Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,2,Mod(277,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("966.277");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.i (of order \(3\), 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: | \(7.71354883526\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.29428272.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 6x^{4} - 4x^{3} - 42x^{2} + 343 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 415.2 | ||
Root | \(2.63435 + 0.245357i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 966.415 |
Dual form | 966.2.i.k.277.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(829\) | \(925\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | −0.955901 | − | 0.293691i | \(-0.905116\pi\) |
0.732294 | + | 0.680989i | \(0.238450\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.10469 | + | 2.40409i | −0.417534 | + | 0.908662i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0.500000 | + | 0.866025i | 0.158114 | + | 0.273861i | ||||
\(11\) | −2.02966 | − | 3.51547i | −0.611966 | − | 1.05996i | −0.990909 | − | 0.134535i | \(-0.957046\pi\) |
0.378943 | − | 0.925420i | \(-0.376288\pi\) | |||||||
\(12\) | 0.500000 | − | 0.866025i | 0.144338 | − | 0.250000i | ||||
\(13\) | −6.26870 | −1.73862 | −0.869312 | − | 0.494263i | \(-0.835438\pi\) | ||||
−0.869312 | + | 0.494263i | \(0.835438\pi\) | |||||||
\(14\) | 1.52966 | + | 2.15874i | 0.408819 | + | 0.576946i | ||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.92497 | − | 3.33415i | −0.466874 | − | 0.808649i | 0.532410 | − | 0.846487i | \(-0.321286\pi\) |
−0.999284 | + | 0.0378374i | \(0.987953\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | −1.60469 | + | 2.77940i | −0.368141 | + | 0.637639i | −0.989275 | − | 0.146065i | \(-0.953339\pi\) |
0.621134 | + | 0.783705i | \(0.286672\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −2.63435 | + | 0.245357i | −0.574862 | + | 0.0535412i | ||||
\(22\) | −4.05932 | −0.865450 | ||||||||
\(23\) | 0.500000 | − | 0.866025i | 0.104257 | − | 0.180579i | ||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 2.00000 | + | 3.46410i | 0.400000 | + | 0.692820i | ||||
\(26\) | −3.13435 | + | 5.42885i | −0.614697 | + | 1.06469i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.63435 | − | 0.245357i | 0.497845 | − | 0.0463680i | ||||
\(29\) | −1.26870 | −0.235592 | −0.117796 | − | 0.993038i | \(-0.537583\pi\) | ||||
−0.117796 | + | 0.993038i | \(0.537583\pi\) | |||||||
\(30\) | −0.500000 | + | 0.866025i | −0.0912871 | + | 0.158114i | ||||
\(31\) | −3.23904 | − | 5.61018i | −0.581749 | − | 1.00762i | −0.995272 | − | 0.0971249i | \(-0.969035\pi\) |
0.413523 | − | 0.910493i | \(-0.364298\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 2.02966 | − | 3.51547i | 0.353318 | − | 0.611966i | ||||
\(34\) | −3.84994 | −0.660259 | ||||||||
\(35\) | −1.52966 | − | 2.15874i | −0.258560 | − | 0.364893i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 5.45463 | − | 9.44770i | 0.896736 | − | 1.55319i | 0.0650940 | − | 0.997879i | \(-0.479265\pi\) |
0.831642 | − | 0.555313i | \(-0.187401\pi\) | |||||||
\(38\) | 1.60469 | + | 2.77940i | 0.260315 | + | 0.450879i | ||||
\(39\) | −3.13435 | − | 5.42885i | −0.501898 | − | 0.869312i | ||||
\(40\) | 0.500000 | − | 0.866025i | 0.0790569 | − | 0.136931i | ||||
\(41\) | −4.79062 | −0.748169 | −0.374085 | − | 0.927395i | \(-0.622043\pi\) | ||||
−0.374085 | + | 0.927395i | \(0.622043\pi\) | |||||||
\(42\) | −1.10469 | + | 2.40409i | −0.170457 | + | 0.370960i | ||||
\(43\) | −8.11864 | −1.23808 | −0.619041 | − | 0.785359i | \(-0.712478\pi\) | ||||
−0.619041 | + | 0.785359i | \(0.712478\pi\) | |||||||
\(44\) | −2.02966 | + | 3.51547i | −0.305983 | + | 0.529978i | ||||
\(45\) | −0.500000 | − | 0.866025i | −0.0745356 | − | 0.129099i | ||||
\(46\) | −0.500000 | − | 0.866025i | −0.0737210 | − | 0.127688i | ||||
\(47\) | −2.73904 | + | 4.74416i | −0.399530 | + | 0.692006i | −0.993668 | − | 0.112357i | \(-0.964160\pi\) |
0.594138 | + | 0.804363i | \(0.297493\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −4.55932 | − | 5.31155i | −0.651331 | − | 0.758793i | ||||
\(50\) | 4.00000 | 0.565685 | ||||||||
\(51\) | 1.92497 | − | 3.33415i | 0.269550 | − | 0.466874i | ||||
\(52\) | 3.13435 | + | 5.42885i | 0.434656 | + | 0.752847i | ||||
\(53\) | 4.55932 | + | 7.89697i | 0.626271 | + | 1.08473i | 0.988294 | + | 0.152564i | \(0.0487529\pi\) |
−0.362023 | + | 0.932169i | \(0.617914\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 4.05932 | 0.547359 | ||||||||
\(56\) | 1.10469 | − | 2.40409i | 0.147620 | − | 0.321260i | ||||
\(57\) | −3.20938 | −0.425093 | ||||||||
\(58\) | −0.634350 | + | 1.09873i | −0.0832942 | + | 0.144270i | ||||
\(59\) | 3.42497 | + | 5.93222i | 0.445893 | + | 0.772310i | 0.998114 | − | 0.0613883i | \(-0.0195528\pi\) |
−0.552221 | + | 0.833698i | \(0.686219\pi\) | |||||||
\(60\) | 0.500000 | + | 0.866025i | 0.0645497 | + | 0.111803i | ||||
\(61\) | −5.00000 | + | 8.66025i | −0.640184 | + | 1.10883i | 0.345207 | + | 0.938527i | \(0.387809\pi\) |
−0.985391 | + | 0.170305i | \(0.945525\pi\) | |||||||
\(62\) | −6.47808 | −0.822717 | ||||||||
\(63\) | −1.52966 | − | 2.15874i | −0.192719 | − | 0.271975i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.13435 | − | 5.42885i | 0.388768 | − | 0.673366i | ||||
\(66\) | −2.02966 | − | 3.51547i | −0.249834 | − | 0.432725i | ||||
\(67\) | 6.73904 | + | 11.6724i | 0.823305 | + | 1.42601i | 0.903208 | + | 0.429203i | \(0.141206\pi\) |
−0.0799032 | + | 0.996803i | \(0.525461\pi\) | |||||||
\(68\) | −1.92497 | + | 3.33415i | −0.233437 | + | 0.404325i | ||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | −2.63435 | + | 0.245357i | −0.314865 | + | 0.0293257i | ||||
\(71\) | 12.3873 | 1.47011 | 0.735053 | − | 0.678009i | \(-0.237157\pi\) | ||||
0.735053 | + | 0.678009i | \(0.237157\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | −4.52966 | − | 7.84560i | −0.530157 | − | 0.918258i | −0.999381 | − | 0.0351792i | \(-0.988800\pi\) |
0.469224 | − | 0.883079i | \(-0.344534\pi\) | |||||||
\(74\) | −5.45463 | − | 9.44770i | −0.634088 | − | 1.09827i | ||||
\(75\) | −2.00000 | + | 3.46410i | −0.230940 | + | 0.400000i | ||||
\(76\) | 3.20938 | 0.368141 | ||||||||
\(77\) | 10.6937 | − | 0.995981i | 1.21866 | − | 0.113503i | ||||
\(78\) | −6.26870 | −0.709791 | ||||||||
\(79\) | −4.69367 | + | 8.12968i | −0.528079 | + | 0.914660i | 0.471385 | + | 0.881928i | \(0.343754\pi\) |
−0.999464 | + | 0.0327324i | \(0.989579\pi\) | |||||||
\(80\) | −0.500000 | − | 0.866025i | −0.0559017 | − | 0.0968246i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −2.39531 | + | 4.14880i | −0.264518 | + | 0.458158i | ||||
\(83\) | 0.0593201 | 0.00651123 | 0.00325562 | − | 0.999995i | \(-0.498964\pi\) | ||||
0.00325562 | + | 0.999995i | \(0.498964\pi\) | |||||||
\(84\) | 1.52966 | + | 2.15874i | 0.166900 | + | 0.235537i | ||||
\(85\) | 3.84994 | 0.417585 | ||||||||
\(86\) | −4.05932 | + | 7.03095i | −0.437728 | + | 0.758167i | ||||
\(87\) | −0.634350 | − | 1.09873i | −0.0680095 | − | 0.117796i | ||||
\(88\) | 2.02966 | + | 3.51547i | 0.216362 | + | 0.374751i | ||||
\(89\) | −5.45463 | + | 9.44770i | −0.578190 | + | 1.00145i | 0.417497 | + | 0.908678i | \(0.362907\pi\) |
−0.995687 | + | 0.0927757i | \(0.970426\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 6.92497 | − | 15.0705i | 0.725934 | − | 1.57982i | ||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 3.23904 | − | 5.61018i | 0.335873 | − | 0.581749i | ||||
\(94\) | 2.73904 | + | 4.74416i | 0.282510 | + | 0.489322i | ||||
\(95\) | −1.60469 | − | 2.77940i | −0.164638 | − | 0.285161i | ||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | −15.8061 | −1.60487 | −0.802433 | − | 0.596742i | \(-0.796462\pi\) | ||||
−0.802433 | + | 0.596742i | \(0.796462\pi\) | |||||||
\(98\) | −6.87960 | + | 1.29271i | −0.694945 | + | 0.130583i | ||||
\(99\) | 4.05932 | 0.407977 | ||||||||
\(100\) | 2.00000 | − | 3.46410i | 0.200000 | − | 0.346410i | ||||
\(101\) | 7.05932 | + | 12.2271i | 0.702429 | + | 1.21664i | 0.967612 | + | 0.252444i | \(0.0812343\pi\) |
−0.265183 | + | 0.964198i | \(0.585432\pi\) | |||||||
\(102\) | −1.92497 | − | 3.33415i | −0.190600 | − | 0.330130i | ||||
\(103\) | −0.260960 | + | 0.451996i | −0.0257132 | + | 0.0445365i | −0.878596 | − | 0.477566i | \(-0.841519\pi\) |
0.852882 | + | 0.522103i | \(0.174852\pi\) | |||||||
\(104\) | 6.26870 | 0.614697 | ||||||||
\(105\) | 1.10469 | − | 2.40409i | 0.107807 | − | 0.234615i | ||||
\(106\) | 9.11864 | 0.885681 | ||||||||
\(107\) | 7.02966 | − | 12.1757i | 0.679583 | − | 1.17707i | −0.295524 | − | 0.955335i | \(-0.595494\pi\) |
0.975107 | − | 0.221737i | \(-0.0711725\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | 6.05932 | + | 10.4951i | 0.580378 | + | 1.00524i | 0.995434 | + | 0.0954480i | \(0.0304284\pi\) |
−0.415057 | + | 0.909795i | \(0.636238\pi\) | |||||||
\(110\) | 2.02966 | − | 3.51547i | 0.193520 | − | 0.335187i | ||||
\(111\) | 10.9093 | 1.03546 | ||||||||
\(112\) | −1.52966 | − | 2.15874i | −0.144539 | − | 0.203981i | ||||
\(113\) | −5.43118 | −0.510922 | −0.255461 | − | 0.966819i | \(-0.582227\pi\) | ||||
−0.255461 | + | 0.966819i | \(0.582227\pi\) | |||||||
\(114\) | −1.60469 | + | 2.77940i | −0.150293 | + | 0.260315i | ||||
\(115\) | 0.500000 | + | 0.866025i | 0.0466252 | + | 0.0807573i | ||||
\(116\) | 0.634350 | + | 1.09873i | 0.0588979 | + | 0.102014i | ||||
\(117\) | 3.13435 | − | 5.42885i | 0.289771 | − | 0.501898i | ||||
\(118\) | 6.84994 | 0.630588 | ||||||||
\(119\) | 10.1421 | − | 0.944608i | 0.929724 | − | 0.0865921i | ||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | −2.73904 | + | 4.74416i | −0.249004 | + | 0.431287i | ||||
\(122\) | 5.00000 | + | 8.66025i | 0.452679 | + | 0.784063i | ||||
\(123\) | −2.39531 | − | 4.14880i | −0.215978 | − | 0.374085i | ||||
\(124\) | −3.23904 | + | 5.61018i | −0.290874 | + | 0.503809i | ||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | −2.63435 | + | 0.245357i | −0.234687 | + | 0.0218581i | ||||
\(127\) | −16.0593 | −1.42503 | −0.712517 | − | 0.701655i | \(-0.752445\pi\) | ||||
−0.712517 | + | 0.701655i | \(0.752445\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −4.05932 | − | 7.03095i | −0.357403 | − | 0.619041i | ||||
\(130\) | −3.13435 | − | 5.42885i | −0.274901 | − | 0.476142i | ||||
\(131\) | 9.43271 | − | 16.3379i | 0.824140 | − | 1.42745i | −0.0784353 | − | 0.996919i | \(-0.524992\pi\) |
0.902575 | − | 0.430533i | \(-0.141674\pi\) | |||||||
\(132\) | −4.05932 | −0.353318 | ||||||||
\(133\) | −4.90926 | − | 6.92820i | −0.425687 | − | 0.600751i | ||||
\(134\) | 13.4781 | 1.16433 | ||||||||
\(135\) | 0.500000 | − | 0.866025i | 0.0430331 | − | 0.0745356i | ||||
\(136\) | 1.92497 | + | 3.33415i | 0.165065 | + | 0.285901i | ||||
\(137\) | −7.79836 | − | 13.5072i | −0.666259 | − | 1.15399i | −0.978942 | − | 0.204137i | \(-0.934561\pi\) |
0.312683 | − | 0.949857i | \(-0.398772\pi\) | |||||||
\(138\) | 0.500000 | − | 0.866025i | 0.0425628 | − | 0.0737210i | ||||
\(139\) | 6.83752 | 0.579951 | 0.289975 | − | 0.957034i | \(-0.406353\pi\) | ||||
0.289975 | + | 0.957034i | \(0.406353\pi\) | |||||||
\(140\) | −1.10469 | + | 2.40409i | −0.0933633 | + | 0.203183i | ||||
\(141\) | −5.47808 | −0.461338 | ||||||||
\(142\) | 6.19367 | − | 10.7278i | 0.519761 | − | 0.900253i | ||||
\(143\) | 12.7233 | + | 22.0375i | 1.06398 | + | 1.84286i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 0.634350 | − | 1.09873i | 0.0526799 | − | 0.0912443i | ||||
\(146\) | −9.05932 | −0.749755 | ||||||||
\(147\) | 2.32028 | − | 6.60426i | 0.191373 | − | 0.544710i | ||||
\(148\) | −10.9093 | −0.896736 | ||||||||
\(149\) | −1.58898 | + | 2.75219i | −0.130174 | + | 0.225469i | −0.923744 | − | 0.383011i | \(-0.874887\pi\) |
0.793569 | + | 0.608480i | \(0.208220\pi\) | |||||||
\(150\) | 2.00000 | + | 3.46410i | 0.163299 | + | 0.282843i | ||||
\(151\) | −5.02966 | − | 8.71163i | −0.409308 | − | 0.708942i | 0.585504 | − | 0.810669i | \(-0.300896\pi\) |
−0.994812 | + | 0.101727i | \(0.967563\pi\) | |||||||
\(152\) | 1.60469 | − | 2.77940i | 0.130158 | − | 0.225439i | ||||
\(153\) | 3.84994 | 0.311249 | ||||||||
\(154\) | 4.48429 | − | 9.75898i | 0.361354 | − | 0.786401i | ||||
\(155\) | 6.47808 | 0.520332 | ||||||||
\(156\) | −3.13435 | + | 5.42885i | −0.250949 | + | 0.434656i | ||||
\(157\) | −1.03587 | − | 1.79418i | −0.0826714 | − | 0.143191i | 0.821725 | − | 0.569884i | \(-0.193012\pi\) |
−0.904397 | + | 0.426693i | \(0.859679\pi\) | |||||||
\(158\) | 4.69367 | + | 8.12968i | 0.373408 | + | 0.646762i | ||||
\(159\) | −4.55932 | + | 7.89697i | −0.361578 | + | 0.626271i | ||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 1.52966 | + | 2.15874i | 0.120554 | + | 0.170132i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −2.03587 | + | 3.52623i | −0.159462 | + | 0.276196i | −0.934675 | − | 0.355504i | \(-0.884309\pi\) |
0.775213 | + | 0.631700i | \(0.217643\pi\) | |||||||
\(164\) | 2.39531 | + | 4.14880i | 0.187042 | + | 0.323967i | ||||
\(165\) | 2.02966 | + | 3.51547i | 0.158009 | + | 0.273679i | ||||
\(166\) | 0.0296601 | − | 0.0513728i | 0.00230207 | − | 0.00398730i | ||||
\(167\) | 18.0155 | 1.39408 | 0.697040 | − | 0.717032i | \(-0.254500\pi\) | ||||
0.697040 | + | 0.717032i | \(0.254500\pi\) | |||||||
\(168\) | 2.63435 | − | 0.245357i | 0.203245 | − | 0.0189297i | ||||
\(169\) | 26.2966 | 2.02282 | ||||||||
\(170\) | 1.92497 | − | 3.33415i | 0.147638 | − | 0.255717i | ||||
\(171\) | −1.60469 | − | 2.77940i | −0.122714 | − | 0.212546i | ||||
\(172\) | 4.05932 | + | 7.03095i | 0.309520 | + | 0.536105i | ||||
\(173\) | 7.26870 | − | 12.5898i | 0.552629 | − | 0.957182i | −0.445455 | − | 0.895304i | \(-0.646958\pi\) |
0.998084 | − | 0.0618771i | \(-0.0197087\pi\) | |||||||
\(174\) | −1.26870 | −0.0961799 | ||||||||
\(175\) | −10.5374 | + | 0.981426i | −0.796553 | + | 0.0741889i | ||||
\(176\) | 4.05932 | 0.305983 | ||||||||
\(177\) | −3.42497 | + | 5.93222i | −0.257437 | + | 0.445893i | ||||
\(178\) | 5.45463 | + | 9.44770i | 0.408842 | + | 0.708135i | ||||
\(179\) | 6.37960 | + | 11.0498i | 0.476834 | + | 0.825900i | 0.999648 | − | 0.0265467i | \(-0.00845105\pi\) |
−0.522814 | + | 0.852447i | \(0.675118\pi\) | |||||||
\(180\) | −0.500000 | + | 0.866025i | −0.0372678 | + | 0.0645497i | ||||
\(181\) | −12.5374 | −0.931898 | −0.465949 | − | 0.884812i | \(-0.654287\pi\) | ||||
−0.465949 | + | 0.884812i | \(0.654287\pi\) | |||||||
\(182\) | −9.58898 | − | 13.5325i | −0.710783 | − | 1.00309i | ||||
\(183\) | −10.0000 | −0.739221 | ||||||||
\(184\) | −0.500000 | + | 0.866025i | −0.0368605 | + | 0.0638442i | ||||
\(185\) | 5.45463 | + | 9.44770i | 0.401032 | + | 0.694608i | ||||
\(186\) | −3.23904 | − | 5.61018i | −0.237498 | − | 0.411358i | ||||
\(187\) | −7.81407 | + | 13.5344i | −0.571421 | + | 0.989731i | ||||
\(188\) | 5.47808 | 0.399530 | ||||||||
\(189\) | 1.10469 | − | 2.40409i | 0.0803544 | − | 0.174872i | ||||
\(190\) | −3.20938 | −0.232833 | ||||||||
\(191\) | −2.03587 | + | 3.52623i | −0.147310 | + | 0.255149i | −0.930233 | − | 0.366971i | \(-0.880395\pi\) |
0.782922 | + | 0.622120i | \(0.213728\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | −11.8873 | − | 20.5895i | −0.855669 | − | 1.48206i | −0.876023 | − | 0.482270i | \(-0.839812\pi\) |
0.0203531 | − | 0.999793i | \(-0.493521\pi\) | |||||||
\(194\) | −7.90305 | + | 13.6885i | −0.567406 | + | 0.982776i | ||||
\(195\) | 6.26870 | 0.448911 | ||||||||
\(196\) | −2.32028 | + | 6.60426i | −0.165734 | + | 0.471733i | ||||
\(197\) | 0.418760 | 0.0298354 | 0.0149177 | − | 0.999889i | \(-0.495251\pi\) | ||||
0.0149177 | + | 0.999889i | \(0.495251\pi\) | |||||||
\(198\) | 2.02966 | − | 3.51547i | 0.144242 | − | 0.249834i | ||||
\(199\) | 2.84994 | + | 4.93624i | 0.202027 | + | 0.349921i | 0.949181 | − | 0.314730i | \(-0.101914\pi\) |
−0.747154 | + | 0.664650i | \(0.768580\pi\) | |||||||
\(200\) | −2.00000 | − | 3.46410i | −0.141421 | − | 0.244949i | ||||
\(201\) | −6.73904 | + | 11.6724i | −0.475335 | + | 0.823305i | ||||
\(202\) | 14.1186 | 0.993384 | ||||||||
\(203\) | 1.40152 | − | 3.05007i | 0.0983674 | − | 0.214073i | ||||
\(204\) | −3.84994 | −0.269550 | ||||||||
\(205\) | 2.39531 | − | 4.14880i | 0.167296 | − | 0.289765i | ||||
\(206\) | 0.260960 | + | 0.451996i | 0.0181819 | + | 0.0314921i | ||||
\(207\) | 0.500000 | + | 0.866025i | 0.0347524 | + | 0.0601929i | ||||
\(208\) | 3.13435 | − | 5.42885i | 0.217328 | − | 0.376423i | ||||
\(209\) | 13.0279 | 0.901159 | ||||||||
\(210\) | −1.52966 | − | 2.15874i | −0.105557 | − | 0.148967i | ||||
\(211\) | −4.41876 | −0.304200 | −0.152100 | − | 0.988365i | \(-0.548604\pi\) | ||||
−0.152100 | + | 0.988365i | \(0.548604\pi\) | |||||||
\(212\) | 4.55932 | − | 7.89697i | 0.313135 | − | 0.542366i | ||||
\(213\) | 6.19367 | + | 10.7278i | 0.424383 | + | 0.735053i | ||||
\(214\) | −7.02966 | − | 12.1757i | −0.480538 | − | 0.832316i | ||||
\(215\) | 4.05932 | − | 7.03095i | 0.276843 | − | 0.479507i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 17.0655 | − | 1.58944i | 1.15848 | − | 0.107898i | ||||
\(218\) | 12.1186 | 0.820778 | ||||||||
\(219\) | 4.52966 | − | 7.84560i | 0.306086 | − | 0.530157i | ||||
\(220\) | −2.02966 | − | 3.51547i | −0.136840 | − | 0.237013i | ||||
\(221\) | 12.0671 | + | 20.9008i | 0.811718 | + | 1.40594i | ||||
\(222\) | 5.45463 | − | 9.44770i | 0.366091 | − | 0.634088i | ||||
\(223\) | 11.7592 | 0.787454 | 0.393727 | − | 0.919227i | \(-0.371185\pi\) | ||||
0.393727 | + | 0.919227i | \(0.371185\pi\) | |||||||
\(224\) | −2.63435 | + | 0.245357i | −0.176015 | + | 0.0163936i | ||||
\(225\) | −4.00000 | −0.266667 | ||||||||
\(226\) | −2.71559 | + | 4.70354i | −0.180638 | + | 0.312875i | ||||
\(227\) | −6.87960 | − | 11.9158i | −0.456615 | − | 0.790881i | 0.542164 | − | 0.840272i | \(-0.317605\pi\) |
−0.998779 | + | 0.0493919i | \(0.984272\pi\) | |||||||
\(228\) | 1.60469 | + | 2.77940i | 0.106273 | + | 0.184071i | ||||
\(229\) | −10.8141 | + | 18.7305i | −0.714614 | + | 1.23775i | 0.248494 | + | 0.968633i | \(0.420064\pi\) |
−0.963108 | + | 0.269114i | \(0.913269\pi\) | |||||||
\(230\) | 1.00000 | 0.0659380 | ||||||||
\(231\) | 6.20938 | + | 8.76300i | 0.408547 | + | 0.576563i | ||||
\(232\) | 1.26870 | 0.0832942 | ||||||||
\(233\) | 13.3046 | − | 23.0442i | 0.871611 | − | 1.50968i | 0.0112822 | − | 0.999936i | \(-0.496409\pi\) |
0.860329 | − | 0.509739i | \(-0.170258\pi\) | |||||||
\(234\) | −3.13435 | − | 5.42885i | −0.204899 | − | 0.354895i | ||||
\(235\) | −2.73904 | − | 4.74416i | −0.178675 | − | 0.309475i | ||||
\(236\) | 3.42497 | − | 5.93222i | 0.222947 | − | 0.386155i | ||||
\(237\) | −9.38734 | −0.609773 | ||||||||
\(238\) | 4.25299 | − | 9.25561i | 0.275680 | − | 0.599952i | ||||
\(239\) | −16.0000 | −1.03495 | −0.517477 | − | 0.855697i | \(-0.673129\pi\) | ||||
−0.517477 | + | 0.855697i | \(0.673129\pi\) | |||||||
\(240\) | 0.500000 | − | 0.866025i | 0.0322749 | − | 0.0559017i | ||||
\(241\) | −14.1124 | − | 24.4434i | −0.909062 | − | 1.57454i | −0.815371 | − | 0.578939i | \(-0.803467\pi\) |
−0.0936910 | − | 0.995601i | \(-0.529867\pi\) | |||||||
\(242\) | 2.73904 | + | 4.74416i | 0.176072 | + | 0.304966i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 10.0000 | 0.640184 | ||||||||
\(245\) | 6.87960 | − | 1.29271i | 0.439522 | − | 0.0825882i | ||||
\(246\) | −4.79062 | −0.305439 | ||||||||
\(247\) | 10.0593 | − | 17.4233i | 0.640059 | − | 1.10862i | ||||
\(248\) | 3.23904 | + | 5.61018i | 0.205679 | + | 0.356247i | ||||
\(249\) | 0.0296601 | + | 0.0513728i | 0.00187963 | + | 0.00325562i | ||||
\(250\) | −4.50000 | + | 7.79423i | −0.284605 | + | 0.492950i | ||||
\(251\) | −8.29660 | −0.523677 | −0.261838 | − | 0.965112i | \(-0.584329\pi\) | ||||
−0.261838 | + | 0.965112i | \(0.584329\pi\) | |||||||
\(252\) | −1.10469 | + | 2.40409i | −0.0695889 | + | 0.151444i | ||||
\(253\) | −4.05932 | −0.255207 | ||||||||
\(254\) | −8.02966 | + | 13.9078i | −0.503826 | + | 0.872652i | ||||
\(255\) | 1.92497 | + | 3.33415i | 0.120546 | + | 0.208792i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −9.51395 | + | 16.4786i | −0.593464 | + | 1.02791i | 0.400298 | + | 0.916385i | \(0.368907\pi\) |
−0.993762 | + | 0.111525i | \(0.964427\pi\) | |||||||
\(258\) | −8.11864 | −0.505444 | ||||||||
\(259\) | 16.6875 | + | 23.5502i | 1.03691 | + | 1.46334i | ||||
\(260\) | −6.26870 | −0.388768 | ||||||||
\(261\) | 0.634350 | − | 1.09873i | 0.0392653 | − | 0.0680095i | ||||
\(262\) | −9.43271 | − | 16.3379i | −0.582755 | − | 1.00936i | ||||
\(263\) | −0.0593201 | − | 0.102746i | −0.00365784 | − | 0.00633556i | 0.864191 | − | 0.503164i | \(-0.167831\pi\) |
−0.867849 | + | 0.496829i | \(0.834498\pi\) | |||||||
\(264\) | −2.02966 | + | 3.51547i | −0.124917 | + | 0.216362i | ||||
\(265\) | −9.11864 | −0.560154 | ||||||||
\(266\) | −8.45463 | + | 0.787443i | −0.518387 | + | 0.0482812i | ||||
\(267\) | −10.9093 | −0.667636 | ||||||||
\(268\) | 6.73904 | − | 11.6724i | 0.411652 | − | 0.713003i | ||||
\(269\) | −1.48429 | − | 2.57087i | −0.0904988 | − | 0.156748i | 0.817222 | − | 0.576323i | \(-0.195513\pi\) |
−0.907721 | + | 0.419574i | \(0.862179\pi\) | |||||||
\(270\) | −0.500000 | − | 0.866025i | −0.0304290 | − | 0.0527046i | ||||
\(271\) | 6.44842 | − | 11.1690i | 0.391714 | − | 0.678468i | −0.600962 | − | 0.799278i | \(-0.705216\pi\) |
0.992676 | + | 0.120810i | \(0.0385491\pi\) | |||||||
\(272\) | 3.84994 | 0.233437 | ||||||||
\(273\) | 16.5140 | − | 1.53807i | 0.999470 | − | 0.0930880i | ||||
\(274\) | −15.5967 | −0.942232 | ||||||||
\(275\) | 8.11864 | − | 14.0619i | 0.489572 | − | 0.847964i | ||||
\(276\) | −0.500000 | − | 0.866025i | −0.0300965 | − | 0.0521286i | ||||
\(277\) | −5.58898 | − | 9.68040i | −0.335809 | − | 0.581639i | 0.647831 | − | 0.761784i | \(-0.275676\pi\) |
−0.983640 | + | 0.180146i | \(0.942343\pi\) | |||||||
\(278\) | 3.41876 | − | 5.92147i | 0.205044 | − | 0.355146i | ||||
\(279\) | 6.47808 | 0.387833 | ||||||||
\(280\) | 1.52966 | + | 2.15874i | 0.0914147 | + | 0.129009i | ||||
\(281\) | −31.4621 | −1.87687 | −0.938437 | − | 0.345450i | \(-0.887726\pi\) | ||||
−0.938437 | + | 0.345450i | \(0.887726\pi\) | |||||||
\(282\) | −2.73904 | + | 4.74416i | −0.163107 | + | 0.282510i | ||||
\(283\) | 5.00774 | + | 8.67366i | 0.297679 | + | 0.515596i | 0.975605 | − | 0.219535i | \(-0.0704541\pi\) |
−0.677925 | + | 0.735131i | \(0.737121\pi\) | |||||||
\(284\) | −6.19367 | − | 10.7278i | −0.367527 | − | 0.636575i | ||||
\(285\) | 1.60469 | − | 2.77940i | 0.0950536 | − | 0.164638i | ||||
\(286\) | 25.4467 | 1.50469 | ||||||||
\(287\) | 5.29215 | − | 11.5171i | 0.312386 | − | 0.679833i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 1.08898 | − | 1.88617i | 0.0640577 | − | 0.110951i | ||||
\(290\) | −0.634350 | − | 1.09873i | −0.0372503 | − | 0.0645194i | ||||
\(291\) | −7.90305 | − | 13.6885i | −0.463285 | − | 0.802433i | ||||
\(292\) | −4.52966 | + | 7.84560i | −0.265078 | + | 0.459129i | ||||
\(293\) | 3.83752 | 0.224190 | 0.112095 | − | 0.993697i | \(-0.464244\pi\) | ||||
0.112095 | + | 0.993697i | \(0.464244\pi\) | |||||||
\(294\) | −4.55932 | − | 5.31155i | −0.265905 | − | 0.309776i | ||||
\(295\) | −6.84994 | −0.398819 | ||||||||
\(296\) | −5.45463 | + | 9.44770i | −0.317044 | + | 0.549136i | ||||
\(297\) | 2.02966 | + | 3.51547i | 0.117773 | + | 0.203989i | ||||
\(298\) | 1.58898 | + | 2.75219i | 0.0920472 | + | 0.159430i | ||||
\(299\) | −3.13435 | + | 5.42885i | −0.181264 | + | 0.313959i | ||||
\(300\) | 4.00000 | 0.230940 | ||||||||
\(301\) | 8.96858 | − | 19.5180i | 0.516940 | − | 1.12500i | ||||
\(302\) | −10.0593 | −0.578849 | ||||||||
\(303\) | −7.05932 | + | 12.2271i | −0.405547 | + | 0.702429i | ||||
\(304\) | −1.60469 | − | 2.77940i | −0.0920353 | − | 0.159410i | ||||
\(305\) | −5.00000 | − | 8.66025i | −0.286299 | − | 0.495885i | ||||
\(306\) | 1.92497 | − | 3.33415i | 0.110043 | − | 0.190600i | ||||
\(307\) | 13.9841 | 0.798112 | 0.399056 | − | 0.916926i | \(-0.369338\pi\) | ||||
0.399056 | + | 0.916926i | \(0.369338\pi\) | |||||||
\(308\) | −6.20938 | − | 8.76300i | −0.353812 | − | 0.499318i | ||||
\(309\) | −0.521920 | −0.0296910 | ||||||||
\(310\) | 3.23904 | − | 5.61018i | 0.183965 | − | 0.318637i | ||||
\(311\) | 13.1937 | + | 22.8521i | 0.748144 | + | 1.29582i | 0.948711 | + | 0.316144i | \(0.102388\pi\) |
−0.200567 | + | 0.979680i | \(0.564278\pi\) | |||||||
\(312\) | 3.13435 | + | 5.42885i | 0.177448 | + | 0.307348i | ||||
\(313\) | −4.57503 | + | 7.92418i | −0.258596 | + | 0.447901i | −0.965866 | − | 0.259042i | \(-0.916593\pi\) |
0.707270 | + | 0.706943i | \(0.249926\pi\) | |||||||
\(314\) | −2.07174 | −0.116915 | ||||||||
\(315\) | 2.63435 | − | 0.245357i | 0.148429 | − | 0.0138243i | ||||
\(316\) | 9.38734 | 0.528079 | ||||||||
\(317\) | −10.1124 | + | 17.5152i | −0.567971 | + | 0.983754i | 0.428796 | + | 0.903401i | \(0.358938\pi\) |
−0.996767 | + | 0.0803526i | \(0.974395\pi\) | |||||||
\(318\) | 4.55932 | + | 7.89697i | 0.255674 | + | 0.442840i | ||||
\(319\) | 2.57503 | + | 4.46008i | 0.144174 | + | 0.249717i | ||||
\(320\) | −0.500000 | + | 0.866025i | −0.0279508 | + | 0.0484123i | ||||
\(321\) | 14.0593 | 0.784715 | ||||||||
\(322\) | 2.63435 | − | 0.245357i | 0.146807 | − | 0.0136732i | ||||
\(323\) | 12.3559 | 0.687502 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | −12.5374 | − | 21.7154i | −0.695450 | − | 1.20455i | ||||
\(326\) | 2.03587 | + | 3.52623i | 0.112756 | + | 0.195300i | ||||
\(327\) | −6.05932 | + | 10.4951i | −0.335081 | + | 0.580378i | ||||
\(328\) | 4.79062 | 0.264518 | ||||||||
\(329\) | −8.37960 | − | 11.8257i | −0.461982 | − | 0.651973i | ||||
\(330\) | 4.05932 | 0.223458 | ||||||||
\(331\) | 10.3046 | − | 17.8480i | 0.566390 | − | 0.981017i | −0.430528 | − | 0.902577i | \(-0.641673\pi\) |
0.996919 | − | 0.0784400i | \(-0.0249939\pi\) | |||||||
\(332\) | −0.0296601 | − | 0.0513728i | −0.00162781 | − | 0.00281945i | ||||
\(333\) | 5.45463 | + | 9.44770i | 0.298912 | + | 0.517731i | ||||
\(334\) | 9.00774 | − | 15.6019i | 0.492882 | − | 0.853696i | ||||
\(335\) | −13.4781 | −0.736386 | ||||||||
\(336\) | 1.10469 | − | 2.40409i | 0.0602658 | − | 0.131154i | ||||
\(337\) | −26.2249 | −1.42856 | −0.714280 | − | 0.699860i | \(-0.753245\pi\) | ||||
−0.714280 | + | 0.699860i | \(0.753245\pi\) | |||||||
\(338\) | 13.1483 | − | 22.7735i | 0.715173 | − | 1.23872i | ||||
\(339\) | −2.71559 | − | 4.70354i | −0.147491 | − | 0.255461i | ||||
\(340\) | −1.92497 | − | 3.33415i | −0.104396 | − | 0.180819i | ||||
\(341\) | −13.1483 | + | 22.7735i | −0.712020 | + | 1.23326i | ||||
\(342\) | −3.20938 | −0.173543 | ||||||||
\(343\) | 17.8061 | − | 5.09341i | 0.961439 | − | 0.275018i | ||||
\(344\) | 8.11864 | 0.437728 | ||||||||
\(345\) | −0.500000 | + | 0.866025i | −0.0269191 | + | 0.0466252i | ||||
\(346\) | −7.26870 | − | 12.5898i | −0.390768 | − | 0.676830i | ||||
\(347\) | −12.7984 | − | 22.1674i | −0.687052 | − | 1.19001i | −0.972787 | − | 0.231700i | \(-0.925571\pi\) |
0.285735 | − | 0.958309i | \(-0.407762\pi\) | |||||||
\(348\) | −0.634350 | + | 1.09873i | −0.0340047 | + | 0.0588979i | ||||
\(349\) | 1.61266 | 0.0863237 | 0.0431618 | − | 0.999068i | \(-0.486257\pi\) | ||||
0.0431618 | + | 0.999068i | \(0.486257\pi\) | |||||||
\(350\) | −4.41876 | + | 9.61637i | −0.236193 | + | 0.514017i | ||||
\(351\) | 6.26870 | 0.334598 | ||||||||
\(352\) | 2.02966 | − | 3.51547i | 0.108181 | − | 0.187375i | ||||
\(353\) | 13.3046 | + | 23.0442i | 0.708131 | + | 1.22652i | 0.965550 | + | 0.260219i | \(0.0837947\pi\) |
−0.257419 | + | 0.966300i | \(0.582872\pi\) | |||||||
\(354\) | 3.42497 | + | 5.93222i | 0.182035 | + | 0.315294i | ||||
\(355\) | −6.19367 | + | 10.7278i | −0.328726 | + | 0.569370i | ||||
\(356\) | 10.9093 | 0.578190 | ||||||||
\(357\) | 5.88910 | + | 8.31100i | 0.311684 | + | 0.439865i | ||||
\(358\) | 12.7592 | 0.674345 | ||||||||
\(359\) | 9.41876 | − | 16.3138i | 0.497103 | − | 0.861008i | −0.502891 | − | 0.864350i | \(-0.667730\pi\) |
0.999994 | + | 0.00334179i | \(0.00106373\pi\) | |||||||
\(360\) | 0.500000 | + | 0.866025i | 0.0263523 | + | 0.0456435i | ||||
\(361\) | 4.34994 | + | 7.53432i | 0.228944 | + | 0.396543i | ||||
\(362\) | −6.26870 | + | 10.8577i | −0.329476 | + | 0.570668i | ||||
\(363\) | −5.47808 | −0.287525 | ||||||||
\(364\) | −16.5140 | + | 1.53807i | −0.865566 | + | 0.0806166i | ||||
\(365\) | 9.05932 | 0.474186 | ||||||||
\(366\) | −5.00000 | + | 8.66025i | −0.261354 | + | 0.452679i | ||||
\(367\) | −0.373390 | − | 0.646731i | −0.0194908 | − | 0.0337591i | 0.856115 | − | 0.516785i | \(-0.172871\pi\) |
−0.875606 | + | 0.483025i | \(0.839538\pi\) | |||||||
\(368\) | 0.500000 | + | 0.866025i | 0.0260643 | + | 0.0451447i | ||||
\(369\) | 2.39531 | − | 4.14880i | 0.124695 | − | 0.215978i | ||||
\(370\) | 10.9093 | 0.567145 | ||||||||
\(371\) | −24.0217 | + | 2.23732i | −1.24714 | + | 0.116156i | ||||
\(372\) | −6.47808 | −0.335873 | ||||||||
\(373\) | −9.47808 | + | 16.4165i | −0.490756 | + | 0.850015i | −0.999943 | − | 0.0106409i | \(-0.996613\pi\) |
0.509187 | + | 0.860656i | \(0.329946\pi\) | |||||||
\(374\) | 7.81407 | + | 13.5344i | 0.404056 | + | 0.699845i | ||||
\(375\) | −4.50000 | − | 7.79423i | −0.232379 | − | 0.402492i | ||||
\(376\) | 2.73904 | − | 4.74416i | 0.141255 | − | 0.244661i | ||||
\(377\) | 7.95310 | 0.409606 | ||||||||
\(378\) | −1.52966 | − | 2.15874i | −0.0786772 | − | 0.111033i | ||||
\(379\) | 11.7154 | 0.601778 | 0.300889 | − | 0.953659i | \(-0.402717\pi\) | ||||
0.300889 | + | 0.953659i | \(0.402717\pi\) | |||||||
\(380\) | −1.60469 | + | 2.77940i | −0.0823189 | + | 0.142580i | ||||
\(381\) | −8.02966 | − | 13.9078i | −0.411372 | − | 0.712517i | ||||
\(382\) | 2.03587 | + | 3.52623i | 0.104164 | + | 0.180418i | ||||
\(383\) | 13.0828 | − | 22.6600i | 0.668498 | − | 1.15787i | −0.309826 | − | 0.950793i | \(-0.600271\pi\) |
0.978324 | − | 0.207080i | \(-0.0663959\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −4.48429 | + | 9.75898i | −0.228541 | + | 0.497364i | ||||
\(386\) | −23.7747 | −1.21010 | ||||||||
\(387\) | 4.05932 | − | 7.03095i | 0.206347 | − | 0.357403i | ||||
\(388\) | 7.90305 | + | 13.6885i | 0.401217 | + | 0.694928i | ||||
\(389\) | 13.8968 | + | 24.0700i | 0.704598 | + | 1.22040i | 0.966837 | + | 0.255396i | \(0.0822059\pi\) |
−0.262239 | + | 0.965003i | \(0.584461\pi\) | |||||||
\(390\) | 3.13435 | − | 5.42885i | 0.158714 | − | 0.274901i | ||||
\(391\) | −3.84994 | −0.194700 | ||||||||
\(392\) | 4.55932 | + | 5.31155i | 0.230280 | + | 0.268274i | ||||
\(393\) | 18.8654 | 0.951635 | ||||||||
\(394\) | 0.209380 | − | 0.362657i | 0.0105484 | − | 0.0182704i | ||||
\(395\) | −4.69367 | − | 8.12968i | −0.236164 | − | 0.409048i | ||||
\(396\) | −2.02966 | − | 3.51547i | −0.101994 | − | 0.176659i | ||||
\(397\) | −1.92497 | + | 3.33415i | −0.0966115 | + | 0.167336i | −0.910280 | − | 0.413993i | \(-0.864134\pi\) |
0.813669 | + | 0.581329i | \(0.197467\pi\) | |||||||
\(398\) | 5.69988 | 0.285709 | ||||||||
\(399\) | 3.54537 | − | 7.71565i | 0.177490 | − | 0.386265i | ||||
\(400\) | −4.00000 | −0.200000 | ||||||||
\(401\) | −3.58898 | + | 6.21630i | −0.179225 | + | 0.310427i | −0.941615 | − | 0.336691i | \(-0.890692\pi\) |
0.762390 | + | 0.647118i | \(0.224026\pi\) | |||||||
\(402\) | 6.73904 | + | 11.6724i | 0.336113 | + | 0.582164i | ||||
\(403\) | 20.3046 | + | 35.1685i | 1.01144 | + | 1.75187i | ||||
\(404\) | 7.05932 | − | 12.2271i | 0.351214 | − | 0.608321i | ||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −1.94068 | − | 2.73879i | −0.0963143 | − | 0.135924i | ||||
\(407\) | −44.2842 | −2.19509 | ||||||||
\(408\) | −1.92497 | + | 3.33415i | −0.0953002 | + | 0.165065i | ||||
\(409\) | 8.18746 | + | 14.1811i | 0.404844 | + | 0.701210i | 0.994303 | − | 0.106588i | \(-0.0339925\pi\) |
−0.589459 | + | 0.807798i | \(0.700659\pi\) | |||||||
\(410\) | −2.39531 | − | 4.14880i | −0.118296 | − | 0.204895i | ||||
\(411\) | 7.79836 | − | 13.5072i | 0.384665 | − | 0.666259i | ||||
\(412\) | 0.521920 | 0.0257132 | ||||||||
\(413\) | −18.0451 | + | 1.68068i | −0.887943 | + | 0.0827008i | ||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | −0.0296601 | + | 0.0513728i | −0.00145596 | + | 0.00252179i | ||||
\(416\) | −3.13435 | − | 5.42885i | −0.153674 | − | 0.266171i | ||||
\(417\) | 3.41876 | + | 5.92147i | 0.167417 | + | 0.289975i | ||||
\(418\) | 6.51395 | − | 11.2825i | 0.318608 | − | 0.551845i | ||||
\(419\) | −25.9372 | −1.26711 | −0.633557 | − | 0.773696i | \(-0.718406\pi\) | ||||
−0.633557 | + | 0.773696i | \(0.718406\pi\) | |||||||
\(420\) | −2.63435 | + | 0.245357i | −0.128543 | + | 0.0119722i | ||||
\(421\) | 3.13764 | 0.152919 | 0.0764596 | − | 0.997073i | \(-0.475638\pi\) | ||||
0.0764596 | + | 0.997073i | \(0.475638\pi\) | |||||||
\(422\) | −2.20938 | + | 3.82676i | −0.107551 | + | 0.186284i | ||||
\(423\) | −2.73904 | − | 4.74416i | −0.133177 | − | 0.230669i | ||||
\(424\) | −4.55932 | − | 7.89697i | −0.221420 | − | 0.383511i | ||||
\(425\) | 7.69988 | − | 13.3366i | 0.373499 | − | 0.646919i | ||||
\(426\) | 12.3873 | 0.600169 | ||||||||
\(427\) | −15.2966 | − | 21.5874i | −0.740254 | − | 1.04469i | ||||
\(428\) | −14.0593 | −0.679583 | ||||||||
\(429\) | −12.7233 | + | 22.0375i | −0.614288 | + | 1.06398i | ||||
\(430\) | −4.05932 | − | 7.03095i | −0.195758 | − | 0.339062i | ||||
\(431\) | 8.53740 | + | 14.7872i | 0.411232 | + | 0.712275i | 0.995025 | − | 0.0996279i | \(-0.0317652\pi\) |
−0.583793 | + | 0.811903i | \(0.698432\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | −34.4746 | −1.65674 | −0.828371 | − | 0.560180i | \(-0.810732\pi\) | ||||
−0.828371 | + | 0.560180i | \(0.810732\pi\) | |||||||
\(434\) | 7.15627 | − | 15.5739i | 0.343512 | − | 0.747571i | ||||
\(435\) | 1.26870 | 0.0608295 | ||||||||
\(436\) | 6.05932 | − | 10.4951i | 0.290189 | − | 0.502622i | ||||
\(437\) | 1.60469 | + | 2.77940i | 0.0767627 | + | 0.132957i | ||||
\(438\) | −4.52966 | − | 7.84560i | −0.216436 | − | 0.374877i | ||||
\(439\) | −1.29836 | + | 2.24883i | −0.0619673 | + | 0.107331i | −0.895345 | − | 0.445374i | \(-0.853071\pi\) |
0.833377 | + | 0.552704i | \(0.186404\pi\) | |||||||
\(440\) | −4.05932 | −0.193520 | ||||||||
\(441\) | 6.87960 | − | 1.29271i | 0.327600 | − | 0.0615576i | ||||
\(442\) | 24.1341 | 1.14794 | ||||||||
\(443\) | −2.01395 | + | 3.48826i | −0.0956857 | + | 0.165732i | −0.909895 | − | 0.414840i | \(-0.863838\pi\) |
0.814209 | + | 0.580572i | \(0.197171\pi\) | |||||||
\(444\) | −5.45463 | − | 9.44770i | −0.258865 | − | 0.448368i | ||||
\(445\) | −5.45463 | − | 9.44770i | −0.258574 | − | 0.447864i | ||||
\(446\) | 5.87960 | − | 10.1838i | 0.278407 | − | 0.482215i | ||||
\(447\) | −3.17796 | −0.150312 | ||||||||
\(448\) | −1.10469 | + | 2.40409i | −0.0521917 | + | 0.113583i | ||||
\(449\) | −22.1655 | −1.04606 | −0.523028 | − | 0.852315i | \(-0.675198\pi\) | ||||
−0.523028 | + | 0.852315i | \(0.675198\pi\) | |||||||
\(450\) | −2.00000 | + | 3.46410i | −0.0942809 | + | 0.163299i | ||||
\(451\) | 9.72333 | + | 16.8413i | 0.457854 | + | 0.793026i | ||||
\(452\) | 2.71559 | + | 4.70354i | 0.127731 | + | 0.221236i | ||||
\(453\) | 5.02966 | − | 8.71163i | 0.236314 | − | 0.409308i | ||||
\(454\) | −13.7592 | −0.645751 | ||||||||
\(455\) | 9.58898 | + | 13.5325i | 0.449538 | + | 0.634412i | ||||
\(456\) | 3.20938 | 0.150293 | ||||||||
\(457\) | −16.3811 | + | 28.3729i | −0.766277 | + | 1.32723i | 0.173292 | + | 0.984871i | \(0.444560\pi\) |
−0.939569 | + | 0.342360i | \(0.888774\pi\) | |||||||
\(458\) | 10.8141 | + | 18.7305i | 0.505308 | + | 0.875220i | ||||
\(459\) | 1.92497 | + | 3.33415i | 0.0898499 | + | 0.155625i | ||||
\(460\) | 0.500000 | − | 0.866025i | 0.0233126 | − | 0.0403786i | ||||
\(461\) | −10.2373 | −0.476798 | −0.238399 | − | 0.971167i | \(-0.576623\pi\) | ||||
−0.238399 | + | 0.971167i | \(0.576623\pi\) | |||||||
\(462\) | 10.6937 | − | 0.995981i | 0.497515 | − | 0.0463372i | ||||
\(463\) | −0.118640 | −0.00551368 | −0.00275684 | − | 0.999996i | \(-0.500878\pi\) | ||||
−0.00275684 | + | 0.999996i | \(0.500878\pi\) | |||||||
\(464\) | 0.634350 | − | 1.09873i | 0.0294490 | − | 0.0510071i | ||||
\(465\) | 3.23904 | + | 5.61018i | 0.150207 | + | 0.260166i | ||||
\(466\) | −13.3046 | − | 23.0442i | −0.616322 | − | 1.06750i | ||||
\(467\) | 4.05932 | − | 7.03095i | 0.187843 | − | 0.325354i | −0.756688 | − | 0.653776i | \(-0.773184\pi\) |
0.944531 | + | 0.328423i | \(0.106517\pi\) | |||||||
\(468\) | −6.26870 | −0.289771 | ||||||||
\(469\) | −35.5060 | + | 3.30694i | −1.63951 | + | 0.152700i | ||||
\(470\) | −5.47808 | −0.252685 | ||||||||
\(471\) | 1.03587 | − | 1.79418i | 0.0477304 | − | 0.0826714i | ||||
\(472\) | −3.42497 | − | 5.93222i | −0.157647 | − | 0.273053i | ||||
\(473\) | 16.4781 | + | 28.5409i | 0.757663 | + | 1.31231i | ||||
\(474\) | −4.69367 | + | 8.12968i | −0.215587 | + | 0.373408i | ||||
\(475\) | −12.8375 | −0.589026 | ||||||||
\(476\) | −5.88910 | − | 8.31100i | −0.269926 | − | 0.380934i | ||||
\(477\) | −9.11864 | −0.417514 | ||||||||
\(478\) | −8.00000 | + | 13.8564i | −0.365911 | + | 0.633777i | ||||
\(479\) | 2.27667 | + | 3.94331i | 0.104024 | + | 0.180174i | 0.913339 | − | 0.407200i | \(-0.133495\pi\) |
−0.809315 | + | 0.587375i | \(0.800162\pi\) | |||||||
\(480\) | −0.500000 | − | 0.866025i | −0.0228218 | − | 0.0395285i | ||||
\(481\) | −34.1934 | + | 59.2248i | −1.55909 | + | 2.70042i | ||||
\(482\) | −28.2249 | −1.28561 | ||||||||
\(483\) | −1.10469 | + | 2.40409i | −0.0502651 | + | 0.109390i | ||||
\(484\) | 5.47808 | 0.249004 | ||||||||
\(485\) | 7.90305 | − | 13.6885i | 0.358859 | − | 0.621562i | ||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | 10.6578 | + | 18.4599i | 0.482951 | + | 0.836496i | 0.999808 | − | 0.0195758i | \(-0.00623158\pi\) |
−0.516857 | + | 0.856072i | \(0.672898\pi\) | |||||||
\(488\) | 5.00000 | − | 8.66025i | 0.226339 | − | 0.392031i | ||||
\(489\) | −4.07174 | −0.184130 | ||||||||
\(490\) | 2.32028 | − | 6.60426i | 0.104820 | − | 0.298350i | ||||
\(491\) | 2.09074 | 0.0943538 | 0.0471769 | − | 0.998887i | \(-0.484978\pi\) | ||||
0.0471769 | + | 0.998887i | \(0.484978\pi\) | |||||||
\(492\) | −2.39531 | + | 4.14880i | −0.107989 | + | 0.187042i | ||||
\(493\) | 2.44221 | + | 4.23003i | 0.109992 | + | 0.190511i | ||||
\(494\) | −10.0593 | − | 17.4233i | −0.452590 | − | 0.783909i | ||||
\(495\) | −2.02966 | + | 3.51547i | −0.0912264 | + | 0.158009i | ||||
\(496\) | 6.47808 | 0.290874 | ||||||||
\(497\) | −13.6842 | + | 29.7803i | −0.613819 | + | 1.33583i | ||||
\(498\) | 0.0593201 | 0.00265820 | ||||||||
\(499\) | 3.56882 | − | 6.18138i | 0.159762 | − | 0.276716i | −0.775021 | − | 0.631936i | \(-0.782261\pi\) |
0.934783 | + | 0.355220i | \(0.115594\pi\) | |||||||
\(500\) | 4.50000 | + | 7.79423i | 0.201246 | + | 0.348569i | ||||
\(501\) | 9.00774 | + | 15.6019i | 0.402436 | + | 0.697040i | ||||
\(502\) | −4.14830 | + | 7.18507i | −0.185148 | + | 0.320685i | ||||
\(503\) | 11.9372 | 0.532252 | 0.266126 | − | 0.963938i | \(-0.414256\pi\) | ||||
0.266126 | + | 0.963938i | \(0.414256\pi\) | |||||||
\(504\) | 1.52966 | + | 2.15874i | 0.0681365 | + | 0.0961577i | ||||
\(505\) | −14.1186 | −0.628271 | ||||||||
\(506\) | −2.02966 | + | 3.51547i | −0.0902294 | + | 0.156282i | ||||
\(507\) | 13.1483 | + | 22.7735i | 0.583937 | + | 1.01141i | ||||
\(508\) | 8.02966 | + | 13.9078i | 0.356259 | + | 0.617058i | ||||
\(509\) | −0.784410 | + | 1.35864i | −0.0347684 | + | 0.0602206i | −0.882886 | − | 0.469587i | \(-0.844403\pi\) |
0.848118 | + | 0.529808i | \(0.177736\pi\) | |||||||
\(510\) | 3.84994 | 0.170478 | ||||||||
\(511\) | 23.8654 | − | 2.22276i | 1.05574 | − | 0.0983293i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.60469 | − | 2.77940i | 0.0708488 | − | 0.122714i | ||||
\(514\) | 9.51395 | + | 16.4786i | 0.419642 | + | 0.726842i | ||||
\(515\) | −0.260960 | − | 0.451996i | −0.0114993 | − | 0.0199173i | ||||
\(516\) | −4.05932 | + | 7.03095i | −0.178702 | + | 0.309520i | ||||
\(517\) | 22.2373 | 0.977994 | ||||||||
\(518\) | 28.7388 | − | 2.67666i | 1.26271 | − | 0.117606i | ||||
\(519\) | 14.5374 | 0.638121 | ||||||||
\(520\) | −3.13435 | + | 5.42885i | −0.137450 | + | 0.238071i | ||||
\(521\) | −3.37960 | − | 5.85364i | −0.148063 | − | 0.256453i | 0.782449 | − | 0.622715i | \(-0.213970\pi\) |
−0.930512 | + | 0.366263i | \(0.880637\pi\) | |||||||
\(522\) | −0.634350 | − | 1.09873i | −0.0277647 | − | 0.0480900i | ||||
\(523\) | −3.85768 | + | 6.68170i | −0.168685 | + | 0.292170i | −0.937958 | − | 0.346750i | \(-0.887285\pi\) |
0.769273 | + | 0.638920i | \(0.220619\pi\) | |||||||
\(524\) | −18.8654 | −0.824140 | ||||||||
\(525\) | −6.11864 | − | 8.63494i | −0.267039 | − | 0.376860i | ||||
\(526\) | −0.118640 | −0.00517296 | ||||||||
\(527\) | −12.4701 | + | 21.5989i | −0.543207 | + | 0.940861i | ||||
\(528\) | 2.02966 | + | 3.51547i | 0.0883296 | + | 0.152991i | ||||
\(529\) | −0.500000 | − | 0.866025i | −0.0217391 | − | 0.0376533i | ||||
\(530\) | −4.55932 | + | 7.89697i | −0.198044 | + | 0.343023i | ||||
\(531\) | −6.84994 | −0.297262 | ||||||||
\(532\) | −3.54537 | + | 7.71565i | −0.153711 | + | 0.334516i | ||||
\(533\) | 30.0310 | 1.30079 | ||||||||
\(534\) | −5.45463 | + | 9.44770i | −0.236045 | + | 0.408842i | ||||
\(535\) | 7.02966 | + | 12.1757i | 0.303919 | + | 0.526403i | ||||
\(536\) | −6.73904 | − | 11.6724i | −0.291082 | − | 0.504169i | ||||
\(537\) | −6.37960 | + | 11.0498i | −0.275300 | + | 0.476834i | ||||
\(538\) | −2.96858 | −0.127985 | ||||||||
\(539\) | −9.41876 | + | 26.8088i | −0.405695 | + | 1.15474i | ||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | 0.924970 | − | 1.60210i | 0.0397676 | − | 0.0688795i | −0.845457 | − | 0.534044i | \(-0.820672\pi\) |
0.885224 | + | 0.465165i | \(0.154005\pi\) | |||||||
\(542\) | −6.44842 | − | 11.1690i | −0.276983 | − | 0.479749i | ||||
\(543\) | −6.26870 | − | 10.8577i | −0.269016 | − | 0.465949i | ||||
\(544\) | 1.92497 | − | 3.33415i | 0.0825324 | − | 0.142950i | ||||
\(545\) | −12.1186 | −0.519106 | ||||||||
\(546\) | 6.92497 | − | 15.0705i | 0.296361 | − | 0.644959i | ||||
\(547\) | −37.6839 | −1.61125 | −0.805624 | − | 0.592427i | \(-0.798170\pi\) | ||||
−0.805624 | + | 0.592427i | \(0.798170\pi\) | |||||||
\(548\) | −7.79836 | + | 13.5072i | −0.333129 | + | 0.576997i | ||||
\(549\) | −5.00000 | − | 8.66025i | −0.213395 | − | 0.369611i | ||||
\(550\) | −8.11864 | − | 14.0619i | −0.346180 | − | 0.599601i | ||||
\(551\) | 2.03587 | − | 3.52623i | 0.0867310 | − | 0.150222i | ||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | −14.3594 | − | 20.2648i | −0.610625 | − | 0.861746i | ||||
\(554\) | −11.1780 | −0.474906 | ||||||||
\(555\) | −5.45463 | + | 9.44770i | −0.231536 | + | 0.401032i | ||||
\(556\) | −3.41876 | − | 5.92147i | −0.144988 | − | 0.251126i | ||||
\(557\) | −10.9982 | − | 19.0495i | −0.466010 | − | 0.807154i | 0.533236 | − | 0.845966i | \(-0.320976\pi\) |
−0.999247 | + | 0.0388128i | \(0.987642\pi\) | |||||||
\(558\) | 3.23904 | − | 5.61018i | 0.137119 | − | 0.237498i | ||||
\(559\) | 50.8933 | 2.15256 | ||||||||
\(560\) | 2.63435 | − | 0.245357i | 0.111322 | − | 0.0103682i | ||||
\(561\) | −15.6281 | −0.659821 | ||||||||
\(562\) | −15.7311 | + | 27.2470i | −0.663575 | + | 1.14935i | ||||
\(563\) | 17.9389 | + | 31.0711i | 0.756035 | + | 1.30949i | 0.944858 | + | 0.327480i | \(0.106200\pi\) |
−0.188823 | + | 0.982011i | \(0.560467\pi\) | |||||||
\(564\) | 2.73904 | + | 4.74416i | 0.115334 | + | 0.199765i | ||||
\(565\) | 2.71559 | − | 4.70354i | 0.114246 | − | 0.197879i | ||||
\(566\) | 10.0155 | 0.420982 | ||||||||
\(567\) | 2.63435 | − | 0.245357i | 0.110632 | − | 0.0103040i | ||||
\(568\) | −12.3873 | −0.519761 | ||||||||
\(569\) | 10.5297 | − | 18.2379i | 0.441426 | − | 0.764573i | −0.556369 | − | 0.830935i | \(-0.687806\pi\) |
0.997796 | + | 0.0663624i | \(0.0211393\pi\) | |||||||
\(570\) | −1.60469 | − | 2.77940i | −0.0672131 | − | 0.116416i | ||||
\(571\) | 17.0312 | + | 29.4989i | 0.712733 | + | 1.23449i | 0.963827 | + | 0.266527i | \(0.0858763\pi\) |
−0.251094 | + | 0.967963i | \(0.580790\pi\) | |||||||
\(572\) | 12.7233 | − | 22.0375i | 0.531989 | − | 0.921432i | ||||
\(573\) | −4.07174 | −0.170099 | ||||||||
\(574\) | −7.32802 | − | 10.3417i | −0.305866 | − | 0.431654i | ||||
\(575\) | 4.00000 | 0.166812 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −17.3577 | − | 30.0644i | −0.722610 | − | 1.25160i | −0.959950 | − | 0.280170i | \(-0.909609\pi\) |
0.237341 | − | 0.971426i | \(-0.423724\pi\) | |||||||
\(578\) | −1.08898 | − | 1.88617i | −0.0452956 | − | 0.0784543i | ||||
\(579\) | 11.8873 | − | 20.5895i | 0.494021 | − | 0.855669i | ||||
\(580\) | −1.26870 | −0.0526799 | ||||||||
\(581\) | −0.0655304 | + | 0.142611i | −0.00271866 | + | 0.00591651i | ||||
\(582\) | −15.8061 | −0.655184 | ||||||||
\(583\) | 18.5077 | − | 32.0563i | 0.766512 | − | 1.32764i | ||||
\(584\) | 4.52966 | + | 7.84560i | 0.187439 | + | 0.324653i | ||||
\(585\) | 3.13435 | + | 5.42885i | 0.129589 | + | 0.224455i | ||||
\(586\) | 1.91876 | − | 3.32339i | 0.0792632 | − | 0.137288i | ||||
\(587\) | −41.5843 | −1.71637 | −0.858184 | − | 0.513342i | \(-0.828407\pi\) | ||||
−0.858184 | + | 0.513342i | \(0.828407\pi\) | |||||||
\(588\) | −6.87960 | + | 1.29271i | −0.283710 | + | 0.0533105i | ||||
\(589\) | 20.7906 | 0.856663 | ||||||||
\(590\) | −3.42497 | + | 5.93222i | −0.141004 | + | 0.244226i | ||||
\(591\) | 0.209380 | + | 0.362657i | 0.00861274 | + | 0.0149177i | ||||
\(592\) | 5.45463 | + | 9.44770i | 0.224184 | + | 0.388298i | ||||
\(593\) | 12.6406 | − | 21.8941i | 0.519086 | − | 0.899083i | −0.480668 | − | 0.876902i | \(-0.659606\pi\) |
0.999754 | − | 0.0221802i | \(-0.00706075\pi\) | |||||||
\(594\) | 4.05932 | 0.166556 | ||||||||
\(595\) | −4.25299 | + | 9.25561i | −0.174356 | + | 0.379443i | ||||
\(596\) | 3.17796 | 0.130174 | ||||||||
\(597\) | −2.84994 | + | 4.93624i | −0.116640 | + | 0.202027i | ||||
\(598\) | 3.13435 | + | 5.42885i | 0.128173 | + | 0.222002i | ||||
\(599\) | −10.7625 | − | 18.6412i | −0.439743 | − | 0.761658i | 0.557926 | − | 0.829891i | \(-0.311597\pi\) |
−0.997669 | + | 0.0682328i | \(0.978264\pi\) | |||||||
\(600\) | 2.00000 | − | 3.46410i | 0.0816497 | − | 0.141421i | ||||
\(601\) | 4.17796 | 0.170423 | 0.0852113 | − | 0.996363i | \(-0.472843\pi\) | ||||
0.0852113 | + | 0.996363i | \(0.472843\pi\) | |||||||
\(602\) | −12.4188 | − | 17.5260i | −0.506151 | − | 0.714306i | ||||
\(603\) | −13.4781 | −0.548870 | ||||||||
\(604\) | −5.02966 | + | 8.71163i | −0.204654 | + | 0.354471i | ||||
\(605\) | −2.73904 | − | 4.74416i | −0.111358 | − | 0.192877i | ||||
\(606\) | 7.05932 | + | 12.2271i | 0.286765 | + | 0.496692i | ||||
\(607\) | 10.6264 | − | 18.4054i | 0.431311 | − | 0.747053i | −0.565675 | − | 0.824628i | \(-0.691384\pi\) |
0.996987 | + | 0.0775749i | \(0.0247177\pi\) | |||||||
\(608\) | −3.20938 | −0.130158 | ||||||||
\(609\) | 3.34220 | − | 0.311284i | 0.135433 | − | 0.0126139i | ||||
\(610\) | −10.0000 | −0.404888 | ||||||||
\(611\) | 17.1702 | − | 29.7397i | 0.694633 | − | 1.20314i | ||||
\(612\) | −1.92497 | − | 3.33415i | −0.0778123 | − | 0.134775i | ||||
\(613\) | −1.17796 | − | 2.04029i | −0.0475774 | − | 0.0824064i | 0.841256 | − | 0.540637i | \(-0.181817\pi\) |
−0.888833 | + | 0.458231i | \(0.848483\pi\) | |||||||
\(614\) | 6.99203 | − | 12.1106i | 0.282175 | − | 0.488742i | ||||
\(615\) | 4.79062 | 0.193176 | ||||||||
\(616\) | −10.6937 | + | 0.995981i | −0.430860 | + | 0.0401292i | ||||
\(617\) | −12.8778 | −0.518442 | −0.259221 | − | 0.965818i | \(-0.583466\pi\) | ||||
−0.259221 | + | 0.965818i | \(0.583466\pi\) | |||||||
\(618\) | −0.260960 | + | 0.451996i | −0.0104974 | + | 0.0181819i | ||||
\(619\) | 5.97187 | + | 10.3436i | 0.240030 | + | 0.415744i | 0.960722 | − | 0.277511i | \(-0.0895095\pi\) |
−0.720693 | + | 0.693255i | \(0.756176\pi\) | |||||||
\(620\) | −3.23904 | − | 5.61018i | −0.130083 | − | 0.225310i | ||||
\(621\) | −0.500000 | + | 0.866025i | −0.0200643 | + | 0.0347524i | ||||
\(622\) | 26.3873 | 1.05804 | ||||||||
\(623\) | −16.6875 | − | 23.5502i | −0.668569 | − | 0.943519i | ||||
\(624\) | 6.26870 | 0.250949 | ||||||||
\(625\) | −5.50000 | + | 9.52628i | −0.220000 | + | 0.381051i | ||||
\(626\) | 4.57503 | + | 7.92418i | 0.182855 | + | 0.316714i | ||||
\(627\) | 6.51395 | + | 11.2825i | 0.260142 | + | 0.450579i | ||||
\(628\) | −1.03587 | + | 1.79418i | −0.0413357 | + | 0.0715956i | ||||
\(629\) | −42.0000 | −1.67465 | ||||||||
\(630\) | 1.10469 | − | 2.40409i | 0.0440119 | − | 0.0957813i | ||||
\(631\) | 10.9841 | 0.437269 | 0.218634 | − | 0.975807i | \(-0.429840\pi\) | ||||
0.218634 | + | 0.975807i | \(0.429840\pi\) | |||||||
\(632\) | 4.69367 | − | 8.12968i | 0.186704 | − | 0.323381i | ||||
\(633\) | −2.20938 | − | 3.82676i | −0.0878150 | − | 0.152100i | ||||
\(634\) | 10.1124 | + | 17.5152i | 0.401616 | + | 0.695619i | ||||
\(635\) | 8.02966 | − | 13.9078i | 0.318647 | − | 0.551913i | ||||
\(636\) | 9.11864 | 0.361578 | ||||||||
\(637\) | 28.5810 | + | 33.2965i | 1.13242 | + | 1.31926i | ||||
\(638\) | 5.15006 | 0.203893 | ||||||||
\(639\) | −6.19367 | + | 10.7278i | −0.245018 | + | 0.424383i | ||||
\(640\) | 0.500000 | + | 0.866025i | 0.0197642 | + | 0.0342327i | ||||
\(641\) | −13.7311 | − | 23.7829i | −0.542345 | − | 0.939369i | −0.998769 | − | 0.0496062i | \(-0.984203\pi\) |
0.456424 | − | 0.889762i | \(-0.349130\pi\) | |||||||
\(642\) | 7.02966 | − | 12.1757i | 0.277439 | − | 0.480538i | ||||
\(643\) | −3.32802 | −0.131244 | −0.0656222 | − | 0.997845i | \(-0.520903\pi\) | ||||
−0.0656222 | + | 0.997845i | \(0.520903\pi\) | |||||||
\(644\) | 1.10469 | − | 2.40409i | 0.0435309 | − | 0.0947345i | ||||
\(645\) | 8.11864 | 0.319671 | ||||||||
\(646\) | 6.17796 | − | 10.7005i | 0.243069 | − | 0.421007i | ||||
\(647\) | −15.9247 | − | 27.5825i | −0.626066 | − | 1.08438i | −0.988334 | − | 0.152304i | \(-0.951331\pi\) |
0.362268 | − | 0.932074i | \(-0.382003\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | 13.9031 | − | 24.0808i | 0.545742 | − | 0.945254i | ||||
\(650\) | −25.0748 | −0.983515 | ||||||||
\(651\) | 9.90926 | + | 13.9845i | 0.388375 | + | 0.548094i | ||||
\(652\) | 4.07174 | 0.159462 | ||||||||
\(653\) | 1.14385 | − | 1.98121i | 0.0447623 | − | 0.0775306i | −0.842776 | − | 0.538264i | \(-0.819080\pi\) |
0.887539 | + | 0.460734i | \(0.152414\pi\) | |||||||
\(654\) | 6.05932 | + | 10.4951i | 0.236938 | + | 0.410389i | ||||
\(655\) | 9.43271 | + | 16.3379i | 0.368566 | + | 0.638376i | ||||
\(656\) | 2.39531 | − | 4.14880i | 0.0935211 | − | 0.161983i | ||||
\(657\) | 9.05932 | 0.353438 | ||||||||
\(658\) | −14.4312 | + | 1.34408i | −0.562586 | + | 0.0523978i | ||||
\(659\) | −8.18148 | −0.318705 | −0.159353 | − | 0.987222i | \(-0.550941\pi\) | ||||
−0.159353 | + | 0.987222i | \(0.550941\pi\) | |||||||
\(660\) | 2.02966 | − | 3.51547i | 0.0790044 | − | 0.136840i | ||||
\(661\) | 13.3404 | + | 23.1063i | 0.518883 | + | 0.898732i | 0.999759 | + | 0.0219432i | \(0.00698531\pi\) |
−0.480876 | + | 0.876788i | \(0.659681\pi\) | |||||||
\(662\) | −10.3046 | − | 17.8480i | −0.400499 | − | 0.693684i | ||||
\(663\) | −12.0671 | + | 20.9008i | −0.468646 | + | 0.811718i | ||||
\(664\) | −0.0593201 | −0.00230207 | ||||||||
\(665\) | 8.45463 | − | 0.787443i | 0.327856 | − | 0.0305357i | ||||
\(666\) | 10.9093 | 0.422725 | ||||||||
\(667\) | −0.634350 | + | 1.09873i | −0.0245621 | + | 0.0425429i | ||||
\(668\) | −9.00774 | − | 15.6019i | −0.348520 | − | 0.603654i | ||||
\(669\) | 5.87960 | + | 10.1838i | 0.227318 | + | 0.393727i | ||||
\(670\) | −6.73904 | + | 11.6724i | −0.260352 | + | 0.450943i | ||||
\(671\) | 40.5932 | 1.56708 | ||||||||
\(672\) | −1.52966 | − | 2.15874i | −0.0590079 | − | 0.0832750i | ||||
\(673\) | −48.6525 | −1.87542 | −0.937708 | − | 0.347423i | \(-0.887057\pi\) | ||||
−0.937708 | + | 0.347423i | \(0.887057\pi\) | |||||||
\(674\) | −13.1124 | + | 22.7114i | −0.505072 | + | 0.874810i | ||||
\(675\) | −2.00000 | − | 3.46410i | −0.0769800 | − | 0.133333i | ||||
\(676\) | −13.1483 | − | 22.7735i | −0.505704 | − | 0.875905i | ||||
\(677\) | −0.618640 | + | 1.07152i | −0.0237763 | + | 0.0411817i | −0.877669 | − | 0.479268i | \(-0.840902\pi\) |
0.853892 | + | 0.520450i | \(0.174236\pi\) | |||||||
\(678\) | −5.43118 | −0.208583 | ||||||||
\(679\) | 17.4608 | − | 37.9993i | 0.670086 | − | 1.45828i | ||||
\(680\) | −3.84994 | −0.147638 | ||||||||
\(681\) | 6.87960 | − | 11.9158i | 0.263627 | − | 0.456615i | ||||
\(682\) | 13.1483 | + | 22.7735i | 0.503474 | + | 0.872043i | ||||
\(683\) | −2.67351 | − | 4.63065i | −0.102299 | − | 0.177187i | 0.810332 | − | 0.585970i | \(-0.199287\pi\) |
−0.912631 | + | 0.408783i | \(0.865953\pi\) | |||||||
\(684\) | −1.60469 | + | 2.77940i | −0.0613569 | + | 0.106273i | ||||
\(685\) | 15.5967 | 0.595920 | ||||||||
\(686\) | 4.49203 | − | 17.9672i | 0.171507 | − | 0.685992i | ||||
\(687\) | −21.6281 | −0.825165 | ||||||||
\(688\) | 4.05932 | − | 7.03095i | 0.154760 | − | 0.268052i | ||||
\(689\) | −28.5810 | − | 49.5038i | −1.08885 | − | 1.88594i | ||||
\(690\) | 0.500000 | + | 0.866025i | 0.0190347 | + | 0.0329690i | ||||
\(691\) | −1.76717 | + | 3.06083i | −0.0672263 | + | 0.116439i | −0.897679 | − | 0.440649i | \(-0.854748\pi\) |
0.830453 | + | 0.557089i | \(0.188082\pi\) | |||||||
\(692\) | −14.5374 | −0.552629 | ||||||||
\(693\) | −4.48429 | + | 9.75898i | −0.170344 | + | 0.370713i | ||||
\(694\) | −25.5967 | −0.971638 | ||||||||
\(695\) | −3.41876 | + | 5.92147i | −0.129681 | + | 0.224614i | ||||
\(696\) | 0.634350 | + | 1.09873i | 0.0240450 | + | 0.0416471i | ||||
\(697\) | 9.22180 | + | 15.9726i | 0.349301 | + | 0.605006i | ||||
\(698\) | 0.806330 | − | 1.39660i | 0.0305200 | − | 0.0528622i | ||||
\(699\) | 26.6091 | 1.00645 | ||||||||
\(700\) | 6.11864 | + | 8.63494i | 0.231263 | + | 0.326370i | ||||
\(701\) | −32.6999 | −1.23506 | −0.617529 | − | 0.786548i | \(-0.711866\pi\) | ||||
−0.617529 | + | 0.786548i | \(0.711866\pi\) | |||||||
\(702\) | 3.13435 | − | 5.42885i | 0.118298 | − | 0.204899i | ||||
\(703\) | 17.5060 | + | 30.3212i | 0.660251 | + | 1.14359i | ||||
\(704\) | −2.02966 | − | 3.51547i | −0.0764957 | − | 0.132494i | ||||
\(705\) | 2.73904 | − | 4.74416i | 0.103158 | − | 0.178675i | ||||
\(706\) | 26.6091 | 1.00145 | ||||||||
\(707\) | −37.1934 | + | 3.46410i | −1.39880 | + | 0.130281i | ||||
\(708\) | 6.84994 | 0.257437 | ||||||||
\(709\) | −21.1107 | + | 36.5648i | −0.792828 | + | 1.37322i | 0.131381 | + | 0.991332i | \(0.458059\pi\) |
−0.924209 | + | 0.381886i | \(0.875275\pi\) | |||||||
\(710\) | 6.19367 | + | 10.7278i | 0.232444 | + | 0.402605i | ||||
\(711\) | −4.69367 | − | 8.12968i | −0.176026 | − | 0.304887i | ||||
\(712\) | 5.45463 | − | 9.44770i | 0.204421 | − | 0.354067i | ||||
\(713\) | −6.47808 | −0.242606 | ||||||||
\(714\) | 10.1421 | − | 0.944608i | 0.379558 | − | 0.0353511i | ||||
\(715\) | −25.4467 | −0.951651 | ||||||||
\(716\) | 6.37960 | − | 11.0498i | 0.238417 | − | 0.412950i | ||||
\(717\) | −8.00000 | − | 13.8564i | −0.298765 | − | 0.517477i | ||||
\(718\) | −9.41876 | − | 16.3138i | −0.351505 | − | 0.608825i | ||||
\(719\) | −11.6483 | + | 20.1754i | −0.434408 | + | 0.752417i | −0.997247 | − | 0.0741494i | \(-0.976376\pi\) |
0.562839 | + | 0.826567i | \(0.309709\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | −0.798360 | − | 1.12669i | −0.0297325 | − | 0.0419600i | ||||
\(722\) | 8.69988 | 0.323776 | ||||||||
\(723\) | 14.1124 | − | 24.4434i | 0.524847 | − | 0.909062i | ||||
\(724\) | 6.26870 | + | 10.8577i | 0.232974 | + | 0.403524i | ||||
\(725\) | −2.53740 | − | 4.39491i | −0.0942367 | − | 0.163223i | ||||
\(726\) | −2.73904 | + | 4.74416i | −0.101655 | + | 0.176072i | ||||
\(727\) | −32.5498 | −1.20721 | −0.603603 | − | 0.797285i | \(-0.706269\pi\) | ||||
−0.603603 | + | 0.797285i | \(0.706269\pi\) | |||||||
\(728\) | −6.92497 | + | 15.0705i | −0.256656 | + | 0.558551i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 4.52966 | − | 7.84560i | 0.167650 | − | 0.290379i | ||||
\(731\) | 15.6281 | + | 27.0687i | 0.578028 | + | 1.00117i | ||||
\(732\) | 5.00000 | + | 8.66025i | 0.184805 | + | 0.320092i | ||||
\(733\) | −4.38289 | + | 7.59139i | −0.161886 | + | 0.280394i | −0.935545 | − | 0.353208i | \(-0.885091\pi\) |
0.773659 | + | 0.633602i | \(0.218424\pi\) | |||||||
\(734\) | −0.746780 | −0.0275642 | ||||||||
\(735\) | 4.55932 | + | 5.31155i | 0.168173 | + | 0.195920i | ||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 27.3559 | − | 47.3818i | 1.00767 | − | 1.74533i | ||||
\(738\) | −2.39531 | − | 4.14880i | −0.0881726 | − | 0.152719i | ||||
\(739\) | 12.5498 | + | 21.7369i | 0.461653 | + | 0.799606i | 0.999043 | − | 0.0437275i | \(-0.0139233\pi\) |
−0.537391 | + | 0.843333i | \(0.680590\pi\) | |||||||
\(740\) | 5.45463 | − | 9.44770i | 0.200516 | − | 0.347304i | ||||
\(741\) | 20.1186 | 0.739077 | ||||||||
\(742\) | −10.0733 | + | 21.9221i | −0.369801 | + | 0.804784i | ||||
\(743\) | 18.3090 | 0.671693 | 0.335846 | − | 0.941917i | \(-0.390978\pi\) | ||||
0.335846 | + | 0.941917i | \(0.390978\pi\) | |||||||
\(744\) | −3.23904 | + | 5.61018i | −0.118749 | + | 0.205679i | ||||
\(745\) | −1.58898 | − | 2.75219i | −0.0582157 | − | 0.100833i | ||||
\(746\) | 9.47808 | + | 16.4165i | 0.347017 | + | 0.601051i | ||||
\(747\) | −0.0296601 | + | 0.0513728i | −0.00108521 | + | 0.00187963i | ||||
\(748\) | 15.6281 | 0.571421 | ||||||||
\(749\) | 21.5060 | + | 30.3504i | 0.785811 | + | 1.10898i | ||||
\(750\) | −9.00000 | −0.328634 | ||||||||
\(751\) | 14.0217 | − | 24.2863i | 0.511659 | − | 0.886219i | −0.488250 | − | 0.872704i | \(-0.662365\pi\) |
0.999909 | − | 0.0135151i | \(-0.00430212\pi\) | |||||||
\(752\) | −2.73904 | − | 4.74416i | −0.0998825 | − | 0.173002i | ||||
\(753\) | −4.14830 | − | 7.18507i | −0.151172 | − | 0.261838i | ||||
\(754\) | 3.97655 | − | 6.88759i | 0.144817 | − | 0.250831i | ||||
\(755\) | 10.0593 | 0.366096 | ||||||||
\(756\) | −2.63435 | + | 0.245357i | −0.0958104 | + | 0.00892353i | ||||
\(757\) | 21.7468 | 0.790400 | 0.395200 | − | 0.918595i | \(-0.370675\pi\) | ||||
0.395200 | + | 0.918595i | \(0.370675\pi\) | |||||||
\(758\) | 5.85768 | − | 10.1458i | 0.212761 | − | 0.368512i | ||||
\(759\) | −2.02966 | − | 3.51547i | −0.0736720 | − | 0.127604i | ||||
\(760\) | 1.60469 | + | 2.77940i | 0.0582082 | + | 0.100820i | ||||
\(761\) | 19.9606 | − | 34.5728i | 0.723572 | − | 1.25326i | −0.235988 | − | 0.971756i | \(-0.575833\pi\) |
0.959559 | − | 0.281507i | \(-0.0908342\pi\) | |||||||
\(762\) | −16.0593 | −0.581768 | ||||||||
\(763\) | −31.9247 | + | 2.97339i | −1.15575 | + | 0.107644i | ||||
\(764\) | 4.07174 | 0.147310 | ||||||||
\(765\) | −1.92497 | + | 3.33415i | −0.0695974 | + | 0.120546i | ||||
\(766\) | −13.0828 | − | 22.6600i | −0.472700 | − | 0.818740i | ||||
\(767\) | −21.4701 | − | 37.1873i | −0.775241 | − | 1.34276i | ||||
\(768\) | 0.500000 | − | 0.866025i | 0.0180422 | − | 0.0312500i | ||||
\(769\) | −29.3245 | −1.05747 | −0.528734 | − | 0.848787i | \(-0.677333\pi\) | ||||
−0.528734 | + | 0.848787i | \(0.677333\pi\) | |||||||
\(770\) | 6.20938 | + | 8.76300i | 0.223771 | + | 0.315797i | ||||
\(771\) | −19.0279 | −0.685273 | ||||||||
\(772\) | −11.8873 | + | 20.5895i | −0.427835 | + | 0.741032i | ||||
\(773\) | −2.67972 | − | 4.64141i | −0.0963828 | − | 0.166940i | 0.813802 | − | 0.581142i | \(-0.197394\pi\) |
−0.910185 | + | 0.414202i | \(0.864061\pi\) | |||||||
\(774\) | −4.05932 | − | 7.03095i | −0.145909 | − | 0.252722i | ||||
\(775\) | 12.9562 | − | 22.4407i | 0.465399 | − | 0.806095i | ||||
\(776\) | 15.8061 | 0.567406 | ||||||||
\(777\) | −12.0514 | + | 26.2269i | −0.432340 | + | 0.940884i | ||||
\(778\) | 27.7937 | 0.996452 | ||||||||
\(779\) | 7.68746 | − | 13.3151i | 0.275432 | − | 0.477062i | ||||
\(780\) | −3.13435 | − | 5.42885i | −0.112228 | − | 0.194384i | ||||
\(781\) | −25.1421 | − | 43.5474i | −0.899655 | − | 1.55825i | ||||
\(782\) | −1.92497 | + | 3.33415i | −0.0688368 | + | 0.119229i | ||||
\(783\) | 1.26870 | 0.0453396 | ||||||||
\(784\) | 6.87960 | − | 1.29271i | 0.245700 | − | 0.0461682i | ||||
\(785\) | 2.07174 | 0.0739436 | ||||||||
\(786\) | 9.43271 | − | 16.3379i | 0.336454 | − | 0.582755i | ||||
\(787\) | −13.9484 | − | 24.1594i | −0.497207 | − | 0.861189i | 0.502787 | − | 0.864410i | \(-0.332308\pi\) |
−0.999995 | + | 0.00322154i | \(0.998975\pi\) | |||||||
\(788\) | −0.209380 | − | 0.362657i | −0.00745885 | − | 0.0129191i | ||||
\(789\) | 0.0593201 | − | 0.102746i | 0.00211185 | − | 0.00365784i | ||||
\(790\) | −9.38734 | −0.333987 | ||||||||
\(791\) | 5.99977 | − | 13.0571i | 0.213327 | − | 0.464256i | ||||
\(792\) | −4.05932 | −0.144242 | ||||||||
\(793\) | 31.3435 | − | 54.2885i | 1.11304 | − | 1.92784i | ||||
\(794\) | 1.92497 | + | 3.33415i | 0.0683146 | + | 0.118324i | ||||
\(795\) | −4.55932 | − | 7.89697i | −0.161702 | − | 0.280077i | ||||
\(796\) | 2.84994 | − | 4.93624i | 0.101013 | − | 0.174960i | ||||
\(797\) | 13.6560 | 0.483722 | 0.241861 | − | 0.970311i | \(-0.422242\pi\) | ||||
0.241861 | + | 0.970311i | \(0.422242\pi\) | |||||||
\(798\) | −4.90926 | − | 6.92820i | −0.173786 | − | 0.245256i | ||||
\(799\) | 21.0903 | 0.746120 | ||||||||
\(800\) | −2.00000 | + | 3.46410i | −0.0707107 | + | 0.122474i | ||||
\(801\) | −5.45463 | − | 9.44770i | −0.192730 | − | 0.333818i | ||||
\(802\) | 3.58898 | + | 6.21630i | 0.126731 | + | 0.219505i | ||||
\(803\) | −18.3873 | + | 31.8478i | −0.648875 | + | 1.12388i | ||||
\(804\) | 13.4781 | 0.475335 | ||||||||
\(805\) | −2.63435 | + | 0.245357i | −0.0928486 | + | 0.00864768i | ||||
\(806\) | 40.6091 | 1.43040 | ||||||||
\(807\) | 1.48429 | − | 2.57087i | 0.0522495 | − | 0.0904988i | ||||
\(808\) | −7.05932 | − | 12.2271i | −0.248346 | − | 0.430148i | ||||
\(809\) | 8.36389 | + | 14.4867i | 0.294059 | + | 0.509325i | 0.974765 | − | 0.223231i | \(-0.0716605\pi\) |
−0.680707 | + | 0.732556i | \(0.738327\pi\) | |||||||
\(810\) | 0.500000 | − | 0.866025i | 0.0175682 | − | 0.0304290i | ||||
\(811\) | −17.3998 | −0.610988 | −0.305494 | − | 0.952194i | \(-0.598822\pi\) | ||||
−0.305494 | + | 0.952194i | \(0.598822\pi\) | |||||||
\(812\) | −3.34220 | + | 0.311284i | −0.117288 | + | 0.0109239i | ||||
\(813\) | 12.8968 | 0.452312 | ||||||||
\(814\) | −22.1421 | + | 38.3512i | −0.776080 | + | 1.34421i | ||||
\(815\) | −2.03587 | − | 3.52623i | −0.0713134 | − | 0.123518i | ||||
\(816\) | 1.92497 | + | 3.33415i | 0.0673874 | + | 0.116718i | ||||
\(817\) | 13.0279 | − | 22.5650i | 0.455789 | − | 0.789449i | ||||
\(818\) | 16.3749 | 0.572536 | ||||||||
\(819\) | 9.58898 | + | 13.5325i | 0.335066 | + | 0.472863i | ||||
\(820\) | −4.79062 | −0.167296 | ||||||||
\(821\) | 14.3656 | − | 24.8820i | 0.501365 | − | 0.868389i | −0.498634 | − | 0.866813i | \(-0.666165\pi\) |
0.999999 | − | 0.00157647i | \(-0.000501806\pi\) | |||||||
\(822\) | −7.79836 | − | 13.5072i | −0.271999 | − | 0.471116i | ||||
\(823\) | 16.0155 | + | 27.7396i | 0.558265 | + | 0.966943i | 0.997642 | + | 0.0686398i | \(0.0218659\pi\) |
−0.439377 | + | 0.898303i | \(0.644801\pi\) | |||||||
\(824\) | 0.260960 | − | 0.451996i | 0.00909097 | − | 0.0157460i | ||||
\(825\) | 16.2373 | 0.565310 | ||||||||
\(826\) | −7.56706 | + | 16.4679i | −0.263292 | + | 0.572991i | ||||
\(827\) | 26.3214 | 0.915286 | 0.457643 | − | 0.889136i | \(-0.348694\pi\) | ||||
0.457643 | + | 0.889136i | \(0.348694\pi\) | |||||||
\(828\) | 0.500000 | − | 0.866025i | 0.0173762 | − | 0.0300965i | ||||
\(829\) | 10.7669 | + | 18.6489i | 0.373951 | + | 0.647703i | 0.990169 | − | 0.139873i | \(-0.0446694\pi\) |
−0.616218 | + | 0.787575i | \(0.711336\pi\) | |||||||
\(830\) | 0.0296601 | + | 0.0513728i | 0.00102952 | + | 0.00178317i | ||||
\(831\) | 5.58898 | − | 9.68040i | 0.193880 | − | 0.335809i | ||||
\(832\) | −6.26870 | −0.217328 | ||||||||
\(833\) | −8.93294 | + | 25.4260i | −0.309508 | + | 0.880959i | ||||
\(834\) | 6.83752 | 0.236764 | ||||||||
\(835\) | −9.00774 | + | 15.6019i | −0.311726 | + | 0.539925i | ||||
\(836\) | −6.51395 | − | 11.2825i | −0.225290 | − | 0.390213i | ||||
\(837\) | 3.23904 | + | 5.61018i | 0.111958 | + | 0.193916i | ||||
\(838\) | −12.9686 | + | 22.4622i | −0.447992 | + | 0.775945i | ||||
\(839\) | 6.25322 | 0.215885 | 0.107943 | − | 0.994157i | \(-0.465574\pi\) | ||||
0.107943 | + | 0.994157i | \(0.465574\pi\) | |||||||
\(840\) | −1.10469 | + | 2.40409i | −0.0381154 | + | 0.0829491i | ||||
\(841\) | −27.3904 | −0.944497 | ||||||||
\(842\) | 1.56882 | − | 2.71728i | 0.0540651 | − | 0.0936435i | ||||
\(843\) | −15.7311 | − | 27.2470i | −0.541807 | − | 0.938437i | ||||
\(844\) | 2.20938 | + | 3.82676i | 0.0760500 | + | 0.131722i | ||||
\(845\) | −13.1483 | + | 22.7735i | −0.452315 | + | 0.783433i | ||||
\(846\) | −5.47808 | −0.188340 | ||||||||
\(847\) | −8.37960 | − | 11.8257i | −0.287926 | − | 0.406337i | ||||
\(848\) | −9.11864 | −0.313135 | ||||||||
\(849\) | −5.00774 | + | 8.67366i | −0.171865 | + | 0.297679i | ||||
\(850\) | −7.69988 | − | 13.3366i | −0.264104 | − | 0.457441i | ||||
\(851\) | −5.45463 | − | 9.44770i | −0.186982 | − | 0.323863i | ||||
\(852\) | 6.19367 | − | 10.7278i | 0.212192 | − | 0.367527i | ||||
\(853\) | 4.65604 | 0.159420 | 0.0797099 | − | 0.996818i | \(-0.474601\pi\) | ||||
0.0797099 | + | 0.996818i | \(0.474601\pi\) | |||||||
\(854\) | −26.3435 | + | 2.45357i | −0.901456 | + | 0.0839593i | ||||
\(855\) | 3.20938 | 0.109758 | ||||||||
\(856\) | −7.02966 | + | 12.1757i | −0.240269 | + | 0.416158i | ||||
\(857\) | 22.8420 | + | 39.5635i | 0.780267 | + | 1.35146i | 0.931786 | + | 0.363008i | \(0.118250\pi\) |
−0.151519 | + | 0.988454i | \(0.548417\pi\) | |||||||
\(858\) | 12.7233 | + | 22.0375i | 0.434367 | + | 0.752346i | ||||
\(859\) | −21.0045 | + | 36.3808i | −0.716663 | + | 1.24130i | 0.245652 | + | 0.969358i | \(0.420998\pi\) |
−0.962315 | + | 0.271938i | \(0.912335\pi\) | |||||||
\(860\) | −8.11864 | −0.276843 | ||||||||
\(861\) | 12.6202 | − | 1.17541i | 0.430094 | − | 0.0400579i | ||||
\(862\) | 17.0748 | 0.581570 | ||||||||
\(863\) | 25.1029 | − | 43.4796i | 0.854514 | − | 1.48006i | −0.0225817 | − | 0.999745i | \(-0.507189\pi\) |
0.877095 | − | 0.480316i | \(-0.159478\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 7.26870 | + | 12.5898i | 0.247143 | + | 0.428065i | ||||
\(866\) | −17.2373 | + | 29.8558i | −0.585747 | + | 1.01454i | ||||
\(867\) | 2.17796 | 0.0739674 | ||||||||
\(868\) | −9.90926 | − | 13.9845i | −0.336342 | − | 0.474664i | ||||
\(869\) | 38.1062 | 1.29266 | ||||||||
\(870\) | 0.634350 | − | 1.09873i | 0.0215065 | − | 0.0372503i | ||||
\(871\) | −42.2450 | − | 73.1705i | −1.43142 | − | 2.47929i | ||||
\(872\) | −6.05932 | − | 10.4951i | −0.205194 | − | 0.355407i | ||||
\(873\) | 7.90305 | − | 13.6885i | 0.267478 | − | 0.463285i | ||||
\(874\) | 3.20938 | 0.108559 | ||||||||
\(875\) | 9.94221 | − | 21.6368i | 0.336108 | − | 0.731458i | ||||
\(876\) | −9.05932 | −0.306086 | ||||||||
\(877\) | 4.22509 | − | 7.31807i | 0.142671 | − | 0.247114i | −0.785831 | − | 0.618442i | \(-0.787764\pi\) |
0.928502 | + | 0.371328i | \(0.121098\pi\) | |||||||
\(878\) | 1.29836 | + | 2.24883i | 0.0438175 | + | 0.0758942i | ||||
\(879\) | 1.91876 | + | 3.32339i | 0.0647182 | + | 0.112095i | ||||
\(880\) | −2.02966 | + | 3.51547i | −0.0684198 | + | 0.118507i | ||||
\(881\) | 1.17796 | 0.0396865 | 0.0198432 | − | 0.999803i | \(-0.493683\pi\) | ||||
0.0198432 | + | 0.999803i | \(0.493683\pi\) | |||||||
\(882\) | 2.32028 | − | 6.60426i | 0.0781279 | − | 0.222377i | ||||
\(883\) | 27.5653 | 0.927646 | 0.463823 | − | 0.885928i | \(-0.346477\pi\) | ||||
0.463823 | + | 0.885928i | \(0.346477\pi\) | |||||||
\(884\) | 12.0671 | − | 20.9008i | 0.405859 | − | 0.702969i | ||||
\(885\) | −3.42497 | − | 5.93222i | −0.115129 | − | 0.199409i | ||||
\(886\) | 2.01395 | + | 3.48826i | 0.0676600 | + | 0.117191i | ||||
\(887\) | −24.1186 | + | 41.7747i | −0.809825 | + | 1.40266i | 0.103160 | + | 0.994665i | \(0.467104\pi\) |
−0.912985 | + | 0.407993i | \(0.866229\pi\) | |||||||
\(888\) | −10.9093 | −0.366091 | ||||||||
\(889\) | 17.7406 | − | 38.6081i | 0.595000 | − | 1.29487i | ||||
\(890\) | −10.9093 | −0.365679 | ||||||||
\(891\) | −2.02966 | + | 3.51547i | −0.0679962 | + | 0.117773i | ||||
\(892\) | −5.87960 | − | 10.1838i | −0.196864 | − | 0.340978i | ||||
\(893\) | −8.79062 | − | 15.2258i | −0.294167 | − | 0.509512i | ||||
\(894\) | −1.58898 | + | 2.75219i | −0.0531434 | + | 0.0920472i | ||||
\(895\) | −12.7592 | −0.426493 | ||||||||
\(896\) | 1.52966 | + | 2.15874i | 0.0511024 | + | 0.0721183i | ||||
\(897\) | −6.26870 | −0.209306 | ||||||||
\(898\) | −11.0828 | + | 19.1959i | −0.369837 | + | 0.640576i | ||||
\(899\) | 4.10937 | + | 7.11764i | 0.137055 | + | 0.237387i | ||||
\(900\) | 2.00000 | + | 3.46410i | 0.0666667 | + | 0.115470i | ||||
\(901\) | 17.5531 | − | 30.4029i | 0.584779 | − | 1.01287i | ||||
\(902\) | 19.4467 | 0.647503 | ||||||||
\(903\) | 21.3873 | − | 1.99196i | 0.711726 | − | 0.0662883i | ||||
\(904\) | 5.43118 | 0.180638 | ||||||||
\(905\) | 6.26870 | − | 10.8577i | 0.208379 | − | 0.360922i | ||||
\(906\) | −5.02966 | − | 8.71163i | −0.167099 | − | 0.289424i | ||||
\(907\) | 12.1344 | + | 21.0173i | 0.402914 | + | 0.697868i | 0.994076 | − | 0.108685i | \(-0.0346639\pi\) |
−0.591162 | + | 0.806553i | \(0.701331\pi\) | |||||||
\(908\) | −6.87960 | + | 11.9158i | −0.228308 | + | 0.395440i | ||||
\(909\) | −14.1186 | −0.468286 | ||||||||
\(910\) | 16.5140 | − | 1.53807i | 0.547432 | − | 0.0509864i | ||||
\(911\) | −6.68088 | −0.221347 | −0.110674 | − | 0.993857i | \(-0.535301\pi\) | ||||
−0.110674 | + | 0.993857i | \(0.535301\pi\) | |||||||
\(912\) | 1.60469 | − | 2.77940i | 0.0531366 | − | 0.0920353i | ||||
\(913\) | −0.120400 | − | 0.208538i | −0.00398465 | − | 0.00690162i | ||||
\(914\) | 16.3811 | + | 28.3729i | 0.541840 | + | 0.938494i | ||||
\(915\) | 5.00000 | − | 8.66025i | 0.165295 | − | 0.286299i | ||||
\(916\) | 21.6281 | 0.714614 | ||||||||
\(917\) | 28.8577 | + | 40.7255i | 0.952965 | + | 1.34487i | ||||
\(918\) | 3.84994 | 0.127067 | ||||||||
\(919\) | −2.14232 | + | 3.71061i | −0.0706686 | + | 0.122402i | −0.899195 | − | 0.437549i | \(-0.855847\pi\) |
0.828526 | + | 0.559951i | \(0.189180\pi\) | |||||||
\(920\) | −0.500000 | − | 0.866025i | −0.0164845 | − | 0.0285520i | ||||
\(921\) | 6.99203 | + | 12.1106i | 0.230395 | + | 0.399056i | ||||
\(922\) | −5.11864 | + | 8.86575i | −0.168573 | + | 0.291978i | ||||
\(923\) | −77.6525 | −2.55596 | ||||||||
\(924\) | 4.48429 | − | 9.75898i | 0.147522 | − | 0.321047i | ||||
\(925\) | 43.6370 | 1.43478 | ||||||||
\(926\) | −0.0593201 | + | 0.102746i | −0.00194938 | + | 0.00337643i | ||||
\(927\) | −0.260960 | − | 0.451996i | −0.00857105 | − | 0.0148455i | ||||
\(928\) | −0.634350 | − | 1.09873i | −0.0208236 | − | 0.0360675i | ||||
\(929\) | 1.59227 | − | 2.75789i | 0.0522407 | − | 0.0904835i | −0.838723 | − | 0.544559i | \(-0.816697\pi\) |
0.890963 | + | 0.454076i | \(0.150030\pi\) | |||||||
\(930\) | 6.47808 | 0.212425 | ||||||||
\(931\) | 22.0793 | − | 4.14880i | 0.723618 | − | 0.135971i | ||||
\(932\) | −26.6091 | −0.871611 | ||||||||
\(933\) | −13.1937 | + | 22.8521i | −0.431941 | + | 0.748144i | ||||
\(934\) | −4.05932 | − | 7.03095i | −0.132825 | − | 0.230060i | ||||
\(935\) | −7.81407 | − | 13.5344i | −0.255547 | − | 0.442621i | ||||
\(936\) | −3.13435 | + | 5.42885i | −0.102449 | + | 0.177448i | ||||
\(937\) | 25.8619 | 0.844871 | 0.422436 | − | 0.906393i | \(-0.361175\pi\) | ||||
0.422436 | + | 0.906393i | \(0.361175\pi\) | |||||||
\(938\) | −14.8891 | + | 32.4025i | −0.486146 | + | 1.05798i | ||||
\(939\) | −9.15006 | −0.298601 | ||||||||
\(940\) | −2.73904 | + | 4.74416i | −0.0893376 | + | 0.154737i | ||||
\(941\) | −1.85170 | − | 3.20724i | −0.0603637 | − | 0.104553i | 0.834264 | − | 0.551365i | \(-0.185893\pi\) |
−0.894628 | + | 0.446812i | \(0.852559\pi\) | |||||||
\(942\) | −1.03587 | − | 1.79418i | −0.0337505 | − | 0.0584575i | ||||
\(943\) | −2.39531 | + | 4.14880i | −0.0780020 | + | 0.135103i | ||||
\(944\) | −6.84994 | −0.222947 | ||||||||
\(945\) | 1.52966 | + | 2.15874i | 0.0497598 | + | 0.0702237i | ||||
\(946\) | 32.9562 | 1.07150 | ||||||||
\(947\) | 25.0077 | − | 43.3147i | 0.812642 | − | 1.40754i | −0.0983661 | − | 0.995150i | \(-0.531362\pi\) |
0.911009 | − | 0.412388i | \(-0.135305\pi\) | |||||||
\(948\) | 4.69367 | + | 8.12968i | 0.152443 | + | 0.264040i | ||||
\(949\) | 28.3951 | + | 49.1817i | 0.921743 | + | 1.59651i | ||||
\(950\) | −6.41876 | + | 11.1176i | −0.208252 | + | 0.360703i | ||||
\(951\) | −20.2249 | −0.655836 | ||||||||
\(952\) | −10.1421 | + | 0.944608i | −0.328707 | + | 0.0306149i | ||||
\(953\) | 24.4188 | 0.791001 | 0.395501 | − | 0.918466i | \(-0.370571\pi\) | ||||
0.395501 | + | 0.918466i | \(0.370571\pi\) | |||||||
\(954\) | −4.55932 | + | 7.89697i | −0.147613 | + | 0.255674i | ||||
\(955\) | −2.03587 | − | 3.52623i | −0.0658792 | − | 0.114106i | ||||
\(956\) | 8.00000 | + | 13.8564i | 0.258738 | + | 0.448148i | ||||
\(957\) | −2.57503 | + | 4.46008i | −0.0832389 | + | 0.144174i | ||||
\(958\) | 4.55334 | 0.147112 | ||||||||
\(959\) | 41.0872 | − | 3.82676i | 1.32678 | − | 0.123572i | ||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | −5.48276 | + | 9.49642i | −0.176863 | + | 0.306336i | ||||
\(962\) | 34.1934 | + | 59.2248i | 1.10244 | + | 1.90948i | ||||
\(963\) | 7.02966 | + | 12.1757i | 0.226528 | + | 0.392357i | ||||
\(964\) | −14.1124 | + | 24.4434i | −0.454531 | + | 0.787270i | ||||
\(965\) | 23.7747 | 0.765334 | ||||||||
\(966\) | 1.52966 | + | 2.15874i | 0.0492160 | + | 0.0694562i | ||||
\(967\) | −18.4152 | −0.592194 | −0.296097 | − | 0.955158i | \(-0.595685\pi\) | ||||
−0.296097 | + | 0.955158i | \(0.595685\pi\) | |||||||
\(968\) | 2.73904 | − | 4.74416i | 0.0880361 | − | 0.152483i | ||||
\(969\) | 6.17796 | + | 10.7005i | 0.198465 | + | 0.343751i | ||||
\(970\) | −7.90305 | − | 13.6885i | −0.253752 | − | 0.439511i | ||||
\(971\) | 8.97034 | − | 15.5371i | 0.287872 | − | 0.498609i | −0.685430 | − | 0.728139i | \(-0.740386\pi\) |
0.973302 | + | 0.229530i | \(0.0737189\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −7.55334 | + | 16.4380i | −0.242149 | + | 0.526979i | ||||
\(974\) | 21.3156 | 0.682996 | ||||||||
\(975\) | 12.5374 | − | 21.7154i | 0.401518 | − | 0.695450i | ||||
\(976\) | −5.00000 | − | 8.66025i | −0.160046 | − | 0.277208i | ||||
\(977\) | −14.2171 | − | 24.6248i | −0.454846 | − | 0.787816i | 0.543833 | − | 0.839193i | \(-0.316972\pi\) |
−0.998679 | + | 0.0513769i | \(0.983639\pi\) | |||||||
\(978\) | −2.03587 | + | 3.52623i | −0.0651000 | + | 0.112756i | ||||
\(979\) | 44.2842 | 1.41533 | ||||||||
\(980\) | −4.55932 | − | 5.31155i | −0.145642 | − | 0.169671i | ||||
\(981\) | −12.1186 | −0.386918 | ||||||||
\(982\) | 1.04537 | − | 1.81063i | 0.0333591 | − | 0.0577796i | ||||
\(983\) | −2.30457 | − | 3.99163i | −0.0735044 | − | 0.127313i | 0.826931 | − | 0.562304i | \(-0.190085\pi\) |
−0.900435 | + | 0.434991i | \(0.856752\pi\) | |||||||
\(984\) | 2.39531 | + | 4.14880i | 0.0763597 | + | 0.132259i | ||||
\(985\) | −0.209380 | + | 0.362657i | −0.00667140 | + | 0.0115552i | ||||
\(986\) | 4.88442 | 0.155552 | ||||||||
\(987\) | 6.05158 | − | 13.1698i | 0.192624 | − | 0.419200i | ||||
\(988\) | −20.1186 | −0.640059 | ||||||||
\(989\) | −4.05932 | + | 7.03095i | −0.129079 | + | 0.223571i | ||||
\(990\) | 2.02966 | + | 3.51547i | 0.0645068 | + | 0.111729i | ||||
\(991\) | 20.9389 | + | 36.2673i | 0.665147 | + | 1.15207i | 0.979246 | + | 0.202678i | \(0.0649643\pi\) |
−0.314099 | + | 0.949390i | \(0.601702\pi\) | |||||||
\(992\) | 3.23904 | − | 5.61018i | 0.102840 | − | 0.178123i | ||||
\(993\) | 20.6091 | 0.654011 | ||||||||
\(994\) | 18.9484 | + | 26.7410i | 0.601007 | + | 0.848173i | ||||
\(995\) | −5.69988 | −0.180698 | ||||||||
\(996\) | 0.0296601 | − | 0.0513728i | 0.000939815 | − | 0.00162781i | ||||
\(997\) | −16.6640 | − | 28.8629i | −0.527754 | − | 0.914098i | −0.999477 | − | 0.0323503i | \(-0.989701\pi\) |
0.471722 | − | 0.881747i | \(-0.343633\pi\) | |||||||
\(998\) | −3.56882 | − | 6.18138i | −0.112969 | − | 0.195668i | ||||
\(999\) | −5.45463 | + | 9.44770i | −0.172577 | + | 0.298912i |
(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 | 966.2.i.k.415.2 | yes | 6 | |
7.2 | even | 3 | 6762.2.a.ce.1.3 | 3 | |||
7.4 | even | 3 | inner | 966.2.i.k.277.2 | ✓ | 6 | |
7.5 | odd | 6 | 6762.2.a.cf.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.i.k.277.2 | ✓ | 6 | 7.4 | even | 3 | inner | |
966.2.i.k.415.2 | yes | 6 | 1.1 | even | 1 | trivial | |
6762.2.a.ce.1.3 | 3 | 7.2 | even | 3 | |||
6762.2.a.cf.1.3 | 3 | 7.5 | odd | 6 |