Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(337,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.r (of order \(3\), 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: | \(8.04892052375\) |
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: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 337.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.337 |
Dual form | 1008.2.r.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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | −0.732294 | − | 0.680989i | \(-0.761550\pi\) |
0.955901 | + | 0.293691i | \(0.0948835\pi\) | |||||||
\(6\) | 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 | −0.821541 | − | 0.570149i | \(-0.806886\pi\) |
−0.0829925 | − | 0.996550i | \(-0.526448\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00000 | + | 5.19615i | −0.832050 | + | 1.44115i | 0.0643593 | + | 0.997927i | \(0.479500\pi\) |
−0.896410 | + | 0.443227i | \(0.853834\pi\) | |||||||
\(14\) | 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 | \(-0.796740\pi\) | ||||
−0.802955 | + | 0.596040i | \(0.796740\pi\) | |||||||
\(20\) | 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 | \(-0.866580\pi\) |
0.809177 | + | 0.587565i | \(0.199913\pi\) | |||||||
\(24\) | 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 | 0.758115 | − | 0.652121i | \(-0.226120\pi\) |
−0.943811 | + | 0.330487i | \(0.892787\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.00000 | − | 8.66025i | 0.898027 | − | 1.55543i | 0.0680129 | − | 0.997684i | \(-0.478334\pi\) |
0.830014 | − | 0.557743i | \(-0.188333\pi\) | |||||||
\(32\) | 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 | −0.363905 | − | 0.931436i | \(-0.618557\pi\) |
0.988600 | − | 0.150567i | \(-0.0481100\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.00000 | − | 8.66025i | −0.762493 | − | 1.32068i | −0.941562 | − | 0.336840i | \(-0.890642\pi\) |
0.179069 | − | 0.983836i | \(-0.442691\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.50000 | + | 2.59808i | −0.223607 | + | 0.387298i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.00000 | + | 6.92820i | 0.583460 | + | 1.01058i | 0.995066 | + | 0.0992202i | \(0.0316348\pi\) |
−0.411606 | + | 0.911362i | \(0.635032\pi\) | |||||||
\(48\) | 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 | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.50000 | − | 6.06218i | −0.448129 | − | 0.776182i | 0.550135 | − | 0.835076i | \(-0.314576\pi\) |
−0.998264 | + | 0.0588933i | \(0.981243\pi\) | |||||||
\(62\) | 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 | 0.222571 | + | 0.974916i | \(0.428555\pi\) |
−0.955588 | + | 0.294706i | \(0.904778\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.50000 | + | 0.866025i | 0.180579 | + | 0.104257i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.0000 | −1.78017 | −0.890086 | − | 0.455792i | \(-0.849356\pi\) | ||||
−0.890086 | + | 0.455792i | \(0.849356\pi\) | |||||||
\(72\) | 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 | \(-0.148751\pi\) |
−0.836527 | + | 0.547926i | \(0.815418\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.00000 | + | 10.3923i | 0.658586 | + | 1.14070i | 0.980982 | + | 0.194099i | \(0.0621783\pi\) |
−0.322396 | + | 0.946605i | \(0.604488\pi\) | |||||||
\(84\) | 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 | 0.912317 | − | 0.409484i | \(-0.134291\pi\) |
−0.810782 | + | 0.585348i | \(0.800958\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.00000 | + | 15.5885i | 0.904534 | + | 1.56670i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.50000 | − | 2.59808i | −0.149256 | − | 0.258518i | 0.781697 | − | 0.623658i | \(-0.214354\pi\) |
−0.930953 | + | 0.365140i | \(0.881021\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.00000 | − | 5.19615i | 0.295599 | − | 0.511992i | −0.679525 | − | 0.733652i | \(-0.737814\pi\) |
0.975124 | + | 0.221660i | \(0.0711475\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 1.73205i | − | 0.169031i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.0000 | −1.16008 | −0.580042 | − | 0.814587i | \(-0.696964\pi\) | ||||
−0.580042 | + | 0.814587i | \(0.696964\pi\) | |||||||
\(108\) | 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 | −0.572938 | − | 0.819599i | \(-0.694196\pi\) |
0.996262 | + | 0.0863794i | \(0.0275297\pi\) | |||||||
\(114\) | 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 | \(-0.571206\pi\) | ||||
−0.221839 | + | 0.975083i | \(0.571206\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −15.0000 | + | 8.66025i | −1.32068 | + | 0.762493i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.50000 | − | 14.7224i | 0.742648 | − | 1.28630i | −0.208637 | − | 0.977993i | \(-0.566903\pi\) |
0.951285 | − | 0.308312i | \(-0.0997640\pi\) | |||||||
\(132\) | 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 | −0.993109 | − | 0.117198i | \(-0.962609\pi\) |
0.395058 | − | 0.918656i | \(-0.370724\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.50000 | − | 2.59808i | 0.127228 | − | 0.220366i | −0.795373 | − | 0.606120i | \(-0.792725\pi\) |
0.922602 | + | 0.385754i | \(0.126059\pi\) | |||||||
\(140\) | 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 | −0.422744 | − | 0.906249i | \(-0.638933\pi\) |
0.996207 | − | 0.0870170i | \(-0.0277334\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.50000 | − | 4.33013i | −0.203447 | − | 0.352381i | 0.746190 | − | 0.665733i | \(-0.231881\pi\) |
−0.949637 | + | 0.313353i | \(0.898548\pi\) | |||||||
\(152\) | 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 | −0.394468 | − | 0.918910i | \(-0.629071\pi\) |
0.993033 | − | 0.117836i | \(-0.0375956\pi\) | |||||||
\(158\) | 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 | \(-0.628089\pi\) | ||||
−0.391630 | + | 0.920123i | \(0.628089\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.3923i | 0.809040i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.00000 | − | 10.3923i | 0.464294 | − | 0.804181i | −0.534875 | − | 0.844931i | \(-0.679641\pi\) |
0.999169 | + | 0.0407502i | \(0.0129748\pi\) | |||||||
\(168\) | 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 | −0.999293 | − | 0.0375896i | \(-0.988032\pi\) |
0.467093 | − | 0.884208i | \(-0.345301\pi\) | |||||||
\(174\) | 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 | \(-0.378083\pi\) | ||||
0.373718 | + | 0.927543i | \(0.378083\pi\) | |||||||
\(180\) | 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 | \(-0.224566\pi\) |
−0.942185 | + | 0.335093i | \(0.891232\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.50000 | + | 7.79423i | −0.323917 | + | 0.561041i | −0.981293 | − | 0.192522i | \(-0.938333\pi\) |
0.657376 | + | 0.753563i | \(0.271667\pi\) | |||||||
\(194\) | 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 | \(-0.522583\pi\) | ||||
−0.0708881 | + | 0.997484i | \(0.522583\pi\) | |||||||
\(200\) | 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 | \(-0.877300\pi\) |
0.788935 | + | 0.614477i | \(0.210633\pi\) | |||||||
\(212\) | 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 | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(224\) | 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 | \(-0.177232\pi\) |
−0.882141 | + | 0.470985i | \(0.843899\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.50000 | + | 4.33013i | −0.165205 | + | 0.286143i | −0.936728 | − | 0.350058i | \(-0.886162\pi\) |
0.771523 | + | 0.636201i | \(0.219495\pi\) | |||||||
\(230\) | 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 | \(-0.781632\pi\) |
0.935483 | + | 0.353373i | \(0.114965\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.00000 | − | 3.46410i | −0.128831 | − | 0.223142i | 0.794393 | − | 0.607404i | \(-0.207789\pi\) |
−0.923224 | + | 0.384262i | \(0.874456\pi\) | |||||||
\(242\) | 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 | \(-0.634568\pi\) | ||||
−0.410276 | + | 0.911961i | \(0.634568\pi\) | |||||||
\(252\) | 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 | 0.435970 | + | 0.899961i | \(0.356405\pi\) |
−0.997374 | + | 0.0724199i | \(0.976928\pi\) | |||||||
\(258\) | 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 | \(-0.0136300\pi\) |
−0.536614 | + | 0.843828i | \(0.680297\pi\) | |||||||
\(264\) | 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 | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | 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 | 0.799666 | − | 0.600446i | \(-0.205010\pi\) |
−0.919834 | + | 0.392308i | \(0.871677\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −15.0000 | + | 25.9808i | −0.898027 | + | 1.55543i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.50000 | + | 2.59808i | 0.0894825 | + | 0.154988i | 0.907293 | − | 0.420500i | \(-0.138145\pi\) |
−0.817810 | + | 0.575488i | \(0.804812\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.50000 | + | 11.2583i | −0.386385 | + | 0.669238i | −0.991960 | − | 0.126550i | \(-0.959610\pi\) |
0.605575 | + | 0.795788i | \(0.292943\pi\) | |||||||
\(284\) | 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 | −0.704117 | − | 0.710084i | \(-0.748657\pi\) |
0.967009 | + | 0.254741i | \(0.0819901\pi\) | |||||||
\(294\) | 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 | \(-0.272104\pi\) | ||||
0.656340 | + | 0.754466i | \(0.272104\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.00000 | − | 5.19615i | −0.511992 | − | 0.295599i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | − | 20.7846i | 0.680458 | − | 1.17859i | −0.294384 | − | 0.955687i | \(-0.595114\pi\) |
0.974841 | − | 0.222900i | \(-0.0715523\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.00000 | − | 1.73205i | −0.0565233 | − | 0.0979013i | 0.836379 | − | 0.548151i | \(-0.184668\pi\) |
−0.892903 | + | 0.450250i | \(0.851335\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.00000 | −0.169031 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.00000 | + | 15.5885i | 0.505490 | + | 0.875535i | 0.999980 | + | 0.00635137i | \(0.00202172\pi\) |
−0.494489 | + | 0.869184i | \(0.664645\pi\) | |||||||
\(318\) | 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 | \(-0.0409527\pi\) |
−0.606980 | + | 0.794717i | \(0.707619\pi\) | |||||||
\(332\) | 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 | −0.891976 | − | 0.452082i | \(-0.850681\pi\) |
0.837503 | + | 0.546433i | \(0.184015\pi\) | |||||||
\(338\) | 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 | −0.340293 | − | 0.940319i | \(-0.610526\pi\) |
0.984487 | − | 0.175457i | \(-0.0561403\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.00000 | + | 8.66025i | 0.267644 | + | 0.463573i | 0.968253 | − | 0.249973i | \(-0.0804216\pi\) |
−0.700609 | + | 0.713545i | \(0.747088\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −27.0000 | − | 15.5885i | −1.44115 | − | 0.832050i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.00000 | − | 5.19615i | −0.159674 | − | 0.276563i | 0.775077 | − | 0.631867i | \(-0.217711\pi\) |
−0.934751 | + | 0.355303i | \(0.884378\pi\) | |||||||
\(354\) | 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 | \(-0.836422\pi\) | ||||
−0.870837 | + | 0.491572i | \(0.836422\pi\) | |||||||
\(360\) | 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 | 0.893873 | + | 0.448320i | \(0.147978\pi\) |
−0.0586798 | + | 0.998277i | \(0.518689\pi\) | |||||||
\(368\) | 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 | −0.890753 | − | 0.454488i | \(-0.849822\pi\) |
0.838975 | + | 0.544170i | \(0.183156\pi\) | |||||||
\(374\) | 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 | \(-0.549248\pi\) | ||||
−0.154100 | + | 0.988055i | \(0.549248\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.66025i | 0.443678i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.00000 | + | 5.19615i | −0.153293 | + | 0.265511i | −0.932436 | − | 0.361335i | \(-0.882321\pi\) |
0.779143 | + | 0.626846i | \(0.215654\pi\) | |||||||
\(384\) | 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 | 0.999967 | + | 0.00812520i | \(0.00258636\pi\) |
−0.492947 | + | 0.870059i | \(0.664080\pi\) | |||||||
\(390\) | 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 | −0.475253 | − | 0.879849i | \(-0.657644\pi\) |
0.999598 | − | 0.0283431i | \(-0.00902310\pi\) | |||||||
\(402\) | 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 | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(410\) | 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 | \(-0.888029\pi\) |
0.767779 | + | 0.640715i | \(0.221362\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.00000 | − | 8.66025i | −0.243685 | − | 0.422075i | 0.718076 | − | 0.695965i | \(-0.245023\pi\) |
−0.961761 | + | 0.273890i | \(0.911690\pi\) | |||||||
\(422\) | 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 | \(-0.833974\pi\) | ||||
−0.867029 | + | 0.498257i | \(0.833974\pi\) | |||||||
\(432\) | 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 | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.50000 | − | 2.59808i | 0.0714286 | − | 0.123718i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.0000 | − | 29.4449i | −0.807694 | − | 1.39897i | −0.914457 | − | 0.404683i | \(-0.867382\pi\) |
0.106763 | − | 0.994285i | \(-0.465952\pi\) | |||||||
\(444\) | 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 | 0.965512 | − | 0.260358i | \(-0.0838407\pi\) |
−0.708233 | + | 0.705979i | \(0.750507\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 10.3923i | − | 0.485071i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.50000 | + | 2.59808i | 0.0698620 | + | 0.121004i | 0.898840 | − | 0.438276i | \(-0.144411\pi\) |
−0.828978 | + | 0.559281i | \(0.811077\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.5000 | − | 19.9186i | 0.534450 | − | 0.925695i | −0.464739 | − | 0.885448i | \(-0.653852\pi\) |
0.999190 | − | 0.0402476i | \(-0.0128147\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −15.0000 | + | 8.66025i | −0.695608 | + | 0.401610i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.0000 | −0.555294 | −0.277647 | − | 0.960683i | \(-0.589555\pi\) | ||||
−0.277647 | + | 0.960683i | \(0.589555\pi\) | |||||||
\(468\) | 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 | 0.933806 | + | 0.357780i | \(0.116466\pi\) |
−0.157056 | + | 0.987590i | \(0.550200\pi\) | |||||||
\(480\) | 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 | \(-0.507213\pi\) | ||||
−0.0226572 | + | 0.999743i | \(0.507213\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.3205i | 0.783260i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.00000 | + | 5.19615i | −0.135388 | + | 0.234499i | −0.925746 | − | 0.378147i | \(-0.876561\pi\) |
0.790358 | + | 0.612646i | \(0.209895\pi\) | |||||||
\(492\) | 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 | \(-0.716748\pi\) |
0.987648 | + | 0.156687i | \(0.0500814\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.0000 | − | 10.3923i | −0.804181 | − | 0.464294i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.0000 | 1.42681 | 0.713405 | − | 0.700752i | \(-0.247152\pi\) | ||||
0.713405 | + | 0.700752i | \(0.247152\pi\) | |||||||
\(504\) | 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 | −0.314459 | − | 0.949271i | \(-0.601823\pi\) |
0.979322 | − | 0.202306i | \(-0.0648436\pi\) | |||||||
\(510\) | 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 | \(-0.718605\pi\) | ||||
−0.634041 | + | 0.773300i | \(0.718605\pi\) | |||||||
\(524\) | 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 | \(-0.221375\pi\) |
−0.938779 | + | 0.344519i | \(0.888042\pi\) | |||||||
\(548\) | 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 | \(-0.994393\pi\) |
0.515178 | + | 0.857083i | \(0.327726\pi\) | |||||||
\(564\) | 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 | −0.987786 | − | 0.155815i | \(-0.950200\pi\) |
0.358954 | − | 0.933355i | \(-0.383134\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.0000 | + | 34.6410i | −0.836974 | + | 1.44968i | 0.0554391 | + | 0.998462i | \(0.482344\pi\) |
−0.892413 | + | 0.451219i | \(0.850989\pi\) | |||||||
\(572\) | 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 | \(-0.199570\pi\) |
−0.912996 | + | 0.407969i | \(0.866237\pi\) | |||||||
\(588\) | 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 | 0.328465 | + | 0.944516i | \(0.393469\pi\) |
−0.982208 | + | 0.187799i | \(0.939865\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.00000 | + | 12.1244i | 0.285536 | + | 0.494563i | 0.972739 | − | 0.231903i | \(-0.0744951\pi\) |
−0.687203 | + | 0.726465i | \(0.741162\pi\) | |||||||
\(602\) | 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 | \(-0.846257\pi\) |
0.845017 | + | 0.534739i | \(0.179590\pi\) | |||||||
\(608\) | 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 | −0.388351 | − | 0.921512i | \(-0.626955\pi\) |
0.992228 | − | 0.124434i | \(-0.0397116\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.5000 | − | 28.5788i | −0.663191 | − | 1.14868i | −0.979772 | − | 0.200115i | \(-0.935868\pi\) |
0.316581 | − | 0.948565i | \(-0.397465\pi\) | |||||||
\(620\) | 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 | \(-0.531732\pi\) | ||||
−0.0995234 | + | 0.995035i | \(0.531732\pi\) | |||||||
\(632\) | 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 | −0.881924 | − | 0.471391i | \(-0.843752\pi\) |
0.0327252 | − | 0.999464i | \(-0.489581\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.00000 | − | 3.46410i | 0.0788723 | − | 0.136611i | −0.823891 | − | 0.566748i | \(-0.808201\pi\) |
0.902764 | + | 0.430137i | \(0.141535\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17.3205i | 0.681994i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.0000 | −0.471769 | −0.235884 | − | 0.971781i | \(-0.575799\pi\) | ||||
−0.235884 | + | 0.971781i | \(0.575799\pi\) | |||||||
\(648\) | 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 | 0.0101092 | + | 0.999949i | \(0.496782\pi\) |
−0.871036 | + | 0.491220i | \(0.836551\pi\) | |||||||
\(654\) | 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 | −0.980029 | − | 0.198852i | \(-0.936279\pi\) |
0.317803 | − | 0.948157i | \(-0.397055\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.5000 | − | 21.6506i | 0.486194 | − | 0.842112i | −0.513680 | − | 0.857982i | \(-0.671718\pi\) |
0.999874 | + | 0.0158695i | \(0.00505163\pi\) | |||||||
\(662\) | 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 | 0.622770 | − | 0.782405i | \(-0.286007\pi\) |
−0.988968 | + | 0.148132i | \(0.952674\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −18.0000 | + | 10.3923i | −0.692820 | + | 0.400000i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.0000 | + | 36.3731i | 0.807096 | + | 1.39793i | 0.914867 | + | 0.403755i | \(0.132295\pi\) |
−0.107772 | + | 0.994176i | \(0.534372\pi\) | |||||||
\(678\) | 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 | \(-0.611909\pi\) | ||||
−0.344375 | + | 0.938832i | \(0.611909\pi\) | |||||||
\(684\) | 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 | 0.932024 | + | 0.362397i | \(0.118041\pi\) |
−0.152167 | + | 0.988355i | \(0.548625\pi\) | |||||||
\(692\) | 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 | 0.900978 | + | 0.433865i | \(0.142851\pi\) |
−0.0747503 | + | 0.997202i | \(0.523816\pi\) | |||||||
\(710\) | 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 | \(-0.428166\pi\) | ||||
0.223762 | + | 0.974644i | \(0.428166\pi\) | |||||||
\(720\) | 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 | −0.999750 | − | 0.0223506i | \(-0.992885\pi\) |
0.480519 | − | 0.876984i | \(-0.340448\pi\) | |||||||
\(728\) | 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 | 0.423802 | + | 0.905755i | \(0.360695\pi\) |
−0.996308 | + | 0.0858539i | \(0.972638\pi\) | |||||||
\(734\) | 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 | \(-0.253662\pi\) | ||||
0.698926 | + | 0.715194i | \(0.253662\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −63.0000 | − | 36.3731i | −2.31436 | − | 1.33620i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.0000 | − | 38.1051i | 0.807102 | − | 1.39794i | −0.107761 | − | 0.994177i | \(-0.534368\pi\) |
0.914863 | − | 0.403764i | \(-0.132298\pi\) | |||||||
\(744\) | 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 | \(-0.804255\pi\) |
0.908027 | + | 0.418911i | \(0.137588\pi\) | |||||||
\(752\) | 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 | −0.915264 | − | 0.402854i | \(-0.868018\pi\) |
0.806514 | + | 0.591215i | \(0.201351\pi\) | |||||||
\(762\) | 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 | −0.941984 | − | 0.335657i | \(-0.891042\pi\) |
0.761680 | + | 0.647954i | \(0.224375\pi\) | |||||||
\(770\) | 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 | \(-0.949350\pi\) |
0.630905 | + | 0.775860i | \(0.282684\pi\) | |||||||
\(788\) | 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 | −0.934652 | − | 0.355564i | \(-0.884289\pi\) |
0.775254 | + | 0.631650i | \(0.217622\pi\) | |||||||
\(798\) | 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 | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.00000 | + | 13.8564i | −0.278862 | + | 0.483004i | −0.971102 | − | 0.238664i | \(-0.923291\pi\) |
0.692240 | + | 0.721668i | \(0.256624\pi\) | |||||||
\(824\) | 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 | \(-0.233083\pi\) |
−0.950813 | + | 0.309764i | \(0.899750\pi\) | |||||||
\(840\) | 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 | 0.992941 | − | 0.118609i | \(-0.0378434\pi\) |
−0.599189 | + | 0.800608i | \(0.704510\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.5000 | − | 18.1865i | 0.359092 | − | 0.621966i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.00000 | + | 5.19615i | 0.102478 | + | 0.177497i | 0.912705 | − | 0.408619i | \(-0.133990\pi\) |
−0.810227 | + | 0.586116i | \(0.800656\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.0000 | + | 17.3205i | −0.341196 | + | 0.590968i | −0.984655 | − | 0.174512i | \(-0.944165\pi\) |
0.643459 | + | 0.765480i | \(0.277499\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 13.8564i | − | 0.472225i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 43.0000 | 1.46374 | 0.731869 | − | 0.681446i | \(-0.238649\pi\) | ||||
0.731869 | + | 0.681446i | \(0.238649\pi\) | |||||||
\(864\) | 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 | −0.959671 | − | 0.281126i | \(-0.909292\pi\) |
0.723298 | + | 0.690536i | \(0.242625\pi\) | |||||||
\(878\) | 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 | \(-0.355869\pi\) | ||||
0.437485 | + | 0.899226i | \(0.355869\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(888\) | 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 | \(-0.320563\pi\) |
−0.999195 | + | 0.0401089i | \(0.987230\pi\) | |||||||
\(908\) | 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 | \(-0.0647463\pi\) |
−0.664635 | + | 0.747168i | \(0.731413\pi\) | |||||||
\(912\) | 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 | \(-0.409536\pi\) | ||||
0.280389 | + | 0.959886i | \(0.409536\pi\) | |||||||
\(920\) | 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 | 0.831350 | − | 0.555749i | \(-0.187569\pi\) |
−0.896968 | + | 0.442096i | \(0.854235\pi\) | |||||||
\(930\) | 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 | −0.461133 | − | 0.887331i | \(-0.652557\pi\) |
0.999018 | − | 0.0443125i | \(-0.0141097\pi\) | |||||||
\(942\) | 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 | \(-0.0163278\pi\) |
−0.543746 | + | 0.839250i | \(0.682994\pi\) | |||||||
\(948\) | 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 | \(-0.848694\pi\) |
0.840899 | + | 0.541192i | \(0.182027\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 24.2487i | − | 0.778981i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −55.0000 | −1.76503 | −0.882517 | − | 0.470281i | \(-0.844153\pi\) | ||||
−0.882517 | + | 0.470281i | \(0.844153\pi\) | |||||||
\(972\) | 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 | −0.910017 | − | 0.414572i | \(-0.863931\pi\) |
0.814038 | + | 0.580812i | \(0.197265\pi\) | |||||||
\(978\) | 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 | \(-0.0739903\pi\) |
−0.686050 | + | 0.727554i | \(0.740657\pi\) | |||||||
\(984\) | 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 | \(-0.224028\pi\) | ||||
0.762385 | + | 0.647124i | \(0.224028\pi\) | |||||||
\(992\) | 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 | 0.675465 | − | 0.737392i | \(-0.263943\pi\) |
−0.976333 | + | 0.216274i | \(0.930610\pi\) | |||||||
\(998\) | 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 | 1008.2.r.c.337.1 | 2 | ||
3.2 | odd | 2 | 3024.2.r.b.1009.1 | 2 | |||
4.3 | odd | 2 | 504.2.r.a.337.1 | yes | 2 | ||
9.2 | odd | 6 | 3024.2.r.b.2017.1 | 2 | |||
9.4 | even | 3 | 9072.2.a.i.1.1 | 1 | |||
9.5 | odd | 6 | 9072.2.a.n.1.1 | 1 | |||
9.7 | even | 3 | inner | 1008.2.r.c.673.1 | 2 | ||
12.11 | even | 2 | 1512.2.r.a.1009.1 | 2 | |||
36.7 | odd | 6 | 504.2.r.a.169.1 | ✓ | 2 | ||
36.11 | even | 6 | 1512.2.r.a.505.1 | 2 | |||
36.23 | even | 6 | 4536.2.a.g.1.1 | 1 | |||
36.31 | odd | 6 | 4536.2.a.d.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.r.a.169.1 | ✓ | 2 | 36.7 | odd | 6 | ||
504.2.r.a.337.1 | yes | 2 | 4.3 | odd | 2 | ||
1008.2.r.c.337.1 | 2 | 1.1 | even | 1 | trivial | ||
1008.2.r.c.673.1 | 2 | 9.7 | even | 3 | inner | ||
1512.2.r.a.505.1 | 2 | 36.11 | even | 6 | |||
1512.2.r.a.1009.1 | 2 | 12.11 | even | 2 | |||
3024.2.r.b.1009.1 | 2 | 3.2 | odd | 2 | |||
3024.2.r.b.2017.1 | 2 | 9.2 | odd | 6 | |||
4536.2.a.d.1.1 | 1 | 36.31 | odd | 6 | |||
4536.2.a.g.1.1 | 1 | 36.23 | even | 6 | |||
9072.2.a.i.1.1 | 1 | 9.4 | even | 3 | |||
9072.2.a.n.1.1 | 1 | 9.5 | odd | 6 |