Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1380,2,Mod(1057,1380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1380, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1380.1057");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1380.t (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: | \(11.0193554789\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1057.3 | ||
Character | \(\chi\) | \(=\) | 1380.1057 |
Dual form | 1380.2.t.a.1333.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(691\) | \(1201\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.62167 | + | 1.53954i | −0.725233 | + | 0.688503i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.42328 | − | 2.42328i | 0.915915 | − | 0.915915i | −0.0808141 | − | 0.996729i | \(-0.525752\pi\) |
0.996729 | + | 0.0808141i | \(0.0257520\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.29399i | − | 1.29469i | −0.762198 | − | 0.647344i | \(-0.775880\pi\) | ||
0.762198 | − | 0.647344i | \(-0.224120\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.97472 | + | 2.97472i | −0.825038 | + | 0.825038i | −0.986826 | − | 0.161788i | \(-0.948274\pi\) |
0.161788 | + | 0.986826i | \(0.448274\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.0580751 | − | 2.23531i | 0.0149949 | − | 0.577156i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.55993 | + | 5.55993i | −1.34848 | + | 1.34848i | −0.461168 | + | 0.887313i | \(0.652570\pi\) |
−0.887313 | + | 0.461168i | \(0.847430\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.90921 | 0.896834 | 0.448417 | − | 0.893824i | \(-0.351988\pi\) | ||||
0.448417 | + | 0.893824i | \(0.351988\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.42704i | 0.747842i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.00108 | + | 3.74079i | 0.625768 | + | 0.780009i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.259632 | − | 4.99325i | 0.0519264 | − | 0.998651i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.44894i | 1.19754i | 0.800921 | + | 0.598769i | \(0.204343\pi\) | ||||
−0.800921 | + | 0.598769i | \(0.795657\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.44378 | −1.33694 | −0.668471 | − | 0.743738i | \(-0.733051\pi\) | ||||
−0.668471 | + | 0.743738i | \(0.733051\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.03631 | + | 3.03631i | 0.528554 | + | 0.528554i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.199026 | + | 7.66051i | −0.0336415 | + | 1.29486i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.45878 | + | 1.45878i | −0.239822 | + | 0.239822i | −0.816777 | − | 0.576954i | \(-0.804241\pi\) |
0.576954 | + | 0.816777i | \(0.304241\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 4.20688i | − | 0.673640i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.04416 | −0.631592 | −0.315796 | − | 0.948827i | \(-0.602272\pi\) | ||||
−0.315796 | + | 0.948827i | \(0.602272\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.37770 | + | 3.37770i | 0.515094 | + | 0.515094i | 0.916083 | − | 0.400989i | \(-0.131333\pi\) |
−0.400989 | + | 0.916083i | \(0.631333\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.53954 | + | 1.62167i | 0.229501 | + | 0.241744i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.41315 | − | 7.41315i | −1.08132 | − | 1.08132i | −0.996387 | − | 0.0849330i | \(-0.972932\pi\) |
−0.0849330 | − | 0.996387i | \(-0.527068\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 4.74461i | − | 0.677801i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 7.86293i | − | 1.10103i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.484238 | + | 0.484238i | 0.0665152 | + | 0.0665152i | 0.739582 | − | 0.673067i | \(-0.235023\pi\) |
−0.673067 | + | 0.739582i | \(0.735023\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.61077 | + | 6.96344i | 0.891397 | + | 0.938950i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.76423 | + | 2.76423i | −0.366131 | + | 0.366131i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 15.1559i | 1.97313i | 0.163357 | + | 0.986567i | \(0.447768\pi\) | ||||
−0.163357 | + | 0.986567i | \(0.552232\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 12.1499i | − | 1.55563i | −0.628494 | − | 0.777815i | \(-0.716328\pi\) | ||
0.628494 | − | 0.777815i | \(-0.283672\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.42328 | − | 2.42328i | −0.305305 | − | 0.305305i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.244315 | − | 9.40370i | 0.0303036 | − | 1.16639i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.35595 | + | 1.35595i | −0.165655 | + | 0.165655i | −0.785067 | − | 0.619411i | \(-0.787371\pi\) |
0.619411 | + | 0.785067i | \(0.287371\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.76722 | − | 0.523058i | −0.573906 | − | 0.0629688i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.1317 | −1.67712 | −0.838560 | − | 0.544809i | \(-0.816602\pi\) | ||||
−0.838560 | + | 0.544809i | \(0.816602\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.24680 | + | 8.24680i | −0.965214 | + | 0.965214i | −0.999415 | − | 0.0342006i | \(-0.989111\pi\) |
0.0342006 | + | 0.999415i | \(0.489111\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.34718 | + | 3.71435i | 0.386499 | + | 0.428896i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.4056 | − | 10.4056i | −1.18582 | − | 1.18582i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.52299 | −0.846403 | −0.423201 | − | 0.906036i | \(-0.639094\pi\) | ||||
−0.423201 | + | 0.906036i | \(0.639094\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.22090 | − | 3.22090i | −0.353540 | − | 0.353540i | 0.507885 | − | 0.861425i | \(-0.330427\pi\) |
−0.861425 | + | 0.507885i | \(0.830427\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.456640 | − | 17.5761i | 0.0495296 | − | 1.90640i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.56009 | − | 4.56009i | −0.488893 | − | 0.488893i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.86653 | −0.833850 | −0.416925 | − | 0.908941i | \(-0.636892\pi\) | ||||
−0.416925 | + | 0.908941i | \(0.636892\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.4172i | 1.51133i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.26355 | − | 5.26355i | 0.545804 | − | 0.545804i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.33945 | + | 6.01839i | −0.650414 | + | 0.617473i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.32463 | + | 4.32463i | −0.439099 | + | 0.439099i | −0.891709 | − | 0.452610i | \(-0.850493\pi\) |
0.452610 | + | 0.891709i | \(0.350493\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.29399 | −0.431563 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.38025 | −0.833866 | −0.416933 | − | 0.908937i | \(-0.636895\pi\) | ||||
−0.416933 | + | 0.908937i | \(0.636895\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.329316 | + | 0.329316i | 0.0324485 | + | 0.0324485i | 0.723145 | − | 0.690696i | \(-0.242696\pi\) |
−0.690696 | + | 0.723145i | \(0.742696\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.27607 | − | 5.55753i | −0.514891 | − | 0.542360i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.62917 | + | 4.62917i | −0.447519 | + | 0.447519i | −0.894529 | − | 0.447010i | \(-0.852489\pi\) |
0.447010 | + | 0.894529i | \(0.352489\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.3838 | 1.85664 | 0.928318 | − | 0.371788i | \(-0.121255\pi\) | ||||
0.928318 | + | 0.371788i | \(0.121255\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 2.06303i | − | 0.195814i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.60107 | + | 7.60107i | 0.715048 | + | 0.715048i | 0.967587 | − | 0.252538i | \(-0.0812654\pi\) |
−0.252538 | + | 0.967587i | \(0.581265\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.6259 | − | 1.44606i | −0.990867 | − | 0.134845i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.97472 | + | 2.97472i | 0.275013 | + | 0.275013i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 26.9466i | 2.47019i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.43838 | −0.676216 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.85965 | − | 2.85965i | 0.257846 | − | 0.257846i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.26628 | + | 8.49713i | 0.649916 | + | 0.760006i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.71025 | + | 4.71025i | 0.417967 | + | 0.417967i | 0.884502 | − | 0.466536i | \(-0.154498\pi\) |
−0.466536 | + | 0.884502i | \(0.654498\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.77678 | −0.420572 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.75315 | 0.327914 | 0.163957 | − | 0.986467i | \(-0.447574\pi\) | ||||
0.163957 | + | 0.986467i | \(0.447574\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.47312 | − | 9.47312i | 0.821424 | − | 0.821424i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.23531 | − | 0.0580751i | −0.192385 | − | 0.00499831i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.5311 | − | 13.5311i | 1.15604 | − | 1.15604i | 0.170724 | − | 0.985319i | \(-0.445389\pi\) |
0.985319 | − | 0.170724i | \(-0.0546106\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 13.4756i | − | 1.14299i | −0.820606 | − | 0.571494i | \(-0.806364\pi\) | ||
0.820606 | − | 0.571494i | \(-0.193636\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.4838 | 0.882894 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.7734 | + | 12.7734i | 1.06817 | + | 1.06817i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.92841 | − | 10.4581i | −0.824509 | − | 0.868495i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.35494 | + | 3.35494i | 0.276711 | + | 0.276711i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.23720 | −0.101355 | −0.0506777 | − | 0.998715i | \(-0.516138\pi\) | ||||
−0.0506777 | + | 0.998715i | \(0.516138\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.50269 | −0.447802 | −0.223901 | − | 0.974612i | \(-0.571879\pi\) | ||||
−0.223901 | + | 0.974612i | \(0.571879\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.55993 | + | 5.55993i | 0.449494 | + | 0.449494i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.0714 | − | 11.4600i | 0.969595 | − | 0.920489i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.05369 | + | 5.05369i | −0.403329 | + | 0.403329i | −0.879404 | − | 0.476076i | \(-0.842059\pi\) |
0.476076 | + | 0.879404i | \(0.342059\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.684816 | −0.0543095 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.3375 | + | 1.79254i | 1.28757 | + | 0.141272i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.132281 | − | 0.132281i | 0.0103611 | − | 0.0103611i | −0.701907 | − | 0.712268i | \(-0.747668\pi\) |
0.712268 | + | 0.701907i | \(0.247668\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.59842 | − | 0.249374i | −0.747236 | − | 0.0194137i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.14511 | + | 9.14511i | 0.707670 | + | 0.707670i | 0.966045 | − | 0.258375i | \(-0.0831870\pi\) |
−0.258375 | + | 0.966045i | \(0.583187\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 4.69787i | − | 0.361374i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 3.90921i | − | 0.298945i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.4998 | + | 10.4998i | −0.798283 | + | 0.798283i | −0.982825 | − | 0.184541i | \(-0.940920\pi\) |
0.184541 | + | 0.982825i | \(0.440920\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.4709 | − | 12.7292i | −0.867119 | − | 0.962240i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.7169 | − | 10.7169i | −0.805529 | − | 0.805529i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 18.6034i | − | 1.39048i | −0.718777 | − | 0.695241i | \(-0.755298\pi\) | ||
0.718777 | − | 0.695241i | \(-0.244702\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.62136i | 0.640820i | 0.947279 | + | 0.320410i | \(0.103821\pi\) | ||||
−0.947279 | + | 0.320410i | \(0.896179\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.59125 | + | 8.59125i | 0.635083 | + | 0.635083i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.119811 | − | 4.61152i | 0.00880866 | − | 0.339046i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 23.8743 | + | 23.8743i | 1.74586 | + | 1.74586i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.42704 | 0.249281 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 7.09143i | − | 0.513118i | −0.966529 | − | 0.256559i | \(-0.917411\pi\) | ||
0.966529 | − | 0.256559i | \(-0.0825888\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.02699 | + | 2.02699i | −0.145906 | + | 0.145906i | −0.776286 | − | 0.630381i | \(-0.782899\pi\) |
0.630381 | + | 0.776286i | \(0.282899\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.47667 | + | 6.82218i | 0.463804 | + | 0.488546i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.1838 | + | 17.1838i | 1.22429 | + | 1.22429i | 0.966091 | + | 0.258203i | \(0.0831302\pi\) |
0.258203 | + | 0.966091i | \(0.416870\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.2591 | −1.71968 | −0.859839 | − | 0.510565i | \(-0.829436\pi\) | ||||
−0.859839 | + | 0.510565i | \(0.829436\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 1.91760i | − | 0.135257i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.6276 | + | 15.6276i | 1.09684 | + | 1.09684i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.55830 | − | 6.22615i | 0.458051 | − | 0.434853i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.74079 | − | 3.00108i | 0.260003 | − | 0.208589i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 16.7861i | − | 1.16112i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.0827 | 1.38255 | 0.691277 | − | 0.722590i | \(-0.257049\pi\) | ||||
0.691277 | + | 0.722590i | \(0.257049\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.99260 | − | 9.99260i | 0.684681 | − | 0.684681i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.6776 | − | 0.277412i | −0.728207 | − | 0.0189194i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18.0384 | + | 18.0384i | −1.22453 | + | 1.22453i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 11.6627i | − | 0.788094i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 33.0784i | − | 2.22510i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.02181 | − | 9.02181i | 0.604145 | − | 0.604145i | −0.337265 | − | 0.941410i | \(-0.609502\pi\) |
0.941410 | + | 0.337265i | \(0.109502\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.99325 | − | 0.259632i | −0.332884 | − | 0.0173088i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.48763 | + | 8.48763i | −0.563343 | + | 0.563343i | −0.930256 | − | 0.366912i | \(-0.880415\pi\) |
0.366912 | + | 0.930256i | \(0.380415\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.8119 | −1.11096 | −0.555480 | − | 0.831530i | \(-0.687466\pi\) | ||||
−0.555480 | + | 0.831530i | \(0.687466\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.7157 | 0.968221 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.3998 | + | 13.3998i | −0.877849 | + | 0.877849i | −0.993312 | − | 0.115463i | \(-0.963165\pi\) |
0.115463 | + | 0.993312i | \(0.463165\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 23.4345 | + | 0.608847i | 1.52870 | + | 0.0397168i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.31956 | − | 5.31956i | 0.345542 | − | 0.345542i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.795147i | 0.0514338i | 0.999669 | + | 0.0257169i | \(0.00818685\pi\) | ||||
−0.999669 | + | 0.0257169i | \(0.991813\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 23.1419i | − | 1.49070i | −0.666674 | − | 0.745350i | \(-0.732282\pi\) | ||
0.666674 | − | 0.745350i | \(-0.267718\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.30451 | + | 7.69419i | 0.466668 | + | 0.491564i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.6288 | + | 11.6288i | −0.739922 | + | 0.739922i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.55504 | 0.288664 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.99742i | 0.315435i | 0.987484 | + | 0.157717i | \(0.0504135\pi\) | ||||
−0.987484 | + | 0.157717i | \(0.949587\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.0629 | − | 12.8866i | 1.00987 | − | 0.810174i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.1053 | + | 12.7511i | 0.758063 | + | 0.798504i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.31312 | + | 9.31312i | 0.580937 | + | 0.580937i | 0.935161 | − | 0.354224i | \(-0.115255\pi\) |
−0.354224 | + | 0.935161i | \(0.615255\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.07009i | 0.439314i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.44894 | 0.399180 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.98627 | − | 2.98627i | −0.184141 | − | 0.184141i | 0.609016 | − | 0.793158i | \(-0.291564\pi\) |
−0.793158 | + | 0.609016i | \(0.791564\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.53078 | − | 0.0397708i | −0.0940350 | − | 0.00244310i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.56247 | − | 5.56247i | 0.340418 | − | 0.340418i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.65419i | 0.405713i | 0.979208 | + | 0.202857i | \(0.0650225\pi\) | ||||
−0.979208 | + | 0.202857i | \(0.934978\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.10057 | 0.188346 | 0.0941731 | − | 0.995556i | \(-0.469979\pi\) | ||||
0.0941731 | + | 0.995556i | \(0.469979\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.1945 | − | 10.1945i | −0.616997 | − | 0.616997i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −21.4410 | − | 1.11486i | −1.29294 | − | 0.0672285i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.2733 | − | 14.2733i | −0.857599 | − | 0.857599i | 0.133456 | − | 0.991055i | \(-0.457393\pi\) |
−0.991055 | + | 0.133456i | \(0.957393\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.44378i | 0.445647i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 5.58516i | − | 0.333183i | −0.986026 | − | 0.166591i | \(-0.946724\pi\) | ||
0.986026 | − | 0.166591i | \(-0.0532760\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.5902 | + | 15.5902i | 0.926739 | + | 0.926739i | 0.997494 | − | 0.0707550i | \(-0.0225408\pi\) |
−0.0707550 | + | 0.997494i | \(0.522541\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.227028 | − | 8.73831i | 0.0134480 | − | 0.517613i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.80015 | + | 9.80015i | −0.578485 | + | 0.578485i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 44.8256i | − | 2.63680i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 6.11595i | − | 0.358523i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.83471 | − | 7.83471i | −0.457708 | − | 0.457708i | 0.440194 | − | 0.897903i | \(-0.354910\pi\) |
−0.897903 | + | 0.440194i | \(0.854910\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −23.3332 | − | 24.5779i | −1.35851 | − | 1.43098i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.03631 | − | 3.03631i | 0.176185 | − | 0.176185i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −20.0551 | − | 2.20044i | −1.15982 | − | 0.127255i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.3702 | 0.943564 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.92573 | − | 5.92573i | 0.340424 | − | 0.340424i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 18.7052 | + | 19.7031i | 1.07106 | + | 1.12819i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.4715 | + | 12.4715i | 0.711788 | + | 0.711788i | 0.966909 | − | 0.255121i | \(-0.0821154\pi\) |
−0.255121 | + | 0.966909i | \(0.582115\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.465723 | −0.0264941 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.97357 | 0.395435 | 0.197717 | − | 0.980259i | \(-0.436647\pi\) | ||||
0.197717 | + | 0.980259i | \(0.436647\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.65841 | − | 3.65841i | −0.206786 | − | 0.206786i | 0.596114 | − | 0.802900i | \(-0.296711\pi\) |
−0.802900 | + | 0.596114i | \(0.796711\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.66051 | + | 0.199026i | 0.431621 | + | 0.0112138i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.0363 | + | 12.0363i | 0.676024 | + | 0.676024i | 0.959098 | − | 0.283074i | \(-0.0913542\pi\) |
−0.283074 | + | 0.959098i | \(0.591354\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 27.6917 | 1.55044 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 6.54664i | − | 0.365398i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.7349 | + | 21.7349i | −1.20936 | + | 1.20936i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.0812 | + | 15.6258i | 0.781083 | + | 0.866766i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13.7064 | + | 13.7064i | −0.757968 | + | 0.757968i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −35.9283 | −1.98079 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.5843 | 1.79100 | 0.895499 | − | 0.445064i | \(-0.146819\pi\) | ||||
0.895499 | + | 0.445064i | \(0.146819\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.45878 | + | 1.45878i | 0.0799408 | + | 0.0799408i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.111365 | − | 4.28643i | 0.00608450 | − | 0.234193i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.03755 | − | 5.03755i | 0.274413 | − | 0.274413i | −0.556461 | − | 0.830874i | \(-0.687841\pi\) |
0.830874 | + | 0.556461i | \(0.187841\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.7495 | −0.583835 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 31.9635i | 1.73092i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.46546 | + | 5.46546i | 0.295107 | + | 0.295107i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.53613 | − | 6.49110i | 0.459570 | − | 0.349469i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.38983 | − | 5.38983i | −0.289341 | − | 0.289341i | 0.547479 | − | 0.836820i | \(-0.315588\pi\) |
−0.836820 | + | 0.547479i | \(0.815588\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.7785i | 1.59400i | 0.603976 | + | 0.797002i | \(0.293582\pi\) | ||||
−0.603976 | + | 0.797002i | \(0.706418\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.20688 | −0.224547 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.8433 | − | 16.8433i | 0.896476 | − | 0.896476i | −0.0986466 | − | 0.995123i | \(-0.531451\pi\) |
0.995123 | + | 0.0986466i | \(0.0314513\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.9169 | − | 21.7563i | 1.21630 | − | 1.15470i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −19.0541 | − | 19.0541i | −1.00845 | − | 1.00845i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.87689 | 0.204615 | 0.102307 | − | 0.994753i | \(-0.467378\pi\) | ||||
0.102307 | + | 0.994753i | \(0.467378\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.71808 | −0.195688 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.25973 | − | 5.25973i | 0.276064 | − | 0.276064i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.677314 | − | 26.0699i | 0.0354522 | − | 1.36456i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.3782 | − | 10.3782i | 0.541738 | − | 0.541738i | −0.382300 | − | 0.924038i | \(-0.624868\pi\) |
0.924038 | + | 0.382300i | \(0.124868\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.04416i | 0.210531i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.34689 | 0.121845 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.9119 | + | 18.9119i | 0.979222 | + | 0.979222i | 0.999788 | − | 0.0205660i | \(-0.00654683\pi\) |
−0.0205660 | + | 0.999788i | \(0.506547\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.1464 | − | 0.870343i | −0.575598 | − | 0.0449443i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −19.1838 | − | 19.1838i | −0.988015 | − | 0.988015i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.0884 | 1.18597 | 0.592985 | − | 0.805213i | \(-0.297949\pi\) | ||||
0.592985 | + | 0.805213i | \(0.297949\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.66129 | −0.341268 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.2739 | − | 15.2739i | −0.780459 | − | 0.780459i | 0.199449 | − | 0.979908i | \(-0.436085\pi\) |
−0.979908 | + | 0.199449i | \(0.936085\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 32.8942 | + | 0.854615i | 1.67644 | + | 0.0435552i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.37770 | − | 3.37770i | 0.171698 | − | 0.171698i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.72655 | −0.391751 | −0.195876 | − | 0.980629i | \(-0.562755\pi\) | ||||
−0.195876 | + | 0.980629i | \(0.562755\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −37.4843 | − | 4.11277i | −1.89566 | − | 0.207991i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.65388 | + | 2.65388i | −0.133870 | + | 0.133870i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.1998 | − | 11.5819i | 0.613839 | − | 0.582751i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.7465 | − | 25.7465i | −1.29218 | − | 1.29218i | −0.933436 | − | 0.358745i | \(-0.883205\pi\) |
−0.358745 | − | 0.933436i | \(-0.616795\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 13.3970i | 0.670690i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 4.30417i | − | 0.214940i | −0.994208 | − | 0.107470i | \(-0.965725\pi\) | ||
0.994208 | − | 0.107470i | \(-0.0342750\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.1431 | − | 22.1431i | 1.10303 | − | 1.10303i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.62167 | − | 1.53954i | 0.0805815 | − | 0.0765004i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.26400 | + | 6.26400i | 0.310495 | + | 0.310495i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 10.1730i | − | 0.503022i | −0.967854 | − | 0.251511i | \(-0.919073\pi\) | ||
0.967854 | − | 0.251511i | \(-0.0809274\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.1359i | 0.943905i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 36.7271 | + | 36.7271i | 1.80722 | + | 1.80722i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.1819 | + | 0.264534i | 0.499812 | + | 0.0129855i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.52871 | + | 9.52871i | 0.466623 | + | 0.466623i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.763920 | −0.0373199 | −0.0186600 | − | 0.999826i | \(-0.505940\pi\) | ||||
−0.0186600 | + | 0.999826i | \(0.505940\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.69690i | 0.131439i | 0.997838 | + | 0.0657194i | \(0.0209342\pi\) | ||||
−0.997838 | + | 0.0657194i | \(0.979066\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.41315 | + | 7.41315i | −0.360440 | + | 0.360440i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 26.3186 | + | 29.2057i | 1.27664 | + | 1.41668i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −29.4425 | − | 29.4425i | −1.42482 | − | 1.42482i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −18.0643 | −0.872154 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 12.1006i | − | 0.582868i | −0.956591 | − | 0.291434i | \(-0.905868\pi\) | ||
0.956591 | − | 0.291434i | \(-0.0941323\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.5487 | + | 16.5487i | 0.795281 | + | 0.795281i | 0.982347 | − | 0.187066i | \(-0.0598980\pi\) |
−0.187066 | + | 0.982347i | \(0.559898\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.4154 | + | 0.374523i | 0.691166 | + | 0.0179570i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.7318 | + | 14.6235i | 0.561210 | + | 0.699539i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.7012i | 1.27438i | 0.770706 | + | 0.637190i | \(0.219904\pi\) | ||||
−0.770706 | + | 0.637190i | \(0.780096\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.74461 | −0.225934 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.58880 | − | 8.58880i | 0.408066 | − | 0.408066i | −0.472998 | − | 0.881064i | \(-0.656828\pi\) |
0.881064 | + | 0.472998i | \(0.156828\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.7569 | − | 12.1108i | 0.604736 | − | 0.574109i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.874832 | − | 0.874832i | 0.0413781 | − | 0.0413781i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 5.02794i | − | 0.237283i | −0.992937 | − | 0.118642i | \(-0.962146\pi\) | ||
0.992937 | − | 0.118642i | \(-0.0378540\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.3656i | 0.817714i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.89099 | − | 3.89099i | 0.182815 | − | 0.182815i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −22.1958 | − | 23.3799i | −1.04055 | − | 1.09607i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.2129 | + | 22.2129i | −1.03907 | + | 1.03907i | −0.0398684 | + | 0.999205i | \(0.512694\pi\) |
−0.999205 | + | 0.0398684i | \(0.987306\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.86293 | −0.367010 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.08115 | −0.143503 | −0.0717517 | − | 0.997423i | \(-0.522859\pi\) | ||||
−0.0717517 | + | 0.997423i | \(0.522859\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.8994 | + | 12.8994i | −0.599486 | + | 0.599486i | −0.940176 | − | 0.340690i | \(-0.889339\pi\) |
0.340690 | + | 0.940176i | \(0.389339\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.432298 | + | 16.6392i | −0.0200473 | + | 0.771623i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.6873 | − | 21.6873i | 1.00357 | − | 1.00357i | 0.00357715 | − | 0.999994i | \(-0.498861\pi\) |
0.999994 | − | 0.00357715i | \(-0.00113865\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.57169i | 0.303452i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 7.14700i | − | 0.329316i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.5038 | − | 14.5038i | 0.666885 | − | 0.666885i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.01496 | − | 19.5197i | 0.0465694 | − | 0.895624i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.484238 | − | 0.484238i | 0.0221717 | − | 0.0221717i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.8616 | 0.861807 | 0.430903 | − | 0.902398i | \(-0.358195\pi\) | ||||
0.430903 | + | 0.902398i | \(0.358195\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 8.67893i | − | 0.395725i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.8198 | + | 10.2848i | −0.583323 | + | 0.467975i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.355184 | − | 13.6711i | 0.0161281 | − | 0.620771i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.9118 | + | 10.9118i | 0.494460 | + | 0.494460i | 0.909708 | − | 0.415248i | \(-0.136305\pi\) |
−0.415248 | + | 0.909708i | \(0.636305\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.187074i | 0.00845976i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.8654 | −0.580605 | −0.290303 | − | 0.956935i | \(-0.593756\pi\) | ||||
−0.290303 | + | 0.956935i | \(0.593756\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −35.8557 | − | 35.8557i | −1.61486 | − | 1.61486i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.96344 | − | 6.61077i | 0.312983 | − | 0.297132i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −34.2450 | + | 34.2450i | −1.53610 | + | 1.53610i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.6623i | 0.745908i | 0.927850 | + | 0.372954i | \(0.121655\pi\) | ||||
−0.927850 | + | 0.372954i | \(0.878345\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.9331 | −0.577810 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.18468 | + | 2.18468i | 0.0974102 | + | 0.0974102i | 0.754133 | − | 0.656722i | \(-0.228058\pi\) |
−0.656722 | + | 0.754133i | \(0.728058\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.5900 | − | 12.9017i | 0.604747 | − | 0.574119i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.32189 | + | 3.32189i | 0.147530 | + | 0.147530i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.5788i | 1.04511i | 0.852605 | + | 0.522557i | \(0.175022\pi\) | ||||
−0.852605 | + | 0.522557i | \(0.824978\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 39.9686i | 1.76811i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.76423 | + | 2.76423i | 0.122044 | + | 0.122044i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.04104 | − | 0.0270469i | −0.0458736 | − | 0.00119183i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −31.8320 | + | 31.8320i | −1.39997 | + | 1.39997i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 14.8489i | − | 0.651796i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 40.5459i | − | 1.77635i | −0.459509 | − | 0.888173i | \(-0.651975\pi\) | ||
0.459509 | − | 0.888173i | \(-0.348025\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.7767 | − | 16.7767i | −0.733592 | − | 0.733592i | 0.237737 | − | 0.971329i | \(-0.423594\pi\) |
−0.971329 | + | 0.237737i | \(0.923594\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 17.1121 | + | 0.889770i | 0.746833 | + | 0.0388327i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 41.3869 | − | 41.3869i | 1.80284 | − | 1.80284i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.98707 | + | 22.4528i | −0.216829 | + | 0.976210i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.1559 | 0.657711 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.0302 | − | 12.0302i | 0.521087 | − | 0.521087i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.380197 | − | 14.6338i | 0.0164373 | − | 0.632674i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.1546 | + | 13.1546i | 0.567662 | + | 0.567662i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20.3733 | −0.877540 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.07553 | −0.218214 | −0.109107 | − | 0.994030i | \(-0.534799\pi\) | ||||
−0.109107 | + | 0.994030i | \(0.534799\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.09622 | − | 6.09622i | −0.261614 | − | 0.261614i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −31.4342 | + | 29.8422i | −1.34649 | + | 1.27830i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.0257 | + | 10.0257i | 0.428667 | + | 0.428667i | 0.888174 | − | 0.459507i | \(-0.151974\pi\) |
−0.459507 | + | 0.888174i | \(0.651974\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.1499 | −0.518543 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 25.2103i | 1.07399i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18.2303 | + | 18.2303i | −0.775233 | + | 0.775233i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.17612 | + | 3.34556i | 0.134819 | + | 0.142011i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.2312 | + | 14.2312i | −0.602996 | + | 0.602996i | −0.941106 | − | 0.338110i | \(-0.890212\pi\) |
0.338110 | + | 0.941106i | \(0.390212\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.0954 | −0.849943 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −33.7634 | −1.42549 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.04643 | − | 4.04643i | −0.170537 | − | 0.170537i | 0.616678 | − | 0.787215i | \(-0.288478\pi\) |
−0.787215 | + | 0.616678i | \(0.788478\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −24.0286 | − | 0.624280i | −1.01089 | − | 0.0262637i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.42328 | + | 2.42328i | −0.101768 | + | 0.101768i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.676811 | 0.0283734 | 0.0141867 | − | 0.999899i | \(-0.495484\pi\) | ||||
0.0141867 | + | 0.999899i | \(0.495484\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.5218i | 0.984357i | 0.870494 | + | 0.492178i | \(0.163799\pi\) | ||||
−0.870494 | + | 0.492178i | \(0.836201\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.01440 | + | 5.01440i | 0.209480 | + | 0.209480i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 19.4579 | − | 14.0139i | 0.811451 | − | 0.584421i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.6048 | − | 11.6048i | −0.483113 | − | 0.483113i | 0.423011 | − | 0.906124i | \(-0.360973\pi\) |
−0.906124 | + | 0.423011i | \(0.860973\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 2.86659i | − | 0.119132i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.6103 | −0.647624 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.07932 | − | 2.07932i | 0.0861164 | − | 0.0861164i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.40370 | − | 0.244315i | −0.388795 | − | 0.0101012i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.63593 | + | 9.63593i | 0.397717 | + | 0.397717i | 0.877427 | − | 0.479710i | \(-0.159258\pi\) |
−0.479710 | + | 0.877427i | \(0.659258\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29.0993 | −1.19902 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.3015 | −0.999631 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.4629 | − | 16.4629i | 0.676049 | − | 0.676049i | −0.283055 | − | 0.959104i | \(-0.591348\pi\) |
0.959104 | + | 0.283055i | \(0.0913478\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −41.4853 | − | 43.6985i | −1.70073 | − | 1.79146i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.1537 | − | 17.1537i | 0.702056 | − | 0.702056i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 23.9384i | − | 0.978097i | −0.872257 | − | 0.489048i | \(-0.837344\pi\) | ||
0.872257 | − | 0.489048i | \(-0.162656\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.29617 | −0.134454 | −0.0672269 | − | 0.997738i | \(-0.521415\pi\) | ||||
−0.0672269 | + | 0.997738i | \(0.521415\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.35595 | + | 1.35595i | 0.0552184 | + | 0.0552184i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.0626 | − | 11.4517i | 0.490414 | − | 0.465577i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.10815 | − | 2.10815i | −0.0855670 | − | 0.0855670i | 0.663028 | − | 0.748595i | \(-0.269271\pi\) |
−0.748595 | + | 0.663028i | \(0.769271\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −22.1008 | −0.895569 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 44.1041 | 1.78426 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.3502 | − | 18.3502i | −0.741157 | − | 0.741157i | 0.231644 | − | 0.972801i | \(-0.425590\pi\) |
−0.972801 | + | 0.231644i | \(0.925590\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.234865 | + | 9.03997i | −0.00947068 | + | 0.364527i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.6621 | − | 31.6621i | 1.27467 | − | 1.27467i | 0.331061 | − | 0.943610i | \(-0.392594\pi\) |
0.943610 | − | 0.331061i | \(-0.107406\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.85168 | 0.114619 | 0.0573093 | − | 0.998356i | \(-0.481748\pi\) | ||||
0.0573093 | + | 0.998356i | \(0.481748\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.523058 | + | 4.76722i | −0.0209896 | + | 0.191302i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −19.0628 | + | 19.0628i | −0.763736 | + | 0.763736i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.8652 | − | 2.59282i | −0.994607 | − | 0.103713i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.8696 | + | 11.8696i | 0.474025 | + | 0.474025i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 16.2215i | − | 0.646792i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 8.75077i | − | 0.348362i | −0.984714 | − | 0.174181i | \(-0.944272\pi\) | ||
0.984714 | − | 0.174181i | \(-0.0557279\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.2006 | + | 14.2006i | −0.564425 | + | 0.564425i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.8901 | − | 0.386855i | −0.590895 | − | 0.0153519i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.1139 | + | 14.1139i | 0.559211 | + | 0.559211i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.1317i | 0.559040i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.3110i | 0.960228i | 0.877206 | + | 0.480114i | \(0.159405\pi\) | ||||
−0.877206 | + | 0.480114i | \(0.840595\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.56365 | − | 1.56365i | −0.0616643 | − | 0.0616643i | 0.675602 | − | 0.737266i | \(-0.263884\pi\) |
−0.737266 | + | 0.675602i | \(0.763884\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.74637 | − | 7.35405i | 0.305013 | − | 0.289565i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −31.7988 | − | 31.7988i | −1.25014 | − | 1.25014i | −0.955657 | − | 0.294483i | \(-0.904853\pi\) |
−0.294483 | − | 0.955657i | \(-0.595147\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 65.0795 | 2.55459 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 25.5101i | − | 0.999821i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.8488 | − | 10.8488i | 0.424546 | − | 0.424546i | −0.462220 | − | 0.886765i | \(-0.652947\pi\) |
0.886765 | + | 0.462220i | \(0.152947\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.08637 | + | 5.77813i | −0.237814 | + | 0.225770i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.24680 | + | 8.24680i | 0.321738 | + | 0.321738i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −38.4656 | −1.49841 | −0.749203 | − | 0.662341i | \(-0.769563\pi\) | ||||
−0.749203 | + | 0.662341i | \(0.769563\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 25.7565i | − | 1.00181i | −0.865502 | − | 0.500905i | \(-0.833001\pi\) | ||
0.865502 | − | 0.500905i | \(-0.166999\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 23.3900 | + | 23.3900i | 0.908391 | + | 0.908391i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.778033 | + | 29.9465i | −0.0301708 | + | 1.16128i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.1242 | + | 19.3538i | −0.934091 | + | 0.749381i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.7588i | 0.493282i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −52.1714 | −2.01405 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.2159 | + | 30.2159i | −1.16474 | + | 1.16474i | −0.181312 | + | 0.983426i | \(0.558034\pi\) |
−0.983426 | + | 0.181312i | \(0.941966\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.71435 | − | 3.34718i | 0.142965 | − | 0.128833i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.437662 | + | 0.437662i | −0.0168207 | + | 0.0168207i | −0.715467 | − | 0.698646i | \(-0.753786\pi\) |
0.698646 | + | 0.715467i | \(0.253786\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.9596i | 0.804355i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 12.0033i | − | 0.459968i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.39542 | + | 4.39542i | −0.168186 | + | 0.168186i | −0.786182 | − | 0.617996i | \(-0.787945\pi\) |
0.617996 | + | 0.786182i | \(0.287945\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.11132 | + | 42.7748i | −0.0424614 | + | 1.63434i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.8878 | − | 11.8878i | 0.453548 | − | 0.453548i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.88094 | −0.109755 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.66838 | 0.253677 | 0.126839 | − | 0.991923i | \(-0.459517\pi\) | ||||
0.126839 | + | 0.991923i | \(0.459517\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.4056 | + | 10.4056i | −0.395275 | + | 0.395275i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20.7463 | + | 21.8530i | 0.786951 | + | 0.828933i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.4853 | − | 22.4853i | 0.851690 | − | 0.851690i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 18.9502i | − | 0.716761i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 14.9673i | − | 0.565309i | −0.959222 | − | 0.282654i | \(-0.908785\pi\) | ||
0.959222 | − | 0.282654i | \(-0.0912150\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.70269 | + | 5.70269i | −0.215081 | + | 0.215081i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −17.0012 | + | 16.1402i | −0.640304 | + | 0.607875i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −20.3077 | + | 20.3077i | −0.763750 | + | 0.763750i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.4512 | 0.617838 | 0.308919 | − | 0.951088i | \(-0.400033\pi\) | ||||
0.308919 | + | 0.951088i | \(0.400033\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.52299i | 0.282134i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −22.3394 | − | 27.8456i | −0.836615 | − | 1.04283i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −40.3794 | − | 1.04909i | −1.51011 | − | 0.0392337i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.562254 | − | 0.562254i | −0.0209978 | − | 0.0209978i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.5756i | 0.506286i | 0.967429 | + | 0.253143i | \(0.0814642\pi\) | ||||
−0.967429 | + | 0.253143i | \(0.918536\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.59605 | 0.0594401 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.3638 | + | 16.3638i | 0.608576 | + | 0.608576i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 32.2012 | + | 1.67435i | 1.19592 | + | 0.0621839i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.54345 | − | 1.54345i | 0.0572435 | − | 0.0572435i | −0.677906 | − | 0.735149i | \(-0.737112\pi\) |
0.735149 | + | 0.677906i | \(0.237112\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −37.5595 | −1.38919 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.44932 | − | 9.44932i | −0.349019 | − | 0.349019i | 0.510725 | − | 0.859744i | \(-0.329377\pi\) |
−0.859744 | + | 0.510725i | \(0.829377\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −10.6057 | − | 0.275544i | −0.391197 | − | 0.0101636i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.82242 | + | 5.82242i | 0.214472 | + | 0.214472i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 39.5398i | − | 1.45450i | −0.686374 | − | 0.727248i | \(-0.740799\pi\) | ||
0.686374 | − | 0.727248i | \(-0.259201\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 16.4456i | − | 0.604144i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.1890 | + | 13.1890i | 0.483858 | + | 0.483858i | 0.906361 | − | 0.422503i | \(-0.138848\pi\) |
−0.422503 | + | 0.906361i | \(0.638848\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.00633 | − | 1.90472i | 0.0735062 | − | 0.0697835i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.22090 | + | 3.22090i | −0.117847 | + | 0.117847i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22.4356i | 0.819779i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.2467i | 1.35915i | 0.733606 | + | 0.679576i | \(0.237836\pi\) | ||||
−0.733606 | + | 0.679576i | \(0.762164\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.53371 | − | 3.53371i | −0.128776 | − | 0.128776i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.92355 | − | 8.47161i | 0.324761 | − | 0.308313i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.5183 | + | 10.5183i | −0.382296 | + | 0.382296i | −0.871929 | − | 0.489633i | \(-0.837131\pi\) |
0.489633 | + | 0.871929i | \(0.337131\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.24601 | + | 20.4704i | −0.0815249 | + | 0.743029i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 52.6037 | 1.90688 | 0.953441 | − | 0.301579i | \(-0.0975136\pi\) | ||||
0.953441 | + | 0.301579i | \(0.0975136\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 46.9725 | − | 46.9725i | 1.70052 | − | 1.70052i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −17.5761 | − | 0.456640i | −0.635466 | − | 0.0165099i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −45.0846 | − | 45.0846i | −1.62791 | − | 1.62791i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.2044 | 0.872833 | 0.436417 | − | 0.899745i | \(-0.356247\pi\) | ||||
0.436417 | + | 0.899745i | \(0.356247\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.1707 | −0.474333 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.19000 | − | 3.19000i | −0.114736 | − | 0.114736i | 0.647408 | − | 0.762144i | \(-0.275853\pi\) |
−0.762144 | + | 0.647408i | \(0.775853\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.93264 | + | 37.1687i | −0.0694226 | + | 1.33514i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.99931 | − | 4.99931i | −0.179349 | − | 0.179349i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.8095 | −0.566433 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 60.6813i | 2.17135i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.56009 | + | 4.56009i | −0.162964 | + | 0.162964i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.415063 | − | 15.9758i | 0.0148142 | − | 0.570200i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.6154 | − | 22.6154i | 0.806151 | − | 0.806151i | −0.177898 | − | 0.984049i | \(-0.556930\pi\) |
0.984049 | + | 0.177898i | \(0.0569297\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.22323 | 0.150351 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 36.8391 | 1.30985 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 36.1424 | + | 36.1424i | 1.28345 | + | 1.28345i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.11055 | − | 1.05430i | 0.0393870 | − | 0.0373922i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.37906 | − | 3.37906i | 0.119693 | − | 0.119693i | −0.644723 | − | 0.764416i | \(-0.723027\pi\) |
0.764416 | + | 0.644723i | \(0.223027\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 82.4332 | 2.91628 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.86653i | 0.277950i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 35.4117 | + | 35.4117i | 1.24965 | + | 1.24965i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −29.2537 | + | 22.2453i | −1.03106 | + | 0.784043i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.70522 | − | 4.70522i | −0.165632 | − | 0.165632i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 47.1962i | − | 1.65933i | −0.558261 | − | 0.829665i | \(-0.688531\pi\) | ||
0.558261 | − | 0.829665i | \(-0.311469\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.16242 | −0.111048 | −0.0555238 | − | 0.998457i | \(-0.517683\pi\) | ||||
−0.0555238 | + | 0.998457i | \(0.517683\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.19243 | + | 2.19243i | −0.0768920 | + | 0.0768920i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.0108643 | + | 0.418168i | −0.000380561 | + | 0.0146478i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.2041 | + | 13.2041i | 0.461954 | + | 0.461954i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 14.4172 | 0.503776 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.8676 | −0.798085 | −0.399043 | − | 0.916932i | \(-0.630657\pi\) | ||||
−0.399043 | + | 0.916932i | \(0.630657\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.2903 | + | 23.2903i | −0.811847 | + | 0.811847i | −0.984911 | − | 0.173064i | \(-0.944633\pi\) |
0.173064 | + | 0.984911i | \(0.444633\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.9494 | − | 14.3728i | 0.555287 | − | 0.500395i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.50826 | − | 3.50826i | 0.121994 | − | 0.121994i | −0.643474 | − | 0.765468i | \(-0.722507\pi\) |
0.765468 | + | 0.643474i | \(0.222507\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 4.58447i | − | 0.159225i | −0.996826 | − | 0.0796126i | \(-0.974632\pi\) | ||
0.996826 | − | 0.0796126i | \(-0.0253683\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.1855 | 0.700227 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26.3797 | + | 26.3797i | 0.914002 | + | 0.914002i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −28.9096 | − | 0.751093i | −1.00046 | − | 0.0259926i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.26355 | − | 5.26355i | −0.181935 | − | 0.181935i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.796335 | 0.0274925 | 0.0137463 | − | 0.999906i | \(-0.495624\pi\) | ||||
0.0137463 | + | 0.999906i | \(0.495624\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.5889 | −0.434099 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.94930 | + | 3.94930i | 0.136021 | + | 0.136021i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.23255 | + | 7.61839i | 0.248807 | + | 0.262081i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.0253 | + | 18.0253i | −0.619356 | + | 0.619356i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22.0478 | −0.756679 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.83493 | − | 1.07908i | −0.337137 | − | 0.0369905i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.75847 | − | 1.75847i | 0.0602089 | − | 0.0602089i | −0.676361 | − | 0.736570i | \(-0.736444\pi\) |
0.736570 | + | 0.676361i | \(0.236444\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.01839 | + | 6.33945i | 0.205824 | + | 0.216805i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.0724985 | + | 0.0724985i | 0.00247650 | + | 0.00247650i | 0.708344 | − | 0.705867i | \(-0.249443\pi\) |
−0.705867 | + | 0.708344i | \(0.749443\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.5671i | 1.55473i | 0.629050 | + | 0.777365i | \(0.283444\pi\) | ||||
−0.629050 | + | 0.777365i | \(0.716556\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 13.8595i | − | 0.472331i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33.9486 | + | 33.9486i | −1.15562 | + | 1.15562i | −0.170217 | + | 0.985407i | \(0.554447\pi\) |
−0.985407 | + | 0.170217i | \(0.945553\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.862353 | − | 33.1920i | 0.0293209 | − | 1.12856i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 31.6965 | + | 31.6965i | 1.07647 | + | 1.07647i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 32.3037i | 1.09583i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 8.06711i | − | 0.273344i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.32463 | + | 4.32463i | 0.146366 | + | 0.146366i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 38.1992 | + | 2.98270i | 1.29137 | + | 0.100834i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32.7483 | − | 32.7483i | −1.10583 | − | 1.10583i | −0.993692 | − | 0.112140i | \(-0.964229\pi\) |
−0.112140 | − | 0.993692i | \(-0.535771\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.0799 | 0.373717 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1.99317i | − | 0.0671517i | −0.999436 | − | 0.0335759i | \(-0.989310\pi\) | ||
0.999436 | − | 0.0335759i | \(-0.0106895\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.5670 | + | 34.5670i | −1.16327 | + | 1.16327i | −0.179519 | + | 0.983754i | \(0.557454\pi\) |
−0.983754 | + | 0.179519i | \(0.942546\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 33.8783 | + | 0.880182i | 1.13881 | + | 0.0295870i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.83938 | + | 5.83938i | 0.196067 | + | 0.196067i | 0.798312 | − | 0.602244i | \(-0.205727\pi\) |
−0.602244 | + | 0.798312i | \(0.705727\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.8285 | 0.765644 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.29399i | 0.143854i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −28.9796 | − | 28.9796i | −0.969764 | − | 0.969764i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 28.6406 | + | 30.1685i | 0.957351 | + | 1.00842i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.7371 | − | 12.6252i | 0.525446 | − | 0.421543i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 48.0045i | − | 1.60104i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.38466 | −0.179389 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11.5755 | + | 11.5755i | −0.385208 | + | 0.385208i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.2729 | − | 13.9810i | −0.441207 | − | 0.464744i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.9819 | + | 19.9819i | −0.663489 | + | 0.663489i | −0.956201 | − | 0.292712i | \(-0.905442\pi\) |
0.292712 | + | 0.956201i | \(0.405442\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.38025i | 0.277955i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 46.9352i | − | 1.55503i | −0.628862 | − | 0.777517i | \(-0.716479\pi\) | ||
0.628862 | − | 0.777517i | \(-0.283521\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.8305 | + | 13.8305i | −0.457723 | + | 0.457723i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −27.1587 | − | 0.705604i | −0.897840 | − | 0.0233266i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.09495 | − | 9.09495i | 0.300342 | − | 0.300342i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30.7173 | −1.01327 | −0.506634 | − | 0.862161i | \(-0.669111\pi\) | ||||
−0.506634 | + | 0.862161i | \(0.669111\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.6374 | −0.581172 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 42.0377 | − | 42.0377i | 1.38369 | − | 1.38369i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.90533 | + | 7.66282i | 0.227046 | + | 0.251952i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.329316 | − | 0.329316i | 0.0108162 | − | 0.0108162i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.8148i | 0.453250i | 0.973982 | + | 0.226625i | \(0.0727692\pi\) | ||||
−0.973982 | + | 0.226625i | \(0.927231\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 18.5477i | − | 0.607875i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.93106 | + | 4.93106i | −0.161436 | + | 0.161436i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −75.4717 | − | 1.96081i | −2.46819 | − | 0.0641254i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.6846 | + | 17.6846i | −0.577730 | + | 0.577730i | −0.934277 | − | 0.356548i | \(-0.883954\pi\) |
0.356548 | + | 0.934277i | \(0.383954\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.17378 | 0.168840 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 28.1623i | − | 0.918064i | −0.888420 | − | 0.459032i | \(-0.848196\pi\) | ||
0.888420 | − | 0.459032i | \(-0.151804\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.1368 | − | 15.1284i | −0.395230 | − | 0.492648i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.55753 | + | 5.27607i | −0.180787 | + | 0.171630i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −43.3171 | − | 43.3171i | −1.40762 | − | 1.40762i | −0.772033 | − | 0.635583i | \(-0.780760\pi\) |
−0.635583 | − | 0.772033i | \(-0.719240\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 49.0637i | − | 1.59268i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.0219 | −0.551971 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36.1667 | − | 36.1667i | −1.17155 | − | 1.17155i | −0.981839 | − | 0.189716i | \(-0.939243\pi\) |
−0.189716 | − | 0.981839i | \(-0.560757\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.9175 | + | 11.5000i | 0.353283 | + | 0.372130i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −19.5810 | + | 19.5810i | −0.632964 | + | 0.632964i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 65.5795i | − | 2.11767i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.4098 | 0.787414 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.62917 | + | 4.62917i | 0.149173 | + | 0.149173i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.166478 | − | 6.40774i | 0.00535911 | − | 0.206272i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.8045 | − | 27.8045i | −0.894133 | − | 0.894133i | 0.100776 | − | 0.994909i | \(-0.467868\pi\) |
−0.994909 | + | 0.100776i | \(0.967868\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 30.7378i | − | 0.987441i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 20.9889i | − | 0.673567i | −0.941582 | − | 0.336784i | \(-0.890661\pi\) | ||
0.941582 | − | 0.336784i | \(-0.109339\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.6553 | − | 32.6553i | −1.04688 | − | 1.04688i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −21.0060 | − | 1.09224i | −0.672732 | − | 0.0349797i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.7848 | + | 12.7848i | −0.409022 | + | 0.409022i | −0.881397 | − | 0.472376i | \(-0.843397\pi\) |
0.472376 | + | 0.881397i | \(0.343397\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 33.7788i | 1.07958i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 19.3838i | − | 0.618878i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.2420 | + | 22.2420i | 0.709411 | + | 0.709411i | 0.966411 | − | 0.257000i | \(-0.0827342\pi\) |
−0.257000 | + | 0.966411i | \(0.582734\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −54.3215 | − | 1.41131i | −1.73083 | − | 0.0449682i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 25.4052 | − | 25.4052i | 0.808656 | − | 0.808656i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.49853 | + | 22.7720i | −0.0794487 | + | 0.724107i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.8734 | −1.20309 | −0.601543 | − | 0.798840i | \(-0.705447\pi\) | ||||
−0.601543 | + | 0.798840i | \(0.705447\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −23.0406 | + | 23.0406i | −0.731172 | + | 0.731172i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 39.3402 | − | 37.3478i | 1.24717 | − | 1.18400i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.5475 | + | 24.5475i | 0.777428 | + | 0.777428i | 0.979393 | − | 0.201965i | \(-0.0647328\pi\) |
−0.201965 | + | 0.979393i | \(0.564733\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.06303 | −0.0652714 |
(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 | 1380.2.t.a.1057.3 | ✓ | 48 | |
5.3 | odd | 4 | inner | 1380.2.t.a.1333.4 | yes | 48 | |
23.22 | odd | 2 | inner | 1380.2.t.a.1057.4 | yes | 48 | |
115.68 | even | 4 | inner | 1380.2.t.a.1333.3 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.t.a.1057.3 | ✓ | 48 | 1.1 | even | 1 | trivial | |
1380.2.t.a.1057.4 | yes | 48 | 23.22 | odd | 2 | inner | |
1380.2.t.a.1333.3 | yes | 48 | 115.68 | even | 4 | inner | |
1380.2.t.a.1333.4 | yes | 48 | 5.3 | odd | 4 | inner |