Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3360,2,Mod(2591,3360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3360, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3360.2591");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3360.ba (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(26.8297350792\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} + 8 x^{18} - 20 x^{17} + 50 x^{16} - 92 x^{15} + 144 x^{14} - 244 x^{13} + 481 x^{12} - 696 x^{11} + 848 x^{10} - 2088 x^{9} + 4329 x^{8} - 6588 x^{7} + 11664 x^{6} + \cdots + 59049 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{15} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2591.13 | ||
Root | \(-0.504688 + 1.65689i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3360.2591 |
Dual form | 3360.2.ba.d.2591.14 |
$q$-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 \(\left(\mathbb{Z}/3360\mathbb{Z}\right)^\times\).
\(n\) | \(421\) | \(1121\) | \(1471\) | \(1921\) | \(2017\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0.814731 | − | 1.52847i | 0.470385 | − | 0.882461i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.67243 | − | 2.49058i | −0.557476 | − | 0.830193i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.02863 | −0.310144 | −0.155072 | − | 0.987903i | \(-0.549561\pi\) | ||||
−0.155072 | + | 0.987903i | \(0.549561\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.05107 | −1.12356 | −0.561782 | − | 0.827285i | \(-0.689884\pi\) | ||||
−0.561782 | + | 0.827285i | \(0.689884\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.52847 | − | 0.814731i | −0.394649 | − | 0.210363i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.17733i | 0.770615i | 0.922788 | + | 0.385308i | \(0.125905\pi\) | ||||
−0.922788 | + | 0.385308i | \(0.874095\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.43512i | − | 0.558656i | −0.960196 | − | 0.279328i | \(-0.909888\pi\) | ||
0.960196 | − | 0.279328i | \(-0.0901116\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.52847 | − | 0.814731i | −0.333539 | − | 0.177789i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.89676 | −1.43807 | −0.719037 | − | 0.694972i | \(-0.755417\pi\) | ||||
−0.719037 | + | 0.694972i | \(0.755417\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.16935 | + | 0.527101i | −0.994842 | + | 0.101441i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.16192i | 0.772849i | 0.922321 | + | 0.386425i | \(0.126290\pi\) | ||||
−0.922321 | + | 0.386425i | \(0.873710\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.76217i | 0.496101i | 0.968747 | + | 0.248051i | \(0.0797899\pi\) | ||||
−0.968747 | + | 0.248051i | \(0.920210\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.838058 | + | 1.57223i | −0.145887 | + | 0.273690i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.949518 | 0.156100 | 0.0780499 | − | 0.996949i | \(-0.475131\pi\) | ||||
0.0780499 | + | 0.996949i | \(0.475131\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.30053 | + | 6.19193i | −0.528508 | + | 0.991502i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.27131i | 0.823240i | 0.911356 | + | 0.411620i | \(0.135037\pi\) | ||||
−0.911356 | + | 0.411620i | \(0.864963\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.82252i | 1.49792i | 0.662615 | + | 0.748960i | \(0.269447\pi\) | ||||
−0.662615 | + | 0.748960i | \(0.730553\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.49058 | + | 1.67243i | −0.371274 | + | 0.249311i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.55610 | 0.810441 | 0.405220 | − | 0.914219i | \(-0.367195\pi\) | ||||
0.405220 | + | 0.914219i | \(0.367195\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.85644 | + | 2.58867i | 0.680038 | + | 0.362486i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 2.52469i | − | 0.346793i | −0.984852 | − | 0.173397i | \(-0.944526\pi\) | ||
0.984852 | − | 0.173397i | \(-0.0554742\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.02863i | 0.138701i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.72201 | − | 1.98397i | −0.492992 | − | 0.262783i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.4623 | 1.75264 | 0.876318 | − | 0.481732i | \(-0.159992\pi\) | ||||
0.876318 | + | 0.481732i | \(0.159992\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.8801 | −1.77717 | −0.888585 | − | 0.458711i | \(-0.848311\pi\) | ||||
−0.888585 | + | 0.458711i | \(0.848311\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.49058 | + | 1.67243i | −0.313783 | + | 0.210706i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.05107i | 0.502473i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 12.3941i | − | 1.51418i | −0.653308 | − | 0.757092i | \(-0.726619\pi\) | ||
0.653308 | − | 0.757092i | \(-0.273381\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.61900 | + | 10.5415i | −0.676448 | + | 1.26904i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.483561 | 0.0573881 | 0.0286941 | − | 0.999588i | \(-0.490865\pi\) | ||||
0.0286941 | + | 0.999588i | \(0.490865\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.55005 | −0.298460 | −0.149230 | − | 0.988802i | \(-0.547680\pi\) | ||||
−0.149230 | + | 0.988802i | \(0.547680\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.814731 | + | 1.52847i | −0.0940770 | + | 0.176492i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.02863i | 0.117224i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 4.87745i | − | 0.548756i | −0.961622 | − | 0.274378i | \(-0.911528\pi\) | ||
0.961622 | − | 0.274378i | \(-0.0884720\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.40597 | + | 8.33063i | −0.378441 | + | 0.925625i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.24143 | −0.904614 | −0.452307 | − | 0.891862i | \(-0.649399\pi\) | ||||
−0.452307 | + | 0.891862i | \(0.649399\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.17733 | 0.344630 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.36136 | + | 3.39084i | 0.682010 | + | 0.363537i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.15948i | 0.228905i | 0.993429 | + | 0.114452i | \(0.0365113\pi\) | ||||
−0.993429 | + | 0.114452i | \(0.963489\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.05107i | 0.424667i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.22189 | + | 2.25043i | 0.437790 | + | 0.233359i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.43512 | −0.249838 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.82636 | 0.185438 | 0.0927191 | − | 0.995692i | \(-0.470444\pi\) | ||||
0.0927191 | + | 0.995692i | \(0.470444\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.72031 | + | 2.56189i | 0.172898 | + | 0.257480i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 10.7091i | − | 1.06560i | −0.846242 | − | 0.532798i | \(-0.821140\pi\) | ||
0.846242 | − | 0.532798i | \(-0.178860\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.39285i | 0.925505i | 0.886488 | + | 0.462753i | \(0.153138\pi\) | ||||
−0.886488 | + | 0.462753i | \(0.846862\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.814731 | + | 1.52847i | −0.0795096 | + | 0.149163i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.05603 | 0.198764 | 0.0993819 | − | 0.995049i | \(-0.468313\pi\) | ||||
0.0993819 | + | 0.995049i | \(0.468313\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.9058 | −1.33194 | −0.665968 | − | 0.745980i | \(-0.731981\pi\) | ||||
−0.665968 | + | 0.745980i | \(0.731981\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.773601 | − | 1.45131i | 0.0734270 | − | 0.137752i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.76305i | 0.542142i | 0.962559 | + | 0.271071i | \(0.0873779\pi\) | ||||
−0.962559 | + | 0.271071i | \(0.912622\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.89676i | 0.643126i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.77512 | + | 10.0895i | 0.626360 | + | 0.932775i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.17733 | 0.291265 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.94192 | −0.903811 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.05702 | + | 4.29470i | 0.726477 | + | 0.387240i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.39012i | 0.655767i | 0.944718 | + | 0.327883i | \(0.106335\pi\) | ||||
−0.944718 | + | 0.327883i | \(0.893665\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 15.0134 | + | 8.00271i | 1.32186 | + | 0.704599i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.6620 | 1.28102 | 0.640511 | − | 0.767949i | \(-0.278723\pi\) | ||||
0.640511 | + | 0.767949i | \(0.278723\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.43512 | −0.211152 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.527101 | + | 5.16935i | 0.0453656 | + | 0.444907i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.50071i | 0.469957i | 0.972001 | + | 0.234979i | \(0.0755020\pi\) | ||||
−0.972001 | + | 0.234979i | \(0.924498\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 20.4943i | − | 1.73831i | −0.494544 | − | 0.869153i | \(-0.664665\pi\) | ||
0.494544 | − | 0.869153i | \(-0.335335\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.52673 | − | 8.49232i | 0.381219 | − | 0.715183i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.16706 | 0.348467 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.16192 | 0.345629 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.814731 | + | 1.52847i | −0.0671979 | + | 0.126066i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 10.3708i | − | 0.849606i | −0.905286 | − | 0.424803i | \(-0.860343\pi\) | ||
0.905286 | − | 0.424803i | \(-0.139657\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.68583i | 0.218570i | 0.994010 | + | 0.109285i | \(0.0348561\pi\) | ||||
−0.994010 | + | 0.109285i | \(0.965144\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.91339 | − | 5.31385i | 0.639759 | − | 0.429599i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.76217 | 0.221863 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −24.8805 | −1.98568 | −0.992842 | − | 0.119438i | \(-0.961891\pi\) | ||||
−0.992842 | + | 0.119438i | \(0.961891\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.85891 | − | 2.05694i | −0.306031 | − | 0.163126i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.89676i | 0.543541i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.77321i | 0.452193i | 0.974105 | + | 0.226097i | \(0.0725965\pi\) | ||||
−0.974105 | + | 0.226097i | \(0.927404\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.57223 | + | 0.838058i | 0.122398 | + | 0.0652427i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.7838 | −1.06663 | −0.533313 | − | 0.845918i | \(-0.679053\pi\) | ||||
−0.533313 | + | 0.845918i | \(0.679053\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.41115 | 0.262396 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.06487 | + | 4.07257i | −0.463792 | + | 0.311437i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 2.64419i | − | 0.201034i | −0.994935 | − | 0.100517i | \(-0.967950\pi\) | ||
0.994935 | − | 0.100517i | \(-0.0320497\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000i | 0.0755929i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.9681 | − | 20.5766i | 0.824414 | − | 1.54663i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 23.8234 | 1.78064 | 0.890322 | − | 0.455332i | \(-0.150479\pi\) | ||||
0.890322 | + | 0.455332i | \(0.150479\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.5767 | −1.23214 | −0.616068 | − | 0.787693i | \(-0.711276\pi\) | ||||
−0.616068 | + | 0.787693i | \(0.711276\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.3086 | + | 21.2154i | −0.835954 | + | 1.56828i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 0.949518i | − | 0.0698100i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3.26830i | − | 0.239002i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.527101 | + | 5.16935i | 0.0383410 | + | 0.376015i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.87494 | −0.425096 | −0.212548 | − | 0.977151i | \(-0.568176\pi\) | ||||
−0.212548 | + | 0.977151i | \(0.568176\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.37509 | −0.0989815 | −0.0494907 | − | 0.998775i | \(-0.515760\pi\) | ||||
−0.0494907 | + | 0.998775i | \(0.515760\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.19193 | + | 3.30053i | 0.443413 | + | 0.236356i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.53554i | 0.394391i | 0.980364 | + | 0.197195i | \(0.0631834\pi\) | ||||
−0.980364 | + | 0.197195i | \(0.936817\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.6010i | 1.03504i | 0.855671 | + | 0.517520i | \(0.173145\pi\) | ||||
−0.855671 | + | 0.517520i | \(0.826855\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −18.9440 | − | 10.0979i | −1.33621 | − | 0.712249i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.16192 | 0.292110 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.27131 | 0.368164 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.5343 | + | 17.1769i | 0.801691 | + | 1.19388i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.50485i | 0.173264i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 20.9843i | − | 1.44462i | −0.691569 | − | 0.722311i | \(-0.743080\pi\) | ||
0.691569 | − | 0.722311i | \(-0.256920\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.393972 | − | 0.739107i | 0.0269945 | − | 0.0506428i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.82252 | 0.669890 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.76217 | 0.187509 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.07760 | + | 3.89766i | −0.140391 | + | 0.263380i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 12.8716i | − | 0.865835i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 4.11921i | − | 0.275843i | −0.990443 | − | 0.137921i | \(-0.955958\pi\) | ||
0.990443 | − | 0.137921i | \(-0.0440421\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.67243 | + | 2.49058i | 0.111495 | + | 0.166039i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.32987 | 0.287384 | 0.143692 | − | 0.989622i | \(-0.454103\pi\) | ||||
0.143692 | + | 0.989622i | \(0.454103\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.56658 | 0.632177 | 0.316089 | − | 0.948730i | \(-0.397630\pi\) | ||||
0.316089 | + | 0.948730i | \(0.397630\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.57223 | + | 0.838058i | 0.103445 | + | 0.0551402i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 14.9942i | − | 0.982303i | −0.871074 | − | 0.491152i | \(-0.836576\pi\) | ||
0.871074 | − | 0.491152i | \(-0.163424\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 5.55610i | − | 0.362440i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.45503 | − | 3.97381i | −0.484256 | − | 0.258127i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.20979 | −0.336993 | −0.168497 | − | 0.985702i | \(-0.553891\pi\) | ||||
−0.168497 | + | 0.985702i | \(0.553891\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.6920 | −1.46172 | −0.730861 | − | 0.682526i | \(-0.760881\pi\) | ||||
−0.730861 | + | 0.682526i | \(0.760881\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.95815 | + | 11.9931i | 0.638816 | + | 0.769360i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000i | 0.0638877i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.86485i | 0.627686i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.71454 | + | 12.5968i | −0.425517 | + | 0.798287i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.35580 | 0.590533 | 0.295267 | − | 0.955415i | \(-0.404592\pi\) | ||||
0.295267 | + | 0.955415i | \(0.404592\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.09423 | 0.446010 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.58867 | − | 4.85644i | 0.162109 | − | 0.304122i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.1927i | 0.822938i | 0.911424 | + | 0.411469i | \(0.134984\pi\) | ||||
−0.911424 | + | 0.411469i | \(0.865016\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 0.949518i | − | 0.0590002i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.3656 | − | 6.96051i | 0.641614 | − | 0.430845i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −24.1870 | −1.49143 | −0.745716 | − | 0.666264i | \(-0.767893\pi\) | ||||
−0.745716 | + | 0.666264i | \(0.767893\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.52469 | −0.155091 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.30070 | + | 1.75940i | 0.201999 | + | 0.107673i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.26475i | 0.138084i | 0.997614 | + | 0.0690420i | \(0.0219942\pi\) | ||||
−0.997614 | + | 0.0690420i | \(0.978006\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.4324i | 1.24118i | 0.784136 | + | 0.620589i | \(0.213106\pi\) | ||||
−0.784136 | + | 0.620589i | \(0.786894\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.19193 | + | 3.30053i | 0.374752 | + | 0.199757i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.02863 | 0.0620289 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.4294 | −1.40774 | −0.703869 | − | 0.710330i | \(-0.748546\pi\) | ||||
−0.703869 | + | 0.710330i | \(0.748546\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.87941 | − | 4.61954i | 0.411860 | − | 0.276564i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 9.47571i | − | 0.565274i | −0.959227 | − | 0.282637i | \(-0.908791\pi\) | ||
0.959227 | − | 0.282637i | \(-0.0912091\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.9834i | 1.12845i | 0.825622 | + | 0.564224i | \(0.190824\pi\) | ||||
−0.825622 | + | 0.564224i | \(0.809176\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.98397 | + | 3.72201i | −0.117520 | + | 0.220473i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.27131 | 0.311155 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.90459 | 0.406152 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.48799 | − | 2.79153i | 0.0872274 | − | 0.163642i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.2408i | 1.12406i | 0.827117 | + | 0.562029i | \(0.189979\pi\) | ||||
−0.827117 | + | 0.562029i | \(0.810021\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 13.4623i | − | 0.783803i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.31736 | − | 0.542193i | 0.308544 | − | 0.0314612i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 27.9392 | 1.61577 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.82252 | 0.566161 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −16.3685 | − | 8.72505i | −0.940348 | − | 0.501241i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.8801i | 0.794775i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.41175i | 0.308865i | 0.988003 | + | 0.154432i | \(0.0493549\pi\) | ||||
−0.988003 | + | 0.154432i | \(0.950645\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.3567 | + | 7.65264i | 0.816722 | + | 0.435344i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.7401 | −1.40288 | −0.701441 | − | 0.712727i | \(-0.747460\pi\) | ||||
−0.701441 | + | 0.712727i | \(0.747460\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.1213 | −0.628616 | −0.314308 | − | 0.949321i | \(-0.601772\pi\) | ||||
−0.314308 | + | 0.949321i | \(0.601772\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.67243 | + | 2.49058i | 0.0942306 | + | 0.140328i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 13.7615i | − | 0.772925i | −0.922305 | − | 0.386463i | \(-0.873697\pi\) | ||
0.922305 | − | 0.386463i | \(-0.126303\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 4.28109i | − | 0.239695i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.67511 | − | 3.14257i | 0.0934955 | − | 0.175401i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.73719 | 0.430509 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.05107 | 0.224713 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.3295 | + | 21.2546i | −0.626523 | + | 1.17538i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 5.55610i | − | 0.306318i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 14.8523i | − | 0.816357i | −0.912902 | − | 0.408179i | \(-0.866164\pi\) | ||
0.912902 | − | 0.408179i | \(-0.133836\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.58800 | − | 2.36485i | −0.0870219 | − | 0.129593i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.3941 | −0.677164 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.2100 | −1.80907 | −0.904533 | − | 0.426403i | \(-0.859780\pi\) | ||||
−0.904533 | + | 0.426403i | \(0.859780\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.80864 | + | 4.69533i | 0.478420 | + | 0.255016i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 2.84126i | − | 0.153863i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10.5415 | + | 5.61900i | 0.567534 | + | 0.302517i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.21271 | 0.118784 | 0.0593922 | − | 0.998235i | \(-0.481084\pi\) | ||||
0.0593922 | + | 0.998235i | \(0.481084\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.24785 | −0.441497 | −0.220749 | − | 0.975331i | \(-0.570850\pi\) | ||||
−0.220749 | + | 0.975331i | \(0.570850\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 20.9414 | − | 2.13532i | 1.11777 | − | 0.113975i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 27.6601i | 1.47220i | 0.676874 | + | 0.736099i | \(0.263334\pi\) | ||||
−0.676874 | + | 0.736099i | \(0.736666\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 0.483561i | − | 0.0256647i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.58867 | − | 4.85644i | 0.137007 | − | 0.257030i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.8086 | 1.20379 | 0.601895 | − | 0.798575i | \(-0.294412\pi\) | ||||
0.601895 | + | 0.798575i | \(0.294412\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0702 | 0.687904 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.09998 | + | 15.1959i | −0.425139 | + | 0.797578i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.55005i | 0.133475i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 34.2006i | − | 1.78526i | −0.450791 | − | 0.892630i | \(-0.648858\pi\) | ||
0.450791 | − | 0.892630i | \(-0.351142\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.1286 | − | 8.81588i | 0.683448 | − | 0.458936i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.52469 | −0.131075 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.5027 | 0.543808 | 0.271904 | − | 0.962324i | \(-0.412347\pi\) | ||||
0.271904 | + | 0.962324i | \(0.412347\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.52847 | + | 0.814731i | 0.0789297 | + | 0.0420725i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 16.8602i | − | 0.868346i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.7093i | 1.16650i | 0.812293 | + | 0.583250i | \(0.198219\pi\) | ||||
−0.812293 | + | 0.583250i | \(0.801781\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.2956 | + | 6.02095i | 0.578689 | + | 0.308463i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.68651 | −0.443860 | −0.221930 | − | 0.975063i | \(-0.571236\pi\) | ||||
−0.221930 | + | 0.975063i | \(0.571236\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.02863 | 0.0524239 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 24.4638 | − | 16.4275i | 1.24356 | − | 0.835055i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.1956i | 0.922555i | 0.887256 | + | 0.461278i | \(0.152609\pi\) | ||||
−0.887256 | + | 0.461278i | \(0.847391\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 21.9133i | − | 1.10820i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.9455 | − | 22.4103i | 0.602573 | − | 1.13045i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.87745 | −0.245411 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.9987 | 0.702577 | 0.351288 | − | 0.936267i | \(-0.385744\pi\) | ||||
0.351288 | + | 0.936267i | \(0.385744\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.98397 | + | 3.72201i | −0.0993227 | + | 0.186333i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 27.7434i | − | 1.38544i | −0.721206 | − | 0.692720i | \(-0.756412\pi\) | ||
0.721206 | − | 0.692720i | \(-0.243588\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 11.1898i | − | 0.557401i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.33063 | + | 3.40597i | 0.413952 | + | 0.169244i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.976705 | −0.0484135 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.9399 | −1.18375 | −0.591877 | − | 0.806028i | \(-0.701613\pi\) | ||||
−0.591877 | + | 0.806028i | \(0.701613\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.40765 | + | 4.48159i | 0.414719 | + | 0.221061i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 13.4623i | − | 0.662434i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.24143i | 0.404556i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −31.3249 | − | 16.6974i | −1.53399 | − | 0.817673i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.1582 | −0.789378 | −0.394689 | − | 0.918815i | \(-0.629148\pi\) | ||||
−0.394689 | + | 0.918815i | \(0.629148\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.9591 | 1.46012 | 0.730060 | − | 0.683383i | \(-0.239492\pi\) | ||||
0.730060 | + | 0.683383i | \(0.239492\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.29218 | − | 13.8379i | −0.451801 | − | 0.672822i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 3.17733i | − | 0.154123i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.8801i | 0.671707i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.39503 | − | 6.36922i | 0.163914 | − | 0.307509i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.19384 | −0.0575053 | −0.0287526 | − | 0.999587i | \(-0.509154\pi\) | ||||
−0.0287526 | + | 0.999587i | \(0.509154\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.3012 | −1.11979 | −0.559893 | − | 0.828565i | \(-0.689158\pi\) | ||||
−0.559893 | + | 0.828565i | \(0.689158\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.39084 | − | 6.36136i | 0.162579 | − | 0.305004i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.7945i | 0.803388i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 1.58614i | − | 0.0757025i | −0.999283 | − | 0.0378512i | \(-0.987949\pi\) | ||
0.999283 | − | 0.0378512i | \(-0.0120513\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.67243 | + | 2.49058i | 0.0796394 | + | 0.118599i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.8564 | −0.610824 | −0.305412 | − | 0.952220i | \(-0.598794\pi\) | ||||
−0.305412 | + | 0.952220i | \(0.598794\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.15948 | 0.102369 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.8514 | − | 8.44938i | −0.749745 | − | 0.399642i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 2.04478i | − | 0.0964993i | −0.998835 | − | 0.0482497i | \(-0.984636\pi\) | ||
0.998835 | − | 0.0482497i | \(-0.0153643\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 5.42224i | − | 0.255323i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.10521 | + | 2.18823i | 0.192879 | + | 0.102812i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.05107 | 0.189917 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.8392 | 1.20871 | 0.604353 | − | 0.796717i | \(-0.293432\pi\) | ||||
0.604353 | + | 0.796717i | \(0.293432\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.67477 | − | 16.4247i | −0.0781717 | − | 0.766640i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 34.7726i | − | 1.61952i | −0.586760 | − | 0.809761i | \(-0.699597\pi\) | ||
0.586760 | − | 0.809761i | \(-0.300403\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 8.82104i | − | 0.409949i | −0.978767 | − | 0.204974i | \(-0.934289\pi\) | ||
0.978767 | − | 0.204974i | \(-0.0657111\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.25043 | − | 4.22189i | 0.104361 | − | 0.195786i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.8590 | −1.10406 | −0.552032 | − | 0.833823i | \(-0.686147\pi\) | ||||
−0.552032 | + | 0.833823i | \(0.686147\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.3941 | −0.572308 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.2709 | + | 38.0291i | −0.934036 | + | 1.75229i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 10.1038i | − | 0.464571i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.43512i | 0.111731i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.28795 | + | 4.22237i | −0.287905 | + | 0.193329i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.3238 | 0.654471 | 0.327236 | − | 0.944943i | \(-0.393883\pi\) | ||||
0.327236 | + | 0.944943i | \(0.393883\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.84656 | −0.175388 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.5415 | + | 5.61900i | 0.479654 | + | 0.255673i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 1.82636i | − | 0.0829305i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 10.6405i | − | 0.482169i | −0.970504 | − | 0.241085i | \(-0.922497\pi\) | ||
0.970504 | − | 0.241085i | \(-0.0775031\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.82417 | + | 4.70361i | 0.399043 | + | 0.212705i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.6682 | −0.887614 | −0.443807 | − | 0.896122i | \(-0.646372\pi\) | ||||
−0.443807 | + | 0.896122i | \(0.646372\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.2238 | −0.595569 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.56189 | − | 1.72031i | 0.115148 | − | 0.0773223i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 0.483561i | − | 0.0216907i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 16.3530i | − | 0.732060i | −0.930603 | − | 0.366030i | \(-0.880717\pi\) | ||
0.930603 | − | 0.366030i | \(-0.119283\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.2301 | + | 21.0682i | −0.501725 | + | 0.941256i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −35.6697 | −1.59043 | −0.795217 | − | 0.606324i | \(-0.792643\pi\) | ||||
−0.795217 | + | 0.606324i | \(0.792643\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.7091 | −0.476549 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.77917 | − | 5.21384i | 0.123427 | − | 0.231555i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 35.4015i | 1.56915i | 0.620037 | + | 0.784573i | \(0.287118\pi\) | ||||
−0.620037 | + | 0.784573i | \(0.712882\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.55005i | 0.112807i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.28356 | + | 12.5880i | 0.0566704 | + | 0.555774i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.39285 | 0.413898 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.71518 | −0.251354 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.04156 | − | 2.15430i | −0.177405 | − | 0.0945634i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.5904i | 1.69068i | 0.534232 | + | 0.845338i | \(0.320601\pi\) | ||||
−0.534232 | + | 0.845338i | \(0.679399\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 7.35480i | − | 0.321603i | −0.986987 | − | 0.160801i | \(-0.948592\pi\) | ||
0.986987 | − | 0.160801i | \(-0.0514079\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.52847 | + | 0.814731i | 0.0667078 | + | 0.0355578i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.77633 | −0.382303 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24.5653 | 1.06806 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −22.5147 | − | 33.5288i | −0.977053 | − | 1.45503i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 21.3544i | − | 0.924963i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 2.05603i | − | 0.0888898i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.4096 | − | 36.4133i | 0.837588 | − | 1.57135i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.02863 | 0.0443063 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.0900 | −0.433801 | −0.216901 | − | 0.976194i | \(-0.569595\pi\) | ||||
−0.216901 | + | 0.976194i | \(0.569595\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.5056 | + | 25.3370i | −0.579579 | + | 1.08731i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.9058i | 0.595660i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 7.00161i | − | 0.299367i | −0.988734 | − | 0.149684i | \(-0.952174\pi\) | ||
0.988734 | − | 0.149684i | \(-0.0478255\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 23.2135 | + | 34.5696i | 0.990730 | + | 1.47539i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.1348 | 0.431757 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.87745 | −0.207410 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.45131 | − | 0.773601i | −0.0616046 | − | 0.0328376i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 23.3180i | − | 0.988017i | −0.869457 | − | 0.494008i | \(-0.835531\pi\) | ||
0.869457 | − | 0.494008i | \(-0.164469\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 39.7917i | − | 1.68301i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.99549 | − | 2.66279i | −0.210910 | − | 0.112423i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.70223 | −0.366755 | −0.183378 | − | 0.983043i | \(-0.558703\pi\) | ||||
−0.183378 | + | 0.983043i | \(0.558703\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.76305 | 0.242453 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.33063 | + | 3.40597i | 0.349854 | + | 0.143037i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.7542i | 1.45697i | 0.685062 | + | 0.728485i | \(0.259775\pi\) | ||||
−0.685062 | + | 0.728485i | \(0.740225\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 29.5985i | − | 1.23866i | −0.785131 | − | 0.619330i | \(-0.787404\pi\) | ||
0.785131 | − | 0.619330i | \(-0.212596\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.78649 | + | 8.97966i | −0.199959 | + | 0.375131i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.89676 | 0.287615 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.2723 | 1.09373 | 0.546864 | − | 0.837221i | \(-0.315821\pi\) | ||||
0.546864 | + | 0.837221i | \(0.315821\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.12033 | + | 2.10179i | −0.0465594 | + | 0.0873473i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.24143i | 0.341912i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.59698i | 0.107556i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.0895 | − | 6.77512i | 0.417150 | − | 0.280117i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.95283 | 0.204425 | 0.102213 | − | 0.994763i | \(-0.467408\pi\) | ||||
0.102213 | + | 0.994763i | \(0.467408\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.72624 | 0.277150 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.46090 | + | 4.50998i | 0.348035 | + | 0.185516i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 30.1056i | − | 1.23629i | −0.786065 | − | 0.618144i | \(-0.787885\pi\) | ||
0.786065 | − | 0.618144i | \(-0.212115\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 3.17733i | − | 0.130258i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 22.3172 | + | 11.8959i | 0.913383 | + | 0.486867i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.31960 | −0.176494 | −0.0882470 | − | 0.996099i | \(-0.528126\pi\) | ||||
−0.0882470 | + | 0.996099i | \(0.528126\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.7553 | −1.25454 | −0.627268 | − | 0.778803i | \(-0.715827\pi\) | ||||
−0.627268 | + | 0.778803i | \(0.715827\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −30.8686 | + | 20.7283i | −1.25707 | + | 0.844121i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.94192i | 0.404196i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.2187i | 0.658298i | 0.944278 | + | 0.329149i | \(0.106762\pi\) | ||||
−0.944278 | + | 0.329149i | \(0.893238\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.39084 | − | 6.36136i | 0.137404 | − | 0.257775i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22.5081 | −0.910582 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.0300119 | 0.00121217 | 0.000606084 | − | 1.00000i | \(-0.499807\pi\) | ||||
0.000606084 | 1.00000i | \(0.499807\pi\) | ||||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.29470 | − | 8.05702i | 0.173179 | − | 0.324891i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 13.9151i | − | 0.560200i | −0.959971 | − | 0.280100i | \(-0.909632\pi\) | ||
0.959971 | − | 0.280100i | \(-0.0903676\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 19.7421i | − | 0.793501i | −0.917926 | − | 0.396750i | \(-0.870138\pi\) | ||
0.917926 | − | 0.396750i | \(-0.129862\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 35.6517 | − | 3.63529i | 1.43066 | − | 0.145879i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.15948 | 0.0865178 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.82858 | + | 2.04078i | 0.152899 | + | 0.0815007i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.01693i | 0.120293i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.60553i | 0.183343i | 0.995789 | + | 0.0916716i | \(0.0292210\pi\) | ||||
−0.995789 | + | 0.0916716i | \(0.970779\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −32.0739 | − | 17.0966i | −1.27482 | − | 0.679528i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.39012 | 0.293268 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.05107 | 0.160509 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.808721 | − | 1.20435i | −0.0319925 | − | 0.0476432i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 41.2011i | 1.62735i | 0.581322 | + | 0.813674i | \(0.302536\pi\) | ||||
−0.581322 | + | 0.813674i | \(0.697464\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 11.2120i | − | 0.442156i | −0.975256 | − | 0.221078i | \(-0.929042\pi\) | ||
0.975256 | − | 0.221078i | \(-0.0709576\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.00271 | − | 15.0134i | 0.315106 | − | 0.591152i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.63691 | −0.260924 | −0.130462 | − | 0.991453i | \(-0.541646\pi\) | ||||
−0.130462 | + | 0.991453i | \(0.541646\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.8477 | −0.543570 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.25043 | − | 4.22189i | 0.0882012 | − | 0.165469i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 37.8238i | − | 1.48016i | −0.672518 | − | 0.740081i | \(-0.734787\pi\) | ||
0.672518 | − | 0.740081i | \(-0.265213\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 14.6620i | − | 0.572890i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.26477 | + | 6.35109i | 0.166384 | + | 0.247780i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.3589 | 1.18262 | 0.591308 | − | 0.806446i | \(-0.298612\pi\) | ||||
0.591308 | + | 0.806446i | \(0.298612\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.8441 | −1.31638 | −0.658192 | − | 0.752850i | \(-0.728679\pi\) | ||||
−0.658192 | + | 0.752850i | \(0.728679\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −19.6738 | − | 10.4869i | −0.764066 | − | 0.407276i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.43512i | 0.0944301i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 28.7038i | − | 1.11141i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.29608 | − | 3.35605i | −0.243421 | − | 0.129752i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.2776 | 0.551179 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.93411 | 0.267290 | 0.133645 | − | 0.991029i | \(-0.457332\pi\) | ||||
0.133645 | + | 0.991029i | \(0.457332\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.16935 | − | 0.527101i | 0.198968 | − | 0.0202881i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 48.8801i | 1.87861i | 0.343079 | + | 0.939307i | \(0.388530\pi\) | ||||
−0.343079 | + | 0.939307i | \(0.611470\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1.82636i | − | 0.0700891i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.52768 | − | 6.61807i | 0.135181 | − | 0.253605i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.4825 | 0.860267 | 0.430134 | − | 0.902765i | \(-0.358466\pi\) | ||||
0.430134 | + | 0.902765i | \(0.358466\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.50071 | 0.210171 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.79418 | − | 14.6222i | 0.297367 | − | 0.557872i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.2277i | 0.389644i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 46.8158i | − | 1.78096i | −0.455024 | − | 0.890479i | \(-0.650369\pi\) | ||
0.455024 | − | 0.890479i | \(-0.349631\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.56189 | − | 1.72031i | 0.0973181 | − | 0.0653493i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −20.4943 | −0.777394 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.7487 | −0.634401 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22.9182 | − | 12.2162i | −0.866845 | − | 0.462061i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 31.7316i | − | 1.19848i | −0.800568 | − | 0.599242i | \(-0.795469\pi\) | ||
0.800568 | − | 0.599242i | \(-0.204531\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 2.31219i | − | 0.0872060i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.49232 | − | 4.52673i | −0.319839 | − | 0.170486i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.7091 | −0.402758 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 45.2570 | 1.69966 | 0.849830 | − | 0.527057i | \(-0.176704\pi\) | ||||
0.849830 | + | 0.527057i | \(0.176704\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.1477 | + | 8.15719i | −0.455574 | + | 0.305919i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 19.0500i | − | 0.713430i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 4.16706i | − | 0.155839i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.24457 | + | 7.96299i | −0.158517 | + | 0.297383i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.35064 | −0.124958 | −0.0624789 | − | 0.998046i | \(-0.519901\pi\) | ||||
−0.0624789 | + | 0.998046i | \(0.519901\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.39285 | 0.349808 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −18.4879 | + | 34.6840i | −0.687572 | + | 1.28991i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 4.16192i | − | 0.154570i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 14.8966i | − | 0.552486i | −0.961088 | − | 0.276243i | \(-0.910911\pi\) | ||
0.961088 | − | 0.276243i | \(-0.0890895\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.4443 | − | 5.44954i | 0.979420 | − | 0.201835i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −31.2094 | −1.15432 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.15703 | −0.264351 | −0.132175 | − | 0.991226i | \(-0.542196\pi\) | ||||
−0.132175 | + | 0.991226i | \(0.542196\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.52847 | + | 0.814731i | 0.0563784 | + | 0.0300518i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.7490i | 0.469615i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 54.2406i | − | 1.99527i | −0.0687121 | − | 0.997637i | \(-0.521889\pi\) | ||
0.0687121 | − | 0.997637i | \(-0.478111\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.0781 | + | 8.03720i | 0.553908 | + | 0.295254i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.20435 | −0.337675 | −0.168837 | − | 0.985644i | \(-0.554001\pi\) | ||||
−0.168837 | + | 0.985644i | \(0.554001\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.3708 | −0.379956 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.7832 | + | 20.5259i | 0.504301 | + | 0.751004i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 2.05603i | − | 0.0751256i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 4.30009i | − | 0.156912i | −0.996918 | − | 0.0784562i | \(-0.975001\pi\) | ||
0.996918 | − | 0.0784562i | \(-0.0249991\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.62246 | − | 14.3000i | 0.277778 | − | 0.521123i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.68583 | 0.0977474 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.7794 | 0.609857 | 0.304929 | − | 0.952375i | \(-0.401367\pi\) | ||||
0.304929 | + | 0.952375i | \(0.401367\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.77988 | − | 10.8433i | 0.209797 | − | 0.393587i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 26.3871i | − | 0.956531i | −0.878215 | − | 0.478266i | \(-0.841266\pi\) | ||
0.878215 | − | 0.478266i | \(-0.158734\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.9058i | 0.503424i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.31385 | − | 7.91339i | −0.192123 | − | 0.286109i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −54.5365 | −1.96920 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.9362 | −0.899221 | −0.449611 | − | 0.893225i | \(-0.648437\pi\) | ||||
−0.449611 | + | 0.893225i | \(0.648437\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.1646 | + | 10.7485i | 0.726211 | + | 0.387098i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 45.5450i | − | 1.63814i | −0.573694 | − | 0.819070i | \(-0.694490\pi\) | ||
0.573694 | − | 0.819070i | \(-0.305510\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 2.76217i | − | 0.0992202i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.45131 | − | 0.773601i | −0.0520654 | − | 0.0277528i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.8363 | 0.459908 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.497406 | −0.0177986 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.19375 | − | 21.5144i | −0.0783983 | − | 0.768863i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24.8805i | 0.888025i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 32.5394i | − | 1.15990i | −0.814651 | − | 0.579952i | \(-0.803071\pi\) | ||
0.814651 | − | 0.579952i | \(-0.196929\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19.7059 | + | 36.9690i | −0.701547 | + | 1.31613i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.76305 | 0.204911 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 56.2294 | 1.99677 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.05694 | + | 3.85891i | −0.0729523 | + | 0.136861i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40.2915i | 1.42720i | 0.700555 | + | 0.713599i | \(0.252936\pi\) | ||||
−0.700555 | + | 0.713599i | \(0.747064\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.6536i | 0.624538i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.37836 | − | 3.61158i | 0.190035 | − | 0.127609i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.62306 | 0.0925657 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.89676 | 0.243079 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.46159 | + | 1.84516i | 0.121854 | + | 0.0649526i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 4.35497i | − | 0.153113i | −0.997065 | − | 0.0765563i | \(-0.975608\pi\) | ||
0.997065 | − | 0.0765563i | \(-0.0243925\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 13.8673i | − | 0.486945i | −0.969908 | − | 0.243473i | \(-0.921713\pi\) | ||
0.969908 | − | 0.243473i | \(-0.0782866\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 31.2302 | + | 16.6469i | 1.09529 | + | 0.583831i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.77321 | 0.202227 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.9191 | 0.836822 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.0895 | − | 6.77512i | 0.352556 | − | 0.236742i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 36.4682i | − | 1.27275i | −0.771380 | − | 0.636375i | \(-0.780433\pi\) | ||
0.771380 | − | 0.636375i | \(-0.219567\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 38.0513i | − | 1.32638i | −0.748449 | − | 0.663192i | \(-0.769201\pi\) | ||
0.748449 | − | 0.663192i | \(-0.230799\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.838058 | − | 1.57223i | 0.0291774 | − | 0.0547381i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19.5344 | −0.679276 | −0.339638 | − | 0.940556i | \(-0.610305\pi\) | ||||
−0.339638 | + | 0.940556i | \(0.610305\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.1218 | 1.56714 | 0.783572 | − | 0.621301i | \(-0.213395\pi\) | ||||
0.783572 | + | 0.621301i | \(0.213395\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.0887 | + | 35.8111i | −0.662179 | + | 1.24227i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 3.17733i | − | 0.110088i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.7838i | 0.477010i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.45594 | − | 14.2786i | −0.0503248 | − | 0.493542i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 48.0813 | 1.65995 | 0.829976 | − | 0.557800i | \(-0.188354\pi\) | ||||
0.829976 | + | 0.557800i | \(0.188354\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.6784 | 0.402704 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.4833 | − | 7.72016i | −0.498832 | − | 0.265896i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 3.41115i | − | 0.117347i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.94192i | 0.341608i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 29.0156 | + | 15.4664i | 0.995811 | + | 0.530805i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.54860 | −0.224483 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.9961 | −1.19824 | −0.599122 | − | 0.800658i | \(-0.704484\pi\) | ||||
−0.599122 | + | 0.800658i | \(0.704484\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.07257 | + | 6.06487i | 0.139279 | + | 0.207414i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 9.60020i | − | 0.327937i | −0.986466 | − | 0.163968i | \(-0.947571\pi\) | ||
0.986466 | − | 0.163968i | \(-0.0524295\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 13.9926i | − | 0.477420i | −0.971091 | − | 0.238710i | \(-0.923275\pi\) | ||
0.971091 | − | 0.238710i | \(-0.0767246\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.29470 | − | 8.05702i | 0.146363 | − | 0.274583i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.3191 | −0.759753 | −0.379876 | − | 0.925037i | \(-0.624033\pi\) | ||||
−0.379876 | + | 0.925037i | \(0.624033\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.64419 | −0.0899051 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.62538 | − | 10.5534i | 0.191048 | − | 0.358414i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.01711i | 0.170194i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 50.2095i | 1.70128i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.05445 | − | 4.54868i | −0.103377 | − | 0.153950i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −39.4987 | −1.33378 | −0.666889 | − | 0.745157i | \(-0.732374\pi\) | ||||
−0.666889 | + | 0.745157i | \(0.732374\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 29.4089 | + | 15.6761i | 0.991938 | + | 0.528740i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.3276i | 1.32498i | 0.749071 | + | 0.662490i | \(0.230500\pi\) | ||||
−0.749071 | + | 0.662490i | \(0.769500\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.7331i | 1.00060i | 0.865852 | + | 0.500300i | \(0.166777\pi\) | ||||
−0.865852 | + | 0.500300i | \(0.833223\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −20.5766 | − | 10.9681i | −0.691676 | − | 0.368689i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.3460 | 0.481693 | 0.240846 | − | 0.970563i | \(-0.422575\pi\) | ||||
0.240846 | + | 0.970563i | \(0.422575\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.39012 | 0.247857 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.50349 | − | 8.56915i | 0.117371 | − | 0.287077i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 13.5298i | − | 0.452757i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 23.8234i | − | 0.796328i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 22.7630 | − | 42.7042i | 0.760033 | − | 1.42585i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11.4960 | −0.383411 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.02177 | 0.267244 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.00271 | − | 15.0134i | 0.266313 | − | 0.499615i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.5767i | 0.551028i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.55934i | 0.0849814i | 0.999097 | + | 0.0424907i | \(0.0135293\pi\) | ||||
−0.999097 | + | 0.0424907i | \(0.986471\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −26.6719 | + | 17.9102i | −0.884651 | + | 0.594045i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.4063 | 1.04054 | 0.520269 | − | 0.854003i | \(-0.325832\pi\) | ||||
0.520269 | + | 0.854003i | \(0.325832\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.47739 | 0.280561 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 21.2154 | + | 11.3086i | 0.701358 | + | 0.373850i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 14.6620i | − | 0.484180i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 19.6050i | − | 0.646710i | −0.946278 | − | 0.323355i | \(-0.895189\pi\) | ||
0.946278 | − | 0.323355i | \(-0.104811\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.27169 | + | 4.40912i | 0.272561 | + | 0.145285i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.95894 | −0.0644792 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.949518 | −0.0312200 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 23.3936 | − | 15.7089i | 0.768348 | − | 0.515947i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 10.7301i | − | 0.352042i | −0.984386 | − | 0.176021i | \(-0.943677\pi\) | ||
0.984386 | − | 0.176021i | \(-0.0563227\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.43512i | 0.0798080i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20.1565 | + | 37.8145i | −0.659895 | + | 1.23799i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.26830 | −0.106885 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.3454 | −0.762662 | −0.381331 | − | 0.924439i | \(-0.624534\pi\) | ||||
−0.381331 | + | 0.924439i | \(0.624534\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.06090 | + | 16.9986i | −0.295691 | + | 0.554729i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 58.0096i | − | 1.89106i | −0.325537 | − | 0.945529i | \(-0.605545\pi\) | ||
0.325537 | − | 0.945529i | \(-0.394455\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 36.3549i | − | 1.18388i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.16935 | − | 0.527101i | 0.168159 | − | 0.0171466i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.23510 | 0.300100 | 0.150050 | − | 0.988678i | \(-0.452056\pi\) | ||||
0.150050 | + | 0.988678i | \(0.452056\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.3304 | 0.335339 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.0341 | − | 11.2120i | −0.682077 | − | 0.363572i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 11.9268i | − | 0.386347i | −0.981165 | − | 0.193174i | \(-0.938122\pi\) | ||
0.981165 | − | 0.193174i | \(-0.0618780\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.87494i | 0.190109i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.54350 | − | 3.48793i | −0.211521 | − | 0.112749i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.50071 | 0.177627 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.3704 | 0.753884 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.43856 | − | 5.12070i | −0.110806 | − | 0.165012i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.37509i | 0.0442659i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.0407i | 0.612308i | 0.951982 | + | 0.306154i | \(0.0990422\pi\) | ||||
−0.951982 | + | 0.306154i | \(0.900958\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.30372 | − | 11.8260i | 0.202505 | − | 0.379907i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.9262 | −0.896193 | −0.448097 | − | 0.893985i | \(-0.647898\pi\) | ||||
−0.448097 | + | 0.893985i | \(0.647898\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.4943 | −0.657018 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.30053 | − | 6.19193i | 0.105702 | − | 0.198300i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 50.4549i | 1.61419i | 0.590419 | + | 0.807097i | \(0.298963\pi\) | ||||
−0.590419 | + | 0.807097i | \(0.701037\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2.22131i | − | 0.0709934i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 23.2565 | + | 34.6335i | 0.742522 | + | 1.10576i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.07518 | 0.193768 | 0.0968840 | − | 0.995296i | \(-0.469112\pi\) | ||||
0.0968840 | + | 0.995296i | \(0.469112\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.53554 | 0.176377 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.49232 | − | 4.52673i | −0.270314 | − | 0.144087i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 67.7435i | − | 2.15412i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.8413i | 0.947939i | 0.880541 | + | 0.473969i | \(0.157179\pi\) | ||||
−0.880541 | + | 0.473969i | \(0.842821\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −22.7013 | − | 12.1006i | −0.720404 | − | 0.384002i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.6010 | 0.462884 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.73412 | 0.276612 | 0.138306 | − | 0.990390i | \(-0.455834\pi\) | ||||
0.138306 | + | 0.990390i | \(0.455834\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.90839 | + | 0.500492i | −0.155295 | + | 0.0158349i |
(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 | 3360.2.ba.d.2591.13 | yes | 20 | |
3.2 | odd | 2 | 3360.2.ba.c.2591.7 | ✓ | 20 | ||
4.3 | odd | 2 | 3360.2.ba.c.2591.8 | yes | 20 | ||
12.11 | even | 2 | inner | 3360.2.ba.d.2591.14 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3360.2.ba.c.2591.7 | ✓ | 20 | 3.2 | odd | 2 | ||
3360.2.ba.c.2591.8 | yes | 20 | 4.3 | odd | 2 | ||
3360.2.ba.d.2591.13 | yes | 20 | 1.1 | even | 1 | trivial | |
3360.2.ba.d.2591.14 | yes | 20 | 12.11 | even | 2 | inner |