0.381980 | + | 0.924170i | \(0.624758\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.61861 | − | 2.65019i | −0.986645 | − | 0.395067i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.57021 | −0.520769 | −0.260384 | − | 0.965505i | \(-0.583849\pi\) | ||||
−0.260384 | + | 0.965505i | \(0.583849\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.2345 | 2.17636 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 17.0388i | 2.38590i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.47921 | − | 1.47921i | 0.203185 | − | 0.203185i | −0.598178 | − | 0.801363i | \(-0.704108\pi\) |
0.801363 | + | 0.598178i | \(0.204108\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.349803 | − | 0.817015i | −0.0471675 | − | 0.110166i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.75213i | − | 0.364528i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.52346 | + | 4.52346i | 0.588904 | + | 0.588904i | 0.937335 | − | 0.348431i | \(-0.113285\pi\) |
−0.348431 | + | 0.937335i | \(0.613285\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.05191 | 0.518794 | 0.259397 | − | 0.965771i | \(-0.416476\pi\) | ||||
0.259397 | + | 0.965771i | \(0.416476\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 15.0344i | − | 1.89416i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.88909 | + | 5.50624i | −0.730452 | + | 0.682964i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 7.84255i | − | 0.958120i | −0.877782 | − | 0.479060i | \(-0.840978\pi\) | ||
0.877782 | − | 0.479060i | \(-0.159022\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.10296 | 0.975482 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.41956 | + | 5.41956i | 0.643184 | + | 0.643184i | 0.951337 | − | 0.308153i | \(-0.0997108\pi\) |
−0.308153 | + | 0.951337i | \(0.599711\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 9.61771i | − | 1.12567i | −0.826570 | − | 0.562834i | \(-0.809711\pi\) | ||
0.826570 | − | 0.562834i | \(-0.190289\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 12.4348 | − | 0.294387i | 1.43584 | − | 0.0339929i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.32524 | − | 1.32524i | 0.151025 | − | 0.151025i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.86018i | 0.209287i | 0.994510 | + | 0.104643i | \(0.0333701\pi\) | ||||
−0.994510 | + | 0.104643i | \(0.966630\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.39930 | 0.933255 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.71033 | 0.736554 | 0.368277 | − | 0.929716i | \(-0.379948\pi\) | ||||
0.368277 | + | 0.929716i | \(0.379948\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.02807 | − | 14.0794i | −0.653836 | − | 1.52713i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.9890 | + | 10.9890i | 1.17815 | + | 1.17815i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.0574 | + | 10.0574i | 1.06608 | + | 1.06608i | 0.997656 | + | 0.0684279i | \(0.0217983\pi\) |
0.0684279 | + | 0.997656i | \(0.478202\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.3957 | − | 7.21263i | −1.61390 | − | 0.756089i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 23.4601 | 2.43270 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.973664 | + | 2.27413i | 0.0998958 | + | 0.233321i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 13.5640i | − | 1.37722i | −0.725134 | − | 0.688608i | \(-0.758222\pi\) | ||
0.725134 | − | 0.688608i | \(-0.241778\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.896092 | − | 0.896092i | −0.0900606 | − | 0.0900606i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 0.932039i | − | 0.0927413i | −0.998924 | − | 0.0463707i | \(-0.985234\pi\) | ||
0.998924 | − | 0.0463707i | \(-0.0147655\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.49429 | − | 4.49429i | −0.442836 | − | 0.442836i | 0.450128 | − | 0.892964i | \(-0.351378\pi\) |
−0.892964 | + | 0.450128i | \(0.851378\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 10.3236 | + | 24.1123i | 1.00748 | + | 2.35312i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.80764 | − | 4.80764i | −0.464772 | − | 0.464772i | 0.435444 | − | 0.900216i | \(-0.356591\pi\) |
−0.900216 | + | 0.435444i | \(0.856591\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.13756 | + | 2.13756i | −0.204741 | + | 0.204741i | −0.802028 | − | 0.597287i | \(-0.796245\pi\) |
0.597287 | + | 0.802028i | \(0.296245\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.54233 | − | 5.54233i | 0.526055 | − | 0.526055i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.15291 | + | 6.15291i | −0.578817 | + | 0.578817i | −0.934577 | − | 0.355760i | \(-0.884222\pi\) |
0.355760 | + | 0.934577i | \(0.384222\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.69561 | + | 2.86671i | −0.624369 | + | 0.267322i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.87700 | + | 10.4102i | −0.450879 | + | 0.962421i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 22.8374 | − | 22.8374i | 2.09350 | − | 2.09350i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.8420i | 0.985639i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −29.4471 | −2.65516 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.1709 | + | 4.64250i | −0.909713 | + | 0.415238i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.83780 | + | 7.83780i | −0.695492 | + | 0.695492i | −0.963435 | − | 0.267943i | \(-0.913656\pi\) |
0.267943 | + | 0.963435i | \(0.413656\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.5081 | −1.10127 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.640461 | −0.0559574 | −0.0279787 | − | 0.999609i | \(-0.508907\pi\) | ||||
−0.0279787 | + | 0.999609i | \(0.508907\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.68874 | + | 3.68874i | −0.319854 | + | 0.319854i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.963411 | − | 0.412483i | 0.0829172 | − | 0.0355008i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.64527 | 0.226001 | 0.113000 | − | 0.993595i | \(-0.463954\pi\) | ||||
0.113000 | + | 0.993595i | \(0.463954\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 5.69897i | − | 0.483381i | −0.970353 | − | 0.241690i | \(-0.922298\pi\) | ||
0.970353 | − | 0.241690i | \(-0.0777018\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.28012 | − | 6.28012i | 0.528882 | − | 0.528882i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.34751 | + | 0.487731i | −0.112685 | + | 0.0407861i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.9682 | − | 5.19265i | −1.07695 | − | 0.431227i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −26.7980 | + | 26.7980i | −2.21026 | + | 2.21026i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.1616 | + | 13.1616i | −1.07824 | + | 1.07824i | −0.0815732 | + | 0.996667i | \(0.525994\pi\) |
−0.996667 | + | 0.0815732i | \(0.974006\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.99575 | − | 7.99575i | 0.650685 | − | 0.650685i | −0.302473 | − | 0.953158i | \(-0.597812\pi\) |
0.953158 | + | 0.302473i | \(0.0978121\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −15.4421 | − | 15.4421i | −1.24842 | − | 1.24842i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.3855 | + | 8.29986i | −1.55708 | + | 0.666661i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.4321 | + | 14.4321i | 1.15181 | + | 1.15181i | 0.986190 | + | 0.165616i | \(0.0529613\pi\) |
0.165616 | + | 0.986190i | \(0.447039\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.20397i | 0.412702i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.8606 | − | 10.8606i | −0.855934 | − | 0.855934i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.33972i | 0.418239i | 0.977890 | + | 0.209120i | \(0.0670598\pi\) | ||||
−0.977890 | + | 0.209120i | \(0.932940\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.05247 | + | 0.821841i | 0.159785 | + | 0.0639802i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.51667 | 0.426893 | 0.213446 | − | 0.976955i | \(-0.431531\pi\) | ||||
0.213446 | + | 0.976955i | \(0.431531\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.32060 | + | 9.98837i | 0.640046 | + | 0.768336i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.49424 | + | 2.49424i | 0.190739 | + | 0.190739i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.95916 | − | 1.95916i | −0.148952 | − | 0.148952i | 0.628698 | − | 0.777650i | \(-0.283588\pi\) |
−0.777650 | + | 0.628698i | \(0.783588\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −17.0612 | − | 16.2720i | −1.28970 | − | 1.23005i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −15.9138 | −1.19616 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.2189 | 1.43649 | 0.718245 | − | 0.695790i | \(-0.244946\pi\) | ||||
0.718245 | + | 0.695790i | \(0.244946\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.95172i | − | 0.219399i | −0.993965 | − | 0.109700i | \(-0.965011\pi\) | ||
0.993965 | − | 0.109700i | \(-0.0349889\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.12745 | + | 7.12745i | −0.526876 | + | 0.526876i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.61892 | + | 6.54052i | −0.192547 | + | 0.480868i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 2.72234i | − | 0.199077i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.56270 | + | 1.56270i | 0.113669 | + | 0.113669i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.18940 | −0.158420 | −0.0792099 | − | 0.996858i | \(-0.525240\pi\) | ||||
−0.0792099 | + | 0.996858i | \(0.525240\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 1.11351i | − | 0.0801521i | −0.999197 | − | 0.0400761i | \(-0.987240\pi\) | ||
0.999197 | − | 0.0400761i | \(-0.0127600\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.673452 | − | 20.0448i | 0.0482269 | − | 1.43544i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 5.59534i | − | 0.398651i | −0.979933 | − | 0.199326i | \(-0.936125\pi\) | ||
0.979933 | − | 0.199326i | \(-0.0638752\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.48117 | 0.530326 | 0.265163 | − | 0.964204i | \(-0.414574\pi\) | ||||
0.265163 | + | 0.964204i | \(0.414574\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.7953 | + | 13.7953i | 0.973046 | + | 0.973046i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 29.4577i | − | 2.06753i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 24.3326 | − | 10.4180i | 1.69946 | − | 0.727623i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.34366 | + | 7.34366i | −0.510420 | + | 0.510420i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.439717i | 0.0304159i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.9472 | −1.02901 | −0.514504 | − | 0.857488i | \(-0.672024\pi\) | ||||
−0.514504 | + | 0.857488i | \(0.672024\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −19.0664 | −1.30641 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.3356 | − | 4.42517i | 0.704883 | − | 0.301794i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −31.4442 | − | 31.4442i | −2.13457 | − | 2.13457i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.9179 | + | 16.9179i | 1.14320 | + | 1.14320i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.2214 | + | 8.40493i | −1.56204 | + | 0.565377i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.7086 | −1.31978 | −0.659892 | − | 0.751360i | \(-0.729398\pi\) | ||||
−0.659892 | + | 0.751360i | \(0.729398\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.0027 | + | 11.5363i | −0.733516 | + | 0.769090i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.2779i | 0.947660i | 0.880616 | + | 0.473830i | \(0.157129\pi\) | ||||
−0.880616 | + | 0.473830i | \(0.842871\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.113080 | − | 0.113080i | −0.00747252 | − | 0.00747252i | 0.703361 | − | 0.710833i | \(-0.251682\pi\) |
−0.710833 | + | 0.703361i | \(0.751682\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.66227i | 0.306755i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.15635 | − | 1.15635i | −0.0757551 | − | 0.0757551i | 0.668214 | − | 0.743969i | \(-0.267059\pi\) |
−0.743969 | + | 0.668214i | \(0.767059\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.96755 | + | 7.41118i | −0.193582 | + | 0.483452i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.27212 | − | 3.27212i | −0.212547 | − | 0.212547i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.16538 | + | 9.16538i | −0.592859 | + | 0.592859i | −0.938403 | − | 0.345543i | \(-0.887695\pi\) |
0.345543 | + | 0.938403i | \(0.387695\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.539502 | + | 0.539502i | −0.0347524 | + | 0.0347524i | −0.724269 | − | 0.689517i | \(-0.757823\pi\) |
0.689517 | + | 0.724269i | \(0.257823\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.7689 | + | 15.7689i | −1.01157 | + | 1.01157i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.6629 | − | 31.6244i | 0.809002 | − | 2.02041i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.75075 | − | 1.35758i | 0.238655 | − | 0.0863807i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.8037 | + | 11.8037i | −0.748029 | + | 0.748029i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 15.2991i | − | 0.965674i | −0.875710 | − | 0.482837i | \(-0.839606\pi\) | ||
0.875710 | − | 0.482837i | \(-0.160394\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.29464 | −0.0813933 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 35.3697 | + | 14.1626i | 2.21494 | + | 0.886894i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.25113 | + | 7.25113i | −0.452313 | + | 0.452313i | −0.896122 | − | 0.443809i | \(-0.853627\pi\) |
0.443809 | + | 0.896122i | \(0.353627\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.8570 | −0.923171 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −19.9186 | −1.23293 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.0473 | − | 11.0473i | 0.681208 | − | 0.681208i | −0.279064 | − | 0.960273i | \(-0.590024\pi\) |
0.960273 | + | 0.279064i | \(0.0900242\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.84109 | − | 4.30013i | −0.113097 | − | 0.264155i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −35.3827 | −2.16538 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.22615i | 0.440586i | 0.975434 | + | 0.220293i | \(0.0707013\pi\) | ||||
−0.975434 | + | 0.220293i | \(0.929299\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.58439 | − | 1.58439i | 0.0962449 | − | 0.0962449i | −0.657345 | − | 0.753590i | \(-0.728321\pi\) |
0.753590 | + | 0.657345i | \(0.228321\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 39.7688 | − | 14.3942i | 2.40692 | − | 0.871179i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.98675 | + | 0.0470352i | −0.119805 | + | 0.00283633i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.0009 | − | 11.0009i | 0.660978 | − | 0.660978i | −0.294633 | − | 0.955611i | \(-0.595197\pi\) |
0.955611 | + | 0.294633i | \(0.0951973\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −21.2618 | + | 21.2618i | −1.27291 | + | 1.27291i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.01859 | − | 5.01859i | 0.299384 | − | 0.299384i | −0.541389 | − | 0.840772i | \(-0.682101\pi\) |
0.840772 | + | 0.541389i | \(0.182101\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.5151 | + | 15.5151i | 0.922274 | + | 0.922274i | 0.997190 | − | 0.0749155i | \(-0.0238687\pi\) |
−0.0749155 | + | 0.997190i | \(0.523869\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.71298 | − | 2.28756i | −0.338407 | − | 0.135503i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 39.4686 | + | 39.4686i | 2.32976 | + | 2.32976i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 29.9134i | − | 1.75961i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 23.8595 | + | 23.8595i | 1.39867 | + | 1.39867i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.864418i | 0.0504999i | 0.999681 | + | 0.0252499i | \(0.00803816\pi\) | ||||
−0.999681 | + | 0.0252499i | \(0.991962\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.1499 | − | 5.63009i | 0.765614 | − | 0.327796i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.186282 | 0.0108092 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.99706 | + | 11.0432i | 0.231156 | + | 0.638643i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.7648 | + | 16.7648i | 0.966310 | + | 0.966310i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.63949 | + | 1.63949i | 0.0941861 | + | 0.0941861i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.36794 | − | 8.41112i | 0.192848 | − | 0.481619i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.2003 | 0.924601 | 0.462300 | − | 0.886723i | \(-0.347024\pi\) | ||||
0.462300 | + | 0.886723i | \(0.347024\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.8112 | 0.899469 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.2345i | 1.60103i | 0.599312 | + | 0.800516i | \(0.295441\pi\) | ||||
−0.599312 | + | 0.800516i | \(0.704559\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.9671 | + | 11.9671i | −0.676423 | + | 0.676423i | −0.959189 | − | 0.282766i | \(-0.908748\pi\) |
0.282766 | + | 0.959189i | \(0.408748\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −31.2091 | − | 12.4966i | −1.75843 | − | 0.704102i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 1.66668i | − | 0.0936100i | −0.998904 | − | 0.0468050i | \(-0.985096\pi\) | ||
0.998904 | − | 0.0468050i | \(-0.0149039\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.75576 | − | 1.75576i | −0.0983036 | − | 0.0983036i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.9136 | 0.944025 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.57753i | 0.421625i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.53507 | + | 16.8016i | 0.362500 | + | 0.931984i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 7.52008i | − | 0.415861i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.8348 | −0.928132 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.0216 | + | 18.0216i | 0.990556 | + | 0.990556i | 0.999956 | − | 0.00939989i | \(-0.00299212\pi\) |
−0.00939989 | + | 0.999956i | \(0.502992\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.0460i | 0.550515i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16.2799 | − | 6.51871i | −0.889465 | − | 0.356155i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.7241 | + | 11.7241i | −0.638653 | + | 0.638653i | −0.950223 | − | 0.311570i | \(-0.899145\pi\) |
0.311570 | + | 0.950223i | \(0.399145\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 21.6464i | − | 1.17567i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.74831 | −0.202982 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 38.8286 | 2.09655 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.73516 | − | 16.8205i | 0.362609 | − | 0.905583i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.40632 | − | 3.40632i | −0.182861 | − | 0.182861i | 0.609740 | − | 0.792601i | \(-0.291274\pi\) |
−0.792601 | + | 0.609740i | \(0.791274\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.7962 | − | 12.7962i | −0.684963 | − | 0.684963i | 0.276151 | − | 0.961114i | \(-0.410941\pi\) |
−0.961114 | + | 0.276151i | \(0.910941\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.575124 | − | 1.58897i | −0.0306979 | − | 0.0848128i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.38245 | 0.286479 | 0.143239 | − | 0.989688i | \(-0.454248\pi\) | ||||
0.143239 | + | 0.989688i | \(0.454248\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.7549 | − | 6.74542i | 0.836182 | − | 0.358010i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 80.3437i | 4.25224i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.2099 | − | 23.2099i | −1.22497 | − | 1.22497i | −0.965842 | − | 0.259131i | \(-0.916564\pi\) |
−0.259131 | − | 0.965842i | \(-0.583436\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.7761i | 0.935582i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −19.0715 | − | 19.0715i | −1.00099 | − | 1.00099i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −19.9648 | − | 7.99422i | −1.04501 | − | 0.418437i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.7526 | − | 23.7526i | −1.23987 | − | 1.23987i | −0.960052 | − | 0.279822i | \(-0.909724\pi\) |
−0.279822 | − | 0.960052i | \(-0.590276\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 26.6877 | − | 26.6877i | 1.38931 | − | 1.38931i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.97500 | − | 6.97500i | 0.362124 | − | 0.362124i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.3318 | + | 17.3318i | −0.897406 | + | 0.897406i | −0.995206 | − | 0.0978000i | \(-0.968819\pi\) |
0.0978000 | + | 0.995206i | \(0.468819\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.72464 | − | 26.0573i | 0.502178 | − | 1.34559i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.55576 | + | 20.3972i | −0.492147 | + | 1.05051i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.1822 | + | 16.1822i | −0.831224 | + | 0.831224i | −0.987684 | − | 0.156460i | \(-0.949992\pi\) |
0.156460 | + | 0.987684i | \(0.449992\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 27.5739i | − | 1.41265i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.5091 | 1.20126 | 0.600628 | − | 0.799528i | \(-0.294917\pi\) | ||||
0.600628 | + | 0.799528i | \(0.294917\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.64944 | − | 3.85251i | −0.0840635 | − | 0.196342i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.3360 | − | 11.3360i | 0.576240 | − | 0.576240i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 33.7108 | 1.70921 | 0.854604 | − | 0.519280i | \(-0.173800\pi\) | ||||
0.854604 | + | 0.519280i | \(0.173800\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.3102 | −1.12827 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.12659 | − | 1.12659i | 0.0568291 | − | 0.0568291i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.86143 | + | 1.54618i | 0.194290 | + | 0.0777966i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.2446 | 1.46774 | 0.733872 | − | 0.679288i | \(-0.237711\pi\) | ||||
0.733872 | + | 0.679288i | \(0.237711\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 12.9772i | − | 0.649675i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.8234 | + | 15.8234i | −0.790184 | + | 0.790184i | −0.981524 | − | 0.191340i | \(-0.938717\pi\) |
0.191340 | + | 0.981524i | \(0.438717\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.5725 | + | 31.9728i | 0.576467 | + | 1.59268i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.98147 | − | 17.4356i | 0.346912 | − | 0.866382i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.885518 | + | 0.885518i | −0.0438935 | + | 0.0438935i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.0977 | + | 22.0977i | −1.09266 | + | 1.09266i | −0.0974166 | + | 0.995244i | \(0.531058\pi\) |
−0.995244 | + | 0.0974166i | \(0.968942\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.65312 | + | 4.65312i | −0.229522 | + | 0.229522i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 21.3297 | + | 21.3297i | 1.04956 | + | 1.04956i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.57761 | − | 13.9296i | 0.273794 | − | 0.683776i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.0247 | + | 10.0247i | 0.490911 | + | 0.490911i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 14.4832i | − | 0.707549i | −0.935331 | − | 0.353775i | \(-0.884898\pi\) | ||
0.935331 | − | 0.353775i | \(-0.115102\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.1266 | − | 22.1266i | −1.07839 | − | 1.07839i | −0.996654 | − | 0.0817310i | \(-0.973955\pi\) |
−0.0817310 | − | 0.996654i | \(-0.526045\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.3833i | 0.553473i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −34.2371 | + | 0.810546i | −1.66074 | + | 0.0393173i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.1062 | 0.924613 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.51239 | − | 3.22826i | 0.0730188 | − | 0.155862i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.2677 | − | 18.2677i | −0.879924 | − | 0.879924i | 0.113603 | − | 0.993526i | \(-0.463761\pi\) |
−0.993526 | + | 0.113603i | \(0.963761\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.20010 | + | 9.20010i | 0.442129 | + | 0.442129i | 0.892727 | − | 0.450598i | \(-0.148789\pi\) |
−0.450598 | + | 0.892727i | \(0.648789\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 31.9455 | − | 13.6774i | 1.53167 | − | 0.655782i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.60358 | 0.172382 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.5148 | 0.692752 | 0.346376 | − | 0.938096i | \(-0.387412\pi\) | ||||
0.346376 | + | 0.938096i | \(0.387412\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 48.5737i | − | 2.31304i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.0331 | + | 16.0331i | −0.761757 | + | 0.761757i | −0.976640 | − | 0.214883i | \(-0.931063\pi\) |
0.214883 | + | 0.976640i | \(0.431063\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 29.2373 | − | 12.5179i | 1.38598 | − | 0.593405i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 46.3034i | − | 2.19008i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.3022 | + | 26.3022i | 1.24128 | + | 1.24128i | 0.959470 | + | 0.281810i | \(0.0909346\pi\) |
0.281810 | + | 0.959470i | \(0.409065\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.70487 | 0.221544 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 28.1296i | 1.32164i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −27.7691 | + | 25.9638i | −1.30184 | + | 1.21720i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 27.9739i | − | 1.30856i | −0.756251 | − | 0.654282i | \(-0.772971\pi\) | ||
0.756251 | − | 0.654282i | \(-0.227029\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.21014 | 0.149837 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.2175 | + | 19.2175i | 0.895046 | + | 0.895046i | 0.994993 | − | 0.0999465i | \(-0.0318672\pi\) |
−0.0999465 | + | 0.994993i | \(0.531867\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 28.8100i | − | 1.33892i | −0.742850 | − | 0.669458i | \(-0.766526\pi\) | ||
0.742850 | − | 0.669458i | \(-0.233474\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 19.5000 | − | 48.6995i | 0.904291 | − | 2.25838i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.2034 | − | 24.2034i | 1.12000 | − | 1.12000i | 0.128259 | − | 0.991741i | \(-0.459061\pi\) |
0.991741 | − | 0.128259i | \(-0.0409390\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 36.9804i | − | 1.70759i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −50.7731 | −2.33950 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.99846 | 0.0918892 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.53003 | − | 0.130921i | 0.253735 | − | 0.00600705i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.71632 | − | 4.71632i | −0.215946 | − | 0.215946i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.9541 | + | 11.9541i | 0.546197 | + | 0.546197i | 0.925339 | − | 0.379142i | \(-0.123781\pi\) |
−0.379142 | + | 0.925339i | \(0.623781\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.2873 | + | 4.81946i | 0.469062 | + | 0.219748i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 38.2083 | 1.73854 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −28.1567 | − | 11.2744i | −1.27853 | − | 0.511942i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.7489i | 0.577709i | 0.957373 | + | 0.288854i | \(0.0932743\pi\) | ||||
−0.957373 | + | 0.288854i | \(0.906726\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.39275 | − | 9.39275i | −0.424755 | − | 0.424755i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.59961i | 0.433224i | 0.976258 | + | 0.216612i | \(0.0695007\pi\) | ||||
−0.976258 | + | 0.216612i | \(0.930499\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −30.2565 | − | 30.2565i | −1.36269 | − | 1.36269i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.60497 | + | 1.11531i | −0.117085 | + | 0.0501296i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 25.5551 | + | 25.5551i | 1.14630 | + | 1.14630i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.5467 | + | 24.5467i | −1.09886 | + | 1.09886i | −0.104319 | + | 0.994544i | \(0.533266\pi\) |
−0.994544 | + | 0.104319i | \(0.966734\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.70401 | + | 9.70401i | −0.433543 | + | 0.433543i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.95718 | − | 3.95718i | 0.176442 | − | 0.176442i | −0.613361 | − | 0.789803i | \(-0.710183\pi\) |
0.789803 | + | 0.613361i | \(0.210183\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.93476 | − | 0.774708i | −0.0860958 | − | 0.0344741i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −32.2061 | − | 2.93366i | −1.43032 | − | 0.130289i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.11209 | − | 3.11209i | 0.137941 | − | 0.137941i | −0.634765 | − | 0.772706i | \(-0.718903\pi\) |
0.772706 | + | 0.634765i | \(0.218903\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 45.3509i | − | 2.00620i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.518508 | −0.0228927 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13.0651 | + | 5.59378i | −0.575716 | + | 0.246492i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.00340 | + | 1.00340i | −0.0441294 | + | 0.0441294i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.89245 | 0.302545 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.7076 | −0.688163 | −0.344081 | − | 0.938940i | \(-0.611810\pi\) | ||||
−0.344081 | + | 0.938940i | \(0.611810\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.02118 | + | 5.02118i | −0.219561 | + | 0.219561i | −0.808313 | − | 0.588752i | \(-0.799619\pi\) |
0.588752 | + | 0.808313i | \(0.299619\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 58.6343 | − | 1.38814i | 2.55901 | − | 0.0605832i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −64.5936 | −2.81374 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 12.3902i | − | 0.538702i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.4226 | − | 14.4226i | 0.625888 | − | 0.625888i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.5258 | − | 40.1322i | −0.629181 | − | 1.73832i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.9760 | + | 5.98379i | −0.604235 | + | 0.258702i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −33.8067 | + | 33.8067i | −1.45887 | + | 1.45887i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.28162 | − | 4.28162i | 0.184422 | − | 0.184422i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.7010 | + | 18.7010i | −0.804018 | + | 0.804018i | −0.983721 | − | 0.179703i | \(-0.942486\pi\) |
0.179703 | + | 0.983721i | \(0.442486\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.19217 | + | 5.19217i | 0.222817 | + | 0.222817i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.66050 | + | 6.21396i | 0.113963 | + | 0.266177i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.8583 | − | 27.8583i | −1.19114 | − | 1.19114i | −0.976749 | − | 0.214386i | \(-0.931225\pi\) |
−0.214386 | − | 0.976749i | \(-0.568775\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 12.9191i | − | 0.551375i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.88708 | + | 4.88708i | 0.208197 | + | 0.208197i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.77139i | 0.372998i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.89822 | − | 16.1118i | −0.292813 | − | 0.683906i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.9228 | 0.801783 | 0.400892 | − | 0.916126i | \(-0.368700\pi\) | ||||
0.400892 | + | 0.916126i | \(0.368700\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.17002 | − | 17.0467i | −0.260964 | − | 0.720998i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.78870 | + | 4.78870i | 0.202179 | + | 0.202179i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.3970 | + | 18.3970i | 0.775341 | + | 0.775341i | 0.979035 | − | 0.203694i | \(-0.0652947\pi\) |
−0.203694 | + | 0.979035i | \(0.565295\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.65818 | + | 17.8867i | 0.322182 | + | 0.752501i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 39.6056 | 1.66328 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.8685 | −0.874854 | −0.437427 | − | 0.899254i | \(-0.644110\pi\) | ||||
−0.437427 | + | 0.899254i | \(0.644110\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.59879i | 0.150605i | 0.997161 | + | 0.0753023i | \(0.0239922\pi\) | ||||
−0.997161 | + | 0.0753023i | \(0.976008\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.85124 | − | 3.85124i | 0.160888 | − | 0.160888i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.385464 | + | 16.2818i | 0.0160750 | + | 0.678999i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 20.9808i | − | 0.873442i | −0.899597 | − | 0.436721i | \(-0.856140\pi\) | ||
0.899597 | − | 0.436721i | \(-0.143860\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.95870 | + | 1.95870i | 0.0814008 | + | 0.0814008i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 31.6415 | 1.31271 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 0.831457i | − | 0.0344354i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 17.5561 | + | 18.7768i | 0.725855 | + | 0.776325i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 6.80302i | − | 0.280791i | −0.990096 | − | 0.140395i | \(-0.955163\pi\) | ||
0.990096 | − | 0.140395i | \(-0.0448374\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.4333 | 0.429895 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.84239 | + | 9.84239i | 0.404862 | + | 0.404862i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.9868i | 0.451174i | 0.974223 | + | 0.225587i | \(0.0724299\pi\) | ||||
−0.974223 | + | 0.225587i | \(0.927570\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −28.4244 | − | 66.3893i | −1.16529 | − | 2.72170i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.1596 | + | 13.1596i | −0.538588 | + | 0.538588i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 46.6176i | 1.90474i | 0.304941 | + | 0.952371i | \(0.401363\pi\) | ||||
−0.304941 | + | 0.952371i | \(0.598637\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.301935 | −0.0123162 | −0.00615809 | − | 0.999981i | \(-0.501960\pi\) | ||||
−0.00615809 | + | 0.999981i | \(0.501960\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −25.0052 | −1.01829 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22.5063 | + | 9.01186i | 0.915012 | + | 0.366384i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.09452 | + | 9.09452i | 0.369135 | + | 0.369135i | 0.867162 | − | 0.498026i | \(-0.165942\pi\) |
−0.498026 | + | 0.867162i | \(0.665942\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 51.8171 | + | 51.8171i | 2.09974 | + | 2.09974i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.6568 | + | 5.46102i | 0.471583 | + | 0.220929i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.3083 | −1.46648 | −0.733240 | − | 0.679970i | \(-0.761993\pi\) | ||||
−0.733240 | + | 0.679970i | \(0.761993\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −24.4764 | + | 61.1275i | −0.986982 | + | 2.46490i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.4457i | 0.460787i | 0.973098 | + | 0.230394i | \(0.0740014\pi\) | ||||
−0.973098 | + | 0.230394i | \(0.925999\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.93208 | + | 9.93208i | 0.399204 | + | 0.399204i | 0.877952 | − | 0.478748i | \(-0.158909\pi\) |
−0.478748 | + | 0.877952i | \(0.658909\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 1.52662i | − | 0.0612611i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 47.4242 | + | 47.4242i | 1.90001 | + | 1.90001i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.18306 | + | 24.9720i | 0.0473225 | + | 0.998880i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.773478 | − | 0.773478i | −0.0308897 | − | 0.0308897i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15.2599 | + | 15.2599i | −0.608452 | + | 0.608452i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.8060 | + | 14.8060i | −0.589419 | + | 0.589419i | −0.937474 | − | 0.348055i | \(-0.886842\pi\) |
0.348055 | + | 0.937474i | \(0.386842\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 26.2926 | − | 26.2926i | 1.04504 | − | 1.04504i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.75526 | + | 22.7848i | 0.387126 | + | 0.904186i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −49.7408 | − | 23.3028i | −1.97080 | − | 0.923291i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 17.2798 | − | 17.2798i | 0.683576 | − | 0.683576i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.1792i | 0.560046i | 0.959993 | + | 0.280023i | \(0.0903422\pi\) | ||||
−0.959993 | + | 0.280023i | \(0.909658\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.488940 | 0.0192819 | 0.00964096 | − | 0.999954i | \(-0.496931\pi\) | ||||
0.00964096 | + | 0.999954i | \(0.496931\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.3967 | + | 25.9647i | −0.409368 | + | 1.02236i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.4849 | − | 22.4849i | 0.883972 | − | 0.883972i | −0.109964 | − | 0.993936i | \(-0.535074\pi\) |
0.993936 | + | 0.109964i | \(0.0350735\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.54261 | 0.0998062 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 110.623 | 4.33564 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.78979 | + | 4.78979i | −0.187439 | + | 0.187439i | −0.794588 | − | 0.607149i | \(-0.792313\pi\) |
0.607149 | + | 0.794588i | \(0.292313\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.532350 | + | 1.32950i | −0.0208006 | + | 0.0519477i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −30.6651 | −1.19636 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 9.69986i | − | 0.377853i | −0.981991 | − | 0.188926i | \(-0.939499\pi\) | ||
0.981991 | − | 0.188926i | \(-0.0605008\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.5418 | − | 27.5418i | 1.07125 | − | 1.07125i | 0.0739913 | − | 0.997259i | \(-0.476426\pi\) |
0.997259 | − | 0.0739913i | \(-0.0235737\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 26.0626 | − | 55.6317i | 1.01219 | − | 2.16056i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.59116 | + | 10.7233i | 0.178038 | + | 0.415832i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.3888 | + | 14.3888i | −0.557137 | + | 0.557137i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 34.6681 | − | 34.6681i | 1.34034 | − | 1.34034i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.13878 | − | 1.13878i | 0.0439621 | − | 0.0439621i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.6307 | − | 17.6307i | −0.679615 | − | 0.679615i | 0.280298 | − | 0.959913i | \(-0.409567\pi\) |
−0.959913 | + | 0.280298i | \(0.909567\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.0554632 | − | 2.34274i | −0.00213478 | − | 0.0901721i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.5028 | − | 11.5028i | −0.442089 | − | 0.442089i | 0.450625 | − | 0.892714i | \(-0.351201\pi\) |
−0.892714 | + | 0.450625i | \(0.851201\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 63.9590i | − | 2.45452i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −25.1154 | − | 25.1154i | −0.962424 | − | 0.962424i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 48.3576i | − | 1.85035i | −0.379540 | − | 0.925175i | \(-0.623918\pi\) | ||
0.379540 | − | 0.925175i | \(-0.376082\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.19874 | − | 5.49116i | 0.0840097 | − | 0.209807i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.397822 | 0.0151779 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.09226 | + | 2.56703i | −0.270194 | + | 0.0977961i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.4135 | − | 19.4135i | −0.738525 | − | 0.738525i | 0.233768 | − | 0.972292i | \(-0.424894\pi\) |
−0.972292 | + | 0.233768i | \(0.924894\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.22538 | − | 4.22538i | −0.160509 | − | 0.160509i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.8302 | − | 4.73697i | −0.448743 | − | 0.179684i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 81.0778 | 3.07104 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.06812 | 0.153871 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 7.83662i | − | 0.295985i | −0.988988 | − | 0.147992i | \(-0.952719\pi\) | ||
0.988988 | − | 0.147992i | \(-0.0472811\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.46480 | − | 2.46480i | 0.0929619 | − | 0.0929619i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.81651 | − | 18.2565i | −0.294387 | − | 0.687581i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 4.39489i | − | 0.165287i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.86339 | − | 8.86339i | −0.332872 | − | 0.332872i | 0.520804 | − | 0.853676i | \(-0.325632\pi\) |
−0.853676 | + | 0.520804i | \(0.825632\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.93100 | 0.222430 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 30.7182i | 1.15041i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.107600 | + | 3.20262i | −0.00402400 | + | 0.119771i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 32.2444i | − | 1.20419i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.10825 | 0.302387 | 0.151193 | − | 0.988504i | \(-0.451688\pi\) | ||||
0.151193 | + | 0.988504i | \(0.451688\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.1921 | − | 21.1921i | −0.789237 | − | 0.789237i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 1.89800i | − | 0.0705875i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −21.5582 | + | 22.6038i | −0.800653 | + | 0.839482i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.70651 | + | 7.70651i | −0.285819 | + | 0.285819i | −0.835424 | − | 0.549606i | \(-0.814778\pi\) |
0.549606 | + | 0.835424i | \(0.314778\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 30.2781i | − | 1.12141i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 34.4389 | 1.27377 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.7323 | 0.470277 | 0.235139 | − | 0.971962i | \(-0.424446\pi\) | ||||
0.235139 | + | 0.971962i | \(0.424446\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 33.3540 | + | 77.9028i | 1.23028 | + | 2.87349i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.20413 | − | 2.20413i | −0.0811901 | − | 0.0811901i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.7053 | + | 10.7053i | 0.393801 | + | 0.393801i | 0.876040 | − | 0.482239i | \(-0.160176\pi\) |
−0.482239 | + | 0.876040i | \(0.660176\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.20967 | + | 8.98573i | −0.154646 | + | 0.330099i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −43.4613 | −1.59444 | −0.797220 | − | 0.603689i | \(-0.793697\pi\) | ||||
−0.797220 | + | 0.603689i | \(0.793697\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.3815 | + | 38.2613i | 0.600171 | + | 1.40178i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 21.3952i | − | 0.782810i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −22.6697 | − | 22.6697i | −0.828333 | − | 0.828333i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.6226i | 1.48234i | 0.671317 | + | 0.741171i | \(0.265729\pi\) | ||||
−0.671317 | + | 0.741171i | \(0.734271\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 26.9117 | + | 26.9117i | 0.980718 | + | 0.980718i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.95186 | − | 23.2440i | −0.362185 | − | 0.845934i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.9354 | − | 12.9354i | −0.470145 | − | 0.470145i | 0.431816 | − | 0.901962i | \(-0.357873\pi\) |
−0.901962 | + | 0.431816i | \(0.857873\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.27732 | − | 2.27732i | 0.0826613 | − | 0.0826613i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31.6508 | − | 31.6508i | 1.14734 | − | 1.14734i | 0.160267 | − | 0.987074i | \(-0.448764\pi\) |
0.987074 | − | 0.160267i | \(-0.0512356\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.0793 | + | 10.0793i | −0.364896 | + | 0.364896i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −44.8908 | + | 19.2199i | −1.62303 | + | 0.694897i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.85003 | − | 21.6883i | −0.283448 | − | 0.783117i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.1433 | + | 10.1433i | −0.365776 | + | 0.365776i | −0.865934 | − | 0.500158i | \(-0.833275\pi\) |
0.500158 | + | 0.865934i | \(0.333275\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 25.5100i | − | 0.918719i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.8119 | 0.748551 | 0.374276 | − | 0.927317i | \(-0.377891\pi\) | ||||
0.374276 | + | 0.927317i | \(0.377891\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.11602 | + | 47.1400i | 0.0400885 | + | 1.69332i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 26.1340 | − | 26.1340i | 0.937553 | − | 0.937553i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13.0958 | −0.469206 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.04631 | 0.109005 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.07036 | − | 2.07036i | 0.0739887 | − | 0.0739887i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 41.9546 | − | 17.9628i | 1.49743 | − | 0.641120i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 40.0291 | 1.42688 | 0.713442 | − | 0.700714i | \(-0.247135\pi\) | ||||
0.713442 | + | 0.700714i | \(0.247135\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 38.8653i | 1.38364i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −29.0131 | + | 29.0131i | −1.03159 | + | 1.03159i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.2295 | − | 6.19783i | −0.469795 | − | 0.220092i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.8026 | + | 4.32553i | 0.383129 | + | 0.153411i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.76153 | + | 5.76153i | −0.204084 | + | 0.204084i | −0.801747 | − | 0.597663i | \(-0.796096\pi\) |
0.597663 | + | 0.801747i | \(0.296096\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.2913 | + | 17.2913i | −0.611722 | + | 0.611722i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 32.0671 | − | 32.0671i | 1.13303 | − | 1.13303i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.70303 | − | 2.70303i | −0.0953879 | − | 0.0953879i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −31.5721 | + | 13.5176i | −1.11277 | + | 0.476431i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.7110 | − | 12.7110i | −0.447450 | − | 0.447450i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 11.4657i | − | 0.403112i | −0.979477 | − | 0.201556i | \(-0.935400\pi\) | ||
0.979477 | − | 0.201556i | \(-0.0645998\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.25440 | − | 5.25440i | −0.184507 | − | 0.184507i | 0.608810 | − | 0.793316i | \(-0.291647\pi\) |
−0.793316 | + | 0.608810i | \(0.791647\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.57399i | 0.195489i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.0844 | + | 4.43836i | 0.388270 | + | 0.155469i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.56263 | −0.194612 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −22.9968 | + | 49.0876i | −0.803572 | + | 1.71526i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.7094 | + | 25.7094i | 0.897263 | + | 0.897263i | 0.995193 | − | 0.0979307i | \(-0.0312223\pi\) |
−0.0979307 | + | 0.995193i | \(0.531222\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.3073 | − | 13.3073i | −0.463865 | − | 0.463865i | 0.436055 | − | 0.899920i | \(-0.356375\pi\) |
−0.899920 | + | 0.436055i | \(0.856375\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.41202 | − | 3.57749i | 0.118791 | − | 0.124552i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40.4261 | 1.40575 | 0.702877 | − | 0.711311i | \(-0.251898\pi\) | ||||
0.702877 | + | 0.711311i | \(0.251898\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.00868 | 0.312884 | 0.156442 | − | 0.987687i | \(-0.449998\pi\) | ||||
0.156442 | + | 0.987687i | \(0.449998\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 38.7018i | 1.34255i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 73.7840 | − | 73.7840i | 2.55646 | − | 2.55646i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.58544 | − | 11.4517i | 0.158686 | − | 0.396303i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 4.41995i | − | 0.152776i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.2917 | + | 15.2917i | 0.527929 | + | 0.527929i | 0.919954 | − | 0.392025i | \(-0.128225\pi\) |
−0.392025 | + | 0.919954i | \(0.628225\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.0275 | −0.345776 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.6557i | 0.608096i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 27.6503 | − | 8.96993i | 0.951200 | − | 0.308575i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 51.1239i | 1.75664i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −54.5830 | −1.87328 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.25701 | + | 7.25701i | 0.248767 | + | 0.248767i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.8763i | 0.920226i | 0.887860 | + | 0.460113i | \(0.152191\pi\) | ||||
−0.887860 | + | 0.460113i | \(0.847809\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.25083 | − | 3.10443i | 0.247973 | − | 0.106169i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.53408 | + | 6.53408i | −0.223200 | + | 0.223200i | −0.809844 | − | 0.586645i | \(-0.800449\pi\) |
0.586645 | + | 0.809844i | \(0.300449\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 10.4798i | − | 0.357565i | −0.983889 | − | 0.178783i | \(-0.942784\pi\) | ||
0.983889 | − | 0.178783i | \(-0.0572159\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −138.853 | −4.73211 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.95053 | −0.236599 | −0.118299 | − | 0.992978i | \(-0.537744\pi\) | ||||
−0.118299 | + | 0.992978i | \(0.537744\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.69535 | + | 2.43845i | −0.193648 | + | 0.0829099i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 52.6188 | + | 52.6188i | 1.78703 | + | 1.78703i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.522798 | + | 0.522798i | 0.0177347 | + | 0.0177347i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.9960 | + | 25.6060i | −0.406470 | + | 0.867627i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −43.2475 | −1.46371 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −47.9593 | + | 21.8910i | −1.62132 | + | 0.740051i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 17.4225i | − | 0.588318i | −0.955757 | − | 0.294159i | \(-0.904961\pi\) | ||
0.955757 | − | 0.294159i | \(-0.0950395\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.52054 | − | 1.52054i | −0.0512866 | − | 0.0512866i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 22.8509i | − | 0.769866i | −0.922944 | − | 0.384933i | \(-0.874225\pi\) | ||
0.922944 | − | 0.384933i | \(-0.125775\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.3552 | − | 24.3552i | −0.819618 | − | 0.819618i | 0.166434 | − | 0.986053i | \(-0.446775\pi\) |
−0.986053 | + | 0.166434i | \(0.946775\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.2275 | + | 33.0346i | −0.444639 | + | 1.11044i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.83517 | + | 9.83517i | 0.330233 | + | 0.330233i | 0.852675 | − | 0.522442i | \(-0.174979\pi\) |
−0.522442 | + | 0.852675i | \(0.674979\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −36.9580 | + | 36.9580i | −1.23953 | + | 1.23953i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.36060 | − | 2.36060i | 0.0790831 | − | 0.0790831i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.79292 | − | 2.79292i | 0.0934614 | − | 0.0934614i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.9747 | − | 39.8954i | 0.533976 | − | 1.33356i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −26.4563 | − | 12.3944i | −0.883349 | − | 0.413835i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −41.6593 | + | 41.6593i | −1.38941 | + | 1.38941i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 14.3283i | − | 0.477344i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −58.9799 | −1.96273 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.12729 | − | 2.45346i | −0.203678 | − | 0.0815557i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.1522 | − | 10.1522i | 0.337098 | − | 0.337098i | −0.518176 | − | 0.855274i | \(-0.673389\pi\) |
0.855274 | + | 0.518176i | \(0.173389\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.97171 | −0.0985656 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.9290 | −0.660277 | −0.330139 | − | 0.943932i | \(-0.607096\pi\) | ||||
−0.330139 | + | 0.943932i | \(0.607096\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.88592 | − | 1.88592i | 0.0624148 | − | 0.0624148i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.87113 | + | 20.7198i | 0.293270 | + | 0.684974i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.02000 | −0.0997292 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 14.8038i | − | 0.488332i | −0.969733 | − | 0.244166i | \(-0.921486\pi\) | ||
0.969733 | − | 0.244166i | \(-0.0785141\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.4969 | + | 28.4969i | −0.939005 | + | 0.939005i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.40514 | − | 25.9847i | −0.309574 | − | 0.855298i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.4002 | + | 10.8729i | 0.374837 | + | 0.357499i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.3296 | + | 14.3296i | −0.470646 | + | 0.470646i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.78926 | − | 7.78926i | 0.255557 | − | 0.255557i | −0.567687 | − | 0.823244i | \(-0.692162\pi\) |
0.823244 | + | 0.567687i | \(0.192162\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.9177 | + | 11.9177i | −0.390587 | + | 0.390587i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −49.6654 | − | 49.6654i | −1.62597 | − | 1.62597i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.65115 | − | 2.26280i | −0.184812 | − | 0.0740016i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.2503 | + | 37.2503i | 1.21692 | + | 1.21692i | 0.968707 | + | 0.248209i | \(0.0798419\pi\) |
0.248209 | + | 0.968707i | \(0.420158\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 42.1012i | − | 1.37392i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.77514 | + | 2.77514i | 0.0904671 | + | 0.0904671i | 0.750892 | − | 0.660425i | \(-0.229624\pi\) |
−0.660425 | + | 0.750892i | \(0.729624\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 38.5574i | − | 1.25560i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.54282 | − | 1.94500i | 0.147778 | − | 0.0632708i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −40.5927 | −1.31909 | −0.659543 | − | 0.751667i | \(-0.729250\pi\) | ||||
−0.659543 | + | 0.751667i | \(0.729250\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.7113 | + | 31.4019i | −0.477550 | + | 1.01935i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.93175 | + | 2.93175i | 0.0950684 | + | 0.0950684i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.4282 | + | 12.4282i | 0.402590 | + | 0.402590i | 0.879145 | − | 0.476555i | \(-0.158115\pi\) |
−0.476555 | + | 0.879145i | \(0.658115\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.81983 | + | 4.54485i | −0.0588882 | + | 0.147068i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.17688 | 0.199670 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.4734 | 0.402786 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 57.9370i | 1.86893i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.3287 | + | 15.3287i | −0.493960 | + | 0.493960i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.31147 | − | 0.925546i | −0.0744087 | − | 0.0297944i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 13.2989i | − | 0.427663i | −0.976871 | − | 0.213832i | \(-0.931406\pi\) | ||
0.976871 | − | 0.213832i | \(-0.0685944\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −13.3291 | − | 13.3291i | −0.428194 | − | 0.428194i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.37939 | −0.204724 | −0.102362 | − | 0.994747i | \(-0.532640\pi\) | ||||
−0.102362 | + | 0.994747i | \(0.532640\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 26.8726i | − | 0.861498i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −41.0500 | − | 18.0591i | −1.31465 | − | 0.578355i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.33256i | − | 0.0426324i | −0.999773 | − | 0.0213162i | \(-0.993214\pi\) | ||
0.999773 | − | 0.0213162i | \(-0.00678566\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.65322 | 0.180678 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.81540 | + | 6.81540i | 0.217599 | + | 0.217599i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 50.5175i | 1.61126i | 0.592420 | + | 0.805630i | \(0.298173\pi\) | ||||
−0.592420 | + | 0.805630i | \(0.701827\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.6150 | − | 4.65083i | −0.370086 | − | 0.148188i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 29.6130 | − | 29.6130i | 0.942591 | − | 0.942591i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 16.3778i | − | 0.520783i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.3018 | 1.05787 | 0.528933 | − | 0.848664i | \(-0.322592\pi\) | ||||
0.528933 | + | 0.848664i | \(0.322592\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −63.4012 | −2.01198 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.21833 | − | 15.5297i | 0.197134 | − | 0.492325i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.1643 | + | 14.1643i | 0.448587 | + | 0.448587i | 0.894885 | − | 0.446297i | \(-0.147258\pi\) |
−0.446297 | + | 0.894885i | \(0.647258\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.04419 | − | 1.04419i | −0.0330367 | − | 0.0330367i |
(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 | 1040.2.cd.p.177.2 | 20 | ||
4.3 | odd | 2 | 520.2.bh.f.177.9 | yes | 20 | ||
5.3 | odd | 4 | 1040.2.bg.p.593.2 | 20 | |||
13.5 | odd | 4 | 1040.2.bg.p.577.2 | 20 | |||
20.3 | even | 4 | 520.2.w.f.73.9 | yes | 20 | ||
52.31 | even | 4 | 520.2.w.f.57.9 | ✓ | 20 | ||
65.18 | even | 4 | inner | 1040.2.cd.p.993.2 | 20 | ||
260.83 | odd | 4 | 520.2.bh.f.473.9 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
520.2.w.f.57.9 | ✓ | 20 | 52.31 | even | 4 | ||
520.2.w.f.73.9 | yes | 20 | 20.3 | even | 4 | ||
520.2.bh.f.177.9 | yes | 20 | 4.3 | odd | 2 | ||
520.2.bh.f.473.9 | yes | 20 | 260.83 | odd | 4 | ||
1040.2.bg.p.577.2 | 20 | 13.5 | odd | 4 | |||
1040.2.bg.p.593.2 | 20 | 5.3 | odd | 4 | |||
1040.2.cd.p.177.2 | 20 | 1.1 | even | 1 | trivial | ||
1040.2.cd.p.993.2 | 20 | 65.18 | even | 4 | inner |