Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(169,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.169");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.r (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.02446026187\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 169.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.169 |
Dual form | 504.2.r.a.337.1 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | − | 1.73205i | − | 1.00000i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | 0.955901 | − | 0.293691i | \(-0.0948835\pi\) |
−0.732294 | + | 0.680989i | \(0.761550\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | + | 0.866025i | −0.188982 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000 | − | 5.19615i | 0.904534 | − | 1.56670i | 0.0829925 | − | 0.996550i | \(-0.473552\pi\) |
0.821541 | − | 0.570149i | \(-0.193114\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00000 | − | 5.19615i | −0.832050 | − | 1.44115i | −0.896410 | − | 0.443227i | \(-0.853834\pi\) |
0.0643593 | − | 0.997927i | \(-0.479500\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.50000 | − | 0.866025i | 0.387298 | − | 0.223607i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.00000 | 1.60591 | 0.802955 | − | 0.596040i | \(-0.203260\pi\) | ||||
0.802955 | + | 0.596040i | \(0.203260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.50000 | + | 0.866025i | 0.327327 | + | 0.188982i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.500000 | + | 0.866025i | 0.104257 | + | 0.180579i | 0.913434 | − | 0.406986i | \(-0.133420\pi\) |
−0.809177 | + | 0.587565i | \(0.800087\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | − | 3.46410i | 0.400000 | − | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | + | 1.73205i | −0.185695 | + | 0.321634i | −0.943811 | − | 0.330487i | \(-0.892787\pi\) |
0.758115 | + | 0.652121i | \(0.226120\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.00000 | − | 8.66025i | −0.898027 | − | 1.55543i | −0.830014 | − | 0.557743i | \(-0.811667\pi\) |
−0.0680129 | − | 0.997684i | \(-0.521666\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9.00000 | − | 5.19615i | −1.56670 | − | 0.904534i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00000 | −0.986394 | −0.493197 | − | 0.869918i | \(-0.664172\pi\) | ||||
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.00000 | + | 5.19615i | −1.44115 | + | 0.832050i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.00000 | + | 6.92820i | 0.624695 | + | 1.08200i | 0.988600 | + | 0.150567i | \(0.0481100\pi\) |
−0.363905 | + | 0.931436i | \(0.618557\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.00000 | − | 8.66025i | 0.762493 | − | 1.32068i | −0.179069 | − | 0.983836i | \(-0.557309\pi\) |
0.941562 | − | 0.336840i | \(-0.109358\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.50000 | − | 2.59808i | −0.223607 | − | 0.387298i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.00000 | + | 6.92820i | −0.583460 | + | 1.01058i | 0.411606 | + | 0.911362i | \(0.364968\pi\) |
−0.995066 | + | 0.0992202i | \(0.968365\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.46410i | 0.485071i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.00000 | 0.809040 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 12.1244i | − | 1.60591i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.50000 | + | 6.06218i | −0.448129 | + | 0.776182i | −0.998264 | − | 0.0588933i | \(-0.981243\pi\) |
0.550135 | + | 0.835076i | \(0.314576\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.50000 | − | 2.59808i | 0.188982 | − | 0.327327i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.00000 | − | 5.19615i | 0.372104 | − | 0.644503i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.00000 | + | 10.3923i | 0.733017 | + | 1.26962i | 0.955588 | + | 0.294706i | \(0.0952216\pi\) |
−0.222571 | + | 0.974916i | \(0.571445\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.50000 | − | 0.866025i | 0.180579 | − | 0.104257i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.0000 | 1.78017 | 0.890086 | − | 0.455792i | \(-0.150644\pi\) | ||||
0.890086 | + | 0.455792i | \(0.150644\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.00000 | −0.234082 | −0.117041 | − | 0.993127i | \(-0.537341\pi\) | ||||
−0.117041 | + | 0.993127i | \(0.537341\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.00000 | − | 3.46410i | −0.692820 | − | 0.400000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.00000 | + | 5.19615i | 0.341882 | + | 0.592157i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.500000 | + | 0.866025i | −0.0562544 | + | 0.0974355i | −0.892781 | − | 0.450490i | \(-0.851249\pi\) |
0.836527 | + | 0.547926i | \(0.184582\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.00000 | + | 10.3923i | −0.658586 | + | 1.14070i | 0.322396 | + | 0.946605i | \(0.395512\pi\) |
−0.980982 | + | 0.194099i | \(0.937822\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.00000 | − | 1.73205i | −0.108465 | − | 0.187867i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.00000 | + | 1.73205i | 0.321634 | + | 0.185695i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.00000 | 0.423999 | 0.212000 | − | 0.977270i | \(-0.432002\pi\) | ||||
0.212000 | + | 0.977270i | \(0.432002\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.00000 | 0.628971 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −15.0000 | + | 8.66025i | −1.55543 | + | 0.898027i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.50000 | + | 6.06218i | 0.359092 | + | 0.621966i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.00000 | − | 1.73205i | 0.101535 | − | 0.175863i | −0.810782 | − | 0.585348i | \(-0.800958\pi\) |
0.912317 | + | 0.409484i | \(0.134291\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.00000 | + | 15.5885i | −0.904534 | + | 1.56670i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.50000 | + | 2.59808i | −0.149256 | + | 0.258518i | −0.930953 | − | 0.365140i | \(-0.881021\pi\) |
0.781697 | + | 0.623658i | \(0.214354\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.00000 | − | 5.19615i | −0.295599 | − | 0.511992i | 0.679525 | − | 0.733652i | \(-0.262186\pi\) |
−0.975124 | + | 0.221660i | \(0.928852\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.73205i | 0.169031i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.0000 | 1.16008 | 0.580042 | − | 0.814587i | \(-0.303036\pi\) | ||||
0.580042 | + | 0.814587i | \(0.303036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.3923i | 0.986394i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.50000 | + | 7.79423i | 0.423324 | + | 0.733219i | 0.996262 | − | 0.0863794i | \(-0.0275297\pi\) |
−0.572938 | + | 0.819599i | \(0.694196\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.500000 | + | 0.866025i | −0.0466252 | + | 0.0807573i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.00000 | + | 15.5885i | 0.832050 | + | 1.44115i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.00000 | − | 1.73205i | 0.0916698 | − | 0.158777i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.5000 | − | 21.6506i | −1.13636 | − | 1.96824i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12.0000 | − | 6.92820i | 1.08200 | − | 0.624695i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.00000 | 0.443678 | 0.221839 | − | 0.975083i | \(-0.428794\pi\) | ||||
0.221839 | + | 0.975083i | \(0.428794\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −15.0000 | − | 8.66025i | −1.32068 | − | 0.762493i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.50000 | − | 14.7224i | −0.742648 | − | 1.28630i | −0.951285 | − | 0.308312i | \(-0.900236\pi\) |
0.208637 | − | 0.977993i | \(-0.433097\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.50000 | + | 6.06218i | −0.303488 | + | 0.525657i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.50000 | + | 2.59808i | −0.387298 | + | 0.223607i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.00000 | + | 12.1244i | −0.598050 | + | 1.03585i | 0.395058 | + | 0.918656i | \(0.370724\pi\) |
−0.993109 | + | 0.117198i | \(0.962609\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.50000 | − | 2.59808i | −0.127228 | − | 0.220366i | 0.795373 | − | 0.606120i | \(-0.207275\pi\) |
−0.922602 | + | 0.385754i | \(0.873941\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.0000 | + | 6.92820i | 1.01058 | + | 0.583460i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −36.0000 | −3.01047 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00000 | −0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.50000 | + | 0.866025i | −0.123718 | + | 0.0714286i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.00000 | + | 12.1244i | 0.573462 | + | 0.993266i | 0.996207 | + | 0.0870170i | \(0.0277334\pi\) |
−0.422744 | + | 0.906249i | \(0.638933\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.50000 | − | 4.33013i | 0.203447 | − | 0.352381i | −0.746190 | − | 0.665733i | \(-0.768119\pi\) |
0.949637 | + | 0.313353i | \(0.101452\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.00000 | 0.485071 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.00000 | − | 8.66025i | 0.401610 | − | 0.695608i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.50000 | + | 12.9904i | 0.598565 | + | 1.03675i | 0.993033 | + | 0.117836i | \(0.0375956\pi\) |
−0.394468 | + | 0.918910i | \(0.629071\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 3.46410i | − | 0.274721i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.0000 | 0.783260 | 0.391630 | − | 0.920123i | \(-0.371911\pi\) | ||||
0.391630 | + | 0.920123i | \(0.371911\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 10.3923i | − | 0.809040i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.00000 | − | 10.3923i | −0.464294 | − | 0.804181i | 0.534875 | − | 0.844931i | \(-0.320359\pi\) |
−0.999169 | + | 0.0407502i | \(0.987025\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.5000 | + | 19.9186i | −0.884615 | + | 1.53220i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −21.0000 | −1.60591 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.00000 | + | 12.1244i | −0.532200 | + | 0.921798i | 0.467093 | + | 0.884208i | \(0.345301\pi\) |
−0.999293 | + | 0.0375896i | \(0.988032\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.00000 | + | 3.46410i | 0.151186 | + | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.0000 | −0.747435 | −0.373718 | − | 0.927543i | \(-0.621917\pi\) | ||||
−0.373718 | + | 0.927543i | \(0.621917\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.00000 | 0.371647 | 0.185824 | − | 0.982583i | \(-0.440505\pi\) | ||||
0.185824 | + | 0.982583i | \(0.440505\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.5000 | + | 6.06218i | 0.776182 | + | 0.448129i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.00000 | − | 5.19615i | −0.220564 | − | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.00000 | + | 10.3923i | −0.438763 | + | 0.759961i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.50000 | − | 2.59808i | −0.327327 | − | 0.188982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.50000 | − | 4.33013i | 0.180894 | − | 0.313317i | −0.761291 | − | 0.648410i | \(-0.775434\pi\) |
0.942185 | + | 0.335093i | \(0.108768\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.50000 | − | 7.79423i | −0.323917 | − | 0.561041i | 0.657376 | − | 0.753563i | \(-0.271667\pi\) |
−0.981293 | + | 0.192522i | \(0.938333\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.00000 | − | 5.19615i | −0.644503 | − | 0.372104i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.00000 | 0.141776 | 0.0708881 | − | 0.997484i | \(-0.477417\pi\) | ||||
0.0708881 | + | 0.997484i | \(0.477417\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 18.0000 | − | 10.3923i | 1.26962 | − | 0.733017i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.00000 | − | 1.73205i | −0.0701862 | − | 0.121566i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.00000 | + | 6.92820i | −0.279372 | + | 0.483887i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.50000 | − | 2.59808i | −0.104257 | − | 0.180579i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.0000 | − | 36.3731i | 1.45260 | − | 2.51598i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | + | 3.46410i | 0.137686 | + | 0.238479i | 0.926620 | − | 0.375999i | \(-0.122700\pi\) |
−0.788935 | + | 0.614477i | \(0.789367\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 25.9808i | − | 1.78017i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.0000 | 0.681994 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.0000 | 0.678844 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.46410i | 0.234082i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.00000 | + | 10.3923i | 0.403604 | + | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.00000 | + | 10.3923i | −0.400000 | + | 0.692820i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.500000 | − | 0.866025i | 0.0331862 | − | 0.0574801i | −0.848955 | − | 0.528465i | \(-0.822768\pi\) |
0.882141 | + | 0.470985i | \(0.156101\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.50000 | − | 4.33013i | −0.165205 | − | 0.286143i | 0.771523 | − | 0.636201i | \(-0.219495\pi\) |
−0.936728 | + | 0.350058i | \(0.886162\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.00000 | − | 5.19615i | 0.592157 | − | 0.341882i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.00000 | −0.458585 | −0.229293 | − | 0.973358i | \(-0.573641\pi\) | ||||
−0.229293 | + | 0.973358i | \(0.573641\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.00000 | −0.521862 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.50000 | + | 0.866025i | 0.0974355 | + | 0.0562544i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.50000 | − | 4.33013i | −0.161712 | − | 0.280093i | 0.773771 | − | 0.633465i | \(-0.218368\pi\) |
−0.935483 | + | 0.353373i | \(0.885035\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.00000 | + | 3.46410i | −0.128831 | + | 0.223142i | −0.923224 | − | 0.384262i | \(-0.874456\pi\) |
0.794393 | + | 0.607404i | \(0.207789\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 15.5885i | − | 1.00000i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.500000 | − | 0.866025i | 0.0319438 | − | 0.0553283i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −21.0000 | − | 36.3731i | −1.33620 | − | 2.31436i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 18.0000 | + | 10.3923i | 1.14070 | + | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.0000 | 0.820553 | 0.410276 | − | 0.911961i | \(-0.365432\pi\) | ||||
0.410276 | + | 0.911961i | \(0.365432\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.00000 | 0.377217 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.00000 | + | 1.73205i | −0.187867 | + | 0.108465i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.00000 | − | 15.5885i | −0.561405 | − | 0.972381i | −0.997374 | − | 0.0724199i | \(-0.976928\pi\) |
0.435970 | − | 0.899961i | \(-0.356405\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.00000 | − | 5.19615i | 0.186411 | − | 0.322873i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.00000 | − | 5.19615i | 0.185695 | − | 0.321634i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.50000 | + | 12.9904i | −0.462470 | + | 0.801021i | −0.999083 | − | 0.0428069i | \(-0.986370\pi\) |
0.536614 | + | 0.843828i | \(0.319703\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.00000 | + | 1.73205i | 0.0614295 | + | 0.106399i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 6.92820i | − | 0.423999i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.00000 | −0.182913 | −0.0914566 | − | 0.995809i | \(-0.529152\pi\) | ||||
−0.0914566 | + | 0.995809i | \(0.529152\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | 0.485965 | 0.242983 | − | 0.970031i | \(-0.421874\pi\) | ||||
0.242983 | + | 0.970031i | \(0.421874\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 10.3923i | − | 0.628971i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.0000 | − | 20.7846i | −0.723627 | − | 1.25336i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.00000 | + | 3.46410i | −0.120168 | + | 0.208138i | −0.919834 | − | 0.392308i | \(-0.871677\pi\) |
0.799666 | + | 0.600446i | \(0.205010\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 15.0000 | + | 25.9808i | 0.898027 | + | 1.55543i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.50000 | − | 2.59808i | 0.0894825 | − | 0.154988i | −0.817810 | − | 0.575488i | \(-0.804812\pi\) |
0.907293 | + | 0.420500i | \(0.138145\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.50000 | + | 11.2583i | 0.386385 | + | 0.669238i | 0.991960 | − | 0.126550i | \(-0.0403903\pi\) |
−0.605575 | + | 0.795788i | \(0.707057\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.5000 | − | 6.06218i | 0.621966 | − | 0.359092i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.00000 | −0.472225 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.00000 | − | 1.73205i | −0.175863 | − | 0.101535i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.50000 | + | 7.79423i | 0.262893 | + | 0.455344i | 0.967009 | − | 0.254741i | \(-0.0819901\pi\) |
−0.704117 | + | 0.710084i | \(0.748657\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 27.0000 | + | 15.5885i | 1.56670 | + | 0.904534i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.00000 | − | 5.19615i | 0.173494 | − | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.00000 | + | 8.66025i | 0.288195 | + | 0.499169i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.50000 | + | 2.59808i | 0.258518 | + | 0.149256i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.00000 | −0.400819 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.0000 | −1.31268 | −0.656340 | − | 0.754466i | \(-0.727896\pi\) | ||||
−0.656340 | + | 0.754466i | \(0.727896\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.00000 | + | 5.19615i | −0.511992 | + | 0.295599i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.0000 | − | 20.7846i | −0.680458 | − | 1.17859i | −0.974841 | − | 0.222900i | \(-0.928448\pi\) |
0.294384 | − | 0.955687i | \(-0.404886\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.00000 | + | 1.73205i | −0.0565233 | + | 0.0979013i | −0.892903 | − | 0.450250i | \(-0.851335\pi\) |
0.836379 | + | 0.548151i | \(0.184668\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.00000 | 0.169031 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.00000 | − | 15.5885i | 0.505490 | − | 0.875535i | −0.494489 | − | 0.869184i | \(-0.664645\pi\) |
0.999980 | − | 0.00635137i | \(-0.00202172\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.00000 | + | 10.3923i | 0.335936 | + | 0.581857i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 20.7846i | − | 1.16008i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.0000 | −0.778981 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −24.0000 | −1.33128 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 17.3205i | − | 0.957826i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.00000 | − | 6.92820i | −0.220527 | − | 0.381964i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.00000 | + | 12.1244i | −0.384755 | + | 0.666415i | −0.991735 | − | 0.128302i | \(-0.959047\pi\) |
0.606980 | + | 0.794717i | \(0.292381\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 18.0000 | 0.986394 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.00000 | + | 10.3923i | −0.327815 | + | 0.567792i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.00000 | − | 1.73205i | −0.0544735 | − | 0.0943508i | 0.837503 | − | 0.546433i | \(-0.184015\pi\) |
−0.891976 | + | 0.452082i | \(0.850681\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.5000 | − | 7.79423i | 0.733219 | − | 0.423324i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −60.0000 | −3.24918 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.50000 | + | 0.866025i | 0.0807573 | + | 0.0466252i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.0000 | − | 20.7846i | −0.644194 | − | 1.11578i | −0.984487 | − | 0.175457i | \(-0.943860\pi\) |
0.340293 | − | 0.940319i | \(-0.389474\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.00000 | − | 8.66025i | 0.267644 | − | 0.463573i | −0.700609 | − | 0.713545i | \(-0.747088\pi\) |
0.968253 | + | 0.249973i | \(0.0804216\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 27.0000 | − | 15.5885i | 1.44115 | − | 0.832050i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.00000 | + | 5.19615i | −0.159674 | + | 0.276563i | −0.934751 | − | 0.355303i | \(-0.884378\pi\) |
0.775077 | + | 0.631867i | \(0.217711\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.50000 | + | 12.9904i | 0.398059 | + | 0.689458i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.00000 | − | 1.73205i | −0.158777 | − | 0.0916698i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 33.0000 | 1.74167 | 0.870837 | − | 0.491572i | \(-0.163578\pi\) | ||||
0.870837 | + | 0.491572i | \(0.163578\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 30.0000 | 1.57895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −37.5000 | + | 21.6506i | −1.96824 | + | 1.13636i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.00000 | − | 1.73205i | −0.0523424 | − | 0.0906597i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.0000 | + | 27.7128i | −0.835193 | + | 1.44660i | 0.0586798 | + | 0.998277i | \(0.481311\pi\) |
−0.893873 | + | 0.448320i | \(0.852022\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.0000 | − | 20.7846i | −0.624695 | − | 1.08200i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.00000 | + | 1.73205i | −0.0519174 | + | 0.0899236i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.00000 | − | 1.73205i | −0.0517780 | − | 0.0896822i | 0.838975 | − | 0.544170i | \(-0.183156\pi\) |
−0.890753 | + | 0.454488i | \(0.849822\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 15.5885i | − | 0.804984i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0000 | 0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.00000 | 0.308199 | 0.154100 | − | 0.988055i | \(-0.450752\pi\) | ||||
0.154100 | + | 0.988055i | \(0.450752\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 8.66025i | − | 0.443678i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.00000 | + | 5.19615i | 0.153293 | + | 0.265511i | 0.932436 | − | 0.361335i | \(-0.117679\pi\) |
−0.779143 | + | 0.626846i | \(0.784346\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.00000 | + | 5.19615i | −0.152894 | + | 0.264820i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −15.0000 | + | 25.9808i | −0.762493 | + | 1.32068i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.0000 | − | 17.3205i | 0.507020 | − | 0.878185i | −0.492947 | − | 0.870059i | \(-0.664080\pi\) |
0.999967 | − | 0.00812520i | \(-0.00258636\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.00000 | − | 1.73205i | −0.0505722 | − | 0.0875936i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −25.5000 | + | 14.7224i | −1.28630 | + | 0.742648i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.00000 | −0.0503155 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.0000 | 1.10415 | 0.552074 | − | 0.833795i | \(-0.313837\pi\) | ||||
0.552074 | + | 0.833795i | \(0.313837\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.5000 | + | 6.06218i | 0.525657 | + | 0.303488i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.5000 | + | 18.1865i | 0.524345 | + | 0.908192i | 0.999598 | + | 0.0283431i | \(0.00902310\pi\) |
−0.475253 | + | 0.879849i | \(0.657644\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −30.0000 | + | 51.9615i | −1.49441 | + | 2.58839i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.50000 | + | 7.79423i | 0.223607 | + | 0.387298i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.0000 | + | 31.1769i | −0.892227 | + | 1.54538i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.0000 | + | 12.1244i | 1.03585 | + | 0.598050i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.0000 | −0.589057 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.50000 | + | 2.59808i | −0.220366 | + | 0.127228i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.50000 | + | 6.06218i | 0.170986 | + | 0.296157i | 0.938765 | − | 0.344558i | \(-0.111971\pi\) |
−0.767779 | + | 0.640715i | \(0.778638\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.00000 | + | 8.66025i | −0.243685 | + | 0.422075i | −0.961761 | − | 0.273890i | \(-0.911690\pi\) |
0.718076 | + | 0.695965i | \(0.245023\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12.0000 | − | 20.7846i | 0.583460 | − | 1.01058i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.00000 | + | 6.92820i | −0.194029 | + | 0.336067i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.50000 | − | 6.06218i | −0.169377 | − | 0.293369i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 62.3538i | 3.01047i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 36.0000 | 1.73406 | 0.867029 | − | 0.498257i | \(-0.166026\pi\) | ||||
0.867029 | + | 0.498257i | \(0.166026\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.0000 | −1.24948 | −0.624740 | − | 0.780833i | \(-0.714795\pi\) | ||||
−0.624740 | + | 0.780833i | \(0.714795\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.46410i | 0.166091i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.50000 | + | 6.06218i | 0.167428 | + | 0.289993i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.50000 | + | 2.59808i | 0.0714286 | + | 0.123718i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.0000 | − | 29.4449i | 0.807694 | − | 1.39897i | −0.106763 | − | 0.994285i | \(-0.534048\pi\) |
0.914457 | − | 0.404683i | \(-0.132618\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.00000 | + | 3.46410i | 0.0948091 | + | 0.164214i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 21.0000 | − | 12.1244i | 0.993266 | − | 0.573462i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.00000 | 0.0471929 | 0.0235965 | − | 0.999722i | \(-0.492488\pi\) | ||||
0.0235965 | + | 0.999722i | \(0.492488\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 48.0000 | 2.26023 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.50000 | − | 4.33013i | −0.352381 | − | 0.203447i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.00000 | + | 5.19615i | 0.140642 | + | 0.243599i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.50000 | − | 9.52628i | 0.257279 | − | 0.445621i | −0.708233 | − | 0.705979i | \(-0.750507\pi\) |
0.965512 | + | 0.260358i | \(0.0838407\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 10.3923i | − | 0.485071i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.50000 | − | 2.59808i | 0.0698620 | − | 0.121004i | −0.828978 | − | 0.559281i | \(-0.811077\pi\) |
0.898840 | + | 0.438276i | \(0.144411\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.5000 | − | 19.9186i | −0.534450 | − | 0.925695i | −0.999190 | − | 0.0402476i | \(-0.987185\pi\) |
0.464739 | − | 0.885448i | \(-0.346148\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −15.0000 | − | 8.66025i | −0.695608 | − | 0.401610i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.0000 | 0.555294 | 0.277647 | − | 0.960683i | \(-0.410445\pi\) | ||||
0.277647 | + | 0.960683i | \(0.410445\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.0000 | −0.554109 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.5000 | − | 12.9904i | 1.03675 | − | 0.598565i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −30.0000 | − | 51.9615i | −1.37940 | − | 2.38919i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.0000 | − | 24.2487i | 0.642364 | − | 1.11261i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.00000 | −0.274721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.0000 | + | 29.4449i | −0.776750 | + | 1.34537i | 0.157056 | + | 0.987590i | \(0.449800\pi\) |
−0.933806 | + | 0.357780i | \(0.883534\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.0000 | + | 31.1769i | 0.820729 | + | 1.42154i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.73205i | 0.0788110i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.00000 | 0.0908153 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.00000 | 0.0453143 | 0.0226572 | − | 0.999743i | \(-0.492787\pi\) | ||||
0.0226572 | + | 0.999743i | \(0.492787\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 17.3205i | − | 0.783260i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.00000 | + | 5.19615i | 0.135388 | + | 0.234499i | 0.925746 | − | 0.378147i | \(-0.123439\pi\) |
−0.790358 | + | 0.612646i | \(0.790105\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.00000 | − | 3.46410i | 0.0900755 | − | 0.156015i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −18.0000 | −0.809040 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.50000 | + | 12.9904i | −0.336421 | + | 0.582698i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.00000 | − | 13.8564i | −0.358129 | − | 0.620298i | 0.629519 | − | 0.776985i | \(-0.283252\pi\) |
−0.987648 | + | 0.156687i | \(0.949919\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.0000 | + | 10.3923i | −0.804181 | + | 0.464294i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −32.0000 | −1.42681 | −0.713405 | − | 0.700752i | \(-0.752848\pi\) | ||||
−0.713405 | + | 0.700752i | \(0.752848\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.00000 | −0.133498 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 34.5000 | + | 19.9186i | 1.53220 | + | 0.884615i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.0000 | + | 25.9808i | 0.664863 | + | 1.15158i | 0.979322 | + | 0.202306i | \(0.0648436\pi\) |
−0.314459 | + | 0.949271i | \(0.601823\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.00000 | − | 1.73205i | 0.0442374 | − | 0.0766214i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 36.3731i | 1.60591i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.00000 | − | 5.19615i | 0.132196 | − | 0.228970i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.0000 | + | 41.5692i | 1.05552 | + | 1.82821i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.0000 | + | 12.1244i | 0.921798 | + | 0.532200i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.0000 | −0.525730 | −0.262865 | − | 0.964833i | \(-0.584667\pi\) | ||||
−0.262865 | + | 0.964833i | \(0.584667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.0000 | 1.26808 | 0.634041 | − | 0.773300i | \(-0.281395\pi\) | ||||
0.634041 | + | 0.773300i | \(0.281395\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.00000 | − | 3.46410i | 0.261861 | − | 0.151186i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.0000 | + | 17.3205i | 0.435607 | + | 0.754493i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | − | 19.0526i | 0.478261 | − | 0.828372i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.0000 | − | 41.5692i | 1.03956 | − | 1.80056i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.00000 | + | 10.3923i | 0.259403 | + | 0.449299i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.3205i | 0.747435i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.00000 | −0.258438 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.0000 | −0.601907 | −0.300954 | − | 0.953639i | \(-0.597305\pi\) | ||||
−0.300954 | + | 0.953639i | \(0.597305\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 8.66025i | − | 0.371647i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.00000 | + | 8.66025i | 0.214176 | + | 0.370965i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.00000 | − | 6.92820i | 0.171028 | − | 0.296229i | −0.767752 | − | 0.640747i | \(-0.778625\pi\) |
0.938779 | + | 0.344519i | \(0.111958\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.5000 | − | 18.1865i | 0.448129 | − | 0.776182i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.00000 | + | 12.1244i | −0.298210 | + | 0.516515i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.500000 | − | 0.866025i | −0.0212622 | − | 0.0368271i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.00000 | + | 5.19615i | −0.382029 | + | 0.220564i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −44.0000 | −1.86434 | −0.932170 | − | 0.362021i | \(-0.882087\pi\) | ||||
−0.932170 | + | 0.362021i | \(0.882087\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −60.0000 | −2.53773 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.0000 | + | 10.3923i | 0.759961 | + | 0.438763i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.5000 | + | 19.9186i | 0.484667 | + | 0.839468i | 0.999845 | − | 0.0176152i | \(-0.00560738\pi\) |
−0.515178 | + | 0.857083i | \(0.672274\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.50000 | + | 7.79423i | −0.189316 | + | 0.327906i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.50000 | + | 7.79423i | −0.188982 | + | 0.327327i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.0000 | + | 25.9808i | −0.628833 | + | 1.08917i | 0.358954 | + | 0.933355i | \(0.383134\pi\) |
−0.987786 | + | 0.155815i | \(0.950200\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.0000 | + | 34.6410i | 0.836974 | + | 1.44968i | 0.892413 | + | 0.451219i | \(0.149011\pi\) |
−0.0554391 | + | 0.998462i | \(0.517656\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.50000 | − | 4.33013i | −0.313317 | − | 0.180894i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.00000 | 0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.0000 | 1.49870 | 0.749350 | − | 0.662174i | \(-0.230366\pi\) | ||||
0.749350 | + | 0.662174i | \(0.230366\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.5000 | + | 7.79423i | −0.561041 | + | 0.323917i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.00000 | − | 10.3923i | −0.248922 | − | 0.431145i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.00000 | − | 10.3923i | 0.248495 | − | 0.430405i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.00000 | + | 15.5885i | −0.372104 | + | 0.644503i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.50000 | − | 4.33013i | 0.103186 | − | 0.178723i | −0.809810 | − | 0.586693i | \(-0.800430\pi\) |
0.912996 | + | 0.407969i | \(0.133763\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −35.0000 | − | 60.6218i | −1.44215 | − | 2.49788i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 10.3923i | − | 0.427482i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.0000 | −0.492781 | −0.246390 | − | 0.969171i | \(-0.579245\pi\) | ||||
−0.246390 | + | 0.969171i | \(0.579245\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.00000 | 0.0819920 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 3.46410i | − | 0.141776i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.0000 | + | 27.7128i | 0.653742 | + | 1.13231i | 0.982208 | + | 0.187799i | \(0.0601353\pi\) |
−0.328465 | + | 0.944516i | \(0.606531\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.00000 | − | 12.1244i | 0.285536 | − | 0.494563i | −0.687203 | − | 0.726465i | \(-0.741162\pi\) |
0.972739 | + | 0.231903i | \(0.0744951\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −18.0000 | − | 31.1769i | −0.733017 | − | 1.26962i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.5000 | − | 21.6506i | 0.508197 | − | 0.880223i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.00000 | + | 1.73205i | 0.0405887 | + | 0.0703018i | 0.885606 | − | 0.464437i | \(-0.153743\pi\) |
−0.845017 | + | 0.534739i | \(0.820410\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.00000 | + | 1.73205i | −0.121566 | + | 0.0701862i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 48.0000 | 1.94187 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.0000 | −0.807792 | −0.403896 | − | 0.914805i | \(-0.632344\pi\) | ||||
−0.403896 | + | 0.914805i | \(0.632344\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.0000 | + | 6.92820i | 0.483887 | + | 0.279372i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.0000 | + | 25.9808i | 0.603877 | + | 1.04595i | 0.992228 | + | 0.124434i | \(0.0397116\pi\) |
−0.388351 | + | 0.921512i | \(0.626955\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.5000 | − | 28.5788i | 0.663191 | − | 1.14868i | −0.316581 | − | 0.948565i | \(-0.602535\pi\) |
0.979772 | − | 0.200115i | \(-0.0641316\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.50000 | + | 2.59808i | −0.180579 | + | 0.104257i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.00000 | + | 3.46410i | −0.0801283 | + | 0.138786i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.50000 | − | 9.52628i | −0.220000 | − | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −63.0000 | − | 36.3731i | −2.51598 | − | 1.45260i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.0000 | 0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.00000 | 0.199047 | 0.0995234 | − | 0.995035i | \(-0.468268\pi\) | ||||
0.0995234 | + | 0.995035i | \(0.468268\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.00000 | − | 3.46410i | 0.238479 | − | 0.137686i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.50000 | + | 4.33013i | 0.0992095 | + | 0.171836i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.00000 | + | 5.19615i | −0.118864 | + | 0.205879i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −45.0000 | −1.78017 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.5000 | + | 37.2391i | −0.849199 | + | 1.47086i | 0.0327252 | + | 0.999464i | \(0.489581\pi\) |
−0.881924 | + | 0.471391i | \(0.843752\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.00000 | − | 3.46410i | −0.0788723 | − | 0.136611i | 0.823891 | − | 0.566748i | \(-0.191799\pi\) |
−0.902764 | + | 0.430137i | \(0.858465\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 17.3205i | − | 0.681994i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.0000 | 0.471769 | 0.235884 | − | 0.971781i | \(-0.424201\pi\) | ||||
0.235884 | + | 0.971781i | \(0.424201\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 17.3205i | − | 0.678844i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.0000 | − | 38.1051i | −0.860927 | − | 1.49117i | −0.871036 | − | 0.491220i | \(-0.836551\pi\) |
0.0101092 | − | 0.999949i | \(-0.496782\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.50000 | − | 14.7224i | 0.332122 | − | 0.575253i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.00000 | 0.234082 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.0000 | − | 29.4449i | 0.662226 | − | 1.14701i | −0.317803 | − | 0.948157i | \(-0.602945\pi\) |
0.980029 | − | 0.198852i | \(-0.0637214\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.5000 | + | 21.6506i | 0.486194 | + | 0.842112i | 0.999874 | − | 0.0158695i | \(-0.00505163\pi\) |
−0.513680 | + | 0.857982i | \(0.671718\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 18.0000 | − | 10.3923i | 0.699062 | − | 0.403604i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.00000 | −0.271448 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.00000 | −0.0774403 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.0000 | + | 36.3731i | 0.810696 | + | 1.40417i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.50000 | + | 16.4545i | −0.366198 | + | 0.634274i | −0.988968 | − | 0.148132i | \(-0.952674\pi\) |
0.622770 | + | 0.782405i | \(0.286007\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 18.0000 | + | 10.3923i | 0.692820 | + | 0.400000i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.0000 | − | 36.3731i | 0.807096 | − | 1.39793i | −0.107772 | − | 0.994176i | \(-0.534372\pi\) |
0.914867 | − | 0.403755i | \(-0.132295\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.00000 | + | 1.73205i | 0.0383765 | + | 0.0664700i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.50000 | − | 0.866025i | −0.0574801 | − | 0.0331862i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.0000 | 0.688751 | 0.344375 | − | 0.938832i | \(-0.388091\pi\) | ||||
0.344375 | + | 0.938832i | \(0.388091\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.0000 | −0.534913 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.50000 | + | 4.33013i | −0.286143 | + | 0.165205i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.00000 | − | 10.3923i | −0.228582 | − | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.5000 | + | 35.5070i | −0.779857 | + | 1.35075i | 0.152167 | + | 0.988355i | \(0.451375\pi\) |
−0.932024 | + | 0.362397i | \(0.881959\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.00000 | − | 15.5885i | −0.341882 | − | 0.592157i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.50000 | − | 2.59808i | 0.0568982 | − | 0.0985506i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.00000 | − | 13.8564i | −0.303022 | − | 0.524849i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.1244i | 0.458585i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.0000 | −0.982006 | −0.491003 | − | 0.871158i | \(-0.663370\pi\) | ||||
−0.491003 | + | 0.871158i | \(0.663370\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −42.0000 | −1.58406 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13.8564i | 0.521862i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.50000 | − | 2.59808i | −0.0564133 | − | 0.0977107i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.0000 | − | 38.1051i | 0.826227 | − | 1.43107i | −0.0747503 | − | 0.997202i | \(-0.523816\pi\) |
0.900978 | − | 0.433865i | \(-0.142851\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.50000 | − | 2.59808i | 0.0562544 | − | 0.0974355i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.00000 | − | 8.66025i | 0.187251 | − | 0.324329i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.0000 | − | 31.1769i | −0.673162 | − | 1.16595i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.50000 | + | 4.33013i | −0.280093 | + | 0.161712i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.0000 | −0.447524 | −0.223762 | − | 0.974644i | \(-0.571834\pi\) | ||||
−0.223762 | + | 0.974644i | \(0.571834\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.00000 | 0.223452 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.00000 | + | 3.46410i | 0.223142 | + | 0.128831i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.00000 | + | 6.92820i | 0.148556 | + | 0.257307i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.0000 | − | 24.2487i | 0.519231 | − | 0.899335i | −0.480519 | − | 0.876984i | \(-0.659552\pi\) |
0.999750 | − | 0.0223506i | \(-0.00711500\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.0000 | + | 17.3205i | −0.369863 | + | 0.640622i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.5000 | − | 26.8468i | −0.572506 | − | 0.991609i | −0.996308 | − | 0.0858539i | \(-0.972638\pi\) |
0.423802 | − | 0.905755i | \(-0.360695\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.50000 | − | 0.866025i | −0.0553283 | − | 0.0319438i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 72.0000 | 2.65215 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −38.0000 | −1.39785 | −0.698926 | − | 0.715194i | \(-0.746338\pi\) | ||||
−0.698926 | + | 0.715194i | \(0.746338\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −63.0000 | + | 36.3731i | −2.31436 | + | 1.33620i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.0000 | − | 38.1051i | −0.807102 | − | 1.39794i | −0.914863 | − | 0.403764i | \(-0.867702\pi\) |
0.107761 | − | 0.994177i | \(-0.465632\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.00000 | + | 12.1244i | −0.256460 | + | 0.444202i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 18.0000 | − | 31.1769i | 0.658586 | − | 1.14070i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.00000 | + | 10.3923i | −0.219235 | + | 0.379727i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.50000 | − | 4.33013i | −0.0912263 | − | 0.158009i | 0.816801 | − | 0.576919i | \(-0.195745\pi\) |
−0.908027 | + | 0.418911i | \(0.862412\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 22.5167i | − | 0.820553i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.00000 | 0.181969 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.0000 | 1.23575 | 0.617876 | − | 0.786276i | \(-0.287994\pi\) | ||||
0.617876 | + | 0.786276i | \(0.287994\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 10.3923i | − | 0.377217i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.00000 | − | 5.19615i | −0.108750 | − | 0.188360i | 0.806514 | − | 0.591215i | \(-0.201351\pi\) |
−0.915264 | + | 0.402854i | \(0.868018\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.00000 | + | 8.66025i | −0.181012 | + | 0.313522i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.00000 | + | 5.19615i | 0.108465 | + | 0.187867i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.00000 | − | 8.66025i | −0.180305 | − | 0.312297i | 0.761680 | − | 0.647954i | \(-0.224375\pi\) |
−0.941984 | + | 0.335657i | \(0.891042\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −27.0000 | + | 15.5885i | −0.972381 | + | 0.561405i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.0000 | 1.11499 | 0.557496 | − | 0.830179i | \(-0.311762\pi\) | ||||
0.557496 | + | 0.830179i | \(0.311762\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −40.0000 | −1.43684 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.00000 | − | 5.19615i | −0.322873 | − | 0.186411i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 28.0000 | + | 48.4974i | 1.00320 | + | 1.73760i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 45.0000 | − | 77.9423i | 1.61023 | − | 2.78899i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.00000 | − | 5.19615i | −0.321634 | − | 0.185695i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.50000 | + | 12.9904i | −0.267686 | + | 0.463647i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.0000 | + | 17.3205i | 0.356462 | + | 0.617409i | 0.987367 | − | 0.158450i | \(-0.0506498\pi\) |
−0.630905 | + | 0.775860i | \(0.717316\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.5000 | + | 12.9904i | 0.801021 | + | 0.462470i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.00000 | −0.320003 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 42.0000 | 1.49146 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.00000 | − | 1.73205i | 0.106399 | − | 0.0614295i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.50000 | − | 7.79423i | −0.159398 | − | 0.276086i | 0.775254 | − | 0.631650i | \(-0.217622\pi\) |
−0.934652 | + | 0.355564i | \(0.884289\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.00000 | − | 13.8564i | 0.283020 | − | 0.490204i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.0000 | −0.423999 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.00000 | + | 10.3923i | −0.211735 | + | 0.366736i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.500000 | − | 0.866025i | −0.0176227 | − | 0.0305234i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.19615i | 0.182913i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.00000 | −0.210949 | −0.105474 | − | 0.994422i | \(-0.533636\pi\) | ||||
−0.105474 | + | 0.994422i | \(0.533636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 13.8564i | − | 0.485965i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.00000 | + | 8.66025i | 0.175142 | + | 0.303355i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 35.0000 | − | 60.6218i | 1.22449 | − | 2.12089i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −18.0000 | −0.628971 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.00000 | + | 13.8564i | 0.278862 | + | 0.483004i | 0.971102 | − | 0.238664i | \(-0.0767093\pi\) |
−0.692240 | + | 0.721668i | \(0.743376\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −36.0000 | + | 20.7846i | −1.25336 | + | 0.723627i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 50.0000 | 1.73657 | 0.868286 | − | 0.496064i | \(-0.165222\pi\) | ||||
0.868286 | + | 0.496064i | \(0.165222\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.00000 | + | 3.46410i | 0.208138 | + | 0.120168i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.00000 | + | 1.73205i | 0.0346479 | + | 0.0600120i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.00000 | − | 10.3923i | 0.207639 | − | 0.359641i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 45.0000 | − | 25.9808i | 1.55543 | − | 0.898027i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.00000 | − | 10.3923i | 0.207143 | − | 0.358782i | −0.743670 | − | 0.668546i | \(-0.766917\pi\) |
0.950813 | + | 0.309764i | \(0.100250\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.5000 | + | 21.6506i | 0.431034 | + | 0.746574i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.50000 | − | 2.59808i | −0.154988 | − | 0.0894825i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −23.0000 | −0.791224 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.0000 | 0.859010 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19.5000 | − | 11.2583i | 0.669238 | − | 0.386385i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.00000 | − | 5.19615i | −0.102839 | − | 0.178122i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.5000 | − | 19.9186i | 0.393753 | − | 0.681999i | −0.599189 | − | 0.800608i | \(-0.704510\pi\) |
0.992941 | + | 0.118609i | \(0.0378434\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.5000 | − | 18.1865i | −0.359092 | − | 0.621966i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.00000 | − | 5.19615i | 0.102478 | − | 0.177497i | −0.810227 | − | 0.586116i | \(-0.800656\pi\) |
0.912705 | + | 0.408619i | \(0.133990\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.0000 | + | 17.3205i | 0.341196 | + | 0.590968i | 0.984655 | − | 0.174512i | \(-0.0558348\pi\) |
−0.643459 | + | 0.765480i | \(0.722501\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.8564i | 0.472225i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −43.0000 | −1.46374 | −0.731869 | − | 0.681446i | \(-0.761351\pi\) | ||||
−0.731869 | + | 0.681446i | \(0.761351\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.0000 | −0.476014 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 22.5167i | 0.764706i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.00000 | + | 5.19615i | 0.101768 | + | 0.176267i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 36.0000 | − | 62.3538i | 1.21981 | − | 2.11278i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.00000 | + | 5.19615i | −0.101535 | + | 0.175863i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.50000 | + | 7.79423i | −0.152128 | + | 0.263493i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.00000 | − | 12.1244i | −0.236373 | − | 0.409410i | 0.723298 | − | 0.690536i | \(-0.242625\pi\) |
−0.959671 | + | 0.281126i | \(0.909292\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.5000 | − | 7.79423i | 0.455344 | − | 0.262893i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.0000 | 1.34763 | 0.673817 | − | 0.738898i | \(-0.264654\pi\) | ||||
0.673817 | + | 0.738898i | \(0.264654\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.0000 | −0.874970 | −0.437485 | − | 0.899226i | \(-0.644131\pi\) | ||||
−0.437485 | + | 0.899226i | \(0.644131\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.50000 | + | 4.33013i | −0.0838473 | + | 0.145228i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 27.0000 | − | 46.7654i | 0.904534 | − | 1.56670i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −28.0000 | + | 48.4974i | −0.936984 | + | 1.62290i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.00000 | − | 8.66025i | −0.167132 | − | 0.289480i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.00000 | − | 5.19615i | −0.300501 | − | 0.173494i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 20.0000 | 0.667037 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.00000 | −0.133259 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15.0000 | − | 8.66025i | 0.499169 | − | 0.288195i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.50000 | + | 4.33013i | 0.0831028 | + | 0.143938i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.0000 | − | 24.2487i | 0.464862 | − | 0.805165i | −0.534333 | − | 0.845274i | \(-0.679437\pi\) |
0.999195 | + | 0.0401089i | \(0.0127705\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.50000 | − | 7.79423i | 0.149256 | − | 0.258518i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.50000 | + | 16.4545i | −0.314749 | + | 0.545161i | −0.979384 | − | 0.202007i | \(-0.935254\pi\) |
0.664635 | + | 0.747168i | \(0.268587\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 36.0000 | + | 62.3538i | 1.19143 | + | 2.06361i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.1244i | 0.400819i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.0000 | 0.561389 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.0000 | −0.560778 | −0.280389 | − | 0.959886i | \(-0.590464\pi\) | ||||
−0.280389 | + | 0.959886i | \(0.590464\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 39.8372i | 1.31268i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −45.0000 | − | 77.9423i | −1.48119 | − | 2.56550i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.0000 | + | 20.7846i | −0.394558 | + | 0.683394i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.00000 | + | 15.5885i | 0.295599 | + | 0.511992i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.00000 | + | 3.46410i | −0.0656179 | + | 0.113653i | −0.896968 | − | 0.442096i | \(-0.854235\pi\) |
0.831350 | + | 0.555749i | \(0.187569\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.50000 | − | 6.06218i | −0.114708 | − | 0.198680i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −36.0000 | + | 20.7846i | −1.17859 | + | 0.680458i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.0000 | −0.392442 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42.0000 | −1.37208 | −0.686040 | − | 0.727564i | \(-0.740653\pi\) | ||||
−0.686040 | + | 0.727564i | \(0.740653\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.00000 | + | 1.73205i | 0.0979013 | + | 0.0565233i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.5000 | + | 28.5788i | 0.537885 | + | 0.931644i | 0.999018 | + | 0.0443125i | \(0.0141097\pi\) |
−0.461133 | + | 0.887331i | \(0.652557\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.00000 | + | 6.92820i | −0.130258 | + | 0.225613i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 5.19615i | − | 0.169031i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.0000 | + | 24.2487i | −0.454939 | + | 0.787977i | −0.998685 | − | 0.0512727i | \(-0.983672\pi\) |
0.543746 | + | 0.839250i | \(0.317006\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.00000 | + | 10.3923i | 0.194768 | + | 0.337348i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −27.0000 | − | 15.5885i | −0.875535 | − | 0.505490i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.0000 | −0.453504 | −0.226752 | − | 0.973952i | \(-0.572811\pi\) | ||||
−0.226752 | + | 0.973952i | \(0.572811\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.00000 | 0.161796 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 18.0000 | − | 10.3923i | 0.581857 | − | 0.335936i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.00000 | − | 12.1244i | −0.226042 | − | 0.391516i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −34.5000 | + | 59.7558i | −1.11290 | + | 1.92760i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −36.0000 | −1.16008 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.50000 | − | 7.79423i | 0.144860 | − | 0.250905i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.50000 | + | 2.59808i | 0.0482367 | + | 0.0835485i | 0.889136 | − | 0.457644i | \(-0.151306\pi\) |
−0.840899 | + | 0.541192i | \(0.817973\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 24.2487i | 0.778981i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 55.0000 | 1.76503 | 0.882517 | − | 0.470281i | \(-0.155847\pi\) | ||||
0.882517 | + | 0.470281i | \(0.155847\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.00000 | 0.0961756 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 41.5692i | 1.33128i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.00000 | − | 5.19615i | −0.0959785 | − | 0.166240i | 0.814038 | − | 0.580812i | \(-0.197265\pi\) |
−0.910017 | + | 0.414572i | \(0.863931\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.0000 | − | 20.7846i | 0.383522 | − | 0.664279i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −30.0000 | −0.957826 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.00000 | + | 15.5885i | −0.287055 | + | 0.497195i | −0.973106 | − | 0.230360i | \(-0.926010\pi\) |
0.686050 | + | 0.727554i | \(0.259343\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.00000 | + | 5.19615i | 0.0955879 | + | 0.165563i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.0000 | + | 6.92820i | −0.381964 | + | 0.220527i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.0000 | 0.317982 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48.0000 | −1.52477 | −0.762385 | − | 0.647124i | \(-0.775972\pi\) | ||||
−0.762385 | + | 0.647124i | \(0.775972\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 21.0000 | + | 12.1244i | 0.666415 | + | 0.384755i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.00000 | + | 1.73205i | 0.0317021 | + | 0.0549097i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.50000 | + | 16.4545i | −0.300868 | + | 0.521119i | −0.976333 | − | 0.216274i | \(-0.930610\pi\) |
0.675465 | + | 0.737392i | \(0.263943\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 31.1769i | − | 0.986394i |
(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 | 504.2.r.a.169.1 | ✓ | 2 | |
3.2 | odd | 2 | 1512.2.r.a.505.1 | 2 | |||
4.3 | odd | 2 | 1008.2.r.c.673.1 | 2 | |||
9.2 | odd | 6 | 4536.2.a.g.1.1 | 1 | |||
9.4 | even | 3 | inner | 504.2.r.a.337.1 | yes | 2 | |
9.5 | odd | 6 | 1512.2.r.a.1009.1 | 2 | |||
9.7 | even | 3 | 4536.2.a.d.1.1 | 1 | |||
12.11 | even | 2 | 3024.2.r.b.2017.1 | 2 | |||
36.7 | odd | 6 | 9072.2.a.i.1.1 | 1 | |||
36.11 | even | 6 | 9072.2.a.n.1.1 | 1 | |||
36.23 | even | 6 | 3024.2.r.b.1009.1 | 2 | |||
36.31 | odd | 6 | 1008.2.r.c.337.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.r.a.169.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
504.2.r.a.337.1 | yes | 2 | 9.4 | even | 3 | inner | |
1008.2.r.c.337.1 | 2 | 36.31 | odd | 6 | |||
1008.2.r.c.673.1 | 2 | 4.3 | odd | 2 | |||
1512.2.r.a.505.1 | 2 | 3.2 | odd | 2 | |||
1512.2.r.a.1009.1 | 2 | 9.5 | odd | 6 | |||
3024.2.r.b.1009.1 | 2 | 36.23 | even | 6 | |||
3024.2.r.b.2017.1 | 2 | 12.11 | even | 2 | |||
4536.2.a.d.1.1 | 1 | 9.7 | even | 3 | |||
4536.2.a.g.1.1 | 1 | 9.2 | odd | 6 | |||
9072.2.a.i.1.1 | 1 | 36.7 | odd | 6 | |||
9072.2.a.n.1.1 | 1 | 36.11 | even | 6 |