Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [260,2,Mod(31,260)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(260, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("260.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 260 = 2^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 260.j (of order \(4\), degree \(2\), 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: | \(2.07611045255\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 31.20 | ||
Character | \(\chi\) | \(=\) | 260.31 |
Dual form | 260.2.j.a.151.20 |
$q$-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 \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).
\(n\) | \(41\) | \(131\) | \(157\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.723264 | − | 1.21527i | 0.511425 | − | 0.859328i | ||||
\(3\) | 1.80245i | 1.04064i | 0.853970 | + | 0.520322i | \(0.174188\pi\) | ||||
−0.853970 | + | 0.520322i | \(0.825812\pi\) | |||||||
\(4\) | −0.953778 | − | 1.75793i | −0.476889 | − | 0.878963i | ||||
\(5\) | 0.707107 | − | 0.707107i | 0.316228 | − | 0.316228i | ||||
\(6\) | 2.19047 | + | 1.30365i | 0.894254 | + | 0.532211i | ||||
\(7\) | 1.20463 | − | 1.20463i | 0.455306 | − | 0.455306i | −0.441805 | − | 0.897111i | \(-0.645662\pi\) |
0.897111 | + | 0.441805i | \(0.145662\pi\) | |||||||
\(8\) | −2.82620 | − | 0.112344i | −0.999211 | − | 0.0397196i | ||||
\(9\) | −0.248815 | −0.0829385 | ||||||||
\(10\) | −0.347903 | − | 1.37075i | −0.110017 | − | 0.433470i | ||||
\(11\) | 2.81846 | − | 2.81846i | 0.849797 | − | 0.849797i | −0.140311 | − | 0.990108i | \(-0.544810\pi\) |
0.990108 | + | 0.140311i | \(0.0448101\pi\) | |||||||
\(12\) | 3.16857 | − | 1.71913i | 0.914687 | − | 0.496271i | ||||
\(13\) | 2.45611 | + | 2.63961i | 0.681201 | + | 0.732096i | ||||
\(14\) | −0.592687 | − | 2.33521i | −0.158402 | − | 0.624112i | ||||
\(15\) | 1.27452 | + | 1.27452i | 0.329080 | + | 0.329080i | ||||
\(16\) | −2.18061 | + | 3.35334i | −0.545154 | + | 0.838336i | ||||
\(17\) | 0.129940i | 0.0315151i | 0.999876 | + | 0.0157576i | \(0.00501599\pi\) | ||||
−0.999876 | + | 0.0157576i | \(0.994984\pi\) | |||||||
\(18\) | −0.179959 | + | 0.302379i | −0.0424168 | + | 0.0712714i | ||||
\(19\) | 0.145035 | + | 0.145035i | 0.0332733 | + | 0.0332733i | 0.723548 | − | 0.690274i | \(-0.242510\pi\) |
−0.690274 | + | 0.723548i | \(0.742510\pi\) | |||||||
\(20\) | −1.91747 | − | 0.568619i | −0.428758 | − | 0.127147i | ||||
\(21\) | 2.17127 | + | 2.17127i | 0.473811 | + | 0.473811i | ||||
\(22\) | −1.38671 | − | 5.46368i | −0.295647 | − | 1.16486i | ||||
\(23\) | −4.57371 | −0.953684 | −0.476842 | − | 0.878989i | \(-0.658219\pi\) | ||||
−0.476842 | + | 0.878989i | \(0.658219\pi\) | |||||||
\(24\) | 0.202494 | − | 5.09407i | 0.0413340 | − | 1.03982i | ||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | 4.98426 | − | 1.07571i | 0.977494 | − | 0.210963i | ||||
\(27\) | 4.95886i | 0.954334i | ||||||||
\(28\) | −3.26659 | − | 0.968698i | −0.617327 | − | 0.183067i | ||||
\(29\) | −3.84278 | −0.713587 | −0.356793 | − | 0.934183i | \(-0.616130\pi\) | ||||
−0.356793 | + | 0.934183i | \(0.616130\pi\) | |||||||
\(30\) | 2.47071 | − | 0.627077i | 0.451088 | − | 0.114488i | ||||
\(31\) | −2.42671 | − | 2.42671i | −0.435851 | − | 0.435851i | 0.454762 | − | 0.890613i | \(-0.349724\pi\) |
−0.890613 | + | 0.454762i | \(0.849724\pi\) | |||||||
\(32\) | 2.49807 | + | 5.07540i | 0.441601 | + | 0.897212i | ||||
\(33\) | 5.08012 | + | 5.08012i | 0.884335 | + | 0.884335i | ||||
\(34\) | 0.157913 | + | 0.0939810i | 0.0270818 | + | 0.0161176i | ||||
\(35\) | − | 1.70360i | − | 0.287961i | ||||||
\(36\) | 0.237315 | + | 0.437399i | 0.0395525 | + | 0.0728999i | ||||
\(37\) | −1.25170 | − | 1.25170i | −0.205778 | − | 0.205778i | 0.596692 | − | 0.802470i | \(-0.296481\pi\) |
−0.802470 | + | 0.596692i | \(0.796481\pi\) | |||||||
\(38\) | 0.281155 | − | 0.0713584i | 0.0456094 | − | 0.0115759i | ||||
\(39\) | −4.75776 | + | 4.42700i | −0.761851 | + | 0.708888i | ||||
\(40\) | −2.07786 | + | 1.91898i | −0.328539 | + | 0.303418i | ||||
\(41\) | −4.46917 | + | 4.46917i | −0.697967 | + | 0.697967i | −0.963972 | − | 0.266005i | \(-0.914296\pi\) |
0.266005 | + | 0.963972i | \(0.414296\pi\) | |||||||
\(42\) | 4.20910 | − | 1.06829i | 0.649477 | − | 0.164840i | ||||
\(43\) | −7.63599 | −1.16448 | −0.582239 | − | 0.813018i | \(-0.697823\pi\) | ||||
−0.582239 | + | 0.813018i | \(0.697823\pi\) | |||||||
\(44\) | −7.64283 | − | 2.26646i | −1.15220 | − | 0.341682i | ||||
\(45\) | −0.175939 | + | 0.175939i | −0.0262275 | + | 0.0262275i | ||||
\(46\) | −3.30800 | + | 5.55830i | −0.487738 | + | 0.819527i | ||||
\(47\) | −4.07898 | + | 4.07898i | −0.594981 | + | 0.594981i | −0.938973 | − | 0.343992i | \(-0.888221\pi\) |
0.343992 | + | 0.938973i | \(0.388221\pi\) | |||||||
\(48\) | −6.04423 | − | 3.93044i | −0.872409 | − | 0.567310i | ||||
\(49\) | 4.09775i | 0.585394i | ||||||||
\(50\) | −1.21527 | − | 0.723264i | −0.171866 | − | 0.102285i | ||||
\(51\) | −0.234210 | −0.0327960 | ||||||||
\(52\) | 2.29766 | − | 6.83526i | 0.318628 | − | 0.947880i | ||||
\(53\) | 3.15397 | 0.433231 | 0.216616 | − | 0.976257i | \(-0.430498\pi\) | ||||
0.216616 | + | 0.976257i | \(0.430498\pi\) | |||||||
\(54\) | 6.02638 | + | 3.58657i | 0.820086 | + | 0.488070i | ||||
\(55\) | − | 3.98590i | − | 0.537459i | ||||||
\(56\) | −3.53984 | + | 3.26917i | −0.473031 | + | 0.436862i | ||||
\(57\) | −0.261417 | + | 0.261417i | −0.0346256 | + | 0.0346256i | ||||
\(58\) | −2.77935 | + | 4.67003i | −0.364946 | + | 0.613205i | ||||
\(59\) | 9.66305 | − | 9.66305i | 1.25802 | − | 1.25802i | 0.305986 | − | 0.952036i | \(-0.401014\pi\) |
0.952036 | − | 0.305986i | \(-0.0989861\pi\) | |||||||
\(60\) | 1.02491 | − | 3.45613i | 0.132315 | − | 0.446184i | ||||
\(61\) | −5.89106 | −0.754273 | −0.377136 | − | 0.926158i | \(-0.623091\pi\) | ||||
−0.377136 | + | 0.926158i | \(0.623091\pi\) | |||||||
\(62\) | −4.70428 | + | 1.19397i | −0.597444 | + | 0.151634i | ||||
\(63\) | −0.299729 | + | 0.299729i | −0.0377624 | + | 0.0377624i | ||||
\(64\) | 7.97476 | + | 0.635013i | 0.996845 | + | 0.0793766i | ||||
\(65\) | 3.60322 | + | 0.129757i | 0.446924 | + | 0.0160943i | ||||
\(66\) | 9.84800 | − | 2.49947i | 1.21221 | − | 0.307663i | ||||
\(67\) | 6.46816 | + | 6.46816i | 0.790212 | + | 0.790212i | 0.981528 | − | 0.191317i | \(-0.0612757\pi\) |
−0.191317 | + | 0.981528i | \(0.561276\pi\) | |||||||
\(68\) | 0.228425 | − | 0.123934i | 0.0277006 | − | 0.0150292i | ||||
\(69\) | − | 8.24386i | − | 0.992444i | ||||||
\(70\) | −2.07034 | − | 1.23215i | −0.247453 | − | 0.147270i | ||||
\(71\) | −6.42532 | − | 6.42532i | −0.762545 | − | 0.762545i | 0.214237 | − | 0.976782i | \(-0.431274\pi\) |
−0.976782 | + | 0.214237i | \(0.931274\pi\) | |||||||
\(72\) | 0.703201 | + | 0.0279530i | 0.0828730 | + | 0.00329429i | ||||
\(73\) | 11.6298 | + | 11.6298i | 1.36117 | + | 1.36117i | 0.872433 | + | 0.488734i | \(0.162541\pi\) |
0.488734 | + | 0.872433i | \(0.337459\pi\) | |||||||
\(74\) | −2.42646 | + | 0.615847i | −0.282071 | + | 0.0715908i | ||||
\(75\) | 1.80245 | 0.208129 | ||||||||
\(76\) | 0.116630 | − | 0.393292i | 0.0133783 | − | 0.0451136i | ||||
\(77\) | − | 6.79037i | − | 0.773835i | ||||||
\(78\) | 1.93890 | + | 8.98387i | 0.219537 | + | 1.01722i | ||||
\(79\) | 3.11122i | 0.350040i | 0.984565 | + | 0.175020i | \(0.0559989\pi\) | ||||
−0.984565 | + | 0.175020i | \(0.944001\pi\) | |||||||
\(80\) | 0.829246 | + | 3.91310i | 0.0927125 | + | 0.437498i | ||||
\(81\) | −9.68454 | −1.07606 | ||||||||
\(82\) | 2.19887 | + | 8.66365i | 0.242825 | + | 0.956740i | ||||
\(83\) | 11.2681 | + | 11.2681i | 1.23684 | + | 1.23684i | 0.961287 | + | 0.275548i | \(0.0888594\pi\) |
0.275548 | + | 0.961287i | \(0.411141\pi\) | |||||||
\(84\) | 1.74603 | − | 5.88785i | 0.190507 | − | 0.642418i | ||||
\(85\) | 0.0918816 | + | 0.0918816i | 0.00996595 | + | 0.00996595i | ||||
\(86\) | −5.52284 | + | 9.27982i | −0.595543 | + | 1.00067i | ||||
\(87\) | − | 6.92641i | − | 0.742589i | ||||||
\(88\) | −8.28215 | + | 7.64887i | −0.882880 | + | 0.815373i | ||||
\(89\) | −10.5657 | − | 10.5657i | −1.11996 | − | 1.11996i | −0.991746 | − | 0.128215i | \(-0.959075\pi\) |
−0.128215 | − | 0.991746i | \(-0.540925\pi\) | |||||||
\(90\) | 0.0865637 | + | 0.341064i | 0.00912461 | + | 0.0359514i | ||||
\(91\) | 6.13843 | + | 0.221053i | 0.643482 | + | 0.0231727i | ||||
\(92\) | 4.36230 | + | 8.04024i | 0.454801 | + | 0.838253i | ||||
\(93\) | 4.37402 | − | 4.37402i | 0.453565 | − | 0.453565i | ||||
\(94\) | 2.00690 | + | 7.90726i | 0.206996 | + | 0.815572i | ||||
\(95\) | 0.205110 | 0.0210439 | ||||||||
\(96\) | −9.14813 | + | 4.50264i | −0.933677 | + | 0.459549i | ||||
\(97\) | −9.62350 | + | 9.62350i | −0.977118 | + | 0.977118i | −0.999744 | − | 0.0226260i | \(-0.992797\pi\) |
0.0226260 | + | 0.999744i | \(0.492797\pi\) | |||||||
\(98\) | 4.97989 | + | 2.96376i | 0.503045 | + | 0.299385i | ||||
\(99\) | −0.701276 | + | 0.701276i | −0.0704809 | + | 0.0704809i | ||||
\(100\) | −1.75793 | + | 0.953778i | −0.175793 | + | 0.0953778i | ||||
\(101\) | − | 13.6153i | − | 1.35477i | −0.735629 | − | 0.677384i | \(-0.763113\pi\) | ||
0.735629 | − | 0.677384i | \(-0.236887\pi\) | |||||||
\(102\) | −0.169396 | + | 0.284629i | −0.0167727 | + | 0.0281825i | ||||
\(103\) | 10.0009 | 0.985416 | 0.492708 | − | 0.870195i | \(-0.336007\pi\) | ||||
0.492708 | + | 0.870195i | \(0.336007\pi\) | |||||||
\(104\) | −6.64489 | − | 7.73598i | −0.651585 | − | 0.758575i | ||||
\(105\) | 3.07064 | 0.299664 | ||||||||
\(106\) | 2.28115 | − | 3.83294i | 0.221565 | − | 0.372288i | ||||
\(107\) | − | 11.8232i | − | 1.14299i | −0.820606 | − | 0.571494i | \(-0.806364\pi\) | ||
0.820606 | − | 0.571494i | \(-0.193636\pi\) | |||||||
\(108\) | 8.71732 | − | 4.72966i | 0.838825 | − | 0.455111i | ||||
\(109\) | 2.62846 | − | 2.62846i | 0.251761 | − | 0.251761i | −0.569931 | − | 0.821692i | \(-0.693030\pi\) |
0.821692 | + | 0.569931i | \(0.193030\pi\) | |||||||
\(110\) | −4.84396 | − | 2.88286i | −0.461853 | − | 0.274870i | ||||
\(111\) | 2.25612 | − | 2.25612i | 0.214141 | − | 0.214141i | ||||
\(112\) | 1.41270 | + | 6.66635i | 0.133488 | + | 0.629911i | ||||
\(113\) | 3.29753 | 0.310206 | 0.155103 | − | 0.987898i | \(-0.450429\pi\) | ||||
0.155103 | + | 0.987898i | \(0.450429\pi\) | |||||||
\(114\) | 0.128620 | + | 0.506768i | 0.0120463 | + | 0.0474631i | ||||
\(115\) | −3.23410 | + | 3.23410i | −0.301581 | + | 0.301581i | ||||
\(116\) | 3.66516 | + | 6.75533i | 0.340302 | + | 0.627217i | ||||
\(117\) | −0.611117 | − | 0.656776i | −0.0564978 | − | 0.0607189i | ||||
\(118\) | −4.75431 | − | 18.7322i | −0.437670 | − | 1.72444i | ||||
\(119\) | 0.156529 | + | 0.156529i | 0.0143490 | + | 0.0143490i | ||||
\(120\) | −3.45886 | − | 3.74523i | −0.315750 | − | 0.341892i | ||||
\(121\) | − | 4.88740i | − | 0.444309i | ||||||
\(122\) | −4.26079 | + | 7.15924i | −0.385754 | + | 0.648168i | ||||
\(123\) | −8.05544 | − | 8.05544i | −0.726334 | − | 0.726334i | ||||
\(124\) | −1.95144 | + | 6.58053i | −0.175244 | + | 0.590949i | ||||
\(125\) | −0.707107 | − | 0.707107i | −0.0632456 | − | 0.0632456i | ||||
\(126\) | 0.147470 | + | 0.581037i | 0.0131376 | + | 0.0517629i | ||||
\(127\) | −11.7740 | −1.04478 | −0.522389 | − | 0.852707i | \(-0.674959\pi\) | ||||
−0.522389 | + | 0.852707i | \(0.674959\pi\) | |||||||
\(128\) | 6.53957 | − | 9.23223i | 0.578022 | − | 0.816021i | ||||
\(129\) | − | 13.7635i | − | 1.21181i | ||||||
\(130\) | 2.76377 | − | 4.28504i | 0.242398 | − | 0.375823i | ||||
\(131\) | 7.98436i | 0.697597i | 0.937198 | + | 0.348798i | \(0.113410\pi\) | ||||
−0.937198 | + | 0.348798i | \(0.886590\pi\) | |||||||
\(132\) | 4.08517 | − | 13.7758i | 0.355569 | − | 1.19903i | ||||
\(133\) | 0.349425 | 0.0302990 | ||||||||
\(134\) | 12.5388 | − | 3.18240i | 1.08319 | − | 0.274917i | ||||
\(135\) | 3.50645 | + | 3.50645i | 0.301787 | + | 0.301787i | ||||
\(136\) | 0.0145980 | − | 0.367236i | 0.00125177 | − | 0.0314902i | ||||
\(137\) | −14.0186 | − | 14.0186i | −1.19769 | − | 1.19769i | −0.974857 | − | 0.222833i | \(-0.928470\pi\) |
−0.222833 | − | 0.974857i | \(-0.571530\pi\) | |||||||
\(138\) | −10.0185 | − | 5.96249i | −0.852835 | − | 0.507561i | ||||
\(139\) | − | 11.8700i | − | 1.00680i | −0.864053 | − | 0.503402i | \(-0.832082\pi\) | ||
0.864053 | − | 0.503402i | \(-0.167918\pi\) | |||||||
\(140\) | −2.99480 | + | 1.62485i | −0.253107 | + | 0.137325i | ||||
\(141\) | −7.35215 | − | 7.35215i | −0.619163 | − | 0.619163i | ||||
\(142\) | −12.4557 | + | 3.16132i | −1.04526 | + | 0.265292i | ||||
\(143\) | 14.3621 | + | 0.517197i | 1.20102 | + | 0.0432502i | ||||
\(144\) | 0.542570 | − | 0.834364i | 0.0452142 | − | 0.0695303i | ||||
\(145\) | −2.71726 | + | 2.71726i | −0.225656 | + | 0.225656i | ||||
\(146\) | 22.5448 | − | 5.72198i | 1.86582 | − | 0.473554i | ||||
\(147\) | −7.38599 | −0.609186 | ||||||||
\(148\) | −1.00655 | + | 3.39424i | −0.0827380 | + | 0.279005i | ||||
\(149\) | 1.95014 | − | 1.95014i | 0.159762 | − | 0.159762i | −0.622699 | − | 0.782461i | \(-0.713964\pi\) |
0.782461 | + | 0.622699i | \(0.213964\pi\) | |||||||
\(150\) | 1.30365 | − | 2.19047i | 0.106442 | − | 0.178851i | ||||
\(151\) | −6.31578 | + | 6.31578i | −0.513971 | + | 0.513971i | −0.915741 | − | 0.401770i | \(-0.868395\pi\) |
0.401770 | + | 0.915741i | \(0.368395\pi\) | |||||||
\(152\) | −0.393603 | − | 0.426190i | −0.0319254 | − | 0.0345686i | ||||
\(153\) | − | 0.0323311i | − | 0.00261382i | ||||||
\(154\) | −8.25216 | − | 4.91123i | −0.664978 | − | 0.395758i | ||||
\(155\) | −3.43189 | −0.275656 | ||||||||
\(156\) | 12.3202 | + | 4.14141i | 0.986405 | + | 0.331578i | ||||
\(157\) | −0.134883 | −0.0107648 | −0.00538240 | − | 0.999986i | \(-0.501713\pi\) | ||||
−0.00538240 | + | 0.999986i | \(0.501713\pi\) | |||||||
\(158\) | 3.78098 | + | 2.25023i | 0.300799 | + | 0.179019i | ||||
\(159\) | 5.68486i | 0.450839i | ||||||||
\(160\) | 5.35525 | + | 1.82244i | 0.423370 | + | 0.144077i | ||||
\(161\) | −5.50960 | + | 5.50960i | −0.434218 | + | 0.434218i | ||||
\(162\) | −7.00448 | + | 11.7694i | −0.550324 | + | 0.924688i | ||||
\(163\) | −13.3308 | + | 13.3308i | −1.04415 | + | 1.04415i | −0.0451734 | + | 0.998979i | \(0.514384\pi\) |
−0.998979 | + | 0.0451734i | \(0.985616\pi\) | |||||||
\(164\) | 12.1191 | + | 3.59387i | 0.946340 | + | 0.280634i | ||||
\(165\) | 7.18437 | 0.559303 | ||||||||
\(166\) | 21.8436 | − | 5.54401i | 1.69540 | − | 0.430299i | ||||
\(167\) | 11.9297 | − | 11.9297i | 0.923150 | − | 0.923150i | −0.0741008 | − | 0.997251i | \(-0.523609\pi\) |
0.997251 | + | 0.0741008i | \(0.0236087\pi\) | |||||||
\(168\) | −5.89251 | − | 6.38037i | −0.454617 | − | 0.492256i | ||||
\(169\) | −0.935082 | + | 12.9663i | −0.0719294 | + | 0.997410i | ||||
\(170\) | 0.178116 | − | 0.0452066i | 0.0136609 | − | 0.00346719i | ||||
\(171\) | −0.0360869 | − | 0.0360869i | −0.00275963 | − | 0.00275963i | ||||
\(172\) | 7.28305 | + | 13.4235i | 0.555327 | + | 1.02353i | ||||
\(173\) | − | 22.1130i | − | 1.68122i | −0.541641 | − | 0.840610i | \(-0.682197\pi\) | ||
0.541641 | − | 0.840610i | \(-0.317803\pi\) | |||||||
\(174\) | −8.41748 | − | 5.00963i | −0.638128 | − | 0.379779i | ||||
\(175\) | −1.20463 | − | 1.20463i | −0.0910611 | − | 0.0910611i | ||||
\(176\) | 3.30529 | + | 15.5972i | 0.249146 | + | 1.17569i | ||||
\(177\) | 17.4171 | + | 17.4171i | 1.30915 | + | 1.30915i | ||||
\(178\) | −20.4820 | + | 5.19842i | −1.53519 | + | 0.389638i | ||||
\(179\) | 12.1902 | 0.911140 | 0.455570 | − | 0.890200i | \(-0.349435\pi\) | ||||
0.455570 | + | 0.890200i | \(0.349435\pi\) | |||||||
\(180\) | 0.477095 | + | 0.141481i | 0.0355606 | + | 0.0105454i | ||||
\(181\) | − | 8.93090i | − | 0.663828i | −0.943310 | − | 0.331914i | \(-0.892306\pi\) | ||
0.943310 | − | 0.331914i | \(-0.107694\pi\) | |||||||
\(182\) | 4.70835 | − | 7.29999i | 0.349006 | − | 0.541111i | ||||
\(183\) | − | 10.6183i | − | 0.784929i | ||||||
\(184\) | 12.9262 | + | 0.513829i | 0.952931 | + | 0.0378800i | ||||
\(185\) | −1.77017 | −0.130145 | ||||||||
\(186\) | −2.15206 | − | 8.47921i | −0.157797 | − | 0.621726i | ||||
\(187\) | 0.366231 | + | 0.366231i | 0.0267814 | + | 0.0267814i | ||||
\(188\) | 11.0610 | + | 3.28011i | 0.806706 | + | 0.239227i | ||||
\(189\) | 5.97357 | + | 5.97357i | 0.434514 | + | 0.434514i | ||||
\(190\) | 0.148349 | − | 0.249265i | 0.0107624 | − | 0.0180836i | ||||
\(191\) | 27.1472i | 1.96430i | 0.188098 | + | 0.982150i | \(0.439768\pi\) | ||||
−0.188098 | + | 0.982150i | \(0.560232\pi\) | |||||||
\(192\) | −1.14458 | + | 14.3741i | −0.0826027 | + | 1.03736i | ||||
\(193\) | 11.0899 | + | 11.0899i | 0.798266 | + | 0.798266i | 0.982822 | − | 0.184556i | \(-0.0590846\pi\) |
−0.184556 | + | 0.982822i | \(0.559085\pi\) | |||||||
\(194\) | 4.73485 | + | 18.6555i | 0.339942 | + | 1.33939i | ||||
\(195\) | −0.233879 | + | 6.49461i | −0.0167485 | + | 0.465088i | ||||
\(196\) | 7.20355 | − | 3.90835i | 0.514540 | − | 0.279168i | ||||
\(197\) | 0.674322 | − | 0.674322i | 0.0480434 | − | 0.0480434i | −0.682677 | − | 0.730720i | \(-0.739184\pi\) |
0.730720 | + | 0.682677i | \(0.239184\pi\) | |||||||
\(198\) | 0.345034 | + | 1.35945i | 0.0245205 | + | 0.0966118i | ||||
\(199\) | 18.1270 | 1.28499 | 0.642495 | − | 0.766290i | \(-0.277899\pi\) | ||||
0.642495 | + | 0.766290i | \(0.277899\pi\) | |||||||
\(200\) | −0.112344 | + | 2.82620i | −0.00794393 | + | 0.199842i | ||||
\(201\) | −11.6585 | + | 11.6585i | −0.822329 | + | 0.822329i | ||||
\(202\) | −16.5463 | − | 9.84743i | −1.16419 | − | 0.692863i | ||||
\(203\) | −4.62911 | + | 4.62911i | −0.324900 | + | 0.324900i | ||||
\(204\) | 0.223385 | + | 0.411724i | 0.0156401 | + | 0.0288265i | ||||
\(205\) | 6.32036i | 0.441433i | ||||||||
\(206\) | 7.23328 | − | 12.1538i | 0.503966 | − | 0.846796i | ||||
\(207\) | 1.13801 | 0.0790971 | ||||||||
\(208\) | −14.2073 | + | 2.48020i | −0.985102 | + | 0.171971i | ||||
\(209\) | 0.817549 | 0.0565510 | ||||||||
\(210\) | 2.22089 | − | 3.73167i | 0.153256 | − | 0.257510i | ||||
\(211\) | − | 16.9704i | − | 1.16829i | −0.811649 | − | 0.584146i | \(-0.801430\pi\) | ||
0.811649 | − | 0.584146i | \(-0.198570\pi\) | |||||||
\(212\) | −3.00819 | − | 5.54445i | −0.206603 | − | 0.380794i | ||||
\(213\) | 11.5813 | − | 11.5813i | 0.793538 | − | 0.793538i | ||||
\(214\) | −14.3684 | − | 8.55126i | −0.982201 | − | 0.584552i | ||||
\(215\) | −5.39946 | + | 5.39946i | −0.368240 | + | 0.368240i | ||||
\(216\) | 0.557099 | − | 14.0147i | 0.0379058 | − | 0.953581i | ||||
\(217\) | −5.84656 | −0.396891 | ||||||||
\(218\) | −1.29323 | − | 5.09537i | −0.0875884 | − | 0.345102i | ||||
\(219\) | −20.9621 | + | 20.9621i | −1.41649 | + | 1.41649i | ||||
\(220\) | −7.00692 | + | 3.80167i | −0.472407 | + | 0.256308i | ||||
\(221\) | −0.342991 | + | 0.319147i | −0.0230721 | + | 0.0214681i | ||||
\(222\) | −1.11003 | − | 4.37357i | −0.0745005 | − | 0.293535i | ||||
\(223\) | −15.0119 | − | 15.0119i | −1.00527 | − | 1.00527i | −0.999986 | − | 0.00528284i | \(-0.998318\pi\) |
−0.00528284 | − | 0.999986i | \(-0.501682\pi\) | |||||||
\(224\) | 9.12319 | + | 3.10471i | 0.609569 | + | 0.207442i | ||||
\(225\) | 0.248815i | 0.0165877i | ||||||||
\(226\) | 2.38499 | − | 4.00740i | 0.158647 | − | 0.266569i | ||||
\(227\) | −3.96857 | − | 3.96857i | −0.263403 | − | 0.263403i | 0.563032 | − | 0.826435i | \(-0.309635\pi\) |
−0.826435 | + | 0.563032i | \(0.809635\pi\) | |||||||
\(228\) | 0.708887 | + | 0.210219i | 0.0469472 | + | 0.0139221i | ||||
\(229\) | 18.9098 | + | 18.9098i | 1.24959 | + | 1.24959i | 0.955900 | + | 0.293692i | \(0.0948841\pi\) |
0.293692 | + | 0.955900i | \(0.405116\pi\) | |||||||
\(230\) | 1.59121 | + | 6.26942i | 0.104921 | + | 0.413393i | ||||
\(231\) | 12.2393 | 0.805286 | ||||||||
\(232\) | 10.8605 | + | 0.431714i | 0.713024 | + | 0.0283434i | ||||
\(233\) | − | 1.37159i | − | 0.0898559i | −0.998990 | − | 0.0449280i | \(-0.985694\pi\) | ||
0.998990 | − | 0.0449280i | \(-0.0143058\pi\) | |||||||
\(234\) | −1.24016 | + | 0.267652i | −0.0810719 | + | 0.0174970i | ||||
\(235\) | 5.76855i | 0.376299i | ||||||||
\(236\) | −26.2033 | − | 7.77053i | −1.70569 | − | 0.505818i | ||||
\(237\) | −5.60781 | −0.364266 | ||||||||
\(238\) | 0.303438 | − | 0.0770138i | 0.0196689 | − | 0.00499206i | ||||
\(239\) | −14.1896 | − | 14.1896i | −0.917847 | − | 0.917847i | 0.0790252 | − | 0.996873i | \(-0.474819\pi\) |
−0.996873 | + | 0.0790252i | \(0.974819\pi\) | |||||||
\(240\) | −7.05316 | + | 1.49467i | −0.455279 | + | 0.0964807i | ||||
\(241\) | 3.26599 | + | 3.26599i | 0.210381 | + | 0.210381i | 0.804429 | − | 0.594048i | \(-0.202471\pi\) |
−0.594048 | + | 0.804429i | \(0.702471\pi\) | |||||||
\(242\) | −5.93953 | − | 3.53488i | −0.381807 | − | 0.227231i | ||||
\(243\) | − | 2.57927i | − | 0.165460i | ||||||
\(244\) | 5.61876 | + | 10.3560i | 0.359704 | + | 0.662978i | ||||
\(245\) | 2.89755 | + | 2.89755i | 0.185118 | + | 0.185118i | ||||
\(246\) | −15.6158 | + | 3.96335i | −0.995625 | + | 0.252694i | ||||
\(247\) | −0.0266144 | + | 0.739056i | −0.00169343 | + | 0.0470250i | ||||
\(248\) | 6.58574 | + | 7.13099i | 0.418195 | + | 0.452819i | ||||
\(249\) | −20.3102 | + | 20.3102i | −1.28710 | + | 1.28710i | ||||
\(250\) | −1.37075 | + | 0.347903i | −0.0866940 | + | 0.0220033i | ||||
\(251\) | 11.0760 | 0.699108 | 0.349554 | − | 0.936916i | \(-0.386333\pi\) | ||||
0.349554 | + | 0.936916i | \(0.386333\pi\) | |||||||
\(252\) | 0.812778 | + | 0.241027i | 0.0512002 | + | 0.0151833i | ||||
\(253\) | −12.8908 | + | 12.8908i | −0.810437 | + | 0.810437i | ||||
\(254\) | −8.51574 | + | 14.3087i | −0.534325 | + | 0.897807i | ||||
\(255\) | −0.165612 | + | 0.165612i | −0.0103710 | + | 0.0103710i | ||||
\(256\) | −6.48984 | − | 14.6247i | −0.405615 | − | 0.914044i | ||||
\(257\) | 4.31539i | 0.269187i | 0.990901 | + | 0.134593i | \(0.0429728\pi\) | ||||
−0.990901 | + | 0.134593i | \(0.957027\pi\) | |||||||
\(258\) | −16.7264 | − | 9.95463i | −1.04134 | − | 0.619748i | ||||
\(259\) | −3.01566 | −0.187384 | ||||||||
\(260\) | −3.20857 | − | 6.45795i | −0.198987 | − | 0.400505i | ||||
\(261\) | 0.956144 | 0.0591838 | ||||||||
\(262\) | 9.70318 | + | 5.77480i | 0.599464 | + | 0.356768i | ||||
\(263\) | 5.51741i | 0.340218i | 0.985425 | + | 0.170109i | \(0.0544120\pi\) | ||||
−0.985425 | + | 0.170109i | \(0.945588\pi\) | |||||||
\(264\) | −13.7867 | − | 14.9281i | −0.848512 | − | 0.918763i | ||||
\(265\) | 2.23019 | − | 2.23019i | 0.137000 | − | 0.137000i | ||||
\(266\) | 0.252727 | − | 0.424647i | 0.0154957 | − | 0.0260368i | ||||
\(267\) | 19.0441 | − | 19.0441i | 1.16548 | − | 1.16548i | ||||
\(268\) | 5.20136 | − | 17.5397i | 0.317724 | − | 1.07141i | ||||
\(269\) | 4.03912 | 0.246270 | 0.123135 | − | 0.992390i | \(-0.460705\pi\) | ||||
0.123135 | + | 0.992390i | \(0.460705\pi\) | |||||||
\(270\) | 6.79738 | − | 1.72520i | 0.413675 | − | 0.104993i | ||||
\(271\) | 7.11595 | − | 7.11595i | 0.432263 | − | 0.432263i | −0.457134 | − | 0.889398i | \(-0.651124\pi\) |
0.889398 | + | 0.457134i | \(0.151124\pi\) | |||||||
\(272\) | −0.435734 | − | 0.283349i | −0.0264203 | − | 0.0171806i | ||||
\(273\) | −0.398436 | + | 11.0642i | −0.0241145 | + | 0.669636i | ||||
\(274\) | −27.1756 | + | 6.89728i | −1.64174 | + | 0.416680i | ||||
\(275\) | −2.81846 | − | 2.81846i | −0.169959 | − | 0.169959i | ||||
\(276\) | −14.4921 | + | 7.86282i | −0.872322 | + | 0.473286i | ||||
\(277\) | 3.87573i | 0.232870i | 0.993198 | + | 0.116435i | \(0.0371467\pi\) | ||||
−0.993198 | + | 0.116435i | \(0.962853\pi\) | |||||||
\(278\) | −14.4253 | − | 8.58517i | −0.865174 | − | 0.514904i | ||||
\(279\) | 0.603804 | + | 0.603804i | 0.0361488 | + | 0.0361488i | ||||
\(280\) | −0.191389 | + | 4.81470i | −0.0114377 | + | 0.287733i | ||||
\(281\) | 11.0563 | + | 11.0563i | 0.659561 | + | 0.659561i | 0.955276 | − | 0.295715i | \(-0.0955580\pi\) |
−0.295715 | + | 0.955276i | \(0.595558\pi\) | |||||||
\(282\) | −14.2524 | + | 3.61733i | −0.848719 | + | 0.215409i | ||||
\(283\) | −7.53745 | −0.448055 | −0.224027 | − | 0.974583i | \(-0.571920\pi\) | ||||
−0.224027 | + | 0.974583i | \(0.571920\pi\) | |||||||
\(284\) | −5.16691 | + | 17.4236i | −0.306600 | + | 1.03390i | ||||
\(285\) | 0.369700i | 0.0218991i | ||||||||
\(286\) | 11.0161 | − | 17.0798i | 0.651395 | − | 1.00995i | ||||
\(287\) | 10.7673i | 0.635576i | ||||||||
\(288\) | −0.621559 | − | 1.26284i | −0.0366257 | − | 0.0744134i | ||||
\(289\) | 16.9831 | 0.999007 | ||||||||
\(290\) | 1.33692 | + | 5.26751i | 0.0785064 | + | 0.309319i | ||||
\(291\) | −17.3458 | − | 17.3458i | −1.01683 | − | 1.01683i | ||||
\(292\) | 9.35210 | − | 31.5366i | 0.547290 | − | 1.84554i | ||||
\(293\) | −8.60612 | − | 8.60612i | −0.502775 | − | 0.502775i | 0.409524 | − | 0.912299i | \(-0.365695\pi\) |
−0.912299 | + | 0.409524i | \(0.865695\pi\) | |||||||
\(294\) | −5.34202 | + | 8.97599i | −0.311553 | + | 0.523490i | ||||
\(295\) | − | 13.6656i | − | 0.795643i | ||||||
\(296\) | 3.39692 | + | 3.67817i | 0.197442 | + | 0.213789i | ||||
\(297\) | 13.9763 | + | 13.9763i | 0.810990 | + | 0.810990i | ||||
\(298\) | −0.959488 | − | 3.78042i | −0.0555816 | − | 0.218994i | ||||
\(299\) | −11.2335 | − | 12.0728i | −0.649651 | − | 0.698188i | ||||
\(300\) | −1.71913 | − | 3.16857i | −0.0992543 | − | 0.182937i | ||||
\(301\) | −9.19851 | + | 9.19851i | −0.530194 | + | 0.530194i | ||||
\(302\) | 3.10742 | + | 12.2434i | 0.178812 | + | 0.704527i | ||||
\(303\) | 24.5408 | 1.40983 | ||||||||
\(304\) | −0.802616 | + | 0.170087i | −0.0460332 | + | 0.00975514i | ||||
\(305\) | −4.16561 | + | 4.16561i | −0.238522 | + | 0.238522i | ||||
\(306\) | −0.0392911 | − | 0.0233839i | −0.00224612 | − | 0.00133677i | ||||
\(307\) | −1.42049 | + | 1.42049i | −0.0810716 | + | 0.0810716i | −0.746480 | − | 0.665408i | \(-0.768258\pi\) |
0.665408 | + | 0.746480i | \(0.268258\pi\) | |||||||
\(308\) | −11.9370 | + | 6.47651i | −0.680172 | + | 0.369033i | ||||
\(309\) | 18.0261i | 1.02547i | ||||||||
\(310\) | −2.48216 | + | 4.17069i | −0.140977 | + | 0.236879i | ||||
\(311\) | −20.6745 | −1.17234 | −0.586172 | − | 0.810186i | \(-0.699366\pi\) | ||||
−0.586172 | + | 0.810186i | \(0.699366\pi\) | |||||||
\(312\) | 13.9437 | − | 11.9771i | 0.789406 | − | 0.678068i | ||||
\(313\) | −24.9530 | −1.41043 | −0.705213 | − | 0.708996i | \(-0.749149\pi\) | ||||
−0.705213 | + | 0.708996i | \(0.749149\pi\) | |||||||
\(314\) | −0.0975557 | + | 0.163919i | −0.00550539 | + | 0.00925049i | ||||
\(315\) | 0.423881i | 0.0238830i | ||||||||
\(316\) | 5.46930 | − | 2.96741i | 0.307672 | − | 0.166930i | ||||
\(317\) | 19.1560 | − | 19.1560i | 1.07591 | − | 1.07591i | 0.0790380 | − | 0.996872i | \(-0.474815\pi\) |
0.996872 | − | 0.0790380i | \(-0.0251848\pi\) | |||||||
\(318\) | 6.90866 | + | 4.11166i | 0.387419 | + | 0.230570i | ||||
\(319\) | −10.8307 | + | 10.8307i | −0.606404 | + | 0.606404i | ||||
\(320\) | 6.08803 | − | 5.18998i | 0.340331 | − | 0.290129i | ||||
\(321\) | 21.3106 | 1.18944 | ||||||||
\(322\) | 2.71078 | + | 10.6806i | 0.151066 | + | 0.595205i | ||||
\(323\) | −0.0188458 | + | 0.0188458i | −0.00104861 | + | 0.00104861i | ||||
\(324\) | 9.23690 | + | 17.0247i | 0.513161 | + | 0.945817i | ||||
\(325\) | 2.63961 | − | 2.45611i | 0.146419 | − | 0.136240i | ||||
\(326\) | 6.55890 | + | 25.8423i | 0.363264 | + | 1.43128i | ||||
\(327\) | 4.73766 | + | 4.73766i | 0.261993 | + | 0.261993i | ||||
\(328\) | 13.1328 | − | 12.1287i | 0.725139 | − | 0.669693i | ||||
\(329\) | 9.82730i | 0.541796i | ||||||||
\(330\) | 5.19620 | − | 8.73098i | 0.286041 | − | 0.480625i | ||||
\(331\) | 10.3712 | + | 10.3712i | 0.570053 | + | 0.570053i | 0.932143 | − | 0.362090i | \(-0.117937\pi\) |
−0.362090 | + | 0.932143i | \(0.617937\pi\) | |||||||
\(332\) | 9.06123 | − | 30.5558i | 0.497300 | − | 1.67697i | ||||
\(333\) | 0.311442 | + | 0.311442i | 0.0170669 | + | 0.0170669i | ||||
\(334\) | −5.86954 | − | 23.1262i | −0.321167 | − | 1.26541i | ||||
\(335\) | 9.14736 | 0.499774 | ||||||||
\(336\) | −12.0157 | + | 2.54632i | −0.655512 | + | 0.138913i | ||||
\(337\) | − | 8.81143i | − | 0.479989i | −0.970774 | − | 0.239995i | \(-0.922854\pi\) | ||
0.970774 | − | 0.239995i | \(-0.0771457\pi\) | |||||||
\(338\) | 15.0813 | + | 10.5145i | 0.820316 | + | 0.571911i | ||||
\(339\) | 5.94363i | 0.322814i | ||||||||
\(340\) | 0.0738864 | − | 0.249156i | 0.00400705 | − | 0.0135124i | ||||
\(341\) | −13.6792 | −0.740769 | ||||||||
\(342\) | −0.0699558 | + | 0.0177551i | −0.00378278 | + | 0.000960085i | ||||
\(343\) | 13.3686 | + | 13.3686i | 0.721839 | + | 0.721839i | ||||
\(344\) | 21.5808 | + | 0.857859i | 1.16356 | + | 0.0462527i | ||||
\(345\) | −5.82929 | − | 5.82929i | −0.313838 | − | 0.313838i | ||||
\(346\) | −26.8733 | − | 15.9935i | −1.44472 | − | 0.859818i | ||||
\(347\) | 26.6526i | 1.43078i | 0.698723 | + | 0.715392i | \(0.253752\pi\) | ||||
−0.698723 | + | 0.715392i | \(0.746248\pi\) | |||||||
\(348\) | −12.1761 | + | 6.60626i | −0.652709 | + | 0.354133i | ||||
\(349\) | −1.40597 | − | 1.40597i | −0.0752601 | − | 0.0752601i | 0.668475 | − | 0.743735i | \(-0.266947\pi\) |
−0.743735 | + | 0.668475i | \(0.766947\pi\) | |||||||
\(350\) | −2.33521 | + | 0.592687i | −0.124822 | + | 0.0316804i | ||||
\(351\) | −13.0895 | + | 12.1795i | −0.698664 | + | 0.650094i | ||||
\(352\) | 21.3455 | + | 7.26408i | 1.13772 | + | 0.387177i | ||||
\(353\) | 1.08177 | − | 1.08177i | 0.0575770 | − | 0.0575770i | −0.677732 | − | 0.735309i | \(-0.737037\pi\) |
0.735309 | + | 0.677732i | \(0.237037\pi\) | |||||||
\(354\) | 33.7638 | − | 8.56939i | 1.79452 | − | 0.455458i | ||||
\(355\) | −9.08677 | −0.482276 | ||||||||
\(356\) | −8.49639 | + | 28.6510i | −0.450308 | + | 1.51850i | ||||
\(357\) | −0.282136 | + | 0.282136i | −0.0149322 | + | 0.0149322i | ||||
\(358\) | 8.81675 | − | 14.8145i | 0.465980 | − | 0.782968i | ||||
\(359\) | −2.87994 | + | 2.87994i | −0.151998 | + | 0.151998i | −0.779010 | − | 0.627012i | \(-0.784278\pi\) |
0.627012 | + | 0.779010i | \(0.284278\pi\) | |||||||
\(360\) | 0.517004 | − | 0.477472i | 0.0272485 | − | 0.0251650i | ||||
\(361\) | − | 18.9579i | − | 0.997786i | ||||||
\(362\) | −10.8535 | − | 6.45940i | −0.570446 | − | 0.339498i | ||||
\(363\) | 8.80929 | 0.462368 | ||||||||
\(364\) | −5.46611 | − | 11.0017i | −0.286502 | − | 0.576648i | ||||
\(365\) | 16.4470 | 0.860877 | ||||||||
\(366\) | −12.9042 | − | 7.67985i | −0.674511 | − | 0.401432i | ||||
\(367\) | 14.7250i | 0.768639i | 0.923200 | + | 0.384319i | \(0.125564\pi\) | ||||
−0.923200 | + | 0.384319i | \(0.874436\pi\) | |||||||
\(368\) | 9.97349 | − | 15.3372i | 0.519904 | − | 0.799508i | ||||
\(369\) | 1.11200 | − | 1.11200i | 0.0578883 | − | 0.0578883i | ||||
\(370\) | −1.28030 | + | 2.15124i | −0.0665596 | + | 0.111838i | ||||
\(371\) | 3.79935 | − | 3.79935i | 0.197253 | − | 0.197253i | ||||
\(372\) | −11.8611 | − | 3.51736i | −0.614967 | − | 0.182367i | ||||
\(373\) | 5.16533 | 0.267450 | 0.133725 | − | 0.991018i | \(-0.457306\pi\) | ||||
0.133725 | + | 0.991018i | \(0.457306\pi\) | |||||||
\(374\) | 0.709952 | − | 0.180189i | 0.0367107 | − | 0.00931735i | ||||
\(375\) | 1.27452 | − | 1.27452i | 0.0658161 | − | 0.0658161i | ||||
\(376\) | 11.9863 | − | 11.0698i | 0.618144 | − | 0.570879i | ||||
\(377\) | −9.43828 | − | 10.1434i | −0.486096 | − | 0.522414i | ||||
\(378\) | 11.5800 | − | 2.93905i | 0.595611 | − | 0.151169i | ||||
\(379\) | −7.51825 | − | 7.51825i | −0.386187 | − | 0.386187i | 0.487138 | − | 0.873325i | \(-0.338041\pi\) |
−0.873325 | + | 0.487138i | \(0.838041\pi\) | |||||||
\(380\) | −0.195630 | − | 0.360569i | −0.0100356 | − | 0.0184968i | ||||
\(381\) | − | 21.2221i | − | 1.08724i | ||||||
\(382\) | 32.9912 | + | 19.6346i | 1.68798 | + | 1.00459i | ||||
\(383\) | 8.07375 | + | 8.07375i | 0.412549 | + | 0.412549i | 0.882626 | − | 0.470076i | \(-0.155774\pi\) |
−0.470076 | + | 0.882626i | \(0.655774\pi\) | |||||||
\(384\) | 16.6406 | + | 11.7872i | 0.849187 | + | 0.601514i | ||||
\(385\) | −4.80152 | − | 4.80152i | −0.244708 | − | 0.244708i | ||||
\(386\) | 21.4981 | − | 5.45632i | 1.09423 | − | 0.277719i | ||||
\(387\) | 1.89995 | 0.0965801 | ||||||||
\(388\) | 26.0961 | + | 7.73872i | 1.32483 | + | 0.392874i | ||||
\(389\) | − | 18.5117i | − | 0.938578i | −0.883045 | − | 0.469289i | \(-0.844510\pi\) | ||
0.883045 | − | 0.469289i | \(-0.155490\pi\) | |||||||
\(390\) | 7.72356 | + | 4.98154i | 0.391098 | + | 0.252250i | ||||
\(391\) | − | 0.594308i | − | 0.0300554i | ||||||
\(392\) | 0.460359 | − | 11.5811i | 0.0232516 | − | 0.584932i | ||||
\(393\) | −14.3914 | −0.725949 | ||||||||
\(394\) | −0.331773 | − | 1.30720i | −0.0167145 | − | 0.0658557i | ||||
\(395\) | 2.19996 | + | 2.19996i | 0.110692 | + | 0.110692i | ||||
\(396\) | 1.90165 | + | 0.563930i | 0.0955617 | + | 0.0283385i | ||||
\(397\) | −23.7739 | − | 23.7739i | −1.19318 | − | 1.19318i | −0.976170 | − | 0.217008i | \(-0.930370\pi\) |
−0.217008 | − | 0.976170i | \(-0.569630\pi\) | |||||||
\(398\) | 13.1106 | − | 22.0293i | 0.657176 | − | 1.10423i | ||||
\(399\) | 0.629820i | 0.0315305i | ||||||||
\(400\) | 3.35334 | + | 2.18061i | 0.167667 | + | 0.109031i | ||||
\(401\) | 18.0427 | + | 18.0427i | 0.901011 | + | 0.901011i | 0.995524 | − | 0.0945126i | \(-0.0301292\pi\) |
−0.0945126 | + | 0.995524i | \(0.530129\pi\) | |||||||
\(402\) | 5.73610 | + | 22.6005i | 0.286091 | + | 1.12721i | ||||
\(403\) | 0.445311 | − | 12.3658i | 0.0221825 | − | 0.615987i | ||||
\(404\) | −23.9346 | + | 12.9859i | −1.19079 | + | 0.646075i | ||||
\(405\) | −6.84800 | + | 6.84800i | −0.340280 | + | 0.340280i | ||||
\(406\) | 2.27757 | + | 8.97371i | 0.113034 | + | 0.445358i | ||||
\(407\) | −7.05572 | −0.349739 | ||||||||
\(408\) | 0.661924 | + | 0.0263121i | 0.0327701 | + | 0.00130265i | ||||
\(409\) | 20.2935 | − | 20.2935i | 1.00345 | − | 1.00345i | 0.00345338 | − | 0.999994i | \(-0.498901\pi\) |
0.999994 | − | 0.00345338i | \(-0.00109925\pi\) | |||||||
\(410\) | 7.68096 | + | 4.57129i | 0.379336 | + | 0.225760i | ||||
\(411\) | 25.2678 | − | 25.2678i | 1.24637 | − | 1.24637i | ||||
\(412\) | −9.53862 | − | 17.5808i | −0.469934 | − | 0.866145i | ||||
\(413\) | − | 23.2807i | − | 1.14557i | ||||||
\(414\) | 0.823081 | − | 1.38299i | 0.0404522 | − | 0.0679703i | ||||
\(415\) | 15.9355 | 0.782243 | ||||||||
\(416\) | −7.26154 | + | 19.0596i | −0.356026 | + | 0.934476i | ||||
\(417\) | 21.3951 | 1.04772 | ||||||||
\(418\) | 0.591304 | − | 0.993545i | 0.0289216 | − | 0.0485959i | ||||
\(419\) | 9.76105i | 0.476858i | 0.971160 | + | 0.238429i | \(0.0766325\pi\) | ||||
−0.971160 | + | 0.238429i | \(0.923367\pi\) | |||||||
\(420\) | −2.92871 | − | 5.39797i | −0.142907 | − | 0.263394i | ||||
\(421\) | 15.5421 | − | 15.5421i | 0.757477 | − | 0.757477i | −0.218385 | − | 0.975863i | \(-0.570079\pi\) |
0.975863 | + | 0.218385i | \(0.0700790\pi\) | |||||||
\(422\) | −20.6237 | − | 12.2741i | −1.00395 | − | 0.597493i | ||||
\(423\) | 1.01491 | − | 1.01491i | 0.0493468 | − | 0.0493468i | ||||
\(424\) | −8.91374 | − | 0.354330i | −0.432889 | − | 0.0172078i | ||||
\(425\) | 0.129940 | 0.00630302 | ||||||||
\(426\) | −5.69811 | − | 22.4508i | −0.276074 | − | 1.08774i | ||||
\(427\) | −7.09652 | + | 7.09652i | −0.343425 | + | 0.343425i | ||||
\(428\) | −20.7842 | + | 11.2767i | −1.00464 | + | 0.545078i | ||||
\(429\) | −0.932220 | + | 25.8869i | −0.0450080 | + | 1.24983i | ||||
\(430\) | 2.65659 | + | 10.4671i | 0.128112 | + | 0.504767i | ||||
\(431\) | −18.6396 | − | 18.6396i | −0.897836 | − | 0.897836i | 0.0974082 | − | 0.995245i | \(-0.468945\pi\) |
−0.995245 | + | 0.0974082i | \(0.968945\pi\) | |||||||
\(432\) | −16.6288 | − | 10.8134i | −0.800053 | − | 0.520259i | ||||
\(433\) | − | 17.1797i | − | 0.825602i | −0.910821 | − | 0.412801i | \(-0.864550\pi\) | ||
0.910821 | − | 0.412801i | \(-0.135450\pi\) | |||||||
\(434\) | −4.22861 | + | 7.10517i | −0.202980 | + | 0.341059i | ||||
\(435\) | −4.89771 | − | 4.89771i | −0.234827 | − | 0.234827i | ||||
\(436\) | −7.12761 | − | 2.11367i | −0.341351 | − | 0.101227i | ||||
\(437\) | −0.663346 | − | 0.663346i | −0.0317322 | − | 0.0317322i | ||||
\(438\) | 10.3136 | + | 40.6359i | 0.492801 | + | 1.94166i | ||||
\(439\) | −15.3214 | −0.731251 | −0.365626 | − | 0.930762i | \(-0.619145\pi\) | ||||
−0.365626 | + | 0.930762i | \(0.619145\pi\) | |||||||
\(440\) | −0.447793 | + | 11.2649i | −0.0213477 | + | 0.537035i | ||||
\(441\) | − | 1.01958i | − | 0.0485517i | ||||||
\(442\) | 0.139777 | + | 0.647656i | 0.00664853 | + | 0.0308058i | ||||
\(443\) | − | 28.2978i | − | 1.34447i | −0.740339 | − | 0.672233i | \(-0.765335\pi\) | ||
0.740339 | − | 0.672233i | \(-0.234665\pi\) | |||||||
\(444\) | −6.11793 | − | 1.81426i | −0.290344 | − | 0.0861008i | ||||
\(445\) | −14.9421 | −0.708326 | ||||||||
\(446\) | −29.1011 | + | 7.38598i | −1.37798 | + | 0.349736i | ||||
\(447\) | 3.51503 | + | 3.51503i | 0.166255 | + | 0.166255i | ||||
\(448\) | 10.3715 | − | 8.84164i | 0.490010 | − | 0.417728i | ||||
\(449\) | −17.5795 | − | 17.5795i | −0.829629 | − | 0.829629i | 0.157836 | − | 0.987465i | \(-0.449548\pi\) |
−0.987465 | + | 0.157836i | \(0.949548\pi\) | |||||||
\(450\) | 0.302379 | + | 0.179959i | 0.0142543 | + | 0.00848336i | ||||
\(451\) | 25.1923i | 1.18626i | ||||||||
\(452\) | −3.14512 | − | 5.79682i | −0.147934 | − | 0.272660i | ||||
\(453\) | −11.3839 | − | 11.3839i | −0.534860 | − | 0.534860i | ||||
\(454\) | −7.69321 | + | 1.95257i | −0.361060 | + | 0.0916387i | ||||
\(455\) | 4.49683 | − | 4.18422i | 0.210815 | − | 0.196159i | ||||
\(456\) | 0.768186 | − | 0.709448i | 0.0359736 | − | 0.0332230i | ||||
\(457\) | 6.18802 | − | 6.18802i | 0.289463 | − | 0.289463i | −0.547405 | − | 0.836868i | \(-0.684384\pi\) |
0.836868 | + | 0.547405i | \(0.184384\pi\) | |||||||
\(458\) | 36.6573 | − | 9.30378i | 1.71288 | − | 0.434737i | ||||
\(459\) | −0.644356 | −0.0300759 | ||||||||
\(460\) | 8.76992 | + | 2.60070i | 0.408900 | + | 0.121258i | ||||
\(461\) | −5.70215 | + | 5.70215i | −0.265576 | + | 0.265576i | −0.827315 | − | 0.561739i | \(-0.810133\pi\) |
0.561739 | + | 0.827315i | \(0.310133\pi\) | |||||||
\(462\) | 8.85223 | − | 14.8741i | 0.411843 | − | 0.692005i | ||||
\(463\) | −12.6056 | + | 12.6056i | −0.585831 | + | 0.585831i | −0.936500 | − | 0.350668i | \(-0.885954\pi\) |
0.350668 | + | 0.936500i | \(0.385954\pi\) | |||||||
\(464\) | 8.37963 | − | 12.8862i | 0.389014 | − | 0.598226i | ||||
\(465\) | − | 6.18580i | − | 0.286860i | ||||||
\(466\) | −1.66686 | − | 0.992022i | −0.0772157 | − | 0.0459545i | ||||
\(467\) | 2.92501 | 0.135353 | 0.0676766 | − | 0.997707i | \(-0.478441\pi\) | ||||
0.0676766 | + | 0.997707i | \(0.478441\pi\) | |||||||
\(468\) | −0.571693 | + | 1.70072i | −0.0264265 | + | 0.0786157i | ||||
\(469\) | 15.5834 | 0.719576 | ||||||||
\(470\) | 7.01037 | + | 4.17219i | 0.323364 | + | 0.192449i | ||||
\(471\) | − | 0.243119i | − | 0.0112023i | ||||||
\(472\) | −28.3953 | + | 26.2241i | −1.30700 | + | 1.20706i | ||||
\(473\) | −21.5217 | + | 21.5217i | −0.989570 | + | 0.989570i | ||||
\(474\) | −4.05593 | + | 6.81502i | −0.186295 | + | 0.313024i | ||||
\(475\) | 0.145035 | − | 0.145035i | 0.00665465 | − | 0.00665465i | ||||
\(476\) | 0.125873 | − | 0.424461i | 0.00576937 | − | 0.0194551i | ||||
\(477\) | −0.784757 | −0.0359315 | ||||||||
\(478\) | −27.5070 | + | 6.98140i | −1.25814 | + | 0.319322i | ||||
\(479\) | 16.7931 | − | 16.7931i | 0.767298 | − | 0.767298i | −0.210332 | − | 0.977630i | \(-0.567454\pi\) |
0.977630 | + | 0.210332i | \(0.0674545\pi\) | |||||||
\(480\) | −3.28486 | + | 9.65255i | −0.149933 | + | 0.440577i | ||||
\(481\) | 0.229691 | − | 6.37830i | 0.0104730 | − | 0.290825i | ||||
\(482\) | 6.33125 | − | 1.60690i | 0.288381 | − | 0.0731922i | ||||
\(483\) | −9.93077 | − | 9.93077i | −0.451866 | − | 0.451866i | ||||
\(484\) | −8.59170 | + | 4.66150i | −0.390532 | + | 0.211886i | ||||
\(485\) | 13.6097i | 0.617984i | ||||||||
\(486\) | −3.13452 | − | 1.86549i | −0.142185 | − | 0.0846206i | ||||
\(487\) | −1.21797 | − | 1.21797i | −0.0551916 | − | 0.0551916i | 0.678972 | − | 0.734164i | \(-0.262426\pi\) |
−0.734164 | + | 0.678972i | \(0.762426\pi\) | |||||||
\(488\) | 16.6493 | + | 0.661826i | 0.753677 | + | 0.0299594i | ||||
\(489\) | −24.0281 | − | 24.0281i | −1.08659 | − | 1.08659i | ||||
\(490\) | 5.61701 | − | 1.42562i | 0.253751 | − | 0.0644030i | ||||
\(491\) | 1.56917 | 0.0708155 | 0.0354077 | − | 0.999373i | \(-0.488727\pi\) | ||||
0.0354077 | + | 0.999373i | \(0.488727\pi\) | |||||||
\(492\) | −6.47777 | + | 21.8440i | −0.292040 | + | 0.984802i | ||||
\(493\) | − | 0.499332i | − | 0.0224888i | ||||||
\(494\) | 0.878906 | + | 0.566876i | 0.0395438 | + | 0.0255050i | ||||
\(495\) | 0.991754i | 0.0445760i | ||||||||
\(496\) | 13.4293 | − | 2.84588i | 0.602995 | − | 0.127784i | ||||
\(497\) | −15.4802 | −0.694382 | ||||||||
\(498\) | 9.99279 | + | 39.3720i | 0.447788 | + | 1.76430i | ||||
\(499\) | 24.2108 | + | 24.2108i | 1.08383 | + | 1.08383i | 0.996149 | + | 0.0876770i | \(0.0279443\pi\) |
0.0876770 | + | 0.996149i | \(0.472056\pi\) | |||||||
\(500\) | −0.568619 | + | 1.91747i | −0.0254294 | + | 0.0857516i | ||||
\(501\) | 21.5027 | + | 21.5027i | 0.960670 | + | 0.960670i | ||||
\(502\) | 8.01084 | − | 13.4603i | 0.357541 | − | 0.600763i | ||||
\(503\) | − | 29.3584i | − | 1.30902i | −0.756052 | − | 0.654512i | \(-0.772874\pi\) | ||
0.756052 | − | 0.654512i | \(-0.227126\pi\) | |||||||
\(504\) | 0.880767 | − | 0.813421i | 0.0392325 | − | 0.0362327i | ||||
\(505\) | −9.62744 | − | 9.62744i | −0.428416 | − | 0.428416i | ||||
\(506\) | 6.34239 | + | 24.9893i | 0.281954 | + | 1.11091i | ||||
\(507\) | −23.3711 | − | 1.68544i | −1.03795 | − | 0.0748528i | ||||
\(508\) | 11.2298 | + | 20.6979i | 0.498243 | + | 0.918321i | ||||
\(509\) | −26.9394 | + | 26.9394i | −1.19407 | + | 1.19407i | −0.218152 | + | 0.975915i | \(0.570003\pi\) |
−0.975915 | + | 0.218152i | \(0.929997\pi\) | |||||||
\(510\) | 0.0814825 | + | 0.321044i | 0.00360810 | + | 0.0142161i | ||||
\(511\) | 28.0191 | 1.23949 | ||||||||
\(512\) | −22.4669 | − | 2.69059i | −0.992905 | − | 0.118908i | ||||
\(513\) | −0.719208 | + | 0.719208i | −0.0317538 | + | 0.0317538i | ||||
\(514\) | 5.24438 | + | 3.12117i | 0.231320 | + | 0.137669i | ||||
\(515\) | 7.07169 | − | 7.07169i | 0.311616 | − | 0.311616i | ||||
\(516\) | −24.1952 | + | 13.1273i | −1.06513 | + | 0.577897i | ||||
\(517\) | 22.9929i | 1.01123i | ||||||||
\(518\) | −2.18112 | + | 3.66485i | −0.0958327 | + | 0.161024i | ||||
\(519\) | 39.8575 | 1.74955 | ||||||||
\(520\) | −10.1688 | − | 0.771518i | −0.445932 | − | 0.0338333i | ||||
\(521\) | 6.81322 | 0.298493 | 0.149246 | − | 0.988800i | \(-0.452315\pi\) | ||||
0.149246 | + | 0.988800i | \(0.452315\pi\) | |||||||
\(522\) | 0.691544 | − | 1.16198i | 0.0302681 | − | 0.0508583i | ||||
\(523\) | 15.8116i | 0.691395i | 0.938346 | + | 0.345697i | \(0.112358\pi\) | ||||
−0.938346 | + | 0.345697i | \(0.887642\pi\) | |||||||
\(524\) | 14.0359 | − | 7.61531i | 0.613162 | − | 0.332676i | ||||
\(525\) | 2.17127 | − | 2.17127i | 0.0947622 | − | 0.0947622i | ||||
\(526\) | 6.70516 | + | 3.99054i | 0.292359 | + | 0.173996i | ||||
\(527\) | 0.315328 | − | 0.315328i | 0.0137359 | − | 0.0137359i | ||||
\(528\) | −28.1132 | + | 5.95761i | −1.22347 | + | 0.259272i | ||||
\(529\) | −2.08122 | −0.0904876 | ||||||||
\(530\) | −1.09728 | − | 4.32331i | −0.0476626 | − | 0.187793i | ||||
\(531\) | −2.40432 | + | 2.40432i | −0.104338 | + | 0.104338i | ||||
\(532\) | −0.333274 | − | 0.614264i | −0.0144493 | − | 0.0266317i | ||||
\(533\) | −22.7736 | − | 0.820108i | −0.986434 | − | 0.0355228i | ||||
\(534\) | −9.36987 | − | 36.9177i | −0.405474 | − | 1.59759i | ||||
\(535\) | −8.36023 | − | 8.36023i | −0.361444 | − | 0.361444i | ||||
\(536\) | −17.5536 | − | 19.0069i | −0.758201 | − | 0.820975i | ||||
\(537\) | 21.9722i | 0.948172i | ||||||||
\(538\) | 2.92135 | − | 4.90864i | 0.125948 | − | 0.211626i | ||||
\(539\) | 11.5493 | + | 11.5493i | 0.497466 | + | 0.497466i | ||||
\(540\) | 2.81970 | − | 9.50845i | 0.121341 | − | 0.409179i | ||||
\(541\) | 3.68712 | + | 3.68712i | 0.158522 | + | 0.158522i | 0.781911 | − | 0.623390i | \(-0.214245\pi\) |
−0.623390 | + | 0.781911i | \(0.714245\pi\) | |||||||
\(542\) | −3.50111 | − | 13.7945i | −0.150386 | − | 0.592526i | ||||
\(543\) | 16.0975 | 0.690809 | ||||||||
\(544\) | −0.659498 | + | 0.324600i | −0.0282757 | + | 0.0139171i | ||||
\(545\) | − | 3.71720i | − | 0.159228i | ||||||
\(546\) | 13.1578 | + | 8.48654i | 0.563104 | + | 0.363191i | ||||
\(547\) | − | 34.5492i | − | 1.47722i | −0.674135 | − | 0.738608i | \(-0.735483\pi\) | ||
0.674135 | − | 0.738608i | \(-0.264517\pi\) | |||||||
\(548\) | −11.2730 | + | 38.0143i | −0.481560 | + | 1.62389i | ||||
\(549\) | 1.46579 | 0.0625582 | ||||||||
\(550\) | −5.46368 | + | 1.38671i | −0.232972 | + | 0.0591294i | ||||
\(551\) | −0.557337 | − | 0.557337i | −0.0237434 | − | 0.0237434i | ||||
\(552\) | −0.926150 | + | 23.2988i | −0.0394195 | + | 0.991661i | ||||
\(553\) | 3.74785 | + | 3.74785i | 0.159375 | + | 0.159375i | ||||
\(554\) | 4.71008 | + | 2.80318i | 0.200112 | + | 0.119096i | ||||
\(555\) | − | 3.19064i | − | 0.135435i | ||||||
\(556\) | −20.8666 | + | 11.3214i | −0.884943 | + | 0.480133i | ||||
\(557\) | 3.70923 | + | 3.70923i | 0.157165 | + | 0.157165i | 0.781309 | − | 0.624144i | \(-0.214552\pi\) |
−0.624144 | + | 0.781309i | \(0.714552\pi\) | |||||||
\(558\) | 1.17050 | − | 0.297077i | 0.0495511 | − | 0.0125763i | ||||
\(559\) | −18.7548 | − | 20.1560i | −0.793244 | − | 0.852510i | ||||
\(560\) | 5.71275 | + | 3.71489i | 0.241408 | + | 0.156983i | ||||
\(561\) | −0.660112 | + | 0.660112i | −0.0278699 | + | 0.0278699i | ||||
\(562\) | 21.4330 | − | 5.43978i | 0.904095 | − | 0.229463i | ||||
\(563\) | −32.6926 | −1.37783 | −0.688914 | − | 0.724843i | \(-0.741912\pi\) | ||||
−0.688914 | + | 0.724843i | \(0.741912\pi\) | |||||||
\(564\) | −5.91222 | + | 19.9369i | −0.248950 | + | 0.839494i | ||||
\(565\) | 2.33171 | − | 2.33171i | 0.0980957 | − | 0.0980957i | ||||
\(566\) | −5.45156 | + | 9.16006i | −0.229146 | + | 0.385026i | ||||
\(567\) | −11.6662 | + | 11.6662i | −0.489936 | + | 0.489936i | ||||
\(568\) | 17.4374 | + | 18.8811i | 0.731655 | + | 0.792231i | ||||
\(569\) | − | 23.3490i | − | 0.978840i | −0.872048 | − | 0.489420i | \(-0.837208\pi\) | ||
0.872048 | − | 0.489420i | \(-0.162792\pi\) | |||||||
\(570\) | 0.449287 | + | 0.267391i | 0.0188186 | + | 0.0111998i | ||||
\(571\) | −0.790107 | −0.0330649 | −0.0165325 | − | 0.999863i | \(-0.505263\pi\) | ||||
−0.0165325 | + | 0.999863i | \(0.505263\pi\) | |||||||
\(572\) | −12.7890 | − | 25.7407i | −0.534736 | − | 1.07627i | ||||
\(573\) | −48.9313 | −2.04414 | ||||||||
\(574\) | 13.0853 | + | 7.78763i | 0.546168 | + | 0.325050i | ||||
\(575\) | 4.57371i | 0.190737i | ||||||||
\(576\) | −1.98424 | − | 0.158001i | −0.0826768 | − | 0.00658338i | ||||
\(577\) | 18.5877 | − | 18.5877i | 0.773815 | − | 0.773815i | −0.204956 | − | 0.978771i | \(-0.565705\pi\) |
0.978771 | + | 0.204956i | \(0.0657051\pi\) | |||||||
\(578\) | 12.2833 | − | 20.6391i | 0.510917 | − | 0.858474i | ||||
\(579\) | −19.9889 | + | 19.9889i | −0.830711 | + | 0.830711i | ||||
\(580\) | 7.36840 | + | 2.18508i | 0.305956 | + | 0.0907305i | ||||
\(581\) | 27.1477 | 1.12628 | ||||||||
\(582\) | −33.6256 | + | 8.53431i | −1.39382 | + | 0.353759i | ||||
\(583\) | 8.88933 | − | 8.88933i | 0.368158 | − | 0.368158i | ||||
\(584\) | −31.5616 | − | 34.1747i | −1.30603 | − | 1.41416i | ||||
\(585\) | −0.896536 | − | 0.0322854i | −0.0370672 | − | 0.00133484i | ||||
\(586\) | −16.6833 | + | 4.23429i | −0.689180 | + | 0.174917i | ||||
\(587\) | 22.8998 | + | 22.8998i | 0.945178 | + | 0.945178i | 0.998573 | − | 0.0533956i | \(-0.0170044\pi\) |
−0.0533956 | + | 0.998573i | \(0.517004\pi\) | |||||||
\(588\) | 7.04459 | + | 12.9840i | 0.290514 | + | 0.535452i | ||||
\(589\) | − | 0.703916i | − | 0.0290043i | ||||||
\(590\) | −16.6075 | − | 9.88385i | −0.683718 | − | 0.406912i | ||||
\(591\) | 1.21543 | + | 1.21543i | 0.0499961 | + | 0.0499961i | ||||
\(592\) | 6.92685 | − | 1.46791i | 0.284692 | − | 0.0603305i | ||||
\(593\) | 9.11235 | + | 9.11235i | 0.374199 | + | 0.374199i | 0.869004 | − | 0.494805i | \(-0.164760\pi\) |
−0.494805 | + | 0.869004i | \(0.664760\pi\) | |||||||
\(594\) | 27.0937 | − | 6.87649i | 1.11167 | − | 0.282146i | ||||
\(595\) | 0.221366 | 0.00907511 | ||||||||
\(596\) | −5.28821 | − | 1.56820i | −0.216614 | − | 0.0642361i | ||||
\(597\) | 32.6730i | 1.33722i | ||||||||
\(598\) | −22.7965 | + | 4.91996i | −0.932220 | + | 0.201192i | ||||
\(599\) | − | 14.7206i | − | 0.601467i | −0.953708 | − | 0.300733i | \(-0.902769\pi\) | ||
0.953708 | − | 0.300733i | \(-0.0972314\pi\) | |||||||
\(600\) | −5.09407 | − | 0.202494i | −0.207964 | − | 0.00826680i | ||||
\(601\) | 12.8224 | 0.523037 | 0.261519 | − | 0.965198i | \(-0.415777\pi\) | ||||
0.261519 | + | 0.965198i | \(0.415777\pi\) | |||||||
\(602\) | 4.52575 | + | 17.8317i | 0.184456 | + | 0.726764i | ||||
\(603\) | −1.60938 | − | 1.60938i | −0.0655390 | − | 0.0655390i | ||||
\(604\) | 17.1265 | + | 5.07883i | 0.696869 | + | 0.206654i | ||||
\(605\) | −3.45592 | − | 3.45592i | −0.140503 | − | 0.140503i | ||||
\(606\) | 17.7495 | − | 29.8238i | 0.721023 | − | 1.21151i | ||||
\(607\) | − | 19.7681i | − | 0.802362i | −0.915999 | − | 0.401181i | \(-0.868600\pi\) | ||
0.915999 | − | 0.401181i | \(-0.131400\pi\) | |||||||
\(608\) | −0.373802 | + | 1.09842i | −0.0151597 | + | 0.0445467i | ||||
\(609\) | −8.34373 | − | 8.34373i | −0.338105 | − | 0.338105i | ||||
\(610\) | 2.04952 | + | 8.07518i | 0.0829825 | + | 0.326955i | ||||
\(611\) | −20.7853 | − | 0.748508i | −0.840885 | − | 0.0302814i | ||||
\(612\) | −0.0568357 | + | 0.0308367i | −0.00229745 | + | 0.00124650i | ||||
\(613\) | 17.7152 | − | 17.7152i | 0.715509 | − | 0.715509i | −0.252173 | − | 0.967682i | \(-0.581145\pi\) |
0.967682 | + | 0.252173i | \(0.0811452\pi\) | |||||||
\(614\) | 0.698894 | + | 2.75367i | 0.0282051 | + | 0.111129i | ||||
\(615\) | −11.3921 | −0.459374 | ||||||||
\(616\) | −0.762858 | + | 19.1909i | −0.0307364 | + | 0.773224i | ||||
\(617\) | −18.7927 | + | 18.7927i | −0.756566 | + | 0.756566i | −0.975696 | − | 0.219130i | \(-0.929678\pi\) |
0.219130 | + | 0.975696i | \(0.429678\pi\) | |||||||
\(618\) | 21.9066 | + | 13.0376i | 0.881212 | + | 0.524449i | ||||
\(619\) | 9.62828 | − | 9.62828i | 0.386993 | − | 0.386993i | −0.486620 | − | 0.873614i | \(-0.661770\pi\) |
0.873614 | + | 0.486620i | \(0.161770\pi\) | |||||||
\(620\) | 3.27326 | + | 6.03301i | 0.131457 | + | 0.242292i | ||||
\(621\) | − | 22.6804i | − | 0.910133i | ||||||
\(622\) | −14.9531 | + | 25.1252i | −0.599566 | + | 1.00743i | ||||
\(623\) | −25.4554 | −1.01985 | ||||||||
\(624\) | −4.47043 | − | 25.6080i | −0.178960 | − | 1.02514i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | −18.0476 | + | 30.3247i | −0.721327 | + | 1.21202i | ||||
\(627\) | 1.47359i | 0.0588494i | ||||||||
\(628\) | 0.128648 | + | 0.237114i | 0.00513361 | + | 0.00946186i | ||||
\(629\) | 0.162646 | − | 0.162646i | 0.00648512 | − | 0.00648512i | ||||
\(630\) | 0.515132 | + | 0.306578i | 0.0205233 | + | 0.0122144i | ||||
\(631\) | 0.441905 | − | 0.441905i | 0.0175920 | − | 0.0175920i | −0.698256 | − | 0.715848i | \(-0.746040\pi\) |
0.715848 | + | 0.698256i | \(0.246040\pi\) | |||||||
\(632\) | 0.349527 | − | 8.79291i | 0.0139034 | − | 0.349763i | ||||
\(633\) | 30.5883 | 1.21577 | ||||||||
\(634\) | −9.42494 | − | 37.1347i | −0.374312 | − | 1.47481i | ||||
\(635\) | −8.32551 | + | 8.32551i | −0.330388 | + | 0.330388i | ||||
\(636\) | 9.99358 | − | 5.42210i | 0.396271 | − | 0.215000i | ||||
\(637\) | −10.8165 | + | 10.0645i | −0.428564 | + | 0.398771i | ||||
\(638\) | 5.32881 | + | 20.9958i | 0.210970 | + | 0.831230i | ||||
\(639\) | 1.59872 | + | 1.59872i | 0.0632443 | + | 0.0632443i | ||||
\(640\) | −1.90400 | − | 11.1523i | −0.0752621 | − | 0.440835i | ||||
\(641\) | 38.3959i | 1.51655i | 0.651936 | + | 0.758274i | \(0.273957\pi\) | ||||
−0.651936 | + | 0.758274i | \(0.726043\pi\) | |||||||
\(642\) | 15.4132 | − | 25.8982i | 0.608310 | − | 1.02212i | ||||
\(643\) | 27.0409 | + | 27.0409i | 1.06639 | + | 1.06639i | 0.997633 | + | 0.0687573i | \(0.0219034\pi\) |
0.0687573 | + | 0.997633i | \(0.478097\pi\) | |||||||
\(644\) | 14.9404 | + | 4.43054i | 0.588735 | + | 0.174588i | ||||
\(645\) | −9.73225 | − | 9.73225i | −0.383207 | − | 0.383207i | ||||
\(646\) | 0.00927233 | + | 0.0365334i | 0.000364815 | + | 0.00143739i | ||||
\(647\) | −17.6171 | −0.692600 | −0.346300 | − | 0.938124i | \(-0.612562\pi\) | ||||
−0.346300 | + | 0.938124i | \(0.612562\pi\) | |||||||
\(648\) | 27.3704 | + | 1.08800i | 1.07521 | + | 0.0427407i | ||||
\(649\) | − | 54.4698i | − | 2.13813i | ||||||
\(650\) | −1.07571 | − | 4.98426i | −0.0421926 | − | 0.195499i | ||||
\(651\) | − | 10.5381i | − | 0.413021i | ||||||
\(652\) | 36.1493 | + | 10.7200i | 1.41572 | + | 0.419827i | ||||
\(653\) | −35.9748 | −1.40780 | −0.703902 | − | 0.710297i | \(-0.748560\pi\) | ||||
−0.703902 | + | 0.710297i | \(0.748560\pi\) | |||||||
\(654\) | 9.18413 | − | 2.33097i | 0.359128 | − | 0.0911483i | ||||
\(655\) | 5.64580 | + | 5.64580i | 0.220599 | + | 0.220599i | ||||
\(656\) | −5.24113 | − | 24.7322i | −0.204632 | − | 0.965630i | ||||
\(657\) | −2.89368 | − | 2.89368i | −0.112893 | − | 0.112893i | ||||
\(658\) | 11.9429 | + | 7.10773i | 0.465581 | + | 0.277088i | ||||
\(659\) | − | 0.973268i | − | 0.0379131i | −0.999820 | − | 0.0189566i | \(-0.993966\pi\) | ||
0.999820 | − | 0.0189566i | \(-0.00603442\pi\) | |||||||
\(660\) | −6.85230 | − | 12.6296i | −0.266725 | − | 0.491607i | ||||
\(661\) | 14.7847 | + | 14.7847i | 0.575059 | + | 0.575059i | 0.933538 | − | 0.358479i | \(-0.116705\pi\) |
−0.358479 | + | 0.933538i | \(0.616705\pi\) | |||||||
\(662\) | 20.1050 | − | 5.10273i | 0.781402 | − | 0.198323i | ||||
\(663\) | −0.575245 | − | 0.618224i | −0.0223407 | − | 0.0240098i | ||||
\(664\) | −30.5800 | − | 33.1118i | −1.18673 | − | 1.28499i | ||||
\(665\) | 0.247081 | − | 0.247081i | 0.00958139 | − | 0.00958139i | ||||
\(666\) | 0.603742 | − | 0.153232i | 0.0233945 | − | 0.00593763i | ||||
\(667\) | 17.5758 | 0.680536 | ||||||||
\(668\) | −32.3499 | − | 9.59327i | −1.25166 | − | 0.371175i | ||||
\(669\) | 27.0581 | − | 27.0581i | 1.04613 | − | 1.04613i | ||||
\(670\) | 6.61596 | − | 11.1165i | 0.255597 | − | 0.429470i | ||||
\(671\) | −16.6037 | + | 16.6037i | −0.640978 | + | 0.640978i | ||||
\(672\) | −5.59608 | + | 16.4441i | −0.215873 | + | 0.634344i | ||||
\(673\) | 1.67990i | 0.0647555i | 0.999476 | + | 0.0323777i | \(0.0103080\pi\) | ||||
−0.999476 | + | 0.0323777i | \(0.989692\pi\) | |||||||
\(674\) | −10.7083 | − | 6.37299i | −0.412468 | − | 0.245478i | ||||
\(675\) | 4.95886 | 0.190867 | ||||||||
\(676\) | 23.6857 | − | 10.7232i | 0.910989 | − | 0.412431i | ||||
\(677\) | 42.4579 | 1.63179 | 0.815896 | − | 0.578199i | \(-0.196244\pi\) | ||||
0.815896 | + | 0.578199i | \(0.196244\pi\) | |||||||
\(678\) | 7.22314 | + | 4.29881i | 0.277403 | + | 0.165095i | ||||
\(679\) | 23.1854i | 0.889775i | ||||||||
\(680\) | −0.249353 | − | 0.269998i | −0.00956225 | − | 0.0103539i | ||||
\(681\) | 7.15313 | − | 7.15313i | 0.274109 | − | 0.274109i | ||||
\(682\) | −9.89366 | + | 16.6239i | −0.378848 | + | 0.636564i | ||||
\(683\) | −24.8104 | + | 24.8104i | −0.949345 | + | 0.949345i | −0.998777 | − | 0.0494324i | \(-0.984259\pi\) |
0.0494324 | + | 0.998777i | \(0.484259\pi\) | |||||||
\(684\) | −0.0290192 | + | 0.0978570i | −0.00110958 | + | 0.00374166i | ||||
\(685\) | −19.8253 | −0.757485 | ||||||||
\(686\) | 25.9156 | − | 6.57749i | 0.989462 | − | 0.251130i | ||||
\(687\) | −34.0838 | + | 34.0838i | −1.30038 | + | 1.30038i | ||||
\(688\) | 16.6512 | − | 25.6061i | 0.634819 | − | 0.976224i | ||||
\(689\) | 7.74649 | + | 8.32525i | 0.295118 | + | 0.317167i | ||||
\(690\) | −11.3003 | + | 2.86807i | −0.430195 | + | 0.109185i | ||||
\(691\) | 21.9436 | + | 21.9436i | 0.834774 | + | 0.834774i | 0.988165 | − | 0.153392i | \(-0.0490196\pi\) |
−0.153392 | + | 0.988165i | \(0.549020\pi\) | |||||||
\(692\) | −38.8730 | + | 21.0909i | −1.47773 | + | 0.801755i | ||||
\(693\) | 1.68955i | 0.0641807i | ||||||||
\(694\) | 32.3901 | + | 19.2768i | 1.22951 | + | 0.731739i | ||||
\(695\) | −8.39338 | − | 8.39338i | −0.318379 | − | 0.318379i | ||||
\(696\) | −0.778142 | + | 19.5754i | −0.0294954 | + | 0.742003i | ||||
\(697\) | −0.580724 | − | 0.580724i | −0.0219965 | − | 0.0219965i | ||||
\(698\) | −2.72553 | + | 0.691752i | −0.103163 | + | 0.0261832i | ||||
\(699\) | 2.47222 | 0.0935079 | ||||||||
\(700\) | −0.968698 | + | 3.26659i | −0.0366133 | + | 0.123465i | ||||
\(701\) | 46.8970i | 1.77128i | 0.464377 | + | 0.885638i | \(0.346278\pi\) | ||||
−0.464377 | + | 0.885638i | \(0.653722\pi\) | |||||||
\(702\) | 5.33428 | + | 24.7163i | 0.201329 | + | 0.932856i | ||||
\(703\) | − | 0.363080i | − | 0.0136938i | ||||||
\(704\) | 24.2663 | − | 20.6868i | 0.914569 | − | 0.779662i | ||||
\(705\) | −10.3975 | −0.391593 | ||||||||
\(706\) | −0.532243 | − | 2.09706i | −0.0200312 | − | 0.0789238i | ||||
\(707\) | −16.4013 | − | 16.4013i | −0.616834 | − | 0.616834i | ||||
\(708\) | 14.0060 | − | 47.2301i | 0.526377 | − | 1.77502i | ||||
\(709\) | 32.2745 | + | 32.2745i | 1.21209 | + | 1.21209i | 0.970337 | + | 0.241755i | \(0.0777231\pi\) |
0.241755 | + | 0.970337i | \(0.422277\pi\) | |||||||
\(710\) | −6.57214 | + | 11.0429i | −0.246648 | + | 0.414433i | ||||
\(711\) | − | 0.774120i | − | 0.0290318i | ||||||
\(712\) | 28.6737 | + | 31.0477i | 1.07459 | + | 1.16356i | ||||
\(713\) | 11.0991 | + | 11.0991i | 0.415664 | + | 0.415664i | ||||
\(714\) | 0.138813 | + | 0.546930i | 0.00519496 | + | 0.0204684i | ||||
\(715\) | 10.5212 | − | 9.78980i | 0.393471 | − | 0.366118i | ||||
\(716\) | −11.6268 | − | 21.4295i | −0.434513 | − | 0.800859i | ||||
\(717\) | 25.5760 | − | 25.5760i | 0.955152 | − | 0.955152i | ||||
\(718\) | 1.41696 | + | 5.58288i | 0.0528805 | + | 0.208351i | ||||
\(719\) | 13.4055 | 0.499939 | 0.249970 | − | 0.968254i | \(-0.419579\pi\) | ||||
0.249970 | + | 0.968254i | \(0.419579\pi\) | |||||||
\(720\) | −0.206329 | − | 0.973640i | −0.00768943 | − | 0.0362854i | ||||
\(721\) | 12.0473 | − | 12.0473i | 0.448666 | − | 0.448666i | ||||
\(722\) | −23.0391 | − | 13.7116i | −0.857425 | − | 0.510293i | ||||
\(723\) | −5.88678 | + | 5.88678i | −0.218932 | + | 0.218932i | ||||
\(724\) | −15.6999 | + | 8.51810i | −0.583481 | + | 0.316573i | ||||
\(725\) | 3.84278i | 0.142717i | ||||||||
\(726\) | 6.37144 | − | 10.7057i | 0.236466 | − | 0.397325i | ||||
\(727\) | −15.7815 | −0.585305 | −0.292653 | − | 0.956219i | \(-0.594538\pi\) | ||||
−0.292653 | + | 0.956219i | \(0.594538\pi\) | |||||||
\(728\) | −17.3236 | − | 1.31436i | −0.642054 | − | 0.0487133i | ||||
\(729\) | −24.4046 | −0.903874 | ||||||||
\(730\) | 11.8956 | − | 19.9876i | 0.440274 | − | 0.739776i | ||||
\(731\) | − | 0.992222i | − | 0.0366987i | ||||||
\(732\) | −18.6662 | + | 10.1275i | −0.689924 | + | 0.374324i | ||||
\(733\) | −7.78597 | + | 7.78597i | −0.287582 | + | 0.287582i | −0.836123 | − | 0.548542i | \(-0.815183\pi\) |
0.548542 | + | 0.836123i | \(0.315183\pi\) | |||||||
\(734\) | 17.8949 | + | 10.6501i | 0.660513 | + | 0.393101i | ||||
\(735\) | −5.22268 | + | 5.22268i | −0.192641 | + | 0.192641i | ||||
\(736\) | −11.4254 | − | 23.2134i | −0.421147 | − | 0.855656i | ||||
\(737\) | 36.4605 | 1.34304 | ||||||||
\(738\) | −0.547113 | − | 2.15565i | −0.0201395 | − | 0.0793505i | ||||
\(739\) | 32.4954 | − | 32.4954i | 1.19536 | − | 1.19536i | 0.219823 | − | 0.975540i | \(-0.429452\pi\) |
0.975540 | − | 0.219823i | \(-0.0705481\pi\) | |||||||
\(740\) | 1.68835 | + | 3.11183i | 0.0620649 | + | 0.114393i | ||||
\(741\) | −1.33211 | − | 0.0479710i | −0.0489363 | − | 0.00176226i | ||||
\(742\) | −1.86932 | − | 7.36519i | −0.0686248 | − | 0.270385i | ||||
\(743\) | 11.9167 | + | 11.9167i | 0.437183 | + | 0.437183i | 0.891063 | − | 0.453880i | \(-0.149961\pi\) |
−0.453880 | + | 0.891063i | \(0.649961\pi\) | |||||||
\(744\) | −12.8532 | + | 11.8704i | −0.471223 | + | 0.435192i | ||||
\(745\) | − | 2.75792i | − | 0.101042i | ||||||
\(746\) | 3.73589 | − | 6.27728i | 0.136781 | − | 0.229828i | ||||
\(747\) | −2.80368 | − | 2.80368i | −0.102581 | − | 0.102581i | ||||
\(748\) | 0.294504 | − | 0.993110i | 0.0107681 | − | 0.0363117i | ||||
\(749\) | −14.2425 | − | 14.2425i | −0.520409 | − | 0.520409i | ||||
\(750\) | −0.627077 | − | 2.47071i | −0.0228976 | − | 0.0902176i | ||||
\(751\) | −26.1761 | −0.955181 | −0.477591 | − | 0.878582i | \(-0.658490\pi\) | ||||
−0.477591 | + | 0.878582i | \(0.658490\pi\) | |||||||
\(752\) | −4.78355 | − | 22.5729i | −0.174438 | − | 0.823150i | ||||
\(753\) | 19.9638i | 0.727522i | ||||||||
\(754\) | −19.1534 | + | 4.13370i | −0.697527 | + | 0.150541i | ||||
\(755\) | 8.93186i | 0.325064i | ||||||||
\(756\) | 4.80364 | − | 16.1986i | 0.174707 | − | 0.589136i | ||||
\(757\) | −22.1030 | −0.803347 | −0.401673 | − | 0.915783i | \(-0.631571\pi\) | ||||
−0.401673 | + | 0.915783i | \(0.631571\pi\) | |||||||
\(758\) | −14.5744 | + | 3.69905i | −0.529367 | + | 0.134356i | ||||
\(759\) | −23.2350 | − | 23.2350i | −0.843376 | − | 0.843376i | ||||
\(760\) | −0.579681 | − | 0.0230429i | −0.0210272 | − | 0.000835855i | ||||
\(761\) | 9.16654 | + | 9.16654i | 0.332287 | + | 0.332287i | 0.853454 | − | 0.521168i | \(-0.174503\pi\) |
−0.521168 | + | 0.853454i | \(0.674503\pi\) | |||||||
\(762\) | −25.7906 | − | 15.3492i | −0.934297 | − | 0.556042i | ||||
\(763\) | − | 6.33262i | − | 0.229256i | ||||||
\(764\) | 47.7227 | − | 25.8924i | 1.72655 | − | 0.936753i | ||||
\(765\) | −0.0228616 | − | 0.0228616i | −0.000826561 | − | 0.000826561i | ||||
\(766\) | 15.6513 | − | 3.97236i | 0.565503 | − | 0.143527i | ||||
\(767\) | 49.2402 | + | 1.77320i | 1.77796 | + | 0.0640267i | ||||
\(768\) | 26.3603 | − | 11.6976i | 0.951194 | − | 0.422101i | ||||
\(769\) | 5.20162 | − | 5.20162i | 0.187575 | − | 0.187575i | −0.607072 | − | 0.794647i | \(-0.707656\pi\) |
0.794647 | + | 0.607072i | \(0.207656\pi\) | |||||||
\(770\) | −9.30792 | + | 2.36239i | −0.335434 | + | 0.0851347i | ||||
\(771\) | −7.77826 | −0.280127 | ||||||||
\(772\) | 8.91790 | − | 30.0725i | 0.320962 | − | 1.08233i | ||||
\(773\) | −7.88292 | + | 7.88292i | −0.283529 | + | 0.283529i | −0.834515 | − | 0.550986i | \(-0.814252\pi\) |
0.550986 | + | 0.834515i | \(0.314252\pi\) | |||||||
\(774\) | 1.37417 | − | 2.30896i | 0.0493934 | − | 0.0829939i | ||||
\(775\) | −2.42671 | + | 2.42671i | −0.0871701 | + | 0.0871701i | ||||
\(776\) | 28.2790 | − | 26.1167i | 1.01516 | − | 0.937536i | ||||
\(777\) | − | 5.43556i | − | 0.195000i | ||||||
\(778\) | −22.4967 | − | 13.3888i | −0.806546 | − | 0.480012i | ||||
\(779\) | −1.29637 | −0.0464472 | ||||||||
\(780\) | 11.6401 | − | 5.78327i | 0.416783 | − | 0.207074i | ||||
\(781\) | −36.2190 | −1.29602 | ||||||||
\(782\) | −0.722247 | − | 0.429842i | −0.0258275 | − | 0.0153711i | ||||
\(783\) | − | 19.0558i | − | 0.681000i | ||||||
\(784\) | −13.7412 | − | 8.93562i | −0.490757 | − | 0.319129i | ||||
\(785\) | −0.0953763 | + | 0.0953763i | −0.00340413 | + | 0.00340413i | ||||
\(786\) | −10.4088 | + | 17.4895i | −0.371269 | + | 0.623829i | ||||
\(787\) | 34.6472 | − | 34.6472i | 1.23504 | − | 1.23504i | 0.273034 | − | 0.962004i | \(-0.411973\pi\) |
0.962004 | − | 0.273034i | \(-0.0880272\pi\) | |||||||
\(788\) | −1.82856 | − | 0.542255i | −0.0651398 | − | 0.0193170i | ||||
\(789\) | −9.94484 | −0.354046 | ||||||||
\(790\) | 4.26471 | − | 1.08240i | 0.151732 | − | 0.0385102i | ||||
\(791\) | 3.97229 | − | 3.97229i | 0.141238 | − | 0.141238i | ||||
\(792\) | 2.06073 | − | 1.90316i | 0.0732247 | − | 0.0676258i | ||||
\(793\) | −14.4691 | − | 15.5501i | −0.513812 | − | 0.552200i | ||||
\(794\) | −46.0866 | + | 11.6970i | −1.63555 | + | 0.415110i | ||||
\(795\) | 4.01981 | + | 4.01981i | 0.142568 | + | 0.142568i | ||||
\(796\) | −17.2892 | − | 31.8660i | −0.612798 | − | 1.12946i | ||||
\(797\) | 43.1803i | 1.52952i | 0.644313 | + | 0.764762i | \(0.277143\pi\) | ||||
−0.644313 | + | 0.764762i | \(0.722857\pi\) | |||||||
\(798\) | 0.765404 | + | 0.455526i | 0.0270950 | + | 0.0161255i | ||||
\(799\) | −0.530024 | − | 0.530024i | −0.0187509 | − | 0.0187509i | ||||
\(800\) | 5.07540 | − | 2.49807i | 0.179442 | − | 0.0883201i | ||||
\(801\) | 2.62891 | + | 2.62891i | 0.0928879 | + | 0.0928879i | ||||
\(802\) | 34.9765 | − | 8.87719i | 1.23506 | − | 0.313465i | ||||
\(803\) | 65.5563 | 2.31343 | ||||||||
\(804\) | 31.6145 | + | 9.37518i | 1.11496 | + | 0.330637i | ||||
\(805\) | 7.79175i | 0.274623i | ||||||||
\(806\) | −14.7058 | − | 9.48495i | −0.517990 | − | 0.334093i | ||||
\(807\) | 7.28031i | 0.256279i | ||||||||
\(808\) | −1.52959 | + | 38.4794i | −0.0538109 | + | 1.35370i | ||||
\(809\) | 1.93088 | 0.0678860 | 0.0339430 | − | 0.999424i | \(-0.489194\pi\) | ||||
0.0339430 | + | 0.999424i | \(0.489194\pi\) | |||||||
\(810\) | 3.36928 | + | 13.2751i | 0.118384 | + | 0.466440i | ||||
\(811\) | 1.00517 | + | 1.00517i | 0.0352961 | + | 0.0352961i | 0.724535 | − | 0.689238i | \(-0.242055\pi\) |
−0.689238 | + | 0.724535i | \(0.742055\pi\) | |||||||
\(812\) | 12.5528 | + | 3.72250i | 0.440517 | + | 0.130634i | ||||
\(813\) | 12.8261 | + | 12.8261i | 0.449832 | + | 0.449832i | ||||
\(814\) | −5.10315 | + | 8.57462i | −0.178865 | + | 0.300540i | ||||
\(815\) | 18.8527i | 0.660380i | ||||||||
\(816\) | 0.510722 | − | 0.785388i | 0.0178789 | − | 0.0274941i | ||||
\(817\) | −1.10748 | − | 1.10748i | −0.0387460 | − | 0.0387460i | ||||
\(818\) | −9.98457 | − | 39.3396i | −0.349102 | − | 1.37548i | ||||
\(819\) | −1.52734 | − | 0.0550014i | −0.0533694 | − | 0.00192190i | ||||
\(820\) | 11.1107 | − | 6.02822i | 0.388003 | − | 0.210515i | ||||
\(821\) | 21.8955 | − | 21.8955i | 0.764157 | − | 0.764157i | −0.212914 | − | 0.977071i | \(-0.568295\pi\) |
0.977071 | + | 0.212914i | \(0.0682954\pi\) | |||||||
\(822\) | −12.4320 | − | 48.9825i | −0.433615 | − | 1.70846i | ||||
\(823\) | −48.9301 | −1.70560 | −0.852798 | − | 0.522241i | \(-0.825096\pi\) | ||||
−0.852798 | + | 0.522241i | \(0.825096\pi\) | |||||||
\(824\) | −28.2644 | − | 1.12354i | −0.984639 | − | 0.0391404i | ||||
\(825\) | 5.08012 | − | 5.08012i | 0.176867 | − | 0.176867i | ||||
\(826\) | −28.2924 | − | 16.8381i | −0.984420 | − | 0.585873i | ||||
\(827\) | 15.7484 | − | 15.7484i | 0.547626 | − | 0.547626i | −0.378128 | − | 0.925753i | \(-0.623432\pi\) |
0.925753 | + | 0.378128i | \(0.123432\pi\) | |||||||
\(828\) | −1.08541 | − | 2.00054i | −0.0377205 | − | 0.0695234i | ||||
\(829\) | 46.9223i | 1.62968i | 0.579686 | + | 0.814840i | \(0.303175\pi\) | ||||
−0.579686 | + | 0.814840i | \(0.696825\pi\) | |||||||
\(830\) | 11.5256 | − | 19.3660i | 0.400059 | − | 0.672204i | ||||
\(831\) | −6.98581 | −0.242335 | ||||||||
\(832\) | 17.9107 | + | 22.6099i | 0.620941 | + | 0.783858i | ||||
\(833\) | −0.532463 | −0.0184487 | ||||||||
\(834\) | 15.4743 | − | 26.0009i | 0.535832 | − | 0.900338i | ||||
\(835\) | − | 16.8712i | − | 0.583851i | ||||||
\(836\) | −0.779760 | − | 1.43719i | −0.0269686 | − | 0.0497063i | ||||
\(837\) | 12.0337 | − | 12.0337i | 0.415947 | − | 0.415947i | ||||
\(838\) | 11.8623 | + | 7.05982i | 0.409778 | + | 0.243877i | ||||
\(839\) | 0.862157 | − | 0.862157i | 0.0297650 | − | 0.0297650i | −0.692068 | − | 0.721833i | \(-0.743300\pi\) |
0.721833 | + | 0.692068i | \(0.243300\pi\) | |||||||
\(840\) | −8.67824 | − | 0.344969i | −0.299428 | − | 0.0119026i | ||||
\(841\) | −14.2330 | −0.490794 | ||||||||
\(842\) | −7.64687 | − | 30.1290i | −0.263529 | − | 1.03831i | ||||
\(843\) | −19.9283 | + | 19.9283i | −0.686367 | + | 0.686367i | ||||
\(844\) | −29.8328 | + | 16.1860i | −1.02689 | + | 0.557146i | ||||
\(845\) | 8.50737 | + | 9.82978i | 0.292663 | + | 0.338155i | ||||
\(846\) | −0.499347 | − | 1.96745i | −0.0171679 | − | 0.0676423i | ||||
\(847\) | −5.88749 | − | 5.88749i | −0.202297 | − | 0.202297i | ||||
\(848\) | −6.87759 | + | 10.5764i | −0.236177 | + | 0.363193i | ||||
\(849\) | − | 13.5858i | − | 0.466265i | ||||||
\(850\) | 0.0939810 | − | 0.157913i | 0.00322352 | − | 0.00541636i | ||||
\(851\) | 5.72490 | + | 5.72490i | 0.196247 | + | 0.196247i | ||||
\(852\) | −31.4051 | − | 9.31309i | −1.07592 | − | 0.319061i | ||||
\(853\) | 19.3938 | + | 19.3938i | 0.664031 | + | 0.664031i | 0.956328 | − | 0.292296i | \(-0.0944194\pi\) |
−0.292296 | + | 0.956328i | \(0.594419\pi\) | |||||||
\(854\) | 3.49155 | + | 13.7569i | 0.119478 | + | 0.470750i | ||||
\(855\) | −0.0510346 | −0.00174535 | ||||||||
\(856\) | −1.32826 | + | 33.4145i | −0.0453991 | + | 1.14209i | ||||
\(857\) | − | 4.80900i | − | 0.164272i | −0.996621 | − | 0.0821362i | \(-0.973826\pi\) | ||
0.996621 | − | 0.0821362i | \(-0.0261742\pi\) | |||||||
\(858\) | 30.7854 | + | 19.8559i | 1.05099 | + | 0.677870i | ||||
\(859\) | − | 5.64419i | − | 0.192577i | −0.995353 | − | 0.0962887i | \(-0.969303\pi\) | ||
0.995353 | − | 0.0962887i | \(-0.0306972\pi\) | |||||||
\(860\) | 14.6418 | + | 4.34197i | 0.499280 | + | 0.148060i | ||||
\(861\) | −19.4076 | −0.661408 | ||||||||
\(862\) | −36.1335 | + | 9.17084i | −1.23071 | + | 0.312360i | ||||
\(863\) | −2.84941 | − | 2.84941i | −0.0969951 | − | 0.0969951i | 0.656944 | − | 0.753939i | \(-0.271849\pi\) |
−0.753939 | + | 0.656944i | \(0.771849\pi\) | |||||||
\(864\) | −25.1682 | + | 12.3876i | −0.856240 | + | 0.421435i | ||||
\(865\) | −15.6362 | − | 15.6362i | −0.531648 | − | 0.531648i | ||||
\(866\) | −20.8780 | − | 12.4254i | −0.709463 | − | 0.422233i | ||||
\(867\) | 30.6112i | 1.03961i | ||||||||
\(868\) | 5.57632 | + | 10.2778i | 0.189273 | + | 0.348852i | ||||
\(869\) | 8.76884 | + | 8.76884i | 0.297463 | + | 0.297463i | ||||
\(870\) | −9.49440 | + | 2.40972i | −0.321890 | + | 0.0816972i | ||||
\(871\) | −1.18693 | + | 32.9599i | −0.0402176 | + | 1.11680i | ||||
\(872\) | −7.72384 | + | 7.13325i | −0.261562 | + | 0.241562i | ||||
\(873\) | 2.39447 | − | 2.39447i | 0.0810407 | − | 0.0810407i | ||||
\(874\) | −1.28592 | + | 0.326373i | −0.0434970 | + | 0.0110397i | ||||
\(875\) | −1.70360 | −0.0575921 | ||||||||
\(876\) | 56.8431 | + | 16.8567i | 1.92055 | + | 0.569534i | ||||
\(877\) | −1.22498 | + | 1.22498i | −0.0413645 | + | 0.0413645i | −0.727487 | − | 0.686122i | \(-0.759312\pi\) |
0.686122 | + | 0.727487i | \(0.259312\pi\) | |||||||
\(878\) | −11.0814 | + | 18.6197i | −0.373980 | + | 0.628385i | ||||
\(879\) | 15.5121 | − | 15.5121i | 0.523209 | − | 0.523209i | ||||
\(880\) | 13.3661 | + | 8.69171i | 0.450571 | + | 0.292998i | ||||
\(881\) | 6.78568i | 0.228615i | 0.993445 | + | 0.114308i | \(0.0364650\pi\) | ||||
−0.993445 | + | 0.114308i | \(0.963535\pi\) | |||||||
\(882\) | −1.23907 | − | 0.737429i | −0.0417218 | − | 0.0248305i | ||||
\(883\) | 19.0036 | 0.639523 | 0.319761 | − | 0.947498i | \(-0.396397\pi\) | ||||
0.319761 | + | 0.947498i | \(0.396397\pi\) | |||||||
\(884\) | 0.888174 | + | 0.298558i | 0.0298725 | + | 0.0100416i | ||||
\(885\) | 24.6316 | 0.827981 | ||||||||
\(886\) | −34.3895 | − | 20.4667i | −1.15534 | − | 0.687594i | ||||
\(887\) | − | 47.7807i | − | 1.60432i | −0.597110 | − | 0.802159i | \(-0.703684\pi\) | ||
0.597110 | − | 0.802159i | \(-0.296316\pi\) | |||||||
\(888\) | −6.62970 | + | 6.12277i | −0.222478 | + | 0.205467i | ||||
\(889\) | −14.1833 | + | 14.1833i | −0.475693 | + | 0.475693i | ||||
\(890\) | −10.8071 | + | 18.1588i | −0.362255 | + | 0.608684i | ||||
\(891\) | −27.2955 | + | 27.2955i | −0.914432 | + | 0.914432i | ||||
\(892\) | −12.0718 | + | 40.7078i | −0.404193 | + | 1.36300i | ||||
\(893\) | −1.18319 | −0.0395939 | ||||||||
\(894\) | 6.81401 | − | 1.72943i | 0.227895 | − | 0.0578407i | ||||
\(895\) | 8.61979 | − | 8.61979i | 0.288128 | − | 0.288128i | ||||
\(896\) | −3.24364 | − | 18.9991i | −0.108363 | − | 0.634716i | ||||
\(897\) | 21.7606 | − | 20.2478i | 0.726565 | − | 0.676055i | ||||
\(898\) | −34.0786 | + | 8.64929i | −1.13722 | + | 0.288630i | ||||
\(899\) | 9.32533 | + | 9.32533i | 0.311017 | + | 0.311017i | ||||
\(900\) | 0.437399 | − | 0.237315i | 0.0145800 | − | 0.00791049i | ||||
\(901\) | 0.409827i | 0.0136533i | ||||||||
\(902\) | 30.6155 | + | 18.2207i | 1.01939 | + | 0.606683i | ||||
\(903\) | −16.5798 | − | 16.5798i | −0.551742 | − | 0.551742i | ||||
\(904\) | −9.31947 | − | 0.370459i | −0.309961 | − | 0.0123213i | ||||
\(905\) | −6.31510 | − | 6.31510i | −0.209921 | − | 0.209921i | ||||
\(906\) | −22.0680 | + | 5.60096i | −0.733161 | + | 0.186080i | ||||
\(907\) | −18.1020 | −0.601067 | −0.300534 | − | 0.953771i | \(-0.597165\pi\) | ||||
−0.300534 | + | 0.953771i | \(0.597165\pi\) | |||||||
\(908\) | −3.19132 | + | 10.7616i | −0.105908 | + | 0.357136i | ||||
\(909\) | 3.38769i | 0.112362i | ||||||||
\(910\) | −1.83257 | − | 8.49118i | −0.0607491 | − | 0.281480i | ||||
\(911\) | 15.6842i | 0.519641i | 0.965657 | + | 0.259821i | \(0.0836634\pi\) | ||||
−0.965657 | + | 0.259821i | \(0.916337\pi\) | |||||||
\(912\) | −0.306572 | − | 1.44667i | −0.0101516 | − | 0.0479042i | ||||
\(913\) | 63.5174 | 2.10212 | ||||||||
\(914\) | −3.04456 | − | 11.9957i | −0.100705 | − | 0.396783i | ||||
\(915\) | −7.50829 | − | 7.50829i | −0.248216 | − | 0.248216i | ||||
\(916\) | 15.2063 | − | 51.2777i | 0.502429 | − | 1.69426i | ||||
\(917\) | 9.61816 | + | 9.61816i | 0.317620 | + | 0.317620i | ||||
\(918\) | −0.466039 | + | 0.783068i | −0.0153816 | + | 0.0258451i | ||||
\(919\) | 38.7998i | 1.27989i | 0.768422 | + | 0.639943i | \(0.221042\pi\) | ||||
−0.768422 | + | 0.639943i | \(0.778958\pi\) | |||||||
\(920\) | 9.50353 | − | 8.77686i | 0.313322 | − | 0.289365i | ||||
\(921\) | −2.56036 | − | 2.56036i | −0.0843667 | − | 0.0843667i | ||||
\(922\) | 2.80551 | + | 11.0538i | 0.0923946 | + | 0.364039i | ||||
\(923\) | 1.17907 | − | 32.7416i | 0.0388095 | − | 1.07770i | ||||
\(924\) | −11.6736 | − | 21.5158i | −0.384032 | − | 0.707817i | ||||
\(925\) | −1.25170 | + | 1.25170i | −0.0411556 | + | 0.0411556i | ||||
\(926\) | 6.20207 | + | 24.4364i | 0.203813 | + | 0.803030i | ||||
\(927\) | −2.48837 | −0.0817289 | ||||||||
\(928\) | −9.59954 | − | 19.5036i | −0.315120 | − | 0.640238i | ||||
\(929\) | 24.4927 | − | 24.4927i | 0.803580 | − | 0.803580i | −0.180073 | − | 0.983653i | \(-0.557633\pi\) |
0.983653 | + | 0.180073i | \(0.0576334\pi\) | |||||||
\(930\) | −7.51744 | − | 4.47397i | −0.246507 | − | 0.146707i | ||||
\(931\) | −0.594317 | + | 0.594317i | −0.0194780 | + | 0.0194780i | ||||
\(932\) | −2.41116 | + | 1.30819i | −0.0789801 | + | 0.0428513i | ||||
\(933\) | − | 37.2647i | − | 1.21999i | ||||||
\(934\) | 2.11555 | − | 3.55468i | 0.0692230 | − | 0.116313i | ||||
\(935\) | 0.517928 | 0.0169381 | ||||||||
\(936\) | 1.65335 | + | 1.92483i | 0.0540415 | + | 0.0629151i | ||||
\(937\) | −49.8771 | −1.62942 | −0.814708 | − | 0.579872i | \(-0.803103\pi\) | ||||
−0.814708 | + | 0.579872i | \(0.803103\pi\) | |||||||
\(938\) | 11.2709 | − | 18.9381i | 0.368009 | − | 0.618352i | ||||
\(939\) | − | 44.9764i | − | 1.46775i | ||||||
\(940\) | 10.1407 | − | 5.50192i | 0.330753 | − | 0.179453i | ||||
\(941\) | 1.82125 | − | 1.82125i | 0.0593711 | − | 0.0593711i | −0.676798 | − | 0.736169i | \(-0.736633\pi\) |
0.736169 | + | 0.676798i | \(0.236633\pi\) | |||||||
\(942\) | −0.295456 | − | 0.175839i | −0.00962646 | − | 0.00572914i | ||||
\(943\) | 20.4407 | − | 20.4407i | 0.665639 | − | 0.665639i | ||||
\(944\) | 11.3322 | + | 53.4749i | 0.368830 | + | 1.74046i | ||||
\(945\) | 8.44791 | 0.274811 | ||||||||
\(946\) | 10.5889 | + | 41.7207i | 0.344274 | + | 1.35646i | ||||
\(947\) | 10.0728 | − | 10.0728i | 0.327321 | − | 0.327321i | −0.524246 | − | 0.851567i | \(-0.675653\pi\) |
0.851567 | + | 0.524246i | \(0.175653\pi\) | |||||||
\(948\) | 5.34861 | + | 9.85812i | 0.173715 | + | 0.320177i | ||||
\(949\) | −2.13411 | + | 59.2622i | −0.0692762 | + | 1.92373i | ||||
\(950\) | −0.0713584 | − | 0.281155i | −0.00231517 | − | 0.00912188i | ||||
\(951\) | 34.5277 | + | 34.5277i | 1.11964 | + | 1.11964i | ||||
\(952\) | −0.424797 | − | 0.459967i | −0.0137677 | − | 0.0149076i | ||||
\(953\) | 22.7318i | 0.736357i | 0.929755 | + | 0.368178i | \(0.120018\pi\) | ||||
−0.929755 | + | 0.368178i | \(0.879982\pi\) | |||||||
\(954\) | −0.567586 | + | 0.953694i | −0.0183763 | + | 0.0308770i | ||||
\(955\) | 19.1959 | + | 19.1959i | 0.621166 | + | 0.621166i | ||||
\(956\) | −11.4105 | + | 38.4779i | −0.369043 | + | 1.24447i | ||||
\(957\) | −19.5218 | − | 19.5218i | −0.631050 | − | 0.631050i | ||||
\(958\) | −8.26238 | − | 32.5541i | −0.266945 | − | 1.05178i | ||||
\(959\) | −33.7743 | −1.09063 | ||||||||
\(960\) | 9.35467 | + | 10.9733i | 0.301921 | + | 0.354163i | ||||
\(961\) | − | 19.2221i | − | 0.620068i | ||||||
\(962\) | −7.58525 | − | 4.89233i | −0.244558 | − | 0.157735i | ||||
\(963\) | 2.94178i | 0.0947977i | ||||||||
\(964\) | 2.62634 | − | 8.85641i | 0.0845889 | − | 0.285246i | ||||
\(965\) | 15.6834 | 0.504868 | ||||||||
\(966\) | −19.2512 | + | 4.88603i | −0.619396 | + | 0.157205i | ||||
\(967\) | 16.9691 | + | 16.9691i | 0.545691 | + | 0.545691i | 0.925192 | − | 0.379500i | \(-0.123904\pi\) |
−0.379500 | + | 0.925192i | \(0.623904\pi\) | |||||||
\(968\) | −0.549071 | + | 13.8128i | −0.0176478 | + | 0.443959i | ||||
\(969\) | −0.0339686 | − | 0.0339686i | −0.00109123 | − | 0.00109123i | ||||
\(970\) | 16.5395 | + | 9.84339i | 0.531051 | + | 0.316052i | ||||
\(971\) | 11.8306i | 0.379662i | 0.981817 | + | 0.189831i | \(0.0607940\pi\) | ||||
−0.981817 | + | 0.189831i | \(0.939206\pi\) | |||||||
\(972\) | −4.53417 | + | 2.46005i | −0.145434 | + | 0.0789063i | ||||
\(973\) | −14.2989 | − | 14.2989i | −0.458403 | − | 0.458403i | ||||
\(974\) | −2.36108 | + | 0.599253i | −0.0756540 | + | 0.0192013i | ||||
\(975\) | 4.42700 | + | 4.75776i | 0.141778 | + | 0.152370i | ||||
\(976\) | 12.8461 | − | 19.7547i | 0.411194 | − | 0.632334i | ||||
\(977\) | 20.7800 | − | 20.7800i | 0.664812 | − | 0.664812i | −0.291699 | − | 0.956510i | \(-0.594220\pi\) |
0.956510 | + | 0.291699i | \(0.0942205\pi\) | |||||||
\(978\) | −46.5795 | + | 11.8221i | −1.48945 | + | 0.378028i | ||||
\(979\) | −59.5579 | −1.90348 | ||||||||
\(980\) | 2.33006 | − | 7.85730i | 0.0744311 | − | 0.250992i | ||||
\(981\) | −0.654002 | + | 0.654002i | −0.0208807 | + | 0.0208807i | ||||
\(982\) | 1.13492 | − | 1.90697i | 0.0362168 | − | 0.0608537i | ||||
\(983\) | −16.0481 | + | 16.0481i | −0.511854 | + | 0.511854i | −0.915094 | − | 0.403240i | \(-0.867884\pi\) |
0.403240 | + | 0.915094i | \(0.367884\pi\) | |||||||
\(984\) | 21.8613 | + | 23.6712i | 0.696911 | + | 0.754611i | ||||
\(985\) | − | 0.953635i | − | 0.0303853i | ||||||
\(986\) | −0.606825 | − | 0.361149i | −0.0193252 | − | 0.0115013i | ||||
\(987\) | −17.7132 | −0.563817 | ||||||||
\(988\) | 1.32459 | − | 0.658109i | 0.0421408 | − | 0.0209373i | ||||
\(989\) | 34.9248 | 1.11054 | ||||||||
\(990\) | 1.20525 | + | 0.717300i | 0.0383054 | + | 0.0227973i | ||||
\(991\) | − | 32.8640i | − | 1.04396i | −0.852958 | − | 0.521980i | \(-0.825194\pi\) | ||
0.852958 | − | 0.521980i | \(-0.174806\pi\) | |||||||
\(992\) | 6.25443 | − | 18.3786i | 0.198578 | − | 0.583522i | ||||
\(993\) | −18.6936 | + | 18.6936i | −0.593222 | + | 0.593222i | ||||
\(994\) | −11.1963 | + | 18.8127i | −0.355124 | + | 0.596702i | ||||
\(995\) | 12.8177 | − | 12.8177i | 0.406350 | − | 0.406350i | ||||
\(996\) | 55.0752 | + | 16.3324i | 1.74512 | + | 0.517512i | ||||
\(997\) | −47.9078 | −1.51726 | −0.758628 | − | 0.651524i | \(-0.774130\pi\) | ||||
−0.758628 | + | 0.651524i | \(0.774130\pi\) | |||||||
\(998\) | 46.9336 | − | 11.9120i | 1.48566 | − | 0.377066i | ||||
\(999\) | 6.20700 | − | 6.20700i | 0.196381 | − | 0.196381i |
(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 | 260.2.j.a.31.20 | ✓ | 56 | |
4.3 | odd | 2 | inner | 260.2.j.a.31.23 | yes | 56 | |
13.8 | odd | 4 | inner | 260.2.j.a.151.23 | yes | 56 | |
52.47 | even | 4 | inner | 260.2.j.a.151.20 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.j.a.31.20 | ✓ | 56 | 1.1 | even | 1 | trivial | |
260.2.j.a.31.23 | yes | 56 | 4.3 | odd | 2 | inner | |
260.2.j.a.151.20 | yes | 56 | 52.47 | even | 4 | inner | |
260.2.j.a.151.23 | yes | 56 | 13.8 | odd | 4 | inner |