Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(361,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.i (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: | \(11.7380090971\) |
Analytic rank: | \(1\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.361 |
Dual form | 1470.2.i.c.961.1 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0.500000 | − | 0.866025i | 0.158114 | − | 0.273861i | ||||
\(11\) | −1.00000 | + | 1.73205i | −0.301511 | + | 0.522233i | −0.976478 | − | 0.215615i | \(-0.930824\pi\) |
0.674967 | + | 0.737848i | \(0.264158\pi\) | |||||||
\(12\) | −0.500000 | − | 0.866025i | −0.144338 | − | 0.250000i | ||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.00000 | + | 3.46410i | −0.485071 | + | 0.840168i | −0.999853 | − | 0.0171533i | \(-0.994540\pi\) |
0.514782 | + | 0.857321i | \(0.327873\pi\) | |||||||
\(18\) | −0.500000 | + | 0.866025i | −0.117851 | + | 0.204124i | ||||
\(19\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.00000 | 0.426401 | ||||||||
\(23\) | −4.00000 | − | 6.92820i | −0.834058 | − | 1.44463i | −0.894795 | − | 0.446476i | \(-0.852679\pi\) |
0.0607377 | − | 0.998154i | \(-0.480655\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 1.00000 | + | 1.73205i | 0.196116 | + | 0.339683i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0.500000 | + | 0.866025i | 0.0912871 | + | 0.158114i | ||||
\(31\) | −1.00000 | + | 1.73205i | −0.179605 | + | 0.311086i | −0.941745 | − | 0.336327i | \(-0.890815\pi\) |
0.762140 | + | 0.647412i | \(0.224149\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −1.00000 | − | 1.73205i | −0.174078 | − | 0.301511i | ||||
\(34\) | 4.00000 | 0.685994 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.00000 | − | 6.92820i | −0.657596 | − | 1.13899i | −0.981236 | − | 0.192809i | \(-0.938240\pi\) |
0.323640 | − | 0.946180i | \(-0.395093\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | − | 1.73205i | 0.160128 | − | 0.277350i | ||||
\(40\) | 0.500000 | + | 0.866025i | 0.0790569 | + | 0.136931i | ||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | −0.304997 | −0.152499 | − | 0.988304i | \(-0.548732\pi\) | ||||
−0.152499 | + | 0.988304i | \(0.548732\pi\) | |||||||
\(44\) | −1.00000 | − | 1.73205i | −0.150756 | − | 0.261116i | ||||
\(45\) | 0.500000 | − | 0.866025i | 0.0745356 | − | 0.129099i | ||||
\(46\) | −4.00000 | + | 6.92820i | −0.589768 | + | 1.02151i | ||||
\(47\) | 5.00000 | + | 8.66025i | 0.729325 | + | 1.26323i | 0.957169 | + | 0.289530i | \(0.0934991\pi\) |
−0.227844 | + | 0.973698i | \(0.573168\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −2.00000 | − | 3.46410i | −0.280056 | − | 0.485071i | ||||
\(52\) | 1.00000 | − | 1.73205i | 0.138675 | − | 0.240192i | ||||
\(53\) | 1.00000 | − | 1.73205i | 0.137361 | − | 0.237915i | −0.789136 | − | 0.614218i | \(-0.789471\pi\) |
0.926497 | + | 0.376303i | \(0.122805\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.00000 | − | 3.46410i | 0.260378 | − | 0.450988i | −0.705965 | − | 0.708247i | \(-0.749486\pi\) |
0.966342 | + | 0.257260i | \(0.0828195\pi\) | |||||||
\(60\) | 0.500000 | − | 0.866025i | 0.0645497 | − | 0.111803i | ||||
\(61\) | −5.00000 | − | 8.66025i | −0.640184 | − | 1.10883i | −0.985391 | − | 0.170305i | \(-0.945525\pi\) |
0.345207 | − | 0.938527i | \(-0.387809\pi\) | |||||||
\(62\) | 2.00000 | 0.254000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.00000 | − | 1.73205i | −0.124035 | − | 0.214834i | ||||
\(66\) | −1.00000 | + | 1.73205i | −0.123091 | + | 0.213201i | ||||
\(67\) | −1.00000 | + | 1.73205i | −0.122169 | + | 0.211604i | −0.920623 | − | 0.390453i | \(-0.872318\pi\) |
0.798454 | + | 0.602056i | \(0.205652\pi\) | |||||||
\(68\) | −2.00000 | − | 3.46410i | −0.242536 | − | 0.420084i | ||||
\(69\) | 8.00000 | 0.963087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.0000 | −1.42414 | −0.712069 | − | 0.702109i | \(-0.752242\pi\) | ||||
−0.712069 | + | 0.702109i | \(0.752242\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | 5.00000 | − | 8.66025i | 0.585206 | − | 1.01361i | −0.409644 | − | 0.912245i | \(-0.634347\pi\) |
0.994850 | − | 0.101361i | \(-0.0323196\pi\) | |||||||
\(74\) | −4.00000 | + | 6.92820i | −0.464991 | + | 0.805387i | ||||
\(75\) | −0.500000 | − | 0.866025i | −0.0577350 | − | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.00000 | −0.226455 | ||||||||
\(79\) | −8.00000 | − | 13.8564i | −0.900070 | − | 1.55897i | −0.827401 | − | 0.561611i | \(-0.810182\pi\) |
−0.0726692 | − | 0.997356i | \(-0.523152\pi\) | |||||||
\(80\) | 0.500000 | − | 0.866025i | 0.0559017 | − | 0.0968246i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −1.00000 | − | 1.73205i | −0.110432 | − | 0.191273i | ||||
\(83\) | −16.0000 | −1.75623 | −0.878114 | − | 0.478451i | \(-0.841198\pi\) | ||||
−0.878114 | + | 0.478451i | \(0.841198\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.00000 | −0.433861 | ||||||||
\(86\) | 1.00000 | + | 1.73205i | 0.107833 | + | 0.186772i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.00000 | + | 1.73205i | −0.106600 | + | 0.184637i | ||||
\(89\) | 7.00000 | + | 12.1244i | 0.741999 | + | 1.28518i | 0.951584 | + | 0.307389i | \(0.0994552\pi\) |
−0.209585 | + | 0.977790i | \(0.567211\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.00000 | 0.834058 | ||||||||
\(93\) | −1.00000 | − | 1.73205i | −0.103695 | − | 0.179605i | ||||
\(94\) | 5.00000 | − | 8.66025i | 0.515711 | − | 0.893237i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | −7.00000 | + | 12.1244i | −0.696526 | + | 1.20642i | 0.273138 | + | 0.961975i | \(0.411939\pi\) |
−0.969664 | + | 0.244443i | \(0.921395\pi\) | |||||||
\(102\) | −2.00000 | + | 3.46410i | −0.198030 | + | 0.342997i | ||||
\(103\) | −10.0000 | − | 17.3205i | −0.985329 | − | 1.70664i | −0.640464 | − | 0.767988i | \(-0.721258\pi\) |
−0.344865 | − | 0.938652i | \(-0.612075\pi\) | |||||||
\(104\) | −2.00000 | −0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.00000 | −0.194257 | ||||||||
\(107\) | −6.00000 | − | 10.3923i | −0.580042 | − | 1.00466i | −0.995474 | − | 0.0950377i | \(-0.969703\pi\) |
0.415432 | − | 0.909624i | \(-0.363630\pi\) | |||||||
\(108\) | −0.500000 | + | 0.866025i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | 1.00000 | − | 1.73205i | 0.0957826 | − | 0.165900i | −0.814152 | − | 0.580651i | \(-0.802798\pi\) |
0.909935 | + | 0.414751i | \(0.136131\pi\) | |||||||
\(110\) | 1.00000 | + | 1.73205i | 0.0953463 | + | 0.165145i | ||||
\(111\) | 8.00000 | 0.759326 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.0000 | −1.31701 | −0.658505 | − | 0.752577i | \(-0.728811\pi\) | ||||
−0.658505 | + | 0.752577i | \(0.728811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.00000 | − | 6.92820i | 0.373002 | − | 0.646058i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | + | 1.73205i | 0.0924500 | + | 0.160128i | ||||
\(118\) | −4.00000 | −0.368230 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | −5.00000 | + | 8.66025i | −0.452679 | + | 0.784063i | ||||
\(123\) | −1.00000 | + | 1.73205i | −0.0901670 | + | 0.156174i | ||||
\(124\) | −1.00000 | − | 1.73205i | −0.0898027 | − | 0.155543i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.0000 | −1.06483 | −0.532414 | − | 0.846484i | \(-0.678715\pi\) | ||||
−0.532414 | + | 0.846484i | \(0.678715\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 1.00000 | − | 1.73205i | 0.0880451 | − | 0.152499i | ||||
\(130\) | −1.00000 | + | 1.73205i | −0.0877058 | + | 0.151911i | ||||
\(131\) | 6.00000 | + | 10.3923i | 0.524222 | + | 0.907980i | 0.999602 | + | 0.0281993i | \(0.00897729\pi\) |
−0.475380 | + | 0.879781i | \(0.657689\pi\) | |||||||
\(132\) | 2.00000 | 0.174078 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.00000 | 0.172774 | ||||||||
\(135\) | 0.500000 | + | 0.866025i | 0.0430331 | + | 0.0745356i | ||||
\(136\) | −2.00000 | + | 3.46410i | −0.171499 | + | 0.297044i | ||||
\(137\) | 1.00000 | − | 1.73205i | 0.0854358 | − | 0.147979i | −0.820141 | − | 0.572161i | \(-0.806105\pi\) |
0.905577 | + | 0.424182i | \(0.139438\pi\) | |||||||
\(138\) | −4.00000 | − | 6.92820i | −0.340503 | − | 0.589768i | ||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.0000 | −0.842152 | ||||||||
\(142\) | 6.00000 | + | 10.3923i | 0.503509 | + | 0.872103i | ||||
\(143\) | 2.00000 | − | 3.46410i | 0.167248 | − | 0.289683i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −10.0000 | −0.827606 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.00000 | 0.657596 | ||||||||
\(149\) | 8.00000 | + | 13.8564i | 0.655386 | + | 1.13516i | 0.981797 | + | 0.189933i | \(0.0608272\pi\) |
−0.326411 | + | 0.945228i | \(0.605840\pi\) | |||||||
\(150\) | −0.500000 | + | 0.866025i | −0.0408248 | + | 0.0707107i | ||||
\(151\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.00000 | 0.323381 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.00000 | −0.160644 | ||||||||
\(156\) | 1.00000 | + | 1.73205i | 0.0800641 | + | 0.138675i | ||||
\(157\) | −5.00000 | + | 8.66025i | −0.399043 | + | 0.691164i | −0.993608 | − | 0.112884i | \(-0.963991\pi\) |
0.594565 | + | 0.804048i | \(0.297324\pi\) | |||||||
\(158\) | −8.00000 | + | 13.8564i | −0.636446 | + | 1.10236i | ||||
\(159\) | 1.00000 | + | 1.73205i | 0.0793052 | + | 0.137361i | ||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 5.00000 | + | 8.66025i | 0.391630 | + | 0.678323i | 0.992665 | − | 0.120900i | \(-0.0385779\pi\) |
−0.601035 | + | 0.799223i | \(0.705245\pi\) | |||||||
\(164\) | −1.00000 | + | 1.73205i | −0.0780869 | + | 0.135250i | ||||
\(165\) | 1.00000 | − | 1.73205i | 0.0778499 | − | 0.134840i | ||||
\(166\) | 8.00000 | + | 13.8564i | 0.620920 | + | 1.07547i | ||||
\(167\) | −18.0000 | −1.39288 | −0.696441 | − | 0.717614i | \(-0.745234\pi\) | ||||
−0.696441 | + | 0.717614i | \(0.745234\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 2.00000 | + | 3.46410i | 0.153393 | + | 0.265684i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.00000 | − | 1.73205i | 0.0762493 | − | 0.132068i | ||||
\(173\) | −3.00000 | − | 5.19615i | −0.228086 | − | 0.395056i | 0.729155 | − | 0.684349i | \(-0.239913\pi\) |
−0.957241 | + | 0.289292i | \(0.906580\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.00000 | 0.150756 | ||||||||
\(177\) | 2.00000 | + | 3.46410i | 0.150329 | + | 0.260378i | ||||
\(178\) | 7.00000 | − | 12.1244i | 0.524672 | − | 0.908759i | ||||
\(179\) | 1.00000 | − | 1.73205i | 0.0747435 | − | 0.129460i | −0.826231 | − | 0.563331i | \(-0.809520\pi\) |
0.900975 | + | 0.433872i | \(0.142853\pi\) | |||||||
\(180\) | 0.500000 | + | 0.866025i | 0.0372678 | + | 0.0645497i | ||||
\(181\) | 22.0000 | 1.63525 | 0.817624 | − | 0.575753i | \(-0.195291\pi\) | ||||
0.817624 | + | 0.575753i | \(0.195291\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.0000 | 0.739221 | ||||||||
\(184\) | −4.00000 | − | 6.92820i | −0.294884 | − | 0.510754i | ||||
\(185\) | 4.00000 | − | 6.92820i | 0.294086 | − | 0.509372i | ||||
\(186\) | −1.00000 | + | 1.73205i | −0.0733236 | + | 0.127000i | ||||
\(187\) | −4.00000 | − | 6.92820i | −0.292509 | − | 0.506640i | ||||
\(188\) | −10.0000 | −0.729325 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(192\) | −0.500000 | + | 0.866025i | −0.0360844 | + | 0.0625000i | ||||
\(193\) | 9.00000 | − | 15.5885i | 0.647834 | − | 1.12208i | −0.335805 | − | 0.941932i | \(-0.609008\pi\) |
0.983639 | − | 0.180150i | \(-0.0576584\pi\) | |||||||
\(194\) | 3.00000 | + | 5.19615i | 0.215387 | + | 0.373062i | ||||
\(195\) | 2.00000 | 0.143223 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | −1.00000 | − | 1.73205i | −0.0710669 | − | 0.123091i | ||||
\(199\) | 5.00000 | − | 8.66025i | 0.354441 | − | 0.613909i | −0.632581 | − | 0.774494i | \(-0.718005\pi\) |
0.987022 | + | 0.160585i | \(0.0513380\pi\) | |||||||
\(200\) | −0.500000 | + | 0.866025i | −0.0353553 | + | 0.0612372i | ||||
\(201\) | −1.00000 | − | 1.73205i | −0.0705346 | − | 0.122169i | ||||
\(202\) | 14.0000 | 0.985037 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.00000 | 0.280056 | ||||||||
\(205\) | 1.00000 | + | 1.73205i | 0.0698430 | + | 0.120972i | ||||
\(206\) | −10.0000 | + | 17.3205i | −0.696733 | + | 1.20678i | ||||
\(207\) | −4.00000 | + | 6.92820i | −0.278019 | + | 0.481543i | ||||
\(208\) | 1.00000 | + | 1.73205i | 0.0693375 | + | 0.120096i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 1.00000 | + | 1.73205i | 0.0686803 | + | 0.118958i | ||||
\(213\) | 6.00000 | − | 10.3923i | 0.411113 | − | 0.712069i | ||||
\(214\) | −6.00000 | + | 10.3923i | −0.410152 | + | 0.710403i | ||||
\(215\) | −1.00000 | − | 1.73205i | −0.0681994 | − | 0.118125i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.00000 | −0.135457 | ||||||||
\(219\) | 5.00000 | + | 8.66025i | 0.337869 | + | 0.585206i | ||||
\(220\) | 1.00000 | − | 1.73205i | 0.0674200 | − | 0.116775i | ||||
\(221\) | 4.00000 | − | 6.92820i | 0.269069 | − | 0.466041i | ||||
\(222\) | −4.00000 | − | 6.92820i | −0.268462 | − | 0.464991i | ||||
\(223\) | −16.0000 | −1.07144 | −0.535720 | − | 0.844396i | \(-0.679960\pi\) | ||||
−0.535720 | + | 0.844396i | \(0.679960\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 7.00000 | + | 12.1244i | 0.465633 | + | 0.806500i | ||||
\(227\) | −6.00000 | + | 10.3923i | −0.398234 | + | 0.689761i | −0.993508 | − | 0.113761i | \(-0.963710\pi\) |
0.595274 | + | 0.803523i | \(0.297043\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.00000 | + | 8.66025i | 0.330409 | + | 0.572286i | 0.982592 | − | 0.185776i | \(-0.0594799\pi\) |
−0.652183 | + | 0.758062i | \(0.726147\pi\) | |||||||
\(230\) | −8.00000 | −0.527504 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.00000 | + | 12.1244i | 0.458585 | + | 0.794293i | 0.998886 | − | 0.0471787i | \(-0.0150230\pi\) |
−0.540301 | + | 0.841472i | \(0.681690\pi\) | |||||||
\(234\) | 1.00000 | − | 1.73205i | 0.0653720 | − | 0.113228i | ||||
\(235\) | −5.00000 | + | 8.66025i | −0.326164 | + | 0.564933i | ||||
\(236\) | 2.00000 | + | 3.46410i | 0.130189 | + | 0.225494i | ||||
\(237\) | 16.0000 | 1.03931 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.00000 | −0.517477 | −0.258738 | − | 0.965947i | \(-0.583307\pi\) | ||||
−0.258738 | + | 0.965947i | \(0.583307\pi\) | |||||||
\(240\) | 0.500000 | + | 0.866025i | 0.0322749 | + | 0.0559017i | ||||
\(241\) | −10.0000 | + | 17.3205i | −0.644157 | + | 1.11571i | 0.340339 | + | 0.940303i | \(0.389458\pi\) |
−0.984496 | + | 0.175409i | \(0.943875\pi\) | |||||||
\(242\) | 3.50000 | − | 6.06218i | 0.224989 | − | 0.389692i | ||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 10.0000 | 0.640184 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.00000 | 0.127515 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1.00000 | + | 1.73205i | −0.0635001 | + | 0.109985i | ||||
\(249\) | 8.00000 | − | 13.8564i | 0.506979 | − | 0.878114i | ||||
\(250\) | 0.500000 | + | 0.866025i | 0.0316228 | + | 0.0547723i | ||||
\(251\) | 20.0000 | 1.26239 | 0.631194 | − | 0.775625i | \(-0.282565\pi\) | ||||
0.631194 | + | 0.775625i | \(0.282565\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.0000 | 1.00591 | ||||||||
\(254\) | 6.00000 | + | 10.3923i | 0.376473 | + | 0.652071i | ||||
\(255\) | 2.00000 | − | 3.46410i | 0.125245 | − | 0.216930i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 6.00000 | + | 10.3923i | 0.374270 | + | 0.648254i | 0.990217 | − | 0.139533i | \(-0.0445601\pi\) |
−0.615948 | + | 0.787787i | \(0.711227\pi\) | |||||||
\(258\) | −2.00000 | −0.124515 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.00000 | 0.124035 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.00000 | − | 10.3923i | 0.370681 | − | 0.642039i | ||||
\(263\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(264\) | −1.00000 | − | 1.73205i | −0.0615457 | − | 0.106600i | ||||
\(265\) | 2.00000 | 0.122859 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.0000 | −0.856786 | ||||||||
\(268\) | −1.00000 | − | 1.73205i | −0.0610847 | − | 0.105802i | ||||
\(269\) | −5.00000 | + | 8.66025i | −0.304855 | + | 0.528025i | −0.977229 | − | 0.212187i | \(-0.931941\pi\) |
0.672374 | + | 0.740212i | \(0.265275\pi\) | |||||||
\(270\) | 0.500000 | − | 0.866025i | 0.0304290 | − | 0.0527046i | ||||
\(271\) | −7.00000 | − | 12.1244i | −0.425220 | − | 0.736502i | 0.571221 | − | 0.820796i | \(-0.306470\pi\) |
−0.996441 | + | 0.0842940i | \(0.973137\pi\) | |||||||
\(272\) | 4.00000 | 0.242536 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.00000 | −0.120824 | ||||||||
\(275\) | −1.00000 | − | 1.73205i | −0.0603023 | − | 0.104447i | ||||
\(276\) | −4.00000 | + | 6.92820i | −0.240772 | + | 0.417029i | ||||
\(277\) | 14.0000 | − | 24.2487i | 0.841178 | − | 1.45696i | −0.0477206 | − | 0.998861i | \(-0.515196\pi\) |
0.888899 | − | 0.458103i | \(-0.151471\pi\) | |||||||
\(278\) | −2.00000 | − | 3.46410i | −0.119952 | − | 0.207763i | ||||
\(279\) | 2.00000 | 0.119737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.0000 | 0.835170 | 0.417585 | − | 0.908638i | \(-0.362877\pi\) | ||||
0.417585 | + | 0.908638i | \(0.362877\pi\) | |||||||
\(282\) | 5.00000 | + | 8.66025i | 0.297746 | + | 0.515711i | ||||
\(283\) | 2.00000 | − | 3.46410i | 0.118888 | − | 0.205919i | −0.800439 | − | 0.599414i | \(-0.795400\pi\) |
0.919327 | + | 0.393494i | \(0.128734\pi\) | |||||||
\(284\) | 6.00000 | − | 10.3923i | 0.356034 | − | 0.616670i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.00000 | −0.236525 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 0.500000 | + | 0.866025i | 0.0294118 | + | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.00000 | − | 5.19615i | 0.175863 | − | 0.304604i | ||||
\(292\) | 5.00000 | + | 8.66025i | 0.292603 | + | 0.506803i | ||||
\(293\) | −30.0000 | −1.75262 | −0.876309 | − | 0.481749i | \(-0.840002\pi\) | ||||
−0.876309 | + | 0.481749i | \(0.840002\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.00000 | 0.232889 | ||||||||
\(296\) | −4.00000 | − | 6.92820i | −0.232495 | − | 0.402694i | ||||
\(297\) | −1.00000 | + | 1.73205i | −0.0580259 | + | 0.100504i | ||||
\(298\) | 8.00000 | − | 13.8564i | 0.463428 | − | 0.802680i | ||||
\(299\) | 8.00000 | + | 13.8564i | 0.462652 | + | 0.801337i | ||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.00000 | − | 12.1244i | −0.402139 | − | 0.696526i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.00000 | − | 8.66025i | 0.286299 | − | 0.495885i | ||||
\(306\) | −2.00000 | − | 3.46410i | −0.114332 | − | 0.198030i | ||||
\(307\) | 20.0000 | 1.14146 | 0.570730 | − | 0.821138i | \(-0.306660\pi\) | ||||
0.570730 | + | 0.821138i | \(0.306660\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20.0000 | 1.13776 | ||||||||
\(310\) | 1.00000 | + | 1.73205i | 0.0567962 | + | 0.0983739i | ||||
\(311\) | −10.0000 | + | 17.3205i | −0.567048 | + | 0.982156i | 0.429808 | + | 0.902920i | \(0.358581\pi\) |
−0.996856 | + | 0.0792356i | \(0.974752\pi\) | |||||||
\(312\) | 1.00000 | − | 1.73205i | 0.0566139 | − | 0.0980581i | ||||
\(313\) | −13.0000 | − | 22.5167i | −0.734803 | − | 1.27272i | −0.954810 | − | 0.297218i | \(-0.903941\pi\) |
0.220006 | − | 0.975499i | \(-0.429392\pi\) | |||||||
\(314\) | 10.0000 | 0.564333 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.0000 | 0.900070 | ||||||||
\(317\) | −3.00000 | − | 5.19615i | −0.168497 | − | 0.291845i | 0.769395 | − | 0.638774i | \(-0.220558\pi\) |
−0.937892 | + | 0.346929i | \(0.887225\pi\) | |||||||
\(318\) | 1.00000 | − | 1.73205i | 0.0560772 | − | 0.0971286i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.500000 | + | 0.866025i | 0.0279508 | + | 0.0484123i | ||||
\(321\) | 12.0000 | 0.669775 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 1.00000 | − | 1.73205i | 0.0554700 | − | 0.0960769i | ||||
\(326\) | 5.00000 | − | 8.66025i | 0.276924 | − | 0.479647i | ||||
\(327\) | 1.00000 | + | 1.73205i | 0.0553001 | + | 0.0957826i | ||||
\(328\) | 2.00000 | 0.110432 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.00000 | −0.110096 | ||||||||
\(331\) | 2.00000 | + | 3.46410i | 0.109930 | + | 0.190404i | 0.915742 | − | 0.401768i | \(-0.131604\pi\) |
−0.805812 | + | 0.592172i | \(0.798271\pi\) | |||||||
\(332\) | 8.00000 | − | 13.8564i | 0.439057 | − | 0.760469i | ||||
\(333\) | −4.00000 | + | 6.92820i | −0.219199 | + | 0.379663i | ||||
\(334\) | 9.00000 | + | 15.5885i | 0.492458 | + | 0.852962i | ||||
\(335\) | −2.00000 | −0.109272 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.00000 | −0.108947 | −0.0544735 | − | 0.998515i | \(-0.517348\pi\) | ||||
−0.0544735 | + | 0.998515i | \(0.517348\pi\) | |||||||
\(338\) | 4.50000 | + | 7.79423i | 0.244768 | + | 0.423950i | ||||
\(339\) | 7.00000 | − | 12.1244i | 0.380188 | − | 0.658505i | ||||
\(340\) | 2.00000 | − | 3.46410i | 0.108465 | − | 0.187867i | ||||
\(341\) | −2.00000 | − | 3.46410i | −0.108306 | − | 0.187592i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.00000 | −0.107833 | ||||||||
\(345\) | 4.00000 | + | 6.92820i | 0.215353 | + | 0.373002i | ||||
\(346\) | −3.00000 | + | 5.19615i | −0.161281 | + | 0.279347i | ||||
\(347\) | 2.00000 | − | 3.46410i | 0.107366 | − | 0.185963i | −0.807337 | − | 0.590091i | \(-0.799092\pi\) |
0.914702 | + | 0.404128i | \(0.132425\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.0000 | −0.535288 | −0.267644 | − | 0.963518i | \(-0.586245\pi\) | ||||
−0.267644 | + | 0.963518i | \(0.586245\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | −1.00000 | − | 1.73205i | −0.0533002 | − | 0.0923186i | ||||
\(353\) | 12.0000 | − | 20.7846i | 0.638696 | − | 1.10625i | −0.347024 | − | 0.937856i | \(-0.612808\pi\) |
0.985719 | − | 0.168397i | \(-0.0538590\pi\) | |||||||
\(354\) | 2.00000 | − | 3.46410i | 0.106299 | − | 0.184115i | ||||
\(355\) | −6.00000 | − | 10.3923i | −0.318447 | − | 0.551566i | ||||
\(356\) | −14.0000 | −0.741999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.00000 | −0.105703 | ||||||||
\(359\) | 10.0000 | + | 17.3205i | 0.527780 | + | 0.914141i | 0.999476 | + | 0.0323801i | \(0.0103087\pi\) |
−0.471696 | + | 0.881761i | \(0.656358\pi\) | |||||||
\(360\) | 0.500000 | − | 0.866025i | 0.0263523 | − | 0.0456435i | ||||
\(361\) | 9.50000 | − | 16.4545i | 0.500000 | − | 0.866025i | ||||
\(362\) | −11.0000 | − | 19.0526i | −0.578147 | − | 1.00138i | ||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.0000 | 0.523424 | ||||||||
\(366\) | −5.00000 | − | 8.66025i | −0.261354 | − | 0.452679i | ||||
\(367\) | −14.0000 | + | 24.2487i | −0.730794 | + | 1.26577i | 0.225750 | + | 0.974185i | \(0.427517\pi\) |
−0.956544 | + | 0.291587i | \(0.905817\pi\) | |||||||
\(368\) | −4.00000 | + | 6.92820i | −0.208514 | + | 0.361158i | ||||
\(369\) | −1.00000 | − | 1.73205i | −0.0520579 | − | 0.0901670i | ||||
\(370\) | −8.00000 | −0.415900 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.00000 | 0.103695 | ||||||||
\(373\) | 18.0000 | + | 31.1769i | 0.932005 | + | 1.61428i | 0.779890 | + | 0.625917i | \(0.215275\pi\) |
0.152115 | + | 0.988363i | \(0.451392\pi\) | |||||||
\(374\) | −4.00000 | + | 6.92820i | −0.206835 | + | 0.358249i | ||||
\(375\) | 0.500000 | − | 0.866025i | 0.0258199 | − | 0.0447214i | ||||
\(376\) | 5.00000 | + | 8.66025i | 0.257855 | + | 0.446619i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.00000 | 0.410932 | 0.205466 | − | 0.978664i | \(-0.434129\pi\) | ||||
0.205466 | + | 0.978664i | \(0.434129\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.00000 | − | 10.3923i | 0.307389 | − | 0.532414i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.00000 | + | 12.1244i | 0.357683 | + | 0.619526i | 0.987573 | − | 0.157159i | \(-0.0502334\pi\) |
−0.629890 | + | 0.776684i | \(0.716900\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −18.0000 | −0.916176 | ||||||||
\(387\) | 1.00000 | + | 1.73205i | 0.0508329 | + | 0.0880451i | ||||
\(388\) | 3.00000 | − | 5.19615i | 0.152302 | − | 0.263795i | ||||
\(389\) | 12.0000 | − | 20.7846i | 0.608424 | − | 1.05382i | −0.383076 | − | 0.923717i | \(-0.625135\pi\) |
0.991500 | − | 0.130105i | \(-0.0415314\pi\) | |||||||
\(390\) | −1.00000 | − | 1.73205i | −0.0506370 | − | 0.0877058i | ||||
\(391\) | 32.0000 | 1.61831 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.0000 | −0.605320 | ||||||||
\(394\) | −9.00000 | − | 15.5885i | −0.453413 | − | 0.785335i | ||||
\(395\) | 8.00000 | − | 13.8564i | 0.402524 | − | 0.697191i | ||||
\(396\) | −1.00000 | + | 1.73205i | −0.0502519 | + | 0.0870388i | ||||
\(397\) | 7.00000 | + | 12.1244i | 0.351320 | + | 0.608504i | 0.986481 | − | 0.163876i | \(-0.0523996\pi\) |
−0.635161 | + | 0.772380i | \(0.719066\pi\) | |||||||
\(398\) | −10.0000 | −0.501255 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 7.00000 | + | 12.1244i | 0.349563 | + | 0.605461i | 0.986172 | − | 0.165726i | \(-0.0529966\pi\) |
−0.636609 | + | 0.771187i | \(0.719663\pi\) | |||||||
\(402\) | −1.00000 | + | 1.73205i | −0.0498755 | + | 0.0863868i | ||||
\(403\) | 2.00000 | − | 3.46410i | 0.0996271 | − | 0.172559i | ||||
\(404\) | −7.00000 | − | 12.1244i | −0.348263 | − | 0.603209i | ||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.0000 | 0.793091 | ||||||||
\(408\) | −2.00000 | − | 3.46410i | −0.0990148 | − | 0.171499i | ||||
\(409\) | −16.0000 | + | 27.7128i | −0.791149 | + | 1.37031i | 0.134107 | + | 0.990967i | \(0.457183\pi\) |
−0.925256 | + | 0.379344i | \(0.876150\pi\) | |||||||
\(410\) | 1.00000 | − | 1.73205i | 0.0493865 | − | 0.0855399i | ||||
\(411\) | 1.00000 | + | 1.73205i | 0.0493264 | + | 0.0854358i | ||||
\(412\) | 20.0000 | 0.985329 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 8.00000 | 0.393179 | ||||||||
\(415\) | −8.00000 | − | 13.8564i | −0.392705 | − | 0.680184i | ||||
\(416\) | 1.00000 | − | 1.73205i | 0.0490290 | − | 0.0849208i | ||||
\(417\) | −2.00000 | + | 3.46410i | −0.0979404 | + | 0.169638i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −36.0000 | −1.75872 | −0.879358 | − | 0.476162i | \(-0.842028\pi\) | ||||
−0.879358 | + | 0.476162i | \(0.842028\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 38.0000 | 1.85201 | 0.926003 | − | 0.377515i | \(-0.123221\pi\) | ||||
0.926003 | + | 0.377515i | \(0.123221\pi\) | |||||||
\(422\) | 2.00000 | + | 3.46410i | 0.0973585 | + | 0.168630i | ||||
\(423\) | 5.00000 | − | 8.66025i | 0.243108 | − | 0.421076i | ||||
\(424\) | 1.00000 | − | 1.73205i | 0.0485643 | − | 0.0841158i | ||||
\(425\) | −2.00000 | − | 3.46410i | −0.0970143 | − | 0.168034i | ||||
\(426\) | −12.0000 | −0.581402 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 12.0000 | 0.580042 | ||||||||
\(429\) | 2.00000 | + | 3.46410i | 0.0965609 | + | 0.167248i | ||||
\(430\) | −1.00000 | + | 1.73205i | −0.0482243 | + | 0.0835269i | ||||
\(431\) | −6.00000 | + | 10.3923i | −0.289010 | + | 0.500580i | −0.973574 | − | 0.228373i | \(-0.926659\pi\) |
0.684564 | + | 0.728953i | \(0.259993\pi\) | |||||||
\(432\) | −0.500000 | − | 0.866025i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | −38.0000 | −1.82616 | −0.913082 | − | 0.407777i | \(-0.866304\pi\) | ||||
−0.913082 | + | 0.407777i | \(0.866304\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.00000 | + | 1.73205i | 0.0478913 | + | 0.0829502i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 5.00000 | − | 8.66025i | 0.238909 | − | 0.413803i | ||||
\(439\) | −13.0000 | − | 22.5167i | −0.620456 | − | 1.07466i | −0.989401 | − | 0.145210i | \(-0.953614\pi\) |
0.368945 | − | 0.929451i | \(-0.379719\pi\) | |||||||
\(440\) | −2.00000 | −0.0953463 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.00000 | −0.380521 | ||||||||
\(443\) | −14.0000 | − | 24.2487i | −0.665160 | − | 1.15209i | −0.979242 | − | 0.202695i | \(-0.935030\pi\) |
0.314082 | − | 0.949396i | \(-0.398303\pi\) | |||||||
\(444\) | −4.00000 | + | 6.92820i | −0.189832 | + | 0.328798i | ||||
\(445\) | −7.00000 | + | 12.1244i | −0.331832 | + | 0.574750i | ||||
\(446\) | 8.00000 | + | 13.8564i | 0.378811 | + | 0.656120i | ||||
\(447\) | −16.0000 | −0.756774 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.00000 | 0.283158 | 0.141579 | − | 0.989927i | \(-0.454782\pi\) | ||||
0.141579 | + | 0.989927i | \(0.454782\pi\) | |||||||
\(450\) | −0.500000 | − | 0.866025i | −0.0235702 | − | 0.0408248i | ||||
\(451\) | −2.00000 | + | 3.46410i | −0.0941763 | + | 0.163118i | ||||
\(452\) | 7.00000 | − | 12.1244i | 0.329252 | − | 0.570282i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12.0000 | 0.563188 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.0000 | + | 36.3731i | 0.982339 | + | 1.70146i | 0.653213 | + | 0.757174i | \(0.273421\pi\) |
0.329125 | + | 0.944286i | \(0.393246\pi\) | |||||||
\(458\) | 5.00000 | − | 8.66025i | 0.233635 | − | 0.404667i | ||||
\(459\) | −2.00000 | + | 3.46410i | −0.0933520 | + | 0.161690i | ||||
\(460\) | 4.00000 | + | 6.92820i | 0.186501 | + | 0.323029i | ||||
\(461\) | 18.0000 | 0.838344 | 0.419172 | − | 0.907907i | \(-0.362320\pi\) | ||||
0.419172 | + | 0.907907i | \(0.362320\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.0000 | 0.743583 | 0.371792 | − | 0.928316i | \(-0.378744\pi\) | ||||
0.371792 | + | 0.928316i | \(0.378744\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.00000 | − | 1.73205i | 0.0463739 | − | 0.0803219i | ||||
\(466\) | 7.00000 | − | 12.1244i | 0.324269 | − | 0.561650i | ||||
\(467\) | 4.00000 | + | 6.92820i | 0.185098 | + | 0.320599i | 0.943610 | − | 0.331061i | \(-0.107406\pi\) |
−0.758512 | + | 0.651660i | \(0.774073\pi\) | |||||||
\(468\) | −2.00000 | −0.0924500 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 10.0000 | 0.461266 | ||||||||
\(471\) | −5.00000 | − | 8.66025i | −0.230388 | − | 0.399043i | ||||
\(472\) | 2.00000 | − | 3.46410i | 0.0920575 | − | 0.159448i | ||||
\(473\) | 2.00000 | − | 3.46410i | 0.0919601 | − | 0.159280i | ||||
\(474\) | −8.00000 | − | 13.8564i | −0.367452 | − | 0.636446i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.00000 | −0.0915737 | ||||||||
\(478\) | 4.00000 | + | 6.92820i | 0.182956 | + | 0.316889i | ||||
\(479\) | 2.00000 | − | 3.46410i | 0.0913823 | − | 0.158279i | −0.816711 | − | 0.577047i | \(-0.804205\pi\) |
0.908093 | + | 0.418769i | \(0.137538\pi\) | |||||||
\(480\) | 0.500000 | − | 0.866025i | 0.0228218 | − | 0.0395285i | ||||
\(481\) | 8.00000 | + | 13.8564i | 0.364769 | + | 0.631798i | ||||
\(482\) | 20.0000 | 0.910975 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.00000 | −0.318182 | ||||||||
\(485\) | −3.00000 | − | 5.19615i | −0.136223 | − | 0.235945i | ||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | −14.0000 | + | 24.2487i | −0.634401 | + | 1.09881i | 0.352241 | + | 0.935909i | \(0.385420\pi\) |
−0.986642 | + | 0.162905i | \(0.947914\pi\) | |||||||
\(488\) | −5.00000 | − | 8.66025i | −0.226339 | − | 0.392031i | ||||
\(489\) | −10.0000 | −0.452216 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.00000 | 0.270776 | 0.135388 | − | 0.990793i | \(-0.456772\pi\) | ||||
0.135388 | + | 0.990793i | \(0.456772\pi\) | |||||||
\(492\) | −1.00000 | − | 1.73205i | −0.0450835 | − | 0.0780869i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.00000 | + | 1.73205i | 0.0449467 | + | 0.0778499i | ||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −16.0000 | −0.716977 | ||||||||
\(499\) | −20.0000 | − | 34.6410i | −0.895323 | − | 1.55074i | −0.833404 | − | 0.552664i | \(-0.813611\pi\) |
−0.0619186 | − | 0.998081i | \(-0.519722\pi\) | |||||||
\(500\) | 0.500000 | − | 0.866025i | 0.0223607 | − | 0.0387298i | ||||
\(501\) | 9.00000 | − | 15.5885i | 0.402090 | − | 0.696441i | ||||
\(502\) | −10.0000 | − | 17.3205i | −0.446322 | − | 0.773052i | ||||
\(503\) | 6.00000 | 0.267527 | 0.133763 | − | 0.991013i | \(-0.457294\pi\) | ||||
0.133763 | + | 0.991013i | \(0.457294\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.0000 | −0.622992 | ||||||||
\(506\) | −8.00000 | − | 13.8564i | −0.355643 | − | 0.615992i | ||||
\(507\) | 4.50000 | − | 7.79423i | 0.199852 | − | 0.346154i | ||||
\(508\) | 6.00000 | − | 10.3923i | 0.266207 | − | 0.461084i | ||||
\(509\) | 9.00000 | + | 15.5885i | 0.398918 | + | 0.690946i | 0.993593 | − | 0.113020i | \(-0.0360525\pi\) |
−0.594675 | + | 0.803966i | \(0.702719\pi\) | |||||||
\(510\) | −4.00000 | −0.177123 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.00000 | − | 10.3923i | 0.264649 | − | 0.458385i | ||||
\(515\) | 10.0000 | − | 17.3205i | 0.440653 | − | 0.763233i | ||||
\(516\) | 1.00000 | + | 1.73205i | 0.0440225 | + | 0.0762493i | ||||
\(517\) | −20.0000 | −0.879599 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.00000 | 0.263371 | ||||||||
\(520\) | −1.00000 | − | 1.73205i | −0.0438529 | − | 0.0759555i | ||||
\(521\) | 15.0000 | − | 25.9808i | 0.657162 | − | 1.13824i | −0.324185 | − | 0.945994i | \(-0.605090\pi\) |
0.981347 | − | 0.192244i | \(-0.0615766\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.0000 | + | 17.3205i | 0.437269 | + | 0.757373i | 0.997478 | − | 0.0709788i | \(-0.0226123\pi\) |
−0.560208 | + | 0.828352i | \(0.689279\pi\) | |||||||
\(524\) | −12.0000 | −0.524222 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.00000 | − | 6.92820i | −0.174243 | − | 0.301797i | ||||
\(528\) | −1.00000 | + | 1.73205i | −0.0435194 | + | 0.0753778i | ||||
\(529\) | −20.5000 | + | 35.5070i | −0.891304 | + | 1.54378i | ||||
\(530\) | −1.00000 | − | 1.73205i | −0.0434372 | − | 0.0752355i | ||||
\(531\) | −4.00000 | −0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.00000 | −0.173259 | ||||||||
\(534\) | 7.00000 | + | 12.1244i | 0.302920 | + | 0.524672i | ||||
\(535\) | 6.00000 | − | 10.3923i | 0.259403 | − | 0.449299i | ||||
\(536\) | −1.00000 | + | 1.73205i | −0.0431934 | + | 0.0748132i | ||||
\(537\) | 1.00000 | + | 1.73205i | 0.0431532 | + | 0.0747435i | ||||
\(538\) | 10.0000 | 0.431131 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | −1.00000 | − | 1.73205i | −0.0429934 | − | 0.0744667i | 0.843728 | − | 0.536771i | \(-0.180356\pi\) |
−0.886721 | + | 0.462304i | \(0.847023\pi\) | |||||||
\(542\) | −7.00000 | + | 12.1244i | −0.300676 | + | 0.520786i | ||||
\(543\) | −11.0000 | + | 19.0526i | −0.472055 | + | 0.817624i | ||||
\(544\) | −2.00000 | − | 3.46410i | −0.0857493 | − | 0.148522i | ||||
\(545\) | 2.00000 | 0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.0000 | −0.598597 | −0.299298 | − | 0.954160i | \(-0.596753\pi\) | ||||
−0.299298 | + | 0.954160i | \(0.596753\pi\) | |||||||
\(548\) | 1.00000 | + | 1.73205i | 0.0427179 | + | 0.0739895i | ||||
\(549\) | −5.00000 | + | 8.66025i | −0.213395 | + | 0.369611i | ||||
\(550\) | −1.00000 | + | 1.73205i | −0.0426401 | + | 0.0738549i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 8.00000 | 0.340503 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −28.0000 | −1.18961 | ||||||||
\(555\) | 4.00000 | + | 6.92820i | 0.169791 | + | 0.294086i | ||||
\(556\) | −2.00000 | + | 3.46410i | −0.0848189 | + | 0.146911i | ||||
\(557\) | −15.0000 | + | 25.9808i | −0.635570 | + | 1.10084i | 0.350824 | + | 0.936442i | \(0.385902\pi\) |
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(558\) | −1.00000 | − | 1.73205i | −0.0423334 | − | 0.0733236i | ||||
\(559\) | 4.00000 | 0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.00000 | 0.337760 | ||||||||
\(562\) | −7.00000 | − | 12.1244i | −0.295277 | − | 0.511435i | ||||
\(563\) | 12.0000 | − | 20.7846i | 0.505740 | − | 0.875967i | −0.494238 | − | 0.869326i | \(-0.664553\pi\) |
0.999978 | − | 0.00664037i | \(-0.00211371\pi\) | |||||||
\(564\) | 5.00000 | − | 8.66025i | 0.210538 | − | 0.364662i | ||||
\(565\) | −7.00000 | − | 12.1244i | −0.294492 | − | 0.510075i | ||||
\(566\) | −4.00000 | −0.168133 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.0000 | −0.503509 | ||||||||
\(569\) | 19.0000 | + | 32.9090i | 0.796521 | + | 1.37962i | 0.921869 | + | 0.387503i | \(0.126662\pi\) |
−0.125347 | + | 0.992113i | \(0.540004\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.00000 | + | 10.3923i | −0.251092 | + | 0.434904i | −0.963827 | − | 0.266529i | \(-0.914123\pi\) |
0.712735 | + | 0.701434i | \(0.247456\pi\) | |||||||
\(572\) | 2.00000 | + | 3.46410i | 0.0836242 | + | 0.144841i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.00000 | 0.333623 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −1.00000 | + | 1.73205i | −0.0416305 | + | 0.0721062i | −0.886090 | − | 0.463513i | \(-0.846589\pi\) |
0.844459 | + | 0.535620i | \(0.179922\pi\) | |||||||
\(578\) | 0.500000 | − | 0.866025i | 0.0207973 | − | 0.0360219i | ||||
\(579\) | 9.00000 | + | 15.5885i | 0.374027 | + | 0.647834i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −6.00000 | −0.248708 | ||||||||
\(583\) | 2.00000 | + | 3.46410i | 0.0828315 | + | 0.143468i | ||||
\(584\) | 5.00000 | − | 8.66025i | 0.206901 | − | 0.358364i | ||||
\(585\) | −1.00000 | + | 1.73205i | −0.0413449 | + | 0.0716115i | ||||
\(586\) | 15.0000 | + | 25.9808i | 0.619644 | + | 1.07326i | ||||
\(587\) | 16.0000 | 0.660391 | 0.330195 | − | 0.943913i | \(-0.392885\pi\) | ||||
0.330195 | + | 0.943913i | \(0.392885\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −2.00000 | − | 3.46410i | −0.0823387 | − | 0.142615i | ||||
\(591\) | −9.00000 | + | 15.5885i | −0.370211 | + | 0.641223i | ||||
\(592\) | −4.00000 | + | 6.92820i | −0.164399 | + | 0.284747i | ||||
\(593\) | −10.0000 | − | 17.3205i | −0.410651 | − | 0.711268i | 0.584310 | − | 0.811530i | \(-0.301365\pi\) |
−0.994961 | + | 0.100262i | \(0.968032\pi\) | |||||||
\(594\) | 2.00000 | 0.0820610 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −16.0000 | −0.655386 | ||||||||
\(597\) | 5.00000 | + | 8.66025i | 0.204636 | + | 0.354441i | ||||
\(598\) | 8.00000 | − | 13.8564i | 0.327144 | − | 0.566631i | ||||
\(599\) | −16.0000 | + | 27.7128i | −0.653742 | + | 1.13231i | 0.328465 | + | 0.944516i | \(0.393469\pi\) |
−0.982208 | + | 0.187799i | \(0.939865\pi\) | |||||||
\(600\) | −0.500000 | − | 0.866025i | −0.0204124 | − | 0.0353553i | ||||
\(601\) | −4.00000 | −0.163163 | −0.0815817 | − | 0.996667i | \(-0.525997\pi\) | ||||
−0.0815817 | + | 0.996667i | \(0.525997\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.00000 | 0.0814463 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.50000 | + | 6.06218i | −0.142295 | + | 0.246463i | ||||
\(606\) | −7.00000 | + | 12.1244i | −0.284356 | + | 0.492518i | ||||
\(607\) | 4.00000 | + | 6.92820i | 0.162355 | + | 0.281207i | 0.935713 | − | 0.352763i | \(-0.114758\pi\) |
−0.773358 | + | 0.633970i | \(0.781424\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −10.0000 | −0.404888 | ||||||||
\(611\) | −10.0000 | − | 17.3205i | −0.404557 | − | 0.700713i | ||||
\(612\) | −2.00000 | + | 3.46410i | −0.0808452 | + | 0.140028i | ||||
\(613\) | 4.00000 | − | 6.92820i | 0.161558 | − | 0.279827i | −0.773869 | − | 0.633345i | \(-0.781681\pi\) |
0.935428 | + | 0.353518i | \(0.115015\pi\) | |||||||
\(614\) | −10.0000 | − | 17.3205i | −0.403567 | − | 0.698999i | ||||
\(615\) | −2.00000 | −0.0806478 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.00000 | 0.241551 | 0.120775 | − | 0.992680i | \(-0.461462\pi\) | ||||
0.120775 | + | 0.992680i | \(0.461462\pi\) | |||||||
\(618\) | −10.0000 | − | 17.3205i | −0.402259 | − | 0.696733i | ||||
\(619\) | −12.0000 | + | 20.7846i | −0.482321 | + | 0.835404i | −0.999794 | − | 0.0202954i | \(-0.993539\pi\) |
0.517473 | + | 0.855699i | \(0.326873\pi\) | |||||||
\(620\) | 1.00000 | − | 1.73205i | 0.0401610 | − | 0.0695608i | ||||
\(621\) | −4.00000 | − | 6.92820i | −0.160514 | − | 0.278019i | ||||
\(622\) | 20.0000 | 0.801927 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.00000 | −0.0800641 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −13.0000 | + | 22.5167i | −0.519584 | + | 0.899947i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.00000 | − | 8.66025i | −0.199522 | − | 0.345582i | ||||
\(629\) | 32.0000 | 1.27592 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.00000 | −0.318475 | −0.159237 | − | 0.987240i | \(-0.550904\pi\) | ||||
−0.159237 | + | 0.987240i | \(0.550904\pi\) | |||||||
\(632\) | −8.00000 | − | 13.8564i | −0.318223 | − | 0.551178i | ||||
\(633\) | 2.00000 | − | 3.46410i | 0.0794929 | − | 0.137686i | ||||
\(634\) | −3.00000 | + | 5.19615i | −0.119145 | + | 0.206366i | ||||
\(635\) | −6.00000 | − | 10.3923i | −0.238103 | − | 0.412406i | ||||
\(636\) | −2.00000 | −0.0793052 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.00000 | + | 10.3923i | 0.237356 | + | 0.411113i | ||||
\(640\) | 0.500000 | − | 0.866025i | 0.0197642 | − | 0.0342327i | ||||
\(641\) | −21.0000 | + | 36.3731i | −0.829450 | + | 1.43665i | 0.0690201 | + | 0.997615i | \(0.478013\pi\) |
−0.898470 | + | 0.439034i | \(0.855321\pi\) | |||||||
\(642\) | −6.00000 | − | 10.3923i | −0.236801 | − | 0.410152i | ||||
\(643\) | 36.0000 | 1.41970 | 0.709851 | − | 0.704352i | \(-0.248762\pi\) | ||||
0.709851 | + | 0.704352i | \(0.248762\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.00000 | 0.0787499 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.00000 | + | 1.73205i | −0.0393141 | + | 0.0680939i | −0.885013 | − | 0.465566i | \(-0.845851\pi\) |
0.845699 | + | 0.533660i | \(0.179184\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | 4.00000 | + | 6.92820i | 0.157014 | + | 0.271956i | ||||
\(650\) | −2.00000 | −0.0784465 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.0000 | −0.391630 | ||||||||
\(653\) | −1.00000 | − | 1.73205i | −0.0391330 | − | 0.0677804i | 0.845796 | − | 0.533507i | \(-0.179126\pi\) |
−0.884929 | + | 0.465727i | \(0.845793\pi\) | |||||||
\(654\) | 1.00000 | − | 1.73205i | 0.0391031 | − | 0.0677285i | ||||
\(655\) | −6.00000 | + | 10.3923i | −0.234439 | + | 0.406061i | ||||
\(656\) | −1.00000 | − | 1.73205i | −0.0390434 | − | 0.0676252i | ||||
\(657\) | −10.0000 | −0.390137 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.0000 | −1.32445 | −0.662226 | − | 0.749304i | \(-0.730388\pi\) | ||||
−0.662226 | + | 0.749304i | \(0.730388\pi\) | |||||||
\(660\) | 1.00000 | + | 1.73205i | 0.0389249 | + | 0.0674200i | ||||
\(661\) | −13.0000 | + | 22.5167i | −0.505641 | + | 0.875797i | 0.494337 | + | 0.869270i | \(0.335411\pi\) |
−0.999979 | + | 0.00652642i | \(0.997923\pi\) | |||||||
\(662\) | 2.00000 | − | 3.46410i | 0.0777322 | − | 0.134636i | ||||
\(663\) | 4.00000 | + | 6.92820i | 0.155347 | + | 0.269069i | ||||
\(664\) | −16.0000 | −0.620920 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.00000 | 0.309994 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 9.00000 | − | 15.5885i | 0.348220 | − | 0.603136i | ||||
\(669\) | 8.00000 | − | 13.8564i | 0.309298 | − | 0.535720i | ||||
\(670\) | 1.00000 | + | 1.73205i | 0.0386334 | + | 0.0669150i | ||||
\(671\) | 20.0000 | 0.772091 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.0000 | 0.385472 | 0.192736 | − | 0.981251i | \(-0.438264\pi\) | ||||
0.192736 | + | 0.981251i | \(0.438264\pi\) | |||||||
\(674\) | 1.00000 | + | 1.73205i | 0.0385186 | + | 0.0667161i | ||||
\(675\) | −0.500000 | + | 0.866025i | −0.0192450 | + | 0.0333333i | ||||
\(676\) | 4.50000 | − | 7.79423i | 0.173077 | − | 0.299778i | ||||
\(677\) | 13.0000 | + | 22.5167i | 0.499631 | + | 0.865386i | 1.00000 | 0.000426509i | \(-0.000135762\pi\) | |
−0.500369 | + | 0.865812i | \(0.666802\pi\) | |||||||
\(678\) | −14.0000 | −0.537667 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −4.00000 | −0.153393 | ||||||||
\(681\) | −6.00000 | − | 10.3923i | −0.229920 | − | 0.398234i | ||||
\(682\) | −2.00000 | + | 3.46410i | −0.0765840 | + | 0.132647i | ||||
\(683\) | −12.0000 | + | 20.7846i | −0.459167 | + | 0.795301i | −0.998917 | − | 0.0465244i | \(-0.985185\pi\) |
0.539750 | + | 0.841825i | \(0.318519\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.00000 | 0.0764161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.0000 | −0.381524 | ||||||||
\(688\) | 1.00000 | + | 1.73205i | 0.0381246 | + | 0.0660338i | ||||
\(689\) | −2.00000 | + | 3.46410i | −0.0761939 | + | 0.131972i | ||||
\(690\) | 4.00000 | − | 6.92820i | 0.152277 | − | 0.263752i | ||||
\(691\) | −14.0000 | − | 24.2487i | −0.532585 | − | 0.922464i | −0.999276 | − | 0.0380440i | \(-0.987887\pi\) |
0.466691 | − | 0.884420i | \(-0.345446\pi\) | |||||||
\(692\) | 6.00000 | 0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.00000 | −0.151838 | ||||||||
\(695\) | 2.00000 | + | 3.46410i | 0.0758643 | + | 0.131401i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.00000 | + | 6.92820i | −0.151511 | + | 0.262424i | ||||
\(698\) | 5.00000 | + | 8.66025i | 0.189253 | + | 0.327795i | ||||
\(699\) | −14.0000 | −0.529529 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.0000 | 0.604312 | 0.302156 | − | 0.953259i | \(-0.402294\pi\) | ||||
0.302156 | + | 0.953259i | \(0.402294\pi\) | |||||||
\(702\) | 1.00000 | + | 1.73205i | 0.0377426 | + | 0.0653720i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −1.00000 | + | 1.73205i | −0.0376889 | + | 0.0652791i | ||||
\(705\) | −5.00000 | − | 8.66025i | −0.188311 | − | 0.326164i | ||||
\(706\) | −24.0000 | −0.903252 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4.00000 | −0.150329 | ||||||||
\(709\) | −21.0000 | − | 36.3731i | −0.788672 | − | 1.36602i | −0.926781 | − | 0.375602i | \(-0.877436\pi\) |
0.138109 | − | 0.990417i | \(-0.455897\pi\) | |||||||
\(710\) | −6.00000 | + | 10.3923i | −0.225176 | + | 0.390016i | ||||
\(711\) | −8.00000 | + | 13.8564i | −0.300023 | + | 0.519656i | ||||
\(712\) | 7.00000 | + | 12.1244i | 0.262336 | + | 0.454379i | ||||
\(713\) | 16.0000 | 0.599205 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.00000 | 0.149592 | ||||||||
\(716\) | 1.00000 | + | 1.73205i | 0.0373718 | + | 0.0647298i | ||||
\(717\) | 4.00000 | − | 6.92820i | 0.149383 | − | 0.258738i | ||||
\(718\) | 10.0000 | − | 17.3205i | 0.373197 | − | 0.646396i | ||||
\(719\) | −24.0000 | − | 41.5692i | −0.895049 | − | 1.55027i | −0.833744 | − | 0.552151i | \(-0.813807\pi\) |
−0.0613050 | − | 0.998119i | \(-0.519526\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −19.0000 | −0.707107 | ||||||||
\(723\) | −10.0000 | − | 17.3205i | −0.371904 | − | 0.644157i | ||||
\(724\) | −11.0000 | + | 19.0526i | −0.408812 | + | 0.708083i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.50000 | + | 6.06218i | 0.129897 | + | 0.224989i | ||||
\(727\) | −32.0000 | −1.18681 | −0.593407 | − | 0.804902i | \(-0.702218\pi\) | ||||
−0.593407 | + | 0.804902i | \(0.702218\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −5.00000 | − | 8.66025i | −0.185058 | − | 0.320530i | ||||
\(731\) | 4.00000 | − | 6.92820i | 0.147945 | − | 0.256249i | ||||
\(732\) | −5.00000 | + | 8.66025i | −0.184805 | + | 0.320092i | ||||
\(733\) | 15.0000 | + | 25.9808i | 0.554038 | + | 0.959621i | 0.997978 | + | 0.0635649i | \(0.0202470\pi\) |
−0.443940 | + | 0.896056i | \(0.646420\pi\) | |||||||
\(734\) | 28.0000 | 1.03350 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.00000 | 0.294884 | ||||||||
\(737\) | −2.00000 | − | 3.46410i | −0.0736709 | − | 0.127602i | ||||
\(738\) | −1.00000 | + | 1.73205i | −0.0368105 | + | 0.0637577i | ||||
\(739\) | −24.0000 | + | 41.5692i | −0.882854 | + | 1.52915i | −0.0347009 | + | 0.999398i | \(0.511048\pi\) |
−0.848153 | + | 0.529751i | \(0.822285\pi\) | |||||||
\(740\) | 4.00000 | + | 6.92820i | 0.147043 | + | 0.254686i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −48.0000 | −1.76095 | −0.880475 | − | 0.474093i | \(-0.842776\pi\) | ||||
−0.880475 | + | 0.474093i | \(0.842776\pi\) | |||||||
\(744\) | −1.00000 | − | 1.73205i | −0.0366618 | − | 0.0635001i | ||||
\(745\) | −8.00000 | + | 13.8564i | −0.293097 | + | 0.507659i | ||||
\(746\) | 18.0000 | − | 31.1769i | 0.659027 | − | 1.14147i | ||||
\(747\) | 8.00000 | + | 13.8564i | 0.292705 | + | 0.506979i | ||||
\(748\) | 8.00000 | 0.292509 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 4.00000 | + | 6.92820i | 0.145962 | + | 0.252814i | 0.929731 | − | 0.368238i | \(-0.120039\pi\) |
−0.783769 | + | 0.621052i | \(0.786706\pi\) | |||||||
\(752\) | 5.00000 | − | 8.66025i | 0.182331 | − | 0.315807i | ||||
\(753\) | −10.0000 | + | 17.3205i | −0.364420 | + | 0.631194i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.0000 | −0.726912 | −0.363456 | − | 0.931611i | \(-0.618403\pi\) | ||||
−0.363456 | + | 0.931611i | \(0.618403\pi\) | |||||||
\(758\) | −4.00000 | − | 6.92820i | −0.145287 | − | 0.251644i | ||||
\(759\) | −8.00000 | + | 13.8564i | −0.290382 | + | 0.502956i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.0000 | − | 25.9808i | −0.543750 | − | 0.941802i | −0.998684 | − | 0.0512772i | \(-0.983671\pi\) |
0.454935 | − | 0.890525i | \(-0.349663\pi\) | |||||||
\(762\) | −12.0000 | −0.434714 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.00000 | + | 3.46410i | 0.0723102 | + | 0.125245i | ||||
\(766\) | 7.00000 | − | 12.1244i | 0.252920 | − | 0.438071i | ||||
\(767\) | −4.00000 | + | 6.92820i | −0.144432 | + | 0.250163i | ||||
\(768\) | −0.500000 | − | 0.866025i | −0.0180422 | − | 0.0312500i | ||||
\(769\) | −16.0000 | −0.576975 | −0.288487 | − | 0.957484i | \(-0.593152\pi\) | ||||
−0.288487 | + | 0.957484i | \(0.593152\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.0000 | −0.432169 | ||||||||
\(772\) | 9.00000 | + | 15.5885i | 0.323917 | + | 0.561041i | ||||
\(773\) | 15.0000 | − | 25.9808i | 0.539513 | − | 0.934463i | −0.459418 | − | 0.888220i | \(-0.651942\pi\) |
0.998930 | − | 0.0462427i | \(-0.0147248\pi\) | |||||||
\(774\) | 1.00000 | − | 1.73205i | 0.0359443 | − | 0.0622573i | ||||
\(775\) | −1.00000 | − | 1.73205i | −0.0359211 | − | 0.0622171i | ||||
\(776\) | −6.00000 | −0.215387 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.0000 | −0.860442 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −1.00000 | + | 1.73205i | −0.0358057 | + | 0.0620174i | ||||
\(781\) | 12.0000 | − | 20.7846i | 0.429394 | − | 0.743732i | ||||
\(782\) | −16.0000 | − | 27.7128i | −0.572159 | − | 0.991008i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.0000 | −0.356915 | ||||||||
\(786\) | 6.00000 | + | 10.3923i | 0.214013 | + | 0.370681i | ||||
\(787\) | −6.00000 | + | 10.3923i | −0.213877 | + | 0.370446i | −0.952925 | − | 0.303207i | \(-0.901942\pi\) |
0.739048 | + | 0.673653i | \(0.235276\pi\) | |||||||
\(788\) | −9.00000 | + | 15.5885i | −0.320612 | + | 0.555316i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −16.0000 | −0.569254 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.00000 | 0.0710669 | ||||||||
\(793\) | 10.0000 | + | 17.3205i | 0.355110 | + | 0.615069i | ||||
\(794\) | 7.00000 | − | 12.1244i | 0.248421 | − | 0.430277i | ||||
\(795\) | −1.00000 | + | 1.73205i | −0.0354663 | + | 0.0614295i | ||||
\(796\) | 5.00000 | + | 8.66025i | 0.177220 | + | 0.306955i | ||||
\(797\) | −2.00000 | −0.0708436 | −0.0354218 | − | 0.999372i | \(-0.511277\pi\) | ||||
−0.0354218 | + | 0.999372i | \(0.511277\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −40.0000 | −1.41510 | ||||||||
\(800\) | −0.500000 | − | 0.866025i | −0.0176777 | − | 0.0306186i | ||||
\(801\) | 7.00000 | − | 12.1244i | 0.247333 | − | 0.428393i | ||||
\(802\) | 7.00000 | − | 12.1244i | 0.247179 | − | 0.428126i | ||||
\(803\) | 10.0000 | + | 17.3205i | 0.352892 | + | 0.611227i | ||||
\(804\) | 2.00000 | 0.0705346 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.00000 | −0.140894 | ||||||||
\(807\) | −5.00000 | − | 8.66025i | −0.176008 | − | 0.304855i | ||||
\(808\) | −7.00000 | + | 12.1244i | −0.246259 | + | 0.426533i | ||||
\(809\) | 5.00000 | − | 8.66025i | 0.175791 | − | 0.304478i | −0.764644 | − | 0.644453i | \(-0.777085\pi\) |
0.940435 | + | 0.339975i | \(0.110418\pi\) | |||||||
\(810\) | 0.500000 | + | 0.866025i | 0.0175682 | + | 0.0304290i | ||||
\(811\) | 28.0000 | 0.983213 | 0.491606 | − | 0.870817i | \(-0.336410\pi\) | ||||
0.491606 | + | 0.870817i | \(0.336410\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.0000 | 0.491001 | ||||||||
\(814\) | −8.00000 | − | 13.8564i | −0.280400 | − | 0.485667i | ||||
\(815\) | −5.00000 | + | 8.66025i | −0.175142 | + | 0.303355i | ||||
\(816\) | −2.00000 | + | 3.46410i | −0.0700140 | + | 0.121268i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 32.0000 | 1.11885 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.00000 | −0.0698430 | ||||||||
\(821\) | −12.0000 | − | 20.7846i | −0.418803 | − | 0.725388i | 0.577016 | − | 0.816733i | \(-0.304217\pi\) |
−0.995819 | + | 0.0913446i | \(0.970884\pi\) | |||||||
\(822\) | 1.00000 | − | 1.73205i | 0.0348790 | − | 0.0604122i | ||||
\(823\) | 8.00000 | − | 13.8564i | 0.278862 | − | 0.483004i | −0.692240 | − | 0.721668i | \(-0.743376\pi\) |
0.971102 | + | 0.238664i | \(0.0767093\pi\) | |||||||
\(824\) | −10.0000 | − | 17.3205i | −0.348367 | − | 0.603388i | ||||
\(825\) | 2.00000 | 0.0696311 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.00000 | 0.278187 | 0.139094 | − | 0.990279i | \(-0.455581\pi\) | ||||
0.139094 | + | 0.990279i | \(0.455581\pi\) | |||||||
\(828\) | −4.00000 | − | 6.92820i | −0.139010 | − | 0.240772i | ||||
\(829\) | −5.00000 | + | 8.66025i | −0.173657 | + | 0.300783i | −0.939696 | − | 0.342012i | \(-0.888892\pi\) |
0.766039 | + | 0.642795i | \(0.222225\pi\) | |||||||
\(830\) | −8.00000 | + | 13.8564i | −0.277684 | + | 0.480963i | ||||
\(831\) | 14.0000 | + | 24.2487i | 0.485655 | + | 0.841178i | ||||
\(832\) | −2.00000 | −0.0693375 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4.00000 | 0.138509 | ||||||||
\(835\) | −9.00000 | − | 15.5885i | −0.311458 | − | 0.539461i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.00000 | + | 1.73205i | −0.0345651 | + | 0.0598684i | ||||
\(838\) | 18.0000 | + | 31.1769i | 0.621800 | + | 1.07699i | ||||
\(839\) | −12.0000 | −0.414286 | −0.207143 | − | 0.978311i | \(-0.566417\pi\) | ||||
−0.207143 | + | 0.978311i | \(0.566417\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | −19.0000 | − | 32.9090i | −0.654783 | − | 1.13412i | ||||
\(843\) | −7.00000 | + | 12.1244i | −0.241093 | + | 0.417585i | ||||
\(844\) | 2.00000 | − | 3.46410i | 0.0688428 | − | 0.119239i | ||||
\(845\) | −4.50000 | − | 7.79423i | −0.154805 | − | 0.268130i | ||||
\(846\) | −10.0000 | −0.343807 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.00000 | −0.0686803 | ||||||||
\(849\) | 2.00000 | + | 3.46410i | 0.0686398 | + | 0.118888i | ||||
\(850\) | −2.00000 | + | 3.46410i | −0.0685994 | + | 0.118818i | ||||
\(851\) | −32.0000 | + | 55.4256i | −1.09695 | + | 1.89997i | ||||
\(852\) | 6.00000 | + | 10.3923i | 0.205557 | + | 0.356034i | ||||
\(853\) | −38.0000 | −1.30110 | −0.650548 | − | 0.759465i | \(-0.725461\pi\) | ||||
−0.650548 | + | 0.759465i | \(0.725461\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.00000 | − | 10.3923i | −0.205076 | − | 0.355202i | ||||
\(857\) | −6.00000 | + | 10.3923i | −0.204956 | + | 0.354994i | −0.950119 | − | 0.311888i | \(-0.899038\pi\) |
0.745163 | + | 0.666883i | \(0.232372\pi\) | |||||||
\(858\) | 2.00000 | − | 3.46410i | 0.0682789 | − | 0.118262i | ||||
\(859\) | −2.00000 | − | 3.46410i | −0.0682391 | − | 0.118194i | 0.829887 | − | 0.557931i | \(-0.188405\pi\) |
−0.898126 | + | 0.439738i | \(0.855071\pi\) | |||||||
\(860\) | 2.00000 | 0.0681994 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.0000 | 0.408722 | ||||||||
\(863\) | −12.0000 | − | 20.7846i | −0.408485 | − | 0.707516i | 0.586235 | − | 0.810141i | \(-0.300609\pi\) |
−0.994720 | + | 0.102624i | \(0.967276\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | 3.00000 | − | 5.19615i | 0.102003 | − | 0.176674i | ||||
\(866\) | 19.0000 | + | 32.9090i | 0.645646 | + | 1.11829i | ||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 32.0000 | 1.08553 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.00000 | − | 3.46410i | 0.0677674 | − | 0.117377i | ||||
\(872\) | 1.00000 | − | 1.73205i | 0.0338643 | − | 0.0586546i | ||||
\(873\) | 3.00000 | + | 5.19615i | 0.101535 | + | 0.175863i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.0000 | −0.337869 | ||||||||
\(877\) | −6.00000 | − | 10.3923i | −0.202606 | − | 0.350923i | 0.746762 | − | 0.665092i | \(-0.231608\pi\) |
−0.949367 | + | 0.314169i | \(0.898274\pi\) | |||||||
\(878\) | −13.0000 | + | 22.5167i | −0.438729 | + | 0.759900i | ||||
\(879\) | 15.0000 | − | 25.9808i | 0.505937 | − | 0.876309i | ||||
\(880\) | 1.00000 | + | 1.73205i | 0.0337100 | + | 0.0583874i | ||||
\(881\) | 46.0000 | 1.54978 | 0.774890 | − | 0.632096i | \(-0.217805\pi\) | ||||
0.774890 | + | 0.632096i | \(0.217805\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.0000 | 1.14419 | 0.572096 | − | 0.820187i | \(-0.306131\pi\) | ||||
0.572096 | + | 0.820187i | \(0.306131\pi\) | |||||||
\(884\) | 4.00000 | + | 6.92820i | 0.134535 | + | 0.233021i | ||||
\(885\) | −2.00000 | + | 3.46410i | −0.0672293 | + | 0.116445i | ||||
\(886\) | −14.0000 | + | 24.2487i | −0.470339 | + | 0.814651i | ||||
\(887\) | −1.00000 | − | 1.73205i | −0.0335767 | − | 0.0581566i | 0.848749 | − | 0.528796i | \(-0.177356\pi\) |
−0.882325 | + | 0.470640i | \(0.844023\pi\) | |||||||
\(888\) | 8.00000 | 0.268462 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 14.0000 | 0.469281 | ||||||||
\(891\) | −1.00000 | − | 1.73205i | −0.0335013 | − | 0.0580259i | ||||
\(892\) | 8.00000 | − | 13.8564i | 0.267860 | − | 0.463947i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 8.00000 | + | 13.8564i | 0.267560 | + | 0.463428i | ||||
\(895\) | 2.00000 | 0.0668526 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.0000 | −0.534224 | ||||||||
\(898\) | −3.00000 | − | 5.19615i | −0.100111 | − | 0.173398i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.500000 | + | 0.866025i | −0.0166667 | + | 0.0288675i | ||||
\(901\) | 4.00000 | + | 6.92820i | 0.133259 | + | 0.230812i | ||||
\(902\) | 4.00000 | 0.133185 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.0000 | −0.465633 | ||||||||
\(905\) | 11.0000 | + | 19.0526i | 0.365652 | + | 0.633328i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.00000 | + | 8.66025i | −0.166022 | + | 0.287559i | −0.937018 | − | 0.349281i | \(-0.886426\pi\) |
0.770996 | + | 0.636841i | \(0.219759\pi\) | |||||||
\(908\) | −6.00000 | − | 10.3923i | −0.199117 | − | 0.344881i | ||||
\(909\) | 14.0000 | 0.464351 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.0000 | 0.530104 | 0.265052 | − | 0.964234i | \(-0.414611\pi\) | ||||
0.265052 | + | 0.964234i | \(0.414611\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.0000 | − | 27.7128i | 0.529523 | − | 0.917160i | ||||
\(914\) | 21.0000 | − | 36.3731i | 0.694618 | − | 1.20311i | ||||
\(915\) | 5.00000 | + | 8.66025i | 0.165295 | + | 0.286299i | ||||
\(916\) | −10.0000 | −0.330409 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 4.00000 | 0.132020 | ||||||||
\(919\) | −28.0000 | − | 48.4974i | −0.923635 | − | 1.59978i | −0.793742 | − | 0.608254i | \(-0.791870\pi\) |
−0.129893 | − | 0.991528i | \(-0.541463\pi\) | |||||||
\(920\) | 4.00000 | − | 6.92820i | 0.131876 | − | 0.228416i | ||||
\(921\) | −10.0000 | + | 17.3205i | −0.329511 | + | 0.570730i | ||||
\(922\) | −9.00000 | − | 15.5885i | −0.296399 | − | 0.513378i | ||||
\(923\) | 24.0000 | 0.789970 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.00000 | 0.263038 | ||||||||
\(926\) | −8.00000 | − | 13.8564i | −0.262896 | − | 0.455350i | ||||
\(927\) | −10.0000 | + | 17.3205i | −0.328443 | + | 0.568880i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.0000 | − | 25.9808i | −0.492134 | − | 0.852401i | 0.507825 | − | 0.861460i | \(-0.330450\pi\) |
−0.999959 | + | 0.00905914i | \(0.997116\pi\) | |||||||
\(930\) | −2.00000 | −0.0655826 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −14.0000 | −0.458585 | ||||||||
\(933\) | −10.0000 | − | 17.3205i | −0.327385 | − | 0.567048i | ||||
\(934\) | 4.00000 | − | 6.92820i | 0.130884 | − | 0.226698i | ||||
\(935\) | 4.00000 | − | 6.92820i | 0.130814 | − | 0.226576i | ||||
\(936\) | 1.00000 | + | 1.73205i | 0.0326860 | + | 0.0566139i | ||||
\(937\) | −42.0000 | −1.37208 | −0.686040 | − | 0.727564i | \(-0.740653\pi\) | ||||
−0.686040 | + | 0.727564i | \(0.740653\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.0000 | 0.848478 | ||||||||
\(940\) | −5.00000 | − | 8.66025i | −0.163082 | − | 0.282466i | ||||
\(941\) | 25.0000 | − | 43.3013i | 0.814977 | − | 1.41158i | −0.0943679 | − | 0.995537i | \(-0.530083\pi\) |
0.909345 | − | 0.416044i | \(-0.136584\pi\) | |||||||
\(942\) | −5.00000 | + | 8.66025i | −0.162909 | + | 0.282166i | ||||
\(943\) | −8.00000 | − | 13.8564i | −0.260516 | − | 0.451227i | ||||
\(944\) | −4.00000 | −0.130189 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.00000 | −0.130051 | ||||||||
\(947\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(948\) | −8.00000 | + | 13.8564i | −0.259828 | + | 0.450035i | ||||
\(949\) | −10.0000 | + | 17.3205i | −0.324614 | + | 0.562247i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.00000 | 0.194563 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −58.0000 | −1.87880 | −0.939402 | − | 0.342817i | \(-0.888619\pi\) | ||||
−0.939402 | + | 0.342817i | \(0.888619\pi\) | |||||||
\(954\) | 1.00000 | + | 1.73205i | 0.0323762 | + | 0.0560772i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4.00000 | − | 6.92820i | 0.129369 | − | 0.224074i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.00000 | −0.129234 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | 13.5000 | + | 23.3827i | 0.435484 | + | 0.754280i | ||||
\(962\) | 8.00000 | − | 13.8564i | 0.257930 | − | 0.446748i | ||||
\(963\) | −6.00000 | + | 10.3923i | −0.193347 | + | 0.334887i | ||||
\(964\) | −10.0000 | − | 17.3205i | −0.322078 | − | 0.557856i | ||||
\(965\) | 18.0000 | 0.579441 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.0000 | 1.02905 | 0.514525 | − | 0.857475i | \(-0.327968\pi\) | ||||
0.514525 | + | 0.857475i | \(0.327968\pi\) | |||||||
\(968\) | 3.50000 | + | 6.06218i | 0.112494 | + | 0.194846i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.00000 | + | 5.19615i | −0.0963242 | + | 0.166838i | ||||
\(971\) | −10.0000 | − | 17.3205i | −0.320915 | − | 0.555842i | 0.659762 | − | 0.751475i | \(-0.270657\pi\) |
−0.980677 | + | 0.195633i | \(0.937324\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 28.0000 | 0.897178 | ||||||||
\(975\) | 1.00000 | + | 1.73205i | 0.0320256 | + | 0.0554700i | ||||
\(976\) | −5.00000 | + | 8.66025i | −0.160046 | + | 0.277208i | ||||
\(977\) | 15.0000 | − | 25.9808i | 0.479893 | − | 0.831198i | −0.519841 | − | 0.854263i | \(-0.674009\pi\) |
0.999734 | + | 0.0230645i | \(0.00734232\pi\) | |||||||
\(978\) | 5.00000 | + | 8.66025i | 0.159882 | + | 0.276924i | ||||
\(979\) | −28.0000 | −0.894884 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.00000 | −0.0638551 | ||||||||
\(982\) | −3.00000 | − | 5.19615i | −0.0957338 | − | 0.165816i | ||||
\(983\) | −23.0000 | + | 39.8372i | −0.733586 | + | 1.27061i | 0.221755 | + | 0.975102i | \(0.428822\pi\) |
−0.955341 | + | 0.295506i | \(0.904512\pi\) | |||||||
\(984\) | −1.00000 | + | 1.73205i | −0.0318788 | + | 0.0552158i | ||||
\(985\) | 9.00000 | + | 15.5885i | 0.286764 | + | 0.496690i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.00000 | + | 13.8564i | 0.254385 | + | 0.440608i | ||||
\(990\) | 1.00000 | − | 1.73205i | 0.0317821 | − | 0.0550482i | ||||
\(991\) | 12.0000 | − | 20.7846i | 0.381193 | − | 0.660245i | −0.610040 | − | 0.792370i | \(-0.708847\pi\) |
0.991233 | + | 0.132125i | \(0.0421802\pi\) | |||||||
\(992\) | −1.00000 | − | 1.73205i | −0.0317500 | − | 0.0549927i | ||||
\(993\) | −4.00000 | −0.126936 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.0000 | 0.317021 | ||||||||
\(996\) | 8.00000 | + | 13.8564i | 0.253490 | + | 0.439057i | ||||
\(997\) | 3.00000 | − | 5.19615i | 0.0950110 | − | 0.164564i | −0.814602 | − | 0.580020i | \(-0.803045\pi\) |
0.909613 | + | 0.415456i | \(0.136378\pi\) | |||||||
\(998\) | −20.0000 | + | 34.6410i | −0.633089 | + | 1.09654i | ||||
\(999\) | −4.00000 | − | 6.92820i | −0.126554 | − | 0.219199i |
(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 | 1470.2.i.c.361.1 | 2 | ||
7.2 | even | 3 | inner | 1470.2.i.c.961.1 | 2 | ||
7.3 | odd | 6 | 1470.2.a.n.1.1 | ✓ | 1 | ||
7.4 | even | 3 | 1470.2.a.p.1.1 | yes | 1 | ||
7.5 | odd | 6 | 1470.2.i.g.961.1 | 2 | |||
7.6 | odd | 2 | 1470.2.i.g.361.1 | 2 | |||
21.11 | odd | 6 | 4410.2.a.n.1.1 | 1 | |||
21.17 | even | 6 | 4410.2.a.e.1.1 | 1 | |||
35.4 | even | 6 | 7350.2.a.o.1.1 | 1 | |||
35.24 | odd | 6 | 7350.2.a.bh.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1470.2.a.n.1.1 | ✓ | 1 | 7.3 | odd | 6 | ||
1470.2.a.p.1.1 | yes | 1 | 7.4 | even | 3 | ||
1470.2.i.c.361.1 | 2 | 1.1 | even | 1 | trivial | ||
1470.2.i.c.961.1 | 2 | 7.2 | even | 3 | inner | ||
1470.2.i.g.361.1 | 2 | 7.6 | odd | 2 | |||
1470.2.i.g.961.1 | 2 | 7.5 | odd | 6 | |||
4410.2.a.e.1.1 | 1 | 21.17 | even | 6 | |||
4410.2.a.n.1.1 | 1 | 21.11 | odd | 6 | |||
7350.2.a.o.1.1 | 1 | 35.4 | even | 6 | |||
7350.2.a.bh.1.1 | 1 | 35.24 | odd | 6 |