Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,2,Mod(379,1134)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("1134.379");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.f (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.05503558921\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 378) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 379.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.379 |
Dual form | 1134.2.f.p.757.1 |
$q$-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 \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||
\(5\) | 2.00000 | + | 3.46410i | 0.894427 | + | 1.54919i | 0.834512 | + | 0.550990i | \(0.185750\pi\) |
0.0599153 | + | 0.998203i | \(0.480917\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | − | 0.866025i | 0.188982 | − | 0.327327i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.00000 | 1.26491 | ||||||||
\(11\) | −2.00000 | + | 3.46410i | −0.603023 | + | 1.04447i | 0.389338 | + | 0.921095i | \(0.372704\pi\) |
−0.992361 | + | 0.123371i | \(0.960630\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.50000 | − | 2.59808i | −0.416025 | − | 0.720577i | 0.579510 | − | 0.814965i | \(-0.303244\pi\) |
−0.995535 | + | 0.0943882i | \(0.969911\pi\) | |||||||
\(14\) | −0.500000 | − | 0.866025i | −0.133631 | − | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 7.00000 | 1.69775 | 0.848875 | − | 0.528594i | \(-0.177281\pi\) | ||||
0.848875 | + | 0.528594i | \(0.177281\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 2.00000 | − | 3.46410i | 0.447214 | − | 0.774597i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.00000 | + | 3.46410i | 0.426401 | + | 0.738549i | ||||
\(23\) | −0.500000 | − | 0.866025i | −0.104257 | − | 0.180579i | 0.809177 | − | 0.587565i | \(-0.199913\pi\) |
−0.913434 | + | 0.406986i | \(0.866580\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.50000 | + | 9.52628i | −1.10000 | + | 1.90526i | ||||
\(26\) | −3.00000 | −0.588348 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 0.500000 | − | 0.866025i | 0.0928477 | − | 0.160817i | −0.815861 | − | 0.578249i | \(-0.803736\pi\) |
0.908708 | + | 0.417432i | \(0.137070\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.50000 | + | 7.79423i | 0.808224 | + | 1.39988i | 0.914093 | + | 0.405505i | \(0.132904\pi\) |
−0.105869 | + | 0.994380i | \(0.533762\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.50000 | − | 6.06218i | 0.600245 | − | 1.03965i | ||||
\(35\) | 4.00000 | 0.676123 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 1.00000 | − | 1.73205i | 0.162221 | − | 0.280976i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.00000 | − | 3.46410i | −0.316228 | − | 0.547723i | ||||
\(41\) | 3.00000 | + | 5.19615i | 0.468521 | + | 0.811503i | 0.999353 | − | 0.0359748i | \(-0.0114536\pi\) |
−0.530831 | + | 0.847477i | \(0.678120\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.50000 | + | 9.52628i | −0.838742 | + | 1.45274i | 0.0522047 | + | 0.998636i | \(0.483375\pi\) |
−0.890947 | + | 0.454108i | \(0.849958\pi\) | |||||||
\(44\) | 4.00000 | 0.603023 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −3.00000 | + | 5.19615i | −0.437595 | + | 0.757937i | −0.997503 | − | 0.0706177i | \(-0.977503\pi\) |
0.559908 | + | 0.828554i | \(0.310836\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 5.50000 | + | 9.52628i | 0.777817 | + | 1.34722i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.50000 | + | 2.59808i | −0.208013 | + | 0.360288i | ||||
\(53\) | 9.00000 | 1.23625 | 0.618123 | − | 0.786082i | \(-0.287894\pi\) | ||||
0.618123 | + | 0.786082i | \(0.287894\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16.0000 | −2.15744 | ||||||||
\(56\) | −0.500000 | + | 0.866025i | −0.0668153 | + | 0.115728i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.500000 | − | 0.866025i | −0.0656532 | − | 0.113715i | ||||
\(59\) | −2.50000 | − | 4.33013i | −0.325472 | − | 0.563735i | 0.656136 | − | 0.754643i | \(-0.272190\pi\) |
−0.981608 | + | 0.190909i | \(0.938857\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.00000 | − | 5.19615i | 0.384111 | − | 0.665299i | −0.607535 | − | 0.794293i | \(-0.707841\pi\) |
0.991645 | + | 0.128994i | \(0.0411748\pi\) | |||||||
\(62\) | 9.00000 | 1.14300 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.00000 | − | 10.3923i | 0.744208 | − | 1.28901i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.50000 | − | 6.06218i | −0.427593 | − | 0.740613i | 0.569066 | − | 0.822292i | \(-0.307305\pi\) |
−0.996659 | + | 0.0816792i | \(0.973972\pi\) | |||||||
\(68\) | −3.50000 | − | 6.06218i | −0.424437 | − | 0.735147i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.00000 | − | 3.46410i | 0.239046 | − | 0.414039i | ||||
\(71\) | 7.00000 | 0.830747 | 0.415374 | − | 0.909651i | \(-0.363651\pi\) | ||||
0.415374 | + | 0.909651i | \(0.363651\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.0000 | −1.63858 | −0.819288 | − | 0.573382i | \(-0.805631\pi\) | ||||
−0.819288 | + | 0.573382i | \(0.805631\pi\) | |||||||
\(74\) | 1.00000 | − | 1.73205i | 0.116248 | − | 0.201347i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | − | 1.73205i | −0.114708 | − | 0.198680i | ||||
\(77\) | 2.00000 | + | 3.46410i | 0.227921 | + | 0.394771i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.00000 | − | 5.19615i | 0.337526 | − | 0.584613i | −0.646440 | − | 0.762964i | \(-0.723743\pi\) |
0.983967 | + | 0.178352i | \(0.0570765\pi\) | |||||||
\(80\) | −4.00000 | −0.447214 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.00000 | 0.662589 | ||||||||
\(83\) | −2.00000 | + | 3.46410i | −0.219529 | + | 0.380235i | −0.954664 | − | 0.297686i | \(-0.903785\pi\) |
0.735135 | + | 0.677920i | \(0.237119\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.0000 | + | 24.2487i | 1.51851 | + | 2.63014i | ||||
\(86\) | 5.50000 | + | 9.52628i | 0.593080 | + | 1.02725i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.00000 | − | 3.46410i | 0.213201 | − | 0.369274i | ||||
\(89\) | 3.00000 | 0.317999 | 0.159000 | − | 0.987279i | \(-0.449173\pi\) | ||||
0.159000 | + | 0.987279i | \(0.449173\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.00000 | −0.314485 | ||||||||
\(92\) | −0.500000 | + | 0.866025i | −0.0521286 | + | 0.0902894i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.00000 | + | 5.19615i | 0.309426 | + | 0.535942i | ||||
\(95\) | 4.00000 | + | 6.92820i | 0.410391 | + | 0.710819i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.00000 | − | 6.92820i | 0.406138 | − | 0.703452i | −0.588315 | − | 0.808632i | \(-0.700208\pi\) |
0.994453 | + | 0.105180i | \(0.0335417\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 11.0000 | 1.10000 | ||||||||
\(101\) | 5.00000 | − | 8.66025i | 0.497519 | − | 0.861727i | −0.502477 | − | 0.864590i | \(-0.667578\pi\) |
0.999996 | + | 0.00286291i | \(0.000911295\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.50000 | − | 14.7224i | −0.837530 | − | 1.45064i | −0.891954 | − | 0.452126i | \(-0.850666\pi\) |
0.0544240 | − | 0.998518i | \(-0.482668\pi\) | |||||||
\(104\) | 1.50000 | + | 2.59808i | 0.147087 | + | 0.254762i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.50000 | − | 7.79423i | 0.437079 | − | 0.757042i | ||||
\(107\) | −12.0000 | −1.16008 | −0.580042 | − | 0.814587i | \(-0.696964\pi\) | ||||
−0.580042 | + | 0.814587i | \(0.696964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.0000 | 1.53252 | 0.766261 | − | 0.642529i | \(-0.222115\pi\) | ||||
0.766261 | + | 0.642529i | \(0.222115\pi\) | |||||||
\(110\) | −8.00000 | + | 13.8564i | −0.762770 | + | 1.32116i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.500000 | + | 0.866025i | 0.0472456 | + | 0.0818317i | ||||
\(113\) | −4.00000 | − | 6.92820i | −0.376288 | − | 0.651751i | 0.614231 | − | 0.789127i | \(-0.289466\pi\) |
−0.990519 | + | 0.137376i | \(0.956133\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.00000 | − | 3.46410i | 0.186501 | − | 0.323029i | ||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.00000 | −0.460287 | ||||||||
\(119\) | 3.50000 | − | 6.06218i | 0.320844 | − | 0.555719i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.50000 | − | 4.33013i | −0.227273 | − | 0.393648i | ||||
\(122\) | −3.00000 | − | 5.19615i | −0.271607 | − | 0.470438i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.50000 | − | 7.79423i | 0.404112 | − | 0.699942i | ||||
\(125\) | −24.0000 | −2.14663 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.00000 | − | 10.3923i | −0.526235 | − | 0.911465i | ||||
\(131\) | 0.500000 | + | 0.866025i | 0.0436852 | + | 0.0756650i | 0.887041 | − | 0.461690i | \(-0.152757\pi\) |
−0.843356 | + | 0.537355i | \(0.819423\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.00000 | − | 1.73205i | 0.0867110 | − | 0.150188i | ||||
\(134\) | −7.00000 | −0.604708 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.00000 | −0.600245 | ||||||||
\(137\) | 11.0000 | − | 19.0526i | 0.939793 | − | 1.62777i | 0.173939 | − | 0.984757i | \(-0.444351\pi\) |
0.765855 | − | 0.643013i | \(-0.222316\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.00000 | − | 8.66025i | −0.424094 | − | 0.734553i | 0.572241 | − | 0.820086i | \(-0.306074\pi\) |
−0.996335 | + | 0.0855324i | \(0.972741\pi\) | |||||||
\(140\) | −2.00000 | − | 3.46410i | −0.169031 | − | 0.292770i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.50000 | − | 6.06218i | 0.293713 | − | 0.508727i | ||||
\(143\) | 12.0000 | 1.00349 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.00000 | 0.332182 | ||||||||
\(146\) | −7.00000 | + | 12.1244i | −0.579324 | + | 1.00342i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.00000 | − | 1.73205i | −0.0821995 | − | 0.142374i | ||||
\(149\) | −1.50000 | − | 2.59808i | −0.122885 | − | 0.212843i | 0.798019 | − | 0.602632i | \(-0.205881\pi\) |
−0.920904 | + | 0.389789i | \(0.872548\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.00000 | + | 8.66025i | −0.406894 | + | 0.704761i | −0.994540 | − | 0.104357i | \(-0.966722\pi\) |
0.587646 | + | 0.809118i | \(0.300055\pi\) | |||||||
\(152\) | −2.00000 | −0.162221 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.00000 | 0.322329 | ||||||||
\(155\) | −18.0000 | + | 31.1769i | −1.44579 | + | 2.50419i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.50000 | − | 14.7224i | −0.678374 | − | 1.17498i | −0.975470 | − | 0.220131i | \(-0.929352\pi\) |
0.297097 | − | 0.954847i | \(-0.403982\pi\) | |||||||
\(158\) | −3.00000 | − | 5.19615i | −0.238667 | − | 0.413384i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.00000 | + | 3.46410i | −0.158114 | + | 0.273861i | ||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.00000 | −0.0783260 | −0.0391630 | − | 0.999233i | \(-0.512469\pi\) | ||||
−0.0391630 | + | 0.999233i | \(0.512469\pi\) | |||||||
\(164\) | 3.00000 | − | 5.19615i | 0.234261 | − | 0.405751i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.00000 | + | 3.46410i | 0.155230 | + | 0.268866i | ||||
\(167\) | −4.00000 | − | 6.92820i | −0.309529 | − | 0.536120i | 0.668730 | − | 0.743505i | \(-0.266838\pi\) |
−0.978259 | + | 0.207385i | \(0.933505\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.00000 | − | 3.46410i | 0.153846 | − | 0.266469i | ||||
\(170\) | 28.0000 | 2.14750 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.0000 | 0.838742 | ||||||||
\(173\) | −4.00000 | + | 6.92820i | −0.304114 | + | 0.526742i | −0.977064 | − | 0.212947i | \(-0.931694\pi\) |
0.672949 | + | 0.739689i | \(0.265027\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.50000 | + | 9.52628i | 0.415761 | + | 0.720119i | ||||
\(176\) | −2.00000 | − | 3.46410i | −0.150756 | − | 0.261116i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.50000 | − | 2.59808i | 0.112430 | − | 0.194734i | ||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.00000 | −0.668965 | −0.334482 | − | 0.942402i | \(-0.608561\pi\) | ||||
−0.334482 | + | 0.942402i | \(0.608561\pi\) | |||||||
\(182\) | −1.50000 | + | 2.59808i | −0.111187 | + | 0.192582i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.500000 | + | 0.866025i | 0.0368605 | + | 0.0638442i | ||||
\(185\) | 4.00000 | + | 6.92820i | 0.294086 | + | 0.509372i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.0000 | + | 24.2487i | −1.02378 | + | 1.77324i | ||||
\(188\) | 6.00000 | 0.437595 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.00000 | 0.580381 | ||||||||
\(191\) | 6.00000 | − | 10.3923i | 0.434145 | − | 0.751961i | −0.563081 | − | 0.826402i | \(-0.690384\pi\) |
0.997225 | + | 0.0744412i | \(0.0237173\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.50000 | − | 4.33013i | −0.179954 | − | 0.311689i | 0.761911 | − | 0.647682i | \(-0.224262\pi\) |
−0.941865 | + | 0.335993i | \(0.890928\pi\) | |||||||
\(194\) | −4.00000 | − | 6.92820i | −0.287183 | − | 0.497416i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.500000 | + | 0.866025i | −0.0357143 | + | 0.0618590i | ||||
\(197\) | −26.0000 | −1.85242 | −0.926212 | − | 0.377004i | \(-0.876954\pi\) | ||||
−0.926212 | + | 0.377004i | \(0.876954\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.00000 | −0.496217 | −0.248108 | − | 0.968732i | \(-0.579809\pi\) | ||||
−0.248108 | + | 0.968732i | \(0.579809\pi\) | |||||||
\(200\) | 5.50000 | − | 9.52628i | 0.388909 | − | 0.673610i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.00000 | − | 8.66025i | −0.351799 | − | 0.609333i | ||||
\(203\) | −0.500000 | − | 0.866025i | −0.0350931 | − | 0.0607831i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.0000 | + | 20.7846i | −0.838116 | + | 1.45166i | ||||
\(206\) | −17.0000 | −1.18445 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.00000 | 0.208013 | ||||||||
\(209\) | −4.00000 | + | 6.92820i | −0.276686 | + | 0.479234i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.500000 | + | 0.866025i | 0.0344214 | + | 0.0596196i | 0.882723 | − | 0.469894i | \(-0.155708\pi\) |
−0.848301 | + | 0.529514i | \(0.822374\pi\) | |||||||
\(212\) | −4.50000 | − | 7.79423i | −0.309061 | − | 0.535310i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.00000 | + | 10.3923i | −0.410152 | + | 0.710403i | ||||
\(215\) | −44.0000 | −3.00078 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.00000 | 0.610960 | ||||||||
\(218\) | 8.00000 | − | 13.8564i | 0.541828 | − | 0.938474i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 8.00000 | + | 13.8564i | 0.539360 | + | 0.934199i | ||||
\(221\) | −10.5000 | − | 18.1865i | −0.706306 | − | 1.22336i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.00000 | + | 6.92820i | −0.267860 | + | 0.463947i | −0.968309 | − | 0.249756i | \(-0.919650\pi\) |
0.700449 | + | 0.713702i | \(0.252983\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.00000 | −0.532152 | ||||||||
\(227\) | −4.50000 | + | 7.79423i | −0.298675 | + | 0.517321i | −0.975833 | − | 0.218517i | \(-0.929878\pi\) |
0.677158 | + | 0.735838i | \(0.263211\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.00000 | + | 12.1244i | 0.462573 | + | 0.801200i | 0.999088 | − | 0.0426906i | \(-0.0135930\pi\) |
−0.536515 | + | 0.843891i | \(0.680260\pi\) | |||||||
\(230\) | −2.00000 | − | 3.46410i | −0.131876 | − | 0.228416i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.500000 | + | 0.866025i | −0.0328266 | + | 0.0568574i | ||||
\(233\) | 4.00000 | 0.262049 | 0.131024 | − | 0.991379i | \(-0.458173\pi\) | ||||
0.131024 | + | 0.991379i | \(0.458173\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.0000 | −1.56559 | ||||||||
\(236\) | −2.50000 | + | 4.33013i | −0.162736 | + | 0.281867i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.50000 | − | 6.06218i | −0.226871 | − | 0.392953i | ||||
\(239\) | 6.00000 | + | 10.3923i | 0.388108 | + | 0.672222i | 0.992195 | − | 0.124696i | \(-0.0397955\pi\) |
−0.604087 | + | 0.796918i | \(0.706462\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.00000 | − | 8.66025i | 0.322078 | − | 0.557856i | −0.658838 | − | 0.752285i | \(-0.728952\pi\) |
0.980917 | + | 0.194429i | \(0.0622852\pi\) | |||||||
\(242\) | −5.00000 | −0.321412 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.00000 | −0.384111 | ||||||||
\(245\) | 2.00000 | − | 3.46410i | 0.127775 | − | 0.221313i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.00000 | − | 5.19615i | −0.190885 | − | 0.330623i | ||||
\(248\) | −4.50000 | − | 7.79423i | −0.285750 | − | 0.494934i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −12.0000 | + | 20.7846i | −0.758947 | + | 1.31453i | ||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.00000 | 0.251478 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 15.0000 | + | 25.9808i | 0.935674 | + | 1.62064i | 0.773427 | + | 0.633885i | \(0.218541\pi\) |
0.162247 | + | 0.986750i | \(0.448126\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.00000 | − | 1.73205i | 0.0621370 | − | 0.107624i | ||||
\(260\) | −12.0000 | −0.744208 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.00000 | 0.0617802 | ||||||||
\(263\) | 4.50000 | − | 7.79423i | 0.277482 | − | 0.480613i | −0.693276 | − | 0.720672i | \(-0.743833\pi\) |
0.970758 | + | 0.240059i | \(0.0771668\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.0000 | + | 31.1769i | 1.10573 | + | 1.91518i | ||||
\(266\) | −1.00000 | − | 1.73205i | −0.0613139 | − | 0.106199i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.50000 | + | 6.06218i | −0.213797 | + | 0.370306i | ||||
\(269\) | −4.00000 | −0.243884 | −0.121942 | − | 0.992537i | \(-0.538912\pi\) | ||||
−0.121942 | + | 0.992537i | \(0.538912\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.00000 | 0.182237 | 0.0911185 | − | 0.995840i | \(-0.470956\pi\) | ||||
0.0911185 | + | 0.995840i | \(0.470956\pi\) | |||||||
\(272\) | −3.50000 | + | 6.06218i | −0.212219 | + | 0.367574i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.0000 | − | 19.0526i | −0.664534 | − | 1.15101i | ||||
\(275\) | −22.0000 | − | 38.1051i | −1.32665 | − | 2.29783i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.00000 | + | 6.92820i | −0.240337 | + | 0.416275i | −0.960810 | − | 0.277207i | \(-0.910591\pi\) |
0.720473 | + | 0.693482i | \(0.243925\pi\) | |||||||
\(278\) | −10.0000 | −0.599760 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.00000 | −0.239046 | ||||||||
\(281\) | −5.00000 | + | 8.66025i | −0.298275 | + | 0.516627i | −0.975741 | − | 0.218926i | \(-0.929745\pi\) |
0.677466 | + | 0.735554i | \(0.263078\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.0000 | − | 24.2487i | −0.832214 | − | 1.44144i | −0.896279 | − | 0.443491i | \(-0.853740\pi\) |
0.0640654 | − | 0.997946i | \(-0.479593\pi\) | |||||||
\(284\) | −3.50000 | − | 6.06218i | −0.207687 | − | 0.359724i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.00000 | − | 10.3923i | 0.354787 | − | 0.614510i | ||||
\(287\) | 6.00000 | 0.354169 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 32.0000 | 1.88235 | ||||||||
\(290\) | 2.00000 | − | 3.46410i | 0.117444 | − | 0.203419i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.00000 | + | 12.1244i | 0.409644 | + | 0.709524i | ||||
\(293\) | 3.00000 | + | 5.19615i | 0.175262 | + | 0.303562i | 0.940252 | − | 0.340480i | \(-0.110589\pi\) |
−0.764990 | + | 0.644042i | \(0.777256\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.0000 | − | 17.3205i | 0.582223 | − | 1.00844i | ||||
\(296\) | −2.00000 | −0.116248 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.00000 | −0.173785 | ||||||||
\(299\) | −1.50000 | + | 2.59808i | −0.0867472 | + | 0.150251i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.50000 | + | 9.52628i | 0.317015 | + | 0.549086i | ||||
\(302\) | 5.00000 | + | 8.66025i | 0.287718 | + | 0.498342i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | + | 1.73205i | −0.0573539 | + | 0.0993399i | ||||
\(305\) | 24.0000 | 1.37424 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.00000 | −0.114146 | −0.0570730 | − | 0.998370i | \(-0.518177\pi\) | ||||
−0.0570730 | + | 0.998370i | \(0.518177\pi\) | |||||||
\(308\) | 2.00000 | − | 3.46410i | 0.113961 | − | 0.197386i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 18.0000 | + | 31.1769i | 1.02233 | + | 1.77073i | ||||
\(311\) | −4.00000 | − | 6.92820i | −0.226819 | − | 0.392862i | 0.730044 | − | 0.683400i | \(-0.239499\pi\) |
−0.956864 | + | 0.290537i | \(0.906166\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.0000 | − | 22.5167i | 0.734803 | − | 1.27272i | −0.220006 | − | 0.975499i | \(-0.570608\pi\) |
0.954810 | − | 0.297218i | \(-0.0960589\pi\) | |||||||
\(314\) | −17.0000 | −0.959366 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.00000 | −0.337526 | ||||||||
\(317\) | −9.00000 | + | 15.5885i | −0.505490 | + | 0.875535i | 0.494489 | + | 0.869184i | \(0.335355\pi\) |
−0.999980 | + | 0.00635137i | \(0.997978\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.00000 | + | 3.46410i | 0.111979 | + | 0.193952i | ||||
\(320\) | 2.00000 | + | 3.46410i | 0.111803 | + | 0.193649i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.500000 | + | 0.866025i | −0.0278639 | + | 0.0482617i | ||||
\(323\) | 14.0000 | 0.778981 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 33.0000 | 1.83051 | ||||||||
\(326\) | −0.500000 | + | 0.866025i | −0.0276924 | + | 0.0479647i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.00000 | − | 5.19615i | −0.165647 | − | 0.286910i | ||||
\(329\) | 3.00000 | + | 5.19615i | 0.165395 | + | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.5000 | − | 26.8468i | 0.851957 | − | 1.47563i | −0.0274825 | − | 0.999622i | \(-0.508749\pi\) |
0.879440 | − | 0.476011i | \(-0.157918\pi\) | |||||||
\(332\) | 4.00000 | 0.219529 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.00000 | −0.437741 | ||||||||
\(335\) | 14.0000 | − | 24.2487i | 0.764902 | − | 1.32485i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.5000 | − | 23.3827i | −0.735392 | − | 1.27374i | −0.954551 | − | 0.298047i | \(-0.903665\pi\) |
0.219159 | − | 0.975689i | \(-0.429669\pi\) | |||||||
\(338\) | −2.00000 | − | 3.46410i | −0.108786 | − | 0.188422i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 14.0000 | − | 24.2487i | 0.759257 | − | 1.31507i | ||||
\(341\) | −36.0000 | −1.94951 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 5.50000 | − | 9.52628i | 0.296540 | − | 0.513623i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.00000 | + | 6.92820i | 0.215041 | + | 0.372463i | ||||
\(347\) | 9.00000 | + | 15.5885i | 0.483145 | + | 0.836832i | 0.999813 | − | 0.0193540i | \(-0.00616095\pi\) |
−0.516667 | + | 0.856186i | \(0.672828\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.5000 | + | 21.6506i | −0.669110 | + | 1.15893i | 0.309044 | + | 0.951048i | \(0.399991\pi\) |
−0.978153 | + | 0.207884i | \(0.933342\pi\) | |||||||
\(350\) | 11.0000 | 0.587975 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.00000 | −0.213201 | ||||||||
\(353\) | 7.50000 | − | 12.9904i | 0.399185 | − | 0.691408i | −0.594441 | − | 0.804139i | \(-0.702627\pi\) |
0.993626 | + | 0.112731i | \(0.0359599\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.0000 | + | 24.2487i | 0.743043 | + | 1.28699i | ||||
\(356\) | −1.50000 | − | 2.59808i | −0.0794998 | − | 0.137698i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.00000 | − | 10.3923i | 0.317110 | − | 0.549250i | ||||
\(359\) | 11.0000 | 0.580558 | 0.290279 | − | 0.956942i | \(-0.406252\pi\) | ||||
0.290279 | + | 0.956942i | \(0.406252\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | −4.50000 | + | 7.79423i | −0.236515 | + | 0.409656i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.50000 | + | 2.59808i | 0.0786214 | + | 0.136176i | ||||
\(365\) | −28.0000 | − | 48.4974i | −1.46559 | − | 2.53847i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.5000 | − | 21.6506i | 0.652495 | − | 1.13015i | −0.330021 | − | 0.943974i | \(-0.607056\pi\) |
0.982516 | − | 0.186180i | \(-0.0596109\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.00000 | 0.415900 | ||||||||
\(371\) | 4.50000 | − | 7.79423i | 0.233628 | − | 0.404656i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.0000 | + | 32.9090i | 0.983783 | + | 1.70396i | 0.647225 | + | 0.762299i | \(0.275929\pi\) |
0.336557 | + | 0.941663i | \(0.390737\pi\) | |||||||
\(374\) | 14.0000 | + | 24.2487i | 0.723923 | + | 1.25387i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.00000 | − | 5.19615i | 0.154713 | − | 0.267971i | ||||
\(377\) | −3.00000 | −0.154508 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.00000 | −0.410932 | −0.205466 | − | 0.978664i | \(-0.565871\pi\) | ||||
−0.205466 | + | 0.978664i | \(0.565871\pi\) | |||||||
\(380\) | 4.00000 | − | 6.92820i | 0.205196 | − | 0.355409i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.00000 | − | 10.3923i | −0.306987 | − | 0.531717i | ||||
\(383\) | −2.00000 | − | 3.46410i | −0.102195 | − | 0.177007i | 0.810394 | − | 0.585886i | \(-0.199253\pi\) |
−0.912589 | + | 0.408879i | \(0.865920\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.00000 | + | 13.8564i | −0.407718 | + | 0.706188i | ||||
\(386\) | −5.00000 | −0.254493 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.00000 | −0.406138 | ||||||||
\(389\) | −7.00000 | + | 12.1244i | −0.354914 | + | 0.614729i | −0.987103 | − | 0.160085i | \(-0.948823\pi\) |
0.632189 | + | 0.774814i | \(0.282157\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.50000 | − | 6.06218i | −0.177003 | − | 0.306578i | ||||
\(392\) | 0.500000 | + | 0.866025i | 0.0252538 | + | 0.0437409i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −13.0000 | + | 22.5167i | −0.654931 | + | 1.13437i | ||||
\(395\) | 24.0000 | 1.20757 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.00000 | 0.301131 | 0.150566 | − | 0.988600i | \(-0.451890\pi\) | ||||
0.150566 | + | 0.988600i | \(0.451890\pi\) | |||||||
\(398\) | −3.50000 | + | 6.06218i | −0.175439 | + | 0.303870i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.50000 | − | 9.52628i | −0.275000 | − | 0.476314i | ||||
\(401\) | 15.0000 | + | 25.9808i | 0.749064 | + | 1.29742i | 0.948272 | + | 0.317460i | \(0.102830\pi\) |
−0.199207 | + | 0.979957i | \(0.563837\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.5000 | − | 23.3827i | 0.672483 | − | 1.16477i | ||||
\(404\) | −10.0000 | −0.497519 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.00000 | −0.0496292 | ||||||||
\(407\) | −4.00000 | + | 6.92820i | −0.198273 | + | 0.343418i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.00000 | − | 1.73205i | −0.0494468 | − | 0.0856444i | 0.840243 | − | 0.542211i | \(-0.182412\pi\) |
−0.889689 | + | 0.456566i | \(0.849079\pi\) | |||||||
\(410\) | 12.0000 | + | 20.7846i | 0.592638 | + | 1.02648i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.50000 | + | 14.7224i | −0.418765 | + | 0.725322i | ||||
\(413\) | −5.00000 | −0.246034 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.0000 | −0.785409 | ||||||||
\(416\) | 1.50000 | − | 2.59808i | 0.0735436 | − | 0.127381i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.00000 | + | 6.92820i | 0.195646 | + | 0.338869i | ||||
\(419\) | −16.5000 | − | 28.5788i | −0.806078 | − | 1.39617i | −0.915561 | − | 0.402179i | \(-0.868253\pi\) |
0.109483 | − | 0.993989i | \(-0.465080\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.00000 | − | 5.19615i | 0.146211 | − | 0.253245i | −0.783613 | − | 0.621249i | \(-0.786625\pi\) |
0.929824 | + | 0.368004i | \(0.119959\pi\) | |||||||
\(422\) | 1.00000 | 0.0486792 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.00000 | −0.437079 | ||||||||
\(425\) | −38.5000 | + | 66.6840i | −1.86752 | + | 3.23465i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.00000 | − | 5.19615i | −0.145180 | − | 0.251459i | ||||
\(428\) | 6.00000 | + | 10.3923i | 0.290021 | + | 0.502331i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −22.0000 | + | 38.1051i | −1.06093 | + | 1.83759i | ||||
\(431\) | −24.0000 | −1.15604 | −0.578020 | − | 0.816023i | \(-0.696174\pi\) | ||||
−0.578020 | + | 0.816023i | \(0.696174\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.00000 | 0.384455 | 0.192228 | − | 0.981350i | \(-0.438429\pi\) | ||||
0.192228 | + | 0.981350i | \(0.438429\pi\) | |||||||
\(434\) | 4.50000 | − | 7.79423i | 0.216007 | − | 0.374135i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.00000 | − | 13.8564i | −0.383131 | − | 0.663602i | ||||
\(437\) | −1.00000 | − | 1.73205i | −0.0478365 | − | 0.0828552i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.50000 | + | 7.79423i | −0.214773 | + | 0.371998i | −0.953202 | − | 0.302333i | \(-0.902235\pi\) |
0.738429 | + | 0.674331i | \(0.235568\pi\) | |||||||
\(440\) | 16.0000 | 0.762770 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −21.0000 | −0.998868 | ||||||||
\(443\) | 13.0000 | − | 22.5167i | 0.617649 | − | 1.06980i | −0.372265 | − | 0.928126i | \(-0.621419\pi\) |
0.989914 | − | 0.141672i | \(-0.0452479\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.00000 | + | 10.3923i | 0.284427 | + | 0.492642i | ||||
\(446\) | 4.00000 | + | 6.92820i | 0.189405 | + | 0.328060i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.500000 | − | 0.866025i | 0.0236228 | − | 0.0409159i | ||||
\(449\) | −4.00000 | −0.188772 | −0.0943858 | − | 0.995536i | \(-0.530089\pi\) | ||||
−0.0943858 | + | 0.995536i | \(0.530089\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −24.0000 | −1.13012 | ||||||||
\(452\) | −4.00000 | + | 6.92820i | −0.188144 | + | 0.325875i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.50000 | + | 7.79423i | 0.211195 | + | 0.365801i | ||||
\(455\) | −6.00000 | − | 10.3923i | −0.281284 | − | 0.487199i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.5000 | − | 25.1147i | 0.678281 | − | 1.17482i | −0.297217 | − | 0.954810i | \(-0.596058\pi\) |
0.975498 | − | 0.220008i | \(-0.0706083\pi\) | |||||||
\(458\) | 14.0000 | 0.654177 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.00000 | −0.186501 | ||||||||
\(461\) | −7.00000 | + | 12.1244i | −0.326023 | + | 0.564688i | −0.981719 | − | 0.190337i | \(-0.939042\pi\) |
0.655696 | + | 0.755025i | \(0.272375\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.0000 | − | 19.0526i | −0.511213 | − | 0.885448i | −0.999916 | − | 0.0129968i | \(-0.995863\pi\) |
0.488702 | − | 0.872451i | \(-0.337470\pi\) | |||||||
\(464\) | 0.500000 | + | 0.866025i | 0.0232119 | + | 0.0402042i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.00000 | − | 3.46410i | 0.0926482 | − | 0.160471i | ||||
\(467\) | 8.00000 | 0.370196 | 0.185098 | − | 0.982720i | \(-0.440740\pi\) | ||||
0.185098 | + | 0.982720i | \(0.440740\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.00000 | −0.323230 | ||||||||
\(470\) | −12.0000 | + | 20.7846i | −0.553519 | + | 0.958723i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.50000 | + | 4.33013i | 0.115072 | + | 0.199310i | ||||
\(473\) | −22.0000 | − | 38.1051i | −1.01156 | − | 1.75208i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.0000 | + | 19.0526i | −0.504715 | + | 0.874191i | ||||
\(476\) | −7.00000 | −0.320844 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12.0000 | 0.548867 | ||||||||
\(479\) | 4.00000 | − | 6.92820i | 0.182765 | − | 0.316558i | −0.760056 | − | 0.649857i | \(-0.774829\pi\) |
0.942821 | + | 0.333300i | \(0.108162\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.00000 | − | 5.19615i | −0.136788 | − | 0.236924i | ||||
\(482\) | −5.00000 | − | 8.66025i | −0.227744 | − | 0.394464i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.50000 | + | 4.33013i | −0.113636 | + | 0.196824i | ||||
\(485\) | 32.0000 | 1.45305 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.0000 | 1.17817 | 0.589086 | − | 0.808070i | \(-0.299488\pi\) | ||||
0.589086 | + | 0.808070i | \(0.299488\pi\) | |||||||
\(488\) | −3.00000 | + | 5.19615i | −0.135804 | + | 0.235219i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.00000 | − | 3.46410i | −0.0903508 | − | 0.156492i | ||||
\(491\) | 12.0000 | + | 20.7846i | 0.541552 | + | 0.937996i | 0.998815 | + | 0.0486647i | \(0.0154966\pi\) |
−0.457263 | + | 0.889332i | \(0.651170\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.50000 | − | 6.06218i | 0.157632 | − | 0.273027i | ||||
\(494\) | −6.00000 | −0.269953 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.00000 | −0.404112 | ||||||||
\(497\) | 3.50000 | − | 6.06218i | 0.156996 | − | 0.271926i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.0000 | − | 24.2487i | −0.626726 | − | 1.08552i | −0.988204 | − | 0.153141i | \(-0.951061\pi\) |
0.361478 | − | 0.932381i | \(-0.382272\pi\) | |||||||
\(500\) | 12.0000 | + | 20.7846i | 0.536656 | + | 0.929516i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.0000 | 1.07011 | 0.535054 | − | 0.844818i | \(-0.320291\pi\) | ||||
0.535054 | + | 0.844818i | \(0.320291\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 40.0000 | 1.77998 | ||||||||
\(506\) | 2.00000 | − | 3.46410i | 0.0889108 | − | 0.153998i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.00000 | − | 5.19615i | −0.132973 | − | 0.230315i | 0.791849 | − | 0.610718i | \(-0.209119\pi\) |
−0.924821 | + | 0.380402i | \(0.875786\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.00000 | + | 12.1244i | −0.309662 | + | 0.536350i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 30.0000 | 1.32324 | ||||||||
\(515\) | 34.0000 | − | 58.8897i | 1.49822 | − | 2.59499i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.0000 | − | 20.7846i | −0.527759 | − | 0.914106i | ||||
\(518\) | −1.00000 | − | 1.73205i | −0.0439375 | − | 0.0761019i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.00000 | + | 10.3923i | −0.263117 | + | 0.455733i | ||||
\(521\) | 15.0000 | 0.657162 | 0.328581 | − | 0.944476i | \(-0.393430\pi\) | ||||
0.328581 | + | 0.944476i | \(0.393430\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.0000 | −0.699631 | −0.349816 | − | 0.936819i | \(-0.613756\pi\) | ||||
−0.349816 | + | 0.936819i | \(0.613756\pi\) | |||||||
\(524\) | 0.500000 | − | 0.866025i | 0.0218426 | − | 0.0378325i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.50000 | − | 7.79423i | −0.196209 | − | 0.339845i | ||||
\(527\) | 31.5000 | + | 54.5596i | 1.37216 | + | 2.37665i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | − | 19.0526i | 0.478261 | − | 0.828372i | ||||
\(530\) | 36.0000 | 1.56374 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.00000 | −0.0867110 | ||||||||
\(533\) | 9.00000 | − | 15.5885i | 0.389833 | − | 0.675211i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.0000 | − | 41.5692i | −1.03761 | − | 1.79719i | ||||
\(536\) | 3.50000 | + | 6.06218i | 0.151177 | + | 0.261846i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.00000 | + | 3.46410i | −0.0862261 | + | 0.149348i | ||||
\(539\) | 4.00000 | 0.172292 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −36.0000 | −1.54776 | −0.773880 | − | 0.633332i | \(-0.781687\pi\) | ||||
−0.773880 | + | 0.633332i | \(0.781687\pi\) | |||||||
\(542\) | 1.50000 | − | 2.59808i | 0.0644305 | − | 0.111597i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.50000 | + | 6.06218i | 0.150061 | + | 0.259914i | ||||
\(545\) | 32.0000 | + | 55.4256i | 1.37073 | + | 2.37417i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.0000 | + | 31.1769i | −0.769624 | + | 1.33303i | 0.168142 | + | 0.985763i | \(0.446223\pi\) |
−0.937767 | + | 0.347266i | \(0.887110\pi\) | |||||||
\(548\) | −22.0000 | −0.939793 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −44.0000 | −1.87617 | ||||||||
\(551\) | 1.00000 | − | 1.73205i | 0.0426014 | − | 0.0737878i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.00000 | − | 5.19615i | −0.127573 | − | 0.220963i | ||||
\(554\) | 4.00000 | + | 6.92820i | 0.169944 | + | 0.294351i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.00000 | + | 8.66025i | −0.212047 | + | 0.367277i | ||||
\(557\) | −1.00000 | −0.0423714 | −0.0211857 | − | 0.999776i | \(-0.506744\pi\) | ||||
−0.0211857 | + | 0.999776i | \(0.506744\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 33.0000 | 1.39575 | ||||||||
\(560\) | −2.00000 | + | 3.46410i | −0.0845154 | + | 0.146385i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.00000 | + | 8.66025i | 0.210912 | + | 0.365311i | ||||
\(563\) | 5.50000 | + | 9.52628i | 0.231797 | + | 0.401485i | 0.958337 | − | 0.285640i | \(-0.0922060\pi\) |
−0.726540 | + | 0.687124i | \(0.758873\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.0000 | − | 27.7128i | 0.673125 | − | 1.16589i | ||||
\(566\) | −28.0000 | −1.17693 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.00000 | −0.293713 | ||||||||
\(569\) | 6.00000 | − | 10.3923i | 0.251533 | − | 0.435668i | −0.712415 | − | 0.701758i | \(-0.752399\pi\) |
0.963948 | + | 0.266090i | \(0.0857319\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.5000 | + | 33.7750i | 0.816050 | + | 1.41344i | 0.908572 | + | 0.417729i | \(0.137174\pi\) |
−0.0925222 | + | 0.995711i | \(0.529493\pi\) | |||||||
\(572\) | −6.00000 | − | 10.3923i | −0.250873 | − | 0.434524i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.00000 | − | 5.19615i | 0.125218 | − | 0.216883i | ||||
\(575\) | 11.0000 | 0.458732 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.0000 | 0.416305 | 0.208153 | − | 0.978096i | \(-0.433255\pi\) | ||||
0.208153 | + | 0.978096i | \(0.433255\pi\) | |||||||
\(578\) | 16.0000 | − | 27.7128i | 0.665512 | − | 1.15270i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.00000 | − | 3.46410i | −0.0830455 | − | 0.143839i | ||||
\(581\) | 2.00000 | + | 3.46410i | 0.0829740 | + | 0.143715i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.0000 | + | 31.1769i | −0.745484 | + | 1.29122i | ||||
\(584\) | 14.0000 | 0.579324 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.00000 | 0.247858 | ||||||||
\(587\) | −12.5000 | + | 21.6506i | −0.515930 | + | 0.893617i | 0.483899 | + | 0.875124i | \(0.339220\pi\) |
−0.999829 | + | 0.0184934i | \(0.994113\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.00000 | + | 15.5885i | 0.370839 | + | 0.642311i | ||||
\(590\) | −10.0000 | − | 17.3205i | −0.411693 | − | 0.713074i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.00000 | + | 1.73205i | −0.0410997 | + | 0.0711868i | ||||
\(593\) | 18.0000 | 0.739171 | 0.369586 | − | 0.929197i | \(-0.379500\pi\) | ||||
0.369586 | + | 0.929197i | \(0.379500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 28.0000 | 1.14789 | ||||||||
\(596\) | −1.50000 | + | 2.59808i | −0.0614424 | + | 0.106421i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.50000 | + | 2.59808i | 0.0613396 | + | 0.106243i | ||||
\(599\) | 10.5000 | + | 18.1865i | 0.429018 | + | 0.743082i | 0.996786 | − | 0.0801071i | \(-0.0255262\pi\) |
−0.567768 | + | 0.823189i | \(0.692193\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.0000 | − | 24.2487i | 0.571072 | − | 0.989126i | −0.425384 | − | 0.905013i | \(-0.639861\pi\) |
0.996456 | − | 0.0841128i | \(-0.0268056\pi\) | |||||||
\(602\) | 11.0000 | 0.448327 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.0000 | 0.406894 | ||||||||
\(605\) | 10.0000 | − | 17.3205i | 0.406558 | − | 0.704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.5000 | − | 33.7750i | −0.791481 | − | 1.37088i | −0.925050 | − | 0.379845i | \(-0.875977\pi\) |
0.133570 | − | 0.991039i | \(-0.457356\pi\) | |||||||
\(608\) | 1.00000 | + | 1.73205i | 0.0405554 | + | 0.0702439i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12.0000 | − | 20.7846i | 0.485866 | − | 0.841544i | ||||
\(611\) | 18.0000 | 0.728202 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.00000 | −0.242338 | −0.121169 | − | 0.992632i | \(-0.538664\pi\) | ||||
−0.121169 | + | 0.992632i | \(0.538664\pi\) | |||||||
\(614\) | −1.00000 | + | 1.73205i | −0.0403567 | + | 0.0698999i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.00000 | − | 3.46410i | −0.0805823 | − | 0.139573i | ||||
\(617\) | 7.00000 | + | 12.1244i | 0.281809 | + | 0.488108i | 0.971830 | − | 0.235681i | \(-0.0757321\pi\) |
−0.690021 | + | 0.723789i | \(0.742399\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.00000 | − | 12.1244i | 0.281354 | − | 0.487319i | −0.690365 | − | 0.723462i | \(-0.742550\pi\) |
0.971718 | + | 0.236143i | \(0.0758832\pi\) | |||||||
\(620\) | 36.0000 | 1.44579 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −8.00000 | −0.320771 | ||||||||
\(623\) | 1.50000 | − | 2.59808i | 0.0600962 | − | 0.104090i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.5000 | − | 35.5070i | −0.820000 | − | 1.42028i | ||||
\(626\) | −13.0000 | − | 22.5167i | −0.519584 | − | 0.899947i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.50000 | + | 14.7224i | −0.339187 | + | 0.587489i | ||||
\(629\) | 14.0000 | 0.558217 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.00000 | −0.159237 | −0.0796187 | − | 0.996825i | \(-0.525370\pi\) | ||||
−0.0796187 | + | 0.996825i | \(0.525370\pi\) | |||||||
\(632\) | −3.00000 | + | 5.19615i | −0.119334 | + | 0.206692i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.00000 | + | 15.5885i | 0.357436 | + | 0.619097i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.50000 | + | 2.59808i | −0.0594322 | + | 0.102940i | ||||
\(638\) | 4.00000 | 0.158362 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4.00000 | 0.158114 | ||||||||
\(641\) | −14.0000 | + | 24.2487i | −0.552967 | + | 0.957767i | 0.445092 | + | 0.895485i | \(0.353171\pi\) |
−0.998059 | + | 0.0622816i | \(0.980162\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.00000 | + | 3.46410i | 0.0788723 | + | 0.136611i | 0.902764 | − | 0.430137i | \(-0.141535\pi\) |
−0.823891 | + | 0.566748i | \(0.808201\pi\) | |||||||
\(644\) | 0.500000 | + | 0.866025i | 0.0197028 | + | 0.0341262i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.00000 | − | 12.1244i | 0.275411 | − | 0.477026i | ||||
\(647\) | −42.0000 | −1.65119 | −0.825595 | − | 0.564263i | \(-0.809160\pi\) | ||||
−0.825595 | + | 0.564263i | \(0.809160\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.0000 | 0.785069 | ||||||||
\(650\) | 16.5000 | − | 28.5788i | 0.647183 | − | 1.12095i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.500000 | + | 0.866025i | 0.0195815 | + | 0.0339162i | ||||
\(653\) | 1.50000 | + | 2.59808i | 0.0586995 | + | 0.101671i | 0.893882 | − | 0.448303i | \(-0.147971\pi\) |
−0.835182 | + | 0.549973i | \(0.814638\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.00000 | + | 3.46410i | −0.0781465 | + | 0.135354i | ||||
\(656\) | −6.00000 | −0.234261 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.00000 | 0.233904 | ||||||||
\(659\) | −14.0000 | + | 24.2487i | −0.545363 | + | 0.944596i | 0.453221 | + | 0.891398i | \(0.350275\pi\) |
−0.998584 | + | 0.0531977i | \(0.983059\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.00000 | + | 12.1244i | 0.272268 | + | 0.471583i | 0.969442 | − | 0.245319i | \(-0.0788928\pi\) |
−0.697174 | + | 0.716902i | \(0.745559\pi\) | |||||||
\(662\) | −15.5000 | − | 26.8468i | −0.602425 | − | 1.04343i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.00000 | − | 3.46410i | 0.0776151 | − | 0.134433i | ||||
\(665\) | 8.00000 | 0.310227 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | −4.00000 | + | 6.92820i | −0.154765 | + | 0.268060i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −14.0000 | − | 24.2487i | −0.540867 | − | 0.936809i | ||||
\(671\) | 12.0000 | + | 20.7846i | 0.463255 | + | 0.802381i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.5000 | + | 19.9186i | −0.443292 | + | 0.767805i | −0.997932 | − | 0.0642860i | \(-0.979523\pi\) |
0.554639 | + | 0.832091i | \(0.312856\pi\) | |||||||
\(674\) | −27.0000 | −1.04000 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.00000 | −0.153846 | ||||||||
\(677\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.00000 | − | 6.92820i | −0.153506 | − | 0.265880i | ||||
\(680\) | −14.0000 | − | 24.2487i | −0.536875 | − | 0.929896i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −18.0000 | + | 31.1769i | −0.689256 | + | 1.19383i | ||||
\(683\) | 48.0000 | 1.83667 | 0.918334 | − | 0.395805i | \(-0.129534\pi\) | ||||
0.918334 | + | 0.395805i | \(0.129534\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 88.0000 | 3.36231 | ||||||||
\(686\) | −0.500000 | + | 0.866025i | −0.0190901 | + | 0.0330650i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.50000 | − | 9.52628i | −0.209686 | − | 0.363186i | ||||
\(689\) | −13.5000 | − | 23.3827i | −0.514309 | − | 0.890809i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.0000 | − | 34.6410i | 0.760836 | − | 1.31781i | −0.181584 | − | 0.983375i | \(-0.558123\pi\) |
0.942420 | − | 0.334431i | \(-0.108544\pi\) | |||||||
\(692\) | 8.00000 | 0.304114 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18.0000 | 0.683271 | ||||||||
\(695\) | 20.0000 | − | 34.6410i | 0.758643 | − | 1.31401i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.0000 | + | 36.3731i | 0.795432 | + | 1.37773i | ||||
\(698\) | 12.5000 | + | 21.6506i | 0.473132 | + | 0.819489i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.50000 | − | 9.52628i | 0.207880 | − | 0.360060i | ||||
\(701\) | 2.00000 | 0.0755390 | 0.0377695 | − | 0.999286i | \(-0.487975\pi\) | ||||
0.0377695 | + | 0.999286i | \(0.487975\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.00000 | 0.150863 | ||||||||
\(704\) | −2.00000 | + | 3.46410i | −0.0753778 | + | 0.130558i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.50000 | − | 12.9904i | −0.282266 | − | 0.488899i | ||||
\(707\) | −5.00000 | − | 8.66025i | −0.188044 | − | 0.325702i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.0000 | − | 34.6410i | 0.751116 | − | 1.30097i | −0.196167 | − | 0.980571i | \(-0.562849\pi\) |
0.947282 | − | 0.320400i | \(-0.103817\pi\) | |||||||
\(710\) | 28.0000 | 1.05082 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.00000 | −0.112430 | ||||||||
\(713\) | 4.50000 | − | 7.79423i | 0.168526 | − | 0.291896i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.0000 | + | 41.5692i | 0.897549 | + | 1.55460i | ||||
\(716\) | −6.00000 | − | 10.3923i | −0.224231 | − | 0.388379i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.50000 | − | 9.52628i | 0.205258 | − | 0.355518i | ||||
\(719\) | −48.0000 | −1.79010 | −0.895049 | − | 0.445968i | \(-0.852860\pi\) | ||||
−0.895049 | + | 0.445968i | \(0.852860\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.0000 | −0.633113 | ||||||||
\(722\) | −7.50000 | + | 12.9904i | −0.279121 | + | 0.483452i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.50000 | + | 7.79423i | 0.167241 | + | 0.289670i | ||||
\(725\) | 5.50000 | + | 9.52628i | 0.204265 | + | 0.353797i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.5000 | − | 25.1147i | 0.537775 | − | 0.931454i | −0.461248 | − | 0.887271i | \(-0.652598\pi\) |
0.999023 | − | 0.0441829i | \(-0.0140684\pi\) | |||||||
\(728\) | 3.00000 | 0.111187 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −56.0000 | −2.07265 | ||||||||
\(731\) | −38.5000 | + | 66.6840i | −1.42397 | + | 2.46640i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.50000 | + | 12.9904i | 0.277019 | + | 0.479811i | 0.970642 | − | 0.240527i | \(-0.0773202\pi\) |
−0.693624 | + | 0.720338i | \(0.743987\pi\) | |||||||
\(734\) | −12.5000 | − | 21.6506i | −0.461383 | − | 0.799140i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.500000 | − | 0.866025i | 0.0184302 | − | 0.0319221i | ||||
\(737\) | 28.0000 | 1.03139 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.0000 | 0.441427 | 0.220714 | − | 0.975339i | \(-0.429161\pi\) | ||||
0.220714 | + | 0.975339i | \(0.429161\pi\) | |||||||
\(740\) | 4.00000 | − | 6.92820i | 0.147043 | − | 0.254686i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.50000 | − | 7.79423i | −0.165200 | − | 0.286135i | ||||
\(743\) | 25.5000 | + | 44.1673i | 0.935504 | + | 1.62034i | 0.773732 | + | 0.633513i | \(0.218388\pi\) |
0.161772 | + | 0.986828i | \(0.448279\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.00000 | − | 10.3923i | 0.219823 | − | 0.380745i | ||||
\(746\) | 38.0000 | 1.39128 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 28.0000 | 1.02378 | ||||||||
\(749\) | −6.00000 | + | 10.3923i | −0.219235 | + | 0.379727i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.00000 | − | 5.19615i | −0.109472 | − | 0.189610i | 0.806085 | − | 0.591800i | \(-0.201583\pi\) |
−0.915556 | + | 0.402190i | \(0.868249\pi\) | |||||||
\(752\) | −3.00000 | − | 5.19615i | −0.109399 | − | 0.189484i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.50000 | + | 2.59808i | −0.0546268 | + | 0.0946164i | ||||
\(755\) | −40.0000 | −1.45575 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.0000 | −0.436147 | −0.218074 | − | 0.975932i | \(-0.569977\pi\) | ||||
−0.218074 | + | 0.975932i | \(0.569977\pi\) | |||||||
\(758\) | −4.00000 | + | 6.92820i | −0.145287 | + | 0.251644i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.00000 | − | 6.92820i | −0.145095 | − | 0.251312i | ||||
\(761\) | −6.50000 | − | 11.2583i | −0.235625 | − | 0.408114i | 0.723829 | − | 0.689979i | \(-0.242380\pi\) |
−0.959454 | + | 0.281865i | \(0.909047\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.00000 | − | 13.8564i | 0.289619 | − | 0.501636i | ||||
\(764\) | −12.0000 | −0.434145 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.00000 | −0.144526 | ||||||||
\(767\) | −7.50000 | + | 12.9904i | −0.270809 | + | 0.469055i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.00000 | − | 3.46410i | −0.0721218 | − | 0.124919i | 0.827709 | − | 0.561157i | \(-0.189644\pi\) |
−0.899831 | + | 0.436239i | \(0.856310\pi\) | |||||||
\(770\) | 8.00000 | + | 13.8564i | 0.288300 | + | 0.499350i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.50000 | + | 4.33013i | −0.0899770 | + | 0.155845i | ||||
\(773\) | −4.00000 | −0.143870 | −0.0719350 | − | 0.997409i | \(-0.522917\pi\) | ||||
−0.0719350 | + | 0.997409i | \(0.522917\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −99.0000 | −3.55618 | ||||||||
\(776\) | −4.00000 | + | 6.92820i | −0.143592 | + | 0.248708i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.00000 | + | 12.1244i | 0.250962 | + | 0.434679i | ||||
\(779\) | 6.00000 | + | 10.3923i | 0.214972 | + | 0.372343i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.0000 | + | 24.2487i | −0.500959 | + | 0.867687i | ||||
\(782\) | −7.00000 | −0.250319 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 34.0000 | − | 58.8897i | 1.21351 | − | 2.10186i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.00000 | − | 15.5885i | −0.320815 | − | 0.555668i | 0.659841 | − | 0.751405i | \(-0.270624\pi\) |
−0.980656 | + | 0.195737i | \(0.937290\pi\) | |||||||
\(788\) | 13.0000 | + | 22.5167i | 0.463106 | + | 0.802123i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12.0000 | − | 20.7846i | 0.426941 | − | 0.739483i | ||||
\(791\) | −8.00000 | −0.284447 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.0000 | −0.639199 | ||||||||
\(794\) | 3.00000 | − | 5.19615i | 0.106466 | − | 0.184405i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.50000 | + | 6.06218i | 0.124054 | + | 0.214868i | ||||
\(797\) | −9.00000 | − | 15.5885i | −0.318796 | − | 0.552171i | 0.661441 | − | 0.749997i | \(-0.269945\pi\) |
−0.980237 | + | 0.197826i | \(0.936612\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.0000 | + | 36.3731i | −0.742927 | + | 1.28679i | ||||
\(800\) | −11.0000 | −0.388909 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 30.0000 | 1.05934 | ||||||||
\(803\) | 28.0000 | − | 48.4974i | 0.988099 | − | 1.71144i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.00000 | − | 3.46410i | −0.0704907 | − | 0.122094i | ||||
\(806\) | −13.5000 | − | 23.3827i | −0.475517 | − | 0.823620i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.00000 | + | 8.66025i | −0.175899 | + | 0.304667i | ||||
\(809\) | 32.0000 | 1.12506 | 0.562530 | − | 0.826777i | \(-0.309828\pi\) | ||||
0.562530 | + | 0.826777i | \(0.309828\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26.0000 | −0.912983 | −0.456492 | − | 0.889728i | \(-0.650894\pi\) | ||||
−0.456492 | + | 0.889728i | \(0.650894\pi\) | |||||||
\(812\) | −0.500000 | + | 0.866025i | −0.0175466 | + | 0.0303915i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.00000 | + | 6.92820i | 0.140200 | + | 0.242833i | ||||
\(815\) | −2.00000 | − | 3.46410i | −0.0700569 | − | 0.121342i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.0000 | + | 19.0526i | −0.384841 | + | 0.666565i | ||||
\(818\) | −2.00000 | −0.0699284 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 24.0000 | 0.838116 | ||||||||
\(821\) | −6.50000 | + | 11.2583i | −0.226852 | + | 0.392918i | −0.956873 | − | 0.290505i | \(-0.906177\pi\) |
0.730022 | + | 0.683424i | \(0.239510\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.0000 | + | 32.9090i | 0.662298 | + | 1.14713i | 0.980010 | + | 0.198947i | \(0.0637522\pi\) |
−0.317712 | + | 0.948187i | \(0.602914\pi\) | |||||||
\(824\) | 8.50000 | + | 14.7224i | 0.296112 | + | 0.512880i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.50000 | + | 4.33013i | −0.0869861 | + | 0.150664i | ||||
\(827\) | −42.0000 | −1.46048 | −0.730242 | − | 0.683189i | \(-0.760592\pi\) | ||||
−0.730242 | + | 0.683189i | \(0.760592\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.0000 | −0.903017 | −0.451509 | − | 0.892267i | \(-0.649114\pi\) | ||||
−0.451509 | + | 0.892267i | \(0.649114\pi\) | |||||||
\(830\) | −8.00000 | + | 13.8564i | −0.277684 | + | 0.480963i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.50000 | − | 2.59808i | −0.0520031 | − | 0.0900721i | ||||
\(833\) | −3.50000 | − | 6.06218i | −0.121268 | − | 0.210042i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.0000 | − | 27.7128i | 0.553703 | − | 0.959041i | ||||
\(836\) | 8.00000 | 0.276686 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −33.0000 | −1.13997 | ||||||||
\(839\) | −5.00000 | + | 8.66025i | −0.172619 | + | 0.298985i | −0.939335 | − | 0.343002i | \(-0.888556\pi\) |
0.766716 | + | 0.641987i | \(0.221890\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.0000 | + | 24.2487i | 0.482759 | + | 0.836162i | ||||
\(842\) | −3.00000 | − | 5.19615i | −0.103387 | − | 0.179071i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.500000 | − | 0.866025i | 0.0172107 | − | 0.0298098i | ||||
\(845\) | 16.0000 | 0.550417 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.00000 | −0.171802 | ||||||||
\(848\) | −4.50000 | + | 7.79423i | −0.154531 | + | 0.267655i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 38.5000 | + | 66.6840i | 1.32054 | + | 2.28724i | ||||
\(851\) | −1.00000 | − | 1.73205i | −0.0342796 | − | 0.0593739i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.5000 | + | 45.8993i | −0.907343 | + | 1.57156i | −0.0896015 | + | 0.995978i | \(0.528559\pi\) |
−0.817741 | + | 0.575586i | \(0.804774\pi\) | |||||||
\(854\) | −6.00000 | −0.205316 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.0000 | 0.410152 | ||||||||
\(857\) | 13.5000 | − | 23.3827i | 0.461151 | − | 0.798737i | −0.537867 | − | 0.843029i | \(-0.680770\pi\) |
0.999019 | + | 0.0442921i | \(0.0141032\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.00000 | − | 1.73205i | −0.0341196 | − | 0.0590968i | 0.848461 | − | 0.529257i | \(-0.177529\pi\) |
−0.882581 | + | 0.470160i | \(0.844196\pi\) | |||||||
\(860\) | 22.0000 | + | 38.1051i | 0.750194 | + | 1.29937i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12.0000 | + | 20.7846i | −0.408722 | + | 0.707927i | ||||
\(863\) | −1.00000 | −0.0340404 | −0.0170202 | − | 0.999855i | \(-0.505418\pi\) | ||||
−0.0170202 | + | 0.999855i | \(0.505418\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −32.0000 | −1.08803 | ||||||||
\(866\) | 4.00000 | − | 6.92820i | 0.135926 | − | 0.235430i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.50000 | − | 7.79423i | −0.152740 | − | 0.264553i | ||||
\(869\) | 12.0000 | + | 20.7846i | 0.407072 | + | 0.705070i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.5000 | + | 18.1865i | −0.355779 | + | 0.616227i | ||||
\(872\) | −16.0000 | −0.541828 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.00000 | −0.0676510 | ||||||||
\(875\) | −12.0000 | + | 20.7846i | −0.405674 | + | 0.702648i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.00000 | + | 6.92820i | 0.135070 | + | 0.233949i | 0.925624 | − | 0.378444i | \(-0.123541\pi\) |
−0.790554 | + | 0.612392i | \(0.790207\pi\) | |||||||
\(878\) | 4.50000 | + | 7.79423i | 0.151868 | + | 0.263042i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8.00000 | − | 13.8564i | 0.269680 | − | 0.467099i | ||||
\(881\) | −15.0000 | −0.505363 | −0.252681 | − | 0.967550i | \(-0.581312\pi\) | ||||
−0.252681 | + | 0.967550i | \(0.581312\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.0000 | −0.639401 | −0.319700 | − | 0.947519i | \(-0.603582\pi\) | ||||
−0.319700 | + | 0.947519i | \(0.603582\pi\) | |||||||
\(884\) | −10.5000 | + | 18.1865i | −0.353153 | + | 0.611679i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.0000 | − | 22.5167i | −0.436744 | − | 0.756462i | ||||
\(887\) | −6.00000 | − | 10.3923i | −0.201460 | − | 0.348939i | 0.747539 | − | 0.664218i | \(-0.231235\pi\) |
−0.948999 | + | 0.315279i | \(0.897902\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 12.0000 | 0.402241 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.00000 | 0.267860 | ||||||||
\(893\) | −6.00000 | + | 10.3923i | −0.200782 | + | 0.347765i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.0000 | + | 41.5692i | 0.802232 | + | 1.38951i | ||||
\(896\) | −0.500000 | − | 0.866025i | −0.0167038 | − | 0.0289319i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.00000 | + | 3.46410i | −0.0667409 | + | 0.115599i | ||||
\(899\) | 9.00000 | 0.300167 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 63.0000 | 2.09883 | ||||||||
\(902\) | −12.0000 | + | 20.7846i | −0.399556 | + | 0.692052i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.00000 | + | 6.92820i | 0.133038 | + | 0.230429i | ||||
\(905\) | −18.0000 | − | 31.1769i | −0.598340 | − | 1.03636i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.00000 | + | 10.3923i | −0.199227 | + | 0.345071i | −0.948278 | − | 0.317441i | \(-0.897176\pi\) |
0.749051 | + | 0.662512i | \(0.230510\pi\) | |||||||
\(908\) | 9.00000 | 0.298675 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −12.0000 | −0.397796 | ||||||||
\(911\) | −24.0000 | + | 41.5692i | −0.795155 | + | 1.37725i | 0.127585 | + | 0.991828i | \(0.459277\pi\) |
−0.922740 | + | 0.385422i | \(0.874056\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.00000 | − | 13.8564i | −0.264761 | − | 0.458580i | ||||
\(914\) | −14.5000 | − | 25.1147i | −0.479617 | − | 0.830722i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.00000 | − | 12.1244i | 0.231287 | − | 0.400600i | ||||
\(917\) | 1.00000 | 0.0330229 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.0000 | 0.725713 | 0.362857 | − | 0.931845i | \(-0.381802\pi\) | ||||
0.362857 | + | 0.931845i | \(0.381802\pi\) | |||||||
\(920\) | −2.00000 | + | 3.46410i | −0.0659380 | + | 0.114208i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7.00000 | + | 12.1244i | 0.230533 | + | 0.399294i | ||||
\(923\) | −10.5000 | − | 18.1865i | −0.345612 | − | 0.598617i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.0000 | + | 19.0526i | −0.361678 | + | 0.626444i | ||||
\(926\) | −22.0000 | −0.722965 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.00000 | 0.0328266 | ||||||||
\(929\) | −15.0000 | + | 25.9808i | −0.492134 | + | 0.852401i | −0.999959 | − | 0.00905914i | \(-0.997116\pi\) |
0.507825 | + | 0.861460i | \(0.330450\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.00000 | − | 1.73205i | −0.0327737 | − | 0.0567657i | ||||
\(932\) | −2.00000 | − | 3.46410i | −0.0655122 | − | 0.113470i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.00000 | − | 6.92820i | 0.130884 | − | 0.226698i | ||||
\(935\) | −112.000 | −3.66279 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −52.0000 | −1.69877 | −0.849383 | − | 0.527777i | \(-0.823026\pi\) | ||||
−0.849383 | + | 0.527777i | \(0.823026\pi\) | |||||||
\(938\) | −3.50000 | + | 6.06218i | −0.114279 | + | 0.197937i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 12.0000 | + | 20.7846i | 0.391397 | + | 0.677919i | ||||
\(941\) | −1.00000 | − | 1.73205i | −0.0325991 | − | 0.0564632i | 0.849266 | − | 0.527966i | \(-0.177045\pi\) |
−0.881865 | + | 0.471503i | \(0.843712\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.00000 | − | 5.19615i | 0.0976934 | − | 0.169210i | ||||
\(944\) | 5.00000 | 0.162736 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −44.0000 | −1.43056 | ||||||||
\(947\) | −1.00000 | + | 1.73205i | −0.0324956 | + | 0.0562841i | −0.881816 | − | 0.471594i | \(-0.843679\pi\) |
0.849320 | + | 0.527878i | \(0.177012\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.0000 | + | 36.3731i | 0.681689 | + | 1.18072i | ||||
\(950\) | 11.0000 | + | 19.0526i | 0.356887 | + | 0.618147i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.50000 | + | 6.06218i | −0.113436 | + | 0.196476i | ||||
\(953\) | −8.00000 | −0.259145 | −0.129573 | − | 0.991570i | \(-0.541361\pi\) | ||||
−0.129573 | + | 0.991570i | \(0.541361\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 48.0000 | 1.55324 | ||||||||
\(956\) | 6.00000 | − | 10.3923i | 0.194054 | − | 0.336111i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.00000 | − | 6.92820i | −0.129234 | − | 0.223840i | ||||
\(959\) | −11.0000 | − | 19.0526i | −0.355209 | − | 0.615239i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.0000 | + | 43.3013i | −0.806452 | + | 1.39682i | ||||
\(962\) | −6.00000 | −0.193448 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.0000 | −0.322078 | ||||||||
\(965\) | 10.0000 | − | 17.3205i | 0.321911 | − | 0.557567i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.0000 | + | 34.6410i | 0.643157 | + | 1.11398i | 0.984724 | + | 0.174123i | \(0.0557089\pi\) |
−0.341567 | + | 0.939857i | \(0.610958\pi\) | |||||||
\(968\) | 2.50000 | + | 4.33013i | 0.0803530 | + | 0.139176i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 16.0000 | − | 27.7128i | 0.513729 | − | 0.889805i | ||||
\(971\) | 15.0000 | 0.481373 | 0.240686 | − | 0.970603i | \(-0.422627\pi\) | ||||
0.240686 | + | 0.970603i | \(0.422627\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.0000 | −0.320585 | ||||||||
\(974\) | 13.0000 | − | 22.5167i | 0.416547 | − | 0.721480i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.00000 | + | 5.19615i | 0.0960277 | + | 0.166325i | ||||
\(977\) | −21.0000 | − | 36.3731i | −0.671850 | − | 1.16368i | −0.977379 | − | 0.211495i | \(-0.932167\pi\) |
0.305530 | − | 0.952183i | \(-0.401167\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.00000 | + | 10.3923i | −0.191761 | + | 0.332140i | ||||
\(980\) | −4.00000 | −0.127775 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 24.0000 | 0.765871 | ||||||||
\(983\) | 18.0000 | − | 31.1769i | 0.574111 | − | 0.994389i | −0.422027 | − | 0.906583i | \(-0.638681\pi\) |
0.996138 | − | 0.0878058i | \(-0.0279855\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −52.0000 | − | 90.0666i | −1.65686 | − | 2.86976i | ||||
\(986\) | −3.50000 | − | 6.06218i | −0.111463 | − | 0.193059i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.00000 | + | 5.19615i | −0.0954427 | + | 0.165312i | ||||
\(989\) | 11.0000 | 0.349780 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.0000 | 0.825917 | 0.412959 | − | 0.910750i | \(-0.364495\pi\) | ||||
0.412959 | + | 0.910750i | \(0.364495\pi\) | |||||||
\(992\) | −4.50000 | + | 7.79423i | −0.142875 | + | 0.247467i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.50000 | − | 6.06218i | −0.111013 | − | 0.192281i | ||||
\(995\) | −14.0000 | − | 24.2487i | −0.443830 | − | 0.768736i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.5000 | + | 30.3109i | −0.554231 | + | 0.959955i | 0.443732 | + | 0.896159i | \(0.353654\pi\) |
−0.997963 | + | 0.0637961i | \(0.979679\pi\) | |||||||
\(998\) | −28.0000 | −0.886325 | ||||||||
\(999\) | 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 | 1134.2.f.p.379.1 | 2 | ||
3.2 | odd | 2 | 1134.2.f.a.379.1 | 2 | |||
9.2 | odd | 6 | 378.2.a.h.1.1 | yes | 1 | ||
9.4 | even | 3 | inner | 1134.2.f.p.757.1 | 2 | ||
9.5 | odd | 6 | 1134.2.f.a.757.1 | 2 | |||
9.7 | even | 3 | 378.2.a.a.1.1 | ✓ | 1 | ||
36.7 | odd | 6 | 3024.2.a.a.1.1 | 1 | |||
36.11 | even | 6 | 3024.2.a.bd.1.1 | 1 | |||
45.29 | odd | 6 | 9450.2.a.bc.1.1 | 1 | |||
45.34 | even | 6 | 9450.2.a.dv.1.1 | 1 | |||
63.20 | even | 6 | 2646.2.a.p.1.1 | 1 | |||
63.34 | odd | 6 | 2646.2.a.o.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.2.a.a.1.1 | ✓ | 1 | 9.7 | even | 3 | ||
378.2.a.h.1.1 | yes | 1 | 9.2 | odd | 6 | ||
1134.2.f.a.379.1 | 2 | 3.2 | odd | 2 | |||
1134.2.f.a.757.1 | 2 | 9.5 | odd | 6 | |||
1134.2.f.p.379.1 | 2 | 1.1 | even | 1 | trivial | ||
1134.2.f.p.757.1 | 2 | 9.4 | even | 3 | inner | ||
2646.2.a.o.1.1 | 1 | 63.34 | odd | 6 | |||
2646.2.a.p.1.1 | 1 | 63.20 | even | 6 | |||
3024.2.a.a.1.1 | 1 | 36.7 | odd | 6 | |||
3024.2.a.bd.1.1 | 1 | 36.11 | even | 6 | |||
9450.2.a.bc.1.1 | 1 | 45.29 | odd | 6 | |||
9450.2.a.dv.1.1 | 1 | 45.34 | even | 6 |