Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7605,2,Mod(1,7605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7605, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7605.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7605 = 3^{2} \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7605.a (trivial) |
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: | yes |
Analytic conductor: | \(60.7262307372\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 65) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7605.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.30278 | −1.62831 | −0.814154 | − | 0.580649i | \(-0.802799\pi\) | ||||
−0.814154 | + | 0.580649i | \(0.802799\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.30278 | 1.65139 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | 0.188982 | − | 0.981981i | \(-0.439481\pi\) | ||||
0.188982 | + | 0.981981i | \(0.439481\pi\) | |||||||
\(8\) | −3.00000 | −1.06066 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.30278 | 0.728202 | ||||||||
\(11\) | 1.60555 | 0.484092 | 0.242046 | − | 0.970265i | \(-0.422182\pi\) | ||||
0.242046 | + | 0.970265i | \(0.422182\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −2.30278 | −0.615443 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.302776 | 0.0756939 | ||||||||
\(17\) | −7.60555 | −1.84462 | −0.922309 | − | 0.386454i | \(-0.873700\pi\) | ||||
−0.922309 | + | 0.386454i | \(0.873700\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.60555 | 1.28600 | 0.643001 | − | 0.765865i | \(-0.277689\pi\) | ||||
0.643001 | + | 0.765865i | \(0.277689\pi\) | |||||||
\(20\) | −3.30278 | −0.738523 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.69722 | −0.788251 | ||||||||
\(23\) | 3.00000 | 0.625543 | 0.312772 | − | 0.949828i | \(-0.398743\pi\) | ||||
0.312772 | + | 0.949828i | \(0.398743\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.30278 | 0.624166 | ||||||||
\(29\) | 6.21110 | 1.15337 | 0.576686 | − | 0.816966i | \(-0.304345\pi\) | ||||
0.576686 | + | 0.816966i | \(0.304345\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | 5.30278 | 0.937407 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 17.5139 | 3.00361 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.60555 | −0.592749 | −0.296374 | − | 0.955072i | \(-0.595778\pi\) | ||||
−0.296374 | + | 0.955072i | \(0.595778\pi\) | |||||||
\(38\) | −12.9083 | −2.09401 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.00000 | 0.474342 | ||||||||
\(41\) | 3.00000 | 0.468521 | 0.234261 | − | 0.972174i | \(-0.424733\pi\) | ||||
0.234261 | + | 0.972174i | \(0.424733\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.2111 | −1.55718 | −0.778589 | − | 0.627534i | \(-0.784064\pi\) | ||||
−0.778589 | + | 0.627534i | \(0.784064\pi\) | |||||||
\(44\) | 5.30278 | 0.799424 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.90833 | −1.01858 | ||||||||
\(47\) | 9.21110 | 1.34358 | 0.671789 | − | 0.740743i | \(-0.265526\pi\) | ||||
0.671789 | + | 0.740743i | \(0.265526\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | −2.30278 | −0.325662 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.21110 | 0.441079 | 0.220539 | − | 0.975378i | \(-0.429218\pi\) | ||||
0.220539 | + | 0.975378i | \(0.429218\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.60555 | −0.216492 | ||||||||
\(56\) | −3.00000 | −0.400892 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −14.3028 | −1.87805 | ||||||||
\(59\) | −10.8167 | −1.40821 | −0.704104 | − | 0.710097i | \(-0.748651\pi\) | ||||
−0.704104 | + | 0.710097i | \(0.748651\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | −0.128037 | −0.0640184 | − | 0.997949i | \(-0.520392\pi\) | ||||
−0.0640184 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(62\) | −9.21110 | −1.16981 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.8167 | −1.60208 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.00000 | 0.855186 | 0.427593 | − | 0.903971i | \(-0.359362\pi\) | ||||
0.427593 | + | 0.903971i | \(0.359362\pi\) | |||||||
\(68\) | −25.1194 | −3.04618 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.30278 | 0.275234 | ||||||||
\(71\) | 4.81665 | 0.571632 | 0.285816 | − | 0.958285i | \(-0.407735\pi\) | ||||
0.285816 | + | 0.958285i | \(0.407735\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.788897 | 0.0923335 | 0.0461667 | − | 0.998934i | \(-0.485299\pi\) | ||||
0.0461667 | + | 0.998934i | \(0.485299\pi\) | |||||||
\(74\) | 8.30278 | 0.965178 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 18.5139 | 2.12369 | ||||||||
\(77\) | 1.60555 | 0.182970 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.21110 | 0.586295 | 0.293147 | − | 0.956067i | \(-0.405297\pi\) | ||||
0.293147 | + | 0.956067i | \(0.405297\pi\) | |||||||
\(80\) | −0.302776 | −0.0338513 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.90833 | −0.762897 | ||||||||
\(83\) | −9.21110 | −1.01105 | −0.505525 | − | 0.862812i | \(-0.668701\pi\) | ||||
−0.505525 | + | 0.862812i | \(0.668701\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.60555 | 0.824938 | ||||||||
\(86\) | 23.5139 | 2.53557 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.81665 | −0.513457 | ||||||||
\(89\) | −6.21110 | −0.658376 | −0.329188 | − | 0.944264i | \(-0.606775\pi\) | ||||
−0.329188 | + | 0.944264i | \(0.606775\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9.90833 | 1.03301 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −21.2111 | −2.18776 | ||||||||
\(95\) | −5.60555 | −0.575117 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.39445 | 0.852327 | 0.426164 | − | 0.904646i | \(-0.359865\pi\) | ||||
0.426164 | + | 0.904646i | \(0.359865\pi\) | |||||||
\(98\) | 13.8167 | 1.39569 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.30278 | 0.330278 | ||||||||
\(101\) | 9.00000 | 0.895533 | 0.447767 | − | 0.894150i | \(-0.352219\pi\) | ||||
0.447767 | + | 0.894150i | \(0.352219\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | −0.394132 | −0.197066 | − | 0.980390i | \(-0.563141\pi\) | ||||
−0.197066 | + | 0.980390i | \(0.563141\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.39445 | −0.718212 | ||||||||
\(107\) | −6.21110 | −0.600450 | −0.300225 | − | 0.953868i | \(-0.597062\pi\) | ||||
−0.300225 | + | 0.953868i | \(0.597062\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.2111 | 1.84009 | 0.920045 | − | 0.391813i | \(-0.128152\pi\) | ||||
0.920045 | + | 0.391813i | \(0.128152\pi\) | |||||||
\(110\) | 3.69722 | 0.352517 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.302776 | 0.0286096 | ||||||||
\(113\) | 1.60555 | 0.151038 | 0.0755188 | − | 0.997144i | \(-0.475939\pi\) | ||||
0.0755188 | + | 0.997144i | \(0.475939\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.00000 | −0.279751 | ||||||||
\(116\) | 20.5139 | 1.90467 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 24.9083 | 2.29300 | ||||||||
\(119\) | −7.60555 | −0.697200 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.42221 | −0.765655 | ||||||||
\(122\) | 2.30278 | 0.208484 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 13.2111 | 1.18639 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.21110 | −0.373675 | −0.186837 | − | 0.982391i | \(-0.559824\pi\) | ||||
−0.186837 | + | 0.982391i | \(0.559824\pi\) | |||||||
\(128\) | 18.9083 | 1.67128 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21.2111 | 1.85322 | 0.926611 | − | 0.376021i | \(-0.122708\pi\) | ||||
0.926611 | + | 0.376021i | \(0.122708\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.60555 | 0.486063 | ||||||||
\(134\) | −16.1194 | −1.39251 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 22.8167 | 1.95651 | ||||||||
\(137\) | −1.60555 | −0.137172 | −0.0685858 | − | 0.997645i | \(-0.521849\pi\) | ||||
−0.0685858 | + | 0.997645i | \(0.521849\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.39445 | 0.542370 | 0.271185 | − | 0.962527i | \(-0.412584\pi\) | ||||
0.271185 | + | 0.962527i | \(0.412584\pi\) | |||||||
\(140\) | −3.30278 | −0.279135 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −11.0917 | −0.930793 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.21110 | −0.515804 | ||||||||
\(146\) | −1.81665 | −0.150347 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −11.9083 | −0.978858 | ||||||||
\(149\) | 3.00000 | 0.245770 | 0.122885 | − | 0.992421i | \(-0.460785\pi\) | ||||
0.122885 | + | 0.992421i | \(0.460785\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.21110 | 0.0985581 | 0.0492791 | − | 0.998785i | \(-0.484308\pi\) | ||||
0.0492791 | + | 0.998785i | \(0.484308\pi\) | |||||||
\(152\) | −16.8167 | −1.36401 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.69722 | −0.297931 | ||||||||
\(155\) | −4.00000 | −0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.2111 | 0.894743 | 0.447372 | − | 0.894348i | \(-0.352360\pi\) | ||||
0.447372 | + | 0.894348i | \(0.352360\pi\) | |||||||
\(158\) | −12.0000 | −0.954669 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.30278 | −0.419221 | ||||||||
\(161\) | 3.00000 | 0.236433 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.78890 | 0.296769 | 0.148385 | − | 0.988930i | \(-0.452593\pi\) | ||||
0.148385 | + | 0.988930i | \(0.452593\pi\) | |||||||
\(164\) | 9.90833 | 0.773710 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 21.2111 | 1.64630 | ||||||||
\(167\) | 9.00000 | 0.696441 | 0.348220 | − | 0.937413i | \(-0.386786\pi\) | ||||
0.348220 | + | 0.937413i | \(0.386786\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −17.5139 | −1.34325 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −33.7250 | −2.57151 | ||||||||
\(173\) | −4.81665 | −0.366203 | −0.183102 | − | 0.983094i | \(-0.558614\pi\) | ||||
−0.183102 | + | 0.983094i | \(0.558614\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0.486122 | 0.0366428 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 14.3028 | 1.07204 | ||||||||
\(179\) | −22.8167 | −1.70540 | −0.852698 | − | 0.522404i | \(-0.825035\pi\) | ||||
−0.852698 | + | 0.522404i | \(0.825035\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.6333 | 1.31067 | 0.655337 | − | 0.755337i | \(-0.272527\pi\) | ||||
0.655337 | + | 0.755337i | \(0.272527\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −9.00000 | −0.663489 | ||||||||
\(185\) | 3.60555 | 0.265085 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.2111 | −0.892964 | ||||||||
\(188\) | 30.4222 | 2.21877 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.9083 | 0.936468 | ||||||||
\(191\) | −16.8167 | −1.21681 | −0.608405 | − | 0.793627i | \(-0.708190\pi\) | ||||
−0.608405 | + | 0.793627i | \(0.708190\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.6056 | −1.12331 | −0.561656 | − | 0.827371i | \(-0.689836\pi\) | ||||
−0.561656 | + | 0.827371i | \(0.689836\pi\) | |||||||
\(194\) | −19.3305 | −1.38785 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −19.8167 | −1.41548 | ||||||||
\(197\) | 1.18335 | 0.0843099 | 0.0421550 | − | 0.999111i | \(-0.486578\pi\) | ||||
0.0421550 | + | 0.999111i | \(0.486578\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.8167 | 0.908549 | 0.454274 | − | 0.890862i | \(-0.349899\pi\) | ||||
0.454274 | + | 0.890862i | \(0.349899\pi\) | |||||||
\(200\) | −3.00000 | −0.212132 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −20.7250 | −1.45820 | ||||||||
\(203\) | 6.21110 | 0.435934 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.00000 | −0.209529 | ||||||||
\(206\) | 9.21110 | 0.641768 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.00000 | 0.622543 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.6056 | −1.62507 | −0.812537 | − | 0.582910i | \(-0.801914\pi\) | ||||
−0.812537 | + | 0.582910i | \(0.801914\pi\) | |||||||
\(212\) | 10.6056 | 0.728392 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 14.3028 | 0.977718 | ||||||||
\(215\) | 10.2111 | 0.696391 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.00000 | 0.271538 | ||||||||
\(218\) | −44.2389 | −2.99623 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.30278 | −0.357513 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.21110 | 0.281996 | 0.140998 | − | 0.990010i | \(-0.454969\pi\) | ||||
0.140998 | + | 0.990010i | \(0.454969\pi\) | |||||||
\(224\) | 5.30278 | 0.354307 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.69722 | −0.245936 | ||||||||
\(227\) | −27.4222 | −1.82008 | −0.910038 | − | 0.414525i | \(-0.863948\pi\) | ||||
−0.910038 | + | 0.414525i | \(0.863948\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.0000 | −0.925146 | −0.462573 | − | 0.886581i | \(-0.653074\pi\) | ||||
−0.462573 | + | 0.886581i | \(0.653074\pi\) | |||||||
\(230\) | 6.90833 | 0.455522 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −18.6333 | −1.22334 | ||||||||
\(233\) | −15.2111 | −0.996512 | −0.498256 | − | 0.867030i | \(-0.666026\pi\) | ||||
−0.498256 | + | 0.867030i | \(0.666026\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.21110 | −0.600866 | ||||||||
\(236\) | −35.7250 | −2.32550 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 17.5139 | 1.13526 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.78890 | −0.115233 | −0.0576165 | − | 0.998339i | \(-0.518350\pi\) | ||||
−0.0576165 | + | 0.998339i | \(0.518350\pi\) | |||||||
\(242\) | 19.3944 | 1.24672 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.30278 | −0.211439 | ||||||||
\(245\) | 6.00000 | 0.383326 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −12.0000 | −0.762001 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.30278 | 0.145640 | ||||||||
\(251\) | 7.18335 | 0.453409 | 0.226704 | − | 0.973964i | \(-0.427205\pi\) | ||||
0.226704 | + | 0.973964i | \(0.427205\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.81665 | 0.302820 | ||||||||
\(254\) | 9.69722 | 0.608458 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −17.9083 | −1.11927 | ||||||||
\(257\) | 16.3944 | 1.02266 | 0.511329 | − | 0.859385i | \(-0.329153\pi\) | ||||
0.511329 | + | 0.859385i | \(0.329153\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.60555 | −0.224038 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −48.8444 | −3.01762 | ||||||||
\(263\) | −11.7889 | −0.726935 | −0.363467 | − | 0.931607i | \(-0.618407\pi\) | ||||
−0.363467 | + | 0.931607i | \(0.618407\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.21110 | −0.197256 | ||||||||
\(266\) | −12.9083 | −0.791460 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 23.1194 | 1.41224 | ||||||||
\(269\) | 9.00000 | 0.548740 | 0.274370 | − | 0.961624i | \(-0.411531\pi\) | ||||
0.274370 | + | 0.961624i | \(0.411531\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.8167 | 1.26452 | 0.632261 | − | 0.774756i | \(-0.282127\pi\) | ||||
0.632261 | + | 0.774756i | \(0.282127\pi\) | |||||||
\(272\) | −2.30278 | −0.139626 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.69722 | 0.223357 | ||||||||
\(275\) | 1.60555 | 0.0968184 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.6056 | 1.65866 | 0.829328 | − | 0.558761i | \(-0.188723\pi\) | ||||
0.829328 | + | 0.558761i | \(0.188723\pi\) | |||||||
\(278\) | −14.7250 | −0.883146 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.00000 | 0.179284 | ||||||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.00000 | 0.297219 | 0.148610 | − | 0.988896i | \(-0.452520\pi\) | ||||
0.148610 | + | 0.988896i | \(0.452520\pi\) | |||||||
\(284\) | 15.9083 | 0.943986 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.00000 | 0.177084 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 40.8444 | 2.40261 | ||||||||
\(290\) | 14.3028 | 0.839888 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.60555 | 0.152478 | ||||||||
\(293\) | 10.3944 | 0.607250 | 0.303625 | − | 0.952792i | \(-0.401803\pi\) | ||||
0.303625 | + | 0.952792i | \(0.401803\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.8167 | 0.629770 | ||||||||
\(296\) | 10.8167 | 0.628705 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.90833 | −0.400189 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.2111 | −0.588558 | ||||||||
\(302\) | −2.78890 | −0.160483 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.69722 | 0.0973425 | ||||||||
\(305\) | 1.00000 | 0.0572598 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.0000 | 0.913168 | 0.456584 | − | 0.889680i | \(-0.349073\pi\) | ||||
0.456584 | + | 0.889680i | \(0.349073\pi\) | |||||||
\(308\) | 5.30278 | 0.302154 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.21110 | 0.523155 | ||||||||
\(311\) | 9.21110 | 0.522314 | 0.261157 | − | 0.965296i | \(-0.415896\pi\) | ||||
0.261157 | + | 0.965296i | \(0.415896\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0000 | 0.791327 | 0.395663 | − | 0.918396i | \(-0.370515\pi\) | ||||
0.395663 | + | 0.918396i | \(0.370515\pi\) | |||||||
\(314\) | −25.8167 | −1.45692 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 17.2111 | 0.968200 | ||||||||
\(317\) | 6.00000 | 0.336994 | 0.168497 | − | 0.985702i | \(-0.446109\pi\) | ||||
0.168497 | + | 0.985702i | \(0.446109\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.97224 | 0.558338 | ||||||||
\(320\) | 12.8167 | 0.716473 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.90833 | −0.384986 | ||||||||
\(323\) | −42.6333 | −2.37218 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.72498 | −0.483232 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.00000 | −0.496942 | ||||||||
\(329\) | 9.21110 | 0.507825 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.0278 | −0.551175 | −0.275588 | − | 0.961276i | \(-0.588872\pi\) | ||||
−0.275588 | + | 0.961276i | \(0.588872\pi\) | |||||||
\(332\) | −30.4222 | −1.66964 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −20.7250 | −1.13402 | ||||||||
\(335\) | −7.00000 | −0.382451 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.6333 | −1.39634 | −0.698168 | − | 0.715934i | \(-0.746001\pi\) | ||||
−0.698168 | + | 0.715934i | \(0.746001\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 25.1194 | 1.36229 | ||||||||
\(341\) | 6.42221 | 0.347782 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.0000 | −0.701934 | ||||||||
\(344\) | 30.6333 | 1.65164 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.0917 | 0.596292 | ||||||||
\(347\) | −5.78890 | −0.310764 | −0.155382 | − | 0.987854i | \(-0.549661\pi\) | ||||
−0.155382 | + | 0.987854i | \(0.549661\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.78890 | 0.202815 | 0.101408 | − | 0.994845i | \(-0.467665\pi\) | ||||
0.101408 | + | 0.994845i | \(0.467665\pi\) | |||||||
\(350\) | −2.30278 | −0.123089 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.51388 | 0.453791 | ||||||||
\(353\) | 16.8167 | 0.895060 | 0.447530 | − | 0.894269i | \(-0.352304\pi\) | ||||
0.447530 | + | 0.894269i | \(0.352304\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.81665 | −0.255641 | ||||||||
\(356\) | −20.5139 | −1.08723 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 52.5416 | 2.77691 | ||||||||
\(359\) | 18.4222 | 0.972287 | 0.486143 | − | 0.873879i | \(-0.338403\pi\) | ||||
0.486143 | + | 0.873879i | \(0.338403\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.4222 | 0.653800 | ||||||||
\(362\) | −40.6056 | −2.13418 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.788897 | −0.0412928 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.4222 | 0.596234 | 0.298117 | − | 0.954529i | \(-0.403641\pi\) | ||||
0.298117 | + | 0.954529i | \(0.403641\pi\) | |||||||
\(368\) | 0.908327 | 0.0473498 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.30278 | −0.431641 | ||||||||
\(371\) | 3.21110 | 0.166712 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.3944 | −1.05598 | −0.527992 | − | 0.849249i | \(-0.677055\pi\) | ||||
−0.527992 | + | 0.849249i | \(0.677055\pi\) | |||||||
\(374\) | 28.1194 | 1.45402 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −27.6333 | −1.42508 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.60555 | −0.493404 | −0.246702 | − | 0.969091i | \(-0.579347\pi\) | ||||
−0.246702 | + | 0.969091i | \(0.579347\pi\) | |||||||
\(380\) | −18.5139 | −0.949742 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 38.7250 | 1.98134 | ||||||||
\(383\) | −24.6333 | −1.25870 | −0.629352 | − | 0.777121i | \(-0.716679\pi\) | ||||
−0.629352 | + | 0.777121i | \(0.716679\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.60555 | −0.0818265 | ||||||||
\(386\) | 35.9361 | 1.82910 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 27.7250 | 1.40752 | ||||||||
\(389\) | 15.2111 | 0.771234 | 0.385617 | − | 0.922659i | \(-0.373989\pi\) | ||||
0.385617 | + | 0.922659i | \(0.373989\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.8167 | −1.15389 | ||||||||
\(392\) | 18.0000 | 0.909137 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.72498 | −0.137283 | ||||||||
\(395\) | −5.21110 | −0.262199 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.0278 | −1.10554 | −0.552771 | − | 0.833333i | \(-0.686429\pi\) | ||||
−0.552771 | + | 0.833333i | \(0.686429\pi\) | |||||||
\(398\) | −29.5139 | −1.47940 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.302776 | 0.0151388 | ||||||||
\(401\) | 12.2111 | 0.609793 | 0.304897 | − | 0.952385i | \(-0.401378\pi\) | ||||
0.304897 | + | 0.952385i | \(0.401378\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 29.7250 | 1.47887 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −14.3028 | −0.709835 | ||||||||
\(407\) | −5.78890 | −0.286945 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.21110 | −0.406013 | −0.203006 | − | 0.979177i | \(-0.565071\pi\) | ||||
−0.203006 | + | 0.979177i | \(0.565071\pi\) | |||||||
\(410\) | 6.90833 | 0.341178 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −13.2111 | −0.650864 | ||||||||
\(413\) | −10.8167 | −0.532253 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.21110 | 0.452155 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −20.7250 | −1.01369 | ||||||||
\(419\) | −17.2389 | −0.842173 | −0.421087 | − | 0.907020i | \(-0.638351\pi\) | ||||
−0.421087 | + | 0.907020i | \(0.638351\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.4222 | −1.58016 | −0.790081 | − | 0.613003i | \(-0.789961\pi\) | ||||
−0.790081 | + | 0.613003i | \(0.789961\pi\) | |||||||
\(422\) | 54.3583 | 2.64612 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.63331 | −0.467835 | ||||||||
\(425\) | −7.60555 | −0.368923 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.00000 | −0.0483934 | ||||||||
\(428\) | −20.5139 | −0.991576 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −23.5139 | −1.13394 | ||||||||
\(431\) | 29.2389 | 1.40839 | 0.704193 | − | 0.710008i | \(-0.251309\pi\) | ||||
0.704193 | + | 0.710008i | \(0.251309\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.60555 | 0.173272 | 0.0866359 | − | 0.996240i | \(-0.472388\pi\) | ||||
0.0866359 | + | 0.996240i | \(0.472388\pi\) | |||||||
\(434\) | −9.21110 | −0.442147 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 63.4500 | 3.03870 | ||||||||
\(437\) | 16.8167 | 0.804450 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.2389 | −1.30004 | −0.650020 | − | 0.759917i | \(-0.725239\pi\) | ||||
−0.650020 | + | 0.759917i | \(0.725239\pi\) | |||||||
\(440\) | 4.81665 | 0.229625 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.42221 | −0.305128 | −0.152564 | − | 0.988294i | \(-0.548753\pi\) | ||||
−0.152564 | + | 0.988294i | \(0.548753\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.21110 | 0.294434 | ||||||||
\(446\) | −9.69722 | −0.459177 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −12.8167 | −0.605530 | ||||||||
\(449\) | 30.6333 | 1.44568 | 0.722838 | − | 0.691018i | \(-0.242837\pi\) | ||||
0.722838 | + | 0.691018i | \(0.242837\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.81665 | 0.226807 | ||||||||
\(452\) | 5.30278 | 0.249422 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 63.1472 | 2.96364 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.8167 | 1.25443 | 0.627215 | − | 0.778846i | \(-0.284195\pi\) | ||||
0.627215 | + | 0.778846i | \(0.284195\pi\) | |||||||
\(458\) | 32.2389 | 1.50642 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.90833 | −0.461978 | ||||||||
\(461\) | 36.2111 | 1.68652 | 0.843260 | − | 0.537507i | \(-0.180634\pi\) | ||||
0.843260 | + | 0.537507i | \(0.180634\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.4222 | 1.59974 | 0.799868 | − | 0.600176i | \(-0.204903\pi\) | ||||
0.799868 | + | 0.600176i | \(0.204903\pi\) | |||||||
\(464\) | 1.88057 | 0.0873033 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 35.0278 | 1.62263 | ||||||||
\(467\) | −2.78890 | −0.129055 | −0.0645274 | − | 0.997916i | \(-0.520554\pi\) | ||||
−0.0645274 | + | 0.997916i | \(0.520554\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.00000 | 0.323230 | ||||||||
\(470\) | 21.2111 | 0.978395 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 32.4500 | 1.49363 | ||||||||
\(473\) | −16.3944 | −0.753818 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.60555 | 0.257200 | ||||||||
\(476\) | −25.1194 | −1.15135 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.8167 | −1.31667 | −0.658333 | − | 0.752727i | \(-0.728738\pi\) | ||||
−0.658333 | + | 0.752727i | \(0.728738\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 4.11943 | 0.187635 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −27.8167 | −1.26439 | ||||||||
\(485\) | −8.39445 | −0.381172 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.00000 | 0.0453143 | 0.0226572 | − | 0.999743i | \(-0.492787\pi\) | ||||
0.0226572 | + | 0.999743i | \(0.492787\pi\) | |||||||
\(488\) | 3.00000 | 0.135804 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −13.8167 | −0.624173 | ||||||||
\(491\) | 16.8167 | 0.758925 | 0.379462 | − | 0.925207i | \(-0.376109\pi\) | ||||
0.379462 | + | 0.925207i | \(0.376109\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −47.2389 | −2.12753 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.21110 | 0.0543801 | ||||||||
\(497\) | 4.81665 | 0.216056 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.42221 | −0.108433 | −0.0542164 | − | 0.998529i | \(-0.517266\pi\) | ||||
−0.0542164 | + | 0.998529i | \(0.517266\pi\) | |||||||
\(500\) | −3.30278 | −0.147705 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −16.5416 | −0.738289 | ||||||||
\(503\) | −3.00000 | −0.133763 | −0.0668817 | − | 0.997761i | \(-0.521305\pi\) | ||||
−0.0668817 | + | 0.997761i | \(0.521305\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.00000 | −0.400495 | ||||||||
\(506\) | −11.0917 | −0.493085 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −13.9083 | −0.617082 | ||||||||
\(509\) | 3.00000 | 0.132973 | 0.0664863 | − | 0.997787i | \(-0.478821\pi\) | ||||
0.0664863 | + | 0.997787i | \(0.478821\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.788897 | 0.0348988 | ||||||||
\(512\) | 3.42221 | 0.151242 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −37.7527 | −1.66520 | ||||||||
\(515\) | 4.00000 | 0.176261 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.7889 | 0.650415 | ||||||||
\(518\) | 8.30278 | 0.364803 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.0000 | −0.788594 | −0.394297 | − | 0.918983i | \(-0.629012\pi\) | ||||
−0.394297 | + | 0.918983i | \(0.629012\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.42221 | −0.0621887 | −0.0310943 | − | 0.999516i | \(-0.509899\pi\) | ||||
−0.0310943 | + | 0.999516i | \(0.509899\pi\) | |||||||
\(524\) | 70.0555 | 3.06039 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 27.1472 | 1.18367 | ||||||||
\(527\) | −30.4222 | −1.32521 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.0000 | −0.608696 | ||||||||
\(530\) | 7.39445 | 0.321194 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 18.5139 | 0.802678 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.21110 | 0.268529 | ||||||||
\(536\) | −21.0000 | −0.907062 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −20.7250 | −0.893517 | ||||||||
\(539\) | −9.63331 | −0.414936 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.6333 | 1.10206 | 0.551031 | − | 0.834485i | \(-0.314235\pi\) | ||||
0.551031 | + | 0.834485i | \(0.314235\pi\) | |||||||
\(542\) | −47.9361 | −2.05903 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −40.3305 | −1.72916 | ||||||||
\(545\) | −19.2111 | −0.822913 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.8444 | 1.40433 | 0.702163 | − | 0.712016i | \(-0.252218\pi\) | ||||
0.702163 | + | 0.712016i | \(0.252218\pi\) | |||||||
\(548\) | −5.30278 | −0.226523 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.69722 | −0.157650 | ||||||||
\(551\) | 34.8167 | 1.48324 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.21110 | 0.221599 | ||||||||
\(554\) | −63.5694 | −2.70080 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 21.1194 | 0.895663 | ||||||||
\(557\) | −1.60555 | −0.0680294 | −0.0340147 | − | 0.999421i | \(-0.510829\pi\) | ||||
−0.0340147 | + | 0.999421i | \(0.510829\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.302776 | −0.0127946 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13.8167 | 0.582820 | ||||||||
\(563\) | −9.42221 | −0.397099 | −0.198549 | − | 0.980091i | \(-0.563623\pi\) | ||||
−0.198549 | + | 0.980091i | \(0.563623\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.60555 | −0.0675460 | ||||||||
\(566\) | −11.5139 | −0.483964 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.4500 | −0.606307 | ||||||||
\(569\) | 27.4222 | 1.14960 | 0.574799 | − | 0.818294i | \(-0.305080\pi\) | ||||
0.574799 | + | 0.818294i | \(0.305080\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.8444 | 0.872311 | 0.436156 | − | 0.899871i | \(-0.356340\pi\) | ||||
0.436156 | + | 0.899871i | \(0.356340\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.90833 | −0.288348 | ||||||||
\(575\) | 3.00000 | 0.125109 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.6333 | 0.567562 | 0.283781 | − | 0.958889i | \(-0.408411\pi\) | ||||
0.283781 | + | 0.958889i | \(0.408411\pi\) | |||||||
\(578\) | −94.0555 | −3.91219 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −20.5139 | −0.851792 | ||||||||
\(581\) | −9.21110 | −0.382141 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.15559 | 0.213523 | ||||||||
\(584\) | −2.36669 | −0.0979344 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −23.9361 | −0.988790 | ||||||||
\(587\) | −33.4222 | −1.37948 | −0.689741 | − | 0.724056i | \(-0.742276\pi\) | ||||
−0.689741 | + | 0.724056i | \(0.742276\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.4222 | 0.923891 | ||||||||
\(590\) | −24.9083 | −1.02546 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.09167 | −0.0448675 | ||||||||
\(593\) | 20.7889 | 0.853698 | 0.426849 | − | 0.904323i | \(-0.359624\pi\) | ||||
0.426849 | + | 0.904323i | \(0.359624\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.60555 | 0.311797 | ||||||||
\(596\) | 9.90833 | 0.405861 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.2111 | 0.866662 | 0.433331 | − | 0.901235i | \(-0.357338\pi\) | ||||
0.433331 | + | 0.901235i | \(0.357338\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.7889 | 0.562461 | 0.281230 | − | 0.959640i | \(-0.409257\pi\) | ||||
0.281230 | + | 0.959640i | \(0.409257\pi\) | |||||||
\(602\) | 23.5139 | 0.958354 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.00000 | 0.162758 | ||||||||
\(605\) | 8.42221 | 0.342411 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −34.2111 | −1.38859 | −0.694293 | − | 0.719693i | \(-0.744283\pi\) | ||||
−0.694293 | + | 0.719693i | \(0.744283\pi\) | |||||||
\(608\) | 29.7250 | 1.20551 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.30278 | −0.0932367 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.60555 | 0.226406 | 0.113203 | − | 0.993572i | \(-0.463889\pi\) | ||||
0.113203 | + | 0.993572i | \(0.463889\pi\) | |||||||
\(614\) | −36.8444 | −1.48692 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.81665 | −0.194069 | ||||||||
\(617\) | −38.4500 | −1.54794 | −0.773969 | − | 0.633224i | \(-0.781731\pi\) | ||||
−0.773969 | + | 0.633224i | \(0.781731\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.4222 | −0.579677 | −0.289839 | − | 0.957076i | \(-0.593602\pi\) | ||||
−0.289839 | + | 0.957076i | \(0.593602\pi\) | |||||||
\(620\) | −13.2111 | −0.530571 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −21.2111 | −0.850488 | ||||||||
\(623\) | −6.21110 | −0.248843 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −32.2389 | −1.28852 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 37.0278 | 1.47757 | ||||||||
\(629\) | 27.4222 | 1.09339 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.0278 | 1.43424 | 0.717121 | − | 0.696949i | \(-0.245459\pi\) | ||||
0.717121 | + | 0.696949i | \(0.245459\pi\) | |||||||
\(632\) | −15.6333 | −0.621860 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −13.8167 | −0.548729 | ||||||||
\(635\) | 4.21110 | 0.167113 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −22.9638 | −0.909147 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −18.9083 | −0.747417 | ||||||||
\(641\) | −9.42221 | −0.372155 | −0.186077 | − | 0.982535i | \(-0.559578\pi\) | ||||
−0.186077 | + | 0.982535i | \(0.559578\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.63331 | −0.103848 | −0.0519238 | − | 0.998651i | \(-0.516535\pi\) | ||||
−0.0519238 | + | 0.998651i | \(0.516535\pi\) | |||||||
\(644\) | 9.90833 | 0.390443 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 98.1749 | 3.86264 | ||||||||
\(647\) | −39.4222 | −1.54985 | −0.774923 | − | 0.632055i | \(-0.782212\pi\) | ||||
−0.774923 | + | 0.632055i | \(0.782212\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.3667 | −0.681702 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.5139 | 0.490081 | ||||||||
\(653\) | 7.18335 | 0.281106 | 0.140553 | − | 0.990073i | \(-0.455112\pi\) | ||||
0.140553 | + | 0.990073i | \(0.455112\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.2111 | −0.828786 | ||||||||
\(656\) | 0.908327 | 0.0354642 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −21.2111 | −0.826895 | ||||||||
\(659\) | 34.8167 | 1.35626 | 0.678132 | − | 0.734940i | \(-0.262790\pi\) | ||||
0.678132 | + | 0.734940i | \(0.262790\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.63331 | 0.180215 | 0.0901074 | − | 0.995932i | \(-0.471279\pi\) | ||||
0.0901074 | + | 0.995932i | \(0.471279\pi\) | |||||||
\(662\) | 23.0917 | 0.897483 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 27.6333 | 1.07238 | ||||||||
\(665\) | −5.60555 | −0.217374 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.6333 | 0.721485 | ||||||||
\(668\) | 29.7250 | 1.15009 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 16.1194 | 0.622748 | ||||||||
\(671\) | −1.60555 | −0.0619816 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.6056 | −0.678644 | −0.339322 | − | 0.940670i | \(-0.610198\pi\) | ||||
−0.339322 | + | 0.940670i | \(0.610198\pi\) | |||||||
\(674\) | 59.0278 | 2.27366 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.63331 | 0.370238 | 0.185119 | − | 0.982716i | \(-0.440733\pi\) | ||||
0.185119 | + | 0.982716i | \(0.440733\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.39445 | 0.322149 | ||||||||
\(680\) | −22.8167 | −0.874979 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −14.7889 | −0.566296 | ||||||||
\(683\) | 36.2111 | 1.38558 | 0.692790 | − | 0.721140i | \(-0.256381\pi\) | ||||
0.692790 | + | 0.721140i | \(0.256381\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.60555 | 0.0613450 | ||||||||
\(686\) | 29.9361 | 1.14296 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.09167 | −0.117869 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.0278 | 1.14231 | 0.571155 | − | 0.820842i | \(-0.306496\pi\) | ||||
0.571155 | + | 0.820842i | \(0.306496\pi\) | |||||||
\(692\) | −15.9083 | −0.604744 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13.3305 | 0.506020 | ||||||||
\(695\) | −6.39445 | −0.242555 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22.8167 | −0.864242 | ||||||||
\(698\) | −8.72498 | −0.330245 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.30278 | 0.124833 | ||||||||
\(701\) | 36.4222 | 1.37565 | 0.687824 | − | 0.725878i | \(-0.258566\pi\) | ||||
0.687824 | + | 0.725878i | \(0.258566\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.2111 | −0.762276 | ||||||||
\(704\) | −20.5778 | −0.775555 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −38.7250 | −1.45743 | ||||||||
\(707\) | 9.00000 | 0.338480 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.8444 | 0.519938 | 0.259969 | − | 0.965617i | \(-0.416288\pi\) | ||||
0.259969 | + | 0.965617i | \(0.416288\pi\) | |||||||
\(710\) | 11.0917 | 0.416263 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 18.6333 | 0.698313 | ||||||||
\(713\) | 12.0000 | 0.449404 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −75.3583 | −2.81627 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −42.4222 | −1.58318 | ||||||||
\(719\) | 25.6056 | 0.954926 | 0.477463 | − | 0.878652i | \(-0.341556\pi\) | ||||
0.477463 | + | 0.878652i | \(0.341556\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.00000 | −0.148968 | ||||||||
\(722\) | −28.6056 | −1.06459 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 58.2389 | 2.16443 | ||||||||
\(725\) | 6.21110 | 0.230675 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.5778 | 0.503573 | 0.251786 | − | 0.967783i | \(-0.418982\pi\) | ||||
0.251786 | + | 0.967783i | \(0.418982\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.81665 | 0.0672374 | ||||||||
\(731\) | 77.6611 | 2.87240 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.8444 | 1.73024 | 0.865119 | − | 0.501567i | \(-0.167243\pi\) | ||||
0.865119 | + | 0.501567i | \(0.167243\pi\) | |||||||
\(734\) | −26.3028 | −0.970853 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15.9083 | 0.586389 | ||||||||
\(737\) | 11.2389 | 0.413989 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.6056 | 1.30977 | 0.654886 | − | 0.755728i | \(-0.272717\pi\) | ||||
0.654886 | + | 0.755728i | \(0.272717\pi\) | |||||||
\(740\) | 11.9083 | 0.437759 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.39445 | −0.271459 | ||||||||
\(743\) | 36.6333 | 1.34395 | 0.671973 | − | 0.740576i | \(-0.265447\pi\) | ||||
0.671973 | + | 0.740576i | \(0.265447\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.00000 | −0.109911 | ||||||||
\(746\) | 46.9638 | 1.71947 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −40.3305 | −1.47463 | ||||||||
\(749\) | −6.21110 | −0.226949 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.4500 | 1.69498 | 0.847492 | − | 0.530809i | \(-0.178112\pi\) | ||||
0.847492 | + | 0.530809i | \(0.178112\pi\) | |||||||
\(752\) | 2.78890 | 0.101701 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.21110 | −0.0440765 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.816654 | 0.0296818 | 0.0148409 | − | 0.999890i | \(-0.495276\pi\) | ||||
0.0148409 | + | 0.999890i | \(0.495276\pi\) | |||||||
\(758\) | 22.1194 | 0.803414 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 16.8167 | 0.610004 | ||||||||
\(761\) | 18.6333 | 0.675457 | 0.337728 | − | 0.941244i | \(-0.390341\pi\) | ||||
0.337728 | + | 0.941244i | \(0.390341\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.2111 | 0.695489 | ||||||||
\(764\) | −55.5416 | −2.00943 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 56.7250 | 2.04956 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.0000 | −0.396670 | −0.198335 | − | 0.980134i | \(-0.563553\pi\) | ||||
−0.198335 | + | 0.980134i | \(0.563553\pi\) | |||||||
\(770\) | 3.69722 | 0.133239 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −51.5416 | −1.85502 | ||||||||
\(773\) | 22.3944 | 0.805472 | 0.402736 | − | 0.915316i | \(-0.368059\pi\) | ||||
0.402736 | + | 0.915316i | \(0.368059\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.00000 | 0.143684 | ||||||||
\(776\) | −25.1833 | −0.904029 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −35.0278 | −1.25581 | ||||||||
\(779\) | 16.8167 | 0.602519 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.73338 | 0.276722 | ||||||||
\(782\) | 52.5416 | 1.87889 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.81665 | −0.0648805 | ||||||||
\(785\) | −11.2111 | −0.400141 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.6333 | −0.521621 | −0.260811 | − | 0.965390i | \(-0.583990\pi\) | ||||
−0.260811 | + | 0.965390i | \(0.583990\pi\) | |||||||
\(788\) | 3.90833 | 0.139228 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12.0000 | 0.426941 | ||||||||
\(791\) | 1.60555 | 0.0570868 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 50.7250 | 1.80016 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 42.3305 | 1.50037 | ||||||||
\(797\) | 14.4500 | 0.511844 | 0.255922 | − | 0.966697i | \(-0.417621\pi\) | ||||
0.255922 | + | 0.966697i | \(0.417621\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −70.0555 | −2.47839 | ||||||||
\(800\) | 5.30278 | 0.187481 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −28.1194 | −0.992932 | ||||||||
\(803\) | 1.26662 | 0.0446979 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.00000 | −0.105736 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −27.0000 | −0.949857 | ||||||||
\(809\) | 55.0555 | 1.93565 | 0.967824 | − | 0.251627i | \(-0.0809655\pi\) | ||||
0.967824 | + | 0.251627i | \(0.0809655\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.4222 | 1.63010 | 0.815052 | − | 0.579388i | \(-0.196708\pi\) | ||||
0.815052 | + | 0.579388i | \(0.196708\pi\) | |||||||
\(812\) | 20.5139 | 0.719896 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 13.3305 | 0.467235 | ||||||||
\(815\) | −3.78890 | −0.132719 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −57.2389 | −2.00253 | ||||||||
\(818\) | 18.9083 | 0.661114 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.90833 | −0.346014 | ||||||||
\(821\) | 21.4222 | 0.747640 | 0.373820 | − | 0.927501i | \(-0.378048\pi\) | ||||
0.373820 | + | 0.927501i | \(0.378048\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.6333 | −0.579801 | −0.289900 | − | 0.957057i | \(-0.593622\pi\) | ||||
−0.289900 | + | 0.957057i | \(0.593622\pi\) | |||||||
\(824\) | 12.0000 | 0.418040 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 24.9083 | 0.866672 | ||||||||
\(827\) | −42.4222 | −1.47516 | −0.737582 | − | 0.675257i | \(-0.764033\pi\) | ||||
−0.737582 | + | 0.675257i | \(0.764033\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.4222 | 1.02188 | 0.510938 | − | 0.859618i | \(-0.329298\pi\) | ||||
0.510938 | + | 0.859618i | \(0.329298\pi\) | |||||||
\(830\) | −21.2111 | −0.736248 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 45.6333 | 1.58110 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.00000 | −0.311458 | ||||||||
\(836\) | 29.7250 | 1.02806 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 39.6972 | 1.37132 | ||||||||
\(839\) | −20.0278 | −0.691435 | −0.345717 | − | 0.938339i | \(-0.612364\pi\) | ||||
−0.345717 | + | 0.938339i | \(0.612364\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.57779 | 0.330269 | ||||||||
\(842\) | 74.6611 | 2.57299 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −77.9638 | −2.68363 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.42221 | −0.289390 | ||||||||
\(848\) | 0.972244 | 0.0333870 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 17.5139 | 0.600721 | ||||||||
\(851\) | −10.8167 | −0.370790 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −47.2111 | −1.61648 | −0.808239 | − | 0.588855i | \(-0.799579\pi\) | ||||
−0.808239 | + | 0.588855i | \(0.799579\pi\) | |||||||
\(854\) | 2.30278 | 0.0787994 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.6333 | 0.636873 | ||||||||
\(857\) | −6.00000 | −0.204956 | −0.102478 | − | 0.994735i | \(-0.532677\pi\) | ||||
−0.102478 | + | 0.994735i | \(0.532677\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.7889 | 0.368112 | 0.184056 | − | 0.982916i | \(-0.441077\pi\) | ||||
0.184056 | + | 0.982916i | \(0.441077\pi\) | |||||||
\(860\) | 33.7250 | 1.15001 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −67.3305 | −2.29329 | ||||||||
\(863\) | 36.0000 | 1.22545 | 0.612727 | − | 0.790295i | \(-0.290072\pi\) | ||||
0.612727 | + | 0.790295i | \(0.290072\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.81665 | 0.163771 | ||||||||
\(866\) | −8.30278 | −0.282140 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 13.2111 | 0.448414 | ||||||||
\(869\) | 8.36669 | 0.283821 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −57.6333 | −1.95171 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −38.7250 | −1.30989 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.97224 | 0.0665979 | 0.0332990 | − | 0.999445i | \(-0.489399\pi\) | ||||
0.0332990 | + | 0.999445i | \(0.489399\pi\) | |||||||
\(878\) | 62.7250 | 2.11687 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.486122 | −0.0163872 | ||||||||
\(881\) | 21.8444 | 0.735957 | 0.367978 | − | 0.929834i | \(-0.380050\pi\) | ||||
0.367978 | + | 0.929834i | \(0.380050\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.6333 | 0.391492 | 0.195746 | − | 0.980655i | \(-0.437287\pi\) | ||||
0.195746 | + | 0.980655i | \(0.437287\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14.7889 | 0.496843 | ||||||||
\(887\) | 37.0555 | 1.24420 | 0.622101 | − | 0.782937i | \(-0.286279\pi\) | ||||
0.622101 | + | 0.782937i | \(0.286279\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.21110 | −0.141236 | ||||||||
\(890\) | −14.3028 | −0.479430 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13.9083 | 0.465685 | ||||||||
\(893\) | 51.6333 | 1.72784 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.8167 | 0.762677 | ||||||||
\(896\) | 18.9083 | 0.631683 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −70.5416 | −2.35400 | ||||||||
\(899\) | 24.8444 | 0.828607 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.4222 | −0.813622 | ||||||||
\(902\) | −11.0917 | −0.369312 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.81665 | −0.160200 | ||||||||
\(905\) | −17.6333 | −0.586151 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38.2666 | −1.27062 | −0.635311 | − | 0.772256i | \(-0.719128\pi\) | ||||
−0.635311 | + | 0.772256i | \(0.719128\pi\) | |||||||
\(908\) | −90.5694 | −3.00565 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36.0000 | 1.19273 | 0.596367 | − | 0.802712i | \(-0.296610\pi\) | ||||
0.596367 | + | 0.802712i | \(0.296610\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.7889 | −0.489441 | ||||||||
\(914\) | −61.7527 | −2.04260 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −46.2389 | −1.52777 | ||||||||
\(917\) | 21.2111 | 0.700452 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.8167 | −1.28044 | −0.640222 | − | 0.768190i | \(-0.721157\pi\) | ||||
−0.640222 | + | 0.768190i | \(0.721157\pi\) | |||||||
\(920\) | 9.00000 | 0.296721 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −83.3860 | −2.74617 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.60555 | −0.118550 | ||||||||
\(926\) | −79.2666 | −2.60486 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 32.9361 | 1.08118 | ||||||||
\(929\) | −15.4222 | −0.505986 | −0.252993 | − | 0.967468i | \(-0.581415\pi\) | ||||
−0.252993 | + | 0.967468i | \(0.581415\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −33.6333 | −1.10229 | ||||||||
\(932\) | −50.2389 | −1.64563 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.42221 | 0.210141 | ||||||||
\(935\) | 12.2111 | 0.399346 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 54.4777 | 1.77971 | 0.889855 | − | 0.456244i | \(-0.150806\pi\) | ||||
0.889855 | + | 0.456244i | \(0.150806\pi\) | |||||||
\(938\) | −16.1194 | −0.526318 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −30.4222 | −0.992263 | ||||||||
\(941\) | −9.63331 | −0.314037 | −0.157018 | − | 0.987596i | \(-0.550188\pi\) | ||||
−0.157018 | + | 0.987596i | \(0.550188\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.00000 | 0.293080 | ||||||||
\(944\) | −3.27502 | −0.106593 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 37.7527 | 1.22745 | ||||||||
\(947\) | −18.6333 | −0.605501 | −0.302751 | − | 0.953070i | \(-0.597905\pi\) | ||||
−0.302751 | + | 0.953070i | \(0.597905\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −12.9083 | −0.418801 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 22.8167 | 0.739492 | ||||||||
\(953\) | 14.4500 | 0.468080 | 0.234040 | − | 0.972227i | \(-0.424805\pi\) | ||||
0.234040 | + | 0.972227i | \(0.424805\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.8167 | 0.544174 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 66.3583 | 2.14394 | ||||||||
\(959\) | −1.60555 | −0.0518460 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.90833 | −0.190294 | ||||||||
\(965\) | 15.6056 | 0.502360 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.4777 | 1.43031 | 0.715153 | − | 0.698967i | \(-0.246357\pi\) | ||||
0.715153 | + | 0.698967i | \(0.246357\pi\) | |||||||
\(968\) | 25.2666 | 0.812100 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 19.3305 | 0.620666 | ||||||||
\(971\) | 44.0278 | 1.41292 | 0.706459 | − | 0.707754i | \(-0.250291\pi\) | ||||
0.706459 | + | 0.707754i | \(0.250291\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.39445 | 0.204997 | ||||||||
\(974\) | −2.30278 | −0.0737857 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.302776 | −0.00969161 | ||||||||
\(977\) | 28.8167 | 0.921926 | 0.460963 | − | 0.887419i | \(-0.347504\pi\) | ||||
0.460963 | + | 0.887419i | \(0.347504\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.97224 | −0.318714 | ||||||||
\(980\) | 19.8167 | 0.633020 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −38.7250 | −1.23576 | ||||||||
\(983\) | 18.4222 | 0.587577 | 0.293789 | − | 0.955870i | \(-0.405084\pi\) | ||||
0.293789 | + | 0.955870i | \(0.405084\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.18335 | −0.0377045 | ||||||||
\(986\) | 108.780 | 3.46428 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −30.6333 | −0.974083 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.0278 | 1.27152 | 0.635762 | − | 0.771885i | \(-0.280686\pi\) | ||||
0.635762 | + | 0.771885i | \(0.280686\pi\) | |||||||
\(992\) | 21.2111 | 0.673453 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −11.0917 | −0.351807 | ||||||||
\(995\) | −12.8167 | −0.406315 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.4500 | −0.584316 | −0.292158 | − | 0.956370i | \(-0.594373\pi\) | ||||
−0.292158 | + | 0.956370i | \(0.594373\pi\) | |||||||
\(998\) | 5.57779 | 0.176562 | ||||||||
\(999\) | 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 | 7605.2.a.bb.1.1 | 2 | ||
3.2 | odd | 2 | 845.2.a.f.1.2 | 2 | |||
13.4 | even | 6 | 585.2.j.d.406.1 | 4 | |||
13.10 | even | 6 | 585.2.j.d.451.1 | 4 | |||
13.12 | even | 2 | 7605.2.a.bg.1.2 | 2 | |||
15.14 | odd | 2 | 4225.2.a.t.1.1 | 2 | |||
39.2 | even | 12 | 845.2.m.d.316.4 | 8 | |||
39.5 | even | 4 | 845.2.c.d.506.1 | 4 | |||
39.8 | even | 4 | 845.2.c.d.506.4 | 4 | |||
39.11 | even | 12 | 845.2.m.d.316.1 | 8 | |||
39.17 | odd | 6 | 65.2.e.b.16.2 | ✓ | 4 | ||
39.20 | even | 12 | 845.2.m.d.361.4 | 8 | |||
39.23 | odd | 6 | 65.2.e.b.61.2 | yes | 4 | ||
39.29 | odd | 6 | 845.2.e.d.191.1 | 4 | |||
39.32 | even | 12 | 845.2.m.d.361.1 | 8 | |||
39.35 | odd | 6 | 845.2.e.d.146.1 | 4 | |||
39.38 | odd | 2 | 845.2.a.c.1.1 | 2 | |||
156.23 | even | 6 | 1040.2.q.o.321.2 | 4 | |||
156.95 | even | 6 | 1040.2.q.o.81.2 | 4 | |||
195.17 | even | 12 | 325.2.o.b.224.1 | 8 | |||
195.23 | even | 12 | 325.2.o.b.74.1 | 8 | |||
195.62 | even | 12 | 325.2.o.b.74.4 | 8 | |||
195.134 | odd | 6 | 325.2.e.a.276.1 | 4 | |||
195.173 | even | 12 | 325.2.o.b.224.4 | 8 | |||
195.179 | odd | 6 | 325.2.e.a.126.1 | 4 | |||
195.194 | odd | 2 | 4225.2.a.x.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.e.b.16.2 | ✓ | 4 | 39.17 | odd | 6 | ||
65.2.e.b.61.2 | yes | 4 | 39.23 | odd | 6 | ||
325.2.e.a.126.1 | 4 | 195.179 | odd | 6 | |||
325.2.e.a.276.1 | 4 | 195.134 | odd | 6 | |||
325.2.o.b.74.1 | 8 | 195.23 | even | 12 | |||
325.2.o.b.74.4 | 8 | 195.62 | even | 12 | |||
325.2.o.b.224.1 | 8 | 195.17 | even | 12 | |||
325.2.o.b.224.4 | 8 | 195.173 | even | 12 | |||
585.2.j.d.406.1 | 4 | 13.4 | even | 6 | |||
585.2.j.d.451.1 | 4 | 13.10 | even | 6 | |||
845.2.a.c.1.1 | 2 | 39.38 | odd | 2 | |||
845.2.a.f.1.2 | 2 | 3.2 | odd | 2 | |||
845.2.c.d.506.1 | 4 | 39.5 | even | 4 | |||
845.2.c.d.506.4 | 4 | 39.8 | even | 4 | |||
845.2.e.d.146.1 | 4 | 39.35 | odd | 6 | |||
845.2.e.d.191.1 | 4 | 39.29 | odd | 6 | |||
845.2.m.d.316.1 | 8 | 39.11 | even | 12 | |||
845.2.m.d.316.4 | 8 | 39.2 | even | 12 | |||
845.2.m.d.361.1 | 8 | 39.32 | even | 12 | |||
845.2.m.d.361.4 | 8 | 39.20 | even | 12 | |||
1040.2.q.o.81.2 | 4 | 156.95 | even | 6 | |||
1040.2.q.o.321.2 | 4 | 156.23 | even | 6 | |||
4225.2.a.t.1.1 | 2 | 15.14 | odd | 2 | |||
4225.2.a.x.1.2 | 2 | 195.194 | odd | 2 | |||
7605.2.a.bb.1.1 | 2 | 1.1 | even | 1 | trivial | ||
7605.2.a.bg.1.2 | 2 | 13.12 | even | 2 |