Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(31,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.p (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.26027151847\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 607.2 | ||
Root | \(1.32288 + 2.29129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.607 |
Dual form | 784.2.p.g.31.2 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.32288 | + | 2.29129i | 0.763763 | + | 1.32288i | 0.940898 | + | 0.338689i | \(0.109984\pi\) |
−0.177136 | + | 0.984186i | \(0.556683\pi\) | |||||||
\(4\) | 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 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.00000 | + | 3.46410i | −0.666667 | + | 1.15470i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.96863 | − | 2.29129i | 1.19659 | − | 0.690849i | 0.236794 | − | 0.971560i | \(-0.423903\pi\) |
0.959792 | + | 0.280711i | \(0.0905701\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.46410i | 0.960769i | 0.877058 | + | 0.480384i | \(0.159503\pi\) | ||||
−0.877058 | + | 0.480384i | \(0.840497\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.58258i | 1.18322i | ||||||||
\(16\) | 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 | −0.673435 | − | 0.739246i | \(-0.735182\pi\) |
0.976924 | + | 0.213589i | \(0.0685153\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.96863 | + | 2.29129i | 0.827516 | + | 0.477767i | 0.853001 | − | 0.521909i | \(-0.174780\pi\) |
−0.0254855 | + | 0.999675i | \(0.508113\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | − | 1.73205i | −0.200000 | − | 0.346410i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.64575 | −0.509175 | ||||||||
\(28\) | 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 | 0.722428 | − | 0.691446i | \(-0.243026\pi\) |
−0.960024 | + | 0.279918i | \(0.909693\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 10.5000 | + | 6.06218i | 1.82782 | + | 1.05529i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 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 | ||||||||
\(39\) | −7.93725 | + | 4.58258i | −1.27098 | + | 0.733799i | ||||
\(40\) | 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 | ||||||||
\(45\) | −6.00000 | + | 3.46410i | −0.894427 | + | 0.516398i | ||||
\(46\) | 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 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.9059 | − | 6.87386i | −1.66716 | − | 0.962533i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.50000 | − | 2.59808i | −0.206041 | − | 0.356873i | 0.744423 | − | 0.667708i | \(-0.232725\pi\) |
−0.950464 | + | 0.310835i | \(0.899391\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.93725 | 1.07026 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.00000 | 0.927173 | ||||||||
\(58\) | 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 | 0.400889 | − | 0.916127i | \(-0.368701\pi\) |
−0.592944 | + | 0.805243i | \(0.702035\pi\) | |||||||
\(62\) | 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 | ||||||||
\(69\) | 12.1244i | 1.45960i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.16515i | − | 1.08770i | −0.839181 | − | 0.543852i | \(-0.816965\pi\) | ||
0.839181 | − | 0.543852i | \(-0.183035\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.50000 | − | 2.59808i | 0.526685 | − | 0.304082i | −0.212980 | − | 0.977056i | \(-0.568317\pi\) |
0.739666 | + | 0.672975i | \(0.234984\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.64575 | − | 4.58258i | 0.305505 | − | 0.529150i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 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 | ||||||||
\(81\) | 2.50000 | + | 4.33013i | 0.277778 | + | 0.481125i | ||||
\(82\) | 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 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.50000 | − | 6.06218i | 0.362933 | − | 0.628619i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.96863 | − | 2.29129i | 0.407173 | − | 0.235081i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.46410i | − | 0.351726i | −0.984415 | − | 0.175863i | \(-0.943728\pi\) | ||
0.984415 | − | 0.175863i | \(-0.0562716\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 18.3303i | 1.84226i | ||||||||
\(100\) | 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 | −0.923810 | − | 0.382851i | \(-0.874942\pi\) |
0.793463 | + | 0.608618i | \(0.208276\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.9059 | + | 6.87386i | 1.15098 | + | 0.664521i | 0.949127 | − | 0.314893i | \(-0.101969\pi\) |
0.201858 | + | 0.979415i | \(0.435302\pi\) | |||||||
\(108\) | 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 | ||||||||
\(111\) | −18.5203 | −1.75787 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.0000 | 1.12887 | 0.564433 | − | 0.825479i | \(-0.309095\pi\) | ||||
0.564433 | + | 0.825479i | \(0.309095\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.96863 | + | 6.87386i | 0.370076 | + | 0.640991i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −12.0000 | − | 6.92820i | −1.10940 | − | 0.640513i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | − | 8.66025i | 0.454545 | − | 0.787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.93725 | − | 4.58258i | 0.715678 | − | 0.413197i | ||||
\(124\) | 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 | ||||||||
\(129\) | 21.0000 | − | 12.1244i | 1.84895 | − | 1.06749i | ||||
\(130\) | 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 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.96863 | − | 2.29129i | −0.341565 | − | 0.197203i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.5000 | − | 18.1865i | −0.897076 | − | 1.55378i | −0.831215 | − | 0.555952i | \(-0.812354\pi\) |
−0.0658609 | − | 0.997829i | \(-0.520979\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.5830 | 0.897639 | 0.448819 | − | 0.893622i | \(-0.351845\pi\) | ||||
0.448819 | + | 0.893622i | \(0.351845\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −21.0000 | −1.76852 | ||||||||
\(142\) | 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 | \(-0.622722\pi\) |
0.990485 | − | 0.137619i | \(-0.0439449\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | − | 20.7846i | − | 1.68034i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 4.58258i | − | 0.368081i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.50000 | − | 2.59808i | 0.359139 | − | 0.207349i | −0.309564 | − | 0.950879i | \(-0.600183\pi\) |
0.668703 | + | 0.743530i | \(0.266850\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.96863 | − | 6.87386i | 0.314733 | − | 0.545133i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 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 | ||||||||
\(165\) | 10.5000 | + | 18.1865i | 0.817424 | + | 1.41582i | ||||
\(166\) | 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 | ||||||||
\(171\) | 5.29150 | + | 9.16515i | 0.404651 | + | 0.700877i | ||||
\(172\) | 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 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.5000 | − | 18.1865i | 0.789228 | − | 1.36698i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.9059 | + | 6.87386i | −0.889887 | + | 0.513777i | −0.873906 | − | 0.486096i | \(-0.838421\pi\) |
−0.0159817 | + | 0.999872i | \(0.505087\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.7846i | 1.54491i | 0.635071 | + | 0.772454i | \(0.280971\pi\) | ||||
−0.635071 | + | 0.772454i | \(0.719029\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 4.58258i | − | 0.338754i | ||||||
\(184\) | 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 | −0.438245 | − | 0.898856i | \(-0.644400\pi\) |
−0.997554 | + | 0.0698969i | \(0.977733\pi\) | |||||||
\(192\) | 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 | ||||||||
\(195\) | −15.8745 | −1.13680 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.0000 | −0.854965 | −0.427482 | − | 0.904024i | \(-0.640599\pi\) | ||||
−0.427482 | + | 0.904024i | \(0.640599\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.61438 | − | 11.4564i | −0.468881 | − | 0.812125i | 0.530486 | − | 0.847693i | \(-0.322009\pi\) |
−0.999367 | + | 0.0355680i | \(0.988676\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.5000 | − | 6.06218i | −0.740613 | − | 0.427593i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.00000 | − | 5.19615i | 0.209529 | − | 0.362915i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.8745 | + | 9.16515i | −1.10335 | + | 0.637022i | ||||
\(208\) | 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 | ||||||||
\(213\) | 21.0000 | − | 12.1244i | 1.43890 | − | 0.830747i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.93725 | − | 13.7477i | 0.541316 | − | 0.937587i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.9059 | + | 6.87386i | 0.804525 | + | 0.464493i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.00000 | − | 15.5885i | −0.605406 | − | 1.04859i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.5830 | −0.708690 | −0.354345 | − | 0.935115i | \(-0.615296\pi\) | ||||
−0.354345 | + | 0.935115i | \(0.615296\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.00000 | 0.533333 | ||||||||
\(226\) | 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 | 0.548742 | − | 0.835992i | \(-0.315107\pi\) |
−0.449619 | + | 0.893220i | \(0.648440\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.5000 | + | 18.1865i | −0.687878 | + | 1.19144i | 0.284645 | + | 0.958633i | \(0.408124\pi\) |
−0.972523 | + | 0.232806i | \(0.925209\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.9059 | + | 6.87386i | −0.776654 | + | 0.448401i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.1244i | 0.787562i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.5000 | − | 9.52628i | 1.06286 | − | 0.613642i | 0.136637 | − | 0.990621i | \(-0.456371\pi\) |
0.926222 | + | 0.376980i | \(0.123037\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.5830 | + | 18.3303i | −0.678900 | + | 1.17589i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 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 | ||||||||
\(255\) | −11.9059 | − | 20.6216i | −0.745575 | − | 1.29137i | ||||
\(256\) | 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 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.96863 | + | 2.29129i | −0.244716 | + | 0.141287i | −0.617342 | − | 0.786695i | \(-0.711791\pi\) |
0.372626 | + | 0.927981i | \(0.378457\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 5.19615i | − | 0.319197i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 4.58258i | − | 0.280449i | ||||||
\(268\) | 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 | \(-0.488209\pi\) |
0.846914 | − | 0.531730i | \(-0.178458\pi\) | |||||||
\(272\) | 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 | ||||||||
\(279\) | 10.5830 | 0.633588 | ||||||||
\(280\) | 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 | 0.599684 | − | 0.800237i | \(-0.295293\pi\) |
−0.992868 | + | 0.119223i | \(0.961960\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.5000 | + | 6.06218i | 0.621966 | + | 0.359092i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.00000 | − | 8.66025i | 0.294118 | − | 0.509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.93725 | − | 4.58258i | 0.465290 | − | 0.268635i | ||||
\(292\) | 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 | ||||||||
\(297\) | −10.5000 | + | 6.06218i | −0.609272 | + | 0.351763i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.93725 | + | 13.7477i | −0.459023 | + | 0.795052i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.9059 | − | 6.87386i | −0.683975 | − | 0.394893i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.50000 | − | 2.59808i | −0.0858898 | − | 0.148765i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.5830 | −0.604004 | −0.302002 | − | 0.953307i | \(-0.597655\pi\) | ||||
−0.302002 | + | 0.953307i | \(0.597655\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.00000 | −0.398216 | ||||||||
\(310\) | 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 | 0.975322 | − | 0.220788i | \(-0.0708628\pi\) |
0.296453 | + | 0.955047i | \(0.404196\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.50000 | + | 12.9904i | −0.421242 | + | 0.729612i | −0.996061 | − | 0.0886679i | \(-0.971739\pi\) |
0.574819 | + | 0.818280i | \(0.305072\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 36.3731i | 2.03015i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.7477i | 0.764944i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.00000 | − | 3.46410i | 0.332820 | − | 0.192154i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.26013 | + | 16.0390i | −0.512086 | + | 0.886960i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 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 | ||||||||
\(333\) | −14.0000 | − | 24.2487i | −0.767195 | − | 1.32882i | ||||
\(334\) | 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 | ||||||||
\(339\) | 15.8745 | + | 27.4955i | 0.862185 | + | 1.49335i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.5000 | − | 6.06218i | −0.568607 | − | 0.328285i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.5000 | + | 18.1865i | −0.565301 | + | 0.979130i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.96863 | + | 2.29129i | −0.213047 | + | 0.123003i | −0.602727 | − | 0.797948i | \(-0.705919\pi\) |
0.389680 | + | 0.920950i | \(0.372586\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 3.46410i | − | 0.185429i | −0.995693 | − | 0.0927146i | \(-0.970446\pi\) | ||
0.995693 | − | 0.0927146i | \(-0.0295544\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 9.16515i | − | 0.489200i | ||||||
\(352\) | 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 | 0.780120 | − | 0.625630i | \(-0.215158\pi\) |
−0.151752 | + | 0.988419i | \(0.548491\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.00000 | + | 10.3923i | 0.315789 | + | 0.546963i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 26.4575 | 1.38866 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.00000 | 0.471082 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.1974 | + | 29.7867i | 0.897696 | + | 1.55486i | 0.830432 | + | 0.557120i | \(0.188094\pi\) |
0.0672642 | + | 0.997735i | \(0.478573\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12.0000 | + | 6.92820i | 0.624695 | + | 0.360668i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 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 | ||||||||
\(375\) | 27.7804 | − | 16.0390i | 1.43457 | − | 0.828251i | ||||
\(376\) | 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 | ||||||||
\(381\) | −21.0000 | + | 12.1244i | −1.07586 | + | 0.621150i | ||||
\(382\) | 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 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 31.7490 | + | 18.3303i | 1.61389 | + | 0.931782i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.5000 | − | 18.1865i | −0.532371 | − | 0.922094i | −0.999286 | − | 0.0377914i | \(-0.987968\pi\) |
0.466915 | − | 0.884302i | \(-0.345366\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.8118 | −1.20421 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.0000 | 1.05931 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.96863 | + | 6.87386i | 0.199683 | + | 0.345862i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.5000 | + | 11.2583i | 0.978677 | + | 0.565039i | 0.901870 | − | 0.432007i | \(-0.142194\pi\) |
0.0768065 | + | 0.997046i | \(0.475528\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.5000 | + | 18.1865i | −0.524345 | + | 0.908192i | 0.475253 | + | 0.879849i | \(0.342356\pi\) |
−0.999598 | + | 0.0283431i | \(0.990977\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.93725 | − | 4.58258i | 0.395383 | − | 0.228274i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.66025i | 0.430331i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 32.0780i | 1.59005i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.5000 | + | 9.52628i | −0.815872 | + | 0.471044i | −0.848991 | − | 0.528407i | \(-0.822789\pi\) |
0.0331186 | + | 0.999451i | \(0.489456\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 27.7804 | − | 48.1170i | 1.37031 | − | 2.37344i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.0000 | + | 24.2487i | 0.685583 | + | 1.18746i | ||||
\(418\) | 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 | ||||||||
\(423\) | −15.8745 | − | 27.4955i | −0.771845 | − | 1.33687i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.00000 | + | 5.19615i | 0.436564 | + | 0.252050i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −21.0000 | + | 36.3731i | −1.01389 | + | 1.75611i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.8431 | − | 11.4564i | 0.955810 | − | 0.551837i | 0.0609292 | − | 0.998142i | \(-0.480594\pi\) |
0.894881 | + | 0.446305i | \(0.147260\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.46410i | 0.166474i | 0.996530 | + | 0.0832370i | \(0.0265259\pi\) | ||||
−0.996530 | + | 0.0832370i | \(0.973474\pi\) | |||||||
\(434\) | 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 | \(0.411046\pi\) |
−0.970345 | + | 0.241724i | \(0.922287\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.96863 | − | 2.29129i | −0.188555 | − | 0.108862i | 0.402751 | − | 0.915310i | \(-0.368054\pi\) |
−0.591306 | + | 0.806447i | \(0.701387\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.50000 | − | 2.59808i | −0.0711068 | − | 0.123161i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 39.6863 | 1.87710 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.0000 | 0.566315 | 0.283158 | − | 0.959073i | \(-0.408618\pi\) | ||||
0.283158 | + | 0.959073i | \(0.408618\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.93725 | − | 13.7477i | −0.373751 | − | 0.647355i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 52.5000 | + | 30.3109i | 2.46667 | + | 1.42413i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 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 | ||||||||
\(459\) | 11.9059 | − | 6.87386i | 0.555719 | − | 0.320844i | ||||
\(460\) | 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 | ||||||||
\(465\) | 10.5000 | − | 6.06218i | 0.486926 | − | 0.281127i | ||||
\(466\) | 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 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.9059 | + | 6.87386i | 0.548594 | + | 0.316731i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.0000 | − | 36.3731i | −0.965581 | − | 1.67244i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.29150 | −0.242791 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.0000 | 0.549442 | ||||||||
\(478\) | 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 | ||||||||
\(489\) | 12.1244i | 0.548282i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 18.3303i | − | 0.827235i | −0.910451 | − | 0.413617i | \(-0.864265\pi\) | ||
0.910451 | − | 0.413617i | \(-0.135735\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −15.8745 | + | 27.4955i | −0.713506 | + | 1.23583i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 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 | ||||||||
\(501\) | 21.0000 | + | 36.3731i | 0.938211 | + | 1.62503i | ||||
\(502\) | 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 | ||||||||
\(507\) | 1.32288 | + | 2.29129i | 0.0587510 | + | 0.101760i | ||||
\(508\) | 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 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.50000 | + | 6.06218i | −0.154529 | + | 0.267652i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.96863 | + | 2.29129i | −0.174879 | + | 0.100966i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 36.3731i | 1.59969i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 59.5735i | − | 2.61499i | ||||||
\(520\) | 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 | −0.684399 | − | 0.729108i | \(-0.739935\pi\) |
0.973625 | + | 0.228153i | \(0.0732686\pi\) | |||||||
\(524\) | 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 | ||||||||
\(531\) | 31.7490 | 1.37779 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.0000 | 0.519778 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.9059 | + | 20.6216i | 0.514736 | + | 0.891549i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −31.5000 | − | 18.1865i | −1.35933 | − | 0.784807i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 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 | ||||||||
\(543\) | −47.6235 | + | 27.4955i | −2.04372 | + | 1.17994i | ||||
\(544\) | 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 | ||||||||
\(549\) | 6.00000 | − | 3.46410i | 0.256074 | − | 0.147844i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −27.7804 | − | 16.0390i | −1.17921 | − | 0.680818i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.50000 | + | 2.59808i | 0.0635570 | + | 0.110084i | 0.896053 | − | 0.443947i | \(-0.146422\pi\) |
−0.832496 | + | 0.554031i | \(0.813089\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.7490 | 1.34284 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −63.0000 | −2.65986 | ||||||||
\(562\) | 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 | −0.557520 | − | 0.830164i | \(-0.688247\pi\) |
0.997703 | + | 0.0677445i | \(0.0215803\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | − | 60.6218i | − | 2.53251i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 9.16515i | − | 0.382213i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.5000 | − | 9.52628i | 0.686904 | − | 0.396584i | −0.115547 | − | 0.993302i | \(-0.536862\pi\) |
0.802451 | + | 0.596718i | \(0.203529\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14.5516 | + | 25.2042i | −0.604745 | + | 1.04745i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.9059 | − | 6.87386i | −0.493091 | − | 0.284686i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −12.0000 | − | 20.7846i | −0.496139 | − | 0.859338i | ||||
\(586\) | 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 | ||||||||
\(591\) | −15.8745 | − | 27.4955i | −0.652990 | − | 1.13101i | ||||
\(592\) | 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 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.5000 | − | 30.3109i | 0.716227 | − | 1.24054i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.96863 | + | 2.29129i | −0.162154 | + | 0.0936195i | −0.578881 | − | 0.815412i | \(-0.696510\pi\) |
0.416727 | + | 0.909032i | \(0.363177\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 3.46410i | − | 0.141304i | −0.997501 | − | 0.0706518i | \(-0.977492\pi\) | ||
0.997501 | − | 0.0706518i | \(-0.0225079\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 18.3303i | − | 0.746468i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.0000 | − | 8.66025i | 0.609837 | − | 0.352089i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.32288 | − | 2.29129i | 0.0536939 | − | 0.0930005i | −0.837929 | − | 0.545779i | \(-0.816234\pi\) |
0.891623 | + | 0.452778i | \(0.149567\pi\) | |||||||
\(608\) | 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 | ||||||||
\(615\) | 15.8745 | 0.640122 | ||||||||
\(616\) | 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 | 0.617707 | − | 0.786408i | \(-0.288062\pi\) |
−0.989903 | + | 0.141746i | \(0.954728\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.5000 | − | 6.06218i | −0.421350 | − | 0.243267i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | − | 9.52628i | 0.220000 | − | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 27.7804 | − | 16.0390i | 1.10944 | − | 0.640537i | ||||
\(628\) | 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 | ||||||||
\(633\) | 21.0000 | − | 12.1244i | 0.834675 | − | 0.481900i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.93725 | + | 13.7477i | −0.314980 | + | 0.545562i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 31.7490 | + | 18.3303i | 1.25597 | + | 0.725136i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.5000 | + | 18.1865i | 0.414725 | + | 0.718325i | 0.995400 | − | 0.0958109i | \(-0.0305444\pi\) |
−0.580674 | + | 0.814136i | \(0.697211\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.1660 | 0.834706 | 0.417353 | − | 0.908744i | \(-0.362958\pi\) | ||||
0.417353 | + | 0.908744i | \(0.362958\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 42.0000 | 1.65375 | ||||||||
\(646\) | 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 | −0.584091 | − | 0.811688i | \(-0.698549\pi\) |
0.994988 | + | 0.0999939i | \(0.0318823\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.9059 | − | 6.87386i | 0.465201 | − | 0.268584i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 20.7846i | 0.810885i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 9.16515i | − | 0.357024i | −0.983938 | − | 0.178512i | \(-0.942872\pi\) | ||
0.983938 | − | 0.178512i | \(-0.0571283\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.50000 | − | 2.59808i | 0.175030 | − | 0.101053i | −0.409926 | − | 0.912119i | \(-0.634445\pi\) |
0.584955 | + | 0.811065i | \(0.301112\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 23.8118 | − | 41.2432i | 0.924772 | − | 1.60175i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.0000 | − | 24.2487i | −0.541271 | − | 0.937509i | ||||
\(670\) | 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 | ||||||||
\(675\) | 2.64575 | + | 4.58258i | 0.101835 | + | 0.176383i | ||||
\(676\) | 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 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 31.5000 | − | 54.5596i | 1.20708 | − | 2.09073i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.96863 | − | 2.29129i | 0.151855 | − | 0.0876737i | −0.422147 | − | 0.906527i | \(-0.638723\pi\) |
0.574002 | + | 0.818854i | \(0.305390\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 36.3731i | − | 1.38974i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.58258i | 0.174836i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.00000 | − | 5.19615i | 0.342873 | − | 0.197958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.32288 | + | 2.29129i | −0.0503246 | + | 0.0871647i | −0.890090 | − | 0.455784i | \(-0.849359\pi\) |
0.839766 | + | 0.542949i | \(0.182692\pi\) | |||||||
\(692\) | 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 | ||||||||
\(699\) | −55.5608 | −2.10150 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.0000 | −1.58632 | −0.793159 | − | 0.609015i | \(-0.791565\pi\) | ||||
−0.793159 | + | 0.609015i | \(0.791565\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.26013 | + | 16.0390i | 0.349252 | + | 0.604923i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −31.5000 | − | 18.1865i | −1.18636 | − | 0.684944i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 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 | ||||||||
\(711\) | −15.8745 | + | 9.16515i | −0.595341 | + | 0.343720i | ||||
\(712\) | 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 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 43.6549 | + | 25.2042i | 1.62354 | + | 0.937353i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.1660 | −0.785004 | −0.392502 | − | 0.919751i | \(-0.628390\pi\) | ||||
−0.392502 | + | 0.919751i | \(0.628390\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −41.0000 | −1.51852 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.8118 | + | 41.2432i | 0.880710 | + | 1.52543i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.5000 | − | 11.2583i | −0.720249 | − | 0.415836i | 0.0945954 | − | 0.995516i | \(-0.469844\pi\) |
−0.814844 | + | 0.579680i | \(0.803178\pi\) | |||||||
\(734\) | 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 | ||||||||
\(741\) | 24.2487i | 0.890799i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 45.8258i | 1.68118i | 0.541669 | + | 0.840592i | \(0.317793\pi\) | ||||
−0.541669 | + | 0.840592i | \(0.682207\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22.5000 | − | 12.9904i | 0.824336 | − | 0.475931i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 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 | ||||||||
\(753\) | 21.0000 | + | 36.3731i | 0.765283 | + | 1.32551i | ||||
\(754\) | 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 | ||||||||
\(759\) | 27.7804 | + | 48.1170i | 1.00836 | + | 1.74654i | ||||
\(760\) | 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 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 18.0000 | − | 31.1769i | 0.650791 | − | 1.12720i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 23.8118 | − | 13.7477i | 0.859793 | − | 0.496402i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 51.9615i | 1.87378i | 0.349624 | + | 0.936890i | \(0.386309\pi\) | ||||
−0.349624 | + | 0.936890i | \(0.613691\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.58258i | 0.165037i | ||||||||
\(772\) | 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 | 0.959498 | − | 0.281715i | \(-0.0909031\pi\) |
−0.723721 | + | 0.690093i | \(0.757570\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.5000 | − | 6.06218i | −0.373810 | − | 0.215819i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.00000 | − | 5.19615i | 0.106533 | − | 0.184521i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 11.9059 | − | 6.87386i | 0.422258 | − | 0.243791i | ||||
\(796\) | 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 | ||||||||
\(801\) | 6.00000 | − | 3.46410i | 0.212000 | − | 0.122398i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.9059 | − | 20.6216i | 0.420149 | − | 0.727720i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −67.4667 | − | 38.9519i | −2.37494 | − | 1.37117i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.5000 | + | 38.9711i | 0.791058 | + | 1.37015i | 0.925312 | + | 0.379206i | \(0.123803\pi\) |
−0.134255 | + | 0.990947i | \(0.542864\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.1660 | −0.743239 | −0.371620 | − | 0.928385i | \(-0.621197\pi\) | ||||
−0.371620 | + | 0.928385i | \(0.621197\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 77.0000 | 2.70051 | ||||||||
\(814\) | 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 | −0.528302 | − | 0.849056i | \(-0.677171\pi\) |
0.999456 | + | 0.0329950i | \(0.0105045\pi\) | |||||||
\(822\) | 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 | ||||||||
\(825\) | − | 24.2487i | − | 0.844232i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.16515i | 0.318704i | 0.987222 | + | 0.159352i | \(0.0509404\pi\) | ||||
−0.987222 | + | 0.159352i | \(0.949060\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.50000 | + | 2.59808i | −0.156291 | + | 0.0902349i | −0.576106 | − | 0.817375i | \(-0.695428\pi\) |
0.419815 | + | 0.907610i | \(0.362095\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.4889 | + | 38.9519i | −0.780131 | + | 1.35123i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.8118 | + | 13.7477i | 0.824040 | + | 0.475760i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.50000 | + | 6.06218i | 0.120978 | + | 0.209540i | ||||
\(838\) | 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 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 17.5000 | − | 30.3109i | 0.600598 | − | 1.04027i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27.7804 | + | 16.0390i | −0.952299 | + | 0.549810i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 51.9615i | − | 1.77913i | −0.456810 | − | 0.889564i | \(-0.651008\pi\) | ||
0.456810 | − | 0.889564i | \(-0.348992\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18.3303i | 0.626883i | ||||||||
\(856\) | 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 | −0.842575 | − | 0.538579i | \(-0.818961\pi\) |
0.887711 | + | 0.460402i | \(0.152295\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.9059 | − | 6.87386i | −0.405281 | − | 0.233989i | 0.283479 | − | 0.958978i | \(-0.408511\pi\) |
−0.688760 | + | 0.724989i | \(0.741845\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.5000 | − | 33.7750i | −0.663020 | − | 1.14838i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 26.4575 | 0.898544 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.0000 | 0.712376 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.93725 | − | 13.7477i | −0.268944 | − | 0.465824i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.0000 | + | 6.92820i | 0.406138 | + | 0.234484i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 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 | ||||||||
\(879\) | 47.6235 | − | 27.4955i | 1.60630 | − | 0.927399i | ||||
\(880\) | 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 | ||||||||
\(885\) | 31.5000 | − | 18.1865i | 1.05886 | − | 0.611334i | ||||
\(886\) | 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 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 19.8431 | + | 11.4564i | 0.664770 | + | 0.383805i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.5000 | + | 18.1865i | 0.351369 | + | 0.608589i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23.8118 | −0.795939 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −42.0000 | −1.40234 | ||||||||
\(898\) | 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 | ||||||||
\(909\) | − | 20.7846i | − | 0.689382i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 27.4955i | − | 0.910965i | −0.890245 | − | 0.455483i | \(-0.849467\pi\) | ||
0.890245 | − | 0.455483i | \(-0.150533\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.96863 | − | 6.87386i | 0.131199 | − | 0.227243i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 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 | ||||||||
\(921\) | −14.0000 | − | 24.2487i | −0.461316 | − | 0.799022i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 31.7490 | 1.04503 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.0000 | 0.460317 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.29150 | − | 9.16515i | −0.173796 | − | 0.301023i | ||||
\(928\) | 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 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −31.5000 | + | 54.5596i | −1.03126 | + | 1.78620i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −35.7176 | + | 20.6216i | −1.16809 | + | 0.674398i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 27.7128i | − | 0.905338i | −0.891679 | − | 0.452669i | \(-0.850472\pi\) | ||
0.891679 | − | 0.452669i | \(-0.149528\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 68.7386i | 2.24320i | ||||||||
\(940\) | 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 | 0.563094 | − | 0.826393i | \(-0.309611\pi\) |
−0.434131 | + | 0.900850i | \(0.642944\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.00000 | + | 15.5885i | 0.292152 | + | 0.506023i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −39.6863 | −1.28692 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.0000 | −0.388718 | −0.194359 | − | 0.980930i | \(-0.562263\pi\) | ||||
−0.194359 | + | 0.980930i | \(0.562263\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.8431 | − | 34.3693i | −0.642109 | − | 1.11217i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.0000 | − | 20.7846i | 0.387097 | − | 0.670471i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −47.6235 | + | 27.4955i | −1.53465 | + | 0.886029i | ||||
\(964\) | 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 | ||||||||
\(969\) | −31.5000 | + | 18.1865i | −1.01193 | + | 0.584236i | ||||
\(970\) | 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 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 15.8745 | + | 9.16515i | 0.508391 | + | 0.293520i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.5000 | − | 18.1865i | −0.335925 | − | 0.581839i | 0.647737 | − | 0.761864i | \(-0.275715\pi\) |
−0.983662 | + | 0.180025i | \(0.942382\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.93725 | −0.253676 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −28.0000 | −0.893971 | ||||||||
\(982\) | 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 | ||||||||
\(993\) | − | 36.3731i | − | 1.15426i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 22.9129i | − | 0.726387i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.5000 | + | 21.6506i | −1.18764 | + | 0.685682i | −0.957769 | − | 0.287539i | \(-0.907163\pi\) |
−0.229868 | + | 0.973222i | \(0.573829\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.26013 | − | 16.0390i | 0.292978 | − | 0.507452i |
(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 | 784.2.p.g.607.2 | 4 | ||
4.3 | odd | 2 | inner | 784.2.p.g.607.1 | 4 | ||
7.2 | even | 3 | 784.2.f.d.783.1 | 4 | |||
7.3 | odd | 6 | inner | 784.2.p.g.31.1 | 4 | ||
7.4 | even | 3 | 112.2.p.c.31.2 | yes | 4 | ||
7.5 | odd | 6 | 784.2.f.d.783.4 | 4 | |||
7.6 | odd | 2 | 112.2.p.c.47.1 | yes | 4 | ||
21.2 | odd | 6 | 7056.2.b.s.1567.3 | 4 | |||
21.5 | even | 6 | 7056.2.b.s.1567.1 | 4 | |||
21.11 | odd | 6 | 1008.2.cs.q.703.2 | 4 | |||
21.20 | even | 2 | 1008.2.cs.q.271.1 | 4 | |||
28.3 | even | 6 | inner | 784.2.p.g.31.2 | 4 | ||
28.11 | odd | 6 | 112.2.p.c.31.1 | ✓ | 4 | ||
28.19 | even | 6 | 784.2.f.d.783.2 | 4 | |||
28.23 | odd | 6 | 784.2.f.d.783.3 | 4 | |||
28.27 | even | 2 | 112.2.p.c.47.2 | yes | 4 | ||
56.5 | odd | 6 | 3136.2.f.f.3135.1 | 4 | |||
56.11 | odd | 6 | 448.2.p.c.255.2 | 4 | |||
56.13 | odd | 2 | 448.2.p.c.383.2 | 4 | |||
56.19 | even | 6 | 3136.2.f.f.3135.3 | 4 | |||
56.27 | even | 2 | 448.2.p.c.383.1 | 4 | |||
56.37 | even | 6 | 3136.2.f.f.3135.4 | 4 | |||
56.51 | odd | 6 | 3136.2.f.f.3135.2 | 4 | |||
56.53 | even | 6 | 448.2.p.c.255.1 | 4 | |||
84.11 | even | 6 | 1008.2.cs.q.703.1 | 4 | |||
84.23 | even | 6 | 7056.2.b.s.1567.4 | 4 | |||
84.47 | odd | 6 | 7056.2.b.s.1567.2 | 4 | |||
84.83 | odd | 2 | 1008.2.cs.q.271.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.p.c.31.1 | ✓ | 4 | 28.11 | odd | 6 | ||
112.2.p.c.31.2 | yes | 4 | 7.4 | even | 3 | ||
112.2.p.c.47.1 | yes | 4 | 7.6 | odd | 2 | ||
112.2.p.c.47.2 | yes | 4 | 28.27 | even | 2 | ||
448.2.p.c.255.1 | 4 | 56.53 | even | 6 | |||
448.2.p.c.255.2 | 4 | 56.11 | odd | 6 | |||
448.2.p.c.383.1 | 4 | 56.27 | even | 2 | |||
448.2.p.c.383.2 | 4 | 56.13 | odd | 2 | |||
784.2.f.d.783.1 | 4 | 7.2 | even | 3 | |||
784.2.f.d.783.2 | 4 | 28.19 | even | 6 | |||
784.2.f.d.783.3 | 4 | 28.23 | odd | 6 | |||
784.2.f.d.783.4 | 4 | 7.5 | odd | 6 | |||
784.2.p.g.31.1 | 4 | 7.3 | odd | 6 | inner | ||
784.2.p.g.31.2 | 4 | 28.3 | even | 6 | inner | ||
784.2.p.g.607.1 | 4 | 4.3 | odd | 2 | inner | ||
784.2.p.g.607.2 | 4 | 1.1 | even | 1 | trivial | ||
1008.2.cs.q.271.1 | 4 | 21.20 | even | 2 | |||
1008.2.cs.q.271.2 | 4 | 84.83 | odd | 2 | |||
1008.2.cs.q.703.1 | 4 | 84.11 | even | 6 | |||
1008.2.cs.q.703.2 | 4 | 21.11 | odd | 6 | |||
3136.2.f.f.3135.1 | 4 | 56.5 | odd | 6 | |||
3136.2.f.f.3135.2 | 4 | 56.51 | odd | 6 | |||
3136.2.f.f.3135.3 | 4 | 56.19 | even | 6 | |||
3136.2.f.f.3135.4 | 4 | 56.37 | even | 6 | |||
7056.2.b.s.1567.1 | 4 | 21.5 | even | 6 | |||
7056.2.b.s.1567.2 | 4 | 84.47 | odd | 6 | |||
7056.2.b.s.1567.3 | 4 | 21.2 | odd | 6 | |||
7056.2.b.s.1567.4 | 4 | 84.23 | even | 6 |