Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(89,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.bo (of order \(6\), 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: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 21 x^{14} - 54 x^{13} + 113 x^{12} - 168 x^{11} + 186 x^{10} - 84 x^{9} + \cdots + 390625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 89.7 | ||
Root | \(1.98669 - 1.02619i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.89 |
Dual form | 630.2.bo.b.269.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.98669 | − | 1.02619i | 0.888474 | − | 0.458928i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.39924 | − | 2.24547i | 0.528863 | − | 0.848707i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.104634 | − | 2.23362i | 0.0330883 | − | 0.706332i | ||||
\(11\) | 1.37897 | − | 0.796151i | 0.415776 | − | 0.240049i | −0.277492 | − | 0.960728i | \(-0.589503\pi\) |
0.693269 | + | 0.720679i | \(0.256170\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.925091 | 0.256574 | 0.128287 | − | 0.991737i | \(-0.459052\pi\) | ||||
0.128287 | + | 0.991737i | \(0.459052\pi\) | |||||||
\(14\) | −1.24501 | − | 2.33451i | −0.332743 | − | 0.623925i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −3.42743 | + | 1.97883i | −0.831273 | + | 0.479936i | −0.854288 | − | 0.519799i | \(-0.826007\pi\) |
0.0230153 | + | 0.999735i | \(0.492673\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.541679 | + | 0.312739i | 0.124270 | + | 0.0717472i | 0.560846 | − | 0.827920i | \(-0.310476\pi\) |
−0.436577 | + | 0.899667i | \(0.643809\pi\) | |||||||
\(20\) | −1.88205 | − | 1.20743i | −0.420840 | − | 0.269988i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 1.59230i | − | 0.339480i | ||||||
\(23\) | −3.89282 | + | 6.74256i | −0.811709 | + | 1.40592i | 0.0999578 | + | 0.994992i | \(0.468129\pi\) |
−0.911667 | + | 0.410930i | \(0.865204\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.89385 | − | 4.07745i | 0.578771 | − | 0.815490i | ||||
\(26\) | 0.462546 | − | 0.801153i | 0.0907127 | − | 0.157119i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.64425 | − | 0.0890445i | −0.499717 | − | 0.0168278i | ||||
\(29\) | − | 9.34805i | − | 1.73589i | −0.496661 | − | 0.867945i | \(-0.665441\pi\) | ||
0.496661 | − | 0.867945i | \(-0.334559\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.94618 | − | 5.16508i | 1.60678 | − | 0.927675i | 0.616696 | − | 0.787201i | \(-0.288471\pi\) |
0.990084 | − | 0.140474i | \(-0.0448626\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.95765i | 0.678732i | ||||||||
\(35\) | 0.475571 | − | 5.89693i | 0.0803862 | − | 0.996764i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.369259 | − | 0.213192i | −0.0607058 | − | 0.0350485i | 0.469340 | − | 0.883018i | \(-0.344492\pi\) |
−0.530046 | + | 0.847969i | \(0.677825\pi\) | |||||||
\(38\) | 0.541679 | − | 0.312739i | 0.0878720 | − | 0.0507329i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.98669 | + | 1.02619i | −0.314123 | + | 0.162255i | ||||
\(41\) | −8.35463 | −1.30477 | −0.652387 | − | 0.757886i | \(-0.726232\pi\) | ||||
−0.652387 | + | 0.757886i | \(0.726232\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.27133i | 0.956369i | 0.878259 | + | 0.478184i | \(0.158705\pi\) | ||||
−0.878259 | + | 0.478184i | \(0.841295\pi\) | |||||||
\(44\) | −1.37897 | − | 0.796151i | −0.207888 | − | 0.120024i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.89282 | + | 6.74256i | 0.573965 | + | 0.994137i | ||||
\(47\) | −2.40868 | − | 1.39065i | −0.351342 | − | 0.202847i | 0.313934 | − | 0.949445i | \(-0.398353\pi\) |
−0.665276 | + | 0.746597i | \(0.731686\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.08425 | − | 6.28390i | −0.440607 | − | 0.897700i | ||||
\(50\) | −2.08425 | − | 4.54488i | −0.294757 | − | 0.642743i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.462546 | − | 0.801153i | −0.0641435 | − | 0.111100i | ||||
\(53\) | 1.67557 | + | 2.90217i | 0.230157 | + | 0.398644i | 0.957854 | − | 0.287255i | \(-0.0927426\pi\) |
−0.727697 | + | 0.685899i | \(0.759409\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.92259 | − | 2.99680i | 0.259241 | − | 0.404088i | ||||
\(56\) | −1.39924 | + | 2.24547i | −0.186981 | + | 0.300063i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.09565 | − | 4.67403i | −1.06301 | − | 0.613730i | ||||
\(59\) | 3.10680 | + | 5.38113i | 0.404471 | + | 0.700564i | 0.994260 | − | 0.106994i | \(-0.0341224\pi\) |
−0.589789 | + | 0.807557i | \(0.700789\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.52671 | + | 5.50025i | 1.21977 | + | 0.704235i | 0.964869 | − | 0.262732i | \(-0.0846236\pi\) |
0.254902 | + | 0.966967i | \(0.417957\pi\) | |||||||
\(62\) | − | 10.3302i | − | 1.31193i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.83787 | − | 0.949323i | 0.227959 | − | 0.117749i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.308459 | + | 0.178089i | −0.0376843 | + | 0.0217570i | −0.518724 | − | 0.854942i | \(-0.673593\pi\) |
0.481039 | + | 0.876699i | \(0.340259\pi\) | |||||||
\(68\) | 3.42743 | + | 1.97883i | 0.415637 | + | 0.239968i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.86911 | − | 3.36032i | −0.581970 | − | 0.401635i | ||||
\(71\) | 9.07975i | 1.07757i | 0.842444 | + | 0.538784i | \(0.181116\pi\) | ||||
−0.842444 | + | 0.538784i | \(0.818884\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.41511 | − | 5.91515i | −0.399709 | − | 0.692316i | 0.593981 | − | 0.804479i | \(-0.297555\pi\) |
−0.993690 | + | 0.112163i | \(0.964222\pi\) | |||||||
\(74\) | −0.369259 | + | 0.213192i | −0.0429255 | + | 0.0247830i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 0.625477i | − | 0.0717472i | ||||||
\(77\) | 0.141786 | − | 4.21045i | 0.0161580 | − | 0.479825i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.52582 | + | 7.83895i | −0.509195 | + | 0.881951i | 0.490749 | + | 0.871301i | \(0.336723\pi\) |
−0.999943 | + | 0.0106498i | \(0.996610\pi\) | |||||||
\(80\) | −0.104634 | + | 2.23362i | −0.0116985 | + | 0.249726i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.17731 | + | 7.23532i | −0.461307 | + | 0.799007i | ||||
\(83\) | − | 0.809898i | − | 0.0888978i | −0.999012 | − | 0.0444489i | \(-0.985847\pi\) | ||
0.999012 | − | 0.0444489i | \(-0.0141532\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.77857 | + | 7.44851i | −0.518308 | + | 0.807904i | ||||
\(86\) | 5.43113 | + | 3.13566i | 0.585654 | + | 0.338127i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.37897 | + | 0.796151i | −0.146999 | + | 0.0848700i | ||||
\(89\) | 2.00721 | − | 3.47659i | 0.212764 | − | 0.368518i | −0.739815 | − | 0.672811i | \(-0.765087\pi\) |
0.952579 | + | 0.304293i | \(0.0984201\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.29443 | − | 2.07726i | 0.135693 | − | 0.217756i | ||||
\(92\) | 7.78564 | 0.811709 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.40868 | + | 1.39065i | −0.248436 | + | 0.143435i | ||||
\(95\) | 1.39708 | + | 0.0654463i | 0.143337 | + | 0.00671465i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.87721 | 0.799809 | 0.399905 | − | 0.916557i | \(-0.369043\pi\) | ||||
0.399905 | + | 0.916557i | \(0.369043\pi\) | |||||||
\(98\) | −6.98414 | − | 0.470912i | −0.705505 | − | 0.0475693i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.97810 | − | 0.467426i | −0.497810 | − | 0.0467426i | ||||
\(101\) | 3.76411 | + | 6.51962i | 0.374543 | + | 0.648727i | 0.990258 | − | 0.139241i | \(-0.0444664\pi\) |
−0.615716 | + | 0.787968i | \(0.711133\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.831805 | + | 1.44073i | −0.0819601 | + | 0.141959i | −0.904092 | − | 0.427338i | \(-0.859451\pi\) |
0.822132 | + | 0.569297i | \(0.192785\pi\) | |||||||
\(104\) | −0.925091 | −0.0907127 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.35114 | 0.325492 | ||||||||
\(107\) | −9.70139 | + | 16.8033i | −0.937869 | + | 1.62444i | −0.168433 | + | 0.985713i | \(0.553871\pi\) |
−0.769436 | + | 0.638724i | \(0.779463\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.00000 | − | 1.73205i | −0.0957826 | − | 0.165900i | 0.814152 | − | 0.580651i | \(-0.197202\pi\) |
−0.909935 | + | 0.414751i | \(0.863869\pi\) | |||||||
\(110\) | −1.63401 | − | 3.16341i | −0.155797 | − | 0.301619i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.24501 | + | 2.33451i | 0.117643 | + | 0.220591i | ||||
\(113\) | 16.0750 | 1.51221 | 0.756104 | − | 0.654451i | \(-0.227100\pi\) | ||||
0.756104 | + | 0.654451i | \(0.227100\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.814645 | + | 17.3902i | −0.0759660 | + | 1.62164i | ||||
\(116\) | −8.09565 | + | 4.67403i | −0.751662 | + | 0.433972i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.21360 | 0.572008 | ||||||||
\(119\) | −0.352407 | + | 10.4650i | −0.0323051 | + | 0.959328i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.23229 | + | 7.33053i | −0.384753 | + | 0.666412i | ||||
\(122\) | 9.52671 | − | 5.50025i | 0.862508 | − | 0.497969i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.94618 | − | 5.16508i | −0.803390 | − | 0.463838i | ||||
\(125\) | 1.56493 | − | 11.0703i | 0.139972 | − | 0.990156i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.2173i | 1.17285i | 0.810004 | + | 0.586424i | \(0.199465\pi\) | ||||
−0.810004 | + | 0.586424i | \(0.800535\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.0967962 | − | 2.06630i | 0.00848959 | − | 0.181227i | ||||
\(131\) | −4.70080 | + | 8.14203i | −0.410711 | + | 0.711372i | −0.994968 | − | 0.100197i | \(-0.968053\pi\) |
0.584257 | + | 0.811569i | \(0.301386\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.46018 | − | 0.778726i | 0.126614 | − | 0.0675241i | ||||
\(134\) | 0.356178i | 0.0307691i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.42743 | − | 1.97883i | 0.293899 | − | 0.169683i | ||||
\(137\) | 4.68636 | + | 8.11701i | 0.400382 | + | 0.693483i | 0.993772 | − | 0.111433i | \(-0.0355440\pi\) |
−0.593390 | + | 0.804915i | \(0.702211\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 14.1106i | − | 1.19685i | −0.801180 | − | 0.598423i | \(-0.795794\pi\) | ||
0.801180 | − | 0.598423i | \(-0.204206\pi\) | |||||||
\(140\) | −5.34468 | + | 2.53661i | −0.451708 | + | 0.214383i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.86330 | + | 4.53988i | 0.659873 | + | 0.380978i | ||||
\(143\) | 1.27568 | − | 0.736513i | 0.106678 | − | 0.0615903i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.59291 | − | 18.5717i | −0.796648 | − | 1.54229i | ||||
\(146\) | −6.83023 | −0.565274 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.426383i | 0.0350485i | ||||||||
\(149\) | 2.14103 | + | 1.23612i | 0.175400 | + | 0.101267i | 0.585130 | − | 0.810940i | \(-0.301044\pi\) |
−0.409730 | + | 0.912207i | \(0.634377\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.4425 | + | 18.0869i | 0.849796 | + | 1.47189i | 0.881391 | + | 0.472388i | \(0.156608\pi\) |
−0.0315949 | + | 0.999501i | \(0.510059\pi\) | |||||||
\(152\) | −0.541679 | − | 0.312739i | −0.0439360 | − | 0.0253664i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.57546 | − | 2.22802i | −0.288119 | − | 0.179539i | ||||
\(155\) | 12.4729 | − | 19.4419i | 1.00185 | − | 1.56161i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.2238 | − | 21.1722i | −0.975563 | − | 1.68972i | −0.678065 | − | 0.735002i | \(-0.737181\pi\) |
−0.297498 | − | 0.954723i | \(-0.596152\pi\) | |||||||
\(158\) | 4.52582 | + | 7.83895i | 0.360055 | + | 0.623634i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.88205 | + | 1.20743i | 0.148789 | + | 0.0954553i | ||||
\(161\) | 9.69321 | + | 18.1757i | 0.763932 | + | 1.43244i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.12267 | + | 2.95758i | 0.401239 | + | 0.231655i | 0.687018 | − | 0.726640i | \(-0.258919\pi\) |
−0.285780 | + | 0.958295i | \(0.592253\pi\) | |||||||
\(164\) | 4.17731 | + | 7.23532i | 0.326193 | + | 0.564983i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.701392 | − | 0.404949i | −0.0544386 | − | 0.0314301i | ||||
\(167\) | − | 12.1440i | − | 0.939733i | −0.882737 | − | 0.469867i | \(-0.844302\pi\) | ||
0.882737 | − | 0.469867i | \(-0.155698\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.1442 | −0.934170 | ||||||||
\(170\) | 4.06132 | + | 7.86262i | 0.311489 | + | 0.603035i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.43113 | − | 3.13566i | 0.414120 | − | 0.239092i | ||||
\(173\) | 14.2014 | + | 8.19918i | 1.07971 | + | 0.623372i | 0.930819 | − | 0.365481i | \(-0.119096\pi\) |
0.148893 | + | 0.988853i | \(0.452429\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.10658 | − | 12.2034i | −0.386021 | − | 0.922490i | ||||
\(176\) | 1.59230i | 0.120024i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.00721 | − | 3.47659i | −0.150447 | − | 0.260581i | ||||
\(179\) | 2.73398 | − | 1.57846i | 0.204347 | − | 0.117980i | −0.394334 | − | 0.918967i | \(-0.629025\pi\) |
0.598682 | + | 0.800987i | \(0.295691\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 8.17916i | − | 0.607952i | −0.952680 | − | 0.303976i | \(-0.901686\pi\) | ||
0.952680 | − | 0.303976i | \(-0.0983143\pi\) | |||||||
\(182\) | −1.15175 | − | 2.15964i | −0.0853733 | − | 0.160083i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.89282 | − | 6.74256i | 0.286983 | − | 0.497068i | ||||
\(185\) | −0.952378 | − | 0.0446143i | −0.0700202 | − | 0.00328011i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.15089 | + | 5.45750i | −0.230416 | + | 0.399092i | ||||
\(188\) | 2.78130i | 0.202847i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.755217 | − | 1.17718i | 0.0547892 | − | 0.0854017i | ||||
\(191\) | 2.44949 | + | 1.41421i | 0.177239 | + | 0.102329i | 0.585995 | − | 0.810315i | \(-0.300704\pi\) |
−0.408756 | + | 0.912644i | \(0.634037\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.3420 | + | 8.85772i | −1.10434 | + | 0.637593i | −0.937358 | − | 0.348367i | \(-0.886736\pi\) |
−0.166985 | + | 0.985959i | \(0.553403\pi\) | |||||||
\(194\) | 3.93860 | − | 6.82186i | 0.282775 | − | 0.489781i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.89989 | + | 5.81299i | −0.278564 | + | 0.415213i | ||||
\(197\) | 4.30350 | 0.306612 | 0.153306 | − | 0.988179i | \(-0.451008\pi\) | ||||
0.153306 | + | 0.988179i | \(0.451008\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.00000 | + | 1.73205i | −0.212664 | + | 0.122782i | −0.602549 | − | 0.798082i | \(-0.705848\pi\) |
0.389885 | + | 0.920864i | \(0.372515\pi\) | |||||||
\(200\) | −2.89385 | + | 4.07745i | −0.204626 | + | 0.288319i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.52821 | 0.529683 | ||||||||
\(203\) | −20.9907 | − | 13.0802i | −1.47326 | − | 0.918048i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.5980 | + | 8.57346i | −1.15926 | + | 0.598797i | ||||
\(206\) | 0.831805 | + | 1.44073i | 0.0579546 | + | 0.100380i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.462546 | + | 0.801153i | −0.0320718 | + | 0.0555499i | ||||
\(209\) | 0.995949 | 0.0688912 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.3886 | 0.715183 | 0.357592 | − | 0.933878i | \(-0.383598\pi\) | ||||
0.357592 | + | 0.933878i | \(0.383598\pi\) | |||||||
\(212\) | 1.67557 | − | 2.90217i | 0.115079 | − | 0.199322i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.70139 | + | 16.8033i | 0.663173 | + | 1.14865i | ||||
\(215\) | 6.43560 | + | 12.4592i | 0.438904 | + | 0.849708i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.919844 | − | 27.3155i | 0.0624431 | − | 1.85430i | ||||
\(218\) | −2.00000 | −0.135457 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.55660 | − | 0.166609i | −0.239786 | − | 0.0112328i | ||||
\(221\) | −3.17068 | + | 1.83059i | −0.213283 | + | 0.123139i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.3555 | 1.22918 | 0.614589 | − | 0.788848i | \(-0.289322\pi\) | ||||
0.614589 | + | 0.788848i | \(0.289322\pi\) | |||||||
\(224\) | 2.64425 | + | 0.0890445i | 0.176677 | + | 0.00594954i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.03750 | − | 13.9214i | 0.534646 | − | 0.926035i | ||||
\(227\) | −2.61803 | + | 1.51152i | −0.173765 | + | 0.100323i | −0.584360 | − | 0.811495i | \(-0.698654\pi\) |
0.410595 | + | 0.911818i | \(0.365321\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.22014 | + | 5.32325i | 0.609284 | + | 0.351770i | 0.772685 | − | 0.634789i | \(-0.218913\pi\) |
−0.163401 | + | 0.986560i | \(0.552246\pi\) | |||||||
\(230\) | 14.6530 | + | 9.40058i | 0.966190 | + | 0.619856i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.34805i | 0.613730i | ||||||||
\(233\) | 1.99293 | − | 3.45185i | 0.130561 | − | 0.226138i | −0.793332 | − | 0.608789i | \(-0.791655\pi\) |
0.923893 | + | 0.382651i | \(0.124989\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.21237 | − | 0.291019i | −0.405250 | − | 0.0189840i | ||||
\(236\) | 3.10680 | − | 5.38113i | 0.202235 | − | 0.350282i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 8.88678 | + | 5.53771i | 0.576044 | + | 0.358956i | ||||
\(239\) | − | 8.24699i | − | 0.533453i | −0.963772 | − | 0.266727i | \(-0.914058\pi\) | ||
0.963772 | − | 0.266727i | \(-0.0859421\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.48785 | + | 5.47782i | −0.611166 | + | 0.352857i | −0.773422 | − | 0.633892i | \(-0.781456\pi\) |
0.162255 | + | 0.986749i | \(0.448123\pi\) | |||||||
\(242\) | 4.23229 | + | 7.33053i | 0.272062 | + | 0.471225i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 11.0005i | − | 0.704235i | ||||||
\(245\) | −12.5759 | − | 9.31911i | −0.803447 | − | 0.595376i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.501103 | + | 0.289312i | 0.0318844 | + | 0.0184085i | ||||
\(248\) | −8.94618 | + | 5.16508i | −0.568083 | + | 0.327983i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −8.80467 | − | 6.89041i | −0.556856 | − | 0.435788i | ||||
\(251\) | −21.7369 | −1.37202 | −0.686012 | − | 0.727590i | \(-0.740640\pi\) | ||||
−0.686012 | + | 0.727590i | \(0.740640\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.3971i | 0.779399i | ||||||||
\(254\) | 11.4465 | + | 6.60867i | 0.718220 | + | 0.414665i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −15.0993 | − | 8.71758i | −0.941868 | − | 0.543787i | −0.0513223 | − | 0.998682i | \(-0.516344\pi\) |
−0.890545 | + | 0.454895i | \(0.849677\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.995397 | + | 0.530852i | −0.0618510 | + | 0.0329856i | ||||
\(260\) | −1.74107 | − | 1.11698i | −0.107977 | − | 0.0692721i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.70080 | + | 8.14203i | 0.290417 | + | 0.503016i | ||||
\(263\) | −9.17557 | − | 15.8926i | −0.565790 | − | 0.979977i | −0.996976 | − | 0.0777137i | \(-0.975238\pi\) |
0.431186 | − | 0.902263i | \(-0.358095\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.30703 | + | 4.04625i | 0.387438 | + | 0.248559i | ||||
\(266\) | 0.0556953 | − | 1.65392i | 0.00341490 | − | 0.101408i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.308459 | + | 0.178089i | 0.0188422 | + | 0.0108785i | ||||
\(269\) | −12.4185 | − | 21.5095i | −0.757171 | − | 1.31146i | −0.944288 | − | 0.329121i | \(-0.893248\pi\) |
0.187117 | − | 0.982338i | \(-0.440086\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.1663 | + | 12.2204i | 1.28576 | + | 0.742335i | 0.977895 | − | 0.209094i | \(-0.0670516\pi\) |
0.307867 | + | 0.951430i | \(0.400385\pi\) | |||||||
\(272\) | − | 3.95765i | − | 0.239968i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.37271 | 0.566226 | ||||||||
\(275\) | 0.744284 | − | 7.92665i | 0.0448820 | − | 0.477995i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.0892 | + | 11.5985i | −1.20704 | + | 0.696888i | −0.962113 | − | 0.272653i | \(-0.912099\pi\) |
−0.244932 | + | 0.969540i | \(0.578766\pi\) | |||||||
\(278\) | −12.2201 | − | 7.05530i | −0.732915 | − | 0.423149i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.475571 | + | 5.89693i | −0.0284208 | + | 0.352409i | ||||
\(281\) | − | 14.0801i | − | 0.839949i | −0.907536 | − | 0.419974i | \(-0.862039\pi\) | ||
0.907536 | − | 0.419974i | \(-0.137961\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.39910 | + | 2.42331i | 0.0831677 | + | 0.144051i | 0.904609 | − | 0.426242i | \(-0.140163\pi\) |
−0.821441 | + | 0.570293i | \(0.806830\pi\) | |||||||
\(284\) | 7.86330 | − | 4.53988i | 0.466601 | − | 0.269392i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 1.47303i | − | 0.0871018i | ||||||
\(287\) | −11.6901 | + | 18.7600i | −0.690047 | + | 1.10737i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.668498 | + | 1.15787i | −0.0393234 | + | 0.0681101i | ||||
\(290\) | −20.8800 | − | 0.978126i | −1.22611 | − | 0.0574376i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.41511 | + | 5.91515i | −0.199854 | + | 0.346158i | ||||
\(293\) | − | 25.5598i | − | 1.49322i | −0.665263 | − | 0.746609i | \(-0.731681\pi\) | ||
0.665263 | − | 0.746609i | \(-0.268319\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.6943 | + | 7.50245i | 0.680870 | + | 0.436810i | ||||
\(296\) | 0.369259 | + | 0.213192i | 0.0214627 | + | 0.0123915i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.14103 | − | 1.23612i | 0.124027 | − | 0.0716068i | ||||
\(299\) | −3.60121 | + | 6.23749i | −0.208264 | + | 0.360723i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.0821 | + | 8.77510i | 0.811677 | + | 0.505788i | ||||
\(302\) | 20.8849 | 1.20179 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.541679 | + | 0.312739i | −0.0310674 | + | 0.0179368i | ||||
\(305\) | 24.5709 | + | 1.15103i | 1.40693 | + | 0.0659077i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −34.2860 | −1.95681 | −0.978403 | − | 0.206704i | \(-0.933726\pi\) | ||||
−0.978403 | + | 0.206704i | \(0.933726\pi\) | |||||||
\(308\) | −3.71725 | + | 1.98243i | −0.211810 | + | 0.112960i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −10.6007 | − | 20.5228i | −0.602081 | − | 1.16562i | ||||
\(311\) | −4.34021 | − | 7.51746i | −0.246110 | − | 0.426276i | 0.716333 | − | 0.697759i | \(-0.245819\pi\) |
−0.962443 | + | 0.271483i | \(0.912486\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.0106 | − | 25.9992i | 0.848452 | − | 1.46956i | −0.0341376 | − | 0.999417i | \(-0.510868\pi\) |
0.882589 | − | 0.470145i | \(-0.155798\pi\) | |||||||
\(314\) | −24.4475 | −1.37965 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.05164 | 0.509195 | ||||||||
\(317\) | −13.8628 | + | 24.0111i | −0.778613 | + | 1.34860i | 0.154128 | + | 0.988051i | \(0.450743\pi\) |
−0.932741 | + | 0.360547i | \(0.882590\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.44246 | − | 12.8907i | −0.416698 | − | 0.721742i | ||||
\(320\) | 1.98669 | − | 1.02619i | 0.111059 | − | 0.0573660i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 20.5872 | + | 0.693269i | 1.14728 | + | 0.0386344i | ||||
\(323\) | −2.47542 | −0.137736 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.67708 | − | 3.77201i | 0.148498 | − | 0.209234i | ||||
\(326\) | 5.12267 | − | 2.95758i | 0.283719 | − | 0.163805i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.35463 | 0.461307 | ||||||||
\(329\) | −6.49298 | + | 3.46275i | −0.357970 | + | 0.190908i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.15175 | + | 5.45899i | −0.173236 | + | 0.300053i | −0.939549 | − | 0.342414i | \(-0.888756\pi\) |
0.766314 | + | 0.642467i | \(0.222089\pi\) | |||||||
\(332\) | −0.701392 | + | 0.404949i | −0.0384939 | + | 0.0222245i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −10.5170 | − | 6.07201i | −0.575467 | − | 0.332246i | ||||
\(335\) | −0.430058 | + | 0.670346i | −0.0234966 | + | 0.0366249i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 27.4097i | − | 1.49310i | −0.665329 | − | 0.746550i | \(-0.731709\pi\) | ||
0.665329 | − | 0.746550i | \(-0.268291\pi\) | |||||||
\(338\) | −6.07210 | + | 10.5172i | −0.330279 | + | 0.572060i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8.83988 | + | 0.414106i | 0.479410 | + | 0.0224580i | ||||
\(341\) | 8.22437 | − | 14.2450i | 0.445374 | − | 0.771411i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.4259 | − | 1.86711i | −0.994905 | − | 0.100815i | ||||
\(344\) | − | 6.27133i | − | 0.338127i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.2014 | − | 8.19918i | 0.763472 | − | 0.440791i | ||||
\(347\) | −4.08336 | − | 7.07258i | −0.219206 | − | 0.379676i | 0.735359 | − | 0.677677i | \(-0.237013\pi\) |
−0.954566 | + | 0.298001i | \(0.903680\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.5885i | 1.47678i | 0.674374 | + | 0.738390i | \(0.264413\pi\) | ||||
−0.674374 | + | 0.738390i | \(0.735587\pi\) | |||||||
\(350\) | −13.1217 | − | 1.67927i | −0.701387 | − | 0.0897605i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.37897 | + | 0.796151i | 0.0734996 | + | 0.0424350i | ||||
\(353\) | 6.09929 | − | 3.52142i | 0.324632 | − | 0.187426i | −0.328823 | − | 0.944391i | \(-0.606652\pi\) |
0.653455 | + | 0.756965i | \(0.273319\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.31758 | + | 18.0386i | 0.494526 | + | 0.957391i | ||||
\(356\) | −4.01442 | −0.212764 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 3.15693i | − | 0.166849i | ||||||
\(359\) | −14.1545 | − | 8.17213i | −0.747048 | − | 0.431308i | 0.0775782 | − | 0.996986i | \(-0.475281\pi\) |
−0.824626 | + | 0.565678i | \(0.808615\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.30439 | − | 16.1157i | −0.489705 | − | 0.848193i | ||||
\(362\) | −7.08336 | − | 4.08958i | −0.372293 | − | 0.214943i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.44618 | − | 0.0823743i | −0.128214 | − | 0.00431759i | ||||
\(365\) | −12.8549 | − | 8.24699i | −0.672854 | − | 0.431667i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.50399 | − | 2.60498i | −0.0785076 | − | 0.135979i | 0.824099 | − | 0.566446i | \(-0.191682\pi\) |
−0.902606 | + | 0.430467i | \(0.858349\pi\) | |||||||
\(368\) | −3.89282 | − | 6.74256i | −0.202927 | − | 0.351480i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.514826 | + | 0.802476i | −0.0267645 | + | 0.0417188i | ||||
\(371\) | 8.86126 | + | 0.298401i | 0.460054 | + | 0.0154922i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.0892 | − | 11.5985i | −1.04018 | − | 0.600549i | −0.120296 | − | 0.992738i | \(-0.538384\pi\) |
−0.919884 | + | 0.392189i | \(0.871718\pi\) | |||||||
\(374\) | 3.15089 | + | 5.45750i | 0.162929 | + | 0.282201i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.40868 | + | 1.39065i | 0.124218 | + | 0.0717174i | ||||
\(377\) | − | 8.64780i | − | 0.445384i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.2718 | 1.40086 | 0.700429 | − | 0.713722i | \(-0.252992\pi\) | ||||
0.700429 | + | 0.713722i | \(0.252992\pi\) | |||||||
\(380\) | −0.641860 | − | 1.24263i | −0.0329267 | − | 0.0637455i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.44949 | − | 1.41421i | 0.125327 | − | 0.0723575i | ||||
\(383\) | −3.69096 | − | 2.13098i | −0.188599 | − | 0.108888i | 0.402727 | − | 0.915320i | \(-0.368062\pi\) |
−0.591327 | + | 0.806432i | \(0.701396\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.03905 | − | 8.51035i | −0.205849 | − | 0.433728i | ||||
\(386\) | 17.7154i | 0.901692i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.93860 | − | 6.82186i | −0.199952 | − | 0.346327i | ||||
\(389\) | 1.80282 | − | 1.04086i | 0.0914066 | − | 0.0527736i | −0.453600 | − | 0.891205i | \(-0.649860\pi\) |
0.545007 | + | 0.838432i | \(0.316527\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 30.8129i | − | 1.55827i | ||||||
\(392\) | 3.08425 | + | 6.28390i | 0.155778 | + | 0.317385i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.15175 | − | 3.72694i | 0.108404 | − | 0.187760i | ||||
\(395\) | −0.947112 | + | 20.2179i | −0.0476544 | + | 1.01727i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.1885 | + | 19.3791i | −0.561537 | + | 0.972610i | 0.435826 | + | 0.900031i | \(0.356456\pi\) |
−0.997363 | + | 0.0725790i | \(0.976877\pi\) | |||||||
\(398\) | 3.46410i | 0.173640i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.08425 | + | 4.54488i | 0.104212 | + | 0.227244i | ||||
\(401\) | −17.0295 | − | 9.83196i | −0.850411 | − | 0.490985i | 0.0103787 | − | 0.999946i | \(-0.496696\pi\) |
−0.860789 | + | 0.508961i | \(0.830030\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.27603 | − | 4.77817i | 0.412258 | − | 0.238017i | ||||
\(404\) | 3.76411 | − | 6.51962i | 0.187271 | − | 0.324363i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −21.8231 | + | 11.6384i | −1.08306 | + | 0.577606i | ||||
\(407\) | −0.678932 | −0.0336534 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.19932 | − | 1.26978i | 0.108750 | − | 0.0627866i | −0.444639 | − | 0.895710i | \(-0.646668\pi\) |
0.553388 | + | 0.832923i | \(0.313335\pi\) | |||||||
\(410\) | −0.874180 | + | 18.6610i | −0.0431727 | + | 0.921604i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.66361 | 0.0819601 | ||||||||
\(413\) | 16.4303 | + | 0.553287i | 0.808483 | + | 0.0272255i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.831112 | − | 1.60901i | −0.0407977 | − | 0.0789834i | ||||
\(416\) | 0.462546 | + | 0.801153i | 0.0226782 | + | 0.0392797i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.497974 | − | 0.862517i | 0.0243567 | − | 0.0421871i | ||||
\(419\) | 32.0568 | 1.56608 | 0.783039 | − | 0.621973i | \(-0.213669\pi\) | ||||
0.783039 | + | 0.621973i | \(0.213669\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.2201 | −1.22915 | −0.614577 | − | 0.788857i | \(-0.710673\pi\) | ||||
−0.614577 | + | 0.788857i | \(0.710673\pi\) | |||||||
\(422\) | 5.19432 | − | 8.99682i | 0.252855 | − | 0.437959i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.67557 | − | 2.90217i | −0.0813729 | − | 0.140942i | ||||
\(425\) | −1.84991 | + | 19.7016i | −0.0897338 | + | 0.955668i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 25.6808 | − | 13.6957i | 1.24278 | − | 0.662784i | ||||
\(428\) | 19.4028 | 0.937869 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 14.0078 | + | 0.656196i | 0.675514 | + | 0.0316446i | ||||
\(431\) | 29.1599 | − | 16.8355i | 1.40458 | − | 0.810937i | 0.409726 | − | 0.912209i | \(-0.365624\pi\) |
0.994859 | + | 0.101271i | \(0.0322910\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.7610 | 1.09382 | 0.546912 | − | 0.837190i | \(-0.315803\pi\) | ||||
0.546912 | + | 0.837190i | \(0.315803\pi\) | |||||||
\(434\) | −23.1960 | − | 14.4544i | −1.11344 | − | 0.693832i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.00000 | + | 1.73205i | −0.0478913 | + | 0.0829502i | ||||
\(437\) | −4.21732 | + | 2.43487i | −0.201742 | + | 0.116476i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.86282 | + | 1.07550i | 0.0889074 | + | 0.0513307i | 0.543795 | − | 0.839218i | \(-0.316987\pi\) |
−0.454887 | + | 0.890549i | \(0.650320\pi\) | |||||||
\(440\) | −1.92259 | + | 2.99680i | −0.0916557 | + | 0.142867i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.66119i | 0.174145i | ||||||||
\(443\) | 3.83239 | − | 6.63790i | 0.182082 | − | 0.315376i | −0.760507 | − | 0.649330i | \(-0.775050\pi\) |
0.942590 | + | 0.333954i | \(0.108383\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.420046 | − | 8.96669i | 0.0199121 | − | 0.425062i | ||||
\(446\) | 9.17777 | − | 15.8964i | 0.434580 | − | 0.752715i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.39924 | − | 2.24547i | 0.0661079 | − | 0.106088i | ||||
\(449\) | − | 18.8337i | − | 0.888817i | −0.895824 | − | 0.444408i | \(-0.853414\pi\) | ||
0.895824 | − | 0.444408i | \(-0.146586\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.5208 | + | 6.65155i | −0.542494 | + | 0.313209i | ||||
\(452\) | −8.03750 | − | 13.9214i | −0.378052 | − | 0.654805i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.02304i | 0.141879i | ||||||||
\(455\) | 0.439947 | − | 5.45520i | 0.0206250 | − | 0.255744i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.3442 | + | 14.6325i | 1.18555 | + | 0.684478i | 0.957292 | − | 0.289123i | \(-0.0933636\pi\) |
0.228258 | + | 0.973601i | \(0.426697\pi\) | |||||||
\(458\) | 9.22014 | − | 5.32325i | 0.430829 | − | 0.248739i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 15.4676 | − | 7.98957i | 0.721182 | − | 0.372516i | ||||
\(461\) | −14.1963 | −0.661188 | −0.330594 | − | 0.943773i | \(-0.607249\pi\) | ||||
−0.330594 | + | 0.943773i | \(0.607249\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 7.65787i | − | 0.355891i | −0.984040 | − | 0.177946i | \(-0.943055\pi\) | ||
0.984040 | − | 0.177946i | \(-0.0569451\pi\) | |||||||
\(464\) | 8.09565 | + | 4.67403i | 0.375831 | + | 0.216986i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.99293 | − | 3.45185i | −0.0923206 | − | 0.159904i | ||||
\(467\) | 15.3410 | + | 8.85713i | 0.709897 | + | 0.409859i | 0.811023 | − | 0.585015i | \(-0.198911\pi\) |
−0.101126 | + | 0.994874i | \(0.532245\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.0317157 | + | 0.941825i | −0.00146450 | + | 0.0434894i | ||||
\(470\) | −3.35821 | + | 5.23456i | −0.154903 | + | 0.241452i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.10680 | − | 5.38113i | −0.143002 | − | 0.247687i | ||||
\(473\) | 4.99293 | + | 8.64800i | 0.229575 | + | 0.397636i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.84272 | − | 1.30365i | 0.130433 | − | 0.0598156i | ||||
\(476\) | 9.23918 | − | 4.92732i | 0.423477 | − | 0.225843i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.14210 | − | 4.12349i | −0.326672 | − | 0.188604i | ||||
\(479\) | 6.41996 | + | 11.1197i | 0.293336 | + | 0.508072i | 0.974596 | − | 0.223969i | \(-0.0719013\pi\) |
−0.681261 | + | 0.732041i | \(0.738568\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.341598 | − | 0.197222i | −0.0155755 | − | 0.00899254i | ||||
\(482\) | 10.9556i | 0.499015i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.46457 | 0.384753 | ||||||||
\(485\) | 15.6495 | − | 8.08354i | 0.710609 | − | 0.367054i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.27235 | + | 1.88929i | −0.148284 | + | 0.0856119i | −0.572306 | − | 0.820040i | \(-0.693951\pi\) |
0.424022 | + | 0.905652i | \(0.360618\pi\) | |||||||
\(488\) | −9.52671 | − | 5.50025i | −0.431254 | − | 0.248985i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −14.3586 | + | 6.23152i | −0.648653 | + | 0.281512i | ||||
\(491\) | 32.1664i | 1.45165i | 0.687880 | + | 0.725824i | \(0.258541\pi\) | ||||
−0.687880 | + | 0.725824i | \(0.741459\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.4982 | + | 32.0398i | 0.833115 | + | 1.44300i | ||||
\(494\) | 0.501103 | − | 0.289312i | 0.0225457 | − | 0.0130168i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.3302i | 0.463838i | ||||||||
\(497\) | 20.3883 | + | 12.7048i | 0.914540 | + | 0.569886i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.9683 | + | 27.6579i | −0.714839 | + | 1.23814i | 0.248183 | + | 0.968713i | \(0.420167\pi\) |
−0.963022 | + | 0.269424i | \(0.913167\pi\) | |||||||
\(500\) | −10.3696 | + | 4.17987i | −0.463743 | + | 0.186929i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −10.8685 | + | 18.8247i | −0.485084 | + | 0.840190i | ||||
\(503\) | − | 5.29834i | − | 0.236241i | −0.992999 | − | 0.118121i | \(-0.962313\pi\) | ||
0.992999 | − | 0.118121i | \(-0.0376870\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.1685 | + | 9.08975i | 0.630490 | + | 0.404489i | ||||
\(506\) | 10.7362 | + | 6.19855i | 0.477282 | + | 0.275559i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11.4465 | − | 6.60867i | 0.507858 | − | 0.293212i | ||||
\(509\) | −18.6321 | + | 32.2718i | −0.825854 | + | 1.43042i | 0.0754100 | + | 0.997153i | \(0.475973\pi\) |
−0.901265 | + | 0.433269i | \(0.857360\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.0608 | − | 0.608195i | −0.798965 | − | 0.0269049i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −15.0993 | + | 8.71758i | −0.666001 | + | 0.384516i | ||||
\(515\) | −0.174070 | + | 3.71587i | −0.00767046 | + | 0.163741i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.42867 | −0.194773 | ||||||||
\(518\) | −0.0379671 | + | 1.12747i | −0.00166818 | + | 0.0495380i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.83787 | + | 0.949323i | −0.0805958 | + | 0.0416305i | ||||
\(521\) | −6.00676 | − | 10.4040i | −0.263161 | − | 0.455808i | 0.703919 | − | 0.710280i | \(-0.251432\pi\) |
−0.967080 | + | 0.254472i | \(0.918098\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.5178 | − | 23.4136i | 0.591093 | − | 1.02380i | −0.402992 | − | 0.915203i | \(-0.632030\pi\) |
0.994085 | − | 0.108600i | \(-0.0346369\pi\) | |||||||
\(524\) | 9.40160 | 0.410711 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18.3511 | −0.800148 | ||||||||
\(527\) | −20.4416 | + | 35.4058i | −0.890449 | + | 1.54230i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.8081 | − | 32.5766i | −0.817744 | − | 1.41637i | ||||
\(530\) | 6.65767 | − | 3.43892i | 0.289191 | − | 0.149377i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.40449 | − | 0.875193i | −0.0608923 | − | 0.0379444i | ||||
\(533\) | −7.72879 | −0.334771 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.03020 | + | 43.3384i | −0.0877730 | + | 1.87368i | ||||
\(536\) | 0.308459 | − | 0.178089i | 0.0133234 | − | 0.00769228i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −24.8371 | −1.07080 | ||||||||
\(539\) | −9.25604 | − | 6.20981i | −0.398686 | − | 0.267475i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.85450 | − | 10.1403i | 0.251705 | − | 0.435965i | −0.712291 | − | 0.701885i | \(-0.752342\pi\) |
0.963995 | + | 0.265919i | \(0.0856755\pi\) | |||||||
\(542\) | 21.1663 | − | 12.2204i | 0.909171 | − | 0.524910i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.42743 | − | 1.97883i | −0.146950 | − | 0.0848415i | ||||
\(545\) | −3.76411 | − | 2.41485i | −0.161237 | − | 0.103441i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 17.6050i | − | 0.752737i | −0.926470 | − | 0.376369i | \(-0.877173\pi\) | ||
0.926470 | − | 0.376369i | \(-0.122827\pi\) | |||||||
\(548\) | 4.68636 | − | 8.11701i | 0.200191 | − | 0.346741i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.49254 | − | 4.60789i | −0.276843 | − | 0.196481i | ||||
\(551\) | 2.92350 | − | 5.06364i | 0.124545 | − | 0.215718i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.2694 | + | 21.1312i | 0.479224 | + | 0.898589i | ||||
\(554\) | 23.1970i | 0.985548i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.2201 | + | 7.05530i | −0.518249 | + | 0.299211i | ||||
\(557\) | −10.0409 | − | 17.3913i | −0.425445 | − | 0.736892i | 0.571017 | − | 0.820938i | \(-0.306549\pi\) |
−0.996462 | + | 0.0840462i | \(0.973216\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.80155i | 0.245380i | ||||||||
\(560\) | 4.86911 | + | 3.36032i | 0.205757 | + | 0.142000i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.1937 | − | 7.04005i | −0.514361 | − | 0.296967i | ||||
\(563\) | −20.6180 | + | 11.9038i | −0.868947 | + | 0.501687i | −0.866998 | − | 0.498312i | \(-0.833954\pi\) |
−0.00194851 | + | 0.999998i | \(0.500620\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 31.9360 | − | 16.4961i | 1.34356 | − | 0.693994i | ||||
\(566\) | 2.79820 | 0.117617 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 9.07975i | − | 0.380978i | ||||||
\(569\) | 35.8766 | + | 20.7134i | 1.50403 | + | 0.868350i | 0.999989 | + | 0.00466765i | \(0.00148577\pi\) |
0.504037 | + | 0.863682i | \(0.331848\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.5784 | − | 35.6428i | −0.861177 | − | 1.49160i | −0.870793 | − | 0.491649i | \(-0.836394\pi\) |
0.00961607 | − | 0.999954i | \(-0.496939\pi\) | |||||||
\(572\) | −1.27568 | − | 0.736513i | −0.0533388 | − | 0.0307951i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 10.4016 | + | 19.5040i | 0.434155 | + | 0.814080i | ||||
\(575\) | 16.2272 | + | 35.3848i | 0.676722 | + | 1.47565i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.20835 | − | 10.7532i | −0.258457 | − | 0.447661i | 0.707372 | − | 0.706842i | \(-0.249881\pi\) |
−0.965829 | + | 0.259181i | \(0.916547\pi\) | |||||||
\(578\) | 0.668498 | + | 1.15787i | 0.0278058 | + | 0.0481611i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −11.2871 | + | 17.5935i | −0.468670 | + | 0.730532i | ||||
\(581\) | −1.81860 | − | 1.13324i | −0.0754482 | − | 0.0470148i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.62114 | + | 2.66802i | 0.191388 | + | 0.110498i | ||||
\(584\) | 3.41511 | + | 5.91515i | 0.141318 | + | 0.244771i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22.1354 | − | 12.7799i | −0.914406 | − | 0.527932i | ||||
\(587\) | − | 4.01980i | − | 0.165915i | −0.996553 | − | 0.0829575i | \(-0.973563\pi\) | ||
0.996553 | − | 0.0829575i | \(-0.0264366\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.46127 | 0.266232 | ||||||||
\(590\) | 12.3445 | − | 6.37635i | 0.508214 | − | 0.262510i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.369259 | − | 0.213192i | 0.0151764 | − | 0.00876213i | ||||
\(593\) | 37.7010 | + | 21.7667i | 1.54819 | + | 0.893850i | 0.998280 | + | 0.0586292i | \(0.0186730\pi\) |
0.549914 | + | 0.835221i | \(0.314660\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.0390 | + | 21.1524i | 0.411560 | + | 0.867163i | ||||
\(596\) | − | 2.47225i | − | 0.101267i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.60121 | + | 6.23749i | 0.147265 | + | 0.255070i | ||||
\(599\) | −27.8218 | + | 16.0629i | −1.13677 | + | 0.656314i | −0.945629 | − | 0.325249i | \(-0.894552\pi\) |
−0.191141 | + | 0.981563i | \(0.561219\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 8.21681i | − | 0.335171i | −0.985858 | − | 0.167585i | \(-0.946403\pi\) | ||
0.985858 | − | 0.167585i | \(-0.0535970\pi\) | |||||||
\(602\) | 14.6405 | − | 7.80788i | 0.596702 | − | 0.318225i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.4425 | − | 18.0869i | 0.424898 | − | 0.735945i | ||||
\(605\) | −0.885684 | + | 18.9066i | −0.0360082 | + | 0.768664i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.1180 | + | 24.4532i | −0.573034 | + | 0.992523i | 0.423219 | + | 0.906028i | \(0.360900\pi\) |
−0.996252 | + | 0.0864957i | \(0.972433\pi\) | |||||||
\(608\) | 0.625477i | 0.0253664i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 13.2823 | − | 20.7035i | 0.537784 | − | 0.838261i | ||||
\(611\) | −2.22825 | − | 1.28648i | −0.0901452 | − | 0.0520454i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.6670 | + | 15.3962i | −1.07707 | + | 0.621846i | −0.930104 | − | 0.367296i | \(-0.880284\pi\) |
−0.146965 | + | 0.989142i | \(0.546950\pi\) | |||||||
\(614\) | −17.1430 | + | 29.6926i | −0.691836 | + | 1.19829i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.141786 | + | 4.21045i | −0.00571272 | + | 0.169644i | ||||
\(617\) | −4.42613 | −0.178189 | −0.0890947 | − | 0.996023i | \(-0.528397\pi\) | ||||
−0.0890947 | + | 0.996023i | \(0.528397\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.47047 | − | 5.46778i | 0.380650 | − | 0.219768i | −0.297451 | − | 0.954737i | \(-0.596136\pi\) |
0.678101 | + | 0.734969i | \(0.262803\pi\) | |||||||
\(620\) | −23.0736 | − | 1.08089i | −0.926659 | − | 0.0434095i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −8.68041 | −0.348053 | ||||||||
\(623\) | −4.99800 | − | 9.37171i | −0.200241 | − | 0.375470i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.25121 | − | 23.5991i | −0.330049 | − | 0.943964i | ||||
\(626\) | −15.0106 | − | 25.9992i | −0.599946 | − | 1.03914i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12.2238 | + | 21.1722i | −0.487781 | + | 0.844862i | ||||
\(629\) | 1.68748 | 0.0672841 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.2293 | −1.52189 | −0.760943 | − | 0.648819i | \(-0.775263\pi\) | ||||
−0.760943 | + | 0.648819i | \(0.775263\pi\) | |||||||
\(632\) | 4.52582 | − | 7.83895i | 0.180028 | − | 0.311817i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.8628 | + | 24.0111i | 0.550563 | + | 0.953603i | ||||
\(635\) | 13.5635 | + | 26.2587i | 0.538253 | + | 1.04205i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.85321 | − | 5.81318i | −0.113048 | − | 0.230327i | ||||
\(638\) | −14.8849 | −0.589300 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.104634 | − | 2.23362i | 0.00413603 | − | 0.0882915i | ||||
\(641\) | 29.0339 | − | 16.7627i | 1.14677 | − | 0.662088i | 0.198671 | − | 0.980066i | \(-0.436337\pi\) |
0.948098 | + | 0.317979i | \(0.103004\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.4072 | −0.686474 | −0.343237 | − | 0.939249i | \(-0.611523\pi\) | ||||
−0.343237 | + | 0.939249i | \(0.611523\pi\) | |||||||
\(644\) | 10.8940 | − | 17.4824i | 0.429283 | − | 0.688903i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.23771 | + | 2.14378i | −0.0486971 | + | 0.0843458i | ||||
\(647\) | 33.1343 | − | 19.1301i | 1.30264 | − | 0.752082i | 0.321787 | − | 0.946812i | \(-0.395716\pi\) |
0.980857 | + | 0.194730i | \(0.0623831\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.56839 | + | 4.94696i | 0.336339 | + | 0.194185i | ||||
\(650\) | −1.92812 | − | 4.20443i | −0.0756271 | − | 0.164911i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 5.91515i | − | 0.231655i | ||||||
\(653\) | 16.1671 | − | 28.0023i | 0.632669 | − | 1.09581i | −0.354335 | − | 0.935119i | \(-0.615293\pi\) |
0.987004 | − | 0.160696i | \(-0.0513739\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.983730 | + | 20.9996i | −0.0384375 | + | 0.820522i | ||||
\(656\) | 4.17731 | − | 7.23532i | 0.163097 | − | 0.282492i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.247660 | + | 7.35446i | −0.00965478 | + | 0.286707i | ||||
\(659\) | 16.4516i | 0.640865i | 0.947271 | + | 0.320433i | \(0.103828\pi\) | ||||
−0.947271 | + | 0.320433i | \(0.896172\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.14550 | + | 1.23870i | −0.0834502 | + | 0.0481800i | −0.541144 | − | 0.840930i | \(-0.682009\pi\) |
0.457694 | + | 0.889110i | \(0.348675\pi\) | |||||||
\(662\) | 3.15175 | + | 5.45899i | 0.122496 | + | 0.212170i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.809898i | 0.0314301i | ||||||||
\(665\) | 2.10181 | − | 3.04552i | 0.0815045 | − | 0.118100i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 63.0298 | + | 36.3903i | 2.44052 | + | 1.40904i | ||||
\(668\) | −10.5170 | + | 6.07201i | −0.406916 | + | 0.234933i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.365508 | + | 0.707615i | 0.0141208 | + | 0.0273375i | ||||
\(671\) | 17.5161 | 0.676202 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.0784i | 0.658326i | 0.944273 | + | 0.329163i | \(0.106767\pi\) | ||||
−0.944273 | + | 0.329163i | \(0.893233\pi\) | |||||||
\(674\) | −23.7375 | − | 13.7048i | −0.914333 | − | 0.527891i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.07210 | + | 10.5172i | 0.233542 | + | 0.404507i | ||||
\(677\) | −40.3639 | − | 23.3041i | −1.55131 | − | 0.895650i | −0.998035 | − | 0.0626524i | \(-0.980044\pi\) |
−0.553276 | − | 0.832998i | \(-0.686623\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.0221 | − | 17.6880i | 0.422990 | − | 0.678803i | ||||
\(680\) | 4.77857 | − | 7.44851i | 0.183250 | − | 0.285637i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.22437 | − | 14.2450i | −0.314927 | − | 0.545470i | ||||
\(683\) | −1.18353 | − | 2.04994i | −0.0452867 | − | 0.0784388i | 0.842494 | − | 0.538706i | \(-0.181087\pi\) |
−0.887780 | + | 0.460268i | \(0.847753\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.6399 | + | 11.3168i | 0.673988 | + | 0.432395i | ||||
\(686\) | −10.8299 | + | 15.0237i | −0.413488 | + | 0.573609i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.43113 | − | 3.13566i | −0.207060 | − | 0.119546i | ||||
\(689\) | 1.55006 | + | 2.68478i | 0.0590524 | + | 0.102282i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.0534 | − | 11.0005i | −0.724826 | − | 0.418479i | 0.0917001 | − | 0.995787i | \(-0.470770\pi\) |
−0.816527 | + | 0.577308i | \(0.804103\pi\) | |||||||
\(692\) | − | 16.3984i | − | 0.623372i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.16672 | −0.310004 | ||||||||
\(695\) | −14.4802 | − | 28.0334i | −0.549266 | − | 1.06337i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 28.6349 | − | 16.5323i | 1.08462 | − | 0.626207i | ||||
\(698\) | 23.8924 | + | 13.7943i | 0.904339 | + | 0.522120i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.01516 | + | 10.5241i | −0.302944 | + | 0.397775i | ||||
\(701\) | 28.7909i | 1.08742i | 0.839274 | + | 0.543708i | \(0.182980\pi\) | ||||
−0.839274 | + | 0.543708i | \(0.817020\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.133347 | − | 0.230963i | −0.00502926 | − | 0.00871094i | ||||
\(704\) | 1.37897 | − | 0.796151i | 0.0519721 | − | 0.0300061i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 7.04285i | − | 0.265061i | ||||||
\(707\) | 19.9065 | + | 0.670346i | 0.748661 | + | 0.0252110i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.64049 | − | 13.2337i | 0.286945 | − | 0.497003i | −0.686134 | − | 0.727475i | \(-0.740694\pi\) |
0.973079 | + | 0.230472i | \(0.0740270\pi\) | |||||||
\(710\) | 20.2807 | + | 0.950053i | 0.761121 | + | 0.0356549i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.00721 | + | 3.47659i | −0.0752234 | + | 0.130291i | ||||
\(713\) | 80.4269i | 3.01201i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.77857 | − | 2.77231i | 0.0665147 | − | 0.103679i | ||||
\(716\) | −2.73398 | − | 1.57846i | −0.102174 | − | 0.0589900i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −14.1545 | + | 8.17213i | −0.528243 | + | 0.304981i | ||||
\(719\) | 8.33730 | − | 14.4406i | 0.310929 | − | 0.538545i | −0.667635 | − | 0.744489i | \(-0.732693\pi\) |
0.978564 | + | 0.205944i | \(0.0660266\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.07121 | + | 3.88372i | 0.0771360 | + | 0.144637i | ||||
\(722\) | −18.6088 | −0.692547 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.08336 | + | 4.08958i | −0.263251 | + | 0.151988i | ||||
\(725\) | −38.1162 | − | 27.0519i | −1.41560 | − | 1.00468i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.4228 | −1.20250 | −0.601248 | − | 0.799062i | \(-0.705330\pi\) | ||||
−0.601248 | + | 0.799062i | \(0.705330\pi\) | |||||||
\(728\) | −1.29443 | + | 2.07726i | −0.0479746 | + | 0.0769885i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −13.5695 | + | 7.00913i | −0.502231 | + | 0.259420i | ||||
\(731\) | −12.4099 | − | 21.4945i | −0.458996 | − | 0.795004i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.1637 | + | 40.1207i | −0.855570 | + | 1.48189i | 0.0205452 | + | 0.999789i | \(0.493460\pi\) |
−0.876115 | + | 0.482102i | \(0.839874\pi\) | |||||||
\(734\) | −3.00798 | −0.111026 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.78564 | −0.286983 | ||||||||
\(737\) | −0.283572 | + | 0.491161i | −0.0104455 | + | 0.0180921i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.23689 | + | 14.2667i | 0.302999 | + | 0.524809i | 0.976814 | − | 0.214091i | \(-0.0686788\pi\) |
−0.673815 | + | 0.738900i | \(0.735345\pi\) | |||||||
\(740\) | 0.437552 | + | 0.847091i | 0.0160847 | + | 0.0311397i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.68905 | − | 7.52488i | 0.172141 | − | 0.276247i | ||||
\(743\) | −38.4778 | −1.41161 | −0.705806 | − | 0.708405i | \(-0.749415\pi\) | ||||
−0.705806 | + | 0.708405i | \(0.749415\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.52206 | + | 0.258682i | 0.202313 | + | 0.00947737i | ||||
\(746\) | −20.0892 | + | 11.5985i | −0.735519 | + | 0.424652i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.30178 | 0.230416 | ||||||||
\(749\) | 24.1567 | + | 45.2960i | 0.882666 | + | 1.65508i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.9145 | + | 32.7608i | −0.690198 | + | 1.19546i | 0.281574 | + | 0.959539i | \(0.409143\pi\) |
−0.971773 | + | 0.235919i | \(0.924190\pi\) | |||||||
\(752\) | 2.40868 | − | 1.39065i | 0.0878355 | − | 0.0507118i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.48922 | − | 4.32390i | −0.272741 | − | 0.157467i | ||||
\(755\) | 39.3065 | + | 25.2170i | 1.43051 | + | 0.917740i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.1485i | 0.405197i | 0.979262 | + | 0.202599i | \(0.0649387\pi\) | ||||
−0.979262 | + | 0.202599i | \(0.935061\pi\) | |||||||
\(758\) | 13.6359 | − | 23.6181i | 0.495278 | − | 0.857846i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.39708 | − | 0.0654463i | −0.0506773 | − | 0.00237399i | ||||
\(761\) | 14.6239 | − | 25.3294i | 0.530117 | − | 0.918189i | −0.469266 | − | 0.883057i | \(-0.655481\pi\) |
0.999383 | − | 0.0351321i | \(-0.0111852\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.28850 | − | 0.178089i | −0.191457 | − | 0.00644726i | ||||
\(764\) | − | 2.82843i | − | 0.102329i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.69096 | + | 2.13098i | −0.133360 | + | 0.0769953i | ||||
\(767\) | 2.87407 | + | 4.97804i | 0.103777 | + | 0.179747i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 0.892823i | − | 0.0321960i | −0.999870 | − | 0.0160980i | \(-0.994876\pi\) | ||
0.999870 | − | 0.0160980i | \(-0.00512438\pi\) | |||||||
\(770\) | −9.38970 | − | 0.757253i | −0.338381 | − | 0.0272895i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 15.3420 | + | 8.85772i | 0.552172 | + | 0.318796i | ||||
\(773\) | −17.1302 | + | 9.89011i | −0.616130 | + | 0.355723i | −0.775361 | − | 0.631519i | \(-0.782432\pi\) |
0.159231 | + | 0.987241i | \(0.449099\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.82858 | − | 51.4246i | 0.173448 | − | 1.84723i | ||||
\(776\) | −7.87721 | −0.282775 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 2.08172i | − | 0.0746332i | ||||||
\(779\) | −4.52553 | − | 2.61281i | −0.162144 | − | 0.0936138i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.22886 | + | 12.5207i | 0.258669 | + | 0.448028i | ||||
\(782\) | −26.6847 | − | 15.4064i | −0.954243 | − | 0.550933i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.98414 | + | 0.470912i | 0.249434 | + | 0.0168183i | ||||
\(785\) | −46.0116 | − | 29.5186i | −1.64222 | − | 1.05356i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.2978 | − | 23.0325i | −0.474017 | − | 0.821021i | 0.525541 | − | 0.850769i | \(-0.323863\pi\) |
−0.999557 | + | 0.0297473i | \(0.990530\pi\) | |||||||
\(788\) | −2.15175 | − | 3.72694i | −0.0766529 | − | 0.132767i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 17.0357 | + | 10.9292i | 0.606102 | + | 0.388843i | ||||
\(791\) | 22.4928 | − | 36.0959i | 0.799752 | − | 1.28342i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.81308 | + | 5.08823i | 0.312962 | + | 0.180688i | ||||
\(794\) | 11.1885 | + | 19.3791i | 0.397066 | + | 0.687739i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.00000 | + | 1.73205i | 0.106332 | + | 0.0613909i | ||||
\(797\) | 21.4698i | 0.760499i | 0.924884 | + | 0.380250i | \(0.124162\pi\) | ||||
−0.924884 | + | 0.380250i | \(0.875838\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.0074 | 0.389415 | ||||||||
\(800\) | 4.97810 | + | 0.467426i | 0.176003 | + | 0.0165260i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −17.0295 | + | 9.83196i | −0.601331 | + | 0.347179i | ||||
\(803\) | −9.41871 | − | 5.43790i | −0.332379 | − | 0.191899i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 37.9091 | + | 26.1623i | 1.33612 | + | 0.922099i | ||||
\(806\) | − | 9.55634i | − | 0.336608i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.76411 | − | 6.51962i | −0.132421 | − | 0.229360i | ||||
\(809\) | −18.2930 | + | 10.5615i | −0.643149 | + | 0.371322i | −0.785827 | − | 0.618447i | \(-0.787762\pi\) |
0.142677 | + | 0.989769i | \(0.454429\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 13.3784i | − | 0.469779i | −0.972022 | − | 0.234889i | \(-0.924527\pi\) | ||
0.972022 | − | 0.234889i | \(-0.0754728\pi\) | |||||||
\(812\) | −0.832393 | + | 24.7186i | −0.0292113 | + | 0.867453i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.339466 | + | 0.587972i | −0.0118983 | + | 0.0206084i | ||||
\(815\) | 13.2122 | + | 0.618927i | 0.462803 | + | 0.0216801i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.96129 | + | 3.39705i | −0.0686167 | + | 0.118848i | ||||
\(818\) | − | 2.53956i | − | 0.0887936i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 15.7239 | + | 10.0876i | 0.549101 | + | 0.352274i | ||||
\(821\) | −5.67591 | − | 3.27699i | −0.198091 | − | 0.114368i | 0.397674 | − | 0.917527i | \(-0.369818\pi\) |
−0.595765 | + | 0.803159i | \(0.703151\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.9915 | − | 21.9344i | 1.32430 | − | 0.764585i | 0.339889 | − | 0.940466i | \(-0.389611\pi\) |
0.984412 | + | 0.175880i | \(0.0562772\pi\) | |||||||
\(824\) | 0.831805 | − | 1.44073i | 0.0289773 | − | 0.0501901i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.69432 | − | 13.9524i | 0.302514 | − | 0.485467i | ||||
\(827\) | 19.1611 | 0.666296 | 0.333148 | − | 0.942875i | \(-0.391889\pi\) | ||||
0.333148 | + | 0.942875i | \(0.391889\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.6635 | − | 8.46597i | 0.509284 | − | 0.294035i | −0.223255 | − | 0.974760i | \(-0.571668\pi\) |
0.732539 | + | 0.680725i | \(0.238335\pi\) | |||||||
\(830\) | −1.80900 | − | 0.0847430i | −0.0627914 | − | 0.00294147i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.925091 | 0.0320718 | ||||||||
\(833\) | 23.0058 | + | 15.4344i | 0.797103 | + | 0.534771i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.4621 | − | 24.1264i | −0.431269 | − | 0.834928i | ||||
\(836\) | −0.497974 | − | 0.862517i | −0.0172228 | − | 0.0298308i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 16.0284 | − | 27.7620i | 0.553692 | − | 0.959023i | ||||
\(839\) | 10.5028 | 0.362596 | 0.181298 | − | 0.983428i | \(-0.441970\pi\) | ||||
0.181298 | + | 0.983428i | \(0.441970\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −58.3861 | −2.01331 | ||||||||
\(842\) | −12.6101 | + | 21.8413i | −0.434572 | + | 0.752700i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.19432 | − | 8.99682i | −0.178796 | − | 0.309683i | ||||
\(845\) | −24.1267 | + | 12.4623i | −0.829985 | + | 0.428716i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.5385 | + | 19.7606i | 0.362107 | + | 0.678984i | ||||
\(848\) | −3.35114 | −0.115079 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 16.1371 | + | 11.4529i | 0.553499 | + | 0.392830i | ||||
\(851\) | 2.87492 | − | 1.65983i | 0.0985509 | − | 0.0568984i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.2419 | −1.03546 | −0.517731 | − | 0.855544i | \(-0.673223\pi\) | ||||
−0.517731 | + | 0.855544i | \(0.673223\pi\) | |||||||
\(854\) | 0.979534 | − | 29.0881i | 0.0335190 | − | 0.995374i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.70139 | − | 16.8033i | 0.331587 | − | 0.574325i | ||||
\(857\) | 19.2816 | − | 11.1322i | 0.658646 | − | 0.380270i | −0.133115 | − | 0.991101i | \(-0.542498\pi\) |
0.791761 | + | 0.610831i | \(0.209165\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.7059 | + | 15.4187i | 0.911195 | + | 0.526078i | 0.880815 | − | 0.473460i | \(-0.156995\pi\) |
0.0303793 | + | 0.999538i | \(0.490328\pi\) | |||||||
\(860\) | 7.57216 | − | 11.8030i | 0.258209 | − | 0.402478i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 33.6710i | − | 1.14684i | ||||||
\(863\) | −11.5580 | + | 20.0190i | −0.393437 | + | 0.681454i | −0.992900 | − | 0.118949i | \(-0.962048\pi\) |
0.599463 | + | 0.800403i | \(0.295381\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.6277 | + | 1.71583i | 1.24538 | + | 0.0583400i | ||||
\(866\) | 11.3805 | − | 19.7116i | 0.386725 | − | 0.669828i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −24.1159 | + | 12.8612i | −0.818546 | + | 0.436536i | ||||
\(869\) | 14.4130i | 0.488926i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.285353 | + | 0.164749i | −0.00966882 | + | 0.00558230i | ||||
\(872\) | 1.00000 | + | 1.73205i | 0.0338643 | + | 0.0586546i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.86974i | 0.164721i | ||||||||
\(875\) | −22.6682 | − | 19.0040i | −0.766326 | − | 0.642452i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.8366 | + | 12.6074i | 0.737369 | + | 0.425720i | 0.821112 | − | 0.570767i | \(-0.193354\pi\) |
−0.0837427 | + | 0.996487i | \(0.526687\pi\) | |||||||
\(878\) | 1.86282 | − | 1.07550i | 0.0628670 | − | 0.0362963i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.63401 | + | 3.16341i | 0.0550825 | + | 0.106638i | ||||
\(881\) | 20.5142 | 0.691140 | 0.345570 | − | 0.938393i | \(-0.387686\pi\) | ||||
0.345570 | + | 0.938393i | \(0.387686\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 43.0491i | − | 1.44872i | −0.689424 | − | 0.724358i | \(-0.742136\pi\) | ||
0.689424 | − | 0.724358i | \(-0.257864\pi\) | |||||||
\(884\) | 3.17068 | + | 1.83059i | 0.106642 | + | 0.0615696i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.83239 | − | 6.63790i | −0.128752 | − | 0.223005i | ||||
\(887\) | −28.9170 | − | 16.6952i | −0.970938 | − | 0.560571i | −0.0714156 | − | 0.997447i | \(-0.522752\pi\) |
−0.899522 | + | 0.436876i | \(0.856085\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 29.6791 | + | 18.4942i | 0.995405 | + | 0.620277i | ||||
\(890\) | −7.55535 | − | 4.84711i | −0.253256 | − | 0.162476i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.17777 | − | 15.8964i | −0.307294 | − | 0.532250i | ||||
\(893\) | −0.869820 | − | 1.50657i | −0.0291074 | − | 0.0504156i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.81176 | − | 5.94151i | 0.127413 | − | 0.198603i | ||||
\(896\) | −1.24501 | − | 2.33451i | −0.0415929 | − | 0.0779906i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −16.3104 | − | 9.41684i | −0.544287 | − | 0.314244i | ||||
\(899\) | −48.2834 | − | 83.6293i | −1.61034 | − | 2.78919i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.4858 | − | 6.63132i | −0.382647 | − | 0.220921i | ||||
\(902\) | 13.3031i | 0.442945i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −16.0750 | −0.534646 | ||||||||
\(905\) | −8.39340 | − | 16.2494i | −0.279006 | − | 0.540149i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.7115 | + | 13.6898i | −0.787327 | + | 0.454563i | −0.839021 | − | 0.544100i | \(-0.816871\pi\) |
0.0516937 | + | 0.998663i | \(0.483538\pi\) | |||||||
\(908\) | 2.61803 | + | 1.51152i | 0.0868825 | + | 0.0501616i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.50437 | − | 3.10861i | −0.149318 | − | 0.103049i | ||||
\(911\) | − | 33.0422i | − | 1.09474i | −0.836892 | − | 0.547368i | \(-0.815630\pi\) | ||
0.836892 | − | 0.547368i | \(-0.184370\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.644801 | − | 1.11683i | −0.0213398 | − | 0.0369616i | ||||
\(914\) | 25.3442 | − | 14.6325i | 0.838311 | − | 0.483999i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 10.6465i | − | 0.351770i | ||||||
\(917\) | 11.7051 | + | 21.9482i | 0.386537 | + | 0.724792i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.2444 | − | 22.9400i | 0.436893 | − | 0.756722i | −0.560555 | − | 0.828117i | \(-0.689412\pi\) |
0.997448 | + | 0.0713958i | \(0.0227453\pi\) | |||||||
\(920\) | 0.814645 | − | 17.3902i | 0.0268580 | − | 0.573336i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −7.09815 | + | 12.2944i | −0.233765 | + | 0.404893i | ||||
\(923\) | 8.39960i | 0.276476i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.93786 | + | 0.888689i | −0.0637165 | + | 0.0292199i | ||||
\(926\) | −6.63191 | − | 3.82893i | −0.217938 | − | 0.125827i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.09565 | − | 4.67403i | 0.265753 | − | 0.153432i | ||||
\(929\) | 15.5952 | − | 27.0117i | 0.511663 | − | 0.886226i | −0.488246 | − | 0.872706i | \(-0.662363\pi\) |
0.999909 | − | 0.0135196i | \(-0.00430354\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.294545 | − | 4.36842i | 0.00965332 | − | 0.143169i | ||||
\(932\) | −3.98585 | −0.130561 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 15.3410 | − | 8.85713i | 0.501973 | − | 0.289814i | ||||
\(935\) | −0.659382 | + | 14.0758i | −0.0215641 | + | 0.460327i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.40017 | 0.209084 | 0.104542 | − | 0.994520i | \(-0.466662\pi\) | ||||
0.104542 | + | 0.994520i | \(0.466662\pi\) | |||||||
\(938\) | 0.799787 | + | 0.498379i | 0.0261140 | + | 0.0162727i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.85415 | + | 5.52558i | 0.0930922 | + | 0.180224i | ||||
\(941\) | 2.56243 | + | 4.43825i | 0.0835327 | + | 0.144683i | 0.904765 | − | 0.425911i | \(-0.140046\pi\) |
−0.821232 | + | 0.570594i | \(0.806713\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.5231 | − | 56.3316i | 1.05910 | − | 1.83441i | ||||
\(944\) | −6.21360 | −0.202235 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.98585 | 0.324668 | ||||||||
\(947\) | 21.1125 | − | 36.5679i | 0.686064 | − | 1.18830i | −0.287037 | − | 0.957919i | \(-0.592670\pi\) |
0.973101 | − | 0.230378i | \(-0.0739962\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.15929 | − | 5.47206i | −0.102555 | − | 0.177630i | ||||
\(950\) | 0.292364 | − | 3.11369i | 0.00948555 | − | 0.101021i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.352407 | − | 10.4650i | 0.0114216 | − | 0.339174i | ||||
\(953\) | 8.12428 | 0.263171 | 0.131586 | − | 0.991305i | \(-0.457993\pi\) | ||||
0.131586 | + | 0.991305i | \(0.457993\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.31763 | + | 0.295950i | 0.204434 | + | 0.00957673i | ||||
\(956\) | −7.14210 | + | 4.12349i | −0.230992 | + | 0.133363i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.8399 | 0.414839 | ||||||||
\(959\) | 24.7838 | + | 0.834589i | 0.800311 | + | 0.0269503i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.8560 | − | 65.5686i | 1.22116 | − | 2.11512i | ||||
\(962\) | −0.341598 | + | 0.197222i | −0.0110136 | + | 0.00635869i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.48785 | + | 5.47782i | 0.305583 | + | 0.176429i | ||||
\(965\) | −21.3901 | + | 33.3414i | −0.688571 | + | 1.07330i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 52.3097i | − | 1.68217i | −0.540905 | − | 0.841084i | \(-0.681918\pi\) | ||
0.540905 | − | 0.841084i | \(-0.318082\pi\) | |||||||
\(968\) | 4.23229 | − | 7.33053i | 0.136031 | − | 0.235612i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.824225 | − | 17.5947i | 0.0264643 | − | 0.564931i | ||||
\(971\) | −8.55280 | + | 14.8139i | −0.274473 | + | 0.475400i | −0.970002 | − | 0.243097i | \(-0.921837\pi\) |
0.695529 | + | 0.718498i | \(0.255170\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −31.6849 | − | 19.7441i | −1.01577 | − | 0.632968i | ||||
\(974\) | 3.77858i | 0.121073i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.52671 | + | 5.50025i | −0.304943 | + | 0.176059i | ||||
\(977\) | −18.1989 | − | 31.5215i | −0.582235 | − | 1.00846i | −0.995214 | − | 0.0977201i | \(-0.968845\pi\) |
0.412979 | − | 0.910741i | \(-0.364488\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 6.39217i | − | 0.204295i | ||||||
\(980\) | −1.78262 | + | 15.5506i | −0.0569437 | + | 0.496747i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 27.8569 | + | 16.0832i | 0.888950 | + | 0.513235i | ||||
\(983\) | 22.2813 | − | 12.8641i | 0.710664 | − | 0.410302i | −0.100643 | − | 0.994923i | \(-0.532090\pi\) |
0.811307 | + | 0.584621i | \(0.198757\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.54971 | − | 4.41622i | 0.272416 | − | 0.140713i | ||||
\(986\) | 36.9963 | 1.17820 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 0.578623i | − | 0.0184085i | ||||||
\(989\) | −42.2848 | − | 24.4132i | −1.34458 | − | 0.776293i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.07375 | + | 10.5200i | 0.192939 | + | 0.334180i | 0.946223 | − | 0.323515i | \(-0.104865\pi\) |
−0.753284 | + | 0.657696i | \(0.771531\pi\) | |||||||
\(992\) | 8.94618 | + | 5.16508i | 0.284041 | + | 0.163991i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 21.1968 | − | 11.3044i | 0.672321 | − | 0.358554i | ||||
\(995\) | −4.18264 | + | 6.51962i | −0.132599 | + | 0.206686i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.57663 | − | 14.8552i | −0.271625 | − | 0.470468i | 0.697653 | − | 0.716435i | \(-0.254228\pi\) |
−0.969278 | + | 0.245968i | \(0.920894\pi\) | |||||||
\(998\) | 15.9683 | + | 27.6579i | 0.505467 | + | 0.875495i | ||||
\(999\) | 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 | 630.2.bo.b.89.7 | yes | 16 | |
3.2 | odd | 2 | 630.2.bo.a.89.2 | ✓ | 16 | ||
5.2 | odd | 4 | 3150.2.bf.f.1601.14 | 32 | |||
5.3 | odd | 4 | 3150.2.bf.f.1601.5 | 32 | |||
5.4 | even | 2 | 630.2.bo.a.89.5 | yes | 16 | ||
7.2 | even | 3 | 4410.2.d.a.4409.3 | 16 | |||
7.3 | odd | 6 | inner | 630.2.bo.b.269.4 | yes | 16 | |
7.5 | odd | 6 | 4410.2.d.a.4409.14 | 16 | |||
15.2 | even | 4 | 3150.2.bf.f.1601.6 | 32 | |||
15.8 | even | 4 | 3150.2.bf.f.1601.13 | 32 | |||
15.14 | odd | 2 | inner | 630.2.bo.b.89.4 | yes | 16 | |
21.2 | odd | 6 | 4410.2.d.b.4409.14 | 16 | |||
21.5 | even | 6 | 4410.2.d.b.4409.3 | 16 | |||
21.17 | even | 6 | 630.2.bo.a.269.5 | yes | 16 | ||
35.3 | even | 12 | 3150.2.bf.f.1151.15 | 32 | |||
35.9 | even | 6 | 4410.2.d.b.4409.4 | 16 | |||
35.17 | even | 12 | 3150.2.bf.f.1151.6 | 32 | |||
35.19 | odd | 6 | 4410.2.d.b.4409.13 | 16 | |||
35.24 | odd | 6 | 630.2.bo.a.269.2 | yes | 16 | ||
105.17 | odd | 12 | 3150.2.bf.f.1151.16 | 32 | |||
105.38 | odd | 12 | 3150.2.bf.f.1151.5 | 32 | |||
105.44 | odd | 6 | 4410.2.d.a.4409.13 | 16 | |||
105.59 | even | 6 | inner | 630.2.bo.b.269.7 | yes | 16 | |
105.89 | even | 6 | 4410.2.d.a.4409.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.bo.a.89.2 | ✓ | 16 | 3.2 | odd | 2 | ||
630.2.bo.a.89.5 | yes | 16 | 5.4 | even | 2 | ||
630.2.bo.a.269.2 | yes | 16 | 35.24 | odd | 6 | ||
630.2.bo.a.269.5 | yes | 16 | 21.17 | even | 6 | ||
630.2.bo.b.89.4 | yes | 16 | 15.14 | odd | 2 | inner | |
630.2.bo.b.89.7 | yes | 16 | 1.1 | even | 1 | trivial | |
630.2.bo.b.269.4 | yes | 16 | 7.3 | odd | 6 | inner | |
630.2.bo.b.269.7 | yes | 16 | 105.59 | even | 6 | inner | |
3150.2.bf.f.1151.5 | 32 | 105.38 | odd | 12 | |||
3150.2.bf.f.1151.6 | 32 | 35.17 | even | 12 | |||
3150.2.bf.f.1151.15 | 32 | 35.3 | even | 12 | |||
3150.2.bf.f.1151.16 | 32 | 105.17 | odd | 12 | |||
3150.2.bf.f.1601.5 | 32 | 5.3 | odd | 4 | |||
3150.2.bf.f.1601.6 | 32 | 15.2 | even | 4 | |||
3150.2.bf.f.1601.13 | 32 | 15.8 | even | 4 | |||
3150.2.bf.f.1601.14 | 32 | 5.2 | odd | 4 | |||
4410.2.d.a.4409.3 | 16 | 7.2 | even | 3 | |||
4410.2.d.a.4409.4 | 16 | 105.89 | even | 6 | |||
4410.2.d.a.4409.13 | 16 | 105.44 | odd | 6 | |||
4410.2.d.a.4409.14 | 16 | 7.5 | odd | 6 | |||
4410.2.d.b.4409.3 | 16 | 21.5 | even | 6 | |||
4410.2.d.b.4409.4 | 16 | 35.9 | even | 6 | |||
4410.2.d.b.4409.13 | 16 | 35.19 | odd | 6 | |||
4410.2.d.b.4409.14 | 16 | 21.2 | odd | 6 |