Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [729,2,Mod(28,729)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(729, base_ring=CyclotomicField(54))
chi = DirichletCharacter(H, H._module([44]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("729.28");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 729 = 3^{6} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 729.g (of order \(27\), degree \(18\), 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: | \(5.82109430735\) |
Analytic rank: | \(0\) |
Dimension: | \(144\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{27})\) |
Twist minimal: | no (minimal twist has level 81) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{27}]$ |
Embedding invariants
Embedding label | 433.2 | ||
Character | \(\chi\) | \(=\) | 729.433 |
Dual form | 729.2.g.b.298.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{27}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.71974 | − | 0.201009i | −1.21604 | − | 0.142135i | −0.516222 | − | 0.856455i | \(-0.672662\pi\) |
−0.699819 | + | 0.714320i | \(0.746736\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.971017 | + | 0.230135i | 0.485509 | + | 0.115068i | ||||
\(5\) | 1.23058 | − | 0.618019i | 0.550331 | − | 0.276386i | −0.151828 | − | 0.988407i | \(-0.548516\pi\) |
0.702159 | + | 0.712020i | \(0.252220\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.943081 | + | 3.15011i | −0.356451 | + | 1.19063i | 0.572337 | + | 0.820019i | \(0.306037\pi\) |
−0.928788 | + | 0.370612i | \(0.879148\pi\) | |||||||
\(8\) | 1.63042 | + | 0.593424i | 0.576441 | + | 0.209807i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.24050 | + | 0.815476i | −0.708509 | + | 0.257876i | ||||
\(11\) | −0.0119397 | − | 0.204997i | −0.00359996 | − | 0.0618089i | 0.996030 | − | 0.0890214i | \(-0.0283740\pi\) |
−0.999630 | + | 0.0272125i | \(0.991337\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.13795 | + | 4.21500i | 0.870310 | + | 1.16903i | 0.984468 | + | 0.175567i | \(0.0561757\pi\) |
−0.114157 | + | 0.993463i | \(0.536417\pi\) | |||||||
\(14\) | 2.25506 | − | 5.22781i | 0.602689 | − | 1.39719i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.46816 | − | 2.24399i | −1.11704 | − | 0.560998i | ||||
\(17\) | −3.88762 | − | 3.26210i | −0.942887 | − | 0.791176i | 0.0351981 | − | 0.999380i | \(-0.488794\pi\) |
−0.978085 | + | 0.208204i | \(0.933238\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.25026 | + | 1.88819i | −0.516245 | + | 0.433181i | −0.863320 | − | 0.504656i | \(-0.831619\pi\) |
0.347075 | + | 0.937837i | \(0.387175\pi\) | |||||||
\(20\) | 1.33714 | − | 0.316908i | 0.298993 | − | 0.0708628i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.0206730 | + | 0.354942i | −0.00440750 | + | 0.0756738i | ||||
\(23\) | −1.07900 | − | 3.60410i | −0.224987 | − | 0.751508i | −0.993716 | − | 0.111933i | \(-0.964296\pi\) |
0.768729 | − | 0.639575i | \(-0.220889\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.85342 | + | 2.48958i | −0.370684 | + | 0.497915i | ||||
\(26\) | −4.54921 | − | 7.87946i | −0.892173 | − | 1.54529i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.64070 | + | 2.84178i | −0.310063 | + | 0.537045i | ||||
\(29\) | 2.49856 | + | 5.79232i | 0.463971 | + | 1.07561i | 0.976223 | + | 0.216771i | \(0.0695524\pi\) |
−0.512251 | + | 0.858836i | \(0.671188\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.48702 | + | 3.69602i | −0.626287 | + | 0.663825i | −0.960373 | − | 0.278717i | \(-0.910091\pi\) |
0.334086 | + | 0.942543i | \(0.391572\pi\) | |||||||
\(32\) | 4.33378 | + | 2.85037i | 0.766111 | + | 0.503879i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.03000 | + | 6.39142i | 1.03414 | + | 1.09612i | ||||
\(35\) | 0.786294 | + | 4.45930i | 0.132908 | + | 0.753759i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.44468 | − | 8.19321i | 0.237505 | − | 1.34696i | −0.599770 | − | 0.800173i | \(-0.704741\pi\) |
0.837274 | − | 0.546783i | \(-0.184148\pi\) | |||||||
\(38\) | 4.24941 | − | 2.79488i | 0.689345 | − | 0.453389i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.37310 | − | 0.277376i | 0.375221 | − | 0.0438570i | ||||
\(41\) | −2.74384 | + | 0.320709i | −0.428515 | + | 0.0500863i | −0.327617 | − | 0.944811i | \(-0.606246\pi\) |
−0.100898 | + | 0.994897i | \(0.532172\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.32558 | − | 0.871847i | 0.202149 | − | 0.132955i | −0.444399 | − | 0.895829i | \(-0.646583\pi\) |
0.646547 | + | 0.762874i | \(0.276212\pi\) | |||||||
\(44\) | 0.0355834 | − | 0.201803i | 0.00536439 | − | 0.0304230i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.13114 | + | 6.41502i | 0.166778 | + | 0.945843i | ||||
\(47\) | −1.42828 | − | 1.51388i | −0.208335 | − | 0.220823i | 0.614777 | − | 0.788701i | \(-0.289246\pi\) |
−0.823113 | + | 0.567878i | \(0.807764\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.18539 | − | 2.09506i | −0.455055 | − | 0.299294i | ||||
\(50\) | 3.68783 | − | 3.90887i | 0.521538 | − | 0.552798i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.07698 | + | 4.81499i | 0.288026 | + | 0.667719i | ||||
\(53\) | −4.51663 | + | 7.82303i | −0.620407 | + | 1.07458i | 0.369003 | + | 0.929428i | \(0.379699\pi\) |
−0.989410 | + | 0.145148i | \(0.953634\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.141385 | − | 0.244885i | −0.0190643 | − | 0.0330203i | ||||
\(56\) | −3.40697 | + | 4.57636i | −0.455276 | + | 0.611541i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.13257 | − | 10.4635i | −0.411327 | − | 1.37393i | ||||
\(59\) | −0.863215 | + | 14.8208i | −0.112381 | + | 1.92951i | 0.200459 | + | 0.979702i | \(0.435757\pi\) |
−0.312840 | + | 0.949806i | \(0.601280\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.46609 | + | 0.347469i | −0.187713 | + | 0.0444888i | −0.323397 | − | 0.946263i | \(-0.604825\pi\) |
0.135684 | + | 0.990752i | \(0.456677\pi\) | |||||||
\(62\) | 6.73971 | − | 5.65528i | 0.855943 | − | 0.718222i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.780406 | + | 0.654838i | 0.0975508 | + | 0.0818548i | ||||
\(65\) | 6.46643 | + | 3.24756i | 0.802062 | + | 0.402811i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.31098 | + | 12.3122i | −0.648840 | + | 1.50418i | 0.202345 | + | 0.979314i | \(0.435144\pi\) |
−0.851185 | + | 0.524866i | \(0.824116\pi\) | |||||||
\(68\) | −3.02423 | − | 4.06224i | −0.366741 | − | 0.492619i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.455864 | − | 7.82689i | −0.0544862 | − | 0.935492i | ||||
\(71\) | −4.39214 | + | 1.59861i | −0.521252 | + | 0.189720i | −0.589228 | − | 0.807967i | \(-0.700568\pi\) |
0.0679763 | + | 0.997687i | \(0.478346\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.3008 | + | 5.56905i | 1.79083 | + | 0.651808i | 0.999165 | + | 0.0408483i | \(0.0130060\pi\) |
0.791662 | + | 0.610960i | \(0.209216\pi\) | |||||||
\(74\) | −4.13139 | + | 13.7998i | −0.480265 | + | 1.60420i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.61958 | + | 1.31560i | −0.300487 | + | 0.150910i | ||||
\(77\) | 0.657023 | + | 0.155717i | 0.0748747 | + | 0.0177456i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.47690 | + | 0.172625i | 0.166164 | + | 0.0194218i | 0.198768 | − | 0.980047i | \(-0.436306\pi\) |
−0.0326039 | + | 0.999468i | \(0.510380\pi\) | |||||||
\(80\) | −6.88524 | −0.769794 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.78316 | 0.528211 | ||||||||
\(83\) | −14.1551 | − | 1.65449i | −1.55372 | − | 0.181604i | −0.704524 | − | 0.709680i | \(-0.748840\pi\) |
−0.849197 | + | 0.528076i | \(0.822914\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.80006 | − | 1.61164i | −0.737570 | − | 0.174807i | ||||
\(86\) | −2.45490 | + | 1.23290i | −0.264719 | + | 0.132947i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.102183 | − | 0.341316i | 0.0108928 | − | 0.0363844i | ||||
\(89\) | 4.83016 | + | 1.75803i | 0.511996 | + | 0.186351i | 0.585082 | − | 0.810974i | \(-0.301062\pi\) |
−0.0730859 | + | 0.997326i | \(0.523285\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −16.2370 | + | 5.90980i | −1.70210 | + | 0.619515i | ||||
\(92\) | −0.218294 | − | 3.74796i | −0.0227587 | − | 0.390752i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.15196 | + | 2.89059i | 0.221958 | + | 0.298141i | ||||
\(95\) | −1.60218 | + | 3.71427i | −0.164380 | + | 0.381076i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.60445 | − | 0.805783i | −0.162907 | − | 0.0818149i | 0.365478 | − | 0.930820i | \(-0.380906\pi\) |
−0.528384 | + | 0.849005i | \(0.677202\pi\) | |||||||
\(98\) | 5.05691 | + | 4.24325i | 0.510825 | + | 0.428633i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.37264 | + | 1.99088i | −0.237264 | + | 0.199088i | ||||
\(101\) | 11.1658 | − | 2.64633i | 1.11103 | − | 0.263320i | 0.366178 | − | 0.930545i | \(-0.380666\pi\) |
0.744856 | + | 0.667225i | \(0.232518\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.0290838 | + | 0.499350i | −0.00286571 | + | 0.0492024i | −0.999438 | − | 0.0335260i | \(-0.989326\pi\) |
0.996572 | + | 0.0827284i | \(0.0263634\pi\) | |||||||
\(104\) | 2.61489 | + | 8.73435i | 0.256411 | + | 0.856473i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.33994 | − | 12.5457i | 0.907175 | − | 1.21855i | ||||
\(107\) | 2.72183 | + | 4.71434i | 0.263129 | + | 0.455752i | 0.967072 | − | 0.254504i | \(-0.0819123\pi\) |
−0.703943 | + | 0.710257i | \(0.748579\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.38980 | + | 14.5316i | −0.803597 | + | 1.39187i | 0.113637 | + | 0.993522i | \(0.463750\pi\) |
−0.917234 | + | 0.398348i | \(0.869584\pi\) | |||||||
\(110\) | 0.193921 | + | 0.449559i | 0.0184896 | + | 0.0428638i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 11.2827 | − | 11.9589i | 1.06611 | − | 1.13001i | ||||
\(113\) | −7.37939 | − | 4.85350i | −0.694195 | − | 0.456579i | 0.152747 | − | 0.988265i | \(-0.451188\pi\) |
−0.846941 | + | 0.531686i | \(0.821559\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.55519 | − | 3.76829i | −0.331524 | − | 0.351395i | ||||
\(116\) | 1.09313 | + | 6.19945i | 0.101495 | + | 0.575604i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.46363 | − | 25.3145i | 0.410910 | − | 2.33039i | ||||
\(119\) | 13.9423 | − | 9.17002i | 1.27809 | − | 0.840614i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.8837 | − | 1.27213i | 0.989431 | − | 0.115648i | ||||
\(122\) | 2.59113 | − | 0.302860i | 0.234590 | − | 0.0274197i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.23654 | + | 2.78642i | −0.380453 | + | 0.250228i | ||||
\(125\) | −1.93778 | + | 10.9897i | −0.173321 | + | 0.982950i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.21170 | − | 6.87190i | −0.107521 | − | 0.609783i | −0.990183 | − | 0.139775i | \(-0.955362\pi\) |
0.882662 | − | 0.470008i | \(-0.155749\pi\) | |||||||
\(128\) | −8.32971 | − | 8.82898i | −0.736249 | − | 0.780379i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −10.4678 | − | 6.88478i | −0.918087 | − | 0.603835i | ||||
\(131\) | 3.87020 | − | 4.10217i | 0.338141 | − | 0.358408i | −0.535882 | − | 0.844293i | \(-0.680021\pi\) |
0.874023 | + | 0.485884i | \(0.161502\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.82584 | − | 8.86929i | −0.331742 | − | 0.769065i | ||||
\(134\) | 11.6084 | − | 20.1063i | 1.00281 | − | 1.73692i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.40265 | − | 7.62561i | −0.377524 | − | 0.653891i | ||||
\(137\) | 0.665511 | − | 0.893937i | 0.0568585 | − | 0.0763742i | −0.772784 | − | 0.634669i | \(-0.781137\pi\) |
0.829643 | + | 0.558294i | \(0.188544\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.36460 | + | 4.55809i | 0.115744 | + | 0.386612i | 0.996156 | − | 0.0875977i | \(-0.0279190\pi\) |
−0.880412 | + | 0.474210i | \(0.842734\pi\) | |||||||
\(140\) | −0.262736 | + | 4.51101i | −0.0222053 | + | 0.381250i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.87469 | − | 1.86634i | 0.660829 | − | 0.156619i | ||||
\(143\) | 0.826595 | − | 0.693595i | 0.0691233 | − | 0.0580014i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.65443 | + | 5.58373i | 0.552621 | + | 0.463704i | ||||
\(146\) | −25.1941 | − | 12.6529i | −2.08507 | − | 1.04716i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.28836 | − | 7.62328i | 0.270302 | − | 0.626630i | ||||
\(149\) | −4.58470 | − | 6.15832i | −0.375593 | − | 0.504510i | 0.573629 | − | 0.819115i | \(-0.305535\pi\) |
−0.949222 | + | 0.314606i | \(0.898128\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.179593 | − | 3.08349i | −0.0146150 | − | 0.250930i | −0.997700 | − | 0.0677814i | \(-0.978408\pi\) |
0.983085 | − | 0.183149i | \(-0.0586291\pi\) | |||||||
\(152\) | −4.78937 | + | 1.74319i | −0.388469 | + | 0.141391i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.09861 | − | 0.399861i | −0.0885285 | − | 0.0322217i | ||||
\(155\) | −2.00683 | + | 6.70328i | −0.161193 | + | 0.538421i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.47868 | − | 2.75149i | 0.437246 | − | 0.219593i | −0.216538 | − | 0.976274i | \(-0.569477\pi\) |
0.653784 | + | 0.756681i | \(0.273180\pi\) | |||||||
\(158\) | −2.50519 | − | 0.593741i | −0.199302 | − | 0.0472355i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7.09463 | + | 0.829244i | 0.560880 | + | 0.0655575i | ||||
\(161\) | 12.3709 | 0.974965 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.171894 | −0.0134638 | −0.00673188 | − | 0.999977i | \(-0.502143\pi\) | ||||
−0.00673188 | + | 0.999977i | \(0.502143\pi\) | |||||||
\(164\) | −2.73812 | − | 0.320040i | −0.213811 | − | 0.0249909i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 24.0105 | + | 5.69059i | 1.86358 | + | 0.441676i | ||||
\(167\) | 0.263030 | − | 0.132098i | 0.0203538 | − | 0.0102221i | −0.438593 | − | 0.898686i | \(-0.644523\pi\) |
0.458947 | + | 0.888464i | \(0.348227\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.19103 | + | 13.9990i | −0.322387 | + | 1.07685i | ||||
\(170\) | 11.3704 | + | 4.13849i | 0.872069 | + | 0.317407i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.48780 | − | 0.541516i | 0.113444 | − | 0.0412902i | ||||
\(173\) | −0.156232 | − | 2.68241i | −0.0118781 | − | 0.203940i | −0.999026 | − | 0.0441291i | \(-0.985949\pi\) |
0.987148 | − | 0.159811i | \(-0.0510883\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.09452 | − | 8.18636i | −0.460702 | − | 0.618830i | ||||
\(176\) | −0.406663 | + | 0.942751i | −0.0306534 | + | 0.0710626i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.95324 | − | 3.99427i | −0.596121 | − | 0.299383i | ||||
\(179\) | 1.83356 | + | 1.53854i | 0.137047 | + | 0.114996i | 0.708734 | − | 0.705476i | \(-0.249267\pi\) |
−0.571687 | + | 0.820471i | \(0.693711\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.8278 | − | 10.7638i | 0.953481 | − | 0.800065i | −0.0263995 | − | 0.999651i | \(-0.508404\pi\) |
0.979880 | + | 0.199586i | \(0.0639598\pi\) | |||||||
\(182\) | 29.1114 | − | 6.89954i | 2.15788 | − | 0.511428i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.379543 | − | 6.51651i | 0.0279803 | − | 0.480403i | ||||
\(185\) | −3.28576 | − | 10.9752i | −0.241574 | − | 0.806914i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.622304 | + | 0.835899i | −0.0455074 | + | 0.0611270i | ||||
\(188\) | −1.03848 | − | 1.79870i | −0.0757391 | − | 0.131184i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.50193 | − | 6.06553i | 0.254057 | − | 0.440040i | ||||
\(191\) | −5.62068 | − | 13.0302i | −0.406698 | − | 0.942833i | −0.991313 | − | 0.131522i | \(-0.958014\pi\) |
0.584615 | − | 0.811311i | \(-0.301246\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.86567 | − | 3.03743i | 0.206275 | − | 0.218639i | −0.615974 | − | 0.787766i | \(-0.711237\pi\) |
0.822249 | + | 0.569127i | \(0.192719\pi\) | |||||||
\(194\) | 2.59726 | + | 1.70825i | 0.186473 | + | 0.122645i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.61092 | − | 2.76741i | −0.186494 | − | 0.197672i | ||||
\(197\) | −3.59768 | − | 20.4035i | −0.256324 | − | 1.45369i | −0.792650 | − | 0.609677i | \(-0.791299\pi\) |
0.536326 | − | 0.844011i | \(-0.319812\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.499478 | − | 2.83268i | 0.0354071 | − | 0.200803i | −0.961973 | − | 0.273145i | \(-0.911936\pi\) |
0.997380 | + | 0.0723417i | \(0.0230472\pi\) | |||||||
\(200\) | −4.49923 | + | 2.95919i | −0.318144 | + | 0.209246i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −19.7341 | + | 2.30659i | −1.38849 | + | 0.162291i | ||||
\(203\) | −20.6028 | + | 2.40812i | −1.44603 | + | 0.169017i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.17830 | + | 2.09040i | −0.221982 | + | 0.146000i | ||||
\(206\) | 0.150390 | − | 0.852907i | 0.0104782 | − | 0.0594248i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.56243 | − | 25.8748i | −0.316347 | − | 1.79409i | ||||
\(209\) | 0.413941 | + | 0.438752i | 0.0286329 | + | 0.0303491i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.86778 | + | 5.83243i | 0.610483 | + | 0.401521i | 0.816764 | − | 0.576972i | \(-0.195766\pi\) |
−0.206281 | + | 0.978493i | \(0.566136\pi\) | |||||||
\(212\) | −6.18608 | + | 6.55687i | −0.424862 | + | 0.450327i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.73321 | − | 8.65456i | −0.255197 | − | 0.591613i | ||||
\(215\) | 1.09241 | − | 1.89211i | 0.0745016 | − | 0.129041i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.35434 | − | 14.4701i | −0.567130 | − | 0.982298i | ||||
\(218\) | 17.3493 | − | 23.3041i | 1.17504 | − | 1.57835i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.0809302 | − | 0.270326i | −0.00545631 | − | 0.0182254i | ||||
\(221\) | 1.55059 | − | 26.6226i | 0.104304 | − | 1.79083i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.0369 | + | 5.45985i | −1.54266 | + | 0.365618i | −0.911919 | − | 0.410371i | \(-0.865399\pi\) |
−0.630746 | + | 0.775989i | \(0.717251\pi\) | |||||||
\(224\) | −13.0661 | + | 10.9638i | −0.873015 | + | 0.732547i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.7150 | + | 9.83009i | 0.779273 | + | 0.653888i | ||||
\(227\) | −0.410190 | − | 0.206005i | −0.0272253 | − | 0.0136730i | 0.435134 | − | 0.900365i | \(-0.356701\pi\) |
−0.462360 | + | 0.886692i | \(0.652997\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.33458 | − | 14.6852i | 0.418601 | − | 0.970426i | −0.570244 | − | 0.821476i | \(-0.693151\pi\) |
0.988845 | − | 0.148951i | \(-0.0475896\pi\) | |||||||
\(230\) | 5.35656 | + | 7.19511i | 0.353201 | + | 0.474431i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.636403 | + | 10.9266i | 0.0417819 | + | 0.717368i | ||||
\(233\) | 7.46875 | − | 2.71840i | 0.489294 | − | 0.178089i | −0.0855784 | − | 0.996331i | \(-0.527274\pi\) |
0.574873 | + | 0.818243i | \(0.305052\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.69321 | − | 0.980249i | −0.175686 | − | 0.0639444i | ||||
\(236\) | −4.24899 | + | 14.1926i | −0.276586 | + | 0.923862i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −25.8205 | + | 12.9675i | −1.67369 | + | 0.840560i | ||||
\(239\) | 20.6455 | + | 4.89308i | 1.33545 | + | 0.316507i | 0.835473 | − | 0.549532i | \(-0.185194\pi\) |
0.499977 | + | 0.866039i | \(0.333342\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.9476 | + | 2.09777i | 1.15611 | + | 0.135129i | 0.672460 | − | 0.740134i | \(-0.265238\pi\) |
0.483647 | + | 0.875263i | \(0.339312\pi\) | |||||||
\(242\) | −18.9729 | −1.21963 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.50356 | −0.0962556 | ||||||||
\(245\) | −5.21465 | − | 0.609505i | −0.333152 | − | 0.0389398i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.0199 | − | 3.55979i | −0.955694 | − | 0.226504i | ||||
\(248\) | −7.87862 | + | 3.95679i | −0.500293 | + | 0.251256i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.54152 | − | 18.5100i | 0.350476 | − | 1.17067i | ||||
\(251\) | −7.58786 | − | 2.76176i | −0.478942 | − | 0.174321i | 0.0912569 | − | 0.995827i | \(-0.470912\pi\) |
−0.570199 | + | 0.821507i | \(0.693134\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.725947 | + | 0.264223i | −0.0456399 | + | 0.0166116i | ||||
\(254\) | 0.702500 | + | 12.0615i | 0.0440788 | + | 0.756803i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.3335 | + | 15.2236i | 0.708346 | + | 0.951474i | ||||
\(257\) | −6.54858 | + | 15.1813i | −0.408489 | + | 0.946984i | 0.582474 | + | 0.812849i | \(0.302085\pi\) |
−0.990963 | + | 0.134135i | \(0.957174\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 24.4471 | + | 12.2778i | 1.51907 | + | 0.762904i | ||||
\(260\) | 5.53164 | + | 4.64160i | 0.343058 | + | 0.287860i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.48032 | + | 6.27673i | −0.462135 | + | 0.387778i | ||||
\(263\) | 0.0163370 | − | 0.00387195i | 0.00100738 | − | 0.000238754i | −0.230112 | − | 0.973164i | \(-0.573909\pi\) |
0.231120 | + | 0.972925i | \(0.425761\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.723278 | + | 12.4182i | −0.0444306 | + | 0.762844i | ||||
\(266\) | 4.79665 | + | 16.0219i | 0.294101 | + | 0.982366i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.99054 | + | 10.7332i | −0.488100 | + | 0.655632i | ||||
\(269\) | 3.16338 | + | 5.47913i | 0.192874 | + | 0.334068i | 0.946202 | − | 0.323578i | \(-0.104886\pi\) |
−0.753327 | + | 0.657646i | \(0.771552\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.98751 | + | 17.2989i | −0.606698 | + | 1.05083i | 0.385082 | + | 0.922882i | \(0.374173\pi\) |
−0.991781 | + | 0.127950i | \(0.959160\pi\) | |||||||
\(272\) | 10.0504 | + | 23.2994i | 0.609394 | + | 1.41273i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.32420 | + | 1.40357i | −0.0799977 | + | 0.0847926i | ||||
\(275\) | 0.532485 | + | 0.350221i | 0.0321100 | + | 0.0211191i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.29297 | − | 4.55028i | −0.257940 | − | 0.273400i | 0.585443 | − | 0.810714i | \(-0.300921\pi\) |
−0.843383 | + | 0.537314i | \(0.819439\pi\) | |||||||
\(278\) | −1.43055 | − | 8.11303i | −0.0857985 | − | 0.486587i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.36427 | + | 7.73713i | −0.0815304 | + | 0.462382i | ||||
\(281\) | −4.86386 | + | 3.19901i | −0.290153 | + | 0.190837i | −0.686238 | − | 0.727377i | \(-0.740739\pi\) |
0.396084 | + | 0.918214i | \(0.370369\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.53883 | − | 0.998046i | 0.507581 | − | 0.0593277i | 0.141551 | − | 0.989931i | \(-0.454791\pi\) |
0.366029 | + | 0.930603i | \(0.380717\pi\) | |||||||
\(284\) | −4.63274 | + | 0.541490i | −0.274903 | + | 0.0321315i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.56095 | + | 1.02665i | −0.0923008 | + | 0.0607072i | ||||
\(287\) | 1.57739 | − | 8.94585i | 0.0931106 | − | 0.528057i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.52028 | + | 8.62194i | 0.0894282 | + | 0.507173i | ||||
\(290\) | −10.3215 | − | 10.9402i | −0.606101 | − | 0.642430i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 13.5757 | + | 8.92891i | 0.794460 | + | 0.522525i | ||||
\(293\) | 4.41654 | − | 4.68126i | 0.258017 | − | 0.273482i | −0.585396 | − | 0.810747i | \(-0.699061\pi\) |
0.843413 | + | 0.537265i | \(0.180543\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.09730 | + | 18.7717i | 0.471443 | + | 1.09293i | ||||
\(296\) | 7.21749 | − | 12.5011i | 0.419508 | − | 0.726610i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.64663 | + | 11.5123i | 0.385029 | + | 0.666889i | ||||
\(299\) | 11.8054 | − | 15.8575i | 0.682726 | − | 0.917061i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.49629 | + | 4.99794i | 0.0862445 | + | 0.288077i | ||||
\(302\) | −0.310955 | + | 5.33890i | −0.0178935 | + | 0.307219i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 14.2916 | − | 3.38717i | 0.819680 | − | 0.194268i | ||||
\(305\) | −1.58939 | + | 1.33366i | −0.0910082 | + | 0.0763649i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.8060 | + | 15.7801i | 1.07332 | + | 0.900619i | 0.995349 | − | 0.0963370i | \(-0.0307127\pi\) |
0.0779670 | + | 0.996956i | \(0.475157\pi\) | |||||||
\(308\) | 0.602145 | + | 0.302409i | 0.0343104 | + | 0.0172313i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.79865 | − | 11.1245i | 0.272545 | − | 0.631831i | ||||
\(311\) | 7.75517 | + | 10.4170i | 0.439755 | + | 0.590694i | 0.965647 | − | 0.259858i | \(-0.0836757\pi\) |
−0.525892 | + | 0.850552i | \(0.676268\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.303986 | − | 5.21924i | −0.0171823 | − | 0.295009i | −0.995942 | − | 0.0899978i | \(-0.971314\pi\) |
0.978760 | − | 0.205011i | \(-0.0657231\pi\) | |||||||
\(314\) | −9.97498 | + | 3.63060i | −0.562921 | + | 0.204886i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.39437 | + | 0.507509i | 0.0784394 | + | 0.0285496i | ||||
\(317\) | −8.76380 | + | 29.2731i | −0.492224 | + | 1.64414i | 0.245764 | + | 0.969330i | \(0.420961\pi\) |
−0.737988 | + | 0.674814i | \(0.764224\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.15758 | − | 0.581356i | 0.0648118 | − | 0.0325497i | ||||
\(320\) | 1.36505 | + | 0.323523i | 0.0763087 | + | 0.0180855i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −21.2748 | − | 2.48667i | −1.18560 | − | 0.138576i | ||||
\(323\) | 14.9076 | 0.829483 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.3095 | −0.904688 | ||||||||
\(326\) | 0.295613 | + | 0.0345522i | 0.0163725 | + | 0.00191367i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.66392 | − | 1.10537i | −0.257522 | − | 0.0610338i | ||||
\(329\) | 6.11588 | − | 3.07151i | 0.337180 | − | 0.169338i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.913088 | + | 3.04992i | −0.0501878 | + | 0.167639i | −0.979409 | − | 0.201884i | \(-0.935294\pi\) |
0.929222 | + | 0.369523i | \(0.120479\pi\) | |||||||
\(332\) | −13.3641 | − | 4.86412i | −0.733449 | − | 0.266953i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.478896 | + | 0.174304i | −0.0262040 | + | 0.00953748i | ||||
\(335\) | 1.07363 | + | 18.4334i | 0.0586585 | + | 1.00713i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.5699 | − | 26.2869i | −1.06604 | − | 1.43194i | −0.894667 | − | 0.446733i | \(-0.852587\pi\) |
−0.171372 | − | 0.985206i | \(-0.554820\pi\) | |||||||
\(338\) | 10.0214 | − | 23.2322i | 0.545093 | − | 1.26367i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.23208 | − | 3.12987i | −0.337982 | − | 0.169741i | ||||
\(341\) | 0.799307 | + | 0.670699i | 0.0432849 | + | 0.0363204i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.02888 | + | 6.73703i | −0.433519 | + | 0.363765i | ||||
\(344\) | 2.67862 | − | 0.634846i | 0.144422 | − | 0.0342286i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.270509 | + | 4.64445i | −0.0145426 | + | 0.249687i | ||||
\(347\) | −6.42646 | − | 21.4659i | −0.344990 | − | 1.15235i | −0.937850 | − | 0.347042i | \(-0.887186\pi\) |
0.592859 | − | 0.805306i | \(-0.297999\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.1779 | − | 17.7010i | 0.705398 | − | 0.947514i | −0.294569 | − | 0.955630i | \(-0.595176\pi\) |
0.999967 | + | 0.00811637i | \(0.00258355\pi\) | |||||||
\(350\) | 8.83546 | + | 15.3035i | 0.472275 | + | 0.818005i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.532573 | − | 0.922444i | 0.0283863 | − | 0.0491664i | ||||
\(353\) | 4.32393 | + | 10.0240i | 0.230139 | + | 0.533523i | 0.993682 | − | 0.112235i | \(-0.0358008\pi\) |
−0.763542 | + | 0.645758i | \(0.776542\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.41690 | + | 4.68164i | −0.234425 | + | 0.248476i | ||||
\(356\) | 4.28558 | + | 2.81867i | 0.227135 | + | 0.149389i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.84399 | − | 3.01445i | −0.150310 | − | 0.159319i | ||||
\(359\) | 4.30460 | + | 24.4126i | 0.227188 | + | 1.28845i | 0.858457 | + | 0.512885i | \(0.171423\pi\) |
−0.631269 | + | 0.775564i | \(0.717466\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.80092 | + | 10.2135i | −0.0947851 | + | 0.537553i | ||||
\(362\) | −24.2241 | + | 15.9324i | −1.27319 | + | 0.837390i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −17.1265 | + | 2.00180i | −0.897673 | + | 0.104923i | ||||
\(365\) | 22.2706 | − | 2.60306i | 1.16570 | − | 0.136251i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.7348 | − | 7.06040i | 0.560353 | − | 0.368550i | −0.237514 | − | 0.971384i | \(-0.576332\pi\) |
0.797866 | + | 0.602834i | \(0.205962\pi\) | |||||||
\(368\) | −3.26645 | + | 18.5250i | −0.170276 | + | 0.965681i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.44455 | + | 19.5350i | 0.179074 | + | 1.01558i | ||||
\(371\) | −20.3839 | − | 21.6057i | −1.05828 | − | 1.12171i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.86370 | − | 1.22577i | −0.0964987 | − | 0.0634682i | 0.500343 | − | 0.865828i | \(-0.333207\pi\) |
−0.596841 | + | 0.802359i | \(0.703578\pi\) | |||||||
\(374\) | 1.23823 | − | 1.31244i | 0.0640271 | − | 0.0678648i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.43031 | − | 3.31584i | −0.0737628 | − | 0.171001i | ||||
\(377\) | −16.5742 | + | 28.7074i | −0.853617 | + | 1.47851i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.67947 | + | 6.37302i | 0.189001 | + | 0.327360i | 0.944918 | − | 0.327308i | \(-0.106142\pi\) |
−0.755916 | + | 0.654668i | \(0.772808\pi\) | |||||||
\(380\) | −2.41053 | + | 3.23790i | −0.123657 | + | 0.166101i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7.04693 | + | 23.5384i | 0.360553 | + | 1.20433i | ||||
\(383\) | 0.840550 | − | 14.4317i | 0.0429501 | − | 0.737425i | −0.906248 | − | 0.422746i | \(-0.861066\pi\) |
0.949198 | − | 0.314679i | \(-0.101897\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.904754 | − | 0.214431i | 0.0461105 | − | 0.0109284i | ||||
\(386\) | −5.53876 | + | 4.64757i | −0.281916 | + | 0.236555i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.37251 | − | 1.15167i | −0.0696784 | − | 0.0584671i | ||||
\(389\) | 7.59957 | + | 3.81665i | 0.385314 | + | 0.193512i | 0.630902 | − | 0.775862i | \(-0.282685\pi\) |
−0.245589 | + | 0.969374i | \(0.578981\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.56223 | + | 17.5312i | −0.382438 | + | 0.886591i | ||||
\(392\) | −3.95026 | − | 5.30611i | −0.199518 | − | 0.267999i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.08580 | + | 35.8119i | 0.105081 | + | 1.80418i | ||||
\(395\) | 1.92413 | − | 0.700325i | 0.0968133 | − | 0.0352372i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.16106 | − | 1.87847i | −0.259026 | − | 0.0942779i | 0.209243 | − | 0.977864i | \(-0.432900\pi\) |
−0.468269 | + | 0.883586i | \(0.655122\pi\) | |||||||
\(398\) | −1.42837 | + | 4.77108i | −0.0715976 | + | 0.239153i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.8680 | − | 6.96476i | 0.693399 | − | 0.348238i | ||||
\(401\) | −9.15526 | − | 2.16984i | −0.457192 | − | 0.108356i | −0.00443443 | − | 0.999990i | \(-0.501412\pi\) |
−0.452758 | + | 0.891634i | \(0.649560\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.5208 | − | 3.09984i | −1.32110 | − | 0.154414i | ||||
\(404\) | 11.4512 | 0.569716 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 35.9155 | 1.78246 | ||||||||
\(407\) | −1.69683 | − | 0.198331i | −0.0841088 | − | 0.00983091i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.0060 | − | 3.55650i | −0.742001 | − | 0.175857i | −0.157805 | − | 0.987470i | \(-0.550442\pi\) |
−0.584196 | + | 0.811613i | \(0.698590\pi\) | |||||||
\(410\) | 5.88604 | − | 2.95608i | 0.290691 | − | 0.145990i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.143159 | + | 0.478184i | −0.00705294 | + | 0.0235584i | ||||
\(413\) | −45.8732 | − | 16.6965i | −2.25727 | − | 0.821580i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.4414 | + | 6.71212i | −0.905253 | + | 0.329485i | ||||
\(416\) | 1.58487 | + | 27.2112i | 0.0777047 | + | 1.33414i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.623678 | − | 0.837746i | −0.0305051 | − | 0.0409755i | ||||
\(419\) | −9.78506 | + | 22.6843i | −0.478031 | + | 1.10820i | 0.493168 | + | 0.869934i | \(0.335839\pi\) |
−0.971200 | + | 0.238267i | \(0.923421\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.166031 | − | 0.0833838i | −0.00809185 | − | 0.00406388i | 0.444749 | − | 0.895655i | \(-0.353293\pi\) |
−0.452841 | + | 0.891592i | \(0.649589\pi\) | |||||||
\(422\) | −14.0779 | − | 11.8128i | −0.685302 | − | 0.575037i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12.0064 | + | 10.0746i | −0.583082 | + | 0.489264i | ||||
\(425\) | 15.3267 | − | 3.63249i | 0.743452 | − | 0.176201i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.288073 | − | 4.94603i | 0.0139408 | − | 0.239355i | ||||
\(428\) | 1.55800 | + | 5.20409i | 0.0753089 | + | 0.251549i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.25899 | + | 3.03435i | −0.108938 | + | 0.146329i | ||||
\(431\) | −7.27612 | − | 12.6026i | −0.350478 | − | 0.607046i | 0.635855 | − | 0.771808i | \(-0.280648\pi\) |
−0.986333 | + | 0.164762i | \(0.947314\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.3096 | − | 29.9811i | 0.831846 | − | 1.44080i | −0.0647264 | − | 0.997903i | \(-0.520617\pi\) |
0.896573 | − | 0.442897i | \(-0.146049\pi\) | |||||||
\(434\) | 11.4587 | + | 26.5642i | 0.550034 | + | 1.27512i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.4909 | + | 12.1796i | −0.550313 | + | 0.583297i | ||||
\(437\) | 9.23327 | + | 6.07282i | 0.441687 | + | 0.290502i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.34902 | + | 1.42987i | 0.0643851 | + | 0.0682442i | 0.758765 | − | 0.651364i | \(-0.225803\pi\) |
−0.694380 | + | 0.719608i | \(0.744321\pi\) | |||||||
\(440\) | −0.0851954 | − | 0.483167i | −0.00406153 | − | 0.0230341i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.01800 | + | 45.4724i | −0.381378 | + | 2.16290i | ||||
\(443\) | 26.5757 | − | 17.4791i | 1.26265 | − | 0.830456i | 0.271399 | − | 0.962467i | \(-0.412514\pi\) |
0.991248 | + | 0.132010i | \(0.0421433\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.03038 | − | 0.821733i | 0.333272 | − | 0.0389539i | ||||
\(446\) | 40.7150 | − | 4.75890i | 1.92791 | − | 0.225340i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.79880 | + | 1.84080i | −0.132231 | + | 0.0869696i | ||||
\(449\) | 5.17251 | − | 29.3348i | 0.244106 | − | 1.38439i | −0.578454 | − | 0.815715i | \(-0.696344\pi\) |
0.822560 | − | 0.568679i | \(-0.192545\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.0985049 | + | 0.558649i | 0.00463841 | + | 0.0263057i | ||||
\(452\) | −6.04855 | − | 6.41109i | −0.284500 | − | 0.301552i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.664012 | + | 0.436727i | 0.0311636 | + | 0.0204966i | ||||
\(455\) | −16.3286 | + | 17.3073i | −0.765495 | + | 0.811377i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.04859 | + | 11.7040i | 0.236163 | + | 0.547488i | 0.994543 | − | 0.104325i | \(-0.0332681\pi\) |
−0.758380 | + | 0.651813i | \(0.774009\pi\) | |||||||
\(458\) | −13.8457 | + | 23.9815i | −0.646968 | + | 1.12058i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.58494 | − | 4.47725i | −0.120523 | − | 0.208753i | ||||
\(461\) | −12.3421 | + | 16.5783i | −0.574828 | + | 0.772129i | −0.990519 | − | 0.137378i | \(-0.956133\pi\) |
0.415690 | + | 0.909506i | \(0.363540\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.77533 | + | 15.9507i | 0.221929 | + | 0.741293i | 0.994347 | + | 0.106179i | \(0.0338617\pi\) |
−0.772418 | + | 0.635114i | \(0.780953\pi\) | |||||||
\(464\) | 1.83395 | − | 31.4878i | 0.0851391 | − | 1.46178i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.3908 | + | 3.17367i | −0.620315 | + | 0.147017i | ||||
\(467\) | 22.4416 | − | 18.8308i | 1.03848 | − | 0.871384i | 0.0466403 | − | 0.998912i | \(-0.485149\pi\) |
0.991835 | + | 0.127527i | \(0.0407041\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −33.7762 | − | 28.3416i | −1.55964 | − | 1.30870i | ||||
\(470\) | 4.43459 | + | 2.22713i | 0.204552 | + | 0.102730i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −10.2024 | + | 23.6519i | −0.469606 | + | 1.08867i | ||||
\(473\) | −0.194553 | − | 0.261330i | −0.00894555 | − | 0.0120160i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.530120 | − | 9.10181i | −0.0243236 | − | 0.417620i | ||||
\(476\) | 15.6486 | − | 5.69562i | 0.717252 | − | 0.261059i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −34.5215 | − | 12.5648i | −1.57897 | − | 0.574700i | ||||
\(479\) | 6.41347 | − | 21.4225i | 0.293039 | − | 0.978819i | −0.677023 | − | 0.735962i | \(-0.736730\pi\) |
0.970062 | − | 0.242857i | \(-0.0780845\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 39.0677 | − | 19.6205i | 1.78133 | − | 0.894619i | ||||
\(482\) | −30.4436 | − | 7.21526i | −1.38667 | − | 0.328646i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.8611 | + | 1.26948i | 0.493685 | + | 0.0577035i | ||||
\(485\) | −2.47238 | −0.112265 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.73936 | 0.169447 | 0.0847233 | − | 0.996405i | \(-0.472999\pi\) | ||||
0.0847233 | + | 0.996405i | \(0.472999\pi\) | |||||||
\(488\) | −2.59653 | − | 0.303491i | −0.117540 | − | 0.0137384i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 8.84533 | + | 2.09638i | 0.399591 | + | 0.0947049i | ||||
\(491\) | 1.07834 | − | 0.541563i | 0.0486648 | − | 0.0244404i | −0.424300 | − | 0.905521i | \(-0.639480\pi\) |
0.472965 | + | 0.881081i | \(0.343184\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.18167 | − | 30.6689i | 0.413522 | − | 1.38126i | ||||
\(494\) | 25.1148 | + | 9.14105i | 1.12997 | + | 0.411275i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 23.8744 | − | 8.68957i | 1.07199 | − | 0.390173i | ||||
\(497\) | −0.893649 | − | 15.3434i | −0.0400856 | − | 0.688244i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.99325 | + | 2.67741i | 0.0892303 | + | 0.119857i | 0.844497 | − | 0.535561i | \(-0.179900\pi\) |
−0.755266 | + | 0.655418i | \(0.772492\pi\) | |||||||
\(500\) | −4.41074 | + | 10.2252i | −0.197254 | + | 0.457287i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.4940 | + | 6.27474i | 0.557636 | + | 0.280055i | ||||
\(503\) | −18.7108 | − | 15.7002i | −0.834274 | − | 0.700039i | 0.121994 | − | 0.992531i | \(-0.461071\pi\) |
−0.956268 | + | 0.292492i | \(0.905516\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.1048 | − | 10.1572i | 0.538658 | − | 0.451988i | ||||
\(506\) | 1.30155 | − | 0.308474i | 0.0578611 | − | 0.0137133i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.404884 | − | 6.95159i | 0.0179638 | − | 0.308427i | ||||
\(509\) | 8.87341 | + | 29.6393i | 0.393307 | + | 1.31374i | 0.893982 | + | 0.448102i | \(0.147900\pi\) |
−0.500675 | + | 0.865635i | \(0.666915\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −31.9731 | + | 42.9473i | −1.41440 | + | 1.89988i | ||||
\(512\) | −4.29252 | − | 7.43487i | −0.189705 | − | 0.328578i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14.3134 | − | 24.7916i | 0.631339 | − | 1.09351i | ||||
\(515\) | 0.272818 | + | 0.632463i | 0.0120218 | + | 0.0278696i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.293288 | + | 0.310867i | −0.0128988 | + | 0.0136719i | ||||
\(518\) | −39.5747 | − | 26.0287i | −1.73881 | − | 1.14364i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.61582 | + | 9.13223i | 0.377829 | + | 0.400475i | ||||
\(521\) | −2.47495 | − | 14.0361i | −0.108430 | − | 0.614934i | −0.989795 | − | 0.142499i | \(-0.954486\pi\) |
0.881365 | − | 0.472435i | \(-0.156625\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.234960 | − | 1.33253i | 0.0102741 | − | 0.0582673i | −0.979240 | − | 0.202706i | \(-0.935026\pi\) |
0.989514 | + | 0.144439i | \(0.0461376\pi\) | |||||||
\(524\) | 4.70209 | − | 3.09261i | 0.205412 | − | 0.135101i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.0288738 | + | 0.00337486i | −0.00125896 | + | 0.000147151i | ||||
\(527\) | 25.6130 | − | 2.99373i | 1.11572 | − | 0.130409i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.39088 | − | 4.86106i | 0.321343 | − | 0.211350i | ||||
\(530\) | 3.74002 | − | 21.2107i | 0.162456 | − | 0.921335i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.67382 | − | 9.49269i | −0.0725692 | − | 0.411560i | ||||
\(533\) | −9.96180 | − | 10.5589i | −0.431493 | − | 0.457356i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.26297 | + | 4.11922i | 0.270772 | + | 0.178089i | ||||
\(536\) | −15.9655 | + | 16.9225i | −0.689605 | + | 0.730939i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.33884 | − | 10.0586i | −0.187060 | − | 0.433655i | ||||
\(539\) | −0.391448 | + | 0.678008i | −0.0168609 | + | 0.0292039i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.5060 | + | 21.6611i | 0.537676 | + | 0.931283i | 0.999029 | + | 0.0440659i | \(0.0140312\pi\) |
−0.461352 | + | 0.887217i | \(0.652636\pi\) | |||||||
\(542\) | 20.6532 | − | 27.7420i | 0.887130 | − | 1.19162i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7.54990 | − | 25.2184i | −0.323699 | − | 1.08123i | ||||
\(545\) | −1.34351 | + | 23.0672i | −0.0575498 | + | 0.988092i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.6336 | − | 6.54928i | 1.18153 | − | 0.280027i | 0.407515 | − | 0.913199i | \(-0.366395\pi\) |
0.774011 | + | 0.633172i | \(0.218247\pi\) | |||||||
\(548\) | 0.851950 | − | 0.714871i | 0.0363935 | − | 0.0305378i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.845339 | − | 0.709324i | −0.0360454 | − | 0.0302457i | ||||
\(551\) | −16.5594 | − | 8.31645i | −0.705455 | − | 0.354293i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.93663 | + | 4.48960i | −0.0823537 | + | 0.190917i | ||||
\(554\) | 6.46815 | + | 8.68824i | 0.274805 | + | 0.369128i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.276075 | + | 4.74003i | 0.0117082 | + | 0.201022i | ||||
\(557\) | 34.6621 | − | 12.6160i | 1.46868 | − | 0.534556i | 0.520938 | − | 0.853594i | \(-0.325582\pi\) |
0.947742 | + | 0.319039i | \(0.103360\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.83442 | + | 2.85150i | 0.331361 | + | 0.120605i | ||||
\(560\) | 6.49335 | − | 21.6893i | 0.274394 | − | 0.916540i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.00761 | − | 4.52379i | 0.379963 | − | 0.190825i | ||||
\(563\) | −21.5598 | − | 5.10976i | −0.908635 | − | 0.215351i | −0.250382 | − | 0.968147i | \(-0.580556\pi\) |
−0.658253 | + | 0.752797i | \(0.728704\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.0805 | − | 1.41200i | −0.508229 | − | 0.0594034i | ||||
\(566\) | −14.8852 | −0.625671 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.10969 | −0.340275 | ||||||||
\(569\) | 6.35985 | + | 0.743360i | 0.266619 | + | 0.0311633i | 0.248352 | − | 0.968670i | \(-0.420111\pi\) |
0.0182670 | + | 0.999833i | \(0.494185\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.37491 | − | 1.27388i | −0.224933 | − | 0.0533101i | 0.116604 | − | 0.993179i | \(-0.462799\pi\) |
−0.341537 | + | 0.939868i | \(0.610947\pi\) | |||||||
\(572\) | 0.962259 | − | 0.483264i | 0.0402341 | − | 0.0202063i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.51091 | + | 15.0675i | −0.188282 | + | 0.628904i | ||||
\(575\) | 10.9725 | + | 3.99368i | 0.457586 | + | 0.166548i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.7599 | − | 13.3795i | 1.53033 | − | 0.556996i | 0.566630 | − | 0.823972i | \(-0.308247\pi\) |
0.963703 | + | 0.266977i | \(0.0860246\pi\) | |||||||
\(578\) | −0.881402 | − | 15.1331i | −0.0366615 | − | 0.629454i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.17656 | + | 6.95332i | 0.214945 | + | 0.288721i | ||||
\(581\) | 18.5612 | − | 43.0297i | 0.770049 | − | 1.78517i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.65763 | + | 0.832491i | 0.0686518 | + | 0.0344782i | ||||
\(584\) | 21.6420 | + | 18.1598i | 0.895551 | + | 0.751457i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.53628 | + | 7.16279i | −0.352631 | + | 0.295892i | ||||
\(587\) | −13.5333 | + | 3.20744i | −0.558578 | + | 0.132385i | −0.500201 | − | 0.865909i | \(-0.666741\pi\) |
−0.0583765 | + | 0.998295i | \(0.518592\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.867894 | − | 14.9012i | 0.0357610 | − | 0.613992i | ||||
\(590\) | −10.1520 | − | 33.9100i | −0.417951 | − | 1.39605i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −24.8406 | + | 33.3667i | −1.02094 | + | 1.37136i | ||||
\(593\) | −8.67989 | − | 15.0340i | −0.356441 | − | 0.617373i | 0.630923 | − | 0.775846i | \(-0.282676\pi\) |
−0.987363 | + | 0.158472i | \(0.949343\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.4899 | − | 19.9010i | 0.471039 | − | 0.815863i | ||||
\(596\) | −3.03458 | − | 7.03494i | −0.124301 | − | 0.288162i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −23.4898 | + | 24.8977i | −0.960570 | + | 1.01814i | ||||
\(599\) | 34.7339 | + | 22.8449i | 1.41919 | + | 0.933415i | 0.999671 | + | 0.0256686i | \(0.00817146\pi\) |
0.419519 | + | 0.907747i | \(0.362199\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.33713 | + | 6.71697i | 0.258497 | + | 0.273991i | 0.843605 | − | 0.536965i | \(-0.180429\pi\) |
−0.585108 | + | 0.810956i | \(0.698948\pi\) | |||||||
\(602\) | −1.56859 | − | 8.89594i | −0.0639311 | − | 0.362571i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.535232 | − | 3.03545i | 0.0217783 | − | 0.123511i | ||||
\(605\) | 12.6071 | − | 8.29181i | 0.512551 | − | 0.337110i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.3985 | − | 1.56606i | 0.543829 | − | 0.0635645i | 0.160257 | − | 0.987075i | \(-0.448768\pi\) |
0.383572 | + | 0.923511i | \(0.374694\pi\) | |||||||
\(608\) | −15.1342 | + | 1.76893i | −0.613772 | + | 0.0717397i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.00142 | − | 1.97406i | 0.121524 | − | 0.0799275i | ||||
\(611\) | 1.89916 | − | 10.7707i | 0.0768317 | − | 0.435734i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.675007 | − | 3.82815i | −0.0272633 | − | 0.154618i | 0.968137 | − | 0.250421i | \(-0.0805691\pi\) |
−0.995400 | + | 0.0958034i | \(0.969458\pi\) | |||||||
\(614\) | −29.1695 | − | 30.9179i | −1.17719 | − | 1.24775i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.978817 | + | 0.643778i | 0.0394377 | + | 0.0259386i | ||||
\(617\) | 16.4797 | − | 17.4674i | 0.663447 | − | 0.703212i | −0.305023 | − | 0.952345i | \(-0.598664\pi\) |
0.968469 | + | 0.249133i | \(0.0801455\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.03156 | − | 9.34620i | −0.162042 | − | 0.375656i | 0.817779 | − | 0.575532i | \(-0.195205\pi\) |
−0.979821 | + | 0.199877i | \(0.935946\pi\) | |||||||
\(620\) | −3.49133 | + | 6.04716i | −0.140215 | + | 0.242860i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11.2430 | − | 19.4734i | −0.450802 | − | 0.780812i | ||||
\(623\) | −10.0932 | + | 13.5576i | −0.404377 | + | 0.543172i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.0435457 | − | 0.145453i | −0.00174183 | − | 0.00581812i | ||||
\(626\) | −0.526337 | + | 9.03685i | −0.0210366 | + | 0.361185i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.95311 | − | 1.41091i | 0.237555 | − | 0.0563015i | ||||
\(629\) | −32.3435 | + | 27.1394i | −1.28962 | + | 1.08212i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.7162 | − | 31.6476i | −1.50146 | − | 1.25987i | −0.878621 | − | 0.477520i | \(-0.841536\pi\) |
−0.622836 | − | 0.782352i | \(-0.714020\pi\) | |||||||
\(632\) | 2.30553 | + | 1.15788i | 0.0917090 | + | 0.0460580i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 20.9556 | − | 48.5806i | 0.832255 | − | 1.92938i | ||||
\(635\) | −5.73806 | − | 7.70755i | −0.227708 | − | 0.305865i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.16490 | − | 20.0006i | −0.0461550 | − | 0.792452i | ||||
\(638\) | −2.10759 | + | 0.767099i | −0.0834402 | + | 0.0303698i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −15.7068 | − | 5.71682i | −0.620867 | − | 0.225977i | ||||
\(641\) | −9.77403 | + | 32.6475i | −0.386051 | + | 1.28950i | 0.515524 | + | 0.856875i | \(0.327597\pi\) |
−0.901574 | + | 0.432624i | \(0.857588\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.7621 | + | 8.92044i | −0.700467 | + | 0.351788i | −0.763128 | − | 0.646247i | \(-0.776338\pi\) |
0.0626611 | + | 0.998035i | \(0.480041\pi\) | |||||||
\(644\) | 12.0124 | + | 2.84699i | 0.473354 | + | 0.112187i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −25.6373 | − | 2.99657i | −1.00869 | − | 0.117898i | ||||
\(647\) | 37.1636 | 1.46105 | 0.730525 | − | 0.682886i | \(-0.239275\pi\) | ||||
0.730525 | + | 0.682886i | \(0.239275\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.04853 | 0.119665 | ||||||||
\(650\) | 28.0481 | + | 3.27835i | 1.10014 | + | 0.128588i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.166912 | − | 0.0395588i | −0.00653677 | − | 0.00154924i | ||||
\(653\) | 4.92172 | − | 2.47178i | 0.192602 | − | 0.0967283i | −0.349885 | − | 0.936793i | \(-0.613779\pi\) |
0.542487 | + | 0.840064i | \(0.317483\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.22736 | − | 7.43989i | 0.0870301 | − | 0.290701i | ||||
\(656\) | 12.9796 | + | 4.72418i | 0.506767 | + | 0.184448i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −11.1351 | + | 4.05286i | −0.434093 | + | 0.157997i | ||||
\(659\) | 2.21435 | + | 38.0190i | 0.0862589 | + | 1.48101i | 0.712661 | + | 0.701509i | \(0.247490\pi\) |
−0.626402 | + | 0.779500i | \(0.715473\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.8265 | − | 22.6020i | −0.654477 | − | 0.879115i | 0.343724 | − | 0.939071i | \(-0.388311\pi\) |
−0.998201 | + | 0.0599557i | \(0.980904\pi\) | |||||||
\(662\) | 2.18334 | − | 5.06154i | 0.0848578 | − | 0.196723i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −22.0969 | − | 11.0975i | −0.857526 | − | 0.430666i | ||||
\(665\) | −10.1894 | − | 8.54990i | −0.395127 | − | 0.331551i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.1802 | − | 15.2550i | 0.703939 | − | 0.590675i | ||||
\(668\) | 0.285807 | − | 0.0677375i | 0.0110582 | − | 0.00262084i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.85893 | − | 31.9166i | 0.0718167 | − | 1.23304i | ||||
\(671\) | 0.0887347 | + | 0.296395i | 0.00342556 | + | 0.0114422i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.8365 | − | 19.9289i | 0.571907 | − | 0.768204i | −0.418225 | − | 0.908343i | \(-0.637348\pi\) |
0.990132 | + | 0.140139i | \(0.0447550\pi\) | |||||||
\(674\) | 28.3712 | + | 49.1404i | 1.09282 | + | 1.89282i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.29123 | + | 12.6288i | −0.280432 | + | 0.485722i | ||||
\(677\) | −13.9756 | − | 32.3992i | −0.537128 | − | 1.24520i | −0.943463 | − | 0.331478i | \(-0.892453\pi\) |
0.406335 | − | 0.913724i | \(-0.366806\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.05143 | − | 4.29426i | 0.155480 | − | 0.164799i | ||||
\(680\) | −10.1306 | − | 6.66298i | −0.388490 | − | 0.255514i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.23979 | − | 1.31410i | −0.0474739 | − | 0.0503193i | ||||
\(683\) | 6.86569 | + | 38.9372i | 0.262708 | + | 1.48989i | 0.775483 | + | 0.631369i | \(0.217507\pi\) |
−0.512774 | + | 0.858523i | \(0.671382\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.266493 | − | 1.51136i | 0.0101822 | − | 0.0577460i | ||||
\(686\) | 15.1618 | − | 9.97208i | 0.578880 | − | 0.380736i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.87931 | + | 0.920960i | −0.300396 | + | 0.0351113i | ||||
\(689\) | −47.1470 | + | 5.51069i | −1.79616 | + | 0.209941i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.1957 | − | 9.33667i | 0.540031 | − | 0.355184i | −0.250005 | − | 0.968245i | \(-0.580432\pi\) |
0.790036 | + | 0.613061i | \(0.210062\pi\) | |||||||
\(692\) | 0.465612 | − | 2.64062i | 0.0176999 | − | 0.100381i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.73702 | + | 38.2075i | 0.255734 | + | 1.45034i | ||||
\(695\) | 4.49623 | + | 4.76573i | 0.170552 | + | 0.180774i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.7132 | + | 7.70389i | 0.443669 | + | 0.291805i | ||||
\(698\) | −26.2207 | + | 27.7923i | −0.992468 | + | 1.05195i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.03391 | − | 9.35166i | −0.152468 | − | 0.353460i | ||||
\(701\) | −16.3741 | + | 28.3608i | −0.618442 | + | 1.07117i | 0.371328 | + | 0.928502i | \(0.378903\pi\) |
−0.989770 | + | 0.142672i | \(0.954431\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.2194 | + | 21.1647i | 0.460865 | + | 0.798241i | ||||
\(704\) | 0.124922 | − | 0.167799i | 0.00470818 | − | 0.00632418i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.42113 | − | 18.1078i | −0.204027 | − | 0.681497i | ||||
\(707\) | −2.19397 | + | 37.6691i | −0.0825129 | + | 1.41669i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.9346 | − | 7.56865i | 1.19933 | − | 0.284246i | 0.418048 | − | 0.908425i | \(-0.362714\pi\) |
0.781282 | + | 0.624178i | \(0.214566\pi\) | |||||||
\(710\) | 8.53698 | − | 7.16337i | 0.320387 | − | 0.268837i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.83193 | + | 5.73267i | 0.256037 | + | 0.214841i | ||||
\(713\) | 17.0833 | + | 8.57958i | 0.639776 | + | 0.321308i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.588533 | − | 1.36437i | 0.0220099 | − | 0.0510247i | ||||
\(716\) | 1.42635 | + | 1.91592i | 0.0533051 | + | 0.0716012i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.49565 | − | 42.8487i | −0.0931368 | − | 1.59910i | ||||
\(719\) | 15.8250 | − | 5.75983i | 0.590173 | − | 0.214806i | −0.0296323 | − | 0.999561i | \(-0.509434\pi\) |
0.619806 | + | 0.784755i | \(0.287211\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.54558 | − | 0.562545i | −0.0575604 | − | 0.0209503i | ||||
\(722\) | 5.15012 | − | 17.2026i | 0.191668 | − | 0.640214i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.9331 | − | 7.49969i | 0.554985 | − | 0.278724i | ||||
\(725\) | −19.0513 | − | 4.51524i | −0.707548 | − | 0.167692i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.34602 | + | 0.975510i | 0.309537 | + | 0.0361797i | 0.269443 | − | 0.963016i | \(-0.413160\pi\) |
0.0400936 | + | 0.999196i | \(0.487234\pi\) | |||||||
\(728\) | −29.9802 | −1.11114 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −38.8230 | −1.43690 | ||||||||
\(731\) | −7.99740 | − | 0.934762i | −0.295795 | − | 0.0345734i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.0138 | + | 2.84732i | 0.443739 | + | 0.105168i | 0.446411 | − | 0.894828i | \(-0.352702\pi\) |
−0.00267116 | + | 0.999996i | \(0.500850\pi\) | |||||||
\(734\) | −19.8803 | + | 9.98427i | −0.733796 | + | 0.368526i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.59690 | − | 18.6949i | 0.206304 | − | 0.689105i | ||||
\(737\) | 2.58738 | + | 0.941730i | 0.0953075 | + | 0.0346891i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.3973 | − | 13.6115i | 1.37568 | − | 0.500707i | 0.454815 | − | 0.890586i | \(-0.349705\pi\) |
0.920866 | + | 0.389879i | \(0.127483\pi\) | |||||||
\(740\) | −0.664749 | − | 11.4133i | −0.0244367 | − | 0.419561i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 30.7121 | + | 41.2535i | 1.12748 | + | 1.51446i | ||||
\(743\) | −7.85752 | + | 18.2158i | −0.288264 | + | 0.668272i | −0.999395 | − | 0.0347882i | \(-0.988924\pi\) |
0.711130 | + | 0.703060i | \(0.248184\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.44779 | − | 4.74486i | −0.346140 | − | 0.173838i | ||||
\(746\) | 2.95869 | + | 2.48263i | 0.108325 | + | 0.0908957i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.796638 | + | 0.668459i | −0.0291280 | + | 0.0244413i | ||||
\(749\) | −17.4176 | + | 4.12805i | −0.636425 | + | 0.150836i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.23147 | + | 38.3128i | −0.0814274 | + | 1.39805i | 0.672014 | + | 0.740539i | \(0.265430\pi\) |
−0.753441 | + | 0.657515i | \(0.771607\pi\) | |||||||
\(752\) | 2.98462 | + | 9.96932i | 0.108838 | + | 0.363544i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 34.2739 | − | 46.0378i | 1.24818 | − | 1.67660i | ||||
\(755\) | −2.12665 | − | 3.68347i | −0.0773969 | − | 0.134055i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.07444 | − | 12.2533i | 0.257125 | − | 0.445353i | −0.708346 | − | 0.705866i | \(-0.750558\pi\) |
0.965470 | + | 0.260513i | \(0.0838915\pi\) | |||||||
\(758\) | −5.04670 | − | 11.6996i | −0.183304 | − | 0.424947i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.81636 | + | 5.10504i | −0.174708 | + | 0.185179i | ||||
\(761\) | 7.91964 | + | 5.20883i | 0.287087 | + | 0.188820i | 0.684881 | − | 0.728655i | \(-0.259854\pi\) |
−0.397795 | + | 0.917474i | \(0.630224\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −37.8638 | − | 40.1332i | −1.37076 | − | 1.45292i | ||||
\(764\) | −2.45907 | − | 13.9461i | −0.0889660 | − | 0.504551i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.34643 | + | 24.6498i | −0.157043 | + | 0.890634i | ||||
\(767\) | −65.1785 | + | 42.8685i | −2.35346 | + | 1.54789i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.4366 | − | 1.45363i | 0.448476 | − | 0.0524193i | 0.111142 | − | 0.993804i | \(-0.464549\pi\) |
0.337334 | + | 0.941385i | \(0.390475\pi\) | |||||||
\(770\) | −1.59905 | + | 0.186902i | −0.0576256 | + | 0.00673547i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.48164 | − | 2.28991i | 0.125307 | − | 0.0824156i | ||||
\(773\) | −6.23462 | + | 35.3583i | −0.224244 | + | 1.27175i | 0.639882 | + | 0.768474i | \(0.278983\pi\) |
−0.864125 | + | 0.503277i | \(0.832128\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.73862 | − | 15.5315i | −0.0983742 | − | 0.557908i | ||||
\(776\) | −2.13775 | − | 2.26588i | −0.0767407 | − | 0.0813404i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −12.3021 | − | 8.09123i | −0.441052 | − | 0.290085i | ||||
\(779\) | 5.56879 | − | 5.90257i | 0.199522 | − | 0.211481i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.380151 | + | 0.881289i | 0.0136029 | + | 0.0315350i | ||||
\(782\) | 16.5290 | − | 28.6291i | 0.591076 | − | 1.02377i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 9.53150 | + | 16.5091i | 0.340411 | + | 0.589609i | ||||
\(785\) | 5.04146 | − | 6.77185i | 0.179937 | − | 0.241698i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.4581 | − | 38.2728i | −0.408438 | − | 1.36428i | −0.876848 | − | 0.480767i | \(-0.840358\pi\) |
0.468410 | − | 0.883511i | \(-0.344827\pi\) | |||||||
\(788\) | 1.20215 | − | 20.6401i | 0.0428248 | − | 0.735273i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.44977 | + | 0.817611i | −0.122737 | + | 0.0290893i | ||||
\(791\) | 22.2484 | − | 18.6687i | 0.791063 | − | 0.663781i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.06508 | − | 5.08921i | −0.215377 | − | 0.180723i | ||||
\(794\) | 8.49811 | + | 4.26791i | 0.301586 | + | 0.151462i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.13690 | − | 2.63563i | 0.0402964 | − | 0.0934176i | ||||
\(797\) | 20.3548 | + | 27.3413i | 0.721005 | + | 0.968478i | 0.999967 | + | 0.00817540i | \(0.00260234\pi\) |
−0.278962 | + | 0.960302i | \(0.589990\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.614153 | + | 10.5446i | 0.0217272 | + | 0.373041i | ||||
\(800\) | −15.1285 | + | 5.50634i | −0.534875 | + | 0.194678i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 15.3085 | + | 5.57185i | 0.540563 | + | 0.196749i | ||||
\(803\) | 0.958950 | − | 3.20312i | 0.0338406 | − | 0.113036i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.2234 | − | 7.64546i | 0.536553 | − | 0.269467i | ||||
\(806\) | 44.9858 | + | 10.6618i | 1.58456 | + | 0.375547i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 19.7753 | + | 2.31140i | 0.695691 | + | 0.0813147i | ||||
\(809\) | −7.57622 | −0.266366 | −0.133183 | − | 0.991091i | \(-0.542520\pi\) | ||||
−0.133183 | + | 0.991091i | \(0.542520\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.5558 | 0.721810 | 0.360905 | − | 0.932602i | \(-0.382468\pi\) | ||||
0.360905 | + | 0.932602i | \(0.382468\pi\) | |||||||
\(812\) | −20.5599 | − | 2.40310i | −0.721510 | − | 0.0843324i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.87825 | + | 0.682157i | 0.100882 | + | 0.0239096i | ||||
\(815\) | −0.211529 | + | 0.106234i | −0.00740952 | + | 0.00372120i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.33668 | + | 4.46483i | −0.0467646 | + | 0.156205i | ||||
\(818\) | 25.0916 | + | 9.13260i | 0.877308 | + | 0.319314i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.56726 | + | 1.29838i | −0.124574 | + | 0.0453412i | ||||
\(821\) | −1.77197 | − | 30.4235i | −0.0618420 | − | 1.06179i | −0.876363 | − | 0.481652i | \(-0.840037\pi\) |
0.814520 | − | 0.580135i | \(-0.197000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.3276 | − | 17.9020i | −0.464570 | − | 0.624026i | 0.506667 | − | 0.862142i | \(-0.330878\pi\) |
−0.971237 | + | 0.238116i | \(0.923470\pi\) | |||||||
\(824\) | −0.343745 | + | 0.796891i | −0.0119749 | + | 0.0277610i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 75.5339 | + | 37.9346i | 2.62816 | + | 1.31991i | ||||
\(827\) | 27.2509 | + | 22.8662i | 0.947606 | + | 0.795136i | 0.978893 | − | 0.204374i | \(-0.0655159\pi\) |
−0.0312864 | + | 0.999510i | \(0.509960\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.4520 | + | 11.2875i | −0.467206 | + | 0.392032i | −0.845774 | − | 0.533541i | \(-0.820861\pi\) |
0.378568 | + | 0.925573i | \(0.376416\pi\) | |||||||
\(830\) | 33.0637 | − | 7.83623i | 1.14766 | − | 0.272000i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.311267 | + | 5.34426i | −0.0107913 | + | 0.185279i | ||||
\(833\) | 5.54927 | + | 18.5359i | 0.192271 | + | 0.642230i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.242039 | − | 0.325114i | 0.00837610 | − | 0.0112510i | ||||
\(836\) | 0.300972 | + | 0.521298i | 0.0104093 | + | 0.0180295i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 21.3875 | − | 37.0443i | 0.738820 | − | 1.27967i | ||||
\(839\) | 15.1824 | + | 35.1966i | 0.524153 | + | 1.21512i | 0.950546 | + | 0.310585i | \(0.100525\pi\) |
−0.426393 | + | 0.904538i | \(0.640216\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.40713 | + | 7.85110i | −0.255418 | + | 0.270728i | ||||
\(842\) | 0.268769 | + | 0.176772i | 0.00926240 | + | 0.00609198i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.26852 | + | 7.70418i | 0.250193 | + | 0.265189i | ||||
\(845\) | 3.49427 | + | 19.8170i | 0.120206 | + | 0.681725i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.25691 | + | 35.4847i | −0.214990 | + | 1.21927i | ||||
\(848\) | 37.7359 | − | 24.8193i | 1.29586 | − | 0.852297i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −27.0881 | + | 3.16614i | −0.929113 | + | 0.108598i | ||||
\(851\) | −31.0880 | + | 3.63367i | −1.06568 | + | 0.124560i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.01364 | + | 4.61295i | −0.240143 | + | 0.157944i | −0.663876 | − | 0.747843i | \(-0.731090\pi\) |
0.423733 | + | 0.905787i | \(0.360719\pi\) | |||||||
\(854\) | −1.48961 | + | 8.44799i | −0.0509733 | + | 0.289084i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.64011 | + | 9.30155i | 0.0560580 | + | 0.317920i | ||||
\(857\) | 33.0230 | + | 35.0023i | 1.12804 | + | 1.19566i | 0.978357 | + | 0.206924i | \(0.0663453\pi\) |
0.149688 | + | 0.988733i | \(0.452173\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −42.6770 | − | 28.0691i | −1.45612 | − | 0.957706i | −0.997616 | − | 0.0690137i | \(-0.978015\pi\) |
−0.458505 | − | 0.888692i | \(-0.651615\pi\) | |||||||
\(860\) | 1.49619 | − | 1.58587i | 0.0510196 | − | 0.0540776i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.97981 | + | 23.1358i | 0.339914 | + | 0.788008i | ||||
\(863\) | 18.3885 | − | 31.8499i | 0.625953 | − | 1.08418i | −0.362403 | − | 0.932022i | \(-0.618043\pi\) |
0.988356 | − | 0.152161i | \(-0.0486232\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.85003 | − | 3.20435i | −0.0629031 | − | 0.108951i | ||||
\(866\) | −35.7945 | + | 48.0804i | −1.21635 | + | 1.63384i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.78212 | − | 15.9734i | −0.162316 | − | 0.542172i | ||||
\(869\) | 0.0177538 | − | 0.304821i | 0.000602257 | − | 0.0103404i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −68.5616 | + | 16.2494i | −2.32312 | + | 0.550590i | ||||
\(872\) | −22.3023 | + | 18.7138i | −0.755250 | + | 0.633730i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −14.6581 | − | 12.2996i | −0.495819 | − | 0.416042i | ||||
\(875\) | −32.7913 | − | 16.4684i | −1.10855 | − | 0.556734i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.60802 | + | 3.72781i | −0.0542990 | + | 0.125879i | −0.943206 | − | 0.332209i | \(-0.892206\pi\) |
0.888907 | + | 0.458088i | \(0.151465\pi\) | |||||||
\(878\) | −2.03254 | − | 2.73018i | −0.0685950 | − | 0.0921391i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.0822078 | + | 1.41145i | 0.00277122 | + | 0.0475801i | ||||
\(881\) | −38.2223 | + | 13.9118i | −1.28774 | + | 0.468700i | −0.892986 | − | 0.450085i | \(-0.851394\pi\) |
−0.394758 | + | 0.918785i | \(0.629171\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.6043 | − | 8.95523i | −0.828000 | − | 0.301367i | −0.106962 | − | 0.994263i | \(-0.534112\pi\) |
−0.721038 | + | 0.692896i | \(0.756335\pi\) | |||||||
\(884\) | 7.63246 | − | 25.4942i | 0.256707 | − | 0.857462i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −49.2167 | + | 24.7176i | −1.65347 | + | 0.830403i | ||||
\(887\) | −21.1533 | − | 5.01341i | −0.710257 | − | 0.168334i | −0.140420 | − | 0.990092i | \(-0.544845\pi\) |
−0.569837 | + | 0.821758i | \(0.692994\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.7900 | + | 2.66377i | 0.764352 | + | 0.0893399i | ||||
\(890\) | −12.2556 | −0.410809 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −23.6257 | −0.791048 | ||||||||
\(893\) | 6.07249 | + | 0.709773i | 0.203208 | + | 0.0237516i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.20718 | + | 0.760117i | 0.107204 | + | 0.0254079i | ||||
\(896\) | 35.6679 | − | 17.9131i | 1.19158 | − | 0.598434i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −14.7919 | + | 49.4085i | −0.493614 | + | 1.64878i | ||||
\(899\) | −30.1211 | − | 10.9632i | −1.00459 | − | 0.365642i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43.0785 | − | 15.6793i | 1.43515 | − | 0.522353i | ||||
\(902\) | −0.0571095 | − | 0.980532i | −0.00190154 | − | 0.0326481i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.15132 | − | 12.2924i | −0.304368 | − | 0.408838i | ||||
\(905\) | 9.13334 | − | 21.1735i | 0.303602 | − | 0.703830i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −47.1055 | − | 23.6573i | −1.56411 | − | 0.785527i | −0.564899 | − | 0.825160i | \(-0.691085\pi\) |
−0.999214 | + | 0.0396329i | \(0.987381\pi\) | |||||||
\(908\) | −0.350892 | − | 0.294434i | −0.0116448 | − | 0.00977113i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 31.5598 | − | 26.4818i | 1.04620 | − | 0.877864i | ||||
\(911\) | −41.8920 | + | 9.92859i | −1.38794 | + | 0.328949i | −0.855626 | − | 0.517595i | \(-0.826827\pi\) |
−0.532319 | + | 0.846544i | \(0.678679\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.170158 | + | 2.92150i | −0.00563141 | + | 0.0966876i | ||||
\(914\) | −6.32968 | − | 21.1426i | −0.209367 | − | 0.699335i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.53058 | − | 12.8018i | 0.314899 | − | 0.422983i | ||||
\(917\) | 9.27238 | + | 16.0602i | 0.306201 | + | 0.530356i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.2136 | + | 43.6712i | −0.831719 | + | 1.44058i | 0.0649552 | + | 0.997888i | \(0.479310\pi\) |
−0.896674 | + | 0.442691i | \(0.854024\pi\) | |||||||
\(920\) | −3.56027 | − | 8.25363i | −0.117379 | − | 0.272114i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 24.5576 | − | 26.0295i | 0.808761 | − | 0.857237i | ||||
\(923\) | −20.5204 | − | 13.4965i | −0.675439 | − | 0.444243i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.7200 | + | 18.7821i | 0.582631 | + | 0.617552i | ||||
\(926\) | −5.00610 | − | 28.3910i | −0.164511 | − | 0.932987i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.68204 | + | 32.2245i | −0.186522 | + | 1.05782i | ||||
\(929\) | −13.2760 | + | 8.73178i | −0.435573 | + | 0.286481i | −0.748298 | − | 0.663363i | \(-0.769128\pi\) |
0.312725 | + | 0.949844i | \(0.398758\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.1238 | − | 1.30019i | 0.364568 | − | 0.0426119i | ||||
\(932\) | 7.87789 | − | 0.920793i | 0.258049 | − | 0.0301616i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −42.3790 | + | 27.8731i | −1.38668 | + | 0.912036i | ||||
\(935\) | −0.249191 | + | 1.41323i | −0.00814943 | + | 0.0462177i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.98093 | + | 22.5770i | 0.130051 | + | 0.737557i | 0.978179 | + | 0.207765i | \(0.0666189\pi\) |
−0.848128 | + | 0.529792i | \(0.822270\pi\) | |||||||
\(938\) | 52.3895 | + | 55.5296i | 1.71058 | + | 1.81311i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.38957 | − | 1.57164i | −0.0779390 | − | 0.0512613i | ||||
\(941\) | 9.70324 | − | 10.2848i | 0.316317 | − | 0.335276i | −0.549634 | − | 0.835406i | \(-0.685233\pi\) |
0.865951 | + | 0.500130i | \(0.166714\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.11646 | + | 9.54303i | 0.134050 | + | 0.310764i | ||||
\(944\) | 37.1148 | − | 64.2848i | 1.20799 | − | 2.09229i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.282051 | + | 0.488527i | 0.00917027 | + | 0.0158834i | ||||
\(947\) | 34.0917 | − | 45.7931i | 1.10783 | − | 1.48808i | 0.254233 | − | 0.967143i | \(-0.418177\pi\) |
0.853598 | − | 0.520932i | \(-0.174416\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.5397 | + | 81.9683i | 0.796593 | + | 2.66080i | ||||
\(950\) | −0.917876 | + | 15.7593i | −0.0297798 | + | 0.511300i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 28.1736 | − | 6.67726i | 0.913111 | − | 0.216411i | ||||
\(953\) | 13.5816 | − | 11.3963i | 0.439951 | − | 0.369163i | −0.395740 | − | 0.918363i | \(-0.629512\pi\) |
0.835691 | + | 0.549200i | \(0.185067\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.9696 | − | 12.5610i | −0.484405 | − | 0.406464i | ||||
\(956\) | 18.9211 | + | 9.50254i | 0.611953 | + | 0.307334i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −15.3356 | + | 35.5520i | −0.495472 | + | 1.14863i | ||||
\(959\) | 2.18837 | + | 2.93949i | 0.0706661 | + | 0.0949211i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.301197 | + | 5.17135i | 0.00971602 | + | 0.166818i | ||||
\(962\) | −71.1302 | + | 25.8893i | −2.29333 | + | 0.834704i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 16.9447 | + | 6.16735i | 0.545751 | + | 0.198637i | ||||
\(965\) | 1.64924 | − | 5.50883i | 0.0530908 | − | 0.177336i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.7655 | + | 9.92662i | −0.635617 | + | 0.319219i | −0.737267 | − | 0.675601i | \(-0.763884\pi\) |
0.101650 | + | 0.994820i | \(0.467588\pi\) | |||||||
\(968\) | 18.5000 | + | 4.38458i | 0.594612 | + | 0.140926i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.25186 | + | 0.496971i | 0.136519 | + | 0.0159568i | ||||
\(971\) | 5.09901 | 0.163635 | 0.0818176 | − | 0.996647i | \(-0.473928\pi\) | ||||
0.0818176 | + | 0.996647i | \(0.473928\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.6454 | −0.501569 | ||||||||
\(974\) | −6.43073 | − | 0.751645i | −0.206054 | − | 0.0240843i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.33043 | + | 1.73734i | 0.234641 | + | 0.0556110i | ||||
\(977\) | −20.7615 | + | 10.4268i | −0.664218 | + | 0.333583i | −0.748764 | − | 0.662837i | \(-0.769352\pi\) |
0.0845457 | + | 0.996420i | \(0.473056\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.302721 | − | 1.01116i | 0.00967500 | − | 0.0323167i | ||||
\(980\) | −4.92325 | − | 1.79191i | −0.157267 | − | 0.0572406i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.96332 | + | 0.714592i | −0.0626522 | + | 0.0228035i | ||||
\(983\) | −0.979980 | − | 16.8256i | −0.0312565 | − | 0.536653i | −0.977200 | − | 0.212321i | \(-0.931898\pi\) |
0.945943 | − | 0.324332i | \(-0.105139\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.0370 | − | 22.8846i | −0.542843 | − | 0.729164i | ||||
\(986\) | −21.9548 | + | 50.8970i | −0.699184 | + | 1.62089i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −13.7654 | − | 6.91323i | −0.437935 | − | 0.219939i | ||||
\(989\) | −4.57252 | − | 3.83680i | −0.145398 | − | 0.122003i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.316451 | + | 0.265534i | −0.0100524 | + | 0.00843496i | −0.647800 | − | 0.761810i | \(-0.724311\pi\) |
0.637748 | + | 0.770245i | \(0.279866\pi\) | |||||||
\(992\) | −25.6470 | + | 6.07845i | −0.814293 | + | 0.192991i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.54731 | + | 26.5663i | −0.0490776 | + | 0.842630i | ||||
\(995\) | −1.13600 | − | 3.79452i | −0.0360137 | − | 0.120294i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.48850 | − | 4.68587i | 0.110482 | − | 0.148403i | −0.743443 | − | 0.668799i | \(-0.766808\pi\) |
0.853925 | + | 0.520397i | \(0.174216\pi\) | |||||||
\(998\) | −2.88970 | − | 5.00511i | −0.0914719 | − | 0.158434i | ||||
\(999\) | 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 | 729.2.g.b.433.2 | 144 | ||
3.2 | odd | 2 | 729.2.g.c.433.7 | 144 | |||
9.2 | odd | 6 | 81.2.g.a.31.2 | ✓ | 144 | ||
9.4 | even | 3 | 729.2.g.a.190.7 | 144 | |||
9.5 | odd | 6 | 729.2.g.d.190.2 | 144 | |||
9.7 | even | 3 | 243.2.g.a.145.7 | 144 | |||
81.7 | even | 27 | 243.2.g.a.181.7 | 144 | |||
81.20 | odd | 54 | 729.2.g.c.298.7 | 144 | |||
81.34 | even | 27 | 729.2.g.a.541.7 | 144 | |||
81.40 | even | 27 | 6561.2.a.d.1.56 | 72 | |||
81.41 | odd | 54 | 6561.2.a.c.1.17 | 72 | |||
81.47 | odd | 54 | 729.2.g.d.541.2 | 144 | |||
81.61 | even | 27 | inner | 729.2.g.b.298.2 | 144 | ||
81.74 | odd | 54 | 81.2.g.a.34.2 | yes | 144 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
81.2.g.a.31.2 | ✓ | 144 | 9.2 | odd | 6 | ||
81.2.g.a.34.2 | yes | 144 | 81.74 | odd | 54 | ||
243.2.g.a.145.7 | 144 | 9.7 | even | 3 | |||
243.2.g.a.181.7 | 144 | 81.7 | even | 27 | |||
729.2.g.a.190.7 | 144 | 9.4 | even | 3 | |||
729.2.g.a.541.7 | 144 | 81.34 | even | 27 | |||
729.2.g.b.298.2 | 144 | 81.61 | even | 27 | inner | ||
729.2.g.b.433.2 | 144 | 1.1 | even | 1 | trivial | ||
729.2.g.c.298.7 | 144 | 81.20 | odd | 54 | |||
729.2.g.c.433.7 | 144 | 3.2 | odd | 2 | |||
729.2.g.d.190.2 | 144 | 9.5 | odd | 6 | |||
729.2.g.d.541.2 | 144 | 81.47 | odd | 54 | |||
6561.2.a.c.1.17 | 72 | 81.41 | odd | 54 | |||
6561.2.a.d.1.56 | 72 | 81.40 | even | 27 |