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 | 1057.5 | ||
Character | \(\chi\) | \(=\) | 1380.1057 |
Dual form | 1380.2.t.a.1333.5 |
$q$-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 | ||||||||
\(5\) | −1.68477 | − | 1.47022i | −0.753451 | − | 0.657504i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.29608 | + | 2.29608i | −0.867835 | + | 0.867835i | −0.992233 | − | 0.124397i | \(-0.960300\pi\) |
0.124397 | + | 0.992233i | \(0.460300\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 5.35971i | − | 1.61601i | −0.589173 | − | 0.808007i | \(-0.700546\pi\) | ||
0.589173 | − | 0.808007i | \(-0.299454\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00694 | + | 2.00694i | −0.556624 | + | 0.556624i | −0.928345 | − | 0.371720i | \(-0.878768\pi\) |
0.371720 | + | 0.928345i | \(0.378768\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.23092 | − | 0.151706i | 0.576020 | − | 0.0391702i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.44837 | − | 3.44837i | 0.836352 | − | 0.836352i | −0.152025 | − | 0.988377i | \(-0.548579\pi\) |
0.988377 | + | 0.152025i | \(0.0485794\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.00250982 | −0.000575793 | −0.000287897 | − | 1.00000i | \(-0.500092\pi\) | ||||
−0.000287897 | 1.00000i | \(0.500092\pi\) | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 3.24714i | − | 0.708585i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.94658 | + | 4.38302i | 0.405890 | + | 0.913922i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.676885 | + | 4.95397i | 0.135377 | + | 0.990794i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.32182i | 0.245456i | 0.992440 | + | 0.122728i | \(0.0391643\pi\) | ||||
−0.992440 | + | 0.122728i | \(0.960836\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.62711 | 1.36987 | 0.684935 | − | 0.728604i | \(-0.259831\pi\) | ||||
0.684935 | + | 0.728604i | \(0.259831\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.78989 | + | 3.78989i | 0.659735 | + | 0.659735i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.24410 | − | 0.492610i | 1.22448 | − | 0.0832663i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.26209 | + | 6.26209i | −1.02948 | + | 1.02948i | −0.0299295 | + | 0.999552i | \(0.509528\pi\) |
−0.999552 | + | 0.0299295i | \(0.990472\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 2.83824i | − | 0.454482i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.53073 | −1.17610 | −0.588051 | − | 0.808824i | \(-0.700105\pi\) | ||||
−0.588051 | + | 0.808824i | \(0.700105\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.265803 | − | 0.265803i | −0.0405345 | − | 0.0405345i | 0.686549 | − | 0.727084i | \(-0.259125\pi\) |
−0.727084 | + | 0.686549i | \(0.759125\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.47022 | + | 1.68477i | −0.219168 | + | 0.251150i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.13733 | + | 8.13733i | 1.18695 | + | 1.18695i | 0.977906 | + | 0.209045i | \(0.0670355\pi\) |
0.209045 | + | 0.977906i | \(0.432964\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 3.54394i | − | 0.506277i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.87673i | 0.682878i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.78761 | + | 2.78761i | 0.382908 | + | 0.382908i | 0.872149 | − | 0.489241i | \(-0.162726\pi\) |
−0.489241 | + | 0.872149i | \(0.662726\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.87997 | + | 9.02987i | −1.06254 | + | 1.21759i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.00177471 | − | 0.00177471i | 0.000235067 | − | 0.000235067i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.7480i | 1.39927i | 0.714498 | + | 0.699637i | \(0.246655\pi\) | ||||
−0.714498 | + | 0.699637i | \(0.753345\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 2.04336i | − | 0.261626i | −0.991407 | − | 0.130813i | \(-0.958241\pi\) | ||
0.991407 | − | 0.130813i | \(-0.0417587\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.29608 | + | 2.29608i | 0.289278 | + | 0.289278i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.33187 | − | 0.430577i | 0.785372 | − | 0.0534065i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.91533 | − | 2.91533i | 0.356164 | − | 0.356164i | −0.506233 | − | 0.862397i | \(-0.668962\pi\) |
0.862397 | + | 0.506233i | \(0.168962\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.47570 | − | 1.72282i | −0.538811 | − | 0.207403i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.55392 | 0.896485 | 0.448243 | − | 0.893912i | \(-0.352050\pi\) | ||||
0.448243 | + | 0.893912i | \(0.352050\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.944453 | + | 0.944453i | −0.110540 | + | 0.110540i | −0.760213 | − | 0.649674i | \(-0.774906\pi\) |
0.649674 | + | 0.760213i | \(0.274906\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.98162 | − | 3.02436i | −0.459757 | − | 0.349223i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.3063 | + | 12.3063i | 1.40243 | + | 1.40243i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.43218 | 0.723677 | 0.361838 | − | 0.932241i | \(-0.382149\pi\) | ||||
0.361838 | + | 0.932241i | \(0.382149\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.53189 | − | 2.53189i | −0.277911 | − | 0.277911i | 0.554364 | − | 0.832274i | \(-0.312962\pi\) |
−0.832274 | + | 0.554364i | \(0.812962\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.8796 | + | 0.739827i | −1.18005 | + | 0.0802455i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.934669 | − | 0.934669i | −0.100207 | − | 0.100207i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.05956 | 0.854312 | 0.427156 | − | 0.904178i | \(-0.359516\pi\) | ||||
0.427156 | + | 0.904178i | \(0.359516\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 9.21617i | − | 0.966117i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.39318 | + | 5.39318i | −0.559247 | + | 0.559247i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.00422847 | + | 0.00369000i | 0.000433832 | + | 0.000378586i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.47299 | − | 9.47299i | 0.961837 | − | 0.961837i | −0.0374612 | − | 0.999298i | \(-0.511927\pi\) |
0.999298 | + | 0.0374612i | \(0.0119271\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.35971 | −0.538671 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.81553 | −0.678171 | −0.339086 | − | 0.940756i | \(-0.610118\pi\) | ||||
−0.339086 | + | 0.940756i | \(0.610118\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.60293 | + | 7.60293i | 0.749139 | + | 0.749139i | 0.974317 | − | 0.225179i | \(-0.0722966\pi\) |
−0.225179 | + | 0.974317i | \(0.572297\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.77403 | + | 5.47068i | −0.465897 | + | 0.533884i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.09059 | + | 7.09059i | −0.685473 | + | 0.685473i | −0.961228 | − | 0.275755i | \(-0.911072\pi\) |
0.275755 | + | 0.961228i | \(0.411072\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.17758 | −0.304357 | −0.152178 | − | 0.988353i | \(-0.548629\pi\) | ||||
−0.152178 | + | 0.988353i | \(0.548629\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 8.85593i | − | 0.840568i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.93769 | + | 4.93769i | 0.464499 | + | 0.464499i | 0.900127 | − | 0.435628i | \(-0.143474\pi\) |
−0.435628 | + | 0.900127i | \(0.643474\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.16448 | − | 10.2463i | 0.295089 | − | 0.955470i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.00694 | + | 2.00694i | 0.185541 | + | 0.185541i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 15.8354i | 1.45163i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −17.7265 | −1.61150 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.32503 | − | 5.32503i | 0.480142 | − | 0.480142i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.14305 | − | 9.34146i | 0.549451 | − | 0.835526i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.89475 | + | 2.89475i | 0.256868 | + | 0.256868i | 0.823779 | − | 0.566911i | \(-0.191862\pi\) |
−0.566911 | + | 0.823779i | \(0.691862\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.375902 | 0.0330963 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.8735 | 1.73635 | 0.868176 | − | 0.496256i | \(-0.165292\pi\) | ||||
0.868176 | + | 0.496256i | \(0.165292\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.00576275 | − | 0.00576275i | 0.000499694 | − | 0.000499694i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.151706 | − | 2.23092i | −0.0130567 | − | 0.192007i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.04908 | − | 1.04908i | 0.0896291 | − | 0.0896291i | −0.660871 | − | 0.750500i | \(-0.729813\pi\) |
0.750500 | + | 0.660871i | \(0.229813\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0772i | 0.854740i | 0.904077 | + | 0.427370i | \(0.140560\pi\) | ||||
−0.904077 | + | 0.427370i | \(0.859440\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.5079 | −0.969141 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.7566 | + | 10.7566i | 0.899513 | + | 0.899513i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.94337 | − | 2.22696i | 0.161388 | − | 0.184939i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.50594 | + | 2.50594i | 0.206687 | + | 0.206687i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.0437 | −1.31435 | −0.657176 | − | 0.753737i | \(-0.728249\pi\) | ||||
−0.657176 | + | 0.753737i | \(0.728249\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.8099 | 0.961074 | 0.480537 | − | 0.876974i | \(-0.340442\pi\) | ||||
0.480537 | + | 0.876974i | \(0.340442\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.44837 | − | 3.44837i | −0.278784 | − | 0.278784i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.8499 | − | 11.2136i | −1.03213 | − | 0.900695i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.6476 | + | 16.6476i | −1.32862 | + | 1.32862i | −0.422052 | + | 0.906571i | \(0.638690\pi\) |
−0.906571 | + | 0.422052i | \(0.861310\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.94227 | −0.312643 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.5332 | − | 5.59425i | −1.14538 | − | 0.440888i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.4608 | − | 17.4608i | 1.36764 | − | 1.36764i | 0.503842 | − | 0.863796i | \(-0.331919\pi\) |
0.863796 | − | 0.503842i | \(-0.168081\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.813099 | − | 11.9571i | −0.0632997 | − | 0.930856i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.50817 | − | 7.50817i | −0.581000 | − | 0.581000i | 0.354178 | − | 0.935178i | \(-0.384761\pi\) |
−0.935178 | + | 0.354178i | \(0.884761\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.94440i | 0.380339i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.00250982i | 0.000191931i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.0750 | − | 16.0750i | 1.22216 | − | 1.22216i | 0.255297 | − | 0.966863i | \(-0.417827\pi\) |
0.966863 | − | 0.255297i | \(-0.0821734\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.9289 | − | 9.82052i | −0.977331 | − | 0.742361i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.60000 | − | 7.60000i | −0.571251 | − | 0.571251i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.0883i | 1.27724i | 0.769521 | + | 0.638621i | \(0.220495\pi\) | ||||
−0.769521 | + | 0.638621i | \(0.779505\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.97758i | 0.592969i | 0.955038 | + | 0.296484i | \(0.0958143\pi\) | ||||
−0.955038 | + | 0.296484i | \(0.904186\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.44488 | + | 1.44488i | 0.106808 | + | 0.106808i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 19.7568 | − | 1.34350i | 1.45255 | − | 0.0987758i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.4823 | − | 18.4823i | −1.35156 | − | 1.35156i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.24714 | −0.236195 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 6.88551i | − | 0.498218i | −0.968475 | − | 0.249109i | \(-0.919862\pi\) | ||
0.968475 | − | 0.249109i | \(-0.0801377\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.1417 | + | 11.1417i | −0.802001 | + | 0.802001i | −0.983408 | − | 0.181407i | \(-0.941935\pi\) |
0.181407 | + | 0.983408i | \(0.441935\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.17285 | + | 4.78177i | −0.298824 | + | 0.342430i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.99038 | + | 8.99038i | 0.640538 | + | 0.640538i | 0.950688 | − | 0.310150i | \(-0.100379\pi\) |
−0.310150 | + | 0.950688i | \(0.600379\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.4973 | −0.744136 | −0.372068 | − | 0.928205i | \(-0.621351\pi\) | ||||
−0.372068 | + | 0.928205i | \(0.621351\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.12290i | 0.290807i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.03501 | − | 3.03501i | −0.213016 | − | 0.213016i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.6875 | + | 11.0719i | 0.886136 | + | 0.773292i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.38302 | − | 1.94658i | 0.304641 | − | 0.135297i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.0134519i | 0.000930490i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.90726 | −0.613201 | −0.306601 | − | 0.951838i | \(-0.599192\pi\) | ||||
−0.306601 | + | 0.951838i | \(0.599192\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.34143 | + | 5.34143i | −0.365989 | + | 0.365989i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.0570264 | + | 0.838605i | 0.00388917 | + | 0.0571924i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.5124 | + | 17.5124i | −1.18882 | + | 1.18882i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 1.33566i | − | 0.0902554i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.8413i | 0.931067i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.05589 | − | 7.05589i | 0.472497 | − | 0.472497i | −0.430225 | − | 0.902722i | \(-0.641566\pi\) |
0.902722 | + | 0.430225i | \(0.141566\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.95397 | − | 0.676885i | 0.330265 | − | 0.0451257i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.93717 | + | 7.93717i | −0.526808 | + | 0.526808i | −0.919619 | − | 0.392811i | \(-0.871503\pi\) |
0.392811 | + | 0.919619i | \(0.371503\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.9540 | 1.31860 | 0.659298 | − | 0.751882i | \(-0.270854\pi\) | ||||
0.659298 | + | 0.751882i | \(0.270854\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −17.4037 | −1.14508 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.44690 | − | 8.44690i | 0.553375 | − | 0.553375i | −0.374038 | − | 0.927413i | \(-0.622027\pi\) |
0.927413 | + | 0.374038i | \(0.122027\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.74582 | − | 25.6732i | −0.113885 | − | 1.67473i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.54824 | + | 4.54824i | −0.295440 | + | 0.295440i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 16.5868i | − | 1.07291i | −0.843928 | − | 0.536457i | \(-0.819762\pi\) | ||
0.843928 | − | 0.536457i | \(-0.180238\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.17292i | 0.397632i | 0.980037 | + | 0.198816i | \(0.0637097\pi\) | ||||
−0.980037 | + | 0.198816i | \(0.936290\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.21038 | + | 5.97071i | −0.332879 | + | 0.381455i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.00503706 | − | 0.00503706i | 0.000320501 | − | 0.000320501i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.58063 | 0.226913 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 21.2737i | − | 1.34278i | −0.741103 | − | 0.671391i | \(-0.765697\pi\) | ||
0.741103 | − | 0.671391i | \(-0.234303\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 23.4917 | − | 10.4331i | 1.47691 | − | 0.655924i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.16988 | − | 8.21615i | 0.448995 | − | 0.514515i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.88088 | − | 5.88088i | −0.366839 | − | 0.366839i | 0.499484 | − | 0.866323i | \(-0.333523\pi\) |
−0.866323 | + | 0.499484i | \(0.833523\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 28.7565i | − | 1.78684i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.32182 | 0.0818187 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.54517 | + | 5.54517i | 0.341930 | + | 0.341930i | 0.857093 | − | 0.515163i | \(-0.172268\pi\) |
−0.515163 | + | 0.857093i | \(0.672268\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.598065 | − | 8.79488i | −0.0367389 | − | 0.540265i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.69897 | + | 5.69897i | −0.348771 | + | 0.348771i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 1.96291i | − | 0.119681i | −0.998208 | − | 0.0598404i | \(-0.980941\pi\) | ||
0.998208 | − | 0.0598404i | \(-0.0190592\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.0313 | −0.609355 | −0.304678 | − | 0.952456i | \(-0.598549\pi\) | ||||
−0.304678 | + | 0.952456i | \(0.598549\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.51681 | + | 6.51681i | 0.394415 | + | 0.394415i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 26.5519 | − | 3.62791i | 1.60114 | − | 0.218771i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.6821 | − | 15.6821i | −0.942248 | − | 0.942248i | 0.0561730 | − | 0.998421i | \(-0.482110\pi\) |
−0.998421 | + | 0.0561730i | \(0.982110\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 7.62711i | − | 0.456623i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 15.5018i | − | 0.924762i | −0.886681 | − | 0.462381i | \(-0.846995\pi\) | ||
0.886681 | − | 0.462381i | \(-0.153005\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.72459 | + | 2.72459i | 0.161960 | + | 0.161960i | 0.783435 | − | 0.621474i | \(-0.213466\pi\) |
−0.621474 | + | 0.783435i | \(0.713466\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.00559921 | 0.000380755i | −0.000331668 | 2.25540e-5i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 17.2911 | − | 17.2911i | 1.02066 | − | 1.02066i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 6.78246i | − | 0.398968i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.3968i | 0.785336i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.12495 | + | 9.12495i | 0.533085 | + | 0.533085i | 0.921489 | − | 0.388404i | \(-0.126974\pi\) |
−0.388404 | + | 0.921489i | \(0.626974\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.8020 | − | 18.1079i | 0.920028 | − | 1.05428i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.78989 | − | 3.78989i | 0.219912 | − | 0.219912i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.7031 | − | 4.88978i | −0.734639 | − | 0.282783i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.22061 | 0.0703546 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.81931 | − | 4.81931i | 0.276862 | − | 0.276862i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.00420 | + | 3.44259i | −0.172020 | + | 0.197122i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.36045 | + | 3.36045i | 0.191791 | + | 0.191791i | 0.796470 | − | 0.604679i | \(-0.206698\pi\) |
−0.604679 | + | 0.796470i | \(0.706698\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.7522 | −0.611669 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 31.5893 | 1.79127 | 0.895633 | − | 0.444794i | \(-0.146723\pi\) | ||||
0.895633 | + | 0.444794i | \(0.146723\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.25763 | + | 8.25763i | 0.466749 | + | 0.466749i | 0.900859 | − | 0.434111i | \(-0.142937\pi\) |
−0.434111 | + | 0.900859i | \(0.642937\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.492610 | − | 7.24410i | −0.0277554 | − | 0.408159i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.33631 | − | 4.33631i | −0.243552 | − | 0.243552i | 0.574766 | − | 0.818318i | \(-0.305093\pi\) |
−0.818318 | + | 0.574766i | \(0.805093\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.08459 | 0.396661 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 10.0276i | − | 0.559687i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.00865480 | + | 0.00865480i | −0.000481566 | + | 0.000481566i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.3008 | − | 8.58384i | −0.626854 | − | 0.476146i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.24689 | − | 2.24689i | 0.124253 | − | 0.124253i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −37.3679 | −2.06016 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.17004 | 0.449066 | 0.224533 | − | 0.974466i | \(-0.427914\pi\) | ||||
0.224533 | + | 0.974466i | \(0.427914\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.26209 | + | 6.26209i | 0.343161 | + | 0.343161i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.19784 | + | 0.625468i | −0.502532 | + | 0.0341729i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.8595 | + | 18.8595i | −1.02734 | + | 1.02734i | −0.0277293 | + | 0.999615i | \(0.508828\pi\) |
−0.999615 | + | 0.0277293i | \(0.991172\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.98295 | −0.379262 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 40.8791i | − | 2.21373i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.93539 | − | 7.93539i | −0.428471 | − | 0.428471i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.00758 | + | 9.48283i | 0.269599 | + | 0.510539i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.0059 | − | 10.0059i | −0.537147 | − | 0.537147i | 0.385543 | − | 0.922690i | \(-0.374014\pi\) |
−0.922690 | + | 0.385543i | \(0.874014\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 8.15361i | − | 0.436453i | −0.975898 | − | 0.218226i | \(-0.929973\pi\) | ||
0.975898 | − | 0.218226i | \(-0.0700271\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.83824 | −0.151494 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.1024 | + | 14.1024i | −0.750592 | + | 0.750592i | −0.974590 | − | 0.223997i | \(-0.928089\pi\) |
0.223997 | + | 0.974590i | \(0.428089\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.7266 | − | 11.1059i | −0.675458 | − | 0.589443i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −11.1973 | − | 11.1973i | −0.592626 | − | 0.592626i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.3502 | −0.968487 | −0.484244 | − | 0.874933i | \(-0.660905\pi\) | ||||
−0.484244 | + | 0.874933i | \(0.660905\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.5345 | − | 12.5345i | 0.657893 | − | 0.657893i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.97974 | − | 0.202627i | 0.155967 | − | 0.0106060i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.6140 | + | 23.6140i | −1.23264 | + | 1.23264i | −0.269695 | + | 0.962946i | \(0.586923\pi\) |
−0.962946 | + | 0.269695i | \(0.913077\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.53073i | 0.392034i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.8011 | −0.664601 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.62175 | + | 7.62175i | 0.394639 | + | 0.394639i | 0.876337 | − | 0.481698i | \(-0.159980\pi\) |
−0.481698 | + | 0.876337i | \(0.659980\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.26162 | + | 10.9492i | 0.116790 | + | 0.565414i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.65281 | − | 2.65281i | −0.136627 | − | 0.136627i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.1086 | −1.28974 | −0.644870 | − | 0.764292i | \(-0.723089\pi\) | ||||
−0.644870 | + | 0.764292i | \(0.723089\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.09380 | −0.209732 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.0351 | + | 16.0351i | 0.819357 | + | 0.819357i | 0.986015 | − | 0.166657i | \(-0.0532974\pi\) |
−0.166657 | + | 0.986015i | \(0.553297\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.64025 | − | 38.8263i | −0.134559 | − | 1.97877i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.265803 | + | 0.265803i | −0.0135115 | + | 0.0135115i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.9369 | −0.808032 | −0.404016 | − | 0.914752i | \(-0.632386\pi\) | ||||
−0.404016 | + | 0.914752i | \(0.632386\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.8268 | + | 8.40173i | 1.10383 | + | 0.424894i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.0527 | + | 14.0527i | −0.708863 | + | 0.708863i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.8367 | − | 9.45674i | −0.545255 | − | 0.475820i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.0995 | + | 19.0995i | 0.958577 | + | 0.958577i | 0.999176 | − | 0.0405981i | \(-0.0129263\pi\) |
−0.0405981 | + | 0.999176i | \(0.512926\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.00814976i | 0.000407998i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.0030i | 1.09878i | 0.835567 | + | 0.549389i | \(0.185139\pi\) | ||||
−0.835567 | + | 0.549389i | \(0.814861\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.3071 | + | 15.3071i | −0.762503 | + | 0.762503i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.68477 | + | 1.47022i | 0.0837168 | + | 0.0730560i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 33.5630 | + | 33.5630i | 1.66366 | + | 1.66366i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.6719i | 1.51663i | 0.651889 | + | 0.758314i | \(0.273977\pi\) | ||||
−0.651889 | + | 0.758314i | \(0.726023\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.48363i | 0.0731819i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −24.6783 | − | 24.6783i | −1.21434 | − | 1.21434i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.543202 | + | 7.98808i | 0.0266647 | + | 0.392119i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.12569 | − | 7.12569i | −0.348946 | − | 0.348946i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.2883 | 0.893444 | 0.446722 | − | 0.894673i | \(-0.352591\pi\) | ||||
0.446722 | + | 0.894673i | \(0.352591\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 9.61292i | − | 0.468505i | −0.972176 | − | 0.234252i | \(-0.924736\pi\) | ||
0.972176 | − | 0.234252i | \(-0.0752642\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.13733 | − | 8.13733i | 0.395650 | − | 0.395650i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 19.4173 | + | 14.7490i | 0.941875 | + | 0.715430i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.69172 | + | 4.69172i | 0.227048 | + | 0.227048i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −15.2121 | −0.734449 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.1350i | 1.45155i | 0.687930 | + | 0.725777i | \(0.258520\pi\) | ||||
−0.687930 | + | 0.725777i | \(0.741480\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.89397 | − | 6.89397i | −0.331303 | − | 0.331303i | 0.521778 | − | 0.853081i | \(-0.325269\pi\) |
−0.853081 | + | 0.521778i | \(0.825269\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.200528 | + | 2.94887i | 0.00961458 | + | 0.141388i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.00488557 | − | 0.0110006i | −0.000233709 | − | 0.000526230i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 34.6386i | − | 1.65321i | −0.562781 | − | 0.826606i | \(-0.690269\pi\) | ||
0.562781 | − | 0.826606i | \(-0.309731\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.54394 | −0.168759 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.400276 | + | 0.400276i | −0.0190177 | + | 0.0190177i | −0.716552 | − | 0.697534i | \(-0.754281\pi\) |
0.697534 | + | 0.716552i | \(0.254281\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.5785 | − | 11.8494i | −0.643682 | − | 0.561713i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.3446 | − | 11.3446i | 0.536582 | − | 0.536582i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 39.8963i | − | 1.88282i | −0.337258 | − | 0.941412i | \(-0.609499\pi\) | ||
0.337258 | − | 0.941412i | \(-0.390501\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 40.3626i | 1.90060i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.35084 | + | 8.35084i | −0.392357 | + | 0.392357i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.5498 | + | 15.5271i | −0.635226 | + | 0.727922i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.8152 | + | 17.8152i | −0.833359 | + | 0.833359i | −0.987975 | − | 0.154616i | \(-0.950586\pi\) |
0.154616 | + | 0.987975i | \(0.450586\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.87673 | 0.227626 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.1416 | 1.45041 | 0.725205 | − | 0.688533i | \(-0.241745\pi\) | ||||
0.725205 | + | 0.688533i | \(0.241745\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.7190 | + | 20.7190i | −0.962895 | + | 0.962895i | −0.999336 | − | 0.0364405i | \(-0.988398\pi\) |
0.0364405 | + | 0.999336i | \(0.488398\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 17.0154 | − | 1.15708i | 0.789072 | − | 0.0536581i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.3240 | + | 14.3240i | −0.662838 | + | 0.662838i | −0.956048 | − | 0.293210i | \(-0.905276\pi\) |
0.293210 | + | 0.956048i | \(0.405276\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.3876i | 0.618184i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 23.5433i | − | 1.08482i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.42463 | + | 1.42463i | −0.0655043 | + | 0.0655043i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.00169886 | − | 0.0124336i | −7.79492e−5 | − | 0.000570493i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.78761 | − | 2.78761i | 0.127636 | − | 0.127636i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37.6682 | 1.72110 | 0.860552 | − | 0.509363i | \(-0.170119\pi\) | ||||
0.860552 | + | 0.509363i | \(0.170119\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 25.1353i | − | 1.14607i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 14.2323 | − | 6.32082i | 0.647591 | − | 0.287607i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −29.8872 | + | 2.03238i | −1.35711 | + | 0.0922855i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.90248 | − | 8.90248i | −0.403410 | − | 0.403410i | 0.476023 | − | 0.879433i | \(-0.342078\pi\) |
−0.879433 | + | 0.476023i | \(0.842078\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.6933i | 1.11667i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.8878 | −0.671878 | −0.335939 | − | 0.941884i | \(-0.609054\pi\) | ||||
−0.335939 | + | 0.941884i | \(0.609054\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.55813 | + | 4.55813i | 0.205288 | + | 0.205288i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.02987 | + | 7.87997i | 0.405862 | + | 0.354179i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −17.3444 | + | 17.3444i | −0.778001 | + | 0.778001i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 11.5637i | − | 0.517663i | −0.965922 | − | 0.258832i | \(-0.916662\pi\) | ||
0.965922 | − | 0.258832i | \(-0.0833375\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.6182 | 0.474384 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.49630 | + | 2.49630i | 0.111305 | + | 0.111305i | 0.760566 | − | 0.649261i | \(-0.224922\pi\) |
−0.649261 | + | 0.760566i | \(0.724922\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.4826 | + | 10.0204i | 0.510969 | + | 0.445900i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.49622 | − | 3.49622i | −0.155273 | − | 0.155273i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 1.80920i | − | 0.0801913i | −0.999196 | − | 0.0400957i | \(-0.987234\pi\) | ||
0.999196 | − | 0.0400957i | \(-0.0127663\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 4.33707i | − | 0.191861i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.00177471 | − | 0.00177471i | −7.83555e−5 | − | 7.83555e-5i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.63116 | − | 23.9872i | −0.0718777 | − | 1.05700i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 43.6137 | − | 43.6137i | 1.91813 | − | 1.91813i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.7335i | 0.997889i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 23.1952i | − | 1.01620i | −0.861298 | − | 0.508100i | \(-0.830348\pi\) | ||
0.861298 | − | 0.508100i | \(-0.169652\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.6106 | − | 17.6106i | −0.770058 | − | 0.770058i | 0.208059 | − | 0.978116i | \(-0.433286\pi\) |
−0.978116 | + | 0.208059i | \(0.933286\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 16.0863 | − | 2.19794i | 0.702062 | − | 0.0959261i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 26.3011 | − | 26.3011i | 1.14569 | − | 1.14569i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.4217 | + | 17.0638i | −0.670507 | + | 0.741903i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.7480 | 0.466425 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.1137 | − | 15.1137i | 0.654647 | − | 0.654647i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.3708 | − | 1.52125i | 0.967172 | − | 0.0657692i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.0833 | − | 12.0833i | −0.521432 | − | 0.521432i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −18.9945 | −0.818150 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.0570 | −1.42123 | −0.710615 | − | 0.703581i | \(-0.751583\pi\) | ||||
−0.710615 | + | 0.703581i | \(0.751583\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.64100 | − | 5.64100i | −0.242079 | − | 0.242079i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.35348 | + | 4.67175i | 0.229318 | + | 0.200116i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.8409 | + | 29.8409i | 1.27590 | + | 1.27590i | 0.942940 | + | 0.332963i | \(0.108048\pi\) |
0.332963 | + | 0.942940i | \(0.391952\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.04336 | −0.0872086 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 0.00331754i | − | 0.000141332i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.7688 | + | 14.7688i | −0.628032 | + | 0.628032i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.0202 | + | 14.9202i | −0.552677 | + | 0.633327i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.0581 | − | 19.0581i | 0.807518 | − | 0.807518i | −0.176740 | − | 0.984258i | \(-0.556555\pi\) |
0.984258 | + | 0.176740i | \(0.0565550\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.06690 | 0.0451250 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 26.1378 | 1.10354 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.0966 | + | 29.0966i | 1.22628 | + | 1.22628i | 0.965362 | + | 0.260914i | \(0.0840240\pi\) |
0.260914 | + | 0.965362i | \(0.415976\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.05935 | − | 15.5784i | −0.0445674 | − | 0.655387i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.29608 | − | 2.29608i | 0.0964262 | − | 0.0964262i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.7185 | −0.533188 | −0.266594 | − | 0.963809i | \(-0.585898\pi\) | ||||
−0.266594 | + | 0.963809i | \(0.585898\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.6397i | 1.78441i | 0.451626 | + | 0.892207i | \(0.350844\pi\) | ||||
−0.451626 | + | 0.892207i | \(0.649156\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.86879 | + | 4.86879i | 0.203397 | + | 0.203397i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −20.3957 | + | 12.6101i | −0.850560 | + | 0.525877i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.1720 | + | 28.1720i | 1.17282 | + | 1.17282i | 0.981535 | + | 0.191282i | \(0.0612646\pi\) |
0.191282 | + | 0.981535i | \(0.438735\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 15.7568i | − | 0.654831i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.6268 | 0.482361 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.9408 | − | 14.9408i | 0.618784 | − | 0.618784i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.430577 | − | 6.33187i | −0.0178022 | − | 0.261791i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.7490 | − | 20.7490i | −0.856403 | − | 0.856403i | 0.134509 | − | 0.990912i | \(-0.457054\pi\) |
−0.990912 | + | 0.134509i | \(0.957054\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.0191427 | −0.000788762 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.7143 | −0.522997 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.8636 | − | 17.8636i | 0.733570 | − | 0.733570i | −0.237755 | − | 0.971325i | \(-0.576412\pi\) |
0.971325 | + | 0.237755i | \(0.0764115\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23.2816 | − | 26.6790i | 0.954453 | − | 1.09373i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.42273 | − | 7.42273i | 0.303792 | − | 0.303792i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.2783i | 0.665114i | 0.943083 | + | 0.332557i | \(0.107911\pi\) | ||||
−0.943083 | + | 0.332557i | \(0.892089\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.3242 | 1.60407 | 0.802035 | − | 0.597278i | \(-0.203751\pi\) | ||||
0.802035 | + | 0.597278i | \(0.203751\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.91533 | − | 2.91533i | −0.118721 | − | 0.118721i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 29.8651 | + | 26.0619i | 1.21419 | + | 1.05957i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.1086 | + | 11.1086i | 0.450885 | + | 0.450885i | 0.895648 | − | 0.444763i | \(-0.146712\pi\) |
−0.444763 | + | 0.895648i | \(0.646712\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.29215 | 0.173927 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −32.6622 | −1.32137 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.92796 | − | 4.92796i | −0.199039 | − | 0.199039i | 0.600549 | − | 0.799588i | \(-0.294949\pi\) |
−0.799588 | + | 0.600549i | \(0.794949\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −16.8004 | + | 1.14245i | −0.677459 | + | 0.0460682i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.7567 | + | 13.7567i | −0.553823 | + | 0.553823i | −0.927542 | − | 0.373719i | \(-0.878082\pi\) |
0.373719 | + | 0.927542i | \(0.378082\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.8009 | −0.675284 | −0.337642 | − | 0.941275i | \(-0.609629\pi\) | ||||
−0.337642 | + | 0.941275i | \(0.609629\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.72282 | + | 4.47570i | −0.0691344 | + | 0.179604i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.5054 | + | 18.5054i | −0.741402 | + | 0.741402i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.0837 | + | 6.70654i | −0.963346 | + | 0.268262i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.00951196 | − | 0.00951196i | −0.000379871 | − | 0.000379871i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 43.1880i | 1.72202i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.8184i | 0.868575i | 0.900774 | + | 0.434288i | \(0.143000\pi\) | ||||
−0.900774 | + | 0.434288i | \(0.857000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.29838 | − | 6.29838i | 0.250338 | − | 0.250338i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.621053 | − | 9.13293i | −0.0246457 | − | 0.362429i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.11246 | + | 7.11246i | 0.281806 | + | 0.281806i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 7.55392i | − | 0.298828i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.4018i | 0.608333i | 0.952619 | + | 0.304167i | \(0.0983780\pi\) | ||||
−0.952619 | + | 0.304167i | \(0.901622\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.6574 | + | 20.6574i | 0.814650 | + | 0.814650i | 0.985327 | − | 0.170677i | \(-0.0545955\pi\) |
−0.170677 | + | 0.985327i | \(0.554596\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.633307 | − | 0.552659i | −0.0249364 | − | 0.0217609i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 31.8099 | + | 31.8099i | 1.25058 | + | 1.25058i | 0.955462 | + | 0.295114i | \(0.0953578\pi\) |
0.295114 | + | 0.955462i | \(0.404642\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 57.6063 | 2.26125 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 24.7663i | − | 0.970669i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.52842 | + | 5.52842i | −0.216344 | + | 0.216344i | −0.806956 | − | 0.590612i | \(-0.798886\pi\) |
0.590612 | + | 0.806956i | \(0.298886\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −33.4822 | − | 29.2184i | −1.30826 | − | 1.14166i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.944453 | + | 0.944453i | 0.0368466 | + | 0.0368466i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.6656 | −1.15561 | −0.577803 | − | 0.816176i | \(-0.696090\pi\) | ||||
−0.577803 | + | 0.816176i | \(0.696090\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 18.4917i | − | 0.719245i | −0.933098 | − | 0.359623i | \(-0.882905\pi\) | ||
0.933098 | − | 0.359623i | \(-0.117095\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.78729 | − | 9.78729i | −0.380107 | − | 0.380107i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.0181814 | + | 0.00123637i | −0.000705046 | + | 4.79442e-5i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.79357 | + | 2.57303i | −0.224328 | + | 0.0996282i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.97853i | 0.385792i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.9518 | −0.422791 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.4881 | − | 16.4881i | 0.635571 | − | 0.635571i | −0.313888 | − | 0.949460i | \(-0.601632\pi\) |
0.949460 | + | 0.313888i | \(0.101632\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.02436 | + | 3.98162i | −0.116408 | + | 0.153252i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.9328 | − | 10.9328i | 0.420180 | − | 0.420180i | −0.465085 | − | 0.885266i | \(-0.653976\pi\) |
0.885266 | + | 0.465085i | \(0.153976\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 43.5014i | 1.66943i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 11.2249i | − | 0.430137i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.3457 | − | 14.3457i | 0.548924 | − | 0.548924i | −0.377205 | − | 0.926130i | \(-0.623115\pi\) |
0.926130 | + | 0.377205i | \(0.123115\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.30984 | + | 0.225074i | −0.126463 | + | 0.00859965i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.1096 | + | 14.1096i | −0.538315 | + | 0.538315i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.1891 | −0.426271 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.3580 | 0.660329 | 0.330165 | − | 0.943923i | \(-0.392896\pi\) | ||||
0.330165 | + | 0.943923i | \(0.392896\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 12.3063 | − | 12.3063i | 0.467478 | − | 0.467478i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.8158 | − | 16.9778i | 0.561995 | − | 0.644005i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −25.9687 | + | 25.9687i | −0.983635 | + | 0.983635i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.9457i | 0.451829i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.4053i | 1.07285i | 0.843947 | + | 0.536426i | \(0.180226\pi\) | ||||
−0.843947 | + | 0.536426i | \(0.819774\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.0157168 | − | 0.0157168i | 0.000592769 | − | 0.000592769i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 19.3882 | + | 16.9192i | 0.730201 | + | 0.637214i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.6490 | − | 15.6490i | 0.588541 | − | 0.588541i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 45.8428 | 1.72166 | 0.860831 | − | 0.508892i | \(-0.169945\pi\) | ||||
0.860831 | + | 0.508892i | \(0.169945\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 6.43218i | − | 0.241226i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.8468 | + | 33.4297i | 0.556016 | + | 1.25195i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.30777 | − | 33.9370i | −0.0863056 | − | 1.26917i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.7287 | + | 11.7287i | 0.438015 | + | 0.438015i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 48.1698i | 1.79643i | 0.439558 | + | 0.898214i | \(0.355135\pi\) | ||||
−0.439558 | + | 0.898214i | \(0.644865\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −34.9138 | −1.30026 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.36491 | − | 4.36491i | −0.162333 | − | 0.162333i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.54827 | + | 0.894722i | −0.243197 | + | 0.0332291i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.87374 | + | 7.87374i | −0.292021 | + | 0.292021i | −0.837878 | − | 0.545857i | \(-0.816204\pi\) |
0.545857 | + | 0.837878i | \(0.316204\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.83317 | −0.0678022 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.0552 | − | 28.0552i | −1.03624 | − | 1.03624i | −0.999318 | − | 0.0369226i | \(-0.988245\pi\) |
−0.0369226 | − | 0.999318i | \(-0.511755\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.537635 | − | 7.90622i | −0.0198310 | − | 0.291625i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15.6253 | − | 15.6253i | −0.575567 | − | 0.575567i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 27.9573i | − | 1.02843i | −0.857662 | − | 0.514214i | \(-0.828084\pi\) | ||
0.857662 | − | 0.514214i | \(-0.171916\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.00712348i | 0.000261688i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.1326 | − | 14.1326i | −0.518476 | − | 0.518476i | 0.398634 | − | 0.917110i | \(-0.369484\pi\) |
−0.917110 | + | 0.398634i | \(0.869484\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.0299 | + | 23.5878i | 0.990299 | + | 0.864191i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.53189 | + | 2.53189i | −0.0926369 | + | 0.0926369i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 32.5611i | − | 1.18976i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.2782i | 1.17785i | 0.808188 | + | 0.588925i | \(0.200449\pi\) | ||||
−0.808188 | + | 0.588925i | \(0.799551\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.0428 | + | 15.0428i | 0.548188 | + | 0.548188i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.8969 | − | 17.3632i | −0.724122 | − | 0.631910i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.19305 | + | 1.19305i | −0.0433621 | + | 0.0433621i | −0.728455 | − | 0.685093i | \(-0.759761\pi\) |
0.685093 | + | 0.728455i | \(0.259761\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.23382 | + | 23.9885i | −0.335167 | + | 0.870726i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.69802 | −0.279053 | −0.139527 | − | 0.990218i | \(-0.544558\pi\) | ||||
−0.139527 | + | 0.990218i | \(0.544558\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.29596 | − | 7.29596i | 0.264132 | − | 0.264132i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.739827 | + | 10.8796i | 0.0267485 | + | 0.393352i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21.5706 | − | 21.5706i | −0.778870 | − | 0.778870i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.8925 | 0.681280 | 0.340640 | − | 0.940194i | \(-0.389356\pi\) | ||||
0.340640 | + | 0.940194i | \(0.389356\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.31682 | 0.299523 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.1025 | − | 12.1025i | −0.435297 | − | 0.435297i | 0.455129 | − | 0.890426i | \(-0.349593\pi\) |
−0.890426 | + | 0.455129i | \(0.849593\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.16268 | + | 37.7845i | 0.185449 | + | 1.35726i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 20.3339 | + | 20.3339i | 0.729475 | + | 0.729475i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.0189008 | 0.000677192 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 40.4868i | − | 1.44873i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.934669 | + | 0.934669i | −0.0334024 | + | 0.0334024i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 52.5231 | − | 3.57165i | 1.87463 | − | 0.127478i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.2130 | − | 34.2130i | 1.21956 | − | 1.21956i | 0.251775 | − | 0.967786i | \(-0.418986\pi\) |
0.967786 | − | 0.251775i | \(-0.0810142\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.84206 | −0.279185 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22.6746 | −0.806218 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.10090 | + | 4.10090i | 0.145627 | + | 0.145627i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.64182 | + | 5.79602i | 0.235561 | + | 0.205564i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32.7305 | + | 32.7305i | −1.15937 | + | 1.15937i | −0.174763 | + | 0.984611i | \(0.555916\pi\) |
−0.984611 | + | 0.174763i | \(0.944084\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 56.1210 | 1.98542 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 8.05956i | − | 0.284771i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.06199 | + | 5.06199i | 0.178634 | + | 0.178634i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.2603 | + | 30.7921i | 0.573102 | + | 1.08528i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.38799 | + | 1.38799i | 0.0488595 | + | 0.0488595i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.67827i | 0.269954i | 0.990849 | + | 0.134977i | \(0.0430960\pi\) | ||||
−0.990849 | + | 0.134977i | \(0.956904\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.3589 | 0.925585 | 0.462792 | − | 0.886467i | \(-0.346848\pi\) | ||||
0.462792 | + | 0.886467i | \(0.346848\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.09317 | − | 7.09317i | 0.248768 | − | 0.248768i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −55.0888 | + | 3.74612i | −1.92968 | + | 0.131221i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.000667118 | 0 | 0.000667118i | 2.33395e−5 | 0 | 2.33395e-5i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.21617 | −0.322039 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.85009 | 0.273970 | 0.136985 | − | 0.990573i | \(-0.456259\pi\) | ||||
0.136985 | + | 0.990573i | \(0.456259\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35.0506 | + | 35.0506i | −1.22179 | + | 1.22179i | −0.254792 | + | 0.966996i | \(0.582007\pi\) |
−0.966996 | + | 0.254792i | \(0.917993\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −16.2097 | + | 21.3403i | −0.564349 | + | 0.742974i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21.5188 | − | 21.5188i | 0.748282 | − | 0.748282i | −0.225874 | − | 0.974157i | \(-0.572524\pi\) |
0.974157 | + | 0.225874i | \(0.0725238\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 30.7941i | − | 1.06952i | −0.845003 | − | 0.534762i | \(-0.820401\pi\) | ||
0.845003 | − | 0.534762i | \(-0.179599\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.1779 | 0.769342 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12.2208 | − | 12.2208i | −0.423425 | − | 0.423425i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.61083 | + | 23.6882i | 0.0557452 | + | 0.819764i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.39318 | + | 5.39318i | 0.186416 | + | 0.186416i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −35.3062 | −1.21891 | −0.609453 | − | 0.792823i | \(-0.708611\pi\) | ||||
−0.609453 | + | 0.792823i | \(0.708611\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.2528 | 0.939751 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.9614 | + | 10.9614i | 0.377532 | + | 0.377532i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.26938 | − | 8.33017i | 0.250074 | − | 0.286567i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 40.7014 | − | 40.7014i | 1.39852 | − | 1.39852i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.85316 | −0.132240 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −39.6365 | − | 15.2572i | −1.35872 | − | 0.523010i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.4531 | + | 19.4531i | −0.666063 | + | 0.666063i | −0.956802 | − | 0.290739i | \(-0.906099\pi\) |
0.290739 | + | 0.956802i | \(0.406099\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.00369000 | − | 0.00422847i | 0.000126195 | − | 0.000144611i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −40.1385 | − | 40.1385i | −1.37111 | − | 1.37111i | −0.858808 | − | 0.512297i | \(-0.828795\pi\) |
−0.512297 | − | 0.858808i | \(-0.671205\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.3298i | 0.386567i | 0.981143 | + | 0.193284i | \(0.0619137\pi\) | ||||
−0.981143 | + | 0.193284i | \(0.938086\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 24.4534i | 0.833368i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.6078 | + | 36.6078i | −1.24615 | + | 1.24615i | −0.288737 | + | 0.957408i | \(0.593235\pi\) |
−0.957408 | + | 0.288737i | \(0.906765\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −50.7165 | + | 3.44880i | −1.72441 | + | 0.117263i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.79592 | + | 4.79592i | 0.162878 | + | 0.162878i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 34.4746i | − | 1.16947i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.7018i | 0.396500i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.47299 | − | 9.47299i | −0.320612 | − | 0.320612i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.34380 | + | 35.5536i | 0.248266 | + | 1.20193i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.9225 | + | 34.9225i | 1.17925 | + | 1.17925i | 0.979935 | + | 0.199315i | \(0.0638717\pi\) |
0.199315 | + | 0.979935i | \(0.436128\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.9046 | −0.435262 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 33.9183i | − | 1.14274i | −0.820694 | − | 0.571368i | \(-0.806413\pi\) | ||
0.820694 | − | 0.571368i | \(-0.193587\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.98943 | + | 1.98943i | −0.0669496 | + | 0.0669496i | −0.739789 | − | 0.672839i | \(-0.765075\pi\) |
0.672839 | + | 0.739789i | \(0.265075\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.63054 | + | 23.9779i | 0.0548099 | + | 0.806010i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.5496 | − | 22.5496i | −0.757142 | − | 0.757142i | 0.218659 | − | 0.975801i | \(-0.429832\pi\) |
−0.975801 | + | 0.218659i | \(0.929832\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.2932 | −0.445838 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.35971i | 0.179557i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.0204233 | − | 0.0204233i | −0.000683439 | − | 0.000683439i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.1237 | − | 28.7899i | 0.839792 | − | 0.962340i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.4400 | − | 5.52486i | 0.415361 | − | 0.184470i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.0817i | 0.336243i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.2254 | 0.640491 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.863099 | + | 0.863099i | −0.0287221 | + | 0.0287221i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.7288 | − | 13.4404i | 0.389879 | − | 0.446773i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.2244 | + | 14.2244i | −0.472314 | + | 0.472314i | −0.902663 | − | 0.430349i | \(-0.858391\pi\) |
0.430349 | + | 0.902663i | \(0.358391\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.81553i | 0.226057i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.7252i | 0.819184i | 0.912269 | + | 0.409592i | \(0.134329\pi\) | ||||
−0.912269 | + | 0.409592i | \(0.865671\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.5702 | + | 13.5702i | −0.449108 | + | 0.449108i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.309990 | − | 4.55857i | −0.0102479 | − | 0.150702i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −45.6310 | + | 45.6310i | −1.50687 | + | 1.50687i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 55.1324 | 1.81865 | 0.909325 | − | 0.416087i | \(-0.136599\pi\) | ||||
0.909325 | + | 0.416087i | \(0.136599\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.75239 | −0.156597 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15.1602 | + | 15.1602i | −0.499005 | + | 0.499005i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −35.2609 | − | 26.7835i | −1.15937 | − | 0.880636i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.60293 | − | 7.60293i | 0.249713 | − | 0.249713i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.0979i | 0.659392i | 0.944087 | + | 0.329696i | \(0.106946\pi\) | ||||
−0.944087 | + | 0.329696i | \(0.893054\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.00889466i | 0.000291511i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22.3370 | + | 22.3370i | −0.731281 | + | 0.731281i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.96526 | + | 58.3113i | 0.129678 | + | 1.90698i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.12645 | + | 7.12645i | −0.232811 | + | 0.232811i | −0.813865 | − | 0.581054i | \(-0.802640\pi\) |
0.581054 | + | 0.813865i | \(0.302640\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.6780 | −0.381099 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 42.1911i | − | 1.37539i | −0.726000 | − | 0.687695i | \(-0.758623\pi\) | ||
0.726000 | − | 0.687695i | \(-0.241377\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.6592 | − | 33.0073i | −0.477368 | − | 1.07487i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.47068 | + | 4.77403i | 0.177961 | + | 0.155299i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.90825 | − | 8.90825i | −0.289479 | − | 0.289479i | 0.547395 | − | 0.836874i | \(-0.315620\pi\) |
−0.836874 | + | 0.547395i | \(0.815620\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 3.79092i | − | 0.123058i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.13247 | 0.198859 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.0737 | + | 13.0737i | 0.423499 | + | 0.423499i | 0.886407 | − | 0.462907i | \(-0.153194\pi\) |
−0.462907 | + | 0.886407i | \(0.653194\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.1232 | + | 11.6005i | −0.327580 | + | 0.375383i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.00956 | + | 5.00956i | −0.161936 | + | 0.161936i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.81754i | 0.155567i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.1728 | 0.876543 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.09059 | + | 7.09059i | 0.228491 | + | 0.228491i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 35.1521 | − | 2.39040i | 1.13159 | − | 0.0769496i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.67247 | − | 4.67247i | −0.150257 | − | 0.150257i | 0.627976 | − | 0.778233i | \(-0.283884\pi\) |
−0.778233 | + | 0.627976i | \(0.783884\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 0.0122397i | − | 0.000393197i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 9.40004i | − | 0.301662i | −0.988560 | − | 0.150831i | \(-0.951805\pi\) | ||
0.988560 | − | 0.150831i | \(-0.0481949\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −23.1381 | − | 23.1381i | −0.741774 | − | 0.741774i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.0606 | − | 1.92116i | 0.450298 | − | 0.0615264i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.4884 | − | 11.4884i | 0.367545 | − | 0.367545i | −0.499036 | − | 0.866581i | \(-0.666312\pi\) |
0.866581 | + | 0.499036i | \(0.166312\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 43.1969i | − | 1.38058i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.17758i | 0.101452i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.8053 | − | 11.8053i | −0.376529 | − | 0.376529i | 0.493319 | − | 0.869848i | \(-0.335784\pi\) |
−0.869848 | + | 0.493319i | \(0.835784\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.92883 | − | 28.3646i | −0.0614578 | − | 0.903770i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 26.4231 | − | 26.4231i | 0.841055 | − | 0.841055i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.647611 | − | 1.68242i | 0.0205928 | − | 0.0534979i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.09464 | 0.0347724 | 0.0173862 | − | 0.999849i | \(-0.494466\pi\) | ||||
0.0173862 | + | 0.999849i | \(0.494466\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.77709 | + | 5.77709i | −0.183331 | + | 0.183331i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.6856 | + | 15.4334i | 0.560670 | + | 0.489272i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.1175 | − | 13.1175i | −0.415434 | − | 0.415434i | 0.468192 | − | 0.883627i | \(-0.344905\pi\) |
−0.883627 | + | 0.468192i | \(0.844905\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.85593 | −0.280189 |
(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.1057.5 | ✓ | 48 | |
5.3 | odd | 4 | inner | 1380.2.t.a.1333.6 | yes | 48 | |
23.22 | odd | 2 | inner | 1380.2.t.a.1057.6 | yes | 48 | |
115.68 | even | 4 | inner | 1380.2.t.a.1333.5 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.t.a.1057.5 | ✓ | 48 | 1.1 | even | 1 | trivial | |
1380.2.t.a.1057.6 | yes | 48 | 23.22 | odd | 2 | inner | |
1380.2.t.a.1333.5 | yes | 48 | 115.68 | even | 4 | inner | |
1380.2.t.a.1333.6 | yes | 48 | 5.3 | odd | 4 | inner |