Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(271,1008)]
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([3, 0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.271");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.cs (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 271.1 | ||
Root | \(1.32288 - 2.29129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.271 |
Dual form | 1008.2.cs.q.703.1 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.50000 | + | 0.866025i | 0.670820 | + | 0.387298i | 0.796387 | − | 0.604787i | \(-0.206742\pi\) |
−0.125567 | + | 0.992085i | \(0.540075\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.64575 | −1.00000 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.96863 | + | 2.29129i | −1.19659 | + | 0.690849i | −0.959792 | − | 0.280711i | \(-0.909430\pi\) |
−0.236794 | + | 0.971560i | \(0.576097\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.46410i | − | 0.960769i | −0.877058 | − | 0.480384i | \(-0.840497\pi\) | ||
0.877058 | − | 0.480384i | \(-0.159503\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.50000 | + | 2.59808i | −1.09141 | + | 0.630126i | −0.933952 | − | 0.357400i | \(-0.883663\pi\) |
−0.157459 | + | 0.987526i | \(0.550330\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.32288 | + | 2.29129i | −0.303488 | + | 0.525657i | −0.976924 | − | 0.213589i | \(-0.931485\pi\) |
0.673435 | + | 0.739246i | \(0.264818\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.96863 | − | 2.29129i | −0.827516 | − | 0.477767i | 0.0254855 | − | 0.999675i | \(-0.491887\pi\) |
−0.853001 | + | 0.521909i | \(0.825220\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | − | 1.73205i | −0.200000 | − | 0.346410i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.32288 | + | 2.29129i | 0.237595 | + | 0.411527i | 0.960024 | − | 0.279918i | \(-0.0903074\pi\) |
−0.722428 | + | 0.691446i | \(0.756974\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.96863 | − | 2.29129i | −0.670820 | − | 0.387298i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.50000 | + | 6.06218i | −0.575396 | + | 0.996616i | 0.420602 | + | 0.907245i | \(0.361819\pi\) |
−0.995998 | + | 0.0893706i | \(0.971514\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.46410i | − | 0.541002i | −0.962720 | − | 0.270501i | \(-0.912811\pi\) | ||
0.962720 | − | 0.270501i | \(-0.0871893\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.16515i | − | 1.39767i | −0.715282 | − | 0.698836i | \(-0.753702\pi\) | ||
0.715282 | − | 0.698836i | \(-0.246298\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.96863 | + | 6.87386i | −0.578884 | + | 1.00266i | 0.416724 | + | 0.909033i | \(0.363178\pi\) |
−0.995608 | + | 0.0936230i | \(0.970155\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000 | 1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.50000 | + | 2.59808i | 0.206041 | + | 0.356873i | 0.950464 | − | 0.310835i | \(-0.100609\pi\) |
−0.744423 | + | 0.667708i | \(0.767275\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.93725 | −1.07026 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.96863 | − | 6.87386i | −0.516671 | − | 0.894901i | −0.999813 | − | 0.0193585i | \(-0.993838\pi\) |
0.483141 | − | 0.875542i | \(-0.339496\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.50000 | + | 0.866025i | 0.192055 | + | 0.110883i | 0.592944 | − | 0.805243i | \(-0.297965\pi\) |
−0.400889 | + | 0.916127i | \(0.631299\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.00000 | − | 5.19615i | 0.372104 | − | 0.644503i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.96863 | + | 2.29129i | −0.484845 | + | 0.279925i | −0.722433 | − | 0.691441i | \(-0.756976\pi\) |
0.237588 | + | 0.971366i | \(0.423643\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.16515i | 1.08770i | 0.839181 | + | 0.543852i | \(0.183035\pi\) | ||||
−0.839181 | + | 0.543852i | \(0.816965\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.50000 | + | 2.59808i | −0.526685 | + | 0.304082i | −0.739666 | − | 0.672975i | \(-0.765016\pi\) |
0.212980 | + | 0.977056i | \(0.431683\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.5000 | − | 6.06218i | 1.19659 | − | 0.690849i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.96863 | + | 2.29129i | 0.446505 | + | 0.257790i | 0.706353 | − | 0.707860i | \(-0.250339\pi\) |
−0.259848 | + | 0.965650i | \(0.583672\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.00000 | −0.976187 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.50000 | − | 0.866025i | −0.159000 | − | 0.0917985i | 0.418389 | − | 0.908268i | \(-0.362595\pi\) |
−0.577389 | + | 0.816469i | \(0.695928\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.16515i | 0.960769i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.96863 | + | 2.29129i | −0.407173 | + | 0.235081i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.46410i | 0.351726i | 0.984415 | + | 0.175863i | \(0.0562716\pi\) | ||||
−0.984415 | + | 0.175863i | \(0.943728\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.50000 | + | 2.59808i | −0.447767 | + | 0.258518i | −0.706887 | − | 0.707327i | \(-0.749901\pi\) |
0.259120 | + | 0.965845i | \(0.416568\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.32288 | − | 2.29129i | 0.130347 | − | 0.225767i | −0.793463 | − | 0.608618i | \(-0.791724\pi\) |
0.923810 | + | 0.382851i | \(0.125058\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.9059 | − | 6.87386i | −1.15098 | − | 0.664521i | −0.201858 | − | 0.979415i | \(-0.564698\pi\) |
−0.949127 | + | 0.314893i | \(0.898031\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.50000 | + | 6.06218i | 0.335239 | + | 0.580651i | 0.983531 | − | 0.180741i | \(-0.0578495\pi\) |
−0.648292 | + | 0.761392i | \(0.724516\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.0000 | −1.12887 | −0.564433 | − | 0.825479i | \(-0.690905\pi\) | ||||
−0.564433 | + | 0.825479i | \(0.690905\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.96863 | − | 6.87386i | −0.370076 | − | 0.640991i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.9059 | − | 6.87386i | 1.09141 | − | 0.630126i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | − | 8.66025i | 0.454545 | − | 0.787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 12.1244i | − | 1.08444i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.16515i | 0.813276i | 0.913589 | + | 0.406638i | \(0.133299\pi\) | ||||
−0.913589 | + | 0.406638i | \(0.866701\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.96863 | − | 6.87386i | 0.346741 | − | 0.600572i | −0.638928 | − | 0.769267i | \(-0.720622\pi\) |
0.985668 | + | 0.168694i | \(0.0539551\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.50000 | − | 6.06218i | 0.303488 | − | 0.525657i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.5000 | + | 18.1865i | 0.897076 | + | 1.55378i | 0.831215 | + | 0.555952i | \(0.187646\pi\) |
0.0658609 | + | 0.997829i | \(0.479021\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.5830 | −0.897639 | −0.448819 | − | 0.893622i | \(-0.648155\pi\) | ||||
−0.448819 | + | 0.893622i | \(0.648155\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.93725 | + | 13.7477i | 0.663747 | + | 1.14964i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.50000 | + | 12.9904i | −0.614424 | + | 1.06421i | 0.376061 | + | 0.926595i | \(0.377278\pi\) |
−0.990485 | + | 0.137619i | \(0.956055\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.8431 | − | 11.4564i | 1.61481 | − | 0.932312i | 0.626578 | − | 0.779359i | \(-0.284455\pi\) |
0.988233 | − | 0.152953i | \(-0.0488783\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.58258i | 0.368081i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.50000 | + | 2.59808i | −0.359139 | + | 0.207349i | −0.668703 | − | 0.743530i | \(-0.733150\pi\) |
0.309564 | + | 0.950879i | \(0.399817\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.5000 | + | 6.06218i | 0.827516 | + | 0.477767i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.96863 | + | 2.29129i | 0.310847 | + | 0.179468i | 0.647305 | − | 0.762231i | \(-0.275896\pi\) |
−0.336459 | + | 0.941698i | \(0.609229\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.8745 | 1.22841 | 0.614203 | − | 0.789148i | \(-0.289478\pi\) | ||||
0.614203 | + | 0.789148i | \(0.289478\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.5000 | − | 11.2583i | −1.48256 | − | 0.855955i | −0.482754 | − | 0.875756i | \(-0.660363\pi\) |
−0.999804 | + | 0.0198012i | \(0.993697\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.64575 | + | 4.58258i | 0.200000 | + | 0.346410i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.9059 | − | 6.87386i | 0.889887 | − | 0.513777i | 0.0159817 | − | 0.999872i | \(-0.494913\pi\) |
0.873906 | + | 0.486096i | \(0.161579\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 20.7846i | − | 1.54491i | −0.635071 | − | 0.772454i | \(-0.719029\pi\) | ||
0.635071 | − | 0.772454i | \(-0.280971\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.5000 | + | 6.06218i | −0.771975 | + | 0.445700i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.9059 | − | 20.6216i | 0.870644 | − | 1.50800i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.8431 | + | 11.4564i | 1.43580 | + | 0.828959i | 0.997554 | − | 0.0698969i | \(-0.0222670\pi\) |
0.438245 | + | 0.898856i | \(0.355600\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.50000 | + | 9.52628i | 0.395899 | + | 0.685717i | 0.993215 | − | 0.116289i | \(-0.0370998\pi\) |
−0.597317 | + | 0.802005i | \(0.703766\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.0000 | 0.854965 | 0.427482 | − | 0.904024i | \(-0.359401\pi\) | ||||
0.427482 | + | 0.904024i | \(0.359401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.61438 | + | 11.4564i | 0.468881 | + | 0.812125i | 0.999367 | − | 0.0355680i | \(-0.0113240\pi\) |
−0.530486 | + | 0.847693i | \(0.677991\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.00000 | − | 5.19615i | 0.209529 | − | 0.362915i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 12.1244i | − | 0.838659i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 9.16515i | − | 0.630955i | −0.948933 | − | 0.315478i | \(-0.897835\pi\) | ||
0.948933 | − | 0.315478i | \(-0.102165\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.93725 | − | 13.7477i | 0.541316 | − | 0.937587i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.50000 | − | 6.06218i | −0.237595 | − | 0.411527i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.00000 | + | 15.5885i | 0.605406 | + | 1.04859i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.5830 | 0.708690 | 0.354345 | − | 0.935115i | \(-0.384704\pi\) | ||||
0.354345 | + | 0.935115i | \(0.384704\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.9059 | − | 20.6216i | −0.790221 | − | 1.36870i | −0.925830 | − | 0.377941i | \(-0.876632\pi\) |
0.135609 | − | 0.990762i | \(-0.456701\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.50000 | − | 0.866025i | −0.0991228 | − | 0.0572286i | 0.449619 | − | 0.893220i | \(-0.351560\pi\) |
−0.548742 | + | 0.835992i | \(0.684893\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.5000 | − | 18.1865i | 0.687878 | − | 1.19144i | −0.284645 | − | 0.958633i | \(-0.591876\pi\) |
0.972523 | − | 0.232806i | \(-0.0747909\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.9059 | + | 6.87386i | −0.776654 | + | 0.448401i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.5000 | + | 9.52628i | −1.06286 | + | 0.613642i | −0.926222 | − | 0.376980i | \(-0.876963\pi\) |
−0.136637 | + | 0.990621i | \(0.543629\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.5000 | + | 6.06218i | 0.670820 | + | 0.387298i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.93725 | + | 4.58258i | 0.505035 | + | 0.291582i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.8745 | 1.00199 | 0.500995 | − | 0.865450i | \(-0.332967\pi\) | ||||
0.500995 | + | 0.865450i | \(0.332967\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.0000 | 1.32026 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.50000 | + | 0.866025i | 0.0935674 | + | 0.0540212i | 0.546054 | − | 0.837750i | \(-0.316129\pi\) |
−0.452486 | + | 0.891771i | \(0.649463\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.26013 | − | 16.0390i | 0.575396 | − | 0.996616i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.96863 | − | 2.29129i | 0.244716 | − | 0.141287i | −0.372626 | − | 0.927981i | \(-0.621543\pi\) |
0.617342 | + | 0.786695i | \(0.288209\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.19615i | 0.319197i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −25.5000 | + | 14.7224i | −1.55476 | + | 0.897643i | −0.557019 | + | 0.830500i | \(0.688055\pi\) |
−0.997743 | + | 0.0671428i | \(0.978612\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.5516 | + | 25.2042i | −0.883949 | + | 1.53104i | −0.0370348 | + | 0.999314i | \(0.511791\pi\) |
−0.846914 | + | 0.531730i | \(0.821542\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.93725 | + | 4.58258i | 0.478634 | + | 0.276340i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.50000 | + | 14.7224i | 0.510716 | + | 0.884585i | 0.999923 | + | 0.0124177i | \(0.00395278\pi\) |
−0.489207 | + | 0.872167i | \(0.662714\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.61438 | + | 11.4564i | 0.393184 | + | 0.681015i | 0.992868 | − | 0.119223i | \(-0.0380402\pi\) |
−0.599684 | + | 0.800237i | \(0.704707\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.16515i | 0.541002i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.00000 | − | 8.66025i | 0.294118 | − | 0.509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 20.7846i | − | 1.21425i | −0.794606 | − | 0.607125i | \(-0.792323\pi\) | ||
0.794606 | − | 0.607125i | \(-0.207677\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 13.7477i | − | 0.800424i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.93725 | + | 13.7477i | −0.459023 | + | 0.795052i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.2487i | 1.39767i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.50000 | + | 2.59808i | 0.0858898 | + | 0.148765i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.5830 | 0.604004 | 0.302002 | − | 0.953307i | \(-0.402345\pi\) | ||||
0.302002 | + | 0.953307i | \(0.402345\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.9059 | + | 20.6216i | 0.675121 | + | 1.16934i | 0.976434 | + | 0.215818i | \(0.0692417\pi\) |
−0.301313 | + | 0.953525i | \(0.597425\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.5000 | − | 12.9904i | −1.27178 | − | 0.734260i | −0.296453 | − | 0.955047i | \(-0.595804\pi\) |
−0.975322 | + | 0.220788i | \(0.929137\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.50000 | − | 12.9904i | 0.421242 | − | 0.729612i | −0.574819 | − | 0.818280i | \(-0.694928\pi\) |
0.996061 | + | 0.0886679i | \(0.0282610\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 13.7477i | − | 0.764944i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.00000 | + | 3.46410i | −0.332820 | + | 0.192154i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.5000 | − | 18.1865i | 0.578884 | − | 1.00266i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.9059 | − | 6.87386i | −0.654406 | − | 0.377822i | 0.135736 | − | 0.990745i | \(-0.456660\pi\) |
−0.790142 | + | 0.612923i | \(0.789993\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.93725 | −0.433659 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.0000 | −1.52526 | −0.762629 | − | 0.646837i | \(-0.776092\pi\) | ||||
−0.762629 | + | 0.646837i | \(0.776092\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.5000 | − | 6.06218i | −0.568607 | − | 0.328285i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.5203 | −1.00000 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.96863 | − | 2.29129i | 0.213047 | − | 0.123003i | −0.389680 | − | 0.920950i | \(-0.627414\pi\) |
0.602727 | + | 0.797948i | \(0.294081\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.46410i | 0.185429i | 0.995693 | + | 0.0927146i | \(0.0295544\pi\) | ||||
−0.995693 | + | 0.0927146i | \(0.970446\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.5000 | + | 9.52628i | −0.878206 | + | 0.507033i | −0.870067 | − | 0.492934i | \(-0.835924\pi\) |
−0.00813978 | + | 0.999967i | \(0.502591\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.93725 | + | 13.7477i | −0.421266 | + | 0.729654i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.9059 | − | 6.87386i | −0.628368 | − | 0.362789i | 0.151752 | − | 0.988419i | \(-0.451509\pi\) |
−0.780120 | + | 0.625630i | \(0.784842\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.00000 | + | 10.3923i | 0.315789 | + | 0.546963i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.00000 | −0.471082 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.1974 | − | 29.7867i | −0.897696 | − | 1.55486i | −0.830432 | − | 0.557120i | \(-0.811906\pi\) |
−0.0672642 | − | 0.997735i | \(-0.521427\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.96863 | − | 6.87386i | −0.206041 | − | 0.356873i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.500000 | − | 0.866025i | 0.0258890 | − | 0.0448411i | −0.852791 | − | 0.522253i | \(-0.825092\pi\) |
0.878680 | + | 0.477412i | \(0.158425\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.3303i | 0.941564i | 0.882249 | + | 0.470782i | \(0.156028\pi\) | ||||
−0.882249 | + | 0.470782i | \(0.843972\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.96863 | + | 6.87386i | −0.202787 | + | 0.351238i | −0.949425 | − | 0.313992i | \(-0.898333\pi\) |
0.746638 | + | 0.665230i | \(0.231667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 21.0000 | 1.07026 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.5000 | + | 18.1865i | 0.532371 | + | 0.922094i | 0.999286 | + | 0.0377914i | \(0.0120322\pi\) |
−0.466915 | + | 0.884302i | \(0.654634\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.8118 | 1.20421 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.96863 | + | 6.87386i | 0.199683 | + | 0.345862i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.5000 | − | 11.2583i | −0.978677 | − | 0.565039i | −0.0768065 | − | 0.997046i | \(-0.524472\pi\) |
−0.901870 | + | 0.432007i | \(0.857806\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 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 | ||||||||
\(403\) | 7.93725 | − | 4.58258i | 0.395383 | − | 0.228274i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 32.0780i | − | 1.59005i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.5000 | − | 9.52628i | 0.815872 | − | 0.471044i | −0.0331186 | − | 0.999451i | \(-0.510544\pi\) |
0.848991 | + | 0.528407i | \(0.177211\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.5000 | + | 18.1865i | 0.516671 | + | 0.894901i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −31.7490 | −1.55104 | −0.775520 | − | 0.631322i | \(-0.782512\pi\) | ||||
−0.775520 | + | 0.631322i | \(0.782512\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.0000 | 0.779792 | 0.389896 | − | 0.920859i | \(-0.372511\pi\) | ||||
0.389896 | + | 0.920859i | \(0.372511\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.00000 | + | 5.19615i | 0.436564 | + | 0.252050i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.96863 | − | 2.29129i | −0.192055 | − | 0.110883i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.8431 | + | 11.4564i | −0.955810 | + | 0.551837i | −0.894881 | − | 0.446305i | \(-0.852740\pi\) |
−0.0609292 | + | 0.998142i | \(0.519406\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3.46410i | − | 0.166474i | −0.996530 | − | 0.0832370i | \(-0.973474\pi\) | ||
0.996530 | − | 0.0832370i | \(-0.0265259\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.5000 | − | 6.06218i | 0.502283 | − | 0.289993i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.5516 | − | 25.2042i | 0.694512 | − | 1.20293i | −0.275834 | − | 0.961205i | \(-0.588954\pi\) |
0.970345 | − | 0.241724i | \(-0.0777128\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.96863 | + | 2.29129i | 0.188555 | + | 0.108862i | 0.591306 | − | 0.806447i | \(-0.298613\pi\) |
−0.402751 | + | 0.915310i | \(0.631946\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.50000 | − | 2.59808i | −0.0711068 | − | 0.123161i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.0000 | −0.566315 | −0.283158 | − | 0.959073i | \(-0.591382\pi\) | ||||
−0.283158 | + | 0.959073i | \(0.591382\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.93725 | + | 13.7477i | 0.373751 | + | 0.647355i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.93725 | + | 13.7477i | −0.372104 | + | 0.644503i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.500000 | − | 0.866025i | 0.0233890 | − | 0.0405110i | −0.854094 | − | 0.520119i | \(-0.825888\pi\) |
0.877483 | + | 0.479608i | \(0.159221\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 3.46410i | − | 0.161339i | −0.996741 | − | 0.0806696i | \(-0.974294\pi\) | ||
0.996741 | − | 0.0806696i | \(-0.0257059\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.4955i | 1.27782i | 0.769281 | + | 0.638911i | \(0.220615\pi\) | ||||
−0.769281 | + | 0.638911i | \(0.779385\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.96863 | − | 6.87386i | 0.183646 | − | 0.318084i | −0.759473 | − | 0.650538i | \(-0.774543\pi\) |
0.943119 | + | 0.332454i | \(0.107877\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.5000 | − | 6.06218i | 0.484845 | − | 0.279925i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21.0000 | + | 36.3731i | 0.965581 | + | 1.67244i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.29150 | 0.242791 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.96863 | − | 6.87386i | −0.181331 | − | 0.314075i | 0.761003 | − | 0.648748i | \(-0.224707\pi\) |
−0.942334 | + | 0.334674i | \(0.891374\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.0000 | + | 12.1244i | 0.957518 | + | 0.552823i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.00000 | + | 5.19615i | −0.136223 | + | 0.235945i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −35.7176 | + | 20.6216i | −1.61852 | + | 0.934453i | −0.631218 | + | 0.775606i | \(0.717445\pi\) |
−0.987303 | + | 0.158848i | \(0.949222\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.3303i | 0.827235i | 0.910451 | + | 0.413617i | \(0.135735\pi\) | ||||
−0.910451 | + | 0.413617i | \(0.864265\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 24.2487i | − | 1.08770i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.7804 | − | 16.0390i | −1.24362 | − | 0.718005i | −0.273791 | − | 0.961789i | \(-0.588278\pi\) |
−0.969830 | + | 0.243784i | \(0.921611\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.7490 | −1.41562 | −0.707809 | − | 0.706404i | \(-0.750316\pi\) | ||||
−0.707809 | + | 0.706404i | \(0.750316\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.00000 | −0.400495 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.5000 | − | 12.9904i | −0.997295 | − | 0.575789i | −0.0898481 | − | 0.995955i | \(-0.528638\pi\) |
−0.907447 | + | 0.420167i | \(0.861972\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.9059 | − | 6.87386i | 0.526685 | − | 0.304082i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.96863 | − | 2.29129i | 0.174879 | − | 0.100966i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 36.3731i | − | 1.59969i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.5000 | + | 21.6506i | −1.64290 | + | 0.948532i | −0.663111 | + | 0.748521i | \(0.730764\pi\) |
−0.979794 | + | 0.200011i | \(0.935902\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.61438 | + | 11.4564i | −0.289227 | + | 0.500955i | −0.973625 | − | 0.228153i | \(-0.926731\pi\) |
0.684399 | + | 0.729108i | \(0.260065\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.9059 | − | 6.87386i | −0.518628 | − | 0.299430i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | − | 1.73205i | −0.0434783 | − | 0.0753066i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.0000 | −0.519778 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.9059 | − | 20.6216i | −0.514736 | − | 0.891549i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −27.7804 | + | 16.0390i | −1.19659 | + | 0.690849i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.50000 | + | 11.2583i | −0.279457 | + | 0.484033i | −0.971250 | − | 0.238062i | \(-0.923488\pi\) |
0.691793 | + | 0.722096i | \(0.256821\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.1244i | 0.519350i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 18.3303i | − | 0.783747i | −0.920019 | − | 0.391874i | \(-0.871827\pi\) | ||
0.920019 | − | 0.391874i | \(-0.128173\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.5000 | − | 6.06218i | −0.446505 | − | 0.257790i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.50000 | − | 2.59808i | −0.0635570 | − | 0.110084i | 0.832496 | − | 0.554031i | \(-0.186911\pi\) |
−0.896053 | + | 0.443947i | \(0.853578\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31.7490 | −1.34284 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.96863 | − | 6.87386i | −0.167258 | − | 0.289699i | 0.770197 | − | 0.637806i | \(-0.220158\pi\) |
−0.937455 | + | 0.348107i | \(0.886825\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.0000 | − | 10.3923i | −0.757266 | − | 0.437208i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.5000 | + | 18.1865i | −0.440183 | + | 0.762419i | −0.997703 | − | 0.0677445i | \(-0.978420\pi\) |
0.557520 | + | 0.830164i | \(0.311753\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.9059 | + | 6.87386i | −0.498246 | + | 0.287662i | −0.727989 | − | 0.685589i | \(-0.759545\pi\) |
0.229743 | + | 0.973251i | \(0.426211\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.16515i | 0.382213i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.5000 | + | 9.52628i | −0.686904 | + | 0.396584i | −0.802451 | − | 0.596718i | \(-0.796471\pi\) |
0.115547 | + | 0.993302i | \(0.463138\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.9059 | − | 6.87386i | −0.493091 | − | 0.284686i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −31.7490 | −1.31042 | −0.655211 | − | 0.755446i | \(-0.727420\pi\) | ||||
−0.655211 | + | 0.755446i | \(0.727420\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.00000 | −0.288430 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.5000 | + | 11.2583i | 0.800769 | + | 0.462324i | 0.843740 | − | 0.536752i | \(-0.180349\pi\) |
−0.0429710 | + | 0.999076i | \(0.513682\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23.8118 | 0.976187 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.96863 | − | 2.29129i | 0.162154 | − | 0.0936195i | −0.416727 | − | 0.909032i | \(-0.636823\pi\) |
0.578881 | + | 0.815412i | \(0.303490\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.46410i | 0.141304i | 0.997501 | + | 0.0706518i | \(0.0225079\pi\) | ||||
−0.997501 | + | 0.0706518i | \(0.977492\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.0000 | − | 8.66025i | 0.609837 | − | 0.352089i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.32288 | + | 2.29129i | −0.0536939 | + | 0.0930005i | −0.891623 | − | 0.452778i | \(-0.850433\pi\) |
0.837929 | + | 0.545779i | \(0.183766\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.8118 | + | 13.7477i | 0.963321 | + | 0.556174i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.50000 | + | 6.06218i | 0.141364 | + | 0.244849i | 0.928010 | − | 0.372554i | \(-0.121518\pi\) |
−0.786647 | + | 0.617403i | \(0.788185\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.26013 | + | 16.0390i | 0.372196 | + | 0.644662i | 0.989903 | − | 0.141746i | \(-0.0452716\pi\) |
−0.617707 | + | 0.786408i | \(0.711938\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.96863 | + | 2.29129i | 0.159000 | + | 0.0917985i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | − | 9.52628i | 0.220000 | − | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 36.3731i | − | 1.45029i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.8258i | 1.82429i | 0.409863 | + | 0.912147i | \(0.365577\pi\) | ||||
−0.409863 | + | 0.912147i | \(0.634423\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.93725 | + | 13.7477i | −0.314980 | + | 0.545562i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 24.2487i | − | 0.960769i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.5000 | − | 18.1865i | −0.414725 | − | 0.718325i | 0.580674 | − | 0.814136i | \(-0.302789\pi\) |
−0.995400 | + | 0.0958109i | \(0.969456\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.1660 | −0.834706 | −0.417353 | − | 0.908744i | \(-0.637042\pi\) | ||||
−0.417353 | + | 0.908744i | \(0.637042\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.8431 | − | 34.3693i | −0.780114 | − | 1.35120i | −0.931875 | − | 0.362780i | \(-0.881828\pi\) |
0.151761 | − | 0.988417i | \(-0.451506\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31.5000 | + | 18.1865i | 1.23648 | + | 0.713884i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.5000 | + | 18.1865i | −0.410897 | + | 0.711694i | −0.994988 | − | 0.0999939i | \(-0.968118\pi\) |
0.584091 | + | 0.811688i | \(0.301451\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.9059 | − | 6.87386i | 0.465201 | − | 0.268584i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.16515i | 0.357024i | 0.983938 | + | 0.178512i | \(0.0571283\pi\) | ||||
−0.983938 | + | 0.178512i | \(0.942872\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.50000 | + | 2.59808i | −0.175030 | + | 0.101053i | −0.584955 | − | 0.811065i | \(-0.698888\pi\) |
0.409926 | + | 0.912119i | \(0.365555\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.5000 | − | 6.06218i | 0.407173 | − | 0.235081i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.93725 | −0.306414 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.0000 | 1.07932 | 0.539660 | − | 0.841883i | \(-0.318553\pi\) | ||||
0.539660 | + | 0.841883i | \(0.318553\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.50000 | + | 0.866025i | 0.0576497 | + | 0.0332841i | 0.528548 | − | 0.848904i | \(-0.322737\pi\) |
−0.470898 | + | 0.882188i | \(0.656070\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 9.16515i | − | 0.351726i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.96863 | + | 2.29129i | −0.151855 | + | 0.0876737i | −0.574002 | − | 0.818854i | \(-0.694610\pi\) |
0.422147 | + | 0.906527i | \(0.361277\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 36.3731i | 1.38974i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.00000 | − | 5.19615i | 0.342873 | − | 0.197958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.32288 | − | 2.29129i | 0.0503246 | − | 0.0871647i | −0.839766 | − | 0.542949i | \(-0.817308\pi\) |
0.890090 | + | 0.455784i | \(0.150641\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.8745 | − | 9.16515i | −0.602154 | − | 0.347654i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.00000 | + | 15.5885i | 0.340899 | + | 0.590455i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.0000 | 1.58632 | 0.793159 | − | 0.609015i | \(-0.208435\pi\) | ||||
0.793159 | + | 0.609015i | \(0.208435\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.26013 | − | 16.0390i | −0.349252 | − | 0.604923i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.9059 | − | 6.87386i | 0.447767 | − | 0.258518i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.5000 | + | 30.3109i | −0.657226 | + | 1.13835i | 0.324104 | + | 0.946021i | \(0.394937\pi\) |
−0.981331 | + | 0.192328i | \(0.938396\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 12.1244i | − | 0.454061i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 27.4955i | 1.02827i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.96863 | − | 6.87386i | 0.148005 | − | 0.256352i | −0.782485 | − | 0.622669i | \(-0.786048\pi\) |
0.930490 | + | 0.366317i | \(0.119382\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.50000 | + | 6.06218i | −0.130347 | + | 0.225767i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.1660 | 0.785004 | 0.392502 | − | 0.919751i | \(-0.371610\pi\) | ||||
0.392502 | + | 0.919751i | \(0.371610\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.8118 | + | 41.2432i | 0.880710 | + | 1.52543i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.5000 | + | 11.2583i | 0.720249 | + | 0.415836i | 0.814844 | − | 0.579680i | \(-0.196822\pi\) |
−0.0945954 | + | 0.995516i | \(0.530156\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.5000 | − | 18.1865i | 0.386772 | − | 0.669910i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.8431 | − | 11.4564i | 0.729942 | − | 0.421432i | −0.0884593 | − | 0.996080i | \(-0.528194\pi\) |
0.818401 | + | 0.574648i | \(0.194861\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 45.8258i | − | 1.68118i | −0.541669 | − | 0.840592i | \(-0.682207\pi\) | ||
0.541669 | − | 0.840592i | \(-0.317793\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.5000 | + | 12.9904i | −0.824336 | + | 0.475931i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 31.5000 | + | 18.1865i | 1.15098 | + | 0.664521i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.9059 | + | 6.87386i | 0.434452 | + | 0.250831i | 0.701241 | − | 0.712924i | \(-0.252630\pi\) |
−0.266790 | + | 0.963755i | \(0.585963\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 39.6863 | 1.44433 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.0000 | −1.01768 | −0.508839 | − | 0.860862i | \(-0.669925\pi\) | ||||
−0.508839 | + | 0.860862i | \(0.669925\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.5000 | − | 12.9904i | −0.815624 | − | 0.470901i | 0.0332809 | − | 0.999446i | \(-0.489404\pi\) |
−0.848905 | + | 0.528545i | \(0.822738\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.26013 | − | 16.0390i | −0.335239 | − | 0.580651i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −23.8118 | + | 13.7477i | −0.859793 | + | 0.496402i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 51.9615i | − | 1.87378i | −0.349624 | − | 0.936890i | \(-0.613691\pi\) | ||
0.349624 | − | 0.936890i | \(-0.386309\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.5000 | − | 14.7224i | 0.917171 | − | 0.529529i | 0.0344397 | − | 0.999407i | \(-0.489035\pi\) |
0.882732 | + | 0.469878i | \(0.155702\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.64575 | − | 4.58258i | 0.0950382 | − | 0.164611i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.93725 | + | 4.58258i | 0.284382 | + | 0.164188i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.0000 | − | 36.3731i | −0.751439 | − | 1.30153i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.00000 | −0.321224 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.61438 | − | 11.4564i | −0.235777 | − | 0.408378i | 0.723721 | − | 0.690093i | \(-0.242430\pi\) |
−0.959498 | + | 0.281715i | \(0.909097\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 31.7490 | 1.12887 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.00000 | − | 5.19615i | 0.106533 | − | 0.184521i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.46410i | 0.122705i | 0.998116 | + | 0.0613524i | \(0.0195413\pi\) | ||||
−0.998116 | + | 0.0613524i | \(0.980459\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 41.2432i | − | 1.45908i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.9059 | − | 20.6216i | 0.420149 | − | 0.727720i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.5000 | + | 18.1865i | 0.370076 | + | 0.640991i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22.5000 | − | 38.9711i | −0.791058 | − | 1.37015i | −0.925312 | − | 0.379206i | \(-0.876197\pi\) |
0.134255 | − | 0.990947i | \(-0.457136\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.1660 | 0.743239 | 0.371620 | − | 0.928385i | \(-0.378803\pi\) | ||||
0.371620 | + | 0.928385i | \(0.378803\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.96863 | + | 6.87386i | 0.139015 | + | 0.240781i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.0000 | + | 12.1244i | 0.734697 | + | 0.424178i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.5000 | + | 23.3827i | −0.471153 | + | 0.816061i | −0.999456 | − | 0.0329950i | \(-0.989495\pi\) |
0.528302 | + | 0.849056i | \(0.322829\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.7804 | − | 16.0390i | 0.968363 | − | 0.559085i | 0.0696265 | − | 0.997573i | \(-0.477819\pi\) |
0.898737 | + | 0.438488i | \(0.144486\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 9.16515i | − | 0.318704i | −0.987222 | − | 0.159352i | \(-0.949060\pi\) | ||
0.987222 | − | 0.159352i | \(-0.0509404\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.50000 | − | 2.59808i | 0.156291 | − | 0.0902349i | −0.419815 | − | 0.907610i | \(-0.637905\pi\) |
0.576106 | + | 0.817375i | \(0.304572\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −31.5000 | + | 18.1865i | −1.09141 | + | 0.630126i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.8118 | + | 13.7477i | 0.824040 | + | 0.475760i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31.7490 | 1.09610 | 0.548049 | − | 0.836446i | \(-0.315371\pi\) | ||||
0.548049 | + | 0.836446i | \(0.315371\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.50000 | + | 0.866025i | 0.0516016 | + | 0.0297922i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.2288 | + | 22.9129i | −0.454545 | + | 0.787296i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27.7804 | − | 16.0390i | 0.952299 | − | 0.549810i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 51.9615i | 1.77913i | 0.456810 | + | 0.889564i | \(0.348992\pi\) | ||||
−0.456810 | + | 0.889564i | \(0.651008\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.5000 | + | 14.7224i | −0.871063 | + | 0.502909i | −0.867701 | − | 0.497086i | \(-0.834403\pi\) |
−0.00336193 | + | 0.999994i | \(0.501070\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.32288 | + | 2.29129i | −0.0451359 | + | 0.0781777i | −0.887711 | − | 0.460402i | \(-0.847705\pi\) |
0.842575 | + | 0.538579i | \(0.181039\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.9059 | + | 6.87386i | 0.405281 | + | 0.233989i | 0.688760 | − | 0.724989i | \(-0.258155\pi\) |
−0.283479 | + | 0.958978i | \(0.591489\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.5000 | − | 33.7750i | −0.663020 | − | 1.14838i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21.0000 | −0.712376 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.93725 | + | 13.7477i | 0.268944 | + | 0.465824i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 32.0780i | 1.08444i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.50000 | − | 6.06218i | 0.118187 | − | 0.204705i | −0.800862 | − | 0.598848i | \(-0.795625\pi\) |
0.919049 | + | 0.394143i | \(0.128959\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.7128i | 0.933668i | 0.884345 | + | 0.466834i | \(0.154606\pi\) | ||||
−0.884345 | + | 0.466834i | \(0.845394\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 27.4955i | − | 0.925296i | −0.886542 | − | 0.462648i | \(-0.846899\pi\) | ||
0.886542 | − | 0.462648i | \(-0.153101\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.9059 | − | 20.6216i | 0.399760 | − | 0.692405i | −0.593936 | − | 0.804512i | \(-0.702427\pi\) |
0.993696 | + | 0.112107i | \(0.0357600\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 24.2487i | − | 0.813276i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.5000 | − | 18.1865i | −0.351369 | − | 0.608589i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.8118 | 0.795939 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.5000 | − | 7.79423i | −0.449750 | − | 0.259663i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.0000 | − | 31.1769i | 0.598340 | − | 1.03636i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.8431 | + | 11.4564i | −0.658880 | + | 0.380405i | −0.791850 | − | 0.610715i | \(-0.790882\pi\) |
0.132970 | + | 0.991120i | \(0.457549\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.4955i | 0.910965i | 0.890245 | + | 0.455483i | \(0.150533\pi\) | ||||
−0.890245 | + | 0.455483i | \(0.849467\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.5000 | + | 18.1865i | −0.346741 | + | 0.600572i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.8431 | − | 11.4564i | −0.654565 | − | 0.377913i | 0.135638 | − | 0.990758i | \(-0.456692\pi\) |
−0.790203 | + | 0.612845i | \(0.790025\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 31.7490 | 1.04503 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.0000 | 0.460317 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 40.5000 | + | 23.3827i | 1.32876 | + | 0.767161i | 0.985108 | − | 0.171935i | \(-0.0550020\pi\) |
0.343654 | + | 0.939096i | \(0.388335\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.26013 | + | 16.0390i | −0.303488 | + | 0.525657i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 35.7176 | − | 20.6216i | 1.16809 | − | 0.674398i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.7128i | 0.905338i | 0.891679 | + | 0.452669i | \(0.149528\pi\) | ||||
−0.891679 | + | 0.452669i | \(0.850472\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.5000 | − | 9.52628i | 0.537885 | − | 0.310548i | −0.206337 | − | 0.978481i | \(-0.566154\pi\) |
0.744221 | + | 0.667933i | \(0.232821\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.93725 | + | 13.7477i | −0.258473 | + | 0.447688i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.96863 | − | 2.29129i | −0.128963 | − | 0.0744569i | 0.434131 | − | 0.900850i | \(-0.357056\pi\) |
−0.563094 | + | 0.826393i | \(0.690389\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.00000 | + | 15.5885i | 0.292152 | + | 0.506023i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.0000 | 0.388718 | 0.194359 | − | 0.980930i | \(-0.437737\pi\) | ||||
0.194359 | + | 0.980930i | \(0.437737\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.8431 | + | 34.3693i | 0.642109 | + | 1.11217i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −27.7804 | − | 48.1170i | −0.897076 | − | 1.55378i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.0000 | − | 20.7846i | 0.387097 | − | 0.670471i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19.0526i | 0.613324i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 45.8258i | − | 1.47366i | −0.676080 | − | 0.736828i | \(-0.736323\pi\) | ||
0.676080 | − | 0.736828i | \(-0.263677\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.7804 | + | 48.1170i | −0.891515 | + | 1.54415i | −0.0534559 | + | 0.998570i | \(0.517024\pi\) |
−0.838059 | + | 0.545579i | \(0.816310\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.0000 | 0.897639 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.5000 | + | 18.1865i | 0.335925 | + | 0.581839i | 0.983662 | − | 0.180025i | \(-0.0576179\pi\) |
−0.647737 | + | 0.761864i | \(0.724285\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.93725 | 0.253676 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.96863 | + | 6.87386i | 0.126580 | + | 0.219242i | 0.922349 | − | 0.386357i | \(-0.126267\pi\) |
−0.795770 | + | 0.605599i | \(0.792933\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.0000 | + | 10.3923i | 0.573528 | + | 0.331126i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21.0000 | + | 36.3731i | −0.667761 | + | 1.15660i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.96863 | + | 2.29129i | −0.126068 | + | 0.0727852i | −0.561708 | − | 0.827336i | \(-0.689855\pi\) |
0.435640 | + | 0.900121i | \(0.356522\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.9129i | 0.726387i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37.5000 | − | 21.6506i | 1.18764 | − | 0.685682i | 0.229868 | − | 0.973222i | \(-0.426171\pi\) |
0.957769 | + | 0.287539i | \(0.0928372\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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.cs.q.271.1 | 4 | ||
3.2 | odd | 2 | 112.2.p.c.47.1 | yes | 4 | ||
4.3 | odd | 2 | inner | 1008.2.cs.q.271.2 | 4 | ||
7.2 | even | 3 | 7056.2.b.s.1567.1 | 4 | |||
7.3 | odd | 6 | inner | 1008.2.cs.q.703.2 | 4 | ||
7.5 | odd | 6 | 7056.2.b.s.1567.3 | 4 | |||
12.11 | even | 2 | 112.2.p.c.47.2 | yes | 4 | ||
21.2 | odd | 6 | 784.2.f.d.783.4 | 4 | |||
21.5 | even | 6 | 784.2.f.d.783.1 | 4 | |||
21.11 | odd | 6 | 784.2.p.g.31.1 | 4 | |||
21.17 | even | 6 | 112.2.p.c.31.2 | yes | 4 | ||
21.20 | even | 2 | 784.2.p.g.607.2 | 4 | |||
24.5 | odd | 2 | 448.2.p.c.383.2 | 4 | |||
24.11 | even | 2 | 448.2.p.c.383.1 | 4 | |||
28.3 | even | 6 | inner | 1008.2.cs.q.703.1 | 4 | ||
28.19 | even | 6 | 7056.2.b.s.1567.4 | 4 | |||
28.23 | odd | 6 | 7056.2.b.s.1567.2 | 4 | |||
84.11 | even | 6 | 784.2.p.g.31.2 | 4 | |||
84.23 | even | 6 | 784.2.f.d.783.2 | 4 | |||
84.47 | odd | 6 | 784.2.f.d.783.3 | 4 | |||
84.59 | odd | 6 | 112.2.p.c.31.1 | ✓ | 4 | ||
84.83 | odd | 2 | 784.2.p.g.607.1 | 4 | |||
168.5 | even | 6 | 3136.2.f.f.3135.4 | 4 | |||
168.59 | odd | 6 | 448.2.p.c.255.2 | 4 | |||
168.101 | even | 6 | 448.2.p.c.255.1 | 4 | |||
168.107 | even | 6 | 3136.2.f.f.3135.3 | 4 | |||
168.131 | odd | 6 | 3136.2.f.f.3135.2 | 4 | |||
168.149 | odd | 6 | 3136.2.f.f.3135.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.p.c.31.1 | ✓ | 4 | 84.59 | odd | 6 | ||
112.2.p.c.31.2 | yes | 4 | 21.17 | even | 6 | ||
112.2.p.c.47.1 | yes | 4 | 3.2 | odd | 2 | ||
112.2.p.c.47.2 | yes | 4 | 12.11 | even | 2 | ||
448.2.p.c.255.1 | 4 | 168.101 | even | 6 | |||
448.2.p.c.255.2 | 4 | 168.59 | odd | 6 | |||
448.2.p.c.383.1 | 4 | 24.11 | even | 2 | |||
448.2.p.c.383.2 | 4 | 24.5 | odd | 2 | |||
784.2.f.d.783.1 | 4 | 21.5 | even | 6 | |||
784.2.f.d.783.2 | 4 | 84.23 | even | 6 | |||
784.2.f.d.783.3 | 4 | 84.47 | odd | 6 | |||
784.2.f.d.783.4 | 4 | 21.2 | odd | 6 | |||
784.2.p.g.31.1 | 4 | 21.11 | odd | 6 | |||
784.2.p.g.31.2 | 4 | 84.11 | even | 6 | |||
784.2.p.g.607.1 | 4 | 84.83 | odd | 2 | |||
784.2.p.g.607.2 | 4 | 21.20 | even | 2 | |||
1008.2.cs.q.271.1 | 4 | 1.1 | even | 1 | trivial | ||
1008.2.cs.q.271.2 | 4 | 4.3 | odd | 2 | inner | ||
1008.2.cs.q.703.1 | 4 | 28.3 | even | 6 | inner | ||
1008.2.cs.q.703.2 | 4 | 7.3 | odd | 6 | inner | ||
3136.2.f.f.3135.1 | 4 | 168.149 | odd | 6 | |||
3136.2.f.f.3135.2 | 4 | 168.131 | odd | 6 | |||
3136.2.f.f.3135.3 | 4 | 168.107 | even | 6 | |||
3136.2.f.f.3135.4 | 4 | 168.5 | even | 6 | |||
7056.2.b.s.1567.1 | 4 | 7.2 | even | 3 | |||
7056.2.b.s.1567.2 | 4 | 28.23 | odd | 6 | |||
7056.2.b.s.1567.3 | 4 | 7.5 | odd | 6 | |||
7056.2.b.s.1567.4 | 4 | 28.19 | even | 6 |