Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,3,Mod(145,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.145");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.be (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.8502001097\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 228) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.145 |
Dual form | 912.3.be.c.673.1 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.50000 | + | 0.866025i | −0.500000 | + | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | + | 1.73205i | 0.200000 | + | 0.346410i | 0.948528 | − | 0.316693i | \(-0.102572\pi\) |
−0.748528 | + | 0.663103i | \(0.769239\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.142857 | 0.0714286 | − | 0.997446i | \(-0.477244\pi\) | ||||
0.0714286 | + | 0.997446i | \(0.477244\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −16.0000 | −1.45455 | −0.727273 | − | 0.686349i | \(-0.759212\pi\) | ||||
−0.727273 | + | 0.686349i | \(0.759212\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.5000 | + | 7.79423i | 1.03846 | + | 0.599556i | 0.919397 | − | 0.393330i | \(-0.128677\pi\) |
0.119064 | + | 0.992887i | \(0.462011\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.00000 | − | 1.73205i | −0.200000 | − | 0.115470i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −11.0000 | − | 19.0526i | −0.647059 | − | 1.12074i | −0.983822 | − | 0.179149i | \(-0.942665\pi\) |
0.336763 | − | 0.941589i | \(-0.390668\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −19.0000 | −1.00000 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.50000 | + | 0.866025i | −0.0714286 | + | 0.0412393i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 20.0000 | − | 34.6410i | 0.869565 | − | 1.50613i | 0.00712357 | − | 0.999975i | \(-0.497732\pi\) |
0.862442 | − | 0.506157i | \(-0.168934\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.5000 | − | 18.1865i | 0.420000 | − | 0.727461i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 15.0000 | + | 8.66025i | 0.517241 | + | 0.298629i | 0.735805 | − | 0.677193i | \(-0.236804\pi\) |
−0.218564 | + | 0.975823i | \(0.570137\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 50.2295i | 1.62031i | 0.586219 | + | 0.810153i | \(0.300616\pi\) | ||||
−0.586219 | + | 0.810153i | \(0.699384\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 24.0000 | − | 13.8564i | 0.727273 | − | 0.419891i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000 | + | 1.73205i | 0.0285714 | + | 0.0494872i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 15.5885i | 0.421310i | 0.977561 | + | 0.210655i | \(0.0675596\pi\) | ||||
−0.977561 | + | 0.210655i | \(0.932440\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −27.0000 | −0.692308 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.0000 | + | 6.92820i | −0.292683 | + | 0.168981i | −0.639151 | − | 0.769081i | \(-0.720714\pi\) |
0.346468 | + | 0.938062i | \(0.387381\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −24.5000 | − | 42.4352i | −0.569767 | − | 0.986866i | −0.996589 | − | 0.0825301i | \(-0.973700\pi\) |
0.426821 | − | 0.904336i | \(-0.359633\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.00000 | 0.133333 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 23.0000 | − | 39.8372i | 0.489362 | − | 0.847599i | −0.510563 | − | 0.859840i | \(-0.670563\pi\) |
0.999925 | + | 0.0122408i | \(0.00389646\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −48.0000 | −0.979592 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 33.0000 | + | 19.0526i | 0.647059 | + | 0.373580i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −42.0000 | − | 24.2487i | −0.792453 | − | 0.457523i | 0.0483725 | − | 0.998829i | \(-0.484597\pi\) |
−0.840825 | + | 0.541307i | \(0.817930\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16.0000 | − | 27.7128i | −0.290909 | − | 0.503869i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 28.5000 | − | 16.4545i | 0.500000 | − | 0.288675i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 57.0000 | − | 32.9090i | 0.966102 | − | 0.557779i | 0.0680561 | − | 0.997681i | \(-0.478320\pi\) |
0.898046 | + | 0.439902i | \(0.144987\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 48.5000 | − | 84.0045i | 0.795082 | − | 1.37712i | −0.127705 | − | 0.991812i | \(-0.540761\pi\) |
0.922787 | − | 0.385310i | \(-0.125906\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.50000 | − | 2.59808i | 0.0238095 | − | 0.0412393i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 31.1769i | 0.479645i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 22.5000 | + | 12.9904i | 0.335821 | + | 0.193886i | 0.658422 | − | 0.752649i | \(-0.271224\pi\) |
−0.322602 | + | 0.946535i | \(0.604557\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 69.2820i | 1.00409i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 42.0000 | − | 24.2487i | 0.591549 | − | 0.341531i | −0.174161 | − | 0.984717i | \(-0.555721\pi\) |
0.765710 | + | 0.643186i | \(0.222388\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −17.5000 | − | 30.3109i | −0.239726 | − | 0.415218i | 0.720910 | − | 0.693029i | \(-0.243724\pi\) |
−0.960636 | + | 0.277811i | \(0.910391\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 36.3731i | 0.484974i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −16.0000 | −0.207792 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 76.5000 | − | 44.1673i | 0.968354 | − | 0.559080i | 0.0696203 | − | 0.997574i | \(-0.477821\pi\) |
0.898734 | + | 0.438494i | \(0.144488\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 146.000 | 1.75904 | 0.879518 | − | 0.475865i | \(-0.157865\pi\) | ||||
0.879518 | + | 0.475865i | \(0.157865\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 22.0000 | − | 38.1051i | 0.258824 | − | 0.448296i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −30.0000 | −0.344828 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −33.0000 | − | 19.0526i | −0.370787 | − | 0.214074i | 0.303015 | − | 0.952986i | \(-0.402007\pi\) |
−0.673802 | + | 0.738912i | \(0.735340\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.5000 | + | 7.79423i | 0.148352 | + | 0.0856509i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −43.5000 | − | 75.3442i | −0.467742 | − | 0.810153i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −19.0000 | − | 32.9090i | −0.200000 | − | 0.346410i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 54.0000 | − | 31.1769i | 0.556701 | − | 0.321411i | −0.195119 | − | 0.980780i | \(-0.562509\pi\) |
0.751820 | + | 0.659368i | \(0.229176\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −24.0000 | + | 41.5692i | −0.242424 | + | 0.419891i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.0000 | + | 24.2487i | −0.138614 | + | 0.240086i | −0.926972 | − | 0.375130i | \(-0.877598\pi\) |
0.788358 | + | 0.615216i | \(0.210931\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 126.440i | − | 1.22757i | −0.789473 | − | 0.613785i | \(-0.789646\pi\) | ||
0.789473 | − | 0.613785i | \(-0.210354\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.00000 | − | 1.73205i | −0.0285714 | − | 0.0164957i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 83.1384i | − | 0.776995i | −0.921450 | − | 0.388497i | \(-0.872994\pi\) | ||
0.921450 | − | 0.388497i | \(-0.127006\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −66.0000 | + | 38.1051i | −0.605505 | + | 0.349588i | −0.771204 | − | 0.636588i | \(-0.780345\pi\) |
0.165699 | + | 0.986176i | \(0.447012\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.5000 | − | 23.3827i | −0.121622 | − | 0.210655i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 183.597i | − | 1.62476i | −0.583131 | − | 0.812378i | \(-0.698173\pi\) | ||
0.583131 | − | 0.812378i | \(-0.301827\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 80.0000 | 0.695652 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 40.5000 | − | 23.3827i | 0.346154 | − | 0.199852i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.0000 | − | 19.0526i | −0.0924370 | − | 0.160106i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 135.000 | 1.11570 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12.0000 | − | 20.7846i | 0.0975610 | − | 0.168981i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 92.0000 | 0.736000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −24.0000 | − | 13.8564i | −0.188976 | − | 0.109106i | 0.402527 | − | 0.915408i | \(-0.368132\pi\) |
−0.591503 | + | 0.806303i | \(0.701465\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 73.5000 | + | 42.4352i | 0.569767 | + | 0.328955i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −64.0000 | − | 110.851i | −0.488550 | − | 0.846193i | 0.511364 | − | 0.859364i | \(-0.329141\pi\) |
−0.999913 | + | 0.0131717i | \(0.995807\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −19.0000 | −0.142857 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9.00000 | + | 5.19615i | −0.0666667 | + | 0.0384900i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 58.0000 | − | 100.459i | 0.423358 | − | 0.733277i | −0.572908 | − | 0.819620i | \(-0.694185\pi\) |
0.996265 | + | 0.0863428i | \(0.0275180\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −87.5000 | + | 151.554i | −0.629496 | + | 1.09032i | 0.358156 | + | 0.933662i | \(0.383405\pi\) |
−0.987653 | + | 0.156658i | \(0.949928\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 79.6743i | 0.565066i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −216.000 | − | 124.708i | −1.51049 | − | 0.872082i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 34.6410i | 0.238904i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 72.0000 | − | 41.5692i | 0.489796 | − | 0.282784i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −74.0000 | − | 128.172i | −0.496644 | − | 0.860213i | 0.503348 | − | 0.864084i | \(-0.332101\pi\) |
−0.999993 | + | 0.00387051i | \(0.998768\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 193.990i | 1.28470i | 0.766411 | + | 0.642350i | \(0.222040\pi\) | ||||
−0.766411 | + | 0.642350i | \(0.777960\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −66.0000 | −0.431373 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −87.0000 | + | 50.2295i | −0.561290 | + | 0.324061i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 96.5000 | + | 167.143i | 0.614650 | + | 1.06460i | 0.990446 | + | 0.137902i | \(0.0440359\pi\) |
−0.375796 | + | 0.926702i | \(0.622631\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 84.0000 | 0.528302 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.0000 | − | 34.6410i | 0.124224 | − | 0.215162i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −233.000 | −1.42945 | −0.714724 | − | 0.699407i | \(-0.753448\pi\) | ||||
−0.714724 | + | 0.699407i | \(0.753448\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 48.0000 | + | 27.7128i | 0.290909 | + | 0.167956i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −63.0000 | − | 36.3731i | −0.377246 | − | 0.217803i | 0.299374 | − | 0.954136i | \(-0.403222\pi\) |
−0.676619 | + | 0.736333i | \(0.736556\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 37.0000 | + | 64.0859i | 0.218935 | + | 0.379206i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −28.5000 | + | 49.3634i | −0.166667 | + | 0.288675i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 99.0000 | − | 57.1577i | 0.572254 | − | 0.330391i | −0.185795 | − | 0.982589i | \(-0.559486\pi\) |
0.758049 | + | 0.652197i | \(0.226153\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.5000 | − | 18.1865i | 0.0600000 | − | 0.103923i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −57.0000 | + | 98.7269i | −0.322034 | + | 0.557779i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 83.1384i | 0.464461i | 0.972661 | + | 0.232230i | \(0.0746023\pi\) | ||||
−0.972661 | + | 0.232230i | \(0.925398\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 42.0000 | + | 24.2487i | 0.232044 | + | 0.133971i | 0.611515 | − | 0.791233i | \(-0.290561\pi\) |
−0.379471 | + | 0.925204i | \(0.623894\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 168.009i | 0.918082i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −27.0000 | + | 15.5885i | −0.145946 | + | 0.0842619i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 176.000 | + | 304.841i | 0.941176 | + | 1.63017i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.19615i | 0.0274929i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −70.0000 | −0.366492 | −0.183246 | − | 0.983067i | \(-0.558661\pi\) | ||||
−0.183246 | + | 0.983067i | \(0.558661\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −262.500 | + | 151.554i | −1.36010 | + | 0.785256i | −0.989637 | − | 0.143590i | \(-0.954135\pi\) |
−0.370466 | + | 0.928846i | \(0.620802\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −27.0000 | − | 46.7654i | −0.138462 | − | 0.239822i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.00000 | −0.0101523 | −0.00507614 | − | 0.999987i | \(-0.501616\pi\) | ||||
−0.00507614 | + | 0.999987i | \(0.501616\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 98.5000 | − | 170.607i | 0.494975 | − | 0.857322i | −0.505008 | − | 0.863114i | \(-0.668511\pi\) |
0.999983 | + | 0.00579283i | \(0.00184392\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −45.0000 | −0.223881 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.0000 | + | 8.66025i | 0.0738916 | + | 0.0426613i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −24.0000 | − | 13.8564i | −0.117073 | − | 0.0675922i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −60.0000 | − | 103.923i | −0.289855 | − | 0.502044i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 304.000 | 1.45455 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 316.500 | − | 182.731i | 1.50000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
1.00000 | \(0\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −42.0000 | + | 72.7461i | −0.197183 | + | 0.341531i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 49.0000 | − | 84.8705i | 0.227907 | − | 0.394746i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 50.2295i | 0.231472i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 52.5000 | + | 30.3109i | 0.239726 | + | 0.138406i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 342.946i | − | 1.55179i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −211.500 | + | 122.110i | −0.948430 | + | 0.547577i | −0.892593 | − | 0.450863i | \(-0.851116\pi\) |
−0.0558375 | + | 0.998440i | \(0.517783\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −31.5000 | − | 54.5596i | −0.140000 | − | 0.242487i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 148.956i | 0.656195i | 0.944644 | + | 0.328098i | \(0.106408\pi\) | ||||
−0.944644 | + | 0.328098i | \(0.893592\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 83.0000 | 0.362445 | 0.181223 | − | 0.983442i | \(-0.441995\pi\) | ||||
0.181223 | + | 0.983442i | \(0.441995\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 24.0000 | − | 13.8564i | 0.103896 | − | 0.0599844i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 40.0000 | + | 69.2820i | 0.171674 | + | 0.297348i | 0.939005 | − | 0.343903i | \(-0.111749\pi\) |
−0.767331 | + | 0.641251i | \(0.778416\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 92.0000 | 0.391489 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −76.5000 | + | 132.502i | −0.322785 | + | 0.559080i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −58.0000 | −0.242678 | −0.121339 | − | 0.992611i | \(-0.538719\pi\) | ||||
−0.121339 | + | 0.992611i | \(0.538719\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −244.500 | − | 141.162i | −1.01452 | − | 0.585735i | −0.102010 | − | 0.994783i | \(-0.532527\pi\) |
−0.912513 | + | 0.409048i | \(0.865861\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.5000 | + | 7.79423i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −48.0000 | − | 83.1384i | −0.195918 | − | 0.339341i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −256.500 | − | 148.090i | −1.03846 | − | 0.599556i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −219.000 | + | 126.440i | −0.879518 | + | 0.507790i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −133.000 | + | 230.363i | −0.529880 | + | 0.917780i | 0.469512 | + | 0.882926i | \(0.344430\pi\) |
−0.999392 | + | 0.0348538i | \(0.988903\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −320.000 | + | 554.256i | −1.26482 | + | 2.19074i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 76.2102i | 0.298864i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −162.000 | − | 93.5307i | −0.630350 | − | 0.363933i | 0.150537 | − | 0.988604i | \(-0.451900\pi\) |
−0.780888 | + | 0.624671i | \(0.785233\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.5885i | 0.0601871i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 45.0000 | − | 25.9808i | 0.172414 | − | 0.0995431i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −82.0000 | − | 142.028i | −0.311787 | − | 0.540031i | 0.666962 | − | 0.745092i | \(-0.267594\pi\) |
−0.978749 | + | 0.205060i | \(0.934261\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 96.9948i | − | 0.366018i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 66.0000 | 0.247191 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −447.000 | + | 258.076i | −1.66171 | + | 0.959389i | −0.689811 | + | 0.723989i | \(0.742307\pi\) |
−0.971899 | + | 0.235400i | \(0.924360\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.00000 | + | 12.1244i | 0.0258303 | + | 0.0447393i | 0.878652 | − | 0.477464i | \(-0.158444\pi\) |
−0.852821 | + | 0.522203i | \(0.825110\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −27.0000 | −0.0989011 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −168.000 | + | 290.985i | −0.610909 | + | 1.05813i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 206.000 | 0.743682 | 0.371841 | − | 0.928296i | \(-0.378727\pi\) | ||||
0.371841 | + | 0.928296i | \(0.378727\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 130.500 | + | 75.3442i | 0.467742 | + | 0.270051i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 87.0000 | + | 50.2295i | 0.309609 | + | 0.178753i | 0.646751 | − | 0.762701i | \(-0.276127\pi\) |
−0.337143 | + | 0.941454i | \(0.609461\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 271.000 | + | 469.386i | 0.957597 | + | 1.65861i | 0.728310 | + | 0.685248i | \(0.240306\pi\) |
0.229288 | + | 0.973359i | \(0.426360\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 57.0000 | + | 32.9090i | 0.200000 | + | 0.115470i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.0000 | + | 6.92820i | −0.0418118 | + | 0.0241401i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −97.5000 | + | 168.875i | −0.337370 | + | 0.584342i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −54.0000 | + | 93.5307i | −0.185567 | + | 0.321411i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 481.510i | 1.64338i | 0.569935 | + | 0.821690i | \(0.306968\pi\) | ||||
−0.569935 | + | 0.821690i | \(0.693032\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 114.000 | + | 65.8179i | 0.386441 | + | 0.223112i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 83.1384i | − | 0.279927i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 540.000 | − | 311.769i | 1.80602 | − | 1.04271i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −24.5000 | − | 42.4352i | −0.0813953 | − | 0.140981i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 48.4974i | − | 0.160058i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 194.000 | 0.636066 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 138.000 | − | 79.6743i | 0.449511 | − | 0.259526i | −0.258112 | − | 0.966115i | \(-0.583100\pi\) |
0.707624 | + | 0.706589i | \(0.249767\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 109.500 | + | 189.660i | 0.354369 | + | 0.613785i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −322.000 | −1.03537 | −0.517685 | − | 0.855571i | \(-0.673206\pi\) | ||||
−0.517685 | + | 0.855571i | \(0.673206\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.0000 | + | 22.5167i | −0.0415335 | + | 0.0719382i | −0.886045 | − | 0.463599i | \(-0.846558\pi\) |
0.844511 | + | 0.535538i | \(0.179891\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.00000 | 0.0190476 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −291.000 | − | 168.009i | −0.917981 | − | 0.529997i | −0.0349907 | − | 0.999388i | \(-0.511140\pi\) |
−0.882990 | + | 0.469391i | \(0.844473\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −240.000 | − | 138.564i | −0.752351 | − | 0.434370i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 72.0000 | + | 124.708i | 0.224299 | + | 0.388497i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 209.000 | + | 361.999i | 0.647059 | + | 1.12074i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 283.500 | − | 163.679i | 0.872308 | − | 0.503627i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 66.0000 | − | 114.315i | 0.201835 | − | 0.349588i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 23.0000 | − | 39.8372i | 0.0699088 | − | 0.121086i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 219.970i | 0.664563i | 0.943180 | + | 0.332282i | \(0.107818\pi\) | ||||
−0.943180 | + | 0.332282i | \(0.892182\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 40.5000 | + | 23.3827i | 0.121622 | + | 0.0702183i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 51.9615i | 0.155109i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −505.500 | + | 291.851i | −1.50000 | + | 0.866025i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 159.000 | + | 275.396i | 0.469027 | + | 0.812378i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 803.672i | − | 2.35681i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −97.0000 | −0.282799 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −120.000 | + | 69.2820i | −0.347826 | + | 0.200817i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −235.000 | − | 407.032i | −0.677233 | − | 1.17300i | −0.975811 | − | 0.218617i | \(-0.929845\pi\) |
0.298577 | − | 0.954385i | \(-0.403488\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −295.000 | −0.845272 | −0.422636 | − | 0.906299i | \(-0.638895\pi\) | ||||
−0.422636 | + | 0.906299i | \(0.638895\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −40.5000 | + | 70.1481i | −0.115385 | + | 0.199852i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 262.000 | 0.742210 | 0.371105 | − | 0.928591i | \(-0.378979\pi\) | ||||
0.371105 | + | 0.928591i | \(0.378979\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 84.0000 | + | 48.4974i | 0.236620 | + | 0.136612i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 33.0000 | + | 19.0526i | 0.0924370 | + | 0.0533685i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −232.000 | − | 401.836i | −0.646240 | − | 1.11932i | −0.984014 | − | 0.178093i | \(-0.943007\pi\) |
0.337774 | − | 0.941227i | \(-0.390326\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 361.000 | 1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −202.500 | + | 116.913i | −0.557851 | + | 0.322076i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 35.0000 | − | 60.6218i | 0.0958904 | − | 0.166087i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 116.500 | − | 201.784i | 0.317439 | − | 0.549820i | −0.662514 | − | 0.749049i | \(-0.730511\pi\) |
0.979953 | + | 0.199229i | \(0.0638439\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 41.5692i | 0.112654i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −42.0000 | − | 24.2487i | −0.113208 | − | 0.0653604i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 533.472i | − | 1.43022i | −0.699013 | − | 0.715109i | \(-0.746377\pi\) | ||
0.699013 | − | 0.715109i | \(-0.253623\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −138.000 | + | 79.6743i | −0.368000 | + | 0.212465i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 135.000 | + | 233.827i | 0.358090 | + | 0.620230i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 161.081i | − | 0.425015i | −0.977159 | − | 0.212508i | \(-0.931837\pi\) | ||
0.977159 | − | 0.212508i | \(-0.0681630\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 48.0000 | 0.125984 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 498.000 | − | 287.520i | 1.30026 | − | 0.750706i | 0.319812 | − | 0.947481i | \(-0.396380\pi\) |
0.980449 | + | 0.196775i | \(0.0630468\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.0000 | − | 27.7128i | −0.0415584 | − | 0.0719813i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −147.000 | −0.379845 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 76.0000 | − | 131.636i | 0.195373 | − | 0.338396i | −0.751650 | − | 0.659562i | \(-0.770742\pi\) |
0.947023 | + | 0.321167i | \(0.104075\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −880.000 | −2.25064 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 192.000 | + | 110.851i | 0.488550 | + | 0.282064i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 153.000 | + | 88.3346i | 0.387342 | + | 0.223632i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 249.500 | + | 432.147i | 0.628463 | + | 1.08853i | 0.987860 | + | 0.155346i | \(0.0496492\pi\) |
−0.359397 | + | 0.933185i | \(0.617017\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 28.5000 | − | 16.4545i | 0.0714286 | − | 0.0412393i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 87.0000 | − | 50.2295i | 0.216958 | − | 0.125261i | −0.387583 | − | 0.921835i | \(-0.626690\pi\) |
0.604541 | + | 0.796574i | \(0.293357\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −391.500 | + | 678.098i | −0.971464 | + | 1.68263i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.00000 | − | 15.5885i | 0.0222222 | − | 0.0384900i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 249.415i | − | 0.612814i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 342.000 | + | 197.454i | 0.836186 | + | 0.482772i | 0.855966 | − | 0.517032i | \(-0.172963\pi\) |
−0.0197801 | + | 0.999804i | \(0.506297\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 200.918i | 0.488851i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 57.0000 | − | 32.9090i | 0.138015 | − | 0.0796827i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 146.000 | + | 252.879i | 0.351807 | + | 0.609348i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 303.109i | − | 0.726880i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −628.000 | −1.49881 | −0.749403 | − | 0.662114i | \(-0.769660\pi\) | ||||
−0.749403 | + | 0.662114i | \(0.769660\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 558.000 | − | 322.161i | 1.32542 | − | 0.765229i | 0.340829 | − | 0.940125i | \(-0.389292\pi\) |
0.984587 | + | 0.174896i | \(0.0559590\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −69.0000 | − | 119.512i | −0.163121 | − | 0.282533i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −462.000 | −1.08706 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 48.5000 | − | 84.0045i | 0.113583 | − | 0.196732i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 432.000 | 1.00699 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 393.000 | + | 226.899i | 0.911833 | + | 0.526447i | 0.881020 | − | 0.473078i | \(-0.156857\pi\) |
0.0308125 | + | 0.999525i | \(0.490191\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 433.500 | + | 250.281i | 1.00115 | + | 0.578017i | 0.908590 | − | 0.417690i | \(-0.137160\pi\) |
0.0925650 | + | 0.995707i | \(0.470493\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −30.0000 | − | 51.9615i | −0.0689655 | − | 0.119452i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −380.000 | + | 658.179i | −0.869565 | + | 1.50613i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −292.500 | + | 168.875i | −0.666287 | + | 0.384681i | −0.794668 | − | 0.607044i | \(-0.792355\pi\) |
0.128381 | + | 0.991725i | \(0.459022\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −72.0000 | + | 124.708i | −0.163265 | + | 0.282784i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 365.000 | − | 632.199i | 0.823928 | − | 1.42708i | −0.0788082 | − | 0.996890i | \(-0.525111\pi\) |
0.902736 | − | 0.430195i | \(-0.141555\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 76.2102i | − | 0.171259i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 222.000 | + | 128.172i | 0.496644 | + | 0.286738i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 446.869i | 0.995254i | 0.867391 | + | 0.497627i | \(0.165795\pi\) | ||||
−0.867391 | + | 0.497627i | \(0.834205\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 192.000 | − | 110.851i | 0.425721 | − | 0.245790i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −168.000 | − | 290.985i | −0.370861 | − | 0.642350i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 31.1769i | 0.0685207i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −397.000 | −0.868709 | −0.434354 | − | 0.900742i | \(-0.643023\pi\) | ||||
−0.434354 | + | 0.900742i | \(0.643023\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 99.0000 | − | 57.1577i | 0.215686 | − | 0.124527i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −287.000 | − | 497.099i | −0.622560 | − | 1.07830i | −0.989007 | − | 0.147866i | \(-0.952759\pi\) |
0.366448 | − | 0.930439i | \(-0.380574\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 367.000 | 0.792657 | 0.396328 | − | 0.918109i | \(-0.370284\pi\) | ||||
0.396328 | + | 0.918109i | \(0.370284\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 87.0000 | − | 150.688i | 0.187097 | − | 0.324061i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −424.000 | −0.907923 | −0.453961 | − | 0.891021i | \(-0.649990\pi\) | ||||
−0.453961 | + | 0.891021i | \(0.649990\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.5000 | + | 12.9904i | 0.0479744 | + | 0.0276980i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −289.500 | − | 167.143i | −0.614650 | − | 0.354868i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 392.000 | + | 678.964i | 0.828753 | + | 1.43544i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −199.500 | + | 345.544i | −0.420000 | + | 0.727461i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −126.000 | + | 72.7461i | −0.264151 | + | 0.152508i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −364.000 | + | 630.466i | −0.759916 | + | 1.31621i | 0.182976 | + | 0.983117i | \(0.441427\pi\) |
−0.942893 | + | 0.333097i | \(0.891906\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −121.500 | + | 210.444i | −0.252599 | + | 0.437514i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 69.2820i | 0.143441i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 108.000 | + | 62.3538i | 0.222680 | + | 0.128565i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 270.200i | − | 0.554825i | −0.960751 | − | 0.277413i | \(-0.910523\pi\) | ||
0.960751 | − | 0.277413i | \(-0.0894769\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 349.500 | − | 201.784i | 0.714724 | − | 0.412646i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 380.000 | + | 658.179i | 0.773931 | + | 1.34049i | 0.935393 | + | 0.353609i | \(0.115046\pi\) |
−0.161463 | + | 0.986879i | \(0.551621\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 381.051i | − | 0.772923i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −96.0000 | −0.193939 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 42.0000 | − | 24.2487i | 0.0845070 | − | 0.0487902i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −231.500 | − | 400.970i | −0.463928 | − | 0.803547i | 0.535225 | − | 0.844710i | \(-0.320227\pi\) |
−0.999152 | + | 0.0411632i | \(0.986894\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 126.000 | 0.251497 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 65.0000 | − | 112.583i | 0.129225 | − | 0.223824i | −0.794152 | − | 0.607720i | \(-0.792084\pi\) |
0.923376 | + | 0.383896i | \(0.125418\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −56.0000 | −0.110891 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −111.000 | − | 64.0859i | −0.218935 | − | 0.126402i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −459.000 | − | 265.004i | −0.901768 | − | 0.520636i | −0.0239947 | − | 0.999712i | \(-0.507638\pi\) |
−0.877773 | + | 0.479076i | \(0.840972\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.5000 | − | 30.3109i | −0.0342466 | − | 0.0593168i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 98.7269i | − | 0.192450i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 219.000 | − | 126.440i | 0.425243 | − | 0.245514i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −368.000 | + | 637.395i | −0.711799 | + | 1.23287i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −99.0000 | + | 171.473i | −0.190751 | + | 0.330391i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 602.754i | − | 1.15692i | −0.815712 | − | 0.578458i | \(-0.803655\pi\) | ||
0.815712 | − | 0.578458i | \(-0.196345\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 277.500 | + | 160.215i | 0.530593 | + | 0.306338i | 0.741258 | − | 0.671220i | \(-0.234230\pi\) |
−0.210665 | + | 0.977558i | \(0.567563\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 36.3731i | 0.0692820i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 957.000 | − | 552.524i | 1.81594 | − | 1.04843i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −535.500 | − | 927.513i | −1.01229 | − | 1.75333i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 197.454i | − | 0.371853i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −216.000 | −0.405253 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 144.000 | − | 83.1384i | 0.269159 | − | 0.155399i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −72.0000 | − | 124.708i | −0.134078 | − | 0.232230i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 768.000 | 1.42486 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −182.500 | + | 316.099i | −0.337338 | + | 0.584287i | −0.983931 | − | 0.178548i | \(-0.942860\pi\) |
0.646593 | + | 0.762835i | \(0.276193\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −84.0000 | −0.154696 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −132.000 | − | 76.2102i | −0.242202 | − | 0.139835i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 199.500 | + | 115.181i | 0.364717 | + | 0.210569i | 0.671148 | − | 0.741324i | \(-0.265802\pi\) |
−0.306431 | + | 0.951893i | \(0.599135\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −145.500 | − | 252.013i | −0.265027 | − | 0.459041i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −285.000 | − | 164.545i | −0.517241 | − | 0.298629i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 76.5000 | − | 44.1673i | 0.138336 | − | 0.0798685i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 27.0000 | − | 46.7654i | 0.0486486 | − | 0.0842619i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −320.000 | + | 554.256i | −0.574506 | + | 0.995074i | 0.421589 | + | 0.906787i | \(0.361473\pi\) |
−0.996095 | + | 0.0882870i | \(0.971861\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 763.834i | − | 1.36643i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −528.000 | − | 304.841i | −0.941176 | − | 0.543388i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 96.9948i | − | 0.172282i | −0.996283 | − | 0.0861411i | \(-0.972546\pi\) | ||
0.996283 | − | 0.0861411i | \(-0.0274536\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 318.000 | − | 183.597i | 0.562832 | − | 0.324951i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.50000 | − | 7.79423i | −0.00793651 | − | 0.0137464i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 152.420i | 0.267874i | 0.990990 | + | 0.133937i | \(0.0427620\pi\) | ||||
−0.990990 | + | 0.133937i | \(0.957238\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −335.000 | −0.586690 | −0.293345 | − | 0.956007i | \(-0.594768\pi\) | ||||
−0.293345 | + | 0.956007i | \(0.594768\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 105.000 | − | 60.6218i | 0.183246 | − | 0.105797i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −420.000 | − | 727.461i | −0.730435 | − | 1.26515i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 746.000 | 1.29289 | 0.646447 | − | 0.762959i | \(-0.276254\pi\) | ||||
0.646447 | + | 0.762959i | \(0.276254\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 262.500 | − | 454.663i | 0.453368 | − | 0.785256i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 146.000 | 0.251291 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 672.000 | + | 387.979i | 1.15266 | + | 0.665488i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 81.0000 | + | 46.7654i | 0.138462 | + | 0.0799408i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 89.0000 | + | 154.153i | 0.151618 | + | 0.262611i | 0.931823 | − | 0.362914i | \(-0.118218\pi\) |
−0.780204 | + | 0.625525i | \(0.784885\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 954.360i | − | 1.62031i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.00000 | − | 1.73205i | 0.00507614 | − | 0.00293071i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −137.000 | + | 237.291i | −0.231029 | + | 0.400153i | −0.958111 | − | 0.286397i | \(-0.907542\pi\) |
0.727082 | + | 0.686550i | \(0.240876\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 22.0000 | − | 38.1051i | 0.0369748 | − | 0.0640422i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 341.214i | 0.571548i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 252.000 | + | 145.492i | 0.420701 | + | 0.242892i | 0.695377 | − | 0.718645i | \(-0.255237\pi\) |
−0.274676 | + | 0.961537i | \(0.588571\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 1020.18i | − | 1.69747i | −0.528820 | − | 0.848734i | \(-0.677366\pi\) | ||
0.528820 | − | 0.848734i | \(-0.322634\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 67.5000 | − | 38.9711i | 0.111940 | − | 0.0646288i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 135.000 | + | 233.827i | 0.223140 | + | 0.386491i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 157.617i | − | 0.259665i | −0.991536 | − | 0.129832i | \(-0.958556\pi\) | ||
0.991536 | − | 0.129832i | \(-0.0414440\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −30.0000 | −0.0492611 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 621.000 | − | 358.535i | 1.01637 | − | 0.586800i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 401.000 | + | 694.552i | 0.654160 | + | 1.13304i | 0.982104 | + | 0.188341i | \(0.0603110\pi\) |
−0.327944 | + | 0.944697i | \(0.606356\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 48.0000 | 0.0780488 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 382.000 | − | 661.643i | 0.619125 | − | 1.07236i | −0.370521 | − | 0.928824i | \(-0.620821\pi\) |
0.989646 | − | 0.143531i | \(-0.0458458\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 127.000 | 0.205170 | 0.102585 | − | 0.994724i | \(-0.467289\pi\) | ||||
0.102585 | + | 0.994724i | \(0.467289\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 180.000 | + | 103.923i | 0.289855 | + | 0.167348i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −33.0000 | − | 19.0526i | −0.0529695 | − | 0.0305820i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −170.500 | − | 295.315i | −0.272800 | − | 0.472503i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −456.000 | + | 263.272i | −0.727273 | + | 0.419891i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 297.000 | − | 171.473i | 0.472178 | − | 0.272612i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 161.500 | − | 279.726i | 0.255943 | − | 0.443306i | −0.709208 | − | 0.704999i | \(-0.750947\pi\) |
0.965151 | + | 0.261693i | \(0.0842807\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −316.500 | + | 548.194i | −0.500000 | + | 0.866025i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 55.4256i | − | 0.0872845i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −648.000 | − | 374.123i | −1.01727 | − | 0.587320i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 145.492i | − | 0.227687i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −873.000 | + | 504.027i | −1.36193 | + | 0.786313i | −0.989881 | − | 0.141898i | \(-0.954679\pi\) |
−0.372053 | + | 0.928211i | \(0.621346\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −222.500 | − | 385.381i | −0.346034 | − | 0.599349i | 0.639507 | − | 0.768785i | \(-0.279139\pi\) |
−0.985541 | + | 0.169437i | \(0.945805\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 169.741i | 0.263164i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −106.000 | −0.163833 | −0.0819165 | − | 0.996639i | \(-0.526104\pi\) | ||||
−0.0819165 | + | 0.996639i | \(0.526104\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −912.000 | + | 526.543i | −1.40524 | + | 0.811315i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −43.5000 | − | 75.3442i | −0.0668203 | − | 0.115736i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 328.000 | 0.502297 | 0.251149 | − | 0.967949i | \(-0.419192\pi\) | ||||
0.251149 | + | 0.967949i | \(0.419192\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 128.000 | − | 221.703i | 0.195420 | − | 0.338477i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −105.000 | −0.159817 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −348.000 | − | 200.918i | −0.528073 | − | 0.304883i | 0.212158 | − | 0.977235i | \(-0.431951\pi\) |
−0.740231 | + | 0.672352i | \(0.765284\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 828.000 | + | 478.046i | 1.25265 | + | 0.723216i | 0.971635 | − | 0.236488i | \(-0.0759963\pi\) |
0.281013 | + | 0.959704i | \(0.409330\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 297.000 | + | 514.419i | 0.447964 | + | 0.775896i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −19.0000 | − | 32.9090i | −0.0285714 | − | 0.0494872i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 600.000 | − | 346.410i | 0.899550 | − | 0.519356i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 211.500 | − | 366.329i | 0.316143 | − | 0.547577i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −776.000 | + | 1344.07i | −1.15648 | + | 2.00309i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 521.347i | − | 0.774662i | −0.921941 | − | 0.387331i | \(-0.873397\pi\) | ||
0.921941 | − | 0.387331i | \(-0.126603\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 94.5000 | + | 54.5596i | 0.140000 | + | 0.0808290i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 439.941i | − | 0.649839i | −0.945742 | − | 0.324919i | \(-0.894663\pi\) | ||
0.945742 | − | 0.324919i | \(-0.105337\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 54.0000 | − | 31.1769i | 0.0795287 | − | 0.0459159i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −129.000 | − | 223.435i | −0.189427 | − | 0.328098i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 717.069i | 1.04988i | 0.851139 | + | 0.524941i | \(0.175913\pi\) | ||||
−0.851139 | + | 0.524941i | \(0.824087\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 232.000 | 0.338686 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −124.500 | + | 71.8801i | −0.181223 | + | 0.104629i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −378.000 | − | 654.715i | −0.548621 | − | 0.950240i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −422.000 | −0.610709 | −0.305355 | − | 0.952239i | \(-0.598775\pi\) | ||||
−0.305355 | + | 0.952239i | \(0.598775\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −24.0000 | + | 41.5692i | −0.0346320 | + | 0.0599844i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −350.000 | −0.503597 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 264.000 | + | 152.420i | 0.378766 | + | 0.218681i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −120.000 | − | 69.2820i | −0.171674 | − | 0.0991159i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −185.000 | − | 320.429i | −0.263909 | − | 0.457103i | 0.703368 | − | 0.710825i | \(-0.251678\pi\) |
−0.967277 | + | 0.253722i | \(0.918345\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 296.181i | − | 0.421310i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −138.000 | + | 79.6743i | −0.195745 | + | 0.113013i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.0000 | + | 24.2487i | −0.0198020 | + | 0.0342980i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 45.5000 | − | 78.8083i | 0.0641749 | − | 0.111154i | −0.832153 | − | 0.554546i | \(-0.812892\pi\) |
0.896328 | + | 0.443392i | \(0.146225\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 265.004i | − | 0.372720i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1740.00 | + | 1004.59i | 2.44039 | + | 1.40896i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 498.831i | − | 0.697665i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 87.0000 | − | 50.2295i | 0.121339 | − | 0.0700551i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −502.000 | − | 869.490i | −0.698192 | − | 1.20930i | −0.969093 | − | 0.246697i | \(-0.920655\pi\) |
0.270901 | − | 0.962607i | \(-0.412678\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 126.440i | − | 0.175367i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 489.000 | 0.676349 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 315.000 | − | 181.865i | 0.434483 | − | 0.250849i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −147.500 | − | 255.477i | −0.202889 | − | 0.351413i | 0.746569 | − | 0.665308i | \(-0.231700\pi\) |
−0.949458 | + | 0.313894i | \(0.898366\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −539.000 | + | 933.575i | −0.737346 | + | 1.27712i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −250.000 | −0.341064 | −0.170532 | − | 0.985352i | \(-0.554549\pi\) | ||||
−0.170532 | + | 0.985352i | \(0.554549\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 144.000 | + | 83.1384i | 0.195918 | + | 0.113114i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −360.000 | − | 207.846i | −0.488467 | − | 0.282016i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −285.500 | − | 494.501i | −0.386333 | − | 0.669148i | 0.605620 | − | 0.795754i | \(-0.292925\pi\) |
−0.991953 | + | 0.126606i | \(0.959592\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 513.000 | 0.692308 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.00000 | + | 3.46410i | −0.00807537 | + | 0.00466232i | −0.504032 | − | 0.863685i | \(-0.668151\pi\) |
0.495957 | + | 0.868347i | \(0.334817\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 148.000 | − | 256.344i | 0.198658 | − | 0.344085i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 219.000 | − | 379.319i | 0.293173 | − | 0.507790i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 83.1384i | − | 0.110999i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 841.500 | + | 485.840i | 1.12051 | + | 0.646924i | 0.941530 | − | 0.336929i | \(-0.109388\pi\) |
0.178976 | + | 0.983853i | \(0.442722\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 460.726i | − | 0.611853i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −336.000 | + | 193.990i | −0.445033 | + | 0.256940i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −119.500 | − | 206.980i | −0.157860 | − | 0.273421i | 0.776237 | − | 0.630442i | \(-0.217126\pi\) |
−0.934097 | + | 0.357020i | \(0.883793\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 1108.51i | − | 1.46049i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1402.00 | 1.84231 | 0.921156 | − | 0.389193i | \(-0.127246\pi\) | ||||
0.921156 | + | 0.389193i | \(0.127246\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −66.0000 | + | 38.1051i | −0.0865007 | + | 0.0499412i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −66.0000 | − | 114.315i | −0.0862745 | − | 0.149432i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1026.00 | 1.33768 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 51.5000 | − | 89.2006i | 0.0669701 | − | 0.115996i | −0.830596 | − | 0.556875i | \(-0.812000\pi\) |
0.897566 | + | 0.440880i | \(0.145333\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 324.000 | 0.420233 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −69.0000 | − | 39.8372i | −0.0892626 | − | 0.0515358i | 0.454704 | − | 0.890642i | \(-0.349745\pi\) |
−0.543967 | + | 0.839107i | \(0.683078\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 913.500 | + | 527.409i | 1.17871 | + | 0.680528i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13.5000 | − | 23.3827i | −0.0173745 | − | 0.0300935i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 228.000 | − | 131.636i | 0.292683 | − | 0.168981i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −672.000 | + | 387.979i | −0.860435 | + | 0.496773i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −45.0000 | + | 77.9423i | −0.0574713 | + | 0.0995431i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −193.000 | + | 334.286i | −0.245860 | + | 0.425842i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 188.794i | − | 0.239890i | −0.992781 | − | 0.119945i | \(-0.961728\pi\) | ||
0.992781 | − | 0.119945i | \(-0.0382718\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 246.000 | + | 142.028i | 0.311787 | + | 0.180010i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 183.597i | − | 0.232108i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1309.50 | − | 756.040i | 1.65132 | − | 0.953392i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 84.0000 | + | 145.492i | 0.105660 | + | 0.183009i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 630.466i | − | 0.791050i | −0.918455 | − | 0.395525i | \(-0.870563\pi\) | ||
0.918455 | − | 0.395525i | \(-0.129437\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1012.00 | −1.26658 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −99.0000 | + | 57.1577i | −0.123596 | + | 0.0713579i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 280.000 | + | 484.974i | 0.348692 | + | 0.603953i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 80.0000 | 0.0993789 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 447.000 | − | 774.227i | 0.553903 | − | 0.959389i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1054.00 | 1.30284 | 0.651422 | − | 0.758716i | \(-0.274173\pi\) | ||||
0.651422 | + | 0.758716i | \(0.274173\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −960.000 | − | 554.256i | −1.18372 | − | 0.683423i | −0.226851 | − | 0.973930i | \(-0.572843\pi\) |
−0.956873 | + | 0.290506i | \(0.906176\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.0000 | − | 12.1244i | −0.0258303 | − | 0.0149131i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −233.000 | − | 403.568i | −0.285890 | − | 0.495175i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 465.500 | + | 806.270i | 0.569767 | + | 0.986866i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 40.5000 | − | 23.3827i | 0.0494505 | − | 0.0285503i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 487.000 | − | 843.509i | 0.593179 | − | 1.02742i | −0.400622 | − | 0.916243i | \(-0.631206\pi\) |
0.993801 | − | 0.111173i | \(-0.0354607\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −317.000 | + | 549.060i | −0.385176 | + | 0.667145i | −0.991794 | − | 0.127849i | \(-0.959193\pi\) |
0.606617 | + | 0.794994i | \(0.292526\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 581.969i | − | 0.705417i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1155.00 | − | 666.840i | −1.39661 | − | 0.806336i | −0.402578 | − | 0.915386i | \(-0.631886\pi\) |
−0.994036 | + | 0.109050i | \(0.965219\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 296.181i | 0.357275i | 0.983915 | + | 0.178637i | \(0.0571689\pi\) | ||||
−0.983915 | + | 0.178637i | \(0.942831\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −309.000 | + | 178.401i | −0.371841 | + | 0.214683i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 528.000 | + | 914.523i | 0.633854 | + | 1.09787i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 145.492i | − | 0.174242i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −261.000 | −0.311828 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1395.00 | + | 805.404i | −1.66269 | + | 0.959957i | −0.691273 | + | 0.722594i | \(0.742950\pi\) |
−0.971421 | + | 0.237363i | \(0.923717\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −270.500 | − | 468.520i | −0.321641 | − | 0.557098i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −174.000 | −0.206406 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −74.0000 | + | 128.172i | −0.0875740 | + | 0.151683i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 135.000 | 0.159386 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −813.000 | − | 469.386i | −0.957597 | − | 0.552869i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 540.000 | + | 311.769i | 0.634548 | + | 0.366356i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 219.500 | + | 380.185i | 0.257327 | + | 0.445704i | 0.965525 | − | 0.260310i | \(-0.0838249\pi\) |
−0.708198 | + | 0.706014i | \(0.750492\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −114.000 | −0.133333 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 531.000 | − | 306.573i | 0.619603 | − | 0.357728i | −0.157111 | − | 0.987581i | \(-0.550218\pi\) |
0.776715 | + | 0.629853i | \(0.216885\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 278.500 | − | 482.376i | 0.324214 | − | 0.561555i | −0.657139 | − | 0.753770i | \(-0.728233\pi\) |
0.981353 | + | 0.192214i | \(0.0615668\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.0000 | − | 20.7846i | 0.0139373 | − | 0.0241401i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1340.61i | 1.55343i | 0.629854 | + | 0.776713i | \(0.283115\pi\) | ||||
−0.629854 | + | 0.776713i | \(0.716885\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 198.000 | + | 114.315i | 0.228902 | + | 0.132156i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 337.750i | − | 0.389562i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1224.00 | + | 706.677i | −1.40852 | + | 0.813207i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 202.500 | + | 350.740i | 0.232491 | + | 0.402687i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 187.061i | − | 0.214274i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 92.0000 | 0.105143 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −397.500 | + | 229.497i | −0.453250 | + | 0.261684i | −0.709202 | − | 0.705006i | \(-0.750944\pi\) |
0.255952 | + | 0.966690i | \(0.417611\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −417.000 | − | 722.265i | −0.474403 | − | 0.821690i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 910.000 | 1.03292 | 0.516459 | − | 0.856312i | \(-0.327250\pi\) | ||||
0.516459 | + | 0.856312i | \(0.327250\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.50000 | − | 4.33013i | 0.00283126 | − | 0.00490388i | −0.864606 | − | 0.502450i | \(-0.832432\pi\) |
0.867438 | + | 0.497546i | \(0.165765\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −228.000 | −0.257627 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 927.000 | + | 535.204i | 1.04510 | + | 0.603386i | 0.921272 | − | 0.388918i | \(-0.127151\pi\) |
0.123823 | + | 0.992304i | \(0.460484\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24.0000 | − | 13.8564i | −0.0269966 | − | 0.0155865i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 72.0000 | + | 124.708i | 0.0808081 | + | 0.139964i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −437.000 | + | 756.906i | −0.489362 | + | 0.847599i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −144.000 | + | 83.1384i | −0.160894 | + | 0.0928921i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −540.000 | + | 935.307i | −0.602007 | + | 1.04271i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −435.000 | + | 753.442i | −0.483871 | + | 0.838089i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1066.94i | 1.18418i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 73.5000 | + | 42.4352i | 0.0813953 | + | 0.0469936i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 96.9948i | 0.107177i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −180.000 | + | 103.923i | −0.198456 | + | 0.114579i | −0.595935 | − | 0.803032i | \(-0.703219\pi\) |
0.397479 | + | 0.917611i | \(0.369885\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 42.0000 | + | 72.7461i | 0.0462046 | + | 0.0800288i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 782.887i | 0.859371i | 0.902979 | + | 0.429685i | \(0.141376\pi\) | ||||
−0.902979 | + | 0.429685i | \(0.858624\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2336.00 | −2.55860 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −291.000 | + | 168.009i | −0.318033 | + | 0.183616i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −64.0000 | − | 110.851i | −0.0697928 | − | 0.120885i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1225.00 | 1.33297 | 0.666485 | − | 0.745518i | \(-0.267798\pi\) | ||||
0.666485 | + | 0.745518i | \(0.267798\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −138.000 | + | 239.023i | −0.149837 | + | 0.259526i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 756.000 | 0.819068 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 283.500 | + | 163.679i | 0.306486 | + | 0.176950i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −328.500 | − | 189.660i | −0.354369 | − | 0.204595i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 145.000 | + | 251.147i | 0.156082 | + | 0.270342i | 0.933452 | − | 0.358701i | \(-0.116780\pi\) |
−0.777371 | + | 0.629043i | \(0.783447\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 912.000 | 0.979592 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 483.000 | − | 278.860i | 0.517685 | − | 0.298886i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −352.000 | + | 609.682i | −0.376471 | + | 0.652066i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 276.500 | − | 478.912i | 0.295091 | − | 0.511112i | −0.679915 | − | 0.733291i | \(-0.737983\pi\) |
0.975006 | + | 0.222179i | \(0.0713168\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 45.0333i | − | 0.0479588i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 972.000 | + | 561.184i | 1.03294 | + | 0.596370i | 0.917827 | − | 0.396982i | \(-0.129942\pi\) |
0.115117 | + | 0.993352i | \(0.463276\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 554.256i | 0.587758i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.00000 | + | 5.19615i | −0.00952381 | + | 0.00549857i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −370.000 | − | 640.859i | −0.390707 | − | 0.676725i | 0.601836 | − | 0.798620i | \(-0.294436\pi\) |
−0.992543 | + | 0.121895i | \(0.961103\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 545.596i | − | 0.574917i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 582.000 | 0.611987 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1086.00 | + | 627.002i | −1.13956 | + | 0.657925i | −0.946321 | − | 0.323227i | \(-0.895232\pi\) |
−0.193238 | + | 0.981152i | \(0.561899\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −70.0000 | − | 121.244i | −0.0732984 | − | 0.126957i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 480.000 | 0.501567 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 58.0000 | − | 100.459i | 0.0604797 | − | 0.104754i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1562.00 | −1.62539 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −216.000 | − | 124.708i | −0.224299 | − | 0.129499i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −525.000 | − | 303.109i | −0.544041 | − | 0.314102i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 167.500 | + | 290.119i | 0.173216 | + | 0.300019i | 0.939542 | − | 0.342432i | \(-0.111251\pi\) |
−0.766326 | + | 0.642451i | \(0.777917\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −627.000 | − | 361.999i | −0.647059 | − | 0.373580i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1083.00 | + | 625.270i | −1.11535 | + | 0.643945i | −0.940209 | − | 0.340599i | \(-0.889370\pi\) |
−0.175136 | + | 0.984544i | \(0.556037\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −87.5000 | + | 151.554i | −0.0899281 | + | 0.155760i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −283.500 | + | 491.036i | −0.290769 | + | 0.503627i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1292.11i | 1.32253i | 0.750153 | + | 0.661264i | \(0.229980\pi\) | ||||
−0.750153 | + | 0.661264i | \(0.770020\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 528.000 | + | 304.841i | 0.539326 | + | 0.311380i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 228.631i | 0.233059i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 414.000 | − | 239.023i | 0.421160 | − | 0.243157i | −0.274414 | − | 0.961612i | \(-0.588484\pi\) |
0.695573 | + | 0.718455i | \(0.255150\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.00000 | − | 3.46410i | −0.00203046 | − | 0.00351685i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 79.6743i | 0.0807237i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1960.00 | −1.98180 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −955.500 | + | 551.658i | −0.964178 | + | 0.556668i | −0.897456 | − | 0.441103i | \(-0.854587\pi\) |
−0.0667213 | + | 0.997772i | \(0.521254\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −190.500 | − | 329.956i | −0.191843 | − | 0.332282i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 394.000 | 0.395980 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 270.500 | − | 468.520i | 0.271314 | − | 0.469930i | −0.697885 | − | 0.716210i | \(-0.745875\pi\) |
0.969199 | + | 0.246281i | \(0.0792085\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −81.0000 | −0.0810811 |
(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 | 912.3.be.c.145.1 | 2 | ||
4.3 | odd | 2 | 228.3.l.b.145.1 | ✓ | 2 | ||
12.11 | even | 2 | 684.3.y.a.145.1 | 2 | |||
19.8 | odd | 6 | inner | 912.3.be.c.673.1 | 2 | ||
76.27 | even | 6 | 228.3.l.b.217.1 | yes | 2 | ||
228.179 | odd | 6 | 684.3.y.a.217.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
228.3.l.b.145.1 | ✓ | 2 | 4.3 | odd | 2 | ||
228.3.l.b.217.1 | yes | 2 | 76.27 | even | 6 | ||
684.3.y.a.145.1 | 2 | 12.11 | even | 2 | |||
684.3.y.a.217.1 | 2 | 228.179 | odd | 6 | |||
912.3.be.c.145.1 | 2 | 1.1 | even | 1 | trivial | ||
912.3.be.c.673.1 | 2 | 19.8 | odd | 6 | inner |