Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2730,2,Mod(1639,2730)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2730, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2730.1639");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2730 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2730.l (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(21.7991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1639.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2730.1639 |
Dual form | 2730.2.l.k.1639.2 |
$q$-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 \(\left(\mathbb{Z}/2730\mathbb{Z}\right)^\times\).
\(n\) | \(547\) | \(911\) | \(1471\) | \(2341\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000 | + | 2.00000i | 0.447214 | + | 0.894427i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 2.00000 | − | 1.00000i | 0.632456 | − | 0.316228i | ||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | − | 1.00000i | − | 0.277350i | ||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −2.00000 | + | 1.00000i | −0.516398 | + | 0.258199i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.00000i | 1.45521i | 0.685994 | + | 0.727607i | \(0.259367\pi\) | ||||
−0.685994 | + | 0.727607i | \(0.740633\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | −4.00000 | −0.917663 | −0.458831 | − | 0.888523i | \(-0.651732\pi\) | ||||
−0.458831 | + | 0.888523i | \(0.651732\pi\) | |||||||
\(20\) | −1.00000 | − | 2.00000i | −0.223607 | − | 0.447214i | ||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | − | 2.00000i | − | 0.426401i | ||||||
\(23\) | 2.00000i | 0.417029i | 0.978019 | + | 0.208514i | \(0.0668628\pi\) | ||||
−0.978019 | + | 0.208514i | \(0.933137\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −3.00000 | + | 4.00000i | −0.600000 | + | 0.800000i | ||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | − | 1.00000i | − | 0.188982i | ||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 1.00000 | + | 2.00000i | 0.182574 | + | 0.365148i | ||||
\(31\) | 8.00000 | 1.43684 | 0.718421 | − | 0.695608i | \(-0.244865\pi\) | ||||
0.718421 | + | 0.695608i | \(0.244865\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 2.00000i | 0.348155i | ||||||||
\(34\) | 6.00000 | 1.02899 | ||||||||
\(35\) | −2.00000 | + | 1.00000i | −0.338062 | + | 0.169031i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 6.00000i | 0.986394i | 0.869918 | + | 0.493197i | \(0.164172\pi\) | ||||
−0.869918 | + | 0.493197i | \(0.835828\pi\) | |||||||
\(38\) | 4.00000i | 0.648886i | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −2.00000 | + | 1.00000i | −0.316228 | + | 0.158114i | ||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 1.00000i | 0.154303i | ||||||||
\(43\) | − | 6.00000i | − | 0.914991i | −0.889212 | − | 0.457496i | \(-0.848747\pi\) | ||
0.889212 | − | 0.457496i | \(-0.151253\pi\) | |||||||
\(44\) | −2.00000 | −0.301511 | ||||||||
\(45\) | −1.00000 | − | 2.00000i | −0.149071 | − | 0.298142i | ||||
\(46\) | 2.00000 | 0.294884 | ||||||||
\(47\) | 2.00000i | 0.291730i | 0.989305 | + | 0.145865i | \(0.0465965\pi\) | ||||
−0.989305 | + | 0.145865i | \(0.953403\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 4.00000 | + | 3.00000i | 0.565685 | + | 0.424264i | ||||
\(51\) | −6.00000 | −0.840168 | ||||||||
\(52\) | 1.00000i | 0.138675i | ||||||||
\(53\) | − | 4.00000i | − | 0.549442i | −0.961524 | − | 0.274721i | \(-0.911414\pi\) | ||
0.961524 | − | 0.274721i | \(-0.0885855\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 2.00000 | + | 4.00000i | 0.269680 | + | 0.539360i | ||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | − | 4.00000i | − | 0.529813i | ||||||
\(58\) | 6.00000i | 0.787839i | ||||||||
\(59\) | −12.0000 | −1.56227 | −0.781133 | − | 0.624364i | \(-0.785358\pi\) | ||||
−0.781133 | + | 0.624364i | \(0.785358\pi\) | |||||||
\(60\) | 2.00000 | − | 1.00000i | 0.258199 | − | 0.129099i | ||||
\(61\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(62\) | − | 8.00000i | − | 1.01600i | ||||||
\(63\) | − | 1.00000i | − | 0.125988i | ||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 2.00000 | − | 1.00000i | 0.248069 | − | 0.124035i | ||||
\(66\) | 2.00000 | 0.246183 | ||||||||
\(67\) | − | 8.00000i | − | 0.977356i | −0.872464 | − | 0.488678i | \(-0.837479\pi\) | ||
0.872464 | − | 0.488678i | \(-0.162521\pi\) | |||||||
\(68\) | − | 6.00000i | − | 0.727607i | ||||||
\(69\) | −2.00000 | −0.240772 | ||||||||
\(70\) | 1.00000 | + | 2.00000i | 0.119523 | + | 0.239046i | ||||
\(71\) | 4.00000 | 0.474713 | 0.237356 | − | 0.971423i | \(-0.423719\pi\) | ||||
0.237356 | + | 0.971423i | \(0.423719\pi\) | |||||||
\(72\) | − | 1.00000i | − | 0.117851i | ||||||
\(73\) | − | 4.00000i | − | 0.468165i | −0.972217 | − | 0.234082i | \(-0.924791\pi\) | ||
0.972217 | − | 0.234082i | \(-0.0752085\pi\) | |||||||
\(74\) | 6.00000 | 0.697486 | ||||||||
\(75\) | −4.00000 | − | 3.00000i | −0.461880 | − | 0.346410i | ||||
\(76\) | 4.00000 | 0.458831 | ||||||||
\(77\) | 2.00000i | 0.227921i | ||||||||
\(78\) | − | 1.00000i | − | 0.113228i | ||||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | 1.00000 | + | 2.00000i | 0.111803 | + | 0.223607i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 2.00000i | − | 0.220863i | ||||||
\(83\) | 12.0000i | 1.31717i | 0.752506 | + | 0.658586i | \(0.228845\pi\) | ||||
−0.752506 | + | 0.658586i | \(0.771155\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | −12.0000 | + | 6.00000i | −1.30158 | + | 0.650791i | ||||
\(86\) | −6.00000 | −0.646997 | ||||||||
\(87\) | − | 6.00000i | − | 0.643268i | ||||||
\(88\) | 2.00000i | 0.213201i | ||||||||
\(89\) | 10.0000 | 1.06000 | 0.529999 | − | 0.847998i | \(-0.322192\pi\) | ||||
0.529999 | + | 0.847998i | \(0.322192\pi\) | |||||||
\(90\) | −2.00000 | + | 1.00000i | −0.210819 | + | 0.105409i | ||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | − | 2.00000i | − | 0.208514i | ||||||
\(93\) | 8.00000i | 0.829561i | ||||||||
\(94\) | 2.00000 | 0.206284 | ||||||||
\(95\) | −4.00000 | − | 8.00000i | −0.410391 | − | 0.820783i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | 1.00000i | 0.101015i | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 3.00000 | − | 4.00000i | 0.300000 | − | 0.400000i | ||||
\(101\) | −10.0000 | −0.995037 | −0.497519 | − | 0.867453i | \(-0.665755\pi\) | ||||
−0.497519 | + | 0.867453i | \(0.665755\pi\) | |||||||
\(102\) | 6.00000i | 0.594089i | ||||||||
\(103\) | 8.00000i | 0.788263i | 0.919054 | + | 0.394132i | \(0.128955\pi\) | ||||
−0.919054 | + | 0.394132i | \(0.871045\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | −1.00000 | − | 2.00000i | −0.0975900 | − | 0.195180i | ||||
\(106\) | −4.00000 | −0.388514 | ||||||||
\(107\) | 8.00000i | 0.773389i | 0.922208 | + | 0.386695i | \(0.126383\pi\) | ||||
−0.922208 | + | 0.386695i | \(0.873617\pi\) | |||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | −16.0000 | −1.53252 | −0.766261 | − | 0.642529i | \(-0.777885\pi\) | ||||
−0.766261 | + | 0.642529i | \(0.777885\pi\) | |||||||
\(110\) | 4.00000 | − | 2.00000i | 0.381385 | − | 0.190693i | ||||
\(111\) | −6.00000 | −0.569495 | ||||||||
\(112\) | 1.00000i | 0.0944911i | ||||||||
\(113\) | 6.00000i | 0.564433i | 0.959351 | + | 0.282216i | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | −4.00000 | −0.374634 | ||||||||
\(115\) | −4.00000 | + | 2.00000i | −0.373002 | + | 0.186501i | ||||
\(116\) | 6.00000 | 0.557086 | ||||||||
\(117\) | 1.00000i | 0.0924500i | ||||||||
\(118\) | 12.0000i | 1.10469i | ||||||||
\(119\) | −6.00000 | −0.550019 | ||||||||
\(120\) | −1.00000 | − | 2.00000i | −0.0912871 | − | 0.182574i | ||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.00000i | 0.180334i | ||||||||
\(124\) | −8.00000 | −0.718421 | ||||||||
\(125\) | −11.0000 | − | 2.00000i | −0.983870 | − | 0.178885i | ||||
\(126\) | −1.00000 | −0.0890871 | ||||||||
\(127\) | 16.0000i | 1.41977i | 0.704317 | + | 0.709885i | \(0.251253\pi\) | ||||
−0.704317 | + | 0.709885i | \(0.748747\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 6.00000 | 0.528271 | ||||||||
\(130\) | −1.00000 | − | 2.00000i | −0.0877058 | − | 0.175412i | ||||
\(131\) | 18.0000 | 1.57267 | 0.786334 | − | 0.617802i | \(-0.211977\pi\) | ||||
0.786334 | + | 0.617802i | \(0.211977\pi\) | |||||||
\(132\) | − | 2.00000i | − | 0.174078i | ||||||
\(133\) | − | 4.00000i | − | 0.346844i | ||||||
\(134\) | −8.00000 | −0.691095 | ||||||||
\(135\) | 2.00000 | − | 1.00000i | 0.172133 | − | 0.0860663i | ||||
\(136\) | −6.00000 | −0.514496 | ||||||||
\(137\) | 6.00000i | 0.512615i | 0.966595 | + | 0.256307i | \(0.0825059\pi\) | ||||
−0.966595 | + | 0.256307i | \(0.917494\pi\) | |||||||
\(138\) | 2.00000i | 0.170251i | ||||||||
\(139\) | −16.0000 | −1.35710 | −0.678551 | − | 0.734553i | \(-0.737392\pi\) | ||||
−0.678551 | + | 0.734553i | \(0.737392\pi\) | |||||||
\(140\) | 2.00000 | − | 1.00000i | 0.169031 | − | 0.0845154i | ||||
\(141\) | −2.00000 | −0.168430 | ||||||||
\(142\) | − | 4.00000i | − | 0.335673i | ||||||
\(143\) | − | 2.00000i | − | 0.167248i | ||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | −6.00000 | − | 12.0000i | −0.498273 | − | 0.996546i | ||||
\(146\) | −4.00000 | −0.331042 | ||||||||
\(147\) | − | 1.00000i | − | 0.0824786i | ||||||
\(148\) | − | 6.00000i | − | 0.493197i | ||||||
\(149\) | −10.0000 | −0.819232 | −0.409616 | − | 0.912258i | \(-0.634337\pi\) | ||||
−0.409616 | + | 0.912258i | \(0.634337\pi\) | |||||||
\(150\) | −3.00000 | + | 4.00000i | −0.244949 | + | 0.326599i | ||||
\(151\) | 2.00000 | 0.162758 | 0.0813788 | − | 0.996683i | \(-0.474068\pi\) | ||||
0.0813788 | + | 0.996683i | \(0.474068\pi\) | |||||||
\(152\) | − | 4.00000i | − | 0.324443i | ||||||
\(153\) | − | 6.00000i | − | 0.485071i | ||||||
\(154\) | 2.00000 | 0.161165 | ||||||||
\(155\) | 8.00000 | + | 16.0000i | 0.642575 | + | 1.28515i | ||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | 2.00000i | 0.159617i | 0.996810 | + | 0.0798087i | \(0.0254309\pi\) | ||||
−0.996810 | + | 0.0798087i | \(0.974569\pi\) | |||||||
\(158\) | 8.00000i | 0.636446i | ||||||||
\(159\) | 4.00000 | 0.317221 | ||||||||
\(160\) | 2.00000 | − | 1.00000i | 0.158114 | − | 0.0790569i | ||||
\(161\) | −2.00000 | −0.157622 | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | 16.0000i | 1.25322i | 0.779334 | + | 0.626608i | \(0.215557\pi\) | ||||
−0.779334 | + | 0.626608i | \(0.784443\pi\) | |||||||
\(164\) | −2.00000 | −0.156174 | ||||||||
\(165\) | −4.00000 | + | 2.00000i | −0.311400 | + | 0.155700i | ||||
\(166\) | 12.0000 | 0.931381 | ||||||||
\(167\) | − | 18.0000i | − | 1.39288i | −0.717614 | − | 0.696441i | \(-0.754766\pi\) | ||
0.717614 | − | 0.696441i | \(-0.245234\pi\) | |||||||
\(168\) | − | 1.00000i | − | 0.0771517i | ||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 6.00000 | + | 12.0000i | 0.460179 | + | 0.920358i | ||||
\(171\) | 4.00000 | 0.305888 | ||||||||
\(172\) | 6.00000i | 0.457496i | ||||||||
\(173\) | − | 2.00000i | − | 0.152057i | −0.997106 | − | 0.0760286i | \(-0.975776\pi\) | ||
0.997106 | − | 0.0760286i | \(-0.0242240\pi\) | |||||||
\(174\) | −6.00000 | −0.454859 | ||||||||
\(175\) | −4.00000 | − | 3.00000i | −0.302372 | − | 0.226779i | ||||
\(176\) | 2.00000 | 0.150756 | ||||||||
\(177\) | − | 12.0000i | − | 0.901975i | ||||||
\(178\) | − | 10.0000i | − | 0.749532i | ||||||
\(179\) | 20.0000 | 1.49487 | 0.747435 | − | 0.664335i | \(-0.231285\pi\) | ||||
0.747435 | + | 0.664335i | \(0.231285\pi\) | |||||||
\(180\) | 1.00000 | + | 2.00000i | 0.0745356 | + | 0.149071i | ||||
\(181\) | −8.00000 | −0.594635 | −0.297318 | − | 0.954779i | \(-0.596092\pi\) | ||||
−0.297318 | + | 0.954779i | \(0.596092\pi\) | |||||||
\(182\) | − | 1.00000i | − | 0.0741249i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.00000 | −0.147442 | ||||||||
\(185\) | −12.0000 | + | 6.00000i | −0.882258 | + | 0.441129i | ||||
\(186\) | 8.00000 | 0.586588 | ||||||||
\(187\) | 12.0000i | 0.877527i | ||||||||
\(188\) | − | 2.00000i | − | 0.145865i | ||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −8.00000 | + | 4.00000i | −0.580381 | + | 0.290191i | ||||
\(191\) | −8.00000 | −0.578860 | −0.289430 | − | 0.957199i | \(-0.593466\pi\) | ||||
−0.289430 | + | 0.957199i | \(0.593466\pi\) | |||||||
\(192\) | − | 1.00000i | − | 0.0721688i | ||||||
\(193\) | 2.00000i | 0.143963i | 0.997406 | + | 0.0719816i | \(0.0229323\pi\) | ||||
−0.997406 | + | 0.0719816i | \(0.977068\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.00000 | + | 2.00000i | 0.0716115 | + | 0.143223i | ||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | − | 22.0000i | − | 1.56744i | −0.621117 | − | 0.783718i | \(-0.713321\pi\) | ||
0.621117 | − | 0.783718i | \(-0.286679\pi\) | |||||||
\(198\) | 2.00000i | 0.142134i | ||||||||
\(199\) | −6.00000 | −0.425329 | −0.212664 | − | 0.977125i | \(-0.568214\pi\) | ||||
−0.212664 | + | 0.977125i | \(0.568214\pi\) | |||||||
\(200\) | −4.00000 | − | 3.00000i | −0.282843 | − | 0.212132i | ||||
\(201\) | 8.00000 | 0.564276 | ||||||||
\(202\) | 10.0000i | 0.703598i | ||||||||
\(203\) | − | 6.00000i | − | 0.421117i | ||||||
\(204\) | 6.00000 | 0.420084 | ||||||||
\(205\) | 2.00000 | + | 4.00000i | 0.139686 | + | 0.279372i | ||||
\(206\) | 8.00000 | 0.557386 | ||||||||
\(207\) | − | 2.00000i | − | 0.139010i | ||||||
\(208\) | − | 1.00000i | − | 0.0693375i | ||||||
\(209\) | −8.00000 | −0.553372 | ||||||||
\(210\) | −2.00000 | + | 1.00000i | −0.138013 | + | 0.0690066i | ||||
\(211\) | −20.0000 | −1.37686 | −0.688428 | − | 0.725304i | \(-0.741699\pi\) | ||||
−0.688428 | + | 0.725304i | \(0.741699\pi\) | |||||||
\(212\) | 4.00000i | 0.274721i | ||||||||
\(213\) | 4.00000i | 0.274075i | ||||||||
\(214\) | 8.00000 | 0.546869 | ||||||||
\(215\) | 12.0000 | − | 6.00000i | 0.818393 | − | 0.409197i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 8.00000i | 0.543075i | ||||||||
\(218\) | 16.0000i | 1.08366i | ||||||||
\(219\) | 4.00000 | 0.270295 | ||||||||
\(220\) | −2.00000 | − | 4.00000i | −0.134840 | − | 0.269680i | ||||
\(221\) | 6.00000 | 0.403604 | ||||||||
\(222\) | 6.00000i | 0.402694i | ||||||||
\(223\) | 12.0000i | 0.803579i | 0.915732 | + | 0.401790i | \(0.131612\pi\) | ||||
−0.915732 | + | 0.401790i | \(0.868388\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 3.00000 | − | 4.00000i | 0.200000 | − | 0.266667i | ||||
\(226\) | 6.00000 | 0.399114 | ||||||||
\(227\) | 8.00000i | 0.530979i | 0.964114 | + | 0.265489i | \(0.0855335\pi\) | ||||
−0.964114 | + | 0.265489i | \(0.914466\pi\) | |||||||
\(228\) | 4.00000i | 0.264906i | ||||||||
\(229\) | 26.0000 | 1.71813 | 0.859064 | − | 0.511868i | \(-0.171046\pi\) | ||||
0.859064 | + | 0.511868i | \(0.171046\pi\) | |||||||
\(230\) | 2.00000 | + | 4.00000i | 0.131876 | + | 0.263752i | ||||
\(231\) | −2.00000 | −0.131590 | ||||||||
\(232\) | − | 6.00000i | − | 0.393919i | ||||||
\(233\) | 10.0000i | 0.655122i | 0.944830 | + | 0.327561i | \(0.106227\pi\) | ||||
−0.944830 | + | 0.327561i | \(0.893773\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | −4.00000 | + | 2.00000i | −0.260931 | + | 0.130466i | ||||
\(236\) | 12.0000 | 0.781133 | ||||||||
\(237\) | − | 8.00000i | − | 0.519656i | ||||||
\(238\) | 6.00000i | 0.388922i | ||||||||
\(239\) | 4.00000 | 0.258738 | 0.129369 | − | 0.991596i | \(-0.458705\pi\) | ||||
0.129369 | + | 0.991596i | \(0.458705\pi\) | |||||||
\(240\) | −2.00000 | + | 1.00000i | −0.129099 | + | 0.0645497i | ||||
\(241\) | 14.0000 | 0.901819 | 0.450910 | − | 0.892570i | \(-0.351100\pi\) | ||||
0.450910 | + | 0.892570i | \(0.351100\pi\) | |||||||
\(242\) | 7.00000i | 0.449977i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | − | 2.00000i | −0.0638877 | − | 0.127775i | ||||
\(246\) | 2.00000 | 0.127515 | ||||||||
\(247\) | 4.00000i | 0.254514i | ||||||||
\(248\) | 8.00000i | 0.508001i | ||||||||
\(249\) | −12.0000 | −0.760469 | ||||||||
\(250\) | −2.00000 | + | 11.0000i | −0.126491 | + | 0.695701i | ||||
\(251\) | 30.0000 | 1.89358 | 0.946792 | − | 0.321847i | \(-0.104304\pi\) | ||||
0.946792 | + | 0.321847i | \(0.104304\pi\) | |||||||
\(252\) | 1.00000i | 0.0629941i | ||||||||
\(253\) | 4.00000i | 0.251478i | ||||||||
\(254\) | 16.0000 | 1.00393 | ||||||||
\(255\) | −6.00000 | − | 12.0000i | −0.375735 | − | 0.751469i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 30.0000i | − | 1.87135i | −0.352865 | − | 0.935674i | \(-0.614792\pi\) | ||
0.352865 | − | 0.935674i | \(-0.385208\pi\) | |||||||
\(258\) | − | 6.00000i | − | 0.373544i | ||||||
\(259\) | −6.00000 | −0.372822 | ||||||||
\(260\) | −2.00000 | + | 1.00000i | −0.124035 | + | 0.0620174i | ||||
\(261\) | 6.00000 | 0.371391 | ||||||||
\(262\) | − | 18.0000i | − | 1.11204i | ||||||
\(263\) | 26.0000i | 1.60323i | 0.597841 | + | 0.801614i | \(0.296025\pi\) | ||||
−0.597841 | + | 0.801614i | \(0.703975\pi\) | |||||||
\(264\) | −2.00000 | −0.123091 | ||||||||
\(265\) | 8.00000 | − | 4.00000i | 0.491436 | − | 0.245718i | ||||
\(266\) | −4.00000 | −0.245256 | ||||||||
\(267\) | 10.0000i | 0.611990i | ||||||||
\(268\) | 8.00000i | 0.488678i | ||||||||
\(269\) | 2.00000 | 0.121942 | 0.0609711 | − | 0.998140i | \(-0.480580\pi\) | ||||
0.0609711 | + | 0.998140i | \(0.480580\pi\) | |||||||
\(270\) | −1.00000 | − | 2.00000i | −0.0608581 | − | 0.121716i | ||||
\(271\) | 20.0000 | 1.21491 | 0.607457 | − | 0.794353i | \(-0.292190\pi\) | ||||
0.607457 | + | 0.794353i | \(0.292190\pi\) | |||||||
\(272\) | 6.00000i | 0.363803i | ||||||||
\(273\) | 1.00000i | 0.0605228i | ||||||||
\(274\) | 6.00000 | 0.362473 | ||||||||
\(275\) | −6.00000 | + | 8.00000i | −0.361814 | + | 0.482418i | ||||
\(276\) | 2.00000 | 0.120386 | ||||||||
\(277\) | 2.00000i | 0.120168i | 0.998193 | + | 0.0600842i | \(0.0191369\pi\) | ||||
−0.998193 | + | 0.0600842i | \(0.980863\pi\) | |||||||
\(278\) | 16.0000i | 0.959616i | ||||||||
\(279\) | −8.00000 | −0.478947 | ||||||||
\(280\) | −1.00000 | − | 2.00000i | −0.0597614 | − | 0.119523i | ||||
\(281\) | −20.0000 | −1.19310 | −0.596550 | − | 0.802576i | \(-0.703462\pi\) | ||||
−0.596550 | + | 0.802576i | \(0.703462\pi\) | |||||||
\(282\) | 2.00000i | 0.119098i | ||||||||
\(283\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(284\) | −4.00000 | −0.237356 | ||||||||
\(285\) | 8.00000 | − | 4.00000i | 0.473879 | − | 0.236940i | ||||
\(286\) | −2.00000 | −0.118262 | ||||||||
\(287\) | 2.00000i | 0.118056i | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −19.0000 | −1.11765 | ||||||||
\(290\) | −12.0000 | + | 6.00000i | −0.704664 | + | 0.352332i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.00000i | 0.234082i | ||||||||
\(293\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | −12.0000 | − | 24.0000i | −0.698667 | − | 1.39733i | ||||
\(296\) | −6.00000 | −0.348743 | ||||||||
\(297\) | − | 2.00000i | − | 0.116052i | ||||||
\(298\) | 10.0000i | 0.579284i | ||||||||
\(299\) | 2.00000 | 0.115663 | ||||||||
\(300\) | 4.00000 | + | 3.00000i | 0.230940 | + | 0.173205i | ||||
\(301\) | 6.00000 | 0.345834 | ||||||||
\(302\) | − | 2.00000i | − | 0.115087i | ||||||
\(303\) | − | 10.0000i | − | 0.574485i | ||||||
\(304\) | −4.00000 | −0.229416 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6.00000 | −0.342997 | ||||||||
\(307\) | 2.00000i | 0.114146i | 0.998370 | + | 0.0570730i | \(0.0181768\pi\) | ||||
−0.998370 | + | 0.0570730i | \(0.981823\pi\) | |||||||
\(308\) | − | 2.00000i | − | 0.113961i | ||||||
\(309\) | −8.00000 | −0.455104 | ||||||||
\(310\) | 16.0000 | − | 8.00000i | 0.908739 | − | 0.454369i | ||||
\(311\) | 24.0000 | 1.36092 | 0.680458 | − | 0.732787i | \(-0.261781\pi\) | ||||
0.680458 | + | 0.732787i | \(0.261781\pi\) | |||||||
\(312\) | 1.00000i | 0.0566139i | ||||||||
\(313\) | − | 2.00000i | − | 0.113047i | −0.998401 | − | 0.0565233i | \(-0.981998\pi\) | ||
0.998401 | − | 0.0565233i | \(-0.0180015\pi\) | |||||||
\(314\) | 2.00000 | 0.112867 | ||||||||
\(315\) | 2.00000 | − | 1.00000i | 0.112687 | − | 0.0563436i | ||||
\(316\) | 8.00000 | 0.450035 | ||||||||
\(317\) | 22.0000i | 1.23564i | 0.786318 | + | 0.617822i | \(0.211985\pi\) | ||||
−0.786318 | + | 0.617822i | \(0.788015\pi\) | |||||||
\(318\) | − | 4.00000i | − | 0.224309i | ||||||
\(319\) | −12.0000 | −0.671871 | ||||||||
\(320\) | −1.00000 | − | 2.00000i | −0.0559017 | − | 0.111803i | ||||
\(321\) | −8.00000 | −0.446516 | ||||||||
\(322\) | 2.00000i | 0.111456i | ||||||||
\(323\) | − | 24.0000i | − | 1.33540i | ||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 4.00000 | + | 3.00000i | 0.221880 | + | 0.166410i | ||||
\(326\) | 16.0000 | 0.886158 | ||||||||
\(327\) | − | 16.0000i | − | 0.884802i | ||||||
\(328\) | 2.00000i | 0.110432i | ||||||||
\(329\) | −2.00000 | −0.110264 | ||||||||
\(330\) | 2.00000 | + | 4.00000i | 0.110096 | + | 0.220193i | ||||
\(331\) | −8.00000 | −0.439720 | −0.219860 | − | 0.975531i | \(-0.570560\pi\) | ||||
−0.219860 | + | 0.975531i | \(0.570560\pi\) | |||||||
\(332\) | − | 12.0000i | − | 0.658586i | ||||||
\(333\) | − | 6.00000i | − | 0.328798i | ||||||
\(334\) | −18.0000 | −0.984916 | ||||||||
\(335\) | 16.0000 | − | 8.00000i | 0.874173 | − | 0.437087i | ||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | 8.00000i | 0.435788i | 0.975972 | + | 0.217894i | \(0.0699187\pi\) | ||||
−0.975972 | + | 0.217894i | \(0.930081\pi\) | |||||||
\(338\) | 1.00000i | 0.0543928i | ||||||||
\(339\) | −6.00000 | −0.325875 | ||||||||
\(340\) | 12.0000 | − | 6.00000i | 0.650791 | − | 0.325396i | ||||
\(341\) | 16.0000 | 0.866449 | ||||||||
\(342\) | − | 4.00000i | − | 0.216295i | ||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 6.00000 | 0.323498 | ||||||||
\(345\) | −2.00000 | − | 4.00000i | −0.107676 | − | 0.215353i | ||||
\(346\) | −2.00000 | −0.107521 | ||||||||
\(347\) | − | 16.0000i | − | 0.858925i | −0.903085 | − | 0.429463i | \(-0.858703\pi\) | ||
0.903085 | − | 0.429463i | \(-0.141297\pi\) | |||||||
\(348\) | 6.00000i | 0.321634i | ||||||||
\(349\) | 6.00000 | 0.321173 | 0.160586 | − | 0.987022i | \(-0.448662\pi\) | ||||
0.160586 | + | 0.987022i | \(0.448662\pi\) | |||||||
\(350\) | −3.00000 | + | 4.00000i | −0.160357 | + | 0.213809i | ||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | − | 2.00000i | − | 0.106600i | ||||||
\(353\) | 10.0000i | 0.532246i | 0.963939 | + | 0.266123i | \(0.0857428\pi\) | ||||
−0.963939 | + | 0.266123i | \(0.914257\pi\) | |||||||
\(354\) | −12.0000 | −0.637793 | ||||||||
\(355\) | 4.00000 | + | 8.00000i | 0.212298 | + | 0.424596i | ||||
\(356\) | −10.0000 | −0.529999 | ||||||||
\(357\) | − | 6.00000i | − | 0.317554i | ||||||
\(358\) | − | 20.0000i | − | 1.05703i | ||||||
\(359\) | 24.0000 | 1.26667 | 0.633336 | − | 0.773877i | \(-0.281685\pi\) | ||||
0.633336 | + | 0.773877i | \(0.281685\pi\) | |||||||
\(360\) | 2.00000 | − | 1.00000i | 0.105409 | − | 0.0527046i | ||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 8.00000i | 0.420471i | ||||||||
\(363\) | − | 7.00000i | − | 0.367405i | ||||||
\(364\) | −1.00000 | −0.0524142 | ||||||||
\(365\) | 8.00000 | − | 4.00000i | 0.418739 | − | 0.209370i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 8.00000i | − | 0.417597i | −0.977959 | − | 0.208798i | \(-0.933045\pi\) | ||
0.977959 | − | 0.208798i | \(-0.0669552\pi\) | |||||||
\(368\) | 2.00000i | 0.104257i | ||||||||
\(369\) | −2.00000 | −0.104116 | ||||||||
\(370\) | 6.00000 | + | 12.0000i | 0.311925 | + | 0.623850i | ||||
\(371\) | 4.00000 | 0.207670 | ||||||||
\(372\) | − | 8.00000i | − | 0.414781i | ||||||
\(373\) | 6.00000i | 0.310668i | 0.987862 | + | 0.155334i | \(0.0496454\pi\) | ||||
−0.987862 | + | 0.155334i | \(0.950355\pi\) | |||||||
\(374\) | 12.0000 | 0.620505 | ||||||||
\(375\) | 2.00000 | − | 11.0000i | 0.103280 | − | 0.568038i | ||||
\(376\) | −2.00000 | −0.103142 | ||||||||
\(377\) | 6.00000i | 0.309016i | ||||||||
\(378\) | − | 1.00000i | − | 0.0514344i | ||||||
\(379\) | −20.0000 | −1.02733 | −0.513665 | − | 0.857991i | \(-0.671713\pi\) | ||||
−0.513665 | + | 0.857991i | \(0.671713\pi\) | |||||||
\(380\) | 4.00000 | + | 8.00000i | 0.205196 | + | 0.410391i | ||||
\(381\) | −16.0000 | −0.819705 | ||||||||
\(382\) | 8.00000i | 0.409316i | ||||||||
\(383\) | 30.0000i | 1.53293i | 0.642287 | + | 0.766464i | \(0.277986\pi\) | ||||
−0.642287 | + | 0.766464i | \(0.722014\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −4.00000 | + | 2.00000i | −0.203859 | + | 0.101929i | ||||
\(386\) | 2.00000 | 0.101797 | ||||||||
\(387\) | 6.00000i | 0.304997i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 38.0000 | 1.92668 | 0.963338 | − | 0.268290i | \(-0.0864585\pi\) | ||||
0.963338 | + | 0.268290i | \(0.0864585\pi\) | |||||||
\(390\) | 2.00000 | − | 1.00000i | 0.101274 | − | 0.0506370i | ||||
\(391\) | −12.0000 | −0.606866 | ||||||||
\(392\) | − | 1.00000i | − | 0.0505076i | ||||||
\(393\) | 18.0000i | 0.907980i | ||||||||
\(394\) | −22.0000 | −1.10834 | ||||||||
\(395\) | −8.00000 | − | 16.0000i | −0.402524 | − | 0.805047i | ||||
\(396\) | 2.00000 | 0.100504 | ||||||||
\(397\) | − | 18.0000i | − | 0.903394i | −0.892171 | − | 0.451697i | \(-0.850819\pi\) | ||
0.892171 | − | 0.451697i | \(-0.149181\pi\) | |||||||
\(398\) | 6.00000i | 0.300753i | ||||||||
\(399\) | 4.00000 | 0.200250 | ||||||||
\(400\) | −3.00000 | + | 4.00000i | −0.150000 | + | 0.200000i | ||||
\(401\) | 36.0000 | 1.79775 | 0.898877 | − | 0.438201i | \(-0.144384\pi\) | ||||
0.898877 | + | 0.438201i | \(0.144384\pi\) | |||||||
\(402\) | − | 8.00000i | − | 0.399004i | ||||||
\(403\) | − | 8.00000i | − | 0.398508i | ||||||
\(404\) | 10.0000 | 0.497519 | ||||||||
\(405\) | 1.00000 | + | 2.00000i | 0.0496904 | + | 0.0993808i | ||||
\(406\) | −6.00000 | −0.297775 | ||||||||
\(407\) | 12.0000i | 0.594818i | ||||||||
\(408\) | − | 6.00000i | − | 0.297044i | ||||||
\(409\) | −26.0000 | −1.28562 | −0.642809 | − | 0.766027i | \(-0.722231\pi\) | ||||
−0.642809 | + | 0.766027i | \(0.722231\pi\) | |||||||
\(410\) | 4.00000 | − | 2.00000i | 0.197546 | − | 0.0987730i | ||||
\(411\) | −6.00000 | −0.295958 | ||||||||
\(412\) | − | 8.00000i | − | 0.394132i | ||||||
\(413\) | − | 12.0000i | − | 0.590481i | ||||||
\(414\) | −2.00000 | −0.0982946 | ||||||||
\(415\) | −24.0000 | + | 12.0000i | −1.17811 | + | 0.589057i | ||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | − | 16.0000i | − | 0.783523i | ||||||
\(418\) | 8.00000i | 0.391293i | ||||||||
\(419\) | 10.0000 | 0.488532 | 0.244266 | − | 0.969708i | \(-0.421453\pi\) | ||||
0.244266 | + | 0.969708i | \(0.421453\pi\) | |||||||
\(420\) | 1.00000 | + | 2.00000i | 0.0487950 | + | 0.0975900i | ||||
\(421\) | −36.0000 | −1.75453 | −0.877266 | − | 0.480004i | \(-0.840635\pi\) | ||||
−0.877266 | + | 0.480004i | \(0.840635\pi\) | |||||||
\(422\) | 20.0000i | 0.973585i | ||||||||
\(423\) | − | 2.00000i | − | 0.0972433i | ||||||
\(424\) | 4.00000 | 0.194257 | ||||||||
\(425\) | −24.0000 | − | 18.0000i | −1.16417 | − | 0.873128i | ||||
\(426\) | 4.00000 | 0.193801 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 8.00000i | − | 0.386695i | ||||||
\(429\) | 2.00000 | 0.0965609 | ||||||||
\(430\) | −6.00000 | − | 12.0000i | −0.289346 | − | 0.578691i | ||||
\(431\) | 12.0000 | 0.578020 | 0.289010 | − | 0.957326i | \(-0.406674\pi\) | ||||
0.289010 | + | 0.957326i | \(0.406674\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | − | 26.0000i | − | 1.24948i | −0.780833 | − | 0.624740i | \(-0.785205\pi\) | ||
0.780833 | − | 0.624740i | \(-0.214795\pi\) | |||||||
\(434\) | 8.00000 | 0.384012 | ||||||||
\(435\) | 12.0000 | − | 6.00000i | 0.575356 | − | 0.287678i | ||||
\(436\) | 16.0000 | 0.766261 | ||||||||
\(437\) | − | 8.00000i | − | 0.382692i | ||||||
\(438\) | − | 4.00000i | − | 0.191127i | ||||||
\(439\) | −2.00000 | −0.0954548 | −0.0477274 | − | 0.998860i | \(-0.515198\pi\) | ||||
−0.0477274 | + | 0.998860i | \(0.515198\pi\) | |||||||
\(440\) | −4.00000 | + | 2.00000i | −0.190693 | + | 0.0953463i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | − | 6.00000i | − | 0.285391i | ||||||
\(443\) | − | 12.0000i | − | 0.570137i | −0.958507 | − | 0.285069i | \(-0.907984\pi\) | ||
0.958507 | − | 0.285069i | \(-0.0920164\pi\) | |||||||
\(444\) | 6.00000 | 0.284747 | ||||||||
\(445\) | 10.0000 | + | 20.0000i | 0.474045 | + | 0.948091i | ||||
\(446\) | 12.0000 | 0.568216 | ||||||||
\(447\) | − | 10.0000i | − | 0.472984i | ||||||
\(448\) | − | 1.00000i | − | 0.0472456i | ||||||
\(449\) | 16.0000 | 0.755087 | 0.377543 | − | 0.925992i | \(-0.376769\pi\) | ||||
0.377543 | + | 0.925992i | \(0.376769\pi\) | |||||||
\(450\) | −4.00000 | − | 3.00000i | −0.188562 | − | 0.141421i | ||||
\(451\) | 4.00000 | 0.188353 | ||||||||
\(452\) | − | 6.00000i | − | 0.282216i | ||||||
\(453\) | 2.00000i | 0.0939682i | ||||||||
\(454\) | 8.00000 | 0.375459 | ||||||||
\(455\) | 1.00000 | + | 2.00000i | 0.0468807 | + | 0.0937614i | ||||
\(456\) | 4.00000 | 0.187317 | ||||||||
\(457\) | 22.0000i | 1.02912i | 0.857455 | + | 0.514558i | \(0.172044\pi\) | ||||
−0.857455 | + | 0.514558i | \(0.827956\pi\) | |||||||
\(458\) | − | 26.0000i | − | 1.21490i | ||||||
\(459\) | 6.00000 | 0.280056 | ||||||||
\(460\) | 4.00000 | − | 2.00000i | 0.186501 | − | 0.0932505i | ||||
\(461\) | −18.0000 | −0.838344 | −0.419172 | − | 0.907907i | \(-0.637680\pi\) | ||||
−0.419172 | + | 0.907907i | \(0.637680\pi\) | |||||||
\(462\) | 2.00000i | 0.0930484i | ||||||||
\(463\) | 16.0000i | 0.743583i | 0.928316 | + | 0.371792i | \(0.121256\pi\) | ||||
−0.928316 | + | 0.371792i | \(0.878744\pi\) | |||||||
\(464\) | −6.00000 | −0.278543 | ||||||||
\(465\) | −16.0000 | + | 8.00000i | −0.741982 | + | 0.370991i | ||||
\(466\) | 10.0000 | 0.463241 | ||||||||
\(467\) | 4.00000i | 0.185098i | 0.995708 | + | 0.0925490i | \(0.0295015\pi\) | ||||
−0.995708 | + | 0.0925490i | \(0.970499\pi\) | |||||||
\(468\) | − | 1.00000i | − | 0.0462250i | ||||||
\(469\) | 8.00000 | 0.369406 | ||||||||
\(470\) | 2.00000 | + | 4.00000i | 0.0922531 | + | 0.184506i | ||||
\(471\) | −2.00000 | −0.0921551 | ||||||||
\(472\) | − | 12.0000i | − | 0.552345i | ||||||
\(473\) | − | 12.0000i | − | 0.551761i | ||||||
\(474\) | −8.00000 | −0.367452 | ||||||||
\(475\) | 12.0000 | − | 16.0000i | 0.550598 | − | 0.734130i | ||||
\(476\) | 6.00000 | 0.275010 | ||||||||
\(477\) | 4.00000i | 0.183147i | ||||||||
\(478\) | − | 4.00000i | − | 0.182956i | ||||||
\(479\) | 32.0000 | 1.46212 | 0.731059 | − | 0.682315i | \(-0.239027\pi\) | ||||
0.731059 | + | 0.682315i | \(0.239027\pi\) | |||||||
\(480\) | 1.00000 | + | 2.00000i | 0.0456435 | + | 0.0912871i | ||||
\(481\) | 6.00000 | 0.273576 | ||||||||
\(482\) | − | 14.0000i | − | 0.637683i | ||||||
\(483\) | − | 2.00000i | − | 0.0910032i | ||||||
\(484\) | 7.00000 | 0.318182 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 8.00000i | 0.362515i | 0.983436 | + | 0.181257i | \(0.0580167\pi\) | ||||
−0.983436 | + | 0.181257i | \(0.941983\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.0000 | −0.723545 | ||||||||
\(490\) | −2.00000 | + | 1.00000i | −0.0903508 | + | 0.0451754i | ||||
\(491\) | 20.0000 | 0.902587 | 0.451294 | − | 0.892375i | \(-0.350963\pi\) | ||||
0.451294 | + | 0.892375i | \(0.350963\pi\) | |||||||
\(492\) | − | 2.00000i | − | 0.0901670i | ||||||
\(493\) | − | 36.0000i | − | 1.62136i | ||||||
\(494\) | 4.00000 | 0.179969 | ||||||||
\(495\) | −2.00000 | − | 4.00000i | −0.0898933 | − | 0.179787i | ||||
\(496\) | 8.00000 | 0.359211 | ||||||||
\(497\) | 4.00000i | 0.179425i | ||||||||
\(498\) | 12.0000i | 0.537733i | ||||||||
\(499\) | 32.0000 | 1.43252 | 0.716258 | − | 0.697835i | \(-0.245853\pi\) | ||||
0.716258 | + | 0.697835i | \(0.245853\pi\) | |||||||
\(500\) | 11.0000 | + | 2.00000i | 0.491935 | + | 0.0894427i | ||||
\(501\) | 18.0000 | 0.804181 | ||||||||
\(502\) | − | 30.0000i | − | 1.33897i | ||||||
\(503\) | − | 32.0000i | − | 1.42681i | −0.700752 | − | 0.713405i | \(-0.747152\pi\) | ||
0.700752 | − | 0.713405i | \(-0.252848\pi\) | |||||||
\(504\) | 1.00000 | 0.0445435 | ||||||||
\(505\) | −10.0000 | − | 20.0000i | −0.444994 | − | 0.889988i | ||||
\(506\) | 4.00000 | 0.177822 | ||||||||
\(507\) | − | 1.00000i | − | 0.0444116i | ||||||
\(508\) | − | 16.0000i | − | 0.709885i | ||||||
\(509\) | 30.0000 | 1.32973 | 0.664863 | − | 0.746965i | \(-0.268490\pi\) | ||||
0.664863 | + | 0.746965i | \(0.268490\pi\) | |||||||
\(510\) | −12.0000 | + | 6.00000i | −0.531369 | + | 0.265684i | ||||
\(511\) | 4.00000 | 0.176950 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 4.00000i | 0.176604i | ||||||||
\(514\) | −30.0000 | −1.32324 | ||||||||
\(515\) | −16.0000 | + | 8.00000i | −0.705044 | + | 0.352522i | ||||
\(516\) | −6.00000 | −0.264135 | ||||||||
\(517\) | 4.00000i | 0.175920i | ||||||||
\(518\) | 6.00000i | 0.263625i | ||||||||
\(519\) | 2.00000 | 0.0877903 | ||||||||
\(520\) | 1.00000 | + | 2.00000i | 0.0438529 | + | 0.0877058i | ||||
\(521\) | −36.0000 | −1.57719 | −0.788594 | − | 0.614914i | \(-0.789191\pi\) | ||||
−0.788594 | + | 0.614914i | \(0.789191\pi\) | |||||||
\(522\) | − | 6.00000i | − | 0.262613i | ||||||
\(523\) | 12.0000i | 0.524723i | 0.964970 | + | 0.262362i | \(0.0845013\pi\) | ||||
−0.964970 | + | 0.262362i | \(0.915499\pi\) | |||||||
\(524\) | −18.0000 | −0.786334 | ||||||||
\(525\) | 3.00000 | − | 4.00000i | 0.130931 | − | 0.174574i | ||||
\(526\) | 26.0000 | 1.13365 | ||||||||
\(527\) | 48.0000i | 2.09091i | ||||||||
\(528\) | 2.00000i | 0.0870388i | ||||||||
\(529\) | 19.0000 | 0.826087 | ||||||||
\(530\) | −4.00000 | − | 8.00000i | −0.173749 | − | 0.347498i | ||||
\(531\) | 12.0000 | 0.520756 | ||||||||
\(532\) | 4.00000i | 0.173422i | ||||||||
\(533\) | − | 2.00000i | − | 0.0866296i | ||||||
\(534\) | 10.0000 | 0.432742 | ||||||||
\(535\) | −16.0000 | + | 8.00000i | −0.691740 | + | 0.345870i | ||||
\(536\) | 8.00000 | 0.345547 | ||||||||
\(537\) | 20.0000i | 0.863064i | ||||||||
\(538\) | − | 2.00000i | − | 0.0862261i | ||||||
\(539\) | −2.00000 | −0.0861461 | ||||||||
\(540\) | −2.00000 | + | 1.00000i | −0.0860663 | + | 0.0430331i | ||||
\(541\) | 32.0000 | 1.37579 | 0.687894 | − | 0.725811i | \(-0.258536\pi\) | ||||
0.687894 | + | 0.725811i | \(0.258536\pi\) | |||||||
\(542\) | − | 20.0000i | − | 0.859074i | ||||||
\(543\) | − | 8.00000i | − | 0.343313i | ||||||
\(544\) | 6.00000 | 0.257248 | ||||||||
\(545\) | −16.0000 | − | 32.0000i | −0.685365 | − | 1.37073i | ||||
\(546\) | 1.00000 | 0.0427960 | ||||||||
\(547\) | − | 30.0000i | − | 1.28271i | −0.767245 | − | 0.641354i | \(-0.778373\pi\) | ||
0.767245 | − | 0.641354i | \(-0.221627\pi\) | |||||||
\(548\) | − | 6.00000i | − | 0.256307i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 8.00000 | + | 6.00000i | 0.341121 | + | 0.255841i | ||||
\(551\) | 24.0000 | 1.02243 | ||||||||
\(552\) | − | 2.00000i | − | 0.0851257i | ||||||
\(553\) | − | 8.00000i | − | 0.340195i | ||||||
\(554\) | 2.00000 | 0.0849719 | ||||||||
\(555\) | −6.00000 | − | 12.0000i | −0.254686 | − | 0.509372i | ||||
\(556\) | 16.0000 | 0.678551 | ||||||||
\(557\) | 2.00000i | 0.0847427i | 0.999102 | + | 0.0423714i | \(0.0134913\pi\) | ||||
−0.999102 | + | 0.0423714i | \(0.986509\pi\) | |||||||
\(558\) | 8.00000i | 0.338667i | ||||||||
\(559\) | −6.00000 | −0.253773 | ||||||||
\(560\) | −2.00000 | + | 1.00000i | −0.0845154 | + | 0.0422577i | ||||
\(561\) | −12.0000 | −0.506640 | ||||||||
\(562\) | 20.0000i | 0.843649i | ||||||||
\(563\) | 36.0000i | 1.51722i | 0.651546 | + | 0.758610i | \(0.274121\pi\) | ||||
−0.651546 | + | 0.758610i | \(0.725879\pi\) | |||||||
\(564\) | 2.00000 | 0.0842152 | ||||||||
\(565\) | −12.0000 | + | 6.00000i | −0.504844 | + | 0.252422i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | 4.00000i | 0.167836i | ||||||||
\(569\) | 6.00000 | 0.251533 | 0.125767 | − | 0.992060i | \(-0.459861\pi\) | ||||
0.125767 | + | 0.992060i | \(0.459861\pi\) | |||||||
\(570\) | −4.00000 | − | 8.00000i | −0.167542 | − | 0.335083i | ||||
\(571\) | 44.0000 | 1.84134 | 0.920671 | − | 0.390339i | \(-0.127642\pi\) | ||||
0.920671 | + | 0.390339i | \(0.127642\pi\) | |||||||
\(572\) | 2.00000i | 0.0836242i | ||||||||
\(573\) | − | 8.00000i | − | 0.334205i | ||||||
\(574\) | 2.00000 | 0.0834784 | ||||||||
\(575\) | −8.00000 | − | 6.00000i | −0.333623 | − | 0.250217i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | − | 24.0000i | − | 0.999133i | −0.866276 | − | 0.499567i | \(-0.833493\pi\) | ||
0.866276 | − | 0.499567i | \(-0.166507\pi\) | |||||||
\(578\) | 19.0000i | 0.790296i | ||||||||
\(579\) | −2.00000 | −0.0831172 | ||||||||
\(580\) | 6.00000 | + | 12.0000i | 0.249136 | + | 0.498273i | ||||
\(581\) | −12.0000 | −0.497844 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 8.00000i | − | 0.331326i | ||||||
\(584\) | 4.00000 | 0.165521 | ||||||||
\(585\) | −2.00000 | + | 1.00000i | −0.0826898 | + | 0.0413449i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 8.00000i | − | 0.330195i | −0.986277 | − | 0.165098i | \(-0.947206\pi\) | ||
0.986277 | − | 0.165098i | \(-0.0527939\pi\) | |||||||
\(588\) | 1.00000i | 0.0412393i | ||||||||
\(589\) | −32.0000 | −1.31854 | ||||||||
\(590\) | −24.0000 | + | 12.0000i | −0.988064 | + | 0.494032i | ||||
\(591\) | 22.0000 | 0.904959 | ||||||||
\(592\) | 6.00000i | 0.246598i | ||||||||
\(593\) | − | 18.0000i | − | 0.739171i | −0.929197 | − | 0.369586i | \(-0.879500\pi\) | ||
0.929197 | − | 0.369586i | \(-0.120500\pi\) | |||||||
\(594\) | −2.00000 | −0.0820610 | ||||||||
\(595\) | −6.00000 | − | 12.0000i | −0.245976 | − | 0.491952i | ||||
\(596\) | 10.0000 | 0.409616 | ||||||||
\(597\) | − | 6.00000i | − | 0.245564i | ||||||
\(598\) | − | 2.00000i | − | 0.0817861i | ||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 3.00000 | − | 4.00000i | 0.122474 | − | 0.163299i | ||||
\(601\) | −2.00000 | −0.0815817 | −0.0407909 | − | 0.999168i | \(-0.512988\pi\) | ||||
−0.0407909 | + | 0.999168i | \(0.512988\pi\) | |||||||
\(602\) | − | 6.00000i | − | 0.244542i | ||||||
\(603\) | 8.00000i | 0.325785i | ||||||||
\(604\) | −2.00000 | −0.0813788 | ||||||||
\(605\) | −7.00000 | − | 14.0000i | −0.284590 | − | 0.569181i | ||||
\(606\) | −10.0000 | −0.406222 | ||||||||
\(607\) | 32.0000i | 1.29884i | 0.760430 | + | 0.649420i | \(0.224988\pi\) | ||||
−0.760430 | + | 0.649420i | \(0.775012\pi\) | |||||||
\(608\) | 4.00000i | 0.162221i | ||||||||
\(609\) | 6.00000 | 0.243132 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.00000 | 0.0809113 | ||||||||
\(612\) | 6.00000i | 0.242536i | ||||||||
\(613\) | − | 42.0000i | − | 1.69636i | −0.529705 | − | 0.848182i | \(-0.677697\pi\) | ||
0.529705 | − | 0.848182i | \(-0.322303\pi\) | |||||||
\(614\) | 2.00000 | 0.0807134 | ||||||||
\(615\) | −4.00000 | + | 2.00000i | −0.161296 | + | 0.0806478i | ||||
\(616\) | −2.00000 | −0.0805823 | ||||||||
\(617\) | 6.00000i | 0.241551i | 0.992680 | + | 0.120775i | \(0.0385381\pi\) | ||||
−0.992680 | + | 0.120775i | \(0.961462\pi\) | |||||||
\(618\) | 8.00000i | 0.321807i | ||||||||
\(619\) | −28.0000 | −1.12542 | −0.562708 | − | 0.826656i | \(-0.690240\pi\) | ||||
−0.562708 | + | 0.826656i | \(0.690240\pi\) | |||||||
\(620\) | −8.00000 | − | 16.0000i | −0.321288 | − | 0.642575i | ||||
\(621\) | 2.00000 | 0.0802572 | ||||||||
\(622\) | − | 24.0000i | − | 0.962312i | ||||||
\(623\) | 10.0000i | 0.400642i | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | −2.00000 | −0.0799361 | ||||||||
\(627\) | − | 8.00000i | − | 0.319489i | ||||||
\(628\) | − | 2.00000i | − | 0.0798087i | ||||||
\(629\) | −36.0000 | −1.43541 | ||||||||
\(630\) | −1.00000 | − | 2.00000i | −0.0398410 | − | 0.0796819i | ||||
\(631\) | −34.0000 | −1.35352 | −0.676759 | − | 0.736204i | \(-0.736616\pi\) | ||||
−0.676759 | + | 0.736204i | \(0.736616\pi\) | |||||||
\(632\) | − | 8.00000i | − | 0.318223i | ||||||
\(633\) | − | 20.0000i | − | 0.794929i | ||||||
\(634\) | 22.0000 | 0.873732 | ||||||||
\(635\) | −32.0000 | + | 16.0000i | −1.26988 | + | 0.634941i | ||||
\(636\) | −4.00000 | −0.158610 | ||||||||
\(637\) | 1.00000i | 0.0396214i | ||||||||
\(638\) | 12.0000i | 0.475085i | ||||||||
\(639\) | −4.00000 | −0.158238 | ||||||||
\(640\) | −2.00000 | + | 1.00000i | −0.0790569 | + | 0.0395285i | ||||
\(641\) | −6.00000 | −0.236986 | −0.118493 | − | 0.992955i | \(-0.537806\pi\) | ||||
−0.118493 | + | 0.992955i | \(0.537806\pi\) | |||||||
\(642\) | 8.00000i | 0.315735i | ||||||||
\(643\) | − | 18.0000i | − | 0.709851i | −0.934895 | − | 0.354925i | \(-0.884506\pi\) | ||
0.934895 | − | 0.354925i | \(-0.115494\pi\) | |||||||
\(644\) | 2.00000 | 0.0788110 | ||||||||
\(645\) | 6.00000 | + | 12.0000i | 0.236250 | + | 0.472500i | ||||
\(646\) | −24.0000 | −0.944267 | ||||||||
\(647\) | − | 36.0000i | − | 1.41531i | −0.706560 | − | 0.707653i | \(-0.749754\pi\) | ||
0.706560 | − | 0.707653i | \(-0.250246\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | −24.0000 | −0.942082 | ||||||||
\(650\) | 3.00000 | − | 4.00000i | 0.117670 | − | 0.156893i | ||||
\(651\) | −8.00000 | −0.313545 | ||||||||
\(652\) | − | 16.0000i | − | 0.626608i | ||||||
\(653\) | 24.0000i | 0.939193i | 0.882881 | + | 0.469596i | \(0.155601\pi\) | ||||
−0.882881 | + | 0.469596i | \(0.844399\pi\) | |||||||
\(654\) | −16.0000 | −0.625650 | ||||||||
\(655\) | 18.0000 | + | 36.0000i | 0.703318 | + | 1.40664i | ||||
\(656\) | 2.00000 | 0.0780869 | ||||||||
\(657\) | 4.00000i | 0.156055i | ||||||||
\(658\) | 2.00000i | 0.0779681i | ||||||||
\(659\) | 36.0000 | 1.40236 | 0.701180 | − | 0.712984i | \(-0.252657\pi\) | ||||
0.701180 | + | 0.712984i | \(0.252657\pi\) | |||||||
\(660\) | 4.00000 | − | 2.00000i | 0.155700 | − | 0.0778499i | ||||
\(661\) | 18.0000 | 0.700119 | 0.350059 | − | 0.936727i | \(-0.386161\pi\) | ||||
0.350059 | + | 0.936727i | \(0.386161\pi\) | |||||||
\(662\) | 8.00000i | 0.310929i | ||||||||
\(663\) | 6.00000i | 0.233021i | ||||||||
\(664\) | −12.0000 | −0.465690 | ||||||||
\(665\) | 8.00000 | − | 4.00000i | 0.310227 | − | 0.155113i | ||||
\(666\) | −6.00000 | −0.232495 | ||||||||
\(667\) | − | 12.0000i | − | 0.464642i | ||||||
\(668\) | 18.0000i | 0.696441i | ||||||||
\(669\) | −12.0000 | −0.463947 | ||||||||
\(670\) | −8.00000 | − | 16.0000i | −0.309067 | − | 0.618134i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 1.00000i | 0.0385758i | ||||||||
\(673\) | 32.0000i | 1.23351i | 0.787155 | + | 0.616755i | \(0.211553\pi\) | ||||
−0.787155 | + | 0.616755i | \(0.788447\pi\) | |||||||
\(674\) | 8.00000 | 0.308148 | ||||||||
\(675\) | 4.00000 | + | 3.00000i | 0.153960 | + | 0.115470i | ||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | − | 30.0000i | − | 1.15299i | −0.817099 | − | 0.576497i | \(-0.804419\pi\) | ||
0.817099 | − | 0.576497i | \(-0.195581\pi\) | |||||||
\(678\) | 6.00000i | 0.230429i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −6.00000 | − | 12.0000i | −0.230089 | − | 0.460179i | ||||
\(681\) | −8.00000 | −0.306561 | ||||||||
\(682\) | − | 16.0000i | − | 0.612672i | ||||||
\(683\) | 4.00000i | 0.153056i | 0.997067 | + | 0.0765279i | \(0.0243834\pi\) | ||||
−0.997067 | + | 0.0765279i | \(0.975617\pi\) | |||||||
\(684\) | −4.00000 | −0.152944 | ||||||||
\(685\) | −12.0000 | + | 6.00000i | −0.458496 | + | 0.229248i | ||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 26.0000i | 0.991962i | ||||||||
\(688\) | − | 6.00000i | − | 0.228748i | ||||||
\(689\) | −4.00000 | −0.152388 | ||||||||
\(690\) | −4.00000 | + | 2.00000i | −0.152277 | + | 0.0761387i | ||||
\(691\) | −12.0000 | −0.456502 | −0.228251 | − | 0.973602i | \(-0.573301\pi\) | ||||
−0.228251 | + | 0.973602i | \(0.573301\pi\) | |||||||
\(692\) | 2.00000i | 0.0760286i | ||||||||
\(693\) | − | 2.00000i | − | 0.0759737i | ||||||
\(694\) | −16.0000 | −0.607352 | ||||||||
\(695\) | −16.0000 | − | 32.0000i | −0.606915 | − | 1.21383i | ||||
\(696\) | 6.00000 | 0.227429 | ||||||||
\(697\) | 12.0000i | 0.454532i | ||||||||
\(698\) | − | 6.00000i | − | 0.227103i | ||||||
\(699\) | −10.0000 | −0.378235 | ||||||||
\(700\) | 4.00000 | + | 3.00000i | 0.151186 | + | 0.113389i | ||||
\(701\) | −14.0000 | −0.528773 | −0.264386 | − | 0.964417i | \(-0.585169\pi\) | ||||
−0.264386 | + | 0.964417i | \(0.585169\pi\) | |||||||
\(702\) | 1.00000i | 0.0377426i | ||||||||
\(703\) | − | 24.0000i | − | 0.905177i | ||||||
\(704\) | −2.00000 | −0.0753778 | ||||||||
\(705\) | −2.00000 | − | 4.00000i | −0.0753244 | − | 0.150649i | ||||
\(706\) | 10.0000 | 0.376355 | ||||||||
\(707\) | − | 10.0000i | − | 0.376089i | ||||||
\(708\) | 12.0000i | 0.450988i | ||||||||
\(709\) | −44.0000 | −1.65245 | −0.826227 | − | 0.563337i | \(-0.809517\pi\) | ||||
−0.826227 | + | 0.563337i | \(0.809517\pi\) | |||||||
\(710\) | 8.00000 | − | 4.00000i | 0.300235 | − | 0.150117i | ||||
\(711\) | 8.00000 | 0.300023 | ||||||||
\(712\) | 10.0000i | 0.374766i | ||||||||
\(713\) | 16.0000i | 0.599205i | ||||||||
\(714\) | −6.00000 | −0.224544 | ||||||||
\(715\) | 4.00000 | − | 2.00000i | 0.149592 | − | 0.0747958i | ||||
\(716\) | −20.0000 | −0.747435 | ||||||||
\(717\) | 4.00000i | 0.149383i | ||||||||
\(718\) | − | 24.0000i | − | 0.895672i | ||||||
\(719\) | 24.0000 | 0.895049 | 0.447524 | − | 0.894272i | \(-0.352306\pi\) | ||||
0.447524 | + | 0.894272i | \(0.352306\pi\) | |||||||
\(720\) | −1.00000 | − | 2.00000i | −0.0372678 | − | 0.0745356i | ||||
\(721\) | −8.00000 | −0.297936 | ||||||||
\(722\) | 3.00000i | 0.111648i | ||||||||
\(723\) | 14.0000i | 0.520666i | ||||||||
\(724\) | 8.00000 | 0.297318 | ||||||||
\(725\) | 18.0000 | − | 24.0000i | 0.668503 | − | 0.891338i | ||||
\(726\) | −7.00000 | −0.259794 | ||||||||
\(727\) | 16.0000i | 0.593407i | 0.954970 | + | 0.296704i | \(0.0958873\pi\) | ||||
−0.954970 | + | 0.296704i | \(0.904113\pi\) | |||||||
\(728\) | 1.00000i | 0.0370625i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −4.00000 | − | 8.00000i | −0.148047 | − | 0.296093i | ||||
\(731\) | 36.0000 | 1.33151 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 26.0000i | − | 0.960332i | −0.877178 | − | 0.480166i | \(-0.840576\pi\) | ||
0.877178 | − | 0.480166i | \(-0.159424\pi\) | |||||||
\(734\) | −8.00000 | −0.295285 | ||||||||
\(735\) | 2.00000 | − | 1.00000i | 0.0737711 | − | 0.0368856i | ||||
\(736\) | 2.00000 | 0.0737210 | ||||||||
\(737\) | − | 16.0000i | − | 0.589368i | ||||||
\(738\) | 2.00000i | 0.0736210i | ||||||||
\(739\) | 44.0000 | 1.61857 | 0.809283 | − | 0.587419i | \(-0.199856\pi\) | ||||
0.809283 | + | 0.587419i | \(0.199856\pi\) | |||||||
\(740\) | 12.0000 | − | 6.00000i | 0.441129 | − | 0.220564i | ||||
\(741\) | −4.00000 | −0.146944 | ||||||||
\(742\) | − | 4.00000i | − | 0.146845i | ||||||
\(743\) | 12.0000i | 0.440237i | 0.975473 | + | 0.220119i | \(0.0706445\pi\) | ||||
−0.975473 | + | 0.220119i | \(0.929356\pi\) | |||||||
\(744\) | −8.00000 | −0.293294 | ||||||||
\(745\) | −10.0000 | − | 20.0000i | −0.366372 | − | 0.732743i | ||||
\(746\) | 6.00000 | 0.219676 | ||||||||
\(747\) | − | 12.0000i | − | 0.439057i | ||||||
\(748\) | − | 12.0000i | − | 0.438763i | ||||||
\(749\) | −8.00000 | −0.292314 | ||||||||
\(750\) | −11.0000 | − | 2.00000i | −0.401663 | − | 0.0730297i | ||||
\(751\) | 40.0000 | 1.45962 | 0.729810 | − | 0.683650i | \(-0.239608\pi\) | ||||
0.729810 | + | 0.683650i | \(0.239608\pi\) | |||||||
\(752\) | 2.00000i | 0.0729325i | ||||||||
\(753\) | 30.0000i | 1.09326i | ||||||||
\(754\) | 6.00000 | 0.218507 | ||||||||
\(755\) | 2.00000 | + | 4.00000i | 0.0727875 | + | 0.145575i | ||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | 2.00000i | 0.0726912i | 0.999339 | + | 0.0363456i | \(0.0115717\pi\) | ||||
−0.999339 | + | 0.0363456i | \(0.988428\pi\) | |||||||
\(758\) | 20.0000i | 0.726433i | ||||||||
\(759\) | −4.00000 | −0.145191 | ||||||||
\(760\) | 8.00000 | − | 4.00000i | 0.290191 | − | 0.145095i | ||||
\(761\) | −26.0000 | −0.942499 | −0.471250 | − | 0.882000i | \(-0.656197\pi\) | ||||
−0.471250 | + | 0.882000i | \(0.656197\pi\) | |||||||
\(762\) | 16.0000i | 0.579619i | ||||||||
\(763\) | − | 16.0000i | − | 0.579239i | ||||||
\(764\) | 8.00000 | 0.289430 | ||||||||
\(765\) | 12.0000 | − | 6.00000i | 0.433861 | − | 0.216930i | ||||
\(766\) | 30.0000 | 1.08394 | ||||||||
\(767\) | 12.0000i | 0.433295i | ||||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | 10.0000 | 0.360609 | 0.180305 | − | 0.983611i | \(-0.442292\pi\) | ||||
0.180305 | + | 0.983611i | \(0.442292\pi\) | |||||||
\(770\) | 2.00000 | + | 4.00000i | 0.0720750 | + | 0.144150i | ||||
\(771\) | 30.0000 | 1.08042 | ||||||||
\(772\) | − | 2.00000i | − | 0.0719816i | ||||||
\(773\) | 40.0000i | 1.43870i | 0.694648 | + | 0.719350i | \(0.255560\pi\) | ||||
−0.694648 | + | 0.719350i | \(0.744440\pi\) | |||||||
\(774\) | 6.00000 | 0.215666 | ||||||||
\(775\) | −24.0000 | + | 32.0000i | −0.862105 | + | 1.14947i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 6.00000i | − | 0.215249i | ||||||
\(778\) | − | 38.0000i | − | 1.36237i | ||||||
\(779\) | −8.00000 | −0.286630 | ||||||||
\(780\) | −1.00000 | − | 2.00000i | −0.0358057 | − | 0.0716115i | ||||
\(781\) | 8.00000 | 0.286263 | ||||||||
\(782\) | 12.0000i | 0.429119i | ||||||||
\(783\) | 6.00000i | 0.214423i | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | −4.00000 | + | 2.00000i | −0.142766 | + | 0.0713831i | ||||
\(786\) | 18.0000 | 0.642039 | ||||||||
\(787\) | 22.0000i | 0.784215i | 0.919919 | + | 0.392108i | \(0.128254\pi\) | ||||
−0.919919 | + | 0.392108i | \(0.871746\pi\) | |||||||
\(788\) | 22.0000i | 0.783718i | ||||||||
\(789\) | −26.0000 | −0.925625 | ||||||||
\(790\) | −16.0000 | + | 8.00000i | −0.569254 | + | 0.284627i | ||||
\(791\) | −6.00000 | −0.213335 | ||||||||
\(792\) | − | 2.00000i | − | 0.0710669i | ||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −18.0000 | −0.638796 | ||||||||
\(795\) | 4.00000 | + | 8.00000i | 0.141865 | + | 0.283731i | ||||
\(796\) | 6.00000 | 0.212664 | ||||||||
\(797\) | − | 42.0000i | − | 1.48772i | −0.668338 | − | 0.743858i | \(-0.732994\pi\) | ||
0.668338 | − | 0.743858i | \(-0.267006\pi\) | |||||||
\(798\) | − | 4.00000i | − | 0.141598i | ||||||
\(799\) | −12.0000 | −0.424529 | ||||||||
\(800\) | 4.00000 | + | 3.00000i | 0.141421 | + | 0.106066i | ||||
\(801\) | −10.0000 | −0.353333 | ||||||||
\(802\) | − | 36.0000i | − | 1.27120i | ||||||
\(803\) | − | 8.00000i | − | 0.282314i | ||||||
\(804\) | −8.00000 | −0.282138 | ||||||||
\(805\) | −2.00000 | − | 4.00000i | −0.0704907 | − | 0.140981i | ||||
\(806\) | −8.00000 | −0.281788 | ||||||||
\(807\) | 2.00000i | 0.0704033i | ||||||||
\(808\) | − | 10.0000i | − | 0.351799i | ||||||
\(809\) | 30.0000 | 1.05474 | 0.527372 | − | 0.849635i | \(-0.323177\pi\) | ||||
0.527372 | + | 0.849635i | \(0.323177\pi\) | |||||||
\(810\) | 2.00000 | − | 1.00000i | 0.0702728 | − | 0.0351364i | ||||
\(811\) | −4.00000 | −0.140459 | −0.0702295 | − | 0.997531i | \(-0.522373\pi\) | ||||
−0.0702295 | + | 0.997531i | \(0.522373\pi\) | |||||||
\(812\) | 6.00000i | 0.210559i | ||||||||
\(813\) | 20.0000i | 0.701431i | ||||||||
\(814\) | 12.0000 | 0.420600 | ||||||||
\(815\) | −32.0000 | + | 16.0000i | −1.12091 | + | 0.560456i | ||||
\(816\) | −6.00000 | −0.210042 | ||||||||
\(817\) | 24.0000i | 0.839654i | ||||||||
\(818\) | 26.0000i | 0.909069i | ||||||||
\(819\) | −1.00000 | −0.0349428 | ||||||||
\(820\) | −2.00000 | − | 4.00000i | −0.0698430 | − | 0.139686i | ||||
\(821\) | 2.00000 | 0.0698005 | 0.0349002 | − | 0.999391i | \(-0.488889\pi\) | ||||
0.0349002 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(822\) | 6.00000i | 0.209274i | ||||||||
\(823\) | − | 8.00000i | − | 0.278862i | −0.990232 | − | 0.139431i | \(-0.955473\pi\) | ||
0.990232 | − | 0.139431i | \(-0.0445274\pi\) | |||||||
\(824\) | −8.00000 | −0.278693 | ||||||||
\(825\) | −8.00000 | − | 6.00000i | −0.278524 | − | 0.208893i | ||||
\(826\) | −12.0000 | −0.417533 | ||||||||
\(827\) | 20.0000i | 0.695468i | 0.937593 | + | 0.347734i | \(0.113049\pi\) | ||||
−0.937593 | + | 0.347734i | \(0.886951\pi\) | |||||||
\(828\) | 2.00000i | 0.0695048i | ||||||||
\(829\) | 32.0000 | 1.11141 | 0.555703 | − | 0.831381i | \(-0.312449\pi\) | ||||
0.555703 | + | 0.831381i | \(0.312449\pi\) | |||||||
\(830\) | 12.0000 | + | 24.0000i | 0.416526 | + | 0.833052i | ||||
\(831\) | −2.00000 | −0.0693792 | ||||||||
\(832\) | 1.00000i | 0.0346688i | ||||||||
\(833\) | − | 6.00000i | − | 0.207888i | ||||||
\(834\) | −16.0000 | −0.554035 | ||||||||
\(835\) | 36.0000 | − | 18.0000i | 1.24583 | − | 0.622916i | ||||
\(836\) | 8.00000 | 0.276686 | ||||||||
\(837\) | − | 8.00000i | − | 0.276520i | ||||||
\(838\) | − | 10.0000i | − | 0.345444i | ||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 2.00000 | − | 1.00000i | 0.0690066 | − | 0.0345033i | ||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 36.0000i | 1.24064i | ||||||||
\(843\) | − | 20.0000i | − | 0.688837i | ||||||
\(844\) | 20.0000 | 0.688428 | ||||||||
\(845\) | −1.00000 | − | 2.00000i | −0.0344010 | − | 0.0688021i | ||||
\(846\) | −2.00000 | −0.0687614 | ||||||||
\(847\) | − | 7.00000i | − | 0.240523i | ||||||
\(848\) | − | 4.00000i | − | 0.137361i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −18.0000 | + | 24.0000i | −0.617395 | + | 0.823193i | ||||
\(851\) | −12.0000 | −0.411355 | ||||||||
\(852\) | − | 4.00000i | − | 0.137038i | ||||||
\(853\) | 18.0000i | 0.616308i | 0.951336 | + | 0.308154i | \(0.0997113\pi\) | ||||
−0.951336 | + | 0.308154i | \(0.900289\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.00000 | + | 8.00000i | 0.136797 | + | 0.273594i | ||||
\(856\) | −8.00000 | −0.273434 | ||||||||
\(857\) | 26.0000i | 0.888143i | 0.895991 | + | 0.444072i | \(0.146466\pi\) | ||||
−0.895991 | + | 0.444072i | \(0.853534\pi\) | |||||||
\(858\) | − | 2.00000i | − | 0.0682789i | ||||||
\(859\) | 40.0000 | 1.36478 | 0.682391 | − | 0.730987i | \(-0.260940\pi\) | ||||
0.682391 | + | 0.730987i | \(0.260940\pi\) | |||||||
\(860\) | −12.0000 | + | 6.00000i | −0.409197 | + | 0.204598i | ||||
\(861\) | −2.00000 | −0.0681598 | ||||||||
\(862\) | − | 12.0000i | − | 0.408722i | ||||||
\(863\) | − | 48.0000i | − | 1.63394i | −0.576681 | − | 0.816970i | \(-0.695652\pi\) | ||
0.576681 | − | 0.816970i | \(-0.304348\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 4.00000 | − | 2.00000i | 0.136004 | − | 0.0680020i | ||||
\(866\) | −26.0000 | −0.883516 | ||||||||
\(867\) | − | 19.0000i | − | 0.645274i | ||||||
\(868\) | − | 8.00000i | − | 0.271538i | ||||||
\(869\) | −16.0000 | −0.542763 | ||||||||
\(870\) | −6.00000 | − | 12.0000i | −0.203419 | − | 0.406838i | ||||
\(871\) | −8.00000 | −0.271070 | ||||||||
\(872\) | − | 16.0000i | − | 0.541828i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −8.00000 | −0.270604 | ||||||||
\(875\) | 2.00000 | − | 11.0000i | 0.0676123 | − | 0.371868i | ||||
\(876\) | −4.00000 | −0.135147 | ||||||||
\(877\) | − | 2.00000i | − | 0.0675352i | −0.999430 | − | 0.0337676i | \(-0.989249\pi\) | ||
0.999430 | − | 0.0337676i | \(-0.0107506\pi\) | |||||||
\(878\) | 2.00000i | 0.0674967i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.00000 | + | 4.00000i | 0.0674200 | + | 0.134840i | ||||
\(881\) | 40.0000 | 1.34763 | 0.673817 | − | 0.738898i | \(-0.264654\pi\) | ||||
0.673817 | + | 0.738898i | \(0.264654\pi\) | |||||||
\(882\) | − | 1.00000i | − | 0.0336718i | ||||||
\(883\) | 14.0000i | 0.471138i | 0.971858 | + | 0.235569i | \(0.0756953\pi\) | ||||
−0.971858 | + | 0.235569i | \(0.924305\pi\) | |||||||
\(884\) | −6.00000 | −0.201802 | ||||||||
\(885\) | 24.0000 | − | 12.0000i | 0.806751 | − | 0.403376i | ||||
\(886\) | −12.0000 | −0.403148 | ||||||||
\(887\) | 20.0000i | 0.671534i | 0.941945 | + | 0.335767i | \(0.108996\pi\) | ||||
−0.941945 | + | 0.335767i | \(0.891004\pi\) | |||||||
\(888\) | − | 6.00000i | − | 0.201347i | ||||||
\(889\) | −16.0000 | −0.536623 | ||||||||
\(890\) | 20.0000 | − | 10.0000i | 0.670402 | − | 0.335201i | ||||
\(891\) | 2.00000 | 0.0670025 | ||||||||
\(892\) | − | 12.0000i | − | 0.401790i | ||||||
\(893\) | − | 8.00000i | − | 0.267710i | ||||||
\(894\) | −10.0000 | −0.334450 | ||||||||
\(895\) | 20.0000 | + | 40.0000i | 0.668526 | + | 1.33705i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 2.00000i | 0.0667781i | ||||||||
\(898\) | − | 16.0000i | − | 0.533927i | ||||||
\(899\) | −48.0000 | −1.60089 | ||||||||
\(900\) | −3.00000 | + | 4.00000i | −0.100000 | + | 0.133333i | ||||
\(901\) | 24.0000 | 0.799556 | ||||||||
\(902\) | − | 4.00000i | − | 0.133185i | ||||||
\(903\) | 6.00000i | 0.199667i | ||||||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | −8.00000 | − | 16.0000i | −0.265929 | − | 0.531858i | ||||
\(906\) | 2.00000 | 0.0664455 | ||||||||
\(907\) | 6.00000i | 0.199227i | 0.995026 | + | 0.0996134i | \(0.0317606\pi\) | ||||
−0.995026 | + | 0.0996134i | \(0.968239\pi\) | |||||||
\(908\) | − | 8.00000i | − | 0.265489i | ||||||
\(909\) | 10.0000 | 0.331679 | ||||||||
\(910\) | 2.00000 | − | 1.00000i | 0.0662994 | − | 0.0331497i | ||||
\(911\) | 16.0000 | 0.530104 | 0.265052 | − | 0.964234i | \(-0.414611\pi\) | ||||
0.265052 | + | 0.964234i | \(0.414611\pi\) | |||||||
\(912\) | − | 4.00000i | − | 0.132453i | ||||||
\(913\) | 24.0000i | 0.794284i | ||||||||
\(914\) | 22.0000 | 0.727695 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −26.0000 | −0.859064 | ||||||||
\(917\) | 18.0000i | 0.594412i | ||||||||
\(918\) | − | 6.00000i | − | 0.198030i | ||||||
\(919\) | −40.0000 | −1.31948 | −0.659739 | − | 0.751495i | \(-0.729333\pi\) | ||||
−0.659739 | + | 0.751495i | \(0.729333\pi\) | |||||||
\(920\) | −2.00000 | − | 4.00000i | −0.0659380 | − | 0.131876i | ||||
\(921\) | −2.00000 | −0.0659022 | ||||||||
\(922\) | 18.0000i | 0.592798i | ||||||||
\(923\) | − | 4.00000i | − | 0.131662i | ||||||
\(924\) | 2.00000 | 0.0657952 | ||||||||
\(925\) | −24.0000 | − | 18.0000i | −0.789115 | − | 0.591836i | ||||
\(926\) | 16.0000 | 0.525793 | ||||||||
\(927\) | − | 8.00000i | − | 0.262754i | ||||||
\(928\) | 6.00000i | 0.196960i | ||||||||
\(929\) | −30.0000 | −0.984268 | −0.492134 | − | 0.870519i | \(-0.663783\pi\) | ||||
−0.492134 | + | 0.870519i | \(0.663783\pi\) | |||||||
\(930\) | 8.00000 | + | 16.0000i | 0.262330 | + | 0.524661i | ||||
\(931\) | 4.00000 | 0.131095 | ||||||||
\(932\) | − | 10.0000i | − | 0.327561i | ||||||
\(933\) | 24.0000i | 0.785725i | ||||||||
\(934\) | 4.00000 | 0.130884 | ||||||||
\(935\) | −24.0000 | + | 12.0000i | −0.784884 | + | 0.392442i | ||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | − | 6.00000i | − | 0.196011i | −0.995186 | − | 0.0980057i | \(-0.968754\pi\) | ||
0.995186 | − | 0.0980057i | \(-0.0312463\pi\) | |||||||
\(938\) | − | 8.00000i | − | 0.261209i | ||||||
\(939\) | 2.00000 | 0.0652675 | ||||||||
\(940\) | 4.00000 | − | 2.00000i | 0.130466 | − | 0.0652328i | ||||
\(941\) | −30.0000 | −0.977972 | −0.488986 | − | 0.872292i | \(-0.662633\pi\) | ||||
−0.488986 | + | 0.872292i | \(0.662633\pi\) | |||||||
\(942\) | 2.00000i | 0.0651635i | ||||||||
\(943\) | 4.00000i | 0.130258i | ||||||||
\(944\) | −12.0000 | −0.390567 | ||||||||
\(945\) | 1.00000 | + | 2.00000i | 0.0325300 | + | 0.0650600i | ||||
\(946\) | −12.0000 | −0.390154 | ||||||||
\(947\) | 12.0000i | 0.389948i | 0.980808 | + | 0.194974i | \(0.0624622\pi\) | ||||
−0.980808 | + | 0.194974i | \(0.937538\pi\) | |||||||
\(948\) | 8.00000i | 0.259828i | ||||||||
\(949\) | −4.00000 | −0.129845 | ||||||||
\(950\) | −16.0000 | − | 12.0000i | −0.519109 | − | 0.389331i | ||||
\(951\) | −22.0000 | −0.713399 | ||||||||
\(952\) | − | 6.00000i | − | 0.194461i | ||||||
\(953\) | − | 30.0000i | − | 0.971795i | −0.874016 | − | 0.485898i | \(-0.838493\pi\) | ||
0.874016 | − | 0.485898i | \(-0.161507\pi\) | |||||||
\(954\) | 4.00000 | 0.129505 | ||||||||
\(955\) | −8.00000 | − | 16.0000i | −0.258874 | − | 0.517748i | ||||
\(956\) | −4.00000 | −0.129369 | ||||||||
\(957\) | − | 12.0000i | − | 0.387905i | ||||||
\(958\) | − | 32.0000i | − | 1.03387i | ||||||
\(959\) | −6.00000 | −0.193750 | ||||||||
\(960\) | 2.00000 | − | 1.00000i | 0.0645497 | − | 0.0322749i | ||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | − | 6.00000i | − | 0.193448i | ||||||
\(963\) | − | 8.00000i | − | 0.257796i | ||||||
\(964\) | −14.0000 | −0.450910 | ||||||||
\(965\) | −4.00000 | + | 2.00000i | −0.128765 | + | 0.0643823i | ||||
\(966\) | −2.00000 | −0.0643489 | ||||||||
\(967\) | 24.0000i | 0.771788i | 0.922543 | + | 0.385894i | \(0.126107\pi\) | ||||
−0.922543 | + | 0.385894i | \(0.873893\pi\) | |||||||
\(968\) | − | 7.00000i | − | 0.224989i | ||||||
\(969\) | 24.0000 | 0.770991 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 46.0000 | 1.47621 | 0.738105 | − | 0.674686i | \(-0.235721\pi\) | ||||
0.738105 | + | 0.674686i | \(0.235721\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | − | 16.0000i | − | 0.512936i | ||||||
\(974\) | 8.00000 | 0.256337 | ||||||||
\(975\) | −3.00000 | + | 4.00000i | −0.0960769 | + | 0.128103i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.0000i | 0.575871i | 0.957650 | + | 0.287936i | \(0.0929689\pi\) | ||||
−0.957650 | + | 0.287936i | \(0.907031\pi\) | |||||||
\(978\) | 16.0000i | 0.511624i | ||||||||
\(979\) | 20.0000 | 0.639203 | ||||||||
\(980\) | 1.00000 | + | 2.00000i | 0.0319438 | + | 0.0638877i | ||||
\(981\) | 16.0000 | 0.510841 | ||||||||
\(982\) | − | 20.0000i | − | 0.638226i | ||||||
\(983\) | − | 26.0000i | − | 0.829271i | −0.909988 | − | 0.414636i | \(-0.863909\pi\) | ||
0.909988 | − | 0.414636i | \(-0.136091\pi\) | |||||||
\(984\) | −2.00000 | −0.0637577 | ||||||||
\(985\) | 44.0000 | − | 22.0000i | 1.40196 | − | 0.700978i | ||||
\(986\) | −36.0000 | −1.14647 | ||||||||
\(987\) | − | 2.00000i | − | 0.0636607i | ||||||
\(988\) | − | 4.00000i | − | 0.127257i | ||||||
\(989\) | 12.0000 | 0.381578 | ||||||||
\(990\) | −4.00000 | + | 2.00000i | −0.127128 | + | 0.0635642i | ||||
\(991\) | 24.0000 | 0.762385 | 0.381193 | − | 0.924496i | \(-0.375513\pi\) | ||||
0.381193 | + | 0.924496i | \(0.375513\pi\) | |||||||
\(992\) | − | 8.00000i | − | 0.254000i | ||||||
\(993\) | − | 8.00000i | − | 0.253872i | ||||||
\(994\) | 4.00000 | 0.126872 | ||||||||
\(995\) | −6.00000 | − | 12.0000i | −0.190213 | − | 0.380426i | ||||
\(996\) | 12.0000 | 0.380235 | ||||||||
\(997\) | 42.0000i | 1.33015i | 0.746775 | + | 0.665077i | \(0.231601\pi\) | ||||
−0.746775 | + | 0.665077i | \(0.768399\pi\) | |||||||
\(998\) | − | 32.0000i | − | 1.01294i | ||||||
\(999\) | 6.00000 | 0.189832 |
(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 | 2730.2.l.k.1639.1 | ✓ | 2 | |
5.4 | even | 2 | inner | 2730.2.l.k.1639.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2730.2.l.k.1639.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
2730.2.l.k.1639.2 | yes | 2 | 5.4 | even | 2 | inner |