Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,2,Mod(1133,1134)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1134, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1134.1133");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.05503558921\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 56 x^{14} - 252 x^{13} + 962 x^{12} - 2860 x^{11} + 7240 x^{10} - 15036 x^{9} + \cdots + 457 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1133.5 | ||
Root | \(0.500000 - 0.221083i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.1133 |
Dual form | 1134.2.d.b.1133.13 |
$q$-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 \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.01976 | 0.456053 | 0.228026 | − | 0.973655i | \(-0.426773\pi\) | ||||
0.228026 | + | 0.973655i | \(0.426773\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.141281 | − | 2.64198i | 0.0533990 | − | 0.998573i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 1.01976i | − | 0.322478i | ||||||
\(11\) | 5.07812i | 1.53111i | 0.643371 | + | 0.765555i | \(0.277535\pi\) | ||||
−0.643371 | + | 0.765555i | \(0.722465\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.45173i | 1.51204i | 0.654550 | + | 0.756019i | \(0.272858\pi\) | ||||
−0.654550 | + | 0.756019i | \(0.727142\pi\) | |||||||
\(14\) | −2.64198 | − | 0.141281i | −0.706098 | − | 0.0377588i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.19825 | 1.50330 | 0.751648 | − | 0.659564i | \(-0.229259\pi\) | ||||
0.751648 | + | 0.659564i | \(0.229259\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.96453i | 1.82719i | 0.406626 | + | 0.913595i | \(0.366705\pi\) | ||||
−0.406626 | + | 0.913595i | \(0.633295\pi\) | |||||||
\(20\) | −1.01976 | −0.228026 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.07812 | 1.08266 | ||||||||
\(23\) | − | 0.835475i | − | 0.174209i | −0.996199 | − | 0.0871043i | \(-0.972239\pi\) | ||
0.996199 | − | 0.0871043i | \(-0.0277613\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.96008 | −0.792016 | ||||||||
\(26\) | 5.45173 | 1.06917 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.141281 | + | 2.64198i | −0.0266995 | + | 0.499287i | ||||
\(29\) | − | 8.91359i | − | 1.65521i | −0.561309 | − | 0.827606i | \(-0.689702\pi\) | ||
0.561309 | − | 0.827606i | \(-0.310298\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.97359i | 0.713678i | 0.934166 | + | 0.356839i | \(0.116146\pi\) | ||||
−0.934166 | + | 0.356839i | \(0.883854\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 6.19825i | − | 1.06299i | ||||||
\(35\) | 0.144073 | − | 2.69419i | 0.0243528 | − | 0.455402i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.64324 | −0.434546 | −0.217273 | − | 0.976111i | \(-0.569716\pi\) | ||||
−0.217273 | + | 0.976111i | \(0.569716\pi\) | |||||||
\(38\) | 7.96453 | 1.29202 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.01976i | 0.161239i | ||||||||
\(41\) | 6.36603 | 0.994206 | 0.497103 | − | 0.867691i | \(-0.334397\pi\) | ||||
0.497103 | + | 0.867691i | \(0.334397\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.67095 | 0.864812 | 0.432406 | − | 0.901679i | \(-0.357665\pi\) | ||||
0.432406 | + | 0.901679i | \(0.357665\pi\) | |||||||
\(44\) | − | 5.07812i | − | 0.765555i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.835475 | −0.123184 | ||||||||
\(47\) | −0.563843 | −0.0822449 | −0.0411224 | − | 0.999154i | \(-0.513093\pi\) | ||||
−0.0411224 | + | 0.999154i | \(0.513093\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.96008 | − | 0.746520i | −0.994297 | − | 0.106646i | ||||
\(50\) | 3.96008i | 0.560040i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 5.45173i | − | 0.756019i | ||||||
\(53\) | 2.19615i | 0.301665i | 0.988559 | + | 0.150832i | \(0.0481954\pi\) | ||||
−0.988559 | + | 0.150832i | \(0.951805\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.17848i | 0.698267i | ||||||||
\(56\) | 2.64198 | + | 0.141281i | 0.353049 | + | 0.0188794i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.91359 | −1.17041 | ||||||||
\(59\) | 7.21801 | 0.939705 | 0.469853 | − | 0.882745i | \(-0.344307\pi\) | ||||
0.469853 | + | 0.882745i | \(0.344307\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 7.94963i | − | 1.01785i | −0.860812 | − | 0.508923i | \(-0.830044\pi\) | ||
0.860812 | − | 0.508923i | \(-0.169956\pi\) | |||||||
\(62\) | 3.97359 | 0.504647 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 5.55948i | 0.689569i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.7091 | 1.30833 | 0.654165 | − | 0.756352i | \(-0.273020\pi\) | ||||
0.654165 | + | 0.756352i | \(0.273020\pi\) | |||||||
\(68\) | −6.19825 | −0.751648 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.69419 | − | 0.144073i | −0.322018 | − | 0.0172200i | ||||
\(71\) | 6.20272i | 0.736127i | 0.929801 | + | 0.368064i | \(0.119979\pi\) | ||||
−0.929801 | + | 0.368064i | \(0.880021\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.05024i | 0.825168i | 0.910920 | + | 0.412584i | \(0.135374\pi\) | ||||
−0.910920 | + | 0.412584i | \(0.864626\pi\) | |||||||
\(74\) | 2.64324i | 0.307270i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 7.96453i | − | 0.913595i | ||||||
\(77\) | 13.4163 | + | 0.717439i | 1.52893 | + | 0.0817598i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.74907 | −0.534312 | −0.267156 | − | 0.963653i | \(-0.586084\pi\) | ||||
−0.267156 | + | 0.963653i | \(0.586084\pi\) | |||||||
\(80\) | 1.01976 | 0.114013 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 6.36603i | − | 0.703010i | ||||||
\(83\) | 11.0089 | 1.20839 | 0.604193 | − | 0.796838i | \(-0.293495\pi\) | ||||
0.604193 | + | 0.796838i | \(0.293495\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.32076 | 0.685582 | ||||||||
\(86\) | − | 5.67095i | − | 0.611514i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.07812 | −0.541329 | ||||||||
\(89\) | 2.11919 | 0.224634 | 0.112317 | − | 0.993672i | \(-0.464173\pi\) | ||||
0.112317 | + | 0.993672i | \(0.464173\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.4033 | + | 0.770223i | 1.50988 | + | 0.0807413i | ||||
\(92\) | 0.835475i | 0.0871043i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.563843i | 0.0581559i | ||||||||
\(95\) | 8.12195i | 0.833295i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 2.78605i | − | 0.282880i | −0.989947 | − | 0.141440i | \(-0.954827\pi\) | ||
0.989947 | − | 0.141440i | \(-0.0451733\pi\) | |||||||
\(98\) | −0.746520 | + | 6.96008i | −0.0754099 | + | 0.703074i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.96008 | 0.396008 | ||||||||
\(101\) | −12.0609 | −1.20011 | −0.600054 | − | 0.799959i | \(-0.704854\pi\) | ||||
−0.600054 | + | 0.799959i | \(0.704854\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.4360i | 1.42242i | 0.702978 | + | 0.711212i | \(0.251853\pi\) | ||||
−0.702978 | + | 0.711212i | \(0.748147\pi\) | |||||||
\(104\) | −5.45173 | −0.534586 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.19615 | 0.213309 | ||||||||
\(107\) | − | 11.0039i | − | 1.06379i | −0.846811 | − | 0.531894i | \(-0.821480\pi\) | ||
0.846811 | − | 0.531894i | \(-0.178520\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.94130 | −0.281726 | −0.140863 | − | 0.990029i | \(-0.544988\pi\) | ||||
−0.140863 | + | 0.990029i | \(0.544988\pi\) | |||||||
\(110\) | 5.17848 | 0.493749 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.141281 | − | 2.64198i | 0.0133498 | − | 0.249643i | ||||
\(113\) | − | 6.93237i | − | 0.652142i | −0.945345 | − | 0.326071i | \(-0.894275\pi\) | ||
0.945345 | − | 0.326071i | \(-0.105725\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 0.851988i | − | 0.0794483i | ||||||
\(116\) | 8.91359i | 0.827606i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 7.21801i | − | 0.664472i | ||||||
\(119\) | 0.875692 | − | 16.3756i | 0.0802745 | − | 1.50115i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14.7873 | −1.34430 | ||||||||
\(122\) | −7.94963 | −0.719726 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 3.97359i | − | 0.356839i | ||||||
\(125\) | −9.13717 | −0.817254 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.3085 | −1.18094 | −0.590471 | − | 0.807059i | \(-0.701058\pi\) | ||||
−0.590471 | + | 0.807059i | \(0.701058\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.55948 | 0.487599 | ||||||||
\(131\) | 12.0609 | 1.05377 | 0.526885 | − | 0.849937i | \(-0.323360\pi\) | ||||
0.526885 | + | 0.849937i | \(0.323360\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 21.0421 | + | 1.12523i | 1.82458 | + | 0.0975701i | ||||
\(134\) | − | 10.7091i | − | 0.925129i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.19825i | 0.531495i | ||||||||
\(137\) | 13.3801i | 1.14314i | 0.820554 | + | 0.571569i | \(0.193665\pi\) | ||||
−0.820554 | + | 0.571569i | \(0.806335\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 9.71592i | − | 0.824093i | −0.911163 | − | 0.412047i | \(-0.864814\pi\) | ||
0.911163 | − | 0.412047i | \(-0.135186\pi\) | |||||||
\(140\) | −0.144073 | + | 2.69419i | −0.0121764 | + | 0.227701i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.20272 | 0.520521 | ||||||||
\(143\) | −27.6845 | −2.31510 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 9.08977i | − | 0.754864i | ||||||
\(146\) | 7.05024 | 0.583482 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.64324 | 0.217273 | ||||||||
\(149\) | − | 18.1357i | − | 1.48574i | −0.669437 | − | 0.742869i | \(-0.733465\pi\) | ||
0.669437 | − | 0.742869i | \(-0.266535\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.1750 | −0.828030 | −0.414015 | − | 0.910270i | \(-0.635874\pi\) | ||||
−0.414015 | + | 0.910270i | \(0.635874\pi\) | |||||||
\(152\) | −7.96453 | −0.646009 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.717439 | − | 13.4163i | 0.0578129 | − | 1.08111i | ||||
\(155\) | 4.05213i | 0.325475i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 9.53079i | − | 0.760640i | −0.924855 | − | 0.380320i | \(-0.875814\pi\) | ||
0.924855 | − | 0.380320i | \(-0.124186\pi\) | |||||||
\(158\) | 4.74907i | 0.377815i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 1.01976i | − | 0.0806195i | ||||||
\(161\) | −2.20731 | − | 0.118036i | −0.173960 | − | 0.00930257i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.33296 | −0.574362 | −0.287181 | − | 0.957876i | \(-0.592718\pi\) | ||||
−0.287181 | + | 0.957876i | \(0.592718\pi\) | |||||||
\(164\) | −6.36603 | −0.497103 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 11.0089i | − | 0.854458i | ||||||
\(167\) | −1.18754 | −0.0918947 | −0.0459474 | − | 0.998944i | \(-0.514631\pi\) | ||||
−0.0459474 | + | 0.998944i | \(0.514631\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −16.7214 | −1.28626 | ||||||||
\(170\) | − | 6.32076i | − | 0.484780i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.67095 | −0.432406 | ||||||||
\(173\) | −3.59488 | −0.273313 | −0.136657 | − | 0.990618i | \(-0.543636\pi\) | ||||
−0.136657 | + | 0.990618i | \(0.543636\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.559482 | + | 10.4624i | −0.0422929 | + | 0.790886i | ||||
\(176\) | 5.07812i | 0.382777i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 2.11919i | − | 0.158840i | ||||||
\(179\) | 9.26770i | 0.692700i | 0.938105 | + | 0.346350i | \(0.112579\pi\) | ||||
−0.938105 | + | 0.346350i | \(0.887421\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 5.81954i | − | 0.432563i | −0.976331 | − | 0.216281i | \(-0.930607\pi\) | ||
0.976331 | − | 0.216281i | \(-0.0693928\pi\) | |||||||
\(182\) | 0.770223 | − | 14.4033i | 0.0570927 | − | 1.06765i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.835475 | 0.0615921 | ||||||||
\(185\) | −2.69548 | −0.198176 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 31.4754i | 2.30171i | ||||||||
\(188\) | 0.563843 | 0.0411224 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.12195 | 0.589228 | ||||||||
\(191\) | 4.31684i | 0.312356i | 0.987729 | + | 0.156178i | \(0.0499173\pi\) | ||||
−0.987729 | + | 0.156178i | \(0.950083\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.9861 | 1.58259 | 0.791296 | − | 0.611433i | \(-0.209407\pi\) | ||||
0.791296 | + | 0.611433i | \(0.209407\pi\) | |||||||
\(194\) | −2.78605 | −0.200027 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.96008 | + | 0.746520i | 0.497149 | + | 0.0533228i | ||||
\(197\) | 9.96399i | 0.709905i | 0.934884 | + | 0.354953i | \(0.115503\pi\) | ||||
−0.934884 | + | 0.354953i | \(0.884497\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 11.6673i | − | 0.827075i | −0.910487 | − | 0.413538i | \(-0.864293\pi\) | ||
0.910487 | − | 0.413538i | \(-0.135707\pi\) | |||||||
\(200\) | − | 3.96008i | − | 0.280020i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.0609i | 0.848605i | ||||||||
\(203\) | −23.5495 | − | 1.25932i | −1.65285 | − | 0.0883867i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.49185 | 0.453410 | ||||||||
\(206\) | 14.4360 | 1.00581 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.45173i | 0.378009i | ||||||||
\(209\) | −40.4448 | −2.79763 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.60332 | −0.110377 | −0.0551885 | − | 0.998476i | \(-0.517576\pi\) | ||||
−0.0551885 | + | 0.998476i | \(0.517576\pi\) | |||||||
\(212\) | − | 2.19615i | − | 0.150832i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −11.0039 | −0.752212 | ||||||||
\(215\) | 5.78304 | 0.394400 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.4981 | + | 0.561391i | 0.712660 | + | 0.0381097i | ||||
\(218\) | 2.94130i | 0.199210i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 5.17848i | − | 0.349133i | ||||||
\(221\) | 33.7912i | 2.27304i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.3042i | 1.22574i | 0.790185 | + | 0.612868i | \(0.209984\pi\) | ||||
−0.790185 | + | 0.612868i | \(0.790016\pi\) | |||||||
\(224\) | −2.64198 | − | 0.141281i | −0.176524 | − | 0.00943970i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.93237 | −0.461134 | ||||||||
\(227\) | 15.8519 | 1.05212 | 0.526062 | − | 0.850446i | \(-0.323668\pi\) | ||||
0.526062 | + | 0.850446i | \(0.323668\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 21.7163i | − | 1.43506i | −0.696529 | − | 0.717528i | \(-0.745273\pi\) | ||
0.696529 | − | 0.717528i | \(-0.254727\pi\) | |||||||
\(230\) | −0.851988 | −0.0561785 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.91359 | 0.585206 | ||||||||
\(233\) | − | 17.0886i | − | 1.11951i | −0.828658 | − | 0.559756i | \(-0.810895\pi\) | ||
0.828658 | − | 0.559756i | \(-0.189105\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.574987 | −0.0375080 | ||||||||
\(236\) | −7.21801 | −0.469853 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −16.3756 | − | 0.875692i | −1.06147 | − | 0.0567627i | ||||
\(239\) | 9.32969i | 0.603488i | 0.953389 | + | 0.301744i | \(0.0975687\pi\) | ||||
−0.953389 | + | 0.301744i | \(0.902431\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.4030i | 1.44310i | 0.692360 | + | 0.721552i | \(0.256571\pi\) | ||||
−0.692360 | + | 0.721552i | \(0.743429\pi\) | |||||||
\(242\) | 14.7873i | 0.950561i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.94963i | 0.508923i | ||||||||
\(245\) | −7.09764 | − | 0.761275i | −0.453452 | − | 0.0486360i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −43.4205 | −2.76278 | ||||||||
\(248\) | −3.97359 | −0.252323 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.13717i | 0.577886i | ||||||||
\(251\) | −5.13108 | −0.323871 | −0.161935 | − | 0.986801i | \(-0.551774\pi\) | ||||
−0.161935 | + | 0.986801i | \(0.551774\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.24264 | 0.266733 | ||||||||
\(254\) | 13.3085i | 0.835053i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.85364 | −0.614653 | −0.307327 | − | 0.951604i | \(-0.599434\pi\) | ||||
−0.307327 | + | 0.951604i | \(0.599434\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.373438 | + | 6.98337i | −0.0232043 | + | 0.433926i | ||||
\(260\) | − | 5.55948i | − | 0.344784i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 12.0609i | − | 0.745128i | ||||||
\(263\) | 11.4639i | 0.706891i | 0.935455 | + | 0.353446i | \(0.114990\pi\) | ||||
−0.935455 | + | 0.353446i | \(0.885010\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.23956i | 0.137575i | ||||||||
\(266\) | 1.12523 | − | 21.0421i | 0.0689925 | − | 1.29017i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10.7091 | −0.654165 | ||||||||
\(269\) | 20.8626 | 1.27201 | 0.636007 | − | 0.771684i | \(-0.280585\pi\) | ||||
0.636007 | + | 0.771684i | \(0.280585\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.27566i | 0.0774907i | 0.999249 | + | 0.0387453i | \(0.0123361\pi\) | ||||
−0.999249 | + | 0.0387453i | \(0.987664\pi\) | |||||||
\(272\) | 6.19825 | 0.375824 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.3801 | 0.808321 | ||||||||
\(275\) | − | 20.1097i | − | 1.21266i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.94457 | −0.477343 | −0.238672 | − | 0.971100i | \(-0.576712\pi\) | ||||
−0.238672 | + | 0.971100i | \(0.576712\pi\) | |||||||
\(278\) | −9.71592 | −0.582722 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.69419 | + | 0.144073i | 0.161009 | + | 0.00861000i | ||||
\(281\) | − | 19.2304i | − | 1.14719i | −0.819139 | − | 0.573596i | \(-0.805548\pi\) | ||
0.819139 | − | 0.573596i | \(-0.194452\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.36116i | 0.318688i | 0.987223 | + | 0.159344i | \(0.0509379\pi\) | ||||
−0.987223 | + | 0.159344i | \(0.949062\pi\) | |||||||
\(284\) | − | 6.20272i | − | 0.368064i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 27.6845i | 1.63702i | ||||||||
\(287\) | 0.899395 | − | 16.8189i | 0.0530896 | − | 0.992788i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.4183 | 1.25990 | ||||||||
\(290\) | −9.08977 | −0.533770 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 7.05024i | − | 0.412584i | ||||||
\(293\) | 0.148630 | 0.00868304 | 0.00434152 | − | 0.999991i | \(-0.498618\pi\) | ||||
0.00434152 | + | 0.999991i | \(0.498618\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.36068 | 0.428555 | ||||||||
\(296\) | − | 2.64324i | − | 0.153635i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −18.1357 | −1.05057 | ||||||||
\(299\) | 4.55479 | 0.263410 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.801195 | − | 14.9825i | 0.0461801 | − | 0.863578i | ||||
\(302\) | 10.1750i | 0.585506i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.96453i | 0.456797i | ||||||||
\(305\) | − | 8.10676i | − | 0.464192i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.623699i | 0.0355964i | 0.999842 | + | 0.0177982i | \(0.00566564\pi\) | ||||
−0.999842 | + | 0.0177982i | \(0.994334\pi\) | |||||||
\(308\) | −13.4163 | − | 0.717439i | −0.764463 | − | 0.0408799i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.05213 | 0.230145 | ||||||||
\(311\) | −20.8303 | −1.18118 | −0.590589 | − | 0.806972i | \(-0.701105\pi\) | ||||
−0.590589 | + | 0.806972i | \(0.701105\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 20.4042i | − | 1.15331i | −0.816987 | − | 0.576657i | \(-0.804357\pi\) | ||
0.816987 | − | 0.576657i | \(-0.195643\pi\) | |||||||
\(314\) | −9.53079 | −0.537854 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.74907 | 0.267156 | ||||||||
\(317\) | − | 10.0593i | − | 0.564989i | −0.959269 | − | 0.282494i | \(-0.908838\pi\) | ||
0.959269 | − | 0.282494i | \(-0.0911619\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 45.2643 | 2.53431 | ||||||||
\(320\) | −1.01976 | −0.0570066 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.118036 | + | 2.20731i | −0.00657791 | + | 0.123008i | ||||
\(323\) | 49.3662i | 2.74681i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 21.5893i | − | 1.19756i | ||||||
\(326\) | 7.33296i | 0.406135i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.36603i | 0.351505i | ||||||||
\(329\) | −0.0796600 | + | 1.48966i | −0.00439180 | + | 0.0821275i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.1229 | 1.43584 | 0.717922 | − | 0.696124i | \(-0.245094\pi\) | ||||
0.717922 | + | 0.696124i | \(0.245094\pi\) | |||||||
\(332\) | −11.0089 | −0.604193 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.18754i | 0.0649794i | ||||||||
\(335\) | 10.9208 | 0.596668 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.3950 | 0.729670 | 0.364835 | − | 0.931072i | \(-0.381125\pi\) | ||||
0.364835 | + | 0.931072i | \(0.381125\pi\) | |||||||
\(338\) | 16.7214i | 0.909522i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.32076 | −0.342791 | ||||||||
\(341\) | −20.1784 | −1.09272 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.95561 | + | 18.2829i | −0.159588 | + | 0.987184i | ||||
\(344\) | 5.67095i | 0.305757i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.59488i | 0.193262i | ||||||||
\(347\) | − | 15.7174i | − | 0.843756i | −0.906653 | − | 0.421878i | \(-0.861371\pi\) | ||
0.906653 | − | 0.421878i | \(-0.138629\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.333758i | 0.0178657i | 0.999960 | + | 0.00893284i | \(0.00284345\pi\) | ||||
−0.999960 | + | 0.00893284i | \(0.997157\pi\) | |||||||
\(350\) | 10.4624 | + | 0.559482i | 0.559241 | + | 0.0299056i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.07812 | 0.270664 | ||||||||
\(353\) | −6.45414 | −0.343519 | −0.171760 | − | 0.985139i | \(-0.554945\pi\) | ||||
−0.171760 | + | 0.985139i | \(0.554945\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.32532i | 0.335713i | ||||||||
\(356\) | −2.11919 | −0.112317 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.26770 | 0.489813 | ||||||||
\(359\) | 0.172817i | 0.00912095i | 0.999990 | + | 0.00456047i | \(0.00145165\pi\) | ||||
−0.999990 | + | 0.00456047i | \(0.998548\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −44.4338 | −2.33862 | ||||||||
\(362\) | −5.81954 | −0.305868 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −14.4033 | − | 0.770223i | −0.754940 | − | 0.0403707i | ||||
\(365\) | 7.18958i | 0.376320i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.3366i | 0.696165i | 0.937464 | + | 0.348083i | \(0.113167\pi\) | ||||
−0.937464 | + | 0.348083i | \(0.886833\pi\) | |||||||
\(368\) | − | 0.835475i | − | 0.0435522i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.69548i | 0.140131i | ||||||||
\(371\) | 5.80218 | + | 0.310274i | 0.301234 | + | 0.0161086i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.3485 | −0.898270 | −0.449135 | − | 0.893464i | \(-0.648268\pi\) | ||||
−0.449135 | + | 0.893464i | \(0.648268\pi\) | |||||||
\(374\) | 31.4754 | 1.62756 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 0.563843i | − | 0.0290780i | ||||||
\(377\) | 48.5945 | 2.50274 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.645891 | 0.0331772 | 0.0165886 | − | 0.999862i | \(-0.494719\pi\) | ||||
0.0165886 | + | 0.999862i | \(0.494719\pi\) | |||||||
\(380\) | − | 8.12195i | − | 0.416647i | ||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.31684 | 0.220869 | ||||||||
\(383\) | −24.3455 | −1.24400 | −0.621999 | − | 0.783018i | \(-0.713679\pi\) | ||||
−0.621999 | + | 0.783018i | \(0.713679\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.6814 | + | 0.731619i | 0.697270 | + | 0.0372868i | ||||
\(386\) | − | 21.9861i | − | 1.11906i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.78605i | 0.141440i | ||||||||
\(389\) | 34.7203i | 1.76039i | 0.474614 | + | 0.880194i | \(0.342588\pi\) | ||||
−0.474614 | + | 0.880194i | \(0.657412\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 5.17848i | − | 0.261887i | ||||||
\(392\) | 0.746520 | − | 6.96008i | 0.0377049 | − | 0.351537i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.96399 | 0.501979 | ||||||||
\(395\) | −4.84293 | −0.243674 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 9.89614i | − | 0.496673i | −0.968674 | − | 0.248337i | \(-0.920116\pi\) | ||
0.968674 | − | 0.248337i | \(-0.0798839\pi\) | |||||||
\(398\) | −11.6673 | −0.584830 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.96008 | −0.198004 | ||||||||
\(401\) | − | 13.3181i | − | 0.665074i | −0.943090 | − | 0.332537i | \(-0.892095\pi\) | ||
0.943090 | − | 0.332537i | \(-0.107905\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −21.6629 | −1.07911 | ||||||||
\(404\) | 12.0609 | 0.600054 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.25932 | + | 23.5495i | −0.0624988 | + | 1.16874i | ||||
\(407\) | − | 13.4227i | − | 0.665337i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.80767i | 0.386064i | 0.981192 | + | 0.193032i | \(0.0618322\pi\) | ||||
−0.981192 | + | 0.193032i | \(0.938168\pi\) | |||||||
\(410\) | − | 6.49185i | − | 0.320610i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 14.4360i | − | 0.711212i | ||||||
\(413\) | 1.01976 | − | 19.0698i | 0.0501793 | − | 0.938365i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.2265 | 0.551088 | ||||||||
\(416\) | 5.45173 | 0.267293 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 40.4448i | 1.97822i | ||||||||
\(419\) | −30.5760 | −1.49374 | −0.746868 | − | 0.664972i | \(-0.768444\pi\) | ||||
−0.746868 | + | 0.664972i | \(0.768444\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.9686 | −1.46058 | −0.730289 | − | 0.683138i | \(-0.760615\pi\) | ||||
−0.730289 | + | 0.683138i | \(0.760615\pi\) | |||||||
\(422\) | 1.60332i | 0.0780483i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.19615 | −0.106655 | ||||||||
\(425\) | −24.5456 | −1.19063 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.0027 | − | 1.12313i | −1.01639 | − | 0.0543520i | ||||
\(428\) | 11.0039i | 0.531894i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 5.78304i | − | 0.278883i | ||||||
\(431\) | − | 19.8981i | − | 0.958457i | −0.877690 | − | 0.479229i | \(-0.840917\pi\) | ||
0.877690 | − | 0.479229i | \(-0.159083\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 26.6176i | − | 1.27916i | −0.768725 | − | 0.639580i | \(-0.779108\pi\) | ||
0.768725 | − | 0.639580i | \(-0.220892\pi\) | |||||||
\(434\) | 0.561391 | − | 10.4981i | 0.0269476 | − | 0.503927i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.94130 | 0.140863 | ||||||||
\(437\) | 6.65417 | 0.318312 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 29.1602i | − | 1.39174i | −0.718168 | − | 0.695870i | \(-0.755019\pi\) | ||
0.718168 | − | 0.695870i | \(-0.244981\pi\) | |||||||
\(440\) | −5.17848 | −0.246875 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 33.7912 | 1.60728 | ||||||||
\(443\) | − | 29.3107i | − | 1.39260i | −0.717753 | − | 0.696298i | \(-0.754829\pi\) | ||
0.717753 | − | 0.696298i | \(-0.245171\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.16108 | 0.102445 | ||||||||
\(446\) | 18.3042 | 0.866727 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.141281 | + | 2.64198i | −0.00667488 | + | 0.124822i | ||||
\(449\) | 14.5485i | 0.686588i | 0.939228 | + | 0.343294i | \(0.111543\pi\) | ||||
−0.939228 | + | 0.343294i | \(0.888457\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.3274i | 1.52224i | ||||||||
\(452\) | 6.93237i | 0.326071i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 15.8519i | − | 0.743965i | ||||||
\(455\) | 14.6880 | + | 0.785447i | 0.688585 | + | 0.0368223i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.21166 | −0.243791 | −0.121896 | − | 0.992543i | \(-0.538897\pi\) | ||||
−0.121896 | + | 0.992543i | \(0.538897\pi\) | |||||||
\(458\) | −21.7163 | −1.01474 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.851988i | 0.0397242i | ||||||||
\(461\) | 34.9906 | 1.62968 | 0.814838 | − | 0.579688i | \(-0.196826\pi\) | ||||
0.814838 | + | 0.579688i | \(0.196826\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.05213 | −0.0953705 | −0.0476852 | − | 0.998862i | \(-0.515184\pi\) | ||||
−0.0476852 | + | 0.998862i | \(0.515184\pi\) | |||||||
\(464\) | − | 8.91359i | − | 0.413803i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17.0886 | −0.791614 | ||||||||
\(467\) | −20.4066 | −0.944307 | −0.472153 | − | 0.881516i | \(-0.656523\pi\) | ||||
−0.472153 | + | 0.881516i | \(0.656523\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.51299 | − | 28.2933i | 0.0698636 | − | 1.30646i | ||||
\(470\) | 0.574987i | 0.0265222i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.21801i | 0.332236i | ||||||||
\(473\) | 28.7977i | 1.32412i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 31.5402i | − | 1.44716i | ||||||
\(476\) | −0.875692 | + | 16.3756i | −0.0401373 | + | 0.750576i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.32969 | 0.426730 | ||||||||
\(479\) | 13.8722 | 0.633836 | 0.316918 | − | 0.948453i | \(-0.397352\pi\) | ||||
0.316918 | + | 0.948453i | \(0.397352\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 14.4102i | − | 0.657049i | ||||||
\(482\) | 22.4030 | 1.02043 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 14.7873 | 0.672148 | ||||||||
\(485\) | − | 2.84112i | − | 0.129008i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.3646 | 1.01344 | 0.506718 | − | 0.862112i | \(-0.330858\pi\) | ||||
0.506718 | + | 0.862112i | \(0.330858\pi\) | |||||||
\(488\) | 7.94963 | 0.359863 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.761275 | + | 7.09764i | −0.0343909 | + | 0.320639i | ||||
\(491\) | − | 7.60770i | − | 0.343330i | −0.985155 | − | 0.171665i | \(-0.945085\pi\) | ||
0.985155 | − | 0.171665i | \(-0.0549147\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 55.2487i | − | 2.48827i | ||||||
\(494\) | 43.4205i | 1.95358i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.97359i | 0.178419i | ||||||||
\(497\) | 16.3874 | + | 0.876324i | 0.735077 | + | 0.0393085i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.3208 | −0.506787 | −0.253393 | − | 0.967363i | \(-0.581547\pi\) | ||||
−0.253393 | + | 0.967363i | \(0.581547\pi\) | |||||||
\(500\) | 9.13717 | 0.408627 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.13108i | 0.229011i | ||||||||
\(503\) | −21.2304 | −0.946616 | −0.473308 | − | 0.880897i | \(-0.656940\pi\) | ||||
−0.473308 | + | 0.880897i | \(0.656940\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.2993 | −0.547313 | ||||||||
\(506\) | − | 4.24264i | − | 0.188608i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.3085 | 0.590471 | ||||||||
\(509\) | 30.3353 | 1.34459 | 0.672294 | − | 0.740284i | \(-0.265309\pi\) | ||||
0.672294 | + | 0.740284i | \(0.265309\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.6266 | + | 0.996061i | 0.823991 | + | 0.0440632i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.85364i | 0.434625i | ||||||||
\(515\) | 14.7214i | 0.648700i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2.86326i | − | 0.125926i | ||||||
\(518\) | 6.98337 | + | 0.373438i | 0.306832 | + | 0.0164079i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.55948 | −0.243799 | ||||||||
\(521\) | 15.3479 | 0.672403 | 0.336201 | − | 0.941790i | \(-0.390858\pi\) | ||||
0.336201 | + | 0.941790i | \(0.390858\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 9.95691i | − | 0.435385i | −0.976017 | − | 0.217693i | \(-0.930147\pi\) | ||
0.976017 | − | 0.217693i | \(-0.0698530\pi\) | |||||||
\(524\) | −12.0609 | −0.526885 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.4639 | 0.499848 | ||||||||
\(527\) | 24.6293i | 1.07287i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.3020 | 0.969651 | ||||||||
\(530\) | 2.23956 | 0.0972802 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −21.0421 | − | 1.12523i | −0.912291 | − | 0.0487851i | ||||
\(533\) | 34.7058i | 1.50328i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 11.2214i | − | 0.485144i | ||||||
\(536\) | 10.7091i | 0.462565i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 20.8626i | − | 0.899449i | ||||||
\(539\) | 3.79091 | − | 35.3441i | 0.163286 | − | 1.52238i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.0521 | −0.475168 | −0.237584 | − | 0.971367i | \(-0.576356\pi\) | ||||
−0.237584 | + | 0.971367i | \(0.576356\pi\) | |||||||
\(542\) | 1.27566 | 0.0547942 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 6.19825i | − | 0.265748i | ||||||
\(545\) | −2.99944 | −0.128482 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.4305 | −0.916302 | −0.458151 | − | 0.888874i | \(-0.651488\pi\) | ||||
−0.458151 | + | 0.888874i | \(0.651488\pi\) | |||||||
\(548\) | − | 13.3801i | − | 0.571569i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −20.1097 | −0.857482 | ||||||||
\(551\) | 70.9926 | 3.02439 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.670951 | + | 12.5469i | −0.0285317 | + | 0.533549i | ||||
\(554\) | 7.94457i | 0.337533i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.71592i | 0.412047i | ||||||||
\(557\) | 27.0543i | 1.14633i | 0.819441 | + | 0.573164i | \(0.194284\pi\) | ||||
−0.819441 | + | 0.573164i | \(0.805716\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 30.9165i | 1.30763i | ||||||||
\(560\) | 0.144073 | − | 2.69419i | 0.00608819 | − | 0.113851i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19.2304 | −0.811187 | ||||||||
\(563\) | 9.97401 | 0.420354 | 0.210177 | − | 0.977663i | \(-0.432596\pi\) | ||||
0.210177 | + | 0.977663i | \(0.432596\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 7.06938i | − | 0.297411i | ||||||
\(566\) | 5.36116 | 0.225346 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.20272 | −0.260260 | ||||||||
\(569\) | − | 9.54635i | − | 0.400204i | −0.979775 | − | 0.200102i | \(-0.935873\pi\) | ||
0.979775 | − | 0.200102i | \(-0.0641273\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.2616 | 1.76859 | 0.884296 | − | 0.466926i | \(-0.154639\pi\) | ||||
0.884296 | + | 0.466926i | \(0.154639\pi\) | |||||||
\(572\) | 27.6845 | 1.15755 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −16.8189 | − | 0.899395i | −0.702007 | − | 0.0375400i | ||||
\(575\) | 3.30855i | 0.137976i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.5258i | 0.979392i | 0.871893 | + | 0.489696i | \(0.162892\pi\) | ||||
−0.871893 | + | 0.489696i | \(0.837108\pi\) | |||||||
\(578\) | − | 21.4183i | − | 0.890884i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.08977i | 0.377432i | ||||||||
\(581\) | 1.55535 | − | 29.0853i | 0.0645267 | − | 1.20666i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.1523 | −0.461882 | ||||||||
\(584\) | −7.05024 | −0.291741 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 0.148630i | − | 0.00613983i | ||||||
\(587\) | 16.1592 | 0.666960 | 0.333480 | − | 0.942757i | \(-0.391777\pi\) | ||||
0.333480 | + | 0.942757i | \(0.391777\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −31.6478 | −1.30402 | ||||||||
\(590\) | − | 7.36068i | − | 0.303034i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.64324 | −0.108636 | ||||||||
\(593\) | 41.7403 | 1.71407 | 0.857034 | − | 0.515260i | \(-0.172305\pi\) | ||||
0.857034 | + | 0.515260i | \(0.172305\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.893000 | − | 16.6993i | 0.0366094 | − | 0.684604i | ||||
\(596\) | 18.1357i | 0.742869i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 4.55479i | − | 0.186259i | ||||||
\(599\) | 7.06261i | 0.288570i | 0.989536 | + | 0.144285i | \(0.0460883\pi\) | ||||
−0.989536 | + | 0.144285i | \(0.953912\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 17.0369i | − | 0.694952i | −0.937689 | − | 0.347476i | \(-0.887039\pi\) | ||
0.937689 | − | 0.347476i | \(-0.112961\pi\) | |||||||
\(602\) | −14.9825 | − | 0.801195i | −0.610642 | − | 0.0326543i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.1750 | 0.414015 | ||||||||
\(605\) | −15.0795 | −0.613070 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 13.0060i | − | 0.527895i | −0.964537 | − | 0.263948i | \(-0.914975\pi\) | ||
0.964537 | − | 0.263948i | \(-0.0850246\pi\) | |||||||
\(608\) | 7.96453 | 0.323004 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.10676 | −0.328233 | ||||||||
\(611\) | − | 3.07392i | − | 0.124357i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.1434 | 0.773194 | 0.386597 | − | 0.922249i | \(-0.373650\pi\) | ||||
0.386597 | + | 0.922249i | \(0.373650\pi\) | |||||||
\(614\) | 0.623699 | 0.0251704 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.717439 | + | 13.4163i | −0.0289064 | + | 0.540557i | ||||
\(617\) | − | 23.4743i | − | 0.945041i | −0.881320 | − | 0.472521i | \(-0.843344\pi\) | ||
0.881320 | − | 0.472521i | \(-0.156656\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 34.7025i | − | 1.39481i | −0.716677 | − | 0.697406i | \(-0.754338\pi\) | ||
0.716677 | − | 0.697406i | \(-0.245662\pi\) | |||||||
\(620\) | − | 4.05213i | − | 0.162737i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 20.8303i | 0.835219i | ||||||||
\(623\) | 0.299400 | − | 5.59885i | 0.0119952 | − | 0.224313i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.4826 | 0.419305 | ||||||||
\(626\) | −20.4042 | −0.815516 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.53079i | 0.380320i | ||||||||
\(629\) | −16.3834 | −0.653251 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.5503 | −0.619046 | −0.309523 | − | 0.950892i | \(-0.600169\pi\) | ||||
−0.309523 | + | 0.950892i | \(0.600169\pi\) | |||||||
\(632\) | − | 4.74907i | − | 0.188908i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10.0593 | −0.399507 | ||||||||
\(635\) | −13.5716 | −0.538572 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.06982 | − | 37.9445i | 0.161252 | − | 1.50341i | ||||
\(638\) | − | 45.2643i | − | 1.79203i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.01976i | 0.0403097i | ||||||||
\(641\) | − | 50.1944i | − | 1.98256i | −0.131770 | − | 0.991280i | \(-0.542066\pi\) | ||
0.131770 | − | 0.991280i | \(-0.457934\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 49.4142i | 1.94871i | 0.225023 | + | 0.974353i | \(0.427754\pi\) | ||||
−0.225023 | + | 0.974353i | \(0.572246\pi\) | |||||||
\(644\) | 2.20731 | + | 0.118036i | 0.0869800 | + | 0.00465129i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 49.3662 | 1.94229 | ||||||||
\(647\) | 32.9511 | 1.29544 | 0.647721 | − | 0.761878i | \(-0.275722\pi\) | ||||
0.647721 | + | 0.761878i | \(0.275722\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 36.6539i | 1.43879i | ||||||||
\(650\) | −21.5893 | −0.846801 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.33296 | 0.287181 | ||||||||
\(653\) | − | 25.3395i | − | 0.991613i | −0.868433 | − | 0.495806i | \(-0.834873\pi\) | ||
0.868433 | − | 0.495806i | \(-0.165127\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.2993 | 0.480575 | ||||||||
\(656\) | 6.36603 | 0.248552 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.48966 | + | 0.0796600i | 0.0580729 | + | 0.00310547i | ||||
\(659\) | 15.1268i | 0.589256i | 0.955612 | + | 0.294628i | \(0.0951958\pi\) | ||||
−0.955612 | + | 0.294628i | \(0.904804\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 35.3585i | − | 1.37528i | −0.726050 | − | 0.687642i | \(-0.758646\pi\) | ||
0.726050 | − | 0.687642i | \(-0.241354\pi\) | |||||||
\(662\) | − | 26.1229i | − | 1.01529i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.0089i | 0.427229i | ||||||||
\(665\) | 21.4580 | + | 1.14747i | 0.832106 | + | 0.0444971i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.44709 | −0.288352 | ||||||||
\(668\) | 1.18754 | 0.0459474 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 10.9208i | − | 0.421908i | ||||||
\(671\) | 40.3692 | 1.55843 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.5512 | −0.483813 | −0.241906 | − | 0.970300i | \(-0.577773\pi\) | ||||
−0.241906 | + | 0.970300i | \(0.577773\pi\) | |||||||
\(674\) | − | 13.3950i | − | 0.515954i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.7214 | 0.643129 | ||||||||
\(677\) | −5.40677 | −0.207799 | −0.103900 | − | 0.994588i | \(-0.533132\pi\) | ||||
−0.103900 | + | 0.994588i | \(0.533132\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.36068 | − | 0.393615i | −0.282477 | − | 0.0151055i | ||||
\(680\) | 6.32076i | 0.242390i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 20.1784i | 0.772669i | ||||||||
\(683\) | 3.51472i | 0.134487i | 0.997737 | + | 0.0672435i | \(0.0214204\pi\) | ||||
−0.997737 | + | 0.0672435i | \(0.978580\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.6446i | 0.521332i | ||||||||
\(686\) | 18.2829 | + | 2.95561i | 0.698044 | + | 0.112846i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.67095 | 0.216203 | ||||||||
\(689\) | −11.9728 | −0.456128 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.7668i | 0.485670i | 0.970068 | + | 0.242835i | \(0.0780774\pi\) | ||||
−0.970068 | + | 0.242835i | \(0.921923\pi\) | |||||||
\(692\) | 3.59488 | 0.136657 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −15.7174 | −0.596626 | ||||||||
\(695\) | − | 9.90795i | − | 0.375830i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 39.4582 | 1.49459 | ||||||||
\(698\) | 0.333758 | 0.0126329 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.559482 | − | 10.4624i | 0.0211464 | − | 0.395443i | ||||
\(701\) | 14.4414i | 0.545446i | 0.962093 | + | 0.272723i | \(0.0879242\pi\) | ||||
−0.962093 | + | 0.272723i | \(0.912076\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 21.0522i | − | 0.793997i | ||||||
\(704\) | − | 5.07812i | − | 0.191389i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.45414i | 0.242905i | ||||||||
\(707\) | −1.70398 | + | 31.8647i | −0.0640846 | + | 1.19840i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.9297 | 0.673365 | 0.336682 | − | 0.941618i | \(-0.390695\pi\) | ||||
0.336682 | + | 0.941618i | \(0.390695\pi\) | |||||||
\(710\) | 6.32532 | 0.237385 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.11919i | 0.0794200i | ||||||||
\(713\) | 3.31984 | 0.124329 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −28.2317 | −1.05581 | ||||||||
\(716\) | − | 9.26770i | − | 0.346350i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.172817 | 0.00644948 | ||||||||
\(719\) | 36.9013 | 1.37619 | 0.688094 | − | 0.725622i | \(-0.258448\pi\) | ||||
0.688094 | + | 0.725622i | \(0.258448\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 38.1396 | + | 2.03953i | 1.42039 | + | 0.0759561i | ||||
\(722\) | 44.4338i | 1.65365i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.81954i | 0.216281i | ||||||||
\(725\) | 35.2985i | 1.31095i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.0100i | 0.705040i | 0.935804 | + | 0.352520i | \(0.114675\pi\) | ||||
−0.935804 | + | 0.352520i | \(0.885325\pi\) | |||||||
\(728\) | −0.770223 | + | 14.4033i | −0.0285464 | + | 0.533823i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.18958 | 0.266098 | ||||||||
\(731\) | 35.1500 | 1.30007 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.2058i | 1.07874i | 0.842068 | + | 0.539371i | \(0.181338\pi\) | ||||
−0.842068 | + | 0.539371i | \(0.818662\pi\) | |||||||
\(734\) | 13.3366 | 0.492263 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.835475 | −0.0307960 | ||||||||
\(737\) | 54.3823i | 2.00320i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.10127 | −0.114082 | −0.0570410 | − | 0.998372i | \(-0.518167\pi\) | ||||
−0.0570410 | + | 0.998372i | \(0.518167\pi\) | |||||||
\(740\) | 2.69548 | 0.0990879 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.310274 | − | 5.80218i | 0.0113905 | − | 0.213005i | ||||
\(743\) | − | 41.8237i | − | 1.53436i | −0.641430 | − | 0.767182i | \(-0.721658\pi\) | ||
0.641430 | − | 0.767182i | \(-0.278342\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 18.4942i | − | 0.677574i | ||||||
\(746\) | 17.3485i | 0.635173i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 31.4754i | − | 1.15086i | ||||||
\(749\) | −29.0721 | − | 1.55464i | −1.06227 | − | 0.0568053i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.61553 | 0.350876 | 0.175438 | − | 0.984491i | \(-0.443866\pi\) | ||||
0.175438 | + | 0.984491i | \(0.443866\pi\) | |||||||
\(752\) | −0.563843 | −0.0205612 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 48.5945i | − | 1.76971i | ||||||
\(755\) | −10.3761 | −0.377626 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.1331 | −1.09521 | −0.547603 | − | 0.836738i | \(-0.684459\pi\) | ||||
−0.547603 | + | 0.836738i | \(0.684459\pi\) | |||||||
\(758\) | − | 0.645891i | − | 0.0234598i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8.12195 | −0.294614 | ||||||||
\(761\) | −4.64689 | −0.168450 | −0.0842249 | − | 0.996447i | \(-0.526841\pi\) | ||||
−0.0842249 | + | 0.996447i | \(0.526841\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.415549 | + | 7.77086i | −0.0150439 | + | 0.281324i | ||||
\(764\) | − | 4.31684i | − | 0.156178i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.3455i | 0.879640i | ||||||||
\(767\) | 39.3507i | 1.42087i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 46.3656i | − | 1.67199i | −0.548740 | − | 0.835993i | \(-0.684892\pi\) | ||
0.548740 | − | 0.835993i | \(-0.315108\pi\) | |||||||
\(770\) | 0.731619 | − | 13.6814i | 0.0263657 | − | 0.493045i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −21.9861 | −0.791296 | ||||||||
\(773\) | −48.4069 | −1.74108 | −0.870538 | − | 0.492102i | \(-0.836229\pi\) | ||||
−0.870538 | + | 0.492102i | \(0.836229\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 15.7357i | − | 0.565244i | ||||||
\(776\) | 2.78605 | 0.100013 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 34.7203 | 1.24478 | ||||||||
\(779\) | 50.7024i | 1.81660i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31.4981 | −1.12709 | ||||||||
\(782\) | −5.17848 | −0.185182 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.96008 | − | 0.746520i | −0.248574 | − | 0.0266614i | ||||
\(785\) | − | 9.71916i | − | 0.346892i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.1997i | 1.11215i | 0.831132 | + | 0.556075i | \(0.187693\pi\) | ||||
−0.831132 | + | 0.556075i | \(0.812307\pi\) | |||||||
\(788\) | − | 9.96399i | − | 0.354953i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.84293i | 0.172304i | ||||||||
\(791\) | −18.3152 | − | 0.979409i | −0.651212 | − | 0.0348238i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 43.3392 | 1.53902 | ||||||||
\(794\) | −9.89614 | −0.351201 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.6673i | 0.413538i | ||||||||
\(797\) | 3.59488 | 0.127337 | 0.0636685 | − | 0.997971i | \(-0.479720\pi\) | ||||
0.0636685 | + | 0.997971i | \(0.479720\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.49484 | −0.123638 | ||||||||
\(800\) | 3.96008i | 0.140010i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −13.3181 | −0.470279 | ||||||||
\(803\) | −35.8019 | −1.26342 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.25093 | − | 0.120369i | −0.0793350 | − | 0.00424246i | ||||
\(806\) | 21.6629i | 0.763045i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 12.0609i | − | 0.424303i | ||||||
\(809\) | − | 47.0398i | − | 1.65383i | −0.562327 | − | 0.826915i | \(-0.690094\pi\) | ||
0.562327 | − | 0.826915i | \(-0.309906\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 7.29343i | − | 0.256107i | −0.991767 | − | 0.128053i | \(-0.959127\pi\) | ||
0.991767 | − | 0.128053i | \(-0.0408729\pi\) | |||||||
\(812\) | 23.5495 | + | 1.25932i | 0.826425 | + | 0.0441934i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −13.4227 | −0.470464 | ||||||||
\(815\) | −7.47790 | −0.261939 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 45.1665i | 1.58018i | ||||||||
\(818\) | 7.80767 | 0.272989 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.49185 | −0.226705 | ||||||||
\(821\) | − | 2.74077i | − | 0.0956537i | −0.998856 | − | 0.0478268i | \(-0.984770\pi\) | ||
0.998856 | − | 0.0478268i | \(-0.0152296\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.8348 | −0.412536 | −0.206268 | − | 0.978496i | \(-0.566132\pi\) | ||||
−0.206268 | + | 0.978496i | \(0.566132\pi\) | |||||||
\(824\) | −14.4360 | −0.502903 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −19.0698 | − | 1.01976i | −0.663524 | − | 0.0354822i | ||||
\(827\) | − | 38.9241i | − | 1.35352i | −0.736202 | − | 0.676761i | \(-0.763383\pi\) | ||
0.736202 | − | 0.676761i | \(-0.236617\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 33.3214i | − | 1.15730i | −0.815576 | − | 0.578650i | \(-0.803580\pi\) | ||
0.815576 | − | 0.578650i | \(-0.196420\pi\) | |||||||
\(830\) | − | 11.2265i | − | 0.389678i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 5.45173i | − | 0.189005i | ||||||
\(833\) | −43.1403 | − | 4.62712i | −1.49472 | − | 0.160320i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.21101 | −0.0419088 | ||||||||
\(836\) | 40.4448 | 1.39881 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 30.5760i | 1.05623i | ||||||||
\(839\) | −24.8404 | −0.857586 | −0.428793 | − | 0.903403i | \(-0.641061\pi\) | ||||
−0.428793 | + | 0.903403i | \(0.641061\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −50.4521 | −1.73973 | ||||||||
\(842\) | 29.9686i | 1.03278i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.60332 | 0.0551885 | ||||||||
\(845\) | −17.0518 | −0.586601 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.08915 | + | 39.0676i | −0.0717841 | + | 1.34238i | ||||
\(848\) | 2.19615i | 0.0754162i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 24.5456i | 0.841906i | ||||||||
\(851\) | 2.20836i | 0.0757016i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 2.43959i | − | 0.0835299i | −0.999127 | − | 0.0417650i | \(-0.986702\pi\) | ||
0.999127 | − | 0.0417650i | \(-0.0132981\pi\) | |||||||
\(854\) | −1.12313 | + | 21.0027i | −0.0384327 | + | 0.718699i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.0039 | 0.376106 | ||||||||
\(857\) | −11.8287 | −0.404059 | −0.202030 | − | 0.979379i | \(-0.564754\pi\) | ||||
−0.202030 | + | 0.979379i | \(0.564754\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.3135i | 1.20488i | 0.798164 | + | 0.602440i | \(0.205805\pi\) | ||||
−0.798164 | + | 0.602440i | \(0.794195\pi\) | |||||||
\(860\) | −5.78304 | −0.197200 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −19.8981 | −0.677732 | ||||||||
\(863\) | 15.5568i | 0.529561i | 0.964309 | + | 0.264780i | \(0.0852994\pi\) | ||||
−0.964309 | + | 0.264780i | \(0.914701\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.66593 | −0.124645 | ||||||||
\(866\) | −26.6176 | −0.904503 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −10.4981 | − | 0.561391i | −0.356330 | − | 0.0190549i | ||||
\(869\) | − | 24.1163i | − | 0.818090i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 58.3834i | 1.97824i | ||||||||
\(872\) | − | 2.94130i | − | 0.0996051i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 6.65417i | − | 0.225081i | ||||||
\(875\) | −1.29090 | + | 24.1402i | −0.0436405 | + | 0.816088i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.5957 | 1.30328 | 0.651642 | − | 0.758527i | \(-0.274081\pi\) | ||||
0.651642 | + | 0.758527i | \(0.274081\pi\) | |||||||
\(878\) | −29.1602 | −0.984109 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.17848i | 0.174567i | ||||||||
\(881\) | 38.9816 | 1.31332 | 0.656662 | − | 0.754185i | \(-0.271968\pi\) | ||||
0.656662 | + | 0.754185i | \(0.271968\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.32421 | 0.0445631 | 0.0222815 | − | 0.999752i | \(-0.492907\pi\) | ||||
0.0222815 | + | 0.999752i | \(0.492907\pi\) | |||||||
\(884\) | − | 33.7912i | − | 1.13652i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −29.3107 | −0.984714 | ||||||||
\(887\) | −32.2584 | −1.08313 | −0.541566 | − | 0.840658i | \(-0.682168\pi\) | ||||
−0.541566 | + | 0.840658i | \(0.682168\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.88024 | + | 35.1609i | −0.0630612 | + | 1.17926i | ||||
\(890\) | − | 2.16108i | − | 0.0724394i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 18.3042i | − | 0.612868i | ||||||
\(893\) | − | 4.49074i | − | 0.150277i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.45088i | 0.315908i | ||||||||
\(896\) | 2.64198 | + | 0.141281i | 0.0882622 | + | 0.00471985i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 14.5485 | 0.485491 | ||||||||
\(899\) | 35.4190 | 1.18129 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.6123i | 0.453491i | ||||||||
\(902\) | 32.3274 | 1.07639 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.93237 | 0.230567 | ||||||||
\(905\) | − | 5.93456i | − | 0.197271i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 53.3164 | 1.77034 | 0.885171 | − | 0.465266i | \(-0.154041\pi\) | ||||
0.885171 | + | 0.465266i | \(0.154041\pi\) | |||||||
\(908\) | −15.8519 | −0.526062 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.785447 | − | 14.6880i | 0.0260373 | − | 0.486903i | ||||
\(911\) | − | 5.24548i | − | 0.173790i | −0.996217 | − | 0.0868952i | \(-0.972305\pi\) | ||
0.996217 | − | 0.0868952i | \(-0.0276945\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 55.9046i | 1.85017i | ||||||||
\(914\) | 5.21166i | 0.172386i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 21.7163i | 0.717528i | ||||||||
\(917\) | 1.70398 | − | 31.8647i | 0.0562703 | − | 1.05227i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.6393 | −0.416933 | −0.208466 | − | 0.978030i | \(-0.566847\pi\) | ||||
−0.208466 | + | 0.978030i | \(0.566847\pi\) | |||||||
\(920\) | 0.851988 | 0.0280892 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 34.9906i | − | 1.15236i | ||||||
\(923\) | −33.8156 | −1.11305 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.4674 | 0.344167 | ||||||||
\(926\) | 2.05213i | 0.0674371i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.91359 | −0.292603 | ||||||||
\(929\) | −50.7221 | −1.66414 | −0.832070 | − | 0.554671i | \(-0.812844\pi\) | ||||
−0.832070 | + | 0.554671i | \(0.812844\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.94568 | − | 55.4338i | 0.194862 | − | 1.81677i | ||||
\(932\) | 17.0886i | 0.559756i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 20.4066i | 0.667726i | ||||||||
\(935\) | 32.0975i | 1.04970i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.88667i | 0.257646i | 0.991668 | + | 0.128823i | \(0.0411199\pi\) | ||||
−0.991668 | + | 0.128823i | \(0.958880\pi\) | |||||||
\(938\) | −28.2933 | − | 1.51299i | −0.923809 | − | 0.0494010i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.574987 | 0.0187540 | ||||||||
\(941\) | 50.4702 | 1.64528 | 0.822641 | − | 0.568561i | \(-0.192500\pi\) | ||||
0.822641 | + | 0.568561i | \(0.192500\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 5.31866i | − | 0.173199i | ||||||
\(944\) | 7.21801 | 0.234926 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 28.7977 | 0.936295 | ||||||||
\(947\) | − | 41.1489i | − | 1.33716i | −0.743641 | − | 0.668579i | \(-0.766903\pi\) | ||
0.743641 | − | 0.668579i | \(-0.233097\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −38.4360 | −1.24768 | ||||||||
\(950\) | −31.5402 | −1.02330 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 16.3756 | + | 0.875692i | 0.530737 | + | 0.0283813i | ||||
\(953\) | − | 2.06918i | − | 0.0670273i | −0.999438 | − | 0.0335136i | \(-0.989330\pi\) | ||
0.999438 | − | 0.0335136i | \(-0.0106697\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.40216i | 0.142451i | ||||||||
\(956\) | − | 9.32969i | − | 0.301744i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 13.8722i | − | 0.448190i | ||||||
\(959\) | 35.3499 | + | 1.89035i | 1.14151 | + | 0.0610425i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.2106 | 0.490664 | ||||||||
\(962\) | −14.4102 | −0.464604 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 22.4030i | − | 0.721552i | ||||||
\(965\) | 22.4206 | 0.721745 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.6936 | 1.17999 | 0.589994 | − | 0.807408i | \(-0.299130\pi\) | ||||
0.589994 | + | 0.807408i | \(0.299130\pi\) | |||||||
\(968\) | − | 14.7873i | − | 0.475281i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.84112 | −0.0912227 | ||||||||
\(971\) | −31.2280 | −1.00215 | −0.501077 | − | 0.865403i | \(-0.667063\pi\) | ||||
−0.501077 | + | 0.865403i | \(0.667063\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25.6692 | − | 1.37267i | −0.822918 | − | 0.0440058i | ||||
\(974\) | − | 22.3646i | − | 0.716608i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 7.94963i | − | 0.254462i | ||||||
\(977\) | 16.0686i | 0.514079i | 0.966401 | + | 0.257039i | \(0.0827470\pi\) | ||||
−0.966401 | + | 0.257039i | \(0.917253\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.7615i | 0.343939i | ||||||||
\(980\) | 7.09764 | + | 0.761275i | 0.226726 | + | 0.0243180i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.60770 | −0.242771 | ||||||||
\(983\) | −27.1207 | −0.865015 | −0.432508 | − | 0.901630i | \(-0.642371\pi\) | ||||
−0.432508 | + | 0.901630i | \(0.642371\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.1609i | 0.323754i | ||||||||
\(986\) | −55.2487 | −1.75948 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 43.4205 | 1.38139 | ||||||||
\(989\) | − | 4.73794i | − | 0.150658i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.3814 | 0.456839 | 0.228419 | − | 0.973563i | \(-0.426644\pi\) | ||||
0.228419 | + | 0.973563i | \(0.426644\pi\) | |||||||
\(992\) | 3.97359 | 0.126162 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.876324 | − | 16.3874i | 0.0277953 | − | 0.519778i | ||||
\(995\) | − | 11.8979i | − | 0.377190i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.3585i | 1.08814i | 0.839038 | + | 0.544072i | \(0.183118\pi\) | ||||
−0.839038 | + | 0.544072i | \(0.816882\pi\) | |||||||
\(998\) | 11.3208i | 0.358352i | ||||||||
\(999\) | 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 | 1134.2.d.b.1133.5 | yes | 16 | |
3.2 | odd | 2 | inner | 1134.2.d.b.1133.12 | yes | 16 | |
7.6 | odd | 2 | inner | 1134.2.d.b.1133.4 | ✓ | 16 | |
9.2 | odd | 6 | 1134.2.m.h.377.7 | 16 | |||
9.4 | even | 3 | 1134.2.m.h.755.6 | 16 | |||
9.5 | odd | 6 | 1134.2.m.i.755.3 | 16 | |||
9.7 | even | 3 | 1134.2.m.i.377.2 | 16 | |||
21.20 | even | 2 | inner | 1134.2.d.b.1133.13 | yes | 16 | |
63.13 | odd | 6 | 1134.2.m.h.755.7 | 16 | |||
63.20 | even | 6 | 1134.2.m.h.377.6 | 16 | |||
63.34 | odd | 6 | 1134.2.m.i.377.3 | 16 | |||
63.41 | even | 6 | 1134.2.m.i.755.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1134.2.d.b.1133.4 | ✓ | 16 | 7.6 | odd | 2 | inner | |
1134.2.d.b.1133.5 | yes | 16 | 1.1 | even | 1 | trivial | |
1134.2.d.b.1133.12 | yes | 16 | 3.2 | odd | 2 | inner | |
1134.2.d.b.1133.13 | yes | 16 | 21.20 | even | 2 | inner | |
1134.2.m.h.377.6 | 16 | 63.20 | even | 6 | |||
1134.2.m.h.377.7 | 16 | 9.2 | odd | 6 | |||
1134.2.m.h.755.6 | 16 | 9.4 | even | 3 | |||
1134.2.m.h.755.7 | 16 | 63.13 | odd | 6 | |||
1134.2.m.i.377.2 | 16 | 9.7 | even | 3 | |||
1134.2.m.i.377.3 | 16 | 63.34 | odd | 6 | |||
1134.2.m.i.755.2 | 16 | 63.41 | even | 6 | |||
1134.2.m.i.755.3 | 16 | 9.5 | odd | 6 |