Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2636035467\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | no (minimal twist has level 4024) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.32661 | 0.765921 | 0.382960 | − | 0.923765i | \(-0.374905\pi\) | ||||
0.382960 | + | 0.923765i | \(0.374905\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.90684 | −0.852764 | −0.426382 | − | 0.904543i | \(-0.640212\pi\) | ||||
−0.426382 | + | 0.904543i | \(0.640212\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.79236 | 1.81134 | 0.905671 | − | 0.423981i | \(-0.139368\pi\) | ||||
0.905671 | + | 0.423981i | \(0.139368\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.24010 | −0.413365 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.55688 | −0.770927 | −0.385464 | − | 0.922723i | \(-0.625959\pi\) | ||||
−0.385464 | + | 0.922723i | \(0.625959\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.665181 | 0.184488 | 0.0922440 | − | 0.995736i | \(-0.470596\pi\) | ||||
0.0922440 | + | 0.995736i | \(0.470596\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.52964 | −0.653150 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.36372 | 1.30089 | 0.650446 | − | 0.759552i | \(-0.274582\pi\) | ||||
0.650446 | + | 0.759552i | \(0.274582\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.67815 | −0.384995 | −0.192497 | − | 0.981297i | \(-0.561659\pi\) | ||||
−0.192497 | + | 0.981297i | \(0.561659\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.35761 | 1.38734 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.24383 | −0.676384 | −0.338192 | − | 0.941077i | \(-0.609815\pi\) | ||||
−0.338192 | + | 0.941077i | \(0.609815\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.36396 | −0.272793 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.62497 | −1.08253 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.72489 | −1.62017 | −0.810086 | − | 0.586311i | \(-0.800580\pi\) | ||||
−0.810086 | + | 0.586311i | \(0.800580\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.57296 | −0.282512 | −0.141256 | − | 0.989973i | \(-0.545114\pi\) | ||||
−0.141256 | + | 0.989973i | \(0.545114\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.39199 | −0.590469 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.13826 | −1.54465 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.50788 | −1.23429 | −0.617144 | − | 0.786850i | \(-0.711710\pi\) | ||||
−0.617144 | + | 0.786850i | \(0.711710\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.882438 | 0.141303 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.1056 | 1.57823 | 0.789113 | − | 0.614248i | \(-0.210541\pi\) | ||||
0.789113 | + | 0.614248i | \(0.210541\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.0082 | −1.52623 | −0.763115 | − | 0.646263i | \(-0.776331\pi\) | ||||
−0.763115 | + | 0.646263i | \(0.776331\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.36466 | 0.352503 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.2502 | 1.64100 | 0.820502 | − | 0.571643i | \(-0.193694\pi\) | ||||
0.820502 | + | 0.571643i | \(0.193694\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.9667 | 2.28096 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.11558 | 0.996380 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.5424 | 1.58547 | 0.792737 | − | 0.609564i | \(-0.208655\pi\) | ||||
0.792737 | + | 0.609564i | \(0.208655\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.87555 | 0.657420 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.22626 | −0.294876 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.37075 | −1.21997 | −0.609984 | − | 0.792414i | \(-0.708824\pi\) | ||||
−0.609984 | + | 0.792414i | \(0.708824\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.7957 | −1.76636 | −0.883182 | − | 0.469030i | \(-0.844603\pi\) | ||||
−0.883182 | + | 0.469030i | \(0.844603\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.94299 | −0.748746 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.26839 | −0.157325 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.41724 | −1.15050 | −0.575249 | − | 0.817978i | \(-0.695095\pi\) | ||||
−0.575249 | + | 0.817978i | \(0.695095\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.30330 | −0.518057 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.91607 | −0.939465 | −0.469732 | − | 0.882809i | \(-0.655650\pi\) | ||||
−0.469732 | + | 0.882809i | \(0.655650\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.999682 | −0.117004 | −0.0585019 | − | 0.998287i | \(-0.518632\pi\) | ||||
−0.0585019 | + | 0.998287i | \(0.518632\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.80945 | −0.208938 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.2535 | −1.39641 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.57821 | 0.402580 | 0.201290 | − | 0.979532i | \(-0.435487\pi\) | ||||
0.201290 | + | 0.979532i | \(0.435487\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.74187 | −0.415764 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.87221 | −0.534794 | −0.267397 | − | 0.963586i | \(-0.586164\pi\) | ||||
−0.267397 | + | 0.963586i | \(0.586164\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.2277 | −1.10935 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.5746 | −1.24092 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.53775 | −0.799000 | −0.399500 | − | 0.916733i | \(-0.630816\pi\) | ||||
−0.399500 | + | 0.916733i | \(0.630816\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.18779 | 0.334171 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.08671 | −0.216382 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.19997 | 0.328310 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.0389 | −1.52697 | −0.763486 | − | 0.645825i | \(-0.776514\pi\) | ||||
−0.763486 | + | 0.645825i | \(0.776514\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.17077 | 0.318675 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.54967 | −0.253701 | −0.126851 | − | 0.991922i | \(-0.540487\pi\) | ||||
−0.126851 | + | 0.991922i | \(0.540487\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.72428 | 0.662563 | 0.331282 | − | 0.943532i | \(-0.392519\pi\) | ||||
0.331282 | + | 0.943532i | \(0.392519\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −12.1229 | −1.18308 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.26681 | 0.412488 | 0.206244 | − | 0.978501i | \(-0.433876\pi\) | ||||
0.206244 | + | 0.978501i | \(0.433876\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.78630 | 0.171097 | 0.0855485 | − | 0.996334i | \(-0.472736\pi\) | ||||
0.0855485 | + | 0.996334i | \(0.472736\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.96006 | −0.945367 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.5409 | −1.17975 | −0.589874 | − | 0.807495i | \(-0.700823\pi\) | ||||
−0.589874 | + | 0.807495i | \(0.700823\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.18545 | 0.576797 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.824888 | −0.0762610 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 25.7049 | 2.35636 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.46238 | −0.405671 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.4062 | 1.20880 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1351 | 1.08539 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.11926 | −0.631732 | −0.315866 | − | 0.948804i | \(-0.602295\pi\) | ||||
−0.315866 | + | 0.948804i | \(0.602295\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.2770 | −1.16897 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.7961 | 1.64222 | 0.821109 | − | 0.570771i | \(-0.193356\pi\) | ||||
0.821109 | + | 0.570771i | \(0.193356\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.04232 | −0.697357 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10.7259 | 0.923140 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.08018 | 0.775772 | 0.387886 | − | 0.921707i | \(-0.373205\pi\) | ||||
0.387886 | + | 0.921707i | \(0.373205\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.21379 | 0.611866 | 0.305933 | − | 0.952053i | \(-0.401032\pi\) | ||||
0.305933 | + | 0.952053i | \(0.401032\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 14.9246 | 1.25688 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.70079 | −0.142227 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.6370 | 1.38163 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 21.1817 | 1.74704 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.02654 | 0.247944 | 0.123972 | − | 0.992286i | \(-0.460437\pi\) | ||||
0.123972 | + | 0.992286i | \(0.460437\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.8973 | 1.45646 | 0.728231 | − | 0.685332i | \(-0.240343\pi\) | ||||
0.728231 | + | 0.685332i | \(0.240343\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.65152 | −0.537744 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.99938 | 0.240916 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.6516 | −1.48856 | −0.744278 | − | 0.667870i | \(-0.767206\pi\) | ||||
−0.744278 | + | 0.667870i | \(0.767206\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.3123 | 1.21435 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.5456 | −1.22516 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.08328 | 0.163175 | 0.0815876 | − | 0.996666i | \(-0.474001\pi\) | ||||
0.0815876 | + | 0.996666i | \(0.474001\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.46798 | 0.503531 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.3445 | −1.49692 | −0.748461 | − | 0.663179i | \(-0.769207\pi\) | ||||
−0.748461 | + | 0.663179i | \(0.769207\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5575 | −0.965964 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.08107 | 0.159143 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.688871 | 0.0523739 | 0.0261869 | − | 0.999657i | \(-0.491663\pi\) | ||||
0.0261869 | + | 0.999657i | \(0.491663\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.53661 | −0.494121 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.4314 | −0.934399 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.42163 | −0.106257 | −0.0531287 | − | 0.998588i | \(-0.516919\pi\) | ||||
−0.0531287 | + | 0.998588i | \(0.516919\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.05657 | 0.673170 | 0.336585 | − | 0.941653i | \(-0.390728\pi\) | ||||
0.336585 | + | 0.941653i | \(0.390728\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −18.3016 | −1.35289 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 14.3163 | 1.05256 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.7144 | −1.00289 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −26.9569 | −1.96083 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.2733 | 1.03278 | 0.516390 | − | 0.856353i | \(-0.327275\pi\) | ||||
0.516390 | + | 0.856353i | \(0.327275\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.4088 | 1.32510 | 0.662549 | − | 0.749019i | \(-0.269475\pi\) | ||||
0.662549 | + | 0.749019i | \(0.269475\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.68267 | −0.120498 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.91118 | 0.349907 | 0.174953 | − | 0.984577i | \(-0.444023\pi\) | ||||
0.174953 | + | 0.984577i | \(0.444023\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.8155 | −1.19202 | −0.596011 | − | 0.802976i | \(-0.703249\pi\) | ||||
−0.596011 | + | 0.802976i | \(0.703249\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.4930 | −0.881191 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −41.8128 | −2.93469 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −19.2697 | −1.34586 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.02265 | 0.279594 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.29083 | 0.296803 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.27971 | 0.569999 | 0.284999 | − | 0.958528i | \(-0.408007\pi\) | ||||
0.284999 | + | 0.958528i | \(0.408007\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.5016 | −0.719556 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 19.0840 | 1.30151 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.53819 | −0.511726 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.32619 | −0.0896157 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.56784 | 0.239999 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.80832 | −0.188059 | −0.0940296 | − | 0.995569i | \(-0.529975\pi\) | ||||
−0.0940296 | + | 0.995569i | \(0.529975\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.69145 | 0.112763 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.1808 | 1.53857 | 0.769283 | − | 0.638908i | \(-0.220613\pi\) | ||||
0.769283 | + | 0.638908i | \(0.220613\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.9513 | −0.789767 | −0.394884 | − | 0.918731i | \(-0.629215\pi\) | ||||
−0.394884 | + | 0.918731i | \(0.629215\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −16.2556 | −1.06954 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.77158 | 0.509133 | 0.254567 | − | 0.967055i | \(-0.418067\pi\) | ||||
0.254567 | + | 0.967055i | \(0.418067\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −21.4523 | −1.39939 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.74691 | 0.308345 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.70866 | −0.498632 | −0.249316 | − | 0.968422i | \(-0.580206\pi\) | ||||
−0.249316 | + | 0.968422i | \(0.580206\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.42632 | −0.542787 | −0.271393 | − | 0.962468i | \(-0.587484\pi\) | ||||
−0.271393 | + | 0.962468i | \(0.587484\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.9109 | 0.764084 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −30.4460 | −1.94512 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.11628 | −0.0710269 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.46354 | −0.409610 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.97037 | −0.503085 | −0.251543 | − | 0.967846i | \(-0.580938\pi\) | ||||
−0.251543 | + | 0.967846i | \(0.580938\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.29406 | 0.521443 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −13.5683 | −0.849678 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.2507 | −0.701799 | −0.350900 | − | 0.936413i | \(-0.614124\pi\) | ||||
−0.350900 | + | 0.936413i | \(0.614124\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −35.9805 | −2.23572 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.8197 | 0.669723 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.7761 | −1.34277 | −0.671385 | − | 0.741108i | \(-0.734300\pi\) | ||||
−0.671385 | + | 0.741108i | \(0.734300\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −22.0095 | −1.35204 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.99969 | −0.611971 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −26.4280 | −1.61134 | −0.805672 | − | 0.592362i | \(-0.798196\pi\) | ||||
−0.805672 | + | 0.592362i | \(0.798196\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.7795 | −1.26227 | −0.631133 | − | 0.775675i | \(-0.717410\pi\) | ||||
−0.631133 | + | 0.775675i | \(0.717410\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.22896 | 0.255949 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.48749 | 0.210303 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −27.3774 | −1.64495 | −0.822474 | − | 0.568802i | \(-0.807407\pi\) | ||||
−0.822474 | + | 0.568802i | \(0.807407\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.95062 | 0.116781 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.8364 | −1.00437 | −0.502187 | − | 0.864759i | \(-0.667471\pi\) | ||||
−0.502187 | + | 0.864759i | \(0.667471\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 33.4332 | 1.98740 | 0.993699 | − | 0.112077i | \(-0.0357504\pi\) | ||||
0.993699 | + | 0.112077i | \(0.0357504\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.24512 | 0.251459 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 48.4296 | 2.85871 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.7694 | 0.692320 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −19.9508 | −1.16954 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.23097 | −0.130335 | −0.0651674 | − | 0.997874i | \(-0.520758\pi\) | ||||
−0.0651674 | + | 0.997874i | \(0.520758\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.8685 | 1.04035 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 14.3824 | 0.834549 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.15773 | −0.124785 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −47.9627 | −2.76453 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.38242 | −0.194315 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 26.3063 | 1.50629 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.6489 | −1.17849 | −0.589247 | − | 0.807953i | \(-0.700575\pi\) | ||||
−0.589247 | + | 0.807953i | \(0.700575\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.92052 | 0.507471 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.49843 | −0.311787 | −0.155894 | − | 0.987774i | \(-0.549826\pi\) | ||||
−0.155894 | + | 0.987774i | \(0.549826\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.2701 | 0.806592 | 0.403296 | − | 0.915070i | \(-0.367865\pi\) | ||||
0.403296 | + | 0.915070i | \(0.367865\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 11.3323 | 0.638504 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.38968 | −0.471211 | −0.235606 | − | 0.971849i | \(-0.575707\pi\) | ||||
−0.235606 | + | 0.971849i | \(0.575707\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.3085 | 1.24904 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.66041 | 0.315933 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.00114 | −0.500837 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.907283 | −0.0503270 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.36974 | 0.131047 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 53.9148 | 2.97242 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.900231 | −0.0494812 | −0.0247406 | − | 0.999694i | \(-0.507876\pi\) | ||||
−0.0247406 | + | 0.999694i | \(0.507876\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.31050 | 0.510212 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.9572 | 0.981105 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.6876 | −1.07245 | −0.536227 | − | 0.844074i | \(-0.680151\pi\) | ||||
−0.536227 | + | 0.844074i | \(0.680151\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.6369 | −0.903594 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.02186 | 0.217796 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 42.9718 | 2.32026 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.20571 | 0.441781 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.2797 | 0.873939 | 0.436970 | − | 0.899476i | \(-0.356052\pi\) | ||||
0.436970 | + | 0.899476i | \(0.356052\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.0899 | 1.02186 | 0.510928 | − | 0.859623i | \(-0.329302\pi\) | ||||
0.510928 | + | 0.859623i | \(0.329302\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.74162 | −0.199713 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 34.0955 | 1.81472 | 0.907360 | − | 0.420355i | \(-0.138095\pi\) | ||||
0.907360 | + | 0.420355i | \(0.138095\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.0947 | 0.801142 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 34.1004 | 1.80479 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.4237 | −1.60570 | −0.802850 | − | 0.596181i | \(-0.796684\pi\) | ||||
−0.802850 | + | 0.596181i | \(0.796684\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.1838 | −0.851779 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.91985 | −0.310712 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.90623 | 0.0997768 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.2337 | −1.47379 | −0.736894 | − | 0.676008i | \(-0.763708\pi\) | ||||
−0.736894 | + | 0.676008i | \(0.763708\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.5319 | −0.652384 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 55.3155 | 2.87184 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.2737 | 0.635506 | 0.317753 | − | 0.948174i | \(-0.397072\pi\) | ||||
0.317753 | + | 0.948174i | \(0.397072\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 16.0985 | 0.831325 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.80363 | −0.298902 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.6268 | −0.648593 | −0.324297 | − | 0.945955i | \(-0.605128\pi\) | ||||
−0.324297 | + | 0.945955i | \(0.605128\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.44451 | −0.483857 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.325768 | −0.0166459 | −0.00832297 | − | 0.999965i | \(-0.502649\pi\) | ||||
−0.00832297 | + | 0.999965i | \(0.502649\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 23.3654 | 1.19081 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.4111 | 0.630891 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.44660 | 0.428260 | 0.214130 | − | 0.976805i | \(-0.431308\pi\) | ||||
0.214130 | + | 0.976805i | \(0.431308\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.3990 | −0.879903 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 24.9351 | 1.25781 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.82308 | −0.343306 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.6227 | 0.583326 | 0.291663 | − | 0.956521i | \(-0.405791\pi\) | ||||
0.291663 | + | 0.956521i | \(0.405791\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.6690 | −0.534121 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.1895 | −1.35778 | −0.678889 | − | 0.734241i | \(-0.737538\pi\) | ||||
−0.678889 | + | 0.734241i | \(0.737538\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.04630 | −0.0521200 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.13515 | 0.354549 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.1967 | 0.951547 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.0754 | −0.844325 | −0.422162 | − | 0.906520i | \(-0.638729\pi\) | ||||
−0.422162 | + | 0.906520i | \(0.638729\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.0459 | 0.594180 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −44.9080 | −2.20978 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.29052 | 0.456054 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.56991 | 0.468641 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.51491 | −0.269421 | −0.134710 | − | 0.990885i | \(-0.543010\pi\) | ||||
−0.134710 | + | 0.990885i | \(0.543010\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.0908 | 0.881690 | 0.440845 | − | 0.897583i | \(-0.354679\pi\) | ||||
0.440845 | + | 0.897583i | \(0.354679\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.9513 | −0.678334 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.31591 | −0.354874 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −66.1142 | −3.19949 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.25629 | −0.108935 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 38.2763 | 1.84371 | 0.921853 | − | 0.387540i | \(-0.126675\pi\) | ||||
0.921853 | + | 0.387540i | \(0.126675\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.2629 | 1.16600 | 0.583001 | − | 0.812471i | \(-0.301878\pi\) | ||||
0.583001 | + | 0.812471i | \(0.301878\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 22.0708 | 1.05822 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.44364 | 0.260404 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.37304 | −0.399624 | −0.199812 | − | 0.979834i | \(-0.564033\pi\) | ||||
−0.199812 | + | 0.979834i | \(0.564033\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.8003 | −0.942870 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 32.2412 | 1.53182 | 0.765912 | − | 0.642945i | \(-0.222288\pi\) | ||||
0.765912 | + | 0.642945i | \(0.222288\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.3733 | 0.681359 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.01505 | 0.189905 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.55834 | −0.167929 | −0.0839643 | − | 0.996469i | \(-0.526758\pi\) | ||||
−0.0839643 | + | 0.996469i | \(0.526758\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.8387 | −1.21670 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 23.7428 | 1.11553 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.07860 | −0.284969 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.5155 | −0.679008 | −0.339504 | − | 0.940605i | \(-0.610259\pi\) | ||||
−0.339504 | + | 0.940605i | \(0.610259\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −30.1707 | −1.40825 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −40.0471 | −1.86518 | −0.932590 | − | 0.360938i | \(-0.882457\pi\) | ||||
−0.932590 | + | 0.360938i | \(0.882457\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.42164 | 0.0660694 | 0.0330347 | − | 0.999454i | \(-0.489483\pi\) | ||||
0.0330347 | + | 0.999454i | \(0.489483\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.97902 | 0.184523 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.53745 | −0.395066 | −0.197533 | − | 0.980296i | \(-0.563293\pi\) | ||||
−0.197533 | + | 0.980296i | \(0.563293\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −45.1308 | −2.08395 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −24.7434 | −1.14012 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 25.5896 | 1.17661 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.28894 | 0.105024 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14.3137 | −0.655380 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.03715 | −0.321536 | −0.160768 | − | 0.986992i | \(-0.551397\pi\) | ||||
−0.160768 | + | 0.986992i | \(0.551397\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.99410 | −0.227711 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −20.6230 | −0.938378 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 28.6768 | 1.30215 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.6355 | −0.753827 | −0.376913 | − | 0.926249i | \(-0.623015\pi\) | ||||
−0.376913 | + | 0.926249i | \(0.623015\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.76371 | 0.124979 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.0646 | 1.71783 | 0.858915 | − | 0.512118i | \(-0.171139\pi\) | ||||
0.858915 | + | 0.512118i | \(0.171139\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −46.7978 | −2.10767 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.04615 | −0.271754 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −37.9367 | −1.70169 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.0886 | 0.496392 | 0.248196 | − | 0.968710i | \(-0.420162\pi\) | ||||
0.248196 | + | 0.968710i | \(0.420162\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −25.6627 | −1.14652 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.86180 | 0.216347 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.6590 | −0.739852 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −41.8784 | −1.85623 | −0.928114 | − | 0.372296i | \(-0.878571\pi\) | ||||
−0.928114 | + | 0.372296i | \(0.878571\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.79084 | −0.211934 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.43956 | 0.416767 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.8221 | −0.565010 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −28.7653 | −1.26510 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.913866 | 0.0401142 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.8325 | 1.74510 | 0.872548 | − | 0.488529i | \(-0.162466\pi\) | ||||
0.872548 | + | 0.488529i | \(0.162466\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.78494 | 0.384139 | 0.192069 | − | 0.981381i | \(-0.438480\pi\) | ||||
0.192069 | + | 0.981381i | \(0.438480\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8.67155 | −0.378458 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.43690 | −0.367517 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.4776 | −0.542504 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.6206 | 0.504292 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.72204 | 0.291164 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.13613 | −0.351755 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.88595 | −0.0813847 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −40.8250 | −1.75846 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.6947 | 0.631776 | 0.315888 | − | 0.948797i | \(-0.397698\pi\) | ||||
0.315888 | + | 0.948797i | \(0.397698\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.0146 | 0.515595 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.40620 | −0.145905 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.3196 | −1.38188 | −0.690942 | − | 0.722910i | \(-0.742804\pi\) | ||||
−0.690942 | + | 0.722910i | \(0.742804\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 17.1080 | 0.730154 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.6417 | 0.623758 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.1481 | 0.729211 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 18.9922 | 0.806176 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.2855 | −0.562926 | −0.281463 | − | 0.959572i | \(-0.590820\pi\) | ||||
−0.281463 | + | 0.959572i | \(0.590820\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.65724 | −0.281571 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.1937 | −0.768137 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.1298 | −0.764080 | −0.382040 | − | 0.924146i | \(-0.624778\pi\) | ||||
−0.382040 | + | 0.924146i | \(0.624778\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 23.9135 | 1.00605 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −17.9324 | −0.753091 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.1648 | 0.803428 | 0.401714 | − | 0.915765i | \(-0.368415\pi\) | ||||
0.401714 | + | 0.915765i | \(0.368415\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.80333 | 0.242862 | 0.121431 | − | 0.992600i | \(-0.461252\pi\) | ||||
0.121431 | + | 0.992600i | \(0.461252\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.9352 | 0.791028 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.42446 | 0.184513 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −42.6964 | −1.77748 | −0.888738 | − | 0.458415i | \(-0.848417\pi\) | ||||
−0.888738 | + | 0.458415i | \(0.848417\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24.4214 | 1.01492 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −23.3494 | −0.968696 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −29.5126 | −1.22229 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.57293 | 0.0650326 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.6861 | 1.26655 | 0.633276 | − | 0.773926i | \(-0.281710\pi\) | ||||
0.633276 | + | 0.773926i | \(0.281710\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.63967 | 0.108766 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.51523 | 0.268001 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 33.8800 | 1.39128 | 0.695642 | − | 0.718389i | \(-0.255120\pi\) | ||||
0.695642 | + | 0.718389i | \(0.255120\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −49.0150 | −2.00942 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −22.3077 | −0.912995 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.40726 | 0.0574991 | 0.0287496 | − | 0.999587i | \(-0.490847\pi\) | ||||
0.0287496 | + | 0.999587i | \(0.490847\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.20083 | −0.0489830 | −0.0244915 | − | 0.999700i | \(-0.507797\pi\) | ||||
−0.0244915 | + | 0.999700i | \(0.507797\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.6783 | 0.475576 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.50904 | 0.345942 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.67375 | −0.352057 | −0.176028 | − | 0.984385i | \(-0.556325\pi\) | ||||
−0.176028 | + | 0.984385i | \(0.556325\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −55.4695 | −2.24774 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.48340 | 0.302746 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.62694 | 0.267660 | 0.133830 | − | 0.991004i | \(-0.457272\pi\) | ||||
0.133830 | + | 0.991004i | \(0.457272\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −25.5635 | −1.03082 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.1730 | 1.25498 | 0.627489 | − | 0.778625i | \(-0.284083\pi\) | ||||
0.627489 | + | 0.778625i | \(0.284083\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.5540 | 1.67020 | 0.835098 | − | 0.550102i | \(-0.185411\pi\) | ||||
0.835098 | + | 0.550102i | \(0.185411\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.2464 | 0.732204 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −36.1236 | −1.44726 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.3198 | −0.652791 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.69228 | 0.227328 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −40.2701 | −1.60568 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.75268 | 0.229011 | 0.114505 | − | 0.993423i | \(-0.463472\pi\) | ||||
0.114505 | + | 0.993423i | \(0.463472\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.9840 | 0.436574 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.5753 | 0.538719 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.6208 | 0.420810 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.81669 | 0.388342 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.8737 | −0.705967 | −0.352983 | − | 0.935630i | \(-0.614833\pi\) | ||||
−0.352983 | + | 0.935630i | \(0.614833\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.176330 | 0.00695376 | 0.00347688 | − | 0.999994i | \(-0.498893\pi\) | ||||
0.00347688 | + | 0.999994i | \(0.498893\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 25.3170 | 0.996857 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.8464 | −0.819556 | −0.409778 | − | 0.912185i | \(-0.634394\pi\) | ||||
−0.409778 | + | 0.912185i | \(0.634394\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23.9599 | 0.940507 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.0003 | −0.391941 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.8852 | −0.699902 | −0.349951 | − | 0.936768i | \(-0.613802\pi\) | ||||
−0.349951 | + | 0.936768i | \(0.613802\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −35.8410 | −1.40043 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.23970 | 0.0483653 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 42.0752 | 1.63902 | 0.819509 | − | 0.573066i | \(-0.194246\pi\) | ||||
0.819509 | + | 0.573066i | \(0.194246\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.0492 | 0.507557 | 0.253778 | − | 0.967262i | \(-0.418327\pi\) | ||||
0.253778 | + | 0.967262i | \(0.418327\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.73315 | 0.183820 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.3354 | 0.594682 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.3020 | 1.09586 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.72556 | −0.144039 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 35.2740 | 1.36174 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.30308 | 0.242966 | 0.121483 | − | 0.992594i | \(-0.461235\pi\) | ||||
0.121483 | + | 0.992594i | \(0.461235\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.67225 | 0.295305 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.7333 | 0.604678 | 0.302339 | − | 0.953200i | \(-0.402232\pi\) | ||||
0.302339 | + | 0.953200i | \(0.402232\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −72.0720 | −2.76587 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 30.7520 | 1.17842 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.0044 | 1.45420 | 0.727098 | − | 0.686534i | \(-0.240869\pi\) | ||||
0.727098 | + | 0.686534i | \(0.240869\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.3144 | −0.661551 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.8548 | −0.604899 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.67780 | 0.292501 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.05114 | 0.268238 | 0.134119 | − | 0.990965i | \(-0.457180\pi\) | ||||
0.134119 | + | 0.990965i | \(0.457180\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15.1955 | 0.577229 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.7555 | −0.521777 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 54.2034 | 2.05310 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.3099 | 0.389956 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.10262 | 0.192723 | 0.0963617 | − | 0.995346i | \(-0.469279\pi\) | ||||
0.0963617 | + | 0.995346i | \(0.469279\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.5994 | 0.475195 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −28.4589 | −1.07182 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.2189 | −0.459540 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.76858 | 0.216644 | 0.108322 | − | 0.994116i | \(-0.465452\pi\) | ||||
0.108322 | + | 0.994116i | \(0.465452\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.43733 | −0.166413 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.10240 | 0.191087 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.24313 | 0.121286 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.2264 | −0.381912 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.79042 | 0.327827 | 0.163914 | − | 0.986475i | \(-0.447588\pi\) | ||||
0.163914 | + | 0.986475i | \(0.447588\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 32.2252 | 1.20013 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.1785 | −0.415732 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11.9004 | 0.441971 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −42.1945 | −1.56491 | −0.782454 | − | 0.622708i | \(-0.786033\pi\) | ||||
−0.782454 | + | 0.622708i | \(0.786033\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0268 | 1.00099 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −53.6809 | −1.98546 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.7361 | −0.544289 | −0.272144 | − | 0.962256i | \(-0.587733\pi\) | ||||
−0.272144 | + | 0.962256i | \(0.587733\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −40.3901 | −1.48981 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.0787 | 0.886951 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.3879 | −1.26498 | −0.632490 | − | 0.774569i | \(-0.717967\pi\) | ||||
−0.632490 | + | 0.774569i | \(0.717967\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.48087 | −0.0544010 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.5162 | 1.22959 | 0.614795 | − | 0.788687i | \(-0.289239\pi\) | ||||
0.614795 | + | 0.788687i | \(0.289239\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.77113 | −0.211438 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.04201 | 0.221065 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20.4481 | 0.747158 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.39197 | −0.196756 | −0.0983778 | − | 0.995149i | \(-0.531365\pi\) | ||||
−0.0983778 | + | 0.995149i | \(0.531365\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.5736 | −0.385323 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −34.1273 | −1.24202 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.89577 | −0.214285 | −0.107143 | − | 0.994244i | \(-0.534170\pi\) | ||||
−0.107143 | + | 0.994244i | \(0.534170\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.0030 | 0.399384 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.1241 | −0.910749 | −0.455375 | − | 0.890300i | \(-0.650495\pi\) | ||||
−0.455375 | + | 0.890300i | \(0.650495\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.56062 | 0.309915 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 12.6834 | 0.458569 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.23325 | −0.225069 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.9719 | −1.29718 | −0.648590 | − | 0.761138i | \(-0.724641\pi\) | ||||
−0.648590 | + | 0.761138i | \(0.724641\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.9253 | −0.537523 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.8023 | −0.964013 | −0.482007 | − | 0.876168i | \(-0.660092\pi\) | ||||
−0.482007 | + | 0.876168i | \(0.660092\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.14546 | 0.0770672 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −47.7322 | −1.71238 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16.9587 | −0.607609 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.2404 | 0.724259 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 49.0773 | 1.75388 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 35.5655 | 1.26939 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.5261 | 1.15943 | 0.579715 | − | 0.814820i | \(-0.303164\pi\) | ||||
0.579715 | + | 0.814820i | \(0.303164\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −28.8884 | −1.02846 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −60.1005 | −2.13693 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.17667 | −0.325873 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −29.1982 | −1.03555 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.1511 | −0.713790 | −0.356895 | − | 0.934145i | \(-0.616165\pi\) | ||||
−0.356895 | + | 0.934145i | \(0.616165\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 60.3427 | 2.13477 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.34754 | 0.330279 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.55606 | 0.0902015 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 29.6429 | 1.04478 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −35.0598 | −1.23416 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −49.5524 | −1.74217 | −0.871084 | − | 0.491134i | \(-0.836583\pi\) | ||||
−0.871084 | + | 0.491134i | \(0.836583\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.6036 | −1.32044 | −0.660220 | − | 0.751072i | \(-0.729537\pi\) | ||||
−0.660220 | + | 0.751072i | \(0.729537\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −27.5664 | −0.966796 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.97248 | −0.139150 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.7952 | 0.587591 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.95316 | −0.138135 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.78688 | 0.0623625 | 0.0311812 | − | 0.999514i | \(-0.490073\pi\) | ||||
0.0311812 | + | 0.999514i | \(0.490073\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.2747 | −0.706732 | −0.353366 | − | 0.935485i | \(-0.614963\pi\) | ||||
−0.353366 | + | 0.935485i | \(0.614963\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.62655 | 0.161076 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 41.7240 | 1.45089 | 0.725443 | − | 0.688283i | \(-0.241635\pi\) | ||||
0.725443 | + | 0.688283i | \(0.241635\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.8918 | −0.760334 | −0.380167 | − | 0.924918i | \(-0.624133\pi\) | ||||
−0.380167 | + | 0.924918i | \(0.624133\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −36.3192 | −1.25990 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 85.6410 | 2.96728 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 36.8869 | 1.27652 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.84785 | 0.305826 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.82934 | 0.339346 | 0.169673 | − | 0.985500i | \(-0.445729\pi\) | ||||
0.169673 | + | 0.985500i | \(0.445729\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 47.1238 | 1.62496 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −22.3354 | −0.769271 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 23.9452 | 0.823740 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.3853 | −0.734809 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 44.3530 | 1.52219 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.3543 | 0.834853 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.7591 | 0.368383 | 0.184191 | − | 0.982890i | \(-0.441033\pi\) | ||||
0.184191 | + | 0.982890i | \(0.441033\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.96827 | −0.135712 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.46366 | −0.289113 | −0.144557 | − | 0.989497i | \(-0.546176\pi\) | ||||
−0.144557 | + | 0.989497i | \(0.546176\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −48.5553 | −1.65668 | −0.828342 | − | 0.560222i | \(-0.810716\pi\) | ||||
−0.828342 | + | 0.560222i | \(0.810716\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 64.2474 | 2.18954 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.3752 | 0.353176 | 0.176588 | − | 0.984285i | \(-0.443494\pi\) | ||||
0.176588 | + | 0.984285i | \(0.443494\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.31357 | −0.0446626 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.6135 | 0.530262 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.14905 | −0.310360 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.26417 | −0.212253 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18.6497 | 0.631197 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 58.1556 | 1.96602 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.38935 | 0.283288 | 0.141644 | − | 0.989918i | \(-0.454761\pi\) | ||||
0.141644 | + | 0.989918i | \(0.454761\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.95964 | −0.0998261 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.7646 | −1.13756 | −0.568778 | − | 0.822491i | \(-0.692584\pi\) | ||||
−0.568778 | + | 0.822491i | \(0.692584\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.4095 | 1.59546 | 0.797728 | − | 0.603017i | \(-0.206035\pi\) | ||||
0.797728 | + | 0.603017i | \(0.206035\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 23.7046 | 0.796822 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.6153 | −0.927232 | −0.463616 | − | 0.886036i | \(-0.653448\pi\) | ||||
−0.463616 | + | 0.886036i | \(0.653448\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −34.1181 | −1.14428 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.56751 | 0.320524 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −18.8795 | −0.631778 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.71081 | 0.0906125 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.86248 | −0.0955753 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.7239 | 0.457718 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 61.9103 | 2.06253 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −63.6280 | −2.11741 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17.2694 | −0.574055 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.91293 | 0.0967221 | 0.0483610 | − | 0.998830i | \(-0.484600\pi\) | ||||
0.0483610 | + | 0.998830i | \(0.484600\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.16183 | 0.104871 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.6566 | −0.353068 | −0.176534 | − | 0.984295i | \(-0.556489\pi\) | ||||
−0.176534 | + | 0.984295i | \(0.556489\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.4576 | 0.412288 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 34.8983 | 1.15370 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 90.0775 | 2.97462 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.5605 | 1.40394 | 0.701970 | − | 0.712206i | \(-0.252304\pi\) | ||||
0.701970 | + | 0.712206i | \(0.252304\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −27.3931 | −0.902633 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.26562 | −0.173320 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.2405 | 0.336705 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.33875 | −0.273881 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.6152 | −0.741980 | −0.370990 | − | 0.928637i | \(-0.620982\pi\) | ||||
−0.370990 | + | 0.928637i | \(0.620982\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26.7946 | −0.878158 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.29429 | −0.238804 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 26.1511 | 0.855232 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 55.9096 | 1.82649 | 0.913244 | − | 0.407413i | \(-0.133569\pi\) | ||||
0.913244 | + | 0.407413i | \(0.133569\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.9309 | 0.617786 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −53.6255 | −1.74814 | −0.874071 | − | 0.485798i | \(-0.838529\pi\) | ||||
−0.874071 | + | 0.485798i | \(0.838529\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −32.7807 | −1.06749 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 51.4025 | 1.67212 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.2338 | 0.592519 | 0.296259 | − | 0.955108i | \(-0.404261\pi\) | ||||
0.296259 | + | 0.955108i | \(0.404261\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.664969 | −0.0215858 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.1299 | −0.360911 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.09947 | 0.100402 | 0.0502009 | − | 0.998739i | \(-0.484014\pi\) | ||||
0.0502009 | + | 0.998739i | \(0.484014\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −27.2169 | −0.880718 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 29.5947 | 0.956662 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 43.5155 | 1.40519 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.5258 | −0.920187 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.29126 | −0.170508 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −35.1027 | −1.13000 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −47.8888 | −1.54000 | −0.770000 | − | 0.638044i | \(-0.779744\pi\) | ||||
−0.770000 | + | 0.638044i | \(0.779744\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.9410 | −0.383601 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.7794 | −0.442202 | −0.221101 | − | 0.975251i | \(-0.570965\pi\) | ||||
−0.221101 | + | 0.975251i | \(0.570965\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 34.5711 | 1.10830 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.20361 | −0.0385465 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 40.1880 | 1.28573 | 0.642863 | − | 0.765981i | \(-0.277746\pi\) | ||||
0.642863 | + | 0.765981i | \(0.277746\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19.2731 | 0.615971 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.21519 | −0.0707255 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.44527 | 0.237467 | 0.118734 | − | 0.992926i | \(-0.462117\pi\) | ||||
0.118734 | + | 0.992926i | \(0.462117\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.36482 | −0.298388 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 71.5242 | 2.27664 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.4647 | 1.03232 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.4370 | −0.617437 | −0.308719 | − | 0.951153i | \(-0.599900\pi\) | ||||
−0.308719 | + | 0.951153i | \(0.599900\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.19426 | −0.0378987 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 32.0645 | 1.01651 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 60.9374 | 1.92991 | 0.964953 | − | 0.262422i | \(-0.0845212\pi\) | ||||
0.964953 | + | 0.262422i | \(0.0845212\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 42.2316 | 1.33615 |
(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 | 8048.2.a.v.1.20 | 28 | ||
4.3 | odd | 2 | 4024.2.a.d.1.9 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.d.1.9 | ✓ | 28 | 4.3 | odd | 2 | ||
8048.2.a.v.1.20 | 28 | 1.1 | even | 1 | trivial |