Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1300,2,Mod(193,1300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1300, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1300.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1300.bs (of order \(12\), degree \(4\), 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: | \(10.3805522628\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 30 x^{18} + 371 x^{16} + 2460 x^{14} + 9517 x^{12} + 21870 x^{10} + 29001 x^{8} + 20400 x^{6} + \cdots + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 260) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 457.4 | ||
Root | \(-1.86950i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1300.457 |
Dual form | 1300.2.bs.d.293.4 |
$q$-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 \(\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(651\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{1}{12}\right)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.41732 | + | 0.647720i | 1.39564 | + | 0.373961i | 0.876778 | − | 0.480895i | \(-0.159688\pi\) |
0.518864 | + | 0.854857i | \(0.326355\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.34088 | − | 1.92886i | −1.26273 | − | 0.729040i | −0.289131 | − | 0.957290i | \(-0.593366\pi\) |
−0.973603 | + | 0.228250i | \(0.926700\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.82584 | + | 1.63150i | 0.941945 | + | 0.543832i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.17419 | − | 4.38214i | 0.354032 | − | 1.32126i | −0.527667 | − | 0.849451i | \(-0.676933\pi\) |
0.881699 | − | 0.471813i | \(-0.156400\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.93090 | − | 2.09996i | −0.812885 | − | 0.582425i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.34075 | − | 5.00375i | −0.325180 | − | 1.21359i | −0.914131 | − | 0.405419i | \(-0.867125\pi\) |
0.588951 | − | 0.808169i | \(-0.299541\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.75335 | − | 1.80956i | 1.54933 | − | 0.415141i | 0.620061 | − | 0.784554i | \(-0.287108\pi\) |
0.929265 | + | 0.369413i | \(0.120441\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.82663 | − | 6.82663i | −1.48969 | − | 1.48969i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.490083 | + | 1.82902i | −0.102189 | + | 0.381376i | −0.998011 | − | 0.0630374i | \(-0.979921\pi\) |
0.895822 | + | 0.444414i | \(0.146588\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.465395 | + | 0.465395i | 0.0895652 | + | 0.0895652i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.71600 | + | 0.990731i | −0.318652 | + | 0.183974i | −0.650792 | − | 0.759256i | \(-0.725563\pi\) |
0.332139 | + | 0.943230i | \(0.392230\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.74684 | + | 2.74684i | −0.493347 | + | 0.493347i | −0.909359 | − | 0.416012i | \(-0.863427\pi\) |
0.416012 | + | 0.909359i | \(0.363427\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.67679 | − | 9.83250i | 0.988203 | − | 1.71162i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.2855 | − | 5.93836i | 1.69093 | − | 0.976260i | 0.737165 | − | 0.675712i | \(-0.236164\pi\) |
0.953767 | − | 0.300548i | \(-0.0971695\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.72474 | − | 6.97469i | −0.916692 | − | 1.11684i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.04912 | + | 1.88880i | 1.10089 | + | 0.294982i | 0.763126 | − | 0.646250i | \(-0.223664\pi\) |
0.337761 | + | 0.941232i | \(0.390330\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.07520 | + | 1.35990i | −0.773961 | + | 0.207382i | −0.624121 | − | 0.781328i | \(-0.714543\pi\) |
−0.149841 | + | 0.988710i | \(0.547876\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.88429i | 0.420717i | 0.977624 | + | 0.210358i | \(0.0674631\pi\) | ||||
−0.977624 | + | 0.210358i | \(0.932537\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.94098 | + | 6.82598i | 0.562997 | + | 0.975140i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 12.9641i | − | 1.81534i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.37298 | + | 3.37298i | −0.463315 | + | 0.463315i | −0.899740 | − | 0.436425i | \(-0.856244\pi\) |
0.436425 | + | 0.899740i | \(0.356244\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 17.4971 | 2.31755 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.22940 | − | 4.58817i | −0.160054 | − | 0.597329i | −0.998619 | − | 0.0525286i | \(-0.983272\pi\) |
0.838565 | − | 0.544801i | \(-0.183395\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.59692 | − | 2.76595i | 0.204465 | − | 0.354144i | −0.745497 | − | 0.666509i | \(-0.767788\pi\) |
0.949962 | + | 0.312365i | \(0.101121\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.29385 | − | 10.9013i | −0.792950 | − | 1.37343i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.60567 | + | 2.78111i | 0.196164 | + | 0.339767i | 0.947282 | − | 0.320402i | \(-0.103818\pi\) |
−0.751117 | + | 0.660169i | \(0.770485\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.36938 | + | 4.10389i | −0.285240 | + | 0.494050i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.70510 | + | 6.36353i | 0.202358 | + | 0.755212i | 0.990239 | + | 0.139383i | \(0.0445120\pi\) |
−0.787880 | + | 0.615829i | \(0.788821\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.35146 | −0.392259 | −0.196129 | − | 0.980578i | \(-0.562837\pi\) | ||||
−0.196129 | + | 0.980578i | \(0.562837\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.3753 | + | 12.3753i | −1.41030 | + | 1.41030i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 0.191160i | − | 0.0215072i | −0.999942 | − | 0.0107536i | \(-0.996577\pi\) | ||
0.999942 | − | 0.0107536i | \(-0.00342304\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.07093 | − | 7.05105i | −0.452325 | − | 0.783450i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 7.50696i | − | 0.823996i | −0.911185 | − | 0.411998i | \(-0.864831\pi\) | ||
0.911185 | − | 0.411998i | \(-0.135169\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.78983 | + | 1.28343i | −0.513524 | + | 0.137598i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.5771 | + | 2.83413i | 1.12117 | + | 0.300418i | 0.771358 | − | 0.636401i | \(-0.219578\pi\) |
0.349816 | + | 0.936819i | \(0.386244\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.74124 | + | 12.6690i | 0.601846 | + | 1.32807i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.41918 | + | 4.86082i | −0.873029 | + | 0.504043i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.13619 | + | 5.43203i | −0.318431 | + | 0.551539i | −0.980161 | − | 0.198203i | \(-0.936489\pi\) |
0.661730 | + | 0.749743i | \(0.269823\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.4675 | − | 10.4675i | 1.05202 | − | 1.05202i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.84851 | + | 3.37664i | −0.581949 | + | 0.335988i | −0.761907 | − | 0.647686i | \(-0.775737\pi\) |
0.179959 | + | 0.983674i | \(0.442404\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.17259 | + | 7.17259i | 0.706736 | + | 0.706736i | 0.965847 | − | 0.259111i | \(-0.0834296\pi\) |
−0.259111 | + | 0.965847i | \(0.583430\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.595458 | − | 2.22228i | 0.0575651 | − | 0.214836i | −0.931152 | − | 0.364632i | \(-0.881195\pi\) |
0.988717 | + | 0.149796i | \(0.0478616\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.63415 | + | 1.63415i | 0.156523 | + | 0.156523i | 0.781024 | − | 0.624501i | \(-0.214698\pi\) |
−0.624501 | + | 0.781024i | \(0.714698\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 28.7099 | − | 7.69279i | 2.72502 | − | 0.730167i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.65149 | + | 9.89551i | 0.249432 | + | 0.930891i | 0.971104 | + | 0.238657i | \(0.0767070\pi\) |
−0.721672 | + | 0.692235i | \(0.756626\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.85615 | − | 10.7159i | −0.448951 | − | 0.990685i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.17224 | + | 19.3031i | −0.474138 | + | 1.76951i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.29812 | − | 4.79092i | −0.754375 | − | 0.435538i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15.8166 | + | 9.13170i | 1.42613 | + | 0.823378i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.33875 | − | 1.69846i | −0.562473 | − | 0.150714i | −0.0336308 | − | 0.999434i | \(-0.510707\pi\) |
−0.528842 | + | 0.848720i | \(0.677374\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.1492 | −1.15773 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.05372 | −0.791027 | −0.395514 | − | 0.918460i | \(-0.629433\pi\) | ||||
−0.395514 | + | 0.918460i | \(0.629433\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −26.0525 | − | 6.98075i | −2.25904 | − | 0.605308i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.92353 | + | 1.68790i | 0.249774 | + | 0.144207i | 0.619661 | − | 0.784870i | \(-0.287270\pi\) |
−0.369887 | + | 0.929077i | \(0.620604\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.53706 | + | 4.92888i | 0.724104 | + | 0.418062i | 0.816261 | − | 0.577683i | \(-0.196043\pi\) |
−0.0921571 | + | 0.995744i | \(0.529376\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.86821 | + | 6.97226i | −0.157332 | + | 0.587170i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.6438 | + | 10.3778i | −1.05732 | + | 0.867838i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.10530 | + | 19.0533i | 0.421078 | + | 1.57149i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.20843 | − | 0.591746i | 0.180921 | − | 0.0484777i | −0.167221 | − | 0.985919i | \(-0.553479\pi\) |
0.348142 | + | 0.937442i | \(0.386813\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.2429 | − | 13.2429i | −1.07769 | − | 1.07769i | −0.996716 | − | 0.0809746i | \(-0.974197\pi\) |
−0.0809746 | − | 0.996716i | \(-0.525803\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.37486 | − | 16.3272i | 0.353687 | − | 1.31998i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.52992 | + | 1.52992i | 0.122101 | + | 0.122101i | 0.765517 | − | 0.643416i | \(-0.222483\pi\) |
−0.643416 | + | 0.765517i | \(0.722483\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.3383 | + | 5.96884i | −0.819884 | + | 0.473360i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.16522 | − | 5.16522i | 0.407076 | − | 0.407076i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.70822 | − | 13.3510i | 0.603755 | − | 1.04573i | −0.388492 | − | 0.921452i | \(-0.627004\pi\) |
0.992247 | − | 0.124282i | \(-0.0396626\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.1902 | − | 7.03801i | 0.943306 | − | 0.544618i | 0.0523106 | − | 0.998631i | \(-0.483341\pi\) |
0.890995 | + | 0.454013i | \(0.150008\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.18031 | + | 12.3095i | 0.321562 | + | 0.946888i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 22.0362 | + | 5.90457i | 1.68515 | + | 0.451534i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.2249 | − | 2.73977i | 0.777388 | − | 0.208301i | 0.151755 | − | 0.988418i | \(-0.451507\pi\) |
0.625633 | + | 0.780118i | \(0.284841\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 11.8874i | − | 0.893512i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.94948 | − | 13.7689i | −0.594172 | − | 1.02914i | −0.993663 | − | 0.112399i | \(-0.964146\pi\) |
0.399491 | − | 0.916737i | \(-0.369187\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.0258i | 1.33985i | 0.742430 | + | 0.669923i | \(0.233673\pi\) | ||||
−0.742430 | + | 0.669923i | \(0.766327\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.65184 | − | 5.65184i | 0.417796 | − | 0.417796i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −23.5014 | −1.71859 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.657147 | − | 2.45251i | −0.0478004 | − | 0.178394i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.25135 | − | 12.5597i | 0.524689 | − | 0.908788i | −0.474898 | − | 0.880041i | \(-0.657515\pi\) |
0.999587 | − | 0.0287469i | \(-0.00915169\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.660752 | + | 1.14446i | 0.0475620 | + | 0.0823798i | 0.888826 | − | 0.458244i | \(-0.151522\pi\) |
−0.841264 | + | 0.540624i | \(0.818188\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.96097 | − | 12.0568i | −0.495949 | − | 0.859009i | 0.504040 | − | 0.863680i | \(-0.331846\pi\) |
−0.999989 | + | 0.00467150i | \(0.998513\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.73532 | − | 11.6659i | 0.477454 | − | 0.826975i | −0.522212 | − | 0.852816i | \(-0.674893\pi\) |
0.999666 | + | 0.0258407i | \(0.00822625\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.08005 | + | 7.76287i | 0.146716 | + | 0.547550i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.64391 | 0.536498 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.36893 | + | 4.36893i | −0.303661 | + | 0.303661i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 31.7189i | − | 2.19404i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.02243 | − | 15.6273i | −0.621129 | − | 1.07583i | −0.989276 | − | 0.146060i | \(-0.953341\pi\) |
0.368146 | − | 0.929768i | \(-0.379993\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.4871i | 1.12968i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.4751 | − | 3.87860i | 0.982635 | − | 0.263296i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.10156 | − | 2.17081i | −0.547453 | − | 0.146690i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.57809 | + | 17.4810i | −0.442490 | + | 1.17590i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.73310 | − | 2.15531i | 0.249987 | − | 0.144330i | −0.369771 | − | 0.929123i | \(-0.620564\pi\) |
0.619758 | + | 0.784793i | \(0.287231\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.6548 | − | 18.4546i | 0.707182 | − | 1.22488i | −0.258716 | − | 0.965953i | \(-0.583299\pi\) |
0.965898 | − | 0.258922i | \(-0.0833673\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.68567 | + | 1.68567i | −0.111392 | + | 0.111392i | −0.760606 | − | 0.649214i | \(-0.775098\pi\) |
0.649214 | + | 0.760606i | \(0.275098\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −37.9310 | + | 21.8995i | −2.49567 | + | 1.44088i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.8733 | + | 19.8733i | 1.30195 | + | 1.30195i | 0.927079 | + | 0.374867i | \(0.122312\pi\) |
0.374867 | + | 0.927079i | \(0.377688\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.123818 | − | 0.462096i | 0.00804286 | − | 0.0300164i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.515620 | + | 0.515620i | 0.0333527 | + | 0.0333527i | 0.723586 | − | 0.690234i | \(-0.242492\pi\) |
−0.690234 | + | 0.723586i | \(0.742492\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.9645 | + | 3.74178i | −0.899533 | + | 0.241029i | −0.678816 | − | 0.734309i | \(-0.737506\pi\) |
−0.220717 | + | 0.975338i | \(0.570840\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.78468 | − | 21.5887i | −0.371087 | − | 1.38492i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −23.5934 | − | 8.87817i | −1.50121 | − | 0.564905i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.86241 | − | 18.1467i | 0.308143 | − | 1.15000i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.3324 | − | 7.12014i | −0.778417 | − | 0.449419i | 0.0574522 | − | 0.998348i | \(-0.481702\pi\) |
−0.835869 | + | 0.548929i | \(0.815036\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.43955 | + | 4.29522i | 0.467720 | + | 0.270038i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.08035 | + | 2.43307i | 0.566417 | + | 0.151771i | 0.530653 | − | 0.847589i | \(-0.321947\pi\) |
0.0357640 | + | 0.999360i | \(0.488614\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −45.8170 | −2.84693 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.46550 | −0.400204 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.2807 | + | 5.16623i | 1.18890 | + | 0.318564i | 0.798449 | − | 0.602062i | \(-0.205654\pi\) |
0.390446 | + | 0.920626i | \(0.372321\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 23.7326 | + | 13.7020i | 1.45241 | + | 0.838551i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.8136 | + | 10.8620i | 1.14708 | + | 0.662270i | 0.948175 | − | 0.317748i | \(-0.102927\pi\) |
0.198909 | + | 0.980018i | \(0.436260\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.58261 | + | 5.90638i | −0.0961367 | + | 0.358787i | −0.997189 | − | 0.0749226i | \(-0.976129\pi\) |
0.901053 | + | 0.433710i | \(0.142796\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.67248 | + | 34.3438i | 0.343314 | + | 2.07858i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.11654 | + | 19.0952i | 0.307423 | + | 1.14732i | 0.930839 | + | 0.365429i | \(0.119078\pi\) |
−0.623416 | + | 0.781891i | \(0.714256\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.2436 | + | 3.28066i | −0.733004 | + | 0.196408i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.1598 | + | 14.1598i | 0.844700 | + | 0.844700i | 0.989466 | − | 0.144766i | \(-0.0462429\pi\) |
−0.144766 | + | 0.989466i | \(0.546243\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.46917 | + | 31.6074i | −0.503440 | + | 1.87886i | −0.0270400 | + | 0.999634i | \(0.508608\pi\) |
−0.476400 | + | 0.879229i | \(0.658059\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −19.9070 | − | 19.9070i | −1.17507 | − | 1.17507i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.51750 | + | 4.91758i | −0.501029 | + | 0.289269i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.0996 | + | 11.0996i | −0.650671 | + | 0.650671i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.02783 | − | 10.4405i | 0.352150 | − | 0.609941i | −0.634476 | − | 0.772943i | \(-0.718784\pi\) |
0.986626 | + | 0.163001i | \(0.0521174\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.58588 | − | 1.49296i | 0.150048 | − | 0.0866304i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.27725 | − | 4.33150i | 0.305191 | − | 0.250497i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.5787 | + | 5.24609i | 1.12850 | + | 0.302380i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −16.3249 | + | 4.37423i | −0.937839 | + | 0.251293i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.5219i | 1.45661i | 0.685252 | + | 0.728306i | \(0.259692\pi\) | ||||
−0.685252 | + | 0.728306i | \(0.740308\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.6926 | + | 21.9843i | 0.722059 | + | 1.25064i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.9993i | 1.07735i | 0.842513 | + | 0.538676i | \(0.181075\pi\) | ||||
−0.842513 | + | 0.538676i | \(0.818925\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.2567 | + | 16.2567i | −0.918883 | + | 0.918883i | −0.996948 | − | 0.0780653i | \(-0.975126\pi\) |
0.0780653 | + | 0.996948i | \(0.475126\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.9422 | −1.17623 | −0.588115 | − | 0.808777i | \(-0.700130\pi\) | ||||
−0.588115 | + | 0.808777i | \(0.700130\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.32661 | + | 8.68303i | 0.130265 | + | 0.486157i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.87883 | − | 4.98628i | 0.160681 | − | 0.278307i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.1091 | − | 31.3660i | −1.00762 | − | 1.74525i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.89179 | + | 5.00873i | 0.159916 | + | 0.276983i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.56338 | − | 9.63606i | 0.306719 | − | 0.531253i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.54739 | + | 9.50699i | 0.140017 | + | 0.522551i | 0.999927 | + | 0.0121049i | \(0.00385320\pi\) |
−0.859910 | + | 0.510446i | \(0.829480\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 38.7537 | 2.12369 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.77242 | − | 8.77242i | 0.477864 | − | 0.477864i | −0.426584 | − | 0.904448i | \(-0.640283\pi\) |
0.904448 | + | 0.426584i | \(0.140283\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 25.6381i | 1.39247i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.81171 | + | 15.2623i | 0.477181 | + | 0.826502i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 3.40236i | − | 0.183710i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.16045 | + | 0.310942i | −0.0622963 | + | 0.0166922i | −0.289833 | − | 0.957077i | \(-0.593600\pi\) |
0.227536 | + | 0.973770i | \(0.426933\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.3696 | − | 4.92212i | −0.983303 | − | 0.263475i | −0.268868 | − | 0.963177i | \(-0.586650\pi\) |
−0.714435 | + | 0.699702i | \(0.753316\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.386712 | − | 2.34133i | −0.0206412 | − | 0.124971i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.40342 | − | 4.85172i | 0.447269 | − | 0.258231i | −0.259407 | − | 0.965768i | \(-0.583527\pi\) |
0.706676 | + | 0.707537i | \(0.250194\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −25.0059 | + | 43.3116i | −1.32345 | + | 2.29229i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.3084 | − | 24.3084i | 1.28295 | − | 1.28295i | 0.343969 | − | 0.938981i | \(-0.388228\pi\) |
0.938981 | − | 0.343969i | \(-0.111772\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 25.8788 | − | 14.9411i | 1.36204 | − | 0.786376i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −16.9561 | − | 16.9561i | −0.889963 | − | 0.889963i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.97860 | + | 7.38424i | −0.103282 | + | 0.385454i | −0.998145 | − | 0.0608877i | \(-0.980607\pi\) |
0.894862 | + | 0.446342i | \(0.147274\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 16.8381 | + | 16.8381i | 0.876554 | + | 0.876554i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 17.7747 | − | 4.76273i | 0.922818 | − | 0.247268i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.11739 | + | 4.17016i | 0.0578563 | + | 0.215923i | 0.988802 | − | 0.149236i | \(-0.0476814\pi\) |
−0.930945 | + | 0.365159i | \(0.881015\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.10990 | + | 0.699798i | 0.366179 | + | 0.0360414i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.78500 | + | 14.1258i | −0.194422 | + | 0.725594i | 0.797993 | + | 0.602666i | \(0.205895\pi\) |
−0.992416 | + | 0.122928i | \(0.960772\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.2227 | − | 8.21147i | −0.728650 | − | 0.420686i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.93423 | − | 1.69408i | −0.149932 | − | 0.0865635i | 0.423157 | − | 0.906056i | \(-0.360922\pi\) |
−0.573089 | + | 0.819493i | \(0.694255\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −16.5604 | − | 4.43734i | −0.841810 | − | 0.225562i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.8218 | 1.15711 | 0.578555 | − | 0.815643i | \(-0.303617\pi\) | ||||
0.578555 | + | 0.815643i | \(0.303617\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.80902 | 0.496064 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −21.8858 | − | 5.86427i | −1.10399 | − | 0.295814i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.77734 | + | 5.06760i | 0.440522 | + | 0.254335i | 0.703819 | − | 0.710379i | \(-0.251477\pi\) |
−0.263297 | + | 0.964715i | \(0.584810\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −58.4558 | − | 33.7495i | −2.92645 | − | 1.68959i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.05785 | − | 30.0723i | 0.402390 | − | 1.50174i | −0.406430 | − | 0.913682i | \(-0.633226\pi\) |
0.808819 | − | 0.588057i | \(-0.200107\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.8190 | − | 2.28244i | 0.688372 | − | 0.113697i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.9455 | − | 52.0454i | −0.691254 | − | 2.57979i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.1424 | + | 4.32535i | −0.798192 | + | 0.213875i | −0.634790 | − | 0.772685i | \(-0.718913\pi\) |
−0.163402 | + | 0.986560i | \(0.552247\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.97383 | + | 5.97383i | 0.294667 | + | 0.294667i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.74267 | + | 17.6999i | −0.233371 | + | 0.870954i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.4443 | + | 17.4443i | 0.854252 | + | 0.854252i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.80652 | − | 2.19769i | 0.185960 | − | 0.107364i | −0.404130 | − | 0.914702i | \(-0.632426\pi\) |
0.590090 | + | 0.807337i | \(0.299092\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.0586 | + | 14.0586i | −0.685175 | + | 0.685175i | −0.961161 | − | 0.275987i | \(-0.910995\pi\) |
0.275987 | + | 0.961161i | \(0.410995\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.70571 | + | 8.15053i | −0.228799 | + | 0.396292i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.6703 | + | 6.16047i | −0.516370 | + | 0.298126i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −37.2860 | + | 16.8970i | −1.80018 | + | 0.815794i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.45418 | − | 0.389648i | −0.0700456 | − | 0.0187687i | 0.223626 | − | 0.974675i | \(-0.428211\pi\) |
−0.293672 | + | 0.955906i | \(0.594877\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.3146 | − | 3.83559i | 0.687917 | − | 0.184327i | 0.102105 | − | 0.994774i | \(-0.467442\pi\) |
0.585812 | + | 0.810447i | \(0.300776\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.2388i | 0.633299i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.62582 | + | 6.28011i | 0.173051 | + | 0.299733i | 0.939485 | − | 0.342590i | \(-0.111304\pi\) |
−0.766434 | + | 0.642323i | \(0.777971\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 25.7188i | 1.22470i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.2198 | + | 12.2198i | −0.580581 | + | 0.580581i | −0.935063 | − | 0.354482i | \(-0.884657\pi\) |
0.354482 | + | 0.935063i | \(0.384657\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.72177 | 0.270630 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.84620 | + | 36.7465i | 0.464671 | + | 1.73417i | 0.657979 | + | 0.753037i | \(0.271412\pi\) |
−0.193308 | + | 0.981138i | \(0.561922\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.5540 | − | 28.6724i | 0.779497 | − | 1.35013i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −23.4347 | − | 40.5900i | −1.10106 | − | 1.90709i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.35050 | + | 10.9994i | 0.297064 | + | 0.514530i | 0.975463 | − | 0.220164i | \(-0.0706592\pi\) |
−0.678399 | + | 0.734694i | \(0.737326\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.70474 | − | 2.95270i | 0.0795705 | − | 0.137820i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.37555 | + | 27.5259i | 0.343513 | + | 1.28201i | 0.894339 | + | 0.447389i | \(0.147646\pi\) |
−0.550826 | + | 0.834620i | \(0.685687\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.9895 | −0.557201 | −0.278601 | − | 0.960407i | \(-0.589871\pi\) | ||||
−0.278601 | + | 0.960407i | \(0.589871\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.12252 | − | 2.12252i | 0.0982186 | − | 0.0982186i | −0.656290 | − | 0.754509i | \(-0.727875\pi\) |
0.754509 | + | 0.656290i | \(0.227875\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 12.3885i | − | 0.572046i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.70736 | + | 4.68928i | 0.124748 | + | 0.216071i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 23.8370i | 1.09603i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −15.0345 | + | 4.02848i | −0.688383 | + | 0.184452i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −36.2773 | − | 9.72046i | −1.65755 | − | 0.444139i | −0.695837 | − | 0.718199i | \(-0.744967\pi\) |
−0.961713 | + | 0.274060i | \(0.911633\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −42.6162 | − | 4.19453i | −1.94313 | − | 0.191254i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.8316 | − | 9.14039i | 0.720364 | − | 0.415902i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.64663 | − | 2.85205i | 0.0746160 | − | 0.129239i | −0.826303 | − | 0.563225i | \(-0.809560\pi\) |
0.900919 | + | 0.433987i | \(0.142894\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 27.2810 | − | 27.2810i | 1.23369 | − | 1.23369i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.1647 | − | 9.91005i | 0.774633 | − | 0.447234i | −0.0598922 | − | 0.998205i | \(-0.519076\pi\) |
0.834525 | + | 0.550971i | \(0.185742\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.25810 | + | 7.25810i | 0.326888 | + | 0.326888i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.57780 | − | 24.5487i | 0.295055 | − | 1.10116i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.58653 | + | 6.58653i | 0.294854 | + | 0.294854i | 0.838994 | − | 0.544141i | \(-0.183144\pi\) |
−0.544141 | + | 0.838994i | \(0.683144\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 34.0263 | − | 9.11732i | 1.52018 | − | 0.407332i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.767145 | − | 2.86302i | −0.0342053 | − | 0.127656i | 0.946712 | − | 0.322081i | \(-0.104382\pi\) |
−0.980917 | + | 0.194425i | \(0.937716\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.13203 | + | 32.4638i | 0.0946867 | + | 1.44177i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.86672 | − | 21.8949i | 0.260038 | − | 0.970475i | −0.705180 | − | 0.709028i | \(-0.749134\pi\) |
0.965218 | − | 0.261446i | \(-0.0841995\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.1968 | + | 6.46449i | 0.495318 | + | 0.285972i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.98513 | + | 2.30082i | 0.175948 | + | 0.101584i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.6393 | + | 3.38670i | 0.555878 | + | 0.148947i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 26.4916 | 1.16285 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.4316 | −1.37704 | −0.688521 | − | 0.725216i | \(-0.741740\pi\) | ||||
−0.688521 | + | 0.725216i | \(0.741740\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.5167 | − | 8.71283i | −1.42186 | − | 0.380985i | −0.535715 | − | 0.844399i | \(-0.679958\pi\) |
−0.886142 | + | 0.463414i | \(0.846624\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.4273 | + | 10.0617i | 0.759147 | + | 0.438294i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.8135 | + | 9.70726i | 0.731020 | + | 0.422055i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.01152 | − | 14.9712i | 0.174085 | − | 0.649694i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.6938 | − | 20.3388i | −0.723089 | − | 0.880970i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.2981 | − | 38.4329i | −0.444395 | − | 1.65850i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 34.5398 | − | 9.25492i | 1.48774 | − | 0.398638i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.00796 | − | 2.00796i | −0.0863288 | − | 0.0863288i | 0.662624 | − | 0.748953i | \(-0.269443\pi\) |
−0.748953 | + | 0.662624i | \(0.769443\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.6757 | + | 43.5742i | −0.501051 | + | 1.86995i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.19675 | + | 9.19675i | 0.393224 | + | 0.393224i | 0.875835 | − | 0.482611i | \(-0.160311\pi\) |
−0.482611 | + | 0.875835i | \(0.660311\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.02528 | − | 5.21075i | 0.385190 | − | 0.222389i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.79595 | + | 9.79595i | −0.417321 | + | 0.417321i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.368721 | + | 0.638643i | −0.0156796 | + | 0.0271579i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.3556 | − | 10.0203i | 0.735381 | − | 0.424572i | −0.0850066 | − | 0.996380i | \(-0.527091\pi\) |
0.820387 | + | 0.571808i | \(0.193758\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.7306 | + | 6.67202i | 0.749926 | + | 0.282197i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −56.8105 | − | 15.2223i | −2.39854 | − | 0.642688i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.9878 | − | 8.57109i | 1.34812 | − | 0.361229i | 0.488682 | − | 0.872462i | \(-0.337478\pi\) |
0.859442 | + | 0.511234i | \(0.170811\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 31.4089i | 1.31905i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.5265 | + | 32.0889i | 0.776672 | + | 1.34524i | 0.933850 | + | 0.357665i | \(0.116427\pi\) |
−0.157178 | + | 0.987570i | \(0.550240\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 24.2209i | − | 1.01361i | −0.862060 | − | 0.506807i | \(-0.830826\pi\) | ||
0.862060 | − | 0.506807i | \(-0.169174\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 25.6640 | − | 25.6640i | 1.07213 | − | 1.07213i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.85093 | 0.118686 | 0.0593429 | − | 0.998238i | \(-0.481099\pi\) | ||||
0.0593429 | + | 0.998238i | \(0.481099\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.855965 | + | 3.19450i | 0.0355727 | + | 0.132759i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.4799 | + | 25.0798i | −0.600726 | + | 1.04049i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.8204 | + | 18.7414i | 0.448133 | + | 0.776189i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.91874 | − | 3.32335i | −0.0791947 | − | 0.137169i | 0.823708 | − | 0.567014i | \(-0.191902\pi\) |
−0.902903 | + | 0.429845i | \(0.858568\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.5798 | + | 23.5209i | −0.559547 | + | 0.969164i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.01752 | − | 33.6539i | −0.370931 | − | 1.38433i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.4597 | 0.675919 | 0.337960 | − | 0.941161i | \(-0.390263\pi\) | ||||
0.337960 | + | 0.941161i | \(0.390263\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 23.8377 | − | 23.8377i | 0.975612 | − | 0.975612i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 37.2957i | − | 1.52386i | −0.647659 | − | 0.761931i | \(-0.724252\pi\) | ||
0.647659 | − | 0.761931i | \(-0.275748\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.218654 | − | 0.378720i | −0.00891908 | − | 0.0154483i | 0.861531 | − | 0.507704i | \(-0.169506\pi\) |
−0.870450 | + | 0.492256i | \(0.836172\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.4786i | 0.426722i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.2280 | − | 8.36751i | 1.26750 | − | 0.339627i | 0.438430 | − | 0.898765i | \(-0.355535\pi\) |
0.829074 | + | 0.559139i | \(0.188868\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 18.4778 | + | 4.95111i | 0.748759 | + | 0.200629i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.05690 | − | 8.45355i | 0.245036 | − | 0.341994i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.2582 | − | 14.5828i | 1.02017 | − | 0.588996i | 0.106017 | − | 0.994364i | \(-0.466190\pi\) |
0.914153 | + | 0.405369i | \(0.132857\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.3229 | + | 35.2002i | −0.818168 | + | 1.41711i | 0.0888631 | + | 0.996044i | \(0.471677\pi\) |
−0.907031 | + | 0.421064i | \(0.861657\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.2874 | + | 14.2874i | −0.574260 | + | 0.574260i | −0.933316 | − | 0.359056i | \(-0.883099\pi\) |
0.359056 | + | 0.933316i | \(0.383099\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.07930 | + | 0.623132i | −0.0433107 | + | 0.0250054i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −29.8703 | − | 29.8703i | −1.19673 | − | 1.19673i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 20.5450 | − | 76.6748i | 0.820486 | − | 3.06210i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −43.5044 | − | 43.5044i | −1.73464 | − | 1.73464i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.8788 | + | 8.27394i | −1.22926 | + | 0.329380i | −0.814293 | − | 0.580454i | \(-0.802875\pi\) |
−0.414971 | + | 0.909834i | \(0.636208\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.6880 | − | 43.6202i | −0.464557 | − | 1.73375i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.78369 | − | 28.2822i | 0.110294 | − | 1.12058i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.56374 | + | 20.7641i | −0.220098 | + | 0.821417i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.7120 | + | 17.7316i | 1.21305 | + | 0.700354i | 0.963422 | − | 0.267988i | \(-0.0863587\pi\) |
0.249627 | + | 0.968342i | \(0.419692\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.3268 | + | 14.6224i | 0.998790 | + | 0.576652i | 0.907890 | − | 0.419208i | \(-0.137692\pi\) |
0.0909000 | + | 0.995860i | \(0.471026\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.0890 | − | 5.65079i | −0.829095 | − | 0.222155i | −0.180776 | − | 0.983524i | \(-0.557861\pi\) |
−0.648319 | + | 0.761369i | \(0.724528\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21.5496 | −0.845894 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 37.5033 | 1.46987 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.64542 | + | 2.58448i | 0.377454 | + | 0.101139i | 0.442558 | − | 0.896740i | \(-0.354071\pi\) |
−0.0651035 | + | 0.997879i | \(0.520738\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.47068 | − | 5.46790i | −0.369486 | − | 0.213323i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.9408 | − | 10.3581i | −0.698873 | − | 0.403494i | 0.108055 | − | 0.994145i | \(-0.465538\pi\) |
−0.806927 | + | 0.590651i | \(0.798871\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.9997 | − | 44.7834i | 0.466734 | − | 1.74187i | −0.184343 | − | 0.982862i | \(-0.559016\pi\) |
0.651077 | − | 0.759012i | \(-0.274318\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −27.2242 | + | 37.9965i | −1.05730 | + | 1.47566i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.971081 | − | 3.62412i | −0.0376004 | − | 0.140327i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.4201 | − | 2.79207i | 0.402866 | − | 0.107948i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.2457 | − | 10.2457i | −0.395530 | − | 0.395530i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.44409 | + | 16.5856i | −0.171307 | + | 0.639327i | 0.825844 | + | 0.563898i | \(0.190699\pi\) |
−0.997151 | + | 0.0754282i | \(0.975968\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.9842 | − | 16.9842i | −0.652756 | − | 0.652756i | 0.300900 | − | 0.953656i | \(-0.402713\pi\) |
−0.953656 | + | 0.300900i | \(0.902713\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.9552 | − | 12.0985i | 0.804188 | − | 0.464298i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 37.7095 | − | 37.7095i | 1.44503 | − | 1.44503i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.7675 | − | 32.5062i | 0.718117 | − | 1.24382i | −0.243628 | − | 0.969869i | \(-0.578338\pi\) |
0.961745 | − | 0.273946i | \(-0.0883291\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.16665 | + | 2.98297i | −0.197120 | + | 0.113807i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.9690 | − | 2.80273i | 0.646468 | − | 0.106775i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.8582 | − | 8.00047i | −1.13586 | − | 0.304352i | −0.358573 | − | 0.933502i | \(-0.616737\pi\) |
−0.777284 | + | 0.629149i | \(0.783403\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −55.1610 | + | 14.7803i | −2.09539 | + | 0.561459i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 37.8044i | − | 1.43195i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 35.1679 | + | 60.9126i | 1.33017 | + | 2.30393i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 38.2090i | − | 1.44313i | −0.692345 | − | 0.721566i | \(-0.743423\pi\) | ||
0.692345 | − | 0.721566i | \(-0.256577\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 58.7161 | − | 58.7161i | 2.21452 | − | 2.21452i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 26.0522 | 0.979795 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.62682 | − | 35.9278i | −0.361543 | − | 1.34930i | −0.872048 | − | 0.489421i | \(-0.837208\pi\) |
0.510505 | − | 0.859875i | \(-0.329458\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.311877 | − | 0.540187i | 0.0116963 | − | 0.0202586i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.67783 | − | 6.37019i | −0.137736 | − | 0.238566i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.912443 | + | 1.58040i | 0.0340758 | + | 0.0590210i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.5751 | − | 39.1012i | 0.841908 | − | 1.45823i | −0.0463715 | − | 0.998924i | \(-0.514766\pi\) |
0.888280 | − | 0.459303i | \(-0.151901\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.1279 | − | 37.7977i | −0.377181 | − | 1.40766i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −36.1803 | −1.34556 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.21203 | + | 2.21203i | −0.0820398 | + | 0.0820398i | −0.746936 | − | 0.664896i | \(-0.768476\pi\) |
0.664896 | + | 0.746936i | \(0.268476\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 31.5082i | − | 1.16697i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.6092 | + | 23.5718i | 0.503354 | + | 0.871834i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 17.9002i | − | 0.661161i | −0.943778 | − | 0.330580i | \(-0.892756\pi\) | ||
0.943778 | − | 0.330580i | \(-0.107244\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.0726 | − | 3.77073i | 0.518370 | − | 0.138897i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.0511 | − | 4.03294i | −0.553665 | − | 0.148354i | −0.0288707 | − | 0.999583i | \(-0.509191\pi\) |
−0.524794 | + | 0.851229i | \(0.675858\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −51.2823 | − | 36.7433i | −1.88390 | − | 1.34980i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.81686 | + | 2.20366i | −0.140027 | + | 0.0808446i | −0.568377 | − | 0.822768i | \(-0.692428\pi\) |
0.428350 | + | 0.903613i | \(0.359095\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.2476 | − | 21.2134i | 0.448116 | − | 0.776159i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.27581 | + | 6.27581i | −0.229313 | + | 0.229313i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.2400 | + | 21.5005i | −1.35891 | + | 0.784565i | −0.989476 | − | 0.144694i | \(-0.953780\pi\) |
−0.369429 | + | 0.929259i | \(0.620447\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −25.1996 | − | 25.1996i | −0.918326 | − | 0.918326i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.50026 | + | 27.9914i | −0.272602 | + | 1.01736i | 0.684830 | + | 0.728703i | \(0.259876\pi\) |
−0.957432 | + | 0.288660i | \(0.906790\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.2017 | + | 15.2017i | 0.551786 | + | 0.551786i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.09438 | − | 2.43683i | 0.329671 | − | 0.0883350i | −0.0901872 | − | 0.995925i | \(-0.528747\pi\) |
0.419858 | + | 0.907590i | \(0.362080\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.30745 | − | 8.61152i | −0.0835353 | − | 0.311758i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.03176 | + | 16.0292i | −0.217794 | + | 0.578779i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.95609 | − | 14.7643i | 0.142660 | − | 0.532416i | −0.857188 | − | 0.515004i | \(-0.827791\pi\) |
0.999848 | − | 0.0174122i | \(-0.00554276\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.3742 | + | 11.7630i | 0.733759 | + | 0.423636i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14.8233 | − | 8.55826i | −0.533158 | − | 0.307819i | 0.209143 | − | 0.977885i | \(-0.432933\pi\) |
−0.742302 | + | 0.670066i | \(0.766266\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −110.754 | − | 29.6766i | −3.97329 | − | 1.06464i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 51.0231 | 1.82809 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 29.8880 | 1.06948 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.25970 | − | 0.337534i | −0.0450179 | − | 0.0120625i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.5805 | − | 7.26333i | −0.448445 | − | 0.258910i | 0.258728 | − | 0.965950i | \(-0.416697\pi\) |
−0.707173 | + | 0.707040i | \(0.750030\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 43.2613 | + | 24.9769i | 1.54014 | + | 0.889202i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.2287 | − | 38.1741i | 0.363691 | − | 1.35731i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.4888 | + | 4.75324i | −0.372469 | + | 0.168793i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.4168 | + | 46.3403i | 0.439827 | + | 1.64146i | 0.729244 | + | 0.684253i | \(0.239872\pi\) |
−0.289418 | + | 0.957203i | \(0.593462\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.4323 | − | 3.86712i | 0.510577 | − | 0.136809i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 25.2654 | + | 25.2654i | 0.892708 | + | 0.892708i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.93525 | + | 14.6866i | −0.138872 | + | 0.518277i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 38.4430 | + | 38.4430i | 1.35326 | + | 1.35326i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39.5328 | + | 22.8242i | −1.38990 | + | 0.802458i | −0.993303 | − | 0.115536i | \(-0.963141\pi\) |
−0.396594 | + | 0.917994i | \(0.629808\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.2035 | − | 35.2035i | 1.23616 | − | 1.23616i | 0.274606 | − | 0.961557i | \(-0.411452\pi\) |
0.961557 | − | 0.274606i | \(-0.0885475\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.65136 | + | 13.2525i | −0.268345 | + | 0.464787i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −31.8138 | + | 18.3677i | −1.11303 | + | 0.642606i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.44563 | + | 45.1673i | −0.155343 | + | 1.57827i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 47.3788 | + | 12.6951i | 1.65353 | + | 0.443062i | 0.960599 | − | 0.277940i | \(-0.0896515\pi\) |
0.692933 | + | 0.721002i | \(0.256318\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.3492 | + | 8.66794i | −1.12762 | + | 0.302145i | −0.773964 | − | 0.633230i | \(-0.781729\pi\) |
−0.353658 | + | 0.935375i | \(0.615062\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.102239i | 0.00355520i | 0.999998 | + | 0.00177760i | \(0.000565828\pi\) | ||||
−0.999998 | + | 0.00177760i | \(0.999434\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.0347 | − | 36.4332i | −0.730567 | − | 1.26538i | −0.956641 | − | 0.291268i | \(-0.905923\pi\) |
0.226075 | − | 0.974110i | \(-0.427411\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 49.4734i | 1.71621i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 28.8716 | − | 28.8716i | 1.00034 | − | 1.00034i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.55673 | −0.0883735 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.59501 | + | 5.95267i | 0.0550660 | + | 0.205509i | 0.987978 | − | 0.154596i | \(-0.0494076\pi\) |
−0.932912 | + | 0.360105i | \(0.882741\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.5369 | + | 21.7146i | −0.432307 | + | 0.748778i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 25.0571 | + | 43.4002i | 0.863014 | + | 1.49478i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.4820 | + | 32.0118i | 0.635049 | + | 1.09994i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −40.9454 | + | 70.9196i | −1.40524 | + | 2.43395i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.82058 | + | 21.7227i | 0.199527 | + | 0.744645i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 44.1436 | 1.51145 | 0.755724 | − | 0.654890i | \(-0.227285\pi\) | ||||
0.755724 | + | 0.654890i | \(0.227285\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.9216 | − | 24.9216i | 0.851305 | − | 0.851305i | −0.138989 | − | 0.990294i | \(-0.544385\pi\) |
0.990294 | + | 0.138989i | \(0.0443854\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.2383i | 1.30467i | 0.757929 | + | 0.652337i | \(0.226211\pi\) | ||||
−0.757929 | + | 0.652337i | \(0.773789\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −35.2275 | − | 61.0158i | −1.20055 | − | 2.07941i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 0.948734i | − | 0.0322953i | −0.999870 | − | 0.0161476i | \(-0.994860\pi\) | ||
0.999870 | − | 0.0161476i | \(-0.00514018\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −23.7748 | + | 6.37043i | −0.807433 | + | 0.216351i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.837690 | − | 0.224458i | −0.0284167 | − | 0.00761423i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.13416 | − | 11.5230i | 0.0384296 | − | 0.390442i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −17.7247 | + | 10.2334i | −0.599890 | + | 0.346347i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.8949 | − | 36.1910i | 0.705569 | − | 1.22208i | −0.260916 | − | 0.965361i | \(-0.584025\pi\) |
0.966486 | − | 0.256721i | \(-0.0826420\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 21.3338 | − | 21.3338i | 0.719570 | − | 0.719570i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.5194 | − | 15.8883i | 0.927151 | − | 0.535291i | 0.0412419 | − | 0.999149i | \(-0.486869\pi\) |
0.885910 | + | 0.463858i | \(0.153535\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.2531 | − | 10.2531i | −0.345043 | − | 0.345043i | 0.513217 | − | 0.858259i | \(-0.328454\pi\) |
−0.858259 | + | 0.513217i | \(0.828454\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.69367 | − | 10.0529i | 0.0904447 | − | 0.337544i | −0.905845 | − | 0.423610i | \(-0.860763\pi\) |
0.996289 | + | 0.0860657i | \(0.0274295\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.9009 | + | 17.9009i | 0.600377 | + | 0.600377i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −35.6787 | + | 9.56008i | −1.19528 | + | 0.320275i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.21928 | + | 19.4786i | 0.174657 | + | 0.651827i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.5624 | − | 7.05246i | 0.519614 | − | 0.235475i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.99219 | − | 7.43494i | 0.0664432 | − | 0.247969i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.3999 | + | 12.3552i | 0.712934 | + | 0.411613i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 43.9300 | + | 25.3630i | 1.46190 | + | 0.844028i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.1887 | + | 2.99801i | 0.371516 | + | 0.0995473i | 0.439746 | − | 0.898122i | \(-0.355069\pi\) |
−0.0682301 | + | 0.997670i | \(0.521735\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −22.0359 | −0.730885 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.9445 | −0.561397 | −0.280699 | − | 0.959796i | \(-0.590566\pi\) | ||||
−0.280699 | + | 0.959796i | \(0.590566\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −32.8965 | − | 8.81460i | −1.08872 | − | 0.291721i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 30.2474 | + | 17.4633i | 0.998857 | + | 0.576690i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.13979 | − | 1.23541i | −0.0705851 | − | 0.0407523i | 0.464292 | − | 0.885682i | \(-0.346309\pi\) |
−0.534877 | + | 0.844930i | \(0.679642\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.5310 | + | 61.6947i | −0.544717 | + | 2.03291i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.36569 | − | 22.2315i | 0.275360 | − | 0.731758i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.56650 | + | 31.9706i | 0.281361 | + | 1.05005i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.19975 | − | 1.66122i | 0.203407 | − | 0.0545028i | −0.155677 | − | 0.987808i | \(-0.549756\pi\) |
0.359084 | + | 0.933305i | \(0.383089\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 38.9668 | + | 38.9668i | 1.27709 | + | 1.27709i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.3062 | + | 45.9275i | −0.402888 | + | 1.50360i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.9242 | + | 29.9242i | 0.977581 | + | 0.977581i | 0.999754 | − | 0.0221727i | \(-0.00705838\pi\) |
−0.0221727 | + | 0.999754i | \(0.507058\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −49.8275 | + | 28.7679i | −1.62606 | + | 0.938805i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.0049 | + | 10.0049i | −0.326150 | + | 0.326150i | −0.851121 | − | 0.524970i | \(-0.824076\pi\) |
0.524970 | + | 0.851121i | \(0.324076\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.90931 | + | 11.9673i | −0.224998 | + | 0.389708i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.33687 | − | 4.81329i | 0.270912 | − | 0.156411i | −0.358390 | − | 0.933572i | \(-0.616674\pi\) |
0.629302 | + | 0.777161i | \(0.283341\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.82279 | + | 7.03794i | 0.318861 | + | 0.228461i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −50.6241 | − | 13.5647i | −1.64160 | − | 0.439865i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.91919 | + | 2.12194i | −0.256528 | + | 0.0687364i | −0.384791 | − | 0.923004i | \(-0.625726\pi\) |
0.128263 | + | 0.991740i | \(0.459060\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 22.4967i | 0.727215i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.51143 | − | 11.2781i | −0.210265 | − | 0.364190i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.9097i | 0.513218i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.30831 | − | 5.30831i | 0.171058 | − | 0.171058i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −53.8159 | −1.73060 | −0.865301 | − | 0.501252i | \(-0.832873\pi\) | ||||
−0.865301 | + | 0.501252i | \(0.832873\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −23.4593 | − | 87.5513i | −0.753621 | − | 2.81255i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.7496 | + | 49.7958i | −0.922619 | + | 1.59802i | −0.127272 | + | 0.991868i | \(0.540622\pi\) |
−0.795347 | + | 0.606154i | \(0.792711\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.0142 | − | 32.9336i | −0.609567 | − | 1.05580i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.46271 | + | 5.99759i | 0.110782 | + | 0.191880i | 0.916086 | − | 0.400982i | \(-0.131331\pi\) |
−0.805304 | + | 0.592862i | \(0.797998\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.8391 | − | 43.0226i | 0.793862 | − | 1.37501i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.95172 | + | 7.28393i | 0.0623138 | + | 0.232558i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.9827 | 1.08388 | 0.541941 | − | 0.840417i | \(-0.317690\pi\) | ||||
0.541941 | + | 0.840417i | \(0.317690\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 19.6900 | − | 19.6900i | 0.626738 | − | 0.626738i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 9.94909i | − | 0.316363i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.93170 | − | 13.7381i | −0.251959 | − | 0.436405i | 0.712106 | − | 0.702072i | \(-0.247741\pi\) |
−0.964065 | + | 0.265666i | \(0.914408\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24.6315i | 0.781656i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.5993 | + | 5.25161i | −0.620715 | + | 0.166320i | −0.555453 | − | 0.831548i | \(-0.687455\pi\) |
−0.0652620 | + | 0.997868i | \(0.520788\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.55051 | + | 2.02315i | 0.238888 | + | 0.0640098i |
(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 | 1300.2.bs.d.457.4 | 20 | ||
5.2 | odd | 4 | 260.2.bf.c.93.4 | ✓ | 20 | ||
5.3 | odd | 4 | 1300.2.bn.d.93.2 | 20 | |||
5.4 | even | 2 | 260.2.bk.c.197.2 | yes | 20 | ||
13.7 | odd | 12 | 1300.2.bn.d.657.2 | 20 | |||
65.7 | even | 12 | 260.2.bk.c.33.2 | yes | 20 | ||
65.33 | even | 12 | inner | 1300.2.bs.d.293.4 | 20 | ||
65.59 | odd | 12 | 260.2.bf.c.137.4 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.bf.c.93.4 | ✓ | 20 | 5.2 | odd | 4 | ||
260.2.bf.c.137.4 | yes | 20 | 65.59 | odd | 12 | ||
260.2.bk.c.33.2 | yes | 20 | 65.7 | even | 12 | ||
260.2.bk.c.197.2 | yes | 20 | 5.4 | even | 2 | ||
1300.2.bn.d.93.2 | 20 | 5.3 | odd | 4 | |||
1300.2.bn.d.657.2 | 20 | 13.7 | odd | 12 | |||
1300.2.bs.d.293.4 | 20 | 65.33 | even | 12 | inner | ||
1300.2.bs.d.457.4 | 20 | 1.1 | even | 1 | trivial |