Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,2,Mod(145,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.145");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.r (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.89907473464\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} + x^{14} + 2 x^{12} - 4 x^{11} - 8 x^{9} + 4 x^{8} - 16 x^{7} - 32 x^{5} + 32 x^{4} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 721.7 | ||
Root | \(0.820200 + 1.15207i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 864.721 |
Dual form | 864.2.r.b.145.7 |
$q$-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 \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.97542 | − | 1.14051i | 0.883437 | − | 0.510052i | 0.0116467 | − | 0.999932i | \(-0.496293\pi\) |
0.871790 | + | 0.489880i | \(0.162959\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.907824 | − | 1.57240i | 0.343125 | − | 0.594311i | −0.641886 | − | 0.766800i | \(-0.721848\pi\) |
0.985011 | + | 0.172490i | \(0.0551811\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.24153 | − | 2.44885i | −1.27887 | − | 0.738355i | −0.302228 | − | 0.953236i | \(-0.597730\pi\) |
−0.976640 | + | 0.214880i | \(0.931064\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.00895 | − | 2.31457i | 1.11188 | − | 0.641946i | 0.172567 | − | 0.984998i | \(-0.444794\pi\) |
0.939317 | + | 0.343052i | \(0.111461\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.92788 | −0.467579 | −0.233790 | − | 0.972287i | \(-0.575113\pi\) | ||||
−0.233790 | + | 0.972287i | \(0.575113\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.12907i | − | 0.488442i | −0.969720 | − | 0.244221i | \(-0.921468\pi\) | ||
0.969720 | − | 0.244221i | \(-0.0785322\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.15765 | − | 2.00511i | −0.241387 | − | 0.418094i | 0.719723 | − | 0.694261i | \(-0.244269\pi\) |
−0.961109 | + | 0.276168i | \(0.910936\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.101535 | − | 0.175863i | 0.0203069 | − | 0.0351726i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.16440 | − | 1.82697i | −0.587615 | − | 0.339260i | 0.176539 | − | 0.984294i | \(-0.443510\pi\) |
−0.764154 | + | 0.645034i | \(0.776843\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.65800 | + | 4.60379i | 0.477391 | + | 0.826865i | 0.999664 | − | 0.0259130i | \(-0.00824928\pi\) |
−0.522273 | + | 0.852778i | \(0.674916\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 4.14154i | − | 0.700048i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 7.98438i | − | 1.31262i | −0.754489 | − | 0.656312i | \(-0.772115\pi\) | ||
0.754489 | − | 0.656312i | \(-0.227885\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.36240 | + | 4.09180i | 0.368946 | + | 0.639033i | 0.989401 | − | 0.145209i | \(-0.0463855\pi\) |
−0.620455 | + | 0.784242i | \(0.713052\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.20800 | + | 1.27479i | 0.336717 | + | 0.194404i | 0.658819 | − | 0.752301i | \(-0.271056\pi\) |
−0.322102 | + | 0.946705i | \(0.604390\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.02005 | + | 3.49884i | −0.294655 | + | 0.510358i | −0.974905 | − | 0.222623i | \(-0.928538\pi\) |
0.680249 | + | 0.732981i | \(0.261871\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.85171 | + | 3.20726i | 0.264530 | + | 0.458179i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 8.95958i | − | 1.23069i | −0.788257 | − | 0.615347i | \(-0.789016\pi\) | ||
0.788257 | − | 0.615347i | \(-0.210984\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.1718 | −1.50640 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.05255 | − | 1.76239i | 0.397408 | − | 0.229444i | −0.287957 | − | 0.957643i | \(-0.592976\pi\) |
0.685365 | + | 0.728200i | \(0.259643\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.71675 | + | 0.991165i | 0.219807 | + | 0.126906i | 0.605861 | − | 0.795571i | \(-0.292829\pi\) |
−0.386054 | + | 0.922476i | \(0.626162\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.27959 | − | 9.14451i | 0.654852 | − | 1.13424i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.72723 | − | 4.46132i | 0.944031 | − | 0.545036i | 0.0528093 | − | 0.998605i | \(-0.483182\pi\) |
0.891222 | + | 0.453568i | \(0.149849\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.3561 | 1.58508 | 0.792539 | − | 0.609821i | \(-0.208759\pi\) | ||||
0.792539 | + | 0.609821i | \(0.208759\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.5592 | −1.35290 | −0.676450 | − | 0.736489i | \(-0.736482\pi\) | ||||
−0.676450 | + | 0.736489i | \(0.736482\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.70112 | + | 4.44625i | −0.877625 | + | 0.506697i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.97330 | − | 8.61401i | 0.559540 | − | 0.969151i | −0.437995 | − | 0.898977i | \(-0.644311\pi\) |
0.997535 | − | 0.0701739i | \(-0.0223554\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.12153 | + | 1.80221i | 0.342632 | + | 0.197819i | 0.661435 | − | 0.750002i | \(-0.269948\pi\) |
−0.318803 | + | 0.947821i | \(0.603281\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.80838 | + | 2.19877i | −0.413077 | + | 0.238490i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.49965 | −0.264962 | −0.132481 | − | 0.991186i | \(-0.542294\pi\) | ||||
−0.132481 | + | 0.991186i | \(0.542294\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 8.40489i | − | 0.881072i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.42823 | − | 4.20582i | −0.249131 | − | 0.431508i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.99370 | − | 12.1134i | 0.710103 | − | 1.22993i | −0.254715 | − | 0.967016i | \(-0.581982\pi\) |
0.964818 | − | 0.262918i | \(-0.0846849\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.13087 | + | 0.652911i | 0.112526 | + | 0.0649671i | 0.555207 | − | 0.831712i | \(-0.312639\pi\) |
−0.442681 | + | 0.896679i | \(0.645972\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.22312 | + | 5.58261i | 0.317584 | + | 0.550071i | 0.979983 | − | 0.199080i | \(-0.0637952\pi\) |
−0.662400 | + | 0.749151i | \(0.730462\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.10427i | 0.300101i | 0.988678 | + | 0.150051i | \(0.0479437\pi\) | ||||
−0.988678 | + | 0.150051i | \(0.952056\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.0837i | 1.73210i | 0.499955 | + | 0.866051i | \(0.333350\pi\) | ||||
−0.499955 | + | 0.866051i | \(0.666650\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.41718 | + | 2.45463i | 0.133317 | + | 0.230913i | 0.924953 | − | 0.380080i | \(-0.124104\pi\) |
−0.791636 | + | 0.610993i | \(0.790770\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.57370 | − | 2.64063i | −0.426500 | − | 0.246240i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.75018 | + | 3.03139i | −0.160438 | + | 0.277887i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.49370 | + | 11.2474i | 0.590337 | + | 1.02249i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.9419i | 0.978674i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.44962 | 0.661047 | 0.330523 | − | 0.943798i | \(-0.392775\pi\) | ||||
0.330523 | + | 0.943798i | \(0.392775\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.12153 | + | 1.80221i | −0.272729 | + | 0.157460i | −0.630127 | − | 0.776492i | \(-0.716997\pi\) |
0.357398 | + | 0.933952i | \(0.383664\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.34774 | − | 1.93282i | −0.290286 | − | 0.167597i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.88147 | + | 10.1870i | −0.502488 | + | 0.870335i | 0.497508 | + | 0.867460i | \(0.334249\pi\) |
−0.999996 | + | 0.00287543i | \(0.999085\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.0400 | + | 6.37395i | −0.936400 | + | 0.540631i | −0.888830 | − | 0.458237i | \(-0.848481\pi\) |
−0.0475703 | + | 0.998868i | \(0.515148\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −22.6721 | −1.89594 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.33472 | −0.692161 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.59790 | − | 3.80930i | 0.540521 | − | 0.312070i | −0.204769 | − | 0.978810i | \(-0.565644\pi\) |
0.745290 | + | 0.666740i | \(0.232311\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.26988 | + | 3.93155i | −0.184720 | + | 0.319945i | −0.943482 | − | 0.331423i | \(-0.892471\pi\) |
0.758762 | + | 0.651368i | \(0.225805\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.5014 | + | 6.06296i | 0.843489 | + | 0.486989i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.4105 | + | 6.58787i | −0.910659 | + | 0.525769i | −0.880643 | − | 0.473780i | \(-0.842889\pi\) |
−0.0300161 | + | 0.999549i | \(0.509556\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.20377 | −0.331303 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.5911i | 1.61282i | 0.591358 | + | 0.806409i | \(0.298592\pi\) | ||||
−0.591358 | + | 0.806409i | \(0.701408\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.53912 | + | 4.39789i | 0.196483 | + | 0.340319i | 0.947386 | − | 0.320094i | \(-0.103715\pi\) |
−0.750903 | + | 0.660413i | \(0.770381\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.21446 | − | 7.29967i | 0.324190 | − | 0.561513i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.0398 | + | 6.37385i | 0.839343 | + | 0.484595i | 0.857041 | − | 0.515248i | \(-0.172300\pi\) |
−0.0176977 | + | 0.999843i | \(0.505634\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.184351 | − | 0.319306i | −0.0139356 | − | 0.0241372i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.82019i | 0.659252i | 0.944112 | + | 0.329626i | \(0.106923\pi\) | ||||
−0.944112 | + | 0.329626i | \(0.893077\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 15.4369i | − | 1.14741i | −0.819061 | − | 0.573707i | \(-0.805505\pi\) | ||
0.819061 | − | 0.573707i | \(-0.194495\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.10628 | − | 15.7725i | −0.669507 | − | 1.15962i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.17715 | + | 4.72108i | 0.597972 | + | 0.345239i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.81698 | − | 8.34326i | 0.348545 | − | 0.603697i | −0.637446 | − | 0.770495i | \(-0.720009\pi\) |
0.985991 | + | 0.166797i | \(0.0533426\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.49335 | + | 6.05066i | 0.251457 | + | 0.435536i | 0.963927 | − | 0.266166i | \(-0.0857570\pi\) |
−0.712470 | + | 0.701702i | \(0.752424\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.31842i | 0.307675i | 0.988096 | + | 0.153837i | \(0.0491632\pi\) | ||||
−0.988096 | + | 0.153837i | \(0.950837\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.90649 | −0.418700 | −0.209350 | − | 0.977841i | \(-0.567135\pi\) | ||||
−0.209350 | + | 0.977841i | \(0.567135\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.74544 | + | 3.31713i | −0.403251 | + | 0.232817i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.33350 | + | 5.38870i | 0.651880 | + | 0.376363i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.21376 | + | 9.03050i | −0.360644 | + | 0.624653i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.8781 | + | 9.16723i | −1.09309 | + | 0.631098i | −0.934399 | − | 0.356229i | \(-0.884062\pi\) |
−0.158696 | + | 0.987328i | \(0.550729\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.81565 | 0.396624 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.65199 | 0.655220 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.72877 | + | 4.46221i | −0.519893 | + | 0.300161i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.63263 | − | 4.55986i | 0.176294 | − | 0.305350i | −0.764314 | − | 0.644844i | \(-0.776922\pi\) |
0.940608 | + | 0.339494i | \(0.110256\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.53638 | − | 0.887027i | −0.101973 | − | 0.0588741i | 0.448146 | − | 0.893960i | \(-0.352084\pi\) |
−0.550119 | + | 0.835086i | \(0.685418\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.30687 | − | 1.90922i | 0.218524 | − | 0.126165i | −0.386742 | − | 0.922188i | \(-0.626400\pi\) |
0.605267 | + | 0.796023i | \(0.293066\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.3207 | 1.33125 | 0.665627 | − | 0.746284i | \(-0.268164\pi\) | ||||
0.665627 | + | 0.746284i | \(0.268164\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.21558i | 0.601158i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.69811 | + | 15.0656i | 0.562634 | + | 0.974510i | 0.997266 | + | 0.0739020i | \(0.0235452\pi\) |
−0.434632 | + | 0.900608i | \(0.643121\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.85611 | + | 11.8751i | −0.441641 | + | 0.764944i | −0.997811 | − | 0.0661240i | \(-0.978937\pi\) |
0.556171 | + | 0.831068i | \(0.312270\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.31583 | + | 4.22379i | 0.467391 | + | 0.269848i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.92788 | − | 8.53534i | −0.313553 | − | 0.543090i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.50751i | 0.284512i | 0.989830 | + | 0.142256i | \(0.0454356\pi\) | ||||
−0.989830 | + | 0.142256i | \(0.954564\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.3396i | 0.712916i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.11258 | + | 7.12320i | 0.256536 | + | 0.444333i | 0.965311 | − | 0.261101i | \(-0.0840856\pi\) |
−0.708776 | + | 0.705434i | \(0.750752\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.5546 | − | 7.24842i | −0.780106 | − | 0.450395i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.51376 | − | 4.35395i | 0.155005 | − | 0.268476i | −0.778056 | − | 0.628195i | \(-0.783794\pi\) |
0.933061 | + | 0.359719i | \(0.117127\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.2185 | − | 17.6990i | −0.627718 | − | 1.08724i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.1577i | 1.41195i | 0.708236 | + | 0.705976i | \(0.249491\pi\) | ||||
−0.708236 | + | 0.705976i | \(0.750509\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.9367 | −1.27181 | −0.635906 | − | 0.771766i | \(-0.719373\pi\) | ||||
−0.635906 | + | 0.771766i | \(0.719373\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.861323 | + | 0.497285i | −0.0519398 | + | 0.0299874i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.2687 | − | 11.1248i | −1.15775 | − | 0.668425i | −0.206983 | − | 0.978345i | \(-0.566364\pi\) |
−0.950763 | + | 0.309920i | \(0.899698\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.28029 | − | 16.0739i | 0.553616 | − | 0.958890i | −0.444394 | − | 0.895831i | \(-0.646581\pi\) |
0.998010 | − | 0.0630590i | \(-0.0200856\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.75962 | − | 1.01592i | 0.104599 | − | 0.0603901i | −0.446788 | − | 0.894640i | \(-0.647432\pi\) |
0.551387 | + | 0.834250i | \(0.314099\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.57859 | 0.506378 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.2833 | −0.781370 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 29.5484 | − | 17.0598i | 1.72623 | − | 0.996642i | 0.822178 | − | 0.569231i | \(-0.192759\pi\) |
0.904057 | − | 0.427411i | \(-0.140574\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.02005 | − | 6.96294i | 0.234057 | − | 0.405398i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.28192 | − | 5.35892i | −0.536787 | − | 0.309914i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00895 | − | 2.31457i | 0.231072 | − | 0.133410i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.52174 | 0.258914 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4.77588i | − | 0.272574i | −0.990669 | − | 0.136287i | \(-0.956483\pi\) | ||
0.990669 | − | 0.136287i | \(-0.0435169\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.1771 | − | 19.3592i | −0.633793 | − | 1.09776i | −0.986769 | − | 0.162130i | \(-0.948164\pi\) |
0.352976 | − | 0.935632i | \(-0.385170\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.22411 | − | 2.12022i | 0.0691907 | − | 0.119842i | −0.829355 | − | 0.558723i | \(-0.811292\pi\) |
0.898545 | + | 0.438881i | \(0.144625\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.2886 | − | 8.24953i | −0.802528 | − | 0.463340i | 0.0418263 | − | 0.999125i | \(-0.486682\pi\) |
−0.844354 | + | 0.535785i | \(0.820016\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.94793 | + | 15.4983i | 0.500988 | + | 0.867737i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.10459i | 0.228385i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 0.940035i | − | 0.0521438i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.66771 | + | 6.35266i | 0.202207 | + | 0.350233i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.329200 | − | 0.190064i | −0.0180945 | − | 0.0104469i | 0.490925 | − | 0.871202i | \(-0.336659\pi\) |
−0.509020 | + | 0.860755i | \(0.669992\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.1764 | − | 17.6260i | 0.555994 | − | 0.963010i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.51872 | − | 4.36255i | −0.137203 | − | 0.237643i | 0.789234 | − | 0.614093i | \(-0.210478\pi\) |
−0.926437 | + | 0.376450i | \(0.877145\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 26.0361i | − | 1.40994i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.4337 | 1.04932 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.40337 | − | 4.85169i | 0.451116 | − | 0.260452i | −0.257185 | − | 0.966362i | \(-0.582795\pi\) |
0.708302 | + | 0.705910i | \(0.249462\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.1239 | + | 15.0827i | 1.39838 | + | 0.807356i | 0.994223 | − | 0.107333i | \(-0.0342312\pi\) |
0.404158 | + | 0.914689i | \(0.367564\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.2376 | + | 22.9282i | −0.704565 | + | 1.22034i | 0.262283 | + | 0.964991i | \(0.415525\pi\) |
−0.966848 | + | 0.255352i | \(0.917809\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 26.3840 | − | 15.2328i | 1.40032 | − | 0.808473i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.4619 | −1.23827 | −0.619135 | − | 0.785285i | \(-0.712517\pi\) | ||||
−0.619135 | + | 0.785285i | \(0.712517\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.4671 | 0.761424 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −22.8343 | + | 13.1834i | −1.19520 | + | 0.690050i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.62599 | + | 16.6727i | −0.502472 | + | 0.870308i | 0.497524 | + | 0.867450i | \(0.334243\pi\) |
−0.999996 | + | 0.00285720i | \(0.999091\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.0880 | − | 8.13373i | −0.731414 | − | 0.422282i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.09206 | − | 5.24930i | 0.470769 | − | 0.271799i | −0.245793 | − | 0.969322i | \(-0.579048\pi\) |
0.716562 | + | 0.697524i | \(0.245715\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16.9146 | −0.871145 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 35.5203i | − | 1.82455i | −0.409574 | − | 0.912277i | \(-0.634323\pi\) | ||
0.409574 | − | 0.912277i | \(-0.365677\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.0395 | + | 31.2453i | 0.921774 | + | 1.59656i | 0.796669 | + | 0.604416i | \(0.206593\pi\) |
0.125105 | + | 0.992144i | \(0.460073\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.1420 | + | 17.5664i | −0.516884 | + | 0.895269i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.5243 | − | 10.1177i | −0.888519 | − | 0.512987i | −0.0150612 | − | 0.999887i | \(-0.504794\pi\) |
−0.873458 | + | 0.486900i | \(0.838128\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.23181 | + | 3.86560i | 0.112867 | + | 0.195492i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 22.6884i | − | 1.14158i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.99499i | 0.200503i | 0.994962 | + | 0.100251i | \(0.0319647\pi\) | ||||
−0.994962 | + | 0.100251i | \(0.968035\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.0124 | − | 24.2702i | −0.699747 | − | 1.21200i | −0.968554 | − | 0.248803i | \(-0.919963\pi\) |
0.268807 | − | 0.963194i | \(-0.413371\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.3116 | + | 12.3042i | 1.06161 | + | 0.612918i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −19.5525 | + | 33.8660i | −0.969183 | + | 1.67867i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.22481 | + | 14.2458i | 0.406691 | + | 0.704409i | 0.994517 | − | 0.104579i | \(-0.0333494\pi\) |
−0.587826 | + | 0.808987i | \(0.700016\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 6.39976i | − | 0.314912i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.22179 | 0.403592 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.5573 | − | 11.8688i | 1.00429 | − | 0.579827i | 0.0947752 | − | 0.995499i | \(-0.469787\pi\) |
0.909515 | + | 0.415672i | \(0.136453\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.9420 | − | 14.9776i | −1.26433 | − | 0.729963i | −0.290424 | − | 0.956898i | \(-0.593796\pi\) |
−0.973910 | + | 0.226935i | \(0.927130\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.195746 | + | 0.339043i | −0.00949509 | + | 0.0164460i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.11701 | − | 1.79961i | 0.150843 | − | 0.0870891i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.0367 | −0.531621 | −0.265810 | − | 0.964025i | \(-0.585640\pi\) | ||||
−0.265810 | + | 0.964025i | \(0.585640\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.9394 | 1.67908 | 0.839541 | − | 0.543297i | \(-0.182824\pi\) | ||||
0.839541 | + | 0.543297i | \(0.182824\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.26901 | + | 2.46472i | −0.204215 | + | 0.117903i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.58518 | − | 11.4059i | 0.314293 | − | 0.544372i | −0.664994 | − | 0.746849i | \(-0.731566\pi\) |
0.979287 | + | 0.202477i | \(0.0648991\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.6849 | + | 13.6745i | 1.12530 | + | 0.649694i | 0.942749 | − | 0.333502i | \(-0.108230\pi\) |
0.182554 | + | 0.983196i | \(0.441564\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.93787 | + | 2.85088i | −0.234077 | + | 0.135145i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.8225 | 0.652323 | 0.326161 | − | 0.945314i | \(-0.394245\pi\) | ||||
0.326161 | + | 0.945314i | \(0.394245\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 23.1407i | − | 1.08965i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.58588 | − | 16.6032i | −0.449393 | − | 0.778371i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.86205 | + | 4.95722i | −0.133881 | + | 0.231889i | −0.925170 | − | 0.379554i | \(-0.876077\pi\) |
0.791288 | + | 0.611443i | \(0.209411\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.3717 | − | 11.1843i | −0.902231 | − | 0.520903i | −0.0243074 | − | 0.999705i | \(-0.507738\pi\) |
−0.877923 | + | 0.478801i | \(0.841071\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.5733 | − | 32.1699i | −0.863174 | − | 1.49506i | −0.868849 | − | 0.495077i | \(-0.835140\pi\) |
0.00567564 | − | 0.999984i | \(-0.498193\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 22.6850i | − | 1.04974i | −0.851184 | − | 0.524868i | \(-0.824115\pi\) | ||
0.851184 | − | 0.524868i | \(-0.175885\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 16.2004i | − | 0.748063i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.24353 | − | 10.8141i | −0.287078 | − | 0.497233i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.374425 | − | 0.216174i | −0.0171798 | − | 0.00991875i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.1576 | − | 22.7897i | 0.601188 | − | 1.04129i | −0.391453 | − | 0.920198i | \(-0.628027\pi\) |
0.992641 | − | 0.121091i | \(-0.0386392\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.4804 | − | 32.0090i | −0.842634 | − | 1.45948i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 31.9056i | − | 1.44876i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.0388 | 1.08930 | 0.544652 | − | 0.838662i | \(-0.316662\pi\) | ||||
0.544652 | + | 0.838662i | \(0.316662\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.2256 | + | 15.7187i | −1.22867 | + | 0.709374i | −0.966752 | − | 0.255715i | \(-0.917689\pi\) |
−0.261920 | + | 0.965090i | \(0.584356\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.10058 | + | 3.52217i | 0.274756 | + | 0.158631i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.1250 | − | 21.0011i | 0.543881 | − | 0.942029i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.08156 | − | 2.93384i | 0.227482 | − | 0.131337i | −0.381928 | − | 0.924192i | \(-0.624740\pi\) |
0.609410 | + | 0.792855i | \(0.291406\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.4317 | 1.44606 | 0.723029 | − | 0.690818i | \(-0.242749\pi\) | ||||
0.723029 | + | 0.690818i | \(0.242749\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.97861 | 0.132546 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.6855 | + | 7.90133i | −0.606599 | + | 0.350220i | −0.771633 | − | 0.636068i | \(-0.780560\pi\) |
0.165034 | + | 0.986288i | \(0.447227\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.4937 | + | 18.1756i | −0.464214 | + | 0.804042i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.7341 | + | 7.35202i | 0.561130 | + | 0.323969i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.1362 | − | 9.89361i | 0.753650 | − | 0.435120i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.50310 | −0.241095 | −0.120548 | − | 0.992708i | \(-0.538465\pi\) | ||||
−0.120548 | + | 0.992708i | \(0.538465\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 38.5894i | 1.68740i | 0.536818 | + | 0.843698i | \(0.319626\pi\) | ||||
−0.536818 | + | 0.843698i | \(0.680374\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.12430 | − | 8.87555i | −0.223218 | − | 0.386625i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.81970 | − | 15.2762i | 0.383465 | − | 0.664181i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.9415 | + | 10.9359i | 0.820449 | + | 0.473686i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.54046 | + | 6.13225i | 0.153067 | + | 0.265120i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 18.1382i | − | 0.781268i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 22.5666i | − | 0.970214i | −0.874455 | − | 0.485107i | \(-0.838781\pi\) | ||
0.874455 | − | 0.485107i | \(-0.161219\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20.6246 | + | 35.7229i | 0.883463 | + | 1.53020i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.2679 | − | 6.50552i | −0.481780 | − | 0.278156i | 0.239378 | − | 0.970927i | \(-0.423057\pi\) |
−0.721158 | + | 0.692770i | \(0.756390\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.88974 | + | 6.73723i | −0.165709 | + | 0.287016i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.02976 | − | 15.6400i | −0.383985 | − | 0.665081i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 5.73693i | − | 0.243081i | −0.992586 | − | 0.121541i | \(-0.961217\pi\) | ||
0.992586 | − | 0.121541i | \(-0.0387835\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.8024 | 0.499186 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.2510 | + | 7.65045i | −0.558462 | + | 0.322428i | −0.752528 | − | 0.658560i | \(-0.771166\pi\) |
0.194066 | + | 0.980988i | \(0.437832\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.59908 | + | 3.23263i | 0.235555 | + | 0.135998i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.63095 | + | 11.4851i | −0.277984 | + | 0.481482i | −0.970884 | − | 0.239552i | \(-0.922999\pi\) |
0.692900 | + | 0.721034i | \(0.256333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.4262 | − | 13.5251i | 0.980357 | − | 0.566009i | 0.0779788 | − | 0.996955i | \(-0.475153\pi\) |
0.902378 | + | 0.430946i | \(0.141820\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.470166 | −0.0196073 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.78434 | −0.199174 | −0.0995872 | − | 0.995029i | \(-0.531752\pi\) | ||||
−0.0995872 | + | 0.995029i | \(0.531752\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.66760 | − | 3.27219i | 0.235132 | − | 0.135753i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21.9406 | + | 38.0023i | −0.908689 | + | 1.57390i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −37.0796 | − | 21.4079i | −1.53044 | − | 0.883598i | −0.999341 | − | 0.0362861i | \(-0.988447\pi\) |
−0.531095 | − | 0.847312i | \(-0.678219\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.80179 | − | 5.65906i | 0.403876 | − | 0.233178i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.825572 | 0.0339022 | 0.0169511 | − | 0.999856i | \(-0.494604\pi\) | ||||
0.0169511 | + | 0.999856i | \(0.494604\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.98438i | 0.327328i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.961228 | − | 1.66490i | −0.0392747 | − | 0.0680258i | 0.845720 | − | 0.533627i | \(-0.179171\pi\) |
−0.884995 | + | 0.465601i | \(0.845838\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.5937 | + | 37.4014i | −0.880825 | + | 1.52563i | −0.0303994 | + | 0.999538i | \(0.509678\pi\) |
−0.850425 | + | 0.526096i | \(0.823655\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 25.6556 | + | 14.8123i | 1.04305 | + | 0.602205i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.5078 | − | 35.5206i | −0.832386 | − | 1.44174i | −0.896141 | − | 0.443770i | \(-0.853641\pi\) |
0.0637546 | − | 0.997966i | \(-0.479693\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.7022i | 0.756611i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.05878i | 0.204322i | 0.994768 | + | 0.102161i | \(0.0325757\pi\) | ||||
−0.994768 | + | 0.102161i | \(0.967424\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.0739 | + | 27.8408i | 0.647112 | + | 1.12083i | 0.983809 | + | 0.179217i | \(0.0573566\pi\) |
−0.336698 | + | 0.941613i | \(0.609310\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.3562 | − | 15.7941i | −1.09954 | − | 0.634820i | −0.163440 | − | 0.986553i | \(-0.552259\pi\) |
−0.936100 | + | 0.351734i | \(0.885592\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.26924 | + | 3.93044i | −0.0909153 | + | 0.157470i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.9871 | + | 22.4942i | 0.519482 | + | 0.899770i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.3929i | 0.613756i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.4885 | 0.616586 | 0.308293 | − | 0.951292i | \(-0.400242\pi\) | ||||
0.308293 | + | 0.951292i | \(0.400242\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.7162 | − | 8.49638i | 0.583993 | − | 0.337168i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.8468 | + | 8.57182i | 0.588253 | + | 0.339628i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.2248 | − | 26.3701i | 0.601344 | − | 1.04156i | −0.391274 | − | 0.920274i | \(-0.627966\pi\) |
0.992618 | − | 0.121284i | \(-0.0387011\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.5911 | + | 8.42419i | −0.575418 | + | 0.332218i | −0.759310 | − | 0.650729i | \(-0.774463\pi\) |
0.183893 | + | 0.982946i | \(0.441130\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.6734 | 0.734126 | 0.367063 | − | 0.930196i | \(-0.380363\pi\) | ||||
0.367063 | + | 0.930196i | \(0.380363\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.2633 | −0.677644 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 31.4276 | − | 18.1448i | 1.22986 | − | 0.710059i | 0.262858 | − | 0.964834i | \(-0.415335\pi\) |
0.967000 | + | 0.254775i | \(0.0820015\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.11089 | + | 7.12028i | −0.160626 | + | 0.278212i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.3088 | − | 11.1480i | −0.752166 | − | 0.434263i | 0.0743103 | − | 0.997235i | \(-0.476324\pi\) |
−0.826476 | + | 0.562972i | \(0.809658\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.19793 | + | 3.00103i | −0.202176 | + | 0.116726i | −0.597670 | − | 0.801742i | \(-0.703907\pi\) |
0.395494 | + | 0.918469i | \(0.370573\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.81762 | −0.341933 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.45996i | 0.327571i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.85442 | − | 8.40810i | −0.187403 | − | 0.324591i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.70444 | + | 6.41629i | −0.142796 | + | 0.247330i | −0.928548 | − | 0.371211i | \(-0.878943\pi\) |
0.785753 | + | 0.618541i | \(0.212276\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.57613 | + | 4.95143i | 0.329607 | + | 0.190299i | 0.655667 | − | 0.755050i | \(-0.272388\pi\) |
−0.326059 | + | 0.945349i | \(0.605721\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.6981 | − | 21.9938i | −0.487309 | − | 0.844043i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 39.0736i | 1.49511i | 0.664200 | + | 0.747555i | \(0.268772\pi\) | ||||
−0.664200 | + | 0.747555i | \(0.731228\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26.8316i | 1.02518i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −20.7376 | − | 35.9185i | −0.790039 | − | 1.36839i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.07502 | + | 1.19801i | 0.0789375 | + | 0.0455746i | 0.538949 | − | 0.842338i | \(-0.318821\pi\) |
−0.460012 | + | 0.887913i | \(0.652155\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.5391 | + | 25.1825i | −0.551500 | + | 0.955227i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.55443 | − | 7.88850i | −0.172511 | − | 0.298798i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.9184i | 1.16777i | 0.811836 | + | 0.583885i | \(0.198468\pi\) | ||||
−0.811836 | + | 0.583885i | \(0.801532\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.9993 | −0.641141 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.05327 | − | 1.18546i | 0.0772212 | − | 0.0445837i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.46959 | + | 2.58052i | 0.167859 | + | 0.0969133i | 0.581576 | − | 0.813492i | \(-0.302436\pi\) |
−0.413717 | + | 0.910406i | \(0.635770\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.15406 | − | 10.6591i | 0.230471 | − | 0.399188i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −44.7870 | + | 25.8578i | −1.67494 | + | 0.967027i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.7871 | 0.551465 | 0.275733 | − | 0.961234i | \(-0.411080\pi\) | ||||
0.275733 | + | 0.961234i | \(0.411080\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.7041 | 0.435884 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.642593 | + | 0.371001i | −0.0238653 | + | 0.0137786i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.06681 | − | 1.84777i | 0.0395658 | − | 0.0685299i | −0.845564 | − | 0.533873i | \(-0.820736\pi\) |
0.885130 | + | 0.465344i | \(0.154069\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.25675 | − | 2.45764i | −0.157442 | − | 0.0908990i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.2298 | + | 12.8344i | −0.821076 | + | 0.474048i | −0.850787 | − | 0.525510i | \(-0.823875\pi\) |
0.0297113 | + | 0.999559i | \(0.490541\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −43.7003 | −1.60972 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 5.46282i | − | 0.200953i | −0.994939 | − | 0.100476i | \(-0.967963\pi\) | ||
0.994939 | − | 0.100476i | \(-0.0320367\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.8170 | − | 29.1279i | −0.616955 | − | 1.06860i | −0.990038 | − | 0.140800i | \(-0.955033\pi\) |
0.373083 | − | 0.927798i | \(-0.378301\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.68910 | − | 15.0500i | 0.318344 | − | 0.551388i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.88115 | + | 2.81813i | 0.178353 | + | 0.102972i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.6727 | + | 21.9498i | 0.462435 | + | 0.800961i | 0.999082 | − | 0.0428462i | \(-0.0136426\pi\) |
−0.536647 | + | 0.843807i | \(0.680309\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.3553i | 0.376868i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 3.95103i | − | 0.143603i | −0.997419 | − | 0.0718014i | \(-0.977125\pi\) | ||
0.997419 | − | 0.0718014i | \(-0.0228748\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.3979 | + | 40.5264i | 0.848175 | + | 1.46908i | 0.882835 | + | 0.469682i | \(0.155632\pi\) |
−0.0346607 | + | 0.999399i | \(0.511035\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.4347 | + | 16.4168i | 1.02941 | + | 0.594328i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.15835 | − | 14.1307i | 0.294581 | − | 0.510229i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.60083 | + | 4.50478i | 0.0937885 | + | 0.162446i | 0.909102 | − | 0.416573i | \(-0.136769\pi\) |
−0.815314 | + | 0.579019i | \(0.803436\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38.8477i | 1.39725i | 0.715486 | + | 0.698627i | \(0.246205\pi\) | ||||
−0.715486 | + | 0.698627i | \(0.753795\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.07952 | 0.0387773 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.71173 | − | 5.02972i | 0.312130 | − | 0.180209i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −56.6503 | − | 32.7071i | −2.02711 | − | 1.17035i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.0271 | + | 26.0277i | −0.536340 | + | 0.928968i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40.8579 | + | 23.5893i | −1.45643 | + | 0.840869i | −0.998833 | − | 0.0482918i | \(-0.984622\pi\) |
−0.457595 | + | 0.889161i | \(0.651289\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.14621 | 0.182978 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.17648 | 0.325866 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.35645 | − | 3.66990i | 0.225157 | − | 0.129995i | −0.383179 | − | 0.923674i | \(-0.625171\pi\) |
0.608336 | + | 0.793680i | \(0.291837\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.89442 | − | 6.74533i | 0.137775 | − | 0.238633i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 49.0286 | + | 28.3067i | 1.73018 | + | 0.998920i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.30423 | + | 4.79445i | −0.292686 | + | 0.168982i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.25520 | −0.0792887 | −0.0396443 | − | 0.999214i | \(-0.512622\pi\) | ||||
−0.0396443 | + | 0.999214i | \(0.512622\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.9986i | 0.561785i | 0.959739 | + | 0.280893i | \(0.0906305\pi\) | ||||
−0.959739 | + | 0.280893i | \(0.909369\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 23.4844 | + | 40.6761i | 0.822622 | + | 1.42482i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.71411 | − | 4.70098i | 0.0949548 | − | 0.164467i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.2413 | − | 14.5731i | −0.880928 | − | 0.508604i | −0.00996351 | − | 0.999950i | \(-0.503172\pi\) |
−0.870964 | + | 0.491347i | \(0.836505\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.15695 | + | 7.20005i | 0.144902 | + | 0.250978i | 0.929336 | − | 0.369234i | \(-0.120380\pi\) |
−0.784434 | + | 0.620212i | \(0.787047\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 43.5035i | 1.51277i | 0.654129 | + | 0.756383i | \(0.273035\pi\) | ||||
−0.654129 | + | 0.756383i | \(0.726965\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.9248i | 0.553092i | 0.961001 | + | 0.276546i | \(0.0891897\pi\) | ||||
−0.961001 | + | 0.276546i | \(0.910810\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.56987 | − | 6.18320i | −0.123689 | − | 0.214235i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.0317 | + | 5.79180i | 0.347161 | + | 0.200433i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.0582 | + | 36.4739i | −0.727009 | + | 1.25922i | 0.231132 | + | 0.972922i | \(0.425757\pi\) |
−0.958142 | + | 0.286295i | \(0.907576\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.82437 | − | 13.5522i | −0.269806 | − | 0.467318i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 19.2266i | − | 0.661415i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.5806 | 0.810238 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16.0095 | + | 9.24311i | −0.548800 | + | 0.316850i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.2013 | + | 19.7461i | 1.17103 | + | 0.676095i | 0.953923 | − | 0.300053i | \(-0.0970043\pi\) |
0.217108 | + | 0.976148i | \(0.430338\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.6170 | − | 21.8532i | 0.430988 | − | 0.746493i | −0.565971 | − | 0.824425i | \(-0.691499\pi\) |
0.996959 | + | 0.0779326i | \(0.0248319\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 47.5539 | − | 27.4552i | 1.62252 | − | 0.936761i | 0.636274 | − | 0.771463i | \(-0.280475\pi\) |
0.986244 | − | 0.165297i | \(-0.0528584\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −54.3877 | −1.85138 | −0.925689 | − | 0.378285i | \(-0.876514\pi\) | ||||
−0.925689 | + | 0.378285i | \(0.876514\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 29.0778 | 0.988675 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −42.1888 | + | 24.3577i | −1.43116 | + | 0.826278i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.6521 | − | 35.7704i | 0.699768 | − | 1.21203i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 17.2050 | + | 9.93334i | 0.581637 | + | 0.335808i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.90001 | + | 3.40637i | −0.199229 | + | 0.115025i | −0.596296 | − | 0.802765i | \(-0.703361\pi\) |
0.397067 | + | 0.917790i | \(0.370028\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.2881 | 1.45841 | 0.729207 | − | 0.684293i | \(-0.239889\pi\) | ||||
0.729207 | + | 0.684293i | \(0.239889\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.1510i | 1.04832i | 0.851621 | + | 0.524158i | \(0.175620\pi\) | ||||
−0.851621 | + | 0.524158i | \(0.824380\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.8886 | − | 43.1083i | −0.835677 | − | 1.44743i | −0.893478 | − | 0.449107i | \(-0.851742\pi\) |
0.0578015 | − | 0.998328i | \(-0.481591\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.76295 | − | 11.7138i | 0.226822 | − | 0.392867i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.44926 | + | 4.30083i | 0.249280 | + | 0.143922i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.0595 | + | 17.4236i | 0.336253 | + | 0.582407i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 19.4243i | − | 0.647838i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.2730i | 0.575447i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17.6059 | − | 30.4944i | −0.585241 | − | 1.01367i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.6712 | − | 9.62515i | −0.553559 | − | 0.319598i | 0.196997 | − | 0.980404i | \(-0.436881\pi\) |
−0.750556 | + | 0.660806i | \(0.770214\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.1396 | − | 19.2944i | 0.369072 | − | 0.639252i | −0.620348 | − | 0.784326i | \(-0.713009\pi\) |
0.989421 | + | 0.145074i | \(0.0463421\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.82669 | − | 15.2883i | −0.292121 | − | 0.505968i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.54438i | 0.216114i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.0122 | −0.924039 | −0.462019 | − | 0.886870i | \(-0.652875\pi\) | ||||
−0.462019 | + | 0.886870i | \(0.652875\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 53.5440 | − | 30.9136i | 1.76242 | − | 1.01753i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.40416 | − | 0.810691i | −0.0461684 | − | 0.0266554i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.94220 | − | 6.82809i | 0.129339 | − | 0.224022i | −0.794081 | − | 0.607811i | \(-0.792048\pi\) |
0.923421 | + | 0.383789i | \(0.125381\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.82847 | − | 3.94242i | 0.223794 | − | 0.129208i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.5378 | 0.704361 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.98600 | −0.293560 | −0.146780 | − | 0.989169i | \(-0.546891\pi\) | ||||
−0.146780 | + | 0.989169i | \(0.546891\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.0227 | + | 12.1375i | −0.685322 | + | 0.395671i | −0.801857 | − | 0.597516i | \(-0.796155\pi\) |
0.116535 | + | 0.993187i | \(0.462821\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.46967 | − | 9.47375i | 0.178117 | − | 0.308508i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.71382 | + | 0.989473i | 0.0556916 | + | 0.0321536i | 0.527587 | − | 0.849501i | \(-0.323097\pi\) |
−0.471896 | + | 0.881654i | \(0.656430\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −46.3402 | + | 26.7545i | −1.50427 | + | 0.868488i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28.9674 | −0.938347 | −0.469173 | − | 0.883106i | \(-0.655448\pi\) | ||||
−0.469173 | + | 0.883106i | \(0.655448\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 21.9753i | − | 0.711104i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.6787 | + | 18.4960i | 0.344833 | + | 0.597268i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.37008 | − | 2.37304i | 0.0441961 | − | 0.0765498i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.8017 | + | 7.96842i | 0.444293 | + | 0.256512i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.00531192 | − | 0.00920052i | −0.000170820 | − | 0.000295869i | 0.865940 | − | 0.500148i | \(-0.166721\pi\) |
−0.866111 | + | 0.499852i | \(0.833388\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 17.0984i | − | 0.548715i | −0.961628 | − | 0.274357i | \(-0.911535\pi\) | ||
0.961628 | − | 0.274357i | \(-0.0884651\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 23.1457i | 0.742017i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.50612 | + | 9.53688i | 0.176156 | + | 0.305112i | 0.940561 | − | 0.339625i | \(-0.110300\pi\) |
−0.764404 | + | 0.644737i | \(0.776967\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.6023 | + | 6.12126i | 0.338852 | + | 0.195636i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.7443 | − | 39.3943i | 0.725432 | − | 1.25648i | −0.233364 | − | 0.972389i | \(-0.574973\pi\) |
0.958796 | − | 0.284095i | \(-0.0916932\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.92521 | + | 8.53071i | 0.156930 | + | 0.271811i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 5.90304i | − | 0.187706i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.93737 | −0.125075 | −0.0625374 | − | 0.998043i | \(-0.519919\pi\) | ||||
−0.0625374 | + | 0.998043i | \(0.519919\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.6678 | + | 6.73642i | −0.369895 | + | 0.213559i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.16558 | − | 1.25030i | −0.0685847 | − | 0.0395974i | 0.465316 | − | 0.885145i | \(-0.345941\pi\) |
−0.533900 | + | 0.845547i | \(0.679274\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 864.2.r.b.721.7 | 16 | ||
3.2 | odd | 2 | 288.2.r.b.241.1 | 16 | |||
4.3 | odd | 2 | 216.2.n.b.181.4 | 16 | |||
8.3 | odd | 2 | 216.2.n.b.181.3 | 16 | |||
8.5 | even | 2 | inner | 864.2.r.b.721.2 | 16 | ||
9.2 | odd | 6 | 2592.2.d.j.1297.2 | 8 | |||
9.4 | even | 3 | inner | 864.2.r.b.145.2 | 16 | ||
9.5 | odd | 6 | 288.2.r.b.49.8 | 16 | |||
9.7 | even | 3 | 2592.2.d.k.1297.7 | 8 | |||
12.11 | even | 2 | 72.2.n.b.61.5 | yes | 16 | ||
24.5 | odd | 2 | 288.2.r.b.241.8 | 16 | |||
24.11 | even | 2 | 72.2.n.b.61.6 | yes | 16 | ||
36.7 | odd | 6 | 648.2.d.k.325.7 | 8 | |||
36.11 | even | 6 | 648.2.d.j.325.2 | 8 | |||
36.23 | even | 6 | 72.2.n.b.13.6 | yes | 16 | ||
36.31 | odd | 6 | 216.2.n.b.37.3 | 16 | |||
72.5 | odd | 6 | 288.2.r.b.49.1 | 16 | |||
72.11 | even | 6 | 648.2.d.j.325.1 | 8 | |||
72.13 | even | 6 | inner | 864.2.r.b.145.7 | 16 | ||
72.29 | odd | 6 | 2592.2.d.j.1297.7 | 8 | |||
72.43 | odd | 6 | 648.2.d.k.325.8 | 8 | |||
72.59 | even | 6 | 72.2.n.b.13.5 | ✓ | 16 | ||
72.61 | even | 6 | 2592.2.d.k.1297.2 | 8 | |||
72.67 | odd | 6 | 216.2.n.b.37.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.2.n.b.13.5 | ✓ | 16 | 72.59 | even | 6 | ||
72.2.n.b.13.6 | yes | 16 | 36.23 | even | 6 | ||
72.2.n.b.61.5 | yes | 16 | 12.11 | even | 2 | ||
72.2.n.b.61.6 | yes | 16 | 24.11 | even | 2 | ||
216.2.n.b.37.3 | 16 | 36.31 | odd | 6 | |||
216.2.n.b.37.4 | 16 | 72.67 | odd | 6 | |||
216.2.n.b.181.3 | 16 | 8.3 | odd | 2 | |||
216.2.n.b.181.4 | 16 | 4.3 | odd | 2 | |||
288.2.r.b.49.1 | 16 | 72.5 | odd | 6 | |||
288.2.r.b.49.8 | 16 | 9.5 | odd | 6 | |||
288.2.r.b.241.1 | 16 | 3.2 | odd | 2 | |||
288.2.r.b.241.8 | 16 | 24.5 | odd | 2 | |||
648.2.d.j.325.1 | 8 | 72.11 | even | 6 | |||
648.2.d.j.325.2 | 8 | 36.11 | even | 6 | |||
648.2.d.k.325.7 | 8 | 36.7 | odd | 6 | |||
648.2.d.k.325.8 | 8 | 72.43 | odd | 6 | |||
864.2.r.b.145.2 | 16 | 9.4 | even | 3 | inner | ||
864.2.r.b.145.7 | 16 | 72.13 | even | 6 | inner | ||
864.2.r.b.721.2 | 16 | 8.5 | even | 2 | inner | ||
864.2.r.b.721.7 | 16 | 1.1 | even | 1 | trivial | ||
2592.2.d.j.1297.2 | 8 | 9.2 | odd | 6 | |||
2592.2.d.j.1297.7 | 8 | 72.29 | odd | 6 | |||
2592.2.d.k.1297.2 | 8 | 72.61 | even | 6 | |||
2592.2.d.k.1297.7 | 8 | 9.7 | even | 3 |