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 | 269.5 | ||
Root | \(0.104634 + 2.23362i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.269 |
Dual form | 630.2.bo.a.89.5 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||
\(5\) | −0.104634 | + | 2.23362i | −0.0467939 | + | 0.998905i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.39924 | − | 2.24547i | −0.528863 | − | 0.848707i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.98669 | − | 1.02619i | 0.628246 | − | 0.324511i | ||||
\(11\) | 1.37897 | + | 0.796151i | 0.415776 | + | 0.240049i | 0.693269 | − | 0.720679i | \(-0.256170\pi\) |
−0.277492 | + | 0.960728i | \(0.589503\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.925091 | −0.256574 | −0.128287 | − | 0.991737i | \(-0.540948\pi\) | ||||
−0.128287 | + | 0.991737i | \(0.540948\pi\) | |||||||
\(14\) | −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 | \(-0.173993\pi\) |
−0.0230153 | + | 0.999735i | \(0.507327\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.541679 | − | 0.312739i | 0.124270 | − | 0.0717472i | −0.436577 | − | 0.899667i | \(-0.643809\pi\) |
0.560846 | + | 0.827920i | \(0.310476\pi\) | |||||||
\(20\) | −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 | 0.911667 | + | 0.410930i | \(0.134796\pi\) |
−0.0999578 | + | 0.994992i | \(0.531871\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.97810 | − | 0.467426i | −0.995621 | − | 0.0934852i | ||||
\(26\) | 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 | \(0.334559\pi\) | ||||
−0.496661 | + | 0.867945i | \(0.665441\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.94618 | + | 5.16508i | 1.60678 | + | 0.927675i | 0.990084 | + | 0.140474i | \(0.0448626\pi\) |
0.616696 | + | 0.787201i | \(0.288471\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 3.95765i | − | 0.678732i | ||||||
\(35\) | 5.16193 | − | 2.89042i | 0.872525 | − | 0.488570i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.369259 | − | 0.213192i | 0.0607058 | − | 0.0350485i | −0.469340 | − | 0.883018i | \(-0.655508\pi\) |
0.530046 | + | 0.847969i | \(0.322175\pi\) | |||||||
\(38\) | −0.541679 | − | 0.312739i | −0.0878720 | − | 0.0507329i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.104634 | + | 2.23362i | −0.0165441 | + | 0.353166i | ||||
\(41\) | −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 | \(-0.601647\pi\) |
0.665276 | + | 0.746597i | \(0.268314\pi\) | |||||||
\(48\) | 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 | \(-0.907257\pi\) |
0.727697 | + | 0.685899i | \(0.240591\pi\) | |||||||
\(54\) | 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 | −0.589789 | − | 0.807557i | \(-0.700789\pi\) |
0.994260 | + | 0.106994i | \(0.0341224\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.52671 | − | 5.50025i | 1.21977 | − | 0.704235i | 0.254902 | − | 0.966967i | \(-0.417957\pi\) |
0.964869 | + | 0.262732i | \(0.0846236\pi\) | |||||||
\(62\) | − | 10.3302i | − | 1.31193i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.0967962 | − | 2.06630i | 0.0120061 | − | 0.256293i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.308459 | + | 0.178089i | 0.0376843 | + | 0.0217570i | 0.518724 | − | 0.854942i | \(-0.326407\pi\) |
−0.481039 | + | 0.876699i | \(0.659741\pi\) | |||||||
\(68\) | −3.42743 | + | 1.97883i | −0.415637 | + | 0.239968i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.08414 | − | 3.02515i | −0.607671 | − | 0.361575i | ||||
\(71\) | − | 9.07975i | − | 1.07757i | −0.842444 | − | 0.538784i | \(-0.818884\pi\) | ||
0.842444 | − | 0.538784i | \(-0.181116\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.41511 | − | 5.91515i | 0.399709 | − | 0.692316i | −0.593981 | − | 0.804479i | \(-0.702445\pi\) |
0.993690 | + | 0.112163i | \(0.0357779\pi\) | |||||||
\(74\) | −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 | −0.999943 | − | 0.0106498i | \(-0.996610\pi\) |
0.490749 | − | 0.871301i | \(-0.336723\pi\) | |||||||
\(80\) | 1.98669 | − | 1.02619i | 0.222118 | − | 0.114732i | ||||
\(81\) | 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 | 0.952579 | − | 0.304293i | \(-0.0984201\pi\) |
−0.739815 | + | 0.672811i | \(0.765087\pi\) | |||||||
\(90\) | 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 | ||||
\(95\) | 0.641860 | + | 1.24263i | 0.0658535 | + | 0.127491i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.87721 | −0.799809 | −0.399905 | − | 0.916557i | \(-0.630957\pi\) | ||||
−0.399905 | + | 0.916557i | \(0.630957\pi\) | |||||||
\(98\) | 6.98414 | − | 0.470912i | 0.705505 | − | 0.0475693i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.89385 | − | 4.07745i | 0.289385 | − | 0.407745i | ||||
\(101\) | 3.76411 | − | 6.51962i | 0.374543 | − | 0.648727i | −0.615716 | − | 0.787968i | \(-0.711133\pi\) |
0.990258 | + | 0.139241i | \(0.0444664\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.831805 | + | 1.44073i | 0.0819601 | + | 0.141959i | 0.904092 | − | 0.427338i | \(-0.140549\pi\) |
−0.822132 | + | 0.569297i | \(0.807215\pi\) | |||||||
\(104\) | −0.925091 | −0.0907127 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.35114 | 0.325492 | ||||||||
\(107\) | 9.70139 | + | 16.8033i | 0.937869 | + | 1.62444i | 0.769436 | + | 0.638724i | \(0.220537\pi\) |
0.168433 | + | 0.985713i | \(0.446129\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.00000 | + | 1.73205i | −0.0957826 | + | 0.165900i | −0.909935 | − | 0.414751i | \(-0.863869\pi\) |
0.814152 | + | 0.580651i | \(0.197202\pi\) | |||||||
\(110\) | 3.55660 | + | 0.166609i | 0.339108 | + | 0.0158856i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.24501 | + | 2.33451i | −0.117643 | + | 0.220591i | ||||
\(113\) | −16.0750 | −1.51221 | −0.756104 | − | 0.654451i | \(-0.772900\pi\) | ||||
−0.756104 | + | 0.654451i | \(0.772900\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.4676 | + | 7.98957i | −1.44236 | + | 0.745031i | ||||
\(116\) | −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 | ||||||||
\(130\) | −1.83787 | + | 0.949323i | −0.161192 | + | 0.0832611i | ||||
\(131\) | −4.70080 | − | 8.14203i | −0.410711 | − | 0.711372i | 0.584257 | − | 0.811569i | \(-0.301386\pi\) |
−0.994968 | + | 0.100197i | \(0.968053\pi\) | |||||||
\(132\) | 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 | \(-0.964456\pi\) |
0.593390 | + | 0.804915i | \(0.297789\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.1106i | 1.19685i | 0.801180 | + | 0.598423i | \(0.204206\pi\) | ||||
−0.801180 | + | 0.598423i | \(0.795794\pi\) | |||||||
\(140\) | −0.0777878 | + | 5.91557i | −0.00657427 | + | 0.499957i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.86330 | + | 4.53988i | −0.659873 | + | 0.380978i | ||||
\(143\) | −1.27568 | − | 0.736513i | −0.106678 | − | 0.0615903i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −20.8800 | − | 0.978126i | −1.73399 | − | 0.0812290i | ||||
\(146\) | −6.83023 | −0.565274 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.426383i | 0.0350485i | ||||||||
\(149\) | 2.14103 | − | 1.23612i | 0.175400 | − | 0.101267i | −0.409730 | − | 0.912207i | \(-0.634377\pi\) |
0.585130 | + | 0.810940i | \(0.301044\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.4425 | − | 18.0869i | 0.849796 | − | 1.47189i | −0.0315949 | − | 0.999501i | \(-0.510059\pi\) |
0.881391 | − | 0.472388i | \(-0.156608\pi\) | |||||||
\(152\) | 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 | 0.297498 | − | 0.954723i | \(-0.403848\pi\) |
0.678065 | − | 0.735002i | \(-0.262819\pi\) | |||||||
\(158\) | −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 | \(-0.741081\pi\) |
0.285780 | + | 0.958295i | \(0.407747\pi\) | |||||||
\(164\) | 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 | ||||||||
\(170\) | 8.83988 | + | 0.414106i | 0.677988 | + | 0.0317605i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.43113 | − | 3.13566i | −0.414120 | − | 0.239092i | ||||
\(173\) | −14.2014 | + | 8.19918i | −1.07971 | + | 0.623372i | −0.930819 | − | 0.365481i | \(-0.880904\pi\) |
−0.148893 | + | 0.988853i | \(0.547571\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.91598 | + | 11.8322i | 0.447206 | + | 0.894431i | ||||
\(176\) | − | 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 | 0.598682 | − | 0.800987i | \(-0.295691\pi\) |
−0.394334 | + | 0.918967i | \(0.629025\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.17916i | 0.607952i | 0.952680 | + | 0.303976i | \(0.0983143\pi\) | ||||
−0.952680 | + | 0.303976i | \(0.901686\pi\) | |||||||
\(182\) | 1.15175 | − | 2.15964i | 0.0853733 | − | 0.160083i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.89282 | + | 6.74256i | 0.286983 | + | 0.497068i | ||||
\(185\) | 0.437552 | + | 0.847091i | 0.0321695 | + | 0.0622793i | ||||
\(186\) | 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 | −0.408756 | − | 0.912644i | \(-0.634037\pi\) |
0.585995 | + | 0.810315i | \(0.300704\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.3420 | + | 8.85772i | 1.10434 | + | 0.637593i | 0.937358 | − | 0.348367i | \(-0.113264\pi\) |
0.166985 | + | 0.985959i | \(0.446597\pi\) | |||||||
\(194\) | 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 | \(-0.548992\pi\) | ||||
−0.153306 | + | 0.988179i | \(0.548992\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.00000 | − | 1.73205i | −0.212664 | − | 0.122782i | 0.389885 | − | 0.920864i | \(-0.372515\pi\) |
−0.602549 | + | 0.798082i | \(0.705848\pi\) | |||||||
\(200\) | −4.97810 | − | 0.467426i | −0.352005 | − | 0.0330520i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.52821 | −0.529683 | ||||||||
\(203\) | 20.9907 | − | 13.0802i | 1.47326 | − | 0.918048i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.874180 | − | 18.6610i | 0.0610554 | − | 1.30334i | ||||
\(206\) | 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 | ||||
\(215\) | −14.0078 | − | 0.656196i | −0.955321 | − | 0.0447522i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.919844 | − | 27.3155i | −0.0624431 | − | 1.85430i | ||||
\(218\) | 2.00000 | 0.135457 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.63401 | − | 3.16341i | −0.110165 | − | 0.213277i | ||||
\(221\) | −3.17068 | − | 1.83059i | −0.213283 | − | 0.123139i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.3555 | −1.22918 | −0.614589 | − | 0.788848i | \(-0.710678\pi\) | ||||
−0.614589 | + | 0.788848i | \(0.710678\pi\) | |||||||
\(224\) | 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 | \(-0.301346\pi\) |
−0.410595 | + | 0.911818i | \(0.634679\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.22014 | − | 5.32325i | 0.609284 | − | 0.351770i | −0.163401 | − | 0.986560i | \(-0.552246\pi\) |
0.772685 | + | 0.634789i | \(0.218913\pi\) | |||||||
\(230\) | 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 | \(-0.208345\pi\) |
−0.923893 | + | 0.382651i | \(0.875011\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.85415 | + | 5.52558i | 0.186184 | + | 0.360449i | ||||
\(236\) | 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 | \(0.0859421\pi\) | ||||
−0.963772 | + | 0.266727i | \(0.914058\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.48785 | − | 5.47782i | −0.611166 | − | 0.352857i | 0.162255 | − | 0.986749i | \(-0.448123\pi\) |
−0.773422 | + | 0.633892i | \(0.781456\pi\) | |||||||
\(242\) | −4.23229 | + | 7.33053i | −0.272062 | + | 0.471225i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.0005i | 0.704235i | ||||||||
\(245\) | −13.7131 | − | 7.54655i | −0.876099 | − | 0.482131i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.501103 | + | 0.289312i | −0.0318844 | + | 0.0184085i | ||||
\(248\) | 8.94618 | + | 5.16508i | 0.568083 | + | 0.327983i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10.3696 | + | 4.17987i | −0.655831 | + | 0.264358i | ||||
\(251\) | −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 | \(-0.483656\pi\) |
0.890545 | + | 0.454895i | \(0.150323\pi\) | |||||||
\(258\) | 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 | −0.431186 | − | 0.902263i | \(-0.641905\pi\) |
0.996976 | − | 0.0777137i | \(-0.0247620\pi\) | |||||||
\(264\) | 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 | 0.187117 | + | 0.982338i | \(0.440086\pi\) |
−0.944288 | + | 0.329121i | \(0.893248\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.1663 | − | 12.2204i | 1.28576 | − | 0.742335i | 0.307867 | − | 0.951430i | \(-0.400385\pi\) |
0.977895 | + | 0.209094i | \(0.0670516\pi\) | |||||||
\(272\) | − | 3.95765i | − | 0.239968i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.37271 | 0.566226 | ||||||||
\(275\) | −6.49254 | − | 4.60789i | −0.391515 | − | 0.277866i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.0892 | + | 11.5985i | 1.20704 | + | 0.696888i | 0.962113 | − | 0.272653i | \(-0.0879010\pi\) |
0.244932 | + | 0.969540i | \(0.421234\pi\) | |||||||
\(278\) | 12.2201 | − | 7.05530i | 0.732915 | − | 0.423149i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.16193 | − | 2.89042i | 0.308484 | − | 0.172736i | ||||
\(281\) | 14.0801i | 0.839949i | 0.907536 | + | 0.419974i | \(0.137961\pi\) | ||||
−0.907536 | + | 0.419974i | \(0.862039\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.39910 | + | 2.42331i | −0.0831677 | + | 0.144051i | −0.904609 | − | 0.426242i | \(-0.859837\pi\) |
0.821441 | + | 0.570293i | \(0.193170\pi\) | |||||||
\(284\) | 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 | ||||
\(290\) | 9.59291 | + | 18.5717i | 0.563315 | + | 1.09057i | ||||
\(291\) | 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 | ||||
\(305\) | 11.2886 | + | 21.8546i | 0.646386 | + | 1.25139i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 34.2860 | 1.95681 | 0.978403 | − | 0.206704i | \(-0.0662738\pi\) | ||||
0.978403 | + | 0.206704i | \(0.0662738\pi\) | |||||||
\(308\) | 3.71725 | + | 1.98243i | 0.211810 | + | 0.112960i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 23.0736 | + | 1.08089i | 1.31049 | + | 0.0613903i | ||||
\(311\) | −4.34021 | + | 7.51746i | −0.246110 | + | 0.426276i | −0.962443 | − | 0.271483i | \(-0.912486\pi\) |
0.716333 | + | 0.697759i | \(0.245819\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.0106 | − | 25.9992i | −0.848452 | − | 1.46956i | −0.882589 | − | 0.470145i | \(-0.844202\pi\) |
0.0341376 | − | 0.999417i | \(-0.489132\pi\) | |||||||
\(314\) | −24.4475 | −1.37965 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.05164 | 0.509195 | ||||||||
\(317\) | 13.8628 | + | 24.0111i | 0.778613 | + | 1.34860i | 0.932741 | + | 0.360547i | \(0.117410\pi\) |
−0.154128 | + | 0.988051i | \(0.549257\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.44246 | + | 12.8907i | −0.416698 | + | 0.721742i | ||||
\(320\) | −0.104634 | + | 2.23362i | −0.00584923 | + | 0.124863i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −20.5872 | + | 0.693269i | −1.14728 | + | 0.0386344i | ||||
\(323\) | 2.47542 | 0.137736 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.60520 | + | 0.432412i | 0.255451 | + | 0.0239859i | ||||
\(326\) | 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 | 0.766314 | − | 0.642467i | \(-0.222089\pi\) |
−0.939549 | + | 0.342414i | \(0.888756\pi\) | |||||||
\(332\) | 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 | ||||||||
\(340\) | −4.06132 | − | 7.86262i | −0.220256 | − | 0.426410i | ||||
\(341\) | 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 | \(-0.762987\pi\) |
0.954566 | + | 0.298001i | \(0.0963199\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 27.5885i | − | 1.47678i | −0.674374 | − | 0.738390i | \(-0.735587\pi\) | ||
0.674374 | − | 0.738390i | \(-0.264413\pi\) | |||||||
\(350\) | 7.28901 | − | 11.0395i | 0.389614 | − | 0.590086i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.37897 | + | 0.796151i | −0.0734996 | + | 0.0424350i | ||||
\(353\) | −6.09929 | − | 3.52142i | −0.324632 | − | 0.187426i | 0.328823 | − | 0.944391i | \(-0.393348\pi\) |
−0.653455 | + | 0.756965i | \(0.726681\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.2807 | + | 0.950053i | 1.07639 | + | 0.0504236i | ||||
\(356\) | −4.01442 | −0.212764 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 3.15693i | − | 0.166849i | ||||||
\(359\) | −14.1545 | + | 8.17213i | −0.747048 | + | 0.431308i | −0.824626 | − | 0.565678i | \(-0.808615\pi\) |
0.0775782 | + | 0.996986i | \(0.475281\pi\) | |||||||
\(360\) | 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 | \(-0.808318\pi\) |
0.902606 | + | 0.430467i | \(0.141651\pi\) | |||||||
\(368\) | 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 | \(-0.461616\pi\) |
0.919884 | + | 0.392189i | \(0.128282\pi\) | |||||||
\(374\) | 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 | \(0.252992\pi\) | |||||||
\(380\) | −1.39708 | − | 0.0654463i | −0.0716686 | − | 0.00335733i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.44949 | − | 1.41421i | −0.125327 | − | 0.0723575i | ||||
\(383\) | 3.69096 | − | 2.13098i | 0.188599 | − | 0.108888i | −0.402727 | − | 0.915320i | \(-0.631938\pi\) |
0.591327 | + | 0.806432i | \(0.298604\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.41938 | + | 0.123862i | 0.480056 | + | 0.00631258i | ||||
\(386\) | − | 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 | 0.545007 | − | 0.838432i | \(-0.316527\pi\) |
−0.453600 | + | 0.891205i | \(0.649860\pi\) | |||||||
\(390\) | 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 | ||||
\(395\) | 17.9828 | − | 9.28874i | 0.904812 | − | 0.467367i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.1885 | + | 19.3791i | 0.561537 | + | 0.972610i | 0.997363 | + | 0.0725790i | \(0.0231229\pi\) |
−0.435826 | + | 0.900031i | \(0.643544\pi\) | |||||||
\(398\) | 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 | −0.860789 | − | 0.508961i | \(-0.830030\pi\) |
0.0103787 | + | 0.999946i | \(0.496696\pi\) | |||||||
\(402\) | 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 | 0.553388 | − | 0.832923i | \(-0.313335\pi\) |
−0.444639 | + | 0.895710i | \(0.646668\pi\) | |||||||
\(410\) | −16.5980 | + | 8.57346i | −0.819718 | + | 0.423413i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.66361 | −0.0819601 | ||||||||
\(413\) | −16.4303 | + | 0.553287i | −0.808483 | + | 0.0272255i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.80900 | + | 0.0847430i | 0.0888004 | + | 0.00415987i | ||||
\(416\) | 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 | ||||
\(425\) | −16.1371 | − | 11.4529i | −0.782766 | − | 0.555546i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −25.6808 | − | 13.6957i | −1.24278 | − | 0.662784i | ||||
\(428\) | −19.4028 | −0.937869 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.43560 | + | 12.4592i | 0.310352 | + | 0.600835i | ||||
\(431\) | 29.1599 | + | 16.8355i | 1.40458 | + | 0.810937i | 0.994859 | − | 0.101271i | \(-0.0322910\pi\) |
0.409726 | + | 0.912209i | \(0.365624\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.7610 | −1.09382 | −0.546912 | − | 0.837190i | \(-0.684197\pi\) | ||||
−0.546912 | + | 0.837190i | \(0.684197\pi\) | |||||||
\(434\) | −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 | −0.454887 | − | 0.890549i | \(-0.650320\pi\) |
0.543795 | + | 0.839218i | \(0.316987\pi\) | |||||||
\(440\) | −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 | \(-0.224950\pi\) |
−0.942590 | + | 0.333954i | \(0.891617\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.97540 | + | 4.11957i | −0.378070 | + | 0.195286i | ||||
\(446\) | 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 | \(0.146586\pi\) | ||||
−0.895824 | + | 0.444408i | \(0.853414\pi\) | |||||||
\(450\) | 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 | ||||||
\(455\) | −4.77525 | + | 2.67390i | −0.223867 | + | 0.125354i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.3442 | + | 14.6325i | −1.18555 | + | 0.684478i | −0.957292 | − | 0.289123i | \(-0.906636\pi\) |
−0.228258 | + | 0.973601i | \(0.573303\pi\) | |||||||
\(458\) | −9.22014 | − | 5.32325i | −0.430829 | − | 0.248739i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.814645 | − | 17.3902i | 0.0379830 | − | 0.810820i | ||||
\(461\) | −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 | \(-0.801089\pi\) |
0.101126 | + | 0.994874i | \(0.467755\pi\) | |||||||
\(468\) | 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 | −0.681261 | − | 0.732041i | \(-0.738568\pi\) |
0.974596 | + | 0.223969i | \(0.0719013\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.341598 | + | 0.197222i | −0.0155755 | + | 0.00899254i | ||||
\(482\) | 10.9556i | 0.499015i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.46457 | 0.384753 | ||||||||
\(485\) | 0.824225 | − | 17.5947i | 0.0374262 | − | 0.798933i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.27235 | + | 1.88929i | 0.148284 | + | 0.0856119i | 0.572306 | − | 0.820040i | \(-0.306049\pi\) |
−0.424022 | + | 0.905652i | \(0.639382\pi\) | |||||||
\(488\) | 9.52671 | − | 5.50025i | 0.431254 | − | 0.248985i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.321058 | + | 15.6492i | 0.0145039 | + | 0.706958i | ||||
\(491\) | − | 32.1664i | − | 1.45165i | −0.687880 | − | 0.725824i | \(-0.741459\pi\) | ||
0.687880 | − | 0.725824i | \(-0.258541\pi\) | |||||||
\(492\) | 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 | −0.963022 | − | 0.269424i | \(-0.913167\pi\) |
0.248183 | − | 0.968713i | \(-0.420167\pi\) | |||||||
\(500\) | 8.80467 | + | 6.89041i | 0.393757 | + | 0.308148i | ||||
\(501\) | 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 | −0.901265 | − | 0.433269i | \(-0.857360\pi\) |
0.0754100 | − | 0.997153i | \(-0.475973\pi\) | |||||||
\(510\) | 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 | ||||
\(515\) | −3.30507 | + | 1.70718i | −0.145639 | + | 0.0752275i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.42867 | 0.194773 | ||||||||
\(518\) | 0.0379671 | + | 1.12747i | 0.00166818 | + | 0.0495380i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.0967962 | − | 2.06630i | 0.00424480 | − | 0.0906133i | ||||
\(521\) | −6.00676 | + | 10.4040i | −0.263161 | + | 0.455808i | −0.967080 | − | 0.254472i | \(-0.918098\pi\) |
0.703919 | + | 0.710280i | \(0.251432\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.5178 | − | 23.4136i | −0.591093 | − | 1.02380i | −0.994085 | − | 0.108600i | \(-0.965363\pi\) |
0.402992 | − | 0.915203i | \(-0.367970\pi\) | |||||||
\(524\) | 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 | ||||
\(530\) | −0.350644 | + | 7.48517i | −0.0152310 | + | 0.325135i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.40449 | − | 0.875193i | 0.0608923 | − | 0.0379444i | ||||
\(533\) | 7.72879 | 0.334771 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −38.5473 | + | 19.9110i | −1.66654 | + | 0.860828i | ||||
\(536\) | 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 | 0.963995 | − | 0.265919i | \(-0.0856755\pi\) |
−0.712291 | + | 0.701885i | \(0.752342\pi\) | |||||||
\(542\) | −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 | ||||||||
\(550\) | −0.744284 | + | 7.92665i | −0.0317364 | + | 0.337993i | ||||
\(551\) | 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 | \(-0.693451\pi\) |
0.996462 | + | 0.0840462i | \(0.0267843\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 5.80155i | − | 0.245380i | ||||||
\(560\) | −5.08414 | − | 3.02515i | −0.214844 | − | 0.127836i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12.1937 | − | 7.04005i | 0.514361 | − | 0.296967i | ||||
\(563\) | 20.6180 | + | 11.9038i | 0.868947 | + | 0.501687i | 0.866998 | − | 0.498312i | \(-0.166046\pi\) |
0.00194851 | + | 0.999998i | \(0.499380\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.68199 | − | 35.9054i | 0.0707621 | − | 1.51055i | ||||
\(566\) | 2.79820 | 0.117617 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 9.07975i | − | 0.380978i | ||||||
\(569\) | 35.8766 | − | 20.7134i | 1.50403 | − | 0.868350i | 0.504037 | − | 0.863682i | \(-0.331848\pi\) |
0.999989 | − | 0.00466765i | \(-0.00148577\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.5784 | + | 35.6428i | −0.861177 | + | 1.49160i | 0.00961607 | + | 0.999954i | \(0.496939\pi\) |
−0.870793 | + | 0.491649i | \(0.836394\pi\) | |||||||
\(572\) | 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 | \(-0.750119\pi\) |
0.965829 | + | 0.259181i | \(0.0834527\pi\) | |||||||
\(578\) | −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 | ||||||||
\(590\) | 0.650155 | − | 13.8788i | 0.0267665 | − | 0.571381i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.369259 | − | 0.213192i | −0.0151764 | − | 0.00876213i | ||||
\(593\) | −37.7010 | + | 21.7667i | −1.54819 | + | 0.893850i | −0.549914 | + | 0.835221i | \(0.685340\pi\) |
−0.998280 | + | 0.0586292i | \(0.981327\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23.4118 | + | 0.307857i | 0.959788 | + | 0.0126209i | ||||
\(596\) | 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 | −0.191141 | − | 0.981563i | \(-0.561219\pi\) |
−0.945629 | + | 0.325249i | \(0.894552\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.21681i | 0.335171i | 0.985858 | + | 0.167585i | \(0.0535970\pi\) | ||||
−0.985858 | + | 0.167585i | \(0.946403\pi\) | |||||||
\(602\) | −14.6405 | − | 7.80788i | −0.596702 | − | 0.318225i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.4425 | + | 18.0869i | 0.424898 | + | 0.735945i | ||||
\(605\) | 16.8165 | − | 8.68629i | 0.683686 | − | 0.353148i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.1180 | + | 24.4532i | 0.573034 | + | 0.992523i | 0.996252 | + | 0.0864957i | \(0.0275669\pi\) |
−0.423219 | + | 0.906028i | \(0.639100\pi\) | |||||||
\(608\) | 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 | \(-0.119716\pi\) |
0.146965 | + | 0.989142i | \(0.453050\pi\) | |||||||
\(614\) | −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 | \(-0.471603\pi\) | ||||
0.0890947 | + | 0.996023i | \(0.471603\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.47047 | + | 5.46778i | 0.380650 | + | 0.219768i | 0.678101 | − | 0.734969i | \(-0.262803\pi\) |
−0.297451 | + | 0.954737i | \(0.596136\pi\) | |||||||
\(620\) | −10.6007 | − | 20.5228i | −0.425736 | − | 0.824215i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.68041 | 0.348053 | ||||||||
\(623\) | 4.99800 | − | 9.37171i | 0.200241 | − | 0.375470i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.5630 | + | 4.65379i | 0.982521 | + | 0.186152i | ||||
\(626\) | −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 | ||||
\(635\) | −29.5225 | − | 1.38299i | −1.17156 | − | 0.0548821i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.85321 | − | 5.81318i | 0.113048 | − | 0.230327i | ||||
\(638\) | 14.8849 | 0.589300 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.98669 | − | 1.02619i | 0.0785307 | − | 0.0405639i | ||||
\(641\) | 29.0339 | + | 16.7627i | 1.14677 | + | 0.662088i | 0.948098 | − | 0.317979i | \(-0.103004\pi\) |
0.198671 | + | 0.980066i | \(0.436337\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.4072 | 0.686474 | 0.343237 | − | 0.939249i | \(-0.388477\pi\) | ||||
0.343237 | + | 0.939249i | \(0.388477\pi\) | |||||||
\(644\) | 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 | \(-0.604284\pi\) |
−0.980857 | + | 0.194730i | \(0.937617\pi\) | |||||||
\(648\) | 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 | −0.987004 | − | 0.160696i | \(-0.948626\pi\) |
0.354335 | − | 0.935119i | \(-0.384707\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.6780 | − | 9.64786i | 0.729812 | − | 0.376973i | ||||
\(656\) | 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 | \(-0.896172\pi\) | ||
0.947271 | − | 0.320433i | \(-0.103828\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.14550 | − | 1.23870i | −0.0834502 | − | 0.0481800i | 0.457694 | − | 0.889110i | \(-0.348675\pi\) |
−0.541144 | + | 0.840930i | \(0.682009\pi\) | |||||||
\(662\) | −3.15175 | + | 5.45899i | −0.122496 | + | 0.212170i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 0.809898i | − | 0.0314301i | ||||||
\(665\) | 1.89216 | − | 3.18001i | 0.0733749 | − | 0.123316i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −63.0298 | + | 36.3903i | −2.44052 | + | 1.40904i | ||||
\(668\) | 10.5170 | + | 6.07201i | 0.406916 | + | 0.234933i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.795566 | + | 0.0372684i | 0.0307354 | + | 0.00143981i | ||||
\(671\) | 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 | 0.553276 | − | 0.832998i | \(-0.313377\pi\) |
0.998035 | − | 0.0626524i | \(-0.0199560\pi\) | |||||||
\(678\) | 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 | \(-0.818913\pi\) |
0.887780 | + | 0.460268i | \(0.152247\pi\) | |||||||
\(684\) | 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 | −0.816527 | − | 0.577308i | \(-0.804103\pi\) |
0.0917001 | + | 0.995787i | \(0.470770\pi\) | |||||||
\(692\) | − | 16.3984i | − | 0.623372i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.16672 | −0.310004 | ||||||||
\(695\) | −31.5177 | − | 1.47645i | −1.19553 | − | 0.0560050i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.6349 | − | 16.5323i | −1.08462 | − | 0.626207i | ||||
\(698\) | −23.8924 | + | 13.7943i | −0.904339 | + | 0.522120i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −13.2050 | − | 0.792719i | −0.499101 | − | 0.0299620i | ||||
\(701\) | − | 28.7909i | − | 1.08742i | −0.839274 | − | 0.543708i | \(-0.817020\pi\) | ||
0.839274 | − | 0.543708i | \(-0.182980\pi\) | |||||||
\(702\) | 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 | 0.973079 | − | 0.230472i | \(-0.0740270\pi\) |
−0.686134 | + | 0.727475i | \(0.740694\pi\) | |||||||
\(710\) | −9.31758 | − | 18.0386i | −0.349683 | − | 0.676978i | ||||
\(711\) | 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 | 0.978564 | − | 0.205944i | \(-0.0660266\pi\) |
−0.667635 | + | 0.744489i | \(0.732693\pi\) | |||||||
\(720\) | 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 | ||||
\(725\) | 4.36952 | − | 46.5356i | 0.162280 | − | 1.72829i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.4228 | 1.20250 | 0.601248 | − | 0.799062i | \(-0.294670\pi\) | ||||
0.601248 | + | 0.799062i | \(0.294670\pi\) | |||||||
\(728\) | 1.29443 | + | 2.07726i | 0.0479746 | + | 0.0769885i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.714676 | − | 15.2561i | 0.0264513 | − | 0.564654i | ||||
\(731\) | −12.4099 | + | 21.4945i | −0.458996 | + | 0.795004i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.1637 | + | 40.1207i | 0.855570 | + | 1.48189i | 0.876115 | + | 0.482102i | \(0.160126\pi\) |
−0.0205452 | + | 0.999789i | \(0.506540\pi\) | |||||||
\(734\) | −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 | −0.673815 | − | 0.738900i | \(-0.735345\pi\) |
0.976814 | + | 0.214091i | \(0.0686788\pi\) | |||||||
\(740\) | −0.952378 | − | 0.0446143i | −0.0350101 | − | 0.00164005i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.68905 | − | 7.52488i | −0.172141 | − | 0.276247i | ||||
\(743\) | 38.4778 | 1.41161 | 0.705806 | − | 0.708405i | \(-0.250585\pi\) | ||||
0.705806 | + | 0.708405i | \(0.250585\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.53701 | + | 4.91159i | 0.0929487 | + | 0.179947i | ||||
\(746\) | −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 | −0.971773 | − | 0.235919i | \(-0.924190\pi\) |
0.281574 | − | 0.959539i | \(-0.409143\pi\) | |||||||
\(752\) | −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 | ||||||||
\(760\) | 0.641860 | + | 1.24263i | 0.0232827 | + | 0.0450748i | ||||
\(761\) | 14.6239 | + | 25.3294i | 0.530117 | + | 0.918189i | 0.999383 | + | 0.0351321i | \(0.0111852\pi\) |
−0.469266 | + | 0.883057i | \(0.655481\pi\) | |||||||
\(762\) | 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 | \(0.00512438\pi\) | ||||
−0.999870 | + | 0.0160980i | \(0.994876\pi\) | |||||||
\(770\) | −4.60242 | − | 8.21935i | −0.165860 | − | 0.296205i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −15.3420 | + | 8.85772i | −0.552172 | + | 0.318796i | ||||
\(773\) | 17.1302 | + | 9.89011i | 0.616130 | + | 0.355723i | 0.775361 | − | 0.631519i | \(-0.217568\pi\) |
−0.159231 | + | 0.987241i | \(0.550901\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −42.1207 | − | 29.8940i | −1.51302 | − | 1.07382i | ||||
\(776\) | −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 | \(-0.676137\pi\) |
0.999557 | + | 0.0297473i | \(0.00947025\pi\) | |||||||
\(788\) | 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 | ||||||||
\(800\) | 2.89385 | − | 4.07745i | 0.102313 | − | 0.144160i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 17.0295 | + | 9.83196i | 0.601331 | + | 0.347179i | ||||
\(803\) | 9.41871 | − | 5.43790i | 0.332379 | − | 0.191899i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 39.5833 | + | 23.5527i | 1.39513 | + | 0.830125i | ||||
\(806\) | 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 | 0.142677 | − | 0.989769i | \(-0.454429\pi\) |
−0.785827 | + | 0.618447i | \(0.787762\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.3784i | 0.469779i | 0.972022 | + | 0.234889i | \(0.0754728\pi\) | ||||
−0.972022 | + | 0.234889i | \(0.924527\pi\) | |||||||
\(812\) | 0.832393 | + | 24.7186i | 0.0292113 | + | 0.867453i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.339466 | − | 0.587972i | −0.0118983 | − | 0.0206084i | ||||
\(815\) | −6.07009 | − | 11.7516i | −0.212626 | − | 0.411639i | ||||
\(816\) | 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 | −0.595765 | − | 0.803159i | \(-0.703151\pi\) |
0.397674 | + | 0.917527i | \(0.369818\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.9915 | − | 21.9344i | −1.32430 | − | 0.764585i | −0.339889 | − | 0.940466i | \(-0.610389\pi\) |
−0.984412 | + | 0.175880i | \(0.943723\pi\) | |||||||
\(824\) | 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 | \(-0.608111\pi\) | ||||
−0.333148 | + | 0.942875i | \(0.608111\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.6635 | + | 8.46597i | 0.509284 | + | 0.294035i | 0.732539 | − | 0.680725i | \(-0.238335\pi\) |
−0.223255 | + | 0.974760i | \(0.571668\pi\) | |||||||
\(830\) | −0.831112 | − | 1.60901i | −0.0288483 | − | 0.0558497i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.925091 | −0.0320718 | ||||||||
\(833\) | −23.0058 | + | 15.4344i | −0.797103 | + | 0.534771i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 27.1251 | + | 1.27068i | 0.938704 | + | 0.0439737i | ||||
\(836\) | −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 | ||||
\(845\) | 1.27070 | − | 27.1255i | 0.0437134 | − | 0.933146i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.5385 | + | 19.7606i | −0.362107 | + | 0.678984i | ||||
\(848\) | 3.35114 | 0.115079 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.84991 | + | 19.7016i | −0.0634514 | + | 0.675759i | ||||
\(851\) | 2.87492 | + | 1.65983i | 0.0985509 | + | 0.0568984i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.2419 | 1.03546 | 0.517731 | − | 0.855544i | \(-0.326777\pi\) | ||||
0.517731 | + | 0.855544i | \(0.326777\pi\) | |||||||
\(854\) | 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 | \(-0.457502\pi\) |
−0.791761 | + | 0.610831i | \(0.790835\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.7059 | − | 15.4187i | 0.911195 | − | 0.526078i | 0.0303793 | − | 0.999538i | \(-0.490328\pi\) |
0.880815 | + | 0.473460i | \(0.156995\pi\) | |||||||
\(860\) | 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 | \(-0.0379525\pi\) |
−0.599463 | + | 0.800403i | \(0.704619\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.8279 | − | 32.5784i | −0.572165 | − | 1.10770i | ||||
\(866\) | 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 | ||||||
\(875\) | −27.0477 | + | 11.9760i | −0.914378 | + | 0.404862i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.8366 | + | 12.6074i | −0.737369 | + | 0.425720i | −0.821112 | − | 0.570767i | \(-0.806646\pi\) |
0.0837427 | + | 0.996487i | \(0.473313\pi\) | |||||||
\(878\) | −1.86282 | − | 1.07550i | −0.0628670 | − | 0.0362963i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.55660 | + | 0.166609i | 0.119893 | + | 0.00561640i | ||||
\(881\) | 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 | \(-0.477248\pi\) |
0.899522 | + | 0.436876i | \(0.143915\pi\) | |||||||
\(888\) | 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 | ||||||||
\(905\) | −18.2691 | − | 0.855820i | −0.607286 | − | 0.0284484i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.7115 | + | 13.6898i | 0.787327 | + | 0.454563i | 0.839021 | − | 0.544100i | \(-0.183129\pi\) |
−0.0516937 | + | 0.998663i | \(0.516462\pi\) | |||||||
\(908\) | −2.61803 | + | 1.51152i | −0.0868825 | + | 0.0501616i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.70329 | + | 2.79854i | 0.155913 | + | 0.0927707i | ||||
\(911\) | 33.0422i | 1.09474i | 0.836892 | + | 0.547368i | \(0.184370\pi\) | ||||
−0.836892 | + | 0.547368i | \(0.815630\pi\) | |||||||
\(912\) | 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 | 0.997448 | − | 0.0713958i | \(-0.0227453\pi\) |
−0.560555 | + | 0.828117i | \(0.689412\pi\) | |||||||
\(920\) | −15.4676 | + | 7.98957i | −0.509953 | + | 0.263408i | ||||
\(921\) | 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 | 0.999909 | + | 0.0135196i | \(0.00430354\pi\) |
−0.488246 | + | 0.872706i | \(0.662363\pi\) | |||||||
\(930\) | 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 | ||||
\(935\) | −12.5197 | + | 6.46684i | −0.409437 | + | 0.211488i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.40017 | −0.209084 | −0.104542 | − | 0.994520i | \(-0.533338\pi\) | ||||
−0.104542 | + | 0.994520i | \(0.533338\pi\) | |||||||
\(938\) | −0.799787 | + | 0.498379i | −0.0261140 | + | 0.0162727i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.21237 | − | 0.291019i | −0.202625 | − | 0.00949201i | ||||
\(941\) | 2.56243 | − | 4.43825i | 0.0835327 | − | 0.144683i | −0.821232 | − | 0.570594i | \(-0.806713\pi\) |
0.904765 | + | 0.425911i | \(0.140046\pi\) | |||||||
\(942\) | 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 | −0.973101 | − | 0.230378i | \(-0.926004\pi\) |
0.287037 | − | 0.957919i | \(-0.407330\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.15929 | + | 5.47206i | −0.102555 | + | 0.177630i | ||||
\(950\) | 2.55035 | + | 1.81004i | 0.0827444 | + | 0.0587254i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.352407 | − | 10.4650i | −0.0114216 | − | 0.339174i | ||||
\(953\) | −8.12428 | −0.263171 | −0.131586 | − | 0.991305i | \(-0.542007\pi\) | ||||
−0.131586 | + | 0.991305i | \(0.542007\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.90251 | + | 5.61920i | 0.0939231 | + | 0.181833i | ||||
\(956\) | −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 | ||||||||
\(970\) | −15.6495 | + | 8.08354i | −0.502477 | + | 0.259547i | ||||
\(971\) | −8.55280 | − | 14.8139i | −0.274473 | − | 0.475400i | 0.695529 | − | 0.718498i | \(-0.255170\pi\) |
−0.970002 | + | 0.243097i | \(0.921837\pi\) | |||||||
\(972\) | 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 | −0.412979 | − | 0.910741i | \(-0.635512\pi\) |
0.995214 | − | 0.0977201i | \(-0.0311550\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.39217i | 0.204295i | ||||||||
\(980\) | 13.3921 | − | 8.10264i | 0.427794 | − | 0.258829i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −27.8569 | + | 16.0832i | −0.888950 | + | 0.513235i | ||||
\(983\) | −22.2813 | − | 12.8641i | −0.710664 | − | 0.410302i | 0.100643 | − | 0.994923i | \(-0.467910\pi\) |
−0.811307 | + | 0.584621i | \(0.801243\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.450293 | − | 9.61237i | 0.0143475 | − | 0.306276i | ||||
\(986\) | 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 | −0.753284 | − | 0.657696i | \(-0.771531\pi\) |
0.946223 | + | 0.323515i | \(0.104865\pi\) | |||||||
\(992\) | −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 | \(-0.745772\pi\) |
0.969278 | + | 0.245968i | \(0.0791058\pi\) | |||||||
\(998\) | −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.a.269.5 | yes | 16 | |
3.2 | odd | 2 | 630.2.bo.b.269.4 | yes | 16 | ||
5.2 | odd | 4 | 3150.2.bf.f.1151.16 | 32 | |||
5.3 | odd | 4 | 3150.2.bf.f.1151.5 | 32 | |||
5.4 | even | 2 | 630.2.bo.b.269.7 | yes | 16 | ||
7.3 | odd | 6 | 4410.2.d.b.4409.14 | 16 | |||
7.4 | even | 3 | 4410.2.d.b.4409.3 | 16 | |||
7.5 | odd | 6 | inner | 630.2.bo.a.89.2 | ✓ | 16 | |
15.2 | even | 4 | 3150.2.bf.f.1151.6 | 32 | |||
15.8 | even | 4 | 3150.2.bf.f.1151.15 | 32 | |||
15.14 | odd | 2 | inner | 630.2.bo.a.269.2 | yes | 16 | |
21.5 | even | 6 | 630.2.bo.b.89.7 | yes | 16 | ||
21.11 | odd | 6 | 4410.2.d.a.4409.14 | 16 | |||
21.17 | even | 6 | 4410.2.d.a.4409.3 | 16 | |||
35.4 | even | 6 | 4410.2.d.a.4409.4 | 16 | |||
35.12 | even | 12 | 3150.2.bf.f.1601.6 | 32 | |||
35.19 | odd | 6 | 630.2.bo.b.89.4 | yes | 16 | ||
35.24 | odd | 6 | 4410.2.d.a.4409.13 | 16 | |||
35.33 | even | 12 | 3150.2.bf.f.1601.13 | 32 | |||
105.47 | odd | 12 | 3150.2.bf.f.1601.14 | 32 | |||
105.59 | even | 6 | 4410.2.d.b.4409.4 | 16 | |||
105.68 | odd | 12 | 3150.2.bf.f.1601.5 | 32 | |||
105.74 | odd | 6 | 4410.2.d.b.4409.13 | 16 | |||
105.89 | even | 6 | inner | 630.2.bo.a.89.5 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.bo.a.89.2 | ✓ | 16 | 7.5 | odd | 6 | inner | |
630.2.bo.a.89.5 | yes | 16 | 105.89 | even | 6 | inner | |
630.2.bo.a.269.2 | yes | 16 | 15.14 | odd | 2 | inner | |
630.2.bo.a.269.5 | yes | 16 | 1.1 | even | 1 | trivial | |
630.2.bo.b.89.4 | yes | 16 | 35.19 | odd | 6 | ||
630.2.bo.b.89.7 | yes | 16 | 21.5 | even | 6 | ||
630.2.bo.b.269.4 | yes | 16 | 3.2 | odd | 2 | ||
630.2.bo.b.269.7 | yes | 16 | 5.4 | even | 2 | ||
3150.2.bf.f.1151.5 | 32 | 5.3 | odd | 4 | |||
3150.2.bf.f.1151.6 | 32 | 15.2 | even | 4 | |||
3150.2.bf.f.1151.15 | 32 | 15.8 | even | 4 | |||
3150.2.bf.f.1151.16 | 32 | 5.2 | odd | 4 | |||
3150.2.bf.f.1601.5 | 32 | 105.68 | odd | 12 | |||
3150.2.bf.f.1601.6 | 32 | 35.12 | even | 12 | |||
3150.2.bf.f.1601.13 | 32 | 35.33 | even | 12 | |||
3150.2.bf.f.1601.14 | 32 | 105.47 | odd | 12 | |||
4410.2.d.a.4409.3 | 16 | 21.17 | even | 6 | |||
4410.2.d.a.4409.4 | 16 | 35.4 | even | 6 | |||
4410.2.d.a.4409.13 | 16 | 35.24 | odd | 6 | |||
4410.2.d.a.4409.14 | 16 | 21.11 | odd | 6 | |||
4410.2.d.b.4409.3 | 16 | 7.4 | even | 3 | |||
4410.2.d.b.4409.4 | 16 | 105.59 | even | 6 | |||
4410.2.d.b.4409.13 | 16 | 105.74 | odd | 6 | |||
4410.2.d.b.4409.14 | 16 | 7.3 | odd | 6 |